2018/day85_bayesian_ab_testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experimenting The Bayesian Way\n",
    "\n",
    "### A/B experiments : \n",
    "Two popular approaches to measuring the differences between theses variants statistically: \n",
    "* **the frequentist approach** : In this approach, you treat the traffic in each variant as a sample of all the traffic you will get in your website’s lifetime. Since we are dealing with samples, the means of the samples can be equal or different due to chance — hence, we must use statistical tests (such as Student t-test), confidence intervals, and p-values to figure out whether this is the case. The difference is statistically significant if we can prove that it is unlikely to be due to chance. If you are taking a frequentist approach, you will have to wait until you collect a certain amount of data before you can determine if a change is statistically significant.\n",
    "\n",
    "* **the Bayesian approach** : if we use a Bayesian approach, we must think more in terms of beliefs. The probabilities we see in our samples are interpreted as beliefs about how different the two variants are. Beliefs can be initialized using our prior knowledge of our website visitors and updated using data. Rather than discussing whether the difference between the two samples is significant or not, we quantify our beliefs about how different the two samples are.\n",
    "\n",
    "## Beta distribution \n",
    "\n",
    "The beta function takes two parameters, alpha (the number of successful penalty kicks) and beta (the number of missed penalty kicks).\n",
    "\n",
    "We are asking Player A to make eight kicks, and then another eight, and then another, all the way up to 10,000 sets of eight kicks. Similarly, for Player B, we are asking him to make 10,000 sets of 85 kicks. Then, we’ll compare the distributions of their penalty kick accuracies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEJCAYAAACZjSCSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3XecU1X6+PHPvckk03uDGYYZeh2KqCCogApKlWIBV8Uuq/JVd9eK4GJddZe1l/1Z1oK7uisiigiCoAIugtL7MJTpvbck9/7+GGYoDtOTm0ye9+vlS5Lce8+TM8l9cs859xxF13UdIYQQXks1OgAhhBDGkkQghBBeThKBEEJ4OUkEQgjh5SQRCCGEl5NEIIQQXk4SgTBUWloaffv2ZerUqUydOpXJkydz1VVXsXXr1ib3PX78OPfcc0+Ly+zduzeTJ09m6tSpTJkyhenTp/PRRx/Vv/7xxx/z1ltvNXqMTz/99LR9TnXq/mPHjmXnzp0tiu/U95Wdnc21117bov2FaCmz0QEI4evry7Jly+ofr1ixgocffphVq1Y1ul9GRgapqamtKvOf//wn4eHhABQUFHDnnXdSXV3NzTffzKxZs5rcf+vWrfTs2bPB15qzf2NOfV8xMTH861//atPxhGiKJALhdoqKioiKiqp/vHbtWl5//XVsNhu+vr48+OCDJCcnM3/+fLKzs7nlllt4++23eeONN1izZg1VVVVUVlby4IMPctlllzVZXnh4OA899BDz5s3jpptu4pVXXqGwsJAFCxawZMkS/vWvf+Hj44PVamXRokWkpqaydu1aNmzYgK+vLwUFBWzbto2cnBx69+5N165d6/cHWLJkCfv27aOmpoabbrqJmTNn8r///Y8nnniCL7/8EqD+8bJly057X3/+85+ZPHkyv/76KzabjWeffZZNmzZhMplITk7m4YcfJjAwkLFjxzJt2jQ2bdpEZmYmU6dO5d5773XOH0h0OJIIhOGqqqqYOnUqACUlJeTm5vLqq68CcOTIERYvXsz7779PWFgYBw8e5KabbmLVqlU8+eSTPPHEE7z99tukp6ezceNGPvjgA3x9ffnqq6946aWXmpUIAPr06UNubi6FhYX1zzkcDp5++mnWrl1LdHQ0n3/+OVu3buWaa65hzZo19OzZk+uuu46XX36Z9PR0vvzyS8xmMy+//PJpx7ZarSxdupTs7GymTZvGoEGDzhqHyWQ67X2lpaXVv/b666+Tk5PDsmXLMJlMPProozz33HMsWrQIgIqKCpYsWUJ2djaXXXYZM2bMoEuXLs37IwivJolAGO7MpqGNGzdy11138cUXX7BhwwZycnKYM2dO/euKonDs2LHTjhEXF8dzzz3H8uXLOXr0KNu3b6e8vLzZMSiKAtSetOuYTCYuv/xyrr32WkaPHs2oUaO4+OKLG9x/8ODBmM0Nf53q2vhjYmIYOXIkmzZtonfv3s2Orc7333/Pfffdh4+PDwDXX389d911V/3rl1xySX05ERERFBcXSyIQzSKdxcLtXHDBBSQkJLBz5040TWPEiBEsW7as/r9PPvnkN+3zu3fv5pprrqGsrIyRI0dy6623tqjMnTt3Eh8fT0BAwGnPv/DCC7zxxhskJCTw1ltvcf/99ze4v7+//1mPraonv2aapmE2m1EUhVOn+bLZbE3GqGlafcKqe3zqfqcmsTOPL0RjJBEIt5Oamkp6ejp9+/ZlxIgRbNiwgZSUFADWr1/PlClTqKqqwmQy1Z8If/75ZwYMGMBNN93Eeeedx5o1a3A4HM0qLzs7mxdeeIGbb775tOcLCgq4+OKLCQ0NZc6cOdx77731I4BMJhN2u71Zx1+6dClQ2wm8adMmRowYQXh4OBkZGeTn56PrOl999VX99qe+r1NdeOGFfPzxx9hsNjRN46OPPmLkyJHNikGIxkjTkDDcqX0EUPtLd9GiRSQlJQGwaNEi7r//fnRdx2w28/rrrxMQEECPHj2wWq3MnDmTN954g1WrVnHFFVegaRpjxoyhuLiYsrIyAgMDf1PmjTfeiKqqmEwmAGbMmMF111132jbh4eHMnTuXOXPm4OvrW99+D3DRRRfx7LPPNuv9VVdXM23aNGw2G/Pnz69/X9deey0zZswgKiqK0aNH1yeZU9/X4sWL648zd+5c/vKXv3DllVdit9tJTk7msccea241C3FWikxDLYQQ3k2ahoQQwstJIhBCCC8niUAIIbycJAIhhPBykgiEEMLLSSIQQggv57b3ERQWlqNpMrI1IiKQ/Pwyo8NwC1IXJ0ldnCR1UUtVFcLCApresAFumwg0TZdEcILUw0lSFydJXZwkddE20jQkhBBeThKBEEJ4ObdtGhJCdEy6rlNYmEtNTRXQ9iadnBwVTdPaHphHULBYfAkLizptJtq2kkQghHCpsrJiFEUhJiYeRWl7o4TZrGK3e0ci0HWNoqI8ysqKCQoKbbfjStOQEMKlKivLCAoKbZck4G0URSUoKIzKyvYdJSV/CSGES2maA5NJGiNay2Qyo2nNW2ujueSvIYQbs2fup3rTErSCNEzxA/AddQNqYITRYbVZe7Zvextn1J1cEQjhpuzHtlH55XPoNZX49BmNI3M/FV88jVaaa3RoHUZmZgajRw9nzpzZ3HTTbH73u6u5997fk5OTDcDMmZPJzMxwaUy33HI9Dzxwn0vLlEQghBtyFGVQueYN1Ih4AqY/ju+o6/Gf/BC6rYrKlYvRqiuMDrHDiIyM4r33lvDuu0v48MNP6N69J6+++qIhsRw6dBCLxYdDhw6QnZ3lsnIlEQjhZnRdo2r9O6Ca8Bv3fygWfwBMkYn4XXoXWlEWOcteRPeaIZOuNXToMFJTU057rry8jPnzH+SOO25ixoxJPPPMInRd54knHuOLL5bWb3f33beze/cu0tKOc++9v+fmm69j7txbOHBgHwBPPfU4DzxwH9ddN5Mff/z+N2WvWPEFw4adz4UXXszy5Z87942eQvoIhHAz9oOb0LIP4Tv6VtTA8NNeM8f1w3rBbCo2fIgl4DOs5800KMr2sWFnJj/uyGzTMRQFGlpwd1RyJ0YO7NSiY9ntdtatW0P//smnPb9x44/07NmLJ5/8Czabjd/97ir279/HxIlTefvtN5kyZRpZWZkUFRXRv/8A5s69mfvue4BevfqQmnqYRx75Ix9//BkAISEhPPfc4gbLXrVqJS+//CYlJSUsXPgwc+bcitns/NO000r49NNP+fDDD+sfp6WlMXXqVBYsWOCsIoXweLqmUf3rctSIBMw9Rza4jU+/S7BUZFP665eo0d3wSRzq4ig7lry8XObMmQ2AzVZD3779mTv37tO2ueyyy9mzZxeffLKEI0dSKS4uprKygiFDziEvL5fMzAy++WYFl18+gYqKCvbu3cPTTy+q37+yspLi4iIA+vUb0GAcGzb8QEREJElJ3dB1HVVV2bDhBy6+eIyT3vlJTksEV111FVdddRUABw8e5K677uLuu+9uYi8hvJv96C/oxVlYL73rrKNDFEUhcvwtlB/bR/UP72GO64fi4+viSNvHyIEt/9V+prbeUFbXR9CY//znX6xbt5YpU6Yxc+Z5pKamoOs6iqJwxRWT+Pbbb1izZhWLF7+KpmlYLNbTjpmTk01wcAgAVqu1wTJWrPiC7OwsZs6cDNQ2Ry1b9plLEoFL+ggef/xx7rvvPsLDw5veWAgvZj+wAcU/FHPiOY1up5h88B11I3plCTW717goOu/188//Y8qU6YwbdwU1NTUcPHigflqLK66YxOef/5eYmFgiI6MIDAwkPr4L33yz4sS+P3HXXbc3evyCgnx+/nkzH3zwb/7zn+X85z/Leeedj9i6dTPp6WlOf39OTwQbN26kqqqKK664wtlFCeHRtKpS7Md2YO4xHEVt+qtpiumBKa4/tt3fSsexk1199WzeffctbrjhGl588a8MGJBcP6w0JiaWmJhYrrhicv32Cxc+yfLln3PjjdfyxhuvsmjR042O/1+5cgUjRlxAVFR0/XNxcfGMGnXRaZ3RzqLoekPdLO1n3rx5jBs3jkmTJjmzGCE8Xsm2b8n76nXibnkea2y3Zu1TtmcDOUv/RqfrHscvcaCTI2wfu3fvoXPnrkaH0S50XScvL4+5c29lyZJPsVgsLik3I+Mo/fv3a7fjObU7uqamhp9//plnn322xfvm55fJYhNAVFQQubmlRofhFjp6XVTu3YriH0qxGonSxPusqws9rDeYreT9+j2+AYmuCbSNNE1r10nijJx07rvvvuWvf32WP/zhIVTV7LI4NE37zXdBVRUiIgJbdTynJoL9+/eTmJiIv7+/M4sRwuPpmoY9fTfmroNbNIWAYrZi6twHe/puJ0YnzmbMmEsZM+ZSo8NoM6f2ERw/fpzY2FhnFiFEh6DlHYHqcszxDQ8tbIw5rh96cTZaaV77Bya8glOvCCZMmMCECROcWYQQHYIjcz8Aps59W7xv3T6OzP2oQZHtGpfwDjLFhBBuwJGTghIUierf8sVG1LA4MFlw5B1p/8CEV5BEIIQbcOQcxhTVvJFCZ1JUE2pkAlrukfYNSngNSQRCGEyrKEIvL8AU3b3VxzBFJeHIPyr3E4hWkUnnhDCYI6d2pktTTBsSQWQiNvtqtKJMTOFx7RVah5eZmcGsWdNJTOyGooDNZicyMpJHHllIdHQMM2dO5uWX36RTp85Oj2XmzMn4+vpiNvtgt9tJSOjKQw89RnBwsNPLlisCIQym5R8HFNSILq0+hhqZeOJYR9snKC/iTusRPP/8i7z3Xm0cMTGxfPjhuy4pV64IhDCYVpCGEhKNYm54MrLmUENiQFHRCl27mlZb2Q5swLb/t/Pyt4SiKDQ0QYJP74vw6dXwDK6NGTp0GG+++cppz5WXl/HMM0+Qm5tDXl4uw4adx0MPPcaTTy5g0KChTJkyDahdj2Du3HmEhITwwgvPUFJSjNXqy333/Ylevfrw1FOPU1xcTHr6cebOnceoURc1GIOmaVRUlJOY2Lp+o5aSRCCEwbTCdExhbWvOUUxm1JAYtKK2ze3v7YxcjwDgT3/6P8xmHwoLCzCZTNx0U+OT1bUXSQRCGEi316AVZ2NOGtbmY6mhndEK09shKtfx6TWyVb/aT9XWKSbcZT0CqG0aquuP+PjjD/nDH+7mww8/dcqC9aeSRCCEgbTiLNA11PD4Nh9LDe2E/eiv6A47ikm+2s3lLusRnGny5Ct59dW/U1xcTGhoy+8vaQnpLBbCQFpB7Vzzalg7JIKwzqBraCXZbT6WOJ2z1yNoyNatm4mOjnF6EgC5IhDCUFphOqim2s7eNlLDOp84Zkab+xzE6a6+ejYvvPAMH374LgEBgc1aj+D5559myZL3MZt9mlyPoE5dH4GqKphMJv7856ed9p5O5fT1CFpLpqGu1dGnXm6JjlgXFSv/jl6aR8BVT7Zov4bqQrdVU/buHViGTcc6dEp7htmusrKOEhvbfusRGDkNta7r5Ofncffdt/P++/922XoEDdVhW6ahlqYhIQykFaajttMNYIqPFSUwQkYOudC6dWuYM2cWd9xxl8uSgDNI05AQBtFtVeiluai9L2y3Y6ohMdJH4EKyHoEQok3qbv5qjxFDddTgGLRi908Ebtoi7RGcUXeSCIQwSN2Iofbs2FVDoqG6HL2qrN2O2d5U1YTDYTc6DI/lcNhRVVO7HlMSgRAGcRSmg8mCEhTVbsdUg2tXBNRKctrtmO3Nzy+Q0tIidF1mSm0pXdcoLS3Ez691ncJnI30EQhhEK0hDDeuMorbf7zElJLr22CXZmKJdM09NSwUGhlBYmEt2dhrQ9mYOVVXrx/R3fAoWiy+BgSHtelSnJoK1a9fyyiuvUFlZyciRI5k/f74zixPCo2iF6Zji+7frMdWgKEBx634CRVEID49ut+N1xGHFrua0pqHjx4+zcOFCXnvtNb744gv27NnD+vXrnVWcEB5FrypDryjC1A53FJ9KMVtQAsPdOhEI9+O0K4LVq1czYcIEYmNr2ywXL17c7Dk2hOjoHCcmh2uvewhOJUNIRUs57Yrg6NGjOBwO7rzzTqZOncqSJUsICWnfdi0hPFXdLKHtMcfQmTxlCKlwH067InA4HGzZsoUPPvgAf39/5s6dy9KlS5k+fXqz9m/trdIdUVRUkNEhuI2OUhd5lTnYrP5EJya0eorhs9VFUecECvZ+R3ggmPw6Rn01paN8LozitEQQGRnJiBEjCA8PB+DSSy9lx44dzU4EMtdQLekIO6kj1UVF+mEI7UxeXuvG+zdWF3ZT7WyVuYcPu+3IofbUkT4XbeGWcw2NGTOGH3/8kZKSEhwOBz/88AP9+7fvCAkhPJGu6zgK0jCFt36N4sbUDyEtznLK8UXH47QrgkGDBnHrrbcye/ZsbDYbI0eOZMaMGc4qTgiPoZcXQE1Fmxarb0z9EFI3vqlMuBen3kcwc+ZMZs6c6cwihPA49YvRtOMcQ6eSIaSipWSKCSFczFFwHGjfOYbOJENIRUtIIhDCxbSCNJTACBRrgNPKkCGkoiUkEQjhYlpBmtOahep4wiykwn1IIhDChXSHHa0wE5OzE4EHzEIq3IckAiFcSCvOBN2B6qSho3VkCKloCUkEQriQll/bUez0piEZQipaQBKBEC6kFaSBakINjXVqOTKEVLSEJAIhXMhRkIYa2hlFdf6aUGpIrCQC0SySCIRwIVeMGKqjhsSgFWfJQvGiSZIIhHARvbocvbzA6R3FddSQGKipQK+WIaSicZIIhHARx4mpJZw9dLSOGhIDgF4kI4dE4yQRCOEi2ompJZw12dyZ1JC6ewmkn0A0ThKBEC6iFaSBNQDFP9Ql5SlBkaCoaHJFIJogiUAIF6ldgyC+1SuStZSimlGCo+SKQDRJEoEQLqDrmktHDNWpnXxOrghE4yQRCOECemk+2KpcNmKoTt29BDKEVDRGEoEQLqC5eMRQHTUkBuw16BVFLi1XeBZJBEK4QN1iNKoTF6NpSP3IIWkeEo1w6n3u119/PQUFBZjNtcUsWrSIQYMGObNIIdySVpCGEhSFYvFzabl19xJoxdnQua9Lyxaew2mJQNd1jhw5wnfffVefCITwVtqJEUOupgSGg8ksVwSiUU5rGjp8+DAAN998M1OmTOHDDz90VlFCuDXdYUMrznL5iCEARVFRg2PQZfI50Qin/VQvKSlhxIgRPPbYY9hsNm644QaSkpIYOXKks4oUwi1pRZmga4YkAjgxcqgo05CyhWdwWiIYMmQIQ4YMqX88c+ZM1q9f3+xEEBER6KzQPE5UVJDRIbgNT6yL0qw8KoDI7r2wtGP8za2L/E5dKD6+ncgIfxTV1G7luxNP/Fy4E6clgi1btmCz2RgxYgRQ22fQkr6C/PwyNE3GPkdFBZGbW2p0GG7BU+ui+ughUE0UaUEo7RR/S+qixicMHHZyUo+iBke1S/nuxFM/F+1NVZVW/4B2Wh9BaWkpzz33HNXV1ZSVlbF06VIuu+wyZxUnhNty5WI0DZEhpKIpTvtkjhkzhu3bt3PllVeiaRqzZ88+ralICG+hFaRh6tTLsPJPG0LaZaBhcQj35dSfKPfeey/33nuvM4sQwq3pNRUnFqMxpqMYQPELAR9fuSIQZyV3FgvhRI6CdABMYQYmAkWpXbZSZiEVZyGJQAgnql+MxsArAjgxC6msSyDOQhKBEE6kFaSDjy9KYIShcaihsehleegOu6FxCPckiUAIJ9IKa9cgcNViNGejBseArqOV5hgah3BPkgiEcBJd12tXJTOwf6COGlo7hFSmmhANkUQghJPoFUVQXW54/wCcuCJA7iUQDZNEIISTaIW1I4bUcNeuQdAQxTcQxRpYey+BEGeQRCCEk9RN9KaGdjY4klpKSIwkAtEgSQRCOIlWlAkWfxS/YKNDAU6uXyzEmSQRCOEkWlEmamis4SOG6qghMejlBej2aqNDEW5GEoEQTlKbCDoZHUa9k5PPyRBScTpJBEI4gV5TiV5R5GaJQEYOiYZJIhDCCU52FLtjIpB+AnE6SQRCOIE7JgLFxxfFP1SuCMRvNCsR3HPPPWzcuNHZsQjRYWhFmaCYUIOjjQ7lNGpoJ7SiDKPDEG6mWYngsssu47XXXmP8+PG8/fbbFBUVOTsuITyaVpSJGhxl2KpkZ6OGxaEVZqDrmtGhCDfSrEQwZcoUPvzwQ1577TXy8/OZOXMmf/rTn9ixY4ez4xPCI2nF7jViqI4aHg+2KvSyfKNDEW6k2X0EmqZx9OhRjhw5gsPhICIigscff5yXXnrJmfEJ4XF0zYFWnO2WicAUVjvdRd30F0JAM5eqXLx4MZ999hldunRh9uzZvPjii/j4+FBRUcGYMWOYN2/eWff9y1/+QmFhIc8++2y7BS2EO9NL80BzuGUiqJv3yFGQjjlhsMHRCHfRrERQUFDAP/7xD/r06XPa8/7+/vz1r389636bNm1i6dKljB49uk1BCuFJ3HHEUB3F4o8SEI5WkGZ0KMKNNKtpyOFw/CYJ1F0FjBo1qsF9ioqKWLx4MXfeeWcbQxTCs9QnghN38robNTxOmobEaRq9Ili4cCHZ2dls3bqVgoKC+uftdjvHjx9v9MALFizgvvvuIzMzs30iFcJDaEWZKH7BKL6BRofSIDUsDlvGXnTNgaKajA5HuIFGE8HMmTM5ePAg+/fvZ/z48fXPm0wmBg8+e/vip59+SqdOnRgxYgSfffZZqwKLiHDPL5ERoqKCjA7BbXhCXaSX52CNind6rK09fmnXHuTuWEmouRxLhPFrJbQHT/hcuLNGE8HAgQMZOHAgI0eOJCYmptkHXbFiBbm5uUydOpXi4mIqKip4+umneeSRR5p9jPz8MjRNb/b2HVVUVBC5uaVGh+EWPKUuanLTMCcNc2qsbakLhzkSgLyUA/ho7jFFdlt4yufC2VRVafUP6EYTwf/93//x4osvcuuttzb4+vLlyxt8/t13363/92effcbmzZtblASE8FRaVSl6dVn9GsHuSA3rBCho+cchaZjR4Qg30GgiuO222wB47LHHXBKMEJ5OK6qdx8edE4FittauViYjh8QJjY4aGjBgAADnnXcenTp14rzzzqOiooKff/6Zvn37NquA6dOnyz0Ewmvo9SOG3G/o6KlMEV1w5B8zOgzhJpo1fHTBggX84x//ICUlhfnz55OWliZNPUI0QCvOAtWEEhRpdCiNUsO7oJfmotdUGh2KcAPNSgS7du3i8ccfZ/Xq1UybNo1nnnmG9HQZhyzEmWonm4tx+2GZpogEABzSPCRoZiLQdR1VVdmwYQPDhw8HoKqqyqmBCeGJtOIst+4fqKNGdAFAK2j8fiDhHZqVCBISErjttttIS0vjvPPO4w9/+AO9e/d2dmxCeBRdc6CV5LjtHcWnUgLCweKPJv0EgmbONfTMM8+wevVqzjnnHHx8fBg2bBhXXnmls2MTwqO482RzZ1IU5USHsVwRiGZeEfj7+zNs2DBKSkrYvXs3ycnJHD582NmxCeFRtGL3nmPoTGpEAlpBmixSI5p3RfDiiy/yzjvvEBERUf+coiisWbPGaYEJ4WlO3kPg/lcEAKbwLtjs1egluSghzZ85QHQ8zUoEy5YtY9WqVS2aZkIIb6MVZaFYA912srkz1XUYO/KPoUoi8GrNahrq1KmTJAEhmqAVZ6J4wIihOmpYHCiKjBwSzbsiGDFiBM899xyXXHIJvr6+9c/379/faYEJ4Wm0oixMXZKNDqPZFLMFNaRT7ZxDwqs1KxHUTSW9cuXK+uekj0CIk/SaSvTKYo+4h+BUakQXHDkpRochDNasRLB27VpnxyGERzu5PKXnJQJ7yv/QaypQLP5GhyMM0qw+gvLychYtWsSNN95IUVERCxYsoLy83NmxCeExtOITI4bcfLK5M5nC6zqMpXnImzUrETz55JMEBQWRn5+P1WqlrKyMBQsWODs2ITyGVpQJiooaHG10KC2inphzSPoJvFuzEsHevXu57777MJvN+Pn58cILL7B3715nxyaEx9CKs1CColBMzWptdRuKfyiKNRCtQKaa8GbNSgSqevpmDofjN88J4c20Is+YbO5MiqLUdhjnyyyk3qxZZ/Nzzz2X559/nqqqKn744Qfuvvtuzj//fGfHJoRH0DVH7fTToZ2NDqVV6qea0GSqCW/VrETwxz/+EX9/f4KCgvj73/9Onz59eOCBB5wdmxAeQS/JAc2OKTzO6FBaxRQeD44a9JJso0MRBmmyQXP16tW8/fbb7N+/H19fX3r37s3QoUOxWq2uiE8It+corF2kyZOvCKB25JCnzJMk2lejieDrr79m8eLFzJs3jz59+qAoCjt37uSpp56iurqacePGNXrwF198kW+++QZFUZg5cyY33XRTuwYvhDvQCjMAUMM8NBGEdQbFVDvVRPfzjA5HGKDRRPD+++/z3nvv0bnzyQ949+7dGTRoEI888kijiWDz5s389NNPfPHFF9jtdiZMmMDFF19Mt27d2i96IdyAVpiOEhSJ4uPb9MZuSDH5oIZ2ksXsvVijfQTl5eWnJYE6SUlJVFdXN3rg8847j/fffx+z2Ux+fj4OhwN/f7lzUXQ8WmF67QRuHkwN61w/jbbwPo1eEZhMZ1+AW9f1Jg/u4+PDSy+9xDvvvMPll1/eohlMIyI8YypfV4iKCjI6BLfhbnWhaw5Ki7MI6T2MCBfH1p51UdApgaLULUSG+6KYfNrtuK7ibp8LT+P0u1/mzZvHbbfdxp133sknn3zCNddc06z98vPL0LSmk01HFxUVRG5uqdFhuAV3rAtHUQY47FRbo1waW3vXhc0nDHSNnMOpHtdh7I6fCyOoqtLqH9CNJoL9+/czdOjQ3zyv6zo1NTWNHjglJYWamhr69u2Ln58f48aNY//+/a0KUgh3pRWcGDHk6U1DJ26G04qzPC4RiLZrNBGsXr261QdOS0vjpZde4uOPPwZgzZo1zJgxo9XHE8Id1Y4YUlDDPPvkWbfOct3kecK7NJoI4uJa/yvn4osvZseOHVx55ZWYTCbGjRvHxIkTW308IdyRVnAcJTgKxezZ99Uo1gAU3yC0IrmpzBs5tY/gnnvu4Z577nFmEUIYypF/DNOJG7JFRtvvAAAgAElEQVQ8nRoSK1cEXkpmjhOilfSaCvSSnPo7cz2dIonAa0kiEKKV6hZzMUV2NTiS9qGGxqBXFKHbqowORbiYJAIhWkk7cSduR7kiONlhLP0E3kYSgRCt5Mg7iuIXjOIfanQo7UJGDnkvSQRCtJKWfww1IgFFUYwOpV3ULrOpyFQTXkgSgRCtoDvsaIXpHWbEEIBitqAEhssVgReSRCBEK2iF6aA5UDtIR3Gd2iGk0kfgbSQRCNEKjrwjAB3qigBADYlBK85q1qSSouOQRCBEK2g5h8HijxLS/Bl1PYEaEgs1FejVZUaHIlxIEoEQreDIScEU3Q1F6VhfIfVEYtOlw9irdKxPsRAuoNdUohWkY4rubnQo7cahaei6LkNIvZTT1yMQoqOp7R/QMcW4dyLQdZ3KageFZdUUlVZTWFpNQWkVBSVV5JdUU1BSRVFZDTU2Bw5NR1HA36LwhL/Cpp92cOxoNN06B9MjPpSoEN8OM0xW/JYkAiFayJGdAoApytj1t6trHOQWV5JbVElBSe2JvrC0mqKyk/+utjl+s19IgIXwYF/iIgPonxiO1WLCx6xid+hU1dgpPxpKQE0BG3ZlsfaX2vUWQgMtDOwWweAekfQ7sY/oOCQRCNFCWk4KSkgsiq9rl1PNL65i26E8DqYVcTS7jOyCitNeN6kKoYEWQoOsxEcFMLBbBGFBVkKDLIQFWgkLshIW5IuPufEW4YqVCYSWFfDqLReRnlfOobQi9h4rYsv+HH7YkYmPWaVv1zAG94hkUI9IwoI8ewpuIYlAiBbRdb22ozh+oEvKq65xsGl3Ft9vz+BIVu1yjBHBVvokRTBqYCxRoX5EhPgSGexLUIAFtR2ab9SQWGzpe1EUnS7RgXSJDmTM0HjsDo0Dx4vYdiiP7Yfy2JGSD9/sp2tMEIN6RDCkZxQJMYHShOSBJBEI0QJ6aR56ZYnT+wcqqmx8/b9jfPdLOhXVdhKiA7lqdHeG9ooiJtzfqev0qiGx4KhBLy9ECYyof95sUumXGE6/xHBmXdKTjPwKth3MZfuhfJZvOMIXG44QFmQluXsEyd0i6JsYhq9FTjGeQP5KQrSAI+dE/4CTRgzZ7A7W/pLOlxuPUF5lZ1jvKC47tws94kJc9ku7bgipVpyNekoiOJWiKMRFBhAXGcDEEYmUlNewIyWf7Yfy+GlPNuu3ZWBSFXp1CWVgtwiSu0fQKcJfrhbclCQCIVrAkZMCJgtqeHy7H3vPkQLe/2Y/OYWV9E8KZ+bF3ekaG9Tu5TTltCGkcf2atU9wgIVRyZ0YldwJu0PjYFoxO1Py2Xk4n0++O8Qn3x0iItiX5O4RDDxxtWD1kQ5nd+HURPDKK6/w9ddfA7VrGD/wwAPOLE4Ip3NkH8IUnYSitt9JrLSihn+vPcTGXVlEh/lx/zWDGJDU8C9xV1ACQsFsafWcQ2ZTbWdy365hXD22B/nFVew8XJsUNu7K4rtf0/G1mDi/XwwXD+5MYmxwO78D0VJOSwQbN27kxx9/ZOnSpSiKwq233srq1au57LLLnFWkEE6l26vR8o5hGXRFux1zy74c3v9mP5XVdiZd0JVJIxKxGPxLWVFU1OCYdrupLCLEl9FD4hg9JA6bXeNAWhGbdmWxaVcW67dl0LdrGJMuSKRPQqg0HRnEaYkgKiqKhx56CIvFAkD37t3JyMhwVnFCOJ0j5zDoDkyxPdp8rIoqOx+tPsCm3VkkxgZx88S+xEe5djhqY9SQGBwFae1+XB+zSv/EcPonhjP70p58vz2TbzYf4/mPf6Vv1zBmXdKT+Gj3qQdvoegumGbwyJEjzJo1i48//pjExERnFyeEUxT++B8K139M1/vfw+TX+rb7HYdyWfzxrxSUVHHNpb24+tJemE3uNdtLwXcfUfTTMpIeWIJicm5XYo3NwcpNR/h41X4qqmxcPiKRGyf2w9/Xx6nlipOc3ll88OBB7rjjDh544IEWJYH8/DI0TabCdeYwQU9jdF1UHN6NGtqZgjKgrOVx2OwO/rv+MKt+Pk5MuD+P/O4cunUOprCgvMXHcnZd2CzhoDnISU2t7zx2phF9oxmYGMayH1L5euMRftqVyZzL+zCgW9N9JUZ/LtyFqipERLTuasqpiWDr1q3MmzePRx55hIkTJzqzKCGcStc1HNmH8Ok2rFX7H80q5R9f7iEjr5yxQ+O4akwPtx41Uz9yqCjLJYkAINDPh+vG9WJ4/xjeWbGXv32ynYsGdWLWJb1kSgsnc1oiyMzM5K677mLx4sWMGDHCWcUI4RJaYSbUVGCK6dmy/XSdVZuP89/1KQT6+3D/1YOa9SvXaGpYZwAchWmYuw52adnd40J4/KZz+fzHVFb+dIz9x4u5c0p/Q4bSegunJYK3336b6upqnn322frnrr32WmbNmuWsIoVwGkf2QQBMsc1PBIWl1fy/L/ew92ghQ3tFMeeKPgT6eUa7t2LxRwmMQMtv/w7j5vAxm7hqdA8GJkXwjy/38OT7W7hqdHcuPbdLu0yjIU7ntEQwf/585s+f76zDC+FSjuyDKL5BKMHNW5HslwO5vLtiLzaHxpwr+nBhciePGxqphsejOWHkUEv06RrGn28+j3dX7OVfaw+x+0ght0zsS3CAxdC4Ohr3GqoghJtyZB3CFNOjyZN5dY2Df67cxyuf7SQy1I+Fc87lokGdPS4JAJjCu6AVZaI77IbGEejnw93TB/K7cb3Yd6yQBe9sZtfhfENj6mhkigkhmqBVFKOXZGPqe3Gj2x3NKuXNL3aTXVDBFecnMO2ibm43LLQl1PB40B1oRZmYIroYGouiKIwdGk+vLqG8uWw3f/tkO5eeE8/M0e69OJCnkEQgRBMc2YcAztpRbLNrLN+Yytc/HSM4wMIfrx1M38RwV4boFOqJk79WcNzwRFAnPiqQx24cxn/Wp/DtljT2HC3kwRvOJcjiuQnXHUgiEKIJjuyDoJpRI7v+5rWUjGLeXbGPjLxyRg6I5ZpLenpMh3BT1JBYMJlx5B/Dp+cFRodTz+JjYvalvUjuHsHbX+3lDy+uZ9pF3Rh/bgKq6nlNcO5AEoEQTXBkH0KNSkQxn+ygLKmoYdkPqazblk5ooJV7rxpEcnf3HxbaEopqQo1IQMtNNTqUBg1IiuCJW87n47WH+PS7FHam5HPLxH5EhPgaHZrHkUQgRCN0ew1a7hF8BtROlmizO1izNZ3lG1OprtEYOzSe6Rd1w8/aMb9Kpuju2PatR9cc7TrjansJ9PPh4RvPZenaAyz59iAL3tnM9eN6Mby/a26C6yg65qdXiHbiyDsCmh1HRDe+/t9RVm0+TnF5DcndI7hmbA86RQQYHaJTmaK7Y9u1Gq0gDVMDTWPuQFEULkzuTO+EMP7f8j28tXwP21Py+d24XgTIfEXNIolAiEYUHd6DFXjiqwJyqkrpnxjGHVP606drmNGhuUTdkpyOnBS3TQR1okP9ePC6IazYdJQvNhzhYFoRt0zsR18v+Vu1hSQCIc5QbXOwZV8O67dnMLpoCzGmYBIS47jj/ASSOnnXIipKYCSKXzCO7BToN9bocJpkUlUmj0xiQLcI3lq+hxc+/pXx59UO5fUxy8iis5FEIMQJx7JLWb89g592Z1NZbSc23Je+vnmYkobx+0sGGB2eIRRFwRTdvX6KDU+R1CmYx+ecy7+/O8TKzcfYlVrA7VP6udWaD+5EEoHwatU1DjbvzWbdtgxSM0swm1TO7RPFRYM6092viMqlVfgmNG/d3o7K1Lkv9qO/opXmogZFGR1Os1ktJm4Y35vk7hG8t2IvT/xzC9eP682o5E5Gh+Z2JBEIr5SWU8a6bels2p1FZbWDThH+zLqkJyMGxNbfB1Cz4yeg9kTozUzx/QGwp+3G0ne0scG0wuAekfz5lvN5c9ku3lmxl0PpRcy+tJfhS4K6E0kEwmvU2Bz8vC+HddvSSUmv/fU/rE8UowfH0TM+5DfzAdkz9qGExKAGeHdnoxraGcU/FEf6bvDARAAQEmDhD9cO5vMfUvlq01GOZJXy+ysHEB3mb3RobkESgejwMvPLWfdrBht3ZVJeZScm3J9rxvZg5MBOZ70LWNc0HJkH8Ol+voujdT+KomCK74/96DZ0TUNRPbPT1aSqzLi4Oz3iQvh/X+7hz+9t4bZJ/RjcM9Lo0AwniUB0SDa7xi8Hclm/LZ19x4owqQrn9K799d87IbTJ2UC1vCNgq8TUuY9rAnZz5viB2A9sQMtJadGaDO5oUI9IFs45l1c/38VL/93BlRcmMemCRK9e50ASgehQcooqWb8tnR93ZFJaYSMyxJcZF3djVHJnQlowh739+A5AwRTn3R3FdcwJyaCasB3Z6vGJACAy1I+HrxvKP1fu5/MfUjmWXcYtE/t22DvEm+Kd71p0KA5NY/uhfNb9ms6u1AIUpbaDcMyQOPolhbfql5792HbU6G6oft5138DZKBb/2tFDR35BP/8aj1xf4UwWHxO3TupL19ggPll7iKc+2Mo9MwYS44X9BpIIhMcqLqvm++0ZrNuWQWFpNWFBVqaOSuLC5E6EB7d+4jGtohgtNxXLsOntGK3nMycNo/qH92qnm3CTaanbSlEUxp3bhfioAF7/fBdPvLeFO6f294h1pduT03t9ysrKmDRpEmlpxi55JzqO1MwS3li2iz++tpGlP6TSOcKfu6YN5Lm5I5g6KqlNSQDAcXwHAOaEQe0Rbodh7joEULAf2Wp0KO2uX2I4C+acS3iwL4s/3c7XPx1F13Wjw3IZp14RbN++nfnz53PkyBFnFiO8gK7r7EzJ46Ov97I7tQA/q5lLzoln9JA4YsPb91LedvhnlMAI1IiEdj2up1P9QzDF9sSeuhXrOVcaHU67iwr149Hrz+GdFXv5dF0KR7NLuWlCX6xecL+BUxPBJ598wsKFC3nggQecWYzo4FIyivn0uxQOHC8i2N+HmaO7M2ZInFM69vSqMhxpu7Ekj+8Q7eDtzZw0jOpNS3AUZmAK62x0OO3OajFx59T+JMQE8tn6w2TlV3D39IFEhvoZHZpTKboLrn/Gjh3L+++/T3x8vLOLEh1IVn45//xqDz9uzyA00MrVl/Zi3PCuTv2FVvLLKvK+fpO4W57HGtvNaeV4KntpIcdevp3QkdMJv3iW0eE41Za92bzw4RZUVeXBG4YxqKfnTK/RUm7bWZyfX4ameU8b3dlERQWRm1tqdBguVWNz8OWmI3z90zFMqsLkCxK5/PwEEuLDnF4XFdvWo4bEUqxGorhxvRv3uTBj6tyH4h0/YO870S2umpxVF10j/Zl/wzBe+u8OFry5iVmX9mTs0Di3eM8NUVWFiIjWTarntolAeKfdqQV88M1+cooqGdE/hpmjexAWZHVJ2VppLo7M/VjOmeq2X3Z3YO5+PtXfv4uWdwRTVJLR4ThVTHhtMvjH8j18tPoAabllXHdZL8wmz7y7+mw61rsRHqukvIa3lu/mr//eBgr88drB3Da5v8uSAIBt73pQwKf3hS4r0xP5JA2rvbns0E9Gh+ISflYzd08fyIThXVm/LYMX/rWNkooao8NqV3JFIAyl6To/7sjk0+8OUVXjYMrIRCaO6IqP2bUjNXTNjm3/D5i6JKMGetcY8pZSrAGYuyRjP7wZffg1KErH/z2pqgozR3cnLiqAd1fs48l/buGeGcl0ie4Y6xu4JBGsXbvWFcUID5OeW8b73+znYFoxvbqEcuPlvQ1bA9h+5Ff0ymIsfccYUr6nMXc/H/vRX3FkHsDsRfMxjegfS2y4Py/9dwdPf7CV2yb3Y2gvz+9E7vipXLidGpuD/65P4fF3fyYjr5ybJvThwdlDDF0I3rZ3HUpAOKYuyYbF4EnMXYeA2YLdS5qHTpXUKZgFN55L50h/XvlsJ8s3pHr8zWfSNCRcatfhfD5YtZ/coipGDojlqrE9CPZv/mRwzuAoysCRvhvLOdM8doplV1N8rJi7DsWW+jPWkb9DMXnXqSQsyMqDs4fy3tf7WPpDKul55R5985l3/fWEYXKKKvnPd4fYsj+XmHB//jRrCH27useCL7YdK8Hkg08/aRZqCZ+ew7Gn/IT92HZ8ks4xOhyXs/iYuG1yP+KjA/nvuhSyCyu5Z/rANk9xYgRJBMKpKqpsLN94hDVb01BVhStHJXHF8ASXdwafjVZRhO3ARnx6XygzjbaQKX4gin8otn3rvTIRQO2kdROGd6VzRABvLt/Non9u4Z7pA+keF2J0aC0i18HCKSqq7Hy58QgPvrGJVZuPM7xfLM/cPoIpo5LcJgkA2HavAc2BJXm80aF4HEU14dPnIhzHd6KV5RsdjqEG94xk/vXnYPVR+cuSX9iwM9PokFpErghEuyqtqOHbLWl8uzWNymo7yd0jmHZhN7rGBhkd2m/oVWXU7PoWc+JQ1JBYo8PxSD69L6Lml+XY9n2Pddg0o8MxVFxUII/deC6vLd3J21/t5WhWKVeP7eERN59JIhBtpus6hzNK+O7XdDbvzcHu0DindxSTRiS6ZQKoU73tS7BXyboDbaAGRWJKSMa2Zy2WwRNQzK67AdAdBfr5cP81g/n0uxRWbznOsexS5l45gJBA964XSQSi1YrKqtm8N4eNOzM5llOG1WLiwkGdGDs0nrhI44aCNodWlo9t97eYe47EFB5ndDgezTJ4IpVfPI1t3/dYBlxmdDiGM5tUZl3ak6TOQby3Yh+Pv/czd105kB7x7ttvIIlAtEhFlZ2tB3L4355s9h4tRNeha0wQ14/vzfB+MR6x5quu61Rv+BBQO+S8+q5mju2FKbYXNdu/xqfPRV5/VVBneL9Y4iIDefWznfxlyS/MurQnY4a456R17v+tFYarrLazPSWPrfty2Z6Sj92hER3qx6QRiQzvH2PojWCtYU/dgv3or1jPvxo1KNLocDoEy7kzqFz+DDXbvsIqTW31ukQHsmDOMN5avocPVx3gwPEibhjfG39fH6NDO40kAtGgkvIath3KY+v+XPYeLcDu0AkJsDB6cGeG948lqVOQW/6yaYpWkkPV9++iRiXhM1BGCrUXc6femHuMoGb7Csw9hmMK7XiL1rSWv68P82Ym8/VPR1n6fSop6SXcNrkfvbqEGh1aPUkEAqhtLsnIK2dXagHbDuZxIK0IXYfIEF8uOSeec3pF0y0uGNUDT/519OpyKle/DIDfJb9HUd1nGGtHYB1+DY60XVR9+xr+Vy5AMRt7x7g7URWFiSMS6dM1jLe+2M1flvzC5AsSmTwyEZMb3M3ukhXKWkMWpqnlzAVIyipt7D1ayM7D+exOLaCwtBqAuKgAzukVxdBeUXSJDnSbX/5tqQu9upzKlX/HkXsYv/H3Yu4ysJ2jcy13XbDIfnwnlV//FXO3c/EdO9clU3a4a12cTWW1nSWrD7BhVxaJsUHMuaIPCTFtH10nC9OIJum6Tn5JFQfTijmUVszBtCLSc8vRqZ1vvV9iGAO7RdA/MZyIEM+7Rb4xWlEmFd+8iF6Si+8ld3h8EnBn5i4DsQ6/luqf/kW1NQDrqBu8YprqlvCzmrllUj+Se0Ty0ar9LHpvC+PP78LUkUlYDJqrSBJBB1VRZeNoVilHsks5klnKofTi+l/8vhYT3eNCGNY7mn6J4SR1DnKLy1NnsB/fSeWa11BUM36THsDcqbfRIXV4luTL0atKqdn2Fbq9Bt+Lb0ZR5VRzpnP7RNO3axiffHeIr386xtZ9uVw1pgdDe0W6/Cpc/joeTtd1SipspOeWcTS7tPbkn1VKTmFl/TYRwVZ6xofQMz6UnvEhxEcFoqru0dzjLLquY9v5DdX/+zdqWDx+4/9PRgi5kOXcmWC2UrPlMyorivG95E5UX/e9udAogX4+3DyhLyP6x/Lhqv28unQnveJDuHpsT7p1dt3cV9JH4Obq2j/rTvgZuWVk5FeQnlde/++ySlv99hHBVhJjg+kaG0RibBAJsUGGT/PcXprbFqzXVFL1wz+xp/yEOWkYvqNvRfHpWM1dntIubtv3PVU/vo/iF4zv6Fsxx/Vr9zI8pS6a4tA0ftieyec/HKakwsaApHAmDO9K74TQZl0htKWPQBKBG9F1ndIKG9mFFeQUVpJdWEFxhZ1jmSXkFFVQWe2o39bfaqZzVACdIwKIiwygc2QACTGBBHWQk35DmvOFd2QfonLdP9BLcrAMm45l8MQO2UbtSSc/R94RKr99Hb0kG3PSMCyDJ2GKSmy343tSXTRHZbWdNVvT+HbLcUoqbCR1CuKiQZ05t08M/r5nb8Rx20SwfPlyXn/9dex2OzfeeCPXXXdds/ftqImg2uagoKSKgpJq8kuqyCuuIqewguyCyt+c7FVFISbcn4gQKzGh/kSH+9E5svbEHxJgcZvRPK5yti+8rutouanU7FqF/dBPKAFh+I65o0MvoehpJz/dXkPN9hXU7FgJtirU8C6YEwZhiu2BGpmI6t/6MfWeVhfNVWNzsGFXFmu2ppGRV46PWWVwj0gG9YhgQFIEwQGn/+hzy0SQnZ3NrFmz+Oyzz7BYLFx77bX87W9/o0ePHs3a3xMSgd2hUW1zUF3joKrGQWW1ndJKG2UVNkora078v/ZxQWntyf/UZhwARakdqx8T5k9MmD/RYX7EhPsRE+ZPRIgvnWJDOuSHvKV0XSPcXyfveBp6RRFaRRF6eRFaaQ6OjH3oZflgtmIZcCmWIZM7XFPQmTz15KfXVGA7sAF76hYcWQdB1wBQ/EIwRXdDjemJKbYHpsjEZt+H4Kl10Vy6rnMkq5QNOzPZsi+Hkorac0hCdCBJnWubgROig+gU4U9CfOsWe3JaIli6dCk///wzTz/9NACvvvoquq5z9913N2v/r75PobzqlJPmiTBPDbahyPUGtqt7oJ+xnd2hYbNr2B0n/u3QsNu1E//WT/7brlFjrz3Z1534q20O7I7Gq86kKgT5+xDoZyEsyEpEsJXwYF8ign0JD7YSEexLaJD1rNPUaiU5BFRnUVJSdcqbOLPMUx6f+VorttVpsFIbeXy21xqo9Ka2BXS7Db2qFL2q7MT/S9EritErikF3cCbFLxhTTE9MXQbi0/18FIvfb+PvgDrCyU+vqcRRcBwt7yiO3FQcOSnoxdm1Lyoqamgn1IgE1MAIFL/g2uSuqqDU/acACsHBvie+I55PMflgShh41lFWmq5zLLuUnYcL2He0kKNZpVRU2wGIDvPj7fnjWlWu00YN5eTkEBUVVf84OjqaHTt2NHv/z75POW3kizOZTQo+ZhWzyYSPWf3tfz4mAgIs+FnM+FpN+FnMWC0m/KxmfK1mfC1m/Ky1j0MCrQQHWAgOsOBnNbep+Sbz27+Tc3hbO75Tz6D4+GLyD8LkF4wpKARTpyTMgaGYgsIxB4ZjCgrDHBSOKSAExeRec7a4UlSUp4/CCYK4aODk6maO8mKq0g9QnXGImuxUqrMPUJNSWH/l0JCOkQJOir3mEfx7nH3Ft5joYM4dWDtjrq7rZBdUcCSzhJLymlaX6bREoGnaaSdBXddbdFKcf+Mw7HaN0/Y4sf/pz/Gb5xoqR/nNdgpmk4LZrLb/tAmaRnlpFeVt/MFmungu8ZdWUlBYfuIZ5Yz/Kac/f9o/6zY68721ZNtGXmvltgpNHMfk02CTgAMIP/VXcDVQXUXHOw00T0e4ImiYCmF9IKwPpv7gT22zINUV6PZq0DTQHbXPnbiiDA8LOOU74tkUkw/lwdGUt+BvawK6x7RtSLjTEkFsbCxbtmypf5ybm0t0dHSz9w/2t7h9H4GzKT5WLFGRmOiIX3ghmkdRVPANRKHhjlBLVJB8R9rIaePqLrjgAjZt2kRBQQGVlZWsWrWKiy66yFnFCSGEaCWnXRHExMRw3333ccMNN2Cz2Zg5cybJycnOKk4IIUQrOXWKicmTJzN58mRnFiGEEKKNOt4tl0IIIVpEEoEQQng5SQRCCOHl3HYa6o4+TXJLSF2cJHVxktTFSVIXbasDt519VAghhGtI05AQQng5SQRCCOHlJBEIIYSXk0QghBBeThKBEEJ4OUkEQgjh5SQRCCGEl5NEIIQQXk4SgRBCeDlDE8Hy5cuZMGEC48aN46OPPvrN63v37mX69OmMHz+eRx99FLvdbkCUrtFUXXz77bdMnTqVKVOm8Pvf/57i4mIDonSNpuqizrp16xg7dqwLI3O9puri8OHDXH/99UyZMoVbbrnFqz8Xu3fvZsaMGUyZMoU77riDkpISA6J0jbKyMiZNmkRaWtpvXmvVeVM3SFZWlj5mzBi9sLBQLy8v1ydPnqwfPHjwtG0mTpyo//rrr7qu6/rDDz+sf/TRR0aE6nRN1UVpaak+cuRIPSsrS9d1Xf/73/+uP/HEE0aF61TN+Vzouq7n5ubql19+uT5mzBgDonSNpupC0zR93Lhx+vr163Vd1/Xnn39ef+6554wK16ma87mYNWuWvm7dOl3Xdf2ZZ57R//a3vxkRqtNt27ZNnzRpkt6/f3/9+PHjv3m9NedNw64INm7cyPDhwwkNDcXf35/x48ezcuXK+tfT09Opqqpi8ODBAEyfPv201zuSpurCZrOxcOFCYmJiAOjduzeZmZlGhetUTdVFnfnz53P33XcbEKHrNFUXu3fvxt/fv34J2DvvvJPrrrvOqHCdqjmfC03TKC+vXcS+srISX19fI0J1uk8++YSFCxc2uAZ8a8+bhiWCnJwcoqKi6h9HR0eTnZ191tejoqJOe70jaaouwsLCuOyyywCoqqrirbfe4tJLL3V5nK7QVF0AvP/++/Tr149Bgwa5OjyXaqoujh07RmRkJI888gjTpk1j4cKF+Pv7GxGq0zXnc/HQQw8xf/58Ro0axcaNG7n22mtdHaZLPPXUUwwbNqzB11p73jQsEWiahqKcnDZV1/XTHjf1ekfS3PdaWlrK7bffTp8+fZg2bZorQ3SZpuriwIEDrFq1it///vdGhOdSTdWF3W5n8+bNzJo1i6VLl9KlS/T/u1EAAAIVSURBVBeeffZZI0J1uqbqoqqqikcffZT33nuPH3/8kdmzZ/Pggw8aEaqhWnveNCwRxMbGkpubW/84Nzf3tEudM1/Py8tr8FKoI2iqLqA208+ePZvevXvz1FNPuTpEl2mqLlauXElubi4zZszg9ttvr6+XjqipuoiKiqJr164MHDgQgEmTJrFjxw6Xx+kKTdXFgQMHsFqtJCcnA3DNNdewefNml8dptNaeNw1LBBdccAGbNm2ioKCAyspKVq1aVd/WCRAXF4fVamXr1q0ALFu27LTXO5Km6sLhcHDnnXdyxRVX8Oijj3bYKyNoui7mzZvHN998w7Jly3jrrbeIjo5myZIlBkbsPE3VxZAhQygoKGDfvn0ArF27lv79+xsVrlM1VRddu3YlKyuLw4cPA7BmzZr6BOlNWn3ebL++7Jb74osv9IkTJ+rjxo3T33rrLV3Xdf3WW2/Vd+zYoeu6ru/du1efMWOGPn78eP3+++/Xq6urjQzXqRqri1WrVum9e/fWp0yZUv/fI488YnDEztPU56LO8ePHO/SoIV1vui62bdumz5gxQ58wYYJ+880363l5eUaG61RN1cW6dev0yZMn65MmTdJvvPFG/dixY0aG63RjxoypHzXU1vOmrFAmhBBeTu4sFkIILyeJQAghvJwkAiGE8HKSCIQQwstJIhBCCC8niUAIIbycJAIhhPBykgiEEMLL/X9ijJdqIkc5jwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set()\n",
    "\n",
    "from numpy.random import beta\n",
    "\n",
    "# How many random samples to generate\n",
    "N = 10000\n",
    "\n",
    "# We define alpha and beta for the two distributions\n",
    "success_a = 5\n",
    "failure_a = 3\n",
    "success_b = 50\n",
    "failure_b = 35\n",
    "\n",
    "# Generate N samples using the predefined alphas and betas\n",
    "a_samples = beta(success_a, failure_a, N)\n",
    "b_samples = beta(success_b, failure_b, N)\n",
    "\n",
    "# Convert to a Pandas Series for better handling later\n",
    "a_samples = pd.Series(a_samples)\n",
    "b_samples = pd.Series(b_samples)\n",
    "\n",
    "# Plot the two distributions using kernel density estimation\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        'Player A': a_samples,\n",
    "        'Player B': b_samples,\n",
    "\n",
    "    }\n",
    ").plot(\n",
    "    kind='kde',\n",
    "    title='Beta Distribution',\n",
    "    xlim=(0,1),\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the distribution means, Player A is slightly better than Player B on average. However, the orange distribution is narrower, which means that we have more confidence that Player B’s accuracy is somewhere above 40% and below 80%, while Player A’s accuracy is all over the place (it can be 20% or even 100%; we're not sure). Obviously, Player A’s accuracy is more likely to be above 60% based on his bigger probability mass\n",
    ">When both alpha and beta equal one, we end up with a uniform distribution\n",
    "\n",
    "## Binomial distribution \n",
    "\n",
    "Say we know that a player has a penalty kick accuracy of 80%. If he shoots 10 penalty kicks in a row, what are the chances that he will score only one out of all of them? What about the chances of only scoring two or three, and so on? \n",
    "\n",
    "Since this is a discrete distribution, we represent it with a probability mass function instead of a probability density function. As you can see, the graph is displayed as discrete bars and — since probabilities should add up to one — the sum of the bars’ heights for each player add up to one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import binomial\n",
    "\n",
    "# How many random samples to generate\n",
    "N = 10000\n",
    "\n",
    "# Binomial distribution parameters\n",
    "n_a = 10\n",
    "p_a = 0.2\n",
    "n_b = 100\n",
    "p_b = 0.2\n",
    "\n",
    "# Generate N samples using the predefined N and p\n",
    "a_samples = binomial(n_a, p_a, N)\n",
    "b_samples = binomial(n_b, p_b, N)\n",
    "\n",
    "# Convert to a Pandas Series for better handling later\n",
    "a_samples = pd.Series(a_samples)\n",
    "b_samples = pd.Series(b_samples)\n",
    "\n",
    "# We get some values around 2 in the A samples\n",
    "# And some values around 20 in the B sample\n",
    "# We want to calculate how often each value appears\n",
    "a_freq = a_samples.value_counts()\n",
    "b_freq = b_samples.value_counts()\n",
    "\n",
    "# For better visualisation\n",
    "# We will pad some of missing frequencies\n",
    "# We will set them to zero\n",
    "a_freq = a_freq.reindex(range(11), fill_value=0)\n",
    "b_freq = b_freq.reindex(range(41), fill_value=0)\n",
    "\n",
    "# Sine we are calculating probabilities here\n",
    "# We will divide by the total number of samples (N)\n",
    "a_hist = a_freq / N\n",
    "b_hist = b_freq / N\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(16,6))\n",
    "\n",
    "# We already calculated our histogram,\n",
    "# So we will use a bar chart here instead.\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        'Player A; P=20% & n=100': a_hist,\n",
    "    }\n",
    ").plot(\n",
    "    kind='bar',\n",
    "    title='Binomial Distribution (P=20%; n=10)',\n",
    "    xlim=(0, 10),\n",
    "    ax=axs[0],\n",
    ")\n",
    "\n",
    "\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        'Player B; P=20% & n=100': b_hist,\n",
    "    }\n",
    ").plot(\n",
    "    kind='bar',\n",
    "    title='Binomial Distribution (P=20%; n=100)',\n",
    "    xlim=(0, 50),\n",
    "    ax=axs[1],\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import binomial\n",
    "from numpy.random import beta\n",
    "\n",
    "# Our priors Beta distribution parameters\n",
    "prior_alpha = 1\n",
    "prior_beta = 1\n",
    "\n",
    "# How many kicks were scored\n",
    "successes_messi = 81\n",
    "successes_ronaldo = 109\n",
    "\n",
    "# How many kicks were not scored\n",
    "fails_messi = 24\n",
    "fails_ronaldo = 23\n",
    "\n",
    "# Calculate Posterior := Likelihood * Prior\n",
    "messi_samples = beta(\n",
    "    a = prior_alpha + successes_messi,\n",
    "    b = prior_beta + fails_messi,\n",
    "    size=10000\n",
    ")\n",
    "ronaldo_samples = beta(\n",
    "    a = prior_alpha + successes_ronaldo,\n",
    "    b = prior_beta + fails_ronaldo,\n",
    "    size=10000\n",
    ")\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12,8))\n",
    "\n",
    "pd.DataFrame(\n",
    "    {\n",
    "        'Posterior Messi': messi_samples,\n",
    "        'Posterior Ronaldo': ronaldo_samples,\n",
    "    }\n",
    ").plot(\n",
    "    kind='hist',\n",
    "    title='Messi vs Ronaldo Penalty Shootout Accuracy',\n",
    "    bins=100,\n",
    "    alpha=0.5,\n",
    "    ax=ax,\n",
    ")\n",
    "\n",
    "# Add lines to show the medians of each distribution\n",
    "ax.vlines(\n",
    "    x=np.median(messi_samples), ymin=0, ymax=500, color='red', alpha=0.75,\n",
    ")\n",
    "\n",
    "ax.vlines(\n",
    "    x=np.median(ronaldo_samples), ymin=0, ymax=500, color='blue', alpha=0.75,\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt0AAAHwCAYAAAB67dOHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3Xt4VNW9//HPzCSTSBNFMAFEyqGAIFrBahFaTBQK4RYDGHJABLHcFLnaihCCHKRciikWFLwVSwUtN7nJwaBg4fcooIhWwCJSBJRbiNxMgGSSmfX7g+PUkAQmkDWTy/v1PDxP9tp79nxnWNnzyZ6113YYY4wAAAAAWOMMdQEAAABAZUfoBgAAACwjdAMAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAXOTQoUO65ZZblJSUpKSkJCUmJqpXr15au3atf5tZs2Zp5cqVkqTly5fr3nvv1YABA3T06FF17dpVSUlJ+uyzz4rse/fu3Ro3bpwkaezYsbrnnnsKPU+7du306quvWnldH330kbp27VrsuiFDhmj58uVl9lzPP/+8mjRporfeeqtQ+7lz53THHXdoyJAhZfZcPxg0aJD+/e9/KycnRwMHDlRubm6ZPwcAXKmwUBcAAOVRZGSkVq1a5V8+fPiw+vfvL5fLpYSEBI0cOdK/buXKlRo9erSSkpK0cuVK3XDDDZo/f36Rffp8Po0fP14vvviiv61///4aMGCAf/nIkSPq3Lmz2rZtq4YNG9p5cUFy4403atWqVXrggQf8be+++66qVatm5fl+/MdK165dNWvWLD311FNWngsASovQDQABqFu3rkaMGKF58+YpISFBY8eOVePGjZWZmamdO3fq0KFDOnXqlObPn6/s7Gz17dtXCxYsKLSPd955RzfddJNq1apV4vMcO3ZMxhhFRUVJktavX68XXnhBPp9PP/nJTzRu3Djdfvvtev7553X48GFlZWXp8OHDqlWrlp599lnFxsbqH//4h15++WV5PB6dPHlS3bp106hRowo9T2ZmpsaOHavjx4/rxhtv1IkTJ/zrPvnkE82YMUPnz59XeHi4Ro0apbi4uFK/Z/fcc4/Wr1+vY8eOqXbt2pKkFStW6P7779fXX38tSfJ4PEpPT9e2bdvk9XrVrFkzpaWlKSoqSm+++aYWLVqk8PBwRURE6JlnnlGjRo1KbG/btq1mzZqln//85+rUqZPS09M1YMAA3XDDDaWuHQDKGqEbAALUtGlTffXVV4XaUlNTtXv3bvXp00cdO3bUtddeq3Xr1unll18u8vh169bp3nvvLdQ2f/58rV69Wjk5OcrJydGdd96pl19+WbVq1dK+ffs0ceJELVq0SPXq1dOWLVs0dOhQZWRkSLoQjleuXKmoqCg9+uijWrRokYYPH67XXntN06dP13/9138pMzNT9913n/r161foeZ955hk1b95co0aN0sGDB9WtWzdJ0qlTpzRixAi9+OKLat68ufbu3auHHnpIy5YtU7169Ur1foWFhalTp05avXq1Bg8erCNHjujs2bNq3LixP3S/8sorcrlcWr58uRwOh2bOnKn09HRNmDBBU6dO1fvvv6/Y2FitXLlS27dvV4MGDYptb9SoUaHnjoiI0G233aZNmzYVOtMOAKFC6AaAADkcDkVGRl7x47/++usi4feH4SXnzp3T6NGj5Xa7dffdd0uStm7dqlatWvnDbuvWrVWjRg3t2rVLktSyZUv/GfFmzZrpzJkzcjgceumll7Rx40atWbNG+/btkzFG58+fL/S8mzdv9g+9qF+/vv85d+zYoZ/+9Kdq3ry5JKlx48b6xS9+oY8//rjUoVuSkpKSNH78eA0ePFirVq3yh/sfbNy4UdnZ2dq8ebMkKT8/XzVr1pTL5VLHjh3Vq1cv3XvvvWrTpo3i4+NLbC/OTTfdpP3795e6ZgCwgQspASBAO3fu1M0333zFj3c4HDLGFLuuWrVqmjFjhrZt2+YfD+7z+eRwOAptZ4xRQUGBJBX6A+CHfZ87d07du3fXF198oWbNmmnMmDEKCwsr8rwX1xIWduEcjNfrveRz/mDDhg3+C0AHDRpU4mu+/fbb5fV6tXv3bq1du7bIhZw+n0+pqalatWqVVq1apaVLl2rWrFmSpPT0dL300kv66U9/qldeeUVPPPHEJdsvFh4eLpfLVWJtABBMhG4ACMD+/fs1d+5c/fa3v73ifTRo0EDffPNNieuvu+46PfXUU5o9e7YyMzPVunVrffDBB/r2228lSVu2bNHRo0f9Z6GLc/DgQeXk5GjUqFFq27atPvroI3k8Hvl8vkLb3XPPPVq8eLGkCxdvfvTRR5KkFi1a6Ouvv9aOHTskSXv37tW2bdvUsmXLQo9v166dPyhfbraVpKQkTZ06VQ0aNFD16tULrWvTpo3eeOMNf40TJkzQzJkzdfLkScXHx6t69erq37+/Ro0apZ07d5bYXpxDhw6pQYMGl6wNAIKF4SUAUIzc3FwlJSVJkpxOpyIiIvTEE08UGZNdGgkJCXrvvfcuOcb4/vvv19KlS/XHP/5RM2fO1MSJEzVs2DB5vV5FRkbqpZdeUnR0dImPb9Kkie6991516tRJbrdbN998sxo1aqSDBw/K7Xb7t5s4caLGjRunTp06qXbt2mratKkkqUaNGpo1a5YmT56s3NxcORwOTZs27arC6/33368///nPmjt3bpF1Q4cO1R//+Ed1795dXq9Xt9xyi8aOHauoqCg99thj6t+/vyIjI+VyufSHP/xBNWrUKLb9Yh6PR//85z81ZcqUK64bAMqSw5T0XScAoEx5vV716NFDr7zyyiVnMMHVW758ufbu3cuUgQDKDYaXAECQuFwuTZ48WTNnzgx1KZXa2bNntWbNGg0fPjzUpQCAH2e6AQAAAMs40w0AAABYRugGAAAALCN0AwAAAJZVmikDT506K5+P4elXq2bNKJ04kRPqMlDB0Y9QVuhLKCv0JZQFp9Oh66//yRU9ttKEbp/PELrLCO8jygL9CGWFvoSyQl9CKDG8BAAAALCM0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWEboBgAAACwjdAMAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGaEbAAAAsCws1AUAqFxcu3ZKNX4i3fizUJdS4ezatVOSdNttPw9xJQCAsmY1dM+aNUvr1q2Tw+FQcnKyHnnkEY0bN07bt2/XNddcI0kaNmyY2rdvr82bN2vatGnKy8tTp06dNHr0aJulAbAkbNcOKTqS0H0Fdu3aIYnQDQCVkbXQ/fHHH2vr1q1avXq1CgoK1LlzZ8XHx2vXrl1auHChYmNj/dvm5uYqNTVVCxYsUJ06dTRkyBBt2rRJ8fHxtsoDAAAAgsbamO6WLVvq9ddfV1hYmE6cOCGv16vIyEgdOXJEqampSkxM1OzZs+Xz+bRjxw7Vr19f9erVU1hYmBITE5WRkWGrNAAAACCorA4vCQ8P1+zZs/Xaa6+pY8eOKigoUKtWrTRx4kRFR0dryJAhWrZsmapVq6aYmBj/42JjY5WZmVmq56pZM6qsy6+yYmKiQ10CKrLoSEn0oysRzXtXLN4PlBX6EkLJ+oWUI0aM0KBBg/Too49qy5YtmjNnjn9d3759tXLlSiUkJMjhcPjbjTGFlgNx4kSOfD5TZnVXVTEx0crKyg51GajAIrJzdW10JP3oCmRn50oS792PcExCWaEvoSw4nY4rPtFrbXjJvn37tHv3bknSNddcow4dOmjt2rVat26dfxtjjMLCwlS7dm1lZWX527OysgqN+QYAAAAqMmuh+9ChQ0pLS5PH45HH49GGDRv0y1/+UlOnTtWZM2eUn5+vxYsXq3379mrevLn279+vgwcPyuv1as2aNYqLi7NVGgAAABBU1oaXxMfHa8eOHerWrZtcLpc6dOigYcOG6frrr1fv3r1VUFCgDh06qGvXrpKk6dOna/jw4crLy1N8fLw6duxoqzQAAAAgqBzGmEoxEJox3WWDMW+4WhGL3rgwprvLA6EupcJZtOgNSVKvXn1CXEn5wTEJZYW+hLJQLsd0AwAAALiA0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWEboBgAAACwLC3UBAFARud2SMb4i7Q6HUx5PCAoCAJRrhG4AuALG+LR06bIi7T17JosvEQEAF+OTAQAAALCM0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZN8cBgHKKu14CQOVB6AaAcoq7XgJA5cFRGwAAALCM0A0AAABYxvASAChDLpdTEuOwAQCFEboBoAz5fIzDBgAUxScAAAAAYBlnugGggmEICwBUPIRuAKhgGMICABUPR2cAAADAMkI3AAAAYBnDSwAgCBiHDQBVG6EbAIKAcdgAULVxpAcAAAAsI3QDAAAAlhG6AQAAAMsY0w0Al+B2S8YUdwFkCIq5QiW/Bi7iBIBgIXQDwCUYU/wFkCkpySGo5sqU9Bq4iBMAgoejLQAAAGAZoRsAAACwjNANAAAAWEboBgAAACwjdAMAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGaEbAAAAsIzQDQAAAFhmNXTPmjVLnTt3VpcuXfTXv/5VkrR582YlJiaqQ4cOeu655/zb7t69Wz169FBCQoLGjx+vgoICm6UBAAAAQWMtdH/88cfaunWrVq9erbfeeksLFizQl19+qdTUVM2dO1dr167Vrl27tGnTJknSk08+qaefflrr1q2TMUZLliyxVRoAAAAQVNZCd8uWLfX6668rLCxMJ06ckNfr1ffff6/69eurXr16CgsLU2JiojIyMnT48GHl5uaqRYsWkqQePXooIyPDVmkAAABAUIXZ3Hl4eLhmz56t1157TR07dtTx48cVExPjXx8bG6vMzMwi7TExMcrMzCzVc9WsGVVmdVd1MTHRoS4BFVl0pKTK04+ys7Pldhd/qCyLdpfLqerVL7xX0Re9d6V97h/v68dK2k9J25c3laUvIfToSwglq6FbkkaMGKFBgwbp0Ucf1YEDB+RwOPzrjDFyOBzy+XzFtpfGiRM58vlMmdVdVcXERCsrKzvUZaACi8jO1bXRkZWmH4WH++TxFH+NSVm1nz59RpJ07ty5QssOR+n25fX6in3fS3oNJW1fnnBMQlmhL6EsOJ2OKz7Ray1079u3Tx6PR7fccouuueYadejQQRkZGXK5XP5tsrKyFBsbq9q1aysrK8vf/t133yk2NtZWaQBQbvh8Pi1dukyStG3bJ5Kk8PAISVJKSnLI6gIAlC1rY7oPHTqktLQ0eTweeTwebdiwQb169dL+/ft18OBBeb1erVmzRnFxcapbt64iIiK0fft2SdKqVasUFxdnqzQAAAAgqKyd6Y6Pj9eOHTvUrVs3uVwudejQQV26dFGNGjU0fPhw5eXlKT4+Xh07dpQkpaenKy0tTTk5Obr11lvVr18/W6UBAAAAQWV1TPfw4cM1fPjwQm2tW7fW6tWri2zbtGlTLVu2zGY5AFAit1syxlekvZSXl4SUy+WUFPhrKHl7pzyesq0NAKo66xdSAkBFYMx/xlb/WEUaV/3j8eE/VtJrKGn7nj2TxQ2LAaBscVQFAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWEboBgAAACwjdAMAAACWcRt4AEAhLpdTkq9Iu8PhlMcT/HoAoDIgdAMACvH5fFq6dFmR9p49k8UXpABwZQjdAKoUt1syprizuCEoBgBQZRC6AVQpxhR/FjclJTkE1QAAqgpCNwAgIIz1BoArR+gGAASEsd4AcOU4SgIAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGbOXAKiUuAkOAKA8IXQDqJS4CQ4AoDxheAkAAABgGaEbAAAAsIzhJQCAq8Lt4QHg8gjdAICrwu3hAeDyOBoCAAAAlhG6AQAAAMsI3QAAAIBlhG4AAADAMkI3AAAAYBmhGwAAALCM0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWEboBgAAACwjdAMAAACWhYW6AAC4Gm63ZIyvSLvDEYJiAAAoAaEbQIVmjE9Lly4r0p6SkhyCagAAKB7DSwAAAADLCN0AAACAZYRuAAAAwDKrY7pfeOEFvfPOO5Kk+Ph4jRkzRuPGjdP27dt1zTXXSJKGDRum9u3ba/PmzZo2bZry8vLUqVMnjR492mZpAAAAQNBYC92bN2/WBx98oBUrVsjhcGjgwIF67733tGvXLi1cuFCxsbH+bXNzc5WamqoFCxaoTp06GjJkiDZt2qT4+Hhb5QEAAABBY214SUxMjMaOHSu3263w8HA1bNhQR44c0ZEjR5SamqrExETNnj1bPp9PO3bsUP369VWvXj2FhYUpMTFRGRkZtkoDAAAAgsrame7GjRv7fz5w4IDeeecdvfHGG/r44481ceJERUdHa8iQIVq2bJmqVaummJgY//axsbHKzMws1fPVrBlVZrVXdTEx0aEuARVZdKSk4PWj7Oxsud3FH8oqWrvL5SyyXahrupp2l8up6tWvvh9wTEJZoS8hlKzP0713714NGTJEY8aM0c9+9jPNmTPHv65v375auXKlEhIS5PjRnSyMMYWWA3HiRI58PlNmdVdVMTHRysrKDnUZqMAisnN1bXRk0PpReLhPHk9BsesqWrvX6yuyXahrupp2r9d31f2AYxLKCn0JZcHpdFzxiV6rs5ds375d/fv31+9+9zt1795de/bs0bp16/zrjTEKCwtT7dq1lZWV5W/PysoqNOYbAAAAqMishe6jR4/q8ccfV3p6urp06SLpQsieOnWqzpw5o/z8fC1evFjt27dX8+bNtX//fh08eFBer1dr1qxRXFycrdIAAACAoLI2vGTevHnKy8vT9OnT/W29evXS4MGD1bt3bxUUFKhDhw7q2rWrJGn69OkaPny48vLyFB8fr44dO9oqDQAAAAgqa6E7LS1NaWlpxa7r06dPkbbWrVtr9erVtsoBAAAAQoY7UgIAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGaEbAAAAsIzQDQAAAFhG6AYAAAAsI3QDAAAAlhG6AQAAAMsI3QAAAIBlYaEuAAB+zO2WjPEVaXc4nPJ4QlAQAABlgNANoFwxxqelS5cVae/ZM1l8OQcAqKj4BAMAAAAsI3QDAAAAlhG6AQAAAMsI3QAAAIBlhG4AAADAMkI3AAAAYBmhGwAAALCM0A0AAABYRugGAAAALOOOlACAoHK7L9x59GIOh1MeTwgKAoAgIHQDAILKGJ+WLl1WpL1nz2TxBSyAyoqjGwAAAGAZZ7oBVAgul1NScUMSgl8LAAClRegGUCH4fMUPSUhJSQ5BNQAAlA7DSwAAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWMaUgQAAK5hbHQD+g9ANALCCudUB4D8YXgIAAABYxpluAEC5UNxwlOzsbLndkscTmpoAoKwQugEA5UJxw1Hc7jAlJXUTX8wCqOg4igEAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGaEbAAAAsCyg0L1gwQLl5OTYrgUAAAColAIK3Xv27FFCQoLGjx+vnTt32q4JAAAAqFQCujnOH/7wB+Xk5Ojtt9/WpEmTZIxR7969lZiYqIiICNs1AgAAABVawGO6o6Ki1LFjR3Xt2lWnT5/Wm2++qY4dO+r999+3WR8AAABQ4QV0pnvLli1avHixtmzZooSEBM2ZM0dNmzbVN998owcffFBt27a1XScAAABQYQV0pnvSpEn6xS9+ofXr1+uZZ55R06ZNJUk//elPlZKSUuLjXnjhBXXp0kVdunTRjBkzJEmbN29WYmKiOnTooOeee86/7e7du9WjRw//2PGCgoKreV0AAABAuRFQ6F69erWqV6+u6OhoZWVlaf78+fL5fJKkESNGFPuYzZs364MPPtCKFSu0cuVKffHFF1qzZo1SU1M1d+5crV27Vrt27dKmTZskSU8++aSefvpprVu3TsYYLVmypIxeIgAAABBaAYXuyZMna+PGjRce4HRq+/btmjp16iUfExMTo7Fjx8rtdis8PFwNGzbUgQMHVL9+fdWrV09hYWFKTExURkaGDh8+rNzcXLVo0UKS1KNHD2VkZFzdKwMAAADKiYDGdH/22Wdas2aNJKlmzZqaNWuWkpKSLvmYxo0b+38+cOCA3nnnHT300EOKiYnxt8fGxiozM1PHjx8v1B4TE6PMzMxSvZCaNaNKtT1KFhMTHeoSUJFFR0q68n6UnZ0tt7v4Q1Nlb3e5nEW2C3VN5aHd5XKqenWOS7h6fL4hlAIK3fn5+fJ4PHK73ZJUqvHWe/fu1ZAhQzRmzBi5XC4dOHDAv84YI4fDIZ/PJ4fDUaS9NE6cyJHPZ0r1GBQVExOtrKzsUJeBCiwiO1fXRkdecT8KD/fJ4yn+GFPZ271eX5HtQl1TqNvd7jB5vT6OS7hqfL6hLDidjis+0RtQ6L733ns1YMAAJSUlyeFwaM2aNYqPj7/s47Zv364RI0YoNTVVXbp00ccff6ysrCz/+qysLMXGxqp27dqF2r/77jvFxsZewcsBAAAAyp+AxnSPGTNG7du314YNG7Rx40a1b99eTzzxxCUfc/ToUT3++ONKT09Xly5dJEnNmzfX/v37dfDgQXm9Xq1Zs0ZxcXGqW7euIiIitH37dknSqlWrFBcXd5UvDQAAACgfAjrT7XK51K9fP/Xr1y/gHc+bN095eXmaPn26v61Xr16aPn26hg8frry8PMXHx6tjx46SpPT0dKWlpSknJ0e33nprqZ4LAAAAKM8CCt3r16/X1KlTdebMGRnzn3HTn376aYmPSUtLU1paWrHrVq9eXaStadOmWrZsWSDlAAAAABVKQKH72Wef1dixY9WsWbNSX+AIAAAAVHUBhe5rr71WHTp0sF0LAAAAUCkFdCFl8+bN/XeOBAAAAFA6AZ3p3rRpkxYuXKjw8HCFh4f759G+1JhuAAAAABcEFLrnz59vuQwAAACg8gpoeEndunW1c+dOLVmyRDVq1NBnn32munXr2q4NQAXhdl+4k2R4uE9hLp/O5+YqPNyn/7uJLXBVXC6nv39d/I8+BqCiCOhM9yuvvKIPP/xQx44dU//+/fXCCy/o4MGDevzxx23XB6ACMManpUsvTPnZeNsnCnM5tdsVrp49kxXg3/ZAiXy+//Svi9HHAFQUAR2p/vd//1evvvqqrrnmGl1//fVasmSJ1qxZY7s2AAAAoFIIKHSHhYXJ/aPv8K699lqFhQV0khwAAACo8gJKznXq1NHGjRvlcDjk8Xg0b948xnQDAAAAAQoodE+YMEFjxozRnj171KJFCzVv3lzp6em2awNQwblcTkm+Ytu93qLtksRNbwEAlVFAobtWrVr629/+pvPnz8vr9SoqKsp2XQAqgZIugEtJSS7xwriUlGTbZQEAEHQBhe6//vWvxbY/8sgjZVoMAAAAUBkFFLq/+uor/88ej0fbtm1T69atrRUFAAAAVCYBhe5p06YVWs7MzNT48eOtFAQAAABUNld0R4FatWrp8OHDZV0LAAAAUCmVeky3MUa7du1SzZo1rRUFAAAAVCalHtMtXZi3e8yYMVYKAgDgarndkjFFp6V0OJzyeEJQEIAq74rGdAMAUJ4ZU/x0lT17JusKR1YCwFUJKHT37dtXjkvcseL1118vs4IAAACAyiag0H3bbbdp3759SklJUXh4uFatWqWCggJ16dLFdn0AAABAhRdQ6P7000/15ptvyuVySZLuuecepaSkKCEhwWpxAAAAQGUQ0MC2kydPKi8vz7989uxZ5ebmWisKAAAAqEwCOtPdtWtX/fd//7fat28vY4zeeecd9evXz3ZtAAAAQKUQUOgeOXKkmjVrpq1btyoiIkLPPPOMWrZsabs2AAAuyeVySipuasDg1wIAlxJQ6JYu3IWycePG6tGjh7744gubNQEAEBCfr/ipAVNSkkNQDQCULKAx3W+99ZbGjRunv/zlL8rOztbQoUO1ZMkS27UBAAAAlUJAoXvhwoVavHixoqKiVLNmTS1fvlx/+9vfbNcGAAAAVAoBhW6n06moqCj/cp06dfzTBwIAAAC4tIBCd/Xq1bV7927/XSlXr16t6667zmphAAAAQGUR0IWUqampGjlypL755hu1adNGERERmjt3ru3aAAAAgEohoNCdm5urVatW6cCBA/J6vWrQoIHCw8Nt1wYAAABUCgENL/n9738vl8ulhg0b6uabbyZwAwAAAKUQUOhu0qSJ3n77bR05ckSnT5/2/wMAAABweQENL9mwYYMyMjIKtTkcDu3evdtKUQAAAEBlElDo3rlzp+06AAAAgErrksNLJkyY4P/55MmT1osBAAAAKqNLhu5du3b5fx4wYID1YgCUb263FB7uK/Lv/6bwBwAAJbjk8BJjTLE/A6iajPFp6dJlRdpTUpJDUA0AABVHQLOXSPLfjRIAAABA6VzyTLfP59OZM2dkjJHX6/X//IPq1atbLxAAAACo6C4Zur/66iu1atXKH7Tvvvtu/zqmDAQAAAACc8nQ/eWXXwarDgAAAKDSCnhMNwAAAIArQ+gGAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGCZ9dCdk5Ojrl276tChQ5KkcePGqUOHDkpKSlJSUpLee+89SdLmzZuVmJioDh066LnnnrNdFgAAABA0l7w5ztX6/PPPlZaWpgMHDvjbdu3apYULFyo2Ntbflpubq9TUVC1YsEB16tTRkCFDtGnTJsXHx9ssDwAAAAgKq2e6lyxZookTJ/oD9vnz53XkyBGlpqYqMTFRs2fPls/n044dO1S/fn1bzZ7XAAAda0lEQVTVq1dPYWFhSkxMVEZGhs3SAAAAgKCxeqZ7ypQphZa/++47tWrVShMnTlR0dLSGDBmiZcuWqVq1aoqJifFvFxsbq8zMzFI9V82aUWVSM6SYmOhQl4ByKjs7W2538YeNH9rDXM5Cy5fbvjTrKnu766L3rjzUVN7bS/sYl8up6tU5xlVVfL4hlKyG7ovVq1dPc+bM8S/37dtXK1euVEJCghwOh7/dGFNoORAnTuTI5zNlVmtVFRMTrays7FCXgXIqPNwnj6eg2HU/tBd4fQpzOf3Ll9u+NOsqe7vX6yuyXahrCnX7D8G5rPqL1+vjGFdF8fmGsuB0Oq74RG9QZy/Zs2eP1q1b5182xigsLEy1a9dWVlaWvz0rK6vQmG8AAACgIgtq6DbGaOrUqTpz5ozy8/O1ePFitW/fXs2bN9f+/ft18OBBeb1erVmzRnFxccEsDaiS3O4LZ68v/ud2h7oyoHzgdwRAWQnq8JKmTZtq8ODB6t27twoKCtShQwd17dpVkjR9+nQNHz5ceXl5io+PV8eOHYNZGlAlGePT0qXLirT37JkspvFHVeJ2X/h9KA6/IwDKQlBC9/vvv+//uU+fPurTp0+RbVq3bq3Vq1cHoxwAAAop6Q/QlJTkEFQDoDIK6pluABXDhVk0ip71K+X1zQAA4P8QugEU4fNx1g8AgLLEgDQAAADAMkI3AAAAYBmhGwAAALCM0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLmKcbAFBlcOMnAKFC6AYAVBnc+AlAqDC8BAAAALCM0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLmL0EqETcbsmY4qZDc8rjCUFBAABAEqEbqFSMKX46tJ49k8UXWwAAhA6fwgAAAIBlhG4AAADAMkI3AAAAYBmhGwAAALCM0A0AAABYRugGAAAALCN0AwAAAJYRugEAAADLCN0AAACAZdyREgCAUnK5nJJ8RdodDqc8nuDXA6D8I3QDAFBKPp9PS5cuK9Les2ey+BIZQHE4MgAAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGaEbAAAAsIzQDQAAAFhG6AYAAAAsI3QDAAAAlhG6AQAAAMsI3QAAAIBlhG4AAADAMkI3AAAAYFlYqAsAYJ/L5ZTkK9LucAS/FgAAqiJCN1AF+Hw+LV26rEh7SkpyCKoBAKDqYXgJAAAAYBmhGwAAALCM0A0AAABYRugGAAAALCN0AwAAAJYxewlQjrndkjHFTfXnlMcTgoIAAMAVsRq6c3Jy1KtXL7300ku66aabtHnzZk2bNk15eXnq1KmTRo8eLUnavXu3xo8fr7Nnz+quu+7SpEmTFBbG3wOAMcVP9dezZ7L4ogoAgIrD2qf2559/rt69e+vAgQOSpNzcXKWmpmru3Llau3atdu3apU2bNkmSnnzyST399NNat26djDFasmSJrbIAAACAoLMWupcsWaKJEycqNjZWkrRjxw7Vr19f9erVU1hYmBITE5WRkaHDhw8rNzdXLVq0kCT16NFDGRkZtsoCAAAAgs7aGI4pU6YUWj5+/LhiYmL8y7GxscrMzCzSHhMTo8zMzFI/X82aUVdeLAqJiYkOdQn4P9nZ2XK7i/6aulxOVa9e9P+ppO0lBa09zOUstFza/QSz1vLW7rrovSsPNZX39vJWU0m/mygf+HxDKAVt4LTP55PD4fAvG2PkcDhKbC+tEydy5POZMqm1KouJiVZWVnaoy8D/CQ/3yeMpKNLu9fqK/X8qaXtJQWsv8PoU5nL6l0u7n2DWWt7avV5fke1CXVOo238IthWlv5T0u4nQ4/MNZcHpdFzxid6gXYlVu3ZtZWVl+ZezsrIUGxtbpP27777zD0kBAAAAKoOghe7mzZtr//79OnjwoLxer9asWaO4uDjVrVtXERER2r59uyRp1apViouLC1ZZQIXkcjkVHu4r8u8KviQCAABBELThJREREZo+fbqGDx+uvLw8xcfHq2PHjpKk9PR0paWlKScnR7feeqv69esXrLKACsnnK34qwZSU5BBUAwAALsd66H7//ff9P7du3VqrV68usk3Tpk21bFnRAAEAAABUBtyBBgCAMnJhBhruIgugKEI3AABlpKShX9xFFgBHAAAAAMAyQjcAAABgGaEbAAAAsIzQDQAAAFjGhZQAAISI2y0Zw2wnQFVA6AYAIESMYbYToKrgNxoAAACwjNANAAAAWMbwEgAALCv5TpXBrwVAaBC6AQCwrKQ7VaakJIegGgChwPASAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWEboBgAAACwjdAMAAACWEboBAAAAywjdAAAAgGWEbgAAAMAyQjcAAABgGaEbAAAAsCws1AUAAIDAuN2SMb5i1zkcTnk8QS4IQMAI3QAAVBDG+LR06bJi1/XsmSy+wAbKL347AQAAAMsI3QAAAIBlhG4AAADAMkI3AAAAYBmhGwAAALCM2UuAICppui+m+gIAoHIjdANBVNJ0X0z1BQBA5canPAAAAGAZoRsAAACwjOElAACUMy6XU1Jx138EvxYAZYPQDQBAOePzFX/9R0pKcgiqAVAWCN1AGStphhKJs1QAAFRVhG6gjJU0Q4lU8lkqvkoGcLVKPo4wJSlQHhC6gXKAr5IBXK2SjiNMSQqUD/wWAgAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZoRsAAACwjNANAAAAWEboBgAAACwjdAMAAACWEboBAAAAy0JyG/i+ffvq5MmTCgu78PTPPPOMvvnmG7344osqKCjQww8/rD59+oSiNAAAAKDMBT10G2N04MAB/eMf//CH7szMTI0ePVrLly+X2+1Wr169dPfdd6tRo0bBLg8AAAAoc0EP3V9//bUk6be//a1Onz6tlJQU/eQnP1GrVq1UvXp1SVJCQoIyMjI0bNiwYJcHAAAAlLmgj+n+/vvv1bp1a82ZM0fz58/XokWLdOTIEcXExPi3iY2NVWZmZrBLAwAAAKwI+pnuO+64Q3fccYd/OTk5WdOmTdNjjz3mbzPGyOFwlGq/NWtGlVmNVV1MTHSoS6jQsrOz5XaX/KtV0rrK0h7mchZaLu1+gllreWt3XfTelYeaynt7eaypvL0XLpdT1atzXJf4fENoBT10f/LJJ8rPz1fr1q0lXQjYdevWVVZWln+brKwsxcbGlmq/J07kyOczZVprVRQTE62srOxQl1GhhYf75PEUlLi+pHWVpb3A61OYy+lfLu1+gllreWv3en1Ftgt1TaFu/yFE0l8u317SOq/Xx3FdfL6hbDidjis+0Rv04SXZ2dmaMWOG8vLylJOToxUrVujZZ5/Vli1bdPLkSZ0/f17vvvuu4uLigl0aAAAAYEXQz3Tfd999+vzzz9WtWzf5fD49+OCDuvPOOzV69Gj169dP+fn5Sk5O1u233x7s0lDFud2SMb4i7S6X038G8sccDqc8nmBUBgAAKrqQzNM9atQojRo1qlBbYmKiEhMTQ1EOIOlC4F66dFmR9pSU5GLbe/ZMFveXAgAAgSAxAAAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGBZSGYvASqDC3cPLG4qweDXAgAAyjdCN3CFfL6SpxgEAAD4MYaXAAAAAJYRugEAAADLCN0AAACAZYRuAAAAwDJCNwAAAGAZs5cAAIDLcrslY4qbJtUpjycEBQEVDKEbAIBKrOR7CpQuLBtT/DSpPXsmiy/OgcsjdAMAUImVdE8BwjIQXIRuAACqoLI6Aw4gMIRuAACqoJLOgPfqlaLw8OLCeDCqAiovQjcAAPArKYynpCSHoBqg8mAwFwAAAGAZZ7pR5ZQ87VUIigEAAFUCoRtVTknTXvHVKQCUHhdkAoEhdAMAgCvGlIRAYPhtAAAAACzjTDcqLcZuAwCA8oLQjUqLsdsAAKC8YHgJAAAAYBmhGwAAALCM4SWo8Bi7DQAAyjtCNyo8xm4DAIDyjuElAAAAgGWEbgAAAMAyQjcAAABgGWO6UWFwwSQAVBwul1NSccdspzye4NcDhBqhGxUGF0wCQMXh8xV/zO7ZM1l80Y6qiNANAACChjPgqKoI3QAAIGg4A46qitANAABCjjPgqOwI3QAAIOQ4A47KjtCNcodZSgAAQGVD6Ea5wywlAIArVdKJm+zsbLndYqgKQobQDQAAyq3SjvUu6cSN2x2mpKRuYqgKQoXQDQAAyi3GeqOyIHQjZBi7DQAAqgpCN0KGsdsAAKCq4HsZAAAAwDLOdKNUSh4Sws0LAADBU/IFllfyGD7DYB+hG6VS0pCQXr1SFB5e9EAmcTADAJS9ki6wvNQQRdsXZXJiCpdC6EaZKOlAJpUcyLlgEgBQmZR0YoqZViARuhEEV3I2AgAAoDIhdFcRfOUFAAAQOuUqdL/99tt68cUXVVBQoIcfflh9+vQJdUnlVmlDdGm/8mIObQAAgLJTbkJ3ZmamnnvuOS1fvlxut1u9evXS3XffrUaNGoW6tHKptBc0ljYsM4c2AKCqK+kElMvllNd79Z+1fAtdtZSb0L1582a1atVK1atXlyQlJCQoIyNDw4YNC+jxTmdoTsGGh0vFTT8kOZWfH/j2TqdTPl/g+3E6HYqKiirSbozRO+9kFGnv0qVTsduHhbnkdP7neXNychQRYSQVv3+Ho3TtV/KYytpeHmuy0R5Zs6ZcLqeioqJ4j0rZXrNmTUnyL5eHmkLdHh7uor8E0F4eaypv7ZfqSxd/Fv7Y2rXFf6ZezWdtIPt3OivGhZdllYPKanvbriZvOowxpgxruWIvv/yyzp07p9GjR0uSli5dqh07dmjy5MkhrgwAAAC4OuXmzyifzyfHj76XMcYUWgYAAAAqqnITumvXrq2srCz/clZWlmJjY0NYEQAAAFA2yk3o/tWvfqUtW7bo5MmTOn/+vN59913FxcWFuiwAAADgqpWbCylr1aql0aNHq1+/fsrPz1dycrJuv/32UJcFAAAAXLVycyElAAAAUFmVm+ElAAAAQGVF6AYAAAAsI3QDAAAAlhG6AQAAAMsI3QAAAIBlhO4q7MiRI+rTp486duyoxx57TGfPni1x2w8//FAPP/xwEKtDRfD222+rc+fO6tChg954440i63fv3q0ePXooISFB48ePV0FBQQiqREVwub70gzFjxmj58uVBrAwVzeX60vr165WUlKT7779fQ4cO1ZkzZ0JQJSqCy/Wl9957T4mJierSpYvGjh0rj8dz6R0aVFmDBw82a9asMcYY88ILL5gZM2YU2cbr9Zp58+aZli1bmoceeijYJaIcO3bsmLnvvvvMqVOnzNmzZ01iYqLZu3dvoW26dOliPvvsM2OMMePGjTNvvPFGKEpFORdIXzp27JgZMmSIuf32281bb70VokpR3l2uL2VnZ5tf//rX5tixY8YYY/785z+byZMnh6pclGOX60tnz541bdq0MVlZWcYYY0aNGmUWLVp0yX1ypruKys/P17Zt25SQkCBJ6tGjhzIyMopst2/fPu3bt0+TJ08Odoko5zZv3qxWrVqpevXqqlatmhISEgr1ocOHDys3N1ctWrSQVHIfAy7Xl6QLZ5zatWunTp06hahKVASX60v5+fmaOHGiatWqJUlq0qSJjh49GqpyUY5dri9Vq1ZN77//vm644QadP39eJ06c0LXXXnvJfRK6q6hTp04pKipKYWEXbkoaExOjzMzMIts1btxYU6ZM0XXXXRfsElHOHT9+XDExMf7l2NjYQn3o4vUl9THgcn1JkgYOHKiePXsGuzRUMJfrS9dff73at28vScrNzdUrr7yi3/zmN0GvE+VfIMel8PBwbdq0Sffee69OnTqlNm3aXHKf5eY28LDnnXfe0bRp0wq11a9fXw6Ho1DbxcvApfh8vkJ9xhhTaPly64Ef0FdQVgLtS9nZ2Xr88cfVtGlTde/ePZglooIItC/Fx8fro48+0syZM/U///M/+tOf/lTiPjnTXQV06tRJ/+///b9C/1577TVlZ2fL6/VKkrKyshQbGxviSlGR1K5dW1lZWf7li/vQxeu/++47+hiKdbm+BAQqkL50/PhxPfjgg2rSpImmTJkS7BJRQVyuL50+fVoffPCBfzkxMVF79uy55D4J3VVUeHi47rrrLq1du1aStHLlSsXFxYW4KlQkv/rVr7RlyxadPHlS58+f17vvvluoD9WtW1cRERHavn27JGnVqlX0MRTrcn0JCNTl+pLX69Wjjz6qTp06afz48XyjghJdri8ZY/Tkk0/qyJEjkqSMjAz94he/uOQ+GV5ShU2cOFFjx47Viy++qDp16mjmzJmSpL///e86fvy4Ro4cGeIKUZ7VqlVLo0ePVr9+/ZSfn6/k5GTdfvvtGjRokEaMGKGf//znSk9PV1pamnJycnTrrbeqX79+oS4b5VAgfQkIxOX60rFjx/Svf/1LXq9X69atkyTddtttnPFGEYEclyZPnqwhQ4bI4XCoUaNGmjRp0iX36TDGmCDVDwAAAFRJDC8BAAAALCN0AwAAAJYRugEAAADLCN0AAACAZYRuAAAAwDKmDARQKTRp0kQ333yznM7C5xLmzJmjm266KSg1LF26VB6PR3369CnV47p27aoJEybo7rvvLtQ+duxYffjhh6pRo4YkKT8/X3fddZeGDx+umJgYZWZmauTIkVq0aJFycnI0cOBAZWdna+TIkdq3b58WL16s1q1bF7kjbXnz97//XdnZ2Ro8eHDAj7n4vfH5fDp37px69eqlQYMGXfKx3377rWbMmKHnn3/+quoGgNIgdAOoNP72t7/5Q1gobN++XY0bNy7Tffbv318DBgyQdOFmDC+//LIGDhyo5cuXq1atWlq0aJEkaffu3Tpx4oTee+89SVK7du2Unp6uu+66q0zrsaF3795X9LgfvzeSdOTIEXXu3Flt27ZVw4YNS3zckSNHtH///it6TgC4UoRuAJXeihUrNGfOHK1atUoOh0MPPPCAhgwZojp16ig9PV033nijvv76a0VGRmr69Olq2LChPB6P0tPTtW3bNnm9XjVr1kxpaWmKiorS/v379fTTT+vkyZNyOp167LHHFB4ervfff18ffvihIiMj1adPH7344ot699135fP5VLduXU2cOFG1atXSv//9b6Wmpur8+fP62c9+pnPnzgX0OhwOhx599FGtWLFCH374oX72s58pMTFRb731llJTU5WZmamkpCQ1aNBAmZmZGj9+vEaOHKl77rlHU6ZM0VdffaX8/Hy1bt1aY8aMUVhYmG677Ta1a9dOX375pdLT01WtWjVNmTJFp0+fltfrVd++fZWcnKyPPvpIzz33nOrVq6e9e/eqoKBAkyZN0p133qmzZ8/qD3/4gz799FO5XC795je/0ejRo5Wfn1/ie/hjzz//vE6dOqWnn35abdu2Vffu3bVlyxYdPXpUSUlJGjVqVEDvz7Fjx2SM8e//pZde0oYNG5Sbm6vz58/rqaeeUtu2bZWWlqbMzEwNGDBA8+bN06effqr09HSdP39eTqdTw4YN03333aesrCw99dRTOnXqlCQpPj4+4FoAoAgDAJXAzTffbLp27Wruv/9+/7+hQ4f61z/xxBNm4sSJZty4cSYtLc0YY8zWrVtN06ZNzbZt24wxxrz55pume/fuxhhjnn/+eTN9+nTj8/mMMcb86U9/MhMnTjTGGNOtWzezcOFCY4wxR44cMe3atTPZ2dnmqaeeMn/5y1+MMcasWLHCjBo1yuTn5xtjjFm0aJEZOHCgMcaYpKQks2TJEmOMMZ988olp0qSJ2bp1a5HX9OP9/djw4cPNq6++ar799lvTokUL/2vp0qWLf5v77rvP7NixwxhjzNixY83rr79ujDGmoKDA/P73vzevvPKK/31bsWKFMcaY/Px807lzZ7Nr1y5jjDHff/+96dSpk/nss8/M1q1bzS233GL+9a9/GWOMmTdvnunTp48xxpipU6ea0aNHm4KCApOXl2f69Oljtm7desn38Mdmz55tJk2a5K97+vTpxhhjjh07Zn7+85+bb775ptj3pk2bNub+++83bdu2NS1btjSPPfaY2bJlizHGmEOHDpm+ffua8+fPG2OMWbNmjenatWuR9+r06dOmQ4cO5ttvv/U/Z1xcnDl8+LB54YUXzIQJE4wxxpw9e9aMGjXKfP/990VqAYBAcKYbQKVxqeElkyZNUlJSkiIjI7V8+XJ/e9OmTf1DMB544AE988wzOnXqlDZu3Kjs7Gxt3rxZ0oXx1DVr1tTp06f15ZdfqmfPnpKkOnXqaP369UWe7x//+Id27typBx54QNKFMcfnz5/XqVOntGfPHnXr1k2SdOedd5Z6SIrD4dA111wT8PYbN27Uzp07tWzZMklSbm5uofU/vP4DBw7om2++UWpqqn9dbm6u/vWvf6lhw4a68cYbdcstt0iSmjVrphUrVkiSNm/erHHjxsnlcsnlcmnhwoWSpGeffbbY9/By2rVrJ+nCbZhr1qypM2fOqF69ekW2+2F4yblz5zR69Gi53W7/uPi6detqxowZevvtt3Xw4EF9/vnnOnv2bJF9/POf/1RWVpYef/xxf5vD4dCePXt0zz33aPDgwTp69Kh+9atf6Xe/+52io6MvWz8AFIfQDaBKOHHihPLy8uTxeHT8+HF/iHO5XEW2dblc8vl8Sk1NVXx8vCTp7NmzysvLU1jYhcOmw+Hwb//111/rxhtvLLQPn8+ngQMH6sEHH5QkeTwenTlzxr/eGOP/+Yd9BsIYoy+++EIPPfRQwI/x+XyaNWuWf5zz999/X6j+atWqSZK8Xq+io6O1atUq/7rvvvtO0dHR+uc//6nIyEh/u8Ph8L+GsLCwQvs7evSoIiMjS3wPLyciIqLY5ylJtWrVNGPGDHXu3Fnz58/XI488oi+++EJDhw5V//799etf/1q//OUvNWnSpCKP9Xq9atiwoZYuXepvy8zMVI0aNRQeHq4NGzZoy5Yt2rp1q3r27KlXX31Vt91222VfAwBcjCkDAVR6+fn5euKJJzRy5EgNGzbMP95Ykr788kt9+eWXkqTFixfrjjvu0LXXXqs2bdrojTfekMfjkc/n04QJEzRz5kxFRUXp1ltv1cqVKyVdCJi9e/dWdna2XC6XCgoKJElt2rTRsmXLlJOTI0maNWuWxowZo+uvv1633nqrP+R98cUX+uqrrwJ6HV6vV3PmzNH111+vX/7ylwG//jZt2mj+/Pkyxsjj8eixxx7zn43+sQYNGigyMtIfuo8ePaquXbtq165dl9x/69attWLFCvl8Pnk8Ho0YMULbtm0r8T204brrrtNTTz2l2bNnKzMzU9u2bdNtt92mRx55RC1bttSGDRvk9XolXfij6of//xYtWujgwYPatm2bpAsXpCYkJCgzM1Pp6emaO3eufvOb32j8+PFq1KiR9u7da6V+AJUfZ7oBVBoPP/xwkSkDn3jiCW3dulU33HCDf0jI+vXr9dxzzyk+Pl433HCD/vznP+vw4cOqUaOGZsyYIUkaOnSo/vjHP6p79+7yer265ZZbNHbsWEnSn/70J02aNEkLFiyQw+HQlClTFBMTo7i4OE2fPl2SNGjQIGVmZiolJUUOh0N16tTxr5s5c6bGjRv3/9u1X1UFgiiO478t60vIBhFMJptBsAj+L3aLUdi6aJQJu9FgEINR2CYm32AeR7CIjusDXJbLDcMF+X7yMJw56cc5o9PppCiKVKvVSt90PB51Pp8VBIGcc2o2m9rv93/qy3q9ljFG4/FYz+dT7XZbi8Xix7kwDLXb7WSM0eFw0Ov1UhzHarVastaW3r9cLmWM0XQ6lXNOg8FAvV5PnU6ntIc+TCYT5XmuNE21Wq10vV7V7/f1fr/V7XZ1u910v99Vr9dVqVQ0m82U57m2262yLNPj8VBRFMqyTNVqVfP5XEmSaDQaKQxDNRoNDYdDb/UD+G5B8dveDgC+lLVWm81Gl8vlv0sBAHw5vpcAAAAAnjHpBgAAADxj0g0AAAB4RugGAAAAPCN0AwAAAJ4RugEAAADPCN0AAACAZx9TJHhSIxXZKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the difference between the two samples\n",
    "samples_diff = pd.Series(ronaldo_samples) - pd.Series(messi_samples)\n",
    "\n",
    "# Find the median of the difference\n",
    "samples_diff_median = samples_diff.median()\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12,8))\n",
    "\n",
    "# Plot the samples difference\n",
    "samples_diff.plot(\n",
    "    kind='hist',\n",
    "    title='Diff (Ronaldo - Messi)',\n",
    "    bins=100,\n",
    "    color='Gray',\n",
    "    alpha=0.75,\n",
    "    ax=ax,\n",
    ")\n",
    "\n",
    "ax.set_xlabel(\"Expected Difference in Rates\")\n",
    "\n",
    "# Draw a black line at the median of the difference\n",
    "diff_vline_min, diff_vline_max = ax.get_ylim()\n",
    "ax.plot(\n",
    "    (samples_diff_median, samples_diff_median),\n",
    "    (diff_vline_min, diff_vline_max),\n",
    "    'Black',\n",
    "    alpha=0.5,\n",
    ")\n",
    "\n",
    "# Draw a red line at zero\n",
    "ax.plot(\n",
    "    (0, 0),\n",
    "    (diff_vline_min, diff_vline_max),\n",
    "    'Red',\n",
    "    alpha=0.5,\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence that Ronaldo > Messi: 100.0%\n",
      "Difference (Ronaldo - Messi) Median 5.37%\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    'Confidence that Ronaldo > Messi: {}%'.format(\n",
    "        (\n",
    "            100 * ((b_samples - a_samples) > 0).mean()\n",
    "        ).round(2)\n",
    "    )\n",
    ")\n",
    "\n",
    "print(\n",
    "    'Difference (Ronaldo - Messi) Median {}%'.format(\n",
    "        round(100 * samples_diff_median, 2)\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}