PI.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "former-municipality",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Assignment 2 \n",
    "## Gargi Vaidya\n",
    "## Part 5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "hindu-cornwall",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Policy stable\n",
      "Convergence Plot of Value Iteration - \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value Function \n",
      "  [0.06874881 0.06125542 0.07426752 0.05555766 0.09171777 0.\n",
      " 0.11212568 0.         0.14531312 0.24739914 0.29953819 0.\n",
      " 0.         0.37986114 0.63897971 0.        ]\n",
      "Policy \n",
      " [0 3 0 3 0 0 0 0 3 1 0 0 0 2 1 0]\n"
     ]
    },
    {
     "data": {
      "image/png": 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XCkoiIiIiLhSURERERFwoKImIiIi4UFASERERcaGgJCIiIuJCQUlERETEhYKSiIiIiAsFJREREREXCkoiIiIiLhSURERERFwoKImIiIi4UFASERERcaGgJCIiIuJCQUlERETEhYKSiIiIiAsFJREREREXCkoiIiIiLhSURERERFwoKImIiIi4UFASERERcaGgJCIiIuJCQUlERETEhYKSiIiIiAsFJREREREXCkoiIiIiLhSURERERFwoKImIiIi4UFASERERcREW6gaE0uq5s5n44btYv5/D+h9H91PPKDXfWsvED99l9ZxZhEVGMnDYDdRp3gKAXbm5jH3rNbLS12KM4birr6N+67ZsXr2S3955E19hAR6vl36XD6Vey9Ysmfw7s374rrjuzLVrOP/RJ0lt2rx42v+eHcnWzRlcNPI5ALZlbmbsqFfJ376NWjGxnHDdzcQmJ1fDnjm0rJo7mwmB49yh/3H0CHKcJ3zwDqvmziYsIoITrrmx1HH+9c3XyEpfA8Zw/LDrqd+6LcumTWHq11+wZf06zn/4Ceq2aAXA6nlzmfLZx/iKivCGhXH0hZfQuMPhAHz16APk5uQQFh4BwBnD7yc6Pp6FE35j0qcfEpOYBEDnEwbT8diB1bV7Dilr/prDlE+cY92u73EccfLppeZba5ny8bus+Ws2YRGR9B96PanNWpCzYT2/vvp8cbltmzPofsa5dBp0UvG0uT9+z9TPP+LSl94iKq426fP/YtqXH+P3FeHxhtH7vEtoeFhHAHxFRUz68G02LF6IMYYeZ51Pix692Z6Vyfg3X2FXXi7W76fXORfSpHPXatk3h5KVc2Yz9r13sH4/nQYcR6/Tzyw131rLuPfeYcXsWYRFRjDkupuo28I5p9+48VoiakVhPB48Xi+XPvEUAJO//Jy/xv5KVO3aAPS94EJaHNGNrRkZvHPbLSQ2aABAg9ZtOOHqawD4bMQD7MjOJizCOafPufcBYuLj2Za5mdGvvMSuvDz8fh/9LryYFkd0q5Z9I5WvxgYlv9/H+Pff5vTh9xOblMTnD9xNi27dSWrYuLjM6rmzydm4gUuefYlNy5cx/r03OXfEEwBM/PBdmnY6giG33I6vqJCiXQUATP70I3qeeQ7NOh/BqjmzmPLpR5x53wja9jmGtn2OASBz7Wp+eO6pUiEpbfo0wmvVKtXGyZ98QLuj+9G+b3/WLpjHlC8+5oTrbq7qXXNI8ft9jH/vLc64+wFik5L47P7htOjaneRGe47zqsBxvuzZl9iYtoxx747i/IdHAjDhw3do2rkLJ91a+jgnN2rCybfewdh33ii1vqi4OE65fTixiUlkrl3Dt08+ytCXRxXPH3z9zcWhqqTWvY/i2MuHVsUuqDH8fj+TP3ybk+64j5ikZL4ZcTfNjuhOYsNGxWXW/jWbrZs2cv6TL5KxfBmTPniLMx54nIT6DTj7kaeL6/no1mto3q1n8XI7sjJJXzCP2OSU4mm14uIYfOtdxCQmsSV9DT888xiXvOC8Hmb93zdE1Y7n/Cf/g/X72Zm7w5n+/de06HkkHQacQPa6dEY/9wQXPaugVBF+v49f3nmTc+99gLjkZD68+y5adu9BSolzeuWcWWRv3MDQ/7zMhmXL+OXtUVz82Mji+ec9MILoQCAqqdtJJ9PzlNP2mZ5Qty6XP/Vs0PacfNMt1GtZ+pz+45uvaHvkURxxwmAy09fy9cjHuOZlBaWDVY299bZpeRoJdesRX6cu3rBw2vTuw4qZM0qVWTFzOu2P7ocxhnqt2rArN5fc7GwK8vJYv2Qhh/UfAIA3LJzImBgAjDEU5OcBUJCXR0xi4j7rXjplMm2O7FP8vGBnPnN+/D96nH5WqXJb1qUX90Y0OqzjPu2T/du0PI34fY7z9FJlVsycTvtj+mOMoX7rNuzKyyM3O5tdeXmsW7yIDv2PA0of56SGjUhs0HCf9dVp1oLYQM9QcqPG+AoLKCosrOKtFICMFWnUrluP2nXq4g0Lo1Wvo1g1u/SxXjV7Bm369MUYQ91WbdiVl0tuTnapMusWzqN2nXrEpaQWT5vy6fv0PvciwBRPS2navLgXMLFhY3yFhfgCx3rJ778V92YZj4eoOOdN2RhDYeD6sCs/+PVByrYhLY3EuvVIqFsPb1g47Y46mrTppY/zsunT6dDXuXY3aNOGnbm57MjOdqmxKhgK8vMB2JWXV3xNkIPTfnuUjDHtgNOAhoAF1gPfW2sXVXHbqlRu9hZik/bcxopNSmLj8mX7lkkuWSaZHdlb8Hg91Iqrza+jXiFzzWrqNGtB30uuILxWLY65+HK+e+pRJn/yIdb6OfvBx/ZZ97JpUzj5X3cWP5/21eccceIphEVEliqX0qQpadOn0mXwSSyf8SeFO/PJ376dqLi4ytoNh7wdW7YQV6IXIDYpeZ/jvGNL1l7HOYkd2Vl4PF6i4mrzyxuvkLlmFXWat6Rf4DiXR9qfU0lt2pyw8PDiab+88SrG46FVz170PP1sjHHeeNOmT2Xd4oUk1mtA30suL9VmKZ+8vc7pmMRkMlbse07HJKWUKpOXvYWYhD2BZfm0ybTqveeDzKrZM4hJTCK5STPXda+cMY2Ups3xhoezKzcXgOnffM6GxQupnVqXPpdcSXR8At1OP4fRzzzK/F9/onDXLk6+8/6/u9k1zt7ndFxyEhvS9jqns/cuk+yc54mJGAxfPvYwxhg6DzyezgNPKC43e8yPLJg4nnotWnHsJZdRKzYWgK2bM3j/rtuJiIrimPMuoFH7w4qX+fG1VzAeD2169ebIM51zus855/HlYw8z66fRFO7axbn3PVhVu0OqQZk9SsaYu4DPcD5G/QlMD/z9qTFmeNU3r+pYu+80U+LTolNm30LGgN/nZ/OqlRx+3CAueOxpwiMjmfl/3wIwb+zPHHPR5Vzx4uscc9HljH3ztVLLb0xbRnhEBMmNmwCwefVKcjZtpGWPXvusq8+Fl7Ju8UI+vfcO1i9aQExiEh5vje0EPEDBjqEJUm6fQvj9PjJWraDTwBO48PFnCI+MZMb//bdca81KX8vkzz5iwFXXFE8bfP0tXPzkc5zzwCOsX7yIxZMmANC8a3eueOE1Lh75HI07Hs7Pr79cvk2TUoKdr+x1Tgc/8feU8RUVsXr2TFr06A1A4a5dzP6/b+h+xnmu692ybi3TvviYYy6/GnBuDeVuyaJeq7acNeJJ6rZqw9TPPgRg+dTJtOnTn4uff50Tb7ubcaNewvr9FdvQmu5vHucLH36My558hrPuvo/ZY35i7cIFAHQ5fhBXv/gKlz/5LLGJCfz24fsAxCQmcs0rb3DZk89w7KWX87+XXmBXntMreNJNt3DFM89z4YhHSV+8iAUTnXN60eTf6djvWK577U3OGn4vo19+Ucf5ILa/d92rgB7W2pHW2o8Cj5FAz8C8oIwxw4wxM4wxM0aNGuVWLKRik5LYsSWr+PmOLVuKu9H3lElmR1bJMlnEJCQRm5REbFIy9Vq1BqBlzyPJWLUCgMW/jy8OPa16Hcmm5Wml6lw2dTKtjzy6+PnGZUvZvHIF7916PV89fD85G9bzzaPOp4/YxCROuvUOLnjsaXqfewEAkdExlbQHaobYpGS2Z2UWP3eOYeI+ZUof5y3EJjjH2DnObQBo1bM3GatW7ned27Oy+N/zT3HCtTeRULdeqfUARERF0faoY9gYeG1ExcUV9zp1HDCQjJUrDnBra7aYpORS53RudtY+t7ZikpLJ3ZJZqkx0idfD2r9mk9K0OdHxCQBsy9jEts0ZfHX/HXz87xvIzc7imwfvIi8nB3BeTz+/+AzHDruB+DrOsa4VG0dYRGTxGKcWPXqTudp53SyeOI6WPY8EoF6rNvgKC9m5Y3vl7ohDXGxy6XN6e9aWfW5t7X3eb8/KKi4Tm+T8GxMfT+uevdgQOA9jEhLweLwYj4dOA45nY6CXKiw8vLgXv16LliTUrUf2hvUAxJU4pw/rc3Rxb/W838bS9sijAGjYpi1FhQXkbddxPljtLyj5gQZBptcPzAvKWjvKWtvdWtt92LBhf6d9VaZui1bkbNzA1oxN+IoKWTp1Ms27di9VpnnX7iyaNAFrLRvTlhIRHU1MYiIxCYnEJiWTvX4dAOkL5pEUGDAak5jEukULA9Pnk1Bvzxul9ftZNu2PUuOTDh84iCtfHsXlL7zK2Q88QkL9Bpx53wgA8rdvK/4UMvP7/3JYv2OrboccooId5xbdepQq06Jrdxb9Ph5rLRuWLSUyas9xjkvec5zXljjObnbl5vL9M49z1HkX0aBtu+Lpfp+P/O3bAKfXYuXsmcUDynNLjJ1YMXMGSUHGPsn+1Wnekq2bNrBtcwa+oiLSpk2h6RGlz+mmXbqzdPJErLVsSltKRFR0qeCcNnUyLUvcdktu3ITLXnqLi559hYuefYWYxGTOHPEk0QkJ7MrN5cfnR9Lz7Auo13rPsTbG0LRLN9Yvdq4D6xbOJ7GB87qJTU5h3cL5AGSvT8dXWEituH0HFYu7+i1bkb1xAzmBc3rxlEm06l76OLfq3oMFE51r9/qlS4mMjiY2MZGCnTuLxw4V7NzJqr/mkhro3S85hmnZ9GmkBKbnbduK3+8DIGfTRrI3bCC+bl38Ph952/ac08tnzSxepnZKKmvm/wVAVno6RYWFQQePy8Fhf2OUbgXGGmOWAWsD05oArYAbq7BdVc7j9dLvsqv4/qnH8Pv9HNbvWJIbNWbe2J8BOPy4E2jWpSur587mg3/fRHhEBMcNu6F4+X6XXcnPr72Ir6iI2nXqMnDY9QAMuOoaJn74Ln6/n7Dw8FK3XtYtXkRsUjLxdeqWq43rFi1gyuefOAMS27anv74VVWEer5f+lw/l2ycfdX4Got8Akhs15q9fxwDQaeAgmnXpyqo5s3j/thsJi4jk+GuuL16+/6VX8dOr/8FXVER8nbocf43zGkibPo0J779N/vZtfPf0E6Q2bcYZw+9n7s8/krNpI3/+9yv+/O9XgPMzAOGRkXw78lF8viKs30+Tjp3oOMD5CYA5Y0azYtZ0PF4vtWJiOf7ag/rUChmP18vRF1/J6Gcew/r9tD3mWJIaNmbhOOecPmzACTTpfARr/prFZ3feTFhkBP2v2nOsC3ftIn3BXxxzefk+3C0Y+xPbNm1k1vdfM+v7rwE46Y77iKodT69zL2LcqJeZ8sl71IqrTf+hznqOPP9SJrz7Bn/9/AMG6D/0+vLdCpZiHq+XgVcO5avHH8Hv93N4/wGkNG7CnF+cc7rL8YNocURXVsyexZu33EB4RCQnXuect3lbc/j2GefnAPx+H+37HEPzLkcAMOHjD8hYtQoMxKfW4YSrrwVg7aKFTP7is+LepuOvHkZUbBwFO3fy1eOPFJ/TTQ/vRKfjnHO6/yWXMeaN15jxw//AGE687kYd54OYCX5fv0QBYzw4t9oa4twITgemW2t95VyHfXn6X3+rkfLPd2OPTrw6Y16omyFV7Pruzrcwn/tjbohbIlXptiM7A/DWnPkhbolUtaFdOirB7cd+v/VmrfUDU6uhLSIiIiL/KPoKlYiIiIgLBSURERERFwpKIiIiIi4UlERERERcKCiJiIiIuFBQEhEREXGhoCQiIiLiQkFJRERExIWCkoiIiIgLBSURERERFwpKIiIiIi4UlEQq0Xev/IfvXvlPqJshIpXkm5f+wzcv6Zyuyfb7n+KKSPl8/fwzjP/8YwB8hYWceevtIW6RiPwdXzz7NGM/3XNOn3ObzumaSEGpillrMcaEuhlSxeaOH8fyObPod+4FAKTNnsXcCb/Rud+xIW6ZVDad0zXD7N/Gsmz2LAac75zTS2fNZM5v4+hy7IAQt0yqm269VSG/z8d79w9nzm+/hropUsU69x/ALa+/RVRsLFGxsdzy+lsKSYcgv8/HRw/ezV/jx4a6KVLFjjj2OG5/822iYuOIio3j9jffVkiqodSjVEX8Ph/vP3A3O/Py6NCnb6ibI9UgMio66N9yaPD7fHz80D3sysvlsKOOCXVzpBronBZQUKoys34Zw6xfxgBw29E9gpa56IGH6X3yadXZLBE5QHPGjmHOWOecvqt/z6Blzrt3BD1P0jktcihRUKoiXY8fxF8Tf6MgP5+hTz1PWHh4qJskIn9Dl+MGMf/38RTk53P5E8/pnBapITRGqYp4vF4uf2QkkdHRzP99QqibIyJ/k8fr5eKHniAyKpqFk3ROi9QU6lGqQh6vl8sffVLfkBE5RHi8Xi5+eKTOaZEaREGpiumCWrOcNOz6UDdBqpjO6Zrl1Gt1Ttd0uvUmIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFsdZW9TqqfAUiIiJyQEyoG/BPFxbqBoiIiEgNtODrinWkdDgrJKGuWoLSw+PnVMdqJIQe6N+FcRvTQt0MqWID6rUC4N8/zg5xS6QqPXviEQA6p2uA3ed0KFifr0LlQ9X1pR4lERERqX6+olC3oFwUlERERKTaWX/FgpJ6lERERKTmqOCtt1BRUBIREZFqZ3XrTURERMSFgpKIiIhIcBUdoxQqCkoiIiJS/TRGSURERCQ4jVESERERcaOgJCIiIhKc9evWm4iIiEhQuvUmIiIi4kZBSURERCQ43XoTERERcaMeJREREZHgNEZJRERExI2CkoiIiEhwB8sYJU+oGyAiIiI1jy3YVaHH/hhj3jHGZBhj5rvMN8aYF40xacaYv4wxXcvTTgUlERERqXbWV1ShRzm8BwwuY/6JQOvAYxjwWnkq1a03ERERqX7+yh2jZK2daIxpVkaR04APrLUWmGqMSTDG1LfWbiirXgUlERERqXbWV7ExSsaYYTg9QbuNstaOqkAVDYG1JZ6nB6YpKImIiMg/TAWDUiAUVSQY7c0Eq3Z/CykoiYiISLULwe8opQONSzxvBKzf30IazC0iIiLVz+er2OPv+x64NPDtt97A1v2NTwL1KImIiEgIVHSM0v4YYz4F+gMpxph04EEgHMBa+zowGhgCpAF5wBXlqVdBSURERKpdZf/gpLX2gv3Mt8ANFa1XQUlERESqXyX3KFUVBSURERGpdpV9662qKCiJiIhItbM+f6ibUC4KSiIiIlL9FJREREREgtOtNxEREREX1rffH8X+R1BQEhERkWqnMUoiIiIiLhSURERERFxYv269iYiIiASlMUoiIiIiLuzB8aU3BSURERGpfupREhEREXHhPzjGcisoiYiISPXzF4S6BeWjoCQiIiLVTj1KIiIiIi40mFtERETEhd9vQt2EclFQEhERkWqnW28iIiIiLnTrTURERMSFbr2JiIiIuPCrR0lEREQkOPUoiYiIiLiwCkoiIiIiwelbbyIiIiIudOtNRERExIWCkoiIiIgLn4KSiIiISHDqURIRERFx4bcKSv946+fPYcYX72H9flodPYAOg08vNd9ay8zP32Pd/NmERURy5OXXkdSkBQCLx44mbdJYsNDq6AG0G3gSAKtn/sG8//uKrRvXMXj4YyQ3awnAymm/s+jn/yuuO3vdGk68dyRJjZsx59vPWDl1IgV5OzjvxQ+Ky+RuyeSPd1+hID8P6/fT5YwLaXj4EVW8Vw49C6bN4IuXRmH9fvqcdAKDLjq31HxrLV+8+AYLps0gIjKSS+/+F03atCpz2dxt23nroZFkbcwguV4dho4YTkxcHAA/ffQFU0b/jPF4OO/mazisZzcAVi9ZxgdPPE9hQQEdenXn3JuvwRhDYUEh7z/+LGuWphFTO46hDw4nuX7datxDh46MRXNY8M37WOunSe8BtBp4Wqn5OzatY84nr7MtfSVtTzqPlgNOKZ4395PX2bRwFpGxtek3/Jni6Qu/+4hNC2bh8YYRnVKXLhdcS3h0DAW525n57vPkrFlOo579OPzsKwHwFexi5nsvkJu5CePxULdDV9qfcmFxfetn/8HSn74CY6jdoAldL725ivfKoUfn9KHhYPnWmyfUDQgVv9/P9E/f4dib7ubkh55j1fTJbF2fXqrM+vlz2JaxkVMf+Q+9Lr6aPz9+G4CcdWtImzSWwXc/zpD7n2LdvFls27QBgIQGjel77b+p07p9qbqa9zqGIfc/xZD7n+LIK28kNjmVpMbNAGjUqSuD735snzbO/+EbmnQ/kiH3PcnRQ29h+qdvV8GeOLT5fT4+e+E1bnxqBA+8/xrTx05kw6o1pcosmDaDjPT1jPj4TS68/SY+fe6V/S475uMvadetMw9/8ibtunXm54+/BGDDqjXMGDeR+997jZuefphPn38Vv8/5+dlPn3uVi26/iREfv0lG+noWTJsJwJQfxhAdF8vDn7zFgHNO579vvFtdu+eQYv1+5n/1Dj2vGU7/4c+ybtZktm8sfU6HR8fS8azLaTHg5H2Wb9SrH72uuXuf6altD6ffXU/T766niE2tR9qv3wLgCQun7ZBzOey0i/dZpsWxJ3PsPc/R9/aRZK9cQsbC2QDs2LyBtF+/46hbRtB/+DN0OOOyStjymkXn9KHDZ02FHqFSY4NS1so04urUJS61Lt6wMJp2P4q1c6eXKpM+dzotevfFGENKizYU5OeSvzWbrRvXkdK8NWERkXi8Xuq0OYy1c/4EIL5+I2rXa1Dmulf/OZmmPfoUP09p0Yao+MR9CxoozM8HoCA/L3gZKdOqRUtJbdiA1Ab1CQsPp/uAvsydNLVUmbmTptJ70ACMMbTo0I68HblszdpS5rJzJ0+l9+CBAPQePJA5u6dPmkr3AX0JjwgnpX49Uhs2YNWipWzN2sLOvDxadGyPMYbegwYwd9Ifgbqm0XvQcQB07Xc0i2fNxVpbXbvokJGzOo2YlHrEpNTFExZGwyOOYtO8GaXKRMbFk9CkJcbj3Wf55JbtCY+O2Wd6arvOeLxO+YRmrcnfugWAsMhaJLVohycsvFR5b0QkKa07AOAJC6N2o+bFy6z5YxzNjj6BiOjY4vZIxeicPnT4/aZCj1CpsUEpP2cL0YnJxc+jE5PJz8kuVSYvJ5vopBJlEpLJy95CQoPGZCxbzK4d2ykq2MX6ebPJ25JV7nWvnvEHzXoctd9ynU45h5XTfuebu65j/Msj6X7+FeVehzhyMrNIrJNS/DwxNYWczKwgZVJLl9mcVeay27NziE9OAiA+OYnt2Tku60smJzOLnM1ZJKTueS0llKir5Pq9YV6iYqLJ3bqtMja/RsnfuoVaJc7pWglJxQGlsqydNp467buUu3xhXi4ZC2aR0rojALkZG9ixeQOT//MAk56/j4xFcyq1fTWBzulDx8HSo1RjxyhZypHug30CMIb4+o04bNCpjH3hUcIia5HQuGnxJ879yVy5DG9EBAkNm+y37Ko/J9PyqH60P/4UNi9fypR3X+bkB57BeGpsvq2wYJ/i9jndgh7nci5bjvVhjEtdpoz1HxyDHP/pTCXux2U//xfj8dKw29HlKu/3+Zj1wYs0O2YwMSnO+BTr95G7eSNH3vgAO3O2MOXFh+h319NBe7IkOJ3Th46DZTB3jX3HdXqH9nwKycvOIiqh9K2t6MSkUj1FeTlZRAfKtDp6AEPue5IT7hhBZHQscXXqlWu9q6dPoVmJ225lWT75N5p0OxKA1JZt8BcWsmvH9nItK47E1BSyMzKLn2dvziQ+JblUmYTUFLIzNpcqk5CSXOaycYkJbM1yeiu2Zm0hLjHBZX1ZJCQnkVjH+US7W87mTOJTkvZZv6/IR35uHjG14ypj82uUqPgkdpY4p3fmbKFW7cq5Xb32zwlsWjCLrpfcWO7wNe/zN4lJrU+L/kOKp9VKSKZex27OwPDkOsTUqU9u5sZKaWNNoXP60FHgNxV6hEqNDUrJzVqyPWMjOzIz8BUVsXrGFBp17l6qTKPO3VkxdSLWWjJXLCUiKrp4nNDObVsB55tpa2f/WWrMkRvr97N65lSaluO2G0B0UgobF88HYOuGdHyFhUTG1a7IZtZ4Tdu1ISN9HZkbNlJUWMiMcRPp1KdXqTKd+vRi6phxWGtZsWAxUTExxCcnlblspz69mPrTrwBM/elXOvfpXTx9xriJFBYUkrlhIxnp62jWvg3xyUnUiopixYLFWGuZOmYcnY/uXWL9YwGYNWESbY/oVKk9ITVFfJOW5GZuJC8rA39REetmT6Fux25/u96MRXNYPvZ7elx9B96IyHIts/iHzyncmUeHMy4tNb3e4d3JSlsIQMGObeRu3kB0cp2/3caaROf0ocNvTYUe5WGMGWyMWWKMSTPGDA8yP94Y83/GmLnGmAXGmP2OaTHVMMDMPjx+TlWv44CsmzebmV+8j/X7admnPx2HnMnSCb8A0Kbf8Vhrmf7pO2xYMBdvRARHXnZd8df9f376QXblbsfj9dLt7Eup1/5wANbO/pPpn73Lrh3biIiKIbFxUwbcci8Am5YsYPZ/P2Hw8NLfcJv19Ues+nMy+VuziYpPpNXRA+h0yjlsXZ/O1I/eoGjXTgyGI866iPqHda7GPVR+D/TvwriNaaFuRlDzp07ny5dG4ff7OWrI8Zx4yflM/G40AH1PG4K1ls9eeI2Ff850vko8/F80bdfadVmAHVu38dZDI9myaTNJdVO5esTdxZ8Yf/zwM6aM/gWP18s5Nw6jY28ngK9evIz3Rz5P4a5ddOjVnfNuudb5KvGuAt577BnWpq0gOi6Oqx68k9QG9UOwp/ZvQD3nK9b//nF2iFsS3KaFs1n4X+ecbtzrWFqfcAarJzvndNM+x7NzWw6Tnr2Hop35YAxhkbXod/czhNeKZtb7L5K1fCEFO7YTGRdPmxPPpknvAYx79Bb8RYVERDvHN6FZazqdOxSAsSNupGhXPv6iIsKjYuh13T2E1Ypi7EM3EFunQfFA72bHDKLJkQOw1rLw2w/ZvHguxuOh1fFn0LBr+T44VadnT3R+hkTndI04p0OW4P7bdWCFAsgZs34ts63GGC+wFDgeSAemAxdYaxeWKHMPEG+tvcsYkwosAepZawtc663JQUkqzz85KEnl+acHJakc//SgJJUnlEHpqyMqFpTOnr3foHQk8JC1dlDg+d0A1tonSpS5G2gM3AA0A34B2lhrXX/VqcYO5hYREZHQ8e13KH2FNQTWlnieDvTaq8zLwPfAeiAOOK+skAQ1eIySiIiIhI7PVuxhjBlmjJlR4jFsryqDJa+9e60GAXOABkAX4GVjTJmDf9WjJCIiItXOV8Hy1tpRwKgyiqTj3FbbrRFOz1FJVwAjrTPuKM0YsxJoB/zpVql6lERERKTa+Sr4KIfpQGtjTHNjTARwPs5ttpLWAMcBGGPqAm2BFWVVqh4lERERqXaVPUbJWltkjLkRGAN4gXestQuMMdcG5r8OPAK8Z4yZh3Or7i5rbaZrpSgoiYiISAj4quBb99ba0cDovaa9XuLv9cAJFalTQUlERESqXUXHKIWKgpKIiIhUOwUlERERERcKSiIiIiIufPv8xNE/k4KSiIiIVDv1KImIiIi4qIpvvVUFBSURERGpdupREgCstRgTsv+cWaqJjnPNoWNdM+g4V72DZYyS/guTKuT3+fjq0btZOHFsqJsiVcjn8/HY9f/i9x/GhLopUsX8Ph+jn7qHZZN1Th/KdE5XDx+2Qo9QUY9SFfH7fHz92D3sysujTe9jQt0cqSI+n4/Hb/g3+Tt20Gtg/1A3R6qQ3+fjx6fvpSA/j+Y9dU4fqnROVx/deqvh5v/2M/N/+xmARwb1Clrm9LtGcMTgU6uzWVLJxn/3A+O/+wGAE5t1DFrmjhdGMvi8s6qzWVIFlkz8mSUTnXP6xdN6By0z6F8P0eF4ndMHM53T1UeDuWu4jseewOLJ4yncmc95Dz9LWHh4qJskVaD/aScxZcxY8vPyGPH2K4RHRIS6SVJF2vY9geVTnXP61Puexatz+pCkc7r6aIxSDefxejn7vseJiIpi6ZQJoW6OVBGv18s9rz5HVEwMf/w8LtTNkSrk8XoZcufjRERFs3zaxFA3R6qIzunqU2j9FXqEinqUqpDH6+Xs+0fqmxOHOK/Xy32vPa/jXAN4vF6G3PWEjvUhTud09ThYepQUlKqYTrSaQce55tCxrhl0nKuegpKIiIiICw3mFhEREXGhHiURERERF371KImIiIgEpx4lERERERcKSiIiIiIudOtNRERExIV6lERERERc6OcBRERERFz41aMkIiIiEpx6lERERERcaDC3iIiIiAsN5hYRERFx4bf+UDehXBSUREREpNppMLeIiIiICw3mFhEREXGhHiURERERF/rWm4iIiIiLg2Mot4KSiIiIhECRvvUmIiIiEpxuvYmIiIi4OFgGc3tC3QARERGpefzYCj3Kwxgz2BizxBiTZowZ7lKmvzFmjjFmgTFmwv7qVI+SiIiIVDt/JXcoGWO8wCvA8UA6MN0Y8721dmGJMgnAq8Bga+0aY0yd/dWrHiURERGpdlXQo9QTSLPWrrDWFgCfAaftVeZC4Btr7RoAa23G/ipVUBIREZFqV9GgZIwZZoyZUeIxbK8qGwJrSzxPD0wrqQ2QaIwZb4yZaYy5dH/t1K03ERERqXYV/dKbtXYUMKqMIibYYns9DwO6AccBUcAfxpip1tqlbpUqKImIiEi1q4JvvaUDjUs8bwSsD1Im01qbC+QaYyYCnQHXoKRbbyIiIlLtbAUf5TAdaG2MaW6MiQDOB77fq8x3wDHGmDBjTDTQC1hUVqXqURIREZFqV9k9StbaImPMjcAYwAu8Y61dYIy5NjD/dWvtImPMT8BfOP+LylvW2vll1augJCIiItWuKn5u0lo7Ghi917TX93r+NPB0eetUUBIREZFqd3D8LreCkoiIiITAwfJfmCgoiYiISLU7OGKSgpKIiIiEwMESlIyt6C8+VdzBsi9ERERqmmA/0lgtmjdtWqF8sHL16pC0VT1KIiIiUu0Oll6UaglKl34xqzpWIyH0wbldOfLuOaFuhlSxP57oAsDgS8aGtiFSpX768DgAxm1MC3FLpKoNqNcq1E34x1OPkoiIiIRAyO76VYiCkoiIiISAgpKIiIiICwUlERERkeCMJ9QtKBcFJREREal2Rj1KIiIiIi6MgpKIiIhIUOpREhEREXGlMUoiIiIiQRndehMRERFxoW+9iYiIiARndOtNREREJDjdehMRERFxo1tvIiIiIsEZBSURERGR4DRGSURERMSFepREREREXBjjDXUTykVBSURERKqdepREREREXCgoiYiIiLjQrTcRERERF+pREhEREXGhHiURERERFwpKIiIiIi48uvUmIiIiEpzHExHqJpSLgpKIiIhUO916ExEREXFhPApKIiIiIkF5DpIepYNjJJWIiIgcUozxVuhRvjrNYGPMEmNMmjFmeBnlehhjfMaYs/dXp3qUREREpNpV9hgl41T4CnA8kA5MN8Z8b61dGKTck8CY8tSrHiURERGpdsaEVehRDj2BNGvtCmttAfAZcFqQcjcBXwMZ5alUPUoiIiJS7apgjFJDYG2J5+lAr5IFjDENgTOAAUCP8lSqoCQiIiLVrqLfejPGDAOGlZg0ylo7qmSRIIvZvZ6/ANxlrfUZE6z4vhSUREREpNqV83ZasUAoGlVGkXSgcYnnjYD1e5XpDnwWCEkpwBBjTJG19lu3ShWUREREpNpVwQ9OTgdaG2OaA+uA84ELSxaw1jbfs37zHvC/skISKCiJiIhICFS0R2l/rLVFxpgbcb7N5gXesdYuMMZcG5j/+oHUq6AkIiIi1a4qfnDSWjsaGL3XtKAByVp7eXnqVFASERGRamc8B0cEOThaKSIiIoeUyr71VlUOjlaKiIjIIaUKBnNXCQUlERERqXbqURIRERFxoTFKIiIiIi7UoyQiIiLiRkFJREREJDjdehMRERFxYby1Qt2EclFQEhERkeqnnwcQERERCU633kRERETcaDC3iIiISHBWPUoiIiIiLjwaoyQiIiISnIKSiIiISHBWQUlEREQkOAUlERERETcKSv98h9erzcVdGuExMGFlFv9bvKnU/PpxkVzdoylNE6P5av56flySUWq+MfDwwHZk5xfy3KTlAJzRoT79miezfVcRAF/OW89fG7fRIimaK7o1KV7uvws2MHPdVgDO7tiAPs2SiAn3Muy/c4vrP7ZlCgNbpuK3ll1Fft6ZuYb123ZW2f44VPVuE8etJzfE6zF8Pz2LDyeUPo4ndEnkkr51AMgv8PPUt2tJ27hnP3sMvHtjGzZvK+T291cC8MgFTWmS4vyqbFyUl+35Pi57aQmHNYrmrjMaA85xfvvXjUxY6Bzn4w5P4PJj6+LxwJTF23jlpw0A1EsI596zmpAQE8a2fB8Pfb6azdsKq3anHKK6HZ7EdZe0weMx/DR+PV/8b3Wp+cceVZdzT2oKQP4uHy+9t4SVa3YAcNoJjTnx2AYY4Mfx6/l2zFoAmjeJ5ebL21GrlpdNmfk89eoC8nb6qJtSi1FP9iZ9Qx4Ai9O28tJ7SwB49I4uJCVE4PUY5i/J4ZX3l+C3kJocye3DOhATHYbXA+98sZzpc7Oqae8cOhZMm8EXL43C+v30OekEBl10bqn51lq+ePENFkybQURkJJfe/S+atGlV5rK527bz1kMjydqYQXK9OgwdMZyYuDgAfvroC6aM/hnj8XDezddwWM9uAKxesowPnniewoICOvTqzrk3X4MxhsKCQt5//FnWLE0jpnYcQx8cTnL9utW4hw4O1uMJdRPKpcYGJWPg0q6NeWrCMrbkFzJiYFtmrd9aKojsKPDx4ex0ujVMCFrHoNZ1WL9tJ1HhpVPxmGUZ+4Sq9K35PPjrYvwW4muF8dgJ7Zm9fh5+C7PX5/BLWgZPn9ih1DJ/rN7Cb8szATiiQTwXdm7IM78vr4Strzk8Bv59aiNueXs5GdsKeeeGNvy+aCurMnYVl9mwZRfXj0pj+04fvdvEMfzMxgx9dVnx/HP7pLIqYxcxtfac1Pd/uucN+KYhDcjd6QNg+aZ8rnxlCT4/JMeF8cHNbZm0eCsxtbzcOKQBV7y8hJxcH/ef04TuLWOZsXwHNw1pyI+ztzB6VjbdWsRy3eD6PPzFmmrYO4cWj4EbLmvLPU/OJnPLLl58uAdTZ2WyZn1ucZmNm3dyx2Oz2JFXRPdOydxyZTtufWgGTRvFcOKxDbjlwekUFlkeu6MLf87JZP2mfP51VXve/HQZ8xbncELf+px9UlM++HoFABsy8rnhvj/3acvjL80jL/CauO/mwzmmV10mTN3EBac1Z+Kfm/hh7DqaNIjhkds7c9ltU6pnBx0i/D4fn73wGjc/+yiJqSmMvOZfdOrTm/rNmhSXWTBtBhnp6xnx8ZusXLiET597hbtef77MZcd8/CXtunVm0EXnMubjL/j54y8549or2bBqDTPGTeT+915ja1YW/7ntXkZ8NAqP18unz73KRbffRPMO7Xj5zgdZMG0mHXt3Z8oPY4iOi+XhT95i+tgJ/PeNdxn60PAQ7rV/poPl1tvBEeeqQMukGDJ27GJzbgE+v2Xqmmy6NogvVWb7riJWZufhs3af5ROjwulcvzbjV2aWa30FPos/UE2410PJGpdvyWPrzqJ9ltlZ5C/+O3KvZaR8DmscTXrWLtZnF1Dks/w6N5u+7Usf53lr8tgeeFNbsCaPOrXDi+el1g6nT9vafD/d/VP/cYcn8PPcbAB2FVp8gcMWEeZh90FrmBTB2sxd5OQ665metp3+HRMAaFYnkulpTq/GzBU79mmflE/blrXZsCmfjZt3UuSzTJi6iSO7pZQqs2jZVnbkOefa4rStpCRGAtCkQQyL07ayq8CP32+Ztzibo7qnAtCwfjTzFucAMGv+Fvr0qLPftuwOSV6vISzMYHdfQyxE13I+n8ZEe8nK2eVWhbhYtWgpqQ0bkNqgPmHh4XQf0Je5k6aWKjN30lR6DxqAMYYWHdqRtyOXrVlbylx27uSp9B48EIDegwcyZ/f0SVPpPqAv4RHhpNSvR2rDBqxatJStWVvYmZdHi47tMcbQe9AA5k76I1DXNHoPOg6Arv2OZvGsuXteA1LM7/VU6BEqNbZHKTEqnKy8guLnW/ILaZkUXe7lL+rSiM//WketsH0T8cBWqfRpmsyq7Fw+mbOOvELnotkiKZqhPZqSEh3BG3+uKg5OZTmuVQqD29QlzGMYOX7Z/heQUlJrh5Oxdc9trIxthXRo7H6cT+mRxB9Ltxc/v/Xkhrz843qiI4N/8unSLIYtO4pIz9rzWjqscTT3ntWYegkRPPzFGnx+SM8soGlqJPUSIti8rYC+h8UT7jUApG3YybEd4/liSib9OsQTU8tL7Wgv2/J8f3fza5TkxFps3rKnRzhzyy7atqztWn5Q/wbM+MsJwKvSd3DZ2S2Jiw2joMBPj84pLF25DYDV6Tvo3TWFqbMy6duzDqlJkcV11EuN4uVHepK3s4j3v1zBgqU5xfMeu6MLbVrWZsbcLCb96fQwf/TNCh676whOPaERtSK93D1ydmXughohJzOLxDp7AnBiagorFy0JUia1VJmczVllLrs9O4f45CQA4pOT2J6dU1xX88PallgmmZzMLLxhYSSkJhdPT0hNIScza5/1e8O8RMVEk7t1G7EJ+hBUkm69HcK61K/N9l1FrMrOp11qbKl5Y9M28+3CDWDhrI4NuLBLQ96a7txGWbElj3vGLKJBXC2u7tmUvzZso3A/aWlsWiZj0zI5skkipx1Wj1F/ri6zvJRmgkxz+2DXtUUsp3RP5po3nEDap11tsnOLWLI+nyOaxwZd5vjOifwS6E3abeHaPC56YQlNUyN54Jwm/LF0G9t3+nj623QevbApfgvzVufSMCkCgJdGr+PfpzbipG5JzF6ZS8bWAnw+ffqsKBPkYLsd607tExnUtwH/fnQGAGvX5/HlD6t44q4jyN/pY8Wa7fgC5+Zzby7iukvacNHpzZk6O5OiImf6lpxdXHLrJLbvKKJVszgevLUT1wyfWtybdO/TcwgP93DXdR3o3CGJ2fO30P/Iuvzy+wa++XEN7VvV5o5rO3Dt3VNd2yn7CtYzs8+hD7ZDTTmXLcf6MMalLlPG+ve3pppHQekfLju/kOToiOLnSVHhZOeXbwBt65RYjmgQT6f6tQn3eIgK93JNr2a8MW0V23btuYU2fkUmtx3Tcp/l12/fyS6fn0bxUazMzivXOqeuyeayrk0ABaWKyNhWSJ34PbfS6tQOJzPIQOmW9Wpx95mNue29FcU9OZ2axnBM+9oc1fYwIsIMMZFeHjy3CSMC44e8HujfIZ7LX14adN2rN+8iv8BPi7q1WLwun0mLtzFpsdNLcVqPZPyBN+LM7UXc/fEqAKIiPBzbMZ7cXf6gdYq7zC07SU2qVfw8JSmSLUFubTVvHMutV7Xj/mfmsH3HnvN1zIQNjJngDLC//JyWZAZ6p9I35HHvU3MAaFgvip6dnV6EwiJLYWD5tFXb2ZCRT8P60SxbuadHsrDQz9RZmzmyawqz529hUL8G3Pu0U9eitG1EhHuoHRfOVg3eL7fE1BSyM/YMecjenEl8SnKpMgmpKWRnbC5VJiElGV9hkeuycYkJbM3aQnxyEluzthCXmOCyviwSkpNIrOP0Uu2WszmT+JSkUutPrJOCr8hHfm4eMbXjKm8nHCL8B0lQOjhaWQVWbMmlbmwkKTHON1N6N0lk9vqt5Vr2y3nrufV/8/n3Dwt4depKFmVs541pqwBnoPZu3RolkL41H4CUmAg8gQ8UydER1I+LZHNu2eMT6sbu6eLvXD+eTTv0jbeKWpSeR+OUSOonRhDmNQzsnMjvi7aVKlM3PpyRFzfn4S9WszZzzzF5bcwGThu5kDOfWsj9n65m5ortxSEJoEerOFZv3lXqG2r1EyPYfSu9XkI4TVJrsSHbuS2XGOO8NuJqeTmzdwrfz9gCQHy0t/jD5qX96/C/wHSpmCUrttOgXjR1U2sR5jX0612XqbNKjyFMTY7k/lsO5+k3FrJuY36pefGBsWmpyZH06Z7K+D82lZpuDFxwWnN+GLfOmR4XXnxO10utRYO6UWzIyKdWpJekeOdDmMdj6NE5hbXrnQ9EGVk7OaKD82bauEE0EeEehaQKatquDRnp68jcsJGiwkJmjJtIpz69SpXp1KcXU8eMw1rLigWLiYqJIT45qcxlO/XpxdSffgVg6k+/0rlP7+LpM8ZNpLCgkMwNG8lIX0ez9m2IT06iVlQUKxYsxlrL1DHj6Hx07xLrHwvArAmTaHtEJ4x6lPZhvZ4KPUKlxvYo+S18MGstd/ZthTGGiSuzWLdtJ8e2dO5f/7Y8k/haYYwY2I6ocC9+axnUug7Df1pYapD13s7v1JAmCdFYIDN3F+/OdN5Y26TEcnK7uvj8Fgu8P3MtOwqcnovzOjXkyCaJRIR5eOHkjkxYmcV/F2xgYKtUOtSNw+e35Bb6dNvtAPj88Oz36bxwZQs8xvC/GVtYmbGTM3o6nyL/+2cWVx5Xj9rRXm4/rXFgGcuVrwTvJSppYKd9b7t1bhbDJf2aU+Rzuuyf+S6drYEeqltPaUjrelEAvDNuY3Eo69oilusGNcBimbMyl2e+S6+07a9J/H7Lqx8s4bE7jsDjgZ8nbmD1ulyGDGgIwOhx67jo9ObExYZz42XOmBOfz3Lzg9MBuP/mTsTFhuPz+Xnl/SXFg777967HKQMbATB5RgY/T3R6nTq2TeDSs1rg81v8fstL7y1hR24RCbUjeOi2zoSHGTwew5yF2cXh6s1P0rjlqnacMbgx1sKzoxZW6z46FHjDvJx/63W8dPv9+P1+jhpyPA2aN2Xid6MB6HvaEDr27sH8qTN44MKhzs8DDP9XmcsCDLrwHN56aCSTf/iFpLqpXD3ibgAaNG9Kt2OP5uHLrsXj9XL+rdfj8TpjFi+47QbeH/k8hbt20aFXdzr06g5AnyEn8N5jz/DAhUOJjovjqgfvrO7ddFCwnoMjPJpqGIlvL/1iVlWvQ0Lsg3O7cuTdc0LdDKlifzzRBYDBl4wNbUOkSv30ofONrXEb00LcEqlqA+q1CllaOfq2WRUKIJOe6xqSttbYHiUREREJnYOlR0lBSURERKqdgpKIiIiIC3tw/DC3gpKIiIhUPxumHiURERGR4NSjJCIiIuLiIPklRwUlERERqX4KSiIiIiLBGQUlERERkeCM5+D436APkjwnIiIihxLjqdijXHUaM9gYs8QYk2aMGR5k/kXGmL8CjynGmM77q1M9SiIiIlLtPJX8rTdjjBd4BTgeSAemG2O+t9aW/E8VVwL9rLXZxpgTgVFAr31r20NBqZrM/vRlAI644MYQt0Sq0qY5XwNQt8tZIW6JiMg/m6fy72n1BNKstSsAjDGfAacBxUHJWjulRPmpQKP9VaqgVA1mfPAci3/8DAB/USHdLvlXiFskVaVg++ZQN0FE5KBQ0TFKxphhwLASk0ZZa0eVeN4QWFvieTpl9xZdBfy4v/UqKFWxNdN/I2PxHNoOPg+ATYtms3b6eBr36B/ahonIAbHWYszB8YvCcuB0nKteRXuUAqFoVBlFgh2woGnMGHMsTlA6en/r1WDuKtakx7Ec/8AbRETHEhEdy/EPvKGQJHKQsn4ff016nE1rfg91U6QK+Xw+Hrv+X/z+w5hQN+WQ5vFU7FEO6UDjEs8bAev3LmSM6QS8BZxmrc3aX6XqUaoG4bWigv4tIgcP6/fx1+QnKCrMI7VhmWM/5SDm8/l4/IZ/k79jB70G9g91cw5pVTBGaTrQ2hjTHFgHnA9cWLKAMaYJ8A1wibV2aXkqVVASESmHDavHs3H1eAB++XRI0DIdj7yDhi0HVWOrpLKN/+4Hxn/3AwAnNusYtMwdL4xk8Hn6wsbfVdlByVpbZIy5ERiD8z/JvWOtXWCMuTYw/3XgASAZeDVwa7XIWtu9rHoVlEQqQc6KyWQu/InI2vUBSPvf/aQcNpiEFn1C3DKpLPWb9mdz+hR8RTvp0vchPN7wUDdJqkD/005iypix5OflMeLtVwiPiAh1kw5ZVdCjhLV2NDB6r2mvl/h7KDC0InVqjJJIJajdpDuFuVlsnPkZG2d+RmFuFrWblPkhRQ4yxuOlU5978IZFkbHuj1A3R6qI1+vlnlefIyomhj9+Hhfq5hzSvB5boUeoqEdJpBJ4wiJpe9bzLPnqVgDanvU8nrDI0DZKKp3xeOl09L36NtQhzuv1ct9rz+s4V7Gq6FGqCgpK1aTzOdeEuglSxTxhkbQ//7VQN0OqmN48awYd56qnoCQiIiLiwqugJCIiIhKc5yDptFNQEhERkWqnHiURERERF+EHSQI5SJopIiIihxL1KImIiIi4UFASERERcaGfBxARERFx4dW33kRERESC0603ERERERcKSiIiIiIuwg6SX5xUUBIREZFqpx4lERERERcazC0iIiLiQj1KIiIiIi4UlERERERceDWYW0RERCQ49SiJiIiIuNBgbhEREREXuvUmIiIi4kK33kRERERcqEdJRERExIV6lERERERceIx6lERERESCUo+SiIiIiAuNURIRERFxERGmoCQiIiISlHqURERERFxojJKIiIiIC496lERERESC0603ERERERe69SYiIiLi4mDpUTpI8pyIiIgcSjweU6FHeRhjBhtjlhhj0owxw4PMN8aYFwPz/zLGdN1fnepREhERkWpX2bfejDFe4BXgeCAdmG6M+d5au7BEsROB1oFHL+C1wL+uFJRERESk2lXBrbeeQJq1dgWAMeYz4DSgZFA6DfjAWmuBqcaYBGNMfWvtBrdKjVO2SlX5CkREROSAHBwDhQBjzDBgWIlJo6y1o0rMPxsYbK0dGnh+CdDLWntjiTL/A0ZaaycFno8F7rLWznBbb7X0KI3bmFYdq5EQGlCvFQP67XM7WA4x4yaMBKB/y/YhbolUpfHLFwG6dtcEA+q1CnUTyi0QikaVUSRY6Nu7s6Y8ZUrRYG4RERE5FKQDjUs8bwSsP4AypSgoiYiIyKFgOtDaGNPcGBMBnA98v1eZ74FLA99+6w1sLWt8Emgwt4iIiBwCrLVFxpgbgTGAF3jHWrvAGHNtYP7rwGhgCJAG5AFX7K9eBSURERE5JFhrR+OEoZLTXi/xtwVuqEiduvUmIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiICwUlERERERcKSiIiIiIuFJREREREXCgoiYiIiLhQUBIRERFxoaAkIiIi4kJBSURERMSFgpKIiIiIi7BQNyCUFkybwRcvjcL6/fQ56QQGXXRuqfnWWr548Q0WTJtBRGQkl979L5q0aVXmsrnbtvPWQyPJ2phBcr06DB0xnJi4OAB++ugLpoz+GePxcN7N13BYz24ArF6yjA+eeJ7CggI69OrOuTdfgzGGwoJC3n/8WdYsTSOmdhxDHxxOcv261biHDg09erbhxptOweMxjP5hOp9+MqHU/KP6HMYVVx2P9Vt8Pj+vvPx/zJ+3msaNU7j/wQuLy9VvkMR77/zC119NpkXL+vzr36cTFRXJpo3ZPPbIZ+Tl7cLr9XD7nWfRuk1DvF4PP4+ZxacfjwcgLMzLzbeeSucuLbB+y9tv/czvE+fTqVNzbrjpZFq0qMcjD3/KxAnzq3P3HFJ69j2aG++/B6/Xww+ff8Unb7y1T5kuvXpw43134w0LZ2t2NrdeeCkRERH857MPCY+IwOsNY8JPY3jvPy8D0Kp9O2575CEiIiPw+Xw8/8DDLP5rHmHh4fz70Ydoe3hH/H4/Lz/yOHOmTQdgwClDuPi6a7DWkpWRwWO33cnW7BzCI8K5+5knadvxMLZm5/Dwzbexcd36at1HhwJdu6U61dgeJb/Px2cvvMaNT43ggfdfY/rYiWxYtaZUmQXTZpCRvp4RH7/JhbffxKfPvbLfZcd8/CXtunXm4U/epF23zvz88ZcAbFi1hhnjJnL/e69x09MP8+nzr+L3+QD49LlXuej2mxjx8ZtkpK9nwbSZAEz5YQzRcbE8/MlbDDjndP77xrvVtXsOGR6P4ZZbT2P4ne9yxWXPM+C4LjRtWqdUmVmz0rj6yv8wbOiLPP3kV9x+x1kArF2bybChLzJs6ItcO+wldu0sZNLvCwC4/c4zefONnxh6xQv8/vsCzju/LwD9jj2c8PAwhl7xAtde/RKnnNKLuvUSAbjokmPJyc7lsouf5YrLnmfu3BUAbMrI4cknvmTs2LnVtVsOSR6Ph1seup+7rhzGZYNOYcApJ9G0VctSZWLj4rh1xAPcM+wGrjjxFB666VYACgoKuO3iKxh68hkMPeUMevY9msO6dAbgmrtu572XXmHoKWfyzgsvce1dtwNw8nnnAHDlkNO4/bKruO6euzDG4PV6uen+e/jXRZdx1Umns3zxUs645CIAhpxzNju2buWiAYP56t0PGBaoS8pP126pbjU2KK1atJTUhg1IbVCfsPBwug/oy9xJU0uVmTtpKr0HDcAYQ4sO7cjbkcvWrC1lLjt38lR6Dx4IQO/BA5mze/qkqXQf0JfwiHBS6tcjtWEDVi1aytasLezMy6NFx/YYY+g9aABzJ/0RqGsavQcdB0DXfkezeNZcrLXVtYsOCe3aN2bduiw2bNhCUZGPcePmctTRh5UqszO/oPjvWlERBNvDXbu2Yv36LDZtygGgceNU/pq7EoCZ05dxTL+OTkELUVEReLweIiPDKSwqIi93JwAnDunOJx//5hSzlm1b8wDYtDGbFSs24vfr2P4d7Tp3Yt3qNWxYm05RYSHj/jeaPgMHlCpz3Kkn8/vPv5KxYQMAOVlbiufl5znHIywsjLCw8OJzzVpLTGwsADFxsWRmZADQtFVLZk2ZWlzPjm3baHt4RzAGg6FWVLSzTGxM8TJ9Bg7gp2++A2DCj2PodmTvKtkXhzJdu6W61diglJOZRWKdlOLniakp5GRmBSmTWrrM5qwyl92enUN8chIA8clJbM/OcVlfMjmZWeRsziIhNbl4ekKJukqu3xvmJSommtyt2ypj82uMlJTaZGRsLX6euXkrqSm19yl39DEdeO+D23h85OU8/eRX+8w/9rjOjCvR47Nq5SaO6uMErn7HHk6dOgkATBg/j/z8Ar765h4+/WI4X3z+O9u35xMTWwuAK646gTfevIkHR1xIYmJsZW5qjZdatw6bN2wsfr554yZS65a+3dG4eTNia9fmhY/f543vvuKEM04rnufxeHjr/77h2z8nMWPyFBbN/QuAlx99gmuH384Xk8Zx3fA7efPp5wFYvngxfQYOwOv1Uq9RQ9p27ECd+vXwFRXx/AMjeGf0d3z9x0SatmrF6C++dtpYry6bAyHN5/OxY/t24hMTqnK3HHJ07ZbqVmODUrB0b/YttO+CppzLlmN9GONSlylj/ftbk5RkguyvYJ/rJv2+gMsvfY4H7v2QK648vtS8sDAvRx3Vngnj5xVPe+rJrzj9jN68PupGoqMiKSwsApweLL/fzzlnPs5F5z/JueceQ/36SXi9HurUSWD+vNVcc/VLLFiwhmuvH1Kp21rjBT3WpY+21+ulbccODB96LXdePpRLb7yORs2aAeD3+xl6ypmc0+dY2nc+nOZtWgNw2kXn88qjIzn36AG88thI7hz5KAA/fvkNmzdu4o1vv+TG++5m/qw5+Hw+vGFhnHrR+Vx96pmcdWRfVixewkXXDdvdyH3bqI6GCtG1W6pbjQ1KiakpZGdkFj/P3pxJfEpyqTIJqSlkZ2wuVSYhJbnMZeMSE9ga6M7fmrWFuMCnxX2XySIhOYnEOs4nnd1yNmcSn5K0z/p9RT7yc/OIqR1XGZtfY2zevJU6deKLn6ekxpOZ6f7J7q+/VtKgYTK146OLp/Xs1ZZly9aRnb2jeNraNZu58/Z3uHbYy4wbO5cN651jftzALkz/cyk+n5+cnFzmz19Nm3YN2bY1j/z8guIxThN+m0fr1g0re3NrtM0bN5Fav17x89R6dcnclLFXmY38OfF3dubnszU7h7l/zqBl+7alyuzYvp05U/+kZ9+jARh05ulMHPMLAONH/0S7TocDTo/QK4+NZOgpZ3LftTcSWzuO9FWradW+HQDr16wF4LfRP9Gh6xHF60+tXx9wQltsXBzbcnIqeU8c2nTtlupWY4NS03ZtyEhfR+aGjRQVFjJj3EQ69elVqkynPr2YOmYc1lpWLFhMVEwM8clJZS7bqU8vpv70KwBTf/qVzn16F0+fMW4ihQWFZG7YSEb6Opq1b0N8chK1oqJYsWAx1lqmjhlH56N7l1j/WABmTZhE2yM6Be0hEXeLF6fTsFEy9eolEhbmZcCAzvwxeWGpMg0a7rnItm7dgPAwb/H4IYABe912A0hIiAGcHquLLx3A999PAyBjUw5HdHUGENeqFU77wxqzdrVzwfxjyiK6dGkBQNdurVi9elMlb23NtuSveTRq1pR6jRoSFh7OgJOHMGXsb6XKTPp1HIf36IbX6yWyVi0O69KJNctXEJ+USGzgG04RkZF063Mka5Y7Y9CyNmXQpVcPALoe1Zv01asBiKxVi1pRUQB063MUviIfq9OWk7lpE81atSI+yRnE3/3oo1idthyAKWN/Y/CZzu2+ficOYtYfpcfWyP7p2i3VzVTDADM7bmNaVa/jgMyfOp0vXxqF3+/nqCHHc+Il5zPxu9EA9D1tCNZaPnvhNRb+OdP5iunwf9G0XWvXZQF2bN3GWw+NZMumzSTVTeXqEXcXf5L48cPPmDL6FzxeL+fcOIyOvbsDsHrxMt4f+TyFu3bRoVd3zrvlWucrprsKeO+xZ1ibtoLouDiuevBOUhvUD8Ge2r8B9VoxoN/wUDcjqF692nL9TSfj9Xj4cfQMPv7oN0451bk4/t/30zj/gn6cMKgrRUU+dhUU8sZro5k/L/BmGBnOZ18O5+ILniI3d1dxnWee1YfTznAuipMmLuDNUT8BzmDwu4afTdOmdcHAmB9n8vlnEwGoWzeBu+89j5jYWmzNyeWpkV+SkbGVtu0a8fAjlxAbF0VBQSHZW3Zw5eXPV+cuKrdxE0YC0L9l+xC3JLhe/fty43134/F4+PGrb/jo1Tc49YLzAPj+088BOO/qKznxrDOw1vLD51/x1Xsf0KJtG+5++gk8Xi8ej4fffviJD15+FYDDu3Xlxgfuwev1UrBrFy88+DBL5y+kXsMGPPXeW1i/n8xNGTw1/D42rXe+6n/qBedx1uWXUFRUxKZ16xl55z1sy8khIiKCe559ktYd2rMtZysP3/JvNqxND83OKsP45YsA0LW7Rly7leD2o0YHJak8/+SgJJXnnx6UpHL804OSVB4Fpf2rsbfeRERERPZHQUlERETEhYKSiIiIiAsFJREREREXCkoiIiIiLhSURERERFwoKImIiIi4UFASERERcaGgJCIiIuJCQUlERETEhYKSiIiIiAsFJREREREXCkoiIhW0flsO67flhLoZIlINwkLdABGRg01BUWGomyAi1UQ9SlXMWhvqJkiI6NiLHLx0/spuCkpVyOfz8dj1/+L3H8aEuilSzXK2ruWv+V/i8xeFuikiUkG6dktJCkpVxOfz8fgN/yZv+w56Dewf6uZINYuv3YiI8Bjmzf9aYUnkIKJrt+xNY5SqyPjvfmD8dz8AcGKzjkHL3PHCSAafd1Z1NksqWdaWFfw1/8syy6xfP5vGjXpUU4tE5O/QtVv2pqBURfqfdhJTxowlPy+PEW+/QnhERKibJFUgOakFx/a9a5/p1loWLxnNroIdNKjfpfobJlViS94OMnZsIzIsHIDFGeupE1ubpOjYELdMKouu3bI33XqrIl6vl3tefY6omBj++HlcqJsj1WzrtnQKCnM5vMOZeL3hoW6OVJKEWtEU+Hys35bN+m3ZFPh8JNSKDnWzpBLp2i17U49SFfJ6vdz32vMYY0LdFKlmCfGNie/YSMf+EOPxeOhYtyHzN6UD0LFuQzwefd481OjaLSUpKFUxnWg1l479ocnj8dCpfpNQN0OqmM5f2U0fhURERERcKCiJiIiIuFBQEhEREXGhoCQiIiLiQkFJRERExIWCkoiIiIgLBSURERERFwpKIiIiIi4UlERERERcKCiJiIiIuFBQEhEREXGhoCQiIiLiQkFJRERExIWCkoiIiIgLBSURERERFwpKIiIiIi4UlERERERcKCiJiIiIuFBQEhEREXGhoCQiIiLiQkFJRERExIWCkoiIiIgLBSURERERFwpKIiIiIi4UlERERERcKCiJiIiIuFBQEhEREXGhoCQiIiLiQkFJRERExIWCkoiIiIgLBSURERERFwpKIiIiIi4UlERERERcKCiJiIiIuDDW2qpeR5WvQERERA6ICXUD/unCqmEdNe4gGGOGWWtHhbodIiIi8vfo1lvVGBbqBoiIiMjfp6AkIiIi4kJBSURERMSFglLV0PgkERGRQ0B1fOtNRERE5KCkHiURERERFwpKlcwYM9gYs8QYk2aMGR7q9oiIiMiB0623SmSM8QJLgeOBdGA6cIG1dmFIGyYiIiIHRD1KlasnkGatXWGtLQA+A04LcZtERETkACkoVa6GwNoSz9MD00REROQgpKBUuYL9dy26tykiInKQUlCqXOlA4xLPGwHrQ9QWERER+ZsUlCrXdKC1Maa5MSYCOB/4PsRtEhERkQMUFuoGHEqstUXGmBuBMYAXeMdauyDEzRIREZEDpJ8HEBEREXGhW28iIiIiLhSURERERFwoKImIiIi4UFASERERcaGgJCIiIuJCQUlERETEhYKSiIiIiAsFJREREREX/w+c8GdjITFX8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 792x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "from numpy import linalg\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "import seaborn\n",
    "from matplotlib.colors import LogNorm\n",
    "env = gym.make('FrozenLake-v0')\n",
    "\n",
    "# print('Number of Actions', env.nA) \n",
    "# print('Number of States ', env.nS)\n",
    "# print('P[10,3]', env.P[10][3])\n",
    "\n",
    "%matplotlib inline\n",
    "import seaborn\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import LogNorm\n",
    "import numpy as np\n",
    "def fancy_visual(value_func,policy_int):    \n",
    "    grid = 4    \n",
    "    f, ax = plt.subplots(figsize=(11, 9))\n",
    "    cmap = seaborn.diverging_palette(220, 10, as_cmap=True)\n",
    "    reshaped = np.reshape(value_func,(grid,grid))\n",
    "    seaborn.heatmap(reshaped, cmap=\"icefire\",vmax=1.1, robust = True,\n",
    "                square=True, xticklabels=grid+1, yticklabels=grid+1,\n",
    "                linewidths=.5, cbar_kws={\"shrink\": .5}, ax=ax, annot=True, fmt=\"f\")\n",
    "    counter = 0\n",
    "    for j in range(0, 4):\n",
    "        for i in range(0, 4):\n",
    "            if int(policy_int[counter]) == 1:\n",
    "                plt.text(i+0.5, j+0.7, u'\\u2193', fontsize=12)\n",
    "            elif int(policy_int[counter]) == 3:\n",
    "                plt.text(i+0.5, j+0.7, u'\\u2191', fontsize=12)\n",
    "            elif int(policy_int[counter]) == 0:\n",
    "                plt.text(i+0.5, j+0.7, u'\\u2190', fontsize=12)\n",
    "            else:\n",
    "                plt.text(i+0.5, j+0.7, u'\\u2192', fontsize=12)\n",
    "            counter=counter+1\n",
    "\n",
    "    plt.title('Heatmap of policy iteration with value function values and directions')\n",
    "    print('Value Function \\n ',value_func)\n",
    "    print('Policy \\n',policy_int)\n",
    "    plt.show()\n",
    "\n",
    "def policy_evaluate(V, pi):\n",
    "    for t in range(1000): \n",
    "        V_ = np.zeros(env.nS)\n",
    "        diff = 0\n",
    "        for x in range(env.nS):\n",
    "            a = pi[x]\n",
    "            q = 0\n",
    "            for i in range(len(env.P[x][a])):\n",
    "                p, s_, r, done = env.P[x][a][i]\n",
    "                q += p * (r + gamma * V[s_])\n",
    "            V_[x] = q\n",
    "        diff = linalg.norm(V_ - V, 2)\n",
    "        if diff < epsilon:\n",
    "#             print(\"Number of iterations to converge: \", t)\n",
    "            break\n",
    "        else:\n",
    "            V = V_.copy()   \n",
    "    return V\n",
    "\n",
    "def policy_improve(pi, V, policy_stable):\n",
    "    policy_stable = True\n",
    "    pi_ = np.zeros(env.nS, dtype=int)\n",
    "    Q_star = np.zeros((env.nS, env.nA))\n",
    "    for x in range(env.nS):\n",
    "        Q = []\n",
    "        for a in range(env.nA):\n",
    "            q = 0\n",
    "            for i in range(len(env.P[x][a])):\n",
    "                p, s_, r, done = env.P[x][a][i]\n",
    "                q += p * (r + gamma * V[s_])\n",
    "            Q.append(q)\n",
    "        Q_star[x, :] = Q\n",
    "        pi_[x] = int(np.argmax(np.asarray(Q)))\n",
    "        if pi[x] != pi_[x]:\n",
    "            policy_stable = False        \n",
    "    pi = pi_.copy()\n",
    "    return pi, policy_stable, Q_star\n",
    "\n",
    "def policy_iteration(env, gamma, epsilon): \n",
    "    V = np.zeros(env.nS)\n",
    "    V_ = np.zeros(env.nS)\n",
    "    pi = np.zeros(env.nS, dtype=int)\n",
    "    policy_stable = True\n",
    "    diff = []\n",
    "    for i in range(1000):        \n",
    "        V_ = policy_evaluate(V, pi)\n",
    "        pi, policy_stable, Q = policy_improve(pi, V_, policy_stable)\n",
    "        diff.append(linalg.norm(V_ - V, 2))        \n",
    "        V = V_.copy()\n",
    "        if policy_stable:\n",
    "            print(\"Policy stable\")\n",
    "#             print(\"Number of iterations to converge: \", i+1)\n",
    "            print(\"Convergence Plot of Value Iteration - \")\n",
    "            plt.plot(range(int(i)), diff[1:])\n",
    "            plt.show()\n",
    "            break\n",
    "    return V, pi, Q\n",
    "\n",
    "gamma = 0.9\n",
    "epsilon = 1e-4\n",
    "V_star, pi_star, Q_star = policy_iteration(env, gamma, epsilon)\n",
    "fancy_visual(V_star, pi_star)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "operational-airport",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal Q-Value Function - \n",
      " [[0.06876462 0.0665166  0.0665166  0.05962591]\n",
      " [0.03900127 0.0429049  0.04065688 0.06128152]\n",
      " [0.07429459 0.06868163 0.07258526 0.05732418]\n",
      " [0.03894755 0.03894755 0.0333346  0.05561485]\n",
      " [0.09173391 0.07110927 0.06421858 0.04813997]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.11214171 0.08986146 0.11214171 0.02228026]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.07110927 0.11781368 0.10173507 0.14532901]\n",
      " [0.15755228 0.24741373 0.2038198  0.13345539]\n",
      " [0.29955136 0.26591365 0.22533162 0.10785745]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.18817808 0.30565225 0.379872   0.26591365]\n",
      " [0.39551371 0.63898559 0.6148887  0.53715313]\n",
      " [0.         0.         0.         0.        ]] \n",
      "\n",
      "Optimal State Value Function - \n",
      " [0.06874881 0.06125542 0.07426752 0.05555766 0.09171777 0.\n",
      " 0.11212568 0.         0.14531312 0.24739914 0.29953819 0.\n",
      " 0.         0.37986114 0.63897971 0.        ] \n",
      "\n",
      "Optimal Policy - : \n",
      " [0 3 0 3 0 0 0 0 3 1 0 0 0 2 1 0] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(\"Optimal Q-Value Function - \\n\", Q_star, \"\\n\")\n",
    "print(\"Optimal State Value Function - \\n\", V_star, \"\\n\")\n",
    "print(\"Optimal Policy - : \\n\", pi_star, \"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "id": "current-convenience",
   "metadata": {},
   "outputs": [],
   "source": [
    "## End of Part 5."
   ]
  }
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