Compare_BW_BW_training_size_5000.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pysindy as ps\n",
    "from scipy.integrate import odeint\n",
    "from math import pi\n",
    "from pysindy.differentiation import FiniteDifference\n",
    "fd = FiniteDifference(order=2, d=1)\n",
    "from sklearn import linear_model\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "import glob\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "np.random.seed(29)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.25, -1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,\n",
       "         1.  ,  1.25]),\n",
       " [Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, '')])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cTETxKoLoYH4ANW9cz+7z9tTjwMmpPJtqDVyv7VXkY/mO3DAybfS8wKj3tsc6kHHif7ZYZipfWiRzsVxhLFeMjbYTTkzmWd/VRmvGmIr13W00N0n1m3dCkjoIitTArVKcnMyzqWe+swfT6XrNhUVFdWTfM9/x2WGN4wl3ficn8ws6+47WZtZ0tiRuaEYsmTd0t1Z/29LXwWi2mPhiXOPBLfRmIPl5xxGrg1vY6XYkTrdYqnA6V4zNaw2CE5MmHNzeMl+maim81vpwcO2/TzTwpOLA8GS+GvIHaG4SNna3JU43LqQGbpUgn1/4wZ2cKiyYpwDY0N3G6HSyOS/2yK62093Ybf7diHY9/6FoTy8M1wFs6mlLfCcFuwPqzcwndmy0DPzpBEfYlYoyMl1YILM9FxZmrjWIDk5M5elsNRmyNs7ua+ekNReWFE5Zujxrgdc678HF8R25oT4cbNOOs7N34r8+HAzzA4tGocI4UD+AAhMebUQ3SR0ERWrgVgnWrFmz4P9Onf2G7lZO55Lt7E/Uzf0BbOgxns1o1r2zr+c/KFTVhOvqjPr6rjZON6AbB05MFWhpFs47a77Q8AarqHWSA4rTuaIJB9d0QCLCpp62qiEIgiA6sDu+2gjBpt42yhVlfCa5912f9ACwrquVjBU2i/odNYJjZ99rOvu45sKc+HcKB9vtq1GoMA7Ue3BgojONvNYkdRAUqYFbJTh58uTC/08ubowbuk1n71UXMgpGpvI0Cazvmg/Xre+yOvsGnW49/0ExMTNHsVRhc0+dzEvgwY1MmXDwqZH5fbrWd9tGPTnaJx1G9oZ2G6dD0A2iAydvxtZzkgMKOxy8qYa2iLCuq5WxXCHyd9QI9fOdYL7zQqnCTEwVXJz4d9LzJitCkGR4tFAqMzk7V41G2DjLw4NLUgdBkRq4VYLzzjuv+u+ZYolcsbzow9zQ3Uapor42LQyLU9MF1ne3kalZWL2uq5UmoWGnW8t/KLrWsxfL3NrQc4wDJ6fzbOptWyCD7cEl2dnbncymnnpD0xoq+SCIDkamC9XMuipdy6iHMa5+0cioj+WKkb8jN1Sq2cEL3/W6LlvmePTsxP/IVIGOlvnsYICW5ib6OloSTTIZz5l+Yl3NYBXMQGYqX3Jda5mUDsIgNXCrBAcPztdztj/69fUf5hJ4FWO54iK6zU1mhH2qQSdQy39YurBY5g3dbWQLpUSTPU5ni2zoblsgg23gwoQKfdO1ZN5Qt8ff+u62UEY9iA7GssXq92TDTrIZTbDTHZuZQwTWdtZ3uq2czhUjf0dumMrPUa4o67oWDxqB2EL/TvyPzZh3XRsOBmsgk2A42K1NresymdnjLnpOSgdhkBq4VYLLL7+8+m975FXfCWy054US9CrGZ4qL6IIZ9TUyrLX8h6JrNba1iwxc8kbdyNyyQIaO1ma6WpsT9eDcZF5vheuChqL96qBYqjBdKLGus77jM9/XWJLvOlekr6Nl0Sa267tbOZ0tRv6O3GB39nbnbiNuD86J//Gcc5ta29XKWILf15jL91XVs4txTUoHYbBqDJyIbBWRz4vIcREpiMigiHxYRNb6vP9aEVEff+fW3dfo2tvc6MWN2i0q7A+vPrSwocd7LiwqxnLFRXQN7daGoauoW2y4ypywUVdVxnNzrO1qXSRD0vN/4zNztDY30VW3u/L67lYqChMBQ9F+dTAxa97lmrp3vaajxYSiE/XgiosMK2DNwRUT26rFTpxZ5DlaA6i4QoVO/I/NzC0yMjAvc1KwvdLFHpwls0ubWk7b5ayKUl3WzgC3ApswNSH7gccCfwc8S0SucaojWYdBzK4BTrgc+APgV1Ypr3ocxdSvrMdDnszHhNotKiZm3Ef2kLQ3M8farsVFWDd0t3HX0ITrfVG32LC9mTWdC2nPz4UlI3OuWKZYrrCus5UdOx6+4Nz6rtZk33WuyNqulsWhK0vmsVzBcbDhBr86qM7N1HX2TU3Cuq5w4VG/MDI7DKCsUPRlj7oyEbpjDeajAEZjClE66WA8V2T7+sWl5tZ3tSa6se54znnQWPVaXYxrul1O/PhPjHF7jao+T1XfpKpPxVTyvwR4t9cDVHVQVd/p9AfYmvyMy+1u9342Btl8YYEHZ3+YdR3Q2k472SOZDqhcUSZcRtgmXT9BDy43R3dbhrbMQm8maa+1Nky4yIPrTnaJwphLOHhDdSATjLZfHcyHrpwGMo099agYn5lzlNnudH9+29J6cB2tzXS0NMcWKnTSgZtRX9fVyniumFi5rrFcERGqOxjU0gVcl4MsJw9uxRs4y3t7BsYD+4+60+8AcsCfi0ioPWJEZAPw+8As8N/hOU0WtaOm8VyRJoHeuu0smpqEvo6WaogpbkzNzlHRxZ4jmLp9uWKZYsk58yrqqM/NW7FLlU3MJJM5ajdy48EtlGFtZ2ti7xqMp+7Y2VezGYPR9u3BuXT2YEJ2yWb2Fas6XUDX0v2W7ZckRhcWezNgzf/FJHO9DtzmO21eShVlarYUC+16nM4VWeMw32m/f7fvK/Xg4sVTrOMPVXVB76mq05g92TqBx4d8/ouBNuAbqjrhcs0aEXmZiLxFRF4tImFphca+ffuq/x6bKbKms3XRhwlmNJZUZ+82D2bomkbhtkShlv9wtJ3nKTpammltbgo8H+Wbbo03Uy/Dms6WxN61TdvpXVfnSAKGzfzqYLyBntd1tSU2B6eqZg7OxcgA7N7fnwjtsZkirZkmOuvmO2E+gzMO1OvAbboBavScUCbluMu7zjQ3sabTfYlC1LYcJ1aDgbOHbG65qYesY9hd+F5hHT/V4JorgM9hQqEfB34pIneLyJKlE1122WXVf4/n5hxHuWA63aTWwVXDdQ6jzT7rtwmXxljLf1ja6xxkFhH6EjQ0td5MvQx9nS0USpXElii4zXfaG1EG1bNfHbjNdxramcS+rxkrAuDc2ZtQdPeGsxOhbb6vxan6hnZr4MGEG+p10GjQGHYg4xens84GDkzEws2wRm3LcWI1GDh7U6JJl/P272uCPlhEnowxoL9S1VtdLvt34BpgI9CD2fz0mxij91MROceDxitFZLeI7B4eHmZ0dJTh4WGOHTvG+Pg4AwMDzM7OcuDAASqVCnv37gXm49x79+6lUqnwy1/+ktnZWQYGBhiZzNGVAft5g4ODZLNZ+vv76WvPcPz05IJn2Mf9+/dTKBQ4dOgQU1NTDA0NMTIywsjICENDQ0xNTXHo0CEKhUJ1W/raZ9gjut72Zvr7+8lmswwODjI6OkpldhqAB0fGHGU6fPjwIpkOHDhQlWl8fJxjx445ylQqlTg5kV0wD1YrU197hodGxkLJBGZEWiqVFsk0PDzM4PFRACZHjnPfffctkGlNh23U50LJZI+EnWSanc0zMVOkq1kXyVSYydGeEU5P5wPJdM899/j69vqPPERXazP33rNvkUztUmFypsjx48cDy+T17d11rxnDzoyPLHqGbdQPDx1z1FPQ9lSvp+Onp+hpFUeZKvkck7NzsbSnm266acEz7rznPgCmR08skqk8Y9rxvYeHQsnk9e2N5Yo0zc04ytTRXGZkcsZRpttvvz10ewqrJ1eo6or+Az4NKPByl/Pvts6/OcSzv2zd+7ch7v2mde+H/N6zY8cODYvp6enqv5/5oZ/ry//rTsfrXvvVu/Q33vuT0HQa4at3HNVtO3fpQ+Mzi87d8+CEbtu5S3947wnHe2v5D4OHv/16/efv3ut47gWfuEX/+NO/jPR8N3zgB/26/U27tFyuLJLhe/cc1207d+l9w5Ox0x3PFXTbzl36uV884Hj+8f/6Y33D1+8O9Ey/OnjdV+/Sa97j/A19+ucDum3nLp2aLQai7QeNvqG5Ulm37dyl7/3e/tjpqqr+wX+6f0Pv+N9f6eXvuCEWOvU62LXPfEP9w1OLrh06ndNtO3fp1+4cioV2PXb88w/1Td+6x/HcX153pz7zQz93PBe1LYcBsFsd+tTV4MHZHprz9rLzv08EeaiIrAOej0ku+WIIvj5pHZ8U4t7AGB0drf573CWTEUz4KrE5OJf0cZgPZ7mFKGv5D4r8XJmZYtkxdAXQ15HgvKO1CLepSRbJsKYjuQSXsQZJD2D0HDRU6FcHbvNgYMKykJDM1XDw4tBoprmJnrYMJ8enY6cL7pmMYJK5pvKlWHZRqNdBVWanULT1HqYSCAmrKuMzc45haDDflxvdKG05bqwGA3e/dXSbY3uYdQxaP8ZOLvm6uieXNMIp6xgqezMouru7gYULj52wprOF6XyJkksduSgYnynSlmmiw2Eivs8jycTmPyxdcJ77g4TnHWeK1U6gXoYkO/vxBskHYBm4gHT96sCtsgbMG/Uk3nejhAswhma2nEyX5rbAHObnPKfz0WWu10Gjee3u1gwiybzrmWKZckWrstWjzzLqTojSluPGajBwP7OOzxCRBfKISA9mfmwGCFpVxE4u+XRIvuxMygdC3h8Ic3PmI7cXHrsmmVgfrNvHGQWTDUZ8PW0ZmpvEtbO3+Q8DO03arTGu6WhJbAsXk9BjOp96Gez1Q5MJLBUYq5Zjiy+ZyK8OxmacU/UhfIKLL7ou6zttGJnjf9eVijI129ibgXhkrtfBxIxZ39nSvLirbmoSetuTGbxNWca6kYHLFpwHylHactxY8QZOVQeAHwLnA6+uO/0ujAf1RVXN2T+KyKUicqnbM0XkN4GH0zi5BBF5lIgs+gJE5FHMLy7/kk9RIqFSMR+aHTZw7ew9shmjYCo/R2+7M12RxmvwbP7D0gXo7XAuzLOms4WZYplCKf5sxqn8XPVd18uQZIjS1p+dyFKPMOsd/erADGTcjIxt1JOQ2daze6c7nY9fx7liiYri+m3HaeDqdTCdn6O33b3gVKNQYRTYsrjJbLc1p4FylLYcN1ZFqS7grzGluj4qIk8D7gMeh1kjdxB4a93191nHxTm/Bq+0jl7e2+uB54jIL4AHgQJwKfAsoBlT+eQr/sUIj85OU8pnvrN3aYx22CyhUZ8bXTAdvltnb/Mfiq5HY+yr6XQ39SwOn0bBdL7EwzaZZlQvQ2drMy3NktC79vBaQ6x39KODSkWZLpRcO92+BI36dL5EtxUJcKM9PDETO137XbsNoOI0cPU68GpTYeZa/cCOiviRuX4+Nkpbjhsr3oODqhd3NaYe5OOANwAXAh8BHq/edSirsIozvwB/ySXfAX4OPBIzZ/caYAdwPfB7qvpKK8MncYyNjQE1H6ZLZ1+dI0mgA5qade/4wBhXt8Zo8x+KrodRT1Tmmg6oXgbjtSaT4GLP93Q3MDRB1+D50UG2WEK1wbuuDqCSihC4f19rOluYTCIy4TWAitGo1+vAtKkzYeC8Q5TgbNSjtOW4sVo8ONQUQX6pz2vdPDdUdRzo8Pmc72CM3BnHli1bgJrG6Bqus0KUCXVAF2x0z6lZ29nKyLTzTsA2/6HoVo26e4gS4vdaVc3cjN0BOcmwNqF5oalZb28GTAfU3uLPa/Wjg2nLm+lxedftLc20ZpoS63QbeTO9HS1kiyY93GlBdhS69vOd4FWlJwjqdTCVn+Osus1da9HbkWF4ssE6sJDwClHa35dTeDRKW44bq8KDSwFHjhwBYLpgPrgelw8zydqMtZ29ExqFKG3+w9IFd5lrF1zHiVyxbOZmrMGEkwxJlevy8mbChM386MDLmwGj58S8ZQ9vpliukJ+Ldw6oGqJcgjm4eh34C1HGnzDmOdXRQOYobTlupAZuleDSS03OjJc3YxuBuDtdVWUqX3L1HME0FrdOwOY/DKbyc6bmZMb5c54PIcXrSdV39k4yJLXucDo/52rQoXbdoX/afnTg5c1AcmGz6XzJ1XOE+YFM3LS9oiK21xpHske9DrzC/mYNXoJzcC60exsYuChtOW6kBm6V4O677wa8vZnmJqGrtbkaaooL9rqZRiPs3vYM2ULJcadpm/8wmJptbFjtTjFumetHuU4y9LS3VL3qWGl7yBzGqPvRwZRHiBIS9lo9DCvEH36v6nkJ5sJqdVCpqMmi9JC5mEC906n8HF2tzWQclifYdMHZwEVpy3EjNXCrBFdddRXg7c2A1enGPOrzCmnYdFVN2nU9bP7D0m7U+XQnZODq56OcZOhpz8ROF7xlDuPN+NHBtM/OPpHMUQ9vpjoXFrNxtfXnltAD8Rm4Wh14LU+w6UL8Xuukx3xn1Wt16EeitOW4kRq4VQK7CKnXyB6S6XTtkEajkX0jTyrKJoleI/uW5iY6WprjN+p1IUonGex3HXcyrVe4LozX6kcHfkKUPe0tZGP2WlXVMyybVGc/NTtnLflw7y7jCkXX6mDaY3kCzH97ScjslkFpw20NXrrhaYrYYW8yOOXRCYDV6cbcAfkZ2dt8OXW6UTZJ9BrZG9oJGPU6r9VJhp72FsoVZTaBEFIjIxPGa/WjAz8hyiTedX1CjxtdSCYU3ei7hvg8uFod+A2NQvz1KP3I3NvuvDVSuuFpithhbycxnffu7Hs7WhLv7J0w3wEtbhQ2/2HgNU9h047bqNdPxDvJkESna7yZxuujWpqbaG9pCuRJ+dHB1KwJgTfyZpLwWv1kb9oDqGwh/uiEV1SkN6bvq1YH84utz4TX6i2zm1GP0pbjRmrgVgmuvPJKwHtkD/YcXDIhykbGtVFnb/MfirZHZ29oJyHzwoQeJxnmvdb4OiA7oaeRF2XTDiKzHx1Me2TKAnS3xe+1+hlAdbe5D6Ci0vb6vrrbM2Rj+L5qdeDHqJ+pOTibthPdKG05bqQGbpWgv78f8F6LBvYI+8wkmdReWwub/6CoLrb2Me8Yd4Hpqfwc7S1N1YQeJxlsIxQnbT/v2qYdxMD50YGfzt6WOY4Ov0rXxxxva6aJ1mZJJkTpY9CYLUT3Wmt1YOs57rlWP/AVouxocdRx2LacBFIDt0qwfft2wHSk3iP7BDr7We/G2NugMdr8B8XsXJmSx/IEQzuBzNG6MkpOMjSSOQpd82yPTrctE2iNlB8dmDle7+/LXBufzH7meG3a00mEKD1k7m7LMFdWCqVoi8xrdeAnoceea40zLFupKNlCydOod7dlHOmGbctJYNUYOBHZKiKfF5HjIlIQkUER+bBVW9LvM24UEW3w51gzR0QeISJfF5EREcmLyP0i8i4R8VXyKw4cP368xpvx7uyLpUqs1fWn8iXaW5poy7iXhWqUZHL8+PFwdH3MUxja8Sc+TBcWvmsnGZIIUU77GNnbtIN0fH50YEKU/jy4OGX267W2NyfkzXi2qXgGMrU68JPQ05Yx6fpxyjxdMPVGvbIou10GymHbchJYFbUoReRCzG4Cm4D/BfqBxwJ/BzxLRK4JUnAZs82OExZpU0QeB/wUaAG+idlV4KnAPwJPE5GnqWohAO1QWLduHfm5ii9vpjas0dYdT3V9P6HR9pYmMk3i2PGtW7cuHN0gI/tEPLj5JuQkQxIhpCAhyhNTzrU/neBHB1Ozc5y/3r3eqKEbf7KHnxAlQG9nK9kY9WwPGr3odtcY9Y09baHp1erAz/IEMJ56nMsy5uf+PAZQbZnqQLl2YBu2LSeBVWHggP/EGLfXqOrH7B9F5N+B12H2ZnuV34ep6jv9XCcizcAXgE7M7gH/Z/3eBHwdeL5F/z1+aYfFzMwMxWbjMPqZjwLT6W7oDt8Ya+FnlCsirp7UzMwMa9f6drbn6XqUUbLR095Cfq7CXLni2WH4pp1fuFWIkwzJeHDeCT2GdjCj7kcHfkPgtXzGAT8hcIDOTLxzcNXlCZ7h4HiMeq0OvDJlbcSV4GJjfu7Pe94RIFdYaODCtuUksOJDlJb39gxgEPiPutPvAHLAn4tI42FnODwZszHqTbZxA1DVCvAP1n9fJXGWNndBU1PToqw+N9iNMdYQko95CnCvotLUFO5TDOLBQfydbu27dpKhq7WZJkmqs/eaI3FOAnCDlw78hsCTyGacLniHwAG62ppj9hz9ecvVubCIeq7VgRk0erep7rZ4w+9ZH6FRm27t9TbCtuUksHw4CY+nWMcfWoalClWdBm7BeFiP9/tAEfkjEXmTiLxeRH5bRNzcnKdaxxvqT6jqA5jNVrcBF/ilHRYtLS01nf0ZGGH78OBs2k50W1q873Wk63sOLgGjXrfm0EkGEYm9A/IzN2Ofz1lLCvzASwf+Q+Duc61hUT+YcENvzMtB5r1lfwOoqIk1tTrwk8kIloGL0ajbpfRsA+ZK1+5H6sKjYdtyElgNBu4S63jQ5fwh63hxgGd+Ffg34IPA94EhEXnBEtEOhWw2e0Y7e3u3ZS+4GbhsNhuSrrXxpwftuI26kzfjJkNPe7wV36fyc7Rlmjz3eQuaru+lAz9p61DrwcU8gPIRIWiVSiLJLZ6DiZhClLU6mJr1Dgcb3oJ56l6w9dbl1aZcPLiwbTkJrAYD12cdJ13O27+v8fGs/wWeA2zFbHp6KcbQrQG+JiLPipu2iLxSRHaLyO7h4WFGR0cZHh7m2LFjjI+PMzAwwOzsLAcOHKBSqVSrBNj13vbu3UulUmFiYoLTUzkAtDDDsWPHsJ83ODhINpulv7+fUqnEQ0eM3d3ff3jBs/bv30+hUODQoUNMTU0xNDTEyMgIIyMjDA0NMTU1xaFDhygUCuzfv3/BvePTs/S0Z9i3bx+lUon+/n6y2SyDg4MLZGprUkancotk2rBhwyKZDhw4wOzsLAMDA4yPjzvKdOShYQCOHDywgJ96maZGTwJweOiYb5nso5NMx06colRRKoWZqp66u7sd9dTTnuGhE6O+ZbL1tG/fPkd+Bo+N0Nue8dSTHd2ays/5kqm5ubnht3fbHsPP6PCDDfV0Yvg4na1NjExM+5bJ69sbm87TQtlTT+t7O8kWSkxPTy/69oK0J1umQ0eMrLPT4w31VJtkEqU9nTx5sspPtlCiNJtt2J7Gx8dhbpbpfNG3TF7f3rS1G0NPe6ahnqRscuceOnl6gUy5XC5we4qqJ1eo6or+Az4NKPByl/Pvts6/OQKNv7GecVfd7z+0fv8tl/u+bJ3/Yz90duzYoWFx33336ZdvO6rbdu7S4xMzDa+dyBV1285d+tlfPBCaXj0ufdv1+s/fvdfzutd99S594r/9ZNHv9913Xyi677+hX7e/aZdWKpWG1+1/aEK37dylN/xqOBSdepyazuu2nbv0uluOVH9zk+GFn7hV/+hTt8ZCV1X11V/eo095/888r/vePcd1285deuD4pK/neulgz9Ex3bZzl/70vpOez3rcu3+sb/z63b7o+sFzP36z/tlnb/O87p+/8UvdtnOXZvNzsdD9v7uP6badu/T+E1MNryvMlXXbzl360R8fjESvVgdX/8uP9E3f2ud5z9u+vV8f/U8/jES3Fp/6+WHdtnOXTnu8w4GRad22c5d+e+9DC34P25ajANitDn3qavDgbC+pz+W8/ftEBBqfxSwRuFJEepaYti9cdNFF5Ar+Qgu1o804YJdl8qIL9iLzxXQvuuiiULSzhRJdbRm88njiDlFmHcI4bjLEvQYvZ8nshaAye+nA7/dl045bZj8h8PPP2QzEqOeCv/mo1kwTbZmmyHNhtTrIFUp0tfpIMrGyZTWm2p/ZfAkR6PQMgVtTHXUyh23LSWA1GLj7raPbPNfDrKPbPJknVDUPTFv/rc3GTJy2X9x7773VD82rUcS96anfSWmYX3xcv+npvffeG462z44v7nlHp47PTYb4O/syXW3e6xeDyuylg3kD54e2c5WLsPBr1CdOnQCIbV1YMKMePcHF1kGloswU/Q0a46qiYiNbKNPdmqGpyd+gsX4OLmxbTgKrwcD9zDo+w1p/VoXlbV0DzAC3hSUgIpcAazFGbrTm1E+tY/3cHCJyAcbwHQUeCEvbL6644gpyhRKdrc00e3yYEO+mp0FH9k6bnl5xxRXhaBeT8WY86ToYODcZ4t5gNuvbqAeT2UsH2YKpfOOHdvcZkvmySy4E4isTlq0OGpfGqNs6sNuHnyQTO/kmrgFFtjDnq021ZUzhhvrBRNi2nARWvIFT1QHMXNj5wKvrTr8L43F9UVVz9o8icqmIXFp7oYhsF5FFS/BFZCNmMTfAV1W19iv6OXAf8CQReW7NPU3Ae63/flLjih00wJ49e3yPciFeryLYyN45hTzsJonZgr9Rrr19TGxGvbhYZjcZ4t4+xrdRt7MZfXZ8XjpwMuqutGP8vlTV+ra9v6/jgwNAfIWec9b6u4yP4gBxVMuxdZANMGiMaw2ejVyh3HD3chsiYoVH42nLSWC1VDL5a0ypro+KyNMwRudxmDVyB4G31l1/n3WsdXWeDHxSRG7GeFxjwHnAszFzabuZX7wNgKqWReSlGE/umyLyTWAIeBpwNWYN3odikrEhduzYwRfu3+ur8wGr+kFsIz7/I/sel9Fm2E0Sc4VStSP3QndbsNqMjeAks5sMPe0tlCpKfq5Chw9PwAv+5+CChSi9dBCk0+2Nsehxfq5CRf3RvfqKR8LPbopxDq5Md5u/dV3dbdEritg6CBIV6Y5piYKN6QADZSeZ0w1PY4blxV0NXIcxbG8ALgQ+Ajxe/dWh3INZ/7YZU2LrDZjQ437gNcA1qjrhQPt24DGYJQbPwJTm6gP+CXi6LkEdSqj14Px1oG6VwMMgWGN0NnChPbh8EJmbq4YpKpxkdpOh2+IvPuPqL1w3X/szHg8uWyiRaRLaMt7dhlncntx8pxsGD5mxa5y0u31+X3F4rfMenD2A8qYd97rDbH7O96Cxp71l0UAm9eASgKo+CLzU57WLJqlUdT/wkpC0DwAvDHNvXNixYwe5O3/pK+sKTCLKyQCFeBshSAdkG4RcTB5cNsBos6sts4huWDgZODcZamWOUogXoFSukJ+r+NLzfO3PeDw423P0U3kuztqfQb6vJzzm0fC9H8Y6ePPvzUSPENR7cH68x7h3b8gVymzqcdw4ZTHt1INLsRTYv3+/75E92J19ct6MO93mBffYsBeFBqZdDCZznF4ULEw+cJOhy8VrDYNcsWw9059XEUTPXjoI+n3BYj2HQZDv68hB48HFmWQSbF47mpGxdTBfTcRfcgvEGyHwbdQdpjrCtuUkkBq4VYKLL77Yd/IB2OG6pU8ymQ9RLux0L744XDWzYCPseD24+uQDNxm6E+jsfc+1BjDqXjoIFgKPLywbxIO79JJLYpkLs+F3GQrMZ1FGSSaydRBEz25h/7DIFvyVCLNp19MN25aTQGrgVgmGhobI5ku+sp9gPlwXR2ZfkCQTt5H90NBQYLqFUpm5sgb0WuNMPlhI102GqszFpfVm7Ov8yuylg5zPjFWbrn1PVASReWhoyOp041sCE8TAVRRmiuFltnUwn6XrP4syjjk4VbU8OJ8DGQevNUxbTgqpgVsl2Lx5c6AQUnd7hlIlnsWh2cIcTQIdHpUPwH20uXnz5sB07c7Tzxolm3aSczNuMsx7M9E7+yDeDAQzcF46CBOijNeD89bz5s2b6Wprji38Hihc1+a8BCYIbB0E0XNbppnW5qZY3nWhVKFcUd+Zoz0OO2WEactJITVwqwSjY+MUSv6SDyDesIY9sveTfNCWaaK5SRZ1uhMTEyHoBvNm4g7L1r9rNxninI+qdny+Q0j+ZfbSgd/SUYZunGFZe97RRyWTiYlYBzJBsii7YgjL2jrI5v1nrIKzJxUGtrEKkjlaKFUo1gyUw7TlpJAauFWCSpMZcflOPmiNt9P1O7IXMWXC6um2t/vL2qqnC8G8mfxchVI5Dq91scxuMiSScBEgW9avN+OlgyDznXF+X0EGMu3t7bGFoqsZqwFlnokQirZ1ECRjFaz5vxhClMEHUIv1HKYtJ4XQBk5E1orIuXEykyI87Lj/mQghBen4wA4VLu3cjE0X5jMRI9Eu+p+nsDu+eMJ1wfUc37yjf28mzgiB3xqrNuLKls2dwTblNMfbCHFtqhtkeQKYkmwQX4JL3Ahk4ESkW0Q+KCInMDUZj9Sce5yIfF9EroqbyRTeGM+aPZECd/YxzQsFMXBOnW4+H3xNXpDKGrXXxRU2q6frJkNzk9DRsthrDUfXf8aqfV2u6C+ZqJEOVJWcz+K/tfzFJbPfGqv5fN5ky8aY0BMkY9XcF75N2ToIkrEK8Rn1IMsTYD6UWWtcw7TlpODbwIlIH/BLTKWO45hyV7Vf3H7gN4E/jpPBFP7Q1NYJBBltxtsB+R3ZG9qLO6A1a9aEoBtuhJ1UWLaRDF0xea1hjHpFTbkrLzTiv5p8ECBLF2LylgMMoNasWUNnazMzZ+RdR29Ttg6CrO8E0waiZG/asHnv8enBOWUIh2nLSSGIB/dW4DLgJap6FfCN2pOqOoMpPvy0+NhL4RfHTo4CwT242JJMfIaPwLmkkb2TcTC64UabSYVlG8kQ1/YxuULA5IMAem7Ef9D5zvlK80s7x3vy5MnYkkyCyhxHm7J1MJ0PFhXpdJjXDoNs4AjBYpnDtOWkEMTA/QHwA1X97wbXHAXOicZSOIjIVhH5vIgcF5GCiAyKyIdFZK3P+7tE5E9F5H9EpF9EciIyLSK7ReQNItLqcp82+Au9RU9QdPaZjRCWizfTkHbr4hDleeedF4ouBJC5NXoICdz36mokg0ldj8+w+k0+CJLs0Yj/oMktIhLb/F+QcN15551HV5vJ7IuaTFQNUfr0WjvboieZ2DoIsv4O4lsCEzbJpNZjDtOWk0IQA7cVuMfjmizuu1snBhG5EFMs+aXAHZgK/g8Afwf8UkTW+3jMbwJfAp4J/Ar4GPA/GIP9AeBnIuKWHnQUszVP/d9nQ4oUGANHjwFnKMkkQAUVm3Z9x3fwYPA9YcPOwUWVeX6D14WdbiMZulrj6oCCJR8EkbkR/0HfNcTX6QaJEBw8eDC2ReZBjbq9A3aUULStg6CJW3ENJmx9+Q1RdrYuDsuGactJwf8bNJt9bvK4ZjsLNwRdKvwnhrfXqOrH7B9F5N8xc4bvBl7l8YwTwJ8B31DVYs0z3gjcCDwRs9/cBx3uHVTVd0bgPzLWbjwLGAuQ2Wd/mEs7RwLOa7Muv/zyUHTbMk2+i/nGtTbLbV1WIxm62zKciKG4ddDkgyAyN+I/mw/mLUN8Xmu2UOLsPn+p55dffjkH7jSVNLLFEn2d/jpqZ7rB5nibmpyXwASBrYPAUZG2DDNzZSoV9dyJuxGy+RJNYnai8AOnsGyYtpwUgnhwdwK/a+2SvQgicjZm77Sb42DMLyzv7RnAIPAfdaffAeSAPxeRrkbPUdW7VfXLtcbN+n2aeaN2bRw8J4GDR0yj9mtoMtYGoFGzzebLZQVNMikvyOwLs8VGmE4AopfMcguNNpIhtnBdYG+5uXqfFxrx77TBqzfteAp654r+S9Dt2bMntvB71lo4HVzm8HT37NlTLZcVLOzfjCrMzkV73zZd3yFwh3e9nLbLCWLgPgKsB74vIg+vPWH9/xtAO/DR+NjzhadYxx+q6oKgu2WcbgE6gcdHoGGXCHD7cteIyMtE5C0i8moRiUIrFPo2bA6UfABmrUvUtTNBqkzY6GrLUK4rExZmi40w6+8ghhClS+iqkQxxZlEGnZsx93nTbsR/UG/GvjaWsGyAhIsdO3bEtu5wfueGpZN5x44dgTZ4tRGbUQ/4fbU0N9GaaVqQLbsit8tR1R9g5pWuwcxRvRlAREat/z8ReLOq3poAn41wiXV0C/weso5RSly/zDre4HL+CuBzmFDoxzHzfneLiKevLiKvtBJZdg8PDzM6Osrw8DDHjh1jfHycgYEBZmdnOXDgAJVKhb179wLzo6S9e/dSqVS4f2CQrtZmHnjgAcbHxzl27Bj28wYHB8lms/T391Mqldi3bx8AGUrkCqXqs/bv30+hUODQoUNMTU0xNDTEyMgIIyMjDA0NMTU1xaFDhygUCtUtMW7bcxcAo8MPAbBv3z5KpRL9/f1ks1kGBwcXyZSfnjC83zMv0549exbJdODAAWZnZxkYGHCUaXKmQEZLC2Syn+EkU3E2S7PAyNhUQ5nqn1Ev08CQkbWQm1ygp9tvv91VT7mJ0+QKJU+ZnPRUy0+uUKKUz/nW04NHDgNw4OBAQ5kGBwe59dZbXb+9eW8m41tPGcpMZGc9ZfL69qbzc7RQ9qWnO++8k9MnzXz0A0ePhW5PBw4cYCKbJ9MEM9OTvvXU2dbM8ZGx0O3pRz/60YLam37a08DAAK1iBotT+bmGMnl9eydGx+lqywTSU0emidGJ6apMN954Y6D25CaTXz3Nzpo1wI5Q1UB/GI/p28AwUAROAd8Fnhr0WXH8AZ8GFHi5y/l3W+ffHPL5f2PdfxfQ4nD+gxjjvgHoxuws/g3rnlPAOX5p7dixQ8PidV+7S5/4bz8JdM+zP3KTvuwLd4Smqap64Pikbtu5S793z3Hf93xj94O6becuHRzNRqL9ok/9Ul/wiVsC3XP5O27Qf/zO/kh0b/jVsG7buUvveXDC9z0f+tH9um3nLi2VK5FoP/HffqKv/9rdvq+fmCnqtp279DM3DUSi+5mbBnTbzl06MVP0fc/rv3a3PuFffxyJ7lyprNt27tIP/+ig73t+dWxCt+3cpdfvH45E++3f2a9XvOsHge75w0/eqi/85K2R6B45ldVtO3fpt/Y86PueH1jf5P6H/H+TTvizz96mz/uPmwPdc817fqKv++pdkehGBbBbHfrUwKW6VPVnqvr7qnq2qraq6kZVfY6q/jTos5Y7ROQPgA9jElCer6qLqpmq6htU9VZVHVXVrKruVtUXAt/CGL03LgWvx0dOB5orgHiqHwQtlwXO69HsEWMg2gHnowzt6KFCt/TxRjJ0xzj/F2i+s9X/2r9G/Dtt8OqF7rbmyAu950Pg/uju27cvtmSibMF/cWkbUfcc3LdvX+DlL7XXRm3PQUOUNu2obTkprIZiy5PW0W15gv37RJCHisjzgK8CI8C1qvpAQL4+aR2fFPC+UGhu6wr1YUbtcKdDNEanNO7LLrssMO2gJcJs2tGzKJ0TLhrJEMcciaoGnnesJhP5oNuIf6cNXr0Qx56D2WKw7+uyyy6LL5koH7yzj/p9XXbZZaEMXHyJNf43O62lXVtFJUxbTgqrwcDdbx3d5tgeZh19L84QkRdiwowngSer6v0etzjhlHVsmL0ZF0YnsyE7+5i8mYiN8fDhw6FodwccYTuVCQsKt4SLRjLE0QEVShVKFU3Ma23Ev1l/Fyzlvqst+p6DQSMEhw8fji+ZKED2po2oyUSHDx8OFRWJa41nGK+1s3Xhsp8wbTkpBKlFWRGRssdfSUTGROQWq/pHW5LMW/iZdXyGiCyQx1rScA0wA/iqKiIifwp8BVNv88mqesjjFjfYmZRBPb9QmKM5hAcXfX+0oOWywGySCAsb49atW0PQ9l/810YcmX25Qslxg9dGMsSx6Wl1EW6ITtePYW3Ef9B6oxDPusOg3szWrVtd9xwMTjv49xV1HdzWrVtDLaq321/UepTZQnCjXh+WDdOWk0IQD+4mTCUTASqY6h13WMeK9ft+4BjwaOB9wC1e68+iQlUHgB8C52MWYtfiXRgP6ouqmrN/FJFLReTS+meJyIuB/waGgCd5hSVF5FEismhYKyKPwiS3gKmOkjimZ4shGmP0cF2Y9HGn0eboaLD6AKpqFaQNOu8YffGxPcqtXyvUSIY49kcLWlmjlrYfuo34DxoaBedQdFBUF5j77HRHR0cREas2Y/ToRPDvK8PsXJlyJVxYdnR0tMp3kIFMnCHwqGHZoG05SQSR5I8xa8q+CrxJVYfsEyJyHvAe4HEYjykH/Dvwl8A/YBZcJ4m/Bm4FPioiT8PsdPA4TMbnQUyh6FrcZ7Nu/yAiTwE+jzH6PwNe6rDYcUJVP1zz/9cDzxGRXwAPAgXgUuBZQDPwGYw3mDhmSxrqw5wpRqt+ECWcUtsouru7A9GdKZbRgGuFbNpxdHxOdBvJYHfQUdYdhhnZg3+vtRH/YeY74yhuHdSo2zLE5amHSTIBU4+ypz14FZXu7m6yQyatIFCbimHt3+xcOfD6O7Dn8ufbVNC2nCSCSPJeYExV/6T+hGXs/kREdgPvVdUXi8irMPUdn0/CBk5VB0TkauCfMMbl2ZhlDB8B3qWq4z4es415j/ZlLtccxWRV2vgO0As8CngqZqH7aeB64DOq+n+BBAkJVbv4b8gQUsjGCKYTaA1QLgucM/vm5hYlqHrSheQ6+4a0XTY7bSRDHOG6oNsD2ehqa+ZUtuB5XSP+c8USm3qC7dQcR7JH0BClLUMcyUTZfLg5ODC6CtOm5ubmqlGRzhb/7bm5SXwnE7kh7ADK3slAVRGRwG05SQSR5JkYD6cRfoRlHFS1LCI3AX8akrdAUNUHMcWW/Vy7yF1R1euA6wLS/A7GyJ1RhKl8ANEbI4RLK3bK7KtUgiUiRJ2PshtjGLgVPG4kQxydfZj5Tpv24OkZz+sa8Z8rlOnaEO77isWD8ymzLUNXnVcRFPMh8OCDCQgvc6VSsTzH5sBRlXpPKihmqgOo4N+XnUzU3tIcuC0niSBzcD0Yb6UR+qzrbIwF5ihFYIRJK4b5sFm2EH7EFbT4b5V2XbZZZ2dnoPuzAUNXtXTjyOxzGkw0kiGOzL7QevbptTbiP+j6O5suRPRaA5bLsmXojjjXGjZcF3WutbOz08yDBRy4QXSv1f5GOkOHZS3PM2BbThJBDFw/8EcissXppIhsBf6I+fktgHMxIbsUCSJMqr65Po7MvmCbndqob4xjY8HGQmHDKV0O23sEhZuBayRDHJl9YcOyfju+RvyHmY+KI/EhWwi2wastQ9QEqtDfV0SZx8bGmA4x3wnRZQ7bj9RvmRO0LSeJIAbug8A6YK+IvFVErhWRh1vHt2H2Y1uDSS5BRDLAb2EyLVMkiPCdfTyZfUEbhE27lu6WLY7jpgZ0w81HdVuh2EiZfS4yN5JBxN5KJfoygTCdrp1M1Ahu/JddNnj1Qnc18SG8zEE3eLVliDrXmgsZrpuf1w4n85YtW8K3qbZo39f8jhHhPDj7fQdty0kiSLHlLwNvwhi5fwJ+gimy/BPr/2uBt1rXgTF2/wj8S4z8pnBA2NBVLHMkIcplweIO6MiRI8HohpyPsjus6QTCsl4yxNXpBimXZehaa6Q8tlJx4z8XsJqIjepWPRE9qSB0bRk6I4Yo5/e/C7q4PZrMR44cCeUtG9rRihiE/b7qvdagbTlJBHqLqvo+EfkGJnHkSsyc2xSmEPH/1K4bU9VR4FPxsZrCDVEyCmvvD4NsocS5a4PH3Osz+y69dNGyRE+6EN6oRxrpuiwA9pIh6hxJrhi8XJZNF7y9bTf+w35fmeYm2jIRM/sClsuyZYi6HCQbegAVbdB46aWXkv3RLZyzpjXwvV1tGYbGvJOJ3BAlBA7zXmvQtpwkwhRbPqKq/6KqL1DVp6vq863/L0nFjhSLUbu9RhDEMUcSNsmkvgO6++67A9O1nxOUbu39QVEsVSiWK44lwrxkiFrcOkzGKvhfI+XGv1txaT+I7LW6LMlwgy1Dd2uGYrlCMWQyUej5qIjf1913302uELweJESvohI+BL7Qaw3alpPEaqhF+WuPMJuOQrDNMBvRjiNEedVVVwWkW0JkfoI7CF0IP8JuZFi9ZIhaaT5MNRHwb9Td+M+GnI+yaUfrdIN9X7YMUQcyYeej7LVrYeleddVV1qL6cO96JkJbtrMgA4co6wZQQdtykghl4ERkq4g8TkSe5PQXN5MpGiOsN9Pe0kSThG+MlYqSLZSqtSWDoL6zD7rNvZ29GXQtW9SOr1Fo1EuGyEkAoedm/K3NcuM/bIkwQzta8eGgCRe2DFG3J6quswz4bTc1mWSisDLv2bMnVNUYmN8dJOzuDblCibZM8BB4/VRH0LacJAK9RRF5BvAhTDmqRgg+/EgRGmHXhIlIpLCZnbQQ1quYKZqafc1NEnib+9Dr7yKWNGo0sveS4UyFKOc7oMadrhv/YUNXhna0sFlQr9WWIepcq51kEv7bDifzo658NMVvXB94lwybbkXNGr6ga9kgQgi8bh1c0LacJILsJvB4YBcmO/LjmDqON2HqLfZb//8uJqNyyWF5lZ8XkeMiUhCRQRH5sIisDficddZ9g9ZzjlvP3Zo07bDIFUq0Z4TmEPUko4TNwnqONl2YNxj2lvR+kQ2ZvTk/XxCu42uUveklQ9T990w4OFzoytzfmLYb/2Hno2zaUUt1BaFryxC1oogdAq/fMcIPosw73nqHzX+4OTiIJnMYuqZUn1TpBm3LSSKIL/pmIA88RlX/zvrtZ6r6KuCRmOUAvwV8M14WvSEiF2LW4b0Us+7uQ5htav4O+KWIrPf5nPXAL637Bqzn3GE9d4+IXJAU7SjIFkr0dATPuoJoHVDYTEabLsx3nldeeWWg+8OuFapm9oWW2X39nZcMkbMoC6XqOr4g8Dvv6MZ/lIFMFK81THV7W4boc3AmBB6mCHmUJQoXXPxwIFqbCjsPlyuWA89p19IO25aTRBAD9wTg/1T1eP39avCPmCom74qRP7/4T2AT8BpVfZ6qvklVn4oxNpcwv3WNF/4Vs3Hqv6vq06znPA9jrDZZdJKiHRrZQokWwn3UUeZIonV8Cyfj+/v7A9MOMycE0UbYjWT2kqG7LcNcWSmUwr3v6ULwclngv7N34z/Mlkg2uiNU1whTLsuWIWoRg7AhcJt22AjB/n6z/WSUZKIo33YYHYORORuyLSeJIAauD7NPmo0iLNqt+hZgSZNMLA/qGcAg8B91p9+B2brnz732pRORbuDPrevfWXf645idBJ5Z68XFRTsqcoUSa7o7Qt0bZY4k7FohQ3dhBuf27dsD0i6HSluHaJ5UI6/VSwa/c2FuCGvU/Wb2ufGfK5gNXttbguekRVmPFmb5iy1D1GzZMDtb24gygFqz8SwgWpuKZtTDyzwTsi0niSBf7AimWknt/y+su6YFCNfThsdTrOMPVXXBohdVncYY3U7md9h2w+MxvN9i3Vf7nArwgzp6cdKOhFyhTAvhPurutkx1Qj0MXfsZQVHvVRw/frzR5Q60I4w2E5p39JKhOsIO8b4rIctlgf/MPjf+7ay+MLsvdLc1h87sC7P8xZYhakWRKJ19lLD/g8MjQLg2Va0JGWHKIWyb6rT0DMHbcpIIYuAOstCg3QY8XUQuBhCRszB7vx2Kjz1fuMQ6HnQ5b/NzcQLPiYt2JGQLJfo6g+3VZSPKHEkcSSY27XXr1gW6P+xaIUO7OQaZF9P2kiHKBqBhy2XZ8GPU3fiPOphQnc+wC4Iw35ctQ311jeC0wyX02LTDeq3NbaYqUJgsyKgRgpkIc3C1XmvQtnzDr07w6i/vJe9RSi4Mghi4G4Ani4jN/UcwHs9dInInJpNyIws3BF0K9FnHSZfz9u9rEnhOZNoi8koR2S0iu4eHhxkdHWV4eJhjx44xPj7OwMAAs7OzHDhwgEqlUs1Qstea7N27ly1r2ulhltnZWQYGBhgfH+fYsWPYzxscHCSbzdLf30+pVGLfvn3VZ3S3ZZicyQOwf/9+CoUChw4dYmpqiqGhIUZGRhgZGWFoaIipqSkOHTpEoVBg//79C8J1Nj/79u2jVCrR399PNptlcHDQUaZmNfdm83Ps3buXmZmZBTJVKhUOHDjgKtN0fo5WUUeZao9OMrVKhYlc3lEmp2fUyjQ2PUtLkzA9Mb5IpomJiYZ6sjPyxqZzgfVU680E1RNARktki6WGejp58qTjtzc8OkZXa7OjTF56ymdNE7j73uB6eujkKAAzk2O+9TQ9PU1/fz9z+Rmam2B0Yjpwe6pUKoxOZunINAXWE0B2YpRcoRRKTwePHAXgyKH7ArWn2dlZjg+ZGpAHDj0QWE+Dg4Nk83MUZ6YD62lkZISMlpnIzjI1NcXAwIDv9pTNZrm9f4jv7R9mdORkYD3ZMrlCVX39YfaCexzQU/Pb72MKLs9iEkxe6fd5cf0BnwYUeLnL+Xdb59/s8Zy3WNf9i8v5V1jnPxU3bftvx44dGhbHjx8Pdd97rr9PL3rL90Ld+8kbD+u2nbt0Oj8X+N6TU7O6becu/e9bj6hqMP6LpbJu27lLP/rjg4Hpqqq++st79Nr3/yzUvW/99j165bt+4HjOS4Y9R8d0285d+tP+k4HpHjo5rdt27tLv3PVQ4HtVVZ/zsV/oiz9/e8Nr3Pj/88/drs/9+M2h6H5770O6becuHRiZDnzvT+47odt27tK9R8d831Mrw+XvuEH/8Tv7A9NVVX3y+36qr/nK3lD3/vsP79dtO3dpqVwJfO9Hrr9bt+3cpaPT+cD3TuSKum3nLv3MTQOB761UKrr9Tbv0/Tf0B75XVfX1X7tbn/hvP1HV4H3Ru793QC952/dD0bUB7FaHPtW3H6yqU8Dtdb99G/i232ckBNtL6nM5b/8+kcBz4qIdGS0t4Xbkrs3sa8sEC0/YIaTOkGuFYD7JJAj/UUKjNu3wIUr3eTAvGaIkAURZiwb+9gpz4z8XsloNRFtwHSZ7s1aG+k11g9IOEya06YIJK/cGXNZhs7vUazzzcxUqaubSwqCrZg4uaF8UZe7PC0EWej9JRM7zuObcM1Cq637r6DbP9TDr6DZPFuU5cdGOjGw2G+q++Q1Aw3VAXa3NodYKdbQ0LygTFoT/KOvvIHoWpRtdLxmirM2KatS72jJMeyS3uPGfzUdImY8y7xhC5loZutujJROFWZIB0fQ8kc0H2uC1FvYazzBVVOKc4w3aF0VJ6PFCkLf4M+AlHtf8hXXdUsKm9wwRWSCPiPQA1wAzmKSYRrgNE2q9xrqv9jlNmOUAtfTipB0ZGzZsCHVf1E437IdpNgCd96SC8B+2uLQNvxuAOtN2l9lLhigbgEY16t01I2w3uPEfds8/Q3dpjXqtDGETqMoVZXYuXMaqoRt+0KjNrXS2NofKWIXw0Yko9UZtunNlpViqBO6LclZd2SQQxMD5eeOCmXNaMqjqAPBD4Hzg1XWn34VZq/dFVc3ZP4rIpSKyoJ6mqmaBL1rXv7PuOX9jPf8HunDPu8C0k8JDDz0U6r4o64WyxWihhdpRXxD+o6y/g/lsxjDp1I0MnJcMUVLXw1a3n6ftndnnxn/ULEoI967na6z613OtDKE7+6jeTIRF5qcmpiO1qbBVVKLUG4WaJQqFUuC+KMqiei/EbTa3AdOeV8WPvwZuBT4qIk/DJLw8DrNO7SDw1rrr77OO9Ub7LcC1wOtF5EpM6a2HA7+HWfdXb8TC0E4EF110Uaj7onpwYRdbgxVCsjqTIPxHno+qmRfqCThHki2UOGet81JPLxmibACarXqt0dO43eDGfy6G+agwhmamWA68wWutDF2tGU5M5gPTjTzH2x6+TTW1ddLVFn483NWaCbU0Ihfx+6qtohK0L8oVS6zrCldq0AsNNSgi/1j307UurnMzcB7wIuDmeFjzD1UdEJGrMYWenwU8GxjGLGV4l6qO+3zOaRF5AqYKyfOA3wROA18A/lFVFw1N4qIdFffeey9XXHFF4PuilPfJ5sNXe7Bp2x13EP7jSDKBsPNC7uEUPzJEDSFFMerFUoW5coUWF4PhxH91g9czMB8VJvmgVoawc61RQ+A2z9MhaJ88PUFXW/haGWGLp0eNENQm1tx776FAfVG2UOLcdZ2h6HrBS5p31vxbMd7NtQ2uPwa8KRJHIaGqD2IKHvu51jXcqqpjmNqTf+d2TRTaSSGMcYNoi0OzhRJb14b/MGvLhAVtEOb+pQ8hNQpR+pEhfKdrymWFqW5v07Wfs6bTebTsxH/UwYSdYRtm3jFXKAX2HGtlCLugf34+aumNelNrR2hvGcyO4pMzxcD3xRkV2RGwL8oVSqG2B/IDL9//KdbfUzHhvOtqfqv9exJwGbBNVZfPbne/Rgi7yWDUeaGwI3tYmLoehP84Mgprn+MXqmrJ7EzXjwxhi1vbtRHDJx94ZzM68R91bsYuE7ZUSUy1MpiSWeXAZcKif1/h29ToRDZ0NRGIwaiHHjTOyxy0L5oJuGt7EDR8qqr+3P63iPwX8J3a31IsH4TdZDByuC7Ch1kbrgvCvz3HEGU+CoLL7FXd3o8MYYtbR02l9rMezYn/qAkXNu3wIcpgOq6Vobs9Q7miFEoV2gN4vtEzVsNny1aaW6K969ZMqLJo1TneGLzWJwVoy/agMakkE9+zt6r6UlX9v0S4SBEZ4T24pZ0jqaedDeHBZQslWpubAi9Mn6cbLovSq7q9Xw8uXPZm+NqINl0I7sFFHdmDMTRLNYCqlSHsQCbqfFT9Gs8gmMzlIw9kQiX0xDivHaQth9kSKQiCryZMsSwR1oNrsTL7sgE73blyhWKpErkx5kJ4cFEWHkP4EbZX8oEfGcJ2QFEHEz0+BjJO/M9XE4n2vsOGzYJ+X7UyhJ1rjZqxKiKh9VwoS8Q2ZSIEQcOy2WLJ2pk7nEmobrZaLAdryzEMoBrBVRoRqYhIOcRfuNIBKSLBLmwaBmG2zIllZN/WXC0TFoT/qOG6sGncXhPxfmQIuwFofCFKd9pO/MehZz9lwpyQKwZPPqiVwebZq4JLPWY89OwHYYx61IxVMDJX1JTeCgKz12B4uva8YbZQCtSWZ2IYQDVCIw3exBIv2k4RHhdfHH5HnjBzJGE2o3SiC8YzCsJ/VG/GDiEFNepeczN+ZAi7lUq2UOLcrigZq97hOif+5xdbRzOuxyYaVHx3Qa5QDlwbsVaGsFVUcoUSEiFjFcK1qWpt1wjvujZdvyOAwYqa6NGWaSLTJOQKpcBtGaLJ3AiuT1XVaxOhmCIRDA0N8bCHPcz7QgeEyeyLulao9t5cocTp48d88x+ldBQsLhPmF17ejB8d1G4AGiQjMleMNsL248E58R81fdzcGzyxxitj1Q21MoSfay1HyliFcB5c1OQWmDcUuUKJDd1tgWhHoWuHZXOFUqC+KI7vqxHSObhVgs2bN4e+N0wHFEfsvNarCMJ/Noa04iheqxttPzKE3QA0asbqfGfvTteJ/1hClCHe9UyxjIZIPqiVIfxca/SsvjALrmeK0QeNYTfVjTpoNLTNsowgbTlqQo8XQhk4EWkRkctF5DdF5FEiEm6vlhSxYWJiIvS9YTL74hh51XoVQfiPUul9nrZ38eF6eI2w/cgQNms16gi7LdNMS7M07Pic+M8WyrQ2N9Eaorq9jTDeTFjDWitD6HcdQ2ffFWI9WtQaq+becIUbzPZA0dpUp7XeMUhbjiOJqRECfbUi0isin8Tsb3Y3cCNwFzAhIp8UkTUx85fCJ9rb20PfGybjK45wSu1oMwj/uUK0EmGGdpiwbOMOyI8MYVLX48hYBUvPDeYdnfiPw5vpastQKFUolf0nPoSd462VIWwy0UzEwQSEm2uNe9AYBHHJHLQtR12e4IUg+8H1ArcArwRKwC+Ar1vHOev3m63rlhQi8kQR+b6IjInIrIjcIyKvFRHfrUNEzhGRvxWR60VkUEQKInJaRH4kIn/gcs+1IqIN/t4Tn5TJIUxmXxwGLvxoM44RdhiZ7cWwSytzHGFCCJfNGMdeXeFkjuFdtwYfTNi04xlAnbkkkzC0o+q5J8T+e2csycQBb8aU4/oE8FZVnbBPiEgf8C+Yavtvtv6WBCLye8C3gDzwNWAMeA7wIcx+bC/0+ai/BXYCRzD7vJ3A7I7wB8BviciHVPX1Lvf+HOPN1uNmn7QjI58PXjXdRpTRZhxzcLlCiXx+ztc9qhpp+xYbXW0ZxnIzge4xtRHdN3j1o4P5Qrz+5IV4MlZt2o06Pif+49htueqpF0v0dfqbzQhbQaVWhuYmoaMl3PzyljXhIyIwPwcXJJkonqhI+BB4lCQmMAOKk1P5QH1RLmIFFS8EeZN/ANymqou2jFHVSeBvReQq4PkskYGzvMXPAGXgWlXdbf3+duCnwAtE5EWq+lUfj7vDesaCUmQi8nDMhqWvE5Evu9TavFFV3xlBlMhYs2ZN6HvDZPZ5hev80Z0fba5Zs97XPfm5SiyVD8KOsBvR9aODMMWt48hYNfc3nnd04j+O5IMwYbOqNxOQdr0MYcLvcclcClgmLJY21R7cgzMZq9ETt8wO6uVAfVGuWAq8JVIQBHnqNpy9lFr8HDg3NDfB8QJgI/BV27gBqGoeeJv137/y8yBV/f+c6myq6n0YzxAa76RwRnHy5MnQ94bJ7MsWyrQ0S+hyWTZdMA3bL/9xeTNdITNHG42u/cgQphBvXNUevJaDOPEfV8aqeVZwmYPquV4GU3w4TBZl9AEUBJM5F0MWpR1aDbK4vVCqUK5oLDJP5+cC9UVxRGMaIYiBywGbPK7ZCASL+0TDU63jDQ7nbrJ4eaKI+F8Q4gw7nuT21VwkIn8jIm8RkZeJSLgFaRFw3nnnhb437Ag7aoNosbLzssWSb/6rE/ERNlqF8GHZRo3RjwyhOr6Y1gp5pa478R9HxmqYsFlYr7VehrDLQeIIgUPwNpVpEtoiZKw2N0k1mzEIXYjn+8oWSpx7rn8fJ8yWSEEQ5E3eCbzQrfMWkQuBP7SuWypcYh0P1p9Q1RJmPi0DXBCWgBUGfT6mqssPXS77U+BjwLuBzwEHReSbIrI2LN2gOHhw0SvwjbCdbtSJeJt2rlDyzX8clTXAJNYUrexEv/AqeOxHhijhujgSHxrRdeI/Dj2HqQkZdo63XoagIcpyRcnPVWJ51xC8TbVliLTAHILLbA8moi4TsMuE7b/vft/3xBEhaIQgBu79QDdwp4j8s4g8VUQeLiJPEZF3YQxbN/CBJBh1QZ91nHQ5b/++JszDxXxpnwU2A5+wwpW1OIXZ4PVyoAfjwf42ZunE84HvikjDdywirxSR3SKye3h4mNHRUYaHhzl27Bjj4+MMDAwwOzvLgQMHqFQq7N27F5ivmr53714qlQrNzc3Mzs4yMDDA+Pg4x44dw37e4OAg2WyW/v5+SqUS+/btW/CMEw8NArDv3vspFAocOnSIqakphoaGGBkZYWRkhKGhIaampjh06BCFQoHjp8bobstUn2Ef9+3bR6lUor+/n2w2y+DgYEOZulqbeXD4FJdffvkimQ4cOLBIpqPHTfgjOzHaUCb7uH//fkeZdM6UjjoxOl6Vya6h5ybT6aks7c3iKtNFF13kqafBw/cjwIMnTvnW068OHgbgyKH7GsrkpKdambraMkzOFFz1dPbZZy+SKVcoUchNNZTJSU+1MjWVDc2pmaJvPR0bOQ1AbmKsoUz1enr4wx++QKY2qTCRnfXdnm69wxynJ0ZDt6c9e/ZUDdxEdta3nrKFMh3NEqk9VSoVWigtqOrvpaeHTp4CIKOl0O1pZGSEuZkpACpNrb7aU39/P1MzBTJaCt3v2TK5QlVd/4DfA5pq/v//MNmK5bq/ClAA/qrR81xoDGK8I79/X6q596D120Uuz77FOv+EoHxZ9/+7df9NQFuA+3qBB6x7f8/vfTt27NCw2L17d+h7bzl8Srft3KW3Hh71fc+ffOaX+vv/cXNomjae+aGf68v/607f/P/4wAndtnOX3j00Honu1+4Y0m07d+nQ6Zzve570vp/qa76y1/W8Xxku+8cb9F3/d69vul+4+QHdtnOXjk7nfd/jhPff0K/b37RLK5WK4/l6/iuVil7w5u/p+2/oj0T3dLag23bu0i/c/IDve/75u/fqpW+7PjCtehn+9n/26pPf91Pf9x+fmNFtO3fp/9x+NDDtWuw9Oqbbdu7Sn9530vc9/++/d+s1774hEl1V1d/96C/0xZ+/3ff1dx45rdt27tKf3z8Sie639z6k23bu0v/72W2+73nOx4Lx6gZgtzr0qV6+4beBYyLyBeBzqvopEbke+HPg0RgPahLjsXxJVY96PM8JA5bR9IvjNf+2PbQ+pwtrfp8IyBMi8j7gdRjj9juqWvB7r6pOicj/AG/F7Hb+v0HpB0XY7XIAetpM6nawJIAyvRHnwWA+bLZjx+N90o0n4SJMtpnXvKNfHQRNcIkj+cC+364071SIt55/O/kgaMHjxXS9y4TVI2xWX70MQeusxrXmcH45SBA9l9jQ1x2Jrk07XBJT9BAlwPkXXer7nlyhxLnrwhcR94JXiPLHwBZMRuKAZdx2AO9R1Reo6tOt47tDGjdU9WmqemmAv3+oud0O9i4qXy0iGWA7JjHkgSA8iciHgL/HrIf7bVXNhhDtlHXsCnFvYITd8BTCZfbFlf1kJwH45T9XLe2z9EkAXskHfmXoassE2n8vG0PyAXjXKaznP451WeCvTFg9wlZQqZchaJ3VuEpHhZ1rrRSi5+h1t2cCZVHGtQzF/k727L83EO2k1sCBh4FT1WdgEjTeDQwDzwS+CTwoIv8qItsT48wffmodn+Vw7klAJ3CrX+9LDP4DeC3wI4znFvaLs12SQMY1LKJ4cGEnxOMwcN1tGaYLJd/8x7FWyNANVpS2VK54Jh/4lSHoCNv2HONIPrCf54R6/uNKbrFpB5Y5BF0nD252rky54m/nr9gSekKUCcsVypy1IXpemil6fGaSmADO2XZhINpnNMlEVY+q6tsx6+CeC+wCNmCSKw6JyA9F5AWWx7TU+CYwCrxIRK62fxSRdkxlFTCVV6g51ykil4rIeXW/C/Bp4K+B64HnqmrDTaxqadb9/mfAHwFFTDmzxGFPCodBKG8mH8+HaYfr/PIfVxZl0PJR86Ncd8PqV4agJbPiSFsH7/Vo9fzHudty0O2JwspcL0PQwVucZdGC0LWvLc5MR6ILwTcwDls1ZhFdy6gfODjg63oNuSVSEPh+sqpWMMZtl4icBbwM+Evgt4CnAaMich3wWVU9lACvTjxNicgrMIbuRhH5KqZU13MxSwi+yfwibRuPxYQef87Chdv/CLwcmMUUkn6Tw4j5blX9Ts3/v2ntYL4beAhoBx5j0SgB/09VB6PI6BeXXXZZ6Hs7W5sR8W/g4vww7fVofvn3Kpflm27A1PWsj07ArwxBNwCd8Vie4Bde69Hq+Y8rHGw/I9i8Y4mNAfYzs1EvQ+3gra/Du0xYXNu3hCkTliuWOGfzWZHoQvA1nvNVY+KZa12z0Z8McVUlaoRQQX1VPaGq/6qqFwJPx3gpvcAbgfpU+kRhGZwnY5JBno+pKTkHvB54kZVh4wd2uLUDU2rsHQ5/z6u75xOYtXbXYOpwvhzj3V4HXK2q1wWXKBwOHz4c+t75DUD9NYrZuXJsH6YdTjl0yN+YKI4ySjZdiHdk71cHQeeF4pK52tm7hK/q+Y8rHGw/I2h5sjAy18sQdJF51oen7hfB16OVmMtF9+B62s0az0LJ3/uOoyoRzCer2Ut5vOna0Zjk5uDiMJ0/B9ZhDMRjY3heYKjqLcCzfV57I7Bo+K+qLwFeEpDue4H3BrknKWzdujXS/UEy++Iql2XomjJh6zdv8Um7HGu4LrDMDTJH/eog6HxUXCFKW19uCQj1/MeVZAJG5iCJD2Flrpch7EAmDpl72v0PGoulCnNlZfOGNZHp2gYjmy/R1u3dRuOaB2tvaaJJINPuLxM0zhC4G0KnZYnIJSLyfuAY8FWMcRsE3h4PaymCYHR0NNL9QTL74sq6gvmO5MHhEZ+0o+9PBtCaaaK1uSmAzN4dn18dBC30HFfVGK95x3r+45qPguAhypmQnW69DMHnWks0CXT4LJDcCEEGjfZ1Wgy/K4iN7vYW65l+PbgSPTEs+RERutsyjE76Szq35wl72pPbLzuQVFbyxh9iQnHXYDyhOeD/Az6jqm6lrFIkjO7uaOtngnRAcXd8ALT4254kLm8GwnVAjQyNXx3UbgDqp4p62HCdE13zPGeZ6/mPNckkwPdVqVjV7UOErupl6AqYLZu1BhNRM1YhWGKNfd3ano7IdINuyTSdL9HdFo+R6Wlvoaj+/CabvziMqxt8PVlErgReAfwxZvG0YBZofxb4gqr6G36nSAxzc/73F3NCkMy+uENXYMo4+aKdj75XVy1t/6Nc74QLvzqo9Sr6Or07A2PUY/AoPDL76vmPc6+uIF7rzFz4CEG9DEHn4GYK5cjJFrW0T0z588jsedE4SAfdkilbmKMnxkGj3wxO+7ozlkUpIq/CeGuPxhi1IvAN4NOq+tNG96ZYWlQq/osGOyFIZl+cHtz8CNufcYgr4QKCdbp+Ei786iDIBqBqbfAadF80J3hVmq/nP869usxedGVfew5G+b7qZfBKrKmHCdfF4810t2fIngrW2XdmonuO81V6/Htwm3vjGTR2B5jqsNvemfTg/tM6HsRsLPpfqhptsidFIujsjFbuJkhmX5xJJvbordzkc6fnGBeGBgmb+QnX+dVBkASXQqlCqaIxhmXdFwHX8x9vODhD2ecGoFEiBPUyVMN1Pr2KqfxcvO/a5/dll/Ra3xu98NF8EQP/c3AXxijzRHbpI0Fu8Bqa/Q/wFKtE1gdT47Z8MTY2Fun+II0xziQT+xkjY24bQixE3J1ukDk4r3JZfnUQZAPQ+bm/+MJmbh1fPf9xDiaCZDNO58OP7OtlaMs00dwkgQYycXkUQSIEtsylvL8EjcZ0rdqyAUKFccnc055hctbfdIMtc9S9HRvBq1TXn6nDLtcplh+2bPGXZu+GcOG6+JJMWjt7Pa/1Uy4rCHqsMmF+4Kdcll8dBJkXinMwYZ7j7qnX8x9X9ibUGDgfne503k4+CB4qrJfBzuzzbeBi7Oy7WjPk50wykR+6ABeeG60dQ/DastOFUmxGpqs1Q6HsL8w6nS/R2twUef1dI0QPrqdYFjhy5Eik++3MvjkfjXG66lXE58E9eOKUx5W1VfXjaRDB1v55r7/zq4NqsoePzn4qQmfvRtttIFPP/1ScnX0ADy5K8oGTDhp5rfUwGYXxDSbAX7KHbdRHTzwUnW6rnUXpJwRepliqxJZkYgo9+0wYK8wlOv8GqYFbNbj0Uv9bVDghmFdhymU1RyyXBdBpzcd09q3zRRfii9kHy6Kc8zSsfnXQE2CrHjuME8fWRNB4OUg9/3F6M0G+ryghSicdBC1iENdgoqpnH0kX2UIJEXj0Ix8emW5Tk/iuRxl3JmN3W4bZUnVfTE/aSYYnITVwqwZ33313pPuDzJHEOTfT1CR0tTYz+NCw57V+qokEgV0mzFdj9NHx+dVBkCSTuGVuNO9Yz/90YS4+zzFANqPtefSGoO2kg0aJNbUoVzT2OV7wb9S72zKRiqYvpO3PqM9/XzFljlqViWZ87P0X57t2w6owcCLyRBH5voiMicisiNwjIq8VkUCxLBHRBn+3Nbjvd0XkRhGZFJGsiNwuIi+OLpl/XHXVVZHuD1LxYTrGkb1Nu8uHBxdlbsaNrt/G6EdmvzoIsgFoEjK7hevq+Y9Tz0Ey+2yZw4SinXTgd37ZNoJnIiw7nS/R05aJ3I5t+JU5irfsSDdAdGIqxnCwG1a8gROR38MUWn4SZgfyjwOtwIcwJcSC4ijwLoe/z7rQ/xvgu8AjgS9hllNsAa4TkQ+EoB8KUTY8hWAVH6by8Y3swTRGP3NwUzE3xjAj7Ebwq4MgG4DG3gE1GNnX8q+qsRq4QF5r3oTAw6y/c9KB3yIG8b/rIJ66aVNR23EtbV/znfZatDOQLRtnCNwNyT49YYhIL8aglIFrVXW39fvbMZuhvkBEXqSqQQzdoKq+0yf984EPYLboudreGkdE/gm4E3iDiHxLVX8ZgH4oRNnwFILPkcQ1JwSm82v1sYYs/vmoeaO+yZO2t1EPogO/SxTiXgxbuwFo/RxqLf/5uQrlisZWwinuwYQbnHTgd651fj4qvnBd7XMbYdqaj4rajqu0230auJhT9YPInIYovfECYCPwVdu4AahqHnib9d+/SpD+y4A24OO1+76p6jjwr9Z/X5Ug/Sr27t0b6f5gHVC82U9dbc2cOD3hiy7Em1EI/sKyUz6MehAd+K1TOJWfizWVujqQcZiTquV//l3Hlz4OPkf2EdaiOemgpz1Tlacx3XhlDuTNWDJHbce1tH21ZUvmuOcd/cucXKFlWOEeHPBU63iDw7mbgBngiSLSpqoFn89cIyIvA84CJoE9quo2/9aI/vV11ySKK6+8MtL9QRfi9sQ0yjW0W5j0UWw5qRCSl8zVVGoPukF04LsDijmMU1vZoz6Jo5b/uMPBdpkwv0sjwnZ8TjrwWyZsKmZvJmhY9rx1nZHbcS1tP9VbEvPgfMqcZlE2xiXW8WD9CVUtYTYjzQAXBHjmFcDngHdj5vN+KSJ3i8jlAekPAzlgq4i4xt9E5JUisltEdg8PDzM6Osrw8DDHjh1jfHycgYEBZmdnOXDgAJVKpTrCs2P1e/fupVKpcPPNNzM7O8vAwADj4+McO3YM+3mDg4Nks1n6+/splUrVTC37GXv27Kk2xslcnkOHDjE1NcXQ0BAjIyOMjIwwNDTE1NQUhw4dYjo/RyE7segZAPv27aNUKtHf3082m2VwcNBTpmJukvHp2UUyHThwYIFMx0+N0yyQmxz3JRPA/v37KRQKjjJNj5vCPIcGhygUCuzfv9/xGbftMc+emRxrKNP+/fs99WTLlKHEeDbvqadsvkSLlH3LVKsnJ5lGhx8EYPe+exfp6a677qrKNHzKVARpa6r4lsnr2+tpyzBobYbZSE+TMwUyWvItU+23d+DAgUXfHnN5yhVleOR0w/ZU7exbm33L1OjbGzzUb47HT3rqaSw7S097CzfeeGPk9rR371562jJMzuQ99XT81DgAYyeOR25PQ0NDMGdoTmRnG+oply9SLFdolYpvmRp9e65Q1RX7hzEsClzkcv4W6/wTfD7vg8ATMbtydwNXY4pLK3AKOKfu+qJ1LuPyvGPW+bP90N+xY4eGxczMTOh7VVULc2XdtnOXfuwnBxteVyyZ6z78o8bXBcFbv32PXvmuH3he9/bv7NcrfFznFwMj07pt5y79//Y+2PC6B05lddvOXfqtPY2vC6KDl3z+dn3Ox37h67rf/aj3dX7xi4OndNvOXXrHkdOLztXyf9PBEdfrwuK3PnijvuqLuz2ve9oHb9S/+pL3dU5w0sH/3H5Ut+3cpcMTsw3v/fJt/q4Lgovf+n391+8d8Lzukrd9X9/9vQOR27GN915/n1745u9ppVKJ5Tq/ODWd1207d+l/3Xokluv8AtitDn3qGffgRGTQIz2//u9LSfGiqm9Q1VtVdVRVs6q6W1VfCHwLY/TemBTtqDh+/Hik+1szTXS0NFfDNG7Ixhy6ArPeaWp2znM9Wtzhut6OlupzG9P1N/cXRAe9HUZmL8RZWcPQNc9yol3Lf9zhYEO7pVqZpRGmIxQ8dtKBLYMXbXsOLs6wmZG58fc1Z5Wg62nLRG7HNrrbM5Ss4taNkLXKdMWx/x34L269FFvlwPKYgxsAgmxjW/sF2BV6+1yutX+fCMhTPT4JPB+zFKEWkxjD1wecbkDfXyXhCFi3znsdmRd6OzKenW5SHV9ZYXauTGeD8l/T+blY5/6qHV9MMgfRQU97xrPjs2lvWx9tp4iFdM37c+rsa/mPO6EHTPbr6Zx3GSeTPh6OrpMO7LlGP3oWia+wtaGd8TasNfNg69atiYVuraFptHtDNuYBVFumiUyT9xKY+ezgVZ5koqpPi3D7/Zgw4sXAggUkIpIBtgMl4IEINMCEJwHq97K4H2PgLgYWLAUQkbOt6x9S1ZmI9D0xMzPD2rVrIz2jt917hB13bUSbLsDUbKmhgYuzNiKY9WjtLU2ehsZvRmEQHdR6rY1Gz3FnmvVWjfpimWv5n05ghN3T3sKR0VzDa8rWbt5h6TrpwPbUvb5t21uOy5uxafsfQLXE0o5hvk1lCyU29rS5Xhf3YmsRoau1yTNrNYnvywlnPEQZEfamq89yOPckoBO4Vf1nULrh8dax3lA2ov/bddckiqam6Ko0jdGrs493LZqh6y+ENB1hZO9Ku927A5qqytyYdhAd9Ha0UKoos3ONlyhMxbwkw35/Th1QLf9JdEC9Hd5ea9R1f046sL9Vz7BZYXFmaVSYQaNHm6pJ1Y+jHcN8m5r0+LaTKHjc3Zbx7EeWYrNTWPkG7pvAKPAiEbna/lFE2oF/sf77idobRKRTRC4VkfPqfn+UiCz6ukXkUZiMSjCVSmrxBaAA/I216Nu+Zy3wFuu/nwwqVBi0tERvmH7CKcmErtw73XracRpW8Dcv5DdEGUQH8zK7dwQVqzZinJ1Aa6bJ1Wut5d/2ZuIoqG2jt72F6XzjuVb7GwhraJx00OM7RBnfZqfztDNMexmZmu8rjnYM/sOySaxF6/MTlo15/Z0bVrSBU9Up4BVAM3CjiHxWRN4H3A08AWMAv1Z322OB+4D/rvv99cAJEfmOiHxMRD4gIruAvcB6TMWUr9TRPwL8PbAO2C0i/yEiHwLuAS4EPqhLUMUEIJvNRn5GsHBK/MkefrzHuEd8ve3eo0270/VqjEF00CjZw8bMXBnV+Ee5bl5rLf9xL+YHY2jmykp+zj3xIWpxaScdzCeZeHsVsb/rgAOoONoxQJ/PsGzcc3AAHRn/89pJr4M743NwUaGq3xGRJwNvxSSCtAOHMQbro+qVmjeP7wC9wKMwi7PbMYkj1wOfUdX/c6H/MREZxGRY/gVm0HAAeJuq/ldIsQJjw4YNkZ/hJ/Eh7goXUDMv1KAxqmoio83ejhbGPBIfpn3WRgyig0bJHvN04/eWwcjs5DnW8p9EGaXaUHSHSyJH1AGUkw7aW5ppyzT56nTXdbWGousGM5goNZxrrRr1tgwb1kRvxzA/aPQKUdolwuLE+t4OBkYbrE0jmYGyE1a0B2dDVW9R1Wer6lpV7VDVy1X1Q6q6aIJDVW9UVVHVa+t+/46q/oGqXqSqvaraqqpnq+pz3Ixbzb3fVdUnq2qPqnap6mOW0rgBPPTQQ5Gf4Sddv3ZCPC7Me3ANvJmiqZ+4VN5MLfx6M0F00CjZY55uMp1Aj0sIqZb/ZLxl71B01PRxNx34SddPwpvp7chQLFcapuvXDmTiaMewMHHLDarK5Oxc1duLC02lgue7npydo70l2d28YZUYuBRw0UUXRX6Gn8SH6UKJtkwTrZn4Ph0/IaQkDCv4S3zwm9wSRAd+Mvv8hkaDws2o1/Lvp7h0UNh6nmzQ6UbN0nXTgZtRX0g7mSQmaDx4qy2LFkc7BmhvaaKlWRrKPFMsU6po7Abu3M3rPQeNkzNzsSf0OCE1cKsE9957b+Rn+Bn1Tefnqp1zXGjLNNPaLA0bRRKhUfDvtfqhG0QHfjq+5Iy6c4iylv9EPDhfRj2a1+qmAy9PXVWZSsCbmZe5gVGfnbOSf5pjacdg0vX7Oloahijtc3EbmtmpMQqlCvkGA+WpfPzv2gmpgVsluOKKKyI/w0+6ftxr0Wys6Wz1pAsJGDg/XqtPbyaIDoJ4rXFnjrp5M7X8J6FnP0bd7nTDdn5uOvAKUebnKhTLlfgNnI/55cnZOdZYdONox/O0Gxt1m6e4Zb5k+7kLnu+EJEKjTkgN3CpBHBsl+vUqkqg+0ELJ03OEBLwZX15rydeGkEF00N7STGumybMTgPg7IDvxoR42/7Y3E7en7mc92tTsHG2WNxMGbjro9dgyZ2LWJBrF/a79LFGo7ezj2vAUoMfDqE/OJPN9nT5h5hEbtanUwKUIhDg2SvQ7LxS3RwGwaW2Pr9BV/Ovg4vNag+rAzdDYqIaQYg+bmcSH+hCSzb/tzazpiDmj0Mf3FbXjc9NBj893HXen29fh7alPzMzLHNeGp4a2vxBl3DJf8YiLAW89x/1dOyE1cKsE8Xhw/kbYiXyYxZlEQ1du8Mrsq87NdHrTDaoDk+DSWOb2lvDejBvclijY/CflzbRlmmhtbmpoaGo7+zBw9eC83rXlzazxoecg8BuWTcKD6/VYZG4b3bj1PHx0AGi8RCH14FIEQqweXIMPc2Jmfr4gTmzdvKFxOCUxb6ZxiHJ2ruzbmwnnwTV618VEOgG3JQo2//a7jruzFxHP3bUnZ+ci0XXTQW97C8UGiQ+JDaACeq1xenBei8zn21S8UZHHXmm2znT7tu0KPakHl8I37M0Fo8Ar8UFVmYjYAbmhNDPl2dl3tDTH7s14JQFMBBjZB9WBWzajDZN8EG+Y0KYLi71Wm/+JhOZmbNpeA5kodN104LU10kRCBs6P11obIYijHduwQ5RuGcK2gYt7Xvv44GHAvR+ZzpdQTeb7qkdq4FYJLr744sjPqFbXdzE02UKJckUT6XTP3byBqQZ1CidmkjGsXl5r1cD5aIxBdeC1NitquM4NvS4DGZv/pLwZm7ZXuC7KyN5NB14DmamEIgQi0jA8Wq4o04VS9V3H0Y5t9HqURpuaNQUM4qw3CnClPQfnouf55QnJF9JKDdwqwdDQUCzP6WmwZU51ZJ+AoSnnsw0b40RCMXsvr7U6H+VD5qA68JNkksS7dpsXsvlPaj4KzPflFaKMomc3HXjNhU3OziGCr2zZoDBFpp31PFU3mIirHYN3AlUS6/4ATg4fa1gaLckBVD1WhYETkSeKyPdFZExEZkXkHhF5rYj4jmeJyDt97CY+UHfPtR7Xvyd+aZ2xefPmWJ7TqPhwdW4mgQ9zy4Y1gHtjnEzIg/PyWqudvQ+vNagO7A1mG4WQknjXdscyUSezzX+SHVBfZ0t1oFSPuXKFbKEUKULgpoNeF5lt2Ia1KWZvBqx0fbcIQd27jqsdw7xRd0v2mJxNpprI5s2bG87/JbX+zgkrvtiyiPwe8C3MruBfA8aA5wAfAq4BXujzUTc2OPcc4CpM4WUn/Nzl/pt90o6MiYkJent7Iz+nt0Fq8fx8VPwhyqay2bJvcnaOzb3ti2nPFrlgQ3fsdMF0BK4yB0i4CKqDNR2tFMsV153Mk8o0s/U3UVdk2uZ/YrZIc5MkspXJ2s4Wxmeci1vPezPh6brpYK2lvwkX2klm9fW2ZxrShZpBR0ztuPaZjTypJGSemJigtz3T0LBCMpGgeqxoAycivZhtbMrAtaq62/r97ZiNRl8gIi9S1a96PUtVb8TBSFle4F9a//20y+03quo7g/IfJ9rbFxuFMFjX2cqJqbzjOTtcl4QntbGvE4Bxl8r+4wl5cABrO1tdO13bqK/1YdSD6mBdl5FnfGZukYErlMrMFMuJyNyaaaKnLcNYncw2/3bHF+fO1jbWdbYyOTtHuaKL5n7i6PjcdGDvEjCecx+8JWXg1nW1cvT0jOO5egMXVzsG7x0FJmfnuHBj/IPG9vZ2+hpsnpxUiTAnrPQQ5QuAjcBXbeMGoKp54G3Wf/8qIo1nA1uB21T1nojPWvZY29XqamSCZBQGxRpr1O5kaFTVClHG7zkCrO1qce/4ZovVTUJjp9tpd7qLZU56nmJNV0tDPScRGgXzfVXU2auYD4EnkDna3kKTOH9fNu2k3vXaTvc2ldSSDJifSnALCSdZD7Kvw91TT+fg/OOp1vEGh3M3ATPAE0WkLQKNV1pHN+8N4CIR+RsReYuIvExEHhaBXijk885eV1Cs62pdNLK3keSH2SFmfdKYg6GprkVLyINrKLPV2fvxZoLqwPYqnPajq4brEjLq6zpbGa/r+Gz+k6wyUZXZ4X3HsdbRTQdNTcLazlbXvf8SK2CAkXm6UKLosGVOvcxxtWOAdd3u35eqJhYVyefzrOtqaxCNKdLSLHS67AkYJ1a6gbvEOh6sP6GqJeAIJgx7QZiHi8hW4LeBSRbvDF6LPwU+Brwb+BxwUES+KSJrfdB4pYjsFpHdw8PDjI6OMjw8zLFjxxgfH2dgYIDZ2VkOHDhApVJh7969wHzFg71791KpVDh9+jSzs7MMDAwwPj7OsWPHsJ83ODhINpulv7+fUqnEvn37FjzDPu7fv5/etibycxVOjI4zNDTEyMgIIyMjDA0NcXIiS3tGoFyqrtepf8a+ffsolUr09/eTzWYZHBz0JdN5Z60HzMdvy3TgwAFmZ2fZd59ZV6OFXCiZCoUChw4dYmpqapFMU1NTNM3NMpYrOMo0MTNHe1PZl0zt7e2eerJlGhgYoLlkOrMHjo0skun0tDnX19ESSqZDhw5RKDjLBJApFxjLFRbIBDA8PMypyRxdLfj+9mpl8vr2xqw6hbft3b9IptGp2SpvYWTat28f3d3drnrqbWvmwZFxR5lGp2fp62gJJZPXt1fKTQDwq0NHFsk08OAwAA8NmC7s+PHjsbQngIO/2kdLs3DfA0OLZDp28jTFUoVMpRB7e5qcnKSvvZnRbAFVXfSMgQdPsK6zlfvvvz+wTG7fnitUdcX+YQybAhe5nL/FOv+EkM9/h3X/x13OXwbsBB4JdAMbgGcBe637bgaa/NLbsWOHhsXBgwdD31uLr90xpNt27tIHx3KLzr3x63frE/71x7HQqcfBgwf1EW+/Xv/pu/cuOnfvsUndtnOXXr//eCK0P/CDft3+pl1aLlcWnfujT92qL/zErb6eE1QHY9mCbtu5Sz9/8wOLzv34wAndtnOX3jU0HuiZfvHar96l17znJwt+s/n/zff+VF/zlb2J0L3nwQndtnOX/vDeE4vOff7mB3Tbzl06Op0P/fxGOnjBJ27RF33ql4t+L5cruv1Nu/T9N/SHptsIu/Yd1207d+l9w5OLzr3r/+7VR7z9+ur/42rHNh7zLz/Sf/jGvkW/D53O6badu/Rrdw7FSk/VyPCfPzus23bu0lxhbtH5v7zuDn3Wh2+KlSawWx361DPuwYnIoI/0/Nq/Ly0RX03MJ5d8yukaVb1XVd+rqr9S1ayqjqrqDcC1GO/xGkwGZuI477zzYnnO2gaT8ROzc4mFzM477zzWdjmHkOZrIyY0B9dp5oWcJuMnZvyvRQuqg96OFkRYFCqE+bDS+q7kZK4PIdn8j+eKvpJqQtG1E2sc9DyWK9Ik/hJ63NBIB27JRBOzc1QU1ncnK7PTtz2WK1RDiRBfO7bhFn4/neD3dd5551WfezrrTDup77oeZ9zAAQPA/QH+jtfcO2kd+1yebf8+EYKv3wbOxSSXBKqfo6pTwP9Y/31SCNqBcfDgoihtKNiZfU6NYmKmmFjywcGDB01jdDJwCZaOgsbzQkESLoLqoLlJWNPhnOxhd0DrEuoI1nW1kCuWKZTmazMePHiQQqnMdKHEhoQ6+0bvejRbZF1Xa6S1aI104PZ9jeUKC3iLG40yOE1nP58iEFc7rqW91DLbbdnQWUx7PFdM7F3X44wvE1DVp0W4/X7gauBiYEEZbhHJANuBEvBAiGfbySWO3psPnLKOXSHvD4TLL788luc0yuw7nS3y8C3xrNGpx+WXX87aO+9wHGHbnX1Sne6811o0ObkWVJWxXJH13f5ylMLoYK3bCDtboL2lKbGJ+OpauJk5NvcaGpdffjnDk2Y+w6/MQdHR0kxbpsnFgytE7vga6WCN5cGp6oKkodGs/X0lI/O6Tnejfjpb5Oy++aUBcbXjKu2uVu49PuVIF1hgXOPC5ZdfTvHoOOAi8xIauOXgwUXBT63jsxzOPQnoBG5V1UKQh4rIFuB38E4uaYTHW8cwxjUw4tpmo9HI61S2wMaEOoE9e/a4jjZHpxMeYXc6yzw1W6JYrvg2rGF0sM4lhfx01ozsk1iLBs563rNnT03Hl8y7FhHXUKEtcxQ00sG6LlObMVdcuKPAWMLe8ppGg8ZcYUFoNM7tcsDo0dGLst6/HT6NE3v27Kl+P2N1IcpiqcJ0vpQaOJ/4JjAKvEhErrZ/FJF24F+s/36i9gYR6RSRS0WkUbD7L4Fm4Iuq6pqiU0uz7vc/A/4IKAJf9yNIVMS1zYbbeqH8XJnpfHKhqx07driuFxrNFljb2UKmOZnPtTovVCfzqBXG8TuyD6MDt3nH0VwxsXcNzp76jh07GM0amZOajwJbZud5x6h0G+nALTpxOmGZqwvr6+jaEYJ1NUY9zu1ywLzrydk55soLlyiczhVpbW5KpFrNjh07XJco2BVdUgPnA9Zc1yswxuhGEfmsiLwPuBt4AsYA1ntgjwXuA/7b6Zl1ySWN1r4BfFNEDovIV0XkAyLycRG5HfgiprrK/1PVweCSBUdcIz+39ULVpIcEPbj13a3kiuVFe3adzhYTCx9BrTezsNO1PUe/tEN7cC4hyqTeNdQa9XmZF3pwSb5v50XAo9lCZM+xsQfn3OlW5zsTSqwBq4BCncxT+RJzZV0gcxIeHCwevI1Z851JRAj27NlDT1uGlmZZFKJMem65HivawAGo6neAJ2MWdj8f+FtgDng98CIrhTQInglsw19yySeYz5Z8NfByzFKB64CrVfW6gLRDI86Rn5NXYY/skzI0tgcHDp5UtpCogbPnheyJ93m6tlH31xjDenDjucUFl09nk52nsJ99ukbmHTt21AxkkvUe67+vYqnCVL4U2ag39ODcDFy2yJoEIwQ2bfdB4/y7jtuDs73D+gSX8Znkvq8dO3ZUQ9H1Icqkw8H1WPEGDkBVb1HVZ6vqWlXtUNXLVfVDqrpo+15VvVFVRVWvdXnW9db5J/ig+15VfbqqnmvRbVfVC1X1paq6LwbRfMNemBkHNnS3Vg2ajXkDl8yHuW/fvmpDH512MHA9yRk4EWFDd1vVoNk4HTBEGUYHm3vbKJYrCzyp+eSW5DqB9V1tNAmMTM3red++fYzmCrRmkgld2djU085IXb3T8ZhCV410YM8fj0wvpD22BGnrm3raFrxrmA+N1socZzuGeU/9tMPgLSkjY8vgtEQhyeUJTlgVBi4FXHbZZbE966ze9kUFl22jk5Qnddlll3GWtYtAPW2TfJBsg9jc28bJRTIXEPHf6YbRgb1zQi3t6YKV3JJgmLC5SdjYs1Dmyy67rPquk0puATirr41csbxgX7jT1UzGaHpupINNveZ9npxaPHhLMiQL1vdVZ1jns4PnacfZjmHeqJ+aXijzyFS++j7ihi3Dxp42R7oAmxx2DEkCqYFbJTh8+HBsz9rc287JqcKCsNmphEOUhw8fduzs83NmXdbGBD04gLP6HIx6rsi6zlbfOx6H0cHmaqc7T9vuFDb0JGvUz+pt52RNB3T48GFOTScbDoZaoz5P2/aqotJupIO2TDPruhbvlnEqW0j+++ptZ2JmbsH88ojDHG+c7RjMdw0Lv69KRRmZLlQHlHHDlsH0Iwvf9YnJPO0tTUuymzekBm7VYOvWrbE9a1NvO8VSZUEV8tFsga7WZjoSWpe1detWNnS3WmGz+UaRdGjUxubedk5O1nV8ATv7MDpwMuonLD7O6u0I/Lwg2FQn89atWzkxmV+wLisRuj3uMp+9JprMXjrY3LswPKqqnJjMVw1BUrA9ltow5YnJ2aonbSPOdgxmB/Wu1maGa/R8OlekVNHEZLZlOLuvnZHpAqWaDM6TlmFNMkJQi9TArRKMjo7G9ix7ZFcbUjkxmY/c+TTC6OgomeYmNnS3LRhh2w3zrL5kO/vNve3kimWyhfk9rIYnZzl7jf9OIIwO7M6t1puxZU7a0BgPrmYwMTpqZE6aroNXMTyZR8TMVUWBlw429y78vqbyJWaK5SV518Cib3tzT9uCCEGc7bhKu2+hJ2X/22lj4Thgy7C5t51yRRfMbZ+czCdG1wmpgVsl6O6Ob+PCzQ5zFccnku34bP5NY1xIF+CcAIYmDKodUM1I9/hEni0BjHoYHTiFzU5Y1USS9io297YtCJs1tXYwlS8lPpiwjdiJOg9uQ3cbLREzGb10cFbvwu+r6i2fAaN+cirP5jq6cbbjWtq1Hpwtc1KGxpbB7i8W6HkqNXApQmBuznlTwzCohs1qGsWxiTznJOjB2fxv6lk42jxmGbizk+50LaNuh6/yc2XGckW2BOj4wuqgPmw2PJlnXVcr7S3J7pdVHzY7PmF2nU7am+lqy9DTllkQrhueiic06qWDTb3tjGYL1YXPdmmypGXe7BCWHXYIB8fZjm2c1duxYOBmG5yk5uBsGWyjbg/YVJWTU8mHg2uRGrhVgkpl8WaKYWF39vaor1AqM5otBPJmgsLm/6y+tgWjzeMTZp+urgTT1mG+sdu0bc8xiMxhdbC5t23RCDupzqcW9WEz27NZig5oU29b1biA6QTjkNlLB2f1tqM6n8hzYolC4L0dGdpbmqr0qnN/dfOscbZjG2f1tTEyXaBcMUljJybzNEly89rVtlzXpiZm5iiUKqkHlyI4Ojs7Y3tWW6aZs/vaOXo6B8x3AkkaOJv/89Z1Mjk7x6SV4DIcMEwYFues7aBJ4OiY8WKOTwSXOawOzlvXydDYTDVr9djELFsSDskCnLvO8Gvr+bRlY7ck3NmDLfP8yP7Y+GwsevbSwbnrDI0hS88PjZtEj6hzf14QEbau7eTBcUN3fGaOmWJ5kZ7jbMc2zu7roFzRqvd4dGyGrWs7E1vYbsuwrquVtkxTdbA4aH1n29bFL6MbUgO3SjA2Nhbr885f38UR64N8cMz2ZpLrdG3+t28w8Xub9tDYTKKhURttmWbOWdvBkVFLZqsjCkI7rA7OX9/FdL7E6VyRSkU5Mppj+4bkN6HYuraDTJNUO56Dw+O0NAvnrE3+fW/f0M3gaA5V5dR0gVyxHIvMXjqwadh6PjKa49y1HZHn/vxg+4YuHjg1Txfggo0LZY67HQNcUCfz0dM5tq1PzsjYMoiI6UeqdE2bOn9DauB8QURaROTvROQLInK3iBStTVFfHuGZTxSR74vImIjMisg9IvJaEXGdEBGR3xWRG0VkUkSyInK7iLw4LA9hsGXLllifd/6GLgatD/PwyDQAF22KfwLchs3/duvjPzKapVSuMHg6lyjdWpy/vlbmLO0tTYEMXFgdbN843wGdmMpTKFU4fwkMXEtzE+et66x2QKOFZrat7/K97i8Ktm/sYnauzMmpAg9Y9OMwcF462NLXQWumaYGBW4p3DcbQHD09Q9kaxID55hbwF3M7BrjQaj8Dp7KoJj+AqpXhwk1dDNQYdRHYujY1cH7RBXwYeAlwFnAiysNE5PcwNS2fBHwb+DjQCnwI+KrLPX8DfBd4JPAl4DPAFuA6EflAFH6C4MiRI7E+b/uGTsZn5piYKXJoJEtveyaxrXJgnv9z13XSJHBkdIajYzPMlXXJDNwFG8xoU1U5PJLlgg3dgTbfDKuD2hG2PcJfCg8OzEDGpnnoxMSiDjcp2DI/MJqtDirikNlLB01Nwvb183oePJ1bMpm3b+iiWK5wfGKWwdEczU1SDRPbiLsdg8la7Wpt5oFTOcZyRabzJbYlKHOtDBdu7GZobIZCqczg6Rxb+joST56qxUo3cDPAs4EtqnoW8PmwDxKRXoxxKgPXqupfqurfA1cCvwReICIvqrvnfOADwBimuPKrVfV1wKMwO5W/QUQ8a1rGgUsvvTTW5z1scw8A9w1Pc2gky0WbuhNdnGnz35YxXsR9w1McOpkFkvUca3HRpm6yhRIPjc9y2JI5CMLq4Jw1HbRlmugfnubAsNmk/mLr/SeNizZ188BojsnZOR6aKnHJWUvzri/caOjcf2Kae49P0d2WiWUOzo8OLtzUxf0nphk8PcNMscwlZy3Nu7Y9qf4T09x7fJILN3YtCo3G3Y7BhAov3NTNoZHp6uanD09Q5loZLtzYTbmiDI7O8Ktjk1y6RO/axoo2cKpatIojD8fwuBdg9nP+qqrurqGRB95m/fev6u55GdAGfLx2WxxVHQf+1frvq2LgzRN33313rM979LlrALjjyBj7H5rkUVvXxPr8etTy/+jz1nDX0Dh3DY3T2ty0ZI3i0eetBeD6Xw1zbGKWR23tC3R/WB1kmpu4Yusa9gyNc/eDE2xd25F4uSwbjz53DcVSha/f+SDlinLluWuXhO5Zfe1s6Wtnz9Fx9j00weXn9MUSGvWjg6vOW8vQ2Aw/OmACPlda33rSeOSWPlqahd1Hx9j30KQj3bjbsY0rz13DXUMT7B0yO20/MuC3HQS1MlxhyfjzgyM8MJpLvB+px4o2cDHjqdbxBodzN2G8xSeKSG3P0+ie6+uuSRRXXXVVrM9b09nKRZu6+dhPDzE7V+ax29fF+vx61PK/Y9taRrNFPn/LES7f2rdkIY1Lz+qhq7WZ9//gfoDAMkfRwY7z17LvwQl+cO9Jrt62NEbGpgvw3hv6ETGDi6XC1eev44ZfneCehya5+vx4ZPajg6vPN3p93w3309Oe4WFLFCHoaG3mkef08blfHGEsV2SHg57jbsc2Hn/BemaKZT7+08NcsrmH3vb4d/K2USvD+es72dzbxvtuuB9VeExMevaL1MDN4xLreLD+hKqWMPu+ZYALfN4zDOSArSKS+Kxq3BslAjz3ii2UKkpHSzNPvnhj7M+vRS3/z7rsLJoE5srKcx51dqJ0a5FpbuLZl5/NXFnZtr6Ty88JNsqNooPnXmEm5ssV5TlXxJ9o4IZNPe08/oJ1lCrKIze2LpnnCPAc6/sC+J2Y9OxHB5ef08e29Z2UKsrvXH52ovvA1eM5j5qX+emPOGvR+STaMcA1F22gvaWJUkV5zhXJtqlaGUSE337k2ZQqyobuNh6T8EC5HqmBm4fdm026nLd/XxPiHteeUkReKSK7RWT38PCwqQc4PMyxY8cYHx9nYGCA2dlZDhw4QKVSYe/evcD8R7R3714qlQodHR3Mzs4yMDDA+Pg4x44dw37e4OAg2WyW/v5+SqVSdb8m+xn2cf/+/RQKBQ4dOsTU1BTPOD/DXzzmLP7tdy/g9MnjTE1NcejQIQqFAvv373d8xr59+yiVSvT395PNZhkcHPQl044dO6rPOHrwXv7zT6/ijy7v4/cftSlWmYaGhhgZGWFkZIShoaFFMv3Dsy7ldx/WyUde9Ojqu/Yr0yMe8QhPPR04cMBRTxtbivz9k7fwuqduZwtjscrkpae3PfNCnv/IdfzTcx4e6ttzk8lLT0+7dBN/8age3vMHlzN36mgsMl1xxRWeeioW8vzdY/v4y984n2eeXYhVJi89PeOCDl7++C38y7POI1POL5LJRtT2VC9TT1szb37SRl5xzTaecg6Jtqfe3t4FMl27cYb/96QLeM3VZs4xLplq9eQKVT2jf8AgoAH+vtTgWe+0rnl5CD4OWvde5HL+Fuv8E2p+K1q/ZVzuOWadP9sPDzt27NCw2LNnT+h7lwNWOv+qK1+Glc6/6sqXYaXzr3pmZAB2q0OfujSb8jTGAJD3vGoexxPiw8vbsn+fqLtng3XudIN73Dy82HDllVcmTSJRrHT+YeXLsNL5h5Uvw0rnH5aXDGc8RKmqT1PVSwP8/UNCrNxvHS+uPyEiGWA7UAIe8HnP2Zh1eg+p6ky8rC5Gf39/0iQSxUrnH1a+DCudf1j5Mqx0/mF5yXDGDdwywk+t47Mczj0J6ARuVdXaPdgb3fPbddckiu3bty8FmcSw0vmHlS/DSucfVr4MK51/WF4y/NoZOBHpE5FLLQ+rFt8ERoEXicjVNde3A/9i/fcTdfd8ASgAf2Mt+rbvWQu8xfrvJ2Nk3xXHjycVuV0arHT+YeXLsNL5h5Uvw0rnH5aXDMthDi4SRORNgL10/krr+FIR+Q3r3zer6mdrbvl9jGH6L0yJLwBUdUpEXoExdDeKyFcxFUqei1kO8E3ga7W0VfWIiPw98FFgt4h8DZN48gJgK/BBVf1lTKI2xLp1S5t+GzdWOv+w8mVY6fzDypdhpfMPy0uG1eDBPQt4sfV3hfXbE2t++w2X+xZBVb8DPBmzsPv5wN8Cc8DrgRdZ2Tr193wMYwTvBf4CeCWmJuZLVPWNoSQKgZmZxKf5EsVK5x9WvgwrnX9Y+TKsdP5hecmw4j04Vb024PXXAdc1OH8Lpr5lkGd+F1Nw+YyhqWllj1VWOv+w8mVY6fzDypdhpfMPy0uG5cNJikhoaUmu9M5SYKXzDytfhpXOP6x8GVY6/7C8ZBCHqFuKMwQROQUcDXn7BkySzErFSucfVr4MK51/WPkyrHT+4czIsE1VF9UTTA3cKoGI7FbVq72vXJ5Y6fzDypdhpfMPK1+Glc4/LC8Z0hBlihQpUqRYlUgNXIoUKVKkWJVIDdzqwafPNAMRsdL5h5Uvw0rnH1a+DCudf1hGMqRzcClSpEiRYlUi9eBSpEiRIsWqRGrgUqRIkSLFqkRq4FKkSJEixapEauBWMERkq4h8XkSOi0hBRAZF5MPWbgbLAiLyAhH5mIj8QkSmRERF5Ese9zxRRL4vImMiMisi94jIa0Wkean4tvhYLyIvF5Fvi8hhi5dJEblZRP5SRBzbz3Lhv4af94rIT0TkQYufMRG5S0TeISLrXe5ZVjLUQ0T+zPqWVERe7nLN74rIjZbOsiJyu4i8eKl5tXgZrOG3/u+Eyz3LTgci8jSrPZyw+pzjIvIDEVlU3nA58J8mmaxQiMiFwK3AJuB/gX7gscBTMBuxXqOqTruMLylE5G5MEews8BBm54cvq+qfuVz/e8C3MLu8fw2zo8NzsHZ0UNUXLgHbNi+vwmyRNAz8DBgCNgN/gNmt/VvAC2uLcC8n/mt4KgJ7gQPACGYj3scDVwPHgcer6oM11y87GWohIucC+4FmoBt4Rd2OIYjI3wAfA05jZKjf5WPJCqFb/AwCa4APO5zOquoH6q5fdjoQkfcBf49px9djqpVsBHYAP67djHrZ8K+q6d8K/AN+ACjwt3W//7v1+yfPNI8WP08BHgYIcK3F25dcru3FdMAF4Oqa39sxxlwxuzosFe9PxTTKprrfz8IYOwWev1z5r6Xv8vu7LZ7+c7nLUMOHAD8GBoD3W/y8vO6a8zEd62ng/Jrf1wKHrXuesMR8DwKDPq9ddjoAXmHRvQ5odTjfshz5PyMfafoXUWlwofWRHHHofHsw3lIO6DrTvNbx5mXgXmad/y+Hc0+1zv38TMth8fMWi5+PrUT+LZ6usHj60UqRAfg7oAI8CXini4H7J+v3dwX5xhLmO4iBW1Y6ANosg3XUybgtZ/5X/HY5v6Z4inX8oapWak+o6rSI3AI8AxOG+slSMxcBT7WONzicuwmYAZ4oIm2qWlg6thwxZx1LNb+tJP7BeKcA99T8tmxlEJGHA+8BPqKqN4nIU10ubSTD9XXXLCXaROTPgPMwA9B7gJtUtVx33XLTwdMxocgPAxUR+R3gkRgv+Q5dvKnzsuE/NXArE5dYx4Mu5w9hDNzFrCwD5yqXqpZE5AhwGXABcN9SMlYLEclgNreFhY14WfMvIm/EzFn1YebffgPTyb6n5rJlKYP1zr+ICQ2/xePyRjIMi0gO2Coinaq6lLtznoWRoRZHROSlqvrzmt+Wmw4eYx3zwF0Y41aFiNwEvEBVT1k/LRv+0yzKlYk+6zjpct7+fU3yrMSKlSLXezCN/Puq+oOa35c7/28E3gG8FmPcbgCeUdMxwfKV4R+BRwMvUdVZj2v9ytDncj4JfAF4GsbIdQGXA5/CzBdeLyJX1Fy73HSwyTr+PSa8+JuYqZBHAT/EhIu/UXP9suE/NXApUgSAiLwGeAMma/XPzzA7gaCqZ6mqYDrZP8CMoO8SkavOLGeNISKPw3htH3QIh60IqOq7VPWnqnpSVWdU9Veq+ipMUlgHZj5xucK2EyXguap6s6pmVXU/8PuYrMoni8gTzhiHLkgN3MqE1wjU/n0ieVZixbKWy0o9/wgm3f4pqjpWd8my5t+G1cl+GxPGXg/8d83pZSWDFZr8b0y46+0+b/Mrg5uHsZT4pHV8Us1vy0oHNXTuUtXB2hNWiNeOYjzWOi4b/lMDtzJxv3W82OX8w6yj2xzdcoWrXFZHtx0zinxgKZmy6L8Ws67qVxjj5rQ4d9ny7wRVPYox1peJyAbr5+UmQ7fFy8OBfO0CaUy4FeAz1m8ftv7fSIazMSHCh5Z4/s0Ndni4q+a35aYDm58Jl/Pj1rGj7vozzn9q4FYmfmYdn1FfTUNEeoBrMJlKty01YxHxU+v4LIdzTwI6gVvPQPbeTuBDwN0Y4zbicumy5N8DW6yjncm33GQoAJ9z+bvLuuZm6/92+LKRDL9dd82ZxuOtY21nv9x08BPM3NsjXKr32EknR6zj8uF/qdZSpH/x/rFCFnrX8XYt3gu9T7EMFojW0H67RXc3sM7j2uXI/8VAn8PvTcwv9L5lOcvQQLZ34rwObjvLaKE3xvtctCYVk2ByyOLnLctZB5hqSQq8ru73Z2DWJY7b39ly4j8t1bVC4VCq6z7gcZg1cgeBJ+ryKNX1POB51n/PAp6JGa3+wvptVGvKJlnXfxPTQX0VU+LnuVglfoA/1CX6aK26hddhvJuP4TxnM6iq19Xc8zyWCf8WP68F/g3j5RzBdPqbgSdjkkxOAE9T1QPLVQY3iMg7MWFKp1Jdfwt8lGVQqsvi8w2YNWBHgWlMsYbfwXT63wd+X1WLNfc8j2WkAxHZiulvzsV4dHdhBhLPY95gfWvZ8b+Uo4D0L94/62P7AqZWYhHTeD4MrD3TvNXw+E6rAbj9DTrccw2m0Y8Ds5i6g68DmpcZ7wrcuFz5t3h5JPBxTHh1FDP3MQncacnn6JUuJxl86OflLuefA/wcY1BylswvPgN8Phn4CibzdgJTJOAU8CPMekpZCTrALPb+mNXPFK3v6dvAY5cr/6kHlyJFihQpViXSJJMUKVKkSLEqkRq4FClSpEixKpEauBQpUqRIsSqRGrgUKVKkSLEqkRq4FClSpEixKpEauBQpUqRIsSqRGrgUKVKkSLEqkRq4FCl+DSEiL7EKFL/kTPOSIkVSSHf0TpFihcOqrB8EL02EkRQplhlSA5cixcrHuxx+ey1m362PsHibk7sxdSlvw5R5S5FiVSIt1ZUixSqEiAwC24DtWrdJZYoUvy5I5+BSpPg1hNscnIgMWn/dIvIhEXlQRGZF5G6rQjwikhGRt4rIIRHJi8iAtdu5G61nisj3RWRURArW9e8XkTWJCpni1x5piDJFihT1aMFUul+H2YqpFfhj4Fsi8gzgrzFbM12P2fPrhcDHROSUqn6t9kEi8g5M1f8xYBcwAjwKeCPwbBF5gqpOLYVQKX79kBq4FClS1GMLsBe4Vq1dl0Xki5j9zL4BDACPVNUJ69y/Y7aCeRNm7zWs35+CMW6/BJ5tX2+dewlmq6d3YbZQSZEidqQhyhQpUjjhtbZxA1DVX2ASU9YCO2uNlao+ANwCPFJEmmue8Rrr+Ira6617rsMku/xpArynSAGkHlyKFCkWY0JVBxx+P47ZxXmPw7ljmP7kLOvfAE/AbO75QhF5ocM9rcBGEVmvy2D3+RSrD6mBS5EiRT0mXX4vAaiq0/mSdWyp+W09po95hwe9biA1cCliR2rgUqRIkRQmgSZVXXemGUnx64l0Di5FihRJ4TZgrYhcdqYZSfHridTApUiRIil8yDp+RkS21J8UkS4RefwS85Ti1whpiDJFihSJQFV/IiJvAv4NOCQi38dkYnZjqqw8GbgZeNaZ4zLFakZq4FKkSJEYVPW9InILZsnAbwC/h5mbOwZ8GvifM8heilWOtBZlihQpUqRYlUjn4FKkSJEixapEauBSpEiRIsWqRGrgUqRIkSLFqkRq4FKkSJEixapEauBSpEiRIsWqRGrgUqRIkSLFqkRq4FKkSJEixapEauBSpEiRIsWqRGrgUqRIkSLFqsT/D3FlXnOcAep0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(linestyle='dotted')\n",
    "t = np.linspace(0,20*pi,5000)\n",
    "x = np.sin(t)\n",
    "plt.plot(t, x)\n",
    "plt.xlabel('Time', fontsize = 20)\n",
    "plt.ylabel('Voltage', fontsize = 20)\n",
    "#plt.legend(['Actual function' , 'Learned function', 'Training Data'], prop={'size': 16})\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "#plt.savefig(\"Results/test2_input.png\", dpi = 300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed750350>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "dx = fd._differentiate(x, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed6e83d0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mdx = np.abs(dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed5f1250>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, mdx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(y, t):\n",
    "    dydt = np.cos(t) - 0.5*np.abs(np.cos(t))*y - 2*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y0 = 0\n",
    "y = odeint(model, y0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed57bed0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed5bb290>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed4a0210>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dy = fd._differentiate(y, t)\n",
    "plt.plot(t, dy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "my = np.abs(y)\n",
    "my = my.reshape(-1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38ed3ade90>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = y.reshape(-1,)\n",
    "dy = dy.reshape(-1,)\n",
    "t1 = dx\n",
    "t2 = mdx*y\n",
    "t3 = dx*my\n",
    "terms = t1-0.5*t2-2*t3\n",
    "plt.plot(t,terms)\n",
    "plt.plot(t, dy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.stack((y, x, dx, mdx, my), axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(x0)' = 1.000 x2 + -0.500 x0 x3 + -1.999 x2 x4\n",
      "(x1)' = 1.000 x2\n",
      "(x2)' = -1.000 x1\n",
      "(x3)' = -16.481 1 + -34.102 x0 + 10.088 x1 + -3.174 x2 + 16.000 x3 + 34.380 x4 + -28.383 x0^2 + 58.886 x0 x1 + 17.832 x0 x2 + 36.360 x0 x3 + -41.138 x0 x4 + -11.344 x1^2 + -11.414 x1 x2 + -12.254 x1 x3 + 23.778 x1 x4 + 3.063 x2 x3 + 8.717 x2 x4 + -35.932 x3 x4 + -28.383 x4^2\n",
      "(x4)' = -332.875 1 + -16.006 x0 + 5.227 x1 + -1.170 x2 + 13.486 x3 + 29.008 x4 + -0.823 x0^2 + 0.828 x0 x1 + 1.517 x0 x2 + 16.149 x0 x3 + -17.505 x0 x4 + 321.379 x1^2 + -1.068 x1 x2 + -5.492 x1 x3 + 9.226 x1 x4 + 159.955 x2^2 + 1.455 x2 x3 + 3.292 x2 x4 + 159.955 x3^2 + -30.258 x3 x4 + -0.823 x4^2\n"
     ]
    }
   ],
   "source": [
    "model = ps.SINDy()\n",
    "model.fit(X,t)\n",
    "model.print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kkk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 1\n",
    "c2 = -0.500\n",
    "c3 = -1.999\n",
    "def test_model(y, t):\n",
    "    dydt = c1*np.cos(t) + c2*np.abs(np.cos(t))*y + c3*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "ytest_0 = 0\n",
    "y_test = odeint(test_model, ytest_0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(linestyle='dotted')\n",
    "plt.plot(x, y, 'r')\n",
    "plt.plot(x, y_test, linewidth=2, linestyle=':')\n",
    "plt.xlabel('Voltage', fontsize = 20)\n",
    "plt.ylabel('Displacement', fontsize = 20)\n",
    "plt.legend(['Ground truth' , 'Learned relation'], loc='upper left', prop={'size': 12})\n",
    "plt.xticks(fontsize=20, rotation='45')\n",
    "plt.yticks(fontsize=20)\n",
    "plt.savefig(\"Pics/Slide10.png\", dpi = 1000, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.25, -1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,\n",
       "         1.  ,  1.25]),\n",
       " [Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, '')])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = c1*t1+c2*t2+c3*t3\n",
    "plt.plot(t,dy, 'b')\n",
    "plt.plot(t,test, '--r')\n",
    "plt.grid(linestyle='dotted')\n",
    "plt.xlabel('Time', fontsize = 20)\n",
    "plt.ylabel('Time derivative of disp.', fontsize = 18)\n",
    "plt.legend(['Ground truth' , 'Learned dynamics'], prop={'size': 12})\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "#plt.savefig(\"Results/test2_Output.jpg\", dpi = 300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test SINDy:  1.0625824645764056e-05 %\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape(-1,1)\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = np.mean((y_test - y)**2)/np.mean(y**2)\n",
    "print(\"Relative Error Test SINDy: \", relative_error_test*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1=t1.reshape(-1,1)\n",
    "t2=t2.reshape(-1,1)\n",
    "t3=t3.reshape(-1,1)\n",
    "Y = np.concatenate((t1, t2, t3), axis=1)\n",
    "Y.shape\n",
    "dy = dy.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(Y, dy, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.97362112 -0.52313496 -1.88256334]]\n",
      "[0.00017209]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "clf = Ridge(alpha=1.0)\n",
    "clf.fit(X_train, y_train)\n",
    "print(clf.coef_)\n",
    "print(clf.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kkk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 0.973\n",
    "c2 = -0.523\n",
    "c3 = -1.882\n",
    "def test_model(y, t):\n",
    "    dydt = c1*np.cos(t) + c2*np.abs(np.cos(t))*y + c3*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "ytest_0 = 0\n",
    "y_test = odeint(test_model, ytest_0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test Ridge:  0.004150430852239582 %\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape(-1,1)\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = np.mean((y_test - y)**2)/np.mean(y**2)\n",
    "print(\"Relative Error Test Ridge: \", relative_error_test*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "linreg = LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.99972998, -0.50020186, -1.99882165]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.04304442e-06])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#kkk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 0.999\n",
    "c2 = -0.500\n",
    "c3 = -1.998\n",
    "def test_model(y, t):\n",
    "    dydt = c1*np.cos(t) + c2*np.abs(np.cos(t))*y + c3*np.cos(t)*np.abs(y)\n",
    "    return dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "ytest_0 = 0\n",
    "y_test = odeint(test_model, ytest_0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test Lin reg:  2.3155479806240086e-05 %\n"
     ]
    }
   ],
   "source": [
    "y = y.reshape(-1,1)\n",
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = np.mean((y_test - y)**2)/np.mean(y**2)\n",
    "print(\"Relative Error Test Lin reg: \", relative_error_test*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(Y, dy, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.utils\n",
    "import torch.utils.data\n",
    "from torch.utils.data import DataLoader\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Type of optimizer (ADAM or LBFGS)\n",
    "opt_type = \"LBFGS\"\n",
    "# Random Seed for dataset generation\n",
    "sampling_seed = 78\n",
    "torch.manual_seed(sampling_seed)\n",
    "\n",
    "# Number of training samples\n",
    "n_samples = 5000\n",
    "\n",
    "x = X_train\n",
    "y = y_train\n",
    "y = y.reshape(-1,1)\n",
    "\n",
    "x = x.astype(np.float32)\n",
    "y = y.astype(np.float32)\n",
    "\n",
    "x = torch.from_numpy(x)\n",
    "y = torch.from_numpy(y)\n",
    "\n",
    "batch_size = n_samples\n",
    "training_set = DataLoader(torch.utils.data.TensorDataset(x, y), batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralNet(nn.Module):\n",
    "\n",
    "    def __init__(self, input_dimension, output_dimension, n_hidden_layers, neurons):\n",
    "        super(NeuralNet, self).__init__()\n",
    "        # Number of input dimensions n\n",
    "        self.input_dimension = input_dimension\n",
    "        # Number of output dimensions m\n",
    "        self.output_dimension = output_dimension\n",
    "        # Number of neurons per layer \n",
    "        self.neurons = neurons\n",
    "        # Number of hidden layers \n",
    "        self.n_hidden_layers = n_hidden_layers\n",
    "        # Activation function \n",
    "        self.activation = nn.Tanh()\n",
    "        \n",
    "        self.input_layer = nn.Linear(self.input_dimension, self.neurons)\n",
    "        self.hidden_layers = nn.ModuleList([nn.Linear(self.neurons, self.neurons) for _ in range(n_hidden_layers)])\n",
    "        self.output_layer = nn.Linear(self.neurons, self.output_dimension)\n",
    "\n",
    "    def forward(self, x):\n",
    "        # The forward function performs the set of affine and non-linear transformations defining the network \n",
    "        # (see equation above)\n",
    "        x = self.activation(self.input_layer(x))\n",
    "        for k, l in enumerate(self.hidden_layers):\n",
    "            x = self.activation(l(x))\n",
    "        return self.output_layer(x)\n",
    "\n",
    "def NeuralNet_Seq(input_dimension, output_dimension, n_hidden_layers, neurons):\n",
    "    modules = list()\n",
    "    modules.append(nn.Linear(input_dimension, neurons))\n",
    "    modules.append(nn.Tanh())\n",
    "    for _ in range(n_hidden_layers):\n",
    "        modules.append(nn.Linear(neurons, neurons))\n",
    "        modules.append(nn.Tanh())\n",
    "    modules.append(nn.Linear(neurons, output_dimension))\n",
    "    model =  nn.Sequential(*modules)\n",
    "    return model\n",
    "\n",
    "  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Model definition\n",
    "my_network = NeuralNet(input_dimension=x.shape[1], output_dimension=y.shape[1], n_hidden_layers=4, neurons=20)\n",
    "# my_network = NeuralNet_Seq(input_dimension=x.shape[1], output_dimension=y.shape[1], n_hidden_layers=4, neurons=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.1218],\n",
      "        [ 0.2674],\n",
      "        [-0.8393],\n",
      "        ...,\n",
      "        [-0.7881],\n",
      "        [ 0.5845],\n",
      "        [ 0.7786]], grad_fn=<AddmmBackward0>)\n"
     ]
    }
   ],
   "source": [
    "def init_xavier(model, retrain_seed):\n",
    "    torch.manual_seed(retrain_seed)\n",
    "    def init_weights(m):\n",
    "        if type(m) == nn.Linear and m.weight.requires_grad and m.bias.requires_grad:\n",
    "            g = nn.init.calculate_gain('tanh')\n",
    "            torch.nn.init.xavier_uniform_(m.weight, gain=g)\n",
    "            #torch.nn.init.xavier_normal_(m.weight, gain=g)\n",
    "            m.bias.data.fill_(0)\n",
    "    model.apply(init_weights)\n",
    "\n",
    "# Random Seed for weight initialization\n",
    "retrain = 128\n",
    "# Xavier weight initialization\n",
    "init_xavier(my_network, retrain)\n",
    "# Model definition\n",
    "\n",
    "# Predict network value of x\n",
    "print(my_network(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "if opt_type == \"ADAM\":\n",
    "    optimizer_ = optim.Adam(my_network.parameters(), lr=0.001)\n",
    "elif opt_type == \"LBFGS\":\n",
    "    optimizer_ = optim.LBFGS(my_network.parameters(), lr=0.1, max_iter=1, max_eval=50000, tolerance_change=1.0 * np.finfo(float).eps)\n",
    "else:\n",
    "    raise ValueError(\"Optimizer not recognized\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(model, training_set, num_epochs, optimizer, p, verbose=True):\n",
    "    history = list()\n",
    "    \n",
    "    # Loop over epochs\n",
    "    for epoch in range(num_epochs):\n",
    "        if verbose: print(\"################################ \", epoch, \" ################################\")\n",
    "\n",
    "        running_loss = list([0])\n",
    "        \n",
    "        # Loop over batches\n",
    "        for j, (x_train_, u_train_) in enumerate(training_set):\n",
    "            \n",
    "            def closure():\n",
    "                # zero the parameter gradients\n",
    "                optimizer.zero_grad()\n",
    "                # forward + backward + optimize\n",
    "                u_pred_ = model(x_train_)\n",
    "                # Item 1. below\n",
    "                loss = torch.mean((u_pred_.reshape(-1, ) - u_train_.reshape(-1, ))**p)\n",
    "                # Item 2. below\n",
    "                loss.backward()\n",
    "                # Compute average training loss over batches for the current epoch\n",
    "                running_loss[0] += loss.item()\n",
    "                return loss\n",
    "            \n",
    "            # Item 3. below\n",
    "            optimizer.step(closure=closure)\n",
    "            \n",
    "        print('Loss: ', (running_loss[0] / len(training_set)))\n",
    "        history.append(running_loss[0])\n",
    "\n",
    "    return history\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "################################  0  ################################\n",
      "Loss:  0.9703947901725769\n",
      "################################  1  ################################\n",
      "Loss:  0.9239943623542786\n",
      "################################  2  ################################\n",
      "Loss:  0.7433448433876038\n",
      "################################  3  ################################\n",
      "Loss:  0.57215416431427\n",
      "################################  4  ################################\n",
      "Loss:  0.4557439088821411\n",
      "################################  5  ################################\n",
      "Loss:  0.38543784618377686\n",
      "################################  6  ################################\n",
      "Loss:  0.3384777307510376\n",
      "################################  7  ################################\n",
      "Loss:  0.30370694398880005\n",
      "################################  8  ################################\n",
      "Loss:  0.27632176876068115\n",
      "################################  9  ################################\n",
      "Loss:  0.25384774804115295\n",
      "################################  10  ################################\n",
      "Loss:  0.23480308055877686\n",
      "################################  11  ################################\n",
      "Loss:  0.21821269392967224\n",
      "################################  12  ################################\n",
      "Loss:  0.20339186489582062\n",
      "################################  13  ################################\n",
      "Loss:  0.18983276188373566\n",
      "################################  14  ################################\n",
      "Loss:  0.17714014649391174\n",
      "################################  15  ################################\n",
      "Loss:  0.1649923473596573\n",
      "################################  16  ################################\n",
      "Loss:  0.15311656892299652\n",
      "################################  17  ################################\n",
      "Loss:  0.14127612113952637\n",
      "################################  18  ################################\n",
      "Loss:  0.1292744278907776\n",
      "################################  19  ################################\n",
      "Loss:  0.11698950827121735\n",
      "################################  20  ################################\n",
      "Loss:  0.10444872826337814\n",
      "################################  21  ################################\n",
      "Loss:  0.09174816310405731\n",
      "################################  22  ################################\n",
      "Loss:  0.07888457179069519\n",
      "################################  23  ################################\n",
      "Loss:  0.06721466034650803\n",
      "################################  24  ################################\n",
      "Loss:  0.057769645005464554\n",
      "################################  25  ################################\n",
      "Loss:  0.04898908734321594\n",
      "################################  26  ################################\n",
      "Loss:  0.04423453286290169\n",
      "################################  27  ################################\n",
      "Loss:  0.04013420268893242\n",
      "################################  28  ################################\n",
      "Loss:  0.035911716520786285\n",
      "################################  29  ################################\n",
      "Loss:  0.031590670347213745\n",
      "################################  30  ################################\n",
      "Loss:  0.027050018310546875\n",
      "################################  31  ################################\n",
      "Loss:  0.0224648118019104\n",
      "################################  32  ################################\n",
      "Loss:  0.018007881939411163\n",
      "################################  33  ################################\n",
      "Loss:  0.01409096084535122\n",
      "################################  34  ################################\n",
      "Loss:  0.010938755236566067\n",
      "################################  35  ################################\n",
      "Loss:  0.008544622920453548\n",
      "################################  36  ################################\n",
      "Loss:  0.006826077122241259\n",
      "################################  37  ################################\n",
      "Loss:  0.005502546671777964\n",
      "################################  38  ################################\n",
      "Loss:  0.004532758146524429\n",
      "################################  39  ################################\n",
      "Loss:  0.003738229861482978\n",
      "################################  40  ################################\n",
      "Loss:  0.003215470816940069\n",
      "################################  41  ################################\n",
      "Loss:  0.002794420812278986\n",
      "################################  42  ################################\n",
      "Loss:  0.0024034129455685616\n",
      "################################  43  ################################\n",
      "Loss:  0.002098704921081662\n",
      "################################  44  ################################\n",
      "Loss:  0.0018463701708242297\n",
      "################################  45  ################################\n",
      "Loss:  0.001639230060391128\n",
      "################################  46  ################################\n",
      "Loss:  0.0014683966292068362\n",
      "################################  47  ################################\n",
      "Loss:  0.0013220771215856075\n",
      "################################  48  ################################\n",
      "Loss:  0.00119783915579319\n",
      "################################  49  ################################\n",
      "Loss:  0.0010890155099332333\n",
      "################################  50  ################################\n",
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      "################################  51  ################################\n",
      "Loss:  0.0008954761433415115\n",
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      "Loss:  0.0007685388554818928\n",
      "################################  54  ################################\n",
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      "################################  55  ################################\n",
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      "################################  56  ################################\n",
      "Loss:  0.0006220539216883481\n",
      "################################  57  ################################\n",
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      "################################  61  ################################\n",
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      "################################  64  ################################\n",
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      "################################  66  ################################\n",
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      "################################  75  ################################\n",
      "Loss:  9.876720287138596e-05\n",
      "################################  76  ################################\n",
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      "################################  77  ################################\n",
      "Loss:  7.704040763201192e-05\n",
      "################################  78  ################################\n",
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      "Loss:  6.171818677103147e-05\n",
      "################################  80  ################################\n",
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      "################################  81  ################################\n",
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      "################################  82  ################################\n",
      "Loss:  4.7499339416390285e-05\n",
      "################################  83  ################################\n",
      "Loss:  4.419839387992397e-05\n",
      "################################  84  ################################\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loss:  4.1423874790780246e-05\n",
      "################################  85  ################################\n",
      "Loss:  3.911456587957218e-05\n",
      "################################  86  ################################\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Loss:  6.223858122211823e-07\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 1000\n",
    "history = fit(my_network, training_set, n_epochs, optimizer_, p=2, verbose=True )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3885c6ea90>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(True, which=\"both\", ls=\":\")\n",
    "plt.plot(np.arange(1,n_epochs+1), np.log10(history), label=\"Train Loss\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = X_test.astype(np.float32)\n",
    "X_test = torch.from_numpy(X_test)\n",
    "\n",
    "y_test = y_test.astype(np.float32)\n",
    "y_test = torch.from_numpy(y_test)\n",
    "\n",
    "y_test_pred = my_network(X_test).reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test = y_test.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relative Error Test DNN:  0.0004834499122807756 %\n"
     ]
    }
   ],
   "source": [
    "# Compute the relative L2 error norm (generalization error)\n",
    "relative_error_test = torch.mean((y_test_pred - y_test)**2)/torch.mean(y_test**2)\n",
    "print(\"Relative Error Test DNN: \", relative_error_test.detach().numpy()*100, \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1250, 1])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1250, 1])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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