{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "rc('text', usetex=True)\n",
    "rc('axes', labelsize=15, titlesize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "np.random.seed(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ABC PMC on a 2D gaussian example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we're looking at a dataset that has been drawn from a 2D gaussian distribution. We're going to assume that we don't have a proper likelihood but that we know the covariance matrix $\\Sigma$ of the distribution. Using the ABC PMC algorithm we will approximate the posterior of the distribtion of the mean values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we generate a new dataset by drawing random variables from a mulitvariate gaussian around mean=[1.1, 1.5]. This is going to be our observed data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar instance at 0x10ad0f9e0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAUwAAAFKCAYAAAB2N2ZCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAF0ZJREFUeJzt3c1uHNeZxvGHlIDZTVrkAEECITDbFt612u1lNiGdbLyj\n",
       "TC+0HDWdXIDl6AZmJHj2iaVcgGlLs8pqSGozsxpJprYvJLUEI0gUQKTa2Q0gm7PoU1KpVd11qtlH\n",
       "rC7+f0DD9Xm6WrYev6dOfSwcHh4KAFBu8bgPAADmBYEJAJEITACIRGACQCQCEwAiEZgA5pKZrZvZ\n",
       "qpn1xqzvhc/V3LJr2brYdvIITABzx8w6kuTuu2H+/Mj6VUk77n5DUjvMS1LPzB5IehTTzigCE8A8\n",
       "2pD0PEz3Ja2NrG/nlvUlrYTpnrufc/fbke285vRRjhgAjklL0kFufjm/MlSWmY6kr8L0Uqg2O+7+\n",
       "RVk7owhMAEmY2WlJZ4/YzF/c/cWYdQsRx9CRdM/d70uvgtTMPsx100vbyRCYAFI5K+nxEdtYkfSk\n",
       "YPlA0lKYPiNpf8z+q+5+RXo50HPg7rfC9u0K7UgiMAEk9t133+nFi3FFYrHTp0/rF7/4xaRNtiR1\n",
       "Je1qGKrbkmRmLXcfhOnN0O3OBoH6ku6G/ZfDPneL2hmHQR8ASf3www9TfSZx9z3pZRAOsi63pJ2w\n",
       "fE3SVTN7aGYHkg7DSPiama1Leubu9ye0U2iBpxUBSMHM3pH0+MmTJ1NVmO+8844krbj7k5kf3JSo\n",
       "MOeQmbXD/zXn3lF/S5P+LFB/BOYccve+pHeO+zhiTbqD4qi/Zd7+LE6ihYWFqT51RGDOKXf/x3Ef\n",
       "QwWfTlp51N8yZ38WJ87i4uJUnzpilHzGzGxT0uUw+427XwnLNsOyz91918y+lvRl7pash+7+npl9\n",
       "o+Fo3YGkj939ezNraTiKt63hpRA9Sd+6+7th36/D8qJ97mh498JNd//9hGO8HI7xkaQNd/8+95ve\n",
       "aEvDyy8+0fAyjV9POI4vJXXM7G44/quSbo/8lnvht/8xTN8I189dd/fuyJ9vW9IfNbwUZF/DOzXy\n",
       "fxbZ7+hreMnI/0q6Eb6z8vGP/ReNaNNUjFSYJ0D4S77p7u+5+3uSrodlF9y9G/7yXzOzn2h4WcTH\n",
       "uf3uSZK7fxy2uy7pSq758xqO7G1oeKHty9E6d9+YsM/VcCybJcfYDfO/k3St4Ofl27os6XkWZtn9\n",
       "t0XH4e6fSuqH338lHPvob8l+x28lfZqFpaQLBcexqeH/aLru/pv8n0UI9rVwjH1Jf3T3/8h9Z+Xj\n",
       "x2w0oTsuUWHO2id6dQuW3P2xmf1Ww4oos6VhBXcje3JK2G9Lenk5xKaGlU4/t98g/OV/Q8k+T8L0\n",
       "QQjqccfYNrP/CouLLp3It9VXuHwjTLcl7U04jqK2Cn+Lhv8T+VbSv44ZHd2W9I2ZfSDpS726D1gj\n",
       "33tP0rsaVpbTHP+jCcePCqgwMc6hpNFu3E/0+q1X/6JXgfRtqG5W3f0/Q2V1WdIlDbuqeYUjwVPs\n",
       "U3SMh5L+3d1/HT6/KdhvtK3X5kuOo6ytvDMahtW7RSvDKYyOhl3qe3q90v5Ww4uQJel9Dbvg0x5/\n",
       "Pf/G4lgRmLO1pdwARwjDb7Jlocu4rlfVzZak3+rV7Vjva3g+7h+SPoj8zir7HI45xqJlVU06joGZ\n",
       "/SRUuGWuS/qVpA+KjsPMVtz9SbiD465yI+Thz3fBzLYlPSq7CLnC8eMIGCVHoXDXwJfh7oKHGlaO\n",
       "u5K2w/yOpMtZ1zDc09rTsGspSV9LuhAGSNb0etd4tJt8WHGfwwnHuKdhN/duaOf9gp9XdiyTjmNH\n",
       "w2rwalhe+FvCoMu/hdDqSbphZv88su1aOM6HGlaiT0baO69h4F4Jg0izOH4cQZMCkzt90BjhnPAD\n",
       "d/9TqGavSdoO/2OaSfvu/vks2joJsjt9/v73v5fe6jjq1KlT+ulPfypxp09zVHm0Pd6KQ4VBoHBJ\n",
       "0EDDc6JHFi7FWp9FWydNkypMAnNKVR9tj/TCdaaf5E4tHLr7n2bU9nVNHvnHGE0KTC4rmt6GpOwy\n",
       "nOzR9nvHdziQhtdSHvcxoLkIzOlVerQ9cJLVtWKsisA8mmb8VwAk1KQL1wnM6VV6tD1wUjUpMBn0\n",
       "md6WhrfQSRGPtsd8M7MLkrpmdum4j2XeNOlpRVyHeQThcqK+pPbIaz2BEy+7DnMwGOjHH3+stO/i\n",
       "4qJarZZUs+sw6ZIfQS4kd4/1QAC8FQQmgKSadA6TwASQFIEJABXUNQCrIjABJDVNWMbsE94vPtCY\n",
       "QdfcMx7ezb2epWjZNXf/3Mx6ZYO39Ry7B9AYKS4rKnuWg5mtStoJAdgOD8l5Y1nYvGdmDxTxlH0C\n",
       "E8A82tCr15Nkz3LIa+eWZa8hGV22EqZ77n7O3W+rBF1yAEkl6pJPfJbDSNe6I+mrkSfwd/Tq3VZL\n",
       "odrshCf5jzWzwDSzf9Lw0f5/k1TtaaEA6uqUpJ9JuuPu/zdNA6nOYSriWQ7ZG1nzYTm6LAtXM/vQ\n",
       "zLK3JBSaZYX5gaT/nmF7AOrjl5L+Z5odEwVm7LMcVsPrnQuXhUGgg/BU/n0Nu+1vJTD/Jknfffed\n",
       "Xrx4McNmUUePHz8+7kPAW/D06VNdvHhRCn+/p5EoMLc0fEPornLPcjCzlrsPwvRm1sXOKsfRZRqe\n",
       "y7wb2lxWyTMhZhmYP0jSixcvCMwT4OzZs8d9CHi7jnSabdbXYbr7npl1Q+gNcl3uHQ0fkrIm6aqZ\n",
       "XdawEr1QtMzdb4dXzUjSs7I3jTLoA2AuFT3Lwd274Z87etVlz3tjWZWX5BGYAJKq66PapkFgAkiq\n",
       "KbdFSgQmgMQITACIRGACQKQmBWZzzsYCQGJUmACSmuYBwnV91xiBCSCpaQJTqmdoEpgAkiIwASDS\n",
       "4uLiVF3yqq/mfRsITABJTVth1hGj5AAQiQoTQFILCwuV7yevY3dcIjABJMZ7yQEgEoEJAJFiXps7\n",
       "LwhMAEk1qcJsRuwDwFtAhQkgKbrkAFBBXbvYVRGYAJKapsKs433kEoEJILFUgz5mti5pIKmde4Nk\n",
       "fn0vTL7r7r8ft09ZO3nNOLEAoLaywKz6mcTMOpLk7rth/vzI+lVJOyEA22a2mm2T36esnVEEJoB5\n",
       "tCHpeZjuS1obWd/OLeuH+U80rCTz+2wULBuLLjmApBKdw2xJOsjNL+dXjnStO5K2JL0vaX9kn4nt\n",
       "jKLCBJBUii551nTZBqHLfc/d92L3mYQKE0BSiZ5WNJC0FKbP6PXKMW/V3a8U7NPK7RPTjiQqTACJ\n",
       "JaowtzQ8LylJK5K2JcnMWtkGZrbp7l+E6dWRfdphn8J2xiEwASSVIjCzLnYIwoG73w+rdsLyNUlX\n",
       "zeyhmR1IOizaZ0I7heiSA5hLuYGd3dyybvjnjl51tcv2eWPZOAQmgKSmGSWv673nBCaApJr0eDcC\n",
       "E0BS04ySE5gATiQqTACI1KTArOeZVQCoISpMAEkxSg4AkZrUJScwASRFhQkAFdS1YqyKwASQFBUm\n",
       "AERq0jnMesY4ANQQFSaApJpUYRKYAJIiMAEgEoEJAJEITACooK4BWBWj5AAQiQoTQFJ0yQEgUpMC\n",
       "ky45gKSyWyOrfsqY2bqZrZpZb8I213LTHTP7Mbx696GZ/SG/zaR2Xv6WWRwUAIyT4r3kZtaRJHff\n",
       "DfPnC7bZlLSeW3TG3Rfd/T1JH0vKwrRnZg8kPSr7LRMDM+agAGCSFIEpaUPS8zDdl7Q2uoG7Xw/r\n",
       "svn8e8e77v4kTPfc/Zy73y770rIKs/SgAOAYtCQd5OaXY3c0s1VJX+cWLYVe9Gdl+5YF5tQHBQBS\n",
       "sgpTkqYdGfrQ3b/PZtz9Rqg+l0OYjhUz6FPP4SoAcyNBWA4kLYXpM5L2KxxOJ5sws56ZZec59yW1\n",
       "J+1YFphHOSgASFVhbulVuK1I2pYkM2tN2snMRgOxL2knTC9LujNp/7LALDwoAIiVIjDdfU96eT5y\n",
       "4O73w6os/GRmFyR1zexSbtdD5UbDQ1d8LVSZz3LtFJp44bq775lZt+CgACBKqgvX3f1GmNzNLevm\n",
       "pm9Kujmyz2NJvxtZdiv2uErv9Ck6KAA4ibg1EkBSTbo1ksAEkBSBCQCRCEwAiERgAkAFdQ3Aqni8\n",
       "GwBEosIEkBRdcgCIRGACQCQCEwAiEZgAEKlJgckoOQBEosIEkFSTKkwCE0BSBCYAVFDXAKyKwASQ\n",
       "FBUmAERqUmAySg4AkagwASTVpAqTwASQFIEJAJGaFJicwwSQ1OLi4lSfMma2bmarZtabsM21ovn8\n",
       "PjHtvPwtpUcFAEeUVZmxnzJm1pEkd98N8+cLttmUtD6yuGdmDyQ9im0nj8AEMI82JD0P031Ja6Mb\n",
       "uPv1sC6v5+7n3P12bDt5BCaApKpWl5FVZkvSQW5+OfJwlkL3+7Np2mHQB0BSCQd9Ko8MufsNSTKz\n",
       "D81stWo7BCaApBIF5kDSUpg+I2m/bIcwqHPg7rfC9u2q7dAlB5BUoi75loaBJ0krkrYlycxaE/bp\n",
       "S9oJ08uS7oxrZxwCE0BSKQLT3fckKXSrB+5+P6zKAlFmdkFS18wuhX12Ja2Z2bqkZ+5+f0I7heiS\n",
       "A5hL2flISbu5Zd3c9E1JN0f2uRXTzjgEJoCkmnSnD4EJICkCEwAqqGsAVkVgAkiKChMAIsU+TGN0\n",
       "nzqq51EBQA1RYQJIii45AEQiMAEgEoEJAJEITACooK4BWBWj5AAQiQoTQFJ0yQEgEoEJAJEITACI\n",
       "RGACQCTuJQeAE4gKE0BSdMkBoIK6BmBVBCaApKgwASBSkwKTQR8ASaV4L7kkmdm6ma2aWW/CNtdG\n",
       "5nvhc3V0m0ntZAhMAHPHzDqS5O67Yf58wTabktZz86uSdsJ7yNthXpJ6ZvZA0qOy7yUwASSVqMLc\n",
       "kPQ8TPclrY1u4O7Xw7pMO7ddX9JKmO65+zl3v132pZzDBJBUonOYLUkHufnlsh1CZZnpSPoqTC+F\n",
       "arPj7l9MaoMKE0BSqc5hSppqZCh05++5+31pGKSha7+c66YXIjABJJUoMAeSlsL0GUn7FQ5p1d2v\n",
       "SC8HgbLznPsadtvHmnmX/PHjxzp79uysm0XN1PWyD8zW6dOn1W5PzJBSCwsLle8Nj/jva0tSV9Ku\n",
       "hucityXJzFruPhi3k5ltZt3uUE32Jd0Nq5ezdsahwgQwd9x9T3oZeoOsey1pJ9vGzC5I6prZpTC/\n",
       "JumqmT00swNJh6ErvhaqzGe5dgox6AMgqVQXrucGcXZzy7q56ZuSbubmd/SqG59v51bscRGYAJJq\n",
       "0p0+BCaApAhMAIjUpAcIE5gAkmpShVnPGAeAGqLCBJBcXSvGqghMAEk1qUtOYAJIisAEgEiMkgNA\n",
       "pCZVmPWMcQCoISpMAEk1qcIkMAEkRWACQKREz8M8FgQmgKSoMAEgUpMCk1FyAIhEhQkgqSZVmAQm\n",
       "gKQITACIxK2RAFBBXSvGqghMAEml6pKHV+MOJLVzb5Ac3eaau38+aZ+YdjL1rHsBYAIz60hSeK+4\n",
       "zOx8wTabktYn7RPTTh6BCSCprMKs+imxIel5mO5LWhvdwN2vh3WT9tnQsLoc204eXXIASSUa9GlJ\n",
       "OsjNL0c0W7RPpXYITABJJbysaJqRpCONPhGYAJJKFJgDSUth+oyk/Yhm8/u0cvtEt8M5TABJJTqH\n",
       "uSWpHaZXJG1Lkpm1Ivdph30K2xmHwAQwd9x9T5LMbFXSwN3vh1U72TZmdkFS18wujdtnQjuF6JID\n",
       "SC7Fheu5ayZ3c8u6uembkm5G7PPGsnEITABJcWskAETi4RsAEInABIBITQrMep4oAIAaosIEkBSD\n",
       "PgBQQV272FXVM8YBoIaoMAEk1aRBHwITQFJNCky65AAQiQoTQFJNqjAJTABJEZgAEInABIBIBCYA\n",
       "RGpSYDJKDgCRCEwAiESXHEByde1iV0VgAkiqSecwCUwASRGYABCpSYEZNehjZtdSHwgA1F1pYJrZ\n",
       "pqT1t3AsABooqzCrfsqY2bqZrZpZL2a9mXXM7Eczexg+fwjLr4V/FraTVxqY7n5dUr/06AGgQIrA\n",
       "NLOOJLn7bpg/H7H+jLsvuvt7kj6WlPWce2b2QNKjst/CdZgAkkpUYW5Ieh6m+5LWytZn4Rl03f1J\n",
       "mO65+zl3v132pQQmgHnUknSQm1+OXW9mq5K+zq1bCl33z8q+lMAEkFSqc5iSyjYat/5Dd/8+m3H3\n",
       "G6H6XA5hOhaBCWAeDSQthekzkvYrrO9kE2bWM7NsUHtfUnvSl8aMkl+Q1DWzS2XbAkCRBNXlll6F\n",
       "24qkbUkys1bJ+tFA7EvaCdPLku5M+tKYUfKb7r7k7n8q2xYARqXokrv7nvTyfOTA3e+HVTsl6w+V\n",
       "Gw0PXfG1UGU+y21XiDt9ACSV6k4fd78RJndzy7ol6x9L+t1IO7dij4vABJBUk26NJDABJNWkwGSU\n",
       "HAAiUWECSKpJFSaBCSCpJgUmXXIAiESFCSCpJlWYBCaA5OoagFXRJQeASFSYAJKiSw4AkQhMAIhE\n",
       "YAJApCYFJoM+ABCJwASASHTJASTVpC45gQkgqSYFJl1yAIhEhQkgqSZVmAQmgOTqGoBV0SUHgEhU\n",
       "mACSalKXnAoTwFwys3UzWzWzXux6M7sW/tmLbSePwASQVFZhVv1MYmYdSXL33TB/PnJ9z8weSHoU\n",
       "084oAhNAUikCU9KGpOdhui9pLXJ9z93PufvtyHZeQ2ACmEctSQe5+eXI9Uuh+/1ZZDuvYdAHwLwq\n",
       "K0PfWO/uNyTJzD40s9XIdl4iMAEklWiUfCBpKUyfkbQ/YX1L0n4Y1Dlw91th+3ZEO6+hSw4gqUTn\n",
       "MLc0DDxJWpG0LUlm1ipY35a0o+E5yp2wbFnSnXHtjENgAkgqRWC6+54khW71wN3vh1U7Y9bvhZHw\n",
       "NTNbl/TM3e9PaKcQXXIAcyk7HylpN7esW7L+Vkw74xCYAJLiTh8AOIGoMAEkV9eKsSoCE0BSdMkB\n",
       "4ASiwgSQVJMqTAITQFJNCky65AAQicAEgEh0yQEk1aQuOYEJICkCEwAiNSkwOYcJAJEITACIRJcc\n",
       "QFJN6pITmACSq2sAVkWXHAAiUWECSIouOQBEalJg0iUHgEgEJgBEoksOIKlUXfLwutyBpHbuzY8T\n",
       "15tZL6x+191/H5Zdc/fPzaxX1E4eFSaAuWNmHUkK7xqXmZ0vWx/ePb4TQrEd5iWpZ2YPJD0q+14C\n",
       "E0BSWYVZ9VNiQ9LzMN2XtBaxvp3bri9pJUz33P2cu98u+1K65ADmUUvSQW5+uWy9u3+Rm+9I+ipM\n",
       "L4VqszOyzRuoMAHMq7IytHB96K7fc/f7kuTuN0LXfTnXTS80ywrzlCQ9ffp0hk2irk6fpnNyEuT+\n",
       "PZ+ato1Egz4DSUth+oyk/QrrV939ivRyEOjA3W+FbdqSdsd96Sz/q/+ZJF28eHGGTaKu2u32cR8C\n",
       "3q6fKWJQ5C3aktTVMNxWJG1Lkpm13H0wYf1m1u0O1WRf0t3Q5nK23TizDMw7kn4p6W+SfphhuwCO\n",
       "zykNw/LOtA2kqDDdfc/MuiH0Bln3WtKOpG7RejNbk3TVzC5rWH1ecPfbZrZuZpL0LNdO8XEdHh5W\n",
       "+iEAEMPM3pH0+M9//rN+/vOfV9r3r3/9qz766CNJWnH3J7M/uulwIgpAUtxLDgAnEIEJAJHokgNI\n",
       "rq5d7KqoMAEgEhUmgKQY9AGAE4jABIBIBCYAROIcJoCkOIcJACcQFSaApKgwAeAEosIEkBQVJgCc\n",
       "QAQmAESiSw4gKbrkAHACUWECSIoKEwBOIAITACLRJQeQVJO65AQmgLlkZuuSBpLa7n4jZn3ssnHo\n",
       "kgNILqsyYz9lzKwjSe6+G+bPl62PXTbpewlMAPNoQ9LzMN2XtBaxfkPDSrJs2Vh0yQEklegcZkvS\n",
       "QW5+OWJ97LKxCEwAST19+jTVPmWpOvORIwITQFIXL15M0exA0lKYPiNpf8L6Vm79pGVF7byGwASQ\n",
       "yl8krcygjSJbkrqSdsN3bEuSmbXcfTCyvh3WL5Qse9nOOAuHh4dH+zkAcAzMrKfhQE3+EqG77t6d\n",
       "sD5q2TgEJgBE4rIiAIhEYAJAJAITACIRmAAQicAEgEgEJgBEIjABIBKBCQCR/h/f4lNn94LgDgAA\n",
       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac6a110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples_size = 1000\n",
    "sigma = np.eye(2) * 0.25\n",
    "means = [1.1, 1.5]\n",
    "\n",
    "data = np.random.multivariate_normal(means, sigma, samples_size)\n",
    "matshow(sigma)\n",
    "title(\"covariance matrix sigma\")\n",
    "colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we need to define our model/simulation. In this case this is simple: we draw again random variables from a multivariate gaussian distribution using the given mean and the sigma from above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def create_new_sample(theta):\n",
    "    return np.random.multivariate_normal(theta, sigma, samples_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need to define a distance measure. We will use the sum of the absolute differences of the means of the simulated and the observed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def dist_measure(x, y):\n",
    "    return np.sum(np.abs(np.mean(x, axis=0) - np.mean(y, axis=0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Verification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify if everything works and to see the effect of the random samples in the simulation we compute the distance for 1000 simulations at the true mean values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "distances = [dist_measure(data, create_new_sample(means)) for _ in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10af34950>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAeYAAAFtCAYAAADS5MnUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XeUW+ed5vkvgMoJlRNDFYvhZaaYlGzJtEnJYRzaVnCa\n",
       "9nZ7Ldk9PXt25+w4bZ/p6TNnpls67uk9s9vjtazOUbYkd7fsti2JlGUlSswU4yWLRRarWDnnCOwf\n",
       "uEVCpUoAgboXwPM5p06hAFzgh1tVePC+973v6wkGg4iIiIg7eJ0uQERERG5RMIuIiLiIgllERMRF\n",
       "FMwiIiIuomAWERFxEQWzxI0x5sfGmMfmuP5JY8xDS3yMOmNMzyL3KTTG1C90/czjGGP8xpgrS33s\n",
       "aBhjdhljjhtjji5yvyvGmIJ41RELS30tMX7OmOyP+f4uluO5RW6Hglni6Sng63Nc/5BlWc8v5QEs\n",
       "y2oAam+3kLDH8QDBuR57rg8RUXoC+LBlWXsXud+cdcwWw7qisdTXEjOx+p0vVfj+Xe7nFpmLglni\n",
       "xrKsQ0CdMcY/c50xZhdwIsLHGYhRPe97nFnXzfUhIhp1kda8yP1jVVc0In4tsbDMz/me/evE6xUJ\n",
       "l+Z0AZL0fgw8DnzP/vnrwDMQ6uoG6oAe4BHLsvqNMYXAIeBl+7bHgBOWZa2dbxv7cYuNMT8ADgAH\n",
       "Lcv6RngR9uMeA3bPvs6yrHXGmKeAXcaYY0Ae8Lv2BwuMMfWWZa2b/cKMMY/brw3g25ZlHTLGPEno\n",
       "w8ixmetmbfMk8BChDyfFc9RRB/zAvq0HaAir62XLsr67yH47au+D5yzL+k5Ynd+yS3jWfoxv2bVf\n",
       "AR4N24+za515Ld+ya775u7Es69F59sH7agG6gc8DPZZlPTjrecJfczfwKPbvfCmPFb7/7Me7Auyc\n",
       "4/XMtd/Cf+8vE+ohCP97W9LrsyzrO7Nfh2VZH51dg8hSqMUs8fYsoTfRGfsty/oJgGVZj1qWtQf4\n",
       "IfDdsPvsBLosy3qUsK7nRbYB+Jb95rzHGLM/kiIty/o60GA/9u9it6LsFv7x2fe3r3/Ysqw99jZP\n",
       "GmMKLMv6NqEw/cgcoXzAfv3r7Nc2l8eBp+zHfdD+gNFg//zdRfbBTuAJex88Hlbn4/ZzrgN+aF+3\n",
       "x/75d4An59kn4a/llbDn6LJDea594A+730wt3wJ67ftgjJkdmuGv+aPM+p1H+FjM2jb89bxvv4X/\n",
       "3u39e/O5I3h9M8E9+3WIREUtZokru4VRZ4xZAxQRFnJ2UD1OqBXTELZZn2VZfzzX4y2wTU9YF+RT\n",
       "wAOEWsjR1vyU/ePngR/NcbfPE2odzfiRfd3TCzz0gVnbzDXI6GXgWWPMXkJv8ldn32GR/XZt5rHt\n",
       "EPk8dg8FgGVZV40x3yDUEn7JvjqSeXnDfzdz7YNHCX0YC6+lATgYdrkOOBm23XteM9A7x3PO91hr\n",
       "gPfto7kssN/ms9TX12OMKZj9Oub63YkshVrMshx+CDxM6E3tKbjZGvkW8DVC3dXh5hwVu8g24TxA\n",
       "1+2VzEG7NXazhT+L336eGaUsLeA8C91ot7J3Eequna+lHsl+CwKzu6mDwB/ZLfIHI2zdhT/HfPsg\n",
       "OEct8450nuM1z96Piz3Wovs9gr+dcJG8vkV/dyJLpWCW5fAj4AvAgbAu0d2EjuUNAEsd8bvQNsVh\n",
       "lx8m1KpaMATn0GefTlVI6APEFwgdg53Ls9zq7i4kdNz44Dz3nfEy8EjYNnWz72CMWWNZ1jXLsr4H\n",
       "HLN7GsLrimS/BQnt+5uDm+wPG3NdF4359kFE+332aybCUdHhx8fn268svN9m9q9/1vURvb45fncR\n",
       "vQ6RGQpmiTvLsk4San2Enwv7Y+Bhe9DNAd7b6pndAgouYRuMMT+wbztuWdapOR4ruMB1EHrTPU6o\n",
       "NXmS0BvxXN3YM62jl+3zZA8SOr59bZ76w7dpsLd5gvd22c5sc8AYc8y+zxW7O/RmXYvsg/ddtl/H\n",
       "U8aYevsx99vXPWs/z3sGxM1hvt9FJPtg3seY6zUD1xZ7XXNosF/LE7z3w9RS/nZm9u8T3GoRR/r6\n",
       "PLNfR9h9RSLiWWzZR2PMw4TeQB6ZGelqjHnSsqxvG2MesyxroWNqIgnLGPPjBQZpiYjExYItZntk\n",
       "637r1vmod9g3PWaMucz83XwiCc3uutQMUCKy7BYclW0H8swpH8Vh3YOPWUucuUkk0djn+D4KfMTp\n",
       "WkQk9SylK9tP6BSDhpkwtqewawB22QMdREREJAYWDeYZ9jmPXw8/N88Y8wSh2YgOzbNNJqERkK3A\n",
       "9O2XKyIi4no+oAo4alnWeKQbL9iVbZ/7F7RHcZ4gNKqxj9BkDs8TOl+vjlvd3bPtBV6PtCgREZEk\n",
       "cB/wRqQbLTbz135uLThQCBwhNFnBzIxKJYTOzZxPK8Df//3fU1lZGWltIiIiCaetrY0vf/nLYGdg\n",
       "pBYL5h8Cj9qTs/fOzIBkjHnIGAOhOXNPLbD9NEBlZSUrV66Mpj4REZFEFdUh3MVGZfczx9y/GpEt\n",
       "IiISH5r5S0RExEUUzCIiIi6iYBYREXERBbOIiIiLKJhFRERcRMEsIiLiIgpmERERF1Ewi4iIuIiC\n",
       "WURExEUUzCIiIi6iYBYREXERBbOIiIiLKJhFRERcRMEsIiLiIgpmERERF1Ewi4iIuIiCWURExEUU\n",
       "zCIiIi6iYBYREXERBbOIiIiLKJhFRERcRMEsIiLiIgpmERERF1Ewi4iIuIiCWURExEUUzCIiIi6i\n",
       "YBYREXERBbOIiIiLKJhFRERcRMEsIiLiIgpmERERF1Ewi4iIuIiCWURExEUUzCIiIi6iYBYREXGR\n",
       "tMXuYIx5GOgFHrEs6xv2dQ8BfUCdZVlPx7dEERGR1LFgi9kYsx/Yb1nWIaDOGLPTGLMLwL4OY8zO\n",
       "+JcpIiKSGhYMZsuyDlmW9Tv2j8WWZZ0EPk+oBQ3QAByIY30iIiIpZSld2X7gceCP7Kv8QE/YXUri\n",
       "UJckqUAgwODgYFTbAXi9kQ+LyM/Pj2o7EREnLBrMlmX1A98zxrxkjDlhX+2Jb1mSrAYHB3nh1fPk\n",
       "5ORGtF1XZzteXxrFxZF9DhwZGebT+zbj9/sj2k5ExCkLBrN9PDlod2GfAB4mNOir2L5LEdAd1wol\n",
       "6eTk5JKbVxDRNsPDg3i96RFvJyKSaBbr39vPrRAuBK4APwLq7OvWAC/HpzQREZHUs1hX9g+BR40x\n",
       "dUCvZVk/ATDG7LFHbPdZlnUq3kWKiIikigWD2T6+/L7zlMPOXT4Uj6JERERSlYaqioiIuMiio7JF\n",
       "3KhvaJzG1gEGhidYUZbHqoo80tN8TpclInLbFMySUJo7Bnnt5A16B8dvXvdufRc+r4c11X4+tGsF\n",
       "WRn6sxaRxKV3MEkYTZ2jvH2xDYKwprqAmsoCCvMzaWofpKGln/rmPjr7Rvg3966hqCDL6XJFRKKi\n",
       "YJaE0NA6xon6IdLSvHzi3lpWluffvG1FWR53bank7bNtnLA6eO5Xl/noXbWsrsxf4BFFRNxJg7/E\n",
       "9a629HO8foiMdC+/cf/a94TyDI/Hwz3bqnjgztVMTwf5+VtX6ewdcaBaEZHbo2AWVxufmObXJ5rx\n",
       "emDf9mLKi3MWvP+G1UV87J5apgNBfnG4kbGJ6WWqVEQkNhTM4mpvnWlheGyKTatzKMxLX9I2tVUF\n",
       "7N1cweDIBK+d7iQQCMa5ShGR2FEwi2s1dwxy/moPJf4sNq7MjmjbvZsqqK0qoKV7lOd/fS0+BYqI\n",
       "xIGCWVxpajrAr4434wE+snsVXm9kC5p5PB4O7F1NXnYaP32jkast/fEpVEQkxjQqW1zpYmMvA8MT\n",
       "bF9XSnlxDh3tvRE/RmaGj7s2FXPoRAf/45nj/Oev7sLrWXrAax1nEXGCgllcJxAIctLqwOf1sGtj\n",
       "+W09VnFugOriNK7cGOT7z59l4+qlLRupdZxFxCkKZnGd+uY+BoYn2FJXQm7W0gZ8LWTPhmJ+ebyL\n",
       "E5d72bimgtzs239MEZF4UT+duEowGOSE1YEH2LmhLCaPmZ3p456tVUxMBjh8pjUmjykiEi8KZnGV\n",
       "xtZBuvvHWLeqEH9eZswed0tdCaWFWVjXe+nqG43Z44qIxJqCWVzlhNUOwO7bPLY8m8fj4Z6t1QBq\n",
       "NYuIqymYxTW6+kZp7R5hdWU+Jf7IzlteitWV+awsz+N6+yBN7YMxf3wRkVhQMItrXLjWA8CWNSVx\n",
       "e457t1UBoVZzMKgZwUTEfRTM4grT0wGs671kZ6ZRU7W0U5qiUVaUw/pVhXT2jVLf3Be35xERiZaC\n",
       "WVyhoaWf8YlpNtYU4Ytwlq9I3bWlEq8Hjp5vJ6BWs4i4jIJZXOHC1VA39qba4rg/lz8vE1NTTO/g\n",
       "OFfUahYRl1Ewi+MGhido6hiiqiSHooKsZXnO3RvL8Xjg6IV2HWsWEVdRMIvjLtqDvjbFcdDXbKFW\n",
       "cxG9A+PUN2uBCxFxDwWzOCoYDGJd7yU9zcvalcs7L/WejRV4PHBMrWYRcREFsziqq2+UgeEJaqsK\n",
       "yEjzLetz+/MyMauL6BkY48oNtZpFxB0UzOKomUBcu8KZVZx2bwq1mo+eV6tZRNxBwSyOCQaDXGnu\n",
       "J83nZXVl/M5dXkihWs0i4jIKZnFMz8AYfUPj1FTmk57m3J/i7o0VeNCxZhFxBwWzOGamhVrnUDf2\n",
       "jML8TDbUFNHdP0aDWs0i4jAFszim4UY/Pq+H2jhOwblUe+xWs85rFhGnKZjFEX2D43T3j7GqIp+M\n",
       "9OUdjT2XwvxMNqxWq1lEnKdgFkdcuRGaCtOp0dhz2bMp1Go+ohHaIuIgBbM44sqNfrweqK12vht7\n",
       "xsyx5p6BMRrbR5wuR0RSlIJZlt3gyCSdvaOsLM8nKyPN6XLeY499XvOp+l6tPCUijlAwy7KbaY06\n",
       "PRp7LjPnNfcNTXLkfKfT5YhIClo0mI0xj9lfT4Rd9+TMbfEsTpJTY/swHtwZzHCr1fyTX19jOqBW\n",
       "s4gsrwWD2RizHzhoWdbTQJ39M8BjxpjLwJV4FyjJpWdgnM6+carL8sjOdFc39gx/XiZrq/No6Rrh\n",
       "jVM3nC5HRFLMYi3mOuCAfbkBWGNffsyyrPWWZb0St8okKR27GOoedtNo7LnsWFuIz+vhmZcttZpF\n",
       "ZFktGMyWZT1tt5YBdgHH7MvFxpj9xphvxrU6STpHLoSC2a3d2DPyc9L54I4KmjuGeP1ks9PliEgK\n",
       "WdLgL2PMLuC4ZVmn4GZgHwJKwrq3RRbUOziGdb2f8sJMcrPTnS5nUb9xX82tVvN0wOlyRCRFLHVU\n",
       "9n7Lsr4LNweDPWRf302ou1tkUW+fbSMYhJrKXKdLWZKywmwO3LmaG53D/PqkjjWLyPJYyqjsxy3L\n",
       "+p59eT+hY80H7ZtLgKPxK0+SyVvvtgBQU5HjcCVL9+j+DaT5PDzzksWUWs0isgwWG5V9AHjCGFNv\n",
       "jOkBgnYX9gG71dw1070tspCB4Qnere9iTXU+eQnQjT2jvDiHj95dS2v3MC++3eh0OSKSAhY8X8Wy\n",
       "rINA8RzXPx+3iiQpHTnXSiAQ5M5NZUBijXL+/AMbOHT0Os+8ZPGRPatce5qXiCQHzfwly+LNd1sB\n",
       "2Lup1OFKIleUn8Vn962jb2icf/61Tt0XkfhSMEvcjYxNcupSJ7VVBVQWJ87x5XC/8aG1+PMy+KdX\n",
       "L9M3OO50OSKSxBTMEndHzrczNR3gAzuqnS4lajlZ6XzhAcPo+DTPvGw5XY6IJDEFs8TdzGjse7dV\n",
       "OVzJ7fno3bVUlebyi8PXuN424HQ5IpKkFMwSV2PjUxy/2MHK8jxWV7pn7eVopKd5+dqntxIIBHn6\n",
       "X84S1LKQIhIHCmaJq+MXO5iYnObe7YnbjR1u7+YKdm4o49SlTo6eb3e6HBFJQgpmias37W7sDyRJ\n",
       "MHs8Hr72ma14vR7+7IWzTE5NO12SiCQZBbPEzcTkNMcutFFZksOa6sTuxg63urKAT9xbS2vXMD99\n",
       "/arT5YhIklEwS9yctDoYHZ/m3m3VeDwep8uJqS99dCP5Oek887JF7+CY0+WISBJRMEvc3OzGTuDT\n",
       "pOaTn5PBlz+2idHxKf725xecLkdEkoiCWeJicirAkXNtlBZms35VodPlxMXH7q6hpjKfg0evU9/c\n",
       "53Q5IpIkFMwSF+/WdzI8NsW926qSrht7hs/n5bHPbCMYhKf/+QzBYJBAIEB/f39UX4GAVq8SkUUW\n",
       "sRCJ1lv23NjJcprUfHZsKOOebVUcPtPK66dusKMunxdePU9OTmRrTo+MDPPpfZvx+/1xqlREEoWC\n",
       "WWJuejrA4TOtFOVnsqn2fYuTJZ2vfmoLxy608xc/PceTv7OHnJxccvOSZxS6iCwvdWVLzJ290s3g\n",
       "yAR3b6vC603ObuxwlSW5fHbfOrr7x3jhjetOlyMiCU7BLDH3+ukbANy3Y4XDlSyfRz6yntLCbH5+\n",
       "uImB4UmnyxGRBKZglpianArw1rstFBdksrmuxOlylk1WZhpf/dQWpqaDHLnY7XQ5IpLAFMwSU6cv\n",
       "dzI4MskHdqzAlwLd2OE+uKOaTTWFNHeOcq1Vq0+JSHQUzBJTr58KdWPff0fqdGPP8Hg8fOVj6/B4\n",
       "4I3TN5ie1ulPIhI5BbPEzMTkNIfPtFJWlI2pKXK6HEesqshj46oC+ocmOH25y+lyRCQBKZglZo5f\n",
       "7GB0fIr7dqxI2klFluKO9YVkZfg4eqGdoVENBBORyCiYJWZmurHvS8Fu7HCZ6T7u2VbF1HRoIJyI\n",
       "SCQ0wYjExNj4FEfOt1FVmsvalYk/e9XM1JqR6u/vJxgMsrG2mLMN3Vxu6mP7ulIqSyKbCUxEUpeC\n",
       "WWLi8NlWxiemuX9ncnRjj44O8+LhXoqLIzvlq6uzndw8P3n5Hj64o5p/evUKb77bwuf2rUuK/SIi\n",
       "8adglph45VgTAB/ZvcrhSmInOzvyqTWHhwdvXq4uzaOu2k9DSz8NN/pZuzI5V9kSkdjSMWa5bd39\n",
       "o7x7uZONNUVUl+U5XY6r3LOtCq8n1KMwrdWjRGQJFMxy2359oplAED68J3lay7FSmJ/JlrWl9A9N\n",
       "cPaKZgQTkcUpmOW2BINBXjnWRJrPk/Kjseezd1MFGWlejl1oZ2Jy2ulyRMTlFMxyW662DNDYNsje\n",
       "zZXk52Q4XY4rZWemsdOUMzYxrUlHRGRRCma5LTcHfakbe0Hb15WSleHj1KUOxiamnC5HRFxMwSxR\n",
       "m5oO8OuTzeTnpLN7Y4XT5bhaRrqPXRvLmZgKcOpSp9PliIiLKZglakfPt9M3OM6+3atIT9Of0mK2\n",
       "1pWSk5XG6ctdjI6r1Swic9O7qUTtpXcaAXjgztUOV5IY0tO87NlYwdR0gOMXO5wuR0RcSsEsUenq\n",
       "G+XExXY2rC5kTXXiT8G5XDavKSYvO51zDWo1i8jcNPOXROXgkUYCQbhve3lEc0rPzCWdqnw+LztN\n",
       "Oa+fusHpy53cvbXK6ZJExGUWDWZjzGP2xbWWZX3Hvu4hoA+osyzr6TjWJy4UCAR56Z1G0rwexsbG\n",
       "OXikccnb3ppLOo4FutzmNcUcu9DOmStd7DTlZKb7nC5JRFxkwWA2xuwHDlqWddUY82P75x4Ay7IO\n",
       "GWPqjDE7Lcs6uRzFSuwFAgEGBwcXv2OYsw29dPaNsW5FHoWFkc3/HD6XdKpK83nZsb6Ut8+2cfZK\n",
       "l0a0i8h7LNZirrO/ngYa7MsPAC/btzcABwAFc4IaHBzkhVfPk5Oz9GUJXz0VGrhUU5YZr7KS3ta1\n",
       "pZywOjh9uYvt68qcLkdEXGTBYJ7VTb0L+BGwGwif9DeydfHEdXJylr6K0sjYJNfbRyjI8VFSkB7n\n",
       "ypJXZrqPbWtLOX6xgwvXullbqQ85IhKypFHZxphdwPGwLmstLJuiLl7rJRAMUleZpfWFb9OO9WX4\n",
       "vB5OX+4ikMID4kTkvZZ6utR+y7K+a1/uA4rty0W8t/UsSSwYDHLuajdpPi81FWrh3a7szDRMTRED\n",
       "wxM0tY84XY6IuMSiwWyMedyyrO/Zl/cT6s6us29ew63jzZLkrrcPMjA8wfpVhWRopq+Y2LE+dHz5\n",
       "XOPSTzkTkeS24LurMeYA8IQxpt4Y0wMEZ7qz7ZDusyzr1DLUKS4ws57w1joNK4iV4oIsVlfm09E7\n",
       "TkPLgNPliIgLLDb46yC3uq3Dr58ZFHYoHkWJ+wyOTNDYOkBZUTblxTl0tPc6XVLSuGN9GdfbBvnl\n",
       "283s3KRVukRSnfojZUnOX+0hiFrL8bCyPI/CvHTeOd9JV9+o0+WIiMMUzLKoQCDIhavdZKR5Wb8q\n",
       "sglFZHEej4fNtX6mA0F+/tZVp8sREYdprmxZ1LW2AYbHpti6toT0NE0fGQ+1Fdmcrvfx4uFrfOKu\n",
       "qiUvo5mfn4/Xq8/XIslEwSyLOtcQGvS1ZY26seNlcmKUykIfV9om+IufXWBtdd6i24yMDPPpfZvx\n",
       "+7W6l0gyUTDLggaGJ7jeNkhFcQ6lhdlOl5PUNq72c6Wtk8vNw2zfUO10OSLiEPWByYLOX7Vbyxr0\n",
       "FXd52WnUVObT1jNCZ68mHBFJVQpmmdd0IMiFaz1kpHtZt1KDvpbD1rWlAJy5ogn1RFKVglnm1dg6\n",
       "wMjYFKameMmDkeT2rK7MpyA3g8tNvYxNTDldjog4QO+2Mq9bg77eN8eMxInX42FLXQlT00GsRk3i\n",
       "IpKKFMwyp4Hhca63D1JZkkOJX4O+ltOm2mK8Xg/nrnYT1KpTIilHwSxzOtfQA2jQlxOyM9NYu8JP\n",
       "78A4bd0aBCaSahTM8j4zg74y030a9OWQzfbhg3NXNQhMJNUomOV9rrX0Mzo+hakpIs2nPxEnrCjL\n",
       "w5+XQX1TnwaBiaQYvevK+9wc9KVubMd4PB42rylhOhDk0nUNAhNJJQpmeY/+oXGaOoaoKs2luCDL\n",
       "6XJS2saaIrweD+caejQITCSFKJjlPS7ap+joFCnn5WSls2ZFAT0DY7T3aBCYSKpQMMtNwWDo3Nk0\n",
       "n5e6FVoYwQ1mFg7RIDCR1KFglptau4YZHJlg3Uq/lnd0iZXleRTkhgaBjU9OO12OiCwDBbPcZNmD\n",
       "jExNkcOVyIzQILBipqY1CEwkVSiYBYCp6QD1zX3kZaezomzxtYBl+WysLcbrCY2W1yAwkeSnYBYA\n",
       "rrYMMDEZYMPqIjwej9PlSJjcrHTWVPvp7h+jo3fU6XJEJM4UzAJws5tU3djutHlmEFiDBoGJJDsF\n",
       "szA6Pk1j2wBlRdk6d9mlVlXkkZ+TweWmPiY0CEwkqSmYhcb2YYJB2LBKrWW3ujUILKBBYCJJTsEs\n",
       "NLYNA7B2pc5ddrNNtcV4PGg5SJEkp2BOcf3DE7T1jFFZnEN+TobT5cgCcrPTWVPlp6tvjE4NAhNJ\n",
       "WgrmFHfsQidBYK2Wd0wIm+u0HKRIslMwp7h3zncC6sZOFKsq8snPSefS9T4mpwJOlyMicaBgTmF9\n",
       "g+NcaOyjrDBT3dgJwmsvBzk1HaChdcjpckQkDhTMKezwmRaCQaitzHW6FInARnsQ2KWmQadLEZE4\n",
       "UDCnsDdOtwBQW6FgTiR52enUVhXQPTDB1RaFs0iyUTCnqP6hcc5e6WLdigJys9OcLkciNDMT2K9O\n",
       "tjhciYjEmoI5RR2/2E4gCLs3ljpdikRhdWU+uVk+3jrTwej4lNPliEgMLSmYjTFPzvWzMeaxeBQl\n",
       "8XfkXDsAuzaUOFyJRMPr8bB+ZT5jE9O8fuqG0+WISAwtGszGmMeBh2Zd/Zgx5jJwJS5VSVxNTk1z\n",
       "wmqnqiSX6tIcp8uRKK1fkY/HAy++fc3pUkQkhhYNZsuyfgg0zLr6Mcuy1luW9Up8ypJ4OnOlm9Hx\n",
       "ae7cUqklHhNYbnYad6wr4dL1Phpu9DtdjojESLTHmIuNMfuNMd+MaTWyLI6eawPgzi0VDlcit+vD\n",
       "u6oA+KVazSJJI6pgtizracuyDgElxpj9Ma5J4igYDPLO+TZys9JujuyVxLVjfTGlhdn86lgTQ6OT\n",
       "TpcjIjEQcTAbYx4zxswcc+4G6mJbksTTtdYBOntH2b2pgjSfBuUnOp/Xyyc/sIaxiWleervR6XJE\n",
       "JAaieWduAA7al0uAo7ErR+LtyEw39uZKhyuRWPno3TVkZvj42ZsNTE9r/myRRLeUUdkPA3uMMV8D\n",
       "sLuwD9it5i7Lsk7FuUaJoSPn2/B5PezeWO50KRIjeTkZ7N+zis7eUQ6fbXW6HBG5TYtO+WRZ1nPA\n",
       "c7Ouez5uFUnc9A+Nc7mpjy11JeRp0Yqk8qn76vj5W9d44bUGPrhjhdPliMht0EHGFHL6cifBIOwy\n",
       "ai0nm5Xl+ezZVMGFaz1cut7rdDkichsUzCnkhNUBwE4Fc1L6zP2hcZg/ebXe4UpE5HZo9YIkEQgE\n",
       "GBycf6WhYDDIiYvtFOSkU5IH/f2hCSn6+/sJBoPLVabE0Y71Zaxb6eetd1toah9kVUW+0yWJSBQU\n",
       "zElicHCQF149T07O3Es49g5O0Ds4QV1VLq8cvX7z+q7OdnLz/OTpPTzheTweHj1g+MO/OsKPD13i\n",
       "//zSbqdLEpEoKJiTSE5OLrl5BXPedqkl1I29ZmXxe+4zPKz1fJPJXVsqqa0q4LUTzXzxQUN1aZ7T\n",
       "JYlIhHSMOUU0tYUCeFW5msbJzOv18Oj+DQSC8Nyhy06XIyJRUDCngMmpAC1dw5T4s8jNTne6HImz\n",
       "e3dUs6Isj1eONdHeM+J0OSISIQVzCmjpGmI6EGS1BgOlBJ/Xw+cf2MB0IMg/vnTR6XJEJEIK5hRw\n",
       "sxtbwZwy7t+5ktqqAl451qQlIUUSjII5BTR1DJHm81BdOveIbUk+Pq+Hr35qC8Eg/PkLZ3VKnEgC\n",
       "UTAnuZGxSXoGxqgqycWn1aRSyk5Tzu6N5bxb38XRC+1OlyMiS6R36iR3o3MIgBXlOm0mFf32p7bg\n",
       "9cBf/vQcU1p5SiQhKJiTXHNHKJhX6jSplFRTWcCDd9fS3DHEC69dcbocEVkCBXOSa+4YIiPNS1lh\n",
       "ttOliEN+8+ObKMzL5O9/efFmD4qIuJeCOYkNDE8wMDxBdVkeXq/H6XLEIQW5GXzjc9uZmArw//zo\n",
       "JIGABoKJuJmCOYnNtI5W6vhyyvvAjmru3V7F+as9/Pytq06XIyILUDAnsRsdCma55Ruf3U5+Tjp/\n",
       "/a/nae49+CUpAAAcCElEQVTQHOkibqVgTlLBYJDmziGyM9MoLshyuhxxgaKCLH7nczsYm5jmD//q\n",
       "KKPjU06XJCJzUDAnqf6hCYZHJ1lRlovHo+PLEnLfzhV88oNraGof5E9/fEoTj4i4kII5Sc10Va7Q\n",
       "aVIyy1c/tZVNtcW8duoGP32jwelyRGQWBXOSujnwq0zHl+W90tO8fPsreyjMy+TPXzjH0fNtTpck\n",
       "ImEUzEkoGAxyo3OYnKw0/HkZTpcjLlTiz+b3fvtO0nxenvibY1xs7HG6JBGxKZiTUP/QBKPjU1SX\n",
       "5un4ssxrY20x3/7KHqamA/yXP3ubpnaN1BZxAwVzEro5P3aZVpOShd25uZL/7ZEdDI5M8p+eeouW\n",
       "Ls0MJuI0BXMSaukaBqCqVMeXZXEH7qzhq5/aQnf/GL/3/Tdptf9+RMQZaU4XILEVDAZp6RwiK8NH\n",
       "cUGm0+WICwUCAQYH39tt/ZGdZYyM1vHMwQa+8z9f5/e+cgcVxe+fXz0/Px+vV5/nReJJwZxkBkcm\n",
       "GRqdpK7ar+PLMqfBwUFeePU8OTnvPdSRlQa7NxRx/FIvv/9nx/jYnVXk56TfvH1kZJhP79uM3+9f\n",
       "7pJFUoqCOcm02MeXq3V8WRaQk5NLbl7B+66/e3sBGRlZHD7byovH2vnsh9ZSkKueF5HlpGBOMjPH\n",
       "l6tLFcwSnV0bywkS5O2zbfzTr6/cDOdAIEB/f39Uj6kucJGlUzAnmRudQ2SkeynR+styG3ZvrADg\n",
       "7bNt/MtrDXxu3zpGR4d58XAvxcUlET2WusBFIqNgTiLDY1MMDE9QU5mPV8eX5Tbt3ljB1HSQYxfa\n",
       "+ekbDXxwUw7Z2XN3gYtI7KhvKYm094wBUK1pOCVG7txcwba1JXT3j/HGuQGmpgNOlySS9BTMSaS9\n",
       "1w5mHV+WGPF4PNx3xwrWryqke3CKdy72a0UqkThTMCeRtp4x0nxeyopynC5FkojH42H/3tWU+dNo\n",
       "7hrj6Pl2p0sSSWoK5iTRPzxB//AkVSU5+Lw6viyx5fN6uGdTAblZPo5eaKe+uc/pkkSS1pIGfxlj\n",
       "nrQs69thPz8E9AF1lmU9Ha/iZOms66HTWHR8OXVEe/pSf3903dGZ6V4+uLWIV071cOhoE0X5mZT4\n",
       "NfpfJNYWDWZjzOPAQ8C37Z93AViWdcgYU2eM2WlZ1sn4limLudgYasHo+HLqiPb0pa7OdnLz/OTl\n",
       "R/6chbnpHNi7ml8cvsZL71znkf3rSfOp400klhb9j7Is64dAQ9hVjwK99uUG4EAc6pIIXWzsw+v1\n",
       "UFGs48upZOb0pUi+snNu72+kboWfbWtL6BkY4813W2L0SkRkRjQfdQuB8FXVI/u4LjE3NDJBU/sw\n",
       "Zf5MfGq9yDK4d3s1xQVZnL3SzdWW6GYDE5G5RfsurtFFLnL+ag9BoLI4y+lSJEWk+bw8eNdqfF4P\n",
       "rxxrYmRs0umSRJJGNMHcBxTbl4uA7tiVI9E42xD6FVQomGUZlfizuWdbFWMT07x+Sl3aIrESTTD/\n",
       "CKizL68BXo5dORKNs1e68Hk9lBdqFSBZXtvWlVJZnEN9c5+6tEViZNFgNsY8DOwxxnwNYGYEtjFm\n",
       "P9BnWdap+JYoCxkZm+TKjX7qqvM1OlaWndfjYd/uVXg9Hl47eYOJyWmnSxJJeIueLmVZ1nPAc7Ou\n",
       "mzl3+VA8ipKlu3itl0AgyMaaQqdLkRRV4s9i98Zyjl5o5/DZVj60c6XTJYkkNDWxEtzZhi4ANtZo\n",
       "ST1xzu6N5RTlZ3L2SjcdvSNOlyOS0BTMCe5MfRder4cNqxTM4hyfz8v9O1cA8PqpG1roQuQ2KJgT\n",
       "2Nj4FJeb+li30k92ppbWFmetLM9n7Qo/bd0jXGrSXNoi0VIwJ7CLjT1MB4JsrSt1uhQRIDTxiM/r\n",
       "4a13WzQQTCRKCuYEduZK6PzlbesUzOIOBbkZ7DLljIxNcfyilocUiYaCOYGdvdKF1wOb1xQvfmeR\n",
       "ZbLTlJOXnc7py10MDE84XY5IwlEwJ6ixiSkuXe+jboWfnKx0p8sRuSk9zcvdWyuZDgQ5cq7N6XJE\n",
       "Eo6COUFZjb1MTQfYulbd2OI+G1YXUeLPwrreS/fAuNPliCQUBXOCOjtzfFnBLC7k8Xi4d1s1AMet\n",
       "3kXuLSLhFMwJ6mxDFx4PbK7TqpviTqsr81lZnkdL9yhnrvQsvoGIAArmhDQxOY3V2Muaaj952Tq+\n",
       "LO5177YqAJ451EAgoElHRJZCwZyArOu9TE4F2LpWrWVxt7KiHOqqcmlsG+K1k81OlyOSEBTMCehs\n",
       "fWh+bE0sIolg5/oi0nwe/vYXFzTpiMgSKJgT0NmGbjwe1GKWhJCfk84De1fQ0TvKz9+66nQ5Iq6n\n",
       "YE4wk1PTXLzWQ01lAfk5GU6XI7Ikn7mvhtzsdH708iWGRjTpiMhCFMwJ5tL1PiamApqGUxJKXnY6\n",
       "j3xkPUOjkzx76LLT5Yi4moI5wZy9MnN8Wd3Yklg+dV8dpYXZ/PSNBjp6tGazyHwUzAlmZmKRLQpm\n",
       "STAZ6T5+8+ObmJwK8Le/uOB0OSKupWBOIJNTAc5f66GmMh9/XqbT5YhEbN+uldSt8PPqiWbqm7Vm\n",
       "s8hcFMwJpL6pj4nJac2PLQnL6/Xw1U9uAeAvf3qOYFCTjojMpmBOIGdmji/rNClJYDs2lLF7Yznv\n",
       "1ndx/GKH0+WIuI6COYHcGvilFrMktt/+5Ba8HvjLn51jejrgdDkirqJgThBT0wEuXOthVUUehfk6\n",
       "viyJraaqgP17V3O9bZCDR5ucLkfEVRTMCcJq7GVsYpod68qcLkUkJr78sY1kZvj4hxcvMDY+5XQ5\n",
       "Iq6hYE4QJy+FjsXt2KBgluRQ4s/mNz60lp6Bcf75tStOlyPiGgrmBHH6Uider4dtGpEtSeRz+9ZR\n",
       "mJfJT351md6BMafLEXGFNKcLkPeanJzkzPl68Nz6zDQ2Mc2l672sKM3Gutww53aDA/1MT2vubEks\n",
       "OVnpfOljG/n+c6f565+f5//4wi6nSxJxnILZZcbHx2loHycvv/DmdQ0t/QSCUFFaQMfw3AO/2jsm\n",
       "SEv3LFeZIjHz4F01/PKtaxw62sTH7qllY02x0yWJOEpd2QmguX0QgFXleQ5XIhK5QCBAf3//vF9D\n",
       "gwN8+cE1AHz/uVP09vXdvC0Q0KlUknrUYk4ATe1DpKd5qSjJdboUkYiNjg7z4uFeiosXnhinriqX\n",
       "hpZBfvCTc2xYlc/IyDCf3rcZv9+/TJWKuIOC2eUGRyboGxqnpjIfn1dd1ZKYsrNzyc0rWPA+9+/K\n",
       "punFi5y43MumtRXkLFNtIm6jrmyXa5rpxq7Id7gSkfjKzU5n76YKxiameevdVqfLEXGMgtnlmjuG\n",
       "AAWzpIYd68soLcziwrUeWrtHnS5HxBEKZhcLBIM0tQ+Sm5VGkabhlBTg9XrYt2sVHuDwuS4mpqad\n",
       "Lklk2SmYXayjZ4SxiWlWVxbg8ej4sqSGiuIctq8rZWBkin95/brT5YgsOwWzizW2DgBQW7XwoBmR\n",
       "ZHPn1kpys3z87M3r1Df3OV2OyLKKKpiNMU/a3x+LbTkS7lrbIF6Ph5U6f1lSTEaajw9sLWM6EORP\n",
       "/uEEE5Pq0pbUEW2L+TFjzGVAM8/HyfDoJF19o1SX5ZKR7nO6HJFlV12azQN7q2lqH+TvfnnR6XJE\n",
       "lk3UwWxZ1nrLsl6JaTVyU2OburFFPr9/LdWlufzzr+s5e6XL6XJElkW0wVxsjNlvjPlmTKuRm67Z\n",
       "x5drKhXMkrqyMnz8hy/twgP8yT+eYHBkwumSROIuqmC2LOtpy7IOASXGmP0xrinlTQeCNLUP4c/L\n",
       "oFCnSUmK21hTzBceMHT2jvI/njlJMBh0uiSRuIo4mI0xjxljHrJ/7AbqYluStPeMMTUdoFatZREA\n",
       "Hn3AsH1dKe+ca+NfXpt76VORZBFNi7kBOGhfLgGOxq4cAWjuDM14VKPjyyIA+Lwe/uOXd1OYn8lf\n",
       "/ewcFxt7nC5JJG4iDma7C/uA3WrusizrVOzLSl3BYJDrHSNkpHmpLtVqUiIzigqy+I9f3k0gGOSP\n",
       "/uooPQNjTpckEhfRHmN+3v7641gXlOoaWgYZHpumttqPz6f5X0TC7Vhfxm/9m830DIzx3/7yHZ3f\n",
       "LElJ7/wu8865DgDWrtQatCJz+ey+dXx490ouXe/jT589pcFgknQUzC4SDAZ553wHaT4Pq7WalMic\n",
       "PB4P//6RO9iwupBfHW/m2UOXnS5JJKYUzC7ScKOfjt5RVpZlk6ZubJF5ZaT7+L9+605KC7P5219c\n",
       "4OCRRqdLEokZvfu7yJvvtgBQW5HjcCUi7lfiz+a/PH4P+Tnp/L/PnubI+TanSxKJCQWzSwSDQd48\n",
       "3UJmupcVZdlOlyOSEFZV5PP7X7ubNJ+XJ//mGOcaup0uSeS2KZhdorFtkJauYe7YUKpubJEIbKwp\n",
       "5jtf2cP0dIA/ePqwwlkSnhLAJd44dQOAuzaXO1yJiDsEAgH6+/uX9LVhRTb//uHNTE7Z4awFLySB\n",
       "pTldgITmxj50rInszDR2bijl1WODTpck4rjR0WFePNxLcXHJkre5f3sZr57q4A/+7G3+0/96F9vX\n",
       "lcWxQpH4UDC7wLuXO+nqG+XBu2rIytDayyIzsrNzyc1b+tS0m9cVEARef7eT//zDt/nmv93Nvdur\n",
       "41egSByoK9sFDh69DsCBvasdrkQk8dVW5vLNL20jzefhyb85yi8PX3O6JJGIKJgdNjQ6ydtnWllR\n",
       "lsfG2iKnyxFJClvrivlvv/MB8nIy+J/PneYvfnqO6YBmCJPEoK5sh71+spmJqQD7967C4/E4XY5I\n",
       "wpsZNFbh9/P7v3UH//2ZM/zTq/U0NPfwuw9tJidz/re9/Px8vF61V8RZCmaHHTx6Ha8HPrJnldOl\n",
       "iCSF2YPG9t1Rxq9Pd3K6vodv/uk77LujnKL8jPdtNzIyzKf3bcbv1zz14iwFs4Ma2wa4dL2PPZsq\n",
       "KPFrUhGRWAkfNJYLfOb+Qt4608rpy53869st3HfHCjbVFquXSlxJfTYO+tc3rwJw4E4N+hKJJ6/X\n",
       "wwd3VPPxe2rxeb386ngzLx+5ztj4lNOlibyPWswO6R8a59DRJsqLc7h7S6XT5YikhLoVfkoLs3np\n",
       "nUYuN/Vxo3OIfbtWsqZa3dfiHmoxO+QXh68xMTnNZ+6rw6cpOEWWTUFuBp/bt457tlUxNjHNz9+6\n",
       "xotvNzI8ptazuINazA6YmJzmX9+4Sm5WmrqxRRzg9XrYZcqpqSzgV8ebqG/u41prPz5fOo8+uJn0\n",
       "NE30I85RU80BvzreTN/QOB+7p5acrHSnyxFJWSX+LB768Do+vHslPq+HZw418I0nX+GVY00671kc\n",
       "oxbzMgsEgvzLa/X4vB4+dV+d0+WIpDyPx8PmNSVU+r30Dgc4eKyF//sfT/CTX13m0QMb+MD2ah1u\n",
       "kmWlv7ZldvhsK03tQ9y/c4VOkRJxkcwMH//2o+t46jv7ObB3NU3tg3zv747zjScP8fO3rjIyNul0\n",
       "iZIiFMzLaHIqwF//63l8Xg+ff8A4XY6IzKG8OIf//Qs7+cF3DvDxe2rp7h/j/3v+XX7rv7zInz57\n",
       "ivqmPqdLlCSnruxl9MvD12jtGuaTH1jDirI8p8sRkQVUleby7x7ewRcfNLz4TiMvvdPIi2+HvupW\n",
       "+PnY3TXcv3MludkaJyKxpWBeJkOjk/zjSxY5WWl84UG1lkXcZmaO7dm8wMfvrOSjeyo4c6WHV060\n",
       "cvJSF99//l2e/uczbF9XzId2r+auLVUazCkxoWBeJs8dusTgyARf+cQm/HmZTpcjIrPMnmN7PtvW\n",
       "5LO2Kpv6G0M0tA5x3OrmuNVNetppdm8s54M7VrB3c4VCWqKmYF4GzR2DvPB6A6WF2Xz6/rVOlyMi\n",
       "8wifY3shuXlQVlrMPTvgRlsXXl86x6xu3j7bxttn28hI87J7UwX32SGdtcCKViKz6a8lzqamA/z3\n",
       "fzjB5FSAr31mK5npmrhAJJkU5mVw4M4afvvTO2hsG+DN0y28cfoGh8+0cvhMKxnpPu7cXMF9d6xg\n",
       "96YKvQfIohTMcfbMyxb1TX18ZM8qPrC92ulyRCSOaioLqKks4Esf3Uhj2wCvn7rBG6du8MbpFt44\n",
       "3UJ2po+7tlZx3x0r2LmhnPQ0nRgj76dgjqOLjT08e/AS5UXZPP4b25wuR0TiYL5BY4XZ8Kl7qvnk\n",
       "3VVcbx/i8NkO3jnfyavHm3n1eDM5WWnsNiXcu7WCLWuK8HqXvgRlfn4+Xq9CPVkpmOOkb3CcP/67\n",
       "4wSB//DFXTqlQiRJLXXQWGlBGp+4q5Ku/nGutg7T0DLI66fbef10O9mZPuqqcqmrzqM4P2PBdaJH\n",
       "Rob59L7N+P1aEStZKZjjYGRskj/4s8O094zwxQcNW9eWOl2SiMTRUgeNAeTlQ+1K2NzWTM8gtA9C\n",
       "fVMf564NcO7aAMUFWZjVRWxYXUheTkacKxc3UjDH2OTUNH/4V0e40tzPg3fV8EWdsywic/B4PJQV\n",
       "prNpfTn37aimsW0Qq7GXa60DHD7byuGzrawoy8PUFLF2hZ8MDRpLGQrmGBobn+KP//44py93cdeW\n",
       "Sv7dQ9sX7JISEQHw+bzUrfBTt8LP2MQU9c39XGrs5UbnEDc6h/j1iWbWVPsxNUWU5GrVq2SnYI6R\n",
       "jp4R/utfvsPVlgG2ryvlm7+5RyvSiEjEsjLS2FpXwta6EvqHxrl0vY9L13upb+6jvrmPrAwvbX2T\n",
       "PHh3HetXRTZoTBKDgjkGTlgd/Mk/HKd/aIKP31PL45/dRppCWURukz8vk72bK9izqZyO3lGs671c\n",
       "auzhpSM3eOnIDYryM9m9sYI9myvYuaFMs40liaiC2RjzENAH1FmW9XRsS0oc7T0j/PkLZzl8phWf\n",
       "18PvPLSdT9y7xumyRCTJeDweKopzqCjOYWddHmXF+Zys7+P4xXYOHr3OwaPXSfOF1pXeacrZWFPE\n",
       "ulWFZGWo7ZWIIv6tGWN2AViWdcgYU2eM2WlZ1snYl+Ze11oH+PlbVzl05DoTUwE21Rbz9c9uY+3K\n",
       "QqdLE5Ek5/V62LmhhH176wgEgtQ393H0fDvHLrTxbn0X79Z3AeDzelhTXcDGmmJMbTF11QVUleZp\n",
       "UpMEEM3HqUeBl+zLDcABIKmDORgMcq11gJNWB4fPtHKxsReA0sJs/pdPbOJDu1ZqkJeILIvZE5pU\n",
       "+L188p4qPnlPFX1D41jX+7ncNMDl5n6utgxQ39zPz968CoRCvaokl1UVeawsz2dleR7lRTmUFGZR\n",
       "6s/WyG+XiCaYC4GesJ8XPqs+QUwHggyPTtI3OEZX3xidfaM0dwxyrWWAq6399A9N3LzvLlPOx++t\n",
       "Ze+mCg3wEpFltZQJTSqL0qksKuWezcX0DEzQ2TdOV98IaekZtHSPcqNzCGh733b+vAxK/NkUF2RR\n",
       "kJsR9pVJQW46OVnpZGemkZnhIzsjjazMNLIyfKSnedU4iaFoD0As9TfgA2hre/8fwHJr7RrmmZct\n",
       "RsenmJwKMDUdYHIq9DU+Oc3Y+NS825b4s9iztojNdSVsXlOMPzcTmKa1tSXmdY6MjNDb3cH42FhE\n",
       "2/X1djE1NcXo8PunBlxIT08XXq+PsZEBbZdg2yVCjdouftt5gtNLun86UF0ARenjHLh7NXl5eQyM\n",
       "TNDWNUJr9zB9A2N0D4zTNzhGz8AADVc7saaW9tgzPF4Pmek+MtO9+Hxe0rxevF4PaT4PHq+HNK8H\n",
       "nzd028wgcg83L9z65oHMDB9ffMBQVJAVUQ1uEpZ5UXVBRBPMfUCxfbkI6F7gvlUAX/7yl6N4Gve4\n",
       "ChxzuggRkdv0p04XsETPf9/pCmKmCrgS6UbRBPOPgD3AIWAN8PIC9z0K3Ae0ApF9BBMREUlMPkKh\n",
       "fDSajT3BYOSzyBhjHiM08CulT5cSERGJtaiCWUREROJDQ4pFRERcRNPCiCSwxWbhW+h2Y8w3Lcv6\n",
       "3vJUKpJcljIDpjHmScuyvh3JNqBgXlbRvImm4vSnUe6nx+yb11qW9Z1lK9ZBi83Ct9DtxpgDwANA\n",
       "SgRzlH9TuwgNcC3W/978t6foe9SiM2AaYx4HHgK+vdRtZsS8K9sY85AxZn/YG+WitxtjHrO/noh1\n",
       "PW4R/kuxf9652O2LbZOMotxP+4GD9ptCnf1zKngU6LUvz8zCt9TbU2ZwSTR/U/ZN37Es63mgUP97\n",
       "8/7v7QQa7OsaUmE/2Rb738OyrB/aty15mxkxDWa9qS4omjfRRwl9Ep1vm2QUzX6qC7tfg/1zKlhs\n",
       "Fr45b7c/qR+Kc21uEvHflN0KPApgWdb3UmQ9gGg/6D1pf69Lkf0E0c2AueRtYt1i1pvq/KJ5E03K\n",
       "6U8XEfF+sizr6bAutF1Eee5gglpsFr65bi+e47pkFs3/3l6gxG48fDPO9blFNP97J4GrxpieWbel\n",
       "gmjmIF3SNrEOZr2pLiyaN9FUFNV+sntkjluWdSr2JbnSYrPwhd9eCHSnYGt5RjR/U11hx+Qfin1J\n",
       "rhTRfjLG+IF64DHgaWNMqqx7G8kMmBFvE4/TpfSmOreI30SXsE0yimQ/zb59v2VZ341vea7yI271\n",
       "MN2chc8YUzjH7XXAQUKHix6yB6YUp8gxwWj+97oJzcY7c/veONfoBtHsp8eBp+xj8Y8ADy9DnW6w\n",
       "2P/ekreZS8TBHDZQK/xr5tOk3lTnF+mb6MvzbZPkItlP4bc/PnPqTxKPU3iPsNbcfqAv7EPtwXlu\n",
       "P2lZ1vP2m2gQ8JMag8Ci+d97Luy6QuDIslTqrGg+6GFZ1oD9/RC3xsQktcX+9+zbHgb2GGO+tsg2\n",
       "7xPTmb/sT997LMt62j4u87JlWaeMMYWWZfUtcPvj9gg2jDH7k7Wrba6pTI0xxyzL2rPA7Sk3/Wmk\n",
       "+8k+9efHhA6TFAMPW5b1ijPVixvdxv9eD6H3rGRuNNwU5X76pn1dypxWFm8xn5JTb6oiIiLR01zZ\n",
       "IiIiLqK5skVERFxEwSwiIuIiCmYREREXUTCLiIi4iIJZRETERRTMIi5kjCk0xrxkX66buSwiyU/B\n",
       "LOJON89jtCyrwbKsB+e743xLrIpIYlIwi7hTJAuafD1uVYjIsktzugARucUY8zKh1nJD2HWFwI8t\n",
       "y3rQninvW/btVwit4FZnjPkx8BRwDLg5LaJlWY/a2x8iNPfxAeCP7PmyMcY8CcwsZPGEZVmvGGOe\n",
       "IjRXcp+9/Xuec2ZOchGJDwWziEvYKz4dsyzru/byeU/NcbeHubWaz8x2ByzLejTsPo/a1//AnjD/\n",
       "OLDGsqzvhD3u8/Yk+wXh3eR2Db2WZX09bIGaB2Y/p4jEj7qyRdxjF7dWp+md5z7fBh4wxtTPd2zZ\n",
       "GPO4MeYJYA+3VpA6Fva4Myu8HQh7vvAa6owxPyAUyEVLeU4RiR21mEXc4zihMDzEreX13sOyrH7g\n",
       "GwDGmHrCuq3t6x4H/Hbr+AkWPlb9sv18M93afrsG5lglaN7nFJHYUjCLuIS92tpL9qlRDbx3reQg\n",
       "3AzemcXof2B/P2Zv8yxwFHjWGLOWUIt5rnWEg/bzPW+MeSDsVKwn7Bp+YIx5hNDauk8R+pDwyKzn\n",
       "FJE40epSIiIiLqJjzCIiIi6iYBYREXERBbOIiIiLKJhFRERcRMEsIiLiIgpmERERF1Ewi4iIuIiC\n",
       "WURExEX+f1eNYmLzA1ILAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac4ef10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(distances, axlabel=\"distances\", )\n",
    "title(\"Variablility of distance from simulations\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're going to set up the ABC PMC sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import abcpmc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a prior we're going to use a gaussian prior using our best guess about the distribution of the means. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "prior = abcpmc.GaussianPrior(mu=[1.0, 1.0], sigma=np.eye(2) * 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As threshold $\\epsilon$ we're going to use the $\\alpha^{th}$ percentile of the sorted distances of the particles of the current iteration. The simplest way to do this is to define a constant $\\epsilon$ and iteratively adapt the theshold. As starting value we're going to define a sufficiently high value so that the acceptance ratio is reasonable and we will sample for T iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alpha = 75\n",
    "T = 20\n",
    "eps_start = 1.0\n",
    "eps = abcpmc.ConstEps(T, eps_start)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we create an instance of your sampler. We want to use 5000 particles and the functions we defined above. Additionally we're going to make use of the built-in parallelization and use 7 cores for the sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sampler = abcpmc.Sampler(N=5000, Y=data, postfn=create_new_sample, dist=dist_measure, threads=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optionally, we can customize the proposal creation. Here we're going to use a \"Optimal Local Covariance Matrix\"-kernel (OLCM) as proposed by (Fillipi et al. 2012). This has shown to yield a high acceptance ratio togheter with a faster decrease of the thresold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sampler.particle_proposal_cls = abcpmc.OLCMParticleProposal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're ready to sample. All we need to do is to iterate over the yielded values of your sampler instance. The sample function returns a namedtuple per iteration that contains all the information that we're interestend in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def launch():\n",
    "    eps = abcpmc.ConstEps(T, eps_start)\n",
    "\n",
    "    pools = []\n",
    "    for pool in sampler.sample(prior, eps):\n",
    "        print(\"T: {0}, eps: {1:>.4f}, ratio: {2:>.4f}\".format(pool.t, eps(pool.eps), pool.ratio))\n",
    "\n",
    "        for i, (mean, std) in enumerate(zip(*abcpmc.weighted_avg_and_std(pool.thetas, pool.ws, axis=0))):\n",
    "            print(u\"    theta[{0}]: {1:>.4f} \\u00B1 {2:>.4f}\".format(i, mean,std))\n",
    "\n",
    "        eps.eps = np.percentile(pool.dists, alpha) # reduce eps value\n",
    "        pools.append(pool)\n",
    "    sampler.close()\n",
    "    return pools\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T: 0, eps: 1.0000, ratio: 0.3780\n",
      "    theta[0]: 1.0626 ± 0.3877\n",
      "    theta[1]: 1.3582 ± 0.3641\n",
      "T: 1, eps: 0.8446, ratio: 0.4938\n",
      "    theta[0]: 1.0789 ± 0.3098\n",
      "    theta[1]: 1.3920 ± 0.3021\n",
      "T: 2, eps: 0.6796, ratio: 0.4560\n",
      "    theta[0]: 1.0735 ± 0.2489\n",
      "    theta[1]: 1.4098 ± 0.2668\n",
      "T: 3, eps: 0.5569, ratio: 0.4649\n",
      "    theta[0]: 1.0690 ± 0.2053\n",
      "    theta[1]: 1.4399 ± 0.2193\n",
      "T: 4, eps: 0.4579, ratio: 0.4680\n",
      "    theta[0]: 1.0848 ± 0.1721\n",
      "    theta[1]: 1.4416 ± 0.1831\n",
      "T: 5, eps: 0.3767, ratio: 0.4684\n",
      "    theta[0]: 1.0771 ± 0.1425\n",
      "    theta[1]: 1.4640 ± 0.1460\n",
      "T: 6, eps: 0.3099, ratio: 0.4490\n",
      "    theta[0]: 1.0817 ± 0.1218\n",
      "    theta[1]: 1.4691 ± 0.1241\n",
      "T: 7, eps: 0.2595, ratio: 0.4433\n",
      "    theta[0]: 1.0861 ± 0.0992\n",
      "    theta[1]: 1.4734 ± 0.1009\n",
      "T: 8, eps: 0.2080, ratio: 0.4411\n",
      "    theta[0]: 1.0898 ± 0.0799\n",
      "    theta[1]: 1.4799 ± 0.0825\n",
      "T: 9, eps: 0.1688, ratio: 0.4418\n",
      "    theta[0]: 1.0921 ± 0.0718\n",
      "    theta[1]: 1.4926 ± 0.0678\n",
      "T: 10, eps: 0.1419, ratio: 0.4369\n",
      "    theta[0]: 1.0880 ± 0.0562\n",
      "    theta[1]: 1.4946 ± 0.0581\n",
      "T: 11, eps: 0.1181, ratio: 0.4272\n",
      "    theta[0]: 1.0927 ± 0.0503\n",
      "    theta[1]: 1.4934 ± 0.0483\n",
      "T: 12, eps: 0.0962, ratio: 0.3870\n",
      "    theta[0]: 1.0927 ± 0.0408\n",
      "    theta[1]: 1.4930 ± 0.0394\n",
      "T: 13, eps: 0.0792, ratio: 0.3830\n",
      "    theta[0]: 1.0903 ± 0.0338\n",
      "    theta[1]: 1.4931 ± 0.0330\n",
      "T: 14, eps: 0.0647, ratio: 0.3789\n",
      "    theta[0]: 1.0918 ± 0.0276\n",
      "    theta[1]: 1.4929 ± 0.0288\n",
      "T: 15, eps: 0.0530, ratio: 0.3490\n",
      "    theta[0]: 1.0930 ± 0.0249\n",
      "    theta[1]: 1.4935 ± 0.0248\n",
      "T: 16, eps: 0.0443, ratio: 0.3006\n",
      "    theta[0]: 1.0928 ± 0.0224\n",
      "    theta[1]: 1.4936 ± 0.0222\n",
      "T: 17, eps: 0.0374, ratio: 0.2688\n",
      "    theta[0]: 1.0926 ± 0.0188\n",
      "    theta[1]: 1.4944 ± 0.0209\n",
      "T: 18, eps: 0.0313, ratio: 0.2617\n",
      "    theta[0]: 1.0912 ± 0.0174\n",
      "    theta[1]: 1.4945 ± 0.0188\n",
      "T: 19, eps: 0.0263, ratio: 0.2039\n",
      "    theta[0]: 1.0924 ± 0.0170\n",
      "    theta[1]: 1.4953 ± 0.0167\n",
      "took 94.172825098\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "t0 = time.time()\n",
    "pools = launch()\n",
    "print \"took\", (time.time() - t0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Postprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How did the sampled values evolve over the iterations? As the threshold is decreasing we expect the errors to shrink while the means converge to the true means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAeUAAAFVCAYAAADR+vcXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XuQXOV95vHndPdMz03SaITQHUkj0MtdSB5xFcZYwiS2\n",
       "2c1GMmzMbmo3i3C2nMqWnSLg2Gtnk3gDixPHWyEuEM5uUkbENmzVFl67CkvYgLgKLISQ0Suk0QXd\n",
       "L6ORRppbd593/+jTPT2jufTM9GjeUX8/VNPnnPf0md90j/rp9+23TwfOOQEAgPEXG+8CAABAFqEM\n",
       "AIAnCGUAADxBKAMA4ImiQtkY89ggbauNMSuNMWtLVxYAAOVnyFA2xjwoafUAbUslNVtrN0pqjtYB\n",
       "AMAIDBnK1tqnJDUPskuuF91ord1SkqoAAChDo3pPOQrhPcaYFkktpSkJAIDyNKpQNsbUS9olaa2k\n",
       "dcaYhSWpCgCAMpQY5e3XSnrSWnvGGNMqaY2kx/vb0RiTlLRc0mFJmVH+XAAAfBeXNEvSZmttVzE3\n",
       "GFEoG2PqrbWtkmStPRNdbzTGNA5ys+WSXh3JzwMAYAK7XdKmYnYcMpSNMWskNRljHrDWPh1t3iCp\n",
       "yVr7uDHmIWUngjVYa9cNcqjDkvTMM89o5syZxdQGAMCEdeTIEd1///1SlH/FGDKUrbXPSXquz7am\n",
       "guV+h6v7kZGkmTNnau7cucXWBwDARFf0W7ac0QsAAE8QygAAeIJQBgDAE4QyAACeIJQBAPAEoQwA\n",
       "gCcIZQAAPEEoAwDgCUIZAABPEMoAAHiCUAYAwBOEMgAAniCUAQDwBKEMAIAnCGUAADxBKAMA4AlC\n",
       "GQAAT3gZyl9+4ev68gtfH+8yAAC4oLwMZQAAyhGhDACAJwhlAAA8QSgDAOAJQhkAAE8QygAAeKKs\n",
       "QpmPWgEAfFZWoQwAgM8IZQAAPEEoAwDgCUIZAABPEMqjxOQxAECpEMoAAHiCUAYAwBOEMgAAniCU\n",
       "PcV71QBQfghlAAA8QSgDAOAJQhkAAE8QygAAeIJQBgDAE4QyAACeIJQBAPAEoQwAgCeKCmVjzGOD\n",
       "tC0zxqw2xqwtXVkYK5yUBAD8NWQoG2MelLR6kF0esdY+L6neGLO0ZJUBAFBmhgxla+1Tkpr7azPG\n",
       "rJG0OdrvcWvtltKWBwBA+Rjte8pNkqYZY5YaYx4qRUEAAJSrUkz0OpHrIRtjBhvmxkWM96oBYPRG\n",
       "G8onJe2JllslLR/l8QAAKFsjCmVjTH20+Jykxmi5XtLbpSgKAIByVMzs6zWSmowxDxRs3iBJ1to9\n",
       "klqjYesGa+3/GZsyAQC4+CWG2sFa+5yyPeLCbU0Fy+uixedLWxrKXe496ifu+fY4VwIAFwZn9AIA\n",
       "wBOEMgAAniCUAQDwBKEMAIAnCGWUHU50AsBXhDIAAJ4glAEA8AShDJTIWA2LM9wOlA9CGQAATxDK\n",
       "QJmiBw74h1AGAMAThDIAAJ4glAGUDEPiwOgQygAAeIJQBuA9euAoF4QyAACeIJQBlC164PANoQwA\n",
       "JUbYY6QIZQCYAAj68kAoA0AZm2jnbL/YX5wQygCAsudL2BPKAAB4glAGAMATifEuYCA7X96u9W3r\n",
       "9cUvflGStH79ekka1frOX2/X4juuKdnxJEmTVNLj5dZ3vrw9e+B7Snv8iVTvWDxehfVOhL+vNfeu\n",
       "UTpMa9+WZn2v7R90x52fUjpM65cv/0ouCHXjzTcpHWb05ttvKpTT9Tdcr3SY1nvvb1Uop8XmCqXD\n",
       "jOxHVqGc5s2fp3SY0b4D+3XozGHVTK3To688oUOHDiuQtOCyBYoFgfbv3a9AgS6//HLFgph2f7RL\n",
       "gQJdfeVVisVi2vGbHQokXX/d9YrH4np/6/sKFKg92SlJ+qtnvyNJWt60XEEgbd78jgJJN954k2JB\n",
       "oLfeekuSdMvNtyhQoDfefEOBAt12662SAr3++muSAt2+YoUCBdrz/m5J0ltLt0iSXn3lVUnSittX\n",
       "ZNdf3SRJuj2//mq0fnuv9dz+m6L9u6q7JUmPr/9eP/sH+ePl9v/kJz8pSXrllVd6refqueOO7Pqe\n",
       "rbskSW8vfU9OLrt/IN16261yTnrt9dfk5HTLzbfIyemNN9+Qk3TjjTfKOae3N78lJ6mpqUmhC/Xu\n",
       "u+9q34G9mr5ohl7YsUG/3vJrSdLSpUslOW3Z8p4k6YYbbpAkvffeFrle69n2JUuWSJK2bt0qJ6cl\n",
       "S5boXKpDJ/cc0zef/Wtde911cs5p2wfb5OR01dVXK3ShPvzwQzk5LV68WKFC7dy5U07SokWNCuW0\n",
       "e/duOUkLFsxX6ELt3bdPB1sPqm76ZH1n05P6+MDHkqS5c+dKkg4cOCDXaz1qnxOtHzwgSZozZ060\n",
       "fjC/frqzTeda2vRH//JnmjlzppxCHT5yRE5O06dPl3NOx04cl5NTQ0ODnHM6eapFktPkKVPknNPp\n",
       "M6fl5FRbVyvnnM6eO6ezXec0bUqDpNL9+839fQxH4Jwb9o1GwhizQNKejRs35h+IgeTG9Z+459sl\n",
       "rWEsjjuRap1ox51ItY7muJkwo+PtLTrcdlSH247pUHR9uO2YTrS3lLRG4GIWKFAsCBQEMQVBoJgC\n",
       "xaLl/tdj0f6BTra3anKyVk/+68dKVs+BAwe0cuVKSVpord1bzG287SkDFxPnnFo7z+hw21EdajuW\n",
       "D+DDbcd05NxxZcLMebdpqK7XNZcu1u6WfQoU6HNmpRKxuCpiFUrE4krEEj3X8T7r+etEdJvEee1f\n",
       "/flfSJL+5re/qdCFyrhQoQsVhmG0nlHoXPY62pbbL5NfL9jHOX3/rX+WJD3Q9HsKnZPksv+57H3g\n",
       "lO0EhC7M3y9OknNh1OJ6bueiWzunH3/wU0nSF6793Hn3U6Cg3/s8CPrfXujH216QJN173T3nPV75\n",
       "ZZ3fcendfv7S89t/JinQmms+m33yD2IKFCgIpEBRKEgKgmwoSCrYp2e/wranNj8jSfrDG//9eb9j\n",
       "7980KGgv3Br02/73b/5vSdIf3/IH+RpiQUF4RUGWC69Yv4GXbY9Fv1ssCPTIi38tSXr87m/0V1qf\n",
       "mvp5HAfY96s//wsFkv7us3/eq57cfTdSPkzykghloKRCF2rXyb3ZwD3bO4A7013n7V9bUa3G+nma\n",
       "NWmGZk26VLMmzdDsSZdqZt10VVVUSep5srj32s+XtNbcE1h19HNKIZmolCTdPG9ZyY4pST+1GyRJ\n",
       "n1386ZIe94Udv5Ak/dYVnyrpcX++85eSpM+ZlSU75j9t+YkkqWnO9SU7piRVxiskSdfNuLKkx40F\n",
       "2SlLdcnaEh83+3dbGf2tXWwIZWAA6Uxabd3n1NZ1Vme6zups97le1219lk+0n5KT059t6D38VRGv\n",
       "0Ky6S6PQvVSzCwJ4UmXtqF7dA7i4EMq4qKXDjDpTnepId6oj1anOdJe6Myk55/TirlfUFgVqLnzb\n",
       "us6prTt73ZHuLOpnJGIJTU7WRUN8Md21aEW+5zt70gw11NTnew0A/FTqOSYjRSjDO+lMWu2pDmXC\n",
       "jEI5bT+2MwrUTnWkuvIB25HujAK3K2qLlnMhnO5SKpMa8Oc8/e6z522riCU0OTlJl9ZdosnJWtVV\n",
       "1mlSslaTk3Wqq8xd12lyslaTknWaVFmrZCKpIAjyw8z/Ydm9Y3bfAOXOl/AcK4QySioTZtSR6tS5\n",
       "VLvaU51qT3VkL90d52+LtvdaT3Wou0+Q/rdffreonx0oUFVFUtWJKk2qrNP02mmqTlSpqqJK1Ylk\n",
       "fnnD7lcVU6A/+MS/1aRkrSZV1mXDNlmrZLyS4WSUlbEKuYs9PMcKoYwRO9VxWh8ctdp2bIdOdrQq\n",
       "dKF+7yd/NOzjJGIJ1VZUq6aiWtOqp6qmskrVFdV6//BvFATZWcdViSpVJ6pUXZHMLkdBW1VRpZoo\n",
       "bIsN1Df2vyNJWjF/+bBrBcYLIVceCGUUrb27Q785vlPbjlptO7pDB84czrcFCpQI4jLTF6m2okY1\n",
       "FdWqqahSTWV1tNznUrA9N/uzr55Zx/f02w74igDFSBHKGFAqk5I90awPju3QtqNWu1v25T9fmoxX\n",
       "6oaZV+vaGVfquhlX6vFXv68gCPStO78yzlUDxSM84RtCGXlhGGpP68fadnSHPjhqtePErvz7u7Eg\n",
       "pisaFuRDePG0hUrEe/58eB8WAEbPy1A+cbq4j6JgdJxzOnz2mLYd2aFtx3Zo+7GdOtfdnm+/bMoc\n",
       "XTvD6LoZV+qq6ZerpqJ6HKtFOaNHi3LhZShj5JxzyoQZpV1G6TCtTJhRJgyVDtP5bekwoyfe+id9\n",
       "cNTqZMep/G2n1zTopjk36NoZV+raGUb1VZPH8TcBgPJDKHvGOac9pz7W2e52pcO0vvXS32ZDNgrY\n",
       "bLBmorDN5MM2u5zJv+c7lJf3vqlJlbW6ed4yXT/jSl0740rNqL2EYWiMCj1aYHQIZU8caTumTfs3\n",
       "a9O+zTrUdjS//cPjHykeiysRxLPXsXh+PZmoVG2spv/2WFzxIPvlA/FYLNqW0Ov731E8iOmbd35F\n",
       "8+vncKYpAPAIoTyOWjtO6/WP39WmfZu1q2WvpOx5km+Z9wltP2pVGa/QE/d8u6S9121HPpQkLZw6\n",
       "r2THxMRErxbwD6F8gbV3d+jtg+9p077N2nZsh5xzigUx3TDzaq2Yf6OWz1mi6oqq/Gd0GU4GgPJB\n",
       "KF8A3ZmU3ju8Xa/ue1u/PrRNqTAtSVo8rVEr5i/XzfOWMakKAFBcKBtjHrPWPjzEPg9Zax8vTVkT\n",
       "XxiG2n58pzbt26y3DmxRe6pDkjRn8kzdPv9G3XZZk2bUTR/nKjERMMwMlI8hQ9kY86Ck1ZIGDGVj\n",
       "zCpJd0kq61B2zqn51H5t2rdZr+9/R6c6T0uSplVP1apFK7Tishs1v34OQ9IAgH4NGcrW2qeMMWuG\n",
       "2M2VqJ4JKR1m9JMPfqpN+zfrcNsxSVJdZa1WLbpdKy5briunL2KWMwBgSKN+T9kYs9Rau9EYM+jw\n",
       "9sWiPdWh5pb92t2yT7ta9ua/Hekn2/+fKuMVuvWyJq24bLlumHl1r9NQAgAwlFKkRkMJjuGldCat\n",
       "facPatfJvdrVsle7W/bp4JkjcgUDA4ECVcYr9GDT/bpxzhJVVVSNY8UAgIlsVKGc6yWXqpjxFLpQ\n",
       "h9uOadfJvfle8N7WA0pHM6UlqSqR1NWXXqFFDQt0ecN8XT5tgb654TsKgkCfXHDTOFYPALgYjCiU\n",
       "jTH11tpWSY3GmEZJ0yQ1RCG9paQVjpGW9lbtasn2gHed3Kvdp/apI9XzRRjxWFwLpszVoih8L29Y\n",
       "oNmTZigW6/3eMJO2AAClUszs6zWSmowxD1hrn442b5DUZK19PtpnraQp8njC1/FzJ9We6lAqTOtL\n",
       "//eR/MzonNmTZmj57CX5EJ5fP1eV8YpxqhYTER9dAjBaxcy+fk7Sc322NfVZXydpXWlLG710mNG7\n",
       "h97Xxt2btPXIh/n3gmsrpeVzlujyhgVa1DBfixrmq7ayZpyrBQCUu4tyevCRs8f1UvNr+uWeN3S6\n",
       "84yk7Nmzdh49ILmYnrzv0XGuEACA8100oZzKpLT54FZt2L1JHxyzkqTayhr99hV3amXjbbqsfo7u\n",
       "++GfjHOVAAAMbMKH8qEzR7Sh+TW9vPdNtXWdlSRdNf0KrWy8TTfPXarKROU4VwgAQHEmZCh3p7v1\n",
       "5oEt2tj8mj48/pEkaVKyTp83q7Sy8TbNmTxznCsEAGD4JlQo7289qI3Nr+mVfW/pXHe7JOm6GUYr\n",
       "G1do+ZwlqmC2NIrALGkAvvI+lDvTXXpj/7va0LxJH53cI0maUjVZv3PV3fp0422ayTctAQAuEt6G\n",
       "slOop995Vq/uf1sdqU4FCrR01jVa2bhCy2Zfp0QsPt4lAgBQUl6Gsot3SrFQL+5+RQ3V9frc4k/r\n",
       "zoW3anrttPEuDQCAMeNlKEuSwrgevuNLumHm1YrTKwYAlAEvQznIZL9p6ROzrxvnSgAAuHBiQ+8C\n",
       "AAAuBC97yoDER5cAlB96ygAAeIJQBgDAE4QyAACeIJQBAPAEoQwAgCeYfT1KJ053jncJAICLBKGM\n",
       "kuDjSwAwegxfAwDgCUIZAABPEMoAAHiCUAYAwBOEMgAAniCUAQDwBKEMAIAnCGUAADxBKAMA4AlC\n",
       "GQAATxDKAAB4gnNfe4ovugCA8kNPGQAATxDKAAB4glAGAMATvKdcZjq33pFduGd86wAAnI+eMgAA\n",
       "niCUAQDwBKEMAIAnCGUAADxBKAMA4AlCGQAATxDKAAB4glAGAMATRZ08xBjzmLX24QHa1kaLi6y1\n",
       "j5SssjJXt/fu8S5hWP7TX70oSfrBNz4zzpUAwMQ1ZE/ZGPOgpNUDtK2UtMFau05SY7QOAABGYMhQ\n",
       "ttY+Jal5gOZGSaui5eZoHQAAjMCozn0d9ZBzlkn6l9GVAwBA+SrJRC9jzDJJ71pr3yvF8QAAKEel\n",
       "mn290lr7tRIdC5CUnTyWm0AGAOVgRKFsjKkvWH7QWvt4tMxELwAARqiY2ddrJDUZYx4o2Lwhalsl\n",
       "6VFjzC5jTIskNzZlAgBw8Rtyope19jlJz/XZ1hRdb5DUMDalAQBQXjijF8oO71UD8BWhDACAJwhl\n",
       "AAA8QSgDAOAJQhkoEd6rBjBahDIAAJ4glAHP0QMHygehDACAJwhlAAA8QSgDAOAJQhkAAE8Mee5r\n",
       "DK5u793jXQIwIrnJYz/4xme8PiZQTugpAwDgCUIZgPf4WBjKBaEMAIAnCGUAADxBKAMoWwyLwzeE\n",
       "MgCU2FiEPS8gygOhDABljLD3C6EMACg5wn5kCGUAwIQxVmHvy4sIQhkAAE94G8r7Xv9Q69evz6+v\n",
       "X79+1Ov7Xv+wpMcby/XdW1/S7q0veVPPeNQ7lr//7q0vlfz+oN6J9fc10erdvfUlOeeUCZ1++Mx6\n",
       "PfPMejnn5Jwru7+viVbvcATOuRHdcLiMMQsk7dm4caPmzp076L73/fBPJEk/+nd/U9IaxuK4Y3Wu\n",
       "X47rf61h6NSdyqizO6PO7rQe/vtX5Zz08O8vVzodKpUJlUpnlEqH518y2e3pQdpyF7uvRUEQaMkV\n",
       "01VVGVd1MqHqZEJVyUR+vaoyUbC9Z1tuOVkRVxAEQ94PqXSo9s6UOrrSau9Mq70zpfZouaMzld3W\n",
       "lVZ7R257z7aOzpQOnzgn56SqZPGn1e9TVr86OtNSINXXJVWRiEWXuBKJmCrisYJt2e0DrvfZ93/9\n",
       "dHv2vvhX1yqTcUqHTmEmVDp0ymScMmGoTOiUzoQKQ6d0blsmG46ZTE97bv90xun9j47LSbpyfoMy\n",
       "Yfa2YRSoYTjwdeiyPzd0TmEYKhNKYf72xd+fQcFKULA9WsovB5K606EkKVkZH3Lfoo4ZXZ85161A\n",
       "UsOUasVjQfYSDxSPxRSL1hPxnuVse0zxWNB/e9T20jv7JUl3fmKeQidlMmHPfZtxyrjovux1/4YK\n",
       "Q+Ufi0zBfZ3b52jLOU2qqdQ///lvFXdHF+HAgQNauXKlJC201u4t5jZ8IQUuemHo1NkdBUtXWql0\n",
       "KOec3t5+RB1daXV2Z9TVnc6Ha1d3FLRdfbf1rGdvk+n35z3yxKYx+C2c3vnw6IhvHQSKgjsehXVC\n",
       "p850ycnpwf++Qe1d2XBNRU/Qw1VZEVdNVUJBECgWk2ZdUlvcDYsMmv1Hz8g5qTqZUCoT6lxnWql0\n",
       "d/TCJlN0YA3ku89uGd0BBrBt9wnFAikWCxSLxRSPSbEgtxxE27OXikRMsSAbXNl9gl4B9dHHrZKk\n",
       "qxY0SJJy/Sknp8K+Va6j1e+2/P96brfn0GlJ0rxL61TQnL19wb6DHbNne89+Z9tTkqR4LFAmdEql\n",
       "M9ELmd4vaDIjfPB+9vreYd8mCLL19L6fs4/FBeqfDqmsQrncvtHJOafjpzrUfOi09hw6oz2HTuvk\n",
       "6U45SV/9u5dVPymp+rqkpk6uUn1dMrtesK02epIdD6l0Jt9zaD54Wh1d2UDtyPXKop5ZfrnvpbNn\n",
       "uXOA8PzLf3yr6HoS8SAbZpVx1VVX6pL6bLglK+Oqjq7f2HZIUqDPr1h4fm8t3rvXlhikrfCSiMf0\n",
       "wLd/Ieec/uFPV2Z/p+60Orsy0e8W/Y5daXV0ZfLr2W2ZaN/sfVB4/5xq61QqEyqQ1JXKaFJNpWY0\n",
       "1KgmWaHqqoRqqhKqqapQTTK7XF1VodpoW3WyoL0q2ztPxLPvhOV639/76qdG+RfQW+64T35tVb/t\n",
       "mUxulKFnhKE7lVE6UzgKcf6oxT++8IEk6T9+/pp8L67wOhE9Yfduy/bg+t0W9ei+/D82SsqOQpTq\n",
       "31DuPvj2f76tJMfre9zvfuVTY3Lcp79+16D7OZcdBQgLRyD6hHZudCIMnf7rk69Lkv7yS7f2euHS\n",
       "0+OOnfeCJhbreaEzVL3jrSxCuSuV0b7DZ9TRlVYQSO/uOKra6grVVlWorrpCtdUVqqyIj3eZo5JK\n",
       "Z7T/SJv2RAGcC+JzHale+wWBFASB9hw6o3Rm8F5RIh7LB/XUKKzz63VVqp8cBfikZP5V83lDnwVD\n",
       "m+25UM0NgUbtPWEb7d+Z7lXbf/nbXw3rvkgWDPE2TKnKL+cur2w5qCCQ7ltlVJWMq6oyrmQUuLng\n",
       "zQ0N57bnQmcwH+w+IUn6/c9ePax6ixEEQbamZEJTS3TMi+lrFuPxmOLxmKqGebtnX9whSbrrpvkl\n",
       "rScXxOP1onYiCYJA8UCKx+KqKCKRKhLZf4vzZ00e48rGx0UXymfbu9V86LSaD57W7oPZ6wPHzios\n",
       "GCL583Vvnne7ikTsvKDOX6oSqq3ub3uFMqFTLMi+2rtQ/wBPn+3S3ih4mw+d1t5DZ/Tx0bZew0BB\n",
       "IM2+pE5LF09X45wpWjh7ihbOnqyH/ucrCoJAT3/9Lp3rTKu1rVOtbV061dal1rYutZ7titY78+v7\n",
       "Dp/Rro+LG9a87+s/G/bvEwTZYcmaZEJT6pKaNa1W1VUJfbjnpIIg0F03zT8vWHP7V1f13laVTCg+\n",
       "yKthSdpij0mSfvfOy4ddKwCMpQkbys45nTzdWRC+rWo+eFrHTnX02q+qMi5z2VQ1zpmiV7YckJP0\n",
       "u5+6XOc6UjrbkdK53KWzZ/loyzmlM8N7g+Hf/OkL+aG83BBfdVUUHMneQ3199+u7nnsl6JzTweNn\n",
       "1XzwdL4HnBuC7vs7XjGvPhu8c6aocfZkzZ85ud/JNoWv4OuiFxpzL5005H3d3pnuFdS9grytS7+2\n",
       "R/OTkc4f+swFaM+2wvujqjLR77BSrif34O9cN6zHAgCGy5cRowkRypnQ6VAUTs0HT+d7wmfOdffa\n",
       "b0pdZb5nuGhOvRrnTtHMabX5ntPm3xyRJH1h5eJBf55zTt3psCewCwO8s/e2X717QKFzapwzJT9s\n",
       "e/xUuzq60iOefFKRiCmdCeWc9IePbuzVdsmUKjVdNSPq/U5W4+zs7zjYeyWjFQRBfnRgoADPBei3\n",
       "Hrh5zOoAMHGMVcj5Ep5jxctQDruqFLbV6/vPb832Eg+fOW+m64yGGl3TOE2L5kxRY3RpmFxVkiHk\n",
       "IAiUrIgrWRFXw+TB36XKDYV+548/2Wu7c05d0eSa3PunudDufZ3qM3kp+97q7gOnFcSk22+Ykw3g\n",
       "WVO0YPZkTalLjvr3AzDxEHLlwbtQDkOnzh3LpDChn328V7FYoMtmTMoHb+790brqivEudVCjnZiT\n",
       "63l+9YufKG1hAMYcQYeR8i6UY7FAlZftlDIJPbr6Ac2fOXnCz4wGAKAY3oWyJCWmZj9acsW8Un34\n",
       "AwDOR48WvvEylAGgEOGJcuHtF1IAAFBuCGUAADzB8DWAkmGYGRgdesoAAHiCnjJQpujVAv6hpwwA\n",
       "gCcIZQAAPFHU8LUx5jFr7cMDtK2W1Cqp0Vq7rpTFAWCYGSgnQ/aUjTEPSlo9QNsySbLWbozWl5a0\n",
       "OgAAysiQoWytfUpS8wDN90o6FS03S1pVoroAACg7o519XS+ppWB92iiPB0xYDDMDGK1STPQa/RcY\n",
       "AwCAUYdyq6SGaHmqpJOjPB4AAGVrRKFsjKmPFn8kqTFaXijpF6UoCgCAclTM7Os1kpqMMQ8UbN4g\n",
       "SdbaLdE+KyW1WmvfK0VRdXvvVt3eu0txKAAAJowhJ3pZa5+T9FyfbU0Fy7nPJm8sbWkAAJQXzn2N\n",
       "ssMsaQC+4jSbAAB4glAGAMAThDIAAJ4glAEA8AShDACAJwhlAAA8wUei4C0+ugSg3NBTBgDAE4Qy\n",
       "AACeIJQBAPAEoQwAgCcIZQAAPMHsa5QEM6UBYPToKQMA4AlCGQAATxDKAAB4glAGAMAThDIAAJ5g\n",
       "9nWZYZY0APiLnjIAAJ4glAEA8AShDACAJwhlAAA8QSgDAOAJQhkAAE8QygAAeIJQBgDAE4QyAACe\n",
       "IJQBAPAEoQwAgCc497WnOEc1AJQfesoAAHiCUAYAwBOEMgAAniCUAQDwBKEMAIAnCGUAADxBKAMA\n",
       "4AlCGQAATxDKAAB4gjN6jRJn3gIAlAo9ZQAAPDFkT9kYs1pSq6RGa+264bYDAIDiDNpTNsYskyRr\n",
       "7cZofWmf9qWSmqP25r7tAACgeEMNX98r6VS03CxpVT/7PBZdN1prt5SqMAAAys1QoVwvqaVgfVph\n",
       "YxTCe4wxLX32AwAAw1TMRK9goAZjTL2kXZLWSlpnjFlYqsIAACg3Q4Vyq6SGaHmqpJN92tdKetJa\n",
       "+7ykL0haU9ryAAAoH0OF8o8kNUbLCyX9Qsr3kCVJ1toz0fVGZUMcAACMwKAfibLWbjHGNBljVkpq\n",
       "tda+FzVtkNRkrX3cGPOQspPAGvhIFAAAIzfk55QLgnZjwbamguXHx6AuAADKDmf0AgDAE4QyAACe\n",
       "IJQBAPAEoQwAgCfK6qsb+ZpFAIDP6CkDAOAJQhkAAE8QygAAeIJQBgDAE4QyAACeIJQBAPAEoQwA\n",
       "gCcIZQAAPEEoAwDgCUIZAABPEMoAAHiCUAYAwBOEMgAAniCUAQDwBKEMAIAnCGUAADxBKAMA4AlC\n",
       "GQAATxDKAAB4glAGAMAThDIAAJ4glAEA8AShDACAJxLjXUB/fvCNz4x3CQAAXHD0lAEA8AShDACA\n",
       "JwhlAAA8QSgDAOAJQhkAAE8QygAAeIJQBgDAE4QyAACeIJQBAPAEoQwAgCcIZQAAPEEoAwDgCUIZ\n",
       "AABPDPmHuyo2AAAC+klEQVQtUcaY1ZJaJTVaa9f1075M0kJJDf21AwCA4gzaU44CV9bajdH60n52\n",
       "e8Ra+7yk+gHaAQBAEYbqKd8r6cVouVnSKklbco3GmDWSNkuStfbxsSgQAIByMdR7yvWSWgrWp/Vp\n",
       "b5I0zRiz1BjzUEkrAwCgzAz5nrKkYIj2E9baLcaYVcaY1dFQdn/iknTkyJFhFQgAwERUkHfxYm8z\n",
       "VCi3SmqIlqdKOtmn/aSkPQX7Lpc0UCjPkqT777+/2NoAALgYzJK0u5gdhwrlHyk7RL1R2RnWv5Ak\n",
       "Y0y9tbZV0nOS1kT71kt6e5BjbZZ0u6TDkjLFFAcAwAQWVzaQNxd7g8A5N+gOxpi1yk7yyn8kyhjz\n",
       "jrW2qaC9RVKTtfZrIywcAICyN2QoAwCAC4MzegEA4AlCGSgzxpjH+qyvNsasjN6Kgmf6ebwei655\n",
       "vC5C3oUyTxATD08SE4cx5kFJqwvWizlrH8ZJ38crstYY85GKnM2LC8sYsza6PFqwrehc8yqUeYKY\n",
       "sHiSmCCstU8pO3Ez515Jp6Ll3Fn74Il+Hi9JWmutvcJa+9J41ISBGWNWStoQTYpujIJ4qVR8rnkV\n",
       "yuIJYqLiSWLiGuqsffBPQ/Rkz1kU/dOontxqjtbvU/Y8Hrltg+aab6HME8TExJPExDbUWfvgEWvt\n",
       "uqjXNS3qmcET0WOT+7bEZZLeUTbXCk+8NWiu+RbKEk8QEw5PEhPaUGftg0ei9ypz7zGfVLYnBs9E\n",
       "b8W+a63NfYFT0bnmWyjzBDHB8CQx4f1IPY9Z/qx98FazpA3R8jQN40xRuKBWFpxMa1i55lso8wQx\n",
       "8fAkMYFEX7faZIx5QJJyr+SjEY5Wa+1741kfeuvn8dooaVX0QvgEj5d/jDEP5r7KOPp3Naxc8+6M\n",
       "Xv2d1hN+K+gpL7TWfmdciwGAcWKMWSXpx8rOjWqQtMZa+9Jwcs27UAYAoFz5NnwNAEDZIpQBAPAE\n",
       "oQwAgCcIZQAAPEEoAwDgCUIZAABPEMoAAHiCUAYAwBP/H8JLs3hCHEFfAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac85ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(means)):\n",
    "    moments = np.array([abcpmc.weighted_avg_and_std(pool.thetas[:,i], pool.ws, axis=0) for pool in pools])\n",
    "    errorbar(range(T), moments[:, 0], moments[:, 1])\n",
    "hlines(means, 0, T, linestyle=\"dotted\", linewidth=0.7)\n",
    "_ = xlim([-.5, T])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does the distribution of the distances look like after we have approximated the posterior? If we're close to the true posterior we expect to have a high bin count around the values we've found in the earlier distribution plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10b012690>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAeQAAAFkCAYAAADxHkghAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3WlwI+d95/FfN26AOAgew7k1M5Ja1rkzlmzntGNJdvao\n",
       "pBLJ2mS9VVupRIrzZiu1VcraL/bVpmrl8qZqU6kkdpTNblXWWR9SslGcODrGUWzJOka3NSO3pOFo\n",
       "TnJ4AgSJG937AgCHGg9vHE3g+6maGoBsAn+QTfz4PP0chuu6AgAA3WV2uwAAAEAgAwDgCQQyAAAe\n",
       "QCADAOABGwpky7K+fNX9Bxv/HmlPWQAA9Jd1A9myrIck3bfi/t2SnrFt+1FJhxv3AQDANqwbyLZt\n",
       "/5mk8RUfOizpnsbt8cZ9AACwDf7NfkGjZdx0TNI3WlcOAAD9acuDuizLOibpVdu232hhPQAA9KVN\n",
       "t5BXuNu27S+tdYBlWSFJd0makFTbxnMBALBT+CTtlnTCtu3SRr9oS4FsWdZDtm1/pXH7btu2j69y\n",
       "6F2SfrCV5wAAYIf7OUnPbfTgdQPZsqz7Jd1pWdZv2bb955Zl3SPpEcuyfk9SWtL9a3z5hCR9/etf\n",
       "19jY2EZrAgBgx5qcnNTnP/95qZGBG7VuINu2/Zikx1bcf0b1IN6ImiSNjY1p3759m6kLAICdblOX\n",
       "almpCwAADyCQAQDwAAIZAAAPIJABAPAAAhkAAA8gkAEA8AACGQAADyCQAQDwAAIZAAAPIJABAPAA\n",
       "AhkAAA8gkAEA8AACGQAADyCQAQDwAAIZAAAPIJABAPAAAhkAAA8gkAEA8AACGQAADyCQAQDwAAIZ\n",
       "AAAPIJABAPAAAhkAAA/wd7uAfuQ4jnK5nCQpHo/LNPm7CAD6HUnQBblcTk88e0pPPHtqOZgBAP2N\n",
       "FnKXRKOxbpcAAPAQWsgAAHgAgQwAgAcQyAAAeACBDACABxDIAAB4AIEMAIAHEMgAAHgAgQwAgAcQ\n",
       "yAAAeACBDACABxDIAAB4AIEMAIAHEMgAAHgAgQwAgAcQyAAAeACBDACAB2wokC3L+vJV9++zLOtu\n",
       "y7IebE9ZAAD0l3UD2bKshyTdt+L+MUmybft44/7RtlUHAECfWDeQbdv+M0njKz70gKT5xu1xSfe0\n",
       "oS4AAPrKVq4hpyTNrbg/1KJaAADoW1sd1GW0tAoAAPrcVgI5IynduD0oabZ15QAA0J+2EsjflHS4\n",
       "cfuQpKdbVw4AAP1pI6Os75d0p2VZvyVJtm2/3vj43ZIytm2/0d4SAQDoff71DrBt+zFJj131sUcb\n",
       "N4+3oygAAPoNK3UBAOABBDIAAB5AIAMA4AEEMgAAHkAgAwDgAQQyAAAeQCADAOABBDIAAB5AIAMA\n",
       "4AEEMgAAHkAgAwDgAQQyAAAeQCADAOABBDIAAB5AIAMA4AEEMgAAHkAgAwDgAQQyAAAeQCADAOAB\n",
       "BDIAAB5AIAMA4AEEMgAAHkAgAwDgAf5uF9DPHMdRNptdvh+Px2Wa/I0EAP2IQO6iQmFJT74wr3R6\n",
       "SPn8kn7pUzcrmUx2uywAQBcQyF0WicQUG0h0uwwAQJfRPwoAgAcQyAAAeACBDACABxDIAAB4AIEM\n",
       "AIAHEMgAAHgAgQwAgAcQyAAAeACBDACABxDIAAB4AIEMAIAHEMgAAHgAgQwAgAcQyAAAeACBDACA\n",
       "BxDIAAB4AIEMAIAH+LfyRZZl3ScpI+mwbduPtrYkAAD6z6ZbyJZlHZU0btv2cUnjjfsAAGAbttpl\n",
       "/eXG/4dt2369VcUAANCvNh3IjQA+Y1nWnKS51pcEAED/2UqXdUrS+5IelPSoZVmHWl4VAAB9Zitd\n",
       "1g9K+ppt249L+pyk+1tbEgAA/WdL15Bt215o/H9c9dHWAABgGzY97cm27a9YlvWwpHFJaaY9AQCw\n",
       "fVuah2zb9ldaXQgAAP2MlboAAPAAAhkAAA8gkAEA8AACGQAAD9jSoC5snuM4yuVykqRsNivXdbtc\n",
       "EQDASwjkDsnlcnri2VOKRmOamb6s2ECy2yUBADyELusOikZjig0kFIlGu10KAMBjCGQAADyAQAYA\n",
       "wAMI5C5zXVfzC8VulwEA6DICucvGJwv6q6dsXZopdLsUAEAXEchddmm23jq+OJPvciUAgG4ikLvI\n",
       "cV1NZ8qSpMvzdFsDQD8jkLsos1hVpVZfIGR2oaxCqdrligAA3UIgd9FUpiJJSsSCcl3p/QsLXa4I\n",
       "ANAtBHIXTWXrgfzRm0YlST8+l+1mOQCALiKQu6TmuJrJVpSI+nVkb0qSZJ/NdLkqAEC3EMhdMper\n",
       "qOZIo6mgQkGf0vGgTl9cUKVa63ZpAIAuIJC7ZCpTkiTtSgUlSaODIVVqrl5/54Ky2awcx+lmeQCA\n",
       "DiOQu2Rqvj7daSQVkiQNNvab+Pvnz+qJZ08tb9UIAOgPBHIX1GquZhbKSsV8CgXqP4LhZECSNLNQ\n",
       "VTQa62Z5AIAuIJC7YCFfk+NKQ4nA8sfCQVPxiE8Ts0tyXLeL1QEAuoFA7oJSpX59OBL88Ld/MB5Q\n",
       "peooX2RgFwD0GwK5C5qB3OyuboqFfJKkpSIrdgFAvyGQu6BUrXdJhwLGhz4eDdcDebFAIANAvyGQ\n",
       "u2C1FnK02UImkAGg7xDIXdAM5OAqLWS6rAGg/xDIXVCqNLusuYYMAKgjkLugXHFkSAr6P9xCDvhN\n",
       "hQI+riEDQB8ikLugVHEVDJgyDOMnPjcQDWixUJXLXGQA6CsEcheUKs5PdFc3xaNBVWuu8iVayQDQ\n",
       "TwjkDnNcV+Wqu2ogD0Trq3fNZkudLAsA0GUEcoeVyvVVuNZqIUvSTKbYsZoAAN1HIHdYodEVvXog\n",
       "N1rIC7SQAaCfEMgdVlwnkAci9RbybJYWMgD0EwK5wzbaQp7hGjIA9BUCucMK61xDjkYCMgxayADQ\n",
       "bwjkDluvy9o0DMXCfs0QyADQVwjkDluvy1qSYmG/MrmyqjWnU2UBALqMQO6wDQVyxCdX0kym0KGq\n",
       "AADdRiB3WLFcD+TgGoE8EPZLkqYJZADoGwRyhxVKNflMye/7yXWsm2KRRiDPE8gA0C8I5A4rlqpr\n",
       "dldL9WvIkjSdyXeiJACAB/i38kWWZR2TdEhS2rbtR1tbUu9yXVeFUlWJqG/N4wZoIQNA39lqC/mL\n",
       "tm0/LillWdbRVhbUy6o1VzXHVSiwene1tKKFTCADQN/YdAvZsqz7JZ2QJNu2v9LyinpYcZ1FQZoC\n",
       "flOxsJ8uawDoI1tpId8paciyrKOWZT3c6oJ6WalSn1e8XgtZkoaSIXZ8AoA+stUu6xnbtl+XJMuy\n",
       "7mthPT2t2UJea8pTUzoRUqFU1VKh0u6yAAAesJVAnpV0pnE7I+mu1pXT29bbC3mldCIkicVBAKBf\n",
       "bCWQH5N0uHE7Jenl1pXT24rlRpe1fwNd1omwJGkmSyADQD/YdCDbtn1GUqbRVZ22bfuvW19WbypW\n",
       "aCEDAK5tS/OQV8w9fryFtfS8jY6ylq4EMstnAkB/YKWuDiqVNzHKuhHIs4y0BoC+QCB3ULFck2FI\n",
       "gQ1cQx6kyxoA+gqB3EHFiqNw0C/DWD+QQwGf4tEgg7oAoE8QyB1UKtcUDq29jvVKI6mIZjIFua7b\n",
       "xqoAAF5AIHeI67oqVx2FAhsP5KFUWMVyjcVBAKAPEMgdUqo4cl0puIlAHk5FJEkzWQZ2AUCvI5A7\n",
       "pFCqStKmWsjDyUYgM7ALAHoegdwh+WI9kLfSQmYuMgD0PgK5Q5ot5KB/49/ykUYgzxLIANDzCOQO\n",
       "yRebOz2t30J2HEfZbFZBX30w1/Q8+yIDQK/b0tKZ2Lz8h64hV9c8tlBY0pMvzCuRHJQkTc4utrs8\n",
       "AECX0ULukOUu6w1eQ45EYkomUwoHTc3lSu0sDQDgAQRyh1wZ1LW5b3k07NdctsTiIADQ4wjkDsmX\n",
       "mjs9bXyUtSTFwn6Vq44WWRwEAHoagdwhm+2yboqF68czFxkAehuB3CFbDeRouD7ujrnIANDbCOQO\n",
       "uTLtaXPf8lgjkJmLDAC9jUDukCsLg2yty5oWMgD0NgK5Q/Klqvw+Q6a5/l7IKw1E6i3ky3MsDgIA\n",
       "vYxA7pB8sbqpZTObomG/fKahy7MEMgD0MgK5QwqlmgJbCGTTMDSSCmtidqkNVQEAvIJA7gDXdbfc\n",
       "QpakkcGwFpbKyheZiwwAvYpA7oBy1VHNcRXY5AjrptHB+q5PXEcGgN5FIHdAvrHK1lZbyLsagTxJ\n",
       "tzUA9CwCuQOWitsL5JHBsCRpYoYWMgD0KgK5A5obS2xlUJckjaYaLeQ5WsgA0KsI5A5YanZZBzY3\n",
       "B7lptNFCZuoTAPQuArkDlrde3GILORLyKzkQZOoTAPQwArkDmteQt9plLUlj6Zim5vKqOeyLDAC9\n",
       "iEDugHwrAnkopprjsskEAPQoArkDlgrb67KWpLGhqCQGdgFAryKQOyC/zWlP0pVAZuoTAPQmArkD\n",
       "lqc9bXGlLknaNRSTJF2mhQwAPYlA7oDtLAziOI6y2axiwZokaZKpTwDQk/zdLqAfbKfLulBY0pMv\n",
       "zCsUCsnvM1g+EwB6FIHcAUuNnZ5Mc2sLg0QiMUUiYY2kFglkAOhRdFl3QL5QUSS8/b99RgcjyuUr\n",
       "WiywDSMA9BoCuQPyxaqiId+2H2d5G0ZayQDQcwjkDlgqVhQNbb+FvCtdD+SL04vbfiwAgLcQyG1W\n",
       "qdZUqTot6bLeN1Kf+nR2MrftxwIAeAuB3GbNVbpa0ULev6seyB9cWtj2YwEAvGVbgWxZ1sOtKqRX\n",
       "Nac8RcLbv4acjAWVGgjpg0kCGQB6zZYD2bKseyTd28JaelJzUZBWtJAl6eDuuKbm8stBDwDoDdtp\n",
       "IbMP4AbkG13WkZYFckKSdI7ryADQU7YUyJZlHbVt+3iri+lFV1rI2++ylqTrxuqB/MEE3dYA0Eu2\n",
       "2kJOt7SKHnblGnJrW8hnCWQA6CmbDmRax5uzVGzdKGtJOjAWl2GIgV0A0GO2khKHLcs6LGlIUroR\n",
       "0K+3uK6ekW8scxkJ+ZVtwWXfcNCvsaGYzk4syHVdGcbW1scGAHjLplvItm0/btv246oP6kqKwV1r\n",
       "Wm4ht2DaU9N1uxPK5SuaWyi27DEBAN215X5U27YflfRoC2vpSfkWTXtq7ossSWODQUn1gV1Dycj2\n",
       "CgQAeALbL7ZZvtFC3u6grua+yOn0kC5Pz0uqD+z66E27tl0jAKD7WDqzzZYKrVsYJBKJKTaQ0K5h\n",
       "pj4BQK8hkNtssVhRMOBTwN+6b3U86lfQb+rsBIuDAECvIJDbbKlQ0UCktVcGTMPQ3pGozl3OqVpz\n",
       "WvrYAIDuIJDbbKlQUSwSaPnjHtoTV7XmaPxituWPDQDoPAK5jVzXrQdyuLWB7DiO9g/XR1q/9s5F\n",
       "OQ6tZADY6QjkNiqVa6o5bstbyIXCki5OzkqSnn31gnI5riUDwE5HILdRc2OJdnRZp5MDGogENJur\n",
       "yHVZmwUAdjoCuY0WG1OeBtoQyIZhaPdwTMWyo4nZQssfHwDQWQRyGzXnILejhSxJu4djkiT7XKYt\n",
       "jw8A6BwCuY2W2thClqQ9jUB+9zwjrQFgpyOQ22ixzS3kdCKsoN+UfY5ABoCdjkBuo3Z3WRuGodHB\n",
       "kKbmi5rNch0ZAHYyArmNlgO5xfOQVxodDEuSTp2Za9tzAADaj0Buo3Z3WUvSruVAnm3bcwAA2o9A\n",
       "bqN2D+qSpOFkSAG/qbfen2nbcwAA2o9AbqN2LgzS5DMN3XpoUOcmc7o0s9i25wEAtBeB3EbLeyG3\n",
       "8RqyJH30pmFJ0os/mmzr8wAA2odAbqOlQkWhYGv3Qr6WYzcOyTSkF9+eaOvzAADah0Buo6VCta0j\n",
       "rJsSsaA+cmhIPz47p/lcse3PBwBoPQK5jRbbtBfytXzi1jG5rvTySbqtAWAnIpDbxHVdLRUrbR1h\n",
       "vdInbt0tSXrxbQIZAHYiArlNiuWanDbshbyasaGYrtud0BvvTmlialaO43TkeQEArUEgt0knVum6\n",
       "2tEbBlWtufqLv31LuVyuY88LANg+ArlNrqxj7e/Yc971kRFJ0oXZSseeEwDQGgRym3Ri2cyrHdg1\n",
       "oOFkSBemC5rJMNoaAHYSArlNmqt0dWpQV5O1Py5J+qfXLnX0eQEA20Mgt0m7t15schxH2Wx2+d91\n",
       "Y1EF/aaefX1C1RoDuwBgp+jcBc4+06lALhSW9OQL80qnhzQzfVmxgaSO7B3QO2cX9NLbk/qZO/a0\n",
       "9fkBAK1BC7lNFjs4yjoSiSk2kFAkGpV0pdv6uy+caftzAwBag0Buk061kK8lNRDUTQeTevO9GZ2/\n",
       "zPQnANgJCOQ2Wd4LOdr5QJakz35snyTpW8ff7crzAwA2h0Buk052WV/LR28a1nW7E/r+axd0YYpW\n",
       "MgB4HYHcJt3sspYk0zD07z5ryXGlbzxFKxkAvI5R1m2yVKwoFDD1nWdeViAQUD43KzM61tEaPnHr\n",
       "bh3ek9T337igB+65QQfGEh19fgDAxtFCbpOlQkXRsF+uPy5fZEg1BTteg2EY+rV7b5TrSn/5D28r\n",
       "m82y6QQAeBSB3CZLhYqioe50QKxcLGRPsqLBAb9ePDmtv3jiTTadAACPosu6DVzX1VKhol3pSFee\n",
       "/+rFQo5en9T33pjVG6eXVKOFDACeRAu5DQqlqhxXioZ8Xath5WIhI8mgbjo4qLlcWcdfYY1rAPAi\n",
       "ArkNlgpVSVI07J0OiJ+6bbeCflPf/qczml9gJygA8BoCuQ2aOz116xrytUTDAR27cVCFUk1//rdv\n",
       "d7scAMBVCOQ2aM5B9lILWZJu3B/X9XsT+v4bF/Xsq+cl/eRuUYzCBoDuIJDb4Eogd+8a8rWYhqHf\n",
       "+ZWPKBLy6U8ef0uTs0vK5XJ64tlTeubls3ri2VOMwgaALtlSIFuW9WDj3yOtLqgXNJfN9FKXddOu\n",
       "dERf+NXbVShV9Qdff1U1x1E0Wh8AFo3Gul0eAPStTQeyZVl3S3rGtu1HJR1u3McKi/myJO91WTe7\n",
       "p49dn9AnbhnVj8/O67F/+qDbZQEAtLUW8mFJ9zRujzfuY4XMYkmSlIh1Zx3r1dTnJ5/W8RPnNJZ0\n",
       "tCsd0d89f05nJha7XRoA9L1NB7Jt2482WseSdEzSidaWtPNlco1AjnZ+ucz1NOcnpxJx/ad/e6vC\n",
       "QZ+ef3tGM5lCt0sDgL625UFdlmUdk/SqbdtvtLCenjDfCOTkgLdayFfbOxLT7/zKR1StufqHH55R\n",
       "sVzrdkkA0Le2M8r6btu2v9SySnpIJldU0G8qHPTWKOtr+ag1rKPXp5TLV/TsG1Oq1pj2BADdsNVR\n",
       "1g/Ztv2Vxm0GdV0lkyspFQ/JMIxul7KqlfOPbzuc1JG9SU3OFfX1p053uzQA6EtbGWV9j6RHLMt6\n",
       "37KsOUlu68vauVzXVWaxpMF4uNulrKk5wOu7z9kqlcr69F37NTgQ0NMnLuqpl852uzwA6Dubnpdj\n",
       "2/YzktJtqKUnLBYqqtZcpeKhbpeyrkgkJsepz5kO+n369LFdevLEpP708Td1YFdcN13HjxkAOoWV\n",
       "ulqsOcJ6JwTy1WJhn37jF6+T47j6/f/1kqbnl7pdEgD0DQK5xXZyIBcKSzp7cUp3WmllF8v6/b94\n",
       "SeUKI68BoBMI5Babz9W3Nhwc2HmBLNW7se+8ZZ+O7BnQ+KWc/vixN+W6DBMAgHbz1tqOPeBKC9nb\n",
       "g7rWYhiGfuqWIckw9L1XzuvgWEK/+gvXd7ssAOhptJBbrLls5k7ssl7J7zP1uw/cqqFkWP/770/q\n",
       "2RPjbNEIAG1EILfY/EI9kAd3eCA7jiPTKep3P3eL/D5Df/jtt/Xt4++xRSMAtAmB3GK90kJuzlM+\n",
       "fWFOt+0PqFpzdfy1KbnGzn5dAOBVBHKLZXJFBQM+RTy4F/JmNTeiOLIvodsPxbVYqOipVyaX93sG\n",
       "ALQOgdxi8ztg2cytuGl/THdcP6zsUkV/8H9/pEKp2u2SAKCnEMgt5LqusoulHX/9+FoMw9DP3LFH\n",
       "h3bH9N6FBf2Xr/1Qi/lyt8sCgJ5BILfQ8rKZO3QO8noMw9DP3Tain75tVPbZeX3pT57X3EKx22UB\n",
       "QE8gkFtovhFOO31A19pc/fov7NG9d+3RBxMLeviPfqD3z2e6XRQA7HgEcgs1R1h7faen7SgUlvT0\n",
       "i+NKhSu675PXaWour4f/6Af6znPjrOgFANuw84cCe8hOXsd6MyKRmEKhoD7+kUEd2ZvQn/6/d/S1\n",
       "v/mR3nh3Wr/zq7fJb9RHYTcXEDFNU/F4XKbJ338AsBoCuYXm+ySQpeY85Xml00P65G0JnZ6s6aWT\n",
       "kzo5PqNbD0ZlHUxrdmZKps+vcDisX/rUzUomk90uGwA8i0BuoWYLuRdHWV9Lc56y4zj67McHdeLd\n",
       "RX3jmXG9+OMFTS0YumV/WJFwSJFI73bhA0Cr0IfYQv3SZX215nVlUzX9zE1BjSSDGr+U1ZOvzuvc\n",
       "VIFrywCwAQRyCzW3XuzVaU9rabaWhwcH9At3pPWzd+xRzXH1wjsZPfvGlLJLzFkGgLUQyC2UWSwp\n",
       "FOyNZTO3wzAM3XHDiD5zbFDDiYDOXs7ri396Qv/82oUPtZYdx1neQYpdpAD0OwK5hTK5klIDvbds\n",
       "5lYNRHz69L8Y0l03pVUq1/Tfv/6qHv6jH+jk+KwkKZfL6YlnT+mZl8+yixSAvtffTbkWchxXmVxJ\n",
       "1+9PdbsUTzEMQ7dcl9Sv3XOD/vr75/X8W5f0xT9+TrccHtLHbkrL9IcVG0hc82sdx/lQSDN1CkAv\n",
       "I5BbZLFQUc1x+2aE9WbtSkf0xf9wl+yzc/o/3/2x3nx/WifHZ2UY0lByWum4X/5AUHdYhvbvistn\n",
       "Gsst6Gg0pnx+ialTAHoagdwizTWde3mVrlawDqb1X7/w05rJFPT0i6f1zIkLml0oaibj6t3ztvR3\n",
       "tsJBn47sS+ngaERLBVcHYmFFIhsfqU3LGsBORCC3yPnJegDsHR3ociXe0xy81bwtSQHT1M/cnFDA\n",
       "3K1ILKHzl6YVj/p1abas8Us5nTozq5PjjQd4c1rhoKk3xxd01NqtO24Y1qE9SZnmta/V07IGsBMR\n",
       "yC3yweSCJOm6sWtfD+1nK1f1mpm+LNPnX74dG0hqIG4oGqgov7ikhL+qY4f8+uQdBzV+blL5alCL\n",
       "ZVOTM0t64705vfHenCQpHg3ohv2DumF/StftSWg4FdFIKqJUo4ciGr2yaEnzjwGJ1jIA7yKQW+Ts\n",
       "RD2QD+yOd7kSb2rOU15aysk0A8u3rz7GcSoyzYBSqZT2lZZkmgENj4wqt5DRTQfiOj9b09un52Sf\n",
       "y+o1e0qv2VMfegyfaSgVD8pvSiPpBYXNks5dmtHBvSMqFPK0lgF4FoHcImcnF5QcCHINuU0KhSW9\n",
       "+Fa9lZ0M5PSJG4OKDozqwuWMxobiWiobml0oaX6hpOlMQXPZii7Pl5a/PvlBRftHIrrl4oKOJhJM\n",
       "TQPgOQRyCxRKVU3O5nX79cPdLqWnXd3KHkoPqlbJq1TMyVeramzAr5sP1LvCw9EhKRDX+LlLms7W\n",
       "NDFX1ttnsnr7f76m3cO2fv7oXn3y6D7tHYkxAAyAJxDILXD+cv0N/eBurh93w8qu7iuBbWg4HZVR\n",
       "ieiGvQGl0sN674PLKlSk196d1TefflfffPpdHRwbUDLi6tCelPwq6tN3Hlju0iacAXQSgdwCHzSu\n",
       "Hx9kQJdn+X2m9o1E9PGPpPUb/+oGvfburF46Oa03T8/qrCO9dWZJQb+h509ldWBXQqmoq3//r29X\n",
       "MpGgBQ2gIwjkFjjbGGF9kAFdntYc7e3UqjJ9ft1xZEgj0bwyxaAWiqbOTWY1OV/V5Hx9JPdzJ5/T\n",
       "4T0J1Wol7RmOKxas6YHP3MqgMABtQSC3wPII610Estdd3b2dTOQ0mKqP5J66fFGFsqF8Layzl+a1\n",
       "VKzp7TPzkqR3zuUlST9854e6YX9KR/YmdPsNY7p+f0oBv29LtaxcwISWNwACuQXOTuQ0mo4qGg50\n",
       "uxRsUyzs18GRtA4M+3XPxw5qsVDRY997X9mCdH5iTrMLFb3w9pReeHtKevJ9+X2GDu4a0OF9gxpJ\n",
       "RTSUiigWCSjkN1WrlhQMmAoFfBpMJRQNBxTwGyoX8zIMQ9lsVv/82gXJMJiOBYBA3q5MrqTMYkkf\n",
       "u3ms26WghVYuKLJ3OCIrntR1QzUZhl+BSErvfXBB0/Ml5UqGzkzkdPrSxneq8pn1hU1Cfkejqaj2\n",
       "jcY0N59Z/jytZaA/EcjbxPXj3rTyenN9NbH6xw3DUCoe0sHRsA6NxTU8MqpsNqPbbxjV3EJJx18+\n",
       "I8MMaCGXk+kLKRiKKF8oaDAelCufFvMlTc4VlStUlak6upzJ6Ucf5PT0q5M6MBrTnrRfv/nLd2h4\n",
       "aLC73wAAHUcgb9NyIDPCuuc0rzevxzSkWKCq2JBPNx8a0kA8qanLF5dXGZu6fFGlUlnpdFIz00u6\n",
       "7bohDQ2P6PyFC5rNOZqcK+pypqLxiSWNT0ivvf+8fur2PfrZ2/fo0FhIfl+9tXx1y3m9TTS2uskG\n",
       "m3MA3UEgb9PZCeYg97vVWtMrrVzURKq3tMNBU/tHQto75Jdh+OX443pn/LIm5ko6fuK8jp84L79p\n",
       "aGQwpMGYqU999KB2j6YUNKvy+QwtLS7q5ZOTikRjKhbz+uxP36hkMiHTMGSahnK5Bf3jc7bi8QEV\n",
       "N7BsaDOIm9e2o7EBNucAOohA3qazEwvymYb2jrDLUz/baGt6NYZhaFc6qoHgkD591wFNzNd0/OUz\n",
       "evnUlCZmi5qYlU6de2eVr65P0/rOSy+s8vkZmYb0nZfnFAn5FQr45PdJoYBPoYBP0UhQ4aBfpuFo\n",
       "ajYrv1FVOjmgI4NRRbf8igBsFoG8DZlcSacvZnVwLKGAny49tIZpGLr50JD2pv3akw7KF4jqg4sz\n",
       "2rcrocxiWe98MCefL6BCYUmSqWAorGIhr1qtpkAwpEqlouFURI4rzS2UJcOnUrmsoN9U1ZEW8yUV\n",
       "SjVVHVfuqttMz+nZt+YUj/h16tyibrpuWNfvS+nIvpQSsWDXpmzRnY5eRiBvwz+++IGqNUf3fvxA\n",
       "t0tBj1g5ujubzcp1XYVDfu0dDutjN9Z7YVJR45rXqa++Zu3Uqrp5f+qq69hXtr0cHhnV5MQF5Qtl\n",
       "xRMpTU0XtxGPAAAMKUlEQVRPy/VFtVQoa7HoaqlkaGo+r5dPTevlU9PLNY4ORnRwV0yFYkGpmE//\n",
       "8hMHtH/PkEzDWDMgNxKm6x3DXtfoZQTyFlWqjv7h+TOKhv369J37u10OesTVe0c3r0lv5Dr1Stfq\n",
       "Qr/6OrYkmaahRHxAw8NpubWCTDMgJ2kuh/tCdl437ItrdlE6M5HThemCTl/M6sSPZ5Yf47mTb8sw\n",
       "pEjQ1L7RAe0aimsoGVY05Fco6JPfZ6pSdbSwmNep8SkZpl+lUlm7R5KquYaKpaqWCmUVyzUVS1UV\n",
       "ShUZhinHdRQNB2WapoIBU9FQQEG/VChVNJgwFPQ5eu98VjcFoxqIsAYAdj4CeYuef/Oi5nMl/fLP\n",
       "H2FBELTUtYKz+fHtXKfeimIxr1dOZpRODymovH7zF/crkbhZZy/O6Pjr05qcyWmx6KpSM5XLl/T+\n",
       "hQW9e35hQ489Pllcvm1ICvhNGYZbH5TmM+S6hirVmkzDUb7o6tL0kmpOo4/94qIk6fm3ZyS9rsF4\n",
       "UHuGo9o7EtPhfWkdHEto/664kgOhFn9HVreyde84jiTJNE261bFhWwpky7Luk5SRdNi27UdbW5L3\n",
       "ua6rJ34wLsOQ/s3PHup2OUBbrfwD4ckXTi+33kcTSQ0PxJZb07mFjO6yBuX6Ijo/MauXT12WPxBW\n",
       "JjMvv98nw3UUiw1oaCitYmFJd1mDGhlOqZhf1GvvZerd5qt0vZs+vwYH05qauizDP6BAJK4LE1Oa\n",
       "z5VVqvo0t1DUyTMZnTyTkV6+uFx7PBrQ3uGodg1FlE7ENBANKhLyyWfUFA35lErGFfD7FPCbCvhN\n",
       "+X2mTEMqFfPL081C4YiqTr1XrFypqVypKZcvK7NYVjZX1PT8onL5inKLRU1nCpLhU61aVsBvKhzy\n",
       "6/brR7V3V0pDyYiGkmENJSNKxIIyTfbkxodtOpAtyzomSbZtH7cs67BlWUdt23699aV5l312Xu+d\n",
       "z+jjt4xpbCjW7XKAjlmt9S7Vu9WffulKd/tYOtkI1lq9K7yxhvjwYFRT5XmdOHle6XR+uWv+Wr3w\n",
       "K9ceH4gnlc8vyjT9Gh6JK+guyNwTXw7vmutTsWJoOBnU3KKrs5MLOnNpUfa5rH58Ltv+b86yZi+G\n",
       "I6mqM5PnJJ370BF+n6nBeFCD8ZDSiaDGhuJKJ8OKhaTBeEjJWECJaECRRu/bZueQO46rcrWmQDCq\n",
       "quMqFPApEvLLZ0qLi4vLx9N695attJAfkPRU4/a4pHsk9U0gn76Q0f/4xmuSpF/++SNdrgbwlrUC\n",
       "ezvHbkTAZ8pnVJTJ5DWcHpJKFd28f1Sp9LA+OHdeS4WywpG45ubmZfjDKleqKldqCoXCWlxakitT\n",
       "wWBI+Xxepi+oQDCoYrEgua4Mw5HPNBWLRlQq5hUK+pROJVTKLyiViGv32Iiy85fl9wc1OjqqycmL\n",
       "qjk+lcoVLSyV5AvGNL+wpKFkTEslV9PzeU3NFzWTKareCT99zdfkMw2FAoZGBqNKJyIK+H0yjHov\n",
       "Xb5YVrlSU6niqFSuqVx1VCpXVSjV5Kwyet40648Z9JvymdKudEzxgbBi4YCiYX8jtA1VqxWZRv1Y\n",
       "0zRkGvXxBn6fKZ9pKBqNKBjwKRELKZ0IKzUQlOGWZBr1Vj9BvzVbCeSUmhMf64ZaVIunZXIlfe+V\n",
       "c/rL776jas3Vr3zqet16pC9eOrCjXB30fp+pRNSv1ECk3pqOXtViv8Yo9atvr36sW2+9R4PK50yZ\n",
       "piHDMOQzDQX8PgX9jpIDyRVd8CUd2j2kmVhesZt2KT00ovMXziu7WFK+WJVjhCVfSLOZBZUrUk2m\n",
       "8oWyJmbzOju5+BOv1VB9bXSfr/58phylBgKKhINyamUZchUOh5TPF1VzpGrNlSNTjmuoWK7p9MUF\n",
       "Oe7Grvmvx5AUCfkUDhq68UBa+8eS2pWOalc6qtF0VOl4WOEQw5bWstXvzkYvfvgkaXJycotP012O\n",
       "4+qrf/OW3j03r8V8vRsqGQvqC790q245ktTFixfX/Pq5+YzmZqcVXopoYW5G1bkFRSJRzc3NyDR9\n",
       "cpyaTNOnYn5h+WOr3fbCsdTTu7VTT+dqN9yasplZ5RYyKuYXlG18PGrUZJqLSiUHNVDLyDR9SqUG\n",
       "NTe3qEqprOhAQtnMvAzTlOM4isYGlB5MaX5+dsWxM43bQc3NLTRuhzQ3t/iheprHlkslxQaSmpub\n",
       "lyNToUhMuVxOwXBETq0mGT5FYzHlFrKSGrdzC6pUqgqGolrILaniGCpXXFVdnyoFQwuZqi5fnrrm\n",
       "e2Io4FMsGlDA51MwYCroN+vX8APmcus6Gg7o1z9z444eLLsi8za1N+tWAjkjKd24PShpdo1jd0vS\n",
       "5z//+S08jXf9x7/rdgUA0Lv+6g+7XUHL7JZ0eqMHbyWQvynpTknHJR2S9PQax56Q9HOSJiTVtvBc\n",
       "AADsND7Vw/jEZr7IcFdfO29VlmU9qPqArr6c9gQAQKttKZABAEBrMS4dAAAPIJCBFrAs6z7Lsu5u\n",
       "XM5Z67iHO1UT0CmWZX15jc9t6HdjJ1vn9T/Y+PfIeo9DILfQeideL5+YG3jtGz4pd5qVq9c17h9d\n",
       "5bh7JN3bwdI6ZgM//2ONY3ru3Jf6/nf/IUn3rfK5Df1u7GTrvP67JT3TGGt1uHF/VW0N5H56k17v\n",
       "xOvlE3MDr31TJ+UO9ICk+cbt5up119KTAzY2eG5/0bbtxyWleunclzZ0/h+VNN74/HivvX7btv9M\n",
       "9fP+Wjb6u7FjrfP6D+vKax5v3F9V2wK5D9+k1zvxevnEXO+1beqk3IHWXb2useb78c6V1FFr/vwt\n",
       "y7pfjekftm1/pQfXvt/I73azS/NwD77+tfTlyo5Ntm0/umIm0jGtMw2qnS3kfnuTXu/E6+UTc83X\n",
       "ttmTcodab/W69Dqf38nWO7fvlDRkWdbRHr2Gvt75/7qkM5ZlzV11XL/o+22tGg3UV23bfmOt49oZ\n",
       "yP34Jr3eidfLJ+a6r22jJ+UOtObqdT3eOm5a7+c/02wZNrZv7TWrvn7LslKS3pf0oKRHLcvqpz1b\n",
       "N7OyYy+727btL613ULsHdfXTm/R6J14vn5gbfW0bOil3oG/qSg/P8up1jTdiqX5J5r7G4I90r11D\n",
       "1Po//1lJZ1Yce1eH6uqU9V7/g5K+1riG/jlJ93ewtq5Yce5f83ej1614/bIs6yHbtr/SuN2+QV0r\n",
       "BmWt/Nf867ff3qTXe1Pu5RNzvde+qZNyp1nR8rtbUmbFH5fPND7/eOPN2JWUVO8N7lrv5//Yis+n\n",
       "JL3c0erab93z37bthcb/x1V/b+wZjTECd1qW9VsrPtw891f73egZa73+xsyKRyzLer9xyWLN3/22\n",
       "rdTVaAXcadv2o43rRk/btv2GZVkp27YzjWMeaoxQk2VZd+/0br1rLSlqWdYrtm3fudrne8Var71x\n",
       "Un5L9UsYaUn327b9ve5Vi1bb4Lk/p/p7Qi/8Af4hG3j9Dzc+n+613320TluXzuRNGgCAjWEtawAA\n",
       "PICVugAA8AACGQAADyCQAQDwAAIZAAAPIJABAPAAAhnwMMuyUpZlPdW4fbh5G0DvIZABb1uel2jb\n",
       "9rht259Z7cBe3GsX6CcEMuBtm9mQ5LfbVgWAtvN3uwAAP8myrKdVbx2Pr/hYStK3bNv+TGOlu99r\n",
       "fP606rupHbYs61uSvibpFUnLSzTatv1A4+uPq77W8j2S/ltjjW1ZlvVlSc1NLx6xbft7lmV9TfW1\n",
       "mTO2bT/Q1hcMgEAGvKaxK9Qrtm1/qbFV39eucdj9urKDUPPr7rkqOB9ofPyrjcX9X5V0yLbtL654\n",
       "3Mcbi+MnVnaHN2qYt237t5ubxqx8LgCtR5c14D3H1NgtRtL8Ksf8Z0n3NnaRuea1Y8uyHrIs6xFJ\n",
       "d+rKLlOvrHjc5m5s96x4vpU1HLYs66uS7lV9xzYAbUQLGfCeV1UPweO6sq3fh9i2nZX0BUmyLOt9\n",
       "reiebnzsIUnJRmv4Ea19LfrpxvM1u6+TjRrEzkRA5xDIgMc0tix9qjHFaVwf3kPVlZYDt7nR/Vcb\n",
       "/7/S+JpvSzoh6duWZR1RvYV8rT2I3cbzPW5Z1r0rplQ90qjhq5ZlfU71/Xu/ttO3RwW8jt2eAADw\n",
       "AK4hAwDgAQQyAAAeQCADAOABBDIAAB5AIAMA4AEEMgAAHkAgAwDgAQQyAAAe8P8BzMTAhoZS54UA\n",
       "AAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b01c450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distances = np.array([pool.dists for pool in pools]).flatten()\n",
    "sns.distplot(distances, axlabel=\"distance\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How did our $\\epsilon$ values behave over the iterations? Using the $\\alpha^{th}$ percentile causes the threshold to decrease relatively fast in the beginning and to plateau later on"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10b490750>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAfQAAAFkCAYAAADWsMnJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8VPWh9/HPmez7SiAhISQshzVKCMjqQlDctaL0Vqv3\n",
       "tgXpbV1ua+329LHL01u1YnvpquJy7WLFre6KEkB2IewQOJAFSIAEyB6yL88fmcRgQRLN5Mzyfb9e\n",
       "vObMnDMn35iX851z5szvZ3R0dCAiIiKezWF3ABEREfniVOgiIiJeQIUuIiLiBVToIiIiXsDlhW6a\n",
       "5qOfsW6+aZrZpmkucnUOERERb+bSQjdN825g/nnWZQJYlpXjvD/JlVlERES8mUsL3bKsp4DC86xe\n",
       "AFQ6lwuBua7MIiIi4s3s/Aw9GqjocT/OriAiIiKezu6L4gybf76IiIhX8LfxZ1cBsc7lGKD8fBua\n",
       "phkETAFOAG2ujyYiImIrPyAR2GpZVlNvnjDghW6aZrRlWVXAciALyAHSgA8/42lTgHUDEE9ERMSd\n",
       "zAbW92ZDlxa6aZq3AlmmaS60LOtp58MrgSzLsnaYppllmmY2UGVZ1s7P2NUJgF//9kkmZ4x0ZWQR\n",
       "ERHblZaWcscdd4Cz/3rDpYVuWdYrwCufeiyrx/Iy52LOBXbVBrAlv56brk3u14wiIiJurNcfM9t9\n",
       "UVyfbD9QxvFTdXbHEBERcTseVegdHfDamny7Y4iIiLgdjyr0hJhQcrYWU1HTaHcUERERt+JRhT5v\n",
       "Wiqtbe28ubbA7igiIiJuxaMKfUZGEjERQby78TB1DS12xxEREXEbHlXoAf4Obrp0BA1Nrby3scju\n",
       "OCIiIm7Dowod4JoZwwkL9ufNtYU0tWjQOBERsce+fftYsmSJ3TG6eVyhhwYHcO3MNKrqmsjZetTu\n",
       "OCIi4qMMw72mI/G4Qge4YXY6Af4OXludT1tbu91xREREbGfn5CyfW0xEMHOnDOO9TYfZsPs4l07S\n",
       "6HEiIp7q2bf2sWHXsX7d58yLhvL1G8ZfcLu8vDxSUlKIiIjofuz+++/nl7/8JRERESxbtowJEyaQ\n",
       "nJzMkiVLqK2t5eqrr2bBggVn7ePFF1/kF7/4BcuWLWPYsGHMmzeP++67j7q6Or785S8TERHB8uXL\n",
       "AVi8eDHjxo3r198XPPQIHeBLl4/EYcArqw7R0dFhdxwREfEgNTU1PPTQQ0RERJxV5gDXXnst7733\n",
       "HgCbNm1i+vTppKSksHTpUp599llefPFFgHN2T9dp+GXLljFr1iyeffZZ3nnnHd5//30WL17M0qVL\n",
       "XVLm4KFH6ACJ8WHMumgoa3ceY7t1ksljBtsdSUREPoev3zC+V0fT/WnJkiWkpqZSUlJCSkrKWevm\n",
       "zZvH17/+daZPn05y8idngJ9++mmqqqooKSm54P6Li4vZu3cve/fu5cyZM3zrW9/iz3/+M8XFxSxd\n",
       "uvRffmZ/8NhCB5g/ZxRrdx7jlVWHVOgiItJr1dXVfOMb3zjv+oiICFasWMFXvvIVoLPMU1JSWLhw\n",
       "IStWrPiXbbscPXqUlJQUJkyYQFRUFPPmzetet3TpUjZt2sTy5cv53ve+18+/kYcXevrQKDLHJLD9\n",
       "wEkOHK5gzPBYuyOJiIgHWLx4MS+99FJ3+Z7rtPvjjz/OwoULAZgxYwb3338/GzZs6D6tbhgGhmGQ\n",
       "kpLCpk2beOihhygpKcEwDBYsWMD999/P8uXLiYiIYOLEiWzcuBGABx980CW/k+EJnz+bpjkcKMrJ\n",
       "yTnr9AfAnoLT/PhPG7hk/BB+8vVLbMknIiLSn0pKSsjOzgZIsyzrcG+e47EXxXWZkB6HmRrDx/tK\n",
       "KS6rtTuOiIiILTy+0A3DYP4VowB4dfUhm9OIiIjYw+MLHeCS8UNITghnzbYSTlU22B1HRERkwHlF\n",
       "oTscnUfpbe0dvL423+44IiIiA84rCh3gssxk4qOCWbH5CDVnmu2OIyIiMqC8ptAD/B3cfPlImprb\n",
       "eGd9od1xREREBpTXFDrAVZekEhEawFvri2hsarU7joiIyIDxqkIPCfLnupnp1NY388GWI3bHERER\n",
       "GTBeVegA189KIzDAj3+uKaBVU6uKiIiP8LpCjwoPYt60VE5XNbB2x4UH0BcREfEGXlfoADdfOgI/\n",
       "h8Erq/Jpb3f/oW1FRES+KK8s9ITYUC7LTKa4rJateaV2xxEREXE5ryx0gFuuGAnAK6sOnXMSehER\n",
       "EW/itYWeOiSSqeOGcOBIJXlFFXbHERERcSmvLXSAW+d0TtryyipN2iIiIt7Nqwt9bFos49PjyN1f\n",
       "RtHxarvjiIiIuIxXFzp8cpT+6ipN2iIiIt7L6wt98pgEhidGsm5nCaXlZ+yOIyIi4hJeX+iGYTB/\n",
       "zijaO+D1jwrsjiMiIuISXl/oALMvSiIhNpQPPz5CVW2T3XFERET6nU8Uup+fg1suG0FzaztvaWpV\n",
       "ERHxQj5R6ADZU4cRFR7IOxuKqG9ssTuOiIhIv/KZQg8O9OeG2emcaWjh/U2aWlVERLyLzxQ6wHUz\n",
       "0ggJ8uONtfm0tLbZHUdERKTf+FShh4cGcvX0NCpqmli9TVOrioiI9/CpQge46dJ0/P0MXlt9iDZN\n",
       "rSoiIl7C5wo9LiqEKyancOzUGTbvPWF3HBERkX7hc4UOnVOrGoamVhUREe/hk4WenBDB9ImJ5BdX\n",
       "sfvQabvjiIiIfGE+WegA86/Q1KoiIuI9fLbQRw+LIWNkPDsPndLUqiIi4vF8ttABbrp0BABvrdNw\n",
       "sCIi4tl8utCzxg4mKT6MNdtLNGmLiIh4NJ8udIfD4MbZ6bS0tvPexiK744iIiHxuPl3oAHOmDCMs\n",
       "JIB3Nx6muUXDwYqIiGfy+UIPCfJn3iWpVNU1sXaHhoMVERHP5POFDnD9rHQcDoM31hZqoBkREfFI\n",
       "KnRgUEwIMzOSOHyiht35GmhGREQ8j78rd26a5nygCki3LGtZX9cPpJsuTWfdzmO8sbaAi0YNsjOK\n",
       "iIhIn7nsCN00zUwAy7JynPcnfWr9JKDQub7w0+sHmpkai5kaw9a8Mo6dqrMzioiISJ+58pT7AqDS\n",
       "uVwIzD3HNo86b9Mty9rhwiy9ooFmRETEU7my0KOBih7343qudBZ4kWmaFZ/azjYzJiYyKCaElVuP\n",
       "UlffbHccERGRXnP1RXHG+VaYphkN5AOLgGWmaaa5OMsF+fk5uH5mOk3NbazYfMTuOCIiIr3mykKv\n",
       "AmKdyzFA+afWLwKetCzrVeA24FYXZum1q6alEhzox9vrC2lta7c7joiISK+4stCXA+nO5TTgQ+g+\n",
       "MgfAsqwa520OnW8AbBceEsDcKcM4Xd3Ixt3H7Y4jIiLSKy4r9K6L3EzTzAaqLMva6Vy10rn+MdM0\n",
       "HzRNc75pmovs/tpaTzdcmo5hwJtrdXGciIh4Bpd+D71HSef0eCyrx/Jjrvz5n1dSfDhTxw3h432l\n",
       "HDhcwZjhsRd+koiIiI00Utx5dH2F7fW1BTYnERERuTAV+nlMGBFHelIUm3Yf52RFvd1xREREPpMK\n",
       "/TwMw+DGS9Np74C31uuzdBERcW8q9M9w6aShREcE8eHHR6hvbLE7joiIyHmp0D9DgL8f181M40xj\n",
       "Kzlbi+2OIyIicl4q9Au4ZvpwAvwdvLWukLZ2zZUuIiLuSYV+AVHhQVwxOYUT5WfYmldqdxwREZFz\n",
       "UqH3wo2zOwe800AzIiLirlTovZCaGMnFowexp+A0hceq7Y4jIiLyL1TovdQ10MwbGmhGRETckAq9\n",
       "lzLNBJITwlm7o4SKmka744iIiJxFhd5LDofBjZeOoLWtg3c3FNkdR0RE5Cwq9D64YnIyEaEBvLfp\n",
       "ME0tbXbHERER6aZC74PgQH+unj6cmjPNrNlWYnccERGRbir0PrpuZhp+DoM31xXQ0aGBZkRExD2o\n",
       "0PsoLiqE2RcP5WhpLTsOnrI7joiICKBC/1z0FTYREXE3KvTPYWRKNOPSYtl+4CTFZbV2xxEREVGh\n",
       "f15dR+lvrtNwsCIiYj8V+ud0yYREBseGsiq3mJozzXbHERERH6dC/5z8HAY3zE6nuaWN9zcdtjuO\n",
       "iIj4OBX6F3Dl1GGEBPnzzoZCWlrb7Y4jIiI+TIX+BYQGB3DlJcOoqGliw65jdscREREfpkL/gm6Y\n",
       "lY7D6PwKmwaaERERu6jQv6AhcWFcMiGR/JJq8ooq7I4jIiI+SoXeDzTQjIiI2E2F3g/GpcUyMiWa\n",
       "zXtPUFp+xu44IiLig1To/cAwDG6anU5HB7y1XgPNiIjIwFOh95OZFw0lNjKYDz8+Sn1ji91xRETE\n",
       "x6jQ+0mAv4PrZ6XR0NTKBx8ftTuOiIj4GBV6P7p6+nACA/x4a30hbe36CpuIiAwcFXo/iggNJDsr\n",
       "hZMV9Xy894TdcURExIeo0PvZDbPTAX2FTUREBpYKvZ+lDI5g8pgE8ooq2JN/2u44IiLiI1ToLnD7\n",
       "vDEYBjz1+h7a2jRpi4iIuJ4K3QVGD4vhyqmpHD5Rw7sbD9sdR0REfIAK3UXuunYsYSEB/P39/VTV\n",
       "NtkdR0REvJwK3UWiwoP46tVjONPYyl/ezbM7joiIeDkVugtdM304wxMj+XDLUawjmolNRERcR4Xu\n",
       "Qn5+Dr55SwYAT7y2W4PNiIiIy6jQXWx8ehyXZyaTX1LNyi1H7I4jIiJeSoU+AP7j+nGEBPnx/Dv7\n",
       "qa1vtjuOiIh4IRX6AIiLCuHfrjSprW/m7+8fsDuOiIh4IRX6ALlh9giGDgrnvY1FFB6rtjuOiIh4\n",
       "GRX6AAnwd3D3lybS3tF5gVxHhy6QExGR/qNCH0CZZgLTJyay/3AFa7aX2B1HRES8iAp9gC28cQKB\n",
       "/g6ee2sf9Y0tdscREREvoUIfYAmxodw2dzSVtU384wPL7jgiIuIlVOg2uOXykQyODeWtdYUUl9Xa\n",
       "HUdERLyACt0GgQF+LLppAm3tHTz1zz26QE5ERL4wFbpNpo4fwuQxCew8dIqNe07YHUdERDycCt0m\n",
       "hmFw980T8fdz8PQbe2lsbrU7koiIeDAVuo2SBoXzpctHcLqqgVdyDtkdR0REPJi/K3dumuZ8oApI\n",
       "tyxr2TnWZwJpQOy51vuCBdmjWZ1bzKur85kzJYWk+HC7I4mIiAdy2RG6s6yxLCvHeX/SOTb7oWVZ\n",
       "rwLR51nv9YKD/Pn6DRNobWvn6Tf22h1HREQ8lCtPuS8AKp3LhcDcnitN07wV2ApgWdZjlmXtcGEW\n",
       "tzbr4iQmjohna14ZW/NK7Y4jIiIeyJWFHg1U9Lgf96n1WUCcaZqTTNN80IU53J5hGCz+0kQcDoNl\n",
       "r++luaXN7kgiIuJhXH1RnHGB9ae7jsydn7f7rNTESK6flcaJ8jO8/lGB3XFERMTDuLLQq4BY53IM\n",
       "UP6p9eVAUY9tp7gwi0e4/aoxRIcHsXzlQU5W1tsdR0REPIgrC305kO5cTgM+BDBNM9r52Cs91kcD\n",
       "W1yYxSOEhQTwH9ePo7mljWff2md3HBER8SAuK/Qep9KzgSrLsnY6V610ri8Cqpyn2mMty3rNVVk8\n",
       "yRWTUzBTY9iw6zi7Dp6yO46IiHgIwxPGETdNczhQlJOTQ3Jyst1xXC6/uIrvLv2I5IQIfvfA5fj7\n",
       "afwfERFfUlJSQnZ2NkCaZVmHe/McNYUbGpkSzbxpwykuq+Xt9UUXfoKIiPg8FbqbuvOasUSEBvDC\n",
       "igNU1jTaHUdERNycCt1NRYYFcuc1Y2loauV/38mzO46IiLg5Fbobu2racNKHRrEqt5i8ok9/609E\n",
       "ROQTKnQ35ucw+OaXMgB48rU9tLW7/wWMIiJiDxW6mxubFsucrBQKj1ezYvNhu+OIiIibUqF7gP+4\n",
       "bhwhQf787b391JxptjuOiIi4IRW6B4iJDOb2eWOorW/hr+/ttzuOiIi4IRW6h7h+VhopgyNYsfkw\n",
       "h4orL/wEERHxKSp0D+Hv5+Cbt0ykowN+88J2Gpta7Y4kIiJuRIXuQTJGDuLGS9MpOVnHk//cY3cc\n",
       "ERFxIyp0D/Mf141jRHIUK7ceZc22YrvjiIiIm1Che5gAfz++f2cWIUF+/OnVXRw/XWd3JBERcQMq\n",
       "dA+UFB/Ot269mIamNn7911xaWtvsjiQiIjZToXuoyzOTmTtlGAUl1Tz/jr7KJiLi61ToHmzxlyYy\n",
       "dFA4b6wtYEteqd1xRETERip0DxYc5M8P7soiwN/B//xjB+XVDXZHEhERm6jQPVxaUhTfuHECtfXN\n",
       "LPn7Nk3gIiLio1ToXuDaGcOZPjGRvQXlvLTyoN1xRETEBip0L2AYBvctuJhBMSG8+MEB9hactjuS\n",
       "iIgMMBW6lwgPDeR7d0wGw2DJ37dpVjYRER+jQvci49LiuGPeGMqrG1n64g46OvR5uoiIr1Che5n5\n",
       "c0Zx0ah4tuSV8tb6QrvjiIjIAFGhexk/h8F3b59MVHggz72VR35Jld2RRERkAKjQvVBsZDDf+Uom\n",
       "rW3tPPbXXOobW+yOJCIiLtbrQjdNM9t5m+a8neSqUPLFTR4zmFsuH8nx02d44rXddscREREX68sR\n",
       "errzNtN5G9vPWaSfffWasYweFs3qbSWsyj1qdxwREXGhvhT6y6ZpfgDMdR6tX+miTNJPAvwdPPjV\n",
       "LEKD/fnzq7spOVlrdyQREXGRXhe6ZVlVwAKgiM6j9IddFUr6z5C4MO659WIam9t47K/baG7RVKsi\n",
       "It7Ivy8bO0v91y7KIi4ye9JQduWfYsXmIzz39j4WfynD7kgiItLPdJW7j1h40wRSBkfw9voiNu05\n",
       "YXccERHpZyp0HxEc6M8P7swi0N/B75bv4GRlvd2RRESkH6nQfUhqYiSLbp5IXUMLS/62jba2drsj\n",
       "iYhIP1Gh+5h501KZeVES+w9X8I8PLLvjiIhIP1Gh+xjDMLjntotJiA3lpZyD7Dp0yu5IIiLSD1To\n",
       "Pig8JIDvf3UyDsPg8b9vo6q2ye5IIiLyBanQfZSZGstd146lsraJ/3lxO+3tmmpVRMSTqdB92M2X\n",
       "jSTTTGDbgZO8sbbA7jgiIvIFqNB9mMNh8J2vZBITEcTz7+Rx8Gil3ZFERORzUqH7uOiIIL57eybt\n",
       "HR08/PxWyqsb7I4kIiKfgwpduHh0AndeM5bTVQ38bNlm6ho0f7qIiKdRoQsAt84ZxXUz0zh8ooZf\n",
       "PbeFllZN4iIi4klU6AJ0fj990c0TmZGRyJ6C0/zmBV35LiLiSVTo0s3PYfDA7ZMZnx7H+l3HeebN\n",
       "vXR0qNRFRDyBCl3OEhjgx0++NpVhQyJ4c10h/1yTb3ckERHpBRW6/Ivw0EB+tnA6cVHBPPd2Hqu3\n",
       "FdsdSURELkCFLuc0KCaEny+aTlhIAEtf3MEO66TdkURE5DOo0OW8UhMj+cnXpuJwGDz8/BbyS6rs\n",
       "jiQiIuehQpfPNGFEPN+7YzKNzW38/OnNlJafsTuSiIicgwpdLmhGRhKLb55IVW0TP31qE9V1mp1N\n",
       "RMTdqNClV66blc5t2aM4fvoMv3hmM41NrXZHEhGRHlxa6KZpzjdNM9s0zUUX2O5BV+aQ/nHnNWOZ\n",
       "k5XCwaNVPPrXXNra2u2OJCIiTi4rdNM0MwEsy8px3p90nu3mAle6Kof0H8MwuHfBxWSOSSB3fxl/\n",
       "fGWXBp4REXETrjxCXwB0zcdZCMw9z3ZqBA/i7+fgh3dNYWRKNB9uOcrfVxywO5KIiODaQo8GKnrc\n",
       "j/v0BqZpTuo6ghfPERLkz0+/MY3EuDCWf3iQ9zYW2R1JRMTnufqiOOMC62Nd/PPFRaIjgvj53dOJ\n",
       "Cg/kidd2s2nPCbsjiYj4NFcWehWfFHYMUN5zpY7OPV9ifBg/XTiNwAA/lvwtl7yi8gs/SUREXMKV\n",
       "hb4cSHcupwEfApimGe18LN15FfzdQOz5LpoT9zYqJYYf/vsU2to7+H/PfMzR0hq7I4mI+CSXFbpl\n",
       "WTsATNPMBqosy9rpXLXSuf5Vy7JepfOiuCh0cZzHmjxmMPcuuJi6hhZ+umwz5dUNdkcSEfE5hid8\n",
       "7cg0zeFAUU5ODsnJyXbHkfN4Oecgf3l3P8MTI3n427MIDwmwO5KIiEcqKSkhOzsbIM2yrMO9eY5G\n",
       "ipN+c+ucUVw3M43DJ2r41XNbaGltszuSiIjPUKFLvzEMg0U3T2RGRiJ7Ck7zmxe2097u/meARES8\n",
       "gQpd+pWfw+CB2yczPj2O9buO88ybezWanIjIAFChS78LDPDjJ1+byrAhEby5rpB/rsm3O5KIiNdT\n",
       "oYtLhIcG8rOF04mPCua5t/N4bfUhuyOJiHg1Fbq4zKCYEH6xeEZ3qT/71j6dfhcRcREVurhUyuAI\n",
       "Hr13NkMHhfPPNfksXb5D066KiLiACl1cLiEmlEfvmcWolGhythbz8PNbaWrRV9pERPqTCl0GRFR4\n",
       "EL/85gwuHjWIj/eV8tOnNnGmocXuWCIiXkOFLgMmNDiAhxZewsyMJPYVlvPjP22gsrbR7lgiIl5B\n",
       "hS4DKsDfjwfvzOKa6cMpPF7ND36/ntLyM3bHEhHxeCp0GXB+DoP/nJ/Bl68czYnyM3z/9+soOl5t\n",
       "dywREY+mQhdbGIbBV68ey6KbJ1BZ28SP/riefYWaT11E5PNSoYutbpw9ggfumExjcxsPPbmRLXml\n",
       "dkcSEfFIKnSx3eWZyfzk65eAYfDfz21hVe5RuyOJiHgcFbq4hayxg/nvb84gNMif3/5jB69/pPHf\n",
       "RUT6QoUubmPM8FgeuWcWsZHBPPPmPp5/J09DxYqI9JIKXdxK6pBIfn3vbJLiw3hl1SH+8PIuDRUr\n",
       "ItILKnRxO4NjQ3n0ntmMSI7ig4+P8Ohfc2nWULEiIp9JhS5uKToiiF/950wyRsazac8Jfv70Zuob\n",
       "NVSsiMj5qNDFbYUGB/DThdOYPjGR3fmn+fGfN1BV22R3LBERt6RCF7cWGODHD+6awlWXpFJQUs0P\n",
       "/rCOsop6u2OJiLgdFbq4PT+HwT23XcRt2aM4frpzqNgjJ2rsjiUi4lZU6OIRDMPgrmvH8Y0bJ1BR\n",
       "08gP/7ie/UUVdscSEXEbKnTxKDdfNoLvfGUS9U2t/OTJjXy0vcTuSCIibkGFLh5nTtYw/s/XpuIw\n",
       "YMnft/HYX3OprW+2O5aIiK1U6OKRpo4bwtIHLmdMagxrdx7jnsdWs8M6aXcsERHbqNDFYyXFh/PI\n",
       "t2dx5zVjqa5r4qGnNvHkP3fT2NxqdzQRkQGnQheP5ufnYMHc0Sy5/1JSBkfw9voi/us3H3GouNLu\n",
       "aCIiA0qFLl5hZHI0v/3OZdx4aTrHTtXx4O/W8Y8PLI0DLyI+Q4UuXiMowI9FN03kl4tnEBMRxAsr\n",
       "DvD9P6zj2Kk6u6OJiLicCl28zkWjB/H7B+dw+eRkDh6t4r7H1/DuxiJNxSoiXk2FLl4pPCSAB26f\n",
       "zPfvzCLQ38GfX93Nz57eTHl1g93RRERcQoUuXm32xUP5w4NXkGkmsP3ASe5dspr1u47ZHUtEpN+p\n",
       "0MXrxUWF8LNF0/jmLRk0tbTz6F9yefyFbdQ1aDpWEfEeKnTxCYZhcN3MNJZ+9zJGD4tmzbYS7l2y\n",
       "ml2HTtkdTUSkX6jQxackJ0Tw63tmc/u8MVTUNPKTJzay7I09NLW02R1NROQLUaGLz/Hzc/CVq0we\n",
       "u3c2QweF8+baQr7z248oKKmyO5qIyOemQhefNXpYDP/z3cu4fmYaxWW1PLB0LS+tPKjBaETEI6nQ\n",
       "xacFB/qz+JYMfn73dKLCg/jre/v54R/Xc+L0GbujiYj0iQpdBMg0E/jDg1cw++KhHDhSyX2Pr+bD\n",
       "j49oMBoR8RgqdBGniNBAvn9nFg/cMRmHw+B3L+3kkb9speaM5loXEfenQhf5lMszk/n9A1cwPj2O\n",
       "jbtPcO+S1ew8qLnWRcS9qdBFziEhNpT//s+Z3HVt51zr//fJTTzz5l5aWvX1NhFxTyp0kfPwcxjc\n",
       "lj2ax+6bzdBBYbz+UQEPLF3LkdIau6OJiPwLFbrIBYxKieF/vnM586alUnS8hu/+9iPeWleoC+ZE\n",
       "xK2o0EV6ITjIn3tuu5j/87WpBAX689Tre/j505uprGm0O5qICKBCF+mTaRMSu2dv23bgJPcsWc2W\n",
       "faV2xxIRUaGL9FVsZDA/XTiNRTdPoKGplf/37Mf88ZVdNDa12h1NRHyYCl3kc3A4DG6cPYLf/tdl\n",
       "DE+M5P1Nh/mv335EfrHGgxcRe6jQRb6A1MRIHr//Um66dATHTtXxvd+t5eWcg7S164I5ERlYKnSR\n",
       "LygwwI+FN03gF3dPJyo8kL+8u5+fPLGBk5X1dkcTER+iQhfpJ5PMBH7/vTlMn5jI3oJy7luymrU7\n",
       "SuyOJSI+QoUu0o8iwwL50b9P4d4FF9PW3sFjf9vG4y9s40xDi93RRMTL+bty56ZpzgeqgHTLspad\n",
       "Y/0i5+IIy7J+6MosIgPFMAyuuiSVCelxPP7CNtZsKyGvsJzv3j6Z8elxdscTES/lsiN00zQzASzL\n",
       "ynHen/Sp9dnASmfRpzvvi3iNpEHhPHrPbL48dzSnqxr48Z/W85d38/T1NhFxCVeecl8AVDqXC4G5\n",
       "n1qf3uOxQud9Ea/i7+fgq9eM5VffmkV8TCgv5xxi8SMreX/TYdra2u2OJyJexJWFHg1U9Lh/1rlG\n",
       "y7KW9TgNnwlsdWEWEVuNT4/j9w9czpfnjuZMYyt/fGUX335sFRt3H9eY8CLSL1x9UZxxoQ2cp+a3\n",
       "WZa108VZRGwVGhzAV68Zy1M/mss104dzoryeh5/fyoO/W8eegtN2xxMRD+fKQq8CYp3LMUD5ebbL\n",
       "tizrRy7MIeJWYiOD+datF/Gn789hZkYS1tFKfvynDfz86c0UHa+2O56IeChXFvpyPvlcPA34EMA0\n",
       "zeiuDUzTvNuyrMecy7ooTnzK0EHh/PDfp7DkvtlMGBFH7v4y7v/NGn77j+2crNCgNCLSNy4rdMuy\n",
       "dkB3UVf1OKW+0vn4XOAR0zTzTdOsAPRBovgkMzWWX/3nTH66cBqpQyJZlVvM4kdyeObNvdScabY7\n",
       "noh4CMMTLsgxTXM4UJSTk0NycrLdcURcpq29g4+2l/C39/dzqrKB0GB/bp0zihtmpxMc6NJhI0TE\n",
       "jZSUlJCdnQ2QZlnW4d48RyPFibgRP4fBnKwUnvhBNt+4cQJ+DoO/vLufxQ/nsGKzvuomIuenQhdx\n",
       "Q4EBftwuHJiqAAAPrklEQVR82QiW/fhKbsseRV1DC394eRfffmw1m/boq24i8q9U6CJuLCwkgLuu\n",
       "HcdTP8rm6unDOVF+hl/971Ye/P069uqrbiLSgwpdxAPERYXw7Vsv4o8PXsGMjESsI5X86E8b+MUz\n",
       "mzlyosbueCLiBnSVjYgHSU6I4Ef/PpUDRyr437fz2JpXRu7+Mq6YnMLNl40gLSnK7ogiYhMVuogH\n",
       "GpMay8Pfmsm2Ayd5/p08VuUWsyq3mLSkSOZkpXBZZjIxEcF2xxSRAaRCF/FQhmGQNXYwk8wEtuwr\n",
       "JWfrUXL3l/HMm/t47u08Ms0EsqekMHXcEAID/OyOKyIupkIX8XB+DoPpExOZPjGR6romPtpRwurc\n",
       "YnL3d56ODwsJYPbFQ8nOSsFMjcEwLjjFgoh4IBW6iBeJCg/ixtkjuHH2CI6cqGFVbjFrthfz/qbD\n",
       "vL/pMEMHhXFFVgpXTE4hISbU7rgi0o9U6CJeKjUxkq/dMJ67rh3LrkOnyck9yuY9J/jbewf4+/sH\n",
       "mDginjlZKczISCIkSC8FIp5O/xeLeDk/PweZYxLIHJPAmYYW1u86zuptxezOP83u/NM88dpuZmQk\n",
       "MScrhYkj4nE4dEpexBOp0EV8SFhIAPOmpTJvWionTp9h9bbi7ivkV+UWEx8dwhWTk8meMoyhg8Lt\n",
       "jisifaBCF/FRifFh3D5vDP92pUleUTmrcotZv+s4L+cc4uWcQ5ipMWRnpTDr4qFEhAbaHVdELkCF\n",
       "LuLjHA6DCSPimTAinru/NJHNe0tZtfUouw6dwjpSyZP/3EPGyHhmZCQxbUIi0RFBdkcWkXNQoYtI\n",
       "t+BAfy7PTObyzGTKqxtYs62E9buPs+PgKXYcPMWfX93FhBHxzJiYyPSMJGIjNXiNiLtQoYvIOcVF\n",
       "hTB/zijmzxlFWUU9m/YcZ8Ou490X0z35+h7GDo9lZkYS0ycmMSgmxO7IIj5NhS4iFzQ4NpSbLxvJ\n",
       "zZeN5HRVA5v2nGDD7uPkFZWTV1TBsjf2Yg6LYUZGEjMyEhkSF2Z3ZBGfo0IXkT6Jjw7hhtnp3DA7\n",
       "ncqaRjbv7Sz3PQXlWEcree7tfYxIjmJmRhIzMpJ0tbzIAFGhi8jnFhMZzDUz0rhmRhrVdU18vK+U\n",
       "DbuPs+vgKQpKqvnLu/sZnhjJjIwkZmYkMmxIpN2RRbyWCl1E+kVUeBBXXZLKVZekUlffzJa8Ujbs\n",
       "OsF26yQvrDjACysOkJwQzsyMJGZelMTwxEiNKy/Sj1ToItLvwkMDmZM1jDlZw6hvbGFrXhkbdh9n\n",
       "24GTLF95kOUrD5IYF8aU8YOZOm4I49Pj8Pdz2B1bxKOp0EXEpUKDA7gsM5nLMpNpbGpl24GTbNh9\n",
       "nNz9Zby5tpA31xYSFuxP5pjBTB0/hKwxCYRrIBuRPlOhi8iACQ7yZ+ZFnafcW1rb2Vtwmi15pWzZ\n",
       "V8q6ncdYt/MYDofBuLRYpo4bwtTxQ3RRnUgvqdBFxBYB/g4mmQlMMhO4++aJHCmtZcu+UrbklbKv\n",
       "sJy9BeU8+9Y+hg4KY8q4IVwyfghjh8fip1PzIuekQhcR2xmGwfDESIYnRrJg7mgqaxvZtr+MLXll\n",
       "bLdO8vpHBbz+UQHhIQFkje383D1zTAJhIQF2RxdxGyp0EXE7MRHBzJ2aytypqTS3tLE7v/PU/NZ9\n",
       "pazZXsKa7SX4OQzGp8cxdfwQpo4bQmK8BrMR36ZCFxG3FhjgR9bYwWSNHUzHLRkUHa/hY+ep+a5h\n",
       "aJ9+Yy8pg8OZOm4IU8YNYfSwGAL8dWpefIsKXUQ8hmEYpA+NIn1oFF+5yqS8uoHc/WVs2VfGzkOn\n",
       "eHV1Pq+uzicwwA9zWAzj0mIZlxaHmRqj0/Pi9VToIuKx4qJCmDdtOPOmDaexuZXd+afZtr+MvKIK\n",
       "9haeZk/BaQAMA4YnRjIuLa675OOjNZmMeBcVuoh4heBA/86vuo0bAkBdQwsHDld0TyBz6GglRcdr\n",
       "eGdDEQAJMSGMS4tjrLPghw2OwOHQyHXiuVToIuKVuq6Izxo7GICW1nYKjlWRV/hJyXddYAcQFhLA\n",
       "2OGxjEuLZezwWEYNiyEowM/OX0GkT1ToIuITAvwdjEmNZUxqLLdcMZKOjg5KTtaRV1TB/sOdBZ+7\n",
       "v4zc/WUA+PsZjEyO7j5NP2Z4LFHhQTb/FiLnp0IXEZ9kGAYpgyNIGRzBvGmpAFTWNJLX4zT9weIq\n",
       "Dhyp5LU1nc9JjA9jZHI0I4ZGdd4mR2mYWnEbKnQREaeYyODO2eAykgBoaGrl4NFK8oo6Sz6/uKp7\n",
       "iNouQ+JCGXFWyUcTGaaSl4GnQhcROY+QIH8uGjWIi0YNAqCjo4OyinoKSqrJL6mioKSK/JJqNuw6\n",
       "zoZdx7uflxAb2l3wXUfyOl0vrqZCFxHpJcMwGBIXxpC4MGZe1HkU39HRwanKBvJLqjpL/lg1BSVV\n",
       "bNpzgk17TnQ/d1BMyFlH8SOTo4mOUMlL/1Ghi4h8AYZhkBAbSkJsKDMyPin501WNzoKv6j6i37y3\n",
       "lM17S7ufGxcVzMjkaNKHRnV/nj90UBgB/rq6XvpOhS4i0s8Mw2BQTAiDYkKYPjER6Cz5ippG8os7\n",
       "j+K7Ttl/vK+Uj/d9UvIOA4bEhZEyOILkhHCGDYkgOaFzOTRYo93J+anQRUQGgGEYxEWFEBcVwiUT\n",
       "Ersfr6hp5PDxGopP1lJc1vWvzln0Z+8jPjqElITwzrIfHMEwZ+nr83kBFbqIiK1iI4OJjQwmc0zC\n",
       "WY9X1zVxtKyWkrJaik/WUVxaS/HJWnYcPMWOg6fO2jYyLLD7lH1X4acMjiAuKhjD0Oh3vkKFLiLi\n",
       "hqLCg5gYHsTEEfFnPX6moYWSk51H8SUna52lX0deUTn7CsvP2jYkyI+EmFAGxYQyKCaEhJhQEmJC\n",
       "GBQdSkJsCDERwRru1ouo0EVEPEhYSABmaixmauxZjze1tHH8VF33KfvislqOnaqjrKKeI6W159yX\n",
       "v59BfHRnwXcVfudt53J8dAiBGv7WY6jQRUS8QFCAH2lJUaQlRf3LurqGFk5V1nOqsoGTlfWcrGw4\n",
       "637XrHTnEh0R1H1U37P046I6PyqICg/C309zz7sDFbqIiJcLDwkgPOTcZQ/Q0trGqaoGTlV0Fvyp\n",
       "KudtZQOnKhsoPFbNwaNV591/ZFggMRFBxEQEEx0ZRGxEMDGRQURHBDsfDyImMpjwkAB9pu9CKnQR\n",
       "ER8X4O9HUnw4SfHh51zf3t5BZW3jWaVfUdtIVU0TlbVNVNY2crq68byn9rv4+zmIiQz6pPydt52P\n",
       "Od8EhHf+Cw5SPfWV/ouJiMhncjg++crdmNTzb9fU0kaVs+Ara5qoqm10Fn4TlTWNnY/XNlF4rIbW\n",
       "tvMf8QMEBfoRFRZIVHiQ818g0T2Wux8P67yvz/pV6CIi0k+CAvwYHBvK4NjQz9yuo6ODMw0t3Uf3\n",
       "lTU93gTUNVHt/FdV18zhEzW0tLZf8GeHBvs7C76z7KMjgogMO/tNQHhoIBGhgYSHBBAa7O91p/9V\n",
       "6CIiMqAMwyA8tLNgUwZHfOa2HR0dNDS1Ul3X7Cz5pu7l6h7LXW8EyirqaW/vuGAGh8MgLDiAiNAA\n",
       "IkIDCQsNICIkkPDQAMKdj4WHOG9DA85adteheVXoIiLitgzDIDQ4gNDgABLjwy64fXt7B2caW6iq\n",
       "baLmTPMnR/y1TdQ1tFDX0EJtfTN19S3UNTRTW9/Cycp6Wtsu/CagS1CgHxEhAYSHBhIZFsi/XWky\n",
       "cWT8hZ/oYip0ERHxGg6HQYTz1HpvdXR00NTcRq2z5HuWfV19s/NNgHO5voVa5zanKus5WlbL4RM1\n",
       "KnQRERG7GYZBcJA/wUH+DIoJ6dNzOzo63OazeI0GICIi8jm5S5mDi4/QTdOcD1QB6ZZlLevrehER\n",
       "Eekdlx2hm6aZCWBZVo7z/qS+rBcREZHec+Up9wVApXO5EJjbx/UiIiLSS64s9Gigosf9uD6uFxER\n",
       "kV5y9VXuF7paoLdXE/gBlJaWfrE0IiIiHqBH3/V6FBtXFnoV0DVhbwxQ3sf1PSUC3HHHHf2ZT0RE\n",
       "xN0lAgW92dCVhb4cyAJygDTgQwDTNKMty6o63/rz2ArMBk4AbS7MLCIi4g786Czzrb19gtHR0fvh\n",
       "7vrKNM1FdF7w1v21NNM0cy3LyjrfehEREek7lxa6iIiIDAyNFCciIuIFVOgi8i9M03z0U/fnm6aZ\n",
       "7fyYTNzYOf52jzpv9bfzcm5f6Hoh8Wx6MfE8pmneDczvcV+jOnqIT//tnBaZpnmIXl4pLfYxTXOR\n",
       "898jPR7rdQe6daHrhcQr6MXEw1iW9RSdF6t20aiOHuIcfzuARZZljbIsa5UdmaR3TNPMBlY6LxBP\n",
       "d5b4JOh9B7p1oaMXEm+gFxPPp1EdPVussxwetDuIfKZ0Pum4Quf9L9M5ZkvXY5/Zge5e6Hoh8Xx6\n",
       "MfEO7jNHpPSJZVnLnEd4cc6jQHFDzr9T19e3M4FcOjuw56Brn9mB7l7ooBcSj6YXE6/Ql1EdxY04\n",
       "P4/t+ky9nM6jPnFjzo+at1mWtcP5UK870N0LXS8kHkwvJl5jOZ/87S40qqO4l0JgpXM5jj6MOia2\n",
       "ybYs60fO5T51oLsXul5IPJteTDyQaZq3AlmmaS4E6DpScJ5hqbIsa6ed+eT8zvG3ywHmOt9Yn9bf\n",
       "zr2Zpnm3ZVmPOZez6WMHuv1IcRoe1rP1OEJPsyxria1hRETclGmac4GX6LxuLBa41bKsVX3pQLcv\n",
       "dBEREbkwdz/lLiIiIr2gQhcREfECKnQREREvoEIXERHxAip0ERERL6BCFxER8QIqdBEvZJpmu4v3\n",
       "n26a5geu/Bki0jcqdBEv119z0ffcj2VZhZZlXdUf+xWR/qFCF/F+i91sPyLiAv52BxAR1zFN81Eg\n",
       "3TTNl4AnLcvKMU3zSTrHha6yLGuBaZrRwMtAAbCNzuEnu4eYdG5z1n66tus6Su+xT4AfAEVADp1j\n",
       "T88FHrYs61XX/8YivktDv4p4IdM02y3LcjiXcy3LynIu303nmNA/dJ5Cr6CzeCucjx/+1H6eAF52\n",
       "vhHouZ9onIXu3GekZVlLTNOMcu4vGyiyLCvWNM00Ot9M6BS9iAvplLuIb8mk80j7CeBKOqdk7AC2\n",
       "9yxz0zTvNk3zESALiLrAPufSWeJYllXtfCwayHUuV/LJFJAi4iI65S7iW7YB9Jy1yXm0XdHj/t1A\n",
       "lPMo/pFe7LPrtPoO576i6JzHWUQGkApdxDv1/Cwt1/kVs5csy1pmmuYTpmneRmfpPsknR9JdtgIv\n",
       "m6Y5gs4j9C2f3g+dn7kDnW8OnPvs+hrbbYDxGXlExAX0GbqIiIgX0GfoIiIiXkCFLiIi4gVU6CIi\n",
       "Il5AhS4iIuIFVOgiIiJeQIUuIiLiBVToIiIiXkCFLiIi4gX+P6LRx9xGHCkQAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b4908d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eps_values = np.array([pool.eps for pool in pools])\n",
    "plot(eps_values, label=r\"$\\epsilon$ values\")\n",
    "xlabel(\"Iteration\")\n",
    "ylabel(r\"$\\epsilon$\")\n",
    "legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about the acceptance ratio? ABC PMC with the OLCM kernel gives us a relatively high acceptance ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10b9dec50>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAfQAAAFkCAYAAADWsMnJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8VPW9//H3JJM9IRu7ICQgX1kVCFpApBpQcL0VQVuu\n",
       "vb9aAX+tLXqrt9pfr/e2vW210NZu1wVq6+21FVz6sFYFIWhVwAUFkQBfgQQkQmTJAiGEbPP7Y04W\n",
       "QkhmQiYzOXk9H4885nuWOecTI/Oe71m+x+Pz+QQAALq3qHAXAAAAzh2BDgCACxDoAAC4AIEOAIAL\n",
       "hDzQjTEPt7FsjjEm1xizINR1AADgZiENdGPMQklzzrJsgiRZa/Oc6fGhrAUAADcLaaBba5+QVHCW\n",
       "xfMklTrtAkkzQlkLAABuFs5z6GmSSppNZ4arEAAAurtwXxTnCfP+AQBwBW8Y910mKcNpp0s6erYV\n",
       "jTFxkiZJOiipLvSlAQAQVtGSBkh631p7KpA3dHmgG2PSrLVlklZIypGUJylL0po23jZJ0ltdUB4A\n",
       "AJFkmqS3A1kxpIFujLlZUo4x5g5r7XJn9lpJOdbazcaYHGNMrqQya+2WNjZ1UJKefvpp9e/fP5Ql\n",
       "AwAQdsXFxZo/f77k5F8gQhro1trnJD3XYl5Os/Yyp5nXzqbqJKl///4aNGhQp9YIAEAEC/g0c7gv\n",
       "igMAAJ2AQAcAwAUIdAAAXIBABwDABQh0AABcgEAHAMAFCHQAQMht2LBBl1xySbjL6FIbN27Ugw8+\n",
       "2GX7I9ABACG3atUqTZkyRdu3b+/0ba9evbrTt9lRzWuZPHmyfvjDH3bZvgl0AEDIFRUVafbs2Xrm\n",
       "mWc6fduvvPJKp2+zo8JZSzgfzgIA6EJPvpSv9R991qnbnHrRebr9+tFtrrNhwwZNnTpVU6ZM0dKl\n",
       "S09b9uCDD6qoqEgej0e///3vz5j+9re/rYqKCt1yyy0aNGiQ/v3f/11jxozRxo0b9eSTT+qZZ57R\n",
       "xo0bdffdd+tHP/qRysrKtHTpUh0/flyzZs3SvHnzlJ+fr6VLl2rw4MHatm2bnnrqKaWkpLS5r6uv\n",
       "vvqM32P79u165plnVF5ervnz5+vpp58+bT9Lliw5rZZPP/1Ur776qu69997GbaekpOhXv/pVp/4N\n",
       "GhDoAICQWrVqlW699ValpKQoJSVF27dv16hRo7RixQoNGTKk8bB0y+lly5bpsssu07x587R48WIt\n",
       "WrRIgwcP1g9/+EOtXr1aK1as0H333acdO3bokUcekaTTAvOmm27SvHnzJEnl5eX6wx/+oKVLl2rb\n",
       "tm369NNP29xXa4Hu8/m0atUqrVu3TsnJyY3XBDTsp2UtHo//CeHLly/Xddddp6uuukqrV6/WypUr\n",
       "G+vqTAQ6APQQt18/ut3edChs3LjxtOlXXnlFo0aNUn5+vm699dbG+S2n9+/fr23btmnbtm2qqKhQ\n",
       "RUWFUlNTJfnPT69YsaLV/S1fvlxlZWUqKipqnDdmzBhJUlpamo4dO9buvo4fP66UlJTTtuvxeDRr\n",
       "1iwlJyefdT+t+fjjj3XLLbdIkkaNGqWlS5cS6ACA7iU/P1+zZs3Sd77zHUnS8ePHddNNN+nee+/V\n",
       "mDFjtGHDBo0aNUqSWp1OTU1t7C3n5+ervLxckrRt2zYNHjz4jP0tX75cgwcP1h133NHmxXLt7as1\n",
       "Pp8v6P1I0rhx47RhwwZdffXV2rBhg8aNG9fm+h1FoAMAQubVV1/Vtdde2zidkpKiwYMHq6ioqPHw\n",
       "9u23365evXrpkUceaXV6xYoVSklJ0aJFi7R//34tXrxYRUVFeuqppxq3e/vtt+sHP/iBpkyZosWL\n",
       "F2v9+vWNh7w9Hk9ju2H6bPtu2Fdr57mbb6e1/bSspeE9X//61xu33bCvUPA0/8YRqYwxQyUV5uXl\n",
       "8fhUAOih8vPztWLFii69FSxcioqKlJubK0lZ1tq9gbyH29YAAN1Cy542TkegAwC6hVGjRjUeysaZ\n",
       "CHQAAFyAQAcAwAUIdAAAXIBABwDABQh0AABcgEAHAMAFCHQAAFyAQAcAwAUIdAAAXIBABwDABQh0\n",
       "AABcgEAHAMAFCHQAAFyAQAcAwAUIdAAAXIBABwDABQh0AABcgEAHAMAFCHQAAFyAQAcAwAUIdAAA\n",
       "XIBABwDABQh0AABcgEAHAMAFCHQAAFyAQAcAwAUIdAAAXIBABwDABQh0AABcgEAHAMAFCHQAAFyA\n",
       "QAcAwAUIdAAAXIBABwDABQh0AABcgEAHAMAFvKHcuDFmjqQySdnW2mXBLgcAAIEJWQ/dGDNBkqy1\n",
       "ec70+BbLx0sqcJYXtFwOAAACF8pD7vMklTrtAkkzWlnnYec121q7OYS1AADgaqEM9DRJJc2mM5sv\n",
       "dAK80BhT0mI9AAAQpFBfFOc52wJjTJqk3ZIWSFpmjMkKcS0AALhWKAO9TFKG006XdLTF8gWSHrfW\n",
       "Pi9prqSbQ1gLAACuFspAXyEp22lnSVojNfbMJUnW2mPOa578XwAAAEAHhOy2NWvtZmNMjjEmV1KZ\n",
       "tXaLs2itpBxr7RJjzH3yXzCXwW1rAAB0XEjvQ28W0nnN5uU0ay8J5f4BAOgpGCkOAAAXINABAHAB\n",
       "Ah0AABcg0AEAcAECHQAAFyDQAQBwAQIdAAAXINABAHABAh0AABcg0AEAcAECHQAAFyDQAQBwAQId\n",
       "AAAXINABAHABAh0AABcg0AEAcAECHQAAFyDQAQBwAQIdAAAXINABAHABAh0AABcg0AEAcAECHQAA\n",
       "FyDQAQBwAQIdAAAXINABAHABAh0AABcg0AEAcAECHQAAFyDQAQBwAQIdAAAXINABAHABAh0AABcg\n",
       "0AEAcAECHQAAFyDQAQBwAQIdAAAXINABAHABAh0AABcg0AEAcAECHQAAFyDQAQBwAQIdAAAXINAB\n",
       "AHABAh0AABcg0AEAcAECHQAAFyDQAQBwAQIdAAAXINABAHCBoAPdGNMrFIUAAICO8wa6ojFmvKRl\n",
       "TjtN0s3W2i2hKgwAAAQumB76w5JyrbU5knIk/Sw0JQEAgGAF3EOXJGttufNaZoxpd31jzBxJZZKy\n",
       "rbXLWlk+QVKWpIzWlgMAgMAE00MvNMbca4wZb4y5T1JBWys7YS1rbZ4zPb6V1e631j4vKe0sywEA\n",
       "QAACDnRr7SJJxyQ9IKnMWntnO2+ZJ6nUaRdImtF8oTHmZknvO9teYq3dHGgtAADgdMEecn9C0hMB\n",
       "rp4mqaTZdGaL5TlSY899hrV2STC1AACAJm320I0xrzVvt/wJYPuedpYfaeiZO+fbAQBAB7TXQ29+\n",
       "WH1ei2W+dt5bJinDaadLOtpi+VFJhc3WnSTp+Xa2CQAAWtFmD91a2/zCt4nW2rKGH0lz29n2CknZ\n",
       "TjtL0hqp8R52SXqu2fI0Se8FUzgAAGgSzFXui1pMt+yxn6bZofRc+S+iaxiEZq2zvFBSmXOoPcNa\n",
       "+0IQtQAAgGbavSjOGLNA/jDPNsZsarZo01ne0qjZveV5zebltLKcQ+0AAJyDdgPdCd1lxpiHrbXf\n",
       "7YKaAABAkAK+bc1a+13n8Hlqs3kcJgcAIAIE83CWlfLfV54j/3nwGZIIdAAAIkBQj091Rodba629\n",
       "XwGcQwcAAF0j6OehSypwxnKf0e6aAACgSwQT6AukxuFfy9X+fegAAKCLBDOW+zxJy6TGUAcAABEi\n",
       "mB76RGPM0FAVAgAAOi6YHvow+c+ffyj/1e4+a+3VoSkLAAAEI5hA55w5AAARKpiBZcpCWQgAAOi4\n",
       "jty2BgAAIgyBDgCACwQV6MaYOcaYO5x2bmhKAgAAwQo40J2x3DMkXeXMavl8dAAAECbB9NDTnEep\n",
       "ljRMh6AeAADQAcEEeqEx5iFJGcaYBZIKQlQTAAAIUsCBbq1dJH+IlzjTd4aqKAAAEJxgzqFfaa19\n",
       "wgnylcaYK0NYFwAACEIwh9zvb2hYa8ubTwMAgPDiPnQAAFwgmLHcNxtjHpW0VtJMcVEcAAARI5iL\n",
       "4r4rKU/+MF/DRXEAAESOYHrostY+J+m5ENUCAAA6KOBAN8bMkX90uAxnls9aOykkVQEAgKAE00N/\n",
       "QP5nopeGqBYAANBBwQT6WmttYcgqAQAAHRZMoM80xiyUtKlhhrX2qjbWj3gVldWSpOTE2DBXAgDA\n",
       "uQkm0Bsel+oLRSFdrbKqRt/+xRsqP35K116WrTlXDFdqcly4ywIAoEOCuW2tTNJE+YN9hpoCvlv6\n",
       "0ys7dLj0pDxRHv31jd1a8JO1+vPqnaqsqgl3aQAABC3Y56HPlfQ9SZOc127J7ivRyxsKdV6fJD31\n",
       "4NVacOMYxcVE6y+vWd3x4zV6ft0uVVXXhrtMAAACFtTQr85gMmuttfer2bn07qS2rl6/ffYj+XzS\n",
       "N2++WEkJMbrh8mF64nszdNvskar3SX98ebsW/mSt/v52gWpq68JdMgAA7erIWO4Fxpj75D/s3u38\n",
       "7c092nvwmGZMOl9jh/dunJ8Q59W8GSO0/P/N1LwZI3TyVK0e/+vHWvRQnta8u091dfVhrBoAgLYF\n",
       "E+gLJMla+4SkcvkPv3crxUdP6OnVVr2SYvW160e3uk5yQoxumz1Sy743UzdePkxlx0/p1yu36JtL\n",
       "1umtzZ+pvt4V1wQCAFwmmEDPaWg4oZ7TxroRx+fz6dEXtqq6pk533DhGvZLavlUtLSVOd9w4Rk88\n",
       "MEOzJg9V8dFK/ex/N+nuX76h9/KL5fMR7ACAyBHMbWuL5H84S4O5kpZ1bjmh89aWz/ThzkO6eEQf\n",
       "fXHCoIDf1zstQd+8+SLd9MXh+vNrO/WPD4v0oyfflRmSrttmjdRFI/qEsOrOV1Nbr1PVtaqqrlOV\n",
       "83rKadfW1ssnyefzfwHyt33y+ST5pHpnnnw++Q9U+FRf73/1+dQ0z9mIT5Kv3qf4OK/GDOutfhmJ\n",
       "YfmdAaAnaDfQjTEL5A/zbGNM8wvhus1FcRWV1Vr24jbFeqP0jTkXyePxBL2NAb2T9J2vTNTNV16g\n",
       "p1ft1MaPD+r7j2/QuOG9ddvskbpwaEb7G+kgn8+n8opqHSqt1OGykzpZVeMEsj+IT7Vsnzo9qP1t\n",
       "/2tdGE8ZDMhM0kUj+ujiC/po3AW9lcKAPgDQaTyBHjo2xjzsPEK1yxljhkoqzMvL06BBgfeuG/z2\n",
       "2S1a/c4+3TZ7pObNGNEpNe3eX6Y/rdqhD3cekiRNGtVP/zxrpLLPSw16W3X1PpUeq9Kh0kodKj2p\n",
       "QyWV/vAuPanPS/whXl0T3NX2UR4pLtar+Nhoxcd6FRcb3aLtVXxcdFM7Nlre6Ch5PJLH45FHzqtH\n",
       "/nbU6fMkj6I8ampHNc2T8/4o581lx0/po12H9fGeI6qs8t8O6PFIwwal6eIL/AE/MitDsTHRQf+3\n",
       "AwA3KioqUm5uriRlWWv3BvKegANdkowxvSRlSyqw1h7rSJEdcS6Bnl9wVPf/7m2d3z9Fj9zzRcV4\n",
       "O3Jhf9vb/9OrO5RfcFSSdNlFA/WVqy/U4H4pjevU1tXrSNnJpoBuCO5Sf3AfKTup2rrW/w4piTHq\n",
       "m5GovumJ6pOeoD5piUpOiFF8XBtBHRutGG9Uh45EhFJdXb12FZXpo08Oa8uuw9q5t6Tx9471RmlU\n",
       "VmZjDz7rvFRFR0VW/QDQVUIa6M6tag9IWitpgqR/s9a+0LFSg9PRQK+prdfiX7yh/Z8f18/umqaR\n",
       "WaE5LO7z+bTZHtafXt2u3UXlivJI401fnTxVq0OlJ1VSflJnO9KdlhKnfk5Y98tIVJ/0RPVNT2gM\n",
       "8YS4oB5Z361UnapVfuFRbfnksD7adViFB5q+I6Ykxmjc8D66eIT/p39mUhgrBYCu1ZFAD+qiOGtt\n",
       "YyI659O7JNA76oXXd2n/58c1e/LQkIW55D8MPeHCvhpv+uidbQf1v6t26oOdhxTlkTJSE3Th0Az1\n",
       "TU90QjpBfdIT/eGdltCjDzPHx3k18cJ+mnhhP0lS6fEqbd11RB/tOqzNnxzW+q0HtH7rAUlSv4xE\n",
       "XTyijy66oI/GDe/NuPsA0EJQj09tMR3RF8UdOFyhFWs/UXpKnL567agu2afH49HksQN16egBKj1e\n",
       "pdTkOHmjO/cQv5ulp8Rr+oRBmj5hkHw+nw4eOaEtuw5ryyeHtXX3Ea1+Z59Wv7NPkpR9XqrGDe+t\n",
       "/plJ6pUUe8ZPjLfnflEC0DMF+/jU5iGe5kz7rLWTOrmuc+Lz+fS75z5STW29Fn5prJITYrp0/1FR\n",
       "HmWmJnTpPt3G4/FoYJ9kDeyTrGumZKmu3qc9RWX6yAn47YUlKvis/KzvT4jznhHyqclxLeY1TScn\n",
       "xnLOHkC3FkygT1TTo1M9TjsiPwFf/2C/tu4+opyR/TR13MBwl4NOEB3l0Yjz0zXi/HTNzR2hqupa\n",
       "7dpfprJjp3TsxCkdO1F9xk/5iVPae/CYamrbH7bX4/GPEtgQ9AnxXsVERyk2xn+BYWxMtGK9UYrx\n",
       "RinGG63YmKbXWG+UvF7/8sb1vf7XmBh/u2F9b7RH9fX+e/Xr633y+Xyq9/nv56/3OdP1PqetxrZ/\n",
       "Xf86p007y+WTEuK9Sk6MUXJCrJISYviCAvQwAQe6tbbMGDNHUrq1drkxJtdam9fuG7tYecUpLX8x\n",
       "X3Gx0brzpnERd6U3Okd8rFdjh/Vudz2fz6eq6jon5FsP/pbzDx6tdMUQv0nxXiUlxio5Icb/44R9\n",
       "SmKMkhJilHyWZYnxMYriywDQ7QQc6M7jU9dImilpuc4cOS4iPPlSvo5XVuv260czMhnk8XiUEOdV\n",
       "Qpw34P8f6ut9qqmrV01tvWpq6lRdW6/qmjrV1NarurbOme+0a5rmNU3Xq6a2TtU1/tea2npVO+vV\n",
       "1fnk8fhPy0R5PIqK8pw+7fG0vryx7b/Xv2G5x5kvn0+Vp2pVUVmjipPVqjhZ47RrdOBwhaqqAx/H\n",
       "wOOREuObgj6zV4L6Zyaqf2ZS42vfjETF9eALOoFIFMwh9zRr7TJjzMSG6VAUdC4+2nVY6zbtV/Z5\n",
       "qbphWna4y0E3FRXlUVxUtD+wuvj6i1Cpqa3XiZMtwr7SaTeGf3Xjl4CGZfs/r9CeotavVchMjVf/\n",
       "zCT1y/CH/AAn7PtlJiotOY6jY0AXCybQC40xD0nKcIaDLQhRTR1SXVOn/37uI0V5pLvmXqRori4H\n",
       "GsV4o5SWEqe0lOBu9/P5fKo4WaPioydUfKRSxSUnVHy00j999IR2FB5tHFSpufjY6DPCvp/Tw++X\n",
       "kchdCEAIBHMOfZExZqGcnrm19s6QVdUBK/M+0YEjJ3TDtGxdMDg93OUAruDxeJSSGKuUxNhW/13V\n",
       "1NbrcFllq2FffPSE9h48c0BJj0fKTE3QsPNS9eWrjIYNiriDfUC3FMw59Cudx6bKGJPqTK8LXWmB\n",
       "+7T4mJ5ft0u9U+M1f9aF4S4H6DFivFEa2DtZA3snn7HM5/Pp2IlqfV5SqYNHTqi45IQ+P1qp4qOV\n",
       "OnikQu/mF+u97cW6YuJg/fOskeqTzq2ewLkI5pD7/ZLWSZK1ttwY0zgdTvX1/nvOa+t8WnTTOCXG\n",
       "u+OcJ9DdeTwepSbHKTU5TiPOP7N3v+WTQ3rypXyt27Rfb2/5TDdOH6abr7yAf8NAB4X0RLMxZo4x\n",
       "Jtc5597Wevd1dB9r3tun7YUlmjx2gL4wZkBHNwOgi108oq9+ec8Xdfet45WSFKtn83Zp4U/X6uX1\n",
       "haqta3/sAACnCybQNxtjHnVC+jG1c1GcMWaCJDXcq26MGX+W9WbIfytc0EqPV+kPf9+uhDivFn1p\n",
       "bEc2ASCMoqM8yp10vh67P1e3zR6p6po6PfbCVt21ZJ3e2XZQwTwNEujpAg5051noefKH75oALoqb\n",
       "J6nUaRdImnGW9Tr8L3b5i9t04mSNvnrNSIZaBbqx+Fiv5s0YoccfmKHZU4bq4NFK/fgP7+mB/16v\n",
       "Tz4tbX8DAAIPdOciuOecIF9rjLmynbekSSppNp3ZyjbHd3S0uQ92fq43N3+mEeenafaUrI5sAkCE\n",
       "SU+J1zfmXKTf3nuFLh3dX/kFR/WdX72pJf+7SZ+XVIa7PCCiBXPI/f6GhrW2vPl0G9obWaJDzzSt\n",
       "qq7Vo89vVVSUR3fNvZgxqwGXGdwvRd+//VL95BtTNXxwmt7c/JnufChPT76Ur4rK6nCXB0SkUF4U\n",
       "V6amwE6XdNroE+fSO3/mNavPSyr1T5cPU9bA1HMsE0CkGjust37+7ct17/yJyugVp7++sVsLf7pW\n",
       "f3tzT0AP3QF6kmBuW9tsjHlU/ueiz1T7I8WtkJQj/3n3LPnHgZcxJs1aWyYp2xiTLf+h+Awn4De3\n",
       "V0ThgXL99R971DcjUV++ygRRPoDuKCrKo+kTBmny2AH6+9sFWrn2Ey17cZv+/nah/uXaUZoybgDD\n",
       "zAIK4UVxDeFsjMmVVGat3eIsWussf95a+7z8F8WlKoCL4+p9Pv3u2Y9UX+/TN+aMU3xcMN9HAHRn\n",
       "sTHRuumKC/TE92bqhmnZOlRaqYf+533922/e0o7CkvY3ALicJ9jbQowxqZIWSppnrZ0UkqrO3OdQ\n",
       "SYXff/iPWvnWIV1+8Xm677acrtg1gAh14EiF/uflHVq/9YAkaeq4gfrqtSNbHbUO6G6KioqUm5sr\n",
       "SVnW2r2BvCeYoV/nyP/I1FxJy+QP9S71/Ou7lZSSqTtuHNPVuwYQYQb2Ttb9/zJJOwpL9PuXtmn9\n",
       "1gN6N/+grv7CUA0flKqE+BglxnmVGO9VYnyMEuP9j9GNj/XyvHe4UpuB7hwuXyT/PeRrJT0h/+Hz\n",
       "sDyYpaq6VndeO0rpveLDsXsAEWhkVoaWfGuaNmw9qD++nK+X1xe2ub7HIyXEef1hn9AQ+jFKiPc2\n",
       "tv1fArxKiGtqJza2/a/xcV7usEFEaa+Hvkb+EM9yblVrGNktLIYPStNVlw4J1+4BRCiPx6OpFw3U\n",
       "JaP7a8snh3TsRLUqq2pVeapGJ6tq/e2qWp2oqtHJU7WqrKpRZVWtSo+d0mdVFaqr79j4Vglx0U1f\n",
       "AFoEfkK8V0mNRwZilJTQfJ1mXww4YoBO0magW2ujnEemPmuM8Ul6Th28d7wzfPWakfyPD+CsYrxR\n",
       "mjSqf1Dv8fl8qqmtb/wCUFlV63wJqFHlqYYvAzU6cdL5MnCqVpUnm9atrKpReUW1Dh45odq64L8Y\n",
       "eDxSv4xEzbxkiGZeer7SUzgCiY4J+KI4Y0ya/OfNb5G0R9JjXfX41IaL4vLy8jRo0KCu2CUABK26\n",
       "pq7pi0GL0K+sqj2jfaKqRpVVNSr4rFxV1XXyRns0ZexAXTM1S6OyMrgdrwcL6UVxzr3jP5P0M+f+\n",
       "8YWKgMenAkCkiI2JVmxMtNJS4oJ634mTNXr9g/16ZcNevbnlM7255TOd3z9F10weqityBvNIWQQk\n",
       "6NvWwoEeOoCewOfzaVvBUb26Ya82bD2gunqf4mOj9cWJg3XNlKGMjNmDhLSHDgAILY/Ho7HDemvs\n",
       "sN4qPVal197bp1Ub92nVxr1atXGvRg7N0OwpQzV13EDFxkSHu1xEGAIdACJQeq943TLD6OYrR2jT\n",
       "9mK9snGvNttD2rG3RMtf3KaZl5yvWZOHqn9mUrhLRYQg0AEggkVHeXTpmAG6dMwAHTxyQqs27tWa\n",
       "9z7V86/v1gtv7NYE01fXTMnSxJH9uC++hyPQAaCbGNA7SV+7frTmz7pQ67ce0CvrC/XBzkP6YOch\n",
       "9UlP0KwvDOXWtx6MQAeAbiY2JlpXTBysKyYOVsFn5XplQ6H+8WGR/vTqDv3ltZ2aPHagrpkyVKOz\n",
       "M7n1rQch0AGgG8s+L1V3zb1YX7tutN74YL9e3rBXb235TG85t77dccMYjTd9w10mugCBDgAukJQQ\n",
       "o2svy9Y1U7OU79z69vbWA3rwiY26+gtDdPv1o7mf3eUIdABwEY/HozHDemvMsN76UlGZfvXMZq1+\n",
       "Z58+tIf0rbkX01t3sahwFwAACI3hg9L0i7un65aZI3S0vEoPPrFRv312iyqrasJdGkKAQAcAF4vx\n",
       "RumfZ43UzxdfrqEDemn1O/v0zSWv60N7KNyloZMR6ADQAzT01m+daVR6rEr/8cRG/WYlvXU3IdAB\n",
       "oIeI8UZp/qwLG3vrr73r9NZ30lt3AwIdAHqYYS1768v8vfUTJ+mtd2cEOgD0QM1761kD/b31u5as\n",
       "o7fejRHoANCDDRuUpp8vnq4vX2VUevyU/mPZRv16xWZ6690QgQ4APVyMN0pfufpC/eLu6coa2Etr\n",
       "3vtUdy1Zpw92fh7u0hAEAh0AIMk/jOzPF0/XV5ze+n8ue4feejdCoAMAGsV4o/TlVnrrm3bQW490\n",
       "BDoA4AzZ56XqF3c39dZ/sNzfW6+gtx6xCHQAQKu80f7e+i/vma7sgan01iMcgQ4AaFPWwFT9/O7L\n",
       "NX/WhSqv8PfW/+vJd/XxniPy+XzhLg8OnrYGAGiXNzpKt840unR0f/3uuY/0bn6x3s0vVvbAVN1w\n",
       "ebYuH3+eYrzR4S6zRyPQAQAByxqYqiXfmqade0v14lt7tHHrAT3yzGb98e/bNXvKUM2eMlTpKfHh\n",
       "LrNHItABAEHxeDwamZWhkVkZOlRSqZfXF2r1u/v0l9esns3bpcvHn6cbpmVr2KC0cJfaoxDoAIAO\n",
       "65uRqK9dP1q3XmW0btN+vfTWHq3btF/rNu3XmGGZumFati4ZPUDRUZ5wl+p6BDoA4JwlxHl17dQs\n",
       "zZ48VB/aQ/rbm3u0+ZPD2rbnqPplJOq6y7I185LzlZQQE+5SXYtABwB0mqgoj3JG9lPOyH7aV3xM\n",
       "L71VoNc37dfv/7ZNf169QzMuGaLrLsvSwN7J4S7VdQh0AEBIDOnfS3fNvVhfvWaUVr+zVy+vL9RL\n",
       "bxXo728X6JJR/XXD5dkaO6y3PB4Ox3cGAh0AEFK9kmI1N3eEvvTF4dqw9YBefHNP421vQwf00g3T\n",
       "sjV9wiDFxnDb27kg0AEAXcIbHaXLxw/S5eMHaee+Ev3tzQKt33pAv165RU+9sl2zJg/VFRMHq09a\n",
       "AuHeAQQ6AKDLXTgkQxfelqHDpSf18voCrX5nn1as+UQr1nwiSUpKiFFGrzilp8Qro1e80nvFKz0l\n",
       "Tum94k+bnxjv5ZC9g0AHAIRNn/QE/Z/rRuvWmUavf1ikHYVHVXrslEqOV6n0WJX2f17R5vtjY6JP\n",
       "D/7mod9oidSTAAAJD0lEQVSrYV68eiXFKsrlt84R6ACAsIuP82r25KGaPXnoafNrautUevyUSo9V\n",
       "qeTYKZUer1LJsSp/6B+rUqkT/HZfierbGFY+Ic6rBTeO0cxLh4T2FwkjAh0AELFivNHqm56ovumJ\n",
       "ba5XV+/TsYqGkHe+ABxvCv6tu4/o1yu3aFdRmRbcOFYxXvc9m4xABwB0e9FRHv959l6tjyNffPSE\n",
       "fvyH9/Tqhr3ae+CYvvvVHGWmJnRxlaHlvq8oAAC00D8zSUu+NU2Xjz9PO/aW6J5f/kPbC4+Gu6xO\n",
       "RaADAHqE+Div7p0/UV+/YYzKT1Tr/z26Xq9sKHTNM90JdABAj+HxePRP04fpR4smKzE+Ro8+v1W/\n",
       "WblF1TV14S7tnBHoAIAeZ9zwPvrlPdM1fFCq1rz3qe7/3ds6XHoy3GWdEwIdANAj9U1P1EN3TVPu\n",
       "pMHatb9M9zzyhj7efSTcZXUYgQ4A6LHiYqK1+JbxuvOmcaqorNH3H9+gF9/c0y3PqxPoAIAezePx\n",
       "6NqpWfrx/52qXkmxWv7iNv386Q9VVV0b7tKCQqADACBpdHamHrlnusyQdP1jc5G++5u3VXz0RLjL\n",
       "ChiBDgCAIzM1QT/9xlTNmjxUBQfK9a+P/EOb7aFwlxUQAh0AgGZivNH65s0X6a65F+vkqTr957KN\n",
       "em7drog/r06gAwDQiqu/MEQPfXOq0nvF66mXt+vh/9mkk6ci97w6gQ4AwFmYIRn65T3TNTo7U+u3\n",
       "HtC9v35TBw63/UjXcAlpoBtj5hhjco0xC86yfIHz81Ao6wAAoKPSU+L1X3dO0fXTsvVp8XH96yP/\n",
       "0Pvbi8Nd1hlCFujGmAmSZK3Nc6bHt1ieK2mttXaZpGxnGgCAiOONjtLCfxqrf/3KBNXU1utHT76r\n",
       "v7xmVd/WQ9i7WCh76PMklTrtAkkzWizPbjavwJkGACBiXTFxsB7+1jT1SUvQn1fv1E/++J5OnKwJ\n",
       "d1mSQhvoaZJKmk1nNl9orV3m9M4laYKk90NYCwAAnWL4oDT94u7puuiC3no3v1gvvLE73CVJkrwh\n",
       "3r6nvRWcQ/MfWGu3hLgWAAA6RWpynH6wYLLe+LBIo7Mz239DFwhloJdJynDa6ZLO9iT5XGvtAyGs\n",
       "AwCAThcdHaXcSeeHu4xGoTzkvkJN58WzJK2RJGNMWsMKxpiF1tolTpuL4gAA6KCQBbq1drPUGNRl\n",
       "zQ6pr3Xmz5D0kDFmtzGmRFLkXCoIAEA3E9Jz6M0uestrNi/HeV2rpkPyAADgHDBSHAAALkCgAwDg\n",
       "AgQ6AAAuQKADAOACBDoAAC5AoAMA4AIEOgAALkCgAwDgAgQ6AAAuQKADAOACBDoAAC5AoAMA4AIE\n",
       "OgAALkCgAwDgAgQ6AAAuQKADAOACBDoAAC5AoAMA4AIEOgAALkCgAwDgAgQ6AAAuQKADAOACBDoA\n",
       "AC5AoAMA4AIEOgAALkCgAwDgAgQ6AAAuQKADAOACBDoAAC5AoAMA4AIEOgAALkCgAwDgAgQ6AAAu\n",
       "QKADAOACBDoAAC5AoAMA4AIEOgAALkCgAwDgAgQ6AAAuQKADAOACBDoAAC5AoAMA4AIEOgAALkCg\n",
       "AwDgAgQ6AAAuQKADAOACBDoAAC5AoAMA4AIEOgAALkCgAwDgAgQ6AAAuQKADAOAC3lBu3BgzR1KZ\n",
       "pGxr7bJglwMAgMCErIdujJkgSdbaPGd6fDDLAQBA4EJ5yH2epFKnXSBpRpDLAQBAgEIZ6GmSSppN\n",
       "Zwa5HAAABCik59Alec5xeYNoSSouLj63agAA6Aaa5V10oO8JZaCXScpw2umSjga5vLkBkjR//vzO\n",
       "rA8AgEg3QNKeQFYMZaCvkJQjKU9SlqQ1kmSMSbPWlp1t+Vm8L2mapIOS6kJYMwAAkSBa/jB/P9A3\n",
       "eHw+X8iqMcYskP+Ct8bb0owxm6y1OWdbDgAAghfSQAcAAF2DkeIAAHABAh3AGYwxD7eYnmOMyXVO\n",
       "kyGCtfK3e9h55W/nchEf6HyQdG98mHQ/xpiFkuY0m2ZUx26i5d/OscAYs0sBXimN8DHGLHB+Hmo2\n",
       "L+AMjOhA54PEFfgw6WastU/If7FqA0Z17CZa+dtJ0gJr7QXW2nXhqAmBMcbkSlrrXCCe7YT4eCnw\n",
       "DIzoQBcfJG7Ah0n3x6iO3VuGEw73hbsQtClbTRlX4EzfIv+YLQ3z2szASA90Pki6Pz5M3CHQUR0R\n",
       "Yay1y5weXqbTC0QEcv5ODbdvT5C0Sf4MbD7oWpsZGOmBLvFB0q3xYeIKwYzqiAjinI9tOKd+VP5e\n",
       "HyKYc6r5A2vtZmdWwBkY6YHOB0k3xoeJa6xQ09+uvVEdEVkKJK112pkKYtQxhE2utfYBpx1UBkZ6\n",
       "oPNB0r3xYdINGWNulpRjjLlDkhp6Cs4RljJr7ZZw1oeza+VvlydphvPF+gh/u8hmjFlorV3itHMV\n",
       "ZAZG/EhxDA/bvTXroWdZa5eGtRgAiFDGmBmSVsp/3ViGpJutteuCycCID3QAANC+SD/kDgAAAkCg\n",
       "AwDgAgQ6AAAuQKADAOACBDoAAC5AoAMA4AIEOuBCxpj6EG8/2xjzWij3ASA4BDrgcp31LPrm27HW\n",
       "Flhrr+qM7QLoHAQ64H6LImw7AELAG+4CAISOMeZhSdnGmJWSHrfW5hljHpd/XOgya+08Y0yapGcl\n",
       "7ZH0gfzDTzYOMemsc9p2GtZr6KU326YkfVdSoaQ8+ceeniHpp9ba50P/GwM9F0O/Ai5kjKm31kY5\n",
       "7U3W2hynvVD+MaHvdw6hl8gfvCXO/L0ttvOYpGedLwLNt5MmJ9Cdbfay1i41xqQ628uVVGitzTDG\n",
       "ZMn/ZYJD9EAIccgd6FkmyN/TfkzSTPkfyeiT9GHzMDfGLDTGPCQpR1JqO9ucIX+Iy1pb7sxLk7TJ\n",
       "aZeq6RGQAEKEQ+5Az/KBJDV/apPT2y5pNr1QUqrTi38ogG02HFbf7GwrVf7nOAPoQgQ64E7Nz6Vt\n",
       "cm4xW2mtXWaMecwYM1f+0H1cTT3pBu9LetYYM0z+Hvp7Lbcj/zl3Sf4vB842G25jmyvJ00Y9AEKA\n",
       "c+gAALgA59ABAHABAh0AABcg0AEAcAECHQAAFyDQAQBwAQIdAAAXINABAHABAh0AABf4/ycHGrt6\n",
       "hm3FAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8f9a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "acc_ratios = np.array([pool.ratio for pool in pools])\n",
    "plot(acc_ratios, label=\"Acceptance ratio\")\n",
    "ylim([0, 1])\n",
    "xlabel(\"Iteration\")\n",
    "ylabel(\"Acceptance ratio\")\n",
    "legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "rc('text', usetex=True)\n",
    "rc('axes', labelsize=15, titlesize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally what does our posterior look like? For the visualization we're using triangle.py (https://github.com/dfm/triangle.py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAUsAAAFLCAYAAABft66eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXmYXEW5/z/VPftksgEhAQLBIdQdAoSQm0jYucgWNm9Q\n",
       "UVQQROUnBsIViQIuXK5IEJSrLF6BoKKAqEGCCF7AAIKRRIEBk9wCRsKSDCYkIctktu6u3x9Vp+f0\n",
       "me6ZM8nM9Czv53n66dNnqzrndH/7rXrfektZaxEEQRC6JlHsCgiCIAwGRCwFQRBiIGIpCIIQAxFL\n",
       "QRCEGJT0d4Fa63JgBtAIpPu7fGHQkwQmAMuNMa3FrowwfOh3scQJ5Z+KUK4wtDgKeLbYlRCGD8UQ\n",
       "y0b/fhTwThHKH3TseeaVzwKseei6I4tdlwHAXrg/28budhSE3qQYYhk0vd8xxqwuQvmDjpOufSQF\n",
       "IPcLtNbBonThCP2KOHgEQRBiIGIpCIIQAxFLQRCEGIhYCoIgxEDEUhAEIQYiloIgCDEQsRQEQYiB\n",
       "iKUgCEIMRCwFQRBiIGIpCIIQAxHLAY5S6rx0W0tluq2lUil1dLHrIwjDlWKMDRd6xoZkWUWzXx5V\n",
       "1JoIwjBGLEtBEIQYiFgKgiDEQMRSEAQhBiKWgiAIMRCxFARBiIGIpSAIQgxELAVBEGIgYikIghAD\n",
       "EUtBEIQYiFgKgiDEQMRSEAQhBiKWgiAIMRCxFARBiIGIpSAIQgxELAVBEGIgYikIghADEUtBEIQY\n",
       "iFgKgiDEQMRSEAQhBiKWgiAIMRCxFARBiIGIpSAIQgxELAVBEGIgYikIghADEUtBEIQYiFgKgiDE\n",
       "QMRSEAQhBiKWgiAIMRCxFARBiIGIpSAIQgxELAVBEGIgYikIghADEUtBEIQYiFgKgiDEQMRSEAQh\n",
       "BiKWgiAIMRCxFARBiIGIpSAIQgxELAVBEGIgYikIghADEUtBEIQYiFgKgiDEQMRSEAQhBiKWgiAI\n",
       "MRCxFARBiIGIpSAIQgxELAVBEGIgYikIghADEUtBEIQYiFgKgiDEQMRSEAQhBiKWgiAIMSgpdgWE\n",
       "ziilDgN29R9HFLMugiA4xLIcmOxmrf2df91f7MoIgiBiKQiCEAsRS0EQhBiIWAqCIMRAxFIQBCEG\n",
       "IpaCIAgxELEUBEGIgYilIAhCDEQsBUEQYiBiKQiCEAMRS0EQhBiIWAqCIMRAxFIQBCEGIpaCIAgx\n",
       "ELEUBEGIgYilIAhCDEQsBUEQYiBiKQiCEAMRS0EQhBiIWAqCIMRAxFIQBCEGIpaCIAgxkKlwBxej\n",
       "lFK7++VN1tq2otZGEIYRIpaDi5XAPkAVoIAlxa2OIAwfRCwHEdbaFwCUUiOAGUWujiAMK6TPUhAE\n",
       "IQYiloIgCDEQsRQEQYiBiKUgCEIMRCwFQRBiIGIpCIIQAxFLQRCEGIhYCoIgxEDEUhAEIQYiloIg\n",
       "CDEQsRQEQYiBiKUgCEIMRCwFQRBiIGIpCIIQAxFLQRCEGIhYCoIgxEDEUhAEIQYiloIgCDEQsRQE\n",
       "QYiBiKUgCEIMZMKyAYJSak9gF/9xVDHrIghCZ8SyHDgcAWz2r8eKXBdBECKIZTlwaLbWvlnsSgiC\n",
       "kB+xLAVBEGIgYikIghADEUtBEIQYiFgKgiDEQMRSEAQhBuINH5xkgClKqRFAFfC4tXZjkeskCEMa\n",
       "EctBiLV2O3ALgFJqCjAaELEUhD5EmuGCIAgxELEUBEGIgYilIAhCDEQsBUEQYiAOniKilNLAZP9x\n",
       "YjHrIghC14hYFpfJ1trfFbsSgiB0jzTDBUEQYiCW5dDgGKXU/n75D9ZaW9TaCMIQRMSyn/Gjbsb7\n",
       "j7v2wilXAq/65ZNxrYV0L5xXEIQQ0gzvf44HSv3rTzt7Mutot9a2A6mdPZ8gCPkRy7L/yVhrVxW7\n",
       "EoIg9AwRy6HFVuA0pVQGKLfW/rrYFRKEoYKIZT+glNoL+CDQBuzXV+VYa58NlXl6X5UjCMMREcv+\n",
       "YQLwnLX23WJXRBCEHUPEso9QSlUDpwNNwF7AG/1chYRSaoxfTltrt/Rz+YIwpBCx7DuqgTestc8X\n",
       "qfxlwBS/fDBwW5HqIQhDAhHLXkYpdSHwLlAB1BerHtbaRqDR12lvpdRMv2mjtfb1YtVLEAYrIpa9\n",
       "gFLqAmC9/7jcWls0kSzAw7jpJ8B5y+v88roiWr6CMKgQsewBSqlD6MgONAlY7ZdXWWuXFqNOcbDW\n",
       "bsWFFQHcFaxXSp0W8pqPx1miCnc9Yn0KQggRS49Saiwww3/cDdjslyuB5mC9tXZhf9etr8iX8Ugp\n",
       "lQDO89ZnDe47sgnXrfB/QDtu5FfgMGq31v6zf2osCMWjGGKZ9O97aa17dOC2bdtGNjU17es/2qqq\n",
       "qtUAra2tu6XT6RqAdDq9G35stLW2SinVDJDJZMYkEolNgLLWViqltltrSwGllGqrqqoaPWbMmD+U\n",
       "lpa2Av8oKytrz1cHrfWkHlW6F9jzzCtL+qvs/fffH2BJdH1zc3NFU1PTeABrbbm1NgnQ3t6+d01N\n",
       "TRtAJpMZ6+9x+H5jrS1XSrX6U2WSyeQGQFVVVb1ZVlbWnE6nk+3t7ZVBWaNGjdoAkEqlkul0Ogmg\n",
       "lLL+mezldwu+R4LQL6j+TlCjtT6SXhgTLQx7jjLGPNv9boLQOxTDslwOHIXrH5PsOEJPSeKC/JcX\n",
       "uyLC8KLfLUtBEITBiKRoEwRBiIGIpSAIQgxELAVBEGIgYikIghCDfveGa63LccHf4g0XdoSsN9wY\n",
       "0xrdKN8vYScp+P0qRujQDCTOUth5jgLyxVnK90voDTp9v4ohlo3+/SjgnSKUP+jY88wrnwVY89B1\n",
       "R0a3NTY2HgYwYcKEv/R3vYrEXjgxbCywXb5fPaSr79cwpOD3qxhiGTSN3jHGrC5C+YOOk659JAVQ\n",
       "4H6tBlBKHQdgre00VHEoERoiW6iJLd+vHtLN92tY0dX3Sxw8g4R0e1u5UmpWseshCMMVyTo0RBjq\n",
       "FqUgFBuxLAcJydKy1oGcM1MQhjoiloMIpdRxQd+kIAj9i4ilIAhCDKTPchAh/ZKCUDzEsuxH+qoZ\n",
       "Lc1zQeh7RCx7kf4ULRFIQehfpBnevyyD3g8gl+a5IPQ9Yln2ItbaJT0Vrh21EMNl5TuHWJ5Cdyil\n",
       "jlVKnZ5ua6lMt7eWF7s+Ax0Ry/5lJjBzR0Q1TAEhnNpTcRRBHfbUWGsfTpZVNGOtaEE3SDO8yPRG\n",
       "E9pau0QpBYBS6hTgIGC5NM8FofcQsewndqafMt3eWhE6zyygJTqaJ9QkPyXueUVMBSE+IpZFpC8y\n",
       "BVlrHwUe7a3zCYLgELHsZQoJYFxBzHd8srS8JXQeGR8uCEVAOnX7GaXUNKXUNOjeox2sDzfDe1iW\n",
       "OHAEoZcQsexlwuLXl+WIEApC/yJi2QvEFS6/z2hr7YvRbSErc6p/ZdcHzXCl1KyeJADe2RAlQRA6\n",
       "2OE+S631kUA18Jox5h+9V6XBTz6BUkpdCOwPPNqNY6c+ZjGjdryGgiD0lB2yLLXWhwLbgQrgNK31\n",
       "J3u1VoMML3otMay+V7uz9KLWoFJqXntL00j/scK/+hVp8gvCjluWewHGGPOQ1vpg4Eyt9aeNMff0\n",
       "Yt0GPYF4WmuXWmvvDNbHaRorpeb5xVqbSYef01SlFNba3/Zm/Xb2XIIw1NlRsdwEHKO1Xge8grNQ\n",
       "T9NaH2mMyTeX85CnNwQnT/O8FkAlkin/uQVoA+YopaZaa2+OWHxBX2d9L8duSr+nMOzZUQfPO8A0\n",
       "4FSgCieY9cB+vVSvQU/gzAFe9o6ZLwbCFqdZa629GVgETLCZdIkPH5oGvAg0FDis1r9i4S3eHou8\n",
       "NMuF4UgssdRajwh/Nsa8AdwCHAF8ApgIPAGM1lpX9XYli8lOCsNBwNHAZGDP7naO9lf65WdDluUq\n",
       "L3A3ezElsu8iYNEOZD7qkZddEIYj3TbDtdanAOdqrZcBTxtjXtBaK2PMCq31D4DjgJNwzcOfG2O2\n",
       "922VBwfh5BaeN4BlXnin4r3eMYY81ieSJW3J0vIWf87s/n55DtAQlNUfTWZplgvDkS7F0ocHbQOu\n",
       "A84FjgVeAJTWOmmMWaW1/j+chTrKGLOxj+vb7+yMMIQC1GfR2Ytdp5Rq6XxUZzLpVFkmnSoLOX3C\n",
       "4UUN5Ak36otx54IwnOnOsmzE9Um+CfwcuElr/ZAxpgHIaK0nAicYYxYCQ04oe4tIv+ASYEnIE50v\n",
       "JrPab2sCiHjDo86b+pAoH6eUOi60PfCch0OR8onoNP8uXnFBKEB3YrkF+CiwxBjzvNZ6IZDQWpcD\n",
       "HwA2A6v6uI5FJSpc0f7LnbDcXu5m+9FKKR0Uk0gkU9F+yq6IdgPky6Qe7Id/hmKNCkJhuhRLY8x6\n",
       "rfUPQv2QTUAzzst7pjHmemBtH9exX+gNodhZIY30ZwZN9PpEh4MnhzznXxbdHnJQTfXrbs5T16Cs\n",
       "D/r3gvWW2ExhuNKtNzzisHkG2Bt4BNd3OeSx1jYFVqX/HHis6/wLyFqgQb9kdnx3IW+6P+fMcDgR\n",
       "kTHh3uu9xIKyoKLnCJ1/XqGMRaFz1hPq2ywwbjxnH0EQOuhpUHoNLjzlk8aYJ/ugPgMOpdQXAay1\n",
       "t/nPeZuz5Fp1YU/3VKA+armGhUwpNRWYhbPSF0fOP+/Yr95bkiwt3x45zvhdgqY6YVEP1yXGEMtO\n",
       "VmIer3sgsGJRCsOSnorlu8AMY8zbfVGZgYa3FstwYVE5RMXTWtsUeLdDgjgv+ByIXMThElhxc/z7\n",
       "a3RYgsExtSqRTCVLy1t8fWbg4lrBBaA3RPsyCwhzr/VFSt+mMBzpkVgaY9qAISmUXfzw7/BC2KMM\n",
       "6CGLsz7YzztcsoIZshIbcBY7wMVAYyiG8u2S8sqtftsngF39vnVAivzxmlHBDSzYaLkFrc48wfGC\n",
       "MKyRaSUK4AWlAtdPW2h7VEiyIuXf66NWJvn7BOu9iH0RSONEsA4noibT3laBUhbYF5jgj1lFxIsd\n",
       "Ph8dU+OG+yy7utbYoijiKQxHRCzjky+AvFCzOp+gHOnX3xyOh1QdU9gehxsW+TRu/Pc0f745qdbt\n",
       "I1GJDDAS+BuhEUB+uRYfnB45b97EGn457CkXBKEbRCwLECfvZGQ4Y3dN8kbyJ8CY4d+X44L/V1lr\n",
       "lyqlKnBiNwGVyKhEIu33C1uIU0PLtUTE2juOCgW+z/PHPIkT5wMiAe0FnTzRbfmuWRCGGkN6Wone\n",
       "TBDhvcAVYUssHH5TKIQn1PcIudbgfKXUIzhnzStBqBDOWr2dDhF9tqS8cmsomUZYAIPzjQNSecKB\n",
       "ugsFCsT7sEid54W6DQqRM/2FIAx1hqVl2RujcIKQIjqPYDpcKTUqkpw3cIqdoZQKYjNHARmcJflo\n",
       "qF61wG64fsvA6RMe8hjks6ygo2tgbahOLwbhPV1dVzQ4PST6eSMAIhbnLL99VVcWplifwlBiSIvl\n",
       "zsQEhoc5dvGjPwbniFkUapYfDkxRSrUCz/j1FcAZuDl49gB+RK6XPHDElAG/B97HOZeWAZ/LpFNl\n",
       "Ps5ykV9fh0v/ttzXYw///lq47sDMSBn54ibzCdmt4ev254yO3HnRdxd01ecZdXgJwqBlSIllHEum\n",
       "t8Z2W2tvU0qV4SzBqaH+yz/79xm+vBZgNs5a3ASsC5cbEspaOizQw3H5L8eCtyqTJW3AF5RSZ1tr\n",
       "3wYewmWEwu+33tdpHnAFLkFzCigJ+i6J4REPUUhIc/6Eurl/MhpIGDIMKbHsDfIJblQQ/D4X45w2\n",
       "q3Be7CD8pxqX8HcmcB7OmjQ46yqIj2zxonakP2Xg/Pkw8LXS0tLR7e3t7LbbbpetX7/+X5Ol5dsz\n",
       "qbYK4OxEIkE6nZ44adKkL61evfpOXFP8QZyTBtxIoL2A1f5zEGq0KGxVBtcRzlDk3/Pm2QysyJC3\n",
       "vdMYcRXNliTNb2EIMaTEMs6Ps5d/wBNwYvkaHdZlMOyxETjgrLPOKvnNb35ThnPCTMUJ5KeASThL\n",
       "cpk/T2lFRcUxmUyGQw45hHHjxvG73/2OqVOn/jWTTm1KtTbXlJaW8vzzz/PLX/6SBQsWAPwrTmQb\n",
       "vJhV49KsrfV1AudhjwafZx0z3urMOoKi3u4I2eB2XLcCSqkKEUVhODCkxLKrkSmF+uxiNt2DfI+j\n",
       "Q/uGrbSgGV2Psyg1zoq85De/+c0JOMtzP7/PyOrq6llNTU3g+v3meitzdktLC9dccw1XXXUVSiku\n",
       "uOACfvrTn3LMSW0VYBMzZsxg6tSp1NXVcddddwEc8t577/0Z2E0pdS4wHjfC50VgBKF+xcAiDPWh\n",
       "grNK84YXdRMiNBXnxW/0++RYlIIwFBmKoUP7EMoGVIDuwl6mRiyr6f6VQ0RAonPfTMSJZjuwEmfh\n",
       "KeBQL5Tst99+s5VSH8U10ycDnH322SilUErxne98h5qaGjLtbZVYOPLII1FKUV5ezqc+9Snee+89\n",
       "Jk6c+EVc830vX+YEnLW6Ftjd1yU733iePtt8KdsKEQ5Fagxd89H+lUUC3oWhxpCyLL3VlHeqhjzx\n",
       "h/nW5w02x8cjdmF9Bv1883BW7c1KqX8JH+Obu4cBu5x99tmMHz+e//7v/2bMmDEP7Lbbbrz66qvM\n",
       "nj2b/fffH2stAOPHj+emm27inv+DhEpw1llnZQu85JJLWL58OQ0NDQAHlJSUfDuVSi0HnqejnzIg\n",
       "OmQzsChro9eaLwrArz8uci3R84XPMQv3hzWkE0MLw4shJZYQL1yoi1Eqead6iI7vtqEsP5HQn2Aa\n",
       "2iXW2v8LHVMKfAGora2t5fbbb2fkyJForfnyl7/Mq6++yiWXXMKCBQuw1pJOp0kknNF//vnn89Qt\n",
       "T5FQiunTp2eFdO+99+ZPf/oTmUyG733ve1xxxRXgRDIQylbgoOionNC1hC+xBfiYF8E7urt/dPzZ\n",
       "FJpHaBrOUhaxFIYMQ04s87Ez4UJ5+uxqo6N4cCN0JgDPErJa/X4nT5w48aS3336b0aNHc//99zN6\n",
       "9GgAvvCFL3DSSSfR2NjIrFmzsgKWSCRyxCwQzqB5HqkfH/7whwOxHIkT5ouBJC58aJvqGCee7csN\n",
       "+l39ObKjnGwk0XEX92+JKjw6ahUuZrQgErAuDDaGVJ/ljvSThQOzrZuTO2qZhvs378AFjeeUSedm\n",
       "b8AFo0ePPuntt9/m8ssv5/XXX+fQQw/N2WHffffl8MMP70mVO1FbW8vHP/5xcGJ5xsEHH3wWztnT\n",
       "HLqGWtzInyAz+25KqQ+rjuxKi22MOX6UUl9UHQmR892vnCzvoeMKPhvp3xQGAztkWfoJy+qAtwb6\n",
       "9Lfh/rOgyRyKFcxrcYa96uQGVh8d2S9IRrE+tM+HlFIXAK8A099//31uu+02LrrooqCMcHnZ5XDT\n",
       "O5VKkUwms8vg9mtvb6ekxD2yTCZDMpkkk8mQSCT4xS9+wX/8x3/w/e9/n/vuu49Ro0Ydtnnz5jE4\n",
       "R8xDOO98tK9xf5zjah2hoZV5Yiw7DYXcWQ+4WJTCYKPHYqm1TuJi7PYFnvOvgUSdUqoln4Wocmc7\n",
       "PIXcIYPB+k5z4YQ2t0T2C1KjaZwl9wDOI703QFVVVd2oUaP4/Oc/n20+52teB8vBtmQymd0WiGZ0\n",
       "n2A5vG769On84he/4OSTT+bCCy+kpKREp1KpreQSvg+BRdwQuc4cz3lo29GAsdY+qpS6wq+7oZDw\n",
       "hQPXuxmnLuPKhQHPjjTDJwK7G2NuAP6stT5Eaz2ml+u1M0wGPhiyfJZaPwUEPvtP6AcYZPsJW5Rz\n",
       "6IiZjIYQ/R34h+oYe93g9wvMv1Zr7c+stZ+21t4wefJk3n33XVasWNF3V5uHT3/60/zqV7/yVinl\n",
       "vo7jcHGitbhrnIoLZ/pRnOZ3HtrIM92GIAxVeiyWxpjVQK3W+hTgEOAk4Mta63N6uW49xoveYjom\n",
       "8wpTT24+yX2BE0P9ZeG+yXx5JwGOwKcz82XVAt8AZpSVlf078IBS6t+yBdbXf81ay7e//W2stVhr\n",
       "yWQy2eVUKkU6nSadTtPe3k4mkyGTydDe3p5d39LSQjqVxmasW/brU6lU1nMeHJdOp7PnPvXUU5k5\n",
       "cyY46/k8X6W7ccI+Lqhinn7FeThLuSUUxB7co2dwQzVneYGtj/yZ5PQ/FurTjEP4T0wQBgI9Ekvf\n",
       "BAc3De4ZwF7GmAW4IOgpWuvderl+Pcb/yB6N9qXlczrgsvVE+/FSuMB28uzfCmwhNIUtkCgvL/9g\n",
       "W1sbuOQXh3vB+CEwY5ddduFXv/oV77//fqe6Bt5tpVS26Z1IJCgpKSGRSLB582bmz5/PO2veYW3j\n",
       "Wp544onsPslkMqcZnm/5s5/9bFDUvwHrrLVv4oZBPo1L7HFBIG5eJK8GTqcjbvSHfn3wRzIT99yn\n",
       "0QuIY0cYTMQSS621AjDGBNm6nwG2AkdorfczxizGeV67GznTaxT6oXXjda32r+Nw4S0/ovPQyNfI\n",
       "I6L+mIMip1wEfKu1tfUdvw90xBaWAcdu2LCBU045hVGjRsW6rkwmwyuvvML3vvc96urquP3220km\n",
       "S0ilUsyZM4c5c+awZs2aWOc655xzmDx5Mriuk3/1jq3bcM/pWNwfQ5j3gJf9/ajDWaDav2rpaLqX\n",
       "BU6yHbX+on3DgjDQ6VIsvdcbY4wNrEqttTLGvAncDmwEZmutPwW86l8DhsBiyiOeU4GpkR97PU44\n",
       "byOUbzJCG755Glm/DHjYWvtj4EvAFXV1dZ8Hxs6ePZt7770XoFOzOZVKZZebmpq47LLL2H333Zk+\n",
       "fTpXXHEFLS0tXH311ewxYQITxk9g1qxZLF68mJkzZ/KnP/2JVCpFW1tb3vOl02mqqqq49957KS0t\n",
       "Zdy4cTcAk7yleCAuBvPHwQX4ZvWPgMWh+3UzrlvjDTq6JrrLvl6QPH9k3c5pLggDhe4sy3O11gvB\n",
       "WZVa66QXzoQx5g3gNuAunEXyuDHm3T6ub5ZCVk1X1o61tsk3zzv94CPHLcNNIREW2mW4vtCo0wec\n",
       "c+dN4H7/edaqVau47LLLeOihh6ipqcnbVC4pKSGZTJJMJrn33nv5wQ9+QGlpKeeccw7/8z//w8qV\n",
       "K7n88stRiQSlZWX8/ve/54YbbmD9+vWcccYZLFu2LKf5HjTNw+VMnz6d66+/nnXr1jFx4sSFQDUu\n",
       "ufBS4Bxcn2vYwgua3JOBj+H+HG4I+ihD26eGmumx7v+O7CcIA4XuQofWAPtorX9ojJkbEsygOa6N\n",
       "MX8DHuvbau4UbbhwokJ5KcNxhLNwAtGIi5PMDl/07wfhmrTQkb/yOPzIHf/5X0tKSo6dNm0aN910\n",
       "E/783VbynnvuQSnFs88+y/jx4ykrcwNgmpubs/sopbj00kuZOHEin/zkJzn99NNZsmQJBx0U7R3I\n",
       "Zd68ebz00kvcc8894KbaDZwuCVyquM8rpU7GZSxaA7yFa4KvJXcGy/BMknkJx6hG73fkPmdzZIa3\n",
       "dYVS6riamprdJ0woNAZAEPqO7izLPxhjjge2a61vhayFWaa1Hg3cpLXeLejTLDYF+isn+Vd3x/0Q\n",
       "J5TgBLEF1yfZ5n/cM3HCu4iOsKJ5dIQaBUHq56dSKY466qi8zeO2tjZSqVROE/q1117jL3/5C0cf\n",
       "fTTjxo1j/fr1bN26la1bt7J69Woy6TSZdJrVq1ezbds2TjzxRL773e+yadMmPvGJT7B169ZOHvWw\n",
       "Z9xay/e//31qamoYN27cd3CWcD0uznISrn/yJGB6XV3dGcA/gaXW2svITQYc/HmAE8O54bAjf/0X\n",
       "43J2Tu2iG6RLgr7lfNtSqdR+PTmXIPQW3YmlBTDGzAeaQ4LZZox5HzjRGLPeGNO96dQLhH5880Je\n",
       "3II/RG+tPAg8GBl1k+2vDFk0BwITvUA00DEjY5CBPEjcGzRDa/3rcH/sJ4H5QN2kSZO47LLL8ja9\n",
       "o17vTZs28alPfQqAc889l7KyMkaMGEFZWRllZWWMHDkSlLMqR44cmV3/mc98hosuuohVq1Zx3nnn\n",
       "Ya3NetGjTXKlFGPHjuWSSy5h3bp1AJ/ApXX79wMPPJCXX36Zxx9/nCOOOIJVq1aBS+1WrzoShwTj\n",
       "3yE00if6bPz9aKRjjHw4uUj4uWRDiuI0x4PnbK1dUlpa2r9Bq4Lg6VIsjTGZkCf8cuA9rfUSrfWn\n",
       "vcOnvS8rV0AMA5HqtK9frFMdMy92GesX/hHihgQ2+vMEVtfFhHJB4pqwp+NEcxzOm/wGUDp+/PjP\n",
       "AuM/9KEP8eyzz7LnnntmYyrDTp3W1lba29vZsGED//Vf/8UBBxzAX//6V+bMmcOHPvQhNmzYwJNP\n",
       "Psnzzz/PH//4R8466yzeeWcNje++y4033khDQwMNDQ28/PLLXHXVVRx++OE89NBDXHzxxWzfvr1T\n",
       "HGY4tnP+/PlMnjwZpdS0RCJxybhx41i8eDFTpkxh+/btPP/88/gm7lt0RDZM9fczhc/sniekKqAB\n",
       "l+My2F5PaDqLuBZmqG8534iq8jjnEITeptvQIe/QCZrZt+MS2C4zxqR3xqJsbGw8rPu9cvE/wEX4\n",
       "H2A4aJpcJ8XkLn6Yd5CbhmyqF8ybybWaGoFd6LCo2oDHcc6sRlys4mvArcDu7777Ll/72td49NFH\n",
       "2WMPN9liNG4ykUhQVlbGkiVLqKur49prr6W9vZ1rrrmGm2++merqaioqKhg9ejRPPPEE5557Li++\n",
       "+CIKSLW3c++999LY2Eh1dTWjRo2ipqaGe+65h4MPPpg777yTb3/72106e0aMGMHPfvazbD1++9vf\n",
       "MmnSJB5//HE++tGPUlpaSmNj49NAEx0WdfDH9ACuHzdfkt/AydOV06xTwuUeCKh4zYWiE2tseEgU\n",
       "NwJnGGO29FYFVJ4ckQGhpnM2aUMXP5rAwQLOKppKN1OwhvaPlnccHU6MoEk+DhdKM4Jcy/bEkpKS\n",
       "/SZOnMg3v/nNnPHehfjJT37Cpk2buOSSS/ja177G6NGj2bBhQ3b73/72NxYsWMCJ//m7nONm/sfP\n",
       "+f7yNCw3XH+aE+SamhoWL17Mhz70Ib773e9y8sknc8wxxxQse+bMmTz55JPU1NRwyCGHALBw4UJ8\n",
       "UP0TwGZc0pGlSqkP+sOCz9GpcafhAt6he0ErFG4UdiAF5y74vCdMmPCXLsoQhD6jRyN4fF9lrwhl\n",
       "nC99pKOYHkFSAAAgAElEQVT/6AJB6NW4pmF3/V7VSqnqcBMPcq2fSLMcXIKJm3FN8iTwF+BEOqaY\n",
       "mAyck0qluOmmmygpKclx5gTLYadOc3Nz1tN99tlnU1ZWxvbt23nzzTd59913efXVV/n2t7/dKW9l\n",
       "lMcff5zNmzezbt06xowZw49//GOUUsydO5fm5uac+MuwsyeTyXDUUUdxyCGHZJvnn/jEJ4LT1uD6\n",
       "G4M/jGx3hCpcoaCPMnB4BffxlEJOmq6s0e7YkRaJIPQGKk5YS2+itZ4EvDHh1MvfKx+zR1O6vbUC\n",
       "IFla3injtrUZBaBUwhbaL7xPsC66b7q9tQJrVaK0rCW8X3tL00ibSZckS8u3J0vLW9LtrRWZdKoM\n",
       "3FzdNpNJAqhEIp0sLd+ebm+tSrc21wTrEiVlzem2lhGVlZWM230crofC+nc6lq3NrrIWNm7cyLat\n",
       "W5kwYQKlXjjT6RRKJdi0cSNNTU1UVFagKgqP+qlKpKiursZam7VmN2zYwLZt2xgzdgwja0aCitSj\n",
       "IJa1a9aSSqUoqRq5XimVCbakWppGZVLtFYnSsmaVSKaSpeXbo0cnS8tb2rZvGQtQVjVyY3tL00is\n",
       "paSiamtwv8PPJLjPiWRJW77n3hWtm9ZWNz5y467Avj5PQQ7B96vQdqEDpdTp1tqHT7r2kdXptpbK\n",
       "J649a/fujxradPX9GdCZ0sPClu9HlW5rqQRIllVkgxELiWo61VaZyaRLSyuqtwT7ZVLtBZ0FKpFM\n",
       "Adh0qhQS6WRpeUuqpWl0sL2kJJkMFKWyqoquxSiX7B9UnkPa2p3PLJlMkum8ueN6Mp231oysYdu2\n",
       "bbS2tjobMSZNTU0diTlam2tQKqNUIq0SiZTNZEoSySQ2nS4L7kkmnSqzmXQJQCCeYRFNJEvaIPdP\n",
       "LkyytLwl2CcO4WeaKClrjX9lgtB7FE0sGx+5cUacf34VSTIbDmJWoZyUkf7GfAHoOX2j4eDpSJF1\n",
       "uOb1m9ZNPBakbWsAfnnBBRes3bJlC7/+9a8fA35aUlJy3/77789LL71EIpEgnU7nJO5NJpO0trZm\n",
       "k/Zu376do446in/84x+sWLHChQYBxhhGjx7NypWbOfvs8ygtLeWYq35T8L4cW/0GZ3/0bLZt2xZ4\n",
       "sFm0aBHnf+WzXHPNNfzHZ0+josLpVCaTyUkaHFiia9euZcGCBfz8llsYOXIkW7ZseYWOCIcErtth\n",
       "AjAKN0Plr0NVCKbSuDXkZAOf8zOIQIg2t0PPaTf/eX13genhZxf65xeEfmXAWJY9GckRYF0S2kiz\n",
       "PDcbemjT88C0YL3NnYPmCn/sDf58k/Fz7fjzfQw4BmDhwoU/wTl72oBjUqnUmytXrtznyiuv5Bvf\n",
       "+AbV1dXZ/saSkhKUUpSVlWUFKp1Os2rVKqZMmcIuu+xCaWkpAPvssw+VlZWMHz+eyy+/nBtuuKHL\n",
       "az/xxBMZNWoUlZWVWVF85hk3ieOsWbNyygy84tCRNPjrX/86CxYsIJVKobXGGHMdblqKILlGCS5k\n",
       "aj3wZ5wnPHyPA8/2HKVU8GeSr/+xno7wq32VT8xsrV0f3THaJx16fjs0Fl0QepMBI5aFsHlSrUU/\n",
       "9yAEZTIuG1B0oq59gfGqYyrbyyLnW4xLTXYkzqFRj8vEA/DnsWPH7nPjjTeyfv16Fi5c2GUFysrK\n",
       "GD16NH//+9958cUXg5yTOZx66qlkMhlejnFB4AT4iiuu4O6772bPPffMe84o99xzD2VlZaRSqV8Z\n",
       "Y57CDYGchftTWOqt6jtwAeqLcJmmZtKRaT0QsCAyIDz8MzykcYlvHVyMs0Rf9Nuzf46RAQPhcxPs\n",
       "E/NWCEKfUfQJy7oTunzbuzsmHH8Z+lEuxYlePivF4LLw1BJKlBH68bfQkVA4sKBacNbWPRs3bnxu\n",
       "8uTJ/PKXv2TTpk2dvOHhZL7WWu6++26stZx33nmsX7+etrY2tmzZQnNzM83NzdlEGZcfVkbbH28k\n",
       "07yZTPNmZrQu5btnTuS7Z05k48aNtLa20tTUxFe+8hVuueUW/uVf/oUlS5ZQWVnZyQMeXS4pKWHs\n",
       "2LFYaz+Gs5Kn44RyP3wKNn+Nb+KSaQRhPPV0ZFqv9fdpbvBccE32wwnlvPR/eMtxk6IFIUj5UuDl\n",
       "PMM4z1oQ+osBb1nif5TRWLwwcS2PSCxfWBA/SG4zMvghh89bj7Msa/37GOAB/+PXr7322vvAqQ8+\n",
       "+CAXXHAB0DGXTmlpabZJXFFRwezZs5k/fz4LFixg3rx53Hvvveyxxx7ZkKJZs2ZRWVkJwB133ME3\n",
       "f+e66D575mfZZZddAGhtbWXEiBH87//+L7feeit1dXU89dRT7Lrrrjll+2vt1AxXStHe3h7chxH+\n",
       "Gpfiuhhm4qbU3QfnKmoI7kWoW0LTOSP9VGA1sALYHB45FRK/YAK5aFxmcM+lyS0MSIouljGELjoP\n",
       "d0HRCx+klJoGvG+tfZH8zPH7gW9eh5w/dbhRQEGzPLAwG0PHr/RC+UPcSJ/fAaeuXbu2m8txfOtb\n",
       "3+K5557jwQcf5Nprrw3m/e4Rra2tXHnllZSWlvLAAw9k5yPvjuXLl9PQ0ADOmp4T2tSAm2eoBHjd\n",
       "r5sGHKmUCrIN1eMsdKy1jwYHhgL859ARn1ooC9Ek/x79M8rbzRLrogShjym6WOZDdZ4VMMfT3cVx\n",
       "PXEShdOMNQINoR92G24oYzA+OkhP1oxLcLwI+KtS6mJcxvFtuOlks7GP4PoSg/fAsguWE4kEP/nJ\n",
       "TzjhhBO47rrrqKqq4ktf+hIAW7Z0xP1v3rw5e76tW7dSU+Nigpqamli4cCGrV69m7ty5TJ48mfb2\n",
       "9qw1mclksmWGPeBNTU189atfDU7/V9x471JgL5zVnB3yaa39pb+vwZS/QbM77wRnYcdP5FmV4cfX\n",
       "+z+YTtNSdOEJl1kehQHBgBRLOvq7up3sKt+PyDsUXsXNlfNFOsY5Z0NabG5qsWCxDtf0fBNn6ZRF\n",
       "Tr2Xfy+bNGnSH1evXh2sfxUnmFRXV2eFKfCGh5vh5eXl2fImTpzII488wnHHHcfVV19NY2Mj3/jG\n",
       "N5gwYUK2SV5ZWUnyWTd/z6RJk7Ke74aGBr7zne8watQorr766pzx58E1RZvemUyGk046iaVLl4Jr\n",
       "Qj/t38txIUNtuCTHM3EJSbJWYhehVlE6OWeUUssi625DEAYZRXfwFGAVHXPZRMk6YHrQ+T+NLibZ\n",
       "CnlkX8QljAh+8NHpXsuASmDy6tWr/xla/zReSMNWYRwmT57MY489Rm1tLbfeeisHH3wwv/71r7tM\n",
       "GNzQ0MAZZ5zB5s2bufHGG7P9mN3xwAMPBEIZZLnfhosE2IzzVO+DS5RR4a91Aj6Eyq/bg47kx4WY\n",
       "SmTK4egQ0zhEw7/EySMUmwFpWcZocgXhK0GTL1gfNPWCH+YSYInK9Yh3VW5O5u5IDGfUonoWGI/L\n",
       "Ev9t4AaAt956Kyt0QfM33CROp9M5MZdKKaZMmcLSpUu57bbbuP7667nwwgv5+c9/zgUXXEA6nWZ7\n",
       "866UJJPZseCzZ89m3bp1fO973+PjH/84GT+aJ5VK5TS9g2Xrp939xje+EYxf/wVwJi7J77N0OFf2\n",
       "AGbTkeA4+KOYSmcruxDhPuZqoArYXmBQQc6AA0EYyAxIseyG+gLL4GIBgfxxfNH1XfWHhSyZZcol\n",
       "4AgL71ScyNQC26y1Vim1ALj8ueeeo62tjfLy8k4JeIHsOiAncHzMmDFcffXVnHPOOcydO5c//OEP\n",
       "PPXUUwAcddldAOy334eD7EBcddVVXHrppTn9kUFfaLAclKOU4g9/+AOvv/46Y8aMYdOmTWfirMkk\n",
       "Ptge59B5E2c5B/cnPFvnREK5KfPdt9D6wLmTN5FGT5H+SmEgMKjEsitR64GDIGyNduqDK9DsO9qP\n",
       "PImW0YDLKB4Et7/w0ksvHXrRRRd1G5xeiA984AM8+OCD/PGPf8QYQ2trK0tTo0m1pzjwwAPZZ599\n",
       "mDZtGl/5yld6dN63334bgG3btgEcdMABB7By5cq5uJhIgL3xji7IXn8ZHfcnbwq27oQz9JnofmJR\n",
       "DiCUskqp0/2npLX2t0WtzwBkUInlThDOmRjug6wHWrzYVdBZPFuAg/Gjdbyn9yS/7XVcczXrEAGu\n",
       "mjFjxqM//elPefTRR5k8eTITJ05k3bp1rF69mtbWVn7/+99zwAEHAK4ZHozZDsaRB8vHH388xx9/\n",
       "PM3Nzaz42QsA3Pvkk9n4yyDgPexpj3rAQ90TXHTRRYDr75w/fz733XcfwGnANbi5h0pwE5TlZKHP\n",
       "J5A7G+8aB7Em+5dkaXmLtfZhcNmIil2fgcigF8vuflSh+L+AF4EpOCGchov5e7CLUwSOoXpgzvXX\n",
       "X3/yV7/61XrgD6F+twpcYPeZy5cvXwgcWlNTc8jSpUt57rnnck724x//mB/84AfZz0HdAm82uMD1\n",
       "3Oa027eqqiorrkHQeVdN73A/acDkyZP5wAc+EHw8wr8vDlUxO3wxeiOUS35xBO6eBaOY6sjjjIsT\n",
       "Cxt3uyAMBHZILLXWVcBhwEvGmI29W6XeIfLDa8El0cgnnqtDjp98zczRuMxGU4GGr371q7NxY8xT\n",
       "vpwmpdS+dFisM4BxDQ0Nt+AcJuNxzdv3gC/E9Vz3Jk8//XR2ubW19R1jzF577rkna9as+TnuzyDc\n",
       "3M7pl4zBZApMNVyInRHHxsbGw2QqXKEY9Dh0SGtdCXwKOA+4Rmt9eDeH7DDR0KAehArlnIPOYUMV\n",
       "QIW19rYYMX/PEMq4g2uS70vuPD+TcUkoDC5zz+4jRoz4kt/2MnAXrk+QKVOmdDlm20YmOEun0y53\n",
       "ryVnfbgZHhxnreXXv/41H/nIR3jllVey6+6///6g7g8CN2UymVPWrFlTgguTynq5A2eYUmof3LDH\n",
       "nDAt4EDfl1WPS4xxDs4qfZuOSd2y9z10fzrNvxMm6oQThIHIjliWRwMPG2N+rLX+CnAWLoXXQGZV\n",
       "YC3FFVsVymPpvbuPhjzhi/22OThr9E3cvXwLF6sYOFJa/b7bRowYcYq1luOPP77bZnNpaWlOQDkh\n",
       "73m02R49xxe+8AU2bdrEokWL+PjHP87IkSO588472WOPPVi7du2t4HIKW2vT/rh9cKOVlvkuhZk4\n",
       "ofwL8AE6wrTyUYLrs40KZdA10aI6psjNjpjaGWGUOXiEYrEjYrkWOFZr/QrwI+DHWuspxphen8+5\n",
       "0DjhGKErSwqdw/N+9BjPVLzY4QTwcOBwpVS2/y4UFjMHOFApNS80wgVcEokpyWSSdDqtgWPGjh07\n",
       "//333+e+++5j9OjRPP3009TX13PGGWcwadKk4LzZSqRSqZxYTGda5jqBAsdO+Djr59O57TZnLAcW\n",
       "5ZQpU1ixYsVNuLnCA293ODyoDDgB2B/XnVBvrX1TKfUB8gxxDIVRBaFB+aaGeMZ3URyHH0IZDjIX\n",
       "ioNSandc1xC4nAZCTHZkBM97uAkRGo0xW4HfAhu11mVa64KjZPqRqaqA9Rj6oU6PbMrXTKzHWcxb\n",
       "QtsqlJv47Dg6kk4E1PnXN4Er0+n0I0D17rvvPn/jxo3ccccdTJs2jRNOOIHjjjuOefPmUVtby+zZ\n",
       "s/n73/+eYyUGzptgSlt3u3PXB5ZlMplk5cqVXHjhhTz55JNcfPHFQX3WA88Bv1mxYsXlwCPkyazk\n",
       "uyHuwHn5Z+K6EkYpl4UeOsKjOlnlwcicaDM6MmJnmX8JA4MjgU3+9UiR6zKoiGVZaq1VMB2uMaZR\n",
       "a32/MSaYBOYN4F3gs8B0rfWXjDHpQufqDboKXemiyRimwfpsRJFjWoDnww6fPCNOjsb1W4ZHqvyQ\n",
       "jqlyK3AJN54ADv3nP//JzTffzPnnn8+pp57KkiVLwIlHi7V21mOPPVY6YcIE7rrrrp7cghyuuuoq\n",
       "HnroIRYuXMhhhx1GZWUlY8eO3W3NmjXX2dzsP9AxHURjyNKbCexGR1alKcALgQUZOb5LCln93Q0M\n",
       "yLef0Ce0WWvfKnYlBiNdWpZa63Jw84ZrrZPBemNMRmsdKMwmnGUyH7irr4WyO7pzFuTb3tUx4aa/\n",
       "t5Y0ubGIRwIHAutsR5Yk/D4JgLlz57Jt2zaefPJJDj74YHAOkSqgdK+99uLrX/96QWePG8roPDxR\n",
       "x4+1lubmZh5//PGgLiv+8pe/0NzczJo1axZFhPJiX9cJODE8nFxr+m1cCFAL0ESkad1TJ0xgidod\n",
       "GBcuCAOR7izLc7XWs4wxFxhj0lrrZCCGgaUJbMdl1/6IMWbAJG4NOWPqQ4KXTf1W4LBOMxHmOWdA\n",
       "EMBeS0eKt3l+XfA6PZlM8tJLL3HdddfR1tbGyy+/DM4pxrhx43jiiSeYNGkS1toc502Og4fO64Mm\n",
       "+xNPPMH27dvBZT5agfO+jwVujdQ3OzoH583fgmteVxNqJtuONGtzehIOFD4+z73Ku090WSk1Tyk1\n",
       "1RZIAScIxaS7Pss1wD5a6x8CBIIZbNRaH2qMWQOcPpCEMh9eKKd0s72OPFmNQlZVBR3ZwQPrchFO\n",
       "hIIs6mEr7OV0Os306dP5zW86z9R40EEHMXny5B2+pr/+9a+cf/75wccXcDk1K3HZhA7GWY+jfH3m\n",
       "0tF1cA/wkF8+2r/CfYv1uD/SGT2pT7hfMxSG1ONwL0EYiHRnWf7BGPN7rfUCrfWtxpiLvWCW4ZqR\n",
       "39dazzHGbOiHuvaIcH9biBVdWJXhkTo5lmlonyBRhw6VgVIqSGm2PGKJXYVvogP/C+wKfBConjJl\n",
       "in7yySf51re+xTXXXJPj1Y4m6/3nP/9JaWkp27dvp6qqivb2du666y6uvPLKIETpb7jZK++go08V\n",
       "XNq49ki8IxHvfYtfnx377kUur5Wdr0+yt8RQLEphINOdWAZOnfla6xtDgtkGtGmtT/DLAx7r0691\n",
       "Eb6yyu8XziwUbsJ/0W+/DefICYvEM/41Mywc/lyfDZUxFTenzVsrVqxora2tvebaa69lxIgROYkx\n",
       "As84wN13301L8whamps54ogjuOmmm5g7dy7GGKqrq8lkMv+Ja3bX4hw1QV9jOMVaUHYwO2VU7AJP\n",
       "fjht2qPkJ9/8RNnrLbQuKrI7M4pHEIpBl2IZOHKMMdYYc7nW+hqt9RJgIXAvLrv2gCbyo+z2hx4S\n",
       "yijhdGXBVAsnA38LHUvo2Dbl8mHW4Ub4BPf6fVxYDw0NDUsnTpw4a/78+VRUVDB37tycAm+99Vbm\n",
       "zZvHkZfdhVKJ1CuvvFJy4oknBpv/0dTU9II/7wQ6PNmBt7vehkYnqY55vhvyCFWhRMv56NTdIoIn\n",
       "DAe6DR3ynvAgdOh2XP7DZcX2eu8gcftVs7GIISfH7yP7ZD3i4X7NSBhSmLCgnQlsAB55++233x4/\n",
       "fvzHLr30UqqqqvjMZz7D8uXL+dnPfsaPfvQjxo0bh0ok2ypG7tKIi+s8FRcwf6E/36f9OaNzChFp\n",
       "ftficnAGn8P3IuibDMKIguVeo6tQIkEYDMSKswx5vjcCZxhjejZ3QhHJ53ntqgkYaZ6GN7WE1gdB\n",
       "6Ysi6/KNKjrHLwZC2UCucL787rvvtu6yyy6f/tznPsfnPve57LH77bcfr7/++mN1Sh3b3tI00tfh\n",
       "Z8BP6ZiVsQFvqeKTfeCEMGh2BwKZwjXL63BxpuF6toWuIUdIC1xX9k/EO8am4YeUEkGa28JQoUfD\n",
       "HYO+yj6qS79QwHGTly5+/NGpXYNmeb75zcMWX+DEiPZ5Nm3YsGEKcGho1+2vv/7614ESlSw5IpNq\n",
       "L/frX8R5ug+MlFEPnBFaF4Q0RWnIsy58L4yv26x8zrACgf89zjwkCIONQZ/Pcgepj2NlRsNgQusM\n",
       "nYfwha2xebgx5g9ER9D4bVhrb/bC80W/bwrglltuYdGiRfzxj3+sAm4CUJl2rE1Em/XBUMuw+L3m\n",
       "38Pz5YQD6IP1ef8oQqOUZobX5dsvtLzUe87zZhUS8RSGCsNOLLv78cYRT9x821W4kS7h8wae9Fq8\n",
       "+IUs0bBoRa2713BNZg4++GBmz57NwoULWb58Odu2bSPVnqK0rLSCjiZ1cP7XyHXOrKJDtN7GBZ8b\n",
       "Oo8HXxL9I8gTD1kRN/FFAWtTEIYUw04so3Q14qSAUEzFBac/k2dbwKI85w2azQ+RG8sZpI/7CMDR\n",
       "Rx+dcyKlFEfOvID29lTQbxykO2vDNcnzTYcBLgfnK4RiQrsRtEBkt/n3Brxg4mIwc5rk0hcpDDeG\n",
       "vVhGyeOgiVpgwX5NhfaLnPJ93LziAVFRm+rDehQuuHw0UI7LjbnZWltXUlIyKW1tGjgdN0zx9zgR\n",
       "zAkcj1i3OUTr14XI/c1vfzHaJO8KEU1hqCNi6elBsHTUKx7ed2po5Et0Nsj6fOXQkXV8Ax1DEFcD\n",
       "z1lr1yulPkxJ+d0Jm0ng0uNtxE1zEZ7Tex9cXGe+/tX6cLO7i+sL6vdi6J40USCEqJBFLqIpDFVE\n",
       "LLshjyiEHS1TCXnAlUsIfAywFC9eof0gv2OlBde/OBHXxM7OgeOPnwRYpRJp3LDJcE7KzwG7AyuD\n",
       "ckJ1yXrtwwIZFrd8DqwdoKtrE4Qhg4hlF+SzwiJ9d1GBCBw3y/OcLu+828A83JjxRmA2cJhS6pu4\n",
       "nJhRD3MDuZbibjhrc6HfPzqTV9SqnEVu/2OO2Hd13V2QYzELwlBFxDImXYTQhNff4ddH8zdGvc1h\n",
       "a2wdkNx1110/+d5774Gb9+YG4E6/z5GZdKo8UVLaimt6t4TOc51/PwjXh/lEvj7JkHU8K1KvcLhT\n",
       "MCa8iS6Ghfag71MQhhQilhHyicyOoDrmp5lJ/hjEQKgagEXvvfde+9ixYz9+4okncv/997+Fb5ID\n",
       "2jfBweXBrMM5eFoiXQQnA6d4Z1GQMCM7wsg3tXM82mGxD9U3XDdBEDwiljEokIUoX1M1PK46KpLh\n",
       "WMf6aP8h8OONGze+f//997+B678MmtSXl1aNmO1H8CRwadeeCVuv/lxBHOeImNc0CzgNeMNae2f0\n",
       "fIWuUSxJYbgiYtkNXWQh6o4WnJf6TRvK0+gtv6lANPEGuBE/S4JRPuFyfTP87zgRnYlr2odHA90Z\n",
       "Ok/cvJB7A6XhFXH6KyXGUhiOiFjGo5NzJp/1lcdzvrirk0bGqU8FzlRKzbEuq3l2e6a9LQhHChxI\n",
       "U3HWa23kXF3GiUbX4RxDIn6CEAMRy26IKSDhVG49OTZqsW6ATrMfksmkA+sv2pe4iC6m/u2OkLgH\n",
       "lmysECIRVWE4ImLZDTtidXWzb32BZQPcYa1tiojfskQi2Y5SNtpsj4woCluOwXxDK7pLhJGnHnGv\n",
       "QxCGFSKWPaSAeBaKoQyOyYblFHKWhL3R0XMlSstalErY8Dal1Cm4kKHlQb3y1GGaUuqDRBxKO2AB\n",
       "C8KwR8SyGwol04gOLcxHyEJc5j8HcY4Vwbm76Wv0I3ASlhhEvPZ3xnFOSX+lIMRDxLKHhJq+efsp\n",
       "AyLC1eTXhXcJEmhAZEhisB3nwKlPt7eVh84ZiPSjys3xk3ecdmjfrGdcBFEQdpwdFkut9TG4TDmv\n",
       "+bnDhw0RweyUNd0Tzh0ZNMOzQeGqY3KzvIkucP2Ibihhur1MJUvbQsfmdehEgsy7S5wRPkYsTEHo\n",
       "hh0SS631DGA7Tiw1MKTFMl9Qekgwg7lwcuIe6WYUjD++xZ8/O2Y75Jk2/r1FJUvaEyUlbXRkZz+a\n",
       "zlmNOp0/VHdBEHaSxA4elwTeMcYsA8ZrradprXf0XIOJnDAdL0iLIH+qspCwNhGZU7wLshYlzoFD\n",
       "srQ8yHR0gn89gxsj/sWwBZnv/HEzCkXjREVkBSGXHluWWmsFpIHvaq33xE1WlQDu0Vq/Yoz5eS/X\n",
       "segEzdtCYhQK37k5EJo8ApW1QEPH5ss+HgSpa9ywx+Xp9tYgKL3VH9ekYk7j0FVQujS5hwdKqTKg\n",
       "0n+s6GpfoTA9Fks/j/iLwKXASUANsMgYs15rfZTWOjlI5xTvlu76/ULkc/50mlUxhmg1WGuX/NtV\n",
       "D5T5/R4NlbkUlzezUx2UmwRtMh0jiLp0RsW4HmFwcxoulR/AP4pZkcFMLLHUWlcZY7aHVmWMMRu0\n",
       "1ouBw71QluIS1b5Ixzwuw4LokMd8Vl9kfHh1px0cLcDzXgizgpVIlvR0+uHJwB6FNooYDjvarbVd\n",
       "zRklxKBbsdRaTweO0Vr/A9hkjHnaGJPxfZRVwPFa67XA4cBiY8ywEsp8BN7tAs3xnP3inC/UZxmX\n",
       "xeF60E3QfIA0zwXPXkqp0/3ya9ba/ytqbQYIXYql1vogXB/H3cAs4CSt9VhjzIPGmAywTmv9Q9yU\n",
       "sA8bY97t8xoPQHoiLpFx39FEuku7OnYHzxn2isdJMycMc6y1twfLSqnTABFLurcstwD/AryAaxZm\n",
       "gH/TWrcZYx7RWu8DHGuM+Wkf13PQsSMC1BPx6mbfHvVRBohoCkJhuhPLjcDBwEZjzJNa62dw07TW\n",
       "aq0D79qrfVnBwUbcIPDocsQTHofs1A/Rc4b7TCP1EY+4IOwgXYqlMWar1vo+4GKtdSvwPO4HdzGw\n",
       "pzHmdeDNvq/m4CZfDGaBXbtMeBHdt1A53QmgD4KvA1Z1tZ8gCB10G0hujFkJ3Ap8AjcHzGhgBbC1\n",
       "b6s2OIkbBB73OKXUcaE4S8KOowJDLHMSZ3RRnxfFqhSE+MQKHTLGrNRaX4dL7HA68CtjzLo+rdkQ\n",
       "oouMQhDxVEecNdX0LIg4VhN+Rx1JgjCciR2U7pNlrNFaP+s94UL/8Ew4dKg3QpGEoY9SaldcBIsF\n",
       "DgEeLm6NBj87MoJHhLIH5OtHjDpbwkT2awL40DcWyRA1oadMAZ621m4BflfsygwFhkPyi0FF3CQW\n",
       "kuxCEPoXEcs+ZkcdPuDGeCulvpgsLW/ZgVE8gtAb7K2UOl0p9RGl1L7FrkwxkUzp/Ux3YUR5hHVy\n",
       "e0vTyDjjwyV2UuhtrLW3ASilxgH7Am8Ut0bFQ8SyyHQlntba2/z28/q9YsKgQym1Gy4T2GZgd/xk\n",
       "dkLvIGLZzxQII+py/5OufWRLofNEMx5F1/VWvYVBQTXwkrX278WuyFBExLJI9FTQ0u2tFV1kMdqh\n",
       "sZjUmtEAAAjjSURBVOCC0ANSwKG+OV4NPGKtHVYDU0QsBzn58meKaA4flFIJ4P8Bb+FSJj7bF+VY\n",
       "azcCt/syZ+AEc1iJpXjDi0RXwxuVUvPCc+uk21srAm/4zsyzIwxZVltrH7bW/tJa21+TB05TSs30\n",
       "wjksEMtyABFKcNEJPz68J1mJhCGGUmoSHXPpnIibIkLRMRNof/ESMDZUj2HhSBKxHHi8GB677R08\n",
       "LV4sJXHvMEMp9a/ABP/xA8Ajfvkn1trNxaiTtbYd+CeAUmqLUupkv2n7UJ6+QsRyANFVgotkaXmX\n",
       "84QLQ5YJ1tqBPK77YdzU2ACzi1mRvkbEcoAR12IU4RxaKKXqgP38x/3pSKq9oTg1ioe1NoObQQGl\n",
       "1JuhuXtG4uI9AXa11v6kCNXrVUQsBaGPUUqVAEFTNYmbxbMdmAa8jhObzAC3ILvFWvsSrj8zB6XU\n",
       "p0MiWoZvwvv3YIrebb55P2ARsRxgiMVYfHw4TtC0DProUEqNBnbxq2txU6yAC6NpyrN8EPAKLurk\n",
       "b8AavxxkkXoe189n++RCBgjW2nuCZaXUSDru7RTcSKMyYH+l1DvACNxU2k04fdqASzNX5t/BCevK\n",
       "/ql9B8UQy+BG7aW1LkLxA5vGxsbDACZMmPCXYN2eZ15ZAqC1nlSkag0k9vLvyQLbkwAbNmz42IgR\n",
       "I7YppVoAMpnMiEQi0QRgra0Ira9OJBJN1toya21pIpFoqqqqqvH7tllrq2tqaloBqqurS8vKyl4H\n",
       "SCaTTWPHju1u/qlXQsslwD75dir276A/v1/7779/+OM7oeV/AKTT6URrq5sZIJ1Ol6VSqQoAa20i\n",
       "mUy2ATQ3N+uamprDADKZzOhEIrHZ71OllNrulyuVUs2A8svbrbWlgFJKtfnljFIqHf4+VFZWlo8Z\n",
       "MwbyfL9Uf/+paa2PBP7Ur4UKQ5GjjDGdArDl+yX0Ep2+X8WwLJcDRwGNQLoI5QuDmyQulKZQbJ98\n",
       "v4SdoeD3q98tS0EQhMGIDHcUBEGIgYilIAhCDEQsBUEQYjDo4yy11mXA4caYp4pdl2Kgta4CDgNe\n",
       "MsZsLFIdynEJQN4qVh2GKsV+vvJsOxj0Dh6tdTXwM+D3xpi7ilSHY3DZX17z86v3V7mVwKeBI4At\n",
       "wH3GmD/3V/m+DklgDm5+lueMMc/1Z/n9RTGecbGf70B4tj4UrBp33//R3+WHGQrN8DZcJpaPaK3/\n",
       "X38XrrWeAWz3r/6OLj4aeNgYcx4u+etZ/Vw+wERgd2PMDcCftdaHaK3HFKEefUYRn3Gxn29Rn63W\n",
       "+lDcPa8ATtNaf7K/ys7HoBdLY0w78EvgM8CxWuuL+rkKSeAdY8wyYLzWeprWur/u61rcNR8I/AjY\n",
       "Q2s9pZ/KBsAYsxqo1VqfAhyCmzDry1rrc/qzHn1MsZ5xUZ/vAHi2ewFNxpiHgKeAD2itP91PZXdi\n",
       "0IulZw9cUtQLgBO01ldrrXfv60K11goX+PxdrfUS4AaclfsdrfWn+rp8XBICBTQaY7YCvwU2aq3L\n",
       "tNbT+rpw30wDeAE4A9jLGLMAWAZM0Vrv1td16GuK/IyL9nwHyLPdBBzjrdlXcOng9vFN835nUIul\n",
       "/yJjjHkNGGmMaQLuBS4C5gXb+wpjjAVeBC4F7gCuBaYaY+YDb4a+cL1G+JqMMY3A/caYII3XG8C7\n",
       "wLnA5/ui/HAdjDHBCJlncPOxHKG13s8YsxhopkDW98FEfz/jYj/fAfZs38FlZjoVN7/QK7iZAvbr\n",
       "6qC+YtCIpda6XGv9Ga31LK31AeC+yFrrwKOvtNan4bKVfBdY6L/ovV2PqsiqjP8yLwbeMMas11qX\n",
       "ApPomAKgN8oth+w1Z38kxphM6Ae2CfeDng/cFfrC91kdtNbKGPMmbjKrjcBsb3G9SkdOxkFFMZ5x\n",
       "sZ/vQHi2WusR4c/GmDeAW3AOrk/g+lCfAEbneUZ9zqDwhvsv5r/hUlwdiEuO+rIx5rehfXYH9vH9\n",
       "Sn1Vj+nAMbgMKZuMMU/79QlgV+DLwD3A4cBiY8y7vVj254BZxpgL/Odk9Meitd4T+AVwqTGm1+fq\n",
       "KVQHrXXC/6hH4NJoHQU8b4zZ1Nt16GuK9YyL/XyL/Wx9v+i5uGb+08aYF7xYW611HXAcrjukDef0\n",
       "eq+L0/UJg8WyrMTlEXwdeAiXB/AIrfWZoX3G9bFQHoTzyt2Ne2Anaa3/Hdy/vzFmHfBDnKA/3JtC\n",
       "6VmD66/5oS8zHbZAtNaH+pCW0/tCKLuqgzEmE1TDGNNkjHlskAplMZ9xsZ9v0Z6t74PcBlyH8z8c\n",
       "6zcprXWJMWYVzrq9E3ioGEIJg8eyTALn47yDj+G+0McAM3H/tOtxIvpR4L0+an7v48v7nV91DM7a\n",
       "fdoY84jffqwx5qe9XbYvP/inXwCMMMZc7NeX4fpzHgLmhPq3ilGH39KHz6CvKeYzLvbzLeaz1VrX\n",
       "+jLexMV03gR8wRjT4LdPBE4wxizszXJ7yqCwLH1z5E/A6bjRDC3An3F9OLsaYzYDJxpj1vfhj3Qj\n",
       "cDButFAzruP7OVxoRdBv1Zd9dBbAOxaatda3+s9txpj3cV+mvp6vpbs69PUz6GuK+YyL/XyL+Wy3\n",
       "4Jw4dd5qXggkvJ+iDtf8XtUH5faIQWFZBmgXY/YlXOjGU8ABuP7LewHb1z9S71i6GLgP1xVQ6T//\n",
       "yhjzel+W7ctXwTVqra/BBS0vxF1/pj9EaiDUoS8p5jMu9r0tZvla6ypjzHa/fCZuGo524HxjzPV9\n",
       "VW5PGBSWZYAxZgXwPWAMcCEwHtfJ3i8/UmPMSuBWnGfuLGA0sAIXWtHn+M7uwDN6Oy4Gb5kxJt1f\n",
       "IjUQ6tCXFPMZF/veFrP8QCg9zwB744yiF/qy3J4wqCzLMFrr0Thrst8nmvdeyVrchFS/8h3//V2H\n",
       "MqDCGLOlv8seSHXoK4r9jIt9b4tZvtZ6b5xX/JPGmCf7u/xCDFqxHAgEYRXFrofQd8gz7n+8UO9u\n",
       "jHm72HUJI2IpCIIQg0HVZykIglAsRCwFQRBiIGIpCIIQAxFLQRCEGIhYCoIgxEDEUhAEIQYiloIg\n",
       "CDH4//rcwmNu92/8AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10af0aa50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import triangle\n",
    "samples = np.vstack([pool.thetas for pool in pools])\n",
    "fig = triangle.corner(samples, truths= means)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Omitting the first couple of iterations.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 1.0924 ± 0.0170\n",
      "mean: 1.4953 ± 0.0167\n"
     ]
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAVIAAAFSCAYAAACg1VfvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXecXHW5/9/PzGxNdjebTbLpRQiHGlq4QZrSBJQizYsK\n",
       "CMK1IMoFuXLlqvf+aApiAUVFpalgA5UL4YpIwIBICSAhlEMa6Qkp27LZNjPP74/vOZOzk9mW2c3s\n",
       "bp736zWvnDlzyjOT2c98v9+niapiGIZh7DyxQhtgGIYx1DEhNQzDyBMTUsMwjDwxITUMw8iTRKEN\n",
       "yMbzvBLgMGAdkCqwOcbQIw5MAF7yfb+t0MYYuweDTkhxIvpMoY0whjxHA88W2ghj92AwCum64N+j\n",
       "gdWFNGQ4MemMa58FWPPwTUcV2pYBZjLuh3hdTwcaRn8xGIU0nM6v9n3/3UIaMpw46fq5SYDh/pl6\n",
       "nhdu2rKQscswZ5NhGEaemJAahmHkiQmpYRhGnpiQGoZh5IkJqWEYRp6YkBqGYeSJCalhGEaemJAa\n",
       "hmHkiQmpYRhGnpiQGoZh5MlgTBE1ABE5HigLno5R1XsLaI5hGN1gQjp4KVfVRwBE5LRCG2MYRtfY\n",
       "1N4wDCNPTEgNwzDyxITUMAwjT0xIDcMw8sSE1DAMI09MSA3DMPLEhNQwDCNPTEgNwzDyxITUMAwj\n",
       "TyyzaYghIkcB1cHTdaq6oJD2GIZhQjoUGdVT6qiIfBJoBIqBZ1V1wy60zzB2O2xqPzxpCMR2AVBb\n",
       "aGMMY7hjQmoYhpEnNrUfGqRF5NRgu7SglhiGsQMmpEMAVZ1baBsMw+gam9obhmHkiQmpYRhGnpiQ\n",
       "GoZh5IkJqWEYRp6YkA5vUsCRInJasr2lXFV3OEBEDhSRU4PHB3e5hYYxDDAhHcao6mpV/bGqPiIS\n",
       "S6EqOQ6boqqPquqjQMWuttEwhgMmpIZhGHliQmoYhpEnJqSGYRh5YkJqGIaRJ5YiOkwQkU8ATcHT\n",
       "9wppi2HsbpiQDh+awjqlhmHsWmxqbxiGkScmpIZhGHliQmoYhpEnJqSGYRh5YkJqGIaRJyakhmEY\n",
       "eWJCahiGkScmpIZhGHliAfkFQERigBfZtVRV2wtlj2EY+WEj0sJQBswGOoBpwJTCmpOhSkQODh6D\n",
       "xSbDGPTYiLRwrFHVJSJSVGhDIswFRgTb7wdWFdAWwxgy2Ih0NyEWTyTTyfZSETlNRK7JdYyq1gVV\n",
       "9VcDrbvYRMMYstiIdDdBYvFUvDje4tqO5Oo4YhjGzmJCWng6gGNEZF/ctPplIA2M7cW5I0Tk1GC7\n",
       "YYDsMwyjB0xIC4yqLgGWAIjISGBq8NKzvTj3NwNommEYvcSEdBChqluBNwtth2EYfcOcTYZhGHli\n",
       "QmoYhpEnJqSGYRh5YkJqGIaRJyakhmEYeWJCahiGkScmpIZhGHliQmoYhpEnFpC/e/KWiJwWbLcV\n",
       "1BLDGAaYkO6GRNNSDcPIH5vaG4Zh5IkJqWEYRp7Y1H6AEZGpQEnw9D1VtXJ3hjHMsBHpwHM87nOO\n",
       "AccV2BbDMAYAG5EOPJtU1QcQkb0KbYxhGP2PjUgNwzDyxEakA4CIfA5YHTy1MCPDGOaYkA4Ma1T1\n",
       "0UIbYRjGrsGm9oZhGHliQmoYhpEnJqSGYRh5YkJqGIaRJyakhmEYeWJCahiGkScmpIZhGHliQmoY\n",
       "hpEnJqSGYRh5YkJqGIaRJ5YiauwUIhIHxkd2rVfVVKHsMYxCYiNSY2cZDZwI1ALHAuMKa45hFA4b\n",
       "kRr58LaqviIi9oNs7NbYH4BhGEaemJAahmHkiQmpYRhGnpiQGoZh5IkJqWEYRp6Y137XcqCIKFAK\n",
       "bCm0MYZh9A8mpLsQVb2h0DYYhtH/2NTeMAwjT2xE2kdE5F9w2TwANap6bwHNGUiKROS0YLsEaA22\n",
       "N6nq8wWyyTAGJSakfWecqj4CEBGaYYeq/iHX/uH8ng1jZ7GpvWEYRp6YkBqGYeSJCalhGEae2Bpp\n",
       "PyEilUB58LS0kLYYhrFrMSHtP04D3gm2FxTSEMMwdi0mpP1Ho6q+VGgjDMPY9dgaqWEYRp7YiDQ/\n",
       "VkTiKlu7PXI3RESOA0YET0eq6q8LaY9hDBQmpHmgqguBhYW2Yxezj4gAjATe7uHYEbtD8oJhmJAa\n",
       "fUJVbym0DYYx2LA1UsMwjDwxITUMw8gTE1LDMIw8MSE1DMPIExNSwzCMPDEhNQzDyBMLfzL6g1bg\n",
       "WBFpxMWO/rbQBhnGrsSEtBeIyCHA/kAdNorfAVVdBCwCEJFTC2yOYexyTEh7Rwx4QlXXFdoQwzAG\n",
       "H8NeSLOa1bWr6uPB/jIgHtnfXgj7DMMY+gx7IaXrZnUXsT1XvBb4TfQkEYkDEyKvrxlYMw3DGKrs\n",
       "zut9q1X1KVV9CmjO8fpo4DhgDE5EN+1K4wzDGDrsDiPSfHhHVf9ZaCMMwxjc7M4jUsMwjH7BhNQw\n",
       "DCNPbGqfhYicCSSBCrY3szMMw+gSE9IdSYZefqNfqRaRDwTb61XVL6g1htGPmJAau4rfAcXB9glA\n",
       "vwmpiOwBTAOorq5OjB07tr8ubRi9woTU2CWoaitBg0AR6ch1jIicD9Tjvpdvqmpvl1YOAJ4AaG9v\n",
       "/2T+1hpG3zBnkzGYaFDVR3GiOLkP56VUtVlVm0UkOUC2GUaX7G4j0vJIdlNpQS0xABCRCran6toP\n",
       "uzEk2a2E1Mq7DUo+BbwWbL9QSEMMY2fZrYS0G8Je7bB9dGTsHDER2S/YntDtkY4VqvrMQBpkGAPN\n",
       "oBXStWvXHi8iL++KFE3r1d6vPAmMC7b/r5CGGMauYtCuSU2cOPFJYEqh7TD6RuD0WR48VhXaHsPY\n",
       "FQzaEakxrBkpIuGPZHG3RxrGEMCE1CgEzwM1wfbfC2mIYfQHJqTGLkdVl/f2WBEZB3wQaAGqgQeA\n",
       "VHAdHQj7DKOvDGkhFZFSYHZk1/OqagHZw4sa4GVVXRqI6knB/gOBmwpnlmFsZ0gLKdt7Mb0BeMAZ\n",
       "ItIOjFHVewpnljEQqOp7wFwAERm0jlJj92OoCylAo6rW4dbdgB16MxnDk4SI7Blsjy6oJcZuj/2q\n",
       "G0OVp4Gi4PG3wppi7O4MhxGpMfxoB8aIyKlACS7IvxPBLKRuVxtmGLkwITUGHaragatfahhDgsEo\n",
       "pGGu++SRI0eO8zxvelcHjhkzZlIymazwPK8xuj96Xk/X2F2YdMa1CYDh/lmUlJSE8alWM8HYZchg\n",
       "C8XzPO8owIpYGPlytO/7zxbaCGP3YDCOSF8CjgbWEQReG0YfiOOqTr1UaEOM3YdBNyI1DMMYalj4\n",
       "k2EYRp6YkBqGYeSJCalhGEaeDDpnk+d5JcBhmLPJ2Dkyzibf99uiL9h3y8iTLr9bg05IcV90C38y\n",
       "8uVoIDv8yb5bRn+ww3drMArpuuDfo4HVhTRkKJJOp+WEE05YNnr0aJYuXcoNN9zARz7ykRmTzrj2\n",
       "WYA1D990VKFtHGAm48RyXY7X7Lu1k+xG35/u6PK7NRiFNJxyrfZ9/91CGjIUEZHLlixZknleWlqK\n",
       "7/vvnnT93CTAcP9MPc8LN3NN3e27tZPsLt+f7ujuu2XOpuHHzwjad0yZMoX77ruvpofjDcPIExPS\n",
       "YUZQ8ONY4MxVq1aNUtUthbbJMIY7g3Fqb+RJIKZ/KrQdhrG7YCNSwzCMPDEh3YWISExEPiYiYwpt\n",
       "y2BEHMeLSFWhbTGMvmBCuosImrXNA347YsSIjSIypdA2DSZERICHgb9WV1fXBx1DDWNIYEK6C4iI\n",
       "6AcAmpubicViK01MHRERPQ2grq6OeDy+wcTUGCqYkO4a5hCIaEg6nQb4XkGsGXzsRyCiIalUCqxv\n",
       "vTFEMCHdNbwMrM2x/5u72pBBylvAsugON0jl1oJYYxh9xIR0F6Cq7cCeuO6YIW+p6ssFMmlQoaop\n",
       "YB+gObJvgaq+XTirDKP3WBzpLkJVW0RkFK69cKmqri+0TYOBYH30PGABMBooBoqCdsvGACAiU4F/\n",
       "AdqAGlW9t7AWDX1MSHchqtoCtHT1uoichSvTNQv4q6r+Ptj/P4CH6+P+VLi/vxGRC4CzcLnEf1LV\n",
       "Xw3EfSL3E2A5ME1EUNXHVfXkgbynAcA44O+quk5ETi20McOBfhdSz/MSwHG+7/+lv6+9GzChtLT0\n",
       "h62trQCzReRBdU21DgQ+GhwzDhgQIQU+A4TVfUYDAyqkwD3ANABVRUROEpFZqrpwgO9rGP1Kv66R\n",
       "BiKaAg7yPM/WX/vOoYGIIiKHAKOC/XuHB4waNersgbixiCSKiooyJdJKSkqODcK2BgQRkREjRnwq\n",
       "ui9oxHjBQN3TMAaK/v5DuQgnpLW+76c9zzva87zRnudJP99nUCMiF4nIP0TkFRF5VETOEZGjReTo\n",
       "yDG14SNy6uPACwcddBCq+qfIOuFPpk6dyuTJk6mvr/9GL+5/o4g8KSKfE5GP9nQ8gKomOzo6MuFY\n",
       "bW1tv1XVdC/fcp9RVW1ubj49a3cL8D8DdU/DGCj6RUiDkSi+7/8c+DzwsOd5h+OqEH2ZrBjB4Uyw\n",
       "7vefwOHAwcBHcFPxK3McXhM8AFDV36rq4a+++qqo6pmR/betWLFCVq1aJap6fQ/3L5k0adK1wHHl\n",
       "5eU/xk3Re4WqXoVzhpWo6nm9PW9nUdVHgNNPOeUUgL8AY1W1ufuzDGPwkbeQep5XBtzked4tnucd\n",
       "C/wU19tkk+/71+FiKA/2PG9EvvcaItTiHEOdmDRp0pk5jh0IatatcwW8t23bBjCpLyeransQrrVL\n",
       "UNVHHnvsMVHVk0xEjaFKXkLqeV4RcCFOPDfjPL4zfN9/Ctjmed5Bvu//AVBcds/uwA5e+UQiwZo1\n",
       "a3KNJDcHj35DVdem0+lbPv3pTwPcDbzen9c3DGNH8hJS3/c7gNeALcC3cTGA/xq8fCww2vO8qcCi\n",
       "4LjdgR1GVclk8ipV/YaqZhqvqeqG8NHfBqjqNXfddZeo6iWqanVJDWOA2Skh9Tyv2PO8owIn0l7A\n",
       "Rb7vp4Hr2D4iWwWswXme/+b7fr+OvAYrqpqcMqVTLZJXge8XyJwBR0TKCm2DYRSaPseRBmFNKeAQ\n",
       "3/ef9Tzvj2xvBtWOG5WCS/lb4/u+3y+WDiFWrVr17QsuuOA/fvnLXz4APBrEgvaIiJwEvA84GRiD\n",
       "y89vwTmAFgSHNanqTwbA7D4jIs+IyFEi8oiqZnvgjaFBTESODbZbVPX5glozRNmZgPwrgFuAb3qe\n",
       "F8f94S/1PK/I9/2Nnuc96XneR3EFJ2b1o61DBlX9CvCVX/ziF309tbq8vPxHgZMom4+NGDGC5ubm\n",
       "r+RtYD8gIp8Ajgp+I04TkQtVtc9v2Cg4jwGlwbZlle0kfRZS3/e/53neKFz9yDm40KZW4J/BvvNx\n",
       "QdVH+b6/vB9t3R1IJRJd/5cUFRUBvCUi38ctmfwJeEZVC7Fs0pr1vMvUV2PwoqpJYCuAiLQV2Jwh\n",
       "S5/WSCPxov8NTAXWAV8DVgD7BV783wJzfN/fXZxL3SIi54nIsyLyIxH5cI7XTxSRi0Xkt8CBjY2N\n",
       "/4pz3L2KC9C/E/gFcFl9ff0pwE9ws4JPAX9MJBKbROQ3A5kzLSKXT548WUXkD2GAv6r+AfjV2Wef\n",
       "DfDAQOX/G8ZQoFcjUs/zxPd99X0/Gdn+k+d543DhTvd6nvdNYD/f922NpTP/D+eQOxL3w/NY1usH\n",
       "jRgx4pbm5maAhar6NeB3uS4kIl8nKy40mUyCi5SIAY/2q+XunrHq6uofrFmzBuBMYDVBh1JVvQBL\n",
       "6TSM7keknueVAPi+r8F6aLgtwejzVGCS53kTgVdwnnqjM+si2+/leF2bm5vfCraX9nCtnFP4oAjy\n",
       "pr6b1jOqmq6rq4vOLtYMxH0MYyjT09T+Qs/z7gbwfT8VFdMghvTPuD+sPYAnd5cQpz7ybeBjuFFj\n",
       "rh+a14B/Bz6Em7Z3xz3Za6glJSUEo9h1IvITEblERD4Yvi4inxKRP3S0NI1KdbSVZl0PEblaROYG\n",
       "NQE+0sV9b8I5D28DdrsoDMPoiZ6m9muAaZ7n/cD3/S+GYur7fhjuNDZYC10ysGYOXVR1bg+vP9GH\n",
       "a7WIyD3AxQATJkxg3bp1e6nqYhH5HXBuaWnpZ1tbW08Jz5kyZcq9q1atItXelowlirMdRODSWcO1\n",
       "283ADvaq6u/oYrnBMIyeR6SP+75/PC7d8w7IjEyLA8/9bZ7njR2K1Z1EJCEi14vIgBfnyJfA1l+K\n",
       "yF+AZZdffjnAj9etW3dKIKLFZWVl5wIEZfgyVaZWrVp115w5c4gVFbfEi0pyCekTe+65J9XV1eDq\n",
       "IhiG0Ud6ElIF8H3/GqAlIqbtvu/XAx/yfX+j7/u9CjgfLIhIAliIizj4tYj8oYC2fEBEbgk8++fk\n",
       "eD0BvI0LKzsRuPaHP/zhV4DfAGHA6YdbWjpFH30usv3ACy+8cLzE4slka3OFiDwlIgtFZL6I/BqY\n",
       "sWTJkg/V1dV9CNeEzjA6ISJHptpby1LtrWUickCh7RmMdCukQU1RCbavBjZ5nveU53kXBOulHbvC\n",
       "yAHgTFzmVea5iIzt7ckiUiIi7+tHe87HefU/m+O1U3Br0CFlQFJV56vq/GBf9nmjRaQEQFXnqeq8\n",
       "WDzRlm5vGQ18EDgAN2o9D1e67onw0X9vyRhGjI4Xl7bEi0tbgOmFNmYw0mMcaeilD57+GBDgRd/3\n",
       "U0NtJBqhMse+XuWMi8ioyZMntwJLReSr/WRPSfDvDs4gYH5l5XZzS0pKAB7KOuY38Xg8+vwFVd0h\n",
       "uDqtSm1tLUcccQQA48aNA3hup60uMCIyQkSmF9oOw+hVQH5EMLcApw+D/PlcWTi51g87ISJV5eXl\n",
       "datXrw533SQi1/RwzunBtP22qDc9wgFsd/rtMCpW1YbGxsYbZs2axYEHHkhbW9t3VHVl1jH3pVKp\n",
       "7330ox8FF6f62+zrpDraRgiwYcMGnnvuOSZPnsx77713Lv1cxm9XISIXjBs3bquILBeRbxbaHmP3\n",
       "pk8por7vt9O5N/tQZWP0SSwWI51ON/XivE9m58GXlpZ+S0Ru6aYwyfG4afuR5A6Y/ycuyH1fOsec\n",
       "ZlDVrwNf786woLr9VV29LrF4R8q1DolNnz6dd999d6Kq5rzfYENE4rjogrcin/Px773nwnInTJjw\n",
       "n0B/zQ4Mo8/sru2Y5+FqpO4PkE6nfxu0Su6J38Tj8TtSqVRmR2tr6+2qqiJyXPRAVZ0XbP4V1zGg\n",
       "mK7XlK/HOY72FpH3B/v2C2wEOAR4M3LtpwFE5LJg1yvB/i6zymLxovaispFbgMvefffd1lBEReSY\n",
       "LLvn57xAQFChahRQHxz/uIiciVsuORV4Q1X/p7tr9AUR+S5uLXcC8LaI7BuI6ZP77LPPp1pbW1m+\n",
       "fPkdIjJNVVf0130Noy/slkKqqikRORjn5Imp6t29PG+LiFwE3BvsWsb2UWDpPvvsM7e9vZ2lS5ee\n",
       "ETnnEeCRbq75bLgtIhtxbZc/AKRx2UolwJ6VlZXv22OPPXj11Ve/CjwducSJuCWaBXRDvKi4DYrb\n",
       "cuTElwHX4no7/UBEnumh7N9ncc66+bhAfYCKmpqaezdv3gxwsIhc1x+N84L+V6GIguumei/wKVX9\n",
       "JfDL4Lhp+d5ruBJ42QX3QzcLlxRSjiVW9Cu7pZBCpurNvTtx6gvAF3AC9KKqhsNT7623MtFDZwD/\n",
       "u5OmfQg4KLojFovR2NjIq6++CjAj8tJ6nPCegBPUXiMiRcC/VVdX31FXFzYr5c7JkyffKSI3AN/I\n",
       "JahTpkw5c9WqVQDH4JyPALMCEQUXYTCJ/kkXnsB2EQWguLj4QhH5dORzx0ai3TIbeBI3g3gplxPS\n",
       "yB/rPd93jsTFad4KROM+F+I6hd5BZBoeRUSOiD6CfTeLyPzi4mIFfhUeW15enjlvxIhM38A36OxI\n",
       "CkOwRgIfFpF/CR5HBiFaJWEYVJYdP8UVjb6jsbGRU045hQsvvJDi4mICR9rXgPUiUhY+wnNXrVr1\n",
       "jUsuuQRcVaqwrcrzwLMHH3wwwN+AjwTOtV61gu4KVV0LvBjd197e3klEjR7ZpKorg4eJ6ACx245I\n",
       "86AJ52kHODDcqapP4n75u6MG+A7wLPDzYN9s4OiOjg7YLoxEnVpNTRk/2I2RtVdwjqqQngqeAK6a\n",
       "E25qPgYglUqxYcMGXn75ZdrbO/kRx+HCrC5ge+A/wK133XXXrdEDVfVB4MHg+p8tLS39SZBhtR9B\n",
       "paidRVXniMi1t956641XX331xap6bz7XM4yBYNCOSFetWnVJMP0cbNREtvvaYnqPK664YiYQXdOb\n",
       "0tXBOXgh63kD8PngEXIozjkFbi2sPOucKhEZE93xyiuvEHrAg+LR4fYp9J3jAxGlqqrqeHEkgrqr\n",
       "c0XkF4EXvteo6k1f/vKXxUTUGKwM2hFpR0fH14CrRaRSVQdTBtUy4L9x09pRInICLpB+a+hN74YX\n",
       "b7vttqOC7X1EJAn8paKiYmZk1LkF5/jJxfUi8iJOwJO4UWUy8vrKwJaoUB0sIk3Hf+3BMoknOoBD\n",
       "VHWBiMyOLIGuIhD0YGRMsP0GnUejUUKBzo52WAhUX3zxxSfcc8899wE/Ky8vvyQrbOzDIlJrU3Rj\n",
       "uDBohTSgFDddPqanA3cVqvo4rnI9InL8yJEj/7p161aAT9PZm57r3EwWkYhU4rzeP2lqavo6272q\n",
       "/0Gk6EgWn4jFYp9Ip51DPJFIkEwmX8NlJ/m4oiMvB/dqA9pEZK8c1/m1qv4WmAjcDbw5ceLE1Nq1\n",
       "a7OPm5sdFhY+D5YIcr3HG4AbAO65554fAZ/P0YOqBvg9cFYX79MYoojIOFzUSStQDdy/O/xgDnYh\n",
       "ZcKECV2JymCgJBBRgNo+nns2Llh/RLDGWCci4ydOnHj0unXr6CoCacyYMZlpeFAd/0AROTCY9obL\n",
       "DptFZG/gnRyXWAosVdV3wdUNAH4Ximg8HicSJ5tz2UFEilS1OddrWbwf3HJBdKQbsHcvzjd2LcXB\n",
       "9wZgW3YGXS+pAV5R1aUicjJu+dCEtJCICOvWrZue5zX2jT5X1Zwe9Z1kGxB29XypF7bMwa1hQiAy\n",
       "uDYkIdeEgjZp0iQ2btxIe3s7ZWVltLS0dABFmzdvRkQYN24cdXV1tLe3o6qIyEWqugY31f8ibnlg\n",
       "Ba5K1EPpdKooGEJ+EhgrIj8GJpWUlDzZ1uacuSNHjqS4uJgtW7ZQWVlJY2Pjx0XkFdzIYjVwFHCi\n",
       "iIwVkSeB+4J4zq4oC6/b1taWcaAFwvqBnj4vY5czj8AJiStu021X2KDWxCLczPE9Vf3bgFo3iBm0\n",
       "zqZDDz0UVZ0+mGMEgzXRBcCCXqyPAoyaMWPGHdXV1XdUVlbui4vt+zqAiLyvoqLizPDAtWvXhl70\n",
       "37S0tFxP0OkxlUqhqmzYsIH29nZOP/300BZE5L9w67fhGus0XMvkl2KJotZ0KlkMXIIL8h9XXFyc\n",
       "EVGAlpYWtmzZAkBjY2O4+9u4gP0fAZ/AVYsCN5reoZlfFmsB6urqMiI6fvx4Ojo6xqnqxm7PNHY5\n",
       "qlqnqotVdTFQ1+MJsChIOHkMqBCRCvrugB0WDFohraurm9HPIrpDcHd/oKpPqepTvTx8z+XLl1NX\n",
       "V0djYyMTJkwYBfxTRC6Ix+NLm5qaiMVi7LHHHtGp/Xk4sa0GN1KNthv53//dHvfvEoF2IA6gyWRJ\n",
       "srV5FDCjvLz8c8AewdJAhmjqayR2tTvG9/D6lsj2ZuCC9evXJ0xEhx2tuB/6Q3ExzTsstg93BvXU\n",
       "fqgiIocDRbhptkZy4DMdQEeMGMG6devOAW4HDk2lUhQXFzNt2jSWLFlCZWUlTU1NGUEtLi5mypQp\n",
       "bNq0iWwBDJxOS9Pp9J8AqaiouKqoqIgtW7asAJ4SkTOOueru0QjMnj2bBQsWUFVVdU9DQ8OzuOl6\n",
       "lIXARc3NzbNxHvkaYM/gtT1wca9jce2iNwdLBH9V1ezSfgTHNOAcYcuCtWBjaNMu21t/vwMu5Zoe\n",
       "HK3DnWEvpJE10f5cG+2JxH777Tf/jTfe+AedKzJlunE2Nzd/Eje1D9dMaW9vZ/HixUCnqXXmtRUr\n",
       "VkRF9F6ct35VMpl8nkgwf1NT0/2491sC3FJaWvonVaWyspKvXncdd999Nw8++CDjxo076r333luI\n",
       "ixYAV/xkjqomRSTMdy0HV2cgvL6IlAMtM2bMSC9fvpyKiorPicjngbtVNRPVr6o39ulTMwY9QdSK\n",
       "kcWgndr3JyKyfxDvmb1/RF+Dw3tJ8o033vg6kD3lXw7MweXHrxk1atRfe3Ox0lJX77m4uDi6ez/g\n",
       "F6r6Z1WtzzqlHLi6vLy8HvhMa2sriUSC0jKX6XnkkUcyZ86c0PufAm7GNdS7PKhBEGUbWbGkqroN\n",
       "OHL58uVAJvPqx1VVVW0iclhv3pNhDCeG/YhURL4bi8WuTKfTiMhDqnpOsP+a0tLSb9XU1BAUwbhn\n",
       "J659FC6V8hBcTOZS3DS2Glc+D2BfcX2X2nE1R9/ErR0+WF9fTywWo7S0lByxlhnCTKFUKhV2DgU4\n",
       "DFglIlOCmFEPNwK9IJFIHJdMJjtdM5lMUl9fz69+9RgvvvgiS5ZkGr8eDPwMeJftlfqzOUJEZuGS\n",
       "EbYEFau+BK6gioiQSqVoaGggFou9KCL/oqo9RjEYxnBhWI9IRaS0qKjoyjCAHThbRA4WkdjIkSO/\n",
       "1draypo1awAu3clb7FFVVfUQ8F+4Ed0N5eXlvwcWq+rzwdqoj+tXfwXwpqq+iCt2Mg7c6PD6669n\n",
       "n31cC6mJEycycuTInDdra2vLnvKPBb4fbC/ZZ5997gGOy15DDWlva+OBBx5gyZIlVFVVUVaWqUVy\n",
       "JbAYt6YJgKq2hg+c2H4PVx/gYBGRoqKicwHS6XQnJ1U6naaqqurFrgL2jYFHRCaIyBQRmcIw/xsf\n",
       "LPT7h+x5Xonnecd4njd6ELRpbuvo6FgTPqmoqABYrqrprVu3Rosg/3OHM3tARA6prKy8t7GxkbPP\n",
       "Pjuzf9u2bc/RuYtABy5Hfnlk31/CjWeeeYabb76ZsATf2rVrL9i6dWumCV1ZWVnYpwmAqqqqbFNO\n",
       "DJYnrguvER4/derUzLIAgMSEPfd0fqOLL76Yiy66KHxpJi4e8FkR+ZuIfFM6NwNc/o1vfAOCpQpV\n",
       "1Y6Ojk6FaoKlAAAgAElEQVTLEiecsH3lJBB7DT4nGaQ1E4YzZ+CchDW4urHGANOvQup5XjEu0Hwy\n",
       "btR1ied5BftFDOpp3gQ8esYZZ9DU1HRNZD3xNlw9zTvpg8dRRI4SkUsqKipebmxs5BOf+ATLli0L\n",
       "X16AG53uIyInBWXkPoz7Mi8m6FyqqnOB/4vF3EcTZioFTe5+DTwQXjCZTCIiiAiJRIL6emd+pLjI\n",
       "HjihPjkU0La2NhKJBG1tbZllAQQqRlawatUqiouL2bBhAw0NDUyfPj0MmxqF6xhwDPCfsVjsPRF5\n",
       "SEROAcZcd911RwM/AEpE5F5cKmom1vCvf92uq8XFxQRdA84FFlVWVraLyO29/YyNvFmjqv8MHr2J\n",
       "BzXypL/XSA8Cinzff8DzvJnA6cAVnufd5vt+3hXTdwZV/REumDx7/29wWT87w1fCIiP3339/uO+f\n",
       "wAdUdZuIxEeMGPHXjo4O2tvb/x1XRzT7/h8WkfG49clTARobG58PqvdnanB2dHRk0iuTySTJZJJT\n",
       "Tz2VxsZG5s/PDDYOra6uJizQHIvFSCaTbNwYCddUaNraRFtbGwcccACzZ89m8+bNqConnHACzz//\n",
       "PK2traxfv57m5maC5ZCzgKk4J9QLACLyBeC8IOTq27hpfydHXiQG9TRg32CEeibBuqrRP4jIBQQt\n",
       "X4BKVb2/u+ONgaNfRotBj3twKYnjPc/bw/f9xbgWG3HgwkEwzQcyHvx9ez6yW36OE84GXOrk48BX\n",
       "Am82wPnNzc1hZlIYp3kokVCngA10bgN9uIhcCpwc7vjYxz5GtB1zaWkpvu/zzjud0+jDnP+KigrG\n",
       "jx/P+PHjCRxskaPc9uLFi7ntttu46aab2Lx5M7/61a944403qKysZOvWrahqZv20qqpqdpbN5eBE\n",
       "vbKy8j+Aa8hqW7Fly5Yrgs1/RJYl/oDR39Sr6iNBdlFjj0cbA0beQhpM5y/yPO9c4AicN/kDnufV\n",
       "+L7/Dm7aPJpBkDomIjfGYrHX4/H4GyJyXR6X+geuatITwC24akdhVaTKRCJxUXhgaWnpOYQKBlNF\n",
       "5JDg8XFcz6Hjs679M1zxZ4qKiigtLSUejxOPx0kkEiQSCRYvXsz69es7nRSOWkeOHMnGjRsz8abh\n",
       "8gFAvLisLhaL0draysqVrh7FvHnzaG1tRVV55ZVXMse2tLiiTw0NDQCHR25VDnDUUUfR2NhIZWXl\n",
       "y8BbwNIDDjgA4HFVDafxq9va2s7EjUZ7FeplGEORvKb2wUj0w7j+RPvggsIV144Dz/P+5vv+As/z\n",
       "DsFVlf9HfubmzacjHvyLgG+ET4Lwnsm4bKRtwPM5Yiqjzeqexa0ZZnN81GserFFuUdU7RSQsuDwb\n",
       "Vyrvk90Zu+eee9LQ0ECkpxKRalMhS3HrpIBbbx05ciSbNm0CYM6cOSxatCiwPZ1Ip9P3Bu8dYIcs\n",
       "qS6IOp62AnieR2VlJY899hhlZWUfbWlpmbNw4cJObUGCkVJOxHUvfU9V3+6NAYYxmMlrROr7fiq4\n",
       "RrXv+/NxDoi3cH9s+wLHep53PrAk2F9oomui0dqgL+KyjubipunPAOtE5AfB6x+IPiLn7dCDKTg/\n",
       "mmv8NnCCiHyWwNkUcBps97CLCOXl5YwaNQpw3vr99tuPRx7ZrkXR0WWEs6O596pKQ0MDJSUlHHHE\n",
       "EdTV1W33+qsKcEUQvRDld7kuHKEysv1CWVkZDz/8MH//+98BN3otLi5+QUS+KCLH9nAtROQ1XG+n\n",
       "t0Tk6Z6ON4zBzk4Jqed5xZ7nhWt/ceAkz/NG+b7/Oq4Rmg/8GdeobSXwqu/72dk3uxxVvRK3xHAK\n",
       "zluPiHwNtxyRzRjgvEjoztG4qXh2xaOLCSo4BffYhiuNdyoucuECXApmNfC2qr6C+2GpAieOgZeb\n",
       "lpaWzIgzlUqxatUqIiPoS9Lp9NTq6urovX+mqq8lk8lMBlU6nSYej9PW1sbLL7/M3nvvzXbhFFXV\n",
       "xqampqo99tgjXD+9m84V9YHtzffGjh0LkaZ8qvqtlpaW72/atCmc9iMitLe3E4vFbmd7umlOROTq\n",
       "rGM+kCvrzDCGEn0W0iCcKYXz1oKbru8FnOV53mjcyG4DMM73/Sbf9+f7vj9oQjBUdVuQVvkUwOjR\n",
       "o6/v5vAxuJAgcJ1DpwD/knXMYcccc8zJBAH2wT2aVXVuUMjjUuCyeDz+TVxYlOCC24Hta5HAu6qa\n",
       "mWq3t7fz0kuZ5KCFwD2quqquru4/Jk+eDM7Z9SMR+eDkyZM7jQJD8W1ra+PPf/7z9v2pjpLAvsal\n",
       "S5cmVHUsIEVFRWeDK35yxBFHMGHChExW1MaNG58FyEqlnRu9X1hYJbjvGTk+xyhfzrHvqz2c0yMi\n",
       "UvA1+GFGnYicJiKn4Ro+Gt2wMyPSK3Bls8Z6npfAjWbuxgnMObgQqAVAwvO8rlIOBw1btmw5p5uX\n",
       "1wDTcd72a4FzcdWaolw9f/78E4H3sk8ORlqfhUyJul8C3yJr1BaI55XZ50dGo2uBR0XkVeDE1atX\n",
       "n42rE/q/wFOrV6+mttYV6K+srOSQQw7JBOIf/dXfs+dFt1NWXUtpZU3xSdfP1ZOun6sfuu7RJK7z\n",
       "58UdHR3EYjEmT54cFtMGMqPR7wBXFhUVJWtqalREHsfFyu5Qti8ej4MrptIdl0SfBMsVnw+uVxl9\n",
       "9HCdDCJyXmlp6dZ58+blbitg9BlVfTaMCOhlrd3dmj47m3zf/57neaOAh3HieQZOcBbh/uBn4Rw2\n",
       "f/R9f9D30VbVh0TknP322+/BN97oFO45D5eh9Afgl6p6YY5zn8veFyIio4uKip7I0WLjK9k7AsEs\n",
       "icViUfHMUFRUdHLWdaaXlZXtFRnNdirIvHjxYlpbWzNpp93wgeD6lJWVUVtbm1n3DHL6pwHjYrHY\n",
       "eR0dHeE9PhSeXFZWxrZt2xARVJVUKvVdVe22qrqqPiYiH5k+ffrcWCzGsmXLPFXN1RKlV4jIR4Bf\n",
       "t7a28rOf/WxnL2MYeSFd9QbKhed5Cd/3k8H2R3HT+FXAhTiHxI9832/3PK/c9/2uq3B0f4/pwPJJ\n",
       "Z1y7pqhiTK9cyv2BqopqOubGWKLpVEdxqnVrbSqZJB6PU1w5psci08m2lhGoxuIlZU3pjray9uaG\n",
       "cd2eIALB5x8vKWtKJ9tLNZXKnU4pgrB9Gt0jIsRjMYorx3R5SEvdBhJFCZIdnT/meCKOJErrispG\n",
       "NnZsa6pOtm2rzLZ3h9vFhJKKMaskFtvpxAtNp0U1HRcRl14ai/fY66d9a/3YVEdbOUBxSTHpVGrN\n",
       "modvmgTM8H3/3eix4Xcr12tDERE5LYyM6Gq7vzjp+rnvAjz+9Y9M74N9JwNP6uDqArzTdPf96dXU\n",
       "Pgym930/Gdn+E64l8XTf9+/GNX87KHhtp0S0kIiIxmLxlMTiKYnF0vGiktZYcdnmovKKTSSKG1Pt\n",
       "rWUdrc2VHS1bK1MdbaXZ57c2bp7Qsa1xTEdL0+jWxk1TJJ7okFh8xx+CQCSATqKUTnaUxOKJ9ljc\n",
       "/ZckEolwqoyIMGJEeeb59mt18V5iMVCluKTnlRVNa6frxIpKtklR2RYRJ4jxkrLt62OBvYlEonME\n",
       "gUDRiFHrskU01d5almzdVtHRsnVUqr01mniQk46Wppq2xs2T2rbW1SbbW3u15llUXrkpnnCfSyRt\n",
       "1jB2Kd1O7T3PK/F9v833ffU8L+77firYluDcU4GlnudtwxUFXtpfhq15+KajBsuoQUQ+BNyKi4V9\n",
       "BvjvaHsREfkcLm8/JDZ58uRJq1evPqC8vPz1SDm714EPJxKJVaFTKUi1BOfA+wrwp6lTp64JA+Zn\n",
       "zJjBkUceycknn8z3vnc7L7/8cuYmJSUlmbz6aDxoONUG+NB1j3b5vp753iXRrqHvAieo6g7/hyLy\n",
       "V7YnDryCa4zWipuJnAH8TxCNkH3e5xOJxI8C236sqpd1ZUtQleuVwO4i4DlVPbWr47POrbrwwgvr\n",
       "77zpTg488MCj6FwgxjAGnJ5GpBd6nnc3uJjRMBXU9331fb8DF+K0BhcQ/qTv+5sH1NrCMRonotTW\n",
       "1h6do0fTJ7JPWL16NcCcbdu2RZcEfqeqq5PJ5A/BCWEk/bMMuByoX7ly5b5hbGhNTQ2+7/OTn/yk\n",
       "U+YRbA9RCkV0xowZwPbp/+jRo+mJsATeqFGjphNkLeVg/jnnnANuvfhKVW1S1Q5VvUtVT88logFT\n",
       "IgI/pwdT9spatpjWo/EBqtpw3333SWlp6aBIQzZ2P3pyNq0Bpnme9wPf978YimkQiA8w1vf913Bx\n",
       "kcOCwHlxHK698hZV/QuucAcAGzZsWJ3jtEW4ONNsfp71/HoRmYpbV6atrY3q6mr22muvMHd+n+C+\n",
       "FyWTSR/wFixY0OkC0b7zDQ0NTJs2LRNvunz5cmKxGGVlZUydOpWPfvSjvEzXFBcXk0wmSafTYVWp\n",
       "hUGVpl8CqGp4800PPvjgF6Dz5YLC1qVAayTjK8qzwPW4oterujEFXFLAZ0pKSo4bPXo069atu7OH\n",
       "443OTAxClQCKuz3S6Hd6EtLHfd9/zPO8mz3Pu8P3/S8EYlqMG73cFuTYb/J9f7iEnvw7cEJtbS0b\n",
       "NmwIp5YvRDzqa3Kc051edUJE/k1Vr8MVeJlWX1/P5s2dBvL74kr8/R74Wvb52UWUV6zo7ANLp9M0\n",
       "Nzfz1ltvsX79eurqvgnA0VfeRVFZxeZ5N33sSFy2FQDV1dXU19dHnVhfAmYAmVoEQQWtXHwkFov9\n",
       "Zzqd/jZONDuhqo/hWvX2SFB274S2tjZZt24dqlqQamFDFVUd1D88InImLpoHYEakHsOwoKepvQL4\n",
       "vn8N0OJ53h3B8/YgU+lDvu9vHCwiKq4H0/slO8Cx8zGx7l4n6PQZ1AjNeHciaZW5zn06O30zmrYZ\n",
       "JRCsZbgUSVpbW8kOkZoxY8b76VuM70rc2m0n6urqOjlgOlqaaoiIqIhki2jIgUQqVYnIniKyRES+\n",
       "n3XcmcGPy0l9sLVL1JHuq4iKSFxEPt3D/6tRWJKRSlXDbg272z9W3/fTES/91cAmz/Oe8jzvgmC9\n",
       "dNCENYjIVWPHjt2Ky6F/JtcflYh8Z/z48alJkyalReQzXVzq1zhn0vk4hwrAAQ0NDWGK6z4i8mUR\n",
       "eZ+InC0ilwMfTqfTD8bjcUSEqVOnkkqlGDVqVKfq9oFJn8VlKmW6cpZkedeXL19+Ky4BoLdsSiQS\n",
       "OywtxGIxysvL+dznPkcs4vGvqqpi2rRpqCqqSiKRyA6uzxQ6FZE94/H4Ytw6+BUiEnVGhfmqBcsq\n",
       "CjKu5gF3XXHFFTaKNQpCj6OeiJcenGdagBdDD/6AWtc3LosUMj6SIFsmyuTJk69av349a9asYdq0\n",
       "aTmnQqp6vapep6r3B+uj4OJlw/l3BS475zvAdVVVVT+oqam5HXgwlUodPWrUKFauXImqUl9fT1tb\n",
       "JifhdVUdrao/VdVXcWm0gBPSWbNcslPgMArXujpRUVHB+eefz8SJE7NDfQ7JVcUpLGDS2NhIcVFR\n",
       "RiwbGho6LQmkUqnMqDQYWX8hqFaVGDVq1OLocgLwPhEJ0zzDH5dChrvdgavqz+rVq1m3bt3hPRxv\n",
       "GP1Or6aPEcHcApzu+77f3fEFIjsfeEP2AatXr870tl+xYsVr2a/3QLQr5j64lsr7tra2snnzZsaP\n",
       "H/8bYFldXd2fwoOiBZlxeftRRcqU0BszZgyrVjlfzPLly/9I57J1GZqamrj//vvZvHlzZjmgpKQk\n",
       "UzEqJBTZWCxGLBZj7ty5tLa1ZcQyewQcndqn0+lHVDUsElwdtjaJsv/++98abP7u4x//OLgC3jkR\n",
       "kf8SkadE5HPimrH1N+vCjWh/KsPYlfQp1z5YGx2slbjvAl73PA/gmaBgSDa34Aon3wU8v99+++nI\n",
       "kSO1rKxMR44cqUEu+UYReU1E/lNEomt/D8EOveWZNWsWp5xyCuvXr2fSpElrcALLtGnTOOqoo6JT\n",
       "5gnA5iCP/BiCYihBmmSm5ujEiRPPBHKmTBYVFZFIJDIOp4qKCtra2i6pr6//OPBUeK9QZMORZkND\n",
       "A6iSKCoiHo/vsCYbEgT8XwiZ2NiLQxtDysvLWbRoESJyHrD617/+9dHA/+W6nog8jyt6/UHcbGZl\n",
       "8Nl+LKcBO8d1wD0ABxxwABMmTHi+h+MNo98ZNq1aVfWHqjrr7bffFlU9potj7lPVz6jqpcDsN998\n",
       "k+bmZlpbW2lubg5zyceIyKyioqJvEpS6U9VnVPVBYGHQPiTDSy+9xIIFCxCRsLUzAHvttRePPfZY\n",
       "tiMnAfzvzJkz/xbuSKfTTJ8+PXPA2rVrIXB4ZRP2bwqn8U1NTZfiRspvAF+OhCtlGD9+PACxeJyS\n",
       "4mIqKioy+fzBj8LDoVCmUqk7dXtzwAzpdJpYLMbMmTM577zzwt2nAQuD4hY7eOyDDgC5YkdnkVW4\n",
       "JB/UfcCXAEdcc8015mwyCsKwEdKdoMtC08cee2w4asuOaM8ZBrRx48awF33GgeT7flf96d9avHhx\n",
       "5kl5eTlnnXUWhxxySPSYKdCpiVzIL3EZSCFfwq1ZHwZ8WURmg3NqTZ48mZkzZ2ZGn+lUiubmZurr\n",
       "68OqTrS3tzNt2rQz0un0f+Bqqt4tIp8SkdNxIV1PAfcDb44ePZrFixfz9tsZp//EXG8uuH/RjBkz\n",
       "Hojuy4pi6Nci34G3v9DdF4zdmN1ZSH+Hqws6HzeiexHcdDlcr8T1e4/yUzr3rA+bxH2hqanps0Ti\n",
       "PleuXMnWrVuzq9o3Eak2X1VVxbZt23j88cdR1U5rfDU1NdlC/FPgEFxZv5BZuGntN4BPhqPf0tLS\n",
       "TDvmTZs2UVRUhMQEicUy66f77+/KrK5YsYJJkyZ9G9intLT0BVwZvIeBG4N73AbcumnTplOnTJnC\n",
       "c89lCl5VEWR7RRGR44HvL1++vFNmVcQZdifwZPZ5hjGU6e92zEOGIJ4t4yQJwqVubGpq+mrYahl4\n",
       "NescDWIpvwJuxNjc3LxP2HdIRGLV1dU/ivZYipTF+w7wwMSJE19ev3496XSagw8+mKeffprq6moO\n",
       "O+wwRISOjg5ef/11tm7dGvX4/x0nXPvleCudhrI1NTVMnz6dY489lkWLFrFy5UqmTJmCSIx0KkVH\n",
       "RwcbN25k5syZHHDAAbz++uvhksQngv5SIScCn1HVdwkcbUFW1srg9YPJna10eCwWuyydTjNx4sRM\n",
       "1lSQ//9JVX0gxzlGFiJyIO6HvA2Ypqo/LLBJ/UlbJAtLVbXrghBDhCE/IhWRU0Tk5d72C+qKYHp4\n",
       "LXDnnDlzwInHDp5/4FGcg+Pa5ubmj2ukeZuqpuvq6j6VZR/ASap6NTB77dq1y8I1x6effpri4mL2\n",
       "2GOPzLF77rkn0EmA1+OcT1XAjhWgsti8eTOvvvoqf/zjH6mqqqKiooJly5btUP6utbWVyy67jMMP\n",
       "Pzxzzb333pt993WdqoORdqZVafBD06mS/fTp0x8TkQlZJrSk0+l/VFRUsGjRIurr60kkEqjqN4C5\n",
       "ItJzAQAD3P/3E8EPfo8lHIcSqvqXSHD+sGBIj0hF5CMi8qiqEovFDkmn01/Crevlw0MvvPBCJ4+/\n",
       "iPwLbjS4B05cdmgtHBwzDre++baI7B2Px0kmk3/BeesPxXVZXQa8LxTKeDzOwoULAbeuGm5HPOt1\n",
       "uBjWSuicIgoQpLLeQ5aHfenSpWzYsCHTxjm7YPTmzZuZN28eCxcuzFxz06ZNmXTVlpaWfwJXikgZ\n",
       "bjlhDHDK2LFjufrqq5k7dy7z589n0qRJa0XkbFUN+9a/BrzW1NQ0FtfG+d1kMrkReP+IESPqU6kU\n",
       "InKVqn4PwxgmDGkhnThx4qOBlzsUis+Tu0Vyr1HVJ7p46SPA2Tjv+A7pmAGTcIJzu6r+NFgXPAjX\n",
       "fhngT7i12Eyzt5EjR9LW1sbGjRszfZL23nvvjFNnypQp+6xatepGXF+sHQim/5miKqFgHnHEETz3\n",
       "3HN0VXW/srKSd955h0iJv0wL5/LyckpKSg6qq6s7KHrO+973Po488kiuv/76TJO+YFngfFxlKFQ1\n",
       "uv6Z6doqIl9obm4On36BSN8qo/eIyCeBMAQx14zJKABDWkjXrl17ORBdO7phAG8XFjA5qJtjluLy\n",
       "iPcAjlHVTGxnhP/DVcvaE5zHP5KRhYjw9ttvU1tbi+d5zJ8/H+AmgsyqaPUnIKzadDwRRITnnnuO\n",
       "ww8/nAULFuQU0nfffZd///d/Z9myZUTWhInFYmzbtu2327Zt+9d9992Xs846iw0bNjBz5kzq6uq4\n",
       "+eabw7CpBbhRch3OOdUJEUkAJ+PKA84FHi0uLn5/Op0mmUz+vZvP0OiehuGwpjjcGNJCqqp3iMgH\n",
       "zz333HN+//vfPzCAjoxDgTAdaM9wp4i8HyesRwOrcc3kIKilKSLNwN440YHtHUn/M3JsJ1SV8vJy\n",
       "xo4dS6SE3tTgkRHF/fffH9/3dwiuLy4uJpVKkUqlWLhwYcZbLiIkyis34lorX9nU1MSiRYsoKiqi\n",
       "qKhoe5hUOv3dmpqaq+rr67nkkkuoqqpixYoVvPnmm9x3330UFRXR2tp6Ga5I9QHBvxlE5CpcsedM\n",
       "LG95eTnbtm37WXt7+9nBLsuJN4YVQ1pIAVT13IG6tojEcJWQyoqLiwmC8aPKdSLw/4Ltn6jqi8F5\n",
       "0cu8raovB/tnB9dbgCuKfXLg+b8f58Q6Hpi9bdu2g3KJZEgikeCwww5j06ZNrF+/vtNr7e3toXBF\n",
       "p+2PlVSN3S+w6/p4PH5lKpXiiSeeyEzRg5HuzcD6zZs3c9xxx5FKpSgpKWHOnDlcddVVlJeX09zc\n",
       "fLGq3htcN1cN0hFERBQI7XhfZB11pwmKlExQ1Vx1YY2hR42IHBZsr1fVnurWDkqGvJD2BRE5AzdC\n",
       "TAPvqOoOU9LIsXHcVH0aUN/e3v5TXNWmiUFB49OB/4iccp6IXKY5atJ1wS+B25ubm0exvbSd4pYq\n",
       "PtbR0XFtKMjRS6oqyWSSefPmUVdXx/jx46mvrycauhRd9wyufaqmkmuCq8xIpVJPAx8MRXTmzJks\n",
       "Xrz4HNyI+RyAt956i3nz5lFcXIznebS3t9Pe3v4a2ytiISIfiNgVZms9B9xy8MEHf2XRokV0dHQw\n",
       "fvx41q9fn1kv3VlE5CbgUmCsiDypqif0dM4wYW0kXKjH3ldDjIdxxcHBFRsakkI65MOf+sjhwLdE\n",
       "5BZcNlBOglCfx9je7mIUbkr/Y9wa578SiGikCtMoglbFqvpi9BEeoKp3Bo+XVfUBVf0/IvVBceL+\n",
       "mqr+F/CtsMwdbvqciRQoLy9nxYoVTJ48mfPOO4+ZM7PzBjLcD+wbiruqCi428QHgrSDs6dbFixcX\n",
       "BbUJHiMIs1q3bh3l5eW0t7ezZEmmAcL/4bzymc9zypQpTwNHRN7jk6p6zSuvvCLt7e0CJNavXx9X\n",
       "1exuAX0iWHO9lO0FXY4XkS/mc82hQvB9CXvM/67Q9vSRU4MfgVm5XlTVelVdr6rryUp2GUrsViNS\n",
       "3NpdKE7dxZyOJNK/PeA43Cj0bOD80OmTNf0+Enh8J20L0zvrgA8Df8SFU+0BbCQYKQKceOKJ/O1v\n",
       "f2PZsmVs3bqVRYsWZV9rHq630sJwh6qKtm8dj/Ok/wH4QiqV2gjUq2q0Bl9mOxzZtrS0UFpaSmtr\n",
       "a/YI/t+CLLBPAN/M9aZUtceWyr1kKjtWxfoMeUZpGAOHqv458nTYxIzmYtiPSEXkuyKyvLa2VoEt\n",
       "48ePZ8KECQC/7eocVW3CdcuMXoeSkpI/AuePHTuWL37xi5mCIAGNwLygQv/7I+fNij4i+z8rIp/F\n",
       "leQLuSQejy8H7igqKnoBl0e/gYiIlpSUMHr0aEpKSlBVXnrppU5FTwBisdhxwGRxnTnPE5Ejky2N\n",
       "4zvanehXVlaehYsc2LFGnnOEPRxd562qqqK1tfVcoCFi/7G4UTi4Gq0DiqouI7ImG+Tu/+tA39cw\n",
       "esPuMCI9B5jy3nvvUVxcfOT69etn00WZuiy+D/wCYNSoUcyaNYv58+czdepUbrzxRn784x9HHT1/\n",
       "w8WIXoRbw8puyTETt/6Zq121r6qvisiGeDz+0zC0KRjpXpx9cFtbG88++yxFRUXEYjH22msvamtr\n",
       "efjhh6mrq2Pr1q2k02lGjBgxt7m5+XhcD6jr0pGQqcbGRoDDsp0/qhrWXH08SAc9BIg3NDQ8nDVq\n",
       "DWkCaoismw4kqnq0iFwENCSTSV9V3+zpHMPYFQxrIRWRouLi4ilh6bvg38PonZD+oaKi4hdbt27l\n",
       "0EMP5bLLLuPggw+murqaG264gaC29VLgQlV9TkSOZHuQ+YtAWI1oHxH5TViUREQW4FJMs0ve7RWN\n",
       "D5VIb/psFi9eTDweJ51O8/vf/57a2loADjroIJ591g3aguD3GbgEgZngRnGB4wciQfRZn9kEXMbs\n",
       "Srbn1e9AECP7Di7rKS8PuohIb510kYgBwxg0DOupvap2tLe3fytSwu2vuLXH3pzb3NTU9PnKykqe\n",
       "fPJJ7rnnHmpra/npT38aiuhjwCWqGpZDii6mvw8yTqsfhhoReNZnA/8L/AUXn7pPcL+niYxYo5Wf\n",
       "cjXSi4ruhg0b2LBhQ0ZEA9bhlicyC/iKRr37bWQhIrfF4/G1iURinYh8t6vPJsL3cGvHt/Z0YFeI\n",
       "yM8rKyvTIvKiiOwwAt+dEJESEZkjInNwMwljiDCshRRAVb+aTCZLgBGqeqKqblDVpmAdtKdzf9LQ\n",
       "0LBvTU0Njz76KNdee21YePlB4PRIyA90rrEZjtDOwo0IczF65MiRd+Iq54f32xP4LpDJNrr00ks5\n",
       "44wzOp0YRArcCCzIamcS5SZ1vaEyo8qYxKKi3KldjIjsFY/Hv5RKpUgmk8Tj8StFxOvq4oG9f1bV\n",
       "p7KcCr1GRCaUlJRcEi41AJ/emesMI8bj2pwvx80WevyOGoODfhdSz/MSnudle7wLiqq2q+oODdpE\n",
       "JCE5cjizzn1r8+bNn6ypqQl3vQ2cn8Mb3XHiiSdy3HHHAYRJ5d121wy84p3iAlX1y8DV4fOSkhJG\n",
       "jPs9daYAACAASURBVBjB7bdvbwPe0dFxvqp+TVUPa2xsLKFzmizAIlX9oYgkamtrvxPujCcS0fqo\n",
       "RVnnTIqOcoPtm7uzvx+ozOo40NWPzu7EZlV9L3hYBtgQoV/XSD3PS+AavB3ked5ffd8ftF8EEflK\n",
       "RUXFzU1NTUtE5Juqenc3h6/fvHnz6bhp8oHA6SJyOK5K/GJc1frSJ5544sjg+P2DYPWluJqmB2df\n",
       "sKysjJaWlvOA4iDj6VDgKJxnOpOt9c4777By5crsMKtMwzdVbReRL40ePfryoFUKbF+fvWXDhg3h\n",
       "+81ec51GZ54eOXJkJtOpoqKCpqamM0TkVuCPqtqr/HgRKceNqgC25foBi9jui8gPZs6c+cVEIsFb\n",
       "b711e1fHGsZgpr9HpGfjhLTW9/2053lHe543OtLOeVAgIiPKy8tvDqbPewJXdHe8qs4LgqEfB14Z\n",
       "P37874CrgPOAr8disbuAmKo+F6yZLhs7duzTBx100LPA5biMoR/gRHI58K2WlpaEqv6WHdtu1AJz\n",
       "wiZ7S5Ys4ZBDDuGII46IHtPp/01VdcuWLf8dPH0XuFNEporIlZFjaGttdY3wHBkhDUbls7Zu3fo8\n",
       "uMpRl156KQD7779/2Hp5QFDVL73zzjvy5ptviqr+eCDvZRgDRb+MSD3PGw1c7Pv+dzzPqwVe9jzv\n",
       "cFzQ+8nACzgHS0EI4jcnBEIIkM5y4PQlo6Jy/fr1jBo1ihkzZvDqq6+GufXRa0yNVHWaraq34/or\n",
       "RW0aKSIXAGuBsGveSuCFqVOnsnKlW9pcvnw5y5cvzziSgpFlrnbYj+McWWHmUUcikdghXz8ylW4I\n",
       "rjcCN4LNtA1ZvHgxhx56KACLFi3Kjqedimt78r3I55lNIfvcG8YuJ+8Rqed5Y4BnCGok+r5/O25q\n",
       "t9H3/etwTdQO9jyv2/XCgUJEfhiLxV4D/iwijwCoaktjY+OVZ511Frhc3zv6cMkpIkJ9fT2vvfZa\n",
       "WG3pZ3R23kR7Ge2dw6aRuID4H+HiT7+PKxx9ADBu5cqVn8L1lMpMp8M+Uqq6HKgVkdkickHw72xc\n",
       "iNP/wy0nnAzUdHR0fDJ7CVhVQ+H/lYiMw5Xny9hbVlbGxo0bufvuzEpHpuGfiEwtLi5eAZyE+zyf\n",
       "7tUnZhjDnLyE1PO8atwo6kvAPzzPOwbA9/0ngGbP8w7yff8PuGD0XK15BxQRGReLxb4Qqcd5qrjm\n",
       "bKjq9x966CFR1Y/2MTaxVSNN5trb2z+orsVz1IO/LrLdqZq+iFQBb+Km8CFHlpaWfhHXFO5t3A/R\n",
       "U6p6FC48akFwLnTRyZTtVaZ8tncaXaiq/0rW8kHgzf8TLne+JPpaS0sLkIlDfVRV7wrXR6dOnboi\n",
       "6hwSkQ+ISPR9oKrboo8ubDWMYUW+I9IxwIW+7z+J6yvzHoDneUW4KvC1nudNBhbRudjFrmKPUEQj\n",
       "rY136Hy5E/z6iiuuYNu2bf+WJaAhsbPPPptzzz0XXJ48ACJSM3Xq1HpgSiwW4/LLL88E0wd27rDE\n",
       "oK4n1OeAa1T1K7hWJ4cGj5DMc3VtiaOf9Zuqum/RiMqNkX1hamiXgfRBQZNrovtWrlz5WPR50PW0\n",
       "EcPYzdmpNVLP84qB9/u+/zfP8/A8L44rhXWc53lp3/ff8TxvLlCNE9unfd/f0t01B4iSHPuKe3uy\n",
       "iNxYW1t77YYNGx4Afq6qT+FaN79x2223dTUyBNj20EMPXUGkC6mI1FRWVm5auXIlsf/f3rnHyVVV\n",
       "+f67ql+hbdKdJoEQGAhJqKXyCngZHgK5TFSUADIYkOESZLyACF7Ay8zAVccBHzCOfIAhV73DICoo\n",
       "EBhBNKIZwMhrUEAlPMZZPAMkkYQYOyF0upN07/vH3qf7dKeru7re3b2/n099+tSpc85edbpq1d5r\n",
       "r/1bmQzTp0/ntddeY926dQBs3br1Lnwv9Qx8yZL/EpHzw+nv0F/C+AD6/2/7Aifje7A7hd7ucvyC\n",
       "gOfTBrme7en3fVD4e14mkzlpsIJ+EGS5Gy8NuAbvjB8Obb0C7Dlp0iS2bNmy2Dm3ZZj7UDDia2C9\n",
       "C3gnraAVidQihU42NQCXqOpeZnZr2PeWqq4AblDVy8xsBb4MRTXp63Gn6gXl1QsXkV2Az4X0oTMI\n",
       "ivbOuaHEjAcQJpcG868h8Zze3l7WrFlDe3t7X8zSOXc5/kfnKrzA83J8nBQGikM/R3960aHA36fa\n",
       "mIcPJfyDc+65cPx0Ebn7mP99c2vquHagxTm3VkSuAK5Ivfbjnp6ezwKXpq59XHhf20RkFiBdXV31\n",
       "ZR6674OfPHsav+Q2EqlZCh3ab8XLYp2hqp9OdprZY3ity6tVdWbx5hXN41OmTOl7Embq78rz3D/R\n",
       "36v7PcVnHezQbiJ/55y7IagbgZfNA6+s9JvwyEXfD6Fq3yKkDwDXikiziJxaX1//B+Av0zmkYdie\n",
       "DMkfAP4hPM5wzn002LJm0aJF4P+ffetKnXPbci1wKDFr8Ct7ytLjjURKSUE9UjPbpqpL8EXNblBV\n",
       "Z2b/L7x8OzXyBXDObRGRLxxwwAFfAXj22Wevcc4NpcA01Lm9IvJ5vD5nfaG6miLyQfzSx2eAh6dO\n",
       "nXpMUq0z8BhwSdh+XyaTmRmG2kOFJRISJ7YAYObMmcn6/4TD8LHZ5qRmE/Q5UHp6elY759Lx2HTl\n",
       "z4RHbr311nlD7K8U3fjeaGTiMDVVCWBVmBQdExSTRzoDX7/ok8AtIQ3qu2a2ijyFQSqBc+6r+HXp\n",
       "hZybsxTJUIhIAz4xPy0Ici5+pdLpwPz169c/iY+F9uDjf+tSx76YilduTcnapW3qu7aIvAK+Iij4\n",
       "EstJ+ID+4X8fqSWgfar8uVYshZho1Yhx0YmHc+47yXZwqGPGkeY1tB9qZZKZvQhMNrN38MO/84EL\n",
       "VXXcC6EMhYicOnXq1K2tra1dIjIn9dLz+F76tUBPEEx5yTn36iAnCt65JuQzdH4UuC7Mnqed6BAG\n",
       "9m82NjbOF5Hj87h+JBLJg2Gdnqo2AZiZCzPzyf7kaymqegJ+VvnrwM21vL6+XIjIHk1NTXeuX7+e\n",
       "jRs3Ul9f/2KYlAH4JfAv5Bdj3S+13Tf+F5FD0o9B5yzp6ur6C/rjwavxpUaOH6AMlVpmH3JBzydS\n",
       "E4jIpaEHdii+IkJkjDHS0P4sVT3CzD5pZj2qWmdmPWaWfC3fBJrM7Al8eeGJysXd3f2j+RCX/Bxw\n",
       "To4801ykl2Omk+iT3NcBNeSdc79OPR2wGB9ARE5raWm5MxEiGcSwEnmRimLOuaXVNiJSOCMNw1cD\n",
       "e6vqYoDEmaZe3zU40XGJiHxGRO7No1rldU1N/XNDYVLnodDTGI3ox9zU9pycR+WJc+6uzZs3nwQM\n",
       "iHcGKb1htT9F5EMicrKIfEREakoWMRKpNUZypMvMbD7QqarfgD5n2qiqbcBiVZ1Wa+pOpUBEZkye\n",
       "PHkxcNLOO+98g4jsmetY59wfuru791iwYAELFiygp6fn0ra2tltU9RpGsQCAgUn0fVkPzrnvhcdv\n",
       "nXO/HeK8nATVqnlNO7evyTQ0bpk1axa9vb1H5yGLlwXu2Weffe7DV1WNRCI5GMmROgAzuwzYknKm\n",
       "W82sA/iQmb2VGuqPJz6STN4Eub0Fwx3snFuzdOlSWbp0qQBzOjo6kpSkQmt1DzhPRFqDyEhBZOob\n",
       "tjW1TFn38ssvSz6LCvCLAnj11VdhYOw2EokMYtgYadAUFTNzZvY3qnqlqi4HbsbP1G8b7vwxzveB\n",
       "L+LrqRvwvVGcex9+HXsjPn90NFyFd6J98U8RuauxsXHh9u3bEZGfOudOCPuPSZ9Y4pSl2/C5nI3A\n",
       "DmlYkUiknxHzSMOMvYRe57fwyxCfMLOCEtTHCs65bhGZjU9JqnNDlyPOde5SYNSTB865h0QkE7aX\n",
       "g88IaGxsXJioLmUymQUiMtc59zQwra2t7d86OjqexQtIlwzn3F3kvwosEikbobJtwnrnXM114PJK\n",
       "yE8N3TcAJ5nZhFD8STnPvJ1oCdpcPmjX3LR0XUjY/wv8qp85HR0d4Gf166hBgvr+qH6IxiIisg/9\n",
       "IZCNzrlHqmnPOOCAlJbubHzO9O54lbnRjvLKzqhWNpnZVgqP+UUK4z58WlSSP7oSSERRHqc/dts3\n",
       "QgglRnbB55M659zynm3dk5zrzYjIVfiwQ7K2/9WhFPdFZGb6uXNu5WgNF5ELgUubm5v3EZErnHNX\n",
       "jvYaY4j9nXM/gb5VOZEicM5dNXifiOwNtA5xeNUpafG7SOlxzrmggH8U3lk+kfTuhomJzgM+itco\n",
       "/adwIent7pwG/J9wzNfxjjYXe4S/q4c5JiehJ/p5YPfOzk4aGxuvEJGbnHMFXS8SqWUm5HLOsYbz\n",
       "PBKK6+UzRJ4N0NTU9OG+a+Ckt2dAWHsKvhBfHyKSEZFvisg/M2BRaUFkWlpa+mJbITxRcNZBLSIi\n",
       "u4vISaEHun+17YlUj9gjLQIRORO4aLfddjt07dq1FznnFo/i3DOAE4F/T4s15Dj2g/j42yF4wZM3\n",
       "8IIO5px7YIhT6qBvYcABwHKRTG/9pJY/4nVVW4FrBrWRwcefknzZhfhecEE453pE5Is777zzl7q7\n",
       "u9m6destY0nNJ08OAn4WJj9+Um1jItUjOtLiOAc4dO3atbS2tt4gIjcOUn4aEhHJzJw58wcrV66k\n",
       "vb39dBG5YwSlea2rq7supd5EfX0927dvv4BBNaEC64D3dHZ29uLrQ1HX0NRFAzjncq2x/w79ThS8\n",
       "utclzrlhS1UPh3PuyyLy1bA94TQYhkNERrNQIzKIILx+eHi63eWuaFsR4tC+ONqTjSCcnO9wWBKn\n",
       "GNblj3ReJhFm/vCHP8yJJ56YnLdD/SkRaWtsbEx0RDN77bXX/SFIn6jx7zTEOfvW1dWdNUS7DXm+\n",
       "n5w453qjEx2Sz+LLlR9LrABQCPvhtXzvY3jtXgBE5HwROTE8FpbamOhIi2Mp8OjChQvZtGnTJc65\n",
       "rhHPwA9733jjjTOBj2/atOnsPNTmf9/b23tVJpNh+fLlaV3R2UMce0U6Xer111+noaFhZVfHur27\n",
       "OtbtXV9f3xlioACIyCnAkp6eHlpbB0yIrqLEuamRAfync25ZeAyWU4zkh3O+h5HPysrVYbn0T/AL\n",
       "TQAIWhILwmPKMOcPSxzaF4Fz7nNFnPuDURx7P3C/iLzQ3d393fvu6yvmOaAmlohMamhouHjbtoH5\n",
       "ytu2bUt6zITVUReJyNMhNns6cDDAxo0bk8J31wOXxp5kZALQiI9vT8Mrov2qkIvEHmmNIyLHisix\n",
       "4MVLgPSE1uClm9unT58+YMe+++7Lcccdl9SrAiAoVSWLKgYo9Pf09OzrnPvsaJ2oiMwSkctEZOfR\n",
       "nFcN1qxZM19EFlXbjkhNkISeiuo0xB5pjRJSav4nPhf0B/iqouBjQr8M2wNCAs657SKyS3Nz8x87\n",
       "O/1Lb775JrNmzUpiqkyaNImurq6/c879MJz2AD4Nqhd4zTn3UgG2frmxsfELIaRwuYjs5Zx7e7TX\n",
       "qRQzZsx48IUXXtghvhyJFEp0pLXLB/FJ9bS2tl4Wktlfcs4NK6DtnNsQZjR/BBz99ttvs2zZMo5+\n",
       "72nU1dXR1dU1O1WxFOfcj4o1tL29/QsbNmxInrbhe81nF3vdWkFEmoEL8bWudsenrK2sqlGRmiIO\n",
       "7WuXP0s2Nm7cSGtr64sicuDgg0RkhohMSu9zzm1wzh0DHNrW1gb4nNKGlvY30k40dY09h7p2vmzY\n",
       "sOE/Bu0ab9USBPhNmKh4hJF1DVpSM8RHlN+8SLWJjrR26Vspk8lk2LhxI42NjSvSivsicnUmk1k9\n",
       "bdq0LSKyg+K9c+6pjo6OM4GFmaZ3rZdMZoc4kIj8S1NT0xsiskJE8l5QMIglwGPvf//7Ae50zt1R\n",
       "4HWqQsrpnSgiRZegds7dnpoh3iXVzpEicoKInADskIYWKZiOcqY25UN0pLVLX4wxKdEcYpD/C3xS\n",
       "f1NT0+W9vb289dZbABcMdRHn3A+ccz+sb9rpnRztnNzd3Y1zjrq6us8M7t3mg3PuBufcUY8++qg4\n",
       "5z4+2vNrgZTjmzziwYUzFfhpeESJwhIRlk8n/7+8UhBLTXSktcsdSZnlQSwDn+je3d39s9T+FQW2\n",
       "07e0saen57EkF1ZE6kXkKyLypIi8KCK/E5GTCmxjPPEWcHCYDGxndLO9Lk15zBvXvAMcFO79HEYQ\n",
       "lheRuakRwNRyGhYnm2qXl7q6uhbh17vvj19f/xIDK41+G7gzbBc6S/4gvmKpw1eFRUTq8Gv5Bwtx\n",
       "3Csi33HODVs4bzzjnFuP1yuIVJhw728dxSl/lkgblpvoSGsU59zdYfP7wxzzw1yvjaKd24fYfQQ5\n",
       "1Iyam5v/mlQFUhFpykdfYAzxTkpPtK4UWQ2R8U8c2peBIEX3mog8FsSNxxpPAC8P9UJnZ2ffRJKI\n",
       "PCwiXSKSTzG9MYFz7hepeNt7glM9npRwdiQymJL3SFW1CTgMeA740zitMJoTEXkXftnlFHzhvBYR\n",
       "+eZYiok557aKyH7ACcBlePESAa4Lq6sQka8AR4e39X4R+Zpz7rJq2VwOnHNXl+Ay00OMDnyObWQc\n",
       "UlJHqqqN+GHhDODdQK+q3mxmE2nN9pF4J5pwIH4d75gSpgjD9R+GxwBERFpaWj6/efPmvn3Nzc1/\n",
       "JyKXj6UfjErgnLup2jZEyk+ph/ZzgQYzuw2/pLEVuFhVJ1II4RfA86nnPy9E3UdEPikivxKR1SJy\n",
       "SWr/xSLykog8IyJDpjyNsp1PiMhSEXlCRM7L5xznnNu8efP/SO/r7Ow8KzrRyESlJA4u9ETBr9ne\n",
       "W1VnmtmL+NSaOuAsVS22dMWYwDnXg1dOnwsc4pz7SIGX+it8iGRGW1vbdSLSJiKTdt111+vx8nkH\n",
       "AJeG2kjF8Al8Ab1Dgc+LSF6jFOfcbcBpwCnA6c650cymRiLjilL1FBeo6r74ZNhZwMmqOsXMXsAL\n",
       "bLQD7ypRWzWPc67HObeimNIakydP/kCyHUou7w/MXLeuv3MrIrMYGEYYFWGIfmxq117A9FzHD8Y5\n",
       "d5dz7h7n3JJCbYhEahkROTxZNbVq1apTcx1XlCNV1UZV/WvgU0Czmb0NXAXMBD6uqrPN7ClgM0Oo\n",
       "uUdys2nTpi+nnt4PPOac+y/g3mSnc+7nzrkNO5ycJ2GI/uVMpu9jcItzblWh14tExiFTkyyOTCaT\n",
       "87tW1GSTmW1V1fnATma2QlXPwTvNJ/GTLMeq6hH4RPLfF9PWRMM590UR+Vp42pnEH51zJ4tIe9gu\n",
       "2IkOaucrYXvrSMdHIjVOXSoPeJdhjywhBTnSEBM92sweNLMzVXWeqi7Cq0vPA1qAnwG/wauvP2tm\n",
       "HaUyeiwQ1JQ6nHOv53i9AZgPPJyr1Ihzbsj18aVwoIM4EthbRG6JE0aRsYxz7t6Rjyo9hQ7tG4AL\n",
       "VPU8ADN7CHjAzJ4DvglsBGab2dtm9rCZ/WmYa407ROR2YEV9ff1rInL9EK83Ai/gf2xWh9zTqiAi\n",
       "P8ZnWHwX+E0JJq8ikQlHoY50K17B5i9VNVm5s01VLwrbDwM7q+qEkwoTkbb6+vrTwddHam9vv3gI\n",
       "5/QJfBwZfJJ2VRLZRWRyfX39ialdB4dHJBIZBQUN7c1sm6ouwTvTG1R1m5ndqKrr8AWkDgS+Z2bD\n",
       "1WrPRSKau6eqFmJeVclmsxx++OE8/fTTAMybN49ly5btnX4vc+bMuX/33XdPZPFYsmTJ36vqzeW0\n",
       "a4+Pfq4eQFVnpm098MADef7556mrq2PatGmsXr16Q/qYMcie4e9Q4st9n62WlpZdk/eZ3o4MzVCf\n",
       "n7HKUP/76dOnt2/ZsmX3we8vfWxTU1MSc93hsyWFhsRCutM2vKzY9/G90J+Y2Uuq2mxmI5UYznXd\n",
       "o/Aq5JFIMRxtZgM0AOJnK1Iidvhs5dUjVVUZvGbezF5U1QPNbKWqfh+4AZiuqpcX6kQDTwJHA38g\n",
       "CkVERk8dvq7S4AqrED9bkeLI+dkatkeqqk1m1h2268ysJ2yLmTlVPQhfW2g7fkj/UzMbdRXKSCQS\n",
       "GcuM5EjPBY4ws0+G533ONDzfDdjbzJ4ou6WRSCRSo4w0a78av3Z+MYCZ9ahqOtC6a3SikUhkojNS\n",
       "j7QuOM+vAS1mdmHY3wg042unnwqsn2i6o5FIJJIwkiPNJFqiqnoNfinohanXG80sLiuMRCITmmGH\n",
       "9mbWm8jfmdnfAOtVdbmqLgpD/GGr+BWKqla8llQ1NFMHhUnGc5s1VxtMVZtU9RhVba81iUdVrVfV\n",
       "D1XbjqGo5fsG1bt3eeWRpmbppwN3AJ8yMyuXUar6KSBjZt8qVxuD2mvCF3SrA+4ys7UVaLMRWASs\n",
       "Ap4ysz9WsM3NwOvAr8odkgmr267EZ3bcNzj/rhqE+3AkvpJDC76kck1Ucgg/Oj3A3wLX1IJNCbV8\n",
       "36C69y6vXljqy7YBOKmcTjTwLHBaaslpuTkMH+/9aYWcaD2+oNrPgD/hU8fK3WZdaPPH+EnEw4Bz\n",
       "y9mrUNUG4CzgRrz+wmk1sjKmlis5fAzvDHYLI8Kja6j3V8v3DeBsqnTvRnUDzGyrmW0qlzEpngW+\n",
       "ChymqpdXoL2DgYXA66p6lqpeoKoLyvUPMLPtwGv4HNzVwKGq+ilVnVHGNnvwBeymhF7hv+Nlxs4p\n",
       "Y5vbgN/hf4C/DjQBHy9HW/lQy5Ucwhf+UjNbAlwC3K2qhwPHApcCJw57gfLaloSDXsMvupldK/ct\n",
       "2FcPYGY3AZ8G7q30vauJX5IQdzlEVdtCpsDbwAr8MPS9qvq3qlpShaTQ5vtCr+ku/Jf8bOBB/MqX\n",
       "+ZT4H5Bqc1dgEnAOvlf6Efx7PS3YUMo2JfxtwKt2HaeqbWb2n8BSvDOdW6Y2W/BFEM8Ow6wv4aso\n",
       "oKrvLmWbeVKTlRxUdSp+6eomADO7AZ8V85aZfYkgR1nq70CetjUCZ6vqqfhh/aHAPFXdpdr3Ldi3\n",
       "E3CVqv6Tqh6LH/3U4TOJKnbvqu5Iwz/qKOAQvCM5J3zpZ+DLaJyL/2W5MXzgStnmXLzjWoRXYZoL\n",
       "7GVm9wAPAPuUor1BbR6Mr5F0IHAhXvnpWuAYM7ueEgpghyHXlaEHsQ14Cu/YPhYcyLOAAe8pU5ub\n",
       "8cI2N4aXu/E/WADzVbVk93cEm2q2koOqTsHHqy8CHlfVYwDM7H7gHVWda2Z3Aw4fjqmkbelw0Fr8\n",
       "UN4B7wc+Ws37FuxLh47+iK8fto+ZLQc6K3nvqu5I8W+wK3TLfw3siu+ev4yX69sPeALI4ntUpWzz\n",
       "2/h1s1vwPYB3gLmqOg+v6t+uqs0lbvMm4LfAbsB5+OHShhDT2Rc4SEskPxh6gTOB21V1jpm9AlyP\n",
       "/9E6U1XnBlvqw4RbqducHSbR3gkjjfXAA6p6MvCP+A942QkpeoMrOZyA/9/vg6/kcCbVqeQwFTjL\n",
       "zB7EfxbWQZ+T+ACwm6ruCTyHH6VVjBAOyuDDQQ/je3e/xzvO91Ld+5aEjlbQHzpqpD90dCz++7sX\n",
       "Fbh3Bas/lYrwIfkA8HP8r95B+CF1B/Amfpj9HCClEoge1OY6fE/0KPzw5CF8D20bXs2qHG0m7/N4\n",
       "/Ad1Mn6IfzDwnVIKYYcP0sF4p31xUOeaif+BmoafTb839NJK3ea5wEVm9oqq1pvZdlW9HjgTmG9m\n",
       "Zf1wa6qSQ3g+D1/g73f0V3L4NQMrOVREhDzYdoSZPRR+QF/BD5FPxYukvxB6q1Pwn4/XzazUlRGG\n",
       "s+3PzezRMKSfDtxqZh3hx/dIvDD5r6nwfUvbBzyGH01ONbNrVXUP4FQzuz707NfiR0Cry50VUwv5\n",
       "fd34Ya4D7gSewQ+z9wWWh15Mudt8Gj9seTfwpJn9hxYhBZhnm8/gvyR7Aveb2Zuq+lsz21iKxjSk\n",
       "rJnZ6/hJtJ3w2rEXh4mCleG4kr3PHG3+X1X9TOgNg0+fW2xmL5eizRFIKjnMNrMbg9Pa3cz+oKrP\n",
       "44f6s83sl3gZyErSAFyiqnuZWVLK+i1VXYH/P10WfmgqWl0ihGZ68A7yUeBxfPjpFFX9Eb5nNxu/\n",
       "PPxtKnzfUvYdEhz9PfQreW3F90rBd4ZWVyDDCKjS0D49w2dmbwHfBg7Hd8unhQ92Cz5OWqk2l+Mn\n",
       "gPYLxxTtXPJscxpemgvCZEMp2kxS1lLP7wC+hw/Mn6Kqs8L+kr3PYdr8x9Dmnmb2qwo5UajtSg5b\n",
       "8bPeZ6jqp5OdZvYYcBtwtVYnVexi/GTcNPWz4XXAzfge4EL86O0pShgOKtC+qSGGOwvIqGpD+I49\n",
       "GEJH1+DzXCtCRR1pcuNDcn9d2Cdm9jywGP8rckq4Ec/gg/CVbnNlhdtcgU/HSefrlqTN1PPEsS3B\n",
       "h0muJcyeF8Mo2nw+tFnRxO0QQ1uCn1A8RlXPCyOcUlRyKKVt/11Vz0+9fDvwr/jYfaXtug4/Efcj\n",
       "vPO8AK/h+hywBn/PjgLusSCxWUX7DgNOx6c4HR8OORO4CTjKzF6tlF0VjZFqDlk+DWv6VXUXvHP/\n",
       "b8DjVoLKoxO9zdTriQ37AxvN7I2x2GYBNpalkkMZbLsFH7v9rpmtqpI99eZznEn9yL+BnxmfDHzT\n",
       "fAn2qty3HPa9jo+TzsBPOL0PnzZWqVGPxzlXsUc2mz0+m80+mM1mF6f21aW2D4ltlq3N942HNkew\n",
       "R3LsPzD8/Vg2m12dzWa/luvYKtu2KpvNXp3NZjPVsm3Q9q7ZbHZO2L46m83+eSXtKsC+udWwzzlX\n",
       "8R5pxWX5Ypvjq80cdtRsJYcCbLsvTAZW1Tb8RPQifBrii/jc0V+Ue/Z7LNk3gAr/smRS29dks9lv\n",
       "DHq9MbYZ2yzAjnOz2ezNqed1g17frYq9qbFs24xsNjsnm80enc1m26N9uR8VnWyyKsjyxTbHV5s5\n",
       "qOVKDmPZtmlm9pKZPWIVymEdY/b1UfH0p/SMLvAtvJDGE2bWU67hX2xzfLU5BMvMbD5+WeA3gl09\n",
       "6peGtgGLVXWaVkdYYyzb9s9VtG0s2NdPNbvD2Wy2MZvNTo5txjaLbLcmQgzRtollX/pR9SWi9RVz\n",
       "bAAAAIlJREFUkUgpSCZvwvaVwDH4RPLbgN4K9o6jbRPIvoRaEC2JRIqmRkIMQxJtK5xaty8h9kgj\n",
       "446QfjXJKiNCPiqibYVTy/ZFRxqJRCJFEof2kUgkUiTRkUYikUiRREcaiUQiRRIdaSQSiRRJdKSR\n",
       "SCRSJNGRRiKRSJFERxqJRCJFEh1pJBKJFMn/Bwf29hRnMpSOAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6951d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = -1\n",
    "samples = pools[idx].thetas\n",
    "fig = triangle.corner(samples, weights=pools[idx].ws, truths= means)\n",
    "\n",
    "for mean, std in zip(*abcpmc.weighted_avg_and_std(samples, pools[idx].ws, axis=0)):\n",
    "    print(u\"mean: {0:>.4f} \\u00B1 {1:>.4f}\".format(mean,std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}