Probability theory in birthday paradox

birthday_paradox.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "powered-actress",
   "metadata": {},
   "source": [
    "# Probability in Birthday Paradox"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "loved-apollo",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "persistent-savannah",
   "metadata": {},
   "source": [
    "## Import packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "altered-jaguar",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data frame manipulation\n",
    "import pandas as pd\n",
    "\n",
    "# Mathematical operations\n",
    "import numpy as np\n",
    "\n",
    "# Data visualization\n",
    "import plotnine\n",
    "from plotnine import *\n",
    "\n",
    "# Randomization\n",
    "import random\n",
    "\n",
    "# List manipulation\n",
    "import collections"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abandoned-completion",
   "metadata": {},
   "source": [
    "## Theoretical simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "guilty-number",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Birthday paradox\n",
    "def birthday_paradox(\n",
    "    day: 365,\n",
    "    person: int\n",
    "    ):\n",
    "    \n",
    "    # List of probability\n",
    "    probability = 1\n",
    "    \n",
    "    # Calculate the probability\n",
    "    for i in range(person):\n",
    "        if i == 0:\n",
    "            pass\n",
    "        else:\n",
    "            probability *= (1 - (i / day))\n",
    "    \n",
    "    return probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "lined-recognition",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4927027656760145"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "birthday_paradox(day = 365, person = 23)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "amended-probability",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dictionary of probability\n",
    "obj = {}\n",
    "\n",
    "# Stop\n",
    "stop = 1000\n",
    "person = 1\n",
    "\n",
    "# Loop\n",
    "while round(number = stop, ndigits = 2) != 0:\n",
    "    # Probability\n",
    "    prob = birthday_paradox(day = 365, person = person)\n",
    "    \n",
    "    # Update values\n",
    "    obj.update(\n",
    "        {\n",
    "            person: prob\n",
    "        }\n",
    "    )\n",
    "    \n",
    "    # Update indexer\n",
    "    stop = prob\n",
    "    person += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "valued-degree",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Create a data frame\n",
    "df_theory = pd.DataFrame.from_dict(\n",
    "    data = obj,\n",
    "    orient = 'index'\n",
    "    ).reset_index().rename(\n",
    "    columns = {\n",
    "        'index': 'number_person',\n",
    "        0: 'probability'\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "second-manual",
   "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>number_person</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.997260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.991796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.983644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.972864</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   number_person  probability\n",
       "0              1     1.000000\n",
       "1              2     0.997260\n",
       "2              3     0.991796\n",
       "3              4     0.983644\n",
       "4              5     0.972864"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show data frame\n",
    "df_theory.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "careful-doctrine",
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA14AAAHVCAYAAADhMCrAAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAA9hAAAPYQGoP6dpAABmNklEQVR4nO3deZgcVdmw8fshCQFDIAFFCaDIJiLKJggqmwvKqzYighsK8roiLrgLKCiCO+oroCIiLqD4IUu7IKjsbuwiu+zLoKyBkEAymTzfH6fGNMNMMjOZnprpuX/XVVdPn6queqpOdU8/fU6disxEkiRJktQ+y9UdgCRJkiR1OhMvSZIkSWozEy9JkiRJajMTL0mSJElqMxMvSZIkSWozEy9JkiRJajMTL0mSJElqMxMvSZIkSWozEy9JkiRJajMTL2mMiogdIyIjYp82rHufat07DnL5EyIi+5QdWq1jneGudyS0+TjdFhHnDXLZdao4Dh2hbY/YflXrOWHZo5q4+nsP1BTHlIi4PiKOHsJrzouI29oY1pgylPftMm5nxD/vRiv2QcTxpM/3EV7/qO1nREyPiPsj4qDR2J60JCZe0iC0fAluneZGxFURcXBErFB3jGNVlZAcGhGb1R3LWBMRm1XHZp26Y9G48QHgmcAXWwsj4iPt+PFhLIqIGdX7Zse6Y1H/xlIdZeYc4GvApyPiGXXHo4ltct0BSOPMKcAZ1d9PB94MHAa8BNilrqBGwbuB9w1iuZ8CvwAWtJStAxwC3AZcOcJxAVwArAh0t2HdQ3F7FcfCIbxmM8qxOY9yfKQBRcTywGeAn2fmPX1mf4RyDp0wulHVYgblfQPlvdPXc4DaWyeHaTzH3moGY6uOvkuJ52PAJ0Zxu9IT2OIlDc0/MvNn1fQN4MWUZOLVEbHVQC+KiBUiYtz+0JGZ3Zn5+CCW68nMxzNz0WjEVW1zUbXNntHa5gBxZBXHUhOviFhpNGKayDr0GO8JrA78pO5ARko7Phszc35mLlj6kmPPeI59KEZ7PzPzEcqPpu+0h4rqZOIlLYPM7Ab+VD1dHxZfTxERz4qIX0TE/cBjwFrV/DUj4riIuDsiFkTEXRFxbESsMdB2IuID1XUd8yPi1oj4XN8vKxGxUUQcHRFXR8TDEfFYRPwzIj4eEZMGWPXkal23Vuu+PiL262f7g7q+pe81D9X1TudWs3/U0k3zvIiYWvW7//sA63pTtey7lrLNJ10L1VpWTf+MiMerY374Eo7HQNvYPCL+EBFzqmN7SkQ8u88yT7rGq7UsInaPiIsjYh7wmyjXXP2oWvTclmNzQj/bH9Q+RMQrI+JvVd3fFxHHR8RTB9in90fEWdX5tyAi7o2IX0XEJn2W+221vpn9rGNWRCyMiJ8t5fi1Hoc3RcQV1b50RcSRETGtn/V+PSIuj4gHq3Pzxmq/V+yzbGtdvzdK99/HgaOq+UN6X0TE0yPixxHxQJTuxH+OiJ2WsG8viojfVHE+HhHXRcRno7RO9S7z7irGr/Z57bRq+Qcj4plLOoaVNwGPABf2PbbAs4Ad4ondodfp57ieVG3vsYg4PyK27Gefoor54uoYzI2Iv0TE6wc4Bm+LiL9HxKPVsn+LiDf3s9zSPhunV3V8Q1XnD0bE6RHxgpZ17APcWj09pGVfb2tZpt/rhyLiBRHx8+q8W1C9l85oPQYRsXX1vrmhZd8viYh39rfvgxURMyPiaxHxr+rYPxwR10bEkX2We1LsvWUR8fwo79lHqvPzuOocioj4RETcVB23ayPidX3WMeA1ozHI67likO/LZayjV0fEudU+PhYRV0b5/xd9ljuhWucqEfHdiPhPFc9lEbHzALvwW2A14BVL2k+pncbtL/DSGLJh9XhfS9lKlC9Hl1K6N0wHHo2INYFLKL9a/wC4CtiU0pXv1RGxVWb+p8/6PwisCXwPeBDYDfg8sC6wT8tyOwI7AL9mcbe3/6H0bV8XeFJCBXwFWLmKZT7wVuDoiFg9Mw8d/CEY0KnAFOBA4FgWf2H8T2bOj4gfAx+NiBdk5lV9Xvsu4FFK18Xheh8wCziOUj9vqGKZA3x5kOtYCziH8mvpJ4GNgfcCL46ILfvp8tWfXYEDKHX4AyCAf1KO+XuAI4DrqmVvHs4+RMRrqhjvo9TrQ5Rz5fcDxPQJ4K/Ad4AHKOfxu4BXRsTmmdkbx/co59Hbgf/rs453ApOqfRqM1wEfBY6p9ucVlOOyaUS8sqWl9AXA7pTz51bK8dqR0s1u8yqevj4MPINynt1FOT4whPdFREynnKPrU7rsXQI8D/gNT64XIuLVQBN4GDga+E+17i9Qzo/XVC2yP4jyY8THI+K8zPxdtYrvAhsBr8/MO5Z04KIkidsBF/dpUb6PUjffBO4HDu8zr9c0SrfcS4GDKV2lDwB+HxHrVtfB9PoR8A7K+XRiVfYG4LSIeH9mfq8lri8An6V8lh1WFe8F/Lxa7xF9dmWgz8aVgYsox/7HwD+AmZTPxr9GxHaZeXm1DwdU+3sa5RyB8lkxoIjYpVp+PvBD4HrgqZRz48XAZdWiu1He4ycDd1K6zO0JHB8RT8vMrzI8v6Sciz8ArgCmVvv6skG+fk3Kj3ynVPuxDfC/lPP5IeClwPeBHsp74VcRsWFm3jbMePsz2PflcOvofynH5zbK+/NR4I2UH1E2pXxW9nUWZf8PB55C6XL764jYoJ/31J+rx50o72lp9GWmk5PTUibKP5ekfEF+ajVtTPnim5R/QlOrZc+ryr7cz3p+Us3bs0/5O6ry4/rZ5lzgWS3ly1G+7CXw0pbyaQPEfiLluqM1Wsr2qV5/JzCjpXwFyheihcA6LeUnlI+LJ6z30God6/Sz3h372Y99+oltA2AR8H99yp9dlR87hLrZp5+ye4CZfY7dtUDXIOv9tmo9H+9Tvkc/9bVOVXZoP2XdwCb9rP9Jx2s4+1CV3UpJNtZuKZ9E+ZU3gRP6rP9J5wslyVgAHN1n3bcDV/VZNoBbgBsGcRx7j8MiYOs+846q5u3VUrYiEP2s54vVslv1c5weAp7Rz2uG8r74QrWuj/RZ9s1VebaUTaqO+Vzg2X2WP76ffVoJuIGSHK1FSVoT+NYgz8XeY/jdJZyr5w0w77zqtZ8ZYL/e01L2+qrsgH7W05tkTm95//ZQkpYVW4855YeFvp8jvXH099n4rerce1Gf8hmUz6lzl/ReW9KxoHwhv7c6R9bpZ/nllvK+WI6STMwGpgzm/dvn9atQzv1jBlHPT6pHFn8OvblP+anVeq8Alm8p36xa/kv9vE/26Webh/Lkz/L+yobyvhxqHa1C+fy6C1i1pXwycDZP/n93QlX2/T7r3aYqP2KA7XYDfxjMe87JqR2TXQ2lofkM5Vfk+4BrgE8B5wOvysz5fZb9SuuTiFiO8qXm+sz8ZZ9lf0r5Rf0NfbtUAD/LzNt7n2T5tbu3pWP3lvK5LduaGhGrRulm9nvKl8QndSmifBGY3bKOx4Ejq+V37Wf5EZWZ/6J0Rdwrntjv/l2UL/bHLuMmjs/Mh1q2t4jyq/EaMfhrgOZQWoX+KzP/H3Aj/ddXf36bmVcPcnt9DWYftqR80flJZt7ZsmwP5ceCJ+k9X6puSitX58p/KMnBi/ps7zjg+RHxopZVvIKSIA+2tQvKF56L+5T1xtd6Lj+WmVnFN6XlXP5DtciLeLIfZ+a/B9rPal1Le1/sTvlyfUyfdfwC+FefVW/B4mN+a595h/azT49SWk6mUVqSjqL8yPHJfvalP0+rHh8Y5PJ9LaK0QLTqPZ4btpTtRen+d3JEPLV1Ak6ntJBvWy37ekpS8tXMfKx3BdUx/xoDf470/WwM4G2UFtib+2yz94v3dtGnm+kQ7Ew5ft/KflqAsqUFsc/5smJErAasSjlfVqEMCjFU8ygtbdtExLrDeD2UH1r6tv5fSPmcPCZbrpfKzCspXVI3GOa2+jXM9+Vg7Uz5ceI7mflgyzYXsngEz937ed3X+8T4N0pL2Yb9LAul18jqyxCntEzsaigNzQmUX8qT8uXkpsy8t5/l7mv9slx5GqVbzTV9F87MjIhrgAale82DLbOv7Wf9vWXr9xZExFMoXX7eTPlC2NeqS1jPEtfdZt+jdMPZHTgxyrVr7wSuzMxLl3Hdt/RT1vvFdTWW0vWlcnM/STWUroEbUo7r0r4M3ziI7QxkMPuwXvW8v/p80vkGEBHbA5+jdLPq+4W2byJxXLXsu4Dea/LeTWmh+PESYu/rSfFlZldEPMwTz+VJwMcpLQob8uTrkfs7l/s9xkN8X6wH/DP7v+j/Wp74Rbb3C3R/7+c7qn1ar0/5PyLiQMqPG/MoLRhDHWBgMIl+f7qyzwA5mflA9bvBai3Fz6WcD3cvYV1Prx4HPAaUFi/ocwzo/7OxtxfB9jyxe2RfT6W0fg1V75fwK5a2YJVIfIGSVPZ33W1/594SZWZ3ROxPSbZvjogbKUnT74AzcnADA/X3OfDQUuat1k/5sA3zfTlYwzmXYODPx4H2PeiMUSM1Tpl4SUNzc2b+cRDLzeunrPcL00h86GefR4CTKInbcZRuMfdTuvpsSWkhG2oL92j9czod+DflS/2JwGsoX3gOW8JrBmtJX2iG+wW2r8Ecp/7Oh8Ea8X2IiBdSWs1uAQ6qHudR9uXblFaZ/8rMeyKiCbw5Ig6gfDHfFTg9M5f0RXkoWo/jNyjXqZxCaR25l5LkrUn58aO/c3mgYzxS74u+x3rI7+eq1fu11dMVKa0nT7p2bAC9x3m4X24Hex4tR+lO+MYlLN/75Xg4n2n91VNvHVzAkt/3wz3XBvU+qVrezgY2obRyX0JJYHoo1y8dwDAHJcvMH0bEr6v1bA+8knKN1sURsUPfpLgfS6q/gea17veS6miw3wWH874crCWdSwPGvoSkdaA6n0l7bmsiDYqJlzR67qV0W9uk74zqH/7zKP/k+/4avHE/63pe9Xhz9fpVKF8uf5aZT7gAOSKW1N1kYxbfl6zv9gb7hXBplvilrPo1+HjgwCrWd1O+nJ00QttfVutFxNR+Wr2eS//1NRQjldz21tWSzpVWb6V8/u+SmU/4xbjqWtXfl8DvUQZYeDPlupvlGVo3w37ji4hZlC5crefbO4ALM3OPPssO6V55w3hf3AysHxHL99MS9dw+z2+qHvt7P6/Nk/cJyqAWL6O0qOwF/DgiNs3MrkHszp0sufvYSJ1LN1IG/LgiM5fWktt6DPq2VPQel8F8jtxHeR/NHOQPW0Pd1xuqx80p16kN5PnVModl5udaZ0TEK4e4zSepekecAJxQfeZ/ldKCtAelu3k79fai6C9xH2z3x6G8L4daR63n0m/7zHt+9bhM/5Oqbp6TWdyCJo06r/GSRkl1HcHpwEYR0ffX5LdRulGc2tuHvsVeEfGs3ifVr+afrp72jhbVe41C3yF3p1NGkRvIfhExo2X5qdXyPSz5C8pQ9HbnW9Iv9T+g7MMhwKuBkzPz4RHa/rKaThlZ8r8iYg9KV5vT+qmvoRjMsRmMyykDYLyj+tIP/PdcObCf5Xt/Je57vryPxd3I+voj5YvPuymtk7ew+FYKg/XKiNi6T1lvfKe2lD3pV+yImEK5xnIohvq+OJWSVO7XZ/k38+SE5wrKAAFvb31/Vnq/tP+qZR07VOW/oVwD9ibK9VInVvW0RNUv+xcCWw2w/KMs+3kEi7uOfrW/6xcjovX8OJ1yjD/eeo1m1b3zE5R67PvDzpNUn40/o1xHuHd/y/TZ7lDfN2dTkruPRD9Dprccz4HeF2tSzvlhiYinVMfkv6rPjcurpyNRb0tzK2VgiScMpV79ALHbINcxlPflUOvoD9VrPhAtt66oujceVD39VX8vHILeaxPPXcb1SMNmi5c0ug6k/OP7eZR7A/2TxcPJ38nifzCtrgf+HhHfZfFw8jtRfsW/ECAz50TE74G3RcR8ynU4a1C6svQdnr7VvcAlVYvTAkpLyBbAF/sZMGC4rqW09O0X5R5Ws4F7M/Oc3gUy87aIOIuSgMLQW1La6WbgoIh4HnAxpeXjfZTj+tllXPcllC+uB1VfNuYCt2Zmv/c2G0hm9kTEhyhDN/89Ir5PaUF4A+WC9b5OpSQeZ0bEsZQWxu0oF7jfTD//G6rrEI9l8cAIBw4j6bwC+GNEHAPcQelu9XrKADWtLZz/D3h/RJxC+dK8KqWFaEhdNofxvvg68BbgyCj3jrqY8gv8Oynv1d5f3nuP+fspP1BcEhHfo7yfdqF0Jzurd58i4mnV312UUeUSuDQiPk253uuzlFtELM3JlK6421GOWau/Ae+KiMMo1x8uAn7dOljEYGTmqRHxA8pn0gsi4nTKsZoFvLDavynVsjdFxOFV/H+LiBMpSctelGN1UH+DWQzgYOAllNagXSlDy88Dngm8vPp7p2q7D0TETZSurzdX8c3NzF8PsE/zotyH61TgHxFxHKUVbCZlOPkzKV0LrweuBj4ZZeCaaygDyLyX8r4YboK0IXBBdSyvpnR3XY/yOfIw5X3bVpn5aPU5/96IOJlyi4xnVjH8E9hqEKsZ9PtyGHX0cER8hPLZf2kV61xKl9eXAD/IzIuGss/9eC3lf+hgWlWl9hjs8IdOThN5YvFQvAcPYtnzgNuWMH8tyvUmXZRfIO+mjN63xgDb3AfYn/KlYD6lZeMQYHKf5VeldAe7i9JV7HrKr84v711Py7L7VGWvqNZ1W7XuG4AP9hPzCQxzOPmq/H8ov+4+Xs0/r59tNKp5/xxm3eyzpLIlxb2Edd9W1efmlF9k51C6e50KrNdn2XUYeDj5Q5ewjb0pyekCWoZ9H84+AK+iJBePU37h/xFlQIL/rrdl2ddREr+5lC8jTUpXwPMY4Pyt1jWfct4+aej2Jezjf48DpaXnyirGeyjDiK/UZ/kVKddf9Z6Xt1JGP9yon2M84HEa6vuiWn4NSrevBylfKP9M+cJ/An3eA9Xy21C6Rj3E4vfQZ6mG96YkImdWx+wl/by+SWlJ2HEQx3EqJbk7vp95q1NaBB6kJF3/PT+WUqdPOjeq8jdTWgZmV/t1B2UwiPf1s+xe1Xk3r5r+Bryln+UGjKOl3j9TnR/zqnPzX5TWsJ37LLt1VTdzq324rWXebfT/GbMF5fqk3muT7qa8l7doWeaZwM8picJjVSz70v+tMp5UNsB+rUZJsC+v6udxyjl9PLBhf585Sytb2vYHWM80yr3j7qv27RJKMnIoT/4s769s0O/LZaijXarzZE51nP5B+f8XfZY7gX7ej0vY95Wrc+rrS3ufOTm1c4rMkeoWLknDF+VmtGcCH87Mvjfq1RhQtcp1AWdm5huG8Lp1KF/SPp8jc2PuCasa3ORwYP0c3LVh0oQXEZ+i/CCyQQ7upvdSW3iNl6Sx4iOUXyR/UnMcGth7KTfZ/m7dgUxgR1Fan/rrliypj+qazk9Qbtxt0qVaeY2XpNpExOqULl/bULrJfSVbbuissaEaXGItynU4f8vMPyzlJWqTzOymdO2SNAiZOYfSTVqqnYmXpDptTBl04BHK9UiH1hqNBvJzyvUWf6UMTCFJkobIa7wkSZIkqc28xkuSJEmS2szES5IkSZLazMRLkiRJktrMxEuSJEmS2szES5IkSZLazMRLkiRJktrMxEuSJEmS2szEa4zp6uqa2tXVdWhXV9fUumNpt+7u7jW6u7sP7e7uXqPuWNrNeu081mlnmij1ap12Juu181inncXEa+yZChxSPXa6NSj72vEfJlivncg67UwTpV6t085kvXYe67SDmHhJkiRJUpuZeEmSJElSm5l4SZIkSVKbmXhJkiRJUpuZeEmSJElSm5l4SZIkSVKbmXhJkiRJUpuZeEmSJElSm5l4SZIkSVKbmXhJkiRJUptNrjuAkdZoNPYH9gGeD5zWbDbfXG9EkiRJkia6jku8gC7gi8ArgKfWHIskSZIkdV7i1Ww2TwVoNBqbYeIlSZIkaQzouMRrtHR1dU0FprZh1dN7H7u6ugb1gnXXXfd7CxcufPZyyy33wHLLLffApEmT7p88efIDU6ZMeWDq1KkPrLTSSg+svvrqD2y55ZYPvOc975kzY8aMNoQ9dDNmzJg2adIkenp6pt13330r1x1Pmw25XserCVSv1mlnmhD1ap12Juu181in48esWbMeWdoykZmjEcuoazQahwIbtesar66urkOBQ9qx7qF62ctexg033DCoZadMmcKsWbNYb731WH/99Vl//fXZYIMNWH/99Vl11VXbHKkkSZLUeWbNmhVLW8YWr+H7EnBkG9Y7HbgLWAuYM5gX3HHHHV+eMmXKuosWLVotM1ddtGjRU4F+fxXp7u7m9ttv5/bbb+ecc855wryIeHC55Za7cfLkyTdOnTr1hpVWWunGddZZ519HHnnkbWuvvfaIZ+gzZszYdNKkSRf09PRsP3v27H+M9PrHmCHX63g1gerVOu1ME6JerdPOZL12Huu0s5h4DdOsWbPmA/NHer0tTatzBtNkCTBv3rz9+pZFxPLAapTr3Hqnp1XTs4HnAhvRkqBl5qo9PT3b9PT0bDN//nweeeQRurq62GabbR4C/gxcVE2XZuYy73t3d/dcgOWWW27uYPd1vBpOvY5XE6VerdPONFHq1TrtTNZr57FOO0vHJV6NRmMyZb8mA8s1Go0VgJ5ms9ldb2SjKzMXAPdUU78iIoBnsDgJ652eS/m1oddM4LXVBDA/Ii5hcSL2l8x8aKT3QZIkSeoUHZd4AQfzxGuv9gB+TLm3l1pkucCvNzl7Qr/DiJgObAhsArwYeCmwcTV7avX8pS3LX83iROyszLy/3fFLkiRJ40XHJV7NZvNQ4NB6oxj/MnMOcFk1/RggIlZjcRL2EmArYPnqJZtU0/uARRFxEXAGcEZm3jy60UuSJEljS8clXmqfzHwA+HU1ERErAC9kcevXS4AZwHLA9tX0jao17AzgdOCy7NShNCVJkqQBmHhp2DLzcRZ3LyQilgO2BHatpk2qRXtbww4C7o6IM4AzbrnlltlrrbXWk9YrSZIkdZrl6g5AnSMzF2XmJZl5cGY+H1gf+BhwAbCoWmxNYD/grA022OBPb3/723nb2962TURMqilsSZIkqe1s8VLbVNd2HQkcGRFPpYyKuCvwKmDFnp6elU4++WSAo4FPR8QJwAmZeUtNIUuSJEltYYuXRkVm3p+ZJ2TmbpR7iu265pprNlde+b+3EVsb+Cxwc0T8KSLeFhEr1hWvJEmSNJJMvDTqMnNeZjZvvfXWz99xxx3suOOOnwXObVnkZcDPgHsi4rsRsVV1zzFJkiRpXDLxUq2e8pSncPbZZ/8uM19GuSbsi8Bd1exVKMPTXwxcFREHVF0WJUmSpHHFxEtjRmbenJmfBdYBXg38ElhQzd6Ecr3YnRHxvYh4Tj1RSpIkSUNn4qUxJzN7MvOszHwTMAv4EPCPavYKwHuB6yLi9Ih4qd0QJUmSNNaZeGlMy8wHMvM7mbkZsDXwC6AHCMoIiRcCf42INzokvSRJksYqEy+NG9U9wt5CuRbsW8DcataLgP8H/Csi9o+IaTWFKEmSJPXLxEvjTmbelpkHUIag/zRwTzXr2cB3KNeBfTEinlFXjJIkSVIrEy+NW5n5UGZ+hZJwvRO4ppo1EzgIuL0ajn7NumKUJEmSwMRLHSAz52fmCcDzgV2AP1WzlqcMR39TRHzdoeglSZJUFxMvdYwsfp+ZrwC2AE6pZq0AfAy4NSK+EBGr1BakJEmSJiQTL3WkzLwiM/cAtgR+VxWvBHyWkoB92kE4JEmSNFpMvNTRMvPyzHwN8FLg/Kp4JvAl4OaI+GBETK0tQEmSJE0IJl6aEDLzz8BOwM7AJVXx04H/A26MiH0jYnJd8UmSJKmzmXhpwqiuAfsD5b5fuwFXV7OeCfwQuCYiXh8RUVeMkiRJ6kwmXppwqgTsdGAz4G3AzdWsDYHTgLMiYuN6opMkSVInMvHShJWZPZl5EvBc4D3Af6pZrwSuiohvRsSMuuKTJElS5zDx0oSXmd2Z+QNKi9fXgW5gEvARyvVf746ISTWGKEmSpHHOxEuqZOYjmfkJYBPgzKr4acCxwMUR8ZLagpMkSdK4ZuIl9ZGZN2bm/wCvBf5VFW8BXBQRJ0bEmvVFJ0mSpPHIxEsaQGb+Fng+8Cng0ar4rcANEXFgRKxQW3CSJEkaV0y8pCXIzPmZ+VXK9V8/qYqnAYdThp9/ZW3BSZIkadww8ZIGITPvycy9gW2BS6vidYGzI+KEiFitvugkSZI01pl4SUOQmX+j3ID5XcDsqnhv4NqIeJM3X5YkSVJ/TLykIcrMRZn5Q8r9v/5fVbw68AvgjIhYq7bgJEmSNCaZeEnDlJn/zsw9gdcDXVXx6yitX/tFhO8vSZIkASZe0jLLzDOAjYHvVUXTgaOBCyJio9oCkyRJ0phh4iWNgMx8ODPfD2wP3FgVvwT4R0QcfPbZZ0+pLzpJkiTVzcRLGkGZeSGwKWW4+YXA8sBh//u//3vBFVdcUWtskiRJqo+JlzTCMvPxzDwY2BK4BGDRokUbNxoNNtxwwwMjwtYvSZKkCcbES2qTzLyKct+vA4B5ixYtYu7cuZ8C/uq1X5IkSROLiZfURpnZk5nfetGLXvSSzTffvLd4S+CKiNjfkQ8lSZImhsl1BzBedXd3rwGsMdLrnTlz5rQ5c+Ywffr0Tbu7u+eO9PrHmN5Wn426u7trDaTdzj333GkPPfQQr33ta394xRVX7AOsAHxn5syZbz3uuOM+v/fee99Xc4gjaULUq+/VzjSB6tU67UzWa+exTseJKVOmXL60ZSIzRyOWjtPd3X0ocEjdcWj8ufTSS9l7773517/+BcDMmTM56qij2GOPPWqOTJIkScMxZcqUWNoyJl7D1K4Wr4ULF06bM2fOBdOnT99+8uTJ4y7bH6KNgBOBtwHX1xxLW/Wt16uvvnqF3Xbb7cO33377nr3LPOMZz/jdT37yk6/suOOOj9YZ6wiYEPXqe7UzTaB6tU47k/XaeazTccIWr3Goq6trZeBhYJVZs2Y9Unc87dTd3b0FcBmw5WBO1vFsoHqNiFcDx7M4ib8L2Dszzxn9KEfGRKlX36udaaLUq3XamazXzmOddhYv7JdqlJm/B54PnFIVrQX8KSKOjIgV6otMkiRJI8nES6pZZj4A7Am8Hej9hecA4O8R8ZzaApMkSdKIMfGSxoAsfkZp/TqvKn4BcFlE7FVbYJIkSRoRJl7SGJKZdwAvBw4CFgHTgJ9GxPERMa3W4CRJkjRsJl7SGJOZizLzCGBH4O6q+J3AxRHxvNoCkyRJ0rCZeEljVGZeCGwGnFkVbQxcEhH7RsRS7xUhSZKkscPESxrDMvN+4LXAJ4GFwIrADyndD6fXGZskSZIGz8RLGuOqrodfA7YH7qiK3wZcGhGb1heZJEmSBsvESxonMvOvwObAGVXRhpQh599n10NJkqSxzcRLGkcy80FgN+AjQDcwFfgucHJErFJjaJIkSVoCEy9pnKnu+fVt4MXALVXxHpRRDzeuLzJJkiQNxMRLGqcy81JgC+CUqmhDSvL1xvqikiRJUn9MvKRxLDMfBvYEPg70UG64/P8i4qsRMbnW4CRJkvRfJl7SOFd1PfwG8Ergvqr4E8DZEfG0+iKTJElSLxMvqUNk5rnAlsDFVdFOwGURsVV9UUmSJAlMvKSOkpl3Uu73dWxVtDZwUUS8q76oJEmSZOIldZjMnJ+Z7wXeDSwAlgd+EBHHRsTUeqOTJEmamEy8pA6VmccBLwXurIreDVwYEWvXF5UkSdLEZOIldbDMvIRy3defqqKtKNd97VRfVJIkSROPiZfU4TLzPuDVwFeroqcBf4iID0VE1BeZJEnSxGHiJU0AmbkwMz8F7AE8CkwCvg18PyKWrzU4SZKkCcDES5pAMvMUYFvg1qro3ZTWL+/3JUmS1EYmXtIEk5lXA1sD51dF2wMXR8Tz64tKkiSps5l4SRNQZt4P7Ax8vypaB/hLROxaW1CSJEkdzMRLmqAycwHwfmB/oAdYCTg9Ig500A1JkqSRZeIlTWBZHA28CnioKj4cODEiVqwvMkmSpM5i4iWJzPwT5bqv66qitwAXRMSa9UUlSZLUOUy8JAGQmTdRRjz8XVX0QuCSiNi6vqgkSZI6g4mXpP/KzIeBBvD1qmgNSsvXW+uLSpIkafwz8ZL0BJnZk5mfAPYBFgBTKdd8HeqgG5IkScNj4iWpX5n5Y2BH4N6q6BDgJxExtbagJEmSxikTL0kDysy/Ai8Crq2K9gL+EBGr1ReVJEnS+GPiJWmJMvM24MXAH6qi7YC/RsQGtQUlSZI0zph4SVqqatCN1wA/qIo2AP4WEdvXF5UkSdL4MbnuAAAajcYM4FhgF+AR4PBms3lMP8u9Dfh+S1EATwF2bzabpzYajR2Bc4B5Lcsc0Ww2j2hT6NKEkZndEfFe4F/AV4FVgT9GxL6Z+bN6o5MkSRrbxkTiBRxFiWUWsD7wx0ajcV2z2Ty3daFms3kicGLv80aj8T/Az4Hftyx2b7PZfEb7Q5YmnsxM4GsRcQvwM2AF4KcRsT7w+Wq+JEmS+qi9q2Gj0ZgG7AEc3Gw25zSbzSuAE4B9B/HydwInN5vNeUtdUtKIycxf4YiHkiRJg1Z74gVsCESz2by2pexKYJMlvajRaKxKudHrj/rMWq3RaPy70Wjc3mg0vl8tJ2mEZebf6WfEwzPPPHOV+qKSJEkam8ZCV8OVKNd1tZoNTF/K6/YCbmk2m39tKbse2Ay4jtJt8fvAj4HXjUSgrbq6uqZSbiw70nr3e3pXV1cbVj92zJgxY9qkSZPo6emZdt99961cdzxt1pH1evfddz94xBFHvOr73//+jxcuXPgyYLs3v/nNP7n44otZd911O71eO7JO++N7tfNYp53Jeu081un4MWvWrL75zJNE3ZdkNBqNzYG/N5vN5VvK9gI+1mw2N1/C664ATmo2m19bwjLPBm4Cpo90d8Surq5DKd2rpAmvu7ubgw46iBNPLJdgzpw5kxNOOIEXvvCFNUcmSZLUfrNmzYqlLTMWWrxuBLLRaDy32WxeV5VtBlw90AsajcZmlK6IP13KuhdRRj5c6oEYhi8BR7ZhvdOBu4C1gDltWP+YMWPGjE0nTZp0QU9Pz/azZ8/+R93xtFlH1+uUKVM48MADaTabH54zZ84XHnroIXbbbbcFq6+++j6XXXbZb+uOr006uk5b+V7tPNZpZ7JeO4912llqT7yazebcRqNxCnBYo9F4J7AusA+w5xJeti9wZrPZ/HdrYaPR2Am4FbgdeDrwf8DZzWZz7kjHPWvWrPnA/JFeb0vT6pzBNFmOZ93d3XMBlltuubmdvq8ToV5nzZrFI488ctgrXvGK7gsvvPBLCxYsWP7f//73iWuuueYHM/PouuMbaROhTnv5Xu081mlnsl47j3XaWcbC4BoAHwASuAc4E/hcs9k8B6DRaDzaaDS2612w0WgsD7wVOL6f9WwOXAg8ClwG3A+8vb2hS2p15plnnv273/2OSZMmzaG0Nh8VEV+JiLHyeSNJkjTqam/xAmg2m7MpQ8r3N2+lPs8XAE8dYNkjaU/3P0lDsP322/OpT31q3yOOOOJIYG3gk8DaEfHOzBzxlmJJkqSxzl+gJbXFoYceeguwDdDbJ/0twO8jYkZtQUmSJNXExEtS22RmF7A98MeqaEfgoohYu7agJEmSamDiJamtMvMR4DXAT6qi5wF/i4gX1BeVJEnS6DLxktR2mbmAMlrpF6uiWZSWr5fXFpQkSdIoMvGSNCqy+CzwXso99qYDZ0bEXvVGJkmS1H4mXpJGVWYeC+wKzAOmAD+NiE9FRDtudC5JkjQmmHhJGnWZ+RvKQBv3VUVfBr7pvb4kSVKn8kuOpFpk5iXAtsDNVdGHgZMiYmp9UUmSJLWHiZek2mTmzcBLgMurojcBv42IleuLSpIkaeSZeEmqVWb+h9LtsPdeXy8HzouIp9cWlCRJ0ggz8ZJUu8ycQ7nX1y+qos2Bv0TE+vVFJUmSNHJMvCSNCdW9vt4GfKsqWhf4c0RsWVtQkiRJI8TES9KYkZmLgI8Cn6qKVqd0O3xlfVFJkiQtOxMvSWNKdaPlrwL7AD3ASpQBN95Sa2CSJEnLwMRL0piUmT8GGiy+0fJJEXFAvVFJkiQNj4mXpDErM39HGeXwwaroyIj4akREjWFJkiQNmYmXpDEtM/9GudfXHVXRJ4AfRcTk+qKSJEkaGhMvSWNeZl4PbAtcXRXtDZwaESvWF5UkSdLgmXhJGhcyswvYHvhzVfQ64KyImFFbUJIkSYNk4iVp3MjMh4Cdgd9WRdtRhpt/Rn1RSZIkLZ2Jl6RxJTPnAbsBP62KNqXcaHm9+qKSJElaMhMvSeNOZnZT7vP1zapoXUrytWltQUmSJC2BiZekcSkzFwEfAw6sip4OnB8R29UXlSRJUv9MvCSNW1l8CXgPsAhYBTg7Il5Xb2SSJElPZOIladzLzB8AewALgBWA0yJin1qDkiRJamHiJakjZOapwC7Ao8Akyk2WP15vVJIkSYWJl6SOkZnnADsC91VFX4uIr0RE1BeVJEmSiZekDpOZlwEvBW6vij4JHBsRk+qLSpIkTXQmXpI6TmbeCLwEuKYqehdwckRMrS8qSZI0kZl4SepImXk3sD3w96pod+A3EbFSfVFJkqSJysRLUsfKzAeBVwB/rIpeAfwxIlarLypJkjQRmXhJ6miZ+SjwWuCUquhFwAURsWZ9UUmSpInGxEtSx8vM+cCbgeOqoo2BP0fEBvVFJUmSJhITL0kTQmb2AO8BvlIVPQu4KCI2qy0oSZI0YZh4SZowsvg0ZYh5gNWB8yNiuxrDkiRJE4CJl6QJJzO/BrwbWASsDJwdEa+pNypJktTJJtcdwHjV3d29BrDGSK935syZ0+bMmcP06dM37e7unjvS6x9jNup97O7urjWQdrNex54FCxZc3mg0PnXWWWcdkZkrAKe/7GUvO/Sss846czCvt0470wSqV+u0M1mvncc6HSemTJly+dKWicwcjVg6Tnd396HAIXXHIWnZ/OlPf+KNb3wjc+eWz/hvfetb7LfffjVHJUmSxpMpU6bE0pYx8RqmdrV4LVy4cNqcOXMumD59+vaTJ08ed9n+EG0EnAi8Dbi+5ljaynod2z784Q8/79hjj/1OT0/PKgAbb7zxdy+55JLjpkyZMuBrrNPONIHq1TrtTNZr57FOx4m2tnhFxKWUoZl/npkPD2slepKurq6VgYeBVWbNmvVI3fG0U3d39xbAZcCWgzlZxzPrdeyLiI2BPwCzqqJvAx/NzEX9LW+ddqaJUq/WaWeyXjuPddpZlmVwjRuBI4GuiPhJROwwQjFJ0qjLzGuBlwA3VUUfBo6PCK+FlSRJy2zYiVdmvpXS1e4TwHOBcyPipoj4TETMWvKrJWnsyczbgO2Aq6qivYFTImKF2oKSJEkdYZmGk8/MhzPzmMzcCtgM+A3wUeD2iPh1RLw+IhyyXtK4kZn/BnYA/lwV7Qr8LiKm1xeVJEka70YyKboLuBX4DzAJ2AD4FfCviNhmBLcjSW2VmbOBnYHfV0U7AedExFNrC0qSJI1ry5x4RcSrIuJk4G7gIOBs4HmZuRGwIfAv4Phl3Y4kjabMnEdp7Tq5KnohcEFErFVfVJIkabwaduIVEV+IiDuA3wFPBd4JrJWZH83M6wAy82bg88BzRiJYSRpNmbmAMoTv96qi5wJ/jogN6otKkiSNR8vS4vVuyn0FNszMl2fmL6ovKX3dAOy7DNuRpNpkZg+wH/ClquiZwEU777zz8+uLSpIkjTfLknitnZmfqVq1BpSZD2bmj5dhO5JUqywOpIziCrD6Nddc89uLL764zrAkSdI4siyJ1/yI2Lq/GRGxZUT0LMO6JWnMycyvA+8CFgGrvOUtb2Hrrbd+Zc1hSZKkcWBZEq9YwrwpgImXpI6TmT8E9gQWPP7449x9992/iIi31B2XJEka2yYPZeGIeAbQenPk50TEwj6LrUC5puv2ZYxNksakzPzVs571rD3uv//+M+bNmzcZODEiZmbmMXXHJkmSxqYhJV7Ae4FDgKymE/pZJiitXfstU2SSNIb99a9/Pe/yyy/nda973UPATODoiFgVODwzs+bwJEnSGDPUxOsE4DxKcnUO8AHg2j7LLABuzMwHljU4SRrLtthiCzbbbLNXX3nlladRegMcBqwWER/LzEU1hydJksaQISVemXk7VRfCiNgJuDwz57QjMEkaD377299ev+aaa74U+AOwHvARYGZEvCsz+3bFliRJE9SwB9fIzPNNuiQJMvNW4KXAVVXR3sApEbFCfVFJkqSxZEiJV0Q8EhFbVn/PqZ4PND3cnpAlaezJzH8DOwB/rop2Bc6MiJXri0qSJI0VQ73G6xvAPS1/ewG5JFUyc3ZE7AycAuwC7AicExG7ZOZ9tQYnSZJqNdRrvD7f8vehIx6NJI1zmTkvIl4P/Bh4M7AlcGFEvDIz76w1OEmSVJtluYGyJKkfmbkA2Av4blX0HODPEfGc+qKSJEl1GuoNlP9vCItnZn54iPFIUkfIzJ6I+ADwAHAwsDZwUUS8OjMvqzc6SZI02oZ6jdfrhrBsAiZekias6kbKn42IB4BvAk8Fzo2IXTPz3HqjkyRJo2mo13g9u12BSFKnysxvRcSDwPHAdOD3EfHmzDyt5tAkSdIo8RovSRoFmfkTYDfgcWB5yn2+/rfeqCRJ0mgZ6jVeWwDXZeZj1d9LlJmXDzsySeowmfnriHgV8GtgZeC4iFgtM79ac2iSJKnNhnqN16XANsDF1d8D3ccrqnmThh+aJHWezLwgInYAzgJWB74SEU8DPlldEyZJkjrQUBOvnYBrW/6WJA1RZl4ZES8B/gCsA3wcWC0i3pOZC2sNTpIktcVQB9c4v7+/JUlDk5k3VcnXWcAmwDuBVatBNx6vNzpJkjTSlnlwjYhYJSJeGhF7VI+rjERgktTpMrML2B74S1W0K2XEQz9HJUnqMMNOvCJiuYg4ArgLuAA4uXq8KyK+FBFe3yVJS5GZDwE7A2dWRTtQ7vW1en1RSZKkkbYsLV5fo1yX8E1gC2Ct6vFbwEcBR+mSpEHIzLmU1q6TqqLNgYsiYp3agpIkSSNqqINrtNoH+GxmfqWlrAu4MiLmUZKyjy3D+iVpwsjM7oh4O/AA8EFgA+DPEfHqzPxnvdFJkqRltSwtXpOAge7TdRkOJS9JQ5KZi4APA5+rimYBF0TES+uLSpIkjYRlSbxOAd48wLw3A6cuw7olaULK4jDg/ZT7Ic4A/hARjVoDkyRJy2RIXQ0j4g0tT88HjoiIc4HTgXspNwPdDVgPOGiEYpSkCSczvxcR91Gu+1oBOK26z9cPaw5NkiQNw1Cv8Tqln7I1KaNw9fUj4CdDjkiSBEBm/ioiXg2cAUwHjqtGO/xyZma90UmSpKEYauL17HYE0Wg0ZgDHArsAjwCHN5vNYwZYNoF5lC44ABc2m81dWubvD3wGWBn4HfDuZrP5SDvilqR2y8xzI2IHynDzTweOAJ4eER+trgmTJEnjwJASr8y8vU1xHFXFMgtYH/hjo9G4rtlsnjvA8ls2m83r+xY2Go1XAocArwRuobS4fQfYuy1RS9IoyMwrIuIlwFmUrtwfBlaPiH0yc0G90UmSpMFYlsE1/isinhIRq/adBvPaRqMxDdgDOLjZbM5pNptXACcA+w4jlH2AHzWbzSurVq7PAm9qNBpPGca6JGnMyMybgZcAV1RFbwF+ExHT64tKkiQN1rDv4xURQRlA433AGgMsNpgh5TcEotlsXttSdiXlJswDOafRaEwCLgU+2Ww2r6nKN6F0L+x1dRXDBsA/BhHLoHV1dU0Fpo7kOiu9X6Kmd3V1tWH1Y8eMGTOmTZo0iZ6enmn33XffynXH02bWa+cZ9Tq9++67H/vqV7/6uqOPPvrEhQsX7gC8ctKkSee96U1veuM3v/nNB9q13QlUpzBB3qvWaWeyXjuPdTp+zJo1a6mXNi3LDZQPoNwg+avA4cAXgR7KUPLLV2WDsRLluq5Ws1l88PvaEfgrJen5FHB2o9F4btXCtRLwcO+CzWYzG43GI0tY17L4DKVbY7vc1cZ1jwmzZ8/u/fOCGsMYbdZr5xnVOv3kJz/Jhz/8YT74wQ/y29/+lp6eni0uvfTSW+68807WXnvttmxzAtYpdPh71TrtTNZr57FOx5VY2gLLknj9LyXxOJqSZJ2emZdHxGFAk3Kt1mA8ShkIo9UqwJz+Fm42m+dXfy4ADm40Gm8HXgz8foB1rTzQupbRl4Aj27De6ZQTbi3aE/eYMWPGjE0nTZp0QU9Pz/azZ88e0RbJMch67Ty11enUqVM54IADlvvTn/701ccff/zdt9xyC9tuu+2/N9lkkzf8/ve/v2bpaxiaCVSnMEHeq9ZpZ7JeO4912lmWJfFaB7gyM3sioptyk08yc1FEHA38EDhwEOu5Eciq1eq6qmwzSjfBwVjE4gzzamBTyn1vaDQam1Ba4f41yHUN2qxZs+YD80d6vS1Nq3MG02Q5nnV3d88FWG655eZ2+r5ar52n7jqdNWsWjz/++HuBO4EvZOYz/vnPf/5+zTXX3DUzzxvJbU2UOoX663W0WKedyXrtPNZpZ1mWxOsBStc+gDuALYBzqudPAwY1oEWz2ZzbaDROAQ5rNBrvBNalDJKxZ99lG43G8yhdDK+idGf8JLAipeshlEE5Tmw0GicCtwKHASc3m815Q9w3SRrzqnt5HRYR/wG+S2nhPysi3pGZJ9cbnSRJarUsoxr+Gdiq+vsk4NCI+HpE9HbB+9MQ1vUByn257qHcq+ZzzWbzHIBGo/Foo9HYrlpu9WpbD1OSvW2AVzWbzdkAzWbzD5Rk6/fVurqBDw53ByVpPMjMY4E3AI9TfpT6RUR8pNagJEnSEyxLi9ehwJrV30dQuhq+hdIC9QeGkPBUidMeA8xbqeXvc4GNlrKu71Du3SVJE0ZmnhERLwd+DawKfDMi1gI+6Y2WJUmq37BbvDLzhsw8p/p7fmZ+ODPXzMxVM/NNmXnvyIUpSVqazPwL5V5fvTe7/xjw04hYvr6oJEkSjNwNlNeKiK0iYs2lLy1JapfMvJ4y0mvv6FdvBX4XEZ1+/xdJksa0ZUq8IuI9EXE75dfVvwF3RMSdEfHeEYlOkjRkmdkF7MDiAY9eDlwQEbPqi0qSpIlt2IlXRHwG+B5wPrA7sF31eB5wTDVfklSDzHwY2AX4eVW0KfCXiFjidbKSJKk9lmVwjQ8CX8vMT/UpPz0i/l3N/9IyrF+StAwyc0FE7AV0Ua73ehbw54h4XXU9mCRJGiXL0tVwZeCPA8w7m3L3aUlSjTJzUWZ+HPhoVbQq8KeI2LXGsCRJmnCWJfE6C3jFAPNeyeJrCyRJNcvMbwJvBhYAKwCnRsT7641KkqSJY0hdDSNii5anxwHfj4jVgdOBeyk3ON4NeBngABuSNIZk5skRcS/lM3tlyvW4zwY+7b2+JElqr6Fe43UpkC3PA9i7mrJ63us3wKRlik6SNKIy89yIeCnwO2At4BPAsyJi78x8vN7oJEnqXENNvHZqSxSSpFGTmf+MiG2A31JGO9wTmBURr8/MB+qNTpKkzjSkxCszz29XIJKk0ZOZd0fEdsD/A14FvJQy3Pz/ZObN9UYnSVLnWZbh5AGIiO0p9/BaFXgQuCAzL1zW9UqS2isz50TE64BjgHcBGwJ/rYab/3u90UmS1FmGnXhFxDTgNMrIhguBB4DVgEkR8Udgt8ycNyJRSpLaIjO7I+I9wG3AF4GnAedGxFsy84xag5MkqYMsy3DyXwFeBLwVWDEz1wBWrJ6/CPjysocnSWq3LA4H9gK6KZ/lp0XEh+qNTJKkzrEsidfulCGIf5GZPQCZ2ZOZJwMHAnuMRICSpNGRmSdSrvd6mDJK7bcj4sh58+bFkl8pSZKWZlkSrxnALQPMu7maL0kaRzLzXODFwO1V0QEbbLDBVx977LEao5IkafxblsTrOsr9u/qzN3DtMqxbklSTzLwW2Aa4HOC+++572c4778ypp546s97IJEkav5Yl8foC8KaI+EtEHBARb4mIj0TEXyj3hPnCyIQoSRptmflvYAfKvb74+9//zt577/2TiNi43sgkSRqfhp14ZebpwG7AVODrwInAN6rnuzkaliSNb5n5KPD6Zz7zmb8EmD9//izKcPOvrDcySZLGn2ElXhGxfETsDlyTmVsCKwNrAytn5paZ+euRDFKSVI/MXHjdddd95cgjjwRYRPm8PzMi3ldvZJIkjS/DSrwycwGlhWvt6vnczLw7M+eOZHCSpPpNmTKF/fffn9e//vUHAI8Ck4DvRsSRETGp5vAkSRoXluUar+upEi9JUuf75S9/eRHwUuCuqugAyv2+VqovKkmSxodlSbw+AxwcEVuOVDCSpLEtM/8BbA1cWhW9DrgwItaqLypJksa+ZUm8vgo8Fbg4Iv4TEf+MiKtapn+MUIySpDEkM++hjHj4q6poM8r/An+IkyRpAJOX4bWXLn0RSVInysx5EbEncDjwaWANSsvX2zLztHqjkyRp7Bly4hURzwPeS2nt6gJOycw/jHRgkqSxLTMXAZ+JiBuBY4EVgV9FxKeAr2dm1hqgJEljyJC6GkbES4HLgQ9Q+vjvC/zeYYUlaeLKzB8BrwQeAoLSFf24iFi+1sAkSRpDhnqN16HAtcA6mfl0YDXgdOCLIxuWJGk8yczzgG2Am6qifYE/RcTqtQUlSdIYMtTE6wXAYZl5J0BmPgJ8DFg1IhxaXpImsMy8kZJ8nVcVvRS4JCI2rS0oSZLGiKEmXk9l8f1bet3ZMk+SNIFl5gPAzsB3q6JnAn+JiDfUF5UkSfUbznDyXiwtSRpQZnZn5n7AfsBC4CmUQTc+FxFRb3SSJNVjOInXuRHxSO9EuZgayjDCj7RMD49gnJKkcSYzv0sZdOOBqujzwMkRMa2+qCRJqsdQh5P/fFuikCR1pMw8LyK2Bs4ANgH2ANaPiNdn5h31RidJ0ugZUuKVmSZekqQhycxbIuLFwM+ABrA5ZdCN3TLzL/VGJ0nS6BhOV0NJkoYkM+cAuwFHVEWrU7qu71NbUJIkjaKhdjVUpbu7ew1gjZFe78yZM6fNmTOH6dOnb9rd3T13pNc/xmzU+9jd3V1rIO1mvXYe63ToFixYAPCrXXbZ5dFzzjnnkMycCvxo3XXXfcVf/vKXb6+22mo9IxDrMplA9Toh3qcwoeoUrNdOZJ2OE1OmTLl8actEpoMUDkd3d/ehwCF1xyFJ49Gll17KG9/4Rrq6ugB4xStewU9/+lNWW221miOTJGnopkyZstRRe028hqldLV4LFy6cNmfOnAumT5++/eTJk8ddtj9EGwEnAm8Drq85lrayXjuPdbrsTjrppKfuv//+X3/00UefDzB16tSu/fbb7+Nf+cpXbhipbQzVBKrXCfE+hQlVp2C9diLrdJywxWsc6urqWhl4GFhl1qxZj9QdTzt1d3dvAVwGbDmYk3U8s147j3U6MiJiBeBoYN+q6HHg3Zn5s5HczmBNlHqdKO9TmDh1CtZrJ7JOO4uDa0iSapOZjwPvAt4PdAMrAD+NiG9FxJRag5MkaQSZeEmSapXF94AdgXuq4g8Df4yIp9cWmCRJI8jES5I0JlT39NoS6L231/bAZdUNmCVJGtdMvCRJY0Zm3gPsBBxTFa0JXBgR76ovKkmSlp2JlyRpTMnMBZn5AeCdwHxgeeAHEfH9iJhab3SSJA2PiZckaUzKzBOAlwJ3VkXvAc6LiDVrC0qSpGEy8ZIkjVmZeSnluq/zqqJtKNd97VBbUJIkDYOJlyRpTMvM+4BXAkdWRU8HzomIz0SE/8ckSeOC/7AkSWNeZi7MzI8BbwHmUv5/HQE0I2LVWoOTJGkQTLwkSeNGZv4CeCFwTVX0GuByh5yXJI11Jl6SpHElM68HXgT8tCp6FnBRROwfEVFfZJIkDczES5I07mTmXGBvykiH84EpwHeAX0TE9DpjkySpPyZekqRxKYsfANsCN1fFewKXRsTz64tMkqQnM/GSJI1rmXkFZcj506qiDYG/R8Q+tQUlSVIfJl6SpHEvMx8Gdgc+CiwEVgR+FBE/jIgVaw1OkiRMvCRJHaLqevhNYAfgrqp4X+BvEbFRfZFJkmTiJUnqMJn5F2Bz4Oyq6AXAZRHxv456KEmqi4mXJKnjZOb9wC7AwUAP8BTgOODnEbFKnbFJkiYmEy9JUkfKzEWZeTiwPXB7Vfwm4IqIeFF9kUmSJiITL0lSR6u6Hm4GnFIVPZtyw+VPR4T/ByVJo8J/OJKkjpeZsyn3+HoP8BgwGfgScHZErFFjaJKkCcLES5I0IbTccPmFwNVV8cuBf0TELvVFJkmaCEy8JEkTSmZeC2wNHFMVPQ34XUQc2Ww2l68vMklSJzPxkiRNOJn5WGZ+ANgNeKgqPmD//ff/w80331xjZJKkTmXiJUmasDLzdGBT4EKAnp6ezV71qlexySabvNN7fkmSRpKJlyRpQsvMO4GXAYcCix577DEeeuihbwG/iYhn1BmbJKlzmHhJkia8zFyYmZ9ff/31d15nnXV6i/8HuDoi3lBfZJKkTmHiJUlS5fzzz7/k7LPPZoUVVvhRVbQa8KuIOCEiVqkzNknS+GbiJUlSi2nTpnHzzTd/BHgd8J+qeG/KsPM71BaYJGlcM/GSJKkfmfkb4PnAaVXRs4BzI+JrETG1vsgkSeORiZckSQPIzPuA3YF9gDlAAB8HLomIF9QYmiRpnDHxkiRpCbL4MfACqmHnKS1hl0bEJyNiUn3RSZLGCxMvSZIGITNvA3YCPgksAKYAXwEuiIjn1BiaJGkcMPGSJGmQMrMnM78GbAX8syp+MWXgjU9GxOT6opMkjWUmXpIkDVFmXkVJvr4I9ABTKa1ff4mITeqMTZI0No2JX+YajcYM4FhgF+AR4PBms3lMP8ttA3weeGFV9DfgI81m81/V/B2Bc4B5LS87otlsHtG24CVJE1Jmzgc+GxGnAj8CNqUkY5dHxBeAr2Rmd50xSpLGjjGReAFHUWKZBawP/LHRaFzXbDbP7bPcTOB4YE/gMeAwoAk8t2WZe5vN5jPaH7IkSZCZV0TEVsCngc9Srv06DNg9IvbNzCtqDVCSNCbUnng1Go1pwB7A5s1mcw5wRaPROAHYF3hC4tVsNs/s89pvAJ9sNBqrNZvNB0YpZEmSnqBq2TosIk6jtH69ENgMuDgivgx8sWohkyRNULUnXsCGQDSbzWtbyq4EPjqI1+4A/LtP0rVao9H4NzAf+D3wmWaz+eBIBStJ0kAy8+qI2JbyP+wLlGu/DgZ2q1q/Lq41QElSbcZC4rUS5bquVrOB6Ut6UaPRWJfSRfGDLcXXU35hvI7SbfH7wI+B141MqIt1dXVNpfxDHWm9+z29q6urDasfO2bMmDFt0qRJ9PT0TLvvvvtWrjueNrNeO4912pmWuV7vvvtugO/tuuuuf7riiiuO6enp2Rp4HvDXadOmfeczn/nMl/bdd9/HRibc4bFOO5P12nms0/Fj1qxZffOZJ4nMHI1YBtRoNDYH/t5sNpdvKdsL+Fiz2dx8gNesBZwPHNVsNr+5hHU/G7gJmN5sNucNtNxwdHV1HQocMpLrlCR1lp6eHo4//ni+/OUv8/jjjwPwzGc+kyOOOIKddtqp5ugkSSNl1qxZsbRlxkKL141ANhqN5zabzeuqss2Aq/tbuNForEm59usHS0q6KouAqKaR9iXgyDasdzpwF7AWMKcN6x8zZsyYsemkSZMu6Onp2X727Nn/qDueNrNeO4912plGtF4nTZrEu9/9bs4+++xnX3zxxd9ZuHDhdnfccQd77bUXyy+//Kk777zzp7///e//Z5mjHiLrtDNZr53HOu0stbd4ATQajRMp3fbeCawL/AnYs9lsntNnuVmUlq6fNZvNz/eznp2AW4HbgadTuhpObTabr27vHoycrq6ulYGHgVUG02Q5nnV3d28BXAZsOWXKlMvrjqedrNfOY512pnbWa0QEsDfwdWC1qvgR4EDge5nZM5LbWxLrtDNZr53HOu0sY+UGyh8AErgHOBP4XG/S1Wg0Hm00GttVy72bMtz8J6ry3umZ1fzNgQuBRykn6f3A20dxPyRJ6lcWJwAbASdUxStTrlf+S0RsVk9kkqTRMBa6GtJsNmdThpTvb95KLX9/nnID5YHWcyTt6f4nSdKIyMz7gXdGxAnA9yiJ2NbApRHxbeCQzHy0xhAlSW0wVlq8JEmaUDLzfMo1zZ+l3AJlEmUY+msjYtcaQ5MktYGJlyRJNcnM+Zn5RWAT4I9V8drA6RFxWkSsXV90kqSRZOIlSVLNMvMmYGfgbcC9VfHrgesi4jMRsUJdsUmSRoaJlyRJY0A1+MZJlGu+vl8VTwOOAK6OiEY1MqIkaRwy8ZIkaQzJzIcy833ANsAlVfF6wBnAmRGxUW3BSZKGzcRLkqQxKDP/Tkm+9mVx98NXAf+MiG9ExCq1BSdJGjITL0mSxqjMXJSZPwI2pNwuZSHlVjAfBW6MiHdGhP/LJWkc8MNakqQxLjMfzsyPAS8Azq6KVweOB/4WES+qLThJ0qCYeEmSNE5k5nXAq4FdgVuq4q0oydcJEbFGbcFJkpbIxEuSpHGkGv2wCTwPOAiYV83aG/hXRBwaESvVFqAkqV8mXpIkjUOZ+XhmHgE8BzipKp4GHALcFBHvjYjJtQUoSXoCEy9JksaxzLwrM98GbAv8uSp+OvA9ygiIu3r/L0mqn4mXJEkdIDP/BmwH7AbcWBVvBJwOnO8AHJJULxMvSZI6RHX91+nAJsD7WXz/r+0oA3CcHBHr1RWfJE1kJl6SJHWYzOzOzO8B6wNfYPEAHHsC12244YYfu//++2uLT5ImIhMvSZI6VGbOycxDKAnYD4BFwJTbbrvtrRtttBGbbbbZuyJi5XqjlKSJwcRLkqQOl5n3ZOZ7gOcDvwZ45JFHuPbaa98P3BoRn4qIabUGKUkdzsRLkqQJIjOvzczG29/+9ndvu+22vcWrAl8GbomIAyJixfoilKTOZeIlSdIE88Mf/vDy8847j913331/4NKqeHXgSMo9wPaLiKn1RShJncfES5KkCSgi+PnPf/5XYGtgV+Af1axZwNHAjRHxroiYUleMktRJTLwkSZrAqiHom8AWwB7AddWsZ1IG5Lg+It4REZPqilGSOoGJlyRJIjMXZeYplAE49gL+Vc1aF/gxcE1E7G0LmCQNj4mXJEn6r8zsycwTgY2BfYHbqlnPAU6gXAP2AQfhkKShMfGSJElPkpkLM/NHlITrvcCt1axnAkcBt0XEpyNilbpilKTxxMRLkiQNKDMXZOaxwIaULojXVLNWB74E3B4RX4yIp9UVoySNByZekiRpqaoWsBOBFwCvBy6uZq0CHERJwL4dEWvXFKIkjWkmXpIkadCqQTjOALYBXg78qZq1IvAh4OaI+GFEPKeuGCVpLDLxkiRJQ1YNQ39OZr6CkoSdUc2aQhmU4/qI+HVEvDwiorZAJWmMMPGSJEnLJDP/npmvpwxF/zOgp5r1WuCPwJUR8c6ImFpTiJJUOxMvSZI0IjLz6sx8O7A+cCTwSDXrBcDxwB0RcUhErF5XjJJUFxMvSZI0ojLztsz8GLA28BEWD0W/OnAoJQH7YUQ8v54IJWn0mXhJkqS2yMxHMvPbwAbAG4ALq1lTKdeBXRURf4iI10SE30kkdTQ/5CRJUltlZk9mnpaZ2wMvpFwHtrCa/QrgN8ANEfHxiHhqXXFKUjuZeEmSpFGTmZdV14E9CzgCeLCatT7wNeDuiPhZRLzU0RAldRITL0mSNOoysyszD6JcB/Zu4PJq1vLA2yjdEq+KiA9ExCo1hSlJI8bES5Ik1SYz52XmcZm5JbAV8EPgsWr2JsBRQFdE/CAitqwrTklaVpPrDmC86u7uXgNYY6TXO3PmzGlz5sxh+vTpm3Z3d88d6fWPMRv1PnZ3d9caSLtZr53HOu1ME6hex2SdLliwYBFwzHnnnfeTAw888DXXXHPNGx977LF1gacA7wLeNX369Gs23XTTU77+9a//Ycstt3xsyWucUHUKY7Re22EC1at1Ok5MmTLl8qUtE5k5GrF0nO7u7kOBQ+qOQ5KkTpWZ/PnPf+bYY4/l1FNPZcGCBf+dN23aNN7whjfwjne8g+22247llrMTj6T6TJkyZanXpJp4DVO7WrwWLlw4bc6cORdMnz59+8mTJ4+7bH+INgJOpPTlv77mWNrKeu081mlnmkD1Ou7q9Iwzzphx2GGHNW644Ybd58+fv1brvKlTp3Y9+9nP/s273vWu33zoQx+6u3XeBKpTGIf1OlwTqF6t03HCFq9xqKura2XgYWCVWbNmPVJ3PO3U3d29BXAZsOVgTtbxzHrtPNZpZ5oo9Tqe67S639cOwD7AGyndEFtdAJwAnJKZcyZKncL4rtehmij1ap12FtvlJUnSuJGZizLz3MzcG3gG5UbMF7Qssj1wPPDviPjxi1/84u0WLVpUR6iS9AQmXpIkaVzKzDmZ+aPM3AFYD/g8cFs1+ynAO26//fbfbLPNNmywwQZfiIgtvDeYpLqYeEmSpHEvM2/JzEMpCdhOlO6GcwHuvvtu5s2b92FKl60bIuKwiHheXbFKmphMvCRJUseouiKel5nvBJ6x2mqrvW+HHXYA6KkW2QA4GLg6Iv4ZEQdFxPp1xStp4jDxkiRJHSkzH73qqqt+ftJJJ7HnnntuALwfOB/oHVlsE+CLwL8i4tKI+HhEPLOueCV1NhMvSZLU8b75zW8+kJnfy8wdgbWAjwB/a1lkS+BrwO0R8deI+FREbDj6kUrqVCZekiRpQsnMrsz8dmZuC6wLfBq4omWRbYAvU64HuzYijoiIrauh7CVpWPwAkSRJE1Zm3pqZX8nMLSg3q/0cT0zCngt8Bvg7cGdEHBMRO0fE8jWEK2kcM/GSJEkCMvOGzDysSsLWAT4MnMvigTlmUa4TOwu4LyJOiog9I2KVWgKWNK6YeEmSJPWRmbdn5v9l5suApwN7A6cDj1WLrAy8BTgZuD8izo+IT0fEpt4rTFJ/TLwkSZKWIDMfyMyfZOZuwFOB11PuE/ZAtchkYHvgS8CVwF0R8cOI2CMiZox6wJLGpMl1ByBJkjReZOY84AzgjIiYDGwL7FJNm1WLzQL2raaeiPgrcGY1XZmZ2Xe9kjqfLV6SJEnDkJkLM/PCzDwwMzdnccL1S2B2tdgk4KXA4cDlwD0RcWJE/G9EPLuOuCXVwxYvSZKkEZCZ9wA/An5UtYa9iMWtYVtUiz0deGs1ERG3AedU07mZ2TXKYUsaJbZ4SZIkjbCqNezPmXlwZm4JPIMyQMeJwD0ti65DaSX7GXB3RFwXEUdHxO4RsdqoBy6pbWzxkiRJarPM/A/wE+An1aiHzwFeVk07AatWi25UTfsBGRFXARcBfwYuysw7Rzt2SSPDxEuSJGkUVYNrXF9Nx0TEcsALWJyI7QCsBASwaTV9ACAi7qQkYr3J2NWZ2dN3G5LGHrsaSpIk1SgzF2XmlZl5ZGa+ltL6tS1wEPB74JGWxdem3D/saMrQ9Q9GxO8j4uB99913y7lz545y9JIGyxYvSZKkMSQzu4G/VRMRMQnYBHgJZYTElwDPrBZfGXgV8Kqf/exnnHTSSaywwgq/mDdv3gXAJcDFlFax7lHeDUl9mHhJkiSNYVVXwn9U0zEAEbE2ixOxl1K6KsaiRYuYN2/eBsAGwP9Wq3g8Iq5gcSJ2CXBTZi4a1R2RJjgTL0mSpHGmGmTjF9VERKzyxje+ca/nPe95Rx111FEXPPDAA8+hDF0PsAKl6+K2LauYHRGXUu4tdgWl2+K/vF5Mah8TL0mSpHEuMx/u7u7+K8BBBx10wPLLL38FsBawNbBV9fhCYHr1khnAK6qp12PVKIpXtkz/zEwvHJNGgImXJElSh6lGTryzmn4FUI2e+BwWJ2JbUboorlC9bEXKTZ9f1LqqiLiRkoT9A7gauAa4za6K0tCYeEmSJE0AVaJ0XTX9BCAiJlOuB9usZdoceFr1st57jj0HeFPL6h6LiOsoSVjrdLsJmdQ/Ey9JkqQJKjMXsjgZ+zlAdYPnZ/DEZGwzSoIW1UtXBLaoplbzWhKya4Ebq+mmzJzfth2RxgETL0mSJP1X1U3xnmo6s7c8Ip4CbAQ8r8/07JaXPwXYspqesNqIuI3FiVjrdIetZJoITLwkSZK0VJk5jzIK4uWt5RExDXguixOxjavHdVoXoyRoz6bcd6zV/Ij4F3ATcAtwa/V4C+VassdHel+kOph4SZIkadiqUQ8vrab/qlrI1gM27Gd6asuiUyk3iN6kv/VHxN0sTsRuBW5Zb731/v2LX/yChx9+eLlZs2aN7A5JbWLiJUmSpBFXtZD9s5qeICJW5cnJ2LrVNLPP4mtW03a9BTfffDNbbbUVwP3AXZTRG+/ob8rMh0dyv6ThMvGSJEnSqMrMB4G/VdMTRMRMSpfE3kSs9e91eOL310nAs6qpXxExh5KY3Q10tTy2/v2fzOxext2SlsjES5IkSWNGZj4EPESfa8kAImISsNaznvWsTQ444IDfHHzwwV989NFHnw48s2Wa1udl0ynXnW28pM1GxL0sTsTuAf4zwPRwNQCJNCQmXpIkSRoXMrMHuL2rq+shgD322ONrs2bNeqR3fjUU/kyemIitXT3OqqY1KcPhtwrg6dXUd4j8vuZHRN9k7F5Kt8f+pjkmagITL0mSJHWIKsF5sJqu7G+ZKjlbmZKAtSZjrX8/g5KErdDPKqayOKkbjAUR0TcZe5DSqtffY+/f8xYsWDDITWg8MPGSJEnShFElZw9X07UDLVclaNNZ3BLWOj2jz/OnVsv2Z3kWJ3VDseApT3nKnPXWW4+urq4T5syZ09US9+yWv/t7PofS0mbmNoZ0XOLVaDRmAMcCuwCPAIc3m81jag1KkiRJ40qVoD1STf9a2vIRMRVYjZKEPa167Dv1ls8EVgVWWsIql1+4cOFqN9xwA8Dzq2lIImIBJQl7pHpsnXrLHgXmtjwu6e+5wAK7Tg5PxyVewFGU/ZoFrA/8sdFoXNdsNs+tNyxJkiR1qsycz+LREgclIqZQkrDeROwJj+uss86GL3nJS9561llnnX///fcDrFJNM6rH5ZayieUpyeBqQ9qZJeuJiMeAedXU+nff548Bj7c8Pj5Q2YYbbjjpqKOO4qCDDlr/kksueRCY3zpl5sIR3IdadFTi1Wg0pgF7AJs3m805wBWNRuMEYF/AxEuSJEljRjWE/b3V9CTd3d1bAG8FPjplypQnjPJYdYWcxhMTsVUo169Nb3nsO/UtX4knjwS5JJOq1yyptW7IbrzxRnbeeWeAy/qbHxE9PDEZuyAz3zSSMbRbRyVelJvvRbPZbO2veyXw0XrCkSRJkkZe1d3v0Wq6e1nWFRHLUUZ6nMbiRKz179bHFYGntDwu6e+nUAYjWZEyUEksQ5iTWtYJT77R9pjXaYnXSpT+qq1mM/DFjsPW1dU1lXIijbTeWKd3dQ26pXpcmjFjxrRJkybR09Mz7b777lu57njazHrtPNZpZ5oQ9WqddibrtfOMVp3effd/87bern/3j/Q2Zs+ezQUXXLD81VdfvUJXV9fUBx98cMW5c+dOfeyxx1aYP3/+CjNnzlztQx/60Mlf/vKX//fee+9dtGjRouUXLVo0ddGiRStk5vKLFi2ampnLZ+bUzJw6derUm7q6usbMed56W4OBRCddG9doNDYH/t5sNpdvKdsL+Fiz2dx8JLfV1dV1KHDISK5TkiRJ0vgza9aspbbmdVqL141ANhqN5zabzeuqss2Aq9uwrS8BR7ZhvdOBu4C1KCPNdKwZM2ZsOmnSpAt6enq2nz179j/qjqfNrNfOY512pglRr9ZpZ7JeO4912lk6KvFqNptzG43GKcBhjUbjncC6wD7AniO9rVmzZvVe2DeiWprL5wymyXI86+7unguw3HLLze30fbVeO4912pkmSr1ap53Jeu081mlnWdoQlOPRB4AE7gHOBD7XbDbPqTckSZIkSRNZR7V4ATSbzdmUIeUlSZIkaUzoxBYvSZIkSRpTTLwkSZIkqc1MvCRJkiSpzUy8JEmSJKnNTLwkSZIkqc1MvCRJkiSpzUy8JEmSJKnNTLwkSZIkqc1MvCRJkiSpzUy8JEmSJKnNIjPrjkGSJEmSOpotXpIkSZLUZiZekiRJktRmJl6SJEmS1GYmXpIkSZLUZiZekiRJktRmJl6SJEmS1GYmXpIkSZLUZiZekiRJktRmJl6SJEmS1GYmXpIkSZLUZiZekiRJktRmJl6SJEmS1GYmXpIkSZLUZiZekiRJktRmJl6SJEmS1GYmXpIkSZLUZiZekiRJktRmJl6SJEmS1GYmXpIkSZLUZiZekiRJktRmJl6SJEmS1GaT6w5AizUajRnAscAuwCPA4c1m85hag9KQNBqN/YF9gOcDpzWbzTe3zNsEOA54AXAL8P5ms3lhHXFq8BqNxlTgaODlwFOBO4Ajms3midV863WcajQaxwKvAaYDDwLHNpvNI6p51us41mg0VgNuAG5qNpvbVGXW6TjUaDROAN4KLGgp3rjZbN5Rzbdex6lGo7E78Hng2cD9wAHNZvPUTq5TW7zGlqMoyfAs4LXAYY1GY6d6Q9IQdQFfBH7QWthoNKYATeA0YCbwZeCMRqMxc9Qj1FBNptTry4FVgPcCxzQajW2t13HvW8D6zWZzZWA7YK9Go7GH9doRvgH8s/eJdTruHdlsNldqmXqTLut1nGo0Gi+jfAa/j/Lj11bAlZ1ep7Z4jRGNRmMasAewebPZnANcUf3Ksy9wbp2xafCazeapAI1GYzNK60ivHYGnAF9rNpuLgJ81Go0DgDcAPxzlMDUEzWZzLvC5lqKLGo3Gn4EXAythvY5bzWbz2j5Fi4AN8P06rjUajR2B9YDjKT+UgHXaqXbEeh2vvgB8odlsXlQ9vxe4t9FovJIOrlMTr7FjQyD6fBG4EvhoPeFohG0C/LP6EOl1ZVWucaT6keSFwLexXse9RqPxJeBDlH/0twM/A3bHeh2Xqq7BRwFvAbZsmeV7dXx7T6PReA9wJ/DtZrN5fFVuvY5DjUZjErA18NtGo3ET5fP3D8BH6PA6tavh2LES5bquVrMpza8a/1YCHu5TNhvrd1xpNBoB/Ai4GDgb63Xcazabn6HU49aUpOshrNfx7DPAWc1m8599yq3T8ev/KD9OPw34MPDV6togsF7Hq6cDU4A9Ka2WG1Pq91t0eJ3a4jV2PAqs3KdsFWBODbFo5Fm/41yVdH0PWBPYudlsZqPRsF47QLPZTOCSRqPxauBQ4C6s13Gn0WhsALwd2LSf2b5Xx6lms3l5y9PzGo3G0ZRLM36F9Tpezasej2o2m3cBNBqNw4HTgSPo4Dq1xWvsuBHIRqPx3JayzYCr6wlHI+xq4PmNRqP1PbcZ1u+4UCVdRwObA7tU132B9dppJgPrY72OVy+h/DByW6PRuB/4DrBl9fctWKedYhEQ1d++V8ehZrM5m9JtNPuZ3dF1aovXGNFsNuc2Go1TKCMZvhNYlzIs+Z61BqYhaTQakynvq8nAco1GYwWgBzgPeBz4WKPR+D/KNSTrUkbt0dh3FLAN8PJms9naJfg8rNdxqdForAI0gDMov5pvC7wfOAzrdbz6JfDHlud7UFrAGsB/sE7HpUajsSdwJjCXMqjR/sAHq9nnYb2OV8cB+zcajd9R6vbTlNEMz6OD69QWr7HlA5Ts/x7Kh8znms3mOfWGpCE6GHgMOIjyT/8x4AfNZrOb8s//jZS+ygcBr282mw/WFKcGqdFoPAvYj9IH/c5Go/FoNR1ovY5rSflx63bK9QQ/pAxBfpT1Oj41m815zWbzrt6Jcr3eguq5dTp+7U9pHXkY+D7w2Waz+QsA63VcOwK4CLgWuJnF9/Hq6DqNzP5a+SRJkiRJI8UWL0mSJElqMxMvSZIkSWozEy9JkiRJajMTL0mSJElqMxMvSZIkSWozEy9JkiRJajMTL0mSJElqMxMvSZIkSWozEy9JapOIODQiMiIuGGDeo6MczwkRcfVobnOoIuKrEXFPRCyKiG/VHc9QVfX98RFYz47Vul44EnFJkuo3ue4AJGkC2C4iXpaZ59QdyFgWEa8CPgEcAPwd6Ko3olpdDmwLXFd3IJKkkWHiJUntNRe4GjgE6OjEKyJWzMzHlmEVz60e/y8zF41ETONVZj4C/K3uOIYrIlbIzMfrjkOSxhK7GkpS+30B2D4idhxogYG6lkXEbyLivJbnh0bEoxGxZUT8PSIei4grqucrRMR3I+LBiLgrIj4ywLZ2iYirI+LxiLgsIrbpZ5l9IuKqapm7I+LwiJjcZ35GxLYR8YeImAt8fQn7t2pEHBcR91UxXxwRO7fMPw/4ZvW0p1p3v8er5RhsVa3n8Yi4LiJe28+yr2k5TvdVx2dan2WeGRH/LyJmR8S8iDinn3q4LSKOiohPVMdjXkScERFrDLTPQ4mhn9c86Xyonn8yIj4fEf+JiPsj4keDWNdGEfGLiLizivvaiPhYRCz1O0BEPC8iLqiO8c0R8Y4lnJNbR8RfI+Jx4IPVvO0i4qJq3x+IiJ9GxNOXtJ9V+UDbWGqdS9JYZeIlSW2Wmb8DLgEOHaFVTgGOB74L7E7pvXAq8EPgMeBNwOnANyPixX1euwZwDPA1YE9gPnBWRKzeu0BEfBQ4DjgLeB3wFeBDwBf7ieVE4E/Aa4Gf9hdsREwCzgR2Aw6qYv4P8LuI2KlabD/gO9Xf21bT5Us5BicDPwbeANwEnBYRm7Rs941AE/hnte1PVsv+sGWZ6cD5wFbAB4C3AFOB8yJioz7b3K2a3l9NW1OO+4AGE8MQ7Q+sD+wNHAa8FfjsUl6zJnAD5Rj/D3As8Dng4KXEviJwNrAasBfwqWravJ/Fl6ecCz8FXg2cHRFbAn8EHqecax8FXgGcExErLCXm/iy1ziVpTMtMJycnJ6c2TJRE69Hq79cCCezQd171fMdq/gv7rOM3wHl91pnAq1vKetf9i5aySZTk5pstZSdUy72spWwGMAc4ono+vfV5y3L7AfOA1arn+1Tr+sQgjkOjWvZ/WsqWA67ts28fL/+WBnVcE9i3z/7eCpxUPQ/gtt7nLcv9D7AIeF71/EOtz6uylYAHgBNaym4DHgFmtJS9vIpj55ayBD4+lBgG2McnnQ/V84v7LPcz4KYhnJNBSdQPBLqWsux+QA/w7Jay9aqy/s7JPfq8/lTgTmD5lrJtq2X3GeZ5P2CdOzk5OY31yRYvSRoFmfkbSgvOISOwukU88XqxG6vHP7Zsrwe4GVi7z2sfzpZBPjJzdrWu3u6GL6YkHv8vIib3TtUyKwJ9Wxd+N4h4twPmZGn5693uIuCXwIurFrHhOK1lfT2UlqXe/dgQeBbwyz77cT7VF/2W2K7JzGta1vUo8OtqXqtzq+PVu9yfKMnYk7pqDjGGoTi7z/NrgbWW9IIoXVA/HxE3UVo4u4HDgTUiYqUlvHQr4KrMvLW3IDNvplyz2J++58J2wOmZuaDl9X8FbufJx3awllTnkjSmObiGJI2eLwCnR8Rwv3T2eqz1yyzQ+/fsPsstAPp26bqvn/XdS0kSAJ5aPQ7Uza9vInfvwGH+10xK61tf/6Z0H1sJeHgQ62nVnZkP9RNL7zVXvftxGv3r3Y+ZVRz9xbZqP+vvq3WbfQ02hqGY3ef5AkrXyCX5CvBu4PPAZdU6dqV0NVwBGOi2Bmsw8PkypU/ZvMyc26dsKMd2MJZW55I0ppl4SdIoycwzIuJKSqvXRX1m944At3yf8lVZnFiNhKf1U7Y6cE/194PV4xso3cT6urXP8xzENh8Ent5P+TMorS/DuZ/ZlIiY2eeLeH/7sT9laPq+ulqW63stV29sD/YpW72f5Vq32ddgY2i3PYDvZ+ZXegsi4jWDeN09wGb9lK8O9E2A+jsPllTvvS2MQznvl1bnkjSm2dVQkkbXFyjXBr20T/ld1WPvkOpUA168YIS3v0pEvKxlG6sAL2NxYvAXyrVca2Xmpf1MDwxjmxcB0yPi1S3bXY6SEPyl6jI2HLu1rG8S5Vqy3v24nnJM1x1gP3qTnouATSJi45Z1TaNcN3dhn+3tVB2v3uVeDqxM/0nVUGJotxVpSWKqY/XmQbzuEuAFEfHslteux5O7mw7kIuD1EfHf1rGIeBGl+2XvsR3qeb+kOpekMc0WL0kaXacDV1GSr/92zcrMuyLi78AhEfEwZQCDTzP0LnhL8yDww4g4hNLl7NNV+beqOB6OiM8BX42ItYBzKdeUrUvpnrZ7Zs4b4jZ/C1wM/DQiDqR82X4f8BzKSILDsQA4uBod71bKQBBrAV+q9iOr0RlPqhKp31KO97OA1wAHZuaNwI8oN2z+TUQcTGl9+yQlWflyn23OAc6MiC9TBiX5CmWwi7P6C3AIMbTbH4B3R8S1lK6DH2Dp3ROhHJuDKMfmc5SBOT5P6So4mPusHU5J5H8XEd+mtGJ9iXJd2i9gyOf9EutcksY6Ey9JGkXVl/EvAKf0M/ttwA8oow/eQ7kG5+2Ua6BGyj2UIcG/Rhmh7hrgVZn532uwMvMbEXE3ZfjvD1K6A95MGWluyN0eM7MnInaptvklyv5cBbwmM88b5n50U4Z+Pxp4PuWL+O6ZeVXLdv9fRMymJA97VcW3Ab+nuuYsM+dExA7ANyjD80+htKDsmJnX99nmaZSk8XuU65f+CLx3SUEOJoZR8EFKzN+htGaeQNmXHyzpRZn5WJR7rX0POAm4m9Jiuy+D+EEgMy+LiFdS6vyUatu/o4z62Hpz5cGe90utc0kayyJzMN3zJUkaGyLiUMqX95FMSJe2zduA32Tm/qO1zbEoIlYDbgGOzMzPj+J2D2WU61ySRpotXpIkqV8R8SlKy9xtlNEDP065Pvz4GsOSpHHJxEuSJA2kh9JNci1gIaUb5ssys78RLyVJS2BXQ0mSJElqM4eTlyRJkqQ2M/GSJEmSpDYz8ZIkSZKkNjPxkiRJkqQ2M/GSJEmSpDYz8ZIkSZKkNjPxkiRJkqQ2M/GSJEmSpDb7/3LxwacXt5hfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1000x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (130656102346)>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotnine.options.figure_size = (10, 4.8)\n",
    "(\n",
    "    ggplot(data = df_theory)+\n",
    "    geom_line(aes(x = 'number_person',\n",
    "                  y = 'probability',\n",
    "                  group = 1),\n",
    "              size = 1)+\n",
    "    scale_x_continuous(breaks = range(0, len(df_theory) + 10, 10))+\n",
    "    labs(title = 'Probability in birthday paradox (theoretical simulation)')+\n",
    "    xlab('Number of people in a group')+\n",
    "    ylab('Probability')+\n",
    "    theme_minimal()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reserved-composer",
   "metadata": {},
   "source": [
    "## Empirical simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "through-cargo",
   "metadata": {},
   "source": [
    "### Scenario 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "changed-stopping",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dictionary of probability\n",
    "obj = {}\n",
    "\n",
    "# Loop\n",
    "for person in range(100):\n",
    "    # --------------------------------------------- Probability ---------------------------------------------\n",
    "    # Dictionary of probability\n",
    "    probability = []\n",
    "\n",
    "    # Number of success\n",
    "    number = 0\n",
    "\n",
    "    for idx in range(1000):\n",
    "        # Create a random number\n",
    "        random_number = [random.randint(a = 1, b = 365) for _ in range(person)]\n",
    "\n",
    "        # Check two or more people share birthday\n",
    "        duplicated_number = [item for item, count in collections.Counter(random_number).items() if count > 1]\n",
    "        if len(duplicated_number) > 0:\n",
    "            number += 1\n",
    "\n",
    "        # Append the probability\n",
    "        probability.append(1 - (number / (idx + 1)))\n",
    "    \n",
    "    prob = np.mean(probability)\n",
    "    \n",
    "    # Update values\n",
    "    obj.update(\n",
    "        {\n",
    "            person: prob\n",
    "        }\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "recovered-order",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Create a data frame\n",
    "df_empirical_full = pd.DataFrame.from_dict(\n",
    "    data = obj,\n",
    "    orient = 'index'\n",
    "    ).reset_index().rename(\n",
    "    columns = {\n",
    "        'index': 'number_person',\n",
    "        0: 'probability'\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "phantom-plenty",
   "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>number_person</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.999698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.993782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.988824</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   number_person  probability\n",
       "0              0     1.000000\n",
       "1              1     1.000000\n",
       "2              2     0.999698\n",
       "3              3     0.993782\n",
       "4              4     0.988824"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show data frame\n",
    "df_empirical_full.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "furnished-wealth",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA14AAAHVCAYAAADhMCrAAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAA9hAAAPYQGoP6dpAABlpUlEQVR4nO3dd5gkVdWA8fdsYIFlYREk7CJBkaBIkCAGksgnKLYgIqioGFHEgJkgQYIYwISggGQQFQVKJEsyIEHABBjIsIQlLCwLuzs7c78/bg3bNNOzk3qqZ+b9PU8/3VVdXX3qdHU4fW/dipQSkiRJkqTWGVd1AJIkSZI02ll4SZIkSVKLWXhJkiRJUotZeEmSJElSi1l4SZIkSVKLWXhJkiRJUotZeEmSJElSi1l4SZIkSVKLWXhJkiRJUotZeEkjUERsHREpIvZswbr3LNe9dR+XPzUiUsO8Q8p1rD7Q9Q6FFufpnoi4uo/Lrl7GccgQPfeQbVe5nlMHH9XY1dN7oKI4JkbEHRHx46pj6Y+B7M89fca0ylC/R4Yz9kXEMaSfSz2sf1i3MyJOjIjbI2LCcDyfNBAWXtIg1f1oqL/MiYi/R8SBEbF41TG2q/KL/5CI2LDqWNpNRGxY5mb1qmPRiPFpYFXg8KoD0dhQ/qH2+arjKB0GvBz4ZNWBSM1YeElD51zgA+XlIGAe+YvgvCqDGgYfB5bow3JnlMtdWzdvdeBgYMMhjyq7tnzOM1q0/r66t4yjPz+INyTnZvUWxKNRJiIWA/YDfp5SeqjqePppIO/Tw8vH3NuSiFprJMfeaE/g803uG9btTCndR/4e3t9WL7UrCy9p6PwtpXRmeTkaeANwK7B9RGza7EERsfhI/pJIKXWklOb2YbnOlNLclFLXcMRVPmdX+Zydw/WcTeJIZRwLFrVsRCw1HDGNZaM0x+8BVgBOrzqQ/urP+7T7tUspLSgfU3kXz/4aybH3R0XbeTqwMrDTMD6n1GcWXlKLpJQ6gN+Xk2sCRMTV5bFBq0XEORHxGPAcsEp5//SIOCkiHoyI+RHxQEScEBErN3ueiPh0eVzHvIi4OyIOaizkImKdiPhxRPwzIp6KiOci4h8R8aWIGN9k1RPKdd1drvuOiNi7h+fv0/Etjcd4lccVXFXefUpdN82rI2JSRDwWEdc3Wddu5bIfW8RzvujYkfp55eUfETG3zPkRveSj2XNsFBGXR8TsMrfnRsQaDcu86FiK+nkRsUtE3BARzwIXlseTnFIuelVdbk7t4fn7tA0RsV1E/KV87WdGxMkRsXyTbfpURFxa7n/zI+LRiPh1RKzXsNzvyvUt28M6pkXEgog4cxH5q8/DbhFxS7ktMyLimIiY3MN6vxsRN0fEE+W++Z9yu5doWLb+td4rcvffucCx5f39el9ExIoRcVpEPB65O/GfImKbXrbtdRFxYRnn3MjHn3w9cutU9zIfL2P8dsNjJ5fLPxERq/aWw9JuwNPAH5rEsk1EXBwRT5Y5uz0ivtq4nbHwM2rViPhVufxT5eu/QrnMR8qczY38+fDRHp4vRf5s2DYi/lzm67Fyv3tpw7KLep/29Nr1ePxQRCxV3vfP8vV8MiJujIh96paZEhGHle+HmeU+fk9EHBsRL+lDrpuKiPdHxHV1r/kDEXFeRKxTt0xPx8B2z1u33L8fjIhny9xtVi7zxvL1eabM5fcjYmLD8/d47Gn043iu6Pv7PwFbAavFC7vab91sO8v5ffqei4F9Vl9J/k7dfVHbKVVhxP7LLo0Qa5XXM+vmLUX+cXQTuSvZFOCZiJgO3Ej+1/pE4O/ABuSufNtHxKYppUca1v8ZYDrwE+AJYGfgUHI/9z3rltua/AX5WxZ2e3sb8J1y2RcVVMC3gKXLWOYB7wN+HBErpJQO6XsKmvoNMBHYHziBhT8YH0kpzYuI04AvRMT6KaW/Nzz2Y8AzwDmDeP5PAtOAk8ivz7vKWGYDR/VxHauQv+gvAL4CvArYC3hDRGzcxy5f7wT2Jb+GJwIB/IOc808ARwK3l8veOZBtiIi3lzHOJL+uT5L3lUuaxPRl4DrgR8Dj5P34Y8B2EbFRSqk7jp+Q96MPAD9sWMeHgfHlNvXFO4AvAMeV2/MWcl42iIjt6lpK1wd2Ie8/d5PztTW5m91GZTyNPgesRN7PHiDnB/rxvoiIKeR9dE3gVPJ79dXAhbz4dSEitgcK4Cngx8Aj5bq/Qd4/3l629JxY/lD9UkRcnVK6qFzF8cA6wE5lF6qmyh+gWwA39NSiHBEfIef0FvJ+MQt4I/BNcs4af6ROBq4G/kTO6zrAPsBKEXEe+ViyE8l5/DhwUkTckVL6U8N6XgvsCpxM7kb4OvJ+8bry8+zZ3rar1Oy16ykPy5Bfo9eQ9/efAZ3AeuT3xrHlotPLuM8Ffk5+r72O/N59UxlbRx9ia3z+9wNnkvN2KPkzajqwLfBK4I4+rOZ0cuHwbfLr8AXg8oj4IPnPmJPIn3s7kHMzEziiv7EuQl/f/x8ADgCWJ79Xu91OEwP8nuvzZ3VKqSMibgS2jogY7a2KGoFSSl68eBnEhfzjLZF/IC9fXl5F/kJI5B+Hk8plry7nHdXDek4v73tPw/wPlvNP6uE55wCr1c0fR/6xl4A31c2f3CT2s4AFwMp18/YsH38/MLVu/uLkYnEBsHrd/FPzR8kL1ntIuY7Ve1jv1j1sx549xPZKoAv4YcP8Ncr5J/Tjtdmzh3kPAcs25O42YEYfX/d7yvV8qWH+rj28XquX8w7pYV4HsF4P639RvgayDeW8u8k/Ul5WN3888LtyPac2rP9F+wu5yJgP/Lhh3fcCf29YNoC7gH/3IY/deegCNmu479jyvj3q5i0BRA/rObxcdtMe8vQksFIPj+nP++Ib5bo+37Ds7uX8VDdvfJnzOcAaDcuf3MM2LQX8G3iMXMx/uFzm+33cF7tzeHwP961E/iF/XmPegC+Wj9uqbt7V5byvNSx7TDn/AWCZuvkrAnPJx5bVL5/Ky7sb5n+5nH9gH9+nzV67Q3jxZ0z3/vK5HpYfV3d7MWBiD8t8rHz8rj1sy6mNy/fw+N+QWx0nLGK5nmLvnndRQ6y1cv4CYPOG9dwCPNQw7x7g6l72kZ4+gw5pWLZP7/+6/eWefmznQL7n+vVZTS7QEjC9L+8fL16G82JXQ2no7Ef+N24m8C/gq8A1wFtTSvMalv1W/UREjCP3Sb8jpfTLhmXPIP+j/q6IiIb7zkwpPX/gcsr/dnf/A7hL3fw5dc81KSJeErmb2SXkH4kb97A9x6WUZtWtYy75x9d4citNS6WU/kvuirhHvHBkyI+Rf9ifMMinODml9GTd83WRu4auHH0/Bmg2+V/h56WUfgX8h55fr578LqX0zz4+X6O+bMPG5B9Yp6eU7q9btpP8Z8GLdO8vkS1d7iuPkIuD1zU830nAayLidXWreAu5QO5raxfA5SmlGxrmdcdXvy8/l1JKZXwT6/bly8tFXseLnZZSerjZdpbrWtT7YhdyS9FxDes4B/hvw6pfy8Kc391w3yE9bNMz5GO0JpNbao4l/8nxlR62pSfdXfce7+G+d5P/NDkJWC4ilu++kFvrAN7a8Jgu4PsN87pbpE9LKT1VF3v3fvHKHp77Pymlcxvm/ZD8vtmlh+V70uNr16j8DH0fueD/UeP9qa4lMKU0P5UtWhExISKmlvm4slykp32oL54kv4a1Mp6B+F56Yatld96vTyn9pWHZa8mtkEN6zGJf3//9NYjvuf5+Vne/D1YYaKxSq1h4SUPnVGA78o/ONwIrppS2Tin9p2G5mfVfIqWXkrsc/qtxpeWPzH8By5aXerf1EEf3vDW7Z0TEkhHxzYi4m/zv9OPkArH7QPyejmvo07pb7Cfkbd4F8o8kcmvArSmlmwa57rt6mNf9hb1cH9dxZw9FNeSuNsvSc14bNe4f/dGXbXhFed3T6/mi/Q0gIraMiCvILTZPsfAPhfV48TadRP43vv54u4+T/x0/bRHx13tRfCmlGeXz1+/L4yMfm3Q7L9yXry4X6SnnPea4n++LVwD/SynN70PsLy+ve3o/31du0ysa5v+N3H3qteWs3Zs8V296KvTXLa8vZOHr2H3p7vq2YsNjZqQXD5jT/ZnV0z73JD2/Z3p6TeeV6+jrZ0hf3x/Lk99zf0t9GMAn8rF1t5BbA58k56O7C91Aj/M6HPgf8GvgsYj4bUTsGxGN+e3NC/Jb913RLO/Q98+rPunn+78/Bvo919/P6u73QRpYmFLreIyXNHTuTCld0YflejquYSi/KFLDNcDZ5C4rJ5H/JX2M/GN5Y3ILWX//hBmuL7TzgYfJP+rPAt5OHrHqsCFYd28jqPWlpaov+pKnvhzn0syQb0NEbEL+N/ku8vEbd5FjTMAPyP/oPy+l9FBEFMDuEbEvuSvgO4HzU0r1xzYORn0ejyYf23IuueX4UXKRN53850dP+3KzHA/V+6Ix1/1+P5etATuWk0sAa9PDsWNNdOe5px/F3dvwMZoP6z2jYbq3/arZff3d3/qam76+P/r8/JHPO/U98n6+N3n755FbOS9hgH9Kp5TuLgeg2Jp8XNcWwHeBwyJih5RSjwOfNGiW376+15vltU+/9/r7/u+ngX7P9fdzrrsYe7SfzyO1nIWX1B4eJXe/Wa/xjrLbxavJ/242tpS9qod1vbq8vrN8/DLkH5dnppQ+0bDunroH1a/7gibP19cfhIvS6xdwygdKn0w+L8sryS0pz5J/MLeDV0TEpB5avdal59erP4aquO1+rXrbV+q9j/zdsENK6QX/NEfEcuSWoUY/IR/wvjswlXwMTX+6GfYYX0RMA5bhhfvbB4E/pJR2bVh2h/482QDeF3cCa0bEYj20RK3bMP2/8rqn9/PLePE2ARwIvJl8LNkewGkRsUHZ6rco95OPLeqxu195/WQf/xgaSj29ppPILYJD9RnSbSb5/bZBRIxbRKvXB8nHQv1f/XIR0fg69lvZhfHy8kLkk8PfSO5iuu1g198HT9BzAf7yHub1pL/v//58Tg30e66/XkluERtp57PTGGBXQ6kNlF/+5wPrRMS7G+5+P7lb0m+6j22ps0dErNY9Uf5r/rVy8jfldfcPixf8M1iO0vaFXsLaOyKm1i0/qVy+kzyAx1B4przurfvKieRtOBjYHvhF/TEmFZtCHlnyeRGxK3kUsPN6eL36oy+56YubyS0dHyx/9APP7yv797B897/LjfvLJ3lxl7RuV5B/SH+c3LJyFwtPpdBX20U5bHad7vh+UzfvRf9+Rx5Se79+Pl9/3xe/IReVezcsvzsvLnhuIf+w/0D9+7N0UHn967p1bFXOv5D8A3038oiiZ/XlWKHyeL0/AJv2sPwvyT+WD+npeJiIWKLc5lZYq4fPs8+S3ze/6WH5ASs/Q88mFxifaby/IS/d+9C4uvuDha/NgETDMPml28jdGQf7Pu6rf5O/R6bXxTWOPJBKX/T3/f8MsGxfjmcdxPdcn5WfBZuQBxixq6Haji1eUvvYn3x82M8jnxvoHywcZvd+crePRncA10fE8SwcTn4b8r/4fwBIKc2OiEuA90fEPOB6cne9j5IPmG7mUeDGssVpPvmf0NcCh/cwYMBA3Ub+B3TvyOewmgU8mlLqPsidlNI9EXEp+YsZ+t+S0kp3AgdExKuBG8gtH58k5/Xrg1z3jeTi4IDI58maA9ydUurx3GbNpJQ6I+Kz5FHtro+In5L/UX4XeTS9Rr8hFx4XR8QJ5BbGLYD/I2/vi743UkqpXLZ70Jj9B/Cj5xbgiog4DriPfLzkTuQBaupbOH8FfCoizgUuI/+g3YN+dtkcwPviu8B7gWMiYn3y670e+ZjDf5CHMO9ed2dEfIr8B8WNEfET8vtpB/KQ8pd2b1P5Y/1scne3Pcu83RQRXyMPZvN18tDki/ILclfcLcg5647lwYjYizya4r8jn6bhLnLe1iV/ZuzEwmPkhtI/yC13W5KPe9wM+BD5c+uYFjzfgeRuft8vP0OvJo8a+mpy183uFqdfkffVS8v9aEny+2ExBufSiJhNzv995PfX7uRC85RBrruvfkjeT68s97sgj7TaV/19//+F3EX22Ij4M7lwuzKl1Kyb30C+5/rjzeSuuo2Dd0htwRYvqU2klB4g/zA5jfxj6EfkrlAnA69LLz63CeUyh5O/aL9L/sfwEPKPwXp7kEcB3L58zPvII6f11krwVfI5afYijy63FPDZlNJgC4rnpZS6T3T5NHkUtZ/T87/OPymv/5lSum6onn8IPED+ol+FfN6dPcmtFm/sYxexpspBGD5C/hFxPDk3nxrgugryD/77ya/518nDnW/fw7LXkX+IP0X+wX84+biOLcjb20x3gb6Agf3I/C3luXzIP8o3Jx9TsmPZotPti+QfzZuQ9+W9yAXOBwfwnH1+X5StrFuQjzXcqYxxI/KPzpt7WP4SYEtyAf0Z8rFpa5L371pKqatsJTidPPrae1NKj9c9/nvknBwU5QlpF+GX5O52H+ohltPJA/78mbxPHUf+cb02+XOj8Tx5Q+Vm8mfYJuTtr5G3d6v6ESWHSjkK6xvIn1frkveTw8nH7NWPrvhd8ufby8jHen0B+Bu5uBiM48itWx8jn7ttf3Jr43tSSo3nuWuJcuTD95MLoG+Rt+0qXnhex94e39/3//fJ7/13k1/bn9Nzt+bu9Q/ke64/PkA+Lvi8Qa5HaomwJVZSu4t8MtqLyefnGZYfMOqfslVuBnBxSuld/Xjc6uQi8NA0NCfmHrPKwU2OANYcbOE/BLEk8lDwe1YZh8aOsiv1f4Evp5RedEoBqR3Y4iVpJPg8ucvL6YtYTtXZi3y+qOOrDmQMO5bcxW2w3bWkkai7Jd/PILUtj/GS1JYiYgXyMRmbk0/w+q1Ud0JntYdycIlVyMfX/CWldPkiHqIWKUfUW6fqOKQqNI5OKrUjCy9J7epV5EEHniYfM3RIpdGomZ+Tj2O5jjwwhSRJ6oHHeEmSJElSi3mMlyRJkiS1mIWXJEmSJLWYhZckSZIktZiFlyRJkiS1mIWXJEmSJLWYhZckSZIktZiFlyRJkiS1mIXXCDdjxoxJM2bMOGTGjBmTqo4FoKOjY+WOjo5DOjo6Vq46FnPTu3bKj7lpztw0Z2561075MTfNmZvetVN+zE1z5qZvLLxGvknAweV1O1iZHE87vPHMTe/aKT/mpjlz05y56V075cfcNGduetdO+TE3zZmbPrDwkiRJkqQWs/CSJEmSpBaz8JIkSZKkFrPwkiRJkqQWs/CSJEmSpBaz8JIkSZKkFrPwkiRJkqQWs/CSJEmSpBaz8JIkSZKkFrPwkiRJkqQWm1B1AEOtVqvtA+wJvAY4ryiK3auNSJIkSdJYN+oKL2AGcDjwFmD5imORJEmSpNFXeBVF8RuAWq22IRZekiRJktrAqCu8hsuMGTMmAZOqjgOY8sEPfpCrr776711dXV09LRARnUAnsABY0D0dEc9OmjTp+pVWWumKY4455qZNNtmkc7DBTJ06dfL48ePp7OycPHPmzKUHu75BmtJ9PWPGjEoDgbbLDbRRfsxNc+amOXPTuzbLj7lpztz0rm3yY26aMzcwbdq0pxe1TKSUhiOWYVer1Q4B1mnVMV4zZsw4BDi4Fevur+22247bbrttUOtYeumledOb3sTWW2/N1ltvzfTp04coOkmSJGl0mzZtWixqGVu8Bu6bwDFVBwFMedvb3vbAgw8+eOa8efM6erg/UkrjgQnl9XhgfEppQldX14qdnZ0bA+OefvppLrroIi666CIAxo0b9+/FFlvsD0sttdRf1l9//evOOOOMB/oSzNSpUzcYP378tZ2dnVvOmjXrb0O1kQM0BXgAWAWYXXEs7ZYbaKP8mJvmzE1z5qZ3bZYfc9Ocueld2+TH3DRnbvrGwmuApk2bNg+YV3UcM2bMYN9992Xffff9dF+aOBtFxFRgW2B74K3AywC6urrWnjt37tpz58792JVXXsn06dPvB/5Yd/lH6qG5tKOjYw7AuHHj5gwknqFU17Q8u+pYoL1yA+2VH3PTnLlpztz0rp3yY26aMze9a6f8mJvmzE3fjLrCq1arTSBv1wRgXK1WWxzoLIqip9agMS+lNAv4NfDriAhgXXIBth3wBmCZctGXAe8tLwBnRsQHeyq+JEmSJL3QaDyB8oHAc8ABwK7l7RMrjWiESNltKaXvpZTeBiwHbAB8Gvg5cH/d4nsA76sgTEmSJGnEGXUtXkVRHAIcUm0Uo0NKqRP4e3k5DiAi1gCuIbeA/SAiLkspzawuSkmSJKn9jcYWL7VQSulu4FPl5HK0xwAjkiRJUluz8FK/pZR+R+56CLBHRLy1yngkSZKkdmfhpYH6PPBEefunEbFUhbFIkiRJbc3CSwOSUnoU2LecXA34RoXhSJIkSW3NwkuDcQZweXn7cxGxWW8LR8QSETGx9WFJkiRJ7cXCSwNWnsNrL+BZ8r500sMPP/yikTIjYqOIOA14CvhPRGwwvJFKkiRJ1bLw0qCUoxx+vZx8zdve9rYPAjz11FPjImKniLgauBn4IDARWB34Y0TsUEG4kiRJUiUsvDQUfgjcBPCvf/3r44cffjirrLLKecB5wFblMvOBC4FOYCngwoj4VE8rkyRJkkYbCy8NWkppAfAxoDOltNg3vvEN5s2bt0p590zgUGC1lNI7gLcDs8n73nERcUxEjK8kcEmSJGmYWHhpSKSU/gZ8q3t6ySWX/C/wYWDVlNIhKaWHy+UuBd4I3F8uui/w64iYPMwhS5IkScPGwktD6evbbbfd137/+98zc+bM3VNKp6aU5jYulFL6B/A64K/lrHcC10TEtOEMVpIkSRouLxqBThqolFJXR0fH5cBRfVj2oYjYCjgT2AnYGLguIl6fUprR2kglSZKk4WWLlyqTUpoDvBs4upy1KvALz/UlSZKk0cbCS5VKKXWmlL4E/KCc9SbqjhWTJEmSRgMLL7WLLwN/Km/vGxHvqTIYSZIkaShZeKktpJQ6gPcAj5azfhYR61YYkiRJkjRkLLzUNspBNXZj4UmWfx0RS1UblSRJkjR4Fl5qKymlq4H9ysl1yS1fUV1EkiRJ0uBZeKkdfRf4TXn7PcBnK4xFkiRJGjQLL7WdlFICPgL8t5z13Yh4Y4UhSZIkSYNi4aW2lFJ6CngX8Cz5RN+/ioiVqo1KkiRJGhgLL7WtlNI/gU+UkysDv4mISRWGJEmSJA2IhZfaWkrpLBaeXPn1wI8dbEOSJEkjjYWXRoIvAVeWtz8KfLrCWCRJkqR+s/BS20spLSCPbnhXOev7EfHmCkOSJEmS+sXCSyNCSulx4J3AHGA8ebCNNaqNSpIkSeobCy+NGOVgGx8oJ18CXBARS1UYkiRJktQnFl4aUVJK5wGHlJOvAU6NCPdjSZIktTV/sGokOgw4r7y9C3BwRCwTEZMc8VCSJEntaELVAUj9lVLqiogPAtcB6wEHlRcAImIuMDci5q299trMnz9/8zvvvPOyisKVJEmSLLw0MqWUnomIdwLXA8s33L04sHhKiTvuuIOIOCMiNkgpPTz8kUqSJEkWXhrBUkp3RcQ6wNuAJSkLLmAJYPFJkyZNnzdv3h4ppRWAsyNiu5RSZ4UhS5IkaYyy8NKIVg4zf0ZP982YMWPp/ffff4/TTjsNYBvg6ywcmEOSJEkaNg6uoVHtoIMOYty4cX/rnoyIbSsNSJIkSWOShZdGtcUXX5zNN9/8Q8DTQABnRcRKFYclSZKkMcauhgPU0dGxMrBy1XEsu+yyk2fPns2UKVM26OjomFN1PMA63dcdHR2VBtKdmyuuuGLpnXba6YjLLrvsW8CKyyyzTPHYY4/tvcwyy3QNc0htkxtou33H3DRnbpozN71rm/yYm+bMTe/aLD/mprkxn5uJEyfevKhlIqU0HLGMOh0dHYcAB1cdh/ruc5/7HMcffzwABxxwAAcf7MsnSZKkwZs4ceIizyVr4TVA7dLitWDBgsmzZ8++dsqUKVtOmDCh6n87IP/jcRbwfuCOKgNpzM0999wzcaONNjplzpw56wJpt9122/uMM864YRhDapvcQNvtO+amOXPTnLnpXdvkx9w0Z25612b5MTfNjfnc2OI1BsyYMWNp4ClgmWnTpj1ddTwdHR2vBf4KbNyXHbCVespNRLwCuBlYGngU2DCl9NBwxNNOuYH22nfMTXPmpjlz07t2yo+5ac7c9K6d8mNumjM3fePgGhpTUkp3Ah8tJ1cAvlVhOJIkSRojLLw05qSUzgV+Xk7uHBGLVxmPJEmSRj8LL41VZ5XXSwGe20uSJEktZeGlser3wOzy9ruqDESSJEmjn4WXxqSU0lzgd+XkOyPCc9pJkiSpZSy8NJb9urxeDtiyykAkSZI0ull4aSy7BJhb3ra7oSRJklrGwktjVkrpGeDScnLniPD9IEmSpJbwh6bGut+U19OAzaoMRJIkSaOXhZfGuguBBeVtuxtKkiSpJSy8NKallJ4Arion3xURUWU8kiRJGp0svKSF3Q1fAbymykAkSZI0Oll4SXABkMrbdjeUJEnSkLPw0piXUnoI+HM5aeElSZKkIWfhJWXd3Q1fExGvrDQSSZIkjToWXlJ2Xt3tnSuLQpIkSaOShZcEpJTuBm4uJ3epMhZJkiSNPhZe0kLd3Q03i4iXVRqJJEmSRhULL2mh39Td3qmqICRJkjT6WHhJpZTS7cAd5aSjG0qSJGnIWHhJL9Td6rVlRLy00kgkSZI0alh4SS/UXXiNA/aMiJUjYsmIiCqDkiRJ0shm4SW90M3AfeXtbwMzgDnAvIiYGRH/i4gbImJvizFJkiT1lYWXVCellICf9XDXRGB54BXApsCPgSMsviRJktQXE6oOQGpDhwOXAtOAZXq4bAesCuwHLB4RXywLNkmSJKlHFl5Sg5RSF3B9s/sjYhXg98BawL7k4muf8nGSJEnSi9jVUOqnlNIDwFbAbeWsTwEnRMT46qKSJElSO7PwkgYgpfQwsDXwt3LWR4FTI8JWZEmSJL2IhZc0QCmlmcCbgZvKWXsAZ0fExOqikiRJUjuy8JIGIaX0BPAW4Lpy1q7AGdVFJEmSpHZk4SUNUkrpKeCtwDXlrN0iYr0KQ5IkSVKbsfCShkBKaTbwPqB7WPndKgxHkiRJbcbCSxoiKaUZLGz12t2TK0uSJKmbhZc0tM4pr9cEXltlIJIkSWofFl7S0Po10Fne3r3KQCRJktQ+2uKcQ7VabSpwArAD8DRwRFEUx/Ww3PuBn9bNCmBJYJeiKH5Tq9W2Bq4Enq1b5siiKI5sUejSC6SUHouIy4HtyYNsfDWl1FV1XJIkSapWWxRewLHkWKaRu2hdUavVbi+K4qr6hYqiOAs4q3u6Vqu9Dfg5cEndYo8WRbFS60OWmjqHXHi9DHg98Kdqw5EkSVLVKu9qWKvVJpPPfXRgURSzi6K4BTgV+EgfHv5h4BdFUTy7yCWl4XM+ML+8bXdDSZIktUWL11pAFEVxW928W4Ev9PagWq32EqAGbN1w13K1Wu1hYB65JWy/oiieGLJoSzNmzJgETBrq9Q7AlO7rGTNmVBoIwNSpUyePHz+ezs7OyTNnzly64nAqyc2DDz6YVl999cs6Ojp2jIjdiqI4aJNNNulss9xAG+075qY5c9Ocueldm+XH3DRnbnrXNvkxN82ZG5g2bdrTi1qmHQqvpcjHddWbxcKENbMHcFdRFNfVzbsD2BC4ndxt8afAacA7hiLQBvsBB7dgvQP1QNUBAMyaNav75rUVhtFo2HPzgx/8gL333puU0kufe+65J6BtcwNtsO+Ym+bMTXPmpndtmh9z05y56V3l+TE3zZkbII890at2KLyeARor42WA2Yt43IeBk+tnFEXxMPBwOflArVbbB/hfrVZbsgXdEb8JHDPE6xyIKeSdahUWnbOWmzp16gbjx4+/trOzc8tZs2b9reJwKsvNQw89tCRwJ7Dkhz70odPuuuuuz7ZZbqCN9h1z05y5ac7c9K7N8mNumjM3vWub/Jib5sxN37RD4fUfINVqtXWLori9nLch8M9mD6jVahsC6wFnLGLdXeTqc8hPZDtt2rR55O6MlaprPp3dlybOVuvo6JgDMG7cuDlVx1Nlbr7xjW88fdhhhxXA7vPmzatNnz79E/Pnz2+b3EB77TvttN+AuemNuWmunXID7ZUfc9OcueldO+XH3DRnbvqm8sKrKIo5tVrtXOCwWq32YeDlwJ7Ae3p52EeAi8sWrufVarVtgLuBe4EVgR8ClxVFMacVsUuLcA55cI1lge2Ah6oNR5IkSVWpfFTD0qeBRP5hejFwUFEUVwLUarVnarXaFt0L1mq1xYD30dDNsLQR8Ady98W/Ao8BH2ht6FJTlwBPlbcd3VCSJGkMq7zFC6AoilnkIeV7um+phun5wPJNlj2G9jjuSiKlNC8iziO34O50xx13HLfOOutUHJUkSZKq0C4tXtJo9YvyeqmvfOUrb6w0EkmSJFXGwktqrd8DjwPcfPPNb604FkmSJFXEwktqoZRSB3AuwMyZM7eYPbttRjSVJEnSMLLwklrvHICU0qTf/va3VcciSZKkClh4Sa33B8qh5H/5y19WHIokSZKqYOEltVhKqRP4JcBll13Gdttt97aIGPKTekuSJKl9WXhJw+NkYMGCBQu45pprDgPOjYiXVh2UJEmShoeFlzQMUkp/f+9737vPy172su5Z7wL+ERE7VhiWJEmShomFlzRMTjvttBtvvvlmVl555QvLWSsCv42IEyNiSpWxSZIkqbUsvKRhtMwyy3DvvfceDOwCPFbO/hjw94jYsrrIJEmS1EoWXlIFUkq/AdYDuseXXx24KiL2deANSZKk0cfCS6pISukR4J3AR4DZ5PfjMcCJEbFYlbFJkiRpaFl4SRVK2SnA64A7y9kfBS6PiOWri0ySJElDycJLagMppdvJxdfV5awtgesj4lWVBSVJkqQhY+EltYmU0uPAW4ETy1kvB66LiB2qi0qSJElDwcJLaiMppfnAXsDngS5gaeDCiPh8hWFJkiRpkCy8pDZTHvf1A+DtwNPk9+n3IuK91UYmSZKkgbLwktpUSukSYHNgRjnrmxGxeIUhSZIkaYAsvKQ2Vg668dVycjVg7wrDkSRJ0gBZeEnt72zg1vL2ARExtbpQJEmSNBAWXlKbSyl1sbDV6yXA1yoMR5IkSQNg4SWNACmly4ArysnPRcTLqoxHkiRJ/WPhJY0c3a1eiwOHVhmIJEmS+sfCSxohUko3k4/3AvhQRKxXZTySJEnqOwsvaWQ5EJhPfu8eVXEskiRJ6iMLL2kESSndDRxXTr49IraqMh5JkiT1jYWXNPIcATxd3v52RESVwUiSJGnRLLykESal9BgLuxluBry7wnAkSZLUBxZe0sj0A+DB8vaRETGxymAkSZLUOwsvaQRKKT0LHFxOrgl80y6HkiRJ7cvCSxq5TgVuLW9/kdzyZfElSZLUhiy8pBEqpdQJvB34bznra8DhFl+SJEntx8JLGsFSSjOAbYD/lbP2B75h8SVJktReLLykES6l9CC5+LqznHUgC4//kiRJUhuw8JJGgZTSA+Ti665y1sERcVCFIUmSJKnOhKoDGKk6OjpWBlauOo5ll1128uzZs5kyZcoGHR0dc6qOB1in+7qjo6PSQMZabubPn88JJ5zwmS9+8YsnzJs3bzpw6HrrrbfiLbfc8rOelm+z/LTNfgPmpjfmprk2yw20UX7MTXPmpndtlh9z09yYz83EiRNvXtQykVIajlhGnY6OjkOwO5fa0L333st2223HPffcA8APfvADPvWpT1UblCRJ0ig2ceLERR5fb+E1QO3S4rVgwYLJs2fPvnbKlClbTpgwoep/OyD/43EW8H7gjioDGcu5Oe6441b+yle+cuL8+fNXjoj5++233/sPOeSQu+qXabP8tM1+A+amN+amuTbLDbRRfsxNc+amd22WH3PT3JjPjS1eY8CMGTOWBp4Clpk2bdrTVcfT0dHxWuCvwMZ92QFbaaznJiI2Aq4HJpLP9/W6lNL87vvbKT/ttN+AuemNuWmunXID7ZUfc9OcueldO+XH3DRnbvpmwINrRMRNEfHJiFhmKAOSNDRSSrewsDvshsCh1UUjSZI0tg1mVMP/AMcAMyLi9IjYaohikjR0vg38qbz91Yh4U5XBSJIkjVUDLrxSSu8jH+P0ZWBd4KqI+F9E7BcR04YqQEkDl1LqBD4IPAMEcEZELF1tVJIkSWPPoM7jlVJ6KqV0XEppU3JXpguBLwD3RsRvI2KniPBcYVKFUkp3AZ8rJ1cHvlddNJIkSWPTUBZFDwB3A48A44FXAr8G/hsRmw/h80jqv1OAC8rbH4mInSqMRZIkacwZdOEVEW+NiF8ADwIHAJcBr04prQOsBfwXOHmwzyNp4FIevvQTwKPlrBP33nvvFSoMSZIkaUwZzKiG34iI+4CLgOWBDwOrpJS+kFK6HSCldCd5JLW1hyJYSQOXUnoU+Gg5ufxFF110rKeTkCRJGh6DafH6OPlEaWullLZNKZ1Tf46gOv8GPjKI55E0RFJKFwInAHR0dLz17LPPrjgiSZKksWEwhdfLUkr7la1aTaWUnkgpnTaI55E0tL4I3Anw7W9/m5NPPnmJiuORJEka9QZTeM2LiM16uiMiNo6IzkGsW1KLpJSeIRdfPPbYY3z3u9/9UMUhSZIkjXqDKbyil/smAhZeUvv67bhx4/4F8PTTT38+IiZVHZAkSdJoNqE/C0fESkD9yZHXjogFDYstTj6m695BxiapRVJKXSuuuOJ3Hn300VNTSiuTB8f5SdVxSZIkjVb9bfHaC7gJuBFIwKnl7frLH4EPAd8esiglDbmzzz77gjXXXLN78msRMbHKeCRJkkaz/hZepwLbANuSuxruA7y54fJGYKWU0olDF6akobbuuut2ffazn+2eXA34QIXhSJIkjWr96mqYUrqXsgthRGwD3JxSmt2KwCS13jvf+U4+//nP39XV1fVyYL+IOD2l1Nh9WJIkSYM04ME1UkrXWHRJI9uECROYOnXqMeXkmsBuVcYjSZI0WvWr8IqIpyNi4/L27HK62eWp1oQsaSgdffTR5wD3lZMHRMRgRjuVJElSD/rV1RA4Gnio7nYa2nAkDbf/+7//6wCOAo4D1gV2AX5VaVCSJEmjTH+P8Tq07vYhQx6NpKqcAnwdWBk4MCLOTSn5x4okSdIQsUuRJFJKc1l4Coj1gXdUGI4kSdKo098TKP+wH4unlNLn+hmPpOqcAOwHrAB8PSJ+a6uXJEnS0OjvMV79+Rc8ARZe0giRUno2Io4GvgVsArwVuKTaqCRJkkaH/h7jtUarApHUFo4Hvgq8BPh+RGyTUnpoEY+RJEnSIniMl6Tnlefm+2Y5uTbwh4hYvbqIJEmSRof+HuP1WuD2lNJz5e1epZRuHnBkkqpyNLAi8CXgFcAfI2K7lNLt1YYlSZI0cvX3GK+bgM2BG8rbzQ68j/K+8QMPTVIVUkopIr4CzAIOB6aTW77emlL6a6XBSZIkjVD9Lby2AW6ruy1pFCpHMzwiIp4CfgQsB1wVETumlK6tNjpJkqSRp7+Da1zT021Jo1NK6diIeBo4GZgCXBoRu6SULqo4NEmSpBFl0INrRMQyEfGmiNi1vF5mKAKT1B5SSqcD7wbmA4sDF0TEu6uNSpIkaWQZcOEVEeMi4kjgAeBa4Bfl9QMR8c2I8PguaZRIKZ0PvB2YQ24pPyUiJlcalCRJ0ggymBav75BHPfse8FpglfL6+8AXgG8PNjhJ7SOldAXwvnJyKWDHCsORJEkaUfo7uEa9PYGvp5S+VTdvBnBrRDxLLsq+OIj1S2o/vwMeIQ83/15yS7ckSZIWYTAtXuOBZufp+isOJS+NOimlTuBX5eQOETG1wnAkSZJGjMEUXucCuze5b3fgN4NYt6T29fPyejFgpwrjkCRJGjH61dUwIt5VN3kNcGREXAWcDzwKrADsDLwCOGCIYpTUXv4C3AesSv6T5dRKo5EkSRoB+nuM17k9zJsObNXD/FOA0/uy0lqtNhU4AdgBeBo4oiiK45osm4BngVTO+kNRFDvU3b8PsB+wNHAR8PGiKJ7uSxySFi2l1BURvwC+DLwlIl6aUppZdVySJEntrL+F1xotiQKOJccyDVgTuKJWq91eFMVVTZbfuCiKOxpn1mq17YCDge2Au8iF34+AD7UkamnsOodceI0nn+Pr+GrDkSRJam/9OsYrpXRvfy59WWetVpsM7AocWBTF7KIobiF3XfpIv7cmj7R4SlEUt5atXF8HdqvVaksOYF2SmrsF+G95u9mxnpIkSSoNZjj550XEksDijfNTSk/04eFrAVEUxW11824lnwusmStrtdp44CbgK0VR/Kucvx65e2G3f5L/kX8l8Lc+xNJnM2bMmARMGsp1DtCU7usZM2ZUGgjA1KlTJ48fP57Ozs7JM2fOXLricMxN7wacnwcffJC11lrr13PmzPkasMVb3/rWdU455ZQBJ3k05WaomZvmzE3v2iw/5qY5c9O7tsmPuWnO3MC0adMWeWjTgAuviAjyABqfBFZuslhfhpRfinxcV71ZLExYo62B68hFz1eBy2q12rplC9dSwFPdCxZFkWq12tO9rGsw9iN3a2wXD1QdAMCsWbO6b15bYRiNzE3vBpSfCy+8kG222QYgNt9889sHE8Boy81QMjfNmZvetWl+zE1z5qZ3lefH3DRnbgCIRS0wmBavfcknSP42cARwONBJ7na0WDmvL54hD4RRbxlgdk8LF0VxTXlzPnBgrVb7APAG4JIm61q62boG6ZvAMS1Yb39NIe9Uq9Ca7eyXqVOnbjB+/PhrOzs7t5w1a9aQtjIOgLnp3aDys9ZaazFu3Lg/dXV1rXfEEUf8da+99nrzQAMZbbkZSuamOXPTuzbLj7lpztz0rm3yY26aMzd9M5jC66PkFp8fk4us81NKN0fEYUBBHiSjL/4DpLLVqvtf8w3J3QT7oouFFeY/gQ2AswFqtdp65GLwvz0/dOCmTZs2D5g31Ovtr7rm09l9aeJstY6OjjkA48aNm1N1POamd0ORn66urrOBIzs7OzeePn36S1NKdw5kPaMxN0PF3DRnbnrXTvkxN82Zm961U37MTXPmpm8GU3itDtyaUuqMiA5gKjw/1PSPgZ8B+y9qJUVRzKnVaucCh9VqtQ8DLycPkvGexmVrtdqryV0M/05uVfsKsAS56yHkQTnOqtVqZwF3A4cBvyiK4tkBb6Wk3pwDHFne3p2+t3RLkiSNKf0a1bDB4+RjqiCfTPW1dfe9FOjPSIKfJp+X6yHgYuCgoiiuBKjVas/UarUtyuVWILdmPVU+5+bAW4uimAVQFMXl5GLrknJdHcBn+rthkvompXQ3cH056eiGkiRJTQymxetPwKbkUQTPBg6JiJXIxc7Hgd/3dUVl4bRrk/uWqrt9FbDOItb1I/K5uyQNj3OA1wHrRcR6KaW+dhOWJEkaMwbT4nUI8Ify9pHkroXvBfYiF12fGlRkkkaKX5JbrMFWL0mSpB4NuPBKKf07pXRleXteSulzKaXpKaWXpJR2Syk9OnRhSmpXKaUZQPdoo7uXp5qQJElSncG0eD0vIlaJiE0jYvpQrE/SiHNOef0KYOMqA5EkSWpHgyq8IuITEXEvcC/wF+C+iLg/IvYakugkjRS/Jp+6AexuKEmS9CIDLrwiYj/gJ+QuRrsAW5TXVwPHlfdLGgNSSo8Bl5eT742IFaqMR5Ikqd0MZlTDzwDfSSl9tWH++RHxcHn/Nwexfkkjy5nA9sA04MaI2CmldEvFMUmSJLWFwXQ1XBq4osl9lwFTBrFuSSPPz4Hjy9urAn+KCLsdSpIkMbjC61LgLU3u2w64chDrljTCpJS6Ukp7k08p0QEsAfw8Io6KiPHVRidJklStfnU1jIjX1k2eBPy0PJbjfOBRYAVgZ+DN5B9fksaYlNIJEXEbecCNFYCvAutHxPtSSrMqDU6SJKki/T3G6yYWnigVIIAPlZdUTne7EPBfbmkMSin9MSI2Ac4jDy+/A3BDRLwzpXR7tdFJkiQNv/4WXtu0JApJo05K6f6I2AI4AdgDeCVwU0R8G/huSmlOpQFKkiQNo34VXimla1oViKTRJ6X0XER8ELgV+DawJHAI8ImIOAA4PaXUVV2EkiRJw2NQJ1AGiIgtI+KAiDi6vN5iKAKTNDqk7Gjg9cCfy9nTgFPILWC2pEuSpFFvwOfxiojJ5OM33gIsAB4HlgPGR8QVwM4ppWeHJEpJI15K6YaIeBPwbuBbwBrARsCV06ZNu+aqq65i7bXXrjRGSZKkVhlMi9e3gNcB7wOWSCmtTB4++n3l/KMGH56k0aRs/foVsC7wZeApgMcee2yrTTfdlH322ec1lQYoSZLUIoMpvHYBvpZSOiel1AmQUupMKf0C2B/YdSgClDT6pJTmpZS+C6wJHAt0zp07l9NPP/3QiFii4vAkSZKG3GAKr6nAXU3uu7O8X5KaSik9llL6zKabbvpdgLlz564GHFZxWJIkSUNuMIXX7eTzd/XkQ8Btg1i3pDHk8ssv/9VWW23VPfmFiHhDlfFIkiQNtQEPrgF8A/h1RKwO/Ap4GFgReA+wGbkroiQt0pJLLplOOOEE1l133ee6urqWAE6NiA0doEeSJI0WA27xSimdD+wMTAK+C5wFHF1O75xSumAoApQ0Nqyxxhpssskm3y8nXwkcXmE4kiRJQ2pAhVdELBYRuwD/SiltDCwNvAxYOqW0cUrpt0MZpKSx4bLLLvs1cGU5+fly+HlJkqQRb0CFV0ppPrmF62Xl9JyU0oMppTlDGZyksWXJJZdMwEeBZ4AATomIJauNSpIkafAGM7jGHZSFlyQNlZTSPcCXysk1gSOri0aSJGloDKbw2g84MCI2HqpgJKl0AnBFefuzEbFFlcFIkiQN1mBGNfw2sDxwQ0Q8BjwKpLr7U0ppg8EEJ2lsSimliPgY8A9gCrnL4QZ2Z5YkSSPVYAqvm4YsCklqkFK6NyK+SG79egVwKAu7IEqSJI0o/S68IuLVwF7k1q4ZwLkppcuHOjBJAk4inxvwLeRRDs9MKd1abUiSJEn9169jvMqhnW8GPk0+SfJHgEsi4pMtiE3SGJdSSsCngHnAeOCnETG+2qgkSZL6r7+DaxwC3AasnlJaEVgOOB9PdCqpRVJK/2PhZ8xmgH/0SJKkEae/hdf6wGEppfsBUkpPA18EXhIRDi0vqVW+Qz6FBcCRETGtymAkSZL6q7+F1/LAAw3z7q+7T5KGXEppHvnYUoClge9XF40kSVL/DeQ8XmnRi0jS0EopXQucXE7uGhFvqzIeSZKk/hhI4XVVRDzdfQGeLOf/oX5+RDw1hHFKEsBXgMfK28dFxOQqg5EkSeqr/g4nf2hLopCkPkgpPV6e2+s0YDXgIOCr1UYlSZK0aP0qvFJKFl6SqnYGsCewDfDFiDgrpfT3akOSJEnqXb9PoKyso6NjZWDlquNYdtllJ8+ePZspU6Zs0NHRMafqeIB1uq87OjoqDcTc9K7N8tPn3MyfP5+jjjrqRwcffPCbUkoTp0yZcuZTTz314SWXXHLIjj8dqbkZDuamuTbLDbRRfsxNc+amd22WH3PT3JjPzcSJE29e1DKRz0+q/uro6DgEOLjqOKSx6rDDDuOwww4D4Mgjj+RLX/pSxRFJkqSxauLEibGoZSy8BqhdWrwWLFgwefbs2ddOmTJlywkTJlT9bwfkfzzOAt7PwvMuVcLc9K7N8tPv3Nxzzz0T119//XPmzp27OsC2226738UXX3zZUAQz0nPTSuamuTbLDbRRfsxNc+amd22WH3PT3JjPjS1eY8CMGTOWBp4Clpk2bdrTVcfT0dHxWuCvwMZ92QFbydz0rp3yM9DcRMTawJ+A5YAOYIeU0u8HG89oyE2rmJvm2ik30F75MTfNmZvetVN+zE1z5qZvBjKcvCS1hZTSv4EdgeeAicB5EbFhpUFJkiT1wMJL0oiWUvoLsBvQBUwBLo6I1SsNSpIkqYGFl6QRL6X0W2CvcnIl4JKIWK7CkCRJkl7AwkvSqJBSOomFI42uDVwYEUtWGJIkSdLzLLwkjSaHASeUtzcHzokIz1coSZIqZ+EladRIeZjWTwNFOesdwJURsUF1UUmSJFl4SRplUkoLgPcCfy5nbQHcHBE/joiXVBeZJEkayyy8JI06KaVnge2Aw4F55M+6vYH/RsQnI2J8lfFJkqSxx8JL0qiUUno2pfR14FXABeXslwDHA3+NiC0qC06SJI05Fl6SRrWU0l0ppZ2A7YF/l7M3AK6NiNMjYvnKgpMkSWOGhZekMSGldCmwPvAlYHY5+wPAHRGxR0REZcFJkqRRz8JL0piRUpqfUjoaWAs4p5y9HHAGcHFErFFZcJIkaVSz8JI05qSUHk4pvRd4O3B/OfutwD8j4os33XSTg29IkqQhZeElacxKKV0EvBr4IZCAJYHvvutd7/r9v//9714fK0mS1B8WXpLGtJTS7JTS54DXA/8A6Ozs3Gj33XfnyCOPXLra6CRJ0mhh4SVJQErpemBj4BsAjz76KCeffPL+1UYlSZJGCwsvSSqllDqAQyZMmHA5wHPPPbdXRGxQcViSJGkUsPCSpDoppbTpppt+ZbHFFoP8Gfljh5qXJEmDZeElSQ3OPffcu/bee+/uyTcCH6wwHEmSNApYeElSD/bZZx8i4t5y8jsRMbXKeCRJ0shm4SVJPVhiiSVYaaWVvlJOvhQ4rMp4JEnSyGbhJUlN3HTTTZcAF5aTe0fEa6uMR5IkjVwWXpLUu88Cc1k40Iafm5Ikqd/8ASFJvUgp3Q18s5zcHNizumgkSdJIZeElSYv2beDO8va3IuIlVQYjSZJGHgsvSVqElNJc4DPl5PLAkRWGI0mSRiALL0nqg5TSxcB55eTHI2LtKuORJEkji4WXJPXdl4BO8mfngRXHIkmSRhALL0nqo5TSXcBp5eT7bPWSJEl9ZeElSf1zBLZ6SZKkfrLwkqR+KFu9Ti8n3xcRa1UZjyRJGhksvCSp/2z1kiRJ/WLhJUn9lFK6EzijnHy/rV6SJGlRLLwkaWDqW70OqDgWSZLU5iy8JGkAUkr/Y2Gr1x4R8coq45EkSe1tQtUBANRqtanACcAOwNPAEUVRHNfDcpsDhwKblLP+Any+KIr/lvdvDVwJPFv3sCOLojiyZcFLGsuOAD4AjCcf6/WhasORJEntqi0KL+BYcizTgDWBK2q12u1FUVzVsNyywMnAe4DngMOAAli3bplHi6JYqfUhSxrrUkr/i4gzyQXXHhFxeErpv1XHJUmS2k/lhVetVpsM7ApsVBTFbOCWWq12KvAR4AWFV1EUFzc89mjgK7VabbmiKB4fppAlqd7hwB7kVq8DgD0rjUaSJLWlygsvYC0giqK4rW7ercAX+vDYrYCHG4qu5Wq12sPAPOASYL+iKJ4YqmC7zZgxYxIwaajXOwBTuq9nzJhRaSAAU6dOnTx+/Hg6Ozsnz5w5c+mKwzE3vWub/Izk3Dz44IOPvvzlL//lvHnz3gvs8YY3vOH755577l1DFchIzk2rmZvetVl+zE1z5qZ3bZMfc9OcuYFp06Y9vahl2qHwWop8XFe9WSxMWI9qtdrLyV0UP1M3+w5gQ+B2crfFnwKnAe8YmlBfYD/g4Basd6AeqDoAgFmzZnXfvLbCMBqZm95Vnp+RnpsrrriCrbbaiq6urvHTp0+/ZSgDGOm5aSVz07s2zY+5ac7c9K7y/Jib5swNALGoBdqh8HoGaKyMlwFmN3tArVZbBbgcOKooil92zy+K4mHg4XLygVqttg/wv1qttmRRFM/2sKrB+CZwzBCvcyCmkHeqVeglZ8Nl6tSpG4wfP/7azs7OLWfNmvW3isMxN71rm/yM9Ny8/OUvZ+LEiT+ZN2/ee88991wuuOCCS1796lcf/Lvf/e6OwQYy0nPTSuamd22WH3PTnLnpXdvkx9w0Z276ph0Kr/8AqVarrVsUxe3lvA2Bf/a0cK1Wm04+9uvEoii+t4h1d5Grz0VWoP01bdq0eeTujJWqaz6d3Zcmzlbr6OiYAzBu3Lg5VcdjbnrXTvkZDbmZN2/eAcBbgJd2dHRsf+utt/7f9OnTTwYOTikNuJ/DaMhNq5ib3rVTfsxNc+amd+2UH3PTnLnpm8oLr6Io5tRqtXOBw2q12oeBl5MPTn9P47K1Wm0acDVwZlEUR/Vw/zbA3cC9wIrAD4HLiqKY07INkCQgpXR3RLyKPMDGp4GJwMeA90XE0cB3Ukpt86+bJEkaXu1yAuVPAwl4CLgYOKgoiisBarXaM7VabYtyuY+Th5v/cjm/+7Jqef9GwB/I3Rf/CjxGPseOJLVcSumxlNK+5FNc/KKcvSTwdeDOiPhoZcFJkqRKVd7iBVAUxSzykPI93bdU3e1DySdQbraeY2iP464kjWEppTuB3SPiGOA7wJbAS4GTIuK5lNLZlQYoSZKGXbu0eEnSqJNSugHYGqixcOCfH0bECpUFJUmSKmHhJUktlLLfAt3dDJcjH38qSZLGEAsvSRoGKaWLgDPLyd0i4p1VxiNJkoaXhZckDZ/PA4+Wt4+PiKnVhSJJkoaThZckDZOU0uPAPuXkysDRFYYjSZKGkYWXJA2vc4HzytsfiYjtqgxGkiQNDwsvSRpGKaVEPnfhrHLWiRGxVPNHSJKk0cDCS5KGWUrpIWDfcnI14MgKw5EkScPAwkuSqnEacGl5e5+IeGOVwUiSpNay8JKkCpRdDj8BPAMEcHJEbBIRUW1kkiSpFSy8JKkiKaX7gK+Wk2sBNwJ3RsRREfFaizBJkkYPCy9JqtZPgJ8CneX0GuRi7K/Af9Zbb71P/+Mf/6gqNkmSNEQsvCSpQimlrpTSJ4GVyF0Pfw90lXev+Z///OcjG2+8MWuuueZXI2LxygKVJEmDYuElSW0gpfRYSunElNJbyCdX/hRwFZAA7rvvvvcAf46IV1YYpiRJGiALL0lqMymlR1NKP0kpvfn4449/+9Zbb91910bAXyNi9+qikyRJA2HhJUlt7KMf/egjF198Meuss84J5NavKcDPI+InEbFExeFJkqQ+svCSpDY3fvx4/v73v/8UeAvwcDl7L+AvEbF2dZFJkqS+svCSpBEipXQlsCFwRTlrfXLXw52qikmSJPWNhZckjSAppUeA7YGvk0c/nAz8OiI+WmlgkiSpVxZekjTCpJQ6U0qHA9sBT5M/y0+KiP086bIkSe3JwkuSRqiy6+FWwCPlrCOBYyLCz3ZJktqMX86SNIKllG4F3gjcWc76PHB6RCxWVUySJOnFLLwkaYRLKd0JvAm4tZz1fuCCiJjcuGxEjI+I6RGxgcWZJEnDZ0LVAUiSBi+l9HBEbA1cQO5+uD3w+4i4HFgNWLW8XoWFn/0XRkQtpZSGP2JJksYWCy9JGiVSSk9FxPbA2cDOwOvKSzM7Av8HXDoM4UmSNKbZ1VCSRpGU0lxgV+BHwHxgLvAf8rm/fgYcDHwUeLx8yFEOxiFJUuvZ4iVJo0xKqRP4bER8GZjfU1fCiJgKHE0+IfNuwM+HM0ZJksYa/+WUpFEqpTSvl+O3jgPuL28f7kAbkiS1loWXJI1BZZfEg8rJlwMfrzAcSZJGPQsvSRq7zgD+Vd4+KCKWqjIYSZJGMwsvSRqjymPB9i8nVwD2rTAcSZJGNQsvSRrbfgv8qbz95Yh4aZXBSJI0Wll4SdIYVg6+8bVycgoLW8AkSdIQsvCSpDEupfRH4Hfl5N4RsVqV8UiSNBpZeEmSAPYDErAY8I2KY5EkadTxBMoD1NHRsTKwctVxLLvsspNnz57NlClTNujo6JhTdTzAOt3XHR0dlQZibnrXZvkxN80NS27mz5/PaqutdtFDDz30duADX/va13532GGH/a9xubGYm75qs9xAG+XH3DRnbnrXZvkxN82N+dxMnDjx5kUtE83PranedHR0HAIcXHUckjRU7rnnHtZbbz3mz5/Pdtttx29/+1vGjbNjhCRJizJx4sRY1DIWXgPULi1eCxYsmDx79uxrp0yZsuWECROq/rcD8j8eZwHvB+6oMhBz07s2y4+5aW5Yc7P22mt/8e67734fwCte8YrTb7/99h/U3z+Wc7MobZYbaKP8mJvmzE3v2iw/5qa5MZ+bvrR42dVwgCZOnPgQ8FDVccycOXNpgCeffPJv06ZNe7rqeOqal+/oyw7YSuamd+2UH3PT3HDn5u677/4k8CpgwzvvvPODiy222PUppeO67x/LuVmUdsoNtFd+zE1z5qZ37ZQfc9Ocuekb+5BIkp6XUpoNvB24v5z1o4h4R4UhSZI0Klh4SZJeIKU0A3gb8DT5e+KciNi02qgkSRrZLLwkSS+SUvonsDPQASwJXBgRa1QblSRJI5eFlySpRymlK4GPlZMrABcdcMABy1YYkiRJI5aFlySpqZTS6cBB5eQ6Z5555lnz5s2rMiRJkkYkCy9J0qIcDpwMsGDBgjd+/vOf5/7771/k+UokSdJCFl6SpF6lfMLHTwKXARRFwTbbbHNYtVFJkjSyeB4vSdIipZQ6ImLXcePG/aGrq2v955577jMRcXdK6Xt9eXxEvA7YGHgSeBx4rLx+HJhTFneSJI1atnhJkvokpfT02972tnevssoq3bOOiYjdentMRIyPiG8BfwF+DJwNXAr8FbgHmA3MjYgbIuLVLQtekqSKWXhJkvrspz/96SNnnXUW5JYrgNMjYuuelo2I5YBLgK8sYrWLAZsCv4uIFYcmUkmS2ouFlySpX9Zcc03WXHPN9wBzyUXT+RHxmvplImIjcqvWW8pZNwJrA2sAmwBvBd4HfAb4SbnMauW6Fm/5RkiSNMw8xkuS1G/XXHPNDdOnT98d+A2wDHBJRLw+pXRfRHwAOAHoLqB+BuyTUppbTt/TuL6I6CAXYZsDJ0fE+z3uS5I0mtjiJUkakJTSBcDe5eQ04OKI+DFwOrno6iCPhvjxuqKrmS+QuyUCvBf4+tBHLElSdSy8JEkDllL6Kfk8XwCvYmEh9hCwVUrpp31puUopLQB2B/5Vzjo0InYf6nglSaqKhZckabAOAk6tm/4TsHFK6br+rCSl9BTwDmBmOevUiNh8SCKUJKliHuMlSRqUlFKKiE8A/yZ3L/xRSmn+ANd1d0TsBFwFTAIuiIjNUkr3DlnAkiRVwBYvSdKgpZQ6UkpHpZSOHmjRVbeuPwMfKSdXAH4bEUsPOkhJkipk4SVJajsppbNYeOzYa4DrPcGyJGkks/CSJLWrg4EzytvrADdExPsrjEeSpAGz8JIktaWUUhfwIeBLQCewJHBmRBzvSZYlSSONhZckqW2l7Ghga/IQ9ZDPDfbH4447buXKApMkqZ8c1VCS1PZSSn+MiI2As4E3Axt/8YtfPHvVVVdlmWWWWWrbbbddidwitkTdJQE3DHawD0mShoKFlyRpREgpPRIR/wccChzQ2dm59Lve9S6Aa3p52G0RsWtK6bZhCVKSpCbsaihJGjFSSp0ppQOBHcePH/90Hx7yKuCmiPhwRESLw5MkqSlbvCRJI05K6XennHLKrs8+++ylZ5xxxpHXX3/9f4Dnysuz5fWW5CHplwBOBraJiL1TSs/0tu6IWBKYWw7u0WezZs1i6aWXZtw4/9OUJL2YhZckaUTaY489HgP4xCc+8euJEyfe3MMif46Ia4BzgFWBDwCbRcR7Ukp/716obAl7NbAj8A7g9cA/yuX+3ZdYImLLcePGnbLqqquy7LLLrn3zzTffOLitkySNNv4tJ0katVJK1wEbAUU5a23yyZj3ioj/i4gfAXcB/wC+CbwBCGB9chfF3Xpbf0SMi4ivAld2dXW9/J577uHWW28tIuIVrdomSdLIZOElSRrVUkpPADsBXwA6gMWBnwCXAvsAq9ctfgtwKtAFLAWcExE/iohJjeuNiOWA3wJHAeOBueXzrQT8PiJWackGSZJGJAsvSdKoV54P7HvAm4B76u6aC1wI7AWsklJ6bUrpw8C2wCPlMvsAf4iI1bofFBGvA24G3lbO+tcmm2zypv322697kdXIxdeKLdokSdIIY+ElSRozUko3kLsefoZ8PNdyKaV3pJROSCk9WLfc1eVy3UPVbwrcEhFvj4jPAX8gHzcGcBqw2QUXXPDfffbZh8mTJ3+3nL8WcFlEvKTlGyZJansWXpKkMSWlNCuldGxK6cKU0rO9LPcQ8BbysV8Ay5Jbx74PTCS3ln00pbRn/XpuuOGGw4AflpPrAxdHxJSh3xJJ0khi4SVJUhMppQUppf3JIx4+WXfXf4HXpZRObnzM1KlTAfYFflbO2gy4sBym/gUiYmJErGSrmCSNfg4nL0nSIqSUfhcRrwW+BTwKHJBSanoC55RSV0TsBUwGdiefU+zaiHgIWL68vBRYpvsxEXEqsH/Z0tarcgj8bcvLbcDFKaXHBrh5kqRhYOElSVIfpJTuAXodXr5h+c6I+CC5+HoHsPEiHrIn8O6IOBz4fkppXuMCdQXXIcAb658uIq4jd4W8EPjn/Pnz+xqqJGkYWHhJktQiKaWOiHgPcCLwOuBxYCbwWN31Y8B2wHvJQ9gfBXw8Ir4IFCmlVBZcbyYXXG+qfwryeceCfA6yNwBHAvetueaa1++9996cf/757/rLX/6yNvB03WU2MAt4KqXUOVTbGxGRUkpDtT5JGk1GXeFVq9WmAicAO5C/XI4oiuK4SoOSJI1ZKaW5wAcWsdgpEXEceeCOjYFXAOcDV0TEycCngC3qlp8FHAP8CFiTfAzajixsVVv1vvvuW/VrX/sawAG9PXFEdBdhT5bXs4B/A1cBf0wpze7lsUuQW+BqwNuBl0TEXcCdwP/K6ztf//rXP/zzn/+ciRMnLiIN1SqPtdsBWIl8HPz48lJ/+z7g1+X54Ra1vvHk3OwDrEEeJfM84PKU0nOt2AZJ7WvUFV7AseTtmkb+MrqiVqvdXhTFVdWGJUlScymlP0bEZsCHyCMprkgeVfEtdYs9RS64fphSmlXOu6m8HBIR08jnFttx/Pjx23Z2di7Vh6eeUl5e1jD/y0BnRNxILsKuAv4ELE0usmrklrolGh73qvLyvOuuu4611lqLzs7Oqzo7O6+vi/m2lNKCPsT4AhExDlilvDxDbkl8vCxy+7uu5ckn2H43uYjsy2+jYyOiIJ9K4NKUUkfDOqcCH+XFJ+heg9yl9NmIuBQ4f88997zmiCOO6G/YkkagUVV41Wq1ycCuwEZFUcwGbqnVaqcCHyF/YUiS1LZSSl3k1q9fk1uq9iUPXf8U8D3gB3UFV0+PnwGcBJzU0dHx2gULFvz1mmuu2XqHHXa4h1xcLV13WYY8RP7UhsvywAbAYuQWns3Ly35ARxlPo2eAS8ijPa5B/uNzzXJ9AJTHnL22vHR7LiJuAf5Obml7przMrrvd1bDONcktgpMag4iIOZRFGAu7cz5CHhDl0e7bhx9++PSXvOQl7L///scBm5Tb2ZNUPn9neYFcaC5GLtTeDTwaEWcBpwLzgM+Si+fJdet5FLiO3F10CrAksDOw86mnntp5xx13cOutt35/7ty5/wPurbvMGMquoO2ibAlckty1djL5tXyO/HrPAZ4r3wvSqBKjqSt2rVbbCLi+KIrF6uZ9APhCURQbDeVzzZgxYxI9fOhXYArwAPlfv6bdQYbL1KlTNxg/fvy1nZ2dW86aNetvFYdjbnrXNvkxN82Zm+bGQm5222231e+4447Ndtlll0sPOuigp/rz2MHk58wzz1z8uOOO2+yxxx7bYu7cuVt2dnZuQsOftRHxwKRJky5afvnlLznggAP+UKvVXjSaxwEHHLDsddddt0ZXV9ertt9++x+feOKJ18ydO3d9csHXViLiviWWWOL8VVZZ5fzvfOc7t6655pqd5akBnjdr1ix23nnnje+77773z507dxfqCsuejBs37m/LLrvs8Ycffviva7Xa/KIoFjviiCO2eOyxx3acN2/e21NKKy4irAUR8TC54B0WkyZNmrTyyitPe+ihh2bMmzfvRQO8sLDb5Qu6YqaUxpGPNeyKiPpitft2AJNTSksCi/chlGcj4tlx48Y9t8oqq7zsgQceuLerq6vSYqwPuRlW48aNG7fKKqusNlZzs9hii11/11137dXk7mH/rpo2bVrTkW67jbbCawvgvKIolq+b9w7ge0VRrDmUzzVjxoxDgIOHcp2SJLWjZ599lhtvvJHrr7+eSZMmse222/LqV7+aPOZH/6SUuP/++/nb3/72/OWuu+7i2Wef5ZlnnqHZ78ell16aNdZYg9VXX/35y/Tp03nuued48sknn7888cQTz18/8cQTzJw5kyeffJKefu+suuqq7Ljjjuy4446sv/76/dqeuXPncvnll/PLX/6Sa665hs7O3DA1btw4tt9+ez72sY+x2WabNV1nV1cXt9xyC5dccgk33ngjDzzwAI888kjT7Zf0QltssQXnnHNO1WE8b9q0aYv8ABlthVdPLV57AF+0xWt4tNk/0Oamd22TH3PTnLlpztz0rs3y06fczJo1i8svv3zSn//856UeeuihpZ566qnJHR0di2244Yb3HXjggU80tkD11U033TT+5JNPXu6uu+566axZs1ZYf/31NzrwwAMPftWrXrXlM888M+jc7L333itcffXVO3d1dS25ySabnHvmmWfe34+HP5+ba6+99rnjjjtu+v333/+y2bNnv2zevHmrLliwYEVy69KwWHnllZd785vfXLvyyiuLhx566PEeFknkY/+6KFuzIqK7ZSuRW78aW8LGA4wbN25O2Yo1Z/z48c+OHz/+mQkTJjw7fvz4eQsWLFhiwYIFkzs7Oyd3dXUtWV6WWmyxxZbecccdP3DhhReeOW/evGFr+etJH3IzrCZNmjRxxx133GOs5mbSpEn/vu22245vcrctXq1WHuP1BLBhURS3l/O+C6xYFMWiRpQakWbMmLE0ue//Mn15wVuto6PjtcBfgY0nTpx4c5WxmJvetVN+zE1z5qY5c9O7dsqPuWnO3PSunfJjbpozN30zbP+gDIeiKOYA5wKH1Wq1KbVabQPy6EGnVBqYJEmSpDFtVBVepU+Tm7ofAi4GDiqK4spqQ5IkSZI0lo2q4eQBiqKYRR5SXpIkSZLawmhs8ZIkSZKktmLhJUmSJEktZuElSZIkSS1m4SVJkiRJLWbhJUmSJEktZuElSZIkSS1m4SVJkiRJLWbhJUmSJEktZuElSZIkSS1m4SVJkiRJLWbhJUmSJEktFimlqmOQJEmSpFHNFi9JkiRJajELL0mSJElqMQsvSZIkSWoxCy9JkiRJajELL0mSJElqMQsvSZIkSWoxCy9JkiRJajELL0mSJElqMQsvSZIkSWoxCy9JkiRJajELL0mSJElqMQsvSZIkSWoxCy9JkiRJajELL0mSJElqMQsvSZIkSWoxCy9JkiRJajELL0mSJElqMQsvSZIkSWoxCy9JkiRJajELL0mSJElqMQsvSZIkSWqxCVUHoIGr1WpTgROAHYCngSOKojiu0qAqUqvV9gH2BF4DnFcUxe51960HnASsD9wFfKooij9UEWcVarXaJODHwLbA8sB9wJFFUZxV3j/W83MC8HZgCvAEcEJRFEeW943p3HSr1WrLAf8G/lcUxeblvDGbm1qtdirwPmB+3exXFUVxX3n/mM1Nt1qttgtwKLAG8Biwb1EUvxnruanVas80zFocuKgoilp5/1jPz+rk76vXAx3AhcBni6KYY25qryTnZjPgKeAbRVH8rLxvTOVmML/5arXau4FvAysCfwI+XBTFg8MVuy1eI9ux5OJ5GrAjcFitVtum2pAqMwM4HDixfmatVpsIFMB5wLLAUcAFtVpt2WGPsDoTyPnZFlgG2As4rlarvd78APB9YM2iKJYGtgD2qNVqu5qbFzga+Ef3hLkB4JiiKJaqu3QXXWM+N7Va7c3k99UnyX9obArcam6gfp8hfx4/AvwS3HdKPyX/ATYdeBWwNvD1sZ6bWq02gbz9V5P/QH0XcHStVttqjOZmQL/5arXaOsApwCfIefwvcPbwhW3hNWLVarXJwK7AgUVRzC6K4hbgVOAjlQZWkaIoflMUxfnkf1brbQ0sCXynKIp5RVGcCdxN/tAaE4qimFMUxUFFUdxVFEVXURR/JP/L8wbMD0VR3FYUxXN1s7qAV2JuAKjValsDrwBOr5u9Neamma0xN98g/xv/x/Iz59GiKO7C3DTaHlgK+HU5vTXm5+XAz4uieK4oisfJP6DXw9ysDawOHFUUxYKiKP5Kzs1HGIO5GcRvvg8AFxdFcUX5vf914A21Wu0VwxO5XQ1HsrWAKIritrp5twJfqCactrUe8I+iKLrq5t1azh+TyqJ9E+AHmB8AarXaN4HPkj+w7wXOBHZhjOem7KZ6LPBeYOO6u9xv4BO1Wu0TwP3AD4qiOLmcP6ZzU6vVxpO7Qv2uVqv9j/yeuhz4PGM8Nz34MHBO3R8/5ie3lL6vVqtdA0wmfw6fibnpbiiJunlB7k431nNTb1G5WA+4ofuOoiieqNVq95Xz7xyOAG3xGrmWIh/XVW8WuVuHFlqK3Be63izGaJ5qtVqQm9lvAC7D/ABQFMV+5FxsRv6SfxJzA7AfcGlRFP9omD/Wc/ND8p9fLwU+B3y7PKYJzM2KwETgPeR/n19FztP3MTfPq9VqywPvAE6um21+4CpgHfLvm0eAx8ndycZ6bu4AHgIOqNVqi9VqtdcBO5P/2Bjruam3qFxUnisLr5HrGWDphnnLALMriKWdmadSWXT9hNx3freiKBLm53lFUaSiKG4E5gGHMMZzUx7I/QHg4B7uHtO5KYri5qIoHiuKorMoiqvJB7zvWt49pnMDPFteH1sUxQNFUcwCjgDehrmp937yYDXX180b0/kpW0svBX5Hbu1aBphJ/jNsTOemKIoO4J3kPzNmAMeQDy95gDGemwaLykXlubLwGrn+A6RarbZu3bwNgX9WE07b+ifwmlqtVr+vb8gYy1NZdP0Y2AjYoSiKOeVd5ufFJgBrYm7eSC7S76nVao8BPwI2Lm/fxdjOTaMuFnYBGtP7TVlo3Q+kHu4e07lp8GFy74N6Yz0/ywKrAD8qimJuURRPA8eTR50d67mhKIp/FEXx5qIoli+K4o3k1uW/YG7qLSoX/wQ26L6jHHRjVYYxVx7jNUKVQ6ueSx7J8MPkA1L3JHfvGHPKEX+6L+NqtdriQCd5BKC5wBdrtdoPyf3FX04+KHUsORbYHNi2/DLrdjVjOD+1Wm0ZoAZcQP4n7PXAp4DDGOO5IY+0dkXd9K7kFrAauQvQmM1NrVZ7D3AxMIc8SM0+wGfKu69mDOemdBKwT61Wu4ico6+xcES2sZ4barXaa4FXA2c03HU1Yzg/RVE8VqvV7gL2rtVqR5G7rH4C+BtjPDcAtVrtNcD/yH9qvJc8UvGnyd0yx1RuBvGb70zg+nLk1evIAwFdVxTFsBzfBbZ4jXSfJr8BHyL/CDioKIorqw2pMgcCzwEHkH8gPgecWDbP14B3k/vxHgDsVBTFExXFOexqtdpqwN7kYy3ur9Vqz5SX/c0PifyHxb3kft8/Iw+dfuxYz01RFM+WXcUeKIriAfJxb/PL6TGdG3KhdT95n/kp8PWiKM6B57sEjeXcABwJ/BG4jXzAevd5vMxN9mHgd0VRPFI/0/wA+bilrYCHye+xacAHzQ2Qzx34IPn99CFgu6IoHh+juRnQb76iKG4HPkr+c+hx8miR7xvOwCOlnnoDSJIkSZKGii1ekiRJktRiFl6SJEmS1GIWXpIkSZLUYhZekiRJktRiFl6SJEmS1GIWXpIkSZLUYhZekiRJktRiFl6SJEmS1GIWXpLUIhFxSESkiLi2yX3PDHM8p0bEP4fzOfsrIr4dEQ9FRFdEfL/qePqrfL2/NATr2bpc1yZDEZckqXoTqg5AksaALSLizSmlK6sOpJ1FxFuBLwP7AtcDM6qNqFI3A68Hbq86EEnS0LDwkqTWmgP8EzgYGNWFV0QskVJ6bhCrWLe8/mFKqWsoYhqpUkpPA3+pOo6BiojFU0pzq45DktqJXQ0lqfW+AWwZEVs3W6BZ17KIuDAirq6bPiQinomIjSPi+oh4LiJuKacXj4jjI+KJiHggIj7f5Ll2iIh/RsTciPhrRGzewzJ7RsTfy2UejIgjImJCw/0pIl4fEZdHxBzgu71s30si4qSImFnGfENE/F/d/VcD3ysnO8t195ivuhxsWq5nbkTcHhE79rDs2+vyNLPMz+SGZVaNiF9FxKyIeDYiruzhdbgnIo6NiC+X+Xg2Ii6IiJWbbXN/YujhMS/aH8rpr0TEoRHxSEQ8FhGn9GFd60TEORFxfxn3bRHxxYhY5G+AiHh1RFxb5vjOiPhgL/vkZhFxXUTMBT5T3rdFRPyx3PbHI+KMiFixt+0s5zd7jkW+5pLUriy8JKnFUkoXATcChwzRKicCJwPHA7uQey/8BvgZ8BywG3A+8L2IeEPDY1cGjgO+A7wHmAdcGhErdC8QEV8ATgIuBd4BfAv4LHB4D7GcBfwe2BE4o6dgI2I8cDGwM3BAGfMjwEURsU252N7Aj8rbry8vNy8iB78ATgPeBfwPOC8i1qt73ncDBfCP8rm/Ui77s7plpgDXAJsCnwbeC0wCro6IdRqec+fy8qnyshk57031JYZ+2gdYE/gQcBjwPuDri3jMdODf5By/DTgBOAg4cBGxLwFcBiwH7AF8tbxs1MPii5H3hTOA7YHLImJj4ApgLnlf+wLwFuDKiFh8ETH3ZJGvuSS1tZSSFy9evHhpwYVcaD1T3t4RSMBWjfeV01uX92/SsI4Lgasb1pmA7evmda/7nLp548nFzffq5p1aLvfmunlTgdnAkeX0lPrpuuX2Bp4Fliun9yzX9eU+5KFWLvu2unnjgNsatu1L+WupT3lNwEcatvdu4OxyOoB7uqfrlnsb0AW8upz+bP10OW8p4HHg1Lp59wBPA1Pr5m1bxvF/dfMS8KX+xNBkG1+0P5TTNzQsdybwv37sk0Eu1PcHZixi2b2BTmCNunmvKOf1tE/u2vD43wD3A4vVzXt9ueyeA9zvm77mXrx48dLuF1u8JGkYpJQuJLfgHDwEq+vihceL/ae8vqLu+TqBO4GXNTz2qVQ3yEdKaVa5ru7uhm8gFx6/iogJ3ZdymSWAxtaFi/oQ7xbA7JRb/rqftwv4JfCGskVsIM6rW18nuWWpezvWAlYDftmwHddQ/tCvi+1fKaV/1a3rGeC35X31rirz1b3c78nF2Iu6avYzhv64rGH6NmCV3h4QuQvqoRHxP3ILZwdwBLByRCzVy0M3Bf6eUrq7e0ZK6U7yMYs9adwXtgDOTynNr3v8dcC9vDi3fdXbay5Jbc3BNSRp+HwDOD8iBvqjs9tz9T9mge7bsxqWmw80duma2cP6HiUXCQDLl9fNuvk1FnKPNg/zecuSW98aPUzuPrYU8FQf1lOvI6X0ZA+xdB9z1b0d59Gz7u1Ytoyjp9he0sP6G9U/Z6O+xtAfsxqm55O7RvbmW8DHgUOBv5breCe5q+HiQLPTGqxM8/1lYsO8Z1NKcxrm9Se3fbGo11yS2pqFlyQNk5TSBRFxK7nV648Nd3ePALdYw/yXsLCwGgov7WHeCsBD5e0nyut3kbuJNbq7YTr14TmfAFbsYf5K5NaXgZzPbGJELNvwQ7yn7diHPDR9oxl1yzUey9Ud2xMN81boYbn652zU1xhabVfgpymlb3XPiIi39+FxDwEb9jB/BaCxAOppP+jtde9uYezPfr+o11yS2ppdDSVpeH2DfGzQmxrmP1Bedw+pTjngxfpD/PzLRMSb655jGeDNLCwM/kw+lmuVlNJNPVweH8Bz/hGYEhHb1z3vOHJB8Oeyy9hA7Fy3vvHkY8m6t+MOck5f3mQ7uouePwLrRcSr6tY1mXzc3B8anm+bMl/dy20LLE3PRVV/Ymi1JagrYspc7d6Hx90IrB8Ra9Q99hW8uLtpM38EdoqI51vHIuJ15O6X3bnt737f22suSW3NFi9JGl7nA38nF1/Pd81KKT0QEdcDB0fEU+QBDL5G/7vgLcoTwM8i4mByl7OvlfO/X8bxVEQcBHw7IlYBriIfU/Zycve0XVJKz/bzOX8H3ACcERH7k39sfxJYmzyS4EDMBw4sR8e7mzwQxCrAN8vtSOXojGeXhdTvyPleDXg7sH9K6T/AKeQTNl8YEQeSW9++Qi5Wjmp4ztnAxRFxFHlQkm+RB7u4tKcA+xFDq10OfDwibiN3Hfw0i+6eCDk3B5BzcxB5YI5DyV0F+3KetSPIhfxFEfEDcivWN8nHpZ0D/d7ve33NJandWXhJ0jAqf4x/Azi3h7vfD5xIHn3wIfIxOB8gHwM1VB4iDwn+HfIIdf8C3ppSev4YrJTS0RHxIHn478+QuwPeSR5prt/dHlNKnRGxQ/mc3yRvz9+Bt6eUrh7gdnSQh37/MfAa8g/xXVJKf6973l9FxCxy8bBHOfse4BLKY85SSrMjYivgaPLw/BPJLShbp5TuaHjO88hF40/Ixy9dAezVW5B9iWEYfIYc84/IrZmnkrflxN4elFJ6LvK51n4CnA08SG6x/Qh9+EMgpfTXiNiO/JqfWz73ReRRH+tPrtzX/X6Rr7kktbNIqS/d8yVJag8RcQj5x/tQFqSLes57gAtTSvsM13O2o4hYDrgLOCaldOgwPu8hDPNrLklDzRYvSZLUo4j4Krll7h7y6IFfIh8ffnKFYUnSiGThJUmSmukkd5NcBVhA7ob55pRSTyNeSpJ6YVdDSZIkSWoxh5OXJEmSpBaz8JIkSZKkFrPwkiRJkqQWs/CSJEmSpBaz8JIkSZKkFrPwkiRJkqQWs/CSJEmSpBaz8JIkSZKkFvt/znKboPcrzREAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1000x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (130651383468)>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotnine.options.figure_size = (10, 4.8)\n",
    "(\n",
    "    ggplot(data = df_empirical_full)+\n",
    "    geom_line(aes(x = 'number_person',\n",
    "                  y = 'probability',\n",
    "                  group = 1),\n",
    "              size = 1)+\n",
    "    ylim([0, 1])+\n",
    "    scale_x_continuous(breaks = range(0, len(df_empirical_full) + 10, 10))+\n",
    "    labs(title = 'Probability in birthday paradox (empirical simulation)')+\n",
    "    xlab('Number of people in a group')+\n",
    "    ylab('Probability')+\n",
    "    theme_minimal()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "binary-canal",
   "metadata": {},
   "source": [
    "### Scenario 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "democratic-gamma",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dictionary of probability\n",
    "obj = {}\n",
    "\n",
    "# Number of success\n",
    "number = 0\n",
    "\n",
    "# Number of person\n",
    "person = 23\n",
    "\n",
    "for idx in range(10000):\n",
    "    # Create a random number\n",
    "    random_number = [random.randint(a = 1, b = 365) for _ in range(person)]\n",
    "    \n",
    "    # Check two or more people share birthday\n",
    "    duplicated_number = [item for item, count in collections.Counter(random_number).items() if count > 1]\n",
    "    if len(duplicated_number) > 0:\n",
    "        number += 1\n",
    "    \n",
    "    # Append the probability\n",
    "    obj.update(\n",
    "        {\n",
    "            idx: (1 - (number / (idx + 1)))\n",
    "        }\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "literary-enforcement",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a data frame\n",
    "df_empirical = pd.DataFrame.from_dict(\n",
    "    data = obj,\n",
    "    orient = 'index'\n",
    "    ).reset_index().rename(\n",
    "    columns = {\n",
    "        'index': 'number_person',\n",
    "        0: 'probability'\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "secret-colorado",
   "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>number_person</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   number_person  probability\n",
       "0              0     1.000000\n",
       "1              1     1.000000\n",
       "2              2     0.666667\n",
       "3              3     0.500000\n",
       "4              4     0.600000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show data frame\n",
    "df_empirical.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "outdoor-reach",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (130651421657)>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotnine.options.figure_size = (10, 4.8)\n",
    "(\n",
    "    ggplot(data = df_empirical)+\n",
    "    geom_line(aes(x = 'number_person',\n",
    "                  y = 'probability',\n",
    "                  group = 1),\n",
    "              size = 1)+\n",
    "    ylim([0, 1])+\n",
    "    scale_x_continuous(breaks = range(0, len(df_empirical) + 1000, 1000))+\n",
    "    labs(title = 'Probability of two people share birthday in a group of 23 people')+\n",
    "    xlab('Number of repetition')+\n",
    "    ylab('Probability')+\n",
    "    theme_minimal()\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}