Quant_Econ_Script.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII\n",
    "# Introduction to Python\n",
    "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting up Your Python Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\daniel.heimgartner\\\\Desktop\\\\Quant Econ'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# general remark on working directory\n",
    "%pwd\n",
    "# same folder as jupyter notebook is located!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hello"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "α = 1\n",
    "print(α)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.normal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11.14600356,  9.95354517,  9.04202717])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(10, 1, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "pip?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pip install quantecon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install --upgrade quantecon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pip install interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An Introductory Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# depict plots within notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate some random noise\n",
    "ϵ_values = np.random.randn(100)\n",
    "plt.plot(ϵ_values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# illustration of a loop, list\n",
    "ts_length = 100\n",
    "ϵ_values = []\n",
    "\n",
    "for i in range(ts_length):\n",
    "    e = np.random.randn(1)\n",
    "    ϵ_values.append(e)\n",
    "    \n",
    "plt.plot(ϵ_values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, '3', True]\n",
      "[1, '3', False]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1, \"3\", True]\n",
    "print(a)\n",
    "type(a)\n",
    "a.pop()\n",
    "a.append(False)\n",
    "print(a)\n",
    "a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# while loop\n",
    "ts_lenght = 100\n",
    "ϵ_values = []\n",
    "i = 0\n",
    "\n",
    "while i < ts_length:\n",
    "    e = np.random.randn()\n",
    "    ϵ_values.append(e)\n",
    "    i = i + 1\n",
    "\n",
    "plt.plot(ϵ_values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 0.04\n",
    "T = 50\n",
    "b = np.empty(T)\n",
    "b0 = 50000\n",
    "\n",
    "for t in range(T):\n",
    "    b0 = b0 * (1 + r)\n",
    "    b[t] = b0\n",
    "    \n",
    "plt.plot(b, label = 'my money')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# alternatively\n",
    "b = np.empty(T+1) # +1 because of the 0...\n",
    "b[0] = 50000\n",
    "\n",
    "for t in range(T):\n",
    "    b[t + 1] = b[t] * (1 + r)\n",
    "    \n",
    "plt.plot(b, 'r+', label = 'my money')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kArnrUu6rtvv4bNouDk3F/IFM6VCOZ9NXlHvHdCynix1vKD9+bhPv+/hxfOXF3XFSMtjnV4u5lM5roWUpwmewNGK37e3MmzYXKMHFy/WI1vDImSJnW5fC9MmLdu1kZ9Fy8d2zG1jJGChYTtmERKD1QP4HXzmJ3/vSydCOd5AZqUCeKdo8MdOuR246LlcdayFtH9nKW5iMKdg7HoXt0o6H4T95bhMAcHY9F8pxDQv1FDngVVzcfHCirferlcwbZfKmA8O3L0z/aU5r4JHrNT3ykrUChFu5wp6MgouyWa7jxFKavyZYNgkEAnmTY1ncLOwaS3Okyg83Ao99jYbT18K0XcwldUQIsJYN5/FxI2fi6GwCe/0qiwvbRcwGKi5a5enXtwCUz5rYDWzmTdwQHa/5d7/yA1e0/X61AtUow6wVSikP5K0kO2t55AsTXg4iVEVew1ph1UevLGf5a4qWUxbsW1HkOcMuVbCZdtMeg2FnpBQ5+8UB7deRG7a3cmoyroW2Rool6/b680AutqgO/v67r+Hvv/sa/zML5K9v5EM5rkHkpYtprKRLeQRKqTf5MB7eqIVagWqUyZveE6rt0pK10kL5YfBGx9auMWslzO5Oo0ayk9ll7MbDFHnwNY0C+WeeWsQXnlvC+a3StdZNfmpYGKlAvhkI5Pk2L1b2+DadUEMJ5KbtImc6mIgpfEJfqyfU3z32Gj7x6DkAwHK6iCW/i+38CCvy9//tE/jNz5/gfy5YDkzHraoh74boLis/ZBUmhu2Wkp0teeQBa6VYYa2E6pFXWyuVyrlouTAst+w1bCdrrWP52LfP4k++fooP2AKAC1uje90wwlj1tp8Q8iAh5AQh5AVCyH8M48A6YTNfW5G/568ew30PnWn4vaYfyGeSGlZDsFZYdn88rmIipkCTIy37dZt5k7cgMzV+7OAEFjcLHSdMB53NnIlnFrdKf66YsxIGsRqBalSxnVLwNiynpWQnt54Cn0/WsKFIBOMxBYpEQt0SVLJWgslOqeo1Rdvho24BQIoQJDUZj5xex30PnSm7JkzbxamVLF5dE4G8XWwA/5lSeiWAWwH8AiHkqhDet21YIE/qMvfIz67l8NAra2XLeythHqIqRzCd0EJJdrJANOnXQc+PR7myZnz8kbP48gsXq753K29hPWfCsB08/foW5AjB3dfsgem4WB3R7eEFy8G59TxPYLGnq7FoeIq8VqAaVYJPpIbtduWRJzSvXn8sGu6wqlIdeXWyM/iaSkUOAAuTMXz37AZ+8/MnyiY2Wo73b/3WyVWocgQRUh7In359ayTFUNeBnFK6RCl90v//DIATAPZ1+76dsJHzOgFnkho/kb/+0goANOwCs10KSj21wqyVbjvYmF/PFOWelF4VyP/im2fwicdeK/uaabu8dnclbeD589u4fE8SR2YTAEbLJ88Ztnfh2S4sx/u8n7+wjYdPreHjj5wFEK4iZ4Gq0U7IUSF4swpaK40CuSp7ix2C1lPWsHm9fkyVQ11eXbQcSBFSZvfUUuRGhSIHgAfefyv+4j03AwCW0yVxw25Yj5xex8J4FHMpHed9S/P0ahY/+qcP42t+TBglQvXICSGH4O3vfKzG391DCDlOCDm+uroa5o/lbOZMTMRUf1u6dzI++LIfyO36KswInOTTCQ2G7eLceh4/+EcP4fRqZ81B3FrxPd694zqWKh7xNnJmVQJ0q1CydZbTRZxdz+HITAL7/WTTKFWuvP3/fQh/9uDpsqDz6Jl1vP9vn8A/HF/EeEzBJTPx0H4em2XN7KpRJli1ZdhOS+WHgHezq/TI2X5PVY6EOqemaJXPIgdKM+WDidfKhiDAW4Jx5Z4UAJQlyVnTHCsnnh+PckW+7Aup10ZIDDFCC+SEkASATwH4IKW0qqOGUnovpfQYpfTYzMxMWD+2jM28icm4ipjitfnmDBuPnfEWEDR6nGZqRfMDOeBNXHtxKY0XLnTWHMQ9Xr/qYu+YjuWMAcd/rCuYDgqWU6XSgx7kaxt5nN8s4NBUjJd/jYoizxo2zq7n8fpmvmzA2X0PvYqsYeNTH3gTnv7I2zCbbL9csxF3XDqNx85s8N/5qBIMxoYVUOQNWvQBr/s1aK3kDBsJXyVrciTUz61Y0egDlJKdR+eS3mt41Ur1cc/6s9RXAlYoe7IDvJLJ+fEoLvhiidlCwcA/KoQSyAkhCrwgfj+l9NNhvGc7uC5FumhhM+8rcn/wzsOn1mA6LpKazLvIalF67JQwnfROjm+e9J4a2q1HZ1RO7tuT0uG4FOs5o+zvM0W77FE/GMiPn9uES4GDU3HoioTphDYyipxV4OQMmwcd9lh/9XwKNx1or9mnVW6/dBoFy8FTr2325P0HhXwda6VRiz5QvQ4va9i8JFCVI1zZh0FwzRsjrkrQ5Aiu3eep7aLtVs1aYeiKhKQuYzUYyAPX+cJEFPPjOpa2vK5qVjq5ElLD3yARRtUKAfBXAE5QSn+/+0Nqn7955Cze+NGv4eRyFhNxhe/9O73qdUJev3+cz3WohVlmrXiB98nXvMfvTgP5Vt6ErkT4icoeGdkwr2DNe9BeCVbePHZmHQBwaNpT4/sno1jcGg1FzsrDsobNP5PrFrwlB++59WDVoKywuPXwFCIEePj0ek/ef1AIdq961or3GTeqWgGqtyh5HrnCvzdMa8UILF5myFIEn/752/CLbznqv8apmexkzCY1rGRKCtt0SjXnCxNR7BuPwnRcrOUMLpKWhSKvye0A3gPgTkLI0/5/PxjC+7bM4mYBBcvBdsHCRExFVJFRMB2sZw1EFQmTcbVhEwg/yeUIZnxrhVkguTanKDI2chYmAzXQlaVvwYAdrC9n3rquRPiN6OCU5xMvTMTw+sZoKPLFMkXuBZ1333IA/+5NB/GjN/YuVz4WVXDdwjgePjXaY4UrrRXL9s7nVpZvVHvkEv/eUAO57ZTNImdcPT+Gybh37eQMpyw4VzKb1LHiJztZ9dmbDk9BjhBctTeF+UAPB7NWRjGQd923Sin9NoAdXbeSLlhI6jKiioQr9iRxcjmLvGljLWtgOqki2mTpLvs7VYpgMq6CEIAVreQ6zNJvVQx8ivreX8H3gzcDFkpwbRX7+uVzSTyzuI2EJmPKP6n3T0TxL88twXEppCHfcMMUec5weIXRpbMJ/Nix/T3/2W88PIn7Hnp1JD7HelRaK0YL5YcA/Gul9L2FQHu7Jksw7fCmHxat+gFakQgipDSqtq4iT2l4yn96dvzqs5sOTOB//PTN0BWJ33gubhew7RcSrKSFtTKQbBcszI9F8ciHvg/vedMhxDQJOdPBes7EVFyDrkQaVq3wjL4SgSxFyroJu/HIJwLt5VWKPGCtLJUFchOqFMEl054KPzgV4zbDwkQMtktxcQQUBVPkQWulleUQYTAZU/3xqKNbT15lrbCEfpNkZzRgrVBKUQy0x3vJzjDnkVd75AxCCKKKxFV0vWobZq1QSnmiU5FLluasn/NazZrcWskYdsfX9aAyEoE8XbQwFlW4uoopMkzbxXK6iOmEBr0igVNJ6ST3Po6ZhAZCgOmE1oVHbpUrcqU8kG/kTBACTMbVso7PrZyF8ZiCOX8LzqGpUvnd/km/BHEjjyfObeDTTy52dGyDALdWzJK1UrkJqFewoDDKK986TnYGSnctx1tGwc7d0JOdNapWguiKxINvvdfNJnUULRcZw+bHFqxLZ0/YqxmjrJlp1BKeoxHICzZS0ZKaYwHh9Y0CphMqNP8Rq16TT2WzxGxKw+HpOGaSWtVG71bZyJtlzSzRiqUGm3kTY1EF+yo6PlnlDZuYGNx8w0sQNwv4k6+fwn//wksdHdsgULJWbK4Ao30K5PouGJ4VXGDcaos+UF61UuAt9KXyQyPE9WqNrBX2c9PNFDkrQUwbvIZclUo3K1mKYCquYjXjJTtZbBg1n3w0AnnRQkqvDpoFy/EVebkCM2wH//TUeR7YKwP5r779Kvzhj9+IhCZ1pMgdl2K70DjZuZEzMekvnQh65J6SV/heyqAinx/XQYgXBF9cSmMrbw7lAtqsYWMzbyGpybAcylVXv6yVXRHITQfM/jdsF5bjIkK8wNaIqFKyVio3+PSk/LCO9w14VidrkKunyGeSrJa8yAN55WCw6YTGFflRv0NaBPIBJF2wkIqWAnmwzXcqofKThV24Xz+xgg8+8DReuujNaDAqAvnle5K4dmEMcX9/YLts5ExQCl6TDnh2D1BeteKtgdN5wwL/ekzF1fNjmE6ouOlgaR63JkuYS+p4dnEby2kDdsg7FPsFqyG/bI/X9LGaMUAIGqqzMNkN1krOdPi4VzZrpVmiEygvP+RPSiyQSyE3BNUoPwyiyyVrpZFHDnjnEKvMqQzk3iA8P5D7jUajlvAc+kDuuhQZwy4L5FGlpOymE1rA1vBOwnU/0chOElZ+WJkZj6tyR3M5WNPPVLwUyPlTgn9j2Mh5pZJ7x6NlTUHenk8F+ydjOP6rb8Wls8my994/GcW3A6VzwaTpsMBslcsDgTyqSD2rHa9kNyjygmkjqSuQIwSm75E3s1UA77MpWi5cl1ZZXmrInZ1GxcKISqJqINlZJ+DP+J2/K2mDX8eKXB3Il7YKyBo29k/EoCsRocgHjYxhg1IgpVd75ADKrBV2YrKTgwXPegOF4prUUR35uj8GdypRslbYQCKmyLd8D33vWGnphLdMof6eSsDzyYMXU5hjRfsFS3RewQJ51ujrBhdN2R2KPOZ3SRq21+auNgiaDBa0Ddut2nKvyRJsl/Iei25pnuws1a3Xe11Kl6HJEaxkijBZrXwNRc6SmxNxBXMpb1zGKDH0gZwlQ4KKvDyQV1srrOkma/iKvE4iKK7JHdWRs8UU04nygBz1O04ppZ5HHlexx09qLm0XkTVs2C7FeLT+xD82PIsRHLI1LCxu5qHJERyY9JK3qxmjbxUrQOnJa7QVuR/I/US/p35bX1CdN22e9Ax65ABCUeWO65ULNkx2Bm489Y6dEILZlBeoebKzojKHNfkBXkPYXFIXinzQYA0DtZKdAHj5IRAM5L4i97efVHrkjLjqzTVvN6HIFXnAWgFKFQEFfxDQRFzFvL95ZWm7yI+r0VYcVrnCguDmECry1zcKWJiIIuk/Ra1kin0N5Cx4NGoSG3ZyfiMPqzRJF23+eTciWjZ1sMIjDzGQ19rXWUnw7xpZMElNQc5w6iY7Z5LlgXzPmD5y27aGP5AXvGAcLD9k1Q9SxBuGr1VcuMxaYRvC6434jGsyXNr+Bb+WNSD7PztITJWQtxw+Z2UypvLyqaWtUiAfbzCDe8GvJX/T4SkApacLxrdfWcOvffb5to633yxu5bEwEeN2StFy+1Z6CJQChBFic8ugwRS56lsrmWJ5QUA9gsslKoMtC+SG0/3nxt+7wVNC0BdvpNw1JVI2qrcqkAcU+XhMxRV7kzi/VeBLTEaBoQ/kLCiP1bBWpuIqIhFSOjn9C5dNQeOK3KptrbAZE+0mPNeznm0SqWj/jqreDJjNHBtxq0KTJUwnVFxMF7DmJ0nZnIlaXD6XxFhUwTuu3+v9WypOxn95fgkff/TcQG9BWdz0FDmbqgf0r/QQCFStjLwiZx65p8hTrShyvkXJrapaCfNzY+/dKDcSbVGR67LkzZNx6letMMaiCq6e94azvbBUf2vYsDH0gbyRtTLl34m5teJ7fuxOnA0ockUiVYGXnWTtliCu5wz+s8vfT0LBsrHhq+hJPqs8igtbRZxdKx+SVYuphIZnfu1t+FdHZ5DQ5LLhW4B3E6EUyIa4ySVMMkULW3kLCxMxPhES6F8zEBA4H0ZdkWsyNNnzyDNFiy8tbkRpAbPNn0TZ11ggD6OWnBURBM+BSsqtlcaKvGg7fIRtrWQnYzyq4Op5b0Tuix3uGhhEhj+Q10x2eicHSzZWXrjcWimWqlZqlWaxk6xdRb6WNasSnd5xecnOzVzFrHK/KejMag5JXa75vbUYjylVipyVPqZD3K0YJuf9bS0LE9Gyev/+euS+tTLKitxwEFNKVSuZVhV5wCPnnZ1yqY4cCMcjZ0UEMa2RRx60Vporcm6tVCQ7x6Le4mjAixPTCQ17UnrHS2MGkeEP5EUbhADJwJ1dipCybT+VyS1W6TG1n1YAACAASURBVFEWyGvc8dmjf7sliOs5g08sDMKSndwj918zP6ZjabuA06tZHJlJtFxP7QXyckW+li3/t7XKyeVMT7eNP3ZmHb/0wNN4bd2rIV+YiEKTJX6B9bX8UGbnw2gqclYDHtNkT61abSjyWh656n1eYSY7Wcd0I0stWLXSqJmJK3KntiInhGAmoSGly3we09XzqYYL2YeN4Q/kBQsJTa6yRW47MoVbLpkEgLLyw6K/AxAoLz+sdaIwtdBuCeJ61qxrreRNB1t5ExFSsoP2jEWRLtp44UIah9vYUTkRU6uqVljpY7uB/P/4+6fw379woq3vaYdvnFzFp586jy88twSgVH1TuaOxHyhSBFKEjKy1UvKfJWiyhM2cCZeitaoVpaTIi5bX5s8CI/Opw6i/L1krzatWFIk0HDfMFbldO9kJePbKWKCI4Op9Yzi9mm04TG+Y6J8M6hHpglVVHQIAf/0zt/D/L5UfumUT0Jhl4q2Sqj6hSoq89aCYN73VZVM17JGoKiNvOtjwm37YzYc1BW0XLByZSbT8s8ZjatkOz6Ll8ACeKbZnraznTCR7WFvLjufzzy35T0ve5xNX5bJhRv0i7AFQgwRrOmNr01b9m3tLVSuBmUAF02vYYU+IYSpylndqqMj9Y2k0jwUIKvL6yzMum0uWNQFdPZ+CS4GXLqZxY4/WCvaTUAI5IeRjAN4BYIVSek0Y79kqlQOzahF8lGaBXJEIr1qpN4ci3kEgZzXk0zUUuWet2NjMWWWTEVkgB4AjbSjy8ajCK3CA8vVx6TYDeaZo8dEFvYDdYCyH4shMacY6U2T9tFYAvxV9RBU5C5JRv46cffZt1ZH7/Q7ByhEeyEMoP+TWSqNkp//zGs1jAbzfpVe1Ul+Rf/RfXws30A9y1V4v4fnSxcxIBPKwrJX/CeDukN6rLSpH2NYi4nvmRcvhycF949GyFv2ayU7/pG7HI6/X1QmU6sjXc0ZZieHesVK35uE2FPlETMF2weIt0+wmArRnrViO14690YdADpRsFWBnrBXACxKj2hDEFDmzVhjte+RuzcqRcJKdrVsrjUoP2XEVA8szFKnahlEDyyYAYH48ClWK4Ox6ru1jH0RCCeSU0m8B2AjjvdqlFUUOsGFADk8OLkzEeHAx6njk3Sjyyq5OwFM7lALLaaOse3NuzHtthJTPH2/GeEwFpaUKFXYTAdoL5Ozft5W3YIc4pjRIpmhhwR8vsBAYM8Dsq36WHwLgreujCBMoSV0uU7OtVK0oUmkmkLfBp/T9vCEopGQnIeW14pXwQN6CIqe0lMuqpcgrkSIEB6ZivOR32OlbspMQcg8h5Dgh5Pjq6mpo71s5wrYeup+9Z9bKvvEo35xSL9mpSBGocqStmmw++bCOIge8ErygImdNQfsnY03VRxDWAbpVI5C3Y60Eg36vWv4zRRtX7k3hQz9wBX7ilgP868wj3QmPvGg5WEkX8cDjrw3lXPd6MMswocll9detKHLvdTLSRcuzVgK/F/bUGlayM67KDSu0om0ocqB0Hrcy5RHwZv2fXcs3f+EQ0LdATim9l1J6jFJ6bGZmJrT33a6T7KyEeaIskDNVmDVsGLZbt+Egrra3XGKtgSJnwcr056wEOTqbxHUL41Xf0wim6llTEPvZMVXiowtaIVgnz25EYZPxZ328/81HcM2+Mf519tTTz85OoPSE9pmnzuO/fuo5/PMzF/r683tJJqjIA0GwmQXJmIh71VDFCo88TGsl73eeNiK4K7QRmn+MmaIFOVLd2FePQ1MxnNvIDXQXdKsMZfnhw6fWkCl6NkDOdFouq2IeuRQhfANPtmjDbBTINZkvBw7iurSmDZE1bMgRUtMqiAaC1UTFPJV7/93N+J13Xdv03xGEKXLWqbqe9eZ6z6X0tqpWgoF8I9sbnzxTxwJjYxD6bq34revsaeajnz/RdqXPoFJS5ErZed2KBQl4AmErb6JQsRyZ3RTCCORZwy4b0VAL9rObLRxhSdGsYbdkqzAOTcdRtFwsZ4Z/EuLQBfLtvIWf/qvH8MDjrwda3Zt3QmqKhIJvrYxFFW7HZAyr4faUhFZ7ucT/+OZpvOOPv1319YLp1A1KscBFUTnhMKkrbVdujFco8vWciemkipQut+WRZ4tBRR5+IKeUImvUnr63Y8lORYJhOUgXLCgSwWrWwH964OmaltR2wcLvfellXhUx6LD+iETAI1ck0tIYW8ATGRs5i5cfMsL0yPOm07CrEyifg96IkiK3ayY668HWKL46Aj55KIGcEPL3AB4BcDkhZJEQ8nNhvG8t1nMGKPW2YFd2SDZCZ1UrfiBnnaBMkdfz1WKqVLMh6OxaDi8vZ6pUecF06iZwgsGqlWNuBnsP9jmsZQ1MxTUkdaUtdRkMXr2oXMmZTt2GlFIg77e1UhomtTARw3/7oavx4MureNeffadKcX7j5RX8yYOnhqYTMON3O8dViZ/XKV1po2PYU+SG7dYuPwxJkTez01gAb3YD0gMeeSvr7BiHpr3CgnPrw++Th3L1UEp/Ioz3aQX2KLyeNbkN0FIgVyRs5U1s+dvrE3ppjkq9ZCfgBZpa6jZvOaAU2MibmE3qZV+vpy71wNcrPfJOSOkyFIlwb3wta2LfuA5FiuBiG8095R55+IGc3VRqJdvY43WjMrReoMme1ZYuWEjpMt572yHYLsVvfO5FLKeL2D9Zqh5a9RtJtgd0fk0lmaJnWxBCuFptxX5kTMQUbOZNjEfVMltDingdlmHUkedNu+y6qQV7sm00ZwUo98jbsVb2jvkliCOgyIeus5P7wTmDB51aicVKWNUKhYXJuMoDiJfsrL87cCKm4sSSp7yDG8jZJMW1THkg96yV2h9rmSJvsDyiVQghmIprWPerVdazBq5fGINLaXseuX+j0pUIf68wadSQ8vbr9oJSyjcl9Qt2PqQDc7rn/NnwhYoZLOxGOSyBPGvY/ImTqdlWK1YAT2QULRdbMKueLrWQ9nbmDQexqWbWSnuKPGvYbVV9sRJEYa3sANwPzprcBqhV6lcJq1pZ2i5iOqFxRZ4uNlbkb79uL9ayBr720krZ11nTxVpF4CtYNqJ1kjOxwFLoMBQ54P3b13MmXJdiPWdiKqEipSvteeR+Te++8WhPrBV2U6mV3JpOaPj3t1/St8XLDF2RYNhMkXtBLhboagzCfseDOlGykmzR5uc3C2ytVqwApfxN0XLLniIB+Isq+pTsbLGzs1OPHPAqV0ahKWjoAvlWoEJjPWeCkMar0RhRRcLF7SJWMwau2ptCUvMu3mzRbpjs/L4rZrF3TMcnHj1X9nWm2qoCuenU9XvZo6IUIS01Z7TCVMJT5Jt5E45LMZ3wPPK86bTc3MMexacSWk+slTRX5K2rwl6jyUyRlzqDowqbP187kA+TIk9UKnKtDUUeqKiqnHOiSiEp8gbXCUOWIlAk0nTWCrN/8qbT0oLpIDNJHRu54fi9NmL4AjlrfsmZ2MgZGI8qDSejMfRAJ9/V8ynoitfBli5asBxaN9kpSxH85C0H8NArazizmuVfL9RR5Hmz/mZwpvgmYmpoCnQ6rmIta2Jp2/PE946VdmG2qsrZo/hUXO2RIvfX8YV08woD9oRWU5Fb5Z/bsAXyjGEj4f+bmJptxyMfDwijygosNQRrhVKKnGnz0tNGfOSHrsa7bl5o+JqgnaK2qcijfvXSsDN0gXzbt1ZM28W59XzL1R/Bx7Or5lMghCChy3zJQ6Ns99uv89aqPfnaFv8aU+SrmfJAXmyQ7GR+Y2UNeTd41orBFzbMj+vtB/KijaSuYDKu9sgjr5/s3ClYW7dhu9wjZ7+3KkWeGTKPvGgFPHJmrbSjyAOBvIZHbnRZhlnwCwViTawVAHjPrQdxpT/gqh7BhGw7yU72vZU5kWFk6AJ5cNrfqZVsS4lOoPSIeGgqxgNKQpN5IqtRQoUplGCHZ8kjN/H8+W187Nuv8q/XC+SRCIGuRELzxwHPYy5aLk6teE8L8+NR/u9jZYUXtgoNlyhkDAsJ3VPkW4EhXGHRzvS9flHeKFM+7yUYyCmlvNt1aAJ5LWulzaoVRmUzjurP/u4GPos8pN6BoCJvP5BLsOs09w0TQxfIg7NAlraLLStyZnewxauAF8jZrOZGgTxeYwlzwa8tX8sa+OuHz+KjXzgBSmlVE0UlUUUKpWKFwRZYPH9+G6ocwVRc5Z5vpmjDclzc/Yffwn0PneHfs5Y18PFHzvL5IlnfI5+Me0O4KveAdku2aEOKkL43/TRCC/yOSorc+9yCyc7tgsXnXA9NIC+Wmq9K1krrijxorVSey6oc6XpnZysjbNuhTJG3UUcOBKY9DvkAtaEL5Nv58n2Yky3ut2SVJFfvKz2mXTaXxAl/b1/DVVKy11jBAjmltMxaObGUhuOv1yo0sFYA4OaDk7j5YHjzj1nFzrOL29g7poMQwj3fdNHCq2s5pIt2WV35vzx/ER/57At4zV9K4XmqMib9m0LYPnmmaPG65kGhVut6LWslmAPZbmN+zU7huBQ50+FVK0yZ11o9WA9VjvDvqwzkXvlhd1YE39cZUhNYNx45uwkM+6agoQvkWwULh6dLM7tbPUFrKfJjhya4umjWERbXJF5vbdgumPtwMV3ktsZGzoTt0oajOe977zH8b99zuKVjboVp31o6v1XgCyqCHvmJJe9GFZypzp4mLmx5wT1b9JKd8Trld92SKdZuz99J9DJFXrIhCCl9PgCw6vvj82P6UJQfMrHBAvHCRAwf+/fHcPc1e9p6HzbHp6ZH3qV6Zedis/LDVpEihJcdtmutsCezouVgabuAx86sh3JM/Wb4AnneKttr2aq1cu3CGG48MI4bD5QmDAaVsSo1fuxP6DJ/JGR+c1Lz1pSxm8Fy2lNv/RwAFayhnx/3Jjqyx+hM0cKJpQyAcluILVRgy5aZpxrmTsYgaT+ZOkjoNRQ5IQRRRaqpyI/MJobCWgnOImfcecVc0+7ISljCs6pqJYTyQ67IQ+zmZeduOy36QOlGZdgO/vJbr+L9n3gitGPqJ0MVyB2XIl20MJvSeVa+1UB+9fwYPvPzt5dNgLtiT6oqKVSPuCrz8aDsQg+2cQPAqj9FrZ+BPPjvnx9jgVyGHCFY3CzgpYtMkQcDuXf8S9sFOC5F3n8UZ36qEfIKtEygimJQqOWRA6UtTgweyGcSyBr2wCfFgpMPu4Ep8qo68i7LDx2X8mmiYSlyoGSRdJLsBICC6Q3U2y5YQznWdqgCebpggVJvVyVToq1WrdRCihCu0JvdyZMBRc788QMVgXzFL0XsZ1JPVyQeJPeOe9aKIkVwx9FpfPH5iwFrpRTImeI+v1UsexRnF23YS4kH0lqpM941qkpl1tJa1vBauf3fdbqNjtmdIDj5sBtKirz8utC6SHZu5y1c/+tfxv/nz34P8zphiryT8kMAKNoOCpYNSlF2Ix8WhiqQs9LDibjCqzW6nSL4hkOTAFrxyEvjbNmFfsBfy8Yez1aYtaL0N2ixmxqzVgDgh6+fx/mtArd7snUUeanGO6jIwwnkX3x+Ce/5q8ewnjMGL5Ar7MInZVUPMUXmy4sBr4Z8Kq6WZr8PuL2SKZZ75J3CrqtaVSud3uhXs55w+NKLFwGEu0yEnbudNAQB3jXNnrSzA36zrsVwBXK/LG48qvIkZytzVhpx5xWziKsS9gWCYC2Cc8mZImfWyk0HPVW/sgPWCuDVkgMlawUA3nrVHL857UnpZcnOoEde8lRLSwjCslYeP7uJh15Zw3LaGDiPnF34leNdo2q1Rz6V0PgWqkEO5K+u5Wp65J3ArZUQyw+ZQGBb9cIqPwS6UeSlZCezfNhTzTAxXIHcv4jGYiVrpZU5K424Zt8Ynv/176/yuytJaCVrhV3ol0zFkdRk3HnFHICdsVaA0s2MWSuAF5jvvHwWgFedU+aR+4H6wlaxYr9juMnOoJc6cIq8TsdjrIa1Mp1QBz6Qv3Qxjbf83jfwheeWAHT/ed9yySRuOTRZtUZRlaSOPfLg9ykSaTsx2Qjukbf5niVrxUXeH83QzsC5QWGwrq4mlBS5gjsuncFGzgzlZGilvjmuyTzosQt9Mq7i4Q/dibgq+3OsmbXS30C+dyyK8ZhStcrrg289imsXxlAwHXzBXAKlFIQQPlsia9i44M9oSeilRb1hzZ4wbAdTcRW3XTqN77ksvD2tYcCUWOX8l5gq8cFshu3g5HIWP3ZsYeADObP1vnrCm9LZrbVy25Fp3HZkuurrmtJ5sjP4fWGqcaBUrNCxIg9aK23s6K3kQ59+Fgcm4/jA9x7p+D06IawNQXcTQl4mhJwihPxKGO9ZC3aBTcRUvP26vfiL9xzr1Y+qIqHJ3qYbl/KhSjFVQkr3hnYlNHlHqlYA4Bfecik+8XNvrPr6FXtS+IW3XIq4JsOlJUuoGPA4WTI0oYXvkRu2i6Qu449/4kbcengqlPcMC3bhVyryqCrzz+n42U0ULAdvvnxm4AM58/VZsOzVMmtV8qyVTio7mCVz7OAELp1JNHl1e7Q6u7ze9xXtgLXSoSKnlOJzzy7hO6fXOvr+buj6t00IkQD8KYC3AlgE8Dgh5J8ppS92+96VsEDezgCgsGAKJ2faKJjeCRkM2Eld5t2T/bZWZpIaZpL1q3cSgREDMVVG0XL4YoUHHn8dEzEFByZjkP0pkmFaK2E+PodJSZFXWCuKxIPiN0+uQpUiuPXwFCL+U9ugNgUFcyAJTW55k3y78HVvjgs90t55zm4yv/qOq3D9wliTV7dHSZG329kZTHb61kqHinwrbyFTtHfkZh/GVXYLgFOU0jOUUhPAJwH8SAjvW8W2v5arlbG1YcPKuXJG6RdeGchZEqff1koz2GMsu9gN28UlfnfsRs7ET77xAHRFgix5o33DSnYattvWxpZ+UlLk5VommOz85suruOWSScRUGboiQZMjA6/IgXDrsyvRAoG8XVgg15VI6OMaSlVIbSpy/99TtFz+JNapImcLKsKeVdQKYfzG9wF4PfDnRQBVz/mEkHsA3AMABw4c6OgH3XXlHA5NNU5K9goWDLOGxT3yYMAOXjz9tlaawZ8mAp2pl0zHcXI5AwLgPbce4q/Vuigvq8SwnYFV5JEIwVhUwUzF3kiW7FzaLuDl5Qz+TWAW9lhU4asGB42cf04mdbnrGvJG8EDewVMbH4fRZrBthU49cra8IlMsDUfr1CNnS5y3duAcCeM3XuvWWmWgUUrvBXAvABw7dqyj1qk7jk7jjqPVCZh+kOSB3BuMpUik7KRh5XUR0psTtRuC+0kBzw+MazIum0vimvkU9oyVgpnmL+BwXYqHTq3he45Od6yeTNtt27PsJ5/6wJswl6oO5LZL8fApb+bG7ZeWzrexqDK4itxf1/cztx3q2BpoBVXuPI/CvqcXN3emyDu59nRZwkZARXcbyDNFu2rHb68JI5AvAtgf+PMCgAshvO9AwRV50a65BYiVe8XUwZryBwStFabIXehKBJ/+wG2QKzxFbyiSg0fPrOO9H/suPnnPrR0nKg3b7eljfrdcOpus+hpbnP3Kijej5pLp0lyfgQ7kpoOYIuGX3nZ5T38OO+/zHQQ7s4eBnCtyuf1rT1elsomfnZYfngvs/kwX7a6bFdshjE/0cQBHCSGXEEJUAO8G8M8hvO9AEVS1tbYAMUXe7nCifhCvVOSWA02WEFWlqkdRNt2O1eyzqpZOMKzBTXbWg9llZ1ZzGIsqZTbZIAfynOm0tHGnW9jk0VdWsk1eWQ0L5FqTAXWd0KlH7n1vpCyQd6rIg0uct/rsk3d9lVFKbQC/COBLAE4A+AdK6Qvdvu+gEQzkedOpSmiWFPngBfJEZbLTcutuJtf8DTAs4XdyOdPxzzWdwU121oP9/s6sZvlYYMYgB/K8aYe2cacRR+cSkCKkoxt8L60Vpsg7tlaCgbzY2e/43HqenzObffbJQ/lEKaVfoJReRik9Qin9aBjvOWiwLUE5w0bBcvgjOIN56IMYyIPH7rjUKx2rE2A1xbNW2Ezuly92HsgNyxloj7wWTIG/tpEvyx0AXtnrIJcfhrWooRG6IuHwdLyjQN5La4Ur8g7eOxqwViKkM0WeKVpYz5m4Yb83rmO7MGSKfLfAKgGyho2C6fCNQwymyAfSWlFLx14qAasTyH1rpaTIs3wlXLuYzvBZK+xGbDm0piLP+DfDQSNv2vyG3Wuu3Jvic+7bwXQcSBHSk/LhbhU5O9+nE1rLHnnOsPHF570BYCzReb0fyPtduTJcV9kOoskSFIl4gdyqVj+JinVhg0TE35eZ8/19oHqpLkOTvaqVnFndxt8uhjW81gqAqooW1t05iKo8Z1Y/JfaKK/emcH6r0LYPbNpuzyq6tC488qDNOJvSWlbkn37qPP7DJ57A0naBr028bp/X6CQC+QDDBmc1qloZtGYgRlyTkTNtPjCrsSJ3ytadnezQXjEGuLOzHsERxLUUOTCYbfp5oz8eOQBcuder9mlXlfey07fTzk6g/JqdS+otB/Ilf8PWRs7k1szhmQQIKQ346xfDdZXtMGxwVu2qFT+QD6AiB9gYXofPWamryJUIT3ayi6OThCel1E92DtcpFvy97hkrH2080IHc7I9HDgBXzXsLzNv1yXtptbGnp05K/oKiZjalIVu0W7IT2bRTtlkIAB9eN3RVK7sJNpM8b9rVVSva4ForgJfwDFor9SwPZq0UTAfTCQ17Ujpe7iCQswqFetUxg0rw91elyAd4uUSujx75bFLHdELFE+c22/o+o4fWyhsvmcRDv/wWHJyKN39xBcFreSapw3ZpSw1Py/5spbQfyDU5Al2RMB5ThLUyyLBAXjCdKuU98NaKKvMaeKCRR+5ZK3nTQVyTcMl0nCdy2oGXmg1Yl2szomWKfJislf4pcgB4500L+PxzS/juqxstf08vO30JIU13CtSDXQuEADP+bP9WEp6rQUWet/j5MR5VhLUyyCT8vZ1e+WE9a2UwOxmZv88CbN3yQ1a14pdYTsbVjh4TefPHgN7Y6sGCYUyVqhZGD2ogtxwXpuP2zSMHgA/edRQLE1H8yqefbXnuyqBOw2TWSkyReGNfKz45U+TMWmFblcZjKraFtTK4xDUZa1kTlkMRq0p2KlAkUrVRZVCI+4GcWyv1kp2KhKLlJTtjXTwmsgmKw+aRSxFvc82eMb1q1MKgBnJWOtePzk5GTJXxS2+9DGdWc3jpYmte+aCWo7JAHlXlUuNfE0Vu2A5v+mGBnCvymFDkA82N+8dx3s9UVypyVY7gk/e8CT/5xs4mO/aaeKvJTl+Rew0mEj8p260l5x75AF64zYipUpU/DngXvCpHBq78kI2w7aciB0rWU3AWeiN6WX7YDSyQxzWJ94tkmuztZLYKUCOQR4VHPtD83B2X4P3fcxgAairvmw9ODKwiT/jJTqOF8kNKvZMzqkqYiKlwXIp0m4OEzCEO5HNJHUfqbLAZxDZ9Fkj7qciBUqNZrsVyvcG1VrxjiipSy4p8pSyQe8sk2MKbsZiKdNHqa+PYYBq6AwohBL/yA1fg+66cw3UhbzjpNXHNW2HGHsPrB3Lv61t501fkXvInmMxphV7O1eg1f/u+W+omDgcxkO+UIuejH8wWA7nj9nRWeqewAoWYKvFcVzOPfMX3x1V/2UilIqfUq2aZ6NMExOG7ynYYQghuuWRyIFvxG8FWmrElvfWUMisXzPl1yeP+ydnu1hOjSZnjIDOb1OuO3x3EQM4Ueb97GNjNjomDZgy+tSJXze6vB1Pkh6fj2MyZyBp2mUcO9LcpaPA+VUFPmE15Oz3PbXijNhtZK4yYKmEi3lkgZ9tghtFaacQgBPLKfEVJkffZWtFG0FphHnkTa2U5XYQUITg8E8fipleeywI5E02VuZTFzTw+/JnnuhpEV4/B+1QFPYF1vr3uz4TQ6ynygIIus1baDF5sXdwgXrjdsNOB/JnXt3DF//1FnnQHSmve+tUQxGDNU60q8kEd2aAHrBVVikCKEL7OsR4raQMzCQ3jMZVXrzAlzt6PVYgxXt8o4P7HXsN61kDYDN6nKugJc/5uynPrecgRUncNVVBBR1UZE34g38x1qsiHz1ppRDCQp4sWfvHvnuzJhVmPV1ayMGy3bP4N29bTz4YgwBtQpcqRtjzyQXxC44Fc87Z7xVSp6b9pOWNgNqWV5Y3Y/zOFX9kdykbbMnEUJl19qoSQf0sIeYEQ4hJCjoV1UILwYdbKSsZo6O8HW+pjqoSU/6jZ7qD8Ya0jb0YqqiBT9EbZPr+4jc89u4THz7bXqt4NrDmrpiLfgWa0uCohPyLlh6w3JK7KTf9NK+kiZpN6nUBeW5FXKvcw6fZTfR7AOwF8K4RjEfQQXZGqFEPN11VYK7IUQUqX2+7uHGVrBfAWCbCSzHbzB93AfNcLgUDOJlXuxMC2mCq3rsgH1FoJVq0AQEwrV+Qr6SI+/+xS2fes+Iqc+eFAtSIvVihyVls+MWiKnFJ6glL6clgHI+gtc74qb2R3lCtyT+FNxNW2M/CjnOwEvJwBq2zoZyDfrhHIc6YD1bc5+k1ca0ORD2xnp3dMrA4/rsplvv/HHj6LX/i7J7nCLloONnIm5sfKFTmrI2fXV6Ui38qbUOVIQyHVKYP3qQp6Bkt4NppIWJnsBFCW0GmVUVfk6YKNjL/bsZ9dfFs8kJeWfeQNG7E+JzoZrSpy23HhuBRqDxYvd0tSV0AIeKktW8LCOLXi5SNYJQu7ic6PR2taK+z6MqoCuYXxqFI1+iEMmppqhJCvAthT468+TCn9bKs/iBByD4B7AODAgcFsYx91WCCvNzALqEx2+oE8qrRfR24Pbx15I8oUuX9hb7SRCL64XcR0Qq2bbG4GU+SVHvlO+OOAr8hbqFphT2iDeGOfjKu4/+feiBsPTADwAvlatvQ7fWUlC8Ars5xJavwmOj8e5Z97VJH4uV7yyCuslYLZE1sFaEGRwTQ10AAAGhxJREFUU0rvopReU+O/loO4/z73UkqPUUqPzczMdH7Ego5h1kqjR7tainwi1n4gN20XhHS2sWWQCQbyjK/aWs0fFEwHb/m9b+B/PbHY8c9ngfxiushbwPOmvWMLTWKq3FIdeS8XL4fBbZdO888wpsm8Nr9oOXyNG7PSmCLfF1DkQWXOhBITM4zNvMVn2ofNYH6qgp7AFXmrVSv+2rPxmNq2fcCWCPTiMXInKQvkPNnZ2meTLlooWA4WNwvNX1wHFsgdl2Il4ynDnOH0vT2fkdBas1YGPZAHiaulp4wzqzmw/iturWwXQIh3PdUK5IpEECHVinw7b2FiEAM5IeRfE0IWAbwJwOcJIV8K57AEvWA22UIgD3Z2aswj90rubKe1udOAF8hHLdEJVAZyL6i2WmPPlOtWofPk6Hbewr5xbwUdU4bL6WLfZnpUEmtSfkgpxb88t8RLJLUBLD+sJPiU8cpKqV4/F1DkMwkNqhxBUpdBSHkgJ4RA98dBB9nMmxiP7pC10ghK6WcopQuUUo1SOkcp/f6wDkwQPp1bK97J107limG7Q7dUohV0JQJVinRUtcJUXqfJUUoptgsWrtzr7cw8v1VE0XJwaiWLq/09mv0m3kSRn1zO4gP3P4kvPOeV7w2FIvd9f0opTvn+OBC0VoqY92+mkQhBQpN5xQpDVyS+6BzwfndbBQvj8QFU5ILhgs2PbpSADF5ozOvjQ4Da8MkN2xnI5o9uIYQg5Xd3skft7UJrI0tZIOi0xT9vOrBdiqv8LfYXtgo4uZyB7VJcPb8z0zhjqoSi5db997NzhtlJwxDIY6oM2/WWh59ayfKJiJmAImdPRQBwdDaBS2fLxx7rcqTMWilYDkzbHUxFLhguphMaCGmsyKUIgSIRRBUJkYjnb/M2/TaUpKfIR/P0GovKSAeqVlxaPSCpFiyB1mndOXsimh+PIqXLuLBVwPPnve081+xQII/zCYi1VTlT6xe3/UA+BDd3PkPGcPDKShY37B8H4FkrlFKc3ypgfry0eOSB978J/+X7Ly97D63CWik1AwlFLugSRYrg9iPTTdWbJktl2+QPz3ibydtftDt61gpQmreSKVo8MLUSnNm42U6tlW3/+8aiCvZNxHByOYMXLmwjqcvYPxlt8t29geVR6pUgZv1/89J2aX73oMNuTlnDxtm1HK7ZNwYpQpAt2tjMWzBsF3vHSp+34g/aCqJVKHJ2fvSiPR8QgXzX8Yn3vRE/fevBhq/R5EhZOdvCRAw3H5zAPz99oeWfM6iT7sKAB3LDxsKEd0G38rTCVOt2p4HcV+RjMQU/eM0ePHpmA189sYxr5sd2rDqo2ZYg9vXl9PAEcnZzOr9VgO1S7EnpiKsSsoZd1gzUCF2RysoPt/mcFWGtCPqEJkeqGkx+5IZ5vLycwYmlFhft2s5IVq0AXiDfKnjLBPZPxgC0VrnCFHnGsGG1UQHE4IE8quCnbj0ITY5gOW3sWKITaD7KNmeUl2gOQyBn5z4b+TwZV5HUFWQNmzdi7WsayCO8uxno7cAsQARyQQ00RapqMHn7tXshRQg+26IqH9XyQ8ALpBe3i6AUOMACeQvWStBH7mSBMxuDOhZVMBlX8a6bFwAA1+zbubWDiSbLJSo37QzDOcFuTiyQT8VVJDQZ2aKNJT+Q7x2vXs4dpLJqhZWcimSnoG9ocqTMIweAqYSG245M4Wsnllt6D8Ma7UBuOV6VBgvktXzvx89u4IHHX+N/zpnBC7uTQF7+eP6BNx/BWy6fwR1Hp9t+r7Bgg6aaKXLGMJwTbFjc636lzWRCRVzzrJWVjAE5QjDZxCLR5drJTqHIBX3jqvlUTZV304EJnFrNttaS7YxusjNYM7xnTIccIdioocj/8ltn8P98sTQcNPi5dZLw3C5YkCKEd3Hun4zhr3/mFkwntLbfKyzYsdTbcZmtaBYaxKFZlTCPPGitJHxrZSVjYDqh8YqueuhKebJzK29CVyI92/U7eCutBTvO7//YDTW/fu2+MVAKvLiUxhsOTTZ8D8N2hsIP7YRgF19Sl/0RBtWB/Nx6HtsFC5RSEEK4Rw6UbJJ22Mp7m9oHaexBSZE3TnYyhuGcYB45q32fiKlIal6556o/h7wZlZ2dm3mrZwOzAKHIBW1w7YKn0p9b3G762lG3VhhJXcZkXKmagEgpxbmNHGyXctshb9o8kHWqyMejvXk07xSmyHN12vSHMZAzRb6cKWIsqkCRIp61UrSxmvF2dTbDKz8st1bGevi7G/xPVTAwzKV0zCY1PHe+eSAf1P2MYVAeyJWyee2UUrguxUrG4I/WzNvOmQ6vdug0kFe2gu80sSYNQZWWy1AEct/+oBSYSngqOqEpyBk2VrMGZpKtKfLgzs6NnIHJHs7DGfxPVTBQXLcw1lIgN6wRriMPJKwSmoz9EzGcXsmCUoqPfPYFvPveR3F2LcdfwwJ53rAxl/K6aztNdvZS1XWCKkegSKQskRska9jYkypVeAxDZ6csRbgImfKDb0KXkTVtrGcNzLYQyDU/kFN/dOJKxuDTR3vB4H+qgoHimn1jOL2arZvcYhi2M7LJzkpr5Q2HJrCeM3F6NYcvvnAR3z27gWcWt/hrmPrOmQ6SuoKUrmC7gzb99AAGcsBT5Q+fWsOx3/wKXg3cwADPWmGVPcDwzKdnVVtMRSc0CZR64xhaU+T+liA/mK+kW7sBdIoI5IK24AnPC/Ubg2zHhUuH4zG6E1gwJcRLjL3hEi/x+8nvvobVjAEA+NQT5/nrubVi2IirEsZjSkeKPF20+QCnQSKuSnh2cRtrWROPnF4v+7us4WDBHx+gysMzn55ZRpNxL/gmtNINtKVAHtjbuZW3YDouZnuoyAfvrBAMNExdsaUGtTCGaIlAJ0QVCYpEoMveYLHD03FMxVV84rFzAIAIAV5ezkCTIzBslzf/5E0bMU3GeFRp2yOnlCJTHDyPHPBG2TJeuFBuu+UMG1NxFTFVgjQkQRzwRtkC5dYKYybZPCAH172xG/lcC9UunTKaV5qgZ/ByswbLBFiVRmVT0ahACMFYVOEXNyEExw5NoGi52D8Zxc0Hvd2PrHW+pMgdJDS/XLFNRW7YLiyHDqQi3zOm46YD47jlkkm8EHhSc1yKguUgpsqYjKtDdWMvKfKStcJoxSJh1krRcvicmdkWbgCd0u2GoN8lhLxECHmWEPIZQsh4WAcmGEx4uVmDZQKsgmGnFgL3g1RUKQuqrK7+9iPTuMW3Wq6eH0OElOaVe0HNs1ba9ciZqk/pg6fI//ynb8b977sV1+4bw4mlNN8kxc6RhCZjasgCOVfkgaoVRisNWFyR2w5WfLttkBX5VwBcQym9DsBJAB/q/pAEg0yp3Ky+ImeJ0Lg2mooc8HzyRMBSeNORKQDAmy+b4UH90HScT0os+DXFcdW3VtpU5Gl/9vkgKvK4JiOqSrh6PgXDdnHGT3jm+HkwvIp8invk3p+T/r+1GazqxbDcvijyrs4KSumXA398FMC/6e5wBIOOKkcgR0jDNn0W5IPe6ajxv995admfr54fw1f+0/fg0tkEDNvFu9+wH2+7ag5/+8hZbBUs5P3PK6ZJSOgy3y7UKuni4CpyBhvr8Pz5bVw2lwwEcgk/dP0830Y/DFRWrbAb6EyLqrrkkTtYSReR1Fu7AXRKmFfazwJ4oN5fEkLuAXAPABw4cCDEHyvoN7HAlvFaMEUeG2Fr5c4r5qq+dnTOW8GmKxJ++13XASjNLudPKaoMXZbguBSW40Jpsa6aBf5UdHA/08PTcWhyBPc99Crue+hVfOB7jwDw1Oz3XVn9eQ0yXJH71goTJa10dQIBj9x2e15DDrQQyAkhXwWwp8ZffZhS+ln/NR8GYAO4v977UErvBXAvABw7dqz5gkPBwBLX5MaK3E+EJkZYkbcK2+8ZfEoJqrXWA7mnyJMDrMhlKYJr943h+LlNAMCXXrgIYDifzOIVi8eZTdhK6SFQ2ovLkp29rCEHWgjklNK7Gv09IeS9AN4B4Psoa2MSjDTNFHmOK/LR9chbZSyqYHGzULIZVClQ0eCiVds0XRhcjzzIH/z4DcgaNt75Z9/hTVHDeEO/+5o9UOQI9/U1WUJCk5sulGCUWSsZo+mQuW7p6hMmhNwN4L8CeDOldHgMMEFXxDW5YdVKsFphtzNWochjFYq8VTJD4JED4BuTjszG+WLoYVTkxw5N4lhF8P34z92Cg4Eu1UYEyw973dUJdF+18icAkgC+Qgh5mhDy5yEck2DAialSwzryXCCxt9sZj1V65BIP5MGdjs3IFG1IETI0TzmXziT4/49K9dJNByYw1bJH7k9QTBs97+oEuq9aubT5qwSjRlyVcTFdv7MzZzpQJDKys1baYSyqwPGnIQKVirz1vZ3pooWkLg9NiztL/AK788mM/Y5ZpU4va8gB0dkp6ICYJqPQxCMf5YqVdmBzWdiux6BHXmjLWhnMOSv1uHTWU+QR4o002G2wOvJTK1kAwN6x3ipyEcgFbRNTJO6Dv3wxUzWLmrWiC0qB/MK2F8hjamceebpgIakNtj8ehAXyuDo8TxFhokgRSBGC585vQ4oQXLW3twuyRSAXtE1M8zzy81sF3P1H38Jtv/11/M13zvK/9xT57lNhtWBDri5sFaFKXhVEaTKei628icfOrDd6CwCeIh/kGvJKDk7GoEhkKBOdYaHLETguxdXzqZ42AwEikAs6IK56VSsXtgqgFHAcij998BT/+5xp7+oLOMh41KtDfvFCmtcgBysa7n/sNfzkfY/V3bDD8Dzy4VHkshTBJdPxkUl0dgJ78rrpwETPf5YI5IK2iWkSXAosbXsJzyv3psoahHKGvasv4CATcS/4pqIy/ujd3lLroLXCBmpd3K6fPAaGzyMHgB+8di/+1dGZnT6MHYMH8oO9D+TDdWYIBoLSlnEvI78wGcV3z27AdSkiEYK86bQ0IW43sCel43fedS3uODrDm0m0QPs2uwEubRdxOFCyx6CUglJPkQ96DXklH7zrsp0+hB2F/Z5vFoFcMIgw/3tx00vg7Z/wmiTylpfkFNZKCUIIfvwN5bOFeB255fBGoaU6ivzf/vkjuOngBLKGjdSQKfLdji5L2JPSMd/jihVABHJBB7AgvbhZgCZHuPebM2wvkBuOsFYaEFwDxhT5Rb+qpZIXl9J4dS0HSjGQ24EE9bntyBR0RepL1Y4I5IK2KSnyPKbiKi81zBo25sB2U4pTqx6KRCBFCIqWW1OR//k3T+OG/eO4Yf848mZJtQ+bR77b+dV3XNW3nyWSnYK2Yc0+5zcLmIirXKHnDBu248KwXWGtNIAQAl2OoGA5vB6fBXJKKX7/Kyfxj8cXsZEr3yI0TFUrgv4iArmgbZgiN2wXk3GV2yhZw0ZuxPd1hoWuSChaDp9ZwwJ5umjDtF2sZo2qQD5syU5B/xCBXNA2QbU9EStZKzmj5PmKzs7GeIHc5YqceeRrWW8my2rGwLofyBcmvGoXYa0I6iECuaBt4gG1PVlhrbDGlpgI5A3RlAiKdsn/3sxbKJgOVjOlQL6R8/7/nTctIELQ8y0zguFFXG2CtgkG6cmKZGeWbwcS1kojdFmC4VetzCQ1rGYMXEwXuSLfyBk8qP/s7Yfwzhv3YU8fytgEw4lQ5IK2CU6zq0x25nfBvs4w0JUIcoYDw3ZxZCYOAFjaLvDg7VLg9EoOUoQgpSs4NB3fycMVDDgikAvaRooQHswnYypi/v/nDJsvUBAeeWN0ReLJzCN+R+fSVkmRA8BLyxlMxFREIrtveqCgPboK5ISQ3yCEPOtvB/oyIWQ+rAMTDDasUmUiriASIYirErJGyfMVVSuN0RWJJzN5IA8ocgB4ZTmDqbi6I8cnGC66VeS/Sym9jlJ6A4DPAfhICMckGALYWM7JONsyLgtF3ga6EsFm3gvkUwkVs0kNr67lsZY1kfQ/u7zp8M9XIGhEV4GcUpoO/DEOgHZ3OIJhgXVuTsa8QJPQZGRNUbXSKroswXG9yyWmyrh8TxIvL6exljVw5d4Uf91kQgRyQXO69sgJIR8lhLwO4KfQQJETQu4hhBwnhBxfXV3t9scKdhhmnUwEFHm2WKpaie3C9V7toAesp7gq4Yo9SZxczuLidhEHpmK8xFNYK4JWaBrICSFfJYQ8X+O/HwEASumHKaX7AdwP4BfrvQ+l9F5K6TFK6bGZmd07o3hUiGsykroMRfJOoYRvreT97UAiQdcYPbCYOqbJuGJPCqbtYiVjYDqh8UFkwloRtELT519K6V0tvtffAfg8gF/r6ogEQ0FSl8tmjsc1GYubeaznTEzERPBpBtsSBHiK/PI9pa3zM0kvkJ9dzwtFLmiJroxMQshRSukr/h9/GMBL3R+SYBj44F2XYTMwCySheQuZX9/I85ZyQX10pVyR759UIUUIHJdiOqFyRT4hArmgBbrNSP02IeRyAC6AcwD+Q/eHJBgGLptLlv057s8hX7QLuOPo9A4d1fAQVOQxRYKuSLhkOo5TK1nMJDTMJIS1ImidrgI5pfRdYR2IYLhJaDLSBQsOpUKRt0C5Ivf+/4o9SS+QJ0se+VRcrMwTNEd0dgpCIa7JsF1vvyRb/SaoD0t2yhEC1U8YXz0/hggBZpM6rppPIanLmB8X81UEzRHFvoJQCI62FYq8OWwxb0wtrQJ7720HcezQBMZiCt5y+Sye+cjbRPWPoCVEIBeEQnDa4f5JocibwayV4A0wpsp4w6FJAN4WoT6sehSMCMJaEYQCC0hyhIi52S3AArmYSSMIAxHIBaHAAvn8eBSSsAOaosvepSd2mwrCQARyQSiwIVn7J4U/3gps6JhQ5IIwEIFcEApsiNbCuPDHW4F75GIBhyAERCAXhIJQ5O3Byg/FlEhBGIhALgiFPWM67rpyDm+5YnanD2UoYJ2dcWGtCEJAyAFBKKhyBPe999hOH8bQoPGqFXEJCrpHKHKBYAfQAw1BAkG3CDkgEOwAmizhQz9wBe4UVpQgBEQgFwh2iPe/+chOH4JgRBDWikAgEAw5IpALBALBkCMCuUAgEAw5oQRyQsj/SQihhBCxGkYgEAj6TNeBnBCyH8BbAbzW/eEIBAKBoF3CUOR/AOCXAdAQ3ksgEAgEbdJVICeE/DCA85TSZ1p47T2EkOOEkOOrq6vd/FiBQCAQBGhaR04I+SqAPTX+6sMA/i8Ab2vlB1FK7wVwLwAcO3ZMqHeBQCAICUJpZzGVEHItgK8ByPtfWgBwAcAtlNKLTb53FcC5jn4wMA1grcPv7SXiuNpDHFd7iONqj0E9LqC7YztIKZ2p/GLHgbzqjf7/9s4vNI4qCuO/j9QW1GqtioRSTSJV6JMNIgVtXxRtgjb+AYkIBhREULCIYKQgfa2iD4JYFItVqi2ixbwI9UH0qdU2Jm1KGpPUgNGYQAUrKGr1+DB3YbLsxK5m7t2B84Nl7pxMsh/fPXNy753ZWWkGuNnMSjVP0jEza7mnM7mu5nBdzeG6mqNVdUE52vw+csdxnIqzbM9aMbOO5fpbjuM4zoVTxRH5G6kFFOC6msN1NYfrao5W1QUlaFu2NXLHcRwnDVUckTuO4zg5vJA7juNUnEoVcknbJE1ImpI0mFDHekmfSRqXdErS0yG+S9L3kkbCqzeBthlJJ8P7HwuxtZI+lTQZtldE1nRjzpMRSeck7Ujhl6S9khYkjeViDf1Rxqsh305I6o6s6yVJp8N7H5K0JsQ7JP2W821PZF2F/Sbp+eDXhKS7Ius6mNM0I2kkxGP6VVQbys0xM6vEC2gDpoEuYCUwCmxMpKUd6A7t1cA3wEZgF/BsYp9mgKvqYi8Cg6E9COxO3I8/Atel8AvYCnQDY//mD9ALfAII2AwcjazrTmBFaO/O6erIH5fAr4b9Fs6BUWAV0BnO17ZYuup+/jLwQgK/impDqTlWpRH5LcCUmZ0xsz+AA0BfCiFmNmdmw6H9CzAOrEuh5QLpA/aF9j7g3oRabgemzey/frL3f2FmXwA/1YWL/OkD3rGMI8AaSe2xdJnZYTM7H3aPkH16OioFfhXRBxwws9/N7Ftgiuy8japLkoAHgffLeO+lWKI2lJpjVSrk64DvcvuztEDxlNQBbAKOhtBTYYq0N/YSRsCAw5KOS3o8xK4xsznIEg1I+Y2//Sw+wVL7BcX+tFLOPUo2cqvRKelrSZ9L2pJAT6N+axW/tgDzZjaZi0X3q642lJpjVSrkahBLeu+kpEuBD4EdZnYOeB24HrgJmCOb3sXmVjPrBnqAJyVtTaChIZJWAtuBD0KoFfxaipbIOUk7gfPA/hCaA641s03AM8B7ki6LKKmo31rCL+AhFg8WovvVoDYUHtog1rRnVSrks8D63H7tIV1JkHQRWUftN7OPAMxs3sz+MrO/gTcpaVq5FGb2Q9guAIeChvnadC1sF2LrCvQAw2Y2HzQm9ytQ5E/ynJM0ANwNPGxhUTUsXZwN7eNka9E3xNK0RL+1gl8rgPuBg7VYbL8a1QZKzrEqFfKvgA2SOsPIrh8YSiEkrMG9BYyb2Su5eH5t6z5grP53S9Z1iaTVtTbZxbIxMp8GwmEDwMcxdeVYNFJK7VeOIn+GgEfCnQWbgZ9r0+MYSNoGPAdsN7Nfc/GrJbWFdhewATgTUVdRvw0B/ZJWSeoMur6MpStwB3DazGZrgZh+FdUGys6xGFdyl/GKcC/ZVeBpYGdCHbeRTX9OACPh1Qu8C5wM8SGgPbKuLrK7BkaBUzWPgCvJHjk8GbZrE3h2MXAWuDwXi+4X2T+SOeBPstHQY0X+kE17Xwv5dpLs6Z4xdU2RrZ/WcmxPOPaB0L+jwDBwT2Rdhf1G9j0F08AE0BNTV4i/DTxRd2xMv4pqQ6k55h/RdxzHqThVWlpxHMdxGuCF3HEcp+J4IXccx6k4Xsgdx3Eqjhdyx3GciuOF3HEcp+J4IXccx6k4/wD3Rp19B2fjTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise 1\n",
    "T = 200\n",
    "α = 0.9\n",
    "x = np.empty(T + 1)\n",
    "x[0] = 0\n",
    "\n",
    "for t in range(T):\n",
    "    x[t + 1] = α * x[t] + np.random.randn()\n",
    "\n",
    "plt.plot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KM+BToudKcyUlphJcAdckzyiehBF+ZLftX479BVfAxYB3IM566XH3UGmupLG0EYhktET1pdjVvYsvvvRFfnDZD7ii+QqGfcPaXcB9++4jLMM4/U6klHmtbx5Nh7MDIG3BVzehDXoHqS6uztu8phsTWR5506ZNbNq0KW5MQUEBv/jFL7J63VTkIsLvFkLUA0S+Jgpr2oE5UT83Ap05eG2dSUT1wSvNlVgLrbgCLkLh0CTPKhZ1jtEevir+6sKtelGIps/TR42lRrsQnHGdiXlcvbt5teNVYCT/fWHFQoJSsUiCMjihKZ2q4KdKyYxGveuZyWUmdGLJheA/CahZNx8D4pNN4RngKiFEZSSL56rIMZ1pjCqUqqUD4ApOrShfFfXoNEU1wtfGJBC8HncP1cXVlBWWUWws5ow7VvDVaP7VjleRUmqC/4mVnwBg9azVwMTuPlYFX70rGQv1IpjogqczM8k0LfMBYAewRAjRLoS4FfgecKUQ4hhwZeRnhBDrhBC/BJBSDgD/AbwZ+fftyDGdaYzm4ZsrKS2MCL5/igm+d5BiY3FMsxPVyigQSvu/VBG+EIJaS21chK8Kfre7mxNDJ2iztyEQXNl8JU+9/yk+uuyjMeMmgg5nB5VFlVhMlrTGq3+HqSb4evvF9Mjm75SRhy+l/EiShzYmGLsT+ETUz78Gfp3R7HSmNIO+QQpEAdZCqxbhOwIO6qmf5JmNMOQbiovoVaF7x+x38ErHK3ERfigcot/br/natSW1cbtS7X679v22zm20OdqoL6mnsKCQueVzaXcqNVEmQvDDMswv9v+Cp089zcKKhWk/r6KoAoGYUr0BzGYz/f39VFVVTdjax3RESkl/fz9mszmj5+k7bXWyZtCr7GA1CIMm+FMtNXPAOxCzYAtQVFDE1y/4OhfWXciOzh1xgjfgHSAsw9QUKwlndZY6dnTtiBnjDDgpLypnVvEsnmt9jrAMx+xa1S6AEyD4b555k5/u/SnvbHgn/7zun9N+XoGhgIqiCgY8UyfCb2xspL29PWEqpE4sZrOZxsb07DsVXfB1skYtqwBols54PetXO15lb89ezEYzt6y4BYMY3zLTkHdIm2M0quVSYY4vs6Buuqq2KBG+WmwsGA5iNCgfGYffgdVk5e8X/z3ffeO7GISBTYtGsi3KCsuAifHwu93K3cc3LvhGxqUS0tl1PJGYTCbmzZs32dOYsejF03SyZtA3UpRME/xxRPgOv4M7ttzBL/b/gh/t/hFHB4/mZI6jLZ1oKs2V9Hv7Y46pm7FmFSt5mHUldYRlOGaTlsPvwFqoCH5DaUN8hF+YfYR/dPAod22/K+0NUX2ePgCqiqsyfq1Kc+WU8/B18ocu+DpZo1o6MGJhjCei3XxyM56gh29coJSIzUU1x+g5JiJR5cwej5JZXGNRLJ1ai1KlMDpTRxV8U4GJL6z9AhBbkthaaNXGZcrzrc/z2LHHOD50PK3xfZ4+io3FWIzpLdZGo/7+Hc4O/nryr0gpOTJwhPv3368vns5AdEtHJ2sGfVGWTg4E/7Fjj7GkcgmXN13Od9/4rmZVZIsv5MMddMfk4I/GVmTjoPNgzLEedw8CoUXMiXLx7X67VrPmmnnX0GhtZGX1Su1xc4EZo8GYleCrJY4P9x9mqW3pmOP7Pf1UmbNb5LSZbbzpfZPfHPgNDx15iC5nFw8ffZgzrjNsWrwpoR2mM33RI3ydrAiGgwz7hjUxLTYWUyAKsrZ09vXu4/DAYT64+INUF1djEIZxlybY0akstM4tn5t0TKW5Mj7Cj+TgmwxKT1hV8KPvONQIH5QqiKtnrY5ZbxBCYDVZs7oAdroUwT8yeCSt8f2e/qx3ylaaKxn2DbOrexcAP97zY+3CNtGlIXTyjy74Olmh1l9RI0AhBCWm7CpmnnGd4Stbv0KVuYr3zn8vRoORKnPVuAXnNwd+w+yS2Vw257KkYyrNlTgCDgKhgHas29Wt2Tmg2DMlppKElk4qrIXWmPTNdImO8NOhz9OXlX8PSoQvkRwfOs4/LvtHLmm4hA8v+TDAuO+wdKYeuuDrZEV04TSVbCtm/vPWf8bhd/CzK36mZbfUWGrGJfh7e/ayu2c3Ny2/SYvUE6HeoURnqnS7uzXfXqXOUqdFvsFwEHfQPabglxaWZvz3CIaD2p3EkcEjWnG2VPR5+8YV4atc3HAxP73ip9y68lZAF/yZiC74OlkxOsIHsqqYGZZhDvQf4IbFN7CsaqT8a42lZlyC89SJpygxlfCBhR9IOS66gJhKtzs2wgdl85Uq+GqROPXilAxroTVjD7/X3UtQBllZvRJXwEW7oz3l+EAowLBvOPsIP6qKqLoGUVVclRNLTWfqoQu+TlZodXSiBD+bipl2n51gOMgsy6yY4+ON8DtdnTRZm8YsM6BG+GpqpjvgxuF3UFsyKsIvGYnwVZtmTEsnCw9frYdzedPlABweSG3rqPPONsJXf//55fO1ekMmg4kqc5Xe83YGogu+TlaoEXF0Bkw2lo6aQ67mvKvUWGqw++14g14APEFPRpUne929cVF6IkZH+OpFJpGl0+/tJxAKaFG7mpmUjGw8/C5XFwCXNl6KURjH7Ona74kIvnl8ls6amjUxx2sttXqEPwPRBV8nK1SBjK5CWWIqydzCiOxqHW1JqGKtis4dW+7giy9+MaPzjr5rSMToEsHq642+WGiZOu5u7XdMx8PP9O+hRvjNZc3MKZtDy3BLyvHj2XQFiuBfN/863r8wtlHdeC01namJLvg6WTHoG1Q2HkUtiFYUVTDsG87oPKpgjbYkVMFVRefU8Cl2dO1Ia/dtIBxgwDug1cJJRVlRGQWiQLNG1NcbHeFrm69cZzQRT8fD9wQ9GbUQ7HR2Ul1cTVFBEXOsczjtOJ1y/HgtHYMw8J1LvsPamrUxx3XBn5nogq+TFYPewbgNTdXF1TgCDnwhX9rn0SyJUYKlCmyPu0epDBgZ9+DbD6Z9znQifIMwsMy2jC2ntyCl1EQuWYR/xn0m7QjfalIez8Tm6nR2ag1MGksbaXe2p9zxOt4IPxm1JbU4/A7cgcxa++lMbXTB18mKQW98jRpVtFXBTYc+Tx/mAnOcHx5t6bgCLrwhL0UFRfz15F/H9MWT2TLJ2LR4E8eHjrO3dy/drm6shda4xd7o3bZpL9qq5RUyyFzqdHXSUKK0KJxjnYMr4EpZ3KzP04e10EpRQVHar5EO0RdcnZmDLvg6WTHgiy87rEaZatSZDn1eZdPQ6LIApaZSio3F9Lh7tPNdPe9qPEEPB3oPpDzn6OJnY3H1vKspMZXwyJFH6HH3xNk5ABaTBWuhlW6X4uELlI1mqci0gFqHs4MOZwfzK5SaPHOsSlfQ0bbOm2fe5MiAsgu3z5N9Dn4qdMGfmeiCr5MVQ96hhJYOZCj47sSCpXaa6nZ3a+dbXrUcIK665WjU4mfpWDqgiPm186/l6Zan2d2zO6HgQyQ1030GZ8BJqal0zNLNWonkNC2dh95+CIHQFlAbrUqt8+hc/GHfMJ9/4fP8aPePgJE6Orlm9BqKzsxAF3ydjJFSJiw7nJXgp4hQG0ob6HB20OdVzrfEtgQYuyVfr7uXAlGQsmjaaD67+rNcUH8BQ76hpE3Aay21WoQ/lp0DmVXMdAfcPHrsUTY2bdTso4ZSxdqJjvAfPvIw7qBbK/OQaJNYLtAFf2aiV8vUyRhHwEEwHIyrpFhprkQgMvPwvX2sq1uX8LFGayP7+/Zr52sua8ZkMI0p+Grxs0yap1QVV/GzjT9jT8+epE1E6krqONh3kNqS2rQEXy3LrN5xpOKZlmdw+B1aYxYAs9FMjaVGE3xv0Mv/Hv5fQKn3E5Zhut3d2gUil1hMFqwma0wPAJ3pjx7h62RMdPPyaEwGE5XmyrQjfH/Iz7BvOGmEP8c6B4ffwanhUxQIpR2fzWwb84LS60lv09VohBCcW3tu0vnUWeoY9A1yaviU5s+notZSS31JPa93vT7m2J3dO6kyV8WlR86xzqHd0U5YhvnO699hwDvAxbMvxu630+HsIBgO5kXwAWzF8b0CdKY34xZ8IcQSIcTeqH92IcSXRo25TAgxHDXmzvG+rs7kkahwmkpVcVXagq9G6skEtrFU8bD39uylyqzUd7GZbUkjfHfAzaB3kB53T9oLtpmgCmu7o50PLvrgmOOFEFzccDGvdb1GIBxIOfZA3wFWVK+IW7xuLG2k1d7Kndvu5PHjj/PpVZ/mvfPfCyglpUG5EOWDyiK9G9ZMY9yCL6U8IqVcI6VcA5wHuIHHEwx9RR0npfz2eF9XZ/JIVFZBpdpcrXnuY6HaBUkFP7JoeWzomJYBZCtOLvj/9eZ/8b6/vI9OZ2faC7aZcGH9hVw8+2Luv+p+rltwXVrPeefsd+IKuNjbszfpGFfAxanhUyyvXh732BzrHPq9/Txx4gk+u/qz3LbmNu3Cs68nIvh5ivArzZUM+HTBn0nk2tLZCJyQUrbm+Lw6Uwg1LzxRN6Tq4mr63OkJfrJdtipqWmJYhjXBrzJXJRX8Tmcng75B3EF33iL8n1/5c86vOz/t51xYfyFGYWRbx7akYw71H0IiWVG1Iu6xixsuZknlEv7fxv/H59Z8TsteAtjft1+bVz6wmW0MeHTBn0nkWvA/DDyQ5LH1Qoh9Qoi/CSHiQ5kIQohPCSF2CiF29vbqC0ZTETXCT9Qrtrq4mj5PX1r9UNU6OskE32KyaHcR6hhV8BOdf8g3pM1JvTuYbEoLS1lTs4ZtnckF/62+twBYUR0v+CuqV/Do9Y9yaeOl2jF1feLowFGKCopS9uwdDzazjSHfUFo1+XWmBzkTfCFEIXA98EiCh3cDzVLK1cBPgL8kO4+U8j4p5Top5bpZs3Ifpc1k+jx9Y9ZeyQWD3kHMBeaEpYeriqvwh/1p7S5td7ZjNBhTbhxSo3x1jM1swxfyJSzDPOQb4tLGS/nz9X/mqrlXpfvr5J01NWs4Png8qY9/oO8ADaUNafePNRvNlBeVE5RBai21WfWyTQeb2UZIhrD7Mu/apTM1yWWEfzWwW0oZl7grpbRLKZ2R7zcDJiFE7rcHnqWEwiG+9vLXuPKRK/n7p/4+45r0mRLdvHw0meTitwy30GRtwmhInh2sRuqa4BcrEX8iW2fIN0R5UTmLKhel7HI10cwvn09QBpNejA/2HUwY3adCtXXyZefAiGWn+/gzh1wK/kdIYucIIepEJAwRQlwQed30k7V14pBS8kzLM7gDbjqdnWw+tZk1NWtwBVw82/JsXl+7192bdHdnJvV0WuwtzCufl3KMGuGrr6daPKMF3xfy4Ql6EmYOTTbq73hq6FTcY8FwkE5XJwvKF2R0zokQfK39o56aOWPIieALISzAlcCfo459RgjxmciPm4ADQoh9wI+BD8t0TF6dpOzs3slXtn6Fzac2a7suP7XqUzSXNfPEiSfy+tptjjbmlM1J+Fi6EX4gHOC0/TRzy+amHKemZkYv2kJ8eYUhr9JyMbo+/1RBE3x7vOCrd2PpbOSKRu3IlawMRC5IdnHVmb7kRPCllG4pZZWUcjjq2M+llD+PfH+vlHK5lHK1lPIiKeX2XLzu2czmU5sBpeCW2nqvrqSO9y14H7u6d3Hanh8v3x/y0+XqormsOeHj6oKi2sgjGR2ODoIyyNzyuSnHvavxXfzD0n/Q+q0mE6FEPXanCiWmEmosNZwajhd8tQXiWIXYRjORlo4e4c8c9J2205BAKMBzrc8BSipidNOO6xZch0DkLcpXd302WROXH7AWWmkobRizNV+LvQVgTEunwlzBNy78BmajGYjqQTvKMlIFP18ZK+NlXvk8Tg6djDuuFlbLOMKfCMGP2GNjFavTmT7ogj8O3AF3WumHuWZH1w6GfcMUFRTR5eqi29VNWWEZFpOFupI61s9ez5MnnsxLOl2rXdlikSzCB1hmWza24Eda941l6YzGVGDCWmiNi/DVvQFTVfDnl8/nlP1U3PtFtXQyjfBXz1rNHOscltmW5WyOo1H/1nqEP3PQBT9LXAEXlz9yOc+3PT/hr/1C2wtYC61c3nQ5nc5OzrjPaJ4uwPsXvp8uVxdvnHkj56/d5mgDUgv+UttSWu2tKcsCt9hbsJltWXnuiTZfDdPsmiMAACAASURBVHsVN3EqWjqgRPiugCuuvrxq6YzVEH008yvms/nvNudlR3E0qTa66Uw/dMHPkj5PH66AS4t4J5LTjtMsqlhEk7WJXk8vHc6OmMW7DXM2YDVZeeJ47m2dFnsLFUUVKYV6WZUSdR4ZPJJ0zKnhUxlH9yqJCqipEX554dRbtIXkC7fqRTGdYmyTQaW5Mu0IPxQO6Zu0pji64GeJ+kGdjE0pPe4eaiw1zC6dTViGOTF0IkbwzUYz75n3Hp5vfT6j/rLp0GZvS1o+WEW1GVLZOumkZCYjUYPtYd8wpaZSTAVTJ/8+mnllyu+qWlkq2Ub4E0WqYnWj+fLWL/Nv2/4tzzPSGQ+64GeJupN0rP6q46HN3kabvS3mmJSSbpfS9KK+pB5Qas2MXrx7Z8M78Ya8vNX7Vk7n1Gpvpdma3M4BpdNUlbmKQ/2HEj4eCAcY8A7E2FCZUFdSR7erO8YPH/QNTsmUTJVZllkYhTHuQpVtls5EUWlOv2LmW71vJVyY1pk66IKfJWqEn26/0kzZ3rGdTU9tiouY7H473pCXWkttTGem0fnY59Weh0Cws3tnzubkCXrodnePGeGDYuski/DVnPlsW/PVldThD/tjhGjINzQlN12pGISBWZZZdLtGCb7fSYEooNhYPEkzS01lUWVa9XS8QS89nh6G/cMpx+lMLrrgZ4kq9PmI8I8MHOG2F27DE/TQ7myPeUxd9KspqYmJ6kdHy+VF5SyuXJxTwVfvNlIt2KrML5+ftJSAKtSZtCCMRv291Q1noFxERjdVn2rUWGriFm1dARclppK81cMZL7WWWs02TEWnsxNQrDWdqYsu+Fmi3ornI8J/6MhDmApMfGjJh+jz9BEMB7XHonPuiwqKtJ2tiZpgnF93Pvt69hEIpW6+kS6vdb0GoG2CSoW10Ion6ImZu4qa151tRo0m+K4owY+qlDlVUZuyR6M2RJ+qXDn3SooKirTWislQAxOH36Ev3E5hdMHPEm3RNscRvifo4W+n/saVzVeyxLaEsAzH9BVVI0TVwpldotg6ifzwdbXr8Ia8HOg/kJO5vdL+CgvKF6RVelgVsUSF3FI1UEkH9eI27QS/RBH86LUHp99JSeHU9O9B+T96/8L389SJp1L2t1Xv5iQybzZnrnn4yMPctf2uyZ7GhKILfpaoi7a5fnM/1/oczoCTDyz8wIiwRVkXqgesNvioL62n1FSacNHvvNrzANjdvTvr+fhCPv50+E/0uHvY1b2LS+dcOvaTGEkzTPT3Ga+lYzPbKDQUan+LQCiAK+Ca+oJvqcUT9MSUjnYFXFhNme2ynWhuOucmQjLEI0cTVT5XaHeMWI9ToZzyyeGTY6ZMb+vYxhPHn8Af8k/QrCYfXfCzRBUyh9+R0922m09uZo51DufVnpfQuuh2d1NlrtLSD29efjPfvOibCc9VYa7AarJqjUayYVvHNr77xne5cfONBGWQSxvSE3xVxFTrK5oB7wBGYaSssCyrOQkhqC2p1f4uU7mOTjTqXVn0wq0j4JiyGToqTWVNNJY2auUwEhEt+FNh4fbrL3+dr7781ZRjHAEHQRnk2NCxCZrV5KMLfpaolk5IhnAH3Tk7b7e7m8WVixFCJBR8NQdfZUX1Cq6df23S81WYK8a1NV4t+NXp6sRaaGVNzZq0nqfaFIl22w54B6g0V45robKupE6781EFfyqnZcJIYbnohVtXwDWlPXyViqIKLbsqEe3Odu2ObbIXbgPhAMeGjnGo/xC97l5+d/B3/ObAb+LGqUFbsvThmYgu+FkSfVs+lq0z7Bvm+dbYEgwH+w9qmQ3RqFkboCx8lphK4iL8TEriqml1iZBSjrkG0WJvocpcxdfO/xpfOvdLKZuVRDNWhJ+tnaNSX1JPl6tLOx9kbxFNFOo6S/TCrdPvnLK7bKOpMFekfB+1O9o5p+ocYPIF/9TwKS1ZYPOpzdy7516eOvlU3Dj1c3u4/3Be53PX9ru4+7W78/oa6aILfpZER65jvcEfOfoIt2+5XasRHwgH+OSzn+TePffGjXUFXFiMI60D6yx1MQLR4+7JaMNSsghfSsk9b97DZQ9dlrJ2/anhU8wrn8c/nvOP3LDkhrRfdywPf7ziXGuppdfdSygcmjaCX1OsRPgxgj/Fs3RUKooSC/6Pd/+Yb+34Ft6Ql+VVSqvqYf8w2zu383L7yxM9TUBJawYoNBRy75578Ya8CZuxq2sN+Y7wd/fs5pmWZ6ZE9pIu+FniDDi1jT5jRfiqLaJ6t7u7d+PwO+jxxOZkSylxB9wxnm5dSZ0W4ftCPoZ8QzGWzlgk+6D+8q1f8sfDfyQQDnCw72DS57fYW8asWZ8I9XdIlKUz4BnQWhVmS11JHSEZotfTO20E31Rgwma2xSw2+0K+Ke/hQ+L3Ub+nn18f+DWPHXsMICbCv3fPvfxw9w8nfJ4AxwaPYTKYuGb+NXhDXkDZiR0tuGEZxhlwYhAGjg4eTdpvOBcMegcZ8g3FldWYDHTBzxKH30F9ab32fSrUbAHVc95yegsQX9M9EA4QlMGEgu8JevjDoT8AZCT4iSwdh9/Bz/b9jMsaL0MgODyQ+JZ20DvIsG84qyJnan33ZJbOeHfFRq9vDHgHMAjDlPfwQbkzUT189WI4LSydogo8QU9MbaZnW58lJEPcft7tvKvxXZxXex4lphKGfcOcdpyOsSInkiODR1hYsZArmq4AlFLSYRmO+Rw4A04kkuVVywmEAzktCRF9Rx0MB7XX3d2TfbZcrtAFP0ucficNpQ3A2Ln4quCr9V9eOv0SEN+1SRUAi2nE0qktqaXf28+nn/s0P9r9I86rPY8NczakPc8Ks/JB9Qa92rGt7VsJhAPcuvJWmsqakpZASLdJSSKKCoowGUxxF0Nv0Is76NZaFmZL9G7bAe8AFUUVGMTUfztHb75S14GmhaUT2cUcvXC7+eRmFlYs5JYVt3DvxnspLyqnrLCMTmcnQ74hHH5HyhLZ+eLo4FEWVy7m0sZL+e17fstHl30UIMbWUd+XF9VfBJCzUuIvtb3Ehoc3aPsSoi8ye3r2xIz9jx3/MWYmUa6Z+p+QKYg/5Mcf9mvFy1JF+EPeIe0/vdvdzfGh43Q4O6gprmHIN0QoHNLGJmqGoebi7+nZw53r7+S37/ltRpGsmpse/cZ7vvV5aoprWDVrFUttS5MKvmpFqZUeM6XUVBpn6Yx305WKKvjdrm4GvYNT3s5RqS2ppcvVhZRyJMKfDoI/6n3U4exgb+9e3jv/vTHjyovKOTQw4omrC+sTRb+nnz5Pn5bpdl7teVrNpugAS/3MLq9azupZq3ng7QdiPovZsqV9CyEZ0mxS9TULDYUxgr+tYxsPH32Yrae3Tqi3rwt+FqhvFlXwU0X40bnLZ1xntEji2gXXxt1mJhT8iLBd1ngZmxZtyniuqnWivo474GZbxzY2Nm/EIAwstS2lw9mRcOG5ZbgFk8EUU6QtE0oLS+Muhrny260mKxajRbN0si3ENtHMLZuLw++g39uvRb9TeaetymjBf7X9VQCuar4qZlx5YXmMlTPRgq8GL0tsS7Rjifogqwu21kIrN55zI6cdp9nSvmVcry2lZEfnDgAtt199zXfMfgenHafpdffiC/m4+7W7EQjcQfeE/o10wc8C1ZcuLyqn1BQvatGodk51cTXd7m6ODR6jsqhSaxIS/SZU8/lLjCMCsLZmLZ9Y+QnuesddWeWtq7fiamS9rXMb3pCXK5uvBEZq16uZDdGcsp+iuayZAkNBxq8LSuQ62sMfbx0dFXWfgir4U33TlcriysUAHB04qv1tpvpOWxgRfLXRzP6+/VSZq5hjnRMzrqwodjPdRPv4b5x5A6PBGFPvSU0QiO7Nq35mrYVWNjZtZHbJbP73UOp6QWPR5mjTxPvYoCL46uduY/NGQLlTf73rddqd7dy68taYsRNBzgRfCNEihHhLCLFXCBFXolEo/FgIcVwIsV8IcW6uXnuiiW48bS20pozwW+2tGIWRtTVr6XZ1c2zoGAsrFya8zUzk4ZuNZr547hez9rxHR/iqTbNq1ipAaUcIJFy47XB2pFU3JxmlhaVxHm4uM2rUXPwBz/jTPCeKRZWLAMVnnuq18KNRL6hqK8n9vftZNWtVXBCi2o1lhWUYDcYJj/B3dO5g9azVMZ+h8sJyDMIQG+FHPrNlRco83zv/vezp2ROz1pUpr3UqxQWX2pZyfOg4MPJ+v3j2xRQVFLGnZw97evZgFEZtbUEdOxHkOsLfIKVcI6Vcl+Cxq4FFkX+fAn6W49eeMKIX28oKy8a0dBqtjTSWNtLt7ubE0AkWVowIfr+nnzOuMwx5h7JuaJ2K0RH+kG8Ii9FCUUERAFXFVdQU13B08Gjcc3vdvRlt8hpNogg/l4JfV1JHu7MdR8AxbSL8SnOl9vd2+adPlo7aOnLQN8iQd4gWe4sWNCQa11zWTK2lNuHmwnwx6B3k7YG3WV+/PuZ4gaGAiqKKhB6+mk12TtU5hGRoXOL7Wtdr1JfUc/mcy2l3tOMOuLUMsqriKlZWr9QEf6ltKdXF1dSX1E/PCD8N3gf8Xiq8BlQIIeon8PVzxugIfyxLp7msmdqSWgJhpcjXospFMb7ibS/cxvfe/B7uQMTSyaHglxWWIRBahD/kja8qObd8blyhKX/Iz5BvSCvSlg3WQmtchN/p7NR2EI+X2pJabe1hukT4AItsi2Ii/OmwaGsqMFFqKmXYN8xbfUoXtdWzVseNUyP8xtJG6kvqJ9TSeb3rdSSS9bPXxz1WVVwVm6UTcCAQ2t9evdMdzyas3T27Ob/ufBZVLkIiOTl8MiaDbG3NWt4eeJsDfQe0EiULKxZO2whfAs8KIXYJIT6V4PEGILojRnvkWAxCiE8JIXYKIXb29mZf9CufqAJfWlia0tLxhXy02luZWzY3JlJeVLFIuZUURjqcHRwbPEanszMvEb7RYKSsqCwmwh+d5TPHOieulaJacC2TnP/RlJhKYkpQgCL4ajrreInuATBdFm1B8fFPDJ9gb+9eSkwl2t3WVKe8qJxB3yD7+/ZjEAZtZ+3oMQCN1kZml86my9XFru5dvNL+St7nt6NrB1aTVdsAFs3o3rwOv4NSU6mWyttQ2oC10JqyD3M0b/W+xRde+IIWcPR5+hjwDrDMtkyz7Y4NHovJIFtbs5aQDOEL+VhbsxaAhZULOTV8Kq8bv6LJpeBfLKU8F8W6uU0IMbqsYqIVx7gyk1LK+6SU66SU62bNyj66zCfRkVlZYVnSCH/XmV34Qj4urL8wpjvVgooFGISBSnMlr3W9hkQy6B1M6OHnguhdksO+4Tj7o7msmUHfYMyFS619PsuS/f+BmpYZXU20w9mRO8GP+ptOF0sHFMEPhoNsOb2FG8+5ccp2uxqNuolvf+9+FlUsSvg+VSugzrHOoa6kjh53D3dsuYPv7/x+XuZ0sP8gHc4OAHae2cm6unUJ6z2NFny7z67ZOaAkAaRKUR7NS6dfYkv7Fr6141tIKbWkhyW2JTSWNmIuMHNs6FhMBtnqmtWIiAyqgr+oYhGBcIDT9sTd4XJNzgRfStkZ+doDPA5cMGpIOxC9pN8ITJzBl0NUm6LUVEp1cTV9nr6Eiz2vdLxCUUER59edr0X4dSV12hvNZrbFLO64gi4KDYWYDKaczreiqELLrkjU7LvJqvSojX7TqbtBx2vphGUYT9ADKGlrOY3wowR/Olk6aqaOzWzj5uU3T+5kMqDcXM4Z5xn29Ozh3NrEORdq1s5i22LqS+oJSaXWUbLCa+Pl9pdu53uvfw+H30Gboy1pN7Yqc1VchB8t+KBkrB0dPJqwS9toVAv0udbneOrkUxwZVAR/ceViCgwFLKpcxIG+AzEZZGWFZSyqXERDaYMWSC2sWAgwYSWacyL4QogSIYRV/R64ChjdZulJ4KZIts5FwLCUcmKX8HOEI+DAYrRQYCjg3NpzCYaD7OvdFzfu5faXuaDuAsxGMzazDaMwav/BQEzmjd1vx+6z5yVjo7KoUrv1TNTsW21K3uYYsXVyZenAiAXW7+3HG/Jmndc/muka4c8rn8dS21K+su4r0yJDR6WyqJITwyfwBD1aWu9oltiW8NINL7G8arnWjU0gsPvsOe0bAYpl2uXqYm/vXi0yV9OdR2Mz23AGnFppCLvfHif4S21L8YV8WiZbKtocbVzccDFLKpfwx8N/5MjAEepK6rRg6qL6i9jfu59uV3dMMPIvF/4Ld73jLu1ntT/0WM1ackWuIvxa4FUhxD7gDeD/pJRPCyE+I4T4TGTMZuAkcBy4H/hcjl57wokuaXte7XkUiIK4rdmt9lbaHG1c0ngJoGQKXD3vat49993amNFRabuzPed2DoxUzAyGgzj8jrhFWzX1MvpN1+3uxmQwjauLlPqBUq0q9da7sTT7VM9oio3FVBRVjKuZymRgMph45LpHuG7BdZM9lYxQ3ws2s41za5JnVat9llfOWskVTVdww5IbCMpgwkJ640F9Pw35hvjbqb8BI/tKRqN+1tS1LEfAEfeeUZ+brLaUipSSVnsr88rmce38aznUf4jXul5jSeXIZq+LGy4mJEN4Q96YYOS82vO0cg6g2Le1ltrpJfhSypNSytWRf8ullP8ZOf5zKeXPI99LKeVtUsoFUsqVUsq4XP3pQvTCZ4mphOVVy3mjK1bwt57eCsA7G96pHfvOJd/h/Qvfr/2svgnVD0i7oz1vEf6Qbyhpo5BiYzG1llqt/gcoHn6NpWZc/rKaAaEu3KopermK8EGJ8m1m27TxwaczquBf0XRFWpvxrIVWfrDhB9ribq5tneguW389+VdqLbVJ96uonzV181UiS2de+TwsRgtv9b6V8nV7Pb14gh6ay5q5cq5ypzPgHdCsOlD2uajv/7Hsxrllc1N2E8sl+k7bLBj2DcdEvufXnc+BvgNaWiXAMy3PsNS2NG4nYjTqm1O94p9xncmL4FcVV+EL+TRBT2R/NJU1xUQZve7ecfn3MJJfrq55qBFZrjx8gPnl88e1OUwnfdT3zVVzrxpjZCzqZyXXjVHU97PJYMIT9CS1c2AkqFKz0RIJfoGhgJXVKxPas9Gon5PmsmYaShu0dYPFthHBNxlM2ud6rAyy0Z+9fKILfhbY/XZtgwnABXUXEJRBrTjSaftp9vft55p516Q8j/omVPOGQzKUF0tHvejs790PJG4F2GRtionwezw948rQgfgIv92htMHL5e/4bxf9Gz/a8KOcnU8nOVc1X8W/XvivnF93fkbPUzf/5Vrw2x3tFBuLuaBOyQ85xxafjqmyrGoZ9SX1PHL0EYJhxV5KZAOumrWKo4NHcQfc7O3Zy7+88i/cseWOmPUHNRpX/ff3zH0PAMttsWmqFzdcDDDmLvnmsmaGfcMpW0jmivT61enEMDqXXd1E8VbfW1zccDGbT20G4Op5V6c8zxVNVxB6R4hLGi7RjkXX0ckVahaOumEmUS36prImBrwDWuTT6+7lHbPfMa7X1Tz8yI7STmentpCXK6bDLtWZQoW5gg8t/VDGz1ODo5xbOs52GkobWF2zmm2d2xLm36sYDUY+vPTD/GDXD9jdrdSlHx3hg/JZDskQm09t5u7X7kYiCctwTJmRNnsbhYZCLWngI8s+wuqa1cwpi72bv27BdYRlOGnmkIrab6LF3sIac3o9o7NFj/AzRErJsG84RvAtJgvVxdWaR7351GbOqz0vJoskERaThQ8s+gDlReUUCMUTzYelo75R1Qg/0UKselFoc7ThDrhxBpzjt3QiEb6a39/h7KDBmjs7R2d6oH5W8uHhN1obeffcd3Nh3YWsrV2bcvwHF30Qc4GZO7ffCSQW/FXVSrmI/37zvykQBfzk8p8AcKB/JOmwxd5CU1mTtmnLZDAl3HVcVFDEDUtuGHO9YyIzdXTBzxBP0EMgHIizRWaXzKbT1cmwb5iTwye5tHH0vrPkGIRBE+F8CL7ZaKbWUqsVslJvsaPRUjPtbTlJyQQl+q4oqqDN0UYwHKTTlbscfJ3pg1pBc9ifO0tHSqlE3aWNzC+fzy/f/csxM7XKi8r5xMpPUFRQxCUNlyS0pirMFcwtm4s76OZ9C9/H+vr1mAymmDagbfY2TaRzQYO1gQJRMCGCr1s6GaL6kKOj5NmlsznYf1BbFMq0LWCluZJ+b39ePHxQoohudzdFBUUUG4vjHld9/jZ7m7a2MF4PH5RF1ZNDJ2mzK6K/oGLBuM+pM70wGUbq8OSKfm8/nqAn4wX7T6/+NJ9e/emUY1bPWk2bo42bl9+MqcDEUttSDvYrgh+WYU47TvOuxndlPffRmAwmGq2NE5Kpo0f4GaJGKdGLtgD1pUqp3tELOumipm7layOOKujJumUVG4upsdTQ5mjTIo1cROMLKhZwfOi4thMxOldZ5+yhvKg8p4KvpmSmyoIbkyN/gy33wKgNYbetuY2fbvypdtd7TtU5HOo/RFiG6XH3EAgHcp4Z1lzWnNaGr/GiC36GJMtlbyhpIBgOsqt7FwKR8RtCTXnLx6ItjFg2qZqHN1mbaLO3cbj/MFaTNScbpBZULMDut7O9cztGYWR++fxxn1Nn+lFeVJ5TD1/NKBvXe/SN+2HLd+D1n8ccri+t1zJsAFZUr8AVcNFib9EuNLkW/DWz1nB86Hjeq4uevYJ/+g3oSa9QUjRqlDJa8OtLlUrPak3sTCsgqhF+viwddVE21c7Z5rJm2hxtHB44zNKqpTnZzKQK/AutLzCvYh6mgtzWCdKZHlQUVeQ0wldrPdWWZN+vgb5jgIBnvgmde5MOUzeOHew7SLszcmdROo47iwRc0XwFAC+0vZDT847m7BX8xz8Nz/1bxk9LJviq/dHh7NCi6UzQIvw8WTrqnBIt2KrMsc5hwDvA4YHDSbeoZ4rq2TsCjplr50gJJ16C8MQ1o55ulBfm1tLp9fRSYirJ/vPid8NwG5x3M8iQEgAmYX75fIqNxRzsP8hpx2kMwkBdaeoMvEyZVz6PhRULea71uZyedzRnp+CHgjDYGrnCZ0bSCL9kpJdLNiv4tqL8evjqrW+qCF+9KATDwZS7FjNhVvEsrWfrjBX8rr3wh/fDsWcneyZTlmhLp9vVzYf++iEtTTgbetw92aUN7/qd4tv3R5qONEf2mniTX4wKDAUssy3jQN8B2h3t1JfU57yiLShR/u7u3fR5+nJ+bpWzU/DtHcpVfagNQpk1Hhj2DVNsLI6zbCwmi+aPq/ZJJqgZMckWVceLxWTh48s/nrTKIcTOO1cRvhCC+RWKrRO99XxG4Yj4rr2ZW4RnCxXmChx+B6FwiHvevIdD/Yc43J+6SFkq+jx92aUN7/w1vPoD6I7k1dcuB5MFxtjlurx6OW8PvE2rvTVnxf9Gc0XTFUgk2zq25eX8cLYK/lAk31UV/UyemqBjlIpaFCybCP/Sxkv54WU/zGsUfMe6O7iw/sKkj6sZD+YCc8ZppalQffwZG+G7lYJcDJyY3HlMYcoLy5FINp/arNkWap+EbOhxZ1H6IxxSLspBD+z9EyDAtgDM5WMLftVyfCEfh/oP5a1204KKBRiFkZPDJ/NyfjhbBX8waoNDf2Yf0mH/cFxKpooq+Nl4+EaDkY3NGye16qPFZKGmuIYltiVpVUNMlw8s+gA3L795zJoi0xZN8POfVpcvnj/UzSd/n78CtmqQdM+b92jBhDvoTvGM5EgpsyvuN3AK1EZFLa9AZTOYzGCuSGnpgJKpAyCReRN8o8FIo7Uxrt1oLjk7BX8oSvAHMruaji6rEM0c6xxlE0Webvkmgs+v/TyfXPnJnJ5zbc1avrzuyzk955RCFfwMg4epxI6T/Tx3qJtgKD8Lz+pnZtg3zJfO+xLFxuKsI3y7344/7M9c8Hsiu2UjO3+pjliM5nLwpI7w51jnaGtR+fx8N5U10erI347bs1PwB1uhvAkKrRnfhqcS/I8v/zi/ec9vpnXq4QcWfYB3zcndLsKzAnekdZ6jU8n+mIY4vMpalicQysv51WSBVdWruHzO5RQbi2PKiWeC2m85Yw+/+yAIA6z5B+XnKqXZuGLppI7wDcLAOdVKcbZ8luNuLmvmtP00YZmfC+9ZKvgtyu1c1fycRvgV5oqERZR0ZiCeIfjLbcpX90iv1EzfT1MFp0/p45ovwZ9XPo8VVSv46gVfRQgxrgi/xxPpt5yph999EGzzYXGk61x1RPCLK8b08AFWVCm2Tj4j/GZrM96QV9tnkGvOzlo6Q62w6Erwu1JuuBiNWilzPG3/dGYIrdth7//C0msUS8ccEY2BE1C3IqNTOX1BzEYDxoLJi78c3ojg+/Mj+NZCKw9c+4D2s8VkydrD1yL84gwj/J5DULsC5r0L3v0dWPF3yvE0InyAm5bfxMpZK1PuZRkv0UUMx6q2mw1nX4Qf8ICzGyrmKiv0GaRmuoNugjKYdNFW5yzCGUnFHO5QBL9xnfJzhj6+lJLL/nsLf3ojfwt16WD35jfCH814Iny1mmu1pTr9J/ldyqJt7XIwFMD62xShh8jF2j7mxjmb2cbGpo1ZzTldtFLJefLxzz7BV9MwK+dC1YKMUjMHvMqte75y5XWmEc7ILffwafAMQEUzlNRkbOkEQpI+p4+OoexTFHOBU/Xw8xThj8ZitGTt4fe4e7AWWhNWfU1K3zFAQk2C/SXmcuUxnz2r+eSSupI6Cg2FecvUGbfgCyHmCCFeEkIcFkIcFEJ8McGYy4QQw0KIvZF/d473dbNGTcmsbFb8PEg7Kjs5pHyY55bPzcPEdKYVzm7l61AreAbBUqUEEBlG+N6gIrC+wOSWZci3pTOaYmNx1pZOn6cv8wwdu9KciPIE/ntxxKKZgBaDY2EQBuZY5+StNn4uPPwg8GUp5W4hhBXYJYR4Tkp5aNS4V6SU1+bg9caHS7kdpLQG1DIGaWbqHB08CsCiikX5mJnOdMIREfzugyDDiuDXLIO3HlNqMqEQAgAAIABJREFU66S5n0IVen+e0iHTxTHBlo7FZMl+0TabTVeqBZeoBo5q7aTh4ydCSokvGMZsys3elaaypqkb4Uspu6SUuyPfO4DDwNRta+R3Kl+LyqCkWvma5Db8d9tb+PELI/V2jgweoaG0Qe+jqjMS4as1WSw2mL0WfMMZ2Tq+KRDhB0NhTegn0sMfj6WTcYTv6AaEEuiNRl2EzVLwXznWx9pvP8ewO7MyLclYZltGWVFZTOP0XJFTD18IMRdYC7ye4OH1Qoh9Qoi/CSGWJ3g8P3QfBFdUMSKfQ/laWKpEYbZ5SW/Df7u9haf2dWo/Hx08yuLKGVoPRicznKPS5lTBB+jck/ZpfMFw5OvECG0i1JRMAPcEevjZRPiBUIBud3fmzXmcZ5QAL9EeGTXCH2PzVTJaB9x4AiF6nd6snj+az675LL+/+vd52XWfM8EXQpQCjwFfklKOXv3YDTRLKVcDPwH+kuI8nxJC7BRC7Ozt7R3/xH7/fth6z8jPPgcUFIKxUPnZtiBhRNbn9HGqz6V9ALxBL632VpbY0qgH8/L34cyBscfpTE+kVASkOKqZjKUKZi0FozkjwfdGImp/cPIifNXOgZH55Bs1S2esKPa51ue44akbCISV6LnD2UFYhjMvX+I4k9jOgSgPP7sI3xvRiIm6WI6HnAi+EMKEIvZ/lFL+efTjUkq7lNIZ+X4zYBJCJMypklLeJ6VcJ6VcN2vWOHuq+t3g6oHh9qhjTiW6V6lKnJq5u3UQALdf+TCcGDpBWIaTR/gduyI1tjvgxf+APf87vrnrTF28QxDyQ8N5I8csVUr0WLcSOnanfaqRCH9qCP6EZemYLEgk3lDqqPjhIw9zeOAwp+1Kh6s2h+JtZ1yR1nEGrEmapWgefnYRvnqRPCsEXyj3Hb8CDksp/78kY+oi4xBCXBB53f7xvvaYqAs10bffPicURQm+bb6SmjkYuyq+q00RfFfkP1FdsE1Y8dE7DL+6Crb9CDoiBagGp28hLZ0xUN9PDetGjlkiheFmr4WufUplxjRQvfvJtHTUsgowcaKlplSm8vHtfjs7zyifJ7WCpNraMONets5usCaJ8AutSsmFLCN8bf3jbBB84GLgRuDyqLTLa4QQnxFCfCYyZhNwQAixD/gx8GGZjxWJ0TgSCL7fqfwHq9iUjkyjbZ1dLYrg+4NhQide5sjAYYqNxYnraAy2QjgIJ16AdlXwW3L0S+hMOdT3VcO5ylejWampDjD7XAi4oO9oWqfSFm0nMcKP9vAn0tKB1CWSX2l/haAcucMGZQdqialEawmaFuGQogHJLB2DQUneyNLD90Yu2tMhwh93WqaU8lUg5eqClPJe4N7xvlbGOLqUr66ekVQ5nyM2wq9SBX9k4dYXDLG/YxizyUBTsJWCP3yNA8svYqltKQaR4BqpVt/s2KXs5AVF8DNIz5tKeAMhHt3Vzj9c0ITBMP3mn3fUAKJyLhTbFMFX/5+bLgJRAA9+FD54f6ztkwBVLKaKhz9haZlG5QKZKBf/YP9BHj/2OMcGj1FlrsJUYOLEcETwHW00WZsyW9B09Sl38ckifIjU0xlfhK/av1OZmb3TVo3Egt6RXXSjPXxLlXJ1j8rUOdzlwB8Mc/5cG/PEGfzAIXdX8sJo6k5dGVY66RRaldd05LcDfb546e0e/vUvB9jbPvkbUaYkakpmaa2ykccSVeffNg9u+oty4f/zp8Y81aRG+F37YeevNUunsMAwoRuvIHGE/9SJp3joyEPs7tnNhqYNLKxYyKlhxSI97Tid+YKtloOfouG52gTFM6gEamMR9EPvEQB8EcGfqLuj8TDDBb9r5HtnJONntIcvhBKpRVkwx7qV1M1zmyppFL0cLiokgGR19crErzPUpmziUm/rl12nfJ2mtk6PwwfAgNM/yTOZgqgZOgVFikice9NIuV2VeZdyZuHfI/tPQtCX8nSTmpa5+/fwf1/G41be77OsRbgncOMVJPbwz7jO0FzWzI82/IgvrP0CC8oXcGr4FP6Qnw5HRxYLtpELtLU++RhzhVJI8fuL4U8fUmrrpGL/g/DTi2DglLZbejpYOjNc8KMibDUqG+3hgxKhRa3QH+91UlhgYGmdlQbRx74ipX/t6mCS28jBVuWi0Xyx8vPKTZHjLUrp3Bf/Ex69RfESvXZ469Hx/255pM8ZEXy3LvgxdO2H7y+Ctzcr0aIQcMEnYf3n4oY+3WlBEI5LBhiNKviTYun47CDDmAePYjQIKiwmLcVwNDtO9NPWn7ta/6ki/DOuMzSWNnJ50+XYzDbmV8zHF/Kx88xOgjKYxYJtRAeSZemAcvF29Shfjz8Pf9yU+pz2TuWO/vCT2l2RLviTjePMyC46Zzc/33qCgMceG+EDmMtirugnepzMrbZgNZtoEH3ssZQxOxBkVnt8up03ECI40AIVTbDu43DO+2DuJcqqf+/b8ItL4eX/ggOPKRedA4/BY7dm3Et3IlEFf9A1tQTfHwzzy1dOEpisMgRd+5TSHAMnUosHcCqsPO7vPZ5ynGoHTIqlE3nPlw2/jdVsxFJYkNTD/8IDu7n3pWMJH8uGVB7+GdeZmNLAak/kLe1bgCxaiDrSsHRKa8Bggn94CN75JTj9umLbJENd4D30hLYOM1HrH+Nhhgt+F9SvAsA7dIbvP/M2BQFXrIcPiocfVSnvRK+LhTWlWIoKlAjfXMgqg0XJwhnFz146jq+vRRH8pe+FG36vbOoqa4Rdv1WqKa76sDLYMzTSDs+Vg01l4+D0gBt7VDoePgfs/DWEw/Q6lDf6VIvwXz/Vz93/d5g3Tw2MPTgfqBbhhZ+F1R9OOfR4UNnC7+hMna2jWTqTUVohsuu8ynEUq9mE2VSQMEqVUjLoDnDGntqeyoRkEb4/5Kff209tyYg4z69QBP+Ro48AIyWE08YR2SRnLEo+5tKvwieeVxbZKyIXFFeKJiSqI9CxixKv8r7QF20nEynB3gU1y0EU0NneiinsxUA4QYRfrkU7vmCI1n4XC2aVYiksoNDYT68Isdp2jpJyOSp1yzncSwkepfpmNJXNypvCNh9W3aAc8w6NvFE8g/n4rdNm08+38+PnoyK2w0/BX2+H1m30TnCE/9FfvsavXx1734KaTRJzoZpI7J2K/Xf19+D8T2iHexxe3v2Dl2npc2nH2n3FDEsLvu7UUfFIhJ+b6NDlC3LHw3vpcaSxzd+nZKXUeo5TWqRE+IkWHj2BEKGwpNeRO8FP5uF3uxXrtc4yEuGXFZZxVfNVvLPhnfx4w4+pLk6zDn4oADt+CideTO3fg3LHNnuN8r2avpkq6cIzpO20vtHxSy4yHNItnUnF51DyoctmQ8ksBnraKSXyISga5eEXlSljQ0Fa+tyEJSysKaUUH31FirgsmbdRSe06tTXmqaVupdZOqGyUr1g5V/l63sdHtuB7hkaE3j2o1Pn56Tvg0BO5+q3TYtDlp9vu0xZngZHotW0HJcPH+XPhnfjt+b8LkVLy+skBDnaOXYvcqQl+5pFUMBTm73++nRff7s74uRqOLrDOjjt8oGOYI90O3j7j0I7ZvUFaZB1iMHZ/R1u/mxcOj8xBjfDDkpw0ED/UZefPuzvYvL9r7MGRCL/RfxJrUQHFpsSWjt2j/L1707mIpEmyCL/bpfxtoiN8gP+57H/4yeU/YUPThvRfpOUVeOYbivCvvTH951kTCP5rP4eet0d+9g4p3bNW/wPvDGznwcK7KXZ1pP8ak8TMFXz1P8taD6U1BIbPUCIib67Ri7bmSBd7n50TvUo1zQWzSin1dtJqVLYqNM+/SnneiRdjnmr1Kv/J3pJRxZzqVysXkjUfja23rd4heAaUNnk9B+Hhm+D+y+HJf8o6FzgTTkYiUVfUhhs1t1y2buMK7zOcazhOrX1/3udi9wQJhiWewNgi7ojM15GF4HcNe3mzZZD/2z+OVFl7J5TFR4qdQ4oQqtGxlFIT/OJRnYt+9epJPvfH3VoNmeiIOhc+vrqAuKstjZRanwOMxVikm3nGPooLE1s66h1Vv8ufk4sSgNFgpNBQGOfhn3Er/z85ae+nZsnd+mzChfWkqIKvdTVrh6e/Bnv/ODLGM6Q4Ax/4GZ8zfhuAKndmvRAmgxks+JEIx1qHp6gaS2CAppJIRkSBJXZsVD3s4z2K4M+fVUKxu4tWk4lCCplVWg/z3wXHX4zJ0y33Rfy7klE7cNfdCrcfhJKqkYVjz9CIoLsHIj6+gMu+AYUlsOcP8Ny/5+xPkAzVenDECH4k6jz9Ju8WrwFQ4c7NwrLT6+d4Z1/8A55BPPsfB9LLcPj/2XvvMDnOMt37V9XVXZ27Z6bTJGmUs2RZsuSEI05gY0xmCSYZ9oNd2AMssJyF77C7wO7Ct3CWJS8YlgWMiQbsNRgcsLEtW5JlybLSjMLk2NM5d9X5462qDtMzGskyZ/HHc12+PJrpVNVV93u/93M/z2My/PRZSDqjxkSp/c+ltiA93rJ4ZywpXru+p0pV0zmpR/EXxxqSf9OZEsWKRtyQy+pB/lwAvnkezV5Q84auCxnTGM24ilM47baWLp1Uvmw9ZeY5ynzJfNk6Xy67i3y5keGPZw3Ad58DwE8MgawsXHDVKjxhYbow7ZzHjV19/USsQk3SOVQVu75w4fkZWnIu4wUM+DWGP6H5CUsJXrxCAH2i2pS8UQXDT6fiPH58hu6gC7dDwZEZ5pRdwW+LIEkS1eVXQnKQseMHrKe2l0ZJ6W5yclNeQJZrO4f65kz1DD8zKdrqXvERuPUXcOG7Yc/tcOqxc3oqmuOEAfj5QrG2TU1PgCQjlbN0SyKxHC4NzX3yaeZ+zok936b6+fPwf3U7erUsbp473yxeZ+9/ELv3NtpJkSsuAvCLAnhMieFMwhwh2D+VaWgl0BypQrm1RbJaFgt0C0lnzGD4phxiMuJTWlTkjOocWSbQjyXFc+pB/lxYM82d0kgibwFry6gUQStD704AllSH53Xp1O+oJp9j4vaTdz/LW29/EjDGHFZyDbLOeHYcv8NvafzPKZJD4O8WM2zPJGSbAH2T4Zsybr03P5+wdu4TZTdTup9oaXGAH8+WePVXHmUofu5srouNFzDgG33sfVGStnZCJFkZEMx8tuJofKwBzO+9/SEeHZjhxs1i2y4lBzllt+O0CblmMHABACf23Gc9NVoaZEDvWtiSJdtqvTrMpK3J8D11Axmu/CgEeuGBT57tUS8qTswIwN+RexC+fJHo8JmZsOoIyrqNQdsSurXRxi380JPwT0u55777+MJvF2HRy0zBL96LVCkQkWYpjewn8ejt8Oxd6JlxCwjbpDS5RUg6meJzZ/i6DgeGW8tmpYrGdZ/7Hf9yXwtnTXoc0FtKOiZ4W4BvLEijNmNx2PUVGBckwQT8cQvw6yWd5570y5dq39eehVi+wVZ1X4yCbsdPFpfdRkXT5yw89Uny59rzvX8yw/CswfAVFyOZEa6+82o+tetT6LrORHbi3Mg5IK6v4BlaOM3wRsV3rutw/EHxO3N3XilCJQ/OIJompl0N6N10lVsQpBbx9FCCJ0/O8vT/hUr2Fy7gp0ZBDYDqI2VrwyFV6ZaErDBTbgJ8g+G7tSy/+ItL+ZuXiEHH5dlTjCg2nIgLcNrRTUG3Y5+teau7K4P0a12nlyScRq+OeoafnQJvXQtohwc2v1Zo+/lZ9g0l2Du4eDdPqaItaurOiSkB+KGSUTwyfVQAfnQjqcAaHtS2MOHbyDJpjKSxnUfT4J4PQjHFwQN7uOPJRVzc06L0/OftbwWgeupxpCEhF8VHBqy21W2kFyfpGLuAs9HwRxIFXMYIuvlknV8dHGcsWaB/Mj33j5ZE2ILhm5JOqZHhE17HgN4FT34dvidsnKbVdSxl6v7nWtIR58YmS+w+uRDgi2Ms2jyk8OAjY43oayYvpqQDz53hjyYKZIoVipUqbsXN3om9pMtpvn/4+9x+8HbGc+NE3QvXOCw6EkMtAT+ZL3PTFx7h8PgCRgFfTAD+1JGa3GlKOuY97Apa39mA1sUSbRh0nUyxwtu+9eS8pGjYIB+Zs7iOn2u8sAE/IJj5tCIuoFBWfAFTpcapNyldOAYu71PZ1BOwfj+SOoUmSdg1wcIT+SrH9S48acN5kU/Qps3Sr3fPW6FohSsAuWkoGWCSMyQdT9PItdXXCTfQwP28/wf7+PtfNo8Gnj/+9bfHuPbzD1HV5u8Fous6Jw2G76sagDB+QFQg+6L8auuXeX/53egdK4hJsySSxmOe/j6M7ROHnU4wkSqgLfA+gNVr5Al5C6N6O7ZDP7NyHjMjxyzAD0rZRfVwyRhAmi6eOcMfSeRZFfXS2+5i/zwM//tPiB3HeKoFizWHYDcxfF3XWzB88fn6umNcXfws6fPfBblp4We3GL646etZvcmsHz8+w9u+9eRZJUjN83heb5B9QwswSIOtxqtOUrqbgJTD7RAGhWZrZr0r6rlYM0sVjQnD6TObLeOyu9DRibqjXN93PZ/b8zmOxI80Mvwj/wW//fvF9bepj0pJLNKBuVW5R8bTHBhJ8vjAAh3avVEB9Kac07W1JumYu3Rn0DpX/XThJ0MuMc5bvvkE9x+e5MGjrV1uI8YOZyFp8fmKFy7gJ4eFJRMYtYmEqmtKuE7GC41NQu86LBK1l/U2Mv9BwzEgVQQLT+bLDOiddOQNrc5ogdt/OkkHBMOvL7PPzxqSTtOQl+5t4O4gc+Bujk9nrarXxcRTQ7NMpIocGW/BUI2YShfJlaqEfSptunHhDgrWjTfKUNlHRnLj6hR9//Njhryx+xtWK2mplKKi6adP4E0fA7uH48UAe7XVqKNPWH/KTZ4QDAwISplGx9A8kTlTl06lKCyvxTSjiTxdARebe1oD4YnpLI8OzOCwyYwnW5xzi+E3An48W7JYnsnWTYa/rlPsHJOaByoFUtkcFWORNN+j2MDwRbL3/73rIPcfnjyrBGmuXEWRJVaGvQtr+AbDny45SOHGq2dxOQQcNO+2UoUyDkUm6LY3WnkXiLv2jXBn0y5wIlWwcHsmW7SqbS/vuZxPv+jTvGXDW9DR6fP3iQf97jPw/dfBw58980LF1AigQ3Au4JsLuikttQxfp3jPY7+GtmXCgmlKOqa12hW07vsJu9hJjN79T3xx/PVsDBSZnE3B/jvn5L3MfNLZ2Iufa7xwAT81WgN8KUYFGXnqEADj+daAH1PrbrBKkZMV8Xu9JAo9BOB3Ea6OQ7lgMdgBfRGSjitYa6Ps7hDbxVIGvGG+8/gp7n3GABTZBiuvQTn+W2S0M2pgdmRcfN4nT85fiWpaMjd1BwhJBmMZNJLE3ijTmSLtbgfOqAD8ytQxwZbGn4E1NwDgM+ytpg49b0wfgdBKEoUquzUxKawgu5jRfTimD1qFP0EyiypLTxfOAPBH9sIXd8Kdb0Z/6rsC8IMu1kZ9jCTyc1jsT/cOI0vwqu09zGSLcxOoqVExGrO+MyY1/R7mavgm4McrwiSQmK0xyvGUyfA1PA4hpRTLGr94epQjRvO+xSyCzZEvVXE5bET8KtOZ0vy7PUOeGC86SOoenNWMJXk177ZS+Qp+p52wV11cQRfwncdO8e+PNNYgmEAHBsM3vPiX916OIit8YPsHuOvld/G6ta8T99f9nxQV62AA+BmEmShvwfAnjO+s/vPMCV9UyJ0D98OqaxjMOdAtwDcZfpt1Hc26+wBY2X87USnB63ribM4+Cj+5TfTm0XUY3AW6zvCsSNb+SdI5V1EpibJov5B00hWZMSkGWoU8TiazjZLASKpCSXKKFXz2FMRPQHKYQbuCqtsplsSFmcyXGdC6kNFFP5Xpo5RQGNIji2P4VQO825ZB1WBKnghfeXCArz9cV2m6+lqc5QTnS0fJlqoUylU+dc8h3nfH/LNSZzJFazfwxDytB+7cPcSn7xGL3sYuPyHMC9h4vDfKVLpIyKvi6VyJpkvI8X6YOiQ+b/f5VBQPXsSNsiCDBMHwQ2tI5srsMQB/QN3AkB6hK7nPelhQylCu6qftkXNGSdsH/9GaX1ycGSRXqtLd5iLqdwJzpYl7D46zY1k7m7oD6Dpzgc20ZDb1YW8F+GbeY0m7YLApjP8nxHn2qUqdS6dKwGU3ftb4wv3HUIwZBGdTuZkvVXE7bIR9KlVNt5LEc8Jg+KN5Oyk82MspXIak03wtpwtl/E6FiF9dtKSTzJeZaNL7R+oY9Uy2iN/hx6W42Nm5k3ypykgiz/LAchw2R42hr32p8YIjPDYww6u+/Oji2hAnjd1FC4Y/sRiGb1bb6hrl5Vfz44MppEpeuLUKNQ3f3NVVvV3kdBXNgNS1jimWYyxSJx+Go/fCN6+FY/dZ5+FszAfPNV6YgG9uvw3Az5WqjBhOm4LsYrruotU0nelMkaLiFaznrvfAj98BySGGFQWv3mYxnmSuJJJwQHH8MEwf5RSdVBEl6bquz6+7msVXINotmO/vDjORKnB0PG0V42SWXElRt3OLKqZnzeZKPHEivqAme3RCsPuIT+WJk/E5w6F1Xedvf/oMU+ki775iBWs7/YSlJi3bYPhhn0qbP8AoHTiTx2tDubu2UrB58BmAP9FK6zajlIXkENWOVaSLFQ7pSyi4O3lSvZBhPUywWmO7bYjPfjqAMwH/tFthrSpkqnU3gr+LQlzceN1BJxG/YNv1gD4wleHoRIbrN8SIGQvCnGObp8rWXPQiPrWWtM2XcTtsFpCnjRxRNiUAf12nn/FkAV3XKZQ1fE7xuEK5yonpLJuNPNK850PXazJBdqahTUeuXMVltxHxzT3OhjAAfyinUFJ8yMWkxfBbafg+l8nwFwf4iXyZZL7c8FqjdYw6ni1x2+bb+Pq1X0e1qXzpwX6u+uyDNTnSBOzeHcaHGOWnTw2z+9Qsz46dvipbyIVSbYdQFzVJZwFbpOndt6lMhy4goRs20UKqjuHXJJ2gx8n3qlfxn4HbyOIiVhlhuWzg0MmHResSoNL/G+sc/knDP1dhbv8MSSdfrjDuEBrbIaeHo7ZPkSkJkEnky5SrOlWHT3yZU0dEEjN+gknFhiqHrBsvmS9zXBcabn70EEwdYUCvLSrfefwUl3/mwTlgC9SKr6AB8FNKGxVNJ12sMGqwvn0TGg9pm7nR/iQSokhnKl2sOWZaxFFDBnjdjiVMpYucamplmy1VKVU13nJJHx+6fi1+exW/lKPoEedIl2zg7mBkNk8s4MTlsHFAX0VP/DEY3EXF4WfXrJ8cbtqUAoosNbDbOTEtEuQ5v9D9Kyj89voH+KX6Uob1Wi+UNC7aZaMuYAHA13WdbLGCLInk34IWxglDLlp6Cfg60YyEa1ewxvDr2eevDopczbUbYtbf5+j48wzBHk0UsNsketpcVl/0VKGM32nHaZeRJUgagJ9PCWBe3+UnV6qSKgi3it8lmHU8V0LToTNgLBDzNeP63mtJ/OSvuOIzD1D6/htFhbYR+VIFl0Mh7BPHMa+rxkhAnszI6E4/FJK4lHk0/LzJ8J1MpYutr++mMK/V+oVzNJmn3eNAlkR7j5gnZg0VGk8WKFY0/vL7e8V1YCT06doqulimRnj8uFgwm9twlKsaDx5panSWHBI6vNLkyKv7TLO58vyymdlZs+8Spgo2a9GmmKxL2gasXkjtHgf/UHkTXy1ez7jSTVthkBWSkegfexoO3w2A1l9rzfInwD9XYTkqamA8rQrAf8DjoGI/yamU0NPNLaru8InnZSeFfDHwW6ZsNlR7rAHwC6gM6yHkk7+DxCmOasaiUqrSP5lhJJG3Bp83RD3DN8cqAhNVv/XzUYPdjCbz3F3dSaA8xfnSMWYyNcCfzxlzdCJNwGXnJqOG4IkmHd90hwTd4gYIaOKiTYTEXNaEHCRdqjKZLrI87AHgXvU63JUk+v4fsKfcx3u+v4+E5iRsLxH1OxfW8A3ATxjaJgjLYLZUZVgXiWpdtnNM6yZiF4vTvACHkDvKVZ2IAWQL6vinHhX/X3ox+GLYjP4sjYBf++y/emacLb1BuoIuYgED8JsZfm4G3HObdo0lxQLpURVrwUrlK/hdCpIk4VEVkppgh4VMDfChBnJ+g+Gb16L5GeZdAKePIJ98mFMzGeTxfQ2DfvJlIemcnuGnQHEykqoiO4OgVXDLJes16sNcwMJelWJFm3eH9c/3Hubf7j9GoVy1ciD118jwbJ7eNhdtbsechHSqIHZFRycy3Ll7SNSGgJgo5u8kNzPEoFGodHCkcWf6m2cneMvtTzIwJZL//3b/MbSZ4xDsbZBNTHAfTxVwGIvbvDq+LwaBJbDpNUyli6QxGb5hrXb4wKZY56rNI+6r0WSeuLMXV/oUy6UxZjwrRS6gkIDO83DEDxNCjE/9U9L2XEUzwy9VmXGJbpbPqkIfnTZ0a/Mmk1xBqzgGoNR/PwmbDa89ZF0oyXyZsE9lQOvCP7ELXfVzd0VsOQvlqmXHa5lorWP4f353DYxHK7UKXbP51kSywG+189FsKi+17eL4VIZSVUPXm9oh1MXRiTRroj5WhL3IEnOGVSQMf36bCfiGJXMiIDoETuhBqwJ3eUh8ppP+bYzKnUh6lT3lPqYzRcYLdoI2AXIt7YtmTB8Fyca0WusxlC9XyZcqZJxiUco5o8R1H6FFMHyTDXUGFwP4vxf+60AP+DpxFqZQFZkOj4M2tx27TbK21eWqxoGRJJeu7DDOjx2HIjdKOlpVyCaeFoCfKNAZcOG028jXuXRMEPeqCrNV8ZkruQROu8zykFhQx5J5imUNvyH9mDmYTgPw52WfxTTerAAUpZITU9yMyNVp+LAAwy+mQPUzliygeMVAcLcmrr9mi3G6IBawVVFxXcyXI7pr3yj3HZq0rjWACVMC0nUi07tY6pdp9zjm5BbShQrrO/3YZEmc++SQYNmKCv5uslMiCRv1q3MY/rTxWrPZEo/0T/O1Xz8Fw08y1baVLZ/4Nf91YIzfHZ1i8yd+za7jM0ykimwNtE+dAAAgAElEQVQxZLN5ZR2bHf7HATjv9Uymi6R08Z1V80lOjoyQU3xUqpql4XcYgK/rkPEsRU6cxCsV2B24TkxHszngmk8AcJF8kDVRn2Uz/kPGCxTwR0UxldPPT4/9lLR+gqS7jzJwRBE30XBSFGGZDEhxB0T1nBHTuvh9wNFBsaJR1XQS+TKro15+Xr2YU6HLKLz9QY7oYudgbtFBJKTmhMHwy7KTA0lxQ+MMMJYRjF1VZEuWGUsVcHiCVLt3sk0+2tiFsYWso+s6R8bTrIp6kWWJdo865zPMZov8vfJNVo7+HABPWdy0R+QVFHU7I2U/z4yIG2mFwfBvvWQ53ypeIc6Tdy1Rv0oaF36pIAB/IYafGgVvlESpdonlSlWypSruiJC0JqQQCXwE6jT841MZZlpYUU1HQ5chd8yb8NJ1wfDN6WO+GKqWY4lXQ5IkJEki4nNagD6eLKDptQSrJElE/WrjseVnAX2OQwcEYPQEBeCbenWqULZA3O2wMWMBfpIOj1rbRSQLFCpV/E4h6Zjkw9yFzKvhFzPIepUbZMPmWqoBfr5UxWm34bSLHMJkushMpjh3WlUxjab6SObLuHyiJ4y7an4PjQuNkHTsXLIyRIfHwU+fGp7zkQrlKqPJPNNN0qPpiNFn+vn/8h/jI+PvZ7kz1ZLh+112vKoiFvfksFiwAfzdyKkRgi6FV27u4Mh4uiHBb14L6UKFVL7MFfLTyHqFPa5L0HT42F3P8Dc/OUBV0/nl/jFKFY1tS8UiN9IicTsUz/HA4ZpEJBi+uO5m49P0Dw5zImPn5i/+3npvk0gBlAPLrJ+f0ZbCqmvE2NO+F1GwebnEdpCVEd9ZFRA+1zgngC9J0vWSJB2RJKlfkqSPtPi7KknSD4y/75Ikqe9cvO+8YXjwn556mo8/+nEy7p+ju9o56uugKAmAHUkJwDdvMtXbVnt+aA2TNpHAalcFq8uVxMW0pN3NL+Ur+O7yf6bgbmSv5pff0hnhFK+flX3MYnTr9IiErSTBBX3tDQw/6neitPUQlhINgN9Kx//F/jFShQobuwVrCXkd1hATMyoTh3iT8hv6HvlrOPQL3AbgH864+S/tAn6vbeRXB8eRJVjSIcDvFef3kN98K58tv5o1L3oVr97WS1p349JzdPqdjBmJx5aRmwFPR0Plb75UJV+q4o2KG+JgNkBC9+DRUtY5fse3d/Pu786dLGYx/MBpGP74flHgZgG+2E2sdtXOYcSvWszXdGp0B2u9W2L+pt2LObSmCfDLVY3xVIGeNhcuu9wo6Rgg7lUVpsvGAl9M0eaxW7LU0GwOXcdaHMxr0TzGloBfLVsOr5tshp22HvANSQdEInkyXeDjPz/I2779ZOPrFFKUFMHYPQFxXE4D8PNNtQHFiobPqWC3ydy0pYvfHJqccx0OxnNGc7UiibrBOebCmp4ReZKu3CE+lPr0nFkLqXwFn1OhQ62SzpebAL8LX3mS94V288E9L+Y2fsKxsWTDc0EsGulChWttu0kr7ewqLcOhyMzmyowm84S8Dv7rGfE5Nnb7cShyS6fONx45wbv+c491bU+li6QQJKh/cAQ/WXRnkIOjKY4ZzRbbvTXAl+ok2/35MLz2P+GV30CXZJ51beN6227Czuofp4YvSZIN+CJwA7AeeL0kSeubHvZ2YFbX9ZXA54B/eq7vu2CkRtF9nXz2yc8CUFX7sSlF9m2vDZsey4ibeDJdxO2wYXcbFbaeCCy9iGkT8F0m4FdJ5ssEXA6ifsEQ60vh86WqdeG1LJgxGH4KLzlUqpICnggTqQIhr8qGLj8DkxkLRGJ+FckXIyIlOTpeu7ibb7RDYyk+9KOnuaCvjVeeL26QkHcuww8M/kaci8gG+PFtqLNCY9+fUPmr8l/wzeoN/L5/mt52N6pSazb1P1+xgw2v+3tefeEq/mznEty+IM5qhljASb5cnb+RWW4a3KGGmz9frpItVVDdPkY7r+FXpc0kdC/2ah4HZXKlKmPJArtOxEVLiUpJABxQGX+WPmnMYsfzMvwDPxIdEk07nwH4y511gO+r+clNDbe7zWX93fx+rcganT6bAN/cHfS0uXHZbY1JWwPEPapCugQoLiimaPeoOBQhawzFxXv7TIZv7GzCPhVZmmeCUrF2HGtkg2m3kHTAWNjSRZ44EZ/LZItpCrJY5PxBcY07yklUReZXB8et82MurObxvOL8bkoVjVu+9HvO+7tfWzsHUw4slLWGZL65cO4fEJJMumMzneXBFpJOmXaHxs+Kt7F96scG4AtLZdXXhYMKN+R+jiRJ/LX9Tvp/+DHe8729FCs1opUpVsjlclwh7+MJx4Ucm8qxLubjM6/azCdfvomXbOpskM16gq6WgD+RKlCqaMwaZGUqXSQriXN1anScAFl8beKcmZ1n2+sYviO6CoCS7ORAyg2SRKpY4ZYvPcpn4pcSJM229APkSlUqVY1jE+lFJcLPRZwLhr8D6Nd1/biu6yXgDuDmpsfcDHzb+PlHwNWS1GRoPkdRLJf5YGWMV2vj7Jvaxy0rb0GSNGb0feyjSMQVRat4mM7VNPywTxV9d0A4aGKbLIYfcYkE40ymRLmqE3DZifpV66IwI1+uWhWWrRm+APy45gIksrYAeAXDj/pV1sR8lKoaJ6ezTKSEZIIvhkIVZ3l+wP/iA/247Da++IbzrURUyOsQF3a5AN+6EXZ/k66J+9mnLYeXfQEqeeT9d5DWXRyZrn3WiqZb+rL1se02btjUiWKT6Qq6eNmOtcjlLDG/AIB5dfzsNLg7SBoLgt+pMJstoevgctjoetePWPviWymr4rwEyDKTLVlJsK88OAD/8TL40VuhUmTdfW/m75Rv0RUUwNyQ8CoXhO9+ZkDMDF75YtGFFCzA71Fq51AAurjxTSA0WTUYDL9+9zIPw7d2B20unA4b+ZKw5poSCAjAzxQr4PSjlNK0u8XvIz6VIUM/dtltOGyyxfADLjtuh0K2VQfROjZvhVYWVcUYhVd2xXgPJ4fGUkyli+TL1cYFpJgiayQi2zvENS4VU/zzqzZzeDzFK770KJWqZkmI5vFs6g6wpSdAsayRLlT47i5hfqif9nXcmCnRFXAymSpSrmo88LQgGN7O1biraTK5HLtPxrnzySFrfkC3PI1fT3N14kdCXjUYfsYh2o/EsofhgndwQF9Be3wvd+8f49RMzroW0oUKHVOP45UK/LJ0Hscm06yM+HjF+T382c4lnL+ktouP+p10t7l4ZjTJM01JYPN7MBe9qUyRroj4DNPTkwSlLMF2cc7Mha7dUwP89lAnOIMk3UuJ58Wu9tH+GfYNJXjRNbeghdZy/tgPAJ1nx1Jc87nf8YvFDKw5B3EuAL8bqK+hHjZ+1/Ixuq5XgCQwVxAFJEl6pyRJuyVJ2j01deYTl1SbjaOKnaKm8tYNb+VD2z+KVvZxOHc3Dw0/xLboNqi6mS0Kl8pUukjEpzKjKLwvEiIe7IUlFzGtKNgkmZBxk5t+64DLTsQAjHproGD4CwG+cGZMVcRN9t3gu+Civ2Q8VSTmd1pVmU8PJ5nOCBeMaQ2LSDX/faKpOdpTgwkuXhmyZAKADq/KTKYE++8QHuB7/prO9DP8Tt6B0r1VuA9yM8xKQetmWRUR2/vl4aY2z/McR7e72nBe5kRuBjwhEvkSXlXB57Rb7MpjFPj8xVWr+PAtFwGi+GrEkldc7Hp2AH3wcTj0C37wd69HLUzSI021lnQO/xIe/LQYIpMagU2v5vbfn+C2/9hN1ehV1CnXvOpRv9PyiI8kckR8qtU4DIRLpljRaourCfhNSVsz4dfT5sKp2ChWNNLFCpqOZbX0qopwH6l+7JWM5eYI+1SL4auKDVWRrQSgOW6w5VAYg83nEUnZnK5av9d1nVypYrVIiPjUhuZs0/UyXzFt9ZAKhQ0LYiHJzed18z9fup7h2TxjyYJ1fZi7EEmS+Nl7LuGRD1/Ji9dF+OGeYYqVKifrcgQDBgiujvkYTxX46d4RihlxDZtyR0BP88EfPs3f3/2sNUIxpgndPFY1wM8A/Gm5dt6l1dcRW3ke57nEY2ezJfLZDNfLT5DOF1k2/RAZ3ck9mdVMpIpWohlg29Ia4Ed8Tq5aG2FkNs+NX3jEsuZCbadlkoKpdJGVsQAZ3YWvmqRDSuFuE0RiMJ7DJkvWggjiu2XdjUx3XwUI547ZCvkNO/uQL/xzOjJHOE8asPo6PbZQX59zGOcC8Fsx9eb9yWIeI36p61/TdX27ruvbw+Fwq4csHLKMm6+hFD7F+7e/n3JFppLZwHT5OFF3lA9sfz8KPtIlcaIn0wXCPpW9lST3e9w85rRDdAOTW15DhyuETzXsVsbWP+i20+a2k8iVGiSdTLFi2TFnWrl0bHY0u4eEYdH7celC6L2AyVSBiN/JyogXh022/MSxBsCfpTtYq/Y1YyJVYCSRb2AuICSdQqmM9sj/hugmy620x3mRqBRddxMACZt4ns+psLlHMG3TkjlvGOMhY8box/rk5r6hBD/ZOyzYZjEF7hDJXNlgrDZL6nI5auAqu8VneLG8l9c+/Rb8ZLllazc75MNI6FQlG6+VxfD4mDRLp7+FpHPwp+BqQ6uW0BQ3rLmB3xya4P7Dk0yVHKR1FyG9BvimZXEqXWQkkW+QcwDL4WL1McoZko6rveFxI4k8kiR88+YxmbkBEwDcDhvZYhVN9eHSspabI+JzWq+v2mVrd+ZVFRSbjEddmOHv10Xi+4C+zPp9qaqh6VhN0MzjMGO6XuYrppitOmlz23Ga+SujdUCfkcMZSeRrDN9VAzQz+f2GnUuJZ0vc+8w4J6ezOO3iGAYmM0iSIBHjqQJffmiAVQHjXjH6MXVIKU7O5EgXKtZCFKk2jZ80AH9CEqSrqrhh6cWEl23CW5rCS47ZXJmNqQf5iuPz9I3/mnWph3lQ20IRcZ5X1hGYnjYXIa9Kh8eBQ5F56yXLePyjVyNJ8Gyd88di+Cmxy5tMF4j4VHKym63yMRSq2Ds3EnTbqWg6TkW2vn9Jgg6vA27+ItmLPgQIx9zQbA6/UyHgtsPKqwFYJ5/imGHU2HNq/nYo5zLOBeAPA/X1yz3A6HyPkSRJAQLA83aEKyNe+icNxlOuUopfwpbAtdx+/e1EPVGcNh+5qri4BcN3MqmLC/uILC7MqXKKiCtifZGmLhlw2cXNWKpagO+y2xr8zvG6G+uHu4cs983glvfxo+rlrI35GJ7NUaxUmcmWiPmd2G0yq2NeHjI67EUDTqvQJyIlWNLuxmGTGwD/KWOM3dYldR5/hKRzrbwbefY4XPZBeP0d3Bl4OwmPkUwyAD9tAH7Ep7ImZjD80GkYvtFKOqQUkaRGSedf7jvK//r5wTpG3GHkPQTgmxXOJsMXJ0+A6DuVX7KscIiX2HZx0YoOLrIdoiyp3NN+KwB7tZW4paLR1dFWY/jFNBy7Dza9hk/HPs97pQ+Dw8OxiQxVTefASJJJPUhbXWVvpM6LPzKbtxZTM8ztubVw5+Lg8ILd2aC1Ds/mifqcOBTZqlI1tX+zytarKmSLFcqKF5+Usxi+WfELwqGlGoBvJntddts8Gr4Apocqm9GQ+X11o/h9KWMljc3PYh6n+Vmm6yySFNPEK06xM7TZwe6xKkhN2Ww0ka9p+HUM1oxLV4ZY2uHm3x8+wYnpLOf1iuvwxHQWv9NOLOCiVNE4MZ3lkh67KKAyQLxDqgGsOZ+hrTxORVI4Qp/4g6Hhj5S9lHUbxSWXCZtmSLTpWCGNksiVaC+IXMb1Q58jUI3ziG2n9dr1DF+SJK5YE2ZtZ23Eacir0ul3Wgw8W6xYyfLJdJFMsUKhrBH2qRRtXjZIRj+s2GarKttpt+FQZBRZot3twG4T3+UKY7EZmMowGM/RazjB8HejSQpLpEmrb9LRicyiWps/1zgXgP8ksEqSpGWSJDmA1wE/b3rMz4FbjZ9fBdyvP49ZipVhL+lCRWiXpQp6Kcyr+95vTbv3KgFKelp45wsVwj6VSbu4EQ/rgslP5acIu8PWzWJm4wMuO16HQqmiWT7poNve0GPElHTKVY0P/3g//2r0xd7d+QZ26eu4cHkHhbLG4THxZUeNm39DZ8C6wQTDF+XdERJE/Cp+l70R8IdmcdhkNnTVirdAXMRXyU9RdrYLcI9u4D/tryDoMUCmdwe0LWNc7ROv73Ny7foY166PsqU3wIJhMHx7JUvIW7Mvlqsae07GRfVo0rC0uUMk8mWCbjsuh83yS7vrGL45Jq5NEuf3FtsjxAJOLnMc4Zi6js/nX8KtpQ/zjcpLAHDmx/A5lRrDP3KvcK1sfAW/jkf4ZXoV/ZMZy2f/1OAsE3ob3lJNHjTP91iywGiiMIfhm4A/ayacczPg7mD/cIK1H7vXSvQOz+as55oga+4ETWD3qArFikZBFi0pagy/DvDtNlTj+bVkb+v5sqakc7+2le9ceh9P6yus35uPr3fpAFy1VshalpmglAVdY7rsqC08zoDF8M0FcGQ2b+WlTImqPmRZ4j1XruTASJLxVIHthtWxWNEIuu3Wee4Ouljuqwo50OgO207K+Jw66p5/J8IsgcIoaUeM71RejB5Zb+VMprIVPlR+J9JVfyveuA7wZ3NlQmUhAfmqCSrYmO68HJssoSoyPW2Nk7M+dcsmvvmWCxp+19vutoq66rvTTqYK1n0d9qmU7X5kSadqc0LHCstAYMqBrrr6BxDXQIfHQf9khqF4jl7zs8g2yr4eeqUpjo6nuVl+BDcF9g4tfvbF2cZzBnxDk/8L4FfAIeBOXdcPSpL0d5Ikvcx42DeADkmS+oH3A3Osm+cyVkYEKPVP1t8EtQs2oAbRpCyTBhsLe1WmNPHFHkmfQtd1pnJThF1hloc8hLyqxbxNhg81QAi47JgFsF5VsW4s08Xx+PEZdKNLniTBjmXixthtTCQyfdfr64C7M+AEh5uS4iUsJYj6nQRcSoMP/6nBBOu7/A2uGhCAv0E+STKw3hrvNpsr0WYkDJFt8O7H+HXoLeL4fSp9IQ9fe/P2hvPUMlRz4HuamGHNBHhmJGlJWknDgodHuHSCbjsuu81KcrcCfIDHtXXslA8TyRxhefUEDxTWMBAv8Zi8lTFdnDMpPY7Paa8x/CP3gDdGPrrNuml/9lSts+LewVnGacdZqPmqo0a+4+BoilJVo2c+hm8CpJGA3j+cFNONjMV/JJGnxwB8p8ME/ELDa5jXSgq3YPjumqRjndIGhm9KQcqciu3+yQxfue9pADI4WdKzhLI5n7lUu9bNXemqiJeY38lrLxBM2WL4xg5stOisAZQraLUMcNpthLwORhJ5Rmbz2GSpISlZH6/Y2m3JgKtjPnzG8QZcdmvheOslfcjFtLh2jDzIMleOd1y6jBXSKBce+UduVX6FJz9CxtXFf1auonjbI1ajuql0kfvsV+Lq2STetK0PXVZYrYyRyJWIaBPs0VYxbQuzx7YFp6+dJe1uVoS92ORGNdmhyHPulyV1gF9P3CZSRevfEZ8T3SA71dA6kG1WPsmUstxNgA+C5R+bzDA0m7fszgBV/xJ6pUl684f4344v8V77zzh89Ch89XIYeoLnK86JD1/X9Xt0XV+t6/oKXdc/afzu47qu/9z4uaDr+qt1XV+p6/oOXdePL/yKzy1WGgnI/qnaNrceZDpcbSBV6Z8yZrf6VSbzAhDihTgjmRESxQRhdxhZlrhqbdgCK7M4BGpb/qC7tt3tC7kthm8ywelMiWPGaLeoz2ndIL82EkUmUzCZuqrItQ6KzjBhKUHEpxJw2UnkxWtXqhr7hxNz5ByADqfOammYCe9a63eJbNlqqwCA3YXHOZdtnjbMOb3FZEPx1a666svsrAH4hkvHdJ2Y0bCoqD6QFVJ4+Uj5HQB4f/AKZHQeKgomd8PGGOMG4JMaMRi+AfiJQYispX8qZ/Va/9m+GuDvH04yqbeh5CasIRpBt52wTxUl/DCHBZqgbHnFjQS0+X3Gs6Lt8FiiYIGa0yrVzzW8hlcV11284sRHTui7NEs6NkvDN5m0R7WRa/Jp7z4ZZ3xK5BOyupOQV8XrF9//r54asNi4udvo8Ko8/tGruXB5Bz5njYiY854HCj6LbNQzfBCsfCSR59BYihVhzxyQNEOxyXzourXYZIkNXX7r+AIuO+f1BvnKG7dx68V9Qopy+oVbTbLxPy5q41XbetkiDQCwXT6Kmhmh4DGcOcUK9z07wXiywHSmRKjO547NjtS+grW2MabSRXqYYEDr4v2+z/BR3ovPaee9V6/k3VeuaP64LWNJu5vJdJFCuWoBfIfHwWS60GCVDYfFTsnevRmAmN/Y3RnYsjbmZ0tP4/24IuJl/3CCUkWjt24nKbX3sUSaZIMsJKI32+7jgmf+TgwZ+u8O+P/dIupX8aqKYPjlRtYDEPWIreLDJ8TJ7gw4mcpN0eEUv390VPRiibjFF3zVWqGly5Jobes2b2KzP42rdjH2dXjIGS2N6z2+jw3MiKrMNpcFErtOxNm+tI3Vxo5kbacfSRILgOlarXoiRKQEYZ9K0O2wJJ2TMzkKZY1N3XMlmFB+ALtU5ZR9JSDklnSx0rAwAXgNvbgefE4bBsuhmKazrr3CruNieAhAISEWT93dQTJfIuByNJz/+p+RJGjr4yHHpZzUO/me9FKk3p2c2vY3PKmLnvyvvaCXSYJoSJAeo8PjqG29MxPgjVlaqNthY3g2j9Mu0x10iT5KUhtStSQqZjNTSCcf4eM3rre+v2ZJx2m34alLMpOLW43lQDD/iVSBiqZbi4WrieGbuylzcZsuq3ikIm1OcY6ip2H4LrsyR9KJ50p4EK+fxUWH18EtO8U5um9fv1Ud2mqXFvKqFniZw7nHqoHaYu8MCIY/fgAKKbqCLkZm8xweT1sOsvni+o0x9n38GlaEvXR4xesFXHYkSeL6jTGhaRdS4j1kWbD83DQhn4MtsgD886QBlPwUJZ8A/Hi2xLu+s5uvPDTAlGGsaDygVSyXRhmfmSUmzTKoRzhVDjJcdOJ3KtyytYcbN8/tbtoqTOY9PJuzztH6Ln8Dww97VfxGgZoUEzsNi+Ebi+G337aDD163puG1V4Q9lKuCaPS014iFrWMZbVKGnfIhypIDN3m2F3cBMDE2yANHJhecXHe28YIEfEmSWBHxMjA1N5EF0O0X28q7D/YT8qqsjviYzE1ySbeozvz2QVEy0O0V7tJLV4Vw2GT8LjuyLFnbdHM+aQPD7xDsfSZbsgAi5ndy94Exjk5k6G5z4XPaCbrFTuFzrz0P2dh2elWFvg6PlQwCcLd3s9SRZueyDgJ1Gr6pFTezUwDH5DMAHJWFg6O5j44Z5nHMuZkWijrAN+2N6UKZ3SdnuWy10GfL6UmQZPZOYTQ8Uxt2WB61iS2+/T6+7f9zAG73vQvecCdt13wAHZmQV2Xnsg4cDpWkHITUiKW56pomAN8X5ehEGocic6WhV68Ie612CQWnMUYyPQaPfxG+83JuXN/ONeujKLI0J2kLonKyxvCFpGMy/JlMscGDD40afsBlR7HVXDcA40Vxjtv2/ht88/qGRTY88BN6EGDdqOE3MvzZbAmvlKeoK5Sw0+5xcMM2UeTjoWC1Fm5YUI0IeR21lhVp4YaZ0Ntq0pIzANP98NXL4KF/ojvoYjCeYySRZ21sYcAHrBbPZo4i4GpK8haSNTnQE4bsNG6Hwnm2E5R0G6okrlEtIFqVHJ/KoulwcDRZq5VpOKDVdGljaHEhFkzaosQzJasq+EzCTKYOxnNMpYvIkmhhPZUucmwyU2t1be5uDcCPGoDf6nybYaoNUGvfAWAPCZfVlfJTTAc3M9T7Mo5rMcrOECdOneRDP9qP/DxUKr0gAR9E4rZRw699Kb3GSj2Tn+WKNWEK1TyZcoblgeV0e7sZTA9y84qbuSAmkjteVeHCFR2EDfZi3sQmIAQaJB0B+PFMiZFEjrBP5UWrQjxxIk6xXOXPdogL+iPXr+VLbzi/lrk34lO3bOLDN9SkGEewi6iUIOYXko6ZyTf97/UFQ1aMPU0GD8fKAoATLRam+uOo15NPGw4vIEEhZb33g0emSBcr3LAxhiyBnp1Gd7XzgR8eoKfNxWsu6G24Kdz2phvS3Y5DFcBpasV+p53lYQ9begLYZInLVoXJqlFIjXKR9hQ7KruZmZ4UQ2W8MY6Mp1kZ9nKesaVeFakBftlj+MzTY2K4jVZBSg7z+deexw///CJr4auPdo9KPFeGUg7KuQaGH8+W5px/M3FntgA2w3ztEWPKmrz7GzD4GM5qBp9ToYtpovf/Fdfk7jGOWzyulYYfz5bxUCCLE5+qiPd0CEDxy0XLWFBPbswIeRxsjd8rmHZ6DE1SiONrTNpW8qKz49F76W5zWeMY13X6RFFbPjHndZujnuE3RNFg+CCSsdlpqJRYJ53kF9rFtccFRZPDAaN469BYmsl00br3rIhuQKHKxYXfAVDwLrEaC/paOIoWCjOZOjiTYzpTpMOrEvM7KVU17t4/xotWhQQpCy4RbqboBqD23c8nd0HNqQM0EAupTRynX8pT7NiA8sqvcEPpH0nYw5RTk1y+OszzUZt6ZkvhH1GsjHj58d5hyy5ZDzjL2wUASLYcV62NMJUXCdmIO8ItK29hPDfO3+78W2Spth7+8ys3W84Q01Y40yTpSFJtFZ/JGh7voIvX7VjCeKrAx25cz+qoYMivM4C/OS5a0VSP5o0KwCmm8bvsorBH0xlNFCz5x4pcHCYPweheTtmXM50pUalqJPKtGb7JhM5Iw5ckwdSKaeu97zkgXBI7l7fT4VWx5ePE8XNyJsf3b7tQFBLVgXwrRmQuyPVg+Y1bL7DA68tvPB/pjhUQH+Dy4U+wRFGZGL2GEFgM/8LlHWzoFiysnllJ3hgkENq12Wc9cRJPaCVbm2oYzGh328X23uiqWnG1WwO4TUkHmOPUKJS1WnKc2m5mMGsXd1vG8JrHTxDxqS/kFlQAAB4hSURBVFxUFsNlArqwKdY3XStVNCpVzdotzOZKeKQ8Wd1Fh884T4oKskLMXuGUYW90tzi/65QR3lv4PDzdDZkJCmoHel6uffftywUgb34tPPE1Viq1JPe6sApf3wF9l4q+MAuEqbU3kwsKqUaGP7IHJp7BQYXfVrdyge0YSxjH3rEU6LcA3+w3E2oG/FXXUJHsvNl2HwB6Wx/EG4vEFhshrwOX3cZgPC92E17Vym0k82WuNiRdtr4J1rykVouyCIbfHXThtIucXH1xH2191o9y9xY6gx46An76s26C2gxXrDmLGqRFxAsW8E3gPWZMgqrXNU1Jx2bPcumqEEcSYtxe2B3mphU3tXy9WMBpfcHNDN+8uH2qYm0944aks6E7wLalbXzn7TtbvOoiwhzEkJkg4LKLFsmFCmPJPGGvanl+AfjN/4K9Qo4aC7yKY5MZdnzqt1ayqBnwX7QqzKu39Vi7kkWH6rNcOgAPHJkk6lfpDrrEZ8rFmcTL+k6/tYCZIGS3SVaCsj7M8XptdYC/rO5zSZIkCsiO3I0KLJFU9k6IHEzGEWIsmWF11MfW3jauXR/l2g0xDhmTkWyBLlEJkhqrTVKaPbngIbZ7VDFFzOijM6v7raRwPFtiPCl6MJmulPqbvt1TAyeTHMS1pl1UfICIr5urEgLw/Sbg1xVsgZhg5Te+43i2RJezQqborC2MkgQOD2GljNHduCXgr0AsdNXpo9jS46Tt4h6wdnc7/xzOv1Xsgp74GiuTjwGraPc4iEw9KvIfh+8WfeoDzYX0tWgp6WhVKKVrkognJM7rqGiS97S2goPKBpaQxNXehQD8bMPrzpF0nAFOBi9k5ezD5HQVb3snDIjv9kwZviRJllNnKl0k5FMbJLcr1hrga7PXJmEh7nePw2Yl7FuFLEusivjmfieuNtKSB5+exbt0KwDb+toZPujhEtsJlqx8fgD/BSvpmIBv6Zp1q6vP4QNdprtDDJ+YzAk2E3FFFvXazUlb8+L2Oe0NRTujicIcy98ZhzllKTFI0HifRL7EWLJAZ/1r67oYuNy9Dba/nUOxm4lnS6QLZZ42yrebWdeykIfPvHpL46KxmHD6LZcOCFa7bWmbaD3sV3FVEoyW3A3JPhMQ57N9uk1nyTz2PwD8nbXHS0X0MTG/4GRBMK5VES8uh42vvXk7q6M+K7/R5veJAq/EyRrDnj214CG2e+yiAZ1hYZyoeKzPN5Mpin5H/lpyvf76avfUM3xxvGlzRJ5iAGz8ON1enYvlgwB4NZPhKw3Py9VV287mSnTYS2h2b6MU6PDRYa/ZCVsxzp6qAMPK5DFIjzMrt+FzKrXHShI43GI4T/sKQmNiMtPamA/p2buEdKTrsOdbC563lpKOUSxmSTqekFgA+u8nrbQzQog7fbfCG3+MzyWef3wyg02WLFtlqzzTUOd14v96uCHxfqYMH4SOf3w6Y8lHZlJ9S09gXslTkiQ++tJ1lu11vvjsq7fwyVs2zvn9lC1GSVcI9oq/bV/axjQBwlKKQIu6h3MRL1jA720XF0D/VAZVkRv8uLIk41f9XLDCKLHP1SSdxYS3zodvt9WSuH6XHb9TocPj4JcHxihVtTkOkDOOrq3CyvbYv1k3UTJfZjSRp6tezokfF+x1y+vhxn9h2YbtbF0S5Fd/dZllA21bCEzPJAyG73Yo1mcy2ztEfCreSoKxskdov0a4LcBvvf01gad5F9IQxgQz8//BGcEQj+YE+NXLOCAWNLtNEi4MXycM76n9cREMv1DWKI0/C8BgRRzfpp4AM9kS46lCzdJII+DXn2fzWjH7qYspXJ0QP8EO/RmcUhndHcJrVH43M/z6KWDxTAkPeVb2xPjEyzbUPqzqJWCr1We00vAjBXG82dHDZGaGmdLb5pfyVl2DMvQoPX6FnUu8cPgeWH8zrLpWAH51/opQc1fWYCYwxilako45OezIPfR3XAlIVLwx6Lukdr6KFUJeh9UaoRXgJ3pfTFG3M6SHrepgODvAv3RlB8ensowlhSMo4lfxOETjwIXiDTuXsr2vfcHHrIn5rNqg+jjlWsfTtg3IRtHn9r42pvUAdioNFtlzGS9YwA+47PhUURHbCmRingjHU4eoaBUm85O4FBce++KkDXMB0XRw2Gpl9X6nYvQYWcLTxsDxVg6QMwpnAC7/MAzcT++ssIsm82XGkoWGi5wTxqzM5VcAcOPmLn767ktYHvby9Tdv5xMv22DdTM85VJ91E5uyjtmYKuJVCJJhBj/r6xj+6QDf1Lo7vAsAfngNIMHlokfJ0sx+sHs4Oos1V7Y+2j0O7vsfl3PL1m6xFZ86LP7g8ELi9AwfgP0/gK6t9JfE8W3sEtXQQ/FcQ/5ErdvW17fKNefaxnU/VckmOnm2L4f4cV7i3E/F5kZacwMeE/BdjXZO02VWMhqzufQ8qsffWFPh8OKXRU7BYZMtzb8+AlnhZgmWJvBWkzyTds2frI+sQ6oUuOftq3n3kiExx3X9y2Hza8QI0ImD8563jd0BHv3IVdZsBqCO4ddp+ADojCwRtZkmSDvqLKpRv9MqRpyj4QO+QDsfLt/GV6s3NXwXrdpAnC5uvbiPd18hfPtdQSdOu40HPngFt71o+Wmeefbhf+W/kn3VHda/13f6uWGnUVyWPfPGkYuJFyzgS5Jk+V5byQi3bbqNw/HDfPOZbzKZmyTijiw6Ky5JEh4DuFS7zQIx82Z944VLsdvEaz1nhg9wwTugrY+lB78KwIGRJLlStdGhc/wh8HVBx8o5T18R9oril3MVnghkjCZvAdFLZkPUBbrOBdnfIUs6k3pbk6RTc5+0CvP3CzL8rq3wwaOw5c/QkIXu7YtyfCrD0g5PS6DrC3mEZOXrxOrX17tzUQx/tTSEY/IAbHk9I7N5wr7atKrJdLGB4ctGKb94bt0wDGOubQoPP9txB+x4J7Qvg5kBvKd+i7LqKvB34aqkkKnNtzWvL7N9h+m0UrVczRprhsODG+EaaplArFZwJU8woncgGwOATpX889df+IR/3V+axm5YfFn2IoiJgiMmn13w3HU1k5xmhm8CflsfWrdwwtWDdL2Z4LLVIWJ+Z0vAb/PY+Zl2KYcdGxskpLMBfEmS+ND1a7njnRdacyUifuecSt1zGdv6Orhifa1WQJIktm8wfPx/AvwzDzNZ2eomuH7Z9Vzfdz1feOoL/Prkrxct55hhsmVVka3su3mhRfxObtrchSSdA4YPoDigdydqboSugJMfPCn0WOvG0jQ48TvB7p+fMQON4e8SyT2tyiu39fDlNU/j+Ode+Jf1XHbgozyhreFxz9UN0oa5C5pX0rHPdem0DG8EFAcZVeQ2qp4oA1MZayzj/J/Z3JpLQlYpJI3Rha2j3WPnFbaH0SQFNr7SclzVV3w2W2JdLZxGUEvcyrH1IvHXvlww5dQIrL4O3B1I6ATIWBq++Vqmrdis+XBUc2KAdn2oPpyaAPyW5zdxCkkrUVx+nfWrST04v6RjJibTo0ImdIfA7hKf26aeFvABeOxL8NBnxM+mPGEyfK9xr216DSHjM9TLML66++iWrT08/tGrWyb6TXLgd9rxqTWQ956FpGPGhcs7Wtp0/2BhLoaZyYUfd5bxgnXpQK2gopWmCfDxiz7O6rbV5Co5Lu+5/Ixe263WtqDmzVl/0X7sxvXcdF7XGTsG5g1XO1JulivWRfjeLjE9yAKc2RPCPrj04gVe4BxGoBv0KmQmeFnuZzDwaVh2OTgDTFec3Hrgei5aHm14yukkna6gC4cit64raBFF3xIojpGxdzAYz3HthtjCTzBBzBeDkChWYvZUQy+f+mj3qFwvP8lk5BJinhAnpvdz/tK2BgdOPcMHcZ0lKM/JlZhylbV7aa8r+V91LZx8BICXrnA0DE65Qt6HNBMEIoZBQEep5kBt6mjq8GKrZFHrunY2hCFlLb/0NXDie4AourrYP8+5Ntppkx4Xi5LpyrEpEF4trL+ni2d/BtPHRLdWS9Ix2g60L4NX3Q6rriWUEDuOelZukqnoaepDzPPpcyrWvedx2J5XVv68h7kYPk8M/4UN+AswfBBunds233ZWr+2pY/jupk6HIBJ3V645s13DguFuh1KaK1cG+J6owK4xfPMGjDRPlnyewkyepkZF87LoJnjTT0G2kZvJkj/wYEPCFk7v0rl2fZRHPnyl5fI4XdhCy2F6F0dzonR9xekGtxiTrwj01DzQiVPQdV7Lh7fbq/ikSZ5y34IjW2IkkefWi5c2sPdYM8M3dylNspQJYB2eOs87QOd5YgEypnP9w7VdmOWVbrvMF+xfYPrQEbjkEmazZVwUkXTNKrayQvUiFTNiEEtLwD8i/t+9TXRgzYzzvpdfygUbe1oeO6520co4NSpsmO11OnZkPZx4uPXz6qOQFCRkZmCupAOw8RUAxAJlVEVumXQ9XcsPv8uOJBn9rYznnDOC9X8rXO2A9CdJ52yi19Lw5y+MONswm2Kpig2fU2FLT4CtvXMbmZ2zMJjoJV027DYJu02qVR9OGYAfXjPPk89xmAwwNSLcQdENVlfOnjY3b7xwiUiU1sXpGL4sS2dU8dvWLY71wRFxCZ92cIvJ8OsBf6Z/3of784PIks6o0s0BYwTexu5Ag2001sSQzRbH7d5mhm/WGBhg1L5c2DPX3Sj+bY5ONOcIAN7yDD4pj5oTfW/iuRJeQ6efy/A9UMqwY1k7a2Jz3SBMHxMLntMvcjySzLUXbJrftSUbOY/0mMHw6xaGyHoh9SwghwE1GWdol0j6Qk3SqQu/085vP3A5N59X07Ithn8awLfJEgHDGWe3yTjt8lk5dP5bhU0R18OfJJ0zj+cT8E1d1qEIV8Rdf3HpOX+PhjBYoLua4sLlHQzFc1YPHqaOiLGFzUDwfIXJ8Gf6BSB01CQKmyzxDy/fNOcpZqXtufoupHbRJ2i8KtwgK043uMVi+L3C+dS1FfZ8Gy5+r9DVm1/fWAyOa50odYDvdSjYZAld1xs7OAIuuxiC4WvSgD3NDF/1wv/zqDXgw5qkVQf4roxwEdlzk9y1b4R4poRXMobNNGv4Dh9US3z6ZWtFvqc5MhO1RbrrPJE/kE/zPfhiMH1UyDH1hVbmLnLyMCy9aP7n1wO+0y+0f6U1gDf3g7I0/EUQgDXRmuXR57T/8QM+CFnnT5LOmUeP1djq3B9mfdL2DxIWC4zzqVu2Ng4znzz8h2P3IHYbigtO/l78u/301jVL0jlXCbHu89GdQQa0FYQcjoZ+Ri3DG4W1N4okKcAVfwPfew3s+x5su3Xu4w3Av2vIxXItwbKQx9KZ29x2bLI0xxXkctho8zjmuL08DhtOu9woLdYtkq0YviMhbJSO/ATvu2Mfq6NeIsZYyTkLu/nvUgaUFp7w7FRtwbv643DZX899THP4O4X/HmoLPEBknfj/gTvh+INw0XvmMvdKSbQDAdHqt3dHrehqEbFYSQfgjndeaJ1vnzE7+Y8+PKE/Af7ZhNuhsDLitYqwzulrW5LOHwjwTRaYj9Pb567NlNSqgomtuOIP8zlAOIH8XTD4uPj3IgDfoci87ZJlvHjdOcprBJcgfeQUNz58vHHxmy9kG7zuu7V/r7pWaNq/+yxsfeNcxjvTT8EV5fisxMn0BC+ta7Xb4VGtgScNH8nlaClDbFva1np6lRkOt1hAczPwbzvg/DchGS0dAlIOv63M0YkMNwfLUKCFLbMO8N0tAD83U7NUKvMz7YbwdYJmnNd6SSfQI7T43d8U/z56L7zxx40D3s0krTcq5EbZ1lLOmS86A058TqW2I1og6hfXt126bOFK7T+W8ESsthPnOl7QgA/wy7+8FOV5yNp76lw6f5Awb+Rc0yjg2ZNixF943R/mc5gR6Ia46GW+GMAH+PhN5z6p/I6zLYyRJNjxLvjpO2F8v5B46mP6GI7oGjpKDmayJTZ11wDrz3YusaYc1cdHX7rOKpSqjzdd1MebLupb+PO4O4RbZ/oIPHtXrYcScOsmJ1/YVyXiqAjAb07aOoz8hTH+sCF0XbBFT8fcvy0UvroK03qGL0lw3afE4uLvgp+8C37+Xnj992qPMeWc1dfB3v8QhORFH1z0W996cR83bek6Y7fNGy9cekaP/28boVUiYf48xAse8Fu6Fs5BeB2mpPP8vP6caKHzAjWHTngtf9AwQcDdIcbj/THGiivF/48/2Aj4ug4zx5A3vopbQt38+yMnGipH5ytie041F+52Me0IYGSvYNJ2D5Sz3Lhc4gv74GJ9D0hyIxhDjfGXGhuOAWLIe7VUV926yDDfo9X7nf+m2s9DT8CurwqQN2UbY1Qia14C614mzm39DuA04bTb5hZv/f8prviI+O95iBe0S+f5DM8fWsN3/J/2zj04rrqK45+TpE0fSWiTNrRNaZuWlFKoQhqYyqOCvNKKbbUoOM4YB7Wj4Gh1nAGm6vCfIqMzKgwdEAZkKqCjHYsMWEBHxkeBtvQR7Ctgq9DSl8OjhAKB4x+/3y+7SXY32SR7783u+czs7M0vN7lnzr373XPPPb/zG+cqO97pFeFHXaETCII/wOg+kVTVQ/1ZTvDT6TzuBGxSE6s+PpuvXzKne4HughHy+FLm5ji8fgBmLAJg7tgTXDvlIJe89ZjralnTS4CDmL/5Kn0IueBxAxdcIHWMqimuciQb81e41M+eJ1Jj3ROtJkDTFXmJvVFYTPAHSVXUKR1wUX5nr3K4qCt0AqHqI30S0Uhk9iVw4J/wfmo5So7tc+91p1NfPYabWucV/jwHwZ+/wtXAg+s/D8iJ1/jR+IeQmga4dE3fv500F5BUr6B0wh3hYCP8HK2QAfccpKbBTbQKdAv+wB/UGtFggj9IxqXV4Ud30Nq+EX7UFTqBYojwwQn+B++68sFAeDZRF+GXWRD8uVc5EQVoaHYPcw//C3l1C7R8KfMX++hxMHFm5hmwIcLPO4fv5y3U9CP4ZWWuk2bH06kJVib4iWVIgi8it4vIbhHZISLrRSRjMldE9ovIThHZJiKbh3LMpNCd0snw8K5gjJ3Y86FtqNCpjzh/Dymhj+PYw8nMC6Cswq0lEHjLTXYKTcQiIUTgsy5yjcrATZKqngK7/+h+npGjdUb9/MwRvq/2yTvCr6x2S/pN6dvHvQ8LPuu+NJ+/x/1sgp9YhqpWTwJnq+pHgL3ALTn2vVRVz1HVliEeMxF0p3TyXTxkKIQIf9NdrjIirgodcD1VvvpnmJd5hbARQ2UVzPgY7N2YGjtxBCpPgVF5rPU7VBa2wbXr3MPaRTfAynvddvVU9xC0fHQq8s/E5Hlu7kDXez3HB5vDB7hhE1z47f73a2iGua3w95+5Gbgn3wApT1UPGYlhSGqlqhtVNazQsAnI0pyj+AgzbaON8GtdhL/lfnjhwVQdfNQVOoGGhe6WfqRzxhL38Du0TD5xONXEKiqq6tNaLdTCgmvcdkitTGvO/QVUfyZ82JVKRwU6j7uZuIP58ho9PvcD23Q+8T0n9P+4I1WxE0XnViMvhvPTej3weJbfKbBRRLaIyKpc/0REVonIZhHZfPRoYWabDQepmbYR5/A7j7tbd/0Qnl3rxuPI4RcTc1vd+94/ufcTR3rUwcdKeHiaq40BpL70e+fxB1ODPximLIDGxdDxVM8STSNR9Cv4IvKUiLRneC1P22cN0AWsy/JvLlTVZmAJcKOILM52PFW9W1VbVLVl8uTCLOQ7HNRVjaZmTEX32rmRMLaW7kU8wE0YiqNCp9iomwN1TW7WKMQT4WcjRPi58vfgKnWkrG8e/+1j+efvB8vkM11ayQQ/sfR7v6aql+f6vYi0AVcDl6mqZtpHVQ/69yMish44H3gmf3OTw/jKCrZ+/4poe2+H2bYVY9zDvY6nLLofLs5odROI3ut0UXFSIvzGxe7V31oHo8bAxMa+i5O8faxna4RCUne6m4F7dE+qI6mRKIZapdMK3AQsU9XOLPuMF5HqsA1cCbQP5bhJoaK8bMDLIg4LYbbt9PNSaYiRXiWTFBpa3IzU13a6XjBJifCnnQNtjw7sLq5hoWtol77IeOex6CY+hTLW1w9YhJ9QhprDvwOoBp70JZdrAURkmoj4VnucCvxNRLYDzwGPqeoTmf+dkZMQ4c+6yC2GXVaRu3LDGDhhLeD/uIXiEyP4+XDWClfFFRa0V/UpnYgEP6wkBib4CWVIvXRUte+K2XSncJb67ZeBjw7lOIZn8jy3lODZK90ycat39u1zYgyOEJ2Gls9JSenkw+mXu06W7evd9sk3XNuDqHL4NdNdurHrpAl+QimCmroSYkwNtG1IRVI106z0bbgYNdYtSBJm3I7ECL+iEuZ9EnY9Cl3vwutu7ePIBL+sLNVqY8wIbahX5JjgG0agbk7PXu4jkbNXuiUFd/wGnv+lW2mqMWtR3PAT7pQswk8kRd8e2TAGTF2T75wpg5uZmgTmXOZmDm9c4yqOFralSjujIDwLMcFPJBbhG0YgiNW4uoHPME0aZWWw7Bfw/kk3Oe+Cb0Z7/JBuNMFPJCP0qjaMAhAEf6SmcwKTmuCa+1zFzsSIV4GasQgmzEytfWskChN8wwhMCoI/Ah/Y9ib05Yma2tmwekc8xzb6xVI6hhE45TTXlbIYBN8wMmARvmEEysqh9Ydw6oK4LTGMgmCCbxjpnPeVuC0wjIJhKR3DMIwSwQTfMAyjRDDBNwzDKBFM8A3DMEoEE3zDMIwSwQTfMAyjRDDBNwzDKBFM8A3DMEoEybLueCIQkaPAgUH++STg2DCaM1yYXflhduWH2ZUfxWjXTFXNuOpNogV/KIjIZlVtiduO3phd+WF25YfZlR+lZpeldAzDMEoEE3zDMIwSoZgF/+64DciC2ZUfZld+mF35UVJ2FW0O3zAMw+hJMUf4hmEYRhom+IZhGCVC0Qm+iLSKyB4R6RCRm2O04zQR+YuI7BKRF0XkW378VhF5VUS2+dfSGGzbLyI7/fE3+7FaEXlSRPb594kR23RGmk+2icibIrI6Ln+JyH0ickRE2tPGMvpIHD/319wOEWmO2K7bRWS3P/Z6EZngx2eJyDtpvlsbsV1Zz52I3OL9tUdErorYrkfSbNovItv8eCT+yqENhb++VLVoXkA58BIwGxgNbAfmx2TLVKDZb1cDe4H5wK3Ad2P2035gUq+xHwM3++2bgdtiPo+vATPj8hewGGgG2vvzEbAUeBwQYBHwbMR2XQlU+O3b0uyalb5fDP7KeO7852A7UAk0+s9seVR29fr9T4AfROmvHNpQ8Our2CL884EOVX1ZVd8DHgaWx2GIqh5S1a1++y1gF9AQhy0DZDnwgN9+AFgRoy2XAS+p6mBnWQ8ZVX0G+F+v4Ww+Wg78Sh2bgAkiMjUqu1R1o6p2+R83AdMLcex87crBcuBhVX1XVf8NdOA+u5HaJSICfA54qBDHzmFTNm0o+PVVbILfAPw37edXSIDIisgs4FzgWT/0DX9rdl/UqROPAhtFZIuIrPJjp6rqIXAXJFAfg12B6+j5IYzbX4FsPkrSdXc9LhoMNIrICyLyVxG5OAZ7Mp27pPjrYuCwqu5LG4vUX720oeDXV7EJvmQYi7XuVESqgN8Bq1X1TeAuYA5wDnAId0sZNReqajOwBLhRRBbHYENGRGQ0sAz4rR9Kgr/6IxHXnYisAbqAdX7oEDBDVc8FvgP8WkRqIjQp27lLhL+Az9MzsIjUXxm0IeuuGcYG5a9iE/xXgNPSfp4OHIzJFkRkFO6ErlPV3wOo6mFV/UBVPwTuoUC3srlQ1YP+/Qiw3ttwONwm+vcjUdvlWQJsVdXD3sbY/ZVGNh/Fft2JSBtwNfAF9YlfnzI57re34HLlc6OyKce5S4K/KoDPAI+EsSj9lUkbiOD6KjbBfx5oEpFGHyleB2yIwxCfH7wX2KWqP00bT8+9fRpo7/23BbZrvIhUh23cA792nJ/a/G5twB+itCuNHlFX3P7qRTYfbQC+6KspFgFvhFvzKBCRVuAmYJmqdqaNTxaRcr89G2gCXo7QrmznbgNwnYhUikijt+u5qOzyXA7sVtVXwkBU/sqmDURxfRX6iXTUL9wT7b24b+c1MdpxEe62awewzb+WAg8CO/34BmBqxHbNxlVIbAdeDD4C6oCngX3+vTYGn40DjgOnpI3F4i/cl84h4H1chPXlbD7C3XLf6a+5nUBLxHZ14HK84Tpb6/dd6c/xdmAr8KmI7cp67oA13l97gCVR2uXH7we+1mvfSPyVQxsKfn1ZawXDMIwSodhSOoZhGEYWTPANwzBKBBN8wzCMEsEE3zAMo0QwwTcMwygRTPANwzBKBBN8wzCMEuH/rGcDgYBTvkgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise 2\n",
    "α = [0.00, 0.80, 0.98]\n",
    "\n",
    "for i in α:\n",
    "    x[0] = 0\n",
    "    for t in range(T):\n",
    "        x[t + 1] = i * x[t] + np.random.randn()\n",
    "    plt.plot(x, label = 'α =' + str(i))\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise 3\n",
    "x[0] = 0\n",
    "\n",
    "for t in range(T):\n",
    "    x[t + 1] = 0.9 * abs(x[t]) + np.random.randn()\n",
    "    \n",
    "plt.plot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "range?\n",
    "for i in range(4):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.14588\n"
     ]
    }
   ],
   "source": [
    "# Exercise 5\n",
    "n = 100000\n",
    "\n",
    "count = 0\n",
    "for i in range(n):\n",
    "    # create two univorm RVs\n",
    "    u, v = np.random.uniform(), np.random.uniform()\n",
    "    # distance from origin > 0.5 == in or outside unit circle?\n",
    "    d = np.sqrt((u - 0.5)**2 + (v - 0.5)**2)\n",
    "    # index if d is in \n",
    "    if d < 0.5:\n",
    "        # equivalent to count = count + 1\n",
    "        count += 1\n",
    "\n",
    "area_estimate = count / n\n",
    "\n",
    "print(area_estimate * 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "basic syntax: def function_name(arguments): body return (indentation matters)\n",
    "- Any number of functions can be defined in a given file.\n",
    "- Functions can be (and often are) defined inside other functions.\n",
    "- Any object can be passed to a function as an argument, including other functions.\n",
    "- A function can return any kind of object, including functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# full list of python built-in functions: https://docs.python.org/3/library/functions.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# basic function syntax (super easy)\n",
    "def f(x):\n",
    "    return 2*x + 1\n",
    "\n",
    "f(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "# absolute function with ifelse like clause\n",
    "def abs_value(x):\n",
    "    x = x if x >= 0 else -x\n",
    "    return x\n",
    "\n",
    "print(abs_value(-1)) # if we don´t use print then only the last evaluation is shown...\n",
    "print(abs_value(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# from last lecture\n",
    "def ts_random(n):\n",
    "    ϵ_values = []\n",
    "    for i in range(n):\n",
    "        ϵ_values.append(np.random.randn())\n",
    "    return ϵ_values\n",
    "        \n",
    "x = ts_random(100)\n",
    "plt.plot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# adding a condition (as string!)\n",
    "def ts_random(n, gen_type):\n",
    "    ϵ_values = []\n",
    "    for i in range(n):\n",
    "        if gen_type == 'U':\n",
    "            ϵ_values.append(np.random.uniform())\n",
    "        else:\n",
    "            ϵ_values.append(np.random.randn())\n",
    "    return ϵ_values\n",
    "        \n",
    "x = ts_random(100, gen_type = 'U')\n",
    "plt.plot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pass gen_type as function\n",
    "def ts_random(n, gen_type):\n",
    "    ϵ_values = []\n",
    "    for i in range(n):\n",
    "        ϵ_values.append(gen_type()) # importantly, we have to set () after gen_type!\n",
    "    return ϵ_values\n",
    "\n",
    "x = ts_random(100, np.random.uniform)\n",
    "plt.plot(x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "120"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exercise 1\n",
    "def factorial(x):\n",
    "    x1 = x - 1\n",
    "    while x1 > 0:\n",
    "        x = x * x1\n",
    "        x1 = x1 - 1\n",
    "    return x\n",
    "\n",
    "factorial(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercise 2\n",
    "from numpy.random import uniform\n",
    "\n",
    "# binomial = number of success in n reps with individual success prob of p\n",
    "def binomial_rv(n, p):\n",
    "    count = 0\n",
    "    for i in range(n):\n",
    "        success = 1 if uniform(0, 1) > p else 0\n",
    "        count = count + success\n",
    "    return count\n",
    "\n",
    "binomial_rv(100, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'winner, winner, chicken dinner'"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exercise 3 (only second part)\n",
    "from numpy.random import uniform\n",
    "\n",
    "def in_tot(k):\n",
    "    head = [None] * 10\n",
    "    for i in range(10):\n",
    "        head[i] = 1 if uniform(1, 0) >= 0.5 else 0\n",
    "    # check whether k 1s in head\n",
    "    if sum(head) >= k:\n",
    "        ret = 'winner, winner, chicken dinner'\n",
    "    else:\n",
    "        ret = 'looser'\n",
    "    \n",
    "    return ret\n",
    "\n",
    "in_tot(1)        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Essentials"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Own Summary:\n",
    "- basic objects are\n",
    "    - lists [] or list(), \n",
    "    - tuples () or tuple(), \n",
    "    - dictionaries {} or dict() (with key value pairs)\n",
    "    - sets {} or set()\n",
    "    - strings\n",
    "- know how to access elements with [], enumerate over objects (preferred way with for loop and directly object), keys, etc.\n",
    "- list comprehensions (mathematical way of building list)\n",
    "- function docstring\n",
    "- lambda functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### List and Tuple (and Strings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'list'> [1, 2, 'dog']\n",
      "<class 'tuple'> (1, 2, 'cat')\n"
     ]
    }
   ],
   "source": [
    "# list\n",
    "list_object = [1, 2, 'dog']\n",
    "print(type(list_object), list_object)\n",
    "\n",
    "# tuples = immutable lists\n",
    "tuple_object = (1, 2, 'cat')\n",
    "print(type(tuple_object), tuple_object)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 dog\n"
     ]
    }
   ],
   "source": [
    "# unpacking the above objects\n",
    "x, y, z = list_object # same for tuple_object\n",
    "print(x, y, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 'dog']"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how to access elements of the objects above (slice)?\n",
    "list_object[1:3] # recall that the first element has index 0\n",
    "\n",
    "# The general rule is that a[m:n] returns n - m elements, starting at a[m].\n",
    "\n",
    "# second last object\n",
    "list_object[-2]\n",
    "\n",
    "# all from second last object and higher\n",
    "list_object[-2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'na'"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# works also for strings\n",
    "string = 'banana'\n",
    "string[-2:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sets and Dictionaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'name': 'Daniel', 'age': 27}"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Dictionaries = named (instead of numbered) lists\n",
    "dict_object = {'name' : 'Daniel', 'age' : 27} # keys (name and age) must be strings!\n",
    "dict_object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# access\n",
    "dict_object['age'] # as string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'set'> {'banana', 'apple'}\n"
     ]
    }
   ],
   "source": [
    "# Sets are unordered collections without duplicates, and set methods provide the usual set-theoretic operations\n",
    "set_object = {'a', 'b'}\n",
    "type(set_object)\n",
    "\n",
    "s1 = set_object\n",
    "s2 = {'b', 'c'}\n",
    "\n",
    "s1.issubset(s2)\n",
    "s1.intersection(s2)\n",
    "\n",
    "# create sets from sequences\n",
    "s3 = set(('banana', 'apple', 'banana'))\n",
    "print(type(s3), s3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Input and Output (reading and writing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'C:\\\\Users\\\\daniel.heimgartner\\\\Desktop\\\\Quant Econ'"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check present wd\n",
    "%pwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = open?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write\n",
    "f = open('newtextfile.txt', 'w') # w stands for writing\n",
    "f.write('first line\\n')\n",
    "f.write('second line')\n",
    "f.close()\n",
    "\n",
    "# check in pwd: newtextfile.txt is created"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first line\n",
      "second line\n"
     ]
    }
   ],
   "source": [
    "# read\n",
    "f = open('newtextfile.txt', 'r')\n",
    "textfile = f.read()\n",
    "print(textfile)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Iterating (over object)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "# if an object is iterable we can directly loop over it\n",
    "x = [1, 2, 3, 4]\n",
    "for i in x:\n",
    "    print(i)\n",
    "    \n",
    "# this is preferred to the indexed loop\n",
    "for i in range(len(x)):\n",
    "    print(x[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5\n",
      "1 6\n",
      "2 7\n",
      "3 8\n"
     ]
    }
   ],
   "source": [
    "# The usefulness of enumerate is yet to be shown to me in a concrete example...\n",
    "# if we actually need the index we can use enumerate()\n",
    "enumerate?\n",
    "# It allows us to loop over something and have an automatic counter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5\n",
      "1 6\n",
      "2 7\n",
      "3 8\n",
      "letter_list[0] = 'a'\n",
      "letter_list[1] = 'b'\n",
      "letter_list[2] = 'c'\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['a', 'b', 'c']"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# some enumerate examples\n",
    "some_list = [5, 6, 7, 8]\n",
    "for counter, value in enumerate(some_list):\n",
    "    print(counter, value)\n",
    "\n",
    "letter_list = ['a', 'b', 'c']\n",
    "for index, letter in enumerate(letter_list):\n",
    "    print(f\"letter_list[{index}] = '{letter}'\") # I guess {} makes a \"break\" in the string!\n",
    "\n",
    "letter_list\n",
    "\n",
    "x = ['hello', 'world']\n",
    "for index, i in enumerate(x):\n",
    "    x[index] = i + 'bla'\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### List Comprehensions (set-builder notation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range(0, 8)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0, 2, 4, 6, 8, 10, 12, 14]"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# list comprehensions are an elegant tool to create lists (from existing lists)\n",
    "animals = ['dog', 'cat', 'bird']\n",
    "plurals = [animal + 's' for animal in animals] # recall that animal is the \"uterative\" element of animals\n",
    "plurals\n",
    "\n",
    "# or (range(8) goes from 0 to 7)\n",
    "doubles = [2 * x for x in range(8)]\n",
    "doubles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### More on Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# docstrings (function descriptions)\n",
    "def f(x):\n",
    "    \"\"\"\n",
    "    This function squares its arguments\n",
    "    \"\"\"\n",
    "    return x**2\n",
    "f(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "# see the docstring (very nice)\n",
    "f?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "# double quotation marks returns even the source code\n",
    "f??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lambda to create one line functions\n",
    "f = lambda x: x**2\n",
    "f(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercise 5 \n",
    "# (mostly because of the nice function formatting...)\n",
    "def linapprox(f, a, b, n, x):\n",
    "    \"\"\"\n",
    "    Evaluates the piecewise linear interpolant of f at x on the interval\n",
    "    [a, b], with n evenly spaced grid points.\n",
    "\n",
    "    Parameters\n",
    "    ==========\n",
    "        f : function\n",
    "            The function to approximate\n",
    "\n",
    "        x, a, b : scalars (floats or integers)\n",
    "            Evaluation point and endpoints, with a <= x <= b\n",
    "\n",
    "        n : integer\n",
    "            Number of grid points\n",
    "\n",
    "    Returns\n",
    "    =======\n",
    "        A float. The interpolant evaluated at x\n",
    "\n",
    "    \"\"\"\n",
    "    length_of_interval = b - a\n",
    "    num_subintervals = n - 1\n",
    "    step = length_of_interval / num_subintervals\n",
    "\n",
    "    # === find first grid point larger than x === #\n",
    "    point = a\n",
    "    while point <= x:\n",
    "        point += step\n",
    "\n",
    "    # === x must lie between the gridpoints (point - step) and point === #\n",
    "    u, v = point - step, point\n",
    "\n",
    "    return f(u) + (x - u) * (f(v) - f(u)) / (v - u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OOP I: Introduction to Object Oriented Programming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast to the procedural paradigm, in the OOP paradigm data and functions are \"bundled together\" into \"objects\" (Functions in this context are referred to as methods). Python blends multiple paradigms but at its core **\"everything is an object\"**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1439603172144"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 2.5\n",
    "id(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1439603172112"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 2.5\n",
    "id(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Methods are functions that are bundled with objects (object.method)\n",
    "- Methods typically act on the data contained in the object they belong to, or combine that data with other data\n",
    "- **Important:** To check which methods are applicable for an object, just type the created object, followed by a dot and then the **tab key** (but does not depict all methods, right?) -> **dir(object)** can be used to access all the attributes!!\n",
    "- Everything in memory is treated as an object (not only lists, tibbles, etc. but also functions, files, modules, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [2.5, 3, 4]\n",
    "callable(x.append)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__add__',\n",
       " '__class__',\n",
       " '__contains__',\n",
       " '__delattr__',\n",
       " '__delitem__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__getitem__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__iadd__',\n",
       " '__imul__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__iter__',\n",
       " '__le__',\n",
       " '__len__',\n",
       " '__lt__',\n",
       " '__mul__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__reversed__',\n",
       " '__rmul__',\n",
       " '__setattr__',\n",
       " '__setitem__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " 'append',\n",
       " 'clear',\n",
       " 'copy',\n",
       " 'count',\n",
       " 'extend',\n",
       " 'index',\n",
       " 'insert',\n",
       " 'pop',\n",
       " 'remove',\n",
       " 'reverse',\n",
       " 'sort']"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# press: x.tabkey\n",
    "dir(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OOP II: Building Classes\n",
    "**Super Important Concept**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- As discussed an earlier lecture, in the OOP paradigm, **data and functions are bundled together into \"objects\"**.\n",
    "- **Classes** are blueprints that help you build objects according to your own specifications.\n",
    "- In Python, the data and methods of an object are collectively referred to as attributes. Attributes are accessed via \"dotted attribute notation\"\n",
    "- Objects are important because they allow us to implement abstractions.\n",
    "- (We can define new functions that take an object as an argument (or alternatively include the function as a method in the class..))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5, 4, 1]\n",
      "[1, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "x = [1, 5, 4]\n",
    "# sort(x) does not work -> OF COURSE NOT: you need to write: np.sort(a)!!!\n",
    "x.sort(reverse = True)\n",
    "print(x)\n",
    "x.sort()\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining Your Own Classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- For me, a `class` is like a unified collection of functions that act on an object...\n",
    "- First, we will define a **consumer** class which can be modified by different methods.\n",
    "- In Python, the data and methods of an object are collectively referred to as attributes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# very cool\n",
    "class Consumer:\n",
    "\n",
    "    def __init__(self, w):\n",
    "        \"Initialize consumer with w dollars of wealth\"\n",
    "        self.wealth = w\n",
    "\n",
    "    def earn(self, y):\n",
    "        \"The consumer earns y dollars\"\n",
    "        self.wealth += y\n",
    "\n",
    "    def spend(self, x):\n",
    "        \"The consumer spends x dollars if feasible\"\n",
    "        new_wealth = self.wealth - x\n",
    "        if new_wealth < 0:\n",
    "            print(\"Insufficent funds\")\n",
    "        else:\n",
    "            self.wealth = new_wealth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This class defines **instance data** `wealth` and **three methods**: `__init__`, `earn` and `spend`. *self* is actually necessary and enables the later use of Consumer.method calls..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# usage\n",
    "c1 = Consumer(11)  # create instance with initial wealth 10\n",
    "c1.spend?\n",
    "c1.spend(5)\n",
    "c1.wealth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25\n",
      "Insufficent funds\n"
     ]
    }
   ],
   "source": [
    "c1.earn(20)\n",
    "print(c1.wealth) # use tab key for feasible methods\n",
    "c1.spend(26)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: The Solow Growth Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let´s write a simple `class` to implement the Solow growth model:\n",
    "- the object (instance) mantains track of the current capital stock in the variable `self.k`\n",
    "\n",
    "there exists several methods that act on this object:\n",
    "- the method `h` implements the RHS of the formula\n",
    "- the method `updata` updates the capital stock with help of `h` according to the formula\n",
    "- the method `steady_state` computes the steady state according to the formula by setting k+1 = k\n",
    "- the method `generate_sequence` generates a time-series according to the formula (iteratively applies and updates k)\n",
    "\n",
    "**Remark**: as seen in this example a class can easily be leveraged to compute time series data (with update method) according to some difference equation (model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Solow:\n",
    "    \"\"\"\n",
    "    Implements the Solow growth model with the update rule\n",
    "\n",
    "        k_{t+1} = [(s z k_t^α) + (1 - δ)k_t] /(1 + n)\n",
    "\n",
    "    \"\"\"\n",
    "    def __init__(self, n=0.05,  # population growth rate\n",
    "                       s=0.25,  # savings rate\n",
    "                       δ=0.1,   # depreciation rate\n",
    "                       α=0.3,   # share of labor\n",
    "                       z=2.0,   # productivity\n",
    "                       k=1.0):  # current capital stock)\n",
    "        \"Initialize parameters and capital stock\"\n",
    "        self.n, self.s, self.δ, self.α, self.z, = n, s, δ, α, z\n",
    "        self.k = k\n",
    "        \n",
    "    def h(self):\n",
    "        \"Implement RHS of formula\"\n",
    "        # unpack parameters\n",
    "        s, z, k, α, δ, n = self.s, self.z, self.k, self.α, self.δ, self.n\n",
    "        return ((s * z * k**α) + (1 - δ) * k) / (1 + n)\n",
    "    \n",
    "    def update(self):\n",
    "        \"Update the capital stock (leveraging method h)\"\n",
    "        self.k = self.h() # no return command here (quietly update)!\n",
    "        \n",
    "    def steady_state(self):\n",
    "        \"Compute st-st of economy\"\n",
    "        # unpack parameters (get rid of self to simplify notation)\n",
    "        n, s, δ, α, z = self.n, self.s, self.δ, self.α, self.z\n",
    "        return ((s * z) / (n + δ))**(1 / (1 - α))\n",
    "    \n",
    "    def generate_sequence(self, t): # note the additional parameter here!\n",
    "        \"Generates capital stock time-series\"\n",
    "        path = []\n",
    "        for i in range(t):\n",
    "            path.append(self.k) # how do these two lines exactly work? -> see test class below (clear)...\n",
    "            self.update() # recall, update basically overwrites (updates) self.k which then is appended in the next iteration\n",
    "        return path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = Solow()\n",
    "# s1. press tab key -> __init__ is not a method but initializes all the parameters (which in turn are methods...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Apply\n",
    "# with prespecified parameters (in class definition)\n",
    "s1 = Solow()\n",
    "# with higher capital stock\n",
    "s2 = Solow(k = 8)\n",
    "\n",
    "T = 60\n",
    "\n",
    "# steady state\n",
    "fig, ax = plt.subplots(figsize = (9, 6))\n",
    "ax.plot([s1.steady_state()] * T, 'k-', label = 'steady state')\n",
    "\n",
    "# sequences\n",
    "for s in s1, s2:\n",
    "    lb = f'capital series from initial state {s.k}'\n",
    "    ax.plot(s.generate_sequence(T), 'o-', lw = 2, alpha = 0.6, label = lb)\n",
    "    \n",
    "ax.set_xlabel('$k_{t+1}$', fontsize=14)\n",
    "ax.set_ylabel('$k_t$', fontsize=14)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Test:\n",
    "    \"\"\"\n",
    "    understand the line in the for loop of the class Solow, method generate_sequence\n",
    "    \"\"\"\n",
    "    def __init__(self, s = 10, a = 3):\n",
    "        self.s = s\n",
    "        self.a = a\n",
    "    \n",
    "    def add(self):\n",
    "        \"Add a to the starting value s\"\n",
    "        self.s = self.s + self.a\n",
    "        return self.s\n",
    "    \n",
    "    def test(self, t):\n",
    "        \"Generates sequence by iteratively overwriting s\"\n",
    "        test = []\n",
    "        for i in range(t):\n",
    "            test.append(self.s)\n",
    "            self.add() # adds a to s (-> new s; overrides self.s!) which is then appended in the next! loop\n",
    "        return test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = Test(s = 0, a = 0)\n",
    "t.test(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: A Market"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 1 good economy where all agents are price takers\n",
    "- a linear demand curve\n",
    "- a linear supply curve (the firm has to pay tax)\n",
    "\n",
    "Methods to include:\n",
    "- equilibrium `price` and `quantity`\n",
    "- `consumer_surp` and `producer_surp`\n",
    "- tax revenue `tax_rev`\n",
    "- inverse demand and supply `inv_demand`, `inv_supply`\n",
    "- tax absent case `inv_supply_no_tax`\n",
    "\n",
    "**Good example to understand how methods can be referred to within methods**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {},
   "outputs": [],
   "source": [
    "# to compute areas under surface (consumer and producer surplus)\n",
    "from scipy.integrate import quad\n",
    "\n",
    "class Market:\n",
    "    \"\"\"\n",
    "    Simulates a simple one good market economy where producers are taxed\n",
    "    AD: Q = ad - bd * p\n",
    "    AS: Q = az - bz * (p - tax)\n",
    "    \"\"\"\n",
    "    def __init__(self, ad, bd, az, bz, tax):\n",
    "        self.ad, self.bd, self.az, self.bz, self.tax = ad, bd, az, bz, tax\n",
    "        if ad < az:\n",
    "            raise ValueError('Insufficient Demand.')\n",
    "            \n",
    "    def price(self):\n",
    "        \"Computes equilibrium price\"\n",
    "        # unpack params\n",
    "        ad, bd, az, bz, tax = self.ad, self.bd, self.az, self.bz, self.tax\n",
    "        return (ad - az + bz * tax) / (bz + bd)\n",
    "    \n",
    "    def quant(self):\n",
    "        \"Computes eq quant\"\n",
    "        # plug in self.price in demand (or supply) -> method referred to in method\n",
    "        return self.ad - self.bd * self.price()\n",
    "    \n",
    "    def cons_surp(self):\n",
    "        \"Computes consumer surplus (= area under invers demand curve)\"\n",
    "        integrand = lambda x: (self.ad / self.bd) - (1 / self.bd) * x # inv. demand (where x is the quantity)\n",
    "        area, error = quad(integrand, 0, self.quant()) # upper bound == self.quantity()!! \n",
    "        # see function documentation: first output argument (as dictionary) = integral, second = estimated error\n",
    "        return area - self.price() * self.quantity()\n",
    "    \n",
    "    def prod_surp(self):\n",
    "        \"Computes producer surplus (= area under inverse supply curve)\"\n",
    "        integrand = lambda x: -(self.az / self.bz) + (1 / self.bz) * x\n",
    "        area, error = quad(integrand, 0, self.quant())\n",
    "        return (self.price() - self.tax) * self.quant() - area\n",
    "    \n",
    "    def tax_rev(self):\n",
    "        \"Computes tax revenue\"\n",
    "        return self.tax * self.quant()\n",
    "    \n",
    "    def inv_demand(self, x):\n",
    "        \"Computes inverse demand\"\n",
    "        return self.ad / self.bd - (1 / self.bd) * x\n",
    "    \n",
    "    def inv_supply(self, x):\n",
    "        \"Computes inverse supply\"\n",
    "        return -(self.az / self.bz) + (1 / self.bz) * x + self.tax\n",
    "    \n",
    "    def inv_supply_no_tax(self, x):\n",
    "        \"Compute inverse supply curve without tax\"\n",
    "        return -(self.az / self.bz) + (1 / self.bz) * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Baseline ad, bd, az, bz, tax\n",
    "baseline_params = 15, .5, -2, .5, 3\n",
    "m = Market(*baseline_params) # !! the * to initialize all the params\n",
    "\n",
    "q_max = m.quant() * 2\n",
    "# quantity grid\n",
    "q_grid = np.linspace(0.0, q_max, 100)\n",
    "# for each grid point compute price demand, price supply\n",
    "pd = m.inv_demand(q_grid)\n",
    "ps = m.inv_supply(q_grid)\n",
    "# supplier price in absence of taxes (again for each grid point)\n",
    "psno = m.inv_supply_no_tax(q_grid)\n",
    "\n",
    "# plot\n",
    "# initiate plot \"ax\"\n",
    "fig, ax = plt.subplots()\n",
    "# add inverse demand\n",
    "ax.plot(q_grid, pd, lw=2, alpha=0.6, label='demand')\n",
    "# add inverse supply with and without tax\n",
    "ax.plot(q_grid, ps, lw=2, alpha=0.6, label='supply')\n",
    "ax.plot(q_grid, psno, '--k', lw=2, alpha=0.6, label='supply without tax')\n",
    "# set information (aes)\n",
    "ax.set_xlabel('quantity', fontsize=14)\n",
    "ax.set_xlim(0, q_max)\n",
    "ax.set_ylabel('price', fontsize=14)\n",
    "ax.legend(loc='lower right', frameon=False, fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**very neat**: we now can create a **function** for applied on an \"Market\" **object** / instance (so the object is actually the argument) that computes the deadweight. We could alternatively write a method in the class definition..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deadw(m):\n",
    "    \"Computes deadweight loss for market m.\"\n",
    "    # == Create analogous market with no tax == #\n",
    "    m_no_tax = Market(m.ad, m.bd, m.az, m.bz, 0)\n",
    "    # == Compare surplus, return difference == #\n",
    "    surp1 = m_no_tax.consumer_surp() + m_no_tax.producer_surp()\n",
    "    surp2 = m.consumer_surp() + m.producer_surp() + m.taxrev()\n",
    "    return surp1 - surp2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [],
   "source": [
    "# deadw is a function!\n",
    "deadw?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Special Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predefined methods `__name__` that have a special meaning:\n",
    "- For example the `__len__` special method enables an object to be passed to the len(object) function and returns the \"length\" of the object.\n",
    "- Or the special method `__call__` which makes your object callable like a function object() and returns whatever you defined in the `__call__` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercise 1 \n",
    "# (only copy pasted; but it makes the point for __call__ special method very nicely)\n",
    "class ECDF:\n",
    "    \"\"\"\n",
    "    Computes the empirical cumulative distribution function for any instance data\n",
    "    \"\"\"\n",
    "    def __init__(self, observations):\n",
    "        self.observations = observations\n",
    "\n",
    "    def __call__(self, x):\n",
    "        counter = 0.0\n",
    "        for obs in self.observations:\n",
    "            if obs <= x:\n",
    "                counter += 1\n",
    "        return counter / len(self.observations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4\n",
      "0.494\n"
     ]
    }
   ],
   "source": [
    "# == test == #\n",
    "\n",
    "from random import uniform\n",
    "\n",
    "# create sample (data instance, observations)\n",
    "samples = [uniform(0, 1) for i in range(10)]\n",
    "\n",
    "# creates an object of class ECDF\n",
    "F = ECDF(samples)\n",
    "\n",
    "# evaluate ecdf at x = 0.5 (object is callable!)\n",
    "print(F(0.5))\n",
    "\n",
    "# overwrite observations in the object with a new sample\n",
    "F.observations = [uniform(0, 1) for i in range(1000)]\n",
    "\n",
    "print(F(0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII\n",
    "# The Scientific Libraries\n",
    "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Scientific Computing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- \"For example, it’s almost always better to use an existing routine for root finding than to write a new one from scratch.\"\n",
    "- Concept of **Vectorization** (speed): is the process of converting an algorithm from operating on a single value at a time to operating on a set of values at one time. Many operations can be vectorized...\n",
    "- There exist many so-called universal functions (f.ex. when you call functions from NumPy) that implement the concept of vectorization (f.ex. by working element wise on vectors / arrays). **General Remark**: don´t use loops when not necessary\n",
    "- The big (4 + 1) 5 in the scientific ecosystem: `NumPy`, `SciPy`, `Matplotlib`, `Pandas` (and `Numba`)\n",
    "\n",
    "**Overview:**\n",
    "- NumPy forms the foundations by providing a basic array data type (think of vectors and matrices) and functions for acting on these arrays (e.g. matrix multiplication).\n",
    "- SciPy builds on NumPy by adding the kinds of numerical methods that are routinely used in science (interpolation, optimization, root finding, etc.).\n",
    "- Matplotlib is used to generate figures, with a focus on plotting data stored in NumPy arrays.\n",
    "- Pandas provides types and functions for empirical work (e.g., manipulating data).\n",
    "- Numba accelerates execution via JIT compilation — we’ll learn about this soon."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- library for numerical programming (here: numerical as opposed to f.ex. text...)\n",
    "- NumPy arrays and its operations (for fast array processing)\n",
    "- if `import numpy as np` stands in the cell, you can use np. + tab key to access subpackages and functions (f.ex. np.zeros is a function, whereas np.random is a subpackage containing more functions s.a. np.random.randn...\n",
    "- another useful subpackage is `linalg` for f.ex. matrix inversion or computation of determinants,... (SciPy has also a package linalg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### NumPy Arrays\n",
    "- somewhat similar to native Python lists with the difference that all elements must be of the same data type (`dtypes` provided by Numpy)\n",
    "- dtypes are f.ex. integers, floats, etc.\n",
    "- you have to give the np.array the dimension manually\n",
    "- `np.arrays` (can also be created from lists and tuples)\n",
    "- `np.zeros`, `np.ones`, `np.empty`, `np.linspace` (grid of evenly spaced numbers = **grid**), `np.identity` or `np.eqe`\n",
    "- operations `+, -, *, \\, **` all act **elementwise**! If A and B are both 2D arrays (matrices) it follows that `A * B` is not the matrix product!\n",
    "- use `@` for matrix multiplication or inner product (if vectors)\n",
    "- **Careful:** when you mute an array and assign a \"copy\" (of a) of the array to a new name b and mute (change) an element of b, then that element is also changed in a!\n",
    "- **\"Solution\":** if you want to make an independent copy, use `np.copy()`\n",
    "- **Very nice:** use `np.vectorize()` in order to vectorize user defined functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0.]\n",
      "<class 'numpy.ndarray'>\n",
      "<class 'numpy.float64'>\n"
     ]
    }
   ],
   "source": [
    "# create an empty np.array of zeros\n",
    "a = np.zeros(3)\n",
    "print(a)\n",
    "print(type(a))\n",
    "print(type(a[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.int32'>\n"
     ]
    }
   ],
   "source": [
    "# specify element type (dtype) manually\n",
    "a = np.zeros(3, dtype = int)\n",
    "print(type(a[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**General remark:** press `shift + tab` to get function arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10,)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# shape and dimension\n",
    "a = np.zeros(10)\n",
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape = (2,5)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0.],\n",
       "       [0., 5., 0., 0., 0.]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1,1] = 5\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.52631579,  1.05263158,  1.57894737,  2.10526316,\n",
       "        2.63157895,  3.15789474,  3.68421053,  4.21052632,  4.73684211,\n",
       "        5.26315789,  5.78947368,  6.31578947,  6.84210526,  7.36842105,\n",
       "        7.89473684,  8.42105263,  8.94736842,  9.47368421, 10.        ])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.linspace\n",
    "np.linspace(0, 10, 20) # (press shift + tab after np.linspace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 20 30 40]\n",
      "[10 20 30 40]\n"
     ]
    }
   ],
   "source": [
    "# np.array\n",
    "a = np.array([10, 20, 30, 40])\n",
    "b = np.array((10, 20, 30, 40)) # equivalently with round brackets (tuple)\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 20],\n",
       "       [30, 40]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape = (2,2)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2D (matrix-) array (from a list of lists)\n",
    "z = np.array([[1, 2], [3, 4]])\n",
    "print(z)\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Array Indexing\n",
    "- very intuitive\n",
    "- use [] brackets to index\n",
    "- you can use other arrays (f.ex. an index array or a boolean array) to index an array\n",
    "- you can overwrite elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.linspace(1, 10, 10)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  7.,  5.,  6.,  7.,  8.,  9., 10.])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[3] = 7 # zero based indexing!\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 3., 8., 9.])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = np.array([0, 1, 1, 0, 0, 0, 0, 1, 1, 0], dtype = bool)\n",
    "z[index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3., 4., 5.])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# index rows (or cols) in a 2D array\n",
    "z = np.linspace(1, 10, 10)\n",
    "z.shape = (2, 5)\n",
    "z[0, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[:,:] = 0\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Array Methods\n",
    "- s.a. `np.sum()`, `np.sort()`, `np.cumsum()`, `np.var()`, `np.searchsorted()`, etc.\n",
    "- many (but not all - vgl. sort - of the methods discussed above have equivalent functions in the NumPy namespace -> np.sum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 1. , 2. , 3. , 4. , 5. , 6. , 7. , 8. , 9. ])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "# np. + press tab (works only if import statement is in cell - cell needs not to be run first...)\n",
    "z = np.linspace(1, 10, 10)\n",
    "z[9] = 0.5\n",
    "z.sort()\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 1. , 2. , 3. , 4. , 5. , 6. , 7. , 8. , 9. ])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# equivalently with function instead of method\n",
    "z = np.linspace(1, 10, 10)\n",
    "z[9] = 0.5\n",
    "a = np.sort(z)\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Additional Functionality\n",
    "- most of np functions are vectorized -> `ufuncs` (universal functions) = they act elementwise\n",
    "- not all user defined functions work element wise -> error will be returned when applying to an array\n",
    "- **Very nice:** use `np.vectorize()` to vectorize a user defined function\n",
    "- `np.where()` is also useful"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.69066642e-01,  1.00000000e+02,  2.80531502e-01,  1.00000000e+02,\n",
       "        1.00000000e+02,  6.88872339e-01, -4.06602915e-01, -2.05600586e-02,\n",
       "        6.38776548e-02, -3.26002249e-01])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randn(10)\n",
    "np.where(x > 1, 100, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False False False False False False  True  True  True  True  True]\n",
      "[ 6.  7.  8.  9. 10.]\n"
     ]
    }
   ],
   "source": [
    "# useful for extraction\n",
    "a = np.linspace(0, 10, 11)\n",
    "b = a > 5\n",
    "print(b)\n",
    "c = a[b]\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercise 2\n",
    "import numpy as np\n",
    "# use np.searchsorted and np.cumsum\n",
    "\n",
    "def sample(q):\n",
    "    a = 0 # lower bound\n",
    "    U = np.random.uniform(0, 1)\n",
    "    q = np.asarray(q) # make sure that q is an array\n",
    "    index = np.searchsorted(q, U)\n",
    "    q = q[0:index]\n",
    "    return np.cumsum(q)\n",
    "\n",
    "class DiscreteRW:\n",
    "    \"\"\"\n",
    "    q is the probability vecotor and the instance data of the class. The Method draw(k) returns an array of k random variables.\n",
    "    \"\"\"\n",
    "    def __init__(self, q):\n",
    "        self.q = q\n",
    "        \n",
    "    def draw(self, q, k):\n",
    "        # unpack params\n",
    "        q, k = self.q, self.k\n",
    "        np.vectorize(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import cumsum\n",
    "from numpy.random import uniform\n",
    "\n",
    "class DiscreteRV:\n",
    "    \"\"\"\n",
    "    Generates an array of draws from a discrete random variable with vector of\n",
    "    probabilities given by q.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, q):\n",
    "        \"\"\"\n",
    "        The argument q is a NumPy array, or array like, nonnegative and sums\n",
    "        to 1\n",
    "        \"\"\"\n",
    "        self.q = q\n",
    "        # self.Q = cumsum(q) this yields a problem when updating q as in next sell (Q is not updated...)\n",
    "\n",
    "    def draw(self, k=1):\n",
    "        \"\"\"\n",
    "        Returns k draws from q. For each such draw, the value i is returned\n",
    "        with probability q[i].\n",
    "        \"\"\"\n",
    "        Q = cumsum(self.q) # see remark above -> that´s why we init. Q here\n",
    "        return self.Q.searchsorted(uniform(0, 1, size=k))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.5, 0.5)\n",
      "[0.1 1. ]\n",
      "[0.1 1. ]\n",
      "[0.5 1. ]\n"
     ]
    }
   ],
   "source": [
    "q = (0.1, 0.9)\n",
    "d = DiscreteRV(q)\n",
    "d.q = (0.5, 0.5)\n",
    "print(d.q)\n",
    "print(d.Q)\n",
    "print(np.cumsum(q))\n",
    "print(np.cumsum((0.5, 0.5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 0, 1, 1, 1, 1, 1], dtype=int64)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.draw(k = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Open Question (probably not too relevant):** when defining a method in a class, can we define a function within the method and then call the function (like when writing a nested function?)? Can we use a function within a method which is defined outside the class?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matplotlib\n",
    "- `fig, ax = plt.subplots()` returns a pair and both `fig` and `ax` are **classes / instances** with different **methods**!\n",
    "- F.ex. `ax.plot()` is a method applicable to the ax object\n",
    "- **Explore:** by `. + tab-key` (only works if the object have been initialized befor = command has been run...)\n",
    "- The plots are built layer by layer -> f.ex. you define in ax.plot(..., label = 'bla') the label but you need to add the line (method) `ax.legend()` to explicitly plot it!\n",
    "- The layers are added via methods supplied to ax -> `as. + tab-key`\n",
    "- You can easily define a `subplot()` function that initializes the plot via `fig, ax = plt.subplots()` makes modifiactions to via different layers (ax.method) and returns `return fig, ax`.\n",
    "- **Further Readings:** \n",
    "    - The [Matplotlib gallery](https://matplotlib.org/gallery.html) provides many examples.\n",
    "    - A nice [Matplotlib tutorial](http://scipy-lectures.org/intro/matplotlib/index.html) by Nicolas Rougier, Mike Muller and Gael Varoquaux.\n",
    "    - [mpltools](http://tonysyu.github.io/mpltools/index.html) allows easy switching between plot styles.\n",
    "    - **Promising:** [Seaborn](https://github.com/mwaskom/seaborn) facilitates common statistics plots in Matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# plt. + tab key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 10, 200)\n",
    "y = np.sin(x)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, y, 'b-', linewidth = 2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.boxplot(np.random.randn(100))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# explicitly add a legend\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, y, 'r+', label = 'sin wave')\n",
    "ax.legend() # without this line, the label 'sin wave is not plotted'; add parameters (similar to ggplot)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# multiple plots\n",
    "z = np.cos(x)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, y, 'r+', label = 'sin wave')\n",
    "ax.plot(x, z, 'b-', label = 'cos wave')\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "from random import uniform\n",
    "\n",
    "num_rows, num_cols = 3, 2\n",
    "fig, axes = plt.subplots(num_rows, num_cols, figsize=(10, 12))\n",
    "\n",
    "# loop over the subplot matrix\n",
    "for i in range(num_rows):\n",
    "    for j in range(num_cols):\n",
    "        m, s = uniform(-1, 1), uniform(1, 2)\n",
    "        x = norm.rvs(loc=m, scale=s, size=100)\n",
    "        axes[i, j].hist(x, alpha=0.6, bins=20) # method applies to axes (see above axes instead of ax...)\n",
    "        t = f'$\\mu = {m:.1}, \\quad \\sigma = {s:.2}$' # see below: title = t (0.2 stands for two decimals); don´t get the syntax fully\n",
    "        axes[i, j].set(title=t, xticks=[-4, 0, 4], yticks=[])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6w3KZnm4M1Z/p2W6XbDs373a7hF3BrpRg5LYBbGZgdy3lLu6//YwUzLuYarWUGxsbrK2tEQ6Heeihh4hEIk2dK0gLM5PJMDc3x+HDh3nkkUe8GI4keCqVurixNfeGKp1Ok8/n6e3t9YR0tz6XdpeV2Lbd1trYSoJdKcGokYHdO5W7GIbh9dMtdenuJ2tUCuZdSLVaykQiQTwe91w/9913XyDnDEIwU6kUQ0NDFAoFjh49yqVLlwJZW9DW0Z1oYdZDuVZyP/rRjzhy5Ai2bXvF+/l8nnA4XOTSbUWpS7tdsu22MC3LqjlEIkRwA7v973k+nyeRSCCEKCp3cdkvzRekYN5FVKulzGQyxONxCoUCg4ODdHV1cfPmzcDO3Yxg5nI5RkZGvFFgrpswCFxxk4LZPB0dHcRiMS+2VmrNlJa6+LsXNVPqIgWz+aSjegZ2a5q2rYORK9qV3LrVyl1+8IMfcPXq1bZltAeJFMy7gGq1lPl8ntHRUTY2NrxaSn+yS1AoirLtrnMnTNNkfHycpaUlzp07x5UrVxBCsLi42NKMW0n9lHsPK1kz5fqxugOf/dZorfHydgvWXjh/K2pr/QlG/haOhmF4n9/09DTpdBrDMBBCMDk5uW3Q+k7lLp/61Kf4nd/5HSmYkvZTqZbSFaPFxUXOnj3Lvffe29K79HosTNu2mZ6e5tatW2XLV1pdorIXj3knUOv3p1Kpi9u9aGVlhYmJiZpLXaSFWbtLNgh0Xaevr69o6PvS0hIrKyuEw+Gi7lP+gd2uS7603CWVSjU9KWivIAXzDsUvlFA8bmtycpLp6WlOnTrFjRs3duVir0XkHMdhcXGR0dFRDh8+XDHzNUhBarSRezX2o2A2K1rlBj7XWuqy37Nk231+wIt3Hjt2zHvMdcm71ujy8jLZbNbLsh4aGiIajZLJZOoWzGeeeYavfe1rHDlyhDfffHPb7x3H4cMf/jDf+MY36Ojo4Atf+AIPPfRQ069zJ6Rg3mFUG7c1MzPDxMRES8swKrGTYK6trTE8PEwsFtsxK3e3LMyNjQ1GR0e9DTqIeJukdiqVuhiG4cVFJycnWV9fRwhBMpksKnXZre93uwVrty3MSmsofb/9LvlyA7t/+MMf8rWvfY2JiQlu3LjBmTNnuHr1Kj/5kz/Je97znqrne/rpp/mVX/kVfuEXfqHs7//yL/+SeDxOPB7n5s2b/NIv/VKgORmVkIJ5h1BNKF2rra+vr20NyCuJXDqdZnh4GMdxuHLlSpGFUe+xGqFcy75cLsfw8DD5fJ4zZ85g2/a2eJtbh+hu0P7NQlqYrUXX9aJSl6mpKa+Ewl/q4lo9fmvUnVMZJHtBMPeChVnrvuJmWT/11FP8/M//PO9973t55ZVXmJyc5LXXXvOaLlTjx37sx5iYmKj4+2effZZf+IVfQAjB9evXWV9fZ25urqhtZCuQgrnHcYXSMAxefPFFrl+/7m0Ia2trxONxotEoDzzwANFotKHjB7HBlIqcm2yUSCQYHBwsqvPbiSAFyX8sf5LRhQsXOHTokJcoVa61XDKZ9G5GLMvyeny6fTubrV29k2h3a7xypS6lbeSmp6cpFApeXM0/qLuZtbdbMFuV9FMPpmk2tL+4KIrCmTNnOHPmTCDrmZmZYWBgwPu5v7+fmZkZKZj7ldISETcW57qm4vE4APfee29R4XI9uNZXEBejK5imaTIxMcHCwgLnzp1rKNmoFRbm1NQUt27dYmBgYMf2epUKwt2klUKhQDwex7KsoqSVrq4uwuHwXVl/1k4qxTArtZHzTwZxC/ebKXVpt2DuFZdsI2to1XtXKWu71UjB3GNUq6W0bZs33niDbDbLhQsXirLYGsFtZxfExSiEIJVK8f3vf5+BgYGmko2CtDALhQKvvvoqhw8f5rHHHms47uUmMsRiMW+KSzQaLUpamZ2dJZ/Po+u6J6C7PbeyVbTbwqznu1QurtZMqcteEMxmp80EsYZGrp10Ol1TGKZe+vv7mZqa8n6enp7mxIkTgZ+nFCmYe4RqtZSFQoGxsTEymQwXL17k0KFDgWxeqqo2fTE6jsPS0pIXp7x+/XrTF3cQFmYymWRoaIhcLseVK1eK6gSDwBWQSv1Zk8mk59J1i/n9IroXm5xXo92C2ey5Gyl1cUW03THEveCSbdTCTCQSDXvAqvHkk0/ymc98hqeeeoqbN2/S09PTcncsSMHcE1SrpZycnGR+fp4zZ84Qi8WKNuZmaVaY1tfXGR4eJhqNct999zE6OhrInXAzpSD5fJ54PE46nebixYtMTU0F3vN0p807FApx8ODBIgvHLQZPJpPcunWLdDqNEKJoY3YHCEuKaZVY11LqMj8/TyqV4rXXXitKAnPHa+0Ge8Ela5pmQxZmMpksijvXyj/6R/+I73znOywvL9Pf389v/uZveo1R/tk/+2c88cQTfOMb3+D8+fN0dHTw+c9/vu5zNIIUzDZSrZbSjbn19/d77s3JyclA3UOuhVkvmUyG4eFhLMvyYqiFQqGlma07YVkWExMTzM/PF3UNmp6eDmxd/vXVK+jlisH9/T3dAcJ+N2FQw5+DYL9MKynnNXjppZd417ve5Ymof7xW6Q1PK0pd2u0Sht23ML/0pS9V/b0Qgs9+9rN1H7dZpGC2Adf16oqVv0RkdnaW8fFxjhw5sq2W0hW4oC6eei3MQqGwrc1eo8cKal2O4zA3N8f4+DgnT57cFjvdyyUg5fp7+t2ES0tLjI2NeeUTtm3T0dHhZYLuJu18D9s9rQQq3/C447XKNTR3b3qaLXXZCxZmM4LZiIW5V5GCuYtUq6VcWlpiZGSE3t7eiiOtgog5ljveTvittzNnznDp0qVtG0DQglnLBr26usrw8DA9PT0V60/vtNZ4fjehf/hzNptlYmKCTCbDj370I2/uod8SLddWLkju5BhmK6in1MVNBPM3NK/1Ne0FwYTGPv9kMnnXtMUDKZi7QrW5lOvr68TjccLhMFevXqWjo6PicRp1oVZiJ5FzuwdNTk6Wtd5KjxVk7WS1dbnNEADuv/9+YrFY1WNVW1cjm8BuW61u+URXVxeapnH8+HEcxyGfz3vJRW5buWY25mrsF5dsOer5rGspdVleXi6aUenvXlROGPeCS7bR77vbneluQQpmC6k2lzKVShGPx7Ftm0uXLtX0pdotwXQch+XlZUZGRjhw4ACPPvrorsbRKm2Ofpdwrc0QWtFLdi8ghCASiRCJRMpm6Lq9Pf01iP72f+3egOthL7hkm6VSqYvbIGN2dpZ0Oo1t28RisSIh3SsWZiMkEomi/rN3OlIwW4B795/P5734hXvB+2c/Xrhwoa4OOEELZrnjbWxsMDw8TDgcbrh7UNC4DeVnZ2cruoQr0UgCUS3H3KsiXC5D161B9CesuHWlfpdutU35Ti8raYZWnVvTtIox7FQqxcrKCpOTk2xsbPDWW2/R3d3tWaK7WdvbzPufSqWkhSkpj1tLaRgGKysrLC0tce+99wKbZQVjY2OsrKwUZXHWQyssTPd47oBpwzC4ePHingjUO47jJVO4DeXrvdO+02KYraBcDaKbsOK6c0szdMsV8u9Hwdztz9kfw3YtsxdffJGLFy96GdXz8/NlBz23ynPQjIUrY5iSbTiOg+M4RbWUuq5jWRaWZTE5Ocnc3BynT59mcHCw4Yu/FRamYRi88847rK2tef1V9wKWZfHiiy/S2dlZMQmqFmoRt3ZbMO2gXMJKpUL+aDRKPp9neXnZa/+3m7QzhrlXvhuVprqUK3VxPQeukDZb6tKsYO6Fm++gkILZJJWaDiiKQjKZ5Pvf/z4nTpxoyDoqJUjBtCyL1dVVVldXGRwc5OLFi3tiY8hms94kkQceeKBpd87dZGFmZ2fpOnWqZcevVMifzWZ57bXXirI+w+FwUVy0lRm67Yxh7oWEm0pUKnWpVJbkj4vW0/PYNM2G9y5ZViIBqtdSzs/PMzIygm3b3LhxY9fLQKrhr1vs7Oykv7+fkydPBrK+ZnBd1qurq1y4cIF0Oh1I7ONuGCCdnJri+X/9r7n1/POc/PEf5/3//t+j7lISlpv1qes6586dA24PDnYzdP0uwtL2f3dDhm67BbOe1+5vweji3vSkUik2NjaYmZkp6nnsCmk0Gi37WhvtIwubFqY/FHCnIwWzTqqViKysrBCPx+nq6uKBBx7grbfeCjS71HWhNsry8jLxeJze3l6uXbvGxsYGa2trga3PFZJ6LnDbtpmenmZqaopTp055Lmu3bCSINQWd9LNbWIbB8G//Nu/81/+KaZrEQiFWnn+e5/7e3+PS3/27HHrsMbrvv3/XxcQ/ONjvwncHP/tLJ/wZuq71Wq8AtdMluxcEs1n8pS5HjhzxHi+XUV2u1EXGMG8jBbNGqgllIpFgeHgYTdO8ukDbtgONN8KmYOZyubr/zl2frutFtZ5BNhvwH6+Wi8vfrKHZSSLVuFNdsnN/8ReM/rt/RyKZxMrlEEBICKKaRufICK//4R+S/8Qn0MJhevr7ufbbv03vgw+2dE07UTr4GYozdGdmZkilUkB9LeX2s0u2ld+zchnVbrtGfzJYoVBAVVUmJyeLBnXXQi6Xu6vmxkrB3IFqtZTpdJp4PI5pmly4cKHoTqoVrkB3HFetZLNZ4vE4+XyewcHBbXd67RLMRCLB0NAQ4XCYhx56qOIFFYQrrhWNC6B1G5lt27z6gQ+Q+N73cIQgqyggBNFwGC2TQbEsTEWhT9dZVlXMfJ6V0VH+5gMf4G/98R9z4NFHW7KuRqk0JcTN+PS3lPP30PVn6O5nl+xun79cu0ZXOMPhMGtra9y6dcsboO6/6SktdXGTIe90C92PFMwKVJtLmc/nGR0dJZFIbOup2koURfEs3Gr4S1jczNdyG06rylQquaFzuRzxeJxcLldWwP004t6tdpxyuCPACoVC0Ua9U3p+Kzfvod/4DRLf+x4AuUgEJ5ulIxIhnMthOQ5sndvKZOjt7mYjncawLIxMhrd++Ze5/Pu/z4H3vrdl6wsCRVHKtpSrNGorl8uxsrJCd3d3031Z66XdgrkXmha4PYz9DQjcWnPXGl1YWCgaY/f6669z4sSJIgOjVp577jk+/OEPY1kWH/zgB/nIRz5S9Ptbt27xgQ98gPX1dSzL4hOf+ARPPPFEIK91J6RgluCvpSwVSsMwGB8f9wYI33vvvbt68WqaVtUitG2bW7duMTMzU1MJi78OMwgqWaymaTIxMcHi4iLnz5/n8OHDO75v7rGa3azKxTALhYI3AuzChQuEQiEymQyJRKKosL+0O467cbXKJbvw3HMsfPnLAJvWZaFAaEssy5LN0iUEaiRCv2Ggr62x+Mu/jPoHf0DP3/7bga+vlfgHdLsbsztq69VXXyWRSHgDukOhUFHDhVYW8bdbMNt9fti8fktLifydpkrj2O70nT/90z9lamqKa9euceXKFR544AF+6qd+igsXLlQ8l2VZfOhDH+Kb3/wm/f39XLt2jSeffJLLly97z/m3//bf8nM/93P80i/9Em+99RZPPPEEExMTgb/uckjB3KJcLaX7RbUsq0iIrl+/XvOXOEh3UiWBczNzx8bG6irwr9fFW8v6/Mfz96Lt7++v630LSpQURfESpfwdg86dO8fly5e9m6NSN5Q/llMaeysUCt5nEdTdf3Z2lqGPfARn6/0zQiEU26Yjn6/4N8IwCMViXDZNUlvfi1Amw+qv/iodz/0l+qnTgaytXbijtvwZukBRD13XsnEzdP09dIMQmnYL1l6wMOvJknVLXX71V3+Vf/JP/gk/+7M/y9/8zd/w1ltv8dprr+2YZPjiiy9y/vx5zp49C8BTTz3Fs88+WySYQggSiQSw2ZnsxIkTDb6y+pGCye2uJ7quF9VS+jf848ePc+PGjbq+vEG5FV3KuVDdzNzu7u6KEzvqOV4z+OO2KysrDA8P09fX11Av2qDiq66Fubi4yMjICEePHq3phqLS6K1UKsXExASrq6ssLS3hOM62FnP1Ji/Zts0b//QXCdsmeV3DMkxMTaMzn0fscNNwKhIhvLJCPhzG2BJXJ59n5dd/nWP/8T/VtY47hUoZuu4NzuTkJJlMpqqXoFb2gmC228JsdhZmOBzmwQcf5MEaktJmZr9CMXQAACAASURBVGYYGBjwfu7v7+fmzZtFz/nYxz7G3/k7f4c//MM/JJ1O861vfavutTXKvhZMt5bSNE1efvllbty44Ymcm4xw8ODBuoXIRdM0TNMMbHahX+CSySTDw8OoqrrjxI5KtCLpJ5VKeevaafrKTscKwsLM5XLMzMzQ19dXNcGo1jV1d3fT09NDJBLh6NGj2LbttZhbWFhgZGRk2xDonbqtLPzvv0l0YhjFsYmpgpQewQSUHeLVUV3n6Po6BhCzbdZ9v8u88H3y3/pvhH/i8YZf751EtQHdrpcgnU4X3eDU0gmn3YJZa9Z5K2m0cUEjXX7KXfOlBseXvvQlnn76af7Fv/gXvPDCC/zjf/yPefPNN3flc9qXgllaIuK+0UIIVldXicfjxGKxpjdYTdNa0sruzTffJJPJMDg42FRRcJCCWSgUWFtbY21tjStXrhRtXI3QbP2kG6dcW1vjwIED3HfffU2tpxT3wlYUZVuheKUh0OWyQI3Jcda/+icozuZrFTh094bJbOTZ6XbhlKIgDAMlFEIUCkQjEbJuvNOyWP7t3+HEj/8E4g6ddNEslbwE7g1O6WdTOvTZfX67Lcx2C2ajjQsaGe3V39/P1NSU9/P09PQ2l+vnPvc5nnvuOQBu3LhBLpdjeXm5qMa0VewrwaxWS2lZFi+//DKKonDlypWi9mCNoqpqTVmttWCaJmNjYySTSc6dO1dT4sxOBGHF+XvlRqNRTp061bRYumtrRDBL45SHDx9mY2Oj6fX4qSVhqdwQ6HJZoN1/8FsYuRyKUDaPK8DsBLVgYmYEVPh8wprGgS0XrKIoWEC0UCCnKF4cND9xi8ynf5fYr32k7DH2I+VucPyfjVs2YRgGkUgEx3EIh8Pkcrm62skFRbsFG5pzydZrYV67do14PM74+DgnT57ky1/+Ml/84heLnnPq1Cn++q//mqeffpq3336bXC5X1GO3lewLwXRLRNzkD79QZjIZRkZGyOVy3H///YG2cQoiRmjbNlNTU0xPT3Pq1Clisdiu3EnthD/RyO2VOzY2FugQ6XqO5W+E4I9TLi8v74nxXuWyQHM/fJnR19/YtKYdG8dysCIhMokNbMvC6YhCKl92kz6oaeB6SCwLExC2TSwaJZXNbj7Jtln/0leI/Pz/jHqiv6nXfDfj/2xc3AzdiYkJ8vk8Q0NDRe3k3H+tHrO1FyzM3XTJaprGZz7zGR5//HEsy+KZZ57hypUrfPSjH+WRRx7hySef5Pd+7/f4xV/8RX7/938fIQRf+MIXdu1G5q4XTLdeqLTpgDuMeH19nfPnz5NKpQJvEuzGMBvBjaOOjY1x5MgRrxOO313RLtbW1hgeHqarq6sovhuki7eeYyWTSd555x0ikcg2N3qrGhcEwfInfwv8hd2aQD+gk8zkNr+roTyGbcNW1rYDCEA4Dgf8741hoOg6jmEQymZRdR1r6+bQzOTJfOxf0/V//+ddf313Mm6GbiwWo6+vz7vJ8ffQXVxcLKo9dOOiQY7Z2guC2WgctdG2eE888cS2usqPf/zj3v9fvnyZ559/vu7jBsFdL5j+rFe4XRO4sLBQNIx4YmIi8Iy0Ri1MV5A6Ozt5+OGHd32cUiUymQzDw8PYtl3Wbb3bgumvp7x48WLZi3OvtsYzJkbZePU172dFCA6eO8jAgTTmhsaGopEwBQuxDlanVz0vieM4CMchnE5jupNxOiNoXToYKrYBMVUnsbEpmFYuT/r7N+mYGEW951yl5UgqUOoSrTSg2xXR0jpefyecRkTHtu2WtIysl0ZuLBOJxK41ddkt2v9J7AJCCCzLYmpqiqmpKQYGBrhx40bRheBag0E2S6836cfNMAUCi6MGgWEYjI6Osra2xuDgYMWLIEjBrCZK5eopK13Qe1Uw03/4CXAcBNB3IEL/YZtIzyqOHUJzLCKWxVEB5/tsfpSOMraW3RRHITja0UEol4POMCJmIJQcFibCKqBGBJ2qQi4SJr9kgW1jopH7vz5N7BP/RzBvwC7S7kHdtcQQNU2rmKHrFvGXDuh2RXSn/cayrLbfMDf6GSSTSc6cORPwatrLvhBMd9yWW9Rf7o4tyASdeo+Zz+cZGRkhlUoxODi4Y9JM0L01Kx3PHz89ffr0jjMzW21hVopT7nScdm+6pYiJd9h44QUA7jkV4XAsB7EIODYiWzyNRogCl7o1dCXC24ubA4IPCtCOhRCa29RARQXQdXAcbBy6exzWDYvsKth5A+W550j+01G6jx1vedwtSNr92TWadFMpQ7fSrEp/XNRfhrYXXLKNcrfNwoR9Ipiqqu5YS9lMvLHaefNVOrX4W8adPXu2qqXkP2Yz8+lKKdcw3XEcFhcXGR0dLYqf1nKsZsaP+Sm14qrFKes5TlBra+bGQPzH3yO9keXYkS2xVBQQeVBUMLZ7JESHzlkji3oozDvrJn09DkIrlDzLAS0EZgEFQbQA2bBAP6qQT+qQz+H8l88z+jM/X9QZJ+jZlUHT7ubdQWapVsqezmaz2zJ0w+EwXV1dpFIpOjs729aAvpnRao0k/ex19oVgHj16dEfXaCsEU9M00un0tsf9MyDrbRnXasHc2NhgaGiIjo6OuutQW2Fh1hKnrEar5mE2LMLJdTZe/AHdPWEGDm7VTEZCQA5H6Ai2f08VzcQGBkJ5uh8+hDpfob2Y/zuUM+noDZNezxPuLuDkooS+/S3u/zf/GwhBoVAglUqRSCS8WYj+9nLd3d17QkTbOakEWl/W4Z9VefToUeB2oqI7V9TtNlY68Hk3Pp9mZ2FKwbxLaZWF6Rdqv+XW6AzIoNvZucezLIvh4WHy+TyXLl1q6IsedAzT7ZyzU5xyp+O0wsJsFP3P/phs2uDcsQLeUVQLHBBWpTisgQjriIjOgdMp8qEIxq1yDdmLX2fYhjSbzRDoEhjLKxS+/v8S+um/TygU2ja70h0AnUqlGB8fLxoA7baeC6pHa63c7YJZDn9j88XFRe655x5isVjZgc/+Ad21TNqpl2Zuzu+24dEgBdOjVRame8z19XWGh4cbstz8BC2YAGNjY6yvr1cdBVYLQQimG6e8desWfX19NTeSr8ReS/pRvvvnHO810JStvw+HwNlyr+Yrf//UAyEECQjrRM/YmPMKTqHkvbaL3bQikSfcoZPPGAjHgr4QmS98jtBP//2y56g0ANq1Qv09WusZh9YM7S7cb8YlGdT53ddfKUPXbf/nz9At7W/c6DXUrIUpBfMOpJYvvKZpVeONjeDGMF999VVs2+bee++tu1VUuWMGIZiO4zA9Pc3a2hpdXV11uYUr0axg+uOUAwMDRCKRphMeahG33doQlR98GzW/hqb5hDGkbBqGQkCuQvxXUaDXgIyKUE0URSFyOUL2tVIr0wE1BNZt4eyIqOQzBopiErsvQuqlSawf/RD1ytWa1uwOgA6Hw1y5cgWovEn7LZ3Ozs5AhK7dFma7Y6g7CVa5Ad3uMIlkMlk2Q9f9nGqpCGhGMNPpdEM9rvcy+0Iwa6FSvLFRCoUC4+PjrK2t8eCDDwZWjxSEYC4vLxOPxzlw4ABHjhzh6NGjgWwKjQpmuTjlrVu3AhvvtVcsTP2b/xkRtiG19YCqgrMlekoIqHDD1hNC6Dns3jAqm118QgezFA6HsZZKkn9UFX8YVNnI0302woF7C6g9FgfOQObr/x6u/J81r7tUtCpt0pXGoTVj6bRbMNtt4TZSG66q6rYB3f4MXX9rxmg0WvQZlZawmKbZVL5Eu9v6BY0UzC2CcslalsXExATz8/OcPn2aTCYTaPFuM4KZTCYZGhpC13UeeOABotEob7/9dmAu3noFs1o9ZVDDrfeMS3Z9CTXzCqR8rykagi0BxKkgCqEQRDdF1ekLe88XCDouOiRXBNj+tRS//+pBne7rDkrWBltBi2bpKnyP3PQb2P3317T0Wl5ruTKKSpaO313Y1dVVVUT3kku0XecPoqzEn6Hr4mboplIpNjY2mJ6eplAoEA6HPRE1DKOh19/ucqBWsS8Es1aXbDMbtH925smTJ7lx4wZA4K3sGhn6nM/niyw4v2UQZKJOrWurpZ4yqBKVnbJkTdNkfX2d7u7uujamejcE/a8/j+jJQN63FlG4nadjVDhez+3HRZcFmdu/UsMG4QtR8kNZ38KK37PoI6BoW8ewLNBA6ElCf/UJcs/8l5rX34hoVbJ06hmH1m6XaLsFE1oXMvBn6Lr9qR3HKWr/t7S0RKFQYH19va4yJPf6aHeWddDsC8GshUYtTMdxWF5eZmRkhAMHDmwblhz0nZaiKDWv02/tnjt3jitXrmz7AgeZRFSL+NZaTxmUZVjpOO4NzsTEBF1dXYyOjnrWT3d3d1UXYt2bgG2jzz2Lk+9ChDOQNyAaue2OBciV+UxjEdC3nqMJFD217Snh43kKowLH3HqNjr1Zz2lb6GcjaIe2/l5VwSxASIBwUMwhtJe+gnnt53ZcfpBu0XrHoYVCIQqFAoZhBNqFq1baLZi7bakJIYoGdOu6jqIoHD582BPRchm6rvXqvlf5fJ5oNLqra98N9oVg1mph1iuYGxsbDA8PE4lEPBdnq9E0bUdRchyHubk5b0ROaRtAP7vV/7Xeesqg1lVOMNfX13nnnXfo7e3l0Ucf9QTBtX4SiUSRC7E0DlevmKuv/xfEsXUIAf0GZMM4GRDu101RwSy5aVEU6PLFJw+GEGoGR9U3RdH7Uxv9ngiFEZ/4qjpgE33w9vfZCeuIjAVOCEQeYa+j//VnMR/+B8X1m22gUkF/Op1maWmJfD7PG2+8gWmaZWeKtpq7zUqqB8uy0HW9YgZ1ubj15z73OY4dO4amaXXPxHzuuef48Ic/jGVZfPCDH+QjH9k+mu4rX/kKH/vYxxBCcPXq1W3jv1rJvhDMWqhHMDOZDPF4HMMwuHTpUtOZr/Wwk6tydXWV4eFhenp6duxuBK23MOvp+1p6rKCTfnK5HMPDwxQKBe677z6vg0qhUPCeW876cTcFV0QNw0BVVUKhEN3d3dUzQo0CoaU/gs4cxLc29w4TJ6Yh5gEHHEXb3rCgMwSKTwS7N4/v6CqUlJOEj5sURvHcu44QhE6HUWK3/16oW8d3ttbpOIjDGdQ3/xLrXT9V9T1sR+KNm3VrmiaGYTA4OFhxpmi11nKS5qg22qtc8pdt2xiGwbe//W2Wl5d5//vfTzab5eLFi/zGb/wGly5dqnguy7L40Ic+xDe/+U36+/u5du0aTz75JJcvX/aeE4/H+a3f+i2ef/55+vr6WFxcDO7F1oAUzC1qnY7hjgRzaxZrIcgNR9M0MpnMtsfT6TRDQ0MIIbj//vtrTucO2sJ0xbeRvq9+gurQ4x5nbGyM+fl5zp8/X9fwbUVRtsXhlpaWWFpaAvDurCuVVWiL/wHFngNbga0JIo4awgnlcLqjiI0swlZKTwodJdmvug0WCM2B0sTYkIk+cLuZgcBCP1P6+gzQNLBs2PoYhJZGf+NP96Rgljt3uZmilVrLRSKRIhFtdwPzRmh3hjDUX1aiKArvfve7vaYLn//857Esi6GhIe8zq8SLL77I+fPnOXv2LABPPfUUzz77bJFg/tEf/REf+tCHvH7buz0beF8IZrNfOsuymJycZG5urmgkWK3nDjoG5LcIXRHf2NhgcHCwyGVSCzv1u613bbZtN9z3tdyxmmVpaclzFQVRawp41mV//+2hzOXKKjQzzcOrf4wtTEiGUbZcqY62+fnZfXnUrI6Tsyn6dnSUWJcAbA0/1w1g+3cpPGBj3Nr8f6FZ6MfLvHdhHTI50LcOkckjOt6AfArCe2MyTik7XTuVWsvlcjmSyeS27M9SEW23IFWj3fFTaLzTTyKR8Dw1qqoWiV4lZmZmGBgY8H7u7+/n5s2bRc9xpzm95z3vwbIsPvaxj/H+97+/7vU1yr4QTGgsicRxHGZnZ5mYmODEiRMNdZ1xXb1BuYlcF6rf1VmviPsJ0sI0DINMJsPbb7/dUN9XP80m/aRSKa+EpqOjw7trbRXlyir07/4ampYGC8w1G8UwsIUGTg5hb86ytHtDKJMloYBYics9poGz9RzhNlkvfo4WKaAeDWEtFNDP6IiQBVbJcRQDHIdNxdwS4I4s2pt/gvnw/1LxtbXT0mmkrMQd/hyNRouyP93+rMlkktnZWfL5PKFQqEhEI5HInhHRoOfzNrqGRodH19tes9z1XvpZmKZJPB7nO9/5DtPT07z3ve/lzTffLHILt5J9I5i14m4ObnF/X19fTbHASjRbrlKKoiikUileeOEFb1xZM3VaQcQw/eKtaRrXrl1retNpVMhN02RkZIT19XUuXbpEb28v3/ve95paSyk1ibmZRV/7H4iQCYpCKKOBrmNrUWwluzkQ2rYxohnUHKiOjRAKxKIoarHF7/SoCHyiqqnbBBMgfFqQWQD9HmczkahUMDG3RoCpILYEM22hrf8FJntTMIMqK/H3Zz18+LD3uF9E5+fnyeVyXpPz7u5ubNtu66SQdo/2arRxQSOjvfr7+4vK8Kanpzlx4sS251y/fh1d1zlz5gwXL14kHo9z7dq1utfYCFIwfaiqyvr6OiMjI4RCIa5evUpHR0fTxwyqR+36+jpvv/02hUKB69evBxKXacbCLBenvHnzZiCbS73r8tfB1jK7s1l2Ekx19CuIcA7c17C+JV66iRCb1qUCON1hlIMgVrM4jo0VyWMbm25XoWw+j2iJE7bCVat35VCPhdEO50FUcIOH1U3j0tWgbAElN4STuYXoOFXTa99NWi1W/hIKF7cOMZFIkM/neemll9A0zUvw6u7u3pWZonthFuZuWpjXrl0jHo972f1f/vKXt2XA/szP/Axf+tKXePrpp1leXmZ4eLjl3iM/+0Ywd7IKstksmUyG4eFhLl26FFjT4CAsuGw2y/DwMKZpMjg4yMTERGBJDI2uL4g4ZTXqccmWlom0utSglo1SX/qL2z8UNMibOEoIRxRbfY6i4HTlUdYVRDiCEs2z6TIFx3ZwHBtTMRBbmdFCCBxRQMFBlMQyBYKOxzSEUsBRBWg6otQSFQZYStGVLzIq+sx/xLzw62Vfy53mkm0Wt8l5b28vq6urPPzww9uK+XdjpuheiGE2uoZkMlkU468FTdP4zGc+w+OPP45lWTzzzDNcuXKFj370ozzyyCM8+eSTPP744/zVX/0Vly9fRlVVfvd3fzfQTmo7rnHXzrRHMQyDsbExVldX6ejo4PLly4GWiTTTcs+/Njcr1zCMwF289Vhyzc6nDHJd5cpEdoMdxTw1g5r+EW6c0Mlqmy5VTfUe8zAB1cbpCCOixccUikCgEtIBR/c+dyEMLFvg2CYC4VmsQtUwH+4mlwhhqRYqCjgh1IKCmnfQkxmwrc0yFmezgQEASRNt6VsYF/7NNhGGu8Ml2wg7TQpxx6GVFvOXimij698LFiY0ljTZ6CzMJ554gieeeKLosY9//ONFa/nUpz7Fpz71qbqPHQT7VjD9cbfTp08zODjIW2+9FfjorEYsOP+A6VOnTjE4OOh9aVs1D7OWNTVST9ko1UTJtm2vg1G9ZSJBra0a+tx/AlWBre47Irn5uK0W14M4h3Q4JHAMHdsQqHaZGZcdKjiuUAIIFEVBiYShsBnrdByHfCRKpltgDSYoTEaJLuUBBaHaOGEHMwJGR5TosrFZxuLoePUpeQMlsYSd+g5q5483+K60hnZbt9XErlIxvyuizY5D2wuC2Wji3d04PBr2kWC6F52/C87x48eLkmZaNROzVoHzxwQrDZgOevrGTpZcs/WUQa9rcXGRkZERL+GpXdZHtc9AX/rL4oboCQdHDW/2jlUEzvkwXHUQJwuIjAk/5pA1uumYVhAvWYjh28Lp9JRpagA4uoLY0juzu5tCl4NzMEo4lkOc1FBWFBxLwTa3MmO3rFDrsEIkEUJbyyP8H2NaQZ3/Ezi/XTDbbWHuVcEsh6Zp9PX1eXWC0Pg4tL3gkm0UKZh3ASsrK8Tj8YpdcFohmLUm/SQSCYaGhgiHwy2JCVaimoXZaJwyiE2u9MbAXyaym+9POapZv07mVURm7nayDw6sGZvNCg7o8DMguremj6AjtjJwsjqE+lVCx1PwQgc8vzWVJFb+fRRbtZz5nm7yMQcQ2Md0IIfencaOhtBzAke4HX7AcTYzPtNdWSiE6UxuNlwQikAkTUKLPyB/ZgOh7p2hv+3MFA1KsGodh1Y6+NntKNUumokfJ5PJXSv12E32jWBOTk6yvLzMu971roqZr60SzGqNAXK5HPF43GsftdsTystZcs3EKd3jBTH42bbtojKRixcvFt25t5NKgqkvf3GzXytbVqKhQ8HCPuHAz9qI2O2bEwcNgYFJB44Q5FSdkC3g3VmcQ2HE1ws4ulMmqgioBrm+bgq+uKc47LpuBeaxKPqEb4qJACEUBJsVJ8Y9vThjNmouie042Mks5rrD1FufxOh4uqgusd0W5l6IYQZNLePQVldXgc2bRbfMpZGZoo3SaNMC2BTM3d7LdoN9I5inT5/eMWurVS7ZcoOpTdNkYmKCxcXFtsThXPwWZhBxyiAFM5fLcfPmzV0pE6mHSutwHBtt5btbzQG2Hkur0BuBf5AvEkvAG12ZYzPjOacIulAQ2IjBPPTq8Lrtaa+frNqLoQm8xCJFoB24LZDqoQL2hEWl7V6QIRkL02saqPamb1ct6PTrP2C158NFdYnuZ7q4uEh3d/eudsi501yyzVA6Dm1qasprzZhIJJifnyeZTHrj0FwB9Y9DC5JmYqipVGrXkvB2k30jmLVOLMnlyuxOTVDq8vTXC7pFuI0OaA1iI3Hdi25ssNk4ZRCdg9wyEcuyePe7392WsU7VqOSSNa2/QtlY9ZJ0NlFxfl5FdG6/ERO2g4NO3v0YhcBUOtDtrTFeRy3MvxVB/2/FmbWWiLCqRYlhomwJpnE4Qki7LZhaJI/REyWykb3tlvWh5bLkwz0ku6BnYx2wIWUTXp+h755ZDh16l/fc5eVlpqenSaVSzM3NeR1y3DForWwz184B0u2OIVqWVdTOz78u1xJdXFz0xqH53bmdnZ1NXzfVGq/vhOM4bU9YagVSMH20ysJ0j7myssLw8DB9fX1N1QsGZcXBpuskk8mwsLAQSGywGcEsLRN5/fXXAxPL3bBUtPU/Q5iqr42dwL5hQ892DwMAlkXBibnprwDk1RD61tvnaDrGPQXUiSjK1pBoB8GK3osjwHJUz4J0jm6/lO1jGmxoUCZpCMDpjmEU8mRiPXSk1xCpAooRgtX/BCc+6T1P13Wi0WhRgXg+nyeRSHht5nK5XFHDc9cSbZa71SVbC5UsvHpnijY6Dq1Rl6zjOLs+x3O32DeCWQutjGG+/PLLqKoaWPegZlPO/XHKSCTC/fff39SaXBoRzFaXiQTdAL+chWk7aSIrL4Nz+xzJUweIRXM4olwMWyAsk6wo/gyzikInAnCwdQWwyP+4SXROg3WLpHqAwtYmbiJwtz83fulHO5DBEZW/I6pqYgGZsEA3OtELKURaR135HzjHDYS4vbmWvnfhcJjDhw97beb8vVoTiQQzMzPk83kikcg2S7Qe2u2SbWcYoB7BrjRTtJlxaM3uMXslhBIkUjB9BNnGDjZFaWxsjLW1NR5++OHAElaaqcUsF6d84YUXAlkX1C+Yu1EmslOjgUaae5cez7S+irqega14oBUNs3y2k85khnJnttFwHB1LKT63IwSWiKA6WezQVimU7pD/SQ37T3USWtizKg0BUQSOcNB6spSiqhbG4R70pe2/A9CzCUxFQdg2yY4QBwwFZT2HctjCSP831M6f3jx/DdZCuV6trogmEomiqSGllmi1Ps37NeEIghGsZsahNeqSdV32dyP7RjB30yXrHwd2+vRpstlsoNmdjQjmbtVT1iqYu1kmUql21bZtbt26xdTUFOFw2LOEGnEnivw3UFKAY4OAhSuHiZoGjlb++yTQyFbo92ooYVQrix2+vWbrpM3EjXN0vrxW8mwNq1dF08rH3u3DFixVWLSTJ997iMhqEluBfKSLcCKFYoZh7WvgE8xGRMsvov6pIf7RW1NTU0UbtvsZuBtuO92i7W4c0IppJfWMQ4PNDkdLS0t1xamTyWSg3dL2EvtGMGuhWcF0HIf5+XnGxsa8cWBCiKIO/EFQr2DWUk8Z1J38ToLZjjKRcsOoV1dXGRoa4tChQzzyyCOYpkkikShyJ0aj0SIRdeM/pRambc8QWY17Wa+ZY30kD4c4ulHAEeW/T7atk6vwfucUjYgFdvj232bUXsRjSXJjHXRs3BZH29GxDqlo5VJpAbUnAYoGdpl1CAdV39wCsoe6WRro5sJLo4hcB9ray9j9m27ZoN3Z5UZv5XI5EolEkdUTjUa9zyEWi+168tdecMnuhmBX+kwmJia8HrpunNpNQnIzdMuNQ7tbmxaAFMwimnF1rq2tMTw8TFdX17amCEEHwGtdZ631lEEmEVUSzN2eJuLHL3C5XI6hoSEsy+Lq1atEo1FvuHBpTM6/iU9OTmKapnd3XigUvNFHpvUloikLbBMnpDF7efN91so6YzcxrE681nQlFBSw1RCOujVwWmisa2GE7ZB7LELHX90WRwsFqvSeVhQH82AP2tJq2d+HzRwzNwZIXNJACN64fJGTQ2m6NiaxfW7ZVuLfsP1WTzabZWhoiEQiwdLSUlH8zb2RaaWI3uku2WZw+xP39fUViah/ksvc3Jw3Ds39PNbW1kin0w0J5nPPPceHP/xhLMvigx/8IB/5yEfKPu+rX/0q//Af/kNeeuklHnnkkaZeZ73sG8GsZXNuZAN3J5zYts2VK1d2pfZIUZSqgllvPWUQSUT+Y5UK5m5PEylFCIFlWYyPjzM3N8eFCxeKhLHS35TbxDOZDKurqxQKBX74wx9i2zb3nv065jqotsHK+eNYoc1NVhdpKmlmrprXWgiMUC+wKXJptRebzQSg0PkEuVe7iCxtHcU5YAAAIABJREFUNqg1EWi95YXX46Ba0S27fvYIa/fGULcs1ExYsH4yQj56nJ4tt2w74oiu6zAcDnPq1Ck6Ozs9EU0kEkVJLM1kglbDtu2W1DfWc/69JNhCiLLj0Nxkr5WVFf75P//nTE1NYds2//Jf/ksefvhhHnroIc6fP1/1tViWxYc+9CG++c1v0t/fz7Vr13jyySe5fPly0fOSySSf/vSneeyxx4J/wTWwbwQT6hsZtROGYTA6Osra2hqDg4O7O2KmQn/aRuOUQdROljtWu6aJlGIYBq+88grHjx/nscceq+k9+dG4wr2nbfzXuJtEoes6KysrPPDAAxjWMGpqCTUNeV1j+ngMzSgAKsJcxxHbb8QcwphWgWoalIl0EGYVW4TY0HwJFAJyj4WIfG3zx7yuEu2q3EkKQO3JbJaulHz3jViU+ctRTEKeYIIg2aUx39HPfcPvoDjbB1XvJn6x9sff/Eks/kzQ8fFxr5zCn53biPDtNcHaq+f3i+jXv/51vv71r/PCCy/wEz/xE7zyyit89atf5bOf/ax341mOF198kfPnz3ulS0899RTPPvvsNsH89V//df7Vv/pXfPKTnyx3mJazrwQzCNxEkZmZmbpci0HepZcTuGbmUwY5AUVRFEzT9Ky5ZstEmnnfstks77zzDtlslqtXrxZNlXBxXU/+85gWfPqrIR6+aPFPn9wuGP4bL8f+M7ScinDgnQcfY6lXQ3UcerIGgnEs29lMBPKN4crSjajirgVIRXXCQFLrpbQ5XuhMguyxbqLzCfKHOoEMldy7AEI1MQ9E0VYyRY9PP3QCWzVxStaSC0G4EGL4zAkup57DcW7s2ebrlTJBM5mM58otV9hfi4i2WzDbmSEMjTcuSCaTHD9+nMcff5zHH3+8pr+ZmZlhYGDA+7m/v5+bN28WPefVV19lamqKn/7pn5aCuRvUYmG6YlR6objdcEZHRzly5EjZSSI7nTeoL7+//CWI+ZRBWpjpdJrJyUlOnTrVdJlIo++bbduMj4+zsLDA4OAgiqLUleb+3ddV1pKCb/1A40C3wz94X+VEMGH8f+RzB7jVF2XxlIYALCFIcYCkcpweFoDNTcct6F4zwmhGEgQoQmz2eFXE5izKrZeaj5iYopOkWv47VnhMI/osWId0bDSUKoJpC2tzlNjK7cdSx/rYOBpmM1PJxEZBcbOWEJiaxlp3F6nkd3Gc63tWMMvhF1G3JrFSYX8sFvMs0c7OzqJrut2C2e46xkYbFzSS9FNuX/a/ftu2+bVf+zW+8IUv1L2eINlXglkLbqasf4Pd2NhgaGiIjo6Ohkogyh2zGVRVpVAoMD4+Hsh8yiAsTLdMpFAoMDAwUNQVplEq3bxUY2lpiXg87o1uUxSF2dnZml3xjgN//vzty+Ir39Y50OXwPz18+/1xhdyyJ1GsaWbNKyyf1T0Xq0BgmSYrohPVMencUiohBIgwWSVKlBwK4OAgbBvL2uqOIgQOgjx5Ju0+VNtGK/Py9VNJMid7EH0WFkrFnrFbrwq114CthggAy+duZyerCCwniiJudyRyRAaIsdAxS+96+9yyQYlWucJ+V0QTiQQLCwuMjIzgOI5niWaz2bu2Y00tNOoSTiaTVd2v5ejv7y+qJpienubEiRNFx3zzzTd53/veB8D8/DxPPvkkf/7nf76riT9SMEvwi1s2myUej5PP57l06VLDqdL1zMTcCcdxSKVSzM7OelZcs3GOZizM0jKRTCaDYQSzwdazrkwmwzvvvIOqqttuauqJXb8aV5heLN6g/+gvdPq6HR68YDO7AQe3Dm0a/w8TkdOsrwpWzwkipkNYAwWNsJljIwcrdi8X1TRdeo6sKVjKxVg1HHptr4EsiqOgKoCylR2qRCmYkLQ76HQ2LVFdOOgKaL6P2nhMocPMFHX8qYSqgtEXRVvLYEbDrB+7XWeqAGZJRyAhctjOcWZ7CnRtfA8hdjcb0aWVbkm/iLr4+7Sm02lGRkYYGxvbZonuRmyx3WLdjEu23r3y2rVrxONxxsfHOXnyJF/+8pf54he/6P2+p6eH5eVl7+f3ve99fPKTn5RZsq2k1uYF+XyemZkZlpaWuHDhAocOHWrqog2qg5AbpwQ4evQo586da/qYsHPWbTkqlYnkcrnALvRahM6yLMbGxlheXubixYsV45S1rulvvquyLhxmLZVD2BwWYNmCP/iTEO/5Wya/93wYBYcDzrv4jd7Pkuo/jNbnADZGXpAqgILKgY11FGvzOzOZO8QJcwaAvNDQfYk0msKmV9QBrE1hK4QiZAhhqbr3vbMdyBQEmmoTVg2EAOtYjuRaDN3ME9353cQ5pMAarJ0+WNS/VsHG3tZv1qGATkTRWO59k6703SeY5fD3aV1fX+fUqVN0dHSQTqe9UopUKoXjONsGQAcpou0WS3cNjVj3iUSibsHUNI3PfOYzPP7441iWxTPPPMOVK1f46Ec/yiOPPMKTTz5Z9zpawb4SzJ1wkwVef/11zpw5E1irtmZdnqVxSsuyWFhYaHpd/vXVY2FWKxNpRHwrUc3C9E9YOXnyJI899ljFz2rzOA5bHk+P4UX4la9qmLbKY/0miwmFP4vrWBrYAuZRCTtwwrEJZeG55yJ0dTgolsBQ1wkfTrG8fozYmaSXluM4kDYF/YUkqJtO0KwaJmt2oAgbW4GIk0MAqgKKU1x5YlsCkxAZNYKNwNka98VWfNO0VRxUIrpDij6WIofoXl+kYNsoqn17ILTYiom668JB7c0DguUzpV1YNt9jixCqLxba7SRJii5Wu+bprNCAodW0M47onrtSs3N3APTs7CzpdNoTUb8l2uja2zk4208jNyuNNi544okneOKJJ4oe+/jHP172ud/5znfqPn4QSMHcwi3HEEIwODjoxTmCoNEOQpXqKTc2NgITJahd0GspEwm6RKXcnXY6nebtt98mHA7zyCOP7NjGbmI9zP/6zT7m0hpHOmGgx+FE1OYv4ioFUyBwmFgIkc6CsWXxKeqmVZcXMO4oiDkHDkNqTdARdvj77/k6a7FOUnYnnWrSO5dlalgFFYGDsMBRAAQrHKDTSlEQYaIijypAEQ62vX1DWqUPxc6hKGBaOmEtj/8tda3NZbWPxa4jONkYmuUgyGwOg7Zs731zM3MRAiVkkrhwmHysdCM2gDCWE0YVtwUzqqwzzT3oYo1s91vA+eofWAtod/P1ajdh7uzKkydPArcHQLvdolKpFEKIbZZoLSLa7oSjZrhbh0fDPhPMchdeMpn0epo+8MADzM/Pt60zj8tO9ZRBloHAziLnCnctZSJBCmZpSzvTNBkdHWV1dZVLly4VtdX77pDgjQXBTFZwzwGHn7vfpisMn/4fCr//389jOiqKIpjegNkNcKZUIt2g9gB5KBQgmxEIFZwI2NZt0VTSDmwIWHcw+gUZR3D20jtYaFi64kulAdtRUfKbDziwOVlLhbwaRnVsLBFC3Zpe4pQRS9sRpDrCdDo5hA02Ojjl6ywXCzHSisJ05B560m+jCQVVwO0MIAfbcXBsB9M2UCyLuYEolmV5Qrr5OW7ZsSWfqYIJjobhdJDpfgPYfbfYXhXMcpQOgIZNEXUt0XIi2t3dTSwW23aedtdgQuNuYdka7y4kn88XuTl7e3uB1s3ErFXgaqmnDFowqx2v3mkirbAw/T16BwYGvB69sFkz+R/+u8Jzr2+u6/hBh5l1hf8+pqA68O24gmmb+IeC6AnImwJjHTpyDokY5Atbk0EsUPJghzdFU1WAWYGZ28x+VWcd+i4tcvDkAhP5sxwJLXquXofNeZVaoeS9tAChkhNdKM7meyOEU1Yws2Yn4ehmvaTjQMHWiVbYN9NKBwUL3lCPM8hQmYtZoAiBrYQw6MBG5Z3uG/SLt3AwsC1rKzMXbCeErdrYAt97ZRAVWZJ00RGdxi7YO+bjtoI7RTDLof7/7L15kJ3Xed75O+fb7tK37+0F3Vi6ARAACYKbKJEQtNiO5XhiS4qZcmLPKKkZucaljKdKlZKXWFK5XE7sipOp+cOJJ544U1omdmSZyjiOZNkybVGRZFMSCe47NmLrBnpf7n6/5Zwzf5zvbr0AjUaTFAW+LBDo2996vu+e57zL87yOQ7FY7PO42iBaqVSYmpqiXq8jhOjjiLb3fbPsZu79bcD8AbG2RFq79+Lhw4e5++67+76QruvSbG7cDmm7tpWinxvhU74eHubaytbtdhPZaQ+zVqtx6tQpstnsOo1egH/3iMN3z3af38ySQAqY2G24HAt2Fw3TPTKqgTaESwJXgm5CtSbwW4Zyz2F1AlKC8sBZMiT1bjbQtAQP3vU9tOdwoXqA2zLne3aUGGHIqn5OpONAkniUnYBBZakbIvVAlbAtNFPZWObcXXhOjBE2j1qTLhnT5mdaCQMJaOMSOvaia47P6WQv97mnaSrwJHjCoWJGKJs8DeOSaFhwJ/mOOMoR7TJIhT1ylaJctsdVgtBowsTDFQ1EqlBUYIllxmlJybJ8gVF9/3Yf51vOXq+w6GYgWq1WqVarTE1NUalUiOOY06dPdzzRXC73hoVpb8bDVUq94fKXb5TdUoBZqVR45pln2LdvH+9973s3fPlezybSG9mN6r62j7fTHmYb5G62m8hOAWaSJJTLZcrlMvfcc8+GC4i/flH0gWXbtIHLM4K9ew0MQRInzNcsuKgFOmCp0yFcmRfIjEGP9hTJxDCcNaxOC4y2AGqwQHfPA89SjooYFzA2dIuBJHLBh6zXwMgUBKUFxbL2MQiW4zwFZwlhhM1vpqc0EpIox1K2RF4u9fShFkTKw5OWR2mwQLqkSyghcNKw2dlgPxPV18BTLMV5lhgjwUXRVcR7Uh6glsD5eIwDboMVMUpGFdgjZ3EQSFcSOB5ZJ8ZgPftANUEZqibgTOXPqcwPdopabrQF2lvN3shwsOM4lEqlTqRrdXWV2dlZxsfHqVQqXLp0iXq9juM4fZ5oPp9/Xa6x3VjgRu37obr39bRbCjDz+fyGXkqvvV4h2Xq93vfZzfSn3Ekvrn28JEmYnp6+6W4iN3ttxhhmZma4cOECvu9z2223bQiWlxbh89++9ngtLQgGhmHXQELgSZZWPJKW6APLKIEkAeoCMWDzl4N5w7HbNEdKmmcWHU4hySwb9g0asvk6h4+c5zlzDyPBEni2xlQC2pdo11CkAg6odD2mtIMWMv23C06a30yLX5HWy1x2BqhnPHJrhj3uAGZ7kKBsBlGAFgIHWMwPMl8bgkhSlkV7AquM0LH53CgYqJHvgH/LCbhoJiklZQZElao2xFLQRvK8K8g60BAFxOgSA80ByuUyly9Pca7pcmfBbNgC7QfF3qxwcNtL6wVRsEDW9kQ3AtG2J3qz170Tzat/EO2WAkzXda+rtvN6eZi9HuHN6L7Czr+MjUaDq1evsmfPnpvuJnIzgFmpVHj11VcpFAq8+93v5vz58xtuZwz80V86RNd5TGEMg6HFjeGcYm/o8rKGRsqPHC0ZsgHUGoZmC5SBzB2QHTLMCMFcWTL1IxLjQFMLllbhvgdOon2YSiZ5QDxjrwdIjCCRoGIX16guUAmIlH3nQuMTEBEpH79N30j5l5HxiaSH8tc8Ww2xWP88ahR6d8cg+UbyAd4lnwNtc6qiByxXRZFGJoNEoxyJMg6OUAhAC8myO0QSeZT8ZSLl4ko7uMstRV2EhF6OFengjdWZGD7Mv3o+w8nQ4Y/vWCKryywvL/e1QCsU2iC6PeHzW902Cwe7rsvQ0FBf5KcNopVKhQsXLtBoNHBdt88TvVEQ3S5gbtczfavYD+6dbdN2UpWn95hJkuyI7utOWpsmUq/XGRoa4s4777zpY24HMOM45uzZs1SrVY4dO9YpGNjsWN98SvDU84LJI4ap1rUngYVV2JOPiV1DvRFw1wFDvWUpHdk0orhryFB3DM/ud1nKWMfPaRhUVSJDgxkVCAErgeCe/U9zWe1HC4eiKHfOo2LXInNTdD1HAAOx8UBAVRcIWKIWDzDsLXd+j4F6nIcAPG+9SlIi139NGyLb2d8YWC4PE3k+KrFA2I6MtefI17zbOsp4QsBisotxdzaNM9s/K2oIL4rJ0GRA1gBwZUyeCqvJABd0nr899xzPnb2LC0YSefBLZ4b46/dm1rVA+/QrPtF0zP+WeR6l1Dp+4ptdAfr9bjcCWBuBaBzHHU90cXFxHYgODg6SzWY3BdHtAl+1Wu3jq/6g2duAucZeDw+zzZ188sknb1r3dSdsLU0kk8lw8eLFHTn2jQBmr1rQbbfdxrFjx/rGZSOFnlZovUuA+cuC3F5oXOdxXVj2SYqS6aItCPIEeA6MVSHfUCzEDU4dLZC4BpTAiw16JVXYiQRyFmQAxo+5Y+QU3+U9OCJhUPbwL7VESHAj3Y3RClDKoUXAaXkHp/3DjHirTNSu8D7xPXK6CcZSSRpuFjTkvFrPANm/tJBo7SClSsdN0HIytnDIwGq1REtnEJ7hQnSQI7xmw749Qg1XM3vsBWkBjqFMkXFmO3hp/zYsqDEKusxAeh1CGByt0UYSOx67hl5jakriaChIQy0n+IWVgP1FQz5nKPrgeB5/XQ5IgKPjRX7xUNinlFOtVjkdF3hwmGtSK25lU0rd1Hh4nsfw8HCf8lUbRNtdXJrNJq7r9rVBa4Podj3M7aj8vJXslgLMrYDUTsnYQTdPeebMGYwxvO9973vTV9Yb0UTq9frr0g/zWlYulzl16hTFYnHTzi8bHetPvylZqdh/hxHsCQ0NZ+PnqoFX84LZkRyyaVD5Hjk4RzBV0Nz+ap3XjhVJ3BQ2EkM8nyJRWnkj6qBWBe848TwNkaVMkRGzhBTptSkwjuWVBEnUOfklb5LHvPdxYeAA2pW04oBVd5Vzo7dxWhxmLFrgR+a+Q77ZBE/QIiArW/ShWGqx8ghSwKzqAYyw/M9qc5BmnAdsDe2Uv5cj4Wsd/qfWYKSkkrUiE8ZYoYZQ9hTspOeTwqCMZMGMMa7m8Z0IDDiJxjcJWkiy+QrhaozWHiCoLcNjsy6xtjq3ng94BpEDsvCZus93X3O4o5DhgdEhfngy4alll988HfDPhsv8tJ7pUCt6FXXaubhb1V6P5tUbgWgURR1PdH5+nmaziedZSca2nnYmk9nyAv9tD/MHzK6nK7qZusyNWm+e8v777+eVV17ZUbBsk/q3ugq9Fk1kp/thXgswoyjizJkzNJtN7r777ms2lV77LFYq8NW/6b/fmRnB3sOGK6HgQh4imQq9KcGKA81A4IaaWAlcl07VaBIbZCI4f6hEItsRVIGsGGgX6ACyZdAxGKN514HHuWT2Y4ygxKq9AAMqcRBpFW1e2+Kup737+e7wu6mYoi34MdiaVUt7pBHnWc2G/Pn+n2RkeoUHo+eoOAMMUIYE1qqpx7gE6fnKqggO1Js5alGhry90I5ul1QrIENrjuHBF7EG3xdXboVppKKsiRafcwWekAQWBjDhdu4O7Bl5BCo00ioKsUqZI4jvce/Qkz7/6/u61JeB5ECvwmoZmTcBK6t26MFWQvGokX/YFeD5iEPyM4bNXitx/n8+PTHYrtKvVKheX67wye4VCvNppgNAWBLiRyfutbEqpN6QK2fd9RkZGGBkZ6XwWRRHnz5/vpEparRae5/V5ops9h3K5/LaH+bZt3TbKU2qtdzwv2ga56wHmVmgiO82d3MiMMUxNTTE1NcXhw4cZHx+/7sS3Vunn/3tUEm7Q9nHliuDUYcGVtLxUaGAOK2Y+CHFiP1cKjLQJRikEMrYVso4DKgAZg24KW/GaWMyKY9HhJN4+eZqTPIgUmqKpdPKPSjmYFHQHdIO/yv5dTpduRyuJ0rLdDhOPxOYcNdRFlhLQ0hme238vl8r7uaf2sgVMgVWr6+1MIrzO+WoMoJRDJSx2ALiLmYLXnEPcrV+1PyZwxd2LTrfrabnJkhmhRJqH1SklIB3uVTXCSjjCSGYBVyQMODVWdAkchwO3n+kDTABHGmIlUD1iDMZAFMNqWZCkxw18QWvBCkJoCf/8tYDbBwzHJjTjoy4XkhxfnXE5UjD8t/c1OXnyJMPDw1SrVebm5mi1Wvi+3/FCBwcH8X1/x0FUa/2mAvPNhmRvxnzfJ5PJMDw8zNjYGGDntUqlQrVaZXZ2dt1zGBgYIAiCH2jRAngbMHfMrsWn3CmvtdfagLlZRetm3UQ2sp2mqay1lZUVTp8+zfDw8A013u69rrllePQJO4EsFuHybsHEvGFsBZ4fhpm8DYm2wdLEIBOQ80CRTussR1oJOKlBt6OnNetc6TZ22LJTdLMLLuO7pwl9n0gEOFIxqFPA1KSUEUMzDvjq4E8ylx8DDHHiWdmc1IXzRdgBpER4xIlPXefBwEqxyKPBB/ifzJfIiwad5iEpaCbS7aBiQ+RYrQ9hsO50bwTXaJjJjXN37dXOOC7IEYTu6tq2rUmOVHjIfuoaC9QCEIYKg+STaofSIrUAaRidmFn3rJLELjSiDV7zRIHvQqKhzUZW2v5ZqklWa/D4VYdMYGCXIHHhxargvV/NIaN3cW8ywNGS4h27FO/fpUGFnVzclStXCMOQbDbbmbwLhcJN9559swHzzRZfX9vay/d9RkdHGR0d7XwWht3n8MILL/DLv/zLFItFSqUSX/7yl3nwwQfZt2/flsbxkUce4ROf+ARKKT72sY/x6U9/uu/3v/M7v8NnP/tZXNdl165dfP7zn+fAgQM7d8NbtFsOMLfa6mmrpOWb4VPejF0rjNruJlIsFrdEE9lpIYS2hWHImTNnCMOQe++9l3w+f0P793qY//FrDmeLMLNX0shiqzqLgskpzeU9ElQqLjCfgqWxXqJODGLOoMcF0hVobT1K3eqexyhwpg00gF3C6sc2e/RkgXfc9zTTTKCVxBUJg7JsvUVli2gMgr/VPwL5tldgiPA7vA8lJI7pX5RU4wKtdmjcwKos8WX903xEPIw0CpFArxJdrDw8J2a+MU5I0Cn6EV1MBiMIBzwq1QKDoopBUMkVMDHggnEMRgmEMGgpiIyPL6JO9Wz7SAWvijaCxXiMfZnLoA0BESEu+UKVwsgc1aVuk+BEQSkwrKrNFmXgC0OL9b/3XFARIAWtir2RIAtVoBrlmZ12+Pq0Q2bQ4DhwRy7DOwcH+KmJMe4/ZIXmW60W1WqVlZWVDr0lm832cURvJCe43dZWO2VvtpasUuq64xUEAUEQMDo6yqFDh3juuef43d/9XaampnjmmWf4zGc+w/z8PI8//vg170Upxcc//nG+/vWvMzExwfHjx3nooYe46667Otu8853v5KmnniKXy/H7v//7fPKTn+RLX/rSjt3vVu2WA8ytWLtS9npAc7N8ypuxjbzCrXQT2ch2eiVtjOHixYtcuXKFI0eOMDY2dsPnWGzA5y+W+O+LGaZOepQTQTQKRPaPdEE4MLVb4iRWJEAuQrvmxsQgjLbdQITAWTCYPWnItgV92GVAvSIs4A6CVF1hgzZoHj54hil3LyKBjG7iyxg0JLGL8AVPRseZE7sZY95yG7WD6plwdehi2q9TOhS1aAAn0y0wM1Iw6+7mr5p/jw+Jv7QfhoBv94m1h9KSZYboYFv77zZoGhtCPuse5gH1HHOMo5wU9WMgERY0vZReosbY6053rkFgwd+TMavRMMP+EqvhMI6rGBAVQoZBwm13nuGF73QBE7imymwUpwVBG5hKw8VRezYyEDaAhiBwFE7BRWSwYKvguarD86sOn78Eh3Kaf7I/5n++TTA2lu2EENv0ljat4sKFCyil+hpBFwqFTSfyN7tbyJt9/u0Advs7/kM/9EN89KMf3fJ+J0+e5MiRIxw6dAiAj3zkI3zlK1/pA8wPfOADnX+/5z3v4Qtf+MINXdtO2duAuYFdDzC3y6fcSamtXvrLjXQTeb1teXmZer1OHMfb8rafX4J/94rLd+YlrbiI0JqwAaoOIteVedMJiGZazJoDZ8mG/KQDJjaoBBxje0MaY+XynCqQgyTseo4ActGga1aqzrloiHf1j52ba+KUYoyQOE7CoE7pJAYUDlPxfr7nv4fxaK79MXHsdVXMDahIIlxbeNsJn1Yl5IQNhWLPLwy86t/FWG2BB/ynrNcXAx7EeEyXD0HQP5H2hWQBEwsWB4ahDNNyrw3H9oCriQTCNRigrAfY23MgIUwHhxs6xzBLrFJiSK2S8ZtoJZCOYfLAOV74zg93rkEYqFyHEytcYQuR1lisYDBrqGzwzppYEC1BYdygfUGc3mPGhWYM5xuSf3064P+54PHh8YRP3hUTuHbyzufz5PN5du/eDdjvSaPRoFKpMDc3x7lz5zbtYflWBKzvh/NvJ4d55coVJicnOz9PTEzwxBNPbLr95z73OT74wQ/e8LXthN1ygLkVINmMi7kd3dfe8+4kYLa/1DfaTeT1slarxenTp1FKkcvluP32229o/5eX4V887/LUqsQxhlhb2bdYS8JYYBxwEkjS77A0dHtEngY9C/KgQQcGEoHrCPRaDYAqmHR/rayXqg2YC+kz0aDOpxJ52e5uh+89xYozhFYSz4kpJLUOOlXFAF+TPwlGEPT0koyM1+cBCqU71a/GgEisF2yaElFQRMpHpPQYVxgey/4Qo80FDviXABAKWs0Mc/FuCOiiI91zdKKdSqByDgvlMRa8XazLQGisp+5B7Hhdb1vY6tn2SkKmaj8GQTUeYMCvIjXgwN6xy8ggRod2UeljCJUgCCDcABQ9p4cUuoG5OezCYM0txVow4BqqTQFNyAxC5HU3FYBwYcFI/nDW5y+vevzasZC/f2B9ikFKycDAQF/kpd0Iem0Py0wmQxiG1Gq1102v9Vr2ZgPmzQgX3ChgbpQi22y8v/CFL/DUU0/x7W9/+4avbSfslgPMrdhawNyJPGX7mDdbjNA2pRSnT59mYGDgDQ8H91qvd3v77beza9cuvvvd7255cTDbgH/xjMO35yQx4EpD1JMHS1pdc2EZAAAgAElEQVQ2p4gEHaZeJhZsAOQyqGnAGMQ5g7xNQCC67mOvxSAWwaQ0NJ2AW4GkkjqDIegY3NOG5P7uNRw4/BqrbgkTC3Bg0Nj8ZdTy+VrwYULHjr0n7EUZLUik0wdoUmsLlO3im5rtgGKaAlGAUAcI13IZRWKVFb5p/gf+F/3/4qIwIeh5h1rGFgkZ6Dt+L16SABqmcgcJiwM42i4QOvgt0+4rsQWbclKk6Nl76gXMQa9Coh0cqUjwiFs+gdsiJCAIQnbdfoG5l+6w99ch5mxsQrKplKEjobrRnsaGh4MBaKYX36qA49nqZ8cFYQyt9D3TQMWBT7yQ4Y8uKH7neIs910mb9zaC7gxfkjA/P98pmmvrtfbmQ6+lkrMT9lb1cLcDmBMTE0xNTXV+np6eZu/eveu2e/TRR/nt3/5tvv3tb79pwv+3HGDeqIe5U3nKnZLcazdRXlhYYGJigiNHjtz0Mbdri4uLnDlzhvHxcU6cONH5grWrgq811krDv3lB8l8uOaymvSgz0mBC8IQVANcJRKHoOCbaB68BKmM9Q1EHdc6khS+WKsJ5cA6BWvNmS2WrYqUCM9R1dsx5QIBjjD0XkNQE7oIh2SUQjiKzu0GMh0xLUgdFBTQ8W3knc6kkHMbgytjm4mJL6gcLBq5jcH37O9P2Mps2jKmbEmkEifHwUnW9NtbX/CLPtN7He52/RS04EApaXrdIqG0iFR0QArQSGGM5p9OFPcSui6MMjgSlbdGT6ZkHTQJL0QhF19JZjLQNpxECKTTL8Qi7/HlWzBDTcxMcnHiNEB8h4dCRUx3AVOn1RHG3CKnXYuy5A2+9B+q5hpYSeK7ldPaaMBD6olteC6gY1BJkBwxqzdexaQSuAyerDv/w0SwHRgz/+LaYf7Bv698913U7uc6jR4/a699AJcfzvD56SxAEOwaib7aHud2ip2q12icWvxU7fvw4Z8+e5cKFC+zbt4+HH36YL37xi33bPPvss/zCL/wCjzzySCdP/WbYLQeYWzHXdQnDkJdffnnHdF9vVkFoLU3k4MGDO64EslWvsNlscurUKcBWr2Wz2b7fXy8H9MhlwW++6LIQ0vEmM46hlQKnMOBoQ622/loSz3qF2jHoVw2oFCgBEwEKkiWQOZAFOvxDk0642gFnGfQIyKqdeAMP4qro83HUWYEswsi75ogzHmiB4yjCZoZMDMv1UR7Lvd+imwZfR7YQSRhUqh3rSHBcg9TgZ0KrpKOFrcAVtmgJAb4WOIG06b01SPOU/y7ua7xEtlHDcw0eErw0JK3WRzmFSD1ZYZg1Y4hQMOhYvozj2CpTYwAlLDgaaCZZG6JNi4tog6qBZpLhO8n7+Rv/R0gCj3yrxgke550Dz7J/93kez8VQ90jauWXNurCsK7upyw1fLzcNRTvrAdOTmlCtEz6yz3sVzIAgyAN1g2wJdGLIJtDSsFSUVGYMc5HPy6sJ/+uhmD1ZtmRr39/NVHLa3MSZmRlarRaZTKYPRF3XZ7uO4ltRoGE7Hqbruvze7/0eP/ETP4FSip//+Z/n7rvv5jd+4zd48MEHeeihh/jVX/1VarUaP/uzPwvA/v37+bM/+7PX4xaufa1v+Bm/z01r3enDeOedd+6Y7uvNUDc2oolMT0/veBPp63G/tNZcuHCBubk57rjjjj5O1kbHWmvzDfjU0y7fnJMMOsZOjunQtsUFIKU31tuf9U+TIoFYa8wpg0iczv7tnKaUwDyocduPUg4CsUHpHq8yLRbisg3F3nlAk8toXj3lsFpOwVcDV2DsH10FCUno0KwP4jYFTTfH15Y+SLUwSlbWcQsxg26I5xkwAuO7+D2tQpLYxRe2KbkjDbIu6IvYNgV60Omet8eUdPn6pZ/gH7h/SisO0BmJm3JATN9rmS42hPXIpdasMkor9ijIriqRFS4QOAKMmwJRXiJxcJRC+JB4Bp0qHDxtTvBq7k5bORtAVM/yrH8cterzjsyzFCdnqH9nP3HPtWjPYqCQdlGQ9wxNR1j3WRkcIToeqb3HdJw2CKMLz3qvgWe7z7RNKpAVyC0bVqsCf1jQFHYcEgFOyfYhVQguLwn+uOnxh5d8fnI84dfuChm7DnBuJSS6lptojOHSQsTTl2JeeUlxeiFkvq7JB4LRAcHeksOxSYcPH4XCdSKKb9W+ktsVLvjQhz7Ehz70ob7Pfuu3fqvz70cfffSmr20n7JYDzGsp0bTzlLlcjv3793eq63bCtiPqfi2aiOM4RNEGsjfbtDagbwaYCwsLnD17lj179ly3uGgjwPzDs5LfedVhORJkHMNqIpDCEAiDFNDomXGVhnpTIJsG3TOxCWVIYnBeEXgVQTxAhz+oUw/SKDpFLQooRFBfM0zGAWcWmIN7DxlGh6wn+q53aubnBRcvC3JZODSpGT46h+cKGuVBlHEZ1atMVyc5VzgMRtJcHSBvmuSHF+y1J15fIk8AUejYQh1sflKHAscF1S5Aakh0Mc1prgENUROcCw7y2vLtZKijMyAigXT7spbrTGjBsjNC1eQ4Kk930NnWChmMMhjXhnERguV4lDF/DmIIjCFyDWfDozzv3k+GFkbaIikVOQjj83j4dxhyq9x27ALV8xPMVCTNll20xDFkMoZWmIaljaDVAQhBNms9UC8DnmeIXJtzjpUVxY9V91oT32ZHU7VCvAY4Vw3JrKAxKdBp4VZryRYEhT44qY5tb0VuoyHIZeBrsy7fXnT4qb0x//LueFPv70ZyiMbA0+ckX3vSZdHPMNtoXyyUSgalNPONGCUbPH7S4Y+eTPjRfRU+fEfM+NAAhcL3Vws0Y8y2ATuO4x/oxuLfP0/pTbS1ecpKpUKlUtnRc9yIh7kVmshOiw1s5hU2Gg1OnTqF4zhbzuFKKTvXttCAX3zS5XtLkkSnqm+qXaQhCA3kVP+XM0p7bRtHYJSxajdGY2KBewr0vPUiZC4NbVrFOZv/S3FELkP+CDx4r2ZhUXF5DuqRh0pvsTSj2T0p2DVi+qpIx8YMY2PpB3vK+JkmjUqBRLkIAQNxnW+JH6Xr3gnqlSyuBEbS6tieRyWx3MjOz6mIj0q61JakZf/R1qPtmIFk0aLqN72/w4nG42BAKmPZko5YF6Zsm04cloMSseNQjQcpeJX0au3/hRQgNNJSGynrQXZpq+CTxFBvDfAX+kPggmq5yJzq5D5rUYAwhr+p/yjvH/kuI/e3KM7b9yKMoNWEZksQRYZ6Q6DjfnBvtax4RJiyc6J0LPw8OL5BCVvo5QlD6Ag8A3LBELwG4ZIgRpAZMSQIG64VFrRaFfCz4O41aGc9hcWEMJAzlBH80VWfC6sOn31vi2CDWXArgJkoePRZh6896TK7IskEhmhdek3gOA77R2E1HuJI3uAD5xsD/KuTCT81OcPh4DWMMX0c0TfTtltwdDNA+1axWxowN+NT1uv1HW/xtdWin7Yndz2ayE4D5trjKaU4f/48i4uLHD16tC93cz1rg++3rsIvPucRaVv9KrEh0FZP+DVwDHUlcLETYKsFUbthhweypjEFiaMl4lRaEUtKzaiDX7ATriMsCLWtVDA88C6DETA6YsjlmgwWClTrtmhkfBGKk5r5eHMvTR2aJ2lkaYWZVFYOLoWTLJWG0S3doVliBJUrOQolSbRWNV3bSs7Oj42e86Xi6FGYQbQk5PsXLKIsMelYlQuDPFN5J5NM4SibcnSkBZeNbKU1jPItws2pPR3AbFsHw1MsC50Mov2u+YZvLPxdKm4eoTTaCIQxaMfuqJEEkaAeDDAdH0AMLRHM7wMg8O2fYtHes+9oYhdaoaDZhGbT/p0oqFYFMqXSaGUBTwhbtONnIOdoqtMaNeXQaAkyvcGPVDfYGHu+sB1hiCCqCZwNSg5cYSivCDLD0JJwsunw049m+eKPNimtWQdeCzSUgm+96PBfH/NYrHTHf2S34Yrq36fkawZCWFqWNGNBvbNwCHAdn+/NHWLo2CTvP5SgI9sC7erVqzQaDZ566qk+jugb1QJtKyo/17K3Yu51q3bLAWZbbu1afMrXoyfm9Yp+6vU6p06d2rCbyGbHez08TGNMh9u5b98+Tpw4ccNfUikl//bVgP8852MEHS/AcUFq06FAOALCuB22g1BD3EjFCABjNGQFTiTg5S5Yds4TQiigWLSeXKLsZJbPwTvuMezzYTqGXu+mkIfJlmGqJnBXgWvRDnavUKlnECkGGuVwzjuAq/Q61ornhdTnCphd/Z9rRaePpWyJjoJQ+3eOC1EUoBsSme05qoZkpT88/kzyAHvVVVsZ44CKDU4AyqyfoBaiXR2e6qwc4win+69L9njkgPGgoXLknAY1M8jL8t5O5bFqGbwU3I3UGAXNioc7qng5uYv9AzOsue2OlXKG+UgSBLYYqFTqLh5UYnACw2xVUm9AvS6IY8itGsKXoJLYJtW5kg1ft2/TAHFP1E/0vJ5OFloRqGXIFAwt3X2/6kJQlIbwkmBozNByBUuO4B/+VZY//ECTiZ7U20aAqTU8/rLk4cc8ZlfWfydiH7CpasYyGrkMs6cluQOaplz/jBIl0Mbw8Es+f3bG41M/IpncV2D37t00Gg3uv//+Dkf0Wi3Qdhqgtluh+2YKxr9RdssBZhzHPP7449fkU75egBmG4brP2zSRlZWVTbuJbHa8nfYw2y3AgiDgwQcf3FYuQmv47csH+F6UQwtbIdn+OnsSQi0YdgzNWCC16QidGyBZMBgpMKQVOkIijMZ9xhAt9E8K0lhP8R1HNWO3bXwtrTKQI61ssRO1ELB60h5r5qJg4B1QXStwAJhMSDUJyJkGHjZsuTC9FzFu1oX6RKJxvZhk2cEtaJJ0rSPT8fCc9AT1DcYrhsS46JZAKLqDtSptPrbHloNhzs7fyT3BS5CeQ0cG6dsm1L22JEZtvFoaam6eelIg73YbXiNAKoHuKU5aTkbIOQ2ebj1ohd3bQ+eBDiVCG1xjBSV0RqBaPq6nuFjbjUzm8ZsZXNfFdT1c10EISeBj3eENLJcxRDnBnrxhxGiyi4Yr35MsTEtaLVguGkxT2OeIDbdmAlAZQ9wDEmG744yik/M2CqgLMlm7vghCQ0sKQkfQAloLgmAYloWgHsH/+K0cv/KOkH+UCh709qPUGv72CYf/9pcuYhRma+tBIZczLLQkA56hUDXMnOqRRczTAdJeGy9pZlt2u1ok+NWvZfjf3x3x/oMxUkocx6FYLPZV6LdboFUqFS5cuECj0ehrAr0TLdDWCq9v1Wq12pseTn697ZYDTN/3OX78+DV1Yl8PwHRdl3q9O2OupYnccccdN/SS7yRgJklCuVxmeXmZe+65Z8ugvdZaMfzcYy7PtAZwHEMpY6iGAIKMMegKmLpgVduf24U+xkC9DrqmbW9KRyJdcEJD9pUYWQ9wfUiM3dZ3oJQ3TO41HNoP85s0Wlksw+igYa6HtL9HGa7Ods87FBmqG4x7a/8qq+VB8iMrJAq0dJiZ20tp93wKTl2g8VoKBiyAuzMCDloui0gXAp4TIbQt9llrRgPGRWiDaAlM1lhqzGr/hKVih9DzeSa+n6PhK0ijMaKtGrQ+n7nsDCMUnVDybLKbw23A1AIRg6PA+GBcu2dNFIi1x5M8gEjjAB0pwpaD4yXodpcXJyFZGSTYU6WuS4hDLXIX8iRJTBSFNBqJDZeiaOkcruviuG7nHR8QhrFEEV2RLL8kWOzx2EaGDSN7NDNOQrOZoFSeahVqNUFUgVIBmhJCkyo1Ab4PUQhRzxovSiB41ZBpQuOYvaOwnSvWEK9CbtKQaMFcC37zlYCLYcyv3BGjtSaOHR79W4evft1lZl4ihcHfRJ55ZMyAMMyeEtTi7r3kC4a55sZel16DSRrBb38z4MOHDT+2a2PAcl2XoaGhvu9ouwl0W/JvoxZoN7L43W5ItlKpvA2YP4h2PVH118vDbAPcjXYTud7xtmvGGGZnZzl//jxBELB///5tg2Ws4J885vJSS1B3HFwpKCeCLAa5ZPNfUQoYRoCv7aLbGGg0DEliMJ7AXRXoIshTMBEaRobqDN3msX+f4fLqesCZX4LRvYbF5saLjUxEH/kver7/97PnNPXdVSJlUu/IxXNdpskxmFts0xJZntqDcUy/LmtqXhzjKEt/SGoCrwFx3mA0qMRFuE1kvZ9K0Td2xnrMpikhq2ClR+g2tVY9B0DNL/Da3O3cUTqNSUWjtOrPZ8bKp+IOIBKD8exJ5xvjHFk4j24IK56AFXeIY5C+QeYMSU7yfOZ+WiJjY5h071UraTuNuViPUYKqa1TVBRSLy5I7zyn8UQd8K5auHDBJTL4eE9UbRLWIZMUhnMmw1PIpHBXMLKdk1DWWGwLKBs+z+VCbQjdEEXh7DZcrEtEQGA+iNOwfZAzN9FhuCPI8mKogyRoCbfOWxkAmA60G+MoQ1gVOCoL1puA/XfI4dUVy8PkhXjxVRNNV5tq1zzCXrAe/Xb4mmYOZhfW/G95rqG+QJx8raubTato9GY2LfeR7MvDnr7hUd+/mvvvW7bahbdQEOgzDDkf0RlugvZEqP281uyUB83otvl6P/pBtMYQXXnjhhruJbGQ3C5jtyuBcLsfx48e5fPnytivctIaPPubybE2i056LARpVltQiqwXaqNPp7RgEhnJT4Dc1S4mdxN79LsNrr0nKV8B7Ae7cbxgdh9U0HDe/KHB8OlWuvRZc41HNLgoyY5qaMewGZs92vctms0lrucXtt2WYlz6JUtbbbtSZVgUeLK5iMOjE4dLUATLDdQuYa87hm6hPB1XPgDhsgUwrF1zQ9c2jBzqwla+6KZAJJOX1E2/YytCuJ3ravIs74tP0zOU2n+lb3uFSNIrxrfspawK9IFlplKg2BsgN9EQ52h1ZIoGOBKxKHlv4UcR90lJOTJfm0vaGTM/azvVimtUMXpCw4A0yNd8ieKV7UcWioFzOYjke6f5GQ6LQOmFxtc7qqkQIiee5nQWLlBLlrh9ngIG8QQ3DgSFLkEkSqNWgqQSJb6hrQbYG8Smb0w5cYAhaK5ApQcvpKh2prCAObS6dyB6j3hB8RUiGa6PcGSl6McUfNFDr/hw4hl2hYfmKoFna+PmWN+tB68I+qalVBDM93vVAzrB7VPO1S2PMf9Hn//rH0bUkeDe1IAjYtWsXu3bZ7PJmLdByuVwfiLadhe0C5tse5i1or0f39pmZGRYWFrjvvvt2pJvIdgEzSRLOnTvXEWZo50duBoB/6XGHZ1cEg46hqcCLNc2KtBw3YwtzHJGSsaWdpJJEUVWgGpL33mE4ZmBPqFnIw+SPGZZW0xBjCuKtECZ2wfTK+vPPzAtyo9DYIBeZKNiHYQFQL9swYxzF1Go1/CBgaGgIs2Jg1OB5Hp7nMT+SIQhigmyMkYK5S3toNF0K+RZaaUzqxVilU0FGhqiec6umwK9D5FnQkZGV+dvwecQuwjeoRCFwMAsbI0UzyVrANIbVoMTFmUPsP3K+bxsV2SKgZT1ivch5gYq6k/FsdQ+HBs71jU2vc7e6MMzyxVFkPsQpaeSoQbU3cMFEEnzdUd3xCgmVSp68nxBnAuYPREwudo83MCAol/vvw4KjxPM8hJOhVLJFeEmSkCQxrVaI1op4HqLEsYtbrTsVvENjhjnTvSfXhVIJhqXG2Qfj5xTPf9eh0bTt2kLXIAMbDg/nwB8wVAKB2zTUEYirhooRiIwthHKlVUlaGnKZG4bJHoBcjdt5XcNez7D0mmC6KZm4QzO9wYJoZEyzFK1f/ExmFStLktqa7i6ZwOCUoF4TlIqa7867/PvvGP7Z++NtgWb/uAuy2SzZ7MYt0BYWFjh//nyncCcIAsrlMgMDA1sGz0ql8raH+YNoW20ivRPWpomMjIxQKpV2TAfxRgHXGMPMzAwXLlzgwIEDHD16tO8Y2/WqP/uK5L/PSSKELb6oGWhApqoQrmTAhXrF5vO8lsEnYXlOEVY9AuNwqGTIa7icTsy5HESmzRbsx45WY+Nr0BpGfcPlTSgiqyuSIRUy9yLUa1WU1gwODuK4diJYmhOM7tEspRSOxaJgMF+xlbdacmX2IAJBUIg7YNkeU4PBN81Ug6/nd7MGJi2lRGxQ7NO2qJVBBgYNSKUwFafjifdaI/XSdMplfbL5IPu5wFp01ZGhEZbgCuhEIILuFrOZcQ5hAbNdIStkN+w6NXcAHTlWkGdV4jcMeo9Jc5wCEzoIXyPaTagLCrGiiUMXPSiYHfSY7Lmea72jxWFNOQUgKSW+73dChPmiphIYhG6ilKJSrWK0xnFdShiSONuXDwXYVTT4VZhakBy/V1OpwsVpSVla+cV255oosp1vtDQkzXQlBxCD6xm0DzonkKHh3IjHQKIZasHwLs1KKNjnampXBVd6vMJ4k1k0NwJLPXV+DoY9NbvMWguWYPOgVxoSgxXzOLDL8NmTHt895/DFj7a2LbG3mW3WAu38+fNEUcTMzAy1Wm3TFmhrrVqt3rSE6Pe73ZKAuVW7mXZca2kijuPw7LPP7vAVbs0qlQqvvvoqhUJh05zpdjzMx6/CfzjjUFaCrGsw8+DXoBwKtJQM1KBcFyRJOpYk5OOIAwNZhvcLPFfjSnAalvDetmoT9uwyzKypjF1chpFxw9IGGrOrq4K1FMju8QTBuSZLq6s2BBUE69JmQdlAHppSU827jA5UQdjK2CgJAIXwQoRwMTptsyysCk3WC21409gwIQjihsKpS7RU6E3yqwBx3I35mZrCcQR6gxV908l0CPoIWPRHuLq4n72jl/q2k8uG+UtFSKP9nX2AyuAAYSNDkGt1sL2zKDFwuXkA7UubFPSN1ea9IBCTBrKgtbC1sw62bFgYPGKiOEAEhkbJp1VokKna629uUuwCMDAI5eWNf1cag7pybIjWcchksxhjUEqR+C1arZAkLaBzXZfAdfCuwtRipvNcBwtw3zHN8Ds0z191mFsQ1GsCFYF8zRDfLvveFwN4saE1ZK9ZeyDH4JSQvG9aMVzQqKtOH1ACBFnDYnWTcGxP5fKg0LjTcHVZENy1fttc1jDbBtF03nEl3DZqeGVB8kv/NeB3f3Z9lf127cKs4OC4Wee5tqtze8O5SinqdcsRnZ6epl6vI4Too7bk8/lt5zAfeeQRPvGJT6CU4mMf+xif/vSn+34fhiEf/ehHefrppxkZGeFLX/oSBw8e3O6t35S9DZibmOM419VW3cg2o4lorXeUBrIVi+OYs2fPUqvVOHbs2DVfZiklcbxBTHMTa0bwSyc9FhNBDoO8ZKiFEpMx6LanNywQdSsNlvEjJnY73DWRY+5i9ziJhr3jhstT/d9cswFvDSC7yRxcqcHYPsN8o3+/RCm8+gLR1Qql0n7kJsedvSjJ3Ws4P6jRUpAfrGAQTM/sxyiDH4QIAwjT52XKUIHRPQsrYZswK2BZ42fD1HNPveY1M1RiXIzRCG1QDTAyQQROn9+oE0nLD9Z53C9V7ukDTGfe0JoPqOTzCKOskGvvDkIwX97NZO5i5/M2q2R5fpSGsKRUc8VF3BbbCtQEzEVwDoAO0mtvfyUMuF5CpANkKDAlwcwBh9tespq+qxsUaXUu5Rozj8jSzRWK7rj5nkPLyzPgtvPQBqFi8s+3uFJIWI1aCCE7udBc3mEFh8m9tqLaJIb6EzB3WDIrLXgqzxahydgQjUp73qzV2XViiCYEL4aC7AWHRmP9/YzuNVxprX8ph0Y1K2k4dg+apVcEUSTYfVAzG6/ffmTUMNWQjPqaVjWhFRny0uC7hl0ThmdPO/zff+3x8b+39e/oRtaK4I+/5ZEo+Kcf3PhYa4t+2q3N1rZAa3NEH3vsMX79138dz/PYv38/Y2NjHD9+nMOHD1/X4VBK8fGPf5yvf/3rTExMcPz4cR566CHuuqu7qvjc5z7H0NAQ586d4+GHH+ZTn/oUX/rSl25qHLZrP9gs003sZppIb2bGGKanp3niiSfI5/OcOHGir+K03fLqjbD2tZw8eZJSqcTx48evu/K7UQ/z159wqMZQqhncRUMtJykOGpIQEALPNTRamqQQsm884t47A0aGXeYasGu4fxyWW4K1ODa3AoUNaqJm5wXBJp6k13P5lqpSp1qpUFiEcllSKGweclYKhmPDctG6ZAODVZbmR2nFWYw2BEGENgKtTJ93mq0n63KOUthtkhpkw8R6oqkoels+rP1HCYHWBtHQHS1Zdw0BM6xngR5XMbVLcoJKy7ZScuYMalWwUh5Ga43WGoFaV20757bzV+k4pZ9PzR3ojl3VQfbK9GnQl0BEBhPKTuGP1iALaQ/QCEwRFoYsEpZKAqU2/57Vr+EsNdrXvOZ+h0YNSY/XlpUw8rJLPFuA3DCl0hCDhQKe51lqRHaFldVVKpUKUaNG8VKToq85+sOa979H8b4TCk/Z4h05ALJikMsgayAqVp/Y1GHpsMPlTeYMtQlbYyBVcphsaWZfkERpJx5ng85XvmdYjWHC0SzNShYrDrWWQ5hAkoNK4jC4G/7zd1z+4pntt/x6/rzkVz4T8MhTLh88vvnctpUqWdd1KZVK7N+/nw9/+MM8++yzfPCDH+Q973kPFy9e5JOf/CQPPfTQda/p5MmTHDlyhEOHDuH7Ph/5yEf4yle+0rfNV77yFX7u534OgJ/5mZ/hG9/4xpsmwfe2h7mJtZV5tsJf2gmayHZtbdi4XC7z6quvUiqVOHHixJb5VDeSw3zsMnzjNUmrCQM+rDp23dXMgpaCYiNhtaEZKkYcPOpze15w+XJ3f2dQQE84rhbC3t2GqzM9OUCgVDRc6vaVBWyhyp4Bw9TK+glsdkEQDEG1GVGr18lkMhwbzzP7YhOtYWS4Tr2++cLhtXJCzQvIBU1cL+HK1f3Y4CsEfos2UkrRVvoxeI0Y1hyy/WU2DYFwW5BrqzaJdSEwE4BIFEmj67cmzRiZlx0xglZaIbtWyEDHgleq9/D+8mOotMtKOe5KGGqlbYrO705+S0MlVCb8MUAAACAASURBVOyCtBOmSZ3fy+GBzkJAaQdXWIGC7oWCmRKwz8GMaqRM86k5hVxWGMdBALWsSysXk8tJljcJubquobxJGNMPDCsp3cLQv6LP9qTHctLgP25YuizZfUwz2/bge/Kho4cyhAik0eTPtZi9aBg6uMTciofjOLiux11HXe4Zhz8/E7BaF0gXdAvIg/IEcs4gd8O5Y5LhJ3Xfwi7IGhY3SA8AtAyML2imrvYUKHmG+Wj99hPDipllh+moW0wmhWBw1HSoJ7ksFHbD//moz6GxFscmtg4YrRD+y1+5/PlLdl66/5BiYnTz/bdbJRuGIR/60If48R//8S3vc+XKFSYnJzs/T0xM8MQTT2y6jeu6FItFlpaWNu2W9HraLelhbsW24mGGYciLL77IuXPnuOeeezh27NgbCpa9XmEURbz00kucOXOGe+65hzvvvPOGyMdb9TC1ht96wqXRhIzuls0HviGMBcJJUEMh7727wtFDGQJfMhULxka6X9DZBowO9X9h4w1W8AtlgSPXg3ilvPEkFcUaWVug2WxRLBbJ57K0Xu1qqC4tNa33t4ldKkmQkkKuQr1cpFwvYdKeU26mG77S2oKbANxmf1hLQHfhUdXENYV7jXOKHMgmSCHswkcITAgqURhtmzk34qwF7rWH0YLTV28nXOy+c6trXBiVaFzZfa5GSpZXx7s/A6vzo7RED/XDF5COcbe2w/I39StWkchxe4QbiDEOmCrIYbgy6WHM5lPL0KhB642fYWncdD1b019I1fbmitIgv2VYvWzP4W0ic7wq7VPavSSoLuTJ5fMUj45SKpU6knIHKmXO1qoc2rvMxGgTXEuKNTO2gM0pCZI5QdiC86P91zx2UJNs4EWPFxWtU4K5q/1jMH5QdxoPtG0SxfKqpNkDpMYYxoZVByw74zYIg6Pwqa8GfTn/a9krZyX//N8EPHe5C4B//8S157XtChdsJ4e5kae4NgK4lW3eKLslAfNmQ7LtvpBPP/004+PjPPDAA1vmVO5kKKHdFeTy5cs8+eSTjI6O8uCDD26L37lVD/M/PCO5tCgIYkM8AF7VMKQMqqoJ3CYHdoccOehSzwcMWa49Bmjl+8Ou3prQ1EINRtaAaCuCkdL6PEu5CmOF/m2bzSblchn0AMXiII6UTIoWq1e6M0u9rhjf3dr03sq7BGgoFCpMXZ1ACtOp4xGFnnfBgJAGmYDv9McWpUwl+ABVT//d2nh2i0MfYRJUzyUJwCiBNAZHWhpOy2Sxfkd/OFc2Q6LI5dyVOzr7L2XXx/x0nCC7BBEWdL/y69zS3nX7mJl0wlwD9okr4Irp129NFxMCcAJYHHapX4N3mrmGfm/QQ+Nb+01ZVYJRoWn9JdTmuxdQ32BuL41o6lowGWqunrHb5gcNC1piO4i4HK77lCaHyJeGKRaLHJoU3HekQUmHGB9U06CERnsGUTfMOoJaei4pDctrKCOBY5iQGr8lqG7gQauBNWCZaBqrgtVwzTRsDEkg8aRhMq8pYtiX0ezLa8YGNCYj+Jdf3lh0oDMmDfiDP/X4zX8fsFoTzNUFGLh/n+K+2679PX8jhQsmJiaYmuqGkaanp9m7d++m27RVyW6kGcRO2i0JmFuxzQBzYWGBxx9/HK01J06cYGxsbMurnZ3OY2qteeqpp2i1Wpw4cYLdu3dve+W1FQ+z3IT/9LzEiSBJBKoKKgsVEbFrrM6P3yk5PJ5Fpu2ZnHw33VeJYU/XsWGmLtYBZHYDznO0iSfit9kAScLK6ipKa4ZKQzSjLKNZQ94zzDy+nrRp9MbclFpBUc96aA05N2J+ZbyTQ5NK4eT7x8ZoW0UaZNYCcLqPThDpvJRUEwt+ayyOAnRFr9O5EWC7hCiNIwwNJ4to/yeE1YENY1QzQquYF8VddpKNHZY3WCwJY8OzAoUQMFccwfSM60xjX//2ApIUhda9TgGoy67lrqbmDKbqE54NydczotsTcgO7RmqTuHee7kk3FIuaYmJY/TNB2ANGftawshZwgMKYYbfQTD3d/d3Qwa73OrGsmbkqWCmk3EohGHEdju/yeNdPeBy5vcagA2bZ9h6NAkHiKV4SCfVGndLuBtVGdwz2ZTXyKly9KDasms3kDfPNdgGTYaKlmTojyW7QcndXKSLngBfD1KKk3LQ0lmoDBvNwdFyxEgl+7TMuX37U5fR5SZJYkPzWEw7/x3/0+ae/luEvvuliDIxPGjwB40Zz4vbrR5FuRrjgRmklx48f5+zZs1y4cIEoinj44YfX5T4feugh/uAP/gCAP/mTP+HHfuzH3jQP85bMYW7Hw7zRbiIbWTsvupkk1VYtDENOnz5No9Hgnnvu6ZR/34xtxcP8149JKnVhKwl3QxIrBrMN9o17HCzm8YRNjR0yirkkZimBiVHD1KId78aadHBQAnow7WpFkM1AsweDVus+h/fByhoC/Ow8tHSFVqQpDBT+f/beLFiy6zrT+/Y+Q87jnaeqQg1AFQCCAEGAkJrUYLLFFqWmJLcl2g5SCot22ApbfqaDEYqwQnJQT36wokMdQblJdbitJq0QSanDZouUKAUpkQQJDiigBtR4h7xD3sybc55xLz+cvHnzDgUUCiA1gOsFhXNPnrPPtNdea/3r/7Htgw88LeDudql5x53U9nZAoRDR7R5+9bdmNMZJgDW9VhmUwoTJ/XCt4FBEBSSUQ5HCzR52mPv3MB4yViYRA8oPUG7qUFpVe/p4mnXffBItytDgp1JMPhorjImHwch5GpqFabZ2FnHsEKkwarBM9lUoJFYJ21Bs0FoIXZu93SmqU7v4/TQNqRwCMikNxtJoAycIoUBPE7UV2hKMq8A1WCZGHJuoB6k8bCwrzt06+eLuVb8EaJ3QnwgwbSJu/alzyNEDVM/IuH45adpVNJ8/vN0vAAIrHcPammbpYcOGaGyEhVDoDWFtLkE7lRdDzjwqNJrC7nVFraOQoo0/sNiKFDO6i9sboL2IYSvNK14Kx7ZZOW+xNTjubKZPCetGYythpi2sr2u0JexGh8eYs4QwFjb3bGz74G/VgqFjKTojpO5KyTBUmi8/D5//ks10WdjYUiemiC0tmLqibyne88z9AfseRHWk0+m8bodp2za///u/z/vf/37iOObXf/3Xeeyxx/it3/ot3vnOd/LBD36Qj370o3zkIx/h/PnzVKtV/viP//h1j+3Nsrekw7wf23eYD6omcq9jvpHWEmMMq6urbGxscP78+QRq/wad7769VoR5qwFfuG7hboB31qCMz0NLMeVijlNZWO8fkH9LZKPvQKkN/kNQTEPHg70A5meErVF/5dZAkctAf7h/fTAzc7zFJJ8X9ibqlr7v0+wPOHvWphWeADvse+xe6R3fTpISL5cGdLuj1NFo0HtzyQSR1j6re/NYlhCP/m6njmcaVAhWN0QXkqhFjKJxc4HGVo5eu8BeIw8CmZf6TGUbTM00WHiujZNJUrgK8OoC98AtxAHoHHj91ChEHNUU45i45x24CBGUNrzce5wz2dVxBLp/bYIkOqFWgu4REcTENOIZquyyvbWQgIuOgpEsBTsWZj7mWHLU1smWpkHNWogGR4V4VjKdOBY0pk92mPmioXeP/sxS1dCe4GoVEh3VpXgX/3YGMcffdadK0hM6Ya4ltK4yRqYCpLLCLoq5yLB+OzmHNwWuCNkG1HxF4bwcy2hMVWH6OWHxVsS3btjoOagHDr27JXSsRjfZYFkhQRhS77ZodR2sESexbdtYlo2XgmwgZLZkzDk795CwOXG9edtQNfCS75DJTETRthClFdHE9ax5mpV8TGYFXAxBdBhQls0I1YqQdoUb1xMH/os/E+L+ACEWvu8/UCDxgQ98gA984AOHtv32b//2+N/pdJrPfvazb3h8b4b9yGHewyzLol6vs76+zqlTp163msi9jvmgpO7NZpNr164xPT09liVrNptvWm/na0WY/+uXLFK7BlMJKBdDFucy5Ow0pwoGTxRzuUR9pOMnfKayBINt6HxHcfaRRBFEBCR7cA+NJEQE/TsH2/aOKHoopdhpgaUhCGN6vR5Ka8rlMvYJPZX5lKH+ndvMzmZZXz95MdFoDNCqgDGJA+k7wqCUTCpx2yUqa7SKAIWODXb2eA1SAnCGIbokNO5Oc+W7jzHwcxgTo4MwAQalYRAXGHQLrHXP8HJbuHTpJqcu3MCOYvzo3u+TIpEN8wcZSBm0laSATdc7nsJVMTfKZ7GHR3XHkggTklYXM+oRNSKspws8TMBmeyFBZTKhdrLfctKwUfPxsbSsKQsqGok/twxS1VjZELwM2obAQJRReCqJ9ietVBV690DP5qehPXEJOTskv73FRj2iWDp34m8GCff7xCULK1bAzebhdMb0GaFuFP1byXVWZw0N0Sz2DbWhZuWMYc1oFpwEWdyb6McRYOY8vM3EvHzXIswI1zqaSyOSCsuysCyL6rQwsHOUygnVYRRFeJ5HKuuzsyWoDZc9PzVyohaUgVGFoGAZWFWEFwX8g1S0QliZMwRGUbKElbLhg49GzOWFtY7mP3zDJojhxncUloaFOUMYKRotxU6D8TdiWcL73/PmCkpM2n6p6Z+yeDS8RWuYr/VQW60WN2/eZDgc8uyzz7KysvKmvAgPwqbjeR7f+973uHPnDm9/+9u5cOHCuL7wZkp8vdqxvnZN+NbNGNXpMf92OLWUZ8nWzPjCDV+z5iu2IkVHwWwxIbzuisXMI4IxcOOK4nwvofvaDmB6QkS4GalDDqDrwezMEUCPD9lUm3anQyabpVgooLVitwnlCQCJUpBtrOEPQrrde/DoAYOBYX6hj5EkOqzN6CS1CKiBQmvBxCMOOgNONiCZNhPgjYoNIgrpK1788tt4/uvP0fMKGBOjRIgjQYfmWNQW9TUvvvI4X/3L/4z2jSJyLxaGfQuEYZhOosIoQPXvwbEnMaI0d2orJ/8dDoLEkRP18znaewW2zHSCHBaDEYOIIY6T6zRB8p6pI/VXsUCaVpK2Hgh6KOhRHVO5EBYVOoTNpePfjLJfZZEwEZwsZD3Cl+7Q2vTIZBw6neNrezctNI8ssJZ1QHACrisuw0xD6I3qiNkVWIkNtT1NqWDYc2HBNmwONOt9jQphxTHkrcRxekZx6aLh7Y/EMA07aU3/yPqyspiAxBQK27ZJp9Pk8wUeebhCuj5FFGUxJuFvHQYNrm116A/6OOGQ6I4hRtgO1QgcrHC0cDZnuFm3WGtoTpUM/9OPhZytCjkXLk4bPv4vAqZnhbNPGGKTKKbs7iXHmJsSBqPr/YlnYqZOSMYctTeKsfiRw3wL2WSbyLlz5yiVSm9qm8jrIUPYR+K+8MILLC4u8o53vINsNntonzfTYd4rwux2u3z8sz0WhkN+/OezlHMpVoawc0cxKB3rLWcngHwWUipiwyiWH0q2t9qKqZeFlAJ34sPtBTA/f/gg9sTEKSK0Wi0ioFKp4B55HkXn4LfLdoOd2y0A2u2QubmT742I0Ov2UCQr+eacAg26AVFOkYQsgqUMRjR2MWQU8yURWyBEWw63v3KBjZ1ltEpqgwioOBqDdo5a7AkSRfTaRf7q6z9N/fqr95HFPgSSSlgVeh5xHKFPaLMxJkIjeC+mj0NL9695lLIz5mCHq/WLBLiIhNh2hGVpLEuP+fJiG4y/r7uZLBiSthmQCVCPaRoUgh1HWKNnp2Jhd+745PlqhAV9A1nHsBjssPm3d/EHyfOrVE5GfScgnoNzzKYj1v9uSFcOO1fLFuxA2NhIxmzbQugw1kWdWRTCULE5kSp2TZxwIrdgqW4orxnSHXjyVMw7njQsPmS4MeH8F04b1huHp9NS1rCUNWyvaoJA49jOSGKryMNPV8gXilRTFuGtiO2tAVFhi1a7SxxH2JFPfjdmbxQhPj4f8z+/O8Q+Uh61Lfgf/3nIzKxw9tGDd2OuatgYXV82I/zXH7w/hiBjzAPVL98Ijeg/JvtRSpbkJbl79y61Wo0LFy4wMzNDv99nZ2fnTT3P/Tq43d1drl+/ztzcHM8999z4BfZC+MoNzV++orD2YNCe4+GlmP/qZ6D6BlV1jlG2jVRN/s0XsnjeKc4t22zbMN9JQDwrDwlrJwAMbAV5gaET4DqwpaBYgnobZoaQ+Qb0n1MUctAdBUxypOyx3U14ZhvNPsYYSqUiXuxQyEHvSJC1s6vQDixnuqx+Y/3Q37QeMiZVJXHuyYcN7bZhYXHI1dUcw6lR2vKKYN4DtH20JxDHWFrjWkOM2EmPpBiC2y71/7AE1WT2MkbQWlAIcTCawk9wXApQ/YgoSKKy299/BG3D1FO7x3ce7R+Rgr6HRDI6V4SlXY6ubdx2iDdMIbcs1Lnj75gYha0lUSgZ37u5sURYGBrQPtqy0UonjshSqM0Ucsof3z+UQQQiG6x9BWsUas/g2CGhchDAuDBQCg/Yf7yuK7Q690A9pwx5GdC/vEVteHj8lp09+TdTjNOxOcfQ+VafdE7R8g57ldklQ/3GgRNYOGNo7WpiUZyai7kxsb8rwhzCS22btRHSq2QL/W5C9ae18NhiTPk9mu+1NTo05D1oThD/51JCxRFqq4r8GaF/AsipY2sqSgjvpIA05YpgL+TJB0Lc2sWs2fRLHXa2XbKu4l+e3qXdzlEoFI4hWF0b/rv3hfwff+JyZiVGIri7cbDPhz4QUrrP+eFBW0r6/f4bkiv8x2JvSYc56Rz21UT2ndP+y/KDEJF+LdDPcDjk6tWrADz11FNkMgfN5Btt+Ph/tOmM0k3FFLT3XK7XFH99xeannzD8F//MMDN10pHv30SE7e1tLl++w/OXL9ItVTmb0UyfFSSE9V2FbcNOSh2iXcsC8ylDo6dZH1q0umkeLQpaKworQqetsBYU9a9D5suw+G6hO+rV2x4o8vvOUKDX9yjIHqlUFTEGrRNu1WpZ6B3p7/N8eHiqz/WvHpa6AtjaGpLP5+h2FVor2u12IhDtONi2TeD3qRVzxFlQA5BdQdd9ohG6VmtDSg8w3QD6ARQc4s0M9T9exgQWypVRihMgHkeXwLH+xfH9DfpYVh4ZRqBS3HzhEZQWqm9vHN8X6IXRMWSokRCtnUNOU3Y8IEX4Ugr33MnpaH3Ei4fXU6hzgmT2o2fBmAgR0NoCLKRtoVRCYCCisKwk4KUMJkh0HSU2xEOw1RDPzqItMPMKdR02ZxUP7STnLU8LO73D0YulhfnpNo7Z5s7fHbn+UdTS75/MtrVfv7SUkF0fUO8aFh9LMTyynxOCP+HQxFJ0+4qSY2hmNJYIc5aQVsLuCMgz2ezTjhQrC4a1dYUxCn9XMZ8R5n8u5qUvKpwW4IEdCXGs6IuiP/p974TAbnrZEMYQ3lZjftr5c0ItSrhk1zdsUoUC6TMFygH86pMd5oua7e1tbty4gYhQKBTG5Oe5XI5CWvM//ELA//YHKVY3NcWiUMwL1ZLhZ95z/1moKIoeiLSg0+n8k9fChLeowwQYDAZcuXIF27ZPbBP5QTjMe4F+4jjmzp07bG9v8/DDDx+jfGoO4Le/eOAsATo+ZJcgvG2IYviL72iuvqx47pLwS//CkH5tRr8Tx/Gtb32bF6/M8NVv/hgzy5rCHOxtJv2WOyNwzvwirJvk5ZkTIe4pRAm3lUa5MJcT3HDIXlCmpIU9UVSnhK2GYmpRaNQUq/9JsfJUzJpKnGFlWmi1Db1eF9uyyc/OEW1rPM8f532bJ9CQrZTatK7fOfF6RIRSaUink6FYLI10F0OCIGAwGNBqC513VhBcnMsGCQIiP5lclE5qQloPAIOJFdELQuPPKph917Nf99QGiSNUfOCQxD6e1tJW0jeJ1Uc8B+3EGLG48a2LnFdXqD5xGA0jwyGe8dHawpiJ44lgJEBbDiZOdB/DejIz+xtp3OEQMscdtokN4ypMBNGmi84Z5KFRTVwL0b5gtImACKUTtiXL1kSj+lqyM9C00QuCEUOCFo0giBFHY1zQHtQrhuWNZBJOZRmTqqdTMTPlPZpbN9i40WNlZZGTdM1sW7O39+r1y/nhkI1bI/KEvMOkx1zOhtT7B8ddLMes9y20CFNVIVAQdhVWEe4GCb1DW4TZok804TjXQ81MxVDf02x6mmrdkD8tzD8KViB0N46PffG0odY5/h4Uq8LmLc1wQsUmLkMhMnhriiCyWDgrbASap+cjfv4JF1hgYWEh2TdOwG/dbpe1tTV6vd6YIP3X/2WJv3p+hucvZ3jHozG/8oGI1xMw/jBJC/4x2lvSYYoIN2/e5OzZs/dsE3kz64OTx/T9w0WcnZ0dbty4wcLCwqH0674NA/jXX7NIO8KpEbnFZlsRxtAKbSqnhgy3E5/SsRR/8v8p/uKrmg/9vOF97zb39bHEccytW7e4dsPh+9eeZL2W5qEVwcwJq5ua+VNCf0uNJ1MvB5kYUruwMUgm7OKZhDpNgJ1A0dRpTufBHyoWQoO/oGg2ILUC1CAMQK4Ly9WArVmHO3s9et2IXL6A49i0hjBdFTqdA/Rmb3jQlqI1LKV3WPvOHQCmp7Ps7u4/LxmnX+v1PradIY4P0Iz79MDbQ5dgUaOHQvg3AdbbPMQkYBa1X8d0hygtSMOi+ecLRMMIZXXR2RyG/ZSsQUcRJmbk3IDUYeeutMGYYeLcwiGOKCLjoLXBGM2N5y/yaP5F8me7AGjdY9CNky9UhcDxFZCJQ7RlAwpaGq1DjHGIX3Swnj2M7NUKTChoJ0hAQrcCVKBR60PUcma0j0YbC7SNKBvBIrYEGhGqYtDaQSmNthRiFMa3gP0QKnkm6c0AfzoLHuiiMBhour6PNejRaLbIOwEStuhstfDqBy9nv29zUh67Ws3TaB5fKFVOC9toViyfte8cfFPt+OCYGccQtXyGoxqorQV3tC4+5RoGWUW9rVioCGuHyA+EukpzfkrodsALk3cwyCrsjhDFitQMrH7b4uyTMeFTMF2Nuf3iRGo3JZwU5y9PGzZvaoYT/abFKUMnUrjbiRQdCP0sLEnMv3rs+ALbsixKpdKhnscwDOl2u3Q6HX7i7Zd5+vyQdNplfa04Vhq5nxa0ByUt+FGE+U/YlFI88cQTr4oI+0EUsG3bpj9COr5WhLtvf3JZ80LtSLN2VvADRRDAjm9z6YKwdl3RHsDKeWHtmuLf/F+aL/614ieeFH76Jw336ideW9vh//1PW1y+fpbvvzRPtZpmeVboWSppXJdE1b49Ig6Yrgr9WJHahdZoRlheFlZPaJHoRgnv+MBWpOowOydsbitK09DehW5osfM3PYzbZf6niyxfKrG5dTBxpcYlkYPnpG2YLfr4G7dYu9E92Dc17gKdqFUqfF9YWgrZ2Dg+WWzpLGFR43x1gMHBVBMmHSFByQrg5CMiz9D8f6aJRtcrcYQOd1Eyg7IUxBFxOMLKiAGjkfTEBKwABsnN1CMeWtUHMomztRQm1rzy1Ud429x3cQttjAzpD7JQhDgO0cpFTmARMCZCa4X07CTCwyG4niYzcphaxSjto9WQMPLRYeLQo2sGMRFRy0b5ATiayE9afQ7GrdFuGjYFqSqUOixRJxlQOgEiySsWtDV6N8D5SYdQW+gFg1wXgnN1Trdexm+n8P2IMAyJoog4jlFKk8ul2NrysW370IJRREin712/XHBC1v76IJwszdq0J+jqKgMPa8oZlw4WRGi4mikxyBR4Q1ieSfpt87GhN+qJlBHvQz3UVIsGbzfJu0+mZjc9TXXacPdFTemUUKoIC283tG8pogAKi0KjNTGWvMEJElKI4RFyhspp6DeF3VE0OjUfkBE4lRbOL90fatVxHKrV6iHKON/36XQ6tNtt1tbWCMOQTCYzdqCFQuFY+vVBeWQ7nc6PIsx/yqaU+qFLxFiWNdao3N3d5ZFHHnlVTsR6D/785eMpneZAkXVgKifUAmF9qJiZFeo7ii1PkS3AoAt31hXGh3//723OnxdOrQinTgn9vmKvFfDtb+9x926OVPrJBCEZNBPUaRZS08J6S7FYENYnSAPyUxBNOMtUCmpKnQhyWXSFRl+h0+BMCcW2YgconBWaO8LqRo+pyhC/W6H9FYv8eY+Vedg1GYaRYqersB0Z1dRgPjdAtncYbDXp9Q6vvDc3PbJZl15PRlJaB2MeDPokasEH2yIDvTkX1Y6QK8lEIVNJqlWpGEGjAbdq6HyhTNBMYSQaT6ZGBYjfQaWzEB3wtIoItkREE5+W1gEmjkYo1WT2DiUaR4QmjtFaE0Up1v5qiod+fhNtwXDENp442DBRNT6ykNNaIa0oIYvQMWCIOxZ6e4DMDzCSUPTFMtbMAhThenp0bIXeHCKncxgxaK0OaqNiMP4A1euiwjTayo6jagBTgKgmRJ+z8b6fT8YSxfAfh+j/XBM97qACw5rO81Q1zeamjLUqx8cwQrWao1ZLehb3NWht28YYw3B48kJSuzH1v+0fgmkXF23a+84xG1L7uk/5J4sQQN4Roi4MDRRCIXITNZK7+2QACkoZIa+FtY6M73Mz1CyWY2rt5LprkSKbFgaeIjUL8a4i3xOGRUWqCcWyIeNCBGSqCUBKGdi4q3BcjjFGaS2EXWG3cSAymi5ENNYU/8t/+8ZKQqlU6pAQtIgwHA7pdDrU63Vu3bqFMYZcLjd2omEY/igl+yr2lnWYP2wTETqdDpubm5w/f553vetdrwnf/ncvWARHssLTacEKFIMBZF2Ycz0G5JPet10II5hZFgZXRrWXhqJYhqvXFFevJTWocqnF7TtCPj9NNnfQpmGMxs4a9jyLlAVOBOn0wZyUtqHVUGNnCTA7LawdiXyKAjnpQ1ym6AjdMOnTXDDC4rTh5pqPiXpkMiVmFvJsXktSarWbUKzX8bo+xak0qaJDQRoMd2P8Xkht1KqxspI55DBFIIoMlYo6kfR7by9keTk8RGSwOcxipgxcD1ADG1UIiG2NYpS+FACDd8Wl98o0WgVYlmDMqDcxpUFCxGti4gzj+ptSxEGEx+qGGQAAIABJREFULloYo9A6xsTJDVM6EZaWyKBsByNdlCojohEJUbpLo14i/80SM+/aY6CTEFuAOPZRykImHJZSYGJB7cRoLZTLkM161God/O+1cUZtHUodPENjDCrURPUJROOOoM4wJpo/anEqg/gexvHQKo2QT1C0bRj873nwdUKnZ5KVjdqL4d8a9K9EkIe+FBh6eaB77NhaK/L5CtnswbcQx/EoNQi37/iIBNiWhT0Ca5VKQv2FAZF/BMSUtmGQkKC3rwwozmpao17S4p6gzsNCJJgV2LE04REwVTtS9BQUnZjJ16irNXpUz4xFMTVtGKwrtjxNZcqwsatYUYZoCkxLcfvmyd/13BnD2kTriWsLK0uGm1sHz3R2ynBrO8sv/kTMfPXNXdArpchms2SzWebnExJbYwz9fp9Op8PGxgZ7ewlXpe/7Y1DRvrLLq9mPHOY/cbuflKtS6oH7kiat1+tx9epVtNZUKhVOnz79mr95pa742gQDzrQjlHNJKnanD34IrZ6NN3B425JwN1AsnRXWbiS8lzOLQr2WRAt2GVQTfD+g1+szHKR47NEM9bo61GZQKocM04rFOeGmpzhlhIalkuUysJwSbhxRne+ngCiBksxHQrynCIxwR+XoTzSVF9PQVwG7V/eIpMDF56ZYe0Gz1YRcAfrdBIVZLJZot3fo1D2oe2jt43ke7gSn186Oj+tqgsCMlDsSp1Cv+7iuSxAcn2gajS6pVBV/NKYtL02YjlHPJ9JozIVYOgMqAfsoQNUC9u4sjOqMBoRxzVFlLQQDEqB1CJQSZyqCxDFxFGPbEcZ4CGBZ+6Ab0AMfITOiteuidAZjOkictLwMdp7Can+NQaY4VihJKO88NNlxatZ1FZkMXDyfIZUujZCs4HlDmnfzpEwXrBP6a+9Gh0hipZ1m/6Jjk2gxHrqDloXajJEVCzFDwMciR/B/lqGrwR2JY49+pVyD+Ar5rKB+BuKczXe7U5w5wWEC9HoWk556v9acz1sEYQlQxFFEGEVYeo8ovMbOxso4WnUcG8fV7HrJdDYdDdloG1aezdAB5tKG+ncV6UeFQQBuVpGxhCxJeWFSlDoWhWXJoQb1bqxYqZixBut2rHAdIQgV6TnYayjCocLNC50slKYN7d0jSiYZYWeivSSfNth9aHgH+5XTBmUlGYB/9c9+cKw8k6a1HiNul5aWWF1dxbZtMpkM3W6X27dvMxgMcBznUCo3lUodmkM7nQ6zs7M/lDH/fdpb1mHej+0jZR+Ur3WSh/bixYuk02leeuml+/rtZ76fEHPPuILVV4iBm3GSMtR5WMgIfhdu96AbKip1obOiKBSh24Ewn7R/RBFsNw35coPWnRSlUgnL0mxuwfQUaEtIp6DdUfRSirJt6KZtpiLBGxxQla1EwtHgrVJMmHpKArIBtZEzXboA1A/2M0bYaPaJowj3wgyyp9n2D8ZXXXLoX03AIzs7Lo6jCMNkAu10FIuLKTqdg0nf9w3LyylWVxPYcPLdJvXKlRWLtbXjk81wGLOyMmRtLYsXaYYC0o9ROwYRjTWlQAvs4yIjQf2dIHMa9AGAxhiTpNUyCqXCERGAAG0sK48xLtrWaDsijpN6tWWppCY68gnKi9FaUam4LC/nSaU0t24HDPohly5VKZfTzKr3MnxqwG7b4HnJ4k1r0JYim0kxPeOSzyWf7+KLitqWNe4xffzxKV54wbDY81h4b5nhMGZ316PV8vG8mOCmHIo6lViwPUDmMyiVpA3liI+NdxVqmZESjSH64yay6iCqgDEaa5KfzlWYoY2K+sR/UcB+n7CdrXKmd+fYc8lmXVqtkyMprbMwUmixHYfpaSEIrlGtnsHzsoRhwvXs+x6lZUO7ZbGYi7jz3QSV6+dstC94V6H6tPC3A4vSijAtsM8iuJAybHrj3iAAGqFiLh0yyUa8KwpXJ1yzgVGszMasbVhseZpy1VDbUxRrMLUsrA40K5cMG9eSNhTbEopLQn1U05wuGPpbisKisDn6ZtKOkImFjZ7i2XNtpooPAHN/EyyOYzKZDJVK5RAgMggCOp0OnU6HWq025o31fZ+NjQ2azSbnz59/4PM2m00+9KEPcefOHc6cOcNnPvOZY4DM7373u/zGb/wGnU4Hy7L4+Mc/zoc+9KEHPueD2I8c5qvYgzpMEWFra4tbt26xsrIy5qENw/C+kLfrbXhhQ3HKElbvKlIuOIsKGQESjcDmQGFZmlLOpz6EU1VoXIPZR4VuR9Hqw/J5w/XvJBGaFEqcPuvSmmj3223A/kyx8hi0NhV+LOx5UG1A6hJgoAI07ii8tx0eZ6EiODG07yr80diKeaiNCA1EktTOYDAgm8nw6EKOVqT48lCR0vD+RwxbLykaPRtthZgYfF+xslJibS1h7EnqkSkmewVEhGYzTKK2I2m1VstHKX0iQKZW61EqpbhyM0eU9rGuJkwxSgHTetTzOerB/KoPkT6ILifM0gGzSzm2tyeRqAZjOmidJlNQDEyIVjAzk+aRixVcR9PrBey1PDJToNJZtBYsK8S2bR69VB7X9gaDAfW2x6OlIttvf22mqd7WgUQVJBHaM8/MszJdplXsUSjA7GwGEQj8mPb3Le5sWQwGEd7Q4AcxejuGkdSUMYfTuFpDHLvYRMnrci0g/HoVCEDtkUrliOSgRmzsBPGqUFjGw3rBZvjuLG1JUVKHUeKVSoHBPVgMu90c+59epeIzHH4TbzhE68xIeMAZZR4yLF/M4gaa3uUmQRASMeCVLcWiFXNzt8Ddd6VQaTh3pLd+09esZAxrE5GeAHVxWXQNeyMQ0dCMosxGco0N0VhaiI0iNw+tpiK/JKy9rFk5Zbi7p6lcEKQp5KaSfuGlskEboXZXE8eKfE6gm6B3833BWlHonuF9b2sCfz/R2r3aSlzXZXp6etzyJiJ4nsfly5f54he/yDe/+U3+9E//lM997nM8++yzvPvd7+bpp5++7/N+4hOf4L3vfS8f+9jH+MQnPsEnPvEJfu/3fu/QPtlslj/6oz/iwoUL1Go1nn76ad7//vdTLt8H59+bZG9Zh/lGRaTvZd1ul6tXr5LNZnnmmWcOOdv7bVX5wkuaZetAtWPmVALsOWqRKPqOxamisN5RVDJC7TuKlTPCrVrEi2s9FmY1w04l0ThMw/yysLV++Fgrl5J0ke5q1CVhxQi1tqLH6AVZheoZWJ8IBPQo8Nq9ow4hK0vzQsck0Ph2u401IkqvpBQbIxTmmSm4Voc/K1s8bhvwYPGURe12cm96vRzQGh9zZ0eYnU3RavnjKKrfNywupqjVDrdPdLsxS0spNjZO6neFMNxhp1ZG/5ghfkGBSfpAzZSF1jGxAXszIvxWGueST2wOd55rrShXhEuXSly4UODW7TbbW33SaZupqQyLizmmZmx6IUShwXEOJp98PkU+n2JpocBGQwNCFMVEUYjneURRSBwbbNtiOZNh+/MuxUuGjnvvd9UR6JxMFMTGSy7TP6YZ2iM2HgX5tCaOKly6uJ8EFYLA4Js82yuGfj9iMIgJgmSRoJQiiiQpZnc6mIIi/sIkd6FBvG1ITQMHRBvKjSFyMOEQWjm4FrOWm6EUH2ZjiqKTUbClUoa7qy5uSjE/12Nv79v4vk+pVKDdPl4i6WBT6Q/ZilxyOZelp1I0cmm+twW191ooMbw91aC9Z2G7zjida2nNuqdZTBlq+60lIhg0ygYdJIsqC2ErUmRsYRgpBrFiec6wvqmoeZpS2VBraYolw9aGZrliCHuK3lCxfvX485tdMex0k/PNIrQ8xd4AfvqxIVPFHy4YcdLul7hAKUUmk+GZZ57hmWee4Td/8zf56Ec/SqlU4vnnn+frX//663KYn//85/nKV74CwK/92q/xUz/1U8cc5sMPHwilLy4uMjs7S71e/5HD/Idir8dhRlHEK6+8QqfT4eLFiyfqwt2PgHRrCDdWFWsjZ1kowMYRZ5nSUE0JdgR3+xHF+UR7MU4pgh3Dze91KVU8dGEaO2eRDsH3oDeAHoqlh4XdVYXvwZnHBBOC2QFdSHr11m4oFh8TNoxipQdrTUg9KjDROnIqbbhz+0idJgUbsaI/GBDHhnw+P14wZFxoj4KL2YKwtqPopeA7T2kuvWiYdQ5kJ/b2NDMzOer1/gjNDLlchr09b5x+BfBO0LsEaDQ8slmHwYTAbxRF9Ho9bm7OQl9D10fjYABdiFFpRRyDCg3mzxW2BrLRIZCN42hmZhx+8n0VdlDYtsXDF6o8fOEA6exYQj9MCOUnneWkeeParhorV8RxH6U05XIBESHqDujs9VH/d5/2L7mJVNQI9KInoJZlH+pyco3dxJrShsvw9EFUV+pY7MUJSGd/FKmUJkWRlXOGVrLWSfp6uwF7ewG7uwPCQBHXDKofI7Uq++5Wa0UUaYw1xLICxBQRUSgXTGCjlSIKPOIXLFrvnSbo1HCdxBnncinuxT5ZKBawLMPy8l3W166NtxeLM+MWp33LVzUFFbP+ysHiZqvs8u2UTfMRhZOBkgPFuSmW3JA7PSGMInzfTxDKlkXgWJRTmh4pHITqMCDdz3C6bbh7VxMZhZMS5mcNUU7RL0BHH2RS8gvQbkF2AdqXFXtdjXjQP4FsQ2shLIHrCTNK2LirWXnKEAE/+44+gff6Uapvlr0R4oJqtcpjjz3GE0888bp/v729PSZmWFhYeE1a0m9+85sEQcC5cyer2Pyg7EcO81XsfhymiFCr1bhz5w6nT5/m4sWLb6iH88svKu5OgH3Ks0LXU1QcKIgw6CksR9gyirls0pd4Zz1pvt7uDbCm2sjGNJVUkYpAM4bps8LGywfH3KgrKrNJ28f6TUU4mmcKS4bWjcRBRdOKhSBxnqkM7Ezwxs7bEJ/Aj1nIe1zfG5JOpUZagEk6cT4j7AaKeSU4IcQRuEXhr76vUbPC91cUG57mzCWb/JXkfrtuAUgc5mAw4ObNkHQ6whg9AmEpms2Q2VmXnZ3DUabnGRYWYDBIns9gMCAMQ/L5PDdr08iUj1p1iEdN7qoaIzJCyH4lwLTSaNsjtpO6oW1rFhbSnDmTw7Y1qYIZA6GOWjElNMyrP//eBGNTGCZArHQ6TbmcY9+NpZVNsaiRW0UuDDzWKlHCUNQfIAi2lYBdVNNmxG5w4rn2vpeCCYdpbx3/5Pff13Jf0Snu9yIKpaKLZYVMT2fJ5/LMpovc+Nc+67NCvxfieXESfao0ShK1EqGJ0mXESZ6RtvbLGhHmhsNqocp5JwmJK5UK9xJgcV1DOv0N1tcOj9f3jzfHV+csai8keV3P1dx4IkerksIPEuyyEuH8dOLgNwKHM0XDhjfK/IgQG0MURZjhgOxGi+1bDq3YIp3yqeQ1ceyiFIS+orapMS0II8X8w4ZSxbDWt9j0FfmCYbOrWbpg2HhFUy4Z3BCCI4oqS5cMAYpoDza6mmxB6MfwnrMxxXxMMzh5AfTDsDfiMF8r0nvf+97H1tbWse2/+7u/+7rOtbm5yUc+8hE+/elPv2FA5uu1t6zDfDNSsp1OhytXrlAoFHj22WffsLKJF8Dn/9Ya4wVTLmwFiiU3SaPumVE9cy6pZ24NoOm4rEwFbGy2yGgXqgusuFCrKZayQvQKqIuKMyuGXmfExqKhtqbYm4gYZ88KjS0H34fqPPQjiK6NUsLnDtKxFQeaz4P7+MFvjRF6vR5O2aNUqo77TUWEOaVwOmA6sHWkrlhIQy8GU0naTlo5l3TFYvFuhNo0pNMaY1K4rksURZRKMaurbYyJR716DmG4j5I9fOzNTZ+ZGc31613S6TSlUolQ0vQaDjIVImKNCAMEey4kMCn0mo/5bhptRaQqPtnpPIsLGWZm04eO/2rzWdoFTpCXGv9dC16UkLj3+33i2FAsFo9NUp3dgyh08LkUuf/eJhrhQARJxM3DiO5ql709P5GDcpJFiuPYIy5Y2F1zWBloWtkkqhvcuvc72lsFHk/+HQYB/UGfbCZLKpVCgPRWipJJU7yUjCKOhd2GT7PhMRy0afs2WsUY00Q7RayUgwkSGHUcD5DbJernypzN76I1dLsuR/tYZmaGZDItVu+u0u/1Dk3CjmOxu3sYT5BKCWHLp4/m1qUs9YUUdgaMN9LMzkDFErIH2WK2PMWca9gONChF2tLM+za1a2UW80LLCYh0DEpRbweUVYtGK9Gx9G2b0zOarZrD1nVNNW9YnjLslhXlZehdge1IUZoytBqaatWQSwthAL0OoJO+zJ1belwjnj1n6DcUP/++iMB7MIf1ZtmDcsl2u90Ts2qT9qUvfemef5ubm2Nzc5OFhQU2NzfvibjtdDr83M/9HL/zO7/Dc88997rH+UbtLesw78fu5TD3yQd6vR6PPvro66aEupcUzpe+pw9FH7NLAjGsrR7sO7UsYzSqEcHEMRvNIdXZKgWxKBpop8Deht1Q4WZg/TIoNMsrwtbWQUS5b5YFrgOdjo1tCdULgrep2BmNJS4n6diMBeFLkC8LzZGzHQ49hsMhhUIWqoVxAjOHYWHX0N/VbJ8g8wTw448ZvnBD4+aSqNMfKKJpi5enLW4MXS62Fql8ew07VriuSxynqFQSBx3HMWEYsbbWo1KJqdcF296vTVkMh0MGA2FpaYrBQFOpKL72TYhCjWUgJmllsGyQKUU+bZh62SX3WIrp6QJn3lll4x56lb1XiSCt11jwFrXQCQL6/T6ZbJZ8PsXR6DBtCd4EJLm3qVl5ybD2+KhtA4VjOzi2QzbKUalYY57cMIzwvOGIACCJQuUKyDsSkejd6/d2mM2aJvdozFavjyCUSuXxCl4Bg79UzBUYE6grLczPZZmby7A0V2J1F5pNj63NAZ43QIuiU6+glY0hg4q7hLU066rM028z1OuCUkKxGFIoDOj3t6nX+6yszCaR6xGbnp5jc/Pg/20bstOr/NX0o9SfcAlslQCdbUUUghYhFcKF04ePFaNoRVCyDKkYhtdhbURM0PRAKcHSesS+laaazxGaxJmEUcTG3oBOS2Fpi8HAZmkAcjWFek6RyyXEIHpWsNtCs6XZZwhOp4VsSli9eeAQc0VhsKf48adjSgXY6v/9OswHjTCHw+EhsYjXax/84Af59Kc/zcc+9jE+/elP8wu/8AvH9gmCgF/6pV/iV3/1V/nlX/7lBz7XG7G3rMO83wjT8w48mIiwsbHB3bt3eeihh7h06dLrTr/u1zGP/i6O4c+eP5htNYAHazsTUeDMgbP0PI/BYIhSOtHttJIPstODkifkLsHqZcXCKWHwUtJXt7amKBRgqiJs7SjKJSjkBDsHtzfVSK9CsEPYGWVO3DTsmETNPb8m1JuKU0/CThTT7XZxHJtKpczCPGyRTKwrnvDyC5paWvHQw0LvpHShJPRms3XY6QjaTXpGJVRobQhdxUtzWfTPnmPueodzr9Tp9YTl5QLr610sy8aybCCJ/paXFc2mh+d59HpBwjojNiJ9KhWbxl6N+tZ7UFYXsQrJ+VMx5866rPzyDIt3hLXZifufN3ACPivlCv0TaAD3LXyVErURQ3e3geelDjmjo1awBO/IPdv4nKbwSETXOdiugPaINlFrjeumcN39doQDQNHtvwP7oRbZjtCsp8aKLZbWh5iDAt/HudXAXZkilTrc1jAzNNRf1qycO0AMq5FUi0LR6igcG2Znc8zO5hARpouGK9+IeeUVhzAM0baP8h12dvPkchvE8TadzoB220zUJYVO5+T7p9SBFE+kYePJgNsLbyMyNvHofiiBOEocp3aFFUtwT1gjBEax7MXcumwdQlT3fcVsKWSrdRDJ7vQ001VDo+XiuC6Q5dFHYzbWIYwiesZjtxay/SeG5TMR6WKGejvF6YuajcuJ88nlBFtBszlBXOAI0zOGZlvzi+9PFuZvRt/3G7UHKSmJyBsa98c+9jF+5Vd+hT/8wz/k1KlTfPaznwXgW9/6Fn/wB3/AJz/5ST7zmc/wN3/zNzQaDT71qU8B8KlPfYonn3zygc/7eu0t6zDvxyYjzHa7zZUrVyiXy7zrXe96oLQFHCiWHG1V+dpVRX00UWjgXFV4Zefwi2sXIOrEiaKHbTNdLcPeFmeLhq1dzXpTsVAVwpxCNWB6xN268nDCNQvQ7UK3qyiVoNVMyAL6o44NpWBuNuD29QMU5MzZBPyz3IP11YROsDbs0PWEQiE/vg9OARwD07vC6i2VqGuIELgKDpcYAViaETZCxbllYeeywhGDjx4BbxTkIbYVom1ql0psnSmycr2Fs9kkm7UYDA68WRAI2azC8wYoZVGtVkcO05DJdOl0Nrl9+yHCwMHO72BUlqlqwGOPVZk9p1AG1v/08L0ObXWiwyyUBP8e9UKA4QkaoSB4vs9wMGA2laVYzN3z9wCpE85rQk3xG5ruuw88cimEVnSvSUpN0NBlOIeGWNFxXcIoot/rEZsYrS1s2yIKI5RSzPuzhKnj77b9QvLfdkNNgmEPrttTVEeTPyST7l5Pceq0plCw+f73PYahxgyH2LbFV/5WcXph3zOq8W/m5spsbx+/AamUy/Z28l5uzzjcfiLFQCsyQ0Vgg7JAG1B2AoBDg+vB/GOwko5Z8yeI0RGmtoWbt20Wq4Za+/Az659wT9NZJoHbSX3b0qQsi5AUjzxm2FxTtHZjpvwhJu6yO/DJZw2YNO29HOAkAt0oFmYM2oLVmsV/818G5EZg4Qflcv37tDeDYnRqaoovf/nLx7a/853v5JOf/CQAH/7wh/nwhz/8hs/1Ruwf15P5IZtt2/i+z+XLlxkOhzz++ONvWCT1JE1MEfj8N5KPVANzRugciWKyacMrOwOCKOLhUgY7ctndUqiU4vqewnKgWhQcC3ptRaUg5GKhqRXrPcWpS8LqlYNjtttJa4hdFqJWsn2hFBMxIeEESDUhLVi7rPCDgFjaeOSpVCZmTQVDhMJt2KwfTH6ua6jfQ+jdpIAwqfnNFIXtlsJOx0RYOAaiviAFhUGh3ISt5vbbptg4W+KdG7u0hz3mV/fG/Jh7ez6PPFIZoy5LJYVtN2g02oShQ239PCm3y/LDaaw8lMsuvV6bQirEfDaN72VwbBs1WiV3zcnjTr/K49cI3SPXa0xMt9dDa02pXJ7kQLinqXvss/ElTfXpmObo1mf7h+bwV7XgSgoVguPuR0nAqJeuPxgk3K0i3LzcIb+sid1Ugsq1LPIGtr+SPNdOS1GeMrQGx51KzoVJgTIRxfSC4HsWzz03zZ3bNndebjDsazY2CizPbmNZB3x8SeYlhcjxMsjs7CK31+Hq2/I0lhziOEKLMDQW+GAZQfKS1KYF7CBmqpyQY2wMNdMpw26oSSshe1PY3EnG75/wfrb9hD+2NVEe2ewo8hmhN0Ks73Q1U1VDYxQxRm7yztu2jRfncY3Q29R4YtA6oloaMvD69AZCPm249UqO6TOauRmHfz6hVxnH8bHo/h+67TvMH4RgxT80e8s6zNd6uIk0VJ2trS0ef/xx5ubm7vuF8APoD6F6Qg38JE3Mv/iu4vaOGjvLXl/R208jCXi+j5NqkLbLnHdLbI7ScNks7Kg0GZJeseZQ0QTymSRlFTYUp6aFjV3Falux/LhQezlJfbouTJ8WaiNwyUpVqG9r9iLYL0XYLqDg7teFbqeLAh55pspm5nCNYz4jdC4rBhPUKAqozhh2T1h8WgrqUVKDBXhoCepthQ4F7RoiZ7R4aIGpgLIUxlWoQPCzFn+3MouTnaGTcph9/hqO41Iul6nXYW7OxXUH1GprxCMqups3F4Aczz13l+rFR+kO9l97YWYYcOOGEEYBg34fAbIFjdd1k5qoZR1KW6oRFeBJVkgL7XGLhzD0khRxPpfDcRIn1R++9mrcv0dKEtG4XxH42RHFXuv+J6jaiy55dbAKMMbQ6yUPrFKpjNNpIsKc8blLgi6O45j0VZ9uOz8GFBVsdaKj9o4qNwMHaluKMw9VePiU4q//sknkx6xuzXFuZWd83lIpw85OBAhdx2bv1AJhOoMyBk9P8533lPGzgomTB6DUPn9vEmGqXkSUs7FiwfLh7Epyrw0KL4KqNsTXoDnB59roambLBz2Ro8EQ6cP31oiiUjX0Ng62p4uMVwi7Hc3somGnpvEDRbEq9HsCaERc2qMUb9oC3zOsnB+yvhvzM++5zre/3SKbzVIqlRKSj+zJvak/aHvQSHE4HP69jfmHbW9Zhwn3VizZ29vj6tWrFItFqtXqmKj4fi3lwu2a4tYGvPPRw8c/Sl6w14N/9xWLggO5AWxuKU49KnQHiihKhGJtS1GdnWVYt9mcgOFXFySRwzpyDb0A8nkoXhDWv6ZZLgiDGNabivmLEO8JKgO9oeL/Z+/Ng+TKrjO/37nvvVwqs/YCUFVAAegNQO9UN3qhhmNxtFDriCOZIiWNgqToCVIcy7JmNNZQCsuO8YSklkcRlhwSRzGU7OFoZIdJ6w/GhE2FQ9IwyKG4qLmjG+jGXoXa19wz33v3Hv9xX2ZlVSXQaKBJatR9IhCIqsrtvXzvfvec853vGy8r5VBYuCxM3Aeb27uvc/ioY+EzLSrbMeVSyZeRR3VPiXUiVAobnrG77+Rib3IPTY46Vpx0C3GUijA5rGxWA8LtJunhAmDQFpgquFFBAm8vFTTA5Q1x4pi/7yiNfJmHLswjacr0NMTxDYIIJicLrK01qNWETuc+fvTtiiVHtbl7yY+ULM2rhnwh6rlNqipjxzqsOJcBRpqVLX3fr40BBpdBh3JQicHalFq9ThSGjI2N0T3SvFEa8SuDXH2A/2M3Vj4fcPg7HWujkGzcPmCWBEZqSoWu+lKDoaHSgWxGRGAjR/EBQ7FYRFCCc5Yosj1C0fWXO9SHij1WbhiGiAgb20KhpLT7jnG9IuQLSieztDo8W+LZZw1LS3m2KudJrZeOK5XyqI7gXMpWAN9425uxRa9XahRyq0JsY1yGwMZaNPC7SgGcWCSMCJuKNh1HTihBsPs5rIPR68qA9Ad6AAAgAElEQVTVzQGElgE4sdUMOTbqWOsTSVit72rIAqxUhHLZUc9IUNqn57C+ZTh20nHj6t7vSBUmD4GaIj/8FsdPveMUqtoTQO96Ws7Pz/fEz29XAP1u404JP68XL0x4nQPm/uh0Orz00kvEccxjjz1GFEV87Wtfu6PXOnNS+dSXhD/5pOGnf8D1kpT9zNt/9xeGCasszQs168ukazHU6w2SOKY8PMwD04YbC2aPUPrEuLLYzIg6+wDz+Igyvy1UIqFxUql/QzhaVliClSXYy8oUtoHSKKw1QjTT3yuYDmuXtmm3hxkf80pBYQTrfaXiiVCp/7UQnj54/EGgbFo/xtKNrk9lVATZV3K+75iydV4IOyF2NcYkAWHV0Nk0RGMKE4KzFqcGNEWMkMsZKoVhnn/0YU5sL9BYOcfCmdOsHjvOPRde5KHmdTY2Jnj0saM4e5GR6fEeoUREKac3WNneK4QvIgxP56hEpteqc9aSpClJHHNjs03TdQG0CxgB4EW7m60mnU6HcrlMFO5lm5Tl1v1P8AzZ5oAZ1/6w/5+Bn3A9ws/txLB1VC7GVCd9Gngr0tHGdaHwgCceHWoqa0shuVy4SyhSZXIspdZMaXfapI0UAcIwYnxUabSGer0664TpGcdiBhxrWyG5nHD06AgPPHCM0sgo7VKNxA1RvbjJurO8/Pbvxg0VMOLL3LkNR7NjEA0Q49CCoBKg2f0QSkriwGCQG0puWjl5bPfc5FCKLysLa4bCkNJO9p63tYphcsSx2ejzwxTB7CMLxalwbMqr+4AXah+ZVLJEnfWqYfa4Y2nev87iqjB30rG1IT0Bg1xeGZtQdtYM7/oJf6+JCOVymXK5TK1WY2ZmhlKp1APPQQLoo6Ojd6xxfbO4mxnM14NTCbwBmIAvT83Pz7O4uMj999/P4cOHe04lr1Yarz/e+qTyiU8Jz/3bgH/y05ZCfm+G+WefEb7waUMfEZfx6SYX1zoUCwXK4+Mczymd1l5XEYChcWGrdTBLnhtV5rMMJbGgRWFlBqI1YfKwsrk2eJGdOA7ba4I6RTrbtDZSmD1EqbR7Ax2aU5azkYouWGoKGwNKceMTjoqDPLtACb66WekDDRFlAphzytp1y/VmhCYxSVlwxoEBWzGI+vEPjQETIAI2VSAgbie8lD9OcO80UhZcx3DtxBmK4RAzU9McSZss3qgzdPR4732PjtforLkDWrQAlNiTRZsgIB8EjAzn6IyWyamSWj8H2Ww1sWkKIph2gzQYYXRkpDcH2R+3Q7ofxJDdH5vnAo6/2TFfv31WYmupzvXzDY794BgNuTXpyDlhsu1YLAi5Fwc9QjhSDkhcRDepUvX3SqvVotGoYzMFnSgMqRf9PG2SN1w+JuRGhtiqOtIjD1Afcb5sm6Tc0/hPLD/9LK6YRzRzadl2tOvGbzgFtG0INcEVi6gVAmNJrBKooFvg8soDkylIgDovFj8271hb9t/HTNGxkBw8v7m+r6srv7hSNYyVHDuNvhJuy2fEaUbuWq4YJicdm1mZd60jTB5ybK57PeOFVf+48WnH8BCQKldfCvjHH4wZNOdvM2/UIAgYGxvbM4faNYSuVqvcuHGDJEkYGhra4yJyNyMpdwOYb2SYr4MQETY3N3nppZc4dOgQzz777J4L5nak7F4p3v5Wx3bN8M//15Dvf8YykivS6Cj/+mMBX+/TmLTW0mjUcEeUsdFRjDHMCWyuCM19N5YRWI93j0FVGSvC2x9yPHhYGSn4n/Ohtwn70y8Lf/pJw2knDI9BbV8DauYeZWHbi8PnXRW3Ns7xhwos7Mt0wgkghakIal8U4qZ/7vIAofPCCOxk1lvdBQiE8bJjOzXkRTncUrZeEjarwibCE6cs818DcQEkDhsZgighbQu66ciPg+TApoZ+PfQgMpgYbBhBXQhjRUp5zs+e4huSx9iYwtyDlGSIziHBDYF+dp7jY4NL7Y2blL66DFmR3TnIghZoNpvESUy+PErQEaq1mjeSzjwcozAkCEPklWWEyd+EbLQ/7CcFKetAkfn+6PYq7cU2o6OjjKcRjdvQ13DLEJ7UHtnnwPvvU+gRMURRjnYccfiQFxu3zpEmCfNbKcv3tFk8MYRGQpgEpMXQKyvVU0yUoHnDtWffApr5agKmYZG6Qft7yE6xjRACweQcmiQYJ0glQJ2SyzvmToQkAokqszuWG1cN4FBgbRvC3C7gdWNlxzBaclRaXuO3W4Upl2Cn71hbiTB32LGQZZkKmCEgMzVIrdAqQGlYafTdP/WGkHPK6krAd77Z8ta3Dr4YbgVagwyhm80m1WqV1dVVLl265D9zudwD0VKpdNulXO9Bemcl2TcyzNdBXLhwgXq9zuOPP/5NbVq/50ccGzvCH/9ZQJROsrEZUChkN5zSK+OdfqzIelAgZ2AqVhZuCMdPK419HpTTM9pzBJkoWn70wTbveGqU3IBv89Rh5Vd+QLmvoPzWHwVMD8F9p5XamlDZ9qXYdWdJGztMiWNjtURuqEh1/8ItsIVwKILKFyDOsspwlH4jER8KncjQaXUAr0DTJWiMFpVy3bH6orDQ2ZshFUeF6XFlZTNAaxbGFfXGFwQoyVZAdEhxGcmpGxYhsm0IfQ5nE0GrBhMawnxKEgjt0hCNrPdoEstnH7mfFyRHIQ+T6zBW8Uuk5pR5YNB+eT9Dtl/WbnxsDJeHUthdSLviCgmtVovUWsJGQiMeOqDGs+c0D8jWB4WpJhwtO25w87Jct1c5OVzEtUfAwPqLKeF3RKSvIN+3dsWX8ecbg7PY9RUhnD4IPKrC1ZNwachggwAXRMg6hCgaCUGspImf+PXAKGg7INdSCEPSvMXEFjVCUDUkbu/7i1MIIoKmJTUWaSmuJgSRwTnl2DFoO8NczuE6wuK5CMkcaFClHStHRy2L/SQf/JxyOQeVVrck6/+yXBWKOaXV15fd7ghGFJdtVtZrhpkZx/Kyf81mWxifdCQdiGNhpOSIHKyuGI4edfzcz92cKv1q5jBFhFKpRKlU6umwWut5D9VqlWvXrh0o5Y6MjNyUhXunIy1vlGRfJ3Hvvfd+S2aeROC//SnLv/g3AV85HzI93WFnp0gcx9QbDQr5AlNT47SKMIeysSAsZfT1yoCFTYt+Yf3hBx1/d2KVUjFPLry1LNU736p8/bzjk182bC0J0yHce8ZS2apSuZKiboy6MaRJg0Nzyvo+88vJGSUQYftzkPQ5NFX3fz71/ctWNERBd5VncI7ZtmXtYp5qXCQIQvZvfLcT4b6TsL4NDoPWU2w5Isw5NBVUhWQDcuOOeN/7atEvmN4OzGBtthi3LCJCoQyNghe+dqmjk49YJ8Qdg+vHvIxarqPYcSEdEs6uOYb3VeO7DNmWOmyjSWhjjo2WKQSGvKTUbdDrUQpCGISEQQgFD+QFLC1NB6jxRISRf2xrn7D4zSJtWupfbWPeFPUW7m74rLKGiDA6OsZ0pCzhv7ROE46GlsX41te9tYJ8Pgb2Lq6VEtw4Igw34cERR7q9+94OeOGUsDGx62BjtsG1IDVCblGJRyXjTHXFOwyhOOKmIKJQN5BLyW3ExLn8Hn6VcQ4nhgDFNlKC9YS0mCMIA2yqDA05js/5J9QbAi/sHXfo/l9tCIERrGpG+PH/L21BIW+patfHxdt3TY25PQIi9Y5w9IhjcaVP8ADx11Z2XW7XDbMnHfm6o1kV1MDxOccv/mJMoY8cdPC8353STxAEjI6OMjo6ytzcHLDXy3JxcZE4jikWi3tKud1xtzstyb6SLN7flnhdA2Y+n78tu62bSdm9mohC+NB7Lb/4r5T55YCJ0gbFouP48QnUBZRHHNsbwkIfQ/LwjLLW3vu+hbz35vuVv2c5O6fMz9+eZRjA//QBx4v/zHClCVe2LctX6ozlC54NGeDHMFTJjQHbe587Vlauf9ZLjnWjNLLrQJKtOagqhw8rq+wqzxw2js452Fm1JJMJnbhFmnoT5W62NTUZUE1C1MVMjXRY7pSgExIUHRKBy0ZNcEKy4zPbrnqaqCUt5jAJICbbpQf+eEQ8yO0YTAQSJZg8aM54YYLuywKtnGA64GL4amQo55TDqXIk9jdKInAtiblKyJu+XKN83dGgTQOYng6prhgK44axUzmiYyEbkzla2ZhJKEozvrkaT7vVxqYJjZdAyPVKuYOyUIDKWkyz5jimMTd2Ob49/9FSqdR7n6C2N6NJllKY8re+zc5hsO/yLoaO+Noa4BfdrTG4OidURgQNYAXhqhiGJpXZqjK9Bl99RNiZEOhmaHWvIezfFNKOIMuKm1Ikb3zmpyBxiGC9ObWzyHXB3YhgBBhOkVAJQkFUCVJImoqoYFsBFL20Y2KVEyf8fWpQzHll6OBlDECjbZg97Fiq7lq2KL5nmndVnPoSsxeTV1ZrSiCO1ElvHain0l+5pdoS5o5ZbswHTJQdRQdrLwpx5rOZyym/+qsxx47dusXT7WG+ljHIy7LValGtVllfX+fy5cuoKkEQEEUR9Xr9VZVyq9Xqt9Ri69sZr2vAvJ3o7rxei0x0qOB4z9uu8Bv/bpJ6MkEul6NVgbkp5crlXTHmbkTjQG3v7x6/3/GPvtsxmfE2ukLntxPGwO/8dw1+5AOG+lDAztAYQ5EylN0XIsLYkZilvvk+I3C0oKxfNHvAEmB8FhpuFyjBrx+5MmD9GMXUurL4Db8AHJmBNYno4sWu/mlCJ95msxmCCHPHCtSajnoSoNUEHVUkCtFsrlJtgNtKCCZCVAyhcdjAYJwjSftryQoCReto5QRxFtcSaEEQGjQEkwPNeUk1BQ+gCh2BFGErEl6O4BAxf/1im53ZIUxg+MabjvD06hqFtn+/KJOsa247/uNEkWjLMf3VJpOnc2yM5khVqKr0JhgEMKlQiISRKGSsAIciZeeaF1ZPEg+izlmIfC+0EPgRjnJBaWTKCjtfbqBP5Kg7x067jXEwPTKWsVR9NBf3bqjWLjnMjOOcBqxHgst5BnQOpeDgvopyjCaLK01ypYTPPpyjVvYEr/5IFaqB0DgsLE4otYm+XiOgGVqJguuA4FARgk2DOwJBJBA70kQwxm90AjXYJYfGgqw4NApRwIrFOc9G9jJsFs0H5KqOeCRkZMwxO+Pv0aMNZeGGoRYq+WGlM0B9qbWvzeGco1arYQshUxNlrOuS6ZROKhybsNxY3+U07DRh5pBjed0wWoBhUXQT5sQyf27vJicMlX/6T2MeeuiVG9R3KzF3OyEiDA0NMTQ01BuZc85x5coV2u02169fp9FoEIbhgVLuIBCt1WqcOHHiwO//NsbrGjBfjWPJ3QLm1tYWL730EhMjI/zzn17nsy8eZmVTEaXnfdkfYxOw1EcaCAy86y2O//LNbk8pMwiCPXq3NwtVZWFhgYWFBf7lzz/Mr/7+ISjDpbrheOg4HEAUQbskRNmqPlqAqAqxg+r+OUsgLSra8AuL5/RkoGHgiDrqXxEWt3dv/nwZ6CNQeP3THKpKbJRSqUwQemGHmUMNLlZLaCpIK8ZFBhMYnO0uOoLbtOg4pJFXJ9Jsyx8E3ZJsduz5AIPrey6oE1wbTAs0AQyYAgRlMjTz/4JAsYllNVU0LREsgMk77DB8/ZkJps83aRdDLk1E7EwYUiO0XEAjDNi5N8IIaB2CvGD7jKBNZqYtqUAEaqDgYPSEcmLVMNzxvclOqHzpIYM1yqkvN8jt1AmGWsyXA1bPjFE/nIOikBIQ5MpoLFxWmHLK0VCZQtme3z0XtSHDyw/maEUBne5wvoXYQlr0ghnbU0KwkJADvnpWqJQEUwEGJLtGQGvQKAjS3p1FDCpK0gWqju9XBsZnaAoEG8A0aKfby/c2HnrNEWE8wxvjJZeGPUs2CAwuG71SDQgC0A6IOKYm69RqAYcD4dpn8xgjfgxkyHFjwJjOdl2YPuRYqQntdodWq0W5XCaMImZHHQvb3WzSG283rNC1IVVVpvKOfMUxvqxsrxoq2TUJwsyMpVYzNBpCsaj80i/FPPbYbbK5vk3RvRfL5XIPRJMk6ZVyl5eXabfbe0q5IyMjhGF4Vz3Mra0t3vWud3Ht2jVOnjzJxz72McbHxwc+tlqt8uCDD/JjP/Zj/N7v/d4dH+vdxOsaMG8nXo2J9KDoznYmScLjjz+eZVWX+Wc/6/jX/0fAp/96MGgPTSs72Y1+ZAz+yd+3nDp6sJyzXwhhUHRtyPp1cFVSfvX3Q8ojymoixAk8+7ByYV6YKys5B0tXhDSFmQeAfYAZ5ZXVBgfAMh8ppS1l/kvZHED/udh3qF2CQhgIZuQIhax8GYURx44W2dlps76ew8beXNqmIAbUKU4ETZRoK8Ed86CrgfESaSr0ptGtkuQDtL1fjjBbqAVMG1wRtAUu+6oNoKnFkaJiyDUNMYKDHuGorhFXj42QTnpDZk2zt3W7Ry6pz2A1VQyKhgaJs/eRTHMi9uzfGFgdE1ZHhXJHObKpLJwIiHMAwvlnhjlyQ3lpUqlnfUBVkNg7kbisPJ4ILCGsGmE8dDxkIGdhdSrgxScK/j1TDugvaAcoghP4q+lRxh7OURkJCHbA3aS1FaSeACadTG1HwEWQ7nig0cRhU7+JERzGOJ+lKeTr0BE/fqEKYWpINhSNfZbl1GK2FB11QOg1YsG/BgZBsFHAsaGYkydGcTbFfbVNo9HCWt+71tSQlvMEA8rbacdRrXaNu0d9GRaoNrvXz+4FW2kJc1MOalB7CbZWQ7aAw4cdQeDNE7JaC8vLQhQ5Tp2yvO99KSdP6sGT/Tcw0jTdQ36MoojJyUkmJ73ovWZSipVKhY2NDT7+8Y/zkY98hJGREaIoYnp6mkceeeRV2Rw+99xzfM/3fA8f+tCHeO6553juuef4rd/6rYGP/bVf+zW+67u+6+4O8i7jDcB8hbhTwOzP6PpnO9vtNmmaks/BL77Xcvoew//+p3tFCaaOKEs1YXIY3vqI48efdRRvIi95K8BM05RLly5RqVQO2JD9g+9TcCn/4t8E2MiwEynPv2iINgwrfTvyoTKs7lOeUVWm5hxLavZk6VMFx3BFuXr54OoaBMpWrwzmeyjtdodyqcTsTMi6HlxQHrg/x9ZGGzecw3YcEgqoEATgHARhSlqxUEyQiRDEZx9JnzVU6CBNHUacz2LojuL4vzv15Ujwz3WAwWFjiypeLUYE7en19J0HEdwOmJpCGRgCHdr7KOdA/It6VqizBInB7atudB/jf4B6QWgOCawB0/5Prg4rYwI5IO3zAXUQtCVT7FP/noCLlW2Ez/+dIeZe7nD18YLfIFQVFwpG6JFzAD+3GAN5RTrKzqEhzIZFQy9CcCAU0mqWZTqg4o/BpFn2jEMSITQOl1o/gmH8fLOo0pl3cCJETCZzd02IgNQaD1cSQGQoVGPaZT97K8Yft1MlCAxRTvmOByMaIpy0AQuVYbrJjnOOJE2YiJosVmWv5ZnCxa02x44VaLi9DPlKU5gZdyxXuwQuZTZS0nOwcUP2MIPX1gxHjzkWF3avX1Xl0UdTfu7nYoaHvW+otbZXbvXENBlYev126rG+EulHRCgWixSLRaanpzl16hTvec97eN/73kcul+N3fud3OHfuHG9729v4zd/8zdt6z0984hN86lOfAuA973kPb33rWwcC5pe+9CVWV1f5gR/4AZ5//vk7Or7XIl7XgHk7F+cg7ddXip2dHS5cuMDExMQBZ5P9APeD3+X4ziccl64LV28IVxaEiVnl7EOOx08qr/QRbwaY3bms48ePc/r06YHH+g++X0kTx//4u1ArGm4oFBsFxif8IgieHbuwsTsC0xvoKAtkABiIMoty47NC7tTgzzl5SFlzhjRNvNl0pv8qIhRKbqDpcj5vOHNfyjdWDIExhEGHhAKgiBGMyYTZU4HtBDcaYLXLlvUA6HNCQY303EdEdvvFJgaNyIgqiliHzfqgRjICS9vhTOjRdF+oAwkFWwGzqsgJ0H3jJ5Iq3ekI6fhzbnIG16dX6lKQcO/ruiaIheAbWQY8lQF6YMGI/3wCpunBWKLuhiB7DRWk40itcnkuh9QthIINjP8Ore5+0VnYBHKJJbHZB64KUeyIZw4upMaTnzFBllslYBrgFh1MCzkHiU17msHALpM5drgwwKymyJEQ146xGxBl2agnrypgaW0IWnQeWElxLiAIDahhbs7ScBFzgWN1X7Wma3mWD3KMjvqsMU1T6vWGJxeJoVOvUneOMAqJwl03ke4GdiRS8vPK4hV/Po7OOhb3tVAWlwzHTzjmrxtyOeWnf9rywz/sEMllx+yzaudc7x/Qu2+7IPpauH7cTdwJS7ZQKJAkCR/4wAc4ftwLg7ya9XJ1dbU3EjMzM8Na1z2hL5xz/NIv/RJ//Md/PNDR5FsZr2vAvJ14NRlmHMdcvHiRZrN5U2eTQQA3OgxPPqI8+cirv2H2v16r1eL8+fOEYcjZs2df0fngHT/isBZ+4/dhq2BoFkMurQj3HVFKZdhq9PcHfZ4R5eixdw8VHPYKLCwaRJSt+mCEz5WUxlqdJE0pl4f3bCLiW1SrnnyyxPxnmlQqOYw1QAOX6ctYETSfvV9iiGqCHTEeSMU7haQiu4Pw6kt5/dmSJKCBL/M5Z729mMgu6CBEHUt6kyqTqhCKoh3QlqAXIJhU3Jz07i5VQdQTXqSjqBFcfBA0JcHPnQJBE2j7rNI6oAlSVdxJz0iSvkxWE98DNap7MlcRT7zRnEECUAum5tBRRR2kLiM9+Ud7+UMH6bbCSLZJ2oAkBlME10eENAm9ErD6PQmqYK9ZzJYhN6TEQYrpy+a7EYiSJB60tWPQVAmWPEs1TYKMPeszSWMUAkOwnuKmA5wzXgnHQL6QcuKEB6X8NSXuDL6QNneEwzOOpYqlVqtTLBQoFAuAkKpjajhmq+FodHYViprNkPtKytpfDVHtu0AXlwwzs47lpb3vNX/D8J1/x/JTP2mZmdl7wN1Msh+MBoFoq9VCxAuIdEH0W+mNeafCBfvHSvbzPb73e7+XlZWVA8/79V//9dt6/Q9/+MP80A/9UG9M5tsZbwDmK8TtAGa/sfS9997LQw89dNPs9bVQD+qPLmA657h+/TrLy8ucPn2613e4nXjX2x0PP+D4R/9DxLWioVODq+vCEycclZr0yQRkIHnc0YyE4oZjuc/0empGWU8O3uBxHHNjYwsTjDJWLtEPWMYom+3B5wqgg3DmwSJf/lJMEgdEUQomxWkIqWCGBJeBXNoxyJYjGoXEQahgQ+P7kQpGHFZ9iaw7nK4oYhw2iRET9bK2bqgC5uCi3x/iBOnsdr3cpsAOmOOKm8zA1yoayh7BBRc7TCS4IPuMFn9HOgiWIOkjSKkqmkD+mhDPeYKSGpDY/w/gUoU+g+kohqQumLK3UxML9qohOJPN8uJLvX67pb43vOUH/k3RQccDGoBZUa/gHmWs1z2fDf9LwKwbn/FeaqP3BXs+T++424oRk/WdBbNoYTtAk+yTZFloEDhs5k2pHYPB4ggJAk8cevxxrxY0FTgufc4wddyxMUBoQVVpbNWot5SRkeHMeLz75RmmyjnafS4z6hxTtRbrX0zZ3q5gLXu0g7e2DaWy9vRhS0PKP/yHKd/3Pe4VK0Ld2A+iS0tLzM/P88ADD/QYw7CbhXbLuN9MEL3TaYBGo0GpdHO5xT//8z+/6d+OHDnC8vIyMzMzLC8vc/jw4QOP+dznPsdnPvMZPvzhD1Ov14njmHK5zHPPPfeqP+vdxt/8TvQ3MV4NS/ZmUa1W+eIXv0itVuOZZ55hZmbmW9qH6LJkv/CFL2Ct5dlnn31VYNmNRx6Cf/+vEv7uw2tER7x4z+e+YkjSXbDMRcrMmKPQVip/BcsX9l4+hX2zy845qtUqadqA4iGKxSL7e2ET43pT1ZnAKFsdoVwKmZ31LEXrIoxr+XJr6nrMTZEAYxRRxVY6GJti3N5si8AQmACR3SxUczGpTTHGZ12aEWm6nCHTVtxNZiG7kaae1LMnLLirgrnqmdBYQdrOl4b7z1GimO64jELQBrO8C5aK4tTPkwqCtRBcUWhneWGzvwnps0zwGaDNxjo0Uw8yVW+yrJfpWZQ5u7sYB00DmSi+NhTdcDh1qDpc4pBr2Xu2ds+Pqi+zGsB0BK0KJB3cjhIs214Jtvc9OIdNDNJ/HtaBRoro7nn2m0qHCcT/iwLCLQiMwanjoYcM+VxWgn4ZUCEaIKBjraVSqbC+HXLv9D6wzGJlSyhk1PBcANM7wub5Mqkd45GHRxkbH6NQ9GSpVqvJymqFZnudRr3OY49U+J+fq/O27719sOyPNE05d+4cW1tbnD17lsnJSXK5HIVCgVwuRxRFBEGwR9s6SRLiOO5tlF+ruFPhgu4M553Ej/7oj/LRj34UgI9+9KO8/e1vP/CYP/mTP2F+fp5r167x27/927z73e/+toAlvJFhvmKEYUirdVCvLE1TLl68SLVaPUCo+VZFHMe89NJLNJtN3vzmN99yl3c7cf898Is/dpH/8IVDfOLPQjpV4ca88PTDDk2VrQ2vWHJlfvDNUe3SYFVpd9qZT16Jex6IWBqQeQIUSwzsXwJMDCvrWfPv/vuLWBtzYzGHs22MNpBgCAJDGDiss32Ze4jUW4hxMLwree4QQiPZaILDNloQhhiBIIhwScaOVO0JwEjbooXIS6HdRBRdWyAqDJJ1dZtC2Ha4k76nagfccS5RQnVQN15cfqt7Gv0cqZG+c+e8OHrwkpI+6sdj+re9LvHjG3YLTDZao9YTcbSrIdwBuQp6v//RACT+ODw2C9QNsqmYwGSgrdBUgmuWdNgTcLqgKVkGLiuKYNHY4lIINhSZtEgp7GXokmRZuNVe304XDaadorO7LyqiWXaZbQACi2sE6JTlnpMBU5P+GpzFsXTZn4CVFWHsqGOn7Z/XbrdptdreOSaKyOlgcEmtMDPkWG9AaUFZvb57QhcWhcNTyvpGlLnP+OtpZMTygfdtcIRcMl8AACAASURBVPLEBouLVa5c6VAqlXoqO7cjhN7lOpw4caLXx+uPm5Vyu/+6Jd00TfdkoHeahd4JYN5ttexDH/oQ73znO/mjP/ojjh8/zsc//nEAnn/+ef7gD/6AP/zDP7yr13+t4w3AfIXYn2GqKsvLy1y9epUTJ05w5syZO8oo70Y9SFVZWlri2rVr3HPPPVSr1bsGy+7Nd+TIYX7k6f+ESef42CdOsLEV8hefDzg9o5QKSnP/bEgWI+NKpSHYNKVerxOEIWOjY4gxSNHBTbQVboKjAF5CrG+v8uiDEdrqsLYckFbrRMWUtD6Caoy6rPyXfbwoikjqCSY0uEK+OyKX/TnBppbACi7rTTo1GMmKz7tkXvygPOAczsguV1ZA8FmvtJSBaJmFbQr2RQhnLPbIwQM2qeI2LLgQh4FEPVVJ9jFzxQMNeOm63CVLcmTvAmcS0LovDru+VrnsKK6vv6xVMEuKO+qNuW3VK+R0lz+zplAHHaV3zCYEFkPMCcUVd3nD6hSrEG1YNI17ozm2CuGCJT2VMVytL7F2P4UYQTYtNCFtR9B2mILJ7g2b9ZvxGx9CUuD0WMqxE76HHYhS/0rfMalQFmXLOeq1GmL2jousrBsmpx2bzYPfQbUKI0vK2vW9f1MndGKIIiXJXE7+i7dY3vfulHJ5DBjL3nvX03JpaYlazUsTdq24RkdHvaJWtkm4evUqm5ubPP7441nl5fbCGLMHDPtLt917uPszsAc8bwdE73RNutPnTU5ODiTynD17diBYvve97+W9733vHb3XaxGva8B8tSXZer3O+fPnGRoa4qmnnrpjP7puH/NOLrLuZyiVSjz99NNEUcS1a9fu6HPALlB2b7STJ09yzz338MQTHR49vcWv/cY4jZbh69cdT52psbY2RBSF2U509/OPHnasLLbpZP2F3iyWKputm/RzRdncB8AiymgIJasU1pSZmqO9A/V1Ie4Ip8nT/DrUKh06gcNEHZDI99uMYgoOKSkUHDKaojHIqENKeQiFNGmjGvisSPoXWz8+0N9jVIDQz/shxhNYun9RcDiMZqQbEWTA5lyy1zaxI/1ygHnS4Q7vLlym7nA1kwFuisSe/TlocTOyl6gri+KJPjNZ0dyC2/ZvaHKy57G6JF7NqD8bXRFMyYuIG8OeGROtgosNgXW4TDVI2pY0FeSaIg/3AR8QbDlcbNHEZiMl/q/pGpjJBA7lINlbkHdWCVe8WD6A2XC4Wa/J2mvmIoRBgHUwO6s8capAl0c5kyo31vaep2tXE5KhKoXiSJ8E4W5EA7or+UAJrvgsfLcTvRvVqnDsqGN7Bz7wX6V857MHM9V+T8vZ2Vl/7GlKtVqlUqmwtrbWE0JvtVqMjY3x+OOP37Wn5SAw7M8+VbUHnl1Q7ZZ4X4teaKfToXArcdy/ZfG6Bkygt+O7WYRhSBzHvPzyy2xtbfHggw/etdBwd1Tl1dws1lquXLnCxsYGDz300GsidtwPlt1STjfy+Tzv/JE8Tz7s+O9/K+RL50K+fmmcI8MdioVGr3wThhHFkvLifJsgLPZGRbpx6MhgIhDA+Liy44TDkSPfhM4qbC8IOx2hZkCKcsANQxAefzzPua/n2aqn2LhFkDOIMeAEbQZIJyBNLRplqjK5BFeukbsvIp4d9oxRB3R7YBmTU7Ixkm6YtoMgyMqJknla7KaqghBor+0H1uF6DNsMBLL38so+Al8Hc9rBEUF3wKXGl2oz/8dwIyUs5bi5n8VuJJuCqwvBkKLD4oVTu6VP6+hf+F0Vr6G7b22T8+DmQIa0l71KS9E4A8Qm3rpFlbSeiQbYALMJ2tcqN5sJqqnP5noMY0Ut6IUYNwIkmfVMljlLx6HrkqG44joBxAp5P0saBIYgcCQJTE9bHnywyNqWMDnsqDhh60v9Gx6l0ajjnOPBe8ZZbA1e2lY2DIdmHOsZOSgyyvCysnHD/zx3wrEwwJi7XIZf+5WYyYnb+GKyCMOQiYkJJib8k7qVqdnZWdI05Wtf+xrWWoaHh3tZaKlUumsgu91S7v7Z0Dspr1ar1deNFya8AZi3DFVle3ubzc1NpqameOaZZ14TQk83a71dwNzY2ODll19mdnaWZ5555q5vqP1Z5X6w7I/77oH/8w9iPvmXhn/5v0RsLBeZGi1w+LBibUq90aA8UidtDWFtB+ccUVc4PAg8Eai++3qCMl7wGWR+CyoXYW0AoE4eUtYqg48zMMJbv3uE//DJqnfJti3CqEjS8Zmjc17sXnJCEqckbYd08sTbBjVtoiMGOxmhRw2aE59tWg70KCUGcuz23wZUXqW5WykwGDD0+p9kFlbqFG17QDSJwhcFhhR91KAGVK0n7IiBjiUmxYxFB82t+xY0iUHjTMThnBAc1z3Se+osRkKf7TVBUz8zSR9gmhTSihBYhQe1Z1klG7uZtm1lJfWOA4LdDcUS6IQnUwXqSLYUibMNRdaK7JVs0xy5yzXciXE/36i+J2oWU9K2Z7p2F+zcdkJ8OMIEfhzIqWV6xvLQg7uLcq4JMygLO/76SNKEeq1OsVigUCiwvgr5Ca8BOygk240Eokxs7e1Z3rguTB91rKx1N1PK2/++5ad+wnKnJiJpmvLSSy9hreWpp57ao4TT1bCtVqtcv37dK1+FYQ9AR0dHX3E07HZiUCm3fx1YXV0lDMOeLvXtlnJfT9Ze8AZg3nRn1Ww2e/OM5XK5N5T7WsTtyNkBtNttLly4gKryxBNPvCalj26JplsSvt0NwA9+t+P739rhI38c8H//XyHXr1tGRmpMH82TFo8yXhDUOZKucHjbC4fLJuTDiLEgwrQithcMWzVhC2HsiPdGHBT5AnALq6vUBbzpTcN87WsV2m2Hc03CaAhnQ1QtqTo0dqhzGNMV9wasYlcSguU66UtjyIwQnBTciF/oDX3kniyz3D15e39EQPsIS5phym6C6cUVrFNIHKaV4NoO53JIQ5CvWPRNApH0Rlxc4DNlSWIkytPPU9G+kqk0MlBLMuGCTYEn8GMfgFOHkRQIkZ3sUFymwtOdD61lj60L4XqMO2RAA7TWPVxPgJK6w2m4W14OFGeF4AbocWCtg7E2M/VWD3Z9l7cJUtLVFA5VCYeGsc4gKgQrQqrS65wqSto0SOqwCGHQ5vBhy0MP7k3rtraE0RXvJNJsNknihJGRkV5GFccwV3QHDNC7sbZpODzjiLZg8eK+niXCziaUy541/d/845SzT9w5E7VSqXD+/HmOHz8+kEFvjBlox1WpVKhUKty4cYNO59UTil4p+kHw0qVLxHHMY489RhiGPRDtL+V2n7O/lPt6Mo+GNwDzQFhruXr1Kuvr65w+fZrx8XE+97nPvabv0XVAuVn0y+o98MADA2eTBj3nVuC3P6u8kyzVGHjPuxocO3yVv/z0YU6dmmBzK2JtW0EUFRBCxIW4BHKBcu2Co1JL2Uhj0rSFESGMIg4dNmzteJHsQdG4CbkI/GJWawjlcsQzz0zwjW/ssFNJca4ClMEFWGMQjTCB7ZVUu+mRcwKxxXXqBNcj7FIJGVbkXoUZ/1hVcMHepqFV6ZqZ+PMhWdbWh68HslDriHY6pH3lUtNlh24L5muKfVOm6LTtUBP4T5oomBQx4e7MaP+63Z2DbMaoy3kge1Fxj0mv5OzU+X5gv5hE258i0+jTzTWQLiiMOAL8PCvo7jUVdzCR6ZFwNNsZuG0wsym6bnF9NWTtbiyy/1VjlAiz0MDNKWGhgG4GuGa4h0RVyDmSJCC/U2PolDI0lHLkSJ56o04UhoRRRGAMh63SrKRUdprkchGjY6MHhAuX5oXxWcd2a/B1PlxXFl8e/Ld2W3jkfscHPpAwMz3wIa8Yqsr169dZX1/nsccee1UG9blcjkOHDnHo0KHea90uoejVRL1e54UXXmB2dpZjx471nt8F49shFFUqlYECLX9b4w3A7Iv19XUuXrzIzMzMa1L6vFncSm6vuyMdHx/n2Wefva2dZDdjHTR03N/8f7VZ5f7XWVhYYGlpiWeffoAf/kHfwGq1Uv63fxvyHz+1z9IoUIZKgqYBhWJEIaPjO+dIkoQg36C61fF9u2wovDtzVijA9i2yy7FRpZ4Z+oah4Tu+Y5yLF2vMzzuUHcIgAuMdD0QCwPXUfiAbnTB5r99qLS6uIS0DO3koB5j7FB0XJAzoH3Pz3cs+GQfHQE1YNWBSh0lSkpaF9QSvv5eRi8Tr4AneBcR8I8E9ZpC6Fz5XHLYNRBaDgkTsaa86z7wNkgTXSTFRgBLgKoKZV7in71jTFI37SoAdMDnFNvsgRhxYg7lukZLLPqtgxGBMjEtTjG2jwVDv/JnAE5+42IGdvbsEdbtZpjFJzyVGKxFuxkGnTXS9hTKEBB4EwZIkHZzrMFEu8OTZSZrWoOqrFmmS0O50iDThxeeFuAP3nM5RaQ8dAEvIDLAbXhhjf6n9WNlx+a8DRkaUKFJq+zLRt7zF8sGfS7nTSmi73eaFF15gZGSEJ5988q7XkVsRiqrVak9drFAo9AC0K4g+KLos+4WFBR5++OGb9iBfiVDUarX48Ic//JqUjP9zidc9YIoIrVaLCxcuICKvWenzVjGoJNud66zVare8iG/1evsBcz+p505v3FqtxoULFxgbG+Opp57aA+LFIvzXH0x58gnHR/4opFLxi8/MrLKwcPD9jDHk8zkwOcbGfKaVpilpmtBoeDLRkemURrPcU1Y5APAD8P7YsZAoClhdzdOsb2BMAeeKqMshprNHqce4BMU7oKjrjkY4tN1C2xDsBIR5S+7hIZrjObR/DrKvLCst/4MoiFpvWeEcxOIJp0EGrUkfu5ZM5L3bnxTFbQSYb1i0LEhOem8g6gf/TZDgrOlJ0JmmYmKLa2ezOjbx7CLAzgvBeOrNlwHZtogEuK7wPAq1FC9z7l9Ps/ppumOQ9YRgyPdPRRwu9TVnmyYEgcV1lSLUAY5gLfUiC4W9Gya/KVFcX+qphAQ3WpgjIel2gNM2xrRJEwVxqMKxY2VOn55gPHY0AxAx5KIcuSiHtY7W8g7zxRKFsuHSdkwUbyN4I/L9erBbW8LcScdCX4Y9M+xYfN7/XK0KpZIyPubY3jGEgfLud1t+6Iduz5B9UKytrXH58mVOnz7dI/t8M2I/oUjVm4d3nUSuXLkykFDknOP8+fMYYw7cy7cT3TXk8uXLvP/97+dnfuZn+Pmf//nX/Pj+psbrHjAXFxe5cuUKp06d6jmSD4q7mZvcH/0lWVVldXWVy5cv3/Fc534AfjWknltFl5m7s7PDmTNnbgnizz7jePSRmP/nkwFf+IJhfoDHZzcOHVbWa7sM1SiKiKIIP46mTEwlVJccnU5MvdFAgDAjEkVRRKW+C2CpTanX6kRRxIkTU5w8KWzvFHj5cotWK0F1BC8HtHt+xDksfoHcXxkXAOewmx2anzYwUkUeBB3LeyZuNl4Ciq7EYEKvZpM9XwEjOZ+FKqhVLEFfdu81bukCVgbkdtUQbFr0gb7Pknriknqyrjc1Bsx2h6SZZoRT8fqnxme+gYCed/Ck8Xd3RXtC46ogrulJRibKiEYZMUkVsYpcDtCHPTKLtvdoCJO2IczmfUURHG5ZPQN4n8ynqhJFMfu9zbWRQ69XUUperUlg7kSZuGMplUNOnPDs7/nrwqEzjq1Mx7Xa6nBjx1LfnMCUDC1gmzyjY2VGqpYhk5KmaU8PtsvgvnY5ZPJEwE47YKrkWP+aoH3ZcKPhLexOnbK872ct999/Z4P41lpefvll4jjm7Nmzr8ri6rUIEaFQ8KSnI0eOAAcJRZVKhU6nw/j4OEePHr0j7VhV5WMf+xi/+7u/y0c+8hGeeuqpb8bh/I2N1z1gdkuft8q+em7wd9lo70a3JNslFuVyubua6+wHzDsl9eyPzc1NLl68yOzsLGfPnr2t1ymV4J3vsLz1uyz//k9C/upzg89XvgTUBr+GMVBrRhTyAlmlp78sZ6TB/A0hyMY9nLOUh4czFRYo5JXxqTGemRqj0UjY2OiwthZSr++WZVW7hsQB1h4kdFjrCCXny7GVHPp5JZht4U5HaC7oXSsu9YK1+3hA3oLKZs4c9cT37/b1ar3Y+66usGk5XCXE5CzuRNZDio0n8RiwNsEEEcQOu5ZgJMj6g12NugSnkc8K20LwssU9FOCavh8pYhFNcc4jmBGvx6tYnPoeatBQXBog8ynRfY64sxftnE0xYYJKhHOWMG7j6pFnvFZS3OjuciLGkcSJN3tml1hncATXHbboJQhPnRplbm6YtoPrCn+VCkkAScEwcV2ZG7E0O23WqzkKmvdM5L6IK8riasBWFHBiKsfIEIBis9J/qxWzNd9Ey7D0Qh6X5A/MEb/lLY73vjflVegH7IlarcaLL77I0aNHOXr06LdUGvNW0SUUjYyMoOoJUg8//HDPGPrVEoqazSa//Mu/TK1W41Of+hRjY2MDH/e3OeQVZm/uTvfoP4Ow1r6iuPrzzz/Po48++prV6m/cuMHKygpxHHPmzJm7Lt10G/cjIyN3nVV2Z07TNOXMmTN3VZ5eWBD+3z8L+PSnDZ1YMIEye1y5sXLzzcncccfC2i3+fsxx5YalXq/1BrDT1CJGiMKIuVnYqBX3boBUefligxs3Em9HlXjJN9/b7MvMM0ECSdtEUiSO917+knOED6dwdAiXgG4ZVA37byGvLBNgrRKuJzh3cCPkzYyjXRLWpvVziIA5Y3GZnZYpOwi9jqhJOpiqkl45uM8VY1BTQKSrL6rITIprhYiAkQRxMc511XMiHEOgce86kXmLVgLEOOTeHXQof1B0XoSwOOQNmhda6Ep2T4jFncwk8wSMtHavRQMgiCjBzjbJ9QIyFXPigUMM3zPKdRFqmf1aV1hB1I90UHCUa0q+FBBvsadXGlnF3hByeaWd+E7mkVFlZlwJ+r7+4ZJStpa0k7C2ZqnVLNZaZmdTfvInGzz7bJ7R0dFXLTyuqszPz7O6usrDDz9812pb34xIkoQXXniBQqHAqVOnDiQGXSCtVCrs7OwcIBTVajXuv/9+Xn75Zd7//vfzsz/7s3zwgx/8lrqofJti4OL5BmDeBmB+9atf5YEHHnhNboitrS3OnTtHoVDg7Nmzr8lM5YULF8jn88zMzBBFA3p+t/k6y8vLPceVruH1axGNBvzFXwZ89bzw9RdvnqVHkRKWoHVT9xKHkxq1hlIul/cIaffMgkebLK7LXjJR6MlEGxttLr64RadT6mWWJrC9gf1uBEkTdUN7CD/9YQ61MMeFFE+CERFfrlWDc35+MIwinBVkyaIDJID8c3K7YgErDs3ATFGCRx1uKsAULOQF2i1cxxFsdNDt8sEZTSDIF/aU5k3NopOClkCTKj7TDDPQVKJ8ebck7RQ9D+IEI00I6vBQsdf77L2mAMYTkfScQztBZgoNZiTBHYogaGPLIXaoCPkAIodBKeXgxHqb0Vqee+4L+IoxXAwDb2qdsEeFSNUL6RdXIF8XRseUSsH08NKoekeX2AtKFIagFQMIZRxjOZg6AuNjim5DPTODNkY5e9bx9NOWZ55pUansUKlUqFarWGv3ME9LpdJN74FOp8MLL7xAuVzm/vvv/xsJINvb21y4cIH77rvvtpj23ehXKPqFX/gFLl26RKPR4B3veAc//uM/ztNPP/16yC7fAMxB0WVt3irOnTvH3NzcXanrdIXS4zhmenqaWq3GmTNn7vj1YLdXWavVWFpaolKpoKq9G35sbOy2dCqbzSYXLlygWCxy//33f1P7L8srwuefN3z+S4Yr1/b2k+ZOOhZukn3GSUwht0UzHc2y3oPXcz6npGS9vi6ZKElI0hRrU4wJmBlPWVwe4sqVmErF9lir/bdBlMQkac4zLAcAkzFCIHXs0RB3aPf8du+lIAgJoxxxHdi4+UIahgFpGngvsvV9O3+jmMcVmQJME5dlu3KtA3EBiA5kf7m8Iba74CxLDlFFzzRQdh1RfCdGCALFasn3RaspOh8SSAdnPVHHHGrBsSGcM9hA0GKE5ECwSGLRiwXM6u6MnlOHOdmhM1tCS/ne6iEGcmXjDbITeLDi6ChcPWS8h3VCz2Bbsw8pgDSF4ctQLiiNbSEqKW4OrBHy60pnn/dqIa+EFurL/vf5nFLOwd99s+X7v88yOQknTzpuhh1dd53uDGSj0SCfz+8REYiiiPX1df7/9t48Pqr63v9/nTNLZkImK9lIQoDsi6BglARE24faVvF6r7X6tfqTFrkgKqK4l6tXekXla6/XKr3gioi29nvtpdVqcauCkUWwCGYPhISELITMktlnzjmf3x+Tz2EmzCSTWTIDfJ6Ph4+HTJI5nzlzznl/3tvrfeTIEZSWloY0GSjaUK1avV6PqqqqCWnVemO1WvHAAw/A5XLh3/7t39DS0oK9e/di//79+Oijj+LSo44gzGD6IxiD2dLSgszMzJBuDu9ZmUVFRcjOzsbw8DC6u7tRXV0d0prHKuqh44xoiMXhcGDKlClITU1FamoqkpKSTufgRmZonjx5EmVlZZO+azRbgJY2Ho0tHNo6eBwf5OAY1X8pEQlWixUSkVBcnIhBQ2Bjnj9NOkNbVIZ48lpJSgcGhwjcghsuJ0FfH2AyifIYMw5kZBwWF9BgchwH3uWCKCaAz7RDmqUGoXqrnEesgBAChUkBya7x66lynCfkKEkJ4IdFSJYzvVBe5YSyZgiCVgtJUnq8wHYCgB8RZlf6bDg4TgCUGhDCgRMJyHEOvGQBkswQi7Se1iKOA5eogaRUA0oRvKgE7BwUXQJglCC6bfL6wEmQLuAhTU8HISMqPwnEY29FjzAt1ydCccABXgT4ZAJXhQpSMg3TAkoFJ+dvVVrP3kAhwiOZN7LvISLkfOzIpwPnAhIGAK2BgHcDKpUn8qBQEySkEdiGz/yeNQKBWw8oVEBqCvDDhSKW3+HGrJn+L4lgcDgc8v1EjSjP85g+fToyMjKQlJQUNzlL4LTnm5ycjFmzZoXs+TY1NWHFihVYvnw5/vVf/zUuPegowwymP4IxmEeOHIFOp5Orz4LFYrGgqakJOp0OJSUlco7EYrHg6NGjmDNnzoTXO9GiHtr0bDQaYTQaYbF4Kko1Gg2MRiOys7PDurEiicsFdPZwONrF4ehxHk1tDhw55kBCwhRkpKthdft6pKPJzJQwaAj8OdJ0EgxDp39OiGc0ksPhQm+vA3q9CMewHaJLCzrcUDHKaPI8ByI4QVxqj4qPCBCVAEWZCJKqkX9HlAhUJ0UIonbke1KMeh+MtPuowZ0kkNzeBpOA520QJSuUGhekC3mIiemAXYLkTABReX6XEwk4EYBAQHQ8JB0HhVGEog9QWESQATskUfBssKo5SIWpIFqlZwIMLUJSA1DwgF2CoskCRY9z5NwQSOkqiKWJQJrK6/FBABXx/D0BwHHgnATKfTa4Z2sBwoFXc+AUHBQKb2MOEMFTnEvTxjwHKNUELv50UZBnMwIQB6A7BiTyBHar5320WgLYCexDPDRTCVza03KGGpHAPsAha6qEf10q4I4loUvZ+YM2+efm5iIlJcXHgKpUKh8vNFxB9VAZGhpCW1tbWJ4vIQTbtm3Dq6++ijfeeCOkZ9Q5AjOY/iCEwOUaW+q6s7MTarVabhoeD1EUcfTo0YBi7bSxed68eRNaZyRaRaiuJRVNttlsIIQgOTlZ9kI1Gk1Md81OpxOtra3gOA5FRWU4qU9ATx+HI90cjvXw6DzBwWrzXZ8uicDiAIj/6xwAUJApofvEWBsDgnStA/v2OXDqlBs2m3RaZQee0V48zwEuK0QhEYAEEE/hEQGBIs8OzNDKD3FFvwiReIfDOPC8YsToj2jLcgpIvUq5mIXnXSDEAokIgFoFSZMASaMEX8Z5CowEP/nQkeNJCQB0PJRdAtQterjNHEQNB1KTApKt8gy+tACyXNGIGg+nPn2jc30uKA6aIRUlQirQAErO83sKQKHgIIkERJI8XqaSAzgOCgAKNw/eQiBpRwqIlPAJGfOAZ+amE8CUkcNLALETIIOAwFO5zLs9CkTafo8aj8t6+ju97XoBOakEz7+ghCRxSJxCMKNUQuEsgsKpBBXlEhb/RIqooSSEoKenB729vaiqqvKrauNyuWA0GmUjKggCkpKSZAPqHdWJBpIk4ejRo3IPd6jFiRaLBffffz94nsemTZvOKwUfPzCD6Y9gDGZPTw8kSQpKT3ZwcBBtbW3Iz8/H9OnT/Roet9uNgwcP4pJLLglqfZFQ6gFON1VPnz4d06ZN8wnjDg8Py16odxiXlppPhgfqXXhUXFwsS4P5/SxDwNHjPI52e7xRuws44kcogcJzBAncWAVFnt/RArIxliSCwUEHBgftGB4WYLdLkCSAczlAiMYzrUTJQRJPH1eZ7IZY5PHAJL0KCgUtsvE6Dk8l5jhwdgGSfsqIobRCIgKIJgGSVuuZlEL7INUSSL5CFijwxrsHFAA4hQjypQlcyRRI5VqPYQMAKzntWXr/sSgBCaenjGBQBJIVntZVpedllYaT/5YIBKJIoJjiMdXEAUAkIMc9AkskaSQsTSteOYBzAZKdrg8giQBMEogF4PN4cIkAXB5jyQlAWicB5wSEEQH1JTcIWPewJxJ04FseqakSimbJgYCo4HK50NTUBI1Gg5KSkqDbyiRJkqM6JpMpaoLqAGC329HQ0ICpU6dixowZIT8bGhoasHLlSqxcuRJ33HFHXIWZYwQzmP4IxmD29/fDZrNh1qxZAX/H4XCgubkZHMeN244hSRL27duH2tracdcWaPzWRHA6nWhpaQHP8ygrKxs3ZBQojEsLiWjxQySx2+1obm6GVqv1CV8HCyFAdz+HlmMcWo/xaDnGY2DIS+ElXULfGO0sAJA3VcKJMYyu2+3GyX49DAM87HbAbpfgcpERD5OHYqRalHASFBkWiDodFAoekuR9ruj4L4IpUzhM1wJHWxxwOAWQhARIiYkgCn7Ek7Z3cAAAIABJREFU+fMSWycSuARAyledYfRGHEUolYAoCCB2B0iXCqjReipsKUbiMZ4jz32OA1QqHsRNPGL1Ks4TrpUADBNgCgdFkie0ygGy8aQatB4xBc/BeTMgDcLTD5IFEPVIPyrPQUkIRC+xCU8kVwIxjXjtKoBkQdbh1egJpvQDbjeH1CSCm64T8KvVY1eyRxoa3hxv4xYs3oLqJpMJLpcr7E3pwMAAOjo6UFFREXL9gSRJ2Lp1K7Zs2YItW7bgggsuCOl9zkH8PmzPe+GCYIzQWNqvtBfrxIkTKCkpCermogOkAxGp8CsNJ504cQLFxcVjKhl5461dmZ+fDwCy7JZer8exY8cgSVJEwrjeGrVU7D4UOA6YnkswPZfg6jrPeTtlBBraeTQe4dHXD/SN8x42S6D1E9hsdjidTlx4QQoGM09vhgghMBqdMJtdsFrdsDskuFyAyqkBL7kgZishKBVwOAQQIqGwUIcpU3hkTlVDqQRUpwAFScLhXic8zReBlkA8YuVGCSSVl40mXXGilkNCAsBZAEubEi6LAqTRBVSoAS0H2Ak8MkAARAJexUOp5DwC8hwHNacAJwACPyKi7+CgsHMgWshTvXgvoXmeAKLFM2NT4gFioj/jwJ2CLGKvURA4TSNi854SWM/fD3Pg7ByQCMAGcD2AlAskJgC/qBNwaYWE+RdLyAruko0YkiThyJEjsFgsmDt3bsQ8wUCC6kajET09PTCbPX3F9J5KSUkJuOkWRRHt7e1wOp1hqQqZzWbce++90Gg02Llz57le9RoRznsPE/Ds/sY6DwaDAX19faisrPR5nQqlZ2RkYNasWRNSAtq9ezfq6urOeD1SSj0WiwXNzc1ISUlBUVFRxFSKKP7CuImJibIBDWbHTNeYmpo64fMXCn2DwOEWHodbeDS08rDaT5/b7DQJA71nrlcQBNnDTkxMRE4awcA4nmrmVBG93SLcggBCnEgttKNX0MJsFlFQ4GmQJ4QD9ARN3/JwODkoMkScHHZ7KkuVHmUpSfTyMsUR3VqlBOQoQbQceAWQkMAjQcMDkgCtESD9KghmQBAJRE6ELRMQ8nlwIsApPLM/eZ6DQuVxJDkJ4ER4KoM5gCR4wqek13NYTgVIhZ7WEG4knckDEKyQ86BKEAgDvtcprwL4acDFlRJEAWg/ChiMwIgWEhQDEnSJAqZm2EE4JWw2FfKqCf75BxzuuSx0LddwsFqtaGxsRHZ2dsB0SjShCjw0lOt0OuV7inqhtP4hJycHBQUFIa/x8OHDWLlyJe6991784he/YCHYM2EeZqjQgc8Ut9uN9vZ2WCwWVFdXRyQ5Hkn9V9qDVV5eHrVZdQqFAmlpabJHSBVDvHfMSqVSNqDeYVxJktDZ2YlTp05FdY2jyc0EcjMl/OgyTy7ySBeHQ808DrXwMA35/i4hBHa7HS6XE0lJSVAqVcjPktBzfPywmYLjoFKroVKrASTCPZiKsmw3LNNdGBh2QN/Hw9CnhsLJw+32eHmchUdamhq8wmNQRhYBl1sCEd1wu5Ry6FXFEai0CiQk83AKEninG4peJdxmBbQ8gQAOSgUHJXikaAnsZg62JEDwckQkAVAoPZWrku3067wEwHJ6p0zcgKIHEPM96VOdlqBiFsHh73nYbJ4FSX0cON5LhIcAnAO4Ik8ESQTsdgdmzXCA53U43qNCfrKI5CLOIzxBkiCKItyCGwkuBwpcrdi/X/DJ90V7GAJt/erp6Znw4INIolKpkJGRIVe4eqvw9Pb2Qq/Xw+l0IisrC2q1Gg6HY8KRHUmS8MYbb2Dbtm14++23UVVVFa2Pc07CPEyM72HS/NpFF12E/v5+dHR0YMaMGT6FMxNl9+7dcg7Tu7AnHK9Sr9ejra0Nubm5KCgoiHmrCK0epDtmURSh0WhgNpuRnZ0dFc83VBwOoLmdQ2Mrj4OHRXzfZINCoUZiYiI4jkOqToLFwMlFKIFITZFg0nM+1bqEAGYrcMoAOEQOjpHKW8HqVdAFQJMtwa1UguPpNTDSgK8gcLpOv58qgcCVARDRjVSXCNMJTwGSkicQrfBpvVGoCJAPCBwHazIgjmyROQC56QTJGoIjHTzk/aAEcEO+Fa4AoEklSCsHKoqIbLibWjgMdHOQekY8T42nBzJJRTAtmyA7U4QyXQ8Tr/VRzcmRJPT3nXltXlgs4d/+PzfcbrdPvo/qnUajCM3tdqOpqQkqlQplZWVxcz16IwgCWlpaAADFxcU+UnYOhwNarVY+N96DtEdjMpmwatUqJCcnY+PGjROa0Xkewop+AuF2u2XPLtDPDxw4IPcvlpaWht1rtXfvXlnpP9yiHrfbLU9KKC8vD1nZI5qIoogjR47AYDAgPT0dNpsNdrt9wmHcaEKFHAYHB1FUXIHBoWQcOcajvYPDsB5oP8LDMUaVLccR5OUQ9PTwKMiXUFVJUF0toaRYwh13qfHd9yP6sAqC6gsktLbxpw0hIeCVBEIGgURGNk/goFYBotvTuuLpb/EY2bQ0G8zdUyC5eCRoCQQloOYAu/nM9al1BO6pHEQesCYD4DwtNsUzPT93uTzGb0jvmc8pGT3Gj7aNTlETzKkgKJ4t4cSoit8ClYRuP4OYnU4nbDYrMqdOgbJADcfImyUnEAwfhd/y1sdvd2FO0ZmPHO98n8lkkvN91EikpqaGdD/q9Xq0trZOWDpuMjGbzWhsbJQr20dDIyF0czE8POzTJmY0GlFWVoZDhw7hnnvuwZo1a3DbbbexEOz4MIMZiLEMpiRJ6OjoQEdHB2pqakIuSvGGEIL9+/dj+vTpSEtLk0XEQ3mfgYEBHDt2DDNnzkR2dnZc3gjU883Ly/OZ7O4dxqXCzzSMSx+EkzUmiYpM0PL8QIbbaAL6BzhYLBxcLsDtBgQRSNQSpKcCqWkE6WkeZRpvnE7ghlvUaGnnsfIOAQ/eJ8BsBl7bpsSf3legZyR/qp5CICYDIjgoFRJEF4EgeFqKEpQCLio+hVuuOYnLF0zH8vvS8Y8RI1xWIqG6XEL9Xh4DfuT4NFMJxCkAMQLuWUDNpWfe2kN6QOgETAbPyCvCAzmZBBkjBZhKJYGumMAw0kbDcwSaAcBm9famJVgsFhACuf8wJ1tCf4LHYy5QS+g+dub6ZmRL+M1dYwuIeON2u316H10uF5KSkuRrZ6zeR3pPm0wmVFVVRT3kGwq0YK+vr2/Cwu60vmBwcBCrV69GZ2cnrFYrbrvtNlx//fWoqamJWo+lw+HAokWL4HQ6IQgCbrzxRqxbty4qx4oyzGAGIpDB1Ov1aGlpQU5ODvr6+rBgwYKwj0WLegwGA/r7+zE8PBww1zcWdOh1QkICSkpKJn3+XjDQXK/T6Qza8/VuAjcajbIgNj0/Wq02opsC73xqRUVFVPNXVivwj+94XLbgzGvt20McvvmWR0sbj+P9HAwihykJwNRUgtxMCdMyjZhT1IgZM3IgSRKMRiOsVgdefLUalWXA6pUiUlKSwfM8DjcC//MXFXr7gOn5QNEMCeWlBLnZEjQaYMDOYf3fVHCOCi+nJhAYW8c+tzodgWsa4JQ45Gol9DWdNkputwsWixVarRYaTQK8nzkFsyT0Ew58P3zCy5R7/sWNKy4MHOUZD0IILBbLGb2P9J6iCjw2mw2NjY1h9y1GExomVqvVKC0tDTlMbDQasWrVKqSnp2PNmjU4dOgQ9uzZg4MHD+Lzzz+PyjODRgOSkpLgdruxcOFC/Pa3v8X8+fMjfqwowwxmIARB8Jny4HK50NLSArfbjYqKCiQmJgasag2WsYp6aI8W9bRGt2x4GxpJknD8+HH09/eH1YYRbahA9YwZM5CTkxPyg4kKYtNzQ8O41ANNTk4OOYxrNpvR3Nw8rlcZS1wuF5qbm6FUKlFaWurzkBs9mml4eBgKhcKnXzZQW8S3XTz+78dKiF5yfQVq/+HV0eTmSuhL4pAjEPR38yPrsI4o3Pifp6jgCQqLJHR0nPmzNB3BpvtdUEY4feh9X5lMJtjtdgiCgPz8fOTk5MSdDizgMXItLS1yxChUvv32W6xatQoPP/wwbrnllph8TpvNhoULF2LTpk249NJLJ/34YcIMZiCowaRhkOPHj6O4uNhnxFWoBpMq9EykqMdfy0ZSUhI0Gg1OnTqFzMzMuNF/HQ3dbABAeXl5xHU1/YVxaT6L/jfeznkyvcpwoMpME2mepwUz1Ei4XC7odDqfUCW9/j5v5rFpp+dccSDQnhqrF9WXmUUiOrt4uAXPbFK1OgGJiVrQ54zTDSR4fQ08R5AuEUg6QG/3vW7v/mc3fnBR6N7leLjdbrS0tIDjOOTl5cmeqMVigVqtjqogR7AQQuRrsrq6OuQ6BEmSsHnzZrz33nvYunUrysrKIrzS8RFFEfPmzcORI0dw9913Y8OGDZO+hgjADGYgaIi0qakJKSkpKC4uPkNpZs+ePbj00ksnZKQipdRDb/jh4WEkJibC6XRCrVb7hHFjXd1HCEF/fz86OzsnvYhitIfuHcZNSUmRK12B015lZmYmCgsL43LT4Xa70draCkmSwt50SJInp0jPj8VikUdWpaam4vOODPy/bxOQoyXobw7++ixIlWCxmdExJEGn08n3iyAC3Sc56Ic55GdKyB6ZjZ6vk9BzjEdCAoFuGsEpm+e8l+RLeHqZO2oSd9Rjo5GO0VBBDu9Kbp1OJ5+fsWZiRgo6YUSn06GoqCjka9JgMOCuu+7CtGnT8F//9V8xz80ajUb8y7/8C1566aWQJzPFEGYwA3HixAkcPXoUFRUVAXsC9+/fjzlz5gT18IpUTyXgCW0ePXoU+fn5yMvLk9/H4XD4tGzwPC/f5KFWDYZKvOVTvcO4JpMJNpsNWq0WoijC6XSiurp60no/JwqVZJs5c6bfB3wkoCOr6Pl5vzUXXT1pMJycMjJsm0eA5wUAQK0UoO82A1ChvFKDHrMShAAGs8dYur1yo9npBDNzJKjMgH1EKEKtJkjJJzhl5fDMcjeK8yL/mJEkCceOHYPBYJjQTEg6X5aeH++ZmDQFEMnrm37fJSUlQStx+eObb77B6tWr8atf/Qo33XRT3ISa161bhylTpuDBBx+M9VImCjOYgXC5XLIXGIiDBw+irKxs3N4lWtQjSRJ4ng9L/7W1tRUAUFZWNq5ElyAIMJlMMBgMMBqNEAQBOp0OaWlpUSmWAXyl90pLS5Genh7R948Uw8PDaGxsRGJiIpRK5Rlh3FiOZKIIgoD29nY4HA5UVlZGTJItuGOLeHW7gA/qlRDcboiiCIVCAaVKBZVKBaVCKV87TqcDSUQPm20qVCrPOSuvELHjG4XsNY6mNFuCTvDtJFEqCRZfI+K2ayKv6mO329HY2Ij09HTMnDkz7Ovee4MxPDw8ZgQjWLwrdaurq0P+viVJwsaNG/H+++9j69atKCkpCel9IsXg4CBUKhVSU1Nht9tx9dVX45FHHsHixYtjuq4QYEo/gVAqlePOxFQqlT6FQaMZ7VWGaiyp6kh3d/eEcldKpdJHJYTulI1GI9rb22Gz2SLa82i1WtHc3Izk5GTU1NTEPCTsD+pl6PV6XHDBBT6l9LQtwWg0oqurS95g0PMTykMwVAwGA1pbW1FQUIDy8vJJ9w6USgVW/kyB6hIem/6khcsNiKIEt+CGw+E4rXJFCBJUBAIyZS+rdq6I5f9HgChw+OteDuZRlbcJSoIjJzjkJBHMyiBwOD2DuW9eLOKffxR5Y0nTAuXl5REbiK7RaKDRaOQiHBrBMJlMOHLkCGw2GzQajY8XOtbwAIfDgYaGBqSnp2Pu3Lkhf99DQ0NYuXIlZs6ciS+++GJSN1mB6Ovrw5IlS2Sn4aabbjobjWVAmIeJ4IZINzc3Iycn54yqVHr+IqH/So0QzWVMdGLHWPgrlqE7QbpTDuZ4tLn/5MmTKC8vP2PWZ7wwPDyM5uZmWRd0vM2B9wbDaDTKYVx6fsKpxg0EnZtqNptRWVkZF4ITx3o5/N9tKgwaTl/DnnYRT4FM7hQ3uns4JKjcuPkaA66YzyM1NRVJSUk4qefwwv9T4pNvlBgyA0kJQFGWhGsWiPg/PxYxRQM0H+WgUgLlfgQKwoGq4RBCUF5ePqlpAULIGV4oFQ+gRpRGeGghV3l5eVgV7nv27MGaNWvwxBNP4IYbboibEOw5BAvJBiIYg9ne3o7U1FQfjy9SRT3UExoaGkJZWdmkGSHa82gwGGAymQAAycnJSEtL86vhOTw8jJaWlrhuw6ChLoPBgMrKypAnMFAFFWpAactGuOoyFJPJhJaWFlnGMJ4eeGYb8JddChxu5/B9ux2CW0BKig4FyRx0WuDSCyXUzRWg5E/3PZrNZrkQLSUlFSf0KZieo0TaJKSK6RCEwsJC5ObmRv+AQUAr3akRpS0tCoUCxcXFyMjICCkqI4oiXnzxRfztb3/DW2+9NebIQUZYMIMZiGBmYnZ0dECr1SI3NzeiRT0GgwFtbW1Be0LRRBRFn2pTp9MJnU6H5ORkmM1mWK1WVFZWxu0kdmqEsrOzUVhYGHEj5K0u450nnkgY1ztMHI5BjzZU+UiXmoNhVyHcLmB2KUHyGF+90+n0Ud+RJMnn/EQ6j+7dilFVVRW32qhWqxUNDQ3IyMhAYmKibEg5jvPxQscTUj916hRWrFiBsrIybNiwIS5CsOcwzGAGIhiDefz4cXAch/z8/IgU9VAVHIfDgYqKirgIx42GEILe3l4cPXoUarUahBBoNBq5kCgaYcpQiJRXGcpxR4dxNRqNTxjX24ugRigzMzNuVWbofNeBgYGwN0eiKPqcH7vdHrRQ+HjQMVcpKSlx25MMeHJ6XV1dqKysPKMym25QvYXUvUU5dLrTIhBff/01HnjgAfz617/G9ddfH5fXzjkGM5hj4XQ6x/z5iRMn4HA4MH36dADhDXU+efKkPPEkHBWcaEKrNu12u2zQaa7GO0zJ8/yERAMiDfUqc3JyYjLD0JtAYdyUlBS4XJ48YCzHR40HNUI6nQ7FxcURN0Le54cKhXMc59MOFYzXNDAwgI6OjrDzgNFEFEW0tLRAkiRUVFQEVR/grdxkMpnwxz/+ER9++CGysrLQ19eHLVu2yBOOGFGHGcyxCGQw6fkZHh5GU1MTCCFISUmRvayJhEVov6JarUZJSUnMWxkCQWXtaE5oLCPkXW3qT9ZvovP6gkUURbksv6KiIm5Dm8PDw2hoaIBSqQTP83IYdzIb44OBVpdOdnsQbYfyHpocSERdFEW0trZCEARUVFTEvN83EGazGU1NTcjPzw9rBODJkyexYsUKZGRkoKysDPv27UNPTw9++ctf4v7774/wqj10d3fj9ttvR39/P3iex/Lly7F69eqoHCvOYQZzLPzNxPRX1EPDKLTf0eVy+RgIf3ksQgi6u7vR29sb1/2KLpcLra2tIIQE1fvpD2/RAIPBAIfDIc8yTEtLi4h+Jy3ymDZtWtwVzFC8e1QrKirkQq6JhnGjjbdsXFlZWcyNkD8RdZVKBa1WC71ej+nTp8f1d37ixAmcOHECVVVVYYWzd+3ahYcffhhPPfUUrrvuOvnz0usnWoWBfX196Ovrw9y5c2E2mzFv3jz8+c9/RmVlZVSOF8cwgzkW3gZzIkU93g9Ag8Egi4NTDxQAWlpa5CbqeOxXjKasnfcsQ2/9zlBk/by9ysrKyrgt8qADx6dMmYLi4uIxP1+gMPdkqDbReZCzZs0KS+g7mhBCcPToUQwMDCA1NRU2my0iwgGRxu12yyL54QyiFkURzz33HHbu3Ilt27bJKaBYcf311+Oee+7BVVddFdN1xABmMMeCjviiSj2h9lRSA6HX69HT0wO73Q6dToepU6ciLS1t0j2I8XA4HGhubpZHCU2Gh0F71gwGA4aHhwHAJ8ztz0BQTdB49yr7+vpw/PjxsCIJowXU3W63HKaMRBiXDvOmVc+x1hwNRCCN1UDSh97CAZN5j9GIRyC92mDp7+/H8uXLMW/ePDz11FMx9/Y7OzuxaNEiNDQ0xK2UZBRhBnMsXC4XBEGISKvI0NAQ2tvb5YHJtNyeGohYF8oAp8NHPT09KCkpkRWCYoF3HstoNMLtdsvtCMnJyejt7YXFYpFHrcUjTqfTZ+MRSdEJKqBOz4/Vag05jEvza/HY/+kNzaOXlpaOe23689K9i4n89RRHAkIIurq6MDg4GHZby5dffolHH30Uzz77LH7yk5/E/HuxWCy4/PLLsXbtWtxwww0xXUuMYAYzEC6XC0uWLMHFF1+MBQsWoKqqKqQdKs0BSpKEsrKygDdpoEIZ6mFFe8dvtVrR0tKCpKSkcUOGsYCGuWk+RaFQ+JyfcGX9Ig2t2gxXQDtYxjMQ/orR6MP95MmTcd1LK4qij6ZuqOHoQMVE9Bx5FxOFgsvlQmNjoxx2D/W9BEHAhg0bsHv3bmzbtg35+fkhrylSuN1uLF68GD/60Y+wZs2aWC8nVjCDGQhJkvD9999j165d+Oqrr9Dc3IyCggLU1dWhrq4Oc+fOHfPGpaG4rq6ukHKAgQQDaKFMpHI0dPj0wMBAXMva0ZAh9Sq1Wu0Z7RpKpdLHS4+kRxcsNG/F83zMC2ZGe+neczA1Gg06OzuRkpIS1vioaEO932nTpiE/Pz/iIgejc+n0GqJGNNjvj+Z+J6L17I/+/n4sW7YMtbW1WLduXUyu4dEQQrBkyRKkp6fjhRdeiPVyYgkzmMFCG+GpAT148CBSU1NRW1uLBQsW4JJLLpHzSM3NzbBYLHLvWiQueu8QnMFgiIhwOp0DmZGRgZkzZ8btQ5MKkdNwdqCHJpX1ox6EJEk+Hla0vXQaMozXghnqpXd3d8sTJLyvoXiYoUqhVeT9/f2T6v3Sa4huNOgszEAV74QQdHR0wGg0oqqqKuRrjBCCL774Ar/61a/w3HPP4eqrr455CJZSX1+Pyy67DBdccIH8jHj66adxzTXXxHhlkw4zmKFCq0ipAf3mm2/kfsyuri688cYbYU0dCOb4gYTTqe5roIefKIryXMCKioq4DsVRrzIUIXKq3Uk3Gd79fGlpaRHrdxQEwacXMF57aan3q1AoUFZWBqVS6SMaQKXZJioaEGloaDMxMTHm6YGxWn60Wi16enqQlpaGWbNmhXwtCYKA9evX48CBA9i2bRumTZsW4U/BiBDMYEaK3bt3Y9WqVaiurkZWVhb27t0Lq9WKuXPnoq6uDgsXLvQZ9hwNvAuJ6MPPO0SpVqvlytLc3NyYq+CMBfUqRw/JDgfvfj4aggu331Gv16OtrQ2FhYVxq9AEnB5KPJ73GyiM653ni+ZnPHXqFNrb2yct9ztRaK6Y9lCrRuaDpqSk+Oi/Bktvby+WLVuGRYsW4YknnoiLECwjIMxgRgJRFHHnnXfikUceQXFxsfy63W7Hvn37sGvXLtTX16O/vx9VVVWoq6vDggULUFpaGtUwqHcrgl6vh81mA8/zKCwsRFZWVlxq1dICD5vNNil6uqPzoN7VymMNkfZeZzy3YXi3i1RVVU3YY/RXjZuQkBDxMK4kST7nM15FxL3XWVVVBbVaDUEQ5EgGrTegwhwpKSl+0yWEEHz66ad44okn8Pzzz+PKK6+M0SdiTABmMCcTQRBw8OBB2YC2t7ejqKgItbW1WLhwIWbPnh2VHeapU6dw5MgR5OXlISkpSb6xHQ5HVEKUoUK9tUh6lRPFe5NBp494qzZptVpZq3a8nGqsiVbBjHc17ugwbijtGlSAPicnJ67bWmw2GxoaGuQpQoHW6V1MRMecKZVKOJ1O9PT0YOHChXj55Zdx6NAhbNu2Law+TcakwgxmLJEkCa2trdi5cyfq6+vx/fffIysrC3V1daitrUVNTU1YHpbL5UJbWxtEUUR5ebnftgLvQiLayzfZk0cEQZCn1MfblJbRsn50EHB+fj6ysrLCbkWIBnTEFe0FjLam7ljar2OFcb1l4yorK+NWgB44ravrLWk4EWhedtOmTdizZw/sdjt+/OMfY8GCBViwYAHKy8ujsGoPS5cuxV//+ldkZWWhoaEhasc5D2AGM56glYG0kOjAgQPQarWYP38+6urqMH/+fKSkpIy7A/eefjKRik3vyREGg0HeGXsXEkXaA6ZeZUFBQVii1NGGemtZWVnIzMz0yYPSYivqYcUyD2W329HY2IjU1NSYjbjylyseHcYVRRFNTU1ISEhAaWlp3FTnjiZS4u6EEOzYsQPr1q3DCy+8gIULF+LQoUPYvXs3+vr68Oyzz0Z45afZtWsXkpKScPvttzODGR7MYMYzhBAMDQ2hvr4eO3fuxN69eyEIgiymUFdXh+zsbB8jY7fb0draCpVKFRFZO5fLJYvKm0wmAJDDb2lpaWE1kXvP/ozXHKAkSfJA4kDtDbTYyt85mqxKU28JvvLyclmzOF7wDuPq9XrY7Xakp6cjNzd3Ulp+QsFisaCxsRF5eXlhpQhcLheefPJJtLS0YOvWrTFpOers7MTixYuZwQwPZjDPNsxmM/bu3SvnQQ0GA+bMmYP58+ejs7MT3333HV577bWoydrR8Bs1ov5yfOM9WKhM4PTp08cdFRZLrFYrmpqaZJH8YL21QLJ+VBs30sLgLpfLR+Q7XistJUnC0aNHYTabUVZW5rPRCDaMOxl4S0SGO6v0+PHjWLZsGX7yk5/g0UcfjZknzQxmRGAG82zH5XJh+/btWLt2rZyrKikpkStxKysro3qTBhrdRfOg3g8+QRDQ1tYGp9MZ114lIQTHjx9Hf38/KioqwhaZ9ldpqtVqfdpZQg2d0jaMSE+UiTRWqxWNjY3IyspCYWGh33F3o8O4oyfYTMZGQBAENDU1QaFQoLy8POR7hxCCDz/8EE899RReeuklXH755RFe6cRgBjMiMIN5tnPgwAGsXLkSL774ImprayGKIhoaGnwk/fLz8+UQ7kUXXRTVECGtEKQeKO11VKvVMBgMmDFjRswqYIPBbrejqakJycnJUZOM884V+5P1S0kjzqddAAAWl0lEQVRJGTeUTtta7HZ7XLdhEELQ29uL7u5uVFZWTmjzQSfY0FA3FQaJlnITnTBCh6SHitPpxBNPPIGOjg68+eabYUnlRQpmMCMCM5hnO4IgQBTFgA/MQJJ+8+fPx8KFC30k/aK1vqamJlitViQlJcFqtcaF5utovMNwscgBulwunzAuFd+nuWJv4zA8PIympqaYtt8EQ6TmQVL86SvTfkcqDxnKuaARhYGBAVRXV4c1YaSzsxPLli3D9ddfj4ceeihuKqiZwYwIzGCeb/iT9OM4Dpdeeqnshaanp0fkIUzDhXQmIH1Pb81Xo9Eoew40jDvZ3hKd/6nValFSUhIXFZvesn60Z3bKlCmQJAkOhwPV1dVxK2kIeJSaWlpaoqqr6x3Gpf2OEw3jesvwlZSUhGzgCCF4//338eyzz+J3v/sdFi5cGNL7RINbbrkFX375JU6dOoXs7GysW7cOd9xxR6yXdTbCDOb5DiEEJpMJX3/9NXbt2oXdu3fLkn5UUGGiTe9utxttbW1wu92oqKgY1wBSz4GGcb1nX/oTvI4UdPPQ2dkZ1IzFWGK1WtHQ0AC1Wg2lUim3anj3zMaDoacRDZPJFJYYeaiMrlimmzEayvXu8aVGPdwJI06nE2vXrkV3dze2bNkSl5J+jIjADCbjTMKR9AvkVU4Eb8Frg8EAu92OxMREn9mX4RpQ78rSSLTfRAvvHODopvnRijs8z/vk+CZbBN5ms6GxsRFTp07FjBkz4iJUTDdjNJRLPXVRFOF0OjFnzpywhDI6OjqwbNky3HjjjVizZk3chGAZUYEZTMb4CIKA7777TlYk8pb0W7BgAWbPng2j0Yi33noLV155pV9VoXCgk1moB2o2m+VG+LS0tAl7VydPnsTRo0fjvrKUGnXaUzteeDEYWb9oGTE6+zVUJZzJwm634/Dhw7JoutVqDUl4ghCC7du347nnnsPLL7+M+fPnT8LqGTGGGcxQefzxx/GXv/wFPM8jKysLb7755nkzlodK+tE8aH19PZxOJ6666irccsstuOSSS6Iub0e9KypX5y2aHmjwr9vtRmtrKyRJQnl5edyO4QJOz9YMJ1zobzRVuDNURyMIAlpaWgAA5eXlcVHAFQga/SgrK0N6err8ur8wrvdGQ6PRnCEO8thjj2FwcBCvv/66z3sxzmmYwQyV4eFhuUT+xRdfRFNTEzZv3hzjVU0uBoMB9913H6xWKx577DE0NzfLkn4ajQa1tbUTkvQLB7fb7VNIRKtMaRjXarWira0NM2fOjGuxa1EU5V7VysrKiBr1sWaohtLrSEfFhduGEW0kSZLnqlZXV497Tv0VXDU2NmJgYABlZWXYuHEjfv7zn+Pee+9lIdjzC2YwI8EzzzyD48ePY9OmTbFeyqTS19eH+vp6/OxnP/N53VvSb9euXdi7dy/cbveYkn6Rhuau9Ho9ent7IQgCMjIykJGRERW1nUhA+wAns13E6XTKBVdU1o9uNAJNHiGE4NixY9Dr9aiqqoorsfzR2O12NDQ0IDMz069gQjAQQtDc3IyXX34ZO3fuBMdxKCgoQF1dHX784x+jrq4uCis/zY4dO7B69WqIoohly5bh0UcfjerxGAFhBjMc1q5di7feegspKSn44osv4qJBOV4ZLemn1+tx4YUXynnQiUjPBQsdQl1QUICcnBx55JLBYIhKeDJUqF7t0NAQqqqqwuoDDJfRvY4ul8tHso7neTQ1NSEtLS0q31kkGRgYQEdHByoqKsLqq7Xb7XjkkUdgNBrx6quvIi0tDQMDA9i9ezcEQThjwxhJRFFEaWkpPv30U+Tn56OmpgZ/+MMfUFlZGbVjMgLCDOZYXHnllejv7z/j9fXr1+P666+X//3MM8/A4XBg3bp1k7m8sxqXy4X9+/fLOdCuri6UlpbK447CkfQTRVHWLK2srPTrAY0VnqTe1WS0adDK0oyMDMyYMSPuDBDtdTQYDOjv74fZbIZOp0NWVtakjoCbCDSs7XK5UFlZGVYFdGtrK5YvX44lS5bgrrvumvTPumfPHjz55JP4+OOPAXieNQDw2GOPTeo6GACYwYwMXV1duPbaa5mKRhgEkvSjrSzBSvoNDw+jubkZubm5Ex5GTIs/aHiS4zifQqJI5xOpslC8V5YKgoDW1lZ5rqooij4j4IIpuJosaL9quEOzCSF49913sXHjRrz22muYN29ehFcaHO+99x527NiB1157DQCwbds27Nu3Dxs3bozJes5z/F5M8VvmFke0t7ejpKQEAPD+++9HdQDs+YBCocCcOXMwZ84crFq1ykfSb9u2bXjggQeQkpISUNLP5XKhu7sber0e1dXVIQ1NTkhIQHZ2tqxM492m0dXVBVEUfQqJQs3duVwueRZkTU1NXAgOBILmVUdPltFqtXKhj3fBVWdnJ0RRPEPzNdr5WO/xZuFOGLHZbHjwwQdht9vx5ZdfxnQz4895ibfc+/kO8zCD4Kc//SlaW1vB8zwKCwuxefNm5OXlxXpZ5yxjSfpNnz4dW7ZswbPPPosf/OAHUQubSZLkk99zOBxyfi8tLS0oTd5ItItMBoQQdHV1YXBwcMJ5VVEUYTab5b5ZKhZAz1OkR3fR1haO48KaMAIAzc3NWL58OZYtW4YVK1bEPNzMQrJxBQvJno089NBD+OCDD6BWq1FUVIQtW7bE3cDgaEMIgV6vx8MPP4wdO3agrKwMRqMxLEm/UNZAtUwNBsOYY7voaDMqFxjPPaC0jSJSE1voBBvvfDEVnqDtLKEaOSpEH25rCyEEb7/9Nl5++WW8/vrruOiii0J+r0giCAJKS0vx+eefIy8vDzU1Nfj973+PqqqqWC/tfIQZzLORTz75BD/84Q+hVCrxyCOPAAA2bNgQ41VNPr/4xS9QUFCAxx9/HGq1+gxJv76+PlRXV6Ourg51dXUoKyuLqsfgb2yXSqWCRqOBwWBAYWFh1I14uFAVpNHN/ZHGW9ZveHgYAHwE+MfbUBBC0N3dLcs2hhKCp1gsFjzwwAMQRREvv/xyWOHcaPDRRx/hvvvugyiKWLp0KdauXRvrJZ2vMIN5trN9+3a89957eOedd2K9lEnH4XCMKe5NJf1oGNefpF80C1Row/ypU6eQnJwMm80GYGKGYbKIZGVpKAiC4BPuHkuA3+12o7GxERqNJuzpMk1NTVixYgVWrFiBZcuWxTwEy4hrmME827nuuutw880347bbbov1UuIeb0m/+vp6HDp0CNnZ2airq0NtbS1qamoi1oRvtVrR1NR0hhA5NQw0v+et90rnXk62B2o2m9HU1IS8vLy4ma8ZSNYvISEBp06dQklJSVhjwwgh2LZtG1599VVs2bIFs2fPjuDqGecozGDGK8H0gK5fvx4HDhzA//7v/8bFQ+5sg4b1qAHdv39/2JJ+hBD09PTgxIkTqKyslOUTAyFJkizDZjAY5AIZ6oFGukBm9Frp4ORww5rRRpIktLe3Y3BwUPbW6SBy2jcbrKyf2WzG/fffD4VCgU2bNsX1XFFGXMEM5tnK1q1bsXnzZnz++ecxVYY5l/An6edyuXDxxRdj4cKF40r6OZ1ONDU1hTWImhbIUA/UYrFAo9H4TGaJRNiQrnXKlCkoLi6O61Ck0+lEY2MjdDqdTxGS9yByk8kESZLOaGcZzffff4+77roLd999N375y1+yjSZjIjCDeTayY8cOrFmzBjt37ozr1oRzAW9Jv6+//hp6vR6zZ8+WBRWoPNxf/vIXZGRkoLy8POIDhGkhEZ3MQj0r+t9EJ4TQ1pZ4H5oNAENDQ2hrawtqraNl/ZxOJ7RaLT777DMsWrQIhw8fxltvvYU333wT1dXVk/QJGOcQzGCejRQXF8PpdMoPkPnz50/apJT/+Z//wZNPPonm5mZ88803uPjiiyfluPHCaEm/jo4OKBQKJCYm4umnn8Yll1wSdSECb8/KaDSCEOJTSBRIEUkURbS3t8Nut6OqqipuCo78IUmSLG9YVVUV0nxVQghOnjyJV155BZ988gk6OztxySWX4PLLL8eCBQtw6aWXTto5ON/vm3MEZjAZE6O5uRk8z2PFihX4zW9+c17f+Hv27MHdd9+NG264AcnJyaivrw9Z0i8cqGdFw7j+KkytVisaGxvDloybDOiEkdEFU6Fw6NAh3HXXXbjvvvtw++23o7u7G/X19aivr8eTTz45aQPE2X1zTsAMJiM0rrjiivP6xieE4KGHHsI999yDGTNmyK9LkoRjx45h586d+Oqrr/Ddd9/Jkn7UqwlGESgcvCtMaRhXFEXk5+cjOzsbOp0ubg0m7QMNd8KIJEl4/fXX8c477+DNN9+Mm+ke5/t9c5bDtGQZjFDgOA6/+c1vznid53kUFRWhqKgIS5cuBSEEAwMD2LVrFz7++GP8x3/8hyzpRwUVMjIyImrAeJ5HSkoKtFotDAYDMjMzkZeXh+HhYRw/ftxHaYcWEsVaz5aGix0OBy6++OKw+kBNJhPuuecepKWl4csvv2RFcYyowgzmeU6wY80Y48NxHHJycnDTTTfhpptuAiEEJpMJu3fvxs6dO7Fx40bYbLaIS/rRYhlvzdrk5GTk5+cDOK2009/fj7a2tphOHKHh4pycHJSVlYX12f/xj3/gnnvuwYMPPohbb711Uj1pdt+cnzCDeZ7z2WefxXoJ5yx0ZNg111yDa665BgBkSb+vvvoKq1atkuXeQpH0o+pCFosFc+fODZg/1Wg0yMnJQU5ODoAzJ44E06IRCXp7e3H8+PGgelbHQpIkvPLKK/jjH/+Id999NybTg9h9c37CDCaDMYlotVpcccUVuOKKKwD4SvqtX78ebW1tQUn6UU8tOzsbJSUlE/KuVCoVMjMzZW/Uu0Wjt7cXTqdTLiRKS0vzkaoLBTphBAAuvvjiCbfGeGM0GnH33XcjOzsbX375ZcTUmhiMYGBFP4yAbN++HatWrcLg4CBSU1Nx4YUXyqOHGNHBn6RfVlYWFixYgNraWsybNw+vvPIKEhMT8fOf/zwq4uGSJPlMZqFSddQD1el0QXvBZrMZjY2NZ8zYDIUDBw7g3nvvxaOPPoqbb745bouZ2H1zTsCqZBnxz44dO7B69WqIoohly5bh0UcfjfWSYoq3pN9nn32GDz/8ENOnT8dll12GRYsWhSTpF8oabDabz8gulUrlI1U3upCIygb29vaiqqoqLEk6SZLw3//939i+fTu2bt2K0tLScD8SgzEezGAy4htRFFFaWopPP/0U+fn5qKmpwR/+8Ie4aROIJTTn+e///u+47LLLfCT93G435s2bF5SkX6RwOp2yB2oymeR8LdXEbW9vh1qtRmlpaVhVuXq9HnfddRfy8/Px/PPPRy2/ymCMghlMRnzDJs4HZu/evcjPz5crX70JVtIvmrjdbphMJvT39+PkyZNQq9VIT0+XFYlCyTXu27cP9913H9auXYuf/exncRuCZZyTsD5MRnxz4sQJFBQUyP/Oz8/Hvn37Yrii+GH+/PkBf6bT6XDVVVfhqquuAuCR0ztw4AB27dqFxx57DJ2dnSgrK5MNaFVVVcR7MZVKJSwWC+x2O2pra5GQkCAXErW0tMDhcCApKUk2oGMJOkiShJdeegkffPAB/vSnP6G4uDiia2UwQoUZTEbc4C/awbyKiaNWq+U2FcAT6m5sbMTOnTvx/PPP+0j61dXVjdmSEgwulwsNDQ3Q6XSYN2+e7M2mpaUhLS0NgOe7pYVEHR0dsFqt0Gq1chhXq9UiISEBQ0NDuPPOO1FUVIQvvvgi6lKDDMZEYAaTETfk5+eju7tb/ndPTw+mTZsWwxWdGygUCsyePRuzZ8/GqlWrZEm/Xbt24e2338aDDz4YsqQfFU0oKSkZc3ILx3HQ6XTQ6XQoKCgAIUSezNLa2orly5cjMTERer0eS5cuxYMPPhgTY/nQQw/hgw8+gFqtRlFREbZs2RKWbB/j3ILlMBlxgyAIKC0txeeff468vDzU1NTg97//PaqqqmK9tHMab0m/r776Cvv27RtX0k+SJHR0dMBkMqGqqiqsYhxRFPHb3/4Wn332GW6++Wa0tbVhz5494DgO7777LgoLCyPxMYPik08+wQ9/+EMolUo88sgjAIANGzZM2vEZcQMr+mHEPx999BHuu+8+iKKIpUuXYu3atZN27KVLl+Kvf/0rsrKy0NDQMGnHjTe8Jf1oP6jVasW8efNQW1uLwsJCPPHEE3juuedw4YUXhhU2HxwcxJ133omKigo8++yzPiO4zGYztFptWEIH4bB9+3a89957eOedd2JyfEZMYQaTwRiLXbt2ISkpCbfffvt5bTD94XA4sHfvXrz66qv429/+hvLychQWFoYk6Uepr6/HQw89hF//+tf4p3/6p7jLV1933XW4+eabcdttt8V6KYzJh1XJMhhjsWjRInR2dsZ6GXGJRqPBxx9/DIvFgvb2dqSkpJwh6Tdr1iy5EjeQpB/gCcH+53/+J/7+97/j/fffn9SQKxCccPr69euhVCpx6623TuraGPEN8zAZDC86OzuxePFi5mH6obGxEZWVlX49wdGSfocPH0ZmZqbsgdbU1ECr1WJgYAArVqzAnDlzsH79ep8QbLywdetWbN68GZ9//jkbF3b+wkKyDMZ4MIMZGbwl/err67F//35IkgS9Xo/f/e53uPbaa+MuBAt4pBnXrFmDnTt3yuL0jPMSZjAZjPFgBjM6UG3Zvr4+XHLJJbFeTkCKi4vhdDqRkZEBwCMYsXnz5hivihEDWA6TwWDEBo7jUFBQ4KPkFI8cOXIk1ktgxDHRFZhkMM4ibrnlFtTW1qK1tRX5+fl4/fXXY70kBoMRR7CQLIMRJ3R3d+P2229Hf38/eJ7H8uXLsXr16lgvi8E4H2E5TAYjnunr60NfXx/mzp0Ls9mMefPm4c9//jMbb8ZgTD5+DSYLyTIYcUJubi7mzp0LwDOBpKKiAidOnIjxqhgMBoUZTAYjDuns7MTBgwdx6aWXxnopZwWPP/44Zs+ejQsvvBBXX301ent7Y70kxjkIC8kyGHGGxWLB5ZdfjrVr1+KGG26I9XLOCoaHh5GcnAwAePHFF9HU1MTaQRjhwEKyDEa843a78dOf/hS33norM5YTgBpLALBarXEpisA4+2EeJoMRJxBCsGTJEqSnp+OFF16I9XLOOtauXYu33noLKSkp+OKLL5hSDyMcWJUsgxHP1NfX47LLLsMFF1wgT/54+umncc0118R4ZfFBMKLpAPDMM8/A4XBg3bp1k7k8xrkFM5gMBmNsHA4HFi1aBKfTCUEQcOONN551hqerqwvXXnstkzdkhAPLYTIYjLFJSEjA3//+dxw6dAjfffcdduzYgb1798Z6WePS3t4u///777+P8vLyGK6Gca7CtGQZDIYMx3FISkoC4ClAcrvdZ0UBzaOPPorW1lbwPI/CwkJWIcuICiwky2AwfBBFEfPmzcORI0dw9913Y8OGDbFeEoMx2bCQLIPBGB+FQoHvvvsOPT09+Oabb1gukMEYgRlMBoPhl9TUVFxxxRXYsWNHrJfCYMQFzGAyGAyZwcFBGI1GAIDdbsdnn33GCmgYjBFY0Q+DwZDp6+vDkiVLIIoiJEnCTTfdhMWLF8d6WQxGXMCKfhgMBoPB8MVv0c94Hmb815MzGAwGgzEJsBwmg8FgMBhBwAwmg8FgMBhBwAwmg8FgMBhBwAwmg8FgMBhBwAwmg8FgMBhBwAwmg8FgMBhB8P8DlFCpmbuzg1gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "\n",
    "def f(x, y):\n",
    "    return np.cos(x**2 + y**2) / (1 + x**2 + y**2)\n",
    "\n",
    "xgrid = np.linspace(-3, 3, 50)\n",
    "ygrid = xgrid\n",
    "x, y = np.meshgrid(xgrid, ygrid)\n",
    "\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot_surface(x,\n",
    "                y,\n",
    "                f(x, y),\n",
    "                rstride=2, cstride=2,\n",
    "                cmap=cm.jet,\n",
    "                alpha=0.7,\n",
    "                linewidth=0.25)\n",
    "ax.set_zlim(-0.5, 1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy\n",
    "- Builds on top of NumPy\n",
    "- Common tools for:\n",
    "    - Linear Algebra\n",
    "    - Numerical Integration\n",
    "    - Interpolation\n",
    "    - Optimization\n",
    "    - Distributions and random number generator\n",
    "    - etc.\n",
    "- Useful functionality in SciPy comes in sub-packages s.a. `scipy.stats`, `scipy.optimize`, `scipy.integrate`, `scipy.linalg`, etc.\n",
    "- These sub-packages are explored below (with summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `scipy.stats`\n",
    "- Full documentation of [scipy.stats](https://docs.scipy.org/doc/scipy/reference/stats.html#statistical-functions-scipy-stats)\n",
    "- Numerous RV objects (s.a. densities, cdf, random sampling, etc.)\n",
    "- Some estimation procedures\n",
    "- Some statistical tests\n",
    "- F.ex. we can create a RV object (instance) and apply different methods on it, s.a. random variable sampling `.rvs` etc.\n",
    "- `linregress` is also a function from the sub-package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# substitutes np.random\n",
    "import numpy as np\n",
    "from scipy.stats import beta\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# creates a continuous RV object -> methods can be applied to that object (s.a. method rvs)\n",
    "beta?\n",
    "q = beta(5, 5) # alternatively, you can initialize the RV object without parameters: q = beta() and then supply 5,5 in q.rvs or another method...\n",
    "obs = q.rvs(100)\n",
    "grid = np.linspace(0.01, 0.99, 100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.hist(obs, bins = 40, density = True)\n",
    "ax.plot(grid, q.pdf(grid), 'b-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general syntax for creating these objects that represent distributions (of type rv_frozen) is `name = scipy.stats.distribution_name(shape_parameters, loc=c, scale=d)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.7022167989888299, 0.4725471180735852)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import linregress # you can also press tab-key after import\n",
    "\n",
    "# generate a relationship\n",
    "x = np.linspace(0, 100, 100)\n",
    "y = 0.4 + 0.7 * x + np.random.randn(len(x))\n",
    "\n",
    "# linregress + shift + tab-key\n",
    "slope, intercept, rval, pval, stderr = linregress(x, y)\n",
    "slope, intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `scipy.optimize`: Roots and Fixed Points\n",
    "- Full documentation of [scipy.optimize](https://docs.scipy.org/doc/scipy/reference/optimize.html)\n",
    "- A **root** or **zero** of a function is the vector (point) in the domain where the function evaluates to 0.\n",
    "- A **fixed point** of a function is a vector in the domain s.a. the function evaluated at that point maps it to itself (f(x) = x)\n",
    "- The fixed point of a function f(x) is the root of the function g(x) = x - f(x)\n",
    "- Different methods to numerically approx. the root (as discussed in Dynamic Macro) s.a. bisection, newton-raphson, etc.\n",
    "- Call f.ex. `from scipy.optimize import bisect`\n",
    "- Multivariate root-finding: `scipy.otpimize.fsolve`\n",
    "- Fixed point: `scipy.optimize.fixed_point` or from scipy.optimize import fixed_point.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define function for testing\n",
    "f = lambda x: np.sin(4 * (x - 1/4)) + x + x**20 - 1\n",
    "x = np.linspace(0, 1, 100)\n",
    "y = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "# own bisection function\n",
    "def bisect(f, a, b, tol=10e-5):\n",
    "    \"\"\"\n",
    "    Implements the bisection root finding algorithm, assuming that f is a\n",
    "    real-valued function on [a, b] satisfying f(a) < 0 < f(b).\n",
    "    \"\"\"\n",
    "    lower, upper = a, b\n",
    "\n",
    "    while upper - lower > tol:\n",
    "        middle = 0.5 * (upper + lower)\n",
    "        if f(middle) > 0:   # root is between lower and middle\n",
    "            lower, upper = lower, middle\n",
    "        else:               # root is between middle and upper\n",
    "            lower, upper = middle, upper\n",
    "\n",
    "    return 0.5 * (upper + lower)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.408294677734375"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare\n",
    "bisect(f, 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4082935042806639"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import bisect\n",
    "bisect(f, 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `scipy.optimize`: Optimization\n",
    "- **Minimization is closely related to root-finding:** For smooth functions, interior optima correspond to roots of the first derivative.\n",
    "- `fminbound` for constrained **univariat** optimization\n",
    "- Several functions for **multivariate** optimization (see [documentation](https://docs.scipy.org/doc/scipy/reference/optimize.html))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# f.ex.\n",
    "from scipy.optimize import fminbound\n",
    "fminbound(lambda x: x**2, -1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `scipy.integrate`\n",
    "- Full documentation of [scipy.integrate](https://docs.scipy.org/doc/scipy/reference/integrate.html)\n",
    "- Most numerical integration methods work by computing the integral of an approximating polynomial.\n",
    "- For univariate functions use: `from scipy.integrate import quad` (or fixed_quad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `scipy.linalg`\n",
    "- Full documentation of [scipy.linalg](https://docs.scipy.org/doc/scipy/reference/linalg.html)\n",
    "- More powerful than the equally named library of NumPy\n",
    "- For solving systems of linear equations, eigenvalue decompositions, matrix functions, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2., -2.,  9.])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for system of linear equations\n",
    "a = np.array([[3, 2, 0], [1, -1, 0], [0, 5, 1]])\n",
    "b = np.array([2, 4, -1])\n",
    "from scipy import linalg\n",
    "x = linalg.solve(a, b)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numba\n",
    "- Vecorization has its limit\n",
    "- Numba works with the concept of **Just in time compilation** (JIT) which is more memory efficient than vectorization\n",
    "- Numba will be a key part of our lectures — especially those lectures involving dynamic programming\n",
    "- Numba is basically a JIT compiler that f.ex. infers the type of a function argument\n",
    "- (Create a jit-compiled version of a function with `numba.jit(function_name)`)\n",
    "- But usually it is done with the **Decorator Notation** `@jit` in the function definition (still, jit needs to be imported from numba first)\n",
    "- Don´t blanket your code with @jit statements!\n",
    "- **Take away:** \n",
    "    - JIT infers type\n",
    "    - JIT implementation is very easy by putting `@njit` in front of a function definition\n",
    "    - JIT implementation is also possible for **class** definitions (there you have to define the instance data type first)\n",
    "    - Careful with global variables in \"jit-ed\" functions: does not overwrite global variable after you changed that very variable!\n",
    "    - There is also a `@vectorize` decorator in numba to create ufuns (vectorized functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOC: Elapsed: 0:00:26.63\n",
      "26.63985514640808\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import quantecon as qe\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "α = 4\n",
    "\n",
    "def qm(x0, n):\n",
    "    x = np.empty(n+1)\n",
    "    x[0] = x0\n",
    "    for t in range(n):\n",
    "      x[t+1] = α * x[t] * (1 - x[t])\n",
    "    return x\n",
    "\n",
    "x = qm(0.1, 250)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, 'b-', lw=2, alpha=0.8)\n",
    "ax.set_xlabel('$t$', fontsize=12)\n",
    "ax.set_ylabel('$x_{t}$', fontsize = 12)\n",
    "plt.show()\n",
    "\n",
    "from numba import jit\n",
    "qm_numba = jit(qm)\n",
    "\n",
    "# compare runtimes\n",
    "n = 10_000_000\n",
    "qe.tic()\n",
    "qm(0.1, n)\n",
    "time1 = qe.toc()\n",
    "print(time1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TOC: Elapsed: 0:00:0.23\n",
      "0.23427557945251465\n"
     ]
    }
   ],
   "source": [
    "qe.tic()\n",
    "qm_numba(0.1, n)\n",
    "time2 = qe.toc()\n",
    "print(time2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Decorator Notation\n",
    "- How to make a function \"jit compilable\"\n",
    "- Use `@jit` in the function definition\n",
    "- If we want to control whether or not effective compilation is achievable we use either `@jit(nopython=True)` or, equivalently, `@njit` instead of `@jit`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import njit\n",
    "\n",
    "@njit\n",
    "def qm(x0, n):\n",
    "    x = np.empty(n+1)\n",
    "    x[0] = x0\n",
    "    for t in range(n):\n",
    "        x[t+1] = α * x[t] * (1 - x[t])\n",
    "    return x\n",
    "\n",
    "# equivalent to jit(qm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compiling Classes\n",
    "- Use `@jitclass` from numba\n",
    "- `from numba import jitclass, float64`, then define the type of the instance data (f.ex. `solow_data = []` as list), and as a last step put `@jitclass(solow_data)` before the class definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import jitclass, float64\n",
    "\n",
    "# f.ex. from our Solow growth model implementation\n",
    "solow_data = [\n",
    "    ('n', float64),\n",
    "    ('s', float64),\n",
    "    ('δ', float64),\n",
    "    ('α', float64),\n",
    "    ('z', float64),\n",
    "    ('k', float64)\n",
    "]\n",
    "\n",
    "@jitclass(solow_data)\n",
    "# here follows a regular class definition..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hint:** you can also learn about Markov-chains in later chapters (interesting!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parallelization\n",
    "- Speed gains...\n",
    "- Implementable again through the `numba` package -> flags in function decorators and other minor adjustments (see below)\n",
    "- Multiprocessing vs. Multithreaing (one shared memory space)\n",
    "- We mostly use multithreading\n",
    "- Use f.ex. `@vectorize('float64(float64, float64)', target='parallel')` in order to vectorize the function `f(x,y)` where we specify in the bracket after @vectorize that dependent and both independent variables are floats and set `target = 'parallel'`\n",
    "- Or do: add the `parallel=True` flag in the `@njit decorator` and change range to `prange` (in the loop) within the function\n",
    "- **Careful** in nested loops -> don´t use prange if the inner loop depends on the outer loop!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pandas\n",
    "- Python´s dplyr\n",
    "- Defines fundamental **structures** for working with data and endows them with **methods** s.a.\n",
    "    - reading in data\n",
    "    - adjusting indices\n",
    "    - working with dates and time series\n",
    "    - sorting, grouping, re-ordering and general data munging [1]\n",
    "    - dealing with missing values, etc., etc.\n",
    "- More sophisticated statistical functionality is left to other packages, such as `statsmodels` and `scikit-learn`, which are built on top of pandas.\n",
    "- Two important data types: `Series` (think of 1 column; buit on top of np.arrays -> directly apply np.functions to Series...) and `DataFrames`\n",
    "- One of the nice things about pandas DataFrame and Series objects is that they have methods for plotting and visualization that work through **Matplotlib**:\n",
    "    - `ax = df['population'].plot(kind = 'bar')` followed by `plt.show()` (compare with Matplotlib section - where we first initialized the plot and then ax.plot(data, specification, etc.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import requests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Series\n",
    "- pd.Series are more flexible and provide even additional functionality than np.arrays, f.ex.:\n",
    "    - `.describe()`\n",
    "    - or additional possibilities for indexing via `.index = ['name1', 'name2', etc.]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0    0.082116\n",
       "1    2.242805\n",
       "2    0.843182\n",
       "3    0.173679\n",
       "Name: daily returns, dtype: float64"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = pd.Series(data = np.random.randn(4), name = 'daily returns')\n",
    "print(type(s))\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08211642028657887"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you can directly apply np.functions to series\n",
    "np.min(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    4.000000\n",
       "mean     0.835445\n",
       "std      0.997691\n",
       "min      0.082116\n",
       "25%      0.150788\n",
       "50%      0.508430\n",
       "75%      1.193087\n",
       "max      2.242805\n",
       "Name: daily returns, dtype: float64"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pd.Series provide additional methods (flexibility) compared to np.arrays...\n",
    "s.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AMAZ    0.082116\n",
      "AAPL    2.242805\n",
      "UBS     0.843182\n",
      "MSF     0.173679\n",
      "Name: daily returns, dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.17367861690914332"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set index of the series\n",
    "s.index = ['AMAZ', 'AAPL', 'UBS', 'MSF']\n",
    "print(s)\n",
    "s['MSF']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### DataFrames\n",
    "- very intuitive\n",
    "- `pd.read_csv` read a .csv file\n",
    "- different possibilities to index:\n",
    "    - `.iloc` indexing both rows and cols using integers\n",
    "    - `.loc` indexing both rows and cols using mixture of integers and labels\n",
    "- `df.set_index('column_name')`\n",
    "- `df.columns = 'name1', 'name2'` change col names\n",
    "- construct new column (out of exisitng ones)\n",
    "- `df.sort_values()`\n",
    "- `df.groupby()` similar to dplyr group_by!\n",
    "- etc.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>country isocode</th>\n",
       "      <th>year</th>\n",
       "      <th>POP</th>\n",
       "      <th>XRAT</th>\n",
       "      <th>tcgdp</th>\n",
       "      <th>cc</th>\n",
       "      <th>cg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Argentina</td>\n",
       "      <td>ARG</td>\n",
       "      <td>2000</td>\n",
       "      <td>37335.653</td>\n",
       "      <td>0.999500</td>\n",
       "      <td>2.950722e+05</td>\n",
       "      <td>75.716805</td>\n",
       "      <td>5.578804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Australia</td>\n",
       "      <td>AUS</td>\n",
       "      <td>2000</td>\n",
       "      <td>19053.186</td>\n",
       "      <td>1.724830</td>\n",
       "      <td>5.418047e+05</td>\n",
       "      <td>67.759026</td>\n",
       "      <td>6.720098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>India</td>\n",
       "      <td>IND</td>\n",
       "      <td>2000</td>\n",
       "      <td>1006300.297</td>\n",
       "      <td>44.941600</td>\n",
       "      <td>1.728144e+06</td>\n",
       "      <td>64.575551</td>\n",
       "      <td>14.072206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Israel</td>\n",
       "      <td>ISR</td>\n",
       "      <td>2000</td>\n",
       "      <td>6114.570</td>\n",
       "      <td>4.077330</td>\n",
       "      <td>1.292539e+05</td>\n",
       "      <td>64.436451</td>\n",
       "      <td>10.266688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Malawi</td>\n",
       "      <td>MWI</td>\n",
       "      <td>2000</td>\n",
       "      <td>11801.505</td>\n",
       "      <td>59.543808</td>\n",
       "      <td>5.026222e+03</td>\n",
       "      <td>74.707624</td>\n",
       "      <td>11.658954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>South Africa</td>\n",
       "      <td>ZAF</td>\n",
       "      <td>2000</td>\n",
       "      <td>45064.098</td>\n",
       "      <td>6.939830</td>\n",
       "      <td>2.272424e+05</td>\n",
       "      <td>72.718710</td>\n",
       "      <td>5.726546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>United States</td>\n",
       "      <td>USA</td>\n",
       "      <td>2000</td>\n",
       "      <td>282171.957</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>9.898700e+06</td>\n",
       "      <td>72.347054</td>\n",
       "      <td>6.032454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Uruguay</td>\n",
       "      <td>URY</td>\n",
       "      <td>2000</td>\n",
       "      <td>3219.793</td>\n",
       "      <td>12.099592</td>\n",
       "      <td>2.525596e+04</td>\n",
       "      <td>78.978740</td>\n",
       "      <td>5.108068</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         country country isocode  year          POP       XRAT         tcgdp  \\\n",
       "0      Argentina             ARG  2000    37335.653   0.999500  2.950722e+05   \n",
       "1      Australia             AUS  2000    19053.186   1.724830  5.418047e+05   \n",
       "2          India             IND  2000  1006300.297  44.941600  1.728144e+06   \n",
       "3         Israel             ISR  2000     6114.570   4.077330  1.292539e+05   \n",
       "4         Malawi             MWI  2000    11801.505  59.543808  5.026222e+03   \n",
       "5   South Africa             ZAF  2000    45064.098   6.939830  2.272424e+05   \n",
       "6  United States             USA  2000   282171.957   1.000000  9.898700e+06   \n",
       "7        Uruguay             URY  2000     3219.793  12.099592  2.525596e+04   \n",
       "\n",
       "          cc         cg  \n",
       "0  75.716805   5.578804  \n",
       "1  67.759026   6.720098  \n",
       "2  64.575551  14.072206  \n",
       "3  64.436451  10.266688  \n",
       "4  74.707624  11.658954  \n",
       "5  72.718710   5.726546  \n",
       "6  72.347054   6.032454  \n",
       "7  78.978740   5.108068  "
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('test_pwt.csv')\n",
    "print(type(df))\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>country isocode</th>\n",
       "      <th>year</th>\n",
       "      <th>POP</th>\n",
       "      <th>XRAT</th>\n",
       "      <th>tcgdp</th>\n",
       "      <th>cc</th>\n",
       "      <th>cg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>India</td>\n",
       "      <td>IND</td>\n",
       "      <td>2000</td>\n",
       "      <td>1006300.297</td>\n",
       "      <td>44.941600</td>\n",
       "      <td>1.728144e+06</td>\n",
       "      <td>64.575551</td>\n",
       "      <td>14.072206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Israel</td>\n",
       "      <td>ISR</td>\n",
       "      <td>2000</td>\n",
       "      <td>6114.570</td>\n",
       "      <td>4.077330</td>\n",
       "      <td>1.292539e+05</td>\n",
       "      <td>64.436451</td>\n",
       "      <td>10.266688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Malawi</td>\n",
       "      <td>MWI</td>\n",
       "      <td>2000</td>\n",
       "      <td>11801.505</td>\n",
       "      <td>59.543808</td>\n",
       "      <td>5.026222e+03</td>\n",
       "      <td>74.707624</td>\n",
       "      <td>11.658954</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  country country isocode  year          POP       XRAT         tcgdp  \\\n",
       "2   India             IND  2000  1006300.297  44.941600  1.728144e+06   \n",
       "3  Israel             ISR  2000     6114.570   4.077330  1.292539e+05   \n",
       "4  Malawi             MWI  2000    11801.505  59.543808  5.026222e+03   \n",
       "\n",
       "          cc         cg  \n",
       "2  64.575551  14.072206  \n",
       "3  64.436451  10.266688  \n",
       "4  74.707624  11.658954  "
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select rows\n",
    "df[2:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>year</th>\n",
       "      <th>POP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Argentina</td>\n",
       "      <td>2000</td>\n",
       "      <td>37335.653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Australia</td>\n",
       "      <td>2000</td>\n",
       "      <td>19053.186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>India</td>\n",
       "      <td>2000</td>\n",
       "      <td>1006300.297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Israel</td>\n",
       "      <td>2000</td>\n",
       "      <td>6114.570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Malawi</td>\n",
       "      <td>2000</td>\n",
       "      <td>11801.505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>South Africa</td>\n",
       "      <td>2000</td>\n",
       "      <td>45064.098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>United States</td>\n",
       "      <td>2000</td>\n",
       "      <td>282171.957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Uruguay</td>\n",
       "      <td>2000</td>\n",
       "      <td>3219.793</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         country  year          POP\n",
       "0      Argentina  2000    37335.653\n",
       "1      Australia  2000    19053.186\n",
       "2          India  2000  1006300.297\n",
       "3         Israel  2000     6114.570\n",
       "4         Malawi  2000    11801.505\n",
       "5   South Africa  2000    45064.098\n",
       "6  United States  2000   282171.957\n",
       "7        Uruguay  2000     3219.793"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select cols by name\n",
    "df[['country', 'year', 'POP']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>country isocode</th>\n",
       "      <th>year</th>\n",
       "      <th>POP</th>\n",
       "      <th>XRAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Argentina</td>\n",
       "      <td>ARG</td>\n",
       "      <td>2000</td>\n",
       "      <td>37335.653</td>\n",
       "      <td>0.99950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Australia</td>\n",
       "      <td>AUS</td>\n",
       "      <td>2000</td>\n",
       "      <td>19053.186</td>\n",
       "      <td>1.72483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>India</td>\n",
       "      <td>IND</td>\n",
       "      <td>2000</td>\n",
       "      <td>1006300.297</td>\n",
       "      <td>44.94160</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     country country isocode  year          POP      XRAT\n",
       "0  Argentina             ARG  2000    37335.653   0.99950\n",
       "1  Australia             AUS  2000    19053.186   1.72483\n",
       "2      India             IND  2000  1006300.297  44.94160"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# index\n",
    "df.iloc[0:3, 0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>POP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Argentina</td>\n",
       "      <td>37335.653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Australia</td>\n",
       "      <td>19053.186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>India</td>\n",
       "      <td>1006300.297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Israel</td>\n",
       "      <td>6114.570</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     country          POP\n",
       "0  Argentina    37335.653\n",
       "1  Australia    19053.186\n",
       "2      India  1006300.297\n",
       "3     Israel     6114.570"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# index\n",
    "df.loc[0:3, ['country', 'POP']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>POP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Argentina</td>\n",
       "      <td>37335.653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Australia</td>\n",
       "      <td>19053.186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>India</td>\n",
       "      <td>1006300.297</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     country          POP\n",
       "0  Argentina    37335.653\n",
       "1  Australia    19053.186\n",
       "2      India  1006300.297"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# df.index...\n",
    "df.loc[df.index[0:3], ['country', 'POP']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RangeIndex(start=0, stop=8, step=1)"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>population</th>\n",
       "      <th>total GDP</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Argentina</th>\n",
       "      <td>37335.653</td>\n",
       "      <td>2.950722e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Australia</th>\n",
       "      <td>19053.186</td>\n",
       "      <td>5.418047e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>India</th>\n",
       "      <td>1006300.297</td>\n",
       "      <td>1.728144e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Israel</th>\n",
       "      <td>6114.570</td>\n",
       "      <td>1.292539e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Malawi</th>\n",
       "      <td>11801.505</td>\n",
       "      <td>5.026222e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Africa</th>\n",
       "      <td>45064.098</td>\n",
       "      <td>2.272424e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United States</th>\n",
       "      <td>282171.957</td>\n",
       "      <td>9.898700e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uruguay</th>\n",
       "      <td>3219.793</td>\n",
       "      <td>2.525596e+04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                population     total GDP\n",
       "country                                 \n",
       "Argentina        37335.653  2.950722e+05\n",
       "Australia        19053.186  5.418047e+05\n",
       "India          1006300.297  1.728144e+06\n",
       "Israel            6114.570  1.292539e+05\n",
       "Malawi           11801.505  5.026222e+03\n",
       "South Africa     45064.098  2.272424e+05\n",
       "United States   282171.957  9.898700e+06\n",
       "Uruguay           3219.793  2.525596e+04"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df[['country', 'POP', 'tcgdp']]\n",
    "df = df.set_index('country')\n",
    "df.columns = 'population', 'total GDP'\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = df.sort_values(by = 'population')\n",
    "ax = df['population'].plot(kind = 'bar')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Online Data Sources\n",
    "- Accessing data with `requests` package\n",
    "- Or using `pandas_datareader`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `requests`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VALUE</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DATE</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1948-01-01</th>\n",
       "      <td>3.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1948-02-01</th>\n",
       "      <td>3.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1948-03-01</th>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1948-04-01</th>\n",
       "      <td>3.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1948-05-01</th>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-11-01</th>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-01</th>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-01-01</th>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-02-01</th>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-01</th>\n",
       "      <td>4.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>867 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            VALUE\n",
       "DATE             \n",
       "1948-01-01    3.4\n",
       "1948-02-01    3.8\n",
       "1948-03-01    4.0\n",
       "1948-04-01    3.9\n",
       "1948-05-01    3.5\n",
       "...           ...\n",
       "2019-11-01    3.5\n",
       "2019-12-01    3.5\n",
       "2020-01-01    3.6\n",
       "2020-02-01    3.5\n",
       "2020-03-01    4.4\n",
       "\n",
       "[867 rows x 1 columns]"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = 'http://research.stlouisfed.org/fred2/series/UNRATE/downloaddata/UNRATE.csv'\n",
    "data = pd.read_csv(url, index_col = 0, parse_dates = True)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = data['2006':'2020'].plot(legend = False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `pandas_datareader`\n",
    "- [Documentation](https://pandas-datareader.readthedocs.io/en/latest/index.html)\n",
    "- Access FRED, OECD, Eurostat, Worldbank, etc.\n",
    "- F.ex. start with `from pandas_datareader import wb` or `import data`\n",
    "- `faodata` is a package that let´s you access the fao database"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercise 1\n",
    "import datetime as dt\n",
    "from pandas_datareader import data\n",
    "\n",
    "# ticker dictionary\n",
    "ticker_list = {'INTC': 'Intel',\n",
    "               'MSFT': 'Microsoft',\n",
    "               'IBM': 'IBM',\n",
    "               'BHP': 'BHP',\n",
    "               'TM': 'Toyota',\n",
    "               'AAPL': 'Apple',\n",
    "               'AMZN': 'Amazon',\n",
    "               'BA': 'Boeing',\n",
    "               'QCOM': 'Qualcomm',\n",
    "               'KO': 'Coca-Cola',\n",
    "               'GOOG': 'Google',\n",
    "               'SNE': 'Sony',\n",
    "               'PTR': 'PetroChina'}\n",
    "\n",
    "# define function\n",
    "def read_data(ticker_list,\n",
    "             start = dt.datetime(2019, 1, 1),\n",
    "             end = dt.datetime(2020, 3, 1)):\n",
    "    \"\"\"\n",
    "    Reads in closing prices from Yahoo for the timerange defined\n",
    "    \"\"\"\n",
    "    ticker = pd.DataFrame()\n",
    "    \n",
    "    for tick in ticker_list:\n",
    "        prices = data.DataReader(tick, 'yahoo', start, end)\n",
    "        closing_prices = prices['Close']\n",
    "        ticker[tick] = closing_prices\n",
    "        \n",
    "    return ticker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [],
   "source": [
    "# apply function\n",
    "df = read_data(ticker_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate percentage price change\n",
    "first_obs = df.iloc[0] # series\n",
    "last_obs = df.iloc[-1] # series\n",
    "change = (last_obs - first_obs) / first_obs * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "INTC    17.926929\n",
       "MSFT    60.215576\n",
       "IBM     12.967620\n",
       "BHP     -9.506893\n",
       "TM      12.444102\n",
       "AAPL    73.100297\n",
       "AMZN    22.390571\n",
       "BA     -15.039688\n",
       "QCOM    36.411152\n",
       "KO      13.978268\n",
       "GOOG    28.061384\n",
       "SNE     27.668307\n",
       "PTR    -35.872597\n",
       "dtype: float64"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot as bargraph\n",
    "change = change.sort_values()\n",
    "ax = change.plot(kind = 'bar')\n",
    "ax.set_xlabel('stock')\n",
    "ax.set_ylabel('pct change')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exercise 2\n",
    "indices_list = {'^GSPC': 'S&P 500',\n",
    "               '^IXIC': 'NASDAQ',\n",
    "               '^DJI': 'Dow Jones',\n",
    "               '^N225': 'Nikkei'}\n",
    "    \n",
    "indices_data = read_data(indices_list,\n",
    "                         start = dt.datetime(1990, 1, 2),\n",
    "                         end = dt.datetime(2020, 1, 31))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [],
   "source": [
    "# what does the items method do:\n",
    "# for sym, name in indices_list.items():\n",
    "    # print(sym)\n",
    "    # print(name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Here** we use the `groupby` method!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S&amp;P 500</th>\n",
       "      <th>NASDAQ</th>\n",
       "      <th>Dow Jones</th>\n",
       "      <th>Nikkei</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>31.000000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>31.000000</td>\n",
       "      <td>31.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.083899</td>\n",
       "      <td>0.131635</td>\n",
       "      <td>0.083763</td>\n",
       "      <td>0.005233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.164331</td>\n",
       "      <td>0.271961</td>\n",
       "      <td>0.143217</td>\n",
       "      <td>0.225798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.375847</td>\n",
       "      <td>-0.401978</td>\n",
       "      <td>-0.327168</td>\n",
       "      <td>-0.396770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.010572</td>\n",
       "      <td>-0.008965</td>\n",
       "      <td>-0.011169</td>\n",
       "      <td>-0.167687</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.110019</td>\n",
       "      <td>0.139988</td>\n",
       "      <td>0.084039</td>\n",
       "      <td>0.009353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.196538</td>\n",
       "      <td>0.306769</td>\n",
       "      <td>0.214162</td>\n",
       "      <td>0.148653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.341574</td>\n",
       "      <td>0.842943</td>\n",
       "      <td>0.333111</td>\n",
       "      <td>0.524246</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         S&P 500     NASDAQ  Dow Jones     Nikkei\n",
       "count  31.000000  31.000000  31.000000  31.000000\n",
       "mean    0.083899   0.131635   0.083763   0.005233\n",
       "std     0.164331   0.271961   0.143217   0.225798\n",
       "min    -0.375847  -0.401978  -0.327168  -0.396770\n",
       "25%    -0.010572  -0.008965  -0.011169  -0.167687\n",
       "50%     0.110019   0.139988   0.084039   0.009353\n",
       "75%     0.196538   0.306769   0.214162   0.148653\n",
       "max     0.341574   0.842943   0.333111   0.524246"
      ]
     },
     "execution_count": 304,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yearly_returns = pd.DataFrame()\n",
    "\n",
    "# we iterate over sym = over cols!\n",
    "for sym, name in indices_list.items():\n",
    "    # indices_data.index -> get index column which is a date -> .year group by year...\n",
    "    p1 = indices_data.groupby(indices_data.index.year)[sym].first()\n",
    "    p2 = indices_data.groupby(indices_data.index.year)[sym].last()\n",
    "    returns = (p2 - p1) / p1\n",
    "    yearly_returns[name] = returns\n",
    "    \n",
    "yearly_returns.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "fig, axes = plt.subplots(2, 2, figsize=(10, 6))\n",
    "\n",
    "for iter_, ax in enumerate(axes.flatten()):            # Flatten 2-D array (of axes) to 1-D array\n",
    "    index_name = yearly_returns.columns[iter_]         # Get index name per iteration\n",
    "    ax.plot(yearly_returns[index_name])                # Plot pct change of yearly returns per index\n",
    "    ax.set_ylabel(\"percent change\", fontsize = 12)\n",
    "    ax.set_title(index_name)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII\n",
    "# Advanced Python Programming\n",
    "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# maybe start with a short recap..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**General Remark:** Be aware when methods are applicable (which implies that we can use the . notation) or when we have to make a function call. It´s quite intuitive: f.ex. when you have a numpy array or a pandas dataframe then there are many methods applicable to such an opbject. Methods can often also be called as functions..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}