study_flat.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "niter = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {},
    "tags": []
   },
   "outputs": [],
   "source": [
    "%autoreload 2\n",
    "import ajcs\n",
    "import sqra\n",
    "import optim\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "nx = 5\n",
    "ny = 5\n",
    "\n",
    "\n",
    "U = np.zeros((ny,nx))\n",
    "s = sqra.sqra2d(U)\n",
    "s.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "nt = 3\n",
    "dt = 1\n",
    "ts = ([dt] * nt)\n",
    "\n",
    "o=optim.SqraOptim(s, ts, penalty = 0.001, nonautonomous=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 23.9 s, sys: 223 ms, total: 24.2 s\nWall time: 37 s\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": " final_simplex: (array([[0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       ...,\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.]]), array([-0.01652403, -0.01652389, -0.01652384, -0.01652384, -0.01652384,\n       -0.01652384, -0.01652381, -0.01652381, -0.01652381, -0.01652381,\n       -0.0165238 , -0.0165238 , -0.0165238 , -0.0165238 , -0.01652378,\n       -0.01652378, -0.01652378, -0.01652378, -0.01652377, -0.01652377,\n       -0.01652377, -0.01652377, -0.01652377, -0.01652377, -0.01652377,\n       -0.01652377, -0.01652373, -0.01652373, -0.01652373, -0.01652373,\n       -0.01652373, -0.0165237 , -0.0165237 , -0.0165237 , -0.0165237 ,\n       -0.01652367, -0.01652367, -0.01652367, -0.01652367, -0.01652367,\n       -0.01652366, -0.01652364, -0.01652364, -0.01652364, -0.01652364,\n       -0.01652363, -0.01652363, -0.01652363, -0.01652363, -0.01652361,\n       -0.01652361, -0.01652361, -0.01652361, -0.01652361, -0.01652361,\n       -0.01652361, -0.01652361, -0.01652358, -0.01652358, -0.01652358,\n       -0.01652358, -0.01652355, -0.01652355, -0.01652355, -0.01652355,\n       -0.01652355, -0.01652355, -0.01652355, -0.01652355, -0.01652354,\n       -0.01652354, -0.01652353, -0.01652353, -0.01652353, -0.01652353,\n       -0.01652353]))\n           fun: -0.016524032890056883\n       message: 'Maximum number of iterations has been exceeded.'\n          nfev: 90\n           nit: 10\n        status: 2\n       success: False\n             x: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n       0., 0., 0., 0., 0., 0., 0.])"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "%time o.optimize(niter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "vscode": {}
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x576 with 5 Axes>",
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1GJzRx7D4nGEYXcVclIZhGEZRoggRSzIx+jLZ4nPp9huGYcQpxWkCvbJ+goiME5FnRWSRiCwUka9624eIyJMi8r737+DeGI9hGEYpoQrhWFnSqxToLQsuAnxDVd8Ukf7AXBF5ErgYeFpVbxCRa4BrgG/30pgKHsu4NAwjFxQhUoLrwfXKFavqelV903u/C1gMjAHOAO7yDrsL+HhvjMcwDKOUUCASK0t6lQK9HoMTkQnADGA2MFJV13u7NgAje3s8xYRlXBqGkRaVkpwm0Ks2q4j0A/4GXKWqO/37VFVxPzTStbtMROaIyJxoQ2MvjNQwDKN4UCCigaRXLojIySKyRESWemGk1P1VIvKgt3+2Z8DE933H275ERE5qr08RudLbpiIyrEsX7NFrFpyIVODE7V5V/bu3eaOIjFLV9SIyCtiUrq2q3gLcAlC1+7i0ImgkY/E5wzDiOBdlx+wZESkDbgZOANYAb4jILFVd5DvsEmC7qk4SkfOBnwPnicgU4HxgP2A08JSI7OW1ydTny8AjwHOdu8q29FYWpQC3A4tV9UbfrlnARd77i4B/9cZ4DMMwSgnFuSj9rxw4BFiqqstVNQQ8gMub8OPPo3gYOM573p8BPKCqQVVdASz1+svYp6q+paoru3alyfSWBXcEcCGwQETmedu+C9wAPCQilwCrgHN7aTwlh8XnDKOEUTqTRTkGWO37vAY4NNMxqhoRkXpgqLf9tZS2Y7z37fXZbfSKwKnqS5BxluFxvTEGwzCMUiWDi3KYiMzxfb7FCwcVDVbJpASx+JxhlBZxF2UKW1R1ZpZma4Fxvs9jvW3pjlkjIuXAQGBrO23b67PbKL2Zf4ZhGCVIVANJrxx4A5gsIhNFpBKXNDIr5Rh/HsXZwDNeRvws4Hwvy3IiMBl4Pcc+uw2z4AyLzxlGkaMK0Q5mUXoxtSuBJ4Ay4A5VXSgi1wFzVHUWLnnwHhFZCmzDCRbecQ8Bi3CVrK5Q1Si46QCpfXrbvwJ8C9gNmC8ij6rqpV25bhM4wzCMokc6LHAAqvoo8GjKth/43rcA52Roez1wfS59ettvAm7q8CCzYAJnJGHxOcMoPhRb8NQwDMMoRhSiJnCGkYzF5wyj8NFOuigLHRM4wzCMEkBLsMihCZyRMxafM4zCRBViZsEZhmEYxUg0ZjE4w8gZi88ZRmGgiFlwhmEYRnFSgiE4Ezije7D4nGH0YRTUXJSGYRhGMRIzgTOM7sHic4bRd1BAbaK3YRiGUXSYi9IwegaLzxlGvhETOMMwDKMIMQvOMHoHi88ZRh4owXkCJnCGYRilgCWZGEbvYvE5w+gFFDAXpWEYhlGM2GoChpFnLD5nGD2EWXCGYRhG0aEgsXwPovcxgTP6LNnic+n2G4aRCSnJJJPSWz/BMAyjFImlvHJARE4WkSUislRErkmzv0pEHvT2zxaRCb593/G2LxGRk9rrU0Qmen0s9fqs7PzFOsyCMwoGy7g0jE7SiSxKESkDbgZOANYAb4jILFVd5DvsEmC7qk4SkfOBnwPnicgU4HxgP2A08JSI7OW1ydTnz4Ffq+oDIvJHr+8/dO6CHWbBGYZhlAASS37lwCHAUlVdrqoh4AHgjJRjzgDu8t4/DBwnIuJtf0BVg6q6Aljq9Ze2T6/NR7w+8Pr8eCcvNYFZcEbBYhmXhtGjjAFW+z6vAQ7NdIyqRkSkHhjqbX8tpe0Y7326PocCO1Q1kub4TmMCZxiGUQJIWxflMBGZ4/t8i6re0otD6nFM4IyiwOJzhpEFJV1iyRZVnZml1VpgnO/zWG9bumPWiEg5MBDY2k7bdNu3AoNEpNyz4tKdq8P0agxORMpE5C0RecT73O1ZM4ZhGEZbRJNfOfAGMNl7TlfikkZmpRwzC7jIe3828Iyqqrf9fC/LciIwGXg9U59em2e9PvD6/FdnrzVOb1twXwUWAwO8z92eNWMYYPE5w2hDByd6ezG1K4EngDLgDlVdKCLXAXNUdRZwO3CPiCwFtuEEC++4h4BFQAS4QlWjAOn69E75beABEfkp8JbXd5foNYETkbHAacD1wNd9WTOf9A65C/gRJnCGYRjdimjaGFy7qOqjwKMp237ge98CnJOh7fW45327fXrbl+OyLLuN3rTgfgN8C+jvfe6RrBnDSMXic4ZRmqW6eiUGJyKnA5tUdW4n218mInNEZE60obGbR2cYhlECaMqrBOgtC+4I4GMicipQjYvB/ZYcs2a81NVbAKp2H1cifxqjp7D4nFFylGix5V6x4FT1O6o6VlUn4IKQz6jqp+iBrBnDMAyjLZ2oZFLw5HseXLdnzRhGR7D4nGEUL70ucKr6HPCc977bs2YMwzCMFErURZlvC84w+hQWnzOKFhM4wzAMo9gQzIIzDMOHxeeMoiH38lxFhQmcYRhGKWAWnGEYmbD4nFHImIvSMAzDKD5KqHqJHxM4w+gEFp8zCg2z4AzDMIyixATOMIxOYfE5oy/TgUVOiwoTOMMwjFLABM4wjK5i8TmjL2IuSsMwDKP4sFqUhmH0BBafM/oE5qI0DMMwihGz4AzD6FEsPte7TP7K7KTPy355eE7ttCzZ3AmEW98v/WSyFX7Uly5LvF97TPIa0v52mvK0TdpXlrIv4tvXHctSl6iLsldW9DYMwzDyjKa8uoCIDBGRJ0Xkfe/fwRmOu8g75n0Ruci3/SARWSAiS0XkJhGRbP2KyD4i8qqIBEXk6lzHaRacYeQRi8/1LO/fdGjKltzMGIlKcquK1vepfxc91tcupXt/O4lm2Zfarjzzvs7QA8vlXAM8rao3iMg13udvJ51TZAjwQ2AmTlLnisgsVd0O/AH4PDAbeBQ4GXgsS7/bgK8AH+/IIM2CMwzDKHYUJKZJry5yBnCX9/4u0gvPScCTqrrNE7UngZNFZBQwQFVfU1UF7va1T9uvqm5S1TcAn2O3fcyCM4w+gsXnjJ6kmy24kaq63nu/ARiZ5pgxwGrf5zXetjHe+9TtufabMyZwhmEYJUCaUl3DRGSO7/MtqnpL4niRp4Dd0nR1rf+DqqpI9xcC645+TeAMo49i8Tmj20ifRblFVWdmbKJ6fKZ9IrJRREap6nrP5bgpzWFrgWN8n8cCz3nbx6ZsX+u9z6XfnLEYnGEYRpETTzLxv7rILCCeFXkR8K80xzwBnCgig71syBOBJzwX5E4ROczLnvyMr30u/eaMWXCGUQBki8+l22+0T7Y5cm0yHqtaPWWBoGTcl/p3+fAVX0i8X3d0crtAh9IlugHtVi/iDcBDInIJsAo4F0BEZgKXq+qlqrpNRH4CvOG1uU5Vt3nvvwTcCdTgsicfa6ff3YA5wAAgJiJXAVNUdWe2QZrAGYZhFDvdPNFbVbcCx6XZPge41Pf5DuCODMdN7UC/G0h2a+aECZxhFCCWcdl1ss2RS50H568m4rfYUve1mSN3TOv7jsyD8/fZXcKUev5SwATOMAyj2PHmwZUaJnCGUQRYxqXRHrait2EYhlF09ECproLABM4wigyLzxlt0G4pz1VwmMAZhmGUAqWnbyZwhlHsWHzOQEGipadwvVbJREQGicjDIvKuiCwWkcNzXVPIMAzD6BrdXMmkIOhNC+63wOOqeraIVAK1wHdpZ00hwzC6D4vPlS6lGIPrFQtORAYCRwG3A6hqSFV3kNuaQoZhGEZXSF3Nu0S0rrcsuInAZuDPInIAMBf4Kt289o9hGB3D4nOlgWAxuJ6kHDgQ+IOqzgAace7IBN7Krmn/AiJymYjMEZE50YbGHh+sYRhGUdH9K3oXBL1lwa0B1qhqvHz3wziBy2ntH28RvlsAqnYfVxp/GcPoZSw+V8xod68mUBD0igXnVYJeLSJ7e5uOAxbRzWv/GIZhGOkxC65n+TJwr5dBuRz4LE5g26z9YxhG/rH4XBFRovPgek3gVHUekG559DZr/xiGYRjdS6lYbX6skolhGO1i8bkioARjcCZwhmEYRY6omovSMAwjFyw+V4DESqQ+lw8TOMMwjGJHgdLTNxM4wzC6hsXnCgMpQQuu11YTMAzDMPKEqnNR+l9dINeVYETkIu+Y90XkIt/2g0RkgYgsFZGbRESy9SsinxKR+V6bV7ySj+1iFpxhGN2Kxef6KN1rwF1DOyvBiMgQ4Ie46WEKzBWRWaq6HfgD8HlgNvAocDLwWJZ+VwBHq+p2ETkFV9nq0PYGaRacYRhGCSCxWNKri+SyEsxJwJOqus0TtSeBk72yjANU9TWvBvHdvvZp+1XVV7w+AF4DxuYySLPgDMPoMSw+10dQhWi3mnC5rAQzBljt+7zG2zbGe5+6Pdd+L8FZe+1iAmcYhlEKtLXahonIHN/nW7zC9gCIyFPAbml6utb/QVVVRLp9kl26fkXkWJzAHZlLHyZwhmH0GhafyxMKtC3VtUVV05VPdE1Uj8+0T0RyWQlmLXCM7/NY4Dlv+9iU7Wu99xn7FZFpwG3AKaq6NdPY/FgMzjAMo+hRiEWTX10jl5VgngBOFJHBXjbkicATngtyp4gc5mVPfsbXPm2/IrI78HfgQlV9L9dBmgVnGEZesPhcL6J0dwzuBtKsBCMiM4HLVfVSVd0mIj8B3vDaXKeq27z3XwLuBGpw8bTHsvUL/AAYCvzem1EQyWZ9xjGBMwzDKAW6sdiy5yJssxKMqs4BLvV9vgO4I8NxUzvQ76X+fnPFBM4wjD5BvuNzk78yO/F++Q2HJ+2LVbWKQyAondq37Pzka/rwFV9IvF9/RHK7bkcVol12SxYcJnCGYRilQAmW6jKBMwyjz5EtPpduf3fw/k2thTFSl5ZRXzqe3yrryL49H0gesx7T+l5StMffLnVfp1BFzYIzDMMwihJb0dswDKPvYRmXXcRicIZhGEaxYi5KwzCMAiDfGZeFh3brNIFCwQTOMAyj2FHMRWkYhlFoZIvP7fHwF5L2+ee6Lftl8lw3P0s/9Yekz/45axsOS65wmJQ5mTKdLRBufa/lmfd96IhFSfvefrB1DnTD+K6nUaplURqGYRjFSikKnGiB+WVFZDOuRtkwYEueh9MXsfuSGbs36bH7kpm+eG/Gq+rwjjQQkcdx1+Jni6qe3H3D6nsUnMDFEZE5uRTbLDXsvmTG7k167L5kxu5NYWPL5RiGYRhFiQmcYRiGUZQUssDd0v4hJYndl8zYvUmP3ZfM2L0pYAo2BmcYhmEY2ShkC84wDMMwMlJwAiciJ4vIEhFZKiLX5Hs8+URExonIsyKySEQWishXve1DRORJEXnf+3dwvseaD0SkTETeEpFHvM8TRWS29915UEQq8z3GfCAig0TkYRF5V0QWi8jh9p0BEfma9//oHRG5X0Sq7TtT2BSUwIlIGXAzcAowBbhARKbkd1R5JQJ8Q1WnAIcBV3j34xrgaVWdDDztfS5Fvgos9n3+OfBrVZ0EbAcuycuo8s9vgcdVdR/gANw9KunvjIiMAb4CzFTVqUAZcD72nSloCkrggEOApaq6XFVDwAPAGXkeU95Q1fWq+qb3fhfuQTUGd0/u8g67C/h4XgaYR0RkLHAacJv3WYCPAA97h5TqfRkIHAXcDqCqIVXdgX1nwFV2qhGRcqAWWI99ZwqaQhO4McBq3+c13raSR0QmADOA2cBIVV3v7doAjMzXuPLIb4BvAfFCfkOBHaoa8T6X6ndnIrAZ+LPnvr1NROoo8e+Mqq4FfgV8gBO2emAu9p0paApN4Iw0iEg/4G/AVaq6079PXZpsSaXKisjpwCZVnZvvsfRByoEDgT+o6gygkRR3ZIl+ZwbjrNiJwGigDijqMlalQKEJ3FpgnO/zWG9bySIiFThxu1dV/+5t3igio7z9o4BN+RpfnjgC+JiIrMS5sT+CizsN8txPULrfnTXAGlWNl9V/GCd4pf6dOR5YoaqbVTUM/B33PbLvTAFTaAL3BjDZy2yqxAWBZ+V5THnDiyvdDixW1Rt9u2YBF3nvLwL+1dtjyyeq+h1VHauqE3DfkWdU9VPAs8DZ3mEld18AVHUDsFpE9vY2HQcsosS/MzjX5GEiUuv9v4rfl5L/zhQyBTfRW0ROxcVXyoA7VPX6/I4of4jIkcCLwAJaY03fxcXhHgJ2x628cK6qbsvLIPOMiBwDXK2qp4vIHjiLbgjwFvBpVQ3mcXh5QUSm45JvKoHlwGdxP3ZL+jsjIj8GzsNlJ78FXIqLuZX8d6ZQKTiBMwzDMIxcKDQXpWEYhmHkhAmcYRiGUZSYwBmGYRhFiQmcYRiGUZSYwBmGYRhFiQmcYRiGUZSYwBmGYRhFiQmcYRiGUZSYwBmGYRhFiQmcYRiGUZSYwBmGYRhFiQmc0ScQkTtF5KdZ9jd4xZK7+7zd3q+IHCMia7Ls/6OIfL87z2kYRlvK2z/EMPKPqvbrah8i8hzwF1W9rTv77Siqenkux3nr2V2qqk/17IgMozgxC84wihDfIp2GUbKYwBm9hojsKyLPicgOEVkoIh9LOWSYiDwpIrtE5HkRGe9rqyIyyXtfJSK/EpEPRGSj5/Kr8R17hojME5GdIrJMRE4WkeuBDwO/89ySv/P3KyKHisgGESnz9fMJEZnvvQ+IyDVef1tF5CERGdLO9X5DRDaJyHoR+axve8IdKyLDROQR755sE5EXvXPdg1ub7d/eeL/lHf8x797t8O7lvr5+V4rIt70xN4rIN0XkbyljuklEfpvL38swCh0TOKNXEJEK4N/Af4ERwJeBe30rSwN8CvgJMAyYB9ybobsbgL2A6cAk3KKUP/DOcwhwN/BNYBBwFLBSVa/FLQ57par2U9Ur/R2q6mygEfiIb/Mngfu8918GPg4cDYwGtgM3Z7nk3YCB3tguAW4WkcFpjvsGsAYYDozELVirqnohbpXpj3rj/YWI7AXcD1zlHf8oTgArff1dAJzmXftfgJNFZJB3b8pxK5zfnWXchlE0FKTAicgd3i/jd7qpv91F5L8islhEFonIhBzb7SMir4pIUESuznKciMj1IvKed46veNuPEZF6z9qYJyLxh/Q4EXnWG8tCEflqN1zjdG+sC0Vkvoic19U+O8hhQD/gBlUNqeozwCO4B3Kc/6jqC96KydcCh4vIOH8nIiLAZcDXVHWbqu4C/gf34AYnJneo6pOqGlPVtar6bo5jvD8+HhHpD5zqbQO4HLhWVdd44/sRcHYWV2AYuE5Vw6r6KNAA7J3huFHAeO/YFzXzKsTn4e7Rk6oaBn4F1AAf8h1zk6quVtVmVV0PvACc4+07GdiiqnPbuQ+GURQUpMABd+L+s3YXdwO/VNV9gUOATTm22wZ8BfegycbFwDhgH+8cD/j2vaiq073Xdd62CPANVZ2CE4YrRGRKjmPKRBPwGVXdD3fvfhP/Zd9LjAZWq2rMt20VzsKJszr+RlUbcPd3dEo/w4FaYK7nptsBPO5tB3efl3VyjPcBZ4pIFXAm8KaqrvL2jQf+4TvnYiCKs7rSsVVVI77PTTiBT+WXwFLgvyKyXESuyTK+0bh7BoB3L1eT4R563AV82nv/aeCeLP0bRlFRkAKnqi/gHn4JRGRPEXlcROZ6cYx9cunLE45yVX3S67tBVZtyHMcmVX0D9ys8G1/E/ZqPxdu10+96VX3Te78L9zAd4423U9epqu+p6vve+3U4ER+evVW3sg4YJyL+79zuwFrf54S1JiL9gCFeOz9bgGZgP1Ud5L0G+rIhVwN7ZhhDJsvI7VRdhBOQU0h2T8b7PcV3zkGqWq2qa9P1lSuquktVv6GqewAfA74uIsdlGO86nNACCWt2HMn3MLXNP4FpIjIVOJ3Mbl/DKDoKUuAycAvwZVU9CLga+H2O7fYCdojI30XkLRH5pT/RoJvYEzhPROaIyGMiMtm373ARedvbvl9qQ89dOgOY7W3q7HX6+zwEqKTzlk5nmI2zYr4lIhUicgzwUZKt2VNF5EgvpvQT4DVVTbJIvB8JtwK/FpERACIyRkRO8g65HfisiBznJWuM8f0I2Ai0N+ftPuCruNjdX33b/whcL17ii4gMF5EzOnD9aRGR08UluQhQj7MK41Zu6ngfAk7zrq0CF78LAq9k6l9VW4CHvet6XVU/6OqYDaNQKAqB837tfwj4q4jMA/6Ei2sgImeKyDtpXk94zctx2XVXAwfjHigXe21/lqFtxgnJGagCWlR1Ju7hfIe3/U1c7OUA4P9wv7ZTr+tvwFWqurOL1xnvcxTOTfXZFHdhj6KqIZygnYKzwn6Pc5n642P3AT/EWecH0epaS+XbOLfeayKyE3gKL76lqq8DnwV+jROM52m1en6Li5ttF5GbMvR9Py6R5BlV3eLb/ltgFs6VuAt4DTg0t6vPymRv/A3Aq8DvVfVZb9/PgO95btGrVXUJ7p78H+4efhSXhBJq5xx3Aftj7kmjxJDM8ey+jWfZPKKqU0VkALBEVUd1op/DgJ+r6tHe5wuBw1T1ig708SOgQVXTxuJE5F2ce2uF90t9h6oOTHPcSmCmqm7xfqE/Ajyhqjd6+zt9nb72zwH/o6oPd6aPfOC5NaO4HwNmgXQQEdkdeBfYTVV35ns8htFbFIUF5/2nXSEi50Aia/GAHJu/AQwSkXg86iPAom4e4j+BY733RwPvAYjIbp7gxd2GAWCrt+12YHFc3KBr1+m5/f4B3F1I4uYxFWgBNuR7IIWG9+Pg68ADJm5GqVGQFpyI3A8cg5svtRHn1noG+APOZVeB+w99XaY+Uvo7AfhfQIC5wGU5uH0Qkd2AOcAAXNykAZjiuRMfxZVZWicuW/FeXFJFA3C5qr4tIlfiElAiuMSJr6vqKyJyJG7O1gJa4zHfVdVHRWRiZ65TRD4N/BlY6Nt8sarOa69tPhGRs3Bxxx+raia3opEGEanD/f9YBZycGs80jGKnIAXOMAzDMNqjKFyUhmEYhpFKwRVkHTZsmE6YMCHfwzAMw8gLc+fO3aKqvTmHtWApOIGbMGECc+bMyfcwDMMw8oKIrGr/KAPMRWkYhmEUKSZwhmEYRlFiAmcYhmEUJSZwhmEYRlHSIwLnFSx+V9y6Y/+QDMuyiFuBeIG4tdAsc8QwjLzxwdYmnly0Md/DMLqRnrLgngSmquo0XFmq72Q59lhvLbSZPTQWwzCMdrnr1ZVc9cBb+R6G0Y30iMCp6n99iz2+BoztifMYhmF0hGhMOf7G53l0wfo2+5pCERpDUay6U/HQGzG4zwGPZdinuOVH5orIZb0wFsMwSpiGlghLNzXw7oZdbfY1h6IABCO9toqU0cN0WuBE5KkM64+d4TvmWlwh4UyrCB+pqgfi1gi7QkSOynCuy8QtFjpn8+bNnR2yYRglTkPIOZaC4Wibfc3etpY0++56ZSWbdrb07OCMbqfTlUxU9fhs+0XkYuB04DjNYPOr6lrv300i8g/gEOCFNMfdgqsoz8yZM81/YBhGp2gMOoFrTiNiLeFYYt8g3/bNu4L8cNZCojHlc0dOTGpz96sreXnpFv50oaUQ9EV6KovyZOBbwMdUtSnDMXUi0j/+HjgReKcnxmMYfZEH3/iANz/Y3qE2d7+6knfW1vfQiHqXaEz55RPvsr2x3ZWpEgQjUW547F12tYQ7dc6GuMCFsllwyS7K+LHpRHHeBzt4fcW2To3F6Hl6Kgb3O6A/8KQ3BeCPACIy2lsnDWAk8JKIvA28DvxHVR/vofEYRp/j548v4f7ZHVug/Pr/LObhuWt6aES9y9JNDdz87DKefy/3sMM7a+v54/PLeGXZ1k6dM7sF5wlZivhlc102h6Np+zL6Bj1SbFlVJ2XYvg441Xu/HMh11W3DKDqaQ1FaOpDQEIspwUiMYKQ4HqjZhCNjm5C7Xw0tkXaOTE9jMPM549taIukFLpPV1xKOEYspgYB0akxGz2GVTAwjD8Ri6n79p3loZiL+4O1Im75MNtdfxjbesZ11UcYtuFQ3pL/vllQLLss4myzzsk9jAmcYeSD+QOyINRZ/KKd7OBciccHuyPXErax4LK2jNIbaTzJJteASrstsbk1zU/ZJTOAMIw9kc3u126ZIHqYtXbHgOilw2ZJMEuMJpSSZZIvBdeIajN7DBM4w8kBTFksiE8X2MO1MDC5hwXU6Bhd3UWbOoky9v4n7niXzsljcxsWGCZxh5IGWLjzc001SLkRaXa4dvwe7uphkkipi4WiMSEzTjieb5dyZv6PRe5jAGUYeiLvBOhN/KjYLrkNu2ngWZWdjcBksOP/nTPvSWnBFZlUXGyZwhpEH4i7KjlkvRZZkkkjL74DIR7rooszgGm7OInCZRExVzUXZxzGBM4w80JmEkaJLMumUBdfVJJPWzM1YrLXqX9D3oyGT+KVuD0VjxLsolr9JsWECZxh5wB+7yXV5lmKL9yRiih2YKhE/tqvz4Fxf6UWtTamuhBAnb2/xfS6Wv0mxYQJnGHkg/tCMqbMEOtKmWB6mnYvBdXEenK+dX9T8Y0i1xjL9sMjU3ug7mMAZRh5oCmW2GDIRz54MR5VIjqLYl8k0sTqXNg0tkU4tTBqPwUHmuFu2GJz/nEkCVyQ/OooNEzjDyAPNocwP1Ixt/A/hIigN1ZXJ7hGvLmdHaQxGGVDtSvC2pAhUORH605TRUovGlHC0VeCaMoil0XcwgTOMPJDNYsjcprhiPsGE66/jUyUAdnYiDtcQjDCsfxXQ9kfGZWX/4T9V300Tg8sUq/O9Nxdln8QEzjDyQFOWmE8mii3m05VKJtDxqQLhaIxQJMoX9GH2lLUpPzJijJYtjJYtNKfE91oyWNv+pBOz4PomJnCGkQc6I1adcWv2ZTq7mkBFmVuWpqOJJo3BCHW0cF7DPZwWmN0mhlYjIcqJEQ4H25wzdcxtthfB36MYMYEzjDyQaj3kgj+dvhgme/tLdeU+VSLG8H7OxdhRC64xFKWOFgCqJZQsVqEoVbiVxWPh5qR2zeEoIwP1BIhlFLXUKQRG38AEzjDyQFNnkkw64dbsy8Svu6NTJYZ7MbSdHRW4YIR+4sSrhmBSok5LJEqNJ3CEmpLaSbCB5yu/yumBV5NjcKEoU2Qln6h8vSgs6mLEBM4w8kBzKMoo2UYdzR1KMhnFVmpoKYoHaks4ykRZD2jOFmlLOMrUyo2AdthF2eC5KAGqCSXH1kJRavBck5GWpHaV4XqqCTFKtiW1aQ5Huajsv3wvcGdR/OAoRkzgDCMPNIej3F91PV8t/3uHkkz+WfV9Liv7T1E8UAeGNvB05dUcE3g7Z8EeG17F9es+xyHyLg0dzKJMsuAk2GbaRV3AWXCS4qKUSFPaNs3hKHXS4rYXQdJPMWICZxh5oDkUZTg7GC47crdeQhGGS73XpvAfqLWRegKiOV9PJBpjkO4AYDfZ3ukkE4Bqwm2SR2rECab4LDhVRSLNXptQmzbVBKnSIM2hzlVWMXoWEzjDyAPNoQjVBNs8NLMRCQcJoFRLuOAFzi8cVSlik4mWSCyRCDK4rLnDa8I1BqPU0RqDS41p1ojruyzakijEHIzEqNZQ2jYt4Sh1gRBlxIiEkjMvjb6BCZxh5IFwOEgZMWoI5S5W4bglESz4LMpgJJYQlJocr6cl3JoIMrQi2OEVBRpDEerECVFtIJRUIsz17fbVSDBRJaUlHKXGa5P6t2oKRamTeOZlcmKK0TcwgTOMfBDyxEpyF7hYKL2rrBBpCUep9sSqmlBOMSznEoxbcMEOTxNwSSbuHtZKqM0E7rh1WOW7v80+UU0Xg4uLNCZwfRITOMPIB+FGwHvQ5ihWiWSHjlh9fZSWcMwnHKGcCi4HI62CMqisucNL5jQGI/QXF1+rlVAbsarStpZaPM4GcSFOrl4Sv4bUxBSjb2ACZxj5IBzP5sst/gQk0tdrAoVvwTWHo1RJqwWXSy3H5lAsYcENlJZOJJlEGVTeKmL+GpOhUJhKnGBWS4oF542zLkUU/VML4vFEo29hAmcYvUwsppRF45ZE7vG0QKTVvRYs8BicP+ZVTTAnC64l0mpN9ZfOJJlEGBhoPaffLRoJtWZOuphga53M+DhrA8mWc3O4dTyVsRbCRbCEUbFhAmcYvUxz0sM9N2ssEo1REfNEMceYVV8mObYVyqnUlUvld2360dRxCy4UYYAncFWEklcS98XQkl2Ura7U2tTyXj63ZrUUvlVdjJjAGUYv0+zLzKvK0T3nT5EvhodpSyglySSH62n2JabUalOHLbiGYJT+AfcjoUqDSasGiE/gqnyC2xyOUi1+t2brOEPBIOVEvH1BWzKnD2ICZxi9THOo1Xqp0hzdcz6Lp7oYkkx8CSO5Js0kuQu1kYZgx1b1bvRlUQZSVg3QsN9F6bPg/JYmLUkCp77EklTxM/oGJnCG0cs0h6PUeg/qCiIEg6H22/gsniot/IdpcyjZIs1V4Kq9aiNV0SaisdxrWEJyJRMA9Vlt/iQRv0XpTyRJ/WHhb586hcDoG5jAGUYv0xxqdXtBsiWQCX+KfBVBggXuDkuyxnIWuFhrUkfUTbPYFcx9qkBjKEKN+u61t2qAqiYSeCA5ycSfRelKcvnjdimiWOB/k2LEBM4wehm/2wtAQ+0LnD9FHiBa4POuXGwrnryR21QJfwyuPBakgkiH4nCNwSg12gQVdUDr3LVgJJawDCHZovRnSlYQJhhq/RsEwsmZl2bB9T16ROBE5CciMl9E5onIf0VkdIbjLhKR973XRT0xFsPoa/izKAHIYQ6VP0UeQEOFXTnDH1OsyXGqREvKD4N+NHWomklDMEJVrAn6DQda3ZLNPjekIp4rMubb13rOeEkul9Xa+ndz0z1M4PoaPWXB/VJVp6nqdOAR4AepB4jIEOCHwKHAIcAPRWRwD43HMPoMLt3dJ3A5WGPOremz+gp8YrG/VFdVB7IoawKt96C/NOc8VSAcjRGJRKiIBaFuBOBWDVDV5MVOawYlWWPxgsoJPGvbnwkLbaucGH2DHhE4Vd3p+1gHpEt1Ogl4UlW3qep24Eng5J4Yj2H0JVKtAklZYDMdqdaLhNtv05dpCbcWW64mRDAHgQuGY9RKCBAA+pP7ZO+kBJN+TuCqJUQwEkuKiUrNEGp8qzU0h6PeOT08C87vLgVzUfZVynuqYxG5HvgMUA8cm+aQMcBq3+c13rZ0fV0GXAaw++67d+9ADaOXSXVRSqTZLR8jkrVNdZIoFrYF5xeOKs1NHNwPgzDUDYPGzfQj93qUjaHWpXKoGwa0Ln+TdG9rh1Arm1tLdYW8cXo/0eP3vSUUS/ob2jSBvkmnLTgReUpE3knzOgNAVa9V1XHAvcCVXRmkqt6iqjNVdebw4cO70pVh5B330PQ9HD1LIhtBn8UDJGX9FSItvuzECiKEQu0LlZs7F4R+IwHoL7lXM2kMRqjzCi3HXZRxUfIXfqZ2qCv+HG6d6F1DCKoHAhCIuLXi/IlCWlbp4oiWRdnn6LQFp6rH53jovcCjuHibn7XAMb7PY4HnOjsewygU/Jl50JqWXl1RlrXNUF+bCg0SjsaoKCvMROhE+r1nGcVySJpJzAXsNwI2Qj+ac04yaQhG6Be34DwXZY2XGOJf842awZ7AtcbgqglC7VBoqacGz63pb1M7lOqQWXB9kZ7Kopzs+3gG8G6aw54AThSRwV5yyYneNsMoaprDUeokDJX9AKjOYUXrVBdloVczCYaTpz3kNFUiHKVKQwkLbnBZ7kkmyRacc1FWJyy4KNWEiZVVQWWdK5/mi8FVxQWO1gnd/sxLqR3aZqUBo2/QUz//bvDclfNxwvVVABGZKSK3AajqNuAnwBve6zpvm2EUNc2hKHWBINQOAaA6hzT5eJKJeq6yQo/5JKxY73pymSoRDHli41lgQytC7OxAkknCgku4KJ0FFx+LlldDeTXVvphgc8grqOwJnF8UWzMvB1MbsInefZEeSTJR1bMybJ8DXOr7fAdwR0+MwTD6KonEhdqhsOODnKpgxFPkpWYItNR7a6gVblp6cyhKpYagZjdoqc9pqkRicnv1IAhUMLishSU5W3DR1izKOhfHj6f2x7NatbwWKmrdUjpev6FQiHKiUOtPTIkkXJSxQCWBqgHUyuqCtqiLlcJ04BtGAeNqUYZa3V60v6J1IkXes/pqJLcizX2VcDjoCYe7nlymSiQmt1fUQvUABgeaacg5i9LnoqweSCxQ6ZbpCUdpicTcHMOKaqioASAa8eJr3srr8XHWSjAhitWE0IpaqKgpeIu6WDGBM4xeJpGgUOO5KHNYMieRIu+1qSrw2oexeMytJi5wze2uDJCY3F5RDVX9GRDIfVXvpCSTqn5oRU3CRRkvqCyeWAEQ9MQ0Ps6Ei9K5L5viUz0qaqCips0CqkbfwATOMHqZ5lCUag1CZR2xsiqXtdeONZZIkY9bcAWeZJJwSSYs0vanSiQmt1fUQlV/+kvua8I1BiP0kxZUAq59eU0inhZP4JHKVoFLiGl8xYDE3DnP6vMWX5WKmla3ZiH/PYoUEzjD6GUSmXkVtWh5tWeNZX+4N4eibnmZqv6olBX8oqeJFRT8Vmw715OY3F5eDVUDvYneucfgBpUHkcp+IOLciknTBEIEKmug3LPgPGFLnLNqACrlLovSmxxeQzAhilVqtSj7IiZwhtHLNAcjLjOvogYtb3WVZaMlEqNaQ1BRQ6y8xrPgCjfJJDFRPckizX49iTaeBVerHZvoPTAQSkzNkMpaZ415YlUnISdungUnkWaiMaU82mo1akVNwnKOt3FuzVoqU1YaMPoGJnCG0ctEwi0EiIH36z8Xa6wlGPFZfTUFPw8u4aKscfXVq9q5B+FojHL1BKSiBqoHUBPLfVXvxlCE/oEWqPIErqI2UT8yUVWlwi9w3uR7aT2nu++t8+BqA16bylogt8nqRu9iAmcYvY0vG1B8VkE2Yn73XEW1N3euMAUuFlPK4pZRwoLLfj3+BVLjSSZVMbeqdy6u2oZglP7S0mrBVVRTEwjTEo61Fn72JZmUx1poDEZ853RCViPO6muJ19KsrGtNTPEVwK5vCjPzp08xe/nWjtwao5sxgTOMXiYRf6qoQSprc7LGElmHFbVIRW0iQaIQCcbT8qHNBOpMJFVy8VyUVZEGQHMq1xVPMqGyLtFHfCXxRAkw3zSBakJsbwq3Tub2/RiJJ6a0ZlE6Cy6RkAIs39LAloYgC9f5F1YxehsTOMPoZQLxB2FFnXtoSg7xtESbap/VV5gxuNQqINB+VmjQXxC5vBqqBhDQCFWE2ZVDHK4xGKGWZqjq7zZU1FDri8G5mGhtIsmkhiDbm0Kt9Sa9HyPxxJTEkkd+t6ZvsvrGna7djiaLy+UTEzjD6EUi0RjlsXjiQg1SUZNbHUNfirxUFvbE4qRi0xW+qRLtWHCtYlObEKpc14RrDEWo1eaEi5KK2taJ3qF4fLMm2YJrDCVZjVJR6/5WodbyXnhJJpA8l2/TLvf32mYCl1dM4AyjF2mJxHwP95qck0z8KfJSUUNNoHCTTJrDUarFq0BSUZ3TVInENAmvTbyGZX9pytFFGaU61pxIMklMzg5HiYSDBFAvvulZcBJ3USb/rWqltRZlPBM20YbWuXwb6p3AbW/MrdKK0TOYwBlGL5K0FlxlHZTXtGu9QEqKvC9+VIgkJ4zUouW1OSaZJMfgwFsyJ9i+iDQEI1TFmnwWXA1V3jk17CsBlrDgPBclvsxNn9UXDIWoJJRkwcXnyEGri3Jbo1lw+cQEzjB6Ef8yK61lnrKLVXKKvKt4XyPhgi0N1eJPGElkheaQZCIhVMqgrKLVRZlDNZNwNEYsEnL3MBGDq3WTs0OR1nJcvoSRasJsa3QxuFhZFQTK3A8LTxQjSW1a3Zrxa4i7KLebizKv9MhqAoZhpKdNNqDnKsuWMJJs8bTWPmxpp7RVX6XFvzp5ebU3Jy3ElqwWnEsyiZXXUAZQNQBwMbidLRFeW76Vf81biyp8YsYYDpk4BBEBvLXg4isJJCy4agIo4XCw1f1bUQNlFaiUUSNB1jeFGEsIjVc38dWclFBbq6/GV65r404TuL6ACZxh9CKJlawh8XCs1OyFk5NEsbzV6itUCy4eT4uVVREIBJDK9q3YuNWn5dVug89FecNjiwlHlbpKtyL6A2+sZvzQWj55yO587siJNIaiSYWWgYSlpqEmyvwCB8TKa6gOuySTxFQAb3+VJ2KtUz38LspQGxfl9sYwqpoQW6N3MYEzjF6kKRShltYsSsprKCdKOBzM2CYpRd6z4Ko0SLBAl8tpiTiLNG4ZuakSDe1asdXiExsvyWT6CGFT/6GcdeBYTtzPrfT92IINPDRnNT977F0emb+eLx2zZ+tSOb4YHADhZhffLKdV9MqrqYnPg4tXOMHtr1bPgos0QxkpSSattS3rm8MMrKmgvjnsBLbKHrX5wO66YfQibZIl4lZDqDljm3j8qbWNq33YkkNyRV/ETawOu7XUcAJXK+F2Y3D98Wo/QkKoLpwxlAuPPjTp2LMOGstZB43l8XfW852/L+CL977JjLjA+WJwANFgI+Ux78dF3Dr0MltdkolXUNnbDhAJNhGItHgC57PgPOtuk2e97bNbf2av2Mb2xpAJXJ6wJBPD6EWaQzGqJeiWbSmvckkjkHVF65akeWPViQdxonxXgdESibk5bRWtglLTTumxeAxO4tZUeaW7D8H6jG1OnjqKJ752FMfuPdxnwcUrmXgLmwabkmOi3r/VBJ2LUnyi6v0bbG6k1h8TLatIWmlgo5dgss9uTkwtDpc/7GeFYfQizkXp3HMi0uoWyyJwcYsHSLIYYsECFbhQlJF+a6y8xmWF5lCqSyoHtm6sGgDBXVnPNaJ/NXdcfDA75n4Aj9DGRVlDMDmBB69OJSF2tkSoqwohFUOS9gebGpInnQOxihpqwi6LMuQlmOwzyiXC2FSB/GECZxi9SMJFmbBEnBUTyGKNxS0elTKkrCJh+UihWnBxsfIlb1QTJJglBhcMu+r9iTbg3I3tCByAiDC43BOZeJKJF/+rlpS5bkCgspZqnGVYGy/CDIl/K7QlaZWBeH/VXgyuIeiE2iy4/GMuSsPoRZrjyRK+or+QXMewTRuv7mGsvCbnNn2ZZq8Sf6AyJf2+HQsuSWwAqgdAS47FjIMN7t/K1lqU4OaupYqVeBVLgJQkk9aKJQmrr7JV/OJZlJt2tlBZHmDiMPc33mbVTPKGCZxh9CLNoRi1BH1xHc9qiLYQi6Vf16xNinz834K14GJOQHzzy9qdKhGKUiPh1muHnC04AELecSnTBGoIJZdO8/bVBMLe/qDPgmutcpI01QN89UFjbNzZwsgBVQyoriAgVnA5n5jAGUYv0hSOeCtBp1gF0lrHMJU2KfJxUfQV9y0kEnMBfe699qZKJGp4JrkoB0CwAxaclCVlSoIrr1WTmmRSXp2w0Kr97mTffLc2cbvKukQW5YadLYzsX00gIAyurbQYXB4xgTOMXqQlsRJ0qlWQuVRVc5qYFUAlIULRwqtmklgpO+V6sk6VSKzZlipwuVpwDc56i0+4TpTkCiWXAPPGE7fQEgWVfeOsIdgm81IqaqjzCmBv2hlk5AAnpIPrKi0Gl0dM4AyjF0nEkuKxm/JWt1emNPnWFPlkUSzUNeEStShThCPbVIlgJJosNuC5KDtgwcXjb75zuixKX3wTvGkCIYSYt4xOfO5dndcmRK20oFLuE0VXALs5FGXjzhZGDKgCYIhZcHnFBM4wepGmUNTNoUp5uFdnSZNvY8GVt1p9hbiiQHPYW/qmPPkeZJsq0RIMU0m4tQ24JJPgLsjFTRva1Rp/850znjCiSQJXTZX6rLSUid5xt6b6xdaz+rY0BGkMRRMW3KDaClsyJ4+YwBlGL9KSiD+lWmOZLbhEinxliqusncnRfZWWUITqNK6/bFMlYin1IgFnwWkMQo3tnzTY0DoHDiBQRixQSbWEqJJQ66RzSFSKqfMt6eP/17kog4lKLPF9NYRYudUVYR5VBzz4afYq32AuyjxiAmcYvUhzOOo93NvG4DKJlUvKCLd50FaRfXJ0XyUcDhEglpRk4nZkEbigr7hxnHjZrVzclKGG1qkZHlpek3BRir9fLxFlkHjxvXTTBFKnLHhTHVZtdWI7IboaFv+baaF5bG8KFWQyUDFgAmcYvUhTKEo1LW0mertFTzNnUbq0+ngGoNemnWV2+iyJpWaShaMsy1SJ1iVt/NMEXKWQnBJNQo2tguih3qoMSfUmISFcg2lIHqd3/6s9F2XCovaOqSZIkzfVYURgOwBDZBfhqNIQbH/VcaP7MYEzjF6kORjxkiW8B6oIsbJqqrIsf9McjiUnZfhicIW4ZE4snOJuTMQhM0+VIJzOguuAwKW6KImvYhCkmjCS5KJ04xmSsOB8f6vyGs+CCyZbfRW1VGoQcAI9OLoNgIHqrEuLw+UHEzjD6EUSD3efxaDevKuWDMvfJIotxwWhrJxYoMJZfQW4ZE7CGitv6/rL5KZtbeMTompP4FoyF1xOkJpkAlDp4ma1gVSxcuMZnOqipNWtmTSX0TsmgFJFmLrKMqqbNwHQP+YJnMXh8kKPCJyI/ERE5ovIPBH5r4iMznBc1DtmnojM6omxGEZfQv0rQce3VdRSTTijNdYSjlKpoTYP2mpCtBSgBUeqBecJXVWGuYCqikRaktuALwbXOQsuUFFLDUGvBFiyWIHfRZmSTCIh6trE4FoTUEYOqIZd6wCojTrx3WYClxd6yoL7papOU9XpuBreP8hwXLOqTvdeH+uhsRhG3yFdNmBFtcuIzOCeC4bCyWn1OKuvOovV15cJpIqVr5pLOgsuHFU3H83fBnJPMokEIRZuY8FJpas5WZM6gdyzEtNZcG718aC33E9bUawh5ObA7drghhjaAcB2mwuXF3pkNQFV9X/j6og7pg2jxAmEm6CCpF//4qWYb8xgjUVTLR7vvSvuW1hJJtGYUh7LIHAZCi43Jy0Sm1LJBGD7Knj9Vpj/oJs2MO182P9sqPWWuUkttBynvIaaQDi5qgr4kkxSYnC0/q1qCCVnZSbKeHkW3I71bnPQJZvYZO/80GMxOBG5XkRWA58iswVXLSJzROQ1Efl4T43FMPoC4WisdfVo/0Ozsiajew78KfI+S8LLACy0aQKJKibQJgaXaapE2jbQasG9+Ct49Grn+oyG4LFvwq/2gr9dCrs2ti20HKeihlpCXgJPbjE4qXQVS9rUxfRZcCMHVMNOJ3DSvI2ygFgMLk902oITkaeA3dLsulZV/6Wq1wLXish3gCuBH6Y5dryqrhWRPYBnRGSBqi5Lc67LgMsAdt99984O2TDySnM4mrwStEegooZa2dl+gkWSwNVmTcroqySJVY5TJdzk+DQuykAZHPpFV1/ygAtg1DS3fcMCmHcfzLkDlj4Nh33Rba9MFbhaaiTYtgRYQuBSpgl47+sCW7wSXm3bVBNkt7oANG2Bilok3MRuNTG2N1kWZT7otMCp6vE5Hnov8ChpBE5V13r/LheR54AZQBuBU9VbgFsAZs6cae7OPsDmXUHKAsKQusqc26za2siA6goGd6BNX2bRup3sMbyO6oqynI5vCfke1CnurVrJYo2FU7IOAamsplq2F5zANacTuPhUiUj6aQ+utFc4uU2cU25oe5Ld9oeTfwYHXQx/vwyevd5tT2PB1dFMBZFkyzCRZNLWRen+VsHkyfq+Y2okxO6VXrsRU2DtHMbXtFgMLk/0VBblZN/HM4B30xwzWESqvPfDgCOART0xHqP7+dydb/Dhnz/DbS8uJ9xORfudLWF+NGshx/7qOY7+5bPc8+pKohkm9BYCq7c1celdczj1phc58dcv8OySTe22WbGlkW/89e30saTy6qwTvTNZcLUZkjL6Mi3hWFprLNtUCVdsOo0F1x7D94ZLn4Kjr4F+u8GwvZL3V9TQTxvb9lveOg9OJQBlvh9kFbUMoq3r0h9HHFXmTVsYuR8AY6uaLQaXJ3oqBneDiLwjIvOBE4GvAojITBG5zTtmX2COiLwNPAvcoKomcAVAOBrj3Q07qSwP8NP/LOaj//cSb36wPe2xj8xfx3H/+zx3vbqS8w/Znf3HDuT7/1rIx29+mbcytMnE+vpm1u3onkU+VZX5a3YQ6cByMy3hKDc/u5QTfv08ryzbwpeO2ZOKMuGzf36DL9wzh007W9q0CUdj3PjfJZz06xeY98EOPnXgMLcj5dd/dQaxypgiX1FDTZYCzX2VtC5Ksk+VSCyVA8mWVi6UVcCx34Grl8CglPBGRS0Sz39LI1YDpMm9jy+x4+0bkm76gGeR1wVCjPaqmDByKgCjKxstBpcneiqL8qwM2+cAl3rvXwH274nzGz3L6m1NhKPKd0/dlwE1Ffx41kI+d+cbzLn2eMrLWn8zrdjSyJX3vcW0sQO5/aKZTBs7CFXl3/PX85NHFvGJ37/CadNG8c0T92bCsLqM59vaEOT/nlnKvbNXMWFoHU9+/eguX8OzSzbxuTvnsMfwOr510t6ctN9uiP9B5iMaU/7x1lpu/O8S1tW3cMrU3fj+6VMYPaiGq47fi9teWs5NT7/P9//1Dn+6cGZS27/OWcNNzyzljOmjufa0fRmxZB28Q4rAVWeMp2VMkS+voVYKr1RXiz8jMqWCf40EqU8zVaIl4gpUxwIVBMq68ZGVpnqJ/30ATf47AVTUEtA07lLv/Q9Omsjg6Fa3zbPgRlY0sc0qmeSFHhE4o7hZttm5dSaN6MeM3QcTjsa48r63mL+2ngN3H5w47sX3NwPwuwsOZPeh3sKQInzsgNEcu/dwbn1hObe9tIIn3tnAZw6fwPdO25dAIFlk7nx5Bb98YgktkRh7jezP4vU7WbujmTGDOvhLPoXnl2ymuiJAQITL//Im08cN4rfnT2f80GShXbRuJ19/aB7vbtjF/mMG8stzDuCIScMS+yvLA3zpmEms2d7MrHnriERjSSL//HubGDOoht+cN90JaNqU/1oqM2REpo1Zee+zZV72VZrDUaokhCJIeVViu3hrsKWbKtHiWXDaUeutPdJkTgIueaWs0mVkprpE00wn8L8fUhmFXeshUAHDXKRmWKCRHV7B5Uw/ooyewUp1GR1m2WbnotljuAvaf2hP98B/+f0tSce99P4Wxg2pSYibn/7VFXz9xL157pvH8IkZY7jj5RU8/W5yLGvllkZ+/MgiDhw/mCeuOopfn3eAO8/SLW366ygvLd3CoROH8vhXP8wvzprG0k0N3PBYm1AxP5z1DlsagvzukzP41xVHJImbnyMnDaMhGOHtNa1lo6Ix5ZVlWzly0rDWB1s4HvNJrl5frUFaQm0L8gYzWjxumkCwwAQuvnirllcnuf7cBOoM0wQirlSZ+st0dQeZxMq/L40Fl/69d3yo0U0R6D8KaoYAwhB2EYkpu6zgcq9jAmd0mGWbGhjev4qBNW414yF1lew3egAv+YQnEo3x6nL3cM/GiP7V/OzM/Rk9sJo/v7wiad+dr6ykPCD877kHMGlEP/Ye2Z9h/Sq7LHDr65tZtrmRIycNo7wswLkHj+PCw8fzxMINrNnelDhuwZp63li5nS8eM4nTp41uY136OXyPoYgki++CtfXsaolwxGTfPQg3Q6Acyv2JCzUEiBEOt43TNIejbiKyd5y/TZWmnxjdl4lbpKnWWCA+cT2dFRuKUS3hjiWY5EKaJXJaPyfP0Wtt09YtmdQ+3OwsuP67QVk51AxiIPGCyxaH621M4IwOs3xLI3sOT3blHTlpGG9+sJ0mzwpJPNzbETiA8rIAFx4+gVeWbWXxevcw2NkS5q9zVvPRaaMZ0d89PESEIyYN4+WlW7u0vtbLS12MxD+2Cw8bj4hw96urEtv+/PIK6irLOGfm2Hb7HFxXydTRA5NEPi52H9pzaOuB4eaM1kKiTqWPjC7K8hoqiBAMduyheesLy9v8kOgsK7Y08vm753RoKZiWUNRbQTtFUCpqqcskcGHXRrpd4DpjwWVoI+I+h5tcma7+3hTh2qH0j3n1KE3geh0TOKNDqCpLNzWw5/DkOUUfmjSMcFR5Y6XLIHtlmRORw/cY2qaPdFxwyDiqKwLc+fJKAB56YzWNoSifPWJi0nFHTBrGloYg721s6PQ1vLJ0C0PrKtlnt9bSTaMH1XDK1N24//UPaAxG2LSzhX/PX8c5M8cxoLoip34/NGkob/lE/uWlW9hnt/4M69caayLclNEq2LK9vk1W58otTRljcAAbtu7okNjf9tJy/uzd467y6IL1PLloI2+s3JZzm5VbG6mRMIGqlKSi8mrqyiKs3NJ2de5VWxupC4QJVLZ1dXeJTNaY/3Ob7RnidvHPcQtugFdfvnYotWEncDtssnevY0kmXeT9jbv42kPzKA8E6F9dTm1lGaFIjIZghF0tET592Hg+fdj4jO1bwlF+/eR7fGjSMI7ea3hiezAS5b7ZH1BTUcb5h2Su3qKqXHn/W6za2ki/qnL6VVUgAg0tERqCEYb3r+LWz8ykLIt7rSNsawxR3xxOxN/iHDxhMJVlAV5euoWj9xrOS+9vYcqoAQz1P9yzMKi2kjMPHMvDc9dw9Ul7c9erKzl4wmD2Hzsw6bi41fXS0i3s7ROoXFFVXlq6hQ9NGtbG5fjZIybyyPz1/P3NNWxuCBGJKRd/aELOfR85aRh/en45r6/YxqEThzJn5XY+c3jK3z6URuDi7rCIc536r2vB2h2ucr3/OEj00dzUwIadLYwa2L51s2lXCxt3uozMHU0hBtV2bcL9/DU7AFi4tp5j9x6RU5sFa+s5qjpKoKKtBde/LMyCtfVtkjHmr6nnvKooUpE507ZTtCdW2banto9/btzsij/HLbiaIVRtc14Bs+B6H7PgusjDc9fw7vpd9K8upyEYYcWWRrY2hqgoC7CzOcytLy7P+gv7n2+t5U8vLOeiO17nwttns2jdTma9vY7jb3yeH/97Ed/75ztsTDO/Ks77mxr4z3xX9y4WgzXbm1i9rYlILEZZQHjm3U0dnm+WjXgGZaqLsraynAPHD+Kl97fQHIoyd9V2jpzcvnvSz2c/NIFQJMYX/zKX1dua+VyK9QYwZlANewyr63QcbummBjbtCnLkpLaW5YG7D+KAcYO44+WV3PvaKo7bZ0TW6QupHDxhCJXlTuTnrNpGKBpLjr+BZ8Gl9OmbJBwXjTjz19Qzpp+6rDx/iryvAv+CNTmshwYsXNtaA33B2tzaZCN+3lz7UlUWrtvJ0MpoGnFw0wS2NIRYX9/6fQ9HYyxav5PBFZHuj8GVZ5gmAK3jy5ZkkmpRVtTAds/923+U+7d2KOXBHYCtCZcPzILrIk8t3shhewzlnksObbPvntdW8f1/vsOyzQ1MGtHW2lBV7nh5BfuOGsDZB43lpqff59SbXgRg31ED+MXZk/n23+Zz96sr+eZJ+2Q8P8BtnzmY3QYm/yre2RLmwOue5KnFm5g5YUhXLxVozaBMdVGCs2B+9d/3eGLhBvdwzyH+5mfyyP4ctddwXnhvM2MG1XDClJFpjzti0jD+9uYawtEYFV5KfnMoSk1l25JZwUiUMpFE6n48RpZubCLC546YwFcfmAeQVmCzUV1Rxszxg3lp6VYCAaGiTDgk9b6HmzM+TAdXRFmwtp5zZo4D3Pdjwdp6Lh8isCvV6mut3/jO2npO3C9dWdhk/EI0f009H548PMvR2dm8K8i6+hYCAu+sbWe5Go919S1sawwxsH8UytvWhayMhRJjG+1NA3lv4y5CkRj9yiJtE0G6SqaMSGg9V9YYXBrrbqtXaTAhcEO8gstmweUDs+C6wMotjSzb3Mhx+6Z3zxy3j9v+1OL0pZxeWrqF9zY2cMmRE7nkyIm88M1j+eZJe3PjuQfwyJeP5NyZ4zhh35HcN/uDjIthPr14E1PHDGgjbgADqis4ZOIQnvZEsDtYtqmBqvJA2nlocdH49VPvUVkW4OAJg9sc0x6fO2ICABd9aHzSfLLU8zSFosxbvQOA215cztQfPcFjC9YnHReLKZ+8dTbH3/g8q7e5BI6Xl25hwtBaxg5OH885df9R7Dagmn1268/he+YWP0wd2+L1O3l0wXpm7D6YuqqU35BpY3Dub7fvsHLm+6yxNdub2dEUZmRNLKMo7jWkjHfW5SYw76ytZ49hdUwcVpez1ZetL4Bj9x7B2h25laKKn7NfIJRWUALRZsoDzi2b2qYmteJ/d5AuCzJ1X+o5K7OIYkUthLzYsM+Ck0gLo2rUBC4PmMB1gbj1dPy+6S2N0YNqmDJqQEaBueOlFQzrV8lHD3D/GQbWVnDFsZM488CxiZjZJUdOZHtTmH/OW9um/daGIG9+sJ3j9kl/foDj9h3J+5sa+GBr2wy9zrBscwN7DO+XNmV+/zED6V9dzqqtTRw4fhC1lR13EBy913Duu/TQNsklfg7fYygBcfPsbnzyPX76n8WUBYTrHllEoy+j76E5q5m7ajvr6ls490+vsmTDLl5bvi2rZVlRFuDezx/KrZ+Z2alJufFpEau3NaefIhFuSi60DIkH5d5DK1i0fmeitmdc7IZVpRM493mfYRU5uwjfWVvP1DED2X/MwC67KOevqUeERHz4nRz6e2dtPWUBSZ/yX1GDaIwpI2qSRH7+2nr6V5e7ZYZ6c5pAe0kmqTUqU4/1ZVECTOoXzBpqMHoGE7gu8NTijew1sh/jhmT+ZXn8viOYu2p7m19vyzY38OySzXz6sPFUlWeuRn/IxCHsN3oAd7y0ok0s79klm1HNLLDx88fH2h0s29x2ikCc8rIAh3lZk0fs2TH3ZBwR4UOThiVcj+kYWFvB/mMGcssLrkTWuTPH8pdLDmV9fQs3P7sUcEkUP3/8XQ6ZMIR/fukIwlHl4ze/TEOw/akLew7P/jfNxtQxAxlQ7YT9iDRxvrQuSu/huudgl6D03kZXzHf+2h1UlgUYUB5pW4PR62OvIWVs3tX+w3Nrg3Mp7j9mINPGDmTtjma2NAQ7cYWOBWt3sOfwfhwycYj3OQeBW1fP5BH9CKR107rPB46uSiSagLPgpo0diKRr01USy/XUQCCQfl/G5JPa5BqV8W3gYqzxteo8gdujtiUptmj0DiZwnaS+KcwbK7dnFReA46eMJKbwbEqVjjtfXkllWSBrhiXE40ITeX9TAy+mVAp5atFGRg6oYuqYARnbjx9ax+QR/Xj63a4LXEs4yurtTWnjb3GO8pIqOppg0lE+PHk4zeEonztiIjecOY1DJg7hzAPHcOuLy1m+uYEbn3yP+uYwP/rYfkwZPYC/Xn44Q+oqKQtIzlMXOkNZwM3V619VzrSxg9oeEGrKGNeZMND9d0wkb6ypZ99R/QlEWjI+aPcYVJbUJhNxAdpvzAD2HzMwaVtnmL+mnmljBjKwpoLdh9S2a8GpasKCJJJZ4PYfWcWOpjBrtjcTjER5d8NO9h8zKH2brpJJxMA30TtDkkm6NvFtA0a1ip8ncOOqm82CywMmcD5iMeXdDTtzmlf03HubiMaU49oRuKmjBzKif1WSwNQ3hXl47hrOmD46eY5UBk4/YBTD+lVxh2+CbjAS5cX3N3PcviPbdaUdt+9IZi/fxs6W9ufhNIXSz0UCN4dJFfbIYMEBnHvwOP588cHM2L3j8beO8KVj9+QvlxzK909vrV95zSn7UFVexlceeIu/vLaKCw8bz5TRTvwnDqvjn1ccwUNfOLzH16P7wUen8JdLD01vhYYzC9ywqij9q8uZv7aeWMwlmOw/dmAGq899HtdPEHHWUTYWenG6qWMGst+YgYi0L4qZ2LizhU27gokpHPuPGdju+TfsbGFLQ8iJa7g5Y+WQqcPdnMP5a+pZsmEX4agybUw/Vxeyu2tRBsqgrCq7WOU6fcC/LR5/A6h1Fu6Yyia2N4ULbnmjQscEziMWU675+3xO/s2L/Pjfi9oVuacXb2JoXSXTxw3KelwgIBy37wheeG8LoUiMYCTK1x+aR3O47STmTFSVl3HR4eN5bslm7nplJQCvLd9GYyiacEFm4/h9RxCJKS+8tznrcdsbQ5z9h1c57sbnE1MP/CzbFJ8ikNmCqyov49h9cpsT1RVqK8s5cvKwJHEf0b+aq46fzDtrdzKotpKvn7B3Upvh/as4aHzPCi/AqIE1HJDpe5HFPSeRFqaNHciCNfWs2tbErpYI0zJZL4kVpEPsObxfuxbUgjX1TBhay4DqCvpVlbPn8H5Jsa6OEG83zRO4qWMGsnpbMzuypMHHxXTq6P5Zq7nsMaiMyrIA89fuSJzngJFVScd0KxXVGcQqwzSBhGWX5kde/Nj+voxWz4IbUe7+72wwN2WvYgKHK4p79cNv89CcNczYfRB3vrKS7//rHWIZFuUMR2M8t2QTx+4zIqcJ1MftM5KGYIQX3tvMF+6Zy9PvbuKnH5+asC5y4QtH78mJU0byw1kLuf2lFTy9eCPVFYFEoeNszNh9MEPqKnk6QzYnuBjNBbe+xtLNDew9sj9feeAtZr29LumY5Ykiy9084bYbuehDEzjzwDH84qxpDKzNrQJJrxGLeWKV4aEZbmL/MYN4d8NO5njVQRIWXKYkiHBzTkkjC+LuQY9pYwYmZSt2hAVrdhAQmDKq1YKD7NMF3lm307UZUQ0otJno7a6nIhZk31H9WbCmngVr6hlSV8noujRrtnUXFbUZBC4+TSBlX1m5Sy7J1YKrHggSYGjA/d+xOFzvUvICF4nG+PpD8/j7m2v5+gl78fcvfogvHL0Hf3ntA67954K0Ijdn5XZ2tkRysp7ApY5XlQe48v43ef69zdxw5v7txt5SqSwPcPOnDuSUqbvxk0cW8dCc1Rw5aTjVFZkTVOKUBYRj9h7Os0s2pV3gc/MuJ24rtjRy+0Uz+evlhzNz/GCueuAt/vHWmsRxyzY3MGZQTaeyI3uLirIAN547neMzzKHLK/GVuVMnCJdXAQJhZ8GFo8pf566hqjzA5BH9slo8RJrZb/QANu4MsmlX+ofn9sYQa3c0Jwnc/mMHsnFn5zL75q+tZ6+R/RPzDvfzfqhlc1O+s7aeSSP6UZMoHJ35evYf6wT77TU72H/MwPQLvnYXFTXpXZ+ZpgnE96Xd7v3w8wtcoAxqBjMg5sTf4nC9S8kKXCymPP7Oej76u5f517x1fPOkvfnKcZMREa45eR+uOHZP7n99NR///cs8tWgjqko0psx6ex3X/mMBleUBjsxxomxNZRkfnjycYCTGz8+alrX0VjYqygLcdMEMTps2ipZwjBOm5O4KPGHfkexoCnP5X+Ym3FlNoQi3vrCcU377Aqu3NfPniw/mw5OHU1dVzp8/ezCH7TGUrz34Nlfc+ybvbtjJss2Nfdp66/Mk1oJLeTiKeHUMmxLW0OsrtrHf6AFuLmC4ua3FU55swUFypRI/ceHZ32/Bee7FjsbhVJUFa+qT+hpcV8nYwTVZrcgFa+uZOnpg6z3IVL0/3My0MYPY1RLh3Q273DgztekOMllwmVYTyNYmYcGlTLqvHUpt1N0bs+B6l777U7wHmbNyG9/75zu8u2EXE4fVcdMFM/jYAaMT+0WEq0/cm4nD+vHbp9/j0rvnMHXMAJpDUZZtbmSvkf3404UH0S91Em8W/ucTU1lXP6ndmF17VJQF+O150znnoLEdqkRx0n678Y0T9uLWF5dz+v+9xBGThvLu+l1sbQxx5KRhfPvkfZLqPtZWlnPHxQfzf8+8z12vrOI/C9YTEPjM4RPcAU9cCw0b4fgfwcD2q+2z7i347/fdscf/GPr3QQsrV1Th3f/AC7+ASSfAh7/R1ipL12bJo+59podjuJmxg2sYXFvB9qZwaxZmOgsuEHAJEuEm9vNlRaaLf8aFZ+ro1r/vlFEDCYizxjpi7a6rb2FrYyghkHH2HzMwYxxw484WNu8KOgsyk8hX+Ny0vr5dUsr69G26g31Oc27EVLIlk1TWtZ3L6D92wOjk7bVDqWjZRv/qcjbUN3dtvEaHKEmBu+6RRWxvCvGb86bz0QNGp42jiQhnHzSWM6aPTtSLrK4o4/efOpCT99st69pg6RgxoJoRA7rnF2h5WYBjcixuGycQEL583GQuPmICd72ykr+89gH7jRnIV4+bxEHj05fxqq4o45sn7cPnP7wHd7y8kgde/8BNXlaFt+6Blnp491E45ttw2JegLE3Mq3kHPPNTeOM2l1G2erYTh498Hw6+xLlwColtK+Cxb8P7T0D/0fDir2DBQ3DKL2DvU9K32fwePPoNWPECjJoOe6U5rrwGIi2ICPuPHcQL721utZIiaWJw4Ky6cAv9qsrZY1hdRoFZuHYn44bUJMUkayrL2Gtkfxak1L5sj/jx+6dMgZg6ZiCPvbOB+uZwYp3AOPFxuXjiutaxJ11LXOBamDyiH1XlAYKRmBP5HSvSt+kOjv1u+u3jPwT7nwvD05TIO/VXUJcm9j1wnIvPDU5JHqsdCttWMGpgtVlwvUzJCVwspry/sYHzDh7Hx2eMaff4irIA58wcl6gPWOj0r67gyo9M5sqPTM65jctI3Iuvn7CX29CwyYnb4VfCtuXw5A/g/Sfh4keSG7bshD98yC0fcshl7mHSuAUe+6Z7vXm3swAnHdd20mwq6+bBs9c7C/D0X3fomtOydRk8+GmYeqYT53S/yP0074CXfwOv/cEtWHri9XDoF+CD1+DRq+H+8+HY78HR30xu98FsuPM0Z32c9r9w0GfTi7rnogSXAPLCe5udlRSLuhT5tDGf2kSbqWMG8vqKbUSisaQSZ9GY8vaaHW0sLnDW0RMLN7ByS2NORaXD0Riz3l5HeUCSlhqKnx/g7dU7OGqvZM/CvNU7EIEpowbApmWtY0+9foBwE+VlAfYbPYDV25sZOaAKNjelb9OT9N8Nzro1/b49j02/ffIJ8PV3oS5lnmXtEFgzh5GDqy0G18uUXAxuXX0zzeEok0ZkTnU32mHLe+7fPT8CF9wPR38bVr4IOz5IPm7F87BzLZx/H5z6C6gZBMMmwaf/Dufc6ZYVufcsuOujsPbN9OfavhIevgRuORre/y+89RcIpZ+n1yEW/RM2LXLW5U0zYM4dEE2zcGckCK/8H/z2AHjpN7Dvx+DKN+BDVzqLdeKH4fKXYMKH4e372rZf8Fd33JfnwMGXZrZYK2og7B5+nzx0d645ZR/3HU249DK4Nb0EjKP3Gs6GnS2c9cdXWbrJZewt39zAOX98hTXbmzkqjTv7M4dPIBAQPva7l3huSeYMW3BZthfePptHF2zgi8fs2Sa5afrYQQyoLueK+97kr3NWo6q0hKP87LHF3PzsUmaO9+pyRjJcTyLJxF3P1SftzXUf289NA+nJJJPuRKStuAHUDIGmrYwaUGUWXC9TcgIX/89vAtcF4gI3zLPopnzc/bv8+eTjlj8Hlf1g0vHJ20Vgv0/AlXPglF/CpsVw+4mwZWnycaEmuO1459L88NVOFKMh+ODVrl/D8udg5P7wuSecS+mRr8FLN7Y97olr4b/fg7Ez4QsvuF/1qTGWsgrY53RnzW5flbxv+XMw/gjo145L2WfBjR5Uw+VH7+ke7tkErrwmsf+sg8byu0/O4IOtjZx604t8++H5nHrTiyzb3Mhvz5/OeQe39UDsP3Yg/77ySMYMruWzd77BH55blnb+58J19Xzsdy/z5gc7uPHcA/jGiXu3OWZgbQX//vKR7LvbAL758Hw+d+cbfPT/XuJPzy/nvIPHccfFB7sDEwkj6Seux+/Bh/Ycxin7j8replCoHQqxMOP6KZsbgolao0bPYwJndJwtS527aIDn4h2xL9SNcA9zP/GHe7rYHEB5JRx6mbOAAF7/U/L++Q+4BSQ//Tc47vsw+SQX40g9T0cJNTnX4h5Hw+6Hweced33P/lPCigKgaZuzGGd82o1h1LTMfe5xjPt3hU/k69fA1vdb92XDZ40lkcniiW8LtyYtnD5tNE987SiO3ms4D85ZzRF7DuPJrx3FGdPHZKx2M25ILX/74uGctv8ofv74u9w7O9kK37SzhQtvf52YKg9ffjhnHpg5oWj80DoeuOwwvn/6FF5ZtpVdLRHu+twh/OzMafSPr4qeSbB9UyXakE3kCwFvsvf4mmZUYdOuztcANTpGyQncss0NDK6tYGgPl2sqara8B0P3bC1QK+Ie4sufc5OZAXashq1Lc3u4DxgF+58Nb93rYl3gElle+6NLyhj/IbetshbGHdp1gVv9mrME42MTgcOvgKYt8M7DrcfNvdMJzGFXtN/n8L2h327JY4tbtLncg/JWCy6JbCnyKQIHrprLLRcexPPfPIbbLprZNrFp40LY9G7SptrKcm46fwYfnjyMn/5nEUs3uWLPsZjyjb++TVMowj2XHNq2tmYk6Kxrn9UXCAiXHDmRF799LE9/4+ikVeqTric1YcQ3VSLjPShwgRtd6a7Nqpn0HiUncEs3NTBpRL9OLYVieGx5r9U9GWePY5xAbFrkPq/owMMd4NDLIdzoLCaAZc/AliVw2BeTE1D2OBo2LHDJKp1l+XNuhezdD2/dNvEoGDHFiaoqRMMu83Pi0TBySvt9JkT++VaRX/4c1A13/bZHzSBoSFNKrXFz6/5Uqge27k8aijB+aF367/g/vgD/aivYgYDwv+ccQG1lOV+5fx7BSJQ7Xl7Bi+9v4funT0nv8Xj7AXjgk24KSAoj+le3XQvPfz3V6a5nUNrroXGzW56mskC9LvFyXWVWrqu3KVmB6zZCjTD7FpeksOBhWPIYLPwnvHkPvPp72Lyk/T42vet+DafSsBl2rmu7PZUlj7sxzLsfFj/iflW//QC8fiss+leHLykr4WaXTNJG4I52/8YtmOXPObfliH1z63f0dNj9Q85NGYu6bMV+I12sLuk8Xgbbihc6eQE4ERp3CFT5vgciTkw3LoCVL8HiWS5B5rAv5d5vQuQXOpFc8bwTyNSlWNKx2zRo2AC7NiRvXzevdX+bNvs7KznYkNv4ws2wcZH7gRBpWzdyxIBqfnn2NBat38lVD8zjF48v4YQpI/lkpsIEa+d6Y2wrcBnZMB8GjE0UIU5i1DRY/3bb7evnwbC9e2aaQG/gXevQgLOM19tcuF6jpKYJbG0Isr0pnLVYcId5616X8p6JJR9umz7vZ/UbcPvxMGg8HPcDmHqWWxX4pd/Aqze7/xxffTtzHKtpm/sVrVmqlF+1AAZ1rnpKG7YuAxSGpUwzGDgWhk5yD/XDr3AissfR7af/+znsi/DQhfDyb2Hpk3DstV5sxseo6VA10Ano1DM7Pv6mbe4hmm7+0/7nwFM/cuLauAmG7AGTT8y974TIP++mEjRsbN3WHqNnuH/XzYO9T27dvu4tJwjpklRGHQCoE6zxh7fdn8rGhe57Eo3C5sVe+2SO23ckFx42nnteW8WI/lX8/Kxpmb0dcWFbP6/9cyfazEt7XsDdg/eecIId//Gh6s4z6YTcz9HX8Cy42vAOqiuGmgXXi5SUwPVIgsmSR92D/aJHILgLQrtcPKWqP8z+o3tYNm+HmgxV7F/9nXtgVw2Av10Cr9zkrLbGzTD+SFj1krMIp52T4aKecg+tT//NPZBbvHJNVf3dw/z2491D45DPd8/1pmZQ+tnjGGdFrn/bCUSu7sk4+5wGA3eHp3/skkkO+mzbY8rKXWp+Z+NwK14ANP3YKmrcOV/8lft8yi9ys77iDBjt7svy51qnA+R6D3bb37nh1r3VVuBGT0/fZpS3ff283ATOb2mteyuj0Hz31H2JxJSzDxrDkEyx6nBLqzs6bmW2R3CXszinnZt+/+gZOMGe3xp33bnW/V+I/wAoRKoHgpQhzdsYNXAq620uXK9RUi7KpZu7WeBadjp31t6nuESJ4XvBmINczGbQOJhyhhOfpU+nb7/jA+cKO+gi+MLz8PE/uF+vw/eBzz8DF/0bhk6G125OCuQnseQx5wrc4yNO4EZPd6+he8K4g2HInu6Y7mLL+4C4flPZ4xgXR4sLxMQcrZc4gTKXVQmuikS/DKXI9jgGdqxyVUXiY/rb59um6INz3T7/i+S4WGV/GH1g+r4PvtRZX1UDYPonOzb++NhWvezm7A3ZI3fLuaqfc8P5Rah5B2xblvnhPmCUc+Omc+ulY/3bbk5W9aCsbsWayjJ+dub+GSvcAM4ajEXcj7tNi9O72Nucfz6grcKcSnx7qhBDYQuciKt8snMdIwdUsdEsuF6jtARuUwM1FWWMHthN2VjLnoFYOH3pJXBiVzsss8C8fisgrspHoMw9UL/ypnNpjjnIWQ+HXe7+k69+vW37aNiJ514nZrY09j7FTcIO7urUJbZhy3tOvNPVXpxwpLNCFv/bPfgGdaL6y4EXOXE76huZj4lbRcufcw/NO0525bIeTXEVb3gHHv+2q4DyryvcRO7lzzkLsCyD82LAKFcr86TrnRXcUfY4xmUCLnum4xbs6Bnubx3/MRMXrmwP91HTc7eg1s/zfgDN6FjcLB3rvIn5B13s/g/Erbms5/euJ5OLsv9IN/UkVeCkDHab2qXh5p3xR8D7TzJmQIVN9u5FSk7g9hxR1+E6khl573H3a3jcoen3B8pgr5NcPCmaspp2sAHevAumfCy7EBxwgXNxvHZz232rXoFgfWaBBdjrZJcSv+zZdi8nJ7a856zKdNQMbn0Yd/ThHqd6gJtMPWSPzMcMneQehHP/DHee7lLoD/mCqw+55HF3jKoTvOpBcMRVrsrIXz4B21e0P7YPXQkHfqZz44+LPHRO4Bo3tSYW5WK9jDrAZZu2V90l3OIsrVEHuP42Lko/5yxX1s1zP972Oa31c3usn+eWkslWaDtVfNe95bJQC3WKQJz9Pg5NW5gp77JxZ0vGtSaN7qWkBG7ZpgYmdVeCSSzqYluTT8xsDYATmJZ6N7HYz9v3u+3tZelV1rlfyYv/3bYU1nuPu4rymWrjgZvIXD3QHdtVYjEXQ0kXf4sTf6h3VuByIZ6Sv/5t5/r53OPO4hq2t7PYwi0uo/WDV+D4H8IJP4aTb2jNvOzJsVUPdNY34sp3dYREoslbrf8OGp8+4zDRZjpozLkMs7FpkXMpjpruzhMLu2zPzrLuLdfP4InumnNxk66bl9k9GWf0DPcda6lvTTAZU8DuyTiTToCKWg5seJ5ITNnSaJO9e4MeFTgR+YaIqIikXXZaRC4Skfe910U9OZbGYIR19S3dF39b/To0b0tOCEjHnh9xCRN+gYnFXALKmINg7MHtn+uQywCB129p3abqXJ8Tj8peKLiswv3neu8JJ8pdYeda535LzaD0c8AnXb3GPbKIbndw8KUw9WwnboPGues85eeuduVz/+PKa42eATMudMcf9kU481aYeUl2ge4ODr8CjvhKdmFKx25TnTvOL3DtxZ4Scat52Y+LZzrGXZTx/jtDqMllYY6e4X5sjDqg/UzKYIOz/jO5J+PEx7b+bRdnbd5e2PG3OJW1MPkEJmx6hgAxNtabwPUGPSZwIjIOOBH4IMP+IcAPgUOBQ4AfikiGVMOusyyXBJNlz8AtxzjXX3u895hLRkits5hKVT/3S37Jo62xlXl/cb9SD/tSbmn0A8e6hJW5d3lp+rj5ddtXtC+w4OJwTVta5y1l46VfO7ffro1t92193/2bTSCGTYLz7kmeY9YTjDkQzr49OX1+z2PdfXr5t25O2am/Si5uPO1cOP3Gjk1d6Az7fQJOuK7j7SpqnDtu3VsuA3bHqvYf7gNGu8nk7QnMunnOXTtovPs+1Q7rvMBtWOCsxvjYRk13FmSauXUJNr4DaOaM0Dh+8S2GBBM/Uz5OVXALB8sSmwvXS/SkBfdr4FtAJmfzScCTqrpNVbcDTwI5PK07R7tTBN5/Eu473z0I/nIWrHgxe4dLHnepzOkWS0xl71NcId4t77s0+n9/1YnelDNyv4Bjv+uslD+f6vp5z0tc2SuHWzbpOGcZZMumVHWV9Z/6kcsMvfM02Lk++ZgtOQhcvjnxepcBeeBFrkByoTF6ukvgiCdxtPdwT1hQ7bgI17/tjhNxr9Ezck9OSSVVeEYd4OK8m9/N0sY7V3suytohToTXvunOU1aZWyWYQmDyiWh5NaeUzWaDTRXoFXpE4ETkDGCtqmb7XzcGWO37vMbb1iMs3dRAecCVMGrDksfdZOkR+8CXXnOp3feek3mu1bblLrC/96m5nTwuQo98Df75RedW/ORDmSdvp2PYZDfXTqNO5Obd76pb5LKads1gJ8aZ4nCqbu7ZC790yRUX/8et4XbnaVC/tvW4Le+5OXvtVcbPJ4PGuYnxp/8m3yPpHKNnOLdcvAJNey49cKKxaXGbupQJIiEXg/NbT6NnuDahNLUf22PdW67u5oBRrX1Bdity/Tw3naX/bu33H080WfcWjNyv7WT/QqWqH0w6gVPKXmf9jk7cd6PDdFrgROQpEXknzesM4LvAD7prkCJymYjMEZE5mzenqVWXA0s3NTB+aC0VvsUgCTe7aiEPftr9R/rMv5zIXfQIDJkI953nUvn9c3yCDc4FBrlZT+AeuiP3d5O29zwWLnggfZp9e4yc4sRHxBPYLNmTqex9invILfxH8py6neth1pXONXnQZ+H038KEI+DCf7iFTe88Fd5/yrXZ8p4T2r5ex7N2SMcmaPcl4mKx4GE31zBdDco2baa7Hz6ZEk02LXIWlt96Gj3Da/NOx8eYGhscPNFZzdkswnXz3Dhz+e6MnuHcs2vmFI970kP2+zgjZQe1G+bkeyglQacrmahq2uCTiOwPTATe9kr8jAXeFJFDVNVfaG8tcIzv81jguQznugW4BWDmzJmdyq8dtP4FThk8CNYPhoo6Z828/FuXlr3nR+DsP7c+TPoNdyL30Gfcas0v3ghHXuVKaL3yO5dcMu18J4K5cvQ3ndvzxJ92rabe8L2dyD17vVvGJVemnu3qZf71Yie2R3zFJcq8ebfLrjviq27+V/wBNO4QJ/h/vcgtSjr6QGe5dkRUjY4zcj9XCDrclPvDPW7lrZ+X3i2bmE83vXVbvO+1b7q/da4Ed7kfOlPPat0WCGR3k4aa3A+yfT+a2zniY+vIPSgU9jqJEBVM2vI00MmpKEbOdHupLlVdACR8WCKyEpipqqnl358A/seXWHIi8J3uHg9AOBLlZ03XUdas4F9ybOLRcPSdzmJJpW6om3C94nl47ufw2Lfc9sknuhWsOxrfmXJGx2Ju2Rg22S3+2RH6j4QvzXbLwbzwS/j7512SzPRPwpFfTy/WYw+CL7/ppjS8+Cto2ZF78WSjc5RXOZFbPy/3h/vAca5CSSYLav0851oe7PsbDxjl3IwdTTRZ/zYuWSRlbKMOcKsvRCNtp81sfMclpeTibo33FafYBK6qP4vrDuGgphedV6Sve0MKnF6tRSkiM4HLVfVSVd0mIj8B3vB2X6eq23rivAERVn78n/QPBBlRGXaW2NBJ7YtUfL7VHsc4d0lZZfZFL/s6ZeVwwPmuqPCK571qI+2UkiqvdKXEpn/StRl3WO+MtZQZPaNjAifirLNMMbB189z3NvVhOnoGrJ3jpq3k6tJd4/13Tc2GHDXdLdi6+d22VUfiwtteBmWcmkHOPbtzrStbV2QMOv06dpVVMcLErcfpcYFT1Qm+93OAS32f7wDu6OkxlJUF2HPGMV3rpBAz8jIRKHNu2Y5QVtH+lAije9jnNFfPMldBAOdCfunXrvbmwZc6wVJ1bukN893cvFQmn+CycR/8FHziT66KTDbevAee/R9nYaUmGo3xans+8xM442Y3AR9cubQ3bnUJJgM6kEM25QyoX92xRKwCYfy+RfQs6eOIZiri20eZOXOmzpljAVrDSKJpG/ztUlj2tMvSPfZaeO4GWP6sm3R/5q1ti1erwuw/wRPfddb8+fe5eYypRMPw+HecUO1xjItXp5vE/sr/wdPXuYST0/7XzZt87ufOIvvEH+0HUjchInNV1VQyB0zgDKNYUHX1TZ+41rnhK+rgxJ/AzM9lj/WseNElE0UjcMkTyXHWWAzuP8+tjnD4lS4RKVtpuo2L3KrhG+a7z/ud6Sbc1w3tnms0TOA6gAmcYRQb21c5oZtxYe6ZvttXwW3HOVfi559pzfR9+bfw5A/c2niHfiG3vqJhN71m4FhXTNzoVkzgcscEzjAMx3v/hfvOcSXkTv6ZSw657XhXDu7ceyzjr49gApc7JbWit2EYWdjrRLfs0Gu/h90Pd9Vt6obDR28ycTMKEhM4wzBaOeE6t0DuQxcCAhfN6viqCIbRRyjQekaGYfQIFdVw1m1Q2Q+OutplZBpGgWIWnGEYyYzcD765tPBX0TZKHrPgDMNoi4mbUQSYwBmGYRhFiQmcYRiGUZSYwBmGYRhFiQmcYRiGUZQUXCUTEdkMrOpk82FA6rp0pUap34NSv36wewCFfQ/Gq+rw9g8zCk7guoKIzCn1Ejelfg9K/frB7gHYPSgVzEVpGIZhFCUmcIZhGEZRUmoCd0u+B9AHKPV7UOrXD3YPwO5BSVBSMTjDMAyjdCg1C84wDMMoEUzgDMMwjKKkJARORE4WkSUislRErsn3eHoDERknIs+KyCIRWSgiX/W2DxGRJ0Xkfe/fwfkea08iImUi8paIPOJ9nigis73vwoMiUpnvMfYkIjJIRB4WkXdFZLGIHF6C34Gvef8H3hGR+0WkutS+B6VK0QuciJQBNwOnAFOAC0RkSn5H1StEgG+o6hTgMOAK77qvAZ5W1cnA097nYuarwGLf558Dv1bVScB24JK8jKr3+C3wuKruAxyAuxcl8x0QkTHAV4CZqjoVKAPOp/S+ByVJ0QsccAiwVFWXq2oIeAA4I89j6nFUdb2qvum934V7sI3BXftd3mF3AR/PywB7AREZC5wG3OZ9FuAjwMPeIcV+/QOBo4DbAVQ1pKo7KKHvgEc5UCMi5UAtsJ4S+h6UMqUgcGOA1b7Pa7xtJYOITABmALOBkaq63tu1ARiZr3H1Ar8BvgXEvM9DgR2qGvE+F/t3YSKwGfiz56a9TUTqKKHvgKquBX4FfIATtnpgLqX1PShZSkHgShoR6Qf8DbhKVXf696mbI1KU80RE5HRgk6rOzfdY8kg5cCDwB1WdATSS4o4s5u8AgBdfPAMn9qOBOuDkvA7K6DVKQeDWAuN8n8d624oeEanAidu9qvp3b/NGERnl7R8FbMrX+HqYI4CPichKnFv6I7h41CDPVQXF/11YA6xR1dne54dxglcq3wGA44EVqrpZVcPA33HfjVL6HpQspSBwbwCTvaypSlyAeVaex9TjePGm24HFqnqjb9cs4CLv/UXAv3p7bL2Bqn5HVceq6gTc3/wZVf0U8CxwtndY0V4/gKpuAFaLyN7epuOARZTId8DjA+AwEan1/k/E70HJfA9KmZKoZCIip+LiMWXAHap6fX5H1POIyJHAi8ACWmNQ38XF4R4CdsctO3Suqm7LyyB7CRE5BrhaVU8XkT1wFt0Q4C3g06oazOPwehQRmY5LsqkElgOfxf2wLZnvgIj8GDgPl1n8FnApLuZWMt+DUqUkBM4wDMMoPUrBRWkYhmGUICZwhmEYRlFiAmcYhmEUJSZwhmEYRlFiAmcYhmEUJSZwhmEYRlFiAmcYhmEUJSZwhmEYRlFiAmcYhmEUJSZwhmEYRlFiAmcYhmGkRUROFpElIrJURNqs/C4iR4nImyISEZGzU/ZdJCLve6+LUtv2BlaL0jAMw2iDiJQB7wEn4JZeegO4QFUX+Y6ZAAwArgZmqerD3vYhwBxgJm69wbnAQaq6vTevwSw4wzAMIx2HAEtVdbmqhnCrL5zhP0BVV6rqfFpXLIlzEvCkqm7zRO1J8rDQrAmcYRiGkY4xwGrf5zXetp5u222Ut3+IYRiGUcicdGydbt0WbbN97vzgQqDFt+kWVb2l1wbWw5jAGYZhFDlbtkWZ/cTYNtsrRi1rUdWZGZqtBcb5Po/1tuXCWuCYlLbP5di22zAXpWEYRpGjKGGNtnm1wxvAZBGZKCKVwPnArBxP+QRwoogMFpHBwInetl7FBM4wDKPI6YzAqWoEuBInTIuBh1R1oYhcJyIfAxCRg0VkDXAO8CcRWei13Qb8BCeSbwDXedt6FZsmYBiGUeTMOKBSn31sZJvtg8esmZvFRVnwWAzOMAyjyFEg3CaTv/gxgTMMwyhyFAiXoLfOBM4wDKPIUZQoJnCGYRhGkaEK4dLTNxM4wzCMYkcRwir5HkavYwJnGIZR5CgQKsFZYSZwhmEYJUDMLDjDMAyj2IghhCjL9zB6HRM4wzCMIsdNEzAXpWEYhlF0CFETOMMwDKPYcJVMzEVpGIZhFBmqQlhN4AzDMIwiQxFCWnqP+9K7YsMwjBJDgZjNgzMMwzCKDWfBmYvSMAzDKDLcNIHSe9yX3hUbhmGUGIoQtUomhmEYRrHhVhMovcd96V2xYRhGieFWE7AYnGEYhlGERC2L0jAMwyg2zIIzDMMwihITOMMwDKMocdMETOAMwzCMIkNViNlqAoZhGEaxYRacYRiGUZQoQjhmAmcYhmEUITZNwDAMwyg6FCFiLkrDMAyj2FCFcKz0LLjSu2LDMIwSIz4PLvXVHiJysogsEZGlInJNmv1VIvKgt3+2iEzwtk8QkWYRmee9/tj9V9U+ZsEZhmEUOQrEOriagIiUATcDJwBrgDdEZJaqLvIddgmwXVUnicj5wM+B87x9y1R1elfH3hXMgjMMwyh6XAwu9dUOhwBLVXW5qoaAB4AzUo45A7jLe/8wcJyI9Jl1eUzgDMMwihwXgytr8wKGicgc3+syX7MxwGrf5zXeNtIdo6oRoB4Y6u2bKCJvicjzIvLhHrmwdjAXpWEYRpGjSCYX5RZVndkDp1wP7K6qW0XkIOCfIrKfqu7sgXNlxCw4wzCMIkeBiAbavNphLTDO93msty3tMSJSDgwEtqpqUFW3AqjqXGAZsFfXr6RjmMAZBYeIfFhElvRQ33eKyE97ou+eRkQaRGSPHI6bICLqPZCMUkCFSKyszasd3gAmi8hEEakEzgdmpRwzC7jIe3828IyqqogM95JU8L6Tk4Hl3XY9OWICZ/R5vIfxpPhnVX1RVffO55g6ioj8SET+0o39PScil/q3qWo/Ve31h4jR9+mMBefF1K4EngAWAw+p6kIRuU5EPuYddjswVESWAl8H4lMJjgLmi8g8XPLJ5aq6rdsvrB3sF5xhGEaR05lpAgCq+ijwaMq2H/jetwDnpGn3N+BvHT5hN2MWnNEriMi+ntWxQ0QW+n4Bxt2CfxSRJ0Vkl5d1Nd7b94J32NueC+48ETlGRNb42q8UkW+KyHwRaRSR20VkpIg85vX3lIgM9h3/VxHZICL1IvKCiOyX4zVcLCIvi8jvvLbvishxvv2jRWSWiGzzJr5+3tt+MvBd4DzvGt72tg/0xrpeRNaKyE99bp2LReQlEfmViGwXkRUicoq373rgw8DvvP5+521PWLoicpqXwbZTRFaLyI86+jczigdFiMQCbV7FTvFfoZF3RKQC+DfwX2AE8GXgXhHxuxk/BfwEGAbMA+4FUNWjvP0HeC64BzOc5izchNS9gI8Cj+FEZTjue/4V37GP4WICI4A34+fKkUNxAfNhwA+Bv4vIEG/fA7hU6tG4eMT/iMhHVPVx4H+AB71rOMA7/k4gAkwCZgAnAn6346HAEu9cvwBuFxFR1WuBF4Ervf6uTDPORuAzwCDgNOCLIvLxDlynUUxop5JMCp7iv0KjL3AY0A+4QVVDqvoM8Ahwge+Y/6jqC6oaBK4FDheRcWn6ysT/qepGVV2Le/jPVtW3PBfKP3ACAoCq3qGqu7xz/Qg4QEQG5nieTcBvVDXsie0S4DRvrEcA31bVFlWdB9yGE5k2iMhI4FTgKlVtVNVNwK9xgfw4q1T1VlWN4ibTjgJG5jJIVX1OVReoakxV5wP3A0fneI1GkRF3Uaa+ih2LwRm9wWhgtarGfNtWkTxpNDGhVFUbRGRbvF2O59joe9+c5nM/SJQfuh4XNxgOxMc0DDdJtT3Wqqr6Pq/yxjka2Kaqu1L2ZZpjNB6oANb7Cj8ESL7eDfE3qtrkHdcvhzEiIocCNwBTgUqgCvhrLm2N4iPuoiw1Su+KjXywDhgnIv7v2+4kz6lJWGsi0g8Y4rXrbj6JKy90PG7OzoT4aXNsPyalFNHuuHGuA4aISP+UffFr9IsiOCELAsNUdZD3GqCqOcUD0/SXyn24FO5xqjoQ+CO5X6NRhEQ10OZV7BT/FRp9gdlAE/AtEakQkWNwcbIHfMecKiJHevNtfgK8pqpxa2Yj0O78rhzpjxOWrUAtLjbWEUYAX/Gu4xxgX+BRb6yvAD8TkWoRmYYrRBufGrARmBAXeVVdj4tJ/q+IDBCRgIjsKSK5uhHbuyf9cRZli4gcghN2o0RRhWgs0OZV7BT/FRp5xyvU+lHgFGAL8HvgM6r6ru+w+3BJG9uAg4BP+/b9CLjLy8A8t4vDuRvnOlwLLAJe62D72bgElS04V+fZ8YoNuJjiBJw19w/gh6r6lLcv7h7cKiJveu8/g3MfLgK24+YLjcpxHL8FzvYyLG9Ks/9LwHUisgv4AfBQjv0aRUnb+FspxOAkOZxgGL2PiNwJrFHV7+V7LNkQkYuBS1X1yHyPxTA6Qt1eo3S/mz7bZvsbp/xsbg/VouwTWJKJYRhGsaMQLQGLLRUTOMMwjCJHATWBM4zeR1UvzvcYckFV78RNzjaMAkOIxkzgDMMwjCJDFWIlkDWZigmcYRhGCVAKWZOpFJzAlfWr0/IhQ9o/0DAMowgJrV6zRVWHd7RdzFyUfZ/yIUMY/Y2r8j0MwzCMvLDyqqtXdbSNUhrz3lLpUaesiJwsIku8pUOuSbO/SkQe9PbPFpEJPTkewzCMkkRBY9LmVez0mMB5RW1vxlWvmAJcICJTUg67BNiuqpNwldR/3lPjMQzDKGVUpc2r2OlJC+4QYKmqLvdKNT2AK3Lr5wzcMiDgyhQdl1LI1jAMw+giiovBpb6KnZ4UuDEkL/2xhuTlUZKOUdUIbrmSoT04JsMwjNKjRF2UBZFkIiKXAZcBlA0enOfRGIZhFCAlWHa4Jy24tfjW+ALGkrz+V9IxIlKOW59ra8oxqOotqjpTVWeW9avroeEahmEUK22tt1Kw4HpS4N4AJovIRG+Nr/NxCzD6mQVc5L0/G3hGbXkDwzCM7sVclN2LqkZE5ErgCaAMuENVF4rIdcAcVZ0F3A7cIyJLceuAnd9T4zEMwyhpSiBrMpUejcGp6qPAoynbfuB73wKc05NjMAzDMCjJGFxBJJkYhmEYXcBzUZYaJnCGYRilgAmcYRiGUYyIuSgNwzCMokOlJC240lsBzzAMoxSJpXm1Q1cK5ovId7ztS0TkpG67jg5gAmcYhlHsKM6CS31loSsF873jzgf2A04Gfu/116uYwBmGYZQAom1f7dCVgvlnAA+oalBVVwBLvf56lXYFTkTaLGGTbpthGIbRh9E0r+x0pWB+Lm17nFwsuBPSbDuluwdiGIZh9BwSkzYvYJiIzPG9Lsv3OLuTjFmUIvJF4EvAHiIy37erP/ByTw/MMAzD6CYyW2xbVHVmhlYdKZi/JqVgfi5te5xs0wTuAx4Dfgb4s2d2qeq2Hh2VYRiG0a1IDlmTKSQK5uPE6XzgkynHxAvmv4qvYL6IzALuE5EbgdHAZOD1zo++c2QUOFWtx/lTL+i94RiGYRg9QgcFrisF873jHgIWARHgClWNdtu15IhN9DYMwyhycsyabENXCuar6vXA9R0/a/dhAmcYhlEKlGAlExM4wzCMEqATMbiCxwTOMAyj2FETOMMwDKNYsdUEDMMwjGLElssxDMMwig9zURqGYRhFi1lwhmEYRrEhmAVnGIZhFCPmojQMwzCKFhM4wzAMoxgpxSzKHlvRW0TGicizIrJIRBaKyFfTHHOMiNSLyDzv9YN0fRmGYRhdQHEWXOqryOlJCy4CfENV3xSR/sBcEXlSVRelHPeiqp7eg+MwDMMoeUoxBtdjFpyqrlfVN733u4DF5GHJcsMwDKN1RQH/q9jplRiciEwAZgCz0+w+XETeBtYBV6vqwjTtLwPiS6k3rLzq6iUZTjUM2NL1ERcsdv12/Xb9xc/4DreIuyhLjB4XOBHpB/wNuEpVd6bsfhMYr6oNInIq8E/cyq9JqOotwC05nGtOluXXix67frt+u/7Svf5sCKVhsaXSYy5KABGpwInbvar699T9qrpTVRu8948CFSIyrCfHZBiGUYpIrO2r2OnJLErBLWe+WFVvzHDMbt5xiMgh3ni29tSYDMMwShZN8ypyetJFeQRwIbBAROZ5274L7A6gqn8Ezga+KCIRoBk4X1W7ctvbdWMWOXb9pY1dv5GeEq1kIl3TE8MwDKOvUztinO599tfbbJ/3h6/PLea4pVUyMQzDKAFKMcnEBM4wDKPYKdFpAj2aRdlbiMjJIrJERJaKyDX5Hk9vIyIrRWSBV+5sTr7H0xuIyB0isklE3vFtGyIiT4rI+96/g/M5xp4kw/X/SETW+krfnZrPMfYUmcoAltLfv6PEl8uxLMoCQ0TKgJuBU4ApwAUiMiW/o8oLx6rq9GL2p6dwJ3ByyrZrgKdVdTLwtPe5WLmTttcP8GvvezDdm3pTjMTLAE4BDgOu8P7Pl9Lfv2MoSEzbvIqdghc44BBgqaouV9UQ8ABwRp7HZPQwqvoCsC1l8xnAXd77u4CP9+aYepMM118SZCkDWDJ//85QiqW6ikHgxgCrfZ/XUHo1LxX4r4jM9cqalSojVXW9934DMDKfg8kTV4rIfM+FWfQuupQygPb3z4K5KI1C5UhVPRDnpr1CRI7K94DyjTefsgR+oybxB2BPYDqwHvjfvI6mh8lWBrBE//6ZURO4QmUtMM73eay3rWRQ1bXev5uAf+DctqXIRhEZBeD9uynP4+lVVHWjqkZVNQbcShF/DzKUASzpv3+7lGAlk2IQuDeAySIyUUQqgfOBWXkeU68hInXeenuISB1wIvBO9lZFyyzgIu/9RcC/8jiWXif+cPf4BEX6PchSBrCk//7ZcFmUpZdkUvDz4FQ1IiJXAk8AZcAd6ZbcKWJGAv/wSnqWA/ep6uP5HVLPIyL3A8cAw0RkDfBD4AbgIRG5BFgFnJu/EfYsGa7/GBGZjvttvhL4Qr7G18NkKgNYMn//DtMDpbpEZAjwIDAB9307V1W3pznuIuB73sefqupd3vbngFG4Mo0AJ3peqO4bo5XqMgzDKG76DRmn0064qs32Vx+6utOlukTkF8A2Vb3Bm388WFW/nXLMEGAOMBP3w2sucJCqbvcE7mpV7bG5u8XgojQMwzDaoQeSTHKZlnES8KSqbvOsuydJP3+zRzCBMwzDKHYyT/QeJiJzfK+OTDPKZVpGe9O4/uxV3fl+fOm07qTgY3CGYRhGduKlutKwJZuLUkSeAnZLs+ta/wdVVZEOTx3/lKqu9ZLk/oaLq97dwT6yYgJnGIZR7Ki6V4eb6fGZ9onIRhEZparrs0zLWItLhoozFnjO6zs+vWmXiNyHm9bSrQJnLkrDMIwSoAdicLlMy3gCOFFEBnuVdU4EnhCRchEZBok5jafTA9NaTOAMwzCKHQWJaptXF7kBOEFE3geO9z4jIjNF5DYAVd0G/AQ3X/kN4DpvWxVO6OYD83CW3q1dHVAq5qI0DMMoBbp5RpiqbgWOS7N9DnCp7/MdwB0pxzQCB3XviNpiFpxh5ICIHOwVMa72qscsFJGp+R6XYeSKVTIxDCMtqvqGiMwCfgrUAH9R1aIshWUUIT1QyaQQMIEzjNy5DhdHaAG+kuexGEbOCHRHzK3gMIEzjNwZCvQDKoBqoDG/wzGM3JESLMtoMTjDyJ0/Ad8H7gV+nuexGEbuqEIszavIMQvOMHJARD4DhFX1PhEpA14RkY+o6jP5Hpth5EIpJJWkYgJnGDmgqnfjVVlQ1ShwaH5HZBgdwJJMDMMwjKLFLDjDMAyjGJFY6ZlwJnCGYRhFjmi3lOYqOEzgDMMwSoESnCZgAmcYhlHsKGAWnGEYhlGMWAzOMAzDKEI6t+BpoWMCZxiGUeyYi9IwDMMoVsxFaRiGYRQfik30NgzDMIoRBbPgDMMwjKJDgagJnGEYhlF0KMSi+R5Er2MCZxiGUexYDM4wDMMoWiwGZxiGYRQdqvD/7dyxalRBFIfx7y8iFhaaCFEUQVHwAXwCsbDTQqyUFLHwEQSfQCzs06XTYKNYGEywsBIEH0AbQYkKmkAqweRY5Aoh2WiyN0GZfD8YdmbuPbunO9yZubvsEqUkqUX+k4kkqT3lKUpJUoMKyiVKSVJz3IOTJDVrD+7B7fvXCUiSdltRy8sbWh9JRpK8SPKu+zyyyX3PkywmebZu/nSS10neJ3mU5ECvhAawwElS64rVJcr1rZ87wFxVnQPmuvEg94GbA+bvAQ+q6iywAEz0TWg9C5wkNa6AWqkNracrwFTXnwKuDvztqjlgae1ckgAXgcd/i+/DPThJal3VbpyiHKuq+a7/GRjbRuwosFhVP7vxR+DETiYHFjhJat4SCzOzK9NHB1w6mOTNmvFkVU3+HiSZBY4NiLu7dlBVleS/O8VigZOkxlXV5SHjLm12LcmXJMeraj7JceDrNr76G3A4yf7uKe4k8GmYHP/EPThJ0jCeAuNdfxx4stXAqirgJXBtmPitSu3BdyMkSf0kGQWmgVPAB+B6VX1PcgG4XVW3uvteAeeBQ6w+uU1U1UySM8BDYAR4C9yoqh87mqMFTpLUIpcoJUlNssBJkppkgZMkNckCJ0lqkgVOktQkC5wkqUkWOElSkyxwkqQm/QJfRD928u56PQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "o.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "o.plot_fin_hit_prob()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result\n",
    "As expected, no perturbation is necessary for optimal coverage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Potential Barrier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "vscode": {}
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "U_p = U.copy()\n",
    "U_p[:,2] = 0.3\n",
    "s_p = sqra.sqra2d(U_p)\n",
    "s_p.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "o_p=optim.SqraOptim(s_p, ts, penalty = 0.0001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 23 s, sys: 843 ms, total: 23.9 s\nWall time: 30.3 s\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": " final_simplex: (array([[0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       ...,\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.]]), array([-0.01638553, -0.0163855 , -0.0163855 , -0.01638549, -0.01638549,\n       -0.01638547, -0.01638547, -0.01638547, -0.01638547, -0.01638546,\n       -0.01638546, -0.01638546, -0.01638546, -0.01638546, -0.01638543,\n       -0.01638543, -0.01638543, -0.01638543, -0.01638542, -0.01638542,\n       -0.01638542, -0.01638542, -0.01638542, -0.01638542, -0.01638542,\n       -0.01638542, -0.01638542, -0.01638538, -0.01638538, -0.01638538,\n       -0.01638537, -0.01638537, -0.01638536, -0.01638535, -0.01638535,\n       -0.01638535, -0.01638535, -0.01638535, -0.01638535, -0.01638533,\n       -0.01638533, -0.01638531, -0.0163853 , -0.0163853 , -0.0163853 ,\n       -0.0163853 , -0.0163853 , -0.0163853 , -0.0163853 , -0.0163853 ,\n       -0.01638529, -0.01638529, -0.01638529, -0.01638529, -0.01638529,\n       -0.01638529, -0.01638529, -0.01638529, -0.01638528, -0.01638528,\n       -0.01638528, -0.01638527, -0.01638527, -0.01638527, -0.01638527,\n       -0.01638524, -0.01638524, -0.01638524, -0.01638524, -0.01638522,\n       -0.01638522, -0.01638522, -0.01638522, -0.01638522, -0.01638522,\n       -0.01638522]))\n           fun: -0.016385529320245625\n       message: 'Maximum number of iterations has been exceeded.'\n          nfev: 85\n           nit: 10\n        status: 2\n       success: False\n             x: array([0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.00025,\n       0.     , 0.     , 0.     , 0.     , 0.     , 0.     , 0.     ,\n       0.     , 0.     , 0.     , 0.     , 0.     ])"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "%time o_p.optimize(niter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x576 with 5 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "o_p.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "o_p.plot_perturbation()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Entropic Barrier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "U_h = U.copy()\n",
    "U_h[:,2] = np.inf\n",
    "U_h[2,2] = 0\n",
    "s_h = sqra.sqra2d(U_h, phi=10)\n",
    "s_h.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "o_h=optim.SqraOptim(s_h, ts, penalty = 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 256 ms, sys: 3.48 ms, total: 259 ms\nWall time: 353 ms\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-0.016524032890056883"
     },
     "metadata": {},
     "execution_count": 15
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "%time o.plot_fin_hit_prob()\n",
    "o.objective(o.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "CPU times: user 1min 5s, sys: 1.98 s, total: 1min 7s\nWall time: 1min 24s\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": " final_simplex: (array([[ 1.00000000e-05,  1.00000000e-05,  1.00000000e-05, ...,\n         1.00000000e-05,  1.00000000e-05,  1.00000000e-05],\n       [ 7.70300052e-06,  7.70300052e-06,  7.70300052e-06, ...,\n         7.70300052e-06,  7.70300052e-06, -5.80811059e-06],\n       [ 8.11930491e-06,  8.11930491e-06,  8.11930491e-06, ...,\n         8.11930491e-06,  8.11930491e-06, -6.12200670e-06],\n       ...,\n       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n         0.00000000e+00,  0.00000000e+00,  0.00000000e+00]]), array([-0.40927797, -0.4092681 , -0.40926728, -0.40926698, -0.40926509,\n       -0.40926189, -0.40926164, -0.40926164, -0.40926164, -0.40926164,\n       -0.40926164, -0.40926164, -0.40926164, -0.40926164, -0.40926164,\n       -0.40926164, -0.40926164, -0.40926164, -0.40926138, -0.40926138,\n       -0.40926093, -0.40926093, -0.40926078, -0.40926078, -0.40926078,\n       -0.40926078, -0.40926046, -0.40926046, -0.40926026, -0.40926026,\n       -0.40926026, -0.40926026, -0.40926026, -0.40926012, -0.40926012,\n       -0.40926012, -0.40926012, -0.40926004, -0.40925999, -0.40925999,\n       -0.40925999, -0.40925999, -0.40925993, -0.40925982, -0.40925982,\n       -0.40925982, -0.40925982, -0.40925972, -0.40925972, -0.40925972,\n       -0.40925972, -0.40925968, -0.40925957, -0.40925947, -0.40925947,\n       -0.40925939, -0.40925939, -0.40925939, -0.40925939, -0.40925893,\n       -0.40925893, -0.40925893, -0.40925893, -0.40925812, -0.40925812,\n       -0.40925812, -0.40925812, -0.40925794, -0.40925794, -0.40925794,\n       -0.40925794, -0.40925673, -0.40925673, -0.40925673, -0.40925673,\n       -0.40925614]))\n           fun: -0.4092779672706748\n       message: 'Maximum number of iterations has been exceeded.'\n          nfev: 86\n           nit: 10\n        status: 2\n       success: False\n             x: array([ 1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05, -5.e-04,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05,\n        1.e-05,  1.e-05,  1.e-05,  1.e-05,  1.e-05])"
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "o.simplex=None\n",
    "o.adaptive=True\n",
    "%time o_h.optimize(niter);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x576 with 5 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "o_h.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-0.4092618863429995"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "o_h.objective(np.zeros_like(o_h.x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "-0.4092792072706748"
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "o_h.objective(o_h.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.2400000000000002e-06"
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "source": [
    "o_h.penaltyfunction(o_h.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "o_h.plot_perturbation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x1261da460>"
     },
     "metadata": {},
     "execution_count": 22
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(np.vstack([x for x in o_h.x.reshape(3,5,5) + 0 * o_h.sqra.u.reshape(5,5)]))\n",
    "plt.colorbar()"
   ]
  },
  {
   "source": [
    "# Experimental"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "{\n  \"shell_port\": 9087,\n  \"iopub_port\": 9089,\n  \"stdin_port\": 9088,\n  \"control_port\": 9086,\n  \"hb_port\": 9085,\n  \"ip\": \"127.0.0.1\",\n  \"key\": \"a8b36c1c-fdbe-4dbd-bf53-d7deba0cacbf\",\n  \"transport\": \"tcp\",\n  \"signature_scheme\": \"hmac-sha256\",\n  \"kernel_name\": \"\"\n}\n\nPaste the above JSON into a file, and connect with:\n    $> jupyter <app> --existing <file>\nor, if you are local, you can connect with just:\n    $> jupyter <app> --existing /var/folders/f1/lgdx8nc94yg_11x4fhdkpck00000gn/T/tmp-2210823KIs552zpn.json\nor even just:\n    $> jupyter <app> --existing\nif this is the most recent Jupyter kernel you have started.\n"
    }
   ],
   "source": [
    "%connect_info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import ode\n",
    "Qs = [s_p.Q] * 3\n",
    "us = [s_p.u] * 3\n",
    "dts = [1,1,1]\n",
    "hpa = ode.finite_time_hitting_prob_adjoint(Qs, dts, us, nquad=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "hp1 = hpa.finite_time_hitting_probs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2.0876343986842016e-09"
     },
     "metadata": {},
     "execution_count": 54
    }
   ],
   "source": [
    "hp2 = ode.finite_time_hitting_probs(Qs, dts)\n",
    "np.max(np.abs(hp1-hp2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x1263e0070>"
     },
     "metadata": {},
     "execution_count": 55
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 2 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(hp1)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "vscode": {
     "end_execution_time": "2020-09-18T15:42:25.574Z",
     "start_execution_time": "2020-09-18T15:42:25.375Z"
    }
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.016385464402537332"
     },
     "metadata": {},
     "execution_count": 62
    }
   ],
   "source": [
    "o, du = hpa.min_and_derivative()\n",
    "o"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(24, 0)"
     },
     "metadata": {},
     "execution_count": 66
    }
   ],
   "source": [
    "hpa.activei, hpa.activej"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(du.reshape(nx,ny))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp = s_p.perturbed_copy(np.ones(25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp = s_p.perturbed_copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "ap = ode.finite_time_hitting_prob_adjoint([sp.Q]*3, dts, [sp.u]*3, nquad=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.016523503214520154\n0.01644251643951651\n0.016523561994866324\n0.01644174162901992\n0.01652314117651878\n0.016442150730722204\n0.016523463097902286\n0.01644167645660027\n0.016522928065518885\n0.016441971332509072\n"
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"248.518125pt\" version=\"1.1\" viewBox=\"0 0 245.2025 248.518125\" width=\"245.2025pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <metadata>\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2020-09-25T14:43:44.343820</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.3.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    ap = ode.finite_time_hitting_prob_adjoint([sp.Q]*3, dts, [sp.u]*3, nquad =100)\n",
    "    m, d = ap.min_and_derivative()\n",
    "    sp = sp.perturbed_copy(d*1)\n",
    "    print(m)\n",
    "    plt.imshow(d.reshape((5,5)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x12af9ea60>"
     },
     "metadata": {},
     "execution_count": 219
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(sp.u)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([12.62034262, 12.57918135, 12.59979571, 12.57918135, 12.6203426 ])"
     },
     "metadata": {},
     "execution_count": 220
    }
   ],
   "source": [
    "sum(sp.u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "[autoreload of ode failed: Traceback (most recent call last):\n  File \"/usr/local/lib/python3.8/site-packages/IPython/extensions/autoreload.py\", line 245, in check\n    superreload(m, reload, self.old_objects)\n  File \"/usr/local/lib/python3.8/site-packages/IPython/extensions/autoreload.py\", line 394, in superreload\n    module = reload(module)\n  File \"/usr/local/Cellar/python@3.8/3.8.5/Frameworks/Python.framework/Versions/3.8/lib/python3.8/imp.py\", line 314, in reload\n    return importlib.reload(module)\n  File \"/usr/local/Cellar/python@3.8/3.8.5/Frameworks/Python.framework/Versions/3.8/lib/python3.8/importlib/__init__.py\", line 169, in reload\n    _bootstrap._exec(spec, module)\n  File \"<frozen importlib._bootstrap>\", line 604, in _exec\n  File \"<frozen importlib._bootstrap_external>\", line 779, in exec_module\n  File \"<frozen importlib._bootstrap_external>\", line 916, in get_code\n  File \"<frozen importlib._bootstrap_external>\", line 846, in source_to_code\n  File \"<frozen importlib._bootstrap>\", line 219, in _call_with_frames_removed\n  File \"/Users/alex/Documents/code/augjuc/ode.py\", line 175\n    def __init__(self, inc=1.2, dec=.5, max=50, min=1e-6)\n                                                        ^\nSyntaxError: invalid syntax\n]\n"
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1e-06"
     },
     "metadata": {},
     "execution_count": 221
    }
   ],
   "source": [
    "1e-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([4, 5])"
     },
     "metadata": {},
     "execution_count": 229
    }
   ],
   "source": [
    "np.sign([1,2]) * np.array([4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2"
     },
     "metadata": {},
     "execution_count": 225
    }
   ],
   "source": [
    "np.maximum(1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 588,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem = ode.Problem(s_p, [3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 592,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.01652403236232746\n"
    }
   ],
   "source": [
    "m, d = problem.obj(np.zeros(25))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 595,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x12e0319a0>"
     },
     "metadata": {},
     "execution_count": 595
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     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(d.reshape(5,5))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 597,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(24, 0)"
     },
     "metadata": {},
     "execution_count": 597
    }
   ],
   "source": [
    "problem.hp.activei, problem.hp.activej"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 580,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.01652403236232746\n"
    }
   ],
   "source": [
    "rprop = ode.Rprop(lambda x: problem.obj(x)[1], np.zeros(25), max=1000, g0=np.random.rand(25)*0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 586,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0.01640230885705224\n0.016370393645884433\n0.016331992367683148\n0.016285764457824547\n0.016230083602830556\n0.01616297388263949\n0.016082030989984217\n0.01598432507254304\n0.015866281428957244\n0.015723535110863475\n0.01555075603492872\n0.01534144347413071\n0.015087620310129838\n0.014779658430516792\n0.014406063067989347\n0.013953320081852755\n0.013405992326167213\n0.012747266648171642\n0.011960296256582091\n0.011030800251835858\n0.009951399521661583\n0.008727351069862508\n0.007374017098057511\n0.005938895010183203\n0.004506941406892576\n0.003184098131415549\n0.002025275937919214\n0.001099113017646502\n0.0004852436656004085\n0.0001655211576137958\n4.1382890412742376e-05\n"
    },
    {
     "output_type": "error",
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/usr/local/lib/python3.8/site-packages/scipy/sparse/sputils.py\u001b[0m in \u001b[0;36misshape\u001b[0;34m(x, nonneg)\u001b[0m\n\u001b[1;32m    214\u001b[0m         \u001b[0;31m# Assume it's a tuple of matrix dimensions (M, N)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 215\u001b[0;31m         \u001b[0;34m(\u001b[0m\u001b[0mM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    216\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: too many values to unpack (expected 2)",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-586-dd9baa75c75f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrprop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, iter)\u001b[0m\n\u001b[1;32m    204\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    205\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0miter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 206\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miterate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    207\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    208\u001b[0m \u001b[0;32mclass\u001b[0m \u001b[0mProblem\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36miterate\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    190\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    191\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0miterate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 192\u001b[0;31m         \u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    193\u001b[0m         \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    194\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-580-cc5876256b07>\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(x)\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrprop\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mRprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mproblem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m25\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m25\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m0.001\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mobj\u001b[0;34m(self, x)\u001b[0m\n\u001b[1;32m    219\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    220\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mperturb\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 221\u001b[0;31m         \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmin_and_derivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    222\u001b[0m         \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    223\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mmin_and_derivative\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    139\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    140\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmin_and_derivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 141\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfinite_time_hitting_probs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    142\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mode_mu\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    143\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madjointintegrate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mfinite_time_hitting_probs\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     91\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     92\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 93\u001b[0;31m             \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mode_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     94\u001b[0m             \u001b[0my0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     95\u001b[0m             \u001b[0mcmin\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mode_y\u001b[0;34m(self, j)\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0myT\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     81\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 82\u001b[0;31m         \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0modeint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdydt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mits\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     83\u001b[0m         \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     84\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.8/site-packages/scipy/integrate/odepack.py\u001b[0m in \u001b[0;36modeint\u001b[0;34m(func, y0, t, args, Dfun, col_deriv, full_output, ml, mu, rtol, atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg, tfirst)\u001b[0m\n\u001b[1;32m    239\u001b[0m     \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    240\u001b[0m     \u001b[0my0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 241\u001b[0;31m     output = _odepack.odeint(func, y0, t, args, Dfun, col_deriv, ml, mu,\n\u001b[0m\u001b[1;32m    242\u001b[0m                              \u001b[0mfull_output\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrtol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0matol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtcrit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhmax\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhmin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    243\u001b[0m                              \u001b[0mixpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxhnil\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxordn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxords\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mdydt\u001b[0;34m(y, t)\u001b[0m\n\u001b[1;32m     72\u001b[0m         \u001b[0;31m# solve the finite time hitting ode for state j\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     73\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mdydt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 74\u001b[0;31m             \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdfdy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     75\u001b[0m             \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     76\u001b[0m             \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnan_to_num\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Documents/code/augjuc/ode.py\u001b[0m in \u001b[0;36mdfdy\u001b[0;34m(self, t)\u001b[0m\n\u001b[1;32m     67\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mdfdy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     68\u001b[0m         \u001b[0;31m# linear part of ode rhs: y' = f(y) = dfdy y\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mQs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimeindex\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     70\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     71\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mode_y\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.8/site-packages/scipy/sparse/data.py\u001b[0m in \u001b[0;36m__neg__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     49\u001b[0m             raise NotImplementedError('negating a sparse boolean '\n\u001b[1;32m     50\u001b[0m                                       'matrix is not supported')\n\u001b[0;32m---> 51\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_with_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__imul__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# self *= other\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.8/site-packages/scipy/sparse/compressed.py\u001b[0m in \u001b[0;36m_with_data\u001b[0;34m(self, data, copy)\u001b[0m\n\u001b[1;32m   1200\u001b[0m         \"\"\"\n\u001b[1;32m   1201\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1202\u001b[0;31m             return self.__class__((data, self.indices.copy(),\n\u001b[0m\u001b[1;32m   1203\u001b[0m                                    self.indptr.copy()),\n\u001b[1;32m   1204\u001b[0m                                   \u001b[0mshape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.8/site-packages/scipy/sparse/compressed.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, arg1, shape, dtype, copy)\u001b[0m\n\u001b[1;32m     36\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 38\u001b[0;31m             \u001b[0;32mif\u001b[0m \u001b[0misshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     39\u001b[0m                 \u001b[0;31m# It's a tuple of matrix dimensions (M, N)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m                 \u001b[0;31m# create empty matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.8/site-packages/scipy/sparse/sputils.py\u001b[0m in \u001b[0;36misshape\u001b[0;34m(x, nonneg)\u001b[0m\n\u001b[1;32m    214\u001b[0m         \u001b[0;31m# Assume it's a tuple of matrix dimensions (M, N)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    215\u001b[0m         \u001b[0;34m(\u001b[0m\u001b[0mM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 216\u001b[0;31m     \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    217\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    218\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "rprop.run(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 587,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.colorbar.Colorbar at 0x12dc7a550>"
     },
     "metadata": {},
     "execution_count": 587
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.imshow(rprop.x.reshape((5,5)))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 585,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1.42587086e-03, 3.49733092e-03, 3.02485830e-03, 4.09512422e-03,\n       2.17066452e-03, 8.17044132e-05, 1.73949853e-03, 1.93120329e-03,\n       2.90439970e-03, 6.68853661e-04, 2.98435458e-03, 4.16193962e-03,\n       3.41039710e-04, 2.39058673e-04, 3.01744525e-03, 1.15739814e-03,\n       4.17630293e-03, 1.54285894e-03, 4.50499155e-04, 2.88798035e-03,\n       2.37127828e-03, 3.19093971e-03, 1.46463791e-04, 1.71341689e-03,\n       2.00429226e-03])"
     },
     "metadata": {},
     "execution_count": 585
    }
   ],
   "source": [
    "rprop.g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.5 64-bit",
   "name": "python_defaultSpec_1600680249488"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5-final"
  },
  "orig_nbformat": 2
 },
 "nbformat": 4,
 "nbformat_minor": 2
}