{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "133e372e-98c8-43d7-9aa2-fef97b714f5c",
   "metadata": {},
   "source": [
    "# Physics-Informed Neural Network (PINN)\n",
    "**Marc BUFFAT** , dpt mécanique, Université Lyon 1\n",
    "\n",
    "\n",
    "![(C) Zhang et al 2026, Nature](images/PINNs.png)\n",
    "\n",
    "*(C) Zhang, P., Zhang, H., Zhou, J. et al., Sci Rep. 16, 12760,  2026 Nature*\n",
    "\n",
    "*Certains contenus ont été coconstruits avec l'appui d'un outil d’IA générative puis relus et validés par l'enseignant.* "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b312889a-3473-468f-af6b-61002b276efe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max threads : 4 / used threads 4\n",
      "Attention: no GPU available! using CPU\n",
      "cpu\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/buffat/venvs/jupyter/lib/python3.10/site-packages/torch/cuda/__init__.py:107: UserWarning: CUDA initialization: The NVIDIA driver on your system is too old (found version 9010). Please update your GPU driver by downloading and installing a new version from the URL: http://www.nvidia.com/Download/index.aspx Alternatively, go to: https://pytorch.org to install a PyTorch version that has been compiled with your version of the CUDA driver. (Triggered internally at ../c10/cuda/CUDAFunctions.cpp:109.)\n",
      "  return torch._C._cuda_getDeviceCount() > 0\n"
     ]
    }
   ],
   "source": [
    "from validation.libIA_GPU import Init_torchGPU\n",
    "\n",
    "try: cuda_dev\n",
    "except NameError: cuda_dev = Init_torchGPU(4, 0)\n",
    "if cuda_dev is None: cuda_dev = \"cpu\" \n",
    "print(cuda_dev)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27186d94-009d-4e18-abf1-64fd16cdb86e",
   "metadata": {},
   "source": [
    "Les **Physics-Informed Neural Networks (PINN)** forment une classe de méthodes qui consiste à entraîner un réseau de neurones non seulement sur des données, mais aussi sur les **lois physiques** décrites par des équations différentielles. L'idée a été popularisée par Maziar Raissi et ses collaborateurs en 2019 {cite:ts}`raissi2019`.\n",
    "\n",
    "**références**\n",
    "- http://neuralnetworksanddeeplearning.com/chap4.html\n",
    "- https://karpathy.github.io/2019/04/25/recipe/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f13f3ea5-3b9e-487e-b722-c742f92362f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "CUDA device:  cpu\n",
      "Torch CUDA device:  cpu  threads: 4 4\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "print(torch.cuda.is_available())\n",
    "device = torch.device(cuda_dev)\n",
    "print(\"CUDA device: \",cuda_dev)\n",
    "print(\"Torch CUDA device: \",device,\" threads:\",torch.get_num_threads(),torch.get_num_interop_threads())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7921d49-42ef-4ed1-9cda-99e26864d460",
   "metadata": {},
   "source": [
    "## Approximation de fonction\n",
    "L'approximation de fonctions est l'une des applications fondamentales des réseaux de neurones. Avec PyTorch, il est simple de construire un réseau capable d'apprendre une fonction à partir de données.\n",
    "\n",
    "Prenons un exemple où l'on souhaite approximer la fonction :\n",
    "$f(x)=sin⁡(x)$\n",
    "\n",
    "On définit les données `xdata` et `ydata` \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "adee5802-2cbc-4b64-bca6-a6a41a32b008",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "# Données d'entraînement: attention sans gradient\n",
    "Nd = 100\n",
    "xdata = torch.linspace(-2 * torch.pi, 2 * torch.pi, Nd,device=device).reshape(-1, 1)\n",
    "ydata = torch.sin(xdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "abb70c37-feef-42fe-9b1f-f0d57595fc6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# réseau de neuronnes\n",
    "class NeuralNet(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.model = nn.Sequential(\n",
    "            nn.Linear(1, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 1)\n",
    "        )\n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "\n",
    "model = NeuralNet().to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "36ad3f3f-36f3-4f63-933a-7de15365b8f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# fonction cout\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "131d7fea-e50b-4a1a-9dac-86a1f7d3a38d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Trainable parameters: 1153\n",
      "Epoch 0 : Loss = 0.527297\n",
      "Epoch 200 : Loss = 0.035841\n",
      "Epoch 400 : Loss = 0.003632\n",
      "Epoch 600 : Loss = 0.022887\n",
      "Epoch 800 : Loss = 0.000258\n",
      "Epoch 1000 : Loss = 0.000510\n",
      "Epoch 1200 : Loss = 0.000087\n",
      "Epoch 1400 : Loss = 0.000205\n",
      "Epoch 1600 : Loss = 0.000047\n",
      "Epoch 1800 : Loss = 0.000135\n",
      "Epoch 2000 : Loss = 0.000034\n",
      "Epoch 2200 : Loss = 0.000084\n",
      "Epoch 2400 : Loss = 0.000021\n",
      "Epoch 2600 : Loss = 0.000051\n",
      "Epoch 2800 : Loss = 0.000018\n",
      "Erreur finale = 0.000030\n"
     ]
    }
   ],
   "source": [
    "# entrainement du réseau\n",
    "num_trainable = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(f\"Model Trainable parameters: {num_trainable}\")\n",
    "epochs = 3000\n",
    "for epoch in range(epochs):\n",
    "    optimizer.zero_grad()\n",
    "    ypred = model(xdata)\n",
    "    loss = torch.mean((ypred-ydata)**2)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch % 200 == 0:\n",
    "        print(f\"Epoch {epoch} : Loss = {loss.item():.6f}\")\n",
    "print(f\"Erreur finale = {loss.item():.6f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2f5ded5-2445-4ea8-8de0-2cb7c29cf49f",
   "metadata": {},
   "source": [
    "### Validation\n",
    "Pour valider, on définit des points de collocation `x` (remarque: `xdata` et `x` ne sont pas forcément identiques).\n",
    "\n",
    "Si on veut calculer les dérivées de la fonction $f(x)$, on définit les points de collocation x avec l'option `x.requires_grad=True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0407b48e-7223-4b48-b59b-82fad80b1bc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# points de collocation où on définit la fonction\n",
    "N = 2*Nd\n",
    "x = torch.linspace(-2 * torch.pi, 2 * torch.pi, N,device=device).reshape(-1, 1)\n",
    "# si on veut calculer les dérivées\n",
    "x.requires_grad=True\n",
    "# tester le modele\n",
    "with torch.no_grad():\n",
    "    y_pred = model(x)\n",
    "xn = xdata.cpu()\n",
    "yn = ydata.cpu()\n",
    "xp = x.detach().cpu()\n",
    "yp = y_pred.cpu()\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.subplot(2,1,1)\n",
    "plt.plot(xn, yn, label=\"sin(x)\")\n",
    "plt.plot(xp, yp, '--', label=\"Approximation NN\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.subplot(2,1,2)\n",
    "yp = model(xdata).detach().cpu()\n",
    "plt.plot(xn, yn - yp)\n",
    "plt.title(\"Erreur\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb84dbb6-dc00-4df5-99c4-09ec25104a57",
   "metadata": {},
   "source": [
    "### Calcul de la dérivée\n",
    "Si on a calculé l'approximation avec  `x.requires_grad=True`, on peut calculer la dérivée avec la fonction `torch.autograd.grad`, qui utilise la différentiation automatique dans PyTorch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "462a6034-d6f5-4714-ac15-eb2614653be4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Erreur')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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J6tevT1xcHPPnz2fz5s14e3vTsmVLAN566y2GDRuG0WhkwIABhT48ZIuMtxITE0OlSpXy3SqvUaMGjRo1YvXq1fnGWN2zZw/Dhw9n+PDhvPXWWwC89tprTJ06tdArk3v27CEpKYlBgwYVeuyS6EP73HPPcfDgQQYOHEj16tWJi4vj+++/p3LlyowdO5YTJ06QlZWVr0vFzWX/LGgzMzM5efJkvi4zpdUWQjik0h9YQQhRFDeHT7r55eTkpAYFBam9evVSv/jiCzU1NbXANgkJCeqzzz6rhoaGqkajUQ0KClJ79uypfv/99/nWuzm80uXLlws9ZmHDEkVFRamAqihKvqGF7ub4RV3vVjZs2KC2bNlSdXJyUmvUqKFOnTo175xK6jj/bItr166po0ePVv38/FR3d3c1PDxcPXr0qFq1alX1scceu+P+bjVsl6qqanR0tBoeHq66u7urbm5uavfu3dWtW7fmW6c4P7Nz586pI0eOVP39/VVnZ2e1Ro0a6rPPPqtmZ2fnrfPuu++qlSpVUnU6Xb7tb/UeKOmMhWnTpo3at2/fAss/++wz1d3dPW/otPPnz6vBwcFqx44d1aysrHzrPv3006rRaFRPnz6db/nrr7+uVqlSJW/oMluYNm2a2qNHj7x2r1Wrlvr888+riYmJqqqq6m+//aYC6qFDh/K2ubns4MGD+fa1c+dOFVCXLVuWb7mjtIUQpU1RVTt6kkAIIYT4h5SUFGrUqMHHH3/MmDFjir19dnY21apV44033uCFF16wQcLSI20hROGkD60QQgi75uXlxWuvvcYnn3xyVyNKzJgxA6PRWKRxl+2dtIUQhZMrtEIIIYQQwqHJFVohhBBCCOHQpKAVQgghhBAOTQpaIYQQQgjh0KSgFUIIIYQQDq1cTqxgsVi4dOkSHh4exZoCUgghhBBClA5VVbl+/TohISHodLe/BlsuC9pLly6V2NzjQgghhBDCds6fP0/lypVvu065LGg9PDwAawOV1BzkJc1kMhEZGUnv3r0xGo1axymzpJ1tT9q4dEg7lw5p59Ih7Wx7jtDGqamphIaG5tVtt1MuC9qb3Qw8PT3tuqB1c3PD09PTbt9oZYG0s+1JG5cOaefSIe1cOqSdbc+R2rgo3UPloTAhhBBCCOHQpKAVQgghhBAOTQpaIYQQQgjh0KSgFUIIIYQQDk0KWiGEEEII4dCkoBVCCCGEEA7NpgXtxo0bGTBgACEhISiKwuLFi++4zfr162nRogXOzs7UqlWLmTNnFljn66+/plq1ari4uNC2bVt27txZ8uGFEEIIIYRDsGlBm56eTtOmTfn666+LtP6ZM2fo378/3bt3Z9++fbz44os88cQTrFq1Km+defPmMX78eCZNmkR0dDRNmzYlPDycxMREW52GEEIIIYSwYzadWKFv37707du3yOtPnTqV6tWr85///AeA+vXrs3nzZj7//HPCw8MB+Oyzzxg7diyjR4/O22b58uVMnz6dN954o+RPoiRkXgOjGxictU4ihBBCCHF3zLmQlQIVKmqdpAC7mils27ZthIWF5VsWHh7Oiy++CEBOTg579uxhwoQJea/rdDrCwsLYtm3bLfebnZ1NdnZ23vepqamAdZYMk8lUgmdQOP1vo9CdWY/q7AkV/FF9qqNW64SlWlcIbAhKwQvlN3OVRr7yTNrZ9qSNbSDjKsqx5eguRUPiEZQrxzCYc7jPYkF3wIDqWxM1oD5qYGMsdfuDTzWtE5cZ8n4uHdLOtnfbNlZVSD6L7swGlDMbUa4eh/TLkJEEbhXJfeloqWYsCrsqaOPj4wkMDMy3LDAwkNTUVDIzM7l27Rpms7nQdY4evXXjfvDBB0yePLnA8sjISNzc3Eom/G10jT+LN6Bkp0J2KkrSKTi1Gj2Q7uTHaf/exFbsSq7etcC2UVFRNs8npJ1Lg7TxPVItBKdEU+XqBgJSD6LDXGAVPUBuLiQeQkk8BAcXoF8ziaQKtYj17cR5385YdPY9xaWjkPdz6ZB2tr2/t7FiyaVS8g5qJq7CO/NsoetbMq7x5/KlqIre5tkyMjKKvK5dFbS2MmHCBMaPH5/3fWpqKqGhofTu3RtPT0+bH/9S+25Y1DQ8LCko6YkoCQdQzmxAObeVCjlXaHxxDo0uL8HS5v+wdHgRjK6YTCaioqLo1auX3c+x7MiknW1P2vgeqSrKmfXo172LEh+Tt9gS1JTsqt2Jd6nJGV0VrpqMHDp2guqhIVQyXyA4+wwh13bhnbgD3/ST+KafpGnKasxdXkdt/BDobP/LqCyS93PpkHa2vXxtbNCj7PsF/caPUdLiAVB1RtTKrVCrdUWt1BLVPRAq+IOrL31L6fPj5h31orCrgjYoKIiEhIR8yxISEvD09MTV1RW9Xo9ery90naCgoFvu19nZGWfngv1XjUZjqfyP8uma06w6GE/Xuv4MaFqHsNadcOv4HJgyIWYebPsG5cox9Jv/g/7QQuj/H6jatVQzlnfSzrYnbXwXrifAknFwIhIAi7ECR0OHsVjtwtJLHsSdzbqxYvqN//rDeRMQeOOrHf6M4BG3nYxSluGTegHDsudg13dw/3cQ1Kj0z6mMkPdz6ZB2tj1j0nGMK1+FCzdGjHIPhDZjUVo+jqJxX9ni/OztqqBt3749K1asyLcsKiqK9u3bA+Dk5ETLli1Zs2YNERERAFgsFtasWcO4ceNKO26RqKpKbFIGOWYLUYcTiDqcgLuzgWGtQxnVsRqVW46C5iPhyBJY9SZcOwu/PIC+6XB0dNc6vhBCK0eWwdLnIeMqZp2Rla738a+r4SQdvnlXyVrM+rk7Ua1iBbxcDVy7nEDVKpXJzLGQnJlDfEoW55Lgi4xwptKdx/SreMawBO+Eg1i+74YSNgml3bOgkyHJhSh3VJVaCcsxTFsAqhmc3KH7W9B6TKEPsV++ns3Kg3FcyzDxfM/aGgS+PZsWtGlpaZw8eTLv+zNnzrBv3z58fX2pUqUKEyZM4OLFi8yaNQuAp556iv/973+89tprPP7446xdu5bffvuN5cuX5+1j/PjxPPbYY7Rq1Yo2bdrw3//+l/T09LxRD+yNoij88WxHjsVfZ+n+SyyNucS5qxn8uPkM07ecYUDTEF7pXZfQhhFQqyes/xC2f4Nu/2w6uW2FlFbgV13r0xBClBaLGVa9BTu+BeAI1Xg+8xlOZFRGUaBlFR861KxI+xoVaVTZC08X6xUMk8nEihUr6NevUb6rGunZuRyNv862U1dYdcifhRe78KHxB3oRDZFvk7h/Ff6jZ6O4eGlyukIIDWRfR//7MzS8tMT6ff0B0Pdj8AzJt1qWycyS/ZdYvPci209fxaKCq1HPE52r4+ZkV9dEbVvQ7t69m+7d/7rKeLMf62OPPcbMmTOJi4sjNjY27/Xq1auzfPlyXnrpJb744gsqV67Mjz/+mDdkF8DQoUO5fPkyEydOJD4+nmbNmrFy5coCD4rZm7pBHtQNqsvLveuw4fhlftx0hs0nr/DHvkv8eSCexzpUZVz32niFvwe1wlAXPI5PxhnU6T3h4bkQ2kbrUxBC2FpOBuYFY9Aft96pmpo7gM9yH6SynzevtapMRLNKhHgXfHj0dio4G2hZ1YeWVX0Y16M255MymLW1KVt2zuB15ScCEjZx7j/d0A2fT2i1WrY4KyGEPUk+D7MfRHf5KBZFj9rnI/RtngBFyVvl8vVsft52ltk7YrmanpO3vGmoNwOaBGNRtQh+e4qqqnYYy7ZSU1Px8vIiJSWlVB4Ku5WDF1P44M8jbDl5FQA/d2f+HdGIPo2CMF0+Rfr0wdanDI0V4JG5UL2LZlnLqr+uavWTflo2Im1cROlXuD59MB5X95OtGnnJ9DRnAnvzXI9a9GkYhE6n3Hbz4rZzSqaJ5X8up9f+5/FXUohTfdna7jsG9+mFotz+WOWZvJ9Lh7SzjVw9BbMGQcp5VPcgNoU8Sfshz+e18fUsEz9sPM2Pm8+QkWMdSaWStyuPtK3CwKYhhPrafmSovytOvSYdpzTUqJIXv4xpy4zRranhX4Eradk89csexs2JJskYxOY6b2Gp0R1M6TB7CJyQ4UuEKItyrl8l/n998Li6n2uqO88Y3iH8oadY8Xwn+jUOvmMxeze8XI08MjiC7MciuWgIJVhJouv2Mbz30x9k5OSW+PGEEBpLPAoz+kHKeahYi9zRkVyrYL0ro6oqc3fG0vWT9Xy59iQZOWaaVvbim+Et2PBqN57tXqvUi9nikoJWY4qi0L1uACue78zT3WqiU2BZTBwR327nVLoz5iG/QN1+kJsFvz4MJ9doHVkIUYLiExM590UfgjJPkKh6M7Ped3z2yv8xqFmlUrlSWrlGPULGb+KKZwP8lFTGnnmBZ79awPmkoo//KISwc1dPwcz+kBYPAQ1h9J95/WXPXk3n4R+288aiAySl51DDrwLfDm/B4mc70q9xMAa9Y5SKjpGyHHAx6nm9Tz0WP9uR6n4ViEvJ4stDen7enYA65CdoEAEWE/w2Ei7t0zquEKIE7D19ibhvBlA79zjX8OBkn9m89PB9eLmW7i1Wxc0Hv6eWk+Fdl0AlmXdT3+KF75YSe1WKWiEcXloi/DIYMq5AUBMYtQzcA1BVlc3xCvf9bxvbTyfhYtTxVr/6rHqpC30bBztc1yMpaO1Mk8reLBnXkd4NAjCrClOWH2XCH0fJjfgOqneFnDRr94NrZ7WOKoS4B1tOJJL40yiac5Q0pQKZwxbQoX0n7QK5+eL2xDJyfWpSWbnCe5n/ZtR3azl7Jf3O2woh7FP232oGn2owYhG4+XI9y8SLv8Uw/4ye7FwLnWr5EfliV8Z2qYHRQa7I/pNjpi7jPFyM/G9YUwZVNaNTYO6u84ydHUP6/TMhsDGkJ8IvD0BmstZRhRB3IfJQPNGz3iBc2UEuBvTD5xFSr53WscA9AMOoJZjd/Kmvi+X1zM8Z9t0WuVIrhCOymGHBaIjbB24VrcWsuz8nE68z4KvNrDiYgE5RebNvXX4e04YqFe27j+ydSEFrpxRFoUeIytcPN8PFqGPdscsM++kw1wbPAa9QuHoSfn8KLBatowohimHdsUSW/vo1z+kXAqDe9zmutTprnOpvvCqjf/hXVL0z4frdjMj8hcd/2kVKpknrZEKI4lj/oXWWQYMrPPIbVKzJ1pNXuP+brZy9mkGIlwsvNDQzukNVh+teUBgpaO1cWP0A5oxth28FJw5cTOHhX8+SPGA66J3h+J+w+TOtIwohimj/+WQ+/2UxH+unAmBpNw5jq5EapypEaGuUgV8BMM7wB7WvrGHcnGhyzfIHtBAO4dhK2Pix9d8DvoDKrZi/+zwjp+/kelYurar68PvT7ajmoW3MkiQFrQNoUcWH+U+1J8DDmaPx1xm6NIvrYR9aX1z7bzi1VtuAQog7Onc1nWdmbOI/yn9xVXKw1OyJrvcUrWPdWtOh0PEFAD4y/sCZk4d5Z+khyuHQ5UI4lqQz8PuT1n+3HgtNhzJt8xleXRBDrkVlQNMQfnmiLb4VnLTNWcKkoHUQNf3d+fXJdgR4OHMs4ToPbK9JduPhgAoLn4DrCVpHFELcwvUsE6Nn7GJczjRq6y5icQ9EN/h70Om1jnZ7Pf4FldvgqWTwlfF/zN1+mt/3XtQ6lRDiVswmmD8KslKgcmsIf59v15/i3WWHAfi/LjX4YmgzXIx2/tlzF6SgdSA1/d2Z+2Q7Aj2dOZ6Qxsj4IVgCGkHGVVj6PMiVEyHsjqqqvLHwAA2SVvOwYR0qCrrBP0AFP62j3ZneCA/8CC5eNNed5GXDfCb+cUgeEhPCXm342PoQmIs3DPmJrzac46OVRwF4oWdt3uhbzyYTtdgDKWgdTA1/d34e0xZPFwM7zmfwjvEFVL0THF8J0T9pHU8I8Q8/bz/HngMH+cD4IwBKl1egRleNUxWDT1W40Z/2acNSGplieH7uXkzSn1YI+3J+F2z61PrvAf9lxsEc/hN1HIBXw+vyUq86ZeLhr1uRgtYB1Qn0YNqo1jgbdMw6VYEVAWOtL6x80zobiBDCLhy4kMK/lx3mA+OPeCiZUKkVdH1D61jF12AQtLA+vPaJ0w8cOx/Pl2tOaBxKCJEnO83ab1a1QOOHWJzThslLrd0Mxveqw7Pda2kc0PakoHVQrav58tXDzdEpMO5Me+J8WoEpHRY/I0N5CWEHskxmnp+7lwHqBrrr91vvpAz6GvQGraPdnd7/Bs9KhJLAq4bf+HrdSQ5eTNE6lRACYPU7kHQaPCuxqc7rvDJ/PwCjO1bjuR5lv5gFKWgdWu+GQbzZrz4qOh5KGInZ4Abnt0P0TK2jCVHufb76OOlXLjDJ6WcAlG4TIKCetqHuhYsXDPgSgFGGVTTnGG/+fgCzRfruC6Gp8zthl7VLU2yXT3hq/klyLSr3N6/Ev/o3KNPdDP5OCloHN6ZTdR5oUZnzFj/+k/uQdWHUO3A9XtNcQpRnMReS+WHjad41zsCTdAhpDh2e1zrWvasdBs1GoEPlU+fvOXbhMr9sP6d1KiHKL7MJlr4AqGQ1eIiHV7uSnmOmQ82KfPxgkzL7AFhhpKB1cIqi8N79jWgW6s3UrDCO6WtBdgqsdMB+ekKUASazhdcWxNBV2Uu4fjfoDI7d1eCfwt8D9yCqE8cT+hV8suoY8SlZWqcSonza+hUkHkZ19eXpy4O5mJxJtYpufDO8BUZ9+SrxytfZllEuRj3fP9oSX3dXxmc8jhk9HPodjkdqHU2Icuf7jac5E3+VKU6zrAvaPQOBDbUNVZJcva1FLfC88Q+8c+LyxrgUQpSipDOw4SMA5vs9zbrzFjxcDPz4WGu83crWpAlFIQVtGRHg6cJ/hzbjMNWYltvHunDl65CbrW0wIcqR+JQs/rf2JP+nX0YoCeARAl1f0zpWyWv0AFTrjDPZ/MvwM8sPxLH7bJLWqYQoX1a9BblZJPq15bUTDVAU+N8jLagV4K51Mk1IQVuGdKrtx7jutfgidzCXVW/rE487pmodS4hy45NVx6iYG8ezxiXWBeHvgXMZmiz9JkWBfp+AzkC4fjfddPt4b8URmRZXiNJyai0cW46q6Bmd8BCg8ELP2nSt4691Ms1IQVvGvNCzNg2rV+Kj3KEAqBs+gbREjVMJUfYduJDCwugLvG2YjTM5UL0rNLxf61i2E1Af2j4FwGTjLA7GXmHFAXkYVQibM+fCygkALDb245ApmE61/HiuR22Ng2mrVArar7/+mmrVquHi4kLbtm3ZuXPnLdft1q0biqIU+Orfv3/eOqNGjSrwep8+fUrjVOyeQa/ji2HNiDJ2Z7+lBkrOdVgzRetYQpRpqqry7rLDtFGO0Ee/CxQ99P3YeiWzLOv2BlQIoKoSzyP6NXy08ig5uTIOthA2tXs6XD5Kut6LSakDCPBw5r/DmqEvRyMaFMbmBe28efMYP348kyZNIjo6mqZNmxIeHk5iYuFXDRctWkRcXFze18GDB9Hr9QwZMiTfen369Mm33q+//mrrU3EYwV6uvDOoMZNN1pl91L2/wKV92oYSogxbdSieXWev8LbTHOuClqMce8zZonL2gO5vAvCScRHJSZf5WYbxEsJ2MpJg/fsAfJA1mOuKO18Ma46fu7PGwbRn84L2s88+Y+zYsYwePZoGDRowdepU3NzcmD59eqHr+/r6EhQUlPcVFRWFm5tbgYLW2dk533o+Pj62PhWHEtGsEgENurDY3AEFFUvURK0jCVEmmS0q/4k8zgDddpoop8DJ3Xrlsrxo/ij418Ob6zxj+INv158kM8esdSohyqbNn0HmNU5ShV/NPRjbuQbta1bUOpVdsGlBm5OTw549ewgLC/vrgDodYWFhbNu2rUj7mDZtGsOGDaNChQr5lq9fv56AgADq1q3L008/zdWrV0s0u6O7OT7tNKcRZKsGdGc2wKl1WscSosxZfiCO2MQkXneaZ13Q6UVwD9A0U6nSG6DXuwA8bliJS/pFZu+Qq7RClLiUC6g7vgfg3zlDqR3kzcu962gcyn7YdKTvK1euYDabCQwMzLc8MDCQo0eP3nH7nTt3cvDgQaZNm5ZveZ8+fRg8eDDVq1fn1KlTvPnmm/Tt25dt27ah1+sL7Cc7O5vs7L+Gr0pNTQXAZDJhMpnu5tRs7maue8nn6azj/wZ0ZfaCMB43rCTzz39heHINKPIs4E0l0c7i9spyG5stKv+NOs5IfSSVuIzqEUxuqydBg3PVtJ2rdUNfrQtOZzfyimEe/95QiYdahODqVPDz2NGV5fezPZF2Lki/9n105mx2WOqxRWnOogcaoVMtmEx312/dEdq4ONkU1YbjrFy6dIlKlSqxdetW2rdvn7f8tddeY8OGDezYseO22//f//0f27ZtIyYm5rbrnT59mpo1a7J69Wp69uxZ4PV33nmHyZMnF1g+Z84c3Nzcing2jklVYf7RNKZmvoyHksnOqs8S59tW61hClAm7Lyv8fjKbTc4v4qOksbfKGGIrdtU6lia8Ms7S7dhELKpCn5wPaVg1hG7BMoyXECXBPesi3Y+8iQ6V+7MnUym0Br0qlf3/vzIyMnjkkUdISUnB09Pztuva9Aqtn58fer2ehISEfMsTEhIICgq67bbp6enMnTuXKVPu/IR+jRo18PPz4+TJk4UWtBMmTGD8+PF536emphIaGkrv3r3v2EBaMZlMREVF0atXL4xG4z3tq0WnLH76ch3jlPnUS1xC84ffBv297bOsKMl2FoUrq21stqh88dUWRuv/wEdJQ/WtSaPh79FIp80Ut/bQzpaFu9EdXcJLhgVMvPI6U0Z2xsVYtq7S2kM7lwfSzvnpFzyGDpVV5lZkBrbg48fb3vPUto7QxjfvqBeFTT95nZycaNmyJWvWrCEiIgIAi8XCmjVrGDdu3G23nT9/PtnZ2YwYMeKOx7lw4QJXr14lODi40NednZ1xdi74BKDRaLTbH+JNJZGxip8Rn7DxXF6zCv/M86Tuno1np7EllLBscIT3gqMra228Yt9Frl5J5EmX5QAo3d/E6OyqcSqN27nHW6hHl9JXv4uv04+yYG8tRnesrk0WGytr72d7Je0MXIyGY8sxqwqfmofynweb4OZScqMa2HMbFyeXzTtTjh8/nh9++IGffvqJI0eO8PTTT5Oens7o0aMBGDlyJBMmTCiw3bRp04iIiKBixfxP76WlpfHqq6+yfft2zp49y5o1axg0aBC1atUiPDzc1qfjsIZ1qs8S92EAmDZ8Crk5GicSwnGpqsr3G08z1rAcDzIhoCE0HKx1LO0F1ENp8hAALxvm8+OmM+SaZVxaIe5F7toPAFhs6UT3Tp1pUtlb20B2yuYF7dChQ/n000+ZOHEizZo1Y9++faxcuTLvQbHY2Fji4uLybXPs2DE2b97MmDFjCuxPr9cTExPDwIEDqVOnDmPGjKFly5Zs2rSp0KuwwkqvU2gz5GUSVW8qmuI5u/ZHrSMJ4bC2nrpK/KXzjNavtC7o8Rbo5GFLALq9garo6a7fT1DKPlYclNnDhLhrF/dgOBVJrqpjfoWHeSlMRjW4lVLp7DVu3LhbdjFYv359gWV169a95Zzgrq6urFq1qiTjlRuNqwWxNGQkA+K+xGX7fzF3H4PeKH8ECFFc3208zVjDCioo2RDSHOr20zqS/fCtgdJ8BET/xAuGRXy8sTUDmgSjlPVZ04SwgfTI96iA9ersEwPDyuTIISVFLimUM+0fepnLeBNkSWD3km+0jiOEwzkSl0rM8dOM0EdZF3R9o+xPcVtcnV9GVfR00R/AcCmabadlnHAhiku9sIcK59aQq+rYXWUMYQ0C77xROSYFbTnj5+PNqTrWB8JCD3xNSlq6xomEcCw/bDzNaMMq3JUsCGwMdaTvfgE+VVGaWvvsP2tYzPcbT2scSAjHc3mZdbjRJWonnh7cS+M09k8K2nKo5eCXuKr4EMJlNi/6Vus4QjiM+JQs1u4/+Vff2S6vyNXZW+k0HhWFXvpoEo/v4lj8da0TCeEwss/vJSB+A2ZV4VrL56lascKdNyrnpKAth4wuFUhqbL1KW+/UNC5dk6u0QhTFnB3neERZhaeSAX51of5ArSPZL79aKI2sIz88a1jMzK1ntc0jhAOJXfI+AGv0nXikbw+N0zgGKWjLqVr9xpGmuFNTuUTkoulaxxHC7uXkWli04wRPGFZYF3R5RUY2uJPOLwPQV7eLA3t3kJJhv1NsCmEvrp0/Qo1Eax99fecX5UGwIpJP43JKcfEirckoAJqfm87RuBRtAwlh5/48GEfPrEh8lTRUn+oy7mxRBDZErdcfnaIyUl3C/D3ntU4khN07ufgD9IrKLmMrunctOPupKJwUtOVYUK8XyVGcaKo7zR+//6p1HCHs2i9bT/OE3np1VunwHOi1meLW0SgdXwIgQr+ZP7dGY7GU/fnnhbhbZ86cpMkV6+yDLt1fQaeTPvpFJQVteebuT1aj4QB0jJvF7rNJGgcSwj4dvJhC0IWVhOouY3GtCM0e0TqS4whtjblyO5wUM72uL2bD8ctaJxLCbh1b/BHOSi4nnBvSuENfreM4FCloyznPnuMxo6eT/hALlv+pdRwh7NLPW8/yf4ZlAOjaPQVGV40TORZ95xcBeES/mnlbDmkbRgg7tf9kLB2SlwJQoeerGqdxPFLQlnfeVciuMwCANvFz2HrqisaBhLAvKZkmEmJW0Uh3FrPBFVo/oXUkx1M7nByf2ngqmYSe/o2zV2RkFSH+6eDSr/BUMklwqkJIq0Fax3E4UtAK3Lq+AMAA3TZ+Wrn1ltMOC1Ee/bHvIo+zBABd8xHg5qtxIgek0+HU2fo5M8bwJ/N2nNI4kBD2ZeuJeLomLwLA2Ok5GUHlLkiLCajUgpxK7TEqZprF/camE3KVVggAVVXZum0TXfQHsKBD6TBO60iOq8lDZLn4E6Rc4/ru+eTkWrROJIRdUFWVbUunU1m5QprBG9/2j2odySFJQSsAcOr8HACP6NfwbeR+uUorBBBzIYWuSQsByK3bH3yqaRvIkRmcMbb/PwCGmpcQdShe40BC2Ie1RxLomTwfAKXVE9JH/y5JQSus6vQl16cGXkoGdeKWsO30Va0TCaG5pdtiGKzfDIBTR7k6e6/0rR7HpHOmse4suzev0DqOEJpTVZXIlYtppjtNruJEhU5PaR3JYUlBK6x0OgwdngVgtH4l36w9rnEgIbSVnp2Lx8FfcFZMpFVsDKFttY7k+CpUJLvBgwC0jp8nD4eJcm/9sct0u7YAgNzGQ8HdX+NEjksKWvGXpg9jcfKkmi4Bw5l17I29pnUiITSzYt85himrAKjQ5TlQZIDzkuDexdq9KVy3iz8379A4jRDaUVWV2ZFb6aXbA4BLp2c1TuTYpKAVf3GqgK7FCAAe1Ufx9Tp5ElmUXxe2/Eqgkky6kx9Kw/u1jlN2BNTnSmBH9IqK+/7p8nCYKLc2n7xC08TfMSgWcip3gID6WkdyaFLQivxujLHZXbePY0djOBqfqnEgIUrfycQ0uidbHwZTWz8BBieNE5UtPt2fB2CQZTWbDp3ROI0QpU9VVb5ZfYhh+rUAON14YFLcPSloRX4Va0LNnugUlRH61Xy7Xq7SivJny8ZImulOY8KIe4exWscpc/R1epPkXBlPJZOLm37ROo4QpW7HmST8z0fir6RirhAE9fprHcnhSUErCmrzJAAP6TcQFXOOS8mZGgcSovSYLSq+h38GIDG0D1Tw0zhRGaTTkdtiNACtEhdy9XqWxoGEKF3frD/FY4ZIAPRtxoDeqHEixycFrSiodi/wroKPkkZ/ZQszt57VOpEQpWbH4VOEma1Ddfn3eFrjNGVXQOfHycFIA905tm5cpXUcIUrN4UupXD2xi5a6E6g6I7R4TOtIZUKpFLRff/011apVw8XFhbZt27Jz585brjtz5kwURcn35eLikm8dVVWZOHEiwcHBuLq6EhYWxokTJ2x9GuWHTg+txgAwUh/JrzvOcT3LpHEoIUpH/IbpuCo5xLvUwqlaB63jlF1uvsSG9AXAdf9MbbMIUYq+23iKR/XWq7NKg4HgEahxorLB5gXtvHnzGD9+PJMmTSI6OpqmTZsSHh5OYmLiLbfx9PQkLi4u7+vcuXP5Xv/444/58ssvmTp1Kjt27KBChQqEh4eTlSW3rUpMi5GoBhca685SK+co83ad1zqREDaXkpFD80TrfOq5LUfLUF02FtD9GQA6Z2/i6Omz2oYRohScT8pgU8wJIvRbrAtudPET987mBe1nn33G2LFjGT16NA0aNGDq1Km4ubkxffr0W26jKApBQUF5X4GBf/31oqoq//3vf3n77bcZNGgQTZo0YdasWVy6dInFixfb+nTKDzdflEYPADDSEMmMLWfJNcvwOqJs271uMdWVODJwpVLnkVrHKfM8a7Uj1rkWzoqJ82t+0DqOEDY3bfMZBivrcVFMECgTtpQkgy13npOTw549e5gwYULeMp1OR1hYGNu2bbvldmlpaVStWhWLxUKLFi14//33adiwIQBnzpwhPj6esLCwvPW9vLxo27Yt27ZtY9iwYQX2l52dTXZ2dt73qanWoahMJhMmk33eSr+ZS8t8SvNRGPbNpr9+B/9OjmfZ/ov0bxykWR5bsId2LuscqY3dYmYCcCqkP/X0ruAAmW9ypHb+u+uNRsKeidS7OJ+MzLcxGmz6a+meOWo7O5qy2M7XMnL4bddZ/tRHAda7QGpurmZ5HKGNi5PNpp8cV65cwWw257vCChAYGMjRo0cL3aZu3bpMnz6dJk2akJKSwqeffkqHDh04dOgQlStXJj4+Pm8f/9znzdf+6YMPPmDy5MkFlkdGRuLm5nY3p1ZqoqKiND1+Z7ea+GacYqh+HV/86YlyPlrTPLaidTuXB/bexllpSTyQtQ0UOO3SgtMrVmgd6a7YezsXkBtMqOpGqJLAnBn/oUKlxlonKhKHa2cHVZbaOfKCQhtzDFWdEsnRuxF5wQNznPafM/bcxhkZGUVe1+7+FG7fvj3t27fP+75Dhw7Ur1+f7777jnffffeu9jlhwgTGjx+f931qaiqhoaH07t0bT0/Pe85sCyaTiaioKHr16oXRqN1wHkpoGix5hkcNq/nu+gCqNutEwxD7bLO7YS/tXJY5ShtH/zwBg2LhqFND+j3seP3aHKWdC7M3fhVtLi+gftoWGvV7Xes4t+XI7exIylo75+RaeO+zTXx44+qsvuVIwntpOwOhI7TxzTvqRWHTgtbPzw+9Xk9CQkK+5QkJCQQFFe3WtdFopHnz5pw8eRIgb7uEhASCg4Pz7bNZs2aF7sPZ2RlnZ+dC922vP8SbNM/Y+AFYPZHgjCuE6aKZvbMqnwxpql0eG9G8ncsBe25jNTeHmuetM4NdazDSbnMWhT23863493gW5i2gSfo2Ui/H4hNSU+tId+SI7eyIyko7Lz94Eee0WLo57wdA3/ZJ9HZyXvbcxsXJZdOHwpycnGjZsiVr1qzJW2axWFizZk2+q7C3YzabOXDgQF7xWr16dYKCgvLtMzU1lR07dhR5n6IYjC7Q4lEAhunX8sf+S1xLz9E4lBAl6+KO3/FTk7iqetKg5wit45Q71eu3IMbYGL2ici7qW63jCFGiVFVl+pYzDNWvR4cKNXtaZ+UUJcrmoxyMHz+eH374gZ9++okjR47w9NNPk56ezujR1lliRo4cme+hsSlTphAZGcnp06eJjo5mxIgRnDt3jieeeAKwjoDw4osv8u9//5slS5Zw4MABRo4cSUhICBEREbY+nfKpubWg7aqPwS83kbkyhJcoY0w7rE/Y7/Lpj5eHu8ZpyqdrDayfM1XOLoBc+aNZlB27z13j0IUkHtJvtC5oKRMp2ILN+9AOHTqUy5cvM3HiROLj42nWrBkrV67Me6grNjYWne6vuvratWuMHTuW+Ph4fHx8aNmyJVu3bqVBgwZ567z22mukp6fz5JNPkpycTKdOnVi5cmWBCRhECalYE6p1Rnd2E0P0G/hleyhjO1fHoJeJ5oTjs1w+QfXUXVhUBdf2Y7SOU2416TmcxH3vE8A1LmybT+XOw7WOJESJmL75DN11+whQroGbH9Tpq3WkMqlUKpJx48Zx7tw5srOz2bFjB23b/jXu2vr165k5c2be959//nneuvHx8SxfvpzmzZvn25+iKEyZMoX4+HiysrJYvXo1derUKY1TKb9ajgJgmHEDccnprD1664kxhHAk8eumArBJaU7bFi00TlN++Xi6s7vifQCYdk7TOI0QJeNiciarDsUzVL/OuqDZI2Bw0jZUGSWX2ETR1LsPXLwJ5gqddAeYszNW60RC3LvcHDyPLQDgTJUHcTHqNQ5Uvnl1GINFVah+fQ+5V05rHUeIezZ7+zn81SR66vdZF7SQCVtsRQpaUTRGF2hqnbRimH4dG45f5nxS0ceHE8IemY7+ibs5mUTVmzqdHtA6TrnXpnkzdijWcWgvrvtR4zRC3JvsXDPzdp3nQf1GdFigSgfwq611rDJLClpRdDf+suyt34OvmsI8eThMOLjkzdZb23/qu9G2VuAd1ha2ZtTrOFfV+oeF57HfwGLWOJEQd2/FgTiS0rN4xLjBukCuztqUFLSi6AIbQqVWGDAzWL+JebvPYzJbtE4lxN1JvUTF+E0ApDd4GL1O0TiQAKjdeSjJagV8ci+TfWy11nGEuGs/bztHe91hKpEAzl7QYJDWkco0KWhF8dz4C3O4cT2Xr2ex5og8HCYcU/bun9FhYaelLl1kDGu70aJmEFGGbgBc3SQPhwnHdPBiCtGxyTxiuPEwWJMh4OSmbagyTgpaUTyNBoOxAtW4RGvlmDwcJhyTxYJp988ArHcLL1PTOTs6RVFIb2jtrx9waQ2kX9E4kRDF9/O2c/iQSrh+t3WBdDewOSloRfE4e1iLWmCYYR2bTsjDYcIBnduCe8Z5rquueLQYgqJIdwN70rFjd2Is1TGQS8buOVrHEaJYUrNM/LH/Ivfrt2BUTRDc1PolbEoKWlF8N8akvc+wEw81nQV7LmibR4hiyto5E4Cl5nb0aylTUNqb2oEebHS3Dj6fs2smqKq2gYQohj/2XiTLZGak882HwWRmsNIgBa0ovkotIaABzmo2A/VbWbDnAhaL/MIRDiIzGcOxpQDs8x9A1YoVNA4kCuPecihZqhHvtFNwMVrrOEIUiaqqzN4RS3PlJNUssWBwhcYPah2rXJCCVhSfouR7OOxicibbTl/VOJQQRXRwAQZLNscslWnYqofWacQt9GlVj5WWNgCkbZ+ucRohimb/hRSOxl/nEeONh8Ea3g8uXtqGKiekoBV3p8lQ0DtRnzM0VM7y224Zk1Y4huydPwEw39Kd/k1DNE4jbiXIy4UDAQMBcDryO+Ska5xIiDv7dUcsbmQxUL/DuqDFo9oGKkekoBV3x80X6vUH4AH9Rv48GE9KhknjUELcQfwBnC/HkKPqias6CD93Z60Tiduo07YP5ywBOJnT4fAfWscR4rauZ5lYsv8SfXU7cVYzwbcmVJEhAUuLFLTi7jV9BIDBxq2ouTksibmkcSAhbk+NngVAlKUlYa3qa5xG3EmfxpVYqHYHIGP7DI3TCHF7S/ZfItNkZoTrFuuCZg9bu+iJUiEFrbh7NXuAeyDeairddPuYL90OhD3Lzca8bx4Ai+lO7wZBGgcSd+LlaiSxxmDMqoJb/E64clLrSELc0rxd56msXKa5+QCgQJNhWkcqV6SgFXdPb4AmDwHwoGETMRdSOJl4XeNQQtzCsT8x5KQQp/riWr83FZwNWicSRdCtdVM2WpoAoO6TMWmFfToWf52YCyk8oN9sXVC9C3iHahuqnJGCVtybG90Oeur24kMqi6IvahxIiMJZbhRDi8ydGNRcftE4im51A1iut3Y7yImeAxaLxomEKGhh9AVAZbjLze4Gj2iapzySglbcm8AGENwMA7kM1G9j8d6LMiatsD9pl1FOrgZgtbEHXer4axxIFJWLUY9zg/tIVd1wzoiDs5u0jiREPrlmC7/vvUgr5RgBuZfAyR3qD9A6VrkjBa24dzf+Eh1q3MillCy2n5ExaYWdOTAfRTWzz1KThk1bYdTLR58j6d+yOsvM7QAw7/tV4zRC5LfpxBUuX8/+6+psgwhwkglbSpt8qot71+hB0BlpwBnqKrH8Lt0OhJ2x3CiCFpo7M6hZJY3TiOJqV70i6116AqAe+gOy0zROJMRfFkRfwIVs+inbrAuku4EmpKAV965CRagTDsAD+k38eTCezByzxqGEuCHhELoE69izu92707KKj9aJRDHpdArVmvfgrCUQgzkDji7TOpIQAKRkmIg6lEC4bhfOlgzwripjz2qkVArar7/+mmrVquHi4kLbtm3ZuXPnLdf94Ycf6Ny5Mz4+Pvj4+BAWFlZg/VGjRqEoSr6vPn362Po0xO3c+Iv0AcMWMrOziTqSoHEgIW7Yb706u9bSgu7N66HTybiQjmhQ80osMncGIDd6tsZphLBaGnOJHLOFkW5brQuaPgw6uVaoBZu3+rx58xg/fjyTJk0iOjqapk2bEh4eTmJiYqHrr1+/nocffph169axbds2QkND6d27Nxcv5r+N3adPH+Li4vK+fv1V+lVpqnZvcPOjIsl00cXwe/QFrRMJAeZcLPutY88uNHcmorl0N3BUDYI92evTGwD9uU2QIp8xQnsL9lwgiKu0yN1vXdBUxp7Vis0L2s8++4yxY8cyevRoGjRowNSpU3Fzc2P69OmFrj979myeeeYZmjVrRr169fjxxx+xWCysWbMm33rOzs4EBQXlffn4yG1ETemN0HgIYJ0Kd9OJK1xLz9E4lCj3Tq9Hl55IkupOnH8n6gR6aJ1I3CVFUWjXsiU7LPVQUCFmntaRRDl3MjGNfeeTecCw2fqerNoRfKtrHavcsmlBm5OTw549ewgLC/vrgDodYWFhbNu2rUj7yMjIwGQy4evrm2/5+vXrCQgIoG7dujz99NNcvSpP1mvuRreDcP0e3CzXWXkoXuNAotzbbx179g9zR+5rUU3bLOKeDWwawgJzFwByo+eAKkMECu3cHHt2hMuN7gbyMJimbDpVzpUrVzCbzQQGBuZbHhgYyNGjR4u0j9dff52QkJB8RXGfPn0YPHgw1atX59SpU7z55pv07duXbdu2odfrC+wjOzub7OzsvO9TU1MBMJlMmEymuzk1m7uZy17zFcqvPoaAhhgTDzFQv42l+6rwYPNgrVPdlkO2s4PRrI2zUtEfWYYOWGTpzNcNA8r0z7k8vJeDPIzEBfcm8/JMXK+dJPfcTtRKLUo1Q3loZ3tg7+1stqgsir5Ac+UkwbnnUY1u5NbuB3aatzD23sZQvGx2Pffjhx9+yNy5c1m/fj0uLi55y4cN+6uPSuPGjWnSpAk1a9Zk/fr19OzZs8B+PvjgAyZPnlxgeWRkJG5ubrYJX0KioqK0jlAsNYxNacwhHtBvYvDpMOYuXoGnk9ap7szR2tkRlXYbV7mynubmbI5bKpFZoRp7t6xlb6km0EZZfy8HGRVWWVoRod/K+WUfERP6mCY5yno72wt7beejyQoJqXpeNFon+rjg3pzoNY456Ye9tjFY79IXlU0LWj8/P/R6PQkJ+Z94T0hIICgo6Lbbfvrpp3z44YesXr2aJk2a3HbdGjVq4Ofnx8mTJwstaCdMmMD48ePzvk9NTc172MzT07MYZ1R6TCYTUVFR9OrVC6PRqHWcoktrhfrlPJrrTlJViccU1J1+7aponeqWHLadHYhWbayf9Q0AC81deKx7I/q1rlxqx9ZCeXkvt0vP4fVPDhOh30qV63uo3HsWGJxL7fjlpZ21Zu/tvHp+DEYuMMhpJ5ghuM9L9KvRTetYxWLvbQx/3VEvCpsWtE5OTrRs2ZI1a9YQEREBkPeA17hx42653ccff8x7773HqlWraNWq1R2Pc+HCBa5evUpwcOG3t52dnXF2LviBZzQa7faHeJMjZMzHpxLU7A4nVxOh38KfhxrweOeaWqe6I4drZwdUqm2cdAbOb8esKiynE8uaVSo3P9+y/l4O9Dair9WN+LNTCcq+hv7MWmgwsNRzlPV2thf22M6pWSYiDyfSVbcfN3MquAdhqN0DdAW7PDoCe2zjm4qTy+ajHIwfP54ffviBn376iSNHjvD000+Tnp7O6NGjARg5ciQTJkzIW/+jjz7iX//6F9OnT6datWrEx8cTHx9PWpp1Zpi0tDReffVVtm/fztmzZ1mzZg2DBg2iVq1ahIeH2/p0RFE0GQpAhH4Lu84mcSk5U+NAoty58QT8Fksj6teth7ebA/R7EUU2sHkoi82dAFD3y5CNonT9eSCO7FwLj7ptty5o/KDDFrNlic0L2qFDh/Lpp58yceJEmjVrxr59+1i5cmXeg2KxsbHExcXlrf/tt9+Sk5PDgw8+SHBwcN7Xp59+CoBerycmJoaBAwdSp04dxowZQ8uWLdm0aVOhV2GFBur1B2MFqikJNFdOsuJA3J23EaKkqGpekbPQ3JkImeq2zOnVIJAVuq7Wb45HQrqMciNKzx/7LuFBBh0tu60LbgxZKbRVKg+FjRs37pZdDNavX5/v+7Nnz952X66urqxataqEkgmbcKoA9e+DmHlE6DezaH8rnuhcQ+tUory4sAvl2lnSVWe2GtvxUf0ArROJEubmZKBmw9YcPFSNRrqzcGgRtBmrdSxRDiSmZrHt9FUe1O/EYMkGv7oQ3FTrWIJSmvpWlENNHgJggH4bhy5cJfZq0Z9UFOKexPwGwEpLa7o0rIaLUW4FlkWDmoXwu7kjAJYbP3MhbG35gThUFUa47bQuaPIQKDKdtj2QglbYRvVuUCEAXyWNLroYlsZc0jqRKA/MJtRDiwDrZAoRzUM0DiRspVMtPzY7d8WiKugu7LQ+CCiEjS3Zf4lAkmhiujHVrXQ3sBtS0Arb0BusHeWB+/WbWRYj/WhFKTi1FiXjKpdVL064taRDTT+tEwkbMeh1tGvakC2WhtYFBxZoG0iUeeeTMtgbm8wgw1brVLdV2oNPVa1jiRukoBW2c6PbQS/dHs7HxXMy8brGgUSZd2N0g6Xm9tzXPBS9Tm4FlmWDmlfiD8vNbgfzZCpcYVNL9lvvND7iusO6QK7O2hUpaIXtBDcDvzq4KCb66HexdL9cpRU2lH0d9egKABabO3J/87I9kYKA5qHeHPLqSpZqRHf1BMTt0zqSKMOW7r9EHeU81UynQGeEhvdrHUn8jRS0wnYUJe8qbYRuM8tiLqHKFRRhK0eWoeRmcsoSTE5AUxqE2OcsgKLkKIpCr2a1WG1paV0QM1/bQKLMOp5wnaPx1xls2GJdULs3uPlqG0rkIwWtsK0bt2Q66A6Tdvk8R+Kk24GwkQPWJ93/MHfk/hZydba8GNS8EotvjnZwYD5YzBonEmXR0v2XULAwxOnGZApNpLuBvZGCVtiWTzWo0h6dojJQv5XlB2S0A2ED1xNQT68H4A9LRwbJZArlRk1/d64Gdeaa6o4uPRHObNA6kihjVFVlyf5LtFaOUdGcCM6eUKeP1rHEP0hBK2zvRreD+/VbWHkwXuMwokw6uBBFtRBtqUVozYYEeblonUiUov7Nq7Lc3Nb6jYxJK0pYzIUUzl3N4AHjVuuCBgPB6KptKFGAFLTC9hpEoOqMNNCdw3DlCCcSpNuBKFnqjdENfjd34v7mcnW2vBnQNITFlk4AWA4vgRyZyEWUnCX7L+GEiQGGm6MbPKRtIFEoKWiF7bn5otQJByBCrtKKknblBErcPnJVHWt0HenTKEjrRKKUBXq64Fy9Pect/uhM6XBshdaRRBlhtqgsi7lEd90+3Cxp4BEC1TppHUsUQgpaUTpudDsYpN/CSulHK0rSjVvMGyxNadOwNhWcDRoHEloY1Lwyi2+MSasekG4HomTsOptEQmo2Dzrd6G7Q+AHQyXTa9kgKWlE6aodjcfYkREnCI3EnsVfllqAoAaqKGiOjGwjo0yiIFXS2fnNiDaRf1TaQKBOW7L+EJ+l0V6KtC5oM1TaQuCUpaEXpMLqguzEIdYRuMysPySQLogRc2IWSfJY01YVotw50rFlR60RCI54uRqrXb84BSzUUNRcOLdI6knBwJrOFPw/E0Ue/E4NqgoAGENhI61jiFqSgFaXnxl+2/fQ7WHMgVuMwoky48TDYKksr+jSrjkEvH2nl2aBmf41Jq8okC+IebT99lWsZJh66ObpB4yHWCYOEXZJPf1F6qrTH7FEZTyUT34vriE/J0jqRcGRmE5aD1qtwi82duL+FjG5Q3nWr6896Y2fMqoJyYQckndE6knBgKw/GE8xVWnHIuqCxTKZgz6SgFaVHp0Pf9OaYtJtZdUhGOxD34OQadJlJXFa9uOLXjgbBMtVteeds0NO6cUO2WhpaFxxYoG0g4bDMFpVVhxIYqL9xdbZqJ/AO1TaUuC0paEXputHtoJtuH5tjjmscRji0G0+yLzF3YFDLKihyK1AAEc0rsdh8Y0zamHmgqhonEo4oOvYaV9KyecC4xbpAprq1e1LQitIVUI8c/0Y4KWaCzq/galq21omEI8q+juXocgCWqh0ZLJMpiBvaVPMlxqMzWaoR3dUTELdP60jCAa08GE89JZY6xILeCRoM0jqSuAMpaEWpc2o+DICB+i2sPpKgcRrhkI4sQ5ebxSlLML612hLgKVPdCiudTqFPy9pEWVpaF8hUuKKYVFVl5cF4IvQ3rs7W7g2uPtqGEnckBa0ofY0eQEWhte44u/bt0zqNcECWG6MbLDZ3ZEgr6dcm8hvconLeaAfmAwvAnKtxIuFIDl5M5VJyOoNu9p+VsWcdQqkUtF9//TXVqlXDxcWFtm3bsnPnztuuP3/+fOrVq4eLiwuNGzdmxYr80xiqqsrEiRMJDg7G1dWVsLAwTpw4YctTECXJM4TMytZfNsGxy0jNMmkcSDiU6/EoZzYAsM6pGz3rB2ocSNib6n4VuF6pC0mqO/r0RLjxfhGiKFYeiqOt7ijBylVw8bJeoRV2z+YF7bx58xg/fjyTJk0iOjqapk2bEh4eTmJiYqHrb926lYcffpgxY8awd+9eIiIiiIiI4ODBg3nrfPzxx3z55ZdMnTqVHTt2UKFCBcLDw8nKkmGgHIVby4cBGKhsZu1h6XYgiuHgQhTVwh5LbVo1b4GTQW40iYIGtqzOcnM76zcHZExaUXQrD8YTodts/abBIDBKlyZHYPPfBJ999hljx45l9OjRNGjQgKlTp+Lm5sb06dMLXf+LL76gT58+vPrqq9SvX593332XFi1a8L///Q+wXp3973//y9tvv82gQYNo0qQJs2bN4tKlSyxevNjWpyNKSv0B5CpO1NZd5GD0Jq3TCAeSu+/v3Q1kqltRuPuaBLP8xlS45sNLIEem2xZ3djLxOhcuX6O/fod1gXQ3cBgGW+48JyeHPXv2MGHChLxlOp2OsLAwtm3bVug227ZtY/z48fmWhYeH5xWrZ86cIT4+nrCwsLzXvby8aNu2Ldu2bWPYsGEF9pmdnU129l9P06empgJgMpkwmezzdvfNXPaa757p3UirGobP2RVUil1KSnoEbk42fTsWqsy3sx0o0Ta+cgJjwn5Mqp4TFcOo4+8mP7sb5L2cXwWjglftDpw/5U+o6TK5h5eiNhx8z/uVdi4dWrXzsv2X6K7bh4eSiepZidyQ1lBGf9aO8F4uTjabVhBXrlzBbDYTGJi/j1tgYCBHjx4tdJv4+PhC14+Pj897/eayW63zTx988AGTJ08usDwyMhI3N7einYxGoqKitI5gM4FKbdoB/ZQtfDl3FU38tBtHtCy3s70oiTaud2kBdYGNliaEuKkF+tcLeS//XahFYbGlI8/pFnN57TfsPFdyt46lnUtHabfzghg9/9JbuxucdGnG4T9XlurxtWDP7+WMjKLfWSn9S2IamDBhQr6rvqmpqYSGhtK7d288Pe1zdiGTyURUVBS9evXCaDRqHcc2zGFkfDKDQHMyvupl+vUbVeoRykU7a6zE2lhVsXz5FgBL1U5MGNYT3wpOJZTS8cl7uaCwXAuPfnyF59TFBF4/SL9ubcGt4j3tU9q5dGjRzuevZXB920q6O+8FoNqgN6gWUL9Ujq0FR3gv37yjXhQ2LWj9/PzQ6/UkJOR/6CchIYGgoKBCtwkKCrrt+jf/m5CQQHBwcL51mjVrVug+nZ2dcXZ2LrDcaDTa7Q/xJkfIeNeMRq7VvA+343OodGEZ6MZg1GvzgE+Zbmc7cc9tHLsD0s6TprpgqdOXQO8KJReuDJH38l+MRmjSvC0Hdlejse4sumNLoc3YEtq3tHNpKM12XnvsKv30O3BSzBDYCGOlJqVyXK3Z83u5OLlsWj04OTnRsmVL1qxZk7fMYrGwZs0a2rdvX+g27du3z7c+WC+H31y/evXqBAUF5VsnNTWVHTt23HKfwn5VbD8CgJ7qDnYev6hxGmHPzPvnArDK0pqINrU0TiMcxeAWf02Fa94/T+M0wp79+ffJFJo8pG0YUWw2vxw2fvx4fvjhB3766SeOHDnC008/TXp6OqNHjwZg5MiR+R4ae+GFF1i5ciX/+c9/OHr0KO+88w67d+9m3LhxACiKwosvvsi///1vlixZwoEDBxg5ciQhISFERETY+nRECdNXbc81YxAeSiaxOxZpHUfYq9wczAes74/1Tt3oUttf40DCUTSu5MUBnzDMqoL+4i5IOq11JGGHElOziD93nLa6o6go0OhBrSOJYrJ5QTt06FA+/fRTJk6cSLNmzdi3bx8rV67Me6grNjaWuLi4vPU7dOjAnDlz+P7772natCkLFixg8eLFNGrUKG+d1157jeeee44nn3yS1q1bk5aWxsqVK3FxkbHiHI5OR2qtCABCzi3FYlG1zSPs06k1OOUkc1n1olLLcAwadU0RjkdRFLq1aswWy43fIQcWaBtI2KVVhxPyZgZTqnUCr0oaJxLFVSq/FcaNG8e5c+fIzs5mx44dtG3bNu+19evXM3PmzHzrDxkyhGPHjpGdnc3Bgwfp169fvtcVRWHKlCnEx8eTlZXF6tWrqVOnTmmcirCB4C6PAtDeEs2BU2e1DSPsUlb0rwD8Ye7Ag62qa5xGOJqIZpX4w2KdndC0dy6o8oezyG/VgTgiboxuIGPPOia5zCE05xTciPPOtXBSzFza8qvWcYS9yUrFcMI6dM5R/77UCnDXOJBwNCHeriRXDSdTdcKYfAou7dU6krAj19JzSD4bTR3dRVS9MzQYqHUkcRekoBV2IbX2/QBUil2KKldPxN9YDi/BYMnmpCWENh26ax1HOKgBresSaWkFgBojD4eJv6w+ksBAxXp1VqnbB1y8NE4k7oYUtMIuVO06Eouq0MRymDOnCp90Q5RPqTtnA7BC6cJ9TUM0TiMcVXjDIFbpugBg2j8fzLkaJxL2IvLgRQbe6D9LYxndwFFJQSvsgrt/FY66NgUgfvPPGqcRdiP1Ep7x1mmyc+oP1mR6ZFE2uDrp8W3ah6uqB05ZV+H0eq0jCTuQlp2L6dRGgpRrmJ29oXZvrSOJuyQFrbAb12tb51mvdH6pPLQhAMjYMw8dKjstdenTuZ3WcYSDe6BVNZaareOV5+yT/voC1h1N5D42AaBrNBgMMvugo5KCVtiNWt0eIVs1UtUcS8KJXVrHEXYgY4+16NjpEUajStKvTdybZqHe7PHsBYDu6HLITtM4kdDamgNn6aPbCYDSVEY3cGRS0Aq7UbGiP9Eu1iHdErdIt4PyTk04hF/aMXJUPQFth2kdR5QBiqLQuG0PzlgCMZgz4ehyrSMJDWWZzBiO/4m7kkW2RyiEtr3zRsJuSUEr7Epa3ZvdDpaDxaxxGqGlm32pN9Kcvm3qa5xGlBX3twjlD4t1Ktz0PXM0TiO0tPnEFfqpGwFwaj4MFEXjROJeSEEr7Eq9ToNJVivga7lKytF1WscRWrFYcDmyEIBLoQPxcDFqHEiUFf4eziRWHwSAa+xGSEvUOJHQyqZ9R+iiiwFAaSJ3gRydFLTCroQG+LDVuTMAV7f+onEaoZW0ExvxyU0kVXWlUXcZRkeUrG7t2rLXUgsdFswxMhVueWQyW3A7vhiDYiHNryn41dI6krhHUtAKu5N+o9tB0MVVYMrSOI3QQtymnwDY4tSJ5jWCNE4jypru9QKIMnQFIG3XbI3TCC3sOJ1EuGUDAG6tHtE4jSgJUtAKu9O4QzgXVD/c1AwyD6/QOo4obaYsgi+uAsDS+CEU6dcmSphRr8PY5AFyVR1e1w7C5eNaRxKlbPeeHTTTncaMHl2jB7SOI0qAFLTC7tQN8mK9k/XqScp26XZQ3pzbvhh3NZ041ZcOPWROdWEb/ds3YYPFOpnLzeHhRPlgsai4H18EQHJIZ3D31ziRKAlS0Aq7oygKGXWtfzH7xW2AjCSNE4nSlLbbegv4UMVwfNxdNE4jyqo6gR7s9bbOCmXeN1cmcylHos8l0TvX2t3Aq+0IjdOIkiIFrbBLLVt34LClKgZyyT24WOs4opSkJV+mdrJ1TnW/Do9qnEaUdZXbDyZNdcEj6xJq7Hat44hScnB7JFV0l8nSuWKo31/rOKKESEEr7FLzUG9WG7oA8tBGeXIwahZOSi6ndNVo2rKD1nFEGdevRU2i1DYAXNkm3ZvKA1VV8Tr5OwBXQ/uAk5vGiURJkYJW2CWdTiGz7v1YVAXvy7shOVbrSMLGVFXF7ah17NmrNSLkYTBhc54uRhKrWcekdTuxBHJzNE4kbO3w+St0z90MgF+HkRqnESVJClpht9o3b8J2i3WGKEvMfI3TCFs7ePgATcyHsKgK9Xo9rnUcUU607DaIRNWbCuZUMo6s1DqOsLETWxbhraSTrK+Ic+2uWscRJUgKWmG32tWoyJ96a7eD7Ohf5aGNMu7c+lkAnHZvhmdgVY3TiPKiZXU/NjpbC5vELT9rnEbYmu+pxQBcrj4QdHptw4gSJQWtsFtOBh05tQeQpRpxTT4Bl/ZqHUnYSFJaNvUSrWMOO7d4WOM0ojxRFAVDM+t7LiR+HWpmsraBhM2cPn+BtqadAAR3fkzjNKKk2bSgTUpKYvjw4Xh6euLt7c2YMWNIS0u77frPPfccdevWxdXVlSpVqvD888+TkpKSbz1FUQp8zZ0715anIjTSvWlNVllaA6Dul7Eiy6q161dTS7lIDkYqdxiqdRxRznTr2oMTamWcMHFh6zyt4wgbObtxDs5KLueN1XGv2lzrOKKE2bSgHT58OIcOHSIqKoply5axceNGnnzyyVuuf+nSJS5dusSnn37KwYMHmTlzJitXrmTMmDEF1p0xYwZxcXF5XxERETY8E6GVbnUDWK5YbweaYxbIQxtlkMWiWscBBeKDuqO4emsbSJQ73hWcORbQF4CcaPnDuazyP/MHAEk1I7QNImzCYKsdHzlyhJUrV7Jr1y5atWoFwFdffUW/fv349NNPCQkJKbBNo0aNWLhwYd73NWvW5L333mPEiBHk5uZiMPwV19vbm6AgmeO9rHMx6nGt15PEY98SkJUEJ1dDvX5axxIlaNPxeHqYNoACgZ3kqWOhjUqdR8KiH6iZvpf0xDNUCKiudSRRgi6dPUbj3INYVIUqXaW7QVlksyu027Ztw9vbO6+YBQgLC0On07Fjx44i7yclJQVPT898xSzAs88+i5+fH23atGH69Omo8sBQmdW3SWUWmzsC0u2gLNq/fhH+SgrpBm+c6/fROo4op5o1bsxefWMATq6epnEaUdIubrI+dHrYuSk+wfLHSllksyu08fHxBAQE5D+YwYCvry/x8fFF2seVK1d49913C3RTmDJlCj169MDNzY3IyEieeeYZ0tLSeP755wvdT3Z2NtnZ2Xnfp6amAmAymTCZTMU5rVJzM5e95itNHWv4MFXXlSdZjnpsJbmpieDqUyL7lna2vdu1cVxKFjUuLgE9ZNW7HycLYJGfxd2Q9/K9u1b7ATh6AL+TCzHlTIRCxkKWdi4dJdrOqkrQWWt3g2s1B8nP7gZHeC8XJ1uxC9o33niDjz766LbrHDlypLi7LSA1NZX+/fvToEED3nnnnXyv/etf/8r7d/PmzUlPT+eTTz65ZUH7wQcfMHny5ALLIyMjcXOz71lCoqKitI5gF3QeIRy+XpUGnOPA/Pc469ejRPcv7Wx7hbXx+nOZfKjbA8ABU3VSVqwo7VhljryX716WEkK66kwlyyUW/PwlRr/at1xX2rl0lEQ761POcJ/5PFmqkfOWEJLkcyYfe34vZ2RkFHndYhe0L7/8MqNGjbrtOjVq1CAoKIjExMR8y3Nzc0lKSrpj39fr16/Tp08fPDw8+P333zEajbddv23btrz77rtkZ2fj7Oxc4PUJEyYwfvz4vO9TU1MJDQ2ld+/eeHp63nbfWjGZTERFRdGrV687nn95oK+awML5nWigO0djyyEa9Pu0RPYr7Wx7t2pjk9nC4Y//hbNiIsWjNh0feLrQK2KiaOS9XDL2XFhAu+uRhKbvp8XIFwq8Lu1cOkqynU/OGgfALuf2DHnwgZKIVyY4wnv55h31oih2Qevv74+/v/8d12vfvj3Jycns2bOHli1bArB27VosFgtt27a95XapqamEh4fj7OzMkiVLcHFxueOx9u3bh4+PT6HFLICzs3OhrxmNRrv9Id7kCBlLQ1jDYD5e1IUJ6q8YLu5Cl3IO/GqV2P6lnW3vn228+mgcvXPXgg4qtB2JwclJw3Rlh7yX741720dhdST1rq7BZMrGzc290PWknUvHPbdzbg6VL1qvyF6vN0R+ZoWw5/dycXLZ7KGw+vXr06dPH8aOHcvOnTvZsmUL48aNY9iwYXkjHFy8eJF69eqxc6d1oOPU1FR69+5Neno606ZNIzU1lfj4eOLj4zGbzQAsXbqUH3/8kYMHD3Ly5Em+/fZb3n//fZ577jlbnYqwAy5GPU3r12WjpYl1QYyMO+zoVm/eQkvdCSzoMTSVsWeFfWjQvj/xij9eSjr7VstDqI4u/eByPCypxKs+NOgUoXUcYUM2HYd29uzZ1KtXj549e9KvXz86derE999/n/e6yWTi2LFjeX0koqOj2bFjBwcOHKBWrVoEBwfnfZ0/fx6wVutff/017du3p1mzZnz33Xd89tlnTJo0yZanIuxA/8ZBLDJ3BkDdPxcsFo0Tibt1+nIa1S4uBSC7WjfwCNQ2kBA36PR6LoYOBMDpoEyy4OhStv0EwAaXHlQLsM8uhqJk2GyUAwBfX1/mzJlzy9erVauWb7itbt263XH4rT59+tCnjwztUx51qxvABEMbUlVXPFPOQ+xWqNZJ61jiLszefpbR+s0AuLYaoXEaIfKrHvYETJ9Gs+w9HDl+gvp1bv1wmLBjaYkEJmwAIKuh3AUq62x6hVaIkuRi1NOpfijLze2sC2RMWoeUZTITu2cVlZUrmIyeUFcmyhD2xbdKA864NsSgWDi1dobWccRdyt47Dz0W9lpq0a5NB63jCBuTglY4lP6Ng//qdnDoD8gp+pAewj4si4mjj3kdAPomD4Dxzg9+ClHalGaPAFA7bikpGTLltsNRVbJ3WSdTWOcaRp3Awh/uE2WHFLTCoXSr688RY31iLf4oOdfhyFKtI4liWrDtKH101gdBdTeKBiHsTdUuw8nBSF0llnXr12gdRxRXfAyeqcfJVo0ojR5AkSEByzwpaIVDcTHq6V4/mAXmrtYF+37RNpAoloMXU6h0KYoKSjZmnxpQubXWkYQolOLqw6Ug6wQu5r2zZXp1B5Mbbf3dEGlpSfdmdTROI0qDFLTC4fRvHMxCc2csKHBmI1w7q3UkUUSzd5zjAf1GAPTNH5GJFIRdC+w8GoCuORvYfqJoU7YLO5Cbg2X/bwCscw6jaWUvjQOJ0iAFrXA43er6k+wUxGZzI+uCfbceSUPYj+tZJnbu3U8H/WFUFGgyTOtIQtyWa71eXDdUxE9JZd+6+VrHEUV1YhVOOckkqN74Ng2X7gblhBS0wuG4GPX0ahDI/JvdDvbOBotZ21Dijhbvi6O/Zb31m+qdwTtU0zxC3JHeQE5D61SpNS/+QUJqlsaBRFGYo2cD8Lu5M/2ayudMeSEFrXBIg5pXItLSihTcIfUCnF6vdSRxG6oKc3ec5SHDegCU5iO1DSREEVXsOAaAHko0f2yO1jiNuKO0RJSTkQBsdA2jeai3tnlEqZGCVjikzrX8cK/gzu+5N8YW3CsPh9mzU9chMGknlZUrqC7eUH+A1pGEKJqAelz1bY5BsZC9Zw4ms8xQaNcOzEenmtlnqUn9pm2ku0E5IgWtcEgGvY4BTUOYb+5mXXB0GWQkaZpJ3NqWeB1D9esBUJo8JGPPCofi2cH6cFg/02rWHknUOI24JVXFstfa3WCBuQv9mwRrHEiUJilohcO6v3klDqnVOKxWA3MOHJCHNuzR1bRsYpPS6K3bZV3QQrobCMdibPwAOTo3auri2LN5pdZxxK1cikaXeIhs1ciuCt2ku0E5IwWtcFhNKntRw68C83JvPhz2s7aBRKEWRF9ioG4LTooZgptBUGOtIwlRPM7u5NSPAKBR4h8kZGobR9zCnp8AWGFpQ6cmdaS7QTkjBa1wWIqiENG8EovNHTFhhPgDELdf61jib8wWlbk7Yxmqt051K1dnhaNyb299OKyfbgd74mS0A7uTnYZ6cCEAc3N7SHeDckgKWuHQIppVIgV3VppbWhfIw2F2ZePxy/inHqSu7gKqwRUaP6h1JCHuTqWWpHvVxlXJIShpG2nZuVonEn93cCFKThqnLMGc92gm3Q3KISlohUOrUtGN1tV8+O3mw2Exv4FJrp7Yi1+2n+Mh/XoA1PoDwUVm7BEOSlFwbWt9OOwBZT2/772kcSCRT7S1u8E8czf6NQmR7gblkBS0wuE91CqULZZGJCh+kJVsHfFAaO7CtQy2H4tlgH4bAJZmwzVOJMS90TUdhlkx0ER3hq1b1mOxqFpHEgDxB+HiHkyqnoXmLvST7gblkhS0wuH1axyMq5ORuaYu1gXycJhd+HVnLP1023FXskhzDkQNba91JCHuTYWKmOv0A6BT2ko2nbyicSAB5F2djbS0xNkrULoblFNS0AqHV8HZwH1NQphvvlHQnl4PSWc0zVTe5eRamLfrAsNuPAx2rmJXkFuAogzQtXgUgPv1m5mz+ZjGaQSmTIiZB8Bccw/6NQ6W7gbllBS0okx4qHUoF9QANqlNrQv2zNQ0T3kXeTge7/RTtNSdQFX0nPftpHUkIUqEWr0r1w1+eCkZuJxawdkr6VpHKt8O/wFZKVxQ/dlsaSTdDcoxKWhFmdCiijc1/Sswy9TTumDvz5CbrW2ocuyX7efyZgZTa/cm2+itZRwhSo6i46JfZwAe0q1n1rZzGgcq526MPTs3txvBXm7S3aAck4JWlAmKovBQq1DWWppzRVcRMq7CkaVaxyqXTiZeJ/p0AoP1mwCwNBuhcSIhSlZsxc6oKHTUH2L77l2kyxBe2rh8HGK3YkHHfHNX6W5Qztm0oE1KSmL48OF4enri7e3NmDFjSEtLu+023bp1Q1GUfF9PPfVUvnViY2Pp378/bm5uBAQE8Oqrr5KbKx8o5d3gFpVRdAZ+zu5mXbBrmqZ5yqtftsfSV7eDisp18AhBrdlT60hClKhMJz8sNXoAMMi8ikXRFzROVE7deBhsvdqcBHxlMoVyzqYF7fDhwzl06BBRUVEsW7aMjRs38uSTT95xu7FjxxIXF5f39fHHH+e9Zjab6d+/Pzk5OWzdupWffvqJmTNnMnHiRFueinAA/h7O9GkUxFxzd8zoIXYrJB7ROla5kpGTy8LoCzxqWG1d0Go06AzahhLCBtRWjwPwkH4Dc7YcQ1VlCK9SlZsN+38FYLapG9X9KtBMuhuUazYraI8cOcLKlSv58ccfadu2LZ06deKrr75i7ty5XLp0+wGp3dzcCAoKyvvy9PTMey0yMpLDhw/zyy+/0KxZM/r27cu7777L119/TU5Ojq1ORziIR9tVJQFf1qgtrAt2z9A2UDmzdP8lQrNP0kp3HFVngBaPaR1JCJtQa4Zh8aqCj5JGw2tr2CxDeJWuo8sh4ypJ+oqstzQjolkl6W5QztmsoN22bRve3t60atUqb1lYWBg6nY4dO3bcdtvZs2fj5+dHo0aNmDBhAhkZGfn227hxYwIDA/OWhYeHk5qayqFDh0r+RIRDaVPdl7qBHvx88+Gw/b9CjjyFXBpUVeWX7bGM0EcBoNQfCB6Bd9hKCAel06Nrbb1KO0IfxU9bz2qbp7zZPR2A2dmdMaMnonmIxoGE1mx2LzA+Pp6AgID8BzMY8PX1JT4+/pbbPfLII1StWpWQkBBiYmJ4/fXXOXbsGIsWLcrb79+LWSDv+1vtNzs7m+zsv554T01NBcBkMmEymYp/cqXgZi57zWfPHm5TmclLG3FRCaJSdjy5+39DvcWDSdLOJWff+WTOXbxEhPNWAHJbjEL92/9j0sa2Je1cOvK1c6Nh6Ne+TzNOc/nYNk7G16FqRTeNE5YNt30/Jx7GeHYTFkXPnNyeNA/1IsTTSd77xeQInxnFyVbsgvaNN97go48+uu06R47cfb/Fv/exbdy4McHBwfTs2ZNTp05Rs2bNu9rnBx98wOTJkwssj4yMxM3Nvj98oqKitI7gcFzN4KTX81NOd940/kra2v+y4ZLvbbeRdr53v5zQMVi/CTclm1SXyqw7cA0Orsh7Xdq4dEg7l46b7dzCqzWh17YwQhfFlLnVeaC6ReNkZUth7+cmsTOoDmxQWxBHRToaklixYkXBjUWR2PNnxt/v0N9JsQval19+mVGjRt12nRo1ahAUFERiYmK+5bm5uSQlJREUFFTk47Vt2xaAkydPUrNmTYKCgti5c2e+dRISEgBuud8JEyYwfvz4vO9TU1MJDQ2ld+/e+frn2hOTyURUVBS9evXCaDRqHcfhHFCOsGBHV141LsA78yz9mwWjhjQvsJ60c8m4mp7DKzvX8+GN7gYVuj1Pv5b9AWnj0iLtXDr+2c7KxQCY2YcB+m18ljSSTo/3x9NV2v9e3fL9nJmM4SvryEdTs/tg0Cm8NqwnPm5OGiV1XI7wmXHzjnpRFLug9ff3x9/f/47rtW/fnuTkZPbs2UPLli0BWLt2LRaLJa9ILYp9+/YBEBwcnLff9957j8TExLwuDVFRUXh6etKgQYNC9+Hs7Iyzs3OB5Uaj0W5/iDc5QkZ7NKpjdX7ZcZ7l5jZE6Ldg2DcLqra55frSzvdm0b5ztFYPUlMXh+rkgb75I+j/0Z7SxqVD2rl05LVz1XaoQU1wiY/hvty1LNjbgv/rend3E0VBBd7Pu38DUwaXXWuyI6seYfUCCPCqoF3AMsCePzOKk8tmD4XVr1+fPn36MHbsWHbu3MmWLVsYN24cw4YNIyTE2nn74sWL1KtXL++K66lTp3j33XfZs2cPZ8+eZcmSJYwcOZIuXbrQpEkTAHr37k2DBg149NFH2b9/P6tWreLtt9/m2WefLbRoFeVTrQAPetQL4JfcGw+HHVgAmcmaZiqrzBaV2dtjefTmw2BNh4Gzh8aphCglioLSZiwAI/SrmbXlNCazdDuwCYsFdv4AwA85YYDCAy0qaZtJ2A2bjkM7e/Zs6tWrR8+ePenXrx+dOnXi+++/z3vdZDJx7NixvD4STk5OrF69mt69e1OvXj1efvllHnjgAZYu/WvGJ71ez7Jly9Dr9bRv354RI0YwcuRIpkyZYstTEQ5obOca7FbrclytDLmZsH+u1pHKpHVHEzEnX6CXfo91Qesx2gYSorQ1ehDV2ZOqukRqpe3iz4O3fvBZ3IOTq+HaGUxGD35Ob0vFCk70rC8jqQgrm4547uvry5w5c275erVq1fINRh0aGsqGDRvuuN+qVatKB3BxR+1q+NK4kjc/x4fxrnEm7PoB2jwJOpnxuSTN2n6Ohw1rMWCBqp0goL7WkYQoXU5uKM1HwPZveFQfyVebuzKgiUzDWuJ2fgfAerfeZF53YUSLSjgZ5PNcWMk7QZRZiqIwtksNFpk7k4YbXD0Jp9ZoHatMOXMlnW3H43hYv866QK7OivKqlfW930O3j6sXThAde03jQGXM1VNwcjUqCh9c7gTA0NahGocS9kQKWlGm9WsUhLe3L/Nyu1oXbP9W20BlzC/bz9Fbt5sAJRncA6H+AK0jCaENv1pQozs6ReUR/Rp+3HRG60Rly42+s7G+HTltCaRlVR9qBUhfffEXKWhFmWbQ6xjTqTozzb2xoFiv0F4+rnWsMiEzx8z83ecZZVhpXdDiMdDb55OyQpSK1k8AMEy/lg2HznE+qehjaIrbyE6DfbMB+DrD+qDv0FZydVbkJwWtKPMeblOFzAqhrDG3sC640Q9L3Js/9l2kWvYxWuuOo+qM0t1AiLp9wbsKvkoag3SbmSnT4ZaMmLmQnUqmRzXmJ9emgpOe/k2CtU4l7IwUtKLMc3XS82SXGkw39wFA3ferDOF1j1RVZda2c4wx/AmA0vhB8Cj6hClClEk6PbS1Dvr/uH4lv+06x/Us+51W1CGoal53g2Uu/VHRMbBZCBWcbfpMu3BAUtCKcmFEu6occ2nGUUsoiikdomdpHcmhRcde41rcGfrrtlsXtHtG20BC2Ivmj6I6eVBbd5GWpmjm7TqvdSKHppzdBJePYjG68e+L1rtsI9tX0zaUsEtS0Ipywc3JwNguNf+6SrtjKpjlysndmrXtHI8ZIjEoFqjWGYKbaB1JCPvg4onSYiQAj+v/ZMaWszLRwj3Qbf8agH2+/UixuNKuhi/1g+1zynqhLSloRbnxaPuqrHfqxmXVCyX1Ihz6XetIDuny9WzWHzjDw/obQ6C1f1bbQELYm7b/h6ro6KI/QIWU4yyLuaR1IofkkXkB3ek1qIqOSYnWkWpGdaiucSphr6SgFeWGu7OBUV3rMSM3HADLli+t/bNEsczbFcsg1uOlZIBvTagdrnUkIeyLT1WUevcB8IR+Bd9tOJ1vEiFRNLUSrX30LwSGcSCzIpW8XQmrH6BxKmGvpKAV5croDtWJdO1HhuqMLuGAtX+WKLJcs4W5288wVn9jpr52T8vMa0IUpsNzANyv38y1+HOsP35Z40AO5nocla9tBeA/6dY/mke2r4pBL583onDyzhDliquTnsd7tWSeuRsAlq1faRvIwaw5mkiLtPWE6i6juvlB8xFaRxLCPoW2gSodMCpmHjf8ydT1p7RO5FB0u6ehU82k+Ldk8eVgXIw6mRlM3JYUtKLceahVZVZ7DsasKjidXYdnZqzWkRzGz1vP8pRhGQBKu6fA6KpxIiHsWKcXARiuX8uRM+fZK9PhFk32dXTRMwD4Prc/AENahuLt5qRlKmHnpKAV5Y5Br2NE3678aWkLQLW4ZRoncgynLqehP7OWBrpzWIwV8mZFEkLcQu3eENAAdyWTEfrVfLfhtNaJHMPu6ShZKSQZg/kmrg5GvcJT3WpqnUrYOSloRbnUp1EQa/yGA1A1ZQckyS+aO5mx5QxPG5YAoGs1Glx9NE4khJ1TFOj4AgCjDX+y/nAspy+naRzKzpkyYev/AJihDkBFx4MtK1PJW+4GiduTglaUS4qiMCJiAGvMzdGhkrL6P1pHsmvJGTmc2LOOdrojWHRGmUhBiKJq9AB4heKvpPKgbgM/bJI/nm9r7y+Qnkh2hRC+TeuEXqfwdNdaWqcSDkAKWlFutazqQ0z1xwHwOrEQNVlm9LmV2TtieZJFAChNHgKvShonEsJB6I15Ix48ZVjKkj3nSLyepXEoO2U2wZYvAZjvPJhcDAxsGkyVim4aBxOOQApaUa49OOh+dljqYySX00s+0jqOXcrJtbBzyxp66veiokPp/LLWkYRwLC1GgnsglZUr9GcDM7ac1TqRfTowH1JiMbn68e6lViioPN1FJlIQRWPQOoAQWgrydGGxzwDaphyh0ul5ZCS9iZtviNax7MqKA3EMz54HerA0HoK+ov08nGE2mzGZZApjAJPJhMFgICsrC7PZrHUcu2A0GtHr9VrHsI4G0vEFWPUm4/SLGbS9O890q4mHi1HrZPbDYoZNnwEwRzeAbJxo62+hul8FjYMJRyEFrSj3gqo05PDB2jRQT7Djtym0fWqq1pHshqqqrFm/mq/0e1BR0Hd9VetIgDVXfHw8ycnJWkexG6qqEhQUxPnz51EURes4dsPb25ugoCDt26TlaNTNn1Ml/TI9cjby8/a6PNNN+obmObAArp4gx+jJJ1c7UsFJz31VcrVOJRyIFLSi3HMyKGR2fBU2P0nTuAWcPPUKtWrKLxqAnWeS6Jv0C+ghp/79OPvV1joSQF4xGxAQgJubm/bFih2wWCykpaXh7u6OTmZvQ1VVMjIySExMBCA4OFjbQE5uKB2eg6iJPGtYzEMbuvFY+2pUcJZfw5hzYcOHAEyzDCANN17uUh3P9KMaBxOORP5PEgJo0uV+Tu36LzWzD3N84RRqvPITOp0USavWrGaificWFJy7v6Z1HMDazeBmMVuxYkWt49gNi8VCTk4OLi4uUtDe4OpqHeopMTGRgIAA7bsftBqDuvm/1MiMp2v2en7eXoenutpPFx7NxMyDpNNkGLz5Kq0nlbxdGd2hKmuipKAVRWfTT72kpCSGDx+Op6cn3t7ejBkzhrS0W4/Bd/bsWRRFKfRr/vz5eesV9vrcuXNteSqirFMUvPq/A0DP9BUs37xb2zx24OyVdDrGfgtAeq0BEFBf40RWN/vMurnJk8/izm6+T+yir7WzO8qNcWlfNCxkxoZjZOSU89vqZhNssD6Q+1V2fzJw4Y2+9XA22kHfZ+FQbFrQDh8+nEOHDhEVFcWyZcvYuHEjTz755C3XDw0NJS4uLt/X5MmTcXd3p2/fvvnWnTFjRr71IiIibHkqohzwa9ybOK/mOCsmMtd+zOXr2VpH0tSayCX01O/FjA6Pvu9oHacA6WYgisLu3idtnkR1DyRUd5ne2auYvb2cT729bzYkn+OazocZpjA61/bjviYadw8RDslmBe2RI0dYuXIlP/74I23btqVTp0589dVXzJ07l0uXLhW6jV6vJygoKN/X77//zkMPPYS7u3u+dW929L/55eLiYqtTEeWFouA/6F0AItQ1fLkgUuNA2knJyKHJsS8ASKw1BOxoZIPyJCcnh/fff58jR47Y/FiLFy/m119/tflxyj0nN5Qu1ocrnzf8zk8bDpGZU05HpTBlwoaPAfgq+z6MzhX46IEm9vdHiHAINutDu23bNry9vWnVqlXesrCwMHQ6HTt27OD++++/4z727NnDvn37+Prrrwu89uyzz/LEE09Qo0YNnnrqKUaPHn3L/wmys7PJzv7raltqaipgvQVlF7ehCnEzl73mKysKtHNoO65X6ozHxU20Pv01S/Y2o2+jIA0TamPjn78yQDlCDkYq9nnznt6HJf1eNplMqKqKxWLBYrGUyD611KNHD5o2bcrnn39e4LXx48dz5coVXn/99Tue6+jRo7ly5QpLliwpdrts376d559/nvXr15eJNv07i8WCqqqYTKYS6UNbIu/nJo+g3/Il/imxDMhaxs/b6jO6Q9V7zuZodFu/QZ96kYuqH7PNPZk0oA7+FQz5fjfL70DbcYQ2Lk42mxW08fHxBAQE5D+YwYCvry/x8fFF2se0adOoX78+HTp0yLd8ypQp9OjRAzc3NyIjI3nmmWdIS0vj+eefL3Q/H3zwAZMnTy6wPDIy0u774UVFRWkdoVz4ezt7uvemK5sZqN/GsIWLuH6qGu7laLhIs9lCvZjPQIEdFcJI2rIf2H/P+y2p97LBYCAoKIi0tDRycnJKZJ9ays3NJScnJ+8P7Zt+//13YmJiWLBgAdevX7/jfqZMmQJQpHX/LikpiTFjxvDzzz/j6+tbIEdx+fj45P3bw8OD+vXr89Zbb9GlSxcAnnnmGVJSUpg9e3be97/++isTJ07kpZdeytt2+fLljBgxgmvXrgGwefNmBgwYQL169di8eXO+4rRq1ap88MEHPPLIIwXy5OTkkJmZycaNG8nNLbn+qvf6fq7s3ZeWKd/xlGEJ/Vd3x+fqIZzKUbdRY+51wg59ih741DSEGt4G3OJjWLEiJt968jvQ9uy5jTMyMoq8brEL2jfeeIOPPrr9jEolcXssMzOTOXPm8K9//avAa39f1rx5c9LT0/nkk09uWdBOmDCB8ePH532fmppKaGgovXv3xtPT856z2oLJZCIqKopevXphNJajaqqU3aqdzYtj0B2azwvKXGZnfcXng5pqmLJ07Vk6lQbKWdJwpfnoT3H2Cryn/ZX0ezkrK4vz58/j7u5eJroaGQwGnJycCnwWPfbYYzz22GN33N5sNqMoCh4eHly/fh0PD49i3bL19PTk0KFDxc59O9OmTaNPnz5cuXKFt99+m2HDhhETE0ONGjUwGo0YDIa88zUajbi4uPDll1/y/PPP5xXEN0couLnezYsPZ8+eZfHixYwePTrveIqi4OLiUujneVZWFq6urnTp0qVE3i8l9n62hGP5YSNeV44wSl1Mst+/GdW+/Fyl1UW9jd6SwWFLVTY4d2PxEx0J9vrr5yO/A23PEdq4OH9gF7ugffnllxk1atRt16lRowZBQUF54//dlJubS1JSEkFBd76Fu2DBAjIyMhg5cuQd123bti3vvvsu2dnZODs7F3jd2dm50OVGo9Fuf4g3OULGsqBAO/eaiOXoEtpzmO8Or2Td8cr0blj2ux6Ys9KoecB66/tgjbG086tcYvsuqffyzQJOp9M53PBU6enpPP300yxatAgPDw9eeeUVgLzzAWsXqbfeeotff/2V5ORkGjVqxEcffUS3bt0AmDlzJi+++CKzZs3ijTfe4Pjx45w8eZJJkyZx5coVli5dyo8//sg777zDhQsX8rXRoEGDqFixItOnTwfgjz/+YPLkyRw+fJiQkBAee+wx3nrrLQwG66+G5ORkXnnlFf744w+ys7Np1aoVn3/+OU2b3v4PPF9fX0JCQggJCWHq1KlUqlSJNWvWUKtWrbyRaW7mUhSFsLAwTp48yUcffcTHH1v7VN58/Z//fe6555g8eTIjRozI97l+q/eDTqdDUZQS/yy99/0Zoc+/4ZcHGKmP5OGN/Xi0fXVcysPT/dfOYt41DYAPcx/mf4+1ooqfR6Gryu9A27PnNi5OrmL/NvD396devXq3/XJycqJ9+/YkJyezZ8+evG3Xrl2LxWKhbdu2dzzOtGnTGDhwIP7+/ndcd9++ffj4+BRatApxV7yroGtrHZHjLcMcJv6+j+QMx7+9fScn//gAf/UqF/Gn0QOvax2nyFRVJSMnV5MvVVWLnPPVV19lw4YN/PHHH0RGRrJ+/Xqio6PzrTNu3Di2bdvG3LlziYmJYciQIfTp04cTJ07krZORkcFHH33Ejz/+yKFDhwp07xoyZAhXr15l3bp1ecuSkpJYuXIlw4cPB2DTpk2MHDmSF154gcOHD/Pdd98xc+ZM3nvvvXz7SUxM5M8//2TPnj20aNGCnj17kpSUVORzvnml9XbdQ/R6Pe+//z5fffUVFy5cuO3+XnzxRXJzc/nqq6+KnMFu1QrDUjMMJ8XM/2XPZO7O8jHiwdU/3kSvmthkbkTnPkPpUNNP60iiDLBZH9r69evTp08fxo4dy9SpUzGZTIwbN45hw4YREhICwMWLF+nZsyezZs2iTZs2eduePHmSjRs3smLFigL7Xbp0KQkJCbRr1w4XFxeioqJ4//338650CFFiOr+Mum8OtTMu0i9zGVOWBfHZQ820TmUzaspFqh75AYB9dV+ifwX3O2xhPzJNZhpMXKXJsQ9PCcfN6c4fpWlpaUybNo1ffvmFnj17AvDTTz9RufJfV8FjY2OZMWMGsbGxeZ+Tr7zyCitXrmTGjBm8//77gPVW4TfffHPLK6U+Pj707duXOXPm5B1rwYIF+Pn50b17dwAmT57MG2+8kdetoUaNGrz77ru89tprTJo0ic2bN7Nz504SExPzLhZ8+umnLF68mAULFtx2CMabMjIyePvtt9Hr9XTt2vW2695///00a9aMSZMmMW3atFuu5+bmxqRJk3jzzTcZO3YsXl5ed8xhz3R93sfyzTp66/fwzLrFDGvzfJm+SnshehWVzy7HrCpsrv4Cb3SurnUkUUbY9H7d7NmzqVevHj179qRfv3506tSJ77//Pu91k8nEsWPHCnT6nT59OpUrV6Z3794F9mk0Gvn6669p3749zZo147vvvuOzzz5j0qRJtjwVUR65+qD0nAjAi4YFbIw+zNqjCRqHsp3439/EhWyi1bp0HPiE1nHKnFOnTpGTk5PvDpWvry9169bN+/7AgQOYzWbq1KmDu7t73teGDRs4depU3npOTk40adLktscbPnw4CxcuzBvhZfbs2QwbNizvtvz+/fuZMmVKvuOMHTuWuLg4MjIy2L9/P2lpaVSsWDHfOmfOnMmXpTAPP/ww7u7ueHh4sHDhQqZNm3bHvAAfffQRP/300x2fwxgzZgwVK1a84/McDsG/LmpLa3/gZ3NmMGvL7dvWkcVdu07WUuuQZZFu/XhxxAMyRJcoMTad+tbX15c5c+bc8vVq1aoVervu/fffz7sS8U99+vShT58+JZZRiNtq/ijsnoFn3D5eM8zl9YUBrHzBm4ruZat7i3p2C8FnFwMQ0/A1WlRwrPNzNeo5PCVcs2OXlLS0NPR6PXv27CkwxNTfx+J2dXW9YyEwYMAAVFVl+fLltG7dmk2bNuUbGiwtLY3JkyczePDgAtu6uLiQlpZGcHAw69evL/C6t7f3bY/9+eefExYWhpeXV5G6jd3UpUsXwsPDmTBhwm2f1TAYDLz33nuMGjWKcePGFXn/9krf/U1y9v9GQ9M5lq7/lpS2H+Plap99Gu9WSoaJRd9N4Vn1HCl40H7MZ7iWp2EdhM3ZtKAVwuHp9NDvE5jWi4cMG5iT1pM3Fnnz/aMty86Vhdwc0he9gDswz9KTfn3v0zpRsSmKUqTb/lqqWbMmRqORHTt2UKVKFQCuXbvG8ePH827HN2/eHLPZTGJiIp07d76n47m4uDB48GBmz57NyZMnqVu3Li1atMh7vUWLFhw7doxatWoVun2LFi2Ij4/HYDBQrVq1Yh07KCjolvu9kw8//JBmzZrlu3JdmCFDhvDJJ58UOiSjw6lQEUOvd2DFeJ5Vf2VW1GCeHXhvP397kpady3PTovgq8xdQwNL9LXz8yv5DtqJ0OdYjwkJoIbQNNH0YgPedprHu8EXm7TqvcaiSY9n2Ne6pJ7iiehLX+nUCPBx/KCx75O7uzpgxY3j11VdZu3YtBw8eZNSoUfmezK9Tpw7Dhw9n5MiRLFq0iDNnzrBz504++OADli9fXuxjDh8+nOXLlzN9+vS8h8FumjhxIrNmzWLy5MkcOnSII0eOMHfuXN5++23AOhFO+/btiYiIIDIykrNnz7J161beeustdu/efW+NcRuNGzdm+PDhfPnll3dc98MPP2T69Omkp6fbLE9p0bUaTbJvUzyUTKrtfo+E1CytI5WIzBwzj8/cxaDEr/FSMsiq2BCfznfufy1EcUlBK0RR9HoXXH1ooJxjrH4Fk5ce5swVx/8lyrVzqOs/BOAzHmVUz+YaByrbPvnkEzp37syAAQMICwujU6dOtGzZMt86M2bMYOTIkbz88svUrVuXiIgIdu3alXdVtzh69OiBr68vx44dKzDpQHh4OMuWLSMyMpLWrVvTrl07Pv/8c6pWtY6FqigKK1asoEuXLowePZo6deowbNgwzp07R2DgvY1NfCdTpkwp0oxlPXr0oEePHiU6YYJmdDq8HvwSMzr667ax/PfZWie6Z9m5Zp78eTeu59bxgH4zKgou939pvfMlRAlT1OKMOVNGpKam4uXlRUpKil1PrLBixQr69etnt+PDlQXFaud9v8Lip8jBSHj2h7gF12XRMx1wNjjoh7OqYvnlAXSn1rDdUp8dnWfxQq86JX6Ykn4vZ2VlcebMGapXr14mJlYoKRaLhdTUVDw9PR1ufF5bKun3i60/m+PnvUTQkenEqv5kPrGJuqHBJX6M0mAyW3j6l2i2HjnHaufXCFGuQLtnoM8HRdtefgfanCO0cXHqNfnUE6Komg6Dmj1wwsQn/9/efYdHVWZ/AP/e6SmT3hspBAi9I8UVBQXLb5fVxd5YFtQFV0VdZdcVO669i7r2srLWtaIsqCjSe0uoISG9l5lMv78/Zt6bBJKQSea2mfN5njy7TCaTd66TmXPPPe85xtexv7wRy78plHtVfbf9bWiOrIGd1+Of2hvwR2qfQ4jsUuY8gDpdErK4GpR8eIdffY6Vwu3hcdvKnfjfgSrcZfiPN5iNzgLO/rvcSyNBjAJaQnqL44CLngH04RiP/bha+z+89WsxVu2tlHtl/ms4Dv67vwEAHnddivPP/g3MJmWeoRMSUoxmuP/vBQDAuZavsO2Hz2RekH88Hh53f7IbX+2uwGRdEa7V+PpD/98zgFE9va2J+lBAS4g/YgcAM+8DANxr+DcGcifw1493obTe2vPPKYnHA/x3ETiHBZs9g7Em+mJcNyVb7lURQnySRs3C9uQ/AAAyf74T9tYGmVfUe/9cVYiPtp1AjMaKN6JeAwceGH0VMHCG3EsjQY4CWkL8NWEBkDcDet6O18JXwGZrw8J3t6HN4ZZ7Zb2z6WWg+GdYeSPucN6Iv100Qr11wIQEqUFXP4VSpCCZr0Xxu4sAFZQe/Ovno3hl3VEAPL7I/gRh1nIgNhs4PwgGYBDFo4CWEH9pNMCcl4HweOS4j2JZ2Ec4UNGMuz/drfx6t9ItwGrv9LNHXFdiwMBhmFmQJPOiCCEnizRH48jUx+HmOQyu+hr1v7wh95J69PmOMjz0tXfC2xtjjiCr/FuA0wIX/wswmmVeHQkFFNAS0hfmZOB3LwEAruK/wrna7fjvznK8/ssxmRfWA2s98PE8wOPCV+5J+Dd/Lu69aGjwDIggJMicNfP/8J+o6wAAkWvvBl+5R+YVdW3dwRrc8dEuAMBfx3I4+8hj3m9MvxvInCDjykgooYCWkL4aPBuYeAMA4MWwFcjjyvDINwfwQ2G1zAvrgscDfH4T0FSKUi4VdzsX4NrJ2chPpswJIUrFcRwmXvMgfvKMhoF3wPLe1YC9Re5ldbKrtBE3vrcNLg+PS4dH4aaqf4BztAIDpgJn3i738kgIoYCWkP447yEgawoMrlb82/w8IngrFn2wHXvLmuReWWc/LgcOroKTM+AG282IjYvHHef1PFqUECK/vKQoFE15AuV8HCJbi+H86E+ARxn1+sdqLZj31hZYHW78ZmAcHsVz4OoOA1HpwNy3aYACkRQFtIT0h84AXPo2EJWOJEcJ3o55DTaHE/Pe2oITDQrpfLDzA2Cd9xLg3xzXYz+fjccuGYUIo07mhRFCeuP6meOwPOJu2Hk99IdXAd/fI/eSUN1swzWvb0K9xYER6dH4V9b30Bz+HtCZgMvfByIT5V4iCTEU0BLSX5FJwGXvAVojxto24YWod1HTYsN1b2xGTYtd3rUdWwd88RcAwDvaS/CRezqunTwAk/Pi5V0XIaTXDDoN5l1+Ke503+S9YeNLwKZXZVtPs82Ja9/YjBMNbciOD8e/R++B4denvN/8v2eBNBqhTaRHAS0hgZA+FrjkXwCnwQWO73B/xCc4UmPB1f/ahLpWmYLail3AyqsBjxNbIqZjmeX3yIwLw12zh8izHiI7juPw+eefy70M0gdjs2KRN/1aPOa8DADAr7oL2Cf90AWb040Fb29FYWULEs1GfDytHJFrlnq/edZd3omKhMiAAlpCAmXob72TxABc5/4US8K/RVFVC6761yY0WBzSrqViF/D2bwFbE8rNI3F13fXQ63R44YqxVGpAiEotOjsPm9Ovw79dZ4PjPeA/ng/s+1yy3+/28Ljlwx3YdKweZqMOH89oQcLqvwDggYkLgelLJVsLISejgJaQQBp3HTDzfgDAXzzv4m9hn6GwshmXvboBZY1t0qxBCGYb0Rg/GufV/AV2GPDwnOEYlRkjzRpIlzweD5YvX46cnByEhYVh1KhR+Pjjj8HzPGbOnIlZs2YJvYzr6+uRkZGBe+/19g12u92YP3++8LODBw/Gs88+e8rveOONNzBs2DAYjUakpqZi8eLFAIDs7GwAwO9//3twHCf8GwD++9//YuzYsTCZTMjNzcX9998Pl8sl7sEgftNpNXj68jF4VHsDPnGfCY53Ax//UZKglud53PP5Xny3rwoGrQafnFmBAd8vADwuYPgfgNn/9I4HJ0QmlKohJNCm3Qq4ncAPD2Eh/xHiw5twZ9W1+P2L6/HG9RMwPD1avN99+H/AR38E7E2wJI7BrOpb0AoDrps8AHPHZ4r3e+XG84BTpk14+vBef5AvX74c7733HlasWIH8/HysW7cOV199NRITE/H2229jxIgReO6553DLLbfgxhtvRHp6uhDQejweZGRk4KOPPkJ8fDx+/fVXLFy4EKmpqbj00ksBAK+//jruuecePProozj//PPR1NSE9evXAwC2bNmCpKQkvPnmm5g9eza0Wu8O9J9//hnXXnstnnvuOZx55pk4cuQIFi5cCABYtmxZoI8W6afMuHD8c+5o/Pk9b8vAS7Q/e4NaSw0wcYFov/fp/x3CvzeXgOOAzybsw6BfHgLAA8Mu9g6a0VB+jMiLAlpCxHDWnUB4HPD17bjE8z3SIhtxY8ufcNkrG/DUZaMxa1hKYH8fzwObVgDf/Q3gPWhJnohzK/+MKrsBk3Pjcc9FQwP7+5TGaQUeSZPnd/+tHDBEnPZudrsdjzzyCP73v/9h8uTJAIDc3Fz88ssveOWVV/DBBx/glVdewbXXXovKykp888032LFjB3Q679u0Xq/H/fffLzxeTk4ONmzYgP/85z9CQPvkk09iyZIluOWWW4T7TZjgbWyfmOjddR4TE4OUlPbX3/3334+7774b1113nbCmBx98EH/9618poFWo2cNTseS8Ibjz+xvghhaXan8EvrkDqD7gHTOr1Qf096346QieW3MIerjwxaDVKNj5rvcbExYA5z9GwSxRBApoCRHLhPlAeDzw6QJMdm3G/yKKsdC6CDe868Y1ZwzA3y8sgEkfgD6NbY3AqruBXf8GANTmz8W5B+egwc5hYk4c/nXdeOi19IEjt8OHD8NqteLcc8/tdLvD4cCYMd5d4XPnzsVnn32GRx99FC+//DLy8/M73ffFF1/EG2+8gZKSErS1tcHhcGD06NEAgOrqalRUVOCcc87xa127du3C+vXr8fDDDwu3ud1u2Gw2WK1WhIeH9+HZErEtOnsgDle34q87F6BMm45b8QG4ra8DNYXAnJeA2Ox+/w6e5/H06oN4bu1hZHA1+DjhVaQc3+f95vSl3k1gVGZAFEK0gPbhhx/G119/jZ07d8JgMKCxsfG0P8PzPJYtW4bXXnsNjY2NmDp16ilv6vX19bj55pvx5ZdfQqPR4JJLLsGzzz6LyMhIsZ4KIX03bI73g+Wj65HYcAwfmx7AS87/w8sbf4vNx+qx/JIRGJsV2/fHL1oFfHUr0FIBHhy2D1mCK/eOh93F44zcOLxx/QSEG0LgvFUf7s2UyvW7e6G1tRUA8PXXXyM9Pb3T94xGIwDAarVi27Zt0Gq1OHToUKf7fPjhh7jjjjvw5JNPYvLkyTCbzXj88cexadMmAEBYWFiflt/a2or7778fF1988SnfM5lMfXpMIj6O4/DoJSNxoqENzx6/EEeN6XhG/yK0x9cDL00BZt4HTPhTn7OnHg+Ph785gDd/OYIrtT/g3rD/wNTSApiivSUGQy4M7BMipJ9E+6RzOByYO3cuJk+ejNdff71XP/PYY4/hueeew9tvv42cnBz84x//wKxZs7B//37hjfWqq65CRUUFVq9eDafTiXnz5mHhwoX44IMPxHoqhPRP2mjghnXAl7dAu+9T3Kz7HJfp1uHRmksx96VGXDQ6E3fNHoK0GD8CkhNbgZ8eAw59BwBwx+bi2Yhb8dzOBAA8zhmShBevHIswQ4hM6uG4Xl32l9PQoUNhNBpRUlKCs846q8v73H777dBoNPj2229xwQUX4MILLxQyruvXr8eUKVPw5z//Wbj/kSNHhP9vNpuRlZWFtWvXYsaMGV0+vl6vh9vdecrU2LFjUVRUhIEDB/b3KRKJmfRavDlvAua/tRVfFo/GIf4RrEx5H9HVm4Fv7wR2vg+c9Vdg8AV+ZVKbrE7ctnIH7IfW4mvDeyjQlAIuAOnjgT+8AcQOEO9JEdJHogW0rNbrrbfe6tX9eZ7HM888g3vuuQe/+93vAADvvPMOkpOT8fnnn+Pyyy/HgQMHsGrVKmzZsgXjx48HADz//PO44IIL8MQTTyAtTaYaOkJOxxTl/SAY9nvg+3uQ1HgcTxlW4E7+P/jP3um4au90jB81GtdNye5+01hbA3Dwe2DXB8DRHwEAPKfBzvQrcVPZbFRWaKDTcLhr9hDMn5YDjYYuBSqJ2WzGHXfcgdtuuw0ejwfTpk0TNm1FRUUhISEBb7zxBjZs2ICxY8fizjvvxHXXXYfdu3cjNjYW+fn5eOedd/Ddd98hJycH7777LrZs2YKcnBzhd9x9991YsmQJkpOTcf7556OlpQXr16/HzTffDMDb6WDNmjWYOnUqjEYjYmNjce+99+Kiiy5CVlYW/vCHP0Cj0WDXrl3Yu3cvHnroIbkOF+kls0mPt/44ATe8uw0/HwLGn7gFrw/bjTOLXwBXsRP48EogeTgw7npg8PlAdEaPj3fgSDG++/A53GX/DoMNJ7w3mmKAs/8GjP9jwOtzCQkUxVyLPHbsGCorKzFz5kzhtujoaEyaNAkbNmzA5Zdfjg0bNiAmJkYIZgFg5syZ0Gg02LRpE37/+9/LsXRCeofjvL1q888DNr0M/Po8Uq11uEX3KW7BpzixNwE7dg/Ezsg8pCUlYEByAtLD7DC2lIKrPQSUbgJ4b3bNw+mwPeY8PNAwC7sPezf75CVG4MlLR2M0teZSrAcffBCJiYlYvnw5jh49ipiYGIwdOxZLly7FZZddhvvuuw9jx44F4E0KfP/997jxxhuxcuVK3HDDDdixYwcuu+wycByHK664An/+85/x7bffCo9/xRVXAACeffZZ3HHHHUhISMAf/vAH4fts09hrr72G9PR0FBcXY9asWfjqq6/wwAMP4J///Cf0ej2GDBmCP/3pT9IeHNJn4QYdXrt2PO74aBe+2l2Ba/eMwnkDXscTGb8gas9bQNVe76axb+4AUkYCycO8pVCRSYDTBjgtsNccQfOhDSiwFaMAADSAR2uCZtx1wPS7vZtcCVEwxQS0lZWVAIDk5OROtycnJwvfq6ysRFJSUqfv63Q6xMXFCffpit1uh93ePq2pubkZAOB0OuF0OgOy/kBj61Lq+oKFPMdZC0xaDIxbAO7gt9BsfxtcyXpkoBYZ2lqgbSNwHN6vkxziM/Cdexw+dJ+NExXev4XchAgsmp6LC0ekQKvhFPeaCfQxdjqd4HkeHo8HHo8nII8ppZtvvlnImHZUXu6tAWbPSavVYvPmzcJter0er7/++iklXA8//DA8Ho/Qv3bhwoW44YYbOt2HPeaFF16ICy+88JTbzz333FM2q3X8vpqxY+N0OoVWZf2h1PdmLYCn/jAcU/Pi8ODXhfj+uBtjS6di7tBzcXPsRqRUrAV3YjO4yt1A5e5Tft4IINH3/0sMeYib9icYx1wGtynKe6PEz1epxzmYqOEY+7M2vwLau+++G//85z97vM+BAwcwZIiyRmsuX768U7sb5vvvv1f8Dt7Vq1fLvYSQIN9xNgBxC6CLvhox1mOIaD4Mp6UWNrsDTqcdDZ4wlHiSUconYhs/CMd5b7ullDAeZ8V4UBDNY3BMEzRlO/BdmUxPoZcCdYx1Oh1SUlLQ2toKh0PiCWwq0NLSIvcSFMXhcKCtrQ3r1q0L6LAIpb43hwNYMhRYeVSDQ80a/HuvBf/GCMQahmNYeCOmag8g3lWNWHc1jK5mNLqNsPAm1CIaJfo8ZGXmIiveDDQAWPuL3E9Hscc5mCj5GFutve8v7ldAe/vtt+P666/v8T65ubn+PKSA9UWsqqpCamqqcHtVVZXQliYlJQXV1dWdfs7lcqG+vr5TX8WTLV26FEuWLBH+3dzcjMzMTJx33nmIiorq03rF5nQ6sXr1apx77rnQ66lmSSxKP85WhwvVLXZUt9hxpU6LmHA94sINMJsUc3HltAJ9jG02G0pLSxEZGUm78DvgeR4tLS0wm83gqJWSwGazISwsDL/5zW8C8npR+nsGcx2AvWXNeH19Mb7dV4UGB/CLIxa/YEqn++m1HCbnxuH/RqZiwchUaBVSe6+W46xmajjG7Ip6b/j1qZiYmCg05w60nJwcpKSkYM2aNUIA29zcjE2bNuGmm24CAEyePBmNjY3Ytm0bxo0bBwBYu3YtPB4PJk2a1O1jG41GoS1OR3q9XrH/ERk1rDEYKPU4R+v1iI4IQ36A5zDIIVDH2O12g+M4aDQaaKihu4CVB7BjQ7w0Gg04jgv437hS3zM6GpMdjxey49Fsc6KwogX7y5tQXGdFhFGL2HADUqJNOHNgIqLDlfs81HCc1U7Jx9ifdYmW5ikpKUF9fT1KSkrgdruxc+dOAMDAgQOFnrFDhgzB8uXLhdnit956Kx566CHk5+cLbbvS0tIwZ84cAEBBQQFmz56NBQsWYMWKFXA6nVi8eDEuv/xy6nBACCGEdCHKpMfEnDhMzKGNXSR4iRbQ3nvvvXj77beFf7NJOD/88AOmT58OACgqKkJTU5Nwn7/+9a+wWCxYuHAhGhsbMW3aNKxatarTZaL3338fixcvxowZM4TBCs8995xYT4MQQgghhCicaAHtW2+9ddoetGxXLsNxHB544AE88MAD3f5MXFwcDVEghATFDnwiPnqdEBIa1LOzhBBCABgMBmg0GpSXlyMxMREGg4E2QcEbuDkcDthsNqqhhTdh4nA4UFNTA41GA4PBIPeSCCEiooCWEKIqGo0GOTk5qKioEHq3Em8A19bWhrCwMArwOwgPD0dWVhYF+YQEOQpoCSGqYzAYkJWVBZfLBbfbLfdyFMHpdGLdunX4zW9+o9gdy1LTarXQ6XQU4BMSAiigJYSokhitmNRMq9XC5XLBZDLRMSGEhBy6BkMIIYQQQlSNAlpCCCGEEKJqFNASQgghhBBVC8kaWtb/1p8ZwVJzOp2wWq1obm6mejgR0XEWHx1jadBxlgYdZ2nQcRafGo4xi9NOnlvQlZAMaFtaWgAAmZmZMq+EEEIIIYT0pKWlBdHR0T3eh+N7E/YGGY/Hg/LycpjNZsW2c2lubkZmZiZKS0sRFRUl93KCFh1n8dExlgYdZ2nQcZYGHWfxqeEY8zyPlpYWpKWlnbaXdEhmaDUaDTIyMuReRq9ERUUp9oUWTOg4i4+OsTToOEuDjrM06DiLT+nH+HSZWYY2hRFCCCGEEFWjgJYQQgghhKgaBbQKZTQasWzZMhiNRrmXEtToOIuPjrE06DhLg46zNOg4iy/YjnFIbgojhBBCCCHBgzK0hBBCCCFE1SigJYQQQgghqkYBLSGEEEIIUTUKaAkhhBBCiKpRQKsSX3/9NSZNmoSwsDDExsZizpw5ci8paNntdowePRocx2Hnzp1yLyeoFBcXY/78+cjJyUFYWBjy8vKwbNkyOBwOuZemei+++CKys7NhMpkwadIkbN68We4lBY3ly5djwoQJMJvNSEpKwpw5c1BUVCT3soLeo48+Co7jcOutt8q9lKBTVlaGq6++GvHx8QgLC8OIESOwdetWuZfVLxTQqsAnn3yCa665BvPmzcOuXbuwfv16XHnllXIvK2j99a9/RVpamtzLCEqFhYXweDx45ZVXsG/fPjz99NNYsWIF/va3v8m9NFVbuXIllixZgmXLlmH79u0YNWoUZs2aherqarmXFhR++uknLFq0CBs3bsTq1avhdDpx3nnnwWKxyL20oLVlyxa88sorGDlypNxLCToNDQ2YOnUq9Ho9vv32W+zfvx9PPvkkYmNj5V5a//BE0ZxOJ5+ens7/61//knspIeGbb77hhwwZwu/bt48HwO/YsUPuJQW9xx57jM/JyZF7Gao2ceJEftGiRcK/3W43n5aWxi9fvlzGVQWv6upqHgD/008/yb2UoNTS0sLn5+fzq1ev5s866yz+lltukXtJQeWuu+7ip02bJvcyAo4ytAq3fft2lJWVQaPRYMyYMUhNTcX555+PvXv3yr20oFNVVYUFCxbg3XffRXh4uNzLCRlNTU2Ii4uTexmq5XA4sG3bNsycOVO4TaPRYObMmdiwYYOMKwteTU1NAECvW5EsWrQIF154YafXNAmcL774AuPHj8fcuXORlJSEMWPG4LXXXpN7Wf1GAa3CHT16FABw33334Z577sFXX32F2NhYTJ8+HfX19TKvLnjwPI/rr78eN954I8aPHy/3ckLG4cOH8fzzz+OGG26QeymqVVtbC7fbjeTk5E63Jycno7KyUqZVBS+Px4Nbb70VU6dOxfDhw+VeTtD58MMPsX37dixfvlzupQSto0eP4uWXX0Z+fj6+++473HTTTfjLX/6Ct99+W+6l9QsFtDK5++67wXFcj1+s3hAA/v73v+OSSy7BuHHj8Oabb4LjOHz00UcyPwvl6+1xfv7559HS0oKlS5fKvWRV6u1x7qisrAyzZ8/G3LlzsWDBAplWToh/Fi1ahL179+LDDz+UeylBp7S0FLfccgvef/99mEwmuZcTtDweD8aOHYtHHnkEY8aMwcKFC7FgwQKsWLFC7qX1i07uBYSq22+/Hddff32P98nNzUVFRQUAYOjQocLtRqMRubm5KCkpEXOJQaG3x3nt2rXYsGHDKTOtx48fj6uuukr1Z65i6+1xZsrLy3H22WdjypQpePXVV0VeXXBLSEiAVqtFVVVVp9urqqqQkpIi06qC0+LFi/HVV19h3bp1yMjIkHs5QWfbtm2orq7G2LFjhdvcbjfWrVuHF154AXa7HVqtVsYVBofU1NROMQUAFBQU4JNPPpFpRYFBAa1MEhMTkZiYeNr7jRs3DkajEUVFRZg2bRoAwOl0ori4GAMGDBB7marX2+P83HPP4aGHHhL+XV5ejlmzZmHlypWYNGmSmEsMCr09zoA3M3v22WcLVxs0GrpQ1B8GgwHjxo3DmjVrhHZ+Ho8Ha9asweLFi+VdXJDgeR4333wzPvvsM/z444/IycmRe0lBacaMGdizZ0+n2+bNm4chQ4bgrrvuomA2QKZOnXpK27mDBw+qPqaggFbhoqKicOONN2LZsmXIzMzEgAED8PjjjwMA5s6dK/PqgkdWVlanf0dGRgIA8vLyKBMTQGVlZZg+fToGDBiAJ554AjU1NcL3KJvYd0uWLMF1112H8ePHY+LEiXjmmWdgsVgwb948uZcWFBYtWoQPPvgA//3vf2E2m4Xa5OjoaISFhcm8uuBhNptPqUuOiIhAfHw81SsH0G233YYpU6bgkUcewaWXXorNmzfj1VdfVf3VMgpoVeDxxx+HTqfDNddcg7a2NkyaNAlr165Vf884EnJWr16Nw4cP4/Dhw6ecKPA8L9Oq1O+yyy5DTU0N7r33XlRWVmL06NFYtWrVKRvFSN+8/PLLAIDp06d3uv3NN988bakNIUozYcIEfPbZZ1i6dCkeeOAB5OTk4JlnnsFVV10l99L6hePpU4QQQgghhKgYFa8RQgghhBBVo4CWEEIIIYSoGgW0hBBCCCFE1SigJYQQQgghqkYBLSGEEEIIUTUKaAkhhBBCiKpRQEsIIYQQQlSNAlpCCCGEEKJqFNASQgghhBBVo4CWEEIIIYSoGgW0hBBCCCFE1SigJYQQQgghqkYBLSGEEEIIUTUKaAkhRCJvvfUWOI7r9mvjxo1yL5EQQlRJJ/cCCCEk1DzwwAPIyck55faBAwfKsBpCCFE/CmgJIURi559/PsaPH9/r+7tcLng8HhgMhlO+Z7FYEBEREcjldctms8FgMECjoYt7hBBloXclQghRkOLiYnAchyeeeALPPPMM8vLyYDQasX//ftx3333gOA779+/HlVdeidjYWEybNk342ffeew/jxo1DWFgY4uLicPnll6O0tLTT42dnZ+P6668/5fdOnz4d06dPF/79448/guM4fPjhh7jnnnuQnp6O8PBwNDc3i/XUCSGkzyhDSwghEmtqakJtbW2n2ziOQ3x8vPDvN998EzabDQsXLoTRaERcXJzwvblz5yI/Px+PPPIIeJ4HADz88MP4xz/+gUsvvRR/+tOfUFNTg+effx6/+c1vsGPHDsTExPRprQ8++CAMBgPuuOMO2O32LrPEhBAiNwpoCSFEYjNnzjzlNqPRCJvNJvz7xIkTOHz4MBITE0+576hRo/DBBx8I/z5+/DiWLVuGhx56CH/729+E2y+++GKMGTMGL730Uqfb/WGz2bB161aEhYX16ecJIUQKFNASQojEXnzxRQwaNKjTbVqtttO/L7nkki6DWQC48cYbO/37008/hcfjwaWXXtop85uSkoL8/Hz88MMPfQ5or7vuOgpmCSGKRwEtIYRIbOLEiafdFNZVF4Tuvnfo0CHwPI/8/Pwu76/X6/1fZC/WQQghSkEBLSGEKFBPWdGTv+fxeMBxHL799ttTMr0AEBkZKfx/juO6fEy3293lz1J2lhCiBhTQEkKIyuXl5YHneeTk5JxSynCy2NhYNDY2nnL78ePHkZubK9IKCSFEXNS2ixBCVO7iiy+GVqvF/fffL3Q9YHieR11dnfDvvLw8bNy4EQ6HQ7jtq6++OqW9FyGEqAllaAkhRGLffvstCgsLT7l9ypQpfRpakJeXh4ceeghLly5FcXEx5syZA7PZjGPHjuGzzz7DwoULcccddwAA/vSnP+Hjjz/G7Nmzcemll+LIkSN47733kJeX1+/nRQghcqGAlhBCJHbvvfd2efubb77ZabiBP+6++24MGjQITz/9NO6//34AQGZmJs477zz89re/Fe43a9YsPPnkk3jqqadw6623Yvz48fjqq69w++239+n3EkKIEnD8ydenCCGEEEIIURGqoSWEEEIIIapGAS0hhBBCCFE1CmgJIYQQQoiqUUBLCCGEEEJUjQJaQgghhBCiahTQEkIIIYQQVQvJPrQejwfl5eUwm83dzjUnhBBCCCHy4XkeLS0tSEtLO+3QmZAMaMvLy5GZmSn3MgghhBBCyGmUlpYiIyOjx/uEZEBrNpsBeA9QVFSUzKshhBBCCCEna25uRmZmphC39SQkA1pWZhAVFUUBLSGEEEKIgvWmPJQ2hRFCCCGEEFWjgJYQQgghhKgaBbSEEEIIIUTVKKAlhBBCCCGqRgEtIYQQQghRNQpoCSGEEEKIqlFASwghhBBCVI0CWkIIIYQQomoU0BJCCCGEhCie5+VeQkBQQEsIIYQQEoLe23gcw5d9h0Xvb0dZY5vcy+kXCmgJIYQQQkIIz/N48YfDuOfzvbA43Ph6TwVmPPkjnltzCC63R+7l9QkFtIQQQgghIYLneTy6qhCPf1cEALh+SjYm5sTB5vTgqdUH8erPR2VeYd9QQEsIIYQQEiJW76/CKz95g9Z7LizAfb8dhpULz8DS84cAAN5cXwy7yy3nEvuEAlpCCCGEkBDxxvpjAIAFZ+bgT2fmAgA4jsO8qTlIiTKhpsWOL3aWy7nEPqGAlhBCCCEkBByoaMbGo/XQarwBbEcGnQbXTckGALz+yzHVdT+ggJYQQgghJAS8/WsxAGD2sBSkxYSd8v0rJ2Yh3KBFYWUL1h+uk3h1/UMBLSGEEEJIkGuwOPD5zjIAwPVTs7u8T3S4HpeOzwQA/OsXdW0Oo4CWEEIIISTIrdxaCpvTg2FpURg/ILbb+82bmg2OA34sqsHh6lYJV9g/FNASQgghhAQxl9uDdzccB+Bt08VxXLf3HRAfgTPzEwEAPxZVS7K+QKCAlhBCCCEkiO0obURZYxuiw/T4v1Fpp73/1Lx4AMDGo/ViLy1gKKAlhBBCCAli6w7WAAB+MygRJr32tPc/I9cb0G4+Vge3Rx3dDiigJYQQQggJYj+xgDY/oVf3H5YWhUijDs02Fw5UNIu5tIChgJYQQgghJEjVtdqxp6wJAHDWoMRe/YxOq8GEbO/GsY1H1dG+iwJaQgghhJAg9cvhWvA8MCTFjKQoU69/jpUdqKWOlgJaQgghhJAgxcoNzhrcu+wswwLaLcX18KigjpYCWkIIIYSQIOTx8Fh3sBYAcFa+fwEtq6NtanPiQKXy62gpoCWEEEIICUIHKptR22pHuEGLcdndD1Poik6rwXihjlb5ZQcU0BJCCCGEBCFWbjA5Nx5G3enbdZ2svY5W+RvDKKAlhBBCCAlC6/pYP8u096NVfh2tJAHtiy++iOzsbJhMJkyaNAmbN2/u8f4fffQRhgwZApPJhBEjRuCbb77p9r433ngjOI7DM888E+BVE0IIIYSok83pxvbjjQAgjLL11/C0KIQbtGhqc+JobWsAVxd4oge0K1euxJIlS7Bs2TJs374do0aNwqxZs1Bd3fV84F9//RVXXHEF5s+fjx07dmDOnDmYM2cO9u7de8p9P/vsM2zcuBFpaacf40YIIYQQEioOVDTD4fYgLsKA7PjwPj2GTqtBfrIZAHCwKsQD2qeeegoLFizAvHnzMHToUKxYsQLh4eF44403urz/s88+i9mzZ+POO+9EQUEBHnzwQYwdOxYvvPBCp/uVlZXh5ptvxvvvvw+9Xi/20yCEEEIIUY2dpY0AgNGZMeA4rs+PMzg5EgBQVNkSiGWJRtSA1uFwYNu2bZg5c2b7L9RoMHPmTGzYsKHLn9mwYUOn+wPArFmzOt3f4/HgmmuuwZ133olhw4aJs3hCCCGEEJXqGND2xyAhQ6vsgFYn5oPX1tbC7XYjOTm50+3JyckoLCzs8mcqKyu7vH9lZaXw73/+85/Q6XT4y1/+0qt12O122O124d/Nzcrvp0YIIYSEOreHx4s/HIZWw+HswUkoSDX3K9sYSnZRQKts27Ztw7PPPovt27f3+kW9fPly3H///SKvjBBCCCGBtHp/FZ5afRAA8Ph3RUiNNuHh3w/HOUOST/OToa3B4kBxnRUAMCojpl+PNTjFG9AW11lhd7n71P5LCqKWHCQkJECr1aKqqqrT7VVVVUhJSenyZ1JSUnq8/88//4zq6mpkZWVBp9NBp9Ph+PHjuP3225Gdnd3lYy5duhRNTU3CV2lpaf+fHCGEEEJE9fMhb9up9JgwmPQaVDTZ8PKPR2RelfLtPNEIAMhNiEB0eP/2GSWZjYgy6eD28DhaYwnA6sQhakBrMBgwbtw4rFmzRrjN4/FgzZo1mDx5cpc/M3ny5E73B4DVq1cL97/mmmuwe/du7Ny5U/hKS0vDnXfeie+++67LxzQajYiKiur0RQghhBBlW3/YO7b1/t8Ow7e3/AYAsKOkEVaHS85lKd7OkkYA/S83AACO44QsrZLLDkQvOViyZAmuu+46jB8/HhMnTsQzzzwDi8WCefPmAQCuvfZapKenY/ny5QCAW265BWeddRaefPJJXHjhhfjwww+xdetWvPrqqwCA+Ph4xMfHd/oder0eKSkpGDx4sNhPhxBCCCESKK23orjOCq2Gw6TcOEQadUiPCUNZYxu2FDfgrEF9660aCnb5MrSjs2IC8nj5yWZsKW5QdKcD0dt2XXbZZXjiiSdw7733YvTo0di5cydWrVolbPwqKSlBRUWFcP8pU6bggw8+wKuvvopRo0bh448/xueff47hw4eLvVRCCCGEKMSvR7zZ2dGZMTCb9OA4DlPyvAmtX32ZW3IqnueFDWH9rZ9lBqugF60km8IWL16MxYsXd/m9H3/88ZTb5s6di7lz5/b68YuLi/u4MkIIIYQo0c+HvEHr1IEJwm1TBsbjo20n8OuROrmWpXjH66xosDph0GlQkBqYEst8Xy9aJZccSDL6lhBCCCGktzweXghaz8zvENDmef//3vImNFmdsqxN6Vj/2WFpUTDoAhPmsQxtaYNVsfXLFNASQgghRFEOVDaj3uJAhEHbaWNTcpQJeYkR4Hlg4zHK0nYlUAMVOoqPNCI+wgCeBw5XK7PsgAJahSmuteC2lTvxzoZixZ4FEUIIIWJi3Q0m5cZDr+0cqrAsLdXRdm032xAWwIAWaB+woNSNYRTQKkhxrQWXvboBn+0ow73/3Ycpj67Fk98XweZ0y700QgghRDJd1c8ywsYwqqM9hcfDo9AXcA5LC2yLUta66xBlaElPSuutuPK1jahqtiMnIQJZceFotDrx/NrDePTbrscEE0IIIcHG7nJjS3E9gM71s8wZufHgOG9gVd1ik3p5inaioQ1WhxsGnQbZ8REBfWy2MYwytKRbjVYHLn91I8qbbMhLjMB/bpiMH+6Yjn9eMgIA8N7G4zhao8wzIkIIISSQSuqssDk9iDTqkJ8Uecr3YyMMGOrbvb+BsrSdHKhsBgDkJ0VCpw1siMc2hh1SaKcDCmgVYOWWUpQ1tiEzLgz/XnAGEs1GaDUcLpuQhXOGJMHl4fHPVZSlJYQQEvxONLQBADLjwsFxXJf3mZAdBwDYc6JJsnWpQWGFN9gckhL4iaj5voC2wepU5B4fCmhlxvM8Vm4tBQD8efpAJEWZOn1/6flDoOGA7/ZVYfOxejmWSAghhEimtMEKAMiIDev2Pnm+zG1xnUWSNalFUZU3QzvEV+8aSNFhevz817Ox9/5ZCDdIMsbALxTQymzb8QYcrbEgTK/FRSNTT/l+frIZl0/MAgA8/PV+eDy81EskhBBCJFNa7w1oM2PDu71PXoK3PvRoDQW0HQkZ2tTAB7SAN2uu1XSdNZcbBbQy+48vO3vhyFSYTfou73PbzEGIMGix60QTfjpYI+XyCCGEEEmV1rOSg+4ztDmJ3oC2pN4Kp9sjybqUrs3hFjLWg0XI0CodBbQyarW78NXuCgDAZRMyu71fotmIueO93/9yd7kkayOEEELkcKLx9BnaZLMJYXotXB5eqLkNdYeqW+DhgfgIAxIjjXIvR3IU0Mro693lsDrcyE2IwPgBsT3e90JfOcLq/VVwuOhslBBCSHBiGdqMHjK0Gg2HbKHsgLoAARD6zw5OMXe7mS6YUUAro5VbvOUGc8dnnvbFNy4rFklmI1psLmGCCiGEEBJMmm1ONLU5AfScoQWAXF/ZwbFaqqMFxO1woAYU0MqkrLEN20saodVwuGRs+mnvr9FwmD08BQDwzZ4KsZdHCCGESI5tCIuLMCDC2PNO+lyWoaWAFoC4HQ7UgAJamWz1TUEZnhZ1Squu7lwwwlt28P3+KiqCJ4QQEnSEHrQ9tOxicnwB7THqdABA/A4HSkcBrUzYWD/WHLo3JmTHISHSgKY2J82wJoQQEnRYhjbjNOUGQHtAe7SWamhrWuyoszjAcUB+EgW0REJbjjUAAMb7EdBqNRxmDfOVHeymsgNCCCHBhWVoe9oQxuQmeIcrVDXbYbErb3KVlAp9I29z4iMQZtDKvBp5UEArgyarE0W+Wcjjs3vubnAyVnbw3f5KKjsghBASVHozVIGJDtcjPsIAgDaGFXXocBCqKKCVwbYSb7lBbkIEEvzsFTcpJw4x4Xo0Wp3YVdoowuoIIYQQeQgZ2l7U0AIdyw5CO6AtpICWAlo5bClm5Qb+ZWcBQKfVYFKOt0xhs68OlxBCCFE7nudR2uDL0MadPkML0MYw5oivF2+o1s8CFNDKgnU48Kd+tqOJOfEAgM3HKKAlhBASHOotDlgdbgBAekzvMrS5id462mMhvDGM53kcqfY+/7ykCJlXIx8KaCVmc7qxq7QJgH8dDjpiGdqtxQ1we/iArU3tNhypw29f+AW3rdwJnqfjQgghalLqKzdIjjLCpO/dxiYhQxvCJQe1rQ4021zQcEB2PAW0RCJ7y5rgcHuQEGlAdnzvLqmcrCA1CmajDq12Fw5UNAd4hepjsbvwj8/34orXNmL3iSZ8tqMMG6itGSGEqMqJht637GLYtLCjNZaQTWSwcoPMuPBenwgEIwpoJcbqZydkx/V51rJWwwn1t5tCvOyA53lc/fomvLvxOABggO8kYcW6o3IuixBCiJ9K63s/VIHJigsHxwEtdhdqWx1iLU3RWECb5yu/CFUU0Eqsv/WzTHsdbWhnIg9WtWJHSSMMOg3emz8J7/5xEjQcsO5gDfaVN8m9PEIIIb3k74YwADDptUJHhKM1oVlHe5jVzyaGbrkBQAGtpHiex/YSX4eDAf53OOhoIut0cKwenhCuo11TWAUAmJoXj2n5CciKD8eFI9MAAK9SlpYQQlTDnx60HQ2I8wZyrAY31BzxdXigDC2RTE2LHQ1WJzRc/3vFjUiPRpheiwarE4dD9KwUANYeqAYAnFOQLNx2w29yAQBf7a4Q3iAJIYQoW5mfPWiZtBgTAKC8MUQDWqHDAQW0RCKHfC+6AfER/S7cNug0GDsgBkDo1tE2WBxCxvucIUnC7cPTo3FmfgLcHh6v/3JMruURQgjpJZ7nUd7kDUjTetmyi2H3r2gKvYC2zeFGmS+QpwwtkcxB37jb/ACdRU3MDu1+tD8drIGHB4akmE/pWThvajYAYPX+KhlWRgghxB9Whxs2p3ece6LZvwmaadHe9/+yRlvA16V0R339d2PD9YjzjQEOVRTQSohlaPOTAxTQCnW0dSHZrmRNobfcYEZB0infG58dB44DyhrbUNtql3pphBBC/MDep016DcIN/l3BFDK0IVhyQPWz7SigldAhX4Z2UHJgRtONzoyBVsOhqtmOqubQCtqcbg9+KvLVzw45NaCNMumFP/DdJxqlXBohhBA/sYA2IdLod0vL1A41tKGW3BHqZymgpYBWKjzP42CV94U3MEAlB2EGLQb6XsR7y0KrRdW24w1otrkQG67H6MyuO0aMzIgGAOwsDa1jQwghasN6yCZE+lduALSXHFgcbjTbXAFdl9IJPWhDeOQtQwGtRGpa7Whq83Y4COSZ1PB0b9C2J8QC2rW+coOzBydBq+n6bH50ZgwAYFdpo0SrIoQQ0hftGVr/60DDDFqhfjTUOh2wkoNAJcrUjAJaiRyuClyHg45GpEcBCL0M7S+HagEA07soN2BGZcQAAHadaAy5y1CEEKImtS19z9ACQGp06LXu8nh4YZgElRxQQCsZ1uEg0GdRLEO7N4SmYjndHmEyymhf0NqVIalmGLQaNFqdwkhFQgghylNnaa+h7Qu2May8KXQ6HZQ1tsHu8sCg1SDDz2EUwYgCWokc9AVggwLU4YAZmhYFjgOqmu2obgmNP+TiWgscbg/CDdoeG3AbdVoUpHo34O2kjWGEEKJYrOQgvg8lBwCQFoIZWlY/m5MQ0W3pXSihgFYirOQgPykwHQ6YcINOuNSwr6w5oI+tVEUdukVoTvNHPIrqaAkhRPH6sykMCM3WXax+NjeRNoQBFNBKgud5HKz2DVUIcIYW8I7BBUJnY1hRpfdYDunF+GChjpYCWkIIUayObbv6Qig5CKHhCsW13oA2J4ECWoACWknUtjrQaA18hwMm1DodFPoC2sG9CWh9Gdq95U1wuT1iLosQQkgf1bb0vcsBAKSxXrQhNP62uM4b0GZTQAuAAlpJsIEKWXHhAe1wwAxP83Y62BciAW2RHwFtbkIEzEYdbE6P0AeYEEKIcjhcHqF/bH8ztJVNNrg9odHV5hhlaDuhgFYCbOTtwADXzzLD0qPBcd7dnXVBPubVYnehpN4KABjci4lrGg2HEb4BC7toYxghhCgO63Cg03CIDtP36TGSzCZoNRxcHh41LcH9OQgAdpdb2AA3IJ46HAAU0ErioLCJSZw+cZFGnXCGFuxlB+xYJkQaEd/LM3lWdrD7RHAfG0IIUSPWgzY+0nDajb7d0Wo4pESFTtlBaX0bPDwQYdAisY9Z7WBDAa0EDlWxll3iZGgBYHiaNwu5rzy4Ox34syGMYScSrAF1sDtc3YqXfjyMhe9sxZTla3Dbyp00WIIQoli1vgxtfET/ArNQGq7ANoQNiI8Ax1HLLgDQyb2AUHBGXjyMeg0KUqNE+x0j0qPxxa5y7AnyLKQ/G8KYnARvQMvqjYJZi82Ji19a32me+Wc7ynDx2HScmZ8o48oIIaRrwoYwc/8C2rSYMOB4AypCoNMB2xBG9bPtKKCVwJJzB4n+O4b5RuDurwiNDK1fAW289w++usUOi92FCGPwvuxXbilFs82FtGgT5k3Nwb7yJny+sxxPrT6IaQMT6EyeEKI47T1o+9bhgGEbw8pCIUMrdDig+lmGSg6CBNsgVdpghdXhOs291YvV0PpTchAdrkdchPeNMpiztC63B2+uLwYALD4nHwt+k4u/XVgAk16DHSWN+PFgjbwLJISQLtT1swctw1p3VYRADW1xrXdz9IB4ytAyFNAGifhIIxIijeB5bw1lMKppsaPO4gDH+T9xLdu3C5Sd1Qaj7/ZVoayxDXERBlw8Nh2Ad+fvNWcMAAA8vfpgUNfSvr/pOKYsX4Nr39iMp1YfpGEahKhE+1CFfmZoo0NnuAKVHJyKAtogMjjFWyvKLssHG/a8suMjEGbwr5+vUEdbE7wB7b9+OQoAuPqMAZ36Hd9wVh7C9FrsPtGENQeq5VqeqErrrXjgy/0ob7Jh3cEaPLfmEH7/0npsOlon99IIIafR37G3TGqIZGg7tuzKpgytgALaIMK6KLDL8sGmsNJbH9yb/rMny/HVGR0L0gzttuMN2FHSCINWI2RkmYRII66bkg0AeP2XYzKsTnz3f7kfdpcHE7Pj8ODvhmH8gFh4eOCFHw7LvTRCJNdgceDmf+/AC2sPqWLIAMvQ9rYVY3fSfTW0ta0O2Jzufq9LqUrrrULLrv5mtYOJJAHtiy++iOzsbJhMJkyaNAmbN2/u8f4fffQRhgwZApPJhBEjRuCbb74Rvud0OnHXXXdhxIgRiIiIQFpaGq699lqUl5eL/TQUjwV6RUE6EUtof+ZH/SwT7J0O3lzvDVTnjElDYhc7hS8dnwEA2FbSEHRv9GsOVOF/B6qg03B4+PfDcc3kbDx92WhoNRx+PlRLpQckpDjdHvz5/e34clc5nvj+IP709hY025xyL6tHgdoUFh2mR7jv6l1FU/CWHbD62ewEatnVkegB7cqVK7FkyRIsW7YM27dvx6hRozBr1ixUV3d96fPXX3/FFVdcgfnz52PHjh2YM2cO5syZg7179wIArFYrtm/fjn/84x/Yvn07Pv30UxQVFeG3v/2t2E9F8VigV1QZnJ0OWM1QXqL/l1jYTtDiIAxonW4Pfij0/j1dfVJ2lslJiECi2QiHy4MdJY0Srk5cNqcb9325DwAwf1oO8n0ndZlx4fjdqDQAwEs/BneWtsXmxBu/HBNGbJPQ9tBX+7HhaB3CDVqY9Br8UFSDOS+uR0mdVe6ldcnt4VHv60Pb3wEBHMch2Tdcobo5iANa1uGAyg06ET2gfeqpp7BgwQLMmzcPQ4cOxYoVKxAeHo433nijy/s/++yzmD17Nu68804UFBTgwQcfxNixY/HCCy8AAKKjo7F69WpceumlGDx4MM444wy88MIL2LZtG0pKSsR+OoqWn+TNQlY129Fodci8msAr9Y28zYzzv00J+8NvsDqD7tjsPtEEi8ONmHC9MGDjZBzHYVJOHABg07HgqSt9f1MJSuvbkBJlwl9m5Hf63k3T8wB4N8sFa7C3t6wJFz3/Cx74aj9+/9Kv2FJcL/eSZNNicwZ1h5fe+PfmEry94TgA4JnLRuPjG6cgNdqEozUWLPtir8yr61qj1QFWFREb0f/L50m+K1RVQTz+ll1ppJZdnYka0DocDmzbtg0zZ85s/4UaDWbOnIkNGzZ0+TMbNmzodH8AmDVrVrf3B4CmpiZwHIeYmJiArFutzCa9UEN0MMjKDuwuNyp8Z9wD+hDQRhh1SI7yvtEFW9nBRt/GpzNy4nscGzkpNx4AsOlo8AQ93+2tBADccFbuKf2F85PNmDUsGQDw8k9HJF+b2D7YVIKLX/oVx+us0Go4tNpduPb1zVh/uFbupUlu2/EGTHpkDYbe+x2m/XMt5r+1JeRKTeotDiz7wnu14o7zBuG8YSkYnh6Nd+dPBACsO1SLeovyTuZZuUFsuB56bf9DklDI0B73ZdspQ9uZqAFtbW0t3G43kpOTO92enJyMysrKLn+msrLSr/vbbDbcdddduOKKKxAV1fUkLrvdjubm5k5fwYoNHCgKsozUiYY28L4i+Lg+nsWzP/5ga9316xFvADNlYHyP95uc683Qbi9pgN2l/jraRqsD20oaAAAzC5K7vM+fpw8EAPx3ZzkaFPhh3lfbSxrwt8/2wOH2YGZBEtbfdQ5+MygRbU435r21BZuPBc9Jy+mUNbbhhne3wurwvqZPNLRhTWE15r+9RZEBnFhW76+Ew+VBQWoUFp09ULh9YJIZw9Oj4Pbw+HZvhYwr7FqgetAyLENbHRIZWgpoO1J1lwOn04lLL70UPM/j5Zdf7vZ+y5cvR3R0tPCVmZkp4SqlJXQ6CLLWXaz+KzMuvM9F8Lm+2ttgat1ld7mxtdgb1E3J6zmgzUuMREKkAXaXB7uDYETyTwdr4PbwGJxs7rYMZVRmDPKTIuH28EImOxi867usfNHIVLx27XikRJvw2rXjMLMgCQ6XB8+uOSjzCqVhsbvwp7e3orbVgYLUKPxy19n4cOEZGJQcidrW9oxlKPhmjzfpc9HI1FPeI/9vpLee/Mtdyts8XSN0OAjMbn2Woa0K0gytzelGeRO17OqKqAFtQkICtFotqqqqOt1eVVWFlJSULn8mJSWlV/dnwezx48exevXqbrOzALB06VI0NTUJX6WlpX18Rson9KINsgxtST2bitL3miH2x39MoZsj+mJHSSPsLg8SzUbkJUb2eF+O4zCR1dEGQXC31rcR7pyCpB7vN3VgAgDg1yPqf86AN6P19W5vpm3BmblC8GLUabHs/4aB44D1h+uEmvNgxfM87vhoFw5UNCMh0oB/XTceGbHhOCM3Hk/MHQWthsOXu8qxSoFZyUBrsjqFUpPzh5/62XrhyFQAwKZj9YoL9ALVg5ZJ8pWWKe15BsqJBqtwtZJadnUmakBrMBgwbtw4rFmzRrjN4/FgzZo1mDx5cpc/M3ny5E73B4DVq1d3uj8LZg8dOoT//e9/iI/vOTNlNBoRFRXV6StYdexFG0xToVhAm9WH+lmGTVQ5Vhs89cUsSJucG9+rzPWkHF8drcovSbvcHvzkG+V7zpCeA9rJvsw1K81Qu4+2nYDD7cHIjGiMyozp9L3MuHBM8wXwH20N3hN3wLsZ8tu9ldBrObxyzXhh/wAAjMyIwY1n5QIA7vl8b9CXHvzvQBVcvqsVuV2c2GbEhmPcgFjwPISTIaUIfMmBr4Y2SEsOOo68pZZdnYlecrBkyRK89tprePvtt3HgwAHcdNNNsFgsmDdvHgDg2muvxdKlS4X733LLLVi1ahWefPJJFBYW4r777sPWrVuxePFiAN5g9g9/+AO2bt2K999/H263G5WVlaisrITDEdxvWr2RlxgJDQc0Wp2oCaI/aFYEn9WPSywsoC2utQZNsL+RBbSnKTdgJvnqaLcdb4DT7RFtXWLbUdqIRqsTMeF6jDkpqDvZGTnx0HDAkRoLKlXem9Lt4fH+Jm+5QXct2i4d7y2p+mjbCVU01e+rD7d4u9pcOCIV4wbEnvL9v8zIF0oPXg7y1m2sNvb8EV1f+QSA//Nlab/crayyAzZUoav+2X3BNv9WNwfP519HLLlDHQ5OJXpAe9lll+GJJ57Avffei9GjR2Pnzp1YtWqVsPGrpKQEFRXtZ4xTpkzBBx98gFdffRWjRo3Cxx9/jM8//xzDhw8HAJSVleGLL77AiRMnMHr0aKSmpgpfv/76q9hPR/FMeq1QKB5MZQelAcjQZsWHg+OAVrtLqNtSszaHGztKe1c/ywxKMiMmXA+rw409Zeqto2UjfKcPSoTuNDujo8P1GJ7ubWe24ai6s7TrDtagtL4NUSadUBd5svOGJSMmXI+KJhvWHaqReIXSaLW78N+d3sDsiolZXd7HqNPijvMGAwA+21EOl4pP4HrSYnNi3UHv6/qCEand3u+CkanQcN4yJSWVo7CSg/gAtOwCgCRfDW2r3YVWe/C1cSvpR/vKYCfJprDFixfj+PHjsNvt2LRpEyZNmiR878cff8Rbb73V6f5z585FUVER7HY79u7diwsuuED4XnZ2Nnie7/Jr+vTpUjwdxRMmhgXJxjCe5wNScmDUaYXLkuyyjZptPV4Pp5tHekxYr4+LRtOhH62K23f9INTPdt3d4GQsg73+sLrraN/b6M3Ozh2fiTDfRKSTGXVazBmdDgD4z5bgLDv4Ymc5rA43chMjhLrwrkwfnIS4CANqW+34JUjbma0trIbD7UFuYoTQi7wrSWYTzvC17lNSt4M6XzlIf8feMpFGHSJ9LfyCsXVXID4Lg5WquxyQrnWsow0GNa12tDnd0HDoVCfXF8FUR8vqZ8/oZf0sM36ANwDYfaJRjGWJrrTeiqKqFmg1HM7KT+zVz0zJ89aVbjhSp9pyk0arAz8UeQP5qyZ1nZVkLpvgLTv434EqoUYxmLBygysnZvX42jfoNPitb2Lcp9vLJFmb1L71dTe4YPip3Q1OdtYg79/L9uONYi+r19igm9hwfcAeM5hbd1FA2z0KaIPQQN9Z+pEgaU/FLo+lRofBoOvfS5Z1SShR0CW3vtp+3FtuMKmHDFVXhqSqu1fxBl8gPzYrBtG9/BCckB0LvZZDWWObav/bbzxaDw/v/fvuauNPRwWpURiZEQ2nm8e3e7vu4a1We8uasPtEEwxaDS4em3Ha+1881put/m5fJVpsTrGXJymX2yOUlcwa1n39LDMyIwYAFFVu1Gj1/jeJCWRAG6SdDjwePiDld8GKAtogxALaw9Wtqs1GdSRsCAvAH3BGrPcxyhra+v1YcvJ4eOwr9w4IGZHR9bjb7rCSlOJaC2xO9Q1Y2OnLLI/tYiNQd8INOozJ9N5frWUHrI/u5Nze1UuzYRPB1H8X8I53BYBZw1N6NWRlRHo08hIjYHd5hGxmsDhY1Qqrw41Iow5D007fvWd4uvc+ZY1twmYsObk9PJptLKANXAuq9mlh8j/HQKpptcPu8kDDAWn9vFoZjCigDUI5CRHgOKCpzRkU7WoC0YOWYSULZY3qDmiL6yxotbtg1Gl6rJvrSqLZiJhwPTw8cKRGfaUXrFRilC/b1Ftskppa23dt8LOjBauX3Hi0PihObAFvAPT1Hm/95+UTejcgh+M4IZP7yfYToq1NDmxT6KjMaGh7GHvNmE16YcCMErK0TW1OsJdmTJgYJQfBlaFln4VpMWEBGRMcbOiIBCGTXouMWG/gFgxlB4Hc1cmOywmVZ2jZh1FBatRpd/mfjOM4oc5abRsHbU43Ciu8ax7pZ2aa1dGqsQdvXatdKBE5o5cZ2lGZ0TDqNKhttQfF+wDgLTdotDphNun8KrWZMyYdHOf9b3+iQZ0lJ11htbBjs3p/tWKkr+PHHgVMC2zw1c+aTTq/38d60j4tLLgytGxiZiCSO8GIAtogxaZGHa5WXwbuZIH8I073BbRVzTY4XOpt47PXF9COSPcvqGOGpKizjvZARTNcHh7xEQa/NwiOSI+GhgNqWuyqy9xs9HWkGJJi7tVldsDb7YD1Zw2WsoOfffWiU/Li/QqA0mPChAD4u31Vp7m3erAM7ZismF7/DKujVcL4azHqZ4H21l3BVkNLG8J6RgFtkGIBrRovKZ8skH/EiZFGGHUaeHiousn+nn4GtEInDJVlaNmH8MiMaL+n5IQZtEKXi/2++mO1YP1ze5udZdj9NwRNQOs9DtN62d2io7MHeyfK/Rok7bsarQ4c9WXeR2f6kaH1XdnYU9YoxrL80t7hILAjXFnJQTANFwKoB+3pUEAbpIIloG1zuIXWK4EIaDmOEzJ7JxrVeenR4+Gxr8wbkA3vY0A7OIW1dlPX62OXr352pJ/1s8ywNO/x2qe2gNbP+lmGBbSbjqq3XRljsbuwvcSbkfxNfoLfPz/VNxJ449E6VU/JY3aWNgLw7pnobdYeAIamRUHDeS/Hy53BbLAGfkMY0LHkQL1Ji65QhrZnFNAGqTxf4b/aA9pSX71blEkXsDe9dJXX0R6vt6LF7oJBp0F+sn8bwphBSd6AtqyxTVWtjFiGdlRm3wJ5thN8f4V6AtrqZhuO1FjAcd4xvv5or6N1qP69YNOxOjjdPDLjwjCgDyOwh6ZGITZcD4vDrdoezB1tL2kEgNOOfj5ZuEGHfN/fv9xlB2L0oAXaM7QWhzuopoVRQNszCmiDVJ5v5/uJhjZVtmZiWP1sVgCL4NnGMLW27uq4IayvO12jw/VI8WUx1DKAo9XuEoKyvmZoh6Z6A9oDKsrQsnKBYWlRve67y3Sso92g4slwQIdyg4H+lxsA3il5bGPgL4fUX4Kxo8T/+lmGtfrbI3NgL9TQBrDDAQBEGHUwB9m0sDaHWyihoIC2axTQBqn4CAOiw/TgeeBYrXp3OItxRir0olVp6672DWGn7zvZE1Z2UFSpjszdnhNN4HnvBp+EPo7JLPAFtMfqLLCoJHPjb//Zk7W371J3EPeLL6DtS7kBw8oO1qu8jtbj4YWSgzF+dDhgRvkC2t0yt+5iXQ4CXXIAAInCcIXgqKNlVyvNJh2iA3wCECwooA1SHMcFRdkBCzpZEBoIQg2tStv3sHY7fd0QxrTX0aojQ7tbqJ/t+/NONBuRZDaC54HCSnVkaTf5Mqv+1s8ywVBHW9HUhkPVrdBw7e3X+mKaL6DdXtKgmhOarhytbUWLzQWTXiN0LPHHCDYx7ESTrK8JlqENdMkBACSbfcMVVNbRpDslHQYM+bshNlRQQBvEhI1h1erN0Jb7Atq0aFPAHpPV0KoxQ8vzPPaWewPavm4IY9TWi7a9w0FMvx5nGKujVUHZQYvNiaO1/u9k7ygY6mhZdnZERu/HHXclKz4cGbFhcHl4bFZhP2KG9Z8dmRHTp/6tQ1LM0Gk41FkcKJex2wvL0Mb6samtt5KDbPxtIAcMBSsKaIMYG4Gr1g8xAMKbbWoAx/yxGtqKRhvcHnVlrI7XWdFi824IYwFpX7ERuEVVLarI3O0SJoT1L5BX08awA74hEmnRJr92sndk1GmFrLbcm4D6ipUInDmw79lZZloQlB2w/rP+DFToyKTXCldo5BywwDK0YlxCTwqy8bfUsuv0KKANYsHQuotlaP1tot+TJLMJOg0Hl4dX3dm7sCEsxdzv0YcDkyLBcUC9xYHaVmWPSK63OISuFMP7G9Cmen9eDRlaVi89NK1/z5m1K1PCuNO+2HrcG8D524e3K6yO9hcVB7Tsv+PoPnb7ANpPaOX8fBCrDy3Q3umgKkh60VKHg9OjgDaIsU4HR2ss8KgsEwkAdlf7rs7UAJYcaDUc0mLU2bqL9U8d1s9yA8A7aCDb1/5I6XW0B3zZ1Oz4cESZ+pfNYRnawsoWuBTej5T99x7ezw2ArN6a9S9Wk9pWO040tIHj+t6uraMpvlrkwsoWVTbed7k9Qv9otsmxL9iQETk3DTcINbRilBwEVy9aCmhPjwLaIJYZGwa9lkOb043yJnUFbgBQ1eT9sDHqNH2+3NodlvEtU9lwhSLfRqah/fgg6yjfd9Kj9DpaFnD3t8wCAAbEhSPCoIXd5RHqU5Vqn69eelg/M7Ss3npfeZPqTm53+vqtDkyMhLmfJzMAEB9pFLKT23yZXzUprrPA4fIg3KBFZj82y+YkyhvQ2pxutPlaSsZEiFByEETTwjweHqUU0J4WBbRBTKfVCBm4IzXK/uDuSlmHcoNA7+pUay/aQl/g2ZedzV3J9ZWlHK9T9uuDZaQCEdBqNJyQ2VJy2YHN6cahau/z7m+GNi8xAkadBhaHG8UK/299MtaearSfAwR6MnZATKfHVhP2HjA4xQyNpu/vi3JnaJvavNlZrYYTesYGUscMrRr2CPSkptUOu8sDDQfh6iI5FQW0Qa6904H66mgrfFnl1JjAlRswapwW1mh1oMK3SW5QgALanATv2f6xOmVnqlmGtq+T0U6mho1hRZUtcHt4xEUYhCEYfaXTaoQgXm11tEJA24cBAt1hwTEbTqAmhRWBOallAW29xSHUskpJ6EEbphelDVWSr8uBNQimhbFyg7SYsH7vnQhmdGSCXK7Ml5X6o71lV+DPSNU4XIFlZjJiw/pdR8qwEaLFCn598Dwf0JIDoL1kQ8kZ2r1CuUFUQD7whTpaBT/nk3k8PHaJkKFlwwh2n2hSfB31yVj/5CEp/cvahxt0wt4EOUpvGiy+KWEi9KAFvM9PmBam8rKDjj1oSfcooA1ycl9W6o+yRm82UoxLLOkq3BRWWBGYD7KO2OvjRIMVDpcyP9irmu1osbmg1XDCCVp/5Stgh/fpCBsA+1k/y7Cyhb0qytAerW1Fi92FML1WqHsNhIGJkTAbdWhzuoVyFrU4EKAMLdDh80GGkjQxOxwwSUHSi5Z60PYOBbRBTs0ZWlZykCZCyUFGh+EKatkkwzK0BamB+2BPMhsRptfCwyt3clqRLzubHR8Oo04bkMdkU/QqmmyKvRy5r4wN0AjMCQwLjPeWyTsdyh87fBvCRqRH92mAQHc0Gg6jWNlBqXrKDpptTuGqUiBObFlAe7RW+qC+sU3cDC3QXker9l60pdSDtlcooA1yOQnemsOyxjbYfDtK1UIoORAhQ5sSbYKGAxwuD2pb1fFmd0DYEBa4DC3HccJZv1I3Cx0KcLkB4J0dnxDpzQwdVWCW1un2CP+9A5WhHZRshkGrQbPNhdJ6dVyZ2CFC/SzTXkfbGPDHFstB32siNdrUr4lpjJxX8IQaWhEztEJAq/Lxt9Syq3cooA1yseF6YQqLUgOW7lSIWHKg12qQ6qvNPaGCOlqPhxc+zIYEMEMLtH+oFdcqM0PbviEssM9byYNHjtS0wuHyINKow4AAfYgZdBphOhSrz1U61rIrkPWzzBhfkKymjWEHAtzlhP0NHJWl5ID1oBUvQysMV1B5hvY4BbS9QgFtkOM4TtY6qb5qtjnR4rsULMamMKC9jrZcBQFtSb0VbU43jLr2VmyBks0CWoWe8LAax0DWUALtg0cOK7ADCBuAMDQ1ql+tmU6mpjraNodbKDcRI6Blj3mkxiK0kFI61od6cICu0uR0+NuXuvSqwSJ+hjYpCIYrtDnaBwxRQNszCmhDQK5QJ6XMgKUrLMiMDdcjzBCYusmTsdpcNQS0bGfzoGQztAEMcABvbSqgzDprnuc7lBwEpmUX097STnnPW+hwEKD6WUZNI3D3lDXB7eGRHGUM6KRAJj7SKAQIu1TSj5a17ApUHX1GbBh0Gg42pwcVEgd90tTQejO0aq6hLfXtbTCbdMLVVtI1CmhDgBo7HbByg1SRsrNAeylDeaPyz94DubP5ZCzje1yBvWjLGttgcbih13JCJjlQBiYpt+SABS6BmgjHDO/QukvpG8N2+jZrjc6MEaVPKdCx7KBRlMcPJJ7nOwxWCczrQqfVIIud0Ep8BU+SLgdm9dfQdmzZJdbfQbCggDYEsBGHStz80p0yETeEMWkx7Z0OlE7oPRngAAdQduuuQ75yg5yEiIA3FGedDorrLIrrRcomhAW6bnhIijfDX29xKL6ukLUtG5kRI9rvGKOiTgcnGtrQandBrw1c+zqg/QreMYk7HTRYpcvQVjXbFX8C1x1q2dV7FNCGADVmaMuFsbeBv9TIqKmGVmjZJUKGNtFsRLjB27qrVGGtuwI9UKGjtOgwhOm1cLp54UNDCZqsTqHzRl4AAxcAMOm1QokJq09VqgO+vsuBbFN3MjZgYWdpo+IDniLfe0BeYmRAT+7Y+GupS9IahUlh4mdo25xuYU+G2pRQy65eo4A2BLCAtsHqFArxlY6NeE2VIEOr9IDWYncJ5QCDRQhova27WNmBsk56ikQMaDUdBjUoaWPY4Rrvc06JMsEcoIlwHbHXEOuaoUR2lxtHfJfAC0S4KsEUpEZBr+XQaHUqfsgKu0oT6OMh9KKVsOSA5/n2LgcR4mVowwxamE2+aWEKvyLRnVLqcNBrFNCGgI4jDo8pLGDpjjQlB95j0mB1wupQ7tk7C+oSzUbERxpF+R05CWxjmHIylUB7yUGgN4Qx7a27lPN3wYJrVuMbaOzkQMkZ2sPVrXB7eESH6ZESJd5Vmk6tzBS+Ue6g8LcgTts+Ka/gtdpdcPm6KohZQwt0HK6gzjpa6kHbexTQhgi1te5iU8LELDkwm/TC2buSN4YVirghjGEZ2mIFlaV4PLwQ3AW6lpRRYi9asQNa9jo6qOCA9kCH3fxib4QZziaoKbw3r1BXHeDXRW6HGnq7S5rhOyw7a9JrYNKL08WGEepoVbgxzOPhKaD1AwW0IUJNdbRuD4/KJvG7HADqqKMtEulSY0c58crrRVve1IY2p7fDQaCGC5xsoAJ70bK15ImcoT1Y1QK3Qsc+F/rqZwM5Fa87w9LZSOBm0X9XX7k9vHDSlR/gqxWJZiMiWA29RLXkDRLUzzLJZvWOv61ptcPu8kDDiXu1MlhQQBsi1BTQ1rba4XTz0Go4YdKLWNRQRxvo6UBdUeJwBfZazYoLhy7AHQ6YvCTv8z5S06qYTUGHfYHLwERxAtoB8REw6DSwOT2SBTD+OlAp/oYwZnha+7AJpbwGTsY6kBh0GmTEBvbkjuM4YcNRqUR1xI0SdDhgEqPUOy2MZWfTYsIC3uUlGNERChFs84sahiuw4DIlyiRaIMMofbgCz/OSZKvYzveyhjbFtO5im1RyRQrsAG8PXg0HtNhcqGmV/wPP5nQLm5PEKjnQajjhsrUS62h5nu9QciB+hrYgNQpaDYc6BbcyY7XkeYmRAR+sAngHLACQbGNcgwQ9aBmWoVVjyUHHHrTk9CigDRE5Cd4PsOJa6Ucc+qtcGKogXv0s096LVplvdhVNNjTbXNBpOCGbKIZOlx0V0rqLZWhzAzxQoSOTXitkp5RQduDNFAPRYXokRIr3Yc/GCCux00FNix31Fgc0nDjdLU5m0muFbLhSN4YJWXuRTnJY1rdM4gytmB0OGLYprEahJys9oR60/qGANkSwEYdtTrfiz1TLJehwwCi9hpa16slLjIRRJ97miY6tu5SyMYzVDAayiXxXlNTpoOOGMDE3Q7Gd/YUKzNCyEpuchAjRNwwxbMSwUjeGsQxtoDeEMe0ZWmlraKMlqKFNUvGmsFLqQesXCmhDhF6rES5bKL3TQbmvw0GqiB0OGKGGtkmZAS279CpG/9mTsdeHUoYMsJIDdnVBLGx4wRElZGirxa2fZQYpuBetUGIjQbkBI3Q6UOjGMJahFSugTZd4aqKQoZWghlYoOWi2KbZGujvU4cA/FNCGEKGBtkIycN1pnxImfoaWBbQVjTZFlmIIs9sl2BzDLmspIaC1Od3CSYbYGVpWo6uEDZNiX1pmWMnBsVqLZK2aekuYECbBSRwz3NfpYJ8CM7Q8z+OwL5MudsmBVDW0jRLW0LIMrc3pUd20MApo/UMBbQhRS6cDNiUsTeSWXQCQbDZCwwEOtwe1FuXVWAktuyRoX8Qua7GNCHIqrrOA54Eokw7xEeJ+6GXHK+fvQuwetExqtAlmkw4uD6+I592RMOZZwgztUF+ng4omG+oUsDmwo4omGywON3Sa9rKgQEv3lRzUtNhhc4p/gtMgYZcDk16LKGFamHrKDtocblS3eF+LmQHubBGsKKANITmJyvng7gnL0EpRcqDTaoRJREobrtBx/KeUGdrjCsjQCuUGieLWkgLtGWDWGkkuLrdH+NsUO6DlOE7I0hYpqOzA7nILQb2UJQeRRp2w+XBfubLKDtjxGBAfDoNOnI/s2HA9wg3eemUp9hOwDG2MBBlaoH1jmFK7WHSF1TObTTpJAv9gQAFtCFFDhtbmdKO21ftmJ0XJAaDcXrRSjf9kBsR5Xx+l9VbZyy/YazRPxA4HTJLZiHBfhwc5yy1K6q1wunmY9BpJXvusjlZJAe2RagtcHh5RJh3SJOhy0pEwYEFhZQftE8LEO6nlOE7YGCZFHW2DhDW0QMeAVllJi550LDcQ+6Q+WFBAG0JyfZtrvB+cyug1ejI2ISzcoEV0mDRvdkoNaDuOvJXiDS01xgSthoPd5REudclFqg4HgPfDXAllBywTl5sQCY0IvUZPNjhZeSNwWVePIalRkn+IswEL+xS2MUyqMhR2EiVFHa3UGVo2oEfu9zV/UP2s/yigDSHJUUaE6bVwe3jFTggSyg2iTZJ9oKVJvMO3twolGHnbkV7bnhmUe2MYCyzF7nDAsHIcOVuWSbUhjGE9XgsVlKGVY0MYM8zX6WCPwnrRHq72/vcJ9Mjbk0nVi9bl9qDZ5t2cJVWGNknlGVrSOxTQhhCO4xRfdlAmYQ9aJl2h08JYoCFFyy6GvXkel3EELs/zHaaEiZ+hBdqHN8jZAUSqTBwzyBcgnWhog0Uhu7/l2BDGsI1hJfVWtNickv/+rvA8L5QciJ6hlagXbVNb+7GV6ipcsq/TQbWKamipB63/KKANMUrfGMY6HEhVPwsAqdGs5EBZZ+8HOpQcSCVLAa276i0O4UMvR4Ia2o6/51itfL1oj0gc0MZHGoVpZEqYkga0Z2il3BDGxEUYhOmESsla11kcaLQ6wXHtA0DEItX4W1Y/azbpRB9tzqixhvY4jb31GwW0IUYJmaietJccSBfQKrGGtrbVjtpWOziJxn8yShiuwE620mPCJJsUlZ3ASg7ked48zwsdLcRqnt8VttFICXW0NS121LY6wHHt9b1SGybU0Sqj7IBNCMuMDRf9b0Gq4QpNbdL1oGWEDK1Kamh5nqeSgz6ggDbECJkohU4LK2c9aCVo2cWwN/I6i0OSHoy9sd/XOmhAXDgijDrJfu8AoeRAvoBW6nIDoP1Er7LZJsvl98pmG1rtLmhF7DXaFVZ2cEgBGVpWM54TH4EwgzQnMicb6ssM769QxsYwKeuqWQ1tZbNN1PZ1DRZpOxwAQJLKpoXVtNhhd3mg4aQtv1M7CmhDTPu0MPk/wLpSLkMNbVSYDpG+oFGqSTmnwz5Q2UYVqbCSAzk3DR7xvTalKjcAvLut2QdssQz1w1L0Gu1KvoI6HQgbwmQoN2BYHa1iAlrffxcpsvYJkQYYdRrwfHu3GTE0+DocREuYoWXTwuwuD5rblFEv3hOWnU2NDpP0/UDtJDlSL774IrKzs2EymTBp0iRs3ry5x/t/9NFHGDJkCEwmE0aMGIFvvvmm0/d5nse9996L1NRUhIWFYebMmTh06JCYTyFosCChqtmumI0gDM/zsgS0HMdJPsv8dFhzd/YBKxV2eavO4kCrTK8PdvUgV8KAFpC3T7OwIUzkOsmTsXIWdmlbToUy1IyfbGiq9wTyYGWrIlobsgxtngQBLcdxkmwMa5S4By0AGHVa4fdVtSi/jpbKDfpG9IB25cqVWLJkCZYtW4bt27dj1KhRmDVrFqqrq7u8/6+//oorrrgC8+fPx44dOzBnzhzMmTMHe/fuFe7z2GOP4bnnnsOKFSuwadMmREREYNasWbDZlP9ClVtMuAFxvlGiStsY1tzmgtXhveSfKnFTdaGpuEIytGym/DCJA1qzSS+8PuTqdMDqu3MlDu7a62hlDGglrJ8F2ksOyhrbZDuBYfbLuCGMyYgNg9mog8PtEXohy4mdaEhVV83KDk6IeGLfKEMNLaCujWEU0PaN6AHtU089hQULFmDevHkYOnQoVqxYgfDwcLzxxhtd3v/ZZ5/F7Nmzceedd6KgoAAPPvggxo4dixdeeAGAN4v3zDPP4J577sHvfvc7jBw5Eu+88w7Ky8vx+eefi/10goJSW3ex7Gh8hEGyzUBMhkQta3rD6nAJ/22kztAC7W1i5Cg7cHt4IZCWsuQAkHfDpFwBbUy4AYm+pvOHZCw7cLjaA8gCCcY8d0ej4VCgkAELTW1OYROTVK8LKYYrsC4HUo9zTVLR+FshoI2ngNYfoga0DocD27Ztw8yZM9t/oUaDmTNnYsOGDV3+zIYNGzrdHwBmzZol3P/YsWOorKzsdJ/o6GhMmjSp28e02+1obm7u9BXKlBrQylFuwAiZCQVkaA9UtIDngUSzUdjMICU5N4adaPCOfzXqpBn/2hEb4iDH38URiYcqdCRsDJOx7OBobSucbh5mk07y/+4nU8rGMHaSkxJlgtkkTfAnxZUqYUqYRD1omWTfiZsaMrTUg7ZvRA1oa2tr4Xa7kZyc3On25ORkVFZWdvkzlZWVPd6f/a8/j7l8+XJER0cLX5mZmX16PsEiV6G9aCuaWEArfRCnpAztfpnKDZgBMvaiZR0OchIiJBn/2lF2gvd5S11y0Gh1oLbV+yEvdq/RriihdVf7hDDpR96eTNgYVi53QCvNhLCOpHgfFLocRMhTclCtgoCWvfcOoIDWLyGxfW7p0qVoamoSvkpLS+VekqyU2ou2zDfYQMoetEy6RE3Fe4NlhobKVEuYKWMv2qO18pQbAEC2r11Wg9WJBotDst/LMnFp0SZJW7QxbGPYQRlbdwkbwmQsN2A6ZmjlbPHEXhdSnuQIGVpRa2hZyYHUAS3L0Cq75MDmdAtrpBpa/4ga0CYkJECr1aKqqqrT7VVVVUhJSenyZ1JSUnq8P/tffx7TaDQiKiqq01coEy6t1rQqqicfy9DKccmRlRxUt9hl70XLOhxI3bKLGSBnQOu79C5lD1omwqhDii+Lc0zCDXFC4CJDuQHQseRAvgytsCEsRf735vzkSOg0HJranEJfbDmw3sDSZmi9f/sVTTa4ROrywEoOpOxyAHSooVV4lwOWHTcbdZLXGaudqAGtwWDAuHHjsGbNGuE2j8eDNWvWYPLkyV3+zOTJkzvdHwBWr14t3D8nJwcpKSmd7tPc3IxNmzZ1+5ikswHx4eA4oNnmQr2EmajTkbOGNjZcj3BfM3c5J4a53B5h7KZcJQdsI0JZQ5toH2rdaS85kCe4y5Gh04FcG8IY1ou2osmGZptTljWw17ycG8IYo04rHBM5yw7kaOWWEGmETsPB7eFR0ypOJrNBqKGVq+RA2Rnakg71s3KX36iN6CUHS5YswWuvvYa3334bBw4cwE033QSLxYJ58+YBAK699losXbpUuP8tt9yCVatW4cknn0RhYSHuu+8+bN26FYsXLwbg7ZV366234qGHHsIXX3yBPXv24Nprr0VaWhrmzJkj9tMJCia9Fmm+y/pKqqMtZyUHMtTQchwnyeW20zlSY4HD5UGkUSfb5aZkswkGnQYuDy/8N5HKsVrpp4R1lC3Dhkkpp0F1JTpML1yOlWNjWG2rHTUt3jHPg2XsQdsRKztg7fOkZnW4hPKnfAnHAGs1nBD4VYiQnbY53bA5vSfJMRESbwoTxt/a4PEo58rkyUrqqGVXX4ke0F522WV44okncO+992L06NHYuXMnVq1aJWzqKikpQUVFhXD/KVOm4IMPPsCrr76KUaNG4eOPP8bnn3+O4cOHC/f561//iptvvhkLFy7EhAkT0NrailWrVsFkkj4QUisWMCiljtbt4VHpK9aXa5ezEjodsA/QglSz5JuiGI2GQ6YvuJey7MBidwmvAamHKjBy1JezIFLqoQodtQ9YkL7sgNXPZsdHINwgfQ1xV+TeGMauVMRHtPcNlwrrAV4hwsksG6qg03AwS1wvnhBpBMcBTjcvZImVqKTe+/lDLbv8J8kravHixUKG9WQ//vjjKbfNnTsXc+fO7fbxOI7DAw88gAceeCBQSww5OQkR+PlQrWIytNUtNrg9PHQaDgmRRlnWoIROB/tlrp9lBsRH4EiNBcfrLZiGBEl+J3stxkUYJN8wwggt7Wqk+buwOlzCFQG5MrSAt9PBz4dqcVCGDG1hJaufVUZ2FpC/ddchX4cDOeqqU2PCgOMNwp6GQBLKDcL1kl9O12s1iI8worbVjqpmO+Jl+pw5nRJq2dVnIdHlgJxK6g/u02F1q6kxJmhlykxK0VT8dISRtzJOSwLaL3dJmaEVJoTJlJ0FOkwLq7NIsmGSZeJiw/WyfsAOTvEGTnK07lLShjCG/f2daGhDU5v0dcVSTwjrSMjQilBywALaaIl70DJCpwMFbwwrpSlhfUYBbYhS2nAFFkSmydCyi5G75IDn+faWXTJtCGOEgFbC4QpydjhgsuLCoeEAq8MtTGkSk9wbwhhWpylHQMtKDpSwIYyJDtcLV2wOyJCllfN10R7QBv59kJUcSD32llF6L1qe52nsbT9QQBuiclnrrjqLIgrk2eYjOacEyV1ycLzOiqY2Jww6jVDTKBc2XEHKaWHHauXtcAAABp1GuNR3VIKrF4oJaH2/v7rFjiardBlJp9sjHIMCma9KnKx9Y5h8AS0beiEl1gdcjAxto1WeHrSM0nvR1rY60OZ0g+Pk/SxUKwpoQ1R6bBj0Wg4OlwflIpyJ+0vOll0MC2irmu2wu6TvRbvrRCMAb7sug07eP02WHSitt0rWq5gFkHJmaIEOrbsk6EUrR/P8rphNeqT5MnMHq6XL0h6tscDh9nb1YH9/SiHXxjC7y43jviydrBlaETaFdayhlQMbJa7U8bcsO5sWHSb7Z4Aa0RELUVoNhwHxyik7YBtj0mX8UIuLMCBM7+1FK8ab+ensLG0EAIzKiJH8d5+MZSlb7C40SJCx43leKDnIkzmgzZbw70Lull0dyVF20HFDmNJ6bsq1May41gq3h4fZqBMyilJibROrWwI/XEGuoQoMKzlQakBbKmwIU9bJnVpQQBvClFRHq4QMLcdxso7AZQHt6MwYyX/3yUx6rfBhKsXGsJoWOywONzSc/Lt7hZZ2IpccON0eYYCDEgLa9olh0nU6EDaEKah+lmEZ2sPVLXC4pBswUuQ7oRiYHClLkJ8QYYRey8HDI+B15A1UctAjqp/tHwpoQ5jQc1MBnQ6EDK0MQxU6kquO1uHyCLV6oxQQ0ALAgDjv6+O4BJfej/heg5lx4TDqtKL/vp5IVXJwvM4Kl4dHWIdBJ3KSJUMrbAhTVv0s4K1hjA7Tw+nmhTZaUjjom5omVxszTafhCoE9sVfKpjClZmgpoO0fCmhDmFIytM02J1psLgDyZmiBjgGttBnaokpvFig6TI9shTTUZo29peh00L4hTN5yA6C95OB4nQVuETdMCvWzSRGyDdHoaJAQ0EqXoT2gwJZdDMdx7WUHEtbRsjHAg2XcGJom0sawRrlraH0Z2tpWu+RjvXuDetD2DwW0ISxHmIokfTP1jli5QWy4XvZJQe2tu6TN0O70bQgblRmjmFpCKXvRCi27ZOxwwKTFeDdkON08ykQ8sTlSI/+EsI5Yp4PaVjsaLOJPUqprtQuXtJU0VKEjVnYgZaeDoirv7xok4zFJEWljmNybwuIjjNBqvOUUdRK8xv1FPWj7hwLaEJbjqxU80dAmy65+Rgn1s4xcGdqdJY0AgNEZ8k4I60ho3SVFQFurjA4HgHfDJMuSi3myJ7RmkrlFGxNh1AmtgqQoOyjyZSIHxIcjQuIxqL0l9cYwi92FUt/oUzmz1mxjWKA74MhdcqDVcEiMZHW0yio7sDndwuhvCmj7hgLaEJYYaUSkUQeel7aB/slYFkwJfffkGq7AWnaNzoqR9Pf2JLND6y6xHalRRvsqRqijFbEcRyktuzpiG8MOVot/1aZ9QpgyAvqusAztgfJmSdrXsROJRLMRcRHyBH1Ae8lBZQBLDnieR2ObvAEtoNyNYWWNbeB5IMKglfW/vZpRQBvCOI7rUHYgXx1tme+ylhIytJm+DG1lsw02pzRZ62abUwjoRiqgZRczwBfQin0sbE63EDQrYbc/0D4CV6z6co+Hby85UMhzBtrraA9JkKFltaJK3BDGDEyKhEGrQYvdJclJbpEC6meB9pKD8gAGtC12l1CTLlfJAQAkKXRjWMf6WaWUnakNBbQhTgkbw8oblZOhjYswIMrkvfwpRWN9ANhzogk87y13SIiUvu9kd+IiDEIGX8wP8+I6Czw8EGXSISFSGZmJXJFP9CqabbA63NBpOKG0Qwmk7HSg5A1hjF6rwaAU7wmHFHW0rGXXYJmz1u0Z2sD93TdavNlZk14Dk16+TiYsQ6u08bdUP9t/FNCGOCGglbF1lxKGKjAcxyHHdwlYzMvNHSmp/2xHHMcJZQcl9eIdiyPV3sfOS5Kn72ZX2PhdsU5qWLlBdkIE9FrlvA1L1YvW5fbgkO8YDFVwhhboOAK3SfTfJWRoZQ5oWYa2usUOZ4C6ATQIQxXkPWlN9k0Lq1RYQMvK/iig7TvlvJMSWbBNOErI0Cqh5AAAcoQNQdIck10KDWiB9rKD4yLWWLPgTim7/QEgO6G9llqMDZNKfM5Ae/lDncWBulbxagwP17TC4VLmyNuTjUj3btTcfUL8gJZlxuUuOYiPMMCg1YDnA3dpntXPyjVUgUmOZgGtsmpohR60CrpiozYU0IY4uWtonW6P8IaZJvNQBYZl56TIWvM8j+0lDQCUGdAKvWhF3BgmbAhTUC2p2BsmhYBWQc8ZAMINOiFDJGY/2r1l3sv3Q9OiFNGDtyesrn33iUZRN4bVttpR2+oAx7XXMstFo+GELG2gNoYJPWjD5KufBYBU4XlJPw2yJ9SDtv8ooA1xLKCtbbWj2eaU/PdXNtng4QGDToOECGXUj7J2ZlLU0B6ttaC21QGjToMRCmrZxQi9aEXM0CqtwwHgLbdgVy/Y+gLpiEIDWqBDpwMR62j3lnmzncPTlPeaP9mQVDP0Wg4NVqeoteRCG7O4cIQZ5J2WBwR+YxjrbRwbIXdAK87QiP7geZ5qaAOAAtoQZzbpkWj2BpJS1Yx2JJQbRJsUk6nJiZeuDGPT0XoAwJisGNlHvnZF7OEKSt3tDwD5SeJNzjqs0OcMtGcHWRcCMbDJW8PTlV0/CwBGnVbYuCZm2QELaOXOzjJpwnCFwATx9b6AVu6WVCxQb7G50Gp3yboWpt7igMXhBscpY3O0WlFAS2TtdMAadyulfhZor5+sbXWInrXefKwOADAxJ17U39NXwhjYeqsoY2DLm9pgc3qg13JCyzSlyGcbpALck7Xe4hA+3JUwSOJkrPfqfpE2QXk8vLDBani68jO0ADAyg9XRNor2O1hAq5S+vCkBzmTWCgGtvFfiIo06mH2dbJRSdsASBilRJlk7QKgdBbSkvUWRDJ0O2FAFJQW0UmWteZ7HpmPeDO2knDjRfk9/pMd6x8A6XB5RxsAKu/3jI6BT0G5/oH0UbKB7srJL+ekxYbKPeu7KMF8ZwIHKloDtcO+ouM4Ci8MNk14jvPco3ShfHe0uEQPaQqFllzKy1mxPQ0WAgr76Vm9Aq4TWfKwtWXmAR/v2FdXPBoayPkGILOTM0LKhCkq7zCLFMTnR0IaKJht0Gg5jFDQhrCOthhNKMI6IMAb2iO8kSsmX3o/WWOAKYGBXJAwUUEYm7mQD4sIRadTB4fKIUj+811duUJAapbiTmO6MzPQG+XvLmuER4UqFx8MLJ06DU5Txt5Aa4GlhSik5ABDwDW/9RfWzgaGOdxMiKllLDhQ0VKEjKepoN/uysyMyohWZqWOEzVEijENV4oYwJj0mDGF6LRxuT0BriAsrlT1QQKPh2nuvlgV+mAArNxiWpszn35WBiZEw6TVotbtE6QhzvN4Kq8MNo04jlPnILTXAm8LqLN42WUoIaNuzz8oIaI9TD9qAoICWdOpFK8W88o7KFNaDlsmRoD8vC2gnKrTcgGHBphgf5KzkIC9JGR/iHWk0nJA5DuTGsEKFNM/vCaujFWM6FguS1dDhgNFpNcJ6xaijZY85NE05WWsW0Na22uFw9f8KBcvQxiugm01KFKsPVkYNLQtolTQ1UI2U8ZdDZJUZFw4NB7TaXagRsZn6yXie7zBUQRk9aBkpstabi5VdP8uwYFOMDO1Rtts/UZnBHaujPVwdmDpaj4dXfMkB0L5Za2+AN4bxPC88plo2hDHt/WgDv1mOPSar1VWCuAgDDLrADFdwuT3CYAUlZGhZsK6UDC1rEamU7LxaUUBLYNRpkRHrPTOUcgRuncUBK2tVorAd7h0DWjGy1tXNNhyrtYDjgHEDlB3Q5iaIk6FttDpQ26rc3f4AkJ8c2NZdpQ3eS8sGBV1a7gorBzhQHtia0bLGNjRandBrOaGLhFqM8tXRirExjGVoRygoyOc4LmCBX4PVCZ4HOA6IDZe3Dy0ApAZ4w1t/WOwuVLd4E0lKfk9QAwpoCQB56mhZXWJqlElxPViz4sLBcd5ehXW+S2WBxLKzQ1OjEC3z5JzTYcFmTYsdTW2Ba2PG6mdTo02IMCqzhljodBCg7DQrN8hPilTMpeWuDEyKhEGnQYvdhdKGwNUPswlhg5LNivubPx2Wod1f3hzQ7g9uDy8cl5EKG67SHtD2L/Bj5QYxYXpFvO6VlKFl5Qax4XpEKyDYVzP5X1lEEeQIaEsV3KrEpNcKG9XEOCZsoILS62cBbxuzJF8bs6MB3PV+pFq5HQ4Y1ungSE1rQPrwFlawXqPK3hCl12qEfqh7A7gxjPW2VVP9LJMdHw6zSQe7yyOUjQTCkZpWtDndiDBokauwzZGBmqqlpA1hQHuPXSUMVxDKDVTSwk7JKKAlANqzcGJs/OlOicJ3dooZ5P98qAYAMDlXmQMVTiZsDAtgScohX12qEjscMBmxYTDpvX14A9HpoKiKdThQbv0sM0zYGBa4mlHWsmuYCiaEnYzjOKHGdUdpY8Aed5fvsYalR0OrkGmJTGqApoUpaUMYoKzhClQ/GzgU0BIA8pYchFpAW1xrQXGdFToNhykDEwL62GIRNoYFMEN7oEJZk5G60rnTQf+zckKGVsEbwpihaWxjWGAytDzPC7Wiw1SYoQWACdneKypbfB1KAmFPGdsQprxjkhoTmAytENAqYKgCo5SyAza8hzoc9B8FtARAe/B2vC6wTeR7IgS0Cv1DFgLaAG+U++mgNzs7PjsWkQqtHT2ZsDEsgMeC9WMtSFV2ti4/yRt8Hu5nHW2bw41jvmyMklt2McM7jMANxMbI43VW1LY6YNBqVNWDtqMJObEAvC33ArVZdJevw8EIBXU4YFKjAhP0sc2fSik5ADqUU8g8LazYd6Uyh0oO+o0CWgLAOwrQoNPA6eaF3rBiU3INLdB+KfxggFo2MSygPWtQUkAfV0x5vixloDK01S021LY6oOHa61SViu3G7+8I3EPVLeB5ID7CgMRIZVx67cmQlChoOG8wwnZh98fW4w0AvINE1DqvfkxmLPRaDpXNNpTW9/990uHy4ECFb0OYgjocMIHqBlDvq6GNV1RAq4wM7fE6lqGlgLa/KKAlALyXVtl0LCnqaO0uNyp8vQ2VWnLAmssfq7UEbOOAzenGhiN1AIDpgxMD8phSyBUy+NaAZPDZpffshAiEGZQd3LAMbX9bd3UsN+A4ZdVKdiXMoBVO6vaW9b+Odttx72X68QNi+/1YcgkzaIVuB5uO1fX78Q5WtcDh8iDKpFPkJWeWxaxtdcDucvf5cZQ09pZJCVAHh/6wOlyoavYG+zkU0PYbBbREINYl9q6UNbSB54Fwg1ZRZ+0dJUQakRptAs97W/UEwtbiBrQ53UgyGxVdO3qy9JgwGHUaONwenGjo/weAUG6g8N3+QHvrrv52OhAmhCUr/zkzLHjbXtLQ78faWux9jPHZyu/s0RPWmWRzAOpo2UCFkRkxijzJiQ3Xw6jzhglVTX3P0texkgMFXZlIC1AHh/5gLbtiqGVXQFBASwRSjHtlOm4IU+IbOSNMTApAhgoAfjpYDQA4a1Ciop/3yTQaTmgpdLS2/2UHatgQxmTGhSPcoIXd5elX2zIWxKthQxgzsUPNaH80Wh1CL99xKs7QAh0C2uL+B7R7yhoBKK//LMNxnDCWvD+ZTJahTVBQ8oJlaCtlDGjbN4RRdjYQKKAlApahDUTAcjqlCu9wwLB+mYELaH31syoqN2BYazfWP7Y/WN2g0jeEAYBWwwknNjv72K6J53khQ6uGrDQzMcfbVm5XaRNszr5fct7mq5/NTYxQ1GXnvhg3IBYazptd628wtKuUZWiVGdACQEoANoax4TRxCupywMatl8tYciBsCFNguYkaUUBLBKxeLhABy+kovWUXMyLDG3zsCUBAW97YhoNVrdBwwDSVtOvqSHh99HNjmMPlER5DLdlK1lKJXSL2V3mTDfUWB3QadY18zY4PR0KkEQ63p8/PHWjfEKbm+lkmyqQX6uv7k6VtsjqFrP3oTOUel9R+Bn5uD48GqxJraOUfrkAZ2sCigJYIBvk+aCubbWiyBm7EaVeU3rKLYZm5IzWtsDr696bHsrOjM2MQE66cN/beyvNlaPs7BvZITSucbh5mk06YxqZ0ozJjAAC7fH1U/cUylEPTolS1w5/jOEwSakb7vglqG6ufHaDu+llmYrY3c92fY7LhaC08vHdSHrv8rUSs1rSv2ehGqwOsw1msgt73Io06mI3yDldgQxWoZVdgUEBLBGaTXggwAt2q6mQlvpY3Sm3ZxSSZTUgyG+Hh2y+T99W3eysBAOcMUU+7ro6G+soDDlQ092tzlFBukBKlmjpiNiHqQEVzny69b/cFtGOzlJuJ686EbF8dbXHfNoY5XB7hRGBctvqef1cCsTHs50O1AJR/tYYF2+V97NfK6mdjwvXQa5UVcrS3JZOnjra4joYqBJKyXl1EdixLG8hZ5SfjeV41NbQAMMKXpd3Tj0uuDRYHfj3s/QC7YERqQNYltdzESITptbA63P3aOCjUkqqk3ADwjsCNjzDA6eb7dGLDugSMVeEld1ZHu624vk8t2/aWN8Hu8iAuwiC0f1M7FuQfrGpFXWvfdv+vP6yOgJbVmlY29y2LWafAll1MioydDjq17AqSvwu5UUBLOmFN7gMx5rM7DVYnWu0ucBxUcclZ6HTQj9Zd3++vhMvDoyA1SugWoDZaDSfUDu4r73twzwLCISrYEMZwHCds3PG3lrTN4Rbavqlxh//gFDPMJh0sDrfQncIfW311pmOzYlWTkT+d+Mj2tns/FtX4/fOl9VYU11mh1XCYlKvsMoyUqP5N1GItu5TYnjFNyD5LX3LAWnZFh+lVWYKmRBTQkk5YQCtmhpbVz6ZEmVRRTxiI1l1f7/GWG1w0Up3ZWYaNQ+1PtpoFRWrocNCRUEfrZ6eD3Sca4fLwSI4yCh+gaqLVcJjg6x3bl2EC7LL8hCApN2DOG5YCAPhuX6XfP/uLLzs7JjMGZpOy+4+yDG2dxdGnchs2JUyJGdqMWG+wHoje2v5iE8KyqdwgYCigJZ2wGfMHq1oCNqv8ZCUKH3l7MlZycKi6tU9v6A0Wh3B5Ua3lBswwIVvdt4C2psWO2lY7OK69vEUtWEC708+NYdt85QbjBqg3Q8kC2i1+7upvc7iF4G2qwi+t+2vWsGQA3s2e/m4YVdMxiQ7TI8yXeKhq9j9L215yoJyhCkxGrPcziJXASelYrfd3UoeDwKGAlnQyMCkSHOctC6j1XSoKNDXVzwJAcpQRCZEGuD19q5/8bl8l3B4eQ1OjVF8rxYL7fWXN8PRhYxhrU5QTH4Fwgy6gaxMb2xh2tMaCprbedwFR84Ywhm2C2lLc4NeJ7rpDNbA5PUiPCcOwNHVl5E9naGoUMuPCYHd5sO5g78sOPB5eqKc/M1/5AS3HcUjtx8YwYaiCgnrQMplx8mVoWevCPJWWoCkRBbSkE5Nei2zfGaNYdbTsUotaAlqO4/pVdvD1ngoAwIUqLzcAvCc8Bp0GLXaXkGn3x/bjjQDaM71qEhdhED4Ae/s64Hke20saAahzQxgzIj0aJr0G9RYHivx4X/h+XxUAYNawFNVmp7vDcRxmDfWWHaza2/uyg/0VzWiwOhFp1AlZf6Vr7wbgf+Cn5E1hmb4MbUVTG5x92PDYH0JAm6TuJIeSUEBLTiF2pwO1DFXoiGUmWT/R3qq3OPDrEW/dodrLDQBAr9WgwFeW0peyA3bJeqJK6ylZlra3E8OK66yotzhg0GlUnaE06DSYmufNJn6zu6JXP+Nye7Cm0BvQnue7PB9sZg/3BrRrCqvhcPUuIGLtus7IjVNcG6vuCBvD+tANoL5VuQFtotkIo04DDy/txjCe53GkmjK0gaaOvyYiqcEidzo4UuMrhlfR5fffDPKOql1bWO3XmfznO8qCptyAEepoy/wrv3C5PUL7qgk5yt7Z3Z3Rfm4MY+UGI9KjYdQpfwNkT347Og0A8N9d5b0qO9hS3IBGqxOx4fqgmBDWlbFZsUg0G9Fic2HD0d5tmFtzwBvkq6F+lknrV4bWuyksXoE1tBzHCRvDSuulC2jrLA4027ydfoLlc0EJKKAlpxjky8D5c2mxt5qsTtS0eN/gBiap58x0bFYsEiINaLa5sLGXH1weD493NhQDAK6YlCXi6qQ1oo/lF/srmmF1uBFl0mFQknp60HbELhFvL2no1XCJjhvC1O7cockI02txvM6KXb3ocsF2/88oSIZOJZlIf2k0HM4d6s0+96bbwf7yZmw93gCdhsP5w9VzxSbN116xPzW08QqsoQXaNyefaJBuYxjLzmbEhqmi049aBOe7DOkXIUNbGfhOB4drvEFyarQJkUb1bArSajic62e93E+HalBcZ4XZpMPFY9LFXJ6khqe1dzrw5/WxhY0/zY6DRqPOespRGTGIMulQ2+oQss09YS2rxmbFiLwy8ecQnyUAACGQSURBVIUbdELpwH93lvV4X57nsXq/r9xgaHCWGzCzfe27vt9Xedqyg3c3FgPw1hQredztydqzmP4FfR4PjwbfGHUl9qEFOjw3KQNa31VKKjcILFED2vr6elx11VWIiopCTEwM5s+fj9bWnufA22w2LFq0CPHx8YiMjMQll1yCqqoq4fu7du3CFVdcgczMTISFhaGgoADPPvusmE8j5GQnRECv5WBxuFEW4Lqiw74zUzVlZxlWL/fdvqpeZefe/rUYAHDp+ExEqCh4P51BKZHQazk0Wp1+vT5Yg/3xKq2fBby1pDN9Ado3e3quJS2sbMbh6lYYtBpMzlXP5eWezBntPTH7cldFj1PD9pU3o6yxDWF6rVCuE6zOyI1HktmI2lYHVm4p6fZ+TVYnPt9RDgC4dvIAqZYXEGzzVGmD1a+T2KY2p/BeGavQgFZ4bhKWHFCHA3GIGtBeddVV2LdvH1avXo2vvvoK69atw8KFC3v8mdtuuw1ffvklPvroI/z0008oLy/HxRdfLHx/27ZtSEpKwnvvvYd9+/bh73//O5YuXYoXXnhBzKcSUvRajfCHFug62kNV6g1oJ+fGw2zSobbVjh2nyc4dq7Xgx6IacJz6PrxOx6jTCgM4/Nnt374hTJ31s8wFvkvFq/ZW9ti67L87vcHL9MGJiA5XdvP83pqWn4DYcD1qW+091ox+tsObwf3NoISgv6Rq0Gmw+JyBAIDn1x5Gm6PrXtUfbStFm9ONISlmoQ2aWqTFhEHDATanBzV+jPplHQ6iTDrFboBjJQfSZmgpoBWDaK+wAwcOYNWqVfjXv/6FSZMmYdq0aXj++efx4Ycfory8vMufaWpqwuuvv46nnnoK55xzDsaNG4c333wTv/76KzZu3AgA+OMf/4hnn30WZ511FnJzc3H11Vdj3rx5+PTTT8V6KiGpfWJYzxl1fx32/SHnq7CG0qDTYGaBNzt3urIDlp09e3BSUDbOZmUHvR0DW1xnRW2rd7f/iAz1tezqaFp+AiIMWlQ02bCrmyELHg+PL3wB7e9GB0+5iV6rEdrPsYD9ZKX1Vry78TgA4PIJwVM73pPLJ2QhPSYM1S12oaygI4+Hx3u+Y3LN5AGqa2Fm0GmQGu3/5qk6X/AbH6m8DWGMvBna4PtskJNoAe2GDRsQExOD8ePHC7fNnDkTGo0GmzZt6vJntm3bBqfTiZkzZwq3DRkyBFlZWdiwYUO3v6upqQlxceo641U6NjGsqNL/QQI9YRnafJVNiWJm+erlVu2r7PbSW4PFgU+2nQAAXDclW6qlSYptcmITj05ni6+WdHRGjOp3+5v0Wszwndh8282JzfaSBpQ1tiHSqMOMgiQplyc6FqB/u6eiy13vT3xfBIfLgyl58Zg+OLjLDRiDToNbZuYDAF7+8QhabJ0Hb/xQVC3U089R6QlO+5jY3mcyWZuvlCjl1guz3tK1rfY+TYL0l83pFgY55KnwSqWSiRbQVlZWIimp8xu5TqdDXFwcKiu7/hCorKyEwWBATExMp9uTk5O7/Zlff/0VK1eu7LGUwW63o7m5udMX6dlQX8/MPX0YJNAdq8Ml1FwOVOmllrMGJcKk1+BEQxv2lXf9Olr2xT602F0YkmLGmSpqzeOP6UO8gcruE029GofJyg0m5Ki3fraj83311N/urejyxIZlL2cNSwm6S+7jsmIxIj0aFocbf/n3jk61tLtKG4Xn/rcLClSXieyPi8ekIzcxAg1WJ5753yGhHGXj0Trc+uFOAMDcceqtp2eX5kvqeh/Qsvd71iVBiaLD9DD7/ptI0engWK0FPO/9vUrdKKdWfge0d999NziO6/GrsLBQjLWeYu/evfjd736HZcuW4bzzzuv2fsuXL0d0dLTwlZmZKcn61Iy1Zjpaazkl29BXR6q9OzsTIg2K3SBwOmEGLc4e7D1Re+jr/adsjPl2TwW+2FUOrYbDPy8Zqdrd/KeTZDYJLazWFlaf9v5bhA1hwXElZfrgJITptSitP/XExun2CNPhfufr3RpMNBoOz18xBpFGHbYUN+CJ7w8C8NZJP/zNAQDe4G64CqfB9YdOq8GScwcBAF7/5RgufP4XvPzjEVz7xma02F2YmBOH287Nl3mVfddxY1hvsWEF6THKzdByHId0CXvRdiw3CKUTPin4HdDefvvtOHDgQI9fubm5SElJQXV15w86l8uF+vp6pKSkdPnYKSkpcDgcaGxs7HR7VVXVKT+zf/9+zJgxAwsXLsQ999zT45qXLl2KpqYm4au0tNTfpx1yEiKNSIs2gefRbSbSX4eqvRvM1F4If/t5gxFh0GLj0Xo89l2RcHttqx1//3wvAOCms/JUM9ayr2YO8Qb2rFF8dyqbbCius4LjgqMfK+A9sWGX07/c3bmW9JdDtai3OJAQacCUvHg5lie67IQIPPaHkQCAFT8dwZ/f34apj67F5mP1MOo0uH3WYJlXKI8LR6TingsLYDbpcKCiGf9cVQiHy4OZBcl4548TYTapd3NgVrz/QZ8Q0MYqN0MLSLsxjCV21P45qER+B7SJiYkYMmRIj18GgwGTJ09GY2Mjtm3bJvzs2rVr4fF4MGnSpC4fe9y4cdDr9VizZo1wW1FREUpKSjB58mThtn379uHss8/Gddddh4cffvi0azYajYiKiur0RU6Pbd7xt4F+d1jLLrXWzzIDkyLxxNxRAIBX1x3Fh5tL8NHWUix4ZyvqLQ4MSTHj5hkDZV6l+Fgd6S+Ha3usPfvc17N0TGYMolT8gX6y/xvlzb6+/vMx/FDkPXlvtDrw9P+8GcuLRqYF7UABwDvK+TpfB49v9lSivMkGg1aDf1w0FOkKvsQsJo7j8Kczc7HuzrMxf1oOwg1aXDExCyuuHqv60pO+ZGjVUHIAdNwYJkFAyzK0VD8bcKIV8xQUFGD27NlYsGABVqxYAafTicWLF+Pyyy9HWpr3g6CsrAwzZszAO++8g4kTJyI6Ohrz58/HkiVLEBcXh6ioKNx8882YPHkyzjjjDADeMoNzzjkHs2bNwpIlS4TaWq1Wi8TE0NiAIJWRGTH4bl9Vr3eyn84h1oM2CM5Mzx+RihvOysUrPx3F3Z/uEW43aDV4Yu4o1W986o2CVDPSok0ob7Jh/eFaIcDtiOd5/GeL94rIpeODq9Rn9rAU/H5MOj7bUYY/v7cdT182Gk+vPoiiqhbEhOuDdkNgR3+7sAAmg/e1PjUvAROy4xBmCP7X/unERhjwj4uG4p4Lg6eOmGUxyxvb4HR7TtuGi+d5lDWoJKCNYxvexC85OFrr/RzMpZG3ASdqdfr777+PxYsXY8aMGdBoNLjkkkvw3HPPCd93Op0oKiqC1dp+VvT0008L97Xb7Zg1axZeeukl4fsff/wxampq8N577+G9994Tbh8wYACKi4vFfDohh9XABWpj2BEhQ6u+ll1dufO8wSisaMFPB2swMiMa0wcl4v9GpQXN8zsdjuMwoyAZ7248jv8dqO4yoN16vAFHay0IN2hx0ajgqifVaDg89oeRqLc48NPBGtz4nvdqVHKUEe/OnxQSM9qNOi2Wnl8g9zIUK1iCWQBIjDTCoNPA4fKgotGGrPjwHu/fbHPB4uvJmxat8IC2D9nnvvB4+PaSA8rQBpyoAW1cXBw++OCDbr+fnZ19yg5hk8mEF198ES+++GKXP3PffffhvvvuC+QySTfYxrBjtRY025z9ulxsd7lRXOf9Q1bjUIWu6LQavHH9BNicbtXuXO6vGQVJeHfjcawtrALPDz/lA3ylLzt74YhUVY067i29VoOXrhqLK/+1CbtKGzEgPhzvzZ8kZLMICRYaDYeM2DAcrbGgtMF62oCW1c/GRRgUn7UXamhF3hRW2WxDm9MNnYZDFr1HBFzwFniRfouLMAi9B/tbR1tca4WHB8wmHZLMym2y7S+thgvZYBbwjv0MN2hR1WzH3rLOmwdbbE58vdu72/+yCcFVbtBRhFGHd+dPxGN/GIlPb5pCwSwJWllxva81ZeUGaqinZp9zTW1ONAeoq09X2D6SAfHhip2cpmZ0REmPRvo2hu3pZx0t63AwMCkyqC7DhTqTvn23/8Pf7BfmtgPAV7sr0OZ0IzcxImi6G3QnyqTHpeMzFT0RiZD+8ufSfHkTq59VbssuJsKoQ5yvlaSYG8OKKr2fg2xwEQksCmhJj1gd7e5+ZmiFDgdBUm5A2t3RoY3Zs2sOAQCarE5h/O9l4zPpJIaQIMA2T5X04tK8WjocMJlCL1rxAtoDvsmbQ1Ko05IYKKAlPRqZHgOg/xnaAxXeP+T8JDozDTa5iZF45OIRAIDn1x7Ciz8cxqxn1qGwsgXhBi0uHpsh8woJIYHgT3ur8kbvBEE1lBwA3vcxADhSYxHtdxRWeDO0QyhDKwoKaEmP2Mawknormqx9qy3ieR7bSxoBAKOzYgK0MqIkvxudjssnZILngce/K0Jlsw05CRF4/0+TkBhENdOEhDJWH96bEbFlvvuoJUPLNiuzbjyB5nR7hCuVBamUoRUDBbSkR9HhemEjQF/bd5U1tqGmxQ6dhhMCZBJ87vvtMAxL875RXz8lG9/85UyMyQru2llCQgkLaGtbHbA6XD3eV20Z2rxEb5u9wzXiBLTFtRY43B5EGnWqOSZqE7rbs0mvjciIRkm9FTtLGzAtP8Hvn2fZ2aFpUaqflkO6Z9Jr8clNU1BvcagmK0MI6b3oMD2iTDo021worW/rdnOT0+1BVYs3oFXLe0HHDC3P8wGv+z/g2xA2KDkSGg3tKRADZWjJaU3KiQMA/Hqkrk8/v6OkAQAwlrJ1Qc+k16rmA4wQ4r/MXrTuqmyygecBg06DeF/3AKXLiouAVsPB4nCjstkW8Mcv9O0jGULlBqKhgJac1pQ8b1Z26/EG2Jxuv3+eZWjHUP0sIYSoWm9adwkdDqJNqslGGnQaDPANi2DTvAKp0JehLaANYaKhgJacVl5iBFKiTHC4PNha3ODXz9qcbuwv99beUoaWEELULcdXa3qwqvtaUzYlLD1WXVdr8nydDg77+qYHEmVoxUcBLTktjuMwZWA8AGD9kVq/fnZfeROcbh4Jke1TxwghhKjT8DTvxt6epkeWCxladb3nszraQG8Ma7I6Ud7kLWOgoQrioYCW9MpUX9nB+sP+BbQ7hHKDWGquTwghKsc61RRVtsDh8nR5n7JGdW0IY1iGNtAlB0VV3oxvekwYokz6gD42aUcBLemVqQO9Ae2esia/+tFu920Io/pZQghRv8y4MESZdHC4PThY1fWleVZDq7b2VGJlaAuFCWGUnRUTBbSkV1KiTchLjADPAxuO9r7bAcvQUv0sIYSoH8dxwkj07soOylU29pbJ9dUH17TY0dTWt0FCXTnAJoSlUkArJgpoSa+xLO2vvayjrWhqQ0WTDVoNh5EZNFCBEEKCASs76GrYDs/zqt0UFmXSIznKO9nwSACztO0ZWtoQJiYKaEmvsYD2l17W0W4/3gjAe5kl3EAzPAghJBj0lKH1ThHztndMjTZJuq5ACPQIXI+HRxFr2UUZWlFRQEt67YzceGg44GiNBZVNp288/b8DVQCACdlxYi+NEEKIRFiG9kBlC5zuzhvDNh3zlqQNSTGrcjKk0LorQBna4joLrA43DDoNsuMjAvKYpGsU0JJeiw7TY2RGDADgq93lPd7XYndh1d5KAMDvRqeJvTRCCCESyYoLh9mog8PlwaGT+tGyTjjsip7aBDpDu7O0EYD3JECnpZBLTHR0iV/mjs8AALy/qQQeD9/t/VbtrUSb042chAiMzoyRaHWEEELEptFwGJburQc9ueyAlaRNU2lAK7TuqglM6y6hdSV9DoqOAlrilzmj0xFp1OFYrQW/Hum+28GnO04AAC4ek079ZwkhJMiwsoO95e0BbUmdFaX1bdBpOEzMUWepGcvQHq+zwO7yf9T7yXaUstaV1OlHbBTQEr9EGHW4ZGw6AODdjcVd3qeiqU0IdueMSZdqaYQQQiQyvItOByw7OzYrFhFGdW4ETjIbYTbp4OGBw/0sO2hzuIWWXdSLXXwU0BK/XX3GAADA6v1VqGhqO+X7n+8oB88DE3PikBkXLvXyCCGEiIwFtAcqmuHybQxTe/0s4O2zy7LPu0q7H+/bG7tPNMLt4ZEcZVRlxwe1oYCW+C0/2YwzcuPg4YF/byrp9D2e5/Hp9vZyA0IIIcEnJz4CkUYdbE4PDlW3wuPhsd7Xo3xafrzMq+sftu9jl29DV1/t8P38WBr9LgkKaEmfXHNGNgDgg82lqG5pb+H1353lOFTdCoNOg/NHpMq0OkIIIWLSaDgh8Fv66R5sLq5Ho9WJSKNO6IajVqN8z2tnfwNaGv0uKQpoSZ+cNywZ6TFhqG2143cvrMfesia8u/E4bvvPTgDAlROzEB2ml3eRhBBCRPOPi4YiJlyPnaWNmP/WFgDAGblx0Ku8PRXrSHCwugWtdlefHoPneWxnHQ5oQ5gk1P2qI7LRazV4d/5E5CZGoKLJhotf+hX/+HwveB64+ows/OOioXIvkRBCiIgGp5jxzh8nwmzUweKbDqbm+lkmKcqEtGgTeN5bB9sX5U021LTYodNwGJ5Go9+lQAEt6bPcxEh8vmgqpg9OhMO3KeAvM/Lx4O+GQ6uheiFCCAl2IzNi8Oa8CQjTa6HhgLMGJcq9pIAY7SsT6OvGMFZuUJAahTCD+iamqZE6+2oQxYgy6fH6dRPwweYSxEcYcAHVzRJCSEgZnx2Hr/8yDbWtDuT6BhOo3ejMGHyzpxI7fX1k/SUMVKD6WclQQEv6TavhcI2vlRchhJDQk5sYidzgSM4CAEZneute+7oxjDaESY9KDgghhBBCOhieHgWthkNVs73Lfus9abW7hIETY2lDmGQooCWEEEII6SDcoMOgZDMAYKevfKC3fj5YA6ebR3Z8OLJouJBkKKAlhBBCCDkJ67O7089OB/87UA0AmFGQTAMVJEQBLSGEEELISVg/Wn8ytG4Pjx+LWECbJMKqSHcooCWEEEIIOQlr3bX7RBNsTnevfmZnaSPqLA6YTTpMyI4TcXXkZBTQEkIIIYScZGBiJNKiTWhzuvFjUU2vfmZtYRUAbz9etU9MUxs62oQQQgghJ9FoOFw40ttb/es9Fb36mTUHqNxALhTQEkIIIYR04aKRaQCANQeq0ObouezgRIMVhZUt0HDA9EEU0EqNAlpCCCGEkC6MzIhGZlwYrA431hZW93hf9v1xA2IRG2GQYnmkAwpoCSGEEEK6wHEcLhzhzdJ+tbu8x/t+4ytLmFGQLPq6yKkooCWEEEII6cZFvjratYXVsNhdXd5n87F6bDxaD52Gw4UjUqVcHvGhgJYQQgghpBvD0qKQHR8Ou8uD/x2oOuX7PM/jye+LAABzx2cik6aDyYICWkIIIYSQbnAcJ2wO+8/WUvA83+n7vx6pw6Zj9TBoNbj5nIFyLJGAAlpCCCGEkB5dPDYdei2H9Yfr8NKPR4TbO2Znr5yUhbSYMLmWGPIooCWEEEII6UFuYiQe+N1wAMAT3xdhbWEVbE433lhfjO0ljTDqNPjz9DyZVxnadHIvgBBCCCFE6a6YmIV95U14b2MJ/vLvnTDoNKi3OAAA103JRlKUSeYVhjYKaAkhhBBCeuHei4bhYGUrNhfXA3YgLdqEq84YgAVn5sq9tJBHAS0hhBBCSC8YdBq8cs04vLn+GEZkxODswYnQaal6UwkooCWEEEII6aXYCAOWnDdY7mWQk9BpBSGEEEIIUTVRA9r6+npcddVViIqKQkxMDObPn4/W1tYef8Zms2HRokWIj49HZGQkLrnkElRVndrIGADq6uqQkZEBjuPQ2NgowjMghBBCCCFKJ2pAe9VVV2Hfvn1YvXo1vvrqK6xbtw4LFy7s8Wduu+02fPnll/joo4/w008/oby8HBdffHGX950/fz5GjhwpxtIJIYQQQohKcPzJIy8C5MCBAxg6dCi2bNmC8ePHAwBWrVqFCy64ACdOnEBaWtopP9PU1ITExER88MEH+MMf/gAAKCwsREFBATZs2IAzzjhDuO/LL7+MlStX4t5778WMGTPQ0NCAmJiYXq2tubkZ0dHRaGpqQlRUVP+fLCGEEEIICSh/4jXRMrQbNmxATEyMEMwCwMyZM6HRaLBp06Yuf2bbtm1wOp2YOXOmcNuQIUOQlZWFDRs2CLft378fDzzwAN555x1oNFQGTAghhBASykTrclBZWYmkpKTOv0ynQ1xcHCorK7v9GYPBcEqmNTk5WfgZu92OK664Ao8//jiysrJw9OjR067FbrfDbrcL/25ubvbz2RBCCCGEEKXyO7159913g+O4Hr8KCwvFWCsAYOnSpSgoKMDVV1/d659Zvnw5oqOjha/MzEzR1kcIIYQQQqTld4b29ttvx/XXX9/jfXJzc5GSkoLq6upOt7tcLtTX1yMlJaXLn0tJSYHD4UBjY2OnLG1VVZXwM2vXrsWePXvw8ccfAwBYCXBCQgL+/ve/4/777z/lcZcuXYolS5YI/25ubqaglhBCCCEkSPgd0CYmJiIxMfG095s8eTIaGxuxbds2jBs3DoA3GPV4PJg0aVKXPzNu3Djo9XqsWbMGl1xyCQCgqKgIJSUlmDx5MgDgk08+QVtbm/AzW7ZswR//+Ef8/PPPyMvL6/JxjUYjjEajX8+TEEIIIYSog2g1tAUFBZg9ezYWLFiAFStWwOl0YvHixbj88suFDgdlZWWYMWMG3nnnHUycOBHR0dGYP38+lixZgri4OERFReHmm2/G5MmThQ4HJwettbW1wu/rbZcDltWlWlpCCCGEEGVicVpvGnKJOvr2/fffx+LFizFjxgxoNBpccskleO6554TvO51OFBUVwWq1Crc9/fTTwn3tdjtmzZqFl156KaDramlpAQAqOyCEEEIIUbiWlhZER0f3eB/R+tAqmcfjQXl5OcxmMziOk3s5XWJ1vqWlpdQrV0R0nMVHx1gadJylQcdZGnScxaeGY8zzPFpaWpCWlnbaNq2iZmiVSqPRICMjQ+5l9EpUVJRiX2jBhI6z+OgYS4OOszToOEuDjrP4lH6MT5eZZWgqASGEEEIIUTUKaAkhhBBCiKpRQKtQRqMRy5Yto3ZjIqPjLD46xtKg4ywNOs7SoOMsvmA7xiG5KYwQQgghhAQPytASQgghhBBVo4CWEEIIIYSoGgW0hBBCCCFE1SigJYQQQgghqkYBrUp8/fXXmDRpEsLCwhAbG4s5c+bIvaSgZbfbMXr0aHAch507d8q9nKBSXFyM+fPnIycnB2FhYcjLy8OyZcvgcDjkXprqvfjii8jOzobJZMKkSZOwefNmuZcUNJYvX44JEybAbDYjKSkJc+bMQVFRkdzLCnqPPvooOI7DrbfeKvdSgk5ZWRmuvvpqxMfHIywsDCNGjMDWrVvlXla/UECrAp988gmuueYazJs3D7t27cL69etx5ZVXyr2soPXXv/4VaWlpci8jKBUWFsLj8eCVV17Bvn378PTTT2PFihX429/+JvfSVG3lypVYsmQJli1bhu3bt2PUqFGYNWsWqqur5V5aUPjpp5+waNEibNy4EatXr4bT6cR5550Hi8Ui99KC1pYtW/DKK69g5MiRci8l6DQ0NGDq1KnQ6/X49ttvsX//fjz55JOIjY2Ve2n9wxNFczqdfHp6Ov+vf/1L7qWEhG+++YYfMmQIv2/fPh4Av2PHDrmXFPQee+wxPicnR+5lqNrEiRP5RYsWCf92u918Wloav3z5chlXFbyqq6t5APxPP/0k91KCUktLC5+fn8+vXr2aP+uss/hbbrlF7iUFlbvuuoufNm2a3MsIOMrQKtz27dtRVlYGjUaDMWPGIDU1Feeffz727t0r99KCTlVVFRYsWIB3330X4eHhci8nZDQ1NSEuLk7uZaiWw+HAtm3bMHPmTOE2jUaDmTNnYsOGDTKuLHg1NTUBAL1uRbJo0SJceOGFnV7TJHC++OILjB8/HnPnzkVSUhLGjBmD1157Te5l9RsFtAp39OhRAMB9992He+65B1999RViY2Mxffp01NfXy7y64MHzPK6//nrceOONGD9+vNzLCRmHDx/G888/jxtuuEHupahWbW0t3G43kpOTO92enJyMyspKmVYVvDweD2699VZMnToVw4cPl3s5QefDDz/E9u3bsXz5crmXErSOHj2Kl19+Gfn5+fjuu+9w00034S9/+QvefvttuZfWLxTQyuTuu+8Gx3E9frF6QwD4+9//jksuuQTjxo3Dm2++CY7j8NFHH8n8LJSvt8f5+eefR0tLC5YuXSr3klWpt8e5o7KyMsyePRtz587FggULZFo5If5ZtGgR9u7diw8//FDupQSd0tJS3HLLLXj//fdhMpnkXk7Q8ng8GDt2LB555BGMGTMGCxcuxIIFC7BixQq5l9YvOrkXEKpuv/12XH/99T3eJzc3FxUVFQCAoUOHCrcbjUbk5uaipKREzCUGhd4e57Vr12LDhg2nzLQeP348rrrqKtWfuYqtt8eZKS8vx9lnn40pU6bg1VdfFXl1wS0hIQFarRZVVVWdbq+qqkJKSopMqwpOixcvxldffYV169YhIyND7uUEnW3btqG6uhpjx44VbnO73Vi3bh1eeOEF2O12aLVaGVcYHFJTUzvFFABQUFCATz75RKYVBQYFtDJJTExEYmLiae83btw4GI1GFBUVYdq0aQAAp9OJ4uJiDBgwQOxlql5vj/Nzzz2Hhx56SPh3eXk5Zs2ahZUrV2LSpEliLjEo9PY4A97M7Nlnny1cbdBo6EJRfxgMBowbNw5r1qwR2vl5PB6sWbMGixcvlndxQYLnedx888347LPP8OOPPyInJ0fuJQWlGTNmYM+ePZ1umzdvHoYMGYK77rqLgtkAmTp16ilt5w4ePKj6mIICWoWLiorCjTfeiGXLliEzMxMDBgzA448/DgCYO3euzKsLHllZWZ3+HRkZCQDIy8ujTEwAlZWVYfr06RgwYACeeOIJ1NTUCN+jbGLfLVmyBNdddx3Gjx+PiRMn4plnnoHFYsG8efPkXlpQWLRoET744AP897//hdlsFmqTo6OjERYWJvPqgofZbD6lLjkiIgLx8fFUrxxAt912G6ZMmYJHHnkEl156KTZv3oxXX31V9VfLKKBVgccffxw6nQ7XXHMN2traMGnSJKxdu1b9PeNIyFm9ejUOHz6Mw4cPn3KiwPO8TKtSv8suuww1NTW49957UVlZidGjR2PVqlWnbBQjffPyyy8DAKZPn97p9jfffPO0pTaEKM2ECRPw2WefYenSpXjggQeQk5ODZ555BldddZXcS+sXjqdPEUIIIYQQomJUvEYIIYQQQlSNAlpCCCGEEKJqFNASQgghhBBVo4CWEEIIIYSoGgW0hBBCCCFE1SigJYQQQgghqkYBLSGEEEIIUTUKaAkhhBBCiKpRQEsIIYQQQlSNAlpCCCGEEKJqFNASQgghhBBVo4CWEEIIIYSo2v8DPvunZCU++gUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ypred = model(x)\n",
    "dypred = torch.autograd.grad(\n",
    "        ypred,\n",
    "        x,\n",
    "        grad_outputs=torch.ones_like(ypred),\n",
    "        create_graph=True\n",
    "    )[0]\n",
    "dyp = dypred.detach().cpu()\n",
    "dye = np.cos(xp)\n",
    "# tracer \n",
    "plt.figure(figsize=(8,8))\n",
    "plt.subplot(2,1,1)\n",
    "plt.title(\"Dérivée de la fonction $f(x)=sin(x)$\")\n",
    "plt.plot(xp,dyp,label='dérivée PINN')\n",
    "plt.plot(xp,dye,label='exacte')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(xp, dye - dyp)\n",
    "plt.title(\"Erreur\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceb3cf15-5b3d-486e-a28b-38293022ce0b",
   "metadata": {},
   "source": [
    "### théorème d'approximation universelle\n",
    "\n",
    "Le théorème d'approximation universelle [Wikipedia](https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_d%27approximation_universelle) indique qu'un réseau de neurones à une couche cachée suffisamment large (avec une fonction d'activation non linéaire comme Tanh, ReLU ou Sigmoid) peut approximer arbitrairement bien toute fonction continue sur un domaine compact.\n",
    "\n",
    "**Principe des combinaisons non linéaires**\n",
    "\n",
    "  - Chaque neurone décale, étire ou contracte l'entrée d'une manière légèrement différente, puis la fait passer par une fonction d'activation non-linéaire pour produire une réponse partielle.\n",
    "  - Ces réponses partielles sont fortement actives dans certaines régions et presque inactives dans d'autres, comme de petits fragments de fonction.\n",
    "  - La couche de sortie combine ensuite ces fragments par somme pondérée pour former la fonction globale.\n",
    "  - Au final, le réseau de neurones ne décrit pas une règle générale d'un seul bloc : il construit une fonction complexe en empilant de nombreuses petites réponses.\n",
    "\n",
    "**Signification de l'approximation**\n",
    "\n",
    "  - Le théorème d'approximation universelle ne signifie pas que le réseau reproduit toujours exactement la fonction d'origine.\n",
    "  - Son sens précis est le suivant : si l'on fixe à l'avance une tolérance d'erreur, il est possible de réduire l'écart entre les fonctions en dessous de cette tolérance.\n",
    "  - L'idée centrale n'est donc pas **exactement identique**, mais **aussi proche que souhaité**.\n",
    "  - Cette distinction permet d'éviter de confondre capacité de représentation et précision réelle.\n",
    "\n",
    "$$ \\hat{f}(x)= \\sum_{i=1}^N w_i \\sigma(a_i x_i + b_i) $$\n",
    "avec\n",
    "$$ \\max_{x\\in K} |f(x)-\\hat{f}(x)| < \\epsilon$$\n",
    "\n",
    "**importance et limite**\n",
    "\n",
    "Le théorème d'approximation universelle fournit une base mathématique solide montrant qu'un réseau de neurones n'est pas seulement un modèle linéaire simple, mais qu'il peut aussi représenter des fonctions continues extrêmement complexes. Il est donc souvent cité comme point de départ théorique pour expliquer pourquoi le Deep Learning peut traiter une grande variété de problèmes. \n",
    "\n",
    "Toutefois, ce théorème garantit uniquement que la représentation est possible : il ne signifie pas que cette représentation sera efficace avec peu de neurones, ni que l'apprentissage sera simple et rapide. Dans les problèmes réels, le nombre de neurones requis peut devenir très important, et des difficultés liées à l'optimisation, à la quantité de données et à la généralisation apparaissent séparément. Autrement dit, **ce théorème est essentiel pour comprendre le potentiel des réseaux de neurones, mais il ne garantit pas automatiquement leurs performances en pratique.**\n",
    "\n",
    "Extrait du programme ZeroMathAI.\n",
    "- https://zeromathai.com/fr/universal-approximation-theorem-fr/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06e4a83a-ee54-4440-93b2-357e0b14879c",
   "metadata": {},
   "source": [
    "### Comparaison de l'approximation\n",
    "\n",
    "On peut comparer l'approximation par réseau de neurones avec une approximation par spline cubique.\n",
    "\n",
    "Dans le cas de la fonction sinus, une approximation avec 20 splines donne un meilleur résultat qu'avec le réseau de neurones avec 1153 paramètres !\n",
    "\n",
    "**Il ne faut donc pas systématiquement utiliser cette approximation réseau de neurones**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b0063c8a-bbce-4424-8123-b0fa4dd04cc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import CubicSpline\n",
    "\n",
    "N = 20\n",
    "x = np.linspace(-2 * np.pi, 2 * np.pi, N)\n",
    "y = np.sin(x)\n",
    "cs = CubicSpline(x, y)\n",
    "xs = torch.linspace(-2 * np.pi, 2 * np.pi,200)\n",
    "ys = np.sin(xs)\n",
    "ypred = cs(xs)\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.subplot(2,1,1)\n",
    "plt.title(\"Approximation classique\")\n",
    "plt.plot(xs,ys, label=\"sin(x)\")\n",
    "plt.plot(xs,ypred, '--', label=\"Splines\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(xs, ys - ypred)\n",
    "plt.title(\"Erreur\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "369b9197-27f8-43bf-94e4-e1ddd1aac510",
   "metadata": {},
   "source": [
    "**Conseils pratiques**\n",
    "\n",
    "- Normalisez les données si les entrées ou sorties ont des échelles très différentes.\n",
    "- Réservez un jeu de validation pour surveiller le sur apprentissage.\n",
    "- Choisissez la capacité du réseau (nombre de couches et de neurones) en fonction de la complexité de la fonction à approximer.\n",
    "- Utilisez torch.utils.data.DataLoader pour les grands ensembles de données.\n",
    "- Surveillez le niveau de perte (loss) sur les jeux d'entraînement et de validation afin d'ajuster les hyper paramètres (taux d'apprentissage, taille du réseau, nombre d'époques).\n",
    "\n",
    "Ce schéma constitue la base de nombreuses applications en régression avec PyTorch, qu'il s'agisse d'approximer une fonction analytique, un modèle physique ou une relation empirique issue de données expérimentales."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aacc56c2-b1e0-42f5-a64c-7b27dadee7fc",
   "metadata": {},
   "source": [
    "## Principe général d'un PINN pour résoudre une EDO\n",
    "\n",
    "Supposons que l'on souhaite résoudre une équation différentielle\n",
    "\n",
    "$$\n",
    "\\mathcal{N}[u(x)] = 0,\n",
    "$$\n",
    "\n",
    "avec des conditions aux limites ou des conditions initiales.\n",
    "\n",
    "Au lieu de discrétiser le domaine (comme avec les méthodes des différences finies ou des éléments finis), on approxime directement la solution par un réseau de neurones :\n",
    "\n",
    "$$\n",
    "u(x) \\approx u_\\theta(x),\n",
    "$$\n",
    "\n",
    "où $\\theta$ représente les poids du réseau.\n",
    "\n",
    "L'objectif est alors de trouver les paramètres $\\theta$ qui rendent cette fonction compatible avec les lois physiques.\n",
    "\n",
    "---\n",
    "\n",
    "### Utilisation de la différentiation automatique\n",
    "\n",
    "L'un des points clés des PINN est que les dérivées sont calculées grâce à la **différentiation automatique** de PyTorch ou TensorFlow.\n",
    "\n",
    "Par exemple, si $u_\\theta = u_\\theta(x),$\n",
    "alors $\\frac{\\partial u_\\theta}{\\partial x}$\n",
    "est obtenue automatiquement par\n",
    "\n",
    "```python\n",
    "du_dx = torch.autograd.grad(\n",
    "    outputs=u,\n",
    "    inputs=x,\n",
    "    grad_outputs=torch.ones_like(u),\n",
    "    create_graph=True\n",
    ")[0]\n",
    "```\n",
    "\n",
    "Ce calcul n'est pas basée sur une approximation numérique des dérivées, mais sur une **différentiation automatique numérique** de l'approximation par réseau de neurones.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81cceb2e-f0d7-43a5-b505-21af93a50ca3",
   "metadata": {},
   "source": [
    "### Calcul du résidu physique\n",
    "\n",
    "Considérons l'ODE\n",
    "\n",
    "$$\n",
    "\\frac{du}{dt}+u=0.\n",
    "$$\n",
    "\n",
    "Le réseau de neurones prédit $u_\\theta(t)$. On calcule ensuite la dérivée:\n",
    "\n",
    "$$\n",
    "\\frac{du_\\theta}{dt},\n",
    "$$\n",
    "\n",
    "puis le **résidu** de l'équation\n",
    "\n",
    "$$\n",
    "r(t)=\\frac{du_\\theta}{dt}+u_\\theta.\n",
    "$$\n",
    "\n",
    "Si $u_\\theta(t)$ est solution de l'EDO, alors $r(t)=0 \\;\\forall t$\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9508d59-4222-4f7f-b1c4-1ed2d21babf5",
   "metadata": {},
   "source": [
    "### Calcul Fonction de coût\n",
    "\n",
    "L'entraînement consiste à minimiser plusieurs termes :\n",
    "\n",
    "$$ \\mathcal{L} = \n",
    "\\mathcal L_{\\mathrm{phys}}\n",
    "+\n",
    "\\mathcal L_{\\mathrm{BC}}\n",
    "+\n",
    "\\mathcal L_{\\mathrm{data}}.\n",
    "$$\n",
    "\n",
    "**1. Perte physique**\n",
    "\n",
    "Elle impose à la fonction $u_\\theta(t)$ de vérifier l'équation différentielle en certains points.\n",
    "\n",
    "$$\n",
    "\\mathcal L_{\\mathrm{phys}} =\n",
    "\\frac1N\n",
    "\\sum_{i=1}^{N}\n",
    "r(x_i)^2.\n",
    "$$\n",
    "\n",
    "Les $x_i$ sont appelés **points de collocation**.\n",
    "\n",
    "---\n",
    "\n",
    "**2. Conditions initiales ou aux limites**\n",
    "\n",
    "Par exemple pour imposer la condition initiale $u(0)=1.$, on ajoute\n",
    "\n",
    "$$\n",
    "\\mathcal L_{\\mathrm{BC}} = \n",
    "(u_\\theta(0)-1)^2.\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "**3. Données expérimentales (optionnel)**\n",
    "\n",
    "Si l'on possède quelques mesures\n",
    "$(x_i,u_i),$\n",
    "on ajoute\n",
    "\n",
    "$$\n",
    "\\mathcal L_{\\mathrm{data}} = \n",
    "\\frac1M\n",
    "\\sum\n",
    "(u_\\theta(x_i)-u_i)^2.\n",
    "$$\n",
    "\n",
    "Ainsi, les PINN peuvent fonctionner :\n",
    "\n",
    "* sans données (la physique seule guide l'apprentissage) ;\n",
    "* avec quelques données (cas hybride) ;\n",
    "* avec beaucoup de données (en renforçant la cohérence physique).\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b857bb43-d109-44f3-b459-5cb9d1948dd7",
   "metadata": {},
   "source": [
    "### Principe de l'algorithme\n",
    "\n",
    "```text\n",
    "            Choix des points x\n",
    "                  │\n",
    "                  ▼\n",
    "         Réseau de neurones\n",
    "              uθ(x)\n",
    "                  │\n",
    "        ┌─────────┴──────────┐\n",
    "        ▼                    ▼\n",
    " Conditions          Dérivées automatiques\n",
    "initiales                 (autograd)\n",
    "        │                    │\n",
    "        └─────────┬──────────┘\n",
    "                  ▼\n",
    "          Résidu de l'équation\n",
    "                  │\n",
    "                  ▼\n",
    "        Fonction de coût totale\n",
    "                  │\n",
    "                  ▼\n",
    "     Descente de gradient (Adam/L-BFGS)\n",
    "                  │\n",
    "                  ▼\n",
    "       Mise à jour des paramètres θ\n",
    "```\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50a25cee-8009-41ed-94db-8d8b4a19e21d",
   "metadata": {},
   "source": [
    "### Pourquoi cela fonctionne ?\n",
    "\n",
    "Le **théorème d'approximation universelle** garantit qu'un réseau de neurones suffisamment grand peut approcher une très large classe de fonctions continues. Les PINN exploitent cette propriété pour chercher la fonction qui satisfait au mieux les équations physiques et les conditions imposées.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56f11af3-1e4b-420e-9a72-2a3f24655380",
   "metadata": {},
   "source": [
    "### Avantages\n",
    "\n",
    "* Pas de maillage complexe à construire.\n",
    "* Les dérivées sont obtenues avec une grande précision grâce à la différentiation automatique.\n",
    "* Faciles à étendre aux problèmes multidimensionnels.\n",
    "* Intègrent naturellement des connaissances physiques.\n",
    "* Peuvent résoudre des **problèmes inverses**, où des paramètres inconnus sont estimés en même temps que la solution.\n",
    "\n",
    "---\n",
    "\n",
    "### Limites\n",
    "\n",
    "* L'entraînement peut être lent, surtout pour des problèmes de grande dimension.\n",
    "* Les équations très raides, fortement non linéaires ou comportant des discontinuités sont difficiles à traiter.\n",
    "* Le choix des poids entre les différentes composantes de la fonction de perte est délicat.\n",
    "* Pour de nombreuses PDE industrielles, les méthodes numériques classiques (éléments finis, volumes finis, différences finies) restent souvent plus rapides et plus précises.\n",
    "\n",
    "**En résumé**, un PINN remplace le solveur numérique traditionnel par un réseau de neurones entraîné à satisfaire directement les équations de la physique. La résolution d'une ODE ou d'une PDE devient alors un problème d'optimisation où l'on ajuste les paramètres du réseau pour minimiser le résidu de l'équation et respecter les conditions initiales ou aux limites."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47527048-a582-42b1-9ffe-756460964708",
   "metadata": {},
   "source": [
    "## Exemple 1: ODE d'ordre 1\n",
    "Voici un exemple complet d'un **Physics-Informed Neural Network (PINN)** en **PyTorch** pour résoudre une équation différentielle ordinaire (ODE).\n",
    "\n",
    "Prenons l'ODE suivante :\n",
    "\n",
    "$$\n",
    "\\frac{dy}{dt} = -y, \\qquad y(0)=1\n",
    "$$\n",
    "\n",
    "La solution analytique est :\n",
    "\n",
    "$$\n",
    "y(t)=e^{-t}.\n",
    "$$\n",
    "\n",
    "Le principe d'un PINN est de minimiser simultanément :\n",
    "\n",
    "* le résidu de l'équation différentielle,\n",
    "* les conditions initiales (ou aux limites)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2ba0b8d1-75a5-47af-8be5-452a7bd71e43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using  cpu\n",
      "Total number of parameters: 2209\n",
      "Epoch     0  Loss=6.286e-01\n",
      "Epoch   500  Loss=6.178e-05\n",
      "Epoch  1000  Loss=1.232e-05\n",
      "Epoch  1500  Loss=4.221e-06\n",
      "Epoch  2000  Loss=2.249e-06\n",
      "Epoch  2500  Loss=1.312e-06\n",
      "Epoch  3000  Loss=7.906e-06\n",
      "Epoch  3500  Loss=2.744e-06\n",
      "Epoch  4000  Loss=5.630e-07\n",
      "Epoch  4500  Loss=4.975e-07\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "# Choix du périphérique\n",
    "print(\"using \",device)\n",
    "# -------------------------\n",
    "# Réseau de neurones\n",
    "# -------------------------\n",
    "class PINN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.net = nn.Sequential(\n",
    "            nn.Linear(1, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 1)\n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.net(x)\n",
    "\n",
    "model = PINN().to(device)\n",
    "# -------------------------\n",
    "# Points de collocation\n",
    "# -------------------------\n",
    "N = 100\n",
    "t = torch.linspace(0, 5, N).view(-1,1).to(device)\n",
    "t.requires_grad = True\n",
    "# Condition initiale\n",
    "t0 = torch.tensor([[0.0]], device=device)\n",
    "y0 = torch.tensor([[1.0]], device=device)\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)\n",
    "# -------------------------\n",
    "# Entraînement\n",
    "# -------------------------\n",
    "epochs = 5000\n",
    "total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(f'Total number of parameters: {total_params}')\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    optimizer.zero_grad()\n",
    "    # Prédiction\n",
    "    y = model(t)\n",
    "    # Dérivée dy/dt\n",
    "    dy_dt = torch.autograd.grad(\n",
    "        outputs=y,\n",
    "        inputs=t,\n",
    "        grad_outputs=torch.ones_like(y),\n",
    "        create_graph=True\n",
    "    )[0]\n",
    "    # Résidu de l'ODE\n",
    "    residual = dy_dt + y\n",
    "    loss_ode = torch.mean(residual**2)\n",
    "    # Condition initiale\n",
    "    pred0 = model(t0)\n",
    "    loss_ic = (pred0 - y0).pow(2).mean()\n",
    "    # Fonction coût\n",
    "    loss = loss_ode + loss_ic\n",
    "    # descente\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    # affichage résidu\n",
    "    if epoch % 500 == 0:\n",
    "        print(f\"Epoch {epoch:5d}  Loss={loss.item():.3e}\")\n",
    "\n",
    "# -------------------------\n",
    "# Évaluation et tracé de la solution\n",
    "# -------------------------\n",
    "with torch.no_grad():\n",
    "    t_test = torch.linspace(0,5,200).view(-1,1).to(device)\n",
    "    y_pred = model(t_test).cpu()\n",
    "\n",
    "t_exact = t_test.cpu()\n",
    "y_exact = torch.exp(-t_exact)\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.plot(t_exact, y_exact, label=\"Solution exacte\")\n",
    "plt.plot(t_exact, y_pred, \"--\", label=\"PINN\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aacf797-0fb1-4dcc-9426-13cdf21b81f9",
   "metadata": {},
   "source": [
    "### Explication\n",
    "\n",
    "Le PINN apprend une fonction $y_\\theta(t)$ paramétrée par un réseau de neurones.\n",
    "\n",
    "À chaque itération :\n",
    "\n",
    "1. Le réseau prédit (y(t)).\n",
    "2. PyTorch calcule automatiquement la dérivée\n",
    "   $\\frac{dy_\\theta}{dt}$\n",
    "   grâce à `torch.autograd.grad`.\n",
    "3. On construit le résidu de l'ODE :\n",
    "   $r(t)=\\frac{dy_\\theta}{dt}+y_\\theta.$\n",
    "4. La fonction de perte est\n",
    "   $$\n",
    "   \\mathcal{L} =\n",
    "   \\underbrace{\\frac1N\\sum_i r(t_i)^2}*{\\text{équation}}\n",
    "   +\n",
    "   \\underbrace{\\left(y*\\theta(0)-1\\right)^2}_{\\text{condition initiale}}.\n",
    "   $$\n",
    "\n",
    "Le réseau est ainsi entraîné à satisfaire simultanément l'équation différentielle et la condition initiale."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a653f76-51df-491a-84fe-5cdab02618ac",
   "metadata": {},
   "source": [
    "### Généralisation\n",
    "\n",
    "Pour une ODE quelconque\n",
    "\n",
    "$$\n",
    "\\frac{dy}{dt}=f(t,y),\n",
    "$$\n",
    "\n",
    "il suffit de remplacer\n",
    "\n",
    "```python\n",
    "residual = dy_dt + y\n",
    "```\n",
    "\n",
    "par\n",
    "\n",
    "```python\n",
    "residual = dy_dt - f(t, y)\n",
    "```\n",
    "\n",
    "où `f(t, y)` est une fonction Python définissant le membre de droite."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece8fd1f-b841-43d3-a800-e8e354c3c8a2",
   "metadata": {},
   "source": [
    "## Exemple 2: l'oscillateur harmonique\n",
    "\n",
    "$$\n",
    "\\frac{d^2y}{dt^2}+y=0,\n",
    "$$\n",
    "\n",
    "avec les conditions initiales\n",
    "\n",
    "$$\n",
    "y(0)=1,\\qquad y'(0)=0.\n",
    "$$\n",
    "\n",
    "La solution exacte est\n",
    "\n",
    "$$\n",
    "y(t)=\\cos(t).\n",
    "$$\n",
    "\n",
    "L'idée est de faire apprendre cette solution par un PINN.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f168b4fc-0613-4c30-a1d3-564ef7dd8441",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using  cpu\n",
      "Total number of parameters: 8513\n",
      "0 1.0324066877365112\n",
      "500 0.026727065443992615\n",
      "1000 0.0198180191218853\n",
      "1500 0.018044354394078255\n",
      "2000 0.01761746034026146\n",
      "2500 0.016555413603782654\n",
      "3000 0.013630836270749569\n",
      "3500 0.011124305427074432\n",
      "4000 0.008537301793694496\n",
      "4500 0.0039275591261684895\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "# Choix du périphérique\n",
    "print(\"using \",device)\n",
    "# =====================================================\n",
    "# Réseau de neurones\n",
    "# =====================================================\n",
    "class PINN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "\n",
    "        self.net = nn.Sequential(\n",
    "            nn.Linear(1,64),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(64,64),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(64,64),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(64,1)\n",
    "        )\n",
    "\n",
    "    def forward(self,x):\n",
    "        return self.net(x)\n",
    "\n",
    "model = PINN().to(device)\n",
    "# =====================================================\n",
    "# Points de collocation\n",
    "# =====================================================\n",
    "N = 200\n",
    "t = torch.linspace(0,10,N).reshape(-1,1).to(device)\n",
    "t.requires_grad = True\n",
    "\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)\n",
    "# =====================================================\n",
    "# Entraînement\n",
    "# =====================================================\n",
    "epochs = 5000\n",
    "total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(f'Total number of parameters: {total_params}')\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    optimizer.zero_grad()\n",
    "    # prédiction\n",
    "    y = model(t)\n",
    "    # première dérivée\n",
    "    dy = torch.autograd.grad(\n",
    "        y,\n",
    "        t,\n",
    "        grad_outputs=torch.ones_like(y),\n",
    "        create_graph=True\n",
    "    )[0]\n",
    "    # seconde dérivée\n",
    "    d2y = torch.autograd.grad(\n",
    "        dy,\n",
    "        t,\n",
    "        grad_outputs=torch.ones_like(dy),\n",
    "        create_graph=True\n",
    "    )[0]\n",
    "    # Résidu de l'ODE\n",
    "    residual = d2y + y\n",
    "    loss_phys = torch.mean(residual**2)\n",
    "    # =====================================================\n",
    "    # Conditions initiales\n",
    "    # =====================================================\n",
    "    t0 = torch.tensor([[0.0]], requires_grad=True,device=device)\n",
    "    y0 = model(t0)\n",
    "    dy0 = torch.autograd.grad(\n",
    "        y0,\n",
    "        t0,\n",
    "        grad_outputs=torch.ones_like(y0),\n",
    "        create_graph=True\n",
    "    )[0]\n",
    "    loss_ic = (y0-1)**2 + dy0**2\n",
    "    # =====================================================\n",
    "    loss = loss_phys + loss_ic\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch % 500 == 0:\n",
    "        print(epoch, loss.item())\n",
    "\n",
    "# =====================================================\n",
    "# verification\n",
    "# =====================================================\n",
    "with torch.no_grad():\n",
    "    t_test = torch.linspace(0,10,300,device=device).view(-1,1)\n",
    "    y_pred = model(t_test).cpu()\n",
    "t_exact = t_test.cpu()\n",
    "y_exact = np.cos(t_exact)\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.plot(t_exact,y_exact,label=\"Exact\")\n",
    "plt.plot(t_exact,y_pred,\"--\",label=\"PINN\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7996812-f03c-4eb4-9f86-12ce335d65da",
   "metadata": {},
   "source": [
    "### Explication\n",
    "\n",
    "Pour une ODE du second ordre, le réseau approxime directement la fonction :\n",
    "\n",
    "$$\n",
    "y(t)\\approx y_\\theta(t).\n",
    "$$\n",
    "\n",
    "Les dérivées sont calculées par différentiation automatique :\n",
    "\n",
    "$$\n",
    "\\frac{dy_\\theta}{dt},\n",
    "\\qquad\n",
    "\\frac{d^2y_\\theta}{dt^2}.\n",
    "$$\n",
    "\n",
    "En PyTorch, cela se fait avec deux appels successifs à `torch.autograd.grad` :\n",
    "\n",
    "```python\n",
    "dy = torch.autograd.grad(\n",
    "    y, t,\n",
    "    grad_outputs=torch.ones_like(y),\n",
    "    create_graph=True\n",
    ")[0]\n",
    "\n",
    "d2y = torch.autograd.grad(\n",
    "    dy, t,\n",
    "    grad_outputs=torch.ones_like(dy),\n",
    "    create_graph=True\n",
    ")[0]\n",
    "```\n",
    "\n",
    "Le résidu de l'équation est alors\n",
    "\n",
    "$$\n",
    "r(t)=\\frac{d^2y_\\theta}{dt^2}+y_\\theta,\n",
    "$$\n",
    "\n",
    "et la perte physique est\n",
    "\n",
    "$$\n",
    "L_{\\mathrm{phys}} =\n",
    "\\frac1N\\sum_i r(t_i)^2.\n",
    "$$\n",
    "\n",
    "Les conditions initiales sont ajoutées sous forme de pénalités :\n",
    "\n",
    "$$\n",
    "L_{\\mathrm{IC}}=\n",
    "(y_\\theta(0)-1)^2\n",
    "+\n",
    "\\left(\\frac{dy_\\theta}{dt}(0)\\right)^2.\n",
    "$$\n",
    "\n",
    "La fonction de coût totale est\n",
    "\n",
    "$$\n",
    "L = L_{\\mathrm{phys}} + L_{\\mathrm{IC}}.\n",
    "$$\n",
    "\n",
    "### Généralisation\n",
    "\n",
    "Pour une ODE du second ordre de la forme\n",
    "\n",
    "$$\n",
    "y'' = f(t,y,y'),\n",
    "$$\n",
    "\n",
    "il suffit de remplacer le résidu par :\n",
    "\n",
    "```python\n",
    "residual = d2y - f(t, y, dy)\n",
    "```\n",
    "\n",
    "où `f` est une fonction Python. Cette structure est valable pour la plupart des ODE du second ordre, qu'elles soient linéaires ou non linéaires. Elle peut ensuite être étendue aux systèmes d'ODE en faisant sortir plusieurs composantes du réseau et en construisant un résidu pour chaque équation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca54c70b-aea0-4d0a-a3c7-41dee47f42a8",
   "metadata": {},
   "source": [
    "## Exemple 3: problème inverse\n",
    "\n",
    "Les **problèmes inverses** sont l'une des applications les plus intéressantes des PINN. Contrairement au problème direct (où les paramètres de l'équation sont connus), le but est ici d'**estimer des paramètres physiques inconnus** à partir de quelques mesures.\n",
    "\n",
    "Considérons l'ODE suivante :\n",
    "\n",
    "$$\n",
    "\\frac{dy}{dt} = -\\lambda y,\n",
    "$$\n",
    "\n",
    "avec $y(0)=1,$ où **$\\lambda$** est inconnu.\n",
    "\n",
    "Supposons que l'on dispose de quelques mesures bruitées de $y(t)$ et que l'on souhaite retrouver $\\lambda$.\n",
    "\n",
    "---\n",
    "\n",
    "### Principe\n",
    "\n",
    "Le réseau approxime la solution\n",
    "$y_\\theta(t).$\n",
    "\n",
    "Mais cette fois, le paramètre physique est lui aussi optimisé :\n",
    "\n",
    "```python\n",
    "lambda_param = nn.Parameter(torch.tensor([0.5]))\n",
    "```\n",
    "\n",
    "Il est ajouté à la liste des paramètres entraînables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "df183b80-2b66-43a6-b5f7-b6072ac1817e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using  cpu\n",
      "Total number of parameters: 1153\n",
      "0 0.8843849897384644 0.5009999871253967\n",
      "500 0.02659468911588192 0.9639050364494324\n",
      "1000 0.010516956448554993 1.2724665403366089\n",
      "1500 0.004431234672665596 1.4954813718795776\n",
      "2000 0.0018966301577165723 1.6611098051071167\n",
      "2500 0.000823379959911108 1.7841399908065796\n",
      "3000 0.00039153601392172277 1.8726096153259277\n",
      "3500 0.00023852310550864786 1.931909203529358\n",
      "4000 0.0002051886112894863 1.9677320718765259\n",
      "4500 0.00019649506430141628 1.9865784645080566\n",
      "\n",
      "Valeur estimée : 1.9943212270736694 exacte: 2.0\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import matplotlib.pyplot as plt\n",
    "# Choix du périphérique\n",
    "print(\"using \",device)\n",
    "# =====================================================\n",
    "# Génération de données\n",
    "# =====================================================\n",
    "lambda_true = 2.0\n",
    "t_data = torch.linspace(0, 2, 20,device=device).reshape(-1,1)\n",
    "y_data = torch.exp(-lambda_true*t_data)\n",
    "# bruit\n",
    "y_data += 0.01*torch.randn_like(y_data)\n",
    "# =====================================================\n",
    "# PINN\n",
    "# =====================================================\n",
    "class PINN(nn.Module):\n",
    "\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.net = nn.Sequential(\n",
    "            nn.Linear(1,32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32,32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32,1)\n",
    "        )\n",
    "\n",
    "    def forward(self,x):\n",
    "        return self.net(x)\n",
    "\n",
    "model = PINN().to(device)\n",
    "# =====================================================\n",
    "# Paramètre inconnu\n",
    "# =====================================================\n",
    "lambda_param = nn.Parameter(torch.tensor([0.5],device=device))\n",
    "# =====================================================\n",
    "# Optimiseur\n",
    "# =====================================================\n",
    "optimizer = torch.optim.Adam(\n",
    "    list(model.parameters())+[lambda_param],\n",
    "    lr=1e-3\n",
    ")\n",
    "# =====================================================\n",
    "# Points de collocation\n",
    "# =====================================================\n",
    "t_phys = torch.linspace(0,2,100,device=device).reshape(-1,1)\n",
    "t_phys.requires_grad=True\n",
    "\n",
    "# =====================================================\n",
    "# Entraînement\n",
    "# =====================================================\n",
    "total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "print(f'Total number of parameters: {total_params}')\n",
    "\n",
    "for epoch in range(5000):\n",
    "    optimizer.zero_grad()\n",
    "    # --------------------------\n",
    "    # Physique\n",
    "    # --------------------------\n",
    "    y = model(t_phys)\n",
    "    dy = torch.autograd.grad(\n",
    "        y,\n",
    "        t_phys,\n",
    "        grad_outputs=torch.ones_like(y),\n",
    "        create_graph=True\n",
    "    )[0]\n",
    "    residual = dy + lambda_param*y\n",
    "    loss_phys = torch.mean(residual**2)\n",
    "    # --------------------------\n",
    "    # Données\n",
    "    # --------------------------\n",
    "    y_pred = model(t_data)\n",
    "    loss_data = torch.mean((y_pred-y_data)**2)\n",
    "    # --------------------------\n",
    "    # Condition initiale\n",
    "    # --------------------------\n",
    "    t0 = torch.tensor([[0.0]],device=device)\n",
    "    loss_ic = (model(t0)-1.)**2\n",
    "    # --------------------------\n",
    "    loss = loss_phys + loss_data + loss_ic\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch%500==0:\n",
    "        print(epoch,\n",
    "              loss.item(),\n",
    "              lambda_param.item())\n",
    "\n",
    "print(\"\\nValeur estimée :\", lambda_param.item(), \"exacte:\",lambda_true)\n",
    "\n",
    "# =====================================================\n",
    "# Comparaison\n",
    "# =====================================================\n",
    "with torch.no_grad():\n",
    "    t_test = torch.linspace(0,2,200,device=device).reshape(-1,1)\n",
    "    y_pred = model(t_test).cpu()\n",
    "\n",
    "t = t_test.cpu()\n",
    "plt.plot(t,np.exp(-lambda_true*t),label=\"Exacte\")\n",
    "plt.plot(t,y_pred,'--',label=\"PINN\")\n",
    "plt.scatter(t_data.cpu(),y_data.cpu(),color='red')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2de00832-ae46-4e88-976a-7e06aa469984",
   "metadata": {},
   "source": [
    "### Explication\n",
    "\n",
    "Le réseau apprend simultanément :\n",
    "\n",
    "* la fonction $y(t)$,\n",
    "* le paramètre $\\lambda$.\n",
    "\n",
    "La fonction de perte s'écrit\n",
    "\n",
    "$$\n",
    "L=\n",
    "L_{\\text{phys}}\n",
    "+\n",
    "L_{\\text{data}}\n",
    "+\n",
    "L_{\\text{IC}}\n",
    "$$\n",
    "\n",
    "avec\n",
    "\n",
    "1. Perte Physique\n",
    "\n",
    "$$\n",
    "L_{\\text{phys}}\n",
    "=\n",
    "\\frac1N\n",
    "\\sum_i\n",
    "\\left(\n",
    "\\frac{dy_\\theta}{dt}\n",
    "+\\lambda y_\\theta\n",
    "\\right)^2.\n",
    "$$\n",
    "\n",
    "2. Perte sur les Données\n",
    "\n",
    "$$\n",
    "L_{\\text{data}}=\n",
    "\\frac1M\n",
    "\\sum_i\n",
    "\\left(\n",
    "y_\\theta(t_i)-y_i\n",
    "\\right)^2.\n",
    "$$\n",
    "\n",
    "3. Perte sur la Condition initiale\n",
    "\n",
    "$$\n",
    "L_{\\text{IC}}=\n",
    "(y_\\theta(0)-1)^2.\n",
    "$$\n",
    "\n",
    "---\n",
    "\n",
    "### Pourquoi cela fonctionne ?\n",
    "\n",
    "Le gradient de la perte dépend de **deux types de paramètres** :\n",
    "\n",
    "* les poids du réseau de neurones $\\theta$ ;\n",
    "* le paramètre physique $\\lambda$.\n",
    "\n",
    "Comme $\\lambda$ est déclaré comme un `nn.Parameter`, PyTorch calcule automatiquement\n",
    "\n",
    "$$\n",
    "\\frac{\\partial L}{\\partial \\lambda},\n",
    "$$\n",
    "\n",
    "et l'optimiseur met à jour $\\lambda$ exactement comme les poids du réseau.\n",
    "\n",
    "---\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67ac413a-0ab0-4767-9eb2-69ef0acf5353",
   "metadata": {},
   "source": [
    "## Applications réelles des PINNs\n",
    "\n",
    "Cette approche est utilisée pour identifier des paramètres physiques à partir de données limitées, par exemple :\n",
    "\n",
    "* coefficient de diffusion dans une équation de chaleur ;\n",
    "* viscosité d'un fluide dans les équations de Navier–Stokes equations ;\n",
    "* module d'Young ou conductivité thermique d'un matériau ;\n",
    "* constantes de réaction en cinétique chimique ;\n",
    "* paramètres d'un modèle épidémiologique (par exemple le taux de transmission dans un modèle SIR model) ;\n",
    "* paramètres d'amortissement et de raideur dans les systèmes mécaniques.\n",
    "\n",
    "C'est précisément dans ce contexte où l'on dispose de peu de mesures mais d'un modèle physique fiable que les PINN offrent souvent leur plus grande valeur.\n",
    "\n",
    "### Extensions possibles\n",
    "\n",
    "Cette structure s'étend facilement à des problèmes plus complexes :\n",
    "\n",
    "* **Systèmes d'ODE** (Lotka-Volterra, pendule, Lorenz, etc.) en faisant sortir plusieurs composantes du réseau.\n",
    "* **Équations différentielles d'ordre supérieur**, en calculant des dérivées successives avec `torch.autograd.grad`.\n",
    "* **Équations aux dérivées partielles (PDE)** comme l'équation de la chaleur, de Burgers ou de Navier-Stokes, en utilisant plusieurs variables d'entrée (`x`, `t`, etc.) et les dérivées partielles correspondantes.\n",
    "* **PINN inverses**, où certains paramètres physiques de l'ODE sont également appris par le réseau en les déclarant comme paramètres optimisables (`torch.nn.Parameter`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "46774e34-1cd0-4363-b577-fc3ecc5e1e7d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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