DeriveesIntegrales1.ipynb

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      "text/markdown": [
       "**Start at:** Saturday 08 July 2023, 17:07:22  \n",
       "**Hostname:** ip-sw-install-nico.insa-toulouse.fr (Linux)"
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   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "print(os.getcwd())\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",
    "import tools4pyPhysChem as t4pPC"
   ]
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   "id": "a1b3496a-7f24-4bef-ae7c-617f267ab7ad",
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   "source": [
    "# Dérivées et intégrales<br>**work in progress....**\n",
    "\n",
    "## **1.** Introduction  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5648866f-8941-4756-9f3f-0d9fb546eb7d",
   "metadata": {},
   "source": [
    "### **1.1.** Dérivées et intégrales ? Rafraîchissons-nous la mémoire avec un point de vue simple"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02430379-dcd0-4d0f-8df8-ff0a2515e4cd",
   "metadata": {},
   "source": [
    "#### **1.1.a.** Qu'est-ce qu'une dérivée d'une fonction ?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f7de407-02a0-4f3e-b0f4-216f3d2119c5",
   "metadata": {},
   "source": [
    "#### **1.1.b.** Qu'est-ce qu'une intégrale d'une fonction?"
   ]
  },
  {
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   "execution_count": 2,
   "id": "18afd352-4dfb-40a8-b050-a3ad305e3863",
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   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbc59925-c398-4af8-925d-7d07aeef3d4c",
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    "tags": []
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   "source": [
    "## **2.** Dérivées"
   ]
  },
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   "id": "f813f8f8-6fee-4e42-8a64-0bc56d191c68",
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   "source": [
    "On va tout au long de ce paragraphe étudier trois fonctions simples :\n",
    "\n",
    "$f_1(x)=x^2$\n",
    "\n",
    "$f_2(x)=\\sin(x)$\n",
    "\n",
    "$f_3(x)=x^3+x^2-x$"
   ]
  },
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   "id": "74797da0-e494-40c1-bce9-e118e79f8c44",
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   "source": [
    "def f1(x):\n",
    "    return x**2\n",
    "\n",
    "def f2(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "def f3(x):\n",
    "    return x**3+x**2-x"
   ]
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   "source": [
    "### **2.1.** Dérivée numérique"
   ]
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      "\u001b[91mf1\u001b[0m\n",
      "6.0\n",
      "0.0\n",
      "-6.0\n",
      "\u001b[91mf2\u001b[0m\n",
      "-0.833049961066805\n",
      "0.8414709848078965\n",
      "-0.833049961066805\n",
      "\u001b[91mf3\u001b[0m\n",
      "33.0\n",
      "0.0\n",
      "21.0\n"
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     "text": [
      "/tmp/ipykernel_28083/3210042646.py:4: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f1,3,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:5: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f1,0,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:6: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f1,-3,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:8: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f2,3,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:9: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f2,0,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f2,-3,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:12: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f3,3,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:13: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f3,0,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:14: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  print(df(f3,-3,dx=1))\n",
      "/tmp/ipykernel_28083/3210042646.py:27: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  graph[f1].plot(x,df(f1,x,dx=1),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
      "/tmp/ipykernel_28083/3210042646.py:34: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  graph[f2].plot(x,df(f2,x,dx=1),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
      "/tmp/ipykernel_28083/3210042646.py:41: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools\n",
      "  graph[f3].plot(x,df(f3,x,dx=1),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n"
     ]
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MYW+88QYDwD788EPNcaY00HW9b4wZ/97J8b4RhDHkp1e9fv2a3bp1i506dYp9/PHHrFKlSuzp06e5jiO9qvAYaqBbi9yGYo1yC++9qaO+5IYMdMJq0MdAZ4wrT8WLF2eJiYmFut6aNWsYABYVFVWoeQiCIPJTlNVqNfvkk09YUFAQi42NzXMOW1aUBVauXMnef/99FhgYyFxdXVmJEiVY48aN2ffff88yMjI0x5nSQM/5vjFm/Hsn1/tGEOamSpUqbMGCBTr3kV5FENaFgjFqsExYB1euXEGdOnXybLMmEBMTgxo1amD69OmYOnWqUdfKyspCtWrVUKdOHezcudNIiQmCIPKHMYbPP/8cf/75J6KiogqsYt6/f3/s3r0bMTEx8PT0NPq6ERERGDZsGKKiohASEmL0PLYCvW8EkT9VqlTBoEGDMG3atFz7SK8iCOvChuvPE/bCixcvcPHiRdy4cQMAcPXqVVy8eDHPth+BgYFYv359oZSw2NhYDBgwAIsXLzZ6DoIgiIL4/PPPsXnzZmzatAlubm549OgRHj16hIyMDJ3Hz5o1C6mpqVi+fLnR18zKysKcOXPw/vvvFxkjk943ghCZNGkSTpw4gZiYGFy4cAHDhg3DgwcP0L17d53Hk15FENYFedAJ2Vm3bh0GDx6ca/vatWsxaNAgywtEEARhIhQKhc7tkZGRaNGihc5927Ztw+PHjzFq1Cijrnn37l1s2LAB/fv3R+XKlY2awxah940gOP3798eRI0fw5MkT+Pr6olGjRpg+fToaNWokt2gEQegBGegEQRAEQRAEQRAEYQVQiDtBEARBEARBEARBWAFkoBMEQRAEQRAEQRCEFUAGOkEQBEEQBGFR0tLSMG7cOISEhMDf3x+urq4oW7YsgoODsXbtWmRmZuY6JzExEePGjUNgYCCUSiWCgoLw5ZdfIjk5Wec11Go1li9fjjp16sDNzQ2lSpVCnz59cPfuXXO/PIIgCKMpcjnoarUa8fHx8PT0zLN4D0EQRF4wxpCUlAR/f384ONjXGifdHwmCKAyG3B+fPXuGgIAANG7cGNWqVUOpUqXw8uVL7NmzBzExMQgNDcWePXs086SkpKBp06a4ePEiQkND8eabb+LChQvYv38/GjVqhKNHj8LV1VXrGsOGDUNERARq1aqFjh07Ij4+Htu2bYOHhwdOnTqFqlWr6v3a6P5IEERh0fseKU/7dfm4f/8+A0APetCDHoV63L9/X+7bmcmh+yM96EEPUzz0uT+qVCqWnp6ea3tmZiZr0aIFA8D+/PNPzfavv/6aAWCTJk3SOn7SpEkMAJszZ47W9sOHDzMALCQkROs6f/31FwPAQkND6f5ID3rQQ5ZHQffIIudBT0hIgI+PD+7fvw8vLy+5xSEIwsZITExEQEAAXr16BW9vb7nFMSl0fyQIojCY6v747bffYsyYMVi6dCnGjBkDxhjKly+PxMREPHr0CO7u7ppjU1JSULZsWZQuXRp37tzRbO/bty82b96MqKioXH3tW7ZsiSNHjiAmJgYVKlTQSya6PxIEUVj0vUc6WVAmq0AIS/Ly8qIbLKGFSqXCsWPHAADNmjWDo6OjzBIR1ow9hjjS/ZHID7pHEvpSmPujWq3G3r17AQC1a9cGANy6dQvx8fFo27atlnEOAO7u7ggODsa+fftw//59BAQEAACOHDmi2ZeTtm3b4siRI4iKikL//v11ypGeno709HTN86SkJAB0fyR0Q/dHwhAKukcWOQOdIPKCMaYpNFPEAksIgiAKhO6RhDnIyMjAnDlzwBjD8+fPcejQIVy/fh2DBw9G69atAXADHUCeOeNVq1bFvn37cOvWLQQEBCAlJQUPHz5E7dq1dRpKwjzCvLqYO3cuvvnmm8K+PKKIQPdHwpSQgU4QBEEQBEHIQkZGhpYhrFAoMGHCBMydO1ezLSEhAQDyDAkVPNrCcYYer4spU6Zg3LhxmudCaCpBEIS5sa8SxARBEARBEITN4OHhAcYYVCoV7t+/jxUrViAiIgItWrRAYmKibHIplUpNODuFtRMEYUmswkCfP38+FAoFFAoFTp06lWu/oX0vCYIgCIIgCNvBwcEB5cuXx6efforVq1fjxIkTmD17NgDRE56Xx1sw5IXjDD2eIAjCmpDdQL9y5QrCwsJyFf0QSElJQfPmzbFkyRLUqFEDX3zxBapXr46FCxeiVatWSEtLs7DEBEEQBEEQhLkIDQ0FwAu9AQXnjOfMUXd3d4efnx/u3bsHlUpV4PEEQRDWhKwGemZmJgYOHIj69eujW7duOo9ZsGABLl68iEmTJmHfvn2YN28e9u3bh0mTJuHMmTNYsmSJhaUmCIIgCIIgzEV8fDwAwNnZGQA3pP39/XHixAmkpKRoHZuSkoITJ06gYsWKWjnizZs31+zLyb59+wAgV/s1giAIa0DWInGzZ8/Gf//9h/Pnz2PBggW59jPGEBERAQ8PD0yfPl1r3/Tp0zV5SlOmTLGUyHZFZmamzpXloopKpdJEcqSnpyMrK0tmiawPR0dHjcJEGM/GjRtx7NgxnDt3DpcvX0ZGRgbWrl2LQYMGGTSPWq3GihUrsHr1aty+fRseHh547733MHv2bFSqVMk8whNFFoVCATc3N82YIArD1atXERQUhGLFimltf/36taY4W4cOHQDwz9vQoUMxY8YMzJw5E/PmzdMcP3PmTCQnJ2Pq1Kla8wwfPhxbtmzB9OnTceDAAbi4uAAA9uzZgyNHjiA0NBSBgYHmfIkASNcqKphSh3R2dqY2bUUc2Qz08+fPY/bs2ZgxYwbeeOMNnccY0/cyJzn7WMpZcMRaSExMxLNnz7TeF4JTtmxZAEBsbKzMklgvSqUSJUuWpII5hWDatGmIiYlByZIl4efnh5iYGKPmGTFiBCIiIlCrVi2MHj0a8fHx2LZtG/bv349Tp05R+CZhUhwdHTVtrwiisGzbtg2LFy9G06ZNERQUBC8vL8TFxWHPnj14/vw5mjVrhi+++EJz/MSJE7Fz507Mnz8fFy5cQIMGDXD+/Hns378fjRo1wtixY7Xmb9myJYYOHYqIiAg0aNAAHTt2xMOHD7F161b4+vpi+fLlZn19pGsVPUylQyoUCnh7e6Ns2bK0GFpEkcVAT09Px4ABA1C/fn1MnDgxz+MM7XupC+pjqU1iYiLi4uLg4eGBkiVLwtnZmb78hF4wxpCZmYmEhATExcUBABnpRhIREYGqVasiMDAQ8+bNMyoKKDIyEhEREQgJCdHyDvXt2xcdOnTAyJEjNWGcBEEQ1kanTp0QHx+PkydP4u+//0ZycjK8vb1Rt25d9O7dG0OGDIGTk6imuru7IyoqCuHh4di+fTsiIyPh5+eH8ePHIywsTBPdIWXVqlWoU6cOVq9ejWXLlsHDwwPdunXD7NmzUblyZbO9NtK1CGNhjCElJQVPnz6Fm5sbfHx85BaJkAFZDPSvv/4at27dwrlz5/IN4bCKPpZpaUBUFNCoEeDrq/95VsqzZ8/g4eGB8uXL048FYTBubm7w9PTEgwcP8OzZM9s30J88Af79FwgJAbINXEvw3nvvFXqONWvWAODhnS4S2du3b48WLVpg//79iI2NRYUKFQp9LYKwCjIygMxMII+isoRt0bBhQzRs2NCgc7y9vbFkyRK96w85ODhg9OjRGD16tDEiGg3pWkRhcHNzQ3p6Op48eQJvb2/6DFkrkZFAtWpAuXImn9riReL+/vtvLFy4ENOmTUPt2rXNfr1C9bH86SegZEmgXTtg1y7zCWkhMjMzkZ6eTl/2PGCMISkpCUlJSWCMyS2O1SKEXqWnpyMzM1NucQrH778DbdoAJUoAW7fKLY1BHDlyRJPqk5O2bdsCAKKiovKdIz09HYmJiVoPqycrC5g2DShfHggKApo1A6ZMAajtptlRqVQ4duwYjh07ZrmcWrUa+OMP4KOP+Pe0RAngyy+BV68sc32CMBDStYomptYhvby8oFKpqH6BtaJSAd27c12kWTOTT29RAz0rKwsDBw5E3bp1MXny5AKPl72PZaVKgFAt9M8/zXMNCyJ8yanIV97QzVA/hM+Qzb9Xwvc6ORmoUkVeWQwgJSUFDx8+RMWKFXVGIRXUkkhg7ty58Pb21jwMii6SgydP+ILK7NlAXBwQEwMcPw7Mmwd06EBGuplhjCEhIQEJCQmWWcRUq4G+fYEuXYBNm/j/Nz0dWLiQf1+3bDG/DARhIKRrFV1MqUMK6R1UsNhKOXcOePmSj/38TD69RQ305ORk3Lp1CxcvXoSLiwsUCoXmsX79egDAO++8A4VCgR07dhjc99LkNGkihrXv28fD6+wAWtElCotdfIZSU4FDh/jYzw9480155TEAU6T/ADwFSDC4EhIScP/+fdMKakoePAAaNgSy+yLDyUk77ejYMaBjR3FRlbB9Zs3SjmwpXhxQKvn4+XOgXz/gn3/kkY0gCsAuficJ2aDPj5Vz8KA4NkHaYk4smoOuVCrx8ccf69x39OhR3Lp1C++//z5KlSqFoKCgXH0vpZXc8+p7aVIcHYH27YGffwaSkrinplUr81yLIAjLEhnJjXSAe18dLJ7xIztKpRJKweCxdsaOBYQFBD8/4JdfgOBg4OxZ7lV/9Qo4ehTo3ZuHRJNyY9v8/jsQFsbHCgWwdi3Qpw/w6BHwxRfAb7/xEMMBA4Dz54EcrboIgiAIwmwcOCCO27Qx+fQW1Ujd3NwQERGh8/Huu+8C4B6diIgI1K9fX9P3Mjk5GTNnztSaS+h7OWzYMPMK3amTOLaDMHeCILKRfp+l33MbQPb0H0uzfz+wfTsfly7NQ8uE3PuGDfkPpVDp9s8/tVe2CdsjJgbo3198Pm8eMHAgL+RYoQIPbW/UiO+7cQPQI2WOIAiCIExCSgpw4gQfV6oEVKxo8ktYvcto4sSJqFevHubPn4+2bdtiypQpaNu2LebPn6+z76XJaduWe9IBMtAJwl5gTPw+u7iYJTzJnLi7u8PPzw/37t3Tme9m9vQfS5KeDowaJT5fsCB3vlfDhsD334vPp0zh+cuEbTJ/vpiq0LcvLwonxdkZ2LABcHXlz5cvF1MfCIIgCMKcHDvGO4oAZvGeAzZgoAt9L8eOHYtr165h0aJFuH79OsaPH49Dhw7p7HtpUooXFz01t24BN2+a93qE2cnMzER4eDiqVq0KpVKpqXkA8CJILVq00FTBNoYbN27AyckJK1euNJHEhMm5ckUMl27RAvDwkFUcY2jevLkm1ScnQv/zkJAQS4tlepYsEe+7wcHanlUpPXsC9evz8blzosedsC0ePgR+/JGPPTy48a0rXaFGDb5YIzB7tmXkIwhCLwrStd566y2EhoYaPT/pWoRsmDm8HbAiA33dunVgjKFJkya59gl9L2NjY5GRkYGYmBgsXLgQnp6elhFOGv66e7dlrkmYjUWLFuGbb76Bv78/JkyYgLCwMNSoUQMAsGXLFly6dAnffPON0fNXr14dffr0wTfffIOkpCRTiU2YEhsKb3/27BmuX7+OZ8+eaW0fPnw4AGD69OnIkBSw3LNnD44cOYLQ0FAEBgZaVFaTk5YG/O9/fOzgAKxYkXetAAcHYO5c8flXX4kr3ITJcHFxgYuLi/kusGQJj5oAgE8/1S4EmJPPPwcqV+bjgweB//4zn1wEQRhEfrrWhg0bcP78ecyYMcPo+a1R1xIKXxN2jmCgKxRAy5bmuQYrYiQkJDAALCEhQf+Trl5ljAfFMtaqlfmEMzOpqans6tWrLDU1VW5RZCU4OJh5eHiw9PR0re0qlYoFBQWxZs2aFfoa//77LwPAZs2aVei5rBGb/yy9+674nb5zx6BTjbqH5GDNmjVs4MCBbODAgaxBgwYMAAsODtZsW7NmjebYsLAwBoCFhYXlmmfo0KEMAKtVqxabOHEi69+/P3NxcWG+vr7sxo0bBstlitdmUjZuFP9PH31U8PFqNWPNm4vnbNhgdhEJE/L8OWMeHvx/p1QyFh9f8DlLl4r/7+HDzS8jkS9Wdw8xIfq+Npv/fTQRpGsVDvocWSkPH4q/OY0aGXy6vvcRq/GgWzU1aogFAI4eBQpoXURYN/Hx8ShRokQuL9CePXsQHR2NAQMGFPoaderUQd26dbFmzRqoKRfWunj2DDh1io9r1uQFPizM8ePHsX79eqxfvx7nz58HAJw4cUKz7fjx43rNs2rVKixbtgwAsGzZMvz111/o1q0b/vnnH1SrVs1s8luMNWvE8YgRBR+vUADSgqJr15peJsJ8fPed2Mt+yBD9essOHiymqPz0E/DihfnkIwhCb0jXIuwSoT0vYNb6RWSg64NCAXTuzMdZWbwnOmFzhIeHQ6FQ4N69e4iJidGEIgUFBQEA1q5dC4VCge7du2udd+LECTg5OaF+/fpIF0Iv9djXs2dPxMTEIDIy0qyvizCQv/4SC4jJFN4upPTk9Vi3bp3m2PDwcDDGEB4enmseBwcHjB49GleuXEFaWhqePXuGLVu2oLIQ9mvL3LgBREXxcY0aQNOm+p3XtCkgLE5ERgKxseaRjzAtarW4IOPomLswXF54eXEjHeBtEyMizCMfQRB6QboWYdfs3y+OzZR/DpCBrj+CgQ4Au3bJJwdhNC1atEBYWBi8vb3h7e2NsLAwhIWFYezYsWCMITIyElWrVoWzszMYY5rzgoODMW3aNFy6dAmTJk3SbH/16hU++ugjKJVKbN68OVc/6XfeeQcAcEi62kbIj/T7+/778slB5I/U0Bo2TP++5gqFdiG5n382rVxFGJVKhZMnT+LkyZM6uwcUipMngQcP+LhdO8Pa1owaJX4+VqygCv4EISP66FrVq1dH8eLFtc6zdV2LMYbk5GQkJydr6ZCEHcGYaKAXKwZktwg3B05mm9neCAnhK/WJibxQXFYW4GRnb1/DhsCjR3JLkT9lywJnzxp1aosWLdCiRQuNd1Lqkbx69SpevHiB1q1bIysrK9e506dPx8GDB/Htt9+ibdu2aN++PUaMGIGYmBisWrUKNWvWzHVOw4YNAUBnlW1CJtLTgb17+bhECSD7h52wMtLTASGKwMUFMDQUsl8/YPp0Pt6wgffJpsI9hYYxhhfZIeQmV0C3bhXHvXoZdm7Vqtyo37OHR0ycOmVWxYkgCgXpWmjfvr3Oc21d19KlPxJ2xL//it/dli2BHItFpsTOLEwz4uLCFYBt24CXL/lqvz20MJLy6BEQFye3FLLwINtzU7p0aZ37HR0d8fPPP6N+/foYNGgQxo4di23btuGDDz7QVNPOiZeXF1xdXTVzE1ZAVJSY49qhAw+lJayP3bt5rQAA+OADoGRJw84PCgKaN+f/7+vXuaLZqJHJxSRMhEoF/PorHyuVQJcuhs/Rqxc30AHgt9/IQCesF9K1UKZMGZ37SdcirBrBwQMAhWjHrA9koBtC587cQAd4mKy9Gehly8otQcGYScbnz58D4C398iIwMBA//PADevfujalTp6J8+fJYIy1ipQNfX99c7bEIGZGGt0vTVgjrIrtXLgBg0CDj5ujfX8xh37CBDHRr5uhR0SvRvj2PVjOUzp35gptKBfz+O2/PR1EThDVCuhZ8fHzyPIZ0LcJqkdYga9fOrJciA90Q2rfnvXbVauCPP8T+vPaCkeFM9oCbmxsAIC0tLd/jWrduDS8vLyQmJqJv377wza9HL4DU1FQUK1bMZHIShYAx/r0FAGdns69+EkaiUvFCfgCvzm1sj9EPPwRGjuS91LdsAZYupYgJa2XLFnHcu7dxc/j6Ai1a8Aq7d+/yUMR69UwiHkGYFNK1SNcibI/kZEDosFOxIlClilkvR0XiDKFECbGS8M2b/EHYBaVKlQIAvHz5Mt/jhgwZgsTERJQoUQJLly7FxYsX8zxWrVYjISFBMzchM5cvixW9W7QwzktHmJ9Tp4BsLwvatuXpRcbg7c3TGAAeLl+ElWKrJjMT2L6dj4sVK1xnhQ8+EMe//144uQiCMDmCPvSigHaIpGsRVkdkJP+9Arj33MwRWmSgG4o0LFbwxhE2T61ateDg4IDbt2/necyKFSuwa9cu9OvXD/uzqzj26dMHr1+/1nn8rVu3oFarUadOHbPITBgIhbfbBqb8P0kLEUlzxwjrISpKXJDp1Alwdzd+Lmnu+m+/FU4ugiBMjqBr3bhxI89jSNcirBJpeLsFIjDJQDcUaVsmMtDtBh8fH9StWxcXL17UWZ34ypUrmDBhAipVqoSVK1eiQYMGmD17Nq5fv46xY8fqnPP06dMAgObNm5tTdEJfdu4Ux2SgWy9//sn/KhSiB9xYpDliQgExolA4OjrC0ZSpAlKlp1u3ws1VrhzQpAkfX74M5LPgShCE5RF0rbNnz0Ktox2iretaQs93wg4RfqucnIxPvTMAMtANpVo1oHp1Pj5xQqw0TNg83bp1Q1JSEq5du6Z1g01LS0OfPn2QlZWFTZs2wdPTEwAwfvx4tGnTBmvWrMF2IURTwoEDB+Dk5IROhQnZJExDfDxw5gwf163Lq3wT1se9e8B///FxkyZAYUMWy5cHatfm43/+ET21hFE4OTmhffv2aN++PZxM1Wb04EH+V6EA3nuv8PNJw9ylxQYJgrAKBF3r1KlTWtttXddSKBSa3u9kpNsZd+6IC77BwRZJkSQD3RiEMDq1WvT2EDbP0KFD4eTkhI0bN2ptnzBhAq5cuYLw8HC8/fbbmu0KhQLr169HyZIlMWzYMNy/f1+z7/Xr19ixYwc6deoEf39/i70GIg+k0S7GtHAiLIM50hAELzpjwIEDppmTMA1PngBCbumbbxreTk8X0u+3YPwTBGE1kK5F2By7d4tjM1dvFyAD3RikCoA0bJawCaKjoxEdHZ1ru7+/P3r37o0tW7YgKSlJs/27774DYwxfffVVrnP8/Pzw9OlTvHjxAgEBAZrtmzZtQnJyMr744guzvAbCQKTfUzLQrRfpgqepDXSAwtytjUOHxLEpvOcAULUqD3UHgGPHgIwM08xLEIRBkK5F2A1CZxkA6NjRIpckA90Y3n5bDL3cvx9ITZVXHsIkMMYwdepUpKam4ttvvzV6nqysLMyZMwfvv/8+QkJCTCghYRRJScDhw3xcvjzQoIG88tgZx48DH3/M/+oo36A/aWm8HzYABAYCtWqZRD40bSoWHtu3j0c+EQazezfQp48KK1f+g99//wcqlarwk0o93G3aFH4+gIfKC/mBr1+LqS2EQTx5AixeDIwfL7ckhD0ya9YspKamYvny5UbPYW26FmMMKSkpSElJ0VnLiLBRUlKAI0f4WJo2Z2bIQDcGR0fRu/P6tbYXgLBp/Pz8sHLlSk3ukzHExsZiwIABWLx4sQklI4xm3z7Ri/b++2ZvjVHUWLMG+PFHoFkzoFEj4NEjIyc6cwZIT+fjli1N939SKoFWrfj48WMxpJrQi/R0YMwYXmD9998ZKlR4AmfnJ4VXQKUpB66uYgtTUyAt4CMszhF6s2ABD0IYPx5Ytox/bQjClAQGBmL9+vV2p2tlZmYiU2jFRdgHhw+LuknHjhbTIclANxYKc7dbunXrhlGjRhl9fqVKlRAeHo7KlSubUCrCaCi83WxkZvIgIoFz57ghl5xsxGRRUeLY1NV4pWHuUoGJfHn+nC+8FCKgKG9u3gSEXNKmTbmRbiqEBRmA964l9GbvXmDSJCAriz9Xqah0A2EeevbsSboWYf1Iw9sL21nGAMhAN5b33gPc3Ph41y4KmyQIayQrSyzu4eUFtGghqzj2hrMzL2z600888gvgRnqPHtx4NwghvB0ATB2u2Lq1OD5+3LRz2zGffipGiCuVwNKluo+7e5c/DMIc4e0CQUFip4aTJ3n6BKEXbdoAI0fy8ciRwPXrQL9+8spEEAQhC4yJBrqLi/bir5khA91YihUDQkP5+PFjIEe7CIIgrICjR4GXL/m4fXt+gyVMirs7V+D37QN8fPi2vXuBL780YJLMTG5IAdzSr1jRtEJWqyZWCD9xghZU9eCXX/gDAHx9gb//BoYO1T5GrQZWrADq1AEGDODeVr2RumVNbaADYph7ejoXntALR0ceMREZCSxfLnaVJQiCKHL89x8QG8vHLVoAHh4WuzQZ6IWha1dx/PvvsolBEEQeSPsgS7+vhMl54w3ezU6p5M+/+w64cUPPk8+f54VYAO49N3WOl0Ih5ji/egVcvWra+e2MJ0+Azz4Tn69Ywbug5SQtjRcSe/2ar3voHQrPGK+wDnDrv169QsucC2keOoW5G4RCQcFGBEEQcoW3A2SgF47OnflyM8ANdKraSBDWA2Oige7iYvGba1GkWTNg+nQ+VqkAHd1ydCPNPzdXNV5pEbITJ8xzDTth9Gjg2TM+/uADoFcv3ccVKwasXSs+nzoVuHNHjwvcvAm8eMHHwcGAgxlUESoUpzfXrgFxcXJLQRAEYWVIW7+SgW5DlCghKpN37vBQCIIgrINz58QiVK1b8xx0wuyMHQuULcvH27cD//yjx0nS/HNTF4gTCA4Wx5SHnidqNU/f9vLiWQHff59/QENICK/yDnCP+oIFelxESGcAgHfeKYy4eVO+PO+JDgCnT3M3P5ELxnjqQpUqwJQp1DWWIAgCAK+SKizmV68u/p5YCDLQCwuFudsNCoUCPj4+8PHxgYJacdk+FN4uC+7uQHg4X79cskSP6GWVSgx3LlXKfEmvDRqIlcLJQM8TBwdg3jy+trVvH1C6tLjPyckJnTp1QqdOneDk5KTZPmMGIHRL2rCBh8jnizQn/N13TSd8ToQF9KwsvmBH5OKPP8Q6ejt38sKPBEEYDumQdsZff4n1aoTW2haEDPTCQgY6QVgnwvdRoaD2ahZmyBAeVDR2rJiTnif//gskJvKxOfLPBVxcgLff5uPoaIrpLQAvL76moe+xw4fzcVoasHJlAScIHnRHR6BhQ6NlLBDh/w1wLzqhBWNAWJj4fO5cQLLuQhAEUXT54w9x/P77Fr88GeiFpUIF4K23+PjCBSAmRl55CILgOa5CIbB33wXKlJFXniKGszPg7a3nwVJvtrnyzwUoD91sjBkjGncrVuQTUZ6QIH4369XjIRfmokkTcUwGei7OnAEuXeLjRo1k0UEJgiCsj4wMHkIG8EKm5krFygcy0E2B1IsuDaslbArGGFJSUpCSkgJGBf9sGwpvtx2kSermDHcGtA10CnPXIiUFmDNHLA6nC5VKhXPnzuHcuXNQ5eipFhAA9OzJx8+e8VB3nZw+LRZUNff/+403xLY41Ao1FxER4vjTT80XvEIQRQHSIe2IqCggKYmPO3SQJbSIDHRT0K2bOP7tN/nkIApNZmYmMjMz5RaDKCzS76H0+0lYnGvXgAkTgB9/zOOAM2f4XxcXoG5d8wrzzjuiFUIGuhY//8yr7leoAKxfr/sYxhgePnyIhw8f6lRAx48Xx999l8eFLFEgTkAaQv/gARAfb97r2RDJycDmzXzs6Qn06CGvPARhD5AOaSfIHN4OkIFuGt54A6hWjY+PHQMeP5ZXHsIooqOjUbx4cXwmbQAMYP/+/QgODkbx4sWhUCjQNYdHdunSpXBxcUF0dLTR127WrBneluZLmoDw8HAoFAocOXLEpPNaPQ8eiOGsdesClSvLK08RJjqa3x4XLeIF43LZdK9eic3S69XjRro58fYG6tTh40uXxN7rBDZt4n9TU4FatYybo0ED3j992TLg4ME8DrJUgTgBCnPXybZt3EgHgD59xEADgjAn0dHRUCgUGDRokNZ20rMIq4ExYNcuPnZ2Btq2lUUMMtBNgUIBdO/Ox4xpr7wQNk10dDS6dOmCu3fvYvDgwQgLC0Pv3r01+1++fImZM2diyJAhCAoKMvo64eHh+Oeff7Bly5Z8jzt79iwUCgW+y9M9RWgVaxS+l4QsBAWJ3c2uXNHRck1aWbtxY8sIJVxHrQYuXrTMNa2cuDix01316mJZFWNYsYL3URda7WmhVouh5mXLAoGBxl9IX6QKOYW5a5CGtw8dKp8cBEF6FmFV/PuvWE+sRQvZWvSSgW4qPvhAHG/fLp8chEk5ePAg0tLSsGjRIixevBjh4eFaPxxLlizBixcv8OWXXxbqOq1bt0aDBg0QFhaWb+7Szp07AQBdqCp53kjD26XfS0IWPv5YHK9Zk2OnEN4O8CpVlkBqfVLrLQDcmyrcdnr3NmMu8tWrYsX+d9+1TNIzVXLPxX//iYEMdeuat5A+QRQE6VmEVSGtYSRj5Uwy0E3FW2/x5D0AOHSIh24SNk98ds6iv79/rn1ZWVmIiIhAcHAwKpsgjLpfv364efMmDh8+nOcxO3fuRIMGDRAQEFDo69klT5+KrsCqVY2P1SVMRs+eYvjs9u2AVnqe1KVuKQNdao2cPWuZa1o5Qi4ywA10syE1kC1VFdfPT/xtPnsWyFHcriji4wPMnMnVlqFDqTgcIS+kZxFWhTQKU8Yiw2SgmwqFQvTWZWWJ+QuE1aFSqTB//nxUqVIFrq6uqFKlCubOnQu1Wq05RsiTCstuEtuyZUsoFAqtXKO9e/fi4cOH6JGjuk56ejrq168PJycnnMjRyim/fcI869at0yn3vXv3cPny5Vyruvfv30efPn3g6+sLDw8PNG/eHEcFI1UCYwwdOnSAQqHA1q1bc+1r3769zn02xc6dPIwW4OHtpHnKjrs70KkTH796xct0aBA86J6ePLbaEtSpw/PKAPKgg/erF/4N9esDNWoUfk7GuC0+diwwY4Zkx/nz4tiSblvBi56Swt3HRZxy5YBp0/h6xciRcktD2CNFWc/q0aMHHBwc7FfPsmfu3dPuPVm+vGyikIFuSqT5rlTN3WoZPnw4Jk+eDLVajc8//xxt27bF4sWLMXbsWM0xPj4+CAsLQ/PmzQEAAwcORFhYGMLCwjQ5UIcOHQIANJEWIQKgVCqxefNmuLi44KOPPkJCQoJm38SJE3Hp0iVMnz4dwUJybjbly5dHQECAZt6c7MgOu5H+cDx8+BDvvPMOtmzZgsaNG2P06NHw9fVFmzZtcCpHvqVCocDatWtRunRpjBgxAjFCjg14AZa9e/di0KBB6NWrlx7vopUiTS+h8HarQarraKLHHj7kBf0A7spzdLSMMEqlWCju2jWxUlYRRZqOaSrveVIS0Lw5Lxa3YgVfswagbaDXr2+ai+kD5aHnCa1hEuYgLz1rzJgxmmPsVc9asWKFfetZ9ow0vF3uDkCsiJGQkMAAsISEBNNPnpXFWJkyjAGMuboylpRk+msUgtTUVHb16lWWmpqa5zGLFjFWrlzBj86dc5/bubN+5y5apH1eYqJx5xlDZGQkA8Dq1avHkpOTNdsfPHjASpYsyQCwgQMHMrVazRhjLCwsjAFgkZGRueZq1KgRc3BwYGlpaTqv9cMPPzAArFevXowxxnbv3s0AsKZNm7KsrCyd53Tr1o0BYHfv3s21r3nz5iwoKEhr28CBAxkANmvWLK3tq1atYgB0yr5nzx6mUCjYu+++y7KystiFCxeYi4sLq1q1KkvS8zOrz2fJ4rx8yZizM//+BQQwlv0/NDVmvYfIjLle26tX4r+mQoXsf83OnXwDwNjEiSa9XoEMHy5e+9gxy17byqhdW3wr7t3L/1i1Ws0yMzNZZmam5h6ZFx98IM574ABjLDOTMTc3vqFyZZPJrxfHjonCDB1q2WsXMej+SLqWvnqWgL3oWWq1WvP466+/7FPPsneaNRN/K65dM8sl9L2PkAfdlDg6iisuaWnAnj3yymMEiYm8om9Bj6dPc5/79Kl+5wo1ggQYM+48Y9iwYQMA4Ouvv4a7u7tme7ly5bRWdhV6uBUePHgAHx8fKJVKnftHjBiBbt26YevWrZg3bx4GDRoEHx8f/Pzzz3DMw1tYpkwZzdxSnj9/juPHj2ut6mZkZGDr1q0oXbo0xksbEAMYOnQoqlatqvMa7dq1w5gxY3Dy5ElMnjwZffr0AWMMmzdvhoct99rZtUtMcO7WjVxDVoS3N9CyJR/HxmYXT5ejQJyAtFBcEc5Dj47m1fUB7mQuqECyQqGAk5MTnJycCrxHSh1Eu3aBt9NLTeUbGjQwVmTjqF9fvB8U8cr9Gzbw/3k+NbIIC2DPupa+epY+2JKeJYTnKxQKtG/f3j71LHvmyRPg+HE+rlHDNPlehcBJ1qvbIx9+CPzwAx//8guQI2/G2vHy4vlpBVGqlO5t+pybs2OBQmHcecZwKTu3pFmzZrn26dqWH8+fP0f5AvJTIiIi8M8//2DKlCkAgK1bt6KCULBIB76+vgCAZ8+eaW3fvXs3VCqV1g/HjRs3kJaWhlatWsHV1VXreAcHBwQHB+PWrVs6rzNv3jwcOXIECxcuBADMnz8fbxWmt5I18Msv4tjGvndFga5dgf37+XjnTuBNOQrECUjzn4twHnqxYsC8eXwtuX17084dGsrXrFUqYO9eAA0l4e2WNtA9PIBq1fgiweXLfCFPqENQhHj+HBg8mJfpCA0F9u2TV564uDj88ssv+Ouvv3D9+nU8evQIvr6+CA4OxsSJE3X2rE5MTER4eDi2b9+OR48ewc/PDz169EBYWJhOw0etVmPFihVYvXo1bt++DQ8PD7z33nuYPXs2KlWqZImXqRN71rVIz+LYpZ5lz/zxh7hyKXd4O8hANz3NmwMlSvBfwt27gdevuRZkI4wbxx/GYGz7d09PMRXV3CQkJMDBwQElS5bMta906dIAeNVQxliBHiI3NzekpaXle4yvry9CQkKwefNmlC9fHt0K+NKnZnuYiuX4zOzYsQO+vr5aP25CzpUgd06EVWJdKJVKtG/fHhcvXoSrqyuG2noj3MREUdv08+MtnAir4v33eeGwLl2A0DYMCMo2jEuVEqtsW4ratQEXFyAjo0h70EuXBiZN4g99UKlUuHz5MgCgTp06eXqoAF4p/N13eVHAmzeBu5Ex0JhDljbQAe5Fv3EDSE/nf2vXtrwMMvPnn2INzXr15JUFAJYvX4758+ejcuXKCA0NRalSpXDr1i3s2LEDO3bswKZNm7RydVNSUtC8eXNcvHgRoaGh6NOnDy5cuICFCxciKioKR48ezWVEjRgxAhEREahVqxZGjx6N+Ph4bNu2Dfv378epU6fyjDQzN/asa+WnZ+Wnl+jClvQsxphmbjc3N/vTs+wdafV2KzDQKcTd1Dg5if/Y16+zXQeEteDt7Q21Wp1r5RQAHj9+DABaVUbzo1SpUnjx4kW+x2zfvh2bN29GiRIl8ODBA3z11Vf5Hi/MV0qybJ6Wlob9+/ejY8eOcHIS19S8vb0BAE+ePNE5l/B6dHH69Gn873//Q4kSJZCWloZPP/00X7msnj//5MYWwIs1OtCtzdooVw5Yt47fHt1fxfFFTIAba5ZOR3Bx4Q2gAW6sJSVZ9vo2CmMMDx48wIMHD/LtIyzQrp043nNM4t18800zSFcA0mteuGD561sB2e2dAWgXbpSLxo0b48iRI7h9+zYiIiIwd+5c/Prrr4iMjISjoyM+/fRTpKena45fsGABLl68iEmTJmHfvn2YN28e9u3bh0mTJuHMmTNYsmSJ1vyRkZGIiIhASEgIzp8/j/nz5+Onn37Cjh078OLFC4ykEvZmQR89S19sTc/KyMhARrYuYnd6lj3z6hVw4AAfBwRYtstIHpAWaw4+/FAc//qrfHIQuaiX7TY4ptXrCXluy486deogLS0NsbGxOvc/ePAAw4YNQ6lSpXDhwgU0adIECxcuzLN6KMDDqZydnVFDkvty8OBBpKSk5Gr7Ua1aNbi6uuLs2bO5VpjVajVOnjyp8xpJSUno27cvnJyccOTIEXTv3h3btm3Djz/+qO9Ltz6k3zPp94+wTqR5wJas5i1F+AFmrMgabOZGGja/Nzq7jV5AgO64XXMj/ZwVwf93Zqaof5YqBeQoii0LH3zwgaaCt5RmzZqhZcuWePnypSZigzGGiIgIeHh4YPr06VrHT58+HR4eHoiIiNDavmbNGgDAzJkz4eLiotnevn17tGjRAvv378/z95swHtKz7FTPsmf++EOsYfThh1ZRw8jiBnpaWhrGjRuHkJAQ+Pv7w9XVFWXLlkVwcDDWrl2LTOENkpCYmIhx48YhMDAQSqUSQUFB+PLLL5Fsre1xWrUCihfn4127xMI4hOz0798fADBjxgykpKRotsfFxeHbb781aC5BsTh9+nSufWq1Gv369cPLly+xdu1aBAQE4Oeff4anpycGDBigc2U5IyMDFy5cQMOGDbVCr3bu3AmlUom2bdtqHa9UKtGzZ088efIEixYt0toXERGBmzdv6pT7s88+w927d7Fw4ULUrl0ba9asQUBAAEaPHp3nOVZNcrJYkLFMGaBpU3nlIQpG6DMKyBdrW8QLxR06xNPv9QwYMop69fhXEgAOZ4UgDUp5wtsBbQ96ESwU988/YkfBNm0s19XQWJyzawQI3sxbt24hPj4ewcHBWoXHAMDd3R3BwcG4e/cu7t+/r9l+5MgRzb6cCL+nUVFRecqQnp6OxMRErQdRMPnpWcuWLTNoLlvVsz7//HP70rPsHSt08ljcQE9OTsb3338PhUKBjh07Yty4cejWrRvi4uIwZMgQdOrUSSvEWMg5WrJkCWrUqIEvvvgC1atXx8KFC9GqVasCc1NkwdmZV0QC+C+iUBmJkJ2WLVti8ODBuHTpEurUqYPx48dj5MiRqF+/fq4+mwXRpUsXODg44IDglpAwZ84cREVFYeTIkejYsSMAoFKlSlixYgXi4+MxZMiQXOccO3YM6enp6Cp8dsB/gHbt2oXWrVvrLIAzb948lCtXDtOmTUP79u0xdepUdOvWDaNGjUJoaGiu4zdu3IiNGzeic+fO+PzzzwEAxYsXx8aNG5Gamoq+ffvqXCSzanbv5l0TAN773No1zyLO48fA5l0eGInlUEMhn4EuNRT//VceGWRk7FgeRFC+vPnWkB0cxDD313DHcTSVz0AvXRrw9+fjCxeKXBlzqUOxdWv55NCH2NhYHDx4EH5+fqhTpw4AaApx5ZUzLmwXjktJScHDhw9RsWJFnbUSch6vi7lz58Lb21vzCAgIMP5FFSGKup61detW+9Oz7JmEBLGGkb+/dYQXAZbvg65SqVh6enqu7ZmZmaxFixYMAPvzzz8127/++msGgE2aNEnr+EmTJjEAbM6cOQZd32I9OnfvFnvp9e1r3mvpCfVU5GRlZbG5c+eySpUqMRcXF1apUiU2Z84cduvWLQaA9enTR68+6Iwx1r59e1a8eHGtHp1///03c3JyYrVr19b5Xn/00UcMAPvuu++0tg8aNIi5uLiwJ0+eaLadOHGCAWCrV6/O8/XExMSwXr16MR8fH1asWDHWrFkzFhUVlUv2u3fvMi8vL+bn58eePn2aa56vvvqKAWATJkzI81oCVvVZ6t5d/K4dOmT2y1Gf38LRrZv47zrn0oT3x5aD1FTGHBy4IPXryyODTMTGiv+Dt9/W/7zMzEy2a9cutmvXLpap5//tr78YG9ngBNuN9iwFbozt2mWk1CagQwfxhUdHyyeHDISEWOalF/YekpGRwUJCQhgAtmHDBs32n3/+mQFgX331lc7zpk6dygCw3377jTHGWFxcHAPAgoODdR6/f/9+BoCNHj06T1nS0tJYQkKC5nH//n2T9UG3d/LSs27fvm1QH3TGbEfPUqvV7OLFi8zT09P+9Cx7ZuNG8eY4apTZL6fvPdLiBnp+LFu2jAFgS5cuZYwxplarmb+/P/Pw8GDJyclaxyYnJzMPDw9WqVIlg65hMeU6PZ0xHx/+D/fwYOz1a/NeTw/oy54/arWavXz5kr18+VJjoBfEwYMHGQC2cePGQl37xYsXzNPTkw0ePFhr+8SJE5lCoWAPHz4s1Pymxmo+S0lJjLm68u9ZqVIWMfbIQC8c3y1K0/wW/q/8UrNdRy9q1uSCuLgwlpEhrywWZM0aUR8JD9f/PGMMdMYYY23aiBeMizNcYFPx1VeiHL//Lp8cFiY5mTFnZ/6yK1c277UKcw9RqVSsb9++DAAbNmyY1j45DPSc6PvarOb30U6wFT3LGB0yP+hzZCG6dBF/F44eNfvl9L2PWE2ROLVajb3ZFc9rZ7c/MSbnKCey5RC5uGiHucvdcJQwC61bt0a7du0wa9Ysvau/62Lx4sVQqVSYOXOm1vadO3fi7bffRtmyZQsrqn3y559ieHv37ryLAmHVtPa/phkfQisZJYFYyT0jg/cCKyIcOSKOdURomh4h57t0ad4GUS6kheKKUB768eNi/SNrDW9Xq9UYMmQINm3ahH79+uGHH37Q2i9U0xbaXuVE0O2E4ww9nrBeSM8izEZSkthtq2xZq2rRK5uBnpGRgfDwcISFhWHkyJGoVasW9uzZg8GDB6N19i+IoTlHupA1h0jSvxNbt1ruuoTReHl5wcvLy6Bzli1bhl69eiEuLs7o6/r6+mLDhg0oV66c1vbr16/j77//Nnpeu0f6vZJ+3wirpfqr0/AH/64cfVJD0x1PFgQDHSgyeeiMAUJdrGLFDOsm4+joiDZt2qBNmzb59kDX4vFj4OlTPq5bV97quEW01ZqXF1+/9PW1TgNdrVZj8ODBWL9+Pfr06YN169bBIUerzIL0vZz6oru7O/z8/HDv3j2oVKoCjyesG1vRs4zRIQkZ+eMPQGjlaGU1jGRzN2VkZOCbb77RPFcoFJgwYQLmzp2r2SasfOa1wil8CfJaIQWAKVOmYNy4cZrniYmJljPSW7fm1dxfvuTV3F+/5hoRYZUoFAoojFAeq1WrhvDw8EJd+4svvijU+UWSxETt6u3NmskrD6EXin8voTXc8BMG4HWGM06flvFfJy1Q9++/QJ8+MgliOaKjgQcP+Pjdd3lNU31RKBRQKpWGXTC7TVYMKiDKcTCcN8v4NlesyK3VxMQi5UF/5x1epFitBnTYqrIiGOcbNmxAr1698NNPP+VZ1M3f3x8nTpxASkqKVlRlSkoKTpw4gYoVK2rpd82bN8eWLVtw4sQJhISEaM23LzuqMed2wjqxBT3LWB2SkJEtW8Rx797yyaED2TzoHh4eYIxBpVLh/v37WLFiBSIiItCiRQuThqErlUrNipbFV7acnfmKDACkpIjGBEEQhWfXLnHl88MPrWrlk8iHixfRGmJJ6Xza1ZqfIuhBP3pUHFvENrl8GYnwREXcw8B9fTF/vgWumRcODuKiTGws8OKFjMJYHgcHwxZkzI0Q1r5hwwb06NEDGzduzDMyQ6FQYOjQoUhOTs4Vojxz5kwkJydj2LBhWtuHDx8OgPdJz5CE6uzZswdHjhxBaGgoAgMDTfyqCIKwCV68ENOPy5UDdLRjlBPZEzYdHBxQvnx5fPrppyhZsiR69uyJ2bNnY/78+faRQ9SzJ/B//8fH27bxODPCKmGMITW735CbmxuthFo727aJ45495ZOD0B+1Gvj3X7RGrGbToUNAIR0jxlO+PODjA7x6RQa6HqhUKly9ehUA8MYbb+gX5n75MryQhPq4iAtogH//5UFlxYsbdm2TUa8ecOwYH1+5YqFVCkIXM2bMwPr16+Hh4YFq1aph1qxZuY7p2rUr6mfXDpg4cSJ27tyJ+fPn48KFC2jQoAHOnz+P/fv3o1GjRhg7dqzWuS1btsTQoUMRERGBBg0aoGPHjnj48CG2bt0KX19fLF++3AKvkigqkA5pY/z+u1ico1cvvoJpRchuoEsR+gkeya5gY2jOkVXSqhVQogTw/DkvaJWSAuQoeGdpWBHr/2oIwiq7m5ubzJJYN7J/hhISxMIefn5A06byykPox927QEoKyiMFVdzjcTvFH//8wwMhDI2cNgkKBfeiHz3K475fvOCJunaMkH/u4gI0bmzYuYwxxMTEAABq1qyp30nZIe4hOIYLaADGeNGyzp0Nu7bJyC5CCwD47z+7N9BjY3kGkCzfrwKIjo4GACQnJ2P27Nk6jwkKCtIY6O7u7oiKikJ4eDi2b9+OyMhI+Pn5Yfz48QgLC9P5u71q1SrUqVMHq1evxrJly+Dh4YFu3bph9uzZqFy5srleGgAr+J0kLI4pdUj6/JgZKw5vB2QMcddFfHw8AMA5OwYrZ86RlLxyjqwOJyfRa/76NQ/LlQnB25EprBgRhJEInyG9C0WZmh07oKku1qOH1a18Enlw6ZJmGFzlCQD+bzx3Ti6BoB3mnm1M2isZGbwoXNmywNtvA2Zfh1SpuBEMoHnZG5rNUi++xZEa6FeuyCeHhejRA/D25nUeZC3IqIN169aB8Xa/eT4GDRqkdY63tzeWLFmC2NhYZGRkICYmBgsXLoSnp6fOazg4OGD06NG4cuUK0tLS8OzZM2zZssWsxjnpWoQpyMrKAgA4UXca0/P4MXD4MB9XrmxYtVQLYXGt9urVq3j9+nWu7a9fv9YUc+vQoQMA43KOrBLpyox0xcbCODs7Q6lUIiEhgVbmCKNhjCEhIQFKpVKzmGZxNm8Wx1a48knkgSSM/L3mmWjdGpg+nRuMsiE10CULCPaIiwv/CYqP58Vrzc7du0B2yGfTBuLvvqwGeq1a4tjODfTXr4Hz53mEyvPn/P9PmB/StQhTkJiYCEdHR/kcIfaMUDUT4DqkFaYjWHxZZtu2bVi8eDGaNm2KoKAgeHl5IS4uDnv27MHz58/RrFkzrUqLhuYcWSUhITwM9+FDXiju1Sue9ygDJUuWRFxcHB48eABvb284OztTnkw2jDFNeFJaWhq9LzlgjCEzMxMJCQlITk7O1arEYjx9Chw8yMeBgUCTJvLIQRhOtjcVAPp97o1+1WSURaAIFopTKCz0EySJSCjVMBBvRANXr/KIiaQkIA+np3nx8eEFgeLiuIHOmFUqZ6bgzBkg2wlnbfWP7B7StYoeptIhGWNISUlBYmIi/Pz86HNjDjZtEsdW2qLX4gZ6p06dEB8fj5MnT+Lvv/9GcnIyvL29UbduXfTu3RtDhgzRCucwJufI6nB05EWsli3jMWa//w4MHiyLKEIV+2fPnhWqn6Q9whhDWloaAMDV1ZVuinmgVCpRrlw5+Xp9bt8u9gqy0pVPIg8EA12p5GFl1kCtWvwzxFiRMdAthjRloE4dNH/KDXSVCvj7byC77IzlqV2bG+gvXgCPHvEFdDvk5Elx/O678slRFCFdq+hhSh1SoVDAx8fHuotg2yp37og3xzp1+MMKsbiB3rBhQzQ0MNZfyDlasmSJmaSyAL17cwMd4DGGMhnoADTt5jIzM6GytqaoMpKVlYVj2dV9mzVrRnk/OnB0dJQvrF2Awtttk/R0QCj4WaOG9bTF8/DgiwW3b3OPqkplPbKZkMxMvgZh0TDnHAZ6SBbw/ff86fHjMhvoQnudK1fs1kA/cUIckwfd8pCuVbQwpQ7p7OxMoe3m4uefxXG/fvLJUQBkgViKt98GgoKA6GjeV+jJE6B0aVlFcnZ2lt/YsiKysrI0P6Kurq5koFsjDx6ILZJq1BB7GhPWz82bYuSDJA9YrQauX+f1NKvJFfJeuzY30FNT+T3aWrz7JuTQIaBrV+DNN4GJE4Fu3SxwUcFAd3UFqlTBO67irtOnLXD9vMhZKK5NG/lkMRNqNY9SAICSJQFrbnZj75CuVTQgHdIGYAzYuJGPFQqgTx955ckHKn1sKRQK0dunUgG//CKvPEQuHB0d0apVK7Rq1YpWLq2VX37hN1iAwtttDUn+uWCg//svNx5q1QIWLpRJLok8AHgMth1y+jQPYjh1CsiOwjQYg+6Rqal80QMA3ngDcHREhQpA9ercHm7d2jgZTEIRqOR+4waP4Ad4eDvdKgnCvJAOaQOcOSNG8rVoAVhxFzAy0C2JNBxXGqZLWAUKhQLFihVDsWLFKP/cWrGBwh5EHugw0CtXBhIT+SZpvqzFeeMNcWynBvqpU+L47beNm8Oge+TVq2KV3OwcP4UCuHYN2L+fe/Flo2ZN0WK1UwOd8s8JwrKQDmkD/PSTOLbi8HaADHTLUreuqAieOMFDKQmC0I+bN4GzZ/m4QQMe4k7YDjoMdHd3HnIt7H75Uga5ALs30BkD/vmHj0uVAipWtMBFpYavpAiPVeit7u5ApUp8/N9/4kKCHUH55wRBEBIyM8VW10ol0L27vPIUABnolkShAPr2FZ+TF92qUKvVuHr1Kq5evQq1HSpsNo/Uey79HtkoZ86cQYcOHeDj4wN3d3c0adIE27Zt0/v8devWQaFQ5Pk4cuSI+YQ3BsFAd3XVshCl3j0hZ9biVK8uWo52aKDfvi2GO7/9tvFGskH3SOn7KE0hsBaEMPeUFCAmRl5ZzMC9e/yvszPw1lvyykIQRQHSIa2cvXuBZ8/4uHNnwMor5FMFA0vTty8wbRofb9oETJkirzyEBrVajbt37wIAqlWrBgcHWr+yGhgTDXRpPQcbJTIyEm3btoWrqyt69+4NT09PbN++Hb169cL9+/cxfvx4vefq0qUL6tevn2t7UFCQ6QQuLGlpYj5yzZpaVdLfeQf49ls+PnMG6NBBBvnc3LhH9c4dHoOtVgN29P2Xhrc3aWL8PAbdI69dE8c1a+qYiweRCY5si1O7NrBzJx9fuWKhsALLERkJPHzI0y1toRstQdg6pENaOWvXiuNBg2QTQ1/IQLc0FStyjfTvv7lScPmy1fbgIwir4dw57cIe5crJKk5hyMrKwrBhw+Dg4ICjR49qjOuvv/4ajRs3xtSpU/Hhhx8iMDBQr/m6du2KQdb+Y3PjhhhGnMOb2qiROD5zxoIy5aRWLW6gp6QAsbG864adIK2Ybmz+ucEIBrq7e65CPJ9+ygPIkpN5DYJixSwkk5ScheI6d5ZBCPPi52e3HeQIgiD05+lTYNcuPi5bFmjbVl559ICWd+Tgo4/EsbQfH0EQupF+T6TfHxvk8OHDuHPnDvr27avl+fb29sbUqVORkZGB9evXyyegOdCRfy5QqRLg68vHZ86IRfotjh3noQsedIVCe0HEbKSlAdmeJNSokSsaISsLSEjgDU3OnbOAPLqQfg6ln0+CIAjCvti0if/wAED//ryvq5VDBroc9Oghhnhu3myXBWoIwmSoVGJhDxcXqy/sURBCbnhoaGiufW2zV3WjoqL0nu/ChQtYtGgR5s+fj61bt+L58+d6n5ueno7ExESth1nIx0BXKICGDfn4yRPg/n3ziFAgdmqgp6YCly7xcc2aFkq7u3lT/F3TEd4u9eJLw+8tSrVq4sKBNByfIAiCsC/WrRPH1h5xmA0Z6HJQujQgKOexscDx4/LKQxDWzOHDwKNHfNyhA+DjI6s4heVWdqh+1apVc+0rW7YsPDw8NMfow7fffosJEyZg8uTJ6N27NwICAjB//ny9zp07dy68vb01jwBz9QTNx0AHtL26QqF+i2OnBvrly6LjoDD55wYhff+k72s2UgNdGn5vUZRKMQH++nW7Wijv0gUYORLYulVuSQiCIGTm4kX+AIDGjXX+JlkjZKDLhTRMV9qXjyAIbWyob6U+JCQkAOAh7brw8vLSHJMfFStWxPLly3Hz5k28fv0aDx48wIYNG+Dr64vJkydj+fLlBc4xZcoUJCQkaB73zeW+Fgz0YsV05nYLBrqvr4yt1qRt++zIQG/cmBcL27EDGDHCQhctoEDcG28AHh58LJuBDoiyvX4NPHggoyCm4/Fj4I8/gBUrgJUr5ZaGIAhCZmysOJwAGehy0bUrL54DAL/8wnP2CILQJiUF+O03PvbxATp1klUca6J58+YYOXIkqlatCjc3N5QrVw79+/fHvn374OrqivDwcGQJrtM8UCqV8PLy0nqYHGk+cs2aOqujt27Ni7w/ewZ8/LHpRdALd3exkvfVqzImw5uesmW5V7VxYwtdsAAPuqOjmNbw4AE3KmVBunhgJ2Hu0kKLFqk3QBAEYa2kpQEbN/KxUmlTHYDIQJcLd3cxlzYhAfjzT3nlIeDo6IjmzZujefPmcJS0gSJkZMcObqQDQM+e/AZr4wie87y85ImJiXl61/WhVq1aaNq0KV68eIFr1mB03L6dbz4ywL2plSsb35/bZAjGZFISEBcnryxWiN73SOFz5+KSZx+1Bg3E8fnzJhTSEKRRE9bwXTEB0hQRMtAJwnKQDmmF/PYb8OIFH3/4IVC8uLzyGAAZ6HLSv784pjB32VEoFPD09ISnpycUslsKBADt74X0+2LDCLnnuvLMHz16hOTkZJ356YZQsmRJAECKsLghJ9evi2OpQWSNSL29VNk7F3rdI7OyeJE4gBdiy6Na7ltviWPZKrmTB50gCBNBOqQVsmaNOB42TD45jIAMdDlp2RLw9+fjv/7i8Z0EQXAePgQOHODjoCDg3XdlFcdUNG/eHACwf//+XPv27dundYwxqFQqnM12o+nbS92sSA0fMtAtyqVLwOjRwPr1FqyOf+cOkJnJx3lETABW6EGXLiTZKIyJBnqJEmLGBkEQRJHj5k0gu2sOqlUDQkJkFcdQyECXE0dHoG9fPs7KopKrMqNWq3Hjxg3cuHEDajuq6GuzSFsQ9uunM3fZFmndujUqVaqETZs24aJQWRQ85H3OnDlwcXHBgAEDNNsfPnyI69ev5wqJP6fD7ahSqTB58mTcvn0bLVu2hJ+fn9leh97o6UF//BiYNAlo1Qr4+msLyKULqYFuBwZbZCSwfDmvi7N3b+Hn0+seKc0/z8dAr1ZNLBR3+3bhZTMKHx+eoA/YhQc9NhZ4+pSPGza0gpQRgihCkA5pZUREiOOhQ23uhmgfGq8tIw3b3bBBPjkIqNVq3Lp1C7du3aKbqzUg/T7YQfV2AScnJ0RERECtViMkJATDhw/H+PHjUa9ePdy8eRNz5sxBkKTS+ZQpU1CzZk38/vvvWvM0bNgQ9erVQ//+/TF58mQMHz4cb7zxBhYuXIjy5csjQvrjJCeCoevgAFSpkudhjo7AggXcqDx82EKy5aR6dXF844ZMQpgOqWda6rE2Fr3ukVJDN592Ng4OvMTE7dtin3ZZEBYRnj4Fnj+XUZDCQ/nnBCEfpENaERkZYu9zZ2dg4EBZxTEGMtDlpm5doF49Pv7nH7vw2hBEobl0SdTa335b23CyA1q2bInjx48jODgYW7duxffff48yZcpgy5YtGD9+vF5zjB8/Hp6enjhw4AAWL16MTZs2wc3NDdOmTcO///6LSnkU57IoarV4T6tUKd8ifyVLih3YLlwAVCrzi5cLb2/Ro2oH92IhyMLZGahd20IXLaDFmpTWra2gOKAd5aFLg2qEKvkEQRBFjh07xHCirl2B0qXllMYodFdvISzLwIHAuHF8vH49MHeuvPIQhNysXy+ObXDlUx8aN26MPXv2FHjcunXrsE5YCZawcOFCM0hlYuLieI9pQK/88zffBKKj+Sm3b8u0LlO9OvDoEfDkCW/KbkNVX6WkpIhrDLVrW7ABghDi7uDA49itHamBfv060LSpfLIUEknGDN58UzYxCIIg5GXlSnE8YoR8chQC8qBbA3378vhOgFetlsV1RBBWQmYm8PPPfOziAvTqJa88hPEYWMFdalRcuGAGefRBKqcNh7lfuiSWcJBWTDcrjInvWcWKgKurhS5cCOyo1dqYMcD06fyWGRAgtzQEQRAy8N9/QFQUH1evzgvb2CBkoFsDZcoA7dvzcVycjAmYBGEF7NvHvZcA8P77gK+vvPIQxmOLBrqd5KFLw50tZqDHxXHXPaB3+MPOncDkyTJ2UbSjEPe2bYEZM4AtW2yuHhJBEIRp+P57cfzZZzZ7MyQD3VqQhvFKw3sJoqhRBMLbiwy2aKDbSestqYFuigJxeiFd0NDTQF+wAJg/H9i4EXjxwkxy5Ye/P+Dpycc2bqATBEEUaZKSxALDxYoBko44tgYZ6NZC585iruNvvwGJifLKQxBy8OIF8McffFy6NHcJEbaLgQa6vz9QqhQfX7jAI6Ytjp2EuAsV3B0deS1Si2CEgS717svSD12hEP/nMTFizQSCIAjCtvj5Z26kA7z7j4+PrOIUBjLQrQWlEujTh49TU4Ft2+SVpwji6OiIpk2bomnTpnAUagIQlmXzZt4eAwA++oiXnyZsF8FAL1kSKFGiwMMVCtGL/uwZEB9vRtnyokIFsaKajXrQU1PFWm21apkuFbzAe6QRBrrUuy+LgQ6IYe6MAbduySRE4Th2jP/PqYQNQcgD6ZAywxiwfLn4/NNP5ZPFBJCBbk0MHiyOf/xRPjmKKAqFAj4+PvDx8YHCRnNWbB7p537IEPnkIApPYqJoYevhPReQPczd0VGsPn77NpCVJYMQhSM9HZg4EejQAQgNNd28Bd4jjTDQpf9v2fqhS6vN37wpkxCFY8gQvhhTtqxYHJAgCMtBOqTMHDworkw3bQrUry+rOIWF2qxZE2+9xfvhXLkC/P03994YoNgShE1z6ZLoQmvY0IKNmwmzIDXWDLiPtW/PDYw33wQaNTKDXPpQvTpw+TLvKHDvHlC1qkyCGIePDzBnjgwXFv7nnp5iP/kCqFmTB8pkZspooNt4YcDERL6WBPC+8g7keiEIoqixbJk4HjNGPjlMBN3GrQmFQttruHatfLIUQdRqNe7cuYM7d+5ATS4IyyP9vJP33PYxMP9coHlzXjisTx/e4EIW7KRQnKnJ9x6ZmspzuAFu8OrpQXJxESPMr18H0tJMKLC+SA10G/SgSxc2qP85QcgD6ZAycvMmsHs3H1eoAHTtKqs4poAMdGujXz/AKTuwYcMGmwyvtFXUajWuXbuGa9eu0c3V0mRk8DLOAE+YFeoxELaLkQa6VWDjHlVzke898vZtsaqfnuHtAkIkokrFW9hanCpVxAUFG/x/S1NBbDyqkyBsFtIhZeTbb8XxyJGiHWUGGOO1jM1dxJYMdGujVCle0R0AHj0C9u6VVx6CsAS7dgHPn/Nxt242XXmTyEbqiTTQYJMdG/agC3XOLK4fGpF/LlCvnjiWJczdzY17XQD+uZWlfYDxSA108qATBFGkePUKWLeOj4sVA4YONevlZs0CunThgZ5CTWNzQAa6NSIN7/2//5NPDoKwFFQczv4QDHQnJyAoyKBTGeOp37/9Bty9a3rRCkRaNMzGPKoxMVx8Ly/gyy8teGETGegXL5pGHIMR/uevXgFPn8okhHEI75mjI1CnjqyiEARBWJZVq4CUFD4eMEBsWW0G1q4Fvv6aj9et490zzAUZ6NZIu3aAnx8f//kn96QThL1y/74YKVKhAtCqlbzyEIVHrRbbVVWubHC42bp1QKVKQPfuwM6dphevQLy8eFN2wOY86IKxlpIidouzCIU00Fu1Ar74AujY0cRy6YuN5qFnZIhpAdWr82AAgiCIIkF6OrB0KR8rFPxHxEzs3QsMGyY+/9//gNatzXY5MtCtEicnYNAgPs7K4rnoBGGvrF0rxuN+/DGVILYH4uJ40TBA2xutJ9IC/pcvm0gmQxEMtmfPgBcvZBLCcKQh4lLPtNkRDHSFwuCq9yVLAocOAYsXA23bmkE2fbDRqIkbN3gFfMDC/2+CIAi5+fln0YnZtatR+oY+nD0LfPghr5MCAKNHA+PHm+VSGkgTtlY+/lgcR0TYXE4cQeiFSiWmcTg4AIMHyysPYRqkHkgjfjBr1RJrdv37r4lkMhSp3EI0gA0gNdAtVjCMMdGorVCB5wHaGjbqQZd+P+rWlU8OgiAIi6JWAwsXis/NlNN18yZv/ypE0XfvzheTzd3qngx0a6VyZTHU99Yt4OhReeUhCHNw6BAQG8vH7doBAQHyykOYhkIa6MWKiU7Y//6TqZmFVG4bMtiEEHd3d/4zYhGePAESEvjY1goCCtioBz05GfD15WMy0AmCKDL89Rdw7RofN20KvPOOyS/x8CGP6nr2jD8PCeENhxwdTX6pXJCBbs1IKxFGRMgnRxHB0dERTZo0QZMmTeBoiW8fAaxZI47NXHmTsCBSA8fIkDPB2EhL4x28LI4NGugJCby4HsCLhZk6WyTPe2Qh8s+lMMZLUsgSsFChgpi0byP/bwAYMYIrj3FxQIsWcktDEEUX0iEtCGPAvHniczN4z1++5MZ5dDR/XqcOr4nj6mryS+mEDHRrpls3sRrhr7/yTwthNhQKBUqWLImSJUtCYe7YFYJ73YQKYKVLA506ySsPYToK6UEHtL2BsoS5S/OobSTEXfo+mSO8Pc97pAn+3w8eACVKcDt58uRCCmoMDg7i//z2bZnCNoxDoeA1DW0xs4Ag7AXSIS3I0aPAiRN8XLOmWfTH1FQx5zwwkBeJs2QHYDLQrRlXV6B/fz5OSwN++kleeQjClKxbJ1Y3GjQIcHaWUxrClAgGm4eH2JHCQGQ30CtWFOPYbMSjKluBOBP0vPfz4wV5AZl6oQOi7JmZvF8dQRAEYX3MmiWOp041S3Fhf3++DtC5M7B/v9jYxVKQgW7tjBghjletomJxZkStViM6OhrR0dFQC1XFCfOgVgOrV4vPpb0rCNsmI0OMs65WzehKKrIb6C4u3EgHuAFqA/de6ftkDgM9z3ukNMLAwAruAtIe3nfu8NxqiyNdXLChPHSCIOSHdEgLcfo0cPAgH1eqBPTubbZLlSgB/PGH2YrD54vFDfS4uDgsXboUoaGhqFChAlxcXFC2bFl0794dp0+f1nlOYmIixo0bh8DAQCiVSgQFBeHLL79Esiy/4BbmjTd48QMAuHpVDOkgTI5arcaVK1dw5coVurmam8OHuRYO8EaSVarIKw9hOu7eFdvmFeJXLTAQ8PTkY9kruaek8GoxVo40V1/aqs5U5HmPFAx0pbJQhR4FAx0Qe3tbFBurOxARwWvJjh1rE+LqZOPGjRgxYgQaNmwIpVIJhUKBdevW5Xm8ofqgWq3G8uXLUadOHbi5uaFUqVLo06cP7t69a6ZXRBRVSIe0ELNni+PJk3lrahPAGLBsmUyLwzqwuIG+fPlyfPHFF7h79y5CQ0Mxfvx4NG3aFDt37sS7776LrVu3ah2fkpKC5s2bY8mSJahRowa++OILVK9eHQsXLkSrVq2QlpZm6ZdgeXJ60QnC1pF+jqWfb8L2MUE+MsAj1urU4VHy5cpxx7zFsbE89IMHefDCvn3i4obZUavFlYHKlQtV3lZqoF++XEi5jMHGPOgnTwKRkVypFIro2xrTpk3D6tWrERMTA78C0mGM0QdHjBiB0aNHgzGG0aNHo127dvjtt9/QqFEj3LLQd1rI5CIIopBcvAjs2sXH5csDAwaYZFrGgHHj+GJnaKh1lPyyuIHeuHFjHDlyBLdv30ZERATmzp2LX3/9FZGRkXB0dMSnn36KdCERDcCCBQtw8eJFTJo0Cfv27cO8efOwb98+TJo0CWfOnMGSJUss/RIsz4cfin1UfvkFeP5cXnkIojA8egTs2MHHpUsDXbrIKg5hYkxkoAP8dzghgQcOubgUUi5jsDGPqoMDEBTEFQyLcf++mDxuZHi7gNRAp8KABSMsYigUQK1a8spiLBEREYiOjsbTp0/xySef5HusofpgZGQkIiIiEBISgvPnz2P+/Pn46aefsGPHDrx48QIjR44050sDwG8bb7wBHDhg9ksRhP0THi6OJ04UO28UkmnTgKVL+fjUKb74KTcWN9A/+OADNG/ePNf2Zs2aoWXLlnj58iUuZ//qMMYQEREBDw8PTJ8+Xev46dOnw8PDAxFFof2YqyswcCAfp6cDGzbIKw9BFIa1a8UKyUOGyGR5EWbDBC3WBHx9zVL7RX9szECXBRMuyMjuQS9RQuycYuUGukoFXLnCx1Wr2m4F9/feew+BgYEFHmeMPrgmu43nzJkz4SL5nWnfvj1atGiB/fv3IzY21gSvQjfR0UDz5jzApEsXICrKbJciCPvn7Fmx80+5ciarXTR7NjBnjvg8IgLo2NEkUxcKqyoS55xdxdkpO5/g1q1biI+PR3BwMNzd3bWOdXd3R3BwMO7evYv79+9bXFaLIw0D/uEHmyhYRBC5UKmoOJy9IzXYCulRlR0b86jKggkKxAmULAmULcvHly/L9DMnLDLExvI+O1bK7du8uQugXVDRXjFGHzxy5IhmX07atm0LAIgyo9Vcrhzwzjt8nJrKO0FZg2eOIGySsDBx/NVXJmlI/r//ce+5wHffcb+RNWA1BnpsbCwOHjwIPz8/1MleRhfyg6rm8aMvbM8vjyg9PR2JiYlaD5ukenWgZUs+vnkTOHRIXnkIwhj27uVuBQBo145X4CTsC8FAL13ask1DzUFAgBhCZ+Ue9HnzeMTfTz+JEecWwYQedEA0Np8/59kwFkeqbwiFLK0QaQpAUTHQAf31wZSUFDx8+BAVK1aEo466CJbQH52dgS1bRG9ccjL/2Tt1yqBpCII4dQr46y8+rlDBJFb0kiX8N1NgwQLg888LPa3JsAoDPTMzE/3790d6ejrmz5+vuZkmZFc98fb21nmel5eX1nG6mDt3Lry9vTWPgEJUmJWdzz4TxytXyicHQRiL9HNrTXdCwjQkJopWlYn6kixcCLRvz9coLe5RdXAQDbbbt3kEiJWyYQP3Bnz8sYXTAkzoQQfEMHdXV3Etz6LYSNSE1ECXpgbYK4bqg9aiP7q4AL/+CrRpw58nJQFt2wL//GPwVARRdJG6uadNK3Tu+bff8qJwAnPmAF9+WagpTY7sBrparcagQYNw9OhRDBs2DP379zfp/FOmTEFCQoLmYdPh8F26AEKV0507gQcP5JXHznBwcECjRo3QqFEjOMia+Gqn3L0L7NnDx4GB3Ooi7Atpny8ThbcfPcoDL27eBGJiTDKlYQivIzNTJgEKJj1ddGTXrMk9d+ZA5z1SuLC7u/j7VAhGjeJlDJKTxfBgi2IjBrqQfw4UDQNdDkylP7q6cpWtVSv+PDGRG+x5dBYmbBTSIc3EgQNi1HClSsCgQYWa7o8/gDFjxOczZgBTphRqSrMg6ydIrVZjyJAh2LRpE/r164cffvhBa7+w8pnXCqcQbpTXCikAKJVKeHl5aT1sFmdnYPhwPlartXN5iULj4OCAMmXKoEyZMnRzNQerVoku0E8+KVQ7JsJKMYOBLu3nLTVKLIY0EsBKDbZr10TnvjmNtVz3yMxM3tcN4P9vhaLQ1wgM5G+5bLcHGzHQhSJ6xYoBFSvKK4slMFQftDb90c2Nd6UQMhUTE3m3hb//NnpKwsogHdIMqNXApEni81mzCr0C3a4d8P77fBwWBuSoOWk1mKa7uxGo1WoMHjwYGzZsQJ8+fbBu3bpcH+iCcoQKykmyS4YN4x9QlQpYs4aHelAVbMLaSUsD/u//+NjFxXqqcBCmxcThzoC2wXnlCi+0ZFFyVnLPLi5lTUgrnhdkoGdmZkJlqlD96GjeixYA3n5brFpmywQG8gfAe/xZ4Wt6/ZqrAIGB/P+dkWHe6zk6OmqK+MqFofqgu7s7/Pz8cO/ePahUqlx56HLoj8WKcSO9c2fevz4xETh2TKZIEYKwBbZtAy5c4OM33wR69Sr0lC4uvGP1b78BvXsXejqzIYuBLjXOe/XqhZ9++inPIh7+/v44ceIEUlJStCp3pqSk4MSJE6hYsaJt55UbSrlyQNeuwPbtPNfT2j9hNoRarUZcXBwAoFy5crQCakq2buVVnwCgRw9eQIywP6TKc5UqJplSdg+6VIG30kJx+hjoiYmJePbsGdILUUGOMaYx7h0dHaFIS+NdRQDA21v0pts6q1dzz42jo1W+Jsa4gpmRYTkRlUolSpYsKVsUojH6YPPmzbFlyxacOHECISEhWvPt27cPAHJtNzfu7sCff3IPXrNm2kWqCNuGdEgTk5HBq7ULzJtndIGVFy9421YBFxfrN50sbqALYe0bNmxAjx49sHHjRp3GOQAoFAoMHToUM2bMwMyZMzFv3jzNvpkzZyI5ORlTp061lOjWw+efcwMdAJYvt/5PmY2gVqtx6dIlAICfnx/dXE0FY/xzKkDF4ewXMxjo1asDTk5AVpZMvbGlBro0hN+KKMhAT0xMRFxcHDw8PFCyZEk4OztDYUQ4OmMMSUlJAABPT08onj/nhizAF4+FHuKFJCWF56CnpfG2a4WsB2Q4jHE3NcArBhfhdBzGGDIzM5GQkKAxPuQw0o3RB4cPH44tW7Zg+vTpOHDggKYX+p49e3DkyBGEhobq1YPd1BQrxsuxyByUQJgY0iFNzMqVvHYRALRuLVZaNADGeKDxhg28no0tpQNZ3ECfMWMG1q9fDw8PD1SrVg2zZs3KdUzXrl1Rv359AMDEiROxc+dOzJ8/HxcuXECDBg1w/vx57N+/H40aNcLYsWMt+wKsgRYtuFvpyhXeVPP8eaBBA7mlIgjdnDoFnDvHx2+9BTRpIq88hPkQDHQ/P8DDwyRTurjwKPOrV4Hr13nas0UV2zJl+GtJTrbanGTBQPf2FiPOpTx79gweHh4oX768UYa5AGNM44F3dXWFQhoq7+lpkr60APd2PH3Kx6VKmWxa/XFzEw10hUIGAawLNzc3eHp64sGDB3j27JlJDfSIiAgcP34cAHA5+4McERGBI0eOAACaNm2KoUOHAjBcH2zZsiWGDh2KiIgINGjQAB07dsTDhw+xdetW+Pr6Yrl04djC6LqH/fUXX5T64APLy0MQVsWzZ8A33/CxQgHMn29wjRO1GvjiC16xHeBFGq9c4VEstoDFDfTo7L4pycnJmD17ts5jgoKCNAa6u7s7oqKiEB4eju3btyMyMhJ+fn4YP348wsLC4ObmZiHJrQiFAhg5khfaArh3cu1aeWUiiLyQKkGjRpmkkBRhhSQkiFaVifM669ThBnpGBndi16xp0unzR6Hg0QAXL/Kca4uvEOTPy5dAtmMTderk/nplZmYiPT0dJUuWLJRxrhNpuLwJ3dzSn/XUVJNNqz9Sgzwtjbs8izgKhQLe3t6Ii4tDZmamyXLSjx8/jvXr12ttO3HiBE6cOKF5LhjoxuiDq1atQp06dbB69WosW7YMHh4e6NatG2bPno3KlSub5DWYgiNHgO7d+T1u7VpgwAC5JSIIGQkPB1694uOBA7lzxwBUKl5T+8cfxW0TJtiOcQ7IUMV93bp1YIzl+xiUo4S+t7c3lixZgtjYWGRkZCAmJgYLFy6Ep6enpcW3Hvr1A3x8+HjzZlExJghrIj6eJ0sCQMmSJinwQVgpZigQJ2A1eegqlUzNufPmv//Esa7wdiFn3CxFvoQCao6OPA/BRMhuoEsXGwqRs28uXr3ib73QFMNSCJ8hkxUZRME64bp167SON1QfdHBwwOjRo3HlyhWkpaXh2bNn2LJli1UZ5wD/mUxL416/gQO117UJokhx9apY28TdHcjDmZsX6elc1RSMcwcHYN0628uupAQJW8XdHfj4Yz5OTwciIuSVhyB0sWoVTx4G+HJmEQ8VtWvM0GJNQGqgy56HbmVh7qVKAePH8+Ly+VWDNrn3XK0Wy4e7upo0MkapFKeTpYh6Tg+6FZGVxb9qV65Y/qNo8s8QoWH5ch4YKTB6NG8BZelFGIKQFcZ4XLqwCDh5MuDvr/fpycm804tQpsvZmdcoHjjQDLKaGTLQbZnPPxe1mBUreOglQVgL0grPjo5iSgZhn5jRg96wITdC162TKfRTWvDOygz06tWBhQuBvXuB/v0teGFpby8TV3FTKEQvuuBVtChW7EGXRhTQeqf94ODAc2WnTRO3zZjBjXYTBiwQhHWzfTuwfz8fV6jAf/j15OlTnmd+8CB/XqwY75jw4YdmkNMCkIFuy1SsyHt1ADwJ8ddf5ZWHIKRs2QI8ecLH3bsDRakdYlHEjAZ6+fLcCB040GTF4Q3DBiq5Wxwz5Z8LSMPcLe7EdnQU6wxYmQedDHT7RaEAZs4EliwRt61cyRv1WNnHkCBMT3Iy954LLFmi/UNQwKlNmwJnzvDnPj7cUA8NNb2YloIMdFtHWrV0yRKKhyoEDg4OaNCgARo0aEDtMQoLY8DSpeLzothtoaghNdCtLL+z0FhxiLulKVasGIoVK6ZtMZjBUrSaPPSsLDFNxwqQvhdFsUZuUWDsWN4WSuju9+uvQPv2Ys0swjohHbKQzJwJPHjAx+3aAd266X2qhwfQpw8flysHHDuWf8qXLUCfIFuneXMgu+I9zpzhLa0Io3BwcIC/vz/8/f3p5lpYjhwBsvuB4u23bf9OSRSMYLiWK2d/Va9LlxbbxlmRgZ6aCty/b7l1WYVCARcXF7i4uEBhZg+61OY3hYGemZmJ8PBwVK1aFUqlEgqFAjt27ADA28e99dZbCJW6W6QC6BHmfuPGDTg5OWHlypWFFzYfyEAvGvTvD+zaJd5KT57ktbMI64V0yELw33/A4sV87OLCizIYWPMiLIzb+CdPatetsVXoE2TrKBS5vegEITfkPS9avHwJPH/OxyYObxdgDIiNBXbvlqFQnEIhvq7oaO38axn5+2+epufjI8Ot38Y86IsWLcI333wDf39/TJgwAWFhYahRowYAYMOGDTh//jxmzJghnmBgHnr16tXRp08ffPPNN0hKSiq8wDpgTHwvXFxMWjifsELatwciI/n64Pr1wLvvyi0RQZgBlQoYOlSMVJo0Sa9ctjt3tJ8rFLyGQ4UKZpBRBshAtwd69+Z3cIAXWIiJkVceG0WtViM+Ph7x8fFQW7wqkR1x+zZf+gd48nD37vLKQ5gfM+afCxw8CAQG8gqtGzaY5RL5I7wutdpqWq0JLecSEwFLdB1ljCEjIwMZGRlgwiKFo6MYi2tCXFwAb2/+01aiROHn+/PPP+Hh4YEDBw5g9uzZCA8PR40aNaBWqxEeHo5mzZqhSZMm4glGVHKfOHEinjx5gm+//bbwAusgM1MsGEb550WDxo357bV3b7klIQqCdEgj+f57Mfq3WjVg6tR8D2eMG+I1awKHD1tAPpkgA90eUCqBzz7jY7UaWLZMXnlsFLVajfPnz+P8+fN0cy0M0loII0eKxZYI+8WMLdYE3nhDHMvSC90KK7lLe6BbKqTv9evXeP36tdlarAkIQQsVKgC+voWfLz4+HiVKlICLi4vW9j179iA6OhoDcrYHMKKSe506dVC3bl2sWbPGLL8hFN5eNPHyyr3t66958x7CeiAd0ghiY4EpU8Tnq1fnu/qYlgZ89BFvjZ6ZCXzwAfDwoQXklAEy0O2Fzz4TP9Rr1lA1EUIenj0D1q7lYw8PYMQIeeUhLIMFPOj+/tyjCmgbphbDCiu5SxcqpAsYFsUM+eemJDw8HAqFAvfu3UNMTAwUCgUUCgWCgoIAAGvXroVCoUD3HJE+J86ehVOTJqjfty/Sc4SsnzhxAk5OTqhfvz7ScxjvPXv2RExMDCIjI03+WqSOfDLQiy5r1/Jc25EjgVGjrKqGIUHoD2O8/W5yMn8+fDivq5UHjx4BLVoAmzfz5woFb0Xo52d+UeWADHR7oVQpYNAgPk5O5qtQBGFpvv9edPMMHcqTYwn7xwIedIUCqFWLj+/f52HdFsXKKrkzJhroFSro9rJZBCs30Fu0aIGwsDB4e3vD29sbYWFhCAsLw9ixY8EYQ2RkJKpXr47ixYtrnRccEoJpQ4fi0q1bmDR/vmb7q1ev8NFHH0GpVGLz5s1Q5nj972QXxDx06JDJX4tazftlA2SgF2Xu3RPH330HdOxIPhnCBvm//wP27OFjPz9Acp/NyaVLvN7w6dP8ebFiwI4dwOjR5hdTLqjEiD3xxRfAqlVcc1u2jBfnyhHORxBmIy2NV94EeE7qmDHyykNYDqmBXqmS2S5Tqxav0ArwisbSlGGzIw1xtwIPelycuEhRqPD2hg25a0JPvIT0FcFt5+goWo1mgAFgZcoi48RZo/KuW7RogRYtWmDdunUAuEdd4OrVq3jx4gXat2+v89zpo0bh4KlT+HbzZrTt0wftO3XCiBEjEBMTg1WrVqFmzZq5zmnYsCEA7mU3NX5+QNmyPLSTCsQVXWbMAIKCuPMxMxPYv58bL3/8AVSvLrd0BKEH9+5p9zxfsyZPh8727cCAAcDr1/x5+fK8zJHQwMpeoVu8PVGtGvD++8DOnUB8PLBlC/9UE4Ql+Okn4OlTPv7wQ65BEEUDwaNcvrxZXXtSQ/TKFQsb6KVL80psSUlW4UGXhrcLkQVG8egRt/b1QJH9sCQKcCMkNpb/xJmSB9k9d8uUKaNzv6O7O36eORP1P/oIg4YMwdgvvsC2bdvwwQcfYPjw4TrP8fLygqurq2ZuU6NQ0Lo7AQwZwtcMu3fnmWU3b/KCcps3Ax06yC0dQeSDWg0MHiyGtn/8MQ8D0XHYN9/wBSmBxo2559xew9qlkIFub0yYwA10APjf/3gzTTMU8CEILVQqYOFC8fmECfLJQlgWaYs1PVqjFAapIWrxPHShatn582KrNRktJZMViCtbVu9DGXgldwBQZGVxY92MRSAZuHGeWaKsSVqt5eR59ufWJ69UHKUSgX5++GHyZPT+6itMnToV5cuXx5o1a/Kd19fXF8+ePTOxtAShTUgI8M8/QJcuvPVkYiLvcjFrFjB5slkDWwjCeBYtAqKi+DgwUOx/noPYWO1d/fsXWEPOriAD3d4IDuZupVOnuIvlr790rkwRhEnZsYMv4QO8ikd2mCdRBJA2IzVT/rmArAY6wBcgzp8XW62Z2qVrACbzoJ89q/+xjCExIQEA4H3nDrcA6tc32yKwAsDd69mOlkweVW/K0G637GiPtLzaqGXnl7du3Bhenp5ITEpC37594VtAWfnU1FQUK1bMdIISRB5UrMjTfgYN4qHAjAFffcUzzqSeR4KwCs6cEduoKRS84mEeBVSCgoD164GePXl6+rhxRcvfSOtr9oZCwZdOBfIpukBo4+DggHr16qFevXpwoKVn/WFM+3Mm/fwR9o803NvMHvQyZcSWW0W9krvwtisUvB+spSjm5oZijx/z771SaXaNSZoxoWc7cr0pVaoUAODFixe6D8h21QyZMQOJSUkoUaIEli5diosXL+Y5p1qtRkJCgmZuU/H0KV8DvX/f9O8DYdt4eADbtvHK7goFv09+8oncUhU9SIcsgMREoE8fsX7J5MlAy5Zah+TsTvfBB8CNG8D48UXLOAfIQLdPOncWNbZjxwAzFKuxRxwcHBAQEICAgAC6uRpCZCRfFQW4Ny00VFZxCAsjNVTNbKArFDyc282N56BZ3FCxokJxUVHcSN+zh1e0tQQKhQIuajVckpJ4eLsFYg2lBrqpw9xr1aoFBwcH3LhxQ/cBSiVWbNuGXceOoV/nzti/fz8AoE+fPrwXvA5u3boFtVqNOnXqmFTW5GSu3z5+zDOKCEKKgwMwbRqwezfw66+8LSVhWUiHzAehpZoQcdekCU8wzyY9nbcN1FXao3JlC8loZdAnyB5xcAAmThSfkxedMCfz5onjSZOK3jJnUccCLdak/P47N1bOnpUhF01qoMtcKM7RkYvTtq2FLyzt+22BFmvS/7GpDXQfHx/UrVsXZ8+ehTqn6wbAlWvXMOHbb1GpXDmsnDwZDRo0wOzZs3H9+nWMHTtW55yns/sANc+nn68xSF87tVgj8qJ9e6BpU+1tz59zlTCPNSWCMD8rV4oNzL28gE2bNPVL7t7l2bkrVvDOaz/+KKOcVgQZ6PZK3768ojLA+xFIExYJnajVajx+/BiPHz/WqawROjh/HjhwgI8rVuTV24mihYVarAn4+spY/MiKPOhywBhDZmYmMosVAwMsYqCb04MOAN26dUNSUhJOnTqltT0tLQ19+vRBlkqFTbNmwdPFBVCpMH78eLRp0wZr1qzB9u3bc8134MABODk5oVOnTiaTkTExWkSppOJfhP4wxgtm/+9/vAL21atyS2S/kA6ZB6dOabdU+/FHri+CR3u8+SZw7hzfZYGsKZuBbvP2iosLT9oQmDtXPllsBLVajTNnzuDMmTN0c9WX2bPF8YQJ1Jy3KCJ4kv39AXd3eWUxN2XK8IRPoEga6ACQ4uyMFH9/rkVZIITB2Vm8rZgjpWHo0KFwcnLCxo0btbZPmDABV65cQfiYMXhbKJOfng6FQoH169ejZMmSGDZsGO7fv6855/Xr19ixYwc6deoEfxPGGGdkiLmZ5D0nDOHaNeDQIT7+7z9ev3X1am64E6aFdEgdPH7MHTeZmfz5hAlA9+54/ZqHs/fowVN3AB6Ad+oUX1AiyEC3b4YNA0qW5OMtW4qsQkmYif/+A377jY/LluWNWYmiRUICr14FmD3/3CpQKMTXGR0tKh0WZtkyXgj355/N41XWGwt40AHRKM3MFOsLGUp0dDSio6Nzbff390fv3r2xZcsWJCUlabZ/9913YIzhK+lCd/YKgZ+fH54+fYoXL14gICBAs3vTpk1ITk7GF1JvkQmg8HbCWN54g6cDCSURUlOBESO4zZRXbUSCMAlpaUC3bkBcHH8eEgLMnYsLF/hCkbRbZe/e3Itev74sklolZKDbM+7uvC8BwJffpbnCBFFYpFEZX35ZdJpTEiIWbLEmZf58XguzcWOLXVJEMNCzsoCYGBkEADZs4F+/AQNkDAd0dLRYxIxglCoU2inwpmLWrFlITU3F8uXLc++ULkLkc/GsrCzMmTMH77//PkJCQkwqn9RAp9ssYSg1awKnTwOffipu++03brQLGWoEYVIY4y7yv//mz8uXh3rzVixY7IS33+aRHQAvcPrjjzwl3dNTPnGtETLQ7Z3PPgO8vfl4/XogNlZeeQj74PZtseBHiRJ8SZ4wmDNnzqBDhw7w8fGBu7s7mjRpgm3bthk0R3p6OmbMmIGqVavC1dUV/v7+GD58OJ48eWImqSVYsMWalH37gD//5M0DBAe+xZA5D12tFpWbypUtbLBJwzYtmCxYpgzv9f7mm+bJoggMDMT69evhqUtDlL7B+RjosbGxGDBgABYvXmxy+ciDThQWNzdep+v338VWlfHxvOnKmDFUQI4wMfPnAz/9xMdubsDOnVD4lcWxY2LgWf363Gs+eDDlneuCDHR7x9sbGD2aj7OygAUL5JWHsA/mzxeV9S++sP/cYzMQGRmJ4OBgHD9+HD179sQnn3yCR48eoVevXli0aJFec6jVanTp0gVhYWEoWbIkxo4di3feeQcRERF455138NTc1qsFW6xJqVVLHFu86JHMvdDv3RMNNun7YBEyMsSxhcLbhUu5uZm3OFrPnj0xatQo3RcXyCcJvlKlSggPD0dlM/QEkl6WPOhEYejaFfj3X6BNG3Hbt98C2R0ECaLwbNwITJkiPv/pJ6BBAygUvEp72bK8q8Dp00CNGvKJae2QgV4UGDNGNKDWrBHzQQjCGKKjgXXr+NjLC/j8czmlsUmysrIwbNgwODg44OjRo1i9ejUWLVqES5cuoVq1apg6dSpi9AifXr9+Pfbt24c+ffrg5MmTmDdvHrZv346VK1fi7t27mDZtmnlfiIVbrAlIDdP//rPYZTkye9Clr9fiBrqFW6xZBY6OmnZAZomvLwDGxAUZV1eq4E4UnnLlgL17eS0LV1deqKtrV7mlIuyCAwc0Vd5iUAFRH28AunfX7C5dGrhxg/t4XFzkEtI2oFt9UaBECWDkSD7OyKBcdKJwzJkjVmoaOxbw8ZFTGpvk8OHDuHPnDvr27Yv6kqoo3t7emDp1KjIyMrB+/foC51mTXWVl7ty5UEhixEaMGIFKlSrh559/RqoRVcSysrJ0PlQqlfZxMTHIUir5Iygo/2PzmFPXsSqVKt9jpYbptWv5H6vvvFk5qo/leWzFisgSjNNsA90k82Y/mKS8sq5jr17NglLJH7Vq5X+sdE7pvMLz/B46j5UYqEypNN281n6sUgkGgGVlgalUFpchMJB7nUqUsPD7oFKBpaSA5fgMG/JdJqwTBwceXHnxIg99l8IYdeYljODsWeCDD6DOUmElPkVt5xvouasfnj3TPszLSx7xbA3qiVRUGD8e+O47ICWF99iYPJkvoxIaHBwcUDu7nY4DuSl0Ex0NrF3Lx15e3EAnDObIkSMAgNDQ0Fz72rZtCwCIiorKd460tDScPn0a1atXR2BgoNY+hUKBNm3aYNWqVTh79iyaNWumc4709HSkS4yuxOx+JwcPHkSxYsVyHV+6dGk0llRmO/D551AJhSiPHdM61tfXF++++67m+eHDh5EhDZGW4O3trSXjkSNH8lxY8PDwQN26LTTP33rrGPbuTdZ5rJubG1q3bq15fvLkSSQkJOg81sXFRev/cfr0abzIo8yx48aNaN+jhyYH/9y5c/nm/Et7Yl+8eBEPHz7M89h27drBKbv42uXLl/HgwQOt/bVr896xAFCuXBsAfLHg6tWrOqMuHB0dUaZMGa22P2lpaVr/95x4enrC0dERAP+MpEmbcGeT6OQEJCTAw8NDI6/WsTpwd3eHc7Y3OiMjI9/FI+mxmZmZeJ1PkmyxYsXgku2OMeTYrKwspKSk5Hmsm5sblEoloFQiS6VCSrlygKTSuxRXV1e4Zsefq1QqJCfr/kzmPFatVmtVj8+JUqlEyZJu2fOqkZCQ97EuLi6a7y1jTPN9LuhYAHl+LwDA+eVLuAOarjDHjh3L0xDXdd8grJfq1XNv+/VXoGdPXuNr/nxag9eXIq1D/vsvEBqKq8kBGIY1OIlgIBNIfgJ88w2gq/4mkT9F7BNUhClVSgxFJi+6ThwcHBAUFISgoKCid3PVl5ze8+LFZRXHVrmVbdhV1REWXrZsWXh4eGiOyYs7d+5ArVbrnEM6d37zzJ07F97e3pqHtGVUgSQlydZM19eXexQBWaKOxTjje/eM7/tlAopCZzuroKiE8+eHEOZP2DXPn4uq4urVvAL81q3UN10fiqwOef06Ult3wrSX41AfF7lxns3QocCsWTLKZsMoGCtaX7vExER4e3sjISEBXkUtzuLpUyAoiJfrdHHhLZLKl5dbKsJWuHcPqFaNGyReXtybXgQNdFPcQ0JDQ3HgwAHcunULVXRYWeXKlUNycnK+Xq2TJ08iODgYH330ETZu3Jhr/5o1azB8+HAsXrw4z77MujzoAQEBeP78uc7XplAoNJ5VvHiBrLlz+X2kTh1g+vS8jwVyhXrnd6wqO4w4v2Pfew84dAhQKlW4d4+hVKnCzQtA4wku8NiPPoKTUG3/7l2oKlQwzbzgHm8hXSHnsSoVr2ielsa/ipcu5X2sQFpaGmJjY1GxYkW4ZZcA1+dnX5hX69j//uMrIo6OQN26mtK7Oo81ZF49jn32TGxCEhCAXP9vs8rw4gXY3bv89ZYrx/8JppjX2o+NjwcePeLHVqmCNKUS9+7dQ0BAgCYCICdJSUnw9fW1Sx2rKOiPKhUPeZ86FZAGgbz3HrBiBb/vEISGK1ewu9k8jHo1A/dQSbO5alW+wNOihXyiWSv63kcoxL0oUaoUz0VfsIB70WfPBr7/Xm6prAbGGJ4/fw4AKFGihFZOLwFg5kzRWzhmTJE0zu0NpVLJQ3hz4OTkpGVU6sTXF07/+5/e1ypwPglSozovatXiBnp6uiOuXwf8/Ewzr17HBgWJ49u34VixomnmLeDYe/cAYc2malXt1jR5zevk5ASFQqF1PzPk3qY5Vq0GS09HlqsroFTCKcecRs+r57GurqIXLzU177Y8ZpFBqYQC4AKkpRXYE8iUMiQl8fV0Fxfzvr86SUsT33TJfSK/+4Mhn2/C+nB0BEaN4kXjRo4E/viDbz94kKfXjBsHfPUV9azWRVHTIeP3X8aITvH4M1N0EDg7M3z5pQLTplFLyMJShGIwCADAl18CHh58HBHBNT4CAPdAnTp1CqdOnaJCNzm5cQMQipb5+PBfaTtArZYnRNrb2xtA3nmfwgprYeeQHmdvWE0l9wJSEUyJszMv7NSqFRAcXPDxJiW7fkBKuXJIyc5FtiRSZc+IuoeFQ7qIZcEbBmPAzZvA5cvAtWsWu6yI9LVSyeUiRUAAsHMnfwglTjIzeU56jRq8kxahTZHSIY8fh2uP9/F35luaTS2aZuLSJQVmzybj3BSQgV7UKFmS960GuDf0m2/klYewDcLDxb7nX35pF1VjDh0CGjeWJz8qv/zwR48eITk5Oc/ccoFKlSrBwcEhzxzz/PLc7YF33+VlENasAdq1s/DFZTLQg4J4a6RDh2RYI5Ml2V/EyUlMg5Y6di12ccFjnE8RPFOTnq7TgW0ZhGgB4eJFKaeW0PD++8DVq9xrLqzRxMcDhw/LKxchI7/9Brz3HnwTozEHU+Hv8hSbIl7j8FFn1Kwpt3D2A91xiyLjxokG1k8/AdevyyoOYeX8+y+wZQsflyrFXXg2zvTpPKfu3Dlg8WIgn6LaZqF58+YAgP379+fat2/fPq1j8sLNzQ2NGzfGjRs3clXvZozhwIEDcHd3R8OGDU0ktXVRuzawZAkvQmPxYmnSRY87dyx8cZmQ2UAHRK9MVpYMtfkECzkzkyfqWgBppIDFPVJZWeKiLBXJK9IUK8YXsq9e5Qa7uzsV/ipKMAb8+SfQqBFD3Iz/Az78UPN78HGb+7gR44Y+HxcrKPOHMBAy0IsiPj7AxIl8rFYDX38tqziElSMt/jVlipgiYcN07SqOq1bl9RMtSevWrVGpUiVs2rQJFy9e1GxPSEjAnDlz4OLiggEDBmi2P3z4ENevX88Vzj58+HAAwJQpU7QKPa1atQp3797FRx99pCkMRpgQf39AKJJlQQ+6rFjQc5wX5ghzj46OhkKhwKBBg7S279+/H8HBwShevDgUCgW6jhkj7szIwNKlS+Hi4oLo6Gijr92sWTO8/fbbee6XvsY8arLlIjw8HAqFQtPK0WikCzL6XpywaypX5iHvV6/yW6CUlSuBIUMAHZ0eCRvm2DGgWTOgc2fg7FkFvg6DGNYzYAAc/9wJj7K2rxNaI2SgF1VGjQJKl+bjX34Bzp6VVx7COjlxQqwS4+8PfPKJvPIYwcuXwJUr2tveeguYMAHYsAE4f54XpLYkTk5OiIiIgFqtRkhICIYPH47x48ejXr16uHnzJubMmYMgSSGyKVOmoGbNmvj999+15hk4cCDatm2LzZs3491338XkyZPx4Ycf4rPPPkPFihUxi9wc5sHBgWurAHD3rkU8qioVj/SQre+KFXjQpXaiOfPQo6Oj0aVLF9y9exeDBw9GWFgYenfrptn/8tEjzJw5E0OGDNH6nhpKeHg4/vnnH2wRIpRyILzGq1fPokQJBb777jujr2Uw0gUZ8qATEipU0H6emAiEhQFr1/IF71GjgLg4eWQjTMPp0zx1LCSEq4ECN1ENmXDiZf7XraPaFGaEDPSiiocHMG2a+HzyZPlkIawTxrQ/F+HhNlX5Iy0NWLiQ21G9euUOif3f/4D+/eVLrWzZsiWOHz+O4OBgbN26Fd9//z3KlCmDLVu2YPz48XrN4eDggJ07dyI8PBxPnz7FkiVLcOLECXz88cf4+++/UUpX7zE7gjGuCO7fL4PnRghzz8gAHjww++Vu3eJrZCVKcGXY4liBgS69/ZjToX/w4EGkpaVh0aJFWLx4McLDw9G7Z0/N/iXLl+PFixf48ssvC3Wd1q1bo0GDBggLC8ujRR7/e/ToTgBAly5dCnU9g5D+v8lAJ/Lh4kWe+QHwv999x393R42yyK2RMCEnTwIdOgBNmgDZ2XYAgBq4hl/RHUeVoXDeuI53gaKYdrNCBnpRZsQIQGgPdOgQcOCAvPIQ1sXu3cDx43xcvToweLC88uiJSsU949Wr83p2L1/ykDyhCL010bhxY+zZswcJCQl4/fo1Tp8+jV69euU6bt26dWCM5QrDBXirtLCwMNy+fRvp6el4+PAh1qxZgzJ59Gq2J9avB8qXB9q2BXbssPDFLVwoTogCefmSt0KyKIxZjYHu4cFLYZizDXV8fDwAwF8ax5vtvs/KykLEzz8jODgYlYUoikLQr18/3Lx5E4dzVN1Sq7UN9AYNGiAgIKDQ19Mb6QoIhbgT+RASwhsCTZnC89UBfrv47jugUiVeJ+TmTXllJPLn8WOxO8iePeL2QETjRwzGZdRB93KnoTh2FPjoI/kELUKQgV6UcXHRrvQxebJYFKYI4uDggJo1a6JmzZpwKOoVa1Uqbe/5nDliFWMrhTFg716gQQNg4EAgNpZvVyiAQYOA0FBZxSPMgLRirKyt1m7fNvvlpK9P2mLOImRkaGLrXVNS4CqTweboyFs8BQYCxYsbdq5KpcL8+fNRpUoVuLq6okqVKpg7dy7Ukt88IR89LDtEoWXLlpoe8kdOnQIA7P37bzx88gQ9evTQmj89PR3169eHk5MTTkhjQgvYJ8yzbt26HOcIESL3cOvW5Vze8/v376NPnz7w9fWFh4cHmjdvjqNHj+Z63YwxdOjQAQqFAlu3bs21r3379jr3UYs1whCKF+dqQnQ0L3Hk7s63Z2YC//d//Hs7dKisIpodW9YhS5Tg/zuBCs4PsRrDcBPVMBjr4NSuDQ+VaNRILhGLHLb1CSJMT+/eQP36fHz+vFituwji4OCAypUro3LlyjZ3czU5GzaIFsHbbwOS/Etr5Px5oE0boH17XnReoH17/puydi3v60rYF2+8IY5z1hkwO9JK7vZuoGd7UxWMwZUxuLq6QmFj4Y3Dhw/H5MmToVar8fnnn6Nt27ZYvHgxxkiKv/n4+CAsLEzTQWHgwIEICwtDWFgYgipXBpyccOjMGQBAkyZNtOZXKpXYvHkzXFxc8NFHH2kVdJw4cSIuXbqE6dOnIzhHA/vy5csjICAAhw4d0tou5J9HRe0AoB3e/vDhQ7zzzjvYsmULGjdujNGjR8PX1xdt2rTBqeyFBAGFQoG1a9eidOnSGDFihFbHh6VLl2Lv3r0YNGiQduSONGKCWqwRBlCqFO+Vfu8eb83m7c23MwaULSuvbObGVnTI58+BTZu0tzk5AeNHZ6Kq7zP86DgMtzIDMQwRcHFiwNy5PKKyZEl5BC6qsCJGQkICA8ASEhLkFsV62LePMX7/ZCwwkLHUVLklIuQkOZkxPz/xM3HkiNwS5cuyZaKowqNhQ8YOHzbP9ez5HmKLr61CBf4/9/JiTK224IVjYsQP3Pvvm/1yb7zBL+Xiwlhmpv7npaamsqtXr7LUfO7rixYxVq5cPg+/LFaudDrr3OwlY0+eaJ3buXMB52Y/Fi3SvmZionHnGUNkZCQDwOrVq8eSk5M12x88eMBKlizJALCBAwdqtoeFhTEALDIyUnuiq1dZozfeYA4ODizt9Wud1/rhhx8YANarVy/GGGO7d+9mAFjTpk1ZVlaWznO6devGALC7d+9qtj15wti5c4w1aNCcVagQpHX8wIEDGQA2a9Ysre2rVq1iAHTKvmfPHqZQKNi7777LsrKy2IULF5iLiwurWrUqS0pK0hYoI4OxM2f448YNzWZ9Pku2eA/RF3t+bebi1SvG5s1jrGJFxh4+1N4XHc3YtGmMxcbKI1tRQq1m7PRpxgYOZEyp5L8l//0nOWD/fpZe5Q2WBQfxd612bcbOn5dLZLtF3/uILEs8GzduxIgRI9CwYUMolUooFIpc4V1SEhMTMW7cOAQGBkKpVCIoKAhffvklkpOTLSe0PRMaypM4AV5p6dtv5ZVHJhhjePXqFV69eqWzYE+RYdEisTF4ly5AAf245SY0VMzJrViRB4GcPg20bCmvXIRlqF2b/01MtHBBovLlxeJZZvagZ2SIOZzVq5s+2yQxkRfby/Px0BFxT1zw9JUTspRKZGVlae6RT58WcG72IzFR+5pCgT9DzxPIzOTviz5s2LABAPD111/DXYi9BVCuXDktD3qBKJV48OQJfDw9kVfZtBEjRqBbt27YunUr5s2bh0GDBsHHxwc///wzHPMoHiDUi3gg+QCXKgVUqPAcly4dR9euovc8IyMDW7duRenSpXMVkxw6dCiqSiM7JLRr1w5jxozByZMnMXnyZPTp0weMMWzevBkeOVtnUoE4wkR4ewOTJvFbZE4P+po1PMsyKAjo1An4/Xex2JwtYo065MuXvBbAm2/yYMj168Wv97JlAK5dAzp2BEJD4XL7Khyh5j8wkycDZ87wEwlZkCWpdNq0aYiJiUHJkiXh5+enFXKVk5SUFDRv3hwXL15EaGgo+vTpgwsXLmDhwoWIiorC0aNHZcuHsysWLuRF4tRqXp1x8GCuIRQhVCoVjmcXRWvXrh2crDzn2iw8fAgsWMDHTk7i2Ep4/ZqHzklDfGvU4MXgypYFPv2U0iWLGrVqAX/9xcf//WfBVAah1drVq8CdO/zeaaawxlu3xC4E5ghv9/ICypXL54CsTIAxlPLJQrIaQHIyvLNjV0uVKuBcyTWkKBTGnZeayhcrMjN5xKU+Xc4uXboEgPcdz4mubXni6ornCQkoX7o013Lz6GoRERGBf/75B1OmTAEAbN26FRVy9qaS4OvrCwB49uyZ1va//toNlUqlZaDfuHEDaWlpaNWqVS7dx8HBAcHBwbiVR9HCefPm4ciRI1i4cCEAYP78+XjrrbdyH0gF4ggTk/PWqFaLhVvVah5BvXs3v5/06QMMGMDrydhSJo216JAZGbyzyfr1vEtuzoVMHx9gUNdXGPl0NlBniXab0HffBVatEle+CdmQ5dMTERGBqlWrIjAwEPPmzdP8iOliwYIFuHjxIiZNmoR58+Zptk+ePBnz58/HkiVL8j2f0JPatYEhQ4CICO6y+OYbvuxGFC2mTwdSUvj4k0+AatXklScblYr/2Hz9NTfAr13TduzMnSufbIS8SPWIK1d471aLUaUKN9DT07n7Ph8jrDCYO/983Dj+yJMrN4C0NDBHRySgotauP/4w7pqensZFPLi4iF42fXuhJyQkwMHBASV15FAa1O1AqYSbUom0jIx8+7z5+voiJCQEmzdvRvny5dGtgBoeqdkvpJhQAjubHTt2wNfXV2sRQchtL126tM658ns9SqUS7du3x8WLF+Hq6oqheVXtIg86YWYcHIBTp7jK+X//B9y/z7c/fcqDOL/9lqsfvXtz1TQwUF55bYlPPwV+/DH39iZNgGHt7qP3zRko9tNabcO8fHmuSPXtSzUnrARZ/gvvvfceAvX4tjHGEBERAQ8PD0yfPl1r3/Tp0+Hh4YGIiAhziVn0mDlTLL35ww8yVF0iZOX8efGu7uUlU7NlbRgD/vwTqFcP+PhjHvJ67x7/eBIEoG2wWrySu4UKxUlfl8UdGzkLhsmMo6MYJZOaqikuny/e3t5Qq9W5PNQA8PjxY/0vrlSiVPHieJGYmG/bue3bt2Pz5s0oUaIEHjx4gK+++irfaV+8eAEAKCWJWktLS8P+/fvRsWNHLU+cELnw5MkTnXPl93pOnz6N//3vfyhRogTS0tLw6aef6j6QDHTCApQrx9WMe/d4B5YePbQ/bjdvAjNmAJcvyyejNfP6NbBrF/DqlfZ2acOHUqWAsaNV+HfJIfztGYoh4RVQbFOEaJwXL86jZm/cAPr1I+PcirDq/8StW7cQHx+P4OBgrbwxAHB3d0dwcDDu3r2L+8LSG1E4ypYFpk7lY5UKGDtWP+2HsH0YA0aPFv/fYWGyV+w8fRpo0QLo3FnbQHn/fV6xnSAA3mpNCIOUtdWaGXuhX70qjuVssWYtxpoQWa5W65eHXq9ePQDAsWPHcu3TtS1PXF1Rp3JlpKWnI/buXZ2HPHjwAMOGDUOpUqVw4cIFNGnSBAsXLsxVpV3KjRs34OzsjBo1agDgCveGDQeRkpKCdu2026tVq1YNrq6uOHv2LNJyePHVajVOnjyp8xpJSUno27cvnJyccOTIEXTv3h3btm3Dj7pcbdJ5reR/XhjOnDmDDh06wMfHB+7u7mjSpAm2bdsmt1hENo6OvAzStm3Ao0fA6tW8t7pCAXh4AO+9p338L7/wLMwtWwAda252C2P8Z+a773jOfsmSXB/avVv7uHbtgMGDGHZ9exdxA6ZgyS8BqPPFezyNVaB4cR4pe+8e1/tzRO8Q8mP1BjqAPIueCNvzyrcCeP/RxMRErQeRD+PGiUl9hw4BO3fKKg5hIbZuBYT+vNWqASNHyibK7dtAz548HEva1vftt/nznTu122sRRZtixYBKlbgdYfH6Axbqhb55M0/r2LaNv1aLYoXGmjT1O59Icw39+/cHAMyYMQMpQgoPgLi4OCxbtkz/Czs5oXnDhgCA0+fO5dqtVqvRr18/vHz5EmvXrkVAQAB+/vlneHp6YsCAATo9+BkZGbhw4QIaNmyoCXFPSQH++msnXFyUCAlpq3W8UqlEz5498eTJEyxatEhrX0REBG4K1QRz8Nlnn+Hu3btYuHAhateujTVr1iAgIACjR4/WPkcaMeHiYvMetcjISAQHB+P48ePo2bMnPvnkEzx69Ai9evXK9f4R8uPjAwwbBkRF8RSYrVtzl0HYsgVYt47nqpcuzXPVx43j6TbPn8shtXlgjJc3Wb+eL0gEBXH1bNQobpQLKT6aNCO1Gjh9Gi7ffIUfT9dCp9GV4bxonlj0F+A/IMuX85yCr78W++ARVodV33mFXCvvPD5AXtnVY6T9RnMyd+5ceHt7ax4B1Aw5f1xdeRVvgXHj9NOACNvl9WteZU1gyRLZKq1t3Mg9or/8Im6rWhX49Vfg778BQ+o5EUWHo0eB5GQguz6P5bBQiLuTEy+G2KOH2LHAYlhhuLPUQNcnD71ly5YYPHgwLl26hDp16mD8+PEYOXIk6tevn6ufeUF0adsWDg4OOHDiBFeIJcyZMwdRUVEYOXIkOnbsCACoVKkSVqxYgfj4eAwZMiTXfMeOHUN6ejq6du2q2ZaSosaxY7vQqFFrlCrlkeucefPmoVy5cpg2bRrat2+PqVOnolu3bhg1ahRCQ0NzHb9x40Zs3LgRnTt3xueffw4AKF68ODZu3IjU1FT07dsXmUJif1aWGP5q4wXisrKyMGzYMDg4OODo0aNYvXo1Fi1ahEuXLqFatWqYOnVqvkWKCXnx9wc6dNDeplKJvgSAG7EXLnC1pUsX7lWuWRMYNAg4csSS0pqeIUP4GvCgQXxBIjZWe3/ZsgxDP3iOIWX+5F6N0qW5Z2POHL6iK+DoCHTrxvMIbt3iDpgcUcmE9WHVBropmDJlChISEjQPCofXg27dgFat+PjePV7hnbBf5swRqzV16JD7F9GCNG0qOmxKlwZWruRhy92721Y1V8Ky+PubvvWYXpQvLy5mmTHEXVbswEAHgDVr1mDu3LlQKBT47rvvsGfPHowbNw5Lly416NpBlSqhbZMm+PXwYaRLIvJOnTqFb/6/vTuPi6p6/wD+mRkYVBDUXHALxERRCdNcEtc0SL/2bdHcM60sy8qSyv2rZm6l2W6ZubS49EvbLM2FxX1JxdRETXMXdwcGkGW4vz8e7tw7wMAMzNx7Z3jerxcvzwyXuQcHDve55znPmT4dLVu2xHvvvWfzNUOHDsWQIUPw66+/4tNPP7X53Lfffguj0YgRI0ZYn9uzZzdu3ryCbt0eK/Zead26dbFz504MGDAAu3fvxocffogbN25g06ZNeOCBB2yO/ffffzF69GjUrVu3SDp7ly5dMGHCBOzfvx8TxeVtGny/yyo+Ph6nTp3C4MGD0apVK+vzQUFBmDhxInJycrBcLCXOPILBAJw5A2zeTPMKrVoVvTZISaFZ58JDcmoqMG0azcofOGB/C0d3EgTgyhW6mbxkCX0PvXvTFrGFx7KCFS9WlYwW9Gx+EbM7/orkNs/ikjkIX66tidiPH6FZDXn6gE4HREfTRdTly8DatbSOwMMzYioSTe8jJc6c25shF9PV7c2wA5QO5ufhf2QUp9PRBomtWtHtypkzgSFDaATxYnq93rpsQl9RBrETJwDxYtLXF3j/fcVOnZtLk44REdJzoaG0/aZOB8TFUaVnxjTLYKCUwZQUt2+1pppCKe6VNFCXRD6x62iAbjAYMH78eIwfP77I5wrvWTxt2jRMmzbN7snjhgxBz9Gj8cP332PI888DADp06CDNQhdDnMWWu3XrFtasWYMhQ4ZYC8RZLMDmzT9Dp9MhJuYRuzcm7777bqxatarI8126dLHpe6NGjUrMMnznnXfwzjvvSE940RZriQVTqMVlFcTG0tKBpKQkp183Ly8PeeK+hzI6nc5mr/vijnHFsRaLxe4+2+46FoBNsUK1jjUYDKhUSYcePYBu3SyYNUvArVvA9q352Bl/B7t3CTh4vDLyLHrcf3AJ8Pox4PZtWNLTsf9CC8xJti04Xc2Qhrt9LyNYuIK6PjdR13gDdf1v49mQjXTztVIloFIlXEMt5BmrwOjvCx8/IwxVKsFSyR+5flWQbfTHHX0VZOiqoHZdX1QN1CF/3z7kGY1Iv1MJr8+rj0tXfXHpmh4XrxqQdaf4vxGHZ/2OdtVOAjduIP/qVXQ6WQO97/ovonOS0DEnAW2xD36n6AaaPjcXuoIMnnyDAfk+PpSu3qULLULv1YtmOUDXs+IZ8/PzkV8o80dOr9dbr3+dOVYQBFjkVeE1eKz8591dxwKl/y47StMBemlrzEtbo87KoWVLKhq2YAH9wR4zpuz76XgIvV6Ppk2bqt0N5QgCLWYSqyy98QagwPcvCMBPPwETJtAd7JMnbbOtpk93excYc50mTShAv3OHthlw8TKqb7+l35GWLem6S/GbVuKMql4PndGIShpIZdHr6br5zh2pkrti3fLzQ4927fDwAw/gnffew6DnnivzDd33338fFosFM2bMsD535w6QlPQzWrZsj4YNg13Va8d50Qx6SdeIwcHBCAgIKLWGUbbs/0OcFNq8eXORLfEA2vquXbt21sebNm2ye2Ffo0YNdOzY0fo4Pj4eOXYqHgYFBdlstZeYmGjdmq+wgIAAdOvWzfp427ZtMJvNxR5buXJl9OjRw/p4586ddm/mGI1Gmxsde/bsse4+UJjBYECvXr2sj/fv32931wEA6NOnj7WdnJyMy/I104U8HBsLn7NngeRkHE5Px4WCG1u+fkDXXvQhCh8yAUijPv49ahSE4W3xAzYU+7rPPvsgrl6l93T0iH3Y8IT9apyjR3fFuXM0EA8adByDB58EIACg+hZXc4BTBbPZbceOw/KTVL308cdPYc4zx4p7SQDA5Qm/A0e+AACc690bt958DC/iNoAomBGFBNmxbadPR53Ll4EOHXDx4YdxKLjQWHHggLXZunVr1KtXDwCQmpqKA7LPFRYVFWVdCnzt2jXs27fP7rEtW7ZEaEHNqhs3bmD37t12j42IiEDjxo0B0KTr9hLWozVp0sR6LW42m0u8iRYWFobmBUWJsrKyEB8fb/fYkJAQREZGAqDaH5vkRfMKadCggTXrxmKxYMOG4n9uAMpoatOmjfVxScfWrl3bWgy0NJq+1d+kSRPUq1cPO3bssCnsAgAZGRnYsWMHGjVqxOvK3WXaNKBuXWr/+it9MO+xZg2wcSO1774bKGUrIFfYuZPS2J94gnb1uHyZ7gExVl7Tp9PqnFK2nHY9+cW/G9LcV66krYb69y+6nY7bFd5iTQPBuUhMcxcExyq5u0xB0PphXBwG/Oc/uHjxYplfqkaNGvj6669Rv35963NZWcAPP6RgyZJdNqn8itFgUcCycqSOEdcw8jB3301j7pNPAn/9VeKhPrA/k1mSynBd3SU/5OIuUHFIX5Q8UEVjR4mft7FiBS1N/OEHSl1nXkcnlJRLooA5c+ZgwoQJWLp0KYYPH17k81OnTsXbb7+NcePGYc6cOdbnx48fj7lz52LWrFmYMGGCw+dLS0tDUFAQTCaTtcgcK8HKlcDgwdQOCaEFwV5aXEIQBOud5oCAAKdSUTxOWhqVQhcvLteudWtkk5JCM+Y//WT7fKdOlGHvZJ0mVXnzGOLJ31tEBP2c+flRwTjF1qR//jkg7if9+efACy+49OVDQqg4UGAgBejODkt37tzBv//+i0aNGqGSsynL2dnSJsTVqkFo3Nia8qjX61UdIzMz6d9KlRReVZCXByQnU7tqVZdnHV24QGtlAYpDFC+y/Pff0n9u69Y2/7mO/CxpaQyJiYnBpk2bcPLkSdwj33GhQP369WE2m+0G6cXNoDds2BA3btwo9nvjFHcXHXvzJrB+PRU127zZZrG4ITsb4qhj8fGBYDDQ8rxGjWiNXMOGVBukdm0YateG7q67gGrVYAkIgODvT3f2fH1tBlKLBbhxw4DUVB0uXwZ0sCCmezbd+cvOBrKy8N4nlZF8xAfZdwTk3hGQnytAL+TBqM+BnyEXlfTZqKzLQqeIc/jP3Ufgf/s2dLm5MNy5g1O3a+Iu3zQEGjMh+Bjo3L6+lELv60t7yVWpAkNgIHTVqwM1aiC/dm3k16pFVe+KGeDKmorOKe7qp7hnZGQ4NEaqkuK+ePFia3rD4YI//osXL7auF+rUqROee+45AMBbb72Fn3/+GXPnzsXBgwfRunVrHDhwABs3bkTbtm3x2muvqfEtVBwDBwKLFwPx8cDZszSrXqgAjrewWCzWVJqHH37Y5o+G15k0SQrOe/UCZBWEXenyZfqR+eorqTAwQMHUnDm0x7k33wdhymnZkgL07GyqbeBgFln5uXEGPS1NqtzbsqUKvyvydOeCgCw9PR1AybVflKDatr0+PvSRl2f7/+MiYmwMQPkZdEGQZtD9/Dy+noIjdYyqV69u9+vt1TDy8fFx6PrAmWsIZ441OLGVg8ccm5EBrF0Lw8qVtF+3vSCnVi3ac/X++2G4914gMpIC81L+/0rqgY8PFRotyAIvOLqKzSAzwYFayXl5ediw4Qq2o43NNWTRW0Ol08PxFGd5kKrWsTqdzuGfYW8+FnDud7nE13HJqzhp+/btRSpn7tixAztkeyeIAbq/vz+SkpIwbdo0rFmzBgkJCahbty7i4uIwdepUVFYlB6wC0emAhQuBe++li5EFC2hG/b771O4ZK6s9ewCxknCVKtR2w5X/unXAgAG2F5x161K67vDhKlXdZl4rMpKy/QCa9PWGAP3oUandsqVLX9oxXpTu7FJ+fhRA5OS4vDCguLRYnBhUVF6etHWcF7zf8jpG8jWiAK3FNZvNNmvGmQoOHaJrzJUriy+rXqMGEBNDOwt160b7jvFdfVYBqHJ7dNmyZRAEwe7HsmXLbI4PCgrCggULcO7cOeTk5ODs2bOYN28eqnKJZ2WEhwOTJ1PbYgGef952OpR5jtxcev/EdLPp091Wnf/++6W/o1Wr0mYA//wDPPccB+fM9QpqvwAAjhxR8MQNGkjVrk+ccOlLy78PVQL0YmbQGWyDVxfOogsCUL8+UKcOZbZqIWPCk3Xt2hUAsFGstSLzxx9/2BzDFJSfT0WHu3en3YK++MI2OG/YkLZx2b4duHqVgveRI+lmKAfnrILw7Pwlppy33qI1ywDw55+Ak3vHMo147z2psEqrVoCLlogIAgXfcsHBtO781VdpB6qJE1VMS2VeTx7AisumFaHXAwXVaXH6tEtvXroyQC9TuRmNz6Cnp9MymtOnpYlfRciDVxcG6DodBeYNG7p8MwDHlPJ+q1yyyGk9evRAWFgYVqxYgWSxbgAo5X3WrFkwGo0YNmyYeh2saPLzKc3pvvuARx8FCpa1AqDaRs88A2zbRhudz5tH+3g7kUrPmDfhAJ05xmgEFi2S7l5OnuyWisXMjY4elfYw0+vp/XTBVHZSEhV5a9++aJXpSZOADz+kZWOMuVNYmLRmV9EZdEBKc8/JkRaNu4ArAnRx/WdJe3TbJQZser0K+dalu3aNSmncvGkbW7qdPHhV9MRuVsoMuvgz5Mz6YzX5+Phg8eLFyM/PR5cuXfD8888jLi4OUVFROHHiBGbNmmXdJoq52aZNVHSwcPX18HDgk0/oTttXX1HlWA+vfcCYK/BvAXNcdDTtmw3QRcmzzyo8bcHKLC+P7k7L9zxv27ZcL3nkCNCnDy0L27uXLpJlGy0wpiiDQUry+ecf29oHbuemdehigF6rVtlvcvn6+sLPzw8mk8m5GdD8fGm80NgWayJ5CRo720K7h5tm0FVXwgy6IAgwmUzw8/ODrwZv1tjTvXt3bN++HdHR0Vi9ejUWLlyIOnXqYNWqVYiLi1O7e94vJQV4+GFaR37okPR8u3aU5n7sGDB6NK2DY4xZ8UpQ5pxZs2g/9H//pVSkTz+VgnamXR98QFE0QNsCTZtW5pe6cAGYOhVYtsz2/kxkJC0pY0wtkZHA/v205OLvv6kOgiIKB+gxMeV+yWvXaPklALRoUb7XqlmzJi5evIgLFy4gKCgIvr6+pW+Rlp0t1arw9QXu3IEgCMgpCNrv3Lmj+laU8onc9HQFdwCV3+jIzHTZLHpGBv1XF9oFSjnyuxz5+db3PDc3FyaTCWaz2WbPdk/Rrl07rF+/Xu1uVCwZGVR4Zt48qn0jat2ariNjYjR5048xreAAnTnH35/SkB58kB6PG0d3R+UXqB5Kr9cjLCzM2vYaR49KRf50OmDJkjLt33P7NjB3LsX68uvRBg2AGTOAp57i5WJMXfI08CNHVAzQXSAvjyaWDh+m5KXyEPdavX79Oi6K2yuWJisLuH6d2rm5QMFexuIer9evX1c9QM/Lk7qYkaHwLPrNmxTE3rrlspc8f55e0tdXvuWTgi5epJsPPj60raqMn58f6tevr/re5swDJCUBI0bQRI4oJIQC84EDvTaF3WuvIZkqOEBnzuveHXjxRdoaIysLGDaMZtM9vDS3Xq9HczFH1lvk5FDkLKZhvvYa0LGj0y+zbRttlX7zpvRcUJBUBI53O2Ra0KULBbUtWwKdOyt44vBwqe2iAL1uXVqa6SqBgYEIDAxEbm4uLI4Usvv6a7qgBoDZs4HHH3ddZ1xEEOh6PyODAtr4eAVPPnEicPAgtQ8cKHcFzNRU2mADoJ/jRYvK2T9nXb0KvPACtTt3Br780vopg8HgUWntTCVZWTRp8/HH0nNGIxUZnjDB66vEeuU1JFONZ0dUTD3vvUdFP/75B9i9m6ZWJ01Su1essBkzpIvIiAhKOSuDli2lrE6jEXj5Zbo+vesuF/WTMRdo27bcpRXKpm5dyi7KyNB88UxfX1/Hgq1Dh6RZ1JAQzW67Va0aLWc4e5buQwYFKXTioCDp/+f8eSAqqlwvl5IivVxwsAr/3WfOSB347381+34zjTp6FBgwgP4VdeoELF5My+oYY07hHAxWNv7+wDffSKlK06bR4k8PJggCMjMzkZmZ6XHbyRRr925pBszHh94vB6e6Cxeirl6dsuSHDgWOHwfmz+fgnDErnQ645x5qnz5tu+bSU8lvNBSk8GtxjLz3Xqmt6PZ6Ls6akPc9MrLcL+e8Yt5vxhyyZAndGRWD80qVgAULaBu1ChSca3F8ZJ6LA3RWdh06UNoSQIsBBw0CzGZ1+1QOFosF8fHxiI+PdywFVMtMJno/xCpu//sf0KZNqV+WnAzExlJRKrFAlej11ynG511pGCuGGNRYLDQbWQ75+cCVK+XvUrmcOEH/BgXR5tzQ5hgpD2ZVC9DF/6tycOWe92Ui/x7k3xtj9uTkAC+9RDv6iAUgWrakyZrXXqtwRWm0OD4yz8UBOiufqVOlnNKTJ2lBMlOXIACjRklBQseO0o0UO86epaXq990HbNxI91neftv2GC64yjzF1avAli2UeawYFxaK++cfSnOuUweYPr2c/SqLO3ekNJrwcE3/8stn0OXbK7ud/P12QYAu3lzQ62k1kuI4QGfOuHqVigUvXCg998ILtFsMr8NmrNw4QGfl4+sLrFwJBATQ46VL6TFTz/LlwKpV1A4KAlassFvA7+ZN2hI9PBz49lvp+dBQWj7GmKdZupQC2549gZ9/VvDELgzQxWCtcBaLYk6flopOaDzdOTISaN8eGDkSeOghBU8sLmkAyh2g5+XROnqA/rtVWf4tfg9GI3D33Sp0gHmM48cpg3LHDnrs50cD7+efc8VYxlyEi8Sx8mvcmO6iPvUUPX7hBUqn5rvwyjt6lMpYi778kgo8FZKVRYVWZ8+m7dNENWrQWvOXXqK/uYx5mmbNpLanzqjK+63KemR5/zUeoAcFUbkNxfn70x6TFy6U+4bMyZPSRhuqvN8WC6VtAHTjoYKlJjMnbN8OPPqotKVLvXrAjz8C7dqp2y/GvAzPoDPXGDpUCtDT04F+/YDMTHX7VNGYzbb/7889Bzz5ZJHDDh2iui3jxknBeaVK9PjUKVprzsE581Ty9buHDil4YhcWDZOvpZancCtG3n++0WqfePPi+nXbPSidJP85LWcx+LI5d47WEwMVqqgXc9Lvv1Oaivizfu+9wJ49HJwz5gYcoDPX+ewzae3R4cO0FxdThiDQJropKfQ4Kgr46KNiD23cWLoW0+mA4cNpwmzOHNqyiDFPVrUq/YwDNAwpVqunVi3pF+j48XK9lDiDXqUKEBZWvm6VCVf0doyLbspcvy6ltasSoPP6c1aa77+nmfM7d+hxTAywbRtlkTDGXI4DdOY6AQHADz9Q6h9Aa5IWLVK3TxXFJ59Ia/8DA4H/+z/rWrDLl20PDQigXfF696aZm6VLgYYNle0uY+4kBjlZWZQVogidTgpuzp0rcwaR2UxLwAHKBtCr8Vfag1Lc5W7dooxzxbiokvvLL9P7fuwY0K1b+bvlNA7QWUm+/ZZ2hcnLo8f9+wO//krXGowxt+AAnblWRIRtUP7yy8DOner1xwk6nQ4hISEICQmBTsNVi4tITKS8dNGSJUCTJjh9mv6mhoUV3df8hReA335Tab0jY24mTwtXNM1dnh4srul10tGjUn021X4/xdlgeVYAtDtGnj9Pdc1q1KCil4px4bIGg4HqJ1StWs4+lQUH6Mye1auBp5+Wtmx95hkqPGs0qtsvDdLq+Mg8EwfozPUGDwbGjKF2bi7Qty9w8aK6fXKAwWBAZGQkIiMjYfCUIjlnz9I6czGPd9w4XO/aF2PG0MXeqlWUkTZliu2X8d8O5s3kacKqrUMvY5q76uvP09OBS5eoXShY0+oYGRws7Ruv6F7oLt5qTTXyn1UO0Jlo7VpgyBApOH/xRSo8q6HffS3R6vjIPBMH6Mw93nsP6N6d2qmpwGOPcdE4VzObaU3Y9esAgMye/8WsgFlo3JiWn+fm0mE1a3INF1axqBagy2fQyxiwaaqCu4cUDPP1lfYOP35cWibrdo0aScGKJwfoYt+DgihrgrHNm4GBA6Wb/yNH0lI6VdbcMFbx8G8acw9fX0qNErf4+vNPYNgw6U6sBgmCgOzsbGRnZ0MQc0y1ymKh/PVDh5AHAxbXmoAmR3/EpCl6pKXRIZUr05Zpp07Z7rzGmLcLCZFShRXdak0e0JZxBv3IEamtygy6vN+FAnQtj5HiTRmLRdpT3O2MRgrSAUpxL8P/yfLldJ91yhTg339d3D9HZGVJa6CaNuX0KkbXa489Jt3lf/pp2uOcg/MSaXl8ZJ6Hf9uY+9SqBfzyC1UlA4A1ayhi1CiLxYJNmzZh06ZNsChW+rmM3nwTWLcO/6AxovSHMfLaLFy6TL/Oej3d7P7nH2DGDK7jwioevZ6CWx8fWkKt2IzqPfdI7TLOqP7xB91UWL0auOsuF/XLGSUE6FoeI1u1ktrJyQqeWExzN5uLVuR0QGIi/Zl85x1rMpSyTp2Sbixwejs7eRLo1QvIyKDHjz0GLF7MwbkDtDw+Ms/Dv3HMve69l640xcF99myu7F5eH30ELFgAAGhouIyMWqHWTz36KM3ALVoE1KunUv8Y04Dvv6drzEOHpC2s3K5KFapWBlCgW4ZZFF9fSm3v39/FfXNUCQG6lqkWoJezkru4BEOvB1q0cFGfnMEF4pjo5k3gP/+R7hR17kwF4Xx81O0XYxUQB+jM/Xr3tt2T+8UXgR9/VK8/HuzG4h+B116zPvb7/EPMnF8ZDzxAW5L+9JO0FpOxiqxePZUKDYtBzu3bKk2JlpMYoBsMKm3CXjbyugOKBujNmkntlBSnvjQvj6r2AzQRX6WKC/vlKA7QGQDk5FBBX3E3ghYtKLWjYLtWxpiyOEBnyhg9mtKyAVqHPmgQkJSkbp88yJUrwEv/vYAGIx/GcaEgpXLKFOC55zB4MLBjB9Cpk7p9ZIzBJevQVZOfLwVsYWEetZVSjRpS8kJysoLlTsrxfh8/TnERYHuDQVEcoDNBAF56idZbAEDt2sC6dTZbLDLGlMUBOlPOnDlUKA4AsrOBRx4B9u5Vt08aZzYD06YBjRtZsPDXBriDypiIWbTIfPp0AFTTh+v6MKYR5Uh5nj0bePttmrhSZQnjxYvSbhselN4uEtPc09MVLLhWjhl0+Q4DmgjQ5dvGsYrj88+Br76itp8fpeKFhqrZI8YqPA7QmXL0eio20rs3PU5PB2JjFc5H9Ay5ucDChVRzavp0ICOLtvLxhxn3Ns2B8OlnHJUzVoovvqC13FFRlE6siHLMqC5cCEydCjz1lEo1mTx0/blIDNANBilT1+2Cg6UtA5x8v+UBuioV+wGpz/XqSQVdWcWxaxcwZoz0+KuvgAceUK8/jDEAHKAzpfn6Av/3f0C3bvT49m3goYcU3gtJuwQBWLsWaNmSMs6uXKHnfZCLl/ApTnV9FlOTH4fOl4u2MFaaLVtouPnrLwWzzcsYoN+4AZw/T+1WrVS6/+bhAfqIEcC+fXTv9+GHFTqpTifNop85Q9uWOejgQal9332u7ZZDrl+X6iTIMwFYxZCaCvTrJ22n9vrrwJAh6vaJMQaAA3SmhipVgF9/BTp2pMfXrwPduwP796vaLZ1OhwYNGqBBgwbQqXB1fOkSEB1NdVrkWYf98H/4G83xadf/Q53flypYkpoxz9a6tdQ+cEChkzZsSGmigFMp7vLZVHlFckXJA/Ri1iOrPUaWJjQUuP9+FepaiTczBIH2t3SAIEg/k7Vrq7Trhvz95gC9YrFYKBi/dIked+0KzJ2rbp88nNbHR+ZZOEBn6ggIAH7/HWjfnh7fvAn06EHpVioxGAxo1aoVWrVqBYPBoPj5a9cGbt2SHnfRb8dutMf/oT+aRNehmxqqlPllzDPJA3T5bKVbGQzSWt5//nE4t16+0kcTAXoxM+hqj5GaVYZ16BcuUNYEQLPnqlzPHzsmtXn7j4pl9mwgPp7a9erRdri+vur2ycPx+MhciQN0pp6gIGDTJtprEwBMJqBnTwrcKwCTyfaxjw/V0WveMA2/+PZFYn5ntMde4MEHgT/+kNY5MsYcIk8bVmwGHZBmn3NzKe3ZAZoK0AMDgTp1VOqEByrDsoaqVWm57+jRwOOPu6lfpZHfTOAZ9Ipj61YqdgFQsYsVK/j3nTGN4QCdqatqVWD9egrMAaog/N//AsuWKd4VQRCQl5eHvLw8CILgtvOkpQGTJwP16xed1fvv5S/w14W78EjuWugAWki5bh3g7++2/jDmrWrVAho0oPbBgwpuvSWfjZTPUpZADNB9fIDmzV3fpVJlZQHnzlG7adNip3SVGiPL49gx4N13gcGDgd27FTppGWbQq1UDnnkG+OQT4IUX3NOtUnGAXvHcukWp7eJg+L//UXo7KzdPGB+Z5+AAnanP35+C0CefpMcWC1X7mTJFwStqwGKxYMOGDdiwYQMsbtjjKCcH+OgjoHFjYOZMICMDGDfOenJg3DjoXhwFg1CQEjtkCPDzzyosqGTMe4iz6Glp2t16KztbiuObN5eWsCvq5ElaGA3YLRDn7jHSFXbvpnF15Upg+3aFTnrPPdINDSe3WlOV2Fd/f7pjzLzf6NG0vgKgYr2TJ6vaHW/iCeMj8xwcoDNt8PMDVq0CXnlFeu6ddyhoz8hQr18ukJ9Py7siImg3E7Forq8vXYzn3kgDHnuMpn1Eb7wBfP01YDSq0mfGvIUqheKcnEH/6y9pqbrq6e2AR1ZwF6myrKFSJaBRI2ofPy7d6NCyO3ekO1bNmvG2nRXBqlV05wqgFI5vvqGaGYwxzeEAnWmHXg98+CHw/vvSJsBr19KenIrtkeRaCQlUB2/gQOD0aen5QYNo8uKD5/+Gb+cOlEEA0B/LTz4B3ntPpY2QGfMuqgTo8gDXgQBdvoFFmzZu6I8j5DO/Hhygt2ghZSAoujGI+H9mNkuVse0wmWhll7iNpir++UfKUOP0du938SLt3Sr69FNp/Q9jTHM4AmDaotPRXpzr1lGhIgA4fJj2zlm9Wt2+OeHWLaB3b6rv9uef0vPi4xUrgLCd3wJt20oX8NWqARs2UAoaY8wl5DOqilVyDwig7dYACnxLmVFt2RJ48UUaDsSNLRQnv5GgyiJ41/D1BaKiqH3iRNFinG4jD3JLuaG8ezf9fQgOpiXAquD15xWHIFChA3GbmAEDaJaAMaZZHKAzberVi65ixAtFs5mmoUeMoMWkGhcUBFy9Kj2+916aMdm8GWjT+DYwdCjw1FNUFA8AIiOBvXulYnmMMZdo0IDueX3yCa2aUYyY5n77dqlTpZ06AZ99RkOA6gG6fJs4DyXPQlDspow866CUdejyTA7VkhU4QK84VqwAfvuN2sHBNNjwkgbGNI0DdKZdERF0xTp0qPTcsmUU7SYkqNat4hReJq/XA3Pn0iTa8uV0Qfbww4Bu8yYKxr/7Tjr42WeBPXs8/qKYMS3S6Sg4Hz2aEnEUU4ZK7qqxWKSArXFjj699IX+f5RlMbuXEDLo8QJdneCiKA/SK4epVKn4jWrgQqFFDvf4wxhzCATrTNn9/Kpa2dKm0D/jZs5QrPny4VHFNJXfuAPPnA3ffDezYYfu5Hj1omd+wYYDh+hW60RATI1VQDQoCvv0WWLyYK7Uz5m3kQY/WA/SzZ2kwAzw6vV0kD9AVW4fuRN0BMUCvXFkDM+h6PVWhZ97p1VeBGzeo3b8/FaRljGkeB+hM+3Q6Csb/+gvo0kV6fvlyurr5+GPaw6zcp9Ghbt26qFu3LnSlpH/l51Ns3awZFVy/eRN4882iS02NQjawYAEdKJ81f/BBWls/ZEi5+808T1paGsaOHYuQkBD4+fkhNDQUb775Jsxms1Ovo9Pp7H4MHz7cPZ1njpHPoJeQ8nz+vO1yGFX8/bfUlve7EGfGSDU1b06F1QEFZ9Dr1AGqV6e2/P+zkFu3pIKhUVEqFdEWBOlnslEj6T+LeZf166XaPTVq0LUScxtPGR+ZZ/BRuwOMOSw0lFLbFy0Cxo+n6j83b9Id4o8+ogWm/fqV+YrHYDCgjQMllDdton125WsbdTqahMjMpEl/5OXRH8YpU2w3X65Rg7ZTGzGCq7RXUBkZGejatSuSk5MRExODQYMG4eDBg5g3bx6SkpKwdetWVHLigjkkJKTYYLyVavt1aVNaGs2mXrtGE0lu52CK+9SplCB09900toSHK9C3whwsEOfoGKk2Hx/arm73bspiun2banC6lU5H/3c7dlDFbJOJsqQKkd8waNvWzX2y5+JFaV0Wp7d7p6ws4OWXpccLFgC1a6vXnwrAU8ZH5hk8JkDft28fpk6dip07dyI3NxeRkZEYO3Ys+itypcU0Q68HRo2iNK0336RpbICuwgYOpBn18eOpQqm4146LHDxIgfmmTbbPx8bSevOoKFCa6FffAXPmUJ9EOh3w9NMUnNeq5dJ+Mc/y7rvvIjk5GePGjcOcOXOsz48fPx5z587FggULMGHCBIdfLzQ0FNOmTXNDT72HIFDge+UKcNddwJNPKlAjqVYtuiF382aJAbqYgn3xolT4XXHy/pUwg+5JHnuM/hy0aaNgPSwxQAfo/7RDhyKH7N0rtdu1U6hfhfH6c+83e7aUqtG1KxWlZYx5DI+YwktISEB0dDS2b9+O/v37Y9SoUUhNTcWAAQMwf/58tbvH1BAcDHzzDbBvH9Ctm/T88eM0O92wITBhgm2QXEaZmbR8vHVr2+C8dWuqyr5hAxBV+QTw1ltUMvq552zP27MnLTpcupSD8wpOEAQsXrwYAQEBmDJlis3npkyZgoCAACxevFil3nkvnU6q7H3jhm1Si1tPKgY/Fy8C6elFDsnMBI4epXaLFiqWopCnZHtJwDZuHNUUfeWVYiey3aNFC6ltJ81dEwG6F77fTObECZo1ACidhKu2M+ZxNB+g5+XlYeTIkdDr9di6dSsWLVqE+fPn49ChQwgPD8fEiRNx9uxZtbvJ1HL//UB8PEXO8kD92jWaxW7ShPII582ji5IS9iPOy8vDunXrsG7dOuTl5Vmfr1yZ1omKQkOB774VsG/pEfTY/y5d+TdtCrz3nlSMBaAqcfHxwMaNlG/JKryTJ0/i0qVLiI6Ohr+/v83n/P39ER0djdOnT+O8/AeuFLdv38aiRYswa9YsfP755zh8+LDDX5udnY20tDSbD28lD4bkQZJblbIO/dAhKqAOKFxhXk4QpBn0kJCCNTrFszdGsgLy5QHFBOiCQBt2AJRyr1ptNvGuEGB7U4F5PkGgqu1iXZ433vCKwo+egMdH5kqaD9Dj4+Nx6tQpDB482GZNZVBQECZOnIicnBwsX75cvQ4y9el0NEudkEDphQMHAr6+0uf//JPS4Vu0oIWegwfTeqykJODy5WKDdvlTOgh4981rqBmUgwWPJiCl7VMY/FYD6KMiaZpGvmeO0UiF33btoun17t35zjWzOnnyJACgiZ0t9cTnxeMccejQIbzwwguYNGkSXnzxRdx7773o1asXrjpQeWz27NkICgqyfjRULcfa/VQP0ItJc5evR1YtQL90iRboA3whX16lBOjp6XQPxGik+8aqlSGRB+j8nnuX33+ntD6AMgknT1a3P4yxMtH8GvTExEQAQExMTJHPxcbGAgCSkpKcft28vLxi73DpdDoYZEXGSroLVp5jLRYLBDuzue46FgB8fHxUP9ZgMFgrXLr82I4dgY4dkX/pEvJXrAB++AFITpYOunYNWLsWhlWroCt4rfyqVZFfvz5yagUDb8UBADZ3+R8eQgJw6xYM58+jfWYmzqES/H7LQ77BgDzAdo1769ZAv34wDBkCXZ069Lr5+cjPz7fbX71eD33BFZoWjhUEARZxOk+jx8p/3t11LFDy73JJr1Mak8kEgG4wFicwMNDmuNLExcWhb9++CA8Ph9FoxJEjRzBjxgysX78effr0wa5du2y+r8ImTJiAsWPHWh+npaV5bZAuL8ilWIBeylZr+/ZJbdVqC3nh+nO59HR6v9u2BQp+vdynXj06SVqabRBcIDCQZtCzs22TrRQlCFLfGjRQMP+fuV1ODvD669LjefNKzIhhjGmX5gP0kmacgoODERAQUOJsU3Z2NrKzs62PxRTOzZs3o0qVKkWOr127NtrJplo2bdpk94K8Ro0a6Nixo/VxfHw8cuxs9xUUFITOnTtbHycmJiIrK6vYYwMCAtBNlq69bds2u9svVa5cGT169LA+3rlzp92Le6PRaHOjY8+ePbh582axxxoMBvTq1cv6eP/+/SXOyPXp08faTk5OxuXLl+0e+/DDD1sD+sOHD+OCuC94MR566CH4FQTCf//9d4nLGR588EHre5py+zZON2tm9+5x19GjUfXcOQDAyT59cHLwYJvPWyZ1xAbQe9tp7FhUO3kSlXEHpx55HMeeecZuHzoYDKhZ0D537hyOHDli99i2bduiTkEwf/HiRRw6dMjusa1bt0a9evUAAKmpqTggn7UvJCoqyhpkXbt2DfvkUUAhLVu2RGhoKADgxo0b2L17t91jIyIi0LhxYwAUQG7fvt3usU2aNEHTgg1+zWZziTfRwsLC0LxgFicrKwvx8fF2jw0JCUFkZCQAICcnB5sKV+yTadCggTXrxmKxYIM4q1CMunXr2lRfLelY8WfsjTfegNFotHuc3JgxY+zOmpfHvHnzbB4/8MADWLduHR588EEkJSXh559/xhNPPGH36/38/Ky/X96uZk0gLIzqJh04AOTm2ibauEUpM6q7dtG/RmNBkUk1OFjB3RPNnUulSAQB+PVXQPZnyj10OsrU2rULOHeO7g5UrVrkMD8/iuVVcfkylbUHOL3d23z8MSBeD3fuTNUwGWMeSfMBuiMzTiXNNs2ePRvTp093S9+YB/vf/4BDh7DvTx1+9H0UHZFp/9iQEFrL3rgx0L69cn1kmvbll186fGy/fv3QpEkT6zhmb8wSbyDaG+8codfrMXLkSCQlJWHHjh0lBugVTbt2FKBnZQFHjgD33efmE4prujMyisyoXrsm1ZJs08blm044zsE90D1Ro0bScqVduxQI0AG6ySHeeUlJUXEvNTt4/bl3unYNePttaut0wIcf8vI6xjyY5gP08rKXwtmzZ09rOqmcrtCA9tBDD9l97cLHPvjggw4f261btxLT1uU6d+7s8LEdO3YsMQ1crn379g4f26ZNG4ePbdWqFaJKmA6Sp9xGRkaiZcuWDh3bvHlzRJRwASk/tlmzZggvYUPhM2cMGLlJh9W7AJ99+TCszoefXx6++24zAKBnp07wqVIF0Oth+M9/rH/oGuXnI6SElHF5H+6++240aNDA7rF62QLE+vXro27dug4dGxwcjIcfftihY2vVquXwsXfddZfDxwYFBTl8bEBAgMPHVq5cucRj5T/vRqPR4WMNBoPDxwIo8dj0gmrcJpOp2DGkJKWtMS9tjbqjatakPI4Mca9jBoAC9FWrqL13rwIBul5PQdDevXRnICPDmnIqFgsDgAcecHM/SuLFKe7y/1cxZna7wlkTHKAzJcyYIdWSePZZBQY3xpg7aT5Ad2TGqXr16na/3l4Kp4+Pj826aXscOaYsx5a0LpSPLf+x8nXNcnl5wNixwOefU4orPadHaKges2ZJx/kEBBT7ftp7XWf6oNVjdTqdwz/D3nwsUPLvsjM/h4U1adIE9erVw44dO5CRkWFTyT0jIwM7duxAo0aNyr0OfE9B9CcuX2BEngCzdy/wwgsKnFQM0MVq6QXV4M6fp9T2nByVA3RxBj04GCjhb6knatgQqF+fdrnbu5cq5pfj19cxdpY1HD0K9OpFN4meegp49FE398MejQToycnJ+P7777F//34cOHAA169fR9euXa11h+z57rvv8OGHH+Lo0aMwGo2Ijo7G22+/jdatWxd7/L59+zB16lTs3LkTubm5iIyMxNixY9G/f383fFcq+ecfYOFCalepIs2kM8Y8luaruJc045Samgqz2eyWtZ3MO/n4AKdOScF5rVrAJ5/QddQTT+hQu3Zt1K5du8iMKmOuoNPp8Nxzz8FsNmPGjBk2n5sxYwbMZjNGjhxp83xmZiZSUlJwrqBmgujw4cPIFX+QZXbu3Im5c+fC19cXT/IaRBv33UdBcfPmVB9LEfIMIVlNihdfpAmvXbtoEwpVXL1KqbGAQ+vPdTrPGyPFmx8ZGTb//e4j/3+UBcN799JNmTVraJtq1WikgvtPP/2E2bNnIzExEcHBwQ59zcyZMzF06FBcvXoVo0aNwpNPPomtW7eiY8eO2LFjR5HjExISEB0dje3bt6N///4YNWoUUlNTMWDAAMyfP9/V35J6Jk2i2QeAtlUrIRuPuY8njo9MwwSN27BhgwBAGDFiRJHPLVu2TAAgTJ8+3eHXM5lMAgDBZDK5sptMo3JzBSE/3/a5v/4ShKpVBWHKFEFIS1OnX8xzlXcMMZvNQlRUlABAiImJEcaPHy/ExMQIAIS2bdsKmZmZNscnJCQIAISuXbvaPP/0008LNWvWFB577DHhlVdeEcaOHSvExsYKOp1O0Ov1wsKFCxX/3jxBRobCJ/zjD0Gg+XNBiItT+OSl2LxZ6tuYMWr3xi3mz5e+xTL8SjgvP18QAgLohI0aWZ8eOVLqR0KCAv2w17fAQOrE3Xe75RSOjiFHjhwR9u/fL+Tk5AiXL18udoyTO3HihODj4yOEh4cLt2/ftj5/8OBBwc/PT4iIiBAsFov1+dzcXKFx48aCn5+fcPDgQevzt2/fFsLDwwWj0SicOXPGLd+bovbskX6watfmixrGNM7RcUTzM+g9evRAWFgYVqxYgWTZdlkmkwmzZs2C0WjEsGHD1Osg0yRBAH7+GYiMpBkLuchISnl8++1iC+wy5lb+/v5ISkrCa6+9hmPHjmH+/PlISUlBXFwctmzZgsqVKzv0Oo8++iiio6Nx6NAhLFmyBB9//DH+/vtvDBw4ELt27cKoUaPc/J14pmI273AvOzPomnD4sNQu2B3B2yi+Dl2nk2amz5yhqXsA4qYXPj6U5q6Kixeldcoqrz9v0aIFWrduDV8Ht1JYunQp8vLyMGnSJJsimq1atcKgQYNw7Ngxm51F4uPjcerUKQwePNi6mwdAyyYnTpyInJwcLF++3GXfj2omTJDaU6fyRQ1jXkLza9B9fHywePFixMbGokuXLhg4cCCqVq2KNWvW4OzZs5g3bx6vs2Q2du0C3nwTEDPeJk6k9X7y6wD+G8bUFBQUhAULFmDBggWlHmuvoOTjjz+Oxx9/3B3dY65Uty6t7b51iwN0FbRuLa31V7RQnFh3ICUF10PaWGvxtWmjwk0ikUbWn5eFuDZdvlWsKDY2FsuWLUNSUhK6dOni0PEAStz+0yPEx9MHQLvMFFoexRjzXJqfQQeA7t27Y/v27YiOjsbq1auxcOFC1KlTB6tWrUJcXJza3WMacfw40Lcv0LGjFJwDtM5cXGZZkry8PKxfvx7r169HnrieizHmtcTJRLfS6aRZ9IsXgVu3EBcHPPEEMG8eYDYr0Ad7xABd3L+7FJ44Rvr5UZAO0BbR168rcFL5zY7Dh23+HnXqpMD57fHgAP3kyZMICAgodr16cbWKStoRIzg4GAEBAXZ30xBlZ2cjLS3N5kMzBAGYMkV6PH267SwEU5wnjo9MuzwiQAeAdu3aYf369TCZTMjMzMSePXswYMAAtbvFNCA1lQoutWgBrF0rPd+0KfDjj5RaWK+eY69lsVhgsVjc01HGmCZMmUI7igUHA9nZCpxQnuZ+9Ch++YXGpsmTaXZXFfn5UsAWFmbd/q00njhGPvCAdJ/k8mUFTnjvvVL7r78gy7zmAL2MTCaTTWq7nLjdpXy3H7Fd0tfY2x1INHv2bAQFBVk/yru7hktt2ADs3Ent5s2BgQPV7Q8D4JnjI9Mmzae4M2aPINBN43nzrMv8ANBF9/TpwDPP0Ho/xhiTO3sWSEmh9oEDCmxzJgvQr+36B//8Q1FamzYqBuinTwOZmdT20vR20fjxtDzXTqzmeoUC9G2yLInoaIX6UBx5gO6CPe/j4uKQXegOV05ODgDgjTfegLHQD/eYMWM8atedCRMmYOzYsdbHaWlp2gjSC8+ev/22AvsHMsaUxOEL81g6HV1ki8F5QADw1lu0z7mDk0GMsQqoUyfgm2+ovW2bsgH61ngp9bFjRzeftyQVYP25qHZtFU5Ypw5w5Qoyk09gv0kAoEOzZrTkShXyjInQUPqDWU5ffPEFMuR3x2W+/PLLIs/169evzAF6UFCQ3RlvMfVcPlsutkv6murVq5d4Tj8/P/j5+ZWlu+61bh2wfz+177sP4FokjHkdj0lxZ0wQ6BpDbuZMKrjz8su0v/mUKRycM8ZKJk8zlqcfu40snTjhr7us7e7dFTi3PRUoQFdFwSz63hthyMujPZE7d1axP6dPSwUPZFXNy8NsNkMQBJsPMSA2mUxFPtetW7cyn6tJkyYwm81ITU0t8rni1psXty5dlJqaCrPZ7FGz+VaCQDPmomnTAD1fyjPmbfi3mnmEbdtotunrr22fb9wYuHAB+PhjFWZJGGMeKSICuKsgTt6xo+iNP5e76y6q5g4g8UozAJSRqup6ZHlF+QoWoCtSv6kgQO+MbUj+bCc+/hgYOlSB89pz6JDUjopSrx9l1LVrVwDAxo0bi3zujz/+sDmmLMd7jD/+AP78k9qtWgGPPKJqdxhj7sEBOtO0v/8G/vtfoEsXYPdumiHPyrI9ppQsNcYYs6HTSWuBb96EdQsst2rZEldRC0cttPa3TRugoLaVOsQZdD8/4J57VOyIMs6eBZ57jr7VqVMVOGFBgG5APqLMO/Dyy/R3TDXJyVLbAwP0ESNGwMfHBzNnzrRJW09OTsbKlSsRERGBTrI7Xj169EBYWBhWrFiBZNn3bjKZMGvWLBiNRgwbNkzJb6H8Cs+eT55MgxljzOvwGnSmSRcv0kXU0qW2s1tBQTRj7o7MNJ1Ohxo1aljbjDHv1akT8Msv1N62TYGi1vfei6RN0hpZVdPb79yhPccAqgDtYDVNTx4jjUbgq6+onZCgwAkLFYpTncZm0FNSUjBnzhwAQFbBXfeUlBQMHz7cesyyZcus7fDwcEybNg2TJ09GVFQU+vbti/T0dKxatQoArXnXy1K9fXx8sHjxYsTGxqJLly4YOHAgqlatijVr1uDs2bOYN28eQkND3f59ulR8PLBrF7VbtOC15xrjyeMj0x4O0JmmmEzA3LnABx/YzpTXr083jp9+2n3FSg0GAzqqWrWJMaYU+WxmfDwwapSbT9iqFRIQZn1YjuW45XfsGCBuBeREersnj5F16wLNmlFh0X37aDm2C+qk2RcRQX+sLBZtBeiBgVQkTmWpqalYvny5zXNXrlyxeU4eoAPApEmTEBoaig8++AALFy6E0WhE586dMWPGDLQWN7uX6d69O7Zv346pU6di9erVyM3NRWRkJObOneuZ2/TOmiW1J0/mteca48njI9MeDtCZZnz6Kc2a37ghPRcYSFvkjBlDxeAYY8wV7r8fqFYNuH0b2LyZ4ii37lR0331IBM2qGHQWdOqk4rZIFbRAXPfuFKDn5VHtgdhYN57Mzw/L6ozDv5eMiDkaj/aZOfCpotKeejdvAufOUfveezUR2HXr1g2CIDj9dUOGDMGQIUMcPr5du3ZYv3690+fRnD//pDuJAK3TePJJdfvDGHMr9UdpxgocPCgF576+wGuvUWX2CRM4OGeMuZbBAPToQe07d4B//nHzCZs2xVrjIHyGFzGu2iL3zt6WRp7uXIECdHnWghJp7l/mDMPbmIpOliRc3nHa/Se0Rz6Dr4H0dlYGc+dK7Tff5H3PGfNyHKAz1RS+eT59OgXigwcDx48DCxYANWsq15+8vDxs3LgRGzduRJ4iZX4ZY2p6802aPb95E2ja1M0n8/FBsyg/vIjPMfPWS0B6uptPWIIDB6T2ffc5/GWePkYqGaCbTMCem1QspRmOoeHV/e49YUk0tv6cOenkSWDNGmrXqQN4WnG7CsLTx0emLRygM8X99RfQqxeltMvVr09btX73HdCokTp9y8nJQU5OjjonZ4wpqn17mkWvVEmhE8qDYbXWJefnSwF6gwZO70/pyWNk7dpUEw8A9u+nINpdEhIASz5dYsVgo7rr0OUBuov2QGcKmjdPmtF47TUFByzmLE8eH5m2cIDOFHPuHDB8OF0fbNhARd/S0myPqVNHjZ4xxpgC5MHRwYPq9OHff6WBt5jCWt6uZ0/612IBitki22U2bZLaD2GT7TZnShPPrdcDLVuq1w/mvCtXALFwXtWqClSzZIxpAQfozO1u3QLeegsID6e/M+KN4MqVaY05Y4x5s7//Bt54A0gUuiJXrM2qVoC+X5ZqXQED9D59pPa6de47jxj8+yIH3ZBI/+9lKIpWbrm5wNGj1A4Ppz+8zHN89hmQnU3tF16gypaMMa/HATpzmzt3KDOrcWPgvfekvzHVq9Pj48edWv7IGGMul54OfP450Lcv7VzkDmvXAvPnA91HN8di3fP0pFozqvL15xUwQO/SBfD3p/aePe6Jmf/9Vyo62LF6CgKQQRVQxUrqSjp+HBBTbnn9uWe5cwdYuJDaBgPw6qvq9ocxphgO0JlbrFpFRZfefJNm0AHAz48enzpFs0m8jIoxprb8fODllymI/uEH95zjt9+kdu+wFGocOUKzm0qr4AG6nx9NSm7dSm+BTuf6c9ikt0ddlR78+afrT1Ya+Y0gXn/uWVasAK5do3a/fkDDhur2hzGmGA7QmVvs3i1NFuh0wNNPAydOAO++SzPojDGmBUFBVCwOoMnGEydc+/pXr9JMLUDLf0PaFRTayMkBjh1z7clKIwhSgF67NlCvnrLn14hhw4DOnQEfH/e8/i+/SO2Y3rKT7Fehkrv8pgCnrHkOQQA++EB6/PrrqnWFMaY8DtCZSxROE5w8GQgMBB5+mG7gL1sG3H23Gj1znE6nQ1BQEIKCgqBzx7QKY0yTHn9caou7GbnK+vXS+NinD2yDJKXXoZ8/T6nWAM2eOznO8RhZOpNJmkFv0ABoM+Ae6ZNqzKDv2ye1779f+fOzstmyBTh8mNoPPCDdRWSaxeMjcyU33T9mFcW//1Iwfu+9wLhx0vM1a1JdmgYN1OubswwGAzp37qx2NxhjCuvbl5bfABSgT5jguteWp7f36QMgs5X0xMGDlF6klHKmt/MYWbrKleln6Icf6Ka0vmF92p7kyhUK0AXBPXn1xcnNld7zxo2Bu+5S5rys/D78UGrz7LlH4PGRuRLPoLMyuXGD/mY0bUrLpGbNAq5ftz3Gk4JzxljF1aiRFK/u3083Hl0hJwf44w9q16gBdOgA28BYPruphAq+/lzu2jXgk08oy2vJEte9rtFIN2KWLaOtRKHTAW3a0Cdv3QLOnHHdyUpz9CgVGgOAtm2VOy8rn3//le7sNWxom+LDGKsQOEBnTsnMBGbPBsLCaHmUWOPIaKSthBhjzBP16ye1XZXmvnGjtOV4r15UiBl33UWzmQAFzEoWiuMA3ercOeCVV+gGynffuflk8tRyJdPc9+6V2hyge46FC6V1MS++6L5iCYwxzeIAnTnEYqFZhvBwYOJE6aKzcmVg0iSqzN6li7p9LC+LxYItW7Zgy5YtsFgsaneHMaagvn2ltququX/9tdQeNEj2CXE96Z07wF9/ueZkjhAD9OrVgdBQp7/cm8bI1q2BJk2onZDg5h3QxBl0QNlCcfIMjXbtlDsvK7usLOCrr6htNALPPaduf5jDvGl8ZOrjAJ2VasMG2j712WeBixfpOb2e/m6cPAm88w4VhPN0giAgKysLWVlZENyxOS5jTLPCw6mWBkBV18+fL9/r3b4tVfOuXRuIiZF9skMHqb17d/lO5Kjz54HLl6ldhgJxgHeNkTodVXMHaLLSFbPo8+fT65hMhT6h1gy6GKDr9VzB3VOsWgXcvEntAQOAWrXU7Q9zmDeNj0x9HKCzUu3YQUvZRI88QsVFv/wSqF9fvX4xxpgriWnuen35l4cHBlI17+eeA154AfD1lX1SXpFZ3IPN3XbulNoPPKDMOTVu6FCp/fXXRXcjcUZ6OvC//9FrtmhR6LXq1QPq1qX2/v3lO5GjMjNpo3eAOuTv7/5zsvIRBCqMIBo9Wr2+MMZUxQE6K9Wbb1JV9vbtga1baVaoeXO1e8UYY641YAAwfjxw+jTwxBPley29nvba/vLLgmJhclFRlL4KKBeg79oltTt2VOacGhcaCnTtSu2UlPJNbn/7LcXEABWJK5KgIKa5375Na8Lc7eBBWpsGcHq7p9i7V1qGcv/9/L4xVoFxgM6srl4FXn4ZmDbN9vnAQLqG3LWLLjgZY8wbhYdTEcyQEDefyM9PSjk+cUJKaXUneYAuT7Gv4MQ0d8C2ZoAzCk98vvhiMQfJi7QpsaxBngLCBeI8w6JFUvvFF5Xbjo8xpjkcoDNkZAAzZlBh4U8/Bd59V1prLgoL478VjDHmMvIgWV5t2x2ysqSZuWbNqEgcA0DLGipVovbKldKuZM5ISpJ2MYmOpgSJIjp1ktrbtzt/EmdxBXfPYjLR+nOAZkUGDFC3P4wxVXGAXoHl5QFffAHccw+tnTOb6Xm93nY3HsYYq4hyc2ltsTPS0yk79YsvgOzsEg5Uch36/v004AOc3l5IYKC0zfSNG8DSpc6/xqefSm27y4bbty/YZw/KBuh+fkBkpPvPx8rnu++kNRJPPcU1Axir4DhAr4AEAfjxR6BlS2DUKCA1lZ43GCir6p9/qBBcRaPT6RAQEICAgADoOF2AsQrr1i1aNx4aCsya5dzXLlxI8fCoUVS/wy4lA3QXFYjz1jEyLo7+9fWVCt076sIF+nsKAHXq2G7XZ8PfX1rWcPSoe5c1XL4srXNv06ZQhUKmOYJAd/REzz+vXl9YmXnr+MjU4aN2B5iydu0C3njD9noNoIJIs2YBTZuq0y8tMBgM6Natm9rdYIypLCeHto/MzaUib+PGAdWqlf51GRnAvHnU1ulKKcLcqBFV37x+nQJ0QXDfOiL5+vNyBOjeOka2aUOz4H36AHff7dzXfvihVIvt+eel2n/F6tRJqkS3cyed0B22bpXaYhU8pl179wJ//UXtDh2k/R6ZR/HW8ZGpg2fQK5itW22D8+ho2kZtzZqKHZwzxpioTh1g4EBq37gBTJ3q2Nd98QVw7Rq1Bw4sZUzV6aR16DdvUrE4dxAEKUAPCgIiItxzHg/30kvOB+fHj1OADlBg/sILpXyBfB36jh3OncwZ8gC9Sxf3nYe5hrw4HM+eM8bAAXqF8+qrQIMGVCfop5+Abdt4SSJjjBU2cyZQpQq1P/lEmuCyx2SiApsAxd6TJjlwEnnAlphYlm6W7t9/gStXqN2hAxUZYS5x5Ig0Y/7WW0D9+qV8QXS01HbnOvSkJPpXr7c9J9MesxlYvZraVasC/fur2x/GmCbwX2ovlZ5Ohd8mTLB9vnJlYMsW4PBh4NFHuTK7nMViQWJiIhITE2ERcxYZYxVSw4bA5MnUzs+ndHVBKP5YQQCeeUaKg/v2BVq0cOAk3btL7YSEcvXXLheltwMVZ4xMSwOeflqqzG5P3740iz56dNG/tcUKDqbtUgBKay5LyfjSXL9Oa9wBoHVrCvqYdv3wA62NAYBBg7g4nAerKOMjUwYH6F4mJ4dmexo3pq3T5s+XasWIwsMBH64+UIQgCDCbzTCbzRDsXYkzxiqMsWOBJk2ovX27NENe2IcfAmvXUrtaNeC99xw8gTyASkiwfwegPMTZVKDc6VIVYYw8fZqq8H/9NW3BJu5uYk/9+vQ3V8y2KJWYNZGTQ9UEXU0+M8/rz7VvyRKp/cwz6vWDlVtFGB+ZcjhA9xKCAHz/PdC8OfDKK9I6SMC9S90YY8xb+fkBH30kPR4/ntajy6+9fvrJtlr7119T9XeH+PhIQdTVq6VP2TpLEIBNm6htNHK6swOCg6V90Y8dA4YNo6r+ouPHaYa9zNy9H7r8hgyvP9e2kydpnSFAtSHatVO3P4wxzeAA3QskJtKOPQMG2M6W9+8vXWAwxhhz3sMPUzaSaM4ciqVF169LW4y/9VYZtqiUp7nHx5e5n8U6fRo4c4ba0dFOTPNWXFWqUNaxmNjw44+URTF5MvDcc5SE8MgjQFZWGU8gD9DF4MyVxAJxOh3QubPrX5+5zrJlUvuZZ3jNIWPMigN0D3b0KO3S0r07sG+f9Hy3brS8bfVqabkbY4yxspk8GfjgA2q3bElV3kUjRgBRUcB//0uF5Zz24INS29Xr0MXZcwB46CHXvrYXCw8HvvuOarYAVMl/5kzgq6+o4P7WrVTjpUyaNpV+gBITgexsV3SZmExAcjK1IyOB6tVd99rMtSwWYPlyahsMwFNPqdsfxpimcIDuwZKSgN9+kx63bAmsW0eTMG3bqtcvxhjzNmPGAN98UzTONRgoDv7ppzLW9rj3XqBGDWonJlJFOlfhAL3MHnmE0tmHDLF9XqcDnngCmDKljC+s0wGxsdTOyHBtmvuOHdLPD6e3a9vmzcDFi9T+z39s7/oxxio8DtA92MiRlHrXoAHVGUlOpnGes6QYY8z1hg6lFPfCatUqx7ir10vr0G/dAg4dKnP/bFgsUsp89erAffe55nUrkIYNgW+/pS32vvkG2L2bdkhZswYIDCzHC/fqJbXXry93P602bJDa3bq57nWZ633zjdQePly1bjDGtIkDdA+QnU3plfJCRADg6wv88gtw4gSlWRoMqnTPa+h0OlSuXBmVK1eGju9yMMaU4o409/37gdu3qd2jh0v+QFTUMTIykm7OtG/vol2wHnpI2o9eHlSXhyBQCh1AqRw9e7rmdZnrpadTcQOAbp717q1uf5hLVNTxkbmHogF6cnIyJk6ciNjYWNSqVQs6nQ7dHLjL+91336Fdu3bw9/dH9erV0adPHxw4cMD9HVZZfj6wYgXQrBnw+uvA++8DR47YHtOsmbROjpWPwWBAjx490KNHDxj4bgdjTCnyQnGuCtjckN7OY6SL3HWXVLH76FHg/Pnyv+bffwP//kvtLl2AoKDyvyZzj7VrgcxMag8YQNtFMI/H4yNzJUUD9J9++gmzZ89GYmIigoODHfqamTNnYujQobh69SpGjRqFJ598Elu3bkXHjh2xw4v3D9uyhdaRDxkiFeHNz7e95mKMMeYFmjcHQkKonZBgu69XWW3eLLV5NlV7Hn5Yarvipsyvv0ptp7cSYIqSp7dzcTjGWDEUDdCffPJJ7N+/H2azGZsciDRPnjyJadOmITw8HIcOHcL8+fOxaNEibC3YRmTkyJHId2VBHQ04dIj+bvfsCciTBB56iB6//rp6fWOMMeYGOh3w+OPUzsuzrf5ZFiYTFQwDgLAw+mDaIl+H7ooAXUxvBzhA17ILF6TaEI0bAw88oG5/GGOapGiA3qJFC7Ru3Rq+vr4OHb906VLk5eVh0qRJCJKla7Vq1QqDBg3CsWPHsN2VFVBVdPYs7Vd+333AH39Iz7dqRY83buQaP+5msViwbds2bNu2DRaLRe3uMMYqkieekNpr15bvtX76CcjNpXafPuV7LRkeI12oTRtKdQco20F8v8ri+nVg1y5qN2vG+6tq2YoVVC8AoNlzXqvsNXh8ZK6k6SJxiYmJAICYmJgin4st2KYkKSmpxNfIzs5GWlqazYcWJSVR1pM4boeE0OP9+4Fivn3mBoIgwGQywWQyQRDfCMYYU0LHjlQOHqAZVXGNalmsXi21BwwoX79keIx0IYNB+uOelkYXAWW1fr20vRrPnmvbt99K7aFD1esHczkeH5kraTpAP3nyJAICAopdr96kSRPrMSWZPXs2goKCrB8NGzZ0S1/La8gQ2g63enVg/nzaf3XoUKnQK2OMMS9mMACPPUbtrCzbVCpn3LghFStp2BDo0MEl3WNuIL7fgG3g5ixef+4Zjh4FDh+mdocOnOnAGLNL0+GfyWSySW2XCyzYhNRkMpX4GhMmTLDe0TKZTDjvimqp5WCxAMuXA6+9Zvu8wQCsXAmcOgWMHctFPRljrMIR16ED0jZMzlq7ltaxA0D//nyXV8seeUSqtr5mDZCR4fxrmM3SXurVq/OaZi1buVJqDxqkXj8YY5rn4+wXxMXFITs72+Hjx4wZY53tVoOfnx/8NBDtCgJlLY4fD/z1Fz03eLC00wpAhXwZY4xVUA8+CAQGUsrzr78COTmA0ejca8jT2wcOdG3/mGtVrkw3Ub78kgLtn36idDpnrFpFXwsA/frRHuhMewRBCtD1enrfGWPMDqdH8i+++AIZTtzl7devX5kD9KCgILsz5OJacnsz7Fqyfz/w1ltS4U7RL7/YBuiMMcYqMD8/Kuq2YgVw+zYFbM5cyF+5Qtu0AVS5vU0bd/SSudKwYRSgA8DXXzsfoItfCwDPP++6fjHX2rcPOH2a2t27Aw5uNcwYq5iczn0zm80QBMHhj27dupW5c02aNIHZbEZqamqRz4lrz9WcnS/N6dOUxXT//bbBedu29Pidd9TrG2OMMQ165hmp/eGHzn3t6tVSsbABA7hCtCeIjgYaNaL25s3ApUuOf+2hQ8DevdRu1YpvyGgZp7czxpyg6cVpXbt2BQBs3LixyOf+KCigIx6jJdev0xrzZs0o+0wUFkbXT3v20A1Upj1GoxFGZ1NKGWPMVR58EGjRgto7dwJ//unY1+XlAQsWSI/dFATwGOliOh1ttwXQzZUVKxz/2sKz53xDRpssFmnpia+v7ZaKzKvw+MhcRdMB+ogRI+Dj44OZM2fapLonJydj5cqViIiIQKdOnVTsYfG2baOJD3Fb05o1gY8+Ao4do2xF/huqTT4+PoiJiUFMTAx8eB0fY0wNOh3w6qvS448+cuzrVq0CzpyhdmwsEBnp8q7xGOkmYoAOAJ98AjhS5yczU6r8XqUKFbVh2rRtG3D5MrV79aJifszr8PjIXEnRAD0lJQXDhw/H8OHDMWbMmCLPDR8+3Ob48PBwTJs2DSdOnEBUVBTi4uLw/PPPo0uXLgCAL7/8EnoNVqh97DHa0rZyZWDSJKrM/sorztf6YYwxVgENHQrUqEHtVauAYpZ52cjPB2bPlh5PnOi+vjHXu+ceCtwA4OxZ4IsvSv+a5csBceJiwACpGrwHyM3NxZo1a/D0008jIiICAQEBqFq1Ktq3b4+FCxfCYrHY/drvvvsO7dq1g7+/P6pXr44+ffrgwIEDdo/ft28fevfujWrVqsHf3x8dOnTA999/745vy77/+z+pzYUbGWMO0AmCICh1ssTERHQvJbe7uO589913+OCDD3D06FEYjUZER0djxowZaN26tdN9SEtLsxafE7dqKytBANato2VjhZcKHjtGfy/r1SvXKRhjGuPKMURrvPl78zjjxwNz50pteQBe2M8/S3tqR0fTjB2nanmWgwcB8ZqmVi26s1+1avHH3rgBhIcDN2/S4z17NFNx1pExJCUlxRqY9+jRA02bNoXJZMKvv/6KS5cuoU+fPvjll1+gK/QzPHPmTEyePBkhISHo27cv0tPTsWrVKuTk5GDLli2Ijo62OT4hIQGxsbGoVKkSBg4ciKpVq2LNmjU4e/Ys5s2bh7i4OJd/b0VYLED9+lTA0c8PuHbN/vvKGPN6Do8jQgVjMpkEAILJZCrX6+zaJQidOwsChemCEB/vog4y1eTl5Qk7duwQduzYIeTl5andHaZR5R1DDh48KEyYMEGIiYkRatasKQAQunbtWub+7N27V+jVq5cQFBQkVKlSRWjfvr2wevXqMr2Wq8ZH5gLnzgmCwUB/YHx8BOHPP4s/LidHENq0kf4Y/fab27rEY6SbDRwovY9vv23/uOefl44bPFi5/jnAkTHkwoULwqeffiqYzWab581ms3D//fcLAITvv//e5nMnTpwQfHx8hPDwcOH27dvW5w8ePCj4+fkJERERgsVisT6fm5srNG7cWPDz8xMOHjxoff727dtCeHi4YDQahTNnzrj8eysiIUF6rx5/3KnzMc/C4yNzhKPjiPbywzXuxAnaavSBB2iSQiQvBsc8kyAIuHnzJm7evFlsJgdjrvDTTz9h9uzZSExMRHA5t9pJSEhAdHQ0tm/fjv79+2PUqFFITU3FgAEDMH/+fBf1mKmiYUOaOQeoANxTTwFZWUWPe+MN2ssTAKKipFRpN+Ax0s1mzJD2MX/vPZpFL2zfPqk4XEAAHedh6tevj5deegn+/v42z/v7+2Ps2LEAgKSkJJvPLV26FHl5eZg0aZLN9rqtWrXCoEGDcOzYMWzfvt36fHx8PE6dOoXBgwejVatW1ueDgoIwceJE5OTkYPny5W747gqRp7c/+aT7z8dUw+MjcyUO0B105QowejQV112zRno+PJwef/65en1jjHmOJ598Evv374fZbMamTZvK/Dp5eXkYOXIk9Ho9tm7dikWLFmH+/Pk4dOgQwsPDMXHiRJw9e9aFPWeK+9//gPvuo/axY8C4cTQXJ1qyRCoi5+sLfPYZp7Z7snvuAZ57jtrp6UC3brZB+okTVJ9A/BmYPt3r1tH5+voCQJEiW4mJiQCAmJiYIl8TGxsLwDaod/Z4t7BYpAtGPz+gTx/3no8x5jU4QC+F2Ux/A++5h6598vLo+Tp16PGRI7RjBl8TMcYc0aJFC7Ru3dp6IVpWmpkhYu5jNFKlbj8/evzxx7TGfNUqumP84ovSsQsXUnVS5tlmzgRatqT2hQu0J+vHH1N19/vvpyAdoNmCV15Rr59usmTJEgBFA+uTJ08iICCg2KyjJk2aWI+RHy//nFxwcDACAgJsji9OdnY20tLSbD6csn07ze4AQO/evPacMeYw3gegFLt3A9OmSY/9/YE33wTi4ii7jDHG1OCKGaLs7Gxky7Z0cvoClLlf8+bA/PnAyy/T41276EPu5ZeBZ59Vvm/M9WrUALZsocD877+B8+dtt90DKDj/+WfKmvAiixYtwvr16/Hggw+id+/eNp8zmUyoXbt2sV8nFlqSb8crtoPsVLcPDAy0Ob44s2fPxvTp0x3ufxHyavGc3s4YcwIH6KXo2RN46CEgIQF4/nlgyhSgnMtGGWOs3FwxQ1TuC1CmjNGjgbAwujN87Jj0fKVKwDPPAO+/r17fmOvVrg3Ex9PFx+HDtp8bMABYvFgTMwRxcXE2N/gAICcnBwDwxhtvwFhob9kxY8YUO14BwLp16/Dyyy8jJCQE34r7u6tswoQJ1jXxAN3AbNiwoWNfzOntjLFy4ADdAZ98Qinsdv6uMMaY4lwxQ1SuC1CmrF69KGBbupRSu3r2pIt+Tpv1TnXqAAcOUDXas2eBS5eoCGDv3ppZU/fFF18gIyOj2M99KRayk+nXr1+xAfrvv/+Ofv36oU6dOoiPj0fdunWLHCNuS1QcMfNHPhaK7ZK+pnr16sV+TuTn5wc/cXmJs/LzgXffpSJx/v78e8oYcwoH6A4ID1e7B0wpBoNB7S4wD1HcDJE9Jc0cqalcF6BMeT4+wMiR9KESHiMV5ONDqe4aZTabizzn7F7hv/32G/r27YuaNWsiISEBYWFhxR7XpEkT7Nq1C6mpqUXWoReXTSRfl96mTRub41NTU2E2m9HOnXvH+/oCw4bRB1f0rjB4fGSuwgE6YwV8fHzQy41bFDHvUtwMkT32Zo7KwxUzRIw5g8dI5kpicF6jRg0kJCTgnnvusXts165dsWvXLmzcuBHDhg2z+dwff/xhPUZ+/OzZs7Fx40YMHDiw1OPdSiMZD8y9eHxkrsRV3BljrAxMJhMEQXDoo1u3bi4/f3GVi0XiDJEWZ+0ZY2z9+vXo27cvqlevjoSEhFLHqhEjRsDHxwczZ860uSmZnJyMlStXIiIiAp06dbI+36NHD4SFhWHFihVITk62Pm8ymTBr1iwYjcYigT5jjGkFz6AzxpgH0tQMEWOMOSglJQWPP/44srOz0a1bN6xcubLIMaGhoRg+fLj1cXh4OKZNm4bJkycjKioKffv2RXp6OlatWgWAMpr0emnOycfHB4sXL0ZsbCy6dOmCgQMHomrVqlizZg3Onj2LefPmITQ01N3fKmOMlQkH6IwVsFgs2L9/PwCgTZs2vJaIaUJubi5OnToFX19fNG7c2Pq8fIbo1Vdfte6FzjNEzF14jGSukJqaaq3+LgbYhXXt2tUmQAeASZMmITQ0FB988AEWLlwIo9GIzp07Y8aMGWjdunWR1+jevTu2b9+OqVOnYvXq1cjNzUVkZCTmzp2LAQMGuPz7YhUbj4/MlThAZ6yAIAi4evWqtc2YO6SkpGDOnDkAgKysLOtz8ovRZcuWWdsXL15EREQEQkJCcObMGevzPEPElMZjJHOFbt26lfnnZ8iQIRgyZIjDx7dr1w7r168v07kYcwaPj8yVOEBnjDEFpaamYvny5TbPXblyxeY5eYBeEp4hYowxxhjzLhygM8aYgpydPQoNDS3xeJ4hYowxxhjzHlzFnTHGGGOMMcYY0wAO0BljjDHGGGOMMQ3gAJ0xxhhjjDHGGNOACrcGXVzLmZaWpnJPmNbk5eUhMzMTAP18+PhUuF8P5gBx7PDGKq08PrKS8BjJSsPjI6uoeHxkjnB0jKxwPz3p6ekAgIYNG6rcE8aYJ0tPT0dQUJDa3XApHh8ZY67A4yNjjNlX2hipE7zxNmcJ8vPzcenSJVStWhU6nU7t7lilpaWhYcOGOH/+PAIDA9XuToXF74N2aPW9EAQB6enpqFevHvR671olxOMjKw2/F9qhxfeCx0flafHnoKLi90I7tPpeODpGVrgZdL1ejwYNGqjdDbsCAwM19YNUUfH7oB1afC+8bWZIxOMjcxS/F9qhtfeCx0d1aO3noCLj90I7tPheODJGetftTcYYY4wxxhhjzENxgM4YY4wxxhhjjGkAB+ga4efnh6lTp8LPz0/trlRo/D5oB78XTMQ/C9rB74V28HvBAP450BJ+L7TD09+LClckjjHGGGOMMcYY0yKeQWeMMcYYY4wxxjSAA3TGGGOMMcYYY0wDOEBnjDHGGGOMMcY0gAN0xhhjjDHGGGNMAzhAZ4wxxhhjjDHGNIADdA2aNm0adDqd3Y8zZ86o3UWvtG/fPvTu3RvVqlWDv78/OnTogO+//17tblU4oaGhdn/2u3Xrpnb3mMp4fFQHj4/awOMjKw2Pkcrj8VEbvGl89FG7A8y+p59+GqGhoUWer1atmuJ98XYJCQmIjY1FpUqVMHDgQFStWhVr1qzBgAEDcP78ecTFxandxQolKCgIr732WpHni/t9YBUTj4/K4fFRW3h8ZI7gMVIZPD5qi7eMj7wPugZNmzYN06dPR0JCgsfd8fFEeXl5aNasGS5cuIDdu3ejVatWAACTyYR27drhzJkzOHHiBEJCQtTtaAUhDqJ8l58Vh8dHZfH4qC08PrLS8BipHB4ftcWbxkdOcWcVXnx8PE6dOoXBgwdbB1eA7sJNnDgROTk5WL58uXodZIwxlfD4yBhjxePxkbkLp7hr2NatW7Fnzx7o9Xo0adIEPXv2REBAgNrd8jqJiYkAgJiYmCKfi42NBQAkJSUp2aUKLzs7G8uWLcOlS5cQGBiItm3bon379mp3i2kIj4/K4PFRe3h8ZI7gMdL9eHzUHm8ZHzlA17CpU6faPK5WrRo+/PBDDBs2TKUeeaeTJ08CAJo0aVLkc8HBwQgICLAew5SRmpqKESNG2DzXtm1brFy5Eo0bN1apV0xLeHxUBo+P2sPjI3MEj5Hux+Oj9njL+Mgp7hoUFRWFJUuW4PTp08jKysK///6Ljz/+GDqdDsOHD8cvv/yidhe9islkAkApScUJDAy0HsPcb8SIEdiyZQuuXLmCjIwMHDx4EE899RT27duHHj16ID09Xe0uMhXx+KgsHh+1hcdHVhoeI5XD46O2eNP4yEXi3CQuLg7Z2dkOHz9mzJhi78DJbdmyBQ899BBatmyJv/76q7xdZAViYmKwadMmnDx5Evfcc0+Rz9evXx9ms5kHWZUNGzYM33zzDebPn4+xY8eq3R1WDjw+eg4eHz0Dj4/ehcdIz8Djo2fwxPGRU9zd5IsvvkBGRobDx/fr16/UwbVHjx5o3LgxDh8+jLS0NAQGBpa3mwzSnU97A2haWhqqV6+uZJdYMV544QV888032LFjh8cMsKx4PD56Dh4fPQOPj96Fx0jPwOOjZ/DE8ZFT3N3EbDZDEASHPxzdCqNmzZoAgMzMTDf2vmIR/6gVt04oNTUVZrO51D98zP3En31nLlqYNvH46Dl4fPQMPD56Fx4jPQOPj57BE8dHDtA9SEZGBo4ePQp/f3/rDxsrv65duwIANm7cWORzf/zxh80xTD179uwBIO1zyZgcj4/uweOjZ+DxkZWGx0jX4/HRM3ji+MgBusakp6fjxIkTRZ7PysrCyJEjkZ6ejv79+8PHh1cnuEqPHj0QFhaGFStWIDk52fq8yWTCrFmzYDQaueqpQlJSUoq9s5+SkoJx48YBAAYPHqx0t5hG8PioPB4ftYPHR1YaHiOVxeOjdnjb+Mi/oRpz48YNNGvWDG3btkVERASCg4Nx5coVbN68GRcuXEBkZCTee+89tbvpVXx8fLB48WLExsaiS5cuGDhwIKpWrYo1a9bg7NmzmDdvnkfddfNkq1atwvvvv48uXbogJCQE/v7+OHHiBH7//Xfk5uZiwoQJ6NKli9rdZCrh8VF5PD5qB4+PrDQ8RiqLx0ft8Lbxkau4a0xaWhomTpyIvXv34syZM7h16xYqV66MiIgI9OvXDy+//DIqV66sdje90t69ezF16lTs3LkTubm5iIyMxNixYzFgwAC1u1ZhJCUl4bPPPsPBgwdx5coVZGZmombNmmjfvj1eeuklxMTEqN1FpiIeH9XD46P6eHxkpeExUh08PqrP28ZHDtAZY4wxxhhjjDEN4DXojDHGGGOMMcaYBnCAzhhjjDHGGGOMaQAH6IwxxhhjjDHGmAZwgM4YY4wxxhhjjGkAB+iMMcYYY4wxxpgGcIDOGGOMMcYYY4xpAAfojDHGGGOMMcaYBnCAzhhjjDHGGGOMaQAH6IwxxhhjjDHGmAZwgM4YY4wxxhhjjGkAB+iMMcYYY4wxxpgGcIDOGGOMMcYYY4xpwP8DZI5yDjrnXM4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.misc import derivative as df\n",
    "\n",
    "print(f\"{color.RED}f1{color.OFF}\")\n",
    "print(df(f1,3,dx=1))\n",
    "print(df(f1,0,dx=1))\n",
    "print(df(f1,-3,dx=1))\n",
    "print(f\"{color.RED}f2{color.OFF}\")\n",
    "print(df(f2,3,dx=1))\n",
    "print(df(f2,0,dx=1))\n",
    "print(df(f2,-3,dx=1))\n",
    "print(f\"{color.RED}f3{color.OFF}\")\n",
    "print(df(f3,3,dx=1))\n",
    "print(df(f3,0,dx=1))\n",
    "print(df(f3,-3,dx=1))\n",
    "\n",
    "xmin = -2*np.pi\n",
    "xmax = 2*np.pi\n",
    "npt = 100\n",
    "# génération de npt points équirépartis entre xmin et xmax\n",
    "x = np.linspace(xmin,xmax,npt)\n",
    "\n",
    "plt.rcParams.update({'font.size': 14})\n",
    "mosaic = [[f1,f2,f3]]\n",
    "fig, graph = plt.subplot_mosaic(mosaic, constrained_layout=False,figsize=(12,4),sharex=False,sharey=False)\n",
    "\n",
    "graph[f1].plot(x, f1(x),linewidth=2,color='red',label=\"f(x)\")\n",
    "graph[f1].plot(x,df(f1,x,dx=1),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
    "graph[f1].set_title(\"$f_1(x)=x^2$\", fontsize=14, color=\"black\")\n",
    "graph[f1].axvline(x = 0, color = '0.7',linestyle='--')\n",
    "graph[f1].axhline(y = 0, color = '0.7',linestyle='--')\n",
    "graph[f1].legend()\n",
    "\n",
    "graph[f2].plot(x, f2(x),linewidth=2,color='red',label=\"f(x)\")\n",
    "graph[f2].plot(x,df(f2,x,dx=1),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
    "graph[f2].set_title(\"$f_2(x)=\\sin(x)$\", fontsize=14, color=\"black\")\n",
    "graph[f2].axvline(x = 0, color = '0.7',linestyle='--')\n",
    "graph[f2].axhline(y = 0, color = '0.7',linestyle='--')\n",
    "graph[f2].legend()\n",
    "\n",
    "graph[f3].plot(x, f3(x),linewidth=2,color='red',label=\"f(x)\")\n",
    "graph[f3].plot(x,df(f3,x,dx=1),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
    "graph[f3].set_title(\"$f_3(x)=x^3+x^2-x-2$\", fontsize=14, color=\"black\")\n",
    "graph[f3].axvline(x = 0, color = '0.7',linestyle='--')\n",
    "graph[f3].axhline(y = 0, color = '0.7',linestyle='--')\n",
    "graph[f3].legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bca9ed95-1ff7-48d2-8df3-0283ff18d059",
   "metadata": {
    "tags": []
   },
   "source": [
    "### **2.2.** Fonction dérivée (calcul symbolique)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2150ca98-d0b8-4494-b8d4-80dd48dc1857",
   "metadata": {},
   "source": [
    "Le symbole est la classe la plus importante de la bibliothèque `SymPy`. Comme mentionné précédemment, les calculs symboliques sont effectués avec des symboles. Les variables `SymPy` sont des objets de la classe `Symbol`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5877021a-bfb2-41ed-be02-9948fdeeb8c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[91mf1\u001b[0m\n",
      "df1/dx =  2*x\n"
     ]
    }
   ],
   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "\n",
    "x = sym.Symbol('x')\n",
    "df1dx = f1(x).diff(x)\n",
    "df3dx = f3(x).diff(x)\n",
    "def f2b(x):\n",
    "    return sym.sin(x)\n",
    "df2dx = f2b(x).diff(x)\n",
    "\n",
    "print(f\"{color.RED}f1{color.OFF}\")\n",
    "print(\"df1/dx = \",df1dx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a17bcc59-48d5-4c77-9ac6-0d086ee75e8c",
   "metadata": {},
   "source": [
    "`df1dx` est un objet au format `SymPy`, qui permet de faire du calcul symbolique. Il n'est pas donc possible de directement utiliser cette fonction `SymPy` comme une fonction classique. La preuve avec l'exécution ci-dessous, qui va conduire à une erreur :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "05e84337-2c81-42a0-be5f-e6cd510cf1d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'sympy.core.mul.Mul'>\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'Mul' object is not callable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[6], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;28mtype\u001b[39m(df1dx))\n\u001b[0;32m----> 2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[43mdf1dx\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m)\u001b[49m)\n",
      "\u001b[0;31mTypeError\u001b[0m: 'Mul' object is not callable"
     ]
    }
   ],
   "source": [
    "print(type(df1dx))\n",
    "print(df1dx(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ebbd9fa-d81e-43e5-88f7-99b99ecd1034",
   "metadata": {},
   "source": [
    "On peut quand même faire des applications numériques d'une fonction `SymPy`, grâce à la fonction `subs`. Par exemple : `df1dx.subs(x,2)` renvoie la valeur de `df1dx` après avoir substitué x par le nombre 2. C'est ce qu'on fait systématiquement ci-dessous :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3b1734c5-4fb4-41d6-b4bf-05aa674d96aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(f\"{color.RED}f1{color.OFF}\")\n",
    "print(\"df1/dx = \",df1dx)\n",
    "print(\"df1/dx for x=2 : \",df1dx.subs(x,2))\n",
    "print(f\"{color.RED}f2{color.OFF}\")\n",
    "print(\"df2/dx = \",df2dx)\n",
    "print(\"df2/dx for x=2 : \",df2dx.subs(x,2))\n",
    "print(f\"{color.RED}f3{color.OFF}\")\n",
    "print(\"df3/dx = \",df3dx)\n",
    "print(\"df3/dx for x=2 : \",df3dx.subs(x,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f44bf72-ce73-4433-a6f9-fcdc540c10c3",
   "metadata": {},
   "source": [
    "Ce n'est pas toujours pratique d'utiliser la commande `subs`, en particulier si on veut tracer la fonction ou bien faire de nombreux calculs numériques. Heureusement, `SymPy` fournit une fonction, `lambdify`, qui crée une fonction classique à partir d'un objet symbolique.\n",
    "\n",
    "`lambdify` transforme une expression symbolique `SymPy` en fonction qui peut être utilisée pour calculer des valeurs numériques très rapidement\n",
    "\n",
    "(dans le monde python, cette fonction qui diffère d'une fonction définie par `def` est appelée fonction `lambda`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f358f2e-4a8f-45ce-89ff-ceb36cb5a499",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import lambdify\n",
    "df1num = lambdify(x, df1dx)\n",
    "df2num = lambdify(x, df2dx)\n",
    "df3num = lambdify(x, df3dx)\n",
    "print(df1num)\n",
    "print(df1num(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "65fc16a7-ab91-4031-a5de-fad3e0d727eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(df2num)\n",
    "print(df2num(np.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4f13cd9-28cc-4e16-a924-7e14252a5f8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "xmin = -2*np.pi\n",
    "xmax = 2*np.pi\n",
    "npt = 100\n",
    "# génération de npt points équirépartis entre xmin et xmax\n",
    "xx = np.linspace(xmin,xmax,npt)\n",
    "\n",
    "plt.rcParams.update({'font.size': 14})\n",
    "mosaic = [[f1,f2,f3]]\n",
    "fig, graph = plt.subplot_mosaic(mosaic, constrained_layout=False,figsize=(12,4),sharex=False,sharey=False)\n",
    "\n",
    "graph[f1].plot(xx, f1(xx),linewidth=2,color='red',label=\"f(x)\")\n",
    "graph[f1].plot(xx,df1num(xx),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
    "graph[f1].set_title(\"$f_1(x)=x^2$\", fontsize=14, color=\"black\")\n",
    "graph[f1].axvline(x = 0, color = '0.7',linestyle='--')\n",
    "graph[f1].axhline(y = 0, color = '0.7',linestyle='--')\n",
    "graph[f1].legend()\n",
    "\n",
    "graph[f2].plot(xx, f2(xx),linewidth=2,color='red',label=\"f(x)\")\n",
    "graph[f2].plot(xx,df2num(xx),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
    "graph[f2].set_title(\"$f_2(x)=\\sin(x)$\", fontsize=14, color=\"black\")\n",
    "graph[f2].axvline(x = 0, color = '0.7',linestyle='--')\n",
    "graph[f2].axhline(y = 0, color = '0.7',linestyle='--')\n",
    "graph[f2].legend()\n",
    "\n",
    "graph[f3].plot(xx, f3(xx),linewidth=2,color='red',label=\"f(x)\")\n",
    "graph[f3].plot(xx,df3num(xx),linewidth=2,color='blue',linestyle=\"--\",label=\"df(x)/dx\")\n",
    "graph[f3].set_title(\"$f_3(x)=x^3+x^2-x$\", fontsize=14, color=\"black\")\n",
    "graph[f3].axvline(x = 0, color = '0.7',linestyle='--')\n",
    "graph[f3].axhline(y = 0, color = '0.7',linestyle='--')\n",
    "graph[f3].legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "161f91d4-2532-47ec-828f-9415fdb96c76",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "\n",
    "def f4(a,n,x):\n",
    "    return a*x**n\n",
    "\n",
    "x = sym.Symbol('x')\n",
    "a = sym.Symbol('a')\n",
    "n = sym.Symbol('n')\n",
    "df4dx1 = f4(a,n,x).diff(x)\n",
    "df4dx2 = f4(a,n,x).diff(x,2)\n",
    "print(\"dérivée première de f4 :\", df4dx1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b612f17-b37a-4f0d-a78e-cfea462dc9d6",
   "metadata": {},
   "source": [
    "<div class=\"rq\">\n",
    "L'affichage de l'équation a*n*x**n/x n'est pas très lisible. Il est assez aisé de convertir une expression `SymPy` au format Latex, qui se prête bien à un un affiche élégant dans un notebook. La commande est simplement :\n",
    "    \n",
    "<br>\n",
    "\n",
    "```\n",
    "from IPython.display import display,Math\n",
    "import sympy as sym\n",
    "display(Math(sym.latex(expression_SymPy)))\n",
    "```\n",
    "    \n",
    "<br>\n",
    "\n",
    "Pour éviter de devoir systématiquement lancer la commande `display(Math(sym.latex(expression_SymPy)))`, cette fonctionalité a été implémentée en tant que fonction `PrintLatexStyleSymPyEquation` dans le fichier `tools4pyPhysChem.py`, disponible dans le sous-répertoire `config`. Il faut donc l'importer dans tout notebook où on veut l'utiliser, et lui donner un nom plus compact - par exemple `ple` comme Print Latex Equation. C'est ce qui est fait dans la cellule suivante. `?ple` permet de connaître son descriptif.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "261a4d7a-c28f-48d0-bda9-f9fb28774857",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "?ple"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acdc0731-4d8d-4580-b509-d7beb87ff12c",
   "metadata": {},
   "source": [
    "On va maintenant s'en servir pour afficher les dérivées première et seconde de la fonction $f_4(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a83a500d-fbb4-4f12-a8e4-c73bf0a0d6c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "ple(df4dx1)\n",
    "ple(sym.simplify(df4dx1))\n",
    "print()\n",
    "print()\n",
    "print(\"dérivée seconde de f4 :\",df4dx2)\n",
    "ple(df4dx2)\n",
    "ple(sym.simplify(df4dx2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a9f92de-7689-4783-8d45-4fa0ed1e8318",
   "metadata": {
    "tags": []
   },
   "source": [
    "## **3.** Intégrales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6d503cf-5f41-4ca4-ae0c-baf15238af01",
   "metadata": {},
   "outputs": [],
   "source": [
    "def g1(x):\n",
    "    return 2*x\n",
    "\n",
    "def g2(x):\n",
    "    return np.cos(x)\n",
    "\n",
    "def g3(x):\n",
    "    return 3*x**2+2*x-1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b1102d5-c06a-44e7-8f74-dc073877cbff",
   "metadata": {
    "tags": []
   },
   "source": [
    "### **3.1.** Intégration numérique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "153a23e9-3ddd-44f7-b6ba-00ef36e57874",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate as integrate\n",
    "\n",
    "Ig1=integrate.quad(g1,-3,3)\n",
    "Ig2=integrate.quad(g2,-np.pi,np.pi)\n",
    "Ig3=integrate.quad(g3,-3,3)\n",
    "print(\"intégration entre -3 et +3\")\n",
    "print(\"∫g1 dx = \",Ig1)\n",
    "print(\"∫g2 dx = \",Ig2)\n",
    "print(\"∫g3 dx = \",Ig3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8066e31c-27a8-44a0-9f10-186857f32331",
   "metadata": {
    "tags": []
   },
   "source": [
    "### **3.2.** Fonction intégrale (calcul symbolique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60262ae7-6072-4358-86ab-20b837a472c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "\n",
    "x = sym.Symbol('x')\n",
    "def g2b(x):\n",
    "    return sym.cos(x)\n",
    "\n",
    "Ig1 = g1(x).integrate(x)\n",
    "Ig2 = g2b(x).integrate(x)\n",
    "Ig3 = g3(x).integrate(x)\n",
    "print(\"∫g1 dx = \",Ig1)\n",
    "print(\"∫g2 dx = \",Ig2)\n",
    "print(\"∫g3 dx = \",Ig3)\n",
    "\n",
    "#\\n = saut de ligne\n",
    "print(\"\\nintégration entre -a et +a\")\n",
    "Ig1 = g1(x).integrate((x,-3,3))\n",
    "Ig2 = g2b(x).integrate((x,-np.pi,np.pi))\n",
    "Ig3 = g3(x).integrate((x,-3,3))\n",
    "print(\"∫g1 dx = \",Ig1)\n",
    "print(\"∫g2 dx = \",Ig2)\n",
    "print(\"∫g3 dx = \",Ig3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b52a79a-00c8-4b4f-a409-84d93771e8b7",
   "metadata": {
    "tags": []
   },
   "source": [
    "## **4.** Exercices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10bef792-7fbf-4a56-a68e-591191d1de0c",
   "metadata": {},
   "source": [
    "### **4.1.** Calcul numérique"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cd7f26a-0a5b-488c-a711-3c4533c6bf31",
   "metadata": {},
   "source": [
    "#### **1.** Pobabilité de présence radiale de l'électron 1s de H"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfae38af-41ea-4773-a0b8-79535d469e8f",
   "metadata": {},
   "source": [
    "La probabilité de présence radiale de l'électron 1s de l'atome d'hydrogène a pour expression :\n",
    "$$\\mathcal{P}_{1s}(r)=4r^{2}\\exp\\left(-2r\\right)$$\n",
    "\n",
    "où $r$ est exprimé en bohr\n",
    "(1 bohr = 5.29177210903 $\\times$ 10$^{-11}$ m)\n",
    "\n",
    "**1.** Implémenter puis tracer cette fonction ainsi que sa dérivée première dP/dr entre 0 bohr et 6 bohr.\n",
    "\n",
    "- Commenter la variation de $\\mathcal{P}_{1s}(r)$\n",
    "- Commenter la variation de $d\\mathcal{P}_{1s}(r)/dr$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f637b118-0d35-4602-ae85-a19025406470",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.misc import derivative as df\n",
    "import scipy.integrate as integrate\n",
    "import scipy.constants as sc\n",
    "\n",
    "print(sc.find(\"bohr\"))\n",
    "print(\"rayon de Bohr : \",sc.physical_constants[\"Bohr radius\"])\n",
    "a0 = sc.value(\"Bohr radius\")\n",
    "\n",
    "def P1s(r):\n",
    "    return 4*r**2*np.exp(-2*r)\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10,5)\n",
    "plt.rcParams.update({'font.size': 14})\n",
    "\n",
    "r = np.linspace(0.,6.,100) # r en bohr\n",
    "plt.plot(r, P1s(r),linewidth=2,color='red',label=\"P1s(r)\")\n",
    "plt.plot(r,df(P1s,r,dx=1e-12),linewidth=2,color='blue',linestyle=\"--\",label=\"dP1s(r)/dr\")\n",
    "plt.axvline(x = 0, color = '0.7',linestyle='--')\n",
    "plt.axhline(y = 0, color = '0.7',linestyle='--')\n",
    "plt.xlabel(\"bohr\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26e9a9af-30f1-4477-b4b1-433276a2e007",
   "metadata": {},
   "source": [
    "**2.** Calculer l'intégrale de la probabilité de présence radiale entre 0 et +$\\infty$. Commenter.\n",
    "\n",
    "NB. On a besoin ici d'une représentation numérique de l'infini. La bibliothèque `numpy` fournit pour cela `np.inf`  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "19e9dacb-d640-48fe-8b4d-8ed8d2e3f595",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate as integrate\n",
    "\n",
    "print(integrate.quad(P1s,0,np.inf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fee82a14-0012-4087-8e11-7a3fd719f875",
   "metadata": {},
   "source": [
    "**3.** Dans le cadre de la physique quantique, il est facile de montrer que la valeur moyenne $\\left\\langle r\\right\\rangle$ de la position de l'électron est donnée par l'intégrale :\n",
    "$$\\left\\langle r\\right\\rangle =\\int_{0}^{\\infty}r\\mathcal{P}_{1s}(r)dr$$\n",
    "\n",
    "- Calculer $\\left\\langle r\\right\\rangle$.\n",
    "- Reporter la valeur trouvée sur le graphe précédent en traçant une ligne verticale. La valeur obtenue vous semble-t-elle qualitativement correcte ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2afa74fb-7b2c-4096-8b42-125991bd62ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def frmoyen(r):\n",
    "    return r*P1s(r)\n",
    "print(integrate.quad(frmoyen,0,np.inf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0748b3e4-623b-4060-9ce4-7c465a3ee098",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (10,5)\n",
    "plt.rcParams.update({'font.size': 14})\n",
    "\n",
    "r = np.linspace(0.,6.,100) # r en bohr\n",
    "plt.plot(r, P1s(r),linewidth=2,color='red',label=\"P1s(r)\")\n",
    "plt.plot(r,df(P1s,r,dx=1e-12),linewidth=2,color='blue',linestyle=\"--\",label=\"dP1s(r)/dr\")\n",
    "plt.axvline(x = 0, color = '0.7',linestyle='--')\n",
    "plt.axvline(x = 1.5, color = 'blue',linestyle='-.',linewidth=1)\n",
    "plt.axhline(y = 0, color = '0.7',linestyle='--')\n",
    "plt.xlabel(\"bohr\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece989db-ae99-4856-9753-8a07732a81d4",
   "metadata": {},
   "source": [
    "### **4.2.** Calcul symbolique\n",
    "#### **1.** Dérivées identiques\n",
    "Donner l'expression de la dérivée en fonction de x de\n",
    "- $h_1(x)=2x^3 -x + 1$\n",
    "- $h_2(x)=2x^3 -x + 7$\n",
    "\n",
    "Comparer les deux dérivées.\n",
    "\n",
    "Donner, sans calcul, l'expression de l'intégrale de $6x^2-1$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6669d8b9-bda3-4a44-856c-401629c879ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "\n",
    "def h1(x):\n",
    "    return 2*x**3-x+1\n",
    "def h2(x):\n",
    "    return 2*x**3-x+7\n",
    "\n",
    "x = sym.Symbol('x')\n",
    "dh1dx = h1(x).diff(x)\n",
    "dh2dx = h2(x).diff(x)\n",
    "print(\"dh1/dx\",dh1dx)\n",
    "ple(dh1dx)\n",
    "print()\n",
    "print(\"dh2/dx = \",dh2dx)\n",
    "ple(dh2dx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36407158-f2fa-4d6d-90e2-8c063ee6d730",
   "metadata": {},
   "source": [
    "#### **2.** Dérivation d'une loi de cinétique chimique\n",
    "\n",
    "**2a.** Donner l'expression de la dérivée en fonction de t de :\n",
    "$$[\\mathrm{B}]_t=\\frac{k_{1}}{k_{2}-k_{1}}a_{0}\\left(\\mathrm{e}^{-k_{1}t}-\\mathrm{e}^{-k_{2}t}\\right)$$\n",
    "où $k_1$, $k_2$ et $a_0$ sont des constantes<br>\n",
    "($a_0$ ici est une concentration, à ne pas confondre donc avec le rayon de Bohr, également noté $a_0$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a07c6da-6208-428b-a377-3d502dd6137c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "from tools4pyPhysChem import PrintLatexStyleSymPyEquation as ple\n",
    "\n",
    "def b(k1,k2,a0,t):\n",
    "    return (k1/(k2-k1))*a0*(sym.exp(-k1*t) - sym.exp(-k2*t))\n",
    "\n",
    "t = sym.Symbol('t')\n",
    "k1 = sym.Symbol('k1')\n",
    "k2 = sym.Symbol('k2')\n",
    "a0 = sym.Symbol('a0')\n",
    "\n",
    "dbdt = b(k1,k2,a0,t).diff(t)\n",
    "print(\"db/dt = \",dbdt)\n",
    "ple(dbdt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3f5791d-1a2e-49e8-a8c9-1941492e86c5",
   "metadata": {},
   "source": [
    "**2b.** On va poser $k_1$ = 10, $k_2$ = 1, $a_0$ = 0,1.\n",
    "\n",
    "Tracer $[\\mathrm{B}]_t$ et $[\\mathrm{B}]_t'=d[\\mathrm{B}]_t/dt$ entre 0 et 5 et avec [-0.1 : 0.2] comme intervalle des ordonnées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69415040-40cc-41de-91e7-148a986fd3f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import lambdify\n",
    "\n",
    "#initialisation des variables. Ne pas écraser les variables symboliques k1, k2 et a0\n",
    "# -> on utilise les variables k1_, k2_ et a0_ pour leur équivalent numérique\n",
    "# convention perso. On aurait très bien pu les appeler titi, tata et toto\n",
    "k1_ = 10\n",
    "k2_ = 1\n",
    "a0_ = 0.1\n",
    "\n",
    "bnum = lambdify([k1,k2,a0,t], b(k1,k2,a0,t))\n",
    "dbnum = lambdify([k1,k2,a0,t], dbdt)\n",
    "xx = np.linspace(0.,5.,100)\n",
    "plt.plot(xx, bnum(k1_,k2_,a0_,xx),linewidth=2,color='red',label=\"b(t)\")\n",
    "plt.plot(xx,dbnum(k1_,k2_,a0_,xx),linewidth=2,color='blue',linestyle=\"--\",label=\"db(t)/dt\")\n",
    "plt.axvline(x = 0, color = '0.7',linestyle='--')\n",
    "plt.axhline(y = 0, color = '0.7',linestyle='--')\n",
    "plt.xlim(0,5)\n",
    "plt.ylim(-0.1,0.2)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9a84d89-53f6-4fd2-9d8f-c0ac7cb6b6ce",
   "metadata": {},
   "source": [
    "#### **3.** Résolution d'une égalité\n",
    "L'objectif est de trouver l'expression de $t$ pour laquelle la dérivée première s'annule, ce qui va nous donner le temps pour lequel la [B] est maximale.\n",
    "\n",
    "On va encore utiliser `SymPy` pour cela."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b278f3a6-eac2-4887-afad-343351de137b",
   "metadata": {},
   "outputs": [],
   "source": [
    "tmax = sym.solveset(sym.Eq(dbdt, 0), t)\n",
    "ple(tmax)\n",
    "# résultat renvoyé dans un dictionnaire. On va le convertir en liste\n",
    "# afin de récupérer le premier élement de la liste pour pouvoir travailler avec\n",
    "tmax1 = list(tmax)[0]\n",
    "ple(tmax1)\n",
    "# comme précédemment, il faut utiliser `lambdify` pour transformer la fonction analytique en une fonction python classique\n",
    "tmaxnum = lambdify([k1,k2],tmax1)\n",
    "print(f\"k1 = {k1_} et k2 = {k2_} --> tmax = {tmaxnum(k1_,k2_)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "898a0af5-6513-4be2-8538-0d741a4c4478",
   "metadata": {},
   "outputs": [],
   "source": [
    "vID.end(cwd0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e0e0f687-17f3-40b6-8ad1-9f06616a7cd4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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