MachLePublic/PW-4/pw4-linear-regression-stud.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "18bdba27",
   "metadata": {},
   "source": [
    "# PW4 - Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3629bfdf",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "id": "d6eb2aab",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e69e5d68",
   "metadata": {},
   "source": [
    "## Load data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba14bf9f",
   "metadata": {},
   "source": [
    "Define the path to the file containing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "id": "5f3f924f",
   "metadata": {},
   "outputs": [],
   "source": [
    "datafile = \"lausanne-appart.csv\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adfab574",
   "metadata": {},
   "source": [
    "Read the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "id": "5108e239",
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = pd.read_csv(datafile)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a97d4cc",
   "metadata": {},
   "source": [
    "Display first rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "id": "34222aff",
   "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>living_area</th>\n",
       "      <th>nb_rooms</th>\n",
       "      <th>rent_price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>69</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>3.5</td>\n",
       "      <td>2945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21</td>\n",
       "      <td>1.5</td>\n",
       "      <td>685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>20</td>\n",
       "      <td>1.0</td>\n",
       "      <td>720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>33</td>\n",
       "      <td>1.5</td>\n",
       "      <td>830</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   living_area  nb_rooms  rent_price\n",
       "0           69       3.0        1810\n",
       "1           95       3.5        2945\n",
       "2           21       1.5         685\n",
       "3           20       1.0         720\n",
       "4           33       1.5         830"
      ]
     },
     "execution_count": 432,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ec4b8eb",
   "metadata": {},
   "source": [
    "## Exercise 1 - Visualize the data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbf6b9cf",
   "metadata": {},
   "source": [
    "a) Plot a histogram to visualize the distribution of the renting price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "id": "ad07d4cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "\n",
    "plt.hist(dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Rent price\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "602770ae",
   "metadata": {},
   "source": [
    "b) Plot a histogram to visualize the distribution of the living area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "id": "ac0c9f07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vL5ckxcbGSpIKCgpUW1sb8De9+vbtq+TkZOXn59e7j+rqavl8voAbAABAyERPXV2d7r33Xv3kJz/RgAEDJEnFxcVq27atYmJiAraNj49XcXFxvfuZP3++PB6P/5aUlNTSowMAgDAQMtGTlZWlffv2afXq1c3aT3Z2tsrLy/23o0ePBmlCAAAQzhy9pue06dOn680339TWrVt1wQUX+JcnJCSopqZGZWVlAWd7SkpKlJCQUO++oqKiFBUV1dIjAwCAMOPomR5jjKZPn65169Zpy5YtZ7zlfejQoYqMjFROTo5/WWFhoY4cOSKv19va4wIAgDDm6JmerKwsrVq1Sq+99po6derkv07H4/Goffv28ng8mjZtmmbNmqXY2Fi53W7NmDFDXq+Xd24BAIBGcTR6nn32WUnS1VdfHbB8xYoVuuWWWyRJixYtUps2bZSRkaHq6mqlp6frmWeeaeVJAQBAuHM0ek7/GYsf0q5dOy1ZskRLlixphYkAAMC5KmTevQUAANCSiB4AAGAFogcAAFiB6AEAAFYgegAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoAAIAViB4AAGAFogcAAFiB6AEAAFYgegAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoAAIAViB4AAGAFogcAAFiB6AEAAFYgegAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoAAIAViB4AAGAFogcAAFiB6AEAAFYgegAAgBUinB4AAJoj5cH1To/QaIcXjHN6BMBKnOkBAABWIHoAAIAViB4AAGAFogcAAFiB6AEAAFYgegAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoAAIAViB4AAGAFogcAAFiB6AEAAFYgegAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoAAIAViB4AAGAFR6Nn69atGj9+vLp37y6Xy6VXX301YL0xRo888ogSExPVvn17paWl6dNPP3VmWAAAENYcjZ6TJ09q8ODBWrJkSb3rn3jiCT311FNaunSptm/fro4dOyo9PV1VVVWtPCkAAAh3EU5+8bFjx2rs2LH1rjPGaPHixXr44Yc1YcIESdKLL76o+Ph4vfrqq7rppptac1QAABDmQvaanqKiIhUXFystLc2/zOPxaPjw4crPzz/r46qrq+Xz+QJuAAAAIRs9xcXFkqT4+PiA5fHx8f519Zk/f748Ho//lpSU1KJzAgCA8BCy0dNU2dnZKi8v99+OHj3q9EgAACAEhGz0JCQkSJJKSkoClpeUlPjX1ScqKkputzvgBgAAELLRk5qaqoSEBOXk5PiX+Xw+bd++XV6v18HJAABAOHL03VuVlZU6ePCg/35RUZF2796t2NhYJScn695779Xjjz+u3r17KzU1VXPmzFH37t01ceJE54YGAABhydHo2blzp6655hr//VmzZkmSpkyZopUrV+p3v/udTp48qdtvv11lZWX66U9/qo0bN6pdu3ZOjQwAAMKUyxhjnB6iJfl8Pnk8HpWXlwf9+p6UB9cHdX8A7HB4wTinRwBCXkv8/x2y1/QAAAAEE9EDAACsQPQAAAArED0AAMAKRA8AALAC0QMAAKxA9AAAACsQPQAAwApEDwAAsALRAwAArED0AAAAKxA9AADACkQPAACwAtEDAACsQPQAAAArED0AAMAKRA8AALAC0QMAAKxA9AAAACsQPQAAwApEDwAAsALRAwAArED0AAAAKxA9AADACkQPAACwQoTTAwCAbVIeXO/0CI12eME4p0cAmo0zPQAAwApEDwAAsALRAwAArED0AAAAKxA9AADACkQPAACwAtEDAACsQPQAAAArED0AAMAKRA8AALAC0QMAAKxA9AAAACsQPQAAwApEDwAAsALRAwAArBDh9AAAgNCX8uB6p0dotMMLxjk9AkIMZ3oAAIAViB4AAGAFogcAAFiB6AEAAFYgegAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoAAIAViB4AAGAFogcAAFghwukBAABoCSkPrnd6hEY7vGCc0yOc0zjTAwAArED0AAAAKxA9AADACkQPAACwAtEDAACsQPQAAAArED0AAMAKfE4PAAAhgs8Walmc6QEAAFYgegAAgBWIHgAAYIWwiJ4lS5YoJSVF7dq10/Dhw/Xvf//b6ZEAAECYCfnoeeWVVzRr1izNnTtXH374oQYPHqz09HSVlpY6PRoAAAgjIR89Cxcu1G233aapU6eqf//+Wrp0qTp06KDly5c7PRoAAAgjIf2W9ZqaGhUUFCg7O9u/rE2bNkpLS1N+fn69j6murlZ1dbX/fnl5uSTJ5/MFfb666q+Dvk8AAMJJS/z/+t39GmOCts+Qjp4vv/xSp06dUnx8fMDy+Ph4HThwoN7HzJ8/X/PmzTtjeVJSUovMCACAzTyLW3b/FRUV8ng8QdlXSEdPU2RnZ2vWrFn++3V1dTpx4oTi4uLkcrkcnMxOPp9PSUlJOnr0qNxut9PjWI1jEVo4HqGDYxE6vnssOnXqpIqKCnXv3j1o+w/p6OnSpYvOO+88lZSUBCwvKSlRQkJCvY+JiopSVFRUwLKYmJiWGhEN5Ha7eTEJERyL0MLxCB0ci9Bx+lgE6wzPaSF9IXPbtm01dOhQ5eTk+JfV1dUpJydHXq/XwckAAEC4CekzPZI0a9YsTZkyRZdddpkuv/xyLV68WCdPntTUqVOdHg0AAISRkI+eG2+8UV988YUeeeQRFRcX65JLLtHGjRvPuLgZoSkqKkpz584941eOaH0ci9DC8QgdHIvQ0dLHwmWC+V4wAACAEBXS1/QAAAAEC9EDAACsQPQAAAArED0AAMAKRA+a7dFHH5XL5Qq49e3b17++qqpKWVlZiouLU3R0tDIyMs74wEk03datWzV+/Hh1795dLpdLr776asB6Y4weeeQRJSYmqn379kpLS9Onn34asM2JEyeUmZkpt9utmJgYTZs2TZWVla34LM4NP3YsbrnlljN+VsaMGROwDcciOObPn69hw4apU6dO6tatmyZOnKjCwsKAbRry2nTkyBGNGzdOHTp0ULdu3fTAAw/o22+/bc2nEvYaciyuvvrqM3427rzzzoBtgnEsiB4ExcUXX6zjx4/7b++9955/3cyZM/XGG29ozZo1ysvL07FjxzRp0iQHpz23nDx5UoMHD9aSJUvqXf/EE0/oqaee0tKlS7V9+3Z17NhR6enpqqqq8m+TmZmp/fv3a9OmTXrzzTe1detW3X777a31FM4ZP3YsJGnMmDEBPysvv/xywHqORXDk5eUpKytL27Zt06ZNm1RbW6vRo0fr5MmT/m1+7LXp1KlTGjdunGpqavTBBx/ohRde0MqVK/XII4848ZTCVkOOhSTddtttAT8bTzzxhH9d0I6FAZpp7ty5ZvDgwfWuKysrM5GRkWbNmjX+ZZ988omRZPLz81tpQntIMuvWrfPfr6urMwkJCebJJ5/0LysrKzNRUVHm5ZdfNsYY8/HHHxtJZseOHf5t3nrrLeNyucznn3/earOfa75/LIwxZsqUKWbChAlnfQzHouWUlpYaSSYvL88Y07DXpg0bNpg2bdqY4uJi/zbPPvuscbvdprq6unWfwDnk+8fCGGN+9rOfmXvuueesjwnWseBMD4Li008/Vffu3dWzZ09lZmbqyJEjkqSCggLV1tYqLS3Nv23fvn2VnJys/Px8p8a1RlFRkYqLiwO+/x6PR8OHD/d///Pz8xUTE6PLLrvMv01aWpratGmj7du3t/rM57rc3Fx169ZNffr00V133aWvvvrKv45j0XLKy8slSbGxsZIa9tqUn5+vgQMHBnwYbnp6unw+n/bv39+K059bvn8sTnvppZfUpUsXDRgwQNnZ2fr666/964J1LEL+E5kR+oYPH66VK1eqT58+On78uObNm6errrpK+/btU3Fxsdq2bXvGH32Nj49XcXGxMwNb5PT3+PufYP7d739xcbG6desWsD4iIkKxsbEcoyAbM2aMJk2apNTUVB06dEi///3vNXbsWOXn5+u8887jWLSQuro63XvvvfrJT36iAQMGSFKDXpuKi4vr/dk5vQ6NV9+xkKRf/epX6tGjh7p37669e/dq9uzZKiws1Nq1ayUF71gQPWi2sWPH+v89aNAgDR8+XD169NA//vEPtW/f3sHJgNBy0003+f89cOBADRo0SL169VJubq5GjRrl4GTntqysLO3bty/gWkM442zH4rvXrQ0cOFCJiYkaNWqUDh06pF69egXt6/PrLQRdTEyMLrroIh08eFAJCQmqqalRWVlZwDYlJSVKSEhwZkCLnP4ef/8dKd/9/ickJKi0tDRg/bfffqsTJ05wjFpYz5491aVLFx08eFASx6IlTJ8+XW+++abeeecdXXDBBf7lDXltSkhIqPdn5/Q6NM7ZjkV9hg8fLkkBPxvBOBZED4KusrJShw4dUmJiooYOHarIyEjl5OT41xcWFurIkSPyer0OTmmH1NRUJSQkBHz/fT6ftm/f7v/+e71elZWVqaCgwL/Nli1bVFdX53/hQcv4z3/+o6+++kqJiYmSOBbBZIzR9OnTtW7dOm3ZskWpqakB6xvy2uT1evXRRx8FhOimTZvkdrvVv3//1nki54AfOxb12b17tyQF/GwE5Vg04cJrIMB9991ncnNzTVFRkXn//fdNWlqa6dKliyktLTXGGHPnnXea5ORks2XLFrNz507j9XqN1+t1eOpzR0VFhdm1a5fZtWuXkWQWLlxodu3aZT777DNjjDELFiwwMTEx5rXXXjN79+41EyZMMKmpqeabb77x72PMmDHm0ksvNdu3bzfvvfee6d27t5k8ebJTTyls/dCxqKioMPfff7/Jz883RUVFZvPmzWbIkCGmd+/epqqqyr8PjkVw3HXXXcbj8Zjc3Fxz/Phx/+3rr7/2b/Njr03ffvutGTBggBk9erTZvXu32bhxo+natavJzs524imFrR87FgcPHjSPPfaY2blzpykqKjKvvfaa6dmzpxkxYoR/H8E6FkQPmu3GG280iYmJpm3btub88883N954ozl48KB//TfffGN++9vfms6dO5sOHTqY66+/3hw/ftzBic8t77zzjpF0xm3KlCnGmP+9bX3OnDkmPj7eREVFmVGjRpnCwsKAfXz11Vdm8uTJJjo62rjdbjN16lRTUVHhwLMJbz90LL7++mszevRo07VrVxMZGWl69OhhbrvttoC34BrDsQiW+o6DJLNixQr/Ng15bTp8+LAZO3asad++venSpYu57777TG1tbSs/m/D2Y8fiyJEjZsSIESY2NtZERUWZCy+80DzwwAOmvLw8YD/BOBau/zcQAADAOY1regAAgBWIHgAAYAWiBwAAWIHoAQAAViB6AACAFYgeAABgBaIHAABYgegBAABWIHoABIXL5dKrr77a4O1TUlK0ePHiFpsHAL6P6AHQILfccosmTpx41vXHjx/X2LFjG7y/HTt26Pbbbw/CZA0zf/58nXfeeXryySdb7WsCCC1ED4CgSEhIUFRUVIO379q1qzp06NCCEwVavny5fve732n58uU/um1NTU0rTASgtRE9AILiu7/euvLKKzV79uyA9V988YUiIyO1detWSWf+esvlcun555/X9ddfrw4dOqh37956/fXXA/bx+uuvq3fv3mrXrp2uueYavfDCC3K5XCorK/vB2fLy8vTNN9/osccek8/n0wcffBCw/tFHH9Ull1yi559/XqmpqWrXrp0kqaysTLfeequ6du0qt9utkSNHas+ePf7HHTp0SBMmTFB8fLyio6M1bNgwbd68uTHfNgCtiOgBEHSZmZlavXq1vvv3jF955RV1795dV1111VkfN2/ePP3yl7/U3r17dd111ykzM1MnTpyQJBUVFemGG27QxIkTtWfPHt1xxx166KGHGjTPsmXLNHnyZEVGRmry5MlatmzZGdscPHhQ//rXv7R27Vrt3r1bkvSLX/xCpaWleuutt1RQUKAhQ4Zo1KhR/pkqKyt13XXXKScnR7t27dKYMWM0fvx4HTlypKHfKgCtKSh/Nx7AOW/KlClmwoQJZ10vyaxbt84YY0xpaamJiIgwW7du9a/3er1m9uzZ/vs9evQwixYtCnj8ww8/7L9fWVlpJJm33nrLGGPM7NmzzYABAwK+5kMPPWQkmf/+979nnau8vNy0b9/e7N692xhjzK5du0x0dLSpqKjwbzN37lwTGRlpSktL/cveffdd43a7TVVVVcD+evXqZZ577rmzfr2LL77YPP3002ddD8A5nOkBEHRdu3bV6NGj9dJLL0n631ma/Px8ZWZm/uDjBg0a5P93x44d5Xa7VVpaKkkqLCzUsGHDAra//PLLf3SWl19+Wb169dLgwYMlSZdccol69OihV155JWC7Hj16qGvXrv77e/bsUWVlpeLi4hQdHe2/FRUV6dChQ5L+d6bn/vvvV79+/RQTE6Po6Gh98sknnOkBQlSE0wMAODdlZmbq7rvv1tNPP61Vq1Zp4MCBGjhw4A8+JjIyMuC+y+VSXV1ds+ZYtmyZ9u/fr4iI//9yV1dXp+XLl2vatGn+ZR07dgx4XGVlpRITE5Wbm3vGPmNiYiRJ999/vzZt2qQ//vGPuvDCC9W+fXvdcMMNXAgNhCiiB0CLmDBhgm6//XZt3LhRq1at0s0339ys/fXp00cbNmwIWLZjx44ffMxHH32knTt3Kjc3V7Gxsf7lJ06c0NVXX60DBw6ob9++9T52yJAhKi4uVkREhFJSUurd5v3339ctt9yi66+/XtL/Qunw4cMNf1IAWhXRA6DBysvL/Rf5nhYXF6ekpKQztu3YsaMmTpyoOXPm6JNPPtHkyZOb9bXvuOMOLVy4ULNnz9a0adO0e/durVy5UtL/zgjVZ9myZbr88ss1YsSIM9YNGzZMy5YtO+vn9qSlpcnr9WrixIl64okndNFFF+nYsWNav369rr/+el122WXq3bu31q5dq/Hjx8vlcmnOnDnNPjMFoOVwTQ+ABsvNzdWll14acJs3b95Zt8/MzNSePXt01VVXKTk5uVlfOzU1Vf/85z+1du1aDRo0SM8++6z/3Vv1fT5QTU2N/v73vysjI6Pe/WVkZOjFF19UbW1tvetdLpc2bNigESNGaOrUqbrooot000036bPPPlN8fLwkaeHChercubOuvPJKjR8/Xunp6RoyZEiznieAluMy5jvvKQWAMPKHP/xBS5cu1dGjR50eBUAY4NdbAMLGM888o2HDhikuLk7vv/++nnzySU2fPt3psQCECaIHQNj49NNP9fjjj+vEiRNKTk7Wfffdp+zsbKfHAhAm+PUWAACwAhcyAwAAKxA9AADACkQPAACwAtEDAACsQPQAAAArED0AAMAKRA8AALAC0QMAAKzwf/Dp0EQ29BBXAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "\n",
    "plt.hist(dataset[\"living_area\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9a954dd",
   "metadata": {},
   "source": [
    "c) Plot a scatter plot of renting price as a function of living area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "id": "6d015af9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "\n",
    "plt.scatter(dataset[\"living_area\"], dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Rent price\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c787c4b",
   "metadata": {},
   "source": [
    "## Exercise 2 - Normal equations for linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "859bbd89",
   "metadata": {},
   "source": [
    "a) Implement the closed form solution to this problem using the following normal equation:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf1d5eda",
   "metadata": {},
   "source": [
    "<div><div style=\"display: table-cell; width: 100%;\"><center>$\\theta = (X^{T}X)^{-1}X^{T}\\vec{y}$</center></div><div style=\"display: table-cell; width: 100%;\">$(3)$</div></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3c8e4c1",
   "metadata": {},
   "source": [
    "Assuming $x$ is the living area and $y$ is the renting price. Use `numpy` for the vector operations. Plot the computed line on top of the scatter plot of exercise 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "id": "19ffbbd9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta : [240.07710727  26.33242457]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "X = dataset[\"living_area\"].to_frame()\n",
    "X.insert(0, \"x0\", 1) # add the column full of ones at the start, this represents x0\n",
    "X = np.array(X)\n",
    "\n",
    "y = np.array(dataset[\"rent_price\"])\n",
    "\n",
    "theta = np.linalg.inv(X.T @ X) @ X.T @ y \n",
    "\n",
    "print(f\"Theta : {theta}\")\n",
    "\n",
    "\n",
    "plt.scatter(dataset[\"living_area\"], dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Rent price\")\n",
    "\n",
    "y_regr = theta[0] + theta[1] * X[:,1]\n",
    "plt.plot(X[:,1], y_regr, color='red', label='Regression line')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccc5d7b9",
   "metadata": {},
   "source": [
    "b) Compute the overall cost value according to the following equation:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31a38211",
   "metadata": {},
   "source": [
    "<div><div style=\"display: table-cell; width: 100%;\"><center>$J(\\theta) = \\frac{1}{2N} \\sum_{n=1}^{N} (h_{\\theta}(\\mathbf{x}_{n}) - y_{n})^{2}$</center></div><div style=\"display: table-cell; width: 100%;\">$(2)$</div></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "id": "db65a2fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Overall cost : 138034.95779787414\n"
     ]
    }
   ],
   "source": [
    "# Your code here\n",
    "def cost_J(y_pred, y):\n",
    "    return (1/(2*len(y))) * np.sum((y_pred - y)**2)\n",
    "\n",
    "y_pred = X @ theta\n",
    "# print(y_pred)\n",
    "# print(X)\n",
    "closed_form_cost = cost_J(y_pred, y)\n",
    "print(f\" Overall cost : {closed_form_cost}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38fed9aa",
   "metadata": {},
   "source": [
    "## Exercise 3 - Gradient descent for linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d946ac48",
   "metadata": {},
   "source": [
    "Implement the _full batch_ gradient descent algorithm for the previous problem. As seen in the\n",
    "theory, the update rules are:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d1618d6",
   "metadata": {},
   "source": [
    "<div><div style=\"display: table-cell; width: 100%;\"><center>$\\theta_{0} \\leftarrow \\theta_{0} - \\alpha \\frac{1}{N} \\sum_{n=1}^{N} (h_{\\theta}(\\mathbf{x}_{n}) - y_{n})$</center></div><div style=\"display: table-cell; width: 100%;\">$(6)$</div></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c0049d3",
   "metadata": {},
   "source": [
    "<div><div style=\"display: table-cell; width: 100%;\"><center>$\\theta_{1} \\leftarrow \\theta_{1} - \\alpha \\frac{1}{N} \\sum_{n=1}^{N} (h_{\\theta}(\\mathbf{x}_{n}) - y_{n}) x_{n,1}$</center></div><div style=\"display: table-cell; width: 100%;\">$(7)$</div></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e0f8c42",
   "metadata": {},
   "source": [
    "**Remark** You need to iterate several times over the training set. If you have problems of convergence, you need to use a smaller value of $\\alpha$. Values such as $0.000001$ are common."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "id": "9ca79a3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta = [240.07710713  26.33242457]\n",
      "Cost = 138034.95779787414\n"
     ]
    },
    {
     "data": {
      "image/png": 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2lToQLDg4WOHh4ZoyZUqp3bnffvutGjVqpNWrV+u6666ryZcAAABUh76m6du3r0pKSnTs2DENHjy4zD4DBw5UcXGx9u/f7znwbe/evZJU6sBBAABQM2rVnpFTp05p3759ks6Fj5deeknDhg1Ts2bN1LZtW91xxx3auHGjpk2bpr59++r48eNau3atevXqpREjRsjtduvqq69WcHCwpk+fLrfbraSkJLlcLq1evdryqwMAoH6qVWEkLS3Nc4DfDyUmJmrevHk6e/asnn76aS1YsEBHjhxR8+bNNWDAAD3xxBPq2bOnJOnrr7/Wfffdp9WrV6tx48YaPny4pk2bVuH7ZAAAgKpVq8IIAACoe+rUdUYAAEDtQxgBAABW1Yqzadxut77++muFhIT4fAlsAABghzFGBQUFatWqVakLK/5QrQgjX3/9daXv4wAAAOw6fPhwmXfMPq9WhJGQkBBJ516Mr/dzAAAAduTn5ysyMtLzOV6eWhFGzn8143K5CCMAANQyP3WIBQewAgAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArKrXYeTxv+/SHW/8r7ZmfmO7FAAA6q16HUb+/VWuNuw7of936oztUgAAqLfqdRgBAAD2EUYAAIBVhBEAAGAVYQQAAFjlUxiZOXOmevXqJZfLJZfLpejoaP3zn/8st/+8efPkcDi8lqCgoIsuGgAA1B0BvnRu06aNnnvuOf3sZz+TMUbz58/XqFGjtH37dl1xxRVljnG5XNqzZ4/nscPhuLiKAQBAneJTGBk5cqTX42eeeUYzZ87Up59+Wm4YcTgcCg8Pr3yFAACgTqv0MSMlJSVKTU1VYWGhoqOjy+136tQptWvXTpGRkRo1apR27dr1k+suKipSfn6+1wIAAOomn8PIjh07FBwcLKfTqXvvvVdLly5V9+7dy+zbtWtXvfXWW/rwww/1zjvvyO12KyYmRl999dUFt5GSkqLQ0FDPEhkZ6WuZAACglnAYY4wvA86cOaOsrCzl5eVpyZIleuONN/TJJ5+UG0h+6OzZs7r88st122236amnniq3X1FRkYqKijyP8/PzFRkZqby8PLlcLl/KvaCbXtuobVm5mj02SnFX8FUSAABVKT8/X6GhoT/5+e3TMSOSFBgYqM6dO0uSoqKi9Nlnn+mVV17R7Nmzf3JsgwYN1LdvX+3bt++C/ZxOp5xOp6+lAQCAWuiirzPidru99mJcSElJiXbs2KGIiIiL3WyV4MweAADs82nPSHJysoYPH662bduqoKBACxcuVFpamlatWiVJSkhIUOvWrZWSkiJJevLJJzVgwAB17txZubm5evHFF5WZmanx48dX/SsBAAC1kk9h5NixY0pISNDRo0cVGhqqXr16adWqVbruuuskSVlZWfLz+35ny8mTJzVhwgRlZ2eradOmioqK0qZNmyp0fAkAAKgffD6A1YaKHgDjq1/P3KStmSc5gBUAgGpQ0c9v7k0DAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsII5Iu/ZObAQCouwgjAADAqnodRrgzDQAA9tXrMAIAAOwjjAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijAiSeJ68AAA2EIYAQAAVhFGAACAVfU6jDi4OQ0AANbV6zACAADsI4wAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowIslwaxoAAKwhjAAAAKsIIwAAwKp6HUYc4uY0AADYVq/DCAAAsI8wAgAArCKMAAAAqwgjAADAKsIIAACwyqcwMnPmTPXq1Usul0sul0vR0dH65z//ecExixcvVrdu3RQUFKSePXtqxYoVF1UwAACoW3wKI23atNFzzz2nrVu3asuWLbr22ms1atQo7dq1q8z+mzZt0m233aa77rpL27dvV3x8vOLj47Vz584qKR4AANR+DmMu7mLozZo104svvqi77rqr1HNjxoxRYWGhli9f7mkbMGCA+vTpo1mzZpW7zqKiIhUVFXke5+fnKzIyUnl5eXK5XBdTrpdbZqVr86FvNPP2KzW8Z0SVrRcAAJz7/A4NDf3Jz+9KHzNSUlKi1NRUFRYWKjo6usw+6enpio2N9WqLi4tTenr6BdedkpKi0NBQzxIZGVnZMiuEW9MAAGCPz2Fkx44dCg4OltPp1L333qulS5eqe/fuZfbNzs5WWFiYV1tYWJiys7MvuI3k5GTl5eV5lsOHD/taJgAAqCUCfB3QtWtXZWRkKC8vT0uWLFFiYqI++eSTcgNJZTidTjmdzipbHwAAuHT5HEYCAwPVuXNnSVJUVJQ+++wzvfLKK5o9e3apvuHh4crJyfFqy8nJUXh4eCXLrWLcmgYAAOsu+jojbrfb62DTH4qOjtbatWu92tasWVPuMSYAAKD+8WnPSHJysoYPH662bduqoKBACxcuVFpamlatWiVJSkhIUOvWrZWSkiJJeuCBBzRkyBBNmzZNI0aMUGpqqrZs2aI5c+ZU/SsBAAC1kk9h5NixY0pISNDRo0cVGhqqXr16adWqVbruuuskSVlZWfLz+35nS0xMjBYuXKg///nPevTRR/Wzn/1My5YtU48ePar2VQAAgFrLpzDy5ptvXvD5tLS0Um2jR4/W6NGjfSoKAADUH9ybBgAAWEUYAQAAVhFGAACAVYQRSRd3dx4AAHAxCCMAAMAqwggAALCKMAIAAKyq12GEW9MAAGBfvQ4jAADAPsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijEgy4uY0AADYQhgBAABWEUYAAIBVhBEAAGBVvQ4jDm5OAwCAdfU6jAAAAPsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsKIJMPV4AEAsIYwAgAArCKMAAAAqwgjAADAKsIIAACwql6HEYe4OQ0AALbV6zACAADsI4wAAACrCCMAAMAqwggAALCKMAIAAKzyKYykpKTo6quvVkhIiFq2bKn4+Hjt2bPngmPmzZsnh8PhtQQFBV1U0QAAoO7wKYx88sknSkpK0qeffqo1a9bo7Nmzuv7661VYWHjBcS6XS0ePHvUsmZmZF1V0VePWNAAA2BPgS+eVK1d6PZ43b55atmyprVu36pprril3nMPhUHh4eOUqBAAAddpFHTOSl5cnSWrWrNkF+506dUrt2rVTZGSkRo0apV27dl2wf1FRkfLz870WAABQN1U6jLjdbj344IMaOHCgevToUW6/rl276q233tKHH36od955R263WzExMfrqq6/KHZOSkqLQ0FDPEhkZWdkyAQDAJa7SYSQpKUk7d+5UamrqBftFR0crISFBffr00ZAhQ/TBBx+oRYsWmj17drljkpOTlZeX51kOHz5c2TIBAMAlzqdjRs6bOHGili9frvXr16tNmzY+jW3QoIH69u2rffv2ldvH6XTK6XRWpjSfOLg1DQAA1vm0Z8QYo4kTJ2rp0qVat26dOnTo4PMGS0pKtGPHDkVERPg8FgAA1D0+7RlJSkrSwoUL9eGHHyokJETZ2dmSpNDQUDVs2FCSlJCQoNatWyslJUWS9OSTT2rAgAHq3LmzcnNz9eKLLyozM1Pjx4+v4pcCAABqI5/CyMyZMyVJQ4cO9WqfO3euxo0bJ0nKysqSn9/3O1xOnjypCRMmKDs7W02bNlVUVJQ2bdqk7t27X1zlAACgTvApjBjz05cHS0tL83r88ssv6+WXX/apKAAAUH9wbxoAAGAVYUQV2+MDAACqB2EEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhVr8MI96YBAMC+eh1GAACAfYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWFWvw4hD3JwGAADb6nUYAQAA9hFGAACAVYQRAABgFWEEAABYRRgBAABWEUYkGWO7AgAA6i/CCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwql6HEQe3pgEAwLp6HUYAAIB9hBEAAGAVYQQAAFhFGAEAAFYRRiQZcT14AABsIYwAAACrfAojKSkpuvrqqxUSEqKWLVsqPj5ee/bs+clxixcvVrdu3RQUFKSePXtqxYoVlS4YAADULT6FkU8++URJSUn69NNPtWbNGp09e1bXX3+9CgsLyx2zadMm3Xbbbbrrrru0fft2xcfHKz4+Xjt37rzo4gEAQO3nMMZU+oCJ48ePq2XLlvrkk090zTXXlNlnzJgxKiws1PLlyz1tAwYMUJ8+fTRr1qwKbSc/P1+hoaHKy8uTy+WqbLmljH3zf/U/X57Qy2N668a+bapsvQAAoOKf3xd1zEheXp4kqVmzZuX2SU9PV2xsrFdbXFyc0tPTyx1TVFSk/Px8rwUAANRNlQ4jbrdbDz74oAYOHKgePXqU2y87O1thYWFebWFhYcrOzi53TEpKikJDQz1LZGRkZcsEAACXuEqHkaSkJO3cuVOpqalVWY8kKTk5WXl5eZ7l8OHDVb4NAABwaQiozKCJEydq+fLlWr9+vdq0ufCxFuHh4crJyfFqy8nJUXh4eLljnE6nnE5nZUoDAAC1jE97RowxmjhxopYuXap169apQ4cOPzkmOjpaa9eu9Wpbs2aNoqOjfasUAADUST7tGUlKStLChQv14YcfKiQkxHPcR2hoqBo2bChJSkhIUOvWrZWSkiJJeuCBBzRkyBBNmzZNI0aMUGpqqrZs2aI5c+ZU8UsBAAC1kU97RmbOnKm8vDwNHTpUERERnmXRokWePllZWTp69KjncUxMjBYuXKg5c+aod+/eWrJkiZYtW3bBg14BAED94dOekYpckiQtLa1U2+jRozV69GhfNlWjKn+lFQAAcLG4Nw0AALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArKrXYcThcNguAQCAeq9ehxEAAGAfYQQAAFhFGAEAAFYRRsTl4AEAsIkwAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMCqeh1GuDMNAAD21eswAgAA7COMAAAAqwgjAADAKsKIJG5NAwCAPYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFbV6zDi4OY0AABYV6/DCAAAsI8wAgAArCKMSDKGC8IDAGALYQQAAFhFGAEAAFYRRgAAgFWEEQAAYJXPYWT9+vUaOXKkWrVqJYfDoWXLll2wf1pamhwOR6klOzu7sjUDAIA6xOcwUlhYqN69e2vGjBk+jduzZ4+OHj3qWVq2bOnrpgEAQB0U4OuA4cOHa/jw4T5vqGXLlmrSpInP4wAAQN1WY8eM9OnTRxEREbruuuu0cePGC/YtKipSfn6+1wIAAOqmag8jERERmjVrlt5//329//77ioyM1NChQ7Vt27Zyx6SkpCg0NNSzREZGVktt3JoGAAD7fP6axlddu3ZV165dPY9jYmK0f/9+vfzyy3r77bfLHJOcnKxJkyZ5Hufn51dbIAEAAHZVexgpS79+/bRhw4Zyn3c6nXI6nTVYEQAAsMXKdUYyMjIUERFhY9Nl4s40AADY4/OekVOnTmnfvn2exwcPHlRGRoaaNWumtm3bKjk5WUeOHNGCBQskSdOnT1eHDh10xRVX6LvvvtMbb7yhdevWafXq1VX3KgAAQK3lcxjZsmWLhg0b5nl8/tiOxMREzZs3T0ePHlVWVpbn+TNnzugPf/iDjhw5okaNGqlXr17617/+5bUOAABQfzmMMZf8txT5+fkKDQ1VXl6eXC5Xla33zrmb9fGe43rh5l665SoOkAUAoCpV9PObe9MAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKvqdRhxOLg7DQAAttXrMAIAAOwjjAAAAKsIIxI3pwEAwCLCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMCqeh1GuDMNAAD21eswAgAA7COMSDJcDx4AAGsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMCqeh1GHNycBgAA6+p1GAEAAPYRRiQZbk0DAIA1hBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWOVzGFm/fr1GjhypVq1ayeFwaNmyZT85Ji0tTVdeeaWcTqc6d+6sefPmVaJUAABQF/kcRgoLC9W7d2/NmDGjQv0PHjyoESNGaNiwYcrIyNCDDz6o8ePHa9WqVT4XCwAA6p4AXwcMHz5cw4cPr3D/WbNmqUOHDpo2bZok6fLLL9eGDRv08ssvKy4urswxRUVFKioq8jzOz8/3tUwAAFBLVPsxI+np6YqNjfVqi4uLU3p6erljUlJSFBoa6lkiIyOrqTpuTgMAgG3VHkays7MVFhbm1RYWFqb8/Hx9++23ZY5JTk5WXl6eZzl8+HC11sjV4AEAsMfnr2lqgtPplNPptF0GAACoAdW+ZyQ8PFw5OTlebTk5OXK5XGrYsGF1bx4AAFziqj2MREdHa+3atV5ta9asUXR0dHVvGgAA1AI+h5FTp04pIyNDGRkZks6dupuRkaGsrCxJ5473SEhI8PS/9957deDAAT3yyCP64osv9Nprr+m9997TQw89VDWvAAAA1Go+h5EtW7aob9++6tu3ryRp0qRJ6tu3r/7yl79Iko4ePeoJJpLUoUMHffTRR1qzZo169+6tadOm6Y033ij3tF4AAFC/+HwA69ChQ2VM+eeflHV11aFDh2r79u2+bgoAANQD3JsGAABYRRgBAABWEUYAAIBVhBEAAGBVvQ4jDm5NAwCAdfU6jJx3gZODAABANSOMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwKp6HUbO35rGiOvBAwBgS70OIwAAwD7CCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKyq12HE8Z+b0xhuTQMAgDX1OowAAAD7CCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArKpUGJkxY4bat2+voKAg9e/fX5s3by6377x58+RwOLyWoKCgShcMAADqFp/DyKJFizRp0iRNmTJF27ZtU+/evRUXF6djx46VO8blcuno0aOeJTMz86KKBgAAdYfPYeSll17ShAkTdOedd6p79+6aNWuWGjVqpLfeeqvcMQ6HQ+Hh4Z4lLCzsoooGAAB1h09h5MyZM9q6datiY2O/X4Gfn2JjY5Wenl7uuFOnTqldu3aKjIzUqFGjtGvXrgtup6ioSPn5+V5LdXDo3M1puDUNAAD2+BRGTpw4oZKSklJ7NsLCwpSdnV3mmK5du+qtt97Shx9+qHfeeUdut1sxMTH66quvyt1OSkqKQkNDPUtkZKQvZQIAgFqk2s+miY6OVkJCgvr06aMhQ4bogw8+UIsWLTR79uxyxyQnJysvL8+zHD58uLrLBAAAlgT40rl58+by9/dXTk6OV3tOTo7Cw8MrtI4GDRqob9++2rdvX7l9nE6nnE6nL6UBAIBayqc9I4GBgYqKitLatWs9bW63W2vXrlV0dHSF1lFSUqIdO3YoIiLCt0oBAECd5NOeEUmaNGmSEhMTddVVV6lfv36aPn26CgsLdeedd0qSEhIS1Lp1a6WkpEiSnnzySQ0YMECdO3dWbm6uXnzxRWVmZmr8+PFV+0oAAECt5HMYGTNmjI4fP66//OUvys7OVp8+fbRy5UrPQa1ZWVny8/t+h8vJkyc1YcIEZWdnq2nTpoqKitKmTZvUvXv3qnsVAACg1nIYYy75M1vz8/MVGhqqvLw8uVyuKlvvvW9v1cpd2XoqvofGDmhXZesFAAAV//zm3jQAAMAqwggAALCKMAIAAKwijEjSpX/YDAAAdVa9DiMOh+0KAABAvQ4jAADAPsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowIok70wAAYE+9DiPcmwYAAPvqdRgBAAD2EUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVgXYLuBSsO/YKW0++I0aNvBXw0A/NQwMOPfnBv5q4O+Qv59DDi7XCgBAtajXYcTf79yOoQXpmVqQnnnBvgF+DgX4OxTg5/efn+f+7O/nUAN/h/z8HPJzOOTQucvMO+Q49/OHbQ55+ugH7T8e95//qvxy9f/ZctWtr6rru8RfLwDUZY//qrs6twyxsu16HUbGDmin4wXfKf/bYn13tkTfni3R6TPnfp4pdnv1LXYbFbuNJHfZKwMAoBbL/67Y2rbrdRjp16GZUu+OLvO54hK3vit2q7jEfS6IlBgVu93/+en955L//NlIchsjnftP5/5o5DaSMeeelznXx3j6mO9//mhcVTJVfGviqr7TsanqAgEAPml/WWNr267XYeRCAvz9FOzP8b0AAFQ3Pm0BAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWFWpMDJjxgy1b99eQUFB6t+/vzZv3nzB/osXL1a3bt0UFBSknj17asWKFZUqFgAA1D0+h5FFixZp0qRJmjJlirZt26bevXsrLi5Ox44dK7P/pk2bdNttt+muu+7S9u3bFR8fr/j4eO3cufOiiwcAALWfw/h4He7+/fvr6quv1l//+ldJktvtVmRkpO677z5Nnjy5VP8xY8aosLBQy5cv97QNGDBAffr00axZsyq0zfz8fIWGhiovL08ul8uXcgEAgCUV/fz2ac/ImTNntHXrVsXGxn6/Aj8/xcbGKj09vcwx6enpXv0lKS4urtz+klRUVKT8/HyvBQAA1E0+hZETJ06opKREYWFhXu1hYWHKzs4uc0x2drZP/SUpJSVFoaGhniUyMtKXMgEAQC1ySZ5Nk5ycrLy8PM9y+PBh2yUBAIBq4tNde5s3by5/f3/l5OR4tefk5Cg8PLzMMeHh4T71lySn0ymn0+l5fP6wFr6uAQCg9jj/uf1Th6f6FEYCAwMVFRWltWvXKj4+XtK5A1jXrl2riRMnljkmOjpaa9eu1YMPPuhpW7NmjaKjoyu83YKCAkni6xoAAGqhgoIChYaGlvu8T2FEkiZNmqTExERdddVV6tevn6ZPn67CwkLdeeedkqSEhAS1bt1aKSkpkqQHHnhAQ4YM0bRp0zRixAilpqZqy5YtmjNnToW32apVKx0+fFghISFyOBy+llyu/Px8RUZG6vDhw5ylU42Y55rDXNcM5rlmMM81ozrn2RijgoICtWrV6oL9fA4jY8aM0fHjx/WXv/xF2dnZ6tOnj1auXOk5SDUrK0t+ft8fihITE6OFCxfqz3/+sx599FH97Gc/07Jly9SjR48Kb9PPz09t2rTxtdQKc7lcvNFrAPNcc5jrmsE81wzmuWZU1zxfaI/IeT5fZ6Qu4folNYN5rjnMdc1gnmsG81wzLoV5viTPpgEAAPVHvQ4jTqdTU6ZM8TpzB1WPea45zHXNYJ5rBvNcMy6Fea7XX9MAAAD76vWeEQAAYB9hBAAAWEUYAQAAVhFGAACAVYQRAABgVZ0PIzNmzFD79u0VFBSk/v37a/PmzRfsv3jxYnXr1k1BQUHq2bOnVqxYUUOV1m6+zPPrr7+uwYMHq2nTpmratKliY2N/8u8F3/P1PX1eamqqHA6H575SuDBf5zk3N1dJSUmKiIiQ0+lUly5d+PejAnyd5+nTp6tr165q2LChIiMj9dBDD+m7776roWprp/Xr12vkyJFq1aqVHA6Hli1b9pNj0tLSdOWVV8rpdKpz586aN29e9RZp6rDU1FQTGBho3nrrLbNr1y4zYcIE06RJE5OTk1Nm/40bNxp/f3/zwgsvmN27d5s///nPpkGDBmbHjh01XHnt4us8/+Y3vzEzZsww27dvN59//rkZN26cCQ0NNV999VUNV177+DrX5x08eNC0bt3aDB482IwaNapmiq3FfJ3noqIic9VVV5kbbrjBbNiwwRw8eNCkpaWZjIyMGq68dvF1nv/2t78Zp9Np/va3v5mDBw+aVatWmYiICPPQQw/VcOW1y4oVK8xjjz1mPvjgAyPJLF269IL9Dxw4YBo1amQmTZpkdu/ebV599VXj7+9vVq5cWW011ukw0q9fP5OUlOR5XFJSYlq1amVSUlLK7H/LLbeYESNGeLX179/f3HPPPdVaZ23n6zz/WHFxsQkJCTHz58+vrhLrjMrMdXFxsYmJiTFvvPGGSUxMJIxUgK/zPHPmTNOxY0dz5syZmiqxTvB1npOSksy1117r1TZp0iQzcODAaq2zLqlIGHnkkUfMFVdc4dU2ZswYExcXV2111dmvac6cOaOtW7cqNjbW0+bn56fY2Filp6eXOSY9Pd2rvyTFxcWV2x+Vm+cfO336tM6ePatmzZpVV5l1QmXn+sknn1TLli1111131USZtV5l5vnvf/+7oqOjlZSUpLCwMPXo0UPPPvusSkpKaqrsWqcy8xwTE6OtW7d6vso5cOCAVqxYoRtuuKFGaq4vbHwW+nzX3trixIkTKikp8dxN+LywsDB98cUXZY7Jzs4us392dna11VnbVWaef+xPf/qTWrVqVerND2+VmesNGzbozTffVEZGRg1UWDdUZp4PHDigdevW6fbbb9eKFSu0b98+/f73v9fZs2c1ZcqUmii71qnMPP/mN7/RiRMnNGjQIBljVFxcrHvvvVePPvpoTZRcb5T3WZifn69vv/1WDRs2rPJt1tk9I6gdnnvuOaWmpmrp0qUKCgqyXU6dUlBQoLFjx+r1119X8+bNbZdTp7ndbrVs2VJz5sxRVFSUxowZo8cee0yzZs2yXVqdkpaWpmeffVavvfaatm3bpg8++EAfffSRnnrqKdul4SLV2T0jzZs3l7+/v3Jycrzac3JyFB4eXuaY8PBwn/qjcvN83tSpU/Xcc8/pX//6l3r16lWdZdYJvs71/v37dejQIY0cOdLT5na7JUkBAQHas2ePOnXqVL1F10KVeU9HRESoQYMG8vf397Rdfvnlys7O1pkzZxQYGFitNddGlZnn//qv/9LYsWM1fvx4SVLPnj1VWFiou+++W4899pj8/Pj9uiqU91nocrmqZa+IVIf3jAQGBioqKkpr1671tLndbq1du1bR0dFljomOjvbqL0lr1qwptz8qN8+S9MILL+ipp57SypUrddVVV9VEqbWer3PdrVs37dixQxkZGZ7lV7/6lYYNG6aMjAxFRkbWZPm1RmXe0wMHDtS+ffs8YU+S9u7dq4iICIJIOSozz6dPny4VOM4HQMM9X6uMlc/Cajs09hKQmppqnE6nmTdvntm9e7e5++67TZMmTUx2drYxxpixY8eayZMne/pv3LjRBAQEmKlTp5rPP//cTJkyhVN7K8DXeX7uuedMYGCgWbJkiTl69KhnKSgosPUSag1f5/rHOJumYnyd56ysLBMSEmImTpxo9uzZY5YvX25atmxpnn76aVsvoVbwdZ6nTJliQkJCzLvvvmsOHDhgVq9ebTp16mRuueUWWy+hVigoKDDbt28327dvN5LMSy+9ZLZv324yMzONMcZMnjzZjB071tP//Km9f/zjH83nn39uZsyYwam9F+vVV181bdu2NYGBgaZfv37m008/9Tw3ZMgQk5iY6NX/vffeM126dDGBgYHmiiuuMB999FENV1w7+TLP7dq1M5JKLVOmTKn5wmshX9/TP0QYqThf53nTpk2mf//+xul0mo4dO5pnnnnGFBcX13DVtY8v83z27Fnz+OOPm06dOpmgoCATGRlpfv/735uTJ0/WfOG1yMcff1zmv7nn5zYxMdEMGTKk1Jg+ffqYwMBA07FjRzN37txqrdFhDPu2AACAPXX2mBEAAFA7EEYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBACAemr9+vUaOXKkWrVqJYfDoWXLlvm8DmOMpk6dqi5dusjpdKp169Z65plnfFpHnb1RHgAAuLDCwkL17t1bv/3tb3XTTTdVah0PPPCAVq9eralTp6pnz5765ptv9M033/i0Dq7ACgAA5HA4tHTpUsXHx3vaioqK9Nhjj+ndd99Vbm6uevTooeeff15Dhw6VJH3++efq1auXdu7cqa5du1Z623xNAwAAyjRx4kSlp6crNTVV//73vzV69Gj94he/0JdffilJ+sc//qGOHTtq+fLl6tChg9q3b6/x48f7vGeEMAIAAErJysrS3LlztXjxYg0ePFidOnXSww8/rEGDBmnu3LmSpAMHDigzM1OLFy/WggULNG/ePG3dulU333yzT9vimBEAAFDKjh07VFJSoi5duni1FxUV6bLLLpMkud1uFRUVacGCBZ5+b775pqKiorRnz54Kf3VDGAEAAKWcOnVK/v7+2rp1q/z9/b2eCw4OliRFREQoICDAK7Bcfvnlks7tWSGMAACASuvbt69KSkp07NgxDR48uMw+AwcOVHFxsfbv369OnTpJkvbu3StJateuXYW3xdk0AADUU6dOndK+ffsknQsfL730koYNG6ZmzZqpbdu2uuOOO7Rx40ZNmzZNffv21fHjx7V27Vr16tVLI0aMkNvt1tVXX63g4GBNnz5dbrdbSUlJcrlcWr16dYXrIIwAAFBPpaWladiwYaXaExMTNW/ePJ09e1ZPP/20FixYoCNHjqh58+YaMGCAnnjiCfXs2VOS9PXXX+u+++7T6tWr1bhxYw0fPlzTpk1Ts2bNKlwHYQQAAFjFqb0AAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACs+v8h63+BToASGwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "\n",
    "def gradient_descent(X, y, max_iter, alpha):\n",
    "    theta = np.zeros((2))\n",
    "    costs = []\n",
    "\n",
    "    for i in range(0, max_iter): # we could also use a delta on the cost function with a while to stop when the cost is not improving but we wanted to see the curve after x iterations\n",
    "        y_pred = X @ theta\n",
    "        theta[0] = theta[0] - alpha * (1/len(y)) * np.sum(y_pred - y)\n",
    "        theta[1] = theta[1] - alpha * (1/len(y)) * np.sum((y_pred - y) * X[:,1])  \n",
    "\n",
    "        c = cost_J(y_pred, y) # to plot the costs over iters\n",
    "        costs.append(c)\n",
    "\n",
    "    y_pred = X @ theta\n",
    "    print(f\"Theta = {theta}\")\n",
    "    print(f\"Cost = {cost_J(y_pred, y)}\")\n",
    "\n",
    "    plt.plot(range(0, len(costs)), costs)\n",
    "    plt.title(\"Cost over iterations\")\n",
    "    plt.show()\n",
    "\n",
    "gradient_descent(X, y, max_iter = 1000000, alpha = 0.0001) # i got the best results with those parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da5121b6",
   "metadata": {},
   "source": [
    "a) Plot the cost value (Equation 2) as a function of the iterations. What do you observe?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "id": "5a34ad43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "plt.plot(range(0, len(costs)), costs)\n",
    "plt.title(\"Cost over iterations\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63917be0",
   "metadata": {},
   "source": [
    "In this scenario, we can clearly observe a plateau of the cost function. This means that we have reached a local minimum while trying to minimise the cost."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5903f37",
   "metadata": {},
   "source": [
    "b) Imagine a stopping criterion, i.e. when do we stop iterating on the training set?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93905b85",
   "metadata": {},
   "source": [
    "The stopping criterion can be a small delta between each calculations of the cost. Like if the cost did not change of at least delta, this means we are in a plateau and should stop."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7667bec1",
   "metadata": {},
   "source": [
    "c) Plot the computed line $h_{\\theta}(\\mathbf{x})$ on top of the scatter plot of exercise 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "id": "e80c04b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2bdqIdvARERE5jZQUwM1NU4dJ6/PPNcFUPQc+G8/ZWSzN3AyHDx8WatWqJXzwwQfC2bNnhVWrVgm+vr7CypUrdX0++ugjISAgQNiwYYNw4sQJYciQIUJYWJhw+/ZtXZ8BAwYInTp1Eg4dOiTs27dPaNWqlRAbG6u7np+fLwQFBQmjRo0SUlNThbVr1wq+vr7CV199JWmc1sjKJyIiMotaLQh9++rvmCsstPfIHI41fn/bNXASBEHYuHGjEBERIXh5eQlt27YVvv76a9F1tVotTJ8+XQgKChK8vLyEvn37CmfOnBH1yc3NFWJjY4XatWsL/v7+wrhx44Tr16+L+hw/flzo1auX4OXlJTRq1Ej46KOPJI+RgRMRubo7ZWrhwLmrwi/HLgkHzl0V7pSp7T0kMmT/fv2A6dtv7T0qh2WN398yQRAE+855Ob7CwkLI5XIUFBTA39/f3sMhIrKoxNRMzN6YhsyCe4WFg+XemDk43DEPqK2JysqAbt2Ao0fvtfn7awpc+vjYb1wOzhq/v+1+5AoREdlPYmomJq08KgqaACCroAiTVh5FYmqmnUZGOklJQK1a4qBp/XqgoIBBkx3wkF8iohqqTC1g9sY0GFp2EADIAMzemIZ+4Qq4u/E8M5srLQVatQL++edeW2go8NdfgIeH3YZV03HGiYiohjqcnqc301SeACCzoAiH0/NsNyjS+PlnwNNTHDT99huQns6gyc4440REVEPlXDceNJnTjyzg9m0gKAi4fv1eW5cuwKFDgLu7/cZFOpxxIiKqoQLreFu0H1XT998Dvr7ioGn/fuCPPxg0ORDOOBER1VDdwuohWO6NrIIig3lOMgAKuTe6hbGYolVdv67ZIVdev37Atm2aw3rJoXDGiYiohnJ3k2HmYM2xVxV/PWu/nzk4nInh1vTll/pB07FjmnwmBk0OiYETEVENNiAiGItGdoZCLl6OU8i9sWhkZ9Zxspa8PE1gNHnyvbb//AdQq4GOHe02LKoal+qIiGq4ARHB6BeuwOH0PORcL0JgHc3yHGearOTDD/UP4D19GmjTxj7jIZMwcCIiKqdMLdTIAMLdTQZli/r2HoZry8wEQkLEbS+8ACxebJ/xkFkYOBER3cWjR8hqpk4F5s8Xt124ADRrZpfhkPmY40REBB49QlZy4YIml6l80PTmm5rjeRk0OSXOOBFRjeeMR4/U1CVFpzJhArBkibgtMxNQKOwzHrIIBk5EVOOZcvSII+QBcUnRwZ0+DbRrJ26bM0cz00ROj0t1RFTjOdPRI662pFimFqA6n4sNKZehOp+LMrWheT8nIQjAk0/qB015eQyaXAhnnIioxnOWo0eccUmxMi41c3b0qOZMufIWLgQmTbLPeMhqOONERDWe9ugRY6GGDJpf6PY+esSUJUVH5zIzZ4IAPPKIftB0/TqDJhfFwImIajxnOXrEmZYUK1PVzBmgmTlz+GW7ffsANzdg9+57bStXaoKp2rXtNiyyLgZORERwnKNHKsv5cZYlxao4/cxZWZnmWJQHH7zXVq8ecPs2MGKE3YZFtsEcJyKiu+x99EhVOT/aJcWsgiKDszUyaAI9ey8pVsWpZ862bQMGDBC3bdgAPPaYfcZDNscZJyKicrRHjwzp2AjKFvVtGjRVlfPjLEuKVXHKmbPSUqBpU3HQ1KIFUFLCoKmGYeBERGRnpuT8OMqSYnU4SzK+zk8/AZ6ewMWL99qSkoBz5wAPD/uNi+yCS3VERHZmagFOey8pVpd25mzSyqOQAaKA0aFmzm7fBho2BG7evNfWtStw8KAmKZxqJH7yRER2Zk7Oj72WFC3F4WfOVqwAfH3FQZNKBRw+zKCphuOMExGRndki58cRz7ZzyJmzwkJALhe3RUcDW7dqDuulGo+BExGRnVl7t5wjV+jWzpzZS/mAMnL9dwh77y1xh+PHgchI+wyOHBLnG4mI7Myau+VcpkK3FSSmZqLX3J2Y9NlvGNKpsThoGj5cU8iSQRNVwMCJiMgBWCPnx2UqdFuBNqB8cstypHz2jOjaIxO+QuLbn9hpZFVzqYORnRCX6oiIHISlc35M3a1XU5SpBXy5ai/S5w4XtX/faRCm93/RoQ9LduRl15qCgRMRkQOxZM6PJSt0O2JyubmyJ8Rh47JForYHJi3DFf9AAI4bUGpnySrOL2mXXR1iN2INwMCJiMhFWWq3nsvMcqSnA82bI6Rc0xfK/+D/eo822N2RjnypatnVkWfJXA1znIiIXJQlKnS7THL5s88CzZuLmrpMXmk0aAIc68gXpz8Y2YUwcCIiclHV3a3nEsnlf/6pqb+0fLmuSf3RR1B+uB15fgEGX+JwR77AyQ9GdjEMnIiIXFh1dus59SyHIACPPw6Eh4vbr12DW0KC0x2W7JQHI7so5jgREbk4c3frOe0sR3IycP/94rbFi4EXXtB9qw0oK+ZuKRw0d8vaRVJJOgZOREQ1gDm79ZxulkMQgIceAn7//V6bmxtQUADUrq3X3SGPfDHCaQ5GrgG4VEdERAZZIrncZn7/XRMklQ+aVq0CysoMBk1aznRYssMfjFxDcMaJiIgMcopZjrIyoEMH4NSpe20NGgCXLgFeXvYbl5U40yyZq7LrjNOsWbMgk8lEX23bttVdLyoqQlxcHOrXr4/atWtj2LBhyM7OFt0jIyMDMTEx8PX1RWBgIN544w3cuXNH1Gf37t3o3LkzvLy80LJlS6xYscIWj0dE5PQcepZj61agVi1x0PTrr8C//7pk0KTlTLNkrsjuM0733Xcftm/frvu+Vq17Q4qPj8fmzZuxbt06yOVyTJ48GU888QT2798PACgrK0NMTAwUCgUOHDiAzMxMjB49Gh4eHvjwww8BAOnp6YiJicHEiROxatUq7NixA8899xyCg4MRHR1t24clInJCDjfLUVIChIYCmeVqSLVpA6SmagIpIiuSCYJgtwIcs2bNwi+//IKUlBS9awUFBWjYsCFWr16NJ598EgBw+vRptGvXDiqVCj169MDWrVvx6KOP4sqVKwgKCgIALF68GAkJCfj333/h6emJhIQEbN68Gampqbp7Dx8+HPn5+UhMTJQ0zsLCQsjlchQUFMDf37/6D05EROZZtw74z3/EbTt3Ao88Yp/xkEOzxu9vuyeHnz17FiEhIWjevDlGjBiBjIwMAEBycjJKS0sRFRWl69u2bVs0bdoUKpUKAKBSqdC+fXtd0AQA0dHRKCwsxKm7U7cqlUp0D20f7T0MKS4uRmFhoeiLiIjs6NYtwMdHHDT16KHJcWLQRDZk18Cpe/fuWLFiBRITE7Fo0SKkp6fjwQcfxPXr15GVlQVPT08EBASIXhMUFISsrCwAQFZWliho0l7XXqusT2FhIW7fvm1wXHPmzIFcLtd9NWnSxBKPS0RE5li2DPDzA4rK1Ys6eBBQqTQ76copUwtQnc/FhpTLUJ3Pdeyq5uSU7LoYPHDgQN1/R0ZGonv37mjWrBl++OEH+Pj42G1c06ZNw5QpU3TfFxYWMngiIrK1ggKgwj+eMWgQsGmT5hiVClzmMGJyaHZfqisvICAArVu3xrlz56BQKFBSUoL8/HxRn+zsbCgUCgCAQqHQ22Wn/b6qPv7+/kaDMy8vL/j7+4u+iIjIhv77X/2g6cQJYPNmo0GTSxxGTA7PoQKnGzdu4Pz58wgODkaXLl3g4eGBHTt26K6fOXMGGRkZUCqVAAClUomTJ08iJydH1ycpKQn+/v4Iv3s+kVKpFN1D20d7DyIiciBXr2oCo/j4e20jRmiqgrdvb/AlLnEYMTkNuwZOr7/+Ovbs2YMLFy7gwIEDePzxx+Hu7o7Y2FjI5XKMHz8eU6ZMwa5du5CcnIxx48ZBqVSiR48eAID+/fsjPDwco0aNwvHjx7Ft2za88847iIuLg9fdGh4TJ07E33//jalTp+L06dNYuHAhfvjhB8SX/0NJRET2N3s20LChuO3sWWDlykpf5tSHEZPTsWuO06VLlxAbG4vc3Fw0bNgQvXr1wsGDB9Hw7h+cBQsWwM3NDcOGDUNxcTGio6OxcOFC3evd3d2xadMmTJo0CUqlEn5+fhgzZgzeffddXZ+wsDBs3rwZ8fHx+PTTT9G4cWMsWbKENZyIyKmVqQXHqatUXZcvA40bi9smTwY+/1zSy532MGJySnat4+QsWMeJiByJSyVBx8dr8pnKu3hRP5CqhOp8LmK/OVhlvzUTeph80DE5N5es40RERNK5TBL0+fOaXKbyQdP06ZpcpsaNTSor4FSHEZPTY216IiInUVUStAyaJOh+4QrHXrYbMwb47jtxW06OLr/J1Bk1pziMmFwGZ5yIiJyE0ydBnzqlmWUqHzT93/9pZpnKBU3mzKg59GHE5FI440RE5CScNglaEIDHHtMUrizv2jVRrabqzqg53GHE5JIYOBEROYnAOt5VdzKhn00cOQJ06yZu++Yb4Lnn9LqaMqNmLMnb3U3GBHCyKgZOREROQpsEnVVQZHBWRgbN0pRDJEGr1UDv3sD+/ffaPDw0s0x+fgZf4rQzalSjMMeJiMhJaJOgAejtIHOoJOg9ewB3d3HQtHYtUFJiNGgCnHRGjWocBk5ERE7EoZOg79wBwsOBhx++1xYUBBQVAU8/XeXLWVaAnAGX6oiInIxDJkFv3gw8+qi4bdMmICZG8i1YVoCcQbUqhxcVFcHb2/WnTFk5nIjIiOJioGlTTR0mrXbtgBMngFrm/dvcpSqjk11Z4/e3yf+vVqvV+OCDD7B48WJkZ2fjr7/+QvPmzTF9+nSEhoZi/PjxFhkYERE5uP/9Dxg+XNy2ezfw0EPVuq1DzqgR3WVyjtP777+PFStWYN68efD09NS1R0REYMmSJRYdHBEROaBbtwBPT3HQ1LMnUFZW7aBJS1tWYEjHRlC2qM+giRyGyYHTd999h6+//hojRoyAu7u7rr1Dhw44ffq0RQdHREQOZskSzc640tJ7bYcPA/v2AW7cb0Suz+SlusuXL6Nly5Z67Wq1GqXl/yAREZHrKCgQVfkGAAweDGzYoDlGhaiGMPmfB+Hh4fj999/12n/88Ud06tTJIoMiIiIH8vHH+kHTyZPAr78yaKIax+QZpxkzZmDMmDG4fPky1Go11q9fjzNnzuC7777DpornEBERkfP6918gMFDcNno08O239hkPkQMwecZpyJAh2LhxI7Zv3w4/Pz/MmDEDf/75JzZu3Ih+/fpZY4xERGRr06frB03nzzNoohqvWnWcagrWcSKiGuPSJaBJE3HbK68A//2vXYZDVB3W+P1t8ozTkSNHcOjQIb32Q4cO4Y8//rDIoIiIyA5eflk/aLp0iUETUTkmB05xcXG4ePGiXvvly5cRFxdnkUEREZENnTunSfL+/PN7bTNnAoIANGpkv3EROSCTk8PT0tLQuXNnvfZOnTohLS3NIoMiIiIbGTUKWLlS3Pbvv0CDBvYZD5GDM3nGycvLC9nZ2XrtmZmZqGXmuURERGRjJ09qZpnKB02ffKKZZWLQRGSUyYFT//79MW3aNBQUFOja8vPz8dZbb3FXHZGdlakFqM7nYkPKZajO56JMzb0fVIEgAIMGAZGR4vb8fCA+3i5DInImJk8R/d///R969+6NZs2a6QpepqSkICgoCN9//73FB0hE0vBEearS4cNA9+7itqVLgWeftc94iJyQWeUIbt68iVWrVuH48ePw8fFBZGQkYmNj4eHhYY0x2h3LEZCjS0zNxKSVR1HxD7O2pvOikZ0ZPDmYMrWAw+l5yLlehMA63ugWVs96B9mq1cADDwDld0T7+ABXrwK+vtZ5TyIHYI3f36zjJAEDJ3JkZWoBvebuFM00lScDoJB7Y19CH54w7yBsOju4axfQp4+47YcfgKeesuz7EDkga/z+lrRU9+uvv2LgwIHw8PDAr7/+Wmnfxx57zCIDIyJpDqfnGQ2aAEAAkFlQhMPpeVC2qG+7gZFBxmYHswqKMGnlUcvNDt65A9x3H/DXX/faQkKA9HTA07P69yeqoSQFTkOHDkVWVhYCAwMxdOhQo/1kMhnKysosNTYikiDnuvGgyZx+pGGNpbQytYDZG9P0giZAE+DKAMzemIZ+4YrqvdemTcDgweK2LVuAgQPNvycRAZAYOKnVaoP/TUT2F1jH26L9yHpLaVafHSwu1hSszM291xYRAaSkAO7upt+PiPSYVI6gtLQUffv2xdmzZ601HiIyUbewegiWe8PY/IQMml/63cLq2XJYTku7lFYxwNEupSWmZpp9b6vODq5ZA3h7i4OmPXs09ZoYNBFZjEmBk4eHB06cOGGtsRCRGdzdZJg5OBwA9IIn7fczB4czMVyCqpbSAM1Smrn1sawyO3jzJuDmBjzzzL223r2BsjLN/xKRRZlcAHPkyJFYunSpNcZCRGYaEBGMRSM7QyEX/8JVyL1ZisAEpiylmcPis4Nffw3Urq0paqn1xx+amSY3k/96JyIJTC6AeefOHSxbtgzbt29Hly5d4OfnJ7r+ySefWGxwRCTdgIhg9AtX2K42kAuydqK9dnZw0sqjkAGimS2TZgfz84G6dcVtjz8O/PST5hgVIrIakwOn1NRU3SG/f5Xf5grNrjoish93NxlLDlSDLRLttbODFZPPFVKTz+fPB6ZOFbedOgWEh5s9JiKSzuTAadeuXdYYBxE5IZtWv7YB7VJaVkGRwTwnbTHR6ibamzU7mJMDBAWJ28aNA5Ytq9ZYiMg0JgdO5V28eBEA0KRJE4sMhoichyuejWexpTSJ7yV5dvDtt4EPPxS3/f03EBZW7XEQkWlMzh68c+cOpk+fDrlcjtDQUISGhkIul+Odd95BaWmpNcZIRA7Gmlv27c2hEu0vXtTkLJUPmqZM0SSDM2gisguTZ5xeeuklrF+/HvPmzYNSqQQAqFQqzJo1C7m5uVi0aJHFB0lEjsNm1a/tyCES7WNjgbVrxW2XL2uOTSEiuzF5xmn16tVYsWIFXnjhBURGRiIyMhIvvPACli5ditWrV5s9kI8++ggymQyvvvqqrq2oqAhxcXGoX78+ateujWHDhiE7O1v0uoyMDMTExMDX1xeBgYF44403cOfOHVGf3bt3o3PnzvDy8kLLli2xYsUKs8dJVNNZe8u+o9AupQ3p2AjKFvVtFzQdOqSZZSofNL37rmaWiUETkd2ZPOPk5eWF0NBQvfawsDB4mnlw5JEjR/DVV18hMjJS1B4fH4/Nmzdj3bp1kMvlmDx5Mp544gns378fAFBWVoaYmBgoFAocOHAAmZmZGD16NDw8PPDh3ant9PR0xMTEYOLEiVi1ahV27NiB5557DsHBwYiOjjZrvEQ1WU05G88uie9eXkBJibjt6lWgPndKEjkKk2ecJk+ejPfeew/FxcW6tuLiYnzwwQeYPHmyyQO4ceMGRowYgW+++QZ1y9UlKSgowNKlS/HJJ5+gT58+6NKlC5YvX44DBw7g4MGDAIDffvsNaWlpWLlyJTp27IiBAwfivffew5dffomSu3/5LF68GGFhYfj444/Rrl07TJ48GU8++SQWLFhg8liJnFWZWoDqfC42pFyG6nyu2ZWvgZpxNl5iaiZ6zd2J2G8O4pW1KYj95iB6zd1pvdytpCTNLFP5oOmZZzSzTAyaiByKyTNOx44dw44dO9C4cWN06NABAHD8+HGUlJSgb9++eOKJJ3R9169fX+X94uLiEBMTg6ioKLz//vu69uTkZJSWliIqKkrX1rZtWzRt2hQqlQo9evSASqVC+/btEVRui250dDQmTZqEU6dOoVOnTlCpVKJ7aPuUXxKsqLi4WBQYFhYWVvkcRI7K0rvfbLVl3160ie8Vn02b+G7RBHFBMFzhOycHaNjQMu9xl6uVjiCyF5MDp4CAAAwbNkzUZm45grVr1+Lo0aM4cuSI3rWsrCx4enoiICBA1B4UFISsrCxdn6AKdU2031fVp7CwELdv34aPj4/ee8+ZMwezZ88265mIHIk1ggBbbtm3NZsmvv/4I/DUU+K2l18GPv20evc1wBVLRxDZi8mB0/Llyy3yxhcvXsQrr7yCpKQkeHs71pT+tGnTMGXKFN33hYWFrFVFTseaQUC1q187KFMS382u0F5WBtQy8FdvQQHg72/ePSth0xk0ohqgWgUwqyM5ORk5OTm641sATbL33r178cUXX2Dbtm0oKSlBfn6+aNYpOzsbCoUCAKBQKHD48GHRfbW77sr3qbgTLzs7G/7+/gZnmwBNAryXl1e1n5HInqwdBDjEln0Ls3ri+5IlwIQJ4rb33gPeece8+1WhJpSOILI1uwVOffv2xcmTJ0Vt48aNQ9u2bZGQkIAmTZrAw8MDO3bs0C0NnjlzBhkZGbr6UUqlEh988AFycnIQGBgIAEhKSoK/vz/C757bpFQqsWXLFtH7JCUl6e5B5KpssfvN1c7Gs1rie0mJZsdcRbdvA1accbfJDBpRDWPyrjpLqVOnDiIiIkRffn5+qF+/PiIiIiCXyzF+/HhMmTIFu3btQnJyMsaNGwelUokePXoAAPr374/w8HCMGjUKx48fx7Zt2/DOO+8gLi5ON2M0ceJE/P3335g6dSpOnz6NhQsX4ocffkB8fLy9Hp3IJmrC7jdL0ya+G5t7kUGTG2RS4vv8+fpB05dfahLDrZymUFNKRxDZkt1mnKRYsGAB3NzcMGzYMBQXFyM6OhoLFy7UXXd3d8emTZswadIkKJVK+Pn5YcyYMXj33Xd1fcLCwrB582bEx8fj008/RePGjbFkyRLWcCKX5+q738xV2e4yiya+37wJ1K6t315aajjHyQoYPBNZnkwQBJMKunz33Xd4+umn9XKASkpKsHbtWowePdqiA3QEhYWFkMvlKCgogL8VkjeJrEWbGAwYDgJqWmKw1N1l1d6F9uabwNy54rZVqzS1mWyoTC2g19ydVQbP+xL6MMeJXJI1fn+bHDi5u7sjMzNTl1OklZubi8DAQJSVlVlkYI6EgRM5M25F1zC2u8xYEGlq3aMytYCjx86j6/2tDFwsQxlkdkmkZ/BMNZk1fn+bPF8sCAJkMv0/7JcuXYJcLrfIoIjIclxx95upzNldZkrie2JqJkrHPovByYmi9uQvv0OXF0fZNXh11dIRRPYiOXDq1KkTZDIZZDIZ+vbti1rl1ujLysqQnp6OAQMGWGWQRFQ9rrb7zVTW3F22a+cxDOjbWa89bOpGIEOG57ek4eu96Xato8TgmchyJAdOQ4cOBQCkpKQgOjoatcslPXp6eiI0NFSvojgRkSOw1u4y4dHBeGTzJlHbkyPm4o/G9+m+/+Z3/aAJsH0dpZoePBNZiuTAaebMmQCA0NBQPP300w5X7ZuIyBiL7y47fx5o2VJUtuBf3wB0fWmlXtfKzlNmHSUi52NyjtOYMWMAaHbR5eTkQK1Wi643bdrUMiMjIrIQi5Zm6N4dqHBiwaCxnyEtqLnZ42MdJSLnYXLgdPbsWTz77LM4cOCAqF2bNO6Ku+qIyLlZpD7TyZNAZKSo6Wa79rjvsTnVHh/rKBE5D5MDp7Fjx6JWrVrYtGkTgoODDe6wIyJyNNXaXda4MXD5srjtr7/g3aIlgiupkwQAbjJNkXAWISVyDSbXcfLz80NycjLatm1rrTE5HNZxInIdJtVnOnAA6NlT3BYdDSTeKztQVZ2k53uH4eu96Uavs44SkfU4RB2n8PBwXL161SJvTkT2ZWqRR1cgaXeZIADu7pr/Le/SJaBRI1GTlJmsTk3rso4SkYswecZp586deOedd/Dhhx+iffv28PDwEF13xRkZzjiRK2JFcSO2bQMq1qQbPRr49ttKX1ZVEFoTg1Qie3OII1fc3Nw0L6yQ2+TKyeEMnMjVmHr8SI0gCMDdv99Erl4F6rNUAJEzcoilul27dlnkjYnIPsw5fsSS7+2Qsy4//AA8/bS4bcoU4OOP7TMeInJYJgdODz30kDXGQUQ2Ys3jRypjytKgzQKsO3eACukGAIDCQpT51cbh87mOF+QRkV2ZHDgBwO+//46vvvoKf//9N9atW4dGjRrh+++/R1hYGHr16mXpMRKRBVnr+JHKGFsaNHRem81yr77+GnjhBXHbhx8C06bdHcNh5n8RkR4DC/qV++mnnxAdHQ0fHx8cPXoUxcXFAICCggJ8+OGHFh8gEVmWxY8fqUJVS4OAZmmwTC3oAqyKM2LaACsxNbP6AyouBmQy/aDp9m1d0GT1MVSiTC1AdT4XG1IuQ3U+F2WVndlCRDZncuD0/vvvY/Hixfjmm29EO+p69uyJo0ePWnRwRGR52uNHjC06yaCZXbFUUUapS4MH/86VHGCZbc4coOI5m4sXaxLDvb1NCvKsITE1E73m7kTsNwfxytoUxH5zEL3m7rR6sEZE0pkcOJ05cwa9e/fWa5fL5cjPz7fEmIjIirTHjwDQC54kHz9iAqlLfqrzuZJzr0x244Zmlumtt8TtpaWimSdT8r8szd4zXUQkjcmBk0KhwLlz5/Ta9+3bh+bNzT/kkoiqZqllHG3RRoVcPPuikHtbvBSB9CU/ac9icu7V668DdeqI29au1cwy1RKnedoj/wswbTmTiOzL5OTwCRMm4JVXXsGyZcsgk8lw5coVqFQqvP7665g+fbo1xkhEsHzS9ICIYPQLV1h995p2adDYeW7a89qUzRvgi13nq7yf5EAsNxdo0EC/Xa3WzD5V496WPpTXXjsdich0JgdOb775JtRqNfr27Ytbt26hd+/e8PLywuuvv46XXnrJGmMkqvEq25U2ceVRPNszFP3CFSYHPpKOH6km7dLgpJVHIYPh89pmDg5Hjxb1JQVYknKvxo7Vr/S9dat+RfAKpAZ5lj6U114zXURkOpOX6mQyGd5++23k5eUhNTUVBw8exL///ov33nsPt2/ftsYYiWo0Kcs4y/ZfcOhEYilLgxbJvbp8WTObVD5ocnPTzDJVETQBts//0rLXTBcRmc7kI1cMKS4uxpdffol58+YhKyvLEuNyKDxyhexJdT4Xsd8clNTX0Y9MkVLY0uwlyYEDgcREcdv+/cADD5g8Tluf41emFtBr7s4qZ7r2JfRhEU4iE9j1yJXi4mLMmjULSUlJ8PT0xNSpUzF06FAsX74cb7/9Ntzd3REfH2+RQRHRPaYsz1j7yJTqkrI0aHLu1dmzQOvW4rZGjYBLl8weZ/kxZBUWIe9GMer5eULu44mSO2ok/3PNonlhUpczHe3zJKqJJAdOM2bMwFdffYWoqCgcOHAATz31FMaNG4eDBw/ik08+wVNPPQV3d3drjpWoRjJ1ecYVEokl51517gwcOyZuO34ciIy0yBgKbpdgXuJp0cyTmwwov7nNUjNR2uXMijNdClYsJ3IokgOndevW4bvvvsNjjz2G1NRUREZG4s6dOzh+/DhkRnaoEFH1VZWwbIxLJxKnpACdOonb7r8fOHLEYm9hLCG/YkUAQ8fGmMtWOx2JyHySk8MvXbqELl26AAAiIiLg5eWF+Ph4Bk1EVlZZwnJlXDaRODhYP2g6d86iQVNlCfkVWbrOkna2bUjHRlC2qM+gicjBSA6cysrK4Onpqfu+Vq1aqF27tlUGRURixnalGWLpI1OswaxCnvv2aXbMld+AEhOjKWTZooVFx1dVXaWKrFlRnIgci+SlOkEQMHbsWHh5eQEAioqKMHHiRPj5+Yn6rV+/3rIjJCIA4mWc7WlZWLr/gl4fZ0gkNnnHmiBoSgpUdPkyEBJilTGau8zp0sujRATAhBmnMWPGIDAwEHK5HHK5HCNHjkRISIjue+0XEVmPdhln+uD7sHhkZwTb4MgUSzJ2Hlvm3UKeW05UqEG1ZYt+0DRunCaYslLQBJi/zOmyy6NEpGOROk6ujnWcyFFJqYvkKO+nrVVU2RKYmwz4IrYTBkUoAEO7dHNzgXrWX4Ksqq5SRayzROSY7FrHiYgcjy2OTNGqblFIKXlDagFIfOe/GLRxvvjC1KnA3LlmjdscldVVqsgZlkeJyHIYOBFRlSo7K0/qVvyq8n/c1WU4P3+I/oXr1wE7bEQxVlepYh0n1lkiqlkYOBHVYFUtvZWpBRw8n4s3fzpp9Kw8qZXKK8v/GXlsC97/baGo7cIbMxA6b7aJT2RZhuoqdWlW1+KVw4nIeTBwIqqhDC29Bfh4YFzPMEzu0xJJaVl61w2RWqlcW8iz/P287pTgzMdP6PVt/drPeL5vO7xu+mNZnKHlUGetyE5E1cfAiagGMrb0ln+7FAu2/4Wv9p7HrZIyk+5Z5VLc3byhiSuPAgAmH1iL139fKerzZvRkrO044O53+nNctk6Gt4ea8IxEzoyBE1ENI6UqtqlBEwA0qO1VZZ8BEcF4QxmMuKFd9K41f2MD1G73dtIpmzcQXa9ucrozqAnPSOTsJNdxIiLXYGpVbMmk7NuPj9cLmiYNeROhCZtEQVOArwd6lFsOM1b/SZucnphaof6TE6oJz0jkCjjjRFTDWKu69dWbxZVcvAo0bKjXHDp1o+YYlQo+eqK9bnmqshkyU5LTHVlNeEYiV2HXGadFixYhMjIS/v7+8Pf3h1KpxNatW3XXi4qKEBcXh/r166N27doYNmwYsrOzRffIyMhATEwMfH19ERgYiDfeeAN37twR9dm9ezc6d+4MLy8vtGzZEitWrLDF4xE5JGtVtzZ631Gj9IOm335D4skremfvKfy9sLhCaYOqZshc4Zy4mvCMRK7CrjNOjRs3xkcffYRWrVpBEAR8++23GDJkCI4dO4b77rsP8fHx2Lx5M9atWwe5XI7JkyfjiSeewP79+wFoDh6OiYmBQqHAgQMHkJmZidGjR8PDwwMffvghACA9PR0xMTGYOHEiVq1ahR07duC5555DcHAwoqOj7fn4RHpskRjcLaweFP7eyCq0zMyTtmq23qHCly4BTZqI2zw9gWLNzNQAQG+rv6HnlTpD5sznxNWEZyRyFXYNnAYPHiz6/oMPPsCiRYtw8OBBNG7cGEuXLsXq1avRp08fAMDy5cvRrl07HDx4ED169MBvv/2GtLQ0bN++HUFBQejYsSPee+89JCQkYNasWfD09MTixYsRFhaGjz/+GADQrl077Nu3DwsWLDAaOBUXF6O4+N6yQ2FhoZV+AkT32CoxOCktC0V3TE/+NsRo1ex+/YDt28WdVSqgRw9Rk5TK51JnyJz5nLia8IxErsJhksPLysqwdu1a3Lx5E0qlEsnJySgtLUVUVJSuT9u2bdG0aVOoVCoAgEqlQvv27REUFKTrEx0djcLCQpw6dUrXp/w9tH209zBkzpw5ooOLm1T8VzORhdkqMVj7Pvm3SiX19/MUnxdXcfJL71Dhv/7S5CyVD5qaNdMcylshaDKkTC1AdT4XG1IuQ3U+F2VqQVf/ydi8mwyaAFNvxsuM97IXaz0jEVme3ZPDT548CaVSiaKiItSuXRs///wzwsPDkZKSAk9PTwQEBIj6BwUFISsrCwCQlZUlCpq017XXKutTWFiI27dvw8fHR29M06ZNw5QpU3TfFxYWMngiq7FVYrCUMgQV1fGuha9H34+rN4qrrprdvj2Qmiq+wcmTQESEpPeqbMbN2Llx5p4T52jb/is7G49n4RE5FrvPOLVp0wYpKSk4dOgQJk2ahDFjxiAtLc2uY/Ly8tIlrGu/iKzFVonB5pQhyCoshptMhiEdG0HZoj48a7lB2aK+7nt3Nxlw7Jhmlql80NS9u2aWqYqgSTvr8+7GU5hYyYwbACwa2Vk/mVzujVejWqP4jlryrJGjbvvXno1n6BmlnAVIRLZh9xknT09PtGzZEgDQpUsXHDlyBJ9++imefvpplJSUID8/XzTrlJ2dDYVCAQBQKBQ4fPiw6H7aXXfl+1TciZednQ1/f3+Ds01EtmaJxGApSeXmJhZX+rqGDTWlBsr7+28gLKzK8Uk50kUbBr25/iS+jO2MPW88opvxunD1JlYfysCC7X/p+iv8vTHrMeOzRo6+7d/Q2XisHE7kWOweOFWkVqtRXFyMLl26wMPDAzt27MCwYcMAAGfOnEFGRgaUSiUAQKlU4oMPPkBOTg4CAwMBAElJSfD390d4eLiuz5YtW0TvkZSUpLsHkb1VNzFY6rKTuYnFBl+3dy/w0EPitiFDgF9+kTS+AF8PyXlWAJB/qxQjlh7SPZdXLTcs2H5Wr19WYREmrjyK+KjWCG3gqxd4mDK71y2snl0CGCkJ80RkP3YNnKZNm4aBAweiadOmuH79OlavXo3du3dj27ZtkMvlGD9+PKZMmYJ69erB398fL730EpRKJXrcTTLt378/wsPDMWrUKMybNw9ZWVl45513EBcXBy8vzfEPEydOxBdffIGpU6fi2Wefxc6dO/HDDz9g8+bN9nx0Ih1tYnBWQZHBmRCj2/1h/Mw57bJT+SWeqt5H0vsKAuBmYIU/MxO4O8srZXymBE3lZRVoAqOKSesVlZ+FKh9ESp11256WhSk/pDhMDhQROQ675jjl5ORg9OjRaNOmDfr27YsjR45g27Zt6NevHwBgwYIFePTRRzFs2DD07t0bCoUC69ev173e3d0dmzZtgru7O5RKJUaOHInRo0fj3Xff1fUJCwvD5s2bkZSUhA4dOuDjjz/GkiVLWMOJHIY2MRiA3q6qyhKDq1p2AjTLTtq8n8repyKD77tpk37QNGGCJpgyEDSZk4xeFe29bppwll753CWps25L919wuBwoInIMMkEQ7LcH10kUFhZCLpejoKCAieJkNabu9FKdz0XsNwervO+aCT1ESz+G3sdNBpTPqxa9r1oNuBuY4cnLA+rWNfq+UsdnC9rZsz1vPIKH5u+qdHZPVuFnYeg++xL6MO+IyAlY4/e3w+U4EdVUpiYGm5tUbuh9jJYZWLUKGDlSfMNp04C7lflNeV970uYuJf9zrdJt/wI0E2hV3edweh7zkIhqKAZORA7ElMTg6iSVG3of0felpYC7p/7NbtwA/PwsOj5byrlehEcjQ/BqVGss35+O/Nv3cq0Ucm8MjFBg2f4Lku5DRDWT3es4EZF5rFZt+osvNGfKlZMaPx2qc1dR5uNr8vgsTYaqc7SMuXD1JnrN3YkF2//SBU0BPh6Ij2qFfQl90C9cP1fLEEcMConINhg4ETkpc5PKjbp9W5Pg89JLouZWr/+MRz27I/abg+g1d6fk5Gh3Nxke62DZHWjaJ3m+d1il/Qy9rq6vBxZsP6uX9F1wuxT/3X4WSWlZPPqEiKrEwInIiVms2vS77wK+4tmkqQNfRmjCJpS6e+jatDvLtpzIrPKctzK1gF+PW3YHmva5pg0Kx+KRnVHX16PqF+Fu7lIl1wDNDkQAlg1GicjlcFedBNxVR45OSuVwgwoLAblcr7nn+9tw+brxWkuV7sK7y5xddRXvq/D3Qmy3pght4GfwuX5KvoTX1h2v8r4DIoKQmJpdZT/tDkRHO8uOiMzDXXVEZJBZ1aZffhn4/HNx208/QdXhIVyuIuCpOMGUebcw5cJnOmNQpCawMCeBWi0A02PaoUEdL0kBYP6tEkn39a5VecFMLe2YefQJERnDwImopsnJAYKC9NvVakAmQ07KZbNvPXnNUXyBThgUGWJ2AvWV/NsY/2BzSX3r+RnY+WdASIDpOxB59AkRGcIcJ6KaJDZWP2javl1TvEimmU2pzo4xtQC8uPoYElMzq0y0Nmbp/guSE9AVcmkHdfds0ZBJ30RkEQyciAwoUwtVJj87lYwMTWC0du29Nh8fTcDUt6+o67WbxajuilRVidZSXi/lZy6l5EGw3Bs9WtRn0jcRWQQDJ6IKElMz0WvuTsR+cxCvrE0xeRu+w+nTB2jWTNx26BBw65Ze18TUTMStPmb0yBGpMguKsGJ/OorvqBETGaydzDL59VUFT9qSDJXNJGkDIovtQCSiGo276iTgrrqaIzE1E5NWHtXbuq79xexUv2BPnwbatRO3tWgBnDtnsHuZWkCvuTv16hzZk9SdbKbsgjN7ByIROR1r/P5m4CQBA6eaoarAwakOeG3XThM4lXfqFBAebrB7mVrAiv3peG/znzYYnHSmBKwMiIioIpYjIKqmyn65Hk7Pq3S2xSkOeE1OBu6/X9zWqxfw++9GX2JotqYy4x5ohm9V/1R7OU8KAZrgafbGNPQLV1QaCHEXHBHZAgMnqjGqWs6RWnfIYQ94DQgACgrEbenpQGio0ZcYW5qsTFS4Al1D6+HF1cfMGaXJnCJgJaIag8nhVCNoA4SKsyraI0QSUzMlb8N3uANed+/W7JgrHzQNG6bZMVdJ0FSmFjB7Y5pJQRMAQAAGRYbg2Z7G720NDhuwElGNwhknckqm5LNUFiCUXwra88YjCJZ7I6ugyGBfbY6Tw9T6EQTAzcC/fbKy9Go1Gfp5VbU0aczVm8UAgH7hCizbf8GckZvF4QJWIqqRGDiR0zH1HDGpuUvJ/1zDzMHhmLTyKGQQHwortdaPNkDJKixC3o1i1PPzhELuIzlRWXJA+OuvwJAh4raJE4FFi/S6Gvt5DYpQVDkeQ7QBjLaGkrFA01IcLmAlohqNgRM5FWM5OdolN0O7r0zJXRrSsREWjeysF2goJGyLryzJWsq2ekkBoVoNuOufu7Z57ynUCwlCN7UgCrSM/bwyC4qw1MTZoooBjLaGkqFAsyrBcm881iEYvx7PrDSoZXFKInI0LEcgAcsROAZzywWozucitopDawFgzYQeuuRjU7e2S0mylsH4tnpJ9aOOJgFjxoiuL3tkJN7tNlz3fflAq0wtoOdHO5FVaLncoPKH+JYfe8WAz00mPghY4e+F2G5NEdrAT/TzLP9zvnD1JtYczkBWYbHB5yEiMhXLEVCNZm65gKqWlAwtBZmytV1qkrUAw9vqq8rB8ii7gwHtQ/SutZvyI257iPN+ys+8ncm6btGgCQDe+vkkzubcwOQ+LXXPMCAiGP3CFaJAs0uzukj+51qVgWfFn/PkPq1Yi4mIHBoDJ3Ia5pYLqGxJyRJLQaYkWRsK7Cp7/bNHNmDGzm9EbepPPkHPokjcNvAabbL7tPUnce1WqeRnkCr/dikWbP8Lyw+k46Mn2utmggwFmuaUDmAtJiJydCxHQE6jOuUCrHlOmanb5Cv2N/R6r9JiXJj7qF7QhJISHHpsdJUzb9YImsrLv1WKiXfLOBAR1SSccSKnYc6SW3mGlpQssRRk6jb5iv0rfh//+yq8cmCNqO21QfF48rO3ofTwcKh6RlIqehMRuRIGTuQ0LLHkZo2lIFO25QffDezKJ0U38POCwt8bN//Nxcn/Pq33mrCpv0IR4It5dwNCR6pnxIreRFTTMHAip6JdcjOnXIC1lA/oKiODJrBLSsvSG/+HOxbjmT82ifpPeOIdJLXqAQB4rEOwLiC0Vf0kqRxpBoyIyNpYjkACliNwPKaWC7AFKXWcAIjKDjS4eQ1/fDFKr3/o1I2aY1TuquvrgT/e6ad7Rm35AsDwzJvc1wMFt0ptEljFR7XCK1GtbfBORESmscbvbwZOEjBwIqkqqxwOQFSHauHPH2LQXwdEr48d/iFUzSIN3nvVc93Rs2UD3feVFcwEYDCwqsywzo2w7+xVZF8vrrpzBYurmWBPRGQNDJzspKYGTo44q+PMtIU4GxXkYP/iZ0XXrnv6oH38ukpfP/mRlng9uo2orbLPqLIZMGPKF6q8cPUmlu1PR8HtO5W+xljhUSIie2MBTLIZU8+Dc1SOFPzlXC/C/1YloPulU6L2waMX4GRwKwl3uPdvnIrP9WhkiN5zld9FuD0tS9IRK9mFxfjv9rNYNLIzXolqjcl9WiHhxxP48eilSkfFJHEiqikYOJEec86Dc0QOFfylpWFIp/tETefrNUbfCYsl30Lu44EytWAwudzYc2l3ESpb1EfXsHqY9esp0ZEmFWk/8/JlBh5s3aDSwEmLSeJEVBOwACaJVHX8B6D5pVqmduwVXm3wV3GZShv82bRwY+vWwH3ioKnvc4tMCpoA4IMtp9Hl/SRMNPO5BkQEY/+bfTE9pl2V75VZUIQvdp4FUL3Co0REroaBE4mYch6co3KY4O/IEc3OuLNndU0XIu5HaMIm/F2/iVm3zDdSEVzqc7m7ydCgjpek91qw/SwSUzN15Q+MLXDKcK8+FRGRq2PgRCLmngfnSBwi+KtdG+jWTdT0wKRleDhmFgBRpQEAgCXSrqQ8V5lawFUTds3N3pgGALqdehWHaYmz/oiInAkDJxJxhWUZuwZ/O3dqoqKbN3VNm9o+iNCETbjiH6hr004KjXsgFNNj2sGSk1/GnisxNRO95u7Ee5v/lHwvbSBmzbP+iIicCZPDSaS658E5AmsGf0Z36QkC4Kb/75BBb61DWpmP0ft9q7qAMcpmJo+jMoaey1jCvxTaQMxaZ/0RETkTBk4kYonz4OzNWsGfsV16X/r+g86vjhd3njwZqldnIe2bg5XeUy0Ayw/8Y9I4jDH2XJXlfElRPhCzxll/RETOhEt1pMfZl2W0wR9guZwcQ7v03NRlUL0VpR805ecDn39u0lJgdePQyp6rqpyvyu7JpG8iIjG7Bk5z5sxB165dUadOHQQGBmLo0KE4c+aMqE9RURHi4uJQv3591K5dG8OGDUN2draoT0ZGBmJiYuDr64vAwEC88cYbuHNHXO149+7d6Ny5M7y8vNCyZUusWLHC2o/n1AZEBGNfQh+smdADnw7viDUTemBfQh+HD5q0pAZ/ZWoBqvO52JByGarzuQZ3pBmasYn+6wD+nj9E1E89Y4ZmyU4uBwA0qC1t9xoAk3OcAnw9RN9XFtSak8vlLLOLRES2Zteluj179iAuLg5du3bFnTt38NZbb6F///5IS0uDn58fACA+Ph6bN2/GunXrIJfLMXnyZDzxxBPYv38/AKCsrAwxMTFQKBQ4cOAAMjMzMXr0aHh4eODDDz8EAKSnpyMmJgYTJ07EqlWrsGPHDjz33HMIDg5GdHS03Z7f0Tn7skxVOTlSC2SWn7FxV5fht6UvokXeZdF7tZnyE1aMfgjK8o1WqnYQH9Uak/u0lJxrZE4ul8IJq8QTEdmCQ51V9++//yIwMBB79uxB7969UVBQgIYNG2L16tV48sknAQCnT59Gu3btoFKp0KNHD2zduhWPPvoorly5gqCgIADA4sWLkZCQgH///Reenp5ISEjA5s2bkZqaqnuv4cOHIz8/H4mJiVWOq6aeVefKjCVLa0OP8rM3G1Iu45W1Kehz7jCW/fSuqP+MqBfwXZfBAIBPh3fEo5EhuoDmbPYNfLHrnEXHrfD3wv43+5o0C1SmFtBr7s5Kc76C/L3w8X864uqNYiZ9E5HLcPmz6goKCgAA9eppciqSk5NRWlqKqKgoXZ+2bduiadOmusBJpVKhffv2uqAJAKKjozFp0iScOnUKnTp1gkqlEt1D2+fVV181OI7i4mIUF9+rdVNYWGipRyQHUFWBTBnER44EecqQ/NkzqH/73v8P/mwYipixn0Lt5q5ru3D1JnrN3WlWPpFUsx67z+SARkrC/6zH7kPPlg0sNUwiIpflMMnharUar776Knr27ImIiAgAQFZWFjw9PREQECDqGxQUhKysLF2f8kGT9rr2WmV9CgsLcfv2bb2xzJkzB3K5XPfVpIl5VZ7JMZlUIHPNGvS4r5EoaPrPMx9h4LNf6IImGYC6vh5YsP2sVYOmh1o3NHvpzNkT/omIHIXDzDjFxcUhNTUV+/bts/dQMG3aNEyZMkX3fWFhIYMnFyIlWdqnpAg9WgcCarWu7VCTCMTGfgi17N6/N7QzNrZY7+5lxoxQxbpTe954BMn/XGMdJiIiMzlE4DR58mRs2rQJe/fuRePGjXXtCoUCJSUlyM/PF806ZWdnQ6FQ6PocPnxYdD/trrvyfSruxMvOzoa/vz98fPSLE3p5ecHLS/qOKGdjtIhjDVFVsnRsSiLmbPtC3PjHH7jmFYKgCsnkCrk3hndtigXb/7LGUEXaBtUxqX9lye9DOjay9PCIiGoEuwZOgiDgpZdews8//4zdu3cjLCxMdL1Lly7w8PDAjh07MGzYMADAmTNnkJGRAaVSs39JqVTigw8+QE5ODgIDNUdaJCUlwd/fH+Hh4bo+W7ZsEd07KSlJd4+aROpOMldVphagVgsI8PFA/m3xgbn+RTdw4tPh4hc8/jjw00+ATIYBgN4uvS7N6uKzHWchxdCOIfD38UBm/m0k/Zlj8tjzbpdI7mss+T2roAiTVh7l8hwRkZnsuqvuxRdfxOrVq7Fhwwa0adNG1y6Xy3UzQZMmTcKWLVuwYsUK+Pv746WXXgIAHDhwAICmHEHHjh0REhKCefPmISsrC6NGjcJzzz0nKkcQERGBuLg4PPvss9i5cydefvllbN68WVI5AlfZVWfKTjJXZCho1Hr+0E94a/dyceOpU8Dd4LuiMrWAL3aew7L96SioEIBZy5oJPSSVh9DuojOWb6WtML4voU+NmmkkoprH5XbVLVq0CADw8MMPi9qXL1+OsWPHAgAWLFgANzc3DBs2DMXFxYiOjsbChQt1fd3d3bFp0yZMmjQJSqUSfn5+GDNmDN5999628bCwMGzevBnx8fH49NNP0bhxYyxZsqRG1XAydSeZo7DUsqKxoLH+zXwkfzFS1Pa/9v3w39gE7GvbDu4V+msCprP4au/fuFVSZvI4zGHqETGmJL87c50uIiJ7sPtSXVW8vb3x5Zdf4ssvvzTap1mzZnpLcRU9/PDDOHbsmMljdGblg46r14ud7peppZYVjQWNr+39Hi+p/idq6/XCElwKUAAFRfhi51m8EtVaNJ43159E/i3bzDAB5lXwllop3JyK4kRENZ1DJIeT5VW2LFWZ/eeumj2rY8mkc0vm6FScgQku/BeqReNEfb7pOhQf9HlO1LZg+1m0UdTBgIhgo+OxNnMqeEutFG5ORXEiopqOgZMLqs4v+S92ncNPRy+Z/Mvakknnll5W3J6Wpfvvd39bhNHHNouud3vxW+TUMTzLNntjGvq0DTI6nsrc36wu/vjnmomv0gjw8cCXIzqjR/P6Jgef3cLqIVjuXWmlcFOW/oiI6B6HKYBJllFZ0CGVdlYnMTVTUn9toFZxdsvU+2iZVKBSwtiW7r+A0LzLuDD3UVHQ9HGvEQhN2GQ0aMLd9/ledcGswpZetcz/45V/uxRuMplZM3baSuHAvaU+LR7eS0RUPQycXExVQYcU2qBr9sY0lKkrD8Gqmh0y5T6q87nYkHIZ+89dlTTOqnJ0tGP79Nf52P3NC6JrHV9ejc97xkp6n3/ybknqV9H+87moTmxSnRwkVgonIrIOLtW5GEsl/EpNFrfEDi5z87GqytFJ3fo7VG+Jzyic1fd5rLj/MZPep1k9X5P6l1dFvFip6uYgDYgI1qs7VdOKnRIRWRoDJxcj9Zft0I4h+CXlSpX99p+7Wukv3eru4DInH6uyHJ0ytYDDf+ei+Zgn0eHAHtG1iFd/wA0v6UGQ9n1GKUOxZF+60ZwhKdxk4iCq4veG3tcSOUjubjKH2SVJROQKGDi5GKmJwU91aSIpcPpi1zndfxtK9q7ODq7q5GMZytFJTM3Ej1/+iCWLXxa1vzYoHj+172vS/WXQzJYNjFAg+Z9rmB4TjrjVR80YqYZaAKbHtEODOl4IrOONazeLEbdaUx6j/PMzB4mIyLExx8nFSE0M7tGiPoLl3np9KmMo2VsbqBm7jwyagMvQ7Im5+VivRrXWy9FJPHEZwf0fEgVNNz280WbKTyYHTQAgu/tAy/ZfQOw3B/He5jTERFYvL6hBHS8M6dgIyhb1MSgyhDlIREROiDNOLkibGFwxb6hiTaCZg8MxaeVR3exKVQyVAtAGaobuU9Xsibn5WKENxMttZdt3YEA/cS7TxKHTkNimp1n3B/SX0bIKirDphGm7AyuqOOvGHCQiIufDwMlFSfmlbCzAqoyhZG+pgVpF5iY/61535w7Qti3cz5/XXbtcpyEefuFrlLp7mHVvY6pT3qGynCXmIBERORcGTi5Myi/ligHW2ezr+GLX+UpfA+jPFpkze9ItrB4CfD0kH2EiCkB+/RUYMkR0ffRTs7G3eRdJ97IV5iwREbkWBk4kCrBU53MlBU62Pq5DG3LM7t8c7g3qA9fuVeS+2a492j/6PtRuFY/kte54DM1CyX1qoeD2Hd335hyZQkREjouBE4mYe1yHOUeuHE7PkzzbpJB7YzH+RIf7HxVf2LcP3soHEDR3Z7ULf/Zu1QB7z1ZdfPPVvq3wvz8uGnxW5iwREbk2Bk4kYk6yt7kH8kpNDv9P2wDMG9dL3PjII8COHYBMBnfcS3SvTi6S1CNSuobWw0t9WxkNkJizRETkuliOoAYof5yJ6nxulcefmHJcR3WOXJGy3Dfi2Bb9oOnoUWDnzns1A8qNOcDX/KRwPy9p/464erNYt7ypLS/AWSUiopqBM04uzpwlNEB6srcpR650C6snul/HJgGo5+eJvJsleq/zL7qBE58OF7Vtaf0A8MM61K3thZyUy3pj0o75i51nsXz/BeTflrYMqNUuuA5+Sam6n63zu4iIyHEwcHJh5i6haUnZlSd1uW17Wham/JAiCrKMHTsy8eCPeHPPClFb3+cW4Xz9JpCtPQah3GsqBoHubjK8EtUak/u0MnmnYGAdb7Pyu4iIqObgUp2Lqs4SminvcfV6saS+S/df0JuZqvjWDW5ew4W5j4qCpjWR/RGasAnn6zcBAFHQBBiuZg5AtJTWs2VDSWNUyH0kVV3nshwRUc3FGScXZcoSmjnJzIaWAI2RUpl86p4VePHgj6K2XhOX4pI8qNLXGapmXpEpOwXd3WRmFfMkIqKagYGTi5K6hGbOsSfGlgCNqaxfSGEODix6VtS2uPswfPTwOMnjqSoINHWnII9CISIiYxg4uZAytaD7ZS91Cc3UROfKlgBN9cG2LzAiJVHU1jXue/xbu65Z96ssCDT1WBgehUJERIYwcHIRhpbOjCVfA+YnOle1BChFWN5l7PrmBVHb/AdH4csHnq7WfasKAgdEBKNP2yB8r7qAf/JuoVk9X4xShsJTYv0mIiIiBk4uwNjSWWVBE2BeorM5S3vlfb5hLgaf/l3U1uHlNSjwqVOt+wbfDQLLz7pVXGIzFFwu2ZfO3CUiIpKMgZOTk7J0VnHmqTqJzubWMGqX8ze2Ln9Z1DYj6gV812WwWferaObgcCSlZRmtWQWgWqUZiIiIAAZOTk/K0plaAKbHtEODOl7VTnSuaoeaHkHA9/+bjgf/SRE13/fqD7jp5WvWGCp6snMjAMYDo4krjyLA18NoaYaqduURERFpMbnDiRg6OkXq0lmDOl4WOR5Eu0MNMFzrSAYgwNcDMgCdL/2JC/MGi4KmKTHxCE3YZLGgSQbgvaHtq6xZVdlhwuV35REREVWGM05OwtjRKcO7NpH0ekseE1LVDjWUlaFR9MNon32vWnehlx+6Tv4exbU8LTYOAHi+dxhSLuZXO2EdqH7+FhERuT4GTk6gsqNTFmw/iwBfDxTcKrXpMSFGax3t3AH06yfq+/zjb+O31koEy70xMEKBZfsvVPv93WTAhAfDMG1QODakXK72/QCeQUdERFVj4OTgqjo6pfxymZTijpYkqnVUWgq0bAGkp+uuX5QH4ZEJX6F2bR/E9wzVnR8nJXDy83LHzeIy3fdBdTzxYKuG8PWqpVdGoLoBD8+gIyIiqRg4OTgpR6fk3ypFfFRrrD2SYdFjQirb2i/yyy/A44+Lmkb+5z3sC+sEACi4XYr/bj+LNoo66NM2qNL6UlpzhkSgodxHUuVuKUeqyO/OygG2DS6JiMi1MHBycFLzbkIb+GJfQh+LHRNiLKdKFIgVFQFBQUBhoa7PCUVLDB31MdRu7rq28jvX6nh7VBk0AcCszWk48nY/SeOXcqTKR0+0B+6OgWfQERGRuRg4OTipy1CBdbwtdkxIZTlVuppHx7YDo0eLrj8xYj6ONm5n8J7anWuq87mSxpB3s9SkA4ilHqnCM+iIiKg6GDg5OCnLUJbMz6kqp6p28S0MaB8iat8b2gmj//MuIJMSgEg/5S7nepH05UJIO5yXZ9AREVF1MHBycFKWoSyZn1NZTtWoo5vwXtJiUdugsZ8hLai55PsrmzfA6sMXkXezpMq+F67eRK+5OytfLqyAgREREVkTC2A6Ae0ylEIuXraT+3rg1ajW6BeusNh7Gcqpkt++jgtzHxUFTRvbPojQhE2SgyYZNEFPjxb18f6QiCr71/X1wILtZ/WCOO1yYWJqpqT3JSIisiQGTg7IUIXwARHB2JfQB/FRrRDg4wFAs5tuwfa/0GvuTosFEhVzql5U/YDjn8WK2vo8txgvDUmQfM+KM2ODIoPxQu+wSvsbW9DTts/emIYyKVnmREREFsSlOgdT2W42APjv9rNWPahWm1N153Imjnw5SnRtVccBeDt6ssn3NLRzbdqgcHRoHIB3NqQi7+a941A01dCbYsH2v4zer/wRKVyWIyIiW2Lg5EAq281mjYNqjSVerzr7E5ovXyTq23PiMlyRB0p+FimHCg+KDEF0RLDeGDaduCLpPXhEChER2RoDJwdR1W42QPpBtdpZmJI7anyvuoB/8m7pVds2NLPVqSwfP//fSJTPWlrY40nMe2gsAM1s0PSYcLy3Oc3oLj9AcxxKsNwbgyJDjPS4x1AytyklGIiIiGzJrjlOe/fuxeDBgxESEgKZTIZffvlFdF0QBMyYMQPBwcHw8fFBVFQUzp49K+qTl5eHESNGwN/fHwEBARg/fjxu3Lgh6nPixAk8+OCD8Pb2RpMmTTBv3jxrP5rJqqoQLpV2FmbOljS0nb4V723+E9+p/sF7m/9E2+lbMWdLGracyMTElUdF7zdn62f4+f9Giu416M3/ofS9D/Dp8I5YM6EH9iX0waDIYN2yoTFqAXhx9TFsOWFe3pV2udDYvJk20ZxHpBARka3ZNXC6efMmOnTogC+//NLg9Xnz5uGzzz7D4sWLcejQIfj5+SE6OhpFRfd+4Y8YMQKnTp1CUlISNm3ahL179+L555/XXS8sLET//v3RrFkzJCcnY/78+Zg1axa+/vprqz+fKSy17BRYxxtztqThq73pehW61QLw1d50vLj6qK6tRe5FXJj7KGJP/KZr++ihsQhN2IQ/BT/8d/tZeNVyg7JFfd1y24CIYHz5TGdUtSI4ec1RbJG47FaetgQDAL3giUekEBGRPckEQXCIrUkymQw///wzhg4dCkAz2xQSEoLXXnsNr7/+OgCgoKAAQUFBWLFiBYYPH44///wT4eHhOHLkCO6//34AQGJiIgYNGoRLly4hJCQEixYtwttvv42srCx4enoCAN5880388ssvOH36tMGxFBcXo7i4WPd9YWEhmjRpgoKCAvj7+1vl+VXncxH7zUGzX68thLnztYdx38zEqo81EQQs/GUOBv11QNQc+cpaFHrX1rvvvoQ+okDl0+1/YcF28eyfMYvNTFqXdOwLERGREYWFhZDL5Rb9/e2w5QjS09ORlZWFqKgoXZtcLkf37t2hUqkAACqVCgEBAbqgCQCioqLg5uaGQ4cO6fr07t1bFzQBQHR0NM6cOYNr164ZfO85c+ZALpfrvpo0aWKNRxSpankKAHw9Nee/VTYLs/rQP1UGTfdln8eFeYNFQdM7/V9EaMImUdAEiHOntBJTMyUHTYD5pQO0JRjWTOghWi5k0ERERPbisIFTVlYWACAoKEjUHhQUpLuWlZWFwEDxTq9atWqhXr16oj6G7lH+PSqaNm0aCgoKdF8XL16s/gNVobLlKa1bJWWa6xU6KOTeulIEv5/91/ibCAJWr3kLm1e8ImoOj1+HlZ0GVTo+7VKiNondFBUDL1Nok8eHdGwkWi4kIiKyB+6qM8DLywteXl42f19jB9VWpJ28Gd8zFFHhCt12/8TUTOz+66rB13S5lIafVk0Vtb3y6GvYcN8jksZ24epNAOYnsbN0ABERuQKHDZwUCs0xItnZ2QgOvrc0k52djY4dO+r65OTkiF53584d5OXl6V6vUCiQnZ0t6qP9XtvHXgzVUdIeVHvw71y8uOooCm4bLkEgA7AlNQtvxWiSpI3NBLmpy7Dp21cRnpOua7vmXQc94r5FcS1Pvf7GLNh+Fm0UdVB8R23ycwIsHUBERK7BYZfqwsLCoFAosGPHDl1bYWEhDh06BKVSCQBQKpXIz89HcnKyrs/OnTuhVqvRvXt3XZ+9e/eitPReAJKUlIQ2bdqgbt26NnoafYmpmeg1dydivzmIV9amIPabg7qjU9zdZPjjQp7RoAnQzz0yNBPU++9k/D1/iChoeu6J6ej0yhqTgiat2RvT0KC2aTNxLB1ARESuxK4zTjdu3MC5c+d036enpyMlJQX16tVD06ZN8eqrr+L9999Hq1atEBYWhunTpyMkJES3865du3YYMGAAJkyYgMWLF6O0tBSTJ0/G8OHDERKiKb74zDPPYPbs2Rg/fjwSEhKQmpqKTz/9FAsWLLDHIwOovEL4pJVH8XzvMHy1N93gayvSLoGVXwqrVXYHe76agEbX7+U7pdcNRr/xi3DH3fyPXBOo5SJY7l1pAUwtlg4gIiJXY9fA6Y8//sAjj9zLsZkyZQoAYMyYMVixYgWmTp2Kmzdv4vnnn0d+fj569eqFxMREeHvfW/ZZtWoVJk+ejL59+8LNzQ3Dhg3DZ599prsul8vx22+/IS4uDl26dEGDBg0wY8YMUa0nW5JSIfyb36UFTcC9JTDt/0afOYCvfvlQ1OeZp9/HgdCOZoxW36c7zuGF3mH4em96pYfxAobPqCMiInJmDlPHyZFZsg5Edes1lRdcrr5S2c1bKK5XH74l92aeUoJb4fFRH0OQWXZFtvzRK+WXBxX+Xojt1hShDfwqPaOOiIjIFqxRx8lhk8NdlSV3l+mWwL79Fu5jx8K33LXHR/4fjjVqa7H3Ki+zoAh1/TyxL6GPwUOCiYiIXBUDJxuz1O6yJzs3Qll+ASATH6T7b8+H0a/fm8i/fUfSfbSVwafHhOOtX05WepBweTnXiwwe0EtEROTKHHZXnauSUiHcTWa8CCagueb3zWLEPNhOfOH4cTTctwvJ0/sjPqoVAnw8Kh1L+eTtQZHBSH6nH57s3FjCU7C8ABER1UwMnGysqgNsZQAmPBhm8DoABNwuRPrcRzF7+1e6tg3tHkJowiZsQUPde7wS1RrJ0/thzYQeWPB0RzzZuRHk3uIJxvIVx7Wvm/tkJBT+xksOsLwAERHVZEwOl8AayWVVHWBr6PrLB9Zgyu+rRPd5eMJXuFCvEQDNTNUXsZ0wKFK8fKdlqOCmoZwkbbkEQLxrTttzkZmH9hIREdmSNX5/M3CSwBo/eKDqQEZ7vfD8BURH3y967bedYzCz3ySD911sgcCmqsCOiIjI0TFwshNrBU6SvP468PHHoiblpOXI9G9o9CXlyxRUh9QZKiIiIkfEcgQ1SXo60Ly5qOkL5X/wf71HV/lS7VEs1d3xxl1zREREYkwOd0Tjx+sFTWWZWVg1WHq1c0vWiyIiIiINBk6O5M8/AZkMWLbsXtvcuYAgwF0RpNuNJwXLBRAREVkeAydHIAjA448D4RUCo2vXgKlTdd8OiAjGwmc6o7I0I5YLICIish4GTvaWnAy4uQG//HKv7auvNMFUQIBe90GRwfgitpPBW5UvaMkkbiIiIstjcrg9lZYC95crM+DuDhQUAH5+lb5sUGQIFrvJ9MoFKFgugIiIyKoYONlTrVpAnz7Azp3A6tVAbKzklw6ICEa/cAXLBRAREdkQAyd7ksmAHTvMfjnLBRAREdkWc5yIiIiIJGLgRERERCQRAyciIiIiiRg4EREREUnEwImIiIhIIgZORERERBIxcCIiIiKSiIETERERkUQMnIiIiIgkYuBEREREJBEDJyIiIiKJGDgRERERScTAiYiIiEgiBk5EREREEtWy9wCcgSAIAIDCwkI7j4SIiIik0v7e1v4etwQGThJcv34dANCkSRM7j4SIiIhMdf36dcjlcovcSyZYMgxzUWq1GleuXEGdOnUgk8nsPZwap7CwEE2aNMHFixfh7+9v7+HUePw8HAc/C8fBz8KxaD+PjIwMyGQyhISEwM3NMtlJnHGSwM3NDY0bN7b3MGo8f39//oXkQPh5OA5+Fo6Dn4VjkcvlFv88mBxOREREJBEDJyIiIiKJGDiRw/Py8sLMmTPh5eVl76EQ+Hk4En4WjoOfhWOx5ufB5HAiIiIiiTjjRERERCQRAyciIiIiiRg4EREREUnEwImIiIhIIgZO5DBmzZoFmUwm+mrbtq3uelFREeLi4lC/fn3Url0bw4YNQ3Z2th1H7Dr27t2LwYMHIyQkBDKZDL/88ovouiAImDFjBoKDg+Hj44OoqCicPXtW1CcvLw8jRoyAv78/AgICMH78eNy4ccOGT+Eaqvosxo4dq/fnZMCAAaI+/CwsY86cOejatSvq1KmDwMBADB06FGfOnBH1kfL3UkZGBmJiYuDr64vAwEC88cYbuHPnji0fxSVI+TwefvhhvT8fEydOFPWp7ufBwIkcyn333YfMzEzd1759+3TX4uPjsXHjRqxbtw579uzBlStX8MQTT9hxtK7j5s2b6NChA7788kuD1+fNm4fPPvsMixcvxqFDh+Dn54fo6GgUFRXp+owYMQKnTp1CUlISNm3ahL179+L555+31SO4jKo+CwAYMGCA6M/JmjVrRNf5WVjGnj17EBcXh4MHDyIpKQmlpaXo378/bt68qetT1d9LZWVliImJQUlJCQ4cOIBvv/0WK1aswIwZM+zxSE5NyucBABMmTBD9+Zg3b57umkU+D4HIQcycOVPo0KGDwWv5+fmCh4eHsG7dOl3bn3/+KQAQVCqVjUZYMwAQfv75Z933arVaUCgUwvz583Vt+fn5gpeXl7BmzRpBEAQhLS1NACAcOXJE12fr1q2CTCYTLl++bLOxu5qKn4UgCMKYMWOEIUOGGH0NPwvrycnJEQAIe/bsEQRB2t9LW7ZsEdzc3ISsrCxdn0WLFgn+/v5CcXGxbR/AxVT8PARBEB566CHhlVdeMfoaS3wenHEih3L27FmEhISgefPmGDFiBDIyMgAAycnJKC0tRVRUlK5v27Zt0bRpU6hUKnsNt0ZIT09HVlaW6Gcvl8vRvXt33c9epVIhICAA999/v65PVFQU3NzccOjQIZuP2dXt3r0bgYGBaNOmDSZNmoTc3FzdNX4W1lNQUAAAqFevHgBpfy+pVCq0b98eQUFBuj7R0dEoLCzEqVOnbDh611Px89BatWoVGjRogIiICEybNg23bt3SXbPE58FDfslhdO/eHStWrECbNm2QmZmJ2bNn48EHH0RqaiqysrLg6emJgIAA0WuCgoKQlZVlnwHXENqfb/m/aLTfa69lZWUhMDBQdL1WrVqoV68ePx8LGzBgAJ544gmEhYXh/PnzeOuttzBw4ECoVCq4u7vzs7AStVqNV199FT179kRERAQASPp7KSsry+CfHe01Mo+hzwMAnnnmGTRr1gwhISE4ceIEEhIScObMGaxfvx6AZT4PBk7kMAYOHKj778jISHTv3h3NmjXDDz/8AB8fHzuOjMhxDB8+XPff7du3R2RkJFq0aIHdu3ejb9++dhyZa4uLi0Nqaqoo75Lsx9jnUT6Xr3379ggODkbfvn1x/vx5tGjRwiLvzaU6clgBAQFo3bo1zp07B4VCgZKSEuTn54v6ZGdnQ6FQ2GeANYT251txp1D5n71CoUBOTo7o+p07d5CXl8fPx8qaN2+OBg0a4Ny5cwD4WVjD5MmTsWnTJuzatQuNGzfWtUv5e0mhUBj8s6O9RqYz9nkY0r17dwAQ/fmo7ufBwIkc1o0bN3D+/HkEBwejS5cu8PDwwI4dO3TXz5w5g4yMDCiVSjuO0vWFhYVBoVCIfvaFhYU4dOiQ7mevVCqRn5+P5ORkXZ+dO3dCrVbr/uIi67h06RJyc3MRHBwMgJ+FJQmCgMmTJ+Pnn3/Gzp07ERYWJrou5e8lpVKJkydPioLZpKQk+Pv7Izw83DYP4iKq+jwMSUlJAQDRn49qfx5mJrMTWdxrr70m7N69W0hPTxf2798vREVFCQ0aNBBycnIEQRCEiRMnCk2bNhV27twp/PHHH4JSqRSUSqWdR+0arl+/Lhw7dkw4duyYAED45JNPhGPHjgn//POPIAiC8NFHHwkBAQHChg0bhBMnTghDhgwRwsLChNu3b+vuMWDAAKFTp07CoUOHhH379gmtWrUSYmNj7fVITquyz+L69evC66+/LqhUKiE9PV3Yvn270LlzZ6FVq1ZCUVGR7h78LCxj0qRJglwuF3bv3i1kZmbqvm7duqXrU9XfS3fu3BEiIiKE/v37CykpKUJiYqLQsGFDYdq0afZ4JKdW1edx7tw54d133xX++OMPIT09XdiwYYPQvHlzoXfv3rp7WOLzYOBEDuPpp58WgoODBU9PT6FRo0bC008/LZw7d053/fbt28KLL74o1K1bV/D19RUef/xxITMz044jdh27du0SAOh9jRkzRhAETUmC6dOnC0FBQYKXl5fQt29f4cyZM6J75ObmCrGxsULt2rUFf39/Ydy4ccL169ft8DTOrbLP4tatW0L//v2Fhg0bCh4eHkKzZs2ECRMmiLZWCwI/C0sx9DkAEJYvX67rI+XvpQsXLggDBw4UfHx8hAYNGgivvfaaUFpaauOncX5VfR4ZGRlC7969hXr16gleXl5Cy5YthTfeeEMoKCgQ3ae6n4fs7mCIiIiIqArMcSIiIiKSiIETERERkUQMnIiIiIgkYuBEREREJBEDJyIiIiKJGDgRERERScTAiYiIiEgiBk5EREREEjFwIiKHIZPJ8Msvv0juHxoaiv/+979WGw8RUUUMnIjIZsaOHYuhQ4cavZ6ZmYmBAwdKvt+RI0fw/PPPW2Bk0syZMwfu7u6YP3++zd6TiBwLAycichgKhQJeXl6S+zds2BC+vr5WHJHYsmXLMHXqVCxbtqzKviUlJTYYERHZGgMnInIY5ZfqHnjgASQkJIiu//vvv/Dw8MDevXsB6C/VyWQyLFmyBI8//jh8fX3RqlUr/Prrr6J7/Prrr2jVqhW8vb3xyCOP4Ntvv4VMJkN+fn6lY9uzZw9u376Nd999F4WFhThw4IDo+qxZs9CxY0csWbIEYWFh8Pb2BgDk5+fjueeeQ8OGDeHv748+ffrg+PHjutedP38eQ4YMQVBQEGrXro2uXbti+/btpvzYiMiGGDgRkUMaMWIE1q5di/LnkP/vf/9DSEgIHnzwQaOvmz17Nv7zn//gxIkTGDRoEEaMGIG8vDwAQHp6Op588kkMHToUx48fxwsvvIC3335b0niWLl2K2NhYeHh4IDY2FkuXLtXrc+7cOfz0009Yv349UlJSAABPPfUUcnJysHXrViQnJ6Nz587o27evbkw3btzAoEGDsGPHDhw7dgwDBgzA4MGDkZGRIfVHRUS2JBAR2ciYMWOEIUOGGL0OQPj5558FQRCEnJwcoVatWsLevXt115VKpZCQkKD7vlmzZsKCBQtEr3/nnXd039+4cUMAIGzdulUQBEFISEgQIiIiRO/59ttvCwCEa9euGR1XQUGB4OPjI6SkpAiCIAjHjh0TateuLVy/fl3XZ+bMmYKHh4eQk5Oja/v9998Ff39/oaioSHS/Fi1aCF999ZXR97vvvvuEzz//3Oh1IrIfzjgRkUNq2LAh+vfvj1WrVgHQzBapVCqMGDGi0tdFRkbq/tvPzw/+/v7IyckBAJw5cwZdu3YV9e/WrVuVY1mzZg1atGiBDh06AAA6duyIZs2a4X//+5+oX7NmzdCwYUPd98ePH8eNGzdQv3591K5dW/eVnp6O8+fPA9DMOL3++uto164dAgICULt2bfz555+ccSJyULXsPQAiImNGjBiBl19+GZ9//jlWr16N9u3bo3379pW+xsPDQ/S9TCaDWq2u1jiWLl2KU6dOoVate39lqtVqLFu2DOPHj9e1+fn5iV5348YNBAcHY/fu3Xr3DAgIAAC8/vrrSEpKwv/93/+hZcuW8PHxwZNPPsnkciIHxcCJiBzWkCFD8PzzzyMxMRGrV6/G6NGjq3W/Nm3aYMuWLaK2I0eOVPqakydP4o8//sDu3btRr149XXteXh4efvhhnD59Gm3btjX42s6dOyMrKwu1atVCaGiowT779+/H2LFj8fjjjwPQBFsXLlyQ/lBEZFMMnIjIpgoKCnSJ01r169dHkyZN9Pr6+flh6NChmD59Ov7880/ExsZW671feOEFfPLJJ0hISMD48eORkpKCFStWANDMTBmydOlSdOvWDb1799a71rVrVyxdutRoXaeoqCgolUoMHToU8+bNQ+vWrXHlyhVs3rwZjz/+OO6//360atUK69evx+DBgyGTyTB9+vRqz5ARkfUwx4mIbGr37t3o1KmT6Gv27NlG+48YMQLHjx/Hgw8+iKZNm1brvcPCwvDjjz9i/fr1iIyMxKJFi3S76gzVjyopKcHKlSsxbNgwg/cbNmwYvvvuO5SWlhq8LpPJsGXLFvTu3Rvjxo1D69atMXz4cPzzzz8ICgoCAHzyySeoW7cuHnjgAQwePBjR0dHo3LlztZ6TiKxHJgjl9voSEdUwH3zwARYvXoyLFy/aeyhE5AS4VEdENcrChQvRtWtX1K9fH/v378f8+fMxefJkew+LiJwEAyciqlHOnj2L999/H3l5eWjatClee+01TJs2zd7DIiInwaU6IiIiIomYHE5EREQkEQMnIiIiIokYOBERERFJxMCJiIiISCIGTkREREQSMXAiIiIikoiBExEREZFEDJyIiIiIJPp/TtKyS+CAe7MAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(dataset[\"living_area\"], dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Rent price\")\n",
    "\n",
    "y_regr = theta[0] + theta[1] * X[:,1]\n",
    "plt.plot(X[:,1], y_regr, color='red', label='Regression line')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1fdf27b",
   "metadata": {},
   "source": [
    "d) Compute the final cost value according to Equation 2 and compare it to the one of exercise 2. What can you conclude?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "id": "5e594f32",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best cost value is inf, the exercice 2 cost value is 138034.95779787414\n"
     ]
    }
   ],
   "source": [
    "# Your code here\n",
    "\n",
    "print(f\"The best cost value is {best_cost}, the exercice 2 cost value is {closed_form_cost}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd10b91b",
   "metadata": {},
   "source": [
    "We took some time to experiment with the alpha and max_iter values to try to get the best possible result. It seems that the closed form formula is the best one but we can get really close by tweaking those two values. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54727ff1",
   "metadata": {},
   "source": [
    "## Exercise 4 - Stochastic gradient descent for linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32a00957",
   "metadata": {},
   "source": [
    "Implement the stochastic gradient descent algorithm for the previous problem. As seen in the theory, the update rules are:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "636920d2",
   "metadata": {},
   "source": [
    "<div><div style=\"display: table-cell; width: 100%;\"><center>$\\theta_{i} \\leftarrow \\theta_{i} - \\alpha (h_{\\theta}(\\mathbf{x}_{n}) - y_{n}) x_{n,i}$</center></div><div style=\"display: table-cell; width: 100%;\">$(8)$</div></div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "id": "3f693388",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta = [ 0.338377   28.68612806]\n",
      "Cost = 144162.5602768206\n"
     ]
    },
    {
     "data": {
      "image/png": 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rbDN8+HBUVVXh9OnTjolvJ0+eBIBaEweJiIjIM7xqZKS4uBinTp0CYA8fb7/9Nm6//XYEBwcjNjYWv/vd7/Ddd99h0aJFGDBgAPLz87F161b07dsXY8eOhc1mwy233AJ/f3+88847sNlsmDlzJvR6PbZs2SLz3hEREbVPXhVGduzY4Zjgd60pU6ZgxYoVqKysxJ///Gd8/PHHuHDhAkJDQzF06FC8+uqr6NOnDwDg4sWLeOqpp7Blyxb4+flhzJgxWLRoUaPvk0FERETu5VVhhIiIiNqeNnWdESIiIvI+DCNEREQkK684m8Zms+HixYsICAhw+RLYREREJA8hBIqKihAdHV3rworX8oowcvHixSbfx4GIiIjkde7cuTrvmF3DK8JIQEAAAPvOuHo/ByIiIpKH2WxGTEyM43O8Pl4RRmoOzej1eoYRIiIiL3OjKRacwEpERESyYhghIiIiWTGMEBERkawYRoiIiEhWDCNEREQkK4YRIiIikhXDCBEREcmKYYSIiIhkxTBCREREsmIYISIiIlkxjBAREZGsGEaIiIhIVu06jKzccxbzvvwRZy6VyF0KERFRu9Wuw8i6wxewev85ZBrNcpdCRETUbrXrMBITrAMAnLtSJnMlRERE7ZdLYWTx4sXo27cv9Ho99Ho9EhMT8c0339TbfsWKFZAkyWnRarXNLtpdYoJ8AQDnCkplroSIiKj9UrnSuGPHjnjzzTfRtWtXCCGwcuVKjBs3DocPH0avXr3q3Eav1yMzM9PxWJKk5lXsRjUjI1mXGUaIiIjk4lIYuffee50ev/HGG1i8eDH27t1bbxiRJAmRkZFNr7AF9YrWAwDSf7mM/CILwgI0MldERETU/jR5zojVasXq1atRUlKCxMTEetsVFxcjLi4OMTExGDduHI4dO3bD17ZYLDCbzU5LS+jTwYDYYB0qqmx4b9vPLfIeRERE1DCXw8iRI0fg7+8PjUaDJ554AuvWrUPPnj3rbNutWzd89NFH2LBhAz799FPYbDYMGzYM58+fb/A9UlNTYTAYHEtMTIyrZTaKJEl4ZHg8AOD4RZ5RQ0REJAdJCCFc2aCiogLZ2dkwmUz44osv8OGHH2Lnzp31BpJrVVZWokePHpg4cSJef/31ettZLBZYLBbHY7PZjJiYGJhMJuj1elfKvaHD2QW474M9iDZosWf+nW59bSIiovbMbDbDYDDc8PPbpTkjAKBWq9GlSxcAwMCBA7F//368++67WLp06Q239fHxwYABA3Dq1KkG22k0Gmg0npm/0SHQfkZNbpEFVVYbVMp2fbYzERGRxzX7k9dmszmNYjTEarXiyJEjiIqKau7buk2ovwZqpQJWm0COqVzucoiIiNodl0ZG5s+fjzFjxiA2NhZFRUVYtWoVduzYgc2bNwMAJk+ejA4dOiA1NRUA8Nprr2Ho0KHo0qULCgsLsXDhQmRlZWH69Onu35MmUigkxIfqcDK3GKfzix2n+xIREZFnuBRG8vLyMHnyZOTk5MBgMKBv377YvHkz7rrrLgBAdnY2FIqrgy0FBQWYMWMGjEYjgoKCMHDgQOzZs6dR80s8qWt4AE7mFuNUXjFGdQuXuxwiIqJ2xeUJrHJo7ASYplq4+QTe334akxPj8Nq43m5/fSIiovaosZ/fnK0JQK/1AQAUl1fJXAkREVH7wzACwE9jP1pVbGEYISIi8jSGEQABWnsYKalgGCEiIvI0hhEAfurqkREepiEiIvI4hhEA/loepiEiIpILwwgAf84ZISIikg3DCK6GkRKLVeZKiIiI2h+GEVw9m6akogpVVpvM1RAREbUvDCMAgv3UCNCoIARwPMcsdzlERETtCsMIAKVCwuCEYADAgbMFMldDRETUvjCMVOsQ5AsAKCitkLkSIiKi9oVhpJpOzTNqiIiI5MAwUs1fowQAlPKMGiIiIo9iGKnmuD8NLwlPRETkUQwj1Ryn9/IwDRERkUcxjFSrufAZD9MQERF5FsNINZ3aPmeEE1iJiIg8i2Gkmv81V2ElIiIiz2EYqVYzZ8RUVgkhhMzVEBERtR8MI9XiQ/ygVipQWFqJs5dL5S6HiIio3WAYqearVmJgXBAA4MP//SJzNURERO0Hw8g1pg2PBwBs/SlP3kKIiIjaEYaRawzpFAIAMJrLUVReKXM1RERE7QPDyDUMvj4IC9AAANJPX5a5GiIiovaBYeQ6idWjI2v2n5O5EiIiovaBYeQ6v+4XDcB+qIaIiIhaHsPIdUL81QCAwlLOGSEiIvIEhpHrBOlqwkiFzJUQERG1Dwwj16kJIyUVVlRU2WSuhoiIqO1jGLlOgFYFhWT/mqMjRERELY9h5DoKhYRgP/voSK7ZInM1REREbR/DSB26R+oBAD9eKJS3ECIionaAYaQO/WMCAQBHzpvkLYSIiKgdYBipQ0ywLwAgr4iHaYiIiFoaw0gdQvzsl4S/XMwwQkRE1NIYRupQc+GzS8U8m4aIiKilMYzUIdTfPjJyqdgCIYTM1RAREbVtDCN1qBkZsVTZUFJhlbkaIiKito1hpA46tQq+PkoAnDdCRETU0lwKI4sXL0bfvn2h1+uh1+uRmJiIb775psFt1q5di+7du0Or1aJPnz7YtGlTswr2FM4bISIi8gyXwkjHjh3x5ptv4uDBgzhw4ADuuOMOjBs3DseOHauz/Z49ezBx4kQ8+uijOHz4MFJSUpCSkoKjR4+6pfiWFOLPM2qIiIg8QRLNnKEZHByMhQsX4tFHH6313IQJE1BSUoKNGzc61g0dOhT9+/fHkiVL6n1Ni8UCi+VqCDCbzYiJiYHJZIJer29OuY326Ir92HoiD6n398HEwbEeeU8iIqK2xGw2w2Aw3PDzu8lzRqxWK1avXo2SkhIkJibW2SY9PR1JSUlO65KTk5Gent7ga6empsJgMDiWmJiYppbZZDWHaTgyQkRE1LJcDiNHjhyBv78/NBoNnnjiCaxbtw49e/ass63RaERERITTuoiICBiNxgbfY/78+TCZTI7l3LlzrpbZbFdP7+WcESIiopakcnWDbt26ISMjAyaTCV988QWmTJmCnTt31htImkKj0UCj0bjt9ZrCMWekhGGEiIioJbkcRtRqNbp06QIAGDhwIPbv3493330XS5curdU2MjISubm5Tutyc3MRGRnZxHI9J5SHaYiIiDyi2dcZsdlsTpNNr5WYmIitW7c6rUtLS6t3jklrcvX+NBwZISIiakkujYzMnz8fY8aMQWxsLIqKirBq1Srs2LEDmzdvBgBMnjwZHTp0QGpqKgBg9uzZGDlyJBYtWoSxY8di9erVOHDgAJYtW+b+PXEzxwTWEo6MEBERtSSXwkheXh4mT56MnJwcGAwG9O3bF5s3b8Zdd90FAMjOzoZCcXWwZdiwYVi1ahX++Mc/4qWXXkLXrl2xfv169O7d27170QKCdPYwUlBaKXMlREREbVuzrzPiCY09T9mdCkoqMOD1NADAqTfGQKXklfOJiIhc0eLXGWnr1KqrXVNhtclYCRERUdvGMFIPpzBSxTBCRETUUhhG6qFSSFBI9q8ZRoiIiFoOw0g9JElyjI5YGEaIiIhaDMNIA9RKhhEiIqKWxjDSALVKCYCHaYiIiFoSw0gDNNWHaXg2DRERUcthGGmAI4xwZISIiKjFMIw0QM0wQkRE1OIYRhpw9Wwaq8yVEBERtV0MIw2oOZuGIyNEREQth2GkAWpOYCUiImpxDCMN0PCiZ0RERC2OYaQBnMBKRETU8hhGGuCnUQEALhaWyVwJERFR28Uw0oBR3cIBAN8cNcpcCRERUdvFMNKAkV3DAABnLpXAVFopczVERERtE8NIAww6H8QG6wAAP14olLcYIiKiNoph5AaGJAQDAL7+MUfmSoiIiNomhpEb+HX/aADArpP5MldCRETUNjGM3MDNsUFQSMBFUznyzOVyl0NERNTmMIzcgJ9GhYRQPwDAydximashIiJqexhGGiHK4AsAyCviyAgREZG7MYw0QliABgCQV2SRuRIiIqK2h2GkEcKrw0g+wwgREZHbMYw0AkdGiIiIWg7DSCOE67UAwLNpiIiIWgDDSCOE+VcfpinmyAgREZG7MYw0Qri+OoyYGUaIiIjcjWGkEWomsBZZqlBWYZW5GiIioraFYaQR/DUqaH3sXcUzaoiIiNyLYaQRJElCeED1JFZe+IyIiMitGEYaKZyn9xIREbUIhpFGCuOFz4iIiFoEw0gjXR0Z4WEaIiIid2IYaaSQ6muNXCmplLkSIiKitoVhpJFqzqaxVPHUXiIiIndiGGkkjUoJALBU2WSuhIiIqG1xKYykpqbilltuQUBAAMLDw5GSkoLMzMwGt1mxYgUkSXJatFpts4qWg0ZVPTJSyZERIiIid3IpjOzcuRMzZ87E3r17kZaWhsrKSowePRolJSUNbqfX65GTk+NYsrKymlW0HDSOwzQcGSEiInInlSuNv/32W6fHK1asQHh4OA4ePIjbbrut3u0kSUJkZGTTKmwlHIdpKhlGiIiI3KlZc0ZMJhMAIDg4uMF2xcXFiIuLQ0xMDMaNG4djx4412N5iscBsNjstcuMEViIiopbR5DBis9kwZ84cDB8+HL179663Xbdu3fDRRx9hw4YN+PTTT2Gz2TBs2DCcP3++3m1SU1NhMBgcS0xMTFPLdJuakZFyjowQERG5lSSEEE3Z8Mknn8Q333yD3bt3o2PHjo3errKyEj169MDEiRPx+uuv19nGYrHAYrl6pVOz2YyYmBiYTCbo9fqmlNtsB85ewYNL0hEfosOO52+XpQYiIiJvYjabYTAYbvj57dKckRqzZs3Cxo0bsWvXLpeCCAD4+PhgwIABOHXqVL1tNBoNNBpNU0prMTy1l4iIqGW4dJhGCIFZs2Zh3bp12LZtGxISElx+Q6vViiNHjiAqKsrlbeXEs2mIiIhahksjIzNnzsSqVauwYcMGBAQEwGg0AgAMBgN8fX0BAJMnT0aHDh2QmpoKAHjttdcwdOhQdOnSBYWFhVi4cCGysrIwffp0N+9Ky+J1RoiIiFqGS2Fk8eLFAIBRo0Y5rV++fDmmTp0KAMjOzoZCcXXApaCgADNmzIDRaERQUBAGDhyIPXv2oGfPns2r3MO0PtUTWDkyQkRE5FZNnsDqSY2dANOSCksr0P+1NADAqTfGQKXklfSJiIga0tjPb36iNlLNyAgAlPJQDRERkdswjDSS1kfpmDdiKq2UuRoiIqK2g2HEBYE6HwCAqYxhhIiIyF0YRlwQ6KsGABRyZISIiMhtGEZcYODICBERkdsxjLgg0NceRgrLKmSuhIiIqO1gGHFBzZwRHqYhIiJyH4YRF4QF2O+Xk2sul7kSIiKitoNhxAVRBvsl7y8WMowQERG5C8OIC6IMWgCA0VwmcyVERERtB8OIC2pGRnI4MkJEROQ2DCMuiA60j4xcLqlAOS8JT0RE5BYMIy4w+PpA62PvMqOJoyNERETuwDDiAkmSEF1zqIZhhIiIyC0YRlwUVX2oJsfESaxERETuwDDioiiOjBAREbkVw4iLak7vvVjIkREiIiJ3YBhxUc3ICCewEhERuQfDiItq5oxc4MgIERGRWzCMuKhruD8A4FReMUorqmSuhoiIyPsxjLioY5AO0QYtqmwCGecK5S6HiIjI6zGMNEGPKD0A4MylEpkrISIi8n4MI00QE6wDAGRfKZW5EiIiIu/HMNIEcSHVYeQywwgREVFzMYw0QfdI+2Ga3T9fQrGFk1iJiIiag2GkCYYkBCMuRIciSxV2ZObJXQ4REZFXYxhpAoVCwuieEQCAbScYRoiIiJqDYaSJbu8eDgDYmZkPq03IXA0REZH3Yhhpolvig+GjlHC5pAK5Zl4anoiIqKkYRprIR6mATq0CAJRWWGWuhoiIyHsxjDSDTq0EAJQxjBARETUZw0gz+FaHEd6jhoiIqOkYRpqhZmSktJIjI0RERE3FMNIMvj48TENERNRcDCPN4Fs9gZVhhIiIqOkYRppB58PDNERERM3FMNIMV8+m4QRWIiKipmIYaQat42wajowQERE1lUthJDU1FbfccgsCAgIQHh6OlJQUZGZm3nC7tWvXonv37tBqtejTpw82bdrU5IJbEx0nsBIRETWbS2Fk586dmDlzJvbu3Yu0tDRUVlZi9OjRKCkpqXebPXv2YOLEiXj00Udx+PBhpKSkICUlBUePHm128XIL8lMDAC6XVMhcCRERkfeShBBNvstbfn4+wsPDsXPnTtx22211tpkwYQJKSkqwceNGx7qhQ4eif//+WLJkSaPex2w2w2AwwGQyQa/XN7Vct/vy4Hk8u/YHDO8Sgn9PHyp3OURERK1KYz+/mzVnxGQyAQCCg4PrbZOeno6kpCSndcnJyUhPT693G4vFArPZ7LS0RlGBWgBATiFvlEdERNRUTQ4jNpsNc+bMwfDhw9G7d+962xmNRkRERDiti4iIgNForHeb1NRUGAwGxxITE9PUMltUtMEXAJBjKkczBpiIiIjatSaHkZkzZ+Lo0aNYvXq1O+sBAMyfPx8mk8mxnDt3zu3v4Q6RBvvISFmlFaaySpmrISIi8k6qpmw0a9YsbNy4Ebt27ULHjh0bbBsZGYnc3Fyndbm5uYiMjKx3G41GA41G05TSPErro0SInxqXSypwsbAcgTq13CURERF5HZdGRoQQmDVrFtatW4dt27YhISHhhtskJiZi69atTuvS0tKQmJjoWqWtVM3oSI6pTOZKiIiIvJNLYWTmzJn49NNPsWrVKgQEBMBoNMJoNKKs7OoH8eTJkzF//nzH49mzZ+Pbb7/FokWLcOLECbzyyis4cOAAZs2a5b69kFFU9byRiyZOYiUiImoKl8LI4sWLYTKZMGrUKERFRTmWNWvWONpkZ2cjJyfH8XjYsGFYtWoVli1bhn79+uGLL77A+vXrG5z06k1Cqq81YuacESIioiZxac5IY84Y2bFjR61148ePx/jx4115K6+h9bHnuXLeLI+IiKhJeG+aZtLykvBERETNwjDSTJrqMFJexTBCRETUFAwjzXT1MI1N5kqIiIi8E8NIM/nWjIxwzggREVGTMIw0k9YRRjgyQkRE1BQMI83Es2mIiIiah2GkmbQqHqYhIiJqDoaRZtLybBoiIqJmYRhpJg3PpiEiImoWhpFm4tk0REREzcMw0ky+ansYKbFUyVwJERGRd2IYaaaau/YWlFaitIKBhIiIyFUMI81k8PWBwdcHAHDuSpnM1RAREXkfhhE3iAvRAQCyLpfIXAkREZH3YRhxgzB/DQCgoLRC5kqIiIi8D8OIG2irJ7GWVfCMGiIiIlcxjLiBrvr03lKe3ktEROQyhhE3qDm9t5wjI0RERC5jGHGDmjBSyjBCRETkMoYRN6i5CmsZD9MQERG5jGHEDXScwEpERNRkDCNuwJERIiKipmMYcQNftQoA54wQERE1BcOIG3BkhIiIqOkYRtxAxzv3EhERNRnDiBvEVt+b5niOGabSSpmrISIi8i4MI27QKdQPHYN8IQSQ+s1PcpdDRETkVRhG3ECSJMy+sysA4OsjObDahMwVEREReQ+GETdJGdABAVoVisqrsHTXabnLISIi8hoMI27io1TgkeEJAICdmfkyV0NEROQ9GEbcKLlXJAD7RFYheKiGiIioMRhG3KhLuD8AoKi8CldKKmSuhoiIyDswjLiRWqVwXHOkmNccISIiahSGETfz09gvDc8wQkRE1DgMI27mXx1GSiy8NDwREVFjMIy4mb9jZIRXYiUiImoMhhE389PUzBnhyAgREVFjMIy4mb/GBwBvmkdERNRYLoeRXbt24d5770V0dDQkScL69esbbL9jxw5IklRrMRqNTa25VfOvGRkpZxghIiJqDJfDSElJCfr164f333/fpe0yMzORk5PjWMLDw119a69QczaNqYxzRoiIiBpD5eoGY8aMwZgxY1x+o/DwcAQGBrq8nbfpHqUHAHyyNwsPDY5BxyCdzBURERG1bh6bM9K/f39ERUXhrrvuwnfffddgW4vFArPZ7LR4i/sGdEC0QQtTWSXe/OaE3OUQERG1ei0eRqKiorBkyRJ8+eWX+PLLLxETE4NRo0bh0KFD9W6TmpoKg8HgWGJiYlq6TLfx16jw/qSbAQD/91MuKq02mSsiIiJq3STRjDu6SZKEdevWISUlxaXtRo4cidjYWHzyySd1Pm+xWGCxWByPzWYzYmJiYDKZoNfrm1qux9hsAgNeT4OprBLrfj8MA2KD5C6JiIjI48xmMwwGww0/v2U5tXfw4ME4depUvc9rNBro9XqnxZsoFBL6xQQCAH7KKZK3GCIiolZOljCSkZGBqKgoOd7aYzqH+QEATucXy1wJERFR6+by2TTFxcVOoxpnzpxBRkYGgoODERsbi/nz5+PChQv4+OOPAQDvvPMOEhIS0KtXL5SXl+PDDz/Etm3bsGXLFvftRSvUOcwfAPBzHsMIERFRQ1wOIwcOHMDtt9/ueDx37lwAwJQpU7BixQrk5OQgOzvb8XxFRQWeffZZXLhwATqdDn379sX//d//Ob1GWzQgNhAAsOfUJeSZyxGu18pbEBERUSvVrAmsntLYCTCtzT3v/g/Hc8xYPOlmjOnTtg9LERERXa9VT2BtL3pF2zv+hJGTWImIiOrDMNKCukUGAAB+PF8obyFEREStGMNIC7rtpjAAwO5Tl5B1uUTmaoiIiFonhpEWdFNEAAbFBaHSKrBk5y9yl0NERNQqMYy0sMdu6wQAOHD2isyVEBERtU4MIy1sYJz9UvA/5xWj2FIlczVEREStD8NICwvx1yDUXwMAOM0LoBEREdXCMOIBXcLtl4Y/xTBCRERUC8OIB3SPtF9v5Aee4ktERFQLw4gHDOscAgDYfMyI0grOGyEiIroWw4gHjOgailB/DXLNFmzIuCh3OURERK0Kw4gH6NQqTLilIwDgUFaBzNUQERG1LgwjHjIgxn6K757Tl2G1tfp7ExIREXkMw4iHDO8SCr1WhQuFZdhz+pLc5RAREbUaDCMe4qtW4p4+UQCArT/lyVwNERFR68Ew4kE1N847yHkjREREDgwjHtQ9MgCA/eJnNs4bISIiAsAw4lGxwTqoVQqUVVpxvqBM7nKIiIhaBYYRD1IpFegUar80/M95RTJXQ0RE1DowjHjYTRH2QzUnc3mfGiIiIoBhxONuivAHABy5UChvIURERK0Ew4iH1ZxRs+1EHq6UVMhcDRERkfwYRjysTwcDenfQo7zShpc3HIUQPKuGiIjaN4YRD5MkCa/+uhdUCgkbf8zB/9t9Ru6SiIiIZMUwIoOBccH449geAID3tp3i6AgREbVrDCMy+e2QOKiVCpjKKpF9pVTucoiIiGTDMCITtUqBHlH203w/Ts+SuRoiIiL5MIzI6LdDYgEAGzIu8lANERG1WwwjMhrXvwNUCgmXii24UMjLwxMRUfvEMCIjrY8SvToYAADbT+TJXA0REZE8GEZk9qs+UQCAv//fzzCXV8pcDRERkecxjMjst0NiEW3Q4kpJBXZm5stdDhERkccxjMjMT6PCr/pFAwA+Tj/LiaxERNTuMIy0Ag8PjYNGpcD+swXIOFcodzlEREQexTDSCsQE63B370gAwJOfHkLW5RKZKyIiIvIchpFW4vnkbkgI9YPRXI5FW07KXQ4REZHHMIy0Eh2DdEi9vw8A4Pszl2WuhoiIyHMYRlqRjkG+AICC0kpOZCUionbD5TCya9cu3HvvvYiOjoYkSVi/fv0Nt9mxYwduvvlmaDQadOnSBStWrGhCqW1foE4NAKiosqGs0ipzNURERJ7hchgpKSlBv3798P777zeq/ZkzZzB27FjcfvvtyMjIwJw5czB9+nRs3rzZ5WLbOj+1Ej5KCQBQWMoLoBERUfugcnWDMWPGYMyYMY1uv2TJEiQkJGDRokUAgB49emD37t34+9//juTkZFffvk2TJAmBOjXyiywoKK1AdKCv3CURERG1uBafM5Keno6kpCSndcnJyUhPT693G4vFArPZ7LS0F0E6HwAcGSEiovajxcOI0WhERESE07qIiAiYzWaUldV9p9rU1FQYDAbHEhMT09JlthqRBvtoyOHsApkrISIi8oxWeTbN/PnzYTKZHMu5c+fkLslj7u1rv3HeluO5MldCRETkGS7PGXFVZGQkcnOdP1hzc3Oh1+vh61v3nAiNRgONRtPSpbVKA2KDAACn8ophswkoFJLMFREREbWsFh8ZSUxMxNatW53WpaWlITExsaXf2ivFheigUkgorbBiz2le/IyIiNo+l8NIcXExMjIykJGRAcB+6m5GRgays7MB2A+xTJ482dH+iSeewC+//IIXXngBJ06cwAcffIDPP/8czzzzjHv2oI3xUSpwc5x9dOSpzw7BXM6JrERE1La5HEYOHDiAAQMGYMCAAQCAuXPnYsCAAXj55ZcBADk5OY5gAgAJCQn4+uuvkZaWhn79+mHRokX48MMPeVpvA/7xkL1vC0or8dPF9nMmERERtU+S8ILrjpvNZhgMBphMJuj1ernL8YgpH+3DzpP5WHBvT0wbniB3OURERC5r7Od3qzybhoBOYX4AgFf/exx5ReUyV0NERNRyGEZaqQdu7ohgP/u9al784kfeOI+IiNoshpFWqncHA9Y8NhRqpQLbM/Pxl00/oZw3zyMiojaIYaQV6xoRgDl3dQUA/Ot/Z/D0Z4dlroiIiMj9GEZaucdv64xnkm4CYL8q65ZjRpkrIiIici+GkVZOqZAwO6krpg2PBwA8+/kPnNBKRERtCsOIl3g+uRsCdT4oslThrc2ZcpdDRETkNgwjXkKnVuHVX/cCAOzIzEdFlU3mioiIiNyDYcSLJPeKRIifGnlFFoxcuB0fp5+VuyQiIqJmYxjxIlofJRaO7wt/jQo5pnK8vOEYDmUXyF0WERFRszCMeJk7ukdg70t3YlS3MADAxh9yZK6IiIioeRhGvJC/RoVJQ+IAAJuPGXl1ViIi8moMI17q1q6h0KmVuFBYhmO8sy8REXkxhhEvpfVRYkSXUADA10d4qIaIiLwXw4gXG9e/AwDg/+0+A1NZpczVEBERNQ3DiBe7p08kOoX5oaLKhl0n8+Uuh4iIqEkYRryYJEkY3tl+qOZ4DueNEBGRd2IY8XLBfmoAgJmHaYiIyEsxjHg5g68PAHDOCBEReS2GES+nrw4j5vIqmSshIiJqGoYRL1czMsLDNERE5K0YRrycXqsCwDBCRETei2HEyxl09pGRgtIK2Gy8LDwREXkfhhEvF2XwhVqlQEFpJd75v5Nyl0NEROQyhhEvZ/D1wSv39gIArDlwTuZqiIiIXMcw0gYk9QgHAOQXWWDloRoiIvIyDCNtQIi/BgoJsAngcrFF7nKIiIhcwjDSBigVEsICNACAXDPDCBEReReGkTYi0uALAFiZfpaHaoiIyKswjLQRDw+NAwB8cfA85n/1I8oqrDJXRERE1DgMI23EgwM7YsG9PQEAnx84jxe//FHmioiIiBqHYaQNmTY8AX97oC8A4D8/XMT720/JXBEREdGNMYy0MeMHdcQDN3cEALyddhKZxiKZKyIiImoYw0gbI0kSFv2mH5J7RcBqE/jbtyfkLomIiKhBDCNt1O9HdQEAHD5XKG8hREREN8Aw0kZ1CvMDAFwpqUBROe/oS0RErRfDSBsVoPVBiJ8aALDtRJ7M1RAREdWPYaQN6x4VAAD46Luz8hZCRETUAIaRNuzVX9vv5nvkfCFMZTxUQ0RErVOTwsj777+P+Ph4aLVaDBkyBPv27au37YoVKyBJktOi1WqbXDA1XpfwAMQG62ATwI/nC+Uuh4iIqE4uh5E1a9Zg7ty5WLBgAQ4dOoR+/fohOTkZeXn1z0vQ6/XIyclxLFlZWc0qmhqvT0cDAOC7U5dlroSIiKhuLoeRt99+GzNmzMC0adPQs2dPLFmyBDqdDh999FG920iShMjISMcSERHR4HtYLBaYzWanhZpmYGwQAOCj787g3JVSmashIiKqzaUwUlFRgYMHDyIpKenqCygUSEpKQnp6er3bFRcXIy4uDjExMRg3bhyOHTvW4PukpqbCYDA4lpiYGFfKpGv8dkgsekXrUVFlw2+WpmP/2Styl0REROTEpTBy6dIlWK3WWiMbERERMBqNdW7TrVs3fPTRR9iwYQM+/fRT2Gw2DBs2DOfPn6/3febPnw+TyeRYzp0750qZdA2tjxLvTOiP2GAdckzleGrVYQgh5C6LiIjIocXPpklMTMTkyZPRv39/jBw5El999RXCwsKwdOnSerfRaDTQ6/VOCzVd14gAbJp9K7Q+ChjN5dh8rO7gSEREJAeXwkhoaCiUSiVyc3Od1ufm5iIyMrJRr+Hj44MBAwbg1CneUdaT/DUqjOgSCgB44tNDmLA0HZuO5MhcFRERkYthRK1WY+DAgdi6datjnc1mw9atW5GYmNio17BarThy5AiioqJcq5Sa7c8pfTC6ZwRUCgnfn7mC3//7EJ79/AcYTeVyl0ZERO2YytUN5s6diylTpmDQoEEYPHgw3nnnHZSUlGDatGkAgMmTJ6NDhw5ITU0FALz22msYOnQounTpgsLCQixcuBBZWVmYPn26e/eEbijSoMWyyYNwsbAMb23JxFeHLuDLQ+fxzdEc/GZQDO6/uQP6dgyUu0wiImpnXA4jEyZMQH5+Pl5++WUYjUb0798f3377rWNSa3Z2NhSKqwMuBQUFmDFjBoxGI4KCgjBw4EDs2bMHPXv2dN9ekEuiA33x9m/6Y9KQODy/9gf8cqkEK/acxYo9Z/HEyM548e5ukCRJ7jKJiKidkIQXnFphNpthMBhgMpk4mdXNSiuqkHY8F2sPnMfuU5cAAK+P64WHE+PlLYyIiLxeYz+/eW+adk6nVmFc/w745NHBGN3TPrr1pw3H8HNukcyVERFRe8EwQgDsV8ldOL6f4/H2zPov709ERORODCPkYPD1wew7uwIAvjnKa5EQEZFnMIyQk+6RAQCAw9mFeGDxHry1OROXiy0yV0VERG0Zwwg5GdktDEk9wqFSSDiYVYB/bj+Fh//fPl5CnoiIWgzDCDnRqVX4cMot2PnC7Xjjvt5QKxU4nmPGs5//gKzLJXKXR0REbRDDCNWpQ6AvJg2Jw739ogEAXx2+gJELd2Disr3YdTJf5uqIiKgtYRihBr06rhdS7++DUd3CIElA+i+XMW3FfpzOL5a7NCIiaiN40TNqtAuFZZi+8gB+yjEDAHpF6/HgwI6YOiyeV2wlIqJaeNEzcrsOgb5Y+ruB6BDoCwA4dtGMV/97HIeyC2SujIiIvBnDCLkkNkSHHc+Pwo7nRiFCrwEAfPi/MzCVVspcGREReSsepqEmW3/4AuasyXA8jtRrEa7XIDxAg5E3heF3Q+N4+IaIqB1r7Oc3wwg1mRACn+zNwke7z+Ds5dJaz8eF6PDXB/piaKcQGaojIiK5MYyQRxWWViDrcinyiyzIOFeIj747g9IKK1QKCRNuicH9N3dATJAOYQEajpYQEbUTDCMkq6LySsz76gi+/jHHaf2guCD8dkgs/DQqROq16NPBAIWC4YSIqC1iGCHZ2WwCXx/Jwer92fglvwQ5pvJabWbd3gXPJXeToToiImppDCPU6uw5dQlvp52EQiEhz1zumGdy+E93IchPLXN1RETkbgwj1OqN/vtOnMy1X8k1LkSHLmH+GN4lFOMHdYTVJqD1UULro5S5SiIiaiqGEWr11h++gJfWHUFphbXO5yUJiA3W4Q/39MDoXpEero6IiJqLYYS8gs0mkFtUjrOXSrHzZD5WfZ8Fc3lVrXYDYgMxfmAM4kN06B6lRzAP6xARtXoMI+S1SiuqYBNAcXkVnlv7A3afulSrzZCEYKQM6IC4EB3CAzToEKiDr5qHdIiIWhOGEWozDmUXYMuxXBy5UIgz+SW4WMdZOWqlAnf2CMfUYfHQ+/rAX6NCaYUV+89eQVF5FUL81QjxU+POHhEy7AERUfvEMEJt1gmjGav3ncPJ3CIYzeUwmsrrnXdyPV8fJUL81VArFRAAOoX6YXiXUATqfBAeoMVNEf4I9lNDpeRtm4iImothhNoNIQS+OHgen+3LRkFpJYrKq1BsqYTVJtA1PADxoTrsP1uA/CJLo15PpZBwV88I6NQq+GmUCPXX4Jb4YARoVQDsE2t9fZSwCQFTWSV8fVTQqZWQJKCiygZLlQ06tRIhfhqYyipRWFYBU1kl/DQqhPppoPFRQK1UQKmUUFllQ4i/piW7h4hINgwj1O4JIZwuPV9aUYUcUzlMZfagcrGwDIeyCnCp2B4WzheU1nmPnZYWG6xDsJ8aGpUCWh8lyiutKKu0QpIk+KmV0KlV8Nco4a9VoW/HQCR2CrGHHYYYImrlGEaImqC80opP92bhdH4xwgO0sNoE9p29gnNXSiEEICAgBHClpAI2IRBl8EWF1YayCiuEEFCrFFCrFDCVVaK80gZfHyUMvj7Q+6pwpaQSpRVVsFTZYLU1/3+7ED81booIgJ/GPjKjUkiQJAkqhQSVUoKP0l6LSiHBahO4UlKBovIqWIWobqOAQgJsArDZdw6SBCgkCUqFdPVrSYKvWomEUD/c2y+6xc9kEkLgUnEFyiqs9hoUEiTYa1FIgCRJUCsVMOh8WrQOImo+hhGiFlReaYVNCOjUqjqft9oEqmw2aFR1n+FjtQlUWm24XFKBX/KLUV5pg6XKirIKK9QqBQK0Klht9tGcEosVJZYqXCq2YN3hCygsrUSF1daSu9eg8AANqmwClVU2VFht8Neo4K9VQaNSoKi8CgZfH2iqL1ZnswnYhIDVZg9xViGurhMCNps9CEkAtGolKqpsKCipQEkj5gCF+quh9VHCR2kPXEqFBI1KAd/q0SSdWglfHyUE4AiS1f9BCHHN+quPcU3gvDZ8AoBSIUGhkKCoHm2zCQFRvW82YX+NmmBX8xiwhyeFdDVMAZI9/AGOcKWQAHvkQvU2qPtrOD249h/He133dB2v0XBb1PN+Nc2FY1/tfVazz+Ka76ftmjZXn695zv61VL3PCoX9X6m6L4QQKK+0otJ69WenZlEqJNwUEQC1SlHn9xRAvd9X+z8ClVaBovJK5BdZHN9bSM79olEp4Fv9s+Wjsh9WVavsIVjrYz8ke/0np1T9vZWu+b5I13xfJal237e2e4Y+MjwBMcE6t74mwwhRG2YqrcSxiybkF1tQWmFFaYUVNpv9A74m6NgXgYoqGxSShBB/NfRaFVRKBaqsNlRd8wu+5gNWCAHrdR8kVVYb8ossWJ9xEaaySo/sn8IxL8f+AXL9h33r/61F5H2++v0w3Bwb5NbXbOznd91/1hFRq2bQ+WBYl1CPvufL9/bCCaMZAOx/MVaPSJRUVKG4vApllVbotT4wl1eiosoGIeA43KNU2A/3SNWHgBTVh19qDgPZqv8aVqsU0Pv6oGOQb72jSgBQWFqB8wVlqKwOVZVWG6qqg1dZ9Zyb4vIqlFdZr/7Vjat/qTr+epWka9ZXP675C/aa54CaUR77qFbNIayakY2afbKPctR8XbMdqkcQhCNQKavfpOax1SbgyFfXJK1rM9e1AezaUYA6n0fttqi3rahnfe32AsKxf4rq76fiur5wfr7+fwE4Qqa4LmT6qu2jEkoFoFQooJTsIyhGUzlyzfaJ6Nd/T2vW2f+VrhmFcP7eKiQJAVoVwgI08FEqHCM9NfssBByjlJXVI4A14b5mBBO4+j41fVwzGlPTX9eOqolrOtFppK6VidBrZXtvhhEiahSlQkKvaIPcZQAAAnVqBOp4FV6itoIXUyAiIiJZMYwQERGRrBhGiIiISFYMI0RERCQrhhEiIiKSFcMIERERyYphhIiIiGTFMEJERESyalIYef/99xEfHw+tVoshQ4Zg3759DbZfu3YtunfvDq1Wiz59+mDTpk1NKpaIiIjaHpfDyJo1azB37lwsWLAAhw4dQr9+/ZCcnIy8vLw62+/ZswcTJ07Eo48+isOHDyMlJQUpKSk4evRos4snIiIi7+fyjfKGDBmCW265Bf/85z8BADabDTExMXjqqacwb968Wu0nTJiAkpISbNy40bFu6NCh6N+/P5YsWdKo9+SN8oiIiLxPYz+/XRoZqaiowMGDB5GUlHT1BRQKJCUlIT09vc5t0tPTndoDQHJycr3tAcBiscBsNjstRERE1Da5FEYuXboEq9WKiIgIp/UREREwGo11bmM0Gl1qDwCpqakwGAyOJSYmxpUyiYiIyIu0yrv2zp8/H3PnznU8NplMiI2N5QgJERGRF6n53L7RjBCXwkhoaCiUSiVyc3Od1ufm5iIyMrLObSIjI11qDwAajQYajcbxuGZnOEJCRETkfYqKimAwGOp93qUwolarMXDgQGzduhUpKSkA7BNYt27dilmzZtW5TWJiIrZu3Yo5c+Y41qWlpSExMbHR7xsdHY1z584hICAAkiS5UnKDzGYzYmJicO7cOU6MbWHsa89gP3sG+9kz2M+e01J9LYRAUVERoqOjG2zn8mGauXPnYsqUKRg0aBAGDx6Md955ByUlJZg2bRoAYPLkyejQoQNSU1MBALNnz8bIkSOxaNEijB07FqtXr8aBAwewbNmyRr+nQqFAx44dXS210fR6PX/QPYR97RnsZ89gP3sG+9lzWqKvGxoRqeFyGJkwYQLy8/Px8ssvw2g0on///vj2228dk1Szs7OhUFydFzts2DCsWrUKf/zjH/HSSy+ha9euWL9+PXr37u3qWxMREVEb5PJ1RtoSXr/Ec9jXnsF+9gz2s2ewnz1H7r5u1/em0Wg0WLBggdNkWWoZ7GvPYD97BvvZM9jPniN3X7frkREiIiKSX7seGSEiIiL5MYwQERGRrBhGiIiISFYMI0RERCQrhhEiIiKSVbsOI++//z7i4+Oh1WoxZMgQ7Nu3T+6SvEZqaipuueUWBAQEIDw8HCkpKcjMzHRqU15ejpkzZyIkJAT+/v544IEHat2nKDs7G2PHjoVOp0N4eDief/55VFVVeXJXvMqbb74JSZKcbq/AfnafCxcu4He/+x1CQkLg6+uLPn364MCBA47nhRB4+eWXERUVBV9fXyQlJeHnn392eo0rV65g0qRJ0Ov1CAwMxKOPPori4mJP70qrZbVa8ac//QkJCQnw9fVF586d8frrrzvdSI393DS7du3Cvffei+joaEiShPXr1zs9765+/fHHH3HrrbdCq9UiJiYGf/vb35pfvGinVq9eLdRqtfjoo4/EsWPHxIwZM0RgYKDIzc2VuzSvkJycLJYvXy6OHj0qMjIyxD333CNiY2NFcXGxo80TTzwhYmJixNatW8WBAwfE0KFDxbBhwxzPV1VVid69e4ukpCRx+PBhsWnTJhEaGirmz58vxy61evv27RPx8fGib9++Yvbs2Y717Gf3uHLlioiLixNTp04V33//vfjll1/E5s2bxalTpxxt3nzzTWEwGMT69evFDz/8IH7961+LhIQEUVZW5mhz9913i379+om9e/eK//3vf6JLly5i4sSJcuxSq/TGG2+IkJAQsXHjRnHmzBmxdu1a4e/vL959911HG/Zz02zatEn84Q9/EF999ZUAINatW+f0vDv61WQyiYiICDFp0iRx9OhR8dlnnwlfX1+xdOnSZtXebsPI4MGDxcyZMx2PrVariI6OFqmpqTJW5b3y8vIEALFz504hhBCFhYXCx8dHrF271tHmp59+EgBEenq6EML+P45CoRBGo9HRZvHixUKv1wuLxeLZHWjlioqKRNeuXUVaWpoYOXKkI4ywn93nxRdfFCNGjKj3eZvNJiIjI8XChQsd6woLC4VGoxGfffaZEEKI48ePCwBi//79jjbffPONkCRJXLhwoeWK9yJjx44VjzzyiNO6+++/X0yaNEkIwX52l+vDiLv69YMPPhBBQUFOvztefPFF0a1bt2bV2y4P01RUVODgwYNISkpyrFMoFEhKSkJ6erqMlXkvk8kEAAgODgYAHDx4EJWVlU593L17d8TGxjr6OD09HX369HHc1wgAkpOTYTabcezYMQ9W3/rNnDkTY8eOdepPgP3sTv/5z38waNAgjB8/HuHh4RgwYAD+9a9/OZ4/c+YMjEajU18bDAYMGTLEqa8DAwMxaNAgR5ukpCQoFAp8//33ntuZVmzYsGHYunUrTp48CQD44YcfsHv3bowZMwYA+7mluKtf09PTcdttt0GtVjvaJCcnIzMzEwUFBU2uz+Ub5bUFly5dgtVqdfrlDAARERE4ceKETFV5L5vNhjlz5mD48OGOGyAajUao1WoEBgY6tY2IiIDRaHS0qet7UPMc2a1evRqHDh3C/v37az3HfnafX375BYsXL8bcuXPx0ksvYf/+/Xj66aehVqsxZcoUR1/V1ZfX9nV4eLjT8yqVCsHBwezravPmzYPZbEb37t2hVCphtVrxxhtvYNKkSQDAfm4h7upXo9GIhISEWq9R81xQUFCT6muXYYTca+bMmTh69Ch2794tdyltzrlz5zB79mykpaVBq9XKXU6bZrPZMGjQIPzlL38BAAwYMABHjx7FkiVLMGXKFJmrazs+//xz/Pvf/8aqVavQq1cvZGRkYM6cOYiOjmY/t2Pt8jBNaGgolEplrTMOcnNzERkZKVNV3mnWrFnYuHEjtm/fjo4dOzrWR0ZGoqKiAoWFhU7tr+3jyMjIOr8HNc+R/TBMXl4ebr75ZqhUKqhUKuzcuRP/+Mc/oFKpEBERwX52k6ioKPTs2dNpXY8ePZCdnQ3gal819HsjMjISeXl5Ts9XVVXhypUr7Otqzz//PObNm4eHHnoIffr0wcMPP4xnnnkGqampANjPLcVd/dpSv0/aZRhRq9UYOHAgtm7d6lhns9mwdetWJCYmyliZ9xBCYNasWVi3bh22bdtWa9hu4MCB8PHxcerjzMxMZGdnO/o4MTERR44ccfrhT0tLg16vr/Wh0F7deeedOHLkCDIyMhzLoEGDMGnSJMfX7Gf3GD58eK3T00+ePIm4uDgAQEJCAiIjI5362mw24/vvv3fq68LCQhw8eNDRZtu2bbDZbBgyZIgH9qL1Ky0thULh/NGjVCphs9kAsJ9birv6NTExEbt27UJlZaWjTVpaGrp169bkQzQA2vepvRqNRqxYsUIcP35cPPbYYyIwMNDpjAOq35NPPikMBoPYsWOHyMnJcSylpaWONk888YSIjY0V27ZtEwcOHBCJiYkiMTHR8XzNKaejR48WGRkZ4ttvvxVhYWE85fQGrj2bRgj2s7vs27dPqFQq8cYbb4iff/5Z/Pvf/xY6nU58+umnjjZvvvmmCAwMFBs2bBA//vijGDduXJ2nRg4YMEB8//33Yvfu3aJr167t/pTTa02ZMkV06NDBcWrvV199JUJDQ8ULL7zgaMN+bpqioiJx+PBhcfjwYQFAvP322+Lw4cMiKytLCOGefi0sLBQRERHi4YcfFkePHhWrV68WOp2Op/Y2x3vvvSdiY2OFWq0WgwcPFnv37pW7JK8BoM5l+fLljjZlZWXi97//vQgKChI6nU7cd999Iicnx+l1zp49K8aMGSN8fX1FaGioePbZZ0VlZaWH98a7XB9G2M/u89///lf07t1baDQa0b17d7Fs2TKn5202m/jTn/4kIiIihEajEXfeeafIzMx0anP58mUxceJE4e/vL/R6vZg2bZooKiry5G60amazWcyePVvExsYKrVYrOnXqJP7whz84nSrKfm6a7du31/l7ecqUKUII9/XrDz/8IEaMGCE0Go3o0KGDePPNN5tduyTENZe9IyIiIvKwdjlnhIiIiFoPhhEiIiKSFcMIERERyYphhIiIiGTFMEJERESyYhghIiIiWTGMEBERkawYRoiIiEhWDCNEREQkK4YRIiIikhXDCBEREcnq/wNdHjmyNwoEowAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "import random\n",
    "def stochastic_gradient_descent(X, y, max_iter, alpha):\n",
    "    \n",
    "    theta = np.zeros((2))\n",
    "\n",
    "    costs = []\n",
    "\n",
    "\n",
    "    for i in range(0, max_iter): # we could also use a delta on the cost function with a while to stop when the cost is not improving but we wanted to see the curve after x iterations\n",
    "        rand = int(random.random() * X.shape[0])\n",
    "        y_pred_stoch = X[rand] @ theta\n",
    "        theta[0] = theta[0] - alpha * (y_pred_stoch - y[rand])\n",
    "        theta[1] = theta[1] - alpha * (y_pred_stoch - y[rand]) * X[rand,1]\n",
    "\n",
    "        y_pred = X @ theta\n",
    "        costs.append(cost_J(y_pred, y))\n",
    "\n",
    "\n",
    "    y_pred = X @ theta\n",
    "    print(f\"Theta = {theta}\")\n",
    "    print(f\"Cost = {cost_J(y_pred, y)}\")\n",
    "\n",
    "    plt.plot(range(0, len(costs)), costs)\n",
    "    plt.title(\"Cost over iterations\")\n",
    "    plt.show()\n",
    "    return theta\n",
    "\n",
    "theta = stochastic_gradient_descent(X, y, max_iter = 1000, alpha = 0.000001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb73d7c1",
   "metadata": {},
   "source": [
    "a) Plot the computed line $h_{\\theta}(\\mathbf{x})$ on top of the scatter plot of exercise 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "id": "f73c6af3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FRUGpVGLnzp3G61qtFocOHYJKpQIAqFQqFBYW4ujRo8Y+u3btgk6nQ7du3Yx99u7di9LSUmOf1NRUPPTQQ6IdfERERE5lKGZZflXFUMwysoqFMsk1HJZmbofDhw8LtWrVEt59913h/Pnzwpo1a4SgoCBh9erVxj7vv/++EBoaKmzcuFE4efKkMHDgQCEqKkq4e/eusU///v2Fjh07CocOHRL27dsntGrVShg2bJjxemFhoRARESE8//zzQkZGhrB+/XohKChI+PTTTyWN0xlZ+UREVMPs2CHeMQcIwunT7h5VteaMv99uDZwEQRA2bdokxMTECHK5XGjdurXw2Wefia7rdDph+vTpQkREhCCXy4U+ffoI586dE/W5fv26MGzYMKF27dpCSEiIMGrUKOHmzZuiPidOnBB69OghyOVyoVGjRsL7778veYwMnIiourtXphMOXLgmfH/8d+HAhWvCvTKdu4dUfeh0ghAXJw6Y/vpXfTs5lTP+fssEQRDcO+fl+bRaLRQKBTQaDUJCQtw9HCIih0rJyMXsTZnI1dwvLBypCMDMAdFVP2etpjt5EmjfXty2ezfwl7+4ZTg1jTP+frv9yBUiInKflIxcTFx9TBQ0AYBaU4SJq48hJSPXTSOrBkaOFAdNkZFAaSmDJi/HwImIqIYq0wmYvSkT5pYdDG2zN2WiTMeFCZsYilmuWnW/be1a/a65Wm6tAkQOwMCJiKiGOpxVYDLTVJ4AIFdThMNZBa4blLdjMctqj6EvEVENlX/TctBkT78ajcUsawwGTkRENVR4nQCH9quxVq0S12UC9MtyrMtULXGpjoiohuoaFYZIRQBkFq7LoN9d1zUqzJXD8h4lJUDduuKgafx4FrOs5hg4ERHVUL4+MswcoD/2qmLwZPh+5oBo+PpYCq1qsB07ALkcKCy833b6NPDpp24bErkGAyciohqsf0wkFo2IhVIhXo5TKgKwaEQs6zhVJAhAXBzQt+/9tr/+FdDpgApnr1L1xBwnIqJyynQCDmcVIP9mEcLr6JepqvuMS/+YSPSNVta457YZi1kSGDgRERnV5Aravj4yqFrUc/cwPNfIkeK6TJGRQHY26zLVQFyqIyICK2iTBSxmSRUwcCKiGs8bK2iX6QSkXbyOjelXkXbxukeNrdp46y0WsyQTDJeJqMazpYK2Jyxn1eQlRZcwV8xy7lzgjTfcMhzyLJxxIqIaz5sqaFe3JUWPmzlbtco0aMrJYdBERpxxIqIaz1sqaFtbUpRBv6TYN1rpFTviPGrmrKQEiIgQ12UaP551mcgEZ5yIqMbzlgra1elQXo+aOWMxS7IBAyciqvG8pYK2Ny0pVsZjkvEFAejWTVzM8tFHWcySKsXAiYgInlNBu7KcH29ZUrTGI2bOTp4EfHyAw4fvt+3eDezapS8/QGQBc5yIiP7k7gra1nJ+DEuKak2R2dkaGfSBnruXFK1x+8wZi1lSFXDGiYioHEMF7YEdGkHVop5LgyZrOT/esqRojdtmzljMkhyAgRMRkZvZkvPjKUuKVeGWZHwWsyQHYYhNRORmthbgdPeSYlUZZs4mrj4GGSAKGB0+c8ZiluRgDJyIiNzMnpwfbz+U1zBzVjGnS+nIOk6ffw68+KK4LSdHn9NEZCcGTkREbuaKnJ8yneBxM1ROmzkrKQEaNNAvxRm89BKweHHV7ksEBk5ERG7n7N1yHlWhuwKHz5zt2CGuywToi1laqMvkiQEleTYGTkREbubMnB/Dbr2KAZlht563JJRbJQhAXJy4LtOjjwI7d1qsy+TJASV5Lu6qIyLyAM7YLecxFbqdzY5ilh515IuNPO5g5BqGM05ERB7C0Tk/tu7Wq4zHLmm98ALwxRf3v2/YEPjtt0rrMnnzYcmcJXM/Bk5ERB7EkTk/jqrQ7ZF/rK9cAZo2FbetWwcMHWr1pY4MKF2pxiy7ejgu1RERVVOO2K3nkUtas2ebBk03b0oKmgAPOPLFDjVm2dULMHAiIqqmqlqh2+P+WGs0+pylWbPut82dq08Mr11b8m288bBkjzgYmQAwcCIiqraqeradR/2x/vxz0wrgOTl2VQB3y5EvVeSNs2TVFQMnIqJqrCq79Tzij3VJCaBQiCuAT5ign2WyswK4Nx6W7I2zZNUVk8OJiKo5e3fruf2PdWoq0K+fuC0zE2jTpsq3dsmRLw7k7CKpJB0DJyKiGsCe3Xpu+2Ntrphl7976quAW6jLZw5sOS3bpwchUKS7VERGRWW5Z0jpxwrSY5Z49lVYArwpDQDmwQyOoWtTz6MDDGUVSyXYyQRC4d9EKrVYLhUIBjUaDkJAQdw+HiMilXFbHyY5iljWRxxYj9UDO+Pvt1hmnWbNmQSaTib5at25tvF5UVISkpCTUq1cPtWvXxpAhQ5CXlye6R3Z2NhITExEUFITw8HC8/vrruHfvnqjP7t27ERsbC7lcjpYtW2LlypWueDwiomqhf0wk9iX3xrpxcfh4aAesGxeHfcm9HRc0Xbmin00qHzStWwdcvcqgyQxvmiWrjtz+/8iHH34YO3bsMH5fq9w/kilTpmDLli34+uuvoVAoMGnSJAwePBj79+8HAJSVlSExMRFKpRIHDhxAbm4uXnjhBfj5+eG9994DAGRlZSExMRETJkzAmjVrsHPnTowdOxaRkZFISEhw7cMSEXkpR1Y0F5k9W1yXCdAXs7ShLhORK7l1qW7WrFn4/vvvkZ6ebnJNo9GgQYMGWLt2LZ5++mkAwNmzZ9GmTRukpaUhLi4O27ZtwxNPPIGcnBxEREQAABYvXozk5GT88ccf8Pf3R3JyMrZs2YKMjAzjvYcOHYrCwkKkpKSYHVdxcTGKi4uN32u1WjRp0oRLdUREjlJYCNStK26bNw94/XW3DIeqp2q3VAcA58+fR8OGDfHAAw9g+PDhyM7OBgAcPXoUpaWliI+PN/Zt3bo1mjZtirS0NABAWloa2rZtawyaACAhIQFarRanT5829il/D0Mfwz3MmTNnDhQKhfGrSZMmDnteIqIab+VK06ApN9chQVOZTkDaxevYmH4VaRev8wgScji3LtV169YNK1euxEMPPYTc3FzMnj0bPXv2REZGBtRqNfz9/RFaoVJsREQE1Go1AECtVouCJsN1w7XK+mi1Wty9exeBgYEm45o2bRqmTp1q/N4w40RERFVQUgI0aABotffbJkwAFi1yyO098jBiqnbcGjg99thjxv/drl07dOvWDc2aNcNXX31lNqBxFblcDrlc7rb3JyKqdpxYzBK4fxhxxfklw2HE3K5PjuL2pbryQkND8eCDD+LChQtQKpUoKSlBYWGhqE9eXh6USiUAQKlUmuyyM3xvrU9ISIhbgzMiohpBEIBu3cRBU+/egE7nsKDJ4w4jpmrNowKnW7du4eLFi4iMjESnTp3g5+eHnTt3Gq+fO3cO2dnZUKlUAACVSoVTp04hPz/f2Cc1NRUhISGIjo429il/D0Mfwz2IiMhJXFTM0qMOI6Zqz62B02uvvYY9e/bg8uXLOHDgAJ566in4+vpi2LBhUCgUGDNmDKZOnYqffvoJR48exahRo6BSqRAXFwcA6NevH6Kjo/H888/jxIkT2L59O958800kJSUZl9omTJiAS5cu4Y033sDZs2excOFCfPXVV5gyZYo7H52IqEo8Pgn6+eeBDh3uf9+oEVBaCvTq5fC38ojDiKnGcGuO0++//45hw4bh+vXraNCgAXr06IGDBw+iQYMGAID58+fDx8cHQ4YMQXFxMRISErBw4ULj6319fbF582ZMnDgRKpUKwcHBGDlyJN566y1jn6ioKGzZsgVTpkzBxx9/jMaNG2Pp0qWs4UREXsujk6CvXAGaNhW3rV8PPPus097S7YcRU43CI1ck4JErROQpLCVBGxa+3JoE7cBilrYcK1KmE9Bj7i6rhxHvS+7NKts1jDP+fru9cjgREUljLQlaBn0SdN9opWsDBAcXs7R1Rs1wGPHE1ccgA0Q/H6cdRkw1lkclhxMRkWUemQS9YoVDi1kaZtQqPqehrEBKRq7Z1/WPicSiEbFQKsTLcUpFAEsRkENxxomIyEt4VBK0E4pZVnVGrX9MJPpGKyUv8RHZg4ETEZGX8Jgk6B9/BCpusHFAMUtbZtQsHTjstMOIif7EpToiIi/RNSoMkYoAWJo/kUGfC9Q1Ksw5AxAEoEsXcdDkwGKWHjWjRmQBAyciIi9hSIIGYBI8OT0J2lDM8pdf7rc5uJilx8yoEVWCgRMRkRdxSxJ0xWKWjRs7pZil22fUiCRgjhMRkZdxWRK0i4tZsqwAeQPOOBEReSFDEvTADo2galHP8cHErFmmQdPNm06tAA6wrAB5Ps44ERHRfeaKWX7wAfDaay4bAssKkCdj4ERERHorVgCjR4vbcnMBpdLlQ2FZAfJUXKojIqrpSkqAkBBx0DRhgr78gBuCJiJPVqUZp6KiIgQEcFsoEZHXclIxS6LqyuYZJ51Oh7fffhuNGjVC7dq1cenSJQDA9OnTsWzZMocPkIiInMBcMcv4eIcVsySqrmwOnN555x2sXLkS8+bNg7+/v7E9JiYGS5cudejgiIjICdLTTYtZ7t0LpKY6rJglUXVlc+C0atUqfPbZZxg+fDh8fX2N7e3bt8fZs2cdOjgiInKwESOAjh3vf28oZtmzp/vGRORFbM5xunr1Klq2bGnSrtPpUFpa6pBBERGRg7m4mCVRdWXzjFN0dDR+/vlnk/ZvvvkGHcv/VwwREXkGNxWzJKqObJ5xmjFjBkaOHImrV69Cp9Nhw4YNOHfuHFatWoXNmzc7Y4xERGQPDyhmSVTd2DzjNHDgQGzatAk7duxAcHAwZsyYgTNnzmDTpk3o27evM8ZIRES2WrHCNGjKzWXQRFRFMkEQBOvdajatVguFQgGNRoOQkBB3D4fIojKdwGMqarriYqB+feDWrfttEycCCxe6b0xEbuKMv982L9UdOXIEOp0O3bp1E7UfOnQIvr6+6Ny5s0MGRkS2ScnIxexNmcjVFBnbIhUBmDkgmgej1hTbtwP9+4vbWMySyKFsXqpLSkrClStXTNqvXr2KpKQkhwyKiGyTkpGLiauPiYImAFBrijBx9TGkZOS6aWTkEoIAdO4sDppYzJLIKWwOnDIzMxEbG2vS3rFjR2RmZjpkUEQkXZlOwOxNmTC35m5om70pE2U6rsp7kjKdgLSL17Ex/SrSLl63//MxFLM8evR+G4tZEjmNzUt1crkceXl5eOCBB0Ttubm5qFWrSkffEZEdDmcVmMw0lScAyNUU4XBWAU+b9xAOW1YdPhxYu/b+902aAJcuAfxdTOQ0Ns849evXD9OmTYNGozG2FRYW4p///Cd31RG5Qf5Ny0GTPf1Iz2EzQhU4ZFk1O1s/m1Q+aPryS307gyYip7L5X9i///1v9OrVC82aNTMWvExPT0dERAS++OILhw+QiCoXXifAof3IeYn21pZVZdAvq/aNVlreDTlzJvDWW+K2mzeB2rXtHhcRSWfzjFOjRo1w8uRJzJs3D9HR0ejUqRM+/vhjnDp1Ck2aNHHGGImoEl2jwhCpCIClbBYZ9H/0u0aFuXJYXsuZifa2LKuaKCzUzzKVD5o++ECfGM6gichl7JrTDQ4Oxvjx4x09FiKyg6+PDDMHRGPi6mOQAaLZDEMwNXNANOs5SeCQGaFK2L2sunw5MGaMuC03F1AqbR4DEVWNpMDphx9+wGOPPQY/Pz/88MMPlfZ98sknHTIwIpKuf0wkFo2INVleUrKOk02cnWhv87KquWKWf/sb8L//2fzeROQYkgKnQYMGQa1WIzw8HIMGDbLYTyaToayszFFjIyIb9I+JRN9oJSuHV4GzE+0Ny6pqTZHZWS0Z9MFu16gw88Usz5wBWre2672JyDEkBU46nc7s/yYiz+LrI2PJgSpwdqK9pGXVxNbw9a2Qftq3rz6QYl0mIrezKTm8tLQUffr0wfnz5501HiLyIs7asu8urki0NyyrKhXi4EupCMDXzQrRv31j8Qv27gV+/JFBE5GHsCk53M/PDydPnnTWWIjIi1THs/FclWhvblk17uFGkBUXizsWFwP+/lV6LyJyLJvLEYwYMQLLli1zxliIyEtU57PxKpsRWjQi1mFBoWFZdaBvAVQt64uDphkz9GUGGDQReRybyxHcu3cPy5cvx44dO9CpUycEBweLrn/00UcOGxwReR5nb9n3BC5LtO/VC/j5Z3FbQQFQt65j34eIHMbmGaeMjAzExsaiTp06+PXXX3H8+HHjV3p6ut0Def/99yGTyTB58mRjW1FREZKSklCvXj3Url0bQ4YMQV5enuh12dnZSExMRFBQEMLDw/H666/j3r17oj67d+9GbGws5HI5WrZsiZUrV9o9TqKarkpFHL2IcUaoQyOoWtRzbNCkVutzlsoHTYMH62eZGDQReTSbZ5x++uknhw/iyJEj+PTTT9GuXTtR+5QpU7BlyxZ8/fXXUCgUmDRpEgYPHoz9+/cDAMrKypCYmAilUokDBw4gNzcXL7zwAvz8/PDee+8BALKyspCYmIgJEyZgzZo12LlzJ8aOHYvIyEgkJCQ4/FmIPFGZTnDY7ElNORvPkT8zkUmTTOswXbgAtGhR9XsTkdNV6TTIK1euAECVjlq5desWhg8fjiVLluCdd94xtms0Gixbtgxr165F7969AQArVqxAmzZtcPDgQcTFxeHHH39EZmYmduzYgYiICHTo0AFvv/02kpOTMWvWLPj7+2Px4sWIiorChx9+CABo06YN9u3bh/nz5zNwohrB0UncNeFsPKckvt+5A1RIbUCzZsDly/YP1AZOCwSJahibl+ru3buH6dOnQ6FQoHnz5mjevDkUCgXefPNNlJaW2jyApKQkJCYmIj4+XtR+9OhRlJaWitpbt26Npk2bIi0tDQCQlpaGtm3bIiIiwtgnISEBWq0Wp0+fNvapeO+EhATjPcwpLi6GVqsVfRF5I2ckcVf3s/Gckvj+v/+ZBk0//+yyoCklIxc95u7CsCUH8cr6dAxbchA95u7y6iR+InexOXB6+eWX8dlnn2HevHnG3KZ58+Zh2bJl+Pvf/27TvdavX49jx45hzpw5JtfUajX8/f0RGhoqao+IiIBarTb2KR80Ga4brlXWR6vV4u7du2bHNWfOHCgUCuMXDy8mb2QtiRvQJ3HbWnvJsGUfgEnw5O1n4zn8Z6bT6XOZJk0ybe/RoypDlaw674AkcgebA6e1a9di5cqVeOmll9CuXTu0a9cOL730knFZTaorV67glVdewZo1axAQ4FlT+tOmTYNGozF+GZYkibyJM5O4XbVl39Uc+jPbtg3w9RW3rV6tTwB3UTFLZwXPRDWZzTlOcrkczZs3N2mPioqCvw01R44ePYr8/HzExsYa28rKyrB3714sWLAA27dvR0lJCQoLC0WzTnl5eVD+eSK4UqnE4cOHRfc17Lor36fiTry8vDyEhIQgMDDQ4jPK5XLJz0LkiZydxF0dz8Zz2M9MLgdKSsRtJSWAn5+dI7OPsw8tJqqJbJ5xmjRpEt5++20UlyvWVlxcjHfffReTKk5HV6JPnz44deoU0tPTjV+dO3fG8OHDjf/bz88PO3fuNL7m3LlzyM7OhkqlAgCoVCqcOnUK+fn5xj6pqakICQlBdHS0sU/5exj6GO5BVF25IonbqVv23aDKP7OTJ/WzSeWDppkz9bNMLg6agJqzA5LIlWyecTp+/Dh27tyJxo0bo3379gCAEydOoKSkBH369MHgwYONfTds2GDxPnXq1EFMTIyoLTg4GPXq1TO2jxkzBlOnTkVYWBhCQkLw8ssvQ6VSIS4uDgDQr18/REdH4/nnn8e8efOgVqvx5ptvIikpyThjNGHCBCxYsABvvPEGRo8ejV27duGrr77Cli1bbH10Iq9iSOJWa4rMLtXIoF9a89Ykbmeo0s+sRw/gz1IpRm4uZlkTdkASuZrNgVNoaCiGDBkianNW8vT8+fPh4+ODIUOGoLi4GAkJCVi4cKHxuq+vLzZv3oyJEydCpVIhODgYI0eOxFtvvWXsExUVhS1btmDKlCn4+OOP0bhxYyxdupSlCKjac9W5a96msm35dv3M1GogskJO1+DBwLffOvMxJGHwTOR4MkEQmBVohVarhUKhgEajQUhIiLuHQ2ST6ngYr72k/iwk/8zMFLNM/WEfake3Nsn3clcdJcOuOsB8IOjNyfxE1jjj7zcDJwkYOJG3Y/HD+wFExV94lgKISn9mZopZXq2rRPfxS43flw+03B28uvv9idyFgZObMHAi8m5lOgE95u6yuMPMsGS1L7m39YBywQLg5ZdFTU8Pn4dfGkeb3BMAxveKwmd7syQHbM7C4JlqImf8/a7SkStERN7AIdvydTrTukwAVO+mIldbbNJuCJSW/GwaNBmuy6Cvo9Q3Wun0IMawA5KIqsbmcgRERN6mytvyzRWzXLMGaReumQ2ayqustmRVipASkXvYHDitWrVKVMPJoKSkBKtWrXLIoIiIHKlK2/LlcuDxx8VtJSXAc885rP4R6ygReQ+bA6dRo0ZBo9GYtN+8eROjRo1yyKCIiBzJroOJJRSzdFT9I9ZRIvIeNgdOgiBAZuacpd9//x0KhcIhgyIiciSbDybu0QP4s8CvUUEBMGuWqMlaQAYAPjLT9yz/3iYBGxF5NMnJ4R07doRMJoNMJkOfPn1Qq9b9l5aVlSErKwv9+/d3yiCJiKrKcDBxxW35yvLb8nNzgYYNxS8cMgT45huz95RSMHNcT/2uOhYhJaoeJAdOgwYNAgCkp6cjISEBtWvXNl7z9/dH8+bNTSqKExF5kkoPJk5KAsqdTAAAuHgReOABq/e0FpB1bFq38oCNiLyGzXWcPv/8czz77LMICKg5a/Ks40TVFWv7wGwxS0RFAZcu2XQbaz9L/qyJXM+jCmCWlJQgPz8fOp1O1N60aVOHDMyTMHCi6ojVpGG2mCX27QO6d3fPeIjIoTyiAOb58+cxevRoHDhwQNRuSBovKytzyMCIyHksHT+i1hRh4upjTqtm7TGzLhaKWUKn0++kIyKywObA6cUXX0StWrWwefNmREZGmt1hR0Seq0wnYPamTJdXs/aYGa6tW4HERHHbmjXAc8+JmjwmyCMij2Jz4JSeno6jR4+idevWzhgPETmZQ44fsZGtM1xOC1r8/IB798RtJSXGukzlx+sRQR4ReRybA6fo6Ghcu3bNGWMhIheo8vEjNrJ1hsspQcvJk6Z1mWbN0he0rMBdy5gGnOki8mw2B05z587FG2+8gffeew9t27aFX4X/UmPyNJFnq9LxI3awZYZLc7fE8UFLjx7A/v3itoICoG5dk67uWsY04EwXkeezuXJ4fHw8Dh48iD59+iA8PBx169ZF3bp1ERoairpmfhERkWex6/iRKpA6c6XWFlUatAD6oKWsslNzy8vN1Sd6lw+ann5af2SKhd9VtgR5jmaY6ar4/oagMSUj1+HvSUS2s3nG6aeffnLGOIhIAkcs40ipdu3IatZSZ64KbhU7Lvfqb38DFi0St0koZunqZUwDd890EZF0NgdOf/nLX5wxDiKywpHLOJKOH3EQwwyXWlNkNjCQ/fm+YcH+ku5XadBirpjlAw/ogyYJXL2MaeCOhH0iso/NgRMA/Pzzz/j0009x6dIlfP3112jUqBG++OILREVFoUePHo4eI1GNV1nC8oTVxzC6e3P0jVbaNANV6fEjDiR1hksRKC1wshi0/Pe/wN//Lm6zsZil1CDP0Yfyumumi4hsZ3OO07fffouEhAQEBgbi2LFjKC4uBgBoNBq89957Dh8gUU1nbRkHAJbvv4xhSw6ix9xdNuXC+PrIoGpRDwM7NIKqRT2nLQMZZriUCnHQo1QEGBO+7c69MhStrBg06XQ2VwA3BHmG96v4/oBzDuV110wXEdnO5sDpnXfeweLFi7FkyRLRjrru3bvj2LFjDh0cEVlfxinPkxOJ+8dEYl9yb6wbF4ePh3bAunFx2Jfc27gsaFfQsnWraQXwtWv1CeB2FueVEuQ5mqsT9onIfjYv1Z07dw69evUyaVcoFCgsLHTEmIioHFuWZzw9kdgww2WJTblXEotZ2qP8MqZaW4SCW8UIC/aHItAfJfd0OPrbDYcub7o6YZ+I7Gdz4KRUKnHhwgU0b95c1L5v3z48YGXHChHZztblGW9PJLaae3XiBNChg/hFs2cDM2Y4dBy+PjJo7pZgXspZURDnIwPKV0RwVJ0lVybsE5H9bA6cxo0bh1deeQXLly+HTCZDTk4O0tLS8Nprr2H69OnOGCNRjWYtYdkSb04ktjgz9cgjQFqauO3GDSA01OFjsJSQX7GMlCMrirsqYZ+I7Gdz4PSPf/wDOp0Offr0wZ07d9CrVy/I5XK89tprePnll50xRqIarbJlnMp4ciKxzfWocnOBhg3Fbc88A3z1ldPGZykhvyJHL49aW84kIveSCYJgy3/EGpWUlODChQu4desWoqOjUbt2bdy9exeBgYGOHqPbabVaKBQKaDQaHilDbmOujpM5hi3z+5J7e+RMhc31qOwsZlkVaRevY9iSgza/bt24OAY9RB7EGX+/bd5VZ+Dv74/o6Gh07doVfn5++OijjxAVFeWQQRGRqfK70sZ0b262j6cnEls6ViT3z3pUW0+W2w14545+Z1z5oOmBB/Q75pycT2nvMqc3L48SkTSSA6fi4mJMmzYNnTt3xiOPPILvv/8eALBixQpERUVh/vz5mDJlirPGSUS4v4wzfcDDWDwiFpEu3DIP6Jew0i5ex8b0q0i7eF36uXGQtvw1ad0xbD2Zoy9mWbEC+P79kiuAV5W9y5yevDxKRI4hOcdpxowZ+PTTTxEfH48DBw7gmWeewahRo3Dw4EF89NFHeOaZZ+BbsZ4KETmNqxOJq3rki5R6VIJOh8fbNzK9YChy6SK2JuQ7q6I4EXkeyTNOX3/9NVatWoVvvvkGP/74I8rKynDv3j2cOHECQ4cOZdBE5AauqvxtaYnNloKb1paxHr14BFnznhQ3VrGYpb0qK8ZZkacvjxKRY0mecfr999/RqVMnAEBMTAzkcjmmTJkCmYt/oRGR40jZ3WbtyBepO8oqW8a6OO9J+Ao6UdvBM7mIa6204Wkcy1JdpYp1nFhniahmkRw4lZWVwd///iGctWrVQu3atZ0yKCJyPnNLb6GBfhjVPQqTereEr48MZToBK/dnVbrEJrXgpmH5q/y92uRfwrYV4jPmPuoxHJ90H4b5d8vsfzgHMbcc2qlZXYdXDici7yE5cBIEAS+++CLkcjkAoKioCBMmTEBwhQTODRs2OHaERORwloo7Ft4txfwdv2LFgSw827kxfjiRK/mcPGtLcYblrwmr9WdafvvFa+iUc1bUp90r66EN0P8HWcGtYmkP42Tm6iqx5ABRzSU5cBo5cqTo+xEjRjh8METkfFJ2txXeKcWne7Nsuq+UHWX9YyLxcusgvDqqt6h9c+uemDQwWdQWFuyPimwunOmFasIzEnkzyYHTihUrnDkOInIRKbvbbOUjAzo1q2u948SJeHXxYlFTj5eW4vdQ01wmpUJcTLequ/q8QU14RiJvZ3cBTCLyTs4o0qgTgKO/3bDc4fZt/c64ckHT5dBINE/ebDZoiqywtd8Ru/o8XU14RqLqwK2B06JFi9CuXTuEhIQgJCQEKpUK27ZtM14vKipCUlIS6tWrh9q1a2PIkCHIy8sT3SM7OxuJiYkICgpCeHg4Xn/9ddy7d0/UZ/fu3YiNjYVcLkfLli2xcuVKVzwekUdyVpFGiwHZJ58AFTaSHPxiIx59aYnZ7jKIt/Zb29UH6Hf12VKM09PUhGckqi7cGjg1btwY77//Po4ePYpffvkFvXv3xsCBA3H69GkAwJQpU7Bp0yZ8/fXX2LNnD3JycjB48GDj68vKypCYmIiSkhIcOHAAn3/+OVauXIkZM2YY+2RlZSExMRGPPvoo0tPTMXnyZIwdOxbbt293+fMSWVOVytxSGXa3OZpJQGYoWvnKKybtcSOexCIzlc8jzVQ+t7a0WH5Xn7eqCc9IVF3Yfcivs4SFheGDDz7A008/jQYNGmDt2rV4+umnAQBnz55FmzZtkJaWhri4OGzbtg1PPPEEcnJyEBERAQBYvHgxkpOT8ccff8Df3x/JycnYsmULMjIyjO8xdOhQFBYWIiUlRdKYeMgvuYIr81u2nszF39Yec8i9zB4qvGUL8MQT4o7r1gFDh4qapCRCb0y/ilfWp1sdx8dDO2BgBzNVx71ATXhGInfwqEN+Ha2srAzr16/H7du3oVKpcPToUZSWliI+Pt7Yp3Xr1mjatCnS0tIAAGlpaWjbtq0xaAKAhIQEaLVa46xVWlqa6B6GPoZ7mFNcXAytViv6InImV+a3pGTk4u0tmQ65l9mq2b6+pkFTSYlJ0ASYVj4HYDLjJnVp0ZvPiasJz0hUXUjeVecsp06dgkqlQlFREWrXro3vvvsO0dHRSE9Ph7+/P0JDQ0X9IyIioFarAQBqtVoUNBmuG65V1ker1eLu3bsIDBTv3AGAOXPmYPbs2Y56RKJKOaoytxSW6jdZEhrkh8I7pcbvK62anZ4OdOwovsFbbwHTp0sem7kZt+mJbSo9N87ec+I8adu/tbPxeBYekedwe+D00EMPIT09HRqNBt988w1GjhyJPXv2uHVM06ZNw9SpU43fa7VaNGnSxI0jourMlvyWqhRelFK/qTwZgIBaPlgzthuu3SquvGq2SgUcPCi+wY0bQIX/8DE3psNZBUjNVGP5/ssm19WaIiStPY7xvaLw2d4syADR+A3fPxajr+4tNfjxtG3/huKgE1cfM/uMAM/CI/IUbg+c/P390bJlSwBAp06dcOTIEXz88cd49tlnUVJSgsLCQtGsU15eHpRK/fZlpVKJw4cPi+5n2HVXvk/FnXh5eXkICQkxO9sEAHK53FghncjZpJYHqKyflNkTW+s3CQDU2mL4yGSivBpR8JaTAzSqkHPzf/8HfPml1fubC17MjQEAvvzld7zSpxXWH7kCtfZ+f5lMfwbw8v2XsXz/ZUnBj6VZN8OyaMXkdFexdDYez8Ij8ixuD5wq0ul0KC4uRqdOneDn54edO3diyJAhAIBz584hOzsbKpUKAKBSqfDuu+8iPz8f4eHhAIDU1FSEhIQgOjra2Gfr1q2i90hNTTXeg8jdqprfInX2xN76TRZfN3GiqC4TAODSJSAqyqRrxcDuxu0SJK2VvmRYeKcU/9l5HsoQOabEt4L2bimW7b+MipsODcHP5PgH0bx+kEkQ6cplUXuYOxuPlcOJPItbA6dp06bhscceQ9OmTXHz5k2sXbsWu3fvxvbt26FQKDBmzBhMnToVYWFhCAkJwcsvvwyVSoW4uDgAQL9+/RAdHY3nn38e8+bNg1qtxptvvomkpCTjjNGECROwYMECvPHGGxg9ejR27dqFr776Clu2bHHnoxMZVSW/xZbZE3sTi01ed/u2SV0mtGwJnD9v9vXmAruKy1FS5WmLMX/HeYQG+Zm9brjn/B2/GtvKB5G2LIt2jQpzSwBj7mw8IvIcbg2c8vPz8cILLyA3NxcKhQLt2rXD9u3b0bdvXwDA/Pnz4ePjgyFDhqC4uBgJCQlYuHCh8fW+vr7YvHkzJk6cCJVKheDgYIwcORJvvfWWsU9UVBS2bNmCKVOm4OOPP0bjxo2xdOlSJCQkuPx5icyxN7/F1tkTawFaRWYDto8/BiZPFnc8cECf42SGpcDO3hoohteVT1i3pnwQWXxPJ+k1OzLVmPpVusfkQBGR5/C4Ok6eiHWcyBVsTVhOu3gdw5YcNGmvaN24OOMMhiGQASoPXgwhmnHGqqwMqGXmv7MMRS7NKNMJ6DF3l8PPxbOHIQj89zPtMXzpIbvvAcBtOVBEZDtn/P32uBwnoprK1vwWe5LKLSUgV1pmYPNmYMAA8U3XrweefbbS93XGYcL2MizBQYDVZVFZhZ9F+Xu4OweKiNyPgRORB7Elv8XepHJzAZrFMgM+Pvpta+WVlAB+5nOMynPGYcJVde12MaYnRputmm5YJq1sDt5RpSGIyHsxcCLyUlVJKjcXoIm+N1PMMnvyP9Dow/ckz7R4YpXry9duY/2RK2avKRUBeCxGabaeVEWeGBQSkWt4zJErRGQbQ1I5cD//xqBKRRNVKpOgqd0r69FL3gM95u6SfPxL16gwi7vf7CX788vW+8oA1A3yw/wd5y0uH05PbIO+0UpJ9/PEoJCIXIOBE5EXM+QsKRXiP+RKRYDtScw5OfoEn3IVwDe17onmyZuhDdCXHzDsUNt6MtfkTDlXMDzX+4PbmgSLlRFgPRn+7S1n0KlZXUQqAizeWwZ9jhSPPiGqubirTgLuqiNPV+Vz1yZMAD79VNTU46Wl+D3U/AxMxWRyc7v/pO76q+y+yhA5hnVtiub1g02eKyUjF8nfnoLmrvXSBP1jIpCSkWe137pxcdDcLTG785C76oi8D3fVEZFZdhdNNFPM8m7zB9Dm2U8qfVnFCaZcTREmrD6Ghc/F4vF2+qDCnjwgnaBfMqtfR241AOwfE4krBXfw7tazVu8bUMtX0vvn3yzCwA6NePQJEVnEwImoprJQzPLHwKbA+nS7bjlp3TEsQEc83q6h3XlAOYV3MabnA5L61q8t7UzJhqG27UDk0SdEZAkDJ6Kaxkoxy/CL1+2+tU4A/rb2OBb7yNA3WmlTpXKDZfsvo0tUmKSZHaXC/EHdFXVv0QDfHc+xaQcijz4hInOYHE5kRplOcEvys9Nt3mwaNK1fry9e9GcF8Bu3i1HViZXZmzIBwOKuPymvl/IzN5RkqEykIgBxLeo5ZwciEdU4nHEiqsDWo0+8hoRilikZuUhae9zus+QMcjVFWLk/C/XryJHYLhJbT+VWWljS0utf7B5VaTBT/pw/SzNJhoDIUtV05i4RkS24q04C7qqrOSwdSuvVO6rMFLPEW28B06eLmjzpbDkDqQGrLcFulXcgEpHXcMbfbwZOEjBwqj4q+6NpLXAw5MHsS+7tPX9ou3UDDh8Wt924AYSGiprKdAJW7s/C21vOuG5sEtgSsDIgIqKKWI6AqAqszUpYO5TWq84py8kBGjUStz37rD6fqQJzP5fKjHqkGT5P+83sQbiOZsvBukzmJiJXYHI41QiGJbiKwYGhEnZKRq7kukMef07ZSy+ZBk2XLlkMmsz9XCoTH63EgmEdrXd0kPIBKxGRuzFwomqvTCdg9qZMs8nDhrbZmzIl1wTy2HPKbt/W74z77LP7ba1a6RPCo6JMulf2c6mUADzeriFGd29eldHazOMDViKqERg4kVeypVyA1CU4CKjyOWVuK2Pwn/+YVADHgQPAr79aHJe1n4sl124XA4DkA3EdxWMDViKqUZjjRF7H1nIBUmcqrt0uNm5tl8H8OWWV1foxN67QQD+M6h6FSb1bSkpUtjXBuaz0Hnz9/Uwv/FnM0tK4IhUBeDzGvsDHEMAYaijZWuDSVuaKUxIRuQtnnMirSMlVqkjqTEV4nQBjrR9lhaKKSkVApTu7LI2r8G4p5u/4FZ3eSTU7tor36DF3F4YtOYhX1qdj2JKD6DF3l8XXHV3wuUnQ9ObQfyHlVI4oaDI3rlxNEZbtv1zpeCqqOONmqKFkuGaLSEUAXuoVZbV4JYtTEpGnYTkCCViOwDPYWy7A8Dprx22Uf50tMz+21D9abCH4srl+lMx0LC1f+x5lvrWM/ftGK9H9/V1Qax2XG1T+EN/yY684o+UjEx8ErAyRY1jXpmheP1j08yz/c7587TbWHc6GWltsfF21KDxKRG7DOk5uwsDJM6RdvI5hSw5a7bduXJzJtnRDYAKYX4KrSmFLqeMC9IGApcBOUkB48oRJMct/9xyBBY8MNen/bOfG+M/OCzY/T2UsLT1WDDQ7NauLo7/dsLmmEmsxEZEjsY4T1WhVKRfgzOM2bNntZa4OlNTk9TuxnVHnxDHRtbaTv8RNebDZ/o4OmoD7S48rDmTh/cFtjT83czWU7KmpxFpMROTpGDiR17AlV8mc/jGR6ButdPiMhq27vSoGWtYCr4ib13Bo4Yuith/a9MLfn3zDpvd1pMI7pZiw+pjFpUciouqKgRN5DWu7uKTsvnLGjIZhXFK39ofXCRAtSV27WWyx73spC/DciRRR27Hdx/D3bTlVGrOjSKnoTURUnTBwIq9h2MVlb7kAV4yrsoRBQ2B343axSU6TTKavU2kQWFKEM/OfFr1eePBByM6dQ3udgMgDBU4vAyCF1xxBQ0TkICxHQF7F3nIBrhpXaJCZmkq4H9g92T4SSWuPm8xOlQ+aRh/ZaBI0DRv1EXRnzgKovAyAO+Z9dmSq3fCuRETuwV11EnBXnefx1N1XZToBC3adx4r9l1F4t9TYHqkIwPTEaLy9xfJhuj66Mlz6YKBJe/M3NgEyGdaM7YbuLesb2y0VtjS8jytnpJjrRESeiOUI3ISBE9nKXGB3OKvAYtmCPhcOYdm3b4vaJj35Bja36XX/+0db4rWEh6y+j6+PzGL5hcoMiW2EfeevIa+SnCtLzJVZICJyN5YjIJfy1FkdW7jrGcwloVvaPXd57hMmbS1f+x73fCv+87wfAlV8rifaNRQ9l6XyC5X59thVKEPkmBLfCs3rB+PytdtYvj8Lmrv3rL6WuU5EVFMwcCKzbD0PzhN52jNULFvwcN5FbFn5iqjtg57P43+PPGv29aoH9Mt0Up+rfPmFHZlqSUesqLXFmL/jPBY+F4tX4h/EpN6tMGntUWzLyLP6WlvqWREReSsmh5MJe86D8zSe+AyGsgUyAN+vmmISNLWd/KXFoCnI3xcAsPWkbc9lmPmaPuBhLB4RC2WIXNJYJ607hq0nc+DrI8MLqihJr7G1nhURkTdi4EQiZToBszdlms2LMbTN3pSJMp3npsZ56jP4+sjwXte6yJr7BDrknje2b2zzFzRP3mxSAby8OyVlGL7sECatM1/yQMpz9Y+JxP5/9MH0xDZWx6oTgL+tPY6UjFxRwGdOxcN/iYiqMwZOJCL1+I/DWQWuG5SNPPEZynQC8oa+gEfjO4nae0xYhleefB11LZQxqKiyWE/qc924U1rp9fJmb8oEAKvlD9xRP4uIyB0YOJFIVc6D8xSe9gyphy/C19cHEV9+YWzLqtcYr32ZjlfHJ2DN2G6Q13LcP0VLz5WSkYsec3dhwU/Sz7AzBGKeWj+LiMjVmBxOIlU9D84TOPMZbN2ldyb5LfSdN1PUNuj5D5He8CHg2O/YcTYPox5pDrXW9hIAlph7LkPOlz2Lk4ZAzFln/REReRMGTiTiiPPg3M1Zz2DTLr2yMqBWLVTMJjIUszQovFOK+TvOwxEsPVdlOV9SlA/EnHHWHxGRN+FSHYlIOc7D0/NZnPEMNu3S27QJqCX+b5KkJ5PRPHmzKGhypMqey1rOV2X3ZNI3EZGYWwOnOXPmoEuXLqhTpw7Cw8MxaNAgnDt3TtSnqKgISUlJqFevHmrXro0hQ4YgL09cUyY7OxuJiYkICgpCeHg4Xn/9ddy7Jy7at3v3bsTGxkIul6Nly5ZYuXKlsx/Pa1WHfBapz1CmE5B28To2pl9F2sXrZnek2bRLTyYDnnxS1Kfla99jS5uejngso4oxX2WfjT25XN4SJBMRuZpbl+r27NmDpKQkdOnSBffu3cM///lP9OvXD5mZmQgO1m/NnjJlCrZs2YKvv/4aCoUCkyZNwuDBg7F//34AQFlZGRITE6FUKnHgwAHk5ubihRdegJ+fH9577z0AQFZWFhITEzFhwgSsWbMGO3fuxNixYxEZGYmEhAS3Pb8nqw75LNaeQerSm5RdemG/noavb7yo/bcp0/AX/+6Ofag/LRjWEXWD5ZI+G3tyuZReVuyUiMhVPOqsuj/++APh4eHYs2cPevXqBY1GgwYNGmDt2rV4+mn9afFnz55FmzZtkJaWhri4OGzbtg1PPPEEcnJyEBERAQBYvHgxkpOT8ccff8Df3x/JycnYsmULMjIyjO81dOhQFBYWIiUlxeq4eFZd9WMpWdoQepSfvdmYfhWvrE+3eK+Nn09Be7U4T2nL3kzkCP54d+tZxw0a+pmmBcNi8Xg76QFNmU5Aj7m7Ks35igiR48P/64Brt4q9MkgmIjLHGX+/PSrHSaPRAADCwvQ5FUePHkVpaSni4+//l3zr1q3RtGlTpKWlAQDS0tLQtm1bY9AEAAkJCdBqtTh9+rSxT/l7GPoY7lFRcXExtFqt6IuqD1sLZFqasYm4eQ2X5z4hCpq2t++N5smbkbTlksODJkA/02RL0ARIy/ma9eTD6N6yPgZ2aARVi3oMmoiILPCYwEmn02Hy5Mno3r07YmJiAABqtRr+/v4IDQ0V9Y2IiIBarTb2KR80Ga4brlXWR6vV4u7duyZjmTNnDhQKhfGrSZMmDnlG8gy2Fsg0Vzn7b2lf4dDCF0Wv6zFhGV7qP9XxA/7TXx5sgMfbNbTrtdUhb42IyBN4TDmCpKQkZGRkYN++fe4eCqZNm4apU+//AdRqtQyeqhFbC2QaZmwmrj4G+b0SZMx/Bn66MmO/C2GN8fQry1BoQ0Vue/RoWd/m11SsO7Xn9Udx9LcbXpu3RkTkbh4ROE2aNAmbN2/G3r170bhxY2O7UqlESUkJCgsLRbNOeXl5UCqVxj6HDx8W3c+w6658n4o78fLy8hASEoLAwECT8cjlcsjl0g5D9Ua2FnGsbuwpkNk/JhLfNC1Ap6QXRH3GTPwv2g1OQOGOXx06RnNaR9SxqX9lye8DOzRy9PCIiGoEty7VCYKASZMm4bvvvsOuXbsQFSU+hb1Tp07w8/PDzp07jW3nzp1DdnY2VCoVAEClUuHUqVPIz8839klNTUVISAiio6ONfcrfw9DHcI+axHDsxrAlB/HK+nQMW3IQPebuEtchqsbKdAJ0OgGhgZWfDSeqX6TTAW3bioImdY/eSDv/BxZ98jeUlumcOWSjgrslkvvaVHeKiIgkc+uMU1JSEtauXYuNGzeiTp06xpwkhUKBwMBAKBQKjBkzBlOnTkVYWBhCQkLw8ssvQ6VSIS4uDgDQr18/REdH4/nnn8e8efOgVqvx5ptvIikpyThrNGHCBCxYsABvvPEGRo8ejV27duGrr77Cli1b3Pbs7mBpJ5nhj2l1z3UxNwNjyZPtI/WzcL/8AnTpIr544AAadIvDl7suYMKaY9Dcde4SnYHUmTJrye8y6JPf+0Yra9RMIxGRI7i1HIHMQhXlFStW4MUXXwSgL4D56quvYt26dSguLkZCQgIWLlxoXIYDgN9++w0TJ07E7t27ERwcjJEjR+L9999HrXLVm3fv3o0pU6YgMzMTjRs3xvTp043vYY23liMovyRXP1iOV78+AbXWfNBgOK5jX3Jvj/pj6qhlRVvPaotUBODAL4sg2/Dt/caWLVGWeQYL9lzCp3sv4U5JmeUbOJCtn03axesYtuSg1X7rxsXx+BQiqtac8ffbo+o4eSpvDJxsmV0pz5P+mNp0NlwlDHWMpP4sGheqse/TseLGDRuQ0ioO/9hwyulJ4OWZqytljbW6UwYfD+3AXCciqtaqfR0ncgxL+S1S7L9wzeyxI1JIOb5EKkfm6NhyVlvy7pWmQdPt20hpFYeJq4+5NGgC7CsXYE/yOxERSeMRu+rIcSrLb5FiwU8X8O2x322e1XHU7BDg+BydHZlqq31C72qR/slzorZZfcZje5//wx7/AMzelGbzz7Rzs7r45bcbNr7qz/EE+uF/w2MR94DtxSgNdacqqxSu5OG9RER24YxTNWPL7Iolts7qOGJ2qPxs1cr9WTYVqLQ2tmX7L1fa57n0bSZBU+zLa7Cy85PI1RThi7TLdv1M5bXs/+dVeLcUPjKZXflcUiqF8/BeIiL7cMapmpFa3LEytszqOGJ2yN58LGvPahibJeaKWS7rPBBv9xkn6vdbwR2bxmWw/+J1+MgAe1csq/JZGiqFV/y58vBeIqKqYeBUzTgqb6X8rE5lyeK2HF9i7j627nYrz9yzlt+Fd+1mscWx9b5wGMu/fUvU9tdxn+JymGmydLOwIDtGp1eFNK8qf5b9YyLRN1pZo4udEhE5GgOnakZKfktEiBxDYhvjf7svWr3f/gvXKv2ja+vxJeXZm49lKUdHysyVTNAhZfkkPHQt29i2o0UXjB0yAzBTHiM0yA8PhteBMiQAeVrzP1MpKs48VTYT5cgcJF8fmcfskiQiqg4YOFUz5c9VkwGiP/SGsGDWkw9DEegvKXBa8NMF4/82l+xdlR1c9uZjCTDN0ZEyc9U29zw2rZoiahs84gMca9TG4msK75Ti+RWHERrkZ3fQBOiDpOmJbVC/jhzhdQJw43YxktYeNz6PAXOQiIg8G5PDqyFDfotSIQ5Wym9tN8xM2fKn2Vyyt7X7yFDh+JJy7M3hGd29uSh4kzJztei790RBU1bdSDzw+sZKg6byNA4oQ1C/jhwDOzSCqkU9PN6uodXPiIiIPA9nnKopa/ktlc1MWWIu2VvKDJel2RN7c3j6RitF31c2c9WkUI2fK9Rleumpf2L7g4/Y9J6OqBJb8XmZg0RE5H0YOFVj1vJbLO28qoy5ZG97d3B1jQpDaJCf5KKSlnJ/LM1cJe9eiYmHvhG1tZ76DYr8XFv4sbKcJeYgERF5FwZONVzFWY/zeTex4CfruU8Vg5X+MZHo3ToCX6Rdxm8Fd9AsLAjPq5rDvwq1jMqrbPaq4kyOpWKWKzs/6ZCx2II5S0RE1QsDJxLNeqRdvC4pcKoYrJjb0bZ0X1alM06HswokzzZVNntlyLPK1RRh+PGtePfHhaLrsS+vQUGQQtL7SGVpeVMRWAuau/ckjZuIiLwPAycSsee4Dks72gzJ5JaSnaUmhw/q0BDznm5vcfbK10eG2f0ewKNdW1ktZlmZnq3q4efz1632m9ynFb785YrZ42WYs0REVL0xcKoByheFtPbH3NZk76pUDpeaHP59eg4OXirArCctzNxs3ox+AwaImiwVs6yMIEgLcKIaBGNfcm+LP1PmLBERVV8MnKo5ew7ftSXZ25bK4V2jwkTBRocmoQgL9kfB7RKrz6HWFmHC6mNYXH72SqcD2rYFMu8fq5LXKx7d4l4xW8zSmkA/aflY4XUCmNRNRFRDMXCqxuxdQgOkb5WXuty2I1ONqV+li4Ise85xm7bhFOrI/XDv8CH8ZcQT4otpaYiIi8NiO8++6xcdgYwcrU3LlEREVLMwcKqmHHH4rrVZlTKdgGs3iyWNZ9n+yyZt9pzjduNOKW4+8ST6/5pmbLvd7AEEX/wV8PUFYBr0XbtZjLe3nLF678ZhwXbXpCIiopqBgVM1VdXDd62Rci6cgdQCm9ZYKmb544OPYNGZfNHsWfmgr0wnYOm+rErHaqhu7usjs6smFRER1QwMnKqpqhy+a42Uc+HKc0TQVFkxS2uzZ+UT3i0twZWfSWJFbyIisoSBUzVSfvec1CU0W489kXIunCNJKWYpZfbMUsK7pUR5Jn8TEZE5DJyqCXNLZ5UlX9ub6GxtCdCRRhzfindsKGZpbfaMM0lERFRVDJyqAUtLZ5UFTYB9ic72LO3ZSn6vBJkfPQ1fQWdsW9p5IN6xUswyvE6ATTWriIiIbMXAyctJWTqrOPNUlURnW5f2bNX7wmEs//YtUdtfxn+G3+o2rPR1kYoA3LhdjB5zd1lcirOnphUREVF5DJy8nJSlM50ATE9sg/p15FWehbF2JIu9ZIIO25dNwoPXs41tO1p0wdghMyQVs3yyfSSS1h63WLNqfK8ofLY3y66aVkRERAaOObqeXKJMJyDt4nVsTL+KtIvXUaYTJC+d1a8jx8AOjaBqUa9KS1eGHWrA/SU/A9mfX6FBfibXKtMu91dkzXtSFDQ9NeLfGPv0TElB08dDO+CHE7kWa1YJAJb8bBo0Ga4D+l15ZfYUliIiohqFM05ewtIy09AuTSS93pFLbNaOZAFgsYhkxdBk8XfviopZXgxrhL5jFkLn4ytpLON6Nkd4nQBJs26WVLWmFRER1RwMnLxAZUenzN9xHqFBftDcKXXpMSGV7VAr0wmYHP8gVuzPQuHdUuNrlIoAPBajxPL9l80Wsxz/1L/w44MqSe/vIwPG9YzCtMejsTH9qkOeyRWJ70RE5N0YOHk4KUenGLj6mBBztY7MzYyFBvphVPfmmNS7FQ5nFSD83ZmYcOhb0esMxSwNguW+uF1cZvw+oo4/erZqgCB5LTQLC8Lzqubwr6VfaXbUbJqzE9+JiMj7MXDycFKOTim8U4op8Q9i/ZFshx4TYuvWfkszY5q7pfjPjvOICShFn54xKD+nNCP+JazqNMDkXnMGxqCBIlDSe0tJWPeRAYJgvoo5D+8lIiKpGDh5OKnLR83rB2Ffcm+H1TCydeu+tZmxEce3os9c6cUsZ23JxJF/9ZU0/vJHqliadRvXU7+rjof3EhFRVTBw8nBSl4/C6wQ47JiQynKqym/dr3jEi7mZMXlpMTLnP2NzMcuC26U2JWtbS1jvHxOJjk3r8vBeIiKqEgZOHs7aMpSjl5mk5FTN3pQJnU7A21vOVLqM2OfCISz79m1R29LlKXjn3D1JY8m/WWTTcqG1I1V45AoREVUVAycPJ2UZypHLTFJyqnI1Rfjb2uMW+8gEHX5cloRW168Y21JbdsO4IdOxpkcnhP1+HAW3S6yO5fK125VWAjfH2qwbD+8lIqKqYAFML2BYhlIqxMt2iiA/TI5/EH2jlQ57r6puyTcUsywfND014t8YP2Q6IhUBiGtRD+8MjLF6n7pBfpi/47xJEGdYLkzJyK3SOImIiOzBwMkDmasQ3j8mEvuSe2NKfCuEBvoB0O+mm7/jV/SYu8thgURVtuQv/u5d/LBqqvH7i2GN8MDrG5HeqDWA+zNjj7eLxEu9oizex1yhTANW+iYiInfiUp2HqWw3GwD8Z8d5p563Zs9ZdNaKWZpbXpv2eDTaNw7FmxszUHD7fpFMfTX0ppi/41eL78dK30RE5C4MnDxIZbvZJqw+htAgP6tJ232jlZLznSwlXleWU1Xx/f/x03JMOLxB1NZ66jd4olsLfPxgg0oTsB9v1xAJMZEmY9h8MkfS+Fnpm4iIXM2tS3V79+7FgAED0LBhQ8hkMnz//fei64IgYMaMGYiMjERgYCDi4+Nx/vx5UZ+CggIMHz4cISEhCA0NxZgxY3Dr1i1Rn5MnT6Jnz54ICAhAkyZNMG/ePGc/ms2s7WYD9EtzlpSfhTEouafDsp8vYcbGDCz7+RJK7t0vCZCSkYsec3dh2JKDeGV9OoYtOYju7+/CxzvOo/ieDpPjH0REiHjZTqkIwMLnYhGpCEDdu1pcnvuEKGiaEf8SmidvRpFfAL45dhV+Pj5WDxU2JGuXP4DYlhIMREREruTWGafbt2+jffv2GD16NAYPHmxyfd68efjkk0/w+eefIyoqCtOnT0dCQgIyMzMREKD/ozl8+HDk5uYiNTUVpaWlGDVqFMaPH4+1a9cCALRaLfr164f4+HgsXrwYp06dwujRoxEaGorx48e79HkrY203m1SGWZg5WzOx5Ocs0eG27249g8fbRqJBbX+sOPCbyWvV2iLREpkyRI4p8a3QvH6waOao2def4+FPpole2/HlNbhRoZjlpHXHsAAd8Xi7hjY9g6tLMBAREUklEwTBIzJsZTIZvvvuOwwaNAiAfrapYcOGePXVV/Haa68BADQaDSIiIrBy5UoMHToUZ86cQXR0NI4cOYLOnTsDAFJSUvD444/j999/R8OGDbFo0SL861//glqthr+/PwDgH//4B77//nucPXtW0ti0Wi0UCgU0Gg1CQkIc//AANqZfxSvr06t8n3Xj4rD7XB4+3ZtV5XsZ5omMuVN37wLBwfqzS/60pMsgvNt7rPkb/GmxHblXhmVLwHwJBkfkcxERUfXmjL/fHrurLisrC2q1GvHx8cY2hUKBbt26IS0tDQCQlpaG0NBQY9AEAPHx8fDx8cGhQ4eMfXr16mUMmgAgISEB586dw40bN8y+d3FxMbRarejL2aq67CSDPrG6Q5NQLPm56kETUGEH28YfgKAgUdD0l/GfWQ2ajK+3cQecpRIMSkUAgyYiInIbj00OV6vVAICIiAhRe0REhPGaWq1GeHi46HqtWrUQFhYm6hMVFWVyD8O1unXrmrz3nDlzMHv2bMc8iERSdrMF+fviTklZpYUw1x76DQ7dpS/osOrDUfAtV5dpbxsVXnjyX5JvYe8OOFb6JiIiT+OxM07uNG3aNGg0GuPXlStXrL+oigy72YD7gVBFd0rK9NcrdCg/C7P31z8cNqb2OedMilme+ma7TUGTgb074MwljxMREbmLx844KZX6ath5eXmIjLy/LJOXl4cOHToY++Tn54ted+/ePRQUFBhfr1QqkZeXJ+pj+N7QpyK5XA65XO6Q56hMxXIAfaOVZg+qrcgwozSme3PERyuNszApGbnYc/6aQ8b26YZ3kHD+oPH7G42bo+7lC7h0Sg0cSbf5ftwBR0RE1YHHzjhFRUVBqVRi586dxjatVotDhw5BpdIXVlSpVCgsLMTRo0eNfXbt2gWdTodu3boZ++zduxelpfe38qempuKhhx4yu0znKubKAfSYuwsAsC+5Nyb3aWlx5gnQz0ptzVAbgyZDOYOqalKoxuW5T4iCpnGD30TH4Quw9XS+zQGQIfeKO+CIiKg6cGvgdOvWLaSnpyM9PR2APiE8PT0d2dnZkMlkmDx5Mt555x388MMPOHXqFF544QU0bNjQuPOuTZs26N+/P8aNG4fDhw9j//79mDRpEoYOHYqGDfVb4J977jn4+/tjzJgxOH36NL788kt8/PHHmDp1qoVROZ9hx5ilc9jmpZzBf3ZeqLRyd8W6TY4oZ/CPn5abVAB/aOq3SG0VB0BfXuD6zSJEKgIqDeoMnHEIMRERkTu5danul19+waOPPmr83hDMjBw5EitXrsQbb7yB27dvY/z48SgsLESPHj2QkpJirOEEAGvWrMGkSZPQp08f+Pj4YMiQIfjkk0+M1xUKBX788UckJSWhU6dOqF+/PmbMmOG2Gk5SCl3asivOkDtUlSraoXe1SP/kOVHbjPiXsKrTAFGbTgAmrU/HS72i8NnerErPlAP0uVcVj1ohIiLyZh5Tx8mTObIORNrF6xi25KD1jhKtGxcHVYt6dt93xLEteCd1kajNXDHL8iIVAZieGI23t4hzsZQhcgzr2tSkYCYREZE7OKOOk8cmh1dXjjxfrXzukK2H88pLi3HuoyGits+6PIX3eo+x+tpcTRHqBvtjX3JvlgogIqIahYGTizlyd9ljMfoaRxUP57Um/vwhLN3wtqit1/glyK4rfUkt/2aRsVQAERFRTeGxu+qqK8PMUGXzMj4yy7Wcylu+/7JxN15KRq6x2nakwnxwJhN02LFkgihoSm3ZDar3duAfSYkIDfKT/BwsL0BERDURc5wkcPQaqbVz2Mb/mXxd8bo1C5+LxePtIo31odTaIhTcKkZ2wW2kf5uKjV+8Kur/1PMfIr3hQ8bimWU6Af/deR4f7zxv8X0NB+zuS+7NZTkiIvJozshxYuAkgTN+8CkZuSaFLiPL7UIzd91HhkqPU/GRAQuGdcTj7RqKLzz1FPD998ZvL4Y1Qt8xCxFRN9jsrretJ3Pwt7XHTe7PA3aJiMibMHByE2f84AHTyuEVk6vLX792sxhvbzkj6b6LDYHNxYtAy5aia2cXrcK5uN5Wk7mtBXZERESejoGTmzgrcLLFxvSreGV9uqS+kYoA7L++DT4ffii+cOcOEBgo+T2tBXZERESejOUIajCpydihd7VIm/uEuHHBAiApyeb35K45IiIiMQZOXsKwG6+yY1XMFbPEH38A9es7eXREREQ1A8sReAlDnSZz5KXFuDz3CVHQlDPmb4AgMGgiIiJyIAZOXqR/TCQWPheL8mlG8ecPmVQAf/rVVYj4bIGLR0dERFT9canOyzzeLhIL0BGTVv+CH5cloWXB78ZrqS27YfyQ6Vg0IpZJ3ERERE7AwMkLPV70Oy59MFDUNuj5D5HXpj0WsVwAERGR0zBw8jaDBgEbNxq/vdOiFVK/3IHk0GCWCyAiInIyBk7ewkwxS2zciKAnn8RA868gIiIiB2NyuDd4/XXToOnOHeDJJ90zHiIiohqKgZMnu3YNkMmAf//7ftuCBfoyAzZUACciIiLH4FKdp1q40LTaN4tZEhERuRUDJ09z9y4QFCRue/VV8awTERERuQUDJ0/yww/AwAqp3hcuAC1auGc8REREJMIcJ09QVga0aSMOmgYO1OcyMWgiIiLyGJxxcrfDh4Fu3cRtBw+athEREZHbMXBypzt3xAFS69ZARgbg6+u+MREREZFFXKpzp/IlBTZuBM6cYdBERETkwTjj5E4ymT6PiYiIiLwCZ5yIiIiIJGLgRERERCQRAyciIiIiiRg4EREREUnEwImIiIhIIgZORERERBIxcCIiIiKSiIETERERkUQMnIiIiIgkYuBEREREJBEDJyIiIiKJGDgRERERScTAiYiIiEgiBk5EREREEtVy9wC8gSAIAACtVuvmkRAREZFUhr/bhr/jjsDASYKbN28CAJo0aeLmkRAREZGtbt68CYVC4ZB7yQRHhmHVlE6nQ05ODurUqQOZTObu4dQ4Wq0WTZo0wZUrVxASEuLu4dR4/Dw8Bz8Lz8HPwrMYPo/s7GzIZDI0bNgQPj6OyU7ijJMEPj4+aNy4sbuHUeOFhITwF5IH4efhOfhZeA5+Fp5FoVA4/PNgcjgRERGRRAyciIiIiCRi4EQeTy6XY+bMmZDL5e4eCoGfhyfhZ+E5+Fl4Fmd+HkwOJyIiIpKIM05EREREEjFwIiIiIpKIgRMRERGRRAyciIiIiCRi4EQeY9asWZDJZKKv1q1bG68XFRUhKSkJ9erVQ+3atTFkyBDk5eW5ccTVx969ezFgwAA0bNgQMpkM33//vei6IAiYMWMGIiMjERgYiPj4eJw/f17Up6CgAMOHD0dISAhCQ0MxZswY3Lp1y4VPUT1Y+yxefPFFk38n/fv3F/XhZ+EYc+bMQZcuXVCnTh2Eh4dj0KBBOHfunKiPlN9L2dnZSExMRFBQEMLDw/H666/j3r17rnyUakHK5/HXv/7V5N/HhAkTRH2q+nkwcCKP8vDDDyM3N9f4tW/fPuO1KVOmYNOmTfj666+xZ88e5OTkYPDgwW4cbfVx+/ZttG/fHv/73//MXp83bx4++eQTLF68GIcOHUJwcDASEhJQVFRk7DN8+HCcPn0aqamp2Lx5M/bu3Yvx48e76hGqDWufBQD0799f9O9k3bp1ouv8LBxjz549SEpKwsGDB5GamorS0lL069cPt2/fNvax9nuprKwMiYmJKCkpwYEDB/D5559j5cqVmDFjhjseyatJ+TwAYNy4caJ/H/PmzTNec8jnIRB5iJkzZwrt27c3e62wsFDw8/MTvv76a2PbmTNnBABCWlqai0ZYMwAQvvvuO+P3Op1OUCqVwgcffGBsKywsFORyubBu3TpBEAQhMzNTACAcOXLE2Gfbtm2CTCYTrl696rKxVzcVPwtBEISRI0cKAwcOtPgafhbOk5+fLwAQ9uzZIwiCtN9LW7duFXx8fAS1Wm3ss2jRIiEkJEQoLi527QNUMxU/D0EQhL/85S/CK6+8YvE1jvg8OONEHuX8+fNo2LAhHnjgAQwfPhzZ2dkAgKNHj6K0tBTx8fHGvq1bt0bTpk2RlpbmruHWCFlZWVCr1aKfvUKhQLdu3Yw/+7S0NISGhqJz587GPvHx8fDx8cGhQ4dcPubqbvfu3QgPD8dDDz2EiRMn4vr168Zr/CycR6PRAADCwsIASPu9lJaWhrZt2yIiIsLYJyEhAVqtFqdPn3bh6Kufip+HwZo1a1C/fn3ExMRg2rRpuHPnjvGaIz4PHvJLHqNbt25YuXIlHnroIeTm5mL27Nno2bMnMjIyoFar4e/vj9DQUNFrIiIioFar3TPgGsLw8y3/i8bwveGaWq1GeHi46HqtWrUQFhbGz8fB+vfvj8GDByMqKgoXL17EP//5Tzz22GNIS0uDr68vPwsn0el0mDx5Mrp3746YmBgAkPR7Sa1Wm/23Y7hG9jH3eQDAc889h2bNmqFhw4Y4efIkkpOTce7cOWzYsAGAYz4PBk7kMR577DHj/27Xrh26deuGZs2a4auvvkJgYKAbR0bkOYYOHWr8323btkW7du3QokUL7N69G3369HHjyKq3pKQkZGRkiPIuyX0sfR7lc/natm2LyMhI9OnTBxcvXkSLFi0c8t5cqiOPFRoaigcffBAXLlyAUqlESUkJCgsLRX3y8vKgVCrdM8AawvDzrbhTqPzPXqlUIj8/X3T93r17KCgo4OfjZA888ADq16+PCxcuAOBn4QyTJk3C5s2b8dNPP6Fx48bGdim/l5RKpdl/O4ZrZDtLn4c53bp1AwDRv4+qfh4MnMhj3bp1CxcvXkRkZCQ6deoEPz8/7Ny503j93LlzyM7OhkqlcuMoq7+oqCgolUrRz16r1eLQoUPGn71KpUJhYSGOHj1q7LNr1y7odDrjLy5yjt9//x3Xr19HZGQkAH4WjiQIAiZNmoTvvvsOu3btQlRUlOi6lN9LKpUKp06dEgWzqampCAkJQXR0tGsepJqw9nmYk56eDgCifx9V/jzsTGYncrhXX31V2L17t5CVlSXs379fiI+PF+rXry/k5+cLgiAIEyZMEJo2bSrs2rVL+OWXXwSVSiWoVCo3j7p6uHnzpnD8+HHh+PHjAgDho48+Eo4fPy789ttvgiAIwvvvvy+EhoYKGzduFE6ePCkMHDhQiIqKEu7evWu8R//+/YWOHTsKhw4dEvbt2ye0atVKGDZsmLseyWtV9lncvHlTeO2114S0tDQhKytL2LFjhxAbGyu0atVKKCoqMt6Dn4VjTJw4UVAoFMLu3buF3Nxc49edO3eMfaz9Xrp3754QExMj9OvXT0hPTxdSUlKEBg0aCNOmTXPHI3k1a5/HhQsXhLfeekv45ZdfhKysLGHjxo3CAw88IPTq1ct4D0d8HgycyGM8++yzQmRkpODv7y80atRIePbZZ4ULFy4Yr9+9e1f429/+JtStW1cICgoSnnrqKSE3N9eNI64+fvrpJwGAydfIkSMFQdCXJJg+fboQEREhyOVyoU+fPsK5c+dE97h+/bowbNgwoXbt2kJISIgwatQo4ebNm254Gu9W2Wdx584doV+/fkKDBg0EPz8/oVmzZsK4ceNEW6sFgZ+Fo5j7HAAIK1asMPaR8nvp8uXLwmOPPSYEBgYK9evXF1599VWhtLTUxU/j/ax9HtnZ2UKvXr2EsLAwQS6XCy1bthRef/11QaPRiO5T1c9D9udgiIiIiMgK5jgRERERScTAiYiIiEgiBk5EREREEjFwIiIiIpKIgRMRERGRRAyciIiIiCRi4EREREQkEQMnIiIiIokYOBGRx5DJZPj+++8l92/evDn+85//OG08REQVMXAiIpd58cUXMWjQIIvXc3Nz8dhjj0m+35EjRzB+/HgHjEyaOXPmwNfXFx988IHL3pOIPAsDJyLyGEqlEnK5XHL/Bg0aICgoyIkjElu+fDneeOMNLF++3GrfkpISF4yIiFyNgRMReYzyS3WPPPIIkpOTRdf/+OMP+Pn5Ye/evQBMl+pkMhmWLl2Kp556CkFBQWjVqhV++OEH0T1++OEHtGrVCgEBAXj00Ufx+eefQyaTobCwsNKx7dmzB3fv3sVbb70FrVaLAwcOiK7PmjULHTp0wNKlSxEVFYWAgAAAQGFhIcaOHYsGDRogJCQEvXv3xokTJ4yvu3jxIgYOHIiIiAjUrl0bXbp0wY4dO2z5sRGRCzFwIiKPNHz4cKxfvx7lzyH/8ssv0bBhQ/Ts2dPi62bPno3/+7//w8mTJ/H4449j+PDhKCgoAABkZWXh6aefxqBBg3DixAm89NJL+Ne//iVpPMuWLcOwYcPg5+eHYcOGYdmyZSZ9Lly4gG+//RYbNmxAeno6AOCZZ55Bfn4+tm3bhqNHjyI2NhZ9+vQxjunWrVt4/PHHsXPnThw/fhz9+/fHgAEDkJ2dLfVHRUSuJBARucjIkSOFgQMHWrwOQPjuu+8EQRCE/Px8oVatWsLevXuN11UqlZCcnGz8vlmzZsL8+fNFr3/zzTeN39+6dUsAIGzbtk0QBEFITk4WYmJiRO/5r3/9SwAg3Lhxw+K4NBqNEBgYKKSnpwuCIAjHjx8XateuLdy8edPYZ+bMmYKfn5+Qn59vbPv555+FkJAQoaioSHS/Fi1aCJ9++qnF93v44YeF//73vxavE5H7cMaJiDxSgwYN0K9fP6xZswaAfrYoLS0Nw4cPr/R17dq1M/7v4OBghISEID8/HwBw7tw5dOnSRdS/a9euVseybt06tGjRAu3btwcAdOjQAc2aNcOXX34p6tesWTM0aNDA+P2JEydw69Yt1KtXD7Vr1zZ+ZWVl4eLFiwD0M06vvfYa2rRpg9DQUNSuXRtnzpzhjBORh6rl7gEQEVkyfPhw/P3vf8d///tfrF27Fm3btkXbtm0rfY2fn5/oe5lMBp1OV6VxLFu2DKdPn0atWvd/Zep0OixfvhxjxowxtgUHB4ted+vWLURGRmL37t0m9wwNDQUAvPbaa0hNTcW///1vtGzZEoGBgXj66aeZXE7koRg4EZHHGjhwIMaPH4+UlBSsXbsWL7zwQpXu99BDD2Hr1q2itiNHjlT6mlOnTuGXX37B7t27ERYWZmwvKCjAX//6V5w9exatW7c2+9rY2Fio1WrUqlULzZs3N9tn//79ePHFF/HUU08B0Adbly9flv5QRORSDJyIyKU0Go0xcdqgXr16aNKkiUnf4OBgDBo0CNOnT8eZM2cwbNiwKr33Sy+9hI8++gjJyckYM2YM0tPTsXLlSgD6mSlzli1bhq5du6JXr14m17p06YJly5ZZrOsUHx8PlUqFQYMGYd68eXjwwQeRk5ODLVu24KmnnkLnzp3RqlUrbNiwAQMGDIBMJsP06dOrPENGRM7DHCcicqndu3ejY8eOoq/Zs2db7D98+HCcOHECPXv2RNOmTav03lFRUfjmm2+wYcMGtGvXDosWLTLuqjNXP6qkpASrV6/GkCFDzN5vyJAhWLVqFUpLS81el8lk2Lp1K3r16oVRo0bhwQcfxNChQ/Hbb78hIiICAPDRRx+hbt26eOSRRzBgwAAkJCQgNja2Ss9JRM4jE4Rye32JiGqYd999F4sXL8aVK1fcPRQi8gJcqiOiGmXhwoXo0qUL6tWrh/379+ODDz7ApEmT3D0sIvISDJyIqEY5f/483nnnHRQUFKBp06Z49dVXMW3aNHcPi4i8BJfqiIiIiCRicjgRERGRRAyciIiIiCRi4EREREQkEQMnIiIiIokYOBERERFJxMCJiIiISCIGTkREREQSMXAiIiIikuj/Abi/1G+CMytiAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here\n",
    "plt.scatter(dataset[\"living_area\"], dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Rent price\")\n",
    "\n",
    "y_regr = theta[0] + theta[1] * X[:,1]\n",
    "plt.plot(X[:,1], y_regr, color='red', label='Regression line')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16e1eec7",
   "metadata": {},
   "source": [
    "b) How many samples do you need to visit for reaching the convergence?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd7870eb",
   "metadata": {},
   "source": [
    "The biggest improvements are made before the first 300ish iterations but smaller improvements still occur after that. If we were very limited in cpu time, we would tell that the convergence vas reached around 300 samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c185d7bc",
   "metadata": {},
   "source": [
    "c) What kind of stopping criterion could we use here?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "235f3ac0",
   "metadata": {},
   "source": [
    "We would use the delta of the global cost function. When we compute the cost function, we can stop the iterations when the result is not improving more than a set delta."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e7ce003",
   "metadata": {},
   "source": [
    "d) Compute the final cost value according to Equation 2 and compare it to the one of exercise 2 and 3. What can you conclude?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "id": "dbcb6f22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta = [ 0.338377   28.68612806]\n",
      "Cost = 144162.5602768206\n"
     ]
    }
   ],
   "source": [
    "# Your code here\n",
    "y_pred = X @ theta\n",
    "print(f\"Theta = {theta}\")\n",
    "print(f\"Cost = {cost_J(y_pred, y)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27a8e7fd",
   "metadata": {},
   "source": [
    "The result is really close to both of the other methods but the stochastic is way faster because we dont loop trough the whole dataset for each update. The stochastic might have a slightly worse final result because it is harder to find the exact perfect values but its speed and efficency compensates this."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8a85676",
   "metadata": {},
   "source": [
    "## Exercise 5 - Review questions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84f82d3d",
   "metadata": {},
   "source": [
    "a) The linear regression has a mathematical _closed form_ solution. Then, in which conditions would we prefer a gradient descent algorithm to compute the regression model?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eecbe019",
   "metadata": {},
   "source": [
    "The closed form solution is great to have to best value possible, but it is very compute hungry. The inverse of a really big matrix is not something simple to do. So, the gradient descent is better when compute time is limited."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3696b258",
   "metadata": {},
   "source": [
    "b) Outliers in a data set can be defined as values that are out of the \"usual\" range in comparison with other values. They typically come from noise or anomalies in the data capturing process. What is the impact of an outlier in the stochastic gradient descent process? What if we have many outliers? _Hint_: look at the equation of the MSE, and to the equation of the update rule."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4873219d",
   "metadata": {},
   "source": [
    "Since for each iterations we update theta based on a random point, the outliers could significantly slow the congergence. If there is a lot of them, each update of the thetha values will not decrease the total cost value. This means that, if we are in a while loop searching to improve the cost value, it might either cause more loops to achieve the desired goal or cause the while loop to exit because the cost value is not getting smaller, but bigger."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22dce221",
   "metadata": {},
   "source": [
    "c) In the case of stochastic gradient descent, what is the danger of having a too large or too small $\\alpha$ value? Could you think of a better (more advanced) strategy as the one stated in Slide 36?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1536554",
   "metadata": {},
   "source": [
    "A too small alpha value would make the descent too slow and remove the speed advantage of this method. An alpha too big would cause the theta values to jump from an extreme to another. This would be highly susceptible to outliers. To mitigate this, we could apply the same logic, but pick a small number of samples (mini-batch) rather than a single one for each operations. This would reduce the impact of outliers while keeping the algorithm faster than the full one."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07bdad8b",
   "metadata": {},
   "source": [
    "d) Let's assume we expect that the target variable $y$ has a dependency to the square and to the cube of one of the feature $x_d$ in our multi-variable training set $(x_1, \\ldots, x_d, \\ldots, x_D)$. How would you proceed? Do we need to take precautions in terms of numerical stability?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4f242c5",
   "metadata": {},
   "source": [
    "If we have a dependency to the square and to the cube of the feature f1, we would augment the matrix to reflect this :  h(f) = theta0 + theta1xf1 + theta2xf1² + theta3xf1³. Yes, we need to take precautions because f1³ could mean huge numbers and cause overflows. The solutions would be to scale down each value to keep the relations between them but reduce their overall values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7cf619b",
   "metadata": {},
   "source": [
    "e) _Advanced_. Could we use a descent algorithm without computing the gradient? If yes, give a pseudo code of the algorithm to find $(\\theta_{0}, \\theta_{1})$ using a linear regression $h_{\\theta}(x) = \\theta_0 + \\theta_1 x$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89317af1",
   "metadata": {},
   "source": [
    "_Your answer here_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b0997fa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "8ce59c65",
   "metadata": {},
   "source": [
    "# Exercice 6 Optional – Mini-batch gradient descent for linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "id": "8604ed56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stochastic : \n",
      "Theta = [ 0.32518013 29.02018324]\n",
      "Cost = 144715.36532107095\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "batch of 1 : \n",
      "Theta = [ 0.31051073 29.06744375]\n",
      "Cost = 144869.2393588724\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "batch of 10 : \n",
      "Theta = [ 0.32754329 28.6711317 ]\n",
      "Cost = 144160.22579802573\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.32754329, 28.6711317 ])"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def batch_gradient_descent(X, y, batch_size, max_iter, alpha):\n",
    "    theta = np.zeros((2))\n",
    "\n",
    "    costs = []\n",
    "\n",
    "    for i in range(0, max_iter): # we could also use a delta on the cost function with a while to stop when the cost is not improving but we wanted to see the curve after x iterations\n",
    "        batch_idx = np.random.choice(y.shape[0], batch_size)\n",
    "        y_stoch = y[batch_idx]\n",
    "        y_pred_stoch = X[batch_idx, :] @ theta\n",
    "\n",
    "        theta[0] = theta[0] - alpha * (1/len(y_stoch)) * np.sum(y_pred_stoch - y_stoch)\n",
    "        theta[1] = theta[1] - alpha * (1/len(y_stoch)) * np.sum((y_pred_stoch - y_stoch) * X[batch_idx, 1])\n",
    "\n",
    "        y_pred = X @ theta\n",
    "        costs.append(cost_J(y_pred, y))\n",
    "\n",
    "\n",
    "    y_pred = X @ theta\n",
    "    print(f\"Theta = {theta}\")\n",
    "    print(f\"Cost = {cost_J(y_pred, y)}\")\n",
    "\n",
    "    plt.plot(range(0, len(costs)), costs)\n",
    "    plt.title(\"Cost over iterations\")\n",
    "    plt.show()\n",
    "    return theta\n",
    "\n",
    "\n",
    "print(\"Stochastic : \")\n",
    "stochastic_gradient_descent(X, y, max_iter = 1000, alpha=0.000001)\n",
    "print(\"batch of 1 : \")\n",
    "batch_gradient_descent(X, y, batch_size = 1, max_iter = 1000, alpha = 0.000001)\n",
    "print(\"batch of 10 : \")\n",
    "batch_gradient_descent(X, y, batch_size = 10, max_iter = 1000, alpha = 0.000001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35e0d314",
   "metadata": {},
   "source": [
    "# Exercice 7 Optional – multi-variable linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de60cd7e",
   "metadata": {},
   "source": [
    "## A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "id": "928deeaa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta = [2302.75644692 1057.56722311   65.54208244]\n",
      "Cost = 133826.31478540495\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7w8/PDzt27EBaWho+++wz1K9fX99mwYIF+Oqrr7BkyRIcPXoUderUQWxsLIqL79bEGD16NM6ePYukpCRs3boVBw4cwKRJk/Tn8/PzMWDAALRs2RLJycn49NNP8e677+Kbb75x6vMSEVENlpEBPPCAdkPewEBg2DDgp58M22g02nPkvgQXSkhIEPr06WPyvEajEWQymfDpp5/qj+Xl5QkBAQHC2rVrBUEQhLS0NAGAcPz4cX2bHTt2CBKJRLh69aogCIKwaNEioX79+kJJSYnBvdu3b2/0vsXFxYJKpdL/XLlyRQAgqFSqaj0vERHVUL/9JgiNGgkCIAjh4YLQrZv2z7qfuDhX99ArqVQqu39/u3TEafPmzbj//vvx1FNPITQ0FF27dsW3336rP5+RkQGlUomYmBj9MalUip49e0KhUAAAFAoFQkJCcP/99+vbxMTEwMfHB0ePHtW36du3L/z9/fVtYmNjkZ6ejlu3blXp1/z58yGVSvU/zZs3t/uzExFRDbFyJdC/P3DjBtClizZ/qWIi+BdfAFu3uqp3ZCWXBk5//vknFi9ejHbt2mHnzp2YMmUKXnnlFaxcuRIAoFQqAQBhYWEG7wsLC9OfUyqVCA0NNThfq1YtNGjQwKCNsWtUvEdFs2fPhkql0v9cuXLFDk9LREQ1iloNJCQAzz0HlJZq6zGlpBi22b8fmDbNFb0jG7l0VZ1Go8H999+Pjz76CADQtWtXpKamYsmSJRg3bpzL+hUQEIAAYztRExERiVFYCIweDWzerH09ejSwerVhm8uXgZYtnd41qh6XjjiFh4cjMjLS4FjHjh2RmZkJAJD9s6ogOzvboE12drb+nEwmQ05OjsH58vJy5ObmGrQxdo2K9yAiIrKLzExt/aXNm4GAAOCFF6oGTYWFDJo8lEsDp969eyM9Pd3g2B9//IGW//zHFBERAZlMht27d+vP5+fn4+jRo5DL5QAAuVyOvLw8JFeYL96zZw80Gg169uypb3PgwAGUlZXp2yQlJaF9+/YGK/iIiIiqRaEAunfXbs4bFgYMGQJUyN0FoJ3Cq1PHNf2j6rNbmrkNjh07JtSqVUv48MMPhQsXLgirV68WateuLaxatUrf5uOPPxZCQkKETZs2CadPnxaGDBkiRERECEVFRfo2AwcOFLp27SocPXpUOHjwoNCuXTth1KhR+vN5eXlCWFiYMHbsWCE1NVVYt26dULt2bWHp0qWi+umIrHwiIvIyP/4oCP7+2lVyUVGC0Lmz4cq5nj1d3cMaxxHf3y4NnARBELZs2SJERUUJAQEBQocOHYRvvvnG4LxGoxHmzJkjhIWFCQEBAUL//v2F9PR0gzY3b94URo0aJdStW1cIDg4Wxo8fLxQUFBi0OXXqlNCnTx8hICBAaNq0qfDxxx+L7iMDJyIiMkmtFoQ337wbID38sGHABAjCG2+4upc1kiO+vyWCIAiuHfNyf/n5+ZBKpVCpVAgODnZ1d4iI7E6tEazbZ420bt8Gxo4FNm7Uvh4xAvj5Z8M2a9YAo0Y5v2/kkO9v7lVHRFTDJaZmYd6WNGSp7u7IEC4NxNzBkRgYFe7Cnrm5K1e026ekpAD+/trg6J9yOnpHjwI9erike+QYLt+rjoiIXCcxNQtTVp0wCJoAQKkqxpRVJ5CYmuWinrm5Y8e0AVFKCtC4sXb7lMpB05UrDJq8EAMnIqIaSq0RMG9LGozla+iOzduSBrWGGR0G1q0DHnoIUCqBDh2Adu20xyoqKACaNXNN/8ihGDgREdVQxzJyq4w0VSQAyFIV41hGrvM65c40GmDuXO2UXHGxtlZTRgZw+PDdNlFR2nIDdeu6rp/kUAyciIhqqJwC00GTLe282p07wMiRwHvvaV8PHgwcOgSUlNxt88YbwJkzgA+/Wr0Zk8OJiGqo0HqBdm3nta5e1RayTE4G/PyAJ58EfvrJsM3WrUBcnGv6R07FwImIqIbqEdEA4dJAKFXFRvOcJABkUm1pghrr99+1QdO1a0DDhkDfvlWDpj//BCIiXNM/cjqOJxIR1VC+PhLMHazdL7RyxSbd67mDI2tuPaf167WB0rVr2gTwVq3u1mvSKSpi0FTDMHAiIqrBBkaFY/GYaMikhtNxMmkgFo+Jrpl1nAQBeP994P/+TxsYde8OXLyonarTiYrSJosH1vBpzBqIU3VERBXUxAraA6PC8WikrMY9t1FFRcDzz98tL/Doo0BSkmGbhATg44+d3zdyCwyciIj+UZMraPv6SCBv09DV3XCtrCxg6FBtcctatYDHHgM2bzZss3mzdkUd1VicqiMiAito13gnT2qrfB87BtSvry1wWTlo+uMPBk3EwImIyBMraKs1AhSXbmJTylUoLt10q755nI0bgT59gL//1iaA168P7N5t2CY/X5sgTjUep+qIqMazpoK2O0xn1eQpRbsSBGD+fOCtt7Sv77sPOHXKsE379kBqqnbqjggccSIi8qgK2t42peiykbPiYmDs2LtB04MPVg2aXnkFOH+eQRMZ4H8NRFTjeUoFbUtTihJopxQfjZR5xIo4l42cZWdrq38rFICvrzafac8ewzZr1mj3pCOqhCNORFTj6Spomwo1JNB+obu6grY3bcrrspGz06e1SeAKBRASoq3HVDloOnGCQROZxMCJiGo8T6mg7UlTiua4LBl/82bggQeAzEygeXOgtLTq9NzVq0DXrva9L3kVBk5ERHCfCtrmcn48ZUrREqePnAkCsGCBtkbT7dtAx47AlSvAnTt327RsCRQWAk2a2Oee5LWY40RE9A9XV9C2lPPjLZvyOnXkrKQEmDwZWLFC+/r++7Ub91b04ovAokWAD8cSyDL+V0JEVIGugvaQLk0hb9PQqUGTpZwfT5lStMRpI2fXrwMxMdqgyccHiI6uGjStWwcsWcKgiUTjfylERC5mTc6Pu0wpVodTkvFTU7VJ4AcPAvXqAaGh2qTvym2eftr2e1CNxKk6IiIXs7YAp6unFKtLN3I2ZdUJSACDgNEuI2fbtgEjR2pzlmQyQKkECgrunq9TR1slPCTEtutTjcYRJyIiF7Ml58dVU4r24pCRM0EAPv9cu59cYSHQpo02aKpo7FhApWLQRDbjiBMRkYt5y2o5a9l15Ky0FHjpJWDZMu3r9u2B9HTDNj/+CIwZU/2OU43GwImIyMWcsVpOrRHccmpPN3JWLTduAMOHAwcOaJO8mzatGjSdOaMtdklUTQyciIhczNE5P169KXBamnZq7s8/tblLt29razRVlJsL1K9v9O3uGlCS+5IIguCkHRU9V35+PqRSKVQqFYKDg13dHSLyUo4IcHRlDir/Q68LDTxlJZ5RiYnaVXH5+UCjRtqRp4qGDgV+/lm7H52xt3toQMlgTzxHfH8zcBKBgRMROYs9vxTVGgF9PtljcsWebgrwYEI/z/riFQTg3/8GZswANBrt1NzVq4ZtWrYELl82eQlPDSg9NdhzFUd8f3NVHRGRG7Hnajl7bm1ibisYpyorA6ZMAaZN0wZNjRtXDZoAICPD5CVctldeNblsY2QywBwnIiIvZa+tTdxmlCM3F3jqKWDPHkAi0Y48Xb9u2Obll4GvvjJ7GWvrZrkDS8GeBNpg79FImWeNHnogjjgREXkpe5Q5cJtRjvR0oGdPbdAUFKQNmirbv99i0AQ4ea88O3H6xshkEgMnIiIvVd2tTdxmSispSRs0XbyoLVxZVFS1TW4u0LevqMt5Yt0sTwz2vBUDJyIiL1XdTYHdYpRj0SJg0CBtte969YC8vKptNBqT5QaMccpeeXbmicGet2LgRETkxaqztYlLRznKy4GpU4H4eECt1h6ruN8cALz+unbKTmJdTk91A0pX8MRgz1sxOZyIyMvZurWJy0Y5bt3S1mdKSrqbBF7Z4cOAXG7zLXQBZeWkd5mbLu13+MbIJBrrOInAOk5EVBPp6kBZ2grGrnWgLlzQVgJPTwf8/bV70FWWlwdIpXa5nacVk3SbFY4eggUwXYSBExHVVLpVdYDxUQ67Forcu1e759ytW0BAAFBSUrWNRmP11Jy38bRgz5VYAJOIiJyqOjlSVvnmG2DAAG3QBFQNmmbPtimfyRvZs0gqWc+lgdO7774LiURi8NOhQwf9+eLiYsTHx6Nhw4aoW7cuhg8fjuzsbINrZGZmIi4uDrVr10ZoaChmzpyJ8vJygzb79u1DdHQ0AgIC0LZtW6xYscIZj0dE5BUGRoXjYEI/rH2hF74c2QVrX+iFgwn97BM0lZcD06cDL76o/bMxR48CH31U/XsR2YHLk8Pvvfde7Nq1S/+6Vq27XZoxYwa2bduG9evXQyqVYurUqRg2bBgOHToEAFCr1YiLi4NMJsPhw4eRlZWFZ599Fn5+fvjon79kGRkZiIuLw+TJk7F69Wrs3r0bEydORHh4OGJjY537sEREHko3ymFXKhUwcqR2s15TTp8GOnWy732JqsGlOU7vvvsufv31V6SkpFQ5p1Kp0LhxY6xZswYjRowAAJw/fx4dO3aEQqFAr169sGPHDjz++OO4du0awsLCAABLlixBQkICrl+/Dn9/fyQkJGDbtm1ITU3VX3vkyJHIy8tDoom/rCUlJSipMEycn5+P5s2bM8eJiMheLl3SJoGfOwf4+GhzlyorLATq1HF+38hreGWO04ULF9CkSRO0bt0ao0ePRmZmJgAgOTkZZWVliImJ0bft0KEDWrRoAYVCAQBQKBTo1KmTPmgCgNjYWOTn5+Ps2bP6NhWvoWuju4Yx8+fPh1Qq1f80b97cbs9LRFTj7d+vrQR+7pz2deWgqWFD7TEbgia32YyYvJZLp+p69uyJFStWoH379sjKysK8efPw4IMPIjU1FUqlEv7+/ggJCTF4T1hYGJRKJQBAqVQaBE2687pz5trk5+ejqKgIQUFBVfo1e/ZsvPrqq/rXuhEnIiKqpmXLgClTgLIy4+e//lpb9NIGXKpPzuDSwGnQoEH6P3fu3Bk9e/ZEy5Yt8dNPPxkNaJwlICAAAQEBLrs/EZHXUauBhATgs89Mt7lwAWjb1qbL68omVB5f0m1GbNcVgFSjuXyqrqKQkBDcc889uHjxImQyGUpLS5FXaV+i7OxsyGQyAIBMJquyyk732lKb4OBglwZnREQ1Rn4+MGSI+aDpzz9tDprcZjNiqhHcKnAqLCzEpUuXEB4ejm7dusHPzw+7d+/Wn09PT0dmZibk/5TZl8vlOHPmDHJycvRtkpKSEBwcjMjISH2bitfQtZFXo1Q/ERGJdPky0Ls3sG2b6TZqNRARYfMt3GIzYqoxXBo4vf7669i/fz8uX76Mw4cP48knn4Svry9GjRoFqVSKCRMm4NVXX8XevXuRnJyM8ePHQy6Xo1evXgCAAQMGIDIyEmPHjsWpU6ewc+dOvP3224iPj9dPtU2ePBl//vknZs2ahfPnz2PRokX46aefMGPGDFc+OhFRtXhEEvTBg0D37kCFVc0G2rbVFrX0qd5XkUs3I6Yax6U5Tn///TdGjRqFmzdvonHjxujTpw+OHDmCxo0bAwAWLlwIHx8fDB8+HCUlJYiNjcWiRYv07/f19cXWrVsxZcoUyOVy1KlTB+PGjcN7772nbxMREYFt27ZhxowZ+PLLL9GsWTN89913rOFERB7LI5KgV64EJk0yvtccAGzYADz5pF1u5bLNiKlG4l51InCvOiJyF6aSoB2yd5wt1GrgzTeBBQtMt1GpADv+W+qSzYjJI3hlHSciIhLH7ZOgCwuBYcPMB02CICposmYq0tdHgrmDtXmtlcMi3eu5gyMZNJFduHzLFSIiEseaJGi7b49iSWamthL46dPGzz/1FPDTT6IuZctUpG4z4srvk7nbFCZ5PAZOREQewm2ToBUKYOhQoMIKZwO//w506ybqUtWpxzQwKhyPRspwLCMXOQXFCK0XiB4RDTjSRHbFwImIyEO4ZRL06tXAs88a32sO0CaH+/mJupSlqUgJtFORj0bKTAZDDtmMmKgC5jgREXmIHhENEC4NrJLHoyOBdkqrR0QDx3dGowHeegsYM8Z00CQIooMmgPWYyDMwcCIi8hBukwR9+7Y2Z+mjj4yff+01bdBkJbediiSqgIETEZEH0SVBy6SG03EyaaBzShFcuQJ07aqtw2TMpUvAv/5l06XdciqSqJJq5TgVFxcjMJD/ARMROZPLkqCPHQN69jR9vrwc8PW1+fK6qUhL9ZicMhVJZILVI04ajQbvv/8+mjZtirp16+LPP/8EAMyZMwfLli2zeweJiKgqXRL0kC5NIW/T0PFB09q15oMmQahW0AS40VQkkRlWB04ffPABVqxYgQULFsDf319/PCoqCt99951dO0dERC6m0QCTJwPPPGP8/Jw5NuUzmeLyqUgiC6zecqVt27ZYunQp+vfvj3r16uHUqVNo3bo1zp8/D7lcjlu3bjmqry7DLVeIqEa6cwdo0kS7RYoxly4BrVs75NZqjcB6TFRtjvj+tjrH6erVq2jbtm2V4xqNBmVlZXbpFBERudjly0BEhOnzJSVAhVkHe2M9JnJXVk/VRUZG4rfffqty/Oeff0bXrl3t0ikiInKhdetMB01SqXZqzoFBE5E7s3rE6Z133sG4ceNw9epVaDQabNiwAenp6fjhhx+wdetWR/SRiIic5YkngC1bjJ+7eBFo08a5/SFyM1bnOAHAb7/9hvfeew+nTp1CYWEhoqOj8c4772DAgAGO6KPLMceJiLyeSgWEhJg+X81SA0Su4Ijvb5sCp5qGgRMRebUDB4CHHjJ9nl8T5KEc8f1tdY7T8ePHcfTo0SrHjx49it9//90unSIiIifQaIAZM0wHTZ98wqCJqBKrA6f4+HhcuXKlyvGrV68iPj7eLp0iIiIHy8oCwsKAL74wfv7yZWDWLGf2iMgjWB04paWlITo6usrxrl27Ii0tzS6dIiIiB9q+XVuf6cYN4+dLSoCWLZ3bJyIPYXXgFBAQgOzs7CrHs7KyUKtWtba+IyIiRyop0U7NxcUZP89SA0QWWR04DRgwALNnz4aqQiXZvLw8vPnmm3j00Uft2jkiIrKT9HSga1fTU3O//grk5TmxQ0Seyeohon/961/o27cvWrZsqS94mZKSgrCwMPz444927yAREVWDIAArVgDPP2+6TUEBULeu07pE5MmsDpyaNm2K06dPY/Xq1Th16hSCgoIwfvx4jBo1Cn5+fo7oIxGJxP29yIBKpd2gd9060224ao7IKjYlJdWpUweTJk2yd1+IqBoSU7Mwb0saslTF+mPh0kDMHRzJHeVroiNHgFGjtKvjjImPB77+2qldIvIGogKnzZs3Y9CgQfDz88PmzZvNtn3iiSfs0jEiEi8xNQtTVp1A5bEDpaoYU1adwOIx0Qyeagq1Wlt/6Z13tH825sIFwMhm7URkmajK4T4+PlAqlQgNDYWPj+l8colEArWpv6gejJXDyZ2pNQL6fLLHYKSpIgkAmTQQBxP6cdrOjThkWvXqVWDsWGDvXtNt7twBgoKqdx8iD+GI729RI04ajcbon4nI9Y5l5JoMmgBAAJClKsaxjFzI2zR0XsfIJIdMq27ZAowfD9y8aboN85mIqs2qcgRlZWXo378/Lly44Kj+EJGVcgpMB022tCPH0k2rVg52ddOqialZ1l2wuBh45RXgiSdMB03ffsugichOrEoO9/Pzw+nTpx3VFyKyQWi9QLu2Iy1HTKWpNQLmbUmrkosGaEcGJQDmbUnDo5Eycfc6dw4YORIw9+9yUREQyM+eyF6sXlU3ZswYLFu2DB9//LEj+kNEVuoR0QDh0kAoVcVGv5B1OU49Iho4u2sey1ErFO02rSoIwHffAdOmaQMjc+2IyK6sDpzKy8vx/fffY9euXejWrRvq1KljcP7zzz+3W+eIyDJfHwnmDo7ElFUnIAEMgifdmMXcwZFMDBfJkSsU7TKteusWMGkS8PPPptu8/jrw6adW9o6IxLA6cEpNTdVv8vvHH38YnJNI+A8zkSsMjArH4jHRVUZJZKzjZBW7T6VVUu1p1UOHgGeeATIzTb85KwuQyazuGxGJY3XgtNfcMlcicpmBUeF4NFLGyuHV4OgVijZPq6rVwEcfAe++C5hb2cypOSKHs6lyuM6VK1cAAM2bN7dLZ4ioenx9JCw5UA2OXqFo07Tq338DY8YA+/ebvnDnzsCpUzb1iYisY1U5AkCb4zRnzhxIpVK0atUKrVq1glQqxdtvv42ysjJH9JGIyCmcsUJRN60qkxpeQyYNrJo/9euvwH33mQ+arl1j0ETkRFaPOL388svYsGEDFixYALlcDgBQKBR49913cfPmTSxevNjunSQi9+Rtmwo7a4WixWnVoiLgtdcAS/+eajQAc0uJnErUlisVSaVSrFu3DoMGDTI4vn37dowaNQoqlcquHXQH3HKFqCpv3VRYt6oOMD6V5vB9/1JTtZvzpqaabvPuu8DcuY7rA5GXcMT3t9VTdQEBAWjVqlWV4xEREfD397dHn4jIzdm9+rUbsWoqzZ4EAViyBOje3XzQdOUKgyYiF7J6xOm9997D+fPnsXz5cgQEBAAASkpKMGHCBLRr1w5zvfAvNEeciO6qKZsKO3UaMjcXmDgR2LjRfDtOzRFZxS1GnE6ePImtW7eiWbNmiImJQUxMDJo1a4YtW7bg1KlTGDZsmP7HGh9//DEkEgmmT5+uP1ZcXIz4+Hg0bNgQdevWxfDhw5GdnW3wvszMTMTFxaF27doIDQ3FzJkzUV5ebtBm3759iI6ORkBAANq2bYsVK1ZY+9hE9A9rluyTCAcOaBPAzQVN48ZpR6QYNBG5nNXJ4SEhIRg+fLjBseqWIzh+/DiWLl2Kzp07GxyfMWMGtm3bhvXr10MqlWLq1KkYNmwYDh06BABQq9WIi4uDTCbD4cOHkZWVhWeffRZ+fn746KOPAAAZGRmIi4vD5MmTsXr1auzevRsTJ05EeHg4YmNjq9VvIk9hz9GTmrCpsFPyt8rLgQ8+AN5/33xtptRU4N577XNPIqo2q6fq7K2wsBDR0dFYtGgRPvjgA3Tp0gVffPEFVCoVGjdujDVr1mDEiBEAgPPnz6Njx45QKBTo1asXduzYgccffxzXrl1DWFgYAGDJkiVISEjA9evX4e/vj4SEBGzbtg2pFXIGRo4ciby8PCQmJorqI6fqyJPZOwhQXLqJUd8esdhu7Qu9PLKmlKktV+yaHP7XX8Do0dpK4Oao1YCP1RMDxi/lZSsgicRwi6k6e4uPj0dcXBxiYmIMjicnJ6OsrMzgeIcOHdCiRQsoFAoA2jIInTp10gdNABAbG4v8/HycPXtW36bytWNjY/XXMKakpAT5+fkGP0SeyBFJ3Lol+6a+ciXQBmaeuKmwpS1XAO2WK2pNNf7/5i+/AF26mA+aoqK0U3N2CpoSU7PQ55M9GPXtEUxbl4JR3x5Bn0/2eHQSP5GruDRwWrduHU6cOIH58+dXOadUKuHv74+QkBCD42FhYVAqlfo2FYMm3XndOXNt8vPzUWRiV/H58+dDKpXqf1gZnTyRo4IAXfVrAFWCJ0/fVNih+Vt37gAvvgiMGAHk5Zlud+kScOaM9dc3wZtXQBK5gssCpytXrmDatGlYvXo1AgNtr8LrCLNnz4ZKpdL/6LaWIfIkjgwCXLZk38Eclr91+jRw//3AN9+YbycIQOvW1l3bDKeMoBHVMNXaq646kpOTkZOTg+joaP0xtVqNAwcO4Ouvv8bOnTtRWlqKvLw8g1Gn7OxsyP7Z+Vsmk+HYsWMG19WtuqvYpvJKvOzsbAQHByMoKMho3wICAvSlFog8laOTuL1xU2G7b7kiCMCiRdoq4CUlptt98gkwa5a4a1rB0ZsWE9VEVo84/fDDDygx8g9AaWkpfvjhB9HX6d+/P86cOYOUlBT9z/3334/Ro0fr/+zn54fdu3fr35Oeno7MzEz9Vi9yuRxnzpxBTk6Ovk1SUhKCg4MRGRmpb1PxGro2umsQeStn7Lum21R4SJemkLdp6NFBE2Dn/K0bN4ChQ4GpU80HTZcvOyRoAmrGCkgiZ7M6cBo/frzRbVUKCgowfvx40depV68eoqKiDH7q1KmDhg0bIioqClKpFBMmTMCrr76KvXv3Ijk5GePHj4dcLkevXr0AAAMGDEBkZCTGjh2LU6dOYefOnXj77bcRHx+vHzGaPHky/vzzT8yaNQvnz5/HokWL8NNPP2HGjBnWPjqRR/HmJG5HsVv+1t692tpMmzebb6fRAC1b2tRXMZwRPBPVNFYHToIgQGKkCNvff/8NqVRql07pLFy4EI8//jiGDx+Ovn37QiaTYcOGDfrzvr6+2Lp1K3x9fSGXyzFmzBg8++yzeO+99/RtIiIisG3bNiQlJeG+++7DZ599hu+++441nMjreXMSd3WoNQIUl25iU8pVKC7drJLfU638rbIy4O23gf79gWvXTLf79FOnFLRk8Exkf6LrOHXt2hUSiQSnTp3Cvffei1q17qZHqdVqZGRkYODAgfjpp58c1llXYR0n8mTeuhmvLaz5XVhb90j9ZwbujHga9U4eN9uHnYnHENy2tdPywVy+aTGRCzni+1t04DRv3jz9/7722muoW7eu/py/vz9atWqF4cOHe+VGvwycyNOx+KFjC1um/GsJ2sx5HfWKb5tt1yphq/7PzgxeGTxTTeXSwEln5cqVePrpp92uhIAjMXAi8mwO25j49m1cefYFNN+w1myzjx5+Ht/0NNy/09kjPgyeqSZyxPe31eUIxo0bB0C7ii4nJweaSnsstWjRwi4dIyKyF4csy09JgTByJJqnp5ttFvXqehT6VS19IkAbPM3bkoZHI2UOD2J0KyCJqHqsDpwuXLiA559/HocPHzY4rksaV6vVduscEZE92HVZviAAX30FzJoFSWmp2aYVp+aMXgqso0TkaawOnJ577jnUqlULW7duRXh4uNEVdkRE7sRuy/KvXwfGjwe2bTPbbNxT87C/dTex3WMdJSIPYnXglJKSguTkZHTo0MER/SEisjvdsnylqtjo9iO6HCezy/J37wbGjgWyzO/t1nrmJmh8fK3qH+soEXkOq+s4RUZG4saNG47oCxGRQ1SrplVZGTB7NvDoo2aDppPh7dEqYWuVoMlHUvWeFe/NOkpEnsXqwOmTTz7BrFmzsG/fPty8eRP5+fkGP0RE7simwpZ//gn06QN8/LE2t8mE3lO+x7BnPzM4Jvnn54UHI/SvK58HamYRUiJPZnU5Ah8fbaxVObfJm5PDWY6AyHuIXpa/Zg0weTJQUGD+goJgsU4S6ygRuYZb1HHav3+/2fMPPfRQtTrkjhg4kbdibR8jCgu1G/OuXGm+Xa9egEKhf2npd8nfNZHzuUXgVBMxcCJvxFEQI5KTgVGjgAsXzLe7fh1o1Mg5fSIimzni+9vqHCcA+O233zBmzBg88MADuHr1KgDgxx9/xMGDB+3SKSJyLN32I5WLQipVxZiy6gQSU82vHLOVpQ12XUajAT7/HJDLLQdNgsCgiagGszpw+uWXXxAbG4ugoCCcOHECJSUlAACVSoWPPvrI7h0kIvtSawTM25JmdFm+7ti8LWl2D2oSU7PQ55M9GPXtEUxbl4JR3x5Bn0/2OCxIEy07G4iLA157TbuCzpTvvzebIE5ENYPVgdMHH3yAJUuW4Ntvv4Wfn5/+eO/evXHixAm7do6I7M+a7UfsxdoRLqeNTP3vf8B99wGJiWabKc4roR73nGP6QEQexeoCmOnp6ejbt2+V41KpFHl5efboExE5kF23HxHB0ghX5f3anJJ7VVoKvPUW8K9/WWzaKmErsPx35n8REQAbRpxkMhkuXrxY5fjBgwfRunVru3SKiBzHbtuPiGTNCJdTcq8uXAB697YYNI0Y/YnBXnOOzv/Scds8MCICYMOI0wsvvIBp06bh+++/h0QiwbVr16BQKPD6669jzpw5jugjEdmRXbYfsYLYkStlfjEWJJ4XPTJlkx9/BF56SVtywAxjm/ParQ9mcKUjkfuzesTpjTfewDPPPIP+/fujsLAQffv2xcSJE/Hiiy/i5ZdfdkQficiOqrX9iA3EjlzlFpY4LvcqP1+7z9yzz5oNmnJGjDYaNNmlDxa4aqUjEVnH6sBJIpHgrbfeQm5uLlJTU3HkyBFcv34d77//PoqKihzRRyL6h72mcWzafsRGuhEuS/u1NajjL+p6VudeHT8OREcDq1aZb1deDsVbnzimDxa4aqUjEVnP6qk6HX9/f0RGav9fa0lJCT7//HMsWLAASqXSbp0jorvsPY0zMCocj0bKHF7NWjfCNWXVCUgAg+Cg4giXNEhc4CQ690qjAT77DHjzTaC83Hzbf8oMODv/S8eaPDB5m4Z2vTcRWUf0iFNJSQlmz56N+++/Hw888AB+/fVXAMDy5csRERGBhQsXYsaMGY7qJ1GNZm4aZ/KqE3hvy1mbRqB8fSSQt2mIIV2aQt6mocO2ABEzwiV2ZEpU7lVWFjBwIDBrlvmgafdug9pMdu2DFZy90pGIbCd6xOmdd97B0qVLERMTg8OHD+Opp57C+PHjceTIEXz++ed46qmn4Ovr68i+EtVIYqZxvj90Gd8fuuzWicSWRrjEjkxZDO527ADGjdNui2KOkWKWduuDlVw10kVE1hM94rR+/Xr88MMP+Pnnn/G///0ParUa5eXlOHXqFEaOHMmgichBLE3jVOTuicSWRriqlXtVUgK8+irw2GPmg6YZM8xWAHdm/peOq0a6iMh6ojf59ff3R0ZGBpo2bQoACAoKwrFjx9CpUyeHdtAdcJNfcqVNKVcxbV2K6Pa6cgIHE/o5bOrN0dQawbrcqz/+AEaOBE6etHBhNeAj7v8v6vqgzC9GbmEJGtTxh0wahG4t6yP5r1t2zwvTTccCxke6HBW0EXkzR3x/i56qU6vV8Pe/m7xZq1Yt1K1b1y6dICLTrJ2e8YZEYt3IlEWCAKxcCUydCty+bbmtlX1QFZViQeJ5gxE/HwlQMZXMXtOjupGuygsAZG48/UpUE4kOnARBwHPPPYeAgAAAQHFxMSZPnow6deoYtNuwYYN9e0hUw1kqWGmK1ycSq1TA5MnAunXm2924ATS0PoDUjQBV/p1Xzr/XTY/aY0TIWSsdich2ogOncePGGbweM2aM3TtDRFWZS1g2x6sTiY8cAUaNAi5fNt/OylEmHXMJ+VVuAftWFBc92kZELiE6cFq+fLkj+0FEZpiaxjHG3lumOILVOUz6N6qBBQu0tZnMWbAAmDnT5v5Zk5APeMf0KBGJY3MBTCJyrorTOLvSlFh26HKVNo5cMm8vNhfyvHZNu23Knj3mb6DRAJLqPbut05xePz1KRNZvuUJErqObxpkz+F4sGRONcCcumbcHU4U8s/4p5Ln9tIkyClu3Ap07Ww6aBKHaQRNg+zSnV0+PEhEAjjgReSxXJBLbPMUGcXlDU9eewNfoisc6N9EeKC4GEhKAr74yf/Hbt4HatcU9hAjWJuR7wvQoEdkHAyciD+bMROLq7pUnJm9IIwAvrTmJJT4SDPTN0yaAnzpl/sI2JoCbY01CvidMjxKR/XCqjogsMrdXnthK5aLzfwQBx95aAERGmg+aUlIcEjTpmKogXjk2cvfpUSKyL444EdVglqbe1BoBRy7dxBu/nDG5V57Ypfhi8n+CiwvxUeLXeDz9oPmGDgyYKjI2HeqoyuFE5BkYOBHVUMam3kKC/DC+dwSm9muLpDSlqPIHYpfi6/KGTF0v+u9z+HrzJ2hScMP0zT780HIpAjszNh3KkgNENRcDJ6IayFRV7LyiMizc9QeWHriEO6Vqq65paSpOlzc0+Z/92HR8NGq8dGQ9Xv9tlfkbCIJ2hOzSTa8e7alOAj4ROR4DJ6IaRszqNmuDJgBoVDfAYpuBUeGY3r8dvth9AQAgy7+BL7b+C72upJp/oyBUOzndE9SEZyTydEwOJ6phrK2KLZrItKOX+7eDNKgWBvyhwJHFz5kPmsrL9UFTdZPT3V1NeEYib8DAiaiGcVR16xu3S0S18y0pxuZza/HNxg/NNxQEwNfX7AiZ7ti8LWlQV95914PUhGck8hYuDZwWL16Mzp07Izg4GMHBwZDL5dixY4f+fHFxMeLj49GwYUPUrVsXw4cPR3Z2tsE1MjMzERcXh9q1ayM0NBQzZ85EeXm5QZt9+/YhOjoaAQEBaNu2LVasWOGMxyNyS46qbi3qumfPAh06oOV/V5pssutgmsGqOUsjZBWT0z1VTXhGIm/h0sCpWbNm+Pjjj5GcnIzff/8d/fr1w5AhQ3D27FkAwIwZM7BlyxasX78e+/fvx7Vr1zBs2DD9+9VqNeLi4lBaWorDhw9j5cqVWLFiBd555x19m4yMDMTFxeGRRx5BSkoKpk+fjokTJ2Lnzp1Of14iS9QaAYpLN7Ep5SoUl246ZIRBt7rNXiTQ5uGYrZotCMDSpUBUFJCZabKZWq1BTO+OBsfEjpB58j5xNeEZibyFRBCcVBBFpAYNGuDTTz/FiBEj0LhxY6xZswYjRowAAJw/fx4dO3aEQqFAr169sGPHDjz++OO4du0awsLCAABLlixBQkICrl+/Dn9/fyQkJGDbtm1ITb2bRzFy5Ejk5eUhMTFRVJ/y8/MhlUqhUqkQHBxs/4cmgnMTg7efzsJLa05YbmiBbq2X2QKQubnAc88BW7aYvtDu3UC/fkZPKS7dxKhvj1jsy9oXenlsmYCa8IxEruCI72+3yXFSq9VYt24dbt++DblcjuTkZJSVlSEmJkbfpkOHDmjRogUUCgUAQKFQoFOnTvqgCQBiY2ORn5+vH7VSKBQG19C10V3DmJKSEuTn5xv8EDmSMxODE1Oz8P62NFFtQ2r7Gby2umr2gQNAw4bmgyZB0AdNxkbcdCNkphbkixrxcnM14RmJvIXLyxGcOXMGcrkcxcXFqFu3LjZu3IjIyEikpKTA398fISEhBu3DwsKgVCoBAEql0iBo0p3XnTPXJj8/H0VFRQgKCqrSp/nz52PevHn2ekQisywlBoutzC2GqfpNpnw0NAr16wRYXzW7vBx47z3g/fdNX3zjRmDoUIO+mRpxM7VvXHX2iXOneknm9sbjXnhE7sXlgVP79u2RkpIClUqFn3/+GePGjcP+/ftd2qfZs2fj1Vdf1b/Oz89H8+bNXdgj8mbWJAZXZ5pGTP2miiQA3t92DgcT+hl8YVvsQ2Ym0KsXkGVmlOyfDAFd8JKUpsT3hy5XaaYbcVs8JhqLx0RXCaxk0kCM7N4CJeUaKC7dFB38uGO9JN3eeMaekXWciNyHywMnf39/tG3bFgDQrVs3HD9+HF9++SWefvpplJaWIi8vz2DUKTs7GzKZDAAgk8lw7Ngxg+vpVt1VbFN5JV52djaCg4ONjjYBQEBAAAICLBfzI7IHeyQGixk9sbZ+k00B2y+/AP/kJBq1YQPw5JMAjAcvxvoAAG9sOIP/jIrG/pmP6Ee8Lt+4jbXHMrFw1x/69mKCH1OjbhWDNFcGT5X3xmPlcCL34vLAqTKNRoOSkhJ069YNfn5+2L17N4YPHw4ASE9PR2ZmJuRyOQBALpfjww8/RE5ODkJDQwEASUlJCA4ORmRkpL7N9u3bDe6RlJSkvwaRq4ktD2CqndjRE1tXZIl63507wNix2sDIBMXFG9pg4NJN3Lpdivg14qcM8+6UYfSyo/rnCqjlgy92XTAZ/EyPuQetGtWuEng4c1rUVsb2xiMi9+HSwGn27NkYNGgQWrRogYKCAqxZswb79u3Dzp07IZVKMWHCBLz66qto0KABgoOD8fLLL0Mul6NXr14AgAEDBiAyMhJjx47FggULoFQq8fbbbyM+Pl4/YjR58mR8/fXXmDVrFp5//nns2bMHP/30E7Zt2+bKRyfS0yUGK1XFRr/QJdBO1xhLDLZm9MTW+k0W33fmDNC5s8nTvy9ejZdvhSGrwqoxH4noQuMGlKpiTF51AiG1/cwWizQ1CmXNtGiPiAYc+SGiKlwaOOXk5ODZZ59FVlYWpFIpOnfujJ07d+LRRx8FACxcuBA+Pj4YPnw4SkpKEBsbi0WLFunf7+vri61bt2LKlCmQy+WoU6cOxo0bh/fee0/fJiIiAtu2bcOMGTPw5ZdfolmzZvjuu+8QGxvr9OclMsbWxGBrR08sBWiVmQvYtDcRgE8/BRISTF4j8cy1fwI7w2DF1vJUurfl3SkT/Z6KQWRJuUbUe3alKfHqTylulQNFRO7B7eo4uSPWcSJnsDZh2ZbaP7oRKsD8iI/F+kw3bwKtWgGFhcYvsH491MOGo88nexyzL56VdEHgv566D6O/O2rzNQALNauIyK044vvb7XKciGoqaxODbUkqN7Vyy0diOApkdiXX//4HmBux/ef/ix27dNMtgibg7hQcBFicFpVIjI+IuUsOFBG5FgMnIjdiTWKwrUnlxgI0UfWZysu1K+Y2bTJ+o6VLgUmT9C/dcXuQG7dLzE6LCjDYJq8Ke5WGICLPxcCJyENVJ6ncWIBmNhDIyABatzZ93ki04ajNhKtDFxROj7kHyw9lIK/obq6UTBqIQVEyo/WkKnPHoJCInMNttlwhIuvoksoBVNmqw17VptUaAZdnzzMdNO3ebXKIxt6bCQP/TKWh6lYwYt4XLg3Erdsl6PPJHizc9Yc+aAoJ8sOMmHY4mNAPj0bKRF3PHYNCInIOBk5EHkyXsySrFKBY3ENOhKRjl+Dr64NWH79r9Lzi4g1satBev6dcZb4+Ejxxn32TqHXP9fGwTib3dTNGAPDEfeGIX3OySt6VqqgMX+y6gKQ0JfeMIyKLuKpOBK6qI3dn733Xjn/7X3SfNNLoueXdBuPLJ6YalAQwtvpPrRHstqpuQu9WiImUGTxXYmoWEn45A1WR5dIEz8lbYmdatsm+6KY1Dyb0Q1Ka0ujKQ66qI/I8XFVHREbZrdq0IECIjkb3lBSjp1slbNX+oVIdpax/ClMueiYaj3XWBhXWbvFijLlyDAOjwnEl9w4+3H7e4nXUgiC68CX3jCMicxg4EZHWPwngxsaptnR4EC8PMV3oUmfq2hP4Gl3xWOcmNidQT32kDdqF1RM1ctaorrg9JcUOq+v6zD3jiMgUBk5EBLzyCvDvfxs9pR9lEkEjAC+tOYklPhKbE6j9fH0wpEtTUW1lUuMbdVcW0bCOqHYV+8w944jIGCaHExmh1ghQXLqJTSlXTSY/e4Xbt7UVH40ETWvuG2hV0FTRvC1p6NayvtlEa1MW7rqAxNQsUW3FrNwLlwZirLwVk76JyC444kRUibVbn3isRYuA+Hijp2wNmHSyVMX4UXFZdF2kyt7YcAb1AvzQq01Ds9NjFff5M1XLau7gSPjX8rFpP0Aiosq4qk4ErqqrOXR7uVX+S+FVK6rUaqCW8f/P9HvrLhjx1AdO7pBpYgNWscFujQmKiQiAY76/GTiJwMCpZrC0fL7iknWPHZn45RfttilGKC7eELVpsDNZE7CKLclg79INROS+WI6AqJrMfWlaWj7v0fuUmRllwp49UD/0MA4l/SHqUuMfaImVir+MboRrb9ZsrCs2mZtJ30RUHQycqMawNE0jdvm8x+1TtmIFMH688XOCoP29WFGoMiZShu6tGuClNSft10czPDpgJSKvw1V1VCPocpcqBwdKVTGmrDqBxNQs0cvnPWafssJC7Yo5Y0HT4cP6oMnY78UsAXiscxM837uV3boqhscFrETklRg4kddTawTM25JmdNWV7piY5fMetWT96aeBevWMnxMEQC43+3sx58btEgAQvSGuvXhMwEpEXo2BE3kka+osic1dSv7rFuYOjgSAKsGT2CXrLq//dPq0dpTpp5+qnDp+9Bw2nfxb3y9bt0TRBTCWNsS1F48KWInI6zHHiTyOtUvKrcldGtKlqc37lBnrV0iQH8b3jsDUfm1FrdyydsWXrv2NG3kY3KutyXbyj3Yha8Ml/etwaSAei7JuxEi3qlAXwFSsoVS5NpIl9Wv74dadMovvY40lInI3LEcgAssRuA9b6iwpLt0Utcx+7Qu99MnH1gYwpvqlE1LbDx8P62R14GUuIExMzcK8zWcxPHElXv9tlfFrnvobU9akWD0dV5m536+xfvtIYLDqThYcgFE9WqBVozr632dSmtLi+1hjiYiqg3WcXISBk3uwtc6S7n1KVbHJ6tLVqc9kqV8VLTFRj8jagDAxNQufL9yI/31vvPK3OjAQuH0HvT/eA2V+9ZOq6/j7YlLfNiZHzioHmt1a1kfyX7esrqkk9n1ERGIwcHIRBk7uwZaRIx1dYAIY326jOhXBxfYL0I6gmArsxAaE6jwVbjdpjuCiAqPtIxK2QiYNxNP3N8MXuy9a/TzmWDv1SETkSo74/mZyOHmM6tRZGhgVjsVjoiGrtCGsTBpY7W1UrFkmr6tHVJHowpuXbgDz58O3fojRoClh4MtolbBV397eQRMA5BWVYeGuP9DtgyTRG/ESEXkTJoeTx6hunaWBUeF4NFJm9+02rF0mXznQEhN43XctHfJ7Hjd5vrqb8lor704ZJq86YXLqkYjIWzFwIo+hW/5uKVfJ3LJ1R2y3oeuX2KX9ofUCDXJ7bhSUmGzb4I4Km1dOR7P860bP95+4GJcaNrep3/YgZisUIiJvwsCJPIa55e+uXLZesV+WltbLpIG4dbukSk6TRKKtS6m/pkaN6QfX4GXFf01eL+KfaTlX4lYoRFTTMMeJPIojc5Xs0a+Q2n5Gz+tCuSfuC0f8mpNVRqcqBk29L6fg0qdDTAdN5eVIPHPN4LqV7+NMu9KULrgrEZFrcFWdCFxV536srbPkzH59vecClh+6jLyiMv3xcGkg5sRF4v1taSan9Jrk5+DXH15D6O1bRs/f6v0w6h/cq39tqu6T7j6mpjQdgblOROSOWI7ARRg4kbWMBXbHMnKNli0IKC/F23u+w9iT201er1XCVkx9pC1ej21v8T6+PhKT5RfMGR7dFAcv3EC2mZwrU4yVWSAicjVHfH8zx4lMctdRHU9gLAm9yuo5QcCg9ENYvOljk9d5efBMbIl8SPcGUfcB7k4dVh6RMueXE1chCw7AjJh2aNWoDi7fuI3vD2VAVVRu8b3MdSKimoKBExll7fYf7sqdgr+KZQva3LyC7ctfRoDadFBSucSAvHUj/Z/FPFfF8gu70pRYduiyxT5m55fgi10XsHhMNKbF3IOp/dph6ppk7EjNtvhea+pZERF5KgZOVIWp7T+UqmJMWXXCpUnY1nC34K9HRAO0CVBj2vrP8MS5AybbdY//Edfr1jc4VtvfF4A2YDK2x5up59KNSMnbNET3iAZ4d/NZKPNNT8XpPvOKZQaelUeICpysrWdFROSJmOMkQk3KcbJ1Pzh3Y8tmwA6l0QDLlgGTJpltZqmQZUhtP+TdKatyXOxzqTUCVhzKwPvbzlns8oyYdpgWc4/D9/ojInIUbrlCDid6+49K24a4E7VGwLwtaUa/5CuOqKg1Tvr/DMePA76+ZoOmru8miqr+bSxoAsQ/l6+PBI3qBVi8DwAs3HUBialZ+jpVgOnyB66on0VE5AoMnMhAdfaDcxduE/zl5AADBwI9ephscjrhfRy6cB0Bfr7Vvp2Y51JrBLOVyivTBWLuWj+LiMjZmONEBqq7H5w7cHnwV1YGfPEFMGuW2WatErZi0TPRqC+RmM07spap5zKW82VJxdVyjtrrj4jIkzBwIgP22A/O1RwZ/FlczbZ7NxATY/Ya972yFqqgegCAqWtPYJy8pdX9MMfYc5nK+RKjYiDmiL3+iIg8CQMnMuCu+8FZw1HBn9lVevVKgf/7P+DYMZPvL/QPQtSM9QbHNAKw/PBfVvXDFFPPZS7nSwx3Hl0kInI25jhRFZ6ez+KIZGbdiE3laa5bN1S49MI0oFUrs0FTq4StVYKmiqobh5p7Lks5X+auGe7mo4tERM7m0sBp/vz56N69O+rVq4fQ0FAMHToU6enpBm2Ki4sRHx+Phg0bom7duhg+fDiysw1rymRmZiIuLg61a9dGaGgoZs6cifJyw8KC+/btQ3R0NAICAtC2bVusWLHC0Y/n0QZGheNgQj+sfaEXvhzZBWtf6IWDCf3cPmjSERv8qTUCFJduYlPKVSgu3TS6Is3oiI0gIDb9MM5/PhzxR0wHREPGfiZqtZy1C/wqbyZsLqi1JZfLU0YXiYiczaVTdfv370d8fDy6d++O8vJyvPnmmxgwYADS0tJQp04dAMCMGTOwbds2rF+/HlKpFFOnTsWwYcNw6NAhAIBarUZcXBxkMhkOHz6MrKwsPPvss/Dz88NHH30EAMjIyEBcXBwmT56M1atXY/fu3Zg4cSLCw8MRGxvrsud3d56ez2IpmVlsgczKIzZtb2Ti2w3vI+JWltn7H/rjOk4tO2rnpwJmxNyDqf3aik7StmWqTeaBVeKJiJzBrQpgXr9+HaGhodi/fz/69u0LlUqFxo0bY82aNRgxYgQA4Pz58+jYsSMUCgV69eqFHTt24PHHH8e1a9cQFhYGAFiyZAkSEhJw/fp1+Pv7IyEhAdu2bUNqaqr+XiNHjkReXh4SExMt9qsmFcCsKawpkLkp5SqmrUtBvZLbmLV/pdnNeAFA8UcOcm6X4kJ2Ib7ee9Gu/ZYFB+DQG/2tGgUSU8AyLDgAn/1fF9woLOFqOSLyGl6/ya9KpQIANGigzalITk5GWVkZYiqsUurQoQNatGihD5wUCgU6deqkD5oAIDY2FlOmTMHZs2fRtWtXKBQKg2vo2kyfPt1oP0pKSlBScnd5eH5+vr0ekdyApQKZEhhuORJaxx9Pnf4fPt3xldnrbvrgG3zs0xpZy0znOlXXu0/ca3VAIybh/90n7kXvto2MvJuIiCpym+RwjUaD6dOno3fv3oiKigIAKJVK+Pv7IyQkxKBtWFgYlEqlvk3FoEl3XnfOXJv8/HwUFRVV6cv8+fMhlUr1P82bN7fLM5J7sKpA5tGj6PVApMWgqeu8nZhW0MSmJGyxHrqnsc1TZ56e8E9E5C7cZsQpPj4eqampOHjwoKu7gtmzZ+PVV1/Vv87Pz2fw5EXEJEs3un0LzeMnADs3VVmZV1HkjJ9R5B8Iqf26Z1IfG0aEKted2j/zEST/dYsFLImIbOQWgdPUqVOxdetWHDhwAM2aNdMfl8lkKC0tRV5ensGoU3Z2NmQymb7NsUrLwHWr7iq2qbwSLzs7G8HBwQgKCqrSn4CAAAQEiNvPyxNZLOLo5cwlS9dSl2Nc8hbM2bvM7DUOtOqKZ59+H+HSQLzYvQUW7vrD3t2sokNYPavam0t+H9Klqb27R0RUI7g0cBIEAS+//DI2btyIffv2ISIiwuB8t27d4Ofnh927d2P48OEAgPT0dGRmZkIulwMA5HI5PvzwQ+Tk5CA0NBQAkJSUhODgYERGRurbbN9umNCblJSkv0ZNInYlmbdSawRoNAJCgvyQV2S4YW6fjJNY9ss8BKjLTbxbS3HxBm4VFGNtvUB0a1kfX+2+IOreQ7s0QXCQH7LyipB0LsfqvucWlYpuayr5XakqxpRVJzg9R0RkI5euqnvppZewZs0abNq0Ce3bt9cfl0ql+pGgKVOmYPv27VixYgWCg4Px8ssvAwAOHz4MQFuOoEuXLmjSpAkWLFgApVKJsWPHYuLEiQblCKKiohAfH4/nn38ee/bswSuvvIJt27aJKkfgLavqrFlJ5o1M7dXWLE+JD/+3CA9lnDB/gYICoG5dANoA7Os9F/H9oQyoKgVgjrL2hV6iykPoVtGZyrfSVRg/mNCvRo00ElHN43Wr6hYvXgwAePjhhw2OL1++HM899xwAYOHChfDx8cHw4cNRUlKC2NhYLFq0SN/W19cXW7duxZQpUyCXy1GnTh2MGzcO7733nr5NREQEtm3bhhkzZuDLL79Es2bN8N1339WoGk7WriRzF/aaVjQWNAaWFWPKkZ8x7fA6828ODweuXdP35+s9F7D0wJ+4U6q2uh+2sHaLGGuS3z25ThcRkSu4fKrOksDAQPznP//Bf/7zH5NtWrZsWWUqrrKHH34YJ0+etLqPnqxi0HGjoMTjvkztNa1YJWgUBDyWfgiLNn1s+c0V/htNTM3CGxvOIO+Oc0aYANsqeIutFG5LRXEioprOLZLDyf5MTUtZcujiDZtHdeyZdG7PHJ2KIzD3XL+MT3b8G12z0s2+p8dLK5FTryGWpGZhYFS4yf44mi0VvMVWCufmvURE1mPg5IWq8yX/9d6L+OXE31Z/Wdsz6dze04q70pQILi7EjIOrMT55i9m2eYF10WXa3am7eVvS0K9DmMn+mHN/y/r4/a9bVr5LKyTID/8ZHY1erRtaHXz2iGiAcGmg2Urh1kz9ERHRXW5TAJPsw1zQIZZuVCcx1fxebDq6QK3y6Ja119GxqkClpb6d+huFi5bi9JcjLQZNrRK2GgRN+Oc+Pyou21TYMqCW7X+98orK4COR2DRip6sUDqBKDSpu3ktEVD0MnLyMpaBDDF3QNW9LGtQa8yGYpdEha66juHQTm1Ku4tDFG6L6aSlHR33oMDo82hufJP7bbLtO0/+LVglbTZ7/K/eOqP5UdujSTVQnNqlODhIrhRMROQan6ryMvRJ+xSaL22MFl635WCZzdLKygIQE+P74I1qZeb+iRSeMGjXf4n1aNqhtVb8qshAvmlXdHKSBUeF4NFJWo4udEhHZGwMnLyP2y3Zolyb4NeWaxXaWArHqruCyJR/LZI5OaSk0X34Jn1mzLF7D3AhT5fuMlbfCdwczTOYMieEjMQyiKr82dl975CD5+kjcZpUkEZE3YODkZcQmBj/VrbmowOlGQQk2pVw1OVpRnRVc1cnHqpKjs3Mnip8dj8Ac8/lUrWdugsbH1+L1JdCOlg2KkiH5r1uYExeJ+DUWCmSaoRGAOXEd0aheAELrBeLW7RLEr9GWx6j4/MxBIiJybwycvIwuMXjKqhP6L3+dil/Kvdo0NBtgAdpRkfe3ndO/NrZKrjoruGzNx5oec8/dPvz5JzBjBrB5M8yFcK8Mfh2bIx8WfQ+JRFvC6ftDl/H9ocsIlwZi4oMRWHYww+bpt0b1Agz2iFvsI6kyRWlL+QEiInIeBk5eSJcYbOlL2VSApVM5QDBWQ0lsoGZs9MTWfKxWjWoDt28D8+cDH35oub2IabnKjD37t79lWH2diiqPujEHiYjI87h0rzpP4al71YkpSGksMVtM/k3lfc5sqeOkuHQTo749Yt1DCQL+11SJe955HVCpzDa1JWByBO4NR0TkGl63Vx05lpjE4MqjHjcKSgym5yoztUrOltGTHhENEFLbT/QWJh1zMvDR3m9xz+XTZtt1fXk1btWWirqmozFniYjIuzBwIoMAa1PKVVHvMTbN5qgVXNKiArx6cDXGnTA/gvRj18cwZ8BLdr9/dTBniYjIuzBwIgPVXSVnzYjTsYxcs6NNPho1Rp7+H+YlLYGfRm22P/KPdlW78Kc1TOWFfT2yCxrWC2TOEhGRl2LgRAZsXSVnS46TueTwbn+n4b2kJbg350/zHdZoAIkEc1OzMHmV7eUCAODBdg3x24WbFttN798O//39il325SMiIs/CwIkM2LJKzlQRS2Or8CoyNmoVWnATb+xfgWFn95rv6JEjQM+e+pcDo8Kx6JloTF17ohrVusWNDEU0roODCf24Go6IqAbiXnU1QMV94BSXblrcN86afc6qs1edbnRLAsC/vAyTj/yMY4vGWQ6aBMEgaNJ5rHM4vh7V1fx7zRC7tUpovUB9PteQLk0hb9OQQRMRUQ3BEScvZ8sUGiB+lZw1e9X1iGhgcL1uLetjZPcWOLl0DebuXoqIW+arfrdK2IoXHoxAv0s3Tfbpsc5NsMRIYUkxHu0Qht3nc2wq5klERDUD6ziJ4Kl1nExNoenCDFNTaGKpNQIWJv2Br/detNh2Qu9W2J6qNAhmIvKu4a1d3yLm0nGz7237+q8o9zUe45sKAismql/ILsDXey9Z7OOXI7sgoJYPpvyTK2VsmrK6vzMiInIeR3x/c6rOS1VnCk2MxNQs9Plkj6igCQCWHbqsD5pqlxZh5v6V2Lt0ktmgadrjr6FVwlaTQRNwN48qMdVwtKriVFrvto1F9TG0XqBV05RERFTzcKrOS1kzhWZt7SVTI1kWCQKeOHcAb+1dhrDCXLNNxVb9FqAdDZq3JQ2PRsqM5hpZu1KQW6EQEZEpDJy8lNh94KzdL87cSJY5HXP+xLtJS9Hz77Nm29myTYqlINCWlYKOKuZJRESejYGTF6mY13OjoETUe8QWvNSxNJJVWUhRPl77bRXGntxutl2rWVsASfVGdMwFgWI3PiYiIjKHgZOXsHWzXmtXiIkdofLRqPHMqZ2YtW8FgkvvmGz38AtLcblBU6v6YEpovUCz1csHRoWjX4cw/Ki4jL9y76Blg9oYK28F/1pM9SMiInEYOHkBUzlH5oImwLaNZ8WMUHW/kop5u5YiMifDZJvP+ozGv3uPsure5oRLA3Hrdgn6fLLHZOkFY8HldwczOOJERESisRyBCO5cjkCtEaoEC5VVHnmqzvYguvsZS7QOK7iBN/cux5Bz+81ew5Y8Jkte7BuBbw5kmCy9MMnCea6YIyLyPo74/uaIk4cTk3OkEYA5cR3RqF5AtVeIGUu09i8vw8TjGzHrwA9m3+uIgAkAXunXFuuT/zZbeuHb36oGTbrzllblERER6TBw8iDG8nfE5hw1qheAIV3sk0tUMdG6Y/IBzNu1FM1V2Sbbt565CRofX/1rf18JStX2GeiUBtVCz4iG+GqP+XpS5spVVac0AxER1SwMnDyEqa1TRnZvLur91q6es2SgfwFif/sckh2mV8s9PWM5jvrfLT6p7W8LLNz1h9368cnwzrhxW9wKQkusLc1AREQ1DwMnD2Aq+VupKsbCXRcQUtsPqjtlztlfraAA+OADYMECmJrU0owZi6PvLsRIVREG3C5Fg7oBkAVr+7D19DW7dEMWHIB3n7gXA6PCobh00y7XtHdwSURE3oeBk5uztHVKxeBFbHFHmwgCsHo1MHas2WaJZ65pR8a+PaI/pktG9/WRoFHdAFG3qxPgi9slav1rWXAARvVogVaN6lTJ07JUGRzQJsgLArh5LxERVQsDJzcnZuuUvDtlmBFzD9Ydz7RrcUddTlXJseO4/6M3UDf1lOnGgmB2ZGzKqhNYPCYa9QL8RN37+d6t8ECbxqK2PBFTGfyFB7Wr6hwaXBIRkddj4OTmxObdtGpUGwcT+tltf7XE1Cx8sU6BZ7d+i2dOJZpuqFYDPj6iRsbmbUnDrIEdRN3/R0Umpse0F91/MZXBu7aoz8rhRERULQyc3JzYvJvQeoF2219tZ8oVKGZ+iMRdS003unYN6jCZwRYvYjYVzi0Ul8idV1Rm9So3S5vzcvNeIiKqLgZObs5S/o6983PUe/chtt8jiDVx/s3Yqdj70FDMuS7g/RXmC28a06COP0KC/JBXVGaxbU5BsdktVIyxFDxy814iIqoOBk5uTkz+jl3yc65cAZ5+Gr4Khckm+gKWqmK8tOakTbeRSYMwvneEqJIEl2/cNruFChERkbNxd1MPoMvfkUkNp+2ktf0wPeYePBops/3ixcXAvHlAixaAiaCpVcLWalf9lkAb9PSIaICp/doipLbpJHEJgPq1/bBw14UqI1q6RPPE1Kxq9YeIiMgW3KtOBGfvVWdqekqtEfD1ngtYfuiywVSXTaMwggBs3gwMHWqyib22SDG2H1xiahYmrzphsq20th/y7hifztNNTx5M6Mf8JCIiMskR398MnERwZuBkqkL43MGRAGB0ub/VG9WePw907Gjy9AMf/A9ZBaUmayJZy1RgZ7oaurjq4mtf6MV8JSIiMomb/Ho5c3WQJq86gZDaftXbqDY/H5BKTd5ffSsPviFSvPNPP4zlVIkNpkZEN8WD9zQ2m9BtapWb2Ori3CKFiIiczaU5TgcOHMDgwYPRpEkTSCQS/PrrrwbnBUHAO++8g/DwcAQFBSEmJgYXLlwwaJObm4vRo0cjODgYISEhmDBhAgoLCw3anD59Gg8++CACAwPRvHlzLFiwwNGPZjVLdZAAmJy60rXRbVSrU1quwbLf/sTcjafxZ784k0HTk2P+hVYJW9F70e/4ctcFlJRrMD3mHoQFG+ZUyaSBWPRMNMKlgSa3W9H5+cRVBNTygbxNQ1Gr4IZ0aapva00JBiIiImdy6YjT7du3cd999+H555/HsGHDqpxfsGABvvrqK6xcuRIRERGYM2cOYmNjkZaWhsBA7Zfm6NGjkZWVhaSkJJSVlWH8+PGYNGkS1qxZA0A7TDdgwADExMRgyZIlOHPmDJ5//nmEhIRg0qRJTn1ecyxVCBdLNwozf3savv0tA/3/OIJvN3xgtO3X8v/Dv/o+q3+tzC82mCKTBQdgRky7Ktuc+PhopwwtsTgCZoKzSzAQERGJ5TY5ThKJBBs3bsTQf5KVBUFAkyZN8Nprr+H1118HAKhUKoSFhWHFihUYOXIkzp07h8jISBw/fhz3338/ACAxMRGPPfYY/v77bzRp0gSLFy/GW2+9BaVSCX9/fwDAG2+8gV9//RXnz58X1Tdn5DhtSrmKaetSqn2dtS/0wr70bGzaehxHFj9ntM31OiHoPnWVxWuZy52auuYEtp62vLJtRkw7TIu5x2K7ynTTloDxEgyi87mIiKjGcsT3t9uWI8jIyIBSqURMTIz+mFQqRc+ePaH4Z9m8QqFASEiIPmgCgJiYGPj4+ODo0aP6Nn379tUHTQAQGxuL9PR03Lp1y+i9S0pKkJ+fb/DjaNWddtIt9+8iq4PZcfeaDJpaJWwVFTQBdwOWeVvSoNbcDV8SU7NEBU0AsHDXBZtKB5gqwSCTBjJoIiIil3Hb5HClUgkACAsLMzgeFhamP6dUKhEaGmpwvlatWmjQoIFBm4iIiCrX0J2rX79+lXvPnz8f8+bNs8+DiGRpegoAavv74k6p2mQhTMWbMcCbxt9ra2mBirlT8jYN9blY1rB1yo5bpBARkbtx28DJlWbPno1XX31V/zo/Px/Nmzd36D3NVQjXuVOqBgBIJNoyTDoZnzxu8rr2qsWky52yJRerYuBlLW6RQkRE7sRtAyeZTFsNOzs7G+Hhd6dlsrOz0aVLF32bnJwcg/eVl5cjNzdX/36ZTIbs7GyDNrrXujaVBQQEICAgwC7PYQ3d9FTl2kaV6WbNFD/PQvgl46M/9gqYdC7fuA3A9hIALB1ARETewG1znCIiIiCTybB79279sfz8fBw9ehRyuRwAIJfLkZeXh+TkZH2bPXv2QKPRoGfPnvo2Bw4cQFnZ3aX8SUlJaN++vdFpOmdSawQoLt3EppSrUFy6CbVGwMCocBxM6IfVE3tCGmR8W5IXj/6My588bjRoajVri92DJuBurpKtuVgsHUBERN7ApSNOhYWFuHjxov51RkYGUlJS0KBBA7Ro0QLTp0/HBx98gHbt2unLETRp0kS/8q5jx44YOHAgXnjhBSxZsgRlZWWYOnUqRo4ciSZNmgAAnnnmGcybNw8TJkxAQkICUlNT8eWXX2LhwoWueGQ9cxXCB0aF4/fLuVAVGdZt6pV5GuvWGk9iUqRnY9T3xx3a53lb0rB/5iMWc7EqYukAIiLyJi4tR7Bv3z488sgjVY6PGzcOK1asgCAImDt3Lr755hvk5eWhT58+WLRoEe655+7y9tzcXEydOhVbtmyBj48Phg8fjq+++gp169bVtzl9+jTi4+Nx/PhxNGrUCC+//DISEhJE99PeyxlNVQjXpTxP6huBpQcy9Meb5SlxcOlEo9favvcMHns4ym7lDCyZEdMO7WX1jJYKqIylA4iIyJW4V52L2PMXr9YI6PPJHrM5TD4SbR5T/TsqnPz3aKNt+kxehr+lYfr92hSXbmLUt0eq1TexloyJBoAqI2a6fuvYtPkwERGRnXCvOi8gZlWaX2kJ0j8fbvTcIy8sRUaDpgC0gYluCkxXzsAe1cctmbclDQcT+lUpFdCtZX0k/3WLpQOIiMhrMXByMnOry2qpy7H414/w6MVjVc71efE7/B1iuApw7uBIfWBSsZyBo4cQK5YXqFwqgKUDiIjIm7ntqjpvZWx1mUTQ4LOtn+Hiv4ZWCZoee+4rtErYWiVoGhHdFCXlGv1qPOBuOYOQ2sZX4xmjqzi+6Bnr3sfyAkREVBNxxMnJKlcIn3D8V8zZ851Bm6JaAXh40jfIrmd89EYC4OcTV/HziasADHOJdNW2v95zAcsPXUZepZV5la8DQP/e2CgZEn4+jZ9P/G3xOVhegIiIaiImh4vgqFV1vho1Ln46xODcgy9+h8eekOObf1bVWfPhLHomGo91vpuIrdYIOJaRC2V+MQ5duI6ktGyoisv1540lb6s1Anp/vBvK/BKj99CVFziY0I/5S0RE5Na4qs5FHPGL19VxejLxBwxP3YNJT76FO23a6QMZY3WeKq9aq8xHAnw9qise69zE6HldIGUpeVsX2AHG98RjeQEiIvIEDJxcxBG/eMByIFPx/I2CEry/7Zyo6y6xQ2BjqUAnERGRu2M5Ai9jaQPbiuc3pVwVfd15W9LwaKSsWlNpulwpMSNURERENQUDJw9hTTJ2xXIB1WEpsCMiIqppWI7AQ+hW44nFcgFERET2x8DJQ+gKXIrFcgFERET2x8DJgwyMCseiZ6JhLs1IV9BStxULERER2Q8DJw/zWOdwfD2qq9FzFQtaMombiIjI/hg4eaDHOjfBkjHRVXKeZNJA1lgiIiJyIK6q81AsF0BEROR8DJw8GMsFEBERORen6oiIiIhEYuBEREREJBIDJyIiIiKRGDgRERERicTAiYiIiEgkBk5EREREIjFwIiIiIhKJgRMRERGRSAyciIiIiERi5XARBEEAAOTn57u4J0RERCSW7ntb9z1uDwycRCgoKAAANG/e3MU9ISIiImsVFBRAKpXa5VoSwZ5hmJfSaDS4du0a6tWrB4mEm+g6W35+Ppo3b44rV64gODjY1d2p8fh5uA9+Fu6Dn4V70X0emZmZkEgkaNKkCXx87JOdxBEnEXx8fNCsWTNXd6PGCw4O5j9IboSfh/vgZ+E++Fm4F6lUavfPg8nhRERERCIxcCIiIiISiYETub2AgADMnTsXAQEBru4KgZ+HO+Fn4T74WbgXR34eTA4nIiIiEokjTkREREQiMXAiIiIiEomBExEREZFIDJyIiIiIRGLgRG7j3XffhUQiMfjp0KGD/nxxcTHi4+PRsGFD1K1bF8OHD0d2drYLe+w9Dhw4gMGDB6NJkyaQSCT49ddfDc4LgoB33nkH4eHhCAoKQkxMDC5cuGDQJjc3F6NHj0ZwcDBCQkIwYcIEFBYWOvEpvIOlz+K5556r8vdk4MCBBm34WdjH/Pnz0b17d9SrVw+hoaEYOnQo0tPTDdqI+XcpMzMTcXFxqF27NkJDQzFz5kyUl5c781G8gpjP4+GHH67y92Py5MkGbar7eTBwIrdy7733IisrS/9z8OBB/bkZM2Zgy5YtWL9+Pfbv349r165h2LBhLuyt97h9+zbuu+8+/Oc//zF6fsGCBfjqq6+wZMkSHD16FHXq1EFsbCyKi4v1bUaPHo2zZ88iKSkJW7duxYEDBzBp0iRnPYLXsPRZAMDAgQMN/p6sXbvW4Dw/C/vYv38/4uPjceTIESQlJaGsrAwDBgzA7du39W0s/bukVqsRFxeH0tJSHD58GCtXrsSKFSvwzjvvuOKRPJqYzwMAXnjhBYO/HwsWLNCfs8vnIRC5iblz5wr33Xef0XN5eXmCn5+fsH79ev2xc+fOCQAEhULhpB7WDACEjRs36l9rNBpBJpMJn376qf5YXl6eEBAQIKxdu1YQBEFIS0sTAAjHjx/Xt9mxY4cgkUiEq1evOq3v3qbyZyEIgjBu3DhhyJAhJt/Dz8JxcnJyBADC/v37BUEQ9+/S9u3bBR8fH0GpVOrbLF68WAgODhZKSkqc+wBepvLnIQiC8NBDDwnTpk0z+R57fB4ccSK3cuHCBTRp0gStW7fG6NGjkZmZCQBITk5GWVkZYmJi9G07dOiAFi1aQKFQuKq7NUJGRgaUSqXB714qlaJnz576371CoUBISAjuv/9+fZuYmBj4+Pjg6NGjTu+zt9u3bx9CQ0PRvn17TJkyBTdv3tSf42fhOCqVCgDQoEEDAOL+XVIoFOjUqRPCwsL0bWJjY5Gfn4+zZ886sffep/LnobN69Wo0atQIUVFRmD17Nu7cuaM/Z4/Pg5v8ktvo2bMnVqxYgfbt2yMrKwvz5s3Dgw8+iNTUVCiVSvj7+yMkJMTgPWFhYVAqla7pcA2h+/1W/IdG91p3TqlUIjQ01OB8rVq10KBBA34+djZw4EAMGzYMERERuHTpEt58800MGjQICoUCvr6+/CwcRKPRYPr06ejduzeioqIAQNS/S0ql0ujfHd05so2xzwMAnnnmGbRs2RJNmjTB6dOnkZCQgPT0dGzYsAGAfT4PBk7kNgYNGqT/c+fOndGzZ0+0bNkSP/30E4KCglzYMyL3MXLkSP2fO3XqhM6dO6NNmzbYt28f+vfv78Keebf4+HikpqYa5F2S65j6PCrm8nXq1Anh4eHo378/Ll26hDZt2tjl3pyqI7cVEhKCe+65BxcvXoRMJkNpaSny8vIM2mRnZ0Mmk7mmgzWE7vdbeaVQxd+9TCZDTk6Owfny8nLk5uby83Gw1q1bo1GjRrh48SIAfhaOMHXqVGzduhV79+5Fs2bN9MfF/Lskk8mM/t3RnSPrmfo8jOnZsycAGPz9qO7nwcCJ3FZhYSEuXbqE8PBwdOvWDX5+fti9e7f+fHp6OjIzMyGXy13YS+8XEREBmUxm8LvPz8/H0aNH9b97uVyOvLw8JCcn69vs2bMHGo1G/w8XOcbff/+NmzdvIjw8HAA/C3sSBAFTp07Fxo0bsWfPHkRERBicF/Pvklwux5kzZwyC2aSkJAQHByMyMtI5D+IlLH0exqSkpACAwd+Pan8eNiazE9nda6+9Juzbt0/IyMgQDh06JMTExAiNGjUScnJyBEEQhMmTJwstWrQQ9uzZI/z++++CXC4X5HK5i3vtHQoKCoSTJ08KJ0+eFAAIn3/+uXDy5Enhr7/+EgRBED7++GMhJCRE2LRpk3D69GlhyJAhQkREhFBUVKS/xsCBA4WuXbsKR48eFQ4ePCi0a9dOGDVqlKseyWOZ+ywKCgqE119/XVAoFEJGRoawa9cuITo6WmjXrp1QXFysvwY/C/uYMmWKIJVKhX379glZWVn6nzt37ujbWPp3qby8XIiKihIGDBggpKSkCImJiULjxo2F2bNnu+KRPJqlz+PixYvCe++9J/z+++9CRkaGsGnTJqF169ZC37599dewx+fBwIncxtNPPy2Eh4cL/v7+QtOmTYWnn35auHjxov58UVGR8NJLLwn169cXateuLTz55JNCVlaWC3vsPfbu3SsAqPIzbtw4QRC0JQnmzJkjhIWFCQEBAUL//v2F9PR0g2vcvHlTGDVqlFC3bl0hODhYGD9+vFBQUOCCp/Fs5j6LO3fuCAMGDBAaN24s+Pn5CS1bthReeOEFg6XVgsDPwl6MfQ4AhOXLl+vbiPl36fLly8KgQYOEoKAgoVGjRsJrr70mlJWVOflpPJ+lzyMzM1Po27ev0KBBAyEgIEBo27atMHPmTEGlUhlcp7qfh+SfzhARERGRBcxxIiIiIhKJgRMRERGRSAyciIiIiERi4EREREQkEgMnIiIiIpEYOBERERGJxMCJiIiISCQGTkREREQiMXAiIrchkUjw66+/im7fqlUrfPHFFw7rDxFRZQyciMhpnnvuOQwdOtTk+aysLAwaNEj09Y4fP45JkybZoWfizJ8/H76+vvj000+ddk8ici8MnIjIbchkMgQEBIhu37hxY9SuXduBPTL0/fffY9asWfj+++8tti0tLXVCj4jI2Rg4EZHbqDhV98ADDyAhIcHg/PXr1+Hn54cDBw4AqDpVJ5FI8N133+HJJ59E7dq10a5dO2zevNngGps3b0a7du0QGBiIRx55BCtXroREIkFeXp7Zvu3fvx9FRUV47733kJ+fj8OHDxucf/fdd9GlSxd89913iIiIQGBgIAAgLy8PEydOROPGjREcHIx+/frh1KlT+vddunQJQ4YMQVhYGOrWrYvu3btj165d1vzaiMiJGDgRkVsaPXo01q1bh4r7kP/3v/9FkyZN8OCDD5p837x58/B///d/OH36NB577DGMHj0aubm5AICMjAyMGDECQ4cOxalTp/Diiy/irbfeEtWfZcuWYdSoUfDz88OoUaOwbNmyKm0uXryIX375BRs2bEBKSgoA4KmnnkJOTg527NiB5ORkREdHo3///vo+FRYW4rHHHsPu3btx8uRJDBw4EIMHD0ZmZqbYXxUROZNAROQk48aNE4YMGWLyPABh48aNgiAIQk5OjlCrVi3hwIED+vNyuVxISEjQv27ZsqWwcOFCg/e//fbb+teFhYUCAGHHjh2CIAhCQkKCEBUVZXDPt956SwAg3Lp1y2S/VCqVEBQUJKSkpAiCIAgnT54U6tatKxQUFOjbzJ07V/Dz8xNycnL0x3777TchODhYKC4uNrhemzZthKVLl5q837333iv8+9//NnmeiFyHI05E5JYaN26MAQMGYPXq1QC0o0UKhQKjR482+77OnTvr/1ynTh0EBwcjJycHAJCeno7u3bsbtO/Ro4fFvqxduxZt2rTBfffdBwDo0qULWrZsif/+978G7Vq2bInGjRvrX586dQqFhYVo2LAh6tatq//JyMjApUuXAGhHnF5//XV07NgRISEhqFu3Ls6dO8cRJyI3VcvVHSAiMmX06NF45ZVX8O9//xtr1qxBp06d0KlTJ7Pv8fPzM3gtkUig0Wiq1Y9ly5bh7NmzqFXr7j+ZGo0G33//PSZMmKA/VqdOHYP3FRYWIjw8HPv27atyzZCQEADA66+/jqSkJPzrX/9C27ZtERQUhBEjRjC5nMhNMXAiIrc1ZMgQTJo0CYmJiVizZg2effbZal2vffv22L59u8Gx48ePm33PmTNn8Pvvv2Pfvn1o0KCB/nhubi4efvhhnD9/Hh06dDD63ujoaCiVStSqVQutWrUy2ubQoUN47rnn8OSTTwLQBluXL18W/1BE5FQMnIjIqVQqlT5xWqdhw4Zo3rx5lbZ16tTB0KFDMWfOHJw7dw6jRo2q1r1ffPFFfP7550hISMCECROQkpKCFStWANCOTBmzbNky9OjRA3379q1yrnv37li2bJnJuk4xMTGQy+UYOnQoFixYgHvuuQfXrl3Dtm3b8OSTT+L+++9Hu3btsGHDBgwePBgSiQRz5syp9ggZETkOc5yIyKn27duHrl27GvzMmzfPZPvRo0fj1KlTePDBB9GiRYtq3TsiIgI///wzNmzYgM6dO2Px4sX6VXXG6keVlpZi1apVGD58uNHrDR8+HD/88APKysqMnpdIJNi+fTv69u2L8ePH45577sHIkSPx119/ISwsDADw+eefo379+njggQcwePBgxMbGIjo6ulrPSUSOIxGECmt9iYhqmA8//BBLlizBlStXXN0VIvIAnKojohpl0aJF6N69Oxo2bIhDhw7h008/xdSpU13dLSLyEAyciKhGuXDhAj744APk5uaiRYsWeO211zB79mxXd4uIPASn6oiIiIhEYnI4ERERkUgMnIiIiIhEYuBEREREJBIDJyIiIiKRGDgRERERicTAiYiIiEgkBk5EREREIjFwIiIiIhLp/wF6vSr8bNpd7gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def multivariate_batch_gradient_descent(X, y, batch_size, max_iter, alpha):\n",
    "    theta = np.zeros((X.shape[1]))\n",
    "\n",
    "    costs = []\n",
    "\n",
    "    for i in range(0, max_iter): # we could also use a delta on the cost function with a while to stop when the cost is not improving but we wanted to see the curve after x iterations\n",
    "        batch_idx = np.random.choice(y.shape[0], batch_size)\n",
    "        y_stoch = y[batch_idx]\n",
    "        y_pred_stoch = X[batch_idx, :] @ theta\n",
    "\n",
    "        for j in range(0, X.shape[1]):\n",
    "            theta[j] = theta[j] - alpha * (1/len(y_stoch)) * np.sum((y_pred_stoch - y_stoch) * X[batch_idx, j])\n",
    "\n",
    "        y_pred = X @ theta\n",
    "        costs.append(cost_J(y_pred, y))\n",
    "\n",
    "\n",
    "    y_pred = X @ theta\n",
    "    print(f\"Theta = {theta}\")\n",
    "    print(f\"Cost = {cost_J(y_pred, y)}\")\n",
    "\n",
    "    plt.plot(range(0, len(costs)), costs)\n",
    "    plt.title(\"Cost over iterations\")\n",
    "    plt.show()\n",
    "\n",
    "    return theta\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# need to normalize the data or else overflows will occur\n",
    "living = dataset[\"living_area\"].to_frame()\n",
    "mean_living = living.mean()\n",
    "std_living = living.std()\n",
    "living_normalized = (living - mean_living) / std_living\n",
    "\n",
    "X_norm = living_normalized\n",
    "X_norm.insert(0, \"x0\", 1) # add the column full of ones at the start, this represents x0\n",
    "X_norm.insert(2, \"x2\", X_norm.iloc[:,1]**2) # add the squared value of column 1 to column 2\n",
    "X_norm = np.array(X_norm)\n",
    "\n",
    "y = np.array(dataset[\"rent_price\"])\n",
    "\n",
    "theta = multivariate_batch_gradient_descent(X_norm, y, batch_size=10, max_iter = 10000, alpha=0.001)\n",
    "\n",
    "plt.scatter(dataset[\"living_area\"], dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Rent price\")\n",
    "\n",
    "y_regr = theta[0] + theta[1] * X_norm[:,1] + theta[2] * X_norm[:,2]\n",
    "plt.plot(dataset[\"living_area\"], y_regr, color='red', label='Regression line')\n",
    "\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64f2201b",
   "metadata": {},
   "source": [
    "The convergence is still happening. We observed that we could use a way bigger alpha to achieve the same results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a48af614",
   "metadata": {},
   "source": [
    "## B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcfa5986",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta = [ 1.05482247  0.33405956 28.44182263]\n",
      "Cost = 144284.47491785986\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = dataset[\"living_area\"].to_frame()\n",
    "X.insert(0, \"x0\", 1) # add the column full of ones at the start, this represents x0\n",
    "X.insert(0, \"x2\", dataset[\"nb_rooms\"].to_frame()) # add the column full of ones at the start, this represents x0\n",
    "X = np.array(X)\n",
    "\n",
    "y = np.array(dataset[\"rent_price\"])\n",
    "\n",
    "theta = multivariate_batch_gradient_descent(X, y, batch_size=10, max_iter = 1000, alpha=0.000001)\n",
    "\n",
    "plt.scatter(dataset[\"living_area\"], dataset[\"rent_price\"])\n",
    "plt.xlabel(\"Living Area\")\n",
    "plt.ylabel(\"Rent price\")\n",
    "\n",
    "y_regr = theta[0] + theta[1] * X[:,1] + theta[2] * X[:,2]\n",
    "plt.plot(dataset[\"living_area\"], y_regr, color='red', label='Regression line')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed1e2d4f",
   "metadata": {},
   "source": [
    "The algorithm still manages to converge, but no clear improvements is seen here"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}