example_1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "device(type='mps')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "device = torch.device(\"mps\")\n",
    "device"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial^2 T(x,y,t)}{\\partial x^2} + \\frac{\\partial^2 T(x,y,t)}{\\partial y^2} -\\frac{1}{\\alpha}\\frac{\\partial T(x,y,t)}{\\partial t} = 0\n",
    "$$\n",
    "\n",
    "$T(x,y,z)$ is neural network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Net(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc_in = torch.nn.Linear(3, 10) # x, y, t\n",
    "        for i in range(12):\n",
    "            setattr(self, f'fc{i}', torch.nn.Linear(10, 10))\n",
    "        self.fc_out = torch.nn.Linear(10, 1) # T\n",
    "        self.act = torch.nn.SiLU() # for continuity\n",
    "        self.norm = torch.nn.BatchNorm1d(10)\n",
    "    \n",
    "    def forward(self, x:torch.Tensor, y:torch.Tensor, t:torch.Tensor) -> torch.Tensor:\n",
    "        x = torch.cat((x, y, t), dim=1)\n",
    "        x = self.act(self.fc_in(x))\n",
    "        for i in range(12):\n",
    "            x = getattr(self, f'fc{i}')(x)\n",
    "            x = self.norm(x)\n",
    "            x = self.act(x)\n",
    "        x = self.fc_out(x)\n",
    "        return x\n",
    "    \n",
    "def func(net:torch.nn.Module, x:torch.Tensor, y:torch.Tensor, t:torch.Tensor) -> torch.Tensor:\n",
    "    T = net(x, y, t)\n",
    "    T_x = torch.autograd.grad(T, x, torch.ones_like(T), create_graph=True)[0]\n",
    "    T_xx = torch.autograd.grad(T_x, x, torch.ones_like(T_x), create_graph=True)[0]\n",
    "    T_y = torch.autograd.grad(T, y, torch.ones_like(T), create_graph=True)[0]\n",
    "    T_yy = torch.autograd.grad(T_y, y, torch.ones_like(T_y), create_graph=True)[0]\n",
    "    T_t = torch.autograd.grad(T, t, torch.ones_like(T), create_graph=True)[0]\n",
    "    return T_t - T_xx - T_yy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VYRiGYRiGsQYWrwzDMAzDMIw1sHhlGIZhGIZhrIHFK8MwDMMwDGMNLF4ZhmEYhmEYa2DxyjAMwzAMw1gDi1eGYRiGYRjGGli8MgzDMAzDMNbA4pVhGIZhGIaxBhavDMMwDMMwjDWweGUYhmEYhmGsgcUrwzAMwzAMYw0sXhmGYRiGYRhrYPHKMAzDMAzDWAOLV4ZhGIZhGMYaWLwyDMMwDMMw1sDilWEYhmEYhrEGFq8MwzAMwzCMNbB4ZRiGYRiGYayBxSvDMAzDMAxjDSxeGYZhGIZhGGtg8cowDMMwDMNYA4tXhmEYhmEYxhpYvDIMwzAMwzDWwOKVYRiGYRiGsQYWrwzDMAzDMIw1sHhlGIZhGIZhrIHFK8MwDMMwDGMNLF4ZhmEYhmEYa2DxyjAMwzAMw1gDi1eGYRiGYRjGGli8MgzDMAzDMNbA4pVhGIZhGIaxBhavDMMwDMMwjDWweGUYhmEYhmGsgcUrwzAMwzAMYw0sXhPC2tqaWFtbU66nn+PtVP9X7UcIIX70ox9pP5P7N31XdUzVOt22YdpvagPdJux2unbi7cK217Renrdue9wvnbRB1Weq4+n2EaV9unEnod/R9YmuvabrEeVamb5r6s8w+1T9q/p/0HUI+xsyje2g9uquR9AYiHod6Tamz6OMIdPnuj4zXZuwv+Gw/a1qp2ob2h9hfgdRxzvdJuy9Pez9u91nBd6Hru10bJjOrZN7o+48gn6vYcZSu2Mr6t+JBdYZTz31FAgh4Kmnnup3U2Jjfn4ecrkcOI4DzWbTs35ychLq9TqUSiXI5XIwNTUFk5OT0Gw2odlswuTkJMzPz3u2leswlUoFUqkUbNu2zXMMeRzHcaBYLEIul1N+N5PJQKVScY+D94HbodtW1T78vWazCblcDrZs2eLrB3ycUqkEW7ZsCb1dLpdzt6Ftl8eU24TpT936qakpyGQyUKvVlNvXajXIZDIwNTXlaytuQzt9FnSOk5OT7rjRnc/09LR73fC4KJVK4DgOVCoV37jC11p1bPq5qb/p8fA4x2O0VCr5+oHuW7aV9qf8jvx8amrKs88ofUf3S68DbV/Y39DU1JTbB/R3SPsgTH+r2k/7Vvc9VdtxW+Q+VJ+rzocel+6bHhd/fsUVV/i+qxuf9HdDjxv0m8DnQK8rPXfVNrQ/wvwOVOPH9FsxjXnVOWSzWe01UN2/Vf2t2h/tM9X5mn5XuVwOisWib1+qZ5Lqt9zO85D+jlTXNGgsyf6m+1fdY+h9TNUX9PuqfrWBKPqsr+L1C1/4Arz85S+HXC4HQgj4xCc+Efidz3/+8/DzP//zMDw8DGeddRb85V/+ZaRjJk28tlotKJfLIIQAIQQUi0VoNpvQarVgcnIShBCQTqfdzzOZjLtdsVgEIQSUy2V3H3LbyclJaLVaAADQaDTc7wkhoFAouD+eVqsFjuO4n8n9qb6byWRgYmIChBBQKpXcH3qpVAIhBDiO4x4/nU67+5U3Ctw+x3E8n9M2yH6QNJtN93yjbuc4DjQaDbc/S6US1Ot1zzELhUJgf66urvquyeTkJHzve9/z9K9qe3z9VldX3bbiNkxMTHj6Un6m6rNSqeReC9M5yv3J9unOB7ev0WhAq9Vyv6saV3RcLC8ve4596NAhz+eLi4va/pZtwceT3y2VStBoNDzflQ87+V36ufwu7i/8e8Htwv0nr3lQ3+HxUSwWoVAoePaDvzs5OQnLy8uhf0O0TfJ3SH+ntL2q/ta1H/et6XuTk5Nw5MgRz+dybMhrXSgUPPttNBra88HHbTabnjGUTqfdflSNMbnI7+rGp+q3i48b9JuQ/U1/m/JFGZ+76tovLi56+uuBBx7w/H3o0CHf70A1fky/lVar5WufPAfZP6pzUG2nu3/T/tbtD49R1fPiyJEjgfckui/VM+nss8/2/Obobzns85Duu1Qqee6DQfuh9w68/0aj4Ts3eh/T9QX9Ph6LNmGNeP3MZz4D73rXu6BarYIQweL16NGj8F/+y3+BPXv2wPLyMtx+++2QSqXgb//2b0MfM2niFcAvuKQgq9frnptJPp+Her0euG06nYZ6ve7umwpH/L1mswnj4+Pu+lQqZfwu/nHr/q/aNp/Pe9qXz+eV+5DraRvxOefz+dDbyb/pzQK3UbUvXX/q1tdqNc/NtlarGdfjvtX14/j4OKRSKfe6yOuk2153jqVSCWq1WuD54Bs6HWe0n1XHUB2b/hvlGuvGhe6YujGo+q6qHVH6ztTeoD4x/YZUfaO7R4Tpb1X7a7VaqO/p+kN1vXTnhs+HXlP5fznGg8YYbZtufNLfqOp8Tb8J3W9Td+6qax/0L+2b8fFx5djF92ZV36jGPL12uH/xcYLu32H2R8do2PsC7X/Zj6Znku43EPV5qNo+zDOYjiU89nVjDJ+7qS/odtTibQvWiFeMEMHi9W1vexv87M/+rGfdpZdeCr/6q78a+jhJEK+qN6oggSZ/UEtLS74f2dLSkvIHgderbvj0GPKmpPsuvmHqHkpB2+IbH/1ep0JVtx0+j2q16rkZVavVtvpTtx7f0GZmZpTCkPat6oEUtc+CzjHs+dB/6YPKNC5Ux56dnY3U3ybxMzY2pj0vVV/Qc1H1IRUnUfqOnofpu1F+Q7RNuv4J29+q9kf5nuo60/Onvz/d+ajOmwo00xjTjdOg3247vwnd7yvMtaf9GeZ3EPXeFGbMR32piPISqhujYe4Lqv5XjSP6TFL1Rzv3b1X7w+4Hn4tcVIJfJerl9+V56e5jNlpdARIsXn/pl34JrrnmGs+6D3/4w7Bp0ybtd37yk5/AU0895S4rKyuhO2cQUfm7SZrNpk+w0psL/nHRdfSmgdfrLDh4f2G+Sz9vd1vd94La2O52KnHZSX/q1lNrgjyW6o1ddd6d9FnQOUY9n6C+MV1r3c09zD6D+kF1Xu30o+l4YftOdR6m9oX9Dam2i9LesO0P8z1T21Xn3841bWeMBX03zPmGuWdGOfeg/gzzO4jyWwkz5sNeg7D9HWaMRr0nRXkmqfqjnedh2Gsadizpro2uL7BhgLbLVr/XxIrXcrkMN910k2fdpz/9aRBCwH/8x38ov3PDDTcoB4iN4hX7S+kGuEq8Li0twdLSUqh1AKBdL6Gfd/rddrY1fS+ojXFsNzMz03F/6tbTfc/MzITq27j7THWOUc4nTN+EPXaU/g7qB915Re1H0/Gi9F3Y74Zpm6lNUdobtv1hv2dqU7vn0+kYC/PdTn8TUc89qD/D/A6i/lbC9E/Usdfu/qLeF0z3nii/uXafh53sh56L6dqovj86Our7Hha5Nvq9snhFJM3yKiMxhQhnERWCLa+4jWx5Df9dtryG60O2vLbfdra8suU1yj7Y8qq/H+Fj0+wdtpBY8dqO2wDFZp9XVQaBUsnvbyPEiSkFmcUBD+52fXxUNwn2eWWfV7qefV7Z55V9XtnnNcr+gp4XYftfNY6S5vPqOI5vdnVsbEwZVMqW1x4hRLiArec+97medb/927+9rgK2VDcauqTTJ6IjOdsAZxvgbAP+7+iOqRuDnG2Asw1E+U3ofpumF2x67YP+pX3D2QbWT7YBOm5VC+5Xm7BGvK6ursKXv/xl+PKXvwxCCHj/+98PX/7yl+Fb3/oWAAC8/e1vh127drnby1RZ1113HRw5cgQ+8IEPrMtUWaYpBPlD4zyvnOeV87ye2BfneeU8r3KR3+U8r5znFe8j7PNwUPK80hcTutB+tQVrxOvnP/95ZcdffvnlAABw+eWXw0UXXeT7zvOf/3wYHh6GUqm0bosUqCxeQpy0zAFwhS2KvNFyhS2usEW/i/fNFba4wpbpfIN+E/gcuMIWV9hSjaU4KmypNIB8ibMx0wCAReK1HyRBvJosr/hNFwA8lhf8f/o53VbF6uqq9jO5f9N3VcdUrdNtG6b9pjbQbcJup2sn3i5se03r5Xnrtsf90kkbVH2mOp5uH1Hapxt3EvodXZ/o2mu6HlGulem7pv4Ms0/Vv6r/B12HsL8h09gOaq/uegSNgajXkW5j+jzKGDJ9rusz07UJ+xsO29+qdqq2of0R5ncQdbzTbcLe28Pev9t9VuB96NpOx4bp3Dq5N+rOI+j3GmYstTu2Wq2WUQPojDI2EEWfbQAAEOuIp59+WmzevFk89dRTYtOmTf1uTmRWVlbExRdfLI4ePSrS6bQ4duyY+5n8u1QqiYWFBVEoFPrYUoZhGIZh4iTJGiCKPhvqUZuYGFhbWxOXXHKJZ9CWSiWxtLQkSqWSOHbsmEin0+Lo0aPikksuEWtra/1uMsMwDMMwMcAa4CQsXi1ieHhY7Ny5UwghPG9XF1xwgVhYWHAHrxBC7Ny5UwwPD/ezuQzDMAzDxARrgJOw24BF/OhHPxJnnHGG+OlPfyrS6bR46KGHxPnnn+9+/vDDD4sLL7xQHDt2TGQyGfH9739fnHbaaX1sMcMwDMMwcZB0DcBuAwnltNNOE7feeqvIZDLi2LFj4rLLLhMrKytCiBN+MJdddpk7aG+99VarBi3DMAzDMHpYA5yELa8W8o1vfEO85CUvEUePHhWlUkncddddYteuXe7f9913nzjrrLP63UyGYRiGYWImqRogij5j8WopOOJQYmuEIcMwDMMw4UmiBmC3gYSztrYmCoWCuOuuuzzr77rrLlEoFBIdYcgwDMMw6xnWACxerePAgQPi3HPPFQ8//LDYtWuX57Ndu3aJhx9+WJx77rniwIEDfWohwzAMwzDdgDXACdhtwCLW1tbEueeeKx555BFPjjfs7yLXT05Oiq997WuJTpXBMAzDMOuFpGsAdhtIKMPDw+KjH/2oOzjT6bS4++67xQUXXCDuvvtuz/qPfvSjVg1ahmEYhmH0sAY4CYtXi1hbWxO7d+92B6dMlXH48GE3RYZcv3v37nXh98IwDMMw6wHWACdh8WoRw8PDYt++fWJyclI89NBDolQqiaNHj4qdO3e6KTIeeughMTk5Kfbt25foty6GYRiGWU+wBjgJ+7xayPe//31xxhlniMOHD7ul4oQQYmlpSVxwwQXu5wzDMAzDJIukagD2eU0w11xzjdi+fbv41Kc+pYw0/NSnPiW2b98urrnmmj61kGEYhmGYbsAa4ARsebUIXNdYQiMNJTbWNWYYhmEYRk3SNQBbXhPKaaedJu69917PultvvVVccMEF4tZbb/Wsv/fee60atAzDMAzD6GENcBK2vFoEzvEmSafTolKpiKuvvlocO3bMXW9jjjeGYRiGYdQkXQOw5TWh4EjDWq3mpsT43d/9XTdFRq1WWxeRhgzDMAyznmANcBK2vFrI2tqaGB4eFn/+538ufvd3f9ddPzMzI974xje6nzMMwzAMkyySqgGi6DMWr5by8MMPiwsvvNAzTZBOp8VDDz0kzj///D62jGEYhmGYbpJEDcBuAwkHD9p0Oi1mZmbc6YMLL7xQPPzww/1uIsMwDMMwXYA1AItX66CD9qGHHhJvfOMbxUMPPbTuBi/DMAzDrCdYA5yA3QYsAud4U00P4EFtY443hmEYhmHUJF0DsNtAQjnttNPEz/zMzwghTjhmU7+W888/X8zMzAghhPiZn/kZqwYtwzAMwzB6WAOchC2vFpH0ty6GYRiGYdQkXQOw5TWhnHbaaeLQoUNKvxbqB3Po0CGrBi3DMAzDMHpYA5yExatlnH/++T7H7D//8z/3OXDbmiqDYRiGYRg1rAFOwG4DlpLEHG8MwzAMwwSTRA3AbgMJZ21tTZx//vmiUql41lcqFXH++eeLtbW1PrWMYRiGYZhuwhqAxat1HDhwQJx77rniU5/6lLj66qs9n1199dXiU5/6lDj33HPFgQMH+tRChmEYhmG6AWuAE7DbgEWsra2Jc889VzzyyCPuunQ6LSqVirj66qs90weTk5Pia1/7mpX1jRmGYRiG8ZJ0DcBuAwlleHhYvPe97/Ws+6u/+ivxxje+UfzVX/2VZ/173/teqwYtwzAMwzB6WAOchC2vFoFzvElKpZK46667xK5du8TRo0fd9TbmeGMYhmEYRk3SNQBbXhPKaaedJt70pjeJTCYjarWaKJVK4ujRo2Lnzp3i6NGjolQqiVqtJjKZjHjTm95k1aBlGIZhGEYPa4CTsOXVQr7//e+LM844Qxw+fFjs3LnTXb+0tCQuuOAC93OGYRiGYZJFUjUAW14TzIEDB8QLX/hC8fDDD4tdu3Z5Ptu1a5d4+OGHxQtf+MLERxoyDMMwzHqDNcAJ2PJqETjSUFbXoP4ucr2NkYYMwzAMw6hJugZgy2tCGR4eFh/96EfdwZlOp8Xdd98tLrjgAnH33Xd71n/0ox+1atAyDMMwDKOHNcBJWLxaxNramti9e7c7OI8dOyYuu+wycfjwYXHZZZd51u/evXtdVNlgGIZhmPUAa4CTsHi1iOHhYbFv3z4xOTkpHnroIWWk4UMPPSQmJyfFvn37Ev3WxTAMwzDrCdYAJ2GfVwtZW1sTw8PD2khD+TnDMAzDMMkiqRqAfV4TzvDwsFhZWVFGGq6srFg5aJNM0NRNkqd2GIZhmHhhDcDi1UpWVlbExRdf7E4TLC0tudMHF198sVhZWel3E5n/5MCBA+Lcc8/VXpOVlRVx7rnn9iStiUkkr62tBX7OMAzD9B/WACxerWNlZUVcdNFF7qBdWFgQF1xwgVhYWHAH70UXXbQuBu+gs7a2Jq6//nrxyCOPKG8o8gb0yCOPiOuvv76rAtEkog8cOCDOOecc8ZznPEcponspsBmGYRg9rAH+E1hnPPXUUyCEgKeeeqrfTYlMq9WCXC4HQggoFovQbDY9nzebTSgWiyCEgFwuB61Wq08tZSTNZhNKpRIIIaBUKrnXrNFoKNdL4rx2rVYLJicnlcdqtVpuO4QQ4DiO59i4/ZOTkzymGIZh+kTSNUAUfcaWV4bpIoVCwfNGfPHFF4t9+/aJc845x/PmXCgU3O/EbekcHh4W999/v3Ja6cknnxTHjh1ztz1+/Lh48skn3Xbgqan7779/XfhSMQzDMANOD8T0QGGz5RXgxJvVxMSEz4qGLWQTExO+NzKmv2BLq1zS6TTU63UAOGlpjcPSqfsOtQIvLS25fxeLRfeNnX6msgwzDMMwvSfJGoAtrwnm8OHDYsOGDaJYLLpWtMOHD7sWsmKxKDZs2CAOHz7c76auO3Q+qwcOHBC/9mu/Jm655RbPeplg+uGHHxbnnnuu+MAHPtCxpdPk21ooFMTdd98tMpmMMjegLm8gtQyHPe+wnzMMwzDhYA3wn/RATA8UNltese8itpTJBa9j/8R4CerLubk5mJycVPquymtGl3Q67fk3k8l0ZOk0+bYCeN/M8bK0tORus7S05PlsYWGhrfPGx5ycnIT5+fnI58MwDMOcJOkaIIo+Y/FqGViA5PN5z8CVf/M0b7wECbTl5WWj8KzVap7rdPDgQaWIDHvtdDekVqsFzWYTHMdRTinJ9VIs02OqxG0mk3FdGyiNRsN43hzsxTAMEy9J1gAsXg3YLl4BvBGFdFFFIDLtMzc3ZxRo9Xrd/Vy1Xb1eV4rFarXqW0+toCrm5+eVQlqur9frUCqVIJvNevxX5XgZGhoK5fO6sLDgng/2zZXgG6jqvHVZFhiGYZjOSKoGYPFqgMUrExY8RSOFpk6YZjIZWFxc9Ag2KgBrtZrW4hrG8qpzC9C1U1pa6eI4jkdk4rGExw8+v3Q6DYuLi+538HnS86bBXo1Go9uXimEYZt2QVA3A4tWA7eI1yVMGg4Qq+h8LwwMHDniEnbRMqqbeU6kUFAoFaDabPp9S+f2RkRGPtdTkQ6qyaFKhWa/XlceiN7agPK/UcnzgwAHP8SuVCkxOTkKtVnOFOhbi9XqdfV4ZhmFiIskagMWrAZvFa9KdtQcFOjWvErBYeNIpdSoazzzzTBBCQKFQ8F2zdDrtJp2emJhQ+qtSTCmvZPuKxaLvxqZqqzxfaalViczFxUWlhbjRaPgsvnipVqvs88owDBMTSdcALF4N2CxeAQCmpqYgk8l43rCweMnn85DJZGBqaqrfTbUS3dS8LlL/wIEDnu+rtisWi7BlyxaPiKSCL5/Pu5bMMIJPdRxp6aQ3tHw+7/FnVYniVqtlvNEdOHDAJ0wB1D699DxttQIwDMMMGknWACxeDdgsXukUL54Cpj4wpVLJureuQUE3NT87O6u0QOqClPANBS9btmyBQqHgsYxKoTc5OelaNIOm2qmFd2lpCZrNps/iKte3G0ClEsrpdNpjWcXrZ2ZmlC4VDMMwTPskXQOweDVgu3jFQTimgUt9F5loULGnEq7Ysliv15VT/jidlGrJ5/OeoC8Z3BR07VSC0nEcpRO/KhWWzqpL19F+OHjwoNJ1QuU6wJZXhmGY+Ei6BmDxasBm8Qpwwj9xYmJCW8qzWCzCxMQEB8jEgM5VYHZ21udjKv/dtm2bT6hVKhVXwMpUVVi8SuFaqVQit4tef7n/YrGoLPFqKhpg8vXFwVd79uxRCuRqtepzLWCfV4ZhmPhIsgZg8WogCeK1XC67+TypgKjX61Aul60cuIPIwYMHPX08Ojrqs2KmUin3c2w9xSwvL0OxWPSJV3mzCZtOKkq2Ad32Oosr9vXFwVhyXNG8rni59957teNRJZaDhCwLXYZhGD9J1gAsXg3YLF6pwGBLV3fRTfnLqRo6TYMLAGDrq9xOfo7FrrS+hplWj5LnFV//sJWuqNCVabDwTRK7AlSrVU8eW5UVQJXnVVdoAbeD02sxDMN4SboGYPFqwGbxChCctol9DOOBVpA6ePCgL5n/0tISFAoFjwilUf00gCqVSvkCqqjvkokwFbZUwi+sIKQCdmFhQSlc5fEPHToUyeKrE+AAJ8vb2nzzZRiG6SZJ1gAsXg3YLl4BTuTdxIKBRnfLSkhMe1DhJS2HuqomOH8rzrNXLBbdHK5UuEoLZTsO9rpt5Pqgz6OcP3aH6MTim8vloFwu+1wusMh3HCdUoQaGYZj1TFI1AItXA7aLVxz8o3vrihL8k2Ta8as0WQYBIFQqKlWBACpcVRGi2Wx2YAQbTcO1d+/eti2+5XLZFfGqzAe0v3D5WoZhGOYkSdYALF4N2CxeV1dXPYOWpm+anZ31DN7V1dV+N7lvdOJXafquyvqqEmR0kVW2dIJYpj8ZhKlyXQEEXVBZGIuvztqqqhDDwpVhGMZP0jUAi1cDNotXgGS/dcVFJ36V8seuEmJYZDqOo0xFRS2Wcslms0aLYq+DlMIGbS0tLQWWrG3HHUHum1qoFxYW2mo3wzDMeiDJGoDFqwHbxSuAP0iG+rscOnSo303sC1jYqCx9c3NznkT+VIzJm4LqR6+b3qfT39jHVQhvEFfQdDhufzdTSeksyzRIrVKpwPz8PJRKJW2fRRXdJuu0PK6uIhdnIWAYhkmuBmDxasB28ZrkSMNOkLnvcDAR7qtCoeDJsVooFDx9hNNi0VyttCRfoVDwCWU6/Y1FKw7iCnNtuplKKkq6rXK5DOVy2XcO0lrdbmYAap3O5/OwsLDgsSZQActZCBiGYZKtAVi8GrBZvCY9x1u7tFot1+JZLBbd/KQ6v0r5I5cWVtXNgAZVbdu2TeuX2Ww2PRbXdDoNjUbDZ5WVabVMpVnDBIx1eo11hQ7wdJQusMpxHJifn9fuI8yxcXox3J+00IKMmG33WAzDMEki6RqAxasBm8UrQLKra7QLtYxiAVqv12FsbMzTT9ICm8lkPHlMaSUpmnAfp8TCuUtxrWmapoQKYyn+KNiaqhNrYUVcGJcDlf+pbt94W+nr244fLH0JwBkYpEtFrVbzXKvrr7+ehSvDMMx/kmQNwOLVQBLEa1LrGncCtbDKKlaqcqz4c/yjV4lE+jm1Ti4tLbm5SYvFIiwuLvqm9LFLgsrvVWVNVQlGnYjDQpG6HFARSUUyFt60ffi7jUbD1yfY9QJnHFC5NaiOJftsdHTU52pBF1sDEBiGYeIkyRqAxasBm8UrtfLh6Wsq3sImvE8SOhcBKVaxBZZaY5eWljz7on6ZS0tLSr9Q3N/4TZhO2WDxZ7KmYl/bZrPpCmOVuJTbSKFIp5Sw+wQ91uTkJDQaDd8UvhSkWATL/1955ZW+Pq1UKm4bKpUKlEolt82yD3C7sO8sdhHA+6V/y8XGaTCGYZi4SLoGYPFqwHbxiq1fpoFbKpWsG7hxoCoiQC194+PjvvVhLa+6aHnsa6Sb3g6aqqdis9VqKcWlfKMOsthiCzF1h6jX675942Ngq6/KYooFrNwPFp1SZMsxiMUwbqPOMk4F7NDQkDYLAcMwzHog6RqAxasBm8UrAChTF9Epg1KpZOWUQRzQ4CmVyMQ/8EKh4PHfNPm8SlGKA4uo2AryyzQVAKCBWjpLstyetguXZZXWT2rdlOeIBXyxWPSVqsVT+Nu3b9f2Jxax1HpL3QdohgaTKFYJWMdxYHl5ubsDiGEYZoBJsgZg8WrAdvEKcCKRvsk6aFtVjbgwuQ1QQYR/4GGyDeAbA532xvsOYx1UuSTQ4xQKBdeimc/nPeJwbGzMV7ELWzZbrRZMTEwoz3/Pnj0e4SozI6j6L5/P+9wrgpZ8Pu9akYOiXnUFHVT7xO264oorAIALFjAMsz5JqgZg8WrAdvGKRYpKBK3XRO5UeI2Pj2stsFJkUp9UXZ5X1f4dx/GlKdFZXqnFkfqxUqG8detW97OtW7dqxfKWLVtcsSrzsUrLquM4nv3orKVUbDcajcAXgCChKftQ9lOQC4VpGRsbU2Yh+MpXvrIuxznDMOubJGsAFq8GbBavusAXuagSya8HqBP7+Pi4p0BAkI+rxFRhC/saZbNZZZoSKS5x3wdF91NL7/LyslLEZTIZXx1rIQQsLy+7QlDnKhBWuOLAK50/bJgFW7dVqcFUlm5dW9PpNNxxxx2ez6+99lqrcxkyDMO0Q9I1AItXAzaLVwC/BVDlr0iT6CcJXXJ/aWU988wzfTlIcZ9ls1n3c9WP+3vf+5722PPz83D22Wd7hCutMZ3JZGD//v0A4A/QksctFAqeoDIs9kzBZiqBR4V62Mj9fD6vzeVaKpW0bgdhF9wuKuZVLhq1Ws2Xvkx1/vfee6/W15dhGCbpJFkDRNFnQ4KxDgDo6HNbOXDggDj33HPFysqKZ/3w8LC49dZbxcTEhBgeHhaveMUrxOTkpFhYWBCFQkEUCgXx0EMPiXK5LN7//veLL3zhC2JyclLs27dPDA8Pe/b/3/7bf/PtX3LBBReIY8eOiVe+8pXi6NGjolQqiUOHDolSqSSOHTsm0um0+OlPfyquvfZa8alPfUpcfPHF4ujRo8JxHAEA4tFHHxXFYlGk02nxzne+UxSLRSGEEMeOHROpVEo0m03x+OOPCyGESKVSvuMfO3ZMCCHE2NiYyOVyQgghHnvsMdFsNkU+nxcA4G6Dv6Pa1+OPPy4uvPBCsbKyIlZWVty2FotFcezYMfHNb35TFItFkc/n3e+o9qPjiSeeEM1mU5RKJXH//feL4eFhsba2Ji655BJx9OhRkclkxLFjx0SpVBJ33323+L3f+z1x/Phx4z7f/e53i7e97W1u3y8sLAghhDj33HPFgQMHQreNYRjGZtarBvDQVRk9gNhsecUWRlVCd2y5y+VyibJIhSmbii2qKof1ubk5T1AT3b/8fjabNe5fCK8vp8l/EwdU4QhRmWdVV7pWXk9VwFSxWIRqtaq0VJpcBVQLHkd4ygn/f3x8XHksXZor3BbqOyyvgUwLRosf5PN5KBQKcOqpp2r3q0pbZuMUGcMwTBSSrgHYbcBAUsSrFDB44OI0UDYO3CDClE3VBQiFEb80IEu1/2w2q/2+ygdW+pVi8YuLEegi7uU21PeUikj69+bNm5UCVm4nP9uwYYPn84mJCbd9juMY87wODQ0FTvELIWB0dFRZUGFubs69JjiATU51LS4uGkW4DErgsrEMw6wnkq4BWLwasFm8AnhFkM6/USfgkoAq0T+2mKrOXf6A6/W6J3F/UCosXZ5X3Q1BJURV+6jX6671UWd5rdfryswEdNGlssrn875sA8Vi0c1EQLffu3evsqoW/v/09DRkMhmYnp52RbXO+irbZbKS4hcKed1wDt10Oq3MmIAtDixcGYZZTyRZA7B4NWC7eJ2fn4dCoeB5wM/MzHj+xlWYkojKykmLDWBhikuXCuFN46QSp6b8eVHapBKyONgL33io2MQBT7KdumCuQqHgcyNQicp8Pg/Ly8vKIgsyPRh2t8AiXa7/6le/6mt/sVj0pSVLpVJue7H1lvYjFslUuNZqNWPaLluDEhiGYdolyRqAxasBm8UrTQlliiy3sa5xFKiVM5/PK0ug6kqlmnKtAgAcOHDA87ksJCChuVvxcavVqnLa++DBg0rhKkVYs9n0uQnIz1QuBFi8mrID0LZs2rTJ87cUuqOjo8o3dvkCsH//fk8/yhcC7CeLLcFSwMq+1r0ArK6uwurqqidzQ61Wc/tqYmJCmY2AZkxgGIZJMknXACxeDdguXrF1j04Z479trGscFp2VU06L63KI4ml/KgSxOJ2enlZaTak1l1bnymQyro8rTapPrZw662Gj0fDdgG677Tb3O9TCKf+mPqx4qVarvrEiBavjOEqnf5VLBS3iQP14cVoyavnVCVdseZ2amoJMJgOLi4ueXIZSKKssz0ke5wzDMJikawAWrwZsFq8AJ+sa66aQZXlOG6cMwqDyeaX57VSWTyo+dRbOQ4cOedbPzs5qrbnlctmtbEUtuyq/UrnccMMNsH37dp+gkzeaSqUC6XQastks3Hnnne6+ZWEBLK51mQDomFC5EUgrq6qsruM4yhcBGUhmCoBrtVq+QILPfe5zvmup8nmV7gnz8/MeYS37YGJiwnPNVZkhGIZhkkqSNQCLVwO2i1cAgOXlZa0vYLFYhOXl5X43sSuYsg0ElTStVqvutnIaO5/Pe95Ux8bGfEJQ56eKU2BNTk56tpFCsVgswi233KK8RhMTE27UPYDXAglwolgCFbNYrB05csR3zlu3boVt27b51un6RFqbZdQ/3Z/Kco1TX9E2q66TXLBVmm6rEqKqoAR6zXV+tAzDMEkmqRqAxasB28WrLGEqxRd945JCQVXi1GbCpLoKqk5Vq9U8FtF8Pq8sHYsFlzwetubKaXPcNgD/lP/o6GgonyR6bvV6HcrlsvvmTC3FjuPAwsKC9vrrMhCobnIy88H8/LzSXYKKeFozm05L0ReMz33ucx5fVlVJWpqiDAfRqbJDqI7FeV4ZhlkPJFkDsHg1YLN4pUEtqoGLBZYqUb/N6Cx9AGrrazqdhtnZWZ+ApGVYVWKPTptjQWu6KWArKW4Hzr+H26HyLZWWW2npVKXxMgnSRqOhFaKpVAq2b9/uE9OO43h8celSrVa1QlFV+hWLTZpFAOe+NZ2b9HXVXXO5DyqoGYZhkkjSNQCLVwM2i1cAvzhS1TVOp9NWvnUFIa2UJmsfTcZfKpWgVqt5+mx2dtbTX9RVYGhoyBVYNKvBwsJCYBsPHjzo+c7Y2JjvGsljUpGH2zI2NubLZ0p9SfP5PCwtLbmuECMjI7BlyxatCL322muhWCz6ArxM7gW0P3WFB0yWcSxgM5kMLCws+IQu7Wvs1hDU5wzDMOuBJGsAFq8GbBevdApZNXALhULifACl1ZVa4nT+ldPT0x5xVKvVfEFLpmAn6uuK1+v6VgYZhS3RigUhvYbUmirzoNL2ymvdbDaN6bLkYspKEBT4Raf96bQ9Lr+rAheJoP3ZTm5dhmGY9UaSNQCLVwM2i1fsG6maZsXrkuQDiM8b+0A2Gg13PRWMk5OTnin3crnsSzOl85HF0zJYXJrKkdIUJtJVQHUMud+RkRGlYKVuDPl83leEYHR01BMY1mw2tem5dIJVJVZpkJZOSOtcBILG3MLCgmd/qlKvQX3NMAyzHkm6BrBKvFYqFdixYwds3LgRzjvvPHj44YeN2996660wOTkJz3rWs+DMM8+E3//934cf//jHoY9ns3gF8Pp9qqZZk+oDiAUOFpWyZCldjy2z5XJZW4qVCrh0Og1//Md/7BGyMjgLt4Em86c+t2eeeSbU63WlHy4OHKPidmxsTFuMAG9zxhlneNadeeaZWsE5NDSkLeOqWmSAmu5zXTWzMNeQphCj5XhVfc0ClmEY5gRJ1gDWiNf5+XkYHh6GD3/4w/D1r38drrzyStiyZQs8+eSTyu0/9rGPwcaNG+FjH/sYPProo/DZz34WcrkcvOUtbwl9TNvFK8AJp23TNKttTtphUQlYXSECCc0XWigUtNPjKvF32223+dog/UtV2QJwMJgUjPR4MhhMJaZxyVWdZRi3E+/b5BKgW/L5POzdu9cznX/ttdf6xlY6nfb5xZpEpcovWfZbsViEhYUFj5ClmQ/o9bbRisAwDNMNkqoBrBGv5513Hlx11VXu38ePH4d8Pg8333yzcvurrroKXvziF3vW7dmzB3bu3Bn6mLaLV5mgGFur8DSrrEhk41tXGHTVtVRiik7lm6bX0+k03HvvvR5heM899/iOj/eJ85LifK8q0Tk+Pg6FQsEj4Kh7AA42q9frUK/XtYJUFWkqhLf0a5APK+6TQ4cOKQs74LFFj0dL5kpoVghqcZVJtCuViifnrmq6y2YrAsMwTNwkWQNYIV5brRakUin4xCc+4Vm/e/dueOUrX6n8zsc+9jHYvHmz61rwjW98A57znOfAe97zHu1xfvKTn8BTTz3lLisrK9aKV50YA/BPW9tYGi4sdKpEJ6ZoHWiZRkpaSfEyMjLiS4qvs/bpEuQ3Gg1tZa18Pu+WVDW5BWDLa5D7gCngbGhoKDDfq/yuLgXX/v373fNVfa7z/cVZB3B/U2uy/JzmsFXtk2EYZr2TdA0QRbwOiT7xb//2b+L48eNibGzMs35sbEw88cQTyu9cdtllYt++feLCCy8UmUxGnHXWWeLiiy8W73znO7XHufnmm8XmzZvdpVAoxHoevQYAYt3ONlZWVsSuXbuUn+3atUusrKy4fw8PD4ubb75ZTExMiGKxKJrNpnjJS14iXv7yl/u++73vfU88+uijolQqiRtuuEGk02kxNTUlhoeHlccCAJHNZsXRo0fFxRdfLA4fPixe8pKXiEcffVSMjIyIdDrt2f7xxx8XL37xi8UnPvEJ8e1vf9vzWT6fFyMjI0II4X632WyKlZUVUSgUfL8RIYRIp9PiscceE8ePH1e275lnnhFPPvmk8jPJ8ePHRSqVEs1mUzSbTZHJZDyff+ADHxBra2u+7xUKBeE4jnvuss/X1tbE8PCwuP/++0WpVBJHjx4VL3nJS8TOnTtFJpMRt99+u6dfjh07Jp588kn3HDZt2iS+8IUv+H6jumvAMAyz3ljvGsCluzpaz2OPPQZCCDh8+LBn/XXXXQfnnXee8juf//znYWxsDD70oQ/BP/7jP0K1WoVCoQD79u3THidJllcAgKmpKUin025lKDplMD4+Dul0Gqampvrd1NhR+bxSv1JawhQHbKn8OG+66SbPuoMHD7pZCfBbLd4fLmcaFICky+8qF5nSpFKpKPPN3nvvvYGFCUzL6aef7usr1TIyMuIJflOlsEqn01AsFmF+ft4XUGXyV6UBdTpLr+M41vpqMQzD9IIka4DEug1ceOGFcO2113rW3XXXXXDKKafA8ePHQx3XZp/XpKfJMKHydcWBWFgYyipYNODnwIEDnu/Pzs4qBS2e2g6alqGpn+R3qTuBSqwNDQ1BsViEI0eOaN0NdKK3ncXkRjA2NuZzhVClKHMcx305wKnI5OeTk5OuAMWf46VWqyn7DQvgJI1dhmGYOEi6BrBCvAKcCNi6+uqr3b+PHz8O4+Pj2oCt//pf/yu87W1v86y7++674ZRTToFjx46FOqbN4hXAK+J0dY2TlloI/2CxyKzX61p/zHQ67RFji4uLvgT5OENBtVr1ZC7AOWFVSaBldLxKnGHBGxTIJYUpjuRPp9Pwute9zredDG7CCw3o0gV4bd26NVRmAlW2Btl+LFSnp6dhcnISarWax1orBagsJrF3715lm1UFI7DF+uyzz7Yy4IBhGKabJFkDWCNe5+fnYePGjXDnnXfC8vIyvOENb4AtW7bAE088AQAAu3btgre//e3u9jfccAOcfvrp8PGPfxyOHj0K9913H5x11lnwW7/1W6GPabt4BdBb8qRwwtPmSUGKKN3UtpxCkWJwdHTUI6iw8JqdnfUIVVk1CleAMqWqosJVTtvgTALUcqnaH7Wm5nK5jlwE5GJyD0ilUq4wlxH/+PODBw8CgDdISv6/0WhoXwAymQzUajWfJZZuT5exsTHPtcvn824/5XI56ywHDMMw3SapGsAa8QoAcPvtt0OxWITh4WE477zzPOUnL7roIrj88svdv3/605/CjTfeCGeddRY861nPgkKhAG9+85vhBz/4Qejj2S5eZd5S/MCnFizHcRJptcIiigpHXTQ8FZnLy8u+qlx0ih9vr6rKhfeJo+NVWQioZbhQKGjbKytp0ZRVYQoMhM3xKvclS+aqxOWrX/1qbZnX6elp7b5pu3W5ePGydetWj6jHgt7GaFmGYZhukmQNYJV47TU2i1ea+on6MOK/ZQL9pKLygaWWzYWFBU/aJtVUvioJvswtesUVVyitozif3sTEhOcmQf1sl5eXlXWodVZd1SKtyGG2CyN0U6kU3HHHHR6r6Z/+6Z8qxT/NmxuUvksnaB3HMZ7z2NiYp69trc3NMAzTLZKuAVi8GrBdvGLBRoXVerNa0XyvVBzJaXGVFTEoCf7y8rK23OrIyAgUi0UYGRlR3iTkPvfv3+9eE5yEX3XN2qmOFceSTqfhjjvu0E7vYwFbr9cjBY5hy3a9XncLKATt4/TTT2fhyjAMQ0i6BmDxasBm8QpwwmpYLBY91ZhmZmZcoZBKpdx0RklGV2lLWjbx1L/K/0fl04n3TS2M+XzeM02DxaYqpRYtWFAoFKBarfrekmnJVSz8rrzyyq6L11tuucVjgf34xz+urLRVrVY9N8awIlYKV9wXQZZk+TIQlDbLthszwzBMpyRZA7B4NWC7eMV+lTofQ1WVoiSBhSsNhJJCkuYhVUXQq/qo1Wp5LKQ4Cp6WdE2lUq7Ixceg7ZPbmN6S+70MDQ1BoVCARqPhCVxTWZ/Hx8ehVqtpLdN4OXjwoCdojU5z4XK2sh31eh0qlYqb8kw3BrhsLMMw640kawAWrwZsFq+09Ca15FWrVaUPZ5LAwtBxHI9IxKmWqICV/dFqtaBcLitFLcAJi6n0G02n025JV5WVN5VKwaFDh3zBYzjivlKpQL1eDyX0urFQX1LdIgPTZJt1pW5TqRQsLi4q+0O1pNNpT1qtMP2QzWY91mBqOcc3b904T+LYZxhmfZN0DcDi1YDN4hVAHWwkF1WlIxvR/eDoD7fZbHqsqCqxSi108/PzUCqVfEIXwFuEIJVKeTJfUP9a2uc6Mec4jvYtGQvCzZs390XcyiWfz3sE4/79+5UBVmNjY5HTeaXTabj77rtda65KTI+MjPjWq7JBNJtNX0oyCltlGYZJKknWACxeDdguXgHUqaKCfDxtwTSlDwDK6WRVsBT+4crPddVJVOm2cKlSbOmjolN+/+DBg77PM5mMJ3WWahu6r24uqVTKFxh20003ec4b+03R7+syGXzwgx/0CXNdAFgmk/GlH5PieXZ21rMul8t5+m9hYcFzHah4lS8rNlseGIZhgkiqBmDxasB28arKJSrXq3KP2oTKsiqn+gH8aajkZ1SgmAJ9cP+pyuvJ9TJLQb1e91j6FhYWPN8xpaa65557jG/JvRawKuvu0NCQxw81n8/7/FJTqZRrhaXi95577vHlzcUVuPbs2ePZ/m/+5m+UlcJU/ZDL5ZQlZkdHR7UuInLftlaYYRiGMZFkDcDi1YDN4rXVarlWK9WUKZ72trU6Ef4BZrNZyGaz4DiOr9gAFiy5XM7jFmCy3MofvhQ5qqpXi4uLPkEmty2VSjA9PR0qtRX2H8Vtr1arofKx9nLZvn270R2gUCj4LKaFQgFarRbMz89DuVz2XKNyuQzLy8s+4YlTjOly3o6NjXny5y4sLHg+z+VysLy87HkJwfuQN24bxz/DMIyOpGsAFq8GWLwOPqppeuz/KIOosNgql8uwurqqLEqA94vfTHUJ94vFIiwuLnoi7rE1MijoCKefSqfTvowErVYLtm/frv0+FbZxC12V8E6lUnDjjTcqp/t1x9+/f7/br+VyGebn5z0vB9gKSi3WsggBvY64j+v1uvLzVCoFIyMjkM1mfcIXZ5uw1e+LYRhGRdI1AItXAzaLV4ATg3NiYsIn0LAwm5iYsHLKAKMSLTJyvVQqKdNjAYAnzZOuf6RTu8rih/c5PT2tTRlFp9ZVQhu7AeBpnEqlEjn7QC+KGKTTaU/e2UKh4I41Kh5xP2JXjiNHjnheCrAVlPqr4u9S66k8Du5nVeYEKqyXlpbY75VhmMSSZA3A4tWA7eJVFS2PnbWLxSKUSqVEWJxUEf5UvGDhin+8WMBSZ/Z6va71daWi+ODBg22luUqn01Cr1SCXy0Eul3Pb2Gg0tMFM/Vhwf6oKL6jSfOGMA9giXqvVPOdGLQOyJrf8Ln3JkFZbVeEGKXZ19bzxdqrcuwzDMEkgyRqAxasBm8WrLloeP7jlOlssTro26nKrUoEo01mpLKuqNCI0fymtyKWyALa7lEolWF5eVmY7GIRFWi2HhoY8Fsx8Pu9LPUZfGkZHRz0VXmZnZz0WZ92bf6vVgkaj4X5XlTEA59qVy8zMjLYtss34uo2MjLBwZRgmUSRRA2BYvBqwWbwCeEUaFVnyb1ssTrrgKmpB3bt3r1ZQqiyrcn/UcruwsKDNE0qzEKjSOemWt7/97UphLds/NzfnnptM9YW37YVLQJQlnU7D/v37fS8DMtAKLyohOT09bbxpYp9fld9WvV7X9onKCq5bZ2u6GIZhGB1J0gAUFq8GbBevACemnnWR4cVi0YqHtiotFoD3h4lL3anEJBUtuv3g7WW/0VQiNAsBFZg0aCtI/OG/ZTAZfWsOu79eLlKM0il9XJkML6op/jBv/Lp0L9hNYWhoCG666SbPvs844wz3/0NDQ8qXGnkONloeGIZhgkiCBlDB4tWA7eJV+rvoLJEynZMN/i50qr/RaPhSVBWLRY+foykX6tLSknK/CwsLrhgbGhpyI90B/IntC4WCZ1t6zHw+71ogqXCbnZ31CeZsNgvbtm1TVgQ7dOhQ38WqaikUCm6eWyzww5S5xa4cUQVstVr1ZGmo1WrK4hCnn366u934+LjPxWDr1q3gOI4VvwGGYZgoJEkDUFi8GrBZvLZaLY84opY7/HepVLLC6kSF5t69e13xSIUrjlDfsmWL70dLfV11Fj0hBNRqNV8AET6eKZBJlalAiBPWShzghdNkye9KK2az2YzNtzaOBZ9vOp2G973vfR5fXZVFXCVc8XUISlVFAw/wfmq1mtt3qheW+fl5baozIexN0s0wDKMjiRoAw+LVgO3iFVuiqIjAfzuOY83AVU3xO46jLQWqmjKRgleVJkuyuLjo+Q7OtVooFDz7HBkZ8fRnOp12ha3jOK6gGhoagjvuuEPpZiDEiZQlZ555puc8Go2GUXj1axkbG/Oc8w033KCsXEWn8uVyxx13+ASubuoeu1BQET87Owujo6Oea0OrcqlK3crrRqtvMQzDJIGkagAJi1cDNotXAHAtTti6NzMz47P22TZlQIOrlpaWYH5+3q1vr/JllZGVuVwOKpWKJ8hLTl1TarWaUnhhd4B8Pu+xxuL/YyGFp8hpFahqtQq5XA62bNniy2AwNjY2cEFaUhDSdVh4O44D9957r/b7mUwG7rnnHk+wmsn3ylSgALdJFitQuRDQ78ltcZ5XU7lghmEYm0iqBgBg8WrEdvGKH+K6ty7bpkxVllccKKRKNSV9ZPHnYUXLgQMHPMfCVr5cLuex3MlqXrq0W7r2O44DO3bscP8eHx8fKDeBKAJ2dHQUHMeBWq0WyudVCtdKpRJ43bF4pemucDEEVVU1vEi/V5wzdnJy0vXdtfFGzjAMQ0miBpCweDVgs3il4q1arXoGbrVata6yEPV51aW9Ajhx/jLgSRVQJHOEmkRLo9EIzB8rj12v192ypyrLMN2fKlk0tbhGEY2DImCLxSJ87nOf890oM5kMHDhwQClo/+RP/iT0dVflK5RiFhc0qFar2j6UJWPxuMHXxpbfA8MwjI4kagAMi1cDNotXgJO5UXVJ+MMEygwKVLjqSrnSKP3V1VVfmq1ms+lWszp06JDyB4xLx+K0WKqlWq168sHSKWtaUQq7KlBhFpQSa9u2bfC+972vrUpe7SxRXBZMbarVagAAvhto0I1TlSaNvhxI0e84TuiKZDhADvtMs+8rwzBJIUkagMLi1YDt4hUAYHl52WitXF5e7ncTA9HleZVgAVgul90co1isYoGIA6Bw1Lsq20Amk4FDhw5pp6ClJU+1P9zXdAnKV6tbhoaGXP/YXohXKQ6DrL1BoltXyUwIAYuLi8brj19GVG4XxWIRJiYmYH5+XimO6TWSy/j4uMcvmYUrwzBJIwkaQAWLVwO2i1dcoUknlsL4Gw4CugpbEum3OD8/r7TGUh9IHC2Pg6kajYbbZzINk9zX+Pi4RwQNDQ25f6dSKU8JVLk/mnYLR9mb0nPRpZdiFS/Yr9e04PPHCy7VivubCtsg0UhTcNGbcCaTgVqtpmwrLk+rE7IsXBmGSRpJ0gAUFq8GbBavq6urHhFGI+qpddGGKOsgnxx8Diqho0o5pbOUSjGksthS8RPG8irXl8tlOHLkiK9t27ZtiywsN2zY0DNRK9ufz+d9if5NrgWlUgnuvfdepWB94IEHtD7L9Hrr3Ebwy4bumuBz0F1D6ZfMMAyTBJKoATAsXg3YLF4Bkv3WRZmbm/NZZlVTzLTSFXZax8LqyJEjrquC4ziuuCwWi76p6Xw+75YiPe2003xiSk6Z53I5yGazMDEx4UnXpVvy+XxbojaO5VnPepZvHQ6WClOu1mRJ3rt3r88XC/u+Ykt6kNsITWkmq37RNs7OzrpjQgZs4WvElleGYZJEkjUAi1cDtotXAHOEO07hZDNzc3PaggM0uIda3EqlEuzZs0dphZOuCocOHXK/Nz4+7puaHhkZUVbbwvujCaMLhYIv3yteNm/eDM1mE+r1us+yed111/U8lVYqlYKJiQkQ4oSYr1QqnsINdNug9uHrtbi46AkaUKUx07mNYGErF8dxPOVj8TEXFxfd6+A4jjFjBcMwjO0kVQOweDWQBPEKYM6NajtYvNDgK11Z1WKxGDqYCv/wsRiS+8CJ+QuFgjK/qbS8YreFMALv7rvv1vqbdqtwwSmnnOL+P51Ow6ZNm0AIAb/5m7/pWo4dx4FcLmdsF3UtUN048ZSVDNqi7gE4GlbnNiKF7eLiou+aptNpmJ2d9Uyf0Wusc0lgGIZJAknUACxeDSRBvMoHvi73qG253VSoovVNaadk+VhVkBQWN3hKm+ZhLRaLsHfvXs/3ca5R3X5p5P7Y2FgoK+r4+LinQEKvFlpKV/5Lp93logvcwhW0VAUE0um0x4WD9n9QHkL5mSqXIcCJiFuT/xe19ibhd8EwDJNUDcDi1YDt4jXJOd4oYdJN0fKtVGhS6xyuQCKnmlVJ8tPptEco6ypMyewFKrGKt6XCcHR01E2kv3nzZqVg7KaApf2h8sPdsGGDth2pVAqy2azHLcCUwYAKV2khCLrJqoK3sHUB+39JgUqDwujvwdYbO8MwTJI1AItXAzaLV910umra1mZLExUfqpr2e/bs8eQJxds4juP+gFVBVNJiiH0u6Rss7stsNqvNZ4oFssoqTK27eJmdndVakt/2trd13QdWnh+ukx12kaJ2cnLS44YhCzpQn2OcXgu7gExOTsLc3JxyHNAABGrFxW4g8maNrykuK4z3GeSywDAMM4gkXQOweDVgs3gF8KbC0OUeVU2h2oIqiEeVpD6bzXoSMTebTdi+fTvkcjn3uzJNCBWme/fudb9Hc41SYUdFk0q47t69G0qlklJszs7Oun6xmzZtChXRLxeaRaFbAlYXpKVacB5clVuAtCarXjiocMXClAYY0M/379/vW48FrLS4yht7Npv1+X/h7zqO45b+ZRiGsYUkawAWrwZsFq9Jf+tSpU8yJfqnJVnL5bJrxZMWNpXl1RTYo+pLleDDoo26GKiWbdu2udbAD3zgA0pRWK/XYWZmxrN+8+bNykAp03L66ad79hvmO5s3bw5VCUz+X5XhQVX5jPr0VqtVnzBVCVE6zmnKLZ0vKxXO0heatku6ONj4O2EYZn2SdA3A4tWAzeIVINn+LgBeYZLP5wMFFa2YRaexsTii6URUPpi0DToBVywW4dChQ8r2pdNpuOaaazzr8vk8tFotqFQqyu987GMfA4AT4kslOLvtAyuX8fHxUFkPVAUBsHDMZDIwPT3t84NNpVJuVgOTH6wulyEeJ3Sc498GPi4NupP+x7ZH5jIMs/5IsgZg8WrAdvEKoJ8Ol5GGtlXVoDSbTV8KKmzZ1AlaKoaCUiiZxJEuawFOJ1UoFHwWVynqHMfxVMpKp9Pw4IMPKitHqUR4t9JmBS2yMINpUYnrQqHgcSfA/avKEoHdO6hVtFAoQDabDRSY2KpArfZUwFLB7TgOC1eGYawkqRqAxasB28Xr/Pw8lMtl41uXzb580ndRZfnE5VxVwhJP5eM0ULTSSFR/y9/8zd/0CLGgQCps6cvlcj4xh8WUKsq/WCzCqaeeGkpsnn/++VpB3Isln8+7xRxUixSfKr/l6elpT59TsakTmLqpMOoCojqm7F8WrgzD2EiSNQCLVwM2i9dWq+Va/oL8XXK5nHX+LjhYa2pqyidQpTiVVjmTYLrxxht9KZQwMkKdRrrjzAW4Ugl2RTBZXFXC7ciRI+7n1Dqp8guNEtSVyWRgbm6uK8J0dHRU664wNDTkinjdNjJowOS3LIPuVMUnpBWBXh/TlFiY9Gqq/TIMwww6SdcALF4N2C5e8XS6LtJQCiybBi6e9nUcR5kzFBcFMImuPXv2hPKXvPPOO31tkJH3xWJRaZGV/a+aOqeiEyeMxp+NjIxAoVAw5kWlQlEej7oT3HLLLZHTXNEFB3jhRfqG6sTp2NiY8jPcN3gb6v4h+3lpaUnZFzIXLu7/MEUHTGJZHpMtrwzD2EaSNQAAi1cjtotXOk2ge/iXSiXrBq7OajY2Nub+rav2pFqCqi5Rl4G5uTl33/l8HhzH8Vj46vW659hUROsi8OVxpcU4rAjHQjCVShkzB6TTabjnnntCC+Kwy4YNG3xFFLAvL10KhQJUKhXPDVa2X7oXmITl9u3bPf1YKBR82QJMfrC6YDta9YwFLMMwtpF0DcDi1YDN4hXgxNS6LqeoFESlUslKfxcAf646bKnD4k3Wtw+yOuqCtWgwF7b80sCeVqvle6vFfq10mZ2dVQqter3uq/iFl9NOO015PVXbUiF74MAB9xhh02O1k8Fg8+bNcODAAe3n0k91YWFBez1UwVRSYMr19CVBrg8K4KJpZPANnh6Xg7YYhrGNJGsAFq8GbBevACcT69PBm8/nQ5XcHFRM4oMuuVzO9U0NI2CxT5AMupICCecopaKqWCxCtVr1WYJxSVp6HdLpNCwuLnp8Z1VZELAQpX6veDtaWla1ZDIZbZla3aLzrTWJWhyAphOeKj9euUhXilqtpj2uTuCGEZs4xZZK+NbrdXAcx7WC25gLkWGY9U1SNQCLVwNJEK8A6gAXOXBtRgZt6SLFhTiR8B/nCr3jjjtCC7ZiseiJjpdCzHEc39SLSmTSnKFYsGExKLeTIkkKKlWwF12y2ay73yAr6gc+8IG2sw0MDQ1F8pfdsmWLb3ssdMfHxwPFc7FYhFqtZiwAIV09dGlgdGDLejabdcUudTloNBqBgV8MwzCDTBI1AItXA0kQryoLIRYHNg9eAG9kv07gTE9Pw+TkpE8I7dmzx+j3iYWjaipZrlft4+DBg1Aulz1iFJchVRUgyOVyHuEaJBalxTJMVgXZF7fccktb4lWIEy8CuvMNWlQWUl2BBZVgl64fuv2aKqNRVNXZsPVBFexlq3WCYZj1TVI1AItXA7aLVzpoVc7aNg9emrAev1niyPV0Og0f/OAHPf6xi4uL7j6CxBguG6pK0aSy/JZKJahUKr4ce47juKm3TMfDxykUCnDw4EHfdkNDQ1AsFuHaa69tW5AGLVJgYqszLUuLFxqgdeWVV7opzWR/n3nmmVpxLc+XuhLccccdPoFKc+KqKqPpxjZOtaYbW2xtZRjGZpKsAVi8GrBZvNJIQzxA6YC2MdJQV38e/398fNznk6nKKmBKlzQ0NAT1el0rclVBUvLvbdu2aaejq9Wq2zaa0gpbHguFgtKyGHbRpajatGmT9juy/bJdusIJqoUeK5PJuPlZAU6IxomJCZ/VNZ/PQ71e92UewPuR4hkLVDyGVcF2YatutfM5wzDMoJJ0DcDi1YDt4lVawVS+LdiKuGXLFqsGLs3zioOdqFCkltKDBw969oW31QUf0cpQ8u0V75tW7cKCFFtuo4hQ6aqAhdji4mKgpVi2RfZL2IwC8hgyUAmLxkwmA1deeWWofaRSKfjgBz/oy5+ry9Ig+3h6etrX1ne/+92eimUyMrbRaHiyMZjSnJXLZeP4tmnsMwzDhCHJGgCAxasR28WrDFRSTQvgNy8bq2vgaV/VFLAUL9QXFFvisJgKU8pViJO5RBuNhi8dlhSoUvjhRVpgaWCRSYAuLi667ctkMq5AwwUQVN+T50kzH+TzeeOUPxaBzWYTyuUyVCqVQMGtEsfj4+OwuLjoC37CVm6dfytesHCV41X6oeJsAapMAM1mE3K5HORyOXYPYBhmXZF0DcDi1YDN4hXAX75UNa1qc/5K/GNTCRd87gsLC8qp5Pn5eXAcx2NZpUnq8fpSqQR33nmnJ02X3FYKqEajoQxMolkG8H6pFVK2c//+/T4Lpkm83nPPPVqxWSwWlcL6yiuvVB5D1rxeXFzUistUKqUV/dK/F6f9ku3GJW91fYIzNeA+weNV+g+rxGer1XKD5nTV08JU4WIYhrGRJGsAFq8GbBevAN5ofFVACy1rmgR0Po+q9SohqEvRJKe6M5kM7N+/HyYnJ32plKSYkhbLbdu2ecSayVqKrZZy3eTkJCwvL3v8e7HQVglUGkC2adMmTyoulY/ugw8+qPQhLpVKHheCG2+80VPCVYiT6bocx4Hp6WlPvezV1VWflZq6Q6gEsdwOC2NaAlZiEp1RxgLDMEzSSKoGYPFqwHbxKqfTdamE6vV64qZMV1dXfWmQMPiHXC6X4eyzz/ZYPLG1zyQ66Y9eNY29urpqzGaAy9eqqoCl02mYm5sDAFCm1sL7wdH5Kt9dOX2Ep+GxxXN0dFRZVWrHjh2+852bm4NyuewRquVyGVZXV90+li4HWNRL8SynsHQuFKOjo8o+S6fT7jGiQIVq2IwEDMMwNpNkDcDi1YDN4pXmsqTWOBxclJQpU/lDlaJJNU2MP5+fn4f5+Xm3Alez2fSVnMWCkqaNwsJHF0CE/Y5U1kWTUJb+tXj6W2e1DVO+dXx83NM39Xrd871CoeBaobPZLFxxxRWQSqWU/lKrq6uuwNywYQNUKhXP5/glQY4vPIWlcxeQ7aGuCKlUyneMKKiC5Vi4MgyTVJKuAVi8GrBZvAJ4H9i6dE5JeYDTHyqdCqH+jdiCJ5PQY6st7S/HceDQoUPuPnS5RakwqtfrgdH+NJ0VtgBjP1pVIQJqraVtqNVq7vFTqRTU63V3f7osC47jwPLysjGan6YXm5iYCDUlr7JEp1Ipz7mphLgU8p0QtQoXwzCMzSRZA7B4NWC7eAUAnyVxZmbG8zcVJTbTiX8jtdqq3lLx56oofOwCIEUoFmK6ilL4b5xWC1uHZYUwVd5alXDF2QmwhTWTycDBgwc94pueqxR1dOzg/eH1OJgqaEpeZgCgfatzr0ilUq41uJObLFteGYZZjyRVA7B4NWC7eMXTtLq3LlsjDXW0499IrbY4xRPtL2y1pZY8LMqoUMV/m6b4sTVQZw0OKhtLxVmr1YLp6WmlwF1cXPRlIMD9FObGF0YYSuu2KtsBTqNF+2bv3r3Kl48oU1zs88owzHokyRqAxasBm8UrzfGmsiTanOPNRDtWNtX0Cs2VSvOg0mOEyRUrI+1121GL8eTkpCcwSvrhBglXuX02mwXHcZSR/bOzsx6/Vd0NTVWBjL6xm6bkcdAADtrC6cvS6TSMjIxo+4MKUJnGK8pY4GwDDMOsF5KuAVi8GkiKeB0fH/dNyeKUSzYO3CDa8W+kVkbs0I4FLa16hS15ukAkIbyFDKh4xXlN6TGw76nJ8prJZHyCUH6GsxHIRWUBxtXEstmsmwqMfn9mZsbtN9PLArZqRxHGtM+xgJUCOCjIgFrUOc8rwzDrhaRrABavBmwWrwD+SkyyrCkexHEEwgwa7VheVSILf1clJnWWPJ24lFZX3P9YQOIbDBZu0s9WlXsWL9PT06HbQhd8bJoJQZYYpAKTugzopuR1mRhU10lWFtO9NKgSbptQVV+jY8XWVDEMwzAmkqwBWLwaYPFqH534N0qhowtgwiJMtS+VFZGKVFWyfnw9cOaBdDrtZk3A2QFUQtIkpvEyOjqqzFpQq9V8pVtVwWHU51VV+Uo1JY9z4NLrItdnMhk3HZZKgJv63kSQRcE2iwPDMEwYkqwBWLwasFm84ikDnHoJD2IpPGycMlARh3+jSiTi78zNzbmWPFqeVlpug5ZUKuVLLUWvz9DQEGSzWd/Uu2pftVpNOf1tKuuq2o+u5Cy1mFKRLt0hdNcCp/tS9a20LJvSm6muBcVULjjM5wzDMEkh6RqAxauBpIjXJDprU+LwbwxbRq/Vanmmo+W+aBWsdDoNe/fu9YnC6elp3/EXFhY828hrJ88FZwvAFk8hTviQ0kop+HwzmQxUq1VlsQSViFWtU+V5lRkUMpmMsvKVakpe54usG39hfZfx9VC5CuC2sKsAwzBJJ+kagMWrAZvFK0Cy02So6MS/kU5rq6y2clobC2UZzU+tilIElkolcBzHE0lfKpU8NwqVhTGVSrnO9OPj4+7+8PpisegJ8lpeXvbtT4puVX7VoaEhZSAXXVSWVYATAjaTycDU1JT2msjzlBW2TIFdqusVxvKKrwfOrKDKVOA4jvub4CAthmGSTJI1AItXA7aLVwCAQ4cOGfN0Hjp0qN9NjJV2/BtXV1dDV5OSVsZGo+HJWVooFGDbtm0e4UrFpbTA4rdcKjRxaq5UKuXJXICFKxZmsh2ZTAaOHDniCjlZqIAK16CKX1KwLi0twcTEhFFkqiyulPn5eXAcx9MXNEOD4ziel4qovst4e9zvuv9zeiyGYdYDSdUALF4N2C5esTVR99aFg2TWM1EsrzhvKfYj2rp1qyfYSlpbsdDE+Ul1vrimwC9V+6Rolp/ddttt7rkUi0VPgFY6nYZ77rknUMDitF5YFJZKpUjT7bQwgawgJtuO+89xHJ+FNorvMm0rdq3APl8sXBmGWQ8kWQOweDVgs3il1kSa2H52dtZnTVzvhPF5pb61VMBiy6tqSgZPo5t8dKl/El6k3ye2uuKbUalUUlbOEkLA3XffrSzDqlqk0Gw0Gp7vlMvl0MFPrVbLM/VvEq+lUslTUQz3i8pSrZr212VZUAl/hmGYpJJ0DcDi1YDN4hUg2W9d3SKMn6Vqqt8k/nTofHSDBJhMsaWaJsdtpjerd7/73e54oCJb/k0LLGzbts1jxZQZEHBbg4Kf5ufnoVQqad0GRkZGPOOQ9gs9RtAxaZCXSvgzDMMknSRrABavBmwXrwAADzzwgNHf5YEHHuh3EweOMBHuYQoBhBFKJsuhqdwsze0aJS3W0NCQp825XM7jFyqPKUvGyoXmA4xSoUoXsKUKsML9ojuG7lhseWUYhjlJUjUAi1cDtovXJL91dYsouUWDfFNNlteg6PpCoaAUlPQa0ipXquVtb3ub529pXZWZElS+raqcr3TKP2zuXIzqxSCO/Lx0e/Z5ZRhmvZNkDcDi1YDN4jXp/i7dIEqEu04wjo2NeUSTqnqJyl0A+8AWCgVf8Fiz2VQK2EKh4CmZesstt4SyvkohqkvZRcUrrqQVpWoZPj/Ti0GQv3FU4crZBhiGWc8kXQOweDVgs3gFSPZbV9xEsf6ZKl6pSr5u27bNMx2uC9SivqGZTMYtjECDm+hSKpWgVqsZLcGzs7Nu5gGdVVieLy0hq/Kr1eUHpFZlnc+rFN0yi0GlUglt9abH4zyvDMMwXpKsAVi8GrBdvAKcKBFq8ndZXFzsdxP7TjvVuW677TafxRWLMyokcYS+SSjjnK3y2lDxdfDgQV+qK/wWnU6n4U1vepNS4NbrdY+lVnWuuA3VatU9NrX8FgoFX9BUo9GAyclJmJubg1ar5cs2IC3Rc3NzMDEx4dlnqVTyVRrbu3dvqGvIFbYYhmH8JFUDsHg1YLt4NQUV0YCf9U6U6ly4X6WIpBkAZP+qEvDL/emmyanYxHlm77jjDqN1dWhoCGZmZrSfT05OeqbosfWR5rTFbdBZfWVuVgDvW34qlXIrj9E8szfeeKN7DliEj4yM+NJ7YetzEEHpu8Km92IYhkkCSdYALF4N2CxeqTVRVdc4bKT4eiFMdS5VnldsycQVsqTw0vkSqXxA6RSP/BunuMJCla4bHR31pMC65ZZbPDet2267zT02tj6qzgv7kMrKXnQZHx93fVZVbSwUCj4XBN2CCzwk4ebKMAzTL5KuAVi8GrBZvAIATE1NQSaTgVqtprTq1Wq1wNr0jB9VHlKVCMXVuHTiy3RDwQKWBmKNjY1BvV43ptKSZf/q9bqyehgV1XNzc5620uIEY2NjntK1cj2O5Fd9vn379lAlaalgxQKaBSzDMEw0kqwBWLwasFm84rcuLAjw9LRcb+NbV7+h/UVTQC0sLAT60qpSbVHRpnMRKBaLsLS0pJ3Op/WqqasAFapSZC8vL7uZAcrlstJq6jiO0pVArpfHoUUQwi66gDkepwzDMOFIugZg8WrAZvEK4BVHMieoaT3THqYUULrgLHoNsMWVClhqcaWikVpf9+zZo2yn9Endv3+/R1TLICspOEdGRtxj5HI5yOVynv2feeaZMD8/ry3mEJR3llpar7zySuV+cP9ygBXDMEw0kqwBWLwasFm8Jv2tq9/oMgeo8pOqysmqbhx0uw9+8INKqyd1NaDiVWXlNfm0Oo6jTLNVLBahVqspLagyEE13XFOJVpWADdN+hmEYJhxJ1wAsXg3YLF4BTk4Fq6x4UsCwRSs6qn6lVlVVkQGVNbJWq3n2bbJa0kAmKiaDEvtTcVyv1123ANU+cfDX0NCQW5lLWmh1gl1nNQ4SsNT6zD6uDMMw7ZNkDcDi1YDt4hXgpMVKN8Vr29tWv8Fvs6ogKJX4lG+1KmtkNpv1ibQ77rjDs83Bgwd9+0yn0x4xKYsOBJVUpTljqUuATshKsTo+Pu7JCqCyGquCtkzCGPcTrbTFApZhGKZ9kqoBWLwaSIJ4BTD7ZDLRoflQsYDDCf7lv5VKxWhRxZWqDh06pLTMqoK7hDiRioqWPMX5VlXTQdgyrFoqlYq2nfL8VNNNujZu3rxZeywpYHGVFw7SYhiGiY8kagAWrwaSIF6DasaHTQDPeFH5uuLSqzRPKk4ltXXrVuX0+8LCgkdUSuGq8l1KpVKwfft219oqRWW5XIZyuewThCof3SBBSZeFhQXPNJQuTywV11TwYoGLP6cFE2ydzmIYhhkUkqoBWLwasF28Ygucbmrb1rrGg4BOCOIpfJwZAItCbDGl1spMJuNLdSVTW0nRKMuvApzwa5JWUVoBDPs1VSoVbQquoaEh2LBhg28d/judTkOlUnGPSy2iUtju378fcrmcO+ao4K1UKuA4Dmzfvt1YrpUtrgzDMO2TZA3A4tWAzeJ1dXXVU62JpsLAU7yZTEZbBYoxQ/2IZOS/fKOlEflU3KrE78LCgucYUvzJN2Ra5lTuA/vPqnxQafUuUwAYPh/sW5tOp41v6ljYqsqxBn3OMAzDdE7SNUAUfTYkGGs47bTTxK233ioymYw4duyYuOyyy8TKyooQQoiVlRVx2WWXiWPHjolMJiNuvfVWcdppp/W5xfaxsrIidu3a5VmXTqdFsVgUR48eFS95yUvEa1/7WpFKpTzbfPzjHxeFQkEUCgVx9913i0wm4/n8d37nd9xrtba2Jq6//nrxyCOPiJe85CViZWVFDA8Pu9s++eST4tixY0IIIb7zne+Iiy66SKysrLj7TqfT7uc//elP3b/luCiVSuLBBx8U6XRae574eMeOHROXXHKJ2z7Vtmtra2J4eNjzPfl//K/qc4ZhGKZzWAMgeiCmBwqbLa+S5eVlo7/L8vJyv5toJab8rtjHVbXo8r/qUl3pMgjg9fiYdF+q41cqFbfCVrPZhJGREeW20nVA7n/Tpk0gxIngLZW1lH1VGYZhBoekagB2GzBgu3hNco63fhJGTNLCAfl8XitwowrVMMUQ5KLyp5XTR7IMrPxOoVCAkZERX8CWnHJaXV1Vuiio+oWzBDAMw/SXJGsAFq8GbBavtKISrcqEE8Kz0AgP7VeVgFNZXbGfK/aDlevpPlTXJky6E1UuWSp2ZWou1bm0Wi343Oc+59uHbAdufxjRzTAMw/SepGsAFq8GbBavAOqgHWqRY6ERHfk2q+q3ZrMJhULBY3GlFtZms+mm1SqVSpGm33WJpuV3VJZXnIcWp/PCmQBU1cGwtRZHo4Z1d2AYhmH6R5I1AItXA7aLVwBvRGE6nYaZmRnP3zQCkQmHTnDKG8W2bdu0vq1yXblcNk7X0GOYLK809Ynq5tRqtTxWXymcVUUGMpkMLCws+NodxQrMMAzD9JekagAWrwZsF69JfusaNHRT8BKVK0CUaZqwAWI4GAv7OWGRK7fFfqv1et0NztKVfS0Wi24uWQCzFZhhGIbpL0nWACxeDdgsXpPu7zKImNwJANqPxDcFcen8Z1UWUp3fKq3slc/nPedA/XjL5bKnagtbXhmGYQaLpGsAFq8GbBavACfEVLlcNkYaBk1dM9EIugFEvUGECRCTfqxR0lfp/GNxkQUskrG1llp02eeVYRhm8EiyBuAiBQnn2LFj4rd+67fE0aNHRalUEktLS6JUKomjR4+K3/qt33IT2DPxEJRsP2oy/uHhYbFv3z4xOTkpFhYWRKFQ8HxeKBTEl770JVEul8XNN9+s3H+hUBBf+9rXxKWXXupZd9ddd3m2u//++0W9XnfHx8UXXywOHz4sLr74YtFsNoXjOOJTn/qUuOyyy9zxtLCwIC644AKxsLDg+Z6uiAHDMAzTO1gDCNF3y2ulUoEdO3bAxo0b4bzzzoOHH37YuP0PfvADePOb3wzbt2+H4eFhKJfL8OlPfzr08Wy2vOKyoYJMKdNpYF3EOzM4xG3RDRv8hT9rNBqBVmCbp6EYhmGSQtI1gDWW1wMHDog9e/aIG264QfzDP/yD+Lmf+znxq7/6q+I73/mOcvu1tTXxK7/yK+Kb3/ymuPfee8W//Mu/iA996ENifHy8xy3vHz/60Y9i3Y7pH3FadFdWVsTFF1+sfBO/+OKLhRDCZ5W96667xFlnnRVoBV5YWBCTk5Ni3759XPKVYRimj7AG+E96IKa1nHfeeXDVVVe5fx8/fhzy+TzcfPPNyu3/7M/+DEqlEqytrbV9TNstr7lczhdViP0T5fpcLmfdWxfTHlFLzQrhD8aK2wrMMAzDxEvSNYAVlte1tTXx93//9+KSSy5x1w0NDYlLLrlEfPGLX1R+51Of+pR44QtfKK666ioxNjYmnvvc54qbbrpJHD9+XHucVqslnn76ac9iK8PDw+Lhhx8WjuOIY8eOiXQ6LY4ePSp27twpjh49KtLptDh27JhwHEc8/PDDbCVbB6ytrYlLLrnE468qrafSalosFkWz2XR9XKlVdmVlJXa/XoZhGCZeWAOcpG/i9d/+7d/E8ePHxdjYmGf92NiYeOKJJ5TfOXr0qLj33nvF8ePHxWc+8xnxh3/4h+J973ufePe73609zs033yw2b97sLnRa1DYKhYL4whe+IEqlks8p+9ixY6JUKokvfOEL1p8nE46g4C9MNpsVX/jCFzgYi2EYxlJYA5zAqmwDzzzzjMhms2J2dla84AUvEJdeeql417veJWZmZrTfecc73iGeeuopd0nCQ7pQKIi7775bpNNpz/p0Oi3uvvvuxA9axsull14qvva1r/muu7TKSovrl770JZ9VVgrYSy65RKytrfWj+QNJUF9wXzEM0y9YA/RRvI6OjopUKiWefPJJz/onn3xSbN++XfmdXC4nJicnRSqVctedc8454oknntA+TDZu3Cg2bdrkWWxnZWVFXHbZZcq3rssuuywRAp2Jhmp6CFtlVW/iHIyl5sCBA+Lcc8/V/o5WVlbEueeeKw4cONDjljEMw7AGEKKP4nV4eFi84AUvEA888IC77plnnhEPPPCAeOELX6j8zs6dO0Wj0RDPPPOMu+6RRx4RuVxu3Tx4V1ZWxEUXXeT6t2Ck/8tFF120LgYvE4zOKitR5Ytdz6ytrYnrr79ePPLII0p3CpnV4ZFHHhHXX389W2AZhukprAFO0Fe3gT179ogPfehD4iMf+Yg4cuSIeNOb3iT+/d//XVxxxRVCCCF2794t3vGOd7jbv+lNbxLf//73xTXXXCMeeeQR8elPf1rcdNNN4qqrrurXKfSUtbU1cf7554tHH31UpFIp179FBuAcO3ZMpFIp8eijj4rzzz+fH6yMECL+IgtJZnh4WNx///1Kf2Cajuz+++/nvmMYpmewBjhJOniT7nHppZeK7373u+L6668XTzzxhHj+858v/vZv/9YN4mo2m2Jo6KS+LhQK4rOf/ax4y1veIp73vOeJ8fFxcc0114g/+IM/6Ncp9ByZWeH48eOiWCy6QToLCwviwgsvFM1m07MdwzDRkL8nKVQvvvhicdddd4ldu3YpszowDMP0CtYAJ+ireBVCiKuvvlpcffXVys8WFhZ86174wheKer3e5VYNLqeeemqs2zEM44cK2J07dwohBAtXhmH6CmuAE1iVbWC9Mzw8LG6++WYxMTHh5u6kteqLxaKYmJgQN998M09pMkwHFAoFZVUyFq4Mw/QD1gAnYfFqIZlMRhw8eND1y5MJikulkjh48KDIZDL9biLDWM/KyorYtWuXZ92uXbsSHwjBMMxgwxpA9Lc8bD+wvTzs5OSkWxKuWq16yn1Wq1W3RNzk5KR1peEYpl/Q3wotubuwsKAswcswDNMrkq4BouizDQAA/RDN/eLpp58WmzdvFk899ZSVOV9lmoxHH33ULQUnwaXh1kOFDYaJgwMHDojrr79e3H///aJQKPiyCtx9991i9+7dYmpqSrz//e/noC2GYfpGkjVAFH3GbgOWcfjwYbemsfx3ZmbG8/exY8fE4cOH+91Uhuk5UStj0byu3/jGN8Qll1ziEa6XXXaZeOSRR8Sf/umfivvuu4+rkjEM0zdYA/wnXbcDDxi2uw04juNOEaTTac+UAf7bcRzrpgwYphPm5+dhcnJSO6XfbDZhcnIS5ufnfeuxS0ClUoHJyUmo1+tKVwHdfrpJ0G+Zf+sMk3ySrgGi6DO2vFrGhg0b3P+PjIx4PsN/4+0YJul0UhlLpsWSFtX3v//9YnZ2Vlx22WVKF4FeVyXjcrUMw0hYA/wnPRDTA4XNlleAE9alUqkE+Xze88Yll3w+D6VSqadWIYYZBKgFFVtKg4KtWq2WZzu5yO37ZcGgARq07bjNNgZoMAwTjSRrALa8JphLL71U3Hfffb6axpJ0Oi3uu+8+rlXPrDuoBRXnPzQFWUnLphBCmddVCNE3yyaXq2UYBsMa4D/pgZgeKGy3vGJLC33zkn9zKh9mPWOyoFKwZbNYLEKxWPR8D6/rp2WTWo+XlpY4dRfDrEOSrAHY8ppQ1tbW3EjoYrHoe/NKp9OiWCxyJDSzrolSGUtaNmW1GlmhZmlpybcuqmUzauYDE9SqjJOSc8ouhlkfsAY4CYtXixgeHhb79u0TpVJJCCFEs9kUpVJJLC0tiVKpJJrNphDiRP31ffv28RQisy4ZhMpY3Qiy4nK1DLO+YQ2A6IEleKBIgtvAxMSEMShlYmLCyikDhumUqNPr3XAb6FaQVRR3CNqeTj7vNoPePoYZJJKsAaLoMxavFtFqtSCXy7kPVdVDUT5oc7kc3/SZdUW72QZwftilpSWPOFxaWmorr2snmQ/C7C+sz2u7uW97xaC3j2EGiaRrABavBli8Mkzy6NTa2Y1UWXEFWbUrhAcxzRY+hqp9+HNOA8YwXpKuAVi8GrBZvAKcGJyywobuQeY4jpVTBgzTCZ1Y8boVzd/uVL+kUwEatwW4E1TXB7ejWCy6+Sn70T6GsYEkawAWrwZsF68AnDaHYXS04z/ZbYGnckWIQlhRPjc3p/283/cLkwjH1iIhBBQKBeXDmWGYEwzCb7obsHg1kATxOqjVgBjGNro9td6p5RW308Tc3JxR4NbrdchkMh23oxNMLwk0UM72hzDDdJOkagDO85pgBrkaEMPYyL59+8Tk5KQyX+rY2JhYWFgQk5OTkVPP0ApYMp0NrZQVBtNx19bWxL59+8Qjjzyi3O/Kyoq47LLLxE9/+lPP+l6n2TJVQGs2myKfz/e1fQxjA6wB/pMeiOmBwmbLqy3VgBjGBvB0vM6dQPrIdmJx7YWvaZjjpdPpgbBsqixGqvsZW14ZxkvSNQC7DRiwWbwCAFQqFc9DqFgswtLSkmcQp9NpqFQq/W4qwwws1F2g0Wh4PqfuAqurq23vu1dR/iY/OHnPGBT/OOoHjMtaDkL7GGZQSbIGYPFqwGbx2mq1lBYLOnDlTd+2ty6G6SVY7GUyGajX6771pVIJ6vV65Fyj/cpfqrJqYuHaz2wDpjbKe9kgtI9hBpWkawAWrwZsF68yClc1DYj/dhzHuoHLML2m0Wi4gUzpdBqq1apPuLZrJe1X5Shq1eyWBbjTzA6O40ChUFCK1zjaxzBJI+kagMWrAZvFK8AJi47jOMroXPkAcByHK9IwTEjq9brSHxQLV5P1b5DKm6qsmtiqrNq+HQtwO5ZllTWV3s9UabS4whbDnCTJGoDFqwHbxSsAwOrqqvKBm06noV6vR/LPY5j1ChaV1WrV81uamZkJlWt0kMqbtpv7sR2La1SfXtN3aNofamW1zXrEMN0mqRqAxasB28Vrkt+6GKZXYNGp88EUQkA2mzWKvn6VXw2qpCUD0ML6jvYim8IgCX2GsZUkawAWrwZsFq9J93dhmF6gSzdTKpVgZmbG85vK5/PG31E/yq9SEUhFNA0wq1Qqrl+vroRs2JRg+PN2LL2D5GLBMLaRdA3A4tWA7eI1yZGGDNMraFWnYrEI9Xrd9zuS03BB++pVqUadtVcKWhpgtrq66m6fyWR86XNw23O5HJTL5bb9WE3BYQzDdE7SNQCLVwM2i1eAZOd4Y5godGLFoxaMfD7v5hoVQsDY2Jj7O8tkMr48sJReijidVbfRaESyAtPIf5PgNrlA0OwGS0tLsZ8zwzAnSLIGYPFqwGbxmvTqGgwTljj8J6XvGBat8nfUbDahXq+70+1hhGgvRVxUa2+Y7dtxgRgkyyu7JDBJJ+kagMWrAZvFKwDA1NSUm/pG9bCUD9ypqal+N5VhukKcgVKrq6ueXKNUdGJrpmlf/RBxUY8ZZvsooriX7hJBcDAYs15IsgZg8WrAZvGa9LcuZn3RiaUsrkCpZrMJ2Ww2UNCZhE8/RVxUa2+Y7dsRuf2sjNXPrA8M00uSrgFYvBqwWbwCqANNqL8LrVTDMINGHJayTkUj9fk0fT+MxbXXIq4blleJSeQOolgcJDHNMN0kyRqAxasBFq8M01/iFD9hBVlQXtR2xE4/RVw3fF5V2+r6dBCn6QfJjYFhukWSNQCLVwM2i9ekTxkw64c4LWV79+41ToVTIRWn6OyHiIvad1HWRxGAgxggNUgBZAwTN0nXACxeDdgsXgGS7azNrC/isJQ1Gg03I4BKrOiEaJyis5ciLqrwxnleg7Z3HEdZEte2qXdO3cUkmSRrABavBmwWr0l/62LWH51YyvB3Zd5D+W+pVILFxUWj6Aqq/41/P+0K1G4I26jCe35+PrD4wNlnnw25XG6g/FjbgS2vTJJJugZg8WrAZvEKkGx/F2Z90o6ljFoDcWUpWjJRJ8bCWlbbtdJ206UgiigOI17L5TJMTU0NnB9rFNjnlVkPJFkDsHg1wOKVYQaHdixluqlz1b6EELC4uKg9ZpB1ol3/2EGJyG/HzSBof4MIZxtg1gtJ1gAsXg3YLF6TPmXArC86sZTprJrUihuHmGlXGA2KoOpWOwYlYGtQXhQYptskXQOweDVgs3gF8D60VdOtgz61xzAA8aWq0u1TLtgHtpNp5HaF9qBMZcfdjkFLlTVo7WGYbpFkDcDi1YDt4hXgxEPbNN1q29sWs77ohqXMJM7C+MCGod1goLDf67YlM65gpkG1dA6KJZhhuk1SNUBXxevu3bvhC1/4QlsNGwSSIF4HxZrDMO0yNzdntJQ1Go3Q1oMwVtyoAWE62k3DFPQ9aU1pNBrac5ycnIS5ubm2295J+1XtGQSXCIZZjyRVA3RVvL7qVa+CTCYDZ599NrznPe+Bf/3Xf22rkf3CdvHabDYDczE6jmPt4GWST5xCLcgKWK/XB97yis9B5m/UfT+TybQtYONOI5XUB2hU2OLL9JIka4Cuuw185zvfgfe9733wvOc9D9LpNPz3//7f4Z577oG1tbV2dtdTbBavrVbLzcWoiibEUYi5XI5vmkxPiPLw7saUs87fkYq+vXv3DqzPKy62kE6nXQGLvy9FeDtT8d0SmnEL4iAGTSiyry3TS5KuAXrq8/r3f//3cPXVV8OznvUsGB0dhd///d+HRx55pNPddg0WrwwTH+08vLsx5WwK3iqVSq6Vd5CzDWArcTqdhmq16hOu7QjDbk/x96qi1aAJxUH1/WWSS9I1QM/E6+OPPw633HILPPvZz4ZTTz0Vdu/eDb/8y78M6XQa3v/+93ey665hs3gFSPaUAWMXnTy8uznlHKeo6HWeV5WbQyfCVdcOeTxT+8PQK8vroApF9v1lek2SNUBXxeva2hrce++98LKXvQwymQy84AUvgD/7sz/zHKxarcKWLVui7ron2C5eAU5MMZoe/DpfQoaJm04e3t0UPnFa6XpdYatarfqCzDrpF9oO+jdtR9i+6bXP6yAIRZUopqJhvfr+Mr0jqRqgq+J1ZGQEtm7dCm9+85vhy1/+snKbH/zgBzAxMRF11z3BdvEqHzy4HCZ+wNXrdfaxYjomim9hJyKmm1POcfpHtruvqN9TCXohBFSr1dBtNR2nXUsspV9Csp9BYqaXETxd2wvfX2b9kmQN0FXx+tGPfhR+/OMft9WwQcBm8UofPNRCg33k2MeKaZdO/VjDPrx7Hewz6KiCs7DrAM1CEMdx2hGe/Z7C78e4CXPO+Xy+J76/zPol6RqAixQYsFm8AgQ/4Na7AGA6oxNhEsWK2k8L2iCi+l3LhxMO4uqWgI3a//0OnupVkBjGJPqp1XW9jmOm+yRZA7B4NWC7eAXwRyXPzMx05QHHrE/ascxFsYYNgu/iIIFfGFQPH/x7z2QysfmzdWrB7NQto93P+2mxV4l+LFyLxeK6fxFjuk9SNQCLVwO2i1ccaah767I10pAZHKJY5qJs2+8p50Flbm7OzfOq6pd6ve5+Hme/9MOCCdC+5XYQLPY6v2Scumi9vogx3SfJGoDFqwGbxSvN8abyd7E5xxvTOaprTosEhPkOQDgLVztW1H5POQ8qcZbMDUO/LJjtvsAMksWeiv58Pt/VF7FBK87A9IekawAWrwaSIl7Hx8d9flbFYhHGx8etHbhMZ6hEIV6nC7QyCSKTZa4TKyo/jNX0ql/6bcGMKkQHyWKvEv2qhPFy205fOPhlj5EkXQOweDVgs3gFOHGjKhQKPh8rPIgLhYKVUwZM+6ge7nhdsVh0x4h8uAc98MNY5gb9wZokkRzXufTaghk23VaQgB6EsaZqsyphPKZTiyv+XVN/Z/obXl1dbftYjB0kWQOweDWQBPGqChCg62wcuExnqMSHarzI9SahENWP1US/BOIgiJ24iOtcem3BDGo39uVVvSDR40f5O+y4DLtdv9wW8P4zmYwbjEOPa3N+TyY8SdYALF4N2CxedZY0PGCpdY1ZX8QRDT1IvoXtMkjTzJ0S97m0K4SjvqREabfKNaUTwR72u1NTU6G2k/7I/RpPjUbDFfnpdNqTz1MKV1vGM9M+SdcALF4N2CxeAQCmpqbct2+VP6K0ZExNTfW7qUyf0PnkhakAlCTRlwQRLon7XKIK0biyA6jaTSOm5fR4J/7Upu/i0pqqDA+6amNBAXXdtuTj9Ei4r7BwtWU8M+2TZA3A4tWAzeI16W9dTHyobmph0yIlabq934FJcdKvc+n0hcbUbpzXlp6PTpSFEey6bSqVikew0mPIqfdKpaINHAvqq25Co8tnZmasHc9MdJKuAVi8GrBZvAIk29+FiYdOLK+Sfj6k4z52mMAzW+jXuXRq+VW1W1WQQeXH2a5gp/taWFjwTL2rfEdxMYiwfduPDBF0sXU8M9FJsgZg8WogCeI1qZGGTOfE4fPaT+K2+krhoLM622aZAOhfYYFOLb+03WEtuXiaP6pYCyuadVPyQcfo1SwF7fuZmRlPW6vVakf7Z+whyRqAxasBm8Vr0nO8MZ2hsoKp3tLl+kETsN0KTMLWOyxMTNHZrVbLuP+gz7tFp5bXTq2E7R5f9T0cOa/aHl+bTgQ7/S4NdsIiPMoxeuUfbrJGY0Fua0lQJjxJ1wAsXg0kRbwmsboG0z7dyPPaD+IKTMLnrvOrlOvpuc/Pz0Mul9OWWGw2T5Rn3L59e0/9fju1fMZlJYwqJNtttypwKg7Lq0kAdiLKOxmvOujvmrpRVKtVj6sDzQPLJIukawAWrwZsFq8Aya5rzHRGNyps9YO4ApPwVDC2TOnWA5x4OJTLZfc3Rct+Ukv29u3be/KAaEckBUXg48/DvshEFZKdijvsMhBmLOjOSX4XFxSgD/52x1u3A+lUMwjU5SGKjy5jN0nWACxeDdguXgH8D9+ZmRntw5hZX6hER1Di9kF8O+/E2ian9HWWV3rjp2Kt0Wh4HgpSwFLhKvfZ7f5rZ3pa9SKDtysWi+A4DszPz7cVdBVWSJrajSP/VYJZJ8p07aUvaioXGsdxIJvNah/8ugIA7bhFxCkkV1dXQ6f/GpRZFKZ7JFUDsHg1YLt4VUXG0rcufvtmkkA7fo5YwJh8XrPZrNHnlQbwjI2NQT6f9+yjlxG9Yab8y+UyzM/Pa0WjdBWhgR1B5U3l/tuxoOrajduYyWSgUql4PsdJ+VXT4VSwY3HnOI5SuMp1hUIh1L0zqltNtwPpkpTCjmmfJGsAFq8GbBav9KGk8nfht28mCbRjyTJNjVNhUSgUAoOuVBHo/RCuElNb5+fnoVwua0Ulzl9KrcdBfdtpYFIYFwSdaIwS1IW/l81mlcIV+35nMhm44oorjFPyYQVhty2vkn7nmWX6S9I1AItXAzaLV4CT1TVqtZryZlmr1aytrsEEsx4eXp34EOqmi1VRuWGEhcovkvrBUnp9DXTiUmWhkdZMakUOshJKq58uIEiKvLm5OV/bTAT5tAYFIJkKIjiO49kftcjKfesqasn1UTIwdMPnlWEwSdYALF4N2CxeO4mgZuxnPUwbxhG9TS1tWKjl83lXyIbZj8pKmUqlQlsDe4Wuf1TW46gFKyRB5VFlSVd57mHHK65mFYfV0mQFjfs3FMd4ZZiwJF0DsHg1YLN4BWgvgpqxn17llOwncZ6jydoaRljohKtJwPb7GpgsgNRyHNVKGPXaBAUY0e0XFhZCWYLD9qnJ/zSu2Yv18JtkBo8kawAWrwZsFq9Jf+tizKwHK09clrFWq+WpQkMFjElY6IRvtVqFVCqlFLCDcg1UVkeV3y52mwjb9qjjL+z6xcVFo+UVT+sPkv8pwPqYDWEGh6RrABavBmwWrwCdVQ1i7Gc9+NfFYRlrNptuSiSdgFEJC5rnlQq9er3uEbDpdBoWFhYG6hqoyrA6juMrKUn7IoyVMOr4C9p+enrak1WAPpRxoFk32hcH68EPnRkckqwBWLwasF28AiSzXjsTnl5almzEFLRD+0n1W5mbm3MFqiqwS5eFYBCugc7yWq/XYX5+Hkqlktbnt1uWTd32i4uLHsGKA1Dw9CcWtnFahhnGVpKqAVi8GkiKeDU9QGwduEx4up1TclCIatWKS8DceeedntRTlCNHjhjdEvoBPkeVFVPeG0xW1jh8SsNsv7CwoJz+VFmTwghkk/9p2HNmCypjC0nVACxeDdguXufn58FxHI/1BFuWcOUcJpmsF8trVH/CuAJowqSFKpVKsG3btoG5BlScVyoVbf5S+eDTWVmjpIbqxPKqa2O1WvVZtsP0bSflkaempth3lbGCJGsAFq8GbBavrVbLrYZDpzRpkInjONa+fTF61oPPK0D7QrTTAJowx6W/s35fA1NFLdlm2b5cLudalFX3h6D+idvnVb4gqARuO1ZtalHVFa2gxzS5JXDWAGZQSLoGYPFqwHbxim/wpoFbKnW/5jrTW9abT1+759vp9K/puPg31k7EfrcIk4O1XC5DLpdrW6R1K9uAXK8KNNNZXsPe28K2wVRhK4m/LcZOkq4BWLwasFm8AoAy6IJOGZRKJSunDBg96zWnZL8szarj6iwequ/08hpEqX7VyQtBN/O84kpbckmn055yl3I/Uafww46hdsYa+8kyvSbJGoDFqwHbxSsAwOrqqtHvbHV1td9NZLrAes0p2S8fX9Vxs9ksOI4zMNegnZeadl8Ioo4/1fZ02p6mwcJpyOSDGFtFcXWwKC8IYcdQlLG2Xn+PTP9JqgZg8WrAdvGKb5iqiF++YSabKJaeJFmF+pVdQXXcQevXdqyp7b4QRD13/LdK7GGLqwzSGhkZ8ZT0lQKW+vNFfXkJO4bCbLdeZ0KY/pNkDcDi1YDN4hXfMFX1ydu1SjDJI0lWoUGyvA6q32MUa2o/ckTqgqfw/Wx0dNT9vNFoeO5vhULBTU2WzWYjX4NuWF7Xmw8603+SrgFYvBqwWbwCqINGlpaWtIEkzPojSVahQfJ5HXRBEkZ49bM6j0rU0bQ/2KJK73VhLa5BgWa6imjtXHMbxwljN0nWACxeDbB4ZdYD3bIKtTNlHuY7urRNsq1U1HRTINhsUTNNeQ9CXXRTIJyqT6O6i9AZB1VWAepnK9e3e81tstAz9pNkDcDi1YDN4jXpUwZMvMRtFWrHFSHMd3K5HORyOd/UNh7rNHq2W9Zjm63WQSKq1Wp5StvKsrG69ZK4z7EbU/iynfjaNRoNz99YoNIMB53meV0vFe+Y/pJ0DcDi1YDN4hUAYGpqCjKZDNTrdeUNs16vQyaTgampqX43lRkA4rIKtSPqwnwHp5+iU8J0SpnejLvlt9trf+E4AsCCXlQqlQqUy2W3v6VQzWazUCgU3ACpoaEhT1+bzrWTdgeJvXZfvOj3TJXG5PadVthiyyvTS5KsAVi8GrBZvCb9rYvpDnFZhTqNatd9B49buo1pShmge5H9vcooEIdQDtPH0rIoU33V63XPiwO+h5TLZZifnzdaHDtpd5DY69RtI6yPq0SeVzvXnH1emV6SdA3A4tWAzeIV4MTNUkbd6vxdCoUC3zQZAIjfKtStoBYqVMOKgEFLWxWFOFwUgvZRqVRc4Sr/lRZu+lKTSqVcNwKTUOyk3UFjgU71t+u20QtrqM2+0Yy9JFkDsHg1YLt4rVQq7pSfbuCm02moVCr9birTZ9oRmmHEYDvCAIsonbXNcRzIZrOh95uEdGBxCCBdP2CRmclkYHp62mPtHhsbU1pe23khMbVbjindd7DvKZ7q7/S6dtMP1WbfaMZukqwBWLwasFm8rq6uugIgnU57EnkLISCfz7uDOpPJWFtlg+mcdkRRFDEYRRjgB73qO7hN2KJg2m8Uf1qT1bLbRH0ZaHfqOYwFUgYt0anGVCqlFLJBxw7Tbly6VnW95JjC0f+yvGw756tqW7csr1HK8kZpOwtdRkfSNQCLVwM2i1cArwVLNXDloLXxrYuJh24FV2FhQv0lg4QBjmbH39GV/gyzX5NAlxZcXcqYXlhlo7wMdFNsUf9iWQxALtVqFZrNpu9+EsZSaWo3HVPUokrHoRS4nV6TXvqhzs3NGa8xPackzBYw/SXJGoDFqwHbxSsA+KrP0Gk/nSWAWT+085BsJ7gq6hQzTseE/21nv6o247yhOvHaiynddl4gujnNjS3RKguryiIbtgSrqd30+sh7k26sdXoteumHGvUar66usqsBEwtJ1QDWiddKpQI7duyAjRs3wnnnnQcPP/xwqO99/OMfByEEvOpVrwp9rCSI12bTX3nG9LBm1idxR0+bsgLohIFq2ppa6vD0VzuCQ2X9a6etUfozyA3BFPSkWt+Lae49e/Z49j8zM6N8qRgZGXEt11FcB3Tt7pUltB9+qFHFci/FNZNckqoBrBKv8/PzMDw8DB/+8Ifh61//Olx55ZWwZcsWePLJJ43fe/TRR2F8fBx+6Zd+aV2JV3yT000Z8M2P6QSVIHEcx5i2KoorArXUmSx9YQWHyvoXp2jClmyVVZu6AKjcAXRtaKedUV9MFhcXlRbXWq3mc+col8u+IKogi3pQu6OK83b9QvsxLR/1+vXSrYFJHknWAFaJ1/POOw+uuuoq9+/jx49DPp+Hm2++WfudY8eOwQUXXAB33HEHXH755etGvCY9xxszOKjEYBwVtlQiJpVKQTabbVtwmIRRJxZNnP9T/u4cx3H3J8U2PgYW+TjRv6l9qpcCuk/c3qjXodFo+DI94KAOvD6TySin9oNSXoWxIAaVrjWdX5TiFP0IiIo6zkzbc0AXoyPpGsAa8dpqtSCVSsEnPvEJz/rdu3fDK1/5Su33rr/+evj1X/91AIBA8fqTn/wEnnrqKXdZWVmxVrwCnKiukU6nYXx8XPnmPj4+Dul02srqGuuJQX5Axf1g1aVKwuM2yL8ybDS9yorVji+pSXQXi0X39zc6Ouo+LHSuCgBq4dZqtSCXy2mn+vDUYC6XixxYpyqBWqvVfK4CWLjSIA+VUGxnet40pnBfq/ats2QP2sM56jiL6wWRWV8kWQNYI14fe+wxEELA4cOHPeuvu+46OO+885TfOXToEIyPj8N3v/tdAAgWrzfccINvusxW8dpqtbTBKNQHxnGcgbqxMycZ5AdUt6Y0u+HrF2afUTMYAOjFGd5vKpXyTdfphKtOuDUajdDidfv27cZ8qSofW5qeSmVRxcJ1eXlZ2x+UdjMpqF5aqOVZd/1KpVJgxbV+EYflFVv1e+Wzy9hF0jVAYsXr008/DRMTE/CZz3zGXbeeLK+tVstzwzMN3FKpZN3AXQ90GlTSTYttNwSmbFPcgTRh9klv5FGEuO6cVSm/TIIl6GUAl2nV9bks6arbb7FYhEKhoAyy0olMavXbu3dvYJ/jvsf/mj6P+oKBBSy+fqaXg34Tp89rNwINmeSQdA1gjXiN6jbw5S9/2bV6yGXDhg2wYcMGSKVSodJD2OzzCnDiYVQqlbRphYrFIpRKJZ5WGmDaFYlhrF2yLr0Ok+DoZqR2N6zNpn3iGzn2p1VZJ3WYRIZuMaWJ0rUBZ2AIY5lUnSMW6bQ/6LWKaiUM2+dy3/I6tps7WPaBKpp60IRb1N9yO2KeA7oYTJI1gDXiFeBEwNbVV1/t/n38+HEYHx9XBmz9+Mc/hq997Wue5VWvehW8+MUvhq997WuhHqi2i1eAE1U2TA8g26pqrEeiWmvCCAFsedOlwTIJxG67M3TDaqzzsZV9lU6noV6vez7HfZ/JZHwVkHTbyiWM5bXVakG5XA79MoB9U+m+TIInamGBTtxC2nnB6bRQQzuFE3pFN/O84peWQRXuTP9IqgawSrzOz8/Dxo0b4c4774Tl5WV4wxveAFu2bIEnnngCAAB27doFb3/727XfX0/ZBgC8AkOXHogd+u2gEz85KmLiSsw/yIFkUZibm3Mj6VV9Wq/X3c+DLMmq1F4jIyMev1c6rV2v1yGXy0Eulwv9MhAl2X87lslO3EJM/rYAYEytFWVM0T6g4tV0fv0Yu1Ff+LpVgplZPyRZA1glXgEAbr/9digWizA8PAznnXeex1Jy0UUXweWXX6797noSr0lPk7EeifqAYn+58OgEVZT+UL1gSJclaYWVAgv3v7TOlstl4+9QJQqxUMNuDapt5HHjsNzrXm5MmRdKpRJUq1Xji0JYOjm/fgZBRhXNYbbvxLWDSS5J1wDWiddeYrN4BThxEy4UCr4bOx7EhUKBb3IW0O4DyvS9TqaFu02UQJ+46KQ/qHuBFK6yz1WlbYvFoieHahg/fFMbM5mM52WevuykUik3vVUcPtNh02KpxmDY8w3qg2Kx6LG4ypkE3fn1o7JWVKII3EH+DTP9J8kagMWrAdvFa6VS8fjcqQZuOp325WtkBotOH1Bhp5gHxWojhVOlUlEKKCmc5OfdqoAUtj/o9ZHtqtfrrm8xdhWgEf+qnKlhjoOn4aVgln671D0En4vKghtXtgpdG6vVqqcd1Wo18HyD+gD7euqyEKjOrxOXiG6je2nAbVf5/eLgu0E4D2YwSLIGYPFqwGbxurq66nmgqUrDYauPrU7bSafTB20YMTZI/nLYMqaaXlZZOOO2kEXpD50lD4sNHBmvCqwJY4EMshjitFzpdNq1tlB/W+rj3I0pcpWrAA1ca0dUqfoAiz2VWNWd3yBaLHXXWJ4jzjRRLpfdIL9isQiO43jOcRAsyEx/SboGYPFqwGbxCnDirUsOXl1d47BWH6b3dDrFGeYBPYiWV9wmeXOVgU2q9XG21RTJD9B+En6ZlkwnjMOIi6Dj0Lyy1Nqry33aqxKo6XQaqtVqRyKxnXKwYSquDeLYly82OBsGFe6lUknrt2hzMA4TD0nWACxeDdguXgFOPIxVkcbygdau3xnTG9oNLgljsR3kHJEqAUv/DdvGsNPf+Eav6o96va4VA6ZjzM/PQ7lc9ohvLJZM+41ynFarBRMTE77fedA0etTjhPkcQO8qEGVa21RCOMznQQzSrIPEZLnG6dyoVV/Vj2xxZZKqAVi8GkiCeG02/cnJdVOIzGDSToRy1IpSg+gvp7KMRbWQhRX/+/fv9/mN0jZIARFlGpbmkVUJ46D9Rrn+8/PzngANKsjCWOPiiMbHfriqaxZGSHc7K8AgWl5NbdONn0FpMzOYJFUDsHg1YLt4xW/muikDVZUdxn5MD35c8xpXlJIMkr+cKm9qWAtZFLcLLFzp9ng6PpPJwJEjRyKdA/VHrdfr0Gq1lOtx2wGCryMVcKpALXruJt82VcEEXXS7HBsmd5VMJqN1FTCJz25nBRhEn1cKHfu4H7sptpOSv5lJtgZg8WrAZvHaarUgl8u5g1SV400O3lwuxzekBBJmKrtbVq04iMPyGjbgTWYImJ6e1roOZDIZmJ6ejtQvKstrNpuFQqHgy/NKg4zm5ua0Am5+fh4cx/H4O2J/XZrRQBXgpGqrfNjJ72WzWffhpsqFqxLP1GfTdB1MY7TTYMVe7zdOdFZh6ooRt5tDP3PgMvGSdA3A4tVAUsRr0HSljQOX6ZxBtrDE6fMa1sqGS3KqouMXFxfbsvbhaHFqFS0Wix6fVywQqSDFllBaJQ3vG/sy43RSExMTWh9JGvxDS46OjY35+p1aP6OUNA3bf3FYSKmPLG1jkGU5boL2Sa+56p7dDcurDTlwmfAkXQOweDVgs3gFUE9XmtYzzCDQjWwDYf0bddbesFHypqIK8/PzcOaZZ/qm7qSAwmVoTX7IS0tLnv1gCystPStFply3adMmX9+1Wi3POcu8jypfuXQ6DY1GQ2ul7IblrhPfVFV7aHot2p5uWhfDZIxQpYij9+xOszbosMEqzYQnyRqAxasBm8VrHIEiDNNr2snzGrasatjIcppyKqxYDpqSNwVN4IjyVCrl80NTCbitW7e6+8QlaOXn09PT7nfpdlgE0qTlUjy3Wi3fNPXY2Fio8rIm2rnXtJMVwGRJpGVV6T2wWxZXk2UTB7nhCmS6oEFdSeNOscEfmAkm6RqAxasBm8UrgDq5NX5oRUnRwzC9wlRhC/uEVioVyOVykMvltD6UeNuolleVgNVZKIKEyeLiomd/uVwOxsfHfUI2lUpp87Gqyr0eOnRI6xecyWQ8rg6O40CtVvOdF94ftuaqigu0Y/1U9VWUzzuxvMbpgxsHYSybuMwvHVf0nt2tqfxO+pwZHJKsAVi8GrBdvAIEW51se9ti1gdyXNI0UFLMyih3HBlverCb8rfqpkap1THoAa4TJtPT0x4BLIMkisUijI6OevZfrVaV+1FN4WOrrU5g6twudAsO4sD7qFarvvXtBAtFdSuIwwpIx0E72Q/iJOicaN5N2me6F7S42x210hwzmCRVA7B4NZAU8Wp6i7Z14DJ2ENcUss6yGWZKVTXlr7LIUQsX/c2EmWKj+/3c5z7n2UetVtP61QpxIqiKBkNRQZnP5z1/U1cAlYDFgo3mX8Xb1Wo1GBsbUwpqVbRyFEtc1IAg3bR4O/6XceSdjZOols1eB1eq2qe73pyBYLBJqgZg8WrAdvFK0+nQt3xVTWyGiYu4g3d0osUUzKLym1XtD6emwsKV/mbClFI0iVPZDmotTaVSMDIyEmhtlQKi2Wwq3Q5M0/xy32FdB/AxcZlZLJyj5ogMGxBEXyaCrl0YcWeq+BVUqaobDGJ1LwBv3zqO4yl6QQVsr0U/E40kawAWrwZsFq+qdDr4QUErLPFNh4mTbqXdMU25qtIIqfxm6f6wgI7L2keFyYEDB9zvj4+P+0RioVDwieZGo6GtlqVzI5idnTUKWFWie52IrVarnmNg4VwqlXw5ZMMS1hUgrpcf+gDHQh+fo6pgR7cYVJ/SMC4rdBwMStsZL0nXACxeDdguXvHN0TRwS6WSdQOXGXzCWtmiPvR0D35dAvewU65xCW7dlGu9XveJ0dHRUa1fKi4WgM8TWyWpCKa5cOlCK4nptpuYmIDV1VXtwy8oWr/da0j7vNPpctUDXBeI1qsHeBx+vN3ANP7pM6NQKPTFWs2EJ+kagMWrAZvFK4A/8bhqyqBUKlk5ZcDYQbce1N0qndmptc805ZrP533+pHIKHrs3yIIDUrg6juPrN1wJjPpyptNpuOOOO7S+rSbBL78vXSNUlbxoUv92/R0XFhaULxuSOB6mOquhKgVYO2Oxk8wJcb7QxYVp/Kus/SxcB5skawAWrwZsF68AJ6oGmawcpjrnDENpxxIW9xSpan+6PIbtHKdda1+YKVfVIq2yWPSqrFrYNxOf76FDh5QC1mRhlcFZun7EIhWnJ1M95NoRmZVKJTCAanJyEu688862roX8TFoSTX678rxplH8QUV90bKlgZTruoPrpMnqSqgFYvBqwXbzim6vqpsNRokwUOrFKxvXQowIRTwHjPKy9tmTRtF10yhUHV6VSKY94ktbASqUC6XRa60vabDZhx44drqsATmSvEoNycRzHTSN2xRVX+Cy20rIrhbEuKC0uMUUj/2dnZz3XimZ62L9/v3I/Ye5ftJoWfZHIZrPGAhSmimntCNFuVCDrFYPqp8voSbIGYPFqwGbxqrM64AembiqQYSidWI3ieuiZItKD0mHFMcZN35+fn4ft27dr+4Za+uhvEFtbs9msL4q/0Wi4ovaMM87wCcxWq6W0wGazWbdNsv2Li4vudjjamLo8dEOU6Kzm2ApMrcRYpKv2E3Rt5Weq61AoFOCBBx7QTuXLLBRB5xLFBaDXaa/iYFD9dBk9SdcALF4N2CxeAdT+XrQUZNRcjcz6pZ2HdVwPPZ14VlWQweViVZaFdm7SMo2Wqr04sGnbtm2ebWjAkMrygfsDuwVIKzK1qo6Pj8OOHTt8ifxpcJcQArZv3+7ps1arBblczj3GGWec4T685PSivD/kcrlYS6bSa4hTdqXTaWWmhDA5esOMIRq8YhLPNMdsJpPRui8kTdQFuf3gl5pB8dNl9CRZA7B4NZAE8Upz9NGBWygUrBy4TH+I8rCOOzhFN+WKhSotF4s/l9tEnSabm5vT5oudn5+HYrHoifrHD/h6ve5+pkrlJaezZZvwlHo6nYYDBw54/sYBX47jQKPR8PyeVVH08jvSWr1t2zbP59u2bXNTitXrdaV4jWt6kV5DnKOXLtSFQI63dqLcm82mK+7lfRDfG6WApaWEZdtU1l9JvV43+u92kzituKrfF7Xe0Zygg+Kny6hJsgZg8WrAZvGKLSz5fF45ZSCn0KiFhWFMhHED6FZwStD0sM7vtN1j4vOgVsBWq+X5XaVSKfdBQf1xcT+pBD9ui0rQqQKvaKUt3L6PfexjSgFbLBZ9GQ8KhYLbb3IfOgtb2IIAJmiAiCrjAU3rQ8ebLidrkOVQVjCT62n/HTx4UClcw4wpvPQikClO/1nT75VGrMeZcYLpHknXACxeDSRFvKrqn+Pk3DYOXKa/hElz1I/glLitvfS7WCBScZrP55VlZVUCP6g99Pd60003eQQsFaC4XdKKescdd3i2GR0dVbarUCjEFvgW9ZrrxJ9MXaWry14oFKDVannuW2Esh6VSyWc5VPkj63Lv6q6hzqreLbrxcmj67QRZu/n5MXgkXQOweDVgs3gFUKfWoTfnbgVmMP2lm0EhYdMczc/P9yU4pRt+iCahkk6nXQFUKpVgZmbGKFxV+8QCQyfoVMemx6BlVd/whjdotx8aGlKmjGq336IKKuxXqjqvrVu3upkSVFYjmUFBjjOT5RDnqsU+0bJd8iEf9mVDVdmt1z6v3X5RS4IP73onyRqAxasB28UrgL/u+8zMjNLCwvSXbvuuYTqxeFKfTFwcgFqpqEjo5JyiEsa1IY59SguGSXBmMhnt78xkiVQJ4ZtuuinwGPjlwlSoYPPmzT4Lrq7YQ6PRCLyWtOqWyXqHx4nJmi2Et4oYnv6kOWnDHBtnX8DXQBVUV61WA69/XAFl7dLtF7W4fjtM/0iqBmDxasB28Zrkt64k0SvfNbmvdgMsdNPnKiGiEgmdnFM7n3cjobrKP1OeJ/1sZmYmlJBQWVxpv+oWLOao5dVkpdUtqunFvXv3guM4UCqV3LRRuM8bjYYbKNdoNHznsbCw4LYxm80GpjjTBXHl83loNpu+hzF++JrEnDwHfDy8PS21m0qlfA92Oqa68TuLSjfEJhcjSAZJ1gAsXg3YLF6T7u+SFHrtuxZFTJnaSf0AscUsk8l4rGxBOTpNFV7aFfYqaxo956hj3hRIlcvllH6POn9JSlD/zs7OevadzWY9FaOwgA0jeqlIw+4DQ0NDynOU1/bQoUNun1MXEllaVmeJdhwHWq2WL4MDHSOHDh1SilfVdH2UvML4s0Kh4PYbFq5jY2OeDBEq/1/cH2Gt6t0kTrHJltdkkHQNwOLVQFLE6/j4uNJnTFb9sXHgJole+661+8ClQlL3MKfiBR9PZV00lR1tR9g3m/60SCqLWxRhQa19eHodiz2Z3gpb+2q1mivUqFhXBRxR4Vqv131CXPp8yvU04fji4mIoy6tsu+M4Pr/PsbExYzCT4zju/1OplLsvmVaKPixphgCZO1c1BprNJoyMjGjbHTR2TGIOjw8qXGWWg1qt5hPs7UzP9+K+GqfYZJ/X5JB0DcDi1YDN4hUA3HKTeLDSHG/SUsL0l175roVN+6Oz8tJ1VCQsLCy4n0Xxj9UdL6qwpxZXKUbw9lEry9DzwEIc51AUQsCWLVugXC5DvV53BRIu57p//35XcKkE9Orqqkew4yn2bDbrsRZu377dE4hUKpWgXC67ojBIuMq2TUxMQKVS8T3cqLDDIh1ba/E9Rm6fz+d90/Aq/zoctKXyXZ2YmIClpSWfiJZiNGjMqMScrnCEaqyYfjftvlzG6d8e532jGy/RTH9JsgZg8WrAZvGqqiijGrjyhmTbW1cS6YXvGhWQnTygwrRXNdUeZTpd1TbdA1pXDhFbW/HYD+PrhfdJLdYqESQFm+M4vhyiDz74oKfd8rtUQFMLN/5birvt27e7x8LJ4+V+3vKWt4QSr0IIOPvss908r8Vi0WeBVaXmkgvNNTs+Pu7bdnR0NHQaLt06ldVIde3CjpVm058iS1Xx7MEHH+z4hQ8Tp397nGKzm77yTH9IugZg8WrAdvGKH6w6Xz35oLVt4CaVXviuqaoWdSJcg/bRbiBTmHOh38XiQNVGHDgU9qVA7lNVYWl+fh6y2Syk02l3mltVUGDDhg1unlWVsKbI3yP9V/5fik087S/3g6e8dQu2BlcqFfccH3zwQZ81GS9btmxRrlfVTsdj2OR2IfuAWp1VPqpYcNKXjyhiTiWIafCb/L6pNLDcfxjBGadA7IbYNI1zfJ4yaI8ZbJKuAVi8GrBZvAL48xuqHji03B/TP7rpu7awsKCdso96rKgigR6n3XMLK+yDgnfaia7V3dhbrRacffbZWgGXSqVgw4YNgQJJhclK12g0XLEs918qleDgwYO+fpYClwZi0etwww03hBa9KoFKC1fQ/eus8M1m0z1XWWBB5epRKpXc0q3SJUN+XyXmdOPAcRyPrzC1wKqsunFN9cdpLe1GSrwgoS7dWPiZYQdJ1gAsXg3YLl4BTtxUdVHS9XrduretpNJN3zVctx6vV6VECiKKxQeLhFLJn7OU5tEMe05RxW830/7Q0pmqAKeowl3mTDUl3d+2bZtSoOqWiYkJpUVV3hfoZ7lcDvbs2aMVsNS1IJfLucEfKqEuXxjomFtaWvKdq8wpq3IBkQFvOMuBtCxSq7sqCMxxHJ/wpeNDpuTqFnH+1uP0n2XXgWSSVA3A4tVAEsQrDohQPUB1U0RM7+im7xqtuIQFLE1gL6PEgwhj8aEiQWXpDZsgu5OHfTf8iCVUYIUVribhjkUX/u1ia6Iq2Mi0pFIpuOGGG6BYLPpErszPSr+Tz+e12Qqk9VVnhc3lcp40XrJfRkZGlL52Ol/X+fl5mJiY8FmqqR8yDjahAV9YZK2urrruFkEzA932AezmuIyrXZ3ei5jBIKkagMWrAdvFK7ZO6Pxd6M2f6S3d9F3TPXhw6ibqnxlFJJs+wyIhKCes6ebZycM0TguX7jzxMaIUBVAJd7yvXC7nZi2g7h+6KUDVIv1sVQt2Z8DCFItZnUDFQpXus16vG/vFcRxt+jK8bu/evdpgKeyziv2XdeMijFtCoVBwXTGi+ES3y6AWAuj274bpHUnWACxeDdgsXldXV5X15/GNSC6ZTMaYKJ7pLt3wXaPiUiUmdFWy4nhA6XKWyv3W63V3fOp8UDsR9t22IOFrhqfkgsTe2NhYYOQ9dbdQWa2DjhO04DynePm93/u90CIcF6Og4lQ3VRkkNFUWSZ3Qp5kjwmShkJYmKlyxe8PExETXhdqgWl4lg94+JpikawAWrwZsFq8AANPT08oHAH2oTE9P97mlTJy+azpwvlLVA6kdK69pG9U0LW2PFFG6aFdpOdBZBlTCvtu+e3j/WGgGiT75OZ6S10XeU2FnCsRqZ9GJX7lP+jm1sNIsBYcOHXL9ZrPZrCdAEAtMLCh110IV+IWvI54GVQXJhfHFVn1f1fd0fMTxO7XFsjmolmEmPEnWACxeDdgsXvEDFlvYwpRXZJLL3r17jQ+kKFbeMBZj6VOps6zKsaiapg0rMlXru2HN1rVNlmrVWTNlGi1a0pWKXSrSg1wSOhGvpiWXy/kCuGjuVlyMAgtRVUne2267zefGgvse/03LzdL7V7Va9bkShBVZ9Jrhgg8qtwSaFko1pqi1P2hM2eJTypZX+0m6BmDxasBm8QqgnrrFNyJTeUUmeYR9IIW1uIa1bpbLZe0+seCJ+2EeZDGLYlHTtV22UWXJ3Lp1q8evTIrWUqkE8/Pzvsh71UMkbJnXOBd5LvJBR7MImK4JtZrKwDSTpVV+bqrIphL6dPo/jMiKsj1OG6Ua71ishnnRsiWa3xbLMBNMkjUAi1cDtotXAHD9WHTWCdv8XJj26MYDqRMrksk/dWlpSSlo26WbVthGo+ETVjjaHlv3sI9vvV73WSmpb+f73vc+nxWyV0s6nYZGowH1et0jzMfGxozWSpO/qmlcqKzMOn9fIQQcPHjQOKZNuXzDWGp1YlXuH19X6qMsxa6KqGOxF+5E9Pg2WIaZ8CRVA7B4NWC7eE3yWxcTnm4+kNoRxapE6CrhE0fEd7etXc1mE7Zu3ep7KNCAIMdx3AT7QpyM9JfCkGZ7eOCBB7TCUmXlPe2002IVr2eccYYnK0QqlXItsKVSySfW6DjA39X59equEQ3ym52dVYpr3B48pk1V1KJYXnUBZTIjgRDqohNBL0NhBWm3XV9Ux7XBMsyEJ8kagMWrAZvFa9L9XZhw9OKBFHUqVpf+iFoGCoVCLOOyW+JdVTtcJ+ik64QqAj+fz3seLuPj4z6BmkqloFqtupHw3VyoGJfWU900ucryCOAPCjH1sym9G16uueYazz7Hx8d9L0E4gAu7rLTzokW/s7CwoHTjUF3zTu6r/RKSvRbMTPdIugZg8WrAZvEK4H146CINwyaKZ+ylFw+kqFOx1NLYbDZ9Sf4LhYI2OEaF6fM43CZU6cdkkFaxWPSV4KVWOHz+VJjW63WoVCrGwKx8Pq8NCotrSaVS8NGPftSzDhdUkNW/5PmXy2U3E4GqH6lfLw70Cupf+t2DBw8CwIn7F86KoHJLwL7Fqusf5QVGJaTpywW1tscxtd6vKfxeuyow3SPJGoDFqwGbxWvS37qYaHTzgdTuVKwcf8Vi0RPNnkqlXCEr9xOHAA9qp6kP5ufnoVwuKwWE9GGVSfCpsMD7VUXTy3NWCVNTXfJeLdh/VOWTia+NzpdZtS8TQWndsC9uJpNRvjjgYLBOrZj05YxmX1C5D8RBHC9dQbBYTSZJ1wAsXg3YLF4Bku3vwgwGnU7F6upth5mWVu0v6CassxCbxDEuyZrNZo0ldycnJz15SHF7VH2lKym7ZcsW91xp0JQQAt797nd3XbRu27bNI8joedJsDbgPVdPtJl9U3fXMZDJaf1lc6EIlcDGdvPzoXBjy+bzv+hWLxVAvQ2E+Nx0/LuHKbgLJJskagMWrAdvFK0ByIw2Z/tPpVKyqOhOeoqb76TSllk4EUDGqEse0mpMsM6qrIEYf+qa+oiVc5d8TExOwtLSktLxiMbtp06aOK26plmKx6Dk/UwlhbOWhFaukmKV9SC21qn6SpYN1/UdTc8n7Wjup0VTrqCsCFqvFYtHn2pDP52ObKcB0o2AAB2itD5KqAVi8GrBdvCb5rYvpL3E8+FR5Tum+dEFCUadQg75LRahKNFFRppqqpn0U1FeqoKZUKgVbtmxRWvrodPWWLVtcUR9X0QJqccWZA2R+VV0f4xeS0dFR16VC1YelUgnK5bLHBSHKmMIWbjx+5ItFp8KRWv9V56DyUZ6YmDBWlosqCrtpeW33BZRdDewgyRqAxasBm8Vr0v1dmP7TiXVJJdp0lr0gP8qowlX3gMY3eN10NbUghhUSqr6iQRPZbFYrQPP5PDQaDV/lq1QqBYuLi7H6xRYKBdi/f7+vn01lenFfS99dfG60D0ulkrsdvv/QflJZZlW+xfi+pstmQa95UNU2KqRx2/C1kz632C3CZJGP4rPaC5/XqMdgVwM7SLoGYPFqwGbxCpDsSENmMGjHAkPHn6qSkunBHGUKNao178iRI0o/SmyJpX6OYadwcV+ofoOtVgsWFxeVgnJ8fBzq9TqceuqpSrFJRW2nSyaTgT/8wz/0rDNlCqB9qirAcOjQIQA4EYwlP89kMu79R/aPnMbUiSBsccXXFK9XjSPd93ToysFSn1wp6PF5q6z5UYVnJ245UQn7UsiuBnaRZA3A4tWAzeI16W9djJ3QEqCqNEemcdmO5TXIUiQzAEgRQt0ZZmdnXWufysIZVUCsrq4q+0CeH3UNkIsq96vq37iWsDlaVdAXDCn09uzZ4547tpDibA3UskrLyKrEk2p6FO+/Wq0aLbI66Pijx6cuFGFdG4KOH0YkSqFsKkcbllarZXwpNFXE66aoZton6RqAxasBm8UrwMn0PiZ/F+xzxjDdhOY5rdVqns+pML3qqqu0n0e1ZIWdHtaVI6ViLp/PQ6FQcKe+oz6sp6amPFZHen5YiMpqXKolLj9XnfAtFosdWQxNwrhWq/keoiphGzRt3Wq1PD6mqrRlWEDrfHbDEnXavN1gK9Nx5ufnoVQ6EcSoy5AQdup+fn5emZINu3nQffXCnYHpnCRrABavBpIiXpvNpvIG2mw2rR24jJ2YKmwBeNMfmdJMtWPt0QlYldVXlYsVC1dTXfuwfO973/O0jYpoWf7UJDTjEq+6xXEc31S56TxNooYupVIJarVaaN9n3bWUQg4HgkmBSq3oOJtFJ5isVLSQAz3/sLludcfBY0W1ryhT9zgNnOplBQen0X11M5CMiYckawAWrwZsFq+61DX4JqW7KTFMt6BWHipEVblA4/CzC7KW1Wo1j3ianZ1VCsPR0VG3jcVi0U2bZTp+UHtUwUrynDZv3qwUfuPj49ogrWKxGFiJa2RkxGjRTafTMDExobW2Bbl04OukCs6jQlUlbMOIIN19TroKUItyFOHYDqZctzjtWVCu2yDimrqnAYgyT61uPaUbKbyYeEi6BmDxasBm8QqgvjHRvJG6mxLDxI1JaNBxWSqVfNa1diOcg8SvqppT0EJv/DJXLD2+LugH90OpdLKMKbVymo6vSjUmA+B0wvbKK690fUNVQV6/8zu/4/r/Yj9TUz9LS6Oqj1VW7TBLFBGEj6F6SAtxoiJWNypgYUzjWyUIOxXSNEBMNXUfZHUN+3uUFnh6fLa8DjZJ1gAsXg2weGWYeAkjNHRVitpJPK86rk5cZTIZmJ2dDRRW6XTaV75WdXyTaKa/TSnWVYJAF6gVJAY3bdrkW1coFGBxcdHo1/vAAw+47dSJb3weUszSbWmfS1/UPXv2BPZxVBGEj0UD3sbGxpSW0G7c97CgxGNZN+47sXi146uq2ofKUozbn81mIZfL+cYvPp9O/L+Z7pFkDcDi1YDN4jXpUwZJJ8lJwPGDj6adkhWKAOLPJxkUZHLo0CHfwzudTvsqYEW56ZtEs+qhohKuOt9XKbh/4zd+I1AM0nOi67LZrC91zurqaqDFWra3XC57fD11Ufmq6HvcLl0p2LDXV2VNxtcpij9ouzSbJ3Pd6gLeoo5dCu5fVeq2qH6vEuoGsLCw4Cu4oBPiMoCMBexgkHQNwOLVgM3iFSDZztpJZj0kAafijQqNbuWT1E11qlIs0ST7KutgmOOaRLPqoYKPL4Wr/B4Vsu973/s8GRzaWcbHx6HZ9CbeT6VSMDExoU22jwPrstmscgocp6+i0f+mPsXH1E2t60q5ql6GVC8O3f79UAusahx3KhZMv6F2XCTC/DZwgKLONaLbLwdMeJKsAVi8GkiKeE1imoyksl6SgIcRGiarZZCFx9Qv9CZOrX0y1yiOhFdN3QdVm6Lnq/MPpO3Zu3cvOI7jWhGx/yIWRCMjI9BsNmF6elorTHHQmSoATVq6ZX9hUSrFSr1e9/Q3LhcrA7t012J5eVn7UkDdH3CWgXq97gqjXC4X6P8cVcj14nejC2aKa1aFnnM+n/f8pqJMBwfNSuBnSDabhUKhoBXISXi5TgpJ1gAsXg3YLF6TnqA4yYTxz7R5Wi6s0Gg0GsqHqpySLRQKyj4wPTxVIpKm7mq1WspqTar2RrkGOssHbY/jOFpBKP0cpbB1HEfZvqGhoVBptJaWlnxiUJ77tm3b3PPEPo34GMViEaanp5XpragQxn3tOI67P5x6DH8uzxGLV9XLHRX1NN1ZP6ZHdS8r8sWo01mVqL7jYfdlut/oBFDUl0emNyRdA7B4NWCzeAUAj0VGVxpOCAHT09N9bilDCbKE2Cpco+SVlAnlVUJAjmlq/dRZplW5SulNvF6vu5YKPDUqrVnZbNZjdZT7ieo6oBPruD26qXh8LuVyGbZv3+55COkEq64IgeM4ynE1NzcHjuN4LHnU95daTuWxqXUWC9f9+/d7AoRwP0txh4Wtqg9kRTQsquT2WLhOT097xpUuoX/cmMaZKcdx2FkVlYCnL0byuoXxdw3r1zw5OQkLCwue44QtGcz0hyRrABavBmwWr7gEJX7QqoJCMpmMW0+cGRxMU822QoNZVFaeQqHgs+TRh7MUTrhiks6CpEpirwqc2rZtmyumstmsR1zK6XNqsQiTr1MlZnTRvnjboFRKc3NzkMvlfG2jy9DQEGzdutWzbuvWrZ58tdTiLQVNUMlZXSYEusj9AuhLjTqOA0tLS+41oBXI5Hepj6/OR5mWZ5VBZd0kjBUTj+2gsatrb5gsAaVSKZRY1/nYm3yWcd9HcZ9hekfSNQCLVwM2i1cAr4VCV8WGbz6DTZKSgEepDKQLDFGNYZNlGpcOpUJRHpPms8TiCVv36BRqUG15ek66aW5Vm4IscKq+fOCBBwIFJv4/9ltUJfjXWXOxENbtO8oLVxhXDkyYogdUOPbCBzOKvzoug6vLsBDU7qDZhE4qedFzwenV6PiIo+Qu0x2SrAFYvBqwXbwCmFPT4Dd/ZvBIouU1SiaFoIAU7Ctp6p8w1l48rUxFRifiQidmaI5OVenNIMGF2zk6Ohq6CAAWqtS6TCPkdYIUHw/nvVWJSWo9VREURGeyYIYRy73y5ws7vvfv36+0iqnOU/cC023feJ21WDUDYft9KckkVQOweDWQBPEKoLZUhH2oMP0hqT6vAOGjrcMEdlHRpPPBw/6Vuv5sp2570LmYxIy0nJkqgwXRbKpzm+oW7Ecs+8NxHDfiWOeeoVvkfUUnXsOMV11fU2s3vWY4G8Qg3dfCjm9aIa1arQJAOPHZq6wkuPqcKg8vvkY2Bv2sF5KoAVi8GkiCeNUFuyRBBCWVbltUbCBMEnaVsFX5SUpU0e+mfozqsmEKsAnzeTtQFwRsGd2wYYNv/eLiIgCctPxKv0hTWVpT1oLZ2VkoFovabYIsc0EvaaYUPzbf11R9HbVIQ6/yQeOpZ1Uf98otg2mPpGoAFq8GbBevpik2nu4ZTNZLntcwmMpf4jyg2WwWFhYWPBYiKmB1N3CdIFVtb/IhxMnAdfvr1gP+iiuu8J1XPp+Hm266ybPuxS9+MQCo/WVpwFwYX1bZ1/RzGjilS8cT9iVNZaG0+b6mOj96HmHb36tKfDTLAP3dJPk+ZDNJ1gAsXg3YLF6TnuMtyayHClsS07gzTfXLsYsFJZ4awwLWdAMPekGQx1X5zOJzwFkKwrxwxCU6VldXQ/u6CiHgyJEjvjbpfGBTqZQnHdbY2Ji7n7GxMeVxdT6RNCikneAmudAAlDD3tUEpt6wT7DoXgkEgib7364GkawAWrwZsFq8A/nyIKsuGrZGGSUMV7RvlbxsxiXTsFoAFIfXBoxZWnNcwk8nAwsKCUkjt3bs3tGvG6uqq5+FNBWyj0fBlLDDtL86Xk2az6cm/ms/nfflYVaJDuglglwMcAFcoFFxfWixScYYCKl51wXByoQ/IoH7Abh70oasSUbr72qC8DOoEu6qv4ozg70S4J9n3fj2QZA3A4tWAzeKVp5/tYVAerr3END5brZbnYe44jmd84hsyta7RHKB0iozmAMWWXZzfVLZpbm7OzXVJBWqr1fIILFPRASwa4/pd0ql+lQ+wtKDec8897ra4AEKz2fRVzioUCp5KV/QlQueCUSwWPe3FlvBUKgVzc3PKcRB0brifgl5eaP+trq4O1H2Q/tZVLgSmNGGdHo9iurew773dJF0DsHg1YLN4BQCYmpoKFcAyNTXV45YxkqTfYEyYHo6maXoAcIUmfeiaghOojxctXjA5OemK1Waz6RFKKj9bVa7LMFOscYgC1bg5dOiQ1uIqCxlgS6sUsLrqTPKcVP68zeaJCl+yhKwQAkZGRjzngsX0xMRE6LEb9JvQvbzgtuGxMWgiDGfT0An0ONrVyb1lPd+XkkSSNQCLVwM2i1e++djDoD1cg4jTf9A0LRmUZF13HFMSe5UFlJYOpZH3VMDS6H5qAQyTpSCO6digKktSiMoXAeyPil8OVBbbQqHgmbZWua3IfqLVwkwVxMISZDHUvbzo2jto09+9uj93cm9ZjzNCSSLpGoDFqwGbxSuAfaJoPTNoD1cd3XighbFWtrOvoLyGeFuTnyrNNzozM+PZLw6uiXIucZy3FJE0MINaXOlUOhWdtABEOp2GQ4cOaftYWqnl3zqXhXaEKz63Tj5XtTuucRYHvRKHndxbBiXQjWmPJGsAFq8GbBevAP4pKHrjsrW6RhIZtIcrpZtv8nGUwW02vdkJaAS3ypob9sFuckeQ27UjEuIq/0sDM1T5UulUus7iigVwrVbz9TG2SGMBS/Px5vP5gRm7kkErt9wrcTjo9xameyRVA7B4NWC7eJVv9qZE3zztM1gM2sOV0o03+bgskLlczrX2qca8TPuUy+XaqqZFxfDMzIz7PRqsFaZf4hIUYa+JfEjhlxDZZ3i8Ud9ZWdhAZdWWLyk2iNf1LuAG/d7CxE+SNQCLVwM2i1dqJTMl+rbR3yWJ2PJwjdPFIa59YfE6Pj7ui/rHVsZsNusb70EPdpUfrcoHVjVNrrJIx3ne7VjD5+fnYdu2bdq8t7VazV03NDSkLAyALc7dcBuIE9rfOIWaqt+Sdj+05d7CxEfSNQCLVwM2i1cA7zSqrrpGUFAM0xts8XmVxPEwjNuK22w23dykWDipgoqiWEDD1HfHQVGqhwD2X4z7vNvxnQxzTtSSGka4xhWwFQe6qP5KpQKTk5OwuLiovQ62WqNU2HZvYeIjyRqAxasB28Xr/Py8x4ctnU7DzMyM5+9CoZCYm7St2OpU38k0ZDf8Z3GlKyykVFP7YS2geLoNp5xRBXWVy2Xjb4kGV+HzVgmtOCtE6dwksBhVVcbCVbWosKf5eGmRAixgdaK+W0hBT3P34r8zmQxMT097+hv7Bw6KNSrOIgO23FuYeEiyBmDxasBm8Uof5Lq3LvnmNQg36fWIrelM4rC8diPaen5+3pNYn7YtqgUUB0HRwAZ6bVZXV9s6b1XiehpcFZclkI43mkkB566VDzYqXmV2BepnrBq78jpQP+NuQs9RWlpl+7ALSCaTgcXFRZicnIRKpdIXQWfqF1WOXYxpbNh6b2HiIekagMWrAdvFKxYX1IKC/+61VYTxYls+xTinIbsRbd1qtYxWYZMFVEIFrC4it91ro6oKFsUSq9tfGKggUr2IpNNpGBkZ0T70pAU6jLgKskiHpV3rMn7x0Fmdg3xgu4Xpt4/FBy6RrDpH3diw7d7CxEfSNQCLVwM2i1cAcCsIqXzXhDgRDVwqlfjGNQAMUj7FoGlInI5qEKchw1qFwz7YVWVNMZ1em7AWYF2VnKgCRCU4qdiXmRmwwKNWWdmeXozddkRYFJeQdmcPOiHMCxQtSdzO722Q7i1Mb0myBmDxasB28QpwIjDDFAlsa443pjt02xIUJ7rAKNkGx3ECrcKD8mA3CS1Trfuofa4STCqxrxN09XrdFbY6i3TcfdbJ9HfQi0wUv+1ujIUwLy40DRsHXDFRSKoGYPFqwHbxiq1kqhyM9G2eWd+EEQlRouqjHDfq5yqRTR/40qIwSFZhEzqhRf1SO7V264RRsVj03SeoL+v8/DwUi0Vfnle8725MQ3cSeKQTqKr+1mVG6Ob0ehg3nDh8zJn1R5I1AItXAzaLVxxMkc/nfW9e+EHVy2AKZrAJIxKCbnZR/S+jTgerRDZeF5RVYJCDU8IIrTisb3RKGt8jisWi6++KxRzu40KhAI7jaKfpu9HH7fRBmBcCx3GUKdZ6dV6mdppcO7jIAGMi6RqAxauBpIhX7LeGb/hyvY0Dl+kecQslHXFNB8vv0kwDdJ9RrWe9cCkImuLW+Tl2an2jwRx0f9hig/te9xLTK+t2lD4wjeMw+WqpxVN3nLjGiUmc9svyOihuNUx0kq4BWLwasFm8AnhTwuAAC916hpH06mHZyXSwSpyogskwYW/QvYjSxsdQnYsUU9u2bTP6aIY9J7qdzAFpEkyqc+zVy42OMBZI3fihxRnwvY8KWGldNp1XXOPE9HvrV39zpgL7SbIGYPFqwGbxiq1aQW9dgzyNyvSPXk1TdvJw7obIbrVaUC6XjRZhlVVStR/TMVRuDjpLYKFQUEbHY99eEzofYZwHUgh/IJ7uHPplCQxz3CCLfqVScQWsyqKvyxFMiSuPqmn8q8aG6jtx9zvniLWfpGsAFq8GbBavAABTU1OQyWSgVqspb/i1Wg0ymQxMTU31u6lMF2ln6q/X4qST48Utsk3uB1jcpFKpjtJXUfGomqrGOVbpAyhsBaugDAM0UCtsAEdQvwdVB4v6sIzykhNkNZSVtlTXJ8p46mTmIOj7qrGh+24vfIx77SLCdE6SNQCLVwM2i1f6wKpWq56Bi2uZ2/jWxYSjG/kxu/WwakeExi2yTRZRKhh1Qi+KqGg2T2ZwoOVsS6UTgUXj4+NKgavy0QzTTzTDgOr/nVq85bir1+ta14MoU87tCKlevbS1+3vpV3aPKPTbRYRpn6RrABavBmwWrwDqajIqKw7fgJJJO1N//bK29FI0RGkLFnR4wdG7nfaTavpefpeWeKQCV5VZIexxVOdgEt6qoC3sPyr3I62aeL0u6Kvd3LS669XJQzjMeIrbjSLMy2VQhbJui45+uYgwnZNkDcDi1YDt4hXA75g9MzNjvaM2E54oYrRffm7tiNBui2y8H1V+RCr0OhXPJqszdWOgAiKK9Q1b83RCRLU/bEmllmHddKTqPtPu9el28FCY8ZTNZo1tppatsO4rNkT0c5oue0mqBmDxasB28Zrkty4mPHH6CsY9TdnudHCvLHEqqyueoo/DKhVmH61WyyggopxjGCFCLa6yv1XVvvDDUS4qi2ynlvG4RB7djo4nWnGIWqxVriKqPujGvbUfQpctr/aSZA1gnXitVCqwY8cO2LhxI5x33nnw8MMPa7ednZ2FCy+8ELZs2QJbtmyBX/7lXzZuT7FZvCbd34WJRpQHUK8ekJ2I0F6I7Gazqa1Kg9vbiVUq7ItFXAKi3f1QVwGVJVUl3nSW2X49LHXjJoyPruM4Hh9UlXhPp9Oee2uc5xrHmI/622afV3tJugawSrzOz8/D8PAwfPjDH4avf/3rcOWVV8KWLVvgySefVG5/2WWXwQc+8AH48pe/DEeOHIHXvva1sHnzZvjXf/3XUMezWbwCqKf66IOF8/StHwZx6q+TB3I3RbbJ6or9RDsRZ9iipxOqjuP4purbFRCdCpGg7+umzQdl3AW9LDUaDePDXOUTXq1WI7tHtDNu45htiPpb67ZrDtN9kqwBrBKv5513Hlx11VXu38ePH4d8Pg8333xzqO8fO3YMTj/9dPjIRz4SanvbxSsAwPLysvGBs7y83O8mMl3AZEEZBAsYZtB8/mj1KVOQFJ5GjyIGcfUbXRoknJKrUwERlxDRjSPTw1G1nk7Nq/qnG8TRD6o+UPkOqgRlJy9rnbQ9qvhdXV3lPK8JIakawBrx2mq1IJVKwSc+8QnP+t27d8MrX/nKUPt4+umn4VnPehb89V//tfLzn/zkJ/DUU0+5y8rKitXiFSfj1t3sMpkMVCqVPreUiRP6gFRZi1TjgjkBDmrS+bfm83mlz1hYEdRqtWDLli3uvlTiQIpbaYFtV0DE7SNMLal0mlxXhhWvx64Hqv4f9PRPqj7QHUueSxzXoZO2RxW/XGHLfpKsAawRr4899hgIIeDw4cOe9ddddx2cd955ofbxpje9CUqlEvz4xz9Wfn7DDTf4pgltFa+rq6vaMogAXj+tTCYDq6urfWopEyf0AWmKDmcB6wf3n04w0uAdVYAPtWKpjkOtu/jBgl0WMpmM1lIZVkB0s4wpTZMFoC8/uby8bLwv9cqi18lMRNTv0gpe3bD8ttP2MOJ30GZFmPAkXQOsG/F68803w9atW+GrX/2qdhu2vDJJgF7fMEKWp/5OEkbo5XI5yOVyUKlUlNtKMSg/100D00IDtBBCsVjsaIpdlac1yue0vXj8LCwseB6O09PTMDk5qc3zKtdPT097Hpry/KIIuDhEVadFMdq12nbD8ttukGBU8cvYRZI1gDXitRO3gfe+972wefNm+Lu/+7tIx2SfV8ZW6M1JFwHNU39qwoijIL/ARqPhWml1LweNRkMZGEatse0Q57SvTljihyN+SErRLgNCKpWK50VpcXEx0F9Ydw3keXVijW5HwMUZwNRLy6+KQQmiY7pPUjWANeIV4ETA1tVXX+3+ffz4cRgfHzcGbP3RH/0RbNq0Cb74xS9GPp7t4jXJkYZMMGEfcmxxbR+ToFH5zdLvSmGnK4TQLnH6uUaJ0seCVIpL/Dn+Pl5Px6dOeNOcs9Ri1C2/0W7kFh4Eyy9bXpNNkjWAVeJ1fn4eNm7cCHfeeScsLy/DG97wBtiyZQs88cQTAACwa9cuePvb3+5uf8stt8Dw8DDce++98O1vf9tdwvp22Cxek57jjQnHerCw9NsvTyUoaElXk9gplUqe4Kw4xKvqGJ1YCsNacbGFNYy4Uo3PIKFIffWiuB100ifdsmT30vIbh/hl7CDpGsAq8QoAcPvtt0OxWITh4WE477zzPE7IF110EVx++eXu3zt27FBOx91www2hjmWzeAVIdnUNJpj1YGEZlIhoVV/TnLAqsVEsFn1W17jcBuix2hUr8qGme+mnn4cdd6btwgi1qNW74rCexvGi1C/Lb5wvM4wdJFkDWCdee4nt4hUguXWNGTPrwcLSqzKxYVFZEU3XgQpXXcBWnAI26kuMfDmIGpgWZPEPMz6DtmmnQETcLzudVqzqleV30H4rTO9IqgZg8WrAdvGa5LcuRs96srAMyrmGtSLKxXEcKBQKSpHabHqzEDiO07GYaMd9hPqXmvpYfi4DqUyiMso1CxLe7Z5XJ59LoorJflt+B2WWgukdSdYALF4N2Cxek+7vwqhZjxYWk8+paRq2m8enIoyKrIWFhdAVtnK5XMelbtu1vOqm6bHVU7de1Rc4jVbY8akTqP10i2n3d9ZvAdlv/3CmdyRdA7B4NWCzeAUAmJqagkwmA7VaTXmTr9VqkMlkYGpqqt9NZWKk3w/IfqDzOdUF7cR1/mGsiNj3Ff/+KpUKlMtl43Uql8swNzfn+yxs/tY43EdUApb+qxKuOouqzgUBH09eH51ADRLJYQVsJ2KuXas/C0imVyRZA7B4NWCzeMVvXbrABpxAnG+YyWI9PiCphU5XdjUua0MY6xud/ldZIk3Mzc35hB5+OVEJceyHGpdLhUpE4odgVItqUMaXVqtlFN6dlOZV9aPunKPki+2H1Z9hdCRdA7B4NWCzeAXQl2jUrWcYW9GJK+pLGocfLL7JqwQQtnpK8ZrNZiO3QyWO8Tps0ZUPH5UfalzuI/TlgE7jx2XxVwlXuc9GoxFLedk43Wv6ZfVnmCCSrAFYvBqwWbwm/a2LYSQq65eq7GocwtUkVmVbJicnXYuptLi2K450QUyqjASdTM8HEWR5lcfo1OI/Pz8P5XJZe62azRPFH1KplLbvwp5Xu9P+Knpt9WeYIJKuAVi8GrBZvAKcfBCYqmuUy2W2AjDWYhIgqrKrnVpco1jrVFP+dPt2RFYUcR53XlKTz2ungVK4f7PZrFK4ynZMTEwY711hH8Rx+wTHafXv5NqtR7chxk+SNQCLVwNJEa+qaGeZg9LWgcswYcQkLQDQaYWxqNa6uESEbmpaFQgWNUAo7HHDZBvoVMDi42GLtap/4xJguqCwMOdCS9/SF4tCodCWIO7EBWM9BmwyapKsAVi8GrBZvOp841QPPhunDBgGwPygVllf4xZYnUS6R0X18Nm7d69RnHciVNrN8xr2XhLWVaIX/RsmXyxtb6VS8fQLLlPbidW/E3/c9Zgqj1GTdA3A4tWAzeIV4MTNFScmVlXwSafTUKlU+t1UZh0Q1QoZdvugUpiqKP84BWycwjjK8QqFgi/xuE5ctvtwarfCVtj96izU9XrdFYbd7t8w15K2d3V11RM4VqvVPOdfr9ddv9x2rP6d+OPG6cvL2E2SNQCLVwM2i9dWq+WmbDENXPlwt+2tiwlmkPzeok5ldjL12auHdzvVndohyOdViiQ8fX/o0CHjuUa59qaXhDCfq7bH1kEqjHU+pHv37g3d5rCEsfLqrJnY8ooDXxqNRluW16BSsgsLC6FdU/o1O8AMDknXACxeDdguXvEDgFoB8N+lUsm6gcuYGSS/t6hTmaurqwM/bdory6tKcNNp6fHxcbfUrM4Sq8qI0E8/N5XLgc6XVi6ZTCYwL267bQh6ydFtu7i46Aleq1arbfm86n6vWCDrrOthXuJ6MTvADBZJ1wAsXg3YLF4BTtwQS6WS0gog38JKpZKVztqMnkH0e4tqDe3Eetpt4d4rq1aUPK+ZTMYVsHhZXFz0nO8g+TyqgsGC/o2rf9v5jZiuOxXa8vqEGbe6tuD1eFlYWNC2kV5PVVliZv2QZA3A4tWA7eIV4MQNECcklotMTGzb2xYTjijiL4x7QZRtdNuqIrNNoq8Tkdgtl4le+xOqhDheh5P208wKVOA6jhNY/anX6FwEqGCt1+uxt72dlxydNZPWjY+a51U3fmq1mq9fqIVabk/PR9XWTCZjpX8j0z5J1QAsXg0kQbyaHg6D8gBjukMY8RfmAZ7L5SCXy4XaJiiwZ3p6OlIgziBNffbLoq3aD16n87HED6t8Pu9uM2i/e13lLtxW2bfZbNbt3zAlZoNo5yWHtrdarfrGaDsVtujvtVqtKgWHyhJNxyYVt3hfcbtfMINNUjUAi1cDtotX1bScyqph6+BlgjGJvzBiDDv86ypF4W3CplTCS1CgU68Co8IwSL7E+JhYvObzeaUVtpu/93Yt3XT8qMYGFXXlchmmpqb6ch1UvydavSjIQhy11KzMZqBaj8t6qu73Oj9ivu+vD5KsAVi8GrBZvCa9NBwTHpP4CzMNjqeew2wT9OA0pXeiDJLlVTJIWRx018AkBuOmXUFP2z42NuZrr2rsdRLQ1wkmyygWkp26kCwsLPgsuwBqCzU9P+xGIgPIcFvw75Hv+8km6RqAxasBm8UrgDfHm0502JrjjQlHGPEXxr0g6jZhAm+66fO6HlBZzqnAoRHGcfdbu64U9NrW63Wf8MZtp9PwvfY9pvttNBpKYaBqRxRhoPu9qsp76vxXO8lQwCSLJGsAFq8GbBavrVYLcrmc8sYP4J1qzOVy1r11McFEEX9RRW6UbUzTVFFFSLfEia1gq6eu79PpNOzdu1fbb51akqNeK5N/ZrFY1Aae9evlRifQZd/rrJlRRSI9H5zXNcpLH4Dfekst7ny/Tz5J1wAsXg2weGVspR3xF8a3tJ1tgix/1ErVr2lhW6FpnKgALBQKSut5sxkuYC+MAIsqJOVxsQVTZz2W56K61lHcSjoR6bp+ChKq7VhccftxlHhY14RBdLVhek/SNQCLVwM2i1cAbzCETsCognAYu+k0h2W3LK+ZTMYTYELbFKbCVlxiIUnQ37PKB1bl2lEul6FcLsf2khBVNMn9BVmPi8UiOI6jFdBhXqjiEOnd8nUOk+dV5ZsY9DtmVxsmyRqAxasB28UrAPsNrleiPKx76fMaRszo/qbnpLLCrTdfPpXw0YlBLHB0175T94x2M0MECS/dAzaMYB7Eoh0U3e8Vuybogt66dS2ZZJBUDcDi1UASxGuQVW09WqrWC2EsRWEeeHFnG2jnhmmDAOkXKuETVA7WlCA/7MOtkyl8SjvCK0q7o+6/HxkldPsMKv4hC4Tw74NRkVQNwOLVgO3idX5+HsrlstKPTOZPLJfL68pSxZyknTyvNLk53SYoKEtGQevKWaraiI9lk2WplwIozqCrdtw8OrHuxFGqNU6xO4i5fMNga7uZ7pFkDcDi1YDN4hU7a+PqOtiPTAZC2OiszcRDlApbpupZuVwOstksZLNZZTUu+eCU+5ifn++4PGcnU2DdFpY2CglVoF0YMUnL/rbzUhGlvzqxMgZZh6Psu1wuG8dJkBtM0PbtMEg5iJn+knQNwOLVgO3ilVauKRaLsLS05BvEjuNYN3CZ+AjzwAvKANBoNNzxpnuo4+nPuAUI9Yk0CQdsjVDRqbC0cQpX1adhUpupsgXo9ht0rlGEVycvB0F+uWGsutls1hjoQo9v48sMYzdJ1wAsXg3YLF4BvGlW5NvX0tKSJ40OLTHIrA/asdDEPW3fyf6oAJHpoAD8QoFa7bAA6Zaw7LeLQyfuGKoKPCort3Qh6Zcw63QMh7Uuq4LHTCVg6Rji1G9Mv0iyBmDxasBm8apKs0IXm0vDMe3TidiIa9q+nf2pUgRRAUstgTSBfKPR8FgdsPUsbmEZd1+FpZNME/I7uEqTqpwvjX4PIyT7PaUd9XqYhG7Ul5N+v8ww64+kawAWrwZsFq8A3jQrtGpNPp/Xpl9hkkscU9phrVdhCbM/VTUjKUCwGB0ZGdFmOKCVnHAGhW4Jy7j7KoioPpuqPK9BD71qtRrZUtjvafN2xaPJxaATMRxlzNkmKpjBIckagMWrAdvFK8DJNBmqgdts2psmg2mfOKxA7ebzbGd/KjGF20enxgqFAlSrVU+OWSy4VNazbgrLuPsqiCjXVycqddZt3TUw0W8f4HaPH2Z8RB1Dqu2jZHVgmKgkVQOweDWQBPHabDZ9ztlyUZWMY9YHnUxp98Py2mg0PNPYqjKZKiuhasob77fbwrLXllfVccO6Y1BoadKZmRllqdJ22tPrafOolt8o/Rd1DLWb1cFWkcH0l6RqABavBmwXr81mEwqFgmeg0mlWHOjCrC/aEVb99HnFfpiqbev1ume8CyFgZmYm1LRvN4Rlv3xeVcePen6ml4J2i030uz/C+txGEdpxWF7DZHXgezTTDknWACxeDdgsXlutFmSzWeUbFn0Ty2az/Fa/ToliNYrbetbO/nBOUSoWms2mLzWMzvIah5Ay/WZwW/opStqxLNNp9mq16tlHOz6vkn5ZosMSxcWgVCp5rnEnPq+mrA6D0jeMXSRdA7B4NWCzeF1dXYVUKqWd4sNTgqlUClZXV/vUUqZfqISELndl3H6LnexPVykGP/BNPq9hyt0GiQbTNDTOr9jNdFxBdCIUVQFyeB840CNqFoFOXTUGocBEqVRyhUGYMRRmfZCLC8NEIekagMWrAZvFK8CJadagKal0Og2VSqXPLWV6jcoKJB/GOj8oOW2vGy9Rg0varbClSryNxeihQ4eUFq16ve75ruo8wwjLMMIbCxtdxoZeRte3Y82jlbNUeV6DrqFMXabyJW1HpPUqa0FQMQVVlgbcBjyGouR57UTUMwwlyRqAxasB28Xr/Pw8TExMaFMCFYtFmJiY4EjWdYbKCoST96uEXVhrYVSrV9Rk+lhgLy0t+cTo4uKixy9WledV7kNXVUYngEyJ/WUf4vWmCkxhzj0sdD+0bbKYQBTLchhLYVCyfuyjrCojW61WPdcqSMD2O2sBJqqIDtq+Xq+7fcGWVyYukqwBWLwasFm84hs9tkyprFUcybp+MAkA6gclxd0gBI9Qi6sU11jQjo+Pu+3PZDIe0Uatf+Vy2XjDpr8HlfjA/VIsFqFQKCinkrsJbRe9vjSPY1yWZZ3fp9yWZoeo1Wqe7+CXiigCNm6/606I6r6g2z4OKznDUJKuAVi8GrBZvAJ4b4qqHG98c1yfmKxAWMBms9mBeJDqbsI4+ApH1DqO4wpXvA/T32GPHyT4w1hc40LXLpW/Ks1fqptal9voxohqH/9/e3cfI1dV/gH86e7MbDH0BYO7nakzMFN2i2lLiDTbtECKppEE5OWvktTUapRiWLIJJCix6ArVQgjBJmylKYqYFt1UsnUNbbC2umm7ZdXU1jRsxQxb3FVsI0bpIrDb3T6/P/jd8czZc859mZd7z53vJ9lQZu6dOfee+/Kdc88918uNSLrWcFXruFvdxCns+W0lty1gQLjinAEQXg1sD6/M8R3jDSrj9U75qFzCFMOUKryIgbsW5TS1+MknhXr2VdSVS75E7yXMq1px5e/SPRJW15dVbmFVPSxC9dl+ljsq26hf8o+P3t7esvUvt5LL/YcBvIhrBkB4NYhDeJWf5S5vuPJJDYC5/k+F8sItLNW6xdMUmsMMUW4tkXIoUs3f3t7O6XTaU1eB9vZ25Y8f3TbjNWj6bVWM4jbql/ODwQmmulDf29tbt/68EC9xzQAIrwa2h1fxhgndJQPT3ePQmGxp1fISXqo9rJLuznDnBrKwLl/r6kwXilTz6W7AEqdpbW1V/khw22aqHTRt2Ua9cHs4gtyKbuMyQjjinAEQXg1sDq8TExNlN0yoNlyxP5ptY7xBbdjSn9BLeOnr6+P29nbPd4R7JQcx5xnhcrnqvb68tHy63eRkqn8v4datj2s1gqYt22gQcV42qK+4ZwCEVwObwytz+RhvYuuQeAnB1jHeoPqidCe313Lq+lHW6kEBqv7AQYcVqya3MO8WisRLh6YuGfLniMFUHlNX9Xq1Hydc7W201g9A8CJOrcoQrjhnAIRXA9vDq3wXdpyeawzVFfYYmkGeO+92B7s87FelQUe+fJ7NZpVP6nKmrdfNNV5b63ShSNUnVm7FzWazyuG2xJYd+fvEJ/jIQ5cFWf+13kbr9QAEL+LQnxfCF+cMgPBqYHN4jfsYb1B9YZ28vX7vnj17Zo1hqmsFdEKVPLRW0JY/VeByGwO33q10ppZIJzjKoWhwcHBWINT16xUf6uDWOigef1R96oIGzVpto2H8ePMy7itaXiGouGcAhFcDm8Mrc/mBXvc8eAy9AqJaXTY1PZHLT2hwAqwupKme2lRpGAi7VdpLuZLJ5Kxnl8stpNu3b1euBzH0iye0XC5X1k9O7h7h1joo3kmvUknQrOR9nXp2m9GFcLnOHnvssUh12QG7xDkDILwa2B5emXlW65B88rbt1xbYx23Ae/HRmOIJWneXtelxqLpwWull2ChdUhbt2bPH+IQqcd2K08kt0HI3i0wmUxZiVQ+G8PKDIAp9SP2oxw1Tuh9DqhvfVI/VRYAFP+KaARBeDeIQXnH3KoTJz1OgxHDl97n3pnBarcuwUQ1iunCjCkO69/P5vHHMWvk4Io46ELdjSj0u26u6dTj7iVtd2XiJF8IT1wyA8Gpge3gV74w2nbRs3XjBDl5P1KohlcQbfbx8vhg2isWi8cAdp23ftJymHwHifOl0uuzmDt2PgNbW1kCX1qMa/lXqccOUvM4ee+wx17qy9RIvhCPOGQDh1cDm8Do5OVl6Yo7qEXBjY/97ZFw6nY7UiQPiR9U31QmuiUSi1F+zv7+/LDT09/f7+lwxtIljG8oH7lo/TrYSQUOen9EE5PmcpziZHgs8OTnJ7e3tnoKw3DoY1W4XurLUq0uE31ZeHKfBq7hnAIRXA4RXgOpRnajFllcx0Ho5keta+4rFYqkFy+m/KX6GuO0T6R93GoZKQ56uxdBt+eSuB7pLi0HKF9Ub3lS8XmKtZhjHsFhQC3HPAAivBjaHV+Z4XzIAO8knavEBA2KgVT14QOQWiIaHh7mpqan0eaoxRnO5HOfz+Ui09jFXHvKC9tX0e5d9kBbHoHfy17Orgdcy+nnkrlsYr0f/Wmhccc4ACK8GtodXZvcWFbf+hADVojtR79q1S9lVwC3YuLV+yaMYqFrRotbaEDTkBb0po56ton7LWM+uBn7Xg5eb5NxCaFxvpIFoiWsGQHg1sD28qu7oFkPD8PBwZPqZQbyZTtTyny4MqMKTn8vhtrRs+Q01QQOvoxohMcgT0tz6k9a7q4Hf9VBJ+Ky0zgC8iHMGQHg1sDm8ygd/1Y0wUelnBvGmOyGLjw8lIt61a5f2hF7JAdbGPoX1DnmVXJ73G/q81kcYAc/veghy2d+mPsBgr7hnAIRXA5vDK7N6nEexXyF+3UOtVWtA9mo8NSnKLa+q5fMa8sK8k7+Sy+1e6sOGS+tBfhzZNPoC2CvOGQDh1cD28Mpc3rqVSCR4586dyiGKAGpFPlHLgUe+dFWtlicbgg+zOsioQrdpWK9a3tjkd6QCXQupeOnST31E+QdIJWWzadxbsFdcMwDCq4Ht4TXOv7rALvKJWBVoRZW2PNnSp1DVcimWMZfLlcaqJar/ncFeWwh7e3uNwVQOrn7rI4pdP2z5cQSNK84ZAOHVwObwGvf+LmC/WrU82danUA6rztiLun/X62RTrS4BlQ4tFcWWV1t+HEHjinsGQHg1sDm8MjN3d3dzMpnkgYEB5cF/YGCAk8kkd3d3h11UgKpStRiKB2cnUMmD6av+XQ9jY2NlT7fKZDKzwmoYodtvSNO1kAbt4xnF1k3bfhxB44pzBkB4NbA5vIpP1xAvD8iPzySy8+kaYLd69PfTPZ7U+bc4vqEYnsK6WWZsbIxbW1uNLYxhlM1rgHRrIa3kTn6xu4QqONfq+KX7XNU2JJcdN1xBmOKeARBeDWwPr9lstqx/i9MxWx6iKJvNWrfhgr3qfae12FKWz+dnPXFGDkPO+/VoNZM/X265HBwcdJ2nHtyCabVbSMU6a21tndXXV/6+9vb2qgdFt+1U1XovLwNAWOKeARBeDWwPr/LJJpfL8dDQUNlz3Z2Dv20bLtgprEuuUexXKocjVUBMJpPc29tb03J4pesSUKv+n319fdze3q58vKX4+U5rdTW3F3QNANvFPQMgvBrYHF6ZPzr4FwqFsruVxb9MJsOFQgGXtqCuqhl2TAfcycnJsvflAOtcUtP1Ma0l1XBh4rL39/eXWkaSyWToj3DUtbxWejOWm8nJSeP2ogu21YCbssB2cc4ACK8GtodXZuaJiQkeGxubtfFmMhkeGxvjiYmJsIsIDagal5lNl3Wdg3Y+ny87MKtCmKmPaS2phrGRg2wUhrNxq6ve3t6adwMJ68atKN4wBuBHXDMAwquB7eFVfK6xasO1+bnGYL9KB3jXtfjJl8vy+XxZi588ZIzqUni9FItFTiaTpaAqDl8jB9kwLk97bX10axmuRrnDGjIrikN1AXgR5wyA8Gpgc3gVT+7y4MTOn/hYTtv6u0A8VDL4vClYiX26crlc6T35RoUwW14dvb29pQCrKkdYd65Hsd9nWA8riOJDEgBM4p4BEF4NbA6vzLNP1JlMhoeGhsp+gdn8eDiwWzVatEyXdeUbsMR+pIlEgtva2sr2jXo/BEA0ODhoDEdhnVjqPTKECVpeAfyJcwZAeDWwObzG/U5DsFs1+xKawoXqvUQiUTp4V2O0gUrHrI16OKrHmLxu0OcVwJ+4ZwCEVwPbw6tzN7XYqiRuxM4J3MYBisFetbiL23RZV27VdPYLVcB1bvLyeimt0pbJaoajKITMWgjrrn+MNgA2i3sGQHg1sDm8Mv9vnMSxsTHlyX1sbKwmg3sD6NSiH6XfllfdoPd+n7BV6bJUMxxF6fK+TpBwHVa/2yj29wXwK84ZAOHVwPbwyjx7nET55I6DLtRbNYOWnz6vg4ODpffk8MpcHp687hdBA2g1w5ENQauSOg8rmNvwgwDATVwzAMKrQRzCK/psQRRV4xJ3kNEGanHJN+g+VssQH6VL3NUI12F1iYhrVwxoHHHNAAivBraH17Ex9RNoxI1Z1QIFEHWVjPNai5bIoDddVTMcRfkkVUm4RoAECCbOGQDh1cDm8Cp21hZbnhxi65SNnbUBgjxhy1GLS75RGAs0yiMXBAnXuHQPEEzcMwDCqwHCK0C0ufUFdXu/WqIUGqMQonX8rCcb+vICRFXcMwDCq4HN4ZU53pcMAKLCa4tivcdDDTtE6/gJ11HuywsQdXHOAAivBraHV+Zo94MDsJ24fyWTydKTauT9rh7PELdhXw8Srm1YLoCoiuv+g/BqEIfwGtdhMgDCJl7WTiaTxtYN5/1KLm+b5vPSwlIoFLhYLAb+jkpVchK1oUUZIIrimgEQXg1sD6/izQ66AYpxswNAcM4+Njw8rAxiw8PDymAb9Ht0fUOd4Nra2mrsG5pMJrUBtpbHg2pc/o9yX16AKIpzBkB4NbA5vIqtQuJg7c6f+BpudgAIztl3anV5zsuNS62traX3VftysVg0huha3vxUjRuv0PIK4E/cMwDCq4HN4ZWZube3lxOJRNnGOjQ0VLYRJxIJ7u3tDbuoANbwevm+miHLS8ul240XxWIxtJufKhnyKq599gBqLc4ZAOHVwObwKl5KNG24zknPtl9dAGHwEsKy2WxNLm9XI8SFGQSDPGwAow0ABBP3DIDwamB7eBUvszU3N5dtrOL/6y41AsD/eLn8LZ8Uqh2uqnH53JZL8BjnFSC4uGcAP/msicAaqVSKtm3bRoVCgXK5HM3MzJS9PzMzQ7lcjgqFAm3bto1SqVRIJQWwQyqVokOHDlGhUKDR0VG65ZZbaHx8nIiIxsfH6aabbqKxsTEiIsrlcjQ0NKScthLZbJZ2795d9tru3bspm83W9TPqIZVK0eOPP04dHR00ODg4q3zZbJYGBwepo6ODHn/8cRzDAATIAII6hOlIsbnl1TE5OcnDw8Nl/V7o//u5DA8PW/drCyBsqkvvYour+DSbal/ebqSWV0eQ7gYA8JG4ZgC0vMbc+fPnacOGDTQ9PV32+vT0NG3YsIHOnz8fUskA7OS0+DmtqjfeeGNZi+uxY8dKrYTytOvWraOpqSnl5+ped7z55pt0yy230OjoKBUKhUAtu+Pj4xV/Rr25tQjFusUIoELIAISWV9uILSyqX10U8RYXgCiTx03MZrOB7qZndr8RTDderJ+WXdz8BNBY4pwBcMOWgc3hVbzZQdxIxbuLnddxswOAP6pL725DVen2Mbcbk8QxWlUPGfBy4xJufgJoLHHPAOg2EFOpVIq6u7spkUjQ9PQ0FQoFGhwcpDVr1tDBgwcpn8/T9PQ0JRIJ6u7uplQqVbpsOTU1VfZvh+rfukud7733nvHyqPgdqnlV36l6TTetl/KbyiBP43U6XTnF6byW1/S6s9y66cX1UkkZVOtM9X26z/BTPt1255Dn0a0TXXlN9eGnrsbHx2nt2rWlS+9Ot4CzZ8/S2rVrS5feve5Dzo1g+XyeRkdHS58xNTVF4+Pj9LnPfY4uXrxIyWSSjh49StlstuxzstksHTx4sOzGJXm/kG9+amtrK1tO1c1PbutPVx9u24DfepSnMb3vZxsyva877pjq1Os+7HZc1C2bbhp5fXjZD/xs76ppvB7bvR6/g54rxM/QlV3eNkzLVsmxUbccbsdNL9tSkG0rlUpRV1dXWQY4ePAgrVmzpnTMkjNAbNUhTEeK7S2v6XR61g0kfX19nE6nOZvNciaTYSLidDrNe/bsKXvMZTqd5u7u7tKlTPGyp/hITNWl0N7eXm5ubuZPfOITs1p4+vr6OJ/Pcy6X43Q6rZw3mUxyb2+v8lKqWA7dtKryifONjY1xOp3mhQsXalvLnJaohQsXep4unU6XrWex7M53OtN4WZ+617u7uzmZTPLAwIBy+oGBAU4mk9zd3T2rrGIZgqwzt2Xs6OgobTe65dm6dWup3sTtolAocD6f597e3lnblVjXqu+W3zetb/n7xO1c3EYLhYJyPTg3ZzU3N/PWrVtLy+o85SqXy5WW3VmW7u7uss9Urbt8Ps/z589nIuLFixdzNpstfWYymeSjR48q68Ep3549e1z3Iec5506ZnHXgrBen9UVeB17Wt6ru5XWrm8/5fvl9ua5V76uWR/5e+bNV3Tic97/85S/Pmle3fcr7jfy9bvuEbt9ULbtqGnl9eNkPVNuPaV+Rp3GWX9V6n06nubW1VVsHquO3an2rPk/V5cbtuCCu/3Q6zblcbtZnqc5J8nqX69br+VDej1R16rYtOetb/nxnXvEYIy77nj17SsNhicckZ37xJq50Oh3rltdIhNfe3l6+6qqruKWlhTs7O/l3v/udcfq9e/fy0qVLuaWlhZcvX8779+/3/F1xC6+Tk5Pc3t4+a5y3RYsWlV4X+8U4lyrFx8i1t7fPmla85CBe4iSpH6Bq0OT29nblvMlkkq+++uqyy5zipc18Pl/6/kQiUfpc50Ahli+fz5e9rxq4WT7Aqsbr9DJdPp/nYrFYdol2eHi47Duz2azr+pyYmJh1yaejo4P/9a9/la1f1fRi/U1MTJTKKpbh6quvLluXznuqdVYoFEp1YVpG5/Oc8umWRyxfsVicNR6hvF3J28XIyEjZdx89erTs/SNHjmjXt1MW8fvEvqTFYrFsXudk59SVvO048+bz+bKHEzjLIJZLXH9OncvrTu6XJu+H4nfk8/myeTs6OnhkZMTzPiSXydkP5f1ULq9qfevqXly3pvk6Ojr4zJkzs7pHiJc+s9ls2ecWi0Xt8sj9g8VtKJFIlNajahtz/px5ddunat8Vv9dtnxAfKyyvb+d7xcd7ynV/5MiRsvV1+PDhsv8/evTorP1Atf2Y9hXnx444jaqvpDyNajrd8Vte37rPkwfSl48LZ86ccT0myZ+lOiddc801pXoVz31+z4fyZxcKhbLjoNvnyMcO8fPFp+XJ0znHMfFcv2jRorJ6LRaLZeeuRYsWIbzWUl9fH6dSKX7hhRf49ddf53vvvZcXLlzI58+fV04/NDTEzc3N/NRTT/HIyAg/+uijnEwm+fTp056+z+bwylx+ABAPIE6LK9FHAXZ4eHjWUBqZTIaHh4eVQwCJ0zrDbTjfpzoJO/ONjY3x4sWLZ323bl5x59b9WzVtJpMpK5+zvPJniOtBLKO4zJlMxvN0zv/rAonuO3XrU/f6wMBA2cF2YGDA+Lq4bnXrcfHixaUfM83NzaV60k2vW8ZCocADAwOuyyMe0OXtTF7Pqu9Qfbf8Xz91rNsu5O90WkLFecTva2trmzWvqhymdScPJt7f368tr9s6Me1DqnXjbC/yfu9lfavqfmBgwNN8uvWhqi/dsonLI9ep2FruZRuTy6bbPuV9VLW8pn1Ct2/qll1V927/ldfN4sWLlduueGxWrRvVcVeuO3H9it/jdvz28nm6Iei8bEfi+nfWo+mcpNsH/J4PVdPrXjdtS+K2r9vGxGU3bbfy66YbTaPMqvDa2dnJXV1dpf+fmZnhTCbDTzzxhHL69evX8+2331722qpVq/i+++7z9H22h1dm9zEpnR1ZPLg5G7lq/EpVZ2+5E7hqx5G/wzko6eYVD5i6k5LbtOKBT56v0qCqm05cjv7+/rKDkRxCvK5P3eviAW3nzp3KYKh6/Kd8QvK7ztyW0evyyP+VT1Sm7UL13bt27fK1vk3hp62tTbtcTsuYKfSo1qEcTty2D9P2ZlrvfvYhuUy69eN1favq3s98qnqWj0Py+tAtj2q55YBm2sZ026nbvhtkn9DtX6pjsNv69LIf+D02qcpnCsteflT4+RGq20a9HBdU61+1HcnnJNX6CHL8VpXf6+eIy+L8qQK/KtQ784vH1ba2Nu2PVttYE14nJye5ubmZ9+3bV/b6F7/4Rb7zzjuV82SzWf7+979f9tq3v/1tvu6665TTf/jhh/zuu++W/sbHxz2vnCgTN2hxo5UDq3xwEaeVX5MPGuLruhYc8fO8zCu/H3Ra3XxuZQw6nSpcVrI+da/LrQnOd6l+sauWu5J15raMfpfHbd2Y6lp3cPfymW7rQbVcQdaj6fvk7yD6qNVK3j9V+6apfF73IdV0fsrrte69zGcqu6oeg9RpkG3MbV4vy+vlmOln2d3Wp5f9wM++4mWb91oHXte3l23U7zHJzzlJtT6CnA+91qnXbUlXN7p1IV/Ncb7f1uDKbFF4/fvf/85ExMePHy97/eGHH+bOzk7lPMlkkn/605+WvbZjxw5ubW1VTt/T06PcQGwPr8yzx6QcGhqa9Zrudd1rus81fW+l8waZ1jSfWxmrMd3OnTsrXp+61+XP3rlzp6d1W+11plpGP8vjZd14/W4/69ttPeiWy+96NH2f/B3OJU15ukwmw/39/b7K53Uf8rN+vKzvSuYzlSno8lS6jXmZt9J9wu+yu61PL/uB333Fy/rxu+0F/Ty/xwXTscdUN9U6H1byOfKymOrG6/y6eW2B8CpAyytaXsUyouXV+7xoefW2Dr20iuj2Dy/LipZXtLz62Q/Q8mre59DyGl3WhNd6dBuQoc8r+rz6nU5cDvR5jWefV9W6qLTPa1NTk/ZGrKGhIfR5Nex/6POKPq9+j0mq7Qh9Xu1iTXhl/uiGrQceeKD0/zMzM7x48WLjDVuf//zny15bvXp1w9ywJW/IzsFHvpsaow0EC6rydG4HZd13YrQBe0YbUK1H3feZyqEqfz6fV647U3nd1olpH8JoAxhtQJwGow005mgDtgZYq8JrX18ft7S08IsvvsgjIyO8efNmXrhwIZ87d46ZmTdu3MiPPPJIafqhoSFOJBL89NNP85kzZ7inp6dhhspSPQ5SHufV2fBVY8wRYZxXcRqv02Gc1/iO8+qMjyi+L47z6rwu7i9+x3mV1524feRyGOdV/FyM84pxXjHOq7dxXsUfEqpxXsXzsC2sCq/MzM8++yzncjlOpVLc2dlZ+pXDzLx27VretGlT2fR79+7ljo4OTqVSvGzZsoZ5SAHz7KeNOK+l0+nSgUv1dI9CAU/Ycg60eMIWnrAlzyt+tvi0IdWTc/w8YUu37tyesiSXz+s+pHrCllgfeMIWnrClKh+esOX9fBjmE7acc73440GeP5/PK8/DNvCTz+YwM1MDuXDhAi1YsIDeffddmj9/ftjFCcR5rrn8GhGVnl/uvO/82+19eVrVM5Hfe+89SqVSyvfk5y+r5r388suN5Xde002rKp/8b1MZ5Gm8TidOI5ddXK9eymt63Vlu3fTielGV1WsZVOvMbRnFz/BTPt12Jy+z7rtV7+uW1e37gs5rWp9ePlO37vzWg9d9SPVZXteBrj7ctgG/9ShPY3rfzzZkej/ocdPLPqw7Zurqwq3u5fXhZT+QP8Otrk3Lr5rGNJ2qLr1+norb9iRvG6rPUr3n99hoWl75O/0cMyrZtvwcx2zjJ58hvAIAAABAqPzks6Y6lQkAAAAAoGIIrwAAAABgDYRXAAAAALAGwisAAAAAWAPhFQAAAACsgfAKAAAAANZAeAUAAAAAayC8AgAAAIA1EF4BAAAAwBoIrwAAAABgDYRXAAAAALAGwisAAAAAWAPhFQAAAACsgfAKAAAAANZAeAUAAAAAayC8AgAAAIA1EF4BAAAAwBoIrwAAAABgDYRXAAAAALAGwisAAAAAWAPhFQAAAACsgfAKAAAAANZAeAUAAAAAayC8AgAAAIA1EF4BAAAAwBoIrwAAAABgDYRXAAAAALAGwisAAAAAWAPhFQAAAACsgfAKAAAAANZAeAUAAAAAayC8AgAAAIA1EF4BAAAAwBoIrwAAAABgDYRXAAAAALAGwisAAAAAWAPhFQAAAACsgfAKAAAAANZAeAUAAAAAayC8AgAAAIA1EF4BAAAAwBoIrwAAAABgDYRXAAAAALBGIuwC1BszExHRhQsXQi4JAAAAABD9L5c5Oc2k4cLrxMQEERFls9mQSwIAAAAAoomJCVqwYIFxmjnsJeLGyKVLl+jtt9+mefPm0Zw5c8IuTsUuXLhA2WyWxsfHaf78+WEXB/4f6iW6UDfRhbqJJtRLdMWpbpiZJiYmKJPJUFOTuVdrw7W8NjU10Sc/+cmwi1F18+fPt37DjSPUS3ShbqILdRNNqJfoikvduLW4OnDDFgAAAABYA+EVAAAAAKyB8Gq5lpYW6unpoZaWlrCLAgLUS3ShbqILdRNNqJfoatS6abgbtgAAAADAXmh5BQAAAABrILwCAAAAgDUQXgEAAADAGgivAAAAAGANhFcL7Nixg66++mqaO3curVq1in7/+98bp//5z39O1157Lc2dO5dWrFhBBw4cqFNJG4ufenn++efp5ptvpiuuuIKuuOIKWrdunWs9QnB+9xlHX18fzZkzh+6+++7aFrBB+a2X//znP9TV1UXpdJpaWlqoo6MDx7Ma8Vs327dvp6VLl9Jll11G2WyWHnzwQfrwww/rVNrGceTIEbrjjjsok8nQnDlz6Be/+IXrPIODg/TpT3+aWlpa6JprrqEXX3yx5uWsO4ZI6+vr41QqxS+88AK//vrrfO+99/LChQv5/PnzyumHhoa4ubmZn3rqKR4ZGeFHH32Uk8kknz59us4ljze/9bJhwwbesWMHnzx5ks+cOcNf+tKXeMGCBfy3v/2tziWPP7914zh79iwvXryYb775Zr7rrrvqU9gG4rdeJicneeXKlXzbbbfxsWPH+OzZszw4OMinTp2qc8njz2/dvPTSS9zS0sIvvfQSnz17ln/1q19xOp3mBx98sM4lj78DBw7wli1buL+/n4mI9+3bZ5x+dHSUP/axj/FDDz3EIyMj/Oyzz3JzczO/+uqr9SlwnSC8RlxnZyd3dXWV/n9mZoYzmQw/8cQTyunXr1/Pt99+e9lrq1at4vvuu6+m5Ww0futFNj09zfPmzeOf/OQntSpiwwpSN9PT07xmzRr+4Q9/yJs2bUJ4rQG/9fLcc89xoVDgqampehWxYfmtm66uLv7sZz9b9tpDDz3EN954Y03L2ei8hNevf/3rvGzZsrLX7rnnHr711ltrWLL6Q7eBCJuamqITJ07QunXrSq81NTXRunXr6LXXXlPO89prr5VNT0R06623aqcH/4LUi+z999+nixcv0sc//vFaFbMhBa2bxx9/nFpbW+krX/lKPYrZcILUyy9/+UtavXo1dXV1UVtbGy1fvpy2bdtGMzMz9Sp2QwhSN2vWrKETJ06UuhaMjo7SgQMH6LbbbqtLmUGvUTJAIuwCgN4777xDMzMz1NbWVvZ6W1sb/fnPf1bOc+7cOeX0586dq1k5G02QepF94xvfoEwmM+sgA5UJUjfHjh2jH/3oR3Tq1Kk6lLAxBamX0dFR+s1vfkNf+MIX6MCBA1QsFun++++nixcvUk9PTz2K3RCC1M2GDRvonXfeoZtuuomYmaanp+lrX/saffOb36xHkcFAlwEuXLhAH3zwAV122WUhlay60PIKUGdPPvkk9fX10b59+2ju3LlhF6ehTUxM0MaNG+n555+nK6+8MuzigODSpUvU2tpKu3btohtuuIHuuece2rJlC+3cuTPsojW8wcFB2rZtG/3gBz+gP/7xj9Tf30/79++nrVu3hl00aBBoeY2wK6+8kpqbm+n8+fNlr58/f54WLVqknGfRokW+pgf/gtSL4+mnn6Ynn3ySDh06RNddd10ti9mQ/NbNm2++SW+99RbdcccdpdcuXbpERESJRILeeOMNWrJkSW0L3QCC7DPpdJqSySQ1NzeXXvvUpz5F586do6mpKUqlUjUtc6MIUjff+ta3aOPGjfTVr36ViIhWrFhB//3vf2nz5s20ZcsWampCu1hYdBlg/vz5sWl1JULLa6SlUim64YYb6PDhw6XXLl26RIcPH6bVq1cr51m9enXZ9EREv/71r7XTg39B6oWI6KmnnqKtW7fSq6++SitXrqxHURuO37q59tpr6fTp03Tq1KnS35133kmf+cxn6NSpU5TNZutZ/NgKss/ceOONVCwWSz8miIj+8pe/UDqdRnCtoiB18/77788KqM6PDGauXWHBVcNkgLDvGAOzvr4+bmlp4RdffJFHRkZ48+bNvHDhQj537hwzM2/cuJEfeeSR0vRDQ0OcSCT46aef5jNnznBPTw+GyqoBv/Xy5JNPciqV4pdffpn/8Y9/lP4mJibCWoTY8ls3Mow2UBt+62VsbIznzZvHDzzwAL/xxhv8yiuvcGtrK3/3u98NaxFiy2/d9PT08Lx58/hnP/sZj46O8sGDB3nJkiW8fv36sBYhtiYmJvjkyZN88uRJJiJ+5pln+OTJk/zXv/6VmZkfeeQR3rhxY2l6Z6ishx9+mM+cOcM7duzAUFkQjmeffZZzuRynUinu7Ozk4eHh0ntr167lTZs2lU2/d+9e7ujo4FQqxcuWLeP9+/fXucSNwU+9XHXVVUxEs/56enrqX/AG4HefESG81o7fejl+/DivWrWKW1pauFAo8Pe+9z2enp6uc6kbg5+6uXjxIn/nO9/hJUuW8Ny5czmbzfL999/P//73v+tf8Jj77W9/qzx3OPWxadMmXrt27ax5rr/+ek6lUlwoFPjHP/5x3ctda3OY0cYPAAAAAHZAn1cAAAAAsAbCKwAAAABYA+EVAAAAAKyB8AoAAAAA1kB4BQAAAABrILwCAAAAgDUQXgEAAADAGgivAAAAAGANhFcAAAAAsAbCKwAAAABYA+EVAAAAAKyB8AoAYJl//vOftGjRItq2bVvptePHj1MqlaLDhw+HWDIAgNqbw8wcdiEAAMCfAwcO0N13303Hjx+npUuX0vXXX0933XUXPfPMM2EXDQCgphBeAQAs1dXVRYcOHaKVK1fS6dOn6Q9/+AO1tLSEXSwAgJpCeAUAsNQHH3xAy5cvp/HxcTpx4gStWLEi7CIBANQc+rwCAFjqzTffpLfffpsuXbpEb731VtjFAQCoC7S8AgBYaGpqijo7O+n666+npUuX0vbt2+n06dPU2toadtEAAGoK4RUAwEIPP/wwvfzyy/SnP/2JLr/8clq7di0tWLCAXnnllbCLBgBQU+g2AABgmcHBQdq+fTvt3r2b5s+fT01NTbR79246evQoPffcc2EXDwCgptDyCgAAAADWQMsrAAAAAFgD4RUAAAAArIHwCgAAAADWQHgFAAAAAGsgvAIAAACANRBeAQAAAMAaCK8AAAAAYA2EVwAAAACwBsIrAAAAAFgD4RUAAAAArIHwCgAAAADW+D9GwH2AywMQ/QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# init condition\n",
    "\n",
    "# boundary box\n",
    "init_cond_coord_0 = sp.stats.qmc.LatinHypercube(d=2).random(n=100)\n",
    "init_cond_coord_0 = sp.stats.qmc.scale(init_cond_coord_0, [0, 0], [1, 1])\n",
    "init_cond_x_0, init_cond_y_0 = init_cond_coord_0[:, 0], init_cond_coord_0[:, 1]\n",
    "init_cond_i_0 = np.zeros_like(init_cond_x_0)\n",
    "init_cond_o_0 = np.full_like(init_cond_x_0, 1)\n",
    "init_cond_t_0 = np.full_like(init_cond_x_0, 0)\n",
    "init_cond_u_0 = np.full_like(init_cond_x_0, 1)\n",
    "\n",
    "# circle 0\n",
    "radius_0 = 0.15\n",
    "center_0 = np.array([0.25, 0.75])\n",
    "init_cond_coord_1 = sp.stats.qmc.LatinHypercube(d=2).random(n=500)\n",
    "init_cond_coord_1 = sp.stats.qmc.scale(init_cond_coord_1, [0, 0], [2 * np.pi, radius_0])\n",
    "init_cond_theta_1, init_cond_r_1 = init_cond_coord_1[:, 0], init_cond_coord_1[:, 1]\n",
    "init_cond_x_1 = center_0[0] + init_cond_r_1 * np.cos(init_cond_theta_1)\n",
    "init_cond_y_1 = center_0[1] + init_cond_r_1 * np.sin(init_cond_theta_1)\n",
    "init_cond_t_1 = np.full_like(init_cond_x_1, 0)\n",
    "init_cond_u_1 = np.full_like(init_cond_x_1, 0)\n",
    "\n",
    "# circle 1\n",
    "radius_1 = 0.3\n",
    "center_1 = np.array([0.5, 0.3])\n",
    "init_cond_coord_2 = sp.stats.qmc.LatinHypercube(d=2).random(n=500)\n",
    "init_cond_coord_2 = sp.stats.qmc.scale(init_cond_coord_2, [0, 0], [2 * np.pi, radius_1])\n",
    "init_cond_theta_2, init_cond_r_2 = init_cond_coord_2[:, 0], init_cond_coord_2[:, 1]\n",
    "init_cond_x_2 = center_1[0] + init_cond_r_2 * np.cos(init_cond_theta_2)\n",
    "init_cond_y_2 = center_1[1] + init_cond_r_2 * np.sin(init_cond_theta_2)\n",
    "init_cond_t_2 = np.full_like(init_cond_x_2, 0)\n",
    "init_cond_u_2 = np.full_like(init_cond_x_2, 0)\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.scatter(init_cond_x_0, init_cond_i_0, s=50, marker='x', c='k')\n",
    "plt.scatter(init_cond_x_0, init_cond_o_0, s=50, marker='x', c='k')\n",
    "plt.scatter(init_cond_i_0, init_cond_y_0, s=50, marker='x', c='k')\n",
    "plt.scatter(init_cond_o_0, init_cond_y_0, s=50, marker='x', c='k')\n",
    "\n",
    "plt.scatter(init_cond_x_1, init_cond_y_1, s=50, marker='x', c='k')\n",
    "plt.scatter(init_cond_x_2, init_cond_y_2, s=50, marker='x', c='k')\n",
    "\n",
    "plt.title('Collocation points')\n",
    "plt.xlim([-0.1, 1.1])\n",
    "plt.ylim([-0.1, 1.1])\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = Net().to(device)\n",
    "criterion = torch.nn.MSELoss()\n",
    "\n",
    "history = []\n",
    "best_loss = float('inf')\n",
    "best_net = None\n",
    "steps = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = torch.optim.Adam(net.parameters(), lr=1e-3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_init_cond(n_samples:int=500, device=None):\n",
    "    init_cond_coord_0 = torch.rand(\n",
    "        (n_samples, 2, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_x_0 = init_cond_coord_0[:, 0, :]\n",
    "    init_cond_y_0 = init_cond_coord_0[:, 1, :]\n",
    "    init_cond_i_0 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_o_0 = torch.ones(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_t_0 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_u_0 = torch.ones(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    \n",
    "    init_cond_x = torch.cat([\n",
    "        init_cond_x_0, init_cond_x_0, init_cond_i_0, init_cond_o_0], dim=0)\n",
    "    init_cond_y = torch.cat([\n",
    "        init_cond_i_0, init_cond_o_0, init_cond_y_0, init_cond_y_0], dim=0)\n",
    "    init_cond_t = torch.cat([\n",
    "        init_cond_t_0, init_cond_t_0, init_cond_t_0, init_cond_t_0], dim=0)\n",
    "    init_cond_u = torch.cat([\n",
    "        init_cond_u_0, init_cond_u_0, init_cond_u_0, init_cond_u_0], dim=0)\n",
    "    \n",
    "    radius_1 = 0.15\n",
    "    center_1 = torch.tensor(\n",
    "        [0.25, 0.75], device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_coord_1 = torch.rand(\n",
    "        (n_samples, 2, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_theta_1 = init_cond_coord_1[:, 0, :] * 2 * np.pi\n",
    "    init_cond_r_1 = init_cond_coord_1[:, 1, :] * radius_1\n",
    "    init_cond_x_1 = center_1[0] + init_cond_r_1 * torch.cos(init_cond_theta_1)\n",
    "    init_cond_y_1 = center_1[1] + init_cond_r_1 * torch.sin(init_cond_theta_1)\n",
    "    init_cond_t_1 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_u_1 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    \n",
    "    radius_2 = 0.1\n",
    "    center_2 = torch.tensor(\n",
    "        [0.5, 0.25], device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_coord_2 = torch.rand(\n",
    "        (n_samples, 2, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_theta_2 = init_cond_coord_2[:, 0, :] * 2 * np.pi\n",
    "    init_cond_r_2 = init_cond_coord_2[:, 1, :] * radius_2\n",
    "    init_cond_x_2 = center_2[0] + init_cond_r_2 * torch.cos(init_cond_theta_2)\n",
    "    init_cond_y_2 = center_2[1] + init_cond_r_2 * torch.sin(init_cond_theta_2)\n",
    "    init_cond_t_2 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    init_cond_u_2 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    \n",
    "    init_cond_x = torch.cat([\n",
    "        init_cond_x, init_cond_x_1, init_cond_x_2], dim=0)\n",
    "    init_cond_y = torch.cat([\n",
    "        init_cond_y, init_cond_y_1, init_cond_y_2], dim=0)\n",
    "    init_cond_t = torch.cat([\n",
    "        init_cond_t, init_cond_t_1, init_cond_t_2], dim=0)\n",
    "    init_cond_u = torch.cat([\n",
    "        init_cond_u, init_cond_u_1, init_cond_u_2], dim=0)\n",
    "    return init_cond_x, init_cond_y, init_cond_t, init_cond_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_bnd_cond(n_samples:int=500, device=None):\n",
    "    bnd_cond_coord_0 = torch.rand(\n",
    "        (n_samples, 3, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_x_0 = bnd_cond_coord_0[:, 0, :]\n",
    "    bnd_cond_y_0 = bnd_cond_coord_0[:, 1, :]\n",
    "    bnd_cond_t_0 = bnd_cond_coord_0[:, 2, :]\n",
    "    bnd_cond_i_0 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_o_0 = torch.ones(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_u_0 = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    \n",
    "    bnd_cond_x = torch.cat([\n",
    "        bnd_cond_x_0, bnd_cond_x_0, bnd_cond_i_0, bnd_cond_o_0], dim=0)\n",
    "    bnd_cond_y = torch.cat([\n",
    "        bnd_cond_i_0, bnd_cond_o_0, bnd_cond_y_0, bnd_cond_y_0], dim=0)\n",
    "    bnd_cond_t = torch.cat([\n",
    "        bnd_cond_t_0, bnd_cond_t_0, bnd_cond_t_0, bnd_cond_t_0], dim=0)\n",
    "    bnd_cond_u = torch.cat([\n",
    "        bnd_cond_u_0, bnd_cond_u_0, bnd_cond_u_0, bnd_cond_u_0], dim=0)\n",
    "    \n",
    "    radius_1 = 0.15\n",
    "    center_1 = torch.tensor(\n",
    "        [0.25, 0.75], device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_coord_1 = torch.rand(\n",
    "        (n_samples, 3, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_theta_1 = bnd_cond_coord_1[:, 0, :] * 2 * torch.pi\n",
    "    bnd_cond_r_1 = bnd_cond_coord_1[:, 1, :] * radius_1\n",
    "    bnd_cond_t_1 = bnd_cond_coord_1[:, 2, :]\n",
    "    bnd_cond_x_1 = center_1[0] + bnd_cond_r_1 * torch.cos(bnd_cond_theta_1)\n",
    "    bnd_cond_y_1 = center_1[1] + bnd_cond_r_1 * torch.sin(bnd_cond_theta_1)\n",
    "    bnd_cond_u_1 = torch.ones(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "\n",
    "    radius_2 = 0.1\n",
    "    center_2 = torch.tensor(\n",
    "        [0.5, 0.3], device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_coord_2 = torch.rand(\n",
    "        (n_samples, 3, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    bnd_cond_theta_2 = bnd_cond_coord_2[:, 0, :] * 2 * torch.pi\n",
    "    bnd_cond_r_2 = bnd_cond_coord_2[:, 1, :] * radius_2\n",
    "    bnd_cond_t_2 = bnd_cond_coord_2[:, 2, :]\n",
    "    bnd_cond_x_2 = center_2[0] + bnd_cond_r_2 * torch.cos(bnd_cond_theta_2)\n",
    "    bnd_cond_y_2 = center_2[1] + bnd_cond_r_2 * torch.sin(bnd_cond_theta_2)\n",
    "    bnd_cond_u_2 = torch.ones(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "\n",
    "    bnd_cond_x = torch.cat([bnd_cond_x, bnd_cond_x_1, bnd_cond_x_2], dim=0)\n",
    "    bnd_cond_y = torch.cat([bnd_cond_y, bnd_cond_y_1, bnd_cond_y_2], dim=0)\n",
    "    bnd_cond_t = torch.cat([bnd_cond_t, bnd_cond_t_1, bnd_cond_t_2], dim=0)\n",
    "    bnd_cond_u = torch.cat([bnd_cond_u, bnd_cond_u_1, bnd_cond_u_2], dim=0)\n",
    "    \n",
    "    return bnd_cond_x, bnd_cond_y, bnd_cond_t, bnd_cond_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_colloc_cond(n_samples:int=3000, device=None):\n",
    "    colloc_coord = torch.rand(\n",
    "        (n_samples, 3, 1), device=device, requires_grad=True, dtype=torch.float32)\n",
    "    colloc_x = colloc_coord[:, 0, :]\n",
    "    colloc_y = colloc_coord[:, 1, :]\n",
    "    colloc_t = colloc_coord[:, 2, :]\n",
    "    colloc_u = torch.zeros(\n",
    "        (n_samples, 1), device=device, requires_grad=False, dtype=torch.float32)\n",
    "    return colloc_x, colloc_y, colloc_t, colloc_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [7476/10000], Steps [7476] Loss: 0.21940"
     ]
    }
   ],
   "source": [
    "EPOCHS = 10000\n",
    "\n",
    "for epoch in range(EPOCHS):\n",
    "    loss_tmp = []\n",
    "    init_x, init_y, init_t, init_u = get_init_cond(n_samples=500, device=device)\n",
    "    bnd_x, bnd_y, bnd_t, bnd_u = get_bnd_cond(n_samples=500, device=device)\n",
    "    colloc_x, colloc_y, colloc_t, colloc_u = get_colloc_cond(n_samples=500, device=device)\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    init_pred = net(init_x, init_y, init_t)\n",
    "    bnd_pred = net(bnd_x, bnd_y, bnd_t)\n",
    "    colloc_pred = func(net, colloc_x, colloc_y, colloc_t)\n",
    "    loss = criterion(init_pred, init_u) + criterion(bnd_pred, bnd_u) + criterion(colloc_pred, colloc_u)\n",
    "    loss.backward()\n",
    "    loss_tmp.append(loss.item())\n",
    "    optimizer.step()\n",
    "    \n",
    "    if np.mean(loss_tmp) < best_loss:\n",
    "        best_loss = np.mean(loss_tmp)\n",
    "        best_net = net\n",
    "    \n",
    "    steps += 1\n",
    "\n",
    "    print(f'\\rEpoch [{epoch+1}/{EPOCHS}], Steps [{steps}] Loss: {np.mean(loss_tmp):.5f}', end='')\n",
    "    history.append(np.mean(loss_tmp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(history)\n",
    "plt.title('Loss history')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss')\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting 300/300\r"
     ]
    }
   ],
   "source": [
    "T = np.linspace(0, 1, 300)\n",
    "\n",
    "for i, ti in enumerate(T):\n",
    "    print(f'Plotting {i+1}/{len(T)}', end='\\r')\n",
    "    fig = plt.figure(figsize=(10, 10))\n",
    "\n",
    "    x = np.arange(0, 1, 0.001)\n",
    "    y = np.arange(0, 1, 0.001)\n",
    "\n",
    "    ms_x, ms_y = np.meshgrid(x, y)\n",
    "    ms_t = np.full_like(ms_x, ti)\n",
    "\n",
    "    x = np.ravel(ms_x).reshape(-1, 1)\n",
    "    y = np.ravel(ms_y).reshape(-1, 1)\n",
    "    t = np.ravel(ms_t).reshape(-1, 1)\n",
    "\n",
    "    pt_x = torch.autograd.Variable(torch.from_numpy(x).float(), requires_grad=True).to(device)\n",
    "    pt_y = torch.autograd.Variable(torch.from_numpy(y).float(), requires_grad=True).to(device)\n",
    "    pt_t = torch.autograd.Variable(torch.from_numpy(t).float(), requires_grad=True).to(device)\n",
    "\n",
    "    with torch.no_grad():\n",
    "        pt_u = best_net.to(device)(pt_x, pt_y, pt_t)\n",
    "    u = pt_u.data.cpu().numpy()\n",
    "    ms_u = u.reshape(ms_x.shape)\n",
    "\n",
    "    plt.imshow(ms_u, vmin=0, extent=[0, 1, 0, 1], cmap='jet')\n",
    "    plt.colorbar()\n",
    "    plt.savefig(f'figs/{i:04d}.png', bbox_inches='tight')\n",
    "    plt.close()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "PINN_examples-wk9cyt7d",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}