QCpy-1(FR)correction-Modele_d-Ising.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f2cf11c7-5743-46ed-a465-d8a979365455",
   "metadata": {},
   "outputs": [
    {
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);\n",
       "    float:left;\n",
       "    margin-left:20px;\n",
       "    margin-right:20px;\n",
       "    margin-top:20px;\n",
       "    margin-bottom:20px;\n",
       "}\n",
       "div.todo{\n",
       "    font-size: 1.1em;\n",
       "    margin-top:40px;\n",
       "    background-color: #b2dbea80;\n",
       "}\n",
       "div.todo ul{\n",
       "    margin: 0.2em;\n",
       "}\n",
       "div.todo li{\n",
       "    margin-left:60px;\n",
       "    margin-top:0;\n",
       "    margin-bottom:0;\n",
       "}\n",
       "\n",
       "figure {\n",
       "    border: 0px;\n",
       "    text-align: center;\n",
       "    margin: 5px; /* adjust as needed */\n",
       "    display: block;\n",
       "    margin: auto;\n",
       "}\n",
       "figure img {\n",
       "    vertical-align: top;\n",
       "    text-align: center;\n",
       "    display: block;\n",
       "    margin: auto;\n",
       "}\n",
       "figure figcaption {\n",
       "    border: 0px;\n",
       "    text-align: center;\n",
       "    font-size: 11px;\n",
       "    margin: auto;\n",
       "}\n",
       "\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "**Start at:** Monday 17 June 2024, 15:14:03  \n",
       "**Hostname:** insa-20474 (Linux)"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "<p style=\"text-align: center\"><img width=\"800px\" src=\"./config/svg/pyPhysChemBanner.svg\" style=\"margin-left:auto; margin-right:auto\"/></p>"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "cwd0 = './config/'\n",
    "sys.path.append(cwd0)\n",
    "\n",
    "import visualID_Eng as vID\n",
    "from visualID_Eng import color\n",
    "vID.init(cwd0)\n",
    "\n",
    "__author__ = \"Matthieu CHARNAY, LPCNO (INSA-CNRS-UT3 lab, Toulouse, France)\""
   ]
  },
  {
   "attachments": {
    "fc1da901-be7b-45ea-bd18-98699fb891ea.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9adc5672-9506-414f-89c6-7c24b6dd5ea3",
   "metadata": {},
   "source": [
    "Le présent Jupyter Notebook est la correction des exercices trouvables __[ici](QCpy-1(FR)-Modele_d-Ising.ipynb)__.\n",
    "\n",
    "# Modèle d'Ising par les portes quantiques (CORRECTION)\n",
    "\n",
    "Nous allons ici modéliser le modèle d'Ising dans le cas 1D pseudo-infini en utilisant les portes quantiques.\n",
    "La résolution exacte du modèle est permise en ce qu'il est intégrable, ce qui n'est pas un élément universel - les résolutions exactes sont souvent limitées.\n",
    "\n",
    "Tout le processus est expliqué dans le papier : A. Cervera-Lierta, Quantum 2, 114 (2018)\n",
    "\n",
    "### Méthode\n",
    "\n",
    "La méthode est la même que celle utilisée pour la résolution analytique du problème.\n",
    "\n",
    "**Idée globale** : par une suite de transformations, passer d'un hamiltonien diagonal (dont on connaît aisément l'état fondamental) à l'hamiltonien de notre système ; cela permet d'en déduire l'état de plus faible énergie du système.\n",
    "\n",
    "**Résolution concrète** : en utilisant la réversibilité des opérateurs, l'on part en réalité de l'hamiltonien de notre modèle, que l'on cherchera à diagonaliser. On fixe ensuite les différents paramètre de sorte à le minimiser. Les différentes opérations utilisées n'auront ensuite plus qu'à être inversées.\n",
    "\n",
    "**Etapes successives** :\n",
    "\n",
    "- Etat initial : hamiltonien présentant les couplages entre premiers voisins.\n",
    "\n",
    "- Etape 1 : réaliser une transformée de Jordan-Wigner pour passer d'un état de particules à spin 1/2 à un état fermionique.\n",
    "\n",
    "- Etape 2 : réaliser une transformée de Fourier pour passer des modes fermioniques à l'espace des moments.\n",
    "\n",
    "- Etape 3 : réaliser une transformée de Bogoliubov pour découpler les termes de moments opposés.\n",
    "\n",
    "- Etat final : hamiltonien diagonal.\n",
    "\n",
    "### Traduction en portes quantiques\n",
    "\n",
    "L'étape 1 n'a aucun impact sur les coefficients des différents états de la fonction d'onde, elle n'utilise donc strictement aucune porte quantique. Cela est expliqué dans la __[fiche associée (Transformation de Jordan-Wigner)](./QCpy-additionalFiles/theoryReminderSheets(FR)/Transformation_de_Jordan-Wigner.pdf)__.\n",
    "\n",
    "L'étape 2 se base sur la méthode présentée dans les papiers : A. J. Ferris, Phys. Rev. Lett. 113, 010401 (2014) ; V. Murg, V. E. Korepin and F. Verstraete, Phys. Rev. B 86, 045125 (2012)\n",
    "Celle-ci est décrite en détail dans la __[fiche associée (Transformées de Fourier - équivalent FFT)](./QCpy-additionalFiles/theoryReminderSheets(FR)/Transformees_de_Fourier_Quantiques.pdf)__.\n",
    "\n",
    "L'étape 3 se base sur la méthode présentée dans le papier : V. Murg, V. E. Korepin and F. Verstraete, Phys. Rev. B 86, 045125 (2012)\n",
    "Elle est décrite en détail dans la __[fiche associée (Transformation de Bogoliubov)](./QCpy-additionalFiles/theoryReminderSheets(FR)/Transformation_de_Bogoliubov.pdf)__.\n",
    "\n",
    "### Comment utiliser ce Jupyter Notebook\n",
    "\n",
    "Nous allons ensemble apprendre les éléments fondamentaux de la programmation avec MyQLM en implémentant ces différentes étapes ainsi que tous les composants nécessaires. Les différents éléments de syntaxe pertinents à cet Jupyter Notebook apparaissent dans l'__[annexe de formation](QCpy-1(FR)appendix-Modele_d-Ising.ipynb)__, sous forme d'exemples variés et partiellement annotés. La combinaison du présent Jupyter Notebook et de son annexe permettent au lecteur autonome et néophyte l'apprentissage des bases de MyQLM.\n",
    "\n",
    "<hr style=\"border:2px solid gray\">\n",
    "\n",
    "## **Partie I** : la transformée de Fourier\n",
    "\n",
    "Réalisons maintenant le circuit de portes quantiques permettant de réaliser la Transformée de Fourier.\n",
    "\n",
    "### **A** - Définition des portes quantiques\n",
    "\n",
    "Afin de construire la Transformée de Fourier en un circuit compréhensible pour l'être humain, nous allons définir des portes quantiques abstraites. Composées d'un enchaînement de portes quantiques classiques, celles-ci allègent la lecture des circuit dans lesquels nous nous en servons, et permettent de résumer des sous-circuit en une boîte noire réalisant une fonction précise.\n",
    "\n",
    "#### 1) Préambule\n",
    "\n",
    "Avant de rentrer dans le vif du sujet, nous allons construire le circuit correspondant à l'une des portes quantiques dont nous nous servirons plus tard. Puis, par des tests successifs, nous allons en retrouver la matrice.\n",
    "\n",
    "**Q1)**\n",
    "\n",
    "**a)** Créer une *routine* contenant le circuit de la porte \"séparatrice de faisceaux\". Afficher le circuit obtenu.\n",
    "\n",
    "**b)** À l'aide d'un processeur quantique (*qpu*) virtuel obtenir la sortie par défaut de la porte quantique.\n",
    "\n",
    "**c)** Créer un *programme* en appliquant des portes \\[X] successivement sur les différentes entrées du circuit et en réutilisant la routine définie à la question 1) a) (voir effet des portes usuelles __[ici](./QCpy-additionalFiles/available_gates.ipynb)__), retrouver par cette méthode la matrice associée à la porte quantique \"séparatrice de faisceaux\".\n",
    "\n",
    "On donne le circuit de la porte :\n",
    "\n",
    "![circuitF2.png](attachment:fc1da901-be7b-45ea-bd18-98699fb891ea.png)\n",
    "\n",
    "Avec, par ordre d'apparition :\n",
    "- une porte CNOT\n",
    "- une porte de Hadamard contrôlée\n",
    "- une porte Z contrôlée\n",
    "\n",
    "Le point noir sur le schéma indique le qubit de contrôle.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Rappel :</b> Une routine est une instance indépendante d'un circuit quantique, elle a la particularité d'être faite pour être réutilisée dans d'autres circuits quantiques, en l'appelant comme une porte quantique. Elle se définit en utilisant le décorateur @qrout sur une procédure (fonction sans return) appliquant des portes quantiques. Plus de détails sont disponibles dans la documentation MyQLM.\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-block alert-warning\">\n",
    "<b>Attention :</b> L'affichage de la porte Z contrôlée peut varier et prendre la forme de deux points noirs reliés ; il ne s'agit pas d'une erreur, la porte reste fonctionnelle. Il faut cependant faire attention à l'avoir bien définie dans le bon sens (quel qubit contrôle quel autre).\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aec2e1c1-4be1-4571-ae19-9ef8531570a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qat.lang import qrout, CNOT, H, Z\n",
    "\n",
    "#Code de la question 1) a) Créer une routine contenant le circuit de la porte \"séparatrice de faisceaux\". Afficher le circuit obtenu.\n",
    "\n",
    "@qrout\n",
    "def routine():\n",
    "    CNOT(0,1)\n",
    "    H.ctrl()(1,0)\n",
    "    CNOT(0,1)\n",
    "    Z.ctrl()(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afe93e21-1f81-4bc6-8507-0cf52c8a4d72",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Conseil :</b> Le résultat d'une soumission à un processeur quantique virtuel est une liste d'objets qat.core.Result ; ces derniers contiennent de multiple champs. Dans un premier temps, nous conseillons pour chaque objet dans cette liste d'utiliser la commande print(\"Etat %s, amplitude %s, probabilité %s\"%(res.state, res.amplitude, res.probability)). Plus de détails sont disponibles dans la documentation MyQLM.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cdee7554-27f2-4dc0-bca7-a9b8895081d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Etat |00>, amplitude (1+0j), probabilité 1.0\n"
     ]
    }
   ],
   "source": [
    "from qat.qpus import get_default_qpu\n",
    "\n",
    "#Code de la question 1) b) À l'aide d'un processeur quantique (qpu) virtuel obtenir la sortie par défaut de ce circuit quantique.\n",
    "\n",
    "qpu=get_default_qpu()\n",
    "results=qpu.submit(routine.to_job())\n",
    "for res in results :\n",
    "    print(\"Etat %s, amplitude %s, probabilité %s\"%(res.state, res.amplitude, res.probability))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21d3e4ce-974c-4427-bcf7-52528ed1f948",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Conseil :</b> Un programme est une instance indépendante d'un circuit quantique, qui ne peut être incluse dans un autre. Il se définit en appelant l'initialisateur de la classe Program : Program(). Plus de détails sont disponibles dans la documentation MyQLM.\n",
    "\n",
    "Dans le cas de cette question, veuillez définir un seul programme en mettant ou non en commentaire les commandes de la porte quantique X sur les qubits.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fee0681e-5e3b-4d1f-a753-2f20a33ab667",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Etat |01>, amplitude (0.7071067811865475+0j), probabilité 0.4999999999999999\n",
      "Etat |10>, amplitude (-0.7071067811865475+0j), probabilité 0.4999999999999999\n"
     ]
    }
   ],
   "source": [
    "from qat.lang import Program, X\n",
    "\n",
    "#Code et réponse pour la question 1) c) Créer un programme en appliquant des portes [X] successivement sur les différentes entrées du circuit \n",
    "#celui-ci doit réutiliser la routine définie à la question 1) a)\n",
    "#retrouver par cette méthode la matrice associée à la porte quantique \"séparatrice de faisceaux\".\n",
    "\n",
    "prog=Program()\n",
    "qreg=prog.qalloc(2)\n",
    "X(qreg[0])\n",
    "#X(qreg[1])\n",
    "routine()(qreg)\n",
    "results=qpu.submit(prog.to_circ().to_job())\n",
    "for res in results :\n",
    "    print(\"Etat %s, amplitude %s, probabilité %s\"%(res.state, res.amplitude, res.probability))\n",
    "\n",
    "# Connaissant les composantes successives des vecteurs sur deux qubits : |00>, |01>, |10>, |11>\n",
    "# Redonner ici les coefficients de la matrice :\n",
    "#\n",
    "# ( 1    0          0      0 )\n",
    "# ( 0 1/sqrt(2)  1/sqrt(2) 0 )\n",
    "# ( 0 1/sqrt(2) -1/sqrt(2) 0 )\n",
    "# ( 0    0          0     -1 )\n",
    "#\n",
    "# On rappelle : 1/sqrt(2)≈0,7071 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e38a5c55-55eb-4520-9b14-9a57a924ddd1",
   "metadata": {},
   "source": [
    "#### 2) Construction des portes quantiques\n",
    "\n",
    "Nous allons maintenant pouvoir construite des \"portes abstraites\", c'est à dire des portes n'existant pas nativement dans les ordinateurs quantiques, mais que nous définissons par soucis de clarté des circuits que nous construisons. Nous allons implémenter les différentes portes de la transformée de Fourier, et ce de manières variées.\n",
    "\n",
    "**Q2)**\n",
    "\n",
    "**a)** Créer une fonction qui *retourne une routine* construisant le circuit de la porte \"séparatrice de faisceaux\" vu précédemment.\n",
    "\n",
    "**b)** Créer une porte abstraite (F2) ayant cette fonction comme valeur du paramètre \"circuit_generator\".\n",
    "\n",
    "**c)** Créer une fonction à deux paramètres (n,k) entiers, qui retourne la matrice de la porte \"retard de phase\" décrite dans __[cette fiche](./QCpy-additionalFiles/theoryReminderSheets(FR)/Transformees_de_Fourier_Quantiques.pdf)__.\n",
    "\n",
    "**d)** Créer une porte abstraite (RP) ayant cette fonction comme valeur du paramètre \"matrix_generator\".\n",
    "\n",
    "**e)** Créer une porte abstraite (fSWAP) ayant une fonction lambda comme paramètre \"matrix_generator\", cette fonction lambda retourne la matrice de la porte \"fSWAP\" décrite dans __[cette fiche](./QCpy-additionalFiles/theoryReminderSheets(FR)/Transformees_de_Fourier_Quantiques.pdf)__.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Rappel :</b> Il est possible de créer un objet routine en appelant l'initialisateur de la classe QRoutine : QRoutine(), puis en allouant des qubits à celle-ci (QRoutine.new_wires(int:n)) et en leur appliquant des portes quantiques (QRoutine.apply(...)).\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a9062de6-f2c0-44d5-83fc-0f681cedc3c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Code de la question 2) a) Créer une fonction qui retourne une routine construisant le circuit de la porte \"séparatrice de faisceaux\" vu précédemment.\n",
    "\n",
    "def F2_generator():\n",
    "    rout = QRoutine()\n",
    "    qreg = rout.new_wires(2)\n",
    "    routine()(qreg)\n",
    "    return rout"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cff127d7-d443-401a-98b7-e25f41ff2b30",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Conseil :</b> Une porte abstraite peut être définie : sans implémentation (auquel cas les calculs par qpu seront impossibles) ; avec un circuit_generator (qui définit le circuit interne de la porte abstraite) ; avec un matrix_generator (qui décrit directement l'effet de la porte sur les qubits).\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e4a89369-ad03-4a85-8f9d-f2f50df05512",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qat.lang.AQASM import *\n",
    "\n",
    "#Code de la question 2) b) Créer une porte abstraite (F2) ayant cette fonction comme valeur du paramètre \"circuit_generator\"\n",
    "\n",
    "F2 = AbstractGate(\"F2\",[],arity=2,circuit_generator=F2_generator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "188b6448-8305-45b0-bbbe-e71b0077bc74",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "#Code de la question 2) c) Créer une fonction à deux paramètres (n,k) entiers, qui retourne la matrice de la porte \"retard de phase\"\n",
    "\n",
    "def RP_generator(n,k):\n",
    "    return(np.array([[1, 0],\n",
    "                    [0, np.exp(2*np.pi*1j*k/n)]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d22e182b-4ddd-4561-9fbe-92b40a9ec3a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Code de la question 2) d) Créer une porte abstraite (RP) ayant cette fonction comme valeur du paramètre \"matrix_generator\".\n",
    "\n",
    "RP = AbstractGate(\"RP\",[int,int],arity=1,matrix_generator=RP_generator)\n",
    "\n",
    "#Par soucis de simplicité, nous avons systématiquement nommé les portes abstraites de la même manière que leur nom d'affichage ; cela n'est pas obligatoire"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dc8c44f-f428-4db7-9f64-20044f0ff2af",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Rappel :</b> Les fonctions lambda sont natives à Python. Il s'agit de petites fonctions anonymes pouvant prendre n'importe quel nombre d'argument, mais n'ayant qu'une unique expression en retour. La syntaxe est telle que ci-dessous :\n",
    "\n",
    "lambda *arguments* : *expression*\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f0749642-a2d0-4ea4-bb90-f837f07492b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Code de la question 2) e) Créer une porte abstraite (fSWAP) ayant une fonction lambda comme paramètre \"matrix_generator\"\n",
    "\n",
    "fSWAP = AbstractGate(\"fSWAP\",[],arity=2,matrix_generator=lambda:np.array([[1,0,0,0],\n",
    "                                                                         [0,0,1,0],\n",
    "                                                                         [0,1,0,0],\n",
    "                                                                        [0,0,0,-1]]))"
   ]
  },
  {
   "attachments": {
    "c4edabc1-1f37-4204-800d-812ea389d0f1.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "06e3f992-2169-4f82-80c6-be9fc15abfb9",
   "metadata": {},
   "source": [
    "### **B** - Construction de la Transformée de Fourier Quantique (équivalent FFT)\n",
    "\n",
    "Finalement, après avoir défini toutes nos portes abstraites, il ne nous reste plus qu'à les combiner pour former la Transformée de Fourier Quantique. Dans un premier temps, nous nous intéresserons au cas à 4 qubits, puis nous nous pencherons sur le cas à N qubits.\n",
    "\n",
    "#### 1) Transformée à 4 qubits\n",
    "\n",
    "**Q3)** À l'aide du schéma ci-dessous de la décomposition de la Transformée de Fourier à 4 qubits, et par la méthode de votre choix, utilisez les portes quantiques préalablement définies pour reproduire cette structure.\n",
    "\n",
    "![QFFT4qubits_bis.png](attachment:c4edabc1-1f37-4204-800d-812ea389d0f1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c9a51490-d2d4-4afb-97c6-c4f8e442c7ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    font-family: \"STIXMathJax_Main-Italic\"; \n",
       "    src: 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\"); \n",
       "}\n",
       "]]></style></defs><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"37\">Q0</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"456\" y1=\"32\" y2=\"32\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"69\">Q1</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"456\" y1=\"64\" y2=\"64\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"101\">Q2</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"456\" y1=\"96\" y2=\"96\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"133\">Q3</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"456\" y1=\"128\" y2=\"128\" /><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"61\" x=\"60\" y=\"52\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"85\">fSWAP</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"131\" y=\"20\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"139\" y=\"53\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"131\" y=\"84\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"139\" y=\"117\">F2</text><rect fill=\"white\" height=\"24\" stroke=\"black\" stroke-width=\"2\" width=\"77\" x=\"175\" y=\"84\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"183\" y=\"101\">RP [4, 0]</text><rect fill=\"white\" height=\"24\" stroke=\"black\" stroke-width=\"2\" width=\"77\" x=\"175\" y=\"116\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"183\" y=\"133\">RP [4, 1]</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"61\" x=\"262\" y=\"52\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"270\" y=\"85\">fSWAP</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"333\" y=\"20\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"341\" y=\"53\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"333\" y=\"84\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"341\" y=\"117\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"61\" x=\"377\" y=\"52\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"385\" y=\"85\">fSWAP</text></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Code de la question 3) utilisez les portes quantiques préalablement définies pour reproduire la Transformée de Fourier Quantique à 4 qubits\n",
    "\n",
    "prog=Program()\n",
    "qreg=prog.qalloc(4)\n",
    "\n",
    "fSWAP()(qreg[1:3])\n",
    "for i in range(2):\n",
    "    F2()(qreg[2*i:2*i+2])\n",
    "for i in range(2):\n",
    "    RP(4,i)(qreg[i+2])\n",
    "fSWAP()(qreg[1:3])\n",
    "for i in range(2):\n",
    "    F2()(qreg[2*i:2*i+2])\n",
    "fSWAP()(qreg[1:3])\n",
    "\n",
    "circ=prog.to_circ()\n",
    "circ.display()"
   ]
  },
  {
   "attachments": {
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     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9d13e535-8c3d-4c27-81d2-8a1402e224c1",
   "metadata": {},
   "source": [
    "\n",
    "#### 2) Transformée à N qubits\n",
    "\n",
    "Nous donnons ci-dessous le programme permettant de réaliser le circuit pour N qubits (puissance de 2), et donnons le schéma du résultat attendu pour N=16. Plusieurs sous-fonctions doivent être réalisées, ce sans quoi le programme principal ne fonctionne pas.\n",
    "\n",
    "(ici la nom des portes \"RP\" a été changé en \"ω\" par soucis de légèreté de la lecture)\n",
    "\n",
    "![QFFT16qubits.png](attachment:c7a436b6-5b1e-48fe-a81f-6c1029de5b42.png)\n",
    "\n",
    "**Q4)** \n",
    "\n",
    "**a)** À l'aide du schéma ci-dessus, compléter la fonction \"F2Build\". Cette fonction construit un mur de portes F2 : du premier jusqu'au dernier qubits.\n",
    "\n",
    "*(optionnel)* **b)** Toujours à l'aide du schéma ci-dessus, prendre successivement deux fermions (sur les qubits 7 et 8 par exemple) et trouver la suite de portes que ceux-ci subissent (rappel : une porte fSWAP va échanger la position de deux fermions)\n",
    "\n",
    "**c)** À l'aide du schéma ci-dessus, compléter la fonction \"fSwapTriangleBuild\". Cette fonction construit une structure en triangle de portes fSWAP. \n",
    "\n",
    "**d)** Définir une porte quantique ayant la QFFT (ou \"Transformée de Fourier Rapide Quantique\" - nom non officiel) comme générateur de circuit.\n",
    "\n",
    "**e)** Définir un *programme* qui utilise cette porte quantique sur 16 qubits. Afficher la programme avec un appel à la méthode Circuit.display() sans paramètres.\n",
    "\n",
    "**f)** Ajouter le paramètre \"depth\" dans la méthode display. Faire varier sa valeur à partir de 0. Que permet-il ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "15ac7f7d-cdc1-4f6b-852f-19441541650f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import log2\n",
    "\n",
    "def QFFTfunction(n):\n",
    "    qrout = QRoutine()\n",
    "    qreg = qrout.new_wires(n)\n",
    "    listPhaseDelay=[0]\n",
    "    for i in range(1,int(log2(n))):\n",
    "        fSwapWallBuild(n,i,qrout,qreg,False)\n",
    "        F2Build(n,qrout,qreg)\n",
    "        for k in range(2**(i-1)):\n",
    "            for j in range(int((2*k+1)*n/(2**i)),int((2*k+2)*n/(2**i))):\n",
    "                qrout.apply(RP(2**(i+1),listPhaseDelay[k]+(j%2)*(2**(i-1))),qreg[j])\n",
    "        fSwapWallBuild(n,i,qrout,qreg,True)\n",
    "        for t in range(len(listPhaseDelay)):\n",
    "            listPhaseDelay=listPhaseDelay[0:2*t+1]+[listPhaseDelay[2*t]+2**(i-1)]+listPhaseDelay[2*t+1:]\n",
    "    F2Build(n,qrout,qreg)\n",
    "    fSwapWallBuild(n,1,qrout,qreg,False)\n",
    "    return(qrout)\n",
    "\n",
    "def fSwapWallBuild(n,step,qrout,qreg,inverse):\n",
    "    for i in range(2**(step-1)):\n",
    "        fSwapTriangleBuild(n/(2**(step-1)),qrout,qreg[int(i*n/(2**(step-1))):int((i+1)*n/(2**(step-1)))],inverse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1f4a8a79-bbea-4420-9ad3-a19b1a5b2a88",
   "metadata": {},
   "outputs": [],
   "source": [
    "#fonction à compléter pour la question 4) a) ; cette fonction construit un mur de portes F2 : du premier jusqu'au dernier qubits\n",
    "#voir case ci-dessous pour tester vos fonctions\n",
    "\n",
    "def F2Build(n,qrout,qreg):\n",
    "    r\"\"\" n : nombre de qubits concernés, qrout : routine dans laquelle écrire les portes, qreg : registre des qubits concernés (taille n)\n",
    "    Cette fonction construit un mur de portes F2, du premier jusqu'au dernier qubits, tous subissent la porte F2 deux à deux.\n",
    "    \"\"\"\n",
    "    for k in range(0,int(n/2)):\n",
    "        qrout.apply(F2(),qreg[2*k:2*k+2])\n",
    "\n",
    "#fonction à compléter pour la question 4) c) ; cette fonction construit une structure en triangle de portes fSWAP\n",
    "#voir case ci-dessous pour tester vos fonctions\n",
    "\n",
    "def fSwapTriangleBuild(n,qrout,qreg,inverse):\n",
    "    r\"\"\" n : nombre de qubits concernés, qrout : routine dans laquelle écrire les portes, qreg : registre des qubits concernés (taille n)\n",
    "    Cette fonction construit un triangle de portes fSWAP : partant d'une porte entre les deux qubits centraux, puis deux portes, etc... \n",
    "    seuls le premier et le dernier qubit ne sont pas concernés par les portes fSWAP\n",
    "    Le sens est inversé si le paramètre inverse vaut True : l'on finira le triangle par sa pointe\n",
    "    \"\"\"\n",
    "    for t in range(1,int(n/2)):\n",
    "        i=t\n",
    "        if(inverse==True):\n",
    "            i=int(n/2)-t\n",
    "        pos=int(n/2)-i\n",
    "        for j in range(i):\n",
    "            qrout.apply(fSWAP(),qreg[pos+2*j],qreg[pos+1+2*j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "77ca6fff-0fcb-473a-93d7-63cb483fc927",
   "metadata": {},
   "outputs": [
    {
     "data": {
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AAAAAAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZGhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj9AQUJDREVGR0hJSktMTU5PUFFSU1RVVldYWVpbXF1eXwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAL9mAGFjAAAAAAAAZ2QAAAAAAAAAYmjFAACbAAAAiwAAAAAAAAAAAAAAAGAAAAAAALm6vb67vAAAAADCAAAAAADAaQAAAAAAAAAAAAAAAAAAAAAAAABsbnNlcHFyAAAAbwAAAAMAAP/vq4X/tQAyAAAAAAAAAAAAAAAAAAAAAAAAAAABAAQEAAEBARhTVElYTWF0aEpheF9NYWluLUl0YWxpYwABAgABADb4awD4bAH4bQL4bgP4bwQe4Woz/wwCWQwD/Fn7Zvoe+cgFHAUnDxwAABAcBroRHAAxHE0hEgBVAgABAAgADwAWAB0AJAArADIAOQBAAEcATgBVAFwAYwBqAHEAeAB/AIYAjQCUAJsAogCpALAAtwC+AMUAzADTANoA4QDoAO8A9gD9AQQBCwESARkBIAEnAS4BNQE8AUMBSgFRAVgBXwFmAW0BdAF7AYIBiQGQAZcBngGlAawBswG6AcEByAHPAdYB3QHkAesB8gH5AgACBwIOAhUCHAIjAioCMQI2A+0EBAQVBBt1bmkwMEEwdW5pMDEyN3VuaTAyMzd1bmkwMzkxdW5pMDM5MnVuaTAzOTN1bmkwMzk0dW5pMDM5NXVuaTAzOTZ1bmkwMzk3dW5pMDM5OHVuaTAzOTl1bmkwMzlBdW5pMDM5QnVuaTAzOUN1bmkwMzlEdW5pMDM5RXVuaTAzOUZ1bmkwM0EwdW5pMDNBMXVuaTAzQTN1bmkwM0E0dW5pMDNBNXVuaTAzQTZ1bmkwM0E3dW5pMDNBOHVuaTAzQTl1bmkwM0IxdW5pMDNCMnVuaTAzQjN1bmkwM0I0dW5pMDNCNXVuaTAzQjZ1bmkwM0I3dW5pMDNCOHVuaTAzQjl1bmkwM0JBdW5pMDNCQnVuaTAzQkN1bmkwM0JEdW5pMDNCRXVuaTAzQkZ1bmkwM0MwdW5pMDNDMXVuaTAzQzJ1bmkwM0MzdW5pMDNDNHVuaTAzQzV1bmkwM0M2dW5pMDNDN3VuaTAzQzh1bmkwM0M5dW5pMDNEMHVuaTAzRDF1bmkwM0QydW5pMDNENXVuaTAzRDZ1bmkwM0Q4dW5pMDNEOXVuaTAzREF1bmkwM0RCdW5pMDNEQ3VuaTAzRER1bmkwM0RFdW5pMDNERnVuaTAzRTB1bmkwM0UxdW5pMDNGMHVuaTAzRjF1bmkwM0Y0dW5pMDNGNXVuaTAzRjZ1bmkyMDNFdW5pMjBEN3VuaTIxMTN1bmkyMjAydW5pMjRDOHVuaUVGRkR1bmlFRkZFdW5pRUZGRjEuMS4xQ29weXJpZ2h0IChjKSAyMDAxLTIwMTEgYnkgdGhlIFNUSSBQdWIgQ29tcGFuaWVzLCBjb25zaXN0aW5nIG9mIHRoZSBBbWVyaWNhbiBDaGVtaWNhbCBTb2NpZXR5LCB0aGUgQW1lcmljYW4gSW5zdGl0dXRlIG9mIFBoeXNpY3MsIHRoZSBBbWVyaWNhbiBNYXRoZW1hdGljYWwgU29jaWV0eSwgdGhlIEFtZXJpY2FuIFBoeXNpY2FsIFNvY2lldHksIEVsc2V2aWVyLCBJbmMuLCBhbmQgVGhlIEluc3RpdHV0ZSBvZiBFbGVjdHJpY2FsIGFuZCBFbGVjdHJvbmljIEVuZ2luZWVycywgSW5jLiAgUG9ydGlvbnMgY29weXJpZ2h0IChjKSAxOTk4LTIwMDMgYnkgTWljcm9QcmVzcywgSW5jLiAgUG9ydGlvbnMgY29weXJpZ2h0IChjKSAxOTkwIGJ5IEVsc2V2aWVyLCBJbmMuICBBbGwgcmlnaHRzIHJlc2VydmVkLgpDb3B5cmlnaHQgKGMpIDIwMTMgVGhlIE1hdGhKYXggQ29uc29ydGl1bVNUSVhNYXRoSmF4X01haW4tSXRhbGljU1RJWCBNYXRoSmF4IE1haW5JdGFsaWMAAAAAAQACAAMABAAFAAYABwBoAAkACgALAAwADQAOAA8AEAARABIAEwAUABUAFgAXABgAGQAaABsAHAAdAB4AHwAgACEAIgAjACQAJQAmACcAKAApACoAKwAsAC0ALgAvADAAMQAyADMANAA1ADYANwA4ADkAOgA7ADwAPQA+AD8AQAB8AEIAQwBEAEUARgBHAEgASQBKAEsATABNAE4ATwBQAFEAUgBTAFQAVQBWAFcAWABZAFoAWwBcAF0AXgBfAYcAYgBkAGYAgwCAAKEAfQCYAHIApwGIAJEBiQB+AIgAgQCCAIQAfwGKAYsBjAGNAY4BjwGQAZEBkgGTAZQBlQGWAZcBmAGZAZoBmwGcAZ0BngGfAaABoQGiAaMBpAGlAaYBpwGoAakBqgGrAawBrQGuAa8BsAGxAbIBswG0AbUBtgG3AbgBuQG6AbsBvAG9Ab4BvwHAAcEBwgHDAcQBxQHGAccByAHJAcoBywHMAc0BzgBvAIkAQQAIAGkAdwBwAHEBzwBjAdAB0QHSAdMB1AHVAdYAygIAAQAEAAcATwCRAPIBjwJYAyUDSwODA8MEmwTABMwE4QUBBRgFdwXQBjIGtgbtB0YHugfkCGwI6wkdCTwJWQl3CZUKEArVCvELDAt3C+sL/Qx7DRQNJw03DZUNpQ38DgwOJA45DlAO+g+CEBcQJhCoEPkRfhGNEgASDxJHEl8SlhK4EscS7xOHE/4UWxT/FWIV5Ba1Fz8XZxeUGBcYbhlFGeQZ/RqPGwYbaBv4HGUdAB14Hhoewx9SH8AgKyBBIK0g7yDyIaEiQiMrI0MjWCOQI7UkQSRjJOolhyXeJfMmECYrJlImZCaeJugnBCcfJ3cnmSerJ7onzShHKFcoZyi2KMYo3ilzKYgp9ioNKlgqZyr0K4ormSw9LMYtQC3bLiwunS8jL5kwMzCkMLcxMzGlMisydDMPMygzpjQPNF40sDUDNXg1/zZwNvM3pzg6OPE5gzoFOqg7BDtHO708RjyrPNM9Vj16Peo+QT6wPxA/XT/BQCZAOUBOQGBAckCMQKZBUkJmQnVCiUK8Q0RDtUSNRKdEwETP+IQO+5IO+z+A9fi8nwGy9QP3HfdFFcf3OKHBue2qzZOmi6mLrXucb4tli3lsfjZ1+yKDZmL7Ugik+yEVqHakbG9xc29sn3SpqaWjpx4ON/kanwH37vg5Fcb3FKbUi5uLm3uXeotyi3R8hXCGc4I8gycI+zAWxvcTptWLm4ubfJd6i3KLc3yFcIZzgjyDJwgOiIuf91XB9yPBAfiw+GQVLIvb92hOizv7aPsWi9v3aE6LO/toIYuAVeyLVfsjIYuAVeuLBTv7acmL2vdp9xaLO/tpyYva92nzi5bBLYvB9yPziwX7ORZV+yP7FovB9yMFDoufAfcP2fdH1gP4hfj3FWuiYZ1clgibz2mLekx5iwVCi2CCYV5xb3tsi1yLP7Bj7UwIRvu9BT2ja6yG9Ah7iHH7DwWva8J0xYAIdTCui6DkBeGLq5DCtbaso76Lxovgcq77CeEIw/eBBcp0n2aNQQiaiQX7GfckFVT7cwVOsHiqi7kIw7nA1B5s++MVkYYFz1OceYtRizRWWyGCCA73j3im97qnh6b3eqW6nxLb0vdRo8PT91KiE9+A+VX3aRXVaLZOKy4jID3AT88e4dn3A/cNH3SNFSFKJkZrc6iyHovPreO3upeZoJSbiwixpGhXH2H4fxVfBi8yfoNNi2aLc5VoqHChf5F2iwglMCf7BR8TN4A9vlDOHqyLpZampbu4q9aL0YubipaInKuAnYili8CLqpmwtgj8Hv0muosF9xb43xX7B04mRGl0p7Uei8Kcxqq8n6yWlbSfnHmYgpmEoIGPhItuCA73pnm8Wr/47KsS1+n3Ltz3BNATvPlcyhVzdHSCdItci2imY86ps6evp7W+1pWVvZAInPtQeAeziJaEi3WLaHpqTURsvGbiePDIqqecpqOwq56vi64IwGG0TilOPvsJHouAi2KSYSZfYHhnblpjcVOLVAgTXCrSU/cDHsuLw5zayQgTvLNWvXG3i8WLtZyrwAj7YvicFYtZdWI2Voepip+LpQjkrLSzpJl1Yx4TXDr8cxVbZmN1WYs8i1q/i9WL2c3Q7LEIr/sTrDmtYAgO+7b5Gp8B9y/4ORXG9xOm0oubi5t+mnWLbot6eoZ1hXOCOYMnCA77P/kdnwG10AP3wvkxFS83VFdkTFc2dSWLJIv7FK77FsskCJ2RBWbxgMiL7Iv3YL/3cfcs9yQIDvs/+R2fAfdw0AP3P/ksFa06mjqLJ4stefsHbCtpIWZINzIImHwF5tq/w7LOveGn6ovwi8GExX/DetV7slzfCA75Gp8B99z4XxW2ppyTupG2kJmbi6GLoX+cdIt+i4GHfHpVUomJX26LupGklasIkqOPmIuWCKJ+nXRygXpyHouCjX6Rd5ldj3mLYGSieJtqsHeifpN7i3eLfniLd4tzn3y0hgi1hq16nIEIl4QFYHF9hVyDYIR4eotzi3abgJ6LnIucl5ygp66XlKqelJCPjY6OCItYhnJ+Z4R2iICLggh1lnulp5Sbox6LlImShZ18tYehisAInX4FqnWZhKVqnnSXgpqLoYubl4uki6J4ml6Ra494lX+RCA73P4uf91zNAffFzQP44vdwFc37b/dwSftw+29J92/7cM33cAcO+5LSywOQ+xUVIAoO+z/3VMoB9673kxX7b4t9TPdwiwUO+5KA9wMBpvcDA/cethWqcaVtbXJya26kcqerpaOpHg77dnmf+RifAfgW+S4VQov8Dv1A1IsFDoSn+QenAava98faA/iF+D0V9zZS5CX7Mfsp+3X7f/sfwzfxHrWLtpm0qPLU2fc9i/cnCDzoFYv7FmT7OVElZkldaV2LW4tqvYvgi/a+91i/6a/Msqm4i8eLo1mLOwgOi58B+CX5OBU+e4eNM3gIdIaLfAWejKGMnYsIjgahmH94H4uEiIGGeAj7HPx8BYBldYA8hQh896uadgdfdZSiH4uVlrKSpAj3I/ibBY+ZjZWLkAiPiY6IHg6L1/ij1AH4AuED8PiPFa7OvqjHi9qLs1eLRot1iHiFfnNVXkxJRQj7Zvt0i3r39ou99xp6kgVzWXd8UIsI+0mQBvdQ91QF9wr3Daq5i86L6knVK4tdi2B/ZG1ocHRpc1AIDoSx+O+1EvfZ23DiE9D3RvjLFa+6rJ+2i8CLrmeLVIthd2hhbmBtYX0xewh7owcT4OvLWfsAH4tcf1txbHJvaHlqi3iLcZRxonCjeZF4iwhxenlyarJz0x/Ti8uevLbEva/Ri9qL1HC4R6UIjgcT0PcGs7Syi9WL01W9PYtBi0trakMIDouf9zLKAfhz+TgVYov8NfxDd0j3mota+0bai7n3RvCLmcoriwWa99YVK/vW+2iLi4/3xPfSBQ6EtfjE0gH38tAD+H/5LhX7lIsj+26LewXpfa95r26rcaBdi1aL+wQ2KDGLb4uBk3Ggc597k3uLCHR6eHRjunrG9zn3GfcS9zkfi/cbM8r7GKQIsuP3eosFDoSl+ByvAanX95/kA/id+UIV+yJ6RHAtQfsIMEf7Gov7Gwj7F8U39wz3IPcG9xP3K/FA1S8eb4tlhnF7CIeNBdH3E/cY7vcMmwj7KPwRFYtJdDhoV2tcanVdi1OLYbyL3YvUoeGpuaOwrp6yi9GLulmLQwgOg5/42dQB+K35JBWElfwJizn7HJqBBbvEpJvNiwj3a4uNiPwD/OrRiwUOhKH5EqISqc+z2fct1njPE+j3dff8FfsMaEBFiy0I+wvsWvH3EObY9wMei9RuuzXaCIwHE9T3DK+3t4vZCNxJwiAgQFMrHotVoGfNQgj3XPc9FYtUcGg0Yj3UeqqLtQjMsbbLy7ZXRB4T6FP8CxVGVkQ8R0S/3R6L4sbV5a0I9wL7Bpd5i1IIDnqf93a5+AulAdDj95jWA/f096QVe15bRktWQU5bcjx6CHgH9xihzKTbyfcP6tD3GIv3H4v3GEvh+wmLVYtWeGFlU1hmO4s7iyLJQeOLCLSLrpfArAjQ94gVi0FzLm9tcm9geWOLS4tnvYvki8qezq24p7Cso7qLyYuwWos4CA77P4D3A/d69wMSvfcDgPcDE9D3mfgUFSEKE+An++kVqnKlbWxycWxupHKoHquko6kfDvs/9973AxLxy3v3AxOg95n4FBUhChPA+3X8lRUgCg73P4GfAfjkgRWL0/w491P4OPdTi9P8kPt6i0kFDvc/9wzN9xrNAfji99QVzfyMSQf4jPtcFc38jEkHDvc/gZ8B+OT3cBWLzfyQ93qLQ/g4+1P8OPtTi0MFDn/0+LmhEvcY9FbL9yrVE9j3bPdCFZKnBZnEqbXVwvcI4pqvi8gI3lS0KT1SXkttl3ijo52fmx6Lk4qRhpaFmImRi5MIqaWdt76oZV8ei1d4XEpKMzOBbHknCBPgsvsfFRPQqHOlbh4T4G50dWofE9BtoXepHqekoacfDvg0ebL3CaxrtfenuPcaqhL3Ct73DNL4CrMT3/lCzxU+aFJ/SYsI+0D7BfcP90L3UPcH9xX3N/cw9xf7Dfsi+wBILk5ze5imH4uQjJaRogjI94BGi4FmBX6wc5psiwj7DT77LSMfEydMtGG9HrWLuKStuQgTz5Vdq3G6iwju4Pb3FPcs+xH3Iftc+1/7NPsu+1X7Uvcw+yf3XB/Si8aY6bcIEzf7FPf3FSRN+wJSZnWrvx6Lvp26qLGmrrKfpIsIqJZyZh8O9ouf92Kv+BafAfjIFiIKvfeaFftWi/cp95sFDvaLqfjlqQH3FvkhFSMK+xj7thUkCltrFSUKDvc3ebj4768B+UX5LBV2BoN7gYV3i4KLf4t3kmGaYY1qizyLP3BLXfsCPT77F4v7IYv7OfcAK/ctiwjyi9u25fUIeZoFNDFPbjmL+wOLS8yL9yCL9wKv9wbT2MLG0bHVi+OLvFOXIAidiAUO926LqfjlqQH3F/khFXsHyImaf4twi3yHeIRyCPsO/FEFe1CBhFOBCHv3lQf3CYvwpdTE7dfJ8Iv3EAj3Q/sJ6ftDHilGFZWuoY+xi8WLtX+qdLxmqEyLO4smZPsKREZNTz1tJotdi3WWi6UIi5iQn5zJCA72i6z3uK/3l6wB+Q75IRUmCg72i5/47KwB+Rn5IRX8hXsGzYWVhYtvi3uId4RyCPsP/E4FfFeBdVGHCHv3j5sHUI95louji5qSn5KkCMb3aQWwiaOKoYu6i6eHi2OLe4l9hWwInIbX9395kAVeMYiJ+zyJCMv3dwWSpZqRuYv3RIuifotCi4WLhoh1CKCJBQ73bnmw+PmtAflm99MV+597BquIBayImX+LeYt1hXN3SHU+hn9/f3V1ZX9ei/sVi0LZi/cXi/cDtPcDzN4Iu8jPsdqLyYu7dqploXCYZ41gCJ2IvPdZfJAFenN6gXGLgIuBjHSUX5xakmKLPIs/cEpe+wBAQPsTi/shi0emPrpbCL5Y1nLii+OL057Ytgi8908FmsSclsyPCA73bouf98a1952fAfmV+SEVJwoO+z+Ln/j5nwH4FPkhFSgKDk95q/j/nwGF6AP4f/khFfuSewbKhZmDi3CLfId3g24I+xP8WgWAY3lzc4tzi4CWi6eLlI6Ri5cIpHOgcHB5c2tWumjRHr6Lt5yosaWto7yg1wjy+AMFnMeTkcSTCA73N4uf+PmfAflm+SEVKQoOv4uv+OmfAfjD90gVd5EFb1F1amt2WmpshieLOYt0lYuqi5mPnJGiCPcM+EEFm8Skm8ePCJv7pXsHyYeagYtui3yId4NwCPsO/EoFeUyDglOFCHv4kQcO992Ln/j5nwH5/PkhFSoKDvc3fJ+Gn/j5nxITYPlr+SEVKwoToCwKDvdueaz4/qwB+U/4NhUtCiLKFS4KDvaLn/exsPetqQH3JvkhFS8KSE4VMAoO9277Ss/5f6wB0Ps9FbGgsJWzi5+LqYe2fcR5wIOxi9iLy6m9uJ+dnJ+aoAh7lgVTUWN4Q4tqi2aWYpVflV6VaYsIcovBxAXWkK6Uwaj3LNvz9zqL9zCL9xsz8fsdiz+LM24+SvsBLUv7Fov7D4v7Fck29wZ0CDA7goQ+VQj4q/kNFYskXvsjTS5TOEhiQItBi1nMi/CL77v3HsXixODJs9aL24u8UYssCA72i5/476kB9xj5IRV7B7WFj4qWhJKGkn+LgIt6hniEcAj7C/xDBXtQfXhUhAh794ebB1KRgZaLqYuVjZmWsgjC91/NhvcP+9j3J4uLmwVei3eidcYIMvd/Bc6arJeqo7SqpLyLuwjgQ8P7GB49TxWQnqCWqosI2bVgRi5FUvsLH3mLg4xyjwgOea74/Kx4nxL3F+P3EeITOPiQ+S8VdAZ9doKGdYt+i3+OdpMIE9h2lGqQbIsrizlQiyKLVZprx0uYfpd9mXwIsmEFuVmZbYtgCD9VVz43T9DtHouSi5KNlAh3jWn7dJ2LBZKim5Sfi5aLlImmgbl7poSqi/cHi+Lci/cGi8x1tjDnMOaDm4u8CMq2sNDsoU4lHp2IBQ6/i5/46q4B+Q35IRUxCg73bnm0+PafAfHlA/mR+SEV+1p7BsCGnICLbYuChGh7UAhL+30FXvs4TUf7BYs9i0+6i9KLoZjJpuoIyvd2BZ7QnJrPkgib+6R7B8mJnX6LcYt/h3yGeQhX+1EFcSx5SItViyzlRvcXi8yLvZq2sLavq8Wh1gje97EFsfcWj5DJmQgO9nmf+QufAflE+SEV+017BriGnIGLeIt4eWBsVgj7Zvv8SvhPBYqQi5CLkIutmJXKkgib+4R7B8OEjoai+yAI3fyLnov4Cfj7BZymm5eijAgO9915n/kLnwH6HvkhFftMewa9ipx7i3KLeIFzfnII+1D8AWP4MAWLjomRi5GLq5yWvpAIm/uAewfFiZaCkVgIk0r7QPvwX/goBYqSi5OLkIuxoJO+kAib+397B6uHlYmUgpl8j3qWLQjI/Jaei/dy+FmQi738WZ+L98H42AWowpWTsZcIDvaLn/j5nwH5I/khFTIKDr+Ln/j5nwH5DfkhFftRewaoiAWoiJaDi3qLcF9NIvsQCGRdbPcCBXPgf7eLmouhl5PHkQib+4N7B8ODkYOaVwjX+59Q+2EFeUt0fkmHCHv3tZsHZ44FZI59lIuki6CSpqLaCK/3D/dv96IFrLSTlaiVCA6/i6/42a8B+PL5ExUzCg77B/stpvmOpgH4G/krFftBi/tZ/cT3UIuSplOLBWt6lJ4fi46NlY+bCPcy+S8FkaWXl6iLCMkGDvt2eZ/5GJ8B99N5Ffu0+UBDi/e1/UAFDvsH+y2m+Y6mAfgS+SsV+1GLhHDEiwWsm4N5H4uHi4aHewj7NP0yBYRugX9tiwhNi4Rw90GLBQ45+RqfAfg698EV+0n4AU+L+0n8Ac+L9yL3tYyL9yP7tQUO+xG9AfiI+xEVvfyIWQcO+z/5GJ8B98v4gBX7B/cpBX6cf5F8i3eLe3+LdYt/kYGYgQj3ICEFDoiAvFuf+C2hEpzf91jUE7j4Y/cDFXBuBW1qfoOCi4OLhZGLkouftfdAuvc/jpWMjY2UCISOToSIiIBbBYOwbqBgiwj7Gfst+0n7Lz+3Y8Mf0YvFt9b3BXY5iYOLcggTWG6Xf6ces4ujntbmCBO4+wP3mRWLRG01XEdtYFxUWYtni3Oei8KLyq7ktcq1yLequIsIrqB0aB8OgKL4ELwB+BjgA/c397YV3/fGoN2GkAVZgmeFSIMIegfGiZCKi3WLgoh9hXMI+yL8n4uFBW3UdMT3L/c590L3MthatkgeRYtUZUf7BQj3dJsVi0FZKE9NZmVgdmCLbIt8louii8en7LfVttS5tbuLt4ulcotOCA5PgK/4H6ABqeH3gdMD9/L2FVVSZXJWi1KLa7WL04vkruDDxqips52zi6KLmYOLf4t4fICLeQh3lnenpaGgprpfrU4eTotSdVpkRFJXNIsuiyXBV+iL1ovAqsjYCA5+wFi7+BGiEpri903XE3j4nfk/FVaAZ4VLhQh6B8KJlIiLdot9jId8Vghe+zeKiwWFsnqeYYsI+xb7NvtB+zY/tWLMH8+LvqzG7oBZiXuLdAgTmHCaeaUevYu7tLzUCH+VBVVNgIJ6i36LhpOLl4ubrfcIqvcGCMf3b7L3LAUTePs/+9AV+ywj+0AvaHSmuR6L3r33Ac3Rp6iunKeLCKKjdmcfDk+AuPgUogGq4vd4zQP3+vcBFUNQbHtfi1OLZq+Lwouai6WVn/dHovTZi+EItW6lVvsq+yn7NPsvOMFV3B7ei8uxxNEI+273LxWt5M/YxIuni5J8i3OLbHhnbG1maGV5NXYIDvt2+2Og+Nqr93ihAfsnzvhH0AO0+EAVhGvmizP8OAV0+wBrVWGLf4uDkouUi5aUkIuYCKB8m3R2enh0aK1xuB7mi87ttfdNCNP31PcAi5GrIIsFqPcysNHDi5mLk4aLg4uCgYaLeghznnydop6goa9mpVoeTotiaW1galx6VHVECA77YqH346D3VrKZoRKTwqzZP9X3Lcdq2hP0APhr+AIVsk8HiIuGjYORcJ5qlGWLJosnRosli1eiZ8N3CBP7AFVydG2Lbot+lHydgClQeHCLWAhDzGfx9xnYy+Iei8ddtyuiX5ZwmIudi6Cen5yLjYuNi46KlImWipaLCBP0gOjn298fi5yLm4KdCEV5FYthfmJ3aXNicHlpiwhldae67sfUybCeeVYfE/kAcPxKFVhVYDo7XKvRHouikJuanpmdta2Ui5aHlYiYhwj2aq9vi10IDoK6ZZ/4Br4S97TajtkTuPhl9woVVUd/f3uLgouEk4uVi5abyZy/qemd1Yuki7B4qV2LTYs9SjH7Jgj3DfhThJEFUX5khE+ECHymB52ig3ofi32GeoNsCBN4+yb8vtaLBbP3Lpuus8i/2svIr4uii5CBi3yLh4h+h3sIVPtjBX5ahGyLfwgTmDQKDvt2gLr46p8BvNYD95z46xWodKVwcHd1bGuedqiloqKnHmH8eRU1Cg77dvtjoflx8wH7EM/3e/MD96v46hWnc6Vwb3J1bWyjdqmlo6KmHmr7NBU2Cg5PgL9inxITQPhh+EAV+0d7mQakl4SAH4t3WlstQwhgavcM+FyFkQVQfmSEUIQIe50HrYuahY15iXqIdH5bCPsh/KTWi7v3SLOrBZtfpU2daAgTgKtMn3ioi7OLpKS53wh8lgWGgoaChoN5bH+AfIt4i3SwZOcIZuMF9yf3F6qfuo4IDvt2gLYBtNgD96v5OhWFkAVQfmaEUIQIe50Hq5yBfx+LiIuFiIEI+x38oAWIgYp/i4OLZpx4q4vBi7Cpx+oIfZVyaAVuYnR7fIuBi4SRi5eLk46ckJ0IDvdugrpln/gFvxL39tjf143aE7z5VPQVfJd2cQVtZnl7eouDi4eQi5aLj4+dkaIIz/ePBYyQjZuLkouvdqZmi3eLeIZzfFpsYllF+wOm2JjDi56Lr3ejY4sITotFSTL7JQjF92WIjfs2bIt7pIsFppmEfB+Lf3w4Y/sZCBN8YPsk1osFu/cyma+tv8PgxsWti5iLlIKLe4t+cyFf+ywIcC7WiwWy9y6fvLzQvdG+uqmLlouUgot/i4aJfoZ3CFH7dwWBZIh6i4EIE5xtmXulHrqLt6zA1QgOgrpln/gGvhL3s9aK3BOw+GD3CRWEgoSChINuZnl7fYt/i4eUi5SLk4+cla8Iw/dfBROokaCPoIudi691pGCLS4tITyf7NAjO926HjQVWgG+HOnsIewe+ipmFi3eLhYqFioYIE2gr+/LWiwW69zKTorjOyui4vLOLmouUgIt5i3+FZ4NsCF/7NgUTkH1XiX6LgYtloXuki7qLpJ/P6AgOgKD4LqABpt/3pd8D+Gj3wRU3CjekFTgKDouAnvgatgH4EuUD92v4QBWMj4yQi4sIjYmNiB77MHWNfKGLBZuniHMfi4aGcYBjCPsH/EQFf1x+fGCKCHv3X5sHXHySoR+LmaLdnNGkfqCHoosI9yb3K/c29znZYrpBH0+LUmtVOgj3WHwVi0V2QltIX01balaLb4t3m4uhi62v9xWo1qLHxsHAi7iLnG+LUggOgMD4DaEBpOED+Hj4QBVCi3taBYG4cZxiiwj7Hfsw+0b7MkSwXsof2Iu+sNv3Ewgx+7YFgGZ6fEyHCHv3gZt8B2Z3l54fi46Mj4yPCMj4khWLOEn7H0dQcXRsfnKLZot7qYu6i9688s/Mq6mrnqiLrIulcItqCA77B4uf+CWfAfdE93MVwvdsiI37L3CLegWajZOMk4ufi52Gi3aLdomCfVcIOvu414sFvfc8nbO21a/Ip6ydi5KLjoeRgZR8k4CdiwipnKOpqXigbx90i215cXBiYGlWeGEIDvsHfp95oPgsonifEvcB1LnXExz4AvhOFX0Gg32Eh3yLg4uCjHiRCBNscpJ9jnqLQYtcYYtJi2ufXrZVslqcaYtri1pub1yLV4tptH3qCHuLBROMd/szm4sFkpuWkJaLlouZip6DCBNsooKaipyL3ovIvovei7J5slnFZLl8qIumi7Cjn66LvIupapU4CJsGDvt2gLz3+qsB97z4QBU7i6fyBYyNi5CLi4uQiI6Fi4eLhYiHhWdVSlprhHOGgoKLgIuLi4iMiAjWiz37vAWDa4Nsi4CLcp5/pou/i6qox+cIfpIFWkx7e3uLgouFjouYi46MkoyPCOL33N+LBQ6AwFi6+BOfErXY9z7ZE1j4YfcLFVhIe317i4SLh5GLlouXmbqQngja979BiwVa+xp9ZVxECBO4TS1dVmmLfIuGlYuai4+NlIyOCOT394eOBVJ+Z4RShAh9B7GLjoqUhpGIkIOLhIuDhXGDagho+x8FeUKCZ4t4i2ade66L0ou9wPcK91Zr+wB+SIt1CBNYbJ16qR66i6WfzO4IDk95n/g3nwH4C74D92PRFYX3G4XCfs529wCLkYKLhouEioOIa4RohF6ECH4HloyVi5WLsIuWepg/mD+W+xmLRghzB3qOgZEenIumrMLGnZ7Dy7jRrsGnxYu2CKZ0q2p2en52Hot7kn6de5h/kISLgYtcSvsCQ0EIDvc3eZ/4N58B+Oy7A/gn+D4VlomOhR6Gi4iJhoMI+1T7xAWH4333EX3PhKuKjYCLhIuCh36IbYNph2yGCH6nB6iLlIaUZpdbliCPNAiPMAWNZI2DlIuWi5ykr9Cer52snakI5PcsqPvKBY1xjYKSi5SLlJWmrAiUlgX3Hvc81fcJi8sIq3WjbXV6fHsei32Qf5t8m3yRg4t/i2BpVvsX+zgIDk+AwvfpwwH3h/f3FX3Pf51yi3SLaoROdQiAh457nZAFnpCXjZOLpIuSg5lPCKf7EDn7CAV2bXh4gIuFi4GOgZF+koGPgosId317d3Gee6ofqouflLfGCOP3C6j7CwWXWZp5q4uxi6WjxeUIfJQFg4GHhYJ/dG2AgX6LfYuCmISnCGv3GgWFo4mZi5K32K+3nYuji5R6nosIn5maoKF6mnMfX4tmZ0UgCA5P+2LC+NCfAfgWswP3h/dOFXrkVvc6fIsIhwZVg2qFd4eBiYCJgIkIegeWjpSMlouzi518nlqmR8L7dItji4CHf4V/g35eUHl4dHJ/g36LCHGLi6doiwh1enl1caB6qR/Ei/b3B/P3QN73Hrv3AovECKl1pG10enx1Hot7kYGffp5/koWLfYtfZkM2+yEIDvsHOqD4QMcB98jCA/gQ+DUVlvuvB2v7CJuHBZ++npS/iwj3HIv7yvwIlIIFm5iYkJuLpYurfrpuvWytfqiLCMOwr7OhfZp2H3uLe3qKeouDjYORf46FjYaLh4uCgIV7i3KLeJdxsWPGdZZRmAgOI77WgtYTQPgr+UMV+wWLXGluIQhb+0YFd0J1c0t6sn2ZfYtui3N/VXVACBOAdT+BX4tzi1Ssd+eICI6WBWWWfJ2LsIubkaSbyAgTQKXpndmLnYumep5knMycpqih3gi49zwFoNqlqMmbCA77eXmf+RifAfTNA/c/eRX5QEn9QAcOI/dk1oLWE0D3cfk4FbGAmniLZot9hW57UQgTgHEteT2LeYtvnHmyekl6cW51OAhe+zwFdjxxbk17CIiABfcEi7utqPUIu/dGBZ/UoaPLnGSZfZmLqIujl8Ch1wgTQKHWlbmLoovCap8vjggOsPdPy4/LAfhm99cVZlN6e2SLbotZqHmTZpxrmV6LXItfcWxPCK9ZBZ29r6Gqi7yLunKcgax4pH24i7mLrZ+4zQgO+5IOg9VDod2n91W196yoEpWhE3Td9/0VgmH3BIty+2AFb5Z4i3yLCFRqa2dko3K0H66LopixvQgTnM5Wp3+8i86LvK+lywiAlIGEBXB4e4Jni2CLXZNEqbTkkZul9wII9xOLkrX7EIsFufd3nsDEi6OLl36PbJBomYKciwikmZmmuGWqVB9Vi2B3Y1tXTXNJd/sFCBNkXvu0FXxpbnRwiwhzeJugpqGdqh+gi5eGp3cIDouf9zaz5bP3rZ8B+PH5IRX7UXsGpIgFqIiYg4t6imhaT/sE+xeDgYWEfXsIbu8FbuuBt4ubi6CUksuRCJv7gXsHzYOSgZpYCMr7bPsfi39j9zaLjoF0O/s3i39j9ziLcjcFeU10fkWECId796+Li5tnjgVijn6bi6WLoZOlotEI90aLl7P7Rouj3ZGT9zyLl7P7KYv3Sfd0BauzlpKrmQgO+zag94Wg95+g94CgEsDIc8SwyLXFq8VlyxP1APeN+CIVeZJ6j3mLUYtbVItHi1yjV7pVCNc0BbFfl3SLbQhWYWZPHhP7gGZpnJ8fi5GPj5aSn5eSl4uhCKZ6m21odnZoTsdc1+TOxtkei7OBoVbOCI2OBZeFkoqZi9KLur2L14u0fLRxqwj7D/cqBXqggqSLpQi+rqvEHhPyQK2lfXofi4WHhoKDfH6FgIt9CHGeeKarn6CtxVW0PzVOV0Iei1+cab1NCBP0gPcS+2UVZG5rZ1Eg9xbSsKiosB6si65zslcItlKZbotpCA77P/iQ7QH27fHtA/gp+MEVOQr7XBY5Cg77P/iovgH4L/jbFfvBi4BY98GLBQ4j+Bqt926tAfCy92SyA/gX+KkV20zKOztMTDs8ykvZ3crJ3B5kFk9cWlFTXL3Gx7q8xMS6WVAeDvs/+RifAfdI+IIVrov3P/UFl5KQlIuXi597m3eLgYuDiISECA6BwgH33OAD+IX4QBUzi0L7zQVoXl9yYIthi3Cmi7WLlYyYjZIIzvewM4s2/AoFhXCBb3lebVGDcotoCGyWfaK2p8LiHouTi52KnIqci5mLloudi5SNoJ5WqnTAi8CLu6fAyYh9ioSLgQhknnexHrKLpZm1tgiOlAVyd32Feot6i4KVi52LlI2Sj50IDvuS91v3AwHR9wMD90n3kRWqcaVtbXJya26kcqiqpaOpHg6AoPguoAGm3/el3gP4dvkRFWunKGAFY6xmnV6VCGh6BbV6pXquagj7D1WsbvcJvgWzV6FWlUYIiYoFeatynF+LCPsk+xz7NPssLcNd5vc69xP3Q/dXH4voc9BN0giO+54Vi0RwKV9KZlNgcV+LXItstYvCi9yg1rzPtca5qbeLtounZotSCA6CumWf+Aa+xsES97TajtkTvPhl9woVVUd/f3uLgouEk4uVi5abyZy/qemd1Yuki7B4qV2LTYs9SjH7JgjU96L3M4uawfszi6z3D4SRBVF+ZIRPhAh8pgedooN6H4t9hnqDbAhNi3xVyosFE2z7GPyI1osFs/cum66zyL/ay8ivi6KLkIGLfIuHiH6HewhU+2MFflqEbIt/CBOMNAoO+3aAuvgVnwG62AP3cfcHFWBSdnV6i4GLhZKLk4uVj5uQngjr9+qGjgUmeHiIZIgIewfBipSIi3eLg4d5hngIW/tDBXtPg22Ld4tln3ipi76LravA3QgO+3b7Y6H48p8B+xDPA/eK+EoVNgoO+z/5FZ8B+BX4gBUz9z1ai/sx+z2yi/cd890jBQ77P/kVnwH4PvkpFWaL+yEiMvRli+r7PbuLBQ77P/iAxgH4GfkeFXVNVmZOi0eLaa+GyghuBiSwVOYe4ovT0ZnjCA77P/iQ7QH3Y+0D98X4wRU5Cg77P/iQrfcXrQH3L633GK0D9/f48xXCXrhTVV5eVVO2X8TCuLjBHmkWZm5vZWZvqLCuqamusKluZh4O+z/4nMd7xhITgPgj+QQVgGp+gHCLfIt6kG2ZCBNAZZxyknSLV4tvbnc+CKgGlaubmqSLnIujhMF1CBOApYGdhpiLu4ussJnOCA72i5/3Yq/4Fp8B+MgWIgq995oV+1aL9yn3mwUO9oup+OWpAfcW+SEVIwr7GPu2FSQKW2sVJQoO9ouf+OysAfkZ+SEV/IV7Bs2FlYWLb4t7iHeEcgj7D/xOBXxXgXVRhwh794+bB1CPeZaLo4uakp+SpAj3GPhtBZKlmpG5i/dEi6J+i0KLhYuGiHUIoIkFDvaL6fi+nwH4ohb7GPkwcYv8JP0wBfhP6RX76ov3k/hEBQ72i6z3uK/3l6wB+Q75IRUmCg6/i6/42a8B+PL5ExUzCg73bouf98a1952fAfmV+SEVJwoO9255rPeb6feZrAH4oPhBFYFmZHdmiwgpBmeLg5eDuAh4Bos8azx2WAieBp64p5iwiwj0Bq6Xe2EfngaLyq3snrwI9zCAFYv3LDrs+ySKNos4ZkZPIzBC+yCL+w6L+ynfNvcWi9WL2qbMt/cL2+P3H4v3JggiyhUuCg77P4uf+PmfAfgU+SEVKAoO9zeLn/j5nwH5ZvkhFSkKDvaLn/kInwH4yBabB1aPgJZ93wgv+L1xi/ux/IQFQPsWfnpdggh7906bB1yNfJeLnoubk6OZpQj3efgu0fxCBYyCjIKLg4tpfXtMiAh7Bw733Yuf+PmfAfn8+SEVKgoO9zd8n4af+PmfEhNg+Wv5IRUrChOgLAoO9yeL6fdm4fdB5QH5PPkhFfyDi2H7L52HBaDDqZi/iwj3sQbIln5nH4uEioSKggiciQU4ahV5jgV2W4N2R4sI+yMGZnKMqx+LlYuTjpYIeI9T+2WdhwWgwaiSsosI9yoGxI9/ch+LgouFiX8InIkF6EsVeZAFbT5ag1GLCPvTBmZyla0fi5WLko+eCHqQX/tH+K2LBQ73bnms+P6sAflP+DYVLQoiyhUuCg73bouf+OWzAfmV+SEV/RJ7BsqFmYWLbot8hnWEcAj7CvxCBXlKf3xThQh794mbB0+TgZKLqIuSjJONkgj3J/in97GL+yX8nAV9Wnp0RIYIe/emmwdKkn2Si6eLk4yTjZMI9xj4dQWbxZaRxJUIDvaLn/exsPetqQH3JvkhFS8KSE4VMAoO9wiL6fifrwH5J/khFfyQfQb3VfvO+/L7yot8+LqLzfdYeI4FZz9mbj6LCPvFi/fA95n7NPea90aLBfcJsX9OH4uBinSJgQihiQUOv4uf+OquAfkN+SEVMQoOv4uf+Oi/XbcSEyD5HPjwFYedhpx6mH2VfI94izuLLPsMXPsWCIqIB42bi5qLmggTwPcJaOX7AB5di2x4YW0Ikn0FoJSSjZ2L24uoVYv7H4tkiWeDVghT+1kFeUt0fUmHCHv3tZsHZ44FZI59lIuki5iNmpOmCLP3IAUTIKv3Bez3lvcbi56Ll3+UfggO94GLn/j5nwH4kvjaFZSrq6LJiwicm/uzewbLkYF0H4uAg2uFdvsLiDVwU1tSWmxTi0mL+xH3Alf3DIp6Pm53T4sIgnv3vZsGR3KVqh+Llo6jk6D3Bo3jo8W8xbysxovMi/cT+wS6+w2QCIFtFemDuVaLOItOfF5eW15bUHxAiwgpFi2SX7yL3ovJl7a4urm7xqHWiwgO9ouf+PmfAfkj+SEVMgoO9z+Ln/j5n4WfEvcL4hMw+Z75LxV+BvsUi2w3cS1r+wT7E2lsiQjO94UFlKqfo8uLCJwGE1Cb+6p7lgfDkIF0H4uHiHuEcQhQ+20FS2Ctyx+LsKC6i60IE7DVZK9OHm57BqKefWMfi2hpUotUCPsG6mvxHlD7agV9V3B1SYsIe/e1mwdBe5upH4uUjpaOlwjG92YF9xWL9x++wfdImbuMwMiaCA73lovp+K+sAfeG6RX7FwZocJGxH4uVjZuNlQh6kGH7R/eji6P3OgVQnnLQi9eL1bDax8q/wcqs2Iv0i64/iyKL+xQz+xj7CnEIY/s696yLw/dCeZAFbj9iiFGFCPsUi5KwBfdFrvT3GIv3Hov3GkTr+zeL+wSLMm1DUDxKVjKLMoswsj73AGgIDruAoHjG+AagEqbdE7D4ufhAFTWLXSEFxmLHNh5Ni0hrX15TUmg2izqLN7BH7IvWi9C5vcgIE1CNTpdfsYu7i6q/odUIe5IFdlR7eH2LCHV/vrsfnQcTsFv0FYtwf3KHeHBTR/sbRYsIWHnFxPcz9wL3HMofy5g7Rx8OjYCe+ASr942gEvgV5GvTE/CC+xMVhXZ7YIJ9CNkGlJqVn5e2CLH3GQWlf56GoIu2i7WTsqHovt/3DYvoi9JZsGWOCIwHE+jHps/Ui9yL10ekVov7MYtG+z9k+x8I9PcBFaHfuuvUiwiuq30+UVwnYB99i3aRg4sIaIJ+gH+XgZ0fnIuak52LCBPwp5dzaPsaI/tD+wZvd5qhHw4t+AjKAfcnrgP4SvhAFSuL+0b7wQWQu5jbi8mL0X67WItZi2tAeksImwaewqagnYuxi5VPi0aLP38+iG9tR0gqi1aLapp6oovai5L3LpDmCA5fgKD4/rMBo9/Krvcq3AP4YPjwFbhEnlpLImsrHotVw2S4XfsUf/sM+xaL+xQIMMFY6fc09Pcn9xcei9lzqmKyTMgkr4vFi7HFn6+L5ItqQ8yLCKmUpqAfI/vmFTw9+0UvXGyvwvce6fch4q2scDQeDk+Ar/dQq/dDoBKp4XTd90bTE/D3/O0VVlJae1aLCGBdn8jX3aq6H6CLkoKdiwisl5Sdl3uUeR9yi3mEgYsIE+xgbJ2u596pxaKZgoAfi3h8got3CHOae6OeqJyou2CuSh77Hos2RIo/i22eb62FCBPwSnpYWItNi1emUPcMi9aLyqHI2AgOWftNzPcB3ETT+MqfEqm+5b7ssxNO97b5PxU8dmNki2EIZLJ4qh6MigX7CfsGLPshi/s0iynNd8OLCBOuOgoTXoSLeYp+i0WLZKSLz4v3F/cK9zzhxeST8MeLt4uagZV2i1iLNEtnYAhtkHmci6WLpKSmu50IDm2Ln/gGvgH3Ati/17ncA/co93gVlq6n44u1i6SCn2yLbYtlcm5nfHmAeYiGCJeBBZqdqbOdi5aLjoOLgot9hHSEcgg5+8XWi6v1BbP3GvcQ9yq+i6OLjHeLfIt+gFqIgQhA+6YFbyWGYItyi3mNfJSACNQGiJKGmIuZi6qY2ZzJCOL31QWSpo6Zi6GLsmqdZYtTi0ZPK/suCA5zgKD3xav3yqABpt/3v98D+IL4kxX3C1e7RB5ji2WCX2r7ATj7BftFi/triyG6SdyL0YvRqszh1e7H9ySL9zYI++/7OBWk5O33ceKLroudYotLi0B+Q3pRCIRrFXMpNftjK4tmi3i+i+SLypW/nr0IDvt2gLr4FZ8BvNYD93L3BhU1Cg5Pfp+En/glnxITYPct93UVwfdpiI4FWYFYgVmECH2nB5mehXkfi4SGcYJpCDX7ydeLx/dn6Ps0BROAnG2jacSLCBNgnouij6aUCJsHYot7lGnHCCn3QAXT1q2usYugi5V4oosIpZ+cqKR6oWYfg4uBiYOIVXU+TSn7EggOXXvKXJ/458oS96mzfK4TsPgz9w8Vd1J0eH2LbYuAqYvRCBOoi/cTn/cbi/cai+VuuGiLVItsQXxMCJsGn8OqnZmLqoudbIs+i2uJbol5CBNQ+8r8QOuL92X3zwWEJYJAi08IE5BIpHCnHr+LqsSd3QgOoYC6XssS973ZE6D4afcJFVdHfH57i4SLh5KLk4uVmr6Pmwja98A+i2r7DgUTYHpL+wH7T1CLb4t/oIumi5SNlI2UCNb3vkCL+xf8nQV7TH1ufXcI0gahpZG7svcqkHmXgZ6Lx4vCzuP3MAiMi2ojBYNzhGiLeggToG+geqceuIuposnrCA5peZ/4N58B+E/4RhVj+yM1+2f7YHgI9PgOiI37N2yLewW2iqGHi3WLh4qDioYIL/vhBYmGioeLh4t8mYSZi/ellfT3hKz3WggOWftNzPcB3ETTEqm+4rBxu+ezE0T3vPk/FTp2Z2WLX4txq3iaiwgTWl5mfmmLZ4txm3SgfShaQCqK+wSLKc13w4sIE7o6ChNahIt5in6LRYtkpIvPjNLf5dCiooSmhaGLCKzdlL6edZZsH2SLUn9hbnWbh56LnQinqM7D9b2msZ59l2oeZItRbV1sCBNEeo5/louai5iNr9KiCA6AoPguoAGm3/el3wP4aPfBFTcKN6QVOAoOi3mfftz3sNUSE6D4rPhAFfujBiaLV2VVMAibBrfBpoy/iwiRizn7ZQWBcXdqYYByhIZwi3yLc6N3pYuWi5mPlpPcy6X3Qrj3Dgjziz/7ZgWEeIFli3QIE2Bkm2e2HtaLutuayQh7BnNVcIR3i3aLgZ6LooufwPdAmb0I8QYOi4Ce+DCgAfgS5AOC+xsVhHGBdH12CNkGmqCVpJGjCK/3IQWifqGHoosI9yL3MPc19y73HSiLVh8giyf7BV37RQj30Pc1FYv7Cjr7TPsZiW+LdpuLoIukp/OdzKn2zNXDi7aLolqLUAgOWftNzPcB3ETT9/KfEqm+94KzE1z4WfgWFbNYmmn7K/tP+yv7SynNd8MeE6w6ChNMhIt5in6LCEVkpM/19wbV9wcfq4uugKWLCKigmbMfDoWAoPfs1QGm3/eI3wP4p/hAFftWBvtR+w37N/sbNL9V6fcg9xL3CvcCH4vWU4pjygj3Pgb7MvsZFTtF+xcrXGypx/ch9wn3BdAeq3ilWYtLCA4tgNf3tdUB9wzdA/g++EAV+24GJ4tGKnBKCJsGqL+5r8GLCMgGXCRY+wqLQotgnG+6i8uLxc6i2Qh7Bnpnampyi3GLgaCLqYuZi8zR9zMI9xkGDnGBoPgunwG42/eB3wP3qPg+FcWFp3mLQAgpQ/tu+wBef7C0Houij6WSpAi990kFkqOMnouUi6l7mm+LZYtdaFxECJiCBbS/mZOZi5OLj4eLgYuEiH2GeQhvLgV6VHxai2EIT61f7/cn9wz3UfcQ9wVIpCQeDvcKi5/4GqCBnxKm3/gf3xO492+VFUxentIfi/cP3PdC9acImwdoi2t9a3kpU0H7EIsli0mkYbx4pYG6irKLCFX7VtiLwPdWBaqLp4+lk/ciudX3MIvwCBNY9wFGnVIe+wKLVPsdavsJCOjTFabuqcm6i6CLoYWLP4slSvs0PmJ1f3KIdYsIDlz7Y8r4nsoB90KxA/iG+EAVLov7WPuSBY3tjZqLlYv3BHWrZ4tRi3REekoImwafxKabmYsIsJNaLR+LMvuz++3oi/dZ94gFhmyIUotni0mcTbmLxYuh05jMCHsGeFRyeH6Lbot7o4v3Eoufi6KMpQgO2/g5nxKs313cE8D5MPhNFXUG+yOLbvsCcfsFdzNjSF5rdXxzhXWLCPcH+DY/i/sH/DYFVm6p2x8ToIvFrvOLxAjFebdKHlaLinsFuYaVXYtkCBPAi0hlTotDi0qjZKh2pXivia+LCJSLVftW14vB91YF9wmL876x9zyf5KL3AuydCA73SoCgAabf+F/fA/hs+EsVewe1i7KEl1yPfIxvi3mLS3ozbFF1YmRcU4thi3S0i7aLkouSjZIIlZqYoZOZobGfyou4i6aAnnOLZottW31Xg22HbItyi32MdY18CHhUUVNei2uLcqSL0IvesPcAvcqxuridvosIm3kH+yGLJCBq+w2EcIhwi3CLKMxhy4vSi7CjsrqbaJ9n2YvLi9i2wO4IpbycvovBi7t/uGqncKJilViLCA5bgbP3zbb3tJ8BuMH3i7OYsAP4SPj9FcRUn1oeaotecnF4+xopWvtMi/szCCul+w/3DPcJ2fcQ9tVm5jQeL4tXRV1GnuOj3MDVlIqVi5WLwYvKkLigs52wsIu6CPuRJRWsw9ry04uei5h7i3mLcXZueXpYWliHR4sI9zD7ixVF+wT7PEBjd7eu1PP3Ndu0oWVmHg6/gaD5DqwB2Nuc3/c43wP4ovdiFXKPdpJ2kqzlme2L0IvpY/L7B4tci2F8amxrbXRdi0uL+wjkJvcLVwhr+wNWJjiLXot/sIu0i6KPpZKkCJ3HBZKjjJ6LlIupe5pvi2WLXWhcRAiYggW0v5mTmYuTi4+Hi4GLhIl9hXkIdkoFh36IdIt6i0+tX++L9weL2e659wKihaOHo4kIKPe9FYtbgzB1MvsEz3X3BIvJCNSm1cXJnDs6Hg7ni5/46L9duRL5AtIT0Pfv+CwVjqKMnoufi/cXYM4ni12LbHhhbQiSfQWglJKNnYvbi6hVi/sfi2SJZ4NWCFP7WQV5S3R9SYcIe/e1mwdnjgVkjn2Ui6SLmIyak6YItPcgBRMwq/cA9veb9xuLkouYiIuBi4VmiothCHGeeKa8mLKwtGyvVh77FYs3+yxd+wAIDvcPi58Bpt/4JN8D+HX5PxU+i0j7hnyLBftL+wT7aCYfi0ukXL96pIOyiLaLCFX7VtmLwfdWBfdZjPcB91mL9wiL0myvWp5vlnCMXYsIhXYVoIumipWFpXuecoteizhK+0U5Ym99e4lyiwg9FnSLeI17kWyXeqiLtQj3IfP3RvcIHg73tICg9+zVAfcT3/hf3wP51PhAFfz6Bi2LOiFxSQibBrC8tbzPiwiuBmljbVZ9WYRwiHCLcIsozGHLi9KLr6GzvZ1hoW3Vi8uL2LbA7gilvJy+i8GLoIinhp8Iywb7JhaOfo54i30IM2T7ZvsSYXS0th6LkouSjZKjsKzDi8EIpoOec1xrQFYei32LbY18fl1PSlqLYIt9uIu8i9mv9wG6yggO9275DawB92b7BhV8U32CVIEIe/eImwdSkn+Pi6eLn5GjlKsInMgFw5XBorys9wvb4/cfi/cmi/csOuz7JIo2izhmRk8jMEL7IIv7Dov7GdE59nsI9/n4hBUuCg74OKABpt/3pd8D5/thFdqLw/dcBbqVuKO2ts3Ms+OL14vjT786i2KLY4JkdiJTQPsHi/sEiz21WdiCCPeC9+MVOAoO9z37Y7j5lsUBwuf33eUD9yH7EBWyUM1zz4v3D4v3FdSL9zGLunHDQKj7E737U2uL9yKL9zj3RvcV9ymL6ouBS8CLCK6doKvAT5s/+2b7nPtJ+30fi/sM82v3A37cgcV/rm+heZVzi2+LPjxXK4tbi0aecq4IDk/7Tcz3AdpG4vf0nxKpvveCsxNc+Gf4XhWBZWso+xOCQ4Y+d1RZZWhxXYtQiz3NbcOLCBOsqYutlaaLCLmpgGRiZW9gH3KLgahtiwhwe3d1Zqx8rR+4i8atqbidpZWsi6WLwW/ANIsIE1xwi2d5dIsIVXSks9rYmOMfwou4jK+exKqszpX3BwgOwIuf98Wv95esAfkZ+SEV/IV7Bs2FlYWLb4t7iHeEcgj7D/xOBXxXgXVRhwh794+bB1CPeZaLo4uakp+SpAjF92b3YIuWr/thi8v3dwWSpZqRuYv3RIuifotCi4WLhoh1CKCJBQ564LD3k8MB+Gz4RRX7uov7Jv0D1ovL96f3SIuUsPtIi8f3k/dviwUO9yF5v/lDvxL3qudo5xPQ+Tf4hhWDmfyX+yX3NvdABeXqoqeLuIutdatRi1yLY3RQWgiTfAWhnbOcqIufi5p9i3aLeXdoeXUI+6r795V++JP3JPs2+0AFE+AzLX9zi1+LaaFmxYu6i7SixbwIg5oFdXljem6Ld4t8louli56gqpyiCA5ci5/3s9UB+FH4ERX7yov3tvfCJ4v7uvwM98qL+7b7x++LBQ73YIuf+N7HAaL4ixXIuM2oxZoIQ/uitovW96wFm46ajJmL9IvpT64s+1pi+yL7mmj7KAjpBqv3Hu/3jfc0p5NokF2LZIv7W/sf+4D7Xl8IdAf3jaH3X/eCi/e0i/dc+xX3Efs8i/sTi/sAZPsVIQgOo/gN0gPo+KgV7FvYR7wjCPtJMZRv90znBZhql2aSaQj7Sy+UcPdI5QWSY49li2aLVoRYfVeDbYB3f2wInYAF1PKr9wOL9wyLu4S6frVr9Tr3DftoywgOqH6fhJ/4JZ8S90+z0rUTePjD+EAV+wCL+6D7ioqMBaPFoNWLvAi9cKZidWx7bmGqi6Odk4dzHotTYvsDfXQI+yj7HPcBi/eQ93mMigVrTHtki1cIE5hUsmu3saCjop97nWh1cJOsHou7teSgrAgOl4Cg+C6gAffAucHfA/fN+2EVnZuaoYuji/cH+5Aqe/c+CI2MBaNitXu3i82Ly6TFxc3Ms+OL14vjT786izKLMlJXR1JBbiyLLwiL+2j3paaLTIuHioeJhwjy+KcVOAoO9255rPfCtfemrAH5T/g2FS0K/IpQFZ/CpsKuurzNyr7Vi9uLvFGLLYtohmCAXwiAYRV1QWk/XVJdU1JkSIs3i13Hi/cBi7ORuZi6CA5PgK/3UKv3QqEBqeED+Dj4TRV7BoiChYN/i3CLfJxbiwj7IvsN+zP7Iji6R+Yf74u3s8PPCHuVBVJSaXJTi1CLbbqL1IujjZ6TpAj3SIuRq/tHiwWb0dDz0IvVi51Okl0ImwYOT4Ch90Kr91CvAffc4QPn99cVxMStpMOLxoupXItCi3OJeINyCPtIi4Vr90eLBXtFRiNGi0GLeciEuQh7i3n7FZuLBY6UkZOXi6aLmnq7iwj3IvcN9zP3It5czzAfJ4tfY1NHCA73WbkB+I33hxX8i4uDXfiLiwUO+BX3WbkB+hL3hxX+EIuDXfoQiwUO+z/5Gp8B9z/LA/fB+S4VOwoO+z/5Gp8B93bLA/c0+EgVPAoOv/kanwH3Osv3JcsD+I35LhU7CvtunBU7Cg6/+RqfAfd2y/clywP4BfhIFTwK+1x6FTwKDvkanwH3R/szFbv3ZgWb0rLtpbF/ooedi7eLq42bkq63i6CHs3qeg5OJlosIp5uapqZ8mGsffIuCiXSBZnyBiWCKlryTnKe7nKiSmIudCKh8m3Bse3dmHouBjIOOeo94jICLgIt0iXiDX2CMgY1mmnWUgY59iwhqfH5wcJt8px+Wi5ONn5Sym5uPtIt+QXVcZGCLhouFjXuNeIx/i4GLVX4vdiEIhGqEaYVpCA75Gp8B9674PxV4N3dgZmcIjYIFlGSQfIt4i3WHbIRqCHEGeIt8j22Yc5V9j36LCG93enJznXumH5mLlY2klbKamI2yjIRfhHpuXHdshXyLeQhvm3mkpaGkqB6LkYqUiZaHoomfi56Lo46fkquyipiJsnyjgpaIl4sIqJ2bo6N3nW8ffot9h3OBbX58h3iLCHgGnt+ftrCvf7WHnouhi6GPqpKrCKUGnouah6l+o4GYh5mLCKefnKSjeZtwH32LgYhygmN8f4lkipK3kp2oup+qkZqLnQimep1zcXVybh6LhYyCjYCPdI12i3mLdol4hGdkjH+NY5pzlICOfosIb3l7c3KfeqcfmYuYj6OVqZiaj56LCA75lr0B+Ij5lhW9/IhZBw775YGfAffl+TgVWIv8W/1CvosFDvyM+QfBAfxZ+T0VVfeyB6ybiH8fi4R6dWtwCJ2D9xj1+xn1eYMFqG6geYuCCH52iW8eDtaAqfkQqwG7xfhHqQPY+BkVpniqgqmKfXV9dX91XDltOotUi1GzbrqLyovGxPT3Dwh2nAUq+wRUVFyLcIuCnouji87m9ye/3/dEpfcm9xWL9Iu5daBhizmL+xv7IiL7Lwhti2yNaqII90V4Fb/cwty8vaSlqKCni6KLl3+LeIsr+wcp+zFoCA5qgKn4Fqn3X6kBs9z3q9ID91f5BRWkk6GQpovxi6guizOLc4hzh3V2sGCWa4sI+yb7A/sj+yE2sT7t937I96P3KPc+TeX7Eh9pi2eFb3oI90r72hWLbIVpgmpvJVAnPosITIfHsfcf4fcp7qatdkofDvdIfbX1q/fZq/cDtQGLtfdoz83P9061A/iA+J8VeQaDgIWJf4uEi4KNgY59kHSOd4tTi1Rri02LapR3smehdstUi2cIZm5yYFpprLkei5OLlI6UCHaLefsdm4sFj5mUkZaLkIuRipuFp4GgiJ6Lz4vDuIvNi7N8plK+VLyEkoukCKmknLAewouVao5SCJ0G92pEFfdT+yv3L/tN+1j7LPsr+1f7VPcr+yz3VPdT9yr3K/dVHmEW+zv7Ffsb+zz7O/sc9xv3O/c89xz3HPc79zz3Ffsc+zweDvdYi+8Bi+/4iO8DiwTv7ycG+OwnFe/vJwYO+2CL7wGL7+/vA4sE7+8nBvdcJxXv7ycGDvwoi+8Bi+8DiwTv7ycGDviIFPiMFXmd+SGZBh4KA5Yl/wwJiwwKqgqikI6Oj5CQkJKPDAy1Cx4KBv8MEhwAMRMAHQIAAQAlADgAfwDDANkA+QF/AgECPQLHAz0DhwObA8oD8wQ+BF4EqAUrBWUFcgW5BgAGJwZNBl8Gkwa3Btvft7nDi8MIs3WtZ251d3Mei3iQfJ98m3+PhIuBi3B0blZpCAurcqRsbHNya22jc6keq6SjqR8LmwdWj4CWfd8IL/i9cYv7sfyEBUD7Fn56XYIIe/dOmwdcjXyXi56Lm5OjmaUIxvcD93CLn/sXBYyCjIKLg4tpfXtMiAh7Bwt7B8qGmYSLbot8h3OEcgj7DfxIBXpNgIFUgwh796QH9zb3Bc33Gh+L0mPANaUIjAe2lLCUqqCvo6eui8EI7ka++x8eC8r3dAWVr5WLsosI3K9pQShFVvsXHwvKi7aGn4Sxfqhfi00I+wM9UPsHYXKZpx6LmJq+n9cIC/yFewbJhZqDi3CLf4ZrhXcI+w/8TgV7UYKFU4EIe/iPB8n3NnuTBWVWc29relhwVX8pi1OLdJWLo4uXlrmk4wir9wTZiwWzi6aGloGQho2Ci3qLeYl/hnUIn4bP93x5jwVlNoB/MYsIPYvN930FkaGVj8SL9zGLrn6LT4t+inuJegihiQUL+4x7BsOHm32Lc4t7hHaEcQhd+zj7sYvB91oFmLumnsePCJv7o3sHyoWZhYtui3yGdYRwCPsK/EIFeUp/fFOFCHv3iZsHT5OBkouoi5KMk42SCM33iPexi0v7fQV+Wnl0RIYIe/emmwdKkn2Si6eLk4yTjZMI9xj4dQWbxZaRxJUIC/uLewbDiJt8i3KLe4V2hHII+wz8TQV8U32CVIEIe/eImwdSkn+Pi6eLn5GjlKsI9wz4QQWcyJSUw5IIC/txewajiAWjiJeGi4CLc1VZMkwI+y37AcD3VgWaw6uZv48Im/uiewfJiJx+i3CLe4R2hHII+xD8UQV8VoWAT4QIe/eLmwdUkHuTi6qLlo6Xk6cIzPeB9w/7awWda55ui3aLenx/bIgIboiLe/eni4ubBUyRgZFswQj7PPe59773dQWooaKapIsIC/s6i/vj/IBT+ID7SYuLewW9iKN/i3iLg4d6g3AI+wb8JQVr+wR7e1eFCHv3WZsHWI94m4uni5aPpJCdCPcK+EDJ/Laci/gM+MX7EvxfBXpNd3pKhAh796MHjJsFTI15mYuli5uSoJKkCPcP+E8Fmb6VmcSUCAv7WnsGxIaXgYtni3+JgIV2CCH8GPtj+If7NIuLewW6i6N4mmgI+wn8MwVn+xR9e1ODCHv3WpsHV495louni5iOn5GgCPcG+DoFC/d6/Lqdi/cm+I8FsPcVjY3KmQgLi/csOuz7JIo2izhmRk8jMEL7IIv7Dov7KeM29xaL1YvWpsy39wvb4/cfi/cmCAuLJV77OTcjXVNSZEiLN4tdx4v3AYvvtPcZ1O68zcq+1Yvbi7xRiy0IC3sHxISZg4twi3yHdn5cCPsI/DIFeUqCglKDCHv3iJsHVZF8l4uii5qSoJKmCMD3VQWlhaGJtYvki9GeubG0rabCi8EI60S/+yceC5GinZOni92Lu2mLMotKcF9fcmx5aIVNi3mLhotukAgL/KiLYfsvnYcFu/cAq5v3MosI+yP8owV8VXR8RoUIe/e0mwdojgVij3+Ti6qLoZOikaAI9x34fsWLBcyvb1Yfi36Ke4l6CJyJBQv7Y3sGtomdfot4i3+EfH17CPsl+ztQ9ycFgKaGm4uYi6SblMKSCJv7m3sHxYade55bCPL7kzgqBfsd+zRwbVOBCHv3aZsHW3mWoR+LmZSdmZsI9yv3QM77OQWTd5F5i36Lc3p/T4oIe/ejmwdHk36Uc8cIJveT9z33VgW9xauitpkIC5n8egde+yeehgWmv5ObqqCpn7uSy4sI9z+L/HP874t9+I2Lwfc9eI4Fc1pxaHB3ZW9bhzSLCPs1BgtxnHumHr6LrabI4ggLYFJzdnqLg4uFkIuVi5mQmJCcCOn364eOBSZ4d4hkiAh7B8GKlYiLd4uDh3mGeQhb+0UFfFOEaIt3i2abeayLvYurqcLfCAuHjgU3fFaDa4kIe6UHr5eCdR+LgYd2f1oIQ/u4BWn7HnRfY4t/i4WQi5KLmpeIi6EIoH+bcHR5d3NnrHK5HuKLxtS09zYIC+NPvzoeYotjgmR2IlNA+weL+wSLNMBX6YvNi8ukxcXNzLPji9cIC4s/by1dTGRVZW5fi1yLbKqLx4vap9q50bPHt6q3i7aLp2qLTggLpHSjcm91dnBvoHWnpqGhph4LqYutlaaLCLmpgGRiZW9gH3KLgahtiwhwe3d1Zqx8rR+4i8atqbidpZWsi6WLwV+xNIsICzZcXlSLUghipG2sqKGfph6LnIWWeJx8mYaTi5WLpqGmwK4IC9+6ucKLxAizcqpqbnV3cR6LeJGBnnqafZCDi4CLcXRwV2gICwAAAQAAAA4AAAAYACAAAAACAAEAAQDJAAEABAAAAAIAAAABAAAAAQAAAAEAAAAKACwALgACREZMVAAObGF0bgAYAAQAAAAA//8AAAAEAAAAAP//AAAAAAAAAAEAAAAKADAAPgACREZMVAAObGF0bgAaAAQAAAAA//8AAQAAAAQAAAAA//8AAQAAAAFrZXJuAAgAAAABAAAAAQAEAAIAAAABAAgAAQc6AAQAAAAzAHAAfgCUAJ4BBAEWASgBRgF8AZIBmAHGAgQCLgJIAmoCpAK6AygDRgOUA+IECARWBGAEcgSABIoEoATKBNwE5gTwBRYFIAUyBUgFZgVwBXoF9AX+BiAGJgZYBoYGmAbKBuAHDgckAAMAEv/iALz/2wC+/9sABQAiAA4ANf/eADf/5AA4/+oAOv/YAAIAvP/dAL7/3QAZAA0AEwAPABMAJP/cACj/4wAw/9sAMv/cADX/8gA2/9IAN/+/ADj/xQA6/+wAQv/7AET/7wBF//wARv/uAEj/4QBQ//AAUv/1AFX/+QBW//cAV//dAFj/4ABa/8oAvP+zAL7/swAEACL/7AA3/+cAOP/tADr/3gAEACL/7QAp//sALP/vADD/+QAHACL/7AAr/+UANf/3ADf/5AA4/+oAOf/mADr/2wANAA3/swAO/+AAD/+wACL/ygAr/8UAMP/gAEL/xABG/70ASv/dAEv/2gBQ/78AU//TAFb/1QAFACL/8QA1//IAN//7ADj//QA6//MAAQAi/+wACwAO/9YAJP/TACj/2gAw/9QANAAGADUAEwBC//sARv/uAFD/8ABW//cAWv/BAA8ADgA4ACIAKQAkAAUAKAALADAACgA0ABIANf/xADb/9wA3/9cAOP/eADr/6wBWABYAWv/xALz/sgC+/7IACgANAAEAD//8ACL/7QAk//sAKAABADD//gBC//gARv/yAFD/9ABW//UABgAi//AANf/7ADf/4wA4/+kAOf/mADr/3gAIAA3/oAAO/9IAD/+dACL/wgAr/7gAQv/KAEb/wwBQ/8oADgAO//AAJP/zACj/+gAw//IANf//ADb/6QA3/9wAOP/iADr/7QBC//wARv/wAFD/8gBW//kAWv//AAUAIv/9ADcABAA4AAcAOv/+AFX//wAbAA3/yAAO/8sAD//FABv/ywAc/9cAIv/fACT/8wAo//wAK//aADD/7AA0//8ANwAnADgAKQA6AB8AQv+8AET/vABG/7UASP+wAEr/8QBL/+8AUP+3AFP/rwBU/7cAVv+8AFf/uwBY/70AWv+8AAcADf/wAA//6gAi/9oATv/uAE//7QBR/+kAU//eABMADf/IAA7/4QAP/78AG//eABz/6gAi/8wAJP/jACj/6gAw/+EANP/vADUAHgBC/80ARv/HAEj/tQBK/+4AUP/JAFP/1wBW/9sAWv/wABMADf/YAA7/7gAP/9QAG//oABz/9AAi/9YAJP/rACj/8gAw/+kANP/vADUAHABC/9YARv/VAEj/xABK/+0AUP/XAFP/2wBW/+AAWv/0AAkADv/lACT/3QAw/+AAMv/bAEL//QBG//AAUP/yAFb/+QBa/78AEwAN/84ADv/RAA//ywAb/9gAHP/jACL/5QAk/94AKP/lADD/3AA0//EANQAeAEL/yABG/8EASP+uAEr/8ABQ/8MAUf/LAFb/ywBX/+EAAgBYAAUAWv/5AAQAS//9AFgAAwBaAAIAvP/qAAMAV//5AFj/+wBa//4AAgBJ/+YATP/kAAUAVf/xAFgAAgBZ//QAWgADALz/8AAKAEL/8gBG/+sARwAdAEoAEABLAA4ATQApAFD/8gBU/+8AVQASALwAEQAEAEL/4gBG/98ATf/eAFP/6wACAFr//AC8/+YAAgA1//UAS//pAAkADQAdAA7/3gAPABoAQgAMAEYABABI/+UAUAAGAFQABgBWAAgAAgBX//UAWv/2AAQAUQADAFf/+gBY//wAWv/9AAUANf/XAFf/9gBY//kAWv/5ALz/5AAHADX/zgBV//sAV//yAFj/9ABZ/+UAWv/4ALz/7QACAFX/+wBa//wAAgBE//4AVv/+AB4ADf/HAA7/1AAP/8IAG//nABz/7QBC/+QARP/nAEX/4wBG/+EARwAWAEj/6ABJ/+8ASgAIAEsAAwBM//AATf/rAE4AEQBPABAAUP/kAFEACwBS/+MAUwADAFT/7wBVAAwAVgALAFcAHQBYAB8AWQAHAFoAHwBb//8AAgBV//oAvP/zAAgAGwAFABwAEQA0//4AQv/9AEb/9gBJ//wAUP/4ALz/9gABALz/6wAMAA3/2gAOAAQAD//YABv/+QAcAAQAQv/yAET/8ABG/+wASP/bAE3/6gBQ//EAVP/oAAsADf/aAA4AAQAP/9cAG//4AEL/7gBE/+8ARv/rAEj/2wBN/+oAUP/tAFT/5wAEAEIABABE//0ARv/9AFD//wAMAA3/9AAOAA4AD//wABsABQAcAAwAQv/9AET//QBG//kASP/oAE3/9wBQ//sAVP/zAAUAIv/AADUAAwA3AAEAOAADADr/9AALAA3/wQAP/7sAIv+8AEX/wABQ/78AU//TAFT/zQBV/94AV//nAFj/7QBa/+kABQAi/7cANf/7ADf/+QA4//sAOv/rAAUAIv+1ADX/9wA3//QAOP/3ADr/5wACAAoADQAPAAAAIgAlAAMAJwAoAAcAKwAtAAkALwAxAAwAMwA7AA8AQgBEABgARgBKABsATABaACAAuwC+AC8AAAABAAAAAMw9os8AAAAAxVMQUAAAAADOoXRVA+gAAAD6AAABTQAnAaQAkAH1AAIB9AAgAvMAUAMKAEwA1gCEAU0AKgFNABAB9ACAAqMAVgD6//sBTQAxAPoAGwEW/78B9AAgAfQAMgH0AAwB9AAQAfQAAQH0AA8B9AAeAfQASwH0AB4B9AAXAU0AMgFNABoCowBUAqMAVgKjAFQB9ACEA5gAdgJj/80CY//4ApsAQgLS//gCY///AmMACALSADQC0v/4AU3/+AG8//oCmwAHAiz/+ANB/+4Cm//sAtIAPAJjAAAC0gA7AmP/8wH0ABECLAA7AtIAZgJjAEwDQQBHAmP/4wIsAE4CLP/6AYUAFQEW/9cBhQAMAaYAAAH0AAABTQB4AfUAEQH0ABcBvAAeAfQADwG8AB8BFv9tAfQACAH0ABMBFgAxARb/hAG8AA4BFgApAtIADAH0AA4B9AAbAfj/tQH0ABkBhQAtAYUAEAEWACYB9AAqAbwAFAKbAA8BvP/lAbz/6AGF//4BkAAzARMAaQGQ//kCHQAoAPoAAAH0AAoB9AAcAfQANQFNAGsBTQBjAZAAZQFNALQB9P/iAPoARgH0ABsB9AATARYALwEW/4QBTQBbAU0AeQFNAHUBTQDPAU0AmwFNAGQCY//NAmP/+AJjAAgCY//gAmP//wIs//oC0v/4AtIAPAFN//gCmwAHAmP/zQNB/+4Cm//sAov/+gLSADwC0v/4AmMAAAJs//oCLAA7AiwATgLlADICY//jAqMATQL6//oCKAAbAfr/2AGaABMBzAAYAbwAHgHGAB4B2gAOAeAAGwEWADEBvAAOAcr/9AIO/98B1gAUAcYAHgH0ABsB+AATAfj/2AHGAB4B8gAbAZoADAHeABMCbgAbAcn/lAJIAA8CrgAbAcgALQIsABMCVABOAnMAGwMYABEC0gA8AfQAGwKhADcBvAAeAi0ACAHnACAChQATAckAHwLEAAcCEABdAhX/8AIEABsC0gA8AbwAHgG8ABgB9P/6A3n/+gFNAKsBTQCXAiwApgIsAJcB9ABlAfQAFgH0AAAAp/9XAAD+OwJDADAB1wAoAqwAAAK8AAABLAAAAGQAAA==\"); \n",
       "}\n",
       "]]></style></defs><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"37\">Q0</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"32\" y2=\"32\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"69\">Q1</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"64\" y2=\"64\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"101\">Q2</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"96\" y2=\"96\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"133\">Q3</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"128\" y2=\"128\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"165\">Q4</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"160\" y2=\"160\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"197\">Q5</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"192\" y2=\"192\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"229\">Q6</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"224\" y2=\"224\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"261\">Q7</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"256\" y2=\"256\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"293\">Q8</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"288\" y2=\"288\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"325\">Q9</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"320\" y2=\"320\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"357\">Q10</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"352\" y2=\"352\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"389\">Q11</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"384\" y2=\"384\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"421\">Q12</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"416\" y2=\"416\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"453\">Q13</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"448\" y2=\"448\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"485\">Q14</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"480\" y2=\"480\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"517\">Q15</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"112\" y1=\"512\" y2=\"512\" /><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"20\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"53\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"84\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"117\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"148\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"181\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"212\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"245\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"276\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"309\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"340\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"373\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"404\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"437\">F2</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"34\" x=\"60\" y=\"468\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"501\">F2</text></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Vous pouvez grâce au code suivant tester le bon fonctionnement de vos fonctions\n",
    "\n",
    "N=16 #elles doivent fonctionner pour tout N puissance de 2 (N=1 non compris)\n",
    "\n",
    "def testQ4ac(n):\n",
    "    qrout=QRoutine()\n",
    "    qreg=qrout.new_wires(n)\n",
    "    F2Build(n,qrout,qreg)\n",
    "    #fSwapTriangleBuild(n,qrout,qreg,False)\n",
    "    #fSwapTriangleBuild(n,qrout,qreg,True)\n",
    "    return(qrout)\n",
    "\n",
    "prog=Program()\n",
    "qreg=prog.qalloc(N)\n",
    "testQ4ac(N)(qreg)\n",
    "prog.to_circ().display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6031ee3d-6326-4b0a-83c8-ae94d7e2babe",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Code de la question 4) d) définir une porte quantique ayant la QFFT comme générateur de circuit\n",
    "\n",
    "QFFT = AbstractGate(\"QFFT\", [int], circuit_generator=QFFTfunction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5c11a4f2-4a4a-4f74-bbe9-b9925b8f28e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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AAAAAAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZGhscHR4fICEiIyQlJicoKSorLC0uLzAxMjM0NTY3ODk6Ozw9Pj9AQUJDREVGR0hJSktMTU5PUFFSU1RVVldYWVpbXF1eXwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAL9mAGFjAAAAAAAAZ2QAAAAAAAAAYmjFAACbAAAAiwAAAAAAAAAAAAAAAGAAAAAAALm6vb67vAAAAADCAAAAAADAaQAAAAAAAAAAAAAAAAAAAAAAAABsbnNlcHFyAAAAbwAAAAMAAP/vq4X/tQAyAAAAAAAAAAAAAAAAAAAAAAAAAAABAAQEAAEBARhTVElYTWF0aEpheF9NYWluLUl0YWxpYwABAgABADb4awD4bAH4bQL4bgP4bwQe4Woz/wwCWQwD/Fn7Zvoe+cgFHAUnDxwAABAcBroRHAAxHE0hEgBVAgABAAgADwAWAB0AJAArADIAOQBAAEcATgBVAFwAYwBqAHEAeAB/AIYAjQCUAJsAogCpALAAtwC+AMUAzADTANoA4QDoAO8A9gD9AQQBCwESARkBIAEnAS4BNQE8AUMBSgFRAVgBXwFmAW0BdAF7AYIBiQGQAZcBngGlAawBswG6AcEByAHPAdYB3QHkAesB8gH5AgACBwIOAhUCHAIjAioCMQI2A+0EBAQVBBt1bmkwMEEwdW5pMDEyN3VuaTAyMzd1bmkwMzkxdW5pMDM5MnVuaTAzOTN1bmkwMzk0dW5pMDM5NXVuaTAzOTZ1bmkwMzk3dW5pMDM5OHVuaTAzOTl1bmkwMzlBdW5pMDM5QnVuaTAzOUN1bmkwMzlEdW5pMDM5RXVuaTAzOUZ1bmkwM0EwdW5pMDNBMXVuaTAzQTN1bmkwM0E0dW5pMDNBNXVuaTAzQTZ1bmkwM0E3dW5pMDNBOHVuaTAzQTl1bmkwM0IxdW5pMDNCMnVuaTAzQjN1bmkwM0I0dW5pMDNCNXVuaTAzQjZ1bmkwM0I3dW5pMDNCOHVuaTAzQjl1bmkwM0JBdW5pMDNCQnVuaTAzQkN1bmkwM0JEdW5pMDNCRXVuaTAzQkZ1bmkwM0MwdW5pMDNDMXVuaTAzQzJ1bmkwM0MzdW5pMDNDNHVuaTAzQzV1bmkwM0M2dW5pMDNDN3VuaTAzQzh1bmkwM0M5dW5pMDNEMHVuaTAzRDF1bmkwM0QydW5pMDNENXVuaTAzRDZ1bmkwM0Q4dW5pMDNEOXVuaTAzREF1bmkwM0RCdW5pMDNEQ3VuaTAzRER1bmkwM0RFdW5pMDNERnVuaTAzRTB1bmkwM0UxdW5pMDNGMHVuaTAzRjF1bmkwM0Y0dW5pMDNGNXVuaTAzRjZ1bmkyMDNFdW5pMjBEN3VuaTIxMTN1bmkyMjAydW5pMjRDOHVuaUVGRkR1bmlFRkZFdW5pRUZGRjEuMS4xQ29weXJpZ2h0IChjKSAyMDAxLTIwMTEgYnkgdGhlIFNUSSBQdWIgQ29tcGFuaWVzLCBjb25zaXN0aW5nIG9mIHRoZSBBbWVyaWNhbiBDaGVtaWNhbCBTb2NpZXR5LCB0aGUgQW1lcmljYW4gSW5zdGl0dXRlIG9mIFBoeXNpY3MsIHRoZSBBbWVyaWNhbiBNYXRoZW1hdGljYWwgU29jaWV0eSwgdGhlIEFtZXJpY2FuIFBoeXNpY2FsIFNvY2lldHksIEVsc2V2aWVyLCBJbmMuLCBhbmQgVGhlIEluc3RpdHV0ZSBvZiBFbGVjdHJpY2FsIGFuZCBFbGVjdHJvbmljIEVuZ2luZWVycywgSW5jLiAgUG9ydGlvbnMgY29weXJpZ2h0IChjKSAxOTk4LTIwMDMgYnkgTWljcm9QcmVzcywgSW5jLiAgUG9ydGlvbnMgY29weXJpZ2h0IChjKSAxOTkwIGJ5IEVsc2V2aWVyLCBJbmMuICBBbGwgcmlnaHRzIHJlc2VydmVkLgpDb3B5cmlnaHQgKGMpIDIwMTMgVGhlIE1hdGhKYXggQ29uc29ydGl1bVNUSVhNYXRoSmF4X01haW4tSXRhbGljU1RJWCBNYXRoSmF4IE1haW5JdGFsaWMAAAAAAQACAAMABAAFAAYABwBoAAkACgALAAwADQAOAA8AEAARABIAEwAUABUAFgAXABgAGQAaABsAHAAdAB4AHwAgACEAIgAjACQAJQAmACcAKAApACoAKwAsAC0ALgAvADAAMQAyADMANAA1ADYANwA4ADkAOgA7ADwAPQA+AD8AQAB8AEIAQwBEAEUARgBHAEgASQBKAEsATABNAE4ATwBQAFEAUgBTAFQAVQBWAFcAWABZAFoAWwBcAF0AXgBfAYcAYgBkAGYAgwCAAKEAfQCYAHIApwGIAJEBiQB+AIgAgQCCAIQAfwGKAYsBjAGNAY4BjwGQAZEBkgGTAZQBlQGWAZcBmAGZAZoBmwGcAZ0BngGfAaABoQGiAaMBpAGlAaYBpwGoAakBqgGrAawBrQGuAa8BsAGxAbIBswG0AbUBtgG3AbgBuQG6AbsBvAG9Ab4BvwHAAcEBwgHDAcQBxQHGAccByAHJAcoBywHMAc0BzgBvAIkAQQAIAGkAdwBwAHEBzwBjAdAB0QHSAdMB1AHVAdYAygIAAQAEAAcATwCRAPIBjwJYAyUDSwODA8MEmwTABMwE4QUBBRgFdwXQBjIGtgbtB0YHugfkCGwI6wkdCTwJWQl3CZUKEArVCvELDAt3C+sL/Qx7DRQNJw03DZUNpQ38DgwOJA45DlAO+g+CEBcQJhCoEPkRfhGNEgASDxJHEl8SlhK4EscS7xOHE/4UWxT/FWIV5Ba1Fz8XZxeUGBcYbhlFGeQZ/RqPGwYbaBv4HGUdAB14Hhoewx9SH8AgKyBBIK0g7yDyIaEiQiMrI0MjWCOQI7UkQSRjJOolhyXeJfMmECYrJlImZCaeJugnBCcfJ3cnmSerJ7onzShHKFcoZyi2KMYo3ilzKYgp9ioNKlgqZyr0K4ormSw9LMYtQC3bLiwunS8jL5kwMzCkMLcxMzGlMisydDMPMygzpjQPNF40sDUDNXg1/zZwNvM3pzg6OPE5gzoFOqg7BDtHO708RjyrPNM9Vj16Peo+QT6wPxA/XT/BQCZAOUBOQGBAckCMQKZBUkJmQnVCiUK8Q0RDtUSNRKdEwETP+IQO+5IO+z+A9fi8nwGy9QP3HfdFFcf3OKHBue2qzZOmi6mLrXucb4tli3lsfjZ1+yKDZmL7Ugik+yEVqHakbG9xc29sn3SpqaWjpx4ON/kanwH37vg5Fcb3FKbUi5uLm3uXeotyi3R8hXCGc4I8gycI+zAWxvcTptWLm4ubfJd6i3KLc3yFcIZzgjyDJwgOiIuf91XB9yPBAfiw+GQVLIvb92hOizv7aPsWi9v3aE6LO/toIYuAVeyLVfsjIYuAVeuLBTv7acmL2vdp9xaLO/tpyYva92nzi5bBLYvB9yPziwX7ORZV+yP7FovB9yMFDoufAfcP2fdH1gP4hfj3FWuiYZ1clgibz2mLekx5iwVCi2CCYV5xb3tsi1yLP7Bj7UwIRvu9BT2ja6yG9Ah7iHH7DwWva8J0xYAIdTCui6DkBeGLq5DCtbaso76Lxovgcq77CeEIw/eBBcp0n2aNQQiaiQX7GfckFVT7cwVOsHiqi7kIw7nA1B5s++MVkYYFz1OceYtRizRWWyGCCA73j3im97qnh6b3eqW6nxLb0vdRo8PT91KiE9+A+VX3aRXVaLZOKy4jID3AT88e4dn3A/cNH3SNFSFKJkZrc6iyHovPreO3upeZoJSbiwixpGhXH2H4fxVfBi8yfoNNi2aLc5VoqHChf5F2iwglMCf7BR8TN4A9vlDOHqyLpZampbu4q9aL0YubipaInKuAnYili8CLqpmwtgj8Hv0muosF9xb43xX7B04mRGl0p7Uei8Kcxqq8n6yWlbSfnHmYgpmEoIGPhItuCA73pnm8Wr/47KsS1+n3Ltz3BNATvPlcyhVzdHSCdItci2imY86ps6evp7W+1pWVvZAInPtQeAeziJaEi3WLaHpqTURsvGbiePDIqqecpqOwq56vi64IwGG0TilOPvsJHouAi2KSYSZfYHhnblpjcVOLVAgTXCrSU/cDHsuLw5zayQgTvLNWvXG3i8WLtZyrwAj7YvicFYtZdWI2Voepip+LpQjkrLSzpJl1Yx4TXDr8cxVbZmN1WYs8i1q/i9WL2c3Q7LEIr/sTrDmtYAgO+7b5Gp8B9y/4ORXG9xOm0oubi5t+mnWLbot6eoZ1hXOCOYMnCA77P/kdnwG10AP3wvkxFS83VFdkTFc2dSWLJIv7FK77FsskCJ2RBWbxgMiL7Iv3YL/3cfcs9yQIDvs/+R2fAfdw0AP3P/ksFa06mjqLJ4stefsHbCtpIWZINzIImHwF5tq/w7LOveGn6ovwi8GExX/DetV7slzfCA75Gp8B99z4XxW2ppyTupG2kJmbi6GLoX+cdIt+i4GHfHpVUomJX26LupGklasIkqOPmIuWCKJ+nXRygXpyHouCjX6Rd5ldj3mLYGSieJtqsHeifpN7i3eLfniLd4tzn3y0hgi1hq16nIEIl4QFYHF9hVyDYIR4eotzi3abgJ6LnIucl5ygp66XlKqelJCPjY6OCItYhnJ+Z4R2iICLggh1lnulp5Sbox6LlImShZ18tYehisAInX4FqnWZhKVqnnSXgpqLoYubl4uki6J4ml6Ra494lX+RCA73P4uf91zNAffFzQP44vdwFc37b/dwSftw+29J92/7cM33cAcO+5LSywOQ+xUVIAoO+z/3VMoB9673kxX7b4t9TPdwiwUO+5KA9wMBpvcDA/cethWqcaVtbXJya26kcqerpaOpHg77dnmf+RifAfgW+S4VQov8Dv1A1IsFDoSn+QenAava98faA/iF+D0V9zZS5CX7Mfsp+3X7f/sfwzfxHrWLtpm0qPLU2fc9i/cnCDzoFYv7FmT7OVElZkldaV2LW4tqvYvgi/a+91i/6a/Msqm4i8eLo1mLOwgOi58B+CX5OBU+e4eNM3gIdIaLfAWejKGMnYsIjgahmH94H4uEiIGGeAj7HPx8BYBldYA8hQh896uadgdfdZSiH4uVlrKSpAj3I/ibBY+ZjZWLkAiPiY6IHg6L1/ij1AH4AuED8PiPFa7OvqjHi9qLs1eLRot1iHiFfnNVXkxJRQj7Zvt0i3r39ou99xp6kgVzWXd8UIsI+0mQBvdQ91QF9wr3Daq5i86L6knVK4tdi2B/ZG1ocHRpc1AIDoSx+O+1EvfZ23DiE9D3RvjLFa+6rJ+2i8CLrmeLVIthd2hhbmBtYX0xewh7owcT4OvLWfsAH4tcf1txbHJvaHlqi3iLcZRxonCjeZF4iwhxenlyarJz0x/Ti8uevLbEva/Ri9qL1HC4R6UIjgcT0PcGs7Syi9WL01W9PYtBi0trakMIDouf9zLKAfhz+TgVYov8NfxDd0j3mota+0bai7n3RvCLmcoriwWa99YVK/vW+2iLi4/3xPfSBQ6EtfjE0gH38tAD+H/5LhX7lIsj+26LewXpfa95r26rcaBdi1aL+wQ2KDGLb4uBk3Ggc597k3uLCHR6eHRjunrG9zn3GfcS9zkfi/cbM8r7GKQIsuP3eosFDoSl+ByvAanX95/kA/id+UIV+yJ6RHAtQfsIMEf7Gov7Gwj7F8U39wz3IPcG9xP3K/FA1S8eb4tlhnF7CIeNBdH3E/cY7vcMmwj7KPwRFYtJdDhoV2tcanVdi1OLYbyL3YvUoeGpuaOwrp6yi9GLulmLQwgOg5/42dQB+K35JBWElfwJizn7HJqBBbvEpJvNiwj3a4uNiPwD/OrRiwUOhKH5EqISqc+z2fct1njPE+j3dff8FfsMaEBFiy0I+wvsWvH3EObY9wMei9RuuzXaCIwHE9T3DK+3t4vZCNxJwiAgQFMrHotVoGfNQgj3XPc9FYtUcGg0Yj3UeqqLtQjMsbbLy7ZXRB4T6FP8CxVGVkQ8R0S/3R6L4sbV5a0I9wL7Bpd5i1IIDnqf93a5+AulAdDj95jWA/f096QVe15bRktWQU5bcjx6CHgH9xihzKTbyfcP6tD3GIv3H4v3GEvh+wmLVYtWeGFlU1hmO4s7iyLJQeOLCLSLrpfArAjQ94gVi0FzLm9tcm9geWOLS4tnvYvki8qezq24p7Cso7qLyYuwWos4CA77P4D3A/d69wMSvfcDgPcDE9D3mfgUFSEKE+An++kVqnKlbWxycWxupHKoHquko6kfDvs/9973AxLxy3v3AxOg95n4FBUhChPA+3X8lRUgCg73P4GfAfjkgRWL0/w491P4OPdTi9P8kPt6i0kFDvc/9wzN9xrNAfji99QVzfyMSQf4jPtcFc38jEkHDvc/gZ8B+OT3cBWLzfyQ93qLQ/g4+1P8OPtTi0MFDn/0+LmhEvcY9FbL9yrVE9j3bPdCFZKnBZnEqbXVwvcI4pqvi8gI3lS0KT1SXkttl3ijo52fmx6Lk4qRhpaFmImRi5MIqaWdt76oZV8ei1d4XEpKMzOBbHknCBPgsvsfFRPQqHOlbh4T4G50dWofE9BtoXepHqekoacfDvg0ebL3CaxrtfenuPcaqhL3Ct73DNL4CrMT3/lCzxU+aFJ/SYsI+0D7BfcP90L3UPcH9xX3N/cw9xf7Dfsi+wBILk5ze5imH4uQjJaRogjI94BGi4FmBX6wc5psiwj7DT77LSMfEydMtGG9HrWLuKStuQgTz5Vdq3G6iwju4Pb3FPcs+xH3Iftc+1/7NPsu+1X7Uvcw+yf3XB/Si8aY6bcIEzf7FPf3FSRN+wJSZnWrvx6Lvp26qLGmrrKfpIsIqJZyZh8O9ouf92Kv+BafAfjIFiIKvfeaFftWi/cp95sFDvaLqfjlqQH3FvkhFSMK+xj7thUkCltrFSUKDvc3ebj4768B+UX5LBV2BoN7gYV3i4KLf4t3kmGaYY1qizyLP3BLXfsCPT77F4v7IYv7OfcAK/ctiwjyi9u25fUIeZoFNDFPbjmL+wOLS8yL9yCL9wKv9wbT2MLG0bHVi+OLvFOXIAidiAUO926LqfjlqQH3F/khFXsHyImaf4twi3yHeIRyCPsO/FEFe1CBhFOBCHv3lQf3CYvwpdTE7dfJ8Iv3EAj3Q/sJ6ftDHilGFZWuoY+xi8WLtX+qdLxmqEyLO4smZPsKREZNTz1tJotdi3WWi6UIi5iQn5zJCA72i6z3uK/3l6wB+Q75IRUmCg72i5/47KwB+Rn5IRX8hXsGzYWVhYtvi3uId4RyCPsP/E4FfFeBdVGHCHv3j5sHUI95louji5qSn5KkCMb3aQWwiaOKoYu6i6eHi2OLe4l9hWwInIbX9395kAVeMYiJ+zyJCMv3dwWSpZqRuYv3RIuifotCi4WLhoh1CKCJBQ73bnmw+PmtAflm99MV+597BquIBayImX+LeYt1hXN3SHU+hn9/f3V1ZX9ei/sVi0LZi/cXi/cDtPcDzN4Iu8jPsdqLyYu7dqploXCYZ41gCJ2IvPdZfJAFenN6gXGLgIuBjHSUX5xakmKLPIs/cEpe+wBAQPsTi/shi0emPrpbCL5Y1nLii+OL057Ytgi8908FmsSclsyPCA73bouf98a1952fAfmV+SEVJwoO+z+Ln/j5nwH4FPkhFSgKDk95q/j/nwGF6AP4f/khFfuSewbKhZmDi3CLfId3g24I+xP8WgWAY3lzc4tzi4CWi6eLlI6Ri5cIpHOgcHB5c2tWumjRHr6Lt5yosaWto7yg1wjy+AMFnMeTkcSTCA73N4uf+PmfAflm+SEVKQoOv4uv+OmfAfjD90gVd5EFb1F1amt2WmpshieLOYt0lYuqi5mPnJGiCPcM+EEFm8Skm8ePCJv7pXsHyYeagYtui3yId4NwCPsO/EoFeUyDglOFCHv4kQcO992Ln/j5nwH5/PkhFSoKDvc3fJ+Gn/j5nxITYPlr+SEVKwoToCwKDvdueaz4/qwB+U/4NhUtCiLKFS4KDvaLn/exsPetqQH3JvkhFS8KSE4VMAoO9277Ss/5f6wB0Ps9FbGgsJWzi5+LqYe2fcR5wIOxi9iLy6m9uJ+dnJ+aoAh7lgVTUWN4Q4tqi2aWYpVflV6VaYsIcovBxAXWkK6Uwaj3LNvz9zqL9zCL9xsz8fsdiz+LM24+SvsBLUv7Fov7D4v7Fck29wZ0CDA7goQ+VQj4q/kNFYskXvsjTS5TOEhiQItBi1nMi/CL77v3HsXixODJs9aL24u8UYssCA72i5/476kB9xj5IRV7B7WFj4qWhJKGkn+LgIt6hniEcAj7C/xDBXtQfXhUhAh794ebB1KRgZaLqYuVjZmWsgjC91/NhvcP+9j3J4uLmwVei3eidcYIMvd/Bc6arJeqo7SqpLyLuwjgQ8P7GB49TxWQnqCWqosI2bVgRi5FUvsLH3mLg4xyjwgOea74/Kx4nxL3F+P3EeITOPiQ+S8VdAZ9doKGdYt+i3+OdpMIE9h2lGqQbIsrizlQiyKLVZprx0uYfpd9mXwIsmEFuVmZbYtgCD9VVz43T9DtHouSi5KNlAh3jWn7dJ2LBZKim5Sfi5aLlImmgbl7poSqi/cHi+Lci/cGi8x1tjDnMOaDm4u8CMq2sNDsoU4lHp2IBQ6/i5/46q4B+Q35IRUxCg73bnm0+PafAfHlA/mR+SEV+1p7BsCGnICLbYuChGh7UAhL+30FXvs4TUf7BYs9i0+6i9KLoZjJpuoIyvd2BZ7QnJrPkgib+6R7B8mJnX6LcYt/h3yGeQhX+1EFcSx5SItViyzlRvcXi8yLvZq2sLavq8Wh1gje97EFsfcWj5DJmQgO9nmf+QufAflE+SEV+017BriGnIGLeIt4eWBsVgj7Zvv8SvhPBYqQi5CLkIutmJXKkgib+4R7B8OEjoai+yAI3fyLnov4Cfj7BZymm5eijAgO9915n/kLnwH6HvkhFftMewa9ipx7i3KLeIFzfnII+1D8AWP4MAWLjomRi5GLq5yWvpAIm/uAewfFiZaCkVgIk0r7QPvwX/goBYqSi5OLkIuxoJO+kAib+397B6uHlYmUgpl8j3qWLQjI/Jaei/dy+FmQi738WZ+L98H42AWowpWTsZcIDvaLn/j5nwH5I/khFTIKDr+Ln/j5nwH5DfkhFftRewaoiAWoiJaDi3qLcF9NIvsQCGRdbPcCBXPgf7eLmouhl5PHkQib+4N7B8ODkYOaVwjX+59Q+2EFeUt0fkmHCHv3tZsHZ44FZI59lIuki6CSpqLaCK/3D/dv96IFrLSTlaiVCA6/i6/42a8B+PL5ExUzCg77B/stpvmOpgH4G/krFftBi/tZ/cT3UIuSplOLBWt6lJ4fi46NlY+bCPcy+S8FkaWXl6iLCMkGDvt2eZ/5GJ8B99N5Ffu0+UBDi/e1/UAFDvsH+y2m+Y6mAfgS+SsV+1GLhHDEiwWsm4N5H4uHi4aHewj7NP0yBYRugX9tiwhNi4Rw90GLBQ45+RqfAfg698EV+0n4AU+L+0n8Ac+L9yL3tYyL9yP7tQUO+xG9AfiI+xEVvfyIWQcO+z/5GJ8B98v4gBX7B/cpBX6cf5F8i3eLe3+LdYt/kYGYgQj3ICEFDoiAvFuf+C2hEpzf91jUE7j4Y/cDFXBuBW1qfoOCi4OLhZGLkouftfdAuvc/jpWMjY2UCISOToSIiIBbBYOwbqBgiwj7Gfst+0n7Lz+3Y8Mf0YvFt9b3BXY5iYOLcggTWG6Xf6ces4ujntbmCBO4+wP3mRWLRG01XEdtYFxUWYtni3Oei8KLyq7ktcq1yLequIsIrqB0aB8OgKL4ELwB+BjgA/c397YV3/fGoN2GkAVZgmeFSIMIegfGiZCKi3WLgoh9hXMI+yL8n4uFBW3UdMT3L/c590L3MthatkgeRYtUZUf7BQj3dJsVi0FZKE9NZmVgdmCLbIt8louii8en7LfVttS5tbuLt4ulcotOCA5PgK/4H6ABqeH3gdMD9/L2FVVSZXJWi1KLa7WL04vkruDDxqips52zi6KLmYOLf4t4fICLeQh3lnenpaGgprpfrU4eTotSdVpkRFJXNIsuiyXBV+iL1ovAqsjYCA5+wFi7+BGiEpri903XE3j4nfk/FVaAZ4VLhQh6B8KJlIiLdot9jId8Vghe+zeKiwWFsnqeYYsI+xb7NvtB+zY/tWLMH8+LvqzG7oBZiXuLdAgTmHCaeaUevYu7tLzUCH+VBVVNgIJ6i36LhpOLl4ubrfcIqvcGCMf3b7L3LAUTePs/+9AV+ywj+0AvaHSmuR6L3r33Ac3Rp6iunKeLCKKjdmcfDk+AuPgUogGq4vd4zQP3+vcBFUNQbHtfi1OLZq+Lwouai6WVn/dHovTZi+EItW6lVvsq+yn7NPsvOMFV3B7ei8uxxNEI+273LxWt5M/YxIuni5J8i3OLbHhnbG1maGV5NXYIDvt2+2Og+Nqr93ihAfsnzvhH0AO0+EAVhGvmizP8OAV0+wBrVWGLf4uDkouUi5aUkIuYCKB8m3R2enh0aK1xuB7mi87ttfdNCNP31PcAi5GrIIsFqPcysNHDi5mLk4aLg4uCgYaLeghznnydop6goa9mpVoeTotiaW1galx6VHVECA77YqH346D3VrKZoRKTwqzZP9X3Lcdq2hP0APhr+AIVsk8HiIuGjYORcJ5qlGWLJosnRosli1eiZ8N3CBP7AFVydG2Lbot+lHydgClQeHCLWAhDzGfx9xnYy+Iei8ddtyuiX5ZwmIudi6Cen5yLjYuNi46KlImWipaLCBP0gOjn298fi5yLm4KdCEV5FYthfmJ3aXNicHlpiwhldae67sfUybCeeVYfE/kAcPxKFVhVYDo7XKvRHouikJuanpmdta2Ui5aHlYiYhwj2aq9vi10IDoK6ZZ/4Br4S97TajtkTuPhl9woVVUd/f3uLgouEk4uVi5abyZy/qemd1Yuki7B4qV2LTYs9SjH7Jgj3DfhThJEFUX5khE+ECHymB52ig3ofi32GeoNsCBN4+yb8vtaLBbP3Lpuus8i/2svIr4uii5CBi3yLh4h+h3sIVPtjBX5ahGyLfwgTmDQKDvt2gLr46p8BvNYD95z46xWodKVwcHd1bGuedqiloqKnHmH8eRU1Cg77dvtjoflx8wH7EM/3e/MD96v46hWnc6Vwb3J1bWyjdqmlo6KmHmr7NBU2Cg5PgL9inxITQPhh+EAV+0d7mQakl4SAH4t3WlstQwhgavcM+FyFkQVQfmSEUIQIe50HrYuahY15iXqIdH5bCPsh/KTWi7v3SLOrBZtfpU2daAgTgKtMn3ioi7OLpKS53wh8lgWGgoaChoN5bH+AfIt4i3SwZOcIZuMF9yf3F6qfuo4IDvt2gLYBtNgD96v5OhWFkAVQfmaEUIQIe50Hq5yBfx+LiIuFiIEI+x38oAWIgYp/i4OLZpx4q4vBi7Cpx+oIfZVyaAVuYnR7fIuBi4SRi5eLk46ckJ0IDvdugrpln/gFvxL39tjf143aE7z5VPQVfJd2cQVtZnl7eouDi4eQi5aLj4+dkaIIz/ePBYyQjZuLkouvdqZmi3eLeIZzfFpsYllF+wOm2JjDi56Lr3ejY4sITotFSTL7JQjF92WIjfs2bIt7pIsFppmEfB+Lf3w4Y/sZCBN8YPsk1osFu/cyma+tv8PgxsWti5iLlIKLe4t+cyFf+ywIcC7WiwWy9y6fvLzQvdG+uqmLlouUgot/i4aJfoZ3CFH7dwWBZIh6i4EIE5xtmXulHrqLt6zA1QgOgrpln/gGvhL3s9aK3BOw+GD3CRWEgoSChINuZnl7fYt/i4eUi5SLk4+cla8Iw/dfBROokaCPoIudi691pGCLS4tITyf7NAjO926HjQVWgG+HOnsIewe+ipmFi3eLhYqFioYIE2gr+/LWiwW69zKTorjOyui4vLOLmouUgIt5i3+FZ4NsCF/7NgUTkH1XiX6LgYtloXuki7qLpJ/P6AgOgKD4LqABpt/3pd8D+Gj3wRU3CjekFTgKDouAnvgatgH4EuUD92v4QBWMj4yQi4sIjYmNiB77MHWNfKGLBZuniHMfi4aGcYBjCPsH/EQFf1x+fGCKCHv3X5sHXHySoR+LmaLdnNGkfqCHoosI9yb3K/c29znZYrpBH0+LUmtVOgj3WHwVi0V2QltIX01balaLb4t3m4uhi62v9xWo1qLHxsHAi7iLnG+LUggOgMD4DaEBpOED+Hj4QBVCi3taBYG4cZxiiwj7Hfsw+0b7MkSwXsof2Iu+sNv3Ewgx+7YFgGZ6fEyHCHv3gZt8B2Z3l54fi46Mj4yPCMj4khWLOEn7H0dQcXRsfnKLZot7qYu6i9688s/Mq6mrnqiLrIulcItqCA77B4uf+CWfAfdE93MVwvdsiI37L3CLegWajZOMk4ufi52Gi3aLdomCfVcIOvu414sFvfc8nbO21a/Ip6ydi5KLjoeRgZR8k4CdiwipnKOpqXigbx90i215cXBiYGlWeGEIDvsHfp95oPgsonifEvcB1LnXExz4AvhOFX0Gg32Eh3yLg4uCjHiRCBNscpJ9jnqLQYtcYYtJi2ufXrZVslqcaYtri1pub1yLV4tptH3qCHuLBROMd/szm4sFkpuWkJaLlouZip6DCBNsooKaipyL3ovIvovei7J5slnFZLl8qIumi7Cjn66LvIupapU4CJsGDvt2gLz3+qsB97z4QBU7i6fyBYyNi5CLi4uQiI6Fi4eLhYiHhWdVSlprhHOGgoKLgIuLi4iMiAjWiz37vAWDa4Nsi4CLcp5/pou/i6qox+cIfpIFWkx7e3uLgouFjouYi46MkoyPCOL33N+LBQ6AwFi6+BOfErXY9z7ZE1j4YfcLFVhIe317i4SLh5GLlouXmbqQngja979BiwVa+xp9ZVxECBO4TS1dVmmLfIuGlYuai4+NlIyOCOT394eOBVJ+Z4RShAh9B7GLjoqUhpGIkIOLhIuDhXGDagho+x8FeUKCZ4t4i2ade66L0ou9wPcK91Zr+wB+SIt1CBNYbJ16qR66i6WfzO4IDk95n/g3nwH4C74D92PRFYX3G4XCfs529wCLkYKLhouEioOIa4RohF6ECH4HloyVi5WLsIuWepg/mD+W+xmLRghzB3qOgZEenIumrMLGnZ7Dy7jRrsGnxYu2CKZ0q2p2en52Hot7kn6de5h/kISLgYtcSvsCQ0EIDvc3eZ/4N58B+Oy7A/gn+D4VlomOhR6Gi4iJhoMI+1T7xAWH4333EX3PhKuKjYCLhIuCh36IbYNph2yGCH6nB6iLlIaUZpdbliCPNAiPMAWNZI2DlIuWi5ykr9Cer52snakI5PcsqPvKBY1xjYKSi5SLlJWmrAiUlgX3Hvc81fcJi8sIq3WjbXV6fHsei32Qf5t8m3yRg4t/i2BpVvsX+zgIDk+AwvfpwwH3h/f3FX3Pf51yi3SLaoROdQiAh457nZAFnpCXjZOLpIuSg5lPCKf7EDn7CAV2bXh4gIuFi4GOgZF+koGPgosId317d3Gee6ofqouflLfGCOP3C6j7CwWXWZp5q4uxi6WjxeUIfJQFg4GHhYJ/dG2AgX6LfYuCmISnCGv3GgWFo4mZi5K32K+3nYuji5R6nosIn5maoKF6mnMfX4tmZ0UgCA5P+2LC+NCfAfgWswP3h/dOFXrkVvc6fIsIhwZVg2qFd4eBiYCJgIkIegeWjpSMlouzi518nlqmR8L7dItji4CHf4V/g35eUHl4dHJ/g36LCHGLi6doiwh1enl1caB6qR/Ei/b3B/P3QN73Hrv3AovECKl1pG10enx1Hot7kYGffp5/koWLfYtfZkM2+yEIDvsHOqD4QMcB98jCA/gQ+DUVlvuvB2v7CJuHBZ++npS/iwj3HIv7yvwIlIIFm5iYkJuLpYurfrpuvWytfqiLCMOwr7OhfZp2H3uLe3qKeouDjYORf46FjYaLh4uCgIV7i3KLeJdxsWPGdZZRmAgOI77WgtYTQPgr+UMV+wWLXGluIQhb+0YFd0J1c0t6sn2ZfYtui3N/VXVACBOAdT+BX4tzi1Ssd+eICI6WBWWWfJ2LsIubkaSbyAgTQKXpndmLnYumep5knMycpqih3gi49zwFoNqlqMmbCA77eXmf+RifAfTNA/c/eRX5QEn9QAcOI/dk1oLWE0D3cfk4FbGAmniLZot9hW57UQgTgHEteT2LeYtvnHmyekl6cW51OAhe+zwFdjxxbk17CIiABfcEi7utqPUIu/dGBZ/UoaPLnGSZfZmLqIujl8Ch1wgTQKHWlbmLoovCap8vjggOsPdPy4/LAfhm99cVZlN6e2SLbotZqHmTZpxrmV6LXItfcWxPCK9ZBZ29r6Gqi7yLunKcgax4pH24i7mLrZ+4zQgO+5IOg9VDod2n91W196yoEpWhE3Td9/0VgmH3BIty+2AFb5Z4i3yLCFRqa2dko3K0H66LopixvQgTnM5Wp3+8i86LvK+lywiAlIGEBXB4e4Jni2CLXZNEqbTkkZul9wII9xOLkrX7EIsFufd3nsDEi6OLl36PbJBomYKciwikmZmmuGWqVB9Vi2B3Y1tXTXNJd/sFCBNkXvu0FXxpbnRwiwhzeJugpqGdqh+gi5eGp3cIDouf9zaz5bP3rZ8B+PH5IRX7UXsGpIgFqIiYg4t6imhaT/sE+xeDgYWEfXsIbu8FbuuBt4ubi6CUksuRCJv7gXsHzYOSgZpYCMr7bPsfi39j9zaLjoF0O/s3i39j9ziLcjcFeU10fkWECId796+Li5tnjgVijn6bi6WLoZOlotEI90aLl7P7Rouj3ZGT9zyLl7P7KYv3Sfd0BauzlpKrmQgO+zag94Wg95+g94CgEsDIc8SwyLXFq8VlyxP1APeN+CIVeZJ6j3mLUYtbVItHi1yjV7pVCNc0BbFfl3SLbQhWYWZPHhP7gGZpnJ8fi5GPj5aSn5eSl4uhCKZ6m21odnZoTsdc1+TOxtkei7OBoVbOCI2OBZeFkoqZi9KLur2L14u0fLRxqwj7D/cqBXqggqSLpQi+rqvEHhPyQK2lfXofi4WHhoKDfH6FgIt9CHGeeKarn6CtxVW0PzVOV0Iei1+cab1NCBP0gPcS+2UVZG5rZ1Eg9xbSsKiosB6si65zslcItlKZbotpCA77P/iQ7QH27fHtA/gp+MEVOQr7XBY5Cg77P/iovgH4L/jbFfvBi4BY98GLBQ4j+Bqt926tAfCy92SyA/gX+KkV20zKOztMTDs8ykvZ3crJ3B5kFk9cWlFTXL3Gx7q8xMS6WVAeDvs/+RifAfdI+IIVrov3P/UFl5KQlIuXi597m3eLgYuDiISECA6BwgH33OAD+IX4QBUzi0L7zQVoXl9yYIthi3Cmi7WLlYyYjZIIzvewM4s2/AoFhXCBb3lebVGDcotoCGyWfaK2p8LiHouTi52KnIqci5mLloudi5SNoJ5WqnTAi8CLu6fAyYh9ioSLgQhknnexHrKLpZm1tgiOlAVyd32Feot6i4KVi52LlI2Sj50IDvuS91v3AwHR9wMD90n3kRWqcaVtbXJya26kcqiqpaOpHg6AoPguoAGm3/el3gP4dvkRFWunKGAFY6xmnV6VCGh6BbV6pXquagj7D1WsbvcJvgWzV6FWlUYIiYoFeatynF+LCPsk+xz7NPssLcNd5vc69xP3Q/dXH4voc9BN0giO+54Vi0RwKV9KZlNgcV+LXItstYvCi9yg1rzPtca5qbeLtounZotSCA6CumWf+Aa+xsES97TajtkTvPhl9woVVUd/f3uLgouEk4uVi5abyZy/qemd1Yuki7B4qV2LTYs9SjH7JgjU96L3M4uawfszi6z3D4SRBVF+ZIRPhAh8pgedooN6H4t9hnqDbAhNi3xVyosFE2z7GPyI1osFs/cum66zyL/ay8ivi6KLkIGLfIuHiH6HewhU+2MFflqEbIt/CBOMNAoO+3aAuvgVnwG62AP3cfcHFWBSdnV6i4GLhZKLk4uVj5uQngjr9+qGjgUmeHiIZIgIewfBipSIi3eLg4d5hngIW/tDBXtPg22Ld4tln3ipi76LravA3QgO+3b7Y6H48p8B+xDPA/eK+EoVNgoO+z/5FZ8B+BX4gBUz9z1ai/sx+z2yi/cd890jBQ77P/kVnwH4PvkpFWaL+yEiMvRli+r7PbuLBQ77P/iAxgH4GfkeFXVNVmZOi0eLaa+GyghuBiSwVOYe4ovT0ZnjCA77P/iQ7QH3Y+0D98X4wRU5Cg77P/iQrfcXrQH3L633GK0D9/f48xXCXrhTVV5eVVO2X8TCuLjBHmkWZm5vZWZvqLCuqamusKluZh4O+z/4nMd7xhITgPgj+QQVgGp+gHCLfIt6kG2ZCBNAZZxyknSLV4tvbnc+CKgGlaubmqSLnIujhMF1CBOApYGdhpiLu4ussJnOCA72i5/3Yq/4Fp8B+MgWIgq995oV+1aL9yn3mwUO9oup+OWpAfcW+SEVIwr7GPu2FSQKW2sVJQoO9ouf+OysAfkZ+SEV/IV7Bs2FlYWLb4t7iHeEcgj7D/xOBXxXgXVRhwh794+bB1CPeZaLo4uakp+SpAj3GPhtBZKlmpG5i/dEi6J+i0KLhYuGiHUIoIkFDvaL6fi+nwH4ohb7GPkwcYv8JP0wBfhP6RX76ov3k/hEBQ72i6z3uK/3l6wB+Q75IRUmCg6/i6/42a8B+PL5ExUzCg73bouf98a1952fAfmV+SEVJwoO9255rPeb6feZrAH4oPhBFYFmZHdmiwgpBmeLg5eDuAh4Bos8azx2WAieBp64p5iwiwj0Bq6Xe2EfngaLyq3snrwI9zCAFYv3LDrs+ySKNos4ZkZPIzBC+yCL+w6L+ynfNvcWi9WL2qbMt/cL2+P3H4v3JggiyhUuCg77P4uf+PmfAfgU+SEVKAoO9zeLn/j5nwH5ZvkhFSkKDvaLn/kInwH4yBabB1aPgJZ93wgv+L1xi/ux/IQFQPsWfnpdggh7906bB1yNfJeLnoubk6OZpQj3efgu0fxCBYyCjIKLg4tpfXtMiAh7Bw733Yuf+PmfAfn8+SEVKgoO9zd8n4af+PmfEhNg+Wv5IRUrChOgLAoO9yeL6fdm4fdB5QH5PPkhFfyDi2H7L52HBaDDqZi/iwj3sQbIln5nH4uEioSKggiciQU4ahV5jgV2W4N2R4sI+yMGZnKMqx+LlYuTjpYIeI9T+2WdhwWgwaiSsosI9yoGxI9/ch+LgouFiX8InIkF6EsVeZAFbT5ag1GLCPvTBmZyla0fi5WLko+eCHqQX/tH+K2LBQ73bnms+P6sAflP+DYVLQoiyhUuCg73bouf+OWzAfmV+SEV/RJ7BsqFmYWLbot8hnWEcAj7CvxCBXlKf3xThQh794mbB0+TgZKLqIuSjJONkgj3J/in97GL+yX8nAV9Wnp0RIYIe/emmwdKkn2Si6eLk4yTjZMI9xj4dQWbxZaRxJUIDvaLn/exsPetqQH3JvkhFS8KSE4VMAoO9wiL6fifrwH5J/khFfyQfQb3VfvO+/L7yot8+LqLzfdYeI4FZz9mbj6LCPvFi/fA95n7NPea90aLBfcJsX9OH4uBinSJgQihiQUOv4uf+OquAfkN+SEVMQoOv4uf+Oi/XbcSEyD5HPjwFYedhpx6mH2VfI94izuLLPsMXPsWCIqIB42bi5qLmggTwPcJaOX7AB5di2x4YW0Ikn0FoJSSjZ2L24uoVYv7H4tkiWeDVghT+1kFeUt0fUmHCHv3tZsHZ44FZI59lIuki5iNmpOmCLP3IAUTIKv3Bez3lvcbi56Ll3+UfggO94GLn/j5nwH4kvjaFZSrq6LJiwicm/uzewbLkYF0H4uAg2uFdvsLiDVwU1tSWmxTi0mL+xH3Alf3DIp6Pm53T4sIgnv3vZsGR3KVqh+Llo6jk6D3Bo3jo8W8xbysxovMi/cT+wS6+w2QCIFtFemDuVaLOItOfF5eW15bUHxAiwgpFi2SX7yL3ovJl7a4urm7xqHWiwgO9ouf+PmfAfkj+SEVMgoO9z+Ln/j5n4WfEvcL4hMw+Z75LxV+BvsUi2w3cS1r+wT7E2lsiQjO94UFlKqfo8uLCJwGE1Cb+6p7lgfDkIF0H4uHiHuEcQhQ+20FS2Ctyx+LsKC6i60IE7DVZK9OHm57BqKefWMfi2hpUotUCPsG6mvxHlD7agV9V3B1SYsIe/e1mwdBe5upH4uUjpaOlwjG92YF9xWL9x++wfdImbuMwMiaCA73lovp+K+sAfeG6RX7FwZocJGxH4uVjZuNlQh6kGH7R/eji6P3OgVQnnLQi9eL1bDax8q/wcqs2Iv0i64/iyKL+xQz+xj7CnEIY/s696yLw/dCeZAFbj9iiFGFCPsUi5KwBfdFrvT3GIv3Hov3GkTr+zeL+wSLMm1DUDxKVjKLMoswsj73AGgIDruAoHjG+AagEqbdE7D4ufhAFTWLXSEFxmLHNh5Ni0hrX15TUmg2izqLN7BH7IvWi9C5vcgIE1CNTpdfsYu7i6q/odUIe5IFdlR7eH2LCHV/vrsfnQcTsFv0FYtwf3KHeHBTR/sbRYsIWHnFxPcz9wL3HMofy5g7Rx8OjYCe+ASr942gEvgV5GvTE/CC+xMVhXZ7YIJ9CNkGlJqVn5e2CLH3GQWlf56GoIu2i7WTsqHovt/3DYvoi9JZsGWOCIwHE+jHps/Ui9yL10ekVov7MYtG+z9k+x8I9PcBFaHfuuvUiwiuq30+UVwnYB99i3aRg4sIaIJ+gH+XgZ0fnIuak52LCBPwp5dzaPsaI/tD+wZvd5qhHw4t+AjKAfcnrgP4SvhAFSuL+0b7wQWQu5jbi8mL0X67WItZi2tAeksImwaewqagnYuxi5VPi0aLP38+iG9tR0gqi1aLapp6oovai5L3LpDmCA5fgKD4/rMBo9/Krvcq3AP4YPjwFbhEnlpLImsrHotVw2S4XfsUf/sM+xaL+xQIMMFY6fc09Pcn9xcei9lzqmKyTMgkr4vFi7HFn6+L5ItqQ8yLCKmUpqAfI/vmFTw9+0UvXGyvwvce6fch4q2scDQeDk+Ar/dQq/dDoBKp4XTd90bTE/D3/O0VVlJae1aLCGBdn8jX3aq6H6CLkoKdiwisl5Sdl3uUeR9yi3mEgYsIE+xgbJ2u596pxaKZgoAfi3h8got3CHOae6OeqJyou2CuSh77Hos2RIo/i22eb62FCBPwSnpYWItNi1emUPcMi9aLyqHI2AgOWftNzPcB3ETT+MqfEqm+5b7ssxNO97b5PxU8dmNki2EIZLJ4qh6MigX7CfsGLPshi/s0iynNd8OLCBOuOgoTXoSLeYp+i0WLZKSLz4v3F/cK9zzhxeST8MeLt4uagZV2i1iLNEtnYAhtkHmci6WLpKSmu50IDm2Ln/gGvgH3Ati/17ncA/co93gVlq6n44u1i6SCn2yLbYtlcm5nfHmAeYiGCJeBBZqdqbOdi5aLjoOLgot9hHSEcgg5+8XWi6v1BbP3GvcQ9yq+i6OLjHeLfIt+gFqIgQhA+6YFbyWGYItyi3mNfJSACNQGiJKGmIuZi6qY2ZzJCOL31QWSpo6Zi6GLsmqdZYtTi0ZPK/suCA5zgKD3xav3yqABpt/3v98D+IL4kxX3C1e7RB5ji2WCX2r7ATj7BftFi/triyG6SdyL0YvRqszh1e7H9ySL9zYI++/7OBWk5O33ceKLroudYotLi0B+Q3pRCIRrFXMpNftjK4tmi3i+i+SLypW/nr0IDvt2gLr4FZ8BvNYD93L3BhU1Cg5Pfp+En/glnxITYPct93UVwfdpiI4FWYFYgVmECH2nB5mehXkfi4SGcYJpCDX7ydeLx/dn6Ps0BROAnG2jacSLCBNgnouij6aUCJsHYot7lGnHCCn3QAXT1q2usYugi5V4oosIpZ+cqKR6oWYfg4uBiYOIVXU+TSn7EggOXXvKXJ/458oS96mzfK4TsPgz9w8Vd1J0eH2LbYuAqYvRCBOoi/cTn/cbi/cai+VuuGiLVItsQXxMCJsGn8OqnZmLqoudbIs+i2uJbol5CBNQ+8r8QOuL92X3zwWEJYJAi08IE5BIpHCnHr+LqsSd3QgOoYC6XssS973ZE6D4afcJFVdHfH57i4SLh5KLk4uVmr6Pmwja98A+i2r7DgUTYHpL+wH7T1CLb4t/oIumi5SNlI2UCNb3vkCL+xf8nQV7TH1ufXcI0gahpZG7svcqkHmXgZ6Lx4vCzuP3MAiMi2ojBYNzhGiLeggToG+geqceuIuposnrCA5peZ/4N58B+E/4RhVj+yM1+2f7YHgI9PgOiI37N2yLewW2iqGHi3WLh4qDioYIL/vhBYmGioeLh4t8mYSZi/ellfT3hKz3WggOWftNzPcB3ETTEqm+4rBxu+ezE0T3vPk/FTp2Z2WLX4txq3iaiwgTWl5mfmmLZ4txm3SgfShaQCqK+wSLKc13w4sIE7o6ChNahIt5in6LRYtkpIvPjNLf5dCiooSmhaGLCKzdlL6edZZsH2SLUn9hbnWbh56LnQinqM7D9b2msZ59l2oeZItRbV1sCBNEeo5/louai5iNr9KiCA6AoPguoAGm3/el3wP4aPfBFTcKN6QVOAoOi3mfftz3sNUSE6D4rPhAFfujBiaLV2VVMAibBrfBpoy/iwiRizn7ZQWBcXdqYYByhIZwi3yLc6N3pYuWi5mPlpPcy6X3Qrj3Dgjziz/7ZgWEeIFli3QIE2Bkm2e2HtaLutuayQh7BnNVcIR3i3aLgZ6LooufwPdAmb0I8QYOi4Ce+DCgAfgS5AOC+xsVhHGBdH12CNkGmqCVpJGjCK/3IQWifqGHoosI9yL3MPc19y73HSiLVh8giyf7BV37RQj30Pc1FYv7Cjr7TPsZiW+LdpuLoIukp/OdzKn2zNXDi7aLolqLUAgOWftNzPcB3ETT9/KfEqm+94KzE1z4WfgWFbNYmmn7K/tP+yv7SynNd8MeE6w6ChNMhIt5in6LCEVkpM/19wbV9wcfq4uugKWLCKigmbMfDoWAoPfs1QGm3/eI3wP4p/hAFftWBvtR+w37N/sbNL9V6fcg9xL3CvcCH4vWU4pjygj3Pgb7MvsZFTtF+xcrXGypx/ch9wn3BdAeq3ilWYtLCA4tgNf3tdUB9wzdA/g++EAV+24GJ4tGKnBKCJsGqL+5r8GLCMgGXCRY+wqLQotgnG+6i8uLxc6i2Qh7Bnpnampyi3GLgaCLqYuZi8zR9zMI9xkGDnGBoPgunwG42/eB3wP3qPg+FcWFp3mLQAgpQ/tu+wBef7C0Houij6WSpAi990kFkqOMnouUi6l7mm+LZYtdaFxECJiCBbS/mZOZi5OLj4eLgYuEiH2GeQhvLgV6VHxai2EIT61f7/cn9wz3UfcQ9wVIpCQeDvcKi5/4GqCBnxKm3/gf3xO492+VFUxentIfi/cP3PdC9acImwdoi2t9a3kpU0H7EIsli0mkYbx4pYG6irKLCFX7VtiLwPdWBaqLp4+lk/ciudX3MIvwCBNY9wFGnVIe+wKLVPsdavsJCOjTFabuqcm6i6CLoYWLP4slSvs0PmJ1f3KIdYsIDlz7Y8r4nsoB90KxA/iG+EAVLov7WPuSBY3tjZqLlYv3BHWrZ4tRi3REekoImwafxKabmYsIsJNaLR+LMvuz++3oi/dZ94gFhmyIUotni0mcTbmLxYuh05jMCHsGeFRyeH6Lbot7o4v3Eoufi6KMpQgO2/g5nxKs313cE8D5MPhNFXUG+yOLbvsCcfsFdzNjSF5rdXxzhXWLCPcH+DY/i/sH/DYFVm6p2x8ToIvFrvOLxAjFebdKHlaLinsFuYaVXYtkCBPAi0hlTotDi0qjZKh2pXivia+LCJSLVftW14vB91YF9wmL876x9zyf5KL3AuydCA73SoCgAabf+F/fA/hs+EsVewe1i7KEl1yPfIxvi3mLS3ozbFF1YmRcU4thi3S0i7aLkouSjZIIlZqYoZOZobGfyou4i6aAnnOLZottW31Xg22HbItyi32MdY18CHhUUVNei2uLcqSL0IvesPcAvcqxuridvosIm3kH+yGLJCBq+w2EcIhwi3CLKMxhy4vSi7CjsrqbaJ9n2YvLi9i2wO4IpbycvovBi7t/uGqncKJilViLCA5bgbP3zbb3tJ8BuMH3i7OYsAP4SPj9FcRUn1oeaotecnF4+xopWvtMi/szCCul+w/3DPcJ2fcQ9tVm5jQeL4tXRV1GnuOj3MDVlIqVi5WLwYvKkLigs52wsIu6CPuRJRWsw9ry04uei5h7i3mLcXZueXpYWliHR4sI9zD7ixVF+wT7PEBjd7eu1PP3Ndu0oWVmHg6/gaD5DqwB2Nuc3/c43wP4ovdiFXKPdpJ2kqzlme2L0IvpY/L7B4tci2F8amxrbXRdi0uL+wjkJvcLVwhr+wNWJjiLXot/sIu0i6KPpZKkCJ3HBZKjjJ6LlIupe5pvi2WLXWhcRAiYggW0v5mTmYuTi4+Hi4GLhIl9hXkIdkoFh36IdIt6i0+tX++L9weL2e659wKihaOHo4kIKPe9FYtbgzB1MvsEz3X3BIvJCNSm1cXJnDs6Hg7ni5/46L9duRL5AtIT0Pfv+CwVjqKMnoufi/cXYM4ni12LbHhhbQiSfQWglJKNnYvbi6hVi/sfi2SJZ4NWCFP7WQV5S3R9SYcIe/e1mwdnjgVkjn2Ui6SLmIyak6YItPcgBRMwq/cA9veb9xuLkouYiIuBi4VmiothCHGeeKa8mLKwtGyvVh77FYs3+yxd+wAIDvcPi58Bpt/4JN8D+HX5PxU+i0j7hnyLBftL+wT7aCYfi0ukXL96pIOyiLaLCFX7VtmLwfdWBfdZjPcB91mL9wiL0myvWp5vlnCMXYsIhXYVoIumipWFpXuecoteizhK+0U5Ym99e4lyiwg9FnSLeI17kWyXeqiLtQj3IfP3RvcIHg73tICg9+zVAfcT3/hf3wP51PhAFfz6Bi2LOiFxSQibBrC8tbzPiwiuBmljbVZ9WYRwiHCLcIsozGHLi9KLr6GzvZ1hoW3Vi8uL2LbA7gilvJy+i8GLoIinhp8Iywb7JhaOfo54i30IM2T7ZvsSYXS0th6LkouSjZKjsKzDi8EIpoOec1xrQFYei32LbY18fl1PSlqLYIt9uIu8i9mv9wG6yggO9275DawB92b7BhV8U32CVIEIe/eImwdSkn+Pi6eLn5GjlKsInMgFw5XBorys9wvb4/cfi/cmi/csOuz7JIo2izhmRk8jMEL7IIv7Dov7GdE59nsI9/n4hBUuCg74OKABpt/3pd8D5/thFdqLw/dcBbqVuKO2ts3Ms+OL14vjT786i2KLY4JkdiJTQPsHi/sEiz21WdiCCPeC9+MVOAoO9z37Y7j5lsUBwuf33eUD9yH7EBWyUM1zz4v3D4v3FdSL9zGLunHDQKj7E737U2uL9yKL9zj3RvcV9ymL6ouBS8CLCK6doKvAT5s/+2b7nPtJ+30fi/sM82v3A37cgcV/rm+heZVzi2+LPjxXK4tbi0aecq4IDk/7Tcz3AdpG4vf0nxKpvveCsxNc+Gf4XhWBZWso+xOCQ4Y+d1RZZWhxXYtQiz3NbcOLCBOsqYutlaaLCLmpgGRiZW9gH3KLgahtiwhwe3d1Zqx8rR+4i8atqbidpZWsi6WLwW/ANIsIE1xwi2d5dIsIVXSks9rYmOMfwou4jK+exKqszpX3BwgOwIuf98Wv95esAfkZ+SEV/IV7Bs2FlYWLb4t7iHeEcgj7D/xOBXxXgXVRhwh794+bB1CPeZaLo4uakp+SpAjF92b3YIuWr/thi8v3dwWSpZqRuYv3RIuifotCi4WLhoh1CKCJBQ564LD3k8MB+Gz4RRX7uov7Jv0D1ovL96f3SIuUsPtIi8f3k/dviwUO9yF5v/lDvxL3qudo5xPQ+Tf4hhWDmfyX+yX3NvdABeXqoqeLuIutdatRi1yLY3RQWgiTfAWhnbOcqIufi5p9i3aLeXdoeXUI+6r795V++JP3JPs2+0AFE+AzLX9zi1+LaaFmxYu6i7SixbwIg5oFdXljem6Ld4t8louli56gqpyiCA5ci5/3s9UB+FH4ERX7yov3tvfCJ4v7uvwM98qL+7b7x++LBQ73YIuf+N7HAaL4ixXIuM2oxZoIQ/uitovW96wFm46ajJmL9IvpT64s+1pi+yL7mmj7KAjpBqv3Hu/3jfc0p5NokF2LZIv7W/sf+4D7Xl8IdAf3jaH3X/eCi/e0i/dc+xX3Efs8i/sTi/sAZPsVIQgOo/gN0gPo+KgV7FvYR7wjCPtJMZRv90znBZhql2aSaQj7Sy+UcPdI5QWSY49li2aLVoRYfVeDbYB3f2wInYAF1PKr9wOL9wyLu4S6frVr9Tr3DftoywgOqH6fhJ/4JZ8S90+z0rUTePjD+EAV+wCL+6D7ioqMBaPFoNWLvAi9cKZidWx7bmGqi6Odk4dzHotTYvsDfXQI+yj7HPcBi/eQ93mMigVrTHtki1cIE5hUsmu3saCjop97nWh1cJOsHou7teSgrAgOl4Cg+C6gAffAucHfA/fN+2EVnZuaoYuji/cH+5Aqe/c+CI2MBaNitXu3i82Ly6TFxc3Ms+OL14vjT786izKLMlJXR1JBbiyLLwiL+2j3paaLTIuHioeJhwjy+KcVOAoO9255rPfCtfemrAH5T/g2FS0K/IpQFZ/CpsKuurzNyr7Vi9uLvFGLLYtohmCAXwiAYRV1QWk/XVJdU1JkSIs3i13Hi/cBi7ORuZi6CA5PgK/3UKv3QqEBqeED+Dj4TRV7BoiChYN/i3CLfJxbiwj7IvsN+zP7Iji6R+Yf74u3s8PPCHuVBVJSaXJTi1CLbbqL1IujjZ6TpAj3SIuRq/tHiwWb0dDz0IvVi51Okl0ImwYOT4Ch90Kr91CvAffc4QPn99cVxMStpMOLxoupXItCi3OJeINy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   "source": [
    "#Code de la question 4) e) Définir un programme qui utilise cette porte quantique sur 16 qubits, appeler la méthode Circuit.display() sans paramètres\n",
    "\n",
    "prog=Program()\n",
    "qreg=prog.qalloc(16)\n",
    "QFFT(16)(qreg)\n",
    "circ=prog.to_circ()\n",
    "circ.display()\n",
    "\n",
    "#Code de la question 4) f) ajouter le paramètre \"depth\" dans la méthode display. Faire varier sa valeur à partir de 0. Que permet-il ?\n",
    "\n",
    "#circ.display(depth=0) #identique à circ.display()\n",
    "circ.display(depth=1)\n",
    "circ.display(depth=2)\n",
    "#le paramètre depth défini la \"profondeur\" d'affichage des portes quantiques : on peut afficher les circuit quantique contenu dans les portes abstraites"
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   "id": "6690dd4c-4fa4-4f68-8617-4379c7b137d3",
   "metadata": {},
   "source": [
    "<hr style=\"border:2px solid gray\">\n",
    "\n",
    "## **Partie II** : la transformation de Bogoliubov\n",
    "\n",
    "Nous allons maintenant pouvoir nous pencher sur la __[transformation de Bogoliubov](./QCpy-additionalFiles/theoryReminderSheets(FR)/Transformation_de_Bogoliubov.pdf)__. Cette partie est un exercice récapitulatif, et est donc moins guidée.\n",
    "\n",
    "**Votre mission** : à l'aide des éléments donnés ci-dessous, faites le travail nécessaire pour intégrer la Transformation de Bogoliubov au circuit de diagonalisation de l'hamiltonien pour N qubits (N puissance de 2).\n",
    "\n",
    "**Éléments nécessaires** :\n",
    "- La transformation de Bogoliubov est implémentée par des portes à 2 qubits.\n",
    "- La matrice de ces portes est la suivante :\n",
    "$$\\begin{bmatrix} cos(\\frac{θ_k}{2}) & 0 & 0 & isin(\\frac{θ_k}{2}) \\\\ 0&1&0&0 \\\\ 0&0&1&0 \\\\  isin(\\frac{θ_k}{2}) & 0 & 0 & cos(\\frac{θ_k}{2})\\end{bmatrix}$$\n",
    "avec : $$θ_k=\\arccos\\left(\\frac{λ-\\cos\\left(\\frac{2πk}{n}\\right)}{\\sqrt{\\left(λ-\\cos\\left(\\frac{2πk}{n}\\right)\\right)^2+\\sin^2\\left(\\frac{2πk}{n}\\right)}}\\right)$$\n",
    "λ : paramètre du modèle physique correspondant à l'intensité du champ transverse, variable.\n",
    "- Les portes à 2 qubits forment un mur allant du premier au dernier qubit, n correspond au nombre de qubits, k à l'index de la porte (la 3ème porte prendra k=2).\n",
    "- La transformation est implémentée après la Transformée de Fourier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ad800e3c-e5fa-42ff-bdc3-c46cfafd6ddb",
   "metadata": {},
   "outputs": [
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\"); 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       "}\n",
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "champTransverse=0.9\n",
    "N=16\n",
    "\n",
    "#Code de la partie II\n",
    "\n",
    "def bogoliubov_Generator(n,k):\n",
    "    thetak=np.arccos((champTransverse-np.cos(2*np.pi*k/n))/(np.sqrt((champTransverse-np.cos(2*np.pi*k/n))**2+(np.sin(2*np.pi*k/n))**2)))\n",
    "    return(np.array([[np.cos(thetak/2),0,0,1j*np.sin(thetak/2)],\n",
    "                    [0,1,0,0],\n",
    "                    [0,0,1,0],\n",
    "                    [1j*np.sin(thetak/2),0,0,np.cos(thetak/2)]]))\n",
    "\n",
    "B = AbstractGate(\"B\",[float,float], arity=2, matrix_generator=bogoliubov_Generator)\n",
    "\n",
    "prog=Program()\n",
    "qreg=prog.qalloc(N)\n",
    "QFFT(N)(qreg)\n",
    "for k in range(1,int(N/2)):\n",
    "    B(N,k)(qreg[2*k:2*k+2])\n",
    "#pour k=0, la porte de la transformation de Bogoliubov correspond à l'identité, on se permet donc de ne pas l'implémenter\n",
    "circ=prog.to_circ()\n",
    "circ.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d4db839-6983-4479-94de-1f075e90e18d",
   "metadata": {},
   "source": [
    "<hr style=\"border:2px solid gray\">\n",
    "\n",
    "## **Partie III** : finitions & exploitation du circuit quantique\n",
    "\n",
    "Nous avons maintenant le circuit quantique permettant de passer de l'hamiltonien de notre modèle physique à un hamiltonien diagonal. Il ne nous reste plus alors qu'à :\n",
    "- trouver l'état qui minimise l'hamiltonien diagonal ; préparer le système dans cet état\n",
    "- y appliquer la transformation inversée\n",
    "- exploiter les résultats obtenus\n",
    "\n",
    "Pour ce premier point, les résolutions analytiques nous donne :\n",
    "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}\n",
    "\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}\n",
    "\\ket{\\psi}_{H_{min}}=\\left\\{\n",
    "    \\begin{array}{ll}\n",
    "        \\ket{00...00} & \\mbox{si λ>1}\\\\\n",
    "        \\ket{00...01} & \\mbox{si λ<1}\n",
    "    \\end{array}\n",
    "\\right.$$\n",
    "\n",
    "**Q1)** Définir le circuit quantique permettant la résolution du problème en fonction de la valeur du paramètre champTransverse.\n",
    "On rappelle l'inverse d'un produit d'opérateurs : $$(\\hat{A}\\hat{B})^\\dagger = \\hat{B}^\\dagger\\hat{A}^\\dagger$$\n",
    "\n",
    "**Q2)** Afficher les différents états obtenus en sortie pour :\n",
    "- un nombre pseudo-infini de mesures ;\n",
    "- 1000 mesures.\n",
    "\n",
    "**Q3)** \n",
    "\n",
    "**a)** Définir un observable \"magnétisation\" correspondant à la moyenne pondérée des valeurs de spin suivant Z de tous les qubits.\n",
    "\n",
    "**b)** Calculer la valeur moyenne de cette observable sur :\n",
    "- un nombre pseudo-infini de mesures ;\n",
    "- 100 mesures.\n",
    "\n",
    "**Pour conclure** : faites varier la valeur du champ transverse et le nombre de qubits, et observez les résultats obtenus.\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Conseil :</b> Pour cette première question, vous aurez besoin de la porte quantique X et de la méthode dag() des portes.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "38639e50-d4a4-47cb-98ac-c86745905c73",
   "metadata": {},
   "outputs": [
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\"); \n",
       "}\n",
       "]]></style></defs><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"37\">Q0</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"32\" y2=\"32\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"69\">Q1</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"64\" y2=\"64\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"101\">Q2</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"96\" y2=\"96\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"133\">Q3</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"128\" y2=\"128\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"165\">Q4</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"160\" y2=\"160\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"197\">Q5</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"192\" y2=\"192\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"229\">Q6</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"224\" y2=\"224\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"10\" y=\"261\">Q7</text><line stroke=\"rgb(0,0,0)\" x1=\"50\" x2=\"344\" y1=\"256\" y2=\"256\" /><rect fill=\"white\" height=\"24\" stroke=\"black\" stroke-width=\"2\" width=\"27\" x=\"60\" y=\"244\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"261\">X</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"77\" x=\"60\" y=\"84\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"117\">B [8, 1]</text><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 10px;\" x=\"124\" y=\"112\">†</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"77\" x=\"60\" y=\"148\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"68\" y=\"181\">B [8, 2]</text><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 10px;\" x=\"124\" y=\"176\">†</text><rect fill=\"white\" height=\"56\" stroke=\"black\" stroke-width=\"2\" width=\"77\" x=\"147\" y=\"212\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"155\" y=\"245\">B [8, 3]</text><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 10px;\" x=\"211\" y=\"240\">†</text><rect fill=\"white\" height=\"248\" stroke=\"black\" stroke-width=\"2\" width=\"92\" x=\"234\" y=\"20\" /><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 16px;\" x=\"242\" y=\"149\">QFFT [8]</text><text style=\"font-family: STIXMathJax_Main-Italic; font-size: 10px;\" x=\"313\" y=\"144\">†</text></svg>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "champTransverse=0.9\n",
    "N=8\n",
    "\n",
    "#Code de la question 1) Définir le circuit quantique permettant la résolution du problème en fonction de la valeur du paramètre champTransverse, l'afficher\n",
    "\n",
    "prog=Program()\n",
    "qreg=prog.qalloc(N)\n",
    "if champTransverse<1:\n",
    "    X(qreg[-1])\n",
    "for k in range(1,int(N/2)):\n",
    "    B(N,k).dag()(qreg[2*k:2*k+2])\n",
    "QFFT(N).dag()(qreg)\n",
    "circ=prog.to_circ()\n",
    "circ.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ec1df7f3-77cd-4f45-9792-61fa522de074",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Etats pour un nombre pseudo-infini de mesures :\n",
      "Etat |00000001>, amplitude (-0.18149533888839128+0.18149533888839126j), probabilité 0.06588111607642398\n",
      "Etat |00000010>, amplitude (1.5716698788891566e-17-0.25667316976346394j), probabilité 0.06588111607642398\n",
      "Etat |00000100>, amplitude (-0.18149533888839126-0.18149533888839128j), probabilité 0.06588111607642398\n",
      "Etat |00000111>, amplitude (0.08942400495347332+9.813077866773593e-18j), probabilité 0.00799665266191882\n",
      "Etat |00001000>, amplitude (0.25667316976346394+0j), probabilité 0.06588111607642398\n",
      "Etat |00001011>, amplitude (0.049008404668216765+0.028892750266804483j), probabilité 0.0032366147461036217\n",
      "Etat |00001101>, amplitude (0.04900840466821677-0.10972395083731758j), probabilité 0.014441169115473775\n",
      "Etat |00001110>, amplitude (0.008592804382960194-4.906538933386797e-18j), probabilité 7.383628716381992e-05\n",
      "Etat |00010000>, amplitude (-0.18149533888839128+0.18149533888839126j), probabilité 0.06588111607642398\n",
      "Etat |00010011>, amplitude (-0.04041560028525658+0.028892750266804466j), probabilité 0.0024682117643975614\n",
      "Etat |00010101>, amplitude (0.09801680933643354+1.9879586398639442e-17j), probabilité 0.009607294912494766\n",
      "Etat |00010110>, amplitude (0.049008404668216744+0.10972395083731762j), probabilité 0.014441169115473782\n",
      "Etat |00011001>, amplitude (0.04041560028525657+0.02889275026680449j), probabilité 0.0024682117643975614\n",
      "Etat |00011010>, amplitude (-0.049008404668216765+0.028892750266804476j), probabilité 0.0032366147461036217\n",
      "Etat |00011100>, amplitude (0.08942400495347334+9.93979319931972e-18j), probabilité 0.007996652661918825\n",
      "Etat |00011111>, amplitude (0.015433666834083678-0.015433666834083676j), probabilité 0.00047639614389098894\n",
      "Etat |00100000>, amplitude (1.5716698788891566e-17-0.25667316976346394j), probabilité 0.06588111607642398\n",
      "Etat |00100011>, amplitude (-0.04041560028525659+0.10972395083731762j), probabilité 0.01367276613376773\n",
      "Etat |00100101>, amplitude (0.008592804382960194+9.813077866773593e-18j), probabilité 7.383628716381992e-05\n",
      "Etat |00100110>, amplitude (0.04041560028525656+0.10972395083731762j), probabilité 0.013672766133767724\n",
      "Etat |00101001>, amplitude (-0.08942400495347334-1.471961680016039e-17j), probabilité 0.007996652661918825\n",
      "Etat |00101010>, amplitude (-0.09801680933643354-6.001798590824987e-18j), probabilité 0.009607294912494766\n",
      "Etat |00101100>, amplitude (0.049008404668216765+0.028892750266804476j), probabilité 0.0032366147461036217\n",
      "Etat |00101111>, amplitude (0.021826500953908975-0.030867333668167345j), probabilité 0.0014291884316729668\n",
      "Etat |00110001>, amplitude (0.04041560028525658-0.028892750266804466j), probabilité 0.0024682117643975614\n",
      "Etat |00110010>, amplitude (0.04041560028525659-0.10972395083731762j), probabilité 0.01367276613376773\n",
      "Etat |00110100>, amplitude (-0.04900840466821677+0.10972395083731758j), probabilité 0.014441169115473775\n",
      "Etat |00110111>, amplitude (0.021826500953908975-0.021826500953908957j), probabilité 0.000952792287781978\n",
      "Etat |00111000>, amplitude (-0.008592804382960197+7.359808400080195e-18j), probabilité 7.383628716381997e-05\n",
      "Etat |00111011>, amplitude (0.030867333668167362+8.98432856542387e-18j), probabilité 0.0009527922877819784\n",
      "Etat |00111101>, amplitude (-0.03726016778799263-0.0063928341198252955j), probabilité 0.0014291884316729663\n",
      "Etat |00111110>, amplitude (-0.021826500953908968-1.134659283286316e-17j), probabilité 0.0004763961438909891\n",
      "Etat |01000000>, amplitude (-0.18149533888839126-0.18149533888839128j), probabilité 0.06588111607642398\n",
      "Etat |01000011>, amplitude (0.04900840466821677-0.10972395083731758j), probabilité 0.014441169115473775\n",
      "Etat |01000101>, amplitude (-0.09801680933643354-1.9879586398639442e-17j), probabilité 0.009607294912494766\n",
      "Etat |01000110>, amplitude (-0.04041560028525657-0.02889275026680449j), probabilité 0.0024682117643975614\n",
      "Etat |01001001>, amplitude (-0.008592804382960192-9.93979319931972e-18j), probabilité 7.383628716381989e-05\n",
      "Etat |01001010>, amplitude (0.08942400495347334+9.813077866773593e-18j), probabilité 0.007996652661918825\n",
      "Etat |01001100>, amplitude (0.04041560028525658-0.028892750266804476j), probabilité 0.0024682117643975614\n",
      "Etat |01001111>, amplitude (-0.0063928341198252955+0.03726016778799263j), probabilité 0.0014291884316729663\n",
      "Etat |01010001>, amplitude (-0.09801680933643354-1.9879586398639442e-17j), probabilité 0.009607294912494766\n",
      "Etat |01010010>, amplitude (-0.008592804382960194-9.813077866773593e-18j), probabilité 7.383628716381992e-05\n",
      "Etat |01010100>, amplitude (0.09801680933643354+1.9879586398639442e-17j), probabilité 0.009607294912494766\n",
      "Etat |01010111>, amplitude (-1.495782026284461e-17+0.04365300190781794j), probabilité 0.0019055845755639568\n",
      "Etat |01011000>, amplitude (0.04900840466821675+0.10972395083731762j), probabilité 0.014441169115473782\n",
      "Etat |01011011>, amplitude (-0.015433666834083686+0.015433666834083676j), probabilité 0.0004763961438909891\n",
      "Etat |01011101>, amplitude (0.04365300190781794+1.2284844809865482e-17j), probabilité 0.0019055845755639568\n",
      "Etat |01011110>, amplitude (0.03726016778799265-0.006392834119825276j), probabilité 0.0014291884316729674\n",
      "Etat |01100001>, amplitude (-0.049008404668216744-0.10972395083731762j), probabilité 0.014441169115473782\n",
      "Etat |01100010>, amplitude (-0.04041560028525656-0.10972395083731762j), probabilité 0.013672766133767724\n",
      "Etat |01100100>, amplitude (0.04041560028525657+0.02889275026680449j), probabilité 0.0024682117643975614\n",
      "Etat |01100111>, amplitude (0.021826500953908957+0.021826500953908975j), probabilité 0.000952792287781978\n",
      "Etat |01101000>, amplitude (-0.049008404668216765+0.028892750266804473j), probabilité 0.0032366147461036217\n",
      "Etat |01101011>, amplitude (0.021826500953908968+9.382519770023186e-19j), probabilité 0.0004763961438909891\n",
      "Etat |01101101>, amplitude (0.015433666834083676+0.015433666834083678j), probabilité 0.00047639614389098894\n",
      "Etat |01101110>, amplitude (0.03086733366816735+3.6248025447235304e-18j), probabilité 0.0009527922877819778\n",
      "Etat |01110000>, amplitude (-0.08942400495347332-9.813077866773593e-18j), probabilité 0.00799665266191882\n",
      "Etat |01110011>, amplitude (0.021826500953908975-0.021826500953908957j), probabilité 0.000952792287781978\n",
      "Etat |01110101>, amplitude (-1.495782026284461e-17+0.04365300190781794j), probabilité 0.0019055845755639568\n",
      "Etat |01110110>, amplitude (0.021826500953908957+0.021826500953908975j), probabilité 0.000952792287781978\n",
      "Etat |01111001>, amplitude (0.006392834119825276+0.03726016778799265j), probabilité 0.0014291884316729674\n",
      "Etat |01111010>, amplitude (0.02182650095390896+0.030867333668167355j), probabilité 0.0014291884316729668\n",
      "Etat |01111100>, amplitude (-0.015433666834083676-0.015433666834083686j), probabilité 0.0004763961438909891\n",
      "Etat |10000000>, amplitude (0.25667316976346394+0j), probabilité 0.06588111607642398\n",
      "Etat |10000011>, amplitude (0.008592804382960197-7.359808400080195e-18j), probabilité 7.383628716381997e-05\n",
      "Etat |10000101>, amplitude (-0.04900840466821675-0.10972395083731762j), probabilité 0.014441169115473782\n",
      "Etat |10000110>, amplitude (0.049008404668216765-0.028892750266804473j), probabilité 0.0032366147461036217\n",
      "Etat |10001001>, amplitude (-0.04041560028525656-0.10972395083731762j), probabilité 0.013672766133767724\n",
      "Etat |10001010>, amplitude (0.09801680933643354+6.001798590824987e-18j), probabilité 0.009607294912494766\n",
      "Etat |10001100>, amplitude (0.040415600285256585-0.10972395083731762j), probabilité 0.01367276613376773\n",
      "Etat |10001111>, amplitude (-9.813077866773593e-18+0.021826500953908964j), probabilité 0.00047639614389098894\n",
      "Etat |10010001>, amplitude (-0.04041560028525657-0.02889275026680449j), probabilité 0.0024682117643975614\n",
      "Etat |10010010>, amplitude (0.08942400495347334+1.471961680016039e-17j), probabilité 0.007996652661918825\n",
      "Etat |10010100>, amplitude (0.008592804382960192+9.93979319931972e-18j), probabilité 7.383628716381989e-05\n",
      "Etat |10010111>, amplitude (0.006392834119825276+0.03726016778799265j), probabilité 0.0014291884316729674\n",
      "Etat |10011000>, amplitude (0.04041560028525656+0.10972395083731762j), probabilité 0.013672766133767724\n",
      "Etat |10011011>, amplitude (-5.514881613470254e-18+0.03086733366816735j), probabilité 0.0009527922877819778\n",
      "Etat |10011101>, amplitude (0.021826500953908975-0.02182650095390896j), probabilité 0.000952792287781978\n",
      "Etat |10011110>, amplitude (0.030867333668167355-0.021826500953908957j), probabilité 0.0014291884316729668\n",
      "Etat |10100001>, amplitude (0.049008404668216765-0.028892750266804476j), probabilité 0.0032366147461036217\n",
      "Etat |10100010>, amplitude (0.09801680933643354+6.001798590824987e-18j), probabilité 0.009607294912494766\n",
      "Etat |10100100>, amplitude (-0.08942400495347334-9.813077866773593e-18j), probabilité 0.007996652661918825\n",
      "Etat |10100111>, amplitude (0.02182650095390896+0.030867333668167355j), probabilité 0.0014291884316729668\n",
      "Etat |10101000>, amplitude (-0.09801680933643354-6.001798590824987e-18j), probabilité 0.009607294912494766\n",
      "Etat |10101011>, amplitude (0.030867333668167362+0.030867333668167365j), probabilité 0.0019055845755639568\n",
      "Etat |10101101>, amplitude -0.021826500953908968j, probabilité 0.0004763961438909891\n",
      "Etat |10101110>, amplitude (0.030867333668167365-0.030867333668167362j), probabilité 0.0019055845755639568\n",
      "Etat |10110000>, amplitude (-0.049008404668216765-0.028892750266804483j), probabilité 0.0032366147461036217\n",
      "Etat |10110011>, amplitude (0.030867333668167362+8.98432856542387e-18j), probabilité 0.0009527922877819784\n",
      "Etat |10110101>, amplitude (-0.015433666834083686+0.015433666834083676j), probabilité 0.0004763961438909891\n",
      "Etat |10110110>, amplitude (0.021826500953908968+9.382519770023186e-19j), probabilité 0.0004763961438909891\n",
      "Etat |10111001>, amplitude (-5.514881613470254e-18+0.03086733366816735j), probabilité 0.0009527922877819778\n",
      "Etat |10111010>, amplitude (0.030867333668167362+0.030867333668167365j), probabilité 0.0019055845755639568\n",
      "Etat |10111100>, amplitude (-0.030867333668167345-0.021826500953908975j), probabilité 0.0014291884316729668\n",
      "Etat |11000001>, amplitude (-0.08942400495347334-9.93979319931972e-18j), probabilité 0.007996652661918825\n",
      "Etat |11000010>, amplitude (-0.049008404668216765-0.028892750266804476j), probabilité 0.0032366147461036217\n",
      "Etat |11000100>, amplitude (-0.04041560028525658+0.028892750266804476j), probabilité 0.0024682117643975614\n",
      "Etat |11000111>, amplitude (-0.015433666834083676-0.015433666834083686j), probabilité 0.0004763961438909891\n",
      "Etat |11001000>, amplitude (-0.040415600285256585+0.10972395083731762j), probabilité 0.01367276613376773\n",
      "Etat |11001011>, amplitude (-0.030867333668167345-0.021826500953908975j), probabilité 0.0014291884316729668\n",
      "Etat |11001101>, amplitude (0.02182650095390896+0.021826500953908975j), probabilité 0.000952792287781978\n",
      "Etat |11001110>, amplitude (-7.094249496677145e-18+0.030867333668167362j), probabilité 0.0009527922877819784\n",
      "Etat |11010000>, amplitude (-0.04900840466821677+0.10972395083731758j), probabilité 0.014441169115473775\n",
      "Etat |11010011>, amplitude (-0.03726016778799263-0.0063928341198252955j), probabilité 0.0014291884316729663\n",
      "Etat |11010101>, amplitude (0.04365300190781794+1.2284844809865482e-17j), probabilité 0.0019055845755639568\n",
      "Etat |11010110>, amplitude (0.015433666834083676+0.015433666834083678j), probabilité 0.00047639614389098894\n",
      "Etat |11011001>, amplitude (0.021826500953908975-0.02182650095390896j), probabilité 0.000952792287781978\n",
      "Etat |11011010>, amplitude -0.021826500953908968j, probabilité 0.0004763961438909891\n",
      "Etat |11011100>, amplitude (0.02182650095390896+0.021826500953908975j), probabilité 0.000952792287781978\n",
      "Etat |11100000>, amplitude (-0.008592804382960194+4.906538933386797e-18j), probabilité 7.383628716381992e-05\n",
      "Etat |11100011>, amplitude (-0.021826500953908968-1.134659283286316e-17j), probabilité 0.0004763961438909891\n",
      "Etat |11100101>, amplitude (0.03726016778799265-0.006392834119825276j), probabilité 0.0014291884316729674\n",
      "Etat |11100110>, amplitude (0.03086733366816735+3.6248025447235304e-18j), probabilité 0.0009527922877819778\n",
      "Etat |11101001>, amplitude (0.030867333668167355-0.021826500953908957j), probabilité 0.0014291884316729668\n",
      "Etat |11101010>, amplitude (0.030867333668167365-0.030867333668167362j), probabilité 0.0019055845755639568\n",
      "Etat |11101100>, amplitude (-7.094249496677145e-18+0.030867333668167362j), probabilité 0.0009527922877819784\n",
      "Etat |11110001>, amplitude (0.015433666834083678-0.015433666834083676j), probabilité 0.00047639614389098894\n",
      "Etat |11110010>, amplitude (0.021826500953908975-0.030867333668167345j), probabilité 0.0014291884316729668\n",
      "Etat |11110100>, amplitude (-0.0063928341198252955+0.03726016778799263j), probabilité 0.0014291884316729663\n",
      "Etat |11111000>, amplitude (-9.813077866773593e-18+0.021826500953908964j), probabilité 0.00047639614389098894\n",
      "\n",
      "Etats pour 1000 mesures :\n",
      "Etat |00000001>, amplitude None, probabilité 0.052\n",
      "Etat |00000010>, amplitude None, probabilité 0.059\n",
      "Etat |00000100>, amplitude None, probabilité 0.063\n",
      "Etat |00000111>, amplitude None, probabilité 0.011\n",
      "Etat |00001000>, amplitude None, probabilité 0.074\n",
      "Etat |00001011>, amplitude None, probabilité 0.004\n",
      "Etat |00001101>, amplitude None, probabilité 0.019\n",
      "Etat |00010000>, amplitude None, probabilité 0.074\n",
      "Etat |00010011>, amplitude None, probabilité 0.003\n",
      "Etat |00010101>, amplitude None, probabilité 0.009\n",
      "Etat |00010110>, amplitude None, probabilité 0.019\n",
      "Etat |00011001>, amplitude None, probabilité 0.002\n",
      "Etat |00011010>, amplitude None, probabilité 0.002\n",
      "Etat |00011100>, amplitude None, probabilité 0.011\n",
      "Etat |00100000>, amplitude None, probabilité 0.066\n",
      "Etat |00100011>, amplitude None, probabilité 0.013\n",
      "Etat |00100110>, amplitude None, probabilité 0.009\n",
      "Etat |00101001>, amplitude None, probabilité 0.011\n",
      "Etat |00101010>, amplitude None, probabilité 0.007\n",
      "Etat |00101100>, amplitude None, probabilité 0.001\n",
      "Etat |00110001>, amplitude None, probabilité 0.002\n",
      "Etat |00110010>, amplitude None, probabilité 0.013\n",
      "Etat |00110100>, amplitude None, probabilité 0.02\n",
      "Etat |00111101>, amplitude None, probabilité 0.001\n",
      "Etat |01000000>, amplitude None, probabilité 0.062\n",
      "Etat |01000011>, amplitude None, probabilité 0.011\n",
      "Etat |01000101>, amplitude None, probabilité 0.003\n",
      "Etat |01000110>, amplitude None, probabilité 0.003\n",
      "Etat |01001010>, amplitude None, probabilité 0.009\n",
      "Etat |01001100>, amplitude None, probabilité 0.002\n",
      "Etat |01010001>, amplitude None, probabilité 0.011\n",
      "Etat |01010010>, amplitude None, probabilité 0.001\n",
      "Etat |01010100>, amplitude None, probabilité 0.01\n",
      "Etat |01010111>, amplitude None, probabilité 0.002\n",
      "Etat |01011000>, amplitude None, probabilité 0.015\n",
      "Etat |01011101>, amplitude None, probabilité 0.002\n",
      "Etat |01011110>, amplitude None, probabilité 0.002\n",
      "Etat |01100001>, amplitude None, probabilité 0.022\n",
      "Etat |01100010>, amplitude None, probabilité 0.013\n",
      "Etat |01100100>, amplitude None, probabilité 0.002\n",
      "Etat |01101000>, amplitude None, probabilité 0.002\n",
      "Etat |01101011>, amplitude None, probabilité 0.002\n",
      "Etat |01101101>, amplitude None, probabilité 0.001\n",
      "Etat |01101110>, amplitude None, probabilité 0.002\n",
      "Etat |01110000>, amplitude None, probabilité 0.007\n",
      "Etat |01110011>, amplitude None, probabilité 0.002\n",
      "Etat |01110101>, amplitude None, probabilité 0.001\n",
      "Etat |01110110>, amplitude None, probabilité 0.003\n",
      "Etat |01111001>, amplitude None, probabilité 0.001\n",
      "Etat |01111010>, amplitude None, probabilité 0.001\n",
      "Etat |10000000>, amplitude None, probabilité 0.064\n",
      "Etat |10000101>, amplitude None, probabilité 0.021\n",
      "Etat |10001001>, amplitude None, probabilité 0.017\n",
      "Etat |10001010>, amplitude None, probabilité 0.007\n",
      "Etat |10001100>, amplitude None, probabilité 0.01\n",
      "Etat |10001111>, amplitude None, probabilité 0.002\n",
      "Etat |10010001>, amplitude None, probabilité 0.002\n",
      "Etat |10010010>, amplitude None, probabilité 0.011\n",
      "Etat |10010111>, amplitude None, probabilité 0.002\n",
      "Etat |10011000>, amplitude None, probabilité 0.012\n",
      "Etat |10011110>, amplitude None, probabilité 0.002\n",
      "Etat |10100001>, amplitude None, probabilité 0.002\n",
      "Etat |10100010>, amplitude None, probabilité 0.013\n",
      "Etat |10100100>, amplitude None, probabilité 0.012\n",
      "Etat |10100111>, amplitude None, probabilité 0.001\n",
      "Etat |10101000>, amplitude None, probabilité 0.006\n",
      "Etat |10101011>, amplitude None, probabilité 0.003\n",
      "Etat |10101110>, amplitude None, probabilité 0.003\n",
      "Etat |10110000>, amplitude None, probabilité 0.003\n",
      "Etat |10111100>, amplitude None, probabilité 0.003\n",
      "Etat |11000001>, amplitude None, probabilité 0.01\n",
      "Etat |11000010>, amplitude None, probabilité 0.006\n",
      "Etat |11000100>, amplitude None, probabilité 0.001\n",
      "Etat |11000111>, amplitude None, probabilité 0.001\n",
      "Etat |11001000>, amplitude None, probabilité 0.018\n",
      "Etat |11001011>, amplitude None, probabilité 0.002\n",
      "Etat |11001110>, amplitude None, probabilité 0.002\n",
      "Etat |11010000>, amplitude None, probabilité 0.013\n",
      "Etat |11010011>, amplitude None, probabilité 0.001\n",
      "Etat |11010101>, amplitude None, probabilité 0.003\n",
      "Etat |11011001>, amplitude None, probabilité 0.002\n",
      "Etat |11100110>, amplitude None, probabilité 0.001\n",
      "Etat |11101001>, amplitude None, probabilité 0.002\n",
      "Etat |11101010>, amplitude None, probabilité 0.001\n",
      "Etat |11101100>, amplitude None, probabilité 0.003\n",
      "Etat |11110100>, amplitude None, probabilité 0.001\n"
     ]
    }
   ],
   "source": [
    "#Code de la question 2) Afficher les différents états obtenus en sortie pour un nombre pseudo-infini et 1000 mesures\n",
    "\n",
    "qpu=get_default_qpu()\n",
    "\n",
    "results=qpu.submit(circ.to_job())\n",
    "print(\"Etats pour un nombre pseudo-infini de mesures :\")\n",
    "for res in results:\n",
    "    print(\"Etat %s, amplitude %s, probabilité %s\"%(res.state, res.amplitude, res.probability))\n",
    "\n",
    "print(\"\\nEtats pour 1000 mesures :\")\n",
    "results=qpu.submit(circ.to_job(nbshots=1000))\n",
    "for res in results:\n",
    "    print(\"Etat %s, amplitude %s, probabilité %s\"%(res.state, res.amplitude, res.probability))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0138e0d-1651-4771-aca5-e7db7cecfea0",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "<b>Attention :</b> Sur l'exploitation de ces résultats, rappelez vous la sphère de Bloch : une valeur 0 correspond à un spin up (σz=1), et une valeur 1 correspond à un spin down (σz=-1).\n",
    "</div>\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Conseil :</b> Un observable est un objet de la classe Observable ; un terme peut y être ajouté par sa méthode add_term(). Un terme est un objet de la classe Term(). Plus de détails sont disponibles dans la documentation MyQLM.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "09e0a94d-af37-4c98-ad7e-205321864c1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.125 * (Z|[0]) +\n",
      "0.125 * (Z|[1]) +\n",
      "0.125 * (Z|[2]) +\n",
      "0.125 * (Z|[3]) +\n",
      "0.125 * (Z|[4]) +\n",
      "0.125 * (Z|[5]) +\n",
      "0.125 * (Z|[6]) +\n",
      "0.125 * (Z|[7])\n"
     ]
    }
   ],
   "source": [
    "from qat.core import Observable, Term\n",
    "\n",
    "#Code de la question 3) Définir un observable \"magnétisation\" correspondant à la moyenne pondérée des valeurs de spin suivant Z de tous les qubits\n",
    "\n",
    "magnetisation=Observable(N)\n",
    "for i in range(N):\n",
    "    magnetisation.add_term(Term(1/N,\"Z\",[i]))\n",
    "print(magnetisation)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2433d9c-b7b1-4b69-ac2f-186295237e4d",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Rappel :</b> Il est possible de soumettre des jobs qui contiennent un circuit quantique et un observable à échantillonner sur les états quantiques de sortie.\n",
    "\n",
    "my_job = circuit.to_job(observable=my_obs)\n",
    "\n",
    "Dans certains cas, il peut arriver qu'un QPU ne supporte pas nativement l'évaluation des observables. Le plugin ObservableSplitter est là pour combler cette lacune et permettre à tout QPU, y compris ceux limités aux échantillonages, d'être capable d'évaluer des observables. \n",
    "\n",
    "Il s'appelle donc en combinaison à un qpu classique : qpu = ObservableSplitter() | get_default_qpu()\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "49416abe-5245-4879-abdc-0dc335fba66a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Magnetisation (\"exacte\") :  0.4830351110966724\n",
      "Magnetisation (100 mesures) :  0.45999999999999996\n"
     ]
    }
   ],
   "source": [
    "from qat.plugins import ObservableSplitter\n",
    "\n",
    "#Code de la question 4) Calculer la valeur moyenne de cette observable sur un nombre pseudo-infini et 100 mesures\n",
    "\n",
    "qpuObs=ObservableSplitter()|get_default_qpu()\n",
    "job=circ.to_job(\"OBS\",observable=magnetisation)\n",
    "job2=circ.to_job(\"OBS\",observable=magnetisation,nbshots=100)\n",
    "print(\"Magnetisation (\\\"exacte\\\") : \",qpuObs.submit(job).value)\n",
    "print(\"Magnetisation (100 mesures) : \",qpuObs.submit(job2).value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9b3cbf3-178d-4763-9f07-f98cb390d809",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "<b>C'est terminé :</b> cela conclut donc la correction de ce premier Jupyter Notebook introductif à la programmation en MyQLM pour l'informatique quantique.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6137c9dd-d57e-464f-b0e3-0275d1fb964a",
   "metadata": {},
   "source": [
    "Si cela n'est pas déjà fait, nous vous invitons vivement à refaire vous même ces exercices, vous avez pour cela un Jupyter Notebook a trou spécialement conçu et disponible __[ici](QCpy-1(FR)-Modele_d-Ising.ipynb)__."
   ]
  }
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