\n",
" \n",
"
\n",
"
\n",
"
RMSE:
\n",
"
0.172082
\n",
"
\n",
"
5
\n",
"
\n",
"
5
\n",
"
\n",
"
\n",
"
\n"
],
"text/plain": [
"Evaluation()"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.evaluate(test_ds)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Prediction vs Actual\n",
"\n",
"Let's see how our model performs\n",
"\n",
"First let's see the features we're gonna use:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
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"data": {
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"
\n",
"\n",
"
\n",
" \n",
" \n",
" \n",
" Stint \n",
" Sector1Time \n",
" Sector2Time \n",
" Sector3Time \n",
" SpeedI1 \n",
" SpeedI2 \n",
" Compound \n",
" TyreLife \n",
" \n",
" \n",
" \n",
" \n",
" 362 \n",
" 2.0 \n",
" 25.556 \n",
" 28.348 \n",
" 27.017 \n",
" 212.0 \n",
" 255.0 \n",
" HARD \n",
" 21.0 \n",
" \n",
" \n",
" 320 \n",
" 1.0 \n",
" 25.783 \n",
" 28.501 \n",
" 27.285 \n",
" 213.0 \n",
" 253.0 \n",
" MEDIUM \n",
" 6.0 \n",
" \n",
" \n",
" 369 \n",
" 2.0 \n",
" 25.617 \n",
" 28.264 \n",
" 27.146 \n",
" 213.0 \n",
" 257.0 \n",
" HARD \n",
" 28.0 \n",
" \n",
" \n",
" 350 \n",
" 2.0 \n",
" 26.525 \n",
" 28.968 \n",
" 27.565 \n",
" 211.0 \n",
" 253.0 \n",
" HARD \n",
" 9.0 \n",
" \n",
" \n",
" 361 \n",
" 2.0 \n",
" 25.578 \n",
" 28.403 \n",
" 27.088 \n",
" 214.0 \n",
" 257.0 \n",
" HARD \n",
" 20.0 \n",
" \n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Stint Sector1Time Sector2Time Sector3Time SpeedI1 SpeedI2 Compound \\\n",
"362 2.0 25.556 28.348 27.017 212.0 255.0 HARD \n",
"320 1.0 25.783 28.501 27.285 213.0 253.0 MEDIUM \n",
"369 2.0 25.617 28.264 27.146 213.0 257.0 HARD \n",
"350 2.0 26.525 28.968 27.565 211.0 253.0 HARD \n",
"361 2.0 25.578 28.403 27.088 214.0 257.0 HARD \n",
"\n",
" TyreLife \n",
"362 21.0 \n",
"320 6.0 \n",
"369 28.0 \n",
"350 9.0 \n",
"361 20.0 "
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"test_ds.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The true values (`y`) are:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([27.017, 27.285, 27.146, 27.565, 27.088])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = test_ds['Sector3Time'].values\n",
"y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And now there's the predictions (`y_hat`) based on our features:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([27.295267, 27.28691 , 27.108194, 27.403025, 27.295267],\n",
" dtype=float32)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_hat = model.predict(test_ds)\n",
"y_hat"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### That's a pretty close value! 👏\n",
"\n",
"Well done, our model can give a pretty good prediction on how Hamilton lap will be with margin of error around:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"------------------------------------------\n",
"| 0.057 seconds\n",
"------------------------------------------\n"
]
}
],
"source": [
"error = np.around(y_hat - y, decimals=3)\n",
"error_mean = error.mean()\n",
"\n",
"print(f\"------------------------------------------\\n\"\n",
" f\"| {error_mean:.3f} seconds\\n\"\n",
" f\"------------------------------------------\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualizations\n",
"\n",
"Let's vizualize how close our predictions are from the true values"
]
},
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"cell_type": "code",
"execution_count": 19,
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dO+SujiwuoSrK0/aYrUj0nTobJpMrYnWdZpXp+AlvYdLkKTKB1DTIX7ZJk7QTSSyRaD1z+pRMMh09cVaubH37rQn4ZttXWu/DN0eMxjszZz/yQhvh0rxFK5nYEeWJR93F/w8Z9KpccSaOdu06YPPWbbnJZJHYFI8gi6SOeKHRF+vWyPNE8mb1mvVYvWqlTARre2xerNoVq4hF8qZr5w4yriLhffDPf+XqzLx90ST4RIw+X70SP36/Dy6urggNCZYrZ4s7NLEU54nYjx87CseOHinuMq1tL2xLB01sRIJz0KsD5L0hLMTqT5H4E/UOGjgAUZGRMvEk7iPRZ+/6DxPOmiScSLh269oRly7GyJ9rvhgomHxd8sly9O7TFzEXzsukmi5HYQlV8YIosfJR3Nvtnmgt6y3K+9ude9HQzw9bvtwkX+4lvnwQ/RT9EfdC187tEREeDrHCV5wnnF/s+1zuCs79Bw+jfgOvIhOq8xe8j9cGDZFJ9i6d2iPh7l3ZvVcHDkLv5/vihT7Pat1DVdf7V5Snaxu12Wo+TwVflrd5yza5slas5v7gPwvkS7dEfLd/8zUmTxovixN/s8QXKVcuX8aXmzcWGz5NTMTfLXEvbflqO554sh127fgWE8aPzr3+jwN/yWT2oYMHclcui7oWvr9IJj/FZ1zb36KgJk11TqiKRGmzZi1kklZziMT6n38flfdSvdo15I+ZUC02tDyBAhSgAAUoQAEKUIACFKAABfQgwIRqIYiahKpI3ohH5gseYiWgSFrlTahqzqlduw46PNUR9ep5olr1Gnj2ud75VphqEqoikTp+7MjcojVvchcJSpHc0xyaF8Os/mwFFi54V/64LAlV8ZIZUaZI/Hbv2jFf1zTlapIomqTdsKGD8OsvP+Weu2zFatmvvG0q7F4cOmw45sydL1eU9Xyma6EvZdLsqSkSnSKxl/cQCVSxEjfQzwvdn+mJRR9/IhN6Hdq11Xrra0uonj4bJhOonTs+KZOMmkO88Gn2nHdx6uQJudpQHJpkkqhXlwRqwcYcPXEGlSpVzt36QeyrOvXtScV+XLW1vaiEasHYaBKIBVfTiheZeXrWz03Mr12/Ua4c3PDFOsyfNzu3beLxbbFaVqwUbuTvXWybizpBJFTFIfaOdStfHvXrN5CJPpEAE4lPkagsylsk5mIux+WuhhZfWGiOr7/ZKcvSJNc1L8AqGN+Ce6gWlnA7dSZUrogW7dGW+Na2h6qu96+4j3RtozZT8SVIRPQl+WVIsyaBciWtMIo8f1n+TKwYF6uTNQlM0RexPYPmcXhdgykSpyKBKr5IadksSF4mtjTYsGmL/DyIz4U4REJbrFwVq9X9fevLlcGFHfpIqGrKFV9+PNWpM3x8fFGzRi306PWs/DJGbINw5cplJlR1DTLPowAFKEABClCAAhSgAAUoQIEyCTChWghfaR75F6ulvtnxnXwkt+CR95F9bQnVt96einHjJ2Hnt9sxccKY3CI0j+eLpNyUyRPlz8uSUNWWuBXlapJPmv0+tSVU5767AEOGDpOPa4vHtrUd4lFzkZzUrOgVq1/DwkLx3rtzclfyasoq6i5+/rke6NP3Rbnva0GfgtdpS0qev3hVtiPvC5LEteKR5d/++DNf8ki0WTz6rln1VtpPWOPGQdi+c498FH/alLfw1dYviyxKHwnVfT/+CrFaevBrr2D/H7/l1qeJrdg3VOyPKh6P9/bx1doesbqwQT330nZdXqdJIBYsRHwRMW7MyNz9T7V5a1YwFtUIcQ9u2rhexrCwrRV0SaiKe0PsM1pUvLUlVHW9f5OSEnVuY1H91axG1Ty6L1bRLvjPhzh54jjE50QcYmsGsUWDOMSXQteuXcXRI0cwd86M3NW3RdXx5dZv8GS79vI++XzVytxTN2zeKj9DfZ/vJfckbt6iJXbs2iu/KHm89f+2BilYtj4SqnK7gi3bIB79L+zQrHbmCtUyfWR5MQUoQAEKUIACFKAABShAAQroKMCEaiFQpUmoapKct27exNatm3Hi2DFc+P/Ho8V+kWLllmYPVG0JVfFyoImT3n4kYTh5yjS5D6e+Eqri0e0+L7xY6F6K4mVXIgko9iP9dvu23Ef+C66CnDV7HoYNH1FsQlXQigTzytVrERjYSK6i0xyrPluO/yyYD017Ll++hKNH/i30thXnzZw1F8/3faHYPSC1JSVFck+scCyYJBQrisXLfvJudaCvhKrojCbh9vfhvzCgX98iP5b6SKju3vcTmjRp+khCVbz4ScRAk1DV7NkqkmZi24CCR1Jiolz9WZZDs0J1/rtz5L64YlW02Dai4EpGbd6aVZFi1eWPP+wrtCnixWZiD2CxZ2jBvXDFBbokVLXdG3kr1JZQ1fX+FS950rWNRZlrkszihXeNA3zw+/4/4eXtk2/7DnG92Pt48SfL5Ep5sSJYHGLLB7E9RHH7AGv2S9XWDvHY/dDBA9GxUxd8sfHLfPshF3aNPhKq23fsRstWreWezWIV/z9//4XIyAj5kjnxZRYTqmX5pPJaClCAAhSgAAUoQAEKUIACFCipABOqhYiVNKEq3kB94NDf8nFb8ehr3kM8smzKhGrBfU41+zCKRFret5yLNmvevi62AhDJL20rVEuSUM1r4duwId6eMl0+ai62UhCPKGseuf/3n7/R78Xntd6/b7w5UiZVRdJV7JGp7dCWlAwJPw8XFxf5GLt4nF1zdOveQ+7BGh4Whqe7dJA/1mdCdfqMWRgxcky+F+eUtO0leeRf14SqeGS+TdvH8d78ufKRfEMc2l5KVbAubd7i8e6zIZH5HjMvrJ1im4Ijx0/Lt8IHBeZfdatLQlXzZYjYO1gk1gs7NAlVscev2OtXc+h6/5akjcXF4sSpYPkCrTffGCrv3aK2ZxDJ1A5PdcKcue9C/J3Ku9VCYfU81/t5fLp8lfx8Hvn373ynODo64fEnnpRJTZ8GdXIfr8+7DUBhZWoSqgX/FomV1GJFtfgy5cm2LfNdWvClVGJbg7yP9mtO1rzgjAnV4u4a/p4CFKAABShAAQpQgAIUoAAF9CnAhGohmiVNqGpWahVMLGj2ItTlkX99r1Bd8dnn6NnrOfnI7oL35uX2UvOIu3iku2ljv9zkoliZKlaoip97eXrIR4XLmlAVL59KTEzKfdGUaITYBiAsMkaumqvrUV0meUQyWtTX65mu8k30mkM8XixelPXRh+/nPpovzhPJF7Ffoubo9exzuBgTI68V+5dWr15D7g+b9wVh3+39EU2bPiZX3ooVuJpDvKHcz98/38rX0iRUR40ehx9//F7u8Zq3/cdOnJXJr+K2RxDXaGu7IRKqI0eNxbR3ZspkZYvHGuXbZ1O89ElssSBeyKU5RELxxZf6I/jc2dytJ4r7Q1TWhKooX5MIF/fAsk+X5KtS7Ad8/PhRuSeueGxfrIDWPI4uThT9+P3AX/IFai+90BtH/v2n0D02NUno/ft/x+CBL+fWIV6ENnjIMKxYvhQ9evbCylVr8yXexYm63r/iXF3bWJyrZtW62LtU7OUs9sGdM+ud3MvEivY9e77LfdGY+IX4jCxf+bl88VaLxxprreK7PT+g6WPNZJ8/fH/hI+dp9hfWrFoXe7qKLS2mT52MrVs25/s7ExTUVH7etP0tEr6iPM0XTpoXAPZ94SW5ujbvFg6a7SNat2iKuLhrsh6x+v2X3w/KL0qYUC3uruHvKUABClCAAhSgAAUoQAEKUECfAkyoFqJZ0oSqSAyIVW4iASj2EwwLDZGP4YqXAInDFAlVzd6KIkH6268/w8HREf8cPozVq1bkvgVcrELb/d1OufJLvM1cJKTWfr4K4hFtcZQ1ofrJ0hXyMX2xAu340aNITklGx06dZSIk74rUz1avxTM9esmk6j9/H5aPbjds6IeAwEYyWSMSr+LY+vW3coWcSCSJ/UHj4+Plnop16tTN3aZAPFbdvv1TEI9EHzywH+7u7pg3dxZSUpLlHpbiEHWEBJ9D+w5PyX1ExYo78aIdzaPopUmoapKhly5dRGREuNxe4Ml2HSDuDVF+86aB+VbGFvYh1tb2Vq3aYMasOflegqYtNrquUBX1Hzt5FtWqVZftO7D/94crHRsFwcfXF7du3cx9IZE4V+zJKfbmFNsDtGreRKe/QfpIqIqk/NJlD1fQilXEp0+fRK1a7nKfWPGSsTGjhmPvnt3QvChN3O9iFbOrmxvEY/aa/XuLSqjWreeJg3/+I5P8F85H459//oa7hwcef/xJiK0PxMpVkZw9fuqcPOfwX3/i3r0EZGRkYtyYEdD1/tW1jcXhintKJJpFW8Rnpkljv3x7o/595IQ0El8wnD51Em5u5dG5S1eZeCxqRbL4/IvH/YVZUKOGhe63unLVGvTo+WzuSvHBQ4dh3rsLZJPFZzoqKhKNGgchKKiJ/CJFbA1Q1N8isQJZrEQWid7g4HMyZuILEXHkTaiKPom/G+ILgGPHjsj71t8/IDe+TKgWd9fw9xSgAAUoQAEKUIACFKAABSigTwEmVAvRLG5vQPHmevEG+317d2P0yOGyBJE0mL/g/dwJviZx17pNW5mw0uyhKlYyihdN7dq5AxPGjcqtffyEt+RqzO3ffI3Jk8bn/lzzsirxQiPxYiNxFHwpleZxeJFYEgkmzbF+w2a0a/+UXMUmDs0LnUQCVew9mPcFLyIx8+XmjZj5ztTc68ULZ8SLZ0RSROybqDlmzJyD4SNG4Yv1azF39gyt92PvPn3x3oIP4Orqmu+c6KhI+QIdzaP3IjE0e867eG3w0Hz7rIo2nTlzGs/17CavF28VX7J0uUzoaPaFFD8XbyN/7ZX+CA8Pg3i0euPmryC2F9CcIx7RFskdkRBctmKVTNJqDvGId/9+fRARHp77s9IkVD9e8mluUjpvZ0WCfcQbQ/OtvNUGpq3tDby85HYHeeOrLTaaFYbC4+DB/blVaV5W1f+lPjKhLA6RyPps9Tp5H+T1FIllsU/ljOlTcq8Xj5aL7RHE6kCxSlCXQ5e9SUU5xXlru4+E7eDXXpYrVMW9seO7fXIPYM0h9jMWR9Vq1fBCn2fl4+6alxYVTAy3a9cBny7/TCZpNYdIzu7csR3iUXVxTJg4We4drLmfNS9jKsn9q0sbdbHd+d0+NGveAiEhwXjm6U75LhEvnus/4JXcz734pfgsiX1oR745TGvxmsRnYXvRai7SPKYvvtQQK9nFIVY7i79dIgaaQ2x/Mn/e7NwXsWn7WyT+1n6+9ovctop2ivtcrKgVCVXNFioiefrtrr3yCwrNIfxdXFzlCmSxal18caMtvrqY8hwKUIACFKAABShAAQpQgAIUoICuAkyo6iqlw3lubm5o3eZxeebRo//q9EZtHYot0yki2SOSordv3873OLooVCQnWrVui/T0NLm6TCSQDHGIJEdQ44erGs+eO4O78fFaqxEvmPHzD8DFixcQHRUlE0EFD9EnPz9/mTwRK03FatSCh+ibeIFPZEQEbt++le/XItnq4+OLkydO4OrVWL12WayW9Q8IlCtUT5088UjdulRWVNt1ub6k5whPX9+GcPeojdCQ4NxHqktajqHPFwngpk2bIeFegmxnwZdbifpr1qyF5i1a4NTJk3K1eEkPUYd4VP3Gzevy3ins/hPJPRsbG5nM1DymrqlHl/u3rG3UtU+iLeJejI+/Iz8nqampul5aqvNEfQ0aeCE6OqrQz5W2v0XiC542bR5/uEL9n8OFxlU0SKycFcn/ihUr4szp0zKByoMCFKAABShAAQpQgAIUoAAFKGAKASZUTaHOOilAAQpQgAIUoAAFKEABClCAAhSgAAUoQAFFCjChqsiwsdEUoAAFKEABClCAAhSgAAUoQAEKUIACFKCAKQSYUDWFOuukAAUoQAEKUIACFKAABShAAQpQgAIUoAAFFCnAhKoiw8ZGU4ACFKAABShAAQpQgAIUoAAFKEABClCAAqYQYELVFOqskwIUoAAFKEABClCAAhSgAAUoQAEKUIDwTHCYAAAgAElEQVQCFFCkABOqigwbG00BClCAAhSgAAUoQAEKUIACFKAABShAAQqYQoAJVVOos04KUIACFKAABShAAQpQgAIUoAAFKEABClBAkQJMqCoybGw0BShAAQpQgAIUoAAFKEABClCAAhSgAAUoYAoBJlRNoc46KUABClCAAhSgAAUoQAEKUIACFKAABShAAUUKMKGqyLCx0RSgAAUoQAEKUIACFKAABShAAQpQgAIUoIApBJhQNYU666QABShAAQpQgAIUoAAFKEABClCAAhSgAAUUKcCEqiLDxkZTgAIUoAAFKEABClCAAhSgAAUoQAEKUIACphBgQtUU6qyTAhSgAAUoQAEKUIACFKAABShAAQpQgAIUUKQAE6qKDBsbTQEKUIACFKAABShAAQpQgAIUoAAFKEABCphCgAlVU6izTgpQgAIUoAAFKEABClCAAhSgAAUoQAEKUECRAkyoKjJsbDQFKEABClCAAhSgAAUoQAEKUIACFKAABShgCgEmVE2hzjopQAEKUIACFKAABShAAQpQgAIUoAAFKEABRQowoarIsLHRFKAABShAAQpQgAIUoAAFKEABClCAAhSggCkEmFA1hTrrpAAFKEABClCAAhSgAAUoQAEKUIACFKAABRQpwISqIsPGRlOAAhSgAAUoQAEKUIACFKAABShAAQpQgAKmEGBC1RTqrJMCFKAABShAAQpQgAIUoAAFKEABClCAAhRQpAATqooMGxtNAQpQgAIUoAAFKEABClCAAhSgAAUoQAEKmEKACVVTqLNOClCAAhSgAAUoQAEKUIACFKAABShAAQpQQJECTKgqMmxsNAUoQAEKUIACFKAABShAAQpQgAIUoAAFKGAKASZUTaHOOilAAQpQgAIUoAAFKEABClCAAhSgAAUoQAFFCjChqsiwsdEUoAAFKEABClCAAhSgAAUoQAEKUIACFKCAKQSYUDWFOuukAAUoQAEKUIACFKAABShAAQpQgAIUoAAFFCnAhKoiw8ZGU4ACFKAABShAAQpQgAIUoAAFKEABClCAAqYQYELVFOqskwIUoAAFKEABClCAAhSgAAUoQAEKUIACFFCkABOqigwbG00BClCAAhSgAAUoQAEKUIACFKAABShAAQqYQoAJVVOos04KUIACFKAABShAAQpQgAIUoAAFKEABClBAkQJMqCoybGw0BShAAQpQgAIUoAAFKEABClCAAhSgAAUoYAoBJlRNoc46KUABClCAAhSgAAUoQAEKUIACFKAABShAAUUKMKGqyLCx0RSgAAUoQAEKUIACFKAABShAAQpQgAIUoIApBJhQNYU666QABShAAQpQgAIUoAAFKEABClCAAhSgAAUUKcCEqiLDxkZTgAIUoAAFKEABClCAAhSgAAUoQAEKUIACphBgQtUU6qyTAhSgAAUoQAEKUIACFKAABShAAQpQgAIUUKQAE6qKDBsbTQEKUIACFKAABShAAQpQgAIUoAAFKEABCphCgAlVU6izTgpQgAIUoAAFKEABClCAAhSgAAUoQAEKUECRAkyoKjJsbDQFKEABClCAAhSgAAUoQAEKUIACFKAABShgCgEmVE2hzjopQAEKUIACFKAABShAAQpQgAIUoAAFKEABRQowoarIsLHRFKAABShAAQpQgAIUoAAFKEABClCAAhSggCkEmFA1hTrrpAAFKEABClCAAhSgAAUoQAEKUIACFKAABRQpwISqIsPGRlOAAhSgAAUoQAEKUIACFKAABShAAQpQgAKmEGBC1RTqrJMCFKAABShAAQpQgAIUoAAFKEABClCAAhRQpAATqooMGxtNAQpQgAIUoAAFKEABClCAAhSgAAUoQAEKmELAYhOqHh61Ub58eYSEBOvNtVy5cvDzD0BEeBiSkpL0Vi4LogAFKEABClCAAhSgAAUoQAEKUIACFKAABZQhYHEJVd+GDbHvh19hb28vI5CWloZvtn2Fme9Mlf8eczkO1tbWj0Rn6OCB+P23XwqNWrt2HbBi1Rq4ubnJ3+/+bhfGjRmhjAizlRSgAAUoQAEKUIACFKAABShAAQpQgAIUoIDeBCwuoervH4DpM2Zj0QcLcevWLSxZuhyt27RF0yB/3I2PR4uWreDg4JAL2KlTFwwdNhw9u3fBuXNnH4Ft1Kgx9v34K65ejcVnK5Zh3749qFChImIunNdbEFgQBShAAQpQgAIUoAAFKEABClCAAhSgAAUooAwBi0uoFmQXCdRvd+6RK1Q3b9rwSFROnQlFQsJdPNX+8UIjJpKpAQGB8PWqi/T0dGVE1UCtdKlUE+Uq1kDy3eu4Hx9noFpYrDkK2DmWg4j/3WvR5tg8tsmAAuIzLw7xueehLoGKtbzk3/qMB8nq6jh7i+oNmuLG+VOUUJkAx3qVBTxPdznWqzf2HOvVG3uO9eqNPXuuPwGLT6h++NES9Ov/Mjp2eALno6PyyQ0eOgzz3l2A55/rgZMnjheqGnn+MjIzM5GUlAhXVzfEXbuKiePH4OzZM/qLgkJKEv+xJZJqYoLN5IpCgqanZnKSpSdIBRbDSZYCg6anJnOSpSdIBRbDSZYCg6aHJnOs1wOiQovgWK/QwOmh2Rzr9YCo0CI41is0cGy2WQlYdEK1S9duWLNuA44dPYIX+z6XD97Kygoh4ecRE3MBPbp11hqUS7E3kJCQgL17vkPagwd4+dXXYGtriyaNGiI5ORluVeuYVUAN2RhbByfYOTgjIy0FmWmphqyKZZuZgLWNHewcnJCWkmhmLVNPc7KzM2FtbWv0Dou4iyODn3mj25u6QgdnNxn37KwMUzeF9RtZwMmtMlIT7xi5VlZnagGO9aaOgOnqN+VYb6r/vjGdtnnVzLHevOJhzNaocaxPvHXZmMSsSwUCFptQbd6iJbZt34W4uGvo8GQbuco07zF1+gyMGj0OXTu3R0R4eJEJ1RXLl+LD9xfKc8QLqjZv3YYRw1/Hjz/sg5NrZRXcJg+76FCuvPxfWvI9+T8e6hGwsXOQsU9JuKmeTptZT7NzsmBtZWP0Vjk4l5d1pqXwM290fBNX6Fyhmvxbn5WRZuKWsHpjC7hVqYPE25x0GNvd1PVxrDd1BExXvynH+uzsLFhbG/+/b0ynbV41c6w3r3gYszVu1eog8aa6xvrUJH5ZbMx7TA11WWRCtVPnrli7fqN8cVS3rh0f2ftUvJQqOCwaZ06fwgt9ni0yzmGRMfjn778wdPBAeV7HTl3wxcYvMWHcaOza+a0a7pHcPvKRf1WFO19n+RigemPPxwDVG3s+Bqje2PMxQHXGnmO9OuMues2xXr2x51iv3thzrFdv7Nlz/QlYXEK1W/ceWL1mPWJjr8ikZ05OjtS6c+eOTLCKY9HHn+DFl/rjybYtceVK/m9lRCK2Veu2aOTvLc8VydMOT3WSWwbcuH4dGzZtQf0GXmga5I+Eu3f1FwkFlMSEqgKCZKAmcpJlIFgFFMtJlgKCZKAmcpJlIFgFFMtJlgKCZIAmcqw3AKpCiuRYr5BAGaCZHOsNgKqQIjnWKyRQbKZZC1hcQnXO3PkYOmz4I+iXL1+SCVQ3NzecCY7AoUMHMOjVAY+ct/eHX9CoUWPUq/3wzdaurq74+bcDcHf3kP8utg6Y+vYkfLt9m1kH1hCNY0LVEKrKKJOTLGXEyRCt5CTLEKrKKJOTLGXEyRCt5CTLEKrmXybHevOPkaFayLHeULLmXy7HevOPkaFayLHeULIsV00CFpdQNVTwREK1arVqcpsAzapXQ9VlruUyoWqukTF8uzjJMryxudbASZa5Rsbw7eIky/DG5loDJ1nmGhnDtotjvWF9zbl0jvXmHB3Dto1jvWF9zbl0jvXmHB22TSkCTKgqJVJm0E4mVM0gCCZqAidZJoI3g2o5yTKDIJioCZxkmQjeDKrlJMsMgmCCJnCsNwG6mVTJsd5MAmGCZnCsNwG6mVTJsd5MAsFmKFqACVVFh8+4jWdC1bje5lQbJ1nmFA3jtoWTLON6m1NtnGSZUzSM2xZOsozrbS61caw3l0gYux1WqOrRWlZ6K/ZfAA/fP8FDHQIc69UR58J6ybFevbFXSs/fmTEb27d/jajISLNtMhOqZhsa82sYE6rmFxNjtYiTLGNJm189TKiaX0yM1SJOsowlbX71cJJlfjExRos41htD2bzqqFApCK3br4OzS23ZsJT7V3D0zzcRf/uEeTWUrTGYAMd6g9GafcEc680+RHpr4NhxEzF5yjSt5Y0ZNRx79+zWW336KuhS7A3MmjENmzZ+oa8i9V4OE6p6J7XcAplQtdzYFtczTrKKE7Lc3zOharmxLa5nnGQVJ2S5v+cky3JjW1TPONarL+5PdtmFqjXa5uv47RtHcOiXZ9WHodIec6xXaeABcKw3z9hXrf44yldqjAepcbhxbT8y0u+VuaGVKldGYEAjWU7L1q0hEqzTpryFq7Gx8menTp1AUlJSmevRdwFMqOpblOWZVIAJVZPym7RyTrJMym/SyplQNSm/SSvnJMuk/CatnJMsk/KbrHKO9SajN1nFvfpFw87eNV/9GemJ2LvN22RtYsXGFeBYb1xvc6qNY705ReNhW1q2WwOPuv/7Qis97S7++L4LUpKv6K2x3br3wOo169GxwxM4Hx0lyw0JP491a1eje/ceqOXugUkTxmLJ0uUYPmww/vrzkDzn62924t69BLz5xlD574MGD8XU6TPh7OyMy5cvYcnHi7Br57ePtHPdF5tQr54nOj31ZO7vvtz6DVxcXDB+3Gj88NNvKFeunPxdYmIipr49CT/+sE/+e96E6u/7/8Shgwcwb+4s+btJk6egT98X8USbFvLfH2vWXParatVqSEhIwDdfb8XCBe/K3y1f+Tme7tYddnZ2SE1NxepVK/DJ4o/0YsoVqnphVEchTKiqI86F9ZKTLPXGnglV9caekyz1xp6TLHXGnmO9euLu4tYAPgHjUK9Bf8Aqf79zsrNw6sgUXIz+Uj0gKu4px3r1Bp9jvWFj7+LaAB6ez+tcib1DZXg1fJiszHvcvvkvbsb9qXM59xPPI/biLq3nF5ZQFYlLcYSGhuBq7BWsW/u5TKCOGjEM3+/bK3936PAR3L17F8/17IZWrdvgm2+/wx+//4qtW77E8DdHyoSml6cHcnLy78Pdr//L+PCjJej1TFecPXsGbm5uOBsSic9WLsOWzZsw99338NOPPyA1NQXvzJyDSpUqw8/HU9aZN6F6LjQKhw7ux+iRw+XvPli0GL2f7wtfr7pwcnKSZcbFXcOiDxaiWbMWGPL6G+j7fC94e/vg/Q8/xuerVuLo0SPo0aMX7OztcsvRGVbLiUyollVQRdczoaqiYBfoKidZ6o09E6rqjT0nWeqNPSdZ6ow9x3rLj3uFSo3gGzgB7nV7ys6Kea9VwYTqf392PzEGoWc+QOzF7/iiKgu+NTjWW3Bwi+kax3rDxr6Ge1e07bhZ90pEHrLA32P5d7rwH2stN+7Kz/jnwGslTqh++P5CrFi+VF7n6uqK4LBorQlVkWxt1rwFJk0YI8+3t3fA4k+W5Ts/bwOiLlzB4cN/YvDAlzF1+gyMHDUWAQ0bIDk5GRUqVpQrTYOCmiIoKAie9Rugrkf1EiVUX3/jTcye8y5mz5yO+Pg7/024LsH+P37DmdOnMWPWHIj+rV2zCmlpabrHRIczmVDVAYmnPBRgQlW9dwInWeqNPROq6o09J1nqjT0nWeqMPcd6y417tZpPwSdwDKrVeEJ2MivrAS5GbUFk6GfyZ7Xqdpc/v3bpR2RmJsM/6G24lveRP0uID0Ho6YW4fvU3ywVScc841qs3+BzrDRt7pa1QnT51MrZueZgALi6h+uffR1G7dh3cv38/H+KKZUvlytOCx8pVa9D16e7wrl8bx06cxcWLMXihz7Po1Lkr1q7fiMzMTFy5fAl29vaoU6duiROqiz7+BC/1G/DIPrDHjh3BmJHD8d2eH+Dj21A26+rVWIwfOwrHjh7Ryw3AhKpeGNVRCBOq6ohzYb3kJEu9sWdCVb2x5yRLvbHnJEudsedYb1lxt7Kyhnvd5+ATMAYVKgXKzon9+M5HrEd02OfISE/I7XDBsd7KygZ1GrwEv8aT4VzOQ54Xf+sEzhyfibu3T1oWlMp7w7FevTcAx3rzi72p9lAVj9bnTaiKR+jDoy7KvVR3fPuNhMr7yP93e3+Eu7s7WjzWWCfEuvU8ceivf/HF+rUYMnQY+r/UB//8fRjf//SbTMw+FuQvk6oiKSqSo4WtUD0THIHjx47g9SEPV9/mfeR/wsTJmDBpsnz8X9sKVJGofa53H4wZNwE3b97Ak21b6tT24k5iQrU4If4+339suVSqifvxcUi+e50yKhLgJEtFwS7QVSZU1Rt7TrLUG3tOstQZe471lhF3GxsH1G3wMrz9R6Kca13ZqZTkq4gOW42YyE3Iykp9pKPaxnprG3vU9xkC38DxcHCsLK+Li/0FwSfnI+lepGWAqbwXHOvVewNwrDfP2Fet/jjKV2qMB6lxuHFtPzLS7+m1odr2UM2bUBUVij1LoyIjMHb0CLz4Un+Mn/iW3ANV7KE68LXBeG/hB9i8aQPmz5uNOnXrYuy4Sdj93U78/tsvhbb3r3+OyeSp2Ie1SaOHq0W3bd+FxkFN8Pyzz8DRyQmfLF2u9ZH/r7btQEBgI/To1hmPNWuG9xZ+CHt7e5lEFeWKVbNhYaEY+HI/WfarAwfBwdEBKckpqFK1KpYsXoSszEz89Ot+pCQno0un9npxZUJVL4zqKIQrVNUR58J6yUmWemPPhKp6Y89Jlnpjz0mWOmPPsV7Zcbezc0ODhsNQ3/d1ODpVkZ1JTIhAVOgKXI7ZgZzsTK0dLG6st7UtB++AUfDyGwE7Oxfk5GTjSswuhJxeiNTkWGXDqbz1HOvVewNwrFdn7LUlVKdNeQtfbf3fywgnT5mG0WPGw9raGunp6cjOzpYJy969Hm4RI1aSikSr1X834hbnDBo4AH8f/qtQWPGSqLnz3pMvh1rw3jx5TlCTpvLlV87OzvLf4+/cQaXKlfOtUJ35zlSZuG3XrgPWrN8IR0dH+eKru/HxMgmreYHVy68MxLz5C2WSVRzinJUrPpUJ3Bkz5+S2U1w3dMhAnDxxXC83ABOqemFURyFMqKojzkyoqjfOhfW8uEkWtSxXgJMsy41tcT3jJKs4Icv8PROqyoyro1MNeAeMhKfXQNjalZOduHPrGCKDlyMu9iedOqXrWG/vUBG+gRNR32cwbGwdkJ2VgYvRXyLs7MdIe3BLp7p4knkJcKw3r3gYszUc642prcy6HBwc4OPji3PnzhbaAZFM9fH1RfL9ZMTGXil1Jx9r1lzuqyoSqsUdjRsHITw8TCZ5Czs8PGrDydkJ0VFRMqkqDtFOL29v3LlzR6c6imtD3t8zoVoSLZWfy4Sqem8ATrLUG3tdJ1nqFbLcnnOSZbmxLa5nnGQVJ2SZv+dYr6y4urjWh0/geNTx7AtrGzs5cbx+9VdEhizHnZsle9lGScd6R+ea8A+aijr1X4K1tQ2yMlMRHf45IoKXITMjSVmQKm8tx3r13gAc69Ube/ZcfwJMqOrP0uJLYkLV4kOstYOcZKk39iWdZKlXyvJ6zkmW5cVU1x5xkqWrlGWdx7FeGfGsWLkJfBtNRE2Pp+Wqm+zsTMRe3IXwc5/gfmJ0qTpR2rFeJHUDms6Ae92est70tASZ0I0OX4PsrAelagsvMq4Ax3rjeptTbRzrzSkabItSBZhQVWrkTNBuJlRNgG4mVXKSZSaBMEEzSjvJMkFTWaWeBTjJ0jOogorjJEtBwdJjUznW6xHTAEXVcO8Cn4AxqFK9tSw9MzMFF6O2yATmg9SyvSy2rGN9+YqBCGq5EFWqtZJtS025jvBzi3ExekuRe7cagIlFllCAY30JwSzodI71FhRMdsVkAkyomoxeeRUzoaq8mOmrxZxk6UtSeeWUdZKlvB6zxRoBTrLUey9wkqXO2HOsN7+4W1nZoLZnH3gHjEH5Cg/fipz2IB4XItcjOmwNMtIT9NJofY31VWu0Q+BjMyBW0YrjfuIFhJ75ALEXd4tXhOilrSxEvwIc6/XrqaTSONYrKVpsq7kKMKFqrpExw3YxoWqGQTFSkzjJMhK0GVajr0mWGXaNTSpGgJMs9d4inGSpM/Yc680n7tY2jvD0Hghv/xFwLuchG5Zy/wqiwlYjJmqz3h+n1/dYX6tOTwQ0mQbX8t6y7QnxwQg5tRA3rv1uPshsiRTgWK/eG4FjvXpjz57rT4AJVf1ZWnxJTKhafIi1dpCTLPXGXt+TLPVKKq/nnGQpL2b6ajEnWfqSVFY5HOtNHy87+wpo0HAYGvi+DgfHSrJB9xLCERm8TO6TmpOTZZBGGmKsF6trxUur/ILehnM5d9nu+FsncProdCTEnzFIP1hoyQU41pfczFKu4FhvKZFkP0wpwISqKfUVVjcTqgoLmB6by0mWHjEVVpQhJlkKI1BtcznJUm3owUmWOmPPsd50cXdyrgVv/1Hw9H4VNrZOsiG3b/wr90e9fvVXgzfMkGO9tY096nsPgW+j8XBwrCz7EnflZwSfeg9J9yIN3jdWULQAx3r13iEc69Ube/ZcfwJMqOrP0uJLYkLV4kOstYOcZKk39oacZKlXVRk95yRLGXEyRCs5yTKEqvmXybHe+DFycfNCw0YT4VGvN6ytbZGTk4O42J8RcW4J7t45bbQGGWOst7UtBy//kfD2Hwk7Oxfk5GTjSsxOhJz+D1KTY43WV1aUX4BjvXrvCI716o09e64/ASZU9Wdp8SUxoWrxIWZCVb0h1tpzY0yyyG6eApxkmWdcjNEqTrKMoWx+dTCharyYVK7WGr6BY1HDvbOsNDsrA5djdiAyeCnuJ10wXkP+W5Mxx3p7h4rwDZyI+j6DYWPrIPseE70Z4WcXI+3BLaP3Xe0VcqxX7x3AsV69sTdEz7t07YYaNWpg86YNsLW1hVv58oi/c6fEVVWqXBn3k5KQnp5e4mtNcQETqqZQV2idTKgqNHB6aDYnWXpAVGgRxpxkKZTIYpvNSZbFhrbYjnGSVSyRRZ7Asd7QYbVCzdrd4BMwBpWrNpeVZWYk42L0l4gMWYkHqdcN3QCt5ZtirHd0rgn/oGmoU/9FWFvbIDMzBdFhn8ttDjIzkkxmobaKOdarLeL/6y/HenXFvkXLVvh2557cTmdkZODA/t8xbOggvUB8tW0HGnh5oWWzIAx/cxRmzJqDdk+0xqWLMVrL/2LTFlyIjsb8d+fIcypUrIgz58Lx6dLF+HjRB3ppl6ELYULV0MIWVD4TqhYUzBJ2hZOsEoJZ0OmmmGRZEJ+iu8JJlqLDV6bGc5JVJj7FXsyx3jChs7a2Q23PvvAJGA3X8j6ykgept3EhYh3Oh69FRkaiYSouQammHOvFtgcBTd+Be50essXpaXdlUvV8+BpkZaWVoBc8tTQCHOtLo2YZ13CsN884tq7ojEBXR9xIy8TBO/eRmJmtl4ZqEqqzZkzDhQvn8VzvPnip3wB8uXkjZkyfUuY68iZUa9SoidZt2uCH7/cVudL06IkzOB8djQH9+sr6ra2t0evZ53D82DFcvaqMrWCYUC3zraOeAphQVU+sC/aUkyz1xt6Ukyz1qptHzznJMo84mKIVnGSZQt30dXKs128MbGyc4OkzCN5+b8KpXC1ZeHLSJUSFrcKl6C1mlSw0h7G+fMVABLVciCrVWkmr1JTrCDv7ES6d/wo52Zn6DQ5LyxXgWK/em4FjvfnFflkjD/So7pbbsISMTPQ6EoOrDzLK3FhNQvWFPs/i2NEjsrzjJ88hKSkRT7V/HCHh57Fu7Wp0794Dtdw9MGbUm7h3LwGr16xH1arVkJCQgG++3oqFC96V11apUhXbtu9EAy9vuf93VlYW4uPvyBWqT3XsjBWffY7GAT7IzMxEk6aPYeWqNahZsxays7MRFRmJw38dwutvvCmvTU1Nxc0b19GhXVsEh0Vj+tS3sHfPbnh41MaXX32DevU8ZflHj/yLQQMHyCTtews/QMdOnZGUmATfhg2RlJSEJYsXYf3az2X73nhzJCZOehvOzs4Qq3H/+ecwXnulf5kdCxbAhKreSS23QCZULTe2xfWMk6zihCz39+YwybJcXfPuGSdZ5h0fQ7aOkyxD6ppv2Rzr9RMbe4dK8PIbjvo+Q2DvUEEWmhAfgqjQ5Yi9uBs5OVn6qUiPpZjTWF+1RjsENJ2BSlWayB4mJZ5H2OkPEHtJPKqao8desyghwLFevfcBx3rDxt7TyQ7P1ihfZCUxKenYc+PhUwr1ne3xW1uvR87fGhuPW2lFf6mUtxxtFRZMqNrb28vkZWhIMHo/+wwuxd6Ql4aGhuBq7BV8vvozbPlqO+LirmHRBwvRrFkLDHn9DfR9vheOHzuK3/44BM/6DbBr57cy0Tl12gxkZWfJhGrv5/tg6bLP4F2/Nuzs7HD6XLhMmn6+aiVsbGxksnPAS33w1Tc7ZRJ2/bo1uHP7lkyiinaIVbSbNn6Bw/8el8nclSs+hbu7B158qT9++H4vRo14A+u+2ITOXZ7G6dOnsGf3LrzyykDUrOUOPx9PlC9fHmdDImXieOWKZWjeogU6deqKp7t00HvQTZJQFRvNpqakSFQeyhFgQlU5sdJ3SznJ0reocsozp0mWctQso6WcZFlGHEvTC06ySqOm/Gs41pcths7lasvH+ut6DYCNjaMs7Nb1w/Lx9RvX/ihb4Qa+2hzH+lp1eiGgyVS4lveWvU+4cw4hpxeavaWBQ6X34jnW651UMQVyrDdsqDpWccHaJnWKrOT3W0l448wVeU6XKi5YXcj5pxJS0LSCs87laDtRk1AVyc+0tDS5atTFxQVixapIkIpE5ofvL8SK5UtlEWL16Ow572L2zOky6SmODxYtwf4/fsOUyRMRGnEB32z7Cm+/NUH+Lu8j/3kTqoOHDJP7qb4y4BEdWiUAACAASURBVEX89eehfM0r+Mi/+KUmoSq2CzhxOhhfrF+LubNnyOt++Pl3NGjgBV+vujKh2qx5SzRp1FD+rn37p7Bpy9d4sm1LuYL1yPHT+PPQQUwYNxq3bxvuhYcGT6iKpbh9X3gJ3bp2lBvS7t73E5o0aSo7vfijD7H0k48NeyezdL0JMKGqN0rFFcRJluJCprcGm+MkS2+dY0FFCnCSpd4bhJMsdcaeY33p4i72RW3Y+C241+klX66Uk5ONa1d+RMS5JUiIP1e6Qo18lbmO9VZWNqhTvx/8gibDuZy7VIm/dQKnj05HQvwZIytZZnUc6y0zrrr0imO9LkqlP8dcV6jG37mDpPtJuHTxIhbMn4vw8DDZSZHInD51MrZu2Sz/fdHHn8g9VsWj9HmPY8eOYOXyT+ULrga9OgAHDjz8wlBbQnXh+4vwwov9UK92jUcwi0qoXoyJweat2/IlYucveB8DXxssyyqYUPX3D8CPv/yBXs90xdmzZ+SWAz17PSfrFH0Qq2w3blhf+oBqudLgCdVTZ0KRnJKMJ9q0QNenu2PNug24cD4a5Vxc4OLiCn/f+nrvFAs0jAATqoZxVUKpnGQpIUqGaaO5TrIM01uWmleAkyz13g+cZKkz9hzrSxb3qjWegE/AGFSv9ZS8MCsrHbExOxAR/CnuJ10oWWEmPtvcx3prG3vU9xkK38BxcHCsLLWuXfkJwSfn435itIn1lF09x3plx68sredYXxY9w1xr7D1U8/aiYEJ1wsTJmDBpslwNKla05j2cnJwQHiUSsvPw+eqV8lfaEqqjxoyTe5l27vik3Ds17yESqhfOn0f/l/rk/lizQvXA/j/w599H5b6onyz+SP5++47dcmWt2EqguISqOF88+t+tew+Mn/iW3L9VXCf2dNXnYfCEanRMLPbt3YMJ40Zh7fqN6NK1G5oG+aNmjZpyyW5hsPrsIMvSnwATqvqzVFpJnGQpLWL6a6+5T7L011OWVFCAkyz13hOcZKkz9hzrdYm7FWrV6QHfwLGoWPnhHp8ZGfdxMWoTIkM+Q9qDm7oUYnbnKGWst7UtB2//UfD2Hwlbu3JyNfCVmB0IOf0+UpOV8UZocws+x3pzi4jx2sOx3njWJampdUVnBLo64kZaJg7euY/EzOySXK713MJeSpX35IIJ1dq168iEZlhYKAa+3E+e+urAQXBwdMAH/1kAkQy1trLGuLEjZbJSPJkuXnBVcA9Vd4/a2H/wMKKjIjFuzEikpafjw0WL5V6sm7dsQ6NGjdHuiVaoWq06zkdH5dtDVezxmpGejiGDX0XdunXx8ZJlCA4+h969uheZULW2scHbU6Zj5oxp8in5T5evQs9ezyKgYQMkJyfrxVNTiMETqmJvhaNH/8XggS/j9Nkw2NjaopG/N0SA/vrnGMaPG4Xvdu7Qa6dYmGEEmFA1jKsSSuUkSwlRMkwblTLJMkzv1V0qJ1nqjT8nWeqMPcd67XEXKyTreL4o90h1cWsgT0x7cAvRYWtxPmIdMjPyPxKptDtIaWO9WKXqGzgBnt6DYGPrIFcHX4zajPBzHyPtwcO9/njoJsCxXjcnSzyLY70lRlV7n3RJqE6b8ha+2vplbiEvvzIQ8+YvhHiBlThycnLkC6LEXqvid+JxfisrK/lzkahMTr4vE6rP9X5eJjHFilCxn+mbI0ZjyrR3YGtrK8tJTEyUOcF27TpgzfqNcHR0lI/lB/p5yYTqzHemYvOmDfL3a7/YBAcHB3ndrZs30avH0/JFWWKxZnOxh2pjP/m7hg398PNvB9CzexdkZGRg7w+/5LY7JSUFq1YuN8h2owZPqIq9FUTwYmOvwMOjNnZ+ux0TJ4yRy4e1Lf1V162tnN4yoaqcWOm7pZxk6VtUOeUpbZKlHFnzbyknWeYfI0O1kJMsQ8mad7kc6x+Nj1gRWd93CLz8hsPRqbo84X5iDKLCPsPl818jKyv/Y5DmHWHtrVPqWO/oXBP+QdNQt8FLsLKyRmZmCqLDViMyZIXik9zGupc41htL2vzq4VhvfjEx1xaJPJ6TsxOio6Jk8lRziEf/AwIb4fSpkzo9Su/t44N7Cfdw8+aNfF0VP4+9ckXrS+sDAgJlEvbKlcslInJ394C9gwNiLpwv0XUlOdngCdVq1apj157vUauWu1xu+3SXp+QeDGGRMTIY3EO1JOEy7blMqJrW35S1c5JlSn3T1q3USZZp1Syjdk6yLCOOpekFJ1mlUVP+NRzr/xdDB8cq8PIbgfo+g2Bn7yZ/Id4yHxmyDFcv75WPmlvSofSx3sXNCwFN34F7nR4yLOlpdxERvAwXItZaTNLbUPcbx3pDyZp/uRzrzT9GbKH5Cxg8oWr+BGyhrgJMqOoqZXnncZJleTHVtUdKn2Tp2k+e96gAJ1nqvSs4yVJn7DnWA+Vc68kXTdXxfEk+Si6Om3F/ykTqzbiDFntjWMpYX75iIIJaLkSVaq1krFJT4hB25iNcuvA1crL1+yISS7kZONZbSiRL3g+O9SU34xUUKChgkIRqnTp14erqqpN2aGhIvmXDOl3Ek0wiwISqSdjNolJOsswiDCZphKVMskyCp/BKOclSeADL0HxOssqAp+BL1TzWu1Xwg1/jt+QLp8Sj42IF6rXL3yMieCkS4s8pOKq6Nd3SxvpqNdsjoOkMVKwcJAGSEs8j9PT7uHppr9gFUDcUlZzFsV4lgS6kmxzr1Rt79lx/AgZJqB47eRbiUX9djifatCjxXgi6lMtz9C/AhKr+TZVSoponWUqJkaHaaWmTLEM5WWK5nGRZYlR16xMnWbo5WdpZahzrReJNrEitVrOdDGdWZhoux2yXK1KTky5aWoi19scyx3or1KrTEwFNp8HVzUv2/e6dswg5tRA34/arJrbFdZRjfXFClvt7jvWWG1v2zHgCBkmoPt/nBdStW0/2YvCQ12Fnb481qz/L16tRY8YhJTkZbVo9pnXzWeMxsCZdBJhQ1UXJMs9R4yTLMiNZ8l5Z5iSr5A5qvIKTLDVG/WGfOclSZ+zVMtaLFajudXrBJ2AsKlRuJIOdkZ6EC5EbEB22CmkPbqvuBrDksd7KygZ16veDf9DbcCpXS8b29s0jOHtsFhLiz6gu1gU7zLFevbcAx3r1xp4915+AQRKqeZsXef4yDh3cj2FDB+Vr9aTJUzB+wlto1bwJrl+P01+PWJLBBJhQNRit2ReslkmW2QfCBA205EmWCTgVVSUnWYoKl14by0mWXjkVU5ilj/U2Ng6o06A/vP1GwsXNU8blQepNRId9LpOpmRlJiomVvhuqhrFexN/TZyh8A8fBwbGSJLx25UcEn3wP9xOj9U2qmPI41ismVHpvKMd6vZOyQBUKGDyhev7iVVy6GIOOHZ7Ix9u7T18s/XQlpk15C19t/VKF9MrrMhOqyouZvlps6ZMsfTlZYjlqmGRZYtz00SdOsvShqMwyOMlSZtzK2mpLHett7VzRwPd1NGg4DI5OVSWT2FMzKvQzXL6wDdlZ6WWlU/z1ahrrbW3LwTtgNLz9RsDWrpzcL/fyhW8ReuYDpCbHKj6WJe0Ax/qSilnO+RzrLSeW7InpBAyeUD3w5z/w9KyPGdOn4OuvtiAzMxMVK1XCvh9+gYdHbbzQ51kcO3rEdAKsWWcBJlR1prK4Ey11kmVxgTJAh9Q0yTIAn6KL5CRL0eErU+M5ySoTn2IvtrSx3sGxGnwCRqGe90DY2bnIuMTfPo3IkOW4dnkfX06U505V41jv4FgZvoET4ekzCDY29sjKSkdM1CZEnFuMtAd3FPs5LmnDOdaXVMxyzudYbzmxZE9MJ2DwhGrDhn74/qffYGtri5ycHLlfqrOzs+zx34f/woB+fU3Xe9ZcIgEmVEvEZVEnW9oky6KCY+DOqHGSZWBSxRTPSZZiQqX3hnKSpXdSRRRoKWO9i2t9+Vi3h2dfmSgTx824gzKRejPukCJiYexGqnmsd3SuiYAm01Gn/osQ++tmZqYgOnSVvF8yM5ONHQqj18ex3ujkZlMhx3qzCQUbomABgydUhY1YkfregvcRENgIri6uuH37Nvbu+Q4rli+VSVYeyhBgQlUZcTJEKy1lkmUIG0svU82TLEuPbXH94ySrOCHL/T0nWZYb26J6pvSxvmLlJvANHI+atbvDysoK2dlZuHble4SfXYzEhDB1BlXHXnOsB1zcvBDYdAZq1XlGqqU9iEdE8KeIiVyPrKw0HSWVdxrHeuXFTF8t5livL0mWo2YBoyRU1QxsSX1nQtWSolmyvih9klWy3vLsvAKcZKn3fuAkS72x5yRLnbFX6lhfvVYn+ASMQdUabWXgRPLr0vmvERm8DCnJV9QZzBL2mmP9/8AqVApC4xbzUaVaK/nD1ORrCDv7kbyncnKySihr/qdzrDf/GBmqhRzrDSXLctUkYJSEaqNGjfHa4KFo0MDrEdshg17BvXv31GSu2L4yoarY0JW54UqdZJW54ywAnGSp9ybgJEu9seckS52xV9JYb2VlA496vWUitXxFfxmw9PR7iIncgKjQVUhPi1dnEEvZa471j8JVq9kBAU3fQcXKQfKX9xPPI+TUf3DVwvbf5Vhfyg+NBVzGsd4CgsgumFzA4AnVGTPnYPiIUbKj2dnZ8n95jyfatEBc3DWTQ7ABxQswoVq8kaWeoaRJlqXGwFT94iTLVPKmr5eTLNPHwFQt4CTLVPKmrVcJY721jSM8vV6Bl/8IlHOpI8FSU64jOmw1YiI3qmLPS0PcJRzrtalawb1OTwQ0nQ4XtwbypLt3ziDk1ELcjDtgiFAYvUyO9UYnN5sKOdabTSjYEAULGDyhGhpxARkZGXiqfVvE31HPGxMVfE9obToTqpYYVd36pIRJlm494VklFeAkq6RilnM+J1mWE8uS9oSTrJKKWcb55jzW29m5wctvOOr7DoV4O7s4khKjERm8AlditiM7O8MygmCiXnCsLxperIiu26A//BpPhlO5WvLk2zeP4OyxWUiIP2OiqOmnWo71+nFUYikc65UYNbbZ3AQMnlCNPH8ZJ44fw4B+fY3adw+P2ihfvjxCQoKNWq8lV8aEqiVHt+i+mfMkS71RMU7POckyjrM51sJJljlGxTht4iTLOM7mVos5jvWOTjXgEzAa9bxfha2tsyS7e/sUIkKW4drlHwDw5bb6uI841uumaGPjAE+fofANHAcHx0ryInEfBp9agPuJ0boVYmZncaw3s4AYsTkc642IzaosVsDgCdXd+36Se6cG+j26f6ohVH0bNsS+H36Fvb29LD4tLQ3fbPsKM9+ZKv895nIcrK2tH6l66OCB+P23X4ps0q7d3+OxZs3RtlUzXL0aa4jmm3WZTKiadXgM2jhznGQZtMMsPFeAkyz13gycZKk39pxkqTP25jTWizeu+waOR+16z8Paxk4G5Ma1PxAZvBy3bhxWZ4AM2GuO9SXDtbUtJ/fv9fJ7E7Z25ZCTk43LF7Yj5PR/8CAlrmSFmfhsjvUmDoAJq+dYb0J8Vm0xAgZPqC58fxFeefU1nD59CldjH33T5tS3JyEpKUlvoP7+AZg+YzYWfbAQt27dwpKly9G6TVs0DfLH3fh4tGjZCg4ODrn1derUBUOHDUfP7l1w7txZre34YNFi9B/wivw9E6pxSL57XW8xY0HmL2BOkyzz17KsFnKSZVnxLElvOMkqiZZlnctJlmXFU9femMNYX7lqS/gEjkUN9y6wsrJCdnYWrl7ag/Bzi5F0L1LXrvC8EgjUdbJDR4+Hj7EfiL2GmFRun6Arn9h+wrfRJHh6vwYbG3tkZaXLvXwjgpcg7YEytrrjWK9rtC3vPI71lhdT9sj4AgZPqB45fho1atTU2rPHWzdHbCGJVn1RiATqtzv3yBWqmzdteKTYU2dCkZBwF0+1f1xrlYOHDsPcee/hi3VrZPKVCVUmVPV1fyqlHHOYZCnFytLayYSqpUVU9/5wkqW7laWdyUmWpUVUt/6Ycqyv6fG0XPFXuVpL2disrAe4GL0VkcHLkJrCl9fqFsGSn9W7hhs+9HeHrbWVvDg7JweTQ67iu+uJJS9MxVc4lfOAf9BU1Kn/AqysrJGZkYyosFWICllh9i9K41iv3huXY716Y8+e60/A4AlV/TW1dCV9+NES9Ov/Mjp2eALno6PyFSISpfPeXYDnn+uBkyeOF1rBE0+2w5dbv8EH/1mAyMgIrN+wmQnVeCZUS3c3KvcqU06ylKtmGS1nQtUy4liaXnCSVRo1y7iGkyzLiGNJe2Hssd7K2hZ1PPvC23803Cr4yuampyXgQsR6RIevQXpafEm7wPNLKPBL6/rwcnHMd1VsSjr6Ho/BrfSsEpbG08VWFYGPzUSt2t0lRtqDeEQEL0VM5BfIykozSyCO9WYZFqM0imO9UZhZiYULGDWh6u3jA1dXN4QEn5N7mxr66NK1G9as24BjR4/gxb7P5atOPEYUEn4eMTEX0KNb50KbUqdOXfxx8DB++vEHjBk1HJ06d30koSr+41Mth5NrZTi5VUZq4h2kJinjMRa1xMbQ/bS1d5KxT7qtvr2Di7Z9uKLDOEeOfPzR2Iej68OXLjxI4sTW2Pamrs+1srv8W5+Z/sDUTWH9RhaoWMsbd6/l/xLayE1gdSYQsLV3hPhvvaQ7Vw1au42NE+rU74/63kPh5PzwUXOx7+SFqPW4dOErZGWlGrR+Fg7UsLdBl8rOmO5ZAdYF/9siJwewssKr527geKLh52s5oj4Y/79vDHkflK8YiIAms1C5SnNZTWpKHCJCPkXspR3IyTFGolr3l7W5VvGQc7vMdH7uDHlPmGPZldx9EH9VXVupZDxINsdQsE0KFjBKQlXsP/pSvwH5XgYVFRmBIYNexZUrlw3C17xFS2zbvgtxcdfQ4ck2yMzMzFfP1OkzMGr0OHTt3B4R4eGFtmHW7HkYNnwEgoPPQQz25cuXh0iyRkaE49Oli7F3z26ISYdaDhtbe9jY2SMrIx1Zmelq6Tb7Kf4z19oaIv5MrBS8HXT/D9ay3khZGRmwsXv4Yg5jHiLu4uBn3pjq5lGXrYOT/Hufk22MyZ959JmteChg7+SK9FT97W9PV2UIWFnbyP/Oy0wzTGLF1tYVtev0g7tHX9jZuUmU5OQYXL60Fdev/wwYJdGkjFgYupUfetigk5sN8N/kad760rNzkJYD9L+QiesZRf93zkZPW1S0sZLn3cjIQVxmDm5lQP7zjcyH/59QzBCSlZkBG1vj//eNoY1F+ZUqtUL9Bm/C1e3hCuzklEuIOb8Wt27+YeDqdU9Qiy9SxH/j5WRnG7hNLN7cBOydXJCeet/cmmXQ9vDLYoPyqrJwgydU5y94H68NGoJ79+7h1KkTuHXzJtq0fRweHrVx+9YtNH+skUxW6vMQK0nXrt+ImAvn0a1rR6Sn50/+iZdSBYdF48zpU3ihz7Naq+7YqQuG/P/+qZqjatVq8PP3lyteV65Yhj9+/1WfzTb7ssSjvy6VauI+H/k3+1jpu4HGfgxQ3+1neaUX4CP/pbdT+pV8DFDpESx9+/kYYOntlHylocZ6sQpV7I9az/sV2Ng8fLz8zq3jiAxZjrgrPwHQ7zxAyTEwVtufqFQOLSo4Iy07GxPqVyv1HqpnOvjC1damyGY/8WckrqXlX9hirH6aRz1WcK/bCwFNpsHFrYFsUvzt0wg9vRA34w6avIkc600eApM1gGO9yehZsQUJGDyhKhKX4gj088rHtuST5ejzwotF7l9aGudu3Xtg9Zr18kVXE8aNzk3W3rlzRyZYxbHo40/w4kv98WTblo+skBWJ2Fat26KR/6MrTwt75L80bVTqNUyoKjVyZW+3oSZZZW8ZSzC0ABOqhhY23/I5yTLf2Bi6ZZxkGVrYPMvX91jvWt4HDRtNhHvd52Bt/TDpFhf7q0yk3rn5r3kiWECrajjY4noJEph1nezQ0ePh1gsHYq8hJjVDZwVnayt4ONmjuoMt3B3tUMPRFjUdxP/boZajHao62KLJgYhiy1sa6I77WdmIe5CBuAeZuPYgA9cfpJeoLcVWYuITrKxsULfBAPgFTYaT88MXNt++eQRnjr6De3eDTdY6jvUmozd5xRzrTR4CNsACBAyeUI25HIcD+3+Xj/fnPYKaNMWefT9hzuwZ2LB+rd4o58ydj6HDhj9S3uXLl2QC1c3NDWeCI3Do0AEMenXAI+ft/eEXNGrUGPVq13jkd0yocoWq3m5UhRWk70mWwrqv6uYyoare8HOSpd7Yc5Klztjra6yvUr0tfAPHonqtjhIyOzsTsRe/Q/i5Jbif+HChBQ/9CrStVA5dqrjg6epuuJeRhe7/XihRBaYc652srRDS0U9rexMyHiZYex6JKVGfzPVkGxsH1Pd9Hb6B42DvUFE28+rl7xFyaqFJPh8c6831TjF8uzjWG96YNVi+gMETqqfOhKKciwsaetdDdp69WTZv2YZ27Tuge9eOCA0NsXxpC+ghV6haQBBL2QV9TbJKWT0vM6GAKSdZJuw2qwbASZZ6bwNOstQZ+7KN9VaoVecZ+Wh/pSqPScCszFTERG9BVMgKpKZcUyeqAXv9VBUXPFPNDZ2ruqK83f8eu0/NysaTf0UhPkP3/a9NPdZ3q+aGmrmrW21Rw+HhClfxP3FcT8tA2z+LflGeWC27tJGHXOV6LU2scP3vSte0TFxONb93P9jaucLHfxS8/EfA1tYZ2dlZuHxhO0LPvC9f0masg2O9saTNrx6O9eYXE7ZIeQIGT6iK/VPFPqoimSoew4+Pj0fDhn5wdHTEhfPReKr948pTU2mLmVBVaeABlG2SpV43S+i5qSdZlmCo1D5wkqXUyJW93Zxkld1QiSWUZqy3trZDbc8X4RM4Gq5uD7f3SnsQj/MR63A+fC0y0hOUSGHWbX63YQ30qVkBzjbWue1MzMjCzzcT8evt+/jtVslfKGfOY73YwqC8rQ0iktOKjIuXsz1+aZt/i7m8F9xOy8DpxAcYfuaKWcXXwbEyfBtNgqf3a7CxsUdWZhpiojYiIvgTpD24Y/C2cqw3OLHZVsCx3mxDw4YpSMDgCVVhMfC1wXjr7WmoUKECrKyskJaWhv1//IZJE8YiOTlZQVzqbioTquqNf2kmWerVsqyem/Mky7Kkza83nGSZX0yM1SJOsowlbV71lGSst7UtB0+fQfDyexNOzg+3yUpJjkV02GpciNyE7KwH5tU5C2rN4oBa6F2zAm6nZ+KnG4kykXr4bkqZemgJY72rrTXaVXKRK13lClcnO9QU+7o62Mk9XsVxPCEFLx2/WKRVFXtb9KzuJvehvZaajri0DNxK1321b2kD4VTOQ764qrZnX1hZWSMzIxlRoZ8hKnQlMjMNN1/mWF/aiCn/Oo71yo8he2B6AYMnVB0cHFClSlXcvn1LJlJFQjUnJwc1a9ZC6oNUJNy9a3oFtkAnASZUdWKyyJNKMsmySAAVd8oSJlkqDl+Zus5JVpn4FH0xJ1mKDl+pG6/LWO/gWAVefsPh6TMY9vblZV33EsIRFbIcVy7uQk62mt/mXmr6El0Y4OoIR2srnLiXWqLrijpZDWO9eGmWvRWKfdHV4xWdsblZvUe4YlPTH74sKy0TxxJSsCXWMHNYFzcvBD42C7Vqd5NtEKtUI84txYWoL5Cdpf+tCzjW6+1jpLiCONYrLmRssBkKGDyhunb9RnTp2g0v9HkWx44eySU4cSoYzuXKwc/H0wxZ2KTCBJhQVe99ocskS706lt1zNUyyLDuCpe8dJ1mlt1P6lZxkKT2CpWt/UWO9c7na8Akci7oN+kO8VEcc4g3lkSHLcT32l9JVyKvyCfi5OKKivQ3+jjfcakRt5Bzr/ycj4jCwdkW5slXu6+poBzfb/+1RK8786WYiRp2NLfIO9nSyQ6uK5XApNQOXUtJwLa1kXzZUqBSExi3mo0q1VrKelOSr+D/2vgM8ruraek2fkTSj3iXbsmRJluRGMR2McSOQ0EIILQmE8AgdEsIPvOSlAaGFElIJCQTyeEkIJARCsSkx1aa5qFjdVu9lZqRpmtH/nTOSbFmyNDO6d+aWfb/PnwU6Ze+1rry115yzd83uB9DS9FeMjwt3YpZivXr/IaJYr17uyXPhEBBdUN1dWYvenm5sWH/qNKu/ctHFeOChR/DFL2zCnj27hfOIVhINARJURYNW8guToCp5ikQzkJIs0aCV/MKUZEmeItEMpCRLNGglvfBssd6WtBylK29FTv5Z0Gp1/JYZE1D37f05Bvt3SdofORi32mbG5gwbv2KeazGiccSDjR82Rt10ivVzQ85OBOeZgyUE2B/W+OrdeYTvi3KScG9ZzrSFG0Y8ODDqRfOolzfK+nTIhRrn3OUxMrJPR8Wau5CUuoKv5RiuR9Wun6Gj5WVB3hOK9YLAKMtFKNbLkjYyWmIIiC6o1je1Yvt/3sY3r/jaNNfLysrx6htv4aYbvo1/vPiCxGAhc2ZDgARV9b4XJKiql3tKstTLPSVZ6uWekix1cn9orM/IPhXF5TeA/c2egN+H1v0voLbyMTjtDeoESCCvT0yJx8a0BGzOtPFTkJMPq+/J6qE+2TIg0E6hL0OxPnSsQh3JeL4wJwmLLEYssRiQbAzWcT30+WNLP35S1z3nkhlGHRL0enjTt2D56tthtRXy8ewDjcrP7kZv1/ZQTZp1HMX6BcEn68kU62VNHxkvEQREF1Q/+WwvrDYbSooWT3N5shTAhvWnoL6uTiJwkBlzIUCCqnrfDxJU1cs9JVnq5Z6SLPVyT0mWOrk3mBOwtPRi5ORciOTUVRyEsbFRNNc9wxvjuF1d6gRGQK/fPamIn0SdfN7vd+KVbju29Tl5k6lYPRTrxUc+QafF0jgjFk/8WWQx4D99I3ilxz7n5jcUpOOWwnQ+Zsg3hoFxK0biSuA05GNIn4G2ETte3vM89nZVReQExfqIYFPEJIr1iqCRnIgxAqILqrd+93u46ebvT31rJwAAIABJREFUYKC/H//5zztoa2vBxo1bUFJaiv6+Phy9piLGEND2oSJAgmqoSClvHAmqyuM0VI8oyQoVKeWNoyRLeZyG6hElWaEipYxxWp0Ri5d+FcUV1yE+IdiMhzXCaax9Eo01T8Dnm1vwUQYK0fHip6XZvOP8qz12vNnrxPCYcLUwF+IBxfqFoCfu3GsWp+LS/BSwplpHel6yXofn+s2o+vxuOB1NYRlEsT4suBQ1mGK9ougkZ2KEgOiCKvPrkcd+hXPPOx8ajWbKzZ6eblx2yVdQu29fjFynbcNFgATVcBFTzngSVJXDZbieUJIVLmLKGU9JlnK4DNcTSrLCRUye4/UGK5YWX4Gi5d+C2ZLBnXC5OlG39xdobvgzAv65azvK02uyejYEKNbL473INLImWcFGWdlmI3LiLChOL8GuzBux33I8AgE/b1pVvfs+uEc7pzn145IsnJFuRbvbhx7PGDo9PnS6fHDEp6G5vxdtdge6wmycJQ/UyMojIUCxnt4NQmDhCERFUGVm2mw2HLv2eCQnJ+PTTz9Bc1P0C64vHC51r0CCqnr5J0FVvdxTkqVe7klQVS/3lGQpm3uTOQPLyq5BwbKvwWC0cmeHB6vRWPcE7M5PMNBBpbhCfQNSDDpsSLfizEwbqu1uPNDYE+pUSY2jWC8pOsI2xmRORemK72DJssuh0xnhH/Ogqe4p1FY+DK9nkK/3w5IsnJOViESD7ojr37S3Df/qphPpYRMg0wkU62VKHJktKQSiIqgWLC3EtdfdgIKCpXj2mad4E6of/eQetLQcwJNP/FZSgJAxR0aABFX1vh0kqKqXe0qy1Ms9Carq5Z6SLGVyH29dgpKKG5FfcCEXXdjT2/UB6qoeR3fHm6BYHxrv7JQgE1A3Z1hxTFIcdBM38NpcXpz6vjwbdlGsD417qY+yxOehfPX/Q37BBdBotPD5nGio+Q3qq36FsbERbr5Vr0WB5WAt1+LUNGRrvVhs1uPbu1vx6bBrTjefWJWP4gQTutw+dLCTrm4fP9ka/NuHTvdYTOsBS50jKdlHsV5KbJAtckVAdEF11eo1+Oe/Xp267v/Mn57Cf995O/7xr1exatVq3qzK6/XKFT9V2U2CqqronuYsJVnq5Z6SLPVyT4KqermnJEtZ3CelrEBJxc3IWfQFLrKMj4+js/VV1FY+yjuFTz4U64/Mu0mjwRWLU7A5w4ZVNsu0gZV2F7b2OvF6jx11Ix5ZvjwU62VJ2xGNtiYWo3zNXcjJ38LHuF19qKt6DE11f0TAPz3vDjfWbzuxiDfXmuu5YGczPrfPLcwqC3F5ekOxXp68kdXSQkB0QfX//voCmKh6+aUX4fdPPo2XX36JC6qspuqjv/g1vnz+l/Dxzh3SQoWsmRUBElTV+2JQkqVe7inJUi/34SZZ6kVKeZ5TkqUMTjOyT0dJxQ1IzzqJO+T3e9Ha/HfUVT42a+MaivVz8/7pqcVINur5oM+GR/Fqtx2v9zjQ5vbJ/oWhWC97Cmd1ICllFVavvRcp6Ufz74+OtKFmz4NoafwrxseDDdHCjfVmrYY3yMoy6ZHD/ma1XCfqumaZWG1XPTZ+0IAe79wN135Smg2DVoMON6vl6p065cp+ntyBcWUSIjGvKNZLjBAyR5YIiC6oNu5vx79feRk3XPdf2LWnZkpQXbRoMd79YCduvvE6vPjC87IET21Gk6CqNsYP+ktJlnq5pyRLvdyHm2SpFynleU5Jlnw51Wh0yF38JRSXX4+klAruCLv2u7/+GdRV/Qoe95FrfFKsn5v3qxalwBMY5ydR5xOL5PYGUayXG2Ph2ZuZsx7lq+9EUuoKPtExXIfqXfehveXlsAXV8HY+8uhd60pg089ez9U+5uclBC759AAGfXMLs0LZo8Z1KNarkXXyWWgERBdUq/Y1oqmpEV/8wqZpguo3rrwKP/rx3di04TTU7tsntF+0nggIkKAqAqgyWZKSLJkQJYKZlGSJAKpMliRBVSZEiWAmJVkigCrykjqdCYuLLsWy5dcg3rqY7+Z29aKx9kk07XsSPt/8jWbUGuuPTrTAORZArUyv6wvxalGsFwJFqa+hQd7iL2H56tthtRVyY4cG9qKp6Vdob34dPnewxmq0no3pVmSbDcicOOmaY9Lz/86zHCwnsHRb9bzm/HplHlpcPrS6vDgw6sUBlw8tLionOC9wACjWh4ISjSEE5kZAdEH1qWf+F+vWrcfvfvMrXHTxpXjt1Vewc8dH+Nn9D/HaqeWlwX/Q6ZE+AiSoSp8jsSxUa5IlFp5yWpeSLDmxJaytJKgKi6ecVqMkSz5sGQw2FJZehaUl34TZksYNdzr2o77612hpfA5+f+g1PdUU64vijDgvOwlfzLJxAefPbYP4/r5O+RAvsKUU6wUGVMLLabR6LCm8BKUrvwNLXBa3tLf7Pez95IdcYJXCk27UId1kQLXDPac5Nr0Wu9aVzjpm/6gH+0d9ODDqwY/quqXgluRsoFgvOUrIIBkiILqgajKZ8Pb2D5CbmzcNHp/Ph6uvugJvvblVhrCp02QSVNXJO/NaTUmWelme3XNKstT7RpCgql7uKcmSPvdmSxaKy6/FkqLLoDfEc4OHBipRV/ULtB94CePjgbCdUHqsZ3Ufz8lKxNmZNpRazVP4OMb8+N+2QdzXcORyCGGDKbMJFOtlRpgA5rJT7YWl30LJipvAPphhDysBUPXZ3bPWWBZgS8GXYPVc2UnXfIsRBXFGLIozYkmcEekTtY7Zht2eMZzwbt2ce7N1LslNRqfHhy73WPBvz5jg9kptQYr1UmOE7JEjAqILqpOgnHv+BTjllNOQlJSE6uoq/OHJJzA4MCBHzFRrMwmqqqWeBFX1Ug9KstRLPgmq6uWekizpcp9gXYriipuwqOACaHUGbmhP13uoq/wFejrfWZDhShVU2Wm3X6/Kx1GJcVP49HvH8FqPA1t77Ng+EN2rzgsiSaTJFOtFAlYGy6YtWoWsjHOwdNkV0OvjEAj40dr0V1Ttvg/uUXme2mYCaUGcCYstBlj0WrzYOTwnE8vijXj9hKIZY3jDLPbH40O13Y3fHOiXAaOhm0ixPnSsaCQhcCQEoiaoHmpASmoqXKOjcLlcxIyMECBBVUZkCWyqUpMsgWFS5HKUZCmS1pCcIkE1JJgUOYiSLOnRmpy6GiUrbkF23mZoNBp+ArWj9d+o3fuIYNd0lRzrd5xaDP/4OF7ptuONHgc+HhqVHskxtIhifQzBj/HWk7FeiziUrrwVBUWX8w9r/GMeNNc/hX17H4bXMxhjK8XdPt9iwNWL05Bt1iPbZOB/Jxn00zb9ZGgUX/lk/5yGZBr12JBhnajl6kWryyeu4QtcnWL9AgGk6YQAANEF1Z/ecx8u+PJXsGXTehzY34x/vvwaVq9ew8H/+YP349FHHiIiZIIACaoyIUoEM5WcZIkAl6KWpCRLUXSG5QwJqmHBpajBlGRJh86s3I0oLr8eaZnHc6OYyNG6/3nUVj6GEcfcyX24Xig51ueYDWCnzeiZHQGK9ep9Mw6P9Zb4PJSvvgP5BedDo9HC53OiofrXqKv6Jfx+dR2GKrAYkGU2Itdi4I3rXuuZu7nfaanx+OOaYFPAyaeZNcoa9aJpxINWtw977S58NiwNHCnWq/fnnjwXDgHRBdXPd1djZHQEJ59wLDZtPhNPPPkUmhobEJ+QgIQEK8pKlgrnDa0kKgIkqIoKr6QXV3KSJWngJWAcJVkSICFGJpCgGiPgJbAtJVmxJYE1jclfch6WlV+PxKRgwxWf14Hm+qd5symPu08UA+UW61dazTgz04Y3+5xgp8foiRwBivWRYyf3mUeK9dbEYlSs+W9k52/mLrpdfairehRNdU8h4PfK3W1R7K+wmvGN/BTkxxnBxNg0U7Asy6EPE2Wv3dM25/7JBh3SjDq0uXxwBcZFsZUtSrFeNGhpYRUhILqg2tDchpf/9RJuvvFa/P4PT2Pjpi1Ys6oM2VnZ+Pfrb2LD+lNQXzd3oWgV8SFpVzPTslCanol9vd3o7uuStK1knLAIyC3JEtZ7da9GSZZ6+SdBVb3cU5IVG+61OjMKll2OZWXXIC4+2MzV7epBQ80TaKr7I8Z8DlENk0OsX5sUhzMzrNiYYQM7dcqev3UM4fbqDlGxUfriFOuVzvCR/Zsv1ielrMLqtfciJf1ovsiosxU1ex5ES9NfI2p+pyakLVoNCuNNYCUFFvOGWSbsHXbhz+1zl1C4KCcJ95blcKjsY/6pRlmsnitrlsX+3jPsQu2IJ2I4rXotjlq2Ap/V74VjLPwmhhFvTBMJAYUhILqgWl3bhJ07P8I3Lr8Eu/bUQKfXY0XZMuTnL8J7H36Mm268Fv944e8Kg1V57vy4NAuX5iZP1O0a591Qv19LoqrymJ7dIzkkWWrhItp+UpIVbcSls998SZZ0LCVLhEaABFWhEZ17PYMxCYWlV6Gw5JswmVP4YKe9iZ9GPdD0f1E7DSbVWL8uNYGfRN2QloDkQ7p3V9pdvCbqS13D6FRBR24x30qK9WKiK+21Q431mTlnoHzNnUhKqQgKfUO1qN59HzpaXpG2gzK07is5SbiuIA35FuMRrf/9gX7cU98dkXeU10cEG00iBGZFQHRB9fkXXsKxa49DW1sr8vLy8cLzf8MtN1+Pm2/9Lm659TY6oSqDF/O4JAueO6ZghqV3VLVjx7ALXn8A3nHAEwjA6x+HZ1y8qwkygEuRJko1yVIk2BJzipIsiRESRXNCTbKiaBJtFSUESFCNDtCWuBwsK78OBUWXQqe38E0H+3ejrvIXaG95GUB0f5+SYqxfZTPjxbUHy4MdGPXgX112/LNrGI2jdO1YqDeVYr1QSMpvnfBivQZ5S85B2arbkWAL/lwODezF7p13or93p/ycl4HFaQYdcizGqYZZWWYDsk16vNptx2u9c99aYKLsJbnJaHV5eQ1pVkLAqAWuXpI+w/PLP92P9wepdIoMXgkyUWIIiC6oZmRk4sWXXkFOTi5vSrV54+nweDyoqWvG+Pg41VCV2AsxmznXLEnF94oyZ3xrHOPQQDPj/z/S1IvHmnrn9OzGpem4eenMf8wPnRTKOudnJ+LCnKQ593q+Yxh/7xyac8wF2Un4UpYN3sA4vOPjXBhmf0+KxOzr7f1OfDRPoDkuOQ7HJ8XNuddHQ6PYMc86uWYDvx4y18OCYts8DRbyzAZkmPRBv6Z8C18Al2KSJYMfHVmbqANwfnYSNuQv4n5sa23BC51D8MvaKzI+HATCS7LCWZnGSh0BElTFZSjBVoTSFbcgb8m50GqDnaR7OrejtvIX6O3aLu7mc6wu1Vj/0toC7Bwaxctdw9hld8cMHyVvTIKqktmd27dIYj2r87yk8BKUrvwOLHFZE/+G/QeVn/2EC6z0SAOBn5XlgJ12PfQ5Uv5+f0M3frO/XxqGkxWEgIwQEF1QlREWZOoRELggOxEPlOfO+G63xwePfxxGnQZGjQZGrRYJei0eauzBL5vnbphwy9J03DCPoPpgQw9+tX/udW4qSMNNhRlzcvfzxh48Po89Qq1z89I03Lh0bntCwUcoe0JZ5+HGXvyieW4B/JbiHNywaG7hOhScv5yTBPY+zfX8tWMIL3YOzzmGiehnZ84tgL/T5+QJ2FzP8clxOG4eAfzDwdF512HCdd48Aniry4f2eQRwJqKnGxcugAvxj9n3KypwRdb0mkpPdevw4730i7IQ+MphjUiSLDn4RTbOjwAJqvNjFMmItMwTUFx+PbJyN/Dp4+MBdLS8jJo9P4d9qCaSJQWdE21BNVGvg9sfoJtNgrIY2WIkqEaGmxJmLSTWs7rPRaVXobj8BhhNSfywFPs3rerze+B0NCkBHtn7wE6zppsMSNJrkW024LS0BGzJsM3w67aqdvx9nvxL9mCQA4SACAiQoCoCqEpbMsWgw1snFsJmCJ6iYI/dN4b1HzRiwBfb82pCCVlsncJ4IxeFuTg8JRIzoTgoFn82PP/J0hNT4nFsYvDa3pEedp1ivm607NPE8+YRHp9rH8RLXfY592LrfDU3mV/vmOlbUAAPRbi+rTgX3140txAaiqAaisAr1Dqh+CWUsC+UkB7KOkLhM986O884EWma6Se7neNx+OrOSlQ76ISQ0v6dn82fhSRZasBHyT6SoCosu9n5Z6Kk4kakpB01tfCBhuewr/IRjDj2C7vZAlaLhqBq1mqwMd2Kc7ITsT7Niqt3t2LbPNdWF+ASTQ0RARJUQwRKgcOEiPUGYyI/db+05ErodCaO0v6G/0P17p/BPdqpQNTk65KU83r5okqWqxkBElTVzH4YvhdYDPhaUR4KrXFodIziTw1taHb5wliBhsoZAaGSrGgJ4CatFh8PjfI/cz1yFMAfaOjBr+c5ub1QoTgl/Vh8tMoLPQ77GWf1kTXBMh8tPhOaRsfwdGsf/tNFvyzL+ef7SLYLkWQpERc1+ESCqjAsL1p6IUoqboI1cRlf0OdzYn/9M6ir+iU87rlvhghjQXirCBXrZ9t1fVoCvpiZiE0ZVlh02qkhjzX14JGmuW8jhecFjY4EARJUI0FNGXOEjPUmcwaWr/oulhZ/fQqc+urforbyEXg9A8oATAFesLz+4rxklKanY19vL55rG6S8XgG8kguxQYAE1djgLstd2S9bCSnZcA50YmSwS5Y+kNGRISBmkhWZRTRLSAT0Bisystchd9EXkJmznl/b+nb/zSj07p62zbA2Ff36XOR5a2GEh3/v2eQf4GPtMfy6qsPeCKe9gXd+dTqa+df0yBcBIZMs+aKgTstJUI2cd53OgiXLLuVXYCdrC7pd3air/CX2NzyLsbGRyBcXeabQsX5JnBFXL07FmRk2JBpYZe7gw278bO1x4NUeB1pc1FhKZFpDWp4E1ZBgUuQgMWJ9fMJilK25E/lLzuWYjY2Noq7qcdRX/Qp+v0uROMrRKYr1cmSNbJYaAiSoSo0RCdtDgqqEyRHZNKGTLJHNpeVDQID9spudtwVZeRuRkX3KtBmjzlZku3bj+sCzSA508+8NajNxv3Mt3m3dC9ZQpSwpGeXxOhywbcKopWDWHQN+H0ac+7HR+TQ8nkHsGnZjR08HugbrMeabuzNpCC7QEJERECPJEtlkWl4gBCjJCh9IoykFRcuvxtLiK/iHUuxx2hv5adSWpr8iEJD+rR6hY32F1YyXjgt2Av9oYARv9DrwWo8dXZ6x8AGmGaIiQIKqqPBKenExY701sRgVR30f2XmbOAZuVy9qKx9Fc/3TCPjpw5RYvxgU62PNAO2vBARIUFUCi1HygQTVKAEtwW2ETrIk6KLiTWIdWdPSj0NW/iZk525Egq1wymfWGGWg71N0tW1FZ9vrsA/tAzQ6LCm4EEcvOY6P+3T/Duxv/hswPrNussmcDmtiERKshbAmLYPVFvw6LmERtFod7uq+CMmBnqn9OvSFaNQWosaXhF1OoGGoiwsPDnsDRp0HeKMWemKPgJhJVuy9IwvmQoCSrNDfj7j4fN5oanHRV6HTmfnEwb7P+Wms9pZXWOup0BeL8UgxYv0F2Ul4s8+BoRjX3I8xtJLfngRVyVMkmoHRiPVJKauweu29SEk/mvvBPriv2fMAWpr+Rr/zicbs/AtTrJ8fIxpBCMyHQNQE1VNPXYcVK1fNsOf3T/wGHk/w6ig90kaABFVp8yOmdWIkWWLaS2sHETAYk3g3aXYyIDPndBiMB7t6+rwO9HS+jc62N9DVvg1ez+CssC0kydJqDUiwLsX5edkot1lQZvZiiW4AlolyAZMbOrVJeCDtjxjRJcE/5uGnWh32ejiGG3jZAPa3fbgW/rG5a+IS78IiEI0kS1iLaTWhEKAka34kbUnLUbLiZuQu+iL/4Ig93R1vcyG1t+u9+ReQ4IhQY328ToMN6Tb8s2tYgl6QSZEgsJBYH8l+NEc6CEQz1rPfSctW34mklHIOACsRVb3rZ+ho/bd0AFGRJRTrVUQ2uSoaAqILqueefwEefOhRGAyGWZ04+YRj0draIpqDtLBwCJCgKhyWclsp1CRLbn4p0V5bYgmy8jZxETU57eipRJ/56rQ3oaudnULdir6eDzEemP/apdBJFmtpxerqrUnNxOqUNFRYjcgyBHCb9lZeSiAuPg8azcGGJYdyxOoQMnGVnWTlJ1qH6ydOtbbK6hSYXN67aCZZcsFELXZSknVkptOzTuEnUjNz1vFBgYAf7S3/wr49D8ExXCfrV2SuWJ9k0GFjWgI2Z9pwUnI8TDotrt/Tin/3UPkWWZM+YbzQsV4JmKjFh+jHeg3ylpyLslXfQ4ItWBJksH8X9nz8ffT37lQL7JLwk2K9JGggI2SOgOiC6sef7UFycgruufvHqKrcO+M06p7duxAI0PVOObxHJKjKgSVxbCRBVRxchViVnQJNyzwZ2XkbeT3U+IRFU8sGAmPo79nBBVQmpEbSJCraSZZWZwyWDLAV8c7Ywa8LkZOQhtuHrkeroRhthhK0G4r5n0FdBvx+DxdYeUOs4Xr+N/vv4aFaBPxuIWBW5RrRT7JUCbMknaYk63BaNMhZdBZKKm5Acupq/k2/340DDc/xGqmjI+xDHfk/h8f6dKMOZ2UmYmO6FSekxE85OOoP4LVuO55qHUClg/6NlT/zQLRjvRIwU4oPsYr1rBTVkqJLsXzld2C2ZHI4uzvewd5Pf8gbndIjPgIU68XHmHZQPgKiC6qN+9ux46MPcclXv6x8NBXuIQmqCid4DvdIUJUW9yZzGrJygwJqZvY66A0HE112db+r/S10tb+B7va34PPZF2S8VJKsNTYL/njUEtj07IzrwWdEE49WYxna9cvQaDoKdaZgfa7JxzXaOXWS9eCp1ka4RtrpVOs8b0askqwFvbA0WRAEKMkKwsg+4FlU8BUsK78W1om6017PEJrq/oiGmt/B6xkQBG+pLHJorP9KThJ+VpYzzbQ3ex14oXMIb/U64RmXT21YqeArZTukEuuljJFSbYt1rNfqzCgq/RY/+c8a+o2Pj6Oj5V+o+vxeOB1NSoVdEn5RrJcEDWSEzBEQXVB978OPodVqceJx05NcmeOmSvNJUFUl7dxpElRjz31Sygpk523mIior7q/RHBQWWQ2qyav8A707BS3wL7UkK8dswAqbGax7dIXNgvIEE9JMwZIy250J+NnoqVMnW5kAotNbZiXPP+YKlg9wBE+2TpYPcAzVIxCgut4MtFgnWbH/qVOvBWpPsvT6eCwtuQJFy6+eOjnFPpypr/4Nmuueht/vUuTLcWisL0sw4aXjluLDgRH8q9uOV3vscIzRjTJFEg86oapUXkPxSyqxXm+w8lsARaVX89/d2C2rlqa/oHrXfWAln+gRHgG1x3rhEaUV1YiA6ILqTTd/B7d+93t49JGHUF9XOwPjV//9CsbG5q/jp0ZypOYzCapSYyR69pCgGj2sJ3din9hnZp/GBVRWxN8Slz1lhN/vRX/Ph7yhVGfr66JeN5WaoDobEzkmPcpsFth9fuwcOrRxlQaW+FxeNsCaWMT/LrcloMCiR491Lfp0uTOWYycjXKPtB2u1TtRsZXVb3aOd0X8RYrijVJKsGEKg2q3VmmSx0/9Fy6/B0uKvTzXxYx+21FX/Eq1NzyMQ8Cn6nTg81mca9ej20u/oiiZ9wjk5xHo18BALH6UW603mdCxf+V1eDkCrM/CyTk21T6K28rEjNlCNBW5K2FOtsV4J3JEP0kFAdEGV1VDNyAjWRZntoaZU0nkZ5rOEBNX5EFLu90lQjQ635rhs3kyK/WGNT3Q609TGblcvutq3obt9G7o63opax3ulJVl3LsvAVYvTOK6OMaDeF4fm8Wx0GEvQHb8Wo4nHgYnZsz0+n3OiGRar0XrwVKvT0YiA3xudlySKu0gtyYqi66rfSm1JVrx1CYrLb8Cigguh0wf/3R3o/RR1VY+jo/VVRZQHYXcajk6Kw5YMK05PTcDZO5rgCky/tk+xXr0/+kqL9eplMnzPpRrrLfF5qFhzF/KWnMdvZfm8DtRX/wr11b9W7C2B8Nlb2Ay1xfqFoUWzCYHZERBdUD35lFORmZl1RPz/9dI/4PUqLxFV4gtHgqoSWQ3NJ0qyQsMp/FEapKQdNXEKdROSUsqnLTE0UIkudgq1fSsG+z6PSVKvtCSL1WI9JS1homSAGVkT5QImgR/xB/CDRi8+GCuYOtXKmmKxBllmS8asFI+PBzDqbAU7xcrKCHCxdeJrj7sn/NdCIjOkmmRJBB5Fm6GWJIuVUimpuIk3nNJotJxT9sEVE1L7uj9UBMenpsRjU4YNmzOsSDXqp3y6dncrXut1TPORYr0iKI/ICaXF+ohAUOkkqcd6a2IxKo76AW++yh52wKC28hFefkXptwbEfiXVEuvFxpHWVzcCoguq6oZXWd6ToKosPsPxhpKscNCaeyyrzZeRc3qwqVTuGTBb0qcmsK7RPZ3vBuuhtr4miZpRSk+ykg06rLSZsYLVY7UG/75hTxs+t8+skci4Y7/YM3GVi6y8lMAyxFsLoNMZZyXe57XzU6324XoutAa/rsOIo1nyiYDUkyzhfipppcMRUHqSlZG9jjdAycg+hbvOavW17f8nT9Idw3WyfyGOTrTgsrwUrE9PgFWvm/LHORbAW30OvNJtx/a+mY2lKNbLnvqIHVB6rI8YGBVMlEusT047CquO+SlS0oN9WUacLajZ/QBam58XtHeACiifclHpsV5NXJKvsUNAFEH19PUbcP0NN+G737kZ51/wZZSUlB7Rw+/eehPs9oV1oY4dfOramQRVdfF9qLeUZC2M+7j4fOQsOpOLqKkZx08T31ijE3YiqqttK7o7/4OA372wzQSeTUnW7ID++ajFMGg1qLS7UOnwoMmfih5DAeJsyw452VoEsyVYXuDwJxDwY9R5gJ9kZSJrsClWsEGWx90nMIuRLSeXJCsy72jWXAgoMcliJ1BzF32RX+1PSl2CozcmAAAgAElEQVTB3WfN6fY3/C8/keoa7VDMS/HNRSm4qzh4O6zfO4atvQ683mPHBwOj8I1Pv+ZPsV4xtC/IEYr1C4JP1pPlFuvZ79Jlq++YutXFGrNW7boXnbw8Cz3hIKDEWB+O/zSWEBACAVEE1Ztv+S5u+c5tuPTiC3H/gw8jNzfviLaedPwxaGtrFcIXWkNkBEhQFRlgCS9Pgmp45Gg0OqRmrOUCKruixE41Tj6s6dHQwG4uoHa2vY6hgb3hLR7l0ZRkzQ742ycWYnHcwRq3bJQnMM4F1mqHG5UON17qHIZfnwBbYgkXWRMOaY4Vn7CEN1uY7fF6Brm4ykRWLrZO1Gsdce7HeCB6DWLklmRF+UdD0dspKclitagXFV6MZWXfRoJ1CeeN/Yw17nsSDfuegM87pDguF1mMuCI/Ga/2OA5r1De3qxTrFfcqhOwQxfqQoVLcQHnGeg3yC87D8pXfQ4KtgHMy2L8Lez7+Pvp7dyqOI7EcUlKsFwsjWpcQmA8BUQRVvV4PW2IiBgcGwMQDepSBAAmqyuAxEi8oyZofNYPBhszcM3hDqcyc9TCakqYmjY2NoqfjHXS2vcGv80vlBOL8XgGUZB0ZpXSjDkcnxuGYpDgcnRyHVTbLtMFLt1UfcTIT3ZmoOlk+wMbKCDDR1VoIkzll1nnsWjITVQ+v0+oYqoXPJ/xND3kmWaG81TRmPgSUkGTpDVYUlnwThaVXTZVWGR1pR0PNb9Fc9yfZNjXJNRvQ7vbNR2FE36dYHxFsiphEsV4RNEbkhJxjvUarx5Kiy7B85a0wW4JNsLs73sbeT38E+1BNRHioaZISYr2a+CJfpYmAKIKqNF0lqxaKAAmqC0VQvvMpyZqdO3bydPIUakr6Wmi1B2vVsdpOwVOoW9HX875su8BTkhXez+3apDgclWhBpkmPH9V1zznZpNHg/JxEVDk82HNIzVaTOZULq+xEqy1pWfDrxCLEJyyGVnuwqcyhi3vc/RPlA4KNsSZLCbBaraxpViSPnJOsSPylOQcRkHOSZTJnoLj8WixZdjkMhgTuFLsSyq71t+5/IaqnvIV6p1ZazdicYcOZmVYsiTNh1Tv74BiL7Od6Lpso1gvFmPzWoVgvP86EslgJsV6rM6Oo9GoUV1wPozGRH+hqb/kXqj77KUacB4SCSnHryDnWK44Mcki2CJCgKlvqom84CarRx1wqO1KSFWRCqzUgNeMEfo2fCamT14zY95hoNdD7CRdQu9rfgH1on1ToW5AdlGQtCL45J6+ymfHi2qVTY6p4PVY3Ku2sZIALu+3T6+mykxgJ1qXBU63WwoO1WhOLeAIx2+P3e3kDrKDAOtkUqx7sVOvY2Mic9ikhyRKPPWWvLMcki/1slFTciLyCC6bqVPf37ORCKiuvIrfn2KQ4bMqw4swMG3LMB8uDsA9fbq/qQO2IR3CXKNYLDqlsFqRYLxuqBDdUSbHeYEzkDQeLSr8Fnd7CGw4eaHyON69yu+b+kFtwYGWwoBxjvQxgJRNVhgAJqiojfCHukqC6EPTkPVfNSRY7LZiVuwFZeZvAOkNPnnhijLIO7t2d76CLX+XfxuvyKe2hJEs8RsusZtxYkIZymwXsGu9sz1/aB3FHTee8RpjM6TPqtDLRNd66GKwZz2yPx90L+1A9nI5GOIZYU6wG/vWIg53mGIeSkqx5AaQB0xCQU5KVnLoaJRU3ITv/TGg0Gn4yiZVWqav8hSxr6V2Zn4JvF6Qh1XjwNPrOwRG81hNsLNXpEa+Osppjvdr/CaBYr943QImxnv1OtHzld7Gk6FJer97vd/O62bWVj8LnHVYv2Yd5LqdYT6QRAlJFQLGCal5ePhITE1FVVblg7E0mE0qXl6G5qRF2u/B16hZsYJQWIEE1SkBLcBu1JVmJyeVcQM3O3YjktDXTBCnWLKi7fdvEVf4PZXl9NJxXjJKscNCKfGySQYcVVjMqbBZU2MyosJqRbzHijy39+Mk8pQPm2pWdqk6wBcsHsJOtVhs72Ro84WowWmed6h/zwOlshsfTgeH+agwN1PDTrezatN/vitxJmikbBOSQZGXmnIGSihuQlnkCxzXg96F1/4s8YWbvq1yfy/OScVdxJj4YGOUC6tZeBwZ8/qi4o7ZYHxVQZbIJxXqZECWCmUoUVCdhYqWSylb/P+QtOY9/4MYOQtRV/woN1b+h32cAyCHWi/DK05KEgKAIKE5QLSktxcv/3gqj0ciB8ng8+OtfnsN/33k7/+/mlk5otTNP61z5jcvx5rY3ZoD79LPPYd269VP/v7OzA1+54Fy0tKivHgsJqoL+7MlqMaUnWawLdHrWKfwaf1beRsTF507xw64L9ffsCF7lb3uDn+BT00NJVuzYtuq1iNNq0e2d+0Ta1YtTcW52Imocbuzl5QLcYOUDXIG5m0KyBg6TTbGsE4IrE1/j4vN54jHb4xrtgmO4Hk57Iz/ROtkga3SkjZ9qpUcZCEg1yWLN3PKWnMuvdCYml3GwWdO//fXPoq7ql3C7umRPgFUX/B3V4Re+Rup84Cg91s/nv5q/T7FevewrWVCdZJX1PFhx9P/wG2dcH3D3Yt+eh9Fc/ycEAuI0+ZPDGyXVWC8H7MhGQmASgagIqiwxO+WU07C8rBwfvP8u9u7dgxNOPAkDA/2o3SdsncGysnLccdcP8MB996C3txcPP/o4jj/hRKxZVYbBgQEcu/Y4sBOnk88ZZ2zElVddjbPP3MjtOvx5+JHHUVm1F39//q9Yu/Z4/PaJP+CtN7fim1d8TXVvEQmqqqN8ymElJlnsOlB2/hZ+CjUj+1Rea2ny8bgHeJfQrrbX0dXxFsZ8DtWST0mW9Kl/tCIXX8yaWUO1fsSDajsTWV14vdcRcmdwrc4IJrBmLTkZek0q4uIWBU+42gqhN8TPCgi7TucYbgyeZB2u44Jr8Ot6BPzTa8FKH1GyUGpJFms4UrDsMixbfg3iEvInEuJ+NNX+AQ37fg+fd0jSpCXqdTgjPQFL44x4sLFXsrYqMdZLFmyJGUaxXmKERNEcNQiqk3Ampx2FVcf8FCnpR/P/xUoc1ex5AC1Nz6vyQ2Gpxfoovva0FSEgGAKiC6oZGZl48533YLPZuNHP/Okpflp056e7kZSUjOLCRYI5M9tCTEB9/oWX+J5s78Ofz3dXY2hoEKefdlJIdrz9n/eRkpqGVRUlIY1X0iASVJXEZni+KCPJ0iApdRUXUNl1/uTUldNAYNeZO3kt1K0Y6P044s7o4SEr/dGUZEmfowSdFuUTZQJYyYAVNguWWAzQHnLK9L92tWBrnzMsZ2ZLsixxOQdrtfJTrUVcbGX/f7ZTrayepWu0g4ur7DTroada2f+nR5oISCXJMhiTUFR6FZaWXAlWz5o9o85W1Nf8Bs31z0parE8z6rE5w4otGTYclxQHvVYD//g41rxTC2cMTp+G8qYpI9aH4imNORwBivXqfSfUJKhOssxupJWvuXPqpsPw0D5Uf34vOtteU9WLIJVYryrQyVnFISC6oPrIo7/EOeedjz8/+yecf8GFeOHvf+Pi5hXf/BZ++KOf4sxN61FdXSUasPc/+DAu+uolWL/uZDQ21E/b5xtXXoUf/fhunHfOWfjs00/mtcFisaCypoGfZD33i2fOO15pA0hQVRqjofsj1yRLp49DZvY6ZOdtQmbuGTBbMqacZt3P+7o/4AJqR8urcI22hw6IikZSkiVPsuO0Gl6PdQUXWi24v6F73mY2Z2faeK3GvcMuft04nCSLnSC0sdqsNiawFsKWWMz/ZqdaDz39fSiaY74RsJrETGxlJ1qDJ1uDomvA75Un8AqxOtZJltmSheLy67Bk2WXQ6+M4qsODNairehxt+1/E+Hh0aoqGS2ee2cBF1M0ZNhyTFLR78tnndGNrjwN/bB3AUJRqooZrv1xjfbh+0viZCFCsV+9bEU6sVxZKGuQXnIflq25HgnUJd22wfxd27bwDg32fKcvVI3gT61ivCpDJScUjILqgWttwAJ98vBOXXnwhdu2pwcsvB0+LFhYtw1vvvIebb7wOL77AjtkL/2zctAVPPPkUPt65AxdecM60DdhJmqp9jWhubsJZW4L1VOZ7mL1LC4vwhc1nTInAqfnL55ummO9rdXqwPwH/GP9Dj4oQ0GiC3I9Jv86QyZSBtLSTkZJ6PJIS1/DunpOP1zuAgf4d6O//EAODHyMgowY7fq8bOqM56i+dRqvje44HpClgRB0QBW/4eiGQog/WTm3zjmOfV4t9rnHUuMdR7QacEZV01MBsyoQlLp+XDoiLy4eF/70IJlParGiyU60eTxdGR1vhGm3ByGgLXKOtGHW1wOvpVzAD0nFNZzDB7/NE3SD2XuQvuhSZmRvA6qWyZ3hoN1pbn0N//0dRtyfcDR/PA46LD/4Msfe42gO87QDedABt0g+fgIxifbjc0Pi5EYhlrPd7PdAZD5ZjI66ii4BWbwjmdePqrIOu0eiRnX02Fi2+HCZT8CbEwMAONDX+FiMjTdElI8q7xSrWR9nNadv1t9bEcnvaW4EIiC6o1jW24P33tuOKr182TVBdf8ZG/PHpZ3HBeV/kgqvQzzHHrsVf/vYiWBOpdaecgLGx6QLg7XfchWuvuxGbNpwWUh3X//vrC7zu6+ECMPuHSC1PXGI62J/R4V7+hx71IGAwxXHuh3uk14xNo9EiOfUosI7P7AoPOxl36DM8WI3ujm3oat+GwYHdsq2RNI5xaDB7oyAx30TGO3voZ15MlKWx9n0l6Si3mlASP3tca3f7sG5Hi2DG6nSWYFMs61Jes5X9zU64xlsLwBrFzfb4vA44nU0TTbEaMeJgJ1wb4XQ0qbqxhGCkTCyUtqgMfS3VQi97xPVS0o/FsuXfRmb2Gbx0BBMjuzreQF3VLzA0MLO+fdQMC3OjS3JsODs9AVv7RvBanxOdHnl9ECXlWB8mFTQ8TARiGetj9ftNmBApdnhixmL+O57PM6pYH0NxjN20KSq5CoWl18BotPE41NHyMqr33IfREeF+9wnFlmiNiXasj5Zfc+0Tiw+LpeA32SAeAqILqq9vfQeFRUU4/5yz8Kdn/4+fUP35Q/fjja3vIDUtDcuW5s8QOxfq7hkbNuH3f3gazU2N2LJpPbze6VcHWVMqdnV/967P8eXzvzTndlqtFv98+TWsWLESN93wbfzzHy8u1DzZzqcr/7KlbsGGS+0aoN5gRVbOel4LNTNnPUzmlCkfWXOcns530dX2BjrbXofb1b1g/9W8AF0DVB/7Jq0GyxNMODZ/EZZp3SiL02FZvAldnjGc9n5DFADRID5hohFWImuGFazTyuq1Hlq241BDxscDvLmE09E4rU4rq9vKuvnSEx4C0boGmJ23GcUVNyA1/VhuYMDvQ0vz31FX+SgXyemJLgJSi/XR9V7du1GsVy//6r3yPzvnBmMiistvQNHyb0GnMyMQGMOBhv9FzZ4HFZdTRCvWq/enizxXAwKiC6oFSwux7a3t0Ov1HE+fz8e/ZicQHn3kIfz8wfsFxXnLmWfht0/8AW1trfw0Kft0iT39/f1cYGXPAw89ggu/8lWccuJatLZO/8SJCbHHHX8iVpQt42Pf2f4BmA/3/+we7Njx4ZSte/fshscT/etwgoIV5mIkqIYJmIKGSyHJSrAWIiuPNZTaiLSM46HVBv9NYY9rtBNdbVvR2b4VPZ3bJd2oRG6vBSVZcmNMOHsPT7IK4oxoHp27tmlhnBHPHL0YVXY39tjdqHK4+N99XmHKxOj18bAmFvOTrbwhlrWQfx081Wqc1XmvdxjOwxpisTqtTLAbDwhjl3CoS2MlMZMsjVaPRQUXYFnZdbAlBRt8snq6zQ3PoK7yl/C4e6QBAgBWi3h9uhUb062w6LS4enerZGwTwxApxHox/KI150eAYv38GCl1BAmqszNrMqdj+arbsKToUp5zsAMbjft+j9rKx+DzDividRAz1isCIHKCEAgBAdEFVWZDckoK7n/g5ygrr4DZZEZnVyceffghbH1D+E56//PDn+DKq66e4XpLywEuoNpsNuyurMX27e/g65ddPGPcv/79Bj+NuiQ/i3+vobkNBsPBGoyTE1hN2Pfe3R4CxMoZQoKqcrgM15NYJFks6WbCabCh1Abe3GbyYR+UDPXv4gIqO4k6NLA3XJdofIgIUJIVIlAKHBZJkvWlTBseWZE3A40ezxgq7S5UOlx4b2AUnwwJe7WQlf6IT1iChAmR1ZbESgkU8pOtZsvstVrZqZMR54EZYis75epxq7tWqxhJFivxULDsaygq+y/Exefyd8Tt6kNT7ZM8SfX57JL4KUrU63BGegLOzLDhjHTrlE0j/gBO2F4Hpz+iYsKS8G0+I2IR6+ezib4fHQQo1kcHZynuEkmsl6IfYtkUn7AYZavvQN6Sc/mBMJ/XjrqqX6K+5jeyP8AhRqwXiwdalxCQKgJREVSl6jzZFR4CJKiGh5eSRkcryTKakpGVuyF4lT97HQxG2xSM7ARTd+c7/CRqV/tWeNx9SoJYsr5QkiVZakQ3LNIkq8JqRpnVjAqbGRVWC1YnWqbZ+rf2Qdxe0ym6/ZMbsBIhtsQSWCdEVnaylZURYALsoU3rDjXI4x6Ak51itTfCPlwfrNk6XI8R537JdpgXElAhkyyjKQWFpVehsORKsH/j2cPKM9RX/xoHGv8Xfr80bvtcmJME9oHASakJU1AO+/zY1uvAv3vseLvPKSTEklwrWrFeks6r3CiK9ep9ASKN9WpDjN2OWXH0//A8hT1uVw/27X0Y++ufkW0NdyFjvdreB/KXEJhEICqCKvs0hzWhKisrn4H87377K9VdnZfr60eCqlyZW7jdYiZZtqRSZOVuQnb+JqSkHQ120mzyGXG2BK/yt21FX/d7sv2FZeEMxG4FSrJih32sdxYyySpNMGGFzYKyBBN2Do3i1R7HnO6ttpmRaTbw0gFtbnHao7Mu8qxUABNXJ0VWdsKV/fek8He4kazGJxNVmbjqYM2w7A38a/twLcZ8yhHchEiyLHE5vD7qkqJLeB069gwNVKKu6nG0H/gnWN1bKT1/XLMIp6UmoMvjw+vddmztc+KDgREpmSi6LWLGetGNpw0WhADF+gXBJ+vJQsZ6WQMRovHJaUdh9dp7kZy6ms9wOvajZvcDaG3+u+wa3woR60OEjYYRAopFQHRB9fKvfQM//um9YM2dZntOPuHYGXVMFYu2zB0jQVXmBC7AfCGTLK3OiPTMk3kt1OzcjYhLyJ+yLBDwY7DvUy6gdrW9zkUKemKLACVZscU/lrvHMsm6e3k2Ls4NnmYc8o2h0uHB3mEXr8nKvm5xzV3LdaG4mcypvFwAKxvAywfwxliFwVOtWt2sy7tdvcGTrBMi6+TXo84DkhMP58NnIUkWO8VTuuIW5C4+Zwqr3q73UVv5C/R0vj3f1jH7/iqbGTqNBp8Nu2JmQ6w3FjLWx9oX2j88BCjWh4eXkkbHMtbLGUd2m6589Z1ITF7O3RgerEHVrnt4KTK5PAuJ9XLxkewkBMRGQHRBtbKmAUajEf/z/TtRW7sPY77pJ0327t0z1ThKbGdp/YUhQILqwvCT8+yFJlkmc1rwFGreRmTkrINeHzcFB6tFxK7yd7a+jq72bfB5h+QMleJspyRLcZSG7FAsk6yv56fgCxlWlNksiNfN/EDWMebHdXva8F6UTxCy2s4J1qW8EVawIRY73coE10IYjYmzYusf8wRPtdrr4RhmZQQaeBkBx3Ad/GPC1pINmdx5BkaSZKVnnoTiiuuRmbOer85OoHa0/Bu1lY/EtM41K0HBGkp9LHDdXqGwltI6C431UvKFbAkPAYr14eGlpNGxjPXyx1GD/ILzsXzV95BgXcLdGezfhV0778Bg32eSdy+SWC95p8hAQiDKCIguqLKmTh/v3IGLL7ogyq7RdkIjQIKq0IjKZ71IkqyklJXIzt+MzJwNSE5dxQu5Tz7sqiyrg8qu8/f1fESdtiX8KlCSJWFyRDZNCkkW+1ejIM44VY+V12e1mWHT63DmR42odUqj/iajgnUEZgIrO81qmxBZ2dfxCYumlTI5lDa3q5uLrOxUa7B8QPDrUSfrJj8uMsNHXj70JEuDnEVfQHH59UhJO4ov6Pd70dr8PGorH8WIY3/UfWDvzFGJFmzOsGFzhhX5FiM+HRrBhZ8ciLotctswklgvNx/J3tkRoFiv3jdDCrFe7uhrtQYsKboMpStvhdmSwd3pan8Tez/9If/wVKpP6LFeqh6QXYRA7BEQXVB9Z/sHSExMwppVZbH3lixYEAIkqC4IPllPDiXJ0urMvJEUu8rPCrZb4rKmfGbdtJlwyhtKtW0F66JNjzwQoCRLHjyJYaWUk6wCiwHNrvlrq/7j2AK4AwHssbtR5XCj0u5C46i45QIO54IlWuwEa4Jt2VStVi68WgthMB7sIn/oPNaoaXr5gGCDrOGh2qh0FZ4vyWI+5RdciOKK63jNWfb4fE401z2N+urfwOPuEeOVnHPNk5LjsImLqDZkmPRTYz2BcWzvc+C/9rRF3Sa5bRhKrJebT2RvaAhQrA8NJyWOknKslxveLBdatvwaLCu/lt9aGR8fR9v+f6B6170YcUrvQ735Yr3c8Cd7CYFYICC6oLpq9Rq89PJrePvtN9HWyk5cTH/uvfvHGBlRV9H/WBAtxJ4kqAqBojzXOFKSZY7LRnbeZn6VPz3rFOh0poNJrHsA3R1v8VpCXR1vYcw3dxMaeSKjfKspyVI+x0fyUO5JllmrQfX6YG2zQx+XP4C9dlaP1Y1Khxsvdg7HjGSzJWvqVKvVxkoIBMsHxMXnTzvVP83+kY5gnVZ+qrUx2CBruAGu0Q7BTrUeKcnS6+NRUPwNFC2/eupDM4+7Fw01T6Cx9g8x+3d+x6nFSDceFFFH/QG83efEq93D/G9XIHanfWP2ckWwMQmqEYCmkCkU6xVCZARuyD3WR+Cy6FMMxkSUVNyIwtKreFNGdrBkf8OfefMqFjOl8pCgKhUmyA45IyC6oHrzLd/FLd+57YgYUVMq+bw+JKjKhyuhLT2YZDUiJe3oYEOpvE1ITJ5+8tw+VItOJqC2b8VA78eya8QiNG5KWI+SLCWwGJkPSkiy8swGsDIBK2wWXjag3GpGyiHCm33Mj9XvSK/5HftwarIRli2xeOKEK6vXWjStBvWhzPrHXMGSAY7GYPmAoTr+tWOoHoFAeKURDk+yWB1sJqIyMXWyVqzT3oz6ml/jQONzCPije+r38Df696vysTrRgjf7nHitx473B0bgJRE17B98ElTDhkwxEyjWK4bKsB1RQqwP2+koTWClgMpWfQ+Liy6BVquH3+/mH0DWVf0CPm/sPsyddJ8E1Si9CLSNohEQXVBlTam0Wi2u/a+reFMq32FNqfr6pPMpjaKZFsA5ElQFAFGGS7ATSTlLvoC8JWchKelYmC1pU16wWnl93R9wAbWj5VW4Rttl6CGZPBcClGSp9/1QapKVy0RWm5kLrVqNBg80zH09Pcmgw8a0BFQ7PfxUa6wfS1wOF1t5Qyz+d/BUK/v/h9aqnrSTXTlk/zZzsXW4/mApAXsD3KOd09xhzTWKln8b1qRiLsi2NP0FtsQSLCq8aOoGwmD/Hp4MdrS8LJkPzTKMOvR4/bGmRvb7k6AqewojdoBifcTQyX6iUmO9lIiJT1iMsjV3Im/xOTxOe73DqK/6JeprfhuVMj5HwoIEVSm9JWSLXBEQXVCtb2rFJx/vpKZUcn1DDrGbBFUFkBiiC/HWAmTnbkJW3gZkZJ86bZbH3R88hdr2Bro735Fsl+oQXaVh8yBASZZ6XxFKsoLcn56WgCdXL+Jfs3qc+5xuXjKgcqIua53TA9947K+Us9pttqRSWG1LEW9dCltSCeITliA5deURX2J2WsY+WAOnoxle9wAKSq7kH4IfFGMB3k5QA/R0vYe6ysfR0/m26D8UrFzDpnQrvpiViL0ONx5rog/fRQcdAAmq0UBZmntQrJcmL9GwimJ9NFAO7sFu9pWtvpOXSmOP29WDmj0P8vrjsXhIUI0F6rSn0hAQXVB95bVtyM9fhJXlxUrDTnX+kKCqXMo1Gh1SM47jAT4rdyM/8XToMzxYhcGhnWiu+QsG+3cJVqdPuYgqxzNKspTDZbieUJIVROyYpDhcszgV5TYLMg9pdnQonr870I+f1XeHC3GUxmsQF5/HT7Gyf9vZqdbJrw9tHsg0YQ1XT6c/QwNV+OT962AfqhHd3jPSEnB2ViIXUy26oLBb7XDh7B3Nou9NG5CgquZ3gGK9etmnWB997pPTjsLqtfciOXU139zp2I+a3fejtfmFqOZYJKhGn3vaUXkIiC6o/uz+h3DxJZfh888/Q0f7zA6rt992KxwOalYjh1eLBFU5sBS6jQZjErJy1yMrdxMyc06H0ZQ0NZmdWurp3I6utq3obHsd/nEnElKyMdjREPoGNFIRCFCSpQgaI3KCkqyZsKUa9VhpNaPCZkG51cT/zjEb8FBDN365vz8inGM5Saez8JOsrITAoqUXIjNn3Qxzdn/8fTTu+50oZjL9dm1yHL6YmYgzM6xIPqS+7Z5hF17vdfCaqM2jsa3RKorzElyUTqhKkJQomUSxPkpAS3AbivWxI4U19i1bfQcSk4MNNIcHq1H1+T28lFo0HhJUo4Ey7aF0BEQXVHd8sgtZWdlHxPGk449BW1ur0nFWhH8kqMqfRmtiMW8mxU6hpqQfC61WN+WUa6QDXe3b0Nm+Fb2d/4Hff7CJCSVZ8uc+Ug8oyYoUOfnPoyQrNA6TDTroNBr0ecfmnHBbUQZOS41Hld2NSoeblwyodrjhkUC5AGY4q5W6/uy3p8WFQMCPt14+HfZhcRp3xes02Ht6MJFkz8dDo3i9247Xeh3ocPtCI4BGCYYAxXrBoJTdQhTrZUeZYAZTrBcMyggX0iC/4ALevCreupivMdD7KXZ/8t8Y7CZkCCkAACAASURBVPsswjVDm0aCamg40ShCYC4ERBdUCX7lIECCqvy41GoNSMs8kQuoWXkbkWBdMuUEa1Qy1L+LC6jsFOrwQOURHaQkS37cC2UxJVlCISm/dSjJEpazZ45ajJNS4mcsus/h5s2umMj6avdwTJsrHd6UqqHm1xNXEIXF4tDVbihIR6/Hh219znlFafGsoJUZAhTr1fseUKxXL/cU66XBPcvZliy7HMtX3gqTOZ0bxQ667P30R3AM14liJAmqosBKi6oMARJUVUb4QtwlQXUh6EVvrsmcGhRQczciI2cdDIaEqc3HfCO8kRS7SsKu83vcfSEZRklWSDApchAlWYqkNSSnKMkKCaaQB1n1Wl4uYIXNwksFVFjNWBRnnDb/Kx8345NhV8hrijVQiCTLotXApNNiyOcXy0xaV2AEKNYLDKiMlqNYLyOyBDaVYr3AgC5wOdZgctnya1Bcfh0MRhvYAZi2/S+ietfPMOI8sMDVp08XItYLahAtRgjIEAFRBNXLv/YN3HHXD3DxRRfgtu/dgdLSg9e5Dsdoy6b16Ouj7q1yeHdIUJUuS4kpFcjO3cRPoSanroHmkM4iI44D/BQqE1D7ut9HIBD+NUpKsqTLvdiWUZIlNsLSXZ+SLPG5seq0WJFoQXmCCasS4/C9qnaMBsbn3Pj87ES0u32otLsw4p97bKQeRJpkMdF4Y7oVm9OtODXNit8f6MNDjfQ7XqQ8RHsexfpoIy6d/SjWS4eLaFtCsT7aiIe2n8GYiJKKG1FYehV0OjMCfh/2N/wZNXsehMctTFyNNNaH5gGNIgTUgYAogupll3+dC6qXfPXL+O5t/w+ly48sqJ656QwSVGXyrpGgKh2idDoT0rNO5QJqdu5GWOJzpoxjNe8G+j7hAmpX2xuC1L6jJEs63EfbEkqyoo24dPajJEs6XBxqSc365TBpWTsn8GZNe+0uLq5WOTz8a6c/sGDDw0my0ox6bM6wYnOGDScfUtJg1B/A0y0DeKCxZ8H20ALRQYBifXRwluIuFOulyEp0bKJYHx2cI93FbMnE8lW3YXHhxdBq9fCPudCw7wnUVj6GMd/CGnuHE+sjtZ/mEQJKR0AUQVWr1cJqtWJ4eFjp+KnKPxJUY0s3C6isGyQTUTOyT+WfVk4+Pq8d3R1vo7PtDV5vx+cdEtRYSrIEhVNWi1GSJSu6BDWWkixB4RRkMXYC9EclWbxkQFG8adY1a51unPlR04L2CyXJyjUb8PPyHBybPL0u7NYeO17qsmNbr0MyDbcWBIaKJlOsVxHZh7lKsV693FOslwf38QmLUb7mLuQu/hK/iej1DqOu8nE07PsdAn53RE6EEusjWpgmEQIqQkAUQZWdUL373vuxYf0pqK8Tp4iyijiSjKskqEabCg2SU1dPnELdhKTUFdMMcNobD17l7/kI44G5O0wvxHpKshaCnrznUpIlb/4WYj0lWQtBT/y5rEZpudWM8ol6rBU2MxdZ2WnV8z7eH5EBOgCnpcZj1aKl2N3ShHcHRuA7QlUBgwbYva4URq0GHw6M4KWuYbzW64BjbOEnZCMyniYtGAGK9QuGULYLUKyXLXULNpxi/YIhjOoCtqTlWHH0D5CZs57v63Z1o2bPz7G/4dmwc0ESVKNKHW2mUAREFVQ3bTgNtfv2KRQ69blFgqr4nOv0ccjMOZ03lMrO2zDV5ZHtHAiMoa/nI36Vv7P1VcELk8/lHSVZ4nMv1R0oyZIqM+LbRUmW+BgLvYNZq0GGyYAWl3fOpY9JisPDFbmocbhRNfGn3uHCr1ctQqn14O2HfQ4Xzt3ZDO8RRNUN6VbsHh5Fr5caTwnNZSzWo1gfC9SlsSfFemnwEAsrKNbHAvWF75mcdhRWr72XH75hj9PejOrd96Ft/z8AhFZfnQTVhfNAKxACJKjSOxAyAiSohgxVWAMtcbnIWXQmF1HTMk+ETnew67PHPYDujrfQ2fY6v9K/0Fo5YRl2yGBKsiJFTv7zKMmSP4eRekBJVqTISX/e1/JT8MOSrMMMZQlYsDbroc+Ne9vwcrdd+k6RhQtGgGL9giGU7QIU62VL3YINp1i/YAhjukB23haUrbkDiUml3I6hgSpU77qHl4Cb7yFBdT6E6PuEwPwIiCqovvbqK+jv75/Tirt/8kOMjIzMbymNiDkCJKgKQ4FGo0VK+rETp1A3wZZUMm1h+1AtF1DZSVTWXGp8PPbXJynJEoZ7Oa5CSZYcWRPGZkqyhMFRqquwcgFlVjOKE0yosJqx2maBSaedYe6jjT14tLlPqm6QXQIiQLFeQDBlthTFepkRJqC5FOsFBDNGS7HcMr/gAixfeRvirYu5FQO9n2L3J/+Nwb7PjmgVCaoxIoy2VRQCogqqoSB18gnHorW1JZShNCbGCJCgGjkBBoMNmbnrkZW7CVm562E0JU8t5h/zoK/nAy6gdrS+Btdoe+QbiTSTkiyRgJXBspRkyYAkkUykJEskYCW67NmZNjy2Im+GdXRCVaKEiWAWxXoRQJXJkhTrZUKUCGZSrBcB1BgtqdUaULDsayhdectU2TjWsLjys5/AMTyzrw0JqjEiirZVFAKiCqrXXnMVGhsa5gSstnYfxsdDq/OhKORl6AwJquGRlmArmjiFuhGpGcdBq9VPLeBx96KrbRtvKsWu8vvHRsNbPMqjKcmKMuAS2o6SLAmREWVTKMmKMuAx3s6oAf6xdmlYNVRjbDJtLzACFOsFBlRGy1GslxFZAptKsV5gQCWwnE5nQVHZNSguuxYGo43fdmxtfhFVu+6Ba6RtykISVCVAFpkgewREFVSpKZXs349pDpCgOjef7FPB1Izjp0TUBNvSaROG+veis/0NsE8Kh/p3h1wwXApvESVZUmAhNjZQkhUb3KWwKyVZUmAhujboAJyWGo9Vi5Zid0sT3h0YgY8+844uCTHcjWJ9DMGP8dYU62NMQAy3p1gfQ/BF3tpgTERJxU0oLP0mdDozAn4f9jc8i5amvyNn8VlIzToK/V2fYX/dM3A6GkW2hpYnBJSJAAmqyuRVFK9IUJ0JK7u6z5pJZedtREb26TAYrVOD/H43ejq3cwG1q+0NuF3dovASjUUpyYoGytLcg5IsafISDasoyYoGytLcg06tSJMXsa2iWC82wtJdn2K9dLkR2zKK9WIjHPv1zZZMLF91GxYXXgyNJnhjUnNID0qvx443/nk8vJ65e9/E3hOygBCQHgKiCKobN23BAw8+jLO/sAltba3S85osiggBElSDsCUml3ERNStvE1LTj5mGpdvVg47WV7mAGkp3xYiIiMEkSrJiALpEtqQkSyJExMAMSrJiALpEtiRBVSJERNkMivVRBlxC21GslxAZUTaFYn2UAY/hdgnWpTj6pMeRmn70DCs+ef9GtDT9JYbW0daEgDwREEVQlScUZPV8CKhZUGWnT9kp1Oz8zYiLn960g3VRZOJpV/tWDA3snQ9GWX6fkixZ0iaI0ZRkCQKjLBehJEuWtAliNAmqgsAou0Uo1suOMsEMplgvGJSyW4hivewoW5DBZavvQumKG2essW/vY6jedfeC1qbJhIAaESBBVY2sR+izmgRVkzkd2XmbkMWv8p8GvT5uCrUx3whvJNXVsY2fRPW4lX89gpKsCH9oFDCNkiwFkBihC5RkRQicAqaRoKoAEiNwgWJ9BKApZArFeoUQGYEbFOsjAE3GU9IyTsSpm1+c4cG7Wy9Eb9d2GXtGphMCsUGABNXY4C7LXZUuqCanrkImr4e6CUkpK6E5pLjMiOMAOtu3oqttK/q630cg4JMlh5EaTUlWpMjJfx4lWfLnMFIPKMmKFDn5zyNBVf4cRuIBxfpIUFPGHIr1yuAxEi8o1keCmrznrF57HwqKv85z3fHxcTTX/Qm7dn5P3k6R9YRAjBAgQTVGwMtxW6UJqjqdBRk56/hV/qzcDWAFuyefQMCPgb5PuIDa2fY6HMN1cqRMMJspyRIMStktREmW7CgTzGBKsgSDUnYLkaAqO8oEMZhivSAwynIRivWypE0QoynWCwKj7BYxGGzIX74FrTWvweezy85+MpgQkAoCJKhKhQkZ2KEEQdUcl42cvC38Kn961snQ6UxTyHu9w+jpeIcLqF3tb8LnHZIBK9ExkZKs6OAsxV0oyZIiK9GxiZKs6OAsxV1IUJUiK+LbRLFefIylugPFeqkyI75dFOvFx1iqO1CslyozZJecECBBVU5sxdhWOQqqGo0WyWlHT5xC3YTE5OXTUHTaG9HZ9kbwKn/vDowHxmKMsjS3pyRLmrxEwypKsqKBsjT3oCRLmrxEwypKsqKBsvT2oFgvPU6iZRHF+mghLb19KNZLj5NoWUSxPlpI0z5KRoAEVSWzK7BvchFU9fp4ZOasRxZrKpV7Bkzm1CkkAn4f+no+mrjK/xpGnAcERkmZy1GSpUxeQ/GKkqxQUFLmGEqylMlrKF5RkhUKSsobQ7FeeZyG6hHF+lCRUt44ivXK4zRUjyjWh4oUjSMEjowACar0doSMgJQF1fiExcjO34Ks3I1IyzgeWp1hyi+Pux/dHW/xk6jdHW9jzOcI2WcaGESAkiz1vgmUZKmXe0qy1Ms9JVnq5J5ivTp5Z15TrFcv9xTr1cs9xXr1ck+eC4cACarCYan4laQkqGo0Oi6cslqo7I/VVjQN/+GhfeiauMrPmkuNjwcUz4+YDlKSJSa60l6bkixp8yOmdZRkiYmutNemJEva/IhlHcV6sZCV/roU66XPkVgWUqwXC1npr0uxXvockYXSR4AEVelzJBkLYy2oGoxJ/Ao/u8qfmXM6jMbEKWz8Yx709XzAr/J3tL4G12i7ZHBTgiGUZCmBxch8oCQrMtyUMIuSLCWwGJkPlGRFhpvcZ1GslzuDkdtPsT5y7OQ+k2K93BmM3H6K9ZFjRzMJgUkESFCldyFkBGIhqNoSS4K1UPM2IiXtGGi1uil73a4edLVv4yIqu8rv97tC9oUGhocAJVnh4aWk0ZRkKYnN8HyhJCs8vJQ0mpIsJbEZui8U60PHSmkjKdYrjdHQ/aFYHzpWShtJsV5pjJI/sUCABNVYoC7TPaMhqGq1BqRlnsQF1OzcjYi3Lp6G1mD/Hn6Vv7N9K4b6dwMYlyma8jKbkix58SWktZRkCYmmvNaiJEtefAlpLSVZQqIpn7Uo1suHK6EtpVgvNKLyWY9ivXy4EtpSivVCI0rrqREBElTVyHqEPoslqJrMacFaqLkbkZm9DnpD/JSF/jEXejq3cwGVCaluV3eE1tO0hSBASdZC0JP3XEqy5M3fQqynJGsh6Ml7LiVZ8uYvUusp1keKnPznUayXP4eRekCxPlLk5D+PYr38OSQPYo8ACaqx50A2FggpqCalrOBX+dkp1KTU1dBoNFM4uEY6JgTUrejt2g6/3yMbjJRqKCVZSmV2fr8oyZofI6WOoCRLqczO7xclWfNjpMQRFOuVyGpoPlGsDw0nJY6iWK9EVkPziWJ9aDjRKEJgLgRIUKX3I2QEFiKoanVmZGSfygVUdhrVEpc9te/4+DgG+z/ntVA7217H8GBVyDbRwOggQElWdHCW4i6UZEmRlejYRElWdHCW4i6UZEmRFfFtolgvPsZS3YFivVSZEd8uivXiYyzVHSjWS5UZsktOCJCgKie2YmxruIKq2ZKJ7Pwt/Cp/RvYp0OnMUx74fE70dLyDLnaVv30rPO7+GHtH28+FACVZ6n0/KMlSL/eUZKmXe0qy1Mk9xXp18s68plivXu4p1quXe4r16uWePBcOARJUhcNS8SvNL6hqkJy2ZuIU6iYkpVRMw2TEcQCdbW9wAbWv+wMEAj7FY6YUBynJUgqT4ftBSVb4mCllBiVZSmEyfD8oyQofMyXMoFivBBYj84FifWS4KWEWxXolsBiZDxTrI8ONZhEChyJAgiq9DyEhkGAtxLKV18CWVAL7UC3q9/wGTkcjdPo4ZOWsRya7yp97BsyW9Kn1AgE/Bno/5gIqE1Idw3Uh7UWDpIcAJVnS4yRaFlGSFS2kpbcPJVnS4yRaFlGSFS2kpbUPxXpp8RFNayjWRxNtae1FsV5afETTGor10USb9lIqAiSoKpVZAf0ymlKx6ZyPYDTZplb1j7kx0P8ZUtKOgU5nnPr/Xu8wujveRhc/ifomfN4hAS2hpWKFACVZsUI+9vtSkhV7DmJlASVZsUI+9vtSkhV7DmJhAcX6WKAujT0p1kuDh1hYQbE+FqhLY0+K9dLggayQNwIkqE7wl5eXj8TERFRVVcqbURGsX7T0Ihxz0mMzVh4fBzQawGlvnLjK/yZ6u94VwQJaMtYIUJIVawZitz8lWbHDPtY7U5IVawZitz8lWbHDPpY7U6yPJfqx3ZtifWzxj+XuFOtjiX5s96ZYH1v8aXdlIKB6QbWktBQv/3srjMbgKUuPx4O//uU5/Pedt/P/bm7phFarncH2ld+4HG9ue0MZb8E8XpStvgulK26cMaq7413s2vEdjDgPqAIHNTtJSZZ62ackS73cU5KlXu4pyVIn9xTr1ck785pivXq5p1ivXu4p1quXe/JcOARUL6iWlZXjjrt+gAfuuwe9vb14+NHHcfwJJ2LNqjIMDgzg2LXHwWQyTSF+xhkbceVVV+PsMzdi7949wjEh4ZXSMk7EqZtfnGHhu1svRG/XdglbTqYJhQAlWUIhKb91KMmSH2dCWUxJllBIym8dSrLkx5kQFlOsFwJFea5BsV6evAlhNcV6IVCU5xoU6+XJG1ktLQRUL6geTgcTUJ9/4SV+QvWZPz01g63Pd1djaGgQp592krSYFNma1WvvQ0Hx16HRaDA+Po7muj9h187vibwrLS8VBCjJkgoT0beDkqzoYy6VHSnJkgoT0beDkqzoYy6FHSnWS4GF2NhAsT42uEthV4r1UmAhNjZQrI8N7rSrshAgQfUwPu9/8GFc9NVLsH7dyWhsqJ/23W9ceRV+9OO7cd45Z+GzTz9R1psQgjeJ6UVIzT4K/Z2fYbi3IYQZNEQpCFCSpRQmw/eDkqzwMVPKDEqylMJk+H5QkhU+ZkqYQbFeCSxG5gPF+shwU8IsivVKYDEyHyjWR4YbzSIEDkWABNVD0Ni4aQueePIpfLxzBy684Jxpbwo7mVm1rxHNzU04a8uGqe/FJWWo5o0yWqwwxdngGbXD63Koxm9yFNDpjTDGWeGy9xMcMUJgfDwAjWZmPWexzWE/9+yhn3mxkZbe+hZbKryjDvjHvNIzjiwSFQFrai4c/e2i7kGLSw8BivXS4yRaFsUy1sfq95toYSv1fSjWS50h8exLSM2Bs79DvA0kuPLoUI8ErSKT5IwACaoT7B1z7Fr85W8vorOzA+tOOQFjY2PTeL39jrtw7XU3YtOG01C7b9/U9xJScuTMf1i2s5MLRksCvC4nfO6RsObSYHkjoNUbYDQnwO0clLcjMrZ+POCHRquLugfs55499DMfdehjvqE5IRletxOBMV/MbSEDootAXHIGRgcp6Ygu6rHfjWJ97DmIlQWxjPWx+v0mVlhLbV+K9VJjJHr2xCdlYmSoO3obSmAn54C6BGQJQK54E0hQBXDGhk34/R+eRnNTI7ZsWg+vd/ppHNaUqrKmAbt3fY4vn/8lxb8UR3KQXQdKSMmGc6ATI4NdqsVBjY7TNUA1sh70ma4Bqpd7ugaoXu7pGqA6uadYr07eKdarl3fmOcV69fJPsV693JPnwiGgekF1y5ln4bdP/AFtba24+cbreMMl9vT393OBlT0PPPQILvzKV3HKiWvR2toiHPoyW4kEVZkRJqC5lGQJCKbMliJBVWaECWguJVkCgimzpSjJkhlhAplLsV4gIGW4DMV6GZImkMkU6wUCUobLUKyXIWlksuQQUL2g+j8//AmuvOrqGcS0tBzgAqrNZsPuylps3/4Ovn7ZxZIjMJoGkaAaTbSltRclWdLiI5rWUJIVTbSltRclWdLiI5rWUJIVTbSlsxfFeulwEW1LKNZHG3Hp7EexXjpcRNsSivXRRpz2UyICqhdUlUiqWD6RoCoWstJfl5Is6XMkloWUZImFrPTXpSRL+hyJZSElWWIhK+11KdZLmx8xraNYLya60l6bYr20+RHTOor1YqJLa6sFARJU1cK0AH6SoCoAiDJdgpIsmRIngNmUZAkAokyXoCRLpsQJYDYlWQKAKMMlKNbLkDSBTKZYLxCQMlyGYr0MSRPIZIr1AgFJy6gaARJUVU1/eM6ToBoeXkoaTUmWktgMzxdKssLDS0mjKclSEpvh+UJJVnh4KWU0xXqlMBm+HxTrw8dMKTMo1iuFyfD9oFgfPmY0gxA4HAESVOmdCBmBhJRs3vF7ZLALzoHOkOfRQPkjQEmW/DmM1ANKsiJFTv7zKMn6/+3dd3QV1d7G8QdQlC54RbASakIvIhcQRaUJCIidqr5ekB56E0RFLkUuRTrSW0JHRFCKFKUKoYYiVakRQgcDCO/a25tzIYTkBHJyzpx8Zy3+gMzM3r/PnjDJc/bscf4Y3m0F/JJ1t3LOPo57vbPH7156z73+XvScfSz3emeP3730nnv9vehxLAJ/CxCociUggAACCCCAAAIIIIAAAggggAACCCCAAAJuChCougnFbggggAACCCCAAAIIIIAAAggggAACCCCAAIEq1wACCCCAAAIIIIAAAggggAACCCCAAAIIIOCmAIGqm1DsJqVMmVIFCxbS7t27FBUVBYkfCmTIkEE5cgRo+/ZtunHjhh9WSEkJFUiRIoVSp07N93xC4Ry0v/m/3fy5du2ag3pNVz0l8MQTTypTpkzasWO7p5rgvF4UMN/ruXLn1p+X/9Tvv//mxZ7QtK8ImHt8YGCQUqZKpe3btnIv8JWBScR+ZMyYUfkCgxQZGal9e39NxDNzKgQQQCB5CxCoJu/xd7v6VsFt1bpte5lwxWxzZs1UcKtmbh/Pjr4tYMZ1ashMlSn7nO3o9evX1bF9G00PnRZrx3PlzqNly3+67WuffdpdY0aP9O1i6V2CBHr26qN369RTrhyPJ+g4dnaGgPneX/rjKtvZl8r//f1/p23BoiX2Q7Wbt/Pnz6tgUG5nFEsv4xTIFxiob79bbD9AMZv54NTcAz7u0hE5PxFo1Lipunzc3fWz3NmzZ9W9W2fNnT2Le72fjHFCyxj01XDVeq226zDzwVrbNi3veE0k9Pzs732B5StXKyBnLldHzp07p+pVK+nQwQOxdo57vffHLKl68EzJZzVz9jfaHLZJtWpUTapmaQcBvxIgUPWr4fRMMZmzZFHYlnAt/mGRmjdtrOA27dS0WUu9UbuGNqxf55lGOWuSCpjArHff/vYX59mzZmhKyEwVKlRYeXI+acPVmFuevHm1ZNkq9e3dS1u2hLm+bGa2njl9Okn7TmOeEShdpqwmTQnV/fffb2erEKh6xtmbZ+368Sf6sNFHdnaqmbESX6D63fdLlfWRrLd8mHbu7Flt3brFm2XQdiIJ5M9fQJ27dle/Pr30xx9/aMCgIfpn6TIqViS/TkdGJlIrnMabAv/3r8YKCMipEcOGKHPmzBo3YYoNV0sUKxhrt7jXe3O0kqZt86Hp8WPHNHXqJKV5MI0WLFysFClTqkjBfEnTAVrxuMDkqdM1c0aIvl+0UEWLFbcTKH5atVL1674da9vc6z0+JD7RQPbsj2nFT2v1wAMPKGzTRgJVnxgVOuFEAQJVJ45aEvc5uHU7OzvVzEIys5HM9uv+37Vk8fdq0vjDJO4NzXlCYO78hfZR/6KFAu3pzS/WC39YpuZNG2n+N/NuazL6l6z6dd7WypXLPdElzullAfMDVr58gWrcpJmqvFKNQNXL4+GJ5rM8/LCeePwJDRv5ta5ERbkVqJplQcqVedYT3eGcPiZQ8tlSduaK+aBt0sTxPtY7upMYAiZMq9/gPfvh6ZUrV7jXJwaqw8+xet1GW0GZUiUcXgndj00gXbp02r5zr+bNnaPglk1jRTKBKvd6/75+zM/4a9eHKTLylNKkTauIEycIVP17yKnOgwIEqh7E9ZdTDxw0VNVerWF/4I7eNmzaqiNHjqjWq6/4S5nJug7zA/T5c+dVuWJ5l8Ohwyc0oH8/DRzw5R1/yYqIOKGLFy5oz57d+qxHdx0+/HuydvTH4j/p8bkavPcBgao/Du5/a1q8dIVSpUrlVqBqQvYjRw7LPCo8I3SaJk4Y58cyybu0vl8O0Nvv1LHXBWvu+ee1sGr1ev3jH48oKG9ArAVGf3jKvd4/x//mqr74d19VqFhJWbI8bIO2Bd/O9/+ik1GFJiAdMWqsnaF68eIF1ahWRcePH7tjoMq93r8vDjNp5rHHHleZUsW1eNlKAlX/Hm6q87AAgaqHgf3h9OMnTVWpUqVv+YHbBHCXL13Syy+W84cSk30Nm7fu1MFDB28JyA/+flwTxo/VJ9263OaTLVt2TZg0TScijitjhowqUrSYnd3yTLGCrlnMyR7VTwAIVP1kIOMow91A1cxmMy8uuXz5ssx6m48+mk2jRgzTFz0/9X+kZFZhxUpVNHrMeLusz5uv10xm1SePcqNnp/bq+ZlGjhgaa9Hc65PHtWCqnD33W+XJm09p0qSx/6ePGzM6+RSfDCo1y7eZ5RweeSSrvYebx/23bP7fkl03E3Cv9+8L4quhI/VK1Wp66YWy+u23QzK/0zND1b/HnOo8K0Cg6llfvzg7M1T9YhjjLMLcTM+dPacqlV507RfXDNWYJ3v++fKaNDVUbVu31MwZof4PlowqJFD1/8F2N1CNKWFmt6VPl96uscnmPwLmJRWhM+bo2LGjKl+uNG/89p+hdVVi1sHv2Lmr5syedcfHfmMrm3u9H14MMUoy622Wfa6cAp7K7v/FJsMKzZrJYVt36szpSJV/voxbAtzr3WJyzE57DxzWhfPndfjIYdtn80H51atXtWHDOjWo+45j6qCjCPiKAIGqr4yED/cjeg3V/Ply6uLFi7an5j9jMCte3wAAFD1JREFU85Iq1lD14YFLQNfsGqpP51DRwkH2qAIFCsqsoXSnNVRjnjpr1kdlloH4tEc3jf16VAJaZldfFyBQ9fURuvf+3W2gGj2jqVD+PPfeCc7gEwIvV6ikr8dO0IH9+1Sl0kuxrqvpEx2lE3ctYF5G1+ijpgqZNkUd27dJ0Hm41yeIy5E7d+7aTR81aX7HdXUdWRSdvkVg0Q8/Klv27K73JsTHw70+PiFnfX3QV8OVJUsWV6fNyyejoqK0dMlitWrRxFnF0FsEfECAQNUHBsHXu2BeXBK2JVzfL/pOLZp9pOA27WRmN7xRu4Z9HJDN+QJ16tbXv/t8qa6dO2jWzOkKmTFHBQsWsj9QX79+3f6CXeqfZRQdnLQKbqv06dPb9RPNo0NmdmpQUH49V7ok66g6/3KwFZhZDGnTprVv/X63Tj0VLpDXfoId24tL/KTkZFfGfffdZ9/uOn/B90qZKpWqValgv5/N97x5++uyFT8rZOpk+0GJ2ebMW6CvBg/UmtU/qfIrVWWeXjBvCq5X561kZ+ePBZuXz40cPdb+Hx7csplu3Lhhyzx16pQNWNmcL9Crdz/VrddAixYu0OhRI1wFHTxwQCdP/sG93vlDnOAKQqbP1pzZM+01YR75N8s5Xbt2TUUK5kvwuTjA9wTMsh0jRo2x70RYv36tXq1RS2Z97Oh7N/d63xuzpO4Rj/wntTjt+ZsAgaq/jaiH6mnbvqNatvrfTIZv5s1Vi2aNPdQap01qAROezZg1T+atzmYzv0h36dReU6dMsn+f/90PKlSosHI8mc3+3Twq2KRpCxu6mc0EML2++EyjRw5P6q7TnocEzEy1seP/Hv/ozay1xBvePQTuhdMOHDxMr9V+/ZaWp4dOU/u2wXrqqadlHvO7+f/68N37Zd4QHL0dOLBfNatXsS+oYnO+gJmN/sGHjW4rhO97549tdAVmNnrefIG3FRQaMlUd2rXmXu8/Q+12JctXrVFAQE7X/ufPn9f7DesyYcJtQd/e0cwqX/HTWvsB+c337hrVKuvcuXPc6317+JKkdwSqScJMI34sQKDqx4Ob2KWZ2Uzm7ZA7w3e4Hv1P7DY4n3cFMmXKpFy582hz2CYbksa1mZltefP+PYNh+/ZtrtlM3q2A1hFAwJMCZjZLjoAA7dq1U6cjIz3ZFOdGAAEfEOBe7wOD4OEumDfABwblV0REhA4dPODh1ji9NwRMsJord27t3r1LkadOxdsF7vXxErEDAgggYAUIVLkQEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABNwUIVN2EYjcEEEAAAQQQQAABBBBAAAEEEEAAAQQQQIBAlWsAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBwU4BA1U0odkMAAQQQQAABBBBAAAEEEEAAAQQQQAABBAhUuQYQQAABBBBAAAEEEEAAAQQQQAABBBBAAAE3BQhU3YRiNwQQQAABBBBAAAEEEEAAAQQQQAABBBBAgECVawABBBBAAAEEEEAAAQQQQAABBBBAAAEEEHBTgEDVTSh2QwABBBBAAAEEEEAAAQQQQAABBBBAAAEECFS5BhBAAAEEEEAAAQQQQAABBBBAAAEEEEAAATcFCFTdhGI3BBBAAAEEEEAAAQQQQAABBBBAAAEEEECAQJVrAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQcFOAQNVNKHZDAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQIVLkGEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABNwUIVN2EYjcEEEAAAQQQQAABBBBAAAEEEEAAAQQQQIBAlWsAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBwU4BA1U0odkMAAQQQQACB5CcQGBik6jVqxln4qpUrtG7tmiTHKVSosEJmzFHXLh00d/asJG/fEw126dpdJ0+e1KiRwzxxes6JAAIIIIAAAggggECiCBCoJgojJ0EAAQQQQAABfxQIbtNOrdu0j7O0+d/MU/Omje6q/A8+bKRPenyut96oleBQtnSZsgqZPls9P++h0SOHu9X+tvBfderkHyr/fBm39k+MnRJS476DR3Q6MlLPFC+kjBkzyvR3yuSJ6tIp7jFIjH5yDgQQQAABBBBAAAEE3BUgUHVXiv0QQAABBBBAINkJpEiRQg8++KCr7uWr1ihjxkwqXiS/69+ioqJ0/fr1u7L5V+Mm+rhbD73zVm2tWf1zgs5xN4Hq9p17ddIEquVKJ6ite9k5ITU+/vgTunr1qiIiTihTpkzaumOPpk2drE4d2t5LFzgWAQQQQAABBBBAAIFEFSBQTVROToYAAggggAAC/iywet1GZc6cRUF5A1xlZs/+mMZPnKrcefLovvvu05kzZ9SlUzst+Ha+3cc8mj90xGiZsDBVqlS6cOGC5s6ZpdBpUzR73gKlTp1aly5d0l9//aUTx4/p5RfLxUr41FNPa+KUEOXI8Xfb586ds6Fj9AzVwoWLaPK0GcqQIYNSpkypa9euaXPYJtWr85YuX76sSVNC9fwL5XXjxg3bB7P16N5Ve3bvivM4s9/b79RR5y7d9FDmzPb4yFOn1Kf3F5oeOs2ep1nzVmrSrIVt2wSiG9av0wfv1VPu3HkSVOOSZSt15OgRNaz3rn7ZtE2PZM1qz/fnn3/adp4rU1JnTp++Y3umzsxZsmjVz+u1/MdleqZkSWXLll1XrlzRsCGDdfDgfvX49Atbhwltv+zb21WDP1+31IYAAggggAACCCCQuAIEqonrydkQQAABBBBAwI8FYgaqJkA1syhNKPrjsiU6ceKEar/+ptKmTavSzxbXsWNHZWaFpkmTRjNnhOrypUt6rtzzNpStXrWSDWIDg4K0ds1qRURE6Pixo/qi56e3CZqA1JwnXbp02rf3V61e/bM9T0BATlegamasDhg0ROvWrtXRo4dVtGhxlSn7nFas+FEN6r6jRo2bqmPnrjIzapcuWWzbGDd2tB544IE4jwvImUvLV67W2bNnbQhswsgKFSppy9bNeq9+HbVo2VrtOnTSb78d0rfz56l06bIqVryEli1drC6dOrhdo+nPjl37FHHiuF58oawGDByi2m+8qcOHf9emjRttfzu0C9aH//roju2937CeTMC9dkOY3d/0aXNYmF56uYLSp09v/834hYeHq2KlyjIzkPPmesqPr1hKQwABBBBAAAEEEPCEAIGqJ1Q5JwIIIIAAAgj4pUDMQLVNuw5qFdxWHdq1VmjIVFtzpcqvaPSY8Ro2dLD69+sjsy7orp07VblieZeJCSXNTEt3H4dv3iJY7Tt21sQJ49Stayd7nrge+c+a9VE9nSOHxk2YoqtXrqjYf5coiO+R/9iOe+vtd9Wv/0CNGjHslrA3uobdew/ZoLho4SBXfSbQzJLlYRtWulujOfjmQPVOj/zH1150oHrz2rbRNYwbM1o9PvnY9jPa9NWqlbR16xa/vF4pCgEEEEAAAQQQQMAzAgSqnnHlrAgggAACCCDghwIxA9Up02bYmaLmkf3ozcwmNeuufr/oOzX68H2ZY8zj/ufPn9fO8B0KmTZFs2ZOt7u7GzaOnzRVL774siq8VE6/7tkTa6BqZpqaALXUP0vbpQeiN7M0QKH8eexfYwtU4zvOzIo1x5m6Tpw4rh3bt2nQwP/Y5QTM18J377dryEY/lm/aMTNyzezPp5941O0azXHxBarutBcdqI4b+7Vd0sBsJZ8tpZmzv1Hf3r00dMgg+281a72mwUNGqG3rlnb2MBsCCCCAAAIIIIAAAu4KEKi6K8V+CCCAAAIIIJDsBWIGqrPnfqsSz5S0a3HG3NavX6t1a9fYR+p79e5n1y995JGsNmjctPEXvVazmtth46w58/VMyWcVmCeHXQ/VbDFnqJrA0ASHy5Yt0bQpk23wGTJjth56KHOcgao7xz355FPq++UAFShYyK7barZBA/tr8sQJ2rBpq/b+ukdz58y+hcCErCa8dDc0NgfHF6iaGbTxtRdboFq8xDOaM2/BLYFqteqvatiIrwlUk/13NQAIIIAAAggggEDCBQhUE27GEQgggAACCCCQTAViBqomKK1br4E+eK++li754RYVE5yaFziZ2aLmBVFmMzMsFy3+UeYFU7lyPK4333pHvfv214cfNNTiHxbdUXXg4GF6rfbratn8I82bO8fuZ9ZHnRY6y7WGqpkpeiUq6pZH71f+vM6u1xo9Q3Xz1p26dPmSypQq4WorvuNu7r85yPR96fKfdObMaZUsXlgHfjtm14q9+Zxmv+j6361Tz60aYwaqJojes+83G9S2atHE1d/42iNQTabfnJSNAAIIIIAAAggkoQCBahJi0xQCCCCAAAIIOFsgZqBqZkyuWb/JPvI+ZPBAbdy4QSVKlNS7devZt8fPCA3RshU/a8rkiVr43bfKmjWr+vQbYMPG/Ply2hclmcfpd4aH6z/9+9qvT5404TakwoWLaP53P9ilBSZOGKsUSqH6Dd+3L7/q+XkPjR45XHPnL1TRosXs2q2HDh60Ya2ZsXrzI/9jx0/SSy9X1CfduujixYsK37Fdvfp8GedxwW3aqWHDDzRi+FCtXbvazpTt/sln2rw5TDWrV9HQ4aNU/dWaCtu0UUOHDFa6dGlVuUpV+3Iqs65qhgwZ3KoxZqBq/h62JVz3p06tzh3bKuuj2TR54nj9Z+BXcbZHoOrs7zF6jwACCCCAAAIIOEGAQNUJo0QfEUAAAQQQQMAnBGIGqqZT5cu/pEFDhuuhhx5y9dEEn61bNbcB5PKVa5Q5c2bX18w6pJ06tNOypYvtv5kXWFWoWNmuUXrhwgUVCMwVa609e/VR/Qbvub524MB+BQTk1GefdteY0SNt0GnWUM2YMaPdx5zLBLdmdmzhAnntv5l9xoyb5Oprr56f2RA4ruPMS7aGDBtply4wmwmP9+/bq7ffrK2TJ/+wM3CHjRhtX8Zl2oveTMBaq0bVBNV48yP/5sDGHzVT2/YdXW2XKFrQzoyNq71s2bJr3S+bdfMLqIoWK6558xeqz7+/sIGz2V6pWl0jRo1Rm+AWrjVtfeIioxMIIIAAAggggAACPi9AoOrzQ0QHEUAAAQQQQMAJAmZt0bz5Au3s0IiIE7d02YSc+QKDtGtnuH05VcwtderUCgwM0u7duxQVFXXHck0bRYoUU1jYxljPYw404eFf165p27atdzxPQM5cunrlig4f/t21T3zHmZmfTzz5pH7ZsN4uZRBzM2FqvnyBSpUqla0jepmD6P3crTG2ThcoUFBHjx3V6chI15fja88J1wx9RAABBBBAAAEEEHCmAIGqM8eNXiOAAAIIIIAAAggggAACCCCAAAIIIICAFwQIVL2ATpMIIIAAAggggAACCCCAAAIIIIAAAggg4EwBAlVnjhu9RgABBBBAAAEEEEAAAQQQQAABBBBAAAEvCBCoegGdJhFAAAEEEEAAAQQQQAABBBBAAAEEEEDAmQIEqs4cN3qNAAIIIIAAAggggAACCCCAAAIIIIAAAl4QIFD1AjpNIoAAAggggAACCCCAAAIIIIAAAggggIAzBQhUnTlu9BoBBBBAAAEEEEAAAQQQQAABBBBAAAEEvCBAoOoFdJpEAAEEEEAAAQQQQAABBBBAAAEEEEAAAWcKEKg6c9zoNQIIIIAAAggggAACCCCAAAIIIIAAAgh4QYBA1QvoNIkAAggggAACCCCAAAIIIIAAAggggAACzhQgUHXmuNFrBBBAAAEEEEAAAQQQQAABBBBAAAEEEPCCAIGqF9BpEgEEEEAAAQQQQAABBBBAAAEEEEAAAQScKUCg6sxxo9cIIIAAAggggAACCCCAAAIIIIAAAggg4AUBAlUvoNMkAggggAACCCCAAAIIIIAAAggggAACCDhTgEDVmeNGrxFAAAEEEEAAAQQQQAABBBBAAAEEEEDACwIEql5Ap0kEEEAAAQQQQAABBBBAAAEEEEAAAQQQcKYAgaozx41eI4AAAggggAACCCCAAAIIIIAAAggggIAXBAhUvYBOkwgggAACCCCAAAIIIIAAAggggAACCCDgTAECVWeOG71GAAEEEEAAAQQQQAABBBBAAAEEEEAAAS8IEKh6AZ0mEUAAAQQQQAABBBBAAAEEEEAAAQQQQMCZAgSqzhw3eo0AAggggAACCCCAAAIIIIAAAggggAACXhAgUPUCOk0igAACCCCAAAIIIIAAAggggAACCCCAgDMFCFSdOW70GgEEEEAAAQQQQAABBBBAAAEEEEAAAQS8IECg6gV0mkQAAQQQQAABBBBAAAEEEEAAAQQQQAABZwoQqDpz3Og1AggggAACCCCAAAIIIIAAAggggAACCHhBgEDVC+g0iQACCCCAAAIIIIAAAggggAACCCCAAALOFCBQdea40WsEEEAAAQQQQAABBBBAAAEEEEAAAQQQ8IIAgaoX0GkSAQQQQAABBBBAAAEEEEAAAQQQQAABBJwpQKDqzHGj1wgggAACCCCAAAIIIIAAAggggAACCCDgBQECVS+g0yQCCCCAAAIIIIAAAggggAACCCCAAAIIOFOAQNWZ40avEUAAAQQQQAABBBBAAAEEEEAAAQQQQMALAgSqXkCnSQQQQAABBBBAAAEEEEAAAQQQQAABBBBwpgCBqjPHjV4jgAACCCCAAAIIIIAAAggggAACCCCAgBcECFS9gE6TCCCAAAIIIIAAAggggAACCCCAAAIIIOBMAQJVZ44bvUYAAQQQQAABBBBAAAEEEEAAAQQQQAABLwgQqHoBnSYRQAABBBBAAAEEEEAAAQQQQAABBBBAwJkCBKrOHDd6jQACCCCAAAIIIIAAAggggAACCCCAAAJeECBQ9QI6TSKAAAIIIIAAAggggAACCCCAAAIIIICAMwUIVJ05bvQaAQQQQAABBBBAAAEEEEAAAQQQQAABBLwg8P/Y0wIOU9tznAAAAABJRU5ErkJggg==",
"text/html": [
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = list(range(len(y)))\n",
"\n",
"layout = dict(\n",
" title=\"Hamilton sector 3 time: Predicted vs Actual\",\n",
" xaxis_title=\"Test dataset item\",\n",
" yaxis_title=\"Time in seconds\",\n",
" template=\"plotly_dark\",\n",
" hovermode='x unified',\n",
")\n",
"data = [\n",
" go.Scatter(x=x, y=y, name='True values'),\n",
" go.Scatter(x=x, y=np.round(y_hat, decimals=3),\n",
" name='Predictions', line=dict(dash='dash')),\n",
"]\n",
"fig = go.Figure(data=data, layout=layout)\n",
"\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Feature Importance\n",
"\n",
"Visualize feature importance to understand which variables most impact lap time predictions.\n",
"\n",
"We can vizualize the loss on the \"Training\" tab"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"
Name : GRADIENT_BOOSTED_TREESTask : REGRESSIONLabel : Sector3TimeFeatures (7) : Stint Sector1Time Sector2Time SpeedI1 SpeedI2 Compound TyreLifeWeights : NoneTrained with tuner : NoModel size : 41 kB
Number of records: 45\n",
"Number of columns: 8\n",
"\n",
"Number of columns by type:\n",
"\tNUMERICAL: 7 (87.5%)\n",
"\tCATEGORICAL: 1 (12.5%)\n",
"\n",
"Columns:\n",
"\n",
"NUMERICAL: 7 (87.5%)\n",
"\t0: "Sector3Time" NUMERICAL mean:27.2233 min:26.849 max:27.749 sd:0.245425\n",
"\t1: "Stint" NUMERICAL mean:1.62222 min:1 max:2 sd:0.484832\n",
"\t2: "Sector1Time" NUMERICAL mean:25.6412 min:25.191 max:25.983 sd:0.160483\n",
"\t3: "Sector2Time" NUMERICAL mean:28.4059 min:27.961 max:29.206 sd:0.256306\n",
"\t4: "SpeedI1" NUMERICAL mean:214.156 min:206 max:220 sd:2.98854\n",
"\t5: "SpeedI2" NUMERICAL mean:254.844 min:247 max:260 sd:2.95865\n",
"\t7: "TyreLife" NUMERICAL mean:17.2667 min:2 max:36 sd:9.71231\n",
"\n",
"CATEGORICAL: 1 (12.5%)\n",
"\t6: "Compound" CATEGORICAL has-dict vocab-size:3 zero-ood-items most-frequent:"HARD" 28 (62.2222%)\n",
"\n",
"Terminology:\n",
"\tnas: Number of non-available (i.e. missing) values.\n",
"\tood: Out of dictionary.\n",
"\tmanually-defined: Attribute whose type is manually defined by the user, i.e., the type was not automatically inferred.\n",
"\ttokenized: The attribute value is obtained through tokenization.\n",
"\thas-dict: The attribute is attached to a string dictionary e.g. a categorical attribute stored as a string.\n",
"\tvocab-size: Number of unique values.\n",
" The following evaluation is computed on the validation or out-of-bag dataset.
Number of predictions (with weights): 1\n",
"Task: REGRESSION\n",
"Loss (SQUARED_ERROR): 0.0863763\n",
"\n",
"RMSE: 0.293898\n",
"Default RMSE: : 0\n",
" Variable importances measure the importance of an input feature for a model.
INV_MEAN_MIN_DEPTH NUM_AS_ROOT NUM_NODES SUM_SCORE 1. "Sector2Time" 1.000000 ################\n",
" 2. "Sector1Time" 0.358417 #\n",
" 3. "TyreLife" 0.291115 \n",
" 4. "SpeedI2" 0.278986 \n",
" 5. "SpeedI1" 0.272727 \n",
" 1. "Sector2Time" 11.000000 \n",
" 1. "Sector1Time" 24.000000 ################\n",
" 2. "Sector2Time" 17.000000 ##########\n",
" 3. "TyreLife" 10.000000 #####\n",
" 4. "SpeedI1" 9.000000 ####\n",
" 5. "SpeedI2" 3.000000 \n",
" 1. "Sector2Time" 8.021375 ################\n",
" 2. "Sector1Time" 1.475066 ##\n",
" 3. "TyreLife" 1.119095 #\n",
" 4. "SpeedI2" 0.310687 \n",
" 5. "SpeedI1" 0.151599 \n",
" Those variable importances are computed during training. More, and possibly more informative, variable importances are available when analyzing a model on a test dataset.
Num trees : 11
Only printing the first tree.
Tree #0:\n",
" "Sector2Time">=28.321 [s:0.0385804 n:43 np:25 miss:1] ; pred:5.32283e-08\n",
" ├─(pos)─ "Sector1Time">=25.8315 [s:0.0108827 n:25 np:5 miss:0] ; pred:0.0166667\n",
" | ├─(pos)─ pred:0.0375307\n",
" | └─(neg)─ "Sector1Time">=25.6365 [s:0.00590318 n:20 np:12 miss:1] ; pred:0.0114507\n",
" | ├─(pos)─ "Sector1Time">=25.757 [s:0.00280898 n:12 np:6 miss:0] ; pred:0.0177241\n",
" | | ├─(pos)─ pred:0.0124241\n",
" | | └─(neg)─ pred:0.0230241\n",
" | └─(neg)─ pred:0.00204077\n",
" └─(neg)─ "SpeedI1">=216.5 [s:0.00187296 n:18 np:9 miss:0] ; pred:-0.0231481\n",
" ├─(pos)─ pred:-0.0274759\n",
" └─(neg)─ pred:-0.0188204\n",
" "
],
"text/plain": [
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]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.describe()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- *Sector1Time*, *Sector2Time*, _SpeedI1_ and _SpeedI2_ are the most important feature for predicting lap times.\n",
"\n",
"We can view the dependence plot"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
" Variable importances measure the importance of an input feature for a model.
MEAN_INCREASE_IN_RMSE [In model] INV_MEAN_MIN_DEPTH [In model] NUM_AS_ROOT [In model] NUM_NODES [In model] SUM_SCORE 1. "Sector1Time" 0.063597 ################\n",
" 2. "SpeedI1" 0.001515 ###\n",
" 3. "SpeedI2" 0.000022 ###\n",
" 4. "Stint" -0.000000 ###\n",
" 5. "Compound" -0.000000 ###\n",
" 6. "Sector2Time" -0.009947 #\n",
" 7. "TyreLife" -0.017248 \n",
" 1. "Sector2Time" 1.000000 ################\n",
" 2. "Sector1Time" 0.358417 #\n",
" 3. "TyreLife" 0.291115 \n",
" 4. "SpeedI2" 0.278986 \n",
" 5. "SpeedI1" 0.272727 \n",
" 1. "Sector2Time" 11.000000 \n",
" 1. "Sector1Time" 24.000000 ################\n",
" 2. "Sector2Time" 17.000000 ##########\n",
" 3. "TyreLife" 10.000000 #####\n",
" 4. "SpeedI1" 9.000000 ####\n",
" 5. "SpeedI2" 3.000000 \n",
" 1. "Sector2Time" 8.021375 ################\n",
" 2. "Sector1Time" 1.475066 ##\n",
" 3. "TyreLife" 1.119095 #\n",
" 4. "SpeedI2" 0.310687 \n",
" 5. "SpeedI1" 0.151599 \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.analyze(test_ds)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Vizualizing model tree"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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" "
],
"text/plain": [
""
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.plot_tree()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Results Interpretation\n",
"### Model Performance Analysis\n",
"\n",
"The Gradient Boosted model had an RMSE ranging from 0.24 to 0.15 in validation, indicating that the model can learn from the patterns presented in our data and predict a value close to the real one.\n",
"### Insights and Conclusions\n",
"\n",
"The model shows that the speed and times of sector 1 and sector 2 are the most significant characteristics. Future work could involve more data from the car, as well as the weather and other cars on the track\n",
"## Conclusion\n",
"In this tutorial we covered data fetching from [fastf1 API](https://github.com/theOehrly/Fast-F1), feature engineering to use data that are relevant to us, using a highly interpretable regression model to inform a race engineer\n",
"\n",
"[YDF](https://ydf.readthedocs.io/en/latest/py_api/) provides other models that you can test and share your results\n",
"\n",
"Happy analyzing, and may your lap time predictions be ever accurate!"
]
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