diff --git a/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md new file mode 100644 index 000000000..dd84ea782 --- /dev/null +++ b/.github/ISSUE_TEMPLATE/bug_report.md @@ -0,0 +1,38 @@ +--- +name: Bug report +about: Create a report to help us improve +title: '' +labels: '' +assignees: '' + +--- + +**Describe the bug** +A clear and concise description of what the bug is. + +**To Reproduce** +Steps to reproduce the behavior: +1. Go to '...' +2. Click on '....' +3. Scroll down to '....' +4. See error + +**Expected behavior** +A clear and concise description of what you expected to happen. + +**Screenshots** +If applicable, add screenshots to help explain your problem. + +**Desktop (please complete the following information):** + - OS: [e.g. iOS] + - Browser [e.g. chrome, safari] + - Version [e.g. 22] + +**Smartphone (please complete the following information):** + - Device: [e.g. iPhone6] + - OS: [e.g. iOS8.1] + - Browser [e.g. stock browser, safari] + - Version [e.g. 22] + +**Additional context** +Add any other context about the problem here. diff --git a/.github/ISSUE_TEMPLATE/feature_request.md b/.github/ISSUE_TEMPLATE/feature_request.md new file mode 100644 index 000000000..bbcbbe7d6 --- /dev/null +++ b/.github/ISSUE_TEMPLATE/feature_request.md @@ -0,0 +1,20 @@ +--- +name: Feature request +about: Suggest an idea for this project +title: '' +labels: '' +assignees: '' + +--- + +**Is your feature request related to a problem? Please describe.** +A clear and concise description of what the problem is. Ex. I'm always frustrated when [...] + +**Describe the solution you'd like** +A clear and concise description of what you want to happen. + +**Describe alternatives you've considered** +A clear and concise description of any alternative solutions or features you've considered. + +**Additional context** +Add any other context or screenshots about the feature request here. diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md new file mode 100644 index 000000000..53b2967a4 --- /dev/null +++ b/.github/PULL_REQUEST_TEMPLATE.md @@ -0,0 +1,79 @@ +# Contributing to the Equational Theories Project + +Thank you for your interest in contributing to the Equational Theories Project! We welcome contributions from all sources: human-generated contributions from either professional mathematicians or interested members of the public, as well as computer-generated contributions from programs in various languages, automated theorem provers, or modern AI tools. (In fact, one of the main goals of this project is to learn how such a diverse pool of contributions can effectively be combined with each other to advance a common objective.) + +This guide provides detailed instructions on how to effectively and efficiently contribute to the project. + +## Project Coordination + +The project is managed using a [GitHub project dashboard](https://github.com/users/teorth/projects/1), which tracks tasks through various stages, from assignment to completion. + +## How to Contribute + +Contributions to the project are made through GitHub pull requests (PRs) that correspond to specific tasks outlined in the project's issues. +The following instructions detail the process for claiming and completing tasks. + +### 1. Task Identification + +- Tasks are posted as GitHub issues and can be found in the `Unclaimed Outstanding Tasks` column of the project dashboard. +- Each issue represents a specific task to be completed. The issue title and description contain relevant details and requirements. + +### 2. Claiming a Task + +- To claim a task, comment the single word `claim` on the relevant GitHub issue. +- If no other user is assigned, you will automatically be assigned to the task, and the issue will move to the `Claimed Tasks` column. +- You may only claim one task at a time. If you decide not to work on a task after claiming it, comment the single word `disclaim` on the issue. This will unassign you and return the issue to the `Unclaimed Outstanding Tasks` column, making it available for others to claim. + +### 3. Working on the Task + +Once you are assigned to an issue, begin working on the corresponding task. You should create a new branch from the `main` branch to develop your solution. + +> [!WARNING] +> Before pushing any changes, you have the following options: +> +> - You might want to install the git pre-push hook by running: +> +> ```bash +> scripts/install_pre-push.sh +> ``` +> This will automatically run checks before every push, reducing the risk of CI check failures. +> +> - You can manually run the following script before pushing, reducing the risk of CI check failures: +> +> ```bash +> scripts/run_before_push.sh +> ``` +> This requires manual execution and won't stop the push if skipped. +> +> - You may push your changes without any safeguards, increasing the risk of CI check failures. + +### 4. Submitting a Pull Request + +- When you are ready to submit your solution, create a PR from your working branch to the project’s `main` branch. +- After submitting the PR, comment the single phrase `propose PR #PR_NUMBER` on the original issue. This links your PR to the task, and the task will move to the `In Progress` column on the dashboard. +- A task can only move to `In Progress` if it has been claimed by the user proposing the PR. + +### 5. Withdrawing or Updating a PR + +- If you need to withdraw your PR, comment the single phrase `withdraw PR #PR_NUMBER` on the issue. The task will return to the `Claimed Tasks` column, but you will remain assigned to the issue. +- To submit an updated PR after withdrawal, comment the single phrase `propose PR #NEW_PR_NUMBER` following the same process outlined in step 4. + +### 6. Review Process + +- After finishing the task and ensuring your PR is ready for review, comment the single word `awaiting-review` on the PR. This will add the `awaiting-review` label to your PR and move the task from `In Progress` to the `PRs in Review` column of the dashboard. +- The project maintainers will review the PR. They may request changes, approve the PR, or provide feedback. + +### 7. Task Completion + +- Once the PR is approved and merged, the task will automatically move to the `Completed` column. +- If further adjustments are needed after merging, a new issue will be created to track additional work. + +### Additional Guidelines and Notes + +1. Please adhere to the issue claiming process. If an issue is already assigned to another contributor, refrain from working on it without prior communication with the current claimant. This ensures a collaborative and respectful workflow that values each contributor’s efforts. +2. Be aware that this contribution process is still in an experimental phase. As a result, occasional issues and inefficiencies may arise. We are committed to continuously refining the process, and your constructive feedback is highly appreciated. You can share your thoughts and suggestions on the [Lean Zulip chat channel](https://leanprover.zulipchat.com/#narrow/stream/458659-Equational/). +3. Until the integration of sufficient CI automation, the management of the project dashboard is handled manually by the maintainers. We ask for your patience and understanding as we work to keep the process running smoothly. + +## Discussion + +The main discussion will be held in this [Lean Zulip channel](https://leanprover.zulipchat.com/#narrow/stream/458659-Equational/). Some secondary discussion will also be held at [this blog post](https://terrytao.wordpress.com/2024/09/25/a-pilot-project-in-universal-algebra-to-explore-new-ways-to-collaborate-and-use-machine-assistance/). diff --git a/.github/workflows/blueprint.yml b/.github/workflows/blueprint.yml index ba141f1ac..ebeadb92c 100644 --- a/.github/workflows/blueprint.yml +++ b/.github/workflows/blueprint.yml @@ -149,6 +149,11 @@ jobs: ruby-version: "3.0" # Specify Ruby version bundler-cache: true # Enable caching for bundler + - name: Generate home_page/graphiti/graph.json + run: | + ~/.elan/bin/lake exe extract_implications --json > /tmp/implications.json + ruby scripts/generate_graphiti_data.rb /tmp/implications.json > home_page/graphiti/graph.json + - name: Build website using Jekyll if: github.event_name == 'push' && env.HOME_PAGE_EXISTS == 'true' working-directory: home_page diff --git a/README.md b/README.md index e59ddbc56..3d48efe8b 100644 --- a/README.md +++ b/README.md @@ -8,14 +8,14 @@ [![Paper](https://img.shields.io/badge/Paper-WIP-blue)](https://teorth.github.io/equational_theories/blueprint.pdf) [![Zulip Channel](https://img.shields.io/badge/Zulip_Channel-Join-blue)](https://leanprover.zulipchat.com/#narrow/stream/458659-Equational) -![Hasse diagram of selected equations](https://teorth.github.io/equational_theories/images/subgraph.png) +![Hasse diagram of selected equations](https://github.com/teorth/equational_theories/blob/main/images/subgraph.png?raw=true) The purpose of this project, launched on Sep 25, 2024, is to explore the space of equational theories of [magmas](https://en.wikipedia.org/wiki/Magma_(algebra)), ordered by implication. To begin with we shall focus only on theories of a single equation, and specifically on the 4694 equational laws -involving at most four magma operations, up to symmetry and relabeling (here is the list [in Lean](equational_theories/AllEquations.lean) and in [plain text](https://github.com/teorth/equational_theories/blob/main/data/equations.txt)). This creates 4694*(4694-1) = 22,028,942 implications that need to be proven or disproven, creating both "implications" and "anti-implications". +involving at most four magma operations, up to symmetry and relabeling (here is the list [in Lean](https://github.com/teorth/equational_theories/tree/main/equational_theories/AllEquations.lean) and in [plain text](https://github.com/teorth/equational_theories/tree/main/data/equations.txt)). This creates 4694*(4694-1) = 22,028,942 implications that need to be proven or disproven, creating both "implications" and "anti-implications". We will accumulate both "proven" and "conjectured" implications and anti-implications: proven assertions will be verified in the proof assistant language [Lean](https://www.lean-lang.org/), and "conjectured" assertions represent all claims (either human-generated or computer-generated) that have not yet been verified in Lean. The current status of the project can be found on the [dashboard](https://teorth.github.io/equational_theories/dashboard/). -Some selected equations of interest are listed [here](equational_theories/Equations.lean) (in Lean form) and [here](https://teorth.github.io/equational_theories/blueprint/subgraph-eq.html) (in a human readable blueprint). Examples include +Some selected equations of interest are listed [here](https://github.com/teorth/equational_theories/tree/main/equational_theories/Equations.lean) (in Lean form) and [here](https://teorth.github.io/equational_theories/blueprint/subgraph-eq.html) (in a human readable blueprint). Examples include - [Equation 1](https://teorth.github.io/equational_theories/implications/?1): `x = x`. The trivial law. - [Equation 2](https://teorth.github.io/equational_theories/implications/?2): `x = y`. The singleton law. - [Equation 43](https://teorth.github.io/equational_theories/implications/?43): `x ◇ y = y ◇ x`. The commutative law. @@ -28,23 +28,23 @@ Current statistics and data files, updated automatically: - [dashboard](https://teorth.github.io/equational_theories/dashboard/) Current visualizations, updated automatically: -- A tool for exploring the graph of equation implications is available [here](https://teorth.github.io/equational_theories/implications). -- An experimental tool to interactively explore a Hasse diagram of the graph is available [here](https://tsyrklevi.ch/eqviz/index.html?2) +- [Equation Explorer](https://teorth.github.io/equational_theories/implications) is a tool for exploring the graph of equation implications. +- [Graphiti](https://teorth.github.io/equational_theories/graphiti) is a tool for visualizing the implication graph. -For guidelines on how to contribute, see the [CONTRIBUTING.md](https://teorth.github.io/equational_theories/CONTRIBUTING.md) file. Participants are requested to abide by [our code of conduct](https://teorth.github.io/equational_theories/CODE_OF_CONDUCT.md). +For guidelines on how to contribute, see the [CONTRIBUTING.md](https://github.com/teorth/equational_theories/tree/main/CONTRIBUTING.md) file. Participants are requested to abide by [our code of conduct](https://github.com/teorth/equational_theories/tree/main/CODE_OF_CONDUCT.md). ## Past progress Some automatically generated progress: -- Sep 28, 2024: [85 laws](equational_theories/Generated/Constant.lean) have been shown to be equivalent to the constant law ([Equation 46](https://teorth.github.io/equational_theories/implications/?46)), and [815 laws](equational_theories/Generated/Singleton.lean) have been shown to be equivalent to the singleton law ([Equation2](https://teorth.github.io/equational_theories/implications/?2)). Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/sect0005.html). -- Sep 28, 2024: [18972 implications](equational_theories/Generated/SimpleRewrites/theorems) were established by simple rewrite laws. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/sect0006.html). -- Sep 28, 2024: [4.2m implications proven by a transitive reduction of 15k theorems](https://teorth.github.io/equational_theories/equational_theories/Generated/TrivialBruteforce) were proven using simple rewrite proof scripts. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/sect0007.html). -- Sep 29, 2024: [13.7m implications were conjectured to be refuted by a collection of 515 magmas](https://teorth.github.io/equational_theories/equational_theories/Generated/All4x4Tables), collected by enumerating all 4^(4*4) operators and reducing to a covering set. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/sect0008.html). (Update, Oct 3, 2024: these anti-implications are now formalized in Lean as theorems, and the number of implications established by this method increased to 13.8m.) -- Oct 1, 2024: Another [~250k transitive implications](https://teorth.github.io/equational_theories/equational_theories/Generated/TrivialBruteforce) were proven by simple proof generation. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/sect0007.html). -- Oct 1, 2024: ~500k transitive implications were proven by [EquationSearch](https://teorth.github.io/equational_theories/equational_theories/Generated/EquationSearch), a custom tool that chooses hypotheses and leverages previously found implications to search by using the implied equations as substitutions. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/sect0009.html). -- Oct 2, 2024: 86 (potentially) new implications in [`Subgraph.lean`](https://teorth.github.io/equational_theories/equational_theories/Subgraph.lean) conclusively (i.e. in Lean) resolved using the [lean-egg tactic](https://github.com/marcusrossel/lean-egg). Some of these were simply missed by the transitive closure computation and technically already implied, but some were genuinely new. -- Oct 3, 2024: Another ~150k transitive implications were proven by [EquationSearch](https://teorth.github.io/equational_theories/equational_theories/Generated/EquationSearch) after improved capabilities were added. -- Oct 3, 2024: [~1m transitive implications](https://teorth.github.io/equational_theories/equational_theories/Generated/MagmaEgg) were proven by a new custom tool that uses egraphs to find a proof and exports it to a Lean term +- Sep 28, 2024: [85 laws](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/Constant.lean) have been shown to be equivalent to the constant law ([Equation 46](https://teorth.github.io/equational_theories/implications/?46)), and [815 laws](https://github.com/teorth/equational_theories/tree/main/Generated/Singleton.lean) have been shown to be equivalent to the singleton law ([Equation2](https://teorth.github.io/equational_theories/implications/?2)). Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/simple-rewrite-chapter.html). +- Sep 28, 2024: [18972 implications](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/SimpleRewrites/theorems) were established by simple rewrite laws. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/simple-rewrite-chapter.html). +- Sep 28, 2024: [4.2m implications proven by a transitive reduction of 15k theorems](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/TrivialBruteforce) were proven using simple rewrite proof scripts. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/trivial-auto-chapter.html). +- Sep 29, 2024: [13.7m implications were conjectured to be refuted by a collection of 515 magmas](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/All4x4Tables), collected by enumerating all 4^(4*4) operators and reducing to a covering set. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/all-small-magmas-chapter.html). (Update, Oct 3, 2024: these anti-implications are now formalized in Lean as theorems, and the number of implications established by this method increased to 13.8m.) +- Oct 1, 2024: Another [~250k transitive implications](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/TrivialBruteforce) were proven by simple proof generation. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/trivial-auto-chapter.html). +- Oct 1, 2024: ~500k transitive implications were proven by [EquationSearch](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/EquationSearch), a custom tool that chooses hypotheses and leverages previously found implications to search by using the implied equations as substitutions. Discussed in the blueprint [here](https://teorth.github.io/equational_theories/blueprint/equation-search-chapter.html). +- Oct 2, 2024: 86 (potentially) new implications in [`Subgraph.lean`](https://github.com/teorth/equational_theories/tree/main/equational_theories/Subgraph.lean) conclusively (i.e. in Lean) resolved using the [lean-egg tactic](https://github.com/marcusrossel/lean-egg). Some of these were simply missed by the transitive closure computation and technically already implied, but some were genuinely new. +- Oct 3, 2024: Another ~150k transitive implications were proven by [EquationSearch](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/EquationSearch) after improved capabilities were added. +- Oct 3, 2024: [~1m transitive implications](https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/MagmaEgg) were proven by a new custom tool that uses egraphs to find a proof and exports it to a Lean term - Oct 5, 2024: 97% of the remaining unknown implications were resolved (transitively) by [Vampire](https://en.wikipedia.org/wiki/Vampire_(theorem_prover)), and then converted to a Lean proof using a custom script and a Lean elaborator implementing the deduction step of superposition calculus. @@ -54,13 +54,14 @@ Some statistics and data files from a given point in time: - Oct 2, 2024: [A list of unknown implications whose converse is proven](https://github.com/amirlb/equational_theories/blob/extract_implications_equivalence_creators_data/scripts/equivalence_creators.json), i.e. implications that would reduce the number of equivalence classes of equations. At the time of creation we had 2969 equivalence classes. This file contains 4526 unknown implications, if all hold then it will reduce the number of equivalence classes to 1300. - Oct 4, 2024: Current dashboard status: 29248 explicitly proven, 7063191 implicitly proven, 605854 explicitly disproven, 13243426 implicitly disproven, 1120090 open (94.923% complete). No conjectures at this time. (A more formal time series of progress is planned.) - Oct 5, 2024: Current dashboard status: 31023 explicitly proven, 8151818 implicitly proven, 581166 explicitly disproven, 13268299 implicitly proven, 29503 open (99.866% complete). Note some pruning of redundant theorems occurred in the explicitly disproven theorems to improve compilation time. -- Oct 6, 2024: Current dashboard status (fixing an accounting error in previous dashboards): 31019 explicitly proven, 8147260 implicitly proven, 582094 explicitly disproven, 13272262 implicitly disproven, 1001 open (99.995% complete). Only [8 implications needed](https://teorth.github.io/equational_theories/data/outstanding_3op_implications.txt) to resolve the graph for laws of length 3, and [440 to resolve the entire graph](https://teorth.github.io/equational_theories/data/unknowns_10_06.txt) (including 36 conjectured to be false by Vampire, marked with an asterisk)! +- Oct 6, 2024: Current dashboard status (fixing an accounting error in previous dashboards): 31019 explicitly proven, 8147260 implicitly proven, 582094 explicitly disproven, 13272262 implicitly disproven, 1001 open (99.995% complete). Up to duality, only [8 implications needed](https://github.com/teorth/equational_theories/tree/main/data/outstanding_3op_implications.txt) to resolve the graph for laws of length 3, and [440 to resolve the entire graph](https://github.com/teorth/equational_theories/tree/main/data/unknowns_10_06.txt) (including 18 conjectured to be false by Vampire, marked with an asterisk)! +- Oct 7, 2024: Current dashboard status: 31019 explicitly proven, 8147260 implicitly proven, 582096 explicitly disproven, 13272262 implicitly disproven, 999 open. Deriving a minimal set of open implications is now partly automated and takes duality into account. With this, after resolving [361 implications](https://github.com/teorth/equational_theories/tree/main/data/unknowns_10_07.json) and formalizing Vampire disproofs and duality, the graph will be complete. Some visualizations from a given point in time: -- Sep 28, 2024: A (manually created) [Hasse diagram](https://en.wikipedia.org/wiki/Hasse_diagram) of the [dependencies obtained up to this date](https://teorth.github.io/equational_theories/equational_theories/Subgraph.lean) for the [selected equations of interest](https://teorth.github.io/equational_theories/equational_theories/Equations.lean) can be found [here](https://teorth.github.io/equational_theories/images/implications.png). Note: the orientation in these legacy images is reversed from that in current guidance. -- Sep 28, 2024: A directed acyclic graph of automatically generated implications is [here](https://teorth.github.io/equational_theories/images/implications_092824.svg?raw=true): circular vertices are for nodes representing multiple equivalent equations and equations in green are from [`Subgraph.lean`](https://teorth.github.io/equational_theories/equational_theories/Subgraph.lean). Note: the orientation in these legacy images is reversed from that in current guidance. -- Oct 1, 2024: An image visualizing the graph of proved results can be found [here](https://teorth.github.io/equational_theories/images/outcomes_20241001.png). This was generated by [`outcomes_to_image.py`](https://teorth.github.io/equational_theories/scripts/outcomes_to_image.py). -- Oct 3, 2024: The current implications represented as a directed acyclic graph were generated using [`generate_graphviz_graph.rb`](https://teorth.github.io/equational_theories/scripts/generate_graphviz_graph.rb) to visualize the [entire graph](https://teorth.github.io/equational_theories/images/implications_100324.svg?raw=true) and the smaller graph of equations [limited to 3 variables and three operations](https://teorth.github.io/equational_theories/images/implications_100324_var3_op3.svg?raw=true). As previously: circular vertices are for nodes representing multiple equivalent equations and vertices in green are from [`Subgraph.lean`](https://teorth.github.io/equational_theories/equational_theories/Subgraph.lean). +- Sep 28, 2024: A (manually created) [Hasse diagram](https://en.wikipedia.org/wiki/Hasse_diagram) of the [dependencies obtained up to this date](https://github.com/teorth/equational_theories/tree/main/equational_theories/Subgraph.lean) for the [selected equations of interest](https://github.com/teorth/equational_theories/tree/main/equational_theories/Equations.lean) can be found [here](https://github.com/teorth/equational_theories/tree/main/images/implications.png). Note: the orientation in these legacy images is reversed from that in current guidance. +- Sep 28, 2024: A directed acyclic graph of automatically generated implications is [here](https://github.com/teorth/equational_theories/tree/main/images/implications_092824.svg?raw=true): circular vertices are for nodes representing multiple equivalent equations and equations in green are from [`Subgraph.lean`](https://github.com/teorth/equational_theories/tree/main/equational_theories/Subgraph.lean). Note: the orientation in these legacy images is reversed from that in current guidance. +- Oct 1, 2024: An image visualizing the graph of proved results can be found [here](https://github.com/teorth/equational_theories/tree/main/images/outcomes_20241001.png). This was generated by [`outcomes_to_image.py`](https://github.com/teorth/equational_theories/tree/main/scripts/outcomes_to_image.py). +- Oct 3, 2024: The current implications represented as a directed acyclic graph were generated using [`generate_graphviz_graph.rb`](https://github.com/teorth/equational_theories/tree/main/scripts/generate_graphviz_graph.rb) to visualize the [entire graph](https://github.com/teorth/equational_theories/tree/main/images/implications_100324.svg?raw=true) and the smaller graph of equations [limited to 3 variables and three operations](https://github.com/teorth/equational_theories/tree/main/images/implications_100324_var3_op3.svg?raw=true). As previously: circular vertices are for nodes representing multiple equivalent equations and vertices in green are from [`Subgraph.lean`](https://github.com/teorth/equational_theories/tree/main/equational_theories/Subgraph.lean). ## Building the project @@ -78,8 +79,8 @@ To build this project after [installing Lean](https://www.lean-lang.org/lean-get - [Blueprint](https://teorth.github.io/equational_theories/blueprint/) - [Documentation](https://teorth.github.io/equational_theories/docs/) - [The Lean Zulip stream for the project](https://leanprover.zulipchat.com/#narrow/stream/458659-Equational/) - - [Instructions on how to contribute](https://teorth.github.io/equational_theories/CONTRIBUTING.md) - - [Code of conduct](https://teorth.github.io/equational_theories/CODE_OF_CONDUCT.md) + - [Instructions on how to contribute](https://github.com/teorth/equational_theories/tree/main/CONTRIBUTING.md) + - [Code of conduct](https://github.com/teorth/equational_theories/tree/main/CODE_OF_CONDUCT.md) - [Wiki](https://github.com/teorth/equational_theories/wiki) - [A blog post describing the project.](https://terrytao.wordpress.com/2024/09/25/a-pilot-project-in-universal-algebra-to-explore-new-ways-to-collaborate-and-use-machine-assistance/), Sep 25, 2024. - [Initial discussion on Zulip](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Proposing.20a.20universal.20algebra.20exploration.20using.20Lean), Sep 26, 2024. @@ -87,31 +88,30 @@ To build this project after [installing Lean](https://www.lean-lang.org/lean-get - [Followup discussion on Mastodon](https://mathstodon.xyz/deck/@tao/113201989529992957), Sep 25, 2024. - [The MathOverflow post that inspired the project](https://mathoverflow.net/questions/450930/is-there-an-identity-between-the-associative-identity-and-the-constant-identity), Jul 17, 2023. - [A related MathOverflow post](https://mathoverflow.net/questions/450890/is-there-an-identity-between-the-commutative-identity-and-the-constant-identity), Jul 16, 2023. -- [Data](https://teorth.github.io/equational_theories/data) - - [Text list of equations](https://teorth.github.io/equational_theories/data/equations.txt) - - [List of duals of equations](https://teorth.github.io/equational_theories/data/dual_equations.md) - - [The smallest magma obeying a given equation (up to N=5)](data/smallest_magma.txt), if it exists -- [Scripts](https://teorth.github.io/equational_theories/scripts) +- [Data](https://github.com/teorth/equational_theories/tree/main/data) + - [Text list of equations](https://github.com/teorth/equational_theories/tree/main/data/equations.txt) + - [List of duals of equations](https://github.com/teorth/equational_theories/tree/main/data/dual_equations.md) + - [The smallest magma obeying a given equation (up to N=5)](https://github.com/teorth/equational_theories/tree/main/data/smallest_magma.txt), if it exists +- [Scripts](https://github.com/teorth/equational_theories/tree/main/scripts) - Shell - - [`run_before_push`](https://teorth.github.io/equational_theories/scripts/run_before_push.sh) - performs some of the CI checks, suitable for running just before pushing a new PR + - [`run_before_push`](https://github.com/teorth/equational_theories/tree/main/scripts/run_before_push.sh) - performs some of the CI checks, suitable for running just before pushing a new PR - Lean - - [`extract_implications`](https://teorth.github.io/equational_theories/scripts/extract_implications.lean) - extracts implications from one or more Lean files. This outputs the "ground truth" of implication data, for use by other scripts + - [`extract_implications`](https://github.com/teorth/equational_theories/tree/main/scripts/extract_implications.lean) - extracts implications from one or more Lean files. This outputs the "ground truth" of implication data, for use by other scripts - Python - - [`explore_magma`](https://teorth.github.io/equational_theories/scripts/explore_magma.py) - test a given magma table against all or a subset of the equations in [`AllEquations.lean`](https://teorth.github.io/equational_theories/equational_theories/AllEquations.lean) - - [`find_dual`](https://teorth.github.io/equational_theories/scripts/find_dual.py) - finds the dual of an equation - - [`find_equation_id`](https://teorth.github.io/equational_theories/scripts/find_equation_id.py) - finds the equation number of an equation string - - [`find_powerful_theorems.py`](https://teorth.github.io/equational_theories/scripts/find_powerful_theorems.py) - finds theorems that, if proved, would imply many others - - [`generate_eqs_list`](https://teorth.github.io/equational_theories/scripts/generate_eqs_list.py) - generates a list of equations - - [`generate_graphviz_graph`](https://teorth.github.io/equational_theories/scripts/generate_graphviz_graph.rb) - generates a graphviz dot file, that can be used to create an implication graph - - [`generate_image`](https://teorth.github.io/equational_theories/scripts/generate_image.py) - generates an image of implications - - [`generate_most_wanted_list`](https://teorth.github.io/equational_theories/scripts/generate_most_wanted_list.py) - generates the "most wanted" implications - - [`generate_z3_counterexample`](https://teorth.github.io/equational_theories/scripts/generate_z3_counterexample.py) - given an implication statement between two equations, calls Z3 to try to generate a counterexample - - [`process_implications`](https://teorth.github.io/equational_theories/scripts/process_implications.py) - processes implications from one or more Lean files + - [`explore_magma`](https://github.com/teorth/equational_theories/tree/main/scripts/explore_magma.py) - test a given magma table against all or a subset of the equations in [`AllEquations.lean`](https://github.com/teorth/equational_theories/tree/main/equational_theories/AllEquations.lean) + - [`find_dual`](https://github.com/teorth/equational_theories/tree/main/scripts/find_dual.py) - finds the dual of an equation + - [`find_equation_id`](https://github.com/teorth/equational_theories/tree/main/scripts/find_equation_id.py) - finds the equation number of an equation string + - [`find_powerful_theorems.py`](https://github.com/teorth/equational_theories/tree/main/scripts/find_powerful_theorems.py) - finds theorems that, if proved, would imply many others + - [`generate_eqs_list`](https://github.com/teorth/equational_theories/tree/main/scripts/generate_eqs_list.py) - generates a list of equations + - [`generate_image`](https://github.com/teorth/equational_theories/tree/main/scripts/generate_image.py) - generates an image of implications + - [`generate_most_wanted_list`](https://github.com/teorth/equational_theories/tree/main/scripts/generate_most_wanted_list.py) - generates the "most wanted" implications + - [`generate_z3_counterexample`](https://github.com/teorth/equational_theories/tree/main/scripts/generate_z3_counterexample.py) - given an implication statement between two equations, calls Z3 to try to generate a counterexample + - [`process_implications`](https://github.com/teorth/equational_theories/tree/main/scripts/process_implications.py) - processes implications from one or more Lean files - Ruby - - [`generate_graphviz_graph`](https://teorth.github.io/equational_theories/scripts/generate_graphviz_graph.rb) - creates a graphviz graph - - [`graph`](https://teorth.github.io/equational_theories/scripts/graph.rb) - graph condensation tools - - [`transitive_closure`](https://teorth.github.io/equational_theories/scripts/transitive_closure.rb) - computes the transitive closure of a set of implications - - [`transitive_reduction`](https://teorth.github.io/equational_theories/scripts/transitive_reduction.rb) - finds a transitive reduction of a set of implications + - [`generate_graphviz_graph`](https://github.com/teorth/equational_theories/tree/main/scripts/generate_graphviz_graph.rb) - creates a graphviz graph + - [`transitive_closure`](https://github.com/teorth/equational_theories/tree/main/scripts/transitive_closure.rb) - computes the transitive closure of a set of implications + - [`transitive_reduction`](https://github.com/teorth/equational_theories/tree/main/scripts/transitive_reduction.rb) - finds a transitive reduction of a set of implications + - [`graph`](https://github.com/teorth/equational_theories/tree/main/scripts/graph.rb) - graph library - Automated provers for equational theories - [Prover9 and Mace4](https://www.cs.unm.edu/~mccune/prover9/) - [aa](https://github.com/gsfk/aa) - a project to use Prover9/Mace4 to brute force axioms for finite mathematical domains diff --git a/blueprint/src/chapter/abstract_nonsense.tex b/blueprint/src/chapter/abstract_nonsense.tex new file mode 100644 index 000000000..2947c2446 --- /dev/null +++ b/blueprint/src/chapter/abstract_nonsense.tex @@ -0,0 +1,156 @@ +\chapter{Some abstract nonsense}\label{abstract-nonsense-chapter} + +This is an alternate presentation of the material of the previous section, where we use the ``abstract nonsense'' of free magmas in the presence of a theory as the conceptual foundation. + +\begin{definition}[Free magma relative to a theory]\label{free-theory}\uses{models-def} + Let $\Gamma$ be a theory with an alphabet $X$. A \emph{free magma} with alphabet $X$ subject to the theory $\Gamma$ is a magma $M_{X,\Gamma}$ together with a function $\iota_{X,\Gamma} : X \to M_{X,\Gamma}$, with the following properties: + \begin{itemize} + \item[(i)] $M_{X,\Gamma}$ obeys the theory $\Gamma$: $M_{X,\Gamma} \models \Gamma$. + \item[(ii)] For any magma $M$ obeying the theory $\Gamma$ and any function $f: X \to M$, there exists a unique magma homomorphism $\tilde{f}: M_{X,\Gamma} \to M$ such that $\tilde{f} \circ \iota_{X,\Gamma} = f$. + \end{itemize} +\end{definition} + +Such magmas exist and are unique up to a suitable isomorphism: + +\begin{theorem}[Existence and uniqueness of free magmas]\label{freemag-exist}\uses{free-theory} + Let $\Gamma$ be a theory with alphabet $X$. + \begin{itemize} + \item[(i)] There exists a free magma $M_{X,\Gamma}$ with alphabet $X$ subject to the theory $\Gamma$. + \item[(ii)] If $M_{X,\Gamma}$ and $M'_{X,\Gamma}$ are two free magmas with alphabet $X$ subject to the theory $\Gamma$, then there exists a unique magma isomorphism $\phi: M_{X,\Gamma} \to M'_{X,\Gamma}$ such that $\phi \circ \iota_{X,\Gamma} = \iota'_{X,\Gamma}$. + \end{itemize} +\end{theorem} + +We remark that the ordinary free magma $M_X$ corresponds to the case when $\Gamma$ is the empty theory. + +\begin{proof}\uses{sound-complete, equiv} + For (i), we define $M_{X,\Gamma} = M_X / \sim$, where the equivalence relation $\sim$ is defined by requiring $w \sim w'$ if and only if $\Gamma \models w \formaleq w'$; this is an equivalence relation thanks to \Cref{equiv}, and from \Cref{sound-complete} we see that this relation respects the magma operations, so that $M_{X,\Gamma}$ is a magma. The map $\iota_{X,\Gamma}: X \to M_{X,\Gamma}$ is defined by setting $\iota_{X,\Gamma}(x)$ to be the equivalence class of $x$ in $M_{X,\Gamma}$ for each $x \in X$. + + We first check that $M_{X,\Gamma}$ obeys $\Gamma$. Let $w \formaleq w'$ be a law in $\Gamma$, and let $f: X \to M_{X,\Gamma}$ be a function. We may lift this function to a function $\tilde{f}: X \to M_X$. From \Cref{derivation-def}, we have $\Gamma \vdash w \formaleq w'$ and hence $\Gamma \vdash \varphi_{\tilde{f}}(w) \formaleq \varphi_{\tilde{f}}(w')$. By \Cref{sound-complete}, we conclude $\Gamma \models \varphi_{\tilde{f}}(w) \formaleq \varphi_{\tilde{f}}(w')$. Quotienting by $\sim$, we conclude that $\varphi_f(w) = \varphi(w')$, giving the claim by \Cref{models-def}. + + Now we check the universal property (ii). Let $M$ be a magma obeying the theory $\Gamma$, and let $f: X \to M$ be a function, then we have a magma homomorphism $\varphi_f: M_X \to M$. If $w, w' \in M_X$ are such that $w \sim w'$, then $\Gamma \models w \formaleq w'$ and hence $\varphi_f(w) = \varphi_f(w')$. Hence $\varphi_f$ descends to a map $\tilde{f}: M_{X,\Gamma} \to M$, which one can check to be a magma homomorphism with $\tilde{f} \circ \iota_{X,\Gamma} = f$. By construction, $M_{X,\Gamma}$ is generated by $\iota_{X,\Gamma}(X)$, and so this homomorphism is unique. +\end{proof} + +\begin{example}[Free associative magma] + Let $\Gamma$ consist solely of the associative law, \Cref{eq4512} (so $X$ contains $0,1,2$). Then one can take $M_{X,\Gamma}$ to be the set of nonempty strings with alphabet $X$, with magma operation given by concatenation, and $\iota_{X,\Gamma}(x)$ being the length one string $x$. It is a routine matter to verify that this obeys the axioms of a free magma subject to $\Gamma$. +\end{example} + +\begin{example}[Free associative commutative magma]\label{facm} + Let $\Gamma$ consist of the associative law (\Cref{eq4512}) and the commutative law (\Cref{eq43}). Then one can take $M_{X,\Gamma}$ to be the free abelian monoid $\N_0^X \backslash 0$ of tuples $(n_x)_{x \in X}$ with the $n_x$ natural numbers, not all zero, with all but finitely many of the $n_x$ vanishing, with the magma operation given by vector addition, and with $\iota_{X,\Gamma}(x)$ being the standard generator of $\N^X$ associated to $x \in X$; one can think of this space as the space of formal non-empty commuting associating sums of $X$. It is a routine matter to verify that this obeys the axioms of a free magma subject to $\Gamma$. +\end{example} + +\begin{example}[Free left absorptive magma]\label{freeleft} + Let $\Gamma$ consist of the left absorptive law (\Cref{eq4}). Then one can take $M_{X,\Gamma}$ to be $X$ with the law $x \op y = x$, and $\iota_{X,\Gamma}$ to be the identity map. It is easy to see that this is indeed a free magma subject to $\Gamma$. +\end{example} + +\begin{example}[Free constant magma]\label{freeconst} + Let $\Gamma$ consist of the constant law (\Cref{eq46}). Then one can take $M_{X,\Gamma}$ to be the disjoint union $X \uplus \{0\}$ of $X$ and another object $0$, with $\iota_{X,\Gamma}$ being the identity embedding, and with the zero magma law $x \op y = 0$ for all $x,y \in X \uplus \{0\}$. +\end{example} + +Free magmas can be used to characterize entailment by $\Gamma$ in terms of a canonical invariant. + +\begin{theorem}[Canonical invariant]\label{canonical-invariant}\uses{free-theory} + Let $\Gamma$ be a theory with some alphabet $X$, and let $M_{X,\Gamma}$ be a free magma with alphabet $X$ subject to $\Gamma$, with associated map $\iota_{X,\Gamma}: X \to M_{X,\Gamma}$. Then for any $w,w' \in M_X$, we have + \[ + \Gamma \models w \formaleq w' \text{ if and only if } \varphi_{\iota_{X,\Gamma}}(w) = \varphi_{\iota_{X,\Gamma}}(w'). + \] +\end{theorem} + +\begin{proof}\uses{freemag-exist} + By \Cref{freemag-exist} we may take $M_{X,\Gamma}$ to be the canonical free magma constructed in the proof of that theorem. The claim is then clear from expanding out definitions. +\end{proof} + +Every theory $\Gamma$ then gives a metatheorem about anti-implication: + +\begin{corollary}[Criterion for anti-implication]\label{anti-impl} + Let $\Gamma$ be a theory with some alphabet $X$, and let $M_{X,\Gamma}$ be a free magma with alphabet $X$ subject to $\Gamma$, with associated map $\iota_{X,\Gamma}: X \to M_{X,\Gamma}$. Let $w \formaleq w'$ and $w'' \formaleq w'''$ be laws with alphabet $X$. If one has + \[ + \varphi_{\iota_{X,\Gamma}}(w) = \varphi_{\iota_{X,\Gamma}}(w') + \] + but + \[ + \varphi_{\iota_{X,\Gamma}}(w'') \neq \varphi_{\iota_{X,\Gamma}}(w'''), + \] + then the law $w \formaleq w'$ cannot imply the law $w'' \formaleq w'''$. +\end{corollary} + +\begin{proof}\uses{canonical-invariant} + By \Cref{canonical-invariant}, the hypothesis $\iota_{X,\Gamma}(w) = \iota_{X,\Gamma}(w')$ is equivalent to $\Gamma \models w \formaleq w'$, and the hypothesis $\iota_{X,\Gamma}(w'') \neq \iota_{X,\Gamma}(w''')$ is equivalent to $\Gamma \not\models w'' \formaleq w'''$. The claim follows. +\end{proof} + +\begin{example} + Let $\Gamma$ be the associative and commutative law, so that we can take $M_{X,\Gamma} = \N_0^X \backslash 0$ as in \Cref{facm}. One can then check that for any word $w \in M_X$, that $\varphi_{\iota_{X,\Gamma}}(w)$ is the tuple that assigns to each letter $x$ of the alphabet, the number of times $x$ appears in $w$. We conclude that if $w,w'$ have the same number of occurrences of each letter of the alphabet, but $w'', w'''$ do not, then $w \formaleq w'$ cannot imply $w'' \formaleq w'''$. This recovers \Cref{variable-impl}. +\end{example} + +\begin{example} + Let $\Gamma$ consist of the left absorption law, so we can take $M_{X,\Gamma} = X$ as in \Cref{freeleft}. Then $\varphi_{\iota_{X,\Gamma}}(w)$ is the first letter of $w$. We conclude that if $w,w'$ have the same first letter, but $w'', w'''$ do not, then $w \formaleq w'$ cannot imply $w'' \formaleq w'''$. +\end{example} + +\begin{example} + Let $\Gamma$ consist of the constant law, so we can take $M_{X,\Gamma} = X \uplus \{0\}$ as in \Cref{freeconst}. Then $\varphi_{\iota_{X,\Gamma}}(w)$ is $x$ if $w$ is just a letter $x$ of the alphabet, and $0$ otherwise. We conclude that if $w,w', w'''$ have order at least one, but $w''$ has order zero, then $w \formaleq w'$ cannot imply $w'' \formaleq w'''$; this is basically \Cref{constant-impl}. +\end{example} + +\begin{example} + Let $\Gamma$ be the theory consisting of the commutative and associative laws, and an additional law $x^n \formaleq y^n$ for a fixed $n$, where $x^n$ denotes the magma operation applied to $n$ copies of $x$ (the order is irrelevant thanks to associativity), then one can check (for finite $X$) that the free magma $M_{X,\Gamma}$ can be taken to be $(\Z/n\Z)^X$ with the addition operation, and $\iota_{X,\Gamma}(x)$ being the standard generator associated to $x$. Then for any word $w$, $\varphi_{\iota_{X,\Gamma}}(w)$ corresponds to a tuple that assigns to each letter $x$ of the alphabet, the number of times $x$ occurs in $w$ modulo $n$. We conclude that if $w,w'$ have the same number of occurrences modulo $n$ of each letter of the alphabet, but $w'', w'''$ do not, then $w \formaleq w'$ cannot imply $w'' \formaleq w'''$. This is a stronger version of \Cref{variable-impl}. +\end{example} + +\section{Confluent theories} + +One promising source of theories $\Gamma$ for which the free magma $M_{X,\Gamma}$ can be understood are the \emph{confluent theories}. + +\begin{definition}[Confluent theory]\label{confluent-theory}\uses{free-magma-def} Let $\Gamma$ be a theory. A word $w$ can be \emph{reduced} to another $w'$ if one can get from $w$ to $w'$ by a series of substitutions of laws in $\Gamma$, where no substitution increases the length of the word {\bf this is a working definition, might not be the best one to keep.}. A theory $\Gamma$ is \emph{confluent} if whenever a word $w$ can be reduced to both $w'$ and $w''$, then both $w'$ and $w''$ can be reduced further to a common reduction $\tilde w$. As such, each word $w \in M_X$ should have a \emph{unique simplification} to a reduced word $w_\Gamma$ in some normal form, for instance the shortest reduction that is minimal with respect to some suitable ordering such as lexicographical ordering. +\end{definition} + +\begin{example} The associative law, \Cref{eq4512}, appears to be confluent {\bf check this}. +\end{example} + +\begin{example} The theory consisting of both the associative and commutative laws, \Cref{eq4512}, \Cref{eq43}, appears to be confluent {\bf check this}. +\end{example} + +\begin{example} The idempotent law, \Cref{eq3}, appears to be confluent {\bf check this}. +\end{example} + +The significance of confluent theories lies in + +\begin{theorem}[Free magma of a confluent theory]\label{free-confluent}\uses{confluent-theory} Let $\Gamma$ be a confluent theory. Then the free magma $M_{X,\Gamma}$ subject to this theory can be described as the space of reduced words in $M_X$ in normal form, where the operation $w \op_\Gamma w'$ on this magma is defined as the normal form reduction of $w \op w'$, and $\iota_{X,\Gamma}$ is the identity embedding (note that every single-letter word is already in normal form). +\end{theorem} + +\begin{proof} Should just be a matter of expanding definitions properly. +\end{proof} + +\begin{corollary}[Criterion for anti-implication]\label{confluent-anti-impl}\uses{models-def} Let $\Gamma$ be a confluent theory. Then a law $w \formaleq w'$ is a consequence of $\Gamma$ if and only if $w,w'$ have the same normal form reduction. In particular, a law with this property cannot imply a law without this property. +\end{corollary} + +\begin{proof}\uses{free-confluent,anti-impl} Follows from \Cref{anti-impl}. +\end{proof} + +It is thus of interest to locate some confluent laws. Here is a non-trivial example: + +\begin{theorem}[477 confluent]\label{477-confl}\uses{confluent-def} \Cref{eq477} is confluent. +\end{theorem} + +\begin{proof}\uses{477-lemma} See the notes \href{https://www.overleaf.com/project/66f847bb14d0d8f0b77f74e1}{here}. A sketch of proof is as follows. + + We induct on the length of the term. +As before we consider terms of the form $XY$. +Also, in both sequences if a simplification is applied to the whole term, then we can assume the sequence is simply final. + +By \Cref{477-lemma}, if any of the two sequences is final, +then right before the last step, the two factors of the outermost product are both simple. This is also true for the result of the non-final sequence. By the induction hypothesis, they can be identified correspondingly, so the two sequences are either both final or both non-final, and in the first case, the same simplification is applied to give the same result. +\end{proof} + +\begin{lemma}[477 lemma]\label{477-lemma} + If $Z$ and $W$ are simple, then $Z(W\cdots(WW))$ is simple. +\end{lemma} + +\begin{proof} + Assume the contrary. Then we have 2 cases. + + \textbf{Case 1: $W\cdots(WW)$ matches the pattern + $y(x(y\cdots(yy)))$, with $k$ occurrences of $W$ ($k \le n$).} + Since $|x(y\cdots(yy))| > n|y|$, but $|\cdots(WW)| \le (n-1)|W|$, this is impossible. + + \textbf{Case 2: $Z(W\cdots(WW))$ matches the pattern + $y(x(y\cdots(yy)))$.} Since $n \ge 3$, we have $Z = y = W$, + so $|W\cdots(WW)| = n|W| = n|Z|$, + contradicting $|x(y\cdots(yy))| > n|y|$. +\end{proof} diff --git a/blueprint/src/chapter/all_small_magmas.tex b/blueprint/src/chapter/all_small_magmas.tex index 30e1b8458..c333a6fb0 100644 --- a/blueprint/src/chapter/all_small_magmas.tex +++ b/blueprint/src/chapter/all_small_magmas.tex @@ -1,3 +1,3 @@ -\chapter{Enumerating Small Finite Magmas} +\chapter{Enumerating Small Finite Magmas}\label{all-small-magmas-chapter} {\bf describe the process of automatically generating these implications here.} diff --git a/blueprint/src/chapter/constant.tex b/blueprint/src/chapter/constant.tex index 693a6dea5..4d8436e6f 100644 --- a/blueprint/src/chapter/constant.tex +++ b/blueprint/src/chapter/constant.tex @@ -1,16 +1,19 @@ -\chapter{Equivalence with the constant and singleton laws} +\chapter{Equivalence with the constant and singleton laws}\label{constant-chapter} -\href{https://github.com/teorth/equational_theories/blob/main/equational_theories/Generated/Constant.lean}{85 laws} have been shown to be equivalent to the constant law (Definition \ref{eq46}), and \href{https://github.com/teorth/equational_theories/blob/main/equational_theories/Generated/Singleton.lean}{815 laws} have been shown to be equivalent to the singleton law (Definition \ref{eq2}). +\href{https://github.com/teorth/equational_theories/blob/main/equational_theories/Generated/Constant.lean}{85 laws} +have been shown to be equivalent to the constant law (\Cref{eq46}), and +\href{https://github.com/teorth/equational_theories/blob/main/equational_theories/Generated/Singleton.lean}{815 laws} +have been shown to be equivalent to the singleton law (\Cref{eq2}). -These are the laws up to 4 operations that follow from diagonalization of \ref{eq2} and of \ref{eq46}. +These are the laws up to 4 operations that follow from diagonalization of \Cref{eq2} and \Cref{eq46}. -In order to formalize these in Lean, a search was run on the list of equations to discover +To formalize these in Lean, a search was run on the list of equations to discover diagonalizations of these two specific laws: equations of the form $x = R$ where $R$ doesn't include -$x$, and equations of the form $x \circ y = R$ where R doesn't include $x$ or $y$. +$x$, and equations of the form $x \circ y = R$ where $R$ doesn't include $x$ or $y$. The proofs themselves all look alike, and correspond exactly to the two steps described in the proof -of \ref{diag}. The Lean proofs were generated semi-manually, using search-and-replace starting from +of \Cref{diag}. The Lean proofs were generated semi-manually, using search-and-replace starting from the output of \texttt{grep} that found the diagonalized laws. -In the case of the constant law, equation \ref{eq41} ($x \circ x = y \circ z$) wasn't detected using +In the case of the constant law, \Cref{eq41} ($x \circ x = y \circ z$) wasn't detected using this method. It was added manually to the file with the existing proof from the sub-graph project. diff --git a/blueprint/src/chapter/counterexamples.tex b/blueprint/src/chapter/counterexamples.tex index ce35bf846..6d19a268f 100644 --- a/blueprint/src/chapter/counterexamples.tex +++ b/blueprint/src/chapter/counterexamples.tex @@ -1,4 +1,4 @@ -\chapter{Selected magmas} +\chapter{Selected magmas}\label{selected-magmas-chapter} Each magma can be used to establish anti-implications: if $\Gamma$ is the set of all laws obeyed by a magma $G$, then we have $\neg E \leq E'$ whenever $E \in \Gamma$ and $E' \not \in \Gamma$. Large numbers of implications can already be obtained from @@ -18,8 +18,8 @@ \chapter{Selected magmas} \item The reals with $x \circ y = (x+y)/2$. \item The natural numbers with $x \circ x$ equal to $x$ when $x=y$ and $x+1$ otherwise. \item The set of strings with $x \circ y$ equal to $y$ when $x=y$ or when $x$ ends with $yyy$, or $xy$ otherwise (see \href{https://leanprover.zulipchat.com/#narrow/stream/458659-Equational/topic/3102.20does.20not.20imply.203176}{this Zulip thread}). - \item Vector spaces ${\mathbb F}_2^n$ over ${\mathbb F}_2$, which obey Definition \ref{eq1571} (and hence all the subsequent laws mentioned in Theorem \ref{1571_impl}). - \item Knuth's construction \cite{knuth} of a central groupoid (Definition \ref{eq168}) as follows. Let $S$ be a (finite) set with a distinguished element $0$, and a binary operation $*$ such that $x*0=0$ and $0*x=x$ for all $x$, and for each $x,y$ there is a unique $z$ with $x*z=y$. One can then define a central groupoid on $S \times S$ by defining $(a,b) \op (c,d)$ to equal $(b,c)$ if $c,d \neq 0$; $(b,e)$ if $b*e=c$ is non-zero and $d=0$; and $(a*b,0)$ if $c=0$. One such example in \cite{knuth} is when $S = \{0,1,2\}$ with $1*1=2*1=2$ and $1*2=2*2=1$. + \item Vector spaces ${\mathbb F}_2^n$ over ${\mathbb F}_2$, which obey \Cref{eq1571} (and hence all the subsequent laws mentioned in \Cref{1571_impl}). + \item Knuth's construction \cite{knuth} of a central groupoid (\Cref{eq168}) as follows. Let $S$ be a (finite) set with a distinguished element $0$, and a binary operation $*$ such that $x*0=0$ and $0*x=x$ for all $x$, and for each $x,y$ there is a unique $z$ with $x*z=y$. One can then define a central groupoid on $S \times S$ by defining $(a,b) \op (c,d)$ to equal $(b,c)$ if $c,d \neq 0$; $(b,e)$ if $b*e=c$ is non-zero and $d=0$; and $(a*b,0)$ if $c=0$. One such example in \cite{knuth} is when $S = \{0,1,2\}$ with $1*1=2*1=2$ and $1*2=2*2=1$. \item Cancellative magmas of orders 7 to 9, found by hand-guided search using various solvers. \item Two magmas of cardinality $8$ were \href{https://leanprover.zulipchat.com/#narrow/stream/458659-Equational/topic/using.20z3}{constructed by Z3}. \item A large number of ad-hoc finite magmas were constructed using the Vampire theorem prover. diff --git a/blueprint/src/chapter/egraphs.tex b/blueprint/src/chapter/egraphs.tex index 4943f850a..1c4c01de6 100644 --- a/blueprint/src/chapter/egraphs.tex +++ b/blueprint/src/chapter/egraphs.tex @@ -1,4 +1,4 @@ -\chapter{E-Graphs} +\chapter{E-Graphs}\label{egraphs-chapter} For proving implications, we used another technique called equality saturation~\cite{DBLP:journals/pacmpl/WillseyNWFTP21} with the lean-egg tactic, to automatically construct proofs. @@ -19,10 +19,10 @@ \subsection{Methodology} \subsection{Results} -Out of the possible implications between the $34$ equations considered in Chapter~\ref{subgraph-eq}, this method found an additional 86 implications that were not found before. +Out of the possible implications between the $34$ equations considered in \Cref{subgraph-eq}, this method found an additional 86 implications that were not found before. Some of these seem to be missing in the computation of the transitive closure of implications of the equalities (an investigation is in progress), but some of these are genuinely new theorems, and the \texttt{lean-egg} tactic finds good proofs of these (these can be rewritten using \texttt{calc} style with a different tactic, \texttt{calcify}: \url{https://github.com/nomeata/lean-calcify}). An example of this is the following proof, found by lean-egg: -\begin{theorem}[14 implies 23]\label{14_implies_23} \uses{eq23,eq14}\lean{Subgraph.Equation14_implies_Equation23}\leanok Definition \ref{eq14} is equivalent to Definition \ref{eq23}. +\begin{theorem}[14 implies 23]\label{14_implies_23} \uses{eq23,eq14}\lean{Subgraph.Equation14_implies_Equation23}\leanok \Cref{eq14} is equivalent to \Cref{eq23}. \end{theorem} \begin{proof}\leanok @@ -30,7 +30,7 @@ \subsection{Results} $$ x = (x \op x) \op (x \op (x \op x)) = (x \op x) \op x $$ \end{proof} -It was also able to (re)prove Theorem~\ref{1689_equiv_2}, albeit with a manually-provided hint (guide, in the sense of~\cite{DBLP:journals/pacmpl/KoehlerGBGTS24}). +It was also able to (re)prove \Cref{1689_equiv_2}, albeit with a manually-provided hint (guide, in the sense of~\cite{DBLP:journals/pacmpl/KoehlerGBGTS24}). \section{MagmaEgg} diff --git a/blueprint/src/chapter/equation_search.tex b/blueprint/src/chapter/equation_search.tex index e3c184446..d71753d2b 100644 --- a/blueprint/src/chapter/equation_search.tex +++ b/blueprint/src/chapter/equation_search.tex @@ -1,4 +1,4 @@ -\chapter{Equation Search} +\chapter{Equation Search}\label{equation-search-chapter} \href{https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/EquationSearch}{Approximately ~650k transitive implications were proven by a custom tool leveraging the implication graph}. After previous brute force had derived many implications expressible as a small number of rewrites, this search tool uses substitutions implied by the implication graph to search further. diff --git a/blueprint/src/chapter/equations.tex b/blueprint/src/chapter/equations.tex index 80e1c54b3..166161a16 100644 --- a/blueprint/src/chapter/equations.tex +++ b/blueprint/src/chapter/equations.tex @@ -28,7 +28,7 @@ \chapter{Selected laws}\label{subgraph-eq} \begin{definition}[Equation 5]\label{eq5}\lean{Equation5}\leanok\uses{magma-def} Equation 5 is the law $0 \formaleq 1 \op 0$ (or the equation $x = y \op x$). \end{definition} -This is the right absorption law (the dual of Definition \ref{eq4}). +This is the right absorption law (the dual of \Cref{eq4}). \begin{definition}[Equation 6]\label{eq6}\lean{Equation6}\leanok\uses{magma-def} Equation 6 is the law $0 \formaleq 1 \op 1$ (or the equation $x = y \op y$). \end{definition} @@ -54,12 +54,12 @@ \chapter{Selected laws}\label{subgraph-eq} \begin{definition}[Equation 23]\label{eq23}\lean{Equation23}\leanok\uses{magma-def} Equation 23 is the law $0 \formaleq (0 \op 0) \op 0$ (or the equation $x = (x \op x) \op x$). \end{definition} -This is the dual of Definition \ref{eq8}. +This is the dual of \Cref{eq8}. \begin{definition}[Equation 29]\label{eq29}\lean{Equation29}\leanok\uses{magma-def} Equation 29 is the law $0 \formaleq (1 \op 0) \op 1$ (or the equation $x = (y \op x) \op y)$. \end{definition} -Appears in Problem A1 from Putnam 2001. Dual to Definition \ref{eq14}. +Appears in Problem A1 from Putnam 2001. Dual to \Cref{eq14}. \begin{definition}[Equation 38]\label{eq38}\lean{Equation38}\leanok\uses{magma-def} Equation 38 is the law $0 \op 0 \formaleq 0 \op 1$ (or the equation $x \op x = x \op y$). \end{definition} @@ -69,7 +69,7 @@ \chapter{Selected laws}\label{subgraph-eq} \begin{definition}[Equation 39]\label{eq39}\lean{Equation39}\leanok\uses{magma-def} Equation 39 is the law $0 \op 0 \formaleq 1 \op 0$ (or the equation $x \op x = y \op x$). \end{definition} -This law asserts that the magma operation is independent of the first argument (the dual of Definition \ref{eq38}). +This law asserts that the magma operation is independent of the first argument (the dual of \Cref{eq38}). \begin{definition}[Equation 40]\label{eq40}\lean{Equation40}\leanok\uses{magma-def} Equation 40 is the law $0 \op 0 \formaleq 1 \op 1$ (or the equation $x \op x = y \op y$). \end{definition} @@ -79,12 +79,12 @@ \chapter{Selected laws}\label{subgraph-eq} \begin{definition}[Equation 41]\label{eq41}\lean{Equation41}\leanok\uses{magma-def} Equation 41 is the law $0 \op 0 \formaleq 1 \op 2$ (or the equation $x \op x = y \op z$). \end{definition} -This law is equivalent to the constant law, Definition \ref{eq46}. +This law is equivalent to the constant law, \Cref{eq46}. \begin{definition}[Equation 42]\label{eq42}\lean{Equation42}\leanok\uses{magma-def} Equation 42 is the law $0 \op 1 \formaleq 0 \op 2$ (or the equation $x \op y = x \op z$). \end{definition} -Equivalent to Definition \ref{eq38}. +Equivalent to \Cref{eq38}. \begin{definition}[Equation 43]\label{eq43}\lean{Equation43}\leanok\uses{magma-def} Equation 43 is the law $0 \op 1 \formaleq 1 \op 0$ (or the equation $x \op y = y \op x$). \end{definition} @@ -94,7 +94,7 @@ \chapter{Selected laws}\label{subgraph-eq} \begin{definition}[Equation 45]\label{eq45}\lean{Equation45}\leanok\uses{magma-def} Equation 45 is the law $0 \op 1 \formaleq 2 \op 1$ (or the equation $x \op y = z \op y$). \end{definition} -This is the dual of Definition \ref{eq42}. +This is the dual of \Cref{eq42}. \begin{definition}[Equation 46]\label{eq46}\lean{Equation46}\leanok\uses{magma-def} Equation 46 is the law $0 \op 1 \formaleq 2 \op 3$ (or the equation $x \op y = z \op w$). \end{definition} @@ -116,6 +116,9 @@ \chapter{Selected laws}\label{subgraph-eq} Introduced in \href{https://mathoverflow.net/a/450905/766}{MathOverflow}. +\begin{definition}[Equation 477]\label{eq477}\lean{Equation477}\leanok\uses{magma-def} Equation 477 is the law $0 \formaleq 1 \op (0 \op (1 \op (1 \op 1)))$ (or the equation $x = y \op (x \op (y \op (y \op y)))$). +\end{definition} + \begin{definition}[Equation 953]\label{eq953}\lean{Equation953}\leanok\uses{magma-def} Equation 953 is the law $0 = 1 \op ((2 \op 0) \op (2 \op 2))$ (or the equation $x = y \op ((z \op x) \op (z \op z))$). \end{definition} @@ -155,17 +158,17 @@ \chapter{Selected laws}\label{subgraph-eq} \begin{definition}[Equation 4522]\label{eq4522}\lean{Equation4522}\leanok\uses{magma-def} Equation 4522 is the law $0 \op (1 \op 2) \formaleq (0 \op 3) \op 4$ (or the equation $x \op (y \op z) = (x \op w) \op u$). \end{definition} -Dual to Definition \ref{eq4579}. +Dual to \Cref{eq4579}. \begin{definition}[Equation 4564]\label{eq4564}\lean{Equation4564}\leanok\uses{magma-def} Equation 4564 is the law $0 \op (1 \op 2) \formaleq (3 \op 1) \op 2$ (or the equation $x \op (y \op z) = (w \op y) \op z$). \end{definition} -Dual to Definition \ref{eq4513}. +Dual to \Cref{eq4513}. \begin{definition}[Equation 4579]\label{eq4579}\lean{Equation4579}\leanok\uses{magma-def} Equation 4579 is the law $0 \op (1 \op 2) \formaleq (3 \op 4) \op 2$ (or the equation $x \op (y \op z) = (w \op u) \op z$). \end{definition} -Dual to Definition \ref{eq4522}. +Dual to \Cref{eq4522}. \begin{definition}[Equation 4582]\label{eq4582}\lean{Equation4582}\leanok\uses{magma-def} Equation 4582 is the law $0 \op (1 \op 2) \formaleq (3 \op 4) \op 5$ (or the equation $x \op (y \op z) = (w \op u) \op v$). \end{definition} diff --git a/blueprint/src/chapter/general_implications.tex b/blueprint/src/chapter/general_implications.tex index 64004078b..5636a7906 100644 --- a/blueprint/src/chapter/general_implications.tex +++ b/blueprint/src/chapter/general_implications.tex @@ -1,4 +1,4 @@ -\chapter{General implications} +\chapter{General implications}\label{generla-implications-chapter} We will be interested in seeing which laws imply which other laws, in the sense that magmas obeying the former law automatically obey the latter. We will also be interested in \emph{anti-implications} showing that one law does \emph{not} imply another, by producing examples of magmas that obey the former law but not the latter. Here is a formal definition. @@ -15,7 +15,7 @@ \chapter{General implications} \begin{proof}\leanok Trivial. \end{proof} -Implications between the laws from Chapter \ref{subgraph-eq} are depicted in Figure \ref{fig:implications}. +Implications between the laws from \Cref{subgraph-eq} are depicted in \Cref{fig:implications}. \begin{figure} \centering @@ -60,16 +60,16 @@ \chapter{General implications} In particular, if $G(y_1,\dots,y_m)$ can be viewed as a specialization of $F(x'_1,\dots,x'_n)$, then these two laws are equivalent. \end{theorem} -\begin{proof} From two applications of \eqref{prediag} one has +\begin{proof} From two applications of \Cref{prediag} one has $$ F(x_1,\dots,x_n) = G(y_1,\dots,y_m)$$ and $$ F(x'_1,\dots,x'_n) = G(y_1,\dots,y_m)$$ whence the claim. \end{proof} -Thus for instance, Definition \ref{eq7} is equivalent to Definition \ref{eq2}. +Thus for instance, \Cref{eq7} is equivalent to \Cref{eq2}. -\begin{theorem}[Laws implied by the constant law]\label{constant-impl}\uses{impl,eq46} If $w, w'$ each have order at least one, then the law $w \formaleq w'$ is implied by the constant law (Definition \ref{eq46}). If exactly one of $w, w'$ has order zero, and the law $w \formaleq w'$ is not implied by the constant law. +\begin{theorem}[Laws implied by the constant law]\label{constant-impl}\uses{impl,eq46} If $w, w'$ each have order at least one, then the law $w \formaleq w'$ is implied by the constant law (\Cref{eq46}). If exactly one of $w, w'$ has order zero, and the law $w \formaleq w'$ is not implied by the constant law. \end{theorem} \begin{proof} Routine. diff --git a/blueprint/src/chapter/implications.tex b/blueprint/src/chapter/implications.tex index 8b301c767..64403318a 100644 --- a/blueprint/src/chapter/implications.tex +++ b/blueprint/src/chapter/implications.tex @@ -1,44 +1,44 @@ -\chapter{Implications between selected laws} +\chapter{Implications between selected laws}\label{implications-chapter} -We collect here some notable implications between the the selected laws in Chapter \ref{subgraph-eq}. By Theorem \ref{sound-complete}, every implication can basically be established by a finite number of rewrites. In most cases, the sequence of rewrites is quite straightforward, and the implication is very easy, but we record some less obvious examples. +We collect here some notable implications between the the selected laws in \Cref{subgraph-eq}. By \Cref{sound-complete}, every implication can basically be established by a finite number of rewrites. In most cases, the sequence of rewrites is quite straightforward, and the implication is very easy, but we record some less obvious examples. -\begin{theorem}[387 implies 43]\label{387_implies_43}\uses{eq387,eq43}\lean{Subgraph.Equation387_implies_Equation43}\leanok Definition \ref{eq387} implies Definition \ref{eq43}. +\begin{theorem}[387 implies 43]\label{387_implies_43}\uses{eq387,eq43}\lean{Subgraph.Equation387_implies_Equation43}\leanok \Cref{eq387} implies \Cref{eq43}. \end{theorem} \begin{proof}\leanok (From \href{https://mathoverflow.net/a/450905/766}{MathOverflow}). - By Definition \ref{eq387}, one has the law + By \Cref{eq387}, one has the law \begin{equation}\label{387-again} (x \op x) \op y = y \op x. \end{equation} Specializing to $y=x \op x$, we conclude $$(x \op x) \op (x \op x) = (x \op x) \op x$$ -and hence by another application of \eqref{eq387} we see that $x \op x$ is idempotent: +and hence by another application of \Cref{eq387} we see that $x \op x$ is idempotent: \begin{equation}\label{idem} (x \op x) \op (x \op x) = x \op x. \end{equation} -Now, replacing $x$ by $x \op x$ in \eqref{387-again} and then using \eqref{idem} we see that +Now, replacing $x$ by $x \op x$ in \Cref{387-again} and then using \Cref{idem} we see that $$ (x \op x) \op y = y \op (x \op x)$$ so in particular $x \op x$ commutes with $y \op y$: \begin{equation}\label{op-idem} (x \op x) \op (y \op y) = (y \op y) \op (x \op x). \end{equation} -Also, from two applications of \eqref{387-again} one has +Also, from two applications of \Cref{387-again} one has $$(x \op x) \op (y \op y) = (y \op y) \op x = x \op y.$$ -Thus \eqref{op-idem} simplifies to $x \op y = y \op x$, which is Definition \ref{eq43}. +Thus \Cref{op-idem} simplifies to $x \op y = y \op x$, which is \Cref{eq43}. \end{proof} -\begin{theorem}[29 equivalent to 14]\label{29_equiv_14} \uses{eq29,eq14}\lean{Subgraph.Equation29_implies_Equation14}\leanok Definition \ref{eq29} is equivalent to Definition \ref{eq14}. +\begin{theorem}[29 equivalent to 14]\label{29_equiv_14} \uses{eq29,eq14}\lean{Subgraph.Equation29_implies_Equation14}\leanok \Cref{eq29} is equivalent to \Cref{eq14}. \end{theorem} This result was posed as Problem A1 from Putnam 2001. -\begin{proof}\leanok\uses{duality} By Lemma \ref{duality} it suffices to show that Definition \ref{eq29} implies Definition \ref{eq14}. From Definition \ref{eq29} one has +\begin{proof}\leanok\uses{duality} By \Cref{duality} it suffices to show that \Cref{eq29} implies \Cref{eq14}. From \Cref{eq29} one has $$ x = ((x \op y) \op x) \op (x \op y)$$ and also $$ y = (x \op y) \op x$$ - giving $x = y \op (x \op y)$, which is Definition \ref{eq14}. + giving $x = y \op (x \op y)$, which is \Cref{eq14}. \end{proof} -\begin{theorem}[14 implies 29]\label{14_implies_29} \uses{eq29,eq14}\lean{Subgraph.Equation14_implies_Equation29}\leanok Definition \ref{eq14} implies Definition \ref{eq29}. +\begin{theorem}[14 implies 29]\label{14_implies_29} \uses{eq29,eq14}\lean{Subgraph.Equation14_implies_Equation29}\leanok \Cref{eq14} implies \Cref{eq29}. \end{theorem} This result was posed as Problem A1 from Putnam 2001. @@ -48,7 +48,7 @@ \chapter{Implications between selected laws} The following result was Problem A4 on Putnam 1978. -\begin{theorem}[3744 implies 3722, 381]\label{3744_implies_3722_381}\uses{eq3744, eq3722, eq381}\lean{Subgraph.Equation3744_implies_Equation3722, Subgraph.Equation3744_implies_Equation381}\leanok Definition \ref{eq3744} implies Definition \ref{eq3722} and Definition \ref{eq381}. +\begin{theorem}[3744 implies 3722, 381]\label{3744_implies_3722_381}\uses{eq3744, eq3722, eq381}\lean{Subgraph.Equation3744_implies_Equation3722, Subgraph.Equation3744_implies_Equation381}\leanok \Cref{eq3744} implies \Cref{eq3722} and \Cref{eq381}. \end{theorem} \begin{proof}\leanok By hypothesis, one has @@ -60,16 +60,16 @@ \chapter{Implications between selected laws} x \op z &= (x \op z) \op (x \op z) \label{381-2} \\ (x \op z) \op y &= ((x \op z) \op (x \op z)) \op (y \op y) \label{381-3}. \end{align} -The equation \eqref{381-2} gives Definition \ref{eq3722}, while \eqref{381-1}, \eqref{381-2}, \eqref{381-3} gives +\Cref{381-2} gives \Cref{eq3722}, while \Cref{381-1}, \Cref{381-2}, \Cref{381-3} gives $$ x \op y = (x\op z) \op y$$ -which is Definition \ref{eq381}. +which is \Cref{eq381}. \end{proof} -\begin{theorem}[1689 is equivalent to 2]\label{1689_equiv_2}\uses{eq1689, eq2}\lean{Subgraph.Equation1689_implies_Equation2, Subgraph.Equation2_implies_Equation1689}\leanok Definition \ref{eq1689} is equivalent to Definition \ref{eq2}. +\begin{theorem}[1689 is equivalent to 2]\label{1689_equiv_2}\uses{eq1689, eq2}\lean{Subgraph.Equation1689_implies_Equation2, Subgraph.Equation2_implies_Equation1689}\leanok \Cref{eq1689} is equivalent to \Cref{eq2}. \end{theorem} -\begin{proof}\leanok The implication of Definition \ref{eq1689} from Definition \ref{eq2} is trivial. The converse is a surprisingly long chain of implications; see pages 326--327 of \cite{Kisielewicz2}. The initial law +\begin{proof}\leanok The implication of \Cref{eq1689} from \Cref{eq2} is trivial. The converse is a surprisingly long chain of implications; see pages 326--327 of \cite{Kisielewicz2}. The initial law $$ x = (y \op x) \op ((x \op z) \op z)$$ is used to obtain, in turn, $$ x \op ((((x \op y) \op y) \op z) \op z) = (x \op y) \op y,$$ @@ -90,10 +90,10 @@ \chapter{Implications between selected laws} The following result was established in \cite{mendelsohn-padmanabhan}. -\begin{theorem}[Consequences of 1571]\label{1571_impl}\uses{eq1571, eq2662, eq40, eq23, eq8, eq16, eq14, eq43, eq4512}\lean{Subgraph.Equation1571_implies_Equation2662, Subgraph.Equation1571_implies_Equation40, Subgraph.Equation1571_implies_Equation23,Subgraph.Equation1571_implies_Equation8, Subgraph.Equation1571_implies_Equation16, Subgraph.Equation1571_implies_Equation43, Subgraph.Equation1571_implies_Equation4512}\leanok Magmas obeying Definition \ref{eq1571} also obey Definitions \ref{eq2662}, \ref{eq40}, \ref{eq23}, \ref{eq8}, \ref{eq16}, \eqref{eq14}, \ref{eq43}, and \ref{eq4512}, and are in fact abelian groups of exponent two. Conversely, all abelian groups of exponent two obey Definition \ref{eq1571}. +\begin{theorem}[Consequences of 1571]\label{1571_impl}\uses{eq1571, eq2662, eq40, eq23, eq8, eq16, eq14, eq43, eq4512}\lean{Subgraph.Equation1571_implies_Equation2662, Subgraph.Equation1571_implies_Equation40, Subgraph.Equation1571_implies_Equation23,Subgraph.Equation1571_implies_Equation8, Subgraph.Equation1571_implies_Equation16, Subgraph.Equation1571_implies_Equation43, Subgraph.Equation1571_implies_Equation4512}\leanok Magmas obeying \Cref{eq1571} also obey \Cref{eq2662}, \Cref{eq40}, \Cref{eq23}, \Cref{eq8}, \Cref{eq16}, \Cref{eq14}, \Cref{eq43}, and \Cref{eq4512}, and are in fact abelian groups of exponent two. Conversely, all abelian groups of exponent two obey \Cref{eq1571}. \end{theorem} -\begin{proof}\leanok Suppose that a magma $G$ obeys Definition \ref{eq1571}, thus +\begin{proof}\leanok Suppose that a magma $G$ obeys \Cref{eq1571}, thus \begin{equation}\label{1571-again} x = (y \op z) \op (y \op (x \op z)). \end{equation} @@ -102,18 +102,18 @@ \chapter{Implications between selected laws} $$ x = (x \op y) \op (x \op (x \op y))$$ whence $$x = ((x \op y) \op (x \op y)) \op x$$ -which is Definition \ref{eq2662}. This gives +which is \Cref{eq2662}. This gives $$y = ((y \op z) \op (y \op z)) \op y$$ -while from \eqref{1571-again} one has +while from \Cref{1571-again} one has $$ (y \op z) \op (y \op z) = (x \op y) \op (x \op ((y \op z) \op (y \op z) \op y))$$ whence $$ (x \op y) \op (x \op y) = (y \op z) \op (y \op z).$$ This implies that $(x \op y) \op (x \op y)$ does not depend on $x$, or on $y$, hence is equal to some constant $e$: $$ (x \op y) \op (x \op y) = e.$$ -From \eqref{1571-again} the magma operation is surjective, hence +From \Cref{1571-again} the magma operation is surjective, hence \begin{equation}\label{xxe} x \op x = e \end{equation} -which gives Definition \ref{eq40}. Applying \eqref{1571-again} with $x=y=z$ we conclude +which gives \Cref{eq40}. Applying \Cref{1571-again} with $x=y=z$ we conclude $$ x = e \op (x \op e)$$ while if we instead take $y=z=e$ we have $$ x = e \op (e \op (x \op e))$$ @@ -121,34 +121,34 @@ \chapter{Implications between selected laws} $$ x = e \op x$$ and then also $$ x = x \op e$$ -from which we readily conclude Definitions \ref{eq23}, \ref{eq8}; thus $e$ is an identity element. From \eqref{1571-again} with $z=e$ we now have +from which we readily conclude \Cref{eq23}, \Cref{eq8}; thus $e$ is an identity element. From \Cref{1571-again} with $z=e$ we now have \begin{equation}\label{16-again} x = y \op (y \op x) \end{equation} -which is Definition \ref{eq16}. If instead we take $y=e$ we have +which is \Cref{eq16}. If instead we take $y=e$ we have \begin{equation}\label{14-again} x = z \op (x \op z) \end{equation} -which is Definition \ref{eq14}. So if we substitute $z = x \op y$ and use \eqref{16-again} we obtain +which is \Cref{eq14}. So if we substitute $z = x \op y$ and use \Cref{16-again} we obtain $$ x = (x \op y) \op y$$ and hence $$ y \op x = y \op ((x \op y) \op y) = x \op y$$ -thanks to \eqref{14-again}. This gives Definition \ref{eq43}, thus $G$ is now commutative. From \eqref{1571-again} once more one has +thanks to \Cref{14-again}. This gives \Cref{eq43}, thus $G$ is now commutative. From \Cref{1571-again} once more one has $$x \op (y \op z) = (y \op x) \op (z \op ((x \op (y \op z)) \op x))$$ -which one can simplify using commutativity and \eqref{16-again} (or \eqref{14-again}) to eventually obtain +which one can simplify using commutativity and \Cref{16-again} (or \Cref{14-again}) to eventually obtain $$x \op (y \op z) = (x \op y) \op z$$ -which is Definition \ref{eq4512}. $G$ is now commutative and associative, and every element is its own inverse and of exponent $2$, hence is an abelian group thanks to \eqref{xxe}, so $G$ is an abelian group of exponent $2$ as claimed. The converse is easily verified. +which is \Cref{eq4512}. $G$ is now commutative and associative, and every element is its own inverse and of exponent $2$, hence is an abelian group thanks to \Cref{xxe}, so $G$ is an abelian group of exponent $2$ as claimed. The converse is easily verified. \end{proof} -\begin{theorem}[953 is equivalent to 2]\label{953_equiv_2}\uses{eq953, eq2}\lean{Subgraph.Equation953_implies_Equation2}\leanok Definition \ref{eq953} is equivalent to Definition \ref{eq2}. +\begin{theorem}[953 is equivalent to 2]\label{953_equiv_2}\uses{eq953, eq2}\lean{Subgraph.Equation953_implies_Equation2}\leanok \Cref{eq953} is equivalent to \Cref{eq2}. \end{theorem} -\begin{proof}\leanok It suffices to show that Definition \ref{eq953} implies Definition \ref{eq2}. Pick an element $0$ of $G$ and define $1 = 0 \op 0$ and $2 = 1 \op 1$ (we do not require $0,1,2$ to be distinct). -From Definition \ref{eq953} with $x=z=0$ we have +\begin{proof}\leanok It suffices to show that \Cref{eq953} implies \Cref{eq2}. Pick an element $0$ of $G$ and define $1 = 0 \op 0$ and $2 = 1 \op 1$ (we do not require $0,1,2$ to be distinct). +From \Cref{eq953} with $x=z=0$ we have $$ 0 = y \op 2.$$ -If we then apply Definition \ref{eq953} with $z=1$ we conclude that +If we then apply \Cref{eq953} with $z=1$ we conclude that $$ x = y \op 0$$ -for all $x,y$, from which one concludes $x=x'$ for any $x,x' \in G$, giving Definition \ref{eq2}. +for all $x,y$, from which one concludes $x=x'$ for any $x,x' \in G$, giving \Cref{eq2}. \end{proof} @@ -157,7 +157,7 @@ \chapter{Implications between selected laws} \begin{theorem}[Sheffer stroke axiom]\label{sheffer} The law $$ 0 \formaleq (1 \op ((0 \op 1) \op 1)) \op (0 \op (2 \op 1))$$ or in equation form -$$ x = y \op ((x \op y) \op y) \op (x \op (z \op y)) $$ +$$ x = (y \op ((x \op y) \op y)) \op (x \op (z \op y)) $$ axiomatizes the Sheffer stroke operation $x \op y = \overline{xy}$ in a Boolean algebra. {\bf TODO: locate the equation number for this law.} \end{theorem} @@ -173,7 +173,7 @@ \chapter{Implications between selected laws} A \emph{natural central groupoid} is, up to isomorphism, a magma with carrier $S \times S$ for some set $S$ and operation $$ (a,b) \op (c,d) = (b,c).$$ -These are examples of central groupoids (Definition \ref{eq168}). +These are examples of central groupoids (\Cref{eq168}). \begin{theorem}[Natural central groupoid axiom]\label{natural-central-groupoid} The law $$ 0 \formaleq (1 \op ((2 \op 0) \op 3)) \op (0 \op 3)$$ @@ -185,12 +185,12 @@ \chapter{Implications between selected laws} \end{theorem} \begin{proof} - See \cite[Theorem 5]{knuth}. The proof is quite lengthy; a sketch is as follows. It is easy to see that natural central groupoids obey \eqref{26302}. Conversely, if this law holds, then + See \cite[Theorem 5]{knuth}. The proof is quite lengthy; a sketch is as follows. It is easy to see that natural central groupoids obey \Cref{26302}. Conversely, if this law holds, then \begin{align*} (y \op z) \op (z \op w) &= (( x \op ((w \op (y \op z)) \op w)) \op ((y \op z) \op w)) \op (z \op w)\\ &= z \end{align*} -so we have a central groupoid. Setting $y = (t \op t) \op t$, $z = t \op (t \op t)$, $w = t \op t$ in \eqref{26302} we also obtain +so we have a central groupoid. Setting $y = (t \op t) \op t$, $z = t \op (t \op t)$, $w = t \op t$ in \Cref{26302} we also obtain $$ (x \op t) \op t = (t \op t) \op t.$$ Using the notation $$ x^{(1)} := (x \op x) \op x, \quad x^{(2)} := x \op (x \op x)$$ diff --git a/blueprint/src/chapter/infinite_models.tex b/blueprint/src/chapter/infinite_models.tex index 37096be61..6de8091b9 100644 --- a/blueprint/src/chapter/infinite_models.tex +++ b/blueprint/src/chapter/infinite_models.tex @@ -1,4 +1,4 @@ -\chapter{Infinite models} +\chapter{Infinite models}\label{infinite-model-chapter} In this chapter we consider non-implications which are refuted only on infinite models, as those are more challenging to prove---they can't be proved by directly giving an operation table and checking @@ -7,15 +7,15 @@ \chapter{Infinite models} We note some selected laws of order more than $5$, used for such non-implications. \begin{definition}[Equation 5105] - \label{eq5105}\uses{magma-def}\lean{Equation28393}\leanok + \label{eq5105}\uses{magma-def}\lean{Equation5105}\leanok Equation 5105 is the law $0 \formaleq 1 \op (1 \op (1 \op (0 \op (2 \op 1))))$ (or the equation $x = y \op (y \op (y \op (x \op (z \op y))))$). \end{definition} This law of order $5$ was mentioned in \cite{Kisielewicz2}. -\begin{definition}[Equation 28393] - \label{eq28393}\uses{magma-def}\lean{Equation28393}\leanok - Equation 28393 is the law $0 \formaleq (((0 \op 0) \op 0) \op 1) \op (0 \op 2)$ (or the equation $x = (((x \op x) \op x) \op y) \op (x \op z)$). +\begin{definition}[Equation 28770] + \label{eq28770}\uses{magma-def}\lean{Equation28770}\leanok + Equation 28770 is the law $0 \formaleq (((1 \op 1) \op 1) \op 0) \op (1 \op 2)$ (or the equation $x = (((y \op y) \op y) \op x) \op (y \op z)$). \end{definition} This law of order $5$ was introduced by Kisielewicz \cite{Kisielewicz}. @@ -35,10 +35,10 @@ \chapter{Infinite models} \begin{theorem}[Kisielewicz's first Austin law] \lean{InfModel.Finite.Equation374794_implies_Equation2,InfModel.Equation374794_not_implies_Equation2}\leanok \label{kis-thm}\uses{eq374794,eq2} - Definition \ref{eq374794} is an Austin law. + \Cref{eq374794} is an Austin law. \end{theorem} -\begin{proof} \leanok First we show that every finite model of Definition \ref{eq374794} is trivial. Write $y^2 := y \op y$ and $y^3 := y^2 \op y$. For any $y,z$, introduce the functions ${f_y: x \mapsto y^3 \op x}$ and ${g_{yz}: x \mapsto x \op (y^2 \op z)}$. Definition \ref{eq374794} says that $g_{yz}(f_y(x))=x$, hence by finiteness $g_{yz}=f_y^{-1}$, showing that $g_{yz}$ does not depend on the value of $z$. Since +\begin{proof} \leanok First we show that every finite model of \Cref{eq374794} is trivial. Write $y^2 := y \op y$ and $y^3 := y^2 \op y$. For any $y,z$, introduce the functions ${f_y: x \mapsto y^3 \op x}$ and ${g_{yz}: x \mapsto x \op (y^2 \op z)}$. \Cref{eq374794} says that $g_{yz}(f_y(x))=x$, hence by finiteness $g_{yz}=f_y^{-1}$, showing that $g_{yz}$ does not depend on the value of $z$. Since $$ f_y(y^2 \op z) = g_{yz}(y^3),$$ it follows that $f_y(y^2 \op z)=f_y(y^3)$ which by injectivity of $f_y$ implies that $z\mapsto y^2 \op z$ is a constant function (with $y$ fixed). Substituting $y^2$ for $y$ shows that the same is true for $z\mapsto (y^2 \op y^2) \op z$, and since $$ f_y(z) = (y^2 \op y) \op z = (y^2 \op y^2) \op z$$ @@ -60,21 +60,21 @@ \chapter{Infinite models} $$ 3^x \op ((y \op y) \op z) = x. $$ The case $x=1$ requires a further argument: observe that $w = (y \op y) \op z$ evaluates to one unless $z = 2^y$, in which case it evaluates to $2^{2^y}$ (which is greater than or equal to four). In particular, $w$ never takes the value two. Thus $$ (((y \op y) \op y) \op 1) \op ((y \op y) \op z) = 2 \op w = 1, $$ -concluding our proof that this magma is a model of Definition \ref{eq374794} +concluding our proof that this magma is a model of \Cref{eq374794} \end{proof} An even shorter law (order $5$) was obtained by the same author in a follow-up paper \cite{Kisielewicz2}: -\begin{theorem}[Kisielewicz's second Austin law]\label{kis-thm2}\uses{eq2, eq28393} Definition \ref{eq28393} is an Austin law. +\begin{theorem}[Kisielewicz's second Austin law]\label{kis-thm2}\uses{eq2, eq28770} \Cref{eq28770} is an Austin law. \end{theorem} \begin{proof} Using the $y^2$ and $y^3$ notation as before, the law reads \begin{equation}\label{kis2-law} x = (y^3 \op x) \op (y \op z). \end{equation} -In particular, for any $y$, the map $T_y \colon x \mapsto y^3 \op x$ is injective, hence bijective in a finite model $G$. In particular we can find a function $f : G \to G$ such that $T_y f(y) = y^3$ for all $y$ Applying \eqref{kis2-law} with $x = f(y)$, we conclude +In particular, for any $y$, the map $T_y \colon x \mapsto y^3 \op x$ is injective, hence bijective in a finite model $G$. In particular we can find a function $f : G \to G$ such that $T_y f(y) = y^3$ for all $y$ Applying \Cref{kis2-law} with $x = f(y)$, we conclude $$ T_y(y \op z) = y^3 \op (y \op z) = f(y) $$ -and thus $y \op z$ is independent of $z$ by injectivity of $T_y$. Thus, the left-hand side of \eqref{kis2-law} does not depend on $x$, and so the model is trivial. This shows there are no non-trivial finite models. +and thus $y \op z$ is independent of $z$ by injectivity of $T_y$. Thus, the left-hand side of \Cref{kis2-law} does not depend on $x$, and so the model is trivial. This shows there are no non-trivial finite models. To establish an infinite model, use $\N$ with $x \op y$ defined by requiring $$ y \op y = 2^y; \quad 2^y \op y = 3^y$$ @@ -84,18 +84,18 @@ \chapter{Infinite models} $$ (3^y 5^x) \op z = x$$ for $z \neq 3^y 5^x$. Finally set $$ 2^{3^y} \op z = 3^y$$ -for $z \neq 3^y, 2^{3^y}$. All other assignments of $\op$ may be made arbitrarily. It is then a routine matter to establish \eqref{kis2-law}. +for $z \neq 3^y, 2^{3^y}$. All other assignments of $\op$ may be made arbitrarily. It is then a routine matter to establish \Cref{kis2-law}. \end{proof} In that paper a computer search was also used to show that no law of order four or less is an Austin law. -An open question is whether Definition \ref{eq5105} is an Austin law. We have the following partial result from \cite{Kisielewicz2}: +An open question is whether \Cref{eq5105} is an Austin law. We have the following partial result from \cite{Kisielewicz2}: -\begin{theorem}[Equation 5105 has no non-trivial finite models]\lean{InfModel.Finite.Equation5105_implies_Equation2}\leanok\label{5105-nontrivial}\uses{eq5105, models-def} Definition \ref{eq5105} has no non-trivial finite models. +\begin{theorem}[Equation 5105 has no non-trivial finite models]\lean{InfModel.Finite.Equation5105_implies_Equation2}\leanok\label{5105-nontrivial}\uses{eq5105, models-def} \Cref{eq5105} has no non-trivial finite models. \end{theorem} -\begin{proof} \leanok From Definition \ref{eq5105} we see that the map $w \mapsto y \op w$ is onto, hence injective in a finite model. Using this injectivity four times in Definition \ref{eq5105}, we see that $z \op y$ does not depend on $z$, hence the expression -$x \op (z \op y)$ does not depend on $x$. By Definition \ref{eq5105} again, this means that $x$ does not depend on $x$, which is absurd in a non-trivial model. +\begin{proof} \leanok From \Cref{eq5105} we see that the map $w \mapsto y \op w$ is onto, hence injective in a finite model. Using this injectivity four times in \Cref{eq5105}, we see that $z \op y$ does not depend on $z$, hence the expression +$x \op (z \op y)$ does not depend on $x$. By \Cref{eq5105} again, this means that $x$ does not depend on $x$, which is absurd in a non-trivial model. \end{proof} We also have such a non-implication involving two laws of order $4$: @@ -111,7 +111,7 @@ \chapter{Infinite models} \begin{theorem}[3994 implies 3588 for finite models]\label{finite_imp_3994_3588_thm}\uses{eq3994,eq3588,models-def} \lean{InfModel.Finite.Equation3994_implies_Equation3588}\leanok - All finite magmas which satisfy definition \ref{eq3994} also satisfy definition \ref{eq3588}. + All finite magmas which satisfy \Cref{eq3994} also satisfy \Cref{eq3588}. \end{theorem} \begin{proof}\label{finite_imp_3994_3588} \leanok @@ -124,16 +124,16 @@ \chapter{Infinite models} \begin{theorem}[3994 does not imply 3588 for infinite models]\label{non_imp_3994_3588_thm}\uses{eq3994,eq3588,models-def} \lean{InfModel.Equation3994_not_implies_Equation3588}\leanok - There exists a magma which satisfies \ref{eq3994} and not \ref{eq3588}. + There exists a magma which satisfies \Cref{eq3994} and not \Cref{eq3588}. \end{theorem} \begin{proof} \leanok Consider $\mathbb{N}$, with $x \op y$ defined as $x \oplus y$ (bitwise XOR) if $x$ and $y$ are even, $y+2$ if only $y$ is even, $x \dot - 2$ if only $x$ is even, and $0$ if both are odd. Note that the range of the operation is the set of even naturals. - Definition \ref{eq3994} is satisfied, because for even $z$ we get $z \oplus (x \op y) \oplus z = x \op y$ + \Cref{eq3994} is satisfied, because for even $z$ we get $z \oplus (x \op y) \oplus z = x \op y$ and for odd $z$ we get $(x \op y) + 2 \dot - 2 = x \op y$. - Setting $x = y = z = 1$, definition \ref{eq3588} isn't satisfied. + Setting $x = y = z = 1$, \Cref{eq3588} isn't satisfied. \end{proof} The following result was established in \cite{austin_finite}: diff --git a/blueprint/src/chapter/intro.tex b/blueprint/src/chapter/intro.tex index 81d70eb4e..bd10edaa5 100644 --- a/blueprint/src/chapter/intro.tex +++ b/blueprint/src/chapter/intro.tex @@ -1,4 +1,4 @@ -\chapter{Basic theory of magmas} +\chapter{Basic theory of magmas}\label{basic-theory-chapter} \begin{definition}[Magma]\label{magma-def}\lean{Magma}\leanok A \emph{magma} is a set $G$ equipped with a binary operation $\op: G \times G \to G$. A \emph{homomorphism} $\varphi : G \to H$ between two magmas is a map such that $\varphi(x \op y) = \varphi(x) \op \varphi(y)$ for all $x,y \in G$. An \emph{isomorphism} is an invertible homomorphism. \end{definition} @@ -67,19 +67,18 @@ \chapter{Basic theory of magmas} \begin{equation}\label{comm-law-2} x \op y = y \op x \end{equation} -for all $x, y \in G$. We refer to \eqref{comm-law-2} as the \emph{equation} associated to the law \eqref{comm-law}. One can think of equations as the ``semantic'' interpretation of a ``syntactic'' law. However, we shall often abuse notation and identify a law with its associated equation. In particular, we shall (somewhat carelessly) also refer to \eqref{comm-law-2} as ``the commutative law'' (rather than ``the commutative equation''). +for all $x, y \in G$. We refer to \Cref{comm-law-2} as the \emph{equation} associated to the law \Cref{comm-law}. One can think of equations as the ``semantic'' interpretation of a ``syntactic'' law. However, we shall often abuse notation and identify a law with its associated equation. In particular, we shall (somewhat carelessly) also refer to \Cref{comm-law-2} as ``the commutative law'' (rather than ``the commutative equation''). \begin{definition}[Models]\label{models-def} \lean{models}\leanok - \uses{law-def} - Given an arbitrary set $\Gamma$ of laws, a magma $G$ is a \emph{model} of $\Gamma$ with the + \uses{law-def} A \emph{theory} is a set $\Gamma$ of laws. Given a theory $\Gamma$, a magma $G$ is a \emph{model} of $\Gamma$ with the (overloaded) notation $G\models\Gamma$ if $G\models w\formaleq w'$ for every $w\formaleq w'$ in $\Gamma$; we also say that $G$ \emph{obeys} $\Gamma$. Given a law $E$, we write $\Gamma \models E$ if every magma $G$ that models $\Gamma$, also models $E$. \end{definition} \begin{definition}[Derivation]\label{derivation-def} \lean{derive}\leanok \uses{law-def} - Given a set $\Gamma$ of laws and a law $w\formaleq w'$ over a fixed alphabet $X$, we say that + Given a theory $\Gamma$ and a law $w\formaleq w'$ over a fixed alphabet $X$, we say that $\Gamma$ \emph{derives} $w\formaleq w'$, and write $\Gamma\vdash w\formaleq w'$, if the law can be obtained using a finite number of applications of the following rules: \begin{enumerate} @@ -87,7 +86,7 @@ \chapter{Basic theory of magmas} \item $\Gamma\vdash w\formaleq w$ for any word $w$. \item if $\Gamma\vdash w\formaleq w'$ then $\Gamma\vdash w'\formaleq w$. \item if $\Gamma\vdash w\formaleq w'$ and $\Gamma\vdash w'\formaleq w''$ then $\Gamma\vdash w\formaleq w''$. - \item if $\Gamma\vdash w\formaleq w'$ then $\Gamma\vdash w\sigma\formaleq w'\sigma$, where $\sigma$ is an arbitrary map from $X$ to words in $M_X$ and $w\sigma$ replaces each occurrence of an element of $X$ with its image by $\sigma$ in $w$. + \item if $\Gamma\vdash w\formaleq w'$ then $\Gamma\vdash \varphi_f w \formaleq \varphi_f w'$ for every $f: X \to M_X$. \item if $\Gamma\vdash w_1\formaleq w_2$ and $\Gamma\vdash w_3\formaleq w_4$ then $\Gamma\vdash w_1 \op w_3\formaleq w_2\op w_4$ \end{enumerate} \end{definition} @@ -95,19 +94,19 @@ \chapter{Basic theory of magmas} This definition is useful because of the following theorem: \begin{theorem}[Birkhoff's completeness theorem]\label{sound-complete}\lean{Completeness}\leanok\uses{models-def, derivation-def} - For any set of laws $\Gamma$ and words $w, w'$ over a fixed alphabet + For any theory $\Gamma$ and words $w, w'$ over a fixed alphabet $$ \Gamma\vdash w\formaleq w'\ \mathrm{iff}\ \Gamma\models w\formaleq w'.$$ \end{theorem} \begin{proof} \leanok - (Sketch) The `only if' component is soundness, and follows from verifying that the rules of inference in Definition \ref{derivation-def} holds for $\models$. The `if' part is completeness, and is proven by constructing the magma of words, quotiented out by the relation $\Gamma \vdash w \formaleq w'$, which is easily seen to be an equivalence relation respecting the magma operation. + (Sketch) The `only if' component is soundness, and follows from verifying that the rules of inference in \Cref{derivation-def} holds for $\models$. The `if' part is completeness, and is proven by constructing the magma of words, quotiented out by the relation $\Gamma \vdash w \formaleq w'$, which is easily seen to be an equivalence relation respecting the magma operation. \end{proof} -\begin{corollary}[Compactness theorem]\label{compactness-thm}\uses{models-def} Let $\Gamma$ be a collection of laws, and let $E$ be a law. Then $\Gamma \models E$ if and only if there exists a finite subset $\Gamma'$ of $\Gamma$ such that $\Gamma' \models E$. +\begin{corollary}[Compactness theorem]\label{compactness-thm}\uses{models-def} Let $\Gamma$ be a theory, and let $E$ be a law. Then $\Gamma \models E$ if and only if there exists a finite subset $\Gamma'$ of $\Gamma$ such that $\Gamma' \models E$. \end{corollary} -\begin{proof}\uses{sound-complete} The claim is obvious for $\vdash$, and the claim then follows from Theorem \ref{sound-complete}. +\begin{proof}\uses{sound-complete} The claim is obvious for $\vdash$, and the claim then follows from \Cref{sound-complete}. \end{proof} @@ -119,7 +118,7 @@ \chapter{Basic theory of magmas} If $\pi$ is a bijection, we will call $\pi_*(w) \formaleq \pi_*(w')$ a \emph{relabeling} of the law $w \formaleq w'$. Thus for instance $$ 5 \op 7 \formaleq 7 \op 5$$ -is a relabeling of the commutative law \eqref{comm-law}. By the above lemma, relabeling does not affect whether a given magna satisfies a given law. +is a relabeling of the commutative law \Cref{comm-law}. By the above lemma, relabeling does not affect whether a given magna satisfies a given law. \begin{lemma}[Equivalence]\label{equiv}\uses{law-def} Let $G$ be a magma and $X$ be an alphabet. Then the relation $G \models w \formaleq w'$ is an equivalence relation on $M_X$. \end{lemma} @@ -139,7 +138,7 @@ \chapter{Basic theory of magmas} $$ 1, 1, 2, 5, 15, 52, 203, \dots$$ (\href{https://oeis.org/A000110}{OEIS A000110}). -The sequence in Lemma \ref{law-count} is +The sequence in \Cref{law-count} is $$ 2, 10, 75, 728, 8526, 115764, \dots$$ (\href{https://oeis.org/A289679}{OEIS A289679}). @@ -157,7 +156,7 @@ \chapter{Basic theory of magmas} The sequence $D_n$ is $$ 1, 1, 2, 4, 11, 32, 117, \dots$$ -(\href{https://oeis.org/A103293}{OEIS A103293}), and the sequence in Lemma \ref{law-count-sym} is +(\href{https://oeis.org/A103293}{OEIS A103293}), and the sequence in \Cref{law-count-sym} is $$ 2, 5, 41, 364, 4294, 57882, 888440, \dots$$ (\href{https://oeis.org/A376620}{OEIS A376620}). diff --git a/blueprint/src/chapter/metatheorems_from_invariants.tex b/blueprint/src/chapter/metatheorems_from_invariants.tex index ddc6283a6..24878e42f 100644 --- a/blueprint/src/chapter/metatheorems_from_invariants.tex +++ b/blueprint/src/chapter/metatheorems_from_invariants.tex @@ -1,4 +1,5 @@ -\chapter{Metatheorems from Invariants} +\chapter{Metatheorems from Invariants}\label{metatheory-chapter} + For the purposes of this chapter, a \emph{theorem} is a (true) statement about particular equations, for example `(387 implies 43)' is a theorem. A \emph{metatheorem} is a general statement about implications; one can usually get many theorems from a single metatheorem. This chapter is all about generating many interesting metatheorems using a \emph{meta-metatheorem}, called the fundamental property of invariants. If all this is making your head spin, don't worry. Look at the sections below for examples of metatheorems you can probably agree are both concrete and interesting. Once you have done that, come back here and we will show you how to prove these and other metatheorems using \emph{invariants}. \section{Invariants} @@ -126,7 +127,7 @@ \section{Proving metatheorems from invariants in Lean} Lists form a lifting magma family. \end{example} -The key consequence of the definition \ref{lifting-magma-family} is that it is significantly easier to check whether an equation is satisfied in a lifting magma family. +The key consequence of the \Cref{lifting-magma-family} is that it is significantly easier to check whether an equation is satisfied in a lifting magma family. \begin{theorem}[Evaluation theorem for lifting magma families]\label{lifting-magma-basis-evaluation} Suppose $E$ is an equation involving a set of variables $X$, and let $G$ be a lifting magma family. @@ -146,7 +147,7 @@ \section{Proving metatheorems from invariants in Lean} If $E$ is true with the substitution $\iota_X$, and $E$ implies $E'$, then so is $E'$. \end{theorem} \begin{proof} - Applying the evaluation theorem \ref{lifting-magma-basis-evaluation}, we see that $E$ is satisfied by $G_X$. Since $E$ implies $E'$, $E'$ is also satisfied by $G_X$, and in particular, $E'$ is true with the substitution $\iota_X$. + Applying the evaluation \Cref{lifting-magma-basis-evaluation}, we see that $E$ is satisfied by $G_X$. Since $E$ implies $E'$, $E'$ is also satisfied by $G_X$, and in particular, $E'$ is true with the substitution $\iota_X$. \end{proof} \begin{remark} diff --git a/blueprint/src/chapter/simple_rewrites.tex b/blueprint/src/chapter/simple_rewrites.tex index 96e345297..1d7ed513d 100644 --- a/blueprint/src/chapter/simple_rewrites.tex +++ b/blueprint/src/chapter/simple_rewrites.tex @@ -1,4 +1,4 @@ -\chapter{Simple rewrites} +\chapter{Simple rewrites}\label{simple-rewrite-chapter} \href{https://github.com/teorth/equational_theories/tree/main/equational_theories/SimpleRewrites/theorems}{53,905 implications} were automatically generated by simple rewrites. diff --git a/blueprint/src/chapter/trivial_auto.tex b/blueprint/src/chapter/trivial_auto.tex index ade86007d..eeecc65aa 100644 --- a/blueprint/src/chapter/trivial_auto.tex +++ b/blueprint/src/chapter/trivial_auto.tex @@ -1,4 +1,4 @@ -\chapter{Trivial auto-generated theorems} +\chapter{Trivial auto-generated theorems}\label{trivial-auto-chapter} \href{https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/TrivialBruteforce}{Approximately 4.5m transitive implications were proven by a transitive reduction of about 15k theorems}. Most of these implications were derived from being the first automated run to connect the largest equivalence classes, hence creating a large set of transitively closed implications. diff --git a/blueprint/src/chapter/vampire.tex b/blueprint/src/chapter/vampire.tex index 065ec386a..060068a71 100644 --- a/blueprint/src/chapter/vampire.tex +++ b/blueprint/src/chapter/vampire.tex @@ -1,4 +1,4 @@ -\chapter{Using the Vampire theorem prover} +\chapter{Using the Vampire theorem prover}\label{vampire-chapter} \href{https://github.com/teorth/equational_theories/tree/main/equational_theories/Generated/VampireProven/}{1,775 implications} were proven using the Vampire theorem prover. diff --git a/blueprint/src/content.tex b/blueprint/src/content.tex index eacc22c99..b51b10b9f 100644 --- a/blueprint/src/content.tex +++ b/blueprint/src/content.tex @@ -14,6 +14,7 @@ \input{chapter/counterexamples.tex} \input{chapter/constant.tex} \input{chapter/metatheorems_from_invariants.tex} +\input{chapter/abstract_nonsense.tex} \input{chapter/simple_rewrites.tex} \input{chapter/trivial_auto.tex} \input{chapter/all_small_magmas.tex} diff --git a/blueprint/src/print.pdf b/blueprint/src/print.pdf index 523fa9dbd..afd990ed8 100644 Binary files a/blueprint/src/print.pdf and b/blueprint/src/print.pdf differ diff --git a/blueprint/src/print.tex b/blueprint/src/print.tex index 7c87eb043..c44de5007 100644 --- a/blueprint/src/print.tex +++ b/blueprint/src/print.tex @@ -13,12 +13,10 @@ \documentclass[a4paper]{report} \usepackage{geometry} - \usepackage{expl3} - \usepackage{amssymb, amsthm, mathtools} \usepackage[unicode,colorlinks=true,linkcolor=blue,urlcolor=magenta, citecolor=blue]{hyperref} - +\usepackage{cleveref} \usepackage[warnings-off={mathtools-colon,mathtools-overbracket}]{unicode-math} \input{macros/common} diff --git a/blueprint/src/web.tex b/blueprint/src/web.tex index ac5b4e3cb..66b4a8567 100644 --- a/blueprint/src/web.tex +++ b/blueprint/src/web.tex @@ -8,10 +8,10 @@ \usepackage{amssymb, amsthm, amsmath} \usepackage{hyperref} +\usepackage{cleveref} \usepackage{graphicx} \usepackage[showmore, dep_graph]{blueprint} - \input{macros/common} \input{macros/web} diff --git a/data/outstanding_3op_implications.txt b/data/outstanding_3op_implications.txt index 0eef18219..21a633685 100644 --- a/data/outstanding_3op_implications.txt +++ b/data/outstanding_3op_implications.txt @@ -1,8 +1,8 @@ -Equation63 => Equation1692 Equation65 => Equation359 -Equation65 => Equation614 -Equation65 => Equation817 -Equation65 => Equation1426 -Equation65 => Equation1491 -Equation65 => Equation3862 -Equation65 => Equation4065 +Equation73 => Equation99 +Equation73 => Equation125 +Equation73 => Equation203 +Equation73 => Equation229 +Equation73 => Equation255 +Equation118 => Equation222 +Equation118 => Equation274 diff --git a/data/unknowns_10_06.txt b/data/unknowns_10_06.txt index ff81f5377..ca7073fbd 100644 --- a/data/unknowns_10_06.txt +++ b/data/unknowns_10_06.txt @@ -26,32 +26,32 @@ Equation476 => Equation359 Equation476 => Equation3862 Equation476 => Equation4065 Equation477 => Equation1426 -Equation477 => Equation1519 +Equation477 => Equation1519 (*) Equation477 => Equation2035 -Equation477 => Equation2128 +Equation477 => Equation2128 (*) Equation477 => Equation3050 -Equation477 => Equation3150 -Equation481 => Equation1488 +Equation477 => Equation3150 (*) +Equation481 => Equation1488 (*) Equation481 => Equation1492 Equation481 => Equation2035 Equation481 => Equation2038 Equation481 => Equation2041 -Equation481 => Equation2124 +Equation481 => Equation2124 (*) Equation481 => Equation2128 -Equation481 => Equation2132 +Equation481 => Equation2132 (*) Equation481 => Equation2135 Equation481 => Equation3050 Equation481 => Equation3056 -Equation481 => Equation3139 +Equation481 => Equation3139 (*) Equation481 => Equation3150 -Equation481 => Equation3161 +Equation481 => Equation3161 (*) Equation503 => Equation359 Equation503 => Equation3862 Equation503 => Equation4065 Equation504 => Equation817 Equation504 => Equation1629 Equation504 => Equation1832 -Equation504 => Equation1925 +Equation504 => Equation1925 (*) Equation511 => Equation614 Equation511 => Equation714 Equation511 => Equation1020 @@ -68,7 +68,7 @@ Equation677 => Equation255 Equation680 => Equation1629 Equation680 => Equation1832 Equation680 => Equation2847 -Equation680 => Equation2947 +Equation680 => Equation2947 (*) Equation707 => Equation1223 Equation707 => Equation1316 Equation707 => Equation2238 @@ -146,7 +146,7 @@ Equation1076 => Equation4435 Equation1076 => Equation4470 Equation1086 => Equation1832 Equation1086 => Equation2644 -Equation1086 => Equation2710 +Equation1086 => Equation2710 (*) Equation1110 => Equation8 Equation1110 => Equation411 Equation1110 => Equation1629 @@ -234,7 +234,7 @@ Equation1443 => Equation1629 Equation1443 => Equation1630 Equation1443 => Equation2441 Equation1443 => Equation3050 -Equation1443 => Equation3055 +Equation1443 => Equation3055 (*) Equation1443 => Equation3522 Equation1443 => Equation4065 Equation1443 => Equation4067 @@ -275,10 +275,10 @@ Equation1486 => Equation2051 Equation1486 => Equation2052 Equation1486 => Equation2087 Equation1486 => Equation2088 -Equation1486 => Equation2089 +Equation1486 => Equation2089 (*) Equation1486 => Equation2124 Equation1486 => Equation2125 -Equation1486 => Equation2126 +Equation1486 => Equation2126 (*) Equation1486 => Equation2162 Equation1486 => Equation2163 Equation1486 => Equation3456 @@ -300,12 +300,12 @@ Equation1518 => Equation614 Equation1518 => Equation817 Equation1518 => Equation3862 Equation1519 => Equation2035 -Equation1519 => Equation2128 +Equation1519 => Equation2128 (*) Equation1523 => Equation2035 Equation1523 => Equation2038 -Equation1523 => Equation2124 +Equation1523 => Equation2124 (*) Equation1523 => Equation2128 -Equation1523 => Equation2132 +Equation1523 => Equation2132 (*) Equation1526 => Equation1223 Equation1526 => Equation1323 Equation1526 => Equation2744 @@ -436,5 +436,5 @@ Equation3588 => Equation3862 Equation3588 => Equation3878 Equation3588 => Equation3917 Equation3588 => Equation3955 -Equation3588 => Equation3994 +Equation3588 => Equation3994 (*) Equation3888 => Equation3659 diff --git a/data/unknowns_10_07.json b/data/unknowns_10_07.json new file mode 100644 index 000000000..8502da635 --- /dev/null +++ b/data/unknowns_10_07.json @@ -0,0 +1 @@ +[{"rhs":"Equation1692","lhs":"Equation63"},{"rhs":"Equation359","lhs":"Equation65"},{"rhs":"Equation614","lhs":"Equation65"},{"rhs":"Equation817","lhs":"Equation65"},{"rhs":"Equation1426","lhs":"Equation65"},{"rhs":"Equation1491","lhs":"Equation65"},{"rhs":"Equation3862","lhs":"Equation65"},{"rhs":"Equation4065","lhs":"Equation65"},{"rhs":"Equation99","lhs":"Equation73"},{"rhs":"Equation125","lhs":"Equation73"},{"rhs":"Equation203","lhs":"Equation73"},{"rhs":"Equation229","lhs":"Equation73"},{"rhs":"Equation255","lhs":"Equation73"},{"rhs":"Equation4380","lhs":"Equation73"},{"rhs":"Equation4435","lhs":"Equation73"},{"rhs":"Equation4273","lhs":"Equation115"},{"rhs":"Equation222","lhs":"Equation118"},{"rhs":"Equation274","lhs":"Equation118"},{"rhs":"Equation4435","lhs":"Equation118"},{"rhs":"Equation1924","lhs":"Equation124"},{"rhs":"Equation2847","lhs":"Equation467"},{"rhs":"Equation359","lhs":"Equation476"},{"rhs":"Equation3862","lhs":"Equation476"},{"rhs":"Equation4065","lhs":"Equation476"},{"rhs":"Equation1426","lhs":"Equation477"},{"rhs":"Equation1519","lhs":"Equation477"},{"rhs":"Equation2035","lhs":"Equation477"},{"rhs":"Equation2128","lhs":"Equation477"},{"rhs":"Equation3050","lhs":"Equation477"},{"rhs":"Equation3150","lhs":"Equation477"},{"rhs":"Equation1488","lhs":"Equation481"},{"rhs":"Equation1492","lhs":"Equation481"},{"rhs":"Equation2035","lhs":"Equation481"},{"rhs":"Equation2038","lhs":"Equation481"},{"rhs":"Equation2041","lhs":"Equation481"},{"rhs":"Equation2124","lhs":"Equation481"},{"rhs":"Equation2128","lhs":"Equation481"},{"rhs":"Equation2132","lhs":"Equation481"},{"rhs":"Equation3050","lhs":"Equation481"},{"rhs":"Equation3056","lhs":"Equation481"},{"rhs":"Equation3139","lhs":"Equation481"},{"rhs":"Equation3150","lhs":"Equation481"},{"rhs":"Equation3161","lhs":"Equation481"},{"rhs":"Equation359","lhs":"Equation503"},{"rhs":"Equation3862","lhs":"Equation503"},{"rhs":"Equation4065","lhs":"Equation503"},{"rhs":"Equation817","lhs":"Equation504"},{"rhs":"Equation1629","lhs":"Equation504"},{"rhs":"Equation1832","lhs":"Equation504"},{"rhs":"Equation1925","lhs":"Equation504"},{"rhs":"Equation614","lhs":"Equation511"},{"rhs":"Equation714","lhs":"Equation511"},{"rhs":"Equation1020","lhs":"Equation511"},{"rhs":"Equation1223","lhs":"Equation511"},{"rhs":"Equation2238","lhs":"Equation511"},{"rhs":"Equation2338","lhs":"Equation511"},{"rhs":"Equation2441","lhs":"Equation511"},{"rhs":"Equation2847","lhs":"Equation511"},{"rhs":"Equation3050","lhs":"Equation511"},{"rhs":"Equation4380","lhs":"Equation511"},{"rhs":"Equation4435","lhs":"Equation511"},{"rhs":"Equation255","lhs":"Equation677"},{"rhs":"Equation1629","lhs":"Equation680"},{"rhs":"Equation1832","lhs":"Equation680"},{"rhs":"Equation2847","lhs":"Equation680"},{"rhs":"Equation2947","lhs":"Equation680"},{"rhs":"Equation1223","lhs":"Equation707"},{"rhs":"Equation1316","lhs":"Equation707"},{"rhs":"Equation2238","lhs":"Equation707"},{"rhs":"Equation2847","lhs":"Equation707"},{"rhs":"Equation2940","lhs":"Equation707"},{"rhs":"Equation359","lhs":"Equation713"},{"rhs":"Equation817","lhs":"Equation713"},{"rhs":"Equation1426","lhs":"Equation713"},{"rhs":"Equation3862","lhs":"Equation713"},{"rhs":"Equation4065","lhs":"Equation713"},{"rhs":"Equation107","lhs":"Equation854"},{"rhs":"Equation413","lhs":"Equation854"},{"rhs":"Equation1045","lhs":"Equation854"},{"rhs":"Equation1055","lhs":"Equation854"},{"rhs":"Equation1248","lhs":"Equation854"},{"rhs":"Equation1251","lhs":"Equation854"},{"rhs":"Equation3316","lhs":"Equation854"},{"rhs":"Equation3925","lhs":"Equation854"},{"rhs":"Equation4065","lhs":"Equation879"},{"rhs":"Equation2035","lhs":"Equation883"},{"rhs":"Equation2101","lhs":"Equation883"},{"rhs":"Equation2238","lhs":"Equation883"},{"rhs":"Equation2304","lhs":"Equation883"},{"rhs":"Equation3862","lhs":"Equation906"},{"rhs":"Equation1629","lhs":"Equation917"},{"rhs":"Equation1729","lhs":"Equation917"},{"rhs":"Equation2441","lhs":"Equation917"},{"rhs":"Equation2541","lhs":"Equation917"},{"rhs":"Equation3","lhs":"Equation1076"},{"rhs":"Equation8","lhs":"Equation1076"},{"rhs":"Equation23","lhs":"Equation1076"},{"rhs":"Equation47","lhs":"Equation1076"},{"rhs":"Equation99","lhs":"Equation1076"},{"rhs":"Equation151","lhs":"Equation1076"},{"rhs":"Equation203","lhs":"Equation1076"},{"rhs":"Equation255","lhs":"Equation1076"},{"rhs":"Equation307","lhs":"Equation1076"},{"rhs":"Equation326","lhs":"Equation1076"},{"rhs":"Equation359","lhs":"Equation1076"},{"rhs":"Equation375","lhs":"Equation1076"},{"rhs":"Equation411","lhs":"Equation1076"},{"rhs":"Equation614","lhs":"Equation1076"},{"rhs":"Equation817","lhs":"Equation1076"},{"rhs":"Equation1223","lhs":"Equation1076"},{"rhs":"Equation1426","lhs":"Equation1076"},{"rhs":"Equation1629","lhs":"Equation1076"},{"rhs":"Equation1832","lhs":"Equation1076"},{"rhs":"Equation2035","lhs":"Equation1076"},{"rhs":"Equation2238","lhs":"Equation1076"},{"rhs":"Equation2294","lhs":"Equation1076"},{"rhs":"Equation2441","lhs":"Equation1076"},{"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7"},{"rhs":"Equation151","lhs":"Equation1485"},{"rhs":"Equation152","lhs":"Equation1485"},{"rhs":"Equation1427","lhs":"Equation1485"},{"rhs":"Equation1429","lhs":"Equation1485"},{"rhs":"Equation1481","lhs":"Equation1485"},{"rhs":"Equation1483","lhs":"Equation1485"},{"rhs":"Equation3456","lhs":"Equation1485"},{"rhs":"Equation3457","lhs":"Equation1485"},{"rhs":"Equation3511","lhs":"Equation1485"},{"rhs":"Equation151","lhs":"Equation1486"},{"rhs":"Equation152","lhs":"Equation1486"},{"rhs":"Equation166","lhs":"Equation1486"},{"rhs":"Equation1427","lhs":"Equation1486"},{"rhs":"Equation1428","lhs":"Equation1486"},{"rhs":"Equation1479","lhs":"Equation1486"},{"rhs":"Equation1481","lhs":"Equation1486"},{"rhs":"Equation1483","lhs":"Equation1486"},{"rhs":"Equation1484","lhs":"Equation1486"},{"rhs":"Equation1485","lhs":"Equation1486"},{"rhs":"Equation2035","lhs":"Equation1486"},{"rhs":"Equation2036","lhs":"Equation1486"},{"rhs":"Equation2050","lhs":"Equation1486"},{"rhs":"Equation2051","lhs":"Equation1486"},{"rhs":"Equation2052","lhs":"Equation1486"},{"rhs":"Equation2087","lhs":"Equation1486"},{"rhs":"Equation2088","lhs":"Equation1486"},{"rhs":"Equation2089","lhs":"Equation1486"},{"rhs":"Equation2124","lhs":"Equation1486"},{"rhs":"Equation2125","lhs":"Equation1486"},{"rhs":"Equation2126","lhs":"Equation1486"},{"rhs":"Equation3456","lhs":"Equation1486"},{"rhs":"Equation3457","lhs":"Equation1486"},{"rhs":"Equation3511","lhs":"Equation1486"},{"rhs":"Equation3512","lhs":"Equation1486"},{"rhs":"Equation3513","lhs":"Equation1486"},{"rhs":"Equation3862","lhs":"Equation1486"},{"rhs":"Equation3877","lhs":"Equation1486"},{"rhs":"Equation3918","lhs":"Equation1486"},{"rhs":"Equation3955","lhs":"Equation1486"},{"rhs":"Equation3993","lhs":"Equation1486"},{"rhs":"Equation65","lhs":"Equation1491"},{"rhs":"Equation4590","lhs":"Equation1515"},{"rhs":"Equation255","lhs":"Equation1516"},{"rhs":"Equation1489","lhs":"Equation1516"},{"rhs":"Equation47","lhs":"Equation1518"},{"rhs":"Equation614","lhs":"Equation1518"},{"rhs":"Equation817","lhs":"Equation1518"},{"rhs":"Equation3862","lhs":"Equation1518"},{"rhs":"Equation2035","lhs":"Equation1519"},{"rhs":"Equation2128","lhs":"Equation1519"},{"rhs":"Equation2035","lhs":"Equation1523"},{"rhs":"Equation2038","lhs":"Equation1523"},{"rhs":"Equation2124","lhs":"Equation1523"},{"rhs":"Equation2128","lhs":"Equation1523"},{"rhs":"Equation2132","lhs":"Equation1523"},{"rhs":"Equation1223","lhs":"Equation1526"},{"rhs":"Equation1323","lhs":"Equation1526"},{"rhs":"Equation2744","lhs":"Equation1526"},{"rhs":"Equation4268","lhs":"Equation1630"},{"rhs":"Equation4268","lhs":"Equation1633"},{"rhs":"Equation23","lhs":"Equation1648"},{"rhs":"Equation151","lhs":"Equation1648"},{"rhs":"Equation203","lhs":"Equation1648"},{"rhs":"Equation206","lhs":"Equation1648"},{"rhs":"Equation307","lhs":"Equation1648"},{"rhs":"Equation1426","lhs":"Equation1648"},{"rhs":"Equation1832","lhs":"Equation1648"},{"rhs":"Equation2238","lhs":"Equation1648"},{"rhs":"Equation2441","lhs":"Equation1648"},{"rhs":"Equation3050","lhs":"Equation1648"},{"rhs":"Equation3253","lhs":"Equation1648"},{"rhs":"Equation3456","lhs":"Equation1648"},{"rhs":"Equation3522","lhs":"Equation1648"},{"rhs":"Equation4065","lhs":"Equation1648"},{"rhs":"Equation4118","lhs":"Equation1648"},{"rhs":"Equation3862","lhs":"Equation1681"},{"rhs":"Equation3877","lhs":"Equation1681"},{"rhs":"Equation23","lhs":"Equation1692"},{"rhs":"Equation47","lhs":"Equation1692"},{"rhs":"Equation63","lhs":"Equation1692"},{"rhs":"Equation1832","lhs":"Equation1692"},{"rhs":"Equation1922","lhs":"Equation1692"},{"rhs":"Equation2441","lhs":"Equation1692"},{"rhs":"Equation3050","lhs":"Equation1692"},{"rhs":"Equation3456","lhs":"Equation1692"},{"rhs":"Equation3522","lhs":"Equation1692"},{"rhs":"Equation4065","lhs":"Equation1692"},{"rhs":"Equation4118","lhs":"Equation1692"},{"rhs":"Equation8","lhs":"Equation1701"},{"rhs":"Equation411","lhs":"Equation1701"},{"rhs":"Equation1020","lhs":"Equation1701"},{"rhs":"Equation1035","lhs":"Equation1701"},{"rhs":"Equation1832","lhs":"Equation1701"},{"rhs":"Equation1884","lhs":"Equation1701"},{"rhs":"Equation3253","lhs":"Equation1701"},{"rhs":"Equation3319","lhs":"Equation1701"},{"rhs":"Equation3862","lhs":"Equation1701"},{"rhs":"Equation3877","lhs":"Equation1701"},{"rhs":"Equation3915","lhs":"Equation1701"},{"rhs":"Equation4587","lhs":"Equation1701"},{"rhs":"Equation1832","lhs":"Equation1722"},{"rhs":"Equation2644","lhs":"Equation1722"},{"rhs":"Equation2737","lhs":"Equation1722"},{"rhs":"Equation3050","lhs":"Equation1722"},{"rhs":"Equation3143","lhs":"Equation1722"},{"rhs":"Equation99","lhs":"Equation1728"},{"rhs":"Equation817","lhs":"Equation1729"},{"rhs":"Equation917","lhs":"Equation1729"},{"rhs":"Equation205","lhs":"Equation2712"},{"rhs":"Equation1647","lhs":"Equation2712"},{"rhs":"Equation2240","lhs":"Equation2712"},{"rhs":"Equation2459","lhs":"Equation2712"},{"rhs":"Equation2462","lhs":"Equation2712"},{"rhs":"Equation3068","lhs":"Equation2712"},{"rhs":"Equation3456","lhs":"Equation3308"},{"rhs":"Equation3511","lhs":"Equation3308"},{"rhs":"Equation3456","lhs":"Equation3342"},{"rhs":"Equation3522","lhs":"Equation3342"},{"rhs":"Equation4065","lhs":"Equation3342"},{"rhs":"Equation4118","lhs":"Equation3342"},{"rhs":"Equation4065","lhs":"Equation3352"},{"rhs":"Equation3659","lhs":"Equation3475"},{"rhs":"Equation3862","lhs":"Equation3545"},{"rhs":"Equation3862","lhs":"Equation3549"},{"rhs":"Equation3955","lhs":"Equation3549"},{"rhs":"Equation3862","lhs":"Equation3555"},{"rhs":"Equation3862","lhs":"Equation3588"},{"rhs":"Equation3878","lhs":"Equation3588"},{"rhs":"Equation3917","lhs":"Equation3588"},{"rhs":"Equation3955","lhs":"Equation3588"}] diff --git a/equational_theories.lean b/equational_theories.lean index a641c6893..92aee1884 100644 --- a/equational_theories.lean +++ b/equational_theories.lean @@ -16,3 +16,4 @@ import equational_theories.Homomorphisms import equational_theories.CentralGroupoids import equational_theories.Z3Counterexamples import equational_theories.LinearOps +import equational_theories.Confluence diff --git a/equational_theories/AllEquations.lean b/equational_theories/AllEquations.lean index cc37d9ea7..cf0121ab0 100644 --- a/equational_theories/AllEquations.lean +++ b/equational_theories/AllEquations.lean @@ -3185,7 +3185,7 @@ equation 3163 := x = (((y ◇ y) ◇ z) ◇ y) ◇ x equation 3164 := x = (((y ◇ y) ◇ z) ◇ y) ◇ y equation 3165 := x = (((y ◇ y) ◇ z) ◇ y) ◇ z equation 3166 := x = (((y ◇ y) ◇ z) ◇ y) ◇ w -equation 3167 := x = (((y ◇ y) ◇ z) ◇ z) ◇ x +-- equation 3167 := x = (((y ◇ y) ◇ z) ◇ z) ◇ x equation 3168 := x = (((y ◇ y) ◇ z) ◇ z) ◇ y equation 3169 := x = (((y ◇ y) ◇ z) ◇ z) ◇ z equation 3170 := x = (((y ◇ y) ◇ z) ◇ z) ◇ w @@ -4674,7 +4674,7 @@ equation 4652 := (x ◇ y) ◇ x = (z ◇ w) ◇ w equation 4653 := (x ◇ y) ◇ x = (z ◇ w) ◇ u equation 4654 := (x ◇ y) ◇ y = (x ◇ y) ◇ z equation 4655 := (x ◇ y) ◇ y = (x ◇ z) ◇ y -equation 4656 := (x ◇ y) ◇ y = (x ◇ z) ◇ z +-- equation 4656 := (x ◇ y) ◇ y = (x ◇ z) ◇ z equation 4657 := (x ◇ y) ◇ y = (x ◇ z) ◇ w equation 4658 := (x ◇ y) ◇ y = (y ◇ x) ◇ x equation 4659 := (x ◇ y) ◇ y = (y ◇ x) ◇ z diff --git a/equational_theories/Closure.lean b/equational_theories/Closure.lean index 8595e810d..ebf34cf9a 100644 --- a/equational_theories/Closure.lean +++ b/equational_theories/Closure.lean @@ -153,6 +153,9 @@ def DenseNumbering.fromArray {α : Type} [BEq α] [Hashable α] (elts : Array α let index := Std.HashMap.ofList (elts.mapIdx (fun i x => (x, i.val))).toList ⟨elts, index⟩ +def DenseNumbering.map {α β : Type} [BEq α] [BEq β] [Hashable α] [Hashable β] (num : DenseNumbering α) (f : α → β) : DenseNumbering β := + DenseNumbering.fromArray (num.in_order.map f) + def ltEquationNames (a b : String) : Bool := assert! a.startsWith "Equation" assert! b.startsWith "Equation" @@ -194,10 +197,10 @@ def toEdges (inp : Array EntryVariant) : Array Edge := Id.run do for f2 in refuted do nonimplies := nonimplies.modify eqs[f1]! (fun x ↦ x.set eqs[f2]!) | _ => continue - for i in [:eqs.size] do - for j in [:eqs.size] do + for hi : i in [:eqs.size] do + for hj : j in [:eqs.size] do if nonimplies[i]!.get j then - edges := edges.push (.nonimplication ⟨eqs.in_order[i]!, eqs.in_order[j]!⟩) + edges := edges.push (.nonimplication ⟨eqs.in_order[i], eqs.in_order[j]⟩) return edges structure Reachability where @@ -249,7 +252,6 @@ def closure_aux (inp : Array EntryVariant) (eqs : DenseNumbering String) : IO Re let mut component : Array Nat := Array.mkArray graph_size 0 let mut last_component : Nat := 0 - for i in order do if component[i]! == 0 then do last_component := last_component + 1 @@ -302,7 +304,6 @@ def closure (inp : Array EntryVariant) : IO (Array Edge) := do let eqs := number_equations inp let n := eqs.size - -- extract the implications let mut ans : Array Edge := Array.mkEmpty (n*n) @@ -339,29 +340,24 @@ def list_outcomes (res : Array Entry) : IO (Array String × Array (Array Outcome return (eqs.in_order, outcomes) -def outcomes_mod_equiv (inp : Array EntryVariant) : IO (Array String × Array (Array (Option Bool))) := do +def outcomes_mod_equiv (inp : Array EntryVariant) : IO (DenseNumbering (Array String) × Array (Array (Option Bool))) := do let eqs := number_equations inp let n := eqs.size let reachable ← closure_aux inp eqs - let mut reprs_id : Std.HashMap Nat Nat := {} - let mut reprs : Array String := Array.mkEmpty (reachable.components.size / 2) - for comp in reachable.components do - if comp[0]! < n then - reprs_id := reprs_id.insert comp[0]! reprs.size - reprs := reprs.push eqs.in_order[comp[0]!]! + let comps := reachable.components.filter (·[0]! < n) |> DenseNumbering.fromArray let mut implies : Array (Array (Option Bool)) := - Array.mkArray reprs.size (Array.mkArray reprs.size none) + Array.mkArray comps.size (Array.mkArray comps.size none) for i in reachable.components, i2 in reachable.reachable do if i[0]! >= reachable.size then continue for j in reachable.components, j2 in [:reachable.components.size] do if i2.get j2 then if j[0]! < n then - implies := implies.modify reprs_id[j[0]!]! (fun x ↦ x.set! reprs_id[i[0]!]! true) + implies := implies.modify comps[j]! (fun x ↦ x.set! comps[i]! true) else if j.back < 2*n then - implies := implies.modify reprs_id[i[0]!]! (fun x ↦ x.set! reprs_id[j[0]! - n]! false) + implies := implies.modify comps[i]! (fun x ↦ x.set! comps[j.map (·-n)]! false) - return (reprs, implies) + return (comps.map (fun ids => ids.map (eqs.in_order[·]!)), implies) end Closure diff --git a/equational_theories/Compactness.lean b/equational_theories/Compactness.lean index 5d4d86694..7285a7149 100644 --- a/equational_theories/Compactness.lean +++ b/equational_theories/Compactness.lean @@ -24,9 +24,9 @@ theorem foo (S T : Set Nat) : S ⊆ S ∪ T := Set.subset_union_left def derive.Weak {α} {Γ Δ : Ctx α}{E : MagmaLaw α}(inc : Γ ⊆ Δ) (h : Γ ⊢ E) : Δ ⊢ E := by cases h - case Ax => apply derive.Ax; apply inc; trivial - case Ref => apply derive.Ref - case Sym => apply derive.Sym; apply derive.Weak <;> trivial + case Ax => refine derive.Ax _ _ (inc ?_); assumption + case Ref => exact derive.Ref _ _ + case Sym => apply derive.Sym ; apply derive.Weak _ <;> trivial case Trans => apply derive.Trans <;> try apply derive.Weak <;> trivial case Subst => apply derive.Subst ; apply derive.Weak <;> trivial case Cong => apply derive.Cong <;> apply derive.Weak <;> trivial @@ -34,7 +34,7 @@ def derive.Weak {α} {Γ Δ : Ctx α}{E : MagmaLaw α}(inc : Γ ⊆ Δ) (h : Γ def derive.getAxiomsEnough {α} [DecidableEq α] {Γ : Ctx α} {E : MagmaLaw α}(h : Γ ⊢ E) : ToCtx (derive.getAxioms h) ⊢ E := by cases h <;> simp [ToCtx, getAxioms] - case Ax => constructor; trivial + case Ax => constructor; rfl case Ref => exact derive.Ref _ _ case Sym _ _ h => exact derive.Sym _ _ _ (derive.getAxiomsEnough _) case Trans _ _ _ h₁ h₂ => @@ -43,13 +43,10 @@ def derive.getAxiomsEnough {α} [DecidableEq α] {Γ : Ctx α} {E : MagmaLaw α} · exact derive.Weak Set.subset_union_right (derive.getAxiomsEnough h₂) case Subst => exact derive.Subst _ _ _ _ (derive.getAxiomsEnough _) case Cong _ _ _ h₁ h₂ => - apply derive.Cong - · exact derive.Weak Set.subset_union_left (derive.getAxiomsEnough h₁) - · exact derive.Weak Set.subset_union_right (derive.getAxiomsEnough h₂) + exact derive.Cong _ _ _ _ _ (derive.Weak Set.subset_union_left (derive.getAxiomsEnough h₁)) + (derive.Weak Set.subset_union_right (derive.getAxiomsEnough h₂)) def Compactness {α} [DecidableEq α] {Γ : Ctx α} {E : MagmaLaw α}(h : Γ ⊧ E) : ∃ (Δ : Finset (MagmaLaw α)), Nonempty <| ToCtx Δ ⊧ E := by have ⟨ h'' ⟩ := Completeness _ _ h - refine ⟨(derive.getAxioms (h'')), ?_⟩ - constructor - apply Soundness _ _ (derive.getAxiomsEnough _) + exact ⟨(derive.getAxioms h''), ⟨Soundness _ _ (derive.getAxiomsEnough _)⟩⟩ diff --git a/equational_theories/Confluence.lean b/equational_theories/Confluence.lean new file mode 100644 index 000000000..cccf77042 --- /dev/null +++ b/equational_theories/Confluence.lean @@ -0,0 +1,174 @@ +import equational_theories.FreeMagma +import equational_theories.AllEquations +import equational_theories.FactsSyntax + +def FreeMagma.length {α : Type} : FreeMagma α → Nat + | .Leaf _ => 1 + | .Fork m1 m2 => FreeMagma.length m1 + FreeMagma.length m2 + +theorem FreeMagma.length_pos {α : Type} : (x : FreeMagma α) → 0 < FreeMagma.length x + | .Leaf _ => by simp [FreeMagma.length] + | .Fork m1 m2 => by + have h1 := FreeMagma.length_pos m1 + have h2 := FreeMagma.length_pos m2 + simp [FreeMagma.length] + omega + +@[simp] +theorem FreeMagma.length_0 {α : Type} (x : FreeMagma α) : ¬ (FreeMagma.length x = 0) := + Nat.not_eq_zero_of_lt x.length_pos + +-- equation 477 := x = y ◇ (x ◇ (y ◇ (y ◇ y))) + +def simp477 {α : Type} [DecidableEq α] : FreeMagma α → FreeMagma α + | .Leaf x => .Leaf x + | .Fork m1 m2 => + let y1 := simp477 m1 + let m2' := simp477 m2 + match m2' with + | .Fork x (.Fork y2 (.Fork y3 y4)) => + if y1 = y2 ∧ y1 = y3 ∧ y1 = y4 then + x + else + .Fork y1 m2' + | _ => + .Fork y1 m2' + +attribute [simp] simp477.eq_1 + +inductive IsNF {α : Type} [DecidableEq α] : FreeMagma α → Prop + | leaf (x : α) : IsNF (.Leaf x) + | fork (m1 m2 : FreeMagma α) : IsNF m1 → IsNF m2 → simp477 (.Fork m1 m2) = (.Fork m1 m2) → IsNF (.Fork m1 m2) + +theorem idem_of_IsNF {α : Type} [DecidableEq α] {x : FreeMagma α} : IsNF x → simp477 x = x + | .leaf x => rfl + | .fork _ _ _ _ h => h + +theorem simp477_NF {α : Type} [DecidableEq α] (x : FreeMagma α) : IsNF (simp477 x) := by + unfold simp477 + split + · constructor + · rename_i x m1 m2 + simp (config := {zetaDelta := true}) + split + · rename_i m2' x y2 y3 y4 heq + split + · have := simp477_NF m2 + rw [heq] at this + cases this + assumption + · constructor + · apply simp477_NF + · apply simp477_NF + · simp [simp477] + rw [idem_of_IsNF (simp477_NF m2)] + rw [idem_of_IsNF (simp477_NF m1)] + simp [*] + · constructor + · apply simp477_NF + · apply simp477_NF + · simp [simp477] + rw [idem_of_IsNF (simp477_NF m2)] + rw [idem_of_IsNF (simp477_NF m1)] + simp [*] + +theorem simp477_idempotent {α : Type} [DecidableEq α] (x : FreeMagma α) : + simp477 (simp477 x) = simp477 x := idem_of_IsNF (simp477_NF x) + +-- def Magma477 (α) [DecidableEq α] := Quot (λ x y => @simp477 α _ x = simp477 y) + +def Magma477 (α) [DecidableEq α] := {x : FreeMagma α // simp477 x = x } + +instance (α) [DecidableEq α] : Coe α (Magma477 α) where + coe x := ⟨x, by rfl⟩ + +instance instMagmaMagma477 {α} [DecidableEq α] : Magma (Magma477 α) where + op := fun x y => ⟨simp477 (x.1 ◇ y.1), simp477_idempotent _⟩ + +instance {α} [DecidableEq α] : DecidableEq (Magma477 α) := + inferInstanceAs (DecidableEq {x : FreeMagma α // simp477 x = x }) + +theorem simp477_yy {α} [DecidableEq α] (y : FreeMagma α) : + simp477 (y ⋆ y) = simp477 y ⋆ simp477 y := by + simp [simp477] + split + · split + · exfalso + rename_i m2' x y2 y3 y4 heq hys + obtain ⟨rfl, rfl, rfl⟩ := hys + have := congrArg FreeMagma.length heq + simp [FreeMagma.length] at this + have := FreeMagma.length_pos (simp477 y) + omega + · rfl + · rfl + +theorem simp477_yyy {α} [DecidableEq α] (y : FreeMagma α) : + simp477 (y ⋆ (y ⋆ y)) = simp477 y ⋆ simp477 (y ⋆ y) := by + simp [simp477_yy] + rw [simp477] + split + · split + · exfalso + rename_i m2' x y2 y3 y4 heq hys + obtain ⟨rfl, rfl, rfl⟩ := hys + simp [simp477_yy] at heq + obtain ⟨rfl, heq⟩ := heq + have := congrArg FreeMagma.length heq + simp [FreeMagma.length] at this + · simp [simp477_yy] + · simp [simp477_yy] + +theorem simp477_xyyy {α} [DecidableEq α] (x y : FreeMagma α) : + simp477 (x ⋆ (y ⋆ (y ⋆ y))) = simp477 x ⋆ simp477 (y ⋆ (y ⋆ y)) := by + simp [simp477_yyy] + rw [simp477] + split + · split + · exfalso + rename_i m2' x y2 y3 y4 heq hys + obtain ⟨rfl, rfl, rfl⟩ := hys + simp [simp477_yyy, simp477_yy] at heq + obtain ⟨rfl, hxy, heq⟩ := heq + rw [hxy] at heq + have := congrArg FreeMagma.length heq + simp [FreeMagma.length] at this + · simp [simp477_yyy] + · simp [simp477_yyy] + +@[equational_result] +theorem Equation477_Facts : + ∃ (G : Type) (_ : Magma G), Facts G [477] [1426, 1519, 2035, 2128, 3050, 3150] := by + use Magma477 Nat, instMagmaMagma477 + repeat' apply And.intro + · rintro ⟨x, hx⟩ ⟨y, hy⟩ + simp [Magma.op] + apply Subtype.ext + simp only + simp [hx, hy, simp477_yy, simp477_idempotent, simp477_yyy, simp477_xyyy] + unfold simp477 + simp [hx, hy, simp477_yy, simp477_idempotent, simp477_yyy, simp477_xyyy] + · intro h + replace h := h (0 : Nat) + revert h + decide + · intro h + replace h := h (0 : Nat) (1 : Nat) + revert h + decide + · intro h + replace h := h (0 : Nat) + revert h + decide + · intro h + replace h := h (0 : Nat) (1 : Nat) + revert h + decide + · intro h + replace h := h (0 : Nat) + revert h + decide + · intro h + replace h := h (0 : Nat) (1 : Nat) + revert h + decide diff --git a/equational_theories/Equations.lean b/equational_theories/Equations.lean index 92a5da5f3..e10c8d54c 100644 --- a/equational_theories/Equations.lean +++ b/equational_theories/Equations.lean @@ -90,6 +90,8 @@ equation 1689 := x = (y ◇ x) ◇ ((x ◇ z) ◇ z) equation 2662 := x = ((x ◇ y) ◇ (x ◇ y)) ◇ x +abbrev Equation3167 (G: Type _) [Magma G] := ∀ x y z : G, x = (((y ◇ y) ◇ z) ◇ z) ◇ x + /-- From Putnam 1978, Problem A4, part (a) -/ equation 3722 := x ◇ y = (x ◇ y) ◇ (x ◇ y) @@ -114,14 +116,17 @@ equation 4579 := x ◇ (y ◇ z) = (w ◇ u) ◇ z /-- all products of three values are the same, regardless bracketing -/ equation 4582 := x ◇ (y ◇ z) = (w ◇ u) ◇ v +abbrev Equation4656 (G: Type _) [Magma G] := ∀ x y z : G, (x ◇ y) ◇ y = (x ◇ z) ◇ z /- Some order 5 laws -/ /-- Mentioned in a paper of Kisielewicz as a conjectural Austin law -/ equation 5105 := x = y ◇ (y ◇ (y ◇ (x ◇ (z ◇ y)))) +equation 28381 := x = (((x ◇ x) ◇ x) ◇ y) ◇ (x ◇ z) + /-- Kisielewicz's second Austin law -/ -equation 28393 := x = (((x ◇ x) ◇ x) ◇ y) ◇ (x ◇ z) +equation 28770 := x = (((y ◇ y) ◇ y) ◇ x) ◇ (y ◇ z) /- Some order 6 laws -/ diff --git a/equational_theories/ForMathlib/Algebra/Group/Nat.lean b/equational_theories/ForMathlib/Algebra/Group/Nat.lean index 6270ed6af..e3afb31e7 100644 --- a/equational_theories/ForMathlib/Algebra/Group/Nat.lean +++ b/equational_theories/ForMathlib/Algebra/Group/Nat.lean @@ -13,5 +13,5 @@ theorem Nat.xor_mod_two_eq (a b : ℕ) : (a ^^^ b) % 2 = (a + b) % 2 := by @[simp] theorem Nat.even_xor (a b : ℕ) : Even (a ^^^ b) ↔ (Even a ↔ Even b) := by simp only [even_iff, xor_mod_two_eq] - simp [← even_iff] + simp only [← even_iff] exact even_add diff --git a/equational_theories/FreeSemigroup.lean b/equational_theories/FreeSemigroup.lean new file mode 100644 index 000000000..1be24ce25 --- /dev/null +++ b/equational_theories/FreeSemigroup.lean @@ -0,0 +1,194 @@ +import Mathlib.Logic.Basic + +import equational_theories.Equations +import equational_theories.FreeMagma +import equational_theories.Homomorphisms +import equational_theories.MagmaLaw + +open FreeMagma +open Law + +def treeConcat {α : Type _} (t : FreeMagma α) : List α := + match t with + | Lf a => [a] + | (tl ⋆ tr) => treeConcat tl ++ treeConcat tr + +def rightJoinTrees {α : Type _} (t1 t2 : FreeMagma α) : FreeMagma α := + match t1 with + | Lf a => Lf a ⋆ t2 + | (tl ⋆ tr) => tl ⋆ (rightJoinTrees tr t2) + +def rightAssociateTree {α : Type _} (t : FreeMagma α) : FreeMagma α := + match t with + | Lf a => Lf a + | (tl ⋆ tr) => rightJoinTrees (rightAssociateTree tl) (rightAssociateTree tr) + +theorem AssocImpliesForkEquivRightJoin {α : Type _} {G : Type _} [Magma G] + (assoc : Equation4512 G) (f : α → G) (tl tr : FreeMagma α) + : evalInMagma f (tl ⋆ tr) = evalInMagma f (rightJoinTrees tl tr) := + match tl with + | Lf _ => Eq.refl _ + | (tl1 ⋆ tl2) => Eq.trans + (Eq.symm $ assoc (evalInMagma f tl1) (evalInMagma f tl2) (evalInMagma f tr)) + (congrArg (fun t ↦ (evalInMagma f tl1) ◇ t) (AssocImpliesForkEquivRightJoin assoc f tl2 tr)) + +/- Associativity allows us to fully right-associate an entire operation tree -/ +theorem AssocFullyRightAssociate {α : Type _} {G : Type _} [Magma G] + (assoc : Equation4512 G) (f : α → G) (t : FreeMagma α) + : evalInMagma f t = evalInMagma f (rightAssociateTree t) := + match t with + | Lf _ => Eq.refl _ + | (tl ⋆ tr) => Eq.trans + (congrArg (fun s ↦ s ◇ (evalInMagma f tr)) (AssocFullyRightAssociate assoc f tl)) $ Eq.trans + (congrArg (fun s ↦ (evalInMagma f (rightAssociateTree tl)) ◇ s) (AssocFullyRightAssociate assoc f tr)) + (AssocImpliesForkEquivRightJoin assoc f (rightAssociateTree tl) (rightAssociateTree tr)) + +/-- Example usage of AssocFullyRightAssociate -/ +theorem Assoc4 {G : Type _} [Magma G] (assoc : Equation4512 G) + : ∀ x y z w : G, ((x ◇ y) ◇ z) ◇ w = x ◇ (y ◇ (z ◇ w)) := + fun x y z w ↦ AssocFullyRightAssociate + assoc + (fun | 0 => x | 1 => y | 2 => z | 3 => w : Fin 4 → G) + (((Lf 0 ⋆ Lf 1) ⋆ Lf 2) ⋆ Lf 3) + +inductive FreeSemigroup (α : Type _) + | Singleton : α → FreeSemigroup α + | Cons : α → FreeSemigroup α → FreeSemigroup α + +local postfix:61 ".+" => FreeSemigroup.Singleton +local infixr:60 " ,+ " => FreeSemigroup.Cons + +def semigroupConcat {α : Type _} (s1 s2 : FreeSemigroup α) : FreeSemigroup α := + match s1 with + | a .+ => a ,+ s2 + | a ,+ s1tail => a ,+ (semigroupConcat s1tail s2) + +instance (α : Type _) : Magma (FreeSemigroup α) where + op := semigroupConcat + +theorem FreeSgrAssoc {α : Type} : Equation4512 (FreeSemigroup α) := + fun ls1 ls2 ls3 ↦ match ls1 with + | _ .+ => Eq.refl _ + | a ,+ ls1' => congrArg (fun ls ↦ a ,+ ls) (FreeSgrAssoc ls1' ls2 ls3) + +/- "Flatten" a FreeMagma tree expression into its semigroup representation -/ +def freeMagmaToFreeSgr {α : Type _} : MagmaHom (FreeMagma α) (FreeSemigroup α) where + toFun := fun t ↦ evalInMagma FreeSemigroup.Singleton t + map_op' := fun s _ ↦ match s with + | Lf _ => Eq.refl _ + | _ ⋆ _ => Eq.refl _ + +local postfix:70 " ↠Sgr " => freeMagmaToFreeSgr.toFun + +def evalInSgr {α : Type _} {G : Type _} [Magma G] (f : α → G) (ls : FreeSemigroup α) : G := + match ls with + | a .+ => f a + | a ,+ lstail => f a ◇ evalInSgr f lstail + +def evalInSgrHom {α : Type _} {G : Type _} [Magma G] (assoc : Equation4512 G) (f : α → G) : MagmaHom (FreeSemigroup α) G where + toFun := evalInSgr f + map_op' := let rec mapper : ∀ ls1 ls2 : FreeSemigroup α, evalInSgr f (ls1 ◇ ls2) = evalInSgr f ls1 ◇ evalInSgr f ls2 := + fun ls1 ls2 ↦ match ls1 with + | _ .+ => Eq.refl _ + | a ,+ ls1' => Eq.trans + (congrArg (fun x ↦ f a ◇ x) (mapper ls1' ls2)) + (assoc (f a) (evalInSgr f ls1') (evalInSgr f ls2)) + mapper + +def foldFreeSemigroup {G : Type _} [Magma G] (ls : FreeSemigroup G) : G := + match ls with + | a .+ => a + | a ,+ lstail => a ◇ (foldFreeSemigroup lstail) + +/- When evaluating in an associative structure, we may reduce a FreeMagma tree to a FreeSemigroup list -/ +theorem AssocImpliesSgrProjFaithful {α : Type _} {G : Type _} [Magma G] (assoc : Equation4512 G) (f : α → G) (t : FreeMagma α) + : evalInMagma f t = evalInSgr f (freeMagmaToFreeSgr t) := + match t with + | Lf a => Eq.refl _ + | Lf a ⋆ tr => congrArg (fun y ↦ (f a) ◇ y) (AssocImpliesSgrProjFaithful assoc f tr) + | (tl1 ⋆ tl2) ⋆ tr => by + apply Eq.symm + apply Eq.trans $ congrArg (evalInSgr f) $ freeMagmaToFreeSgr.map_op' (tl1 ⋆ tl2) tr + apply Eq.trans $ congrArg (fun s ↦ evalInSgr f (s ◇ tr ↠Sgr)) $ freeMagmaToFreeSgr.map_op' tl1 tl2 + apply Eq.trans $ (evalInSgrHom assoc f).map_op' (tl1 ↠Sgr ◇ tl2 ↠Sgr) (tr ↠Sgr) + apply Eq.trans $ congrArg (fun s ↦ s ◇ (evalInSgr f (tr ↠Sgr))) $ (evalInSgrHom assoc f).map_op' (tl1 ↠Sgr) (tl2 ↠Sgr) + apply Eq.symm + apply Eq.trans $ congrArg (fun s ↦ _ ◇ s) (AssocImpliesSgrProjFaithful assoc f tr) + apply Eq.trans $ congrArg (fun s ↦ (s ◇ _) ◇ _) (AssocImpliesSgrProjFaithful assoc f tl1) + apply Eq.trans $ congrArg (fun s ↦ (_ ◇ s) ◇ _) (AssocImpliesSgrProjFaithful assoc f tl2) + trivial + +def insertSgrSorted {n : Nat} (i : Fin n) (ls : FreeSemigroup (Fin n)) : FreeSemigroup (Fin n) := + match ls with + | j .+ => if i ≤ j then i ,+ j .+ else j ,+ i .+ + | j ,+ lstail => if i ≤ j then i ,+ j ,+ lstail else j ,+ i ,+ lstail + +def insertionSortSgr {n : Nat} (ls : FreeSemigroup (Fin n)) : FreeSemigroup (Fin n) := + match ls with + | i .+ => i .+ + | i ,+ lstail => insertSgrSorted i (insertionSortSgr lstail) + +theorem CommSgrImpliesInsertSortedFaithful {n : Nat} {G : Type _} [Magma G] (assoc : Equation4512 G) (comm : Equation43 G) (f : Fin n → G) + : ∀ i : Fin n, ∀ ls : FreeSemigroup (Fin n), evalInSgr f (insertSgrSorted i ls) = (f i) ◇ evalInSgr f ls := + fun i ls ↦ match ls with + | j .+ => by + have eqor := ite_eq_or_eq (i ≤ j) (i ,+ j .+) (j ,+ i .+) + cases eqor with + | inl eq1 => apply Eq.trans (congrArg (evalInSgr f) eq1); exact Eq.refl _ + | inr eq2 => apply Eq.trans (congrArg (evalInSgr f) eq2); exact comm (f j) (f i) + | j ,+ lstail => by + have eqor := ite_eq_or_eq (i ≤ j) (i ,+ j ,+ lstail) (j ,+ i ,+ lstail) + cases eqor with + | inl eq1 => + apply Eq.trans (congrArg (evalInSgr f) eq1); + exact Eq.refl _ + | inr eq2 => + apply Eq.trans (congrArg (evalInSgr f) eq2); + apply Eq.trans $ assoc (f j) (f i) _; + rw [comm (f j) (f i)]; + exact Eq.symm $ assoc (f i) (f j) _ + +theorem CommSgrImpliesInsertionSortFaithful {n : Nat} {G : Type _} [Magma G] (assoc : Equation4512 G) (comm : Equation43 G) (f : Fin n → G) + : ∀ ls : FreeSemigroup (Fin n), evalInSgr f ls = evalInSgr f (insertionSortSgr ls) + | _ .+ => Eq.refl _ + | i ,+ lstail => Eq.trans + (congrArg (fun s ↦ (f i) ◇ s) (CommSgrImpliesInsertionSortFaithful assoc comm f lstail)) + (Eq.symm $ CommSgrImpliesInsertSortedFaithful assoc comm f i (insertionSortSgr lstail)) + +def involutionReduce {α : Type _} [DecidableEq α] (ls : FreeSemigroup α) : FreeSemigroup α := + match ls with + | a .+ => a .+ + | a ,+ b .+ => a ,+ b .+ + | a ,+ b ,+ lstail => if (a = b) then involutionReduce lstail else a ,+ involutionReduce (b ,+ lstail) + +def InvolutiveImpliesInvolutionReduceFaithful {α : Type _} [DecidableEq α] {G : Type _} [Magma G] (ls : FreeSemigroup α) (invol : Equation16 G) (f : α → G) + : evalInSgr f ls = evalInSgr f (involutionReduce ls) := + match ls with + | a .+ => Eq.refl _ + | a ,+ b .+ => Eq.refl _ + | a ,+ b ,+ lstail => by + have eqor := dite_eq_or_eq (P := a = b) (A := fun _ ↦ involutionReduce lstail) (B := fun _ ↦ a ,+ involutionReduce (b ,+ lstail)) + cases eqor with + | inl eqcase => + apply Eq.trans $ congrArg (fun s ↦ (f s) ◇ (f b ◇ (evalInSgr f lstail))) eqcase.1 + apply Eq.trans $ Eq.symm $ invol (evalInSgr f lstail) (f b) + apply Eq.trans $ InvolutiveImpliesInvolutionReduceFaithful lstail invol f + exact Eq.symm $ congrArg (evalInSgr f) eqcase.2 + | inr neqcase => + apply Eq.symm + apply Eq.trans $ congrArg (evalInSgr f) neqcase.2 + exact congrArg (fun s ↦ f a ◇ s) $ Eq.symm $ InvolutiveImpliesInvolutionReduceFaithful (b ,+ lstail) invol f + +def equation1571Reducer {n : Nat} (t : FreeMagma (Fin (n+1))) : FreeSemigroup (Fin (n+1)) := + involutionReduce $ insertionSortSgr $ freeMagmaToFreeSgr (t ⋆ (Lf (Fin.last n) ⋆ Lf (Fin.last n))) + +def AbGrpPow2ImpliesEquation1571ReducerFaithful {n : Nat} {G : Type _} [Magma G] (t : FreeMagma (Fin (n+1))) (f : Fin (n+1) → G) + (assoc : Equation4512 G) (comm : Equation43 G) (invol : Equation16 G) + : evalInMagma f t = evalInSgr f (equation1571Reducer t) := by + apply Eq.symm + apply Eq.trans $ Eq.symm $ InvolutiveImpliesInvolutionReduceFaithful _ invol f + apply Eq.trans $ Eq.symm $ CommSgrImpliesInsertionSortFaithful assoc comm f _ + apply Eq.trans $ Eq.symm $ AssocImpliesSgrProjFaithful assoc f _ + apply Eq.trans $ comm (evalInMagma f t) _ + apply Eq.trans $ Eq.symm $ assoc _ _ _ + exact Eq.symm $ invol (evalInMagma f t) (f $ Fin.last n) diff --git a/equational_theories/Generated.lean b/equational_theories/Generated.lean index e3a2eced4..002434b8b 100644 --- a/equational_theories/Generated.lean +++ b/equational_theories/Generated.lean @@ -9,3 +9,4 @@ import equational_theories.Generated.Equation1 import equational_theories.Generated.VampireProven import equational_theories.Generated.FinSearch import equational_theories.Generated.MagmaEgg.small +import equational_theories.Generated.Confluence diff --git a/equational_theories/Generated/All4x4Tables/src/check_correct.py b/equational_theories/Generated/All4x4Tables/src/check_correct.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/check_redundant.py b/equational_theories/Generated/All4x4Tables/src/check_redundant.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/double_check_3x3.py b/equational_theories/Generated/All4x4Tables/src/double_check_3x3.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/drive_c_parallel.py b/equational_theories/Generated/All4x4Tables/src/drive_c_parallel.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/dump_tables.py b/equational_theories/Generated/All4x4Tables/src/dump_tables.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/generate_combined_refutations.sh b/equational_theories/Generated/All4x4Tables/src/generate_combined_refutations.sh old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/generate_lean.py b/equational_theories/Generated/All4x4Tables/src/generate_lean.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/prune.py b/equational_theories/Generated/All4x4Tables/src/prune.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/All4x4Tables/src/write_equations.py b/equational_theories/Generated/All4x4Tables/src/write_equations.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/Confluence.lean b/equational_theories/Generated/Confluence.lean new file mode 100644 index 000000000..03ba86ad3 --- /dev/null +++ b/equational_theories/Generated/Confluence.lean @@ -0,0 +1 @@ +import equational_theories.Generated.Confluence.ManuallySampled diff --git a/equational_theories/Generated/Confluence/ManuallySampled.lean b/equational_theories/Generated/Confluence/ManuallySampled.lean new file mode 100644 index 000000000..adefcdac7 --- /dev/null +++ b/equational_theories/Generated/Confluence/ManuallySampled.lean @@ -0,0 +1,67 @@ +import equational_theories.Magma +import equational_theories.AllEquations +import Mathlib.Tactic + +namespace Confluence + +@[equational_result] +conjecture Equation467_not_implies_Equation2847 : ∃ (G : Type) (_ : Magma G), Equation467 G ∧ ¬Equation2847 G + +@[equational_result] +conjecture Equation477_not_implies_Equation1426 : ∃ (G : Type) (_ : Magma G), Equation477 G ∧ ¬Equation1426 G + +@[equational_result] +conjecture Equation477_not_implies_Equation1519 : ∃ (G : Type) (_ : Magma G), Equation477 G ∧ ¬Equation1519 G + +@[equational_result] +conjecture Equation477_not_implies_Equation2035 : ∃ (G : Type) (_ : Magma G), Equation477 G ∧ ¬Equation2035 G + +@[equational_result] +conjecture Equation477_not_implies_Equation2128 : ∃ (G : Type) (_ : Magma G), Equation477 G ∧ ¬Equation2128 G + +@[equational_result] +conjecture Equation477_not_implies_Equation3050 : ∃ (G : Type) (_ : Magma G), Equation477 G ∧ ¬Equation3050 G + +@[equational_result] +conjecture Equation477_not_implies_Equation3150 : ∃ (G : Type) (_ : Magma G), Equation477 G ∧ ¬Equation3150 G + +@[equational_result] +conjecture Equation504_not_implies_Equation817 : ∃ (G : Type) (_ : Magma G), Equation504 G ∧ ¬Equation817 G + +@[equational_result] +conjecture Equation504_not_implies_Equation1629 : ∃ (G : Type) (_ : Magma G), Equation504 G ∧ ¬Equation1629 G + +@[equational_result] +conjecture Equation504_not_implies_Equation1832 : ∃ (G : Type) (_ : Magma G), Equation504 G ∧ ¬Equation1832 G + +@[equational_result] +conjecture Equation504_not_implies_Equation1925 : ∃ (G : Type) (_ : Magma G), Equation504 G ∧ ¬Equation1925 G + +@[equational_result] +conjecture Equation1515_not_implies_Equation4590 : ∃ (G : Type) (_ : Magma G), Equation1515 G ∧ ¬Equation4590 G + +@[equational_result] +conjecture Equation2038_not_implies_Equation4270 : ∃ (G : Type) (_ : Magma G), Equation2038 G ∧ ¬Equation4270 G + +@[equational_result] +conjecture Equation3140_not_implies_Equation614 : ∃ (G : Type) (_ : Magma G), Equation3140 G ∧ ¬Equation614 G + +@[equational_result] +conjecture Equation3143_not_implies_Equation1629 : ∃ (G : Type) (_ : Magma G), Equation3143 G ∧ ¬Equation1629 G + +@[equational_result] +conjecture Equation3143_not_implies_Equation1832 : ∃ (G : Type) (_ : Magma G), Equation3143 G ∧ ¬Equation1832 G + +@[equational_result] +conjecture Equation3143_not_implies_Equation2644 : ∃ (G : Type) (_ : Magma G), Equation3143 G ∧ ¬Equation2644 G + +@[equational_result] +conjecture Equation3150_not_implies_Equation411 : ∃ (G : Type) (_ : Magma G), Equation3150 G ∧ ¬Equation411 G + +@[equational_result] +conjecture Equation3150_not_implies_Equation1426 : ∃ (G : Type) (_ : Magma G), Equation3150 G ∧ ¬Equation1426 G + +@[equational_result] +conjecture Equation3150_not_implies_Equation2035 : ∃ (G : Type) (_ : Magma G), Equation3150 G ∧ ¬Equation2035 G + +end Confluence diff --git a/equational_theories/Generated/Confluence/README.md b/equational_theories/Generated/Confluence/README.md new file mode 100644 index 000000000..b426cb58b --- /dev/null +++ b/equational_theories/Generated/Confluence/README.md @@ -0,0 +1,18 @@ +This directory implements Fan Zheng's idea, from the Equation 477 thread on Zulip. (TBD: write +this up in the blueprint and link there) + +The idea is: +1. Chains of equality that use only an equation of the form `x = E` can be written down + as two different simplifications of the same expression, contracting `E → x` on + a sequence of points in the expression tree. +2. If the expression `E` cannot be matched to any of its sub-expressions, there is a unique + fully-simplified form (the order of simplifications doesn't matter). +3. Therefore, if an equation `A = B` follows from such a law `x = E`, then the fully-reduced + form of `A` and `B` will be equal. For expressions `E` with order 3 or 4 this means only + trivial substitutions follow. + +The script generates `confluent_equations.txt`. It checks condition 2 very naively, luckily +we have relatively few equations to check and computers are fast enough. + +The file `ManuallySampled.lean` includes the implications that were unknown at the time and +are covered by these arguments. diff --git a/equational_theories/Generated/Confluence/confluent_equations.txt b/equational_theories/Generated/Confluence/confluent_equations.txt new file mode 100644 index 000000000..3b202df9a --- /dev/null +++ b/equational_theories/Generated/Confluence/confluent_equations.txt @@ -0,0 +1,53 @@ +x = x ◇ x (3) +x = x ◇ y (4) +x = y ◇ x (5) +x = y ◇ y (6) +x = y ◇ z (7) +x = x ◇ (x ◇ x) (8) +x = y ◇ (y ◇ y) (17) +x = (x ◇ x) ◇ x (23) +x = (y ◇ y) ◇ y (32) +x = x ◇ (x ◇ (x ◇ x)) (47) +x = y ◇ (y ◇ (y ◇ y)) (76) +x = ((x ◇ x) ◇ x) ◇ x (255) +x = ((y ◇ y) ◇ y) ◇ y (284) +x = x ◇ (x ◇ (x ◇ (x ◇ x))) (411) +x = x ◇ (x ◇ (y ◇ (x ◇ x))) (416) +x = x ◇ (y ◇ (x ◇ (x ◇ x))) (426) +x = x ◇ (y ◇ (y ◇ (x ◇ x))) (436) +x = y ◇ (x ◇ (x ◇ (y ◇ y))) (467) +x = y ◇ (x ◇ (y ◇ (y ◇ y))) (477) +x = y ◇ (y ◇ (x ◇ (y ◇ y))) (504) +x = y ◇ (y ◇ (y ◇ (y ◇ y))) (514) +x = y ◇ (y ◇ (z ◇ (y ◇ y))) (525) +x = y ◇ (z ◇ (y ◇ (y ◇ y))) (559) +x = y ◇ (z ◇ (z ◇ (y ◇ y))) (576) +x = x ◇ ((x ◇ x) ◇ (x ◇ x)) (817) +x = y ◇ ((y ◇ y) ◇ (y ◇ y)) (920) +x = (x ◇ x) ◇ (x ◇ (x ◇ x)) (1426) +x = (x ◇ x) ◇ (y ◇ (y ◇ y)) (1435) +x = (y ◇ y) ◇ (x ◇ (x ◇ x)) (1515) +x = (y ◇ y) ◇ (y ◇ (y ◇ y)) (1529) +x = (y ◇ y) ◇ (z ◇ (z ◇ z)) (1545) +x = (x ◇ x) ◇ ((x ◇ x) ◇ x) (1629) +x = (y ◇ y) ◇ ((y ◇ y) ◇ y) (1732) +x = (x ◇ (x ◇ x)) ◇ (x ◇ x) (1832) +x = (y ◇ (y ◇ y)) ◇ (y ◇ y) (1935) +x = ((x ◇ x) ◇ x) ◇ (x ◇ x) (2035) +x = ((x ◇ x) ◇ x) ◇ (y ◇ y) (2038) +x = ((y ◇ y) ◇ y) ◇ (x ◇ x) (2134) +x = ((y ◇ y) ◇ y) ◇ (y ◇ y) (2138) +x = ((y ◇ y) ◇ y) ◇ (z ◇ z) (2142) +x = ((x ◇ x) ◇ (x ◇ x)) ◇ x (2644) +x = ((y ◇ y) ◇ (y ◇ y)) ◇ y (2747) +x = (((x ◇ x) ◇ x) ◇ x) ◇ x (3050) +x = (((x ◇ x) ◇ x) ◇ y) ◇ x (3052) +x = (((x ◇ x) ◇ y) ◇ x) ◇ x (3055) +x = (((x ◇ x) ◇ y) ◇ y) ◇ x (3058) +x = (((y ◇ y) ◇ x) ◇ x) ◇ y (3140) +x = (((y ◇ y) ◇ x) ◇ y) ◇ y (3143) +x = (((y ◇ y) ◇ y) ◇ x) ◇ y (3150) +x = (((y ◇ y) ◇ y) ◇ y) ◇ y (3153) +x = (((y ◇ y) ◇ y) ◇ z) ◇ y (3156) +x = (((y ◇ y) ◇ z) ◇ y) ◇ y (3164) +x = (((y ◇ y) ◇ z) ◇ z) ◇ y (3168) diff --git a/equational_theories/Generated/Confluence/src/find_confluent_equations.py b/equational_theories/Generated/Confluence/src/find_confluent_equations.py new file mode 100644 index 000000000..0efd4fff0 --- /dev/null +++ b/equational_theories/Generated/Confluence/src/find_confluent_equations.py @@ -0,0 +1,72 @@ +from scripts.generate_eqs_list import eqs, format_expr + + +def leafs(x): + if isinstance(x, int): + yield x + else: + yield from leafs(x[0]) + yield from leafs(x[1]) + + +def subexprs(expr, strict=False): + if not strict: + yield expr + if isinstance(expr, tuple): + yield from subexprs(expr[0]) + yield from subexprs(expr[1]) + + +def u(expr): + if isinstance(expr, int): + return expr + 10 + else: + return (u(expr[0]), u(expr[1])) + + +def subst(expr, v, term): + if isinstance(expr, int): + if expr == v: + return term + else: + return expr + else: + return (subst(expr[0], v, term), subst(expr[1], v, term)) + + +def unify(expr1, expr2): + components = {} + def equate(e1, e2): + if e1 not in components: + components[e1] = {e1} + if e2 not in components: + components[e2] = {e2} + e1_comp = components[e1] + e2_comp = components[e2] + if e1_comp is not e2_comp: + joint = e1_comp | e2_comp + for x in joint: + components[x] = joint + for a in e1_comp: + if isinstance(a, tuple): + for b in e2_comp: + if isinstance(b, tuple): + equate(a[0], b[0]) + equate(a[1], b[1]) + equate(expr1, u(expr2)) + for c in set(map(frozenset, components.values())): + for a in c: + for b in c: + if a in subexprs(b, strict=True): + return False + return True + + +def is_confluent(expr): + return not any(unify(expr, sub) for sub in subexprs(expr, strict=True) if isinstance(sub, tuple)) + + +for i, eq in enumerate(eqs): + if isinstance(eq[0], int) and isinstance(eq[1], tuple): + if is_confluent(eq[1]): + print(format_expr(eq[0]), '=', format_expr(eq[1]), f' ({i+1})') diff --git a/equational_theories/Generated/FinSearch/src/finite_magma.py b/equational_theories/Generated/FinSearch/src/finite_magma.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/FinSearch/src/finsearch.py b/equational_theories/Generated/FinSearch/src/finsearch.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/FinSearch/src/generate_lean.py b/equational_theories/Generated/FinSearch/src/generate_lean.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/FinSearch/src/parser.py b/equational_theories/Generated/FinSearch/src/parser.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/FinitePoly/src/finite_poly_generate_lean.py b/equational_theories/Generated/FinitePoly/src/finite_poly_generate_lean.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/FinitePoly/src/generate_refutations.py b/equational_theories/Generated/FinitePoly/src/generate_refutations.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/FinitePoly/src/utils.py b/equational_theories/Generated/FinitePoly/src/utils.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/LinearOps/README.md b/equational_theories/Generated/LinearOps/README.md new file mode 100644 index 000000000..0fdd2de70 --- /dev/null +++ b/equational_theories/Generated/LinearOps/README.md @@ -0,0 +1,19 @@ +# Brute Force Linear Ops + +This code enumerates all linear operators `op(x,y) = a*x + b*y` via brute force. + +First compile everything +``` +gcc -O3 -c -o equations.o equations.c +gcc -O3 -g brute_force_linear_equations.c equations.o -fopenmp -lm +``` + +Then run the script +``` +./a.out > log +python3 export.py +# output is in new.lean +``` + +This should generate refutations for ~13.3 million implications. +Many of these are covered by previous refutations, but a few are new. \ No newline at end of file diff --git a/equational_theories/Generated/LinearOps/src/brute_force_linear_equations.c b/equational_theories/Generated/LinearOps/src/brute_force_linear_equations.c new file mode 100644 index 000000000..57eb96cef --- /dev/null +++ b/equational_theories/Generated/LinearOps/src/brute_force_linear_equations.c @@ -0,0 +1,350 @@ +#include +#include +#include +#include +#include +#include +#include +#include "header.h" + +extern FunctionPtr* functions; +extern int* nvar_list; +extern void setup(); + +#define USED_EQUATIONS 4694 +//397 + +#define TABLE_SIZE (N * N) +#define BITS_PER_WORD 64 +//#define WORD_COUNT ((NUM_FUNCTIONS + BITS_PER_WORD - 1) / BITS_PER_WORD) +#define WORD_COUNT ((USED_EQUATIONS + BITS_PER_WORD - 1) / BITS_PER_WORD) +#define BLOOM_SIZE (1<<28) +#define BLOOM_WORDS (BLOOM_SIZE / BITS_PER_WORD) +#define NUM_PROBES 8 +#define NUM_THREADS 176 + + +volatile uint64_t unique_tables_found = 0; + +typedef uint64_t word_t; + + +bool check_rule(int nvar, FunctionPtr fn, int pk, int inv, int a, int b) { + int v1, v2, v3, v4, v5, v6; + + switch (nvar) { + case 1: + for (v1 = 0; v1 < pk; v1++) { + if (!fn(pk, inv, a, b, v1, 0, 0, 0, 0, 0)) return false; + } + break; + + case 2: + for (v1 = 0; v1 < pk; v1++) { + for (v2 = 0; v2 < pk; v2++) { + if (!fn(pk, inv, a, b, v1, v2, 0, 0, 0, 0)) return false; + } + } + break; + + case 3: + for (v1 = 0; v1 < pk; v1++) { + for (v2 = 0; v2 < pk; v2++) { + for (v3 = 0; v3 < pk; v3++) { + if (!fn(pk, inv, a, b, v1, v2, v3, 0, 0, 0)) return false; + } + } + } + break; + + case 4: + for (v1 = 0; v1 < pk; v1++) { + for (v2 = 0; v2 < pk; v2++) { + for (v3 = 0; v3 < pk; v3++) { + for (v4 = 0; v4 < pk; v4++) { + if (!fn(pk, inv, a, b, v1, v2, v3, v4, 0, 0)) return false; + } + } + } + } + break; + + case 5: + for (v1 = 0; v1 < pk; v1++) { + for (v2 = 0; v2 < pk; v2++) { + for (v3 = 0; v3 < pk; v3++) { + for (v4 = 0; v4 < pk; v4++) { + for (v5 = 0; v5 < pk; v5++) { + if (!fn(pk, inv, a, b, v1, v2, v3, v4, v5, 0)) return false; + } + } + } + } + } + break; + + case 6: + for (v1 = 0; v1 < pk; v1++) { + for (v2 = 0; v2 < pk; v2++) { + for (v3 = 0; v3 < pk; v3++) { + for (v4 = 0; v4 < pk; v4++) { + for (v5 = 0; v5 < pk; v5++) { + for (v6 = 0; v6 < pk; v6++) { + if (!fn(pk, inv, a, b, v1, v2, v3, v4, v5, v6)) return false; + } + } + } + } + } + } + break; + + default: + // Handle invalid nvar values + return false; + } + + return true; +} + + +// Function to check if a number is prime +bool is_prime(int n) { + // Handle edge cases + if (n <= 1) { + return false; + } + if (n <= 3) { + return true; + } + // If the number is divisible by 2 or 3, it is not prime + if (n % 2 == 0 || n % 3 == 0) { + return false; + } + // Check from 5 to sqrt(n) in steps of 6 (i and i+2) + for (int i = 5; i * i <= n; i += 6) { + if (n % i == 0 || n % (i + 2) == 0) { + return false; + } + } + return true; +} + +// Function to check if a number is a prime power +bool is_prime_power(int n) { + if (n < 2) return false; + for (int base = 2; base <= (int)sqrt(n); base++) { + int power = 2; + while (1) { + int value = (int)pow(base, power); + if (value == n) return is_prime(base); + if (value > n || value < 0) break; // value < 0 handles overflow cases + power++; + } + } + return is_prime(n); +} + +// Function to find the next prime power greater than n +int next_prime_power(int n) { + n++; + while (!is_prime_power(n)) { + n++; + } + return n; +} + + +uint64_t hash_function(word_t* ok, int seed) { + uint64_t hash = seed; + for (int i = 0; i < WORD_COUNT; i++) { + hash ^= ok[i]; + hash *= 0x5bd1e995; + hash ^= hash >> 15; + } + return hash; +} + +bool check_and_set_bloom(word_t* bloom_filter, word_t* ok) { + bool seen = true; + for (int i = 0; i < NUM_PROBES; i++) { + uint64_t hash = hash_function(ok, i) % BLOOM_SIZE; + uint64_t word_index = hash / BITS_PER_WORD; + uint64_t bit_index = hash % BITS_PER_WORD; + + if (!(bloom_filter[word_index] & (1ULL << bit_index))) { + seen = false; + bloom_filter[word_index] |= (1ULL << bit_index); + } + } + return seen; +} + +//int unsolved[USED_EQUATIONS] = {474-1, 2126-1, 1076-1, 2531-1, 1133-1, 1167-1, 1659-1, 1661-1, 1485-1, 481-1, 3161-1, 1648-1, 1924-1, 2712-1, 1701-1, 1839-1, 511-1, 3116-1, 1443-1, 2093-1, 1692-1, 1895-1, 477-1, 1112-1, 2460-1, 3150-1, 854-1, 1110-1, 2497-1, 65-1, 73-1, 261-1, 274-1, 680-1, 707-1, 2940-1, 2947-1, 1523-1, 2132-1, 504-1, 1117-1, 1289-1, 1722-1, 1925-1, 2338-1, 2538-1, 3143-1, 3588-1, 3994-1, 713-1, 2856-1, 883-1, 917-1, 2710-1, 2744-1, 1086-1, 2541-1, 704-1, 1518-1, 2054-1, 2903-1, 3342-1, 4167-1, 118-1, 229-1, 1431-1, 1526-1, 2040-1, 2101-1, 115-1, 219-1, 476-1, 503-1, 907-1, 1447-1, 2056-1, 2700-1, 3069-1, 3076-1, 1519-1, 2128-1, 1630-1, 1633-1, 1681-1, 1833-1, 1884-1, 1958-1, 1113-1, 1515-1, 1729-1, 1898-1, 2038-1, 2534-1, 3549-1, 3917-1, 464-1, 706-1, 1276-1, 1437-1, 1441-1, 1516-1, 2037-1, 2070-1, 2091-1, 2291-1, 3103-1, 3308-1, 4158-1, 714-1, 1323-1, 2304-1, 2507-1, 63-1, 124-1, 206-1, 271-1, 1491-1, 2061-1, 467-1, 670-1, 677-1, 879-1, 906-1, 1728-1, 1841-1, 2504-1, 2647-1, 2650-1, 2866-1, 2910-1, 2937-1, 3140-1, 3352-1, 3475-1, 3545-1, 3555-1, 3888-1, 4164-1, 3862-1, 3862-1, 3456-1, 1832-1, 1629-1, 3253-1, 4065-1, 1426-1, 2035-1, 411-1, 3050-1, 817-1, 2644-1, 614-1, 1020-1, 2441-1, 2847-1, 4435-1, 1223-1, 2238-1, 3319-1, 3522-1, 3915-1, 4118-1, 8-1, 23-1, 47-1, 151-1, 255-1, 3457-1, 3877-1, 4268-1, 4587-1, 99-1, 203-1, 307-1, 359-1, 3511-1, 3955-1, 1657-1, 1860-1, 4380-1, 1519-1, 2128-1, 1055-1, 1429-1, 2124-1, 2452-1, 1701-1, 1839-1, 1630-1, 1633-1, 1681-1, 1833-1, 1884-1, 1958-1, 152-1, 166-1, 1096-1, 1427-1, 1481-1, 1483-1, 1492-1, 1634-1, 1656-1, 1660-1, 1668-1, 1721-1, 1837-1, 1851-1, 2051-1, 2087-1, 3460-1, 3520-1, 3524-1, 3527-1, 3659-1, 3897-1, USED_EQUATIONS2-1, 4006-1, 4040-1, 4314-1, 4315-1, 4606-1, 4615-1, 513-1, 1035-1, 1428-1, 2050-1, 2443-1, 3079-1, 3519-1, 3925-1, 4269-1, 4584-1, 1133-1, 1167-1, 1659-1, 1661-1, 1485-1, 477-1, 1112-1, 2460-1, 3150-1, 1523-1, 2132-1, 883-1, 917-1, 2710-1, 2744-1, 1113-1, 1515-1, 1729-1, 1898-1, 2038-1, 2534-1, 714-1, 1323-1, 2304-1, 2507-1, 3-1, 125-1, 167-1, 168-1, 222-1, 326-1, 375-1, 910-1, 1025-1, 1085-1, 1316-1, 1479-1, 1480-1, 1484-1, 1488-1, 1496-1, 1631-1, 1655-1, 1695-1, 1847-1, 1897-1, 2041-1, 2052-1, 2088-1, 2089-1, 2446-1, 2467-1, 2737-1, 3258-1, 3458-1, 3512-1, 3513-1, 3521-1, 3523-1, 3525-1, 3715-1, 3722-1, 3867-1, 3918-1, 3935-1, 3952-1, 3989-1, 3993-1, 4067-1, 4273-1, 4470-1, 4588-1, 1486-1, 2126-1, 481-1, 3161-1, 1648-1, 1924-1, 511-1, 3116-1, 1692-1, 1895-1, 65-1, 73-1, 261-1, 274-1, 680-1, 707-1, 2940-1, 2947-1, 504-1, 1117-1, 1289-1, 1722-1, 1925-1, 2338-1, 2538-1, 3143-1, 3588-1, 3994-1, 1086-1, 2541-1, 118-1, 229-1, 1431-1, 1526-1, 2040-1, 2101-1, 3549-1, 3917-1, 63-1, 124-1, 206-1, 271-1, 1491-1, 2061-1, 107-1, 205-1, 211-1, 413-1, 414-1, 416-1, 466-1, 473-1, 880-1, 1023-1, 1045-1, 1075-1, 1109-1, 1248-1, 1251-1, 1313-1, 1478-1, 1482-1, 1489-1, 1647-1, 1685-1, 1922-1, 2036-1, 2098-1, 2125-1, 2240-1, 2246-1, 2266-1, 2294-1, 2444-1, 2449-1, 2457-1, 2459-1, 2462-1, 2530-1, 2707-1, 3055-1, 3056-1, 3065-1, 3066-1, 3068-1, 3139-1, 3316-1, 3472-1, 3878-1, 4128-1, 4270-1, 4590-1}; + +void print_result(int pk, int a, int b, word_t* ok, int ok_count) { + printf("Variables %d %d %d", pk, a, b); + printf("\nSatisfied equations: "); + bool first = true; + for (int i = 0; i < USED_EQUATIONS; i++) { + if ((ok[i / BITS_PER_WORD] >> (i % BITS_PER_WORD)) & 1) { + if (!first) { + printf(", "); + } + //printf("%d", unsolved[i]); + printf("%d", i); + first = false; + } + } + printf("\n\n"); + fflush(stdout); +} + +/* +int64_t mod(int64_t x, int64_t q, int64_t y) { + return x%y; +} + +int64_t MOD2(int64_t x, int64_t inv, int64_t pk) { + const uint64_t reciprocal = inv; // Precomputed value (2^32 / 47) + printf("input %ld %ld\n", x, reciprocal); + x = abs(x); + int64_t product = ((u_int64_t)x * reciprocal) >> 32; // Multiply and shift + int64_t out = x - product * pk; // Correct the result + printf("Out %ld %ld\n", out, mod(x, 0, pk)); + return out == pk ? 0 : out; +} +*/ + +int main() { + setup(); + word_t* bloom_filter = malloc(sizeof(word_t)*BLOOM_WORDS); + + /* + int inverse_for_div = (int)((1L << 32) / (long)11); + printf("check_rule(%d, %d, %d, %d, %d, %d)\n", nvar_list[473], 0, 11, inverse_for_div, 10, 2); + printf("%d\n", check_rule(nvar_list[473], my, 11, inverse_for_div, 10, 2)); + + exit(0); + //*/ + + { + + + int current_prime_power = 2; + + while (current_prime_power < 320) { + printf("Loop %d\n", current_prime_power); + #pragma omp parallel for schedule(dynamic) + //for (int const_a = 0; const_a < current_prime_power; const_a++) { + //for (int const_b = 0; const_b < current_prime_power; const_b++) { + for (int dual = 0; dual < current_prime_power*current_prime_power; dual++) { + //for (int dual = 123; dual < 144; dual++) { + + int inverse_for_div = (int)((1L << 32) / (long)current_prime_power); + + int const_a = dual/current_prime_power; + int const_b = dual%current_prime_power; + + #pragma omp critical + { + //printf("Try %d %d %d (from %d)\n", current_prime_power, const_a, const_b, dual); + } + + + word_t ok[WORD_COUNT]; + int ok_count; + ok_count = 0; + memset(ok, 0, sizeof(ok)); // Reset all words + + size_t main_loop_end = USED_EQUATIONS - (USED_EQUATIONS % BITS_PER_WORD); + + // Main loop processing BITS_PER_WORD functions at a time + for (size_t i = 0; i < main_loop_end; i += BITS_PER_WORD) { + unsigned long long temp = 0; + + for (int j = 0; j < BITS_PER_WORD; j++) { + //bool bit_ok = check_rule(nvar_list[unsolved[i+j]], functions[unsolved[i+j]], current_prime_power, inverse_for_div, const_a, const_b); + bool bit_ok = check_rule(nvar_list[i+j], functions[i+j], current_prime_power, inverse_for_div, const_a, const_b); + temp |= (unsigned long long)bit_ok << j; + } + + ok[i / BITS_PER_WORD] = temp; + ok_count += __builtin_popcountll(temp); + } + + // Handle remaining functions + unsigned long long temp = 0; + for (size_t i = main_loop_end; i < USED_EQUATIONS; i++) { + //temp |= (unsigned long long)check_rule(nvar_list[unsolved[i]], functions[unsolved[i]], current_prime_power, inverse_for_div, const_a, const_b) << (i % BITS_PER_WORD); + temp |= (unsigned long long)check_rule(nvar_list[i], functions[i], current_prime_power, inverse_for_div, const_a, const_b) << (i % BITS_PER_WORD); + } + + + if (main_loop_end < NUM_FUNCTIONS) { + ok[main_loop_end / BITS_PER_WORD] = temp; + ok_count += __builtin_popcountll(temp); + } + + /* + #pragma omp critical + { + printf("OK %d: ", ok_count); + for (int i = 0; i < WORD_COUNT; i++) { + printf("%lx ", ok[i]); + } + printf("\n"); + } + */ + + if (ok_count > 0 && !check_and_set_bloom(bloom_filter, ok)) { +#pragma omp atomic + unique_tables_found++; + +#pragma omp critical + { + print_result(current_prime_power, const_a, const_b, ok, ok_count); + } + } + + + #pragma omp critical + { + //printf("Done %d %d %d (from %d)\n", current_prime_power, const_a, const_b, dual); + } + /* + // Progress reporting + if ((current_index - start_index + 1) % progress_step == 0) { +#pragma omp critical + { + int progress = (int)((current_index - start_index + 1) * 100 / tables_to_check); + printf("ThreadID %d: status: %d%%\n", thread_id, progress); + } + } + + // Thread 0 reports additional statistics + if (thread_id == 0 && (current_index - start_index + 1) % progress_step == 0) { + double bloom_filter_fullness = 0; + for (int i = 0; i < BLOOM_WORDS; i++) { + bloom_filter_fullness += __builtin_popcountll(bloom_filter[i]); + } + bloom_filter_fullness /= BLOOM_SIZE; + +#pragma omp critical + { + printf("Thread 0 Report:\n"); + printf(" Unique tables found: %lu\n", unique_tables_found); + printf(" Bloom filter fullness: %.2f%%\n", bloom_filter_fullness * 100); + } + } + */ + + + } + + current_prime_power = next_prime_power(current_prime_power); + } + } + + return 0; +} diff --git a/equational_theories/Generated/LinearOps/src/check_correct.py b/equational_theories/Generated/LinearOps/src/check_correct.py new file mode 100644 index 000000000..748c31e57 --- /dev/null +++ b/equational_theories/Generated/LinearOps/src/check_correct.py @@ -0,0 +1,208 @@ +#!/usr/bin/env python3 + +import numpy as np +import collections +import ast +from itertools import product + +from itertools import product +import re +from typing import List, Callable + +import re + +DEBUG = True + +# Define the expression node +class ExprNode: + def __init__(self, value, left=None, right=None): + self.value = value # Operator or operand + self.left = left + self.right = right + + def __repr__(self): + if self.left and self.right: + return f"({self.left} {self.value} {self.right})" + return self.value + +# Parser implementation +class Parser: + def __init__(self, expression): + self.expression = expression.replace(' ', '') + self.index = 0 + self.length = len(self.expression) + + def parse(self): + return self.parse_expression() + + def parse_expression(self): + nodes = [self.parse_term()] + + while self.current_char() == '◇': + op = self.current_char() + self.advance() + right = self.parse_term() + nodes.append(op) + nodes.append(right) + + # Build the tree (left-associative) + node = nodes[0] + for i in range(1, len(nodes), 2): + node = ExprNode(nodes[i], left=node, right=nodes[i+1]) + + return node + + def parse_term(self): + char = self.current_char() + if char == '(': + self.advance() + node = self.parse_expression() + if self.current_char() != ')': + raise ValueError("Mismatched parentheses") + self.advance() + return node + else: + return self.parse_variable() + + def parse_variable(self): + match = re.match(r'[a-zA-Z_]\w*', self.expression[self.index:]) + if not match: + raise ValueError(f"Invalid character at index {self.index}") + var = match.group(0) + self.index += len(var) + return ExprNode(var) + + def current_char(self): + if self.index < self.length: + return self.expression[self.index] + return None + + def advance(self): + self.index += 1 + +# Function to convert expression tree to prefix notation +def expr_to_prefix(node): + if node.value == '◇': + left = expr_to_prefix(node.left) + right = expr_to_prefix(node.right) + return f"f({left}, {right})" + else: + return node.value + +# Function to convert equations to lambdas +ctr = 0 +def convert(vars_list, equation): + global ctr + if True: + lhs_expr, rhs_expr = equation.split('=') + + # Parse LHS + parser_lhs = Parser(lhs_expr) + tree_lhs = parser_lhs.parse() + prefix_lhs = expr_to_prefix(tree_lhs) + + # Parse RHS + parser_rhs = Parser(rhs_expr) + tree_rhs = parser_rhs.parse() + prefix_rhs = expr_to_prefix(tree_rhs) + + # Create lambda string + lambda_str = f"lambda f,{', '.join(vars_list)}: {prefix_lhs} == {prefix_rhs}" + + # Compile the lambda function + try: + lambda_func = eval(lambda_str) + except Exception as e: + print(f"Error compiling lambda{idx}: {e}") + lambda_func = None + + # Store with a name + lambda_name = f"lambda" + #print(ctr, lambda_str) + ctr += 1 + + return lambda_func + +def get_fns(): + equations = open("equations.txt", "r").read().split("\n")[:-1] + fns = [] + for eq in equations: + oeq = eq + eq = eq.split("∀")[1] + variables, eq = eq.split(":") + variables = variables.strip().split() + rule = eq.split(",")[1] + fns.append((oeq, len(variables), convert(variables, rule))) + + return fns + +fns = get_fns() + +def check_rule(nvar, check, S, op): + for args in product(S, repeat=nvar): + if DEBUG: + VARS = "xyzwuv" + print("Checking equation on assignments", + ", ".join([f"{VARS[i]}={args[i]}" for i in range(nvar)])) + if not check(op, *args): + return False + return True + +""" +S = list(range(4)) + +for row in open("../data/refutations4x4.txt").readlines(): + if 'Table' in row: + table = np.array(eval(row.split("Table")[1])) + elif 'Proves' in row: + proves = eval(row.split("Proves")[1]) + + ok = [] + for x in proves: + if DEBUG: + print(f"Showing that {fns[x-1][0]}") + print(f"is correct on Magma\n{table}") + string, nvar, fn = fns[x-1] + def op(x, y): + if DEBUG: + print(f"table[{x}, {y}] = {table[x, y]}") + return table[x, y] + + this = check_rule(nvar, fn, S, op) + assert this + + ok.append(this) + print(collections.Counter(ok)) +""" + +lines = """ +Variables 11 4 6 +Satisfied equations: 1075 +""".split("\n") + +#for row in open("h4").readlines(): +for row in lines: + print() + print() + if 'Variables' in row: + pk, a, b = map(int,(row.split("Variables")[1].split())) + S = list(range(pk)) + elif 'Satisfied' in row: + proves = list(map(int,row.split(":")[1].split(", "))) + + ok = [] + for x in proves: + if DEBUG: + print(f"Showing that {fns[x][0]}") + print(f"is correct on Magma\n{[pk, a, b]}") + string, nvar, fn = fns[x] + def op(x, y): + if DEBUG: + print(f"{a}*{x}+{b}*{y}={(a*x + b*y)%pk}") + return (a*x + b*y)%pk + + this = check_rule(nvar, fn, S, op) + assert this + + ok.append(this) + print(collections.Counter(ok)) diff --git a/equational_theories/Generated/LinearOps/src/equations.c b/equational_theories/Generated/LinearOps/src/equations.c new file mode 100644 index 000000000..87b802e14 --- /dev/null +++ b/equational_theories/Generated/LinearOps/src/equations.c @@ -0,0 +1,14118 @@ +#include +#include +#include +#include +#include "header.h" + +#define uint64_t int64_t + +FunctionPtr* functions; +int* nvar_list; + + +int64_t MOD(int64_t x, int64_t inv, int64_t pk) { + return x%pk; + /* + const uint64_t reciprocal = inv; // Precomputed value (2^32 / 47) + int64_t product = ((u_int64_t)x * reciprocal) >> 32; // Multiply and shift + int64_t out = x - product * pk; // Correct the result + return out == pk ? 0 : out; + */ +} + + +bool fn0(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (x),inv,pk) == 0; } int nvar_0 = 1; +bool fn1(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (y),inv,pk) == 0; } int nvar_1 = 2; +bool fn2(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(x)),inv,pk) == 0; } int nvar_2 = 1; +bool fn3(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(y)),inv,pk) == 0; } int nvar_3 = 2; +bool fn4(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(x)),inv,pk) == 0; } int nvar_4 = 2; +bool fn5(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(y)),inv,pk) == 0; } int nvar_5 = 2; +bool fn6(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(z)),inv,pk) == 0; } int nvar_6 = 3; +bool fn7(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_7 = 1; +bool fn8(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_8 = 2; +bool fn9(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_9 = 2; +bool fn10(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_10 = 2; +bool fn11(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_11 = 3; +bool fn12(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_12 = 2; +bool fn13(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_13 = 2; +bool fn14(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_14 = 3; +bool fn15(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_15 = 2; +bool fn16(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_16 = 2; +bool fn17(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_17 = 3; +bool fn18(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_18 = 3; +bool fn19(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_19 = 3; +bool fn20(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_20 = 3; +bool fn21(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_21 = 4; +bool fn22(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_22 = 1; +bool fn23(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_23 = 2; +bool fn24(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_24 = 2; +bool fn25(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_25 = 2; +bool fn26(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_26 = 3; +bool fn27(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_27 = 2; +bool fn28(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_28 = 2; +bool fn29(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_29 = 3; +bool fn30(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_30 = 2; +bool fn31(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_31 = 2; +bool fn32(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_32 = 3; +bool fn33(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_33 = 3; +bool fn34(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_34 = 3; +bool fn35(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_35 = 3; +bool fn36(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_36 = 4; +bool fn37(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(y)),inv,pk) == 0; } int nvar_37 = 2; +bool fn38(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(x)),inv,pk) == 0; } int nvar_38 = 2; +bool fn39(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(y)),inv,pk) == 0; } int nvar_39 = 2; +bool fn40(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(z)),inv,pk) == 0; } int nvar_40 = 3; +bool fn41(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(z)),inv,pk) == 0; } int nvar_41 = 3; +bool fn42(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(x)),inv,pk) == 0; } int nvar_42 = 2; +bool fn43(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(z)),inv,pk) == 0; } int nvar_43 = 3; +bool fn44(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(y)),inv,pk) == 0; } int nvar_44 = 3; +bool fn45(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(w)),inv,pk) == 0; } int nvar_45 = 4; +bool fn46(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_46 = 1; +bool fn47(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_47 = 2; +bool fn48(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_48 = 2; +bool fn49(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_49 = 2; +bool fn50(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_50 = 3; +bool fn51(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_51 = 2; +bool fn52(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_52 = 2; +bool fn53(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_53 = 3; +bool fn54(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_54 = 2; +bool fn55(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_55 = 2; +bool fn56(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_56 = 3; +bool fn57(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_57 = 3; +bool fn58(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_58 = 3; +bool fn59(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_59 = 3; +bool fn60(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_60 = 4; +bool fn61(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_61 = 2; +bool fn62(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_62 = 2; +bool fn63(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_63 = 3; +bool fn64(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_64 = 2; +bool fn65(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_65 = 2; +bool fn66(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_66 = 3; +bool fn67(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_67 = 3; +bool fn68(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_68 = 3; +bool fn69(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_69 = 3; +bool fn70(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_70 = 4; +bool fn71(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_71 = 2; +bool fn72(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_72 = 2; +bool fn73(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_73 = 3; +bool fn74(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_74 = 2; +bool fn75(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_75 = 2; +bool fn76(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_76 = 3; +bool fn77(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_77 = 3; +bool fn78(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_78 = 3; +bool fn79(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_79 = 3; +bool fn80(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_80 = 4; +bool fn81(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_81 = 3; +bool fn82(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_82 = 3; +bool fn83(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_83 = 3; +bool fn84(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_84 = 4; +bool fn85(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_85 = 3; +bool fn86(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_86 = 3; +bool fn87(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_87 = 3; +bool fn88(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_88 = 4; +bool fn89(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_89 = 3; +bool fn90(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_90 = 3; +bool fn91(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_91 = 3; +bool fn92(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_92 = 4; +bool fn93(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_93 = 4; +bool fn94(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_94 = 4; +bool fn95(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_95 = 4; +bool fn96(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_96 = 4; +bool fn97(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_97 = 5; +bool fn98(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_98 = 1; +bool fn99(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_99 = 2; +bool fn100(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_100 = 2; +bool fn101(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_101 = 2; +bool fn102(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_102 = 3; +bool fn103(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_103 = 2; +bool fn104(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_104 = 2; +bool fn105(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_105 = 3; +bool fn106(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_106 = 2; +bool fn107(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_107 = 2; +bool fn108(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_108 = 3; +bool fn109(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_109 = 3; +bool fn110(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_110 = 3; +bool fn111(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_111 = 3; +bool fn112(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_112 = 4; +bool fn113(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_113 = 2; +bool fn114(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_114 = 2; +bool fn115(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_115 = 3; +bool fn116(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_116 = 2; +bool fn117(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_117 = 2; +bool fn118(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_118 = 3; +bool fn119(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_119 = 3; +bool fn120(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_120 = 3; +bool fn121(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_121 = 3; +bool fn122(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_122 = 4; +bool fn123(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_123 = 2; +bool fn124(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_124 = 2; +bool fn125(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_125 = 3; +bool fn126(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_126 = 2; +bool fn127(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_127 = 2; +bool fn128(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_128 = 3; +bool fn129(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_129 = 3; +bool fn130(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_130 = 3; +bool fn131(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_131 = 3; +bool fn132(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_132 = 4; +bool fn133(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_133 = 3; +bool fn134(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_134 = 3; +bool fn135(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_135 = 3; +bool fn136(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_136 = 4; +bool fn137(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_137 = 3; +bool fn138(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_138 = 3; +bool fn139(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_139 = 3; +bool fn140(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_140 = 4; +bool fn141(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_141 = 3; +bool fn142(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_142 = 3; +bool fn143(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_143 = 3; +bool fn144(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_144 = 4; +bool fn145(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_145 = 4; +bool fn146(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_146 = 4; +bool fn147(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_147 = 4; +bool fn148(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_148 = 4; +bool fn149(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_149 = 5; +bool fn150(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_150 = 1; +bool fn151(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_151 = 2; +bool fn152(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_152 = 2; +bool fn153(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_153 = 2; +bool fn154(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_154 = 3; +bool fn155(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_155 = 2; +bool fn156(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_156 = 2; +bool fn157(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_157 = 3; +bool fn158(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_158 = 2; +bool fn159(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_159 = 2; +bool fn160(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_160 = 3; +bool fn161(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_161 = 3; +bool fn162(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_162 = 3; +bool fn163(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_163 = 3; +bool fn164(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_164 = 4; +bool fn165(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_165 = 2; +bool fn166(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_166 = 2; +bool fn167(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_167 = 3; +bool fn168(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_168 = 2; +bool fn169(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_169 = 2; +bool fn170(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_170 = 3; +bool fn171(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_171 = 3; +bool fn172(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_172 = 3; +bool fn173(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_173 = 3; +bool fn174(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_174 = 4; +bool fn175(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_175 = 2; +bool fn176(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_176 = 2; +bool fn177(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_177 = 3; +bool fn178(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_178 = 2; +bool fn179(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_179 = 2; +bool fn180(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_180 = 3; +bool fn181(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_181 = 3; +bool fn182(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_182 = 3; +bool fn183(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_183 = 3; +bool fn184(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_184 = 4; +bool fn185(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_185 = 3; +bool fn186(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_186 = 3; +bool fn187(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_187 = 3; +bool fn188(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_188 = 4; +bool fn189(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_189 = 3; +bool fn190(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_190 = 3; +bool fn191(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_191 = 3; +bool fn192(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_192 = 4; +bool fn193(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_193 = 3; +bool fn194(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_194 = 3; +bool fn195(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_195 = 3; +bool fn196(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_196 = 4; +bool fn197(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_197 = 4; +bool fn198(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_198 = 4; +bool fn199(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_199 = 4; +bool fn200(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_200 = 4; +bool fn201(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_201 = 5; +bool fn202(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_202 = 1; +bool fn203(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_203 = 2; +bool fn204(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_204 = 2; +bool fn205(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_205 = 2; +bool fn206(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_206 = 3; +bool fn207(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_207 = 2; +bool fn208(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_208 = 2; +bool fn209(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_209 = 3; +bool fn210(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_210 = 2; +bool fn211(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_211 = 2; +bool fn212(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_212 = 3; +bool fn213(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_213 = 3; +bool fn214(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_214 = 3; +bool fn215(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_215 = 3; +bool fn216(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_216 = 4; +bool fn217(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_217 = 2; +bool fn218(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_218 = 2; +bool fn219(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_219 = 3; +bool fn220(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_220 = 2; +bool fn221(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_221 = 2; +bool fn222(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_222 = 3; +bool fn223(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_223 = 3; +bool fn224(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_224 = 3; +bool fn225(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_225 = 3; +bool fn226(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_226 = 4; +bool fn227(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_227 = 2; +bool fn228(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_228 = 2; +bool fn229(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_229 = 3; +bool fn230(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_230 = 2; +bool fn231(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_231 = 2; +bool fn232(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_232 = 3; +bool fn233(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_233 = 3; +bool fn234(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_234 = 3; +bool fn235(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_235 = 3; +bool fn236(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_236 = 4; +bool fn237(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_237 = 3; +bool fn238(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_238 = 3; +bool fn239(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_239 = 3; +bool fn240(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_240 = 4; +bool fn241(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_241 = 3; +bool fn242(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_242 = 3; +bool fn243(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_243 = 3; +bool fn244(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_244 = 4; +bool fn245(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_245 = 3; +bool fn246(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_246 = 3; +bool fn247(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_247 = 3; +bool fn248(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_248 = 4; +bool fn249(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_249 = 4; +bool fn250(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_250 = 4; +bool fn251(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_251 = 4; +bool fn252(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_252 = 4; +bool fn253(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_253 = 5; +bool fn254(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_254 = 1; +bool fn255(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_255 = 2; +bool fn256(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_256 = 2; +bool fn257(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_257 = 2; +bool fn258(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_258 = 3; +bool fn259(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_259 = 2; +bool fn260(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_260 = 2; +bool fn261(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_261 = 3; +bool fn262(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_262 = 2; +bool fn263(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_263 = 2; +bool fn264(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_264 = 3; +bool fn265(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_265 = 3; +bool fn266(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_266 = 3; +bool fn267(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_267 = 3; +bool fn268(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_268 = 4; +bool fn269(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_269 = 2; +bool fn270(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_270 = 2; +bool fn271(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_271 = 3; +bool fn272(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_272 = 2; +bool fn273(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_273 = 2; +bool fn274(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_274 = 3; +bool fn275(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_275 = 3; +bool fn276(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_276 = 3; +bool fn277(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_277 = 3; +bool fn278(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_278 = 4; +bool fn279(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_279 = 2; +bool fn280(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_280 = 2; +bool fn281(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_281 = 3; +bool fn282(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_282 = 2; +bool fn283(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_283 = 2; +bool fn284(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_284 = 3; +bool fn285(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_285 = 3; +bool fn286(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_286 = 3; +bool fn287(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_287 = 3; +bool fn288(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_288 = 4; +bool fn289(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_289 = 3; +bool fn290(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_290 = 3; +bool fn291(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_291 = 3; +bool fn292(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_292 = 4; +bool fn293(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_293 = 3; +bool fn294(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_294 = 3; +bool fn295(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_295 = 3; +bool fn296(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_296 = 4; +bool fn297(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_297 = 3; +bool fn298(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_298 = 3; +bool fn299(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_299 = 3; +bool fn300(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_300 = 4; +bool fn301(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_301 = 4; +bool fn302(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_302 = 4; +bool fn303(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_303 = 4; +bool fn304(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_304 = 4; +bool fn305(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_305 = 5; +bool fn306(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_306 = 1; +bool fn307(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_307 = 2; +bool fn308(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_308 = 2; +bool fn309(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_309 = 2; +bool fn310(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_310 = 3; +bool fn311(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_311 = 2; +bool fn312(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_312 = 2; +bool fn313(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_313 = 3; +bool fn314(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_314 = 2; +bool fn315(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_315 = 2; +bool fn316(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_316 = 3; +bool fn317(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_317 = 3; +bool fn318(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_318 = 3; +bool fn319(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_319 = 3; +bool fn320(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_320 = 4; +bool fn321(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_321 = 2; +bool fn322(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_322 = 2; +bool fn323(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_323 = 3; +bool fn324(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_324 = 2; +bool fn325(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_325 = 2; +bool fn326(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_326 = 3; +bool fn327(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_327 = 3; +bool fn328(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_328 = 3; +bool fn329(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_329 = 3; +bool fn330(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_330 = 4; +bool fn331(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_331 = 2; +bool fn332(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_332 = 2; +bool fn333(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_333 = 3; +bool fn334(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_334 = 2; +bool fn335(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_335 = 2; +bool fn336(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_336 = 3; +bool fn337(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_337 = 3; +bool fn338(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_338 = 3; +bool fn339(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_339 = 3; +bool fn340(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_340 = 4; +bool fn341(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_341 = 3; +bool fn342(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_342 = 3; +bool fn343(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_343 = 3; +bool fn344(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_344 = 4; +bool fn345(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_345 = 3; +bool fn346(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_346 = 3; +bool fn347(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_347 = 3; +bool fn348(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_348 = 4; +bool fn349(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_349 = 3; +bool fn350(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_350 = 3; +bool fn351(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_351 = 3; +bool fn352(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_352 = 4; +bool fn353(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_353 = 4; +bool fn354(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_354 = 4; +bool fn355(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_355 = 4; +bool fn356(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_356 = 4; +bool fn357(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_357 = 5; +bool fn358(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_358 = 1; +bool fn359(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_359 = 2; +bool fn360(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_360 = 2; +bool fn361(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_361 = 2; +bool fn362(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_362 = 3; +bool fn363(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_363 = 2; +bool fn364(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_364 = 2; +bool fn365(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_365 = 3; +bool fn366(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_366 = 2; +bool fn367(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_367 = 2; +bool fn368(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_368 = 3; +bool fn369(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_369 = 3; +bool fn370(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_370 = 3; +bool fn371(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_371 = 3; +bool fn372(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_372 = 4; +bool fn373(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_373 = 2; +bool fn374(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_374 = 2; +bool fn375(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_375 = 3; +bool fn376(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_376 = 2; +bool fn377(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_377 = 2; +bool fn378(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_378 = 3; +bool fn379(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_379 = 3; +bool fn380(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_380 = 3; +bool fn381(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_381 = 3; +bool fn382(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_382 = 4; +bool fn383(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_383 = 2; +bool fn384(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_384 = 2; +bool fn385(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_385 = 3; +bool fn386(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_386 = 2; +bool fn387(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_387 = 2; +bool fn388(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_388 = 3; +bool fn389(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_389 = 3; +bool fn390(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_390 = 3; +bool fn391(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_391 = 3; +bool fn392(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_392 = 4; +bool fn393(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_393 = 3; +bool fn394(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_394 = 3; +bool fn395(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_395 = 3; +bool fn396(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_396 = 4; +bool fn397(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_397 = 3; +bool fn398(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_398 = 3; +bool fn399(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_399 = 3; +bool fn400(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_400 = 4; +bool fn401(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_401 = 3; +bool fn402(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_402 = 3; +bool fn403(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_403 = 3; +bool fn404(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_404 = 4; +bool fn405(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_405 = 4; +bool fn406(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_406 = 4; +bool fn407(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_407 = 4; +bool fn408(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_408 = 4; +bool fn409(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_409 = 5; +bool fn410(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_410 = 1; +bool fn411(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_411 = 2; +bool fn412(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_412 = 2; +bool fn413(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_413 = 2; +bool fn414(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_414 = 3; +bool fn415(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_415 = 2; +bool fn416(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_416 = 2; +bool fn417(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_417 = 3; +bool fn418(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_418 = 2; +bool fn419(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_419 = 2; +bool fn420(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_420 = 3; +bool fn421(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_421 = 3; +bool fn422(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_422 = 3; +bool fn423(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_423 = 3; +bool fn424(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_424 = 4; +bool fn425(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_425 = 2; +bool fn426(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_426 = 2; +bool fn427(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_427 = 3; +bool fn428(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_428 = 2; +bool fn429(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_429 = 2; +bool fn430(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_430 = 3; +bool fn431(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_431 = 3; +bool fn432(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_432 = 3; +bool fn433(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_433 = 3; +bool fn434(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_434 = 4; +bool fn435(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_435 = 2; +bool fn436(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_436 = 2; +bool fn437(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_437 = 3; +bool fn438(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_438 = 2; +bool fn439(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_439 = 2; +bool fn440(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_440 = 3; +bool fn441(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_441 = 3; +bool fn442(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_442 = 3; +bool fn443(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_443 = 3; +bool fn444(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_444 = 4; +bool fn445(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_445 = 3; +bool fn446(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_446 = 3; +bool fn447(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_447 = 3; +bool fn448(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_448 = 4; +bool fn449(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_449 = 3; +bool fn450(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_450 = 3; +bool fn451(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_451 = 3; +bool fn452(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_452 = 4; +bool fn453(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_453 = 3; +bool fn454(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_454 = 3; +bool fn455(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_455 = 3; +bool fn456(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_456 = 4; +bool fn457(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_457 = 4; +bool fn458(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_458 = 4; +bool fn459(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_459 = 4; +bool fn460(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_460 = 4; +bool fn461(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_461 = 5; +bool fn462(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_462 = 2; +bool fn463(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_463 = 2; +bool fn464(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_464 = 3; +bool fn465(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_465 = 2; +bool fn466(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_466 = 2; +bool fn467(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_467 = 3; +bool fn468(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_468 = 3; +bool fn469(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_469 = 3; +bool fn470(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_470 = 3; +bool fn471(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_471 = 4; +bool fn472(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_472 = 2; +bool fn473(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_473 = 2; +bool fn474(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_474 = 3; +bool fn475(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_475 = 2; +bool fn476(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_476 = 2; +bool fn477(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_477 = 3; +bool fn478(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_478 = 3; +bool fn479(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_479 = 3; +bool fn480(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_480 = 3; +bool fn481(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_481 = 4; +bool fn482(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_482 = 3; +bool fn483(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_483 = 3; +bool fn484(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_484 = 3; +bool fn485(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_485 = 4; +bool fn486(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_486 = 3; +bool fn487(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_487 = 3; +bool fn488(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_488 = 3; +bool fn489(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_489 = 4; +bool fn490(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_490 = 3; +bool fn491(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_491 = 3; +bool fn492(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_492 = 3; +bool fn493(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_493 = 4; +bool fn494(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_494 = 4; +bool fn495(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_495 = 4; +bool fn496(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_496 = 4; +bool fn497(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_497 = 4; +bool fn498(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_498 = 5; +bool fn499(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_499 = 2; +bool fn500(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_500 = 2; +bool fn501(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_501 = 3; +bool fn502(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_502 = 2; +bool fn503(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_503 = 2; +bool fn504(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_504 = 3; +bool fn505(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_505 = 3; +bool fn506(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_506 = 3; +bool fn507(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_507 = 3; +bool fn508(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_508 = 4; +bool fn509(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_509 = 2; +bool fn510(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_510 = 2; +bool fn511(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_511 = 3; +bool fn512(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_512 = 2; +bool fn513(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_513 = 2; +bool fn514(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_514 = 3; +bool fn515(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_515 = 3; +bool fn516(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_516 = 3; +bool fn517(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_517 = 3; +bool fn518(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_518 = 4; +bool fn519(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_519 = 3; +bool fn520(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_520 = 3; +bool fn521(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_521 = 3; +bool fn522(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_522 = 4; +bool fn523(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_523 = 3; +bool fn524(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_524 = 3; +bool fn525(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_525 = 3; +bool fn526(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_526 = 4; +bool fn527(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_527 = 3; +bool fn528(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_528 = 3; +bool fn529(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_529 = 3; +bool fn530(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_530 = 4; +bool fn531(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_531 = 4; +bool fn532(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_532 = 4; +bool fn533(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_533 = 4; +bool fn534(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_534 = 4; +bool fn535(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_535 = 5; +bool fn536(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_536 = 3; +bool fn537(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_537 = 3; +bool fn538(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_538 = 3; +bool fn539(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_539 = 4; +bool fn540(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_540 = 3; +bool fn541(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_541 = 3; +bool fn542(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_542 = 3; +bool fn543(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_543 = 4; +bool fn544(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_544 = 3; +bool fn545(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_545 = 3; +bool fn546(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_546 = 3; +bool fn547(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_547 = 4; +bool fn548(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_548 = 4; +bool fn549(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_549 = 4; +bool fn550(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_550 = 4; +bool fn551(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_551 = 4; +bool fn552(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_552 = 5; +bool fn553(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_553 = 3; +bool fn554(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_554 = 3; +bool fn555(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_555 = 3; +bool fn556(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_556 = 4; +bool fn557(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_557 = 3; +bool fn558(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_558 = 3; +bool fn559(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_559 = 3; +bool fn560(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_560 = 4; +bool fn561(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_561 = 3; +bool fn562(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_562 = 3; +bool fn563(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_563 = 3; +bool fn564(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_564 = 4; +bool fn565(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_565 = 4; +bool fn566(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_566 = 4; +bool fn567(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_567 = 4; +bool fn568(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_568 = 4; +bool fn569(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_569 = 5; +bool fn570(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_570 = 3; +bool fn571(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_571 = 3; +bool fn572(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_572 = 3; +bool fn573(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_573 = 4; +bool fn574(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_574 = 3; +bool fn575(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_575 = 3; +bool fn576(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_576 = 3; +bool fn577(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_577 = 4; +bool fn578(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_578 = 3; +bool fn579(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_579 = 3; +bool fn580(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_580 = 3; +bool fn581(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_581 = 4; +bool fn582(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_582 = 4; +bool fn583(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_583 = 4; +bool fn584(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_584 = 4; +bool fn585(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_585 = 4; +bool fn586(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_586 = 5; +bool fn587(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(x)+b*(x))))),inv,pk) == 0; } int nvar_587 = 4; +bool fn588(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(x)+b*(y))))),inv,pk) == 0; } int nvar_588 = 4; +bool fn589(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(x)+b*(z))))),inv,pk) == 0; } int nvar_589 = 4; +bool fn590(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(x)+b*(w))))),inv,pk) == 0; } int nvar_590 = 4; +bool fn591(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(x)+b*(u))))),inv,pk) == 0; } int nvar_591 = 5; +bool fn592(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(y)+b*(x))))),inv,pk) == 0; } int nvar_592 = 4; +bool fn593(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(y)+b*(y))))),inv,pk) == 0; } int nvar_593 = 4; +bool fn594(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(y)+b*(z))))),inv,pk) == 0; } int nvar_594 = 4; +bool fn595(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(y)+b*(w))))),inv,pk) == 0; } int nvar_595 = 4; +bool fn596(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(y)+b*(u))))),inv,pk) == 0; } int nvar_596 = 5; +bool fn597(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(z)+b*(x))))),inv,pk) == 0; } int nvar_597 = 4; +bool fn598(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(z)+b*(y))))),inv,pk) == 0; } int nvar_598 = 4; +bool fn599(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(z)+b*(z))))),inv,pk) == 0; } int nvar_599 = 4; +bool fn600(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(z)+b*(w))))),inv,pk) == 0; } int nvar_600 = 4; +bool fn601(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(z)+b*(u))))),inv,pk) == 0; } int nvar_601 = 5; +bool fn602(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(w)+b*(x))))),inv,pk) == 0; } int nvar_602 = 4; +bool fn603(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(w)+b*(y))))),inv,pk) == 0; } int nvar_603 = 4; +bool fn604(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(w)+b*(z))))),inv,pk) == 0; } int nvar_604 = 4; +bool fn605(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(w)+b*(w))))),inv,pk) == 0; } int nvar_605 = 4; +bool fn606(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(w)+b*(u))))),inv,pk) == 0; } int nvar_606 = 5; +bool fn607(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(u)+b*(x))))),inv,pk) == 0; } int nvar_607 = 5; +bool fn608(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(u)+b*(y))))),inv,pk) == 0; } int nvar_608 = 5; +bool fn609(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(u)+b*(z))))),inv,pk) == 0; } int nvar_609 = 5; +bool fn610(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(u)+b*(w))))),inv,pk) == 0; } int nvar_610 = 5; +bool fn611(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(u)+b*(u))))),inv,pk) == 0; } int nvar_611 = 5; +bool fn612(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(a*(u)+b*(v))))),inv,pk) == 0; } int nvar_612 = 6; +bool fn613(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(x)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_613 = 1; +bool fn614(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(x)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_614 = 2; +bool fn615(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(x)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_615 = 2; +bool fn616(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(x)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_616 = 2; +bool fn617(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(x)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_617 = 3; +bool fn618(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_618 = 2; +bool fn619(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_619 = 2; +bool fn620(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_620 = 3; +bool fn621(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_621 = 2; +bool fn622(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_622 = 2; +bool fn623(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_623 = 3; +bool fn624(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_624 = 3; +bool fn625(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_625 = 3; +bool fn626(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_626 = 3; +bool fn627(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_627 = 4; +bool fn628(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_628 = 2; +bool fn629(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_629 = 2; +bool fn630(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_630 = 3; +bool fn631(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_631 = 2; +bool fn632(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_632 = 2; +bool fn633(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_633 = 3; +bool fn634(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_634 = 3; +bool fn635(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_635 = 3; +bool fn636(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_636 = 3; +bool fn637(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_637 = 4; +bool fn638(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_638 = 2; +bool fn639(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_639 = 2; +bool fn640(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_640 = 3; +bool fn641(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_641 = 2; +bool fn642(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_642 = 2; +bool fn643(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_643 = 3; +bool fn644(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_644 = 3; +bool fn645(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_645 = 3; +bool fn646(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_646 = 3; +bool fn647(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_647 = 4; +bool fn648(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_648 = 3; +bool fn649(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_649 = 3; +bool fn650(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_650 = 3; +bool fn651(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_651 = 4; +bool fn652(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_652 = 3; +bool fn653(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_653 = 3; +bool fn654(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_654 = 3; +bool fn655(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_655 = 4; +bool fn656(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_656 = 3; +bool fn657(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_657 = 3; +bool fn658(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_658 = 3; +bool fn659(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_659 = 4; +bool fn660(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_660 = 4; +bool fn661(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_661 = 4; +bool fn662(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_662 = 4; +bool fn663(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_663 = 4; +bool fn664(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_664 = 5; +bool fn665(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_665 = 2; +bool fn666(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_666 = 2; +bool fn667(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_667 = 3; +bool fn668(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_668 = 2; +bool fn669(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_669 = 2; +bool fn670(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_670 = 3; +bool fn671(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_671 = 3; +bool fn672(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_672 = 3; +bool fn673(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_673 = 3; +bool fn674(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(x)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_674 = 4; +bool fn675(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_675 = 2; +bool fn676(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_676 = 2; +bool fn677(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_677 = 3; +bool fn678(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_678 = 2; +bool fn679(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_679 = 2; +bool fn680(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_680 = 3; +bool fn681(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_681 = 3; +bool fn682(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_682 = 3; +bool fn683(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_683 = 3; +bool fn684(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_684 = 4; +bool fn685(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_685 = 3; +bool fn686(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_686 = 3; +bool fn687(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_687 = 3; +bool fn688(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_688 = 4; +bool fn689(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_689 = 3; +bool fn690(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_690 = 3; +bool fn691(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_691 = 3; +bool fn692(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_692 = 4; +bool fn693(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_693 = 3; +bool fn694(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_694 = 3; +bool fn695(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_695 = 3; +bool fn696(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_696 = 4; +bool fn697(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_697 = 4; +bool fn698(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_698 = 4; +bool fn699(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_699 = 4; +bool fn700(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_700 = 4; +bool fn701(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(x)+b*(a*(a*(z)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_701 = 5; +bool fn702(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_702 = 2; +bool fn703(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_703 = 2; +bool fn704(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_704 = 3; +bool fn705(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_705 = 2; +bool fn706(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_706 = 2; +bool fn707(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_707 = 3; +bool fn708(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_708 = 3; +bool fn709(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_709 = 3; +bool fn710(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_710 = 3; +bool fn711(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_711 = 4; +bool fn712(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_712 = 2; +bool fn713(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_713 = 2; +bool fn714(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_714 = 3; +bool fn715(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_715 = 2; +bool fn716(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_716 = 2; +bool fn717(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_717 = 3; +bool fn718(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_718 = 3; +bool fn719(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_719 = 3; +bool fn720(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_720 = 3; +bool fn721(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_721 = 4; +bool fn722(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_722 = 3; +bool fn723(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_723 = 3; +bool fn724(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_724 = 3; +bool fn725(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_725 = 4; +bool fn726(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_726 = 3; +bool fn727(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_727 = 3; +bool fn728(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_728 = 3; +bool fn729(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_729 = 4; +bool fn730(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_730 = 3; +bool fn731(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_731 = 3; +bool fn732(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_732 = 3; +bool fn733(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_733 = 4; +bool fn734(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_734 = 4; +bool fn735(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_735 = 4; +bool fn736(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_736 = 4; +bool fn737(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_737 = 4; +bool fn738(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_738 = 5; +bool fn739(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_739 = 3; +bool fn740(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_740 = 3; +bool fn741(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_741 = 3; +bool fn742(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_742 = 4; +bool fn743(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_743 = 3; +bool fn744(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_744 = 3; +bool fn745(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_745 = 3; +bool fn746(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_746 = 4; +bool fn747(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_747 = 3; +bool fn748(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_748 = 3; +bool fn749(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_749 = 3; +bool fn750(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_750 = 4; +bool fn751(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_751 = 4; +bool fn752(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_752 = 4; +bool fn753(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_753 = 4; +bool fn754(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_754 = 4; +bool fn755(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(x)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_755 = 5; +bool fn756(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_756 = 3; +bool fn757(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_757 = 3; +bool fn758(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_758 = 3; +bool fn759(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_759 = 4; +bool fn760(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_760 = 3; +bool fn761(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_761 = 3; +bool fn762(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_762 = 3; +bool fn763(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_763 = 4; +bool fn764(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_764 = 3; +bool fn765(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_765 = 3; +bool fn766(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_766 = 3; +bool fn767(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_767 = 4; +bool fn768(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_768 = 4; +bool fn769(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_769 = 4; +bool fn770(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_770 = 4; +bool fn771(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_771 = 4; +bool fn772(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(y)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_772 = 5; +bool fn773(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_773 = 3; +bool fn774(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_774 = 3; +bool fn775(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_775 = 3; +bool fn776(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_776 = 4; +bool fn777(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_777 = 3; +bool fn778(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_778 = 3; +bool fn779(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_779 = 3; +bool fn780(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_780 = 4; +bool fn781(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_781 = 3; +bool fn782(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_782 = 3; +bool fn783(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_783 = 3; +bool fn784(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_784 = 4; +bool fn785(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_785 = 4; +bool fn786(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_786 = 4; +bool fn787(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_787 = 4; +bool fn788(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_788 = 4; +bool fn789(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(z)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_789 = 5; +bool fn790(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(x))+b*(x)))),inv,pk) == 0; } int nvar_790 = 4; +bool fn791(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(x))+b*(y)))),inv,pk) == 0; } int nvar_791 = 4; +bool fn792(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(x))+b*(z)))),inv,pk) == 0; } int nvar_792 = 4; +bool fn793(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(x))+b*(w)))),inv,pk) == 0; } int nvar_793 = 4; +bool fn794(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(x))+b*(u)))),inv,pk) == 0; } int nvar_794 = 5; +bool fn795(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(y))+b*(x)))),inv,pk) == 0; } int nvar_795 = 4; +bool fn796(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(y))+b*(y)))),inv,pk) == 0; } int nvar_796 = 4; +bool fn797(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(y))+b*(z)))),inv,pk) == 0; } int nvar_797 = 4; +bool fn798(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(y))+b*(w)))),inv,pk) == 0; } int nvar_798 = 4; +bool fn799(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(y))+b*(u)))),inv,pk) == 0; } int nvar_799 = 5; +bool fn800(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(z))+b*(x)))),inv,pk) == 0; } int nvar_800 = 4; +bool fn801(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(z))+b*(y)))),inv,pk) == 0; } int nvar_801 = 4; +bool fn802(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(z))+b*(z)))),inv,pk) == 0; } int nvar_802 = 4; +bool fn803(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(z))+b*(w)))),inv,pk) == 0; } int nvar_803 = 4; +bool fn804(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(z))+b*(u)))),inv,pk) == 0; } int nvar_804 = 5; +bool fn805(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(w))+b*(x)))),inv,pk) == 0; } int nvar_805 = 4; +bool fn806(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(w))+b*(y)))),inv,pk) == 0; } int nvar_806 = 4; +bool fn807(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(w))+b*(z)))),inv,pk) == 0; } int nvar_807 = 4; +bool fn808(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(w))+b*(w)))),inv,pk) == 0; } int nvar_808 = 4; +bool fn809(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(w))+b*(u)))),inv,pk) == 0; } int nvar_809 = 5; +bool fn810(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(u))+b*(x)))),inv,pk) == 0; } int nvar_810 = 5; +bool fn811(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(u))+b*(y)))),inv,pk) == 0; } int nvar_811 = 5; +bool fn812(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(u))+b*(z)))),inv,pk) == 0; } int nvar_812 = 5; +bool fn813(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(u))+b*(w)))),inv,pk) == 0; } int nvar_813 = 5; +bool fn814(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(u))+b*(u)))),inv,pk) == 0; } int nvar_814 = 5; +bool fn815(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(z)+b*(a*(a*(w)+b*(u))+b*(v)))),inv,pk) == 0; } int nvar_815 = 6; +bool fn816(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_816 = 1; +bool fn817(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_817 = 2; +bool fn818(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_818 = 2; +bool fn819(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_819 = 2; +bool fn820(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_820 = 3; +bool fn821(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_821 = 2; +bool fn822(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_822 = 2; +bool fn823(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_823 = 3; +bool fn824(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_824 = 2; +bool fn825(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_825 = 2; +bool fn826(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_826 = 3; +bool fn827(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_827 = 3; +bool fn828(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_828 = 3; +bool fn829(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_829 = 3; +bool fn830(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_830 = 4; +bool fn831(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_831 = 2; +bool fn832(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_832 = 2; +bool fn833(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_833 = 3; +bool fn834(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_834 = 2; +bool fn835(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_835 = 2; +bool fn836(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_836 = 3; +bool fn837(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_837 = 3; +bool fn838(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_838 = 3; +bool fn839(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_839 = 3; +bool fn840(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_840 = 4; +bool fn841(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_841 = 2; +bool fn842(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_842 = 2; +bool fn843(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_843 = 3; +bool fn844(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_844 = 2; +bool fn845(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_845 = 2; +bool fn846(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_846 = 3; +bool fn847(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_847 = 3; +bool fn848(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_848 = 3; +bool fn849(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_849 = 3; +bool fn850(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_850 = 4; +bool fn851(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_851 = 3; +bool fn852(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_852 = 3; +bool fn853(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_853 = 3; +bool fn854(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_854 = 4; +bool fn855(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_855 = 3; +bool fn856(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_856 = 3; +bool fn857(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_857 = 3; +bool fn858(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_858 = 4; +bool fn859(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_859 = 3; +bool fn860(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_860 = 3; +bool fn861(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_861 = 3; +bool fn862(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_862 = 4; +bool fn863(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_863 = 4; +bool fn864(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_864 = 4; +bool fn865(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_865 = 4; +bool fn866(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_866 = 4; +bool fn867(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_867 = 5; +bool fn868(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_868 = 2; +bool fn869(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_869 = 2; +bool fn870(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_870 = 3; +bool fn871(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_871 = 2; +bool fn872(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_872 = 2; +bool fn873(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_873 = 3; +bool fn874(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_874 = 3; +bool fn875(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_875 = 3; +bool fn876(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_876 = 3; +bool fn877(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_877 = 4; +bool fn878(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_878 = 2; +bool fn879(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_879 = 2; +bool fn880(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_880 = 3; +bool fn881(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_881 = 2; +bool fn882(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_882 = 2; +bool fn883(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_883 = 3; +bool fn884(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_884 = 3; +bool fn885(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_885 = 3; +bool fn886(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_886 = 3; +bool fn887(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_887 = 4; +bool fn888(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_888 = 3; +bool fn889(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_889 = 3; +bool fn890(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_890 = 3; +bool fn891(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_891 = 4; +bool fn892(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_892 = 3; +bool fn893(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_893 = 3; +bool fn894(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_894 = 3; +bool fn895(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_895 = 4; +bool fn896(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_896 = 3; +bool fn897(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_897 = 3; +bool fn898(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_898 = 3; +bool fn899(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_899 = 4; +bool fn900(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_900 = 4; +bool fn901(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_901 = 4; +bool fn902(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_902 = 4; +bool fn903(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_903 = 4; +bool fn904(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_904 = 5; +bool fn905(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_905 = 2; +bool fn906(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_906 = 2; +bool fn907(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_907 = 3; +bool fn908(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_908 = 2; +bool fn909(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_909 = 2; +bool fn910(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_910 = 3; +bool fn911(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_911 = 3; +bool fn912(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_912 = 3; +bool fn913(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_913 = 3; +bool fn914(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_914 = 4; +bool fn915(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_915 = 2; +bool fn916(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_916 = 2; +bool fn917(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_917 = 3; +bool fn918(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_918 = 2; +bool fn919(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_919 = 2; +bool fn920(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_920 = 3; +bool fn921(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_921 = 3; +bool fn922(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_922 = 3; +bool fn923(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_923 = 3; +bool fn924(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_924 = 4; +bool fn925(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_925 = 3; +bool fn926(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_926 = 3; +bool fn927(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_927 = 3; +bool fn928(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_928 = 4; +bool fn929(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_929 = 3; +bool fn930(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_930 = 3; +bool fn931(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_931 = 3; +bool fn932(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_932 = 4; +bool fn933(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_933 = 3; +bool fn934(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_934 = 3; +bool fn935(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_935 = 3; +bool fn936(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_936 = 4; +bool fn937(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_937 = 4; +bool fn938(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_938 = 4; +bool fn939(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_939 = 4; +bool fn940(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_940 = 4; +bool fn941(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_941 = 5; +bool fn942(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_942 = 3; +bool fn943(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_943 = 3; +bool fn944(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_944 = 3; +bool fn945(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_945 = 4; +bool fn946(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_946 = 3; +bool fn947(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_947 = 3; +bool fn948(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_948 = 3; +bool fn949(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_949 = 4; +bool fn950(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_950 = 3; +bool fn951(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_951 = 3; +bool fn952(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_952 = 3; +bool fn953(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_953 = 4; +bool fn954(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_954 = 4; +bool fn955(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_955 = 4; +bool fn956(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_956 = 4; +bool fn957(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_957 = 4; +bool fn958(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_958 = 5; +bool fn959(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_959 = 3; +bool fn960(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_960 = 3; +bool fn961(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_961 = 3; +bool fn962(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_962 = 4; +bool fn963(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_963 = 3; +bool fn964(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_964 = 3; +bool fn965(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_965 = 3; +bool fn966(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_966 = 4; +bool fn967(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_967 = 3; +bool fn968(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_968 = 3; +bool fn969(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_969 = 3; +bool fn970(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_970 = 4; +bool fn971(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_971 = 4; +bool fn972(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_972 = 4; +bool fn973(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_973 = 4; +bool fn974(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_974 = 4; +bool fn975(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_975 = 5; +bool fn976(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_976 = 3; +bool fn977(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_977 = 3; +bool fn978(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_978 = 3; +bool fn979(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_979 = 4; +bool fn980(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_980 = 3; +bool fn981(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_981 = 3; +bool fn982(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_982 = 3; +bool fn983(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_983 = 4; +bool fn984(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_984 = 3; +bool fn985(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_985 = 3; +bool fn986(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_986 = 3; +bool fn987(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_987 = 4; +bool fn988(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_988 = 4; +bool fn989(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_989 = 4; +bool fn990(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_990 = 4; +bool fn991(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_991 = 4; +bool fn992(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_992 = 5; +bool fn993(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_993 = 4; +bool fn994(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_994 = 4; +bool fn995(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_995 = 4; +bool fn996(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_996 = 4; +bool fn997(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(x)+b*(u)))),inv,pk) == 0; } int nvar_997 = 5; +bool fn998(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_998 = 4; +bool fn999(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_999 = 4; +bool fn1000(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1000 = 4; +bool fn1001(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1001 = 4; +bool fn1002(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(y)+b*(u)))),inv,pk) == 0; } int nvar_1002 = 5; +bool fn1003(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1003 = 4; +bool fn1004(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1004 = 4; +bool fn1005(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1005 = 4; +bool fn1006(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1006 = 4; +bool fn1007(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(z)+b*(u)))),inv,pk) == 0; } int nvar_1007 = 5; +bool fn1008(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1008 = 4; +bool fn1009(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1009 = 4; +bool fn1010(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1010 = 4; +bool fn1011(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1011 = 4; +bool fn1012(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1012 = 5; +bool fn1013(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(u)+b*(x)))),inv,pk) == 0; } int nvar_1013 = 5; +bool fn1014(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(u)+b*(y)))),inv,pk) == 0; } int nvar_1014 = 5; +bool fn1015(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(u)+b*(z)))),inv,pk) == 0; } int nvar_1015 = 5; +bool fn1016(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(u)+b*(w)))),inv,pk) == 0; } int nvar_1016 = 5; +bool fn1017(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(u)+b*(u)))),inv,pk) == 0; } int nvar_1017 = 5; +bool fn1018(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(a*(u)+b*(v)))),inv,pk) == 0; } int nvar_1018 = 6; +bool fn1019(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1019 = 1; +bool fn1020(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1020 = 2; +bool fn1021(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1021 = 2; +bool fn1022(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1022 = 2; +bool fn1023(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1023 = 3; +bool fn1024(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1024 = 2; +bool fn1025(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1025 = 2; +bool fn1026(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1026 = 3; +bool fn1027(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1027 = 2; +bool fn1028(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1028 = 2; +bool fn1029(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1029 = 3; +bool fn1030(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1030 = 3; +bool fn1031(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1031 = 3; +bool fn1032(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1032 = 3; +bool fn1033(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1033 = 4; +bool fn1034(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1034 = 2; +bool fn1035(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1035 = 2; +bool fn1036(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1036 = 3; +bool fn1037(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1037 = 2; +bool fn1038(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1038 = 2; +bool fn1039(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1039 = 3; +bool fn1040(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1040 = 3; +bool fn1041(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1041 = 3; +bool fn1042(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1042 = 3; +bool fn1043(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1043 = 4; +bool fn1044(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1044 = 2; +bool fn1045(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1045 = 2; +bool fn1046(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1046 = 3; +bool fn1047(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1047 = 2; +bool fn1048(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1048 = 2; +bool fn1049(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1049 = 3; +bool fn1050(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1050 = 3; +bool fn1051(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1051 = 3; +bool fn1052(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1052 = 3; +bool fn1053(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1053 = 4; +bool fn1054(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1054 = 3; +bool fn1055(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1055 = 3; +bool fn1056(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1056 = 3; +bool fn1057(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1057 = 4; +bool fn1058(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1058 = 3; +bool fn1059(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1059 = 3; +bool fn1060(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1060 = 3; +bool fn1061(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1061 = 4; +bool fn1062(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1062 = 3; +bool fn1063(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1063 = 3; +bool fn1064(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1064 = 3; +bool fn1065(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1065 = 4; +bool fn1066(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1066 = 4; +bool fn1067(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1067 = 4; +bool fn1068(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1068 = 4; +bool fn1069(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1069 = 4; +bool fn1070(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1070 = 5; +bool fn1071(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1071 = 2; +bool fn1072(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1072 = 2; +bool fn1073(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1073 = 3; +bool fn1074(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1074 = 2; +bool fn1075(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1075 = 2; +bool fn1076(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1076 = 3; +bool fn1077(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1077 = 3; +bool fn1078(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1078 = 3; +bool fn1079(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1079 = 3; +bool fn1080(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(x)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1080 = 4; +bool fn1081(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1081 = 2; +bool fn1082(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1082 = 2; +bool fn1083(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1083 = 3; +bool fn1084(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1084 = 2; +bool fn1085(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1085 = 2; +bool fn1086(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1086 = 3; +bool fn1087(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1087 = 3; +bool fn1088(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1088 = 3; +bool fn1089(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1089 = 3; +bool fn1090(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1090 = 4; +bool fn1091(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1091 = 3; +bool fn1092(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1092 = 3; +bool fn1093(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1093 = 3; +bool fn1094(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1094 = 4; +bool fn1095(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1095 = 3; +bool fn1096(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1096 = 3; +bool fn1097(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1097 = 3; +bool fn1098(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1098 = 4; +bool fn1099(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1099 = 3; +bool fn1100(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1100 = 3; +bool fn1101(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1101 = 3; +bool fn1102(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1102 = 4; +bool fn1103(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1103 = 4; +bool fn1104(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1104 = 4; +bool fn1105(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1105 = 4; +bool fn1106(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1106 = 4; +bool fn1107(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(x)+b*(a*(z)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1107 = 5; +bool fn1108(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1108 = 2; +bool fn1109(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1109 = 2; +bool fn1110(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1110 = 3; +bool fn1111(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1111 = 2; +bool fn1112(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1112 = 2; +bool fn1113(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1113 = 3; +bool fn1114(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1114 = 3; +bool fn1115(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1115 = 3; +bool fn1116(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1116 = 3; +bool fn1117(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1117 = 4; +bool fn1118(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1118 = 2; +bool fn1119(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1119 = 2; +bool fn1120(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1120 = 3; +bool fn1121(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1121 = 2; +bool fn1122(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1122 = 2; +bool fn1123(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1123 = 3; +bool fn1124(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1124 = 3; +bool fn1125(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1125 = 3; +bool fn1126(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1126 = 3; +bool fn1127(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1127 = 4; +bool fn1128(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1128 = 3; +bool fn1129(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1129 = 3; +bool fn1130(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1130 = 3; +bool fn1131(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1131 = 4; +bool fn1132(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1132 = 3; +bool fn1133(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1133 = 3; +bool fn1134(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1134 = 3; +bool fn1135(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1135 = 4; +bool fn1136(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1136 = 3; +bool fn1137(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1137 = 3; +bool fn1138(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1138 = 3; +bool fn1139(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1139 = 4; +bool fn1140(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1140 = 4; +bool fn1141(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1141 = 4; +bool fn1142(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1142 = 4; +bool fn1143(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1143 = 4; +bool fn1144(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1144 = 5; +bool fn1145(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1145 = 3; +bool fn1146(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1146 = 3; +bool fn1147(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1147 = 3; +bool fn1148(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1148 = 4; +bool fn1149(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1149 = 3; +bool fn1150(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1150 = 3; +bool fn1151(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1151 = 3; +bool fn1152(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1152 = 4; +bool fn1153(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1153 = 3; +bool fn1154(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1154 = 3; +bool fn1155(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1155 = 3; +bool fn1156(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1156 = 4; +bool fn1157(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1157 = 4; +bool fn1158(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1158 = 4; +bool fn1159(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1159 = 4; +bool fn1160(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1160 = 4; +bool fn1161(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(x)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1161 = 5; +bool fn1162(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1162 = 3; +bool fn1163(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1163 = 3; +bool fn1164(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1164 = 3; +bool fn1165(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1165 = 4; +bool fn1166(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1166 = 3; +bool fn1167(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1167 = 3; +bool fn1168(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1168 = 3; +bool fn1169(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1169 = 4; +bool fn1170(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1170 = 3; +bool fn1171(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1171 = 3; +bool fn1172(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1172 = 3; +bool fn1173(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1173 = 4; +bool fn1174(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1174 = 4; +bool fn1175(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1175 = 4; +bool fn1176(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1176 = 4; +bool fn1177(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1177 = 4; +bool fn1178(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(y)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1178 = 5; +bool fn1179(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1179 = 3; +bool fn1180(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1180 = 3; +bool fn1181(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1181 = 3; +bool fn1182(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1182 = 4; +bool fn1183(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1183 = 3; +bool fn1184(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1184 = 3; +bool fn1185(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1185 = 3; +bool fn1186(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1186 = 4; +bool fn1187(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1187 = 3; +bool fn1188(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1188 = 3; +bool fn1189(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1189 = 3; +bool fn1190(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1190 = 4; +bool fn1191(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1191 = 4; +bool fn1192(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1192 = 4; +bool fn1193(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1193 = 4; +bool fn1194(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1194 = 4; +bool fn1195(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(z)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1195 = 5; +bool fn1196(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(x)))+b*(x))),inv,pk) == 0; } int nvar_1196 = 4; +bool fn1197(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(x)))+b*(y))),inv,pk) == 0; } int nvar_1197 = 4; +bool fn1198(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(x)))+b*(z))),inv,pk) == 0; } int nvar_1198 = 4; +bool fn1199(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(x)))+b*(w))),inv,pk) == 0; } int nvar_1199 = 4; +bool fn1200(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(x)))+b*(u))),inv,pk) == 0; } int nvar_1200 = 5; +bool fn1201(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(y)))+b*(x))),inv,pk) == 0; } int nvar_1201 = 4; +bool fn1202(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(y)))+b*(y))),inv,pk) == 0; } int nvar_1202 = 4; +bool fn1203(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(y)))+b*(z))),inv,pk) == 0; } int nvar_1203 = 4; +bool fn1204(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(y)))+b*(w))),inv,pk) == 0; } int nvar_1204 = 4; +bool fn1205(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(y)))+b*(u))),inv,pk) == 0; } int nvar_1205 = 5; +bool fn1206(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(z)))+b*(x))),inv,pk) == 0; } int nvar_1206 = 4; +bool fn1207(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(z)))+b*(y))),inv,pk) == 0; } int nvar_1207 = 4; +bool fn1208(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(z)))+b*(z))),inv,pk) == 0; } int nvar_1208 = 4; +bool fn1209(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(z)))+b*(w))),inv,pk) == 0; } int nvar_1209 = 4; +bool fn1210(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(z)))+b*(u))),inv,pk) == 0; } int nvar_1210 = 5; +bool fn1211(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(w)))+b*(x))),inv,pk) == 0; } int nvar_1211 = 4; +bool fn1212(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(w)))+b*(y))),inv,pk) == 0; } int nvar_1212 = 4; +bool fn1213(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(w)))+b*(z))),inv,pk) == 0; } int nvar_1213 = 4; +bool fn1214(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(w)))+b*(w))),inv,pk) == 0; } int nvar_1214 = 4; +bool fn1215(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(w)))+b*(u))),inv,pk) == 0; } int nvar_1215 = 5; +bool fn1216(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(u)))+b*(x))),inv,pk) == 0; } int nvar_1216 = 5; +bool fn1217(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(u)))+b*(y))),inv,pk) == 0; } int nvar_1217 = 5; +bool fn1218(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(u)))+b*(z))),inv,pk) == 0; } int nvar_1218 = 5; +bool fn1219(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(u)))+b*(w))),inv,pk) == 0; } int nvar_1219 = 5; +bool fn1220(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(u)))+b*(u))),inv,pk) == 0; } int nvar_1220 = 5; +bool fn1221(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(z)+b*(a*(w)+b*(u)))+b*(v))),inv,pk) == 0; } int nvar_1221 = 6; +bool fn1222(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(x))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1222 = 1; +bool fn1223(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(x))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1223 = 2; +bool fn1224(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(x))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1224 = 2; +bool fn1225(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(x))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1225 = 2; +bool fn1226(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(x))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1226 = 3; +bool fn1227(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1227 = 2; +bool fn1228(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1228 = 2; +bool fn1229(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1229 = 3; +bool fn1230(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1230 = 2; +bool fn1231(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1231 = 2; +bool fn1232(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1232 = 3; +bool fn1233(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1233 = 3; +bool fn1234(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1234 = 3; +bool fn1235(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1235 = 3; +bool fn1236(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1236 = 4; +bool fn1237(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1237 = 2; +bool fn1238(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1238 = 2; +bool fn1239(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1239 = 3; +bool fn1240(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1240 = 2; +bool fn1241(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1241 = 2; +bool fn1242(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1242 = 3; +bool fn1243(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1243 = 3; +bool fn1244(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1244 = 3; +bool fn1245(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1245 = 3; +bool fn1246(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1246 = 4; +bool fn1247(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1247 = 2; +bool fn1248(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1248 = 2; +bool fn1249(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1249 = 3; +bool fn1250(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1250 = 2; +bool fn1251(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1251 = 2; +bool fn1252(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1252 = 3; +bool fn1253(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1253 = 3; +bool fn1254(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1254 = 3; +bool fn1255(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1255 = 3; +bool fn1256(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1256 = 4; +bool fn1257(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1257 = 3; +bool fn1258(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1258 = 3; +bool fn1259(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1259 = 3; +bool fn1260(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1260 = 4; +bool fn1261(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1261 = 3; +bool fn1262(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1262 = 3; +bool fn1263(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1263 = 3; +bool fn1264(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1264 = 4; +bool fn1265(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1265 = 3; +bool fn1266(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1266 = 3; +bool fn1267(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1267 = 3; +bool fn1268(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1268 = 4; +bool fn1269(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1269 = 4; +bool fn1270(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1270 = 4; +bool fn1271(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1271 = 4; +bool fn1272(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1272 = 4; +bool fn1273(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(x)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1273 = 5; +bool fn1274(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1274 = 2; +bool fn1275(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1275 = 2; +bool fn1276(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1276 = 3; +bool fn1277(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1277 = 2; +bool fn1278(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1278 = 2; +bool fn1279(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1279 = 3; +bool fn1280(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1280 = 3; +bool fn1281(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1281 = 3; +bool fn1282(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1282 = 3; +bool fn1283(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(x))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1283 = 4; +bool fn1284(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1284 = 2; +bool fn1285(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1285 = 2; +bool fn1286(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1286 = 3; +bool fn1287(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1287 = 2; +bool fn1288(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1288 = 2; +bool fn1289(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1289 = 3; +bool fn1290(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1290 = 3; +bool fn1291(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1291 = 3; +bool fn1292(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1292 = 3; +bool fn1293(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1293 = 4; +bool fn1294(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1294 = 3; +bool fn1295(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1295 = 3; +bool fn1296(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1296 = 3; +bool fn1297(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1297 = 4; +bool fn1298(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1298 = 3; +bool fn1299(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1299 = 3; +bool fn1300(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1300 = 3; +bool fn1301(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1301 = 4; +bool fn1302(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1302 = 3; +bool fn1303(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1303 = 3; +bool fn1304(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1304 = 3; +bool fn1305(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1305 = 4; +bool fn1306(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1306 = 4; +bool fn1307(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1307 = 4; +bool fn1308(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1308 = 4; +bool fn1309(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1309 = 4; +bool fn1310(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(x)+b*(z))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1310 = 5; +bool fn1311(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1311 = 2; +bool fn1312(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1312 = 2; +bool fn1313(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1313 = 3; +bool fn1314(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1314 = 2; +bool fn1315(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1315 = 2; +bool fn1316(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1316 = 3; +bool fn1317(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1317 = 3; +bool fn1318(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1318 = 3; +bool fn1319(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1319 = 3; +bool fn1320(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1320 = 4; +bool fn1321(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1321 = 2; +bool fn1322(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1322 = 2; +bool fn1323(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1323 = 3; +bool fn1324(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1324 = 2; +bool fn1325(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1325 = 2; +bool fn1326(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1326 = 3; +bool fn1327(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1327 = 3; +bool fn1328(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1328 = 3; +bool fn1329(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1329 = 3; +bool fn1330(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1330 = 4; +bool fn1331(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1331 = 3; +bool fn1332(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1332 = 3; +bool fn1333(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1333 = 3; +bool fn1334(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1334 = 4; +bool fn1335(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1335 = 3; +bool fn1336(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1336 = 3; +bool fn1337(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1337 = 3; +bool fn1338(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1338 = 4; +bool fn1339(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1339 = 3; +bool fn1340(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1340 = 3; +bool fn1341(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1341 = 3; +bool fn1342(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1342 = 4; +bool fn1343(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1343 = 4; +bool fn1344(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1344 = 4; +bool fn1345(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1345 = 4; +bool fn1346(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1346 = 4; +bool fn1347(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1347 = 5; +bool fn1348(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1348 = 3; +bool fn1349(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1349 = 3; +bool fn1350(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1350 = 3; +bool fn1351(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1351 = 4; +bool fn1352(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1352 = 3; +bool fn1353(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1353 = 3; +bool fn1354(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1354 = 3; +bool fn1355(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1355 = 4; +bool fn1356(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1356 = 3; +bool fn1357(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1357 = 3; +bool fn1358(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1358 = 3; +bool fn1359(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1359 = 4; +bool fn1360(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1360 = 4; +bool fn1361(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1361 = 4; +bool fn1362(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1362 = 4; +bool fn1363(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1363 = 4; +bool fn1364(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(x))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1364 = 5; +bool fn1365(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1365 = 3; +bool fn1366(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1366 = 3; +bool fn1367(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1367 = 3; +bool fn1368(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1368 = 4; +bool fn1369(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1369 = 3; +bool fn1370(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1370 = 3; +bool fn1371(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1371 = 3; +bool fn1372(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1372 = 4; +bool fn1373(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1373 = 3; +bool fn1374(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1374 = 3; +bool fn1375(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1375 = 3; +bool fn1376(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1376 = 4; +bool fn1377(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1377 = 4; +bool fn1378(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1378 = 4; +bool fn1379(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1379 = 4; +bool fn1380(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1380 = 4; +bool fn1381(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(y))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1381 = 5; +bool fn1382(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1382 = 3; +bool fn1383(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1383 = 3; +bool fn1384(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1384 = 3; +bool fn1385(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1385 = 4; +bool fn1386(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1386 = 3; +bool fn1387(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1387 = 3; +bool fn1388(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1388 = 3; +bool fn1389(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1389 = 4; +bool fn1390(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1390 = 3; +bool fn1391(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1391 = 3; +bool fn1392(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1392 = 3; +bool fn1393(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1393 = 4; +bool fn1394(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1394 = 4; +bool fn1395(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1395 = 4; +bool fn1396(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1396 = 4; +bool fn1397(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1397 = 4; +bool fn1398(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(z))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1398 = 5; +bool fn1399(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1399 = 4; +bool fn1400(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1400 = 4; +bool fn1401(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1401 = 4; +bool fn1402(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1402 = 4; +bool fn1403(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(x))+b*(u))),inv,pk) == 0; } int nvar_1403 = 5; +bool fn1404(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1404 = 4; +bool fn1405(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1405 = 4; +bool fn1406(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1406 = 4; +bool fn1407(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1407 = 4; +bool fn1408(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(y))+b*(u))),inv,pk) == 0; } int nvar_1408 = 5; +bool fn1409(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1409 = 4; +bool fn1410(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1410 = 4; +bool fn1411(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1411 = 4; +bool fn1412(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1412 = 4; +bool fn1413(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(z))+b*(u))),inv,pk) == 0; } int nvar_1413 = 5; +bool fn1414(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1414 = 4; +bool fn1415(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1415 = 4; +bool fn1416(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1416 = 4; +bool fn1417(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1417 = 4; +bool fn1418(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1418 = 5; +bool fn1419(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(u))+b*(x))),inv,pk) == 0; } int nvar_1419 = 5; +bool fn1420(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(u))+b*(y))),inv,pk) == 0; } int nvar_1420 = 5; +bool fn1421(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(u))+b*(z))),inv,pk) == 0; } int nvar_1421 = 5; +bool fn1422(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(u))+b*(w))),inv,pk) == 0; } int nvar_1422 = 5; +bool fn1423(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(u))+b*(u))),inv,pk) == 0; } int nvar_1423 = 5; +bool fn1424(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(y)+b*(a*(a*(a*(z)+b*(w))+b*(u))+b*(v))),inv,pk) == 0; } int nvar_1424 = 6; +bool fn1425(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1425 = 1; +bool fn1426(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1426 = 2; +bool fn1427(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1427 = 2; +bool fn1428(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1428 = 2; +bool fn1429(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1429 = 3; +bool fn1430(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1430 = 2; +bool fn1431(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1431 = 2; +bool fn1432(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1432 = 3; +bool fn1433(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1433 = 2; +bool fn1434(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1434 = 2; +bool fn1435(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1435 = 3; +bool fn1436(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1436 = 3; +bool fn1437(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1437 = 3; +bool fn1438(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1438 = 3; +bool fn1439(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1439 = 4; +bool fn1440(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1440 = 2; +bool fn1441(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1441 = 2; +bool fn1442(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1442 = 3; +bool fn1443(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1443 = 2; +bool fn1444(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1444 = 2; +bool fn1445(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1445 = 3; +bool fn1446(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1446 = 3; +bool fn1447(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1447 = 3; +bool fn1448(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1448 = 3; +bool fn1449(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1449 = 4; +bool fn1450(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1450 = 2; +bool fn1451(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1451 = 2; +bool fn1452(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1452 = 3; +bool fn1453(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1453 = 2; +bool fn1454(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1454 = 2; +bool fn1455(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1455 = 3; +bool fn1456(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1456 = 3; +bool fn1457(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1457 = 3; +bool fn1458(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1458 = 3; +bool fn1459(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1459 = 4; +bool fn1460(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1460 = 3; +bool fn1461(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1461 = 3; +bool fn1462(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1462 = 3; +bool fn1463(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1463 = 4; +bool fn1464(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1464 = 3; +bool fn1465(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1465 = 3; +bool fn1466(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1466 = 3; +bool fn1467(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1467 = 4; +bool fn1468(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1468 = 3; +bool fn1469(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1469 = 3; +bool fn1470(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1470 = 3; +bool fn1471(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1471 = 4; +bool fn1472(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1472 = 4; +bool fn1473(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1473 = 4; +bool fn1474(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1474 = 4; +bool fn1475(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1475 = 4; +bool fn1476(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1476 = 5; +bool fn1477(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1477 = 2; +bool fn1478(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1478 = 2; +bool fn1479(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1479 = 3; +bool fn1480(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1480 = 2; +bool fn1481(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1481 = 2; +bool fn1482(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1482 = 3; +bool fn1483(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1483 = 3; +bool fn1484(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1484 = 3; +bool fn1485(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1485 = 3; +bool fn1486(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1486 = 4; +bool fn1487(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1487 = 2; +bool fn1488(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1488 = 2; +bool fn1489(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1489 = 3; +bool fn1490(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1490 = 2; +bool fn1491(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1491 = 2; +bool fn1492(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1492 = 3; +bool fn1493(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1493 = 3; +bool fn1494(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1494 = 3; +bool fn1495(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1495 = 3; +bool fn1496(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1496 = 4; +bool fn1497(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1497 = 3; +bool fn1498(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1498 = 3; +bool fn1499(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1499 = 3; +bool fn1500(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1500 = 4; +bool fn1501(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1501 = 3; +bool fn1502(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1502 = 3; +bool fn1503(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1503 = 3; +bool fn1504(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1504 = 4; +bool fn1505(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1505 = 3; +bool fn1506(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1506 = 3; +bool fn1507(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1507 = 3; +bool fn1508(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1508 = 4; +bool fn1509(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1509 = 4; +bool fn1510(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1510 = 4; +bool fn1511(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1511 = 4; +bool fn1512(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1512 = 4; +bool fn1513(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1513 = 5; +bool fn1514(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1514 = 2; +bool fn1515(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1515 = 2; +bool fn1516(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1516 = 3; +bool fn1517(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1517 = 2; +bool fn1518(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1518 = 2; +bool fn1519(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1519 = 3; +bool fn1520(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1520 = 3; +bool fn1521(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1521 = 3; +bool fn1522(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1522 = 3; +bool fn1523(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1523 = 4; +bool fn1524(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1524 = 2; +bool fn1525(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1525 = 2; +bool fn1526(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1526 = 3; +bool fn1527(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1527 = 2; +bool fn1528(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1528 = 2; +bool fn1529(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1529 = 3; +bool fn1530(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1530 = 3; +bool fn1531(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1531 = 3; +bool fn1532(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1532 = 3; +bool fn1533(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1533 = 4; +bool fn1534(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1534 = 3; +bool fn1535(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1535 = 3; +bool fn1536(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1536 = 3; +bool fn1537(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1537 = 4; +bool fn1538(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1538 = 3; +bool fn1539(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1539 = 3; +bool fn1540(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1540 = 3; +bool fn1541(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1541 = 4; +bool fn1542(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1542 = 3; +bool fn1543(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1543 = 3; +bool fn1544(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1544 = 3; +bool fn1545(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1545 = 4; +bool fn1546(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1546 = 4; +bool fn1547(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1547 = 4; +bool fn1548(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1548 = 4; +bool fn1549(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1549 = 4; +bool fn1550(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1550 = 5; +bool fn1551(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1551 = 3; +bool fn1552(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1552 = 3; +bool fn1553(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1553 = 3; +bool fn1554(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1554 = 4; +bool fn1555(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1555 = 3; +bool fn1556(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1556 = 3; +bool fn1557(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1557 = 3; +bool fn1558(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1558 = 4; +bool fn1559(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1559 = 3; +bool fn1560(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1560 = 3; +bool fn1561(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1561 = 3; +bool fn1562(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1562 = 4; +bool fn1563(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1563 = 4; +bool fn1564(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1564 = 4; +bool fn1565(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1565 = 4; +bool fn1566(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1566 = 4; +bool fn1567(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1567 = 5; +bool fn1568(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1568 = 3; +bool fn1569(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1569 = 3; +bool fn1570(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1570 = 3; +bool fn1571(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1571 = 4; +bool fn1572(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1572 = 3; +bool fn1573(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1573 = 3; +bool fn1574(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1574 = 3; +bool fn1575(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1575 = 4; +bool fn1576(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1576 = 3; +bool fn1577(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1577 = 3; +bool fn1578(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1578 = 3; +bool fn1579(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1579 = 4; +bool fn1580(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1580 = 4; +bool fn1581(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1581 = 4; +bool fn1582(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1582 = 4; +bool fn1583(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1583 = 4; +bool fn1584(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1584 = 5; +bool fn1585(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1585 = 3; +bool fn1586(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1586 = 3; +bool fn1587(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1587 = 3; +bool fn1588(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1588 = 4; +bool fn1589(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1589 = 3; +bool fn1590(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1590 = 3; +bool fn1591(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1591 = 3; +bool fn1592(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1592 = 4; +bool fn1593(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1593 = 3; +bool fn1594(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1594 = 3; +bool fn1595(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1595 = 3; +bool fn1596(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1596 = 4; +bool fn1597(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1597 = 4; +bool fn1598(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1598 = 4; +bool fn1599(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1599 = 4; +bool fn1600(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1600 = 4; +bool fn1601(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1601 = 5; +bool fn1602(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_1602 = 4; +bool fn1603(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_1603 = 4; +bool fn1604(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_1604 = 4; +bool fn1605(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_1605 = 4; +bool fn1606(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(x)+b*(u)))),inv,pk) == 0; } int nvar_1606 = 5; +bool fn1607(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_1607 = 4; +bool fn1608(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_1608 = 4; +bool fn1609(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_1609 = 4; +bool fn1610(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_1610 = 4; +bool fn1611(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(y)+b*(u)))),inv,pk) == 0; } int nvar_1611 = 5; +bool fn1612(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_1612 = 4; +bool fn1613(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_1613 = 4; +bool fn1614(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_1614 = 4; +bool fn1615(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_1615 = 4; +bool fn1616(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(z)+b*(u)))),inv,pk) == 0; } int nvar_1616 = 5; +bool fn1617(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_1617 = 4; +bool fn1618(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_1618 = 4; +bool fn1619(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_1619 = 4; +bool fn1620(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_1620 = 4; +bool fn1621(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_1621 = 5; +bool fn1622(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(u)+b*(x)))),inv,pk) == 0; } int nvar_1622 = 5; +bool fn1623(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(u)+b*(y)))),inv,pk) == 0; } int nvar_1623 = 5; +bool fn1624(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(u)+b*(z)))),inv,pk) == 0; } int nvar_1624 = 5; +bool fn1625(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(u)+b*(w)))),inv,pk) == 0; } int nvar_1625 = 5; +bool fn1626(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(u)+b*(u)))),inv,pk) == 0; } int nvar_1626 = 5; +bool fn1627(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(a*(u)+b*(v)))),inv,pk) == 0; } int nvar_1627 = 6; +bool fn1628(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1628 = 1; +bool fn1629(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1629 = 2; +bool fn1630(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1630 = 2; +bool fn1631(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1631 = 2; +bool fn1632(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1632 = 3; +bool fn1633(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1633 = 2; +bool fn1634(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1634 = 2; +bool fn1635(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1635 = 3; +bool fn1636(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1636 = 2; +bool fn1637(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1637 = 2; +bool fn1638(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1638 = 3; +bool fn1639(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1639 = 3; +bool fn1640(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1640 = 3; +bool fn1641(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1641 = 3; +bool fn1642(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(x))+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1642 = 4; +bool fn1643(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1643 = 2; +bool fn1644(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1644 = 2; +bool fn1645(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1645 = 3; +bool fn1646(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1646 = 2; +bool fn1647(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1647 = 2; +bool fn1648(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1648 = 3; +bool fn1649(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1649 = 3; +bool fn1650(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1650 = 3; +bool fn1651(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1651 = 3; +bool fn1652(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1652 = 4; +bool fn1653(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1653 = 2; +bool fn1654(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1654 = 2; +bool fn1655(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1655 = 3; +bool fn1656(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1656 = 2; +bool fn1657(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1657 = 2; +bool fn1658(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1658 = 3; +bool fn1659(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1659 = 3; +bool fn1660(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1660 = 3; +bool fn1661(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1661 = 3; +bool fn1662(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1662 = 4; +bool fn1663(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1663 = 3; +bool fn1664(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1664 = 3; +bool fn1665(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1665 = 3; +bool fn1666(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1666 = 4; +bool fn1667(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1667 = 3; +bool fn1668(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1668 = 3; +bool fn1669(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1669 = 3; +bool fn1670(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1670 = 4; +bool fn1671(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1671 = 3; +bool fn1672(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1672 = 3; +bool fn1673(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1673 = 3; +bool fn1674(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1674 = 4; +bool fn1675(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1675 = 4; +bool fn1676(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1676 = 4; +bool fn1677(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1677 = 4; +bool fn1678(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1678 = 4; +bool fn1679(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(y))+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1679 = 5; +bool fn1680(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1680 = 2; +bool fn1681(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1681 = 2; +bool fn1682(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1682 = 3; +bool fn1683(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1683 = 2; +bool fn1684(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1684 = 2; +bool fn1685(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1685 = 3; +bool fn1686(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1686 = 3; +bool fn1687(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1687 = 3; +bool fn1688(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1688 = 3; +bool fn1689(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1689 = 4; +bool fn1690(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1690 = 2; +bool fn1691(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1691 = 2; +bool fn1692(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1692 = 3; +bool fn1693(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1693 = 2; +bool fn1694(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1694 = 2; +bool fn1695(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1695 = 3; +bool fn1696(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1696 = 3; +bool fn1697(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1697 = 3; +bool fn1698(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1698 = 3; +bool fn1699(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1699 = 4; +bool fn1700(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1700 = 3; +bool fn1701(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1701 = 3; +bool fn1702(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1702 = 3; +bool fn1703(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1703 = 4; +bool fn1704(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1704 = 3; +bool fn1705(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1705 = 3; +bool fn1706(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1706 = 3; +bool fn1707(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1707 = 4; +bool fn1708(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1708 = 3; +bool fn1709(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1709 = 3; +bool fn1710(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1710 = 3; +bool fn1711(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1711 = 4; +bool fn1712(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1712 = 4; +bool fn1713(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1713 = 4; +bool fn1714(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1714 = 4; +bool fn1715(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1715 = 4; +bool fn1716(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(x))+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1716 = 5; +bool fn1717(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1717 = 2; +bool fn1718(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1718 = 2; +bool fn1719(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1719 = 3; +bool fn1720(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1720 = 2; +bool fn1721(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1721 = 2; +bool fn1722(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1722 = 3; +bool fn1723(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1723 = 3; +bool fn1724(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1724 = 3; +bool fn1725(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1725 = 3; +bool fn1726(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1726 = 4; +bool fn1727(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1727 = 2; +bool fn1728(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1728 = 2; +bool fn1729(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1729 = 3; +bool fn1730(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1730 = 2; +bool fn1731(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1731 = 2; +bool fn1732(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1732 = 3; +bool fn1733(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1733 = 3; +bool fn1734(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1734 = 3; +bool fn1735(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1735 = 3; +bool fn1736(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1736 = 4; +bool fn1737(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1737 = 3; +bool fn1738(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1738 = 3; +bool fn1739(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1739 = 3; +bool fn1740(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1740 = 4; +bool fn1741(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1741 = 3; +bool fn1742(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1742 = 3; +bool fn1743(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1743 = 3; +bool fn1744(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1744 = 4; +bool fn1745(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1745 = 3; +bool fn1746(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1746 = 3; +bool fn1747(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1747 = 3; +bool fn1748(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1748 = 4; +bool fn1749(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1749 = 4; +bool fn1750(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1750 = 4; +bool fn1751(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1751 = 4; +bool fn1752(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1752 = 4; +bool fn1753(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(y))+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1753 = 5; +bool fn1754(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1754 = 3; +bool fn1755(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1755 = 3; +bool fn1756(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1756 = 3; +bool fn1757(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1757 = 4; +bool fn1758(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1758 = 3; +bool fn1759(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1759 = 3; +bool fn1760(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1760 = 3; +bool fn1761(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1761 = 4; +bool fn1762(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1762 = 3; +bool fn1763(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1763 = 3; +bool fn1764(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1764 = 3; +bool fn1765(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1765 = 4; +bool fn1766(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1766 = 4; +bool fn1767(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1767 = 4; +bool fn1768(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1768 = 4; +bool fn1769(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1769 = 4; +bool fn1770(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(x)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1770 = 5; +bool fn1771(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1771 = 3; +bool fn1772(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1772 = 3; +bool fn1773(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1773 = 3; +bool fn1774(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1774 = 4; +bool fn1775(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1775 = 3; +bool fn1776(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1776 = 3; +bool fn1777(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1777 = 3; +bool fn1778(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1778 = 4; +bool fn1779(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1779 = 3; +bool fn1780(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1780 = 3; +bool fn1781(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1781 = 3; +bool fn1782(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1782 = 4; +bool fn1783(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1783 = 4; +bool fn1784(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1784 = 4; +bool fn1785(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1785 = 4; +bool fn1786(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1786 = 4; +bool fn1787(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(y)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1787 = 5; +bool fn1788(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1788 = 3; +bool fn1789(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1789 = 3; +bool fn1790(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1790 = 3; +bool fn1791(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1791 = 4; +bool fn1792(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1792 = 3; +bool fn1793(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1793 = 3; +bool fn1794(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1794 = 3; +bool fn1795(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1795 = 4; +bool fn1796(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1796 = 3; +bool fn1797(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1797 = 3; +bool fn1798(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1798 = 3; +bool fn1799(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1799 = 4; +bool fn1800(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1800 = 4; +bool fn1801(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1801 = 4; +bool fn1802(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1802 = 4; +bool fn1803(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1803 = 4; +bool fn1804(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1804 = 5; +bool fn1805(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_1805 = 4; +bool fn1806(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_1806 = 4; +bool fn1807(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_1807 = 4; +bool fn1808(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_1808 = 4; +bool fn1809(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(x))+b*(u))),inv,pk) == 0; } int nvar_1809 = 5; +bool fn1810(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_1810 = 4; +bool fn1811(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_1811 = 4; +bool fn1812(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_1812 = 4; +bool fn1813(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_1813 = 4; +bool fn1814(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(y))+b*(u))),inv,pk) == 0; } int nvar_1814 = 5; +bool fn1815(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_1815 = 4; +bool fn1816(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_1816 = 4; +bool fn1817(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_1817 = 4; +bool fn1818(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_1818 = 4; +bool fn1819(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(z))+b*(u))),inv,pk) == 0; } int nvar_1819 = 5; +bool fn1820(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_1820 = 4; +bool fn1821(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_1821 = 4; +bool fn1822(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_1822 = 4; +bool fn1823(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_1823 = 4; +bool fn1824(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_1824 = 5; +bool fn1825(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(u))+b*(x))),inv,pk) == 0; } int nvar_1825 = 5; +bool fn1826(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(u))+b*(y))),inv,pk) == 0; } int nvar_1826 = 5; +bool fn1827(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(u))+b*(z))),inv,pk) == 0; } int nvar_1827 = 5; +bool fn1828(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(u))+b*(w))),inv,pk) == 0; } int nvar_1828 = 5; +bool fn1829(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(u))+b*(u))),inv,pk) == 0; } int nvar_1829 = 5; +bool fn1830(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(z))+b*(a*(a*(w)+b*(u))+b*(v))),inv,pk) == 0; } int nvar_1830 = 6; +bool fn1831(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1831 = 1; +bool fn1832(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1832 = 2; +bool fn1833(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1833 = 2; +bool fn1834(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1834 = 2; +bool fn1835(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1835 = 3; +bool fn1836(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1836 = 2; +bool fn1837(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1837 = 2; +bool fn1838(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1838 = 3; +bool fn1839(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1839 = 2; +bool fn1840(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1840 = 2; +bool fn1841(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1841 = 3; +bool fn1842(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1842 = 3; +bool fn1843(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1843 = 3; +bool fn1844(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1844 = 3; +bool fn1845(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1845 = 4; +bool fn1846(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1846 = 2; +bool fn1847(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1847 = 2; +bool fn1848(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1848 = 3; +bool fn1849(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1849 = 2; +bool fn1850(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1850 = 2; +bool fn1851(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1851 = 3; +bool fn1852(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1852 = 3; +bool fn1853(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1853 = 3; +bool fn1854(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1854 = 3; +bool fn1855(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1855 = 4; +bool fn1856(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1856 = 2; +bool fn1857(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1857 = 2; +bool fn1858(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1858 = 3; +bool fn1859(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1859 = 2; +bool fn1860(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1860 = 2; +bool fn1861(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1861 = 3; +bool fn1862(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1862 = 3; +bool fn1863(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1863 = 3; +bool fn1864(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1864 = 3; +bool fn1865(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1865 = 4; +bool fn1866(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1866 = 3; +bool fn1867(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1867 = 3; +bool fn1868(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1868 = 3; +bool fn1869(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_1869 = 4; +bool fn1870(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1870 = 3; +bool fn1871(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1871 = 3; +bool fn1872(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1872 = 3; +bool fn1873(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_1873 = 4; +bool fn1874(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1874 = 3; +bool fn1875(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1875 = 3; +bool fn1876(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1876 = 3; +bool fn1877(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1877 = 4; +bool fn1878(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_1878 = 4; +bool fn1879(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_1879 = 4; +bool fn1880(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_1880 = 4; +bool fn1881(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_1881 = 4; +bool fn1882(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_1882 = 5; +bool fn1883(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1883 = 2; +bool fn1884(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1884 = 2; +bool fn1885(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1885 = 3; +bool fn1886(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1886 = 2; +bool fn1887(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1887 = 2; +bool fn1888(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1888 = 3; +bool fn1889(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1889 = 3; +bool fn1890(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1890 = 3; +bool fn1891(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1891 = 3; +bool fn1892(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1892 = 4; +bool fn1893(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1893 = 2; +bool fn1894(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1894 = 2; +bool fn1895(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1895 = 3; +bool fn1896(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1896 = 2; +bool fn1897(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1897 = 2; +bool fn1898(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1898 = 3; +bool fn1899(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1899 = 3; +bool fn1900(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1900 = 3; +bool fn1901(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1901 = 3; +bool fn1902(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1902 = 4; +bool fn1903(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1903 = 3; +bool fn1904(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1904 = 3; +bool fn1905(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1905 = 3; +bool fn1906(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_1906 = 4; +bool fn1907(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1907 = 3; +bool fn1908(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1908 = 3; +bool fn1909(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1909 = 3; +bool fn1910(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_1910 = 4; +bool fn1911(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1911 = 3; +bool fn1912(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1912 = 3; +bool fn1913(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1913 = 3; +bool fn1914(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1914 = 4; +bool fn1915(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_1915 = 4; +bool fn1916(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_1916 = 4; +bool fn1917(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_1917 = 4; +bool fn1918(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_1918 = 4; +bool fn1919(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_1919 = 5; +bool fn1920(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1920 = 2; +bool fn1921(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1921 = 2; +bool fn1922(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1922 = 3; +bool fn1923(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1923 = 2; +bool fn1924(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1924 = 2; +bool fn1925(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1925 = 3; +bool fn1926(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1926 = 3; +bool fn1927(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1927 = 3; +bool fn1928(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1928 = 3; +bool fn1929(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1929 = 4; +bool fn1930(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1930 = 2; +bool fn1931(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1931 = 2; +bool fn1932(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1932 = 3; +bool fn1933(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1933 = 2; +bool fn1934(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1934 = 2; +bool fn1935(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1935 = 3; +bool fn1936(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1936 = 3; +bool fn1937(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1937 = 3; +bool fn1938(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1938 = 3; +bool fn1939(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1939 = 4; +bool fn1940(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1940 = 3; +bool fn1941(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1941 = 3; +bool fn1942(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1942 = 3; +bool fn1943(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_1943 = 4; +bool fn1944(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1944 = 3; +bool fn1945(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1945 = 3; +bool fn1946(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1946 = 3; +bool fn1947(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_1947 = 4; +bool fn1948(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1948 = 3; +bool fn1949(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1949 = 3; +bool fn1950(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1950 = 3; +bool fn1951(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1951 = 4; +bool fn1952(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_1952 = 4; +bool fn1953(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_1953 = 4; +bool fn1954(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_1954 = 4; +bool fn1955(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_1955 = 4; +bool fn1956(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_1956 = 5; +bool fn1957(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1957 = 3; +bool fn1958(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1958 = 3; +bool fn1959(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1959 = 3; +bool fn1960(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_1960 = 4; +bool fn1961(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1961 = 3; +bool fn1962(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1962 = 3; +bool fn1963(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1963 = 3; +bool fn1964(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_1964 = 4; +bool fn1965(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1965 = 3; +bool fn1966(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1966 = 3; +bool fn1967(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1967 = 3; +bool fn1968(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1968 = 4; +bool fn1969(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_1969 = 4; +bool fn1970(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_1970 = 4; +bool fn1971(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_1971 = 4; +bool fn1972(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_1972 = 4; +bool fn1973(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_1973 = 5; +bool fn1974(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1974 = 3; +bool fn1975(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1975 = 3; +bool fn1976(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1976 = 3; +bool fn1977(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_1977 = 4; +bool fn1978(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1978 = 3; +bool fn1979(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1979 = 3; +bool fn1980(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1980 = 3; +bool fn1981(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_1981 = 4; +bool fn1982(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1982 = 3; +bool fn1983(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_1983 = 3; +bool fn1984(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_1984 = 3; +bool fn1985(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_1985 = 4; +bool fn1986(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_1986 = 4; +bool fn1987(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_1987 = 4; +bool fn1988(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_1988 = 4; +bool fn1989(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_1989 = 4; +bool fn1990(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_1990 = 5; +bool fn1991(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_1991 = 3; +bool fn1992(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_1992 = 3; +bool fn1993(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_1993 = 3; +bool fn1994(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_1994 = 4; +bool fn1995(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_1995 = 3; +bool fn1996(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_1996 = 3; +bool fn1997(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_1997 = 3; +bool fn1998(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_1998 = 4; +bool fn1999(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_1999 = 3; +bool fn2000(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2000 = 3; +bool fn2001(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2001 = 3; +bool fn2002(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2002 = 4; +bool fn2003(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2003 = 4; +bool fn2004(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2004 = 4; +bool fn2005(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2005 = 4; +bool fn2006(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2006 = 4; +bool fn2007(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2007 = 5; +bool fn2008(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2008 = 4; +bool fn2009(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2009 = 4; +bool fn2010(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2010 = 4; +bool fn2011(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2011 = 4; +bool fn2012(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(x)+b*(u))),inv,pk) == 0; } int nvar_2012 = 5; +bool fn2013(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2013 = 4; +bool fn2014(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2014 = 4; +bool fn2015(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2015 = 4; +bool fn2016(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2016 = 4; +bool fn2017(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(y)+b*(u))),inv,pk) == 0; } int nvar_2017 = 5; +bool fn2018(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2018 = 4; +bool fn2019(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2019 = 4; +bool fn2020(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2020 = 4; +bool fn2021(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2021 = 4; +bool fn2022(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(z)+b*(u))),inv,pk) == 0; } int nvar_2022 = 5; +bool fn2023(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2023 = 4; +bool fn2024(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2024 = 4; +bool fn2025(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2025 = 4; +bool fn2026(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2026 = 4; +bool fn2027(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2027 = 5; +bool fn2028(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(u)+b*(x))),inv,pk) == 0; } int nvar_2028 = 5; +bool fn2029(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(u)+b*(y))),inv,pk) == 0; } int nvar_2029 = 5; +bool fn2030(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(u)+b*(z))),inv,pk) == 0; } int nvar_2030 = 5; +bool fn2031(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(u)+b*(w))),inv,pk) == 0; } int nvar_2031 = 5; +bool fn2032(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(u)+b*(u))),inv,pk) == 0; } int nvar_2032 = 5; +bool fn2033(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(a*(u)+b*(v))),inv,pk) == 0; } int nvar_2033 = 6; +bool fn2034(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2034 = 1; +bool fn2035(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2035 = 2; +bool fn2036(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2036 = 2; +bool fn2037(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2037 = 2; +bool fn2038(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2038 = 3; +bool fn2039(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2039 = 2; +bool fn2040(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2040 = 2; +bool fn2041(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2041 = 3; +bool fn2042(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2042 = 2; +bool fn2043(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2043 = 2; +bool fn2044(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2044 = 3; +bool fn2045(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2045 = 3; +bool fn2046(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2046 = 3; +bool fn2047(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2047 = 3; +bool fn2048(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2048 = 4; +bool fn2049(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2049 = 2; +bool fn2050(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2050 = 2; +bool fn2051(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2051 = 3; +bool fn2052(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2052 = 2; +bool fn2053(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2053 = 2; +bool fn2054(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2054 = 3; +bool fn2055(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2055 = 3; +bool fn2056(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2056 = 3; +bool fn2057(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2057 = 3; +bool fn2058(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2058 = 4; +bool fn2059(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2059 = 2; +bool fn2060(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2060 = 2; +bool fn2061(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2061 = 3; +bool fn2062(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2062 = 2; +bool fn2063(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2063 = 2; +bool fn2064(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2064 = 3; +bool fn2065(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2065 = 3; +bool fn2066(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2066 = 3; +bool fn2067(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2067 = 3; +bool fn2068(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2068 = 4; +bool fn2069(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2069 = 3; +bool fn2070(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2070 = 3; +bool fn2071(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2071 = 3; +bool fn2072(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2072 = 4; +bool fn2073(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2073 = 3; +bool fn2074(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2074 = 3; +bool fn2075(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2075 = 3; +bool fn2076(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2076 = 4; +bool fn2077(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2077 = 3; +bool fn2078(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2078 = 3; +bool fn2079(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2079 = 3; +bool fn2080(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2080 = 4; +bool fn2081(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2081 = 4; +bool fn2082(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2082 = 4; +bool fn2083(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2083 = 4; +bool fn2084(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2084 = 4; +bool fn2085(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2085 = 5; +bool fn2086(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2086 = 2; +bool fn2087(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2087 = 2; +bool fn2088(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2088 = 3; +bool fn2089(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2089 = 2; +bool fn2090(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2090 = 2; +bool fn2091(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2091 = 3; +bool fn2092(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2092 = 3; +bool fn2093(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2093 = 3; +bool fn2094(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2094 = 3; +bool fn2095(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2095 = 4; +bool fn2096(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2096 = 2; +bool fn2097(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2097 = 2; +bool fn2098(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2098 = 3; +bool fn2099(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2099 = 2; +bool fn2100(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2100 = 2; +bool fn2101(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2101 = 3; +bool fn2102(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2102 = 3; +bool fn2103(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2103 = 3; +bool fn2104(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2104 = 3; +bool fn2105(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2105 = 4; +bool fn2106(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2106 = 3; +bool fn2107(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2107 = 3; +bool fn2108(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2108 = 3; +bool fn2109(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2109 = 4; +bool fn2110(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2110 = 3; +bool fn2111(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2111 = 3; +bool fn2112(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2112 = 3; +bool fn2113(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2113 = 4; +bool fn2114(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2114 = 3; +bool fn2115(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2115 = 3; +bool fn2116(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2116 = 3; +bool fn2117(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2117 = 4; +bool fn2118(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2118 = 4; +bool fn2119(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2119 = 4; +bool fn2120(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2120 = 4; +bool fn2121(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2121 = 4; +bool fn2122(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2122 = 5; +bool fn2123(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2123 = 2; +bool fn2124(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2124 = 2; +bool fn2125(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2125 = 3; +bool fn2126(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2126 = 2; +bool fn2127(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2127 = 2; +bool fn2128(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2128 = 3; +bool fn2129(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2129 = 3; +bool fn2130(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2130 = 3; +bool fn2131(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2131 = 3; +bool fn2132(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2132 = 4; +bool fn2133(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2133 = 2; +bool fn2134(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2134 = 2; +bool fn2135(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2135 = 3; +bool fn2136(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2136 = 2; +bool fn2137(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2137 = 2; +bool fn2138(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2138 = 3; +bool fn2139(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2139 = 3; +bool fn2140(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2140 = 3; +bool fn2141(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2141 = 3; +bool fn2142(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2142 = 4; +bool fn2143(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2143 = 3; +bool fn2144(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2144 = 3; +bool fn2145(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2145 = 3; +bool fn2146(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2146 = 4; +bool fn2147(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2147 = 3; +bool fn2148(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2148 = 3; +bool fn2149(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2149 = 3; +bool fn2150(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2150 = 4; +bool fn2151(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2151 = 3; +bool fn2152(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2152 = 3; +bool fn2153(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2153 = 3; +bool fn2154(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2154 = 4; +bool fn2155(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2155 = 4; +bool fn2156(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2156 = 4; +bool fn2157(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2157 = 4; +bool fn2158(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2158 = 4; +bool fn2159(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2159 = 5; +bool fn2160(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2160 = 3; +bool fn2161(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2161 = 3; +bool fn2162(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2162 = 3; +bool fn2163(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2163 = 4; +bool fn2164(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2164 = 3; +bool fn2165(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2165 = 3; +bool fn2166(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2166 = 3; +bool fn2167(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2167 = 4; +bool fn2168(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2168 = 3; +bool fn2169(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2169 = 3; +bool fn2170(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2170 = 3; +bool fn2171(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2171 = 4; +bool fn2172(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2172 = 4; +bool fn2173(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2173 = 4; +bool fn2174(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2174 = 4; +bool fn2175(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2175 = 4; +bool fn2176(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2176 = 5; +bool fn2177(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2177 = 3; +bool fn2178(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2178 = 3; +bool fn2179(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2179 = 3; +bool fn2180(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2180 = 4; +bool fn2181(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2181 = 3; +bool fn2182(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2182 = 3; +bool fn2183(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2183 = 3; +bool fn2184(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2184 = 4; +bool fn2185(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2185 = 3; +bool fn2186(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2186 = 3; +bool fn2187(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2187 = 3; +bool fn2188(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2188 = 4; +bool fn2189(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2189 = 4; +bool fn2190(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2190 = 4; +bool fn2191(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2191 = 4; +bool fn2192(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2192 = 4; +bool fn2193(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2193 = 5; +bool fn2194(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2194 = 3; +bool fn2195(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2195 = 3; +bool fn2196(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2196 = 3; +bool fn2197(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2197 = 4; +bool fn2198(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2198 = 3; +bool fn2199(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2199 = 3; +bool fn2200(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2200 = 3; +bool fn2201(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2201 = 4; +bool fn2202(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2202 = 3; +bool fn2203(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2203 = 3; +bool fn2204(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2204 = 3; +bool fn2205(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2205 = 4; +bool fn2206(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2206 = 4; +bool fn2207(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2207 = 4; +bool fn2208(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2208 = 4; +bool fn2209(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2209 = 4; +bool fn2210(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2210 = 5; +bool fn2211(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_2211 = 4; +bool fn2212(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_2212 = 4; +bool fn2213(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_2213 = 4; +bool fn2214(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_2214 = 4; +bool fn2215(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(x)+b*(u))),inv,pk) == 0; } int nvar_2215 = 5; +bool fn2216(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_2216 = 4; +bool fn2217(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_2217 = 4; +bool fn2218(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_2218 = 4; +bool fn2219(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_2219 = 4; +bool fn2220(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(y)+b*(u))),inv,pk) == 0; } int nvar_2220 = 5; +bool fn2221(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_2221 = 4; +bool fn2222(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_2222 = 4; +bool fn2223(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_2223 = 4; +bool fn2224(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_2224 = 4; +bool fn2225(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(z)+b*(u))),inv,pk) == 0; } int nvar_2225 = 5; +bool fn2226(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_2226 = 4; +bool fn2227(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_2227 = 4; +bool fn2228(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_2228 = 4; +bool fn2229(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_2229 = 4; +bool fn2230(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_2230 = 5; +bool fn2231(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(u)+b*(x))),inv,pk) == 0; } int nvar_2231 = 5; +bool fn2232(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(u)+b*(y))),inv,pk) == 0; } int nvar_2232 = 5; +bool fn2233(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(u)+b*(z))),inv,pk) == 0; } int nvar_2233 = 5; +bool fn2234(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(u)+b*(w))),inv,pk) == 0; } int nvar_2234 = 5; +bool fn2235(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(u)+b*(u))),inv,pk) == 0; } int nvar_2235 = 5; +bool fn2236(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(a*(u)+b*(v))),inv,pk) == 0; } int nvar_2236 = 6; +bool fn2237(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(x)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2237 = 1; +bool fn2238(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(x)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2238 = 2; +bool fn2239(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(x)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2239 = 2; +bool fn2240(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(x)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2240 = 2; +bool fn2241(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(x)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2241 = 3; +bool fn2242(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2242 = 2; +bool fn2243(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2243 = 2; +bool fn2244(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2244 = 3; +bool fn2245(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2245 = 2; +bool fn2246(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2246 = 2; +bool fn2247(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2247 = 3; +bool fn2248(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2248 = 3; +bool fn2249(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2249 = 3; +bool fn2250(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2250 = 3; +bool fn2251(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2251 = 4; +bool fn2252(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2252 = 2; +bool fn2253(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2253 = 2; +bool fn2254(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2254 = 3; +bool fn2255(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2255 = 2; +bool fn2256(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2256 = 2; +bool fn2257(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2257 = 3; +bool fn2258(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2258 = 3; +bool fn2259(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2259 = 3; +bool fn2260(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2260 = 3; +bool fn2261(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2261 = 4; +bool fn2262(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2262 = 2; +bool fn2263(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2263 = 2; +bool fn2264(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2264 = 3; +bool fn2265(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2265 = 2; +bool fn2266(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2266 = 2; +bool fn2267(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2267 = 3; +bool fn2268(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2268 = 3; +bool fn2269(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2269 = 3; +bool fn2270(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2270 = 3; +bool fn2271(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2271 = 4; +bool fn2272(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2272 = 3; +bool fn2273(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2273 = 3; +bool fn2274(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2274 = 3; +bool fn2275(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2275 = 4; +bool fn2276(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2276 = 3; +bool fn2277(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2277 = 3; +bool fn2278(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2278 = 3; +bool fn2279(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2279 = 4; +bool fn2280(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2280 = 3; +bool fn2281(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2281 = 3; +bool fn2282(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2282 = 3; +bool fn2283(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2283 = 4; +bool fn2284(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2284 = 4; +bool fn2285(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2285 = 4; +bool fn2286(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2286 = 4; +bool fn2287(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2287 = 4; +bool fn2288(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2288 = 5; +bool fn2289(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2289 = 2; +bool fn2290(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2290 = 2; +bool fn2291(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2291 = 3; +bool fn2292(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2292 = 2; +bool fn2293(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2293 = 2; +bool fn2294(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2294 = 3; +bool fn2295(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2295 = 3; +bool fn2296(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2296 = 3; +bool fn2297(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2297 = 3; +bool fn2298(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(x)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2298 = 4; +bool fn2299(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2299 = 2; +bool fn2300(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2300 = 2; +bool fn2301(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2301 = 3; +bool fn2302(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2302 = 2; +bool fn2303(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2303 = 2; +bool fn2304(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2304 = 3; +bool fn2305(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2305 = 3; +bool fn2306(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2306 = 3; +bool fn2307(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2307 = 3; +bool fn2308(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(y)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2308 = 4; +bool fn2309(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2309 = 3; +bool fn2310(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2310 = 3; +bool fn2311(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2311 = 3; +bool fn2312(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2312 = 4; +bool fn2313(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2313 = 3; +bool fn2314(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2314 = 3; +bool fn2315(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2315 = 3; +bool fn2316(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2316 = 4; +bool fn2317(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2317 = 3; +bool fn2318(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2318 = 3; +bool fn2319(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2319 = 3; +bool fn2320(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2320 = 4; +bool fn2321(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2321 = 4; +bool fn2322(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2322 = 4; +bool fn2323(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2323 = 4; +bool fn2324(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2324 = 4; +bool fn2325(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(x)+b*(a*(z)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2325 = 5; +bool fn2326(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2326 = 2; +bool fn2327(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2327 = 2; +bool fn2328(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2328 = 3; +bool fn2329(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2329 = 2; +bool fn2330(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2330 = 2; +bool fn2331(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2331 = 3; +bool fn2332(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2332 = 3; +bool fn2333(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2333 = 3; +bool fn2334(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2334 = 3; +bool fn2335(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(x)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2335 = 4; +bool fn2336(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2336 = 2; +bool fn2337(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2337 = 2; +bool fn2338(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2338 = 3; +bool fn2339(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2339 = 2; +bool fn2340(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2340 = 2; +bool fn2341(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2341 = 3; +bool fn2342(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2342 = 3; +bool fn2343(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2343 = 3; +bool fn2344(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2344 = 3; +bool fn2345(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(y)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2345 = 4; +bool fn2346(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2346 = 3; +bool fn2347(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2347 = 3; +bool fn2348(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2348 = 3; +bool fn2349(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2349 = 4; +bool fn2350(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2350 = 3; +bool fn2351(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2351 = 3; +bool fn2352(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2352 = 3; +bool fn2353(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2353 = 4; +bool fn2354(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2354 = 3; +bool fn2355(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2355 = 3; +bool fn2356(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2356 = 3; +bool fn2357(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2357 = 4; +bool fn2358(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2358 = 4; +bool fn2359(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2359 = 4; +bool fn2360(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2360 = 4; +bool fn2361(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2361 = 4; +bool fn2362(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(y)+b*(a*(z)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2362 = 5; +bool fn2363(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2363 = 3; +bool fn2364(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2364 = 3; +bool fn2365(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2365 = 3; +bool fn2366(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2366 = 4; +bool fn2367(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2367 = 3; +bool fn2368(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2368 = 3; +bool fn2369(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2369 = 3; +bool fn2370(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2370 = 4; +bool fn2371(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2371 = 3; +bool fn2372(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2372 = 3; +bool fn2373(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2373 = 3; +bool fn2374(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2374 = 4; +bool fn2375(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2375 = 4; +bool fn2376(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2376 = 4; +bool fn2377(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2377 = 4; +bool fn2378(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2378 = 4; +bool fn2379(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(x)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2379 = 5; +bool fn2380(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2380 = 3; +bool fn2381(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2381 = 3; +bool fn2382(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2382 = 3; +bool fn2383(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2383 = 4; +bool fn2384(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2384 = 3; +bool fn2385(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2385 = 3; +bool fn2386(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2386 = 3; +bool fn2387(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2387 = 4; +bool fn2388(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2388 = 3; +bool fn2389(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2389 = 3; +bool fn2390(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2390 = 3; +bool fn2391(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2391 = 4; +bool fn2392(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2392 = 4; +bool fn2393(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2393 = 4; +bool fn2394(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2394 = 4; +bool fn2395(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2395 = 4; +bool fn2396(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(y)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2396 = 5; +bool fn2397(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2397 = 3; +bool fn2398(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2398 = 3; +bool fn2399(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2399 = 3; +bool fn2400(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2400 = 4; +bool fn2401(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2401 = 3; +bool fn2402(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2402 = 3; +bool fn2403(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2403 = 3; +bool fn2404(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2404 = 4; +bool fn2405(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2405 = 3; +bool fn2406(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2406 = 3; +bool fn2407(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2407 = 3; +bool fn2408(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2408 = 4; +bool fn2409(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2409 = 4; +bool fn2410(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2410 = 4; +bool fn2411(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2411 = 4; +bool fn2412(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2412 = 4; +bool fn2413(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(z)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2413 = 5; +bool fn2414(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))+b*(x)),inv,pk) == 0; } int nvar_2414 = 4; +bool fn2415(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))+b*(y)),inv,pk) == 0; } int nvar_2415 = 4; +bool fn2416(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))+b*(z)),inv,pk) == 0; } int nvar_2416 = 4; +bool fn2417(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))+b*(w)),inv,pk) == 0; } int nvar_2417 = 4; +bool fn2418(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(x))))+b*(u)),inv,pk) == 0; } int nvar_2418 = 5; +bool fn2419(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))+b*(x)),inv,pk) == 0; } int nvar_2419 = 4; +bool fn2420(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))+b*(y)),inv,pk) == 0; } int nvar_2420 = 4; +bool fn2421(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))+b*(z)),inv,pk) == 0; } int nvar_2421 = 4; +bool fn2422(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))+b*(w)),inv,pk) == 0; } int nvar_2422 = 4; +bool fn2423(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(y))))+b*(u)),inv,pk) == 0; } int nvar_2423 = 5; +bool fn2424(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))+b*(x)),inv,pk) == 0; } int nvar_2424 = 4; +bool fn2425(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))+b*(y)),inv,pk) == 0; } int nvar_2425 = 4; +bool fn2426(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))+b*(z)),inv,pk) == 0; } int nvar_2426 = 4; +bool fn2427(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))+b*(w)),inv,pk) == 0; } int nvar_2427 = 4; +bool fn2428(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(z))))+b*(u)),inv,pk) == 0; } int nvar_2428 = 5; +bool fn2429(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))+b*(x)),inv,pk) == 0; } int nvar_2429 = 4; +bool fn2430(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))+b*(y)),inv,pk) == 0; } int nvar_2430 = 4; +bool fn2431(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))+b*(z)),inv,pk) == 0; } int nvar_2431 = 4; +bool fn2432(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))+b*(w)),inv,pk) == 0; } int nvar_2432 = 4; +bool fn2433(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(w))))+b*(u)),inv,pk) == 0; } int nvar_2433 = 5; +bool fn2434(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))+b*(x)),inv,pk) == 0; } int nvar_2434 = 5; +bool fn2435(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))+b*(y)),inv,pk) == 0; } int nvar_2435 = 5; +bool fn2436(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))+b*(z)),inv,pk) == 0; } int nvar_2436 = 5; +bool fn2437(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))+b*(w)),inv,pk) == 0; } int nvar_2437 = 5; +bool fn2438(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))+b*(u)),inv,pk) == 0; } int nvar_2438 = 5; +bool fn2439(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(z)+b*(a*(w)+b*(u))))+b*(v)),inv,pk) == 0; } int nvar_2439 = 6; +bool fn2440(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(x))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2440 = 1; +bool fn2441(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(x))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2441 = 2; +bool fn2442(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(x))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2442 = 2; +bool fn2443(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(x))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2443 = 2; +bool fn2444(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(x))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2444 = 3; +bool fn2445(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2445 = 2; +bool fn2446(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2446 = 2; +bool fn2447(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2447 = 3; +bool fn2448(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2448 = 2; +bool fn2449(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2449 = 2; +bool fn2450(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2450 = 3; +bool fn2451(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2451 = 3; +bool fn2452(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2452 = 3; +bool fn2453(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2453 = 3; +bool fn2454(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2454 = 4; +bool fn2455(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2455 = 2; +bool fn2456(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2456 = 2; +bool fn2457(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2457 = 3; +bool fn2458(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2458 = 2; +bool fn2459(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2459 = 2; +bool fn2460(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2460 = 3; +bool fn2461(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2461 = 3; +bool fn2462(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2462 = 3; +bool fn2463(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2463 = 3; +bool fn2464(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2464 = 4; +bool fn2465(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2465 = 2; +bool fn2466(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2466 = 2; +bool fn2467(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2467 = 3; +bool fn2468(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2468 = 2; +bool fn2469(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2469 = 2; +bool fn2470(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2470 = 3; +bool fn2471(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2471 = 3; +bool fn2472(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2472 = 3; +bool fn2473(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2473 = 3; +bool fn2474(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2474 = 4; +bool fn2475(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2475 = 3; +bool fn2476(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2476 = 3; +bool fn2477(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2477 = 3; +bool fn2478(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2478 = 4; +bool fn2479(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2479 = 3; +bool fn2480(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2480 = 3; +bool fn2481(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2481 = 3; +bool fn2482(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2482 = 4; +bool fn2483(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2483 = 3; +bool fn2484(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2484 = 3; +bool fn2485(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2485 = 3; +bool fn2486(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2486 = 4; +bool fn2487(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2487 = 4; +bool fn2488(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2488 = 4; +bool fn2489(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2489 = 4; +bool fn2490(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2490 = 4; +bool fn2491(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(x)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2491 = 5; +bool fn2492(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2492 = 2; +bool fn2493(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2493 = 2; +bool fn2494(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2494 = 3; +bool fn2495(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2495 = 2; +bool fn2496(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2496 = 2; +bool fn2497(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2497 = 3; +bool fn2498(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2498 = 3; +bool fn2499(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2499 = 3; +bool fn2500(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2500 = 3; +bool fn2501(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(x))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2501 = 4; +bool fn2502(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2502 = 2; +bool fn2503(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2503 = 2; +bool fn2504(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2504 = 3; +bool fn2505(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2505 = 2; +bool fn2506(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2506 = 2; +bool fn2507(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2507 = 3; +bool fn2508(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2508 = 3; +bool fn2509(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2509 = 3; +bool fn2510(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2510 = 3; +bool fn2511(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(y))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2511 = 4; +bool fn2512(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2512 = 3; +bool fn2513(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2513 = 3; +bool fn2514(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2514 = 3; +bool fn2515(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2515 = 4; +bool fn2516(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2516 = 3; +bool fn2517(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2517 = 3; +bool fn2518(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2518 = 3; +bool fn2519(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2519 = 4; +bool fn2520(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2520 = 3; +bool fn2521(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2521 = 3; +bool fn2522(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2522 = 3; +bool fn2523(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2523 = 4; +bool fn2524(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2524 = 4; +bool fn2525(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2525 = 4; +bool fn2526(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2526 = 4; +bool fn2527(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2527 = 4; +bool fn2528(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(x)+b*(z))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2528 = 5; +bool fn2529(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2529 = 2; +bool fn2530(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2530 = 2; +bool fn2531(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2531 = 3; +bool fn2532(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2532 = 2; +bool fn2533(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2533 = 2; +bool fn2534(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2534 = 3; +bool fn2535(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2535 = 3; +bool fn2536(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2536 = 3; +bool fn2537(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2537 = 3; +bool fn2538(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(x))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2538 = 4; +bool fn2539(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2539 = 2; +bool fn2540(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2540 = 2; +bool fn2541(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2541 = 3; +bool fn2542(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2542 = 2; +bool fn2543(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2543 = 2; +bool fn2544(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2544 = 3; +bool fn2545(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2545 = 3; +bool fn2546(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2546 = 3; +bool fn2547(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2547 = 3; +bool fn2548(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(y))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2548 = 4; +bool fn2549(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2549 = 3; +bool fn2550(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2550 = 3; +bool fn2551(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2551 = 3; +bool fn2552(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2552 = 4; +bool fn2553(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2553 = 3; +bool fn2554(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2554 = 3; +bool fn2555(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2555 = 3; +bool fn2556(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2556 = 4; +bool fn2557(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2557 = 3; +bool fn2558(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2558 = 3; +bool fn2559(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2559 = 3; +bool fn2560(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2560 = 4; +bool fn2561(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2561 = 4; +bool fn2562(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2562 = 4; +bool fn2563(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2563 = 4; +bool fn2564(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2564 = 4; +bool fn2565(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(y)+b*(z))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2565 = 5; +bool fn2566(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2566 = 3; +bool fn2567(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2567 = 3; +bool fn2568(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2568 = 3; +bool fn2569(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2569 = 4; +bool fn2570(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2570 = 3; +bool fn2571(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2571 = 3; +bool fn2572(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2572 = 3; +bool fn2573(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2573 = 4; +bool fn2574(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2574 = 3; +bool fn2575(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2575 = 3; +bool fn2576(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2576 = 3; +bool fn2577(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2577 = 4; +bool fn2578(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2578 = 4; +bool fn2579(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2579 = 4; +bool fn2580(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2580 = 4; +bool fn2581(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2581 = 4; +bool fn2582(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(x))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2582 = 5; +bool fn2583(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2583 = 3; +bool fn2584(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2584 = 3; +bool fn2585(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2585 = 3; +bool fn2586(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2586 = 4; +bool fn2587(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2587 = 3; +bool fn2588(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2588 = 3; +bool fn2589(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2589 = 3; +bool fn2590(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2590 = 4; +bool fn2591(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2591 = 3; +bool fn2592(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2592 = 3; +bool fn2593(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2593 = 3; +bool fn2594(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2594 = 4; +bool fn2595(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2595 = 4; +bool fn2596(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2596 = 4; +bool fn2597(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2597 = 4; +bool fn2598(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2598 = 4; +bool fn2599(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(y))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2599 = 5; +bool fn2600(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2600 = 3; +bool fn2601(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2601 = 3; +bool fn2602(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2602 = 3; +bool fn2603(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2603 = 4; +bool fn2604(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2604 = 3; +bool fn2605(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2605 = 3; +bool fn2606(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2606 = 3; +bool fn2607(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2607 = 4; +bool fn2608(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2608 = 3; +bool fn2609(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2609 = 3; +bool fn2610(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2610 = 3; +bool fn2611(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2611 = 4; +bool fn2612(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2612 = 4; +bool fn2613(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2613 = 4; +bool fn2614(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2614 = 4; +bool fn2615(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2615 = 4; +bool fn2616(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(z))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2616 = 5; +bool fn2617(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2617 = 4; +bool fn2618(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2618 = 4; +bool fn2619(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2619 = 4; +bool fn2620(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2620 = 4; +bool fn2621(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(x)))+b*(u)),inv,pk) == 0; } int nvar_2621 = 5; +bool fn2622(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2622 = 4; +bool fn2623(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2623 = 4; +bool fn2624(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2624 = 4; +bool fn2625(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2625 = 4; +bool fn2626(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(y)))+b*(u)),inv,pk) == 0; } int nvar_2626 = 5; +bool fn2627(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2627 = 4; +bool fn2628(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2628 = 4; +bool fn2629(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2629 = 4; +bool fn2630(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2630 = 4; +bool fn2631(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(z)))+b*(u)),inv,pk) == 0; } int nvar_2631 = 5; +bool fn2632(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2632 = 4; +bool fn2633(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2633 = 4; +bool fn2634(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2634 = 4; +bool fn2635(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2635 = 4; +bool fn2636(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2636 = 5; +bool fn2637(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))+b*(x)),inv,pk) == 0; } int nvar_2637 = 5; +bool fn2638(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))+b*(y)),inv,pk) == 0; } int nvar_2638 = 5; +bool fn2639(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))+b*(z)),inv,pk) == 0; } int nvar_2639 = 5; +bool fn2640(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))+b*(w)),inv,pk) == 0; } int nvar_2640 = 5; +bool fn2641(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))+b*(u)),inv,pk) == 0; } int nvar_2641 = 5; +bool fn2642(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(y)+b*(a*(a*(z)+b*(w))+b*(u)))+b*(v)),inv,pk) == 0; } int nvar_2642 = 6; +bool fn2643(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2643 = 1; +bool fn2644(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2644 = 2; +bool fn2645(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2645 = 2; +bool fn2646(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2646 = 2; +bool fn2647(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2647 = 3; +bool fn2648(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2648 = 2; +bool fn2649(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2649 = 2; +bool fn2650(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2650 = 3; +bool fn2651(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2651 = 2; +bool fn2652(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2652 = 2; +bool fn2653(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2653 = 3; +bool fn2654(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2654 = 3; +bool fn2655(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2655 = 3; +bool fn2656(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2656 = 3; +bool fn2657(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(x))+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2657 = 4; +bool fn2658(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2658 = 2; +bool fn2659(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2659 = 2; +bool fn2660(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2660 = 3; +bool fn2661(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2661 = 2; +bool fn2662(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2662 = 2; +bool fn2663(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2663 = 3; +bool fn2664(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2664 = 3; +bool fn2665(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2665 = 3; +bool fn2666(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2666 = 3; +bool fn2667(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2667 = 4; +bool fn2668(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2668 = 2; +bool fn2669(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2669 = 2; +bool fn2670(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2670 = 3; +bool fn2671(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2671 = 2; +bool fn2672(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2672 = 2; +bool fn2673(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2673 = 3; +bool fn2674(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2674 = 3; +bool fn2675(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2675 = 3; +bool fn2676(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2676 = 3; +bool fn2677(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2677 = 4; +bool fn2678(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2678 = 3; +bool fn2679(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2679 = 3; +bool fn2680(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2680 = 3; +bool fn2681(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2681 = 4; +bool fn2682(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2682 = 3; +bool fn2683(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2683 = 3; +bool fn2684(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2684 = 3; +bool fn2685(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2685 = 4; +bool fn2686(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2686 = 3; +bool fn2687(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2687 = 3; +bool fn2688(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2688 = 3; +bool fn2689(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2689 = 4; +bool fn2690(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2690 = 4; +bool fn2691(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2691 = 4; +bool fn2692(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2692 = 4; +bool fn2693(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2693 = 4; +bool fn2694(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(y))+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2694 = 5; +bool fn2695(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2695 = 2; +bool fn2696(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2696 = 2; +bool fn2697(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2697 = 3; +bool fn2698(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2698 = 2; +bool fn2699(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2699 = 2; +bool fn2700(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2700 = 3; +bool fn2701(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2701 = 3; +bool fn2702(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2702 = 3; +bool fn2703(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2703 = 3; +bool fn2704(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2704 = 4; +bool fn2705(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2705 = 2; +bool fn2706(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2706 = 2; +bool fn2707(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2707 = 3; +bool fn2708(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2708 = 2; +bool fn2709(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2709 = 2; +bool fn2710(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2710 = 3; +bool fn2711(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2711 = 3; +bool fn2712(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2712 = 3; +bool fn2713(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2713 = 3; +bool fn2714(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2714 = 4; +bool fn2715(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2715 = 3; +bool fn2716(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2716 = 3; +bool fn2717(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2717 = 3; +bool fn2718(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2718 = 4; +bool fn2719(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2719 = 3; +bool fn2720(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2720 = 3; +bool fn2721(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2721 = 3; +bool fn2722(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2722 = 4; +bool fn2723(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2723 = 3; +bool fn2724(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2724 = 3; +bool fn2725(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2725 = 3; +bool fn2726(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2726 = 4; +bool fn2727(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2727 = 4; +bool fn2728(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2728 = 4; +bool fn2729(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2729 = 4; +bool fn2730(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2730 = 4; +bool fn2731(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(x))+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2731 = 5; +bool fn2732(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2732 = 2; +bool fn2733(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2733 = 2; +bool fn2734(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2734 = 3; +bool fn2735(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2735 = 2; +bool fn2736(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2736 = 2; +bool fn2737(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2737 = 3; +bool fn2738(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2738 = 3; +bool fn2739(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2739 = 3; +bool fn2740(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2740 = 3; +bool fn2741(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2741 = 4; +bool fn2742(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2742 = 2; +bool fn2743(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2743 = 2; +bool fn2744(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2744 = 3; +bool fn2745(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2745 = 2; +bool fn2746(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2746 = 2; +bool fn2747(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2747 = 3; +bool fn2748(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2748 = 3; +bool fn2749(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2749 = 3; +bool fn2750(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2750 = 3; +bool fn2751(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2751 = 4; +bool fn2752(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2752 = 3; +bool fn2753(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2753 = 3; +bool fn2754(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2754 = 3; +bool fn2755(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2755 = 4; +bool fn2756(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2756 = 3; +bool fn2757(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2757 = 3; +bool fn2758(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2758 = 3; +bool fn2759(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2759 = 4; +bool fn2760(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2760 = 3; +bool fn2761(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2761 = 3; +bool fn2762(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2762 = 3; +bool fn2763(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2763 = 4; +bool fn2764(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2764 = 4; +bool fn2765(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2765 = 4; +bool fn2766(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2766 = 4; +bool fn2767(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2767 = 4; +bool fn2768(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(y))+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2768 = 5; +bool fn2769(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2769 = 3; +bool fn2770(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2770 = 3; +bool fn2771(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2771 = 3; +bool fn2772(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2772 = 4; +bool fn2773(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2773 = 3; +bool fn2774(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2774 = 3; +bool fn2775(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2775 = 3; +bool fn2776(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2776 = 4; +bool fn2777(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2777 = 3; +bool fn2778(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2778 = 3; +bool fn2779(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2779 = 3; +bool fn2780(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2780 = 4; +bool fn2781(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2781 = 4; +bool fn2782(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2782 = 4; +bool fn2783(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2783 = 4; +bool fn2784(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2784 = 4; +bool fn2785(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(x)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2785 = 5; +bool fn2786(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2786 = 3; +bool fn2787(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2787 = 3; +bool fn2788(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2788 = 3; +bool fn2789(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2789 = 4; +bool fn2790(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2790 = 3; +bool fn2791(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2791 = 3; +bool fn2792(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2792 = 3; +bool fn2793(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2793 = 4; +bool fn2794(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2794 = 3; +bool fn2795(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2795 = 3; +bool fn2796(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2796 = 3; +bool fn2797(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2797 = 4; +bool fn2798(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2798 = 4; +bool fn2799(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2799 = 4; +bool fn2800(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2800 = 4; +bool fn2801(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2801 = 4; +bool fn2802(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(y)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2802 = 5; +bool fn2803(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2803 = 3; +bool fn2804(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2804 = 3; +bool fn2805(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2805 = 3; +bool fn2806(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2806 = 4; +bool fn2807(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2807 = 3; +bool fn2808(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2808 = 3; +bool fn2809(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2809 = 3; +bool fn2810(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2810 = 4; +bool fn2811(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2811 = 3; +bool fn2812(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2812 = 3; +bool fn2813(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2813 = 3; +bool fn2814(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2814 = 4; +bool fn2815(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2815 = 4; +bool fn2816(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2816 = 4; +bool fn2817(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2817 = 4; +bool fn2818(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2818 = 4; +bool fn2819(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2819 = 5; +bool fn2820(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_2820 = 4; +bool fn2821(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_2821 = 4; +bool fn2822(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_2822 = 4; +bool fn2823(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_2823 = 4; +bool fn2824(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(x)))+b*(u)),inv,pk) == 0; } int nvar_2824 = 5; +bool fn2825(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_2825 = 4; +bool fn2826(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_2826 = 4; +bool fn2827(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_2827 = 4; +bool fn2828(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_2828 = 4; +bool fn2829(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(y)))+b*(u)),inv,pk) == 0; } int nvar_2829 = 5; +bool fn2830(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_2830 = 4; +bool fn2831(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_2831 = 4; +bool fn2832(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_2832 = 4; +bool fn2833(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_2833 = 4; +bool fn2834(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(z)))+b*(u)),inv,pk) == 0; } int nvar_2834 = 5; +bool fn2835(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_2835 = 4; +bool fn2836(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_2836 = 4; +bool fn2837(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_2837 = 4; +bool fn2838(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_2838 = 4; +bool fn2839(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_2839 = 5; +bool fn2840(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))+b*(x)),inv,pk) == 0; } int nvar_2840 = 5; +bool fn2841(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))+b*(y)),inv,pk) == 0; } int nvar_2841 = 5; +bool fn2842(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))+b*(z)),inv,pk) == 0; } int nvar_2842 = 5; +bool fn2843(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))+b*(w)),inv,pk) == 0; } int nvar_2843 = 5; +bool fn2844(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))+b*(u)),inv,pk) == 0; } int nvar_2844 = 5; +bool fn2845(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(z))+b*(a*(w)+b*(u)))+b*(v)),inv,pk) == 0; } int nvar_2845 = 6; +bool fn2846(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2846 = 1; +bool fn2847(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2847 = 2; +bool fn2848(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2848 = 2; +bool fn2849(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2849 = 2; +bool fn2850(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(x)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2850 = 3; +bool fn2851(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2851 = 2; +bool fn2852(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2852 = 2; +bool fn2853(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2853 = 3; +bool fn2854(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2854 = 2; +bool fn2855(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2855 = 2; +bool fn2856(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2856 = 3; +bool fn2857(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2857 = 3; +bool fn2858(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2858 = 3; +bool fn2859(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2859 = 3; +bool fn2860(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(x)+b*(y)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2860 = 4; +bool fn2861(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2861 = 2; +bool fn2862(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2862 = 2; +bool fn2863(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2863 = 3; +bool fn2864(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2864 = 2; +bool fn2865(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2865 = 2; +bool fn2866(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2866 = 3; +bool fn2867(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2867 = 3; +bool fn2868(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2868 = 3; +bool fn2869(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2869 = 3; +bool fn2870(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(x)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2870 = 4; +bool fn2871(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2871 = 2; +bool fn2872(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2872 = 2; +bool fn2873(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2873 = 3; +bool fn2874(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2874 = 2; +bool fn2875(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2875 = 2; +bool fn2876(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2876 = 3; +bool fn2877(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2877 = 3; +bool fn2878(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2878 = 3; +bool fn2879(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2879 = 3; +bool fn2880(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(y)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2880 = 4; +bool fn2881(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2881 = 3; +bool fn2882(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2882 = 3; +bool fn2883(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2883 = 3; +bool fn2884(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_2884 = 4; +bool fn2885(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2885 = 3; +bool fn2886(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2886 = 3; +bool fn2887(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2887 = 3; +bool fn2888(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_2888 = 4; +bool fn2889(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2889 = 3; +bool fn2890(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2890 = 3; +bool fn2891(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2891 = 3; +bool fn2892(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2892 = 4; +bool fn2893(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_2893 = 4; +bool fn2894(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_2894 = 4; +bool fn2895(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_2895 = 4; +bool fn2896(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_2896 = 4; +bool fn2897(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(x)+b*(a*(y)+b*(z)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_2897 = 5; +bool fn2898(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2898 = 2; +bool fn2899(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2899 = 2; +bool fn2900(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2900 = 3; +bool fn2901(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2901 = 2; +bool fn2902(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2902 = 2; +bool fn2903(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2903 = 3; +bool fn2904(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2904 = 3; +bool fn2905(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2905 = 3; +bool fn2906(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2906 = 3; +bool fn2907(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(x)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2907 = 4; +bool fn2908(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2908 = 2; +bool fn2909(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2909 = 2; +bool fn2910(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2910 = 3; +bool fn2911(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2911 = 2; +bool fn2912(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2912 = 2; +bool fn2913(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2913 = 3; +bool fn2914(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2914 = 3; +bool fn2915(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2915 = 3; +bool fn2916(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2916 = 3; +bool fn2917(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(y)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2917 = 4; +bool fn2918(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2918 = 3; +bool fn2919(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2919 = 3; +bool fn2920(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2920 = 3; +bool fn2921(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_2921 = 4; +bool fn2922(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2922 = 3; +bool fn2923(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2923 = 3; +bool fn2924(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2924 = 3; +bool fn2925(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_2925 = 4; +bool fn2926(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2926 = 3; +bool fn2927(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2927 = 3; +bool fn2928(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2928 = 3; +bool fn2929(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2929 = 4; +bool fn2930(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_2930 = 4; +bool fn2931(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_2931 = 4; +bool fn2932(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_2932 = 4; +bool fn2933(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_2933 = 4; +bool fn2934(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(x)+b*(z)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_2934 = 5; +bool fn2935(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2935 = 2; +bool fn2936(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2936 = 2; +bool fn2937(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2937 = 3; +bool fn2938(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2938 = 2; +bool fn2939(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2939 = 2; +bool fn2940(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2940 = 3; +bool fn2941(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2941 = 3; +bool fn2942(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2942 = 3; +bool fn2943(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2943 = 3; +bool fn2944(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(x)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2944 = 4; +bool fn2945(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2945 = 2; +bool fn2946(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2946 = 2; +bool fn2947(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2947 = 3; +bool fn2948(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2948 = 2; +bool fn2949(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2949 = 2; +bool fn2950(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2950 = 3; +bool fn2951(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2951 = 3; +bool fn2952(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2952 = 3; +bool fn2953(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2953 = 3; +bool fn2954(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(y)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2954 = 4; +bool fn2955(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2955 = 3; +bool fn2956(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2956 = 3; +bool fn2957(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2957 = 3; +bool fn2958(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_2958 = 4; +bool fn2959(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2959 = 3; +bool fn2960(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2960 = 3; +bool fn2961(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2961 = 3; +bool fn2962(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_2962 = 4; +bool fn2963(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2963 = 3; +bool fn2964(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2964 = 3; +bool fn2965(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2965 = 3; +bool fn2966(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2966 = 4; +bool fn2967(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_2967 = 4; +bool fn2968(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_2968 = 4; +bool fn2969(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_2969 = 4; +bool fn2970(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_2970 = 4; +bool fn2971(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(y)+b*(z)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_2971 = 5; +bool fn2972(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2972 = 3; +bool fn2973(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2973 = 3; +bool fn2974(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2974 = 3; +bool fn2975(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_2975 = 4; +bool fn2976(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2976 = 3; +bool fn2977(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2977 = 3; +bool fn2978(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2978 = 3; +bool fn2979(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_2979 = 4; +bool fn2980(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2980 = 3; +bool fn2981(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2981 = 3; +bool fn2982(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2982 = 3; +bool fn2983(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_2983 = 4; +bool fn2984(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_2984 = 4; +bool fn2985(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_2985 = 4; +bool fn2986(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_2986 = 4; +bool fn2987(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_2987 = 4; +bool fn2988(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(x)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_2988 = 5; +bool fn2989(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_2989 = 3; +bool fn2990(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_2990 = 3; +bool fn2991(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_2991 = 3; +bool fn2992(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_2992 = 4; +bool fn2993(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_2993 = 3; +bool fn2994(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_2994 = 3; +bool fn2995(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_2995 = 3; +bool fn2996(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_2996 = 4; +bool fn2997(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_2997 = 3; +bool fn2998(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_2998 = 3; +bool fn2999(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_2999 = 3; +bool fn3000(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3000 = 4; +bool fn3001(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3001 = 4; +bool fn3002(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3002 = 4; +bool fn3003(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3003 = 4; +bool fn3004(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3004 = 4; +bool fn3005(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(y)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3005 = 5; +bool fn3006(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3006 = 3; +bool fn3007(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3007 = 3; +bool fn3008(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3008 = 3; +bool fn3009(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3009 = 4; +bool fn3010(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3010 = 3; +bool fn3011(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3011 = 3; +bool fn3012(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3012 = 3; +bool fn3013(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3013 = 4; +bool fn3014(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3014 = 3; +bool fn3015(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3015 = 3; +bool fn3016(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3016 = 3; +bool fn3017(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3017 = 4; +bool fn3018(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3018 = 4; +bool fn3019(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3019 = 4; +bool fn3020(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3020 = 4; +bool fn3021(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3021 = 4; +bool fn3022(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(z)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3022 = 5; +bool fn3023(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3023 = 4; +bool fn3024(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3024 = 4; +bool fn3025(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3025 = 4; +bool fn3026(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3026 = 4; +bool fn3027(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(x))+b*(u)),inv,pk) == 0; } int nvar_3027 = 5; +bool fn3028(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3028 = 4; +bool fn3029(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3029 = 4; +bool fn3030(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3030 = 4; +bool fn3031(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3031 = 4; +bool fn3032(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(y))+b*(u)),inv,pk) == 0; } int nvar_3032 = 5; +bool fn3033(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3033 = 4; +bool fn3034(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3034 = 4; +bool fn3035(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3035 = 4; +bool fn3036(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3036 = 4; +bool fn3037(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(z))+b*(u)),inv,pk) == 0; } int nvar_3037 = 5; +bool fn3038(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3038 = 4; +bool fn3039(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3039 = 4; +bool fn3040(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3040 = 4; +bool fn3041(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3041 = 4; +bool fn3042(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3042 = 5; +bool fn3043(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))+b*(x)),inv,pk) == 0; } int nvar_3043 = 5; +bool fn3044(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))+b*(y)),inv,pk) == 0; } int nvar_3044 = 5; +bool fn3045(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))+b*(z)),inv,pk) == 0; } int nvar_3045 = 5; +bool fn3046(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))+b*(w)),inv,pk) == 0; } int nvar_3046 = 5; +bool fn3047(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))+b*(u)),inv,pk) == 0; } int nvar_3047 = 5; +bool fn3048(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(y)+b*(a*(z)+b*(w)))+b*(u))+b*(v)),inv,pk) == 0; } int nvar_3048 = 6; +bool fn3049(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3049 = 1; +bool fn3050(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3050 = 2; +bool fn3051(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3051 = 2; +bool fn3052(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3052 = 2; +bool fn3053(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3053 = 3; +bool fn3054(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3054 = 2; +bool fn3055(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3055 = 2; +bool fn3056(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3056 = 3; +bool fn3057(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3057 = 2; +bool fn3058(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3058 = 2; +bool fn3059(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3059 = 3; +bool fn3060(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3060 = 3; +bool fn3061(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3061 = 3; +bool fn3062(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3062 = 3; +bool fn3063(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(x))+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3063 = 4; +bool fn3064(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3064 = 2; +bool fn3065(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3065 = 2; +bool fn3066(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3066 = 3; +bool fn3067(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3067 = 2; +bool fn3068(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3068 = 2; +bool fn3069(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3069 = 3; +bool fn3070(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3070 = 3; +bool fn3071(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3071 = 3; +bool fn3072(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3072 = 3; +bool fn3073(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3073 = 4; +bool fn3074(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3074 = 2; +bool fn3075(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3075 = 2; +bool fn3076(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3076 = 3; +bool fn3077(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3077 = 2; +bool fn3078(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3078 = 2; +bool fn3079(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3079 = 3; +bool fn3080(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3080 = 3; +bool fn3081(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3081 = 3; +bool fn3082(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3082 = 3; +bool fn3083(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3083 = 4; +bool fn3084(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3084 = 3; +bool fn3085(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3085 = 3; +bool fn3086(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3086 = 3; +bool fn3087(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3087 = 4; +bool fn3088(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3088 = 3; +bool fn3089(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3089 = 3; +bool fn3090(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3090 = 3; +bool fn3091(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3091 = 4; +bool fn3092(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3092 = 3; +bool fn3093(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3093 = 3; +bool fn3094(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3094 = 3; +bool fn3095(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3095 = 4; +bool fn3096(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3096 = 4; +bool fn3097(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3097 = 4; +bool fn3098(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3098 = 4; +bool fn3099(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3099 = 4; +bool fn3100(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(x)+b*(y))+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3100 = 5; +bool fn3101(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3101 = 2; +bool fn3102(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3102 = 2; +bool fn3103(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3103 = 3; +bool fn3104(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3104 = 2; +bool fn3105(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3105 = 2; +bool fn3106(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3106 = 3; +bool fn3107(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3107 = 3; +bool fn3108(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3108 = 3; +bool fn3109(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3109 = 3; +bool fn3110(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3110 = 4; +bool fn3111(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3111 = 2; +bool fn3112(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3112 = 2; +bool fn3113(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3113 = 3; +bool fn3114(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3114 = 2; +bool fn3115(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3115 = 2; +bool fn3116(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3116 = 3; +bool fn3117(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3117 = 3; +bool fn3118(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3118 = 3; +bool fn3119(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3119 = 3; +bool fn3120(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3120 = 4; +bool fn3121(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3121 = 3; +bool fn3122(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3122 = 3; +bool fn3123(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3123 = 3; +bool fn3124(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3124 = 4; +bool fn3125(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3125 = 3; +bool fn3126(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3126 = 3; +bool fn3127(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3127 = 3; +bool fn3128(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3128 = 4; +bool fn3129(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3129 = 3; +bool fn3130(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3130 = 3; +bool fn3131(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3131 = 3; +bool fn3132(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3132 = 4; +bool fn3133(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3133 = 4; +bool fn3134(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3134 = 4; +bool fn3135(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3135 = 4; +bool fn3136(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3136 = 4; +bool fn3137(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(x))+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3137 = 5; +bool fn3138(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3138 = 2; +bool fn3139(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3139 = 2; +bool fn3140(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3140 = 3; +bool fn3141(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3141 = 2; +bool fn3142(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3142 = 2; +bool fn3143(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3143 = 3; +bool fn3144(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3144 = 3; +bool fn3145(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3145 = 3; +bool fn3146(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3146 = 3; +bool fn3147(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3147 = 4; +bool fn3148(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3148 = 2; +bool fn3149(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3149 = 2; +bool fn3150(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3150 = 3; +bool fn3151(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3151 = 2; +bool fn3152(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3152 = 2; +bool fn3153(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3153 = 3; +bool fn3154(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3154 = 3; +bool fn3155(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3155 = 3; +bool fn3156(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3156 = 3; +bool fn3157(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3157 = 4; +bool fn3158(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3158 = 3; +bool fn3159(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3159 = 3; +bool fn3160(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3160 = 3; +bool fn3161(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3161 = 4; +bool fn3162(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3162 = 3; +bool fn3163(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3163 = 3; +bool fn3164(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3164 = 3; +bool fn3165(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3165 = 4; +bool fn3166(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3166 = 3; +bool fn3167(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3167 = 3; +bool fn3168(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3168 = 3; +bool fn3169(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3169 = 4; +bool fn3170(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3170 = 4; +bool fn3171(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3171 = 4; +bool fn3172(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3172 = 4; +bool fn3173(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3173 = 4; +bool fn3174(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(y))+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3174 = 5; +bool fn3175(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3175 = 3; +bool fn3176(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3176 = 3; +bool fn3177(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3177 = 3; +bool fn3178(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3178 = 4; +bool fn3179(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3179 = 3; +bool fn3180(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3180 = 3; +bool fn3181(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3181 = 3; +bool fn3182(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3182 = 4; +bool fn3183(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3183 = 3; +bool fn3184(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3184 = 3; +bool fn3185(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3185 = 3; +bool fn3186(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3186 = 4; +bool fn3187(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3187 = 4; +bool fn3188(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3188 = 4; +bool fn3189(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3189 = 4; +bool fn3190(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3190 = 4; +bool fn3191(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(x))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3191 = 5; +bool fn3192(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3192 = 3; +bool fn3193(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3193 = 3; +bool fn3194(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3194 = 3; +bool fn3195(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3195 = 4; +bool fn3196(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3196 = 3; +bool fn3197(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3197 = 3; +bool fn3198(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3198 = 3; +bool fn3199(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3199 = 4; +bool fn3200(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3200 = 3; +bool fn3201(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3201 = 3; +bool fn3202(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3202 = 3; +bool fn3203(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3203 = 4; +bool fn3204(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3204 = 4; +bool fn3205(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3205 = 4; +bool fn3206(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3206 = 4; +bool fn3207(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3207 = 4; +bool fn3208(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(y))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3208 = 5; +bool fn3209(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3209 = 3; +bool fn3210(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3210 = 3; +bool fn3211(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3211 = 3; +bool fn3212(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3212 = 4; +bool fn3213(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3213 = 3; +bool fn3214(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3214 = 3; +bool fn3215(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3215 = 3; +bool fn3216(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3216 = 4; +bool fn3217(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3217 = 3; +bool fn3218(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3218 = 3; +bool fn3219(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3219 = 3; +bool fn3220(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3220 = 4; +bool fn3221(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3221 = 4; +bool fn3222(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3222 = 4; +bool fn3223(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3223 = 4; +bool fn3224(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3224 = 4; +bool fn3225(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3225 = 5; +bool fn3226(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_3226 = 4; +bool fn3227(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_3227 = 4; +bool fn3228(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_3228 = 4; +bool fn3229(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_3229 = 4; +bool fn3230(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(x))+b*(u)),inv,pk) == 0; } int nvar_3230 = 5; +bool fn3231(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_3231 = 4; +bool fn3232(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_3232 = 4; +bool fn3233(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_3233 = 4; +bool fn3234(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_3234 = 4; +bool fn3235(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(y))+b*(u)),inv,pk) == 0; } int nvar_3235 = 5; +bool fn3236(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_3236 = 4; +bool fn3237(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_3237 = 4; +bool fn3238(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_3238 = 4; +bool fn3239(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_3239 = 4; +bool fn3240(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(z))+b*(u)),inv,pk) == 0; } int nvar_3240 = 5; +bool fn3241(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_3241 = 4; +bool fn3242(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_3242 = 4; +bool fn3243(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_3243 = 4; +bool fn3244(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_3244 = 4; +bool fn3245(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_3245 = 5; +bool fn3246(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))+b*(x)),inv,pk) == 0; } int nvar_3246 = 5; +bool fn3247(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))+b*(y)),inv,pk) == 0; } int nvar_3247 = 5; +bool fn3248(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))+b*(z)),inv,pk) == 0; } int nvar_3248 = 5; +bool fn3249(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))+b*(w)),inv,pk) == 0; } int nvar_3249 = 5; +bool fn3250(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))+b*(u)),inv,pk) == 0; } int nvar_3250 = 5; +bool fn3251(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((x) - (a*(a*(a*(a*(y)+b*(z))+b*(w))+b*(u))+b*(v)),inv,pk) == 0; } int nvar_3251 = 6; +bool fn3252(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3252 = 1; +bool fn3253(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3253 = 2; +bool fn3254(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3254 = 2; +bool fn3255(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3255 = 2; +bool fn3256(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3256 = 3; +bool fn3257(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3257 = 2; +bool fn3258(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3258 = 2; +bool fn3259(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3259 = 3; +bool fn3260(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3260 = 2; +bool fn3261(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3261 = 2; +bool fn3262(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3262 = 3; +bool fn3263(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3263 = 3; +bool fn3264(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3264 = 3; +bool fn3265(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3265 = 3; +bool fn3266(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3266 = 4; +bool fn3267(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3267 = 2; +bool fn3268(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3268 = 2; +bool fn3269(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3269 = 3; +bool fn3270(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3270 = 2; +bool fn3271(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3271 = 2; +bool fn3272(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3272 = 3; +bool fn3273(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3273 = 3; +bool fn3274(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3274 = 3; +bool fn3275(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3275 = 3; +bool fn3276(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3276 = 4; +bool fn3277(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3277 = 2; +bool fn3278(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3278 = 2; +bool fn3279(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3279 = 3; +bool fn3280(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3280 = 2; +bool fn3281(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3281 = 2; +bool fn3282(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3282 = 3; +bool fn3283(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3283 = 3; +bool fn3284(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3284 = 3; +bool fn3285(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3285 = 3; +bool fn3286(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3286 = 4; +bool fn3287(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3287 = 3; +bool fn3288(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3288 = 3; +bool fn3289(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3289 = 3; +bool fn3290(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3290 = 4; +bool fn3291(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3291 = 3; +bool fn3292(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3292 = 3; +bool fn3293(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3293 = 3; +bool fn3294(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3294 = 4; +bool fn3295(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3295 = 3; +bool fn3296(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3296 = 3; +bool fn3297(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3297 = 3; +bool fn3298(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3298 = 4; +bool fn3299(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3299 = 4; +bool fn3300(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3300 = 4; +bool fn3301(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3301 = 4; +bool fn3302(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3302 = 4; +bool fn3303(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3303 = 5; +bool fn3304(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3304 = 2; +bool fn3305(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3305 = 2; +bool fn3306(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3306 = 3; +bool fn3307(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3307 = 2; +bool fn3308(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3308 = 2; +bool fn3309(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3309 = 3; +bool fn3310(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3310 = 3; +bool fn3311(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3311 = 3; +bool fn3312(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3312 = 3; +bool fn3313(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3313 = 4; +bool fn3314(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3314 = 2; +bool fn3315(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3315 = 2; +bool fn3316(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3316 = 3; +bool fn3317(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3317 = 2; +bool fn3318(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3318 = 2; +bool fn3319(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3319 = 3; +bool fn3320(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3320 = 3; +bool fn3321(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3321 = 3; +bool fn3322(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3322 = 3; +bool fn3323(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3323 = 4; +bool fn3324(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3324 = 3; +bool fn3325(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3325 = 3; +bool fn3326(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3326 = 3; +bool fn3327(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3327 = 4; +bool fn3328(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3328 = 3; +bool fn3329(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3329 = 3; +bool fn3330(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3330 = 3; +bool fn3331(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3331 = 4; +bool fn3332(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3332 = 3; +bool fn3333(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3333 = 3; +bool fn3334(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3334 = 3; +bool fn3335(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3335 = 4; +bool fn3336(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3336 = 4; +bool fn3337(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3337 = 4; +bool fn3338(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3338 = 4; +bool fn3339(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3339 = 4; +bool fn3340(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3340 = 5; +bool fn3341(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3341 = 2; +bool fn3342(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3342 = 2; +bool fn3343(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3343 = 3; +bool fn3344(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3344 = 2; +bool fn3345(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3345 = 2; +bool fn3346(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3346 = 3; +bool fn3347(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3347 = 3; +bool fn3348(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3348 = 3; +bool fn3349(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3349 = 3; +bool fn3350(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3350 = 4; +bool fn3351(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3351 = 2; +bool fn3352(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3352 = 2; +bool fn3353(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3353 = 3; +bool fn3354(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3354 = 2; +bool fn3355(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3355 = 2; +bool fn3356(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3356 = 3; +bool fn3357(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3357 = 3; +bool fn3358(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3358 = 3; +bool fn3359(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3359 = 3; +bool fn3360(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3360 = 4; +bool fn3361(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3361 = 3; +bool fn3362(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3362 = 3; +bool fn3363(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3363 = 3; +bool fn3364(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3364 = 4; +bool fn3365(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3365 = 3; +bool fn3366(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3366 = 3; +bool fn3367(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3367 = 3; +bool fn3368(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3368 = 4; +bool fn3369(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3369 = 3; +bool fn3370(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3370 = 3; +bool fn3371(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3371 = 3; +bool fn3372(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3372 = 4; +bool fn3373(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3373 = 4; +bool fn3374(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3374 = 4; +bool fn3375(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3375 = 4; +bool fn3376(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3376 = 4; +bool fn3377(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3377 = 5; +bool fn3378(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3378 = 3; +bool fn3379(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3379 = 3; +bool fn3380(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3380 = 3; +bool fn3381(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3381 = 4; +bool fn3382(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3382 = 3; +bool fn3383(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3383 = 3; +bool fn3384(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3384 = 3; +bool fn3385(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3385 = 4; +bool fn3386(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3386 = 3; +bool fn3387(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3387 = 3; +bool fn3388(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3388 = 3; +bool fn3389(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3389 = 4; +bool fn3390(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3390 = 4; +bool fn3391(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3391 = 4; +bool fn3392(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3392 = 4; +bool fn3393(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3393 = 4; +bool fn3394(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(x)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3394 = 5; +bool fn3395(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3395 = 3; +bool fn3396(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3396 = 3; +bool fn3397(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3397 = 3; +bool fn3398(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3398 = 4; +bool fn3399(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3399 = 3; +bool fn3400(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3400 = 3; +bool fn3401(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3401 = 3; +bool fn3402(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3402 = 4; +bool fn3403(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3403 = 3; +bool fn3404(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3404 = 3; +bool fn3405(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3405 = 3; +bool fn3406(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3406 = 4; +bool fn3407(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3407 = 4; +bool fn3408(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3408 = 4; +bool fn3409(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3409 = 4; +bool fn3410(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3410 = 4; +bool fn3411(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(y)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3411 = 5; +bool fn3412(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3412 = 3; +bool fn3413(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3413 = 3; +bool fn3414(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3414 = 3; +bool fn3415(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3415 = 4; +bool fn3416(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3416 = 3; +bool fn3417(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3417 = 3; +bool fn3418(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3418 = 3; +bool fn3419(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3419 = 4; +bool fn3420(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3420 = 3; +bool fn3421(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3421 = 3; +bool fn3422(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3422 = 3; +bool fn3423(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3423 = 4; +bool fn3424(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3424 = 4; +bool fn3425(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3425 = 4; +bool fn3426(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3426 = 4; +bool fn3427(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3427 = 4; +bool fn3428(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(z)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3428 = 5; +bool fn3429(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(x)+b*(x)))),inv,pk) == 0; } int nvar_3429 = 4; +bool fn3430(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(x)+b*(y)))),inv,pk) == 0; } int nvar_3430 = 4; +bool fn3431(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(x)+b*(z)))),inv,pk) == 0; } int nvar_3431 = 4; +bool fn3432(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(x)+b*(w)))),inv,pk) == 0; } int nvar_3432 = 4; +bool fn3433(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(x)+b*(u)))),inv,pk) == 0; } int nvar_3433 = 5; +bool fn3434(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(y)+b*(x)))),inv,pk) == 0; } int nvar_3434 = 4; +bool fn3435(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(y)+b*(y)))),inv,pk) == 0; } int nvar_3435 = 4; +bool fn3436(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(y)+b*(z)))),inv,pk) == 0; } int nvar_3436 = 4; +bool fn3437(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(y)+b*(w)))),inv,pk) == 0; } int nvar_3437 = 4; +bool fn3438(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(y)+b*(u)))),inv,pk) == 0; } int nvar_3438 = 5; +bool fn3439(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(z)+b*(x)))),inv,pk) == 0; } int nvar_3439 = 4; +bool fn3440(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(z)+b*(y)))),inv,pk) == 0; } int nvar_3440 = 4; +bool fn3441(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(z)+b*(z)))),inv,pk) == 0; } int nvar_3441 = 4; +bool fn3442(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(z)+b*(w)))),inv,pk) == 0; } int nvar_3442 = 4; +bool fn3443(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(z)+b*(u)))),inv,pk) == 0; } int nvar_3443 = 5; +bool fn3444(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(w)+b*(x)))),inv,pk) == 0; } int nvar_3444 = 4; +bool fn3445(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(w)+b*(y)))),inv,pk) == 0; } int nvar_3445 = 4; +bool fn3446(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(w)+b*(z)))),inv,pk) == 0; } int nvar_3446 = 4; +bool fn3447(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(w)+b*(w)))),inv,pk) == 0; } int nvar_3447 = 4; +bool fn3448(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(w)+b*(u)))),inv,pk) == 0; } int nvar_3448 = 5; +bool fn3449(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(u)+b*(x)))),inv,pk) == 0; } int nvar_3449 = 5; +bool fn3450(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(u)+b*(y)))),inv,pk) == 0; } int nvar_3450 = 5; +bool fn3451(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(u)+b*(z)))),inv,pk) == 0; } int nvar_3451 = 5; +bool fn3452(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(u)+b*(w)))),inv,pk) == 0; } int nvar_3452 = 5; +bool fn3453(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(u)+b*(u)))),inv,pk) == 0; } int nvar_3453 = 5; +bool fn3454(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(w)+b*(a*(u)+b*(v)))),inv,pk) == 0; } int nvar_3454 = 6; +bool fn3455(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3455 = 1; +bool fn3456(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3456 = 2; +bool fn3457(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3457 = 2; +bool fn3458(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3458 = 2; +bool fn3459(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3459 = 3; +bool fn3460(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3460 = 2; +bool fn3461(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3461 = 2; +bool fn3462(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3462 = 3; +bool fn3463(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3463 = 2; +bool fn3464(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3464 = 2; +bool fn3465(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3465 = 3; +bool fn3466(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3466 = 3; +bool fn3467(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3467 = 3; +bool fn3468(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3468 = 3; +bool fn3469(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3469 = 4; +bool fn3470(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3470 = 2; +bool fn3471(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3471 = 2; +bool fn3472(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3472 = 3; +bool fn3473(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3473 = 2; +bool fn3474(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3474 = 2; +bool fn3475(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3475 = 3; +bool fn3476(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3476 = 3; +bool fn3477(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3477 = 3; +bool fn3478(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3478 = 3; +bool fn3479(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3479 = 4; +bool fn3480(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3480 = 2; +bool fn3481(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3481 = 2; +bool fn3482(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3482 = 3; +bool fn3483(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3483 = 2; +bool fn3484(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3484 = 2; +bool fn3485(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3485 = 3; +bool fn3486(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3486 = 3; +bool fn3487(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3487 = 3; +bool fn3488(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3488 = 3; +bool fn3489(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3489 = 4; +bool fn3490(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3490 = 3; +bool fn3491(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3491 = 3; +bool fn3492(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3492 = 3; +bool fn3493(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3493 = 4; +bool fn3494(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3494 = 3; +bool fn3495(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3495 = 3; +bool fn3496(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3496 = 3; +bool fn3497(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3497 = 4; +bool fn3498(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3498 = 3; +bool fn3499(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3499 = 3; +bool fn3500(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3500 = 3; +bool fn3501(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3501 = 4; +bool fn3502(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3502 = 4; +bool fn3503(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3503 = 4; +bool fn3504(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3504 = 4; +bool fn3505(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3505 = 4; +bool fn3506(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3506 = 5; +bool fn3507(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3507 = 2; +bool fn3508(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3508 = 2; +bool fn3509(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3509 = 3; +bool fn3510(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3510 = 2; +bool fn3511(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3511 = 2; +bool fn3512(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3512 = 3; +bool fn3513(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3513 = 3; +bool fn3514(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3514 = 3; +bool fn3515(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3515 = 3; +bool fn3516(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3516 = 4; +bool fn3517(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3517 = 2; +bool fn3518(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3518 = 2; +bool fn3519(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3519 = 3; +bool fn3520(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3520 = 2; +bool fn3521(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3521 = 2; +bool fn3522(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3522 = 3; +bool fn3523(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3523 = 3; +bool fn3524(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3524 = 3; +bool fn3525(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3525 = 3; +bool fn3526(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3526 = 4; +bool fn3527(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3527 = 3; +bool fn3528(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3528 = 3; +bool fn3529(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3529 = 3; +bool fn3530(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3530 = 4; +bool fn3531(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3531 = 3; +bool fn3532(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3532 = 3; +bool fn3533(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3533 = 3; +bool fn3534(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3534 = 4; +bool fn3535(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3535 = 3; +bool fn3536(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3536 = 3; +bool fn3537(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3537 = 3; +bool fn3538(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3538 = 4; +bool fn3539(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3539 = 4; +bool fn3540(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3540 = 4; +bool fn3541(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3541 = 4; +bool fn3542(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3542 = 4; +bool fn3543(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(x)+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3543 = 5; +bool fn3544(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3544 = 2; +bool fn3545(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3545 = 2; +bool fn3546(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3546 = 3; +bool fn3547(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3547 = 2; +bool fn3548(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3548 = 2; +bool fn3549(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3549 = 3; +bool fn3550(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3550 = 3; +bool fn3551(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3551 = 3; +bool fn3552(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3552 = 3; +bool fn3553(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3553 = 4; +bool fn3554(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3554 = 2; +bool fn3555(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3555 = 2; +bool fn3556(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3556 = 3; +bool fn3557(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3557 = 2; +bool fn3558(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3558 = 2; +bool fn3559(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3559 = 3; +bool fn3560(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3560 = 3; +bool fn3561(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3561 = 3; +bool fn3562(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3562 = 3; +bool fn3563(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3563 = 4; +bool fn3564(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3564 = 3; +bool fn3565(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3565 = 3; +bool fn3566(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3566 = 3; +bool fn3567(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3567 = 4; +bool fn3568(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3568 = 3; +bool fn3569(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3569 = 3; +bool fn3570(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3570 = 3; +bool fn3571(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3571 = 4; +bool fn3572(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3572 = 3; +bool fn3573(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3573 = 3; +bool fn3574(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3574 = 3; +bool fn3575(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3575 = 4; +bool fn3576(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3576 = 4; +bool fn3577(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3577 = 4; +bool fn3578(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3578 = 4; +bool fn3579(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3579 = 4; +bool fn3580(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(y)+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3580 = 5; +bool fn3581(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3581 = 3; +bool fn3582(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3582 = 3; +bool fn3583(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3583 = 3; +bool fn3584(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3584 = 4; +bool fn3585(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3585 = 3; +bool fn3586(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3586 = 3; +bool fn3587(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3587 = 3; +bool fn3588(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3588 = 4; +bool fn3589(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3589 = 3; +bool fn3590(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3590 = 3; +bool fn3591(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3591 = 3; +bool fn3592(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3592 = 4; +bool fn3593(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3593 = 4; +bool fn3594(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3594 = 4; +bool fn3595(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3595 = 4; +bool fn3596(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3596 = 4; +bool fn3597(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(x)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3597 = 5; +bool fn3598(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3598 = 3; +bool fn3599(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3599 = 3; +bool fn3600(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3600 = 3; +bool fn3601(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3601 = 4; +bool fn3602(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3602 = 3; +bool fn3603(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3603 = 3; +bool fn3604(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3604 = 3; +bool fn3605(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3605 = 4; +bool fn3606(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3606 = 3; +bool fn3607(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3607 = 3; +bool fn3608(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3608 = 3; +bool fn3609(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3609 = 4; +bool fn3610(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3610 = 4; +bool fn3611(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3611 = 4; +bool fn3612(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3612 = 4; +bool fn3613(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3613 = 4; +bool fn3614(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(y)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3614 = 5; +bool fn3615(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3615 = 3; +bool fn3616(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3616 = 3; +bool fn3617(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3617 = 3; +bool fn3618(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3618 = 4; +bool fn3619(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3619 = 3; +bool fn3620(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3620 = 3; +bool fn3621(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3621 = 3; +bool fn3622(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3622 = 4; +bool fn3623(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3623 = 3; +bool fn3624(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3624 = 3; +bool fn3625(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3625 = 3; +bool fn3626(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3626 = 4; +bool fn3627(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3627 = 4; +bool fn3628(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3628 = 4; +bool fn3629(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3629 = 4; +bool fn3630(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3630 = 4; +bool fn3631(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(z)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3631 = 5; +bool fn3632(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(x))+b*(x))),inv,pk) == 0; } int nvar_3632 = 4; +bool fn3633(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(x))+b*(y))),inv,pk) == 0; } int nvar_3633 = 4; +bool fn3634(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(x))+b*(z))),inv,pk) == 0; } int nvar_3634 = 4; +bool fn3635(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(x))+b*(w))),inv,pk) == 0; } int nvar_3635 = 4; +bool fn3636(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(x))+b*(u))),inv,pk) == 0; } int nvar_3636 = 5; +bool fn3637(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(y))+b*(x))),inv,pk) == 0; } int nvar_3637 = 4; +bool fn3638(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(y))+b*(y))),inv,pk) == 0; } int nvar_3638 = 4; +bool fn3639(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(y))+b*(z))),inv,pk) == 0; } int nvar_3639 = 4; +bool fn3640(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(y))+b*(w))),inv,pk) == 0; } int nvar_3640 = 4; +bool fn3641(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(y))+b*(u))),inv,pk) == 0; } int nvar_3641 = 5; +bool fn3642(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(z))+b*(x))),inv,pk) == 0; } int nvar_3642 = 4; +bool fn3643(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(z))+b*(y))),inv,pk) == 0; } int nvar_3643 = 4; +bool fn3644(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(z))+b*(z))),inv,pk) == 0; } int nvar_3644 = 4; +bool fn3645(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(z))+b*(w))),inv,pk) == 0; } int nvar_3645 = 4; +bool fn3646(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(z))+b*(u))),inv,pk) == 0; } int nvar_3646 = 5; +bool fn3647(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(w))+b*(x))),inv,pk) == 0; } int nvar_3647 = 4; +bool fn3648(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(w))+b*(y))),inv,pk) == 0; } int nvar_3648 = 4; +bool fn3649(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(w))+b*(z))),inv,pk) == 0; } int nvar_3649 = 4; +bool fn3650(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(w))+b*(w))),inv,pk) == 0; } int nvar_3650 = 4; +bool fn3651(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(w))+b*(u))),inv,pk) == 0; } int nvar_3651 = 5; +bool fn3652(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(u))+b*(x))),inv,pk) == 0; } int nvar_3652 = 5; +bool fn3653(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(u))+b*(y))),inv,pk) == 0; } int nvar_3653 = 5; +bool fn3654(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(u))+b*(z))),inv,pk) == 0; } int nvar_3654 = 5; +bool fn3655(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(u))+b*(w))),inv,pk) == 0; } int nvar_3655 = 5; +bool fn3656(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(u))+b*(u))),inv,pk) == 0; } int nvar_3656 = 5; +bool fn3657(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(z)+b*(a*(a*(w)+b*(u))+b*(v))),inv,pk) == 0; } int nvar_3657 = 6; +bool fn3658(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3658 = 1; +bool fn3659(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3659 = 2; +bool fn3660(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3660 = 2; +bool fn3661(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3661 = 2; +bool fn3662(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3662 = 3; +bool fn3663(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3663 = 2; +bool fn3664(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3664 = 2; +bool fn3665(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3665 = 3; +bool fn3666(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3666 = 2; +bool fn3667(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3667 = 2; +bool fn3668(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3668 = 3; +bool fn3669(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3669 = 3; +bool fn3670(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3670 = 3; +bool fn3671(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3671 = 3; +bool fn3672(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3672 = 4; +bool fn3673(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3673 = 2; +bool fn3674(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3674 = 2; +bool fn3675(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3675 = 3; +bool fn3676(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3676 = 2; +bool fn3677(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3677 = 2; +bool fn3678(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3678 = 3; +bool fn3679(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3679 = 3; +bool fn3680(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3680 = 3; +bool fn3681(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3681 = 3; +bool fn3682(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3682 = 4; +bool fn3683(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3683 = 2; +bool fn3684(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3684 = 2; +bool fn3685(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3685 = 3; +bool fn3686(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3686 = 2; +bool fn3687(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3687 = 2; +bool fn3688(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3688 = 3; +bool fn3689(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3689 = 3; +bool fn3690(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3690 = 3; +bool fn3691(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3691 = 3; +bool fn3692(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3692 = 4; +bool fn3693(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3693 = 3; +bool fn3694(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3694 = 3; +bool fn3695(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3695 = 3; +bool fn3696(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3696 = 4; +bool fn3697(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3697 = 3; +bool fn3698(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3698 = 3; +bool fn3699(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3699 = 3; +bool fn3700(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3700 = 4; +bool fn3701(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3701 = 3; +bool fn3702(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3702 = 3; +bool fn3703(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3703 = 3; +bool fn3704(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3704 = 4; +bool fn3705(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3705 = 4; +bool fn3706(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3706 = 4; +bool fn3707(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3707 = 4; +bool fn3708(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3708 = 4; +bool fn3709(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3709 = 5; +bool fn3710(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3710 = 2; +bool fn3711(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3711 = 2; +bool fn3712(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3712 = 3; +bool fn3713(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3713 = 2; +bool fn3714(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3714 = 2; +bool fn3715(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3715 = 3; +bool fn3716(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3716 = 3; +bool fn3717(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3717 = 3; +bool fn3718(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3718 = 3; +bool fn3719(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3719 = 4; +bool fn3720(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3720 = 2; +bool fn3721(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3721 = 2; +bool fn3722(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3722 = 3; +bool fn3723(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3723 = 2; +bool fn3724(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3724 = 2; +bool fn3725(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3725 = 3; +bool fn3726(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3726 = 3; +bool fn3727(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3727 = 3; +bool fn3728(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3728 = 3; +bool fn3729(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3729 = 4; +bool fn3730(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3730 = 3; +bool fn3731(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3731 = 3; +bool fn3732(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3732 = 3; +bool fn3733(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3733 = 4; +bool fn3734(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3734 = 3; +bool fn3735(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3735 = 3; +bool fn3736(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3736 = 3; +bool fn3737(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3737 = 4; +bool fn3738(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3738 = 3; +bool fn3739(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3739 = 3; +bool fn3740(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3740 = 3; +bool fn3741(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3741 = 4; +bool fn3742(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3742 = 4; +bool fn3743(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3743 = 4; +bool fn3744(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3744 = 4; +bool fn3745(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3745 = 4; +bool fn3746(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3746 = 5; +bool fn3747(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3747 = 2; +bool fn3748(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3748 = 2; +bool fn3749(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3749 = 3; +bool fn3750(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3750 = 2; +bool fn3751(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3751 = 2; +bool fn3752(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3752 = 3; +bool fn3753(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3753 = 3; +bool fn3754(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3754 = 3; +bool fn3755(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3755 = 3; +bool fn3756(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3756 = 4; +bool fn3757(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3757 = 2; +bool fn3758(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3758 = 2; +bool fn3759(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3759 = 3; +bool fn3760(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3760 = 2; +bool fn3761(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3761 = 2; +bool fn3762(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3762 = 3; +bool fn3763(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3763 = 3; +bool fn3764(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3764 = 3; +bool fn3765(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3765 = 3; +bool fn3766(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3766 = 4; +bool fn3767(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3767 = 3; +bool fn3768(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3768 = 3; +bool fn3769(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3769 = 3; +bool fn3770(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3770 = 4; +bool fn3771(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3771 = 3; +bool fn3772(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3772 = 3; +bool fn3773(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3773 = 3; +bool fn3774(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3774 = 4; +bool fn3775(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3775 = 3; +bool fn3776(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3776 = 3; +bool fn3777(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3777 = 3; +bool fn3778(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3778 = 4; +bool fn3779(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3779 = 4; +bool fn3780(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3780 = 4; +bool fn3781(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3781 = 4; +bool fn3782(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3782 = 4; +bool fn3783(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3783 = 5; +bool fn3784(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3784 = 3; +bool fn3785(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3785 = 3; +bool fn3786(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3786 = 3; +bool fn3787(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3787 = 4; +bool fn3788(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3788 = 3; +bool fn3789(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3789 = 3; +bool fn3790(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3790 = 3; +bool fn3791(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3791 = 4; +bool fn3792(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3792 = 3; +bool fn3793(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3793 = 3; +bool fn3794(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3794 = 3; +bool fn3795(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3795 = 4; +bool fn3796(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3796 = 4; +bool fn3797(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3797 = 4; +bool fn3798(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3798 = 4; +bool fn3799(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3799 = 4; +bool fn3800(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(x))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3800 = 5; +bool fn3801(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3801 = 3; +bool fn3802(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3802 = 3; +bool fn3803(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3803 = 3; +bool fn3804(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3804 = 4; +bool fn3805(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3805 = 3; +bool fn3806(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3806 = 3; +bool fn3807(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3807 = 3; +bool fn3808(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3808 = 4; +bool fn3809(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3809 = 3; +bool fn3810(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3810 = 3; +bool fn3811(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3811 = 3; +bool fn3812(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3812 = 4; +bool fn3813(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3813 = 4; +bool fn3814(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3814 = 4; +bool fn3815(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3815 = 4; +bool fn3816(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3816 = 4; +bool fn3817(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(y))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3817 = 5; +bool fn3818(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3818 = 3; +bool fn3819(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3819 = 3; +bool fn3820(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3820 = 3; +bool fn3821(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3821 = 4; +bool fn3822(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3822 = 3; +bool fn3823(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3823 = 3; +bool fn3824(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3824 = 3; +bool fn3825(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3825 = 4; +bool fn3826(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3826 = 3; +bool fn3827(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3827 = 3; +bool fn3828(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3828 = 3; +bool fn3829(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3829 = 4; +bool fn3830(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3830 = 4; +bool fn3831(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3831 = 4; +bool fn3832(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3832 = 4; +bool fn3833(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3833 = 4; +bool fn3834(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(z))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3834 = 5; +bool fn3835(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_3835 = 4; +bool fn3836(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_3836 = 4; +bool fn3837(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_3837 = 4; +bool fn3838(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_3838 = 4; +bool fn3839(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(x)+b*(u))),inv,pk) == 0; } int nvar_3839 = 5; +bool fn3840(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_3840 = 4; +bool fn3841(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_3841 = 4; +bool fn3842(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_3842 = 4; +bool fn3843(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_3843 = 4; +bool fn3844(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(y)+b*(u))),inv,pk) == 0; } int nvar_3844 = 5; +bool fn3845(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_3845 = 4; +bool fn3846(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_3846 = 4; +bool fn3847(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_3847 = 4; +bool fn3848(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_3848 = 4; +bool fn3849(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(z)+b*(u))),inv,pk) == 0; } int nvar_3849 = 5; +bool fn3850(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_3850 = 4; +bool fn3851(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_3851 = 4; +bool fn3852(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_3852 = 4; +bool fn3853(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_3853 = 4; +bool fn3854(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_3854 = 5; +bool fn3855(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(u)+b*(x))),inv,pk) == 0; } int nvar_3855 = 5; +bool fn3856(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(u)+b*(y))),inv,pk) == 0; } int nvar_3856 = 5; +bool fn3857(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(u)+b*(z))),inv,pk) == 0; } int nvar_3857 = 5; +bool fn3858(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(u)+b*(w))),inv,pk) == 0; } int nvar_3858 = 5; +bool fn3859(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(u)+b*(u))),inv,pk) == 0; } int nvar_3859 = 5; +bool fn3860(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(w))+b*(a*(u)+b*(v))),inv,pk) == 0; } int nvar_3860 = 6; +bool fn3861(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3861 = 1; +bool fn3862(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3862 = 2; +bool fn3863(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3863 = 2; +bool fn3864(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3864 = 2; +bool fn3865(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3865 = 3; +bool fn3866(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3866 = 2; +bool fn3867(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3867 = 2; +bool fn3868(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3868 = 3; +bool fn3869(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3869 = 2; +bool fn3870(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3870 = 2; +bool fn3871(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3871 = 3; +bool fn3872(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3872 = 3; +bool fn3873(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3873 = 3; +bool fn3874(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3874 = 3; +bool fn3875(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3875 = 4; +bool fn3876(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3876 = 2; +bool fn3877(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3877 = 2; +bool fn3878(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3878 = 3; +bool fn3879(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3879 = 2; +bool fn3880(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3880 = 2; +bool fn3881(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3881 = 3; +bool fn3882(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3882 = 3; +bool fn3883(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3883 = 3; +bool fn3884(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3884 = 3; +bool fn3885(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3885 = 4; +bool fn3886(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3886 = 2; +bool fn3887(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3887 = 2; +bool fn3888(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3888 = 3; +bool fn3889(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3889 = 2; +bool fn3890(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3890 = 2; +bool fn3891(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3891 = 3; +bool fn3892(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3892 = 3; +bool fn3893(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3893 = 3; +bool fn3894(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3894 = 3; +bool fn3895(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3895 = 4; +bool fn3896(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3896 = 3; +bool fn3897(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3897 = 3; +bool fn3898(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3898 = 3; +bool fn3899(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_3899 = 4; +bool fn3900(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3900 = 3; +bool fn3901(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3901 = 3; +bool fn3902(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3902 = 3; +bool fn3903(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_3903 = 4; +bool fn3904(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3904 = 3; +bool fn3905(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3905 = 3; +bool fn3906(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3906 = 3; +bool fn3907(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3907 = 4; +bool fn3908(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_3908 = 4; +bool fn3909(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_3909 = 4; +bool fn3910(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_3910 = 4; +bool fn3911(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_3911 = 4; +bool fn3912(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_3912 = 5; +bool fn3913(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3913 = 2; +bool fn3914(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3914 = 2; +bool fn3915(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3915 = 3; +bool fn3916(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3916 = 2; +bool fn3917(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3917 = 2; +bool fn3918(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3918 = 3; +bool fn3919(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3919 = 3; +bool fn3920(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3920 = 3; +bool fn3921(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3921 = 3; +bool fn3922(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3922 = 4; +bool fn3923(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3923 = 2; +bool fn3924(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3924 = 2; +bool fn3925(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3925 = 3; +bool fn3926(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3926 = 2; +bool fn3927(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3927 = 2; +bool fn3928(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3928 = 3; +bool fn3929(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3929 = 3; +bool fn3930(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3930 = 3; +bool fn3931(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3931 = 3; +bool fn3932(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3932 = 4; +bool fn3933(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3933 = 3; +bool fn3934(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3934 = 3; +bool fn3935(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3935 = 3; +bool fn3936(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_3936 = 4; +bool fn3937(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3937 = 3; +bool fn3938(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3938 = 3; +bool fn3939(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3939 = 3; +bool fn3940(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_3940 = 4; +bool fn3941(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3941 = 3; +bool fn3942(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3942 = 3; +bool fn3943(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3943 = 3; +bool fn3944(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3944 = 4; +bool fn3945(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_3945 = 4; +bool fn3946(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_3946 = 4; +bool fn3947(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_3947 = 4; +bool fn3948(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_3948 = 4; +bool fn3949(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(x)+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_3949 = 5; +bool fn3950(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3950 = 2; +bool fn3951(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3951 = 2; +bool fn3952(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3952 = 3; +bool fn3953(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3953 = 2; +bool fn3954(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3954 = 2; +bool fn3955(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3955 = 3; +bool fn3956(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3956 = 3; +bool fn3957(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3957 = 3; +bool fn3958(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3958 = 3; +bool fn3959(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3959 = 4; +bool fn3960(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3960 = 2; +bool fn3961(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3961 = 2; +bool fn3962(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3962 = 3; +bool fn3963(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3963 = 2; +bool fn3964(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3964 = 2; +bool fn3965(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3965 = 3; +bool fn3966(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3966 = 3; +bool fn3967(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3967 = 3; +bool fn3968(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3968 = 3; +bool fn3969(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3969 = 4; +bool fn3970(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3970 = 3; +bool fn3971(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3971 = 3; +bool fn3972(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3972 = 3; +bool fn3973(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_3973 = 4; +bool fn3974(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3974 = 3; +bool fn3975(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3975 = 3; +bool fn3976(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3976 = 3; +bool fn3977(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_3977 = 4; +bool fn3978(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3978 = 3; +bool fn3979(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3979 = 3; +bool fn3980(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3980 = 3; +bool fn3981(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3981 = 4; +bool fn3982(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_3982 = 4; +bool fn3983(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_3983 = 4; +bool fn3984(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_3984 = 4; +bool fn3985(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_3985 = 4; +bool fn3986(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(y)+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_3986 = 5; +bool fn3987(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_3987 = 3; +bool fn3988(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_3988 = 3; +bool fn3989(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_3989 = 3; +bool fn3990(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_3990 = 4; +bool fn3991(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_3991 = 3; +bool fn3992(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_3992 = 3; +bool fn3993(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_3993 = 3; +bool fn3994(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_3994 = 4; +bool fn3995(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_3995 = 3; +bool fn3996(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_3996 = 3; +bool fn3997(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_3997 = 3; +bool fn3998(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_3998 = 4; +bool fn3999(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_3999 = 4; +bool fn4000(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_4000 = 4; +bool fn4001(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_4001 = 4; +bool fn4002(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_4002 = 4; +bool fn4003(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(x)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_4003 = 5; +bool fn4004(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_4004 = 3; +bool fn4005(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_4005 = 3; +bool fn4006(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_4006 = 3; +bool fn4007(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_4007 = 4; +bool fn4008(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_4008 = 3; +bool fn4009(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_4009 = 3; +bool fn4010(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_4010 = 3; +bool fn4011(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_4011 = 4; +bool fn4012(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_4012 = 3; +bool fn4013(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_4013 = 3; +bool fn4014(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_4014 = 3; +bool fn4015(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_4015 = 4; +bool fn4016(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_4016 = 4; +bool fn4017(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_4017 = 4; +bool fn4018(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_4018 = 4; +bool fn4019(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_4019 = 4; +bool fn4020(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(y)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_4020 = 5; +bool fn4021(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_4021 = 3; +bool fn4022(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_4022 = 3; +bool fn4023(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_4023 = 3; +bool fn4024(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_4024 = 4; +bool fn4025(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_4025 = 3; +bool fn4026(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_4026 = 3; +bool fn4027(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_4027 = 3; +bool fn4028(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_4028 = 4; +bool fn4029(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_4029 = 3; +bool fn4030(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_4030 = 3; +bool fn4031(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_4031 = 3; +bool fn4032(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_4032 = 4; +bool fn4033(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_4033 = 4; +bool fn4034(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_4034 = 4; +bool fn4035(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_4035 = 4; +bool fn4036(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_4036 = 4; +bool fn4037(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(z)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_4037 = 5; +bool fn4038(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(x)))+b*(x)),inv,pk) == 0; } int nvar_4038 = 4; +bool fn4039(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(x)))+b*(y)),inv,pk) == 0; } int nvar_4039 = 4; +bool fn4040(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(x)))+b*(z)),inv,pk) == 0; } int nvar_4040 = 4; +bool fn4041(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(x)))+b*(w)),inv,pk) == 0; } int nvar_4041 = 4; +bool fn4042(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(x)))+b*(u)),inv,pk) == 0; } int nvar_4042 = 5; +bool fn4043(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(y)))+b*(x)),inv,pk) == 0; } int nvar_4043 = 4; +bool fn4044(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(y)))+b*(y)),inv,pk) == 0; } int nvar_4044 = 4; +bool fn4045(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(y)))+b*(z)),inv,pk) == 0; } int nvar_4045 = 4; +bool fn4046(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(y)))+b*(w)),inv,pk) == 0; } int nvar_4046 = 4; +bool fn4047(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(y)))+b*(u)),inv,pk) == 0; } int nvar_4047 = 5; +bool fn4048(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(z)))+b*(x)),inv,pk) == 0; } int nvar_4048 = 4; +bool fn4049(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(z)))+b*(y)),inv,pk) == 0; } int nvar_4049 = 4; +bool fn4050(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(z)))+b*(z)),inv,pk) == 0; } int nvar_4050 = 4; +bool fn4051(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(z)))+b*(w)),inv,pk) == 0; } int nvar_4051 = 4; +bool fn4052(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(z)))+b*(u)),inv,pk) == 0; } int nvar_4052 = 5; +bool fn4053(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(w)))+b*(x)),inv,pk) == 0; } int nvar_4053 = 4; +bool fn4054(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(w)))+b*(y)),inv,pk) == 0; } int nvar_4054 = 4; +bool fn4055(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(w)))+b*(z)),inv,pk) == 0; } int nvar_4055 = 4; +bool fn4056(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(w)))+b*(w)),inv,pk) == 0; } int nvar_4056 = 4; +bool fn4057(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(w)))+b*(u)),inv,pk) == 0; } int nvar_4057 = 5; +bool fn4058(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(u)))+b*(x)),inv,pk) == 0; } int nvar_4058 = 5; +bool fn4059(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(u)))+b*(y)),inv,pk) == 0; } int nvar_4059 = 5; +bool fn4060(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(u)))+b*(z)),inv,pk) == 0; } int nvar_4060 = 5; +bool fn4061(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(u)))+b*(w)),inv,pk) == 0; } int nvar_4061 = 5; +bool fn4062(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(u)))+b*(u)),inv,pk) == 0; } int nvar_4062 = 5; +bool fn4063(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(z)+b*(a*(w)+b*(u)))+b*(v)),inv,pk) == 0; } int nvar_4063 = 6; +bool fn4064(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4064 = 1; +bool fn4065(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4065 = 2; +bool fn4066(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4066 = 2; +bool fn4067(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4067 = 2; +bool fn4068(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4068 = 3; +bool fn4069(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4069 = 2; +bool fn4070(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4070 = 2; +bool fn4071(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4071 = 3; +bool fn4072(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4072 = 2; +bool fn4073(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4073 = 2; +bool fn4074(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4074 = 3; +bool fn4075(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4075 = 3; +bool fn4076(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4076 = 3; +bool fn4077(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4077 = 3; +bool fn4078(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4078 = 4; +bool fn4079(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4079 = 2; +bool fn4080(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4080 = 2; +bool fn4081(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4081 = 3; +bool fn4082(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4082 = 2; +bool fn4083(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4083 = 2; +bool fn4084(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4084 = 3; +bool fn4085(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4085 = 3; +bool fn4086(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4086 = 3; +bool fn4087(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4087 = 3; +bool fn4088(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4088 = 4; +bool fn4089(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4089 = 2; +bool fn4090(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4090 = 2; +bool fn4091(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4091 = 3; +bool fn4092(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4092 = 2; +bool fn4093(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4093 = 2; +bool fn4094(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4094 = 3; +bool fn4095(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4095 = 3; +bool fn4096(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4096 = 3; +bool fn4097(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4097 = 3; +bool fn4098(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4098 = 4; +bool fn4099(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4099 = 3; +bool fn4100(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4100 = 3; +bool fn4101(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4101 = 3; +bool fn4102(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4102 = 4; +bool fn4103(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4103 = 3; +bool fn4104(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4104 = 3; +bool fn4105(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4105 = 3; +bool fn4106(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4106 = 4; +bool fn4107(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4107 = 3; +bool fn4108(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4108 = 3; +bool fn4109(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4109 = 3; +bool fn4110(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4110 = 4; +bool fn4111(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4111 = 4; +bool fn4112(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4112 = 4; +bool fn4113(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4113 = 4; +bool fn4114(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4114 = 4; +bool fn4115(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(x)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4115 = 5; +bool fn4116(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4116 = 2; +bool fn4117(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4117 = 2; +bool fn4118(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4118 = 3; +bool fn4119(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4119 = 2; +bool fn4120(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4120 = 2; +bool fn4121(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4121 = 3; +bool fn4122(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4122 = 3; +bool fn4123(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4123 = 3; +bool fn4124(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4124 = 3; +bool fn4125(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4125 = 4; +bool fn4126(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4126 = 2; +bool fn4127(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4127 = 2; +bool fn4128(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4128 = 3; +bool fn4129(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4129 = 2; +bool fn4130(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4130 = 2; +bool fn4131(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4131 = 3; +bool fn4132(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4132 = 3; +bool fn4133(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4133 = 3; +bool fn4134(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4134 = 3; +bool fn4135(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4135 = 4; +bool fn4136(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4136 = 3; +bool fn4137(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4137 = 3; +bool fn4138(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4138 = 3; +bool fn4139(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4139 = 4; +bool fn4140(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4140 = 3; +bool fn4141(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4141 = 3; +bool fn4142(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4142 = 3; +bool fn4143(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4143 = 4; +bool fn4144(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4144 = 3; +bool fn4145(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4145 = 3; +bool fn4146(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4146 = 3; +bool fn4147(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4147 = 4; +bool fn4148(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4148 = 4; +bool fn4149(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4149 = 4; +bool fn4150(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4150 = 4; +bool fn4151(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4151 = 4; +bool fn4152(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(x)+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4152 = 5; +bool fn4153(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4153 = 2; +bool fn4154(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4154 = 2; +bool fn4155(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4155 = 3; +bool fn4156(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4156 = 2; +bool fn4157(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4157 = 2; +bool fn4158(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4158 = 3; +bool fn4159(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4159 = 3; +bool fn4160(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4160 = 3; +bool fn4161(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4161 = 3; +bool fn4162(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4162 = 4; +bool fn4163(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4163 = 2; +bool fn4164(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4164 = 2; +bool fn4165(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4165 = 3; +bool fn4166(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4166 = 2; +bool fn4167(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4167 = 2; +bool fn4168(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4168 = 3; +bool fn4169(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4169 = 3; +bool fn4170(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4170 = 3; +bool fn4171(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4171 = 3; +bool fn4172(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4172 = 4; +bool fn4173(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4173 = 3; +bool fn4174(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4174 = 3; +bool fn4175(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4175 = 3; +bool fn4176(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4176 = 4; +bool fn4177(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4177 = 3; +bool fn4178(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4178 = 3; +bool fn4179(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4179 = 3; +bool fn4180(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4180 = 4; +bool fn4181(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4181 = 3; +bool fn4182(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4182 = 3; +bool fn4183(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4183 = 3; +bool fn4184(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4184 = 4; +bool fn4185(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4185 = 4; +bool fn4186(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4186 = 4; +bool fn4187(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4187 = 4; +bool fn4188(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4188 = 4; +bool fn4189(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(y)+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4189 = 5; +bool fn4190(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4190 = 3; +bool fn4191(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4191 = 3; +bool fn4192(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4192 = 3; +bool fn4193(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4193 = 4; +bool fn4194(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4194 = 3; +bool fn4195(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4195 = 3; +bool fn4196(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4196 = 3; +bool fn4197(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4197 = 4; +bool fn4198(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4198 = 3; +bool fn4199(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4199 = 3; +bool fn4200(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4200 = 3; +bool fn4201(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4201 = 4; +bool fn4202(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4202 = 4; +bool fn4203(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4203 = 4; +bool fn4204(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4204 = 4; +bool fn4205(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4205 = 4; +bool fn4206(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(x))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4206 = 5; +bool fn4207(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4207 = 3; +bool fn4208(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4208 = 3; +bool fn4209(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4209 = 3; +bool fn4210(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4210 = 4; +bool fn4211(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4211 = 3; +bool fn4212(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4212 = 3; +bool fn4213(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4213 = 3; +bool fn4214(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4214 = 4; +bool fn4215(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4215 = 3; +bool fn4216(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4216 = 3; +bool fn4217(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4217 = 3; +bool fn4218(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4218 = 4; +bool fn4219(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4219 = 4; +bool fn4220(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4220 = 4; +bool fn4221(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4221 = 4; +bool fn4222(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4222 = 4; +bool fn4223(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(y))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4223 = 5; +bool fn4224(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4224 = 3; +bool fn4225(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4225 = 3; +bool fn4226(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4226 = 3; +bool fn4227(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4227 = 4; +bool fn4228(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4228 = 3; +bool fn4229(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4229 = 3; +bool fn4230(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4230 = 3; +bool fn4231(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4231 = 4; +bool fn4232(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4232 = 3; +bool fn4233(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4233 = 3; +bool fn4234(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4234 = 3; +bool fn4235(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4235 = 4; +bool fn4236(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4236 = 4; +bool fn4237(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4237 = 4; +bool fn4238(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4238 = 4; +bool fn4239(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4239 = 4; +bool fn4240(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(z))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4240 = 5; +bool fn4241(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4241 = 4; +bool fn4242(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4242 = 4; +bool fn4243(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4243 = 4; +bool fn4244(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4244 = 4; +bool fn4245(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(x))+b*(u)),inv,pk) == 0; } int nvar_4245 = 5; +bool fn4246(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4246 = 4; +bool fn4247(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4247 = 4; +bool fn4248(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4248 = 4; +bool fn4249(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4249 = 4; +bool fn4250(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(y))+b*(u)),inv,pk) == 0; } int nvar_4250 = 5; +bool fn4251(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4251 = 4; +bool fn4252(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4252 = 4; +bool fn4253(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4253 = 4; +bool fn4254(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4254 = 4; +bool fn4255(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(z))+b*(u)),inv,pk) == 0; } int nvar_4255 = 5; +bool fn4256(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4256 = 4; +bool fn4257(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4257 = 4; +bool fn4258(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4258 = 4; +bool fn4259(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4259 = 4; +bool fn4260(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4260 = 5; +bool fn4261(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(u))+b*(x)),inv,pk) == 0; } int nvar_4261 = 5; +bool fn4262(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(u))+b*(y)),inv,pk) == 0; } int nvar_4262 = 5; +bool fn4263(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(u))+b*(z)),inv,pk) == 0; } int nvar_4263 = 5; +bool fn4264(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(u))+b*(w)),inv,pk) == 0; } int nvar_4264 = 5; +bool fn4265(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(u))+b*(u)),inv,pk) == 0; } int nvar_4265 = 5; +bool fn4266(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(y)) - (a*(a*(a*(z)+b*(w))+b*(u))+b*(v)),inv,pk) == 0; } int nvar_4266 = 6; +bool fn4267(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(x)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4267 = 2; +bool fn4268(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(x)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4268 = 2; +bool fn4269(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(x)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4269 = 2; +bool fn4270(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4270 = 3; +bool fn4271(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_4271 = 2; +bool fn4272(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4272 = 2; +bool fn4273(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4273 = 3; +bool fn4274(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4274 = 2; +bool fn4275(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4275 = 2; +bool fn4276(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4276 = 3; +bool fn4277(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4277 = 3; +bool fn4278(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4278 = 3; +bool fn4279(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4279 = 3; +bool fn4280(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4280 = 4; +bool fn4281(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4281 = 3; +bool fn4282(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4282 = 2; +bool fn4283(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4283 = 2; +bool fn4284(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4284 = 3; +bool fn4285(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4285 = 3; +bool fn4286(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4286 = 3; +bool fn4287(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4287 = 3; +bool fn4288(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(x)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4288 = 4; +bool fn4289(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_4289 = 2; +bool fn4290(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4290 = 2; +bool fn4291(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4291 = 3; +bool fn4292(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4292 = 2; +bool fn4293(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4293 = 3; +bool fn4294(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4294 = 3; +bool fn4295(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4295 = 3; +bool fn4296(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4296 = 3; +bool fn4297(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4297 = 4; +bool fn4298(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_4298 = 3; +bool fn4299(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4299 = 3; +bool fn4300(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4300 = 3; +bool fn4301(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_4301 = 4; +bool fn4302(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4302 = 3; +bool fn4303(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4303 = 3; +bool fn4304(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4304 = 3; +bool fn4305(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_4305 = 4; +bool fn4306(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4306 = 3; +bool fn4307(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4307 = 4; +bool fn4308(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_4308 = 4; +bool fn4309(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_4309 = 4; +bool fn4310(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_4310 = 4; +bool fn4311(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_4311 = 4; +bool fn4312(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(z)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_4312 = 5; +bool fn4313(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(x)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4313 = 2; +bool fn4314(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4314 = 3; +bool fn4315(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(x)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4315 = 3; +bool fn4316(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(x)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4316 = 3; +bool fn4317(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(x)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4317 = 3; +bool fn4318(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(x)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4318 = 4; +bool fn4319(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_4319 = 2; +bool fn4320(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4320 = 2; +bool fn4321(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4321 = 3; +bool fn4322(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4322 = 3; +bool fn4323(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4323 = 3; +bool fn4324(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4324 = 3; +bool fn4325(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4325 = 4; +bool fn4326(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_4326 = 3; +bool fn4327(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4327 = 3; +bool fn4328(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_4328 = 4; +bool fn4329(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4329 = 3; +bool fn4330(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4330 = 3; +bool fn4331(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4331 = 3; +bool fn4332(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_4332 = 4; +bool fn4333(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_4333 = 4; +bool fn4334(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_4334 = 4; +bool fn4335(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_4335 = 4; +bool fn4336(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_4336 = 4; +bool fn4337(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(z)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_4337 = 5; +bool fn4338(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(x)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4338 = 3; +bool fn4339(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(x)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4339 = 3; +bool fn4340(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(x)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4340 = 3; +bool fn4341(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(x)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4341 = 4; +bool fn4342(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(y)+b*(a*(x)+b*(x))),inv,pk) == 0; } int nvar_4342 = 2; +bool fn4343(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4343 = 3; +bool fn4344(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4344 = 3; +bool fn4345(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(y)+b*(a*(z)+b*(z))),inv,pk) == 0; } int nvar_4345 = 3; +bool fn4346(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4346 = 4; +bool fn4347(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(x)+b*(y))),inv,pk) == 0; } int nvar_4347 = 3; +bool fn4348(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_4348 = 4; +bool fn4349(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4349 = 3; +bool fn4350(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(y)+b*(y))),inv,pk) == 0; } int nvar_4350 = 3; +bool fn4351(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_4351 = 4; +bool fn4352(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_4352 = 4; +bool fn4353(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_4353 = 4; +bool fn4354(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(w)+b*(w))),inv,pk) == 0; } int nvar_4354 = 4; +bool fn4355(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(z)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_4355 = 5; +bool fn4356(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(x)+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_4356 = 4; +bool fn4357(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(x)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4357 = 3; +bool fn4358(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(x)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4358 = 4; +bool fn4359(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(x)+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_4359 = 4; +bool fn4360(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(x)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_4360 = 5; +bool fn4361(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(x)+b*(z))),inv,pk) == 0; } int nvar_4361 = 3; +bool fn4362(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(x)+b*(w))),inv,pk) == 0; } int nvar_4362 = 4; +bool fn4363(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(z)+b*(x))),inv,pk) == 0; } int nvar_4363 = 3; +bool fn4364(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(z)+b*(w))),inv,pk) == 0; } int nvar_4364 = 4; +bool fn4365(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_4365 = 4; +bool fn4366(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(w)+b*(z))),inv,pk) == 0; } int nvar_4366 = 4; +bool fn4367(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(y)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_4367 = 5; +bool fn4368(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(z)+b*(a*(y)+b*(x))),inv,pk) == 0; } int nvar_4368 = 3; +bool fn4369(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(z)+b*(a*(y)+b*(w))),inv,pk) == 0; } int nvar_4369 = 4; +bool fn4370(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(z)+b*(a*(w)+b*(x))),inv,pk) == 0; } int nvar_4370 = 4; +bool fn4371(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(z)+b*(a*(w)+b*(y))),inv,pk) == 0; } int nvar_4371 = 4; +bool fn4372(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(z)+b*(a*(w)+b*(u))),inv,pk) == 0; } int nvar_4372 = 5; +bool fn4373(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(w)+b*(a*(y)+b*(z))),inv,pk) == 0; } int nvar_4373 = 4; +bool fn4374(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(w)+b*(a*(y)+b*(u))),inv,pk) == 0; } int nvar_4374 = 5; +bool fn4375(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(w)+b*(a*(z)+b*(y))),inv,pk) == 0; } int nvar_4375 = 4; +bool fn4376(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(w)+b*(a*(z)+b*(u))),inv,pk) == 0; } int nvar_4376 = 5; +bool fn4377(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(w)+b*(a*(u)+b*(z))),inv,pk) == 0; } int nvar_4377 = 5; +bool fn4378(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(w)+b*(a*(u)+b*(v))),inv,pk) == 0; } int nvar_4378 = 6; +bool fn4379(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4379 = 1; +bool fn4380(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4380 = 2; +bool fn4381(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4381 = 2; +bool fn4382(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4382 = 2; +bool fn4383(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4383 = 3; +bool fn4384(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4384 = 2; +bool fn4385(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4385 = 2; +bool fn4386(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4386 = 3; +bool fn4387(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4387 = 2; +bool fn4388(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4388 = 2; +bool fn4389(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4389 = 3; +bool fn4390(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4390 = 3; +bool fn4391(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4391 = 3; +bool fn4392(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4392 = 3; +bool fn4393(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(x))) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4393 = 4; +bool fn4394(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4394 = 2; +bool fn4395(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4395 = 2; +bool fn4396(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4396 = 3; +bool fn4397(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4397 = 2; +bool fn4398(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4398 = 2; +bool fn4399(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4399 = 3; +bool fn4400(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4400 = 3; +bool fn4401(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4401 = 3; +bool fn4402(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4402 = 3; +bool fn4403(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4403 = 4; +bool fn4404(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4404 = 2; +bool fn4405(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4405 = 2; +bool fn4406(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4406 = 3; +bool fn4407(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4407 = 2; +bool fn4408(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4408 = 2; +bool fn4409(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4409 = 3; +bool fn4410(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4410 = 3; +bool fn4411(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4411 = 3; +bool fn4412(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4412 = 3; +bool fn4413(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4413 = 4; +bool fn4414(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4414 = 3; +bool fn4415(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4415 = 3; +bool fn4416(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4416 = 3; +bool fn4417(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4417 = 4; +bool fn4418(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4418 = 3; +bool fn4419(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4419 = 3; +bool fn4420(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4420 = 3; +bool fn4421(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4421 = 4; +bool fn4422(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4422 = 3; +bool fn4423(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4423 = 3; +bool fn4424(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4424 = 3; +bool fn4425(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4425 = 4; +bool fn4426(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4426 = 4; +bool fn4427(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4427 = 4; +bool fn4428(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4428 = 4; +bool fn4429(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4429 = 4; +bool fn4430(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(x)+b*(y))) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4430 = 5; +bool fn4431(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4431 = 2; +bool fn4432(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4432 = 2; +bool fn4433(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4433 = 3; +bool fn4434(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4434 = 2; +bool fn4435(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4435 = 2; +bool fn4436(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4436 = 3; +bool fn4437(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4437 = 3; +bool fn4438(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4438 = 3; +bool fn4439(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4439 = 3; +bool fn4440(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4440 = 4; +bool fn4441(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4441 = 2; +bool fn4442(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4442 = 2; +bool fn4443(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4443 = 3; +bool fn4444(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4444 = 2; +bool fn4445(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4445 = 2; +bool fn4446(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4446 = 3; +bool fn4447(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4447 = 3; +bool fn4448(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4448 = 3; +bool fn4449(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4449 = 3; +bool fn4450(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4450 = 4; +bool fn4451(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4451 = 3; +bool fn4452(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4452 = 3; +bool fn4453(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4453 = 3; +bool fn4454(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4454 = 4; +bool fn4455(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4455 = 3; +bool fn4456(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4456 = 3; +bool fn4457(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4457 = 3; +bool fn4458(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4458 = 4; +bool fn4459(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4459 = 3; +bool fn4460(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4460 = 3; +bool fn4461(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4461 = 3; +bool fn4462(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4462 = 4; +bool fn4463(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4463 = 4; +bool fn4464(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4464 = 4; +bool fn4465(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4465 = 4; +bool fn4466(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4466 = 4; +bool fn4467(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(x))) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4467 = 5; +bool fn4468(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4468 = 2; +bool fn4469(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4469 = 2; +bool fn4470(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4470 = 3; +bool fn4471(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4471 = 2; +bool fn4472(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4472 = 2; +bool fn4473(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4473 = 3; +bool fn4474(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4474 = 3; +bool fn4475(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4475 = 3; +bool fn4476(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4476 = 3; +bool fn4477(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4477 = 4; +bool fn4478(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4478 = 2; +bool fn4479(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4479 = 2; +bool fn4480(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4480 = 3; +bool fn4481(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4481 = 2; +bool fn4482(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4482 = 2; +bool fn4483(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4483 = 3; +bool fn4484(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4484 = 3; +bool fn4485(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4485 = 3; +bool fn4486(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4486 = 3; +bool fn4487(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4487 = 4; +bool fn4488(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4488 = 3; +bool fn4489(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4489 = 3; +bool fn4490(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4490 = 3; +bool fn4491(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4491 = 4; +bool fn4492(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4492 = 3; +bool fn4493(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4493 = 3; +bool fn4494(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4494 = 3; +bool fn4495(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4495 = 4; +bool fn4496(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4496 = 3; +bool fn4497(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4497 = 3; +bool fn4498(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4498 = 3; +bool fn4499(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4499 = 4; +bool fn4500(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4500 = 4; +bool fn4501(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4501 = 4; +bool fn4502(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4502 = 4; +bool fn4503(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4503 = 4; +bool fn4504(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(y))) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4504 = 5; +bool fn4505(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4505 = 3; +bool fn4506(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4506 = 3; +bool fn4507(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4507 = 3; +bool fn4508(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4508 = 4; +bool fn4509(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4509 = 3; +bool fn4510(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4510 = 3; +bool fn4511(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4511 = 3; +bool fn4512(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4512 = 4; +bool fn4513(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4513 = 3; +bool fn4514(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4514 = 3; +bool fn4515(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4515 = 3; +bool fn4516(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4516 = 4; +bool fn4517(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4517 = 4; +bool fn4518(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4518 = 4; +bool fn4519(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4519 = 4; +bool fn4520(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4520 = 4; +bool fn4521(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(x)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4521 = 5; +bool fn4522(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4522 = 3; +bool fn4523(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4523 = 3; +bool fn4524(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4524 = 3; +bool fn4525(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4525 = 4; +bool fn4526(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4526 = 3; +bool fn4527(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4527 = 3; +bool fn4528(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4528 = 3; +bool fn4529(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4529 = 4; +bool fn4530(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4530 = 3; +bool fn4531(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4531 = 3; +bool fn4532(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4532 = 3; +bool fn4533(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4533 = 4; +bool fn4534(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4534 = 4; +bool fn4535(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4535 = 4; +bool fn4536(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4536 = 4; +bool fn4537(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4537 = 4; +bool fn4538(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(y)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4538 = 5; +bool fn4539(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4539 = 3; +bool fn4540(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4540 = 3; +bool fn4541(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4541 = 3; +bool fn4542(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4542 = 4; +bool fn4543(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4543 = 3; +bool fn4544(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4544 = 3; +bool fn4545(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4545 = 3; +bool fn4546(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4546 = 4; +bool fn4547(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4547 = 3; +bool fn4548(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4548 = 3; +bool fn4549(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4549 = 3; +bool fn4550(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4550 = 4; +bool fn4551(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4551 = 4; +bool fn4552(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4552 = 4; +bool fn4553(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4553 = 4; +bool fn4554(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4554 = 4; +bool fn4555(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4555 = 5; +bool fn4556(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4556 = 4; +bool fn4557(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4557 = 4; +bool fn4558(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4558 = 4; +bool fn4559(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4559 = 4; +bool fn4560(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(x))+b*(u)),inv,pk) == 0; } int nvar_4560 = 5; +bool fn4561(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4561 = 4; +bool fn4562(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4562 = 4; +bool fn4563(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4563 = 4; +bool fn4564(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4564 = 4; +bool fn4565(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(y))+b*(u)),inv,pk) == 0; } int nvar_4565 = 5; +bool fn4566(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4566 = 4; +bool fn4567(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4567 = 4; +bool fn4568(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4568 = 4; +bool fn4569(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4569 = 4; +bool fn4570(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(z))+b*(u)),inv,pk) == 0; } int nvar_4570 = 5; +bool fn4571(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4571 = 4; +bool fn4572(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4572 = 4; +bool fn4573(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4573 = 4; +bool fn4574(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4574 = 4; +bool fn4575(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4575 = 5; +bool fn4576(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(u))+b*(x)),inv,pk) == 0; } int nvar_4576 = 5; +bool fn4577(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(u))+b*(y)),inv,pk) == 0; } int nvar_4577 = 5; +bool fn4578(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(u))+b*(z)),inv,pk) == 0; } int nvar_4578 = 5; +bool fn4579(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(u))+b*(w)),inv,pk) == 0; } int nvar_4579 = 5; +bool fn4580(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(u))+b*(u)),inv,pk) == 0; } int nvar_4580 = 5; +bool fn4581(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(x)+b*(a*(y)+b*(z))) - (a*(a*(w)+b*(u))+b*(v)),inv,pk) == 0; } int nvar_4581 = 6; +bool fn4582(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(x)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4582 = 2; +bool fn4583(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4583 = 2; +bool fn4584(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4584 = 2; +bool fn4585(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4585 = 3; +bool fn4586(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4586 = 2; +bool fn4587(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4587 = 2; +bool fn4588(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4588 = 3; +bool fn4589(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4589 = 2; +bool fn4590(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4590 = 2; +bool fn4591(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4591 = 3; +bool fn4592(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4592 = 3; +bool fn4593(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4593 = 3; +bool fn4594(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4594 = 3; +bool fn4595(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(x)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4595 = 4; +bool fn4596(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4596 = 3; +bool fn4597(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4597 = 2; +bool fn4598(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4598 = 2; +bool fn4599(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4599 = 3; +bool fn4600(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4600 = 3; +bool fn4601(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4601 = 3; +bool fn4602(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4602 = 3; +bool fn4603(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4603 = 4; +bool fn4604(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4604 = 2; +bool fn4605(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4605 = 2; +bool fn4606(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4606 = 3; +bool fn4607(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4607 = 2; +bool fn4608(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4608 = 3; +bool fn4609(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4609 = 3; +bool fn4610(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4610 = 3; +bool fn4611(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4611 = 3; +bool fn4612(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4612 = 4; +bool fn4613(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4613 = 3; +bool fn4614(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4614 = 3; +bool fn4615(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4615 = 3; +bool fn4616(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4616 = 4; +bool fn4617(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4617 = 3; +bool fn4618(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4618 = 3; +bool fn4619(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4619 = 3; +bool fn4620(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4620 = 4; +bool fn4621(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4621 = 3; +bool fn4622(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4622 = 4; +bool fn4623(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4623 = 4; +bool fn4624(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4624 = 4; +bool fn4625(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4625 = 4; +bool fn4626(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4626 = 4; +bool fn4627(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(x))+b*(y)) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4627 = 5; +bool fn4628(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(x)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4628 = 2; +bool fn4629(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4629 = 3; +bool fn4630(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(x)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4630 = 3; +bool fn4631(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4631 = 3; +bool fn4632(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4632 = 3; +bool fn4633(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4633 = 4; +bool fn4634(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4634 = 2; +bool fn4635(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4635 = 2; +bool fn4636(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4636 = 3; +bool fn4637(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4637 = 3; +bool fn4638(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4638 = 3; +bool fn4639(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4639 = 3; +bool fn4640(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4640 = 4; +bool fn4641(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4641 = 3; +bool fn4642(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4642 = 3; +bool fn4643(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4643 = 4; +bool fn4644(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4644 = 3; +bool fn4645(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4645 = 3; +bool fn4646(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4646 = 3; +bool fn4647(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4647 = 4; +bool fn4648(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4648 = 4; +bool fn4649(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4649 = 4; +bool fn4650(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4650 = 4; +bool fn4651(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4651 = 4; +bool fn4652(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(x)) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4652 = 5; +bool fn4653(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(x)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4653 = 3; +bool fn4654(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4654 = 3; +bool fn4655(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(x)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4655 = 3; +bool fn4656(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4656 = 4; +bool fn4657(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(y)+b*(x))+b*(x)),inv,pk) == 0; } int nvar_4657 = 2; +bool fn4658(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4658 = 3; +bool fn4659(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4659 = 3; +bool fn4660(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(y)+b*(z))+b*(z)),inv,pk) == 0; } int nvar_4660 = 3; +bool fn4661(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4661 = 4; +bool fn4662(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(x))+b*(y)),inv,pk) == 0; } int nvar_4662 = 3; +bool fn4663(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4663 = 4; +bool fn4664(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4664 = 3; +bool fn4665(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(y))+b*(y)),inv,pk) == 0; } int nvar_4665 = 3; +bool fn4666(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4666 = 4; +bool fn4667(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4667 = 4; +bool fn4668(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4668 = 4; +bool fn4669(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(w))+b*(w)),inv,pk) == 0; } int nvar_4669 = 4; +bool fn4670(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(y)) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4670 = 5; +bool fn4671(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(x)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4671 = 4; +bool fn4672(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(x)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4672 = 3; +bool fn4673(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(x)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4673 = 4; +bool fn4674(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(x)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4674 = 4; +bool fn4675(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(x)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4675 = 5; +bool fn4676(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(x))+b*(z)),inv,pk) == 0; } int nvar_4676 = 3; +bool fn4677(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(x))+b*(w)),inv,pk) == 0; } int nvar_4677 = 4; +bool fn4678(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(z))+b*(x)),inv,pk) == 0; } int nvar_4678 = 3; +bool fn4679(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(z))+b*(w)),inv,pk) == 0; } int nvar_4679 = 4; +bool fn4680(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4680 = 4; +bool fn4681(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(w))+b*(z)),inv,pk) == 0; } int nvar_4681 = 4; +bool fn4682(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(y)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4682 = 5; +bool fn4683(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(z)+b*(y))+b*(x)),inv,pk) == 0; } int nvar_4683 = 3; +bool fn4684(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(z)+b*(y))+b*(w)),inv,pk) == 0; } int nvar_4684 = 4; +bool fn4685(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(z)+b*(w))+b*(x)),inv,pk) == 0; } int nvar_4685 = 4; +bool fn4686(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(z)+b*(w))+b*(y)),inv,pk) == 0; } int nvar_4686 = 4; +bool fn4687(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(z)+b*(w))+b*(u)),inv,pk) == 0; } int nvar_4687 = 5; +bool fn4688(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(w)+b*(y))+b*(z)),inv,pk) == 0; } int nvar_4688 = 4; +bool fn4689(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(w)+b*(y))+b*(u)),inv,pk) == 0; } int nvar_4689 = 5; +bool fn4690(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(w)+b*(z))+b*(y)),inv,pk) == 0; } int nvar_4690 = 4; +bool fn4691(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(w)+b*(z))+b*(u)),inv,pk) == 0; } int nvar_4691 = 5; +bool fn4692(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(w)+b*(u))+b*(z)),inv,pk) == 0; } int nvar_4692 = 5; +bool fn4693(uint64_t pk, int64_t inv, uint64_t a, uint64_t b, uint64_t x, uint64_t y, uint64_t z, uint64_t w, uint64_t u, uint64_t v) { return MOD((a*(a*(x)+b*(y))+b*(z)) - (a*(a*(w)+b*(u))+b*(v)),inv,pk) == 0; } int nvar_4693 = 6; + + +void setup() { + functions = (FunctionPtr*)malloc(NUM_FUNCTIONS * sizeof(FunctionPtr)); + nvar_list = (int*)malloc(NUM_FUNCTIONS * sizeof(int)); + + if (!functions || !nvar_list) { + fprintf(stderr, "Memory allocation failed\n"); + return; + } + + functions[0] = fn0; + nvar_list[0] = nvar_0; + functions[1] = fn1; + nvar_list[1] = nvar_1; + functions[2] = fn2; + nvar_list[2] = nvar_2; + functions[3] = fn3; + nvar_list[3] = nvar_3; + functions[4] = fn4; + nvar_list[4] = nvar_4; + functions[5] = fn5; + nvar_list[5] = nvar_5; + functions[6] = fn6; + nvar_list[6] = nvar_6; + functions[7] = fn7; + nvar_list[7] = nvar_7; + functions[8] = fn8; + nvar_list[8] = nvar_8; + functions[9] = fn9; + nvar_list[9] = nvar_9; + functions[10] = fn10; + nvar_list[10] = nvar_10; + functions[11] = fn11; + nvar_list[11] = nvar_11; + functions[12] = fn12; + nvar_list[12] = nvar_12; + functions[13] = fn13; + nvar_list[13] = nvar_13; + functions[14] = fn14; + nvar_list[14] = nvar_14; + functions[15] = fn15; + nvar_list[15] = nvar_15; + functions[16] = fn16; + nvar_list[16] = nvar_16; + functions[17] = fn17; + nvar_list[17] = nvar_17; + functions[18] = fn18; + nvar_list[18] = nvar_18; + functions[19] = fn19; + nvar_list[19] = nvar_19; + functions[20] = fn20; + nvar_list[20] = nvar_20; + functions[21] = fn21; + nvar_list[21] = nvar_21; + functions[22] = fn22; + nvar_list[22] = nvar_22; + functions[23] = fn23; + nvar_list[23] = nvar_23; + functions[24] = fn24; + nvar_list[24] = nvar_24; + functions[25] = fn25; + nvar_list[25] = nvar_25; + functions[26] = fn26; + nvar_list[26] = nvar_26; + functions[27] = fn27; + nvar_list[27] = nvar_27; + functions[28] = fn28; + nvar_list[28] = nvar_28; + functions[29] = fn29; + nvar_list[29] = nvar_29; + functions[30] = fn30; + nvar_list[30] = nvar_30; + functions[31] = fn31; + nvar_list[31] = nvar_31; + functions[32] = fn32; + nvar_list[32] = nvar_32; + functions[33] = fn33; + nvar_list[33] = nvar_33; + functions[34] = fn34; + nvar_list[34] = nvar_34; + functions[35] = fn35; + nvar_list[35] = nvar_35; + functions[36] = fn36; + nvar_list[36] = nvar_36; + functions[37] = fn37; + nvar_list[37] = nvar_37; + functions[38] = fn38; + nvar_list[38] = nvar_38; + functions[39] = fn39; + nvar_list[39] = nvar_39; + functions[40] = fn40; + nvar_list[40] = nvar_40; + functions[41] = fn41; + nvar_list[41] = nvar_41; + functions[42] = fn42; + nvar_list[42] = nvar_42; + functions[43] = fn43; + nvar_list[43] = nvar_43; + functions[44] = fn44; + nvar_list[44] = nvar_44; + functions[45] = fn45; + nvar_list[45] = nvar_45; + functions[46] = fn46; + nvar_list[46] = nvar_46; + functions[47] = fn47; + nvar_list[47] = nvar_47; + functions[48] = fn48; + nvar_list[48] = nvar_48; + functions[49] = fn49; + nvar_list[49] = nvar_49; + functions[50] = fn50; + nvar_list[50] = nvar_50; + functions[51] = fn51; + nvar_list[51] = nvar_51; + functions[52] = fn52; + nvar_list[52] = nvar_52; + functions[53] = fn53; + nvar_list[53] = nvar_53; + functions[54] = fn54; + nvar_list[54] = nvar_54; + functions[55] = fn55; + nvar_list[55] = nvar_55; + functions[56] = fn56; + nvar_list[56] = nvar_56; + functions[57] = fn57; + nvar_list[57] = nvar_57; + functions[58] = fn58; + nvar_list[58] = nvar_58; + functions[59] = fn59; + nvar_list[59] = nvar_59; + functions[60] = fn60; + nvar_list[60] = nvar_60; + functions[61] = fn61; + nvar_list[61] = nvar_61; + functions[62] = fn62; + nvar_list[62] = nvar_62; + functions[63] = fn63; + nvar_list[63] = nvar_63; + functions[64] = fn64; + nvar_list[64] = nvar_64; + functions[65] = fn65; + nvar_list[65] = nvar_65; + functions[66] = fn66; + nvar_list[66] = nvar_66; + functions[67] = fn67; + nvar_list[67] = nvar_67; + functions[68] = fn68; + nvar_list[68] = nvar_68; + functions[69] = fn69; + nvar_list[69] = nvar_69; + functions[70] = fn70; + nvar_list[70] = nvar_70; + functions[71] = fn71; + nvar_list[71] = nvar_71; + functions[72] = fn72; + nvar_list[72] = nvar_72; + functions[73] = fn73; + nvar_list[73] = nvar_73; + functions[74] = fn74; + nvar_list[74] = nvar_74; + functions[75] = fn75; + nvar_list[75] = nvar_75; + functions[76] = fn76; + nvar_list[76] = nvar_76; + functions[77] = fn77; + nvar_list[77] = nvar_77; + functions[78] = fn78; + nvar_list[78] = nvar_78; + functions[79] = fn79; + nvar_list[79] = nvar_79; + functions[80] = fn80; + nvar_list[80] = nvar_80; + functions[81] = fn81; + nvar_list[81] = nvar_81; + functions[82] = fn82; + nvar_list[82] = nvar_82; + functions[83] = fn83; + nvar_list[83] = nvar_83; + functions[84] = fn84; + nvar_list[84] = nvar_84; + functions[85] = fn85; + nvar_list[85] = nvar_85; + functions[86] = fn86; + nvar_list[86] = nvar_86; + functions[87] = fn87; + nvar_list[87] = nvar_87; + functions[88] = fn88; + nvar_list[88] = nvar_88; + functions[89] = fn89; + nvar_list[89] = nvar_89; + functions[90] = fn90; + nvar_list[90] = nvar_90; + functions[91] = fn91; + nvar_list[91] = nvar_91; + functions[92] = fn92; + nvar_list[92] = nvar_92; + functions[93] = fn93; + nvar_list[93] = nvar_93; + functions[94] = fn94; + nvar_list[94] = nvar_94; + functions[95] = fn95; + nvar_list[95] = nvar_95; + functions[96] = fn96; + nvar_list[96] = nvar_96; + functions[97] = fn97; + nvar_list[97] = nvar_97; + functions[98] = fn98; + nvar_list[98] = nvar_98; + functions[99] = fn99; + nvar_list[99] = nvar_99; + functions[100] = fn100; + nvar_list[100] = nvar_100; + functions[101] = fn101; + nvar_list[101] = nvar_101; + functions[102] = fn102; + nvar_list[102] = nvar_102; + functions[103] = fn103; + nvar_list[103] = nvar_103; + functions[104] = fn104; + nvar_list[104] = nvar_104; + functions[105] = fn105; + nvar_list[105] = nvar_105; + functions[106] = fn106; + nvar_list[106] = nvar_106; + functions[107] = fn107; + nvar_list[107] = nvar_107; + functions[108] = fn108; + nvar_list[108] = nvar_108; + functions[109] = fn109; + nvar_list[109] = nvar_109; + functions[110] = fn110; + nvar_list[110] = nvar_110; + functions[111] = fn111; + nvar_list[111] = nvar_111; + functions[112] = fn112; + nvar_list[112] = nvar_112; + functions[113] = fn113; + nvar_list[113] = nvar_113; + functions[114] = fn114; + nvar_list[114] = nvar_114; + functions[115] = fn115; + nvar_list[115] = nvar_115; + functions[116] = fn116; + nvar_list[116] = nvar_116; + functions[117] = fn117; + nvar_list[117] = nvar_117; + functions[118] = fn118; + nvar_list[118] = nvar_118; + functions[119] = fn119; + nvar_list[119] = nvar_119; + functions[120] = fn120; + nvar_list[120] = nvar_120; + functions[121] = fn121; + nvar_list[121] = nvar_121; + functions[122] = fn122; + nvar_list[122] = nvar_122; + functions[123] = fn123; + nvar_list[123] = nvar_123; + functions[124] = fn124; + nvar_list[124] = nvar_124; + functions[125] = fn125; + nvar_list[125] = nvar_125; + functions[126] = fn126; + nvar_list[126] = nvar_126; + functions[127] = fn127; + nvar_list[127] = nvar_127; + functions[128] = fn128; + nvar_list[128] = nvar_128; + functions[129] = fn129; + nvar_list[129] = nvar_129; + functions[130] = fn130; + nvar_list[130] = nvar_130; + functions[131] = fn131; + nvar_list[131] = nvar_131; + functions[132] = fn132; + nvar_list[132] = nvar_132; + functions[133] = fn133; + nvar_list[133] = nvar_133; + functions[134] = fn134; + nvar_list[134] = nvar_134; + functions[135] = fn135; + nvar_list[135] = nvar_135; + functions[136] = fn136; + nvar_list[136] = nvar_136; + functions[137] = fn137; + nvar_list[137] = nvar_137; + functions[138] = fn138; + nvar_list[138] = nvar_138; + functions[139] = fn139; + nvar_list[139] = nvar_139; + functions[140] = fn140; + nvar_list[140] = nvar_140; + functions[141] = fn141; + nvar_list[141] = nvar_141; + functions[142] = fn142; + nvar_list[142] = nvar_142; + functions[143] = fn143; + nvar_list[143] = nvar_143; + functions[144] = fn144; + nvar_list[144] = nvar_144; + functions[145] = fn145; + nvar_list[145] = nvar_145; + functions[146] = fn146; + nvar_list[146] = nvar_146; + functions[147] = fn147; + nvar_list[147] = nvar_147; + functions[148] = fn148; + nvar_list[148] = nvar_148; + functions[149] = fn149; + nvar_list[149] = nvar_149; + functions[150] = fn150; + nvar_list[150] = nvar_150; + functions[151] = fn151; + nvar_list[151] = nvar_151; + functions[152] = fn152; + nvar_list[152] = nvar_152; + functions[153] = fn153; + nvar_list[153] = nvar_153; + functions[154] = fn154; + nvar_list[154] = nvar_154; + functions[155] = fn155; + nvar_list[155] = nvar_155; + functions[156] = fn156; + nvar_list[156] = nvar_156; + functions[157] = fn157; + nvar_list[157] = nvar_157; + functions[158] = fn158; + nvar_list[158] = nvar_158; + functions[159] = fn159; + nvar_list[159] = nvar_159; + functions[160] = fn160; + nvar_list[160] = nvar_160; + functions[161] = fn161; + nvar_list[161] = nvar_161; + functions[162] = fn162; + nvar_list[162] = nvar_162; + functions[163] = fn163; + nvar_list[163] = nvar_163; + functions[164] = fn164; + nvar_list[164] = nvar_164; + functions[165] = fn165; + nvar_list[165] = nvar_165; + functions[166] = fn166; + nvar_list[166] = nvar_166; + functions[167] = fn167; + nvar_list[167] = nvar_167; + functions[168] = fn168; + nvar_list[168] = nvar_168; + functions[169] = fn169; + nvar_list[169] = nvar_169; + functions[170] = fn170; + nvar_list[170] = nvar_170; + functions[171] = fn171; + nvar_list[171] = nvar_171; + functions[172] = fn172; + nvar_list[172] = nvar_172; + functions[173] = fn173; + nvar_list[173] = nvar_173; + functions[174] = fn174; + nvar_list[174] = nvar_174; + functions[175] = fn175; + nvar_list[175] = nvar_175; + functions[176] = fn176; + nvar_list[176] = nvar_176; + functions[177] = fn177; + nvar_list[177] = nvar_177; + functions[178] = fn178; + nvar_list[178] = nvar_178; + functions[179] = fn179; + nvar_list[179] = nvar_179; + functions[180] = fn180; + nvar_list[180] = nvar_180; + functions[181] = fn181; + nvar_list[181] = nvar_181; + functions[182] = fn182; + nvar_list[182] = nvar_182; + functions[183] = fn183; + nvar_list[183] = nvar_183; + functions[184] = fn184; + nvar_list[184] = nvar_184; + functions[185] = fn185; + nvar_list[185] = nvar_185; + functions[186] = fn186; + nvar_list[186] = nvar_186; + functions[187] = fn187; + nvar_list[187] = nvar_187; + functions[188] = fn188; + nvar_list[188] = nvar_188; + functions[189] = fn189; + nvar_list[189] = nvar_189; + functions[190] = fn190; + nvar_list[190] = nvar_190; + functions[191] = fn191; + nvar_list[191] = nvar_191; + functions[192] = fn192; + nvar_list[192] = nvar_192; + functions[193] = fn193; + nvar_list[193] = nvar_193; + functions[194] = fn194; + nvar_list[194] = nvar_194; + functions[195] = fn195; + nvar_list[195] = nvar_195; + functions[196] = fn196; + nvar_list[196] = nvar_196; + functions[197] = fn197; + nvar_list[197] = nvar_197; + functions[198] = fn198; + nvar_list[198] = nvar_198; + functions[199] = fn199; + nvar_list[199] = nvar_199; + functions[200] = fn200; + nvar_list[200] = nvar_200; + functions[201] = fn201; + nvar_list[201] = nvar_201; + functions[202] = fn202; + nvar_list[202] = nvar_202; + functions[203] = fn203; + nvar_list[203] = nvar_203; + functions[204] = fn204; + nvar_list[204] = nvar_204; + functions[205] = fn205; + nvar_list[205] = nvar_205; + functions[206] = fn206; + nvar_list[206] = nvar_206; + functions[207] = fn207; + nvar_list[207] = nvar_207; + functions[208] = fn208; + nvar_list[208] = nvar_208; + functions[209] = fn209; + nvar_list[209] = nvar_209; + functions[210] = fn210; + nvar_list[210] = nvar_210; + functions[211] = fn211; + nvar_list[211] = nvar_211; + functions[212] = fn212; + nvar_list[212] = nvar_212; + functions[213] = fn213; + nvar_list[213] = nvar_213; + functions[214] = fn214; + nvar_list[214] = nvar_214; + functions[215] = fn215; + nvar_list[215] = nvar_215; + functions[216] = fn216; + nvar_list[216] = nvar_216; + functions[217] = fn217; + nvar_list[217] = nvar_217; + functions[218] = fn218; + nvar_list[218] = nvar_218; + functions[219] = fn219; + nvar_list[219] = nvar_219; + functions[220] = fn220; + nvar_list[220] = nvar_220; + functions[221] = fn221; + nvar_list[221] = nvar_221; + functions[222] = fn222; + nvar_list[222] = nvar_222; + functions[223] = fn223; + nvar_list[223] = nvar_223; + functions[224] = fn224; + nvar_list[224] = nvar_224; + functions[225] = fn225; + nvar_list[225] = nvar_225; + functions[226] = fn226; + nvar_list[226] = nvar_226; + functions[227] = fn227; + nvar_list[227] = nvar_227; + functions[228] = fn228; + nvar_list[228] = nvar_228; + functions[229] = fn229; + nvar_list[229] = nvar_229; + functions[230] = fn230; + nvar_list[230] = nvar_230; + functions[231] = fn231; + nvar_list[231] = nvar_231; + functions[232] = fn232; + nvar_list[232] = nvar_232; + functions[233] = fn233; + nvar_list[233] = nvar_233; + functions[234] = fn234; + nvar_list[234] = nvar_234; + functions[235] = fn235; + nvar_list[235] = nvar_235; + functions[236] = fn236; + nvar_list[236] = nvar_236; + functions[237] = fn237; + nvar_list[237] = nvar_237; + functions[238] = fn238; + nvar_list[238] = nvar_238; + functions[239] = fn239; + nvar_list[239] = nvar_239; + functions[240] = fn240; + nvar_list[240] = nvar_240; + functions[241] = fn241; + nvar_list[241] = nvar_241; + functions[242] = fn242; + nvar_list[242] = nvar_242; + functions[243] = fn243; + nvar_list[243] = nvar_243; + functions[244] = fn244; + nvar_list[244] = nvar_244; + functions[245] = fn245; + nvar_list[245] = nvar_245; + functions[246] = fn246; + nvar_list[246] = nvar_246; + functions[247] = fn247; + nvar_list[247] = nvar_247; + functions[248] = fn248; + nvar_list[248] = nvar_248; + functions[249] = fn249; + nvar_list[249] = nvar_249; + functions[250] = fn250; + nvar_list[250] = nvar_250; + functions[251] = fn251; + nvar_list[251] = nvar_251; + functions[252] = fn252; + nvar_list[252] = nvar_252; + functions[253] = fn253; + nvar_list[253] = nvar_253; + functions[254] = fn254; + nvar_list[254] = nvar_254; + functions[255] = fn255; + nvar_list[255] = nvar_255; + functions[256] = fn256; + nvar_list[256] = nvar_256; + functions[257] = fn257; + nvar_list[257] = nvar_257; + functions[258] = fn258; + nvar_list[258] = nvar_258; + functions[259] = fn259; + nvar_list[259] = nvar_259; + functions[260] = fn260; + nvar_list[260] = nvar_260; + functions[261] = fn261; + nvar_list[261] = nvar_261; + functions[262] = fn262; + nvar_list[262] = nvar_262; + functions[263] = fn263; + nvar_list[263] = nvar_263; + functions[264] = fn264; + nvar_list[264] = nvar_264; + functions[265] = fn265; + nvar_list[265] = nvar_265; + functions[266] = fn266; + nvar_list[266] = nvar_266; + functions[267] = fn267; + nvar_list[267] = nvar_267; + functions[268] = fn268; + nvar_list[268] = nvar_268; + functions[269] = fn269; + nvar_list[269] = nvar_269; + functions[270] = fn270; + nvar_list[270] = nvar_270; + functions[271] = fn271; + nvar_list[271] = nvar_271; + functions[272] = fn272; + nvar_list[272] = nvar_272; + functions[273] = fn273; + nvar_list[273] = nvar_273; + functions[274] = fn274; + nvar_list[274] = nvar_274; + functions[275] = fn275; + nvar_list[275] = nvar_275; + functions[276] = fn276; + nvar_list[276] = nvar_276; + functions[277] = fn277; + nvar_list[277] = nvar_277; + functions[278] = fn278; + nvar_list[278] = nvar_278; + functions[279] = fn279; + nvar_list[279] = nvar_279; + functions[280] = fn280; + nvar_list[280] = nvar_280; + functions[281] = fn281; + nvar_list[281] = nvar_281; + functions[282] = fn282; + nvar_list[282] = nvar_282; + functions[283] = fn283; + nvar_list[283] = nvar_283; + functions[284] = fn284; + nvar_list[284] = nvar_284; + functions[285] = fn285; + nvar_list[285] = nvar_285; + functions[286] = fn286; + nvar_list[286] = nvar_286; + functions[287] = fn287; + nvar_list[287] = nvar_287; + functions[288] = fn288; + nvar_list[288] = nvar_288; + functions[289] = fn289; + nvar_list[289] = nvar_289; + functions[290] = fn290; + nvar_list[290] = nvar_290; + functions[291] = fn291; + nvar_list[291] = nvar_291; + functions[292] = fn292; + nvar_list[292] = nvar_292; + functions[293] = fn293; + nvar_list[293] = nvar_293; + functions[294] = fn294; + nvar_list[294] = nvar_294; + functions[295] = fn295; + nvar_list[295] = nvar_295; + functions[296] = fn296; + nvar_list[296] = nvar_296; + functions[297] = fn297; + nvar_list[297] = nvar_297; + functions[298] = fn298; + nvar_list[298] = nvar_298; + functions[299] = fn299; + nvar_list[299] = nvar_299; + functions[300] = fn300; + nvar_list[300] = nvar_300; + functions[301] = fn301; + nvar_list[301] = nvar_301; + functions[302] = fn302; + nvar_list[302] = nvar_302; + functions[303] = fn303; + nvar_list[303] = nvar_303; + functions[304] = fn304; + nvar_list[304] = nvar_304; + functions[305] = fn305; + nvar_list[305] = nvar_305; + functions[306] = fn306; + nvar_list[306] = nvar_306; + functions[307] = fn307; + nvar_list[307] = nvar_307; + functions[308] = fn308; + nvar_list[308] = nvar_308; + functions[309] = fn309; + nvar_list[309] = nvar_309; + functions[310] = fn310; + nvar_list[310] = nvar_310; + functions[311] = fn311; + nvar_list[311] = nvar_311; + functions[312] = fn312; + nvar_list[312] = nvar_312; + functions[313] = fn313; + nvar_list[313] = nvar_313; + functions[314] = fn314; + nvar_list[314] = nvar_314; + functions[315] = fn315; + nvar_list[315] = nvar_315; + functions[316] = fn316; + nvar_list[316] = nvar_316; + functions[317] = fn317; + nvar_list[317] = nvar_317; + functions[318] = fn318; + nvar_list[318] = nvar_318; + functions[319] = fn319; + nvar_list[319] = nvar_319; + functions[320] = fn320; + nvar_list[320] = nvar_320; + functions[321] = fn321; + nvar_list[321] = nvar_321; + functions[322] = fn322; + nvar_list[322] = nvar_322; + functions[323] = fn323; + nvar_list[323] = nvar_323; + functions[324] = fn324; + nvar_list[324] = nvar_324; + functions[325] = fn325; + nvar_list[325] = nvar_325; + functions[326] = fn326; + nvar_list[326] = nvar_326; + functions[327] = fn327; + nvar_list[327] = nvar_327; + functions[328] = fn328; + nvar_list[328] = nvar_328; + functions[329] = fn329; + nvar_list[329] = nvar_329; + functions[330] = fn330; + nvar_list[330] = nvar_330; + functions[331] = fn331; + nvar_list[331] = nvar_331; + functions[332] = fn332; + nvar_list[332] = nvar_332; + functions[333] = fn333; + nvar_list[333] = nvar_333; + functions[334] = fn334; + nvar_list[334] = nvar_334; + functions[335] = fn335; + nvar_list[335] = nvar_335; + functions[336] = fn336; + nvar_list[336] = nvar_336; + functions[337] = fn337; + nvar_list[337] = nvar_337; + functions[338] = fn338; + nvar_list[338] = nvar_338; + functions[339] = fn339; + nvar_list[339] = nvar_339; + functions[340] = fn340; + nvar_list[340] = nvar_340; + functions[341] = fn341; + nvar_list[341] = nvar_341; + functions[342] = fn342; + nvar_list[342] = nvar_342; + functions[343] = fn343; + nvar_list[343] = nvar_343; + functions[344] = fn344; + nvar_list[344] = nvar_344; + functions[345] = fn345; + nvar_list[345] = nvar_345; + functions[346] = fn346; + nvar_list[346] = nvar_346; + functions[347] = fn347; + nvar_list[347] = nvar_347; + functions[348] = fn348; + nvar_list[348] = nvar_348; + functions[349] = fn349; + nvar_list[349] = nvar_349; + functions[350] = fn350; + nvar_list[350] = nvar_350; + functions[351] = fn351; + nvar_list[351] = nvar_351; + functions[352] = fn352; + nvar_list[352] = nvar_352; + functions[353] = fn353; + nvar_list[353] = nvar_353; + functions[354] = fn354; + nvar_list[354] = nvar_354; + functions[355] = fn355; + nvar_list[355] = nvar_355; + functions[356] = fn356; + nvar_list[356] = nvar_356; + functions[357] = fn357; + nvar_list[357] = nvar_357; + functions[358] = fn358; + nvar_list[358] = nvar_358; + functions[359] = fn359; + nvar_list[359] = nvar_359; + functions[360] = fn360; + nvar_list[360] = nvar_360; + functions[361] = fn361; + nvar_list[361] = nvar_361; + functions[362] = fn362; + nvar_list[362] = nvar_362; + functions[363] = fn363; + nvar_list[363] = nvar_363; + functions[364] = fn364; + nvar_list[364] = nvar_364; + functions[365] = fn365; + nvar_list[365] = nvar_365; + functions[366] = fn366; + nvar_list[366] = nvar_366; + functions[367] = fn367; + nvar_list[367] = nvar_367; + functions[368] = fn368; + nvar_list[368] = nvar_368; + functions[369] = fn369; + nvar_list[369] = nvar_369; + functions[370] = fn370; + nvar_list[370] = nvar_370; + functions[371] = fn371; + nvar_list[371] = nvar_371; + functions[372] = fn372; + nvar_list[372] = nvar_372; + functions[373] = fn373; + nvar_list[373] = nvar_373; + functions[374] = fn374; + nvar_list[374] = nvar_374; + functions[375] = fn375; + nvar_list[375] = nvar_375; + functions[376] = fn376; + nvar_list[376] = nvar_376; + functions[377] = fn377; + nvar_list[377] = nvar_377; + functions[378] = fn378; + nvar_list[378] = nvar_378; + functions[379] = fn379; + nvar_list[379] = nvar_379; + functions[380] = fn380; + nvar_list[380] = nvar_380; + functions[381] = fn381; + nvar_list[381] = nvar_381; + functions[382] = fn382; + nvar_list[382] = nvar_382; + functions[383] = fn383; + nvar_list[383] = nvar_383; + functions[384] = fn384; + nvar_list[384] = nvar_384; + functions[385] = fn385; + nvar_list[385] = nvar_385; + functions[386] = fn386; + nvar_list[386] = nvar_386; + functions[387] = fn387; + nvar_list[387] = nvar_387; + functions[388] = fn388; + nvar_list[388] = nvar_388; + functions[389] = fn389; + nvar_list[389] = nvar_389; + functions[390] = fn390; + nvar_list[390] = nvar_390; + functions[391] = fn391; + nvar_list[391] = nvar_391; + functions[392] = fn392; + nvar_list[392] = nvar_392; + functions[393] = fn393; + nvar_list[393] = nvar_393; + functions[394] = fn394; + nvar_list[394] = nvar_394; + functions[395] = fn395; + nvar_list[395] = nvar_395; + functions[396] = fn396; + nvar_list[396] = nvar_396; + functions[397] = fn397; + nvar_list[397] = nvar_397; + functions[398] = fn398; + nvar_list[398] = nvar_398; + functions[399] = fn399; + nvar_list[399] = nvar_399; + functions[400] = fn400; + nvar_list[400] = nvar_400; + functions[401] = fn401; + nvar_list[401] = nvar_401; + functions[402] = fn402; + nvar_list[402] = nvar_402; + functions[403] = fn403; + nvar_list[403] = nvar_403; + functions[404] = fn404; + nvar_list[404] = nvar_404; + functions[405] = fn405; + nvar_list[405] = nvar_405; + functions[406] = fn406; + nvar_list[406] = nvar_406; + functions[407] = fn407; + nvar_list[407] = nvar_407; + functions[408] = fn408; + nvar_list[408] = nvar_408; + functions[409] = fn409; + nvar_list[409] = nvar_409; + functions[410] = fn410; + nvar_list[410] = nvar_410; + functions[411] = fn411; + nvar_list[411] = nvar_411; + functions[412] = fn412; + nvar_list[412] = nvar_412; + functions[413] = fn413; + nvar_list[413] = nvar_413; + functions[414] = fn414; + nvar_list[414] = nvar_414; + functions[415] = fn415; + nvar_list[415] = nvar_415; + functions[416] = fn416; + nvar_list[416] = nvar_416; + functions[417] = fn417; + nvar_list[417] = nvar_417; + functions[418] = fn418; + nvar_list[418] = nvar_418; + functions[419] = fn419; + nvar_list[419] = nvar_419; + functions[420] = fn420; + nvar_list[420] = nvar_420; + functions[421] = fn421; + nvar_list[421] = nvar_421; + functions[422] = fn422; + nvar_list[422] = nvar_422; + functions[423] = fn423; + nvar_list[423] = nvar_423; + functions[424] = fn424; + nvar_list[424] = nvar_424; + functions[425] = fn425; + nvar_list[425] = nvar_425; + functions[426] = fn426; + nvar_list[426] = nvar_426; + functions[427] = fn427; + nvar_list[427] = nvar_427; + functions[428] = fn428; + nvar_list[428] = nvar_428; + functions[429] = fn429; + nvar_list[429] = nvar_429; + functions[430] = fn430; + nvar_list[430] = nvar_430; + functions[431] = fn431; + nvar_list[431] = nvar_431; + functions[432] = fn432; + nvar_list[432] = nvar_432; + functions[433] = fn433; + nvar_list[433] = nvar_433; + functions[434] = fn434; + nvar_list[434] = nvar_434; + functions[435] = fn435; + nvar_list[435] = nvar_435; + functions[436] = fn436; + nvar_list[436] = nvar_436; + functions[437] = fn437; + nvar_list[437] = nvar_437; + functions[438] = fn438; + nvar_list[438] = nvar_438; + functions[439] = fn439; + nvar_list[439] = nvar_439; + functions[440] = fn440; + nvar_list[440] = nvar_440; + functions[441] = fn441; + nvar_list[441] = nvar_441; + functions[442] = fn442; + nvar_list[442] = nvar_442; + functions[443] = fn443; + nvar_list[443] = nvar_443; + functions[444] = fn444; + nvar_list[444] = nvar_444; + functions[445] = fn445; + nvar_list[445] = nvar_445; + functions[446] = fn446; + nvar_list[446] = nvar_446; + functions[447] = fn447; + nvar_list[447] = nvar_447; + functions[448] = fn448; + nvar_list[448] = nvar_448; + functions[449] = fn449; + nvar_list[449] = nvar_449; + functions[450] = fn450; + nvar_list[450] = nvar_450; + functions[451] = fn451; + nvar_list[451] = nvar_451; + functions[452] = fn452; + nvar_list[452] = nvar_452; + functions[453] = fn453; + nvar_list[453] = nvar_453; + functions[454] = fn454; + nvar_list[454] = nvar_454; + functions[455] = fn455; + nvar_list[455] = nvar_455; + functions[456] = fn456; + nvar_list[456] = nvar_456; + functions[457] = fn457; + nvar_list[457] = nvar_457; + functions[458] = fn458; + nvar_list[458] = nvar_458; + functions[459] = fn459; + nvar_list[459] = nvar_459; + functions[460] = fn460; + nvar_list[460] = nvar_460; + functions[461] = fn461; + nvar_list[461] = nvar_461; + functions[462] = fn462; + nvar_list[462] = nvar_462; + functions[463] = fn463; + nvar_list[463] = nvar_463; + functions[464] = fn464; + nvar_list[464] = nvar_464; + functions[465] = fn465; + nvar_list[465] = nvar_465; + functions[466] = fn466; + nvar_list[466] = nvar_466; + functions[467] = fn467; + nvar_list[467] = nvar_467; + functions[468] = fn468; + nvar_list[468] = nvar_468; + functions[469] = fn469; + nvar_list[469] = nvar_469; + functions[470] = fn470; + nvar_list[470] = nvar_470; + functions[471] = fn471; + nvar_list[471] = nvar_471; + functions[472] = fn472; + nvar_list[472] = nvar_472; + functions[473] = fn473; + nvar_list[473] = nvar_473; + functions[474] = fn474; + nvar_list[474] = nvar_474; + functions[475] = fn475; + nvar_list[475] = nvar_475; + functions[476] = fn476; + nvar_list[476] = nvar_476; + functions[477] = fn477; + nvar_list[477] = nvar_477; + functions[478] = fn478; + nvar_list[478] = nvar_478; + functions[479] = fn479; + nvar_list[479] = nvar_479; + functions[480] = fn480; + nvar_list[480] = nvar_480; + functions[481] = fn481; + nvar_list[481] = nvar_481; + functions[482] = fn482; + nvar_list[482] = nvar_482; + functions[483] = fn483; + nvar_list[483] = nvar_483; + functions[484] = fn484; + nvar_list[484] = nvar_484; + functions[485] = fn485; + nvar_list[485] = nvar_485; + functions[486] = fn486; + nvar_list[486] = nvar_486; + functions[487] = fn487; + nvar_list[487] = nvar_487; + functions[488] = fn488; + nvar_list[488] = nvar_488; + functions[489] = fn489; + nvar_list[489] = nvar_489; + functions[490] = fn490; + nvar_list[490] = nvar_490; + functions[491] = fn491; + nvar_list[491] = nvar_491; + functions[492] = fn492; + nvar_list[492] = nvar_492; + functions[493] = fn493; + nvar_list[493] = nvar_493; + functions[494] = fn494; + nvar_list[494] = nvar_494; + functions[495] = fn495; + nvar_list[495] = nvar_495; + functions[496] = fn496; + nvar_list[496] = nvar_496; + functions[497] = fn497; + nvar_list[497] = nvar_497; + functions[498] = fn498; + nvar_list[498] = nvar_498; + functions[499] = fn499; + nvar_list[499] = nvar_499; + functions[500] = fn500; + nvar_list[500] = nvar_500; + functions[501] = fn501; + nvar_list[501] = nvar_501; + functions[502] = fn502; + nvar_list[502] = nvar_502; + functions[503] = fn503; + nvar_list[503] = nvar_503; + functions[504] = fn504; + nvar_list[504] = nvar_504; + functions[505] = fn505; + nvar_list[505] = nvar_505; + functions[506] = fn506; + nvar_list[506] = nvar_506; + functions[507] = fn507; + nvar_list[507] = nvar_507; + functions[508] = fn508; + nvar_list[508] = nvar_508; + functions[509] = fn509; + nvar_list[509] = nvar_509; + functions[510] = fn510; + nvar_list[510] = nvar_510; + functions[511] = fn511; + nvar_list[511] = nvar_511; + functions[512] = fn512; + nvar_list[512] = nvar_512; + functions[513] = fn513; + nvar_list[513] = nvar_513; + functions[514] = fn514; + nvar_list[514] = nvar_514; + functions[515] = fn515; + nvar_list[515] = nvar_515; + functions[516] = fn516; + nvar_list[516] = nvar_516; + functions[517] = fn517; + nvar_list[517] = nvar_517; + functions[518] = fn518; + nvar_list[518] = nvar_518; + functions[519] = fn519; + nvar_list[519] = nvar_519; + functions[520] = fn520; + nvar_list[520] = nvar_520; + functions[521] = fn521; + nvar_list[521] = nvar_521; + functions[522] = fn522; + nvar_list[522] = nvar_522; + functions[523] = fn523; + nvar_list[523] = nvar_523; + functions[524] = fn524; + nvar_list[524] = nvar_524; + functions[525] = fn525; + nvar_list[525] = nvar_525; + functions[526] = fn526; + nvar_list[526] = nvar_526; + functions[527] = fn527; + nvar_list[527] = nvar_527; + functions[528] = fn528; + nvar_list[528] = nvar_528; + functions[529] = fn529; + nvar_list[529] = nvar_529; + functions[530] = fn530; + nvar_list[530] = nvar_530; + functions[531] = fn531; + nvar_list[531] = nvar_531; + functions[532] = fn532; + nvar_list[532] = nvar_532; + functions[533] = fn533; + nvar_list[533] = nvar_533; + functions[534] = fn534; + nvar_list[534] = nvar_534; + functions[535] = fn535; + nvar_list[535] = nvar_535; + functions[536] = fn536; + nvar_list[536] = nvar_536; + functions[537] = fn537; + nvar_list[537] = nvar_537; + functions[538] = fn538; + nvar_list[538] = nvar_538; + functions[539] = fn539; + nvar_list[539] = nvar_539; + functions[540] = fn540; + nvar_list[540] = nvar_540; + functions[541] = fn541; + nvar_list[541] = nvar_541; + functions[542] = fn542; + nvar_list[542] = nvar_542; + functions[543] = fn543; + nvar_list[543] = nvar_543; + functions[544] = fn544; + nvar_list[544] = nvar_544; + functions[545] = fn545; + nvar_list[545] = nvar_545; + functions[546] = fn546; + nvar_list[546] = nvar_546; + functions[547] = fn547; + nvar_list[547] = nvar_547; + functions[548] = fn548; + nvar_list[548] = nvar_548; + functions[549] = fn549; + nvar_list[549] = nvar_549; + functions[550] = fn550; + nvar_list[550] = nvar_550; + functions[551] = fn551; + nvar_list[551] = nvar_551; + functions[552] = fn552; + nvar_list[552] = nvar_552; + functions[553] = fn553; + nvar_list[553] = nvar_553; + functions[554] = fn554; + nvar_list[554] = nvar_554; + functions[555] = fn555; + nvar_list[555] = nvar_555; + functions[556] = fn556; + nvar_list[556] = nvar_556; + functions[557] = fn557; + nvar_list[557] = nvar_557; + functions[558] = fn558; + nvar_list[558] = nvar_558; + functions[559] = fn559; + nvar_list[559] = nvar_559; + functions[560] = fn560; + nvar_list[560] = nvar_560; + functions[561] = fn561; + nvar_list[561] = nvar_561; + functions[562] = fn562; + nvar_list[562] = nvar_562; + functions[563] = fn563; + nvar_list[563] = nvar_563; + functions[564] = fn564; + nvar_list[564] = nvar_564; + functions[565] = fn565; + nvar_list[565] = nvar_565; + functions[566] = fn566; + nvar_list[566] = nvar_566; + functions[567] = fn567; + nvar_list[567] = nvar_567; + functions[568] = fn568; + nvar_list[568] = nvar_568; + functions[569] = fn569; + nvar_list[569] = nvar_569; + functions[570] = fn570; + nvar_list[570] = nvar_570; + functions[571] = fn571; + nvar_list[571] = nvar_571; + functions[572] = fn572; + nvar_list[572] = nvar_572; + functions[573] = fn573; + nvar_list[573] = nvar_573; + functions[574] = fn574; + nvar_list[574] = nvar_574; + functions[575] = fn575; + nvar_list[575] = nvar_575; + functions[576] = fn576; + nvar_list[576] = nvar_576; + functions[577] = fn577; + nvar_list[577] = nvar_577; + functions[578] = fn578; + nvar_list[578] = nvar_578; + functions[579] = fn579; + nvar_list[579] = nvar_579; + functions[580] = fn580; + nvar_list[580] = nvar_580; + functions[581] = fn581; + nvar_list[581] = nvar_581; + functions[582] = fn582; + nvar_list[582] = nvar_582; + functions[583] = fn583; + nvar_list[583] = nvar_583; + functions[584] = fn584; + nvar_list[584] = nvar_584; + functions[585] = fn585; + nvar_list[585] = nvar_585; + functions[586] = fn586; + nvar_list[586] = nvar_586; + functions[587] = fn587; + nvar_list[587] = nvar_587; + functions[588] = fn588; + nvar_list[588] = nvar_588; + functions[589] = fn589; + nvar_list[589] = nvar_589; + functions[590] = fn590; + nvar_list[590] = nvar_590; + functions[591] = fn591; + nvar_list[591] = nvar_591; + functions[592] = fn592; + nvar_list[592] = nvar_592; + functions[593] = fn593; + nvar_list[593] = nvar_593; + functions[594] = fn594; + nvar_list[594] = nvar_594; + functions[595] = fn595; + nvar_list[595] = nvar_595; + functions[596] = fn596; + nvar_list[596] = nvar_596; + functions[597] = fn597; + nvar_list[597] = nvar_597; + functions[598] = fn598; + nvar_list[598] = nvar_598; + functions[599] = fn599; + nvar_list[599] = nvar_599; + functions[600] = fn600; + nvar_list[600] = nvar_600; + functions[601] = fn601; + nvar_list[601] = nvar_601; + functions[602] = fn602; + nvar_list[602] = nvar_602; + functions[603] = fn603; + nvar_list[603] = nvar_603; + functions[604] = fn604; + nvar_list[604] = nvar_604; + functions[605] = fn605; + nvar_list[605] = nvar_605; + functions[606] = fn606; + nvar_list[606] = nvar_606; + functions[607] = fn607; + nvar_list[607] = nvar_607; + functions[608] = fn608; + nvar_list[608] = nvar_608; + functions[609] = fn609; + nvar_list[609] = nvar_609; + functions[610] = fn610; + nvar_list[610] = nvar_610; + functions[611] = fn611; + nvar_list[611] = nvar_611; + functions[612] = fn612; + nvar_list[612] = nvar_612; + functions[613] = fn613; + nvar_list[613] = nvar_613; + functions[614] = fn614; + nvar_list[614] = nvar_614; + functions[615] = fn615; + nvar_list[615] = nvar_615; + functions[616] = fn616; + nvar_list[616] = nvar_616; + functions[617] = fn617; + nvar_list[617] = nvar_617; + functions[618] = fn618; + nvar_list[618] = nvar_618; + functions[619] = fn619; + nvar_list[619] = nvar_619; + functions[620] = fn620; + nvar_list[620] = nvar_620; + functions[621] = fn621; + nvar_list[621] = nvar_621; + functions[622] = fn622; + nvar_list[622] = nvar_622; + functions[623] = fn623; + nvar_list[623] = nvar_623; + functions[624] = fn624; + nvar_list[624] = nvar_624; + functions[625] = fn625; + nvar_list[625] = nvar_625; + functions[626] = fn626; + nvar_list[626] = nvar_626; + functions[627] = fn627; + nvar_list[627] = nvar_627; + functions[628] = fn628; + nvar_list[628] = nvar_628; + functions[629] = fn629; + nvar_list[629] = nvar_629; + functions[630] = fn630; + nvar_list[630] = nvar_630; + functions[631] = fn631; + nvar_list[631] = nvar_631; + functions[632] = fn632; + nvar_list[632] = nvar_632; + functions[633] = fn633; + nvar_list[633] = nvar_633; + functions[634] = fn634; + nvar_list[634] = nvar_634; + functions[635] = fn635; + nvar_list[635] = nvar_635; + functions[636] = fn636; + nvar_list[636] = nvar_636; + functions[637] = fn637; + nvar_list[637] = nvar_637; + functions[638] = fn638; + nvar_list[638] = nvar_638; + functions[639] = fn639; + nvar_list[639] = nvar_639; + functions[640] = fn640; + nvar_list[640] = nvar_640; + functions[641] = fn641; + nvar_list[641] = nvar_641; + functions[642] = fn642; + nvar_list[642] = nvar_642; + functions[643] = fn643; + nvar_list[643] = nvar_643; + functions[644] = fn644; + nvar_list[644] = nvar_644; + functions[645] = fn645; + nvar_list[645] = nvar_645; + functions[646] = fn646; + nvar_list[646] = nvar_646; + functions[647] = fn647; + nvar_list[647] = nvar_647; + functions[648] = fn648; + nvar_list[648] = nvar_648; + functions[649] = fn649; + nvar_list[649] = nvar_649; + functions[650] = fn650; + nvar_list[650] = nvar_650; + functions[651] = fn651; + nvar_list[651] = nvar_651; + functions[652] = fn652; + nvar_list[652] = nvar_652; + functions[653] = fn653; + nvar_list[653] = nvar_653; + functions[654] = fn654; + nvar_list[654] = nvar_654; + functions[655] = fn655; + nvar_list[655] = nvar_655; + functions[656] = fn656; + nvar_list[656] = nvar_656; + functions[657] = fn657; + nvar_list[657] = nvar_657; + functions[658] = fn658; + nvar_list[658] = nvar_658; + functions[659] = fn659; + nvar_list[659] = nvar_659; + functions[660] = fn660; + nvar_list[660] = nvar_660; + functions[661] = fn661; + nvar_list[661] = nvar_661; + functions[662] = fn662; + nvar_list[662] = nvar_662; + functions[663] = fn663; + nvar_list[663] = nvar_663; + functions[664] = fn664; + nvar_list[664] = nvar_664; + functions[665] = fn665; + nvar_list[665] = nvar_665; + functions[666] = fn666; + nvar_list[666] = nvar_666; + functions[667] = fn667; + nvar_list[667] = nvar_667; + functions[668] = fn668; + nvar_list[668] = nvar_668; + functions[669] = fn669; + nvar_list[669] = nvar_669; + functions[670] = fn670; + nvar_list[670] = nvar_670; + functions[671] = fn671; + nvar_list[671] = nvar_671; + functions[672] = fn672; + nvar_list[672] = nvar_672; + functions[673] = fn673; + nvar_list[673] = nvar_673; + functions[674] = fn674; + nvar_list[674] = nvar_674; + functions[675] = fn675; + nvar_list[675] = nvar_675; + functions[676] = fn676; + nvar_list[676] = nvar_676; + functions[677] = fn677; + nvar_list[677] = nvar_677; + functions[678] = fn678; + nvar_list[678] = nvar_678; + functions[679] = fn679; + nvar_list[679] = nvar_679; + functions[680] = fn680; + nvar_list[680] = nvar_680; + functions[681] = fn681; + nvar_list[681] = nvar_681; + functions[682] = fn682; + nvar_list[682] = nvar_682; + functions[683] = fn683; + nvar_list[683] = nvar_683; + functions[684] = fn684; + nvar_list[684] = nvar_684; + functions[685] = fn685; + nvar_list[685] = nvar_685; + functions[686] = fn686; + nvar_list[686] = nvar_686; + functions[687] = fn687; + nvar_list[687] = nvar_687; + functions[688] = fn688; + nvar_list[688] = nvar_688; + functions[689] = fn689; + nvar_list[689] = nvar_689; + functions[690] = fn690; + nvar_list[690] = nvar_690; + functions[691] = fn691; + nvar_list[691] = nvar_691; + functions[692] = fn692; + nvar_list[692] = nvar_692; + functions[693] = fn693; + nvar_list[693] = nvar_693; + functions[694] = fn694; + nvar_list[694] = nvar_694; + functions[695] = fn695; + nvar_list[695] = nvar_695; + functions[696] = fn696; + nvar_list[696] = nvar_696; + functions[697] = fn697; + nvar_list[697] = nvar_697; + functions[698] = fn698; + nvar_list[698] = nvar_698; + functions[699] = fn699; + nvar_list[699] = nvar_699; + functions[700] = fn700; + nvar_list[700] = nvar_700; + functions[701] = fn701; + nvar_list[701] = nvar_701; + functions[702] = fn702; + nvar_list[702] = nvar_702; + functions[703] = fn703; + nvar_list[703] = nvar_703; + functions[704] = fn704; + nvar_list[704] = nvar_704; + functions[705] = fn705; + nvar_list[705] = nvar_705; + functions[706] = fn706; + nvar_list[706] = nvar_706; + functions[707] = fn707; + nvar_list[707] = nvar_707; + functions[708] = fn708; + nvar_list[708] = nvar_708; + functions[709] = fn709; + nvar_list[709] = nvar_709; + functions[710] = fn710; + nvar_list[710] = nvar_710; + functions[711] = fn711; + nvar_list[711] = nvar_711; + functions[712] = fn712; + nvar_list[712] = nvar_712; + functions[713] = fn713; + nvar_list[713] = nvar_713; + functions[714] = fn714; + nvar_list[714] = nvar_714; + functions[715] = fn715; + nvar_list[715] = nvar_715; + functions[716] = fn716; + nvar_list[716] = nvar_716; + functions[717] = fn717; + nvar_list[717] = nvar_717; + functions[718] = fn718; + nvar_list[718] = nvar_718; + functions[719] = fn719; + nvar_list[719] = nvar_719; + functions[720] = fn720; + nvar_list[720] = nvar_720; + functions[721] = fn721; + nvar_list[721] = nvar_721; + functions[722] = fn722; + nvar_list[722] = nvar_722; + functions[723] = fn723; + nvar_list[723] = nvar_723; + functions[724] = fn724; + nvar_list[724] = nvar_724; + functions[725] = fn725; + nvar_list[725] = nvar_725; + functions[726] = fn726; + nvar_list[726] = nvar_726; + functions[727] = fn727; + nvar_list[727] = nvar_727; + functions[728] = fn728; + nvar_list[728] = nvar_728; + functions[729] = fn729; + nvar_list[729] = nvar_729; + functions[730] = fn730; + nvar_list[730] = nvar_730; + functions[731] = fn731; + nvar_list[731] = nvar_731; + functions[732] = fn732; + nvar_list[732] = nvar_732; + functions[733] = fn733; + nvar_list[733] = nvar_733; + functions[734] = fn734; + nvar_list[734] = nvar_734; + functions[735] = fn735; + nvar_list[735] = nvar_735; + functions[736] = fn736; + nvar_list[736] = nvar_736; + functions[737] = fn737; + nvar_list[737] = nvar_737; + functions[738] = fn738; + nvar_list[738] = nvar_738; + functions[739] = fn739; + nvar_list[739] = nvar_739; + functions[740] = fn740; + nvar_list[740] = nvar_740; + functions[741] = fn741; + nvar_list[741] = nvar_741; + functions[742] = fn742; + nvar_list[742] = nvar_742; + functions[743] = fn743; + nvar_list[743] = nvar_743; + functions[744] = fn744; + nvar_list[744] = nvar_744; + functions[745] = fn745; + nvar_list[745] = nvar_745; + functions[746] = fn746; + nvar_list[746] = nvar_746; + functions[747] = fn747; + nvar_list[747] = nvar_747; + functions[748] = fn748; + nvar_list[748] = nvar_748; + functions[749] = fn749; + nvar_list[749] = nvar_749; + functions[750] = fn750; + nvar_list[750] = nvar_750; + functions[751] = fn751; + nvar_list[751] = nvar_751; + functions[752] = fn752; + nvar_list[752] = nvar_752; + functions[753] = fn753; + nvar_list[753] = nvar_753; + functions[754] = fn754; + nvar_list[754] = nvar_754; + functions[755] = fn755; + nvar_list[755] = nvar_755; + functions[756] = fn756; + nvar_list[756] = nvar_756; + functions[757] = fn757; + nvar_list[757] = nvar_757; + functions[758] = fn758; + nvar_list[758] = nvar_758; + functions[759] = fn759; + nvar_list[759] = nvar_759; + functions[760] = fn760; + nvar_list[760] = nvar_760; + functions[761] = fn761; + nvar_list[761] = nvar_761; + functions[762] = fn762; + nvar_list[762] = nvar_762; + functions[763] = fn763; + nvar_list[763] = nvar_763; + functions[764] = fn764; + nvar_list[764] = nvar_764; + functions[765] = fn765; + nvar_list[765] = nvar_765; + functions[766] = fn766; + nvar_list[766] = nvar_766; + functions[767] = fn767; + nvar_list[767] = nvar_767; + functions[768] = fn768; + nvar_list[768] = nvar_768; + functions[769] = fn769; + nvar_list[769] = nvar_769; + functions[770] = fn770; + nvar_list[770] = nvar_770; + functions[771] = fn771; + nvar_list[771] = nvar_771; + functions[772] = fn772; + nvar_list[772] = nvar_772; + functions[773] = fn773; + nvar_list[773] = nvar_773; + functions[774] = fn774; + nvar_list[774] = nvar_774; + functions[775] = fn775; + nvar_list[775] = nvar_775; + functions[776] = fn776; + nvar_list[776] = nvar_776; + functions[777] = fn777; + nvar_list[777] = nvar_777; + functions[778] = fn778; + nvar_list[778] = nvar_778; + functions[779] = fn779; + nvar_list[779] = nvar_779; + functions[780] = fn780; + nvar_list[780] = nvar_780; + functions[781] = fn781; + nvar_list[781] = nvar_781; + functions[782] = fn782; + nvar_list[782] = nvar_782; + functions[783] = fn783; + nvar_list[783] = nvar_783; + functions[784] = fn784; + nvar_list[784] = nvar_784; + functions[785] = fn785; + nvar_list[785] = nvar_785; + functions[786] = fn786; + nvar_list[786] = nvar_786; + functions[787] = fn787; + nvar_list[787] = nvar_787; + functions[788] = fn788; + nvar_list[788] = nvar_788; + functions[789] = fn789; + nvar_list[789] = nvar_789; + functions[790] = fn790; + nvar_list[790] = nvar_790; + functions[791] = fn791; + nvar_list[791] = nvar_791; + functions[792] = fn792; + nvar_list[792] = nvar_792; + functions[793] = fn793; + nvar_list[793] = nvar_793; + functions[794] = fn794; + nvar_list[794] = nvar_794; + functions[795] = fn795; + nvar_list[795] = nvar_795; + functions[796] = fn796; + nvar_list[796] = nvar_796; + functions[797] = fn797; + nvar_list[797] = nvar_797; + functions[798] = fn798; + nvar_list[798] = nvar_798; + functions[799] = fn799; + nvar_list[799] = nvar_799; + functions[800] = fn800; + nvar_list[800] = nvar_800; + functions[801] = fn801; + nvar_list[801] = nvar_801; + functions[802] = fn802; + nvar_list[802] = nvar_802; + functions[803] = fn803; + nvar_list[803] = nvar_803; + functions[804] = fn804; + nvar_list[804] = nvar_804; + functions[805] = fn805; + nvar_list[805] = nvar_805; + functions[806] = fn806; + nvar_list[806] = nvar_806; + functions[807] = fn807; + nvar_list[807] = nvar_807; + functions[808] = fn808; + nvar_list[808] = nvar_808; + functions[809] = fn809; + nvar_list[809] = nvar_809; + functions[810] = fn810; + nvar_list[810] = nvar_810; + functions[811] = fn811; + nvar_list[811] = nvar_811; + functions[812] = fn812; + nvar_list[812] = nvar_812; + functions[813] = fn813; + nvar_list[813] = nvar_813; + functions[814] = fn814; + nvar_list[814] = nvar_814; + functions[815] = fn815; + nvar_list[815] = nvar_815; + functions[816] = fn816; + nvar_list[816] = nvar_816; + functions[817] = fn817; + nvar_list[817] = nvar_817; + functions[818] = fn818; + nvar_list[818] = nvar_818; + functions[819] = fn819; + nvar_list[819] = nvar_819; + functions[820] = fn820; + nvar_list[820] = nvar_820; + functions[821] = fn821; + nvar_list[821] = nvar_821; + functions[822] = fn822; + nvar_list[822] = nvar_822; + functions[823] = fn823; + nvar_list[823] = nvar_823; + functions[824] = fn824; + nvar_list[824] = nvar_824; + functions[825] = fn825; + nvar_list[825] = nvar_825; + functions[826] = fn826; + nvar_list[826] = nvar_826; + functions[827] = fn827; + nvar_list[827] = nvar_827; + functions[828] = fn828; + nvar_list[828] = nvar_828; + functions[829] = fn829; + nvar_list[829] = nvar_829; + functions[830] = fn830; + nvar_list[830] = nvar_830; + functions[831] = fn831; + nvar_list[831] = nvar_831; + functions[832] = fn832; + nvar_list[832] = nvar_832; + functions[833] = fn833; + nvar_list[833] = nvar_833; + functions[834] = fn834; + nvar_list[834] = nvar_834; + functions[835] = fn835; + nvar_list[835] = nvar_835; + functions[836] = fn836; + nvar_list[836] = nvar_836; + functions[837] = fn837; + nvar_list[837] = nvar_837; + functions[838] = fn838; + nvar_list[838] = nvar_838; + functions[839] = fn839; + nvar_list[839] = nvar_839; + functions[840] = fn840; + nvar_list[840] = nvar_840; + functions[841] = fn841; + nvar_list[841] = nvar_841; + functions[842] = fn842; + nvar_list[842] = nvar_842; + functions[843] = fn843; + nvar_list[843] = nvar_843; + functions[844] = fn844; + nvar_list[844] = nvar_844; + functions[845] = fn845; + nvar_list[845] = nvar_845; + functions[846] = fn846; + nvar_list[846] = nvar_846; + functions[847] = fn847; + nvar_list[847] = nvar_847; + functions[848] = fn848; + nvar_list[848] = nvar_848; + functions[849] = fn849; + nvar_list[849] = nvar_849; + functions[850] = fn850; + nvar_list[850] = nvar_850; + functions[851] = fn851; + nvar_list[851] = nvar_851; + functions[852] = fn852; + nvar_list[852] = nvar_852; + functions[853] = fn853; + nvar_list[853] = nvar_853; + functions[854] = fn854; + nvar_list[854] = nvar_854; + functions[855] = fn855; + nvar_list[855] = nvar_855; + functions[856] = fn856; + nvar_list[856] = nvar_856; + functions[857] = fn857; + nvar_list[857] = nvar_857; + functions[858] = fn858; + nvar_list[858] = nvar_858; + functions[859] = fn859; + nvar_list[859] = nvar_859; + functions[860] = fn860; + nvar_list[860] = nvar_860; + functions[861] = fn861; + nvar_list[861] = nvar_861; + functions[862] = fn862; + nvar_list[862] = nvar_862; + functions[863] = fn863; + nvar_list[863] = nvar_863; + functions[864] = fn864; + nvar_list[864] = nvar_864; + functions[865] = fn865; + nvar_list[865] = nvar_865; + functions[866] = fn866; + nvar_list[866] = nvar_866; + functions[867] = fn867; + nvar_list[867] = nvar_867; + functions[868] = fn868; + nvar_list[868] = nvar_868; + functions[869] = fn869; + nvar_list[869] = nvar_869; + functions[870] = fn870; + nvar_list[870] = nvar_870; + functions[871] = fn871; + nvar_list[871] = nvar_871; + functions[872] = fn872; + nvar_list[872] = nvar_872; + functions[873] = fn873; + nvar_list[873] = nvar_873; + functions[874] = fn874; + nvar_list[874] = nvar_874; + functions[875] = fn875; + nvar_list[875] = nvar_875; + functions[876] = fn876; + nvar_list[876] = nvar_876; + functions[877] = fn877; + nvar_list[877] = nvar_877; + functions[878] = fn878; + nvar_list[878] = nvar_878; + functions[879] = fn879; + nvar_list[879] = nvar_879; + functions[880] = fn880; + nvar_list[880] = nvar_880; + functions[881] = fn881; + nvar_list[881] = nvar_881; + functions[882] = fn882; + nvar_list[882] = nvar_882; + functions[883] = fn883; + nvar_list[883] = nvar_883; + functions[884] = fn884; + nvar_list[884] = nvar_884; + functions[885] = fn885; + nvar_list[885] = nvar_885; + functions[886] = fn886; + nvar_list[886] = nvar_886; + functions[887] = fn887; + nvar_list[887] = nvar_887; + functions[888] = fn888; + nvar_list[888] = nvar_888; + functions[889] = fn889; + nvar_list[889] = nvar_889; + functions[890] = fn890; + nvar_list[890] = nvar_890; + functions[891] = fn891; + nvar_list[891] = nvar_891; + functions[892] = fn892; + nvar_list[892] = nvar_892; + functions[893] = fn893; + nvar_list[893] = nvar_893; + functions[894] = fn894; + nvar_list[894] = nvar_894; + functions[895] = fn895; + nvar_list[895] = nvar_895; + functions[896] = fn896; + nvar_list[896] = nvar_896; + functions[897] = fn897; + nvar_list[897] = nvar_897; + functions[898] = fn898; + nvar_list[898] = nvar_898; + functions[899] = fn899; + nvar_list[899] = nvar_899; + functions[900] = fn900; + nvar_list[900] = nvar_900; + functions[901] = fn901; + nvar_list[901] = nvar_901; + functions[902] = fn902; + nvar_list[902] = nvar_902; + functions[903] = fn903; + nvar_list[903] = nvar_903; + functions[904] = fn904; + nvar_list[904] = nvar_904; + functions[905] = fn905; + nvar_list[905] = nvar_905; + functions[906] = fn906; + nvar_list[906] = nvar_906; + functions[907] = fn907; + nvar_list[907] = nvar_907; + functions[908] = fn908; + nvar_list[908] = nvar_908; + functions[909] = fn909; + nvar_list[909] = nvar_909; + functions[910] = fn910; + nvar_list[910] = nvar_910; + functions[911] = fn911; + nvar_list[911] = nvar_911; + functions[912] = fn912; + nvar_list[912] = nvar_912; + functions[913] = fn913; + nvar_list[913] = nvar_913; + functions[914] = fn914; + nvar_list[914] = nvar_914; + functions[915] = fn915; + nvar_list[915] = nvar_915; + functions[916] = fn916; + nvar_list[916] = nvar_916; + functions[917] = fn917; + nvar_list[917] = nvar_917; + functions[918] = fn918; + nvar_list[918] = nvar_918; + functions[919] = fn919; + nvar_list[919] = nvar_919; + functions[920] = fn920; + nvar_list[920] = nvar_920; + functions[921] = fn921; + nvar_list[921] = nvar_921; + functions[922] = fn922; + nvar_list[922] = nvar_922; + functions[923] = fn923; + nvar_list[923] = nvar_923; + functions[924] = fn924; + nvar_list[924] = nvar_924; + functions[925] = fn925; + nvar_list[925] = nvar_925; + functions[926] = fn926; + nvar_list[926] = nvar_926; + functions[927] = fn927; + nvar_list[927] = nvar_927; + functions[928] = fn928; + nvar_list[928] = nvar_928; + functions[929] = fn929; + nvar_list[929] = nvar_929; + functions[930] = fn930; + nvar_list[930] = nvar_930; + functions[931] = fn931; + nvar_list[931] = nvar_931; + functions[932] = fn932; + nvar_list[932] = nvar_932; + functions[933] = fn933; + nvar_list[933] = nvar_933; + functions[934] = fn934; + nvar_list[934] = nvar_934; + functions[935] = fn935; + nvar_list[935] = nvar_935; + functions[936] = fn936; + nvar_list[936] = nvar_936; + functions[937] = fn937; + nvar_list[937] = nvar_937; + functions[938] = fn938; + nvar_list[938] = nvar_938; + functions[939] = fn939; + nvar_list[939] = nvar_939; + functions[940] = fn940; + nvar_list[940] = nvar_940; + functions[941] = fn941; + nvar_list[941] = nvar_941; + functions[942] = fn942; + nvar_list[942] = nvar_942; + functions[943] = fn943; + nvar_list[943] = nvar_943; + functions[944] = fn944; + nvar_list[944] = nvar_944; + functions[945] = fn945; + nvar_list[945] = nvar_945; + functions[946] = fn946; + nvar_list[946] = nvar_946; + functions[947] = fn947; + nvar_list[947] = nvar_947; + functions[948] = fn948; + nvar_list[948] = nvar_948; + functions[949] = fn949; + nvar_list[949] = nvar_949; + functions[950] = fn950; + nvar_list[950] = nvar_950; + functions[951] = fn951; + nvar_list[951] = nvar_951; + functions[952] = fn952; + nvar_list[952] = nvar_952; + functions[953] = fn953; + nvar_list[953] = nvar_953; + functions[954] = fn954; + nvar_list[954] = nvar_954; + functions[955] = fn955; + nvar_list[955] = nvar_955; + functions[956] = fn956; + nvar_list[956] = nvar_956; + functions[957] = fn957; + nvar_list[957] = nvar_957; + functions[958] = fn958; + nvar_list[958] = nvar_958; + functions[959] = fn959; + nvar_list[959] = nvar_959; + functions[960] = fn960; + nvar_list[960] = nvar_960; + functions[961] = fn961; + nvar_list[961] = nvar_961; + functions[962] = fn962; + nvar_list[962] = nvar_962; + functions[963] = fn963; + nvar_list[963] = nvar_963; + functions[964] = fn964; + nvar_list[964] = nvar_964; + functions[965] = fn965; + nvar_list[965] = nvar_965; + functions[966] = fn966; + nvar_list[966] = nvar_966; + functions[967] = fn967; + nvar_list[967] = nvar_967; + functions[968] = fn968; + nvar_list[968] = nvar_968; + functions[969] = fn969; + nvar_list[969] = nvar_969; + functions[970] = fn970; + nvar_list[970] = nvar_970; + functions[971] = fn971; + nvar_list[971] = nvar_971; + functions[972] = fn972; + nvar_list[972] = nvar_972; + functions[973] = fn973; + nvar_list[973] = nvar_973; + functions[974] = fn974; + nvar_list[974] = nvar_974; + functions[975] = fn975; + nvar_list[975] = nvar_975; + functions[976] = fn976; + nvar_list[976] = nvar_976; + functions[977] = fn977; + nvar_list[977] = nvar_977; + functions[978] = fn978; + nvar_list[978] = nvar_978; + functions[979] = fn979; + nvar_list[979] = nvar_979; + functions[980] = fn980; + nvar_list[980] = nvar_980; + functions[981] = fn981; + nvar_list[981] = nvar_981; + functions[982] = fn982; + nvar_list[982] = nvar_982; + functions[983] = fn983; + nvar_list[983] = nvar_983; + functions[984] = fn984; + nvar_list[984] = nvar_984; + functions[985] = fn985; + nvar_list[985] = nvar_985; + functions[986] = fn986; + nvar_list[986] = nvar_986; + functions[987] = fn987; + nvar_list[987] = nvar_987; + functions[988] = fn988; + nvar_list[988] = nvar_988; + functions[989] = fn989; + nvar_list[989] = nvar_989; + functions[990] = fn990; + nvar_list[990] = nvar_990; + functions[991] = fn991; + nvar_list[991] = nvar_991; + functions[992] = fn992; + nvar_list[992] = nvar_992; + functions[993] = fn993; + nvar_list[993] = nvar_993; + functions[994] = fn994; + nvar_list[994] = nvar_994; + functions[995] = fn995; + nvar_list[995] = nvar_995; + functions[996] = fn996; + nvar_list[996] = nvar_996; + functions[997] = fn997; + nvar_list[997] = nvar_997; + functions[998] = fn998; + nvar_list[998] = nvar_998; + functions[999] = fn999; + nvar_list[999] = nvar_999; + functions[1000] = fn1000; + nvar_list[1000] = nvar_1000; + functions[1001] = fn1001; + nvar_list[1001] = nvar_1001; + functions[1002] = fn1002; + nvar_list[1002] = nvar_1002; + functions[1003] = fn1003; + nvar_list[1003] = nvar_1003; + functions[1004] = fn1004; + nvar_list[1004] = nvar_1004; + functions[1005] = fn1005; + nvar_list[1005] = nvar_1005; + functions[1006] = fn1006; + nvar_list[1006] = nvar_1006; + functions[1007] = fn1007; + nvar_list[1007] = nvar_1007; + functions[1008] = fn1008; + nvar_list[1008] = nvar_1008; + functions[1009] = fn1009; + nvar_list[1009] = nvar_1009; + functions[1010] = fn1010; + nvar_list[1010] = nvar_1010; + functions[1011] = fn1011; + nvar_list[1011] = nvar_1011; + functions[1012] = fn1012; + nvar_list[1012] = nvar_1012; + functions[1013] = fn1013; + nvar_list[1013] = nvar_1013; + functions[1014] = fn1014; + nvar_list[1014] = nvar_1014; + functions[1015] = fn1015; + nvar_list[1015] = nvar_1015; + functions[1016] = fn1016; + nvar_list[1016] = nvar_1016; + functions[1017] = fn1017; + nvar_list[1017] = nvar_1017; + functions[1018] = fn1018; + nvar_list[1018] = nvar_1018; + functions[1019] = fn1019; + nvar_list[1019] = nvar_1019; + functions[1020] = fn1020; + nvar_list[1020] = nvar_1020; + functions[1021] = fn1021; + nvar_list[1021] = nvar_1021; + functions[1022] = fn1022; + nvar_list[1022] = nvar_1022; + functions[1023] = fn1023; + nvar_list[1023] = nvar_1023; + functions[1024] = fn1024; + nvar_list[1024] = nvar_1024; + functions[1025] = fn1025; + nvar_list[1025] = nvar_1025; + functions[1026] = fn1026; + nvar_list[1026] = nvar_1026; + functions[1027] = fn1027; + nvar_list[1027] = nvar_1027; + functions[1028] = fn1028; + nvar_list[1028] = nvar_1028; + functions[1029] = fn1029; + nvar_list[1029] = nvar_1029; + functions[1030] = fn1030; + nvar_list[1030] = nvar_1030; + functions[1031] = fn1031; + nvar_list[1031] = nvar_1031; + functions[1032] = fn1032; + nvar_list[1032] = nvar_1032; + functions[1033] = fn1033; + nvar_list[1033] = nvar_1033; + functions[1034] = fn1034; + nvar_list[1034] = nvar_1034; + functions[1035] = fn1035; + nvar_list[1035] = nvar_1035; + functions[1036] = fn1036; + nvar_list[1036] = nvar_1036; + functions[1037] = fn1037; + nvar_list[1037] = nvar_1037; + functions[1038] = fn1038; + nvar_list[1038] = nvar_1038; + functions[1039] = fn1039; + nvar_list[1039] = nvar_1039; + functions[1040] = fn1040; + nvar_list[1040] = nvar_1040; + functions[1041] = fn1041; + nvar_list[1041] = nvar_1041; + functions[1042] = fn1042; + nvar_list[1042] = nvar_1042; + functions[1043] = fn1043; + nvar_list[1043] = nvar_1043; + functions[1044] = fn1044; + nvar_list[1044] = nvar_1044; + functions[1045] = fn1045; + nvar_list[1045] = nvar_1045; + functions[1046] = fn1046; + nvar_list[1046] = nvar_1046; + functions[1047] = fn1047; + nvar_list[1047] = nvar_1047; + functions[1048] = fn1048; + nvar_list[1048] = nvar_1048; + functions[1049] = fn1049; + nvar_list[1049] = nvar_1049; + functions[1050] = fn1050; + nvar_list[1050] = nvar_1050; + functions[1051] = fn1051; + nvar_list[1051] = nvar_1051; + functions[1052] = fn1052; + nvar_list[1052] = nvar_1052; + functions[1053] = fn1053; + nvar_list[1053] = nvar_1053; + functions[1054] = fn1054; + nvar_list[1054] = nvar_1054; + functions[1055] = fn1055; + nvar_list[1055] = nvar_1055; + functions[1056] = fn1056; + nvar_list[1056] = nvar_1056; + functions[1057] = fn1057; + nvar_list[1057] = nvar_1057; + functions[1058] = fn1058; + nvar_list[1058] = nvar_1058; + functions[1059] = fn1059; + nvar_list[1059] = nvar_1059; + functions[1060] = fn1060; + nvar_list[1060] = nvar_1060; + functions[1061] = fn1061; + nvar_list[1061] = nvar_1061; + functions[1062] = fn1062; + nvar_list[1062] = nvar_1062; + functions[1063] = fn1063; + nvar_list[1063] = nvar_1063; + functions[1064] = fn1064; + nvar_list[1064] = nvar_1064; + functions[1065] = fn1065; + nvar_list[1065] = nvar_1065; + functions[1066] = fn1066; + nvar_list[1066] = nvar_1066; + functions[1067] = fn1067; + nvar_list[1067] = nvar_1067; + functions[1068] = fn1068; + nvar_list[1068] = nvar_1068; + functions[1069] = fn1069; + nvar_list[1069] = nvar_1069; + functions[1070] = fn1070; + nvar_list[1070] = nvar_1070; + functions[1071] = fn1071; + nvar_list[1071] = nvar_1071; + functions[1072] = fn1072; + nvar_list[1072] = nvar_1072; + functions[1073] = fn1073; + nvar_list[1073] = nvar_1073; + functions[1074] = fn1074; + nvar_list[1074] = nvar_1074; + functions[1075] = fn1075; + nvar_list[1075] = nvar_1075; + functions[1076] = fn1076; + nvar_list[1076] = nvar_1076; + functions[1077] = fn1077; + nvar_list[1077] = nvar_1077; + functions[1078] = fn1078; + nvar_list[1078] = nvar_1078; + functions[1079] = fn1079; + nvar_list[1079] = nvar_1079; + functions[1080] = fn1080; + nvar_list[1080] = nvar_1080; + functions[1081] = fn1081; + nvar_list[1081] = nvar_1081; + functions[1082] = fn1082; + nvar_list[1082] = nvar_1082; + functions[1083] = fn1083; + nvar_list[1083] = nvar_1083; + functions[1084] = fn1084; + nvar_list[1084] = nvar_1084; + functions[1085] = fn1085; + nvar_list[1085] = nvar_1085; + functions[1086] = fn1086; + nvar_list[1086] = nvar_1086; + functions[1087] = fn1087; + nvar_list[1087] = nvar_1087; + functions[1088] = fn1088; + nvar_list[1088] = nvar_1088; + functions[1089] = fn1089; + nvar_list[1089] = nvar_1089; + functions[1090] = fn1090; + nvar_list[1090] = nvar_1090; + functions[1091] = fn1091; + nvar_list[1091] = nvar_1091; + functions[1092] = fn1092; + nvar_list[1092] = nvar_1092; + functions[1093] = fn1093; + nvar_list[1093] = nvar_1093; + functions[1094] = fn1094; + nvar_list[1094] = nvar_1094; + functions[1095] = fn1095; + nvar_list[1095] = nvar_1095; + functions[1096] = fn1096; + nvar_list[1096] = nvar_1096; + functions[1097] = fn1097; + nvar_list[1097] = nvar_1097; + functions[1098] = fn1098; + nvar_list[1098] = nvar_1098; + functions[1099] = fn1099; + nvar_list[1099] = nvar_1099; + functions[1100] = fn1100; + nvar_list[1100] = nvar_1100; + functions[1101] = fn1101; + nvar_list[1101] = nvar_1101; + functions[1102] = fn1102; + nvar_list[1102] = nvar_1102; + functions[1103] = fn1103; + nvar_list[1103] = nvar_1103; + functions[1104] = fn1104; + nvar_list[1104] = nvar_1104; + functions[1105] = fn1105; + nvar_list[1105] = nvar_1105; + functions[1106] = fn1106; + nvar_list[1106] = nvar_1106; + functions[1107] = fn1107; + nvar_list[1107] = nvar_1107; + functions[1108] = fn1108; + nvar_list[1108] = nvar_1108; + functions[1109] = fn1109; + nvar_list[1109] = nvar_1109; + functions[1110] = fn1110; + nvar_list[1110] = nvar_1110; + functions[1111] = fn1111; + nvar_list[1111] = nvar_1111; + functions[1112] = fn1112; + nvar_list[1112] = nvar_1112; + functions[1113] = fn1113; + nvar_list[1113] = nvar_1113; + functions[1114] = fn1114; + nvar_list[1114] = nvar_1114; + functions[1115] = fn1115; + nvar_list[1115] = nvar_1115; + functions[1116] = fn1116; + nvar_list[1116] = nvar_1116; + functions[1117] = fn1117; + nvar_list[1117] = nvar_1117; + functions[1118] = fn1118; + nvar_list[1118] = nvar_1118; + functions[1119] = fn1119; + nvar_list[1119] = nvar_1119; + functions[1120] = fn1120; + nvar_list[1120] = nvar_1120; + functions[1121] = fn1121; + nvar_list[1121] = nvar_1121; + functions[1122] = fn1122; + nvar_list[1122] = nvar_1122; + functions[1123] = fn1123; + nvar_list[1123] = nvar_1123; + functions[1124] = fn1124; + nvar_list[1124] = nvar_1124; + functions[1125] = fn1125; + nvar_list[1125] = nvar_1125; + functions[1126] = fn1126; + nvar_list[1126] = nvar_1126; + functions[1127] = fn1127; + nvar_list[1127] = nvar_1127; + functions[1128] = fn1128; + nvar_list[1128] = nvar_1128; + functions[1129] = fn1129; + nvar_list[1129] = nvar_1129; + functions[1130] = fn1130; + nvar_list[1130] = nvar_1130; + functions[1131] = fn1131; + nvar_list[1131] = nvar_1131; + functions[1132] = fn1132; + nvar_list[1132] = nvar_1132; + functions[1133] = fn1133; + nvar_list[1133] = nvar_1133; + functions[1134] = fn1134; + nvar_list[1134] = nvar_1134; + functions[1135] = fn1135; + nvar_list[1135] = nvar_1135; + functions[1136] = fn1136; + nvar_list[1136] = nvar_1136; + functions[1137] = fn1137; + nvar_list[1137] = nvar_1137; + functions[1138] = fn1138; + nvar_list[1138] = nvar_1138; + functions[1139] = fn1139; + nvar_list[1139] = nvar_1139; + functions[1140] = fn1140; + nvar_list[1140] = nvar_1140; + functions[1141] = fn1141; + nvar_list[1141] = nvar_1141; + functions[1142] = fn1142; + nvar_list[1142] = nvar_1142; + functions[1143] = fn1143; + nvar_list[1143] = nvar_1143; + functions[1144] = fn1144; + nvar_list[1144] = nvar_1144; + functions[1145] = fn1145; + nvar_list[1145] = nvar_1145; + functions[1146] = fn1146; + nvar_list[1146] = nvar_1146; + functions[1147] = fn1147; + nvar_list[1147] = nvar_1147; + functions[1148] = fn1148; + nvar_list[1148] = nvar_1148; + functions[1149] = fn1149; + nvar_list[1149] = nvar_1149; + functions[1150] = fn1150; + nvar_list[1150] = nvar_1150; + functions[1151] = fn1151; + nvar_list[1151] = nvar_1151; + functions[1152] = fn1152; + nvar_list[1152] = nvar_1152; + functions[1153] = fn1153; + nvar_list[1153] = nvar_1153; + functions[1154] = fn1154; + nvar_list[1154] = nvar_1154; + functions[1155] = fn1155; + nvar_list[1155] = nvar_1155; + functions[1156] = fn1156; + nvar_list[1156] = nvar_1156; + functions[1157] = fn1157; + nvar_list[1157] = nvar_1157; + functions[1158] = fn1158; + nvar_list[1158] = nvar_1158; + functions[1159] = fn1159; + nvar_list[1159] = nvar_1159; + functions[1160] = fn1160; + nvar_list[1160] = nvar_1160; + functions[1161] = fn1161; + nvar_list[1161] = nvar_1161; + functions[1162] = fn1162; + nvar_list[1162] = nvar_1162; + functions[1163] = fn1163; + nvar_list[1163] = nvar_1163; + functions[1164] = fn1164; + nvar_list[1164] = nvar_1164; + functions[1165] = fn1165; + nvar_list[1165] = nvar_1165; + functions[1166] = fn1166; + nvar_list[1166] = nvar_1166; + functions[1167] = fn1167; + nvar_list[1167] = nvar_1167; + functions[1168] = fn1168; + nvar_list[1168] = nvar_1168; + functions[1169] = fn1169; + nvar_list[1169] = nvar_1169; + functions[1170] = fn1170; + nvar_list[1170] = nvar_1170; + functions[1171] = fn1171; + nvar_list[1171] = nvar_1171; + functions[1172] = fn1172; + nvar_list[1172] = nvar_1172; + functions[1173] = fn1173; + nvar_list[1173] = nvar_1173; + functions[1174] = fn1174; + nvar_list[1174] = nvar_1174; + functions[1175] = fn1175; + nvar_list[1175] = nvar_1175; + functions[1176] = fn1176; + nvar_list[1176] = nvar_1176; + functions[1177] = fn1177; + nvar_list[1177] = nvar_1177; + functions[1178] = fn1178; + nvar_list[1178] = nvar_1178; + functions[1179] = fn1179; + nvar_list[1179] = nvar_1179; + functions[1180] = fn1180; + nvar_list[1180] = nvar_1180; + functions[1181] = fn1181; + nvar_list[1181] = nvar_1181; + functions[1182] = fn1182; + nvar_list[1182] = nvar_1182; + functions[1183] = fn1183; + nvar_list[1183] = nvar_1183; + functions[1184] = fn1184; + nvar_list[1184] = nvar_1184; + functions[1185] = fn1185; + nvar_list[1185] = nvar_1185; + functions[1186] = fn1186; + nvar_list[1186] = nvar_1186; + functions[1187] = fn1187; + nvar_list[1187] = nvar_1187; + functions[1188] = fn1188; + nvar_list[1188] = nvar_1188; + functions[1189] = fn1189; + nvar_list[1189] = nvar_1189; + functions[1190] = fn1190; + nvar_list[1190] = nvar_1190; + functions[1191] = fn1191; + nvar_list[1191] = nvar_1191; + functions[1192] = fn1192; + nvar_list[1192] = nvar_1192; + functions[1193] = fn1193; + nvar_list[1193] = nvar_1193; + functions[1194] = fn1194; + nvar_list[1194] = nvar_1194; + functions[1195] = fn1195; + nvar_list[1195] = nvar_1195; + functions[1196] = fn1196; + nvar_list[1196] = nvar_1196; + functions[1197] = fn1197; + nvar_list[1197] = nvar_1197; + functions[1198] = fn1198; + nvar_list[1198] = nvar_1198; + functions[1199] = fn1199; + nvar_list[1199] = nvar_1199; + functions[1200] = fn1200; + nvar_list[1200] = nvar_1200; + functions[1201] = fn1201; + nvar_list[1201] = nvar_1201; + functions[1202] = fn1202; + nvar_list[1202] = nvar_1202; + functions[1203] = fn1203; + nvar_list[1203] = nvar_1203; + functions[1204] = fn1204; + nvar_list[1204] = nvar_1204; + functions[1205] = fn1205; + nvar_list[1205] = nvar_1205; + functions[1206] = fn1206; + nvar_list[1206] = nvar_1206; + functions[1207] = fn1207; + nvar_list[1207] = nvar_1207; + functions[1208] = fn1208; + nvar_list[1208] = nvar_1208; + functions[1209] = fn1209; + nvar_list[1209] = nvar_1209; + functions[1210] = fn1210; + nvar_list[1210] = nvar_1210; + functions[1211] = fn1211; + nvar_list[1211] = nvar_1211; + functions[1212] = fn1212; + nvar_list[1212] = nvar_1212; + functions[1213] = fn1213; + nvar_list[1213] = nvar_1213; + functions[1214] = fn1214; + nvar_list[1214] = nvar_1214; + functions[1215] = fn1215; + nvar_list[1215] = nvar_1215; + functions[1216] = fn1216; + nvar_list[1216] = nvar_1216; + functions[1217] = fn1217; + nvar_list[1217] = nvar_1217; + functions[1218] = fn1218; + nvar_list[1218] = nvar_1218; + functions[1219] = fn1219; + nvar_list[1219] = nvar_1219; + functions[1220] = fn1220; + nvar_list[1220] = nvar_1220; + functions[1221] = fn1221; + nvar_list[1221] = nvar_1221; + functions[1222] = fn1222; + nvar_list[1222] = nvar_1222; + functions[1223] = fn1223; + nvar_list[1223] = nvar_1223; + functions[1224] = fn1224; + nvar_list[1224] = nvar_1224; + functions[1225] = fn1225; + nvar_list[1225] = nvar_1225; + functions[1226] = fn1226; + nvar_list[1226] = nvar_1226; + functions[1227] = fn1227; + nvar_list[1227] = nvar_1227; + functions[1228] = fn1228; + nvar_list[1228] = nvar_1228; + functions[1229] = fn1229; + nvar_list[1229] = nvar_1229; + functions[1230] = fn1230; + nvar_list[1230] = nvar_1230; + functions[1231] = fn1231; + nvar_list[1231] = nvar_1231; + functions[1232] = fn1232; + nvar_list[1232] = nvar_1232; + functions[1233] = fn1233; + nvar_list[1233] = nvar_1233; + functions[1234] = fn1234; + nvar_list[1234] = nvar_1234; + functions[1235] = fn1235; + nvar_list[1235] = nvar_1235; + functions[1236] = fn1236; + nvar_list[1236] = nvar_1236; + functions[1237] = fn1237; + nvar_list[1237] = nvar_1237; + functions[1238] = fn1238; + nvar_list[1238] = nvar_1238; + functions[1239] = fn1239; + nvar_list[1239] = nvar_1239; + functions[1240] = fn1240; + nvar_list[1240] = nvar_1240; + functions[1241] = fn1241; + nvar_list[1241] = nvar_1241; + functions[1242] = fn1242; + nvar_list[1242] = nvar_1242; + functions[1243] = fn1243; + nvar_list[1243] = nvar_1243; + functions[1244] = fn1244; + nvar_list[1244] = nvar_1244; + functions[1245] = fn1245; + nvar_list[1245] = nvar_1245; + functions[1246] = fn1246; + nvar_list[1246] = nvar_1246; + functions[1247] = fn1247; + nvar_list[1247] = nvar_1247; + functions[1248] = fn1248; + nvar_list[1248] = nvar_1248; + functions[1249] = fn1249; + nvar_list[1249] = nvar_1249; + functions[1250] = fn1250; + nvar_list[1250] = nvar_1250; + functions[1251] = fn1251; + nvar_list[1251] = nvar_1251; + functions[1252] = fn1252; + nvar_list[1252] = nvar_1252; + functions[1253] = fn1253; + nvar_list[1253] = nvar_1253; + functions[1254] = fn1254; + nvar_list[1254] = nvar_1254; + functions[1255] = fn1255; + nvar_list[1255] = nvar_1255; + functions[1256] = fn1256; + nvar_list[1256] = nvar_1256; + functions[1257] = fn1257; + nvar_list[1257] = nvar_1257; + functions[1258] = fn1258; + nvar_list[1258] = nvar_1258; + functions[1259] = fn1259; + nvar_list[1259] = nvar_1259; + functions[1260] = fn1260; + nvar_list[1260] = nvar_1260; + functions[1261] = fn1261; + nvar_list[1261] = nvar_1261; + functions[1262] = fn1262; + nvar_list[1262] = nvar_1262; + functions[1263] = fn1263; + nvar_list[1263] = nvar_1263; + functions[1264] = fn1264; + nvar_list[1264] = nvar_1264; + functions[1265] = fn1265; + nvar_list[1265] = nvar_1265; + functions[1266] = fn1266; + nvar_list[1266] = nvar_1266; + functions[1267] = fn1267; + nvar_list[1267] = nvar_1267; + functions[1268] = fn1268; + nvar_list[1268] = nvar_1268; + functions[1269] = fn1269; + nvar_list[1269] = nvar_1269; + functions[1270] = fn1270; + nvar_list[1270] = nvar_1270; + functions[1271] = fn1271; + nvar_list[1271] = nvar_1271; + functions[1272] = fn1272; + nvar_list[1272] = nvar_1272; + functions[1273] = fn1273; + nvar_list[1273] = nvar_1273; + functions[1274] = fn1274; + nvar_list[1274] = nvar_1274; + functions[1275] = fn1275; + nvar_list[1275] = nvar_1275; + functions[1276] = fn1276; + nvar_list[1276] = nvar_1276; + functions[1277] = fn1277; + nvar_list[1277] = nvar_1277; + functions[1278] = fn1278; + nvar_list[1278] = nvar_1278; + functions[1279] = fn1279; + nvar_list[1279] = nvar_1279; + functions[1280] = fn1280; + nvar_list[1280] = nvar_1280; + functions[1281] = fn1281; + nvar_list[1281] = nvar_1281; + functions[1282] = fn1282; + nvar_list[1282] = nvar_1282; + functions[1283] = fn1283; + nvar_list[1283] = nvar_1283; + functions[1284] = fn1284; + nvar_list[1284] = nvar_1284; + functions[1285] = fn1285; + nvar_list[1285] = nvar_1285; + functions[1286] = fn1286; + nvar_list[1286] = nvar_1286; + functions[1287] = fn1287; + nvar_list[1287] = nvar_1287; + functions[1288] = fn1288; + nvar_list[1288] = nvar_1288; + functions[1289] = fn1289; + nvar_list[1289] = nvar_1289; + functions[1290] = fn1290; + nvar_list[1290] = nvar_1290; + functions[1291] = fn1291; + nvar_list[1291] = nvar_1291; + functions[1292] = fn1292; + nvar_list[1292] = nvar_1292; + functions[1293] = fn1293; + nvar_list[1293] = nvar_1293; + functions[1294] = fn1294; + nvar_list[1294] = nvar_1294; + functions[1295] = fn1295; + nvar_list[1295] = nvar_1295; + functions[1296] = fn1296; + nvar_list[1296] = nvar_1296; + functions[1297] = fn1297; + nvar_list[1297] = nvar_1297; + functions[1298] = fn1298; + nvar_list[1298] = nvar_1298; + functions[1299] = fn1299; + nvar_list[1299] = nvar_1299; + functions[1300] = fn1300; + nvar_list[1300] = nvar_1300; + functions[1301] = fn1301; + nvar_list[1301] = nvar_1301; + functions[1302] = fn1302; + nvar_list[1302] = nvar_1302; + functions[1303] = fn1303; + nvar_list[1303] = nvar_1303; + functions[1304] = fn1304; + nvar_list[1304] = nvar_1304; + functions[1305] = fn1305; + nvar_list[1305] = nvar_1305; + functions[1306] = fn1306; + nvar_list[1306] = nvar_1306; + functions[1307] = fn1307; + nvar_list[1307] = nvar_1307; + functions[1308] = fn1308; + nvar_list[1308] = nvar_1308; + functions[1309] = fn1309; + nvar_list[1309] = nvar_1309; + functions[1310] = fn1310; + nvar_list[1310] = nvar_1310; + functions[1311] = fn1311; + nvar_list[1311] = nvar_1311; + functions[1312] = fn1312; + nvar_list[1312] = nvar_1312; + functions[1313] = fn1313; + nvar_list[1313] = nvar_1313; + functions[1314] = fn1314; + nvar_list[1314] = nvar_1314; + functions[1315] = fn1315; + nvar_list[1315] = nvar_1315; + functions[1316] = fn1316; + nvar_list[1316] = nvar_1316; + functions[1317] = fn1317; + nvar_list[1317] = nvar_1317; + functions[1318] = fn1318; + nvar_list[1318] = nvar_1318; + functions[1319] = fn1319; + nvar_list[1319] = nvar_1319; + functions[1320] = fn1320; + nvar_list[1320] = nvar_1320; + functions[1321] = fn1321; + nvar_list[1321] = nvar_1321; + functions[1322] = fn1322; + nvar_list[1322] = nvar_1322; + functions[1323] = fn1323; + nvar_list[1323] = nvar_1323; + functions[1324] = fn1324; + nvar_list[1324] = nvar_1324; + functions[1325] = fn1325; + nvar_list[1325] = nvar_1325; + functions[1326] = fn1326; + nvar_list[1326] = nvar_1326; + functions[1327] = fn1327; + nvar_list[1327] = nvar_1327; + functions[1328] = fn1328; + nvar_list[1328] = nvar_1328; + functions[1329] = fn1329; + nvar_list[1329] = nvar_1329; + functions[1330] = fn1330; + nvar_list[1330] = nvar_1330; + functions[1331] = fn1331; + nvar_list[1331] = nvar_1331; + functions[1332] = fn1332; + nvar_list[1332] = nvar_1332; + functions[1333] = fn1333; + nvar_list[1333] = nvar_1333; + functions[1334] = fn1334; + nvar_list[1334] = nvar_1334; + functions[1335] = fn1335; + nvar_list[1335] = nvar_1335; + functions[1336] = fn1336; + nvar_list[1336] = nvar_1336; + functions[1337] = fn1337; + nvar_list[1337] = nvar_1337; + functions[1338] = fn1338; + nvar_list[1338] = nvar_1338; + functions[1339] = fn1339; + nvar_list[1339] = nvar_1339; + functions[1340] = fn1340; + nvar_list[1340] = nvar_1340; + functions[1341] = fn1341; + nvar_list[1341] = nvar_1341; + functions[1342] = fn1342; + nvar_list[1342] = nvar_1342; + functions[1343] = fn1343; + nvar_list[1343] = nvar_1343; + functions[1344] = fn1344; + nvar_list[1344] = nvar_1344; + functions[1345] = fn1345; + nvar_list[1345] = nvar_1345; + functions[1346] = fn1346; + nvar_list[1346] = nvar_1346; + functions[1347] = fn1347; + nvar_list[1347] = nvar_1347; + functions[1348] = fn1348; + nvar_list[1348] = nvar_1348; + functions[1349] = fn1349; + nvar_list[1349] = nvar_1349; + functions[1350] = fn1350; + nvar_list[1350] = nvar_1350; + functions[1351] = fn1351; + nvar_list[1351] = nvar_1351; + functions[1352] = fn1352; + nvar_list[1352] = nvar_1352; + functions[1353] = fn1353; + nvar_list[1353] = nvar_1353; + functions[1354] = fn1354; + nvar_list[1354] = nvar_1354; + functions[1355] = fn1355; + nvar_list[1355] = nvar_1355; + functions[1356] = fn1356; + nvar_list[1356] = nvar_1356; + functions[1357] = fn1357; + nvar_list[1357] = nvar_1357; + functions[1358] = fn1358; + nvar_list[1358] = nvar_1358; + functions[1359] = fn1359; + nvar_list[1359] = nvar_1359; + functions[1360] = fn1360; + nvar_list[1360] = nvar_1360; + functions[1361] = fn1361; + nvar_list[1361] = nvar_1361; + functions[1362] = fn1362; + nvar_list[1362] = nvar_1362; + functions[1363] = fn1363; + nvar_list[1363] = nvar_1363; + functions[1364] = fn1364; + nvar_list[1364] = nvar_1364; + functions[1365] = fn1365; + nvar_list[1365] = nvar_1365; + functions[1366] = fn1366; + nvar_list[1366] = nvar_1366; + functions[1367] = fn1367; + nvar_list[1367] = nvar_1367; + functions[1368] = fn1368; + nvar_list[1368] = nvar_1368; + functions[1369] = fn1369; + nvar_list[1369] = nvar_1369; + functions[1370] = fn1370; + nvar_list[1370] = nvar_1370; + functions[1371] = fn1371; + nvar_list[1371] = nvar_1371; + functions[1372] = fn1372; + nvar_list[1372] = nvar_1372; + functions[1373] = fn1373; + nvar_list[1373] = nvar_1373; + functions[1374] = fn1374; + nvar_list[1374] = nvar_1374; + functions[1375] = fn1375; + nvar_list[1375] = nvar_1375; + functions[1376] = fn1376; + nvar_list[1376] = nvar_1376; + functions[1377] = fn1377; + nvar_list[1377] = nvar_1377; + functions[1378] = fn1378; + nvar_list[1378] = nvar_1378; + functions[1379] = fn1379; + nvar_list[1379] = nvar_1379; + functions[1380] = fn1380; + nvar_list[1380] = nvar_1380; + functions[1381] = fn1381; + nvar_list[1381] = nvar_1381; + functions[1382] = fn1382; + nvar_list[1382] = nvar_1382; + functions[1383] = fn1383; + nvar_list[1383] = nvar_1383; + functions[1384] = fn1384; + nvar_list[1384] = nvar_1384; + functions[1385] = fn1385; + nvar_list[1385] = nvar_1385; + functions[1386] = fn1386; + nvar_list[1386] = nvar_1386; + functions[1387] = fn1387; + nvar_list[1387] = nvar_1387; + functions[1388] = fn1388; + nvar_list[1388] = nvar_1388; + functions[1389] = fn1389; + nvar_list[1389] = nvar_1389; + functions[1390] = fn1390; + nvar_list[1390] = nvar_1390; + functions[1391] = fn1391; + nvar_list[1391] = nvar_1391; + functions[1392] = fn1392; + nvar_list[1392] = nvar_1392; + functions[1393] = fn1393; + nvar_list[1393] = nvar_1393; + functions[1394] = fn1394; + nvar_list[1394] = nvar_1394; + functions[1395] = fn1395; + nvar_list[1395] = nvar_1395; + functions[1396] = fn1396; + nvar_list[1396] = nvar_1396; + functions[1397] = fn1397; + nvar_list[1397] = nvar_1397; + functions[1398] = fn1398; + nvar_list[1398] = nvar_1398; + functions[1399] = fn1399; + nvar_list[1399] = nvar_1399; + functions[1400] = fn1400; + nvar_list[1400] = nvar_1400; + functions[1401] = fn1401; + nvar_list[1401] = nvar_1401; + functions[1402] = fn1402; + nvar_list[1402] = nvar_1402; + functions[1403] = fn1403; + nvar_list[1403] = nvar_1403; + functions[1404] = fn1404; + nvar_list[1404] = nvar_1404; + functions[1405] = fn1405; + nvar_list[1405] = nvar_1405; + functions[1406] = fn1406; + nvar_list[1406] = nvar_1406; + functions[1407] = fn1407; + nvar_list[1407] = nvar_1407; + functions[1408] = fn1408; + nvar_list[1408] = nvar_1408; + functions[1409] = fn1409; + nvar_list[1409] = nvar_1409; + functions[1410] = fn1410; + nvar_list[1410] = nvar_1410; + functions[1411] = fn1411; + nvar_list[1411] = nvar_1411; + functions[1412] = fn1412; + nvar_list[1412] = nvar_1412; + functions[1413] = fn1413; + nvar_list[1413] = nvar_1413; + functions[1414] = fn1414; + nvar_list[1414] = nvar_1414; + functions[1415] = fn1415; + nvar_list[1415] = nvar_1415; + functions[1416] = fn1416; + nvar_list[1416] = nvar_1416; + functions[1417] = fn1417; + nvar_list[1417] = nvar_1417; + functions[1418] = fn1418; + nvar_list[1418] = nvar_1418; + functions[1419] = fn1419; + nvar_list[1419] = nvar_1419; + functions[1420] = fn1420; + nvar_list[1420] = nvar_1420; + functions[1421] = fn1421; + nvar_list[1421] = nvar_1421; + functions[1422] = fn1422; + nvar_list[1422] = nvar_1422; + functions[1423] = fn1423; + nvar_list[1423] = nvar_1423; + functions[1424] = fn1424; + nvar_list[1424] = nvar_1424; + functions[1425] = fn1425; + nvar_list[1425] = nvar_1425; + functions[1426] = fn1426; + nvar_list[1426] = nvar_1426; + functions[1427] = fn1427; + nvar_list[1427] = nvar_1427; + functions[1428] = fn1428; + nvar_list[1428] = nvar_1428; + functions[1429] = fn1429; + nvar_list[1429] = nvar_1429; + functions[1430] = fn1430; + nvar_list[1430] = nvar_1430; + functions[1431] = fn1431; + nvar_list[1431] = nvar_1431; + functions[1432] = fn1432; + nvar_list[1432] = nvar_1432; + functions[1433] = fn1433; + nvar_list[1433] = nvar_1433; + functions[1434] = fn1434; + nvar_list[1434] = nvar_1434; + functions[1435] = fn1435; + nvar_list[1435] = nvar_1435; + functions[1436] = fn1436; + nvar_list[1436] = nvar_1436; + functions[1437] = fn1437; + nvar_list[1437] = nvar_1437; + functions[1438] = fn1438; + nvar_list[1438] = nvar_1438; + functions[1439] = fn1439; + nvar_list[1439] = nvar_1439; + functions[1440] = fn1440; + nvar_list[1440] = nvar_1440; + functions[1441] = fn1441; + nvar_list[1441] = nvar_1441; + functions[1442] = fn1442; + nvar_list[1442] = nvar_1442; + functions[1443] = fn1443; + nvar_list[1443] = nvar_1443; + functions[1444] = fn1444; + nvar_list[1444] = nvar_1444; + functions[1445] = fn1445; + nvar_list[1445] = nvar_1445; + functions[1446] = fn1446; + nvar_list[1446] = nvar_1446; + functions[1447] = fn1447; + nvar_list[1447] = nvar_1447; + functions[1448] = fn1448; + nvar_list[1448] = nvar_1448; + functions[1449] = fn1449; + nvar_list[1449] = nvar_1449; + functions[1450] = fn1450; + nvar_list[1450] = nvar_1450; + functions[1451] = fn1451; + nvar_list[1451] = nvar_1451; + functions[1452] = fn1452; + nvar_list[1452] = nvar_1452; + functions[1453] = fn1453; + nvar_list[1453] = nvar_1453; + functions[1454] = fn1454; + nvar_list[1454] = nvar_1454; + functions[1455] = fn1455; + nvar_list[1455] = nvar_1455; + functions[1456] = fn1456; + nvar_list[1456] = nvar_1456; + functions[1457] = fn1457; + nvar_list[1457] = nvar_1457; + functions[1458] = fn1458; + nvar_list[1458] = nvar_1458; + functions[1459] = fn1459; + nvar_list[1459] = nvar_1459; + functions[1460] = fn1460; + nvar_list[1460] = nvar_1460; + functions[1461] = fn1461; + nvar_list[1461] = nvar_1461; + functions[1462] = fn1462; + nvar_list[1462] = nvar_1462; + functions[1463] = fn1463; + nvar_list[1463] = nvar_1463; + functions[1464] = fn1464; + nvar_list[1464] = nvar_1464; + functions[1465] = fn1465; + nvar_list[1465] = nvar_1465; + functions[1466] = fn1466; + nvar_list[1466] = nvar_1466; + functions[1467] = fn1467; + nvar_list[1467] = nvar_1467; + functions[1468] = fn1468; + nvar_list[1468] = nvar_1468; + functions[1469] = fn1469; + nvar_list[1469] = nvar_1469; + functions[1470] = fn1470; + nvar_list[1470] = nvar_1470; + functions[1471] = fn1471; + nvar_list[1471] = nvar_1471; + functions[1472] = fn1472; + nvar_list[1472] = nvar_1472; + functions[1473] = fn1473; + nvar_list[1473] = nvar_1473; + functions[1474] = fn1474; + nvar_list[1474] = nvar_1474; + functions[1475] = fn1475; + nvar_list[1475] = nvar_1475; + functions[1476] = fn1476; + nvar_list[1476] = nvar_1476; + functions[1477] = fn1477; + nvar_list[1477] = nvar_1477; + functions[1478] = fn1478; + nvar_list[1478] = nvar_1478; + functions[1479] = fn1479; + nvar_list[1479] = nvar_1479; + functions[1480] = fn1480; + nvar_list[1480] = nvar_1480; + functions[1481] = fn1481; + nvar_list[1481] = nvar_1481; + functions[1482] = fn1482; + nvar_list[1482] = nvar_1482; + functions[1483] = fn1483; + nvar_list[1483] = nvar_1483; + functions[1484] = fn1484; + nvar_list[1484] = nvar_1484; + functions[1485] = fn1485; + nvar_list[1485] = nvar_1485; + functions[1486] = fn1486; + nvar_list[1486] = nvar_1486; + functions[1487] = fn1487; + nvar_list[1487] = nvar_1487; + functions[1488] = fn1488; + nvar_list[1488] = nvar_1488; + functions[1489] = fn1489; + nvar_list[1489] = nvar_1489; + functions[1490] = fn1490; + nvar_list[1490] = nvar_1490; + functions[1491] = fn1491; + nvar_list[1491] = nvar_1491; + functions[1492] = fn1492; + nvar_list[1492] = nvar_1492; + functions[1493] = fn1493; + nvar_list[1493] = nvar_1493; + functions[1494] = fn1494; + nvar_list[1494] = nvar_1494; + functions[1495] = fn1495; + nvar_list[1495] = nvar_1495; + functions[1496] = fn1496; + nvar_list[1496] = nvar_1496; + functions[1497] = fn1497; + nvar_list[1497] = nvar_1497; + functions[1498] = fn1498; + nvar_list[1498] = nvar_1498; + functions[1499] = fn1499; + nvar_list[1499] = nvar_1499; + functions[1500] = fn1500; + nvar_list[1500] = nvar_1500; + functions[1501] = fn1501; + nvar_list[1501] = nvar_1501; + functions[1502] = fn1502; + nvar_list[1502] = nvar_1502; + functions[1503] = fn1503; + nvar_list[1503] = nvar_1503; + functions[1504] = fn1504; + nvar_list[1504] = nvar_1504; + functions[1505] = fn1505; + nvar_list[1505] = nvar_1505; + functions[1506] = fn1506; + nvar_list[1506] = nvar_1506; + functions[1507] = fn1507; + nvar_list[1507] = nvar_1507; + functions[1508] = fn1508; + nvar_list[1508] = nvar_1508; + functions[1509] = fn1509; + nvar_list[1509] = nvar_1509; + functions[1510] = fn1510; + nvar_list[1510] = nvar_1510; + functions[1511] = fn1511; + nvar_list[1511] = nvar_1511; + functions[1512] = fn1512; + nvar_list[1512] = nvar_1512; + functions[1513] = fn1513; + nvar_list[1513] = nvar_1513; + functions[1514] = fn1514; + nvar_list[1514] = nvar_1514; + functions[1515] = fn1515; + nvar_list[1515] = nvar_1515; + functions[1516] = fn1516; + nvar_list[1516] = nvar_1516; + functions[1517] = fn1517; + nvar_list[1517] = nvar_1517; + functions[1518] = fn1518; + nvar_list[1518] = nvar_1518; + functions[1519] = fn1519; + nvar_list[1519] = nvar_1519; + functions[1520] = fn1520; + nvar_list[1520] = nvar_1520; + functions[1521] = fn1521; + nvar_list[1521] = nvar_1521; + functions[1522] = fn1522; + nvar_list[1522] = nvar_1522; + functions[1523] = fn1523; + nvar_list[1523] = nvar_1523; + functions[1524] = fn1524; + nvar_list[1524] = nvar_1524; + functions[1525] = fn1525; + nvar_list[1525] = nvar_1525; + functions[1526] = fn1526; + nvar_list[1526] = nvar_1526; + functions[1527] = fn1527; + nvar_list[1527] = nvar_1527; + functions[1528] = fn1528; + nvar_list[1528] = nvar_1528; + functions[1529] = fn1529; + nvar_list[1529] = nvar_1529; + functions[1530] = fn1530; + nvar_list[1530] = nvar_1530; + functions[1531] = fn1531; + nvar_list[1531] = nvar_1531; + functions[1532] = fn1532; + nvar_list[1532] = nvar_1532; + functions[1533] = fn1533; + nvar_list[1533] = nvar_1533; + functions[1534] = fn1534; + nvar_list[1534] = nvar_1534; + functions[1535] = fn1535; + nvar_list[1535] = nvar_1535; + functions[1536] = fn1536; + nvar_list[1536] = nvar_1536; + functions[1537] = fn1537; + nvar_list[1537] = nvar_1537; + functions[1538] = fn1538; + nvar_list[1538] = nvar_1538; + functions[1539] = fn1539; + nvar_list[1539] = nvar_1539; + functions[1540] = fn1540; + nvar_list[1540] = nvar_1540; + functions[1541] = fn1541; + nvar_list[1541] = nvar_1541; + functions[1542] = fn1542; + nvar_list[1542] = nvar_1542; + functions[1543] = fn1543; + nvar_list[1543] = nvar_1543; + functions[1544] = fn1544; + nvar_list[1544] = nvar_1544; + functions[1545] = fn1545; + nvar_list[1545] = nvar_1545; + functions[1546] = fn1546; + nvar_list[1546] = nvar_1546; + functions[1547] = fn1547; + nvar_list[1547] = nvar_1547; + functions[1548] = fn1548; + nvar_list[1548] = nvar_1548; + functions[1549] = fn1549; + nvar_list[1549] = nvar_1549; + functions[1550] = fn1550; + nvar_list[1550] = nvar_1550; + functions[1551] = fn1551; + nvar_list[1551] = nvar_1551; + functions[1552] = fn1552; + nvar_list[1552] = nvar_1552; + functions[1553] = fn1553; + nvar_list[1553] = nvar_1553; + functions[1554] = fn1554; + nvar_list[1554] = nvar_1554; + functions[1555] = fn1555; + nvar_list[1555] = nvar_1555; + functions[1556] = fn1556; + nvar_list[1556] = nvar_1556; + functions[1557] = fn1557; + nvar_list[1557] = nvar_1557; + functions[1558] = fn1558; + nvar_list[1558] = nvar_1558; + functions[1559] = fn1559; + nvar_list[1559] = nvar_1559; + functions[1560] = fn1560; + nvar_list[1560] = nvar_1560; + functions[1561] = fn1561; + nvar_list[1561] = nvar_1561; + functions[1562] = fn1562; + nvar_list[1562] = nvar_1562; + functions[1563] = fn1563; + nvar_list[1563] = nvar_1563; + functions[1564] = fn1564; + nvar_list[1564] = nvar_1564; + functions[1565] = fn1565; + nvar_list[1565] = nvar_1565; + functions[1566] = fn1566; + nvar_list[1566] = nvar_1566; + functions[1567] = fn1567; + nvar_list[1567] = nvar_1567; + functions[1568] = fn1568; + nvar_list[1568] = nvar_1568; + functions[1569] = fn1569; + nvar_list[1569] = nvar_1569; + functions[1570] = fn1570; + nvar_list[1570] = nvar_1570; + functions[1571] = fn1571; + nvar_list[1571] = nvar_1571; + functions[1572] = fn1572; + nvar_list[1572] = nvar_1572; + functions[1573] = fn1573; + nvar_list[1573] = nvar_1573; + functions[1574] = fn1574; + nvar_list[1574] = nvar_1574; + functions[1575] = fn1575; + nvar_list[1575] = nvar_1575; + functions[1576] = fn1576; + nvar_list[1576] = nvar_1576; + functions[1577] = fn1577; + nvar_list[1577] = nvar_1577; + functions[1578] = fn1578; + nvar_list[1578] = nvar_1578; + functions[1579] = fn1579; + nvar_list[1579] = nvar_1579; + functions[1580] = fn1580; + nvar_list[1580] = nvar_1580; + functions[1581] = fn1581; + nvar_list[1581] = nvar_1581; + functions[1582] = fn1582; + nvar_list[1582] = nvar_1582; + functions[1583] = fn1583; + nvar_list[1583] = nvar_1583; + functions[1584] = fn1584; + nvar_list[1584] = nvar_1584; + functions[1585] = fn1585; + nvar_list[1585] = nvar_1585; + functions[1586] = fn1586; + nvar_list[1586] = nvar_1586; + functions[1587] = fn1587; + nvar_list[1587] = nvar_1587; + functions[1588] = fn1588; + nvar_list[1588] = nvar_1588; + functions[1589] = fn1589; + nvar_list[1589] = nvar_1589; + functions[1590] = fn1590; + nvar_list[1590] = nvar_1590; + functions[1591] = fn1591; + nvar_list[1591] = nvar_1591; + functions[1592] = fn1592; + nvar_list[1592] = nvar_1592; + functions[1593] = fn1593; + nvar_list[1593] = nvar_1593; + functions[1594] = fn1594; + nvar_list[1594] = nvar_1594; + functions[1595] = fn1595; + nvar_list[1595] = nvar_1595; + functions[1596] = fn1596; + nvar_list[1596] = nvar_1596; + functions[1597] = fn1597; + nvar_list[1597] = nvar_1597; + functions[1598] = fn1598; + nvar_list[1598] = nvar_1598; + functions[1599] = fn1599; + nvar_list[1599] = nvar_1599; + functions[1600] = fn1600; + nvar_list[1600] = nvar_1600; + functions[1601] = fn1601; + nvar_list[1601] = nvar_1601; + functions[1602] = fn1602; + nvar_list[1602] = nvar_1602; + functions[1603] = fn1603; + nvar_list[1603] = nvar_1603; + functions[1604] = fn1604; + nvar_list[1604] = nvar_1604; + functions[1605] = fn1605; + nvar_list[1605] = nvar_1605; + functions[1606] = fn1606; + nvar_list[1606] = nvar_1606; + functions[1607] = fn1607; + nvar_list[1607] = nvar_1607; + functions[1608] = fn1608; + nvar_list[1608] = nvar_1608; + functions[1609] = fn1609; + nvar_list[1609] = nvar_1609; + functions[1610] = fn1610; + nvar_list[1610] = nvar_1610; + functions[1611] = fn1611; + nvar_list[1611] = nvar_1611; + functions[1612] = fn1612; + nvar_list[1612] = nvar_1612; + functions[1613] = fn1613; + nvar_list[1613] = nvar_1613; + functions[1614] = fn1614; + nvar_list[1614] = nvar_1614; + functions[1615] = fn1615; + nvar_list[1615] = nvar_1615; + functions[1616] = fn1616; + nvar_list[1616] = nvar_1616; + functions[1617] = fn1617; + nvar_list[1617] = nvar_1617; + functions[1618] = fn1618; + nvar_list[1618] = nvar_1618; + functions[1619] = fn1619; + nvar_list[1619] = nvar_1619; + functions[1620] = fn1620; + nvar_list[1620] = nvar_1620; + functions[1621] = fn1621; + nvar_list[1621] = nvar_1621; + functions[1622] = fn1622; + nvar_list[1622] = nvar_1622; + functions[1623] = fn1623; + nvar_list[1623] = nvar_1623; + functions[1624] = fn1624; + nvar_list[1624] = nvar_1624; + functions[1625] = fn1625; + nvar_list[1625] = nvar_1625; + functions[1626] = fn1626; + nvar_list[1626] = nvar_1626; + functions[1627] = fn1627; + nvar_list[1627] = nvar_1627; + functions[1628] = fn1628; + nvar_list[1628] = nvar_1628; + functions[1629] = fn1629; + nvar_list[1629] = nvar_1629; + functions[1630] = fn1630; + nvar_list[1630] = nvar_1630; + functions[1631] = fn1631; + nvar_list[1631] = nvar_1631; + functions[1632] = fn1632; + nvar_list[1632] = nvar_1632; + functions[1633] = fn1633; + nvar_list[1633] = nvar_1633; + functions[1634] = fn1634; + nvar_list[1634] = nvar_1634; + functions[1635] = fn1635; + nvar_list[1635] = nvar_1635; + functions[1636] = fn1636; + nvar_list[1636] = nvar_1636; + functions[1637] = fn1637; + nvar_list[1637] = nvar_1637; + functions[1638] = fn1638; + nvar_list[1638] = nvar_1638; + functions[1639] = fn1639; + nvar_list[1639] = nvar_1639; + functions[1640] = fn1640; + nvar_list[1640] = nvar_1640; + functions[1641] = fn1641; + nvar_list[1641] = nvar_1641; + functions[1642] = fn1642; + nvar_list[1642] = nvar_1642; + functions[1643] = fn1643; + nvar_list[1643] = nvar_1643; + functions[1644] = fn1644; + nvar_list[1644] = nvar_1644; + functions[1645] = fn1645; + nvar_list[1645] = nvar_1645; + functions[1646] = fn1646; + nvar_list[1646] = nvar_1646; + functions[1647] = fn1647; + nvar_list[1647] = nvar_1647; + functions[1648] = fn1648; + nvar_list[1648] = nvar_1648; + functions[1649] = fn1649; + nvar_list[1649] = nvar_1649; + functions[1650] = fn1650; + nvar_list[1650] = nvar_1650; + functions[1651] = fn1651; + nvar_list[1651] = nvar_1651; + functions[1652] = fn1652; + nvar_list[1652] = nvar_1652; + functions[1653] = fn1653; + nvar_list[1653] = nvar_1653; + functions[1654] = fn1654; + nvar_list[1654] = nvar_1654; + functions[1655] = fn1655; + nvar_list[1655] = nvar_1655; + functions[1656] = fn1656; + nvar_list[1656] = nvar_1656; + functions[1657] = fn1657; + nvar_list[1657] = nvar_1657; + functions[1658] = fn1658; + nvar_list[1658] = nvar_1658; + functions[1659] = fn1659; + nvar_list[1659] = nvar_1659; + functions[1660] = fn1660; + nvar_list[1660] = nvar_1660; + functions[1661] = fn1661; + nvar_list[1661] = nvar_1661; + functions[1662] = fn1662; + nvar_list[1662] = nvar_1662; + functions[1663] = fn1663; + nvar_list[1663] = nvar_1663; + functions[1664] = fn1664; + nvar_list[1664] = nvar_1664; + functions[1665] = fn1665; + nvar_list[1665] = nvar_1665; + functions[1666] = fn1666; + nvar_list[1666] = nvar_1666; + functions[1667] = fn1667; + nvar_list[1667] = nvar_1667; + functions[1668] = fn1668; + nvar_list[1668] = nvar_1668; + functions[1669] = fn1669; + nvar_list[1669] = nvar_1669; + functions[1670] = fn1670; + nvar_list[1670] = nvar_1670; + functions[1671] = fn1671; + nvar_list[1671] = nvar_1671; + functions[1672] = fn1672; + nvar_list[1672] = nvar_1672; + functions[1673] = fn1673; + nvar_list[1673] = nvar_1673; + functions[1674] = fn1674; + nvar_list[1674] = nvar_1674; + functions[1675] = fn1675; + nvar_list[1675] = nvar_1675; + functions[1676] = fn1676; + nvar_list[1676] = nvar_1676; + functions[1677] = fn1677; + nvar_list[1677] = nvar_1677; + functions[1678] = fn1678; + nvar_list[1678] = nvar_1678; + functions[1679] = fn1679; + nvar_list[1679] = nvar_1679; + functions[1680] = fn1680; + nvar_list[1680] = nvar_1680; + functions[1681] = fn1681; + nvar_list[1681] = nvar_1681; + functions[1682] = fn1682; + nvar_list[1682] = nvar_1682; + functions[1683] = fn1683; + nvar_list[1683] = nvar_1683; + functions[1684] = fn1684; + nvar_list[1684] = nvar_1684; + functions[1685] = fn1685; + nvar_list[1685] = nvar_1685; + functions[1686] = fn1686; + nvar_list[1686] = nvar_1686; + functions[1687] = fn1687; + nvar_list[1687] = nvar_1687; + functions[1688] = fn1688; + nvar_list[1688] = nvar_1688; + functions[1689] = fn1689; + nvar_list[1689] = nvar_1689; + functions[1690] = fn1690; + nvar_list[1690] = nvar_1690; + functions[1691] = fn1691; + nvar_list[1691] = nvar_1691; + functions[1692] = fn1692; + nvar_list[1692] = nvar_1692; + functions[1693] = fn1693; + nvar_list[1693] = nvar_1693; + functions[1694] = fn1694; + nvar_list[1694] = nvar_1694; + functions[1695] = fn1695; + nvar_list[1695] = nvar_1695; + functions[1696] = fn1696; + nvar_list[1696] = nvar_1696; + functions[1697] = fn1697; + nvar_list[1697] = nvar_1697; + functions[1698] = fn1698; + nvar_list[1698] = nvar_1698; + functions[1699] = fn1699; + nvar_list[1699] = nvar_1699; + functions[1700] = fn1700; + nvar_list[1700] = nvar_1700; + functions[1701] = fn1701; + nvar_list[1701] = nvar_1701; + functions[1702] = fn1702; + nvar_list[1702] = nvar_1702; + functions[1703] = fn1703; + nvar_list[1703] = nvar_1703; + functions[1704] = fn1704; + nvar_list[1704] = nvar_1704; + functions[1705] = fn1705; + nvar_list[1705] = nvar_1705; + functions[1706] = fn1706; + nvar_list[1706] = nvar_1706; + functions[1707] = fn1707; + nvar_list[1707] = nvar_1707; + functions[1708] = fn1708; + nvar_list[1708] = nvar_1708; + functions[1709] = fn1709; + nvar_list[1709] = nvar_1709; + functions[1710] = fn1710; + nvar_list[1710] = nvar_1710; + functions[1711] = fn1711; + nvar_list[1711] = nvar_1711; + functions[1712] = fn1712; + nvar_list[1712] = nvar_1712; + functions[1713] = fn1713; + nvar_list[1713] = nvar_1713; + functions[1714] = fn1714; + nvar_list[1714] = nvar_1714; + functions[1715] = fn1715; + nvar_list[1715] = nvar_1715; + functions[1716] = fn1716; + nvar_list[1716] = nvar_1716; + functions[1717] = fn1717; + nvar_list[1717] = nvar_1717; + functions[1718] = fn1718; + nvar_list[1718] = nvar_1718; + functions[1719] = fn1719; + nvar_list[1719] = nvar_1719; + functions[1720] = fn1720; + nvar_list[1720] = nvar_1720; + functions[1721] = fn1721; + nvar_list[1721] = nvar_1721; + functions[1722] = fn1722; + nvar_list[1722] = nvar_1722; + functions[1723] = fn1723; + nvar_list[1723] = nvar_1723; + functions[1724] = fn1724; + nvar_list[1724] = nvar_1724; + functions[1725] = fn1725; + nvar_list[1725] = nvar_1725; + functions[1726] = fn1726; + nvar_list[1726] = nvar_1726; + functions[1727] = fn1727; + nvar_list[1727] = nvar_1727; + functions[1728] = fn1728; + nvar_list[1728] = nvar_1728; + functions[1729] = fn1729; + nvar_list[1729] = nvar_1729; + functions[1730] = fn1730; + nvar_list[1730] = nvar_1730; + functions[1731] = fn1731; + nvar_list[1731] = nvar_1731; + functions[1732] = fn1732; + nvar_list[1732] = nvar_1732; + functions[1733] = fn1733; + nvar_list[1733] = nvar_1733; + functions[1734] = fn1734; + nvar_list[1734] = nvar_1734; + functions[1735] = fn1735; + nvar_list[1735] = nvar_1735; + functions[1736] = fn1736; + nvar_list[1736] = nvar_1736; + functions[1737] = fn1737; + nvar_list[1737] = nvar_1737; + functions[1738] = fn1738; + nvar_list[1738] = nvar_1738; + functions[1739] = fn1739; + nvar_list[1739] = nvar_1739; + functions[1740] = fn1740; + nvar_list[1740] = nvar_1740; + functions[1741] = fn1741; + nvar_list[1741] = nvar_1741; + functions[1742] = fn1742; + nvar_list[1742] = nvar_1742; + functions[1743] = fn1743; + nvar_list[1743] = nvar_1743; + functions[1744] = fn1744; + nvar_list[1744] = nvar_1744; + functions[1745] = fn1745; + nvar_list[1745] = nvar_1745; + functions[1746] = fn1746; + nvar_list[1746] = nvar_1746; + functions[1747] = fn1747; + nvar_list[1747] = nvar_1747; + functions[1748] = fn1748; + nvar_list[1748] = nvar_1748; + functions[1749] = fn1749; + nvar_list[1749] = nvar_1749; + functions[1750] = fn1750; + nvar_list[1750] = nvar_1750; + functions[1751] = fn1751; + nvar_list[1751] = nvar_1751; + functions[1752] = fn1752; + nvar_list[1752] = nvar_1752; + functions[1753] = fn1753; + nvar_list[1753] = nvar_1753; + functions[1754] = fn1754; + nvar_list[1754] = nvar_1754; + functions[1755] = fn1755; + nvar_list[1755] = nvar_1755; + functions[1756] = fn1756; + nvar_list[1756] = nvar_1756; + functions[1757] = fn1757; + nvar_list[1757] = nvar_1757; + functions[1758] = fn1758; + nvar_list[1758] = nvar_1758; + functions[1759] = fn1759; + nvar_list[1759] = nvar_1759; + functions[1760] = fn1760; + nvar_list[1760] = nvar_1760; + functions[1761] = fn1761; + nvar_list[1761] = nvar_1761; + functions[1762] = fn1762; + nvar_list[1762] = nvar_1762; + functions[1763] = fn1763; + nvar_list[1763] = nvar_1763; + functions[1764] = fn1764; + nvar_list[1764] = nvar_1764; + functions[1765] = fn1765; + nvar_list[1765] = nvar_1765; + functions[1766] = fn1766; + nvar_list[1766] = nvar_1766; + functions[1767] = fn1767; + nvar_list[1767] = nvar_1767; + functions[1768] = fn1768; + nvar_list[1768] = nvar_1768; + functions[1769] = fn1769; + nvar_list[1769] = nvar_1769; + functions[1770] = fn1770; + nvar_list[1770] = nvar_1770; + functions[1771] = fn1771; + nvar_list[1771] = nvar_1771; + functions[1772] = fn1772; + nvar_list[1772] = nvar_1772; + functions[1773] = fn1773; + nvar_list[1773] = nvar_1773; + functions[1774] = fn1774; + nvar_list[1774] = nvar_1774; + functions[1775] = fn1775; + nvar_list[1775] = nvar_1775; + functions[1776] = fn1776; + nvar_list[1776] = nvar_1776; + functions[1777] = fn1777; + nvar_list[1777] = nvar_1777; + functions[1778] = fn1778; + nvar_list[1778] = nvar_1778; + functions[1779] = fn1779; + nvar_list[1779] = nvar_1779; + functions[1780] = fn1780; + nvar_list[1780] = nvar_1780; + functions[1781] = fn1781; + nvar_list[1781] = nvar_1781; + functions[1782] = fn1782; + nvar_list[1782] = nvar_1782; + functions[1783] = fn1783; + nvar_list[1783] = nvar_1783; + functions[1784] = fn1784; + nvar_list[1784] = nvar_1784; + functions[1785] = fn1785; + nvar_list[1785] = nvar_1785; + functions[1786] = fn1786; + nvar_list[1786] = nvar_1786; + functions[1787] = fn1787; + nvar_list[1787] = nvar_1787; + functions[1788] = fn1788; + nvar_list[1788] = nvar_1788; + functions[1789] = fn1789; + nvar_list[1789] = nvar_1789; + functions[1790] = fn1790; + nvar_list[1790] = nvar_1790; + functions[1791] = fn1791; + nvar_list[1791] = nvar_1791; + functions[1792] = fn1792; + nvar_list[1792] = nvar_1792; + functions[1793] = fn1793; + nvar_list[1793] = nvar_1793; + functions[1794] = fn1794; + nvar_list[1794] = nvar_1794; + functions[1795] = fn1795; + nvar_list[1795] = nvar_1795; + functions[1796] = fn1796; + nvar_list[1796] = nvar_1796; + functions[1797] = fn1797; + nvar_list[1797] = nvar_1797; + functions[1798] = fn1798; + nvar_list[1798] = nvar_1798; + functions[1799] = fn1799; + nvar_list[1799] = nvar_1799; + functions[1800] = fn1800; + nvar_list[1800] = nvar_1800; + functions[1801] = fn1801; + nvar_list[1801] = nvar_1801; + functions[1802] = fn1802; + nvar_list[1802] = nvar_1802; + functions[1803] = fn1803; + nvar_list[1803] = nvar_1803; + functions[1804] = fn1804; + nvar_list[1804] = nvar_1804; + functions[1805] = fn1805; + nvar_list[1805] = nvar_1805; + functions[1806] = fn1806; + nvar_list[1806] = nvar_1806; + functions[1807] = fn1807; + nvar_list[1807] = nvar_1807; + functions[1808] = fn1808; + nvar_list[1808] = nvar_1808; + functions[1809] = fn1809; + nvar_list[1809] = nvar_1809; + functions[1810] = fn1810; + nvar_list[1810] = nvar_1810; + functions[1811] = fn1811; + nvar_list[1811] = nvar_1811; + functions[1812] = fn1812; + nvar_list[1812] = nvar_1812; + functions[1813] = fn1813; + nvar_list[1813] = nvar_1813; + functions[1814] = fn1814; + nvar_list[1814] = nvar_1814; + functions[1815] = fn1815; + nvar_list[1815] = nvar_1815; + functions[1816] = fn1816; + nvar_list[1816] = nvar_1816; + functions[1817] = fn1817; + nvar_list[1817] = nvar_1817; + functions[1818] = fn1818; + nvar_list[1818] = nvar_1818; + functions[1819] = fn1819; + nvar_list[1819] = nvar_1819; + functions[1820] = fn1820; + nvar_list[1820] = nvar_1820; + functions[1821] = fn1821; + nvar_list[1821] = nvar_1821; + functions[1822] = fn1822; + nvar_list[1822] = nvar_1822; + functions[1823] = fn1823; + nvar_list[1823] = nvar_1823; + functions[1824] = fn1824; + nvar_list[1824] = nvar_1824; + functions[1825] = fn1825; + nvar_list[1825] = nvar_1825; + functions[1826] = fn1826; + nvar_list[1826] = nvar_1826; + functions[1827] = fn1827; + nvar_list[1827] = nvar_1827; + functions[1828] = fn1828; + nvar_list[1828] = nvar_1828; + functions[1829] = fn1829; + nvar_list[1829] = nvar_1829; + functions[1830] = fn1830; + nvar_list[1830] = nvar_1830; + functions[1831] = fn1831; + nvar_list[1831] = nvar_1831; + functions[1832] = fn1832; + nvar_list[1832] = nvar_1832; + functions[1833] = fn1833; + nvar_list[1833] = nvar_1833; + functions[1834] = fn1834; + nvar_list[1834] = nvar_1834; + functions[1835] = fn1835; + nvar_list[1835] = nvar_1835; + functions[1836] = fn1836; + nvar_list[1836] = nvar_1836; + functions[1837] = fn1837; + nvar_list[1837] = nvar_1837; + functions[1838] = fn1838; + nvar_list[1838] = nvar_1838; + functions[1839] = fn1839; + nvar_list[1839] = nvar_1839; + functions[1840] = fn1840; + nvar_list[1840] = nvar_1840; + functions[1841] = fn1841; + nvar_list[1841] = nvar_1841; + functions[1842] = fn1842; + nvar_list[1842] = nvar_1842; + functions[1843] = fn1843; + nvar_list[1843] = nvar_1843; + functions[1844] = fn1844; + nvar_list[1844] = nvar_1844; + functions[1845] = fn1845; + nvar_list[1845] = nvar_1845; + functions[1846] = fn1846; + nvar_list[1846] = nvar_1846; + functions[1847] = fn1847; + nvar_list[1847] = nvar_1847; + functions[1848] = fn1848; + nvar_list[1848] = nvar_1848; + functions[1849] = fn1849; + nvar_list[1849] = nvar_1849; + functions[1850] = fn1850; + nvar_list[1850] = nvar_1850; + functions[1851] = fn1851; + nvar_list[1851] = nvar_1851; + functions[1852] = fn1852; + nvar_list[1852] = nvar_1852; + functions[1853] = fn1853; + nvar_list[1853] = nvar_1853; + functions[1854] = fn1854; + nvar_list[1854] = nvar_1854; + functions[1855] = fn1855; + nvar_list[1855] = nvar_1855; + functions[1856] = fn1856; + nvar_list[1856] = nvar_1856; + functions[1857] = fn1857; + nvar_list[1857] = nvar_1857; + functions[1858] = fn1858; + nvar_list[1858] = nvar_1858; + functions[1859] = fn1859; + nvar_list[1859] = nvar_1859; + functions[1860] = fn1860; + nvar_list[1860] = nvar_1860; + functions[1861] = fn1861; + nvar_list[1861] = nvar_1861; + functions[1862] = fn1862; + nvar_list[1862] = nvar_1862; + functions[1863] = fn1863; + nvar_list[1863] = nvar_1863; + functions[1864] = fn1864; + nvar_list[1864] = nvar_1864; + functions[1865] = fn1865; + nvar_list[1865] = nvar_1865; + functions[1866] = fn1866; + nvar_list[1866] = nvar_1866; + functions[1867] = fn1867; + nvar_list[1867] = nvar_1867; + functions[1868] = fn1868; + nvar_list[1868] = nvar_1868; + functions[1869] = fn1869; + nvar_list[1869] = nvar_1869; + functions[1870] = fn1870; + nvar_list[1870] = nvar_1870; + functions[1871] = fn1871; + nvar_list[1871] = nvar_1871; + functions[1872] = fn1872; + nvar_list[1872] = nvar_1872; + functions[1873] = fn1873; + nvar_list[1873] = nvar_1873; + functions[1874] = fn1874; + nvar_list[1874] = nvar_1874; + functions[1875] = fn1875; + nvar_list[1875] = nvar_1875; + functions[1876] = fn1876; + nvar_list[1876] = nvar_1876; + functions[1877] = fn1877; + nvar_list[1877] = nvar_1877; + functions[1878] = fn1878; + nvar_list[1878] = nvar_1878; + functions[1879] = fn1879; + nvar_list[1879] = nvar_1879; + functions[1880] = fn1880; + nvar_list[1880] = nvar_1880; + functions[1881] = fn1881; + nvar_list[1881] = nvar_1881; + functions[1882] = fn1882; + nvar_list[1882] = nvar_1882; + functions[1883] = fn1883; + nvar_list[1883] = nvar_1883; + functions[1884] = fn1884; + nvar_list[1884] = nvar_1884; + functions[1885] = fn1885; + nvar_list[1885] = nvar_1885; + functions[1886] = fn1886; + nvar_list[1886] = nvar_1886; + functions[1887] = fn1887; + nvar_list[1887] = nvar_1887; + functions[1888] = fn1888; + nvar_list[1888] = nvar_1888; + functions[1889] = fn1889; + nvar_list[1889] = nvar_1889; + functions[1890] = fn1890; + nvar_list[1890] = nvar_1890; + functions[1891] = fn1891; + nvar_list[1891] = nvar_1891; + functions[1892] = fn1892; + nvar_list[1892] = nvar_1892; + functions[1893] = fn1893; + nvar_list[1893] = nvar_1893; + functions[1894] = fn1894; + nvar_list[1894] = nvar_1894; + functions[1895] = fn1895; + nvar_list[1895] = nvar_1895; + functions[1896] = fn1896; + nvar_list[1896] = nvar_1896; + functions[1897] = fn1897; + nvar_list[1897] = nvar_1897; + functions[1898] = fn1898; + nvar_list[1898] = nvar_1898; + functions[1899] = fn1899; + nvar_list[1899] = nvar_1899; + functions[1900] = fn1900; + nvar_list[1900] = nvar_1900; + functions[1901] = fn1901; + nvar_list[1901] = nvar_1901; + functions[1902] = fn1902; + nvar_list[1902] = nvar_1902; + functions[1903] = fn1903; + nvar_list[1903] = nvar_1903; + functions[1904] = fn1904; + nvar_list[1904] = nvar_1904; + functions[1905] = fn1905; + nvar_list[1905] = nvar_1905; + functions[1906] = fn1906; + nvar_list[1906] = nvar_1906; + functions[1907] = fn1907; + nvar_list[1907] = nvar_1907; + functions[1908] = fn1908; + nvar_list[1908] = nvar_1908; + functions[1909] = fn1909; + nvar_list[1909] = nvar_1909; + functions[1910] = fn1910; + nvar_list[1910] = nvar_1910; + functions[1911] = fn1911; + nvar_list[1911] = nvar_1911; + functions[1912] = fn1912; + nvar_list[1912] = nvar_1912; + functions[1913] = fn1913; + nvar_list[1913] = nvar_1913; + functions[1914] = fn1914; + nvar_list[1914] = nvar_1914; + functions[1915] = fn1915; + nvar_list[1915] = nvar_1915; + functions[1916] = fn1916; + nvar_list[1916] = nvar_1916; + functions[1917] = fn1917; + nvar_list[1917] = nvar_1917; + functions[1918] = fn1918; + nvar_list[1918] = nvar_1918; + functions[1919] = fn1919; + nvar_list[1919] = nvar_1919; + functions[1920] = fn1920; + nvar_list[1920] = nvar_1920; + functions[1921] = fn1921; + nvar_list[1921] = nvar_1921; + functions[1922] = fn1922; + nvar_list[1922] = nvar_1922; + functions[1923] = fn1923; + nvar_list[1923] = nvar_1923; + functions[1924] = fn1924; + nvar_list[1924] = nvar_1924; + functions[1925] = fn1925; + nvar_list[1925] = nvar_1925; + functions[1926] = fn1926; + nvar_list[1926] = nvar_1926; + functions[1927] = fn1927; + nvar_list[1927] = nvar_1927; + functions[1928] = fn1928; + nvar_list[1928] = nvar_1928; + functions[1929] = fn1929; + nvar_list[1929] = nvar_1929; + functions[1930] = fn1930; + nvar_list[1930] = nvar_1930; + functions[1931] = fn1931; + nvar_list[1931] = nvar_1931; + functions[1932] = fn1932; + nvar_list[1932] = nvar_1932; + functions[1933] = fn1933; + nvar_list[1933] = nvar_1933; + functions[1934] = fn1934; + nvar_list[1934] = nvar_1934; + functions[1935] = fn1935; + nvar_list[1935] = nvar_1935; + functions[1936] = fn1936; + nvar_list[1936] = nvar_1936; + functions[1937] = fn1937; + nvar_list[1937] = nvar_1937; + functions[1938] = fn1938; + nvar_list[1938] = nvar_1938; + functions[1939] = fn1939; + nvar_list[1939] = nvar_1939; + functions[1940] = fn1940; + nvar_list[1940] = nvar_1940; + functions[1941] = fn1941; + nvar_list[1941] = nvar_1941; + functions[1942] = fn1942; + nvar_list[1942] = nvar_1942; + functions[1943] = fn1943; + nvar_list[1943] = nvar_1943; + functions[1944] = fn1944; + nvar_list[1944] = nvar_1944; + functions[1945] = fn1945; + nvar_list[1945] = nvar_1945; + functions[1946] = fn1946; + nvar_list[1946] = nvar_1946; + functions[1947] = fn1947; + nvar_list[1947] = nvar_1947; + functions[1948] = fn1948; + nvar_list[1948] = nvar_1948; + functions[1949] = fn1949; + nvar_list[1949] = nvar_1949; + functions[1950] = fn1950; + nvar_list[1950] = nvar_1950; + functions[1951] = fn1951; + nvar_list[1951] = nvar_1951; + functions[1952] = fn1952; + nvar_list[1952] = nvar_1952; + functions[1953] = fn1953; + nvar_list[1953] = nvar_1953; + functions[1954] = fn1954; + nvar_list[1954] = nvar_1954; + functions[1955] = fn1955; + nvar_list[1955] = nvar_1955; + functions[1956] = fn1956; + nvar_list[1956] = nvar_1956; + functions[1957] = fn1957; + nvar_list[1957] = nvar_1957; + functions[1958] = fn1958; + nvar_list[1958] = nvar_1958; + functions[1959] = fn1959; + nvar_list[1959] = nvar_1959; + functions[1960] = fn1960; + nvar_list[1960] = nvar_1960; + functions[1961] = fn1961; + nvar_list[1961] = nvar_1961; + functions[1962] = fn1962; + nvar_list[1962] = nvar_1962; + functions[1963] = fn1963; + nvar_list[1963] = nvar_1963; + functions[1964] = fn1964; + nvar_list[1964] = nvar_1964; + functions[1965] = fn1965; + nvar_list[1965] = nvar_1965; + functions[1966] = fn1966; + nvar_list[1966] = nvar_1966; + functions[1967] = fn1967; + nvar_list[1967] = nvar_1967; + functions[1968] = fn1968; + nvar_list[1968] = nvar_1968; + functions[1969] = fn1969; + nvar_list[1969] = nvar_1969; + functions[1970] = fn1970; + nvar_list[1970] = nvar_1970; + functions[1971] = fn1971; + nvar_list[1971] = nvar_1971; + functions[1972] = fn1972; + nvar_list[1972] = nvar_1972; + functions[1973] = fn1973; + nvar_list[1973] = nvar_1973; + functions[1974] = fn1974; + nvar_list[1974] = nvar_1974; + functions[1975] = fn1975; + nvar_list[1975] = nvar_1975; + functions[1976] = fn1976; + nvar_list[1976] = nvar_1976; + functions[1977] = fn1977; + nvar_list[1977] = nvar_1977; + functions[1978] = fn1978; + nvar_list[1978] = nvar_1978; + functions[1979] = fn1979; + nvar_list[1979] = nvar_1979; + functions[1980] = fn1980; + nvar_list[1980] = nvar_1980; + functions[1981] = fn1981; + nvar_list[1981] = nvar_1981; + functions[1982] = fn1982; + nvar_list[1982] = nvar_1982; + functions[1983] = fn1983; + nvar_list[1983] = nvar_1983; + functions[1984] = fn1984; + nvar_list[1984] = nvar_1984; + functions[1985] = fn1985; + nvar_list[1985] = nvar_1985; + functions[1986] = fn1986; + nvar_list[1986] = nvar_1986; + functions[1987] = fn1987; + nvar_list[1987] = nvar_1987; + functions[1988] = fn1988; + nvar_list[1988] = nvar_1988; + functions[1989] = fn1989; + nvar_list[1989] = nvar_1989; + functions[1990] = fn1990; + nvar_list[1990] = nvar_1990; + functions[1991] = fn1991; + nvar_list[1991] = nvar_1991; + functions[1992] = fn1992; + nvar_list[1992] = nvar_1992; + functions[1993] = fn1993; + nvar_list[1993] = nvar_1993; + functions[1994] = fn1994; + nvar_list[1994] = nvar_1994; + functions[1995] = fn1995; + nvar_list[1995] = nvar_1995; + functions[1996] = fn1996; + nvar_list[1996] = nvar_1996; + functions[1997] = fn1997; + nvar_list[1997] = nvar_1997; + functions[1998] = fn1998; + nvar_list[1998] = nvar_1998; + functions[1999] = fn1999; + nvar_list[1999] = nvar_1999; + functions[2000] = fn2000; + nvar_list[2000] = nvar_2000; + functions[2001] = fn2001; + nvar_list[2001] = nvar_2001; + functions[2002] = fn2002; + nvar_list[2002] = nvar_2002; + functions[2003] = fn2003; + nvar_list[2003] = nvar_2003; + functions[2004] = fn2004; + nvar_list[2004] = nvar_2004; + functions[2005] = fn2005; + nvar_list[2005] = nvar_2005; + functions[2006] = fn2006; + nvar_list[2006] = nvar_2006; + functions[2007] = fn2007; + nvar_list[2007] = nvar_2007; + functions[2008] = fn2008; + nvar_list[2008] = nvar_2008; + functions[2009] = fn2009; + nvar_list[2009] = nvar_2009; + functions[2010] = fn2010; + nvar_list[2010] = nvar_2010; + functions[2011] = fn2011; + nvar_list[2011] = nvar_2011; + functions[2012] = fn2012; + nvar_list[2012] = nvar_2012; + functions[2013] = fn2013; + nvar_list[2013] = nvar_2013; + functions[2014] = fn2014; + nvar_list[2014] = nvar_2014; + functions[2015] = fn2015; + nvar_list[2015] = nvar_2015; + functions[2016] = fn2016; + nvar_list[2016] = nvar_2016; + functions[2017] = fn2017; + nvar_list[2017] = nvar_2017; + functions[2018] = fn2018; + nvar_list[2018] = nvar_2018; + functions[2019] = fn2019; + nvar_list[2019] = nvar_2019; + functions[2020] = fn2020; + nvar_list[2020] = nvar_2020; + functions[2021] = fn2021; + nvar_list[2021] = nvar_2021; + functions[2022] = fn2022; + nvar_list[2022] = nvar_2022; + functions[2023] = fn2023; + nvar_list[2023] = nvar_2023; + functions[2024] = fn2024; + nvar_list[2024] = nvar_2024; + functions[2025] = fn2025; + nvar_list[2025] = nvar_2025; + functions[2026] = fn2026; + nvar_list[2026] = nvar_2026; + functions[2027] = fn2027; + nvar_list[2027] = nvar_2027; + functions[2028] = fn2028; + nvar_list[2028] = nvar_2028; + functions[2029] = fn2029; + nvar_list[2029] = nvar_2029; + functions[2030] = fn2030; + nvar_list[2030] = nvar_2030; + functions[2031] = fn2031; + nvar_list[2031] = nvar_2031; + functions[2032] = fn2032; + nvar_list[2032] = nvar_2032; + functions[2033] = fn2033; + nvar_list[2033] = nvar_2033; + functions[2034] = fn2034; + nvar_list[2034] = nvar_2034; + functions[2035] = fn2035; + nvar_list[2035] = nvar_2035; + functions[2036] = fn2036; + nvar_list[2036] = nvar_2036; + functions[2037] = fn2037; + nvar_list[2037] = nvar_2037; + functions[2038] = fn2038; + nvar_list[2038] = nvar_2038; + functions[2039] = fn2039; + nvar_list[2039] = nvar_2039; + functions[2040] = fn2040; + nvar_list[2040] = nvar_2040; + functions[2041] = fn2041; + nvar_list[2041] = nvar_2041; + functions[2042] = fn2042; + nvar_list[2042] = nvar_2042; + functions[2043] = fn2043; + nvar_list[2043] = nvar_2043; + functions[2044] = fn2044; + nvar_list[2044] = nvar_2044; + functions[2045] = fn2045; + nvar_list[2045] = nvar_2045; + functions[2046] = fn2046; + nvar_list[2046] = nvar_2046; + functions[2047] = fn2047; + nvar_list[2047] = nvar_2047; + functions[2048] = fn2048; + nvar_list[2048] = nvar_2048; + functions[2049] = fn2049; + nvar_list[2049] = nvar_2049; + functions[2050] = fn2050; + nvar_list[2050] = nvar_2050; + functions[2051] = fn2051; + nvar_list[2051] = nvar_2051; + functions[2052] = fn2052; + nvar_list[2052] = nvar_2052; + functions[2053] = fn2053; + nvar_list[2053] = nvar_2053; + functions[2054] = fn2054; + nvar_list[2054] = nvar_2054; + functions[2055] = fn2055; + nvar_list[2055] = nvar_2055; + functions[2056] = fn2056; + nvar_list[2056] = nvar_2056; + functions[2057] = fn2057; + nvar_list[2057] = nvar_2057; + functions[2058] = fn2058; + nvar_list[2058] = nvar_2058; + functions[2059] = fn2059; + nvar_list[2059] = nvar_2059; + functions[2060] = fn2060; + nvar_list[2060] = nvar_2060; + functions[2061] = fn2061; + nvar_list[2061] = nvar_2061; + functions[2062] = fn2062; + nvar_list[2062] = nvar_2062; + functions[2063] = fn2063; + nvar_list[2063] = nvar_2063; + functions[2064] = fn2064; + nvar_list[2064] = nvar_2064; + functions[2065] = fn2065; + nvar_list[2065] = nvar_2065; + functions[2066] = fn2066; + nvar_list[2066] = nvar_2066; + functions[2067] = fn2067; + nvar_list[2067] = nvar_2067; + functions[2068] = fn2068; + nvar_list[2068] = nvar_2068; + functions[2069] = fn2069; + nvar_list[2069] = nvar_2069; + functions[2070] = fn2070; + nvar_list[2070] = nvar_2070; + functions[2071] = fn2071; + nvar_list[2071] = nvar_2071; + functions[2072] = fn2072; + nvar_list[2072] = nvar_2072; + functions[2073] = fn2073; + nvar_list[2073] = nvar_2073; + functions[2074] = fn2074; + nvar_list[2074] = nvar_2074; + functions[2075] = fn2075; + nvar_list[2075] = nvar_2075; + functions[2076] = fn2076; + nvar_list[2076] = nvar_2076; + functions[2077] = fn2077; + nvar_list[2077] = nvar_2077; + functions[2078] = fn2078; + nvar_list[2078] = nvar_2078; + functions[2079] = fn2079; + nvar_list[2079] = nvar_2079; + functions[2080] = fn2080; + nvar_list[2080] = nvar_2080; + functions[2081] = fn2081; + nvar_list[2081] = nvar_2081; + functions[2082] = fn2082; + nvar_list[2082] = nvar_2082; + functions[2083] = fn2083; + nvar_list[2083] = nvar_2083; + functions[2084] = fn2084; + nvar_list[2084] = nvar_2084; + functions[2085] = fn2085; + nvar_list[2085] = nvar_2085; + functions[2086] = fn2086; + nvar_list[2086] = nvar_2086; + functions[2087] = fn2087; + nvar_list[2087] = nvar_2087; + functions[2088] = fn2088; + nvar_list[2088] = nvar_2088; + functions[2089] = fn2089; + nvar_list[2089] = nvar_2089; + functions[2090] = fn2090; + nvar_list[2090] = nvar_2090; + functions[2091] = fn2091; + nvar_list[2091] = nvar_2091; + functions[2092] = fn2092; + nvar_list[2092] = nvar_2092; + functions[2093] = fn2093; + nvar_list[2093] = nvar_2093; + functions[2094] = fn2094; + nvar_list[2094] = nvar_2094; + functions[2095] = fn2095; + nvar_list[2095] = nvar_2095; + functions[2096] = fn2096; + nvar_list[2096] = nvar_2096; + functions[2097] = fn2097; + nvar_list[2097] = nvar_2097; + functions[2098] = fn2098; + nvar_list[2098] = nvar_2098; + functions[2099] = fn2099; + nvar_list[2099] = nvar_2099; + functions[2100] = fn2100; + nvar_list[2100] = nvar_2100; + functions[2101] = fn2101; + nvar_list[2101] = nvar_2101; + functions[2102] = fn2102; + nvar_list[2102] = nvar_2102; + functions[2103] = fn2103; + nvar_list[2103] = nvar_2103; + functions[2104] = fn2104; + nvar_list[2104] = nvar_2104; + functions[2105] = fn2105; + nvar_list[2105] = nvar_2105; + functions[2106] = fn2106; + nvar_list[2106] = nvar_2106; + functions[2107] = fn2107; + nvar_list[2107] = nvar_2107; + functions[2108] = fn2108; + nvar_list[2108] = nvar_2108; + functions[2109] = fn2109; + nvar_list[2109] = nvar_2109; + functions[2110] = fn2110; + nvar_list[2110] = nvar_2110; + functions[2111] = fn2111; + nvar_list[2111] = nvar_2111; + functions[2112] = fn2112; + nvar_list[2112] = nvar_2112; + functions[2113] = fn2113; + nvar_list[2113] = nvar_2113; + functions[2114] = fn2114; + nvar_list[2114] = nvar_2114; + functions[2115] = fn2115; + nvar_list[2115] = nvar_2115; + functions[2116] = fn2116; + nvar_list[2116] = nvar_2116; + functions[2117] = fn2117; + nvar_list[2117] = nvar_2117; + functions[2118] = fn2118; + nvar_list[2118] = nvar_2118; + functions[2119] = fn2119; + nvar_list[2119] = nvar_2119; + functions[2120] = fn2120; + nvar_list[2120] = nvar_2120; + functions[2121] = fn2121; + nvar_list[2121] = nvar_2121; + functions[2122] = fn2122; + nvar_list[2122] = nvar_2122; + functions[2123] = fn2123; + nvar_list[2123] = nvar_2123; + functions[2124] = fn2124; + nvar_list[2124] = nvar_2124; + functions[2125] = fn2125; + nvar_list[2125] = nvar_2125; + functions[2126] = fn2126; + nvar_list[2126] = nvar_2126; + functions[2127] = fn2127; + nvar_list[2127] = nvar_2127; + functions[2128] = fn2128; + nvar_list[2128] = nvar_2128; + functions[2129] = fn2129; + nvar_list[2129] = nvar_2129; + functions[2130] = fn2130; + nvar_list[2130] = nvar_2130; + functions[2131] = fn2131; + nvar_list[2131] = nvar_2131; + functions[2132] = fn2132; + nvar_list[2132] = nvar_2132; + functions[2133] = fn2133; + nvar_list[2133] = nvar_2133; + functions[2134] = fn2134; + nvar_list[2134] = nvar_2134; + functions[2135] = fn2135; + nvar_list[2135] = nvar_2135; + functions[2136] = fn2136; + nvar_list[2136] = nvar_2136; + functions[2137] = fn2137; + nvar_list[2137] = nvar_2137; + functions[2138] = fn2138; + nvar_list[2138] = nvar_2138; + functions[2139] = fn2139; + nvar_list[2139] = nvar_2139; + functions[2140] = fn2140; + nvar_list[2140] = nvar_2140; + functions[2141] = fn2141; + nvar_list[2141] = nvar_2141; + functions[2142] = fn2142; + nvar_list[2142] = nvar_2142; + functions[2143] = fn2143; + nvar_list[2143] = nvar_2143; + functions[2144] = fn2144; + nvar_list[2144] = nvar_2144; + functions[2145] = fn2145; + nvar_list[2145] = nvar_2145; + functions[2146] = fn2146; + nvar_list[2146] = nvar_2146; + functions[2147] = fn2147; + nvar_list[2147] = nvar_2147; + functions[2148] = fn2148; + nvar_list[2148] = nvar_2148; + functions[2149] = fn2149; + nvar_list[2149] = nvar_2149; + functions[2150] = fn2150; + nvar_list[2150] = nvar_2150; + functions[2151] = fn2151; + nvar_list[2151] = nvar_2151; + functions[2152] = fn2152; + nvar_list[2152] = nvar_2152; + functions[2153] = fn2153; + nvar_list[2153] = nvar_2153; + functions[2154] = fn2154; + nvar_list[2154] = nvar_2154; + functions[2155] = fn2155; + nvar_list[2155] = nvar_2155; + functions[2156] = fn2156; + nvar_list[2156] = nvar_2156; + functions[2157] = fn2157; + nvar_list[2157] = nvar_2157; + functions[2158] = fn2158; + nvar_list[2158] = nvar_2158; + functions[2159] = fn2159; + nvar_list[2159] = nvar_2159; + functions[2160] = fn2160; + nvar_list[2160] = nvar_2160; + functions[2161] = fn2161; + nvar_list[2161] = nvar_2161; + functions[2162] = fn2162; + nvar_list[2162] = nvar_2162; + functions[2163] = fn2163; + nvar_list[2163] = nvar_2163; + functions[2164] = fn2164; + nvar_list[2164] = nvar_2164; + functions[2165] = fn2165; + nvar_list[2165] = nvar_2165; + functions[2166] = fn2166; + nvar_list[2166] = nvar_2166; + functions[2167] = fn2167; + nvar_list[2167] = nvar_2167; + functions[2168] = fn2168; + nvar_list[2168] = nvar_2168; + functions[2169] = fn2169; + nvar_list[2169] = nvar_2169; + functions[2170] = fn2170; + nvar_list[2170] = nvar_2170; + functions[2171] = fn2171; + nvar_list[2171] = nvar_2171; + functions[2172] = fn2172; + nvar_list[2172] = nvar_2172; + functions[2173] = fn2173; + nvar_list[2173] = nvar_2173; + functions[2174] = fn2174; + nvar_list[2174] = nvar_2174; + functions[2175] = fn2175; + nvar_list[2175] = nvar_2175; + functions[2176] = fn2176; + nvar_list[2176] = nvar_2176; + functions[2177] = fn2177; + nvar_list[2177] = nvar_2177; + functions[2178] = fn2178; + nvar_list[2178] = nvar_2178; + functions[2179] = fn2179; + nvar_list[2179] = nvar_2179; + functions[2180] = fn2180; + nvar_list[2180] = nvar_2180; + functions[2181] = fn2181; + nvar_list[2181] = nvar_2181; + functions[2182] = fn2182; + nvar_list[2182] = nvar_2182; + functions[2183] = fn2183; + nvar_list[2183] = nvar_2183; + functions[2184] = fn2184; + nvar_list[2184] = nvar_2184; + functions[2185] = fn2185; + nvar_list[2185] = nvar_2185; + functions[2186] = fn2186; + nvar_list[2186] = nvar_2186; + functions[2187] = fn2187; + nvar_list[2187] = nvar_2187; + functions[2188] = fn2188; + nvar_list[2188] = nvar_2188; + functions[2189] = fn2189; + nvar_list[2189] = nvar_2189; + functions[2190] = fn2190; + nvar_list[2190] = nvar_2190; + functions[2191] = fn2191; + nvar_list[2191] = nvar_2191; + functions[2192] = fn2192; + nvar_list[2192] = nvar_2192; + functions[2193] = fn2193; + nvar_list[2193] = nvar_2193; + functions[2194] = fn2194; + nvar_list[2194] = nvar_2194; + functions[2195] = fn2195; + nvar_list[2195] = nvar_2195; + functions[2196] = fn2196; + nvar_list[2196] = nvar_2196; + functions[2197] = fn2197; + nvar_list[2197] = nvar_2197; + functions[2198] = fn2198; + nvar_list[2198] = nvar_2198; + functions[2199] = fn2199; + nvar_list[2199] = nvar_2199; + functions[2200] = fn2200; + nvar_list[2200] = nvar_2200; + functions[2201] = fn2201; + nvar_list[2201] = nvar_2201; + functions[2202] = fn2202; + nvar_list[2202] = nvar_2202; + functions[2203] = fn2203; + nvar_list[2203] = nvar_2203; + functions[2204] = fn2204; + nvar_list[2204] = nvar_2204; + functions[2205] = fn2205; + nvar_list[2205] = nvar_2205; + functions[2206] = fn2206; + nvar_list[2206] = nvar_2206; + functions[2207] = fn2207; + nvar_list[2207] = nvar_2207; + functions[2208] = fn2208; + nvar_list[2208] = nvar_2208; + functions[2209] = fn2209; + nvar_list[2209] = nvar_2209; + functions[2210] = fn2210; + nvar_list[2210] = nvar_2210; + functions[2211] = fn2211; + nvar_list[2211] = nvar_2211; + functions[2212] = fn2212; + nvar_list[2212] = nvar_2212; + functions[2213] = fn2213; + nvar_list[2213] = nvar_2213; + functions[2214] = fn2214; + nvar_list[2214] = nvar_2214; + functions[2215] = fn2215; + nvar_list[2215] = nvar_2215; + functions[2216] = fn2216; + nvar_list[2216] = nvar_2216; + functions[2217] = fn2217; + nvar_list[2217] = nvar_2217; + functions[2218] = fn2218; + nvar_list[2218] = nvar_2218; + functions[2219] = fn2219; + nvar_list[2219] = nvar_2219; + functions[2220] = fn2220; + nvar_list[2220] = nvar_2220; + functions[2221] = fn2221; + nvar_list[2221] = nvar_2221; + functions[2222] = fn2222; + nvar_list[2222] = nvar_2222; + functions[2223] = fn2223; + nvar_list[2223] = nvar_2223; + functions[2224] = fn2224; + nvar_list[2224] = nvar_2224; + functions[2225] = fn2225; + nvar_list[2225] = nvar_2225; + functions[2226] = fn2226; + nvar_list[2226] = nvar_2226; + functions[2227] = fn2227; + nvar_list[2227] = nvar_2227; + functions[2228] = fn2228; + nvar_list[2228] = nvar_2228; + functions[2229] = fn2229; + nvar_list[2229] = nvar_2229; + functions[2230] = fn2230; + nvar_list[2230] = nvar_2230; + functions[2231] = fn2231; + nvar_list[2231] = nvar_2231; + functions[2232] = fn2232; + nvar_list[2232] = nvar_2232; + functions[2233] = fn2233; + nvar_list[2233] = nvar_2233; + functions[2234] = fn2234; + nvar_list[2234] = nvar_2234; + functions[2235] = fn2235; + nvar_list[2235] = nvar_2235; + functions[2236] = fn2236; + nvar_list[2236] = nvar_2236; + functions[2237] = fn2237; + nvar_list[2237] = nvar_2237; + functions[2238] = fn2238; + nvar_list[2238] = nvar_2238; + functions[2239] = fn2239; + nvar_list[2239] = nvar_2239; + functions[2240] = fn2240; + nvar_list[2240] = nvar_2240; + functions[2241] = fn2241; + nvar_list[2241] = nvar_2241; + functions[2242] = fn2242; + nvar_list[2242] = nvar_2242; + functions[2243] = fn2243; + nvar_list[2243] = nvar_2243; + functions[2244] = fn2244; + nvar_list[2244] = nvar_2244; + functions[2245] = fn2245; + nvar_list[2245] = nvar_2245; + functions[2246] = fn2246; + nvar_list[2246] = nvar_2246; + functions[2247] = fn2247; + nvar_list[2247] = nvar_2247; + functions[2248] = fn2248; + nvar_list[2248] = nvar_2248; + functions[2249] = fn2249; + nvar_list[2249] = nvar_2249; + functions[2250] = fn2250; + nvar_list[2250] = nvar_2250; + functions[2251] = fn2251; + nvar_list[2251] = nvar_2251; + functions[2252] = fn2252; + nvar_list[2252] = nvar_2252; + functions[2253] = fn2253; + nvar_list[2253] = nvar_2253; + functions[2254] = fn2254; + nvar_list[2254] = nvar_2254; + functions[2255] = fn2255; + nvar_list[2255] = nvar_2255; + functions[2256] = fn2256; + nvar_list[2256] = nvar_2256; + functions[2257] = fn2257; + nvar_list[2257] = nvar_2257; + functions[2258] = fn2258; + nvar_list[2258] = nvar_2258; + functions[2259] = fn2259; + nvar_list[2259] = nvar_2259; + functions[2260] = fn2260; + nvar_list[2260] = nvar_2260; + functions[2261] = fn2261; + nvar_list[2261] = nvar_2261; + functions[2262] = fn2262; + nvar_list[2262] = nvar_2262; + functions[2263] = fn2263; + nvar_list[2263] = nvar_2263; + functions[2264] = fn2264; + nvar_list[2264] = nvar_2264; + functions[2265] = fn2265; + nvar_list[2265] = nvar_2265; + functions[2266] = fn2266; + nvar_list[2266] = nvar_2266; + functions[2267] = fn2267; + nvar_list[2267] = nvar_2267; + functions[2268] = fn2268; + nvar_list[2268] = nvar_2268; + functions[2269] = fn2269; + nvar_list[2269] = nvar_2269; + functions[2270] = fn2270; + nvar_list[2270] = nvar_2270; + functions[2271] = fn2271; + nvar_list[2271] = nvar_2271; + functions[2272] = fn2272; + nvar_list[2272] = nvar_2272; + functions[2273] = fn2273; + nvar_list[2273] = nvar_2273; + functions[2274] = fn2274; + nvar_list[2274] = nvar_2274; + functions[2275] = fn2275; + nvar_list[2275] = nvar_2275; + functions[2276] = fn2276; + nvar_list[2276] = nvar_2276; + functions[2277] = fn2277; + nvar_list[2277] = nvar_2277; + functions[2278] = fn2278; + nvar_list[2278] = nvar_2278; + functions[2279] = fn2279; + nvar_list[2279] = nvar_2279; + functions[2280] = fn2280; + nvar_list[2280] = nvar_2280; + functions[2281] = fn2281; + nvar_list[2281] = nvar_2281; + functions[2282] = fn2282; + nvar_list[2282] = nvar_2282; + functions[2283] = fn2283; + nvar_list[2283] = nvar_2283; + functions[2284] = fn2284; + nvar_list[2284] = nvar_2284; + functions[2285] = fn2285; + nvar_list[2285] = nvar_2285; + functions[2286] = fn2286; + nvar_list[2286] = nvar_2286; + functions[2287] = fn2287; + nvar_list[2287] = nvar_2287; + functions[2288] = fn2288; + nvar_list[2288] = nvar_2288; + functions[2289] = fn2289; + nvar_list[2289] = nvar_2289; + functions[2290] = fn2290; + nvar_list[2290] = nvar_2290; + functions[2291] = fn2291; + nvar_list[2291] = nvar_2291; + functions[2292] = fn2292; + nvar_list[2292] = nvar_2292; + functions[2293] = fn2293; + nvar_list[2293] = nvar_2293; + functions[2294] = fn2294; + nvar_list[2294] = nvar_2294; + functions[2295] = fn2295; + nvar_list[2295] = nvar_2295; + functions[2296] = fn2296; + nvar_list[2296] = nvar_2296; + functions[2297] = fn2297; + nvar_list[2297] = nvar_2297; + functions[2298] = fn2298; + nvar_list[2298] = nvar_2298; + functions[2299] = fn2299; + nvar_list[2299] = nvar_2299; + functions[2300] = fn2300; + nvar_list[2300] = nvar_2300; + functions[2301] = fn2301; + nvar_list[2301] = nvar_2301; + functions[2302] = fn2302; + nvar_list[2302] = nvar_2302; + functions[2303] = fn2303; + nvar_list[2303] = nvar_2303; + functions[2304] = fn2304; + nvar_list[2304] = nvar_2304; + functions[2305] = fn2305; + nvar_list[2305] = nvar_2305; + functions[2306] = fn2306; + nvar_list[2306] = nvar_2306; + functions[2307] = fn2307; + nvar_list[2307] = nvar_2307; + functions[2308] = fn2308; + nvar_list[2308] = nvar_2308; + functions[2309] = fn2309; + nvar_list[2309] = nvar_2309; + functions[2310] = fn2310; + nvar_list[2310] = nvar_2310; + functions[2311] = fn2311; + nvar_list[2311] = nvar_2311; + functions[2312] = fn2312; + nvar_list[2312] = nvar_2312; + functions[2313] = fn2313; + nvar_list[2313] = nvar_2313; + functions[2314] = fn2314; + nvar_list[2314] = nvar_2314; + functions[2315] = fn2315; + nvar_list[2315] = nvar_2315; + functions[2316] = fn2316; + nvar_list[2316] = nvar_2316; + functions[2317] = fn2317; + nvar_list[2317] = nvar_2317; + functions[2318] = fn2318; + nvar_list[2318] = nvar_2318; + functions[2319] = fn2319; + nvar_list[2319] = nvar_2319; + functions[2320] = fn2320; + nvar_list[2320] = nvar_2320; + functions[2321] = fn2321; + nvar_list[2321] = nvar_2321; + functions[2322] = fn2322; + nvar_list[2322] = nvar_2322; + functions[2323] = fn2323; + nvar_list[2323] = nvar_2323; + functions[2324] = fn2324; + nvar_list[2324] = nvar_2324; + functions[2325] = fn2325; + nvar_list[2325] = nvar_2325; + functions[2326] = fn2326; + nvar_list[2326] = nvar_2326; + functions[2327] = fn2327; + nvar_list[2327] = nvar_2327; + functions[2328] = fn2328; + nvar_list[2328] = nvar_2328; + functions[2329] = fn2329; + nvar_list[2329] = nvar_2329; + functions[2330] = fn2330; + nvar_list[2330] = nvar_2330; + functions[2331] = fn2331; + nvar_list[2331] = nvar_2331; + functions[2332] = fn2332; + nvar_list[2332] = nvar_2332; + functions[2333] = fn2333; + nvar_list[2333] = nvar_2333; + functions[2334] = fn2334; + nvar_list[2334] = nvar_2334; + functions[2335] = fn2335; + nvar_list[2335] = nvar_2335; + functions[2336] = fn2336; + nvar_list[2336] = nvar_2336; + functions[2337] = fn2337; + nvar_list[2337] = nvar_2337; + functions[2338] = fn2338; + nvar_list[2338] = nvar_2338; + functions[2339] = fn2339; + nvar_list[2339] = nvar_2339; + functions[2340] = fn2340; + nvar_list[2340] = nvar_2340; + functions[2341] = fn2341; + nvar_list[2341] = nvar_2341; + functions[2342] = fn2342; + nvar_list[2342] = nvar_2342; + functions[2343] = fn2343; + nvar_list[2343] = nvar_2343; + functions[2344] = fn2344; + nvar_list[2344] = nvar_2344; + functions[2345] = fn2345; + nvar_list[2345] = nvar_2345; + functions[2346] = fn2346; + nvar_list[2346] = nvar_2346; + functions[2347] = fn2347; + nvar_list[2347] = nvar_2347; + functions[2348] = fn2348; + nvar_list[2348] = nvar_2348; + functions[2349] = fn2349; + nvar_list[2349] = nvar_2349; + functions[2350] = fn2350; + nvar_list[2350] = nvar_2350; + functions[2351] = fn2351; + nvar_list[2351] = nvar_2351; + functions[2352] = fn2352; + nvar_list[2352] = nvar_2352; + functions[2353] = fn2353; + nvar_list[2353] = nvar_2353; + functions[2354] = fn2354; + nvar_list[2354] = nvar_2354; + functions[2355] = fn2355; + nvar_list[2355] = nvar_2355; + functions[2356] = fn2356; + nvar_list[2356] = nvar_2356; + functions[2357] = fn2357; + nvar_list[2357] = nvar_2357; + functions[2358] = fn2358; + nvar_list[2358] = nvar_2358; + functions[2359] = fn2359; + nvar_list[2359] = nvar_2359; + functions[2360] = fn2360; + nvar_list[2360] = nvar_2360; + functions[2361] = fn2361; + nvar_list[2361] = nvar_2361; + functions[2362] = fn2362; + nvar_list[2362] = nvar_2362; + functions[2363] = fn2363; + nvar_list[2363] = nvar_2363; + functions[2364] = fn2364; + nvar_list[2364] = nvar_2364; + functions[2365] = fn2365; + nvar_list[2365] = nvar_2365; + functions[2366] = fn2366; + nvar_list[2366] = nvar_2366; + functions[2367] = fn2367; + nvar_list[2367] = nvar_2367; + functions[2368] = fn2368; + nvar_list[2368] = nvar_2368; + functions[2369] = fn2369; + nvar_list[2369] = nvar_2369; + functions[2370] = fn2370; + nvar_list[2370] = nvar_2370; + functions[2371] = fn2371; + nvar_list[2371] = nvar_2371; + functions[2372] = fn2372; + nvar_list[2372] = nvar_2372; + functions[2373] = fn2373; + nvar_list[2373] = nvar_2373; + functions[2374] = fn2374; + nvar_list[2374] = nvar_2374; + functions[2375] = fn2375; + nvar_list[2375] = nvar_2375; + functions[2376] = fn2376; + nvar_list[2376] = nvar_2376; + functions[2377] = fn2377; + nvar_list[2377] = nvar_2377; + functions[2378] = fn2378; + nvar_list[2378] = nvar_2378; + functions[2379] = fn2379; + nvar_list[2379] = nvar_2379; + functions[2380] = fn2380; + nvar_list[2380] = nvar_2380; + functions[2381] = fn2381; + nvar_list[2381] = nvar_2381; + functions[2382] = fn2382; + nvar_list[2382] = nvar_2382; + functions[2383] = fn2383; + nvar_list[2383] = nvar_2383; + functions[2384] = fn2384; + nvar_list[2384] = nvar_2384; + functions[2385] = fn2385; + nvar_list[2385] = nvar_2385; + functions[2386] = fn2386; + nvar_list[2386] = nvar_2386; + functions[2387] = fn2387; + nvar_list[2387] = nvar_2387; + functions[2388] = fn2388; + nvar_list[2388] = nvar_2388; + functions[2389] = fn2389; + nvar_list[2389] = nvar_2389; + functions[2390] = fn2390; + nvar_list[2390] = nvar_2390; + functions[2391] = fn2391; + nvar_list[2391] = nvar_2391; + functions[2392] = fn2392; + nvar_list[2392] = nvar_2392; + functions[2393] = fn2393; + nvar_list[2393] = nvar_2393; + functions[2394] = fn2394; + nvar_list[2394] = nvar_2394; + functions[2395] = fn2395; + nvar_list[2395] = nvar_2395; + functions[2396] = fn2396; + nvar_list[2396] = nvar_2396; + functions[2397] = fn2397; + nvar_list[2397] = nvar_2397; + functions[2398] = fn2398; + nvar_list[2398] = nvar_2398; + functions[2399] = fn2399; + nvar_list[2399] = nvar_2399; + functions[2400] = fn2400; + nvar_list[2400] = nvar_2400; + functions[2401] = fn2401; + nvar_list[2401] = nvar_2401; + functions[2402] = fn2402; + nvar_list[2402] = nvar_2402; + functions[2403] = fn2403; + nvar_list[2403] = nvar_2403; + functions[2404] = fn2404; + nvar_list[2404] = nvar_2404; + functions[2405] = fn2405; + nvar_list[2405] = nvar_2405; + functions[2406] = fn2406; + nvar_list[2406] = nvar_2406; + functions[2407] = fn2407; + nvar_list[2407] = nvar_2407; + functions[2408] = fn2408; + nvar_list[2408] = nvar_2408; + functions[2409] = fn2409; + nvar_list[2409] = nvar_2409; + functions[2410] = fn2410; + nvar_list[2410] = nvar_2410; + functions[2411] = fn2411; + nvar_list[2411] = nvar_2411; + functions[2412] = fn2412; + nvar_list[2412] = nvar_2412; + functions[2413] = fn2413; + nvar_list[2413] = nvar_2413; + functions[2414] = fn2414; + nvar_list[2414] = nvar_2414; + functions[2415] = fn2415; + nvar_list[2415] = nvar_2415; + functions[2416] = fn2416; + nvar_list[2416] = nvar_2416; + functions[2417] = fn2417; + nvar_list[2417] = nvar_2417; + functions[2418] = fn2418; + nvar_list[2418] = nvar_2418; + functions[2419] = fn2419; + nvar_list[2419] = nvar_2419; + functions[2420] = fn2420; + nvar_list[2420] = nvar_2420; + functions[2421] = fn2421; + nvar_list[2421] = nvar_2421; + functions[2422] = fn2422; + nvar_list[2422] = nvar_2422; + functions[2423] = fn2423; + nvar_list[2423] = nvar_2423; + functions[2424] = fn2424; + nvar_list[2424] = nvar_2424; + functions[2425] = fn2425; + nvar_list[2425] = nvar_2425; + functions[2426] = fn2426; + nvar_list[2426] = nvar_2426; + functions[2427] = fn2427; + nvar_list[2427] = nvar_2427; + functions[2428] = fn2428; + nvar_list[2428] = nvar_2428; + functions[2429] = fn2429; + nvar_list[2429] = nvar_2429; + functions[2430] = fn2430; + nvar_list[2430] = nvar_2430; + functions[2431] = fn2431; + nvar_list[2431] = nvar_2431; + functions[2432] = fn2432; + nvar_list[2432] = nvar_2432; + functions[2433] = fn2433; + nvar_list[2433] = nvar_2433; + functions[2434] = fn2434; + nvar_list[2434] = nvar_2434; + functions[2435] = fn2435; + nvar_list[2435] = nvar_2435; + functions[2436] = fn2436; + nvar_list[2436] = nvar_2436; + functions[2437] = fn2437; + nvar_list[2437] = nvar_2437; + functions[2438] = fn2438; + nvar_list[2438] = nvar_2438; + functions[2439] = fn2439; + nvar_list[2439] = nvar_2439; + functions[2440] = fn2440; + nvar_list[2440] = nvar_2440; + functions[2441] = fn2441; + nvar_list[2441] = nvar_2441; + functions[2442] = fn2442; + nvar_list[2442] = nvar_2442; + functions[2443] = fn2443; + nvar_list[2443] = nvar_2443; + functions[2444] = fn2444; + nvar_list[2444] = nvar_2444; + functions[2445] = fn2445; + nvar_list[2445] = nvar_2445; + functions[2446] = fn2446; + nvar_list[2446] = nvar_2446; + functions[2447] = fn2447; + nvar_list[2447] = nvar_2447; + functions[2448] = fn2448; + nvar_list[2448] = nvar_2448; + functions[2449] = fn2449; + nvar_list[2449] = nvar_2449; + functions[2450] = fn2450; + nvar_list[2450] = nvar_2450; + functions[2451] = fn2451; + nvar_list[2451] = nvar_2451; + functions[2452] = fn2452; + nvar_list[2452] = nvar_2452; + functions[2453] = fn2453; + nvar_list[2453] = nvar_2453; + functions[2454] = fn2454; + nvar_list[2454] = nvar_2454; + functions[2455] = fn2455; + nvar_list[2455] = nvar_2455; + functions[2456] = fn2456; + nvar_list[2456] = nvar_2456; + functions[2457] = fn2457; + nvar_list[2457] = nvar_2457; + functions[2458] = fn2458; + nvar_list[2458] = nvar_2458; + functions[2459] = fn2459; + nvar_list[2459] = nvar_2459; + functions[2460] = fn2460; + nvar_list[2460] = nvar_2460; + functions[2461] = fn2461; + nvar_list[2461] = nvar_2461; + functions[2462] = fn2462; + nvar_list[2462] = nvar_2462; + functions[2463] = fn2463; + nvar_list[2463] = nvar_2463; + functions[2464] = fn2464; + nvar_list[2464] = nvar_2464; + functions[2465] = fn2465; + nvar_list[2465] = nvar_2465; + functions[2466] = fn2466; + nvar_list[2466] = nvar_2466; + functions[2467] = fn2467; + nvar_list[2467] = nvar_2467; + functions[2468] = fn2468; + nvar_list[2468] = nvar_2468; + functions[2469] = fn2469; + nvar_list[2469] = nvar_2469; + functions[2470] = fn2470; + nvar_list[2470] = nvar_2470; + functions[2471] = fn2471; + nvar_list[2471] = nvar_2471; + functions[2472] = fn2472; + nvar_list[2472] = nvar_2472; + functions[2473] = fn2473; + nvar_list[2473] = nvar_2473; + functions[2474] = fn2474; + nvar_list[2474] = nvar_2474; + functions[2475] = fn2475; + nvar_list[2475] = nvar_2475; + functions[2476] = fn2476; + nvar_list[2476] = nvar_2476; + functions[2477] = fn2477; + nvar_list[2477] = nvar_2477; + functions[2478] = fn2478; + nvar_list[2478] = nvar_2478; + functions[2479] = fn2479; + nvar_list[2479] = nvar_2479; + functions[2480] = fn2480; + nvar_list[2480] = nvar_2480; + functions[2481] = fn2481; + nvar_list[2481] = nvar_2481; + functions[2482] = fn2482; + nvar_list[2482] = nvar_2482; + functions[2483] = fn2483; + nvar_list[2483] = nvar_2483; + functions[2484] = fn2484; + nvar_list[2484] = nvar_2484; + functions[2485] = fn2485; + nvar_list[2485] = nvar_2485; + functions[2486] = fn2486; + nvar_list[2486] = nvar_2486; + functions[2487] = fn2487; + nvar_list[2487] = nvar_2487; + functions[2488] = fn2488; + nvar_list[2488] = nvar_2488; + functions[2489] = fn2489; + nvar_list[2489] = nvar_2489; + functions[2490] = fn2490; + nvar_list[2490] = nvar_2490; + functions[2491] = fn2491; + nvar_list[2491] = nvar_2491; + functions[2492] = fn2492; + nvar_list[2492] = nvar_2492; + functions[2493] = fn2493; + nvar_list[2493] = nvar_2493; + functions[2494] = fn2494; + nvar_list[2494] = nvar_2494; + functions[2495] = fn2495; + nvar_list[2495] = nvar_2495; + functions[2496] = fn2496; + nvar_list[2496] = nvar_2496; + functions[2497] = fn2497; + nvar_list[2497] = nvar_2497; + functions[2498] = fn2498; + nvar_list[2498] = nvar_2498; + functions[2499] = fn2499; + nvar_list[2499] = nvar_2499; + functions[2500] = fn2500; + nvar_list[2500] = nvar_2500; + functions[2501] = fn2501; + nvar_list[2501] = nvar_2501; + functions[2502] = fn2502; + nvar_list[2502] = nvar_2502; + functions[2503] = fn2503; + nvar_list[2503] = nvar_2503; + functions[2504] = fn2504; + nvar_list[2504] = nvar_2504; + functions[2505] = fn2505; + nvar_list[2505] = nvar_2505; + functions[2506] = fn2506; + nvar_list[2506] = nvar_2506; + functions[2507] = fn2507; + nvar_list[2507] = nvar_2507; + functions[2508] = fn2508; + nvar_list[2508] = nvar_2508; + functions[2509] = fn2509; + nvar_list[2509] = nvar_2509; + functions[2510] = fn2510; + nvar_list[2510] = nvar_2510; + functions[2511] = fn2511; + nvar_list[2511] = nvar_2511; + functions[2512] = fn2512; + nvar_list[2512] = nvar_2512; + functions[2513] = fn2513; + nvar_list[2513] = nvar_2513; + functions[2514] = fn2514; + nvar_list[2514] = nvar_2514; + functions[2515] = fn2515; + nvar_list[2515] = nvar_2515; + functions[2516] = fn2516; + nvar_list[2516] = nvar_2516; + functions[2517] = fn2517; + nvar_list[2517] = nvar_2517; + functions[2518] = fn2518; + nvar_list[2518] = nvar_2518; + functions[2519] = fn2519; + nvar_list[2519] = nvar_2519; + functions[2520] = fn2520; + nvar_list[2520] = nvar_2520; + functions[2521] = fn2521; + nvar_list[2521] = nvar_2521; + functions[2522] = fn2522; + nvar_list[2522] = nvar_2522; + functions[2523] = fn2523; + nvar_list[2523] = nvar_2523; + functions[2524] = fn2524; + nvar_list[2524] = nvar_2524; + functions[2525] = fn2525; + nvar_list[2525] = nvar_2525; + functions[2526] = fn2526; + nvar_list[2526] = nvar_2526; + functions[2527] = fn2527; + nvar_list[2527] = nvar_2527; + functions[2528] = fn2528; + nvar_list[2528] = nvar_2528; + functions[2529] = fn2529; + nvar_list[2529] = nvar_2529; + functions[2530] = fn2530; + nvar_list[2530] = nvar_2530; + functions[2531] = fn2531; + nvar_list[2531] = nvar_2531; + functions[2532] = fn2532; + nvar_list[2532] = nvar_2532; + functions[2533] = fn2533; + nvar_list[2533] = nvar_2533; + functions[2534] = fn2534; + nvar_list[2534] = nvar_2534; + functions[2535] = fn2535; + nvar_list[2535] = nvar_2535; + functions[2536] = fn2536; + nvar_list[2536] = nvar_2536; + functions[2537] = fn2537; + nvar_list[2537] = nvar_2537; + functions[2538] = fn2538; + nvar_list[2538] = nvar_2538; + functions[2539] = fn2539; + nvar_list[2539] = nvar_2539; + functions[2540] = fn2540; + nvar_list[2540] = nvar_2540; + functions[2541] = fn2541; + nvar_list[2541] = nvar_2541; + functions[2542] = fn2542; + nvar_list[2542] = nvar_2542; + functions[2543] = fn2543; + nvar_list[2543] = nvar_2543; + functions[2544] = fn2544; + nvar_list[2544] = nvar_2544; + functions[2545] = fn2545; + nvar_list[2545] = nvar_2545; + functions[2546] = fn2546; + nvar_list[2546] = nvar_2546; + functions[2547] = fn2547; + nvar_list[2547] = nvar_2547; + functions[2548] = fn2548; + nvar_list[2548] = nvar_2548; + functions[2549] = fn2549; + nvar_list[2549] = nvar_2549; + functions[2550] = fn2550; + nvar_list[2550] = nvar_2550; + functions[2551] = fn2551; + nvar_list[2551] = nvar_2551; + functions[2552] = fn2552; + nvar_list[2552] = nvar_2552; + functions[2553] = fn2553; + nvar_list[2553] = nvar_2553; + functions[2554] = fn2554; + nvar_list[2554] = nvar_2554; + functions[2555] = fn2555; + nvar_list[2555] = nvar_2555; + functions[2556] = fn2556; + nvar_list[2556] = nvar_2556; + functions[2557] = fn2557; + nvar_list[2557] = nvar_2557; + functions[2558] = fn2558; + nvar_list[2558] = nvar_2558; + functions[2559] = fn2559; + nvar_list[2559] = nvar_2559; + functions[2560] = fn2560; + nvar_list[2560] = nvar_2560; + functions[2561] = fn2561; + nvar_list[2561] = nvar_2561; + functions[2562] = fn2562; + nvar_list[2562] = nvar_2562; + functions[2563] = fn2563; + nvar_list[2563] = nvar_2563; + functions[2564] = fn2564; + nvar_list[2564] = nvar_2564; + functions[2565] = fn2565; + nvar_list[2565] = nvar_2565; + functions[2566] = fn2566; + nvar_list[2566] = nvar_2566; + functions[2567] = fn2567; + nvar_list[2567] = nvar_2567; + functions[2568] = fn2568; + nvar_list[2568] = nvar_2568; + functions[2569] = fn2569; + nvar_list[2569] = nvar_2569; + functions[2570] = fn2570; + nvar_list[2570] = nvar_2570; + functions[2571] = fn2571; + nvar_list[2571] = nvar_2571; + functions[2572] = fn2572; + nvar_list[2572] = nvar_2572; + functions[2573] = fn2573; + nvar_list[2573] = nvar_2573; + functions[2574] = fn2574; + nvar_list[2574] = nvar_2574; + functions[2575] = fn2575; + nvar_list[2575] = nvar_2575; + functions[2576] = fn2576; + nvar_list[2576] = nvar_2576; + functions[2577] = fn2577; + nvar_list[2577] = nvar_2577; + functions[2578] = fn2578; + nvar_list[2578] = nvar_2578; + functions[2579] = fn2579; + nvar_list[2579] = nvar_2579; + functions[2580] = fn2580; + nvar_list[2580] = nvar_2580; + functions[2581] = fn2581; + nvar_list[2581] = nvar_2581; + functions[2582] = fn2582; + nvar_list[2582] = nvar_2582; + functions[2583] = fn2583; + nvar_list[2583] = nvar_2583; + functions[2584] = fn2584; + nvar_list[2584] = nvar_2584; + functions[2585] = fn2585; + nvar_list[2585] = nvar_2585; + functions[2586] = fn2586; + nvar_list[2586] = nvar_2586; + functions[2587] = fn2587; + nvar_list[2587] = nvar_2587; + functions[2588] = fn2588; + nvar_list[2588] = nvar_2588; + functions[2589] = fn2589; + nvar_list[2589] = nvar_2589; + functions[2590] = fn2590; + nvar_list[2590] = nvar_2590; + functions[2591] = fn2591; + nvar_list[2591] = nvar_2591; + functions[2592] = fn2592; + nvar_list[2592] = nvar_2592; + functions[2593] = fn2593; + nvar_list[2593] = nvar_2593; + functions[2594] = fn2594; + nvar_list[2594] = nvar_2594; + functions[2595] = fn2595; + nvar_list[2595] = nvar_2595; + functions[2596] = fn2596; + nvar_list[2596] = nvar_2596; + functions[2597] = fn2597; + nvar_list[2597] = nvar_2597; + functions[2598] = fn2598; + nvar_list[2598] = nvar_2598; + functions[2599] = fn2599; + nvar_list[2599] = nvar_2599; + functions[2600] = fn2600; + nvar_list[2600] = nvar_2600; + functions[2601] = fn2601; + nvar_list[2601] = nvar_2601; + functions[2602] = fn2602; + nvar_list[2602] = nvar_2602; + functions[2603] = fn2603; + nvar_list[2603] = nvar_2603; + functions[2604] = fn2604; + nvar_list[2604] = nvar_2604; + functions[2605] = fn2605; + nvar_list[2605] = nvar_2605; + functions[2606] = fn2606; + nvar_list[2606] = nvar_2606; + functions[2607] = fn2607; + nvar_list[2607] = nvar_2607; + functions[2608] = fn2608; + nvar_list[2608] = nvar_2608; + functions[2609] = fn2609; + nvar_list[2609] = nvar_2609; + functions[2610] = fn2610; + nvar_list[2610] = nvar_2610; + functions[2611] = fn2611; + nvar_list[2611] = nvar_2611; + functions[2612] = fn2612; + nvar_list[2612] = nvar_2612; + functions[2613] = fn2613; + nvar_list[2613] = nvar_2613; + functions[2614] = fn2614; + nvar_list[2614] = nvar_2614; + functions[2615] = fn2615; + nvar_list[2615] = nvar_2615; + functions[2616] = fn2616; + nvar_list[2616] = nvar_2616; + functions[2617] = fn2617; + nvar_list[2617] = nvar_2617; + functions[2618] = fn2618; + nvar_list[2618] = nvar_2618; + functions[2619] = fn2619; + nvar_list[2619] = nvar_2619; + functions[2620] = fn2620; + nvar_list[2620] = nvar_2620; + functions[2621] = fn2621; + nvar_list[2621] = nvar_2621; + functions[2622] = fn2622; + nvar_list[2622] = nvar_2622; + functions[2623] = fn2623; + nvar_list[2623] = nvar_2623; + functions[2624] = fn2624; + nvar_list[2624] = nvar_2624; + functions[2625] = fn2625; + nvar_list[2625] = nvar_2625; + functions[2626] = fn2626; + nvar_list[2626] = nvar_2626; + functions[2627] = fn2627; + nvar_list[2627] = nvar_2627; + functions[2628] = fn2628; + nvar_list[2628] = nvar_2628; + functions[2629] = fn2629; + nvar_list[2629] = nvar_2629; + functions[2630] = fn2630; + nvar_list[2630] = nvar_2630; + functions[2631] = fn2631; + nvar_list[2631] = nvar_2631; + functions[2632] = fn2632; + nvar_list[2632] = nvar_2632; + functions[2633] = fn2633; + nvar_list[2633] = nvar_2633; + functions[2634] = fn2634; + nvar_list[2634] = nvar_2634; + functions[2635] = fn2635; + nvar_list[2635] = nvar_2635; + functions[2636] = fn2636; + nvar_list[2636] = nvar_2636; + functions[2637] = fn2637; + nvar_list[2637] = nvar_2637; + functions[2638] = fn2638; + nvar_list[2638] = nvar_2638; + functions[2639] = fn2639; + nvar_list[2639] = nvar_2639; + functions[2640] = fn2640; + nvar_list[2640] = nvar_2640; + functions[2641] = fn2641; + nvar_list[2641] = nvar_2641; + functions[2642] = fn2642; + nvar_list[2642] = nvar_2642; + functions[2643] = fn2643; + nvar_list[2643] = nvar_2643; + functions[2644] = fn2644; + nvar_list[2644] = nvar_2644; + functions[2645] = fn2645; + nvar_list[2645] = nvar_2645; + functions[2646] = fn2646; + nvar_list[2646] = nvar_2646; + functions[2647] = fn2647; + nvar_list[2647] = nvar_2647; + functions[2648] = fn2648; + nvar_list[2648] = nvar_2648; + functions[2649] = fn2649; + nvar_list[2649] = nvar_2649; + functions[2650] = fn2650; + nvar_list[2650] = nvar_2650; + functions[2651] = fn2651; + nvar_list[2651] = nvar_2651; + functions[2652] = fn2652; + nvar_list[2652] = nvar_2652; + functions[2653] = fn2653; + nvar_list[2653] = nvar_2653; + functions[2654] = fn2654; + nvar_list[2654] = nvar_2654; + functions[2655] = fn2655; + nvar_list[2655] = nvar_2655; + functions[2656] = fn2656; + nvar_list[2656] = nvar_2656; + functions[2657] = fn2657; + nvar_list[2657] = nvar_2657; + functions[2658] = fn2658; + nvar_list[2658] = nvar_2658; + functions[2659] = fn2659; + nvar_list[2659] = nvar_2659; + functions[2660] = fn2660; + nvar_list[2660] = nvar_2660; + functions[2661] = fn2661; + nvar_list[2661] = nvar_2661; + functions[2662] = fn2662; + nvar_list[2662] = nvar_2662; + functions[2663] = fn2663; + nvar_list[2663] = nvar_2663; + functions[2664] = fn2664; + nvar_list[2664] = nvar_2664; + functions[2665] = fn2665; + nvar_list[2665] = nvar_2665; + functions[2666] = fn2666; + nvar_list[2666] = nvar_2666; + functions[2667] = fn2667; + nvar_list[2667] = nvar_2667; + functions[2668] = fn2668; + nvar_list[2668] = nvar_2668; + functions[2669] = fn2669; + nvar_list[2669] = nvar_2669; + functions[2670] = fn2670; + nvar_list[2670] = nvar_2670; + functions[2671] = fn2671; + nvar_list[2671] = nvar_2671; + functions[2672] = fn2672; + nvar_list[2672] = nvar_2672; + functions[2673] = fn2673; + nvar_list[2673] = nvar_2673; + functions[2674] = fn2674; + nvar_list[2674] = nvar_2674; + functions[2675] = fn2675; + nvar_list[2675] = nvar_2675; + functions[2676] = fn2676; + nvar_list[2676] = nvar_2676; + functions[2677] = fn2677; + nvar_list[2677] = nvar_2677; + functions[2678] = fn2678; + nvar_list[2678] = nvar_2678; + functions[2679] = fn2679; + nvar_list[2679] = nvar_2679; + functions[2680] = fn2680; + nvar_list[2680] = nvar_2680; + functions[2681] = fn2681; + nvar_list[2681] = nvar_2681; + functions[2682] = fn2682; + nvar_list[2682] = nvar_2682; + functions[2683] = fn2683; + nvar_list[2683] = nvar_2683; + functions[2684] = fn2684; + nvar_list[2684] = nvar_2684; + functions[2685] = fn2685; + nvar_list[2685] = nvar_2685; + functions[2686] = fn2686; + nvar_list[2686] = nvar_2686; + functions[2687] = fn2687; + nvar_list[2687] = nvar_2687; + functions[2688] = fn2688; + nvar_list[2688] = nvar_2688; + functions[2689] = fn2689; + nvar_list[2689] = nvar_2689; + functions[2690] = fn2690; + nvar_list[2690] = nvar_2690; + functions[2691] = fn2691; + nvar_list[2691] = nvar_2691; + functions[2692] = fn2692; + nvar_list[2692] = nvar_2692; + functions[2693] = fn2693; + nvar_list[2693] = nvar_2693; + functions[2694] = fn2694; + nvar_list[2694] = nvar_2694; + functions[2695] = fn2695; + nvar_list[2695] = nvar_2695; + functions[2696] = fn2696; + nvar_list[2696] = nvar_2696; + functions[2697] = fn2697; + nvar_list[2697] = nvar_2697; + functions[2698] = fn2698; + nvar_list[2698] = nvar_2698; + functions[2699] = fn2699; + nvar_list[2699] = nvar_2699; + functions[2700] = fn2700; + nvar_list[2700] = nvar_2700; + functions[2701] = fn2701; + nvar_list[2701] = nvar_2701; + functions[2702] = fn2702; + nvar_list[2702] = nvar_2702; + functions[2703] = fn2703; + nvar_list[2703] = nvar_2703; + functions[2704] = fn2704; + nvar_list[2704] = nvar_2704; + functions[2705] = fn2705; + nvar_list[2705] = nvar_2705; + functions[2706] = fn2706; + nvar_list[2706] = nvar_2706; + functions[2707] = fn2707; + nvar_list[2707] = nvar_2707; + functions[2708] = fn2708; + nvar_list[2708] = nvar_2708; + functions[2709] = fn2709; + nvar_list[2709] = nvar_2709; + functions[2710] = fn2710; + nvar_list[2710] = nvar_2710; + functions[2711] = fn2711; + nvar_list[2711] = nvar_2711; + functions[2712] = fn2712; + nvar_list[2712] = nvar_2712; + functions[2713] = fn2713; + nvar_list[2713] = nvar_2713; + functions[2714] = fn2714; + nvar_list[2714] = nvar_2714; + functions[2715] = fn2715; + nvar_list[2715] = nvar_2715; + functions[2716] = fn2716; + nvar_list[2716] = nvar_2716; + functions[2717] = fn2717; + nvar_list[2717] = nvar_2717; + functions[2718] = fn2718; + nvar_list[2718] = nvar_2718; + functions[2719] = fn2719; + nvar_list[2719] = nvar_2719; + functions[2720] = fn2720; + nvar_list[2720] = nvar_2720; + functions[2721] = fn2721; + nvar_list[2721] = nvar_2721; + functions[2722] = fn2722; + nvar_list[2722] = nvar_2722; + functions[2723] = fn2723; + nvar_list[2723] = nvar_2723; + functions[2724] = fn2724; + nvar_list[2724] = nvar_2724; + functions[2725] = fn2725; + nvar_list[2725] = nvar_2725; + functions[2726] = fn2726; + nvar_list[2726] = nvar_2726; + functions[2727] = fn2727; + nvar_list[2727] = nvar_2727; + functions[2728] = fn2728; + nvar_list[2728] = nvar_2728; + functions[2729] = fn2729; + nvar_list[2729] = nvar_2729; + functions[2730] = fn2730; + nvar_list[2730] = nvar_2730; + functions[2731] = fn2731; + nvar_list[2731] = nvar_2731; + functions[2732] = fn2732; + nvar_list[2732] = nvar_2732; + functions[2733] = fn2733; + nvar_list[2733] = nvar_2733; + functions[2734] = fn2734; + nvar_list[2734] = nvar_2734; + functions[2735] = fn2735; + nvar_list[2735] = nvar_2735; + functions[2736] = fn2736; + nvar_list[2736] = nvar_2736; + functions[2737] = fn2737; + nvar_list[2737] = nvar_2737; + functions[2738] = fn2738; + nvar_list[2738] = nvar_2738; + functions[2739] = fn2739; + nvar_list[2739] = nvar_2739; + functions[2740] = fn2740; + nvar_list[2740] = nvar_2740; + functions[2741] = fn2741; + nvar_list[2741] = nvar_2741; + functions[2742] = fn2742; + nvar_list[2742] = nvar_2742; + functions[2743] = fn2743; + nvar_list[2743] = nvar_2743; + functions[2744] = fn2744; + nvar_list[2744] = nvar_2744; + functions[2745] = fn2745; + nvar_list[2745] = nvar_2745; + functions[2746] = fn2746; + nvar_list[2746] = nvar_2746; + functions[2747] = fn2747; + nvar_list[2747] = nvar_2747; + functions[2748] = fn2748; + nvar_list[2748] = nvar_2748; + functions[2749] = fn2749; + nvar_list[2749] = nvar_2749; + functions[2750] = fn2750; + nvar_list[2750] = nvar_2750; + functions[2751] = fn2751; + nvar_list[2751] = nvar_2751; + functions[2752] = fn2752; + nvar_list[2752] = nvar_2752; + functions[2753] = fn2753; + nvar_list[2753] = nvar_2753; + functions[2754] = fn2754; + nvar_list[2754] = nvar_2754; + functions[2755] = fn2755; + nvar_list[2755] = nvar_2755; + functions[2756] = fn2756; + nvar_list[2756] = nvar_2756; + functions[2757] = fn2757; + nvar_list[2757] = nvar_2757; + functions[2758] = fn2758; + nvar_list[2758] = nvar_2758; + functions[2759] = fn2759; + nvar_list[2759] = nvar_2759; + functions[2760] = fn2760; + nvar_list[2760] = nvar_2760; + functions[2761] = fn2761; + nvar_list[2761] = nvar_2761; + functions[2762] = fn2762; + nvar_list[2762] = nvar_2762; + functions[2763] = fn2763; + nvar_list[2763] = nvar_2763; + functions[2764] = fn2764; + nvar_list[2764] = nvar_2764; + functions[2765] = fn2765; + nvar_list[2765] = nvar_2765; + functions[2766] = fn2766; + nvar_list[2766] = nvar_2766; + functions[2767] = fn2767; + nvar_list[2767] = nvar_2767; + functions[2768] = fn2768; + nvar_list[2768] = nvar_2768; + functions[2769] = fn2769; + nvar_list[2769] = nvar_2769; + functions[2770] = fn2770; + nvar_list[2770] = nvar_2770; + functions[2771] = fn2771; + nvar_list[2771] = nvar_2771; + functions[2772] = fn2772; + nvar_list[2772] = nvar_2772; + functions[2773] = fn2773; + nvar_list[2773] = nvar_2773; + functions[2774] = fn2774; + nvar_list[2774] = nvar_2774; + functions[2775] = fn2775; + nvar_list[2775] = nvar_2775; + functions[2776] = fn2776; + nvar_list[2776] = nvar_2776; + functions[2777] = fn2777; + nvar_list[2777] = nvar_2777; + functions[2778] = fn2778; + nvar_list[2778] = nvar_2778; + functions[2779] = fn2779; + nvar_list[2779] = nvar_2779; + functions[2780] = fn2780; + nvar_list[2780] = nvar_2780; + functions[2781] = fn2781; + nvar_list[2781] = nvar_2781; + functions[2782] = fn2782; + nvar_list[2782] = nvar_2782; + functions[2783] = fn2783; + nvar_list[2783] = nvar_2783; + functions[2784] = fn2784; + nvar_list[2784] = nvar_2784; + functions[2785] = fn2785; + nvar_list[2785] = nvar_2785; + functions[2786] = fn2786; + nvar_list[2786] = nvar_2786; + functions[2787] = fn2787; + nvar_list[2787] = nvar_2787; + functions[2788] = fn2788; + nvar_list[2788] = nvar_2788; + functions[2789] = fn2789; + nvar_list[2789] = nvar_2789; + functions[2790] = fn2790; + nvar_list[2790] = nvar_2790; + functions[2791] = fn2791; + nvar_list[2791] = nvar_2791; + functions[2792] = fn2792; + nvar_list[2792] = nvar_2792; + functions[2793] = fn2793; + nvar_list[2793] = nvar_2793; + functions[2794] = fn2794; + nvar_list[2794] = nvar_2794; + functions[2795] = fn2795; + nvar_list[2795] = nvar_2795; + functions[2796] = fn2796; + nvar_list[2796] = nvar_2796; + functions[2797] = fn2797; + nvar_list[2797] = nvar_2797; + functions[2798] = fn2798; + nvar_list[2798] = nvar_2798; + functions[2799] = fn2799; + nvar_list[2799] = nvar_2799; + functions[2800] = fn2800; + nvar_list[2800] = nvar_2800; + functions[2801] = fn2801; + nvar_list[2801] = nvar_2801; + functions[2802] = fn2802; + nvar_list[2802] = nvar_2802; + functions[2803] = fn2803; + nvar_list[2803] = nvar_2803; + functions[2804] = fn2804; + nvar_list[2804] = nvar_2804; + functions[2805] = fn2805; + nvar_list[2805] = nvar_2805; + functions[2806] = fn2806; + nvar_list[2806] = nvar_2806; + functions[2807] = fn2807; + nvar_list[2807] = nvar_2807; + functions[2808] = fn2808; + nvar_list[2808] = nvar_2808; + functions[2809] = fn2809; + nvar_list[2809] = nvar_2809; + functions[2810] = fn2810; + nvar_list[2810] = nvar_2810; + functions[2811] = fn2811; + nvar_list[2811] = nvar_2811; + functions[2812] = fn2812; + nvar_list[2812] = nvar_2812; + functions[2813] = fn2813; + nvar_list[2813] = nvar_2813; + functions[2814] = fn2814; + nvar_list[2814] = nvar_2814; + functions[2815] = fn2815; + nvar_list[2815] = nvar_2815; + functions[2816] = fn2816; + nvar_list[2816] = nvar_2816; + functions[2817] = fn2817; + nvar_list[2817] = nvar_2817; + functions[2818] = fn2818; + nvar_list[2818] = nvar_2818; + functions[2819] = fn2819; + nvar_list[2819] = nvar_2819; + functions[2820] = fn2820; + nvar_list[2820] = nvar_2820; + functions[2821] = fn2821; + nvar_list[2821] = nvar_2821; + functions[2822] = fn2822; + nvar_list[2822] = nvar_2822; + functions[2823] = fn2823; + nvar_list[2823] = nvar_2823; + functions[2824] = fn2824; + nvar_list[2824] = nvar_2824; + functions[2825] = fn2825; + nvar_list[2825] = nvar_2825; + functions[2826] = fn2826; + nvar_list[2826] = nvar_2826; + functions[2827] = fn2827; + nvar_list[2827] = nvar_2827; + functions[2828] = fn2828; + nvar_list[2828] = nvar_2828; + functions[2829] = fn2829; + nvar_list[2829] = nvar_2829; + functions[2830] = fn2830; + nvar_list[2830] = nvar_2830; + functions[2831] = fn2831; + nvar_list[2831] = nvar_2831; + functions[2832] = fn2832; + nvar_list[2832] = nvar_2832; + functions[2833] = fn2833; + nvar_list[2833] = nvar_2833; + functions[2834] = fn2834; + nvar_list[2834] = nvar_2834; + functions[2835] = fn2835; + nvar_list[2835] = nvar_2835; + functions[2836] = fn2836; + nvar_list[2836] = nvar_2836; + functions[2837] = fn2837; + nvar_list[2837] = nvar_2837; + functions[2838] = fn2838; + nvar_list[2838] = nvar_2838; + functions[2839] = fn2839; + nvar_list[2839] = nvar_2839; + functions[2840] = fn2840; + nvar_list[2840] = nvar_2840; + functions[2841] = fn2841; + nvar_list[2841] = nvar_2841; + functions[2842] = fn2842; + nvar_list[2842] = nvar_2842; + functions[2843] = fn2843; + nvar_list[2843] = nvar_2843; + functions[2844] = fn2844; + nvar_list[2844] = nvar_2844; + functions[2845] = fn2845; + nvar_list[2845] = nvar_2845; + functions[2846] = fn2846; + nvar_list[2846] = nvar_2846; + functions[2847] = fn2847; + nvar_list[2847] = nvar_2847; + functions[2848] = fn2848; + nvar_list[2848] = nvar_2848; + functions[2849] = fn2849; + nvar_list[2849] = nvar_2849; + functions[2850] = fn2850; + nvar_list[2850] = nvar_2850; + functions[2851] = fn2851; + nvar_list[2851] = nvar_2851; + functions[2852] = fn2852; + nvar_list[2852] = nvar_2852; + functions[2853] = fn2853; + nvar_list[2853] = nvar_2853; + functions[2854] = fn2854; + nvar_list[2854] = nvar_2854; + functions[2855] = fn2855; + nvar_list[2855] = nvar_2855; + functions[2856] = fn2856; + nvar_list[2856] = nvar_2856; + functions[2857] = fn2857; + nvar_list[2857] = nvar_2857; + functions[2858] = fn2858; + nvar_list[2858] = nvar_2858; + functions[2859] = fn2859; + nvar_list[2859] = nvar_2859; + functions[2860] = fn2860; + nvar_list[2860] = nvar_2860; + functions[2861] = fn2861; + nvar_list[2861] = nvar_2861; + functions[2862] = fn2862; + nvar_list[2862] = nvar_2862; + functions[2863] = fn2863; + nvar_list[2863] = nvar_2863; + functions[2864] = fn2864; + nvar_list[2864] = nvar_2864; + functions[2865] = fn2865; + nvar_list[2865] = nvar_2865; + functions[2866] = fn2866; + nvar_list[2866] = nvar_2866; + functions[2867] = fn2867; + nvar_list[2867] = nvar_2867; + functions[2868] = fn2868; + nvar_list[2868] = nvar_2868; + functions[2869] = fn2869; + nvar_list[2869] = nvar_2869; + functions[2870] = fn2870; + nvar_list[2870] = nvar_2870; + functions[2871] = fn2871; + nvar_list[2871] = nvar_2871; + functions[2872] = fn2872; + nvar_list[2872] = nvar_2872; + functions[2873] = fn2873; + nvar_list[2873] = nvar_2873; + functions[2874] = fn2874; + nvar_list[2874] = nvar_2874; + functions[2875] = fn2875; + nvar_list[2875] = nvar_2875; + functions[2876] = fn2876; + nvar_list[2876] = nvar_2876; + functions[2877] = fn2877; + nvar_list[2877] = nvar_2877; + functions[2878] = fn2878; + nvar_list[2878] = nvar_2878; + functions[2879] = fn2879; + nvar_list[2879] = nvar_2879; + functions[2880] = fn2880; + nvar_list[2880] = nvar_2880; + functions[2881] = fn2881; + nvar_list[2881] = nvar_2881; + functions[2882] = fn2882; + nvar_list[2882] = nvar_2882; + functions[2883] = fn2883; + nvar_list[2883] = nvar_2883; + functions[2884] = fn2884; + nvar_list[2884] = nvar_2884; + functions[2885] = fn2885; + nvar_list[2885] = nvar_2885; + functions[2886] = fn2886; + nvar_list[2886] = nvar_2886; + functions[2887] = fn2887; + nvar_list[2887] = nvar_2887; + functions[2888] = fn2888; + nvar_list[2888] = nvar_2888; + functions[2889] = fn2889; + nvar_list[2889] = nvar_2889; + functions[2890] = fn2890; + nvar_list[2890] = nvar_2890; + functions[2891] = fn2891; + nvar_list[2891] = nvar_2891; + functions[2892] = fn2892; + nvar_list[2892] = nvar_2892; + functions[2893] = fn2893; + nvar_list[2893] = nvar_2893; + functions[2894] = fn2894; + nvar_list[2894] = nvar_2894; + functions[2895] = fn2895; + nvar_list[2895] = nvar_2895; + functions[2896] = fn2896; + nvar_list[2896] = nvar_2896; + functions[2897] = fn2897; + nvar_list[2897] = nvar_2897; + functions[2898] = fn2898; + nvar_list[2898] = nvar_2898; + functions[2899] = fn2899; + nvar_list[2899] = nvar_2899; + functions[2900] = fn2900; + nvar_list[2900] = nvar_2900; + functions[2901] = fn2901; + nvar_list[2901] = nvar_2901; + functions[2902] = fn2902; + nvar_list[2902] = nvar_2902; + functions[2903] = fn2903; + nvar_list[2903] = nvar_2903; + functions[2904] = fn2904; + nvar_list[2904] = nvar_2904; + functions[2905] = fn2905; + nvar_list[2905] = nvar_2905; + functions[2906] = fn2906; + nvar_list[2906] = nvar_2906; + functions[2907] = fn2907; + nvar_list[2907] = nvar_2907; + functions[2908] = fn2908; + nvar_list[2908] = nvar_2908; + functions[2909] = fn2909; + nvar_list[2909] = nvar_2909; + functions[2910] = fn2910; + nvar_list[2910] = nvar_2910; + functions[2911] = fn2911; + nvar_list[2911] = nvar_2911; + functions[2912] = fn2912; + nvar_list[2912] = nvar_2912; + functions[2913] = fn2913; + nvar_list[2913] = nvar_2913; + functions[2914] = fn2914; + nvar_list[2914] = nvar_2914; + functions[2915] = fn2915; + nvar_list[2915] = nvar_2915; + functions[2916] = fn2916; + nvar_list[2916] = nvar_2916; + functions[2917] = fn2917; + nvar_list[2917] = nvar_2917; + functions[2918] = fn2918; + nvar_list[2918] = nvar_2918; + functions[2919] = fn2919; + nvar_list[2919] = nvar_2919; + functions[2920] = fn2920; + nvar_list[2920] = nvar_2920; + functions[2921] = fn2921; + nvar_list[2921] = nvar_2921; + functions[2922] = fn2922; + nvar_list[2922] = nvar_2922; + functions[2923] = fn2923; + nvar_list[2923] = nvar_2923; + functions[2924] = fn2924; + nvar_list[2924] = nvar_2924; + functions[2925] = fn2925; + nvar_list[2925] = nvar_2925; + functions[2926] = fn2926; + nvar_list[2926] = nvar_2926; + functions[2927] = fn2927; + nvar_list[2927] = nvar_2927; + functions[2928] = fn2928; + nvar_list[2928] = nvar_2928; + functions[2929] = fn2929; + nvar_list[2929] = nvar_2929; + functions[2930] = fn2930; + nvar_list[2930] = nvar_2930; + functions[2931] = fn2931; + nvar_list[2931] = nvar_2931; + functions[2932] = fn2932; + nvar_list[2932] = nvar_2932; + functions[2933] = fn2933; + nvar_list[2933] = nvar_2933; + functions[2934] = fn2934; + nvar_list[2934] = nvar_2934; + functions[2935] = fn2935; + nvar_list[2935] = nvar_2935; + functions[2936] = fn2936; + nvar_list[2936] = nvar_2936; + functions[2937] = fn2937; + nvar_list[2937] = nvar_2937; + functions[2938] = fn2938; + nvar_list[2938] = nvar_2938; + functions[2939] = fn2939; + nvar_list[2939] = nvar_2939; + functions[2940] = fn2940; + nvar_list[2940] = nvar_2940; + functions[2941] = fn2941; + nvar_list[2941] = nvar_2941; + functions[2942] = fn2942; + nvar_list[2942] = nvar_2942; + functions[2943] = fn2943; + nvar_list[2943] = nvar_2943; + functions[2944] = fn2944; + nvar_list[2944] = nvar_2944; + functions[2945] = fn2945; + nvar_list[2945] = nvar_2945; + functions[2946] = fn2946; + nvar_list[2946] = nvar_2946; + functions[2947] = fn2947; + nvar_list[2947] = nvar_2947; + functions[2948] = fn2948; + nvar_list[2948] = nvar_2948; + functions[2949] = fn2949; + nvar_list[2949] = nvar_2949; + functions[2950] = fn2950; + nvar_list[2950] = nvar_2950; + functions[2951] = fn2951; + nvar_list[2951] = nvar_2951; + functions[2952] = fn2952; + nvar_list[2952] = nvar_2952; + functions[2953] = fn2953; + nvar_list[2953] = nvar_2953; + functions[2954] = fn2954; + nvar_list[2954] = nvar_2954; + functions[2955] = fn2955; + nvar_list[2955] = nvar_2955; + functions[2956] = fn2956; + nvar_list[2956] = nvar_2956; + functions[2957] = fn2957; + nvar_list[2957] = nvar_2957; + functions[2958] = fn2958; + nvar_list[2958] = nvar_2958; + functions[2959] = fn2959; + nvar_list[2959] = nvar_2959; + functions[2960] = fn2960; + nvar_list[2960] = nvar_2960; + functions[2961] = fn2961; + nvar_list[2961] = nvar_2961; + functions[2962] = fn2962; + nvar_list[2962] = nvar_2962; + functions[2963] = fn2963; + nvar_list[2963] = nvar_2963; + functions[2964] = fn2964; + nvar_list[2964] = nvar_2964; + functions[2965] = fn2965; + nvar_list[2965] = nvar_2965; + functions[2966] = fn2966; + nvar_list[2966] = nvar_2966; + functions[2967] = fn2967; + nvar_list[2967] = nvar_2967; + functions[2968] = fn2968; + nvar_list[2968] = nvar_2968; + functions[2969] = fn2969; + nvar_list[2969] = nvar_2969; + functions[2970] = fn2970; + nvar_list[2970] = nvar_2970; + functions[2971] = fn2971; + nvar_list[2971] = nvar_2971; + functions[2972] = fn2972; + nvar_list[2972] = nvar_2972; + functions[2973] = fn2973; + nvar_list[2973] = nvar_2973; + functions[2974] = fn2974; + nvar_list[2974] = nvar_2974; + functions[2975] = fn2975; + nvar_list[2975] = nvar_2975; + functions[2976] = fn2976; + nvar_list[2976] = nvar_2976; + functions[2977] = fn2977; + nvar_list[2977] = nvar_2977; + functions[2978] = fn2978; + nvar_list[2978] = nvar_2978; + functions[2979] = fn2979; + nvar_list[2979] = nvar_2979; + functions[2980] = fn2980; + nvar_list[2980] = nvar_2980; + functions[2981] = fn2981; + nvar_list[2981] = nvar_2981; + functions[2982] = fn2982; + nvar_list[2982] = nvar_2982; + functions[2983] = fn2983; + nvar_list[2983] = nvar_2983; + functions[2984] = fn2984; + nvar_list[2984] = nvar_2984; + functions[2985] = fn2985; + nvar_list[2985] = nvar_2985; + functions[2986] = fn2986; + nvar_list[2986] = nvar_2986; + functions[2987] = fn2987; + nvar_list[2987] = nvar_2987; + functions[2988] = fn2988; + nvar_list[2988] = nvar_2988; + functions[2989] = fn2989; + nvar_list[2989] = nvar_2989; + functions[2990] = fn2990; + nvar_list[2990] = nvar_2990; + functions[2991] = fn2991; + nvar_list[2991] = nvar_2991; + functions[2992] = fn2992; + nvar_list[2992] = nvar_2992; + functions[2993] = fn2993; + nvar_list[2993] = nvar_2993; + functions[2994] = fn2994; + nvar_list[2994] = nvar_2994; + functions[2995] = fn2995; + nvar_list[2995] = nvar_2995; + functions[2996] = fn2996; + nvar_list[2996] = nvar_2996; + functions[2997] = fn2997; + nvar_list[2997] = nvar_2997; + functions[2998] = fn2998; + nvar_list[2998] = nvar_2998; + functions[2999] = fn2999; + nvar_list[2999] = nvar_2999; + functions[3000] = fn3000; + nvar_list[3000] = nvar_3000; + functions[3001] = fn3001; + nvar_list[3001] = nvar_3001; + functions[3002] = fn3002; + nvar_list[3002] = nvar_3002; + functions[3003] = fn3003; + nvar_list[3003] = nvar_3003; + functions[3004] = fn3004; + nvar_list[3004] = nvar_3004; + functions[3005] = fn3005; + nvar_list[3005] = nvar_3005; + functions[3006] = fn3006; + nvar_list[3006] = nvar_3006; + functions[3007] = fn3007; + nvar_list[3007] = nvar_3007; + functions[3008] = fn3008; + nvar_list[3008] = nvar_3008; + functions[3009] = fn3009; + nvar_list[3009] = nvar_3009; + functions[3010] = fn3010; + nvar_list[3010] = nvar_3010; + functions[3011] = fn3011; + nvar_list[3011] = nvar_3011; + functions[3012] = fn3012; + nvar_list[3012] = nvar_3012; + functions[3013] = fn3013; + nvar_list[3013] = nvar_3013; + functions[3014] = fn3014; + nvar_list[3014] = nvar_3014; + functions[3015] = fn3015; + nvar_list[3015] = nvar_3015; + functions[3016] = fn3016; + nvar_list[3016] = nvar_3016; + functions[3017] = fn3017; + nvar_list[3017] = nvar_3017; + functions[3018] = fn3018; + nvar_list[3018] = nvar_3018; + functions[3019] = fn3019; + nvar_list[3019] = nvar_3019; + functions[3020] = fn3020; + nvar_list[3020] = nvar_3020; + functions[3021] = fn3021; + nvar_list[3021] = nvar_3021; + functions[3022] = fn3022; + nvar_list[3022] = nvar_3022; + functions[3023] = fn3023; + nvar_list[3023] = nvar_3023; + functions[3024] = fn3024; + nvar_list[3024] = nvar_3024; + functions[3025] = fn3025; + nvar_list[3025] = nvar_3025; + functions[3026] = fn3026; + nvar_list[3026] = nvar_3026; + functions[3027] = fn3027; + nvar_list[3027] = nvar_3027; + functions[3028] = fn3028; + nvar_list[3028] = nvar_3028; + functions[3029] = fn3029; + nvar_list[3029] = nvar_3029; + functions[3030] = fn3030; + nvar_list[3030] = nvar_3030; + functions[3031] = fn3031; + nvar_list[3031] = nvar_3031; + functions[3032] = fn3032; + nvar_list[3032] = nvar_3032; + functions[3033] = fn3033; + nvar_list[3033] = nvar_3033; + functions[3034] = fn3034; + nvar_list[3034] = nvar_3034; + functions[3035] = fn3035; + nvar_list[3035] = nvar_3035; + functions[3036] = fn3036; + nvar_list[3036] = nvar_3036; + functions[3037] = fn3037; + nvar_list[3037] = nvar_3037; + functions[3038] = fn3038; + nvar_list[3038] = nvar_3038; + functions[3039] = fn3039; + nvar_list[3039] = nvar_3039; + functions[3040] = fn3040; + nvar_list[3040] = nvar_3040; + functions[3041] = fn3041; + nvar_list[3041] = nvar_3041; + functions[3042] = fn3042; + nvar_list[3042] = nvar_3042; + functions[3043] = fn3043; + nvar_list[3043] = nvar_3043; + functions[3044] = fn3044; + nvar_list[3044] = nvar_3044; + functions[3045] = fn3045; + nvar_list[3045] = nvar_3045; + functions[3046] = fn3046; + nvar_list[3046] = nvar_3046; + functions[3047] = fn3047; + nvar_list[3047] = nvar_3047; + functions[3048] = fn3048; + nvar_list[3048] = nvar_3048; + functions[3049] = fn3049; + nvar_list[3049] = nvar_3049; + functions[3050] = fn3050; + nvar_list[3050] = nvar_3050; + functions[3051] = fn3051; + nvar_list[3051] = nvar_3051; + functions[3052] = fn3052; + nvar_list[3052] = nvar_3052; + functions[3053] = fn3053; + nvar_list[3053] = nvar_3053; + functions[3054] = fn3054; + nvar_list[3054] = nvar_3054; + functions[3055] = fn3055; + nvar_list[3055] = nvar_3055; + functions[3056] = fn3056; + nvar_list[3056] = nvar_3056; + functions[3057] = fn3057; + nvar_list[3057] = nvar_3057; + functions[3058] = fn3058; + nvar_list[3058] = nvar_3058; + functions[3059] = fn3059; + nvar_list[3059] = nvar_3059; + functions[3060] = fn3060; + nvar_list[3060] = nvar_3060; + functions[3061] = fn3061; + nvar_list[3061] = nvar_3061; + functions[3062] = fn3062; + nvar_list[3062] = nvar_3062; + functions[3063] = fn3063; + nvar_list[3063] = nvar_3063; + functions[3064] = fn3064; + nvar_list[3064] = nvar_3064; + functions[3065] = fn3065; + nvar_list[3065] = nvar_3065; + functions[3066] = fn3066; + nvar_list[3066] = nvar_3066; + functions[3067] = fn3067; + nvar_list[3067] = nvar_3067; + functions[3068] = fn3068; + nvar_list[3068] = nvar_3068; + functions[3069] = fn3069; + nvar_list[3069] = nvar_3069; + functions[3070] = fn3070; + nvar_list[3070] = nvar_3070; + functions[3071] = fn3071; + nvar_list[3071] = nvar_3071; + functions[3072] = fn3072; + nvar_list[3072] = nvar_3072; + functions[3073] = fn3073; + nvar_list[3073] = nvar_3073; + functions[3074] = fn3074; + nvar_list[3074] = nvar_3074; + functions[3075] = fn3075; + nvar_list[3075] = nvar_3075; + functions[3076] = fn3076; + nvar_list[3076] = nvar_3076; + functions[3077] = fn3077; + nvar_list[3077] = nvar_3077; + functions[3078] = fn3078; + nvar_list[3078] = nvar_3078; + functions[3079] = fn3079; + nvar_list[3079] = nvar_3079; + functions[3080] = fn3080; + nvar_list[3080] = nvar_3080; + functions[3081] = fn3081; + nvar_list[3081] = nvar_3081; + functions[3082] = fn3082; + nvar_list[3082] = nvar_3082; + functions[3083] = fn3083; + nvar_list[3083] = nvar_3083; + functions[3084] = fn3084; + nvar_list[3084] = nvar_3084; + functions[3085] = fn3085; + nvar_list[3085] = nvar_3085; + functions[3086] = fn3086; + nvar_list[3086] = nvar_3086; + functions[3087] = fn3087; + nvar_list[3087] = nvar_3087; + functions[3088] = fn3088; + nvar_list[3088] = nvar_3088; + functions[3089] = fn3089; + nvar_list[3089] = nvar_3089; + functions[3090] = fn3090; + nvar_list[3090] = nvar_3090; + functions[3091] = fn3091; + nvar_list[3091] = nvar_3091; + functions[3092] = fn3092; + nvar_list[3092] = nvar_3092; + functions[3093] = fn3093; + nvar_list[3093] = nvar_3093; + functions[3094] = fn3094; + nvar_list[3094] = nvar_3094; + functions[3095] = fn3095; + nvar_list[3095] = nvar_3095; + functions[3096] = fn3096; + nvar_list[3096] = nvar_3096; + functions[3097] = fn3097; + nvar_list[3097] = nvar_3097; + functions[3098] = fn3098; + nvar_list[3098] = nvar_3098; + functions[3099] = fn3099; + nvar_list[3099] = nvar_3099; + functions[3100] = fn3100; + nvar_list[3100] = nvar_3100; + functions[3101] = fn3101; + nvar_list[3101] = nvar_3101; + functions[3102] = fn3102; + nvar_list[3102] = nvar_3102; + functions[3103] = fn3103; + nvar_list[3103] = nvar_3103; + functions[3104] = fn3104; + nvar_list[3104] = nvar_3104; + functions[3105] = fn3105; + nvar_list[3105] = nvar_3105; + functions[3106] = fn3106; + nvar_list[3106] = nvar_3106; + functions[3107] = fn3107; + nvar_list[3107] = nvar_3107; + functions[3108] = fn3108; + nvar_list[3108] = nvar_3108; + functions[3109] = fn3109; + nvar_list[3109] = nvar_3109; + functions[3110] = fn3110; + nvar_list[3110] = nvar_3110; + functions[3111] = fn3111; + nvar_list[3111] = nvar_3111; + functions[3112] = fn3112; + nvar_list[3112] = nvar_3112; + functions[3113] = fn3113; + nvar_list[3113] = nvar_3113; + functions[3114] = fn3114; + nvar_list[3114] = nvar_3114; + functions[3115] = fn3115; + nvar_list[3115] = nvar_3115; + functions[3116] = fn3116; + nvar_list[3116] = nvar_3116; + functions[3117] = fn3117; + nvar_list[3117] = nvar_3117; + functions[3118] = fn3118; + nvar_list[3118] = nvar_3118; + functions[3119] = fn3119; + nvar_list[3119] = nvar_3119; + functions[3120] = fn3120; + nvar_list[3120] = nvar_3120; + functions[3121] = fn3121; + nvar_list[3121] = nvar_3121; + functions[3122] = fn3122; + nvar_list[3122] = nvar_3122; + functions[3123] = fn3123; + nvar_list[3123] = nvar_3123; + functions[3124] = fn3124; + nvar_list[3124] = nvar_3124; + functions[3125] = fn3125; + nvar_list[3125] = nvar_3125; + functions[3126] = fn3126; + nvar_list[3126] = nvar_3126; + functions[3127] = fn3127; + nvar_list[3127] = nvar_3127; + functions[3128] = fn3128; + nvar_list[3128] = nvar_3128; + functions[3129] = fn3129; + nvar_list[3129] = nvar_3129; + functions[3130] = fn3130; + nvar_list[3130] = nvar_3130; + functions[3131] = fn3131; + nvar_list[3131] = nvar_3131; + functions[3132] = fn3132; + nvar_list[3132] = nvar_3132; + functions[3133] = fn3133; + nvar_list[3133] = nvar_3133; + functions[3134] = fn3134; + nvar_list[3134] = nvar_3134; + functions[3135] = fn3135; + nvar_list[3135] = nvar_3135; + functions[3136] = fn3136; + nvar_list[3136] = nvar_3136; + functions[3137] = fn3137; + nvar_list[3137] = nvar_3137; + functions[3138] = fn3138; + nvar_list[3138] = nvar_3138; + functions[3139] = fn3139; + nvar_list[3139] = nvar_3139; + functions[3140] = fn3140; + nvar_list[3140] = nvar_3140; + functions[3141] = fn3141; + nvar_list[3141] = nvar_3141; + functions[3142] = fn3142; + nvar_list[3142] = nvar_3142; + functions[3143] = fn3143; + nvar_list[3143] = nvar_3143; + functions[3144] = fn3144; + nvar_list[3144] = nvar_3144; + functions[3145] = fn3145; + nvar_list[3145] = nvar_3145; + functions[3146] = fn3146; + nvar_list[3146] = nvar_3146; + functions[3147] = fn3147; + nvar_list[3147] = nvar_3147; + functions[3148] = fn3148; + nvar_list[3148] = nvar_3148; + functions[3149] = fn3149; + nvar_list[3149] = nvar_3149; + functions[3150] = fn3150; + nvar_list[3150] = nvar_3150; + functions[3151] = fn3151; + nvar_list[3151] = nvar_3151; + functions[3152] = fn3152; + nvar_list[3152] = nvar_3152; + functions[3153] = fn3153; + nvar_list[3153] = nvar_3153; + functions[3154] = fn3154; + nvar_list[3154] = nvar_3154; + functions[3155] = fn3155; + nvar_list[3155] = nvar_3155; + functions[3156] = fn3156; + nvar_list[3156] = nvar_3156; + functions[3157] = fn3157; + nvar_list[3157] = nvar_3157; + functions[3158] = fn3158; + nvar_list[3158] = nvar_3158; + functions[3159] = fn3159; + nvar_list[3159] = nvar_3159; + functions[3160] = fn3160; + nvar_list[3160] = nvar_3160; + functions[3161] = fn3161; + nvar_list[3161] = nvar_3161; + functions[3162] = fn3162; + nvar_list[3162] = nvar_3162; + functions[3163] = fn3163; + nvar_list[3163] = nvar_3163; + functions[3164] = fn3164; + nvar_list[3164] = nvar_3164; + functions[3165] = fn3165; + nvar_list[3165] = nvar_3165; + functions[3166] = fn3166; + nvar_list[3166] = nvar_3166; + functions[3167] = fn3167; + nvar_list[3167] = nvar_3167; + functions[3168] = fn3168; + nvar_list[3168] = nvar_3168; + functions[3169] = fn3169; + nvar_list[3169] = nvar_3169; + functions[3170] = fn3170; + nvar_list[3170] = nvar_3170; + functions[3171] = fn3171; + nvar_list[3171] = nvar_3171; + functions[3172] = fn3172; + nvar_list[3172] = nvar_3172; + functions[3173] = fn3173; + nvar_list[3173] = nvar_3173; + functions[3174] = fn3174; + nvar_list[3174] = nvar_3174; + functions[3175] = fn3175; + nvar_list[3175] = nvar_3175; + functions[3176] = fn3176; + nvar_list[3176] = nvar_3176; + functions[3177] = fn3177; + nvar_list[3177] = nvar_3177; + functions[3178] = fn3178; + nvar_list[3178] = nvar_3178; + functions[3179] = fn3179; + nvar_list[3179] = nvar_3179; + functions[3180] = fn3180; + nvar_list[3180] = nvar_3180; + functions[3181] = fn3181; + nvar_list[3181] = nvar_3181; + functions[3182] = fn3182; + nvar_list[3182] = nvar_3182; + functions[3183] = fn3183; + nvar_list[3183] = nvar_3183; + functions[3184] = fn3184; + nvar_list[3184] = nvar_3184; + functions[3185] = fn3185; + nvar_list[3185] = nvar_3185; + functions[3186] = fn3186; + nvar_list[3186] = nvar_3186; + functions[3187] = fn3187; + nvar_list[3187] = nvar_3187; + functions[3188] = fn3188; + nvar_list[3188] = nvar_3188; + functions[3189] = fn3189; + nvar_list[3189] = nvar_3189; + functions[3190] = fn3190; + nvar_list[3190] = nvar_3190; + functions[3191] = fn3191; + nvar_list[3191] = nvar_3191; + functions[3192] = fn3192; + nvar_list[3192] = nvar_3192; + functions[3193] = fn3193; + nvar_list[3193] = nvar_3193; + functions[3194] = fn3194; + nvar_list[3194] = nvar_3194; + functions[3195] = fn3195; + nvar_list[3195] = nvar_3195; + functions[3196] = fn3196; + nvar_list[3196] = nvar_3196; + functions[3197] = fn3197; + nvar_list[3197] = nvar_3197; + functions[3198] = fn3198; + nvar_list[3198] = nvar_3198; + functions[3199] = fn3199; + nvar_list[3199] = nvar_3199; + functions[3200] = fn3200; + nvar_list[3200] = nvar_3200; + functions[3201] = fn3201; + nvar_list[3201] = nvar_3201; + functions[3202] = fn3202; + nvar_list[3202] = nvar_3202; + functions[3203] = fn3203; + nvar_list[3203] = nvar_3203; + functions[3204] = fn3204; + nvar_list[3204] = nvar_3204; + functions[3205] = fn3205; + nvar_list[3205] = nvar_3205; + functions[3206] = fn3206; + nvar_list[3206] = nvar_3206; + functions[3207] = fn3207; + nvar_list[3207] = nvar_3207; + functions[3208] = fn3208; + nvar_list[3208] = nvar_3208; + functions[3209] = fn3209; + nvar_list[3209] = nvar_3209; + functions[3210] = fn3210; + nvar_list[3210] = nvar_3210; + functions[3211] = fn3211; + nvar_list[3211] = nvar_3211; + functions[3212] = fn3212; + nvar_list[3212] = nvar_3212; + functions[3213] = fn3213; + nvar_list[3213] = nvar_3213; + functions[3214] = fn3214; + nvar_list[3214] = nvar_3214; + functions[3215] = fn3215; + nvar_list[3215] = nvar_3215; + functions[3216] = fn3216; + nvar_list[3216] = nvar_3216; + functions[3217] = fn3217; + nvar_list[3217] = nvar_3217; + functions[3218] = fn3218; + nvar_list[3218] = nvar_3218; + functions[3219] = fn3219; + nvar_list[3219] = nvar_3219; + functions[3220] = fn3220; + nvar_list[3220] = nvar_3220; + functions[3221] = fn3221; + nvar_list[3221] = nvar_3221; + functions[3222] = fn3222; + nvar_list[3222] = nvar_3222; + functions[3223] = fn3223; + nvar_list[3223] = nvar_3223; + functions[3224] = fn3224; + nvar_list[3224] = nvar_3224; + functions[3225] = fn3225; + nvar_list[3225] = nvar_3225; + functions[3226] = fn3226; + nvar_list[3226] = nvar_3226; + functions[3227] = fn3227; + nvar_list[3227] = nvar_3227; + functions[3228] = fn3228; + nvar_list[3228] = nvar_3228; + functions[3229] = fn3229; + nvar_list[3229] = nvar_3229; + functions[3230] = fn3230; + nvar_list[3230] = nvar_3230; + functions[3231] = fn3231; + nvar_list[3231] = nvar_3231; + functions[3232] = fn3232; + nvar_list[3232] = nvar_3232; + functions[3233] = fn3233; + nvar_list[3233] = nvar_3233; + functions[3234] = fn3234; + nvar_list[3234] = nvar_3234; + functions[3235] = fn3235; + nvar_list[3235] = nvar_3235; + functions[3236] = fn3236; + nvar_list[3236] = nvar_3236; + functions[3237] = fn3237; + nvar_list[3237] = nvar_3237; + functions[3238] = fn3238; + nvar_list[3238] = nvar_3238; + functions[3239] = fn3239; + nvar_list[3239] = nvar_3239; + functions[3240] = fn3240; + nvar_list[3240] = nvar_3240; + functions[3241] = fn3241; + nvar_list[3241] = nvar_3241; + functions[3242] = fn3242; + nvar_list[3242] = nvar_3242; + functions[3243] = fn3243; + nvar_list[3243] = nvar_3243; + functions[3244] = fn3244; + nvar_list[3244] = nvar_3244; + functions[3245] = fn3245; + nvar_list[3245] = nvar_3245; + functions[3246] = fn3246; + nvar_list[3246] = nvar_3246; + functions[3247] = fn3247; + nvar_list[3247] = nvar_3247; + functions[3248] = fn3248; + nvar_list[3248] = nvar_3248; + functions[3249] = fn3249; + nvar_list[3249] = nvar_3249; + functions[3250] = fn3250; + nvar_list[3250] = nvar_3250; + functions[3251] = fn3251; + nvar_list[3251] = nvar_3251; + functions[3252] = fn3252; + nvar_list[3252] = nvar_3252; + functions[3253] = fn3253; + nvar_list[3253] = nvar_3253; + functions[3254] = fn3254; + nvar_list[3254] = nvar_3254; + functions[3255] = fn3255; + nvar_list[3255] = nvar_3255; + functions[3256] = fn3256; + nvar_list[3256] = nvar_3256; + functions[3257] = fn3257; + nvar_list[3257] = nvar_3257; + functions[3258] = fn3258; + nvar_list[3258] = nvar_3258; + functions[3259] = fn3259; + nvar_list[3259] = nvar_3259; + functions[3260] = fn3260; + nvar_list[3260] = nvar_3260; + functions[3261] = fn3261; + nvar_list[3261] = nvar_3261; + functions[3262] = fn3262; + nvar_list[3262] = nvar_3262; + functions[3263] = fn3263; + nvar_list[3263] = nvar_3263; + functions[3264] = fn3264; + nvar_list[3264] = nvar_3264; + functions[3265] = fn3265; + nvar_list[3265] = nvar_3265; + functions[3266] = fn3266; + nvar_list[3266] = nvar_3266; + functions[3267] = fn3267; + nvar_list[3267] = nvar_3267; + functions[3268] = fn3268; + nvar_list[3268] = nvar_3268; + functions[3269] = fn3269; + nvar_list[3269] = nvar_3269; + functions[3270] = fn3270; + nvar_list[3270] = nvar_3270; + functions[3271] = fn3271; + nvar_list[3271] = nvar_3271; + functions[3272] = fn3272; + nvar_list[3272] = nvar_3272; + functions[3273] = fn3273; + nvar_list[3273] = nvar_3273; + functions[3274] = fn3274; + nvar_list[3274] = nvar_3274; + functions[3275] = fn3275; + nvar_list[3275] = nvar_3275; + functions[3276] = fn3276; + nvar_list[3276] = nvar_3276; + functions[3277] = fn3277; + nvar_list[3277] = nvar_3277; + functions[3278] = fn3278; + nvar_list[3278] = nvar_3278; + functions[3279] = fn3279; + nvar_list[3279] = nvar_3279; + functions[3280] = fn3280; + nvar_list[3280] = nvar_3280; + functions[3281] = fn3281; + nvar_list[3281] = nvar_3281; + functions[3282] = fn3282; + nvar_list[3282] = nvar_3282; + functions[3283] = fn3283; + nvar_list[3283] = nvar_3283; + functions[3284] = fn3284; + nvar_list[3284] = nvar_3284; + functions[3285] = fn3285; + nvar_list[3285] = nvar_3285; + functions[3286] = fn3286; + nvar_list[3286] = nvar_3286; + functions[3287] = fn3287; + nvar_list[3287] = nvar_3287; + functions[3288] = fn3288; + nvar_list[3288] = nvar_3288; + functions[3289] = fn3289; + nvar_list[3289] = nvar_3289; + functions[3290] = fn3290; + nvar_list[3290] = nvar_3290; + functions[3291] = fn3291; + nvar_list[3291] = nvar_3291; + functions[3292] = fn3292; + nvar_list[3292] = nvar_3292; + functions[3293] = fn3293; + nvar_list[3293] = nvar_3293; + functions[3294] = fn3294; + nvar_list[3294] = nvar_3294; + functions[3295] = fn3295; + nvar_list[3295] = nvar_3295; + functions[3296] = fn3296; + nvar_list[3296] = nvar_3296; + functions[3297] = fn3297; + nvar_list[3297] = nvar_3297; + functions[3298] = fn3298; + nvar_list[3298] = nvar_3298; + functions[3299] = fn3299; + nvar_list[3299] = nvar_3299; + functions[3300] = fn3300; + nvar_list[3300] = nvar_3300; + functions[3301] = fn3301; + nvar_list[3301] = nvar_3301; + functions[3302] = fn3302; + nvar_list[3302] = nvar_3302; + functions[3303] = fn3303; + nvar_list[3303] = nvar_3303; + functions[3304] = fn3304; + nvar_list[3304] = nvar_3304; + functions[3305] = fn3305; + nvar_list[3305] = nvar_3305; + functions[3306] = fn3306; + nvar_list[3306] = nvar_3306; + functions[3307] = fn3307; + nvar_list[3307] = nvar_3307; + functions[3308] = fn3308; + nvar_list[3308] = nvar_3308; + functions[3309] = fn3309; + nvar_list[3309] = nvar_3309; + functions[3310] = fn3310; + nvar_list[3310] = nvar_3310; + functions[3311] = fn3311; + nvar_list[3311] = nvar_3311; + functions[3312] = fn3312; + nvar_list[3312] = nvar_3312; + functions[3313] = fn3313; + nvar_list[3313] = nvar_3313; + functions[3314] = fn3314; + nvar_list[3314] = nvar_3314; + functions[3315] = fn3315; + nvar_list[3315] = nvar_3315; + functions[3316] = fn3316; + nvar_list[3316] = nvar_3316; + functions[3317] = fn3317; + nvar_list[3317] = nvar_3317; + functions[3318] = fn3318; + nvar_list[3318] = nvar_3318; + functions[3319] = fn3319; + nvar_list[3319] = nvar_3319; + functions[3320] = fn3320; + nvar_list[3320] = nvar_3320; + functions[3321] = fn3321; + nvar_list[3321] = nvar_3321; + functions[3322] = fn3322; + nvar_list[3322] = nvar_3322; + functions[3323] = fn3323; + nvar_list[3323] = nvar_3323; + functions[3324] = fn3324; + nvar_list[3324] = nvar_3324; + functions[3325] = fn3325; + nvar_list[3325] = nvar_3325; + functions[3326] = fn3326; + nvar_list[3326] = nvar_3326; + functions[3327] = fn3327; + nvar_list[3327] = nvar_3327; + functions[3328] = fn3328; + nvar_list[3328] = nvar_3328; + functions[3329] = fn3329; + nvar_list[3329] = nvar_3329; + functions[3330] = fn3330; + nvar_list[3330] = nvar_3330; + functions[3331] = fn3331; + nvar_list[3331] = nvar_3331; + functions[3332] = fn3332; + nvar_list[3332] = nvar_3332; + functions[3333] = fn3333; + nvar_list[3333] = nvar_3333; + functions[3334] = fn3334; + nvar_list[3334] = nvar_3334; + functions[3335] = fn3335; + nvar_list[3335] = nvar_3335; + functions[3336] = fn3336; + nvar_list[3336] = nvar_3336; + functions[3337] = fn3337; + nvar_list[3337] = nvar_3337; + functions[3338] = fn3338; + nvar_list[3338] = nvar_3338; + functions[3339] = fn3339; + nvar_list[3339] = nvar_3339; + functions[3340] = fn3340; + nvar_list[3340] = nvar_3340; + functions[3341] = fn3341; + nvar_list[3341] = nvar_3341; + functions[3342] = fn3342; + nvar_list[3342] = nvar_3342; + functions[3343] = fn3343; + nvar_list[3343] = nvar_3343; + functions[3344] = fn3344; + nvar_list[3344] = nvar_3344; + functions[3345] = fn3345; + nvar_list[3345] = nvar_3345; + functions[3346] = fn3346; + nvar_list[3346] = nvar_3346; + functions[3347] = fn3347; + nvar_list[3347] = nvar_3347; + functions[3348] = fn3348; + nvar_list[3348] = nvar_3348; + functions[3349] = fn3349; + nvar_list[3349] = nvar_3349; + functions[3350] = fn3350; + nvar_list[3350] = nvar_3350; + functions[3351] = fn3351; + nvar_list[3351] = nvar_3351; + functions[3352] = fn3352; + nvar_list[3352] = nvar_3352; + functions[3353] = fn3353; + nvar_list[3353] = nvar_3353; + functions[3354] = fn3354; + nvar_list[3354] = nvar_3354; + functions[3355] = fn3355; + nvar_list[3355] = nvar_3355; + functions[3356] = fn3356; + nvar_list[3356] = nvar_3356; + functions[3357] = fn3357; + nvar_list[3357] = nvar_3357; + functions[3358] = fn3358; + nvar_list[3358] = nvar_3358; + functions[3359] = fn3359; + nvar_list[3359] = nvar_3359; + functions[3360] = fn3360; + nvar_list[3360] = nvar_3360; + functions[3361] = fn3361; + nvar_list[3361] = nvar_3361; + functions[3362] = fn3362; + nvar_list[3362] = nvar_3362; + functions[3363] = fn3363; + nvar_list[3363] = nvar_3363; + functions[3364] = fn3364; + nvar_list[3364] = nvar_3364; + functions[3365] = fn3365; + nvar_list[3365] = nvar_3365; + functions[3366] = fn3366; + nvar_list[3366] = nvar_3366; + functions[3367] = fn3367; + nvar_list[3367] = nvar_3367; + functions[3368] = fn3368; + nvar_list[3368] = nvar_3368; + functions[3369] = fn3369; + nvar_list[3369] = nvar_3369; + functions[3370] = fn3370; + nvar_list[3370] = nvar_3370; + functions[3371] = fn3371; + nvar_list[3371] = nvar_3371; + functions[3372] = fn3372; + nvar_list[3372] = nvar_3372; + functions[3373] = fn3373; + nvar_list[3373] = nvar_3373; + functions[3374] = fn3374; + nvar_list[3374] = nvar_3374; + functions[3375] = fn3375; + nvar_list[3375] = nvar_3375; + functions[3376] = fn3376; + nvar_list[3376] = nvar_3376; + functions[3377] = fn3377; + nvar_list[3377] = nvar_3377; + functions[3378] = fn3378; + nvar_list[3378] = nvar_3378; + functions[3379] = fn3379; + nvar_list[3379] = nvar_3379; + functions[3380] = fn3380; + nvar_list[3380] = nvar_3380; + functions[3381] = fn3381; + nvar_list[3381] = nvar_3381; + functions[3382] = fn3382; + nvar_list[3382] = nvar_3382; + functions[3383] = fn3383; + nvar_list[3383] = nvar_3383; + functions[3384] = fn3384; + nvar_list[3384] = nvar_3384; + functions[3385] = fn3385; + nvar_list[3385] = nvar_3385; + functions[3386] = fn3386; + nvar_list[3386] = nvar_3386; + functions[3387] = fn3387; + nvar_list[3387] = nvar_3387; + functions[3388] = fn3388; + nvar_list[3388] = nvar_3388; + functions[3389] = fn3389; + nvar_list[3389] = nvar_3389; + functions[3390] = fn3390; + nvar_list[3390] = nvar_3390; + functions[3391] = fn3391; + nvar_list[3391] = nvar_3391; + functions[3392] = fn3392; + nvar_list[3392] = nvar_3392; + functions[3393] = fn3393; + nvar_list[3393] = nvar_3393; + functions[3394] = fn3394; + nvar_list[3394] = nvar_3394; + functions[3395] = fn3395; + nvar_list[3395] = nvar_3395; + functions[3396] = fn3396; + nvar_list[3396] = nvar_3396; + functions[3397] = fn3397; + nvar_list[3397] = nvar_3397; + functions[3398] = fn3398; + nvar_list[3398] = nvar_3398; + functions[3399] = fn3399; + nvar_list[3399] = nvar_3399; + functions[3400] = fn3400; + nvar_list[3400] = nvar_3400; + functions[3401] = fn3401; + nvar_list[3401] = nvar_3401; + functions[3402] = fn3402; + nvar_list[3402] = nvar_3402; + functions[3403] = fn3403; + nvar_list[3403] = nvar_3403; + functions[3404] = fn3404; + nvar_list[3404] = nvar_3404; + functions[3405] = fn3405; + nvar_list[3405] = nvar_3405; + functions[3406] = fn3406; + nvar_list[3406] = nvar_3406; + functions[3407] = fn3407; + nvar_list[3407] = nvar_3407; + functions[3408] = fn3408; + nvar_list[3408] = nvar_3408; + functions[3409] = fn3409; + nvar_list[3409] = nvar_3409; + functions[3410] = fn3410; + nvar_list[3410] = nvar_3410; + functions[3411] = fn3411; + nvar_list[3411] = nvar_3411; + functions[3412] = fn3412; + nvar_list[3412] = nvar_3412; + functions[3413] = fn3413; + nvar_list[3413] = nvar_3413; + functions[3414] = fn3414; + nvar_list[3414] = nvar_3414; + functions[3415] = fn3415; + nvar_list[3415] = nvar_3415; + functions[3416] = fn3416; + nvar_list[3416] = nvar_3416; + functions[3417] = fn3417; + nvar_list[3417] = nvar_3417; + functions[3418] = fn3418; + nvar_list[3418] = nvar_3418; + functions[3419] = fn3419; + nvar_list[3419] = nvar_3419; + functions[3420] = fn3420; + nvar_list[3420] = nvar_3420; + functions[3421] = fn3421; + nvar_list[3421] = nvar_3421; + functions[3422] = fn3422; + nvar_list[3422] = nvar_3422; + functions[3423] = fn3423; + nvar_list[3423] = nvar_3423; + functions[3424] = fn3424; + nvar_list[3424] = nvar_3424; + functions[3425] = fn3425; + nvar_list[3425] = nvar_3425; + functions[3426] = fn3426; + nvar_list[3426] = nvar_3426; + functions[3427] = fn3427; + nvar_list[3427] = nvar_3427; + functions[3428] = fn3428; + nvar_list[3428] = nvar_3428; + functions[3429] = fn3429; + nvar_list[3429] = nvar_3429; + functions[3430] = fn3430; + nvar_list[3430] = nvar_3430; + functions[3431] = fn3431; + nvar_list[3431] = nvar_3431; + functions[3432] = fn3432; + nvar_list[3432] = nvar_3432; + functions[3433] = fn3433; + nvar_list[3433] = nvar_3433; + functions[3434] = fn3434; + nvar_list[3434] = nvar_3434; + functions[3435] = fn3435; + nvar_list[3435] = nvar_3435; + functions[3436] = fn3436; + nvar_list[3436] = nvar_3436; + functions[3437] = fn3437; + nvar_list[3437] = nvar_3437; + functions[3438] = fn3438; + nvar_list[3438] = nvar_3438; + functions[3439] = fn3439; + nvar_list[3439] = nvar_3439; + functions[3440] = fn3440; + nvar_list[3440] = nvar_3440; + functions[3441] = fn3441; + nvar_list[3441] = nvar_3441; + functions[3442] = fn3442; + nvar_list[3442] = nvar_3442; + functions[3443] = fn3443; + nvar_list[3443] = nvar_3443; + functions[3444] = fn3444; + nvar_list[3444] = nvar_3444; + functions[3445] = fn3445; + nvar_list[3445] = nvar_3445; + functions[3446] = fn3446; + nvar_list[3446] = nvar_3446; + functions[3447] = fn3447; + nvar_list[3447] = nvar_3447; + functions[3448] = fn3448; + nvar_list[3448] = nvar_3448; + functions[3449] = fn3449; + nvar_list[3449] = nvar_3449; + functions[3450] = fn3450; + nvar_list[3450] = nvar_3450; + functions[3451] = fn3451; + nvar_list[3451] = nvar_3451; + functions[3452] = fn3452; + nvar_list[3452] = nvar_3452; + functions[3453] = fn3453; + nvar_list[3453] = nvar_3453; + functions[3454] = fn3454; + nvar_list[3454] = nvar_3454; + functions[3455] = fn3455; + nvar_list[3455] = nvar_3455; + functions[3456] = fn3456; + nvar_list[3456] = nvar_3456; + functions[3457] = fn3457; + nvar_list[3457] = nvar_3457; + functions[3458] = fn3458; + nvar_list[3458] = nvar_3458; + functions[3459] = fn3459; + nvar_list[3459] = nvar_3459; + functions[3460] = fn3460; + nvar_list[3460] = nvar_3460; + functions[3461] = fn3461; + nvar_list[3461] = nvar_3461; + functions[3462] = fn3462; + nvar_list[3462] = nvar_3462; + functions[3463] = fn3463; + nvar_list[3463] = nvar_3463; + functions[3464] = fn3464; + nvar_list[3464] = nvar_3464; + functions[3465] = fn3465; + nvar_list[3465] = nvar_3465; + functions[3466] = fn3466; + nvar_list[3466] = nvar_3466; + functions[3467] = fn3467; + nvar_list[3467] = nvar_3467; + functions[3468] = fn3468; + nvar_list[3468] = nvar_3468; + functions[3469] = fn3469; + nvar_list[3469] = nvar_3469; + functions[3470] = fn3470; + nvar_list[3470] = nvar_3470; + functions[3471] = fn3471; + nvar_list[3471] = nvar_3471; + functions[3472] = fn3472; + nvar_list[3472] = nvar_3472; + functions[3473] = fn3473; + nvar_list[3473] = nvar_3473; + functions[3474] = fn3474; + nvar_list[3474] = nvar_3474; + functions[3475] = fn3475; + nvar_list[3475] = nvar_3475; + functions[3476] = fn3476; + nvar_list[3476] = nvar_3476; + functions[3477] = fn3477; + nvar_list[3477] = nvar_3477; + functions[3478] = fn3478; + nvar_list[3478] = nvar_3478; + functions[3479] = fn3479; + nvar_list[3479] = nvar_3479; + functions[3480] = fn3480; + nvar_list[3480] = nvar_3480; + functions[3481] = fn3481; + nvar_list[3481] = nvar_3481; + functions[3482] = fn3482; + nvar_list[3482] = nvar_3482; + functions[3483] = fn3483; + nvar_list[3483] = nvar_3483; + functions[3484] = fn3484; + nvar_list[3484] = nvar_3484; + functions[3485] = fn3485; + nvar_list[3485] = nvar_3485; + functions[3486] = fn3486; + nvar_list[3486] = nvar_3486; + functions[3487] = fn3487; + nvar_list[3487] = nvar_3487; + functions[3488] = fn3488; + nvar_list[3488] = nvar_3488; + functions[3489] = fn3489; + nvar_list[3489] = nvar_3489; + functions[3490] = fn3490; + nvar_list[3490] = nvar_3490; + functions[3491] = fn3491; + nvar_list[3491] = nvar_3491; + functions[3492] = fn3492; + nvar_list[3492] = nvar_3492; + functions[3493] = fn3493; + nvar_list[3493] = nvar_3493; + functions[3494] = fn3494; + nvar_list[3494] = nvar_3494; + functions[3495] = fn3495; + nvar_list[3495] = nvar_3495; + functions[3496] = fn3496; + nvar_list[3496] = nvar_3496; + functions[3497] = fn3497; + nvar_list[3497] = nvar_3497; + functions[3498] = fn3498; + nvar_list[3498] = nvar_3498; + functions[3499] = fn3499; + nvar_list[3499] = nvar_3499; + functions[3500] = fn3500; + nvar_list[3500] = nvar_3500; + functions[3501] = fn3501; + nvar_list[3501] = nvar_3501; + functions[3502] = fn3502; + nvar_list[3502] = nvar_3502; + functions[3503] = fn3503; + nvar_list[3503] = nvar_3503; + functions[3504] = fn3504; + nvar_list[3504] = nvar_3504; + functions[3505] = fn3505; + nvar_list[3505] = nvar_3505; + functions[3506] = fn3506; + nvar_list[3506] = nvar_3506; + functions[3507] = fn3507; + nvar_list[3507] = nvar_3507; + functions[3508] = fn3508; + nvar_list[3508] = nvar_3508; + functions[3509] = fn3509; + nvar_list[3509] = nvar_3509; + functions[3510] = fn3510; + nvar_list[3510] = nvar_3510; + functions[3511] = fn3511; + nvar_list[3511] = nvar_3511; + functions[3512] = fn3512; + nvar_list[3512] = nvar_3512; + functions[3513] = fn3513; + nvar_list[3513] = nvar_3513; + functions[3514] = fn3514; + nvar_list[3514] = nvar_3514; + functions[3515] = fn3515; + nvar_list[3515] = nvar_3515; + functions[3516] = fn3516; + nvar_list[3516] = nvar_3516; + functions[3517] = fn3517; + nvar_list[3517] = nvar_3517; + functions[3518] = fn3518; + nvar_list[3518] = nvar_3518; + functions[3519] = fn3519; + nvar_list[3519] = nvar_3519; + functions[3520] = fn3520; + nvar_list[3520] = nvar_3520; + functions[3521] = fn3521; + nvar_list[3521] = nvar_3521; + functions[3522] = fn3522; + nvar_list[3522] = nvar_3522; + functions[3523] = fn3523; + nvar_list[3523] = nvar_3523; + functions[3524] = fn3524; + nvar_list[3524] = nvar_3524; + functions[3525] = fn3525; + nvar_list[3525] = nvar_3525; + functions[3526] = fn3526; + nvar_list[3526] = nvar_3526; + functions[3527] = fn3527; + nvar_list[3527] = nvar_3527; + functions[3528] = fn3528; + nvar_list[3528] = nvar_3528; + functions[3529] = fn3529; + nvar_list[3529] = nvar_3529; + functions[3530] = fn3530; + nvar_list[3530] = nvar_3530; + functions[3531] = fn3531; + nvar_list[3531] = nvar_3531; + functions[3532] = fn3532; + nvar_list[3532] = nvar_3532; + functions[3533] = fn3533; + nvar_list[3533] = nvar_3533; + functions[3534] = fn3534; + nvar_list[3534] = nvar_3534; + functions[3535] = fn3535; + nvar_list[3535] = nvar_3535; + functions[3536] = fn3536; + nvar_list[3536] = nvar_3536; + functions[3537] = fn3537; + nvar_list[3537] = nvar_3537; + functions[3538] = fn3538; + nvar_list[3538] = nvar_3538; + functions[3539] = fn3539; + nvar_list[3539] = nvar_3539; + functions[3540] = fn3540; + nvar_list[3540] = nvar_3540; + functions[3541] = fn3541; + nvar_list[3541] = nvar_3541; + functions[3542] = fn3542; + nvar_list[3542] = nvar_3542; + functions[3543] = fn3543; + nvar_list[3543] = nvar_3543; + functions[3544] = fn3544; + nvar_list[3544] = nvar_3544; + functions[3545] = fn3545; + nvar_list[3545] = nvar_3545; + functions[3546] = fn3546; + nvar_list[3546] = nvar_3546; + functions[3547] = fn3547; + nvar_list[3547] = nvar_3547; + functions[3548] = fn3548; + nvar_list[3548] = nvar_3548; + functions[3549] = fn3549; + nvar_list[3549] = nvar_3549; + functions[3550] = fn3550; + nvar_list[3550] = nvar_3550; + functions[3551] = fn3551; + nvar_list[3551] = nvar_3551; + functions[3552] = fn3552; + nvar_list[3552] = nvar_3552; + functions[3553] = fn3553; + nvar_list[3553] = nvar_3553; + functions[3554] = fn3554; + nvar_list[3554] = nvar_3554; + functions[3555] = fn3555; + nvar_list[3555] = nvar_3555; + functions[3556] = fn3556; + nvar_list[3556] = nvar_3556; + functions[3557] = fn3557; + nvar_list[3557] = nvar_3557; + functions[3558] = fn3558; + nvar_list[3558] = nvar_3558; + functions[3559] = fn3559; + nvar_list[3559] = nvar_3559; + functions[3560] = fn3560; + nvar_list[3560] = nvar_3560; + functions[3561] = fn3561; + nvar_list[3561] = nvar_3561; + functions[3562] = fn3562; + nvar_list[3562] = nvar_3562; + functions[3563] = fn3563; + nvar_list[3563] = nvar_3563; + functions[3564] = fn3564; + nvar_list[3564] = nvar_3564; + functions[3565] = fn3565; + nvar_list[3565] = nvar_3565; + functions[3566] = fn3566; + nvar_list[3566] = nvar_3566; + functions[3567] = fn3567; + nvar_list[3567] = nvar_3567; + functions[3568] = fn3568; + nvar_list[3568] = nvar_3568; + functions[3569] = fn3569; + nvar_list[3569] = nvar_3569; + functions[3570] = fn3570; + nvar_list[3570] = nvar_3570; + functions[3571] = fn3571; + nvar_list[3571] = nvar_3571; + functions[3572] = fn3572; + nvar_list[3572] = nvar_3572; + functions[3573] = fn3573; + nvar_list[3573] = nvar_3573; + functions[3574] = fn3574; + nvar_list[3574] = nvar_3574; + functions[3575] = fn3575; + nvar_list[3575] = nvar_3575; + functions[3576] = fn3576; + nvar_list[3576] = nvar_3576; + functions[3577] = fn3577; + nvar_list[3577] = nvar_3577; + functions[3578] = fn3578; + nvar_list[3578] = nvar_3578; + functions[3579] = fn3579; + nvar_list[3579] = nvar_3579; + functions[3580] = fn3580; + nvar_list[3580] = nvar_3580; + functions[3581] = fn3581; + nvar_list[3581] = nvar_3581; + functions[3582] = fn3582; + nvar_list[3582] = nvar_3582; + functions[3583] = fn3583; + nvar_list[3583] = nvar_3583; + functions[3584] = fn3584; + nvar_list[3584] = nvar_3584; + functions[3585] = fn3585; + nvar_list[3585] = nvar_3585; + functions[3586] = fn3586; + nvar_list[3586] = nvar_3586; + functions[3587] = fn3587; + nvar_list[3587] = nvar_3587; + functions[3588] = fn3588; + nvar_list[3588] = nvar_3588; + functions[3589] = fn3589; + nvar_list[3589] = nvar_3589; + functions[3590] = fn3590; + nvar_list[3590] = nvar_3590; + functions[3591] = fn3591; + nvar_list[3591] = nvar_3591; + functions[3592] = fn3592; + nvar_list[3592] = nvar_3592; + functions[3593] = fn3593; + nvar_list[3593] = nvar_3593; + functions[3594] = fn3594; + nvar_list[3594] = nvar_3594; + functions[3595] = fn3595; + nvar_list[3595] = nvar_3595; + functions[3596] = fn3596; + nvar_list[3596] = nvar_3596; + functions[3597] = fn3597; + nvar_list[3597] = nvar_3597; + functions[3598] = fn3598; + nvar_list[3598] = nvar_3598; + functions[3599] = fn3599; + nvar_list[3599] = nvar_3599; + functions[3600] = fn3600; + nvar_list[3600] = nvar_3600; + functions[3601] = fn3601; + nvar_list[3601] = nvar_3601; + functions[3602] = fn3602; + nvar_list[3602] = nvar_3602; + functions[3603] = fn3603; + nvar_list[3603] = nvar_3603; + functions[3604] = fn3604; + nvar_list[3604] = nvar_3604; + functions[3605] = fn3605; + nvar_list[3605] = nvar_3605; + functions[3606] = fn3606; + nvar_list[3606] = nvar_3606; + functions[3607] = fn3607; + nvar_list[3607] = nvar_3607; + functions[3608] = fn3608; + nvar_list[3608] = nvar_3608; + functions[3609] = fn3609; + nvar_list[3609] = nvar_3609; + functions[3610] = fn3610; + nvar_list[3610] = nvar_3610; + functions[3611] = fn3611; + nvar_list[3611] = nvar_3611; + functions[3612] = fn3612; + nvar_list[3612] = nvar_3612; + functions[3613] = fn3613; + nvar_list[3613] = nvar_3613; + functions[3614] = fn3614; + nvar_list[3614] = nvar_3614; + functions[3615] = fn3615; + nvar_list[3615] = nvar_3615; + functions[3616] = fn3616; + nvar_list[3616] = nvar_3616; + functions[3617] = fn3617; + nvar_list[3617] = nvar_3617; + functions[3618] = fn3618; + nvar_list[3618] = nvar_3618; + functions[3619] = fn3619; + nvar_list[3619] = nvar_3619; + functions[3620] = fn3620; + nvar_list[3620] = nvar_3620; + functions[3621] = fn3621; + nvar_list[3621] = nvar_3621; + functions[3622] = fn3622; + nvar_list[3622] = nvar_3622; + functions[3623] = fn3623; + nvar_list[3623] = nvar_3623; + functions[3624] = fn3624; + nvar_list[3624] = nvar_3624; + functions[3625] = fn3625; + nvar_list[3625] = nvar_3625; + functions[3626] = fn3626; + nvar_list[3626] = nvar_3626; + functions[3627] = fn3627; + nvar_list[3627] = nvar_3627; + functions[3628] = fn3628; + nvar_list[3628] = nvar_3628; + functions[3629] = fn3629; + nvar_list[3629] = nvar_3629; + functions[3630] = fn3630; + nvar_list[3630] = nvar_3630; + functions[3631] = fn3631; + nvar_list[3631] = nvar_3631; + functions[3632] = fn3632; + nvar_list[3632] = nvar_3632; + functions[3633] = fn3633; + nvar_list[3633] = nvar_3633; + functions[3634] = fn3634; + nvar_list[3634] = nvar_3634; + functions[3635] = fn3635; + nvar_list[3635] = nvar_3635; + functions[3636] = fn3636; + nvar_list[3636] = nvar_3636; + functions[3637] = fn3637; + nvar_list[3637] = nvar_3637; + functions[3638] = fn3638; + nvar_list[3638] = nvar_3638; + functions[3639] = fn3639; + nvar_list[3639] = nvar_3639; + functions[3640] = fn3640; + nvar_list[3640] = nvar_3640; + functions[3641] = fn3641; + nvar_list[3641] = nvar_3641; + functions[3642] = fn3642; + nvar_list[3642] = nvar_3642; + functions[3643] = fn3643; + nvar_list[3643] = nvar_3643; + functions[3644] = fn3644; + nvar_list[3644] = nvar_3644; + functions[3645] = fn3645; + nvar_list[3645] = nvar_3645; + functions[3646] = fn3646; + nvar_list[3646] = nvar_3646; + functions[3647] = fn3647; + nvar_list[3647] = nvar_3647; + functions[3648] = fn3648; + nvar_list[3648] = nvar_3648; + functions[3649] = fn3649; + nvar_list[3649] = nvar_3649; + functions[3650] = fn3650; + nvar_list[3650] = nvar_3650; + functions[3651] = fn3651; + nvar_list[3651] = nvar_3651; + functions[3652] = fn3652; + nvar_list[3652] = nvar_3652; + functions[3653] = fn3653; + nvar_list[3653] = nvar_3653; + functions[3654] = fn3654; + nvar_list[3654] = nvar_3654; + functions[3655] = fn3655; + nvar_list[3655] = nvar_3655; + functions[3656] = fn3656; + nvar_list[3656] = nvar_3656; + functions[3657] = fn3657; + nvar_list[3657] = nvar_3657; + functions[3658] = fn3658; + nvar_list[3658] = nvar_3658; + functions[3659] = fn3659; + nvar_list[3659] = nvar_3659; + functions[3660] = fn3660; + nvar_list[3660] = nvar_3660; + functions[3661] = fn3661; + nvar_list[3661] = nvar_3661; + functions[3662] = fn3662; + nvar_list[3662] = nvar_3662; + functions[3663] = fn3663; + nvar_list[3663] = nvar_3663; + functions[3664] = fn3664; + nvar_list[3664] = nvar_3664; + functions[3665] = fn3665; + nvar_list[3665] = nvar_3665; + functions[3666] = fn3666; + nvar_list[3666] = nvar_3666; + functions[3667] = fn3667; + nvar_list[3667] = nvar_3667; + functions[3668] = fn3668; + nvar_list[3668] = nvar_3668; + functions[3669] = fn3669; + nvar_list[3669] = nvar_3669; + functions[3670] = fn3670; + nvar_list[3670] = nvar_3670; + functions[3671] = fn3671; + nvar_list[3671] = nvar_3671; + functions[3672] = fn3672; + nvar_list[3672] = nvar_3672; + functions[3673] = fn3673; + nvar_list[3673] = nvar_3673; + functions[3674] = fn3674; + nvar_list[3674] = nvar_3674; + functions[3675] = fn3675; + nvar_list[3675] = nvar_3675; + functions[3676] = fn3676; + nvar_list[3676] = nvar_3676; + functions[3677] = fn3677; + nvar_list[3677] = nvar_3677; + functions[3678] = fn3678; + nvar_list[3678] = nvar_3678; + functions[3679] = fn3679; + nvar_list[3679] = nvar_3679; + functions[3680] = fn3680; + nvar_list[3680] = nvar_3680; + functions[3681] = fn3681; + nvar_list[3681] = nvar_3681; + functions[3682] = fn3682; + nvar_list[3682] = nvar_3682; + functions[3683] = fn3683; + nvar_list[3683] = nvar_3683; + functions[3684] = fn3684; + nvar_list[3684] = nvar_3684; + functions[3685] = fn3685; + nvar_list[3685] = nvar_3685; + functions[3686] = fn3686; + nvar_list[3686] = nvar_3686; + functions[3687] = fn3687; + nvar_list[3687] = nvar_3687; + functions[3688] = fn3688; + nvar_list[3688] = nvar_3688; + functions[3689] = fn3689; + nvar_list[3689] = nvar_3689; + functions[3690] = fn3690; + nvar_list[3690] = nvar_3690; + functions[3691] = fn3691; + nvar_list[3691] = nvar_3691; + functions[3692] = fn3692; + nvar_list[3692] = nvar_3692; + functions[3693] = fn3693; + nvar_list[3693] = nvar_3693; + functions[3694] = fn3694; + nvar_list[3694] = nvar_3694; + functions[3695] = fn3695; + nvar_list[3695] = nvar_3695; + functions[3696] = fn3696; + nvar_list[3696] = nvar_3696; + functions[3697] = fn3697; + nvar_list[3697] = nvar_3697; + functions[3698] = fn3698; + nvar_list[3698] = nvar_3698; + functions[3699] = fn3699; + nvar_list[3699] = nvar_3699; + functions[3700] = fn3700; + nvar_list[3700] = nvar_3700; + functions[3701] = fn3701; + nvar_list[3701] = nvar_3701; + functions[3702] = fn3702; + nvar_list[3702] = nvar_3702; + functions[3703] = fn3703; + nvar_list[3703] = nvar_3703; + functions[3704] = fn3704; + nvar_list[3704] = nvar_3704; + functions[3705] = fn3705; + nvar_list[3705] = nvar_3705; + functions[3706] = fn3706; + nvar_list[3706] = nvar_3706; + functions[3707] = fn3707; + nvar_list[3707] = nvar_3707; + functions[3708] = fn3708; + nvar_list[3708] = nvar_3708; + functions[3709] = fn3709; + nvar_list[3709] = nvar_3709; + functions[3710] = fn3710; + nvar_list[3710] = nvar_3710; + functions[3711] = fn3711; + nvar_list[3711] = nvar_3711; + functions[3712] = fn3712; + nvar_list[3712] = nvar_3712; + functions[3713] = fn3713; + nvar_list[3713] = nvar_3713; + functions[3714] = fn3714; + nvar_list[3714] = nvar_3714; + functions[3715] = fn3715; + nvar_list[3715] = nvar_3715; + functions[3716] = fn3716; + nvar_list[3716] = nvar_3716; + functions[3717] = fn3717; + nvar_list[3717] = nvar_3717; + functions[3718] = fn3718; + nvar_list[3718] = nvar_3718; + functions[3719] = fn3719; + nvar_list[3719] = nvar_3719; + functions[3720] = fn3720; + nvar_list[3720] = nvar_3720; + functions[3721] = fn3721; + nvar_list[3721] = nvar_3721; + functions[3722] = fn3722; + nvar_list[3722] = nvar_3722; + functions[3723] = fn3723; + nvar_list[3723] = nvar_3723; + functions[3724] = fn3724; + nvar_list[3724] = nvar_3724; + functions[3725] = fn3725; + nvar_list[3725] = nvar_3725; + functions[3726] = fn3726; + nvar_list[3726] = nvar_3726; + functions[3727] = fn3727; + nvar_list[3727] = nvar_3727; + functions[3728] = fn3728; + nvar_list[3728] = nvar_3728; + functions[3729] = fn3729; + nvar_list[3729] = nvar_3729; + functions[3730] = fn3730; + nvar_list[3730] = nvar_3730; + functions[3731] = fn3731; + nvar_list[3731] = nvar_3731; + functions[3732] = fn3732; + nvar_list[3732] = nvar_3732; + functions[3733] = fn3733; + nvar_list[3733] = nvar_3733; + functions[3734] = fn3734; + nvar_list[3734] = nvar_3734; + functions[3735] = fn3735; + nvar_list[3735] = nvar_3735; + functions[3736] = fn3736; + nvar_list[3736] = nvar_3736; + functions[3737] = fn3737; + nvar_list[3737] = nvar_3737; + functions[3738] = fn3738; + nvar_list[3738] = nvar_3738; + functions[3739] = fn3739; + nvar_list[3739] = nvar_3739; + functions[3740] = fn3740; + nvar_list[3740] = nvar_3740; + functions[3741] = fn3741; + nvar_list[3741] = nvar_3741; + functions[3742] = fn3742; + nvar_list[3742] = nvar_3742; + functions[3743] = fn3743; + nvar_list[3743] = nvar_3743; + functions[3744] = fn3744; + nvar_list[3744] = nvar_3744; + functions[3745] = fn3745; + nvar_list[3745] = nvar_3745; + functions[3746] = fn3746; + nvar_list[3746] = nvar_3746; + functions[3747] = fn3747; + nvar_list[3747] = nvar_3747; + functions[3748] = fn3748; + nvar_list[3748] = nvar_3748; + functions[3749] = fn3749; + nvar_list[3749] = nvar_3749; + functions[3750] = fn3750; + nvar_list[3750] = nvar_3750; + functions[3751] = fn3751; + nvar_list[3751] = nvar_3751; + functions[3752] = fn3752; + nvar_list[3752] = nvar_3752; + functions[3753] = fn3753; + nvar_list[3753] = nvar_3753; + functions[3754] = fn3754; + nvar_list[3754] = nvar_3754; + functions[3755] = fn3755; + nvar_list[3755] = nvar_3755; + functions[3756] = fn3756; + nvar_list[3756] = nvar_3756; + functions[3757] = fn3757; + nvar_list[3757] = nvar_3757; + functions[3758] = fn3758; + nvar_list[3758] = nvar_3758; + functions[3759] = fn3759; + nvar_list[3759] = nvar_3759; + functions[3760] = fn3760; + nvar_list[3760] = nvar_3760; + functions[3761] = fn3761; + nvar_list[3761] = nvar_3761; + functions[3762] = fn3762; + nvar_list[3762] = nvar_3762; + functions[3763] = fn3763; + nvar_list[3763] = nvar_3763; + functions[3764] = fn3764; + nvar_list[3764] = nvar_3764; + functions[3765] = fn3765; + nvar_list[3765] = nvar_3765; + functions[3766] = fn3766; + nvar_list[3766] = nvar_3766; + functions[3767] = fn3767; + nvar_list[3767] = nvar_3767; + functions[3768] = fn3768; + nvar_list[3768] = nvar_3768; + functions[3769] = fn3769; + nvar_list[3769] = nvar_3769; + functions[3770] = fn3770; + nvar_list[3770] = nvar_3770; + functions[3771] = fn3771; + nvar_list[3771] = nvar_3771; + functions[3772] = fn3772; + nvar_list[3772] = nvar_3772; + functions[3773] = fn3773; + nvar_list[3773] = nvar_3773; + functions[3774] = fn3774; + nvar_list[3774] = nvar_3774; + functions[3775] = fn3775; + nvar_list[3775] = nvar_3775; + functions[3776] = fn3776; + nvar_list[3776] = nvar_3776; + functions[3777] = fn3777; + nvar_list[3777] = nvar_3777; + functions[3778] = fn3778; + nvar_list[3778] = nvar_3778; + functions[3779] = fn3779; + nvar_list[3779] = nvar_3779; + functions[3780] = fn3780; + nvar_list[3780] = nvar_3780; + functions[3781] = fn3781; + nvar_list[3781] = nvar_3781; + functions[3782] = fn3782; + nvar_list[3782] = nvar_3782; + functions[3783] = fn3783; + nvar_list[3783] = nvar_3783; + functions[3784] = fn3784; + nvar_list[3784] = nvar_3784; + functions[3785] = fn3785; + nvar_list[3785] = nvar_3785; + functions[3786] = fn3786; + nvar_list[3786] = nvar_3786; + functions[3787] = fn3787; + nvar_list[3787] = nvar_3787; + functions[3788] = fn3788; + nvar_list[3788] = nvar_3788; + functions[3789] = fn3789; + nvar_list[3789] = nvar_3789; + functions[3790] = fn3790; + nvar_list[3790] = nvar_3790; + functions[3791] = fn3791; + nvar_list[3791] = nvar_3791; + functions[3792] = fn3792; + nvar_list[3792] = nvar_3792; + functions[3793] = fn3793; + nvar_list[3793] = nvar_3793; + functions[3794] = fn3794; + nvar_list[3794] = nvar_3794; + functions[3795] = fn3795; + nvar_list[3795] = nvar_3795; + functions[3796] = fn3796; + nvar_list[3796] = nvar_3796; + functions[3797] = fn3797; + nvar_list[3797] = nvar_3797; + functions[3798] = fn3798; + nvar_list[3798] = nvar_3798; + functions[3799] = fn3799; + nvar_list[3799] = nvar_3799; + functions[3800] = fn3800; + nvar_list[3800] = nvar_3800; + functions[3801] = fn3801; + nvar_list[3801] = nvar_3801; + functions[3802] = fn3802; + nvar_list[3802] = nvar_3802; + functions[3803] = fn3803; + nvar_list[3803] = nvar_3803; + functions[3804] = fn3804; + nvar_list[3804] = nvar_3804; + functions[3805] = fn3805; + nvar_list[3805] = nvar_3805; + functions[3806] = fn3806; + nvar_list[3806] = nvar_3806; + functions[3807] = fn3807; + nvar_list[3807] = nvar_3807; + functions[3808] = fn3808; + nvar_list[3808] = nvar_3808; + functions[3809] = fn3809; + nvar_list[3809] = nvar_3809; + functions[3810] = fn3810; + nvar_list[3810] = nvar_3810; + functions[3811] = fn3811; + nvar_list[3811] = nvar_3811; + functions[3812] = fn3812; + nvar_list[3812] = nvar_3812; + functions[3813] = fn3813; + nvar_list[3813] = nvar_3813; + functions[3814] = fn3814; + nvar_list[3814] = nvar_3814; + functions[3815] = fn3815; + nvar_list[3815] = nvar_3815; + functions[3816] = fn3816; + nvar_list[3816] = nvar_3816; + functions[3817] = fn3817; + nvar_list[3817] = nvar_3817; + functions[3818] = fn3818; + nvar_list[3818] = nvar_3818; + functions[3819] = fn3819; + nvar_list[3819] = nvar_3819; + functions[3820] = fn3820; + nvar_list[3820] = nvar_3820; + functions[3821] = fn3821; + nvar_list[3821] = nvar_3821; + functions[3822] = fn3822; + nvar_list[3822] = nvar_3822; + functions[3823] = fn3823; + nvar_list[3823] = nvar_3823; + functions[3824] = fn3824; + nvar_list[3824] = nvar_3824; + functions[3825] = fn3825; + nvar_list[3825] = nvar_3825; + functions[3826] = fn3826; + nvar_list[3826] = nvar_3826; + functions[3827] = fn3827; + nvar_list[3827] = nvar_3827; + functions[3828] = fn3828; + nvar_list[3828] = nvar_3828; + functions[3829] = fn3829; + nvar_list[3829] = nvar_3829; + functions[3830] = fn3830; + nvar_list[3830] = nvar_3830; + functions[3831] = fn3831; + nvar_list[3831] = nvar_3831; + functions[3832] = fn3832; + nvar_list[3832] = nvar_3832; + functions[3833] = fn3833; + nvar_list[3833] = nvar_3833; + functions[3834] = fn3834; + nvar_list[3834] = nvar_3834; + functions[3835] = fn3835; + nvar_list[3835] = nvar_3835; + functions[3836] = fn3836; + nvar_list[3836] = nvar_3836; + functions[3837] = fn3837; + nvar_list[3837] = nvar_3837; + functions[3838] = fn3838; + nvar_list[3838] = nvar_3838; + functions[3839] = fn3839; + nvar_list[3839] = nvar_3839; + functions[3840] = fn3840; + nvar_list[3840] = nvar_3840; + functions[3841] = fn3841; + nvar_list[3841] = nvar_3841; + functions[3842] = fn3842; + nvar_list[3842] = nvar_3842; + functions[3843] = fn3843; + nvar_list[3843] = nvar_3843; + functions[3844] = fn3844; + nvar_list[3844] = nvar_3844; + functions[3845] = fn3845; + nvar_list[3845] = nvar_3845; + functions[3846] = fn3846; + nvar_list[3846] = nvar_3846; + functions[3847] = fn3847; + nvar_list[3847] = nvar_3847; + functions[3848] = fn3848; + nvar_list[3848] = nvar_3848; + functions[3849] = fn3849; + nvar_list[3849] = nvar_3849; + functions[3850] = fn3850; + nvar_list[3850] = nvar_3850; + functions[3851] = fn3851; + nvar_list[3851] = nvar_3851; + functions[3852] = fn3852; + nvar_list[3852] = nvar_3852; + functions[3853] = fn3853; + nvar_list[3853] = nvar_3853; + functions[3854] = fn3854; + nvar_list[3854] = nvar_3854; + functions[3855] = fn3855; + nvar_list[3855] = nvar_3855; + functions[3856] = fn3856; + nvar_list[3856] = nvar_3856; + functions[3857] = fn3857; + nvar_list[3857] = nvar_3857; + functions[3858] = fn3858; + nvar_list[3858] = nvar_3858; + functions[3859] = fn3859; + nvar_list[3859] = nvar_3859; + functions[3860] = fn3860; + nvar_list[3860] = nvar_3860; + functions[3861] = fn3861; + nvar_list[3861] = nvar_3861; + functions[3862] = fn3862; + nvar_list[3862] = nvar_3862; + functions[3863] = fn3863; + nvar_list[3863] = nvar_3863; + functions[3864] = fn3864; + nvar_list[3864] = nvar_3864; + functions[3865] = fn3865; + nvar_list[3865] = nvar_3865; + functions[3866] = fn3866; + nvar_list[3866] = nvar_3866; + functions[3867] = fn3867; + nvar_list[3867] = nvar_3867; + functions[3868] = fn3868; + nvar_list[3868] = nvar_3868; + functions[3869] = fn3869; + nvar_list[3869] = nvar_3869; + functions[3870] = fn3870; + nvar_list[3870] = nvar_3870; + functions[3871] = fn3871; + nvar_list[3871] = nvar_3871; + functions[3872] = fn3872; + nvar_list[3872] = nvar_3872; + functions[3873] = fn3873; + nvar_list[3873] = nvar_3873; + functions[3874] = fn3874; + nvar_list[3874] = nvar_3874; + functions[3875] = fn3875; + nvar_list[3875] = nvar_3875; + functions[3876] = fn3876; + nvar_list[3876] = nvar_3876; + functions[3877] = fn3877; + nvar_list[3877] = nvar_3877; + functions[3878] = fn3878; + nvar_list[3878] = nvar_3878; + functions[3879] = fn3879; + nvar_list[3879] = nvar_3879; + functions[3880] = fn3880; + nvar_list[3880] = nvar_3880; + functions[3881] = fn3881; + nvar_list[3881] = nvar_3881; + functions[3882] = fn3882; + nvar_list[3882] = nvar_3882; + functions[3883] = fn3883; + nvar_list[3883] = nvar_3883; + functions[3884] = fn3884; + nvar_list[3884] = nvar_3884; + functions[3885] = fn3885; + nvar_list[3885] = nvar_3885; + functions[3886] = fn3886; + nvar_list[3886] = nvar_3886; + functions[3887] = fn3887; + nvar_list[3887] = nvar_3887; + functions[3888] = fn3888; + nvar_list[3888] = nvar_3888; + functions[3889] = fn3889; + nvar_list[3889] = nvar_3889; + functions[3890] = fn3890; + nvar_list[3890] = nvar_3890; + functions[3891] = fn3891; + nvar_list[3891] = nvar_3891; + functions[3892] = fn3892; + nvar_list[3892] = nvar_3892; + functions[3893] = fn3893; + nvar_list[3893] = nvar_3893; + functions[3894] = fn3894; + nvar_list[3894] = nvar_3894; + functions[3895] = fn3895; + nvar_list[3895] = nvar_3895; + functions[3896] = fn3896; + nvar_list[3896] = nvar_3896; + functions[3897] = fn3897; + nvar_list[3897] = nvar_3897; + functions[3898] = fn3898; + nvar_list[3898] = nvar_3898; + functions[3899] = fn3899; + nvar_list[3899] = nvar_3899; + functions[3900] = fn3900; + nvar_list[3900] = nvar_3900; + functions[3901] = fn3901; + nvar_list[3901] = nvar_3901; + functions[3902] = fn3902; + nvar_list[3902] = nvar_3902; + functions[3903] = fn3903; + nvar_list[3903] = nvar_3903; + functions[3904] = fn3904; + nvar_list[3904] = nvar_3904; + functions[3905] = fn3905; + nvar_list[3905] = nvar_3905; + functions[3906] = fn3906; + nvar_list[3906] = nvar_3906; + functions[3907] = fn3907; + nvar_list[3907] = nvar_3907; + functions[3908] = fn3908; + nvar_list[3908] = nvar_3908; + functions[3909] = fn3909; + nvar_list[3909] = nvar_3909; + functions[3910] = fn3910; + nvar_list[3910] = nvar_3910; + functions[3911] = fn3911; + nvar_list[3911] = nvar_3911; + functions[3912] = fn3912; + nvar_list[3912] = nvar_3912; + functions[3913] = fn3913; + nvar_list[3913] = nvar_3913; + functions[3914] = fn3914; + nvar_list[3914] = nvar_3914; + functions[3915] = fn3915; + nvar_list[3915] = nvar_3915; + functions[3916] = fn3916; + nvar_list[3916] = nvar_3916; + functions[3917] = fn3917; + nvar_list[3917] = nvar_3917; + functions[3918] = fn3918; + nvar_list[3918] = nvar_3918; + functions[3919] = fn3919; + nvar_list[3919] = nvar_3919; + functions[3920] = fn3920; + nvar_list[3920] = nvar_3920; + functions[3921] = fn3921; + nvar_list[3921] = nvar_3921; + functions[3922] = fn3922; + nvar_list[3922] = nvar_3922; + functions[3923] = fn3923; + nvar_list[3923] = nvar_3923; + functions[3924] = fn3924; + nvar_list[3924] = nvar_3924; + functions[3925] = fn3925; + nvar_list[3925] = nvar_3925; + functions[3926] = fn3926; + nvar_list[3926] = nvar_3926; + functions[3927] = fn3927; + nvar_list[3927] = nvar_3927; + functions[3928] = fn3928; + nvar_list[3928] = nvar_3928; + functions[3929] = fn3929; + nvar_list[3929] = nvar_3929; + functions[3930] = fn3930; + nvar_list[3930] = nvar_3930; + functions[3931] = fn3931; + nvar_list[3931] = nvar_3931; + functions[3932] = fn3932; + nvar_list[3932] = nvar_3932; + functions[3933] = fn3933; + nvar_list[3933] = nvar_3933; + functions[3934] = fn3934; + nvar_list[3934] = nvar_3934; + functions[3935] = fn3935; + nvar_list[3935] = nvar_3935; + functions[3936] = fn3936; + nvar_list[3936] = nvar_3936; + functions[3937] = fn3937; + nvar_list[3937] = nvar_3937; + functions[3938] = fn3938; + nvar_list[3938] = nvar_3938; + functions[3939] = fn3939; + nvar_list[3939] = nvar_3939; + functions[3940] = fn3940; + nvar_list[3940] = nvar_3940; + functions[3941] = fn3941; + nvar_list[3941] = nvar_3941; + functions[3942] = fn3942; + nvar_list[3942] = nvar_3942; + functions[3943] = fn3943; + nvar_list[3943] = nvar_3943; + functions[3944] = fn3944; + nvar_list[3944] = nvar_3944; + functions[3945] = fn3945; + nvar_list[3945] = nvar_3945; + functions[3946] = fn3946; + nvar_list[3946] = nvar_3946; + functions[3947] = fn3947; + nvar_list[3947] = nvar_3947; + functions[3948] = fn3948; + nvar_list[3948] = nvar_3948; + functions[3949] = fn3949; + nvar_list[3949] = nvar_3949; + functions[3950] = fn3950; + nvar_list[3950] = nvar_3950; + functions[3951] = fn3951; + nvar_list[3951] = nvar_3951; + functions[3952] = fn3952; + nvar_list[3952] = nvar_3952; + functions[3953] = fn3953; + nvar_list[3953] = nvar_3953; + functions[3954] = fn3954; + nvar_list[3954] = nvar_3954; + functions[3955] = fn3955; + nvar_list[3955] = nvar_3955; + functions[3956] = fn3956; + nvar_list[3956] = nvar_3956; + functions[3957] = fn3957; + nvar_list[3957] = nvar_3957; + functions[3958] = fn3958; + nvar_list[3958] = nvar_3958; + functions[3959] = fn3959; + nvar_list[3959] = nvar_3959; + functions[3960] = fn3960; + nvar_list[3960] = nvar_3960; + functions[3961] = fn3961; + nvar_list[3961] = nvar_3961; + functions[3962] = fn3962; + nvar_list[3962] = nvar_3962; + functions[3963] = fn3963; + nvar_list[3963] = nvar_3963; + functions[3964] = fn3964; + nvar_list[3964] = nvar_3964; + functions[3965] = fn3965; + nvar_list[3965] = nvar_3965; + functions[3966] = fn3966; + nvar_list[3966] = nvar_3966; + functions[3967] = fn3967; + nvar_list[3967] = nvar_3967; + functions[3968] = fn3968; + nvar_list[3968] = nvar_3968; + functions[3969] = fn3969; + nvar_list[3969] = nvar_3969; + functions[3970] = fn3970; + nvar_list[3970] = nvar_3970; + functions[3971] = fn3971; + nvar_list[3971] = nvar_3971; + functions[3972] = fn3972; + nvar_list[3972] = nvar_3972; + functions[3973] = fn3973; + nvar_list[3973] = nvar_3973; + functions[3974] = fn3974; + nvar_list[3974] = nvar_3974; + functions[3975] = fn3975; + nvar_list[3975] = nvar_3975; + functions[3976] = fn3976; + nvar_list[3976] = nvar_3976; + functions[3977] = fn3977; + nvar_list[3977] = nvar_3977; + functions[3978] = fn3978; + nvar_list[3978] = nvar_3978; + functions[3979] = fn3979; + nvar_list[3979] = nvar_3979; + functions[3980] = fn3980; + nvar_list[3980] = nvar_3980; + functions[3981] = fn3981; + nvar_list[3981] = nvar_3981; + functions[3982] = fn3982; + nvar_list[3982] = nvar_3982; + functions[3983] = fn3983; + nvar_list[3983] = nvar_3983; + functions[3984] = fn3984; + nvar_list[3984] = nvar_3984; + functions[3985] = fn3985; + nvar_list[3985] = nvar_3985; + functions[3986] = fn3986; + nvar_list[3986] = nvar_3986; + functions[3987] = fn3987; + nvar_list[3987] = nvar_3987; + functions[3988] = fn3988; + nvar_list[3988] = nvar_3988; + functions[3989] = fn3989; + nvar_list[3989] = nvar_3989; + functions[3990] = fn3990; + nvar_list[3990] = nvar_3990; + functions[3991] = fn3991; + nvar_list[3991] = nvar_3991; + functions[3992] = fn3992; + nvar_list[3992] = nvar_3992; + functions[3993] = fn3993; + nvar_list[3993] = nvar_3993; + functions[3994] = fn3994; + nvar_list[3994] = nvar_3994; + functions[3995] = fn3995; + nvar_list[3995] = nvar_3995; + functions[3996] = fn3996; + nvar_list[3996] = nvar_3996; + functions[3997] = fn3997; + nvar_list[3997] = nvar_3997; + functions[3998] = fn3998; + nvar_list[3998] = nvar_3998; + functions[3999] = fn3999; + nvar_list[3999] = nvar_3999; + functions[4000] = fn4000; + nvar_list[4000] = nvar_4000; + functions[4001] = fn4001; + nvar_list[4001] = nvar_4001; + functions[4002] = fn4002; + nvar_list[4002] = nvar_4002; + functions[4003] = fn4003; + nvar_list[4003] = nvar_4003; + functions[4004] = fn4004; + nvar_list[4004] = nvar_4004; + functions[4005] = fn4005; + nvar_list[4005] = nvar_4005; + functions[4006] = fn4006; + nvar_list[4006] = nvar_4006; + functions[4007] = fn4007; + nvar_list[4007] = nvar_4007; + functions[4008] = fn4008; + nvar_list[4008] = nvar_4008; + functions[4009] = fn4009; + nvar_list[4009] = nvar_4009; + functions[4010] = fn4010; + nvar_list[4010] = nvar_4010; + functions[4011] = fn4011; + nvar_list[4011] = nvar_4011; + functions[4012] = fn4012; + nvar_list[4012] = nvar_4012; + functions[4013] = fn4013; + nvar_list[4013] = nvar_4013; + functions[4014] = fn4014; + nvar_list[4014] = nvar_4014; + functions[4015] = fn4015; + nvar_list[4015] = nvar_4015; + functions[4016] = fn4016; + nvar_list[4016] = nvar_4016; + functions[4017] = fn4017; + nvar_list[4017] = nvar_4017; + functions[4018] = fn4018; + nvar_list[4018] = nvar_4018; + functions[4019] = fn4019; + nvar_list[4019] = nvar_4019; + functions[4020] = fn4020; + nvar_list[4020] = nvar_4020; + functions[4021] = fn4021; + nvar_list[4021] = nvar_4021; + functions[4022] = fn4022; + nvar_list[4022] = nvar_4022; + functions[4023] = fn4023; + nvar_list[4023] = nvar_4023; + functions[4024] = fn4024; + nvar_list[4024] = nvar_4024; + functions[4025] = fn4025; + nvar_list[4025] = nvar_4025; + functions[4026] = fn4026; + nvar_list[4026] = nvar_4026; + functions[4027] = fn4027; + nvar_list[4027] = nvar_4027; + functions[4028] = fn4028; + nvar_list[4028] = nvar_4028; + functions[4029] = fn4029; + nvar_list[4029] = nvar_4029; + functions[4030] = fn4030; + nvar_list[4030] = nvar_4030; + functions[4031] = fn4031; + nvar_list[4031] = nvar_4031; + functions[4032] = fn4032; + nvar_list[4032] = nvar_4032; + functions[4033] = fn4033; + nvar_list[4033] = nvar_4033; + functions[4034] = fn4034; + nvar_list[4034] = nvar_4034; + functions[4035] = fn4035; + nvar_list[4035] = nvar_4035; + functions[4036] = fn4036; + nvar_list[4036] = nvar_4036; + functions[4037] = fn4037; + nvar_list[4037] = nvar_4037; + functions[4038] = fn4038; + nvar_list[4038] = nvar_4038; + functions[4039] = fn4039; + nvar_list[4039] = nvar_4039; + functions[4040] = fn4040; + nvar_list[4040] = nvar_4040; + functions[4041] = fn4041; + nvar_list[4041] = nvar_4041; + functions[4042] = fn4042; + nvar_list[4042] = nvar_4042; + functions[4043] = fn4043; + nvar_list[4043] = nvar_4043; + functions[4044] = fn4044; + nvar_list[4044] = nvar_4044; + functions[4045] = fn4045; + nvar_list[4045] = nvar_4045; + functions[4046] = fn4046; + nvar_list[4046] = nvar_4046; + functions[4047] = fn4047; + nvar_list[4047] = nvar_4047; + functions[4048] = fn4048; + nvar_list[4048] = nvar_4048; + functions[4049] = fn4049; + nvar_list[4049] = nvar_4049; + functions[4050] = fn4050; + nvar_list[4050] = nvar_4050; + functions[4051] = fn4051; + nvar_list[4051] = nvar_4051; + functions[4052] = fn4052; + nvar_list[4052] = nvar_4052; + functions[4053] = fn4053; + nvar_list[4053] = nvar_4053; + functions[4054] = fn4054; + nvar_list[4054] = nvar_4054; + functions[4055] = fn4055; + nvar_list[4055] = nvar_4055; + functions[4056] = fn4056; + nvar_list[4056] = nvar_4056; + functions[4057] = fn4057; + nvar_list[4057] = nvar_4057; + functions[4058] = fn4058; + nvar_list[4058] = nvar_4058; + functions[4059] = fn4059; + nvar_list[4059] = nvar_4059; + functions[4060] = fn4060; + nvar_list[4060] = nvar_4060; + functions[4061] = fn4061; + nvar_list[4061] = nvar_4061; + functions[4062] = fn4062; + nvar_list[4062] = nvar_4062; + functions[4063] = fn4063; + nvar_list[4063] = nvar_4063; + functions[4064] = fn4064; + nvar_list[4064] = nvar_4064; + functions[4065] = fn4065; + nvar_list[4065] = nvar_4065; + functions[4066] = fn4066; + nvar_list[4066] = nvar_4066; + functions[4067] = fn4067; + nvar_list[4067] = nvar_4067; + functions[4068] = fn4068; + nvar_list[4068] = nvar_4068; + functions[4069] = fn4069; + nvar_list[4069] = nvar_4069; + functions[4070] = fn4070; + nvar_list[4070] = nvar_4070; + functions[4071] = fn4071; + nvar_list[4071] = nvar_4071; + functions[4072] = fn4072; + nvar_list[4072] = nvar_4072; + functions[4073] = fn4073; + nvar_list[4073] = nvar_4073; + functions[4074] = fn4074; + nvar_list[4074] = nvar_4074; + functions[4075] = fn4075; + nvar_list[4075] = nvar_4075; + functions[4076] = fn4076; + nvar_list[4076] = nvar_4076; + functions[4077] = fn4077; + nvar_list[4077] = nvar_4077; + functions[4078] = fn4078; + nvar_list[4078] = nvar_4078; + functions[4079] = fn4079; + nvar_list[4079] = nvar_4079; + functions[4080] = fn4080; + nvar_list[4080] = nvar_4080; + functions[4081] = fn4081; + nvar_list[4081] = nvar_4081; + functions[4082] = fn4082; + nvar_list[4082] = nvar_4082; + functions[4083] = fn4083; + nvar_list[4083] = nvar_4083; + functions[4084] = fn4084; + nvar_list[4084] = nvar_4084; + functions[4085] = fn4085; + nvar_list[4085] = nvar_4085; + functions[4086] = fn4086; + nvar_list[4086] = nvar_4086; + functions[4087] = fn4087; + nvar_list[4087] = nvar_4087; + functions[4088] = fn4088; + nvar_list[4088] = nvar_4088; + functions[4089] = fn4089; + nvar_list[4089] = nvar_4089; + functions[4090] = fn4090; + nvar_list[4090] = nvar_4090; + functions[4091] = fn4091; + nvar_list[4091] = nvar_4091; + functions[4092] = fn4092; + nvar_list[4092] = nvar_4092; + functions[4093] = fn4093; + nvar_list[4093] = nvar_4093; + functions[4094] = fn4094; + nvar_list[4094] = nvar_4094; + functions[4095] = fn4095; + nvar_list[4095] = nvar_4095; + functions[4096] = fn4096; + nvar_list[4096] = nvar_4096; + functions[4097] = fn4097; + nvar_list[4097] = nvar_4097; + functions[4098] = fn4098; + nvar_list[4098] = nvar_4098; + functions[4099] = fn4099; + nvar_list[4099] = nvar_4099; + functions[4100] = fn4100; + nvar_list[4100] = nvar_4100; + functions[4101] = fn4101; + nvar_list[4101] = nvar_4101; + functions[4102] = fn4102; + nvar_list[4102] = nvar_4102; + functions[4103] = fn4103; + nvar_list[4103] = nvar_4103; + functions[4104] = fn4104; + nvar_list[4104] = nvar_4104; + functions[4105] = fn4105; + nvar_list[4105] = nvar_4105; + functions[4106] = fn4106; + nvar_list[4106] = nvar_4106; + functions[4107] = fn4107; + nvar_list[4107] = nvar_4107; + functions[4108] = fn4108; + nvar_list[4108] = nvar_4108; + functions[4109] = fn4109; + nvar_list[4109] = nvar_4109; + functions[4110] = fn4110; + nvar_list[4110] = nvar_4110; + functions[4111] = fn4111; + nvar_list[4111] = nvar_4111; + functions[4112] = fn4112; + nvar_list[4112] = nvar_4112; + functions[4113] = fn4113; + nvar_list[4113] = nvar_4113; + functions[4114] = fn4114; + nvar_list[4114] = nvar_4114; + functions[4115] = fn4115; + nvar_list[4115] = nvar_4115; + functions[4116] = fn4116; + nvar_list[4116] = nvar_4116; + functions[4117] = fn4117; + nvar_list[4117] = nvar_4117; + functions[4118] = fn4118; + nvar_list[4118] = nvar_4118; + functions[4119] = fn4119; + nvar_list[4119] = nvar_4119; + functions[4120] = fn4120; + nvar_list[4120] = nvar_4120; + functions[4121] = fn4121; + nvar_list[4121] = nvar_4121; + functions[4122] = fn4122; + nvar_list[4122] = nvar_4122; + functions[4123] = fn4123; + nvar_list[4123] = nvar_4123; + functions[4124] = fn4124; + nvar_list[4124] = nvar_4124; + functions[4125] = fn4125; + nvar_list[4125] = nvar_4125; + functions[4126] = fn4126; + nvar_list[4126] = nvar_4126; + functions[4127] = fn4127; + nvar_list[4127] = nvar_4127; + functions[4128] = fn4128; + nvar_list[4128] = nvar_4128; + functions[4129] = fn4129; + nvar_list[4129] = nvar_4129; + functions[4130] = fn4130; + nvar_list[4130] = nvar_4130; + functions[4131] = fn4131; + nvar_list[4131] = nvar_4131; + functions[4132] = fn4132; + nvar_list[4132] = nvar_4132; + functions[4133] = fn4133; + nvar_list[4133] = nvar_4133; + functions[4134] = fn4134; + nvar_list[4134] = nvar_4134; + functions[4135] = fn4135; + nvar_list[4135] = nvar_4135; + functions[4136] = fn4136; + nvar_list[4136] = nvar_4136; + functions[4137] = fn4137; + nvar_list[4137] = nvar_4137; + functions[4138] = fn4138; + nvar_list[4138] = nvar_4138; + functions[4139] = fn4139; + nvar_list[4139] = nvar_4139; + functions[4140] = fn4140; + nvar_list[4140] = nvar_4140; + functions[4141] = fn4141; + nvar_list[4141] = nvar_4141; + functions[4142] = fn4142; + nvar_list[4142] = nvar_4142; + functions[4143] = fn4143; + nvar_list[4143] = nvar_4143; + functions[4144] = fn4144; + nvar_list[4144] = nvar_4144; + functions[4145] = fn4145; + nvar_list[4145] = nvar_4145; + functions[4146] = fn4146; + nvar_list[4146] = nvar_4146; + functions[4147] = fn4147; + nvar_list[4147] = nvar_4147; + functions[4148] = fn4148; + nvar_list[4148] = nvar_4148; + functions[4149] = fn4149; + nvar_list[4149] = nvar_4149; + functions[4150] = fn4150; + nvar_list[4150] = nvar_4150; + functions[4151] = fn4151; + nvar_list[4151] = nvar_4151; + functions[4152] = fn4152; + nvar_list[4152] = nvar_4152; + functions[4153] = fn4153; + nvar_list[4153] = nvar_4153; + functions[4154] = fn4154; + nvar_list[4154] = nvar_4154; + functions[4155] = fn4155; + nvar_list[4155] = nvar_4155; + functions[4156] = fn4156; + nvar_list[4156] = nvar_4156; + functions[4157] = fn4157; + nvar_list[4157] = nvar_4157; + functions[4158] = fn4158; + nvar_list[4158] = nvar_4158; + functions[4159] = fn4159; + nvar_list[4159] = nvar_4159; + functions[4160] = fn4160; + nvar_list[4160] = nvar_4160; + functions[4161] = fn4161; + nvar_list[4161] = nvar_4161; + functions[4162] = fn4162; + nvar_list[4162] = nvar_4162; + functions[4163] = fn4163; + nvar_list[4163] = nvar_4163; + functions[4164] = fn4164; + nvar_list[4164] = nvar_4164; + functions[4165] = fn4165; + nvar_list[4165] = nvar_4165; + functions[4166] = fn4166; + nvar_list[4166] = nvar_4166; + functions[4167] = fn4167; + nvar_list[4167] = nvar_4167; + functions[4168] = fn4168; + nvar_list[4168] = nvar_4168; + functions[4169] = fn4169; + nvar_list[4169] = nvar_4169; + functions[4170] = fn4170; + nvar_list[4170] = nvar_4170; + functions[4171] = fn4171; + nvar_list[4171] = nvar_4171; + functions[4172] = fn4172; + nvar_list[4172] = nvar_4172; + functions[4173] = fn4173; + nvar_list[4173] = nvar_4173; + functions[4174] = fn4174; + nvar_list[4174] = nvar_4174; + functions[4175] = fn4175; + nvar_list[4175] = nvar_4175; + functions[4176] = fn4176; + nvar_list[4176] = nvar_4176; + functions[4177] = fn4177; + nvar_list[4177] = nvar_4177; + functions[4178] = fn4178; + nvar_list[4178] = nvar_4178; + functions[4179] = fn4179; + nvar_list[4179] = nvar_4179; + functions[4180] = fn4180; + nvar_list[4180] = nvar_4180; + functions[4181] = fn4181; + nvar_list[4181] = nvar_4181; + functions[4182] = fn4182; + nvar_list[4182] = nvar_4182; + functions[4183] = fn4183; + nvar_list[4183] = nvar_4183; + functions[4184] = fn4184; + nvar_list[4184] = nvar_4184; + functions[4185] = fn4185; + nvar_list[4185] = nvar_4185; + functions[4186] = fn4186; + nvar_list[4186] = nvar_4186; + functions[4187] = fn4187; + nvar_list[4187] = nvar_4187; + functions[4188] = fn4188; + nvar_list[4188] = nvar_4188; + functions[4189] = fn4189; + nvar_list[4189] = nvar_4189; + functions[4190] = fn4190; + nvar_list[4190] = nvar_4190; + functions[4191] = fn4191; + nvar_list[4191] = nvar_4191; + functions[4192] = fn4192; + nvar_list[4192] = nvar_4192; + functions[4193] = fn4193; + nvar_list[4193] = nvar_4193; + functions[4194] = fn4194; + nvar_list[4194] = nvar_4194; + functions[4195] = fn4195; + nvar_list[4195] = nvar_4195; + functions[4196] = fn4196; + nvar_list[4196] = nvar_4196; + functions[4197] = fn4197; + nvar_list[4197] = nvar_4197; + functions[4198] = fn4198; + nvar_list[4198] = nvar_4198; + functions[4199] = fn4199; + nvar_list[4199] = nvar_4199; + functions[4200] = fn4200; + nvar_list[4200] = nvar_4200; + functions[4201] = fn4201; + nvar_list[4201] = nvar_4201; + functions[4202] = fn4202; + nvar_list[4202] = nvar_4202; + functions[4203] = fn4203; + nvar_list[4203] = nvar_4203; + functions[4204] = fn4204; + nvar_list[4204] = nvar_4204; + functions[4205] = fn4205; + nvar_list[4205] = nvar_4205; + functions[4206] = fn4206; + nvar_list[4206] = nvar_4206; + functions[4207] = fn4207; + nvar_list[4207] = nvar_4207; + functions[4208] = fn4208; + nvar_list[4208] = nvar_4208; + functions[4209] = fn4209; + nvar_list[4209] = nvar_4209; + functions[4210] = fn4210; + nvar_list[4210] = nvar_4210; + functions[4211] = fn4211; + nvar_list[4211] = nvar_4211; + functions[4212] = fn4212; + nvar_list[4212] = nvar_4212; + functions[4213] = fn4213; + nvar_list[4213] = nvar_4213; + functions[4214] = fn4214; + nvar_list[4214] = nvar_4214; + functions[4215] = fn4215; + nvar_list[4215] = nvar_4215; + functions[4216] = fn4216; + nvar_list[4216] = nvar_4216; + functions[4217] = fn4217; + nvar_list[4217] = nvar_4217; + functions[4218] = fn4218; + nvar_list[4218] = nvar_4218; + functions[4219] = fn4219; + nvar_list[4219] = nvar_4219; + functions[4220] = fn4220; + nvar_list[4220] = nvar_4220; + functions[4221] = fn4221; + nvar_list[4221] = nvar_4221; + functions[4222] = fn4222; + nvar_list[4222] = nvar_4222; + functions[4223] = fn4223; + nvar_list[4223] = nvar_4223; + functions[4224] = fn4224; + nvar_list[4224] = nvar_4224; + functions[4225] = fn4225; + nvar_list[4225] = nvar_4225; + functions[4226] = fn4226; + nvar_list[4226] = nvar_4226; + functions[4227] = fn4227; + nvar_list[4227] = nvar_4227; + functions[4228] = fn4228; + nvar_list[4228] = nvar_4228; + functions[4229] = fn4229; + nvar_list[4229] = nvar_4229; + functions[4230] = fn4230; + nvar_list[4230] = nvar_4230; + functions[4231] = fn4231; + nvar_list[4231] = nvar_4231; + functions[4232] = fn4232; + nvar_list[4232] = nvar_4232; + functions[4233] = fn4233; + nvar_list[4233] = nvar_4233; + functions[4234] = fn4234; + nvar_list[4234] = nvar_4234; + functions[4235] = fn4235; + nvar_list[4235] = nvar_4235; + functions[4236] = fn4236; + nvar_list[4236] = nvar_4236; + functions[4237] = fn4237; + nvar_list[4237] = nvar_4237; + functions[4238] = fn4238; + nvar_list[4238] = nvar_4238; + functions[4239] = fn4239; + nvar_list[4239] = nvar_4239; + functions[4240] = fn4240; + nvar_list[4240] = nvar_4240; + functions[4241] = fn4241; + nvar_list[4241] = nvar_4241; + functions[4242] = fn4242; + nvar_list[4242] = nvar_4242; + functions[4243] = fn4243; + nvar_list[4243] = nvar_4243; + functions[4244] = fn4244; + nvar_list[4244] = nvar_4244; + functions[4245] = fn4245; + nvar_list[4245] = nvar_4245; + functions[4246] = fn4246; + nvar_list[4246] = nvar_4246; + functions[4247] = fn4247; + nvar_list[4247] = nvar_4247; + functions[4248] = fn4248; + nvar_list[4248] = nvar_4248; + functions[4249] = fn4249; + nvar_list[4249] = nvar_4249; + functions[4250] = fn4250; + nvar_list[4250] = nvar_4250; + functions[4251] = fn4251; + nvar_list[4251] = nvar_4251; + functions[4252] = fn4252; + nvar_list[4252] = nvar_4252; + functions[4253] = fn4253; + nvar_list[4253] = nvar_4253; + functions[4254] = fn4254; + nvar_list[4254] = nvar_4254; + functions[4255] = fn4255; + nvar_list[4255] = nvar_4255; + functions[4256] = fn4256; + nvar_list[4256] = nvar_4256; + functions[4257] = fn4257; + nvar_list[4257] = nvar_4257; + functions[4258] = fn4258; + nvar_list[4258] = nvar_4258; + functions[4259] = fn4259; + nvar_list[4259] = nvar_4259; + functions[4260] = fn4260; + nvar_list[4260] = nvar_4260; + functions[4261] = fn4261; + nvar_list[4261] = nvar_4261; + functions[4262] = fn4262; + nvar_list[4262] = nvar_4262; + functions[4263] = fn4263; + nvar_list[4263] = nvar_4263; + functions[4264] = fn4264; + nvar_list[4264] = nvar_4264; + functions[4265] = fn4265; + nvar_list[4265] = nvar_4265; + functions[4266] = fn4266; + nvar_list[4266] = nvar_4266; + functions[4267] = fn4267; + nvar_list[4267] = nvar_4267; + functions[4268] = fn4268; + nvar_list[4268] = nvar_4268; + functions[4269] = fn4269; + nvar_list[4269] = nvar_4269; + functions[4270] = fn4270; + nvar_list[4270] = nvar_4270; + functions[4271] = fn4271; + nvar_list[4271] = nvar_4271; + functions[4272] = fn4272; + nvar_list[4272] = nvar_4272; + functions[4273] = fn4273; + nvar_list[4273] = nvar_4273; + functions[4274] = fn4274; + nvar_list[4274] = nvar_4274; + functions[4275] = fn4275; + nvar_list[4275] = nvar_4275; + functions[4276] = fn4276; + nvar_list[4276] = nvar_4276; + functions[4277] = fn4277; + nvar_list[4277] = nvar_4277; + functions[4278] = fn4278; + nvar_list[4278] = nvar_4278; + functions[4279] = fn4279; + nvar_list[4279] = nvar_4279; + functions[4280] = fn4280; + nvar_list[4280] = nvar_4280; + functions[4281] = fn4281; + nvar_list[4281] = nvar_4281; + functions[4282] = fn4282; + nvar_list[4282] = nvar_4282; + functions[4283] = fn4283; + nvar_list[4283] = nvar_4283; + functions[4284] = fn4284; + nvar_list[4284] = nvar_4284; + functions[4285] = fn4285; + nvar_list[4285] = nvar_4285; + functions[4286] = fn4286; + nvar_list[4286] = nvar_4286; + functions[4287] = fn4287; + nvar_list[4287] = nvar_4287; + functions[4288] = fn4288; + nvar_list[4288] = nvar_4288; + functions[4289] = fn4289; + nvar_list[4289] = nvar_4289; + functions[4290] = fn4290; + nvar_list[4290] = nvar_4290; + functions[4291] = fn4291; + nvar_list[4291] = nvar_4291; + functions[4292] = fn4292; + nvar_list[4292] = nvar_4292; + functions[4293] = fn4293; + nvar_list[4293] = nvar_4293; + functions[4294] = fn4294; + nvar_list[4294] = nvar_4294; + functions[4295] = fn4295; + nvar_list[4295] = nvar_4295; + functions[4296] = fn4296; + nvar_list[4296] = nvar_4296; + functions[4297] = fn4297; + nvar_list[4297] = nvar_4297; + functions[4298] = fn4298; + nvar_list[4298] = nvar_4298; + functions[4299] = fn4299; + nvar_list[4299] = nvar_4299; + functions[4300] = fn4300; + nvar_list[4300] = nvar_4300; + functions[4301] = fn4301; + nvar_list[4301] = nvar_4301; + functions[4302] = fn4302; + nvar_list[4302] = nvar_4302; + functions[4303] = fn4303; + nvar_list[4303] = nvar_4303; + functions[4304] = fn4304; + nvar_list[4304] = nvar_4304; + functions[4305] = fn4305; + nvar_list[4305] = nvar_4305; + functions[4306] = fn4306; + nvar_list[4306] = nvar_4306; + functions[4307] = fn4307; + nvar_list[4307] = nvar_4307; + functions[4308] = fn4308; + nvar_list[4308] = nvar_4308; + functions[4309] = fn4309; + nvar_list[4309] = nvar_4309; + functions[4310] = fn4310; + nvar_list[4310] = nvar_4310; + functions[4311] = fn4311; + nvar_list[4311] = nvar_4311; + functions[4312] = fn4312; + nvar_list[4312] = nvar_4312; + functions[4313] = fn4313; + nvar_list[4313] = nvar_4313; + functions[4314] = fn4314; + nvar_list[4314] = nvar_4314; + functions[4315] = fn4315; + nvar_list[4315] = nvar_4315; + functions[4316] = fn4316; + nvar_list[4316] = nvar_4316; + functions[4317] = fn4317; + nvar_list[4317] = nvar_4317; + functions[4318] = fn4318; + nvar_list[4318] = nvar_4318; + functions[4319] = fn4319; + nvar_list[4319] = nvar_4319; + functions[4320] = fn4320; + nvar_list[4320] = nvar_4320; + functions[4321] = fn4321; + nvar_list[4321] = nvar_4321; + functions[4322] = fn4322; + nvar_list[4322] = nvar_4322; + functions[4323] = fn4323; + nvar_list[4323] = nvar_4323; + functions[4324] = fn4324; + nvar_list[4324] = nvar_4324; + functions[4325] = fn4325; + nvar_list[4325] = nvar_4325; + functions[4326] = fn4326; + nvar_list[4326] = nvar_4326; + functions[4327] = fn4327; + nvar_list[4327] = nvar_4327; + functions[4328] = fn4328; + nvar_list[4328] = nvar_4328; + functions[4329] = fn4329; + nvar_list[4329] = nvar_4329; + functions[4330] = fn4330; + nvar_list[4330] = nvar_4330; + functions[4331] = fn4331; + nvar_list[4331] = nvar_4331; + functions[4332] = fn4332; + nvar_list[4332] = nvar_4332; + functions[4333] = fn4333; + nvar_list[4333] = nvar_4333; + functions[4334] = fn4334; + nvar_list[4334] = nvar_4334; + functions[4335] = fn4335; + nvar_list[4335] = nvar_4335; + functions[4336] = fn4336; + nvar_list[4336] = nvar_4336; + functions[4337] = fn4337; + nvar_list[4337] = nvar_4337; + functions[4338] = fn4338; + nvar_list[4338] = nvar_4338; + functions[4339] = fn4339; + nvar_list[4339] = nvar_4339; + functions[4340] = fn4340; + nvar_list[4340] = nvar_4340; + functions[4341] = fn4341; + nvar_list[4341] = nvar_4341; + functions[4342] = fn4342; + nvar_list[4342] = nvar_4342; + functions[4343] = fn4343; + nvar_list[4343] = nvar_4343; + functions[4344] = fn4344; + nvar_list[4344] = nvar_4344; + functions[4345] = fn4345; + nvar_list[4345] = nvar_4345; + functions[4346] = fn4346; + nvar_list[4346] = nvar_4346; + functions[4347] = fn4347; + nvar_list[4347] = nvar_4347; + functions[4348] = fn4348; + nvar_list[4348] = nvar_4348; + functions[4349] = fn4349; + nvar_list[4349] = nvar_4349; + functions[4350] = fn4350; + nvar_list[4350] = nvar_4350; + functions[4351] = fn4351; + nvar_list[4351] = nvar_4351; + functions[4352] = fn4352; + nvar_list[4352] = nvar_4352; + functions[4353] = fn4353; + nvar_list[4353] = nvar_4353; + functions[4354] = fn4354; + nvar_list[4354] = nvar_4354; + functions[4355] = fn4355; + nvar_list[4355] = nvar_4355; + functions[4356] = fn4356; + nvar_list[4356] = nvar_4356; + functions[4357] = fn4357; + nvar_list[4357] = nvar_4357; + functions[4358] = fn4358; + nvar_list[4358] = nvar_4358; + functions[4359] = fn4359; + nvar_list[4359] = nvar_4359; + functions[4360] = fn4360; + nvar_list[4360] = nvar_4360; + functions[4361] = fn4361; + nvar_list[4361] = nvar_4361; + functions[4362] = fn4362; + nvar_list[4362] = nvar_4362; + functions[4363] = fn4363; + nvar_list[4363] = nvar_4363; + functions[4364] = fn4364; + nvar_list[4364] = nvar_4364; + functions[4365] = fn4365; + nvar_list[4365] = nvar_4365; + functions[4366] = fn4366; + nvar_list[4366] = nvar_4366; + functions[4367] = fn4367; + nvar_list[4367] = nvar_4367; + functions[4368] = fn4368; + nvar_list[4368] = nvar_4368; + functions[4369] = fn4369; + nvar_list[4369] = nvar_4369; + functions[4370] = fn4370; + nvar_list[4370] = nvar_4370; + functions[4371] = fn4371; + nvar_list[4371] = nvar_4371; + functions[4372] = fn4372; + nvar_list[4372] = nvar_4372; + functions[4373] = fn4373; + nvar_list[4373] = nvar_4373; + functions[4374] = fn4374; + nvar_list[4374] = nvar_4374; + functions[4375] = fn4375; + nvar_list[4375] = nvar_4375; + functions[4376] = fn4376; + nvar_list[4376] = nvar_4376; + functions[4377] = fn4377; + nvar_list[4377] = nvar_4377; + functions[4378] = fn4378; + nvar_list[4378] = nvar_4378; + functions[4379] = fn4379; + nvar_list[4379] = nvar_4379; + functions[4380] = fn4380; + nvar_list[4380] = nvar_4380; + functions[4381] = fn4381; + nvar_list[4381] = nvar_4381; + functions[4382] = fn4382; + nvar_list[4382] = nvar_4382; + functions[4383] = fn4383; + nvar_list[4383] = nvar_4383; + functions[4384] = fn4384; + nvar_list[4384] = nvar_4384; + functions[4385] = fn4385; + nvar_list[4385] = nvar_4385; + functions[4386] = fn4386; + nvar_list[4386] = nvar_4386; + functions[4387] = fn4387; + nvar_list[4387] = nvar_4387; + functions[4388] = fn4388; + nvar_list[4388] = nvar_4388; + functions[4389] = fn4389; + nvar_list[4389] = nvar_4389; + functions[4390] = fn4390; + nvar_list[4390] = nvar_4390; + functions[4391] = fn4391; + nvar_list[4391] = nvar_4391; + functions[4392] = fn4392; + nvar_list[4392] = nvar_4392; + functions[4393] = fn4393; + nvar_list[4393] = nvar_4393; + functions[4394] = fn4394; + nvar_list[4394] = nvar_4394; + functions[4395] = fn4395; + nvar_list[4395] = nvar_4395; + functions[4396] = fn4396; + nvar_list[4396] = nvar_4396; + functions[4397] = fn4397; + nvar_list[4397] = nvar_4397; + functions[4398] = fn4398; + nvar_list[4398] = nvar_4398; + functions[4399] = fn4399; + nvar_list[4399] = nvar_4399; + functions[4400] = fn4400; + nvar_list[4400] = nvar_4400; + functions[4401] = fn4401; + nvar_list[4401] = nvar_4401; + functions[4402] = fn4402; + nvar_list[4402] = nvar_4402; + functions[4403] = fn4403; + nvar_list[4403] = nvar_4403; + functions[4404] = fn4404; + nvar_list[4404] = nvar_4404; + functions[4405] = fn4405; + nvar_list[4405] = nvar_4405; + functions[4406] = fn4406; + nvar_list[4406] = nvar_4406; + functions[4407] = fn4407; + nvar_list[4407] = nvar_4407; + functions[4408] = fn4408; + nvar_list[4408] = nvar_4408; + functions[4409] = fn4409; + nvar_list[4409] = nvar_4409; + functions[4410] = fn4410; + nvar_list[4410] = nvar_4410; + functions[4411] = fn4411; + nvar_list[4411] = nvar_4411; + functions[4412] = fn4412; + nvar_list[4412] = nvar_4412; + functions[4413] = fn4413; + nvar_list[4413] = nvar_4413; + functions[4414] = fn4414; + nvar_list[4414] = nvar_4414; + functions[4415] = fn4415; + nvar_list[4415] = nvar_4415; + functions[4416] = fn4416; + nvar_list[4416] = nvar_4416; + functions[4417] = fn4417; + nvar_list[4417] = nvar_4417; + functions[4418] = fn4418; + nvar_list[4418] = nvar_4418; + functions[4419] = fn4419; + nvar_list[4419] = nvar_4419; + functions[4420] = fn4420; + nvar_list[4420] = nvar_4420; + functions[4421] = fn4421; + nvar_list[4421] = nvar_4421; + functions[4422] = fn4422; + nvar_list[4422] = nvar_4422; + functions[4423] = fn4423; + nvar_list[4423] = nvar_4423; + functions[4424] = fn4424; + nvar_list[4424] = nvar_4424; + functions[4425] = fn4425; + nvar_list[4425] = nvar_4425; + functions[4426] = fn4426; + nvar_list[4426] = nvar_4426; + functions[4427] = fn4427; + nvar_list[4427] = nvar_4427; + functions[4428] = fn4428; + nvar_list[4428] = nvar_4428; + functions[4429] = fn4429; + nvar_list[4429] = nvar_4429; + functions[4430] = fn4430; + nvar_list[4430] = nvar_4430; + functions[4431] = fn4431; + nvar_list[4431] = nvar_4431; + functions[4432] = fn4432; + nvar_list[4432] = nvar_4432; + functions[4433] = fn4433; + nvar_list[4433] = nvar_4433; + functions[4434] = fn4434; + nvar_list[4434] = nvar_4434; + functions[4435] = fn4435; + nvar_list[4435] = nvar_4435; + functions[4436] = fn4436; + nvar_list[4436] = nvar_4436; + functions[4437] = fn4437; + nvar_list[4437] = nvar_4437; + functions[4438] = fn4438; + nvar_list[4438] = nvar_4438; + functions[4439] = fn4439; + nvar_list[4439] = nvar_4439; + functions[4440] = fn4440; + nvar_list[4440] = nvar_4440; + functions[4441] = fn4441; + nvar_list[4441] = nvar_4441; + functions[4442] = fn4442; + nvar_list[4442] = nvar_4442; + functions[4443] = fn4443; + nvar_list[4443] = nvar_4443; + functions[4444] = fn4444; + nvar_list[4444] = nvar_4444; + functions[4445] = fn4445; + nvar_list[4445] = nvar_4445; + functions[4446] = fn4446; + nvar_list[4446] = nvar_4446; + functions[4447] = fn4447; + nvar_list[4447] = nvar_4447; + functions[4448] = fn4448; + nvar_list[4448] = nvar_4448; + functions[4449] = fn4449; + nvar_list[4449] = nvar_4449; + functions[4450] = fn4450; + nvar_list[4450] = nvar_4450; + functions[4451] = fn4451; + nvar_list[4451] = nvar_4451; + functions[4452] = fn4452; + nvar_list[4452] = nvar_4452; + functions[4453] = fn4453; + nvar_list[4453] = nvar_4453; + functions[4454] = fn4454; + nvar_list[4454] = nvar_4454; + functions[4455] = fn4455; + nvar_list[4455] = nvar_4455; + functions[4456] = fn4456; + nvar_list[4456] = nvar_4456; + functions[4457] = fn4457; + nvar_list[4457] = nvar_4457; + functions[4458] = fn4458; + nvar_list[4458] = nvar_4458; + functions[4459] = fn4459; + nvar_list[4459] = nvar_4459; + functions[4460] = fn4460; + nvar_list[4460] = nvar_4460; + functions[4461] = fn4461; + nvar_list[4461] = nvar_4461; + functions[4462] = fn4462; + nvar_list[4462] = nvar_4462; + functions[4463] = fn4463; + nvar_list[4463] = nvar_4463; + functions[4464] = fn4464; + nvar_list[4464] = nvar_4464; + functions[4465] = fn4465; + nvar_list[4465] = nvar_4465; + functions[4466] = fn4466; + nvar_list[4466] = nvar_4466; + functions[4467] = fn4467; + nvar_list[4467] = nvar_4467; + functions[4468] = fn4468; + nvar_list[4468] = nvar_4468; + functions[4469] = fn4469; + nvar_list[4469] = nvar_4469; + functions[4470] = fn4470; + nvar_list[4470] = nvar_4470; + functions[4471] = fn4471; + nvar_list[4471] = nvar_4471; + functions[4472] = fn4472; + nvar_list[4472] = nvar_4472; + functions[4473] = fn4473; + nvar_list[4473] = nvar_4473; + functions[4474] = fn4474; + nvar_list[4474] = nvar_4474; + functions[4475] = fn4475; + nvar_list[4475] = nvar_4475; + functions[4476] = fn4476; + nvar_list[4476] = nvar_4476; + functions[4477] = fn4477; + nvar_list[4477] = nvar_4477; + functions[4478] = fn4478; + nvar_list[4478] = nvar_4478; + functions[4479] = fn4479; + nvar_list[4479] = nvar_4479; + functions[4480] = fn4480; + nvar_list[4480] = nvar_4480; + functions[4481] = fn4481; + nvar_list[4481] = nvar_4481; + functions[4482] = fn4482; + nvar_list[4482] = nvar_4482; + functions[4483] = fn4483; + nvar_list[4483] = nvar_4483; + functions[4484] = fn4484; + nvar_list[4484] = nvar_4484; + functions[4485] = fn4485; + nvar_list[4485] = nvar_4485; + functions[4486] = fn4486; + nvar_list[4486] = nvar_4486; + functions[4487] = fn4487; + nvar_list[4487] = nvar_4487; + functions[4488] = fn4488; + nvar_list[4488] = nvar_4488; + functions[4489] = fn4489; + nvar_list[4489] = nvar_4489; + functions[4490] = fn4490; + nvar_list[4490] = nvar_4490; + functions[4491] = fn4491; + nvar_list[4491] = nvar_4491; + functions[4492] = fn4492; + nvar_list[4492] = nvar_4492; + functions[4493] = fn4493; + nvar_list[4493] = nvar_4493; + functions[4494] = fn4494; + nvar_list[4494] = nvar_4494; + functions[4495] = fn4495; + nvar_list[4495] = nvar_4495; + functions[4496] = fn4496; + nvar_list[4496] = nvar_4496; + functions[4497] = fn4497; + nvar_list[4497] = nvar_4497; + functions[4498] = fn4498; + nvar_list[4498] = nvar_4498; + functions[4499] = fn4499; + nvar_list[4499] = nvar_4499; + functions[4500] = fn4500; + nvar_list[4500] = nvar_4500; + functions[4501] = fn4501; + nvar_list[4501] = nvar_4501; + functions[4502] = fn4502; + nvar_list[4502] = nvar_4502; + functions[4503] = fn4503; + nvar_list[4503] = nvar_4503; + functions[4504] = fn4504; + nvar_list[4504] = nvar_4504; + functions[4505] = fn4505; + nvar_list[4505] = nvar_4505; + functions[4506] = fn4506; + nvar_list[4506] = nvar_4506; + functions[4507] = fn4507; + nvar_list[4507] = nvar_4507; + functions[4508] = fn4508; + nvar_list[4508] = nvar_4508; + functions[4509] = fn4509; + nvar_list[4509] = nvar_4509; + functions[4510] = fn4510; + nvar_list[4510] = nvar_4510; + functions[4511] = fn4511; + nvar_list[4511] = nvar_4511; + functions[4512] = fn4512; + nvar_list[4512] = nvar_4512; + functions[4513] = fn4513; + nvar_list[4513] = nvar_4513; + functions[4514] = fn4514; + nvar_list[4514] = nvar_4514; + functions[4515] = fn4515; + nvar_list[4515] = nvar_4515; + functions[4516] = fn4516; + nvar_list[4516] = nvar_4516; + functions[4517] = fn4517; + nvar_list[4517] = nvar_4517; + functions[4518] = fn4518; + nvar_list[4518] = nvar_4518; + functions[4519] = fn4519; + nvar_list[4519] = nvar_4519; + functions[4520] = fn4520; + nvar_list[4520] = nvar_4520; + functions[4521] = fn4521; + nvar_list[4521] = nvar_4521; + functions[4522] = fn4522; + nvar_list[4522] = nvar_4522; + functions[4523] = fn4523; + nvar_list[4523] = nvar_4523; + functions[4524] = fn4524; + nvar_list[4524] = nvar_4524; + functions[4525] = fn4525; + nvar_list[4525] = nvar_4525; + functions[4526] = fn4526; + nvar_list[4526] = nvar_4526; + functions[4527] = fn4527; + nvar_list[4527] = nvar_4527; + functions[4528] = fn4528; + nvar_list[4528] = nvar_4528; + functions[4529] = fn4529; + nvar_list[4529] = nvar_4529; + functions[4530] = fn4530; + nvar_list[4530] = nvar_4530; + functions[4531] = fn4531; + nvar_list[4531] = nvar_4531; + functions[4532] = fn4532; + nvar_list[4532] = nvar_4532; + functions[4533] = fn4533; + nvar_list[4533] = nvar_4533; + functions[4534] = fn4534; + nvar_list[4534] = nvar_4534; + functions[4535] = fn4535; + nvar_list[4535] = nvar_4535; + functions[4536] = fn4536; + nvar_list[4536] = nvar_4536; + functions[4537] = fn4537; + nvar_list[4537] = nvar_4537; + functions[4538] = fn4538; + nvar_list[4538] = nvar_4538; + functions[4539] = fn4539; + nvar_list[4539] = nvar_4539; + functions[4540] = fn4540; + nvar_list[4540] = nvar_4540; + functions[4541] = fn4541; + nvar_list[4541] = nvar_4541; + functions[4542] = fn4542; + nvar_list[4542] = nvar_4542; + functions[4543] = fn4543; + nvar_list[4543] = nvar_4543; + functions[4544] = fn4544; + nvar_list[4544] = nvar_4544; + functions[4545] = fn4545; + nvar_list[4545] = nvar_4545; + functions[4546] = fn4546; + nvar_list[4546] = nvar_4546; + functions[4547] = fn4547; + nvar_list[4547] = nvar_4547; + functions[4548] = fn4548; + nvar_list[4548] = nvar_4548; + functions[4549] = fn4549; + nvar_list[4549] = nvar_4549; + functions[4550] = fn4550; + nvar_list[4550] = nvar_4550; + functions[4551] = fn4551; + nvar_list[4551] = nvar_4551; + functions[4552] = fn4552; + nvar_list[4552] = nvar_4552; + functions[4553] = fn4553; + nvar_list[4553] = nvar_4553; + functions[4554] = fn4554; + nvar_list[4554] = nvar_4554; + functions[4555] = fn4555; + nvar_list[4555] = nvar_4555; + functions[4556] = fn4556; + nvar_list[4556] = nvar_4556; + functions[4557] = fn4557; + nvar_list[4557] = nvar_4557; + functions[4558] = fn4558; + nvar_list[4558] = nvar_4558; + functions[4559] = fn4559; + nvar_list[4559] = nvar_4559; + functions[4560] = fn4560; + nvar_list[4560] = nvar_4560; + functions[4561] = fn4561; + nvar_list[4561] = nvar_4561; + functions[4562] = fn4562; + nvar_list[4562] = nvar_4562; + functions[4563] = fn4563; + nvar_list[4563] = nvar_4563; + functions[4564] = fn4564; + nvar_list[4564] = nvar_4564; + functions[4565] = fn4565; + nvar_list[4565] = nvar_4565; + functions[4566] = fn4566; + nvar_list[4566] = nvar_4566; + functions[4567] = fn4567; + nvar_list[4567] = nvar_4567; + functions[4568] = fn4568; + nvar_list[4568] = nvar_4568; + functions[4569] = fn4569; + nvar_list[4569] = nvar_4569; + functions[4570] = fn4570; + nvar_list[4570] = nvar_4570; + functions[4571] = fn4571; + nvar_list[4571] = nvar_4571; + functions[4572] = fn4572; + nvar_list[4572] = nvar_4572; + functions[4573] = fn4573; + nvar_list[4573] = nvar_4573; + functions[4574] = fn4574; + nvar_list[4574] = nvar_4574; + functions[4575] = fn4575; + nvar_list[4575] = nvar_4575; + functions[4576] = fn4576; + nvar_list[4576] = nvar_4576; + functions[4577] = fn4577; + nvar_list[4577] = nvar_4577; + functions[4578] = fn4578; + nvar_list[4578] = nvar_4578; + functions[4579] = fn4579; + nvar_list[4579] = nvar_4579; + functions[4580] = fn4580; + nvar_list[4580] = nvar_4580; + functions[4581] = fn4581; + nvar_list[4581] = nvar_4581; + functions[4582] = fn4582; + nvar_list[4582] = nvar_4582; + functions[4583] = fn4583; + nvar_list[4583] = nvar_4583; + functions[4584] = fn4584; + nvar_list[4584] = nvar_4584; + functions[4585] = fn4585; + nvar_list[4585] = nvar_4585; + functions[4586] = fn4586; + nvar_list[4586] = nvar_4586; + functions[4587] = fn4587; + nvar_list[4587] = nvar_4587; + functions[4588] = fn4588; + nvar_list[4588] = nvar_4588; + functions[4589] = fn4589; + nvar_list[4589] = nvar_4589; + functions[4590] = fn4590; + nvar_list[4590] = nvar_4590; + functions[4591] = fn4591; + nvar_list[4591] = nvar_4591; + functions[4592] = fn4592; + nvar_list[4592] = nvar_4592; + functions[4593] = fn4593; + nvar_list[4593] = nvar_4593; + functions[4594] = fn4594; + nvar_list[4594] = nvar_4594; + functions[4595] = fn4595; + nvar_list[4595] = nvar_4595; + functions[4596] = fn4596; + nvar_list[4596] = nvar_4596; + functions[4597] = fn4597; + nvar_list[4597] = nvar_4597; + functions[4598] = fn4598; + nvar_list[4598] = nvar_4598; + functions[4599] = fn4599; + nvar_list[4599] = nvar_4599; + functions[4600] = fn4600; + nvar_list[4600] = nvar_4600; + functions[4601] = fn4601; + nvar_list[4601] = nvar_4601; + functions[4602] = fn4602; + nvar_list[4602] = nvar_4602; + functions[4603] = fn4603; + nvar_list[4603] = nvar_4603; + functions[4604] = fn4604; + nvar_list[4604] = nvar_4604; + functions[4605] = fn4605; + nvar_list[4605] = nvar_4605; + functions[4606] = fn4606; + nvar_list[4606] = nvar_4606; + functions[4607] = fn4607; + nvar_list[4607] = nvar_4607; + functions[4608] = fn4608; + nvar_list[4608] = nvar_4608; + functions[4609] = fn4609; + nvar_list[4609] = nvar_4609; + functions[4610] = fn4610; + nvar_list[4610] = nvar_4610; + functions[4611] = fn4611; + nvar_list[4611] = nvar_4611; + functions[4612] = fn4612; + nvar_list[4612] = nvar_4612; + functions[4613] = fn4613; + nvar_list[4613] = nvar_4613; + functions[4614] = fn4614; + nvar_list[4614] = nvar_4614; + functions[4615] = fn4615; + nvar_list[4615] = nvar_4615; + functions[4616] = fn4616; + nvar_list[4616] = nvar_4616; + functions[4617] = fn4617; + nvar_list[4617] = nvar_4617; + functions[4618] = fn4618; + nvar_list[4618] = nvar_4618; + functions[4619] = fn4619; + nvar_list[4619] = nvar_4619; + functions[4620] = fn4620; + nvar_list[4620] = nvar_4620; + functions[4621] = fn4621; + nvar_list[4621] = nvar_4621; + functions[4622] = fn4622; + nvar_list[4622] = nvar_4622; + functions[4623] = fn4623; + nvar_list[4623] = nvar_4623; + functions[4624] = fn4624; + nvar_list[4624] = nvar_4624; + functions[4625] = fn4625; + nvar_list[4625] = nvar_4625; + functions[4626] = fn4626; + nvar_list[4626] = nvar_4626; + functions[4627] = fn4627; + nvar_list[4627] = nvar_4627; + functions[4628] = fn4628; + nvar_list[4628] = nvar_4628; + functions[4629] = fn4629; + nvar_list[4629] = nvar_4629; + functions[4630] = fn4630; + nvar_list[4630] = nvar_4630; + functions[4631] = fn4631; + nvar_list[4631] = nvar_4631; + functions[4632] = fn4632; + nvar_list[4632] = nvar_4632; + functions[4633] = fn4633; + nvar_list[4633] = nvar_4633; + functions[4634] = fn4634; + nvar_list[4634] = nvar_4634; + functions[4635] = fn4635; + nvar_list[4635] = nvar_4635; + functions[4636] = fn4636; + nvar_list[4636] = nvar_4636; + functions[4637] = fn4637; + nvar_list[4637] = nvar_4637; + functions[4638] = fn4638; + nvar_list[4638] = nvar_4638; + functions[4639] = fn4639; + nvar_list[4639] = nvar_4639; + functions[4640] = fn4640; + nvar_list[4640] = nvar_4640; + functions[4641] = fn4641; + nvar_list[4641] = nvar_4641; + functions[4642] = fn4642; + nvar_list[4642] = nvar_4642; + functions[4643] = fn4643; + nvar_list[4643] = nvar_4643; + functions[4644] = fn4644; + nvar_list[4644] = nvar_4644; + functions[4645] = fn4645; + nvar_list[4645] = nvar_4645; + functions[4646] = fn4646; + nvar_list[4646] = nvar_4646; + functions[4647] = fn4647; + nvar_list[4647] = nvar_4647; + functions[4648] = fn4648; + nvar_list[4648] = nvar_4648; + functions[4649] = fn4649; + nvar_list[4649] = nvar_4649; + functions[4650] = fn4650; + nvar_list[4650] = nvar_4650; + functions[4651] = fn4651; + nvar_list[4651] = nvar_4651; + functions[4652] = fn4652; + nvar_list[4652] = nvar_4652; + functions[4653] = fn4653; + nvar_list[4653] = nvar_4653; + functions[4654] = fn4654; + nvar_list[4654] = nvar_4654; + functions[4655] = fn4655; + nvar_list[4655] = nvar_4655; + functions[4656] = fn4656; + nvar_list[4656] = nvar_4656; + functions[4657] = fn4657; + nvar_list[4657] = nvar_4657; + functions[4658] = fn4658; + nvar_list[4658] = nvar_4658; + functions[4659] = fn4659; + nvar_list[4659] = nvar_4659; + functions[4660] = fn4660; + nvar_list[4660] = nvar_4660; + functions[4661] = fn4661; + nvar_list[4661] = nvar_4661; + functions[4662] = fn4662; + nvar_list[4662] = nvar_4662; + functions[4663] = fn4663; + nvar_list[4663] = nvar_4663; + functions[4664] = fn4664; + nvar_list[4664] = nvar_4664; + functions[4665] = fn4665; + nvar_list[4665] = nvar_4665; + functions[4666] = fn4666; + nvar_list[4666] = nvar_4666; + functions[4667] = fn4667; + nvar_list[4667] = nvar_4667; + functions[4668] = fn4668; + nvar_list[4668] = nvar_4668; + functions[4669] = fn4669; + nvar_list[4669] = nvar_4669; + functions[4670] = fn4670; + nvar_list[4670] = nvar_4670; + functions[4671] = fn4671; + nvar_list[4671] = nvar_4671; + functions[4672] = fn4672; + nvar_list[4672] = nvar_4672; + functions[4673] = fn4673; + nvar_list[4673] = nvar_4673; + functions[4674] = fn4674; + nvar_list[4674] = nvar_4674; + functions[4675] = fn4675; + nvar_list[4675] = nvar_4675; + functions[4676] = fn4676; + nvar_list[4676] = nvar_4676; + functions[4677] = fn4677; + nvar_list[4677] = nvar_4677; + functions[4678] = fn4678; + nvar_list[4678] = nvar_4678; + functions[4679] = fn4679; + nvar_list[4679] = nvar_4679; + functions[4680] = fn4680; + nvar_list[4680] = nvar_4680; + functions[4681] = fn4681; + nvar_list[4681] = nvar_4681; + functions[4682] = fn4682; + nvar_list[4682] = nvar_4682; + functions[4683] = fn4683; + nvar_list[4683] = nvar_4683; + functions[4684] = fn4684; + nvar_list[4684] = nvar_4684; + functions[4685] = fn4685; + nvar_list[4685] = nvar_4685; + functions[4686] = fn4686; + nvar_list[4686] = nvar_4686; + functions[4687] = fn4687; + nvar_list[4687] = nvar_4687; + functions[4688] = fn4688; + nvar_list[4688] = nvar_4688; + functions[4689] = fn4689; + nvar_list[4689] = nvar_4689; + functions[4690] = fn4690; + nvar_list[4690] = nvar_4690; + functions[4691] = fn4691; + nvar_list[4691] = nvar_4691; + functions[4692] = fn4692; + nvar_list[4692] = nvar_4692; + functions[4693] = fn4693; + nvar_list[4693] = nvar_4693; + +} diff --git a/equational_theories/Generated/LinearOps/src/export.py b/equational_theories/Generated/LinearOps/src/export.py new file mode 100644 index 000000000..3dee7e287 --- /dev/null +++ b/equational_theories/Generated/LinearOps/src/export.py @@ -0,0 +1,127 @@ +import numpy as np +import os +import random + +def parse_line(line): + # Extract the list from the line using string manipulation + try: + if 'Proves' in line: + return [x-1 for x in list(map(int, line.split('[')[1].split(']')[0].split(', ')))] + else: + return list(map(int, line.split(': ')[1].split(']')[0].split(', '))) + except: + print("Failed on", line) + return [] + +def prune_rows(lines, matrix_size=4694): + matrix = np.zeros((matrix_size, matrix_size), dtype=bool) + matrix = np.load("/tmp/r.npy") != 8 + matrix[:] = 0 + print("ct", np.sum(matrix)) + + random.shuffle(lines) + keep = [] + for i,line in enumerate(lines): + L = parse_line(line) + L_array = np.array(L) + + # Create a boolean mask for elements not in L + mask = np.ones(matrix_size, dtype=bool) + mask[L_array] = False + + # Use advanced indexing to set values + if np.any(matrix[L_array[:, None], mask] == 0): + matrix[L_array[:, None], mask] = True + keep.append(line) + + return matrix, keep + +def trim(lines): + """ + Compute an approximate covering set. Each table gives a set of refutations. + Repeatedly do the following: + 1. Randomly shuffle the table order + 2. Process the tables in linear order and drop those that don't add new rules + 3. Any time it doesn't improve things, increment a counter + 4. If we've made no progress 10 times, then call it "good enough" + """ + print("Start with", len(lines)) + matrix, lines = prune_rows(lines) + identity_count = 0 + while identity_count < 10: + print("Current round", len(lines), np.sum(matrix)) + matrix2, lines2 = prune_rows(lines) + assert np.all(matrix2 == matrix) + if len(lines2) == len(lines): + identity_count += 1 + lines = lines2 + #exit(0) + return matrix, lines + +print("Reading files...") +lines = [] + +for line in open("log").readlines(): + if "Loop" in line: continue + if 'Variables' in line: + vs = line[:-1] + if 'Satisfied equations' not in line: continue + lines.append(vs + " " + line) + + + + +print("Trimming...") +matrix, lines = trim(lines) + +print("Covering set") +for line in lines: + print(line) + +template = """theorem MoreLinearInvariance{COUNT} : ∃ (G : Type) (_ : Magma G), Facts G {YES} {NOT} := + ⟨ZMod {PK}, {{ op := fun x y => {CONST1} * x + {CONST2} * y }}, by decide!⟩""" + +#unsolved = {1486-1, 2126-1, 1076-1, 2531-1, 1133-1, 1167-1, 1659-1, 1661-1, 1485-1, 481-1, 3161-1, 1648-1, 1924-1, 2712-1, 1701-1, 1839-1, 511-1, 3116-1, 1443-1, 2093-1, 1692-1, 1895-1, 477-1, 1112-1, 2460-1, 3150-1, 854-1, 1110-1, 2497-1, 65-1, 73-1, 261-1, 274-1, 680-1, 707-1, 2940-1, 2947-1, 1523-1, 2132-1, 504-1, 1117-1, 1289-1, 1722-1, 1925-1, 2338-1, 2538-1, 3143-1, 3588-1, 3994-1, 713-1, 2856-1, 883-1, 917-1, 2710-1, 2744-1, 1086-1, 2541-1, 704-1, 1518-1, 2054-1, 2903-1, 3342-1, 4167-1, 118-1, 229-1, 1431-1, 1526-1, 2040-1, 2101-1, 115-1, 219-1, 476-1, 503-1, 907-1, 1447-1, 2056-1, 2700-1, 3069-1, 3076-1, 1519-1, 2128-1, 1630-1, 1633-1, 1681-1, 1833-1, 1884-1, 1958-1, 1113-1, 1515-1, 1729-1, 1898-1, 2038-1, 2534-1, 3549-1, 3917-1, 464-1, 706-1, 1276-1, 1437-1, 1441-1, 1516-1, 2037-1, 2070-1, 2091-1, 2291-1, 3103-1, 3308-1, 4158-1, 714-1, 1323-1, 2304-1, 2507-1, 63-1, 124-1, 206-1, 271-1, 1491-1, 2061-1, 467-1, 670-1, 677-1, 879-1, 906-1, 1728-1, 1841-1, 2504-1, 2647-1, 2650-1, 2866-1, 2910-1, 2937-1, 3140-1, 3352-1, 3475-1, 3545-1, 3555-1, 3888-1, 4164-1, 3862-1, 3862-1, 3456-1, 1832-1, 1629-1, 3253-1, 4065-1, 1426-1, 2035-1, 411-1, 3050-1, 817-1, 2644-1, 614-1, 1020-1, 2441-1, 2847-1, 4435-1, 1223-1, 2238-1, 3319-1, 3522-1, 3915-1, 4118-1, 8-1, 23-1, 47-1, 151-1, 255-1, 3457-1, 3877-1, 4268-1, 4587-1, 99-1, 203-1, 307-1, 359-1, 3511-1, 3955-1, 1657-1, 1860-1, 4380-1, 1519-1, 2128-1, 1055-1, 1429-1, 2124-1, 2452-1, 1701-1, 1839-1, 1630-1, 1633-1, 1681-1, 1833-1, 1884-1, 1958-1, 152-1, 166-1, 1096-1, 1427-1, 1481-1, 1483-1, 1492-1, 1634-1, 1656-1, 1660-1, 1668-1, 1721-1, 1837-1, 1851-1, 2051-1, 2087-1, 3460-1, 3520-1, 3524-1, 3527-1, 3659-1, 3897-1, 3972-1, 4006-1, 4040-1, 4314-1, 4315-1, 4606-1, 4615-1, 513-1, 1035-1, 1428-1, 2050-1, 2443-1, 3079-1, 3519-1, 3925-1, 4269-1, 4584-1, 1133-1, 1167-1, 1659-1, 1661-1, 1485-1, 477-1, 1112-1, 2460-1, 3150-1, 1523-1, 2132-1, 883-1, 917-1, 2710-1, 2744-1, 1113-1, 1515-1, 1729-1, 1898-1, 2038-1, 2534-1, 714-1, 1323-1, 2304-1, 2507-1, 3-1, 125-1, 167-1, 168-1, 222-1, 326-1, 375-1, 910-1, 1025-1, 1085-1, 1316-1, 1479-1, 1480-1, 1484-1, 1488-1, 1496-1, 1631-1, 1655-1, 1695-1, 1847-1, 1897-1, 2041-1, 2052-1, 2088-1, 2089-1, 2446-1, 2467-1, 2737-1, 3258-1, 3458-1, 3512-1, 3513-1, 3521-1, 3523-1, 3525-1, 3715-1, 3722-1, 3867-1, 3918-1, 3935-1, 3952-1, 3989-1, 3993-1, 4067-1, 4273-1, 4470-1, 4588-1, 1486-1, 2126-1, 481-1, 3161-1, 1648-1, 1924-1, 511-1, 3116-1, 1692-1, 1895-1, 65-1, 73-1, 261-1, 274-1, 680-1, 707-1, 2940-1, 2947-1, 504-1, 1117-1, 1289-1, 1722-1, 1925-1, 2338-1, 2538-1, 3143-1, 3588-1, 3994-1, 1086-1, 2541-1, 118-1, 229-1, 1431-1, 1526-1, 2040-1, 2101-1, 3549-1, 3917-1, 63-1, 124-1, 206-1, 271-1, 1491-1, 2061-1, 107-1, 205-1, 211-1, 413-1, 414-1, 416-1, 466-1, 473-1, 880-1, 1023-1, 1045-1, 1075-1, 1109-1, 1248-1, 1251-1, 1313-1, 1478-1, 1482-1, 1489-1, 1647-1, 1685-1, 1922-1, 2036-1, 2098-1, 2125-1, 2240-1, 2246-1, 2266-1, 2294-1, 2444-1, 2449-1, 2457-1, 2459-1, 2462-1, 2530-1, 2707-1, 3055-1, 3056-1, 3065-1, 3066-1, 3068-1, 3139-1, 3316-1, 3472-1, 3878-1, 4128-1, 4270-1, 4590-1} +unsolved = set(list(range(4694))) + +solved = np.load("/tmp/r.npy") != 8 +solved[:] = 0 + +fout = open("new.lean","w") +for count,line in list(enumerate(lines)): + print("COUNT", count) + PK, CONST1, CONST2 = map(int,line.split()[1:4]) + yes = list(map(int,line.split(": ")[1].split(", "))) + no = list(set(unsolved)-set(yes)) + + for _ in range(10): + keepyes = [] + for x in yes: + if not np.all(solved[x, no]): + keepyes.append(x) + yes = keepyes + + keepno = [] + for x in no: + if not np.all(solved[yes, x]): + keepno.append(x) + no = keepno + + continue + print("Intro", keepyes, keepno) + if len(keepyes) == 0 or len(keepno) == 0: + continue + + fout.write("@[equational_result]\n") + fout.write(template.format(PK=PK, CONST1=CONST1, CONST2=CONST2, YES=[x+1 for x in yes], NOT=sorted([x+1 for x in no]), COUNT=count)+"\n\n") + + + + +#/eq/tables committed Current round 2204 13732880 +#current set in .txt Current round 515 13732566 +# Current round 513 13737261 + +# 5x5: 14,187,469 +# 14,472,076 +# 22024116 diff --git a/equational_theories/Generated/LinearOps/src/header.h b/equational_theories/Generated/LinearOps/src/header.h new file mode 100644 index 000000000..d140d05f1 --- /dev/null +++ b/equational_theories/Generated/LinearOps/src/header.h @@ -0,0 +1,7 @@ +#define MAX_ARGS 6 +#define NUM_FUNCTIONS 4694 + + +typedef bool (*FunctionPtr)(int64_t, int64_t, int64_t, int64_t, + int64_t, int64_t, int64_t, int64_t, int64_t, int64_t + ); diff --git a/equational_theories/Generated/LinearOps/src/write_equations.py b/equational_theories/Generated/LinearOps/src/write_equations.py new file mode 100644 index 000000000..53dc6cd8c --- /dev/null +++ b/equational_theories/Generated/LinearOps/src/write_equations.py @@ -0,0 +1,161 @@ +#!/usr/bin/env python3 + +import re + +class Expr: + pass + +class Var(Expr): + def __init__(self, name): + self.name = name + +class Op(Expr): + def __init__(self, op, left, right): + self.op = op + self.left = left + self.right = right + +def tokenize(expr_str): + tokens = [] + i = 0 + while i < len(expr_str): + if expr_str[i].isspace(): + i += 1 + elif expr_str[i].isalnum() or expr_str[i] in ("'", "_"): + # Read variable name + var = '' + while i < len(expr_str) and (expr_str[i].isalnum() or expr_str[i] in ("'", "_")): + var += expr_str[i] + i += 1 + tokens.append(('VAR', var)) + elif expr_str[i] == '◇': + tokens.append(('OP', '◇')) + i += 1 + elif expr_str[i] == '(': + tokens.append(('LPAREN', '(')) + i += 1 + elif expr_str[i] == ')': + tokens.append(('RPAREN', ')')) + i += 1 + elif expr_str[i] == '=': + tokens.append(('EQUALS', '=')) + i += 1 + else: + # Skip unknown characters + i += 1 + return tokens + +def parse_expr(tokens, pos=0): + def parse_factor(tokens, pos): + if pos >= len(tokens): + raise Exception('Unexpected end of tokens') + token = tokens[pos] + if token[0] == 'VAR': + return Var(token[1]), pos + 1 + elif token[0] == 'LPAREN': + expr, pos = parse_expr(tokens, pos + 1) + if pos >= len(tokens) or tokens[pos][0] != 'RPAREN': + raise Exception('Expected ) at position {}'.format(pos)) + return expr, pos + 1 + else: + raise Exception('Unexpected token: {}'.format(token)) + + left, pos = parse_factor(tokens, pos) + while pos < len(tokens) and tokens[pos][0] == 'OP': + op = tokens[pos][1] + pos += 1 + right, pos = parse_factor(tokens, pos) + left = Op(op, left, right) + return left, pos + +def parse_equation_line(line): + # First, extract the equation name + match = re.match(r'def\s+(\w+)\s*\(.*?\)\s*(?:\[.*?\])?\s*:=\s*∀(.*)', line) + if not match: + return None + equation_name = match.group(1) + rest = match.group(2).strip() + # Now, split the rest into variables declaration and equation + var_equation = rest.split(',', 1) + if len(var_equation) != 2: + return None + var_decl = var_equation[0].strip() + equation = var_equation[1].strip() + # Extract variables + vars_and_types = var_decl.split(':', 1) + vars_str = vars_and_types[0].strip() + variables = vars_str.replace(',', ' ').split() + # Now, split the equation at '=' + equation_match = re.match(r'(.*)=(.*)', equation) + if not equation_match: + return None + lhs = equation_match.group(1).strip() + rhs = equation_match.group(2).strip() + return { + 'equation_name': equation_name, + 'variables': variables, + 'lhs': lhs, + 'rhs': rhs + } + +def process_equation_line(line, equation_index): + eq = parse_equation_line(line) + if eq is None: + print(f"Failed to parse line: {line}") + return None + variables = eq['variables'] + lhs_expr_str = eq['lhs'] + rhs_expr_str = eq['rhs'] + # Assign indices to variables + variable_indices = {var: idx for idx, var in enumerate(variables)} + # Tokenize and parse lhs and rhs expressions + lhs_tokens = tokenize(lhs_expr_str) + rhs_tokens = tokenize(rhs_expr_str) + try: + lhs_expr, lhs_pos = parse_expr(lhs_tokens) + rhs_expr, rhs_pos = parse_expr(rhs_tokens) + except Exception as e: + print(f"Error parsing expression: {e}") + return None + if lhs_pos != len(lhs_tokens): + print(f"Unparsed tokens remain in LHS expression '{lhs_expr_str}'") + return None + if rhs_pos != len(rhs_tokens): + print(f"Unparsed tokens remain in RHS expression '{rhs_expr_str}'") + return None + # Generate c code for lhs and rhs + lhs_c_code = generate_c_code(lhs_expr, variable_indices) + rhs_c_code = generate_c_code(rhs_expr, variable_indices) + # Generate c code for function + nvar = len(variables) + allvars = ", ".join("uint64_t " + x for x in "xyzwuv") + func_code = f'bool fn{equation_index}(uint64_t pk, int inv, uint64_t a, uint64_t b, {allvars}) {{ return MOD(({lhs_c_code}) - ({rhs_c_code}),inv,pk) == 0; }} int nvar_{equation_index} = {nvar};' + return func_code + +def generate_c_code(expr, variable_indices): + if isinstance(expr, Var): + if expr.name in variable_indices: + idx = variable_indices[expr.name] + # Use expressions involving K and variable index + return 'xyzwuv'[idx] + else: + # Handle constants or variables not in variable_positions + return expr.name + elif isinstance(expr, Op): + if expr.op == '◇': + # For '◇' operation, we need to generate table[...] + left_code = generate_c_code(expr.left, variable_indices) + right_code = generate_c_code(expr.right, variable_indices) + return f'a*({left_code})+b*({right_code})' + else: + # Unknown operator + raise Exception(f'Unknown operator: {expr.op}') + else: + raise Exception('Unknown expression type') + +for idx,line in enumerate(open("equations.txt")): + func_code = process_equation_line(line, idx) + if func_code: + print(func_code) + else: + print(f"Failed to process equation at line {idx}: {line}") diff --git a/equational_theories/Generated/SimpleRewrites/src/find_redundant.py b/equational_theories/Generated/SimpleRewrites/src/find_redundant.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/SimpleRewrites/src/find_simple_rewrites.py b/equational_theories/Generated/SimpleRewrites/src/find_simple_rewrites.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/SimpleRewrites/src/utils.py b/equational_theories/Generated/SimpleRewrites/src/utils.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/TrivialBruteforce/src/generate_refutations.py b/equational_theories/Generated/TrivialBruteforce/src/generate_refutations.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/VampireProven/Conjectures.lean b/equational_theories/Generated/VampireProven/Conjectures.lean index 9f069a061..f96f07cb6 100644 --- a/equational_theories/Generated/VampireProven/Conjectures.lean +++ b/equational_theories/Generated/VampireProven/Conjectures.lean @@ -9,7 +9,6 @@ import Mathlib.Tactic.TypeStar @[equational_result] conjecture Equation477_not_implies_Equation1492 : ∃ (G: Type) (_: Magma G), Equation477 G ∧ ¬ Equation1492 G @[equational_result] conjecture Equation3161_not_implies_Equation1496 : ∃ (G: Type) (_: Magma G), Equation3161 G ∧ ¬ Equation1496 G @[equational_result] conjecture Equation481_not_implies_Equation1496 : ∃ (G: Type) (_: Magma G), Equation481 G ∧ ¬ Equation1496 G -@[equational_result] conjecture Equation3994_not_implies_Equation3588 : ∃ (G: Type) (_: Magma G), Equation3994 G ∧ ¬ Equation3588 G @[equational_result] conjecture Equation2093_not_implies_Equation416 : ∃ (G: Type) (_: Magma G), Equation2093 G ∧ ¬ Equation416 G @[equational_result] conjecture Equation3150_not_implies_Equation2128 : ∃ (G: Type) (_: Magma G), Equation3150 G ∧ ¬ Equation2128 G @[equational_result] conjecture Equation3150_not_implies_Equation1519 : ∃ (G: Type) (_: Magma G), Equation3150 G ∧ ¬ Equation1519 G diff --git a/equational_theories/Generated/VampireProven/src/vampire_fin_counterexamples.py b/equational_theories/Generated/VampireProven/src/vampire_fin_counterexamples.py old mode 100755 new mode 100644 diff --git a/equational_theories/Generated/VampireProven/src/vampire_proofs.py b/equational_theories/Generated/VampireProven/src/vampire_proofs.py old mode 100755 new mode 100644 diff --git a/equational_theories/InfModel.lean b/equational_theories/InfModel.lean index 74fc44a61..167e47ac2 100644 --- a/equational_theories/InfModel.lean +++ b/equational_theories/InfModel.lean @@ -123,6 +123,345 @@ theorem Finite.Equation5105_implies_Equation2 (G : Type*) [Magma G] [Finite G] ( _= x ◇ (x ◇ (x ◇ (y ◇ (x ◇ x)))) := by rw [hhhh] _= y := by rw [← h y x x] +theorem Finite.Equation28770_implies_Equation2 (G : Type*) [Magma G] [Finite G] (h : Equation28770 G) : + Equation2 G := by + have : ∀ (y z u : G), y ◇ z = y ◇ u := by + intro y + let f (x : G) := ((y ◇ y) ◇ y) ◇ x + let g (x : G) := x ◇ (y ◇ y) + have : Function.RightInverse f g := by + intro x + simp [f, g, ← h] + intro z u + apply this.injective + obtain ⟨finv, hf⟩ := (Finite.surjective_of_injective this.injective).hasRightInverse + let fy := finv ((y ◇ y) ◇ y) + replace hf : ((y ◇ y) ◇ y) ◇ fy = (y ◇ y) ◇ y := hf _ + have := h fy y + simp only [hf] at this + simp [f, ← this] + intro x u + have y := x + have z := x + rw [h x y z, this ((y ◇ y) ◇ y) x u, ← this ((y ◇ y) ◇ y) u u, ← h] + +theorem Equation28770_not_implies_Equation2 : ∃ (G : Type) (_ : Magma G), Equation28770 G ∧ ¬Equation2 G := by + have : Fact (Nat.Prime 2) := ⟨Nat.prime_two⟩ + have : Fact (Nat.Prime 3) := ⟨Nat.prime_three⟩ + have : Fact (Nat.Prime 5) := ⟨Nat.prime_five⟩ + letI : Magma ℕ+ := { op := fun a b ↦ if a = b then 2^b.val else + if a = 2^b.val then 3^b.val else + if a = 3^(padicValNat 3 a) then a * 5^b.val else + if a = 3^(padicValNat 3 a) * 5^(padicValNat 5 a) then Nat.toPNat' (padicValNat 5 a) else + if a = 2^(3^(padicValNat 3 (padicValNat 2 a))) then 3^(padicValNat 3 (padicValNat 2 a)) else 1} + refine ⟨ℕ+, this, ⟨?_, fun x ↦ nomatch (x 1 2)⟩⟩ + intro x y z + -- t1 is from the proof of Equation374794_not_implies_Equation2 + have t1 (y : ℕ+) : 2 ^ (y : ℕ) ≠ y := by + apply_fun PNat.val + simp [ne_of_gt, Nat.lt_pow_self] + have h1 : ∀ (y: ℕ+), y ◇ y = 2^y.val := by + intro y + unfold Magma.op + simp only [ite_true] + have h2 : ∀ (y: ℕ+), (2^y.val) ◇ y = 3^y.val := by + intro y + unfold Magma.op + simp [t1] + have h3 : ∀ (x y: ℕ+), x ≠ 3^y.val → (3^y.val) ◇ x = 3^y.val * 5^x.val := by + intro x y hxy + unfold Magma.op + simp + rw [if_neg] + case hnc => + intro h'' + apply hxy + simp [h''] + simp + contrapose + intro _ + apply_fun PNat.val + simp only [PNat.pow_coe, PNat.val_ofNat, ne_eq] + intro nh + apply eq_of_prime_pow_eq at nh + · contradiction + · exact Nat.prime_three.prime + · exact Nat.prime_two.prime + · simp + have h4 : ∀ (x y z: ℕ+), z ≠ 3^y.val * 5^x.val → (3^y.val * 5^x.val) ◇ z = x := by + intro x y z hxyz + unfold Magma.op + simp + rw [if_neg] + case hnc => + intro h' + apply hxyz + simp [h'] + rw [if_neg] + case hnc => + apply_fun PNat.val + simp [PNat.pow_coe, PNat.val_ofNat, ne_eq] + intro nh + apply PNat.ne_zero z + calc ↑z + _ = padicValNat 2 (3^y.val * 5^x.val) := by simp [nh] + _ = 0 := by simp [padicValNat.mul, padicValNat_prime_prime_pow] + rw [if_neg] + case hnc => + intro hc + apply PNat.ne_zero x + calc ↑x + _ = padicValNat 5 ↑((3: ℕ+)^y.val * (5: ℕ+)^x.val) := by simp [padicValNat_prime_prime_pow, padicValNat.mul] + _ = padicValNat 5 ((3: ℕ+)^(padicValNat (3: ℕ) ((3: ℕ)^y.val * (5: ℕ)^x.val))) := by simp [hc] + _ = 0 := by simp [padicValNat_prime_prime_pow] + rw [if_pos] + case hc => + simp [padicValNat.mul, padicValNat_prime_prime_pow] + simp [this, Subtype.ext_iff, padicValNat.mul, padicValNat_prime_prime_pow] + have h5 : ∀ (y z: ℕ+), z ≠ 3^y.val ∧ z ≠ 2^(3^y.val) → (2^(3^y.val)) ◇ z = 3^y.val := by + intro y z hyz + unfold Magma.op + simp + rw [if_neg, if_neg, if_neg, if_neg] + . + intro hc + apply PNat.ne_zero ((3: ℕ+)^y.val) + calc ↑((3: ℕ+)^y.val) + _ = padicValNat 2 ↑(2^3^y.val: ℕ+) := by simp + _ = padicValNat 2 _ := by rw [hc] + _ = 0 := by simp [padicValNat_prime_prime_pow] + . + intro hc + apply PNat.ne_zero ((3: ℕ+)^y.val) + calc ↑((3: ℕ+)^y.val) + _ = padicValNat 2 ↑(2^3^y.val: ℕ+) := by simp + _ = padicValNat 2 _ := by rw [hc] + _ = 0 := by simp [padicValNat_prime_prime_pow] + . + intro hc + apply hyz.1 + calc z + _ = z.val.toPNat' := by simp + _ = (padicValNat 2 (2^z.val: ℕ+)).toPNat' := by simp + _ = (padicValNat 2 ↑(2^3^y.val: ℕ+)).toPNat' := by rw [←hc] + _ = (3^y.val: ℕ).toPNat' := by simp + _ = 3^↑y := by rw [←PNat.coe_inj]; simp + . + intro hc + apply hyz.2 + simp [hc] + rw [h1, h2] + by_cases hx : x = 3^y.val + . + rw [hx, h1] + by_cases hyz : y ◇ z = 2^(3^y.val) + . + simp [hyz, h1] + exfalso + have : padicValNat 2 ↑(y ◇ z) = ↑(3^y.val) := by simp [hyz] + unfold Magma.op at this + simp at this + repeat rw [apply_ite PNat.val] at this + repeat rw [apply_ite (padicValNat 2)] at this + simp only [PNat.pow_coe, PNat.val_ofNat] at this + simp only [padicValNat.prime_pow] at this + simp [padicValNat_prime_prime_pow] at this + repeat rw [apply_ite (padicValNat 2)] at this + simp [padicValNat.mul, padicValNat_prime_prime_pow] at this + repeat simp only [ite_eq_iff] at this + simp at this + have this' : (0: ℕ) = (3: ℕ)^y.val ↔ False := by + apply Iff.intro + . + simp + intro h + apply pow_ne_zero y.val (by simp: 3 ≠ 0) + simp [h] + . + intro h + contradiction + simp [this'] at this + repeat simp [and_or_left, and_or_left] at this + cases this with + | inl h => + rw [h.1] at h + simp at h + have this2 := Nat.lt_pow_self (by simp: 1 < 3) z.val + have this3 := ne_of_gt this2 + exact this3 (Eq.symm h) + | inr this => _ + cases this with + | inl h => + have h1 := h.2.2.1 + have h2 := h.2.2.2 + rw [h1] at h2 + simp at h2 + simp [padicValNat_prime_prime_pow] at h2 + have h2 := Eq.symm h2 + have := pow_ne_zero (3^padicValNat 3 y.val) (by simp: 3 ≠ 0) + apply pow_ne_zero y.val (by simp: 3 ≠ 0) + contradiction + | inr this => _ + have this' := this.2.2.2.2.2 + apply_fun padicValNat 3 at this' + simp [padicValNat.prime_pow] at this' + have this' := Eq.symm this' + have this2 := calc y.val + _ > Nat.log 5 y.val := by simp [Nat.log_lt_self] + _ ≥ padicValNat 5 y.val := by simp [padicValNat_le_nat_log] + _ ≥ Nat.log 2 (padicValNat 5 y.val) := by simp [Nat.log_le_self] + _ ≥ padicValNat 2 (padicValNat 5 y.val) := by simp [padicValNat_le_nat_log] + _ ≥ Nat.log 3 (padicValNat 2 (padicValNat 5 y.val)) := by simp [Nat.log_le_self] + _ ≥ padicValNat 3 (padicValNat 2 (padicValNat 5 y.val)) := by simp [padicValNat_le_nat_log] + have this3 := ne_of_gt this2 + exact this3 this' + . + by_cases hyz' : y ◇ z = 3^y.val + . + rw [←hyz', h2, hyz'] + exfalso + have : padicValNat 3 ↑(y ◇ z) = ↑y.val := by simp [hyz'] + unfold Magma.op at this + simp at this + repeat rw [apply_ite PNat.val] at this + repeat rw [apply_ite (padicValNat 3)] at this + simp only [PNat.pow_coe, PNat.val_ofNat] at this + simp only [padicValNat.prime_pow] at this + simp [padicValNat_prime_prime_pow] at this + repeat rw [apply_ite (padicValNat 3)] at this + simp [padicValNat.mul, padicValNat_prime_prime_pow] at this + repeat simp only [ite_eq_iff] at this + simp at this + have this' : ((0: ℕ) = y.val) ↔ False := by + simp [false_iff] + intro hc + have hc := Eq.symm hc + have hc' := PNat.ne_zero y + contradiction + simp [this'] at this + repeat simp [and_or_left, and_or_left] at this + cases this with + | inl h => + have h1 := h.2.1 + have h2 := h.2.2 + rw [h2] at h1 + have h1 := Eq.symm h1 + apply_fun PNat.val at h1 + simp at h1 + have this2 := Nat.lt_pow_self (by simp: 1 < 2) y.val + have this3 := ne_of_gt this2 + exact this3 h1 + | inr this => _ + cases this with + | inl h => + have h1 := h.2.2.1 + have h2 := h.2.2.2 + rw [h2] at h1 + have h1 := Eq.symm h1 + apply_fun PNat.val at h1 + simp at h1 + have this2 := Nat.lt_pow_self (by simp: 1 < 3) y.val + have this3 := ne_of_gt this2 + exact this3 h1 + | inr this => _ + cases this with + | inl h => + have h := Eq.symm h.2.2.2.2.2 + have h' := calc y.val + _ > Nat.log 5 y.val := by simp [Nat.log_lt_self] + _ ≥ padicValNat 5 y.val := by simp [padicValNat_le_nat_log] + _ ≥ Nat.log 3 (padicValNat 5 y.val) := by simp [Nat.log_le_self] + _ ≥ padicValNat 3 (padicValNat 5 y.val) := by simp [padicValNat_le_nat_log] + exact (ne_of_gt h') h + | inr this => _ + have this := Eq.symm this.2.2.2.2.2 + have this' := calc y.val + _ > Nat.log 2 y.val := by simp [Nat.log_lt_self] + _ ≥ padicValNat 2 y.val := by simp [padicValNat_le_nat_log] + _ ≥ Nat.log 3 (padicValNat 2 y.val) := by simp [Nat.log_le_self] + _ ≥ padicValNat 3 (padicValNat 2 y.val) := by simp [padicValNat_le_nat_log] + exact (ne_of_gt this') this + . + have : (y ◇ z) ≠ 3^y.val ∧ (y ◇ z) ≠ 2^(3^y.val) := And.intro hyz' hyz + simp [h5 y (y ◇ z) this] + . + rw [h3 x y hx] + by_cases hyz : y ◇ z = 3^y.val * 5^x.val + . + rw [hyz, h1] + exfalso + unfold Magma.op at hyz + simp at hyz + simp only [PNat.pow_coe, PNat.val_ofNat] at hyz + repeat simp only [ite_eq_iff] at hyz + cases hyz with + | inl h => + have h' := h.2 + apply_fun padicValNat 2 at h' + simp [padicValNat_prime_prime_pow, padicValNat.mul] at h' + | inr hyz => _ + have hyz := hyz.2 + cases hyz with + | inl h => + have h' := Eq.symm h.2 + apply_fun padicValNat 5 at h' + simp [padicValNat_prime_prime_pow, padicValNat.mul] at h' + | inr hyz => _ + have hyz := hyz.2 + cases hyz with + | inl h => + rw [h.1] at h + have h' := h.2 + apply_fun padicValNat 3 at h' + simp [padicValNat_prime_prime_pow, padicValNat.mul] at h' + have this2 := Nat.lt_pow_self (by simp: 1 < 3) (padicValNat 3 y.val) + have this2 := ne_of_gt this2 + exact this2 (Eq.symm h') + | inr hyz => _ + have hyz := hyz.2 + cases hyz with + | inl h => + rw [h.1] at h + have h' := h.2 + simp [padicValNat_prime_prime_pow, padicValNat.mul, Nat.pow_mul] at h' + apply_fun PNat.val at h' + simp at h' + repeat simp only [ite_eq_iff] at h' + cases h' with + | inl this => + have this := this.2 + have this' := calc 3 ^ (3 ^ padicValNat 3 y.val * 5 ^ padicValNat 5 y.val) * 5 ^ x.val + _ ≥ 3 ^ (3 ^ padicValNat 3 y.val * 5 ^ padicValNat 5 y.val) := by simp [one_le_pow₀] + _ = 3 ^ (5 ^ padicValNat 5 y.val * 3 ^ padicValNat 3 y.val) := by simp [mul_comm] + _ = (3 ^ (5 ^ padicValNat 5 y.val)) ^ (3 ^ padicValNat 3 y.val) := by simp [pow_mul] + _ ≥ 3 ^ (5 ^ padicValNat 5 y.val) := by apply le_self_pow; simp [one_le_pow₀]; apply pow_ne_zero; simp + _ > 5 ^ padicValNat 5 y.val := by simp [Nat.lt_pow_self (by simp: 1 < 3)] + _ > padicValNat 5 y.val := by simp [Nat.lt_pow_self (by simp: 1 < 5)] + exact (ne_of_gt this') (Eq.symm this) + | inr this => + have this := Eq.symm this.2 + apply_fun padicValNat 5 at this + simp [padicValNat_prime_prime_pow, padicValNat.mul] at this + | inr hyz => _ + have hyz := hyz.2 + cases hyz with + | inl h => + have h := Eq.symm h.2 + apply_fun padicValNat 3 at h + simp [padicValNat_prime_prime_pow, padicValNat.mul, Nat.pow_mul] at h + have this' := calc y.val + _ > Nat.log 2 y.val := by simp [Nat.log_lt_self] + _ ≥ padicValNat 2 y.val := by simp [padicValNat_le_nat_log] + _ ≥ Nat.log 3 (padicValNat 2 y.val) := by simp [Nat.log_le_self] + _ ≥ padicValNat 3 (padicValNat 2 y.val) := by simp [padicValNat_le_nat_log] + exact (ne_of_gt this') h + | inr hyz => _ + have h := Eq.symm hyz.2 + apply_fun padicValNat 3 at h + simp [padicValNat_prime_prime_pow, padicValNat.mul, Nat.pow_mul] at h + . + rw [h4 x y (y ◇ z) hyz] + theorem Finite.Equation3994_implies_Equation3588 (G : Type*) [Magma G] [Finite G] (h : Equation3994 G) : Equation3588 G := by intro x y z @@ -144,6 +483,7 @@ theorem Finite.Equation3994_implies_Equation3588 (G : Type*) [Magma G] [Finite G apply (this _).symm simp [S] +@[equational_result] theorem Equation3994_not_implies_Equation3588 : ∃ (G : Type) (_ : Magma G), Equation3994 G ∧ ¬Equation3588 G := by let magN : Magma ℕ := ⟨fun x y ↦ if Even x ∧ Even y then x ^^^ y else if Even y then y + 2 else if Even x then x - 2 else 0⟩ @@ -173,4 +513,38 @@ theorem Equation3994_not_implies_Equation3588 : ∃ (G : Type) (_ : Magma G), Eq use 1, 1, 1 simp [magN] +/-- +Dual of the above, obtained by swapping x and y in the proof. +TODO: find a way to avoid this kind of code duplication. +-/ +@[equational_result] +theorem Equation3588_not_implies_Equation3944 : ∃ (G : Type) (_ : Magma G), Equation3588 G ∧ ¬ Equation3994 G := by + let magN : Magma ℕ := ⟨fun y x ↦ if Even x ∧ Even y then x ^^^ y else if Even y then y + 2 + else if Even x then x - 2 else 0⟩ + use ℕ, magN + have range : ∀ x y : ℕ, Even (x ◇ y : ℕ) := by + intro x y + simp only [magN] + split_ifs + · simp_all + · simpa [Nat.even_add] + · by_cases y < 2 + · rw [Nat.sub_eq_zero_of_le] + simp + omega + rw [Nat.even_sub] + · simp_all + · omega + · exact even_zero + constructor + · intro x y z + generalize h : x ◇ y = v + have : Even v := by rw [← h]; apply range + by_cases hz : Even z + · simp [magN, this, hz, Nat.xor_comm, Nat.xor_cancel_left] + · simp [magN, hz, this, Nat.even_add] + simp only [not_forall] + use 1, 1, 1 + simp [magN] + end InfModel diff --git a/equational_theories/LinearOps.lean b/equational_theories/LinearOps.lean index 5386174c4..e0bb6d64f 100644 --- a/equational_theories/LinearOps.lean +++ b/equational_theories/LinearOps.lean @@ -15,6 +15,11 @@ https://leanprover.zulipchat.com/#narrow/stream/458659-Equational/topic/An.20old namespace LinearOps +-- The following tactic can be faster for larger magmas (roughly `Fin n` with `n ≥ 17`, although +-- it of course depends on the number of variables in the equation) +macro "ringFin" : tactic => + `(tactic | (constructor; · solve | intro x; revert x; simp only [Magma.op]; ring_nf; simp) ) + /-- Found using the Rust program: ``` @@ -39,128 +44,128 @@ fn main() { -/ @[equational_result] theorem Equation1286_not_implies_Equation3 : ∃ (G : Type) (_ : Magma G), Facts G [1279, 1286] [3, 8, 23, 47, 99, 151, 203, 255, 326, 359, 375, 411, 614, 817, 1020, 1083, 1426, 1629, 1832, 2035, 2238, 2301, 2441, 2504, 2644, 2847, 3050, 3253, 3319, 3456, 3522, 3659, 3715, 3722, 3862, 3915, 4065, 4118, 4380, 4435, 4470] := - ⟨ZMod 11, { op := fun x y => 1 * x + 7 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 1 * x + 7 * y }, by decideFin!⟩ /-- Dual of the above. -/ @[equational_result] theorem Equation2301_not_implies_Equation3 : ∃ (G : Type) (_ : Magma G), Facts G [2328, 2301] [3, 8, 23, 47, 99, 151, 203, 255, 307, 326, 359, 375, 411, 614, 817, 1020, 1083, 1223, 1426, 1629, 1832, 2035, 2441, 2504, 2644, 2847, 3050, 3253, 3319, 3456, 3522, 3659, 3715, 3722, 3862, 3915, 4065, 4118, 4380, 4435, 4470] := - ⟨ZMod 11, { op := fun x y => 7 * x + 1 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 7 * x + 1 * y }, by decideFin!⟩ @[equational_result] theorem Equation3116_not_implies_Equation513 : ∃ (G : Type) (_ : Magma G), Facts G [3116] [513] := - ⟨ZMod 11, { op := fun x y => 3 * x + 9 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 3 * x + 9 * y }, by decideFin!⟩ -- dual of the above @[equational_result] theorem Equation511_not_implies_Equation3079 : ∃ (G : Type) (_ : Magma G), Facts G [511] [3079] := - ⟨ZMod 11, { op := fun x y => 9 * x + 3 * y }, by decide!⟩ - + ⟨Fin 11, { op := fun x y => 9 * x + 3 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance0 : ∃ (G : Type) (_ : Magma G), Facts G [1076] [26, 65, 73, 102, 117, 125, 160, 167, 212, 229, 258, 263, 335, 362, 429, 437, 464, 473, 504, 513, 546, 562, 617, 632, 640, 679, 704, 826, 833, 872, 879, 910, 917, 949, 962, 1029, 1046, 1085, 1110, 1119, 1226, 1231, 1278, 1323, 1455, 1482, 1491, 1518, 1526, 1632, 1654, 1658, 1662, 1682, 1721, 1729, 1790, 1838, 1850, 1861, 1873, 1885, 1897, 1925, 1967, 2044, 2053, 2060, 2100, 2125, 2267, 2300, 2328, 2330, 2449, 2457, 2470, 2485, 2503, 2533, 2541, 2586, 2653, 2663, 2672, 2699, 2744, 2850, 2863, 2875, 2910, 2939, 3053, 3058, 3066, 3075, 3079, 3083, 3094, 3113, 3271, 3279, 3343, 3352, 3459, 3474, 3482, 3518, 3526, 3558, 3607, 3668, 3675, 3761, 3871, 3888, 3924, 3954, 4068, 4073, 4127, 4131, 4135, 4146, 4157, 4290, 4321, 4369, 4383, 4408, 4443, 4585, 4636, 4656] := - ⟨ZMod 43, { op := fun x y => 17 * x + 27 * y }, by decide!⟩ + ⟨Fin 43, { op := fun x y => 17 * x + 27 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance1 : ∃ (G : Type) (_ : Magma G), Facts G [2531, 3103] [16, 55, 72, 118, 127, 167, 179, 209, 222, 228, 261, 274, 315, 384, 419, 436, 466, 474, 500, 513, 528, 575, 633, 642, 669, 677, 703, 833, 845, 883, 909, 916, 1026, 1039, 1045, 1075, 1086, 1098, 1122, 1184, 1229, 1242, 1279, 1325, 1434, 1444, 1452, 1482, 1525, 1647, 1655, 1682, 1691, 1722, 1731, 1764, 1780, 1840, 1851, 1885, 1898, 1913, 1921, 1934, 1949, 2054, 2061, 2101, 2125, 2137, 2254, 2263, 2304, 2327, 2450, 2467, 2497, 2506, 2540, 2650, 2660, 2699, 2710, 2722, 2737, 2743, 2776, 2865, 2873, 2903, 2912, 2936, 3056, 3068, 3079, 3091, 3115, 3143, 3185, 3261, 3278, 3306, 3334, 3353, 3414, 3475, 3484, 3556, 3675, 3687, 3748, 3868, 3881, 3887, 3951, 3962, 3973, 4023, 4071, 4084, 4130, 4164, 4275, 4307, 4321, 4409, 4443, 4479, 4605, 4636, 4684] := - ⟨ZMod 25, { op := fun x y => 12 * x + 14 * y }, by decide!⟩ + ⟨Fin 25, { op := fun x y => 12 * x + 14 * y }, by ringFin; ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance2 : ∃ (G : Type) (_ : Magma G), Facts G [2700] [47, 2035, 2847] := - ⟨ZMod 19, { op := fun x y => 14 * x + 8 * y }, by decide!⟩ + ⟨Fin 19, { op := fun x y => 14 * x + 8 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance3 : ∃ (G : Type) (_ : Magma G), Facts G [2866] [255, 307, 326, 2035, 2644, 3253, 3319, 3456, 3522] := - ⟨ZMod 23, { op := fun x y => 4 * x + 3 * y }, by decide!⟩ + ⟨Fin 23, { op := fun x y => 4 * x + 3 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance4 : ∃ (G : Type) (_ : Magma G), Facts G [3113] [3079] := - ⟨ZMod 41, { op := fun x y => 31 * x + 11 * y }, by decide!⟩ + ⟨Fin 41, { op := fun x y => 31 * x + 11 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance5 : ∃ (G : Type) (_ : Magma G), Facts G [882] [3862, 3915] := - ⟨ZMod 11, { op := fun x y => 6 * x + 7 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 6 * x + 7 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance6 : ∃ (G : Type) (_ : Magma G), Facts G [2264] [3050] := - ⟨ZMod 16, { op := fun x y => 5 * x + 6 * y }, by decide!⟩ + ⟨Fin 16, { op := fun x y => 5 * x + 6 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance7 : ∃ (G : Type) (_ : Magma G), Facts G [706] [47, 359, 375, 817, 1426, 3862, 3915, 4065, 4118] := - ⟨ZMod 17, { op := fun x y => 10 * x + 11 * y }, by decide!⟩ + ⟨Fin 17, { op := fun x y => 10 * x + 11 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance8 : ∃ (G : Type) (_ : Magma G), Facts G [464] [2457, 3066] := - ⟨ZMod 19, { op := fun x y => 3 * x + 17 * y }, by decide!⟩ + ⟨Fin 19, { op := fun x y => 3 * x + 17 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance9 : ∃ (G : Type) (_ : Magma G), Facts G [704] [203, 817, 1426, 3050] := - ⟨ZMod 23, { op := fun x y => 2 * x + 6 * y }, by decide!⟩ + ⟨Fin 23, { op := fun x y => 2 * x + 6 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance10 : ∃ (G : Type) (_ : Magma G), Facts G [2504] [23, 47, 1629, 1832, 3050, 3456, 3522, 4065, 4118] := - ⟨ZMod 27, { op := fun x y => 20 * x + 13 * y }, by decide!⟩ + ⟨Fin 27, { op := fun x y => 20 * x + 13 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance11 : ∃ (G : Type) (_ : Magma G), Facts G [2531] [16, 55, 72, 118, 127, 167, 179, 209, 222, 228, 261, 274, 315, 384, 419, 436, 466, 474, 500, 513, 528, 575, 633, 642, 669, 677, 703, 833, 845, 883, 909, 916, 1026, 1039, 1045, 1075, 1086, 1098, 1122, 1184, 1229, 1242, 1279, 1325, 1434, 1444, 1452, 1482, 1525, 1647, 1655, 1682, 1691, 1722, 1731, 1764, 1780, 1840, 1851, 1885, 1898, 1913, 1921, 1934, 1949, 2054, 2061, 2101, 2125, 2137, 2254, 2263, 2304, 2327, 2450, 2467, 2497, 2506, 2540, 2650, 2660, 2699, 2710, 2722, 2737, 2743, 2776, 2865, 2873, 2903, 2912, 2936, 3056, 3068, 3079, 3091, 3103, 3115, 3143, 3185, 3261, 3278, 3306, 3334, 3345, 3353, 3414, 3475, 3484, 3548, 3556, 3675, 3687, 3748, 3868, 3881, 3887, 3951, 3962, 3973, 4023, 4071, 4084, 4130, 4164, 4275, 4307, 4321, 4409, 4443, 4479, 4605, 4636, 4684] := - ⟨ZMod 43, { op := fun x y => 27 * x + 17 * y }, by decide!⟩ + ⟨Fin 43, { op := fun x y => 27 * x + 17 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance12 : ∃ (G : Type) (_ : Magma G), Facts G [2467] [3050, 3079] := - ⟨ZMod 7, { op := fun x y => 2 * x + 3 * y }, by decide!⟩ + ⟨Fin 7, { op := fun x y => 2 * x + 3 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance13 : ∃ (G : Type) (_ : Magma G), Facts G [412] [48, 413, 414, 415, 615, 818, 1427, 2240, 3254] := - ⟨ZMod 16, { op := fun x y => 3 * x + 14 * y }, by decide!⟩ + ⟨Fin 16, { op := fun x y => 3 * x + 14 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance14 : ∃ (G : Type) (_ : Magma G), Facts G [2903] [99, 411, 2035, 2644] := - ⟨ZMod 13, { op := fun x y => 6 * x + 10 * y }, by decide!⟩ + ⟨Fin 13, { op := fun x y => 6 * x + 10 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance15 : ∃ (G : Type) (_ : Magma G), Facts G [907] [255, 614, 1426] := - ⟨ZMod 17, { op := fun x y => 4 * x + 7 * y }, by decide!⟩ + ⟨Fin 17, { op := fun x y => 4 * x + 7 * y }, by ringFin; decideFin!⟩ +-- TODO: Here ringFin fails due to https://github.com/leanprover/lean4/issues/5630 +-- we can use it once that's fixed.How? @[equational_result] theorem LinearInvariance16 : ∃ (G : Type) (_ : Magma G), Facts G [667] [411, 2847, 3050, 4380] := - ⟨ZMod 25, { op := fun x y => 17 * x + 2 * y }, by decide!⟩ + ⟨Fin 25, { op := fun x y => 17 * x + 2 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance17 : ∃ (G : Type) (_ : Magma G), Facts G [511, 714, 1120, 2338] [3079] := - ⟨ZMod 29, { op := fun x y => 19 * x + 11 * y }, by decide!⟩ + ⟨Fin 29, { op := fun x y => 19 * x + 11 * y }, by ringFin; ringFin; ringFin; ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance18 : ∃ (G : Type) (_ : Magma G), Facts G [1289, 2507, 2913, 3116] [513] := - ⟨ZMod 27, { op := fun x y => 2 * x + 17 * y }, by decide!⟩ + ⟨Fin 27, { op := fun x y => 2 * x + 17 * y }, by ringFin; ringFin; ringFin; ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance19 : ∃ (G : Type) (_ : Magma G), Facts G [2670, 2866] [255, 307, 326, 3253, 3319, 3456, 3522] := - ⟨ZMod 27, { op := fun x y => 7 * x + 24 * y }, by decide!⟩ + ⟨Fin 27, { op := fun x y => 7 * x + 24 * y }, by ringFin; ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance20 : ∃ (G : Type) (_ : Magma G), Facts G [474] [513] := - ⟨ZMod 11, { op := fun x y => 10 * x + 2 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 10 * x + 2 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance21 : ∃ (G : Type) (_ : Magma G), Facts G [2328] [99, 1426] := - ⟨ZMod 29, { op := fun x y => 14 * x + 23 * y }, by decide!⟩ + ⟨Fin 29, { op := fun x y => 14 * x + 23 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance22 : ∃ (G : Type) (_ : Magma G), Facts G [670] [817] := - ⟨ZMod 11, { op := fun x y => 9 * x + 4 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 9 * x + 4 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance23 : ∃ (G : Type) (_ : Magma G), Facts G [3102] [270, 1238, 2087, 2696, 2899, 3065, 3139, 3176, 4080] := - ⟨ZMod 16, { op := fun x y => 10 * x + 7 * y }, by decide!⟩ + ⟨Fin 16, { op := fun x y => 10 * x + 7 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance24 : ∃ (G : Type) (_ : Magma G), Facts G [2937] [2644] := - ⟨ZMod 11, { op := fun x y => 4 * x + 9 * y }, by decide!⟩ + ⟨Fin 11, { op := fun x y => 4 * x + 9 * y }, by decideFin!⟩ @[equational_result] theorem LinearInvariance25 : ∃ (G : Type) (_ : Magma G), Facts G [2301] [3, 8, 23, 47, 99, 151, 203, 255, 307, 326, 359, 375, 411, 614, 817, 1020, 1083, 1223, 1286, 1426, 1629, 1832, 2035, 2441, 2504, 2644, 2847, 3050, 3253, 3319, 3456, 3522, 3659, 3715, 3722, 3862, 3915, 4065, 4118, 4380, 4435, 4470] := - ⟨ZMod 23, { op := fun x y => 2 * x + 7 * y }, by decide!⟩ + ⟨Fin 23, { op := fun x y => 2 * x + 7 * y }, by ringFin; decideFin!⟩ @[equational_result] theorem LinearInvariance26 : ∃ (G : Type) (_ : Magma G), Facts G [1279, 1286, 1288] [3, 8, 23, 47, 99, 151, 203, 255, 307, 326, 359, 375, 411, 614, 817, 1020, 1083, 1426, 1629, 1832, 2035, 2238, 2301, 2441, 2504, 2644, 2847, 3050, 3253, 3319, 3456, 3522, 3659, 3715, 3722, 3862, 3915, 4065, 4118, 4380, 4435, 4470] := - ⟨ZMod 11, { op := fun x y => 1 * x + 7 * y }, by decide!⟩ - + ⟨Fin 11, { op := fun x y => 1 * x + 7 * y }, by decideFin!⟩ diff --git a/equational_theories/MagmaLaw.lean b/equational_theories/MagmaLaw.lean index a600415c1..796ec89cd 100644 --- a/equational_theories/MagmaLaw.lean +++ b/equational_theories/MagmaLaw.lean @@ -101,16 +101,16 @@ def MagmaLaw.fmap {α β : Type} (f : α → β) (l : MagmaLaw α) : MagmaLaw β def MagmaLaw.symm {α : Type} (l : MagmaLaw α) : MagmaLaw α := {lhs := l.rhs, rhs:=l.lhs} @[simp] -theorem MagmaLaw.symm_symm {α : Type} (l : MagmaLaw α) : l.symm.symm = l := by - simp [symm] +theorem MagmaLaw.symm_symm {α : Type} (l : MagmaLaw α) : l.symm.symm = l := + rfl theorem satisfiesPhi_symm_law {α G : Type} [Magma G] (φ : α → G) (E : MagmaLaw α) - (h : satisfiesPhi φ E) : satisfiesPhi φ E.symm := by - simp only [satisfiesPhi, MagmaLaw.symm]; exact h.symm + (h : satisfiesPhi φ E) : satisfiesPhi φ E.symm := + h.symm theorem satisfiesPhi_symm {α G : Type} [Magma G] (φ : α → G) (w₁ w₂ : FreeMagma α) (h : satisfiesPhi φ (w₁ ≃ w₂)) : satisfiesPhi φ (w₂ ≃ w₁) := - Law.satisfiesPhi_symm_law φ (w₁ ≃ w₂) h + satisfiesPhi_symm_law φ (w₁ ≃ w₂) h theorem satisfies_symm_law {α : Type} (G : Type) [Magma G] (E : MagmaLaw α) (h : G ⊧ E) : G ⊧ E.symm := @@ -130,7 +130,7 @@ theorem models_symm_law {α} (Γ : Ctx α) (E : MagmaLaw α) (h : Γ ⊧ E) : Γ fun G [Magma G] hsatisfiesSet ↦ satisfies_symm_law G E (h G hsatisfiesSet) theorem models_symm {α} (Γ : Ctx α) (w₁ w₂ : FreeMagma α) (h : Γ ⊧ w₁ ≃ w₂) : Γ ⊧ w₂ ≃ w₁ := - Law.models_symm_law Γ (w₁ ≃ w₂) h + models_symm_law Γ (w₁ ≃ w₂) h def Fin.valHom {n} : FreeMagma (Fin n) →◇ FreeMagma ℕ := evalHom (Lf ∘ Fin.val) @@ -143,14 +143,11 @@ private def fin_split {n} {α} (hn : n ≠ 0) (f : Fin n → α) : ∃ g : ℕ theorem satisfies_fin_satisfies_nat {n : Nat} (hn : n ≠ 0) (G : Type) [Magma G] (E : MagmaLaw (Fin n)) : G ⊧ E ↔ G ⊧ E.fmap Fin.val := by - apply Iff.intro - · intro h φ - simp [satisfies, satisfiesPhi, MagmaLaw.fmap] at * - repeat rw [← evalInMagma_comp Fin.val φ] + apply Iff.intro <;> intro h φ; simp only [ne_eq, satisfies, satisfiesPhi, MagmaLaw.fmap] at * + · repeat rw [← evalInMagma_comp Fin.val φ] exact h (φ ∘ Fin.val) - · intro h φ - simp [satisfies, satisfiesPhi, MagmaLaw.fmap] at * - have ⟨φ', hφ'_val_eq_phi⟩ := fin_split hn φ + · simp only [ne_eq, satisfies, satisfiesPhi, MagmaLaw.fmap] at * + obtain ⟨φ', hφ'_val_eq_phi⟩ := fin_split hn φ have hφ' := h φ' repeat rw [← evalInMagma_comp Fin.val φ', hφ'_val_eq_phi] at hφ' exact hφ' diff --git a/equational_theories/Subgraph.lean b/equational_theories/Subgraph.lean index 5a3898827..954888f5c 100644 --- a/equational_theories/Subgraph.lean +++ b/equational_theories/Subgraph.lean @@ -4,6 +4,8 @@ import equational_theories.EquationalResult import equational_theories.Closure import equational_theories.Equations import equational_theories.FactsSyntax +import equational_theories.FreeSemigroup +import equational_theories.MagmaLaw /- This is a subproject of the main project to completely describe a small subgraph of the entire implication graph. The list of equations under consideration can be found at https://teorth.github.io/equational_theories/blueprint/subgraph-eq.html @@ -282,44 +284,68 @@ theorem Lemma_eq1689_implies_h8 (G: Type*) [Magma G] (h: Equation1689 G) : ∀ a /-- The below results for Equation1571 are out of order because early ones are lemmas for later ones -/ @[equational_result] -theorem Equation1571_implies_Equation2662 (G: Type*) [Magma G] (h: Equation1571 G) : Equation2662 G := - fun _ _ ↦ (h _ _ _).trans (congrArg _ (h _ _ _).symm) +theorem Equation1571_implies_Equation2662 (G: Type _) [Magma G] (h: Equation1571 G) : Equation2662 G := + fun x y ↦ Eq.trans (h x (x ◇ y) (x ◇ y)) (congrArg (fun z ↦ ((x ◇ y) ◇ (x ◇ y)) ◇ z) + (Eq.symm $ h x x y)) @[equational_result] -theorem Equation1571_implies_Equation40 (G: Type*) [Magma G] (h: Equation1571 G) : Equation40 G := by - have sqRotate (x y z : G) : (x ◇ y) ◇ (x ◇ y) = (y ◇ z) ◇ (y ◇ z) := - (congrArg (fun w ↦ (x ◇ y) ◇ (x ◇ w)) (Equation1571_implies_Equation2662 G h _ _)).trans - (h _ _ _).symm - exact fun x y ↦ h x x x ▸ h y y y ▸ (sqRotate _ _ _).trans (sqRotate _ _ _) +theorem Equation1571_implies_Equation40 (G: Type _) [Magma G] (h: Equation1571 G) : Equation40 G := by + have sqRotate : ∀ x y z : G, (x ◇ y) ◇ (x ◇ y) = (y ◇ z) ◇ (y ◇ z) := + fun x y z ↦ Eq.trans (congrArg (fun w ↦ (x ◇ y) ◇ (x ◇ w)) + (Equation1571_implies_Equation2662 G h y z)) (Eq.symm $ h ((y ◇ z) ◇ (y ◇ z)) x y) + have sqConstInImage : ∀ x y z w : G, (x ◇ y) ◇ (x ◇ y) = (z ◇ w) ◇ (z ◇ w) := + fun x y z w ↦ Eq.trans (sqRotate x y z) (sqRotate y z w) + exact fun x y ↦ h x x x ▸ h y y y ▸ sqConstInImage (x ◇ x) (x ◇ (x ◇ x)) (y ◇ y) (y ◇ (y ◇ y)) @[equational_result] -theorem Equation1571_implies_Equation23 (G: Type*) [Magma G] (h: Equation1571 G) : Equation23 G := by +theorem Equation1571_implies_Equation23 (G: Type _) [Magma G] (h: Equation1571 G) : Equation23 G := by refine fun x ↦ (h x (x ◇ x) (x ◇ x)).trans ?_ rw [← h x x x, ← Equation1571_implies_Equation40 G h x (x ◇ x)] @[equational_result] -theorem Equation1571_implies_Equation8 (G: Type*) [Magma G] (h: Equation1571 G) : Equation8 G := - fun x ↦ (h x x x).trans ((congrArg (· ◇ (x ◇ (x ◇ x))) (Equation1571_implies_Equation40 G h x - (x ◇ (x ◇ x)))).trans (Equation1571_implies_Equation23 G h (x ◇ (x ◇ x))).symm) +theorem Equation1571_implies_Equation8 (G: Type _) [Magma G] (h: Equation1571 G) : Equation8 G := + fun x ↦ Eq.trans (h x x x) (((congrArg (fun a ↦ a ◇ (x ◇ (x ◇ x)))) + (Equation1571_implies_Equation40 G h x (x ◇ (x ◇ x)))).trans + (((Equation1571_implies_Equation23 G h (x ◇ (x ◇ x))).symm).trans rfl)) @[equational_result] -theorem Equation1571_implies_Equation16 (G: Type*) [Magma G] (h: Equation1571 G) : Equation16 G := +theorem Equation1571_implies_Equation16 (G: Type _) [Magma G] (h: Equation1571 G) : Equation16 G := fun x y ↦ ((congrArg (fun w ↦ y ◇ (y ◇ w)) (Equation1571_implies_Equation8 G h x)).trans - (Equation1571_implies_Equation40 G h x y ▸ ((congrArg (· ◇ (y ◇ (x ◇ (y ◇ y))))) - (Equation1571_implies_Equation8 G h y)).trans (h x y (y ◇ y)).symm)).symm + ((Equation1571_implies_Equation40 G h x y ▸ ((congrArg (fun w ↦ w ◇ (y ◇ (x ◇ (y ◇ y))))) + (Equation1571_implies_Equation8 G h y)).trans (h x y (y ◇ y)).symm))).symm @[equational_result] -theorem Equation1571_implies_Equation43 (G: Type*) [Magma G] (h: Equation1571 G) : Equation43 G := by +theorem Equation1571_implies_Equation43 (G: Type _) [Magma G] (h: Equation1571 G) : Equation43 G := by refine fun x y ↦ (h _ (x ◇ x) (x ◇ (x ◇ y))).trans ?_ rw [← h x x y, ← Equation1571_implies_Equation23 G h x, ← Equation1571_implies_Equation16 G h y x, Equation1571_implies_Equation40 G h x y, ← Equation1571_implies_Equation23 G h y] @[equational_result] -theorem Equation1571_implies_Equation4512 (G: Type*) [Magma G] (h: Equation1571 G) : Equation4512 G := by +theorem Equation1571_implies_Equation4512 (G: Type _) [Magma G] (h: Equation1571 G) : Equation4512 G := by refine fun x y z ↦ (h (x ◇ (y ◇ z)) y x).trans ?_ rw [Equation1571_implies_Equation43 G h (x ◇ (y ◇ z)) x, ← Equation1571_implies_Equation16 G h (y ◇ z) x, ← Equation1571_implies_Equation16 G h z y, - Equation1571_implies_Equation43 G h y x] + Equation1571_implies_Equation43 G h y x] + +theorem ProveEquation1571Consequence {n : Nat} {G : Type _} [Magma G] (eq1571 : Equation1571 G) + (law : Law.MagmaLaw (Fin (n+1))) (eq : equation1571Reducer law.lhs = equation1571Reducer law.rhs) + : G ⊧ law := + fun _ ↦ (AbGrpPow2ImpliesEquation1571ReducerFaithful law.lhs _ + (Equation1571_implies_Equation4512 G eq1571) (Equation1571_implies_Equation43 G eq1571) + (Equation1571_implies_Equation16 G eq1571)).trans ((congrArg (evalInSgr _) eq).trans + (AbGrpPow2ImpliesEquation1571ReducerFaithful law.rhs _ + (Equation1571_implies_Equation4512 G eq1571) (Equation1571_implies_Equation43 G eq1571) + (Equation1571_implies_Equation16 G eq1571)).symm) + +/- Example usage of the general-purpose prover ProveEquation1571Consequence -/ +theorem Equation1571_implies_Equation3167 {G : Type} [Magma G] (h : Equation1571 G) : Equation3167 G := + fun x y z ↦ ProveEquation1571Consequence (n := 2) h + {lhs := Lf 0, rhs := (((Lf 1 ⋆ Lf 1) ⋆ Lf 2) ⋆ Lf 2) ⋆ Lf 0} rfl fun | 0 => x | 1 => y | 2 => z + +/- Example usage of the general-purpose prover ProveEquation1571Consequence -/ +theorem Equation1571_implies_Equation4656 {G : Type} [Magma G] (h : Equation1571 G) : Equation4656 G := + fun x y z ↦ ProveEquation1571Consequence (n := 2) h + {lhs := (Lf 0 ⋆ Lf 1) ⋆ Lf 1, rhs := (Lf 0 ⋆ Lf 2) ⋆ Lf 2} rfl fun | 0 => x | 1 => y | 2 => z /-- This result was first obtained by Kisielewicz in 1997 via computer assistance. -/ @[equational_result] @@ -390,6 +416,17 @@ theorem Equation4582_implies_Equation4564 (G: Type*) [Magma G] (h: Equation4582 theorem Equation4582_implies_Equation4579 (G: Type*) [Magma G] (h: Equation4582 G) : Equation4579 G := fun _ _ _ _ _ ↦ h _ _ _ _ _ _ +@[equational_result] +theorem Equation953_implies_Equation2 (G : Type _) [Magma G] (h: Equation953 G) : Equation2 G := by + intro x y + let i := x ◇ x + let n := i ◇ i + have znx (z : G) : z ◇ n = x := (h x z x).symm + have hzzi := h x x i + have hyzi := h y x i + rw [znx] at hzzi hyzi + exact hzzi.trans hyzi.symm + /- Obtained with lean-egg -/ @[equational_result] theorem Equation14_implies_Equation23 (G: Type*) [Magma G] (h: Equation14 G) : Equation23 G := @@ -423,7 +460,7 @@ theorem Equation2_implies_Equation5105 (G: Type _) [Magma G] (h: Equation2 G) : fun _ _ _ ↦ h _ _ @[equational_result] -theorem Equation2_implies_Equation28393 (G: Type _) [Magma G] (h: Equation2 G) : Equation28393 G := +theorem Equation2_implies_Equation28381 (G: Type _) [Magma G] (h: Equation2 G) : Equation28381 G := fun _ _ _ ↦ h _ _ @[equational_result] @@ -451,7 +488,7 @@ theorem Equation4_implies_Equation3744 (G: Type _) [Magma G] (h: Equation4 G) : _ = (x ◇ z) ◇ (w ◇ y) := h (x ◇ z) (w ◇ y) @[equational_result] -theorem Equation4_implies_Equation28393 (G: Type _) [Magma G] (h: Equation4 G) : Equation28393 G := +theorem Equation4_implies_Equation28381 (G: Type _) [Magma G] (h: Equation4 G) : Equation28381 G := fun x y z ↦ calc x _ = x ◇ x := (h x x) @@ -550,17 +587,6 @@ theorem Equation4579_implies_Equation4512 (G: Type _) [Magma G] (h: Equation4579 theorem Equation4579_implies_Equation4564 (G: Type _) [Magma G] (h: Equation4579 G) : Equation4564 G := fun _ _ _ _ ↦ h _ _ _ _ _ -@[equational_result] -theorem Equation953_implies_Equation2 (G : Type _) [Magma G] (h: Equation953 G) : Equation2 G := by - intro x y - let i := x ◇ x - let n := i ◇ i - have znx (z : G) : z ◇ n = x := (h x z x).symm - have hzzi := h x x i - have hyzi := h y x i - rw [znx] at hzzi hyzi - exact hzzi.trans hyzi.symm - /- Counterexamples -/ @[equational_result] diff --git a/home_page/_layouts/default.html b/home_page/_layouts/default.html index 809f2d113..825b04af2 100644 --- a/home_page/_layouts/default.html +++ b/home_page/_layouts/default.html @@ -31,7 +31,8 @@

{{ page.description | default: site.description | de Blueprint (pdf) Documentation Dashboard - Equation Viewer + Equation Explorer + Graphiti {% if site.github.is_project_page %} GitHub {% endif %} diff --git a/home_page/graphiti/.gitignore b/home_page/graphiti/.gitignore new file mode 100644 index 000000000..4d0c51e71 --- /dev/null +++ b/home_page/graphiti/.gitignore @@ -0,0 +1,2 @@ +*.swp +graph.json diff --git a/home_page/graphiti/index.html b/home_page/graphiti/index.html new file mode 100644 index 000000000..ba5ed3974 --- /dev/null +++ b/home_page/graphiti/index.html @@ -0,0 +1,727 @@ + + + + + + + Graphiti + + + + + + + + + + + + + +
+

+ Last updated at: (local time), Git + commit: +

+
+ + + + diff --git a/home_page/graphiti/logo.png b/home_page/graphiti/logo.png new file mode 100644 index 000000000..eff00e986 Binary files /dev/null and b/home_page/graphiti/logo.png differ diff --git a/home_page/implications/im-feeling-lucky.html b/home_page/implications/im-feeling-lucky.html new file mode 100644 index 000000000..45505dd5c --- /dev/null +++ b/home_page/implications/im-feeling-lucky.html @@ -0,0 +1,54 @@ +

Redirecting you to a random implication to prove...

+ + + + diff --git a/home_page/implications/index.html b/home_page/implications/index.html index e83103e72..34f25f7b3 100644 --- a/home_page/implications/index.html +++ b/home_page/implications/index.html @@ -3,7 +3,7 @@ - Advanced Equation Implication Table + Equation Explorer