differential equation numerical method.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAloAAAEUCAYAAADz4ZhrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAENpJREFUeJzt3V+sZld5HvDnwTYiqaNYiMgEe1KjYhSQkHCpjAVpmDRN\n",
       "CqPK9AKpRkoUcdEgJAtKpRQFIeFcpepNKY2CLBUiBypQFFTLCEeEpAwiFzVNsI0Bk2AJItsE0wYw\n",
       "f1waG95ezGc4OR7PGTzfOmc++/eTts7ea69v73X8zkjPrL2/5c5MAADYvqcd9QAAAJ6sBC0AgEUE\n",
       "LQCARQQtAIBFBC0AgEUELQCARc4YtNo+o+1tbe9o+7m2v/04/d7Z9gtt72x71ZqhAgDslgvPdHJm\n",
       "vtv2F2bmobYXJvmztj83M3/2aJ+2J5I8b2aubPvSJO9Kcs3aYQMAnP8OfHQ4Mw9tdp+e5IIkX9vX\n",
       "5dokN2363pbkkraXbnOQAAC76MCg1fZpbe9I8kCSj83M5/Z1uSzJvXuO70ty+faGCACwm85mRuv7\n",
       "M/PinApPP9/2+Gm6df/HtjA2AICddsZ3tPaamQfbfjjJP0lycs+p+5Mc23N8+abt72krfAEAO2Nm\n",
       "9k8k/cjOGLTaPivJIzPzjbY/luSXkvzWvm63JLk+yQfaXpPkGzPzwKoBc/ja3jAzNxz1OHhi1G+3\n",
       "qd/uUrvdtq0JooNmtH46yU1tn5ZTjxnfOzN/2vb1STIzN87MrW1PtL0nyXeSvG4bAwMA2HUHLe9w\n",
       "V5J/fJr2G/cdX7/lcQEA7Dwrw3M2Th71ADgnJ496AJyTk0c9AJ6wk0c9AI5eZw7nHfW24x0tAGAX\n",
       "bCu3mNECAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIA\n",
       "WETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE\n",
       "0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBY5IxBq+2xth9r+9m2n2n7xtP0\n",
       "Od72wba3b7a3rRsuAMDuuPCA8w8nefPM3NH24iR/0fajM3P3vn4fn5lr1wwRAGA3nXFGa2a+MjN3\n",
       "bPa/neTuJM85TdcuGBsAwE4763e02l6R5Kokt+07NUle1vbOtre2feH2hgcAsLsOenSYJNk8NvzD\n",
       "JG/azGzt9akkx2bmobavSnJzkudvd5gAALvnwKDV9qIkH0zyvpm5ef/5mfnWnv0/avu7bZ85M187\n",
       "zbVu2HN4cmZOPqFRAwBsUdvjSY5v/bozc6abNslNSf52Zt78OH0uTfLVmZm2Vyf5g5m54jT9Zma8\n",
       "ywUAnPe2lVsOmtF6eZJfSfLptrdv2t6a5GeSZGZuTPKaJG9o+0iSh5Jcd66DAgB4MjjjjNZWb2RG\n",
       "CwDYEdvKLVaGBwBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBY\n",
       "RNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQ\n",
       "AgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBYRNACAFhE0AIAWETQAgBY5IxBq+2xth9r\n",
       "+9m2n2n7xsfp9862X2h7Z9ur1gwVAGC3XHjA+YeTvHlm7mh7cZK/aPvRmbn70Q5tTyR53sxc2fal\n",
       "Sd6V5Jp1QwYA2A1nnNGama/MzB2b/W8nuTvJc/Z1uzbJTZs+tyW5pO2lC8YKALBTzvodrbZXJLkq\n",
       "yW37Tl2W5N49x/clufxcBwYAsOsOenSYJNk8NvzDJG/azGw9psu+4zntdX6r/zYPP+OC/PUrfjbf\n",
       "veQn870LL/rRhgsAsDsODFptL0rywSTvm5mbT9Pl/iTH9hxfvml7rA/munz3H/1scv8FefaDX81l\n",
       "P/XNx0Q0AIDD9uUHLs5X/s/F275sZ047+XTqZNucev/qb2fmzY/T50SS62fmRNtrkrxjZh7zMnzb\n",
       "Sebnk9yY5EUz+d5WfgMAgC1rOzNzztNBB81ovTzJryT5dNvbN21vTfIzSTIzN87MrW1PtL0nyXeS\n",
       "vO4M1/vFJLcIWQDAU8EZZ7S2eqNTM1ofSPLhmbzvUG4KAPAEbGtG67BXhv+HSf76kO8JAHAkBC0A\n",
       "gEUO+9Hh95I8YyaPHMpNAQCegF19dPgdIQsAeKo47KD1zUO+HwDAkRG0AAAWEbQAABYRtAAAFhG0\n",
       "AAAWEbQAABY57KD1rUO+HwDAkTnsoPV/D/l+AABH5rCD1v875PsBABwZQQsAYBFBCwBgEUELAGAR\n",
       "QQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgkcMO\n",
       "Wn93yPcDADgyhx20Hjnk+wEAHBlBCwBgEUELAGARQQsAYJEDg1bb97R9oO1dj3P+eNsH296+2d52\n",
       "hssJWgDAU8aFZ9Hn95L8lyS/f4Y+H5+Za8/iWt87q1EBADwJHDijNTOfSPL1A7r1bG42kzmbfgAA\n",
       "TwbbeEdrkrys7Z1tb237wi1cEwBg553No8ODfCrJsZl5qO2rktyc5Pmn69j2hj2HJ2fm5BbuDwBw\n",
       "TtoeT3J869edOfhpXtsrknxoZl50Fn2/mOQlM/O1fe0zM2f1iBEA4ChtK7ec86PDtpe27Wb/6pwK\n",
       "b1874GMAAE96Bz46bPv+JK9I8qy29yZ5e5KLkmRmbkzymiRvaPtIkoeSXLduuAAAu+OsHh1u5UYe\n",
       "HQIAO+K8eXQIAMDpCVoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwhaAACL\n",
       "CFoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwha\n",
       "AACLCFoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwhaAACLCFoAAIsIWgAAiwhaAACLHBi02r6n7QNt\n",
       "7zpDn3e2/ULbO9tetd0hAgDsprOZ0fq9JK98vJNtTyR53sxcmeTXk7xrS2MDANhpBwatmflEkq+f\n",
       "ocu1SW7a9L0tySVtL93O8AAAdtc23tG6LMm9e47vS3L5Fq4LALDTtvUyfPcdz5auCwCwsy7cwjXu\n",
       "T3Jsz/Hlm7bHaHvDnsOTM3NyC/cHADgnbY8nOb71684cPPnU9ookH5qZF53m3Ikk18/MibbXJHnH\n",
       "zFxzmn4zM/tnvgAAzjvbyi0Hzmi1fX+SVyR5Vtt7k7w9yUVJMjM3zsytbU+0vSfJd5K87lwHBQDw\n",
       "ZHBWM1pbuZEZLQBgR2wrt1gZHgBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGAR\n",
       "QQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUEL\n",
       "AGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBg\n",
       "kQODVttXtv182y+0fctpzh9v+2Db2zfb29YMFQBgt1x4ppNtL0jyO0n+eZL7k/yvtrfMzN37un58\n",
       "Zq5dNEYAgJ100IzW1UnumZkvzczDST6Q5NWn6detjwwAYMcdFLQuS3LvnuP7Nm17TZKXtb2z7a1t\n",
       "X7jNAQIA7KozPjrMqRB1kE8lOTYzD7V9VZKbkzz/nEcGALDjDgpa9yc5tuf4WE7Nav3AzHxrz/4f\n",
       "tf3dts+cma/tv1jbG/YcnpyZkz/yiAEAtqzt8STHt37dmceftGp7YZK/TPKLSb6c5JNJXrv3Zfi2\n",
       "lyb56sxM26uT/MHMXHGaa83MeJcLADjvbSu3nHFGa2YeaXt9ko8kuSDJu2fm7rav35y/Mclrkryh\n",
       "7SNJHkpy3bkOCgDgyeCMM1pbvZEZLQBgR2wrt1gZHgBgEUELAGARQQsAYBFBCwBgEUELAGARQQsA\n",
       "YBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGAR\n",
       "QQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUELAGARQQsAYBFBCwBgEUEL\n",
       "AGARQQsAYBFBCwBgEUELAGCRA4NW21e2/XzbL7R9y+P0eefm/J1tr9r+MAEAds8Zg1bbC5L8TpJX\n",
       "Jnlhkte2fcG+PieSPG9mrkzy60netWisHJG2x496DDxx6rfb1G93qR3JwTNaVye5Z2a+NDMPJ/lA\n",
       "klfv63NtkpuSZGZuS3JJ20u3PlKO0vGjHgDn5PhRD4BzcvyoB8ATdvyoB8DROyhoXZbk3j3H923a\n",
       "Dupz+bkPDQBgtx0UtOYsr9Mn+DkAgCetCw84f3+SY3uOj+XUjNWZ+ly+aXuMtgLYjmr79qMeA0+c\n",
       "+u029dtdasdBQevPk1zZ9ookX07yr5O8dl+fW5Jcn+QDba9J8o2ZeWD/hWZm/6wXAMCT2hmD1sw8\n",
       "0vb6JB9JckGSd8/M3W1fvzl/48zc2vZE23uSfCfJ65aPGgBgB3TG0zwAgBWWrwx/Nguecvjavqft\n",
       "A23v2tP2zLYfbftXbf+47SV7zv3mpoafb/vLe9pf0vauzbn/fNi/x1NR22NtP9b2s20/0/aNm3b1\n",
       "2wFtn9H2trZ3tP1c29/etKvfjmh7Qdvb235oc6x2O6Ltl9p+elO/T27a1tZvZpZtOfW48Z4kVyS5\n",
       "KMkdSV6w8p62s67NP01yVZK79rT9xyT/frP/liT/YbP/wk3tLtrU8p78cDb0k0mu3uzfmuSVR/27\n",
       "Pdm3JM9O8uLN/sVJ/jLJC9Rvd7YkP775eWGS/5nk59Rvd7Yk/y7Jf0tyy+ZY7XZkS/LFJM/c17a0\n",
       "fqtntM5mwVOOwMx8IsnX9zX/YPHZzc9/tdl/dZL3z8zDM/OlnPrD9tK2P53kJ2bmk5t+v7/nMywy\n",
       "M1+ZmTs2+99OcndOrWenfjtiZh7a7D49p/5B+vWo305oe3mSE0n+a364tJHa7Zb9X85bWr/VQets\n",
       "Fjzl/HHp/PAbow8keXSF/+fk7y/r8Wgd97ffH/U9VJtvBF+V5Lao385o+7S2d+RUnT42M5+N+u2K\n",
       "/5TkN5J8f0+b2u2OSfInbf+87b/ZtC2t30HLO5wrb9rvqJkZ656d39penOSDSd40M99qf/iPNPU7\n",
       "v83M95O8uO1PJvlI21/Yd179zkNt/2WSr87M7Y/3/zFUu/Pey2fmb9r+VJKPtv383pMr6rd6Ruts\n",
       "Fjzl/PFA22cnyWZq9Kub9tMtSnvfpv3yfe2nXayW7Wp7UU6FrPfOzM2bZvXbMTPzYJIPJ3lJ1G8X\n",
       "vCzJtW2/mOT9Sf5Z2/dG7XbGzPzN5uf/TvLfc+oVp6X1Wx20frDgadun59SCp7csvidP3C1Jfm2z\n",
       "/2tJbt7Tfl3bp7d9bpIrk3xyZr6S5JttX9pT0ym/uuczLLL5b/3uJJ+bmXfsOaV+O6Dtsx79VlPb\n",
       "H0vyS0luj/qd92bmrTNzbGaem+S6JP9jZn41arcT2v5425/Y7P+DJL+c5K6srt8hvOH/qpz6VtQ9\n",
       "SX7zqL9xYPtBXd6fU6v9/11OvUf3uiTPTPInSf4qyR8nuWRP/7duavj5JP9iT/tLNn9Q70nyzqP+\n",
       "vZ4KW059Q+37OfVtmNs32yvVbze2JC9K8qlN/T6d5Dc27eq3Q1uSV+SH3zpUux3Ykjx38/fujiSf\n",
       "eTSTrK6fBUsBABZZvmApAMBTlaAFALCIoAUAsIigBQCwiKAFALCIoAUAsIigBQCwiKAFALDI/wdV\n",
       "cOEdDXO+mAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1062350d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAloAAAEUCAYAAADz4ZhrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAE3FJREFUeJzt3W+spmWdH/Dvj5lhhUWgLCuLzGywARtIzUKxQNHWWbur\n",
       "OGnRF6bFxI3hRdfaEK3bbO0aE9m+2WbTZC01a0iqW9QGu9GWYsS6bJexbNMd1oUBlEGZjbYwytAu\n",
       "ygps3Rnn1xfnAQ6HM+ecmXmu85znzOeT3Jn7z/U89+9wDcl3rvu6r1PdHQAApu+UWRcAALBZCVoA\n",
       "AIMIWgAAgwhaAACDCFoAAIMIWgAAg6wYtKrqFVW1p6r2VtXDVfUbR2l3c1U9WlUPVNXlY0oFAJgv\n",
       "W1e62N3/r6p+vrufq6qtSf6wqt7Y3X/4fJuq2pXkou6+uKquSvKJJFePLRsAYONb9dFhdz832T01\n",
       "yZYkTy1pcl2SWydt9yQ5u6rOm2aRAADzaNWgVVWnVNXeJAeT3N3dDy9pckGSxxYdP55k+/RKBACY\n",
       "T2sZ0TrS3ZdlITz9narauUyzWvqxKdQGADDXVpyjtVh3P11VX0ry+iS7F106kGTHouPtk3MvUVXC\n",
       "FwAwN7p76UDSMVsxaFXVuUkOd/cPquq0JL+Y5NeXNLsjyY1JPldVVyf5QXcfHFUw66+qburum2Zd\n",
       "B8dH/803/Te/9N18m9YA0WojWucnubWqTsnCY8bPdPd/q6r3Jkl339Ldd1bVrqran+TZJDdMozAA\n",
       "gHm32vIODyX5G8ucv2XJ8Y1TrgsAYO5ZGZ612D3rAjghu2ddACdk96wL4LjtnnUBzF51r88c9apq\n",
       "c7QAgHkwrdxiRAsAYBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGAQQQsA\n",
       "YBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGAQ\n",
       "QQsAYBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGAQQQsAYBBBCwBgEEELAGCQFYNWVe2oqrur6htV\n",
       "9fWqev8ybXZW1dNVdf9k+8i4cgEA5sfWVa4fSvLB7t5bVWck+ZOququ79y1p99Xuvm5MiQAA82nF\n",
       "Ea3ufqK79072n0myL8mrl2laA2oDAJhra56jVVUXJrk8yZ4llzrJNVX1QFXdWVWXTq88AID5tdqj\n",
       "wyTJ5LHh55N8YDKytdh9SXZ093NV9bYktyd57XTLBACYP6sGraraluQLST7b3bcvvd7dP1y0/+Wq\n",
       "+u2qOqe7n1rmu25adLi7u3cfV9UAAFNUVTuT7Jz693b3SjetJLcm+bPu/uBR2pyX5Mnu7qq6Msnv\n",
       "dveFy7Tr7jaXCwDY8KaVW1Yb0XpDkncnebCq7p+c+3CSn02S7r4lyTuTvK+qDid5Lsn1J1oUAMBm\n",
       "sOKI1lRvZEQLAJgT08otVoYHABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQ\n",
       "AgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIA\n",
       "GETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhk\n",
       "xaBVVTuq6u6q+kZVfb2q3n+UdjdX1aNV9UBVXT6mVACA+bJ1leuHknywu/dW1RlJ/qSq7urufc83\n",
       "qKpdSS7q7our6qokn0hy9biSAQDmw4ojWt39RHfvnew/k2RfklcvaXZdklsnbfYkObuqzhtQKwDA\n",
       "XFnzHK2qujDJ5Un2LLl0QZLHFh0/nmT7iRYGADDvVnt0mCSZPDb8fJIPTEa2XtZkyXEv+z2/Xv/0\n",
       "2Mqboq7kR2f+RP7ir5yWH535ihw6/RU5sm1Ljmzdkh9v3ZojW7fkyLatObJlS3LKKema/ExVCz9N\n",
       "1cL+cudfOF763wEAOImtGrSqaluSLyT5bHffvkyTA0l2LDrePjn3cv8p17+w/1fzeC7L48dS7Ko6\n",
       "yTPnn5U/v+BVefZVr8pfvvKsHDrtlTl82pn58bbTUkcO55TDP8oph36UU358KHXkx5PtyEv3u1Pd\n",
       "k7zYqU4qnfSiANnPx6qXtgMA5s93D56RJ/7vGdP+2uo+ejioqsrC/Ks/6+4PHqXNriQ3dveuqro6\n",
       "yce6+2WT4auqu3vqIz5VqSR/K8m7k+xKsiXJ15Lcn+SbSf73ZHuyO4emfX8AYPOZVm5ZLWi9Mcl/\n",
       "T/JgXnwc+OEkP5sk3X3LpN3Hk1yb5NkkN3T3faMKfvH7Ukn+fpJ/meT0JJ9KckeSfd3LP7oEAFiL\n",
       "dQla0zTNoFWVVyf591mYiP8vknypO0em8d0AANPKLXO3MnxV3pDkviT3JPm57nxRyAIANqI1vXW4\n",
       "UVTlrUk+m+Td3fnKrOsBAFjJ3Dw6rMoVSf5rknd0539MrzIAgJc6qR4dVuWnktye5B8LWQDAvNjw\n",
       "I1qTtwv/Y5LHu/Mr068MAOClpjWiNQ9ztN6R5HVJ3jPrQgAAjsWGDlpVOTXJbyb5J935i1nXAwBw\n",
       "LDb6HK33JtnfnbtmXQgAwLHasHO0JqNZf5rk7d152UrzAACjnAxvHf6DJN8SsgCAebUhg9bkTcN/\n",
       "luRfz7oWAIDjtSGDVpIrkpyZWP0dAJhfGzVovSfJp/0OQwBgnm24yfBV+YkkB5L8ze58e3xlAAAv\n",
       "tZknw1+b5GEhCwCYdxsxaL0jyednXQQAwInaUI8Oq7IlyRNJXt+d/7UuhQEALLFZHx1ek+SAkAUA\n",
       "bAYbLWhdl+S/zLoIAIBp2GhB6y1JvjzrIgAApmHDzNGqyrlZ+N2GP9Wdw+tSFADAMjbjHK2dSe4R\n",
       "sgCAzWIjBa03J/mDWRcBADAtghYAwCAbImhV5fwkr0ry4KxrAQCYlg0RtJJcneR/+iXSAMBmspGC\n",
       "1p5ZFwEAME0bJWhdleSPZl0EAMA0zXwdrapsTfL9JDu684N1KQYAYAWbaR2tv57kMSELANhsNkLQ\n",
       "ujoeGwIAm9BGCFqvT/LHsy4CAGDaVg1aVfWpqjpYVQ8d5frOqnq6qu6fbB85xhouS7L3GD8DALDh\n",
       "bV1Dm99J8m+TfHqFNl/t7uuO9eZV2Zbk0iTLhjgAgHm26ohWd9+ThbcCV3K8s/L/WhYmwj9znJ8H\n",
       "ANiwpjFHq5NcU1UPVNWdVXXpMXz25+KxIQCwSa3l0eFq7kuyo7ufq6q3Jbk9yWuXa1hVNy063J30\n",
       "ZUkemEINAADHrap2Jtk59e9dy4KlVXVhki929+vW0PbbSa7o7qeWnH/Zwl9VuSvJb3XnzmMpGgBg\n",
       "pA2zYGlVnVdVNdm/Mgvh7alVPpaqVDw6BAA2sVUfHVbVbUnelOTcqnosyUeTbEuS7r4lyTuTvK+q\n",
       "Did5Lsn1a7z3+VmYRP+946gbAGDDm9nvOqzKW5N8qDtvXpcCAADWaMM8OjwBlyR5eIb3BwAYapZB\n",
       "69IIWgDAJjbrEa19M7w/AMBQMwlakzcOjWgBAJvarEa0fjoLbxw+OaP7AwAMN6ugdUmSfd1Zn1ce\n",
       "AQBmYJZBy2NDAGBTm1XQujQmwgMAm9xMHx3O6N4AAOtiliNaHh0CAJvaugetqpyZ5Kwkj633vQEA\n",
       "1tMsRrRem+TR7hyZwb0BANbNLILWRUn2z+C+AADrahZB6+Ikj87gvgAA68qIFgDAIEa0AAAGMaIF\n",
       "ADDIugatqpyV5PQkT6znfQEAZmG9R7QuSrLfL5MGAE4G6x20zM8CAE4aMxnRWud7AgDMhKAFADCI\n",
       "R4cAAIMY0QIAGGS9g9ZPJvneOt8TAGAm1jto/amlHQCAk8V6By3zswCAk8Z6By3zswCAk4YRLQCA\n",
       "QYxoAQAMYkQLAGCQVYNWVX2qqg5W1UMrtLm5qh6tqgeq6vIVvs7SDgDASWMtI1q/k+Tao12sql1J\n",
       "Lurui5P8cpJPHK2tpR0AgJPJqkGru+9J8v0VmlyX5NZJ2z1Jzq6q86ZTHgDA/JrGHK0Lkjy26Pjx\n",
       "JNun8L0AAHNtWpPha8mxR4QAwElv6xS+40CSHYuOt0/OvUxV3bTocHd3757C/QEATkhV7Uyyc+rf\n",
       "27364FNVXZjki939umWu7UpyY3fvqqqrk3ysu69epl1399KRLwCADWdauWXVEa2qui3Jm5KcW1WP\n",
       "Jflokm1J0t23dPedVbWrqvYneTbJDSdaFADAZrCmEa2p3MiIFgAwJ6aVW9Z7ZXgAgJOGoAUAMIig\n",
       "BQAwiKAFADCIoAUAMIigBQAwiKAFADCIoAUAMIigBQAwiKAFADCIoAUAMIigBQAwiKAFADCIoAUA\n",
       "MIigBQAwiKAFADCIoAUAMIigBQAwiKAFADCIoAUAMIigBQAwiKAFADCIoAUAMIigBQAwiKAFADCI\n",
       "oAUAMIigBQAwiKAFADCIoAUAMIigBQAwiKAFADDIqkGrqq6tqkeq6tGq+tAy13dW1dNVdf9k+8iY\n",
       "UgEA5svWlS5W1ZYkH0/yC0kOJPnjqrqju/ctafrV7r5uUI0AAHNptRGtK5Ps7+7vdPehJJ9L8vZl\n",
       "2tXUKwMAmHOrBa0Lkjy26PjxybnFOsk1VfVAVd1ZVZdOs0AAgHm14qPDLISo1dyXZEd3P1dVb0ty\n",
       "e5LXnnBlAABzbrWgdSDJjkXHO7IwqvWC7v7hov0vV9VvV9U53f3U0i+rqpsWHe7u7t3HXDEAwJRV\n",
       "1c4kO6f+vd1HH7Sqqq1Jvpnk7yb5bpJ7k7xr8WT4qjovyZPd3VV1ZZLf7e4Ll/mu7m5zuQCADW9a\n",
       "uWXFEa3uPlxVNyb5SpItST7Z3fuq6r2T67ckeWeS91XV4STPJbn+RIsCANgMVhzRmuqNjGgBAHNi\n",
       "WrnFyvAAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAA\n",
       "gwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMI\n",
       "WgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAg6watKrq2qp6\n",
       "pKoeraoPHaXNzZPrD1TV5dMvEwBg/qwYtKpqS5KPJ7k2yaVJ3lVVlyxpsyvJRd19cZJfTvKJQbUy\n",
       "I1W1c9Y1cPz033zTf/NL35GsPqJ1ZZL93f2d7j6U5HNJ3r6kzXVJbk2S7t6T5OyqOm/qlTJLO2dd\n",
       "ACdk56wL4ITsnHUBHLedsy6A2VstaF2Q5LFFx49Pzq3WZvuJlwYAMN9WC1q9xu+p4/wcAMCmtXWV\n",
       "6weS7Fh0vCMLI1Yrtdk+OfcyVSWAzamq+uisa+D46b/5pv/ml75jtaD1tSQXV9WFSb6b5B8medeS\n",
       "NnckuTHJ56rq6iQ/6O6DS7+ou5eOegEAbGorBq3uPlxVNyb5SpItST7Z3fuq6r2T67d0951Vtauq\n",
       "9id5NskNw6sGAJgD1e1pHgDACMNXhl/Lgqesv6r6VFUdrKqHFp07p6ruqqpvVdXvVdXZi6792qQP\n",
       "H6mqtyw6f0VVPTS59m/W++c4GVXVjqq6u6q+UVVfr6r3T87rvzlQVa+oqj1VtbeqHq6q35ic139z\n",
       "oqq2VNX9VfXFybG+mxNV9Z2qenDSf/dOzo3tv+4etmXhceP+JBcm2ZZkb5JLRt7Ttua++dtJLk/y\n",
       "0KJzv5nkn0/2P5TkX032L5303bZJX+7Pi6Oh9ya5crJ/Z5JrZ/2zbfYtyc8kuWyyf0aSbya5RP/N\n",
       "z5bk9MmfW5P8UZI36r/52ZL8SpL/kOSOybG+m5MtybeTnLPk3ND+Gz2itZYFT5mB7r4nyfeXnH5h\n",
       "8dnJn++Y7L89yW3dfai7v5OFv2xXVdX5SV7Z3fdO2n160WcYpLuf6O69k/1nkuzLwnp2+m9OdPdz\n",
       "k91Ts/AP0u9H/82FqtqeZFeSf5cXlzbSd/Nl6ct5Q/tvdNBay4KnbBzn9YtvjB5M8vwK/6/OS5f1\n",
       "eL4fl54/EP27riZvBF+eZE/039yoqlOqam8W+unu7v5G9N+8+K0kv5rkyKJz+m5+dJLfr6qvVdU/\n",
       "mpwb2n+rLe9wosy0n1Pd3dY929iq6owkX0jyge7+YdWL/0jTfxtbdx9JcllVnZXkK1X180uu678N\n",
       "qKr+XpInu/v+o/0eQ3234b2hu79XVT+d5K6qemTxxRH9N3pEay0LnrJxHKyqn0mSydDok5Pzyy1K\n",
       "+/jk/PYl55ddrJbpqqptWQhZn+nu2yen9d+c6e6nk3wpyRXRf/PgmiTXVdW3k9yW5M1V9Znou7nR\n",
       "3d+b/Pl/kvznLExxGtp/o4PWCwueVtWpWVjw9I7B9+T43ZHkPZP99yS5fdH566vq1Kp6TZKLk9zb\n",
       "3U8k+fOquqoWhlN+adFnGGTy3/qTSR7u7o8tuqT/5kBVnfv8W01VdVqSX0xyf/TfhtfdH+7uHd39\n",
       "miTXJ/mD7v6l6Lu5UFWnV9UrJ/s/meQtSR7K6P5bhxn+b8vCW1H7k/zarN84sL3QL7dlYbX/v8zC\n",
       "PLobkpyT5PeTfCvJ7yU5e1H7D0/68JEkb110/orJX9T9SW6e9c91MmxZeEPtSBbehrl/sl2r/+Zj\n",
       "S/K6JPdN+u/BJL86Oa//5mhL8qa8+NahvpuDLclrJv/f7U3y9eczyej+s2ApAMAgwxcsBQA4WQla\n",
       "AACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACD/H/UOeBG8rPZ+wAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106332bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAloAAAEUCAYAAADz4ZhrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAGCVJREFUeJzt3XuwXWd93vHvcyQbAya4jkFcJCoopsEpF9XEdsFgQQLI\n",
       "KhgaaGNnSgmTEsrEhUKSUggzOGkbOp1mAoRAnSlkHJPaJUA8pnG4BlGuNmBLNr6AlUDGMraMbXDA\n",
       "4mKjX/9YS9LW1jlnSzr71T7r6PuZWbPX5d17/Y5fyefRu9Z+V6oKSZIkTd/crAuQJElaqQxakiRJ\n",
       "jRi0JEmSGjFoSZIkNWLQkiRJasSgJUmS1MiiQSvJcUmuTLI1yQ1J3rpAu3ckuTnJtiQb2pQqSZI0\n",
       "LKsXO1hVP0zy7KralWQ18NkkZ1bVZ/e0SbIZeHxVnZzkdODdwBlty5YkSVr+Jl46rKpd/eqxwCrg\n",
       "7rEm5wAX9W2vBE5IsmaaRUqSJA3RxKCVZC7JVmAn8KmqumGsyaOBW0a2dwBrp1eiJEnSMB3MiNbu\n",
       "qnoqXXh6VpKN8zTL+NumUJskSdKgLXqP1qiquifJXwJPA7aMHLoVWDeyvbbft58khi9JkjQYVTU+\n",
       "kHTIFg1aSU4C7q+q7yZ5IPBc4HfGml0OnA9cmuQM4LtVtbNVwTryklxQVRfMug4dHvtv2Oy/4bLv\n",
       "hm1aA0STRrQeCVyUZI7uMuPFVfXJJK8CqKoLq+qKJJuTbAfuBV4xjcIkSZKGbtL0DtcB/3Se/ReO\n",
       "bZ8/5bokSZIGz5nhdTC2zLoALcmWWRegJdky6wJ02LbMugDNXqqOzD3qScp7tCRJ0hBMK7c4oiVJ\n",
       "ktSIQUuSJKkRg5YkSVIjBi1JkqRGDFqSJEmNGLQkSZIaMWhJkiQ1YtCSJElqxKAlSZLUiEFLkiSp\n",
       "EYOWJElSIwYtSZKkRgxakiRJjRi0JEmSGjFoSZIkNWLQkiRJasSgJUmS1IhBS5IkqRGDliRJUiMG\n",
       "LUmSpEYMWpIkSY0YtCRJkhoxaEmSJDVi0JIkSWrEoCVJktSIQUuSJKkRg5YkSVIjBi1JkqRGDFqS\n",
       "JEmNGLQkSZIaWTRoJVmX5FNJrk/y1SSvmafNxiT3JLmmX97crlxJkqThWD3h+H3A66pqa5Ljga8k\n",
       "+XhV3TjW7tNVdU6bEiVJkoZp0RGtqrq9qrb2698HbgQeNU/TNKhNkiRp0A76Hq0k64ENwJVjhwp4\n",
       "epJtSa5Icsr0ypMkSRquSZcOAegvG34AeG0/sjXqamBdVe1KcjZwGfCE6ZYpSZI0PBODVpJjgA8C\n",
       "76uqy8aPV9X3Rtb/Ksm7kpxYVXfP81kXjGxuqaoth1W1JEnSFCXZCGyc+udW1WInDXARcFdVvW6B\n",
       "NmuAO6qqkpwGvL+q1s/TrqrKe7kkSdKyN63cMmlE6xnAvwauTXJNv+9NwGMAqupC4KXAq5PcD+wC\n",
       "zl1qUZIkSSvBoiNaUz2RI1qSJGkgppVbnBlekiSpEYOWJElSIwYtSZKkRgxakiRJjRi0JEmSGjFo\n",
       "SZIkNWLQkiRJasSgJUmS1IhBS5IkqRGDliRJUiMGLUmSpEYMWpIkSY0YtCRJkhoxaEmSJDVi0JIk\n",
       "SWrEoCVJktSIQUuSJKkRg5YkSVIjBi1JkqRGDFqSJEmNGLQkSZIaMWhJkiQ1YtCSJElqxKAlSZLU\n",
       "iEFLkiSpEYOWJElSIwYtSZKkRgxakiRJjRi0JEmSGjFoSZIkNWLQkiRJamTRoJVkXZJPJbk+yVeT\n",
       "vGaBdu9IcnOSbUk2tClVkiRpWFZPOH4f8Lqq2prkeOArST5eVTfuaZBkM/D4qjo5yenAu4Ez2pUs\n",
       "SZI0DIuOaFXV7VW1tV//PnAj8KixZucAF/VtrgROSLKmQa2SJEmDctD3aCVZD2wArhw79GjglpHt\n",
       "HcDapRYmSZI0dJMuHQLQXzb8APDafmTrgCZj2zXv5/xO/sOhlSdJR6EK1FzYvSrUXKhVc/vW5+ao\n",
       "vevzLXNUgGTvK/T/V04gUMl+x/e+7m0z3749tfWfQcY+b8++PZ/Zv2HPZzHStt+EzP/e0Tr2rI8a\n",
       "/5UzsqMWOTbfZu332RPaju4YP89YjQf8FjyU84z/vId9ngnvXcp5DsVi52lpVufd38SgleQY4IPA\n",
       "+6rqsnma3AqsG9le2+870Ic4d+/649jBU9lxKMVKWoEqsHv1KnavnmP36lX85Jg5alW/vWpVd2zV\n",
       "XBc2Vq/qjq3q28x1r7VqrgsYe5bMdaEjczA3R2VPAMm+7b3H9t9P9r2fjLTNyPG5uT4EZG8g2Bsa\n",
       "GA8IOaDt3vUF2nb/YQooqP7XexWwmxR793fHal9bIFUj74f9fkXu+aw9+2p0vX//AscWfN/48Tqw\n",
       "3bzH9nvfWL21QB2jav99i8aCA96+SGwYO5RF206KHwvXcWAE2HcwxeI1j33O0mpcuP1iNR6yJSW1\n",
       "I3Peb+08np13Hn/455pfapE+SBK6+6/uqqrXLdBmM3B+VW1Ocgbwtqo64Gb4JFV14D81JC0PCauA\n",
       "BwHHAw/ul+P7fQ8EjuuXB469Tto3vn7s2LIK+HG/3Deyvti++fbf3++7H/hJ/zq+fijHJrXd3e/7\n",
       "Sb9+KMui76la2m8lSUs3rdwyKWidCfw/4Fr2xcI3AY8BqKoL+3bvBDYB9wKvqKqrWxUsqZMQujD0\n",
       "0EWWn6ILS3vC0/jr6PpxwC7g+3R/l+/t13cBPwB+OM/rQusL7ftRv4wGpfsNFpKWmyMStKbJoCXN\n",
       "L+FBwInATy+y/APmD1E/Bu5ZZPl74HvsC0/jIWr09QdV7G7980rSEBi0pGUq4Vjg4cAjgDX98oiR\n",
       "14exf4iaA+6asNzNPCGqivuO1M8lSUcTg5Z0hPX3MD2S7gsfa+m+BLKWbm650TD1U8C3gZ3A7f3r\n",
       "6Pq32T9E3eulM0laXgxa0pQlPBR4HPBYYD0HBqo1wJ10c8XtoJs/bgfwLfYPUnd5CU6Shs2gJR2i\n",
       "hGOAf0gXpB438rpn/VjgG8DfAn9HF6T2hKkdwG1V/PjIVy5JOtIMWtICEk4C/nG//MzI+nrgNrog\n",
       "9bfsC1V71u/0Ep4kCQxaEgkPA54MPKlf9oSq1cBNwNdGXr8GbK/iR7OpVpI0JAYtHTUSjgNOoQtT\n",
       "Tx55fQDdHG/X9cuNdIHqDkemJElLYdDSipTwALog9bSR5QnAdrowde3I660GKklSCwYtDV7CHPCz\n",
       "wOnsC1WnADcDXx5Zrqvih7OqU5J09DFoaXASHgycBjyjX86gm1Pqi8CX6ELVtip2zaxISZIwaGkA\n",
       "En4aOAt4Fl2wOgXYBnyuXz5fxR2zq1CSpPkZtLTsJDwEeCbwnH75R8Bn6R5M/jngy14ClCQNgUFL\n",
       "M5ewGvhnwPPogtVT6C4BfhL4a+BLPotPkjREBi3NRMIjgE3AZuC5dBN9foQuXH2+ih/MsDxJkqbC\n",
       "oKUjov9m4GnAPwfOprsc+AngCuAjVdw2w/IkSWrCoKVm+mcCngX8IvBi4DvAh+nC1Re8HChJWumm\n",
       "lVtWT6MYDV/CA+nutfoXwAvpJgj9ELCxiq/PsjZJkobKEa2jWMKxdOHql+nuuboa+AvgsipumWVt\n",
       "kiTNkpcOdVj6e66eSReuXkL3fMD/DXygim/PsjZJkpYLLx3qkCQ8GXgZcC5wF3AJcGoVfzfTwiRJ\n",
       "WsEMWitYwgnAecCvAg8HLgY2VXH9TAuTJOko4aXDFaa/NHgWXbh6AfBR4D3AJ6v4ySxrkyRpKLxH\n",
       "S/tJWEMXrn4V+D5duPqzKu6aaWGSJA2Q92iJhNA9AufX6b41+OfALwFfqeLIJGhJkrQgg9YAJTyI\n",
       "7luDvw4cD7wLOL+K78y0MEmStB+D1oAkPAZ4DfArwBeANwIfq2L3LOuSJEnzm5t1AZosYUPC+4Ct\n",
       "dH32c1W8sIqPGLIkSVq+DFrLVEISNiV8gu45g9uAx1Xx+iq+MePyJEnSQfDS4TLTP9D5l4HfBAr4\n",
       "H8ClVfx4poVJkqRDZtBaJvrnDv4K8J+AbwK/AXzcbw9KkjRcBq0ZSziObu6rNwA3AC+r4nOzrUqS\n",
       "JE2DQWtG+ikaXkV3ifArwEuruGq2VUmSpGmaeDN8kvcm2ZnkugWOb0xyT5Jr+uXN0y9z5Uh4QMK/\n",
       "B/4GOBN4QRXnGLIkSVp5DmZE60+APwT+dJE2n66qc6ZT0sqUsBp4GXABcC3dw523zbQoSZLU1MSg\n",
       "VVWfSbJ+QjOfYbiA/iHPLwH+M3A7cF4Vn59tVZIk6UiYxj1aBTw9yTbgVuA3q+qGKXzuoPXPIXw+\n",
       "8HvAbroZ3f0WoSRJR5FpBK2rgXVVtSvJ2cBlwBPma5jkgpHNLVW1ZQrnX3YSngL8PrAW+G3gQwYs\n",
       "SZKWryQbgY1T/9yqyb//+0uHH66qJx1E228Ap1bV3WP7q6pW9CXGhEfRXSJ8AfC7wB9Xcd9sq5Ik\n",
       "SYdqWrllyY/gSbImSfr10+jC290T3raiJDw44S3AdcCdwBOq+CNDliRJR7eJlw6TXAKcBZyU5Bbg\n",
       "LcAxAFV1IfBS4NVJ7gd2Aee2K3d56W90/zfAfwE+CzzN5xBKkqQ9DurS4VROtMIuHSacDrwTuA94\n",
       "fRVfnHFJkiRpSqaVW5wZ/hAlPBx4K3A23WNz3ueN7pIkaT5LvkfraJGwup/R/Xrgu8ATq7jYkCVJ\n",
       "khbiiNZBSHgW3WXCO4GNVVw/45IkSdIAGLQWkbCGbj6ss4DfAP7cESxJknSwvHQ4j4S5hFfSTdfw\n",
       "LbrLhO83ZEmSpEPhiNaYhCcCfwwcCzzXBz9LkqTD5YhWL+G4hN8FPgP8H+DphixJkrQUjmgBCc8G\n",
       "LqS7VPiUKm6dcUmSJGkFOKqDVsKJdDe7/zxwfhWXz7gkSZK0ghy1lw4TXkw3gvU94GcNWZIkadqO\n",
       "uhGthJOAPwSeBpxbxWdmXJIkSVqhjqoRrYR/yb4pG55iyJIkSS0dFSNa/fMJ/wj4J8AvVvGFGZck\n",
       "SZKOAit6RCshCecB1wJ/A2wwZEmSpCNlxY5o9Y/P+Z/AycALq/jSjEuSJElHmRU5otV/o3ArcBNw\n",
       "qiFLkiTNwooa0Up4KPB24EzgJVV8fsYlSZKko9iKGdFK2AhsA34IPNWQJUmSZm3wI1oJxwH/FTgX\n",
       "eGUVV8y4JEmSJGDgQSthA/A+4Aa6ebHunHFJkiRJew3y0mHC6oTfBj4K/B7wrwxZkiRpuRnciFbC\n",
       "44GLgXvpvlF4y4xLkiRJmtdgRrT6yUdfDnwBuAR4niFLkiQtZ4MY0Uo4AXg38CTgOVVcN+OSJEmS\n",
       "Jlr2I1oJZ9JNPnon8HOGLEmSNBTLdkQrYTXwZuDfAf+2iv8745IkSZIOybIMWgmPpZu24V66B0Hf\n",
       "NuOSJEmSDtmyu3SYcB5wJfBBYJMhS5IkDdWyGdFKeAjwTuB04PlVXDPjkiRJkpZkWYxoJZxOd8P7\n",
       "j+jmxjJkSZKkwZvpiFbCKuANwGuBV1fxoVnWI0mSNE0TR7SSvDfJziQLTquQ5B1Jbk6yLcmGgzlx\n",
       "wjrgk8Bz6UaxDFmSJGlFOZhLh38CbFroYJLNwOOr6mTg1+gmFl1UwkuBL9M9q/AXqthxcOVKkiQN\n",
       "x8RLh1X1mSTrF2lyDnBR3/bKJCckWVNVO8cbJjwYeDuwEXhhFVcdTtGSJElDMI2b4R8N+z1zcAew\n",
       "doG2V9OFuw2GLEmStNJN62b4jG3XAu3eUsWlUzqnJEnSsjaNoHUrsG5ke22/bx75mYQL+o0tVbVl\n",
       "CueXJElakiQb6W5tmu7nVi00+LTfydcDH66qJ81zbDNwflVtTnIG8LaqOmOedlVV4yNfkiRJy860\n",
       "csvEEa0klwBnAScluQV4C3AMQFVdWFVXJNmcZDvdswlfsdSiJEmSVoKDGtGayokc0ZIkSQMxrdyy\n",
       "LB7BI0mStBIZtCRJkhoxaEmSJDVi0JIkSWrEoCVJktSIQUuSJKkRg5YkSVIjBi1JkqRGDFqSJEmN\n",
       "GLQkSZIaMWhJkiQ1YtCSJElqxKAlSZLUiEFLkiSpEYOWJElSIwYtSZKkRgxakiRJjRi0JEmSGjFo\n",
       "SZIkNWLQkiRJasSgJUmS1IhBS5IkqRGDliRJUiMGLUmSpEYMWpIkSY0YtCRJkhoxaEmSJDVi0JIk\n",
       "SWrEoCVJktSIQUuSJKkRg5YkSVIjE4NWkk1Jbkpyc5I3zHN8Y5J7klzTL29uU6okSdKwrF7sYJJV\n",
       "wDuBXwBuBb6U5PKqunGs6aer6pxGNUqSJA3SpBGt04DtVfXNqroPuBR40TztMvXKJEmSBm5S0Ho0\n",
       "cMvI9o5+36gCnp5kW5IrkpwyzQIlSZKGatFLh3QhapKrgXVVtSvJ2cBlwBOWXJkkSdLATQpatwLr\n",
       "RrbX0Y1q7VVV3xtZ/6sk70pyYlXdPf5hSS4Y2dxSVVsOuWJJkqQpS7IR2Dj1z61aeNAqyWrga8DP\n",
       "A98CrgLOG70ZPska4I6qqiSnAe+vqvXzfFZVlfdySZKkZW9auWXREa2quj/J+cBHgVXAe6rqxiSv\n",
       "6o9fCLwUeHWS+4FdwLlLLUqSJGklWHREa6onckRLkiQNxLRyizPDS5IkNWLQkiRJasSgJUmS1IhB\n",
       "S5IkqRGDliRJUiMGLUmSpEYMWpIkSY0YtCRJkhoxaEmSJDVi0JIkSWrEoCVJktSIQUuSJKkRg5Yk\n",
       "SVIjBi1JkqRGDFqSJEmNGLQkSZIaMWhJkiQ1YtCSJElqxKAlSZLUiEFLkiSpEYOWJElSIwYtSZKk\n",
       "RgxakiRJjRi0JEmSGjFoSZIkNWLQkiRJasSgJUmS1IhBS5IkqRGDliRJUiMGLUmSpEYMWpIkSY0Y\n",
       "tCRJkhqZGLSSbEpyU5Kbk7xhgTbv6I9vS7Jh+mVKkiQNz6JBK8kq4J3AJuAU4LwkTxxrsxl4fFWd\n",
       "DPwa8O5GtWpGkmycdQ06fPbfsNl/w2XfCSaPaJ0GbK+qb1bVfcClwIvG2pwDXARQVVcCJyRZM/VK\n",
       "NUsbZ12AlmTjrAvQkmycdQE6bBtnXYBmb1LQejRwy8j2jn7fpDZrl16aJEnSsE0KWnWQn5PDfJ8k\n",
       "SdKKtXrC8VuBdSPb6+hGrBZrs7bfd4AkBrCBSvKWWdegw2f/DZv9N1z2nSYFrS8DJydZD3wL+CXg\n",
       "vLE2lwPnA5cmOQP4blXtHP+gqhof9ZIkSVrRFg1aVXV/kvOBjwKrgPdU1Y1JXtUfv7CqrkiyOcl2\n",
       "4F7gFc2rliRJGoBUeTVPkiSpheYzwx/MhKc68pK8N8nOJNeN7DsxyceTfD3Jx5KcMHLsjX0f3pTk\n",
       "eSP7T01yXX/s7Uf65zgaJVmX5FNJrk/y1SSv6ffbfwOQ5LgkVybZmuSGJG/t99t/A5FkVZJrkny4\n",
       "37bvBiLJN5Nc2/ffVf2+tv1XVc0WusuN24H1wDHAVuCJLc/pctB980xgA3DdyL7/DvzHfv0NwH/r\n",
       "10/p++6Yvi+3s2809CrgtH79CmDTrH+2lb4AjwCe2q8fD3wNeKL9N5wFeFD/uhr4InCm/TecBXg9\n",
       "8GfA5f22fTeQBfgGcOLYvqb913pE62AmPNUMVNVngO+M7d47+Wz/+uJ+/UXAJVV1X1V9k+4P2+lJ\n",
       "Hgk8pKqu6tv96ch71EhV3V5VW/v17wM30s1nZ/8NRFXt6lePpfsH6Xew/wYhyVpgM/C/2De1kX03\n",
       "LONfzmvaf62D1sFMeKrlY03t+8boTmDPDP+PYv9pPfb04/j+W7F/j6j+G8EbgCux/wYjyVySrXT9\n",
       "9Kmquh77byj+APgtYPfIPvtuOAr4RJIvJ3llv69p/02a3mGpvNN+oKqqnPdseUtyPPBB4LVV9b1k\n",
       "3z/S7L/lrap2A09N8lDgo0mePXbc/luGkrwAuKOqrlnoOYb23bL3jKq6LcnDgI8nuWn0YIv+az2i\n",
       "dTATnmr52JnkEQD90Ogd/f75JqXd0e9fO7Z/3slqNV1JjqELWRdX1WX9bvtvYKrqHuAvgVOx/4bg\n",
       "6cA5Sb4BXAI8J8nF2HeDUVW39a/fBv6C7hanpv3XOmjtnfA0ybF0E55e3vicOnyXAy/v118OXDay\n",
       "/9wkxyZ5LHAycFVV3Q78fZLT0w2nvGzkPWqk/2/9HuCGqnrbyCH7bwCSnLTnW01JHgg8F7gG+2/Z\n",
       "q6o3VdW6qnoscC7w11X1Muy7QUjyoCQP6dcfDDwPuI7W/XcE7vA/m+5bUduBN876Gwcue/vlErrZ\n",
       "/n9Mdx/dK4ATgU8AXwc+Bpww0v5NfR/eBDx/ZP+p/R/U7cA7Zv1zHQ0L3TfUdtN9G+aaftlk/w1j\n",
       "AZ4EXN3337XAb/X77b8BLcBZ7PvWoX03gAV4bP/3bivw1T2ZpHX/OWGpJElSI80nLJUkSTpaGbQk\n",
       "SZIaMWhJkiQ1YtCSJElqxKAlSZLUiEFLkiSpEYOWJElSIwYtSZKkRv4/xzaH3P0Y/ZIAAAAASUVO\n",
       "RK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106355f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAloAAAEUCAYAAADz4ZhrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAFEJJREFUeJzt3V+sZVd9H/Dvzx47/LGxcaicwExkKoyEJSRcKmMRUiZt\n",
       "kxqnMn1AqpEapX5oEZIFpVKKgpAgT6n6UkpQkKVCZEgFikLrGuGIkJSh5CGmxB5jwCS4QGIbMBEz\n",
       "Y2wPf+z614e7x3M4c+49986cNfeemc9H2jp7r73uOet42dLXa629TnV3AABYvQt2uwEAAOcqQQsA\n",
       "YBBBCwBgEEELAGAQQQsAYBBBCwBgkC2DVlU9p6rurqrDVfXVqvqdTeq9v6q+XlX3VdW1Y5oKALBe\n",
       "9m11s7t/VFW/3N3Hq2pfkj+vqtd195+fqFNVNyZ5WXdfXVWvSfLBJNePbTYAwN63dOqwu49Ppxcn\n",
       "uTDJkbkqNyW5fap7d5LLq+rKVTYSAGAdLQ1aVXVBVR1O8miSz3b3V+eqvCTJQzPXDyfZv7omAgCs\n",
       "p+2MaD3T3a/KRnj6R1V1cEG1mv+zFbQNAGCtbblGa1Z3P1ZVn0ryD5Mcmrn1SJIDM9f7p7KfUlXC\n",
       "FwCwNrp7fiBpx7YMWlX1oiRPd/exqnpukl9J8ttz1e5McmuSj1fV9UmOdfejoxrM2VdV7+3u9+52\n",
       "Ozg9+m+96b/1pe/W26oGiJaNaP18ktur6oJsTDN+tLv/rKrekiTdfVt331VVN1bVg0meTHLLKhoG\n",
       "ALDulm3vcH+Sf7Cg/La561tX3C4AgLVnZ3i249BuN4Azcmi3G8AZObTbDeC0HdrtBrD7qvvsrFGv\n",
       "qrZGCwBYB6vKLUa0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0\n",
       "AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAA\n",
       "BhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABtkyaFXVgar6bFV9\n",
       "paq+XFVvW1DnYFU9VlX3Tse7xzUXAGB97Fty/6kk7+juw1V1SZK/rKrPdPcDc/U+1903jWkiAMB6\n",
       "2nJEq7u/292Hp/MnkjyQ5MULqtaAtgEArLVtr9GqqquSXJvk7rlbneS1VXVfVd1VVdesrnkAAOtr\n",
       "2dRhkmSaNvyjJG+fRrZm3ZPkQHcfr6o3JLkjyctX20wAgPWzNGhV1UVJPpHkD7r7jvn73f34zPkf\n",
       "V9XvVdUV3X1kwXu9d+byUHcfOq1WAwCsUFUdTHJw5e/b3Vt9aCW5Pcn3u/sdm9S5Msn3urur6rok\n",
       "f9jdVy2o191tLRcAsOetKrcsG9H6xST/KsmXqureqexdSX4hSbr7tiRvSvLWqno6yfEkN59powAA\n",
       "zgVbjmit9IOMaAEAa2JVucXO8AAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACD\n",
       "CFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwha\n",
       "AACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAA\n",
       "g2wZtKrqQFV9tqq+UlVfrqq3bVLv/VX19aq6r6quHdNUAID1sm/J/aeSvKO7D1fVJUn+sqo+090P\n",
       "nKhQVTcmeVl3X11Vr0nywSTXj2syAMB62HJEq7u/292Hp/MnkjyQ5MVz1W5KcvtU5+4kl1fVlQPa\n",
       "CgCwVra9RquqrkpybZK75269JMlDM9cPJ9l/pg0DAFh3y6YOkyTTtOEfJXn7NLJ1SpW56174Pr9d\n",
       "/25nzQMAWF9Lg1ZVXZTkE0n+oLvvWFDlkSQHZq73T2Wn+u+5+dnzv5+H86o8vJPGAgAMcTj7843V\n",
       "z8htGbSqqpJ8KMlXu/t9m1S7M8mtST5eVdcnOdbdjy6q2Pe1RfIAwJ5XVQtn53b8Pt2bv09VvS7J\n",
       "/07ypZycDnxXkl9Iku6+bar3gSQ3JHkyyS3dfc+iBnf3/BQjAMCes6rcsmXQWiVBCwBYF6vKLXaG\n",
       "BwAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIA\n",
       "GETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE\n",
       "0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhE0AIAGETQAgAYRNACABhkadCqqg9X1aNVdf8m\n",
       "9w9W1WNVde90vHv1zQQAWD/7tlHn95P8bpKPbFHnc91902qaBABwblg6otXdn09ydEm1Wk1zAADO\n",
       "HatYo9VJXltV91XVXVV1zQreEwBg7W1n6nCZe5Ic6O7jVfWGJHckefmiilX13pnLQ919aAWfDwBw\n",
       "RqrqYJKDK3/f7t7Oh1+V5JPd/cpt1P1mkld395G58u5uU4wAwJ63qtxyxlOHVXVlVdV0fl02wtuR\n",
       "JX8GAHDOWzp1WFUfS/L6JC+qqoeSvCfJRUnS3bcleVOSt1bV00mOJ7l5XHMBALZWlQuSXJLksk2O\n",
       "F2xx78T91bRlO1OHK/kgU4cAwBJVuTCbB6FlAelEnUuT/DDJY1scP9j6fv3dKnLLKhbDAwCkKhfl\n",
       "9EeRTtR5XpInsjwkPbTF/ce78/QZfpeVMKIFAKQqlY2Qc3k2Qs/s66KyRfd+JktHipbef6I7z4z+\n",
       "vsusKrcY0QKAc8A05XZiZOh0QtJlSZ7KRtg5Nh2PLXj9203uHUvyZHfOzgjOmjCiBQC7bBpNek7O\n",
       "LCQ9PydHi+YD0KLAdMq97vxk+JddE0a0AGCPmJ5yuzSnH5Iun97qaLYORd/Z4t6emHLjpxnRAuC8\n",
       "N40onQhKL5x7nT+fPU6EpEtzcgH3stGkhSNM3fnR+G/KdhnRAoAZVXlOtheUFt2/LBt7QZ4IQkfn\n",
       "Xo8l+cbM+Xxwerw7/+8sfE3WjBEtAPaEaTH37GjRsnA0f145NSDNBqVF5ydeHzvT7QA4txjRAmBP\n",
       "mabfLsnpB6XnZWMx91ZB6dub3e/OD8/C14QdMaIFwLOq8jM5/aB0WZIfZ/ko0mZB6nGLudkrVpVb\n",
       "BC2Ac0xVnpuN4LPZccXc9Wxo2pedhaPZ82PdeepsfEcYzdQhwDlsWti9VTjaKkAlGwFos+P/zl0f\n",
       "mzn/oQ0nYXWMaAEMsiAsbWd06cRxQX46DB3J1uHp2TrWKsGZM3UIcBZMa5a2G47m68yHpU3D0YLD\n",
       "yBLsIkELYJs2CUvbHV06sWZpp6NLR5McF5ZgPQlawHmlKvtyMgzNBqLtjC5dnO2Ho/l6whKchwQt\n",
       "YO1M+yw9NyfD0omQdMWSshdm4wdzNwtEy0LUk8ISsBOeOgR2zfQDupfl9ALTMzkZjI7MHUeT/M2C\n",
       "siOxxxKwhoxowXlsZu3STgPTC5I8nq0D06JrT8QBa8HUIZDkp372ZDujSfN1LsrycLSo7Jgf0AXO\n",
       "ZYIWnGOmxd6X5/Sm436U0wtM1i4BLCBowR40s9j7dKbjnp+NHbq3Ox337ALw7vzkrHxBgPOExfAw\n",
       "0Nx03M/OvS4LTEny/Wwejh5aUHY0yQ8s9gY4txjR4pw2BabnZXFY2qrsiiQ/ycnAdOL1yMz1whEm\n",
       "i70B1p+pQ84rc/sv7TQ0PZ1Tw9KiADVbdrQ7Pz473w6AvUbQYm1NP7S707D0s0k6ywPSfNmR7vzo\n",
       "LH01AM4R1mix66Y9mLYzBTd//8JsBKHNwtKDC8qOmJIDYN0IWqQqF2d7AWm+7KJsPZr0jQVlR+K3\n",
       "4wA4Twha55CqXJSNJ+B2OsL0nGw9Hfe3C8rswQQAS1ijtQdNG1ee2DJgJyNMz83JJ+F2svD7CYEJ\n",
       "AE6yGH4NVOXCbOz0vZOwdEU29m86liWLvBfc/4HABABn7qwFrar6cJJfS/K97n7lJnXen+QNSY4n\n",
       "+dfdfe+oBu+GqlyQkz+NspPQdGmSx7LzESYbVwLALjqbTx3+fpLfTfKRTRpyY5KXdffVVfWaJB9M\n",
       "cv2ZNmyEKTC9IDsfYbosyePZPCB9PYsD1GN+eBcAzl9Lg1Z3f76qrtqiyk1Jbp/q3l1Vl1fVld39\n",
       "6GqaeKpp88oXZOcjTJcneSJbPyX3xZwamo4JTADATq3iqcOXZOO32054OMn+JEuD1szvye10hOmF\n",
       "SX6YzUeY/ibJPTk1SB3tztNn8mUBALZrVds7zM9hLlz4VZX/mVN/mPfH2XyE6eEkX8qpI0xHu/PU\n",
       "itoOADDEKoLWI0kOzFzvn8oW+KXjyZPfT37ww+RFf5b8xaf8nhwAsNuq6mCSgyt/3+1s7zCt0frk\n",
       "oqcOp8Xwt3b3jVV1fZL3dfcpi+HX+alDAOD8ctaeOqyqjyV5fZIXVdVDSd6TjZ9eSXff1t13VdWN\n",
       "VfVgkieT3HKmjQIAOBfYsBQAYM6qcssFq2gMAACnErQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0\n",
       "AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAA\n",
       "BhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYRtAAABhG0AAAGEbQAAAYR\n",
       "tAAABhG0AAAGWRq0quqGqvpaVX29qt654P7Bqnqsqu6djnePaSoAwHrZt9XNqrowyQeS/NMkjyT5\n",
       "P1V1Z3c/MFf1c91906A2AgCspWUjWtclebC7v9XdTyX5eJI3LqhXK28ZAMCaWxa0XpLkoZnrh6ey\n",
       "WZ3ktVV1X1XdVVXXrLKBAADrasupw2yEqGXuSXKgu49X1RuS3JHk5WfcMgCANbcsaD2S5MDM9YFs\n",
       "jGo9q7sfnzn/46r6vaq6oruPzL9ZVb135vJQdx/acYsBAFasqg4mObjy9+3efNCqqvYl+ask/yTJ\n",
       "t5N8IcmbZxfDV9WVSb7X3V1V1yX5w+6+asF7dXdbywUA7Hmryi1bjmh199NVdWuSTye5MMmHuvuB\n",
       "qnrLdP+2JG9K8taqejrJ8SQ3n2mjAADOBVuOaK30g4xoAQBrYlW5xc7wAACDCFoAAIMIWgAAgwha\n",
       "AACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAA\n",
       "gwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMI\n",
       "WgAAgwhaAACDCFoAAIMIWgAAgwhaAACDCFoAAIMsDVpVdUNVfa2qvl5V79ykzvun+/dV1bWrbyYA\n",
       "wPrZMmhV1YVJPpDkhiTXJHlzVb1irs6NSV7W3Vcn+bdJPjioreySqjq4223g9Om/9ab/1pe+I1k+\n",
       "onVdkge7+1vd/VSSjyd541ydm5LcniTdfXeSy6vqypW3lN10cLcbwBk5uNsN4Iwc3O0GcNoO7nYD\n",
       "2H3LgtZLkjw0c/3wVLaszv4zbxoAwHpbFrR6m+9Tp/l3AADnrH1L7j+S5MDM9YFsjFhtVWf/VHaK\n",
       "qhLA1lRVvWe328Dp03/rTf+tL33HsqD1xSRXV9VVSb6d5F8mefNcnTuT3Jrk41V1fZJj3f3o/Bt1\n",
       "9/yoFwDAOW3LoNXdT1fVrUk+neTCJB/q7geq6i3T/du6+66qurGqHkzyZJJbhrcaAGANVLfZPACA\n",
       "EYbvDL+dDU85+6rqw1X1aFXdP1N2RVV9pqr+uqr+pKoun7n3W1Mffq2qfnWm/NVVdf9077+c7e9x\n",
       "PqqqA1X12ar6SlV9uareNpXrvzVQVc+pqrur6nBVfbWqfmcq139roqourKp7q+qT07W+WxNV9a2q\n",
       "+tLUf1+Yysb2X3cPO7Ix3fhgkquSXJTkcJJXjPxMx7b75peSXJvk/pmy/5TkP0zn70zyH6fza6a+\n",
       "u2jqywdzcjT0C0mum87vSnLDbn+3c/1I8nNJXjWdX5Lkr5K8Qv+tz5HkedPrviR/keR1+m99jiT/\n",
       "Psl/S3LndK3v1uRI8s0kV8yVDe2/0SNa29nwlF3Q3Z9PcnSu+NnNZ6fXfzGdvzHJx7r7qe7+Vjb+\n",
       "ZXtNVf18kku7+wtTvY/M/A2DdPd3u/vwdP5EkgeysZ+d/lsT3X18Or04G/9DejT6by1U1f4kNyb5\n",
       "rzm5tZG+Wy/zD+cN7b/RQWs7G56yd1zZJ58YfTTJiR3+X5yf3tbjRD/Olz8S/XtWTU8EX5vk7ui/\n",
       "tVFVF1TV4Wz002e7+yvRf+viPyf5zSTPzJTpu/XRSf60qr5YVf9mKhvaf8u2dzhTVtqvqe5u+57t\n",
       "bVV1SZJPJHl7dz9edfJ/0vTf3tbdzyR5VVVdluTTVfXLc/f13x5UVf88yfe6+97NfsdQ3+15v9jd\n",
       "36mqv5fkM1X1tdmbI/pv9IjWdjY8Ze94tKp+LkmmodHvTeWLNqV9eCrfP1e+cLNaVquqLspGyPpo\n",
       "d98xFeu/NdPdjyX5VJJXR/+tg9cmuamqvpnkY0n+cVV9NPpubXT3d6bXv0vyP7KxxGlo/40OWs9u\n",
       "eFpVF2djw9M7B38mp+/OJL8xnf9Gkjtmym+uqour6qVJrk7yhe7+bpIfVNVramM45ddn/oZBpn/W\n",
       "H0ry1e5+38wt/bcGqupFJ55qqqrnJvmVJPdG/+153f2u7j7Q3S9NcnOS/9Xdvx59txaq6nlVdel0\n",
       "/vwkv5rk/ozuv7Owwv8N2Xgq6sEkv7XbTxw4nu2Xj2Vjt/+fZGMd3S1Jrkjyp0n+OsmfJLl8pv67\n",
       "pj78WpJ/NlP+6ulf1AeTvH+3v9f5cGTjCbVnsvE0zL3TcYP+W48jySuT3DP135eS/OZUrv/W6Ejy\n",
       "+px86lDfrcGR5KXTf3eHk3z5RCYZ3X82LAUAGGT4hqUAAOcrQQsAYBBBCwBgEEELAGAQQQsAYBBB\n",
       "CwBgEEELAGAQQQsAYJD/D78CJ0Nqj9UMAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10656bc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ordinary differential equation \n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "time = 5000\n",
    "\n",
    "# analytical solution\n",
    "x = np.arange(0,time, 1)\n",
    "y_anal = [2] *time\n",
    "\n",
    "#numerical solution\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "for num, j in enumerate(steps):\n",
    "    value = 1\n",
    "    step = j\n",
    "    y_num = [0] * time\n",
    "    y_num[0] = value\n",
    "    for i in range(time - 1):\n",
    "        update_value = step * value * (2 - value) + value\n",
    "        y_num[i + 1] = update_value\n",
    "        value = update_value\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_num)\n",
    "    plt.plot(x, y_anal)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAlQAAAEUCAYAAADtKKjYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHCxJREFUeJzt3XmcZGV97/HPFwZQBEGDQYXBMeJGREFckKgMEePAjagJ\n",
       "cUmigDdxueKCyY3LyyiJJt6Yq5erRiURlYjRuNwQUNwvg0vioLKv4oIB1MGIjCwuoL/8cc44TdPd\n",
       "1T2nq05V9ef9ep1X13K66tdnnun69vM85zmpKiRJkrT1tum7AEmSpElnoJIkSerIQCVJktSRgUqS\n",
       "JKkjA5UkSVJHBipJkqSOFgxUSe6QZEOS85JckuT18+z35iRXJDk/yf7DKVWSJGk8rVroyar6SZJD\n",
       "qurmJKuALyR5dFV9YfM+SQ4H9q6q+yZ5JPB24MDhli1JkjQ+Bg75VdXN7c3tgW2B62btcgRwcrvv\n",
       "BmDXJLsvZ5GSJEnjbGCgSrJNkvOAjcCZVXXJrF32AK6acf9qYM/lK1GSJGm8LaaH6hdVtR9NSHps\n",
       "krVz7JbZ37YMtUmSJE2EBedQzVRVm5J8DHgYsH7GU9cAq2fc37N97DaSGLIkSdLEqKrZHUbzWjBQ\n",
       "JdkNuLWqrk9yR+DxwF/M2u004FjgA0kOBK6vqo1dC9NtJTm+qo7vu45J5LHrxuPXjcdv63nsuvH4\n",
       "dbPUjqBBPVT3AE5Osg3N8OB7q+qzSZ4LUFUnVtUZSQ5P8nXgJuCYrSlckiRpUg1aNuFC4KFzPH7i\n",
       "rPvHLnNdkiRJE8OV0ifH+r4LmGDr+y5gwq3vu4AJt77vAibY+r4LmHDr+y5gJUnVaOaKJynnUEmS\n",
       "pEmw1NxiD5UkSVJHBipJkqSODFSSJEkdGagkSZI6MlBJkiR1ZKCSJEnqyEAlSZLUkYFKkiSpIwOV\n",
       "JElSRwYqSZKkjgxUkiRJHRmoJEmSOjJQSZIkdWSgkiRJ6shAJUmS1JGBSpIkqSMDlSRJUkcGKkmS\n",
       "pI4MVJIkSR0ZqCRJkjoyUEmSJHVkoJIkSerIQCVJktSRgUqSJKkjA5UkSVJHBipJkqSODFSSJEkd\n",
       "GagkSZI6MlBJkiR1ZKCSJEnqaMFAlWR1kjOTXJzkoiQvmmOftUk2JTm33V41vHIlSZLGz6oBz98C\n",
       "HFdV5yXZCfhqkk9X1aWz9jurqo4YTomSJEnjbcEeqqr6XlWd196+EbgUuOccu2YItUmSJE2ERc+h\n",
       "SrIG2B/YMOupAg5Kcn6SM5Lss3zlSZIkjb9BQ34AtMN9HwZe3PZUzXQOsLqqbk5yGHAqcL/lLVOS\n",
       "JGl8DQxUSbYDPgKcUlWnzn6+qm6YcfvjSd6W5K5Vdd0cr3X8jLvrq2r9VlUtSZK0jJKsBdZu9fdX\n",
       "1UIvHuBk4AdVddw8++wOXFtVleQRwAeras0c+1VVOddKkiSNvaXmlkE9VL8B/CFwQZJz28deCewF\n",
       "UFUnAkcCz09yK3Az8PQlVy1JkjTBFuyhWtY3sodKkiRNiKXmFldKlyRJ6shAJUmS1JGBSpIkqSMD\n",
       "lSRJUkcGKkmSpI4MVJIkSR0ZqCRJkjoyUEmSJHVkoJIkSerIQCVJktSRgUqSJKkjA5UkSVJHBipJ\n",
       "kqSODFSSJEkdGagkSZI6MlBJkiR1ZKCSJEnqyEAlSZLUkYFKkiSpIwOVJElSRwYqSZKkjgxUkiRJ\n",
       "HRmoJEmSOjJQSZIkdWSgkiRJ6shAJUmS1JGBSpIkqSMDlSRJUkcGKkmSpI4MVJIkSR0ZqCRJkjpa\n",
       "MFAlWZ3kzCQXJ7koyYvm2e/NSa5Icn6S/YdTqiRJ0nhaNeD5W4Djquq8JDsBX03y6aq6dPMOSQ4H\n",
       "9q6q+yZ5JPB24MDhlSxJkjReFuyhqqrvVdV57e0bgUuBe87a7Qjg5HafDcCuSXYfQq2SJEljadFz\n",
       "qJKsAfYHNsx6ag/gqhn3rwb27FqYJEnSpFhUoGqH+z4MvLjtqbrdLrPuV9fCJEmSJsWgOVQk2Q74\n",
       "CHBKVZ06xy7XAKtn3N+zfWyu1zp+xt31VbV+0ZVKkiQNSZK1wNqt/v6q+TuTkoRmftQPquq4efY5\n",
       "HDi2qg5PciBwQlXdblJ6kqqq2T1ZkiRJY2epuWVQoHo08DngArYM470S2Augqk5s93srsA64CTim\n",
       "qs7pWpgkSVJfljVQLScDlSRJmhRLzS2ulC5JktSRgUqSJKkjA5UkSVJHBipJkqSODFSSJEkdGagk\n",
       "SZI6MlBJkiR1ZKCSJEnqyEAlSZLUkYFKkiSpIwOVJElSRwYqSZKkjgxUkiRJHRmoJEmSOjJQSZIk\n",
       "dWSgkiRJ6shAJUmS1JGBSpIkqSMDlSRJUkcGKkmSpI5W9V2AtFlCgHsCD5617Ql8H/jegO3aKm4d\n",
       "feWSpJUuVTWaN0qqqjKSN9PYS7gT8OvAvtw2PN0CXABc2H69APgPYDfg7gO23YAfcvug9U3g01V8\n",
       "YzQ/nSRp0i01txioNHQJa4D9uH2v02VsCU0XABdWsbHD+2zL3MHrgcATgBuBT7Tb+ipu2tr3kiRN\n",
       "NwOVxkLCzsDTgecAq4GvcNvwdEUVt4ywntAEuXU04erhwAa2BKyLqxjNfwZJ0tgzUKlXCQfQhKjf\n",
       "A9YDf08z3PbzPuuarQ18h9AErHXA9sAnacLVZ6r4YY/lSZJ6ZqDSyLXh5PdpgtRdgX8A3l3Fd3st\n",
       "bJHa3qu92RKuHkMzh+sTNCHrq+MWCCVJw2Wg0ki0IeRhNCHqSOD/s6U36hd91tZVwh1oQtUTaALW\n",
       "/YBNwPXtttTbN0z6MZGklcZApaFK2IUtvVG70PRGvWdSeqO2Rhuwdmm3XWd8XcztXYA7AFcD36Y5\n",
       "Y3Hz1823r6rix6P7iSRJgxiotOza3qiH04So3wU+Q9Mb9Vl7XgZLuCPNWY33Avaa4+ueND1aM0PW\n",
       "zNuXeUaiJI2WgUrLpg1ShwOvA+7MlrlRW720gW4vYRtgd24bsjbfvhfNWZLvAd5SxZX9VClJK4uB\n",
       "Sssi4UHAm2g+2P8M+Ki9Uf1IuBdwLPBs4EzgBOCLLvMgScOz1Nzitfx0Gwl3S3g7zSTz04F9qzjN\n",
       "MNWfKr5dxf8E1tAsRfFu4OyEP0jYvs/aJEmNgYEqybuSbExy4TzPr02yKcm57faq5S9Tw5awQ8Kf\n",
       "ApcAPwUeUMVbRrn4phZWxQ1VvBV4APCXwH8HvpnwioRf6bc6SVrZFtND9W6aU8cXclZV7d9ur1uG\n",
       "ujQiCUl4CnAxcDDw6CpeUsV1PZemeVTx8ypOr+I3gf9Gs6zD1xNOTHhgz+VJ0oo0MFBV1edh4KrR\n",
       "zo2aQAn70wzt/SXw/CqeWMXlPZelJaji/CqOoem1+i5wZsInEp7QnlQgSRqB5ZhDVcBBSc5PckaS\n",
       "fZbhNTVECXdPOAn4OPABYP8qPt1zWeqgio1VHE8zz+qfgTcAFyc8p122QZI0RKuW4TXOAVZX1c1J\n",
       "DgNOpRmCuJ0kx8+4u76q1i/D+2uR2g/W44CXAu8C7l/Fpn6r0nKq4ifAuxPeQ3OtwuOAVyW8Evgn\n",
       "Ty6QpLklWQus3ervX8yyCUnWAKdX1b6L2PdbwAFVdd2sx102oSft0M9Tgb8Bvgr8WRXf6LcqjUrC\n",
       "QcD/oRmaP66KL/ZckiSNvaXmls49VEl2B66tqkryCJqQ5oTmniXsRrO6+cNpJi5vBxxVxVm9FqaR\n",
       "q+LfEh4FPAN4f8KXgJdV8a2eS5OkqTGwhyrJ+2nO/toN2Ai8hubDmao6MckLgOcDtwI3Ay+tqi/N\n",
       "8Tr2UA1Jws7AQ4FHsCVE3YWmN+ps4N+AM6r4eW9Faiwk7Aj8CfASmpXv/7qKH/VblSSNH1dKn3IJ\n",
       "OwAPYUtwejjNROQLaMLTl9vtCufLaD4J9wT+CjiM5o+kk6q4dZnfY2fgscAd2XJ9wu/bLiVNAgPV\n",
       "GGuv2bY9sMOMrzvMc3/mYzsD+9GEp18HruC24ekiF+DU1kh4KM0lhn4FeGmXsz0TVtG00ce32340\n",
       "7XQTW65PeGfgKrZc/Hnm9m3gqip+vLU1SNJyMVCNkYR7A88DnkXzgbUdcAvNSuRzbT+b5/GbgQtp\n",
       "wtO5Vdw80h9EU609aeHJwN8ClwN/UsVli/y++7IlQK0FrgQ+3W5fmN1W2yHH1WwJWLO31cCPuG3Q\n",
       "+hLwyaqB6+GNjYQ1wFHA02iWp/nPdvv+jNtzPXbDOFyjMWEnmrO1VwPfBC6v4mf9ViWNloGqZ20v\n",
       "1G8BLwAOAk4GTqT5oLnF4Q6Nq3Y4+Vjg5TTrkx1fxQ9m7XM34HHAoTQhalu2BKjPVrGxYw3bAL/K\n",
       "loC1hmYO58E0S7R8lOYak18bh+AxU8KdgN8FjgYeDLwfOAW4gWYO6uztbnM8tgO3D1nXAFe32+bb\n",
       "3+naK52wLc0xvv8c211pesKvBn6N5t/hCpo/7C6Y8fWacft3kJaLgaonCXcBjqGZoH8j8Hc06/7Y\n",
       "m6SJ0p4hejxN78pf03x4bu6Fug9wFvAZmhB12Sg+UNuerUOA3263n9CEq48Cn++r96TtpXs0TYj6\n",
       "HeCLwHuA06v46Va83h24fei6J7DnrG134AdsCVpzbddU8ZOEXZg7NO3dvsbl7XbZjNtXzfzjr13D\n",
       "7oE0QXHfdnswTQDcHLA2h6yLqrhhqT+7NG4MVCOWsB9Nb9SRwBk0Qerf/atNky5hH+B/0Xywb+6F\n",
       "2tD3fL02xDyELeHqAW1tpwMfr+L7I6hhL5qh/KNphurfDZxSxXeH/d7t+6+iCVWzg9Yes27/lGb9\n",
       "sa+xJSxt3r5WxU0d6/hVbhuw9gX2oTkj/EKaXsV/quKKLu8j9cFANQIJ29MEqBfQdJm/A3hn1+EO\n",
       "SUuXsDtwOE24OpTmQt+be68uXK4/btpesqfQhKiH0lzi5z3Al8fxD6h2+HQX4PpR1tcOJd6HJmAd\n",
       "BPwBcAnNMh3/r13NXxp7BqohStgTeC7wxzS/tP8OOG25TzeXtHXaeWAH04SrJ9LM8foazUT3xWw3\n",
       "bL5dxU/b3rBH0YSoI4ENNCHqXw0Gi9P+Afok4I+AA4D3Af9QxUW9FiYNYKBaZu0v1IOBF9LM4Xgf\n",
       "8LYqLu21MEkLav/v3p/mTLU7t9vOM24vtO0C/IJmrtZ3aULUe6u4ZqQ/xJRpz3x+Ns1806tpeq3+\n",
       "uYobey1MmoOBapm0v4zXAX9Os+TBCTRzJJxsKU259v//DsBOwA/GcUhvkrVzwNbR9PY/BvgQ8E7g\n",
       "Kx5rjQsDVUftL9In0gSpOwKvAz7kZVskafm1q/YfTTMk+COaXqv3VXF9n3VJBqqt1E7g/B3gVUAB\n",
       "rwVOdd0oSRq+9nfwITS9VuuA04C3VnF2r4VpxTJQLVF7RspTaYLUTTRB6qN2O0tSP9q10J4JvBq4\n",
       "fxXX9lySViAD1SIlbAf8PvBKmlWJXwt8yiAlSeMh4USaVeH/ou9atPIYqAbWwfY019h6Bc3lYF4L\n",
       "rDdISdJ4SXgAsB64txfN1qgtNbdsM8xixknCHRL+B/B1mvVknlXFb1ZxpmFKksZPe5HurwB/2Hct\n",
       "0iBTH6gStk14AfAN4DDgyCqeUMUXei5NkjTYm4Dj2knr0tha1XcBw5SwN801tgp4YhXn9FySJGlp\n",
       "zqS5JuE6muulSmNpKhN/wjYJLwS+BHwYWGuYkqTJ007JeCPw0r5rkRYydZPS20sbvItmleOjq/ja\n",
       "sN9TkjQ87clE3wR+u4rz+q5HK8OKnZSekITnAWcDHwMeY5iSpMlXxc+At2AvlcbYVPRQJewFnERz\n",
       "QdOjq7hkGO8jSepHwl1oTi7a14tUaxRWVA9V2yv1bOCrNBMXDzJMSdL0qeKHwCnAsX3XIs1lYnuo\n",
       "EvYA/h64B3BUFRcu12tLksZPwn2ADcCaKm7sux5Nt6nvoWp7pZ4JnEvzH+uRhilJmn5VfAM4Czi6\n",
       "51Kk25moHqqEuwPvAH6Nplfq3GUpTpI0ERIOAt4L3K+Kn/ddj6bXVPZQtb1STwfOBy4CHmaYkqQV\n",
       "6d9pLmh/RN+FSDONfQ9Vu67UG4EH0PRKfXnZi5MkTYyE3wNeXMWj+65F02tqeqgSdkr4K+DLwDnA\n",
       "Qw1TkiTgX4A9Eh7ZdyHSZmMXqNrLxjwLuBzYC3hIFa+r4ic9lyZJGgNV3Ar8X1zoU2NkrIb8Eh4F\n",
       "nEBzMeOXVPGlkRQnSZooCXcGvgUcUMWVPZejKTSRQ34JeyacAnyI5vICBxmmJEnzqeJHNNdtfVHf\n",
       "tUiwiECV5F1JNiaZd62nJG9OckWS85Psv9g3T9gx4dXAeTR/aTygilOq+MViX0OStGK9BTg6YZe+\n",
       "C5EW00P1bmDdfE8mORzYu6ruCzwHePugF2yXQXgacCnwIJplEP7clW8lSYtVxX8AnwD+qO9apIGB\n",
       "qqo+D/xwgV2OAE5u990A7Jpk9/l2TjgA+BzwcuCZVTzV8W9J0lZ6E/DihO36LkQr23LModoDuGrG\n",
       "/auBPefaMeEk4KM0AexhVXxuGd5fkrRCVfEVmikjR/Zdi1a25ZqUPnsW/HynDl5HM0/qnV4yQJK0\n",
       "TN4IvDS53WeRNDKrluE1rgFWz7i/Z/vYHHITcFyaJr++qtYvw/tLkla2jwL/G3gMOPKhrZNkLbB2\n",
       "q79/MetQJVkDnF5V+87x3OHAsVV1eJIDgROq6sA59ut8cWRJkuaS8HzgCVU8ue9aNB2WmlsGBqok\n",
       "7wcOBnYDNgKvgWbyX1Wd2O7zVpozAW8Cjqmqc7oWJknSYiXsCHybZh3DK/quR5Nv2QPVcjFQSZKG\n",
       "KeF1wF2qeEHftWjyGagkSStSwt1p1jfcu4of9F2PJttEXnpGkqSuqvgecCrwvL5r0cpjD5UkaWok\n",
       "7At8ClhTxU/7rkeTyx4qSdKKVcWFwIXAM/quRSuLgUqSNG1c6FMjZ6CSJE2bT9F8vh3adyFaOQxU\n",
       "kqSpUkXRXDT5JX3XopXDQCVJmkZnAg/quwitHAYqSdI02gTs0ncRWjkMVJKkafQjYOfEzzmNhg1N\n",
       "kjR1qrgV+DGwU9+1aGUwUEmSppXDfhoZA5UkaVoZqDQyBipJ0rQyUGlkDFSSpGlloNLIGKgkSdPK\n",
       "QKWRMVBJkqaVgUojY6CSJE0rA5VGxkAlSZpWBiqNjIFKkjStDFQaGQOVJGlaGag0MgYqSdK0MlBp\n",
       "ZAxUkqRpZaDSyBioJEnTykClkTFQSZKmlYFKI2OgkiRNKwOVRsZAJUmaVj8C7pyQvgvR9DNQSZKm\n",
       "UhW3AD8Bduq7Fk0/A5UkaZo57KeRMFBJkqaZgUojYaCSJE0zA5VGYmCgSrIuyWVJrkjysjmeX5tk\n",
       "U5Jz2+1VwylVkqQlM1BpJFYt9GSSbYG3AocC1wBfTnJaVV06a9ezquqIIdUoSdLWMlBpJAb1UD0C\n",
       "+HpVXVlVtwAfAJ40x36ekipJGkcGKo3EoEC1B3DVjPtXt4/NVMBBSc5PckaSfZazQEmSOjBQaSQW\n",
       "HPKjCUuDnAOsrqqbkxwGnArcr3NlkiR1Z6DSSAwKVNcAq2fcX03TS/VLVXXDjNsfT/K2JHetqutm\n",
       "v1iS42fcXV9V65dcsSRJi7cJ2L3vIjT+kqwF1m7191fN3wmVZBVwOfA44DvA2cAzZk5KT7I7cG1V\n",
       "VZJHAB+sqjVzvFZVlXOtJEkjk3AUcGgVz+y7Fk2WpeaWBXuoqurWJMcCnwS2BU6qqkuTPLd9/kTg\n",
       "SOD5SW4FbgaevtXVS5K0vBzy00gs2EO1rG9kD5UkacQSDgGOr+LgvmvRZFlqbnGldEnSNLOHSiNh\n",
       "oJIkTTMDlUbCQCVJmmYGKo2EgUqSNM02AXdOvKKHhstAJUmaWlXcAvwMuFPftWi6GagkSdPOYT8N\n",
       "nYFKkjTtDFQaOgOVJGnaGag0dAYqSdK0M1Bp6AxUkqRpZ6DS0BmoJEnTzkCloTNQSZKmnYFKQ2eg\n",
       "kiRNOwOVhs5AJUmadgYqDZ2BSpI07QxUGjoDlSRp2hmoNHQGKknStDNQaegMVJKkaWeg0tAZqCRJ\n",
       "085ApaEzUEmSpp2BSkNnoJIkTbtNwC4J6bsQTS8DlSRpqlXxM+AWYMe+a9H0MlBJklYCh/00VAYq\n",
       "SdJKYKDSUBmoJEkrgYFKQ2WgkiStBAYqDZWBSpK0EhioNFQGKknSSmCg0lAZqCRJK4GBSkNloJIk\n",
       "rQQGKg2VgUqStBIYqDRUBipJ0kpgoNJQDQxUSdYluSzJFUleNs8+b26fPz/J/stfpiRJnRioNFQL\n",
       "Bqok2wJvBdYB+wDPSPLAWfscDuxdVfcFngO8fUi1rmhJ1vZdw6Ty2HXj8evG47f1lvnYrbhAZdsb\n",
       "rUE9VI8Avl5VV1bVLcAHgCfN2ucI4GSAqtoA7Jpk92WvVGv7LmCCre27gAm3tu8CJtzavguYYGuX\n",
       "8bVWXKDCtjdSgwLVHsBVM+5f3T42aJ89u5cmSdKyWYmBSiM0KFDVIl8nW/l9kiSNwvUYqDREqZo/\n",
       "+yQ5EDi+qta1918B/KKq/mbGPu8A1lfVB9r7lwEHV9XGWa9lyJIkSROjqmZ3GM1r1YDnvwLcN8ka\n",
       "4DvA04BnzNrnNOBY4ANtALt+dphaalGSJEmTZMFAVVW3JjkW+CSwLXBSVV2a5Lnt8ydW1RlJDk/y\n",
       "deAm4JihVy1JkjRGFhzykyRJ0mBDXyl9MQuDan5JrkxyQZJzk5zddz3jLsm7kmxMcuGMx+6a5NNJ\n",
       "vpbkU0l27bPGcTbP8Ts+ydVtGzw3ybo+axxXSVYnOTPJxUkuSvKi9nHb3yIscPxsfwMkuUOSDUnO\n",
       "S3JJkte3j9v2FmGB47ektjfUHqp2YdDLgUOBa4AvA8+oqkuH9qZTJsm3gAOq6rq+a5kESR4D3Aj8\n",
       "Y1Xt2z72BuA/q+oNbai/S1W9vM86x9U8x+81wA1V9aZeixtzSe4O3L2qzkuyE/BV4Mk00yBsfwMs\n",
       "cPyeiu1voCQ7VtXNSVYBXwD+lGadSNveIsxz/B7HEtresHuoFrMwqAZzQv8iVdXngR/OeviXi8+2\n",
       "X5880qImyDzHD2yDA1XV96rqvPb2jcClNOv02f4WYYHjB7a/garq5vbm9jRznn+IbW/R5jl+sIS2\n",
       "N+xAtZiFQbWwAj6T5CtJ/rjvYibU7jPOPN0IuJL/0r2wvVbnSQ4bDNaeGb0/sAHb35LNOH5fah+y\n",
       "/Q2QZJsk59G0sTOr6mJse4s2z/GDJbS9YQcqZ7x39xtVtT9wGPCCdkhGW6maMW7b5dK8Hbg3sB/w\n",
       "XeCN/ZYz3trhqo8AL66qG2Y+Z/sbrD1+H6Y5fjdi+1uUqvpFVe1Hc6WSxyY5ZNbztr0FzHH81rLE\n",
       "tjfsQHUNsHrG/dU0vVRapKr6bvv1+8C/0Ayjamk2tvMzSHIP4Nqe65koVXVttYB3YhucV5LtaMLU\n",
       "e6vq1PZh298izTh+p2w+fra/pamqTcDHgAOw7S3ZjOP3sKW2vWEHql8uDJpke5qFQU8b8ntOjSQ7\n",
       "Jtm5vX0n4LeACxf+Ls3hNOCo9vZRwKkL7KtZ2l/Emz0F2+CckgQ4Cbikqk6Y8ZTtbxHmO362v8GS\n",
       "7LZ5OCrJHYHHA+di21uU+Y7f5jDaGtj2hr4OVZLDgBPYsjDo64f6hlMkyb1peqWgWYT1fR6/hSV5\n",
       "P3AwsBvNWPirgX8FPgjsBVwJPLWqru+rxnE2x/F7Dc0V6/ejGS74FvDcua6GsNIleTTwOeACtgyt\n",
       "vAI4G9vfQPMcv1fSXJ3D9reAJPvSTDrfpt3eW1V/m+Su2PYGWuD4/SNLaHsu7ClJktTR0Bf2lCRJ\n",
       "mnYGKkmSpI4MVJIkSR0ZqCRJkjoyUEmSJHVkoJIkSerIQCVJktSRgUqSJKmj/wKSdCKFN+UW+QAA\n",
       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106295a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XfYJFWZ9/HvzQwMDCCIIGkGhqgEleyIgUFBcUTQFVd0\n",
       "lWBCXRRRzLqyhjXtruiy8KIrLuJKEHQEwVVERjAhLjkKAgJDzhkGud8/6pzu06eruqufp7ueML/P\n",
       "dfXV1RVPd1VX3XVSmbsjIiIiIqO33EQnQERERGRZocBLREREpCEKvEREREQaosBLREREpCEKvERE\n",
       "REQaosBLREREpCE9Ay8zW9HMzjezi83sSjP7UsV83zSza83sEjPbdjRJFREREZnaZvaa6O6Pm9mu\n",
       "7v6omc0EfmNmL3H338R5zGwhsKm7b2ZmLwSOBuaPNtkiIiIiU0/fokZ3fzQMrgDMAO7NZtkLOC7M\n",
       "ez6wupmtPcxEioiIiEwHfQMvM1vOzC4G7gDOcfcrs1nWB25OPt8CzBleEkVERESmhzo5Xk+7+zYU\n",
       "wdTLzGxByWyWLzaEtImIiIhMKz3reKXc/QEzOwPYAVicTFoCzE0+zwnjOpiZgjERERGZMtw9z1ga\n",
       "t56Bl5mtCTzl7veb2UrA7sA/Z7OdBhwMnGhm84H73f2OsvWN4gvI6JnZ4e5++ESnQ8ZG+29q0/6b\n",
       "urTvprZRZRj1y/FaFzjOzJajKJY83t3PNrODANz9GHc/08wWmtl1wCPAgaNIqIiIiMhU1687icuA\n",
       "7UrGH5N9PnjI6RIRERGZdtRzvdSxeKITIOOyeKITIOOyeKITIGO2eKITIJOPuTdT593MXHW8RERE\n",
       "ZCoYVdyiHC8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGR\n",
       "hijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8R\n",
       "ERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmI\n",
       "Ai8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhER\n",
       "EWlIz8DLzOaa2TlmdoWZXW5mHyiZZ4GZPWBmF4XXp0eXXBEREZGpa2af6UuBQ939YjNbBfg/MzvL\n",
       "3a/K5vu1u+81miSKiIiITA89c7zc/XZ3vzgMPwxcBaxXMquNIG0iIiIi00rtOl5mNg/YFjg/m+TA\n",
       "zmZ2iZmdaWZbDi95IiIiItNHv6JGAEIx4ynAISHnK3UhMNfdHzWzVwOLgM2Hm0wRERGRqa9v4GVm\n",
       "ywOnAt9390X5dHd/KBn+mZkdZWZruPu9Jes6PPm42N0XjynVIiIiIkNkZguABSPfjrv3SoQBxwH3\n",
       "uPuhFfOsDdzp7m5mOwEnu/u8kvnc3VUXTERERCa9UcUt/XK8Xgy8FbjUzC4K4z4JbADg7scA+wDv\n",
       "NbOngEeBfYedSBEREZHpoGeO11A3pBwvERERmSJGFbeo53oRERGRhijwEhEREWmIAi8RERGRhijw\n",
       "EhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGR\n",
       "hijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8R\n",
       "ERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmI\n",
       "Ai8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhvQMvMxsrpmdY2ZXmNnlZvaBivm+\n",
       "aWbXmtklZrbtaJIqIiIiMrXN7DN9KXCou19sZqsA/2dmZ7n7VXEGM1sIbOrum5nZC4GjgfmjS7KI\n",
       "iIjI1NQzx8vdb3f3i8Pww8BVwHrZbHsBx4V5zgdWN7O1R5BWERERkSmtdh0vM5sHbAucn01aH7g5\n",
       "+XwLMGe8CRMRERGZbmoFXqGY8RTgkJDz1TVL9tnHmzARERGR6aZfHS/MbHngVOD77r6oZJYlwNzk\n",
       "85wwrmxdhycfF7v74topFRERERkRM1sALBj5dtyrM6fMzCjqb93j7odWzLMQONjdF5rZfOAId++q\n",
       "XG9m7u55zpiIiIjIpDOquKVf4PUS4FzgUtrFh58ENgBw92PCfEcCewCPAAe6+4Ul61LgJSIiIlPC\n",
       "hAReQ92QAi8RERGZIkYVt6jnehEREZGGKPASERERaYgCLxEREZGGKPASERERaYgCLxEREZGGKPAS\n",
       "ERERaYgCLxEREZGGKPASERERaYgCLxEREZGGKPASERERaYgCLxEREZGGKPASERERaYgCr3Ey44tm\n",
       "7DPR6RAREZHJz9y9mQ2N6CnfE80MBy50Z/uJTouIyHRhxhzgZmBN4DF3Hp3gJMkyZlRxi3K8hmO7\n",
       "iU6AiMg0s2F4vxu4fyITIlOfGc804zMTnQ5Q4CUiIpPT7GR4+QlLhUwXrwQ+N9GJAAVeY2LGFmb8\n",
       "OhQziojIEJkxEzh+otMh08qkuV4r8BqbfwFeNsgCZqxuxsojSk/dNMw0Y+FEpkFEpIaPAmvXmdGM\n",
       "Dc3491EmxowZZky7OsrLmKcBzNh7ohOiwGtsxvIHvA84fdgJGdAC4IwJToOISD+bDDDvm4FDR5WQ\n",
       "4Fbg6yPehoxWjHc2zSc0HVgr8Bqb/He7oNfMZqwTBueNJDX16Y6th/DnW+b+EyE39vKJTocIgBm7\n",
       "Am8vGT+zYpEvhemj/O8+G9hthOuXETFjDTMW0a4zODub/nrgKeA/m0rTMneRGa8QFT87G/1In/m3\n",
       "Ch83GlW6avrbBG9/sjsP+PFEJ2ICHE77GBWZaLsmw6cmw2/ps9yBI0hLSv+RqWkbYG9g1fD5Gdn0\n",
       "H4X3VvUhM9Y3Y5dRJUiB1+C+BrwwG7dSj/nfC/wyfjBjVq+Vm7GpGSv0S0Q4MMZUWbDHnWMjzDAz\n",
       "fKLTUeJFwCsmOhETYNX+s4hMiPOT4Wf2mbd2Pa9QL2zLGvNtoUZUU96M8D4nvF9dMd/jyfBRwOJR\n",
       "JUiB1wDM2Ar4cMmkXsFUXlfhxX02cy1wWI3kjCX3LKbzoDEsOy4hu3fb8PEN4b3fibTfOs8yY/74\n",
       "UiYUOX2Yqcn+IMxYod+NVJPCzdh0qE6QfofVkuE9KuY/Obx/f4Bt/Bq4osZ8F4b3rs5bzfi+Weui\n",
       "LpNX3EcfDe9VOZePJcMj/R8p8BrMLyvGzwIwY0UzXh5HmrEaRcXP1NlVrSrMeGUY/KJZz1w0aLfQ\n",
       "GORiGdd55ADLDMu/0z6JrRHe1xznOneD4bTSrJPLOI3Fi8ohE5qKqecs4I8TnYjELUyPekjpdelD\n",
       "yXBVhfunw/tDA2xjw/6zALBi9g60zrv/ABPfQk76yoPjf6iY79Jk+LUjSgugwGtQafPmnwEbUBQ7\n",
       "xrvek4Gzk3mOAtYtWc+rK9b/82T4I33SEgOuv/aZL7Vi/1lG5ulkeEl4X3/I68WMLUMxZq3vGuZ9\n",
       "A7BXGDWhXX5MkFjZ9GsTmoqGmXGl2UCt53IvA54/rPQMyez+s0wOZvzKrDS9m4f3dWnfLB5C5/kx\n",
       "tV54r6xrOwT5tTKeJ07NZxyEGWupKHPk8sDrpIr53jfqhETTIvAyY2uzge52xurcZPjr7twM3E47\n",
       "8Mqj5Fclwzcmw0/V2Fa/E2gMvMoCuyr9ctFG6YFk+APhfZ2yGQf02ezzvPA+SBHkZ4G58YMZ7zQb\n",
       "SlA4VYzkuDBjYzMOHsW6h2QL4LJYPBeC8DHf6YZ+8j7Qf86RemKCtz+IXYFPlozfB8Cd2ykqQp9N\n",
       "kStbdVOUVop+5iiL/8w4Kgyukoxzs+4uCmrKG2oNhRk7Ja3pl3VpqdD9wCpmLDHjOWbt/Zj5wygT\n",
       "NGUDLzNmJZWzt4bKH3CY7gIOCMOxIt4TVNfxelYy/NVkeEszvpjOmNR/ivrtm7EUja1IUTzSRJCa\n",
       "ewJarTxjkerAPVObsbIZz83G/XPyMbbcPKfGujYLg3+is2Lut4H3D5q2KawV5A+jyDWc9P8X+CDw\n",
       "H+Nd3ygk+34lOv9LA+dgJfWqNgW+Mc6kjUlS5eDpnjM2yIxVzdgsBCbLZdNiELV6yaKnEerSuvOQ\n",
       "O7tR5GZ1BV5mrBUGvwdsDNwLnGfGcyrS9BqzVpWHOsf7z7LP7w3veVpe0Gc9VWI1lRXS6iWhAdJ6\n",
       "1Yu15tvdrLRO8Pn07+bIzbpa+E0rZjwCvCkZ9UGKWGE9ijqB6bXw7rDM3fSutz1ukz7wMuPlFVmx\n",
       "NwP/HYbjRX3U3TWsCtwZhmOu1VJgTTO+1WO597lzdPJ5V+CTZh39el3YuUjfulutojQzTjBj6z7z\n",
       "Q3GRWQKsmm27VHJSG4Z4gKct6BaH7XzJjI1rrueLwFXZuH9Khlt3uzXqv/05vC8pmTZpLmANSHO8\n",
       "Dh90YTPem13oDqDI7X1/mD4ZKyB/PBmu3cjDjGeU/NdmmfE+Qq6pTcwTKuL/al0zvjMB2y/zKdr/\n",
       "sdlmvCaZFs9fN5Qsdz9wTzbuEcpLAWLXE/vRvil+EXBmRZr2ho6b3JUBzNirxzloacm4/EZ/rNU4\n",
       "4nKLgGtCWowi129JuP6tGcb/nRlXZst/keoqAnNqBFbjrWc7EDM+P6rSqRDofyIbPRvYPfl8F/DG\n",
       "MLxDMv4vtG8CnkX5DcHQTPrAi3buCGb8o1nrIrsW7bvTmL3+5RGnZWXg4TAcf7v7wvu74kyhiOX/\n",
       "xc9J0JUHDGUnnedk713Cb5DWLdgXeGfPlBdWStJbtu10Gy8B7qxRyb+nUPxyIrQaHfw2mbzAjDkU\n",
       "F8G6Dy/tl7OZnpzr5t6UtWBZJgIvM14AvDUZlZ+46jgK+Ezyefts+kgrqo5RejG9KBnu15rpixTF\n",
       "k+9Oxs2j6HzxF+Fz35yKEYh1S3egpPPRKOSkvKpq+pCl546XAD8NaXgP7ab9N5csN4Pu/19pjhfV\n",
       "9XU2rqi/l54fnqDdp9NPCB2xZlYmuwk2YyeKYP1PyejKa6kVXQS5Gb8umRzPZ9sDc81YleK7x3Sd\n",
       "DfzQjA2BXSiKx1P9uuTZtyJN8Tt9sM/y42LGm8w6GqB8mvCdzYZXzBoCzF0pHueXewbt697DJdMB\n",
       "NgMsuWkaaSbOVAi8/gqtLOEjoaNYaVY4gOIffKzl7HWtQrsC598A3Etz495JeZcNd/XbgHvrDrGq\n",
       "Aj50/gZRnbvsFWkfgPGEUHXHE8fnOXGDOoAiqzcGXjG3IBa1xhaOt1StIBZTmPFV4B1hOD0Z3pEM\n",
       "z6aohPsY9bOL43xpq9XG/hshOJ2oznWPoUeQP4CdzDjZjC8BO2XT7h3C+oct7Ux4kLow8bg7JhmX\n",
       "31BNRAvZbcL7StBR/JnbH/hfMxY0kKa0LuvPoPVfPhq4OIxPc+4t1Etaju7OnrvqeGXfMS8SBNiz\n",
       "ZFxad3MWnRfqLc1YLwQ5UVku2/kUVTbSXLle54vDw3vH831DVZlYRzUGIWXXsgUUdYTLboL75Sbn\n",
       "x2YUGxONukrFicCO+chww31H9+zdzJhrVp0DFY6DByiC5zLL0d4/pYFXuI4/AvxbnTSN16QNvKzo\n",
       "mmEN2hfFS0pm2xx4knb5+nYjTtbKtAOvsuKpKP3jpv3Q/F8+Y6irtn/dBJh1FIvcSlEfAooKgztZ\n",
       "SWVBK1pvrUlRkfVRaN2tX0t1MBhzMJ5bMb2uqmKceKcb9+tNZTOZsQ/tk3Da0jO9WK5t7fp+sylO\n",
       "Ug/SI/DKTtqHUfxp00dGPE5zDgKub3B7QHFCo33HfByhQukYiwY3o8jC/3jJtIls1FHlzvRDyGmA\n",
       "/jleT9ZY97hbFpqx0KwIHMxYpUaR0XXh/R3hvaroK9Ztq91p7liKTs3Ykc6uIKI8lyP9j54L3EbR\n",
       "BU9+E/0IRXA/LxmXHmtl3TqUBdSbZZ/fbNZqoLQ1xXn9xmR6+t3zc/5LkuH3mHX3DxUyDKrOQ/OA\n",
       "nbNxcb+V/Y/eVTKuX45X1bbLik+bcHd4XwFawfbxZj0fiH4TSYZBKlRDKr1pt856hfH8WhZ4xe6V\n",
       "ngG8Lhk/smvApA28KHIs7qGd5RoDgLIT32dKxnUIdTM8Kaoci5WBh92x0KKxStoRW3qAf5jui9As\n",
       "2tnBscz55JDmVm5UOEBfT2fuwQ8o6kMQ1ns+5X0xbUE7wHoaODadWFGXa7tk+ng6k/tqxfjHss9V\n",
       "LT33CGnIj9VY1BrvnGPwPTus+0kqch7C3X4eoK5E5x/tsTDvC834QUXaYq5h7cC5whr9Z6knXKT7\n",
       "Nk8PRYw30T5xr027yP67NtyOQZto+DKo5eg8NmNA0K/FcZ0L1px8hBnrmPHDmmmD4mH2p4ec0N/Q\n",
       "WRyar3s23YFKVf3MGBQO8p9+2KwrQOjntIrxeVFZepylgUy+vXjDewO0zkkxt+qZ7iyl++JcFrxc\n",
       "l00zihvYLma8PaT3tjAqf4RMGpTNh/bzTkPgvB9wAqGVZonVSsa9tGLeNF1pR7JVgVf8L1f1zn93\n",
       "xfhhOzb7HIsdDwjvsymqOozn8TwdRfvJTXha6rSY4npQ1uVI+p9PA8Abx5GmnvoGXmZ2rJndYWaX\n",
       "VUxfYGYPmNlF4fXpIacxL1Zboc6FpURs2VBWTIcZL6ux3rSosZdW/QT3doDhjrt3RdErEf487q0c\n",
       "sVj58IxkvmfTfqZUXN9HaHfTEO/4vpDOY9b1CJzl3buy8e+kt6oApmeFUrOOukOpG6ArmDmmbEba\n",
       "wVDe6nPHsJ79wudF4X0tiovjXKo7XDyH4mS6lHYA+Aw6A694QXgPxV1x1X/lU8B/95hex7j78THj\n",
       "ODM+Q8jJsP6PY4rBUJzvatrdn7wN+J/xpin4PSMIvCz0fzSOm4JZtG9aoH2Dt4IZz+uxXFkuTu5H\n",
       "JeNeTPUFuJfrKXJiNrbqFnhlPbpX9e8X11ErxyscUzB4vbWqXM65wK+Sz1XnkLx1aN5zfOvc4t7a\n",
       "j1Xd+qQeAt7qzleA/+0xH7S7vdkT2MGdv2TTe918n0GRi9xVjJ/sx9+VLFen9/3PmrFPKNYvC96g\n",
       "CCYWAfPMWM66n/DRasVtRUvxUfXUPiNs46RQpyu29I/HVcxFLK3yMsZ0xf12VDLu6Yrg/E7aRcG3\n",
       "0ln3+TZGpM7F4rtUP6oh+rW7bxteX+gz76h8nawuiRnHWrup7d+yaZvTqaziYzq/0VnUmIqBy34U\n",
       "TXjLsoSr3E53b9PxJJPetX67YvmqZtPPDHdseYXRDcJ72oKnKuiJOk6iIffNgcfM2NGS1kBZWfzr\n",
       "k+FtkrTOdOcpuh9WGtN9tlnr8Q6xN+FYkTWtdLsR7buVmMvwcdpFkqUVS4PYUOKU8Hl1OvtAit95\n",
       "u2T+MjFYe0PF9J7MOBD4/FiWzexHUYQc0/lys44LXH4Si8WJsXjka+4d37/W98mKvsv8hXbr46p1\n",
       "1G3RmoqVgrcN61iurIjUquswfoyicc67KR4dEy9ghwOXlp3wQ/FZqizAqlJ5AbGiP6Fe5+L4vaoC\n",
       "r646NGG978g+v4L2fq37eJ3Y6KVXMFqmKiBYj866UWmOVxrY5PUC8/NuDATTxiAxNy/esJY9aWRP\n",
       "2n39VRYbm7GQdi7oNclNceqTFDlUP06W2zi7ge+4AQrTnrCiv7ex1gWcT9F9xsehu4guHEuzKb7/\n",
       "xhQN1H6fTN+CzucNP0zozd2My834t3HeSKbiPvl7ijpd+XOO43FSVd8rnsN7Ve3J5dd2CNcNdx6l\n",
       "s67dPu6tzIsVKa4psV5z2g3FUPX9cd39PCrKVxNjjpbN2Nus7yNs6uQI3A2sYaHStRUdNx4IfC1k\n",
       "xb8o2eaKwDV1o+nwZ3kamBGi5ty/AEe7czwVJ8ESv+kxLV4A0wrXeYXlqOqi9Q/Ad0rSE3N40jpV\n",
       "O/T5o+V3r2kQ8kPCCTNc+O5LLsbxe9wPLEkaDtwLRR89Jdt6FUVF/K+Ez/kJPK8j0gqokxPeiRRZ\n",
       "2l0n3qyo2Wk/F/OZFEHUCeFzvBOPLWerTpIx8Bprrk4rK96M35uNq07dHNpFTm8Hdg1BspnxFuDp\n",
       "pD5L/n3yjjePq7nNqgvs9hQXubcCmPE8K+/PaWPoykmoIxYxx45vTwA6cuXNeB29G7RsTnHh34ru\n",
       "46qsyL6jxac7b6C4sJxBu0UjhG4BMrGT1rJzztUkd+c9zksPWXmfTWVFagD/FdZ3jhn/TvF/KLtQ\n",
       "r9IjQI3+yYxbzfhwclM0Fl+iM6hKA680Byl/FNNDFA1yYl2deLPbVWQWKkofCOxixg5mrZvNKOa6\n",
       "7EW1M2hfd/JqEbEU4a/u/IZ2pe6f0H0sx5vN/PvU6e/tVsr7lTuP9jm5rG7oKtCqcL43ScMDK7pC\n",
       "uTKMuy5ZJp43tqLI1U27WqgUAs1edTjLbljz3xOqc1Rj7wDnVkwvc5B1P5avFey7F8+mzYdpV/m4\n",
       "KUzr2xhurIYR1Tqws5ldYmZnmlnfJ75nFgH/mI4oCQJeRrm0IlwsG48X1rTjxiNod7fwY9oX1eXN\n",
       "2M+sfXdfo4imizvfcB/ocQNrQlcRYLqTWzkgZq2Aq6ryYR4IxjuDvDgRinoX3wLIihu3j/MnuVnQ\n",
       "fiB4Xlk4zalK67Mcmk2Pd+rPcu84Qaa5VnMocqjihT8viu1ozeLOPXQ+2qHse36NouFARz0lK56d\n",
       "mRY1r+HeOoGvHbb9NorclHjCOCK8Vz3f68G4+orpg5hPdSukuuJJNt6tPUHxG8aiw/lW1HFLczAO\n",
       "C78rFDnHEI5HK+omxaBhdzPyqgSlAak7F7p3FJXHvnNarVHD/3wsQRe0j/vlQpH239Ndf+jHYTsd\n",
       "aUyCjHMocrqvpLtbgrLiqvi/aHXl4s5j7uzpzqvcMYrj68SwHbeif6i3UP3Mv3jBSTu7fFvJtqOv\n",
       "WUX/dKHuadlxuID2f7PMmdRocU3xlIyv0b4pKmX9GwLEC+9FdDZEWpmieGeLvLV4+HwUsJpZq3oB\n",
       "dPf3FStP30BxrF0A/NWM35oVgShFXdg61gvbzru2uJTiJjxetH9AcSPQ67mN760YfynF/3N/up+h\n",
       "+2n31s1E2gdaWg+s7MY75uB0nEutaKwRz4mb03kezs/xVTdUub9QPFt4Zjje8xuYssCr7Jzd9aQQ\n",
       "M/6FdgbF8834lFmR023GjOwG5fXZ4rGO4KUUVU7+PZu+L9Uled+juprKUAwj8LoQmOvuL6AIdhZV\n",
       "zWhmhyevBT3WmfdDU9pqwZ2fUBTB3QStCs5lP1h6V/AY7YNqRYo7+1OS6XUPuDFz5x73rmzuO5Pp\n",
       "DybjN6q4A47NkOMjN2LAFU/sXQe8O3u7c202utWxazihpXdYsQhygRnPt6Ii+Rw6A6+0eCfe3cU/\n",
       "8ephu/mJq3VSdWcJRfcP8e4rv3v6OHTclUA72PsJ5Xd8T1AEBK0WTGY8SGednjKPh4B0Du2KmbEo\n",
       "s1Vsaca9Zq0+4+J3G+nT7MdheTrvXu+mCDjSE1H6m8dcyflW1HW6jXZO2VF03hSsRP/m6G8J77FO\n",
       "R3pcpj11D3ouiheQ2ST1rsLJfy3r7Gcrz43cALjVncMoivXL7tjLOm5+LkWR91uozmnOG3WcQhH0\n",
       "xhuIz4V0rmdFo5ZYQXzVcBM4g/65ja8K6zCz0rpaZX0ZdbF2twl9K3Sni5Wsx2NQY8UTAeKF/08U\n",
       "F7FcvPBuS6ijGc5xqwK7u3N1xbYfo8itOo52AN86V4bAM/4e+Q3czrRbfJ4c3vPi07KOSDsyBcI2\n",
       "7k7PaaEUZJuuJTtV1bm7250H3Pke3fXdYoC4P8U5chcorzdrxgFmHY0ToLvBxem0z9eb0Fkklx9H\n",
       "vVqEz8iK9Z9H+7p5RjZ7WeAV/4/xpusHlP8HPwEspF0x/gsUQd7yFOflWMT7S3cWhZuOGFzHXNm9\n",
       "3Lk+L6ly5yT3rmd/blZsaru9wPYzs8NL0jQcHmp893pRlIlfVnPeG4A1SsZ7+fzu4fWsZNy3wrjH\n",
       "wNcJ4+aEcR+Ky1Ss66vgyyfrLXudEd7XKZm2fY80zuv//f0vYd7jwfftM+89ybp3zqatEMafC75i\n",
       "Mt+h4Nsk820axl8f3p8I4/8uWeb3Fb+XgZ+Sff8/JsMzw/sV2Tw7gv8pG/dAMrxvWP9v8u2Cfx/8\n",
       "Pdm4TcGfDsPvT/dvto39w7htwucbwueNsvnWy4+RbPoJFdtYN3w+Iny2ZNqpJetaC/yzYfjddf4f\n",
       "2To+XHZ8DriemWXryF6PJMP5/nbwI5P1bZKMf23F+v4UfpsfJONWBX82+NKSfZ4uu10yfrVk/JUD\n",
       "fu8L4n4pORZvzz5vkCwXzw2/DZ/Xy+at3Bdh3I190nUY+L+Cv77XOsPwzeAnZtP/ocb+/HNYx5t6\n",
       "pPU08MtLfv90v95G+1xbetz1+Q4LwD+fjftQMt8hFev4dDhW7kiWuzpM27DHbzsrWccHw/uLK+Z9\n",
       "Qc19+q9h/CYV3/mAmsfj1j3213t6/JZnJev4eFU6k3nmUfzH7q1Y3zOT4U1Kpr8hGc6P0W8nw/v0\n",
       "+K6/AP9N9p3itu7N5r2yx+/y/PB+JPhRPY69H4IvCcMPh2MnTnug1zE74DklxgNbt8cx0Drqvsad\n",
       "42Vma5tZKIqwnQBz91odJlpnz8Jd2bTurOTFg1Jx5xaKbMcjqO5V/EsUuRr9+g1aGN7LovGOVo9p\n",
       "bpN7realMQfqo+5FkUMP85Lh36cTvMgRe4oih+KFyfivu7fqt0CR4/NGOoteZtF5113adNgdp7to\n",
       "a8dkeszt8Wye9em+I0pzwWI9qRvJKo6781b3dq/+wVLAQq7KN0uS+ubwfldYR/z+sdVJRx1E9/Lm\n",
       "4Ym8omysuxOLO2Oz/7SOXSyKTf8z69L+HY7pU9cBK/pse3Ey6l9LZsuLTvqpU8SdFiOkleZ/TvFf\n",
       "auVKeNFyK3YiWFVxfnuKCrut59N58Uy9OylyCPLe79PzwTrJfyotMsuLCfuJuXh/R3eLqD9nn9Mc\n",
       "r1jHLdb5TOu2xXo4aS7wXuE97veuriIyT1KcVyor3pu1WlE9Qndufp1K7zEnNy2eeXc2z+G0c2vz\n",
       "LjJi453ymwgFAAAduElEQVR1yBoChdyM9Pd6knYuQu4caBc9m7EbnR1Qxv0Qc5/i//7BcKy8Pixn\n",
       "tHPLe/WTlk77VHgv7f+Pmg8L9yLX81o6K3enjxvKW1NWuaLHtHh+ipW20+M+zXWp03nnQxQV9qty\n",
       "2OO5/gG6076YztKdi7Pp6dNPenUnszt0nMdupF3ilJ8zVqa6CDam9T7gWXmVgMRs2tfqlensn61O\n",
       "LwN1xeN09B0+948COYGikt+TFJUf305RDHNQmP6PFP2XXEzRPHZ+xXq6Ikfwl2cR8Nw0Yu0RmX4S\n",
       "/Isl4z8F/kXwryfrfDIZfkW2veeVReLZOmOOwhM1o+aVw/yr15x/zfi9K77Pb8GfDuv8U4/1fBn8\n",
       "l+B3hzuC/ZPv9Crw9SqW26/ibuS7YfpvwT/Q466l6jWTIrfudTV+gxWS5X6RDG8Z3tcI73tmdzUX\n",
       "heGVkmW+UnYMZWn7aTqdcOeVpelq2nfh6bxH9fjOb+zzPd8V5qvKSXLwO+reNYE/p2T52eCX1txH\n",
       "n65Y79wayz5e9Z8pWd/7S5Z/Dd05lYdWLB9zN/4LfMWS/bk0+/yZ7POuYZk9S/ZnmqsZcy3+uWS+\n",
       "eCw+3ue7vgf8vmT567O0OMX/1MFvAv9oxe/7mpLvmacpzTHdPUvHxuA3UOTK5ssv7LHOTyTDt4Vp\n",
       "y2VpuTV8vq7XMZKkZW3w3cLwQvDZYfi5Yd79k+Vm9Pl9022c22O+rfqlq8ey6THx2gH+jxaOk19k\n",
       "29w9TF+NdglOnGZV369iG6v2+s2T1wbgq4fhW+KxW7K/zyhZ9lrw8+N+6rEPtgvvaYnIN5L5Vgnj\n",
       "4jF4JcX/I84bc5g+Et6PT5b9aTLfGXT+x3+UDF/XI309z8cly8Xr0Iz2OPoeL2N5DX2F1V+q+wvQ\n",
       "HQhdE8bfDP6Lwbfhh4B/I1vn7eB/JWRJZ9Ouo/ukfR34AcmBGQ/eAwf48zn4SuP/zVoXHA+/ycwa\n",
       "y1wHvhn4u3v9gZP5l6OkuCWZ/o3wu5b9ue/KPqdFTzE7+JU1v2tc7shkOH7/GFjtlcx/Gfh/JN8h\n",
       "T3dcx3LgO2Tp/Dz468DfmeyzrbP0nF32m1T8Dj1Plsk643f7fsmy5ybD6fdcHnz3MH5N8P2SaS/O\n",
       "1rFLMq1X0Ud8HVaRzrIieAe/s2L8SX2+9+yK5R4qGdd1vFTsh//Oxi9Ohg/Ppr0+LPOZfD1h/FNh\n",
       "3DoUwcYHSrZ3Vvi8bZ/velCN3z0GXk+Df7NinhnZd/9pNn0xxcUxfl6YpeNZFMVRi7Ll7qIIykqP\n",
       "XfBjk+Gq/9Rf03krXvvX+M9vXpaGPsvsU2d+youQn6yzjey7Lqwzf7bs8nQWo+9Qtf6K8Y+Bf79i\n",
       "3Wlx6xyqA7FZIR1LKW7Q7gO/qGR/50Fi+npXn9+m7HV0Ml8MzGaDb08oRg5pmwn+jDA9LY60knXm\n",
       "5+KTkuGr6/62NffdjM7PjGk9fbczipWWfyHijl41+ZL5hcPDDnLwD47hR+s4iYVx14cD+Xl9DpqT\n",
       "aNe5uj9ZfmPCiWaAdIw76ArreVf+fWos838Ugcb7B1zud2XboshJO7Lk9/oCWQ4CRf2wJ8JwvHjt\n",
       "UXP76UXk4vAeg+j4Z+w6gSXL5+l+ZRj3Bopc0DSdG9dIzx+S+X8Y3mfSrsNX9VqnYn1p/Y2YI3JD\n",
       "Mm598F1Kvsdl+TaSaelNxteqfpP4fypJ6yEVaS07+fV67d3ntxxofdmyXReWMP4kkrp6yfG+JJv/\n",
       "KkI9HfC3JuNfkGzj8jBupbL/He06hX3/S3TWk8lf/0MR+Hy3z2/wy2R9F9O7jlB8vS5LR17P9RUk\n",
       "gXbFOtK6M619lixzVRj3FEVdo7zuZ/qyGr/VGvlyNc8Vcf639JnvDdn6fzqGbbymzvwV64jH5yYl\n",
       "0/5clhaKm+ZVa6Tthl77smSZUyv+R+f02IcHZP/hDUnq9FW8jkuWiTlTy/X5Phsmy+e54GWvC/t8\n",
       "1yvq7uf++5ChrCd/NfrIIDOeAzyY1Jc4uGS22FHm7WPYxPYl4zaiaC0SW9pUldnfQbv8O23Z+Bfo\n",
       "6gemJ/fSfkrGIk1rv3pL0QMULahmUbT4qdv77gLadXPSTlkfgq7WMlB02xFbtsS6FzvSrscR+6mp\n",
       "Wwb/r3Q3894T+LE7Dqzl3jo2qqT1nc4K76fQ3SdNnfofNyTDsa7eblS3Zos66o+ZtfqGSTuyjS3c\n",
       "5sUR7ixx7+zEN3RtsjWZ0Ipsb9q99n+b8r6c4nF7ljtH0N2/VOkzBcPvHXvV3oGiTmTsbqCsH7uy\n",
       "fqvy9Y1V1cNxV6azd/1Y1ydvzv5L2v/n40N6zL3j2a9/H95jHY/Ts3VUPq6nRK///kco6qPdT2c9\n",
       "tPdk87XqTbmzjbfrRF5KuSUU9a1avLu/wVvcS+sUptJWfmX90sWuGmZQ/D9i10E/zubbqs4+d+de\n",
       "ir4GxypvoZ2v/1SK/2tMyyD9MsXez8dzjYzdgpTV28yfGQmAO9d6ef+GuRuT4ZfR2bVSmarjMu+a\n",
       "ZFXa/eHNTcbvFrbZ68k07yfUxQrnrtcDeHer9g7uHS0+u7qVoOjuJbUtvc85W1N93pgUmn5WYzzY\n",
       "YjPXXj2L93tmWpmqvpYgBF7urOzdfd38nqIuW/qIgdh78URKA6B+zZWjXSk65ZwFHOle71Ef7jzp\n",
       "zpfDRSm9KDxI+wK9KJn/adq9MqePo+hoNu3e1RVElSdpNyI4nyJwa5283Xs/Wyyk++jkc3rif2V4\n",
       "3zXZVj/pxfan4f3kZFxsEn8nnX305L/3PWZ9K46nTy54B+2e3ntVtH8/7f/v9737MVAQmtq7t75/\n",
       "fjHu1QVG7AfnGnd+Rvv7rkrWr55XN/+v6509plV17/IaOi8m8UbtD8m4+yiCz44e3HPuXBmOn3CL\n",
       "y+0l54jx+hbtLmM+SGeDkLMozomHh89Vz4Ms6z0d4A3e7n27Sq+bjfg7ph0Ov7Jkvqrew5fSvrHF\n",
       "vetC2UtVNwt19HvUGe7cQPs4r329c+c/KCrMX9Jv3h7reArY3r20G5vDGfvzEjenaFQSt3OeF10r\n",
       "xU588z4iobOR0ykUT6SBzkZYd7jzMO0uKz5n7cfC1QlkrqddCX7QbpniE2/yXuffSXkGTeW+DJlK\n",
       "/f4PE6rpwCs+b+8aKx6VEuV3mNDZsqQW72x1mN/N508lT1vqvNad39N9wqtqzdOUeEL8Nx+sF925\n",
       "FLl8tVr29PEgRS7C6e5dndTFZ0ymQUpZv1p1pMHQJyhalmxCd8d4Y3WyO4sp+pnp158XtHMbt/P2\n",
       "o3RiXzcbUQS2a7mzdsiRSFvC5Y+uKXsIdqvDTHfOTsY/DqwYTni9OqKcS5Hjc757ea/O4eSTnljz\n",
       "47ssWMvF3yE+cuMJ6Lgjr+y3ry53vkNJTmLIIV+D4gJV9qSHDZPheAec5npuR9E7+fPMaj8iZ7xO\n",
       "TYZjZ7bvcOcgOn/v9NEpj3nRmjReOKsCr8PobE0W1TmP5zcbm4fXCnQfn+dSfmzsRzt3MLUz7d7g\n",
       "B5X2t1W3P7GY0zVoz+LHUfR+X4s7W7tXtpqsu44LKyZ9ju7c2brrvNa99GkysU+zslKOOO1Id97o\n",
       "3uorcxFFQL837ZbF6XUjtuyuyulKW+U+Aqwc+nKLQWXVo4Byse+5NAf0s+58x51zaOf2xsyV22D8\n",
       "z7idKE0HXulBnD61/ECyYkL32s14S+XFfXmOgHtHM+p4UOa91sem56eNJy3jEC82/9Rzrk7xRDaL\n",
       "4QReD1DcvcQiw61oNxn+EVlOnHvHhbjqiQNl0mPxAYbfpPcvAF70Ml51YUvF79uVDndudOdvWS5c\n",
       "GtjPMmNe6CATwo1FyEWJx1r+zLJoc4qc4LJgLXU3Rbcp3+o1U/Zd01zk35M8SqTH8rGYIM3Ji03n\n",
       "bysJxqtcCHyV7ub/cf2ti4W1n/d5NUXnqH9y56UUnftennRHEYtE/kY7GEy7R0n3STxhD3InPjf7\n",
       "vKDfAklx8QW0i90XhWlVF4r4P43pLT0+3bnXnd/R+agXoPsZlZk1PetiJVy8r3VnqXtH8HM/RZC2\n",
       "HsXx8rpkmQfpzqX5JsUDpOP5tXZgE+yfrL/XY9RS/wL8bdBrhDu/cu9ZVNaYWN1nyKuNNx1lAWk8\n",
       "n+VFi19yZwd3TkuCuWuB34bh75lxJuWPLoLOB30/QpHjlQZP/Y5NoLx6jnvrOaHQLm2I1SeqngQw\n",
       "JTQdeJXVj9nNi8eVxFyT99K7HHmYdoaOi1PpQeLe81EQIxOykG3AE0zsz2dYgVcMFB4JaboyZp2H\n",
       "k3ZZVvz7gEsHKGaEdn2Ry8NJPGY5lz26pa70BDRoIB+LrvI6alVBeFpkMouiDsz/hs+tvm3cWS0t\n",
       "1ioRv3dax+ZBil6196J9Ub4UOIDB+r9qnRDd2dm9ss4QFP197Vw2Ifm/1C6Oc2d7dz5G5934ebSD\n",
       "0sdp92N0nxn/GYb3pl2M9QRF/Y2Y+3ZBGI5PHNjQvSO4fITuJ1nkOd+90nwL7RP+az2rg9fHjbTr\n",
       "TJUVe8Q6kFcnaeoZeCVeBB2PzXmwakbgafdafcPFAOgGiqLv/wTuD0VYqWvpzNX+lHtHrsbZDCbm\n",
       "RA6SE/Xf7gM92u0L/WeZ+ty5K5xbyoow43nsoGyZrvNQuNmKddxmA68uWV8svZpJUey/P8X1czs6\n",
       "j/exxBi/ovu8+yWKOr+xmtJ1FEWqZcWqk98oauxXtQ6oaKHw6qx1xpbj247nLXFurWrhQNGc9djk\n",
       "c1crm2G1jmjud271I+ZUNEkecH2xK4Zv9JlvXL8V+DvCOr4bPse+lF46jnWuAf7zsJ5TBlx2j7Bc\n",
       "7Dcq9gv0uYr5l6NoFXYnFd0xlCxzWz6edt9cOybLLk9oJQb+/7L1/t2A3+uPY9lPhD6Aks9nkPR4\n",
       "P8B6YrcIp1O0lLJkWlXrxx+E6Rvkv2f4vTavOhbpbKk3lu8du/l43gDLrBv+hwtK9u8WFM36Z5C0\n",
       "rAzTYn9HG9bYRuxiZcce8/wM/LyaaT48rC9tzbukx/xxnnT/PavOtrL1vDCsZ+BlB9jGCuBzRrX+\n",
       "qfIKv/N2A85f9ro9mb4omX/dMO5jyby/HWB7sZ+x51LREhL8JeO5zgz+mzGSbTWd4/XbknH53eB4\n",
       "K7WuTucDpbcii/Ijdx70dlk3XrSyiVnrrxpnOiaEe8edQv4sqrGI+6df68Q/9pneT6ygHbPCYxFa\n",
       "7RyKXNifsS5V3dad+Try3oz3r5jvaS96436C3r0+p/LnXkK7tVurzowXOYux4vd76PwfldWP7GXH\n",
       "/rOU+gZJS2N3XuNeWum1n/0ocrHeFs9DyTqrcgHjkwu6ci3duca9q6f6dWgXKY6rygJFi1EYoBK4\n",
       "O7e584g7iz2rpO/OVe5s60VRdZ5bHI/1vi2BvV00c3mP2V5DjeLRIOY8pUXglQ1zwvdaI9t/gz51\n",
       "Adr/lZFVhvai4VDp836XMRt5dZ2zMh9MhtNc1fS4SM8J8Ry7bjK9rJFGlXgs3ObVLSF/x2DPFp2U\n",
       "mg68yv5cFyTDr6C76ehAvHjgaPrA6fvce9eDyfyB4pExsejziPGkZ4LVKl/vI5b7lzUvT+1J/64W\n",
       "Krm3gomYdRyLCfM6CWM1aJ2xxdARlMeTSr+uRR6nZuAVLr4PZeOcokJqrDv3+a4F6Wi9Wae+Wscm\n",
       "Bpw/budj7h0n1DHxop7SaV7e0qtKfIRTWYXism3c4d5q0fkw/R/z02tdx3tRfNOrOG9YHqeoz1kr\n",
       "gAnpquy+ItwM1GlAAZ0NTsqa9Jetv9b+6ON84J3uY2rFLgPweo+8S6U3AM8APgysnwRFz6YzOIsO\n",
       "oTh/75plBNRV+V8Lx3TduoCT1iDl5MOQPhvxAuBl6YXDnV81nJ4uXtRX+Hsons/W4y58KhhzblHk\n",
       "zt3FkzjL6/sk893F4K2MyqwT1vekGV+n9zPQ6og5Hl8ZZKGQ0/Xdkkllz5JMDZLjVWVtQr9f7qUN\n",
       "K35aMq4uo/pZp5PVYVAEqtbOPzq07sLuLLFhdw4xAuFcUxZoN6F1Y+LOrU39Xl60kh1PX14yOvn1\n",
       "49eeNNLw3i3tv+1FK/JBXADsOMWvubU0neO1Nu0o+iLvbE0z6UyDA6DyQb1jcMMQ11VlE5JuQNz5\n",
       "0BjvmFJfp+gSYrxFTlC0NDyszzx54LUX2QPQB1CV81Gng8UquzBYa9OmpfspVv7vugN2Hzgn+mym\n",
       "eEuoUepRtCPLrvzcW+d6Hc+PpZ0z9zGf4ZTSTHpNB17PpejEchad/e3IcD0fhnoynQ+8ZUjrquTO\n",
       "9b2KTsa4zsfcB+p5vNe67qtRtLc1nb1SLw8D5+TG9B5dNnE8+9Wdc5Ni3UnHvSNXPDYnT++8t4JW\n",
       "p46DrHc3b/cAL+XSqiB5a0ZZ9uQ5XnW6YoklAgPHFqEYcZm4AWg68HoUuCpUdqxb90AG5M5leaXe\n",
       "ca7v/DHUJVpWrUBRAT/WmbmYot7OIMFCrAicP0omtSLjL9Kc7G4CSOv/eNGdyTC6SZFu+1HUz4Gi\n",
       "D7J+xeoyvcUcr13C+wVVM0bhOnEotLqDkRKhiXoDGzLzUK93qtebEqlkxlcoWiQucG/1OTPoOuL/\n",
       "42b3wZ4TOh3E7++OmTFTFa9FmmfG1hSdFK8O/Jc7b5zgJDXOzNzdh17jsenK9dOh3pRIL2tRPIlh\n",
       "PDm6N1G0nvznoaRo6tmf0FBDQZfIhFkKRU8BsOwFXaPUeI7XMIvARCYbM/5GKMIf67Fuxg7AM905\n",
       "a5hpExGpKzzy7M5l+Zo9qhwvBV4iQ2TGK4BfwtgDLxGRySB0qbRMVHgvM6rAq+nK9V9ueHsiTYs9\n",
       "OasxgohMacty0DVKTQdeY+3PSGSq+Et4H/RRPiIisgxoOvAab2eYIpNa6BT4Eobbea2IiEwTTbdq\n",
       "HEbv4SKTmnvrOYsiIiIdJqIDVREREZFlUtOB16R+NqOIiIjIKCnwEhEREWlI04HXUB+ALCIiIjKV\n",
       "KMdLREREpCEKvEREREQa0nTgpd68RUREZJnVaODlTjMPhhQRERGZhJrO8RIRERFZZinwEhEREWlI\n",
       "38DLzI41szvM7LIe83zTzK41s0vMbNvhJlFERERkeqiT4/VdYI+qiWa2ENjU3TcD3g0cPaS0iYiI\n",
       "iEwrfQMvdz8PuK/HLHsBx4V5zwdWN7O1h5M8ERERkeljGHW81gduTj7fAswZwnpFREREppVhVa63\n",
       "7LO6jRARERHJzBzCOpYAc5PPc8K4LmZ2ePJxsbsvHsL2RURERMbFzBYAC0a+Hff+mVNmNg843d2f\n",
       "VzJtIXCwuy80s/nAEe4+v2Q+d/c8Z0xERERk0hlV3NI3x8vMTgB2AdY0s5uBzwLLA7j7Me5+ppkt\n",
       "NLPrgEeAA4edSBEREZHpoFaO11A2pBwvERERmSJGFbeo53oRERGRhijwEhEREWmIAi8RERGRhijw\n",
       "EhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGR\n",
       "hijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8R\n",
       "ERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmI\n",
       "Ai8RERGRhijwEhEREWmIAi8RERGRhijwEhEREWmIAi8RERGRhvQNvMxsDzO72syuNbOPlUxfYGYP\n",
       "mNlF4fXp0SRVREREZGqb2Wuimc0AjgR2A5YAF5jZae5+VTbrr919rxGlUURERGRa6JfjtRNwnbvf\n",
       "6O5LgROBvUvms6GnTERERGSa6Rd4rQ/cnHy+JYxLObCzmV1iZmea2ZbDTKCIiIjIdNGzqJEiqOrn\n",
       "QmCuuz9qZq8GFgGbjztlIiIiItNMv8BrCTA3+TyXIterxd0fSoZ/ZmZHmdka7n5vvjIzOzz5uNjd\n",
       "Fw+cYhEREZEhM7MFwIKRb8e9OlPLzGYC1wCvAG4F/gi8Oa1cb2ZrA3e6u5vZTsDJ7j6vZF3u7qoL\n",
       "JiIiIpPeqOKWnjle7v6UmR0M/ByYAXzH3a8ys4PC9GOAfYD3mtlTwKPAvsNOpIiIiMh00DPHa6gb\n",
       "Uo6XiIiITBGjilvUc72IiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDRE\n",
       "gZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiI\n",
       "iDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4\n",
       "iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhIQxR4iYiIiDREgZeIiIhI\n",
       "QxR4iYiIiDREgZeIiIhIQxR4iYiIiDSkb+BlZnuY2dVmdq2Zfaxinm+G6ZeY2bbDT6aIiIjI1Ncz\n",
       "8DKzGcCRwB7AlsCbzWyLbJ6FwKbuvhnwbuDoEaVVJoiZLZjoNMjYaf9Nbdp/U5f2nZTpl+O1E3Cd\n",
       "u9/o7kuBE4G9s3n2Ao4DcPfzgdXNbO2hp1Qm0oKJToCMy4KJToCMy4KJToCM2YKJToBMPv0Cr/WB\n",
       "m5PPt4Rx/eaZM/6kiYiIiEwv/QIvr7keG+NyIiIiIsuMmX2mLwHmJp/nUuRo9ZpnThjXxcwUkE1R\n",
       "ZvbZiU6DjJ3239Sm/Td1ad9Jrl/g9SdgMzObB9wKvAl4czbPacDBwIlmNh+4393vyFfk7nmumIiI\n",
       "iMgypWfg5e5PmdnBwM+BGcB33P0qMzsoTD/G3c80s4Vmdh3wCHDgyFMtIiIiMgWZu0r/RERERJow\n",
       "8p7r63TAKs0ys7lmdo6ZXWFml5vZB8L4NczsLDP7s5n9wsxWT5b5RNiHV5vZK5Px25vZZWHaNybi\n",
       "+yyrzGyGmV1kZqeHz9p/U4SZrW5mp5jZVWZ2pZm9UPtvagj74orwu//AzGZp301eZnasmd1hZpcl\n",
       "44a2v8L+PymM/4OZbdg3Ue4+shdF8eR1wDxgeeBiYItRblOvWvtlHWCbMLwKcA2wBfBV4KNh/MeA\n",
       "L4fhLcO+Wz7sy+to55b+EdgpDJ8J7DHR329ZeQEfAv4HOC181v6bIi+Kvg/fHoZnAqtp/03+V/j9\n",
       "rwdmhc8nAftr303eF/BSYFvgsmTc0PYX8D7gqDD8JuDEfmkadY5XnQ5YpWHufru7XxyGHwauouiP\n",
       "rdUZbnh/XRjeGzjB3Ze6+40UB+MLzWxdYFV3/2OY73vJMjJCZjYHWAj8F+3uXLT/pgAzWw14qbsf\n",
       "C0VdWnd/AO2/qeBBYCkw28xmArMpGp5p301S7n4ecF82epj7K13XqcAr+qVp1IFXnQ5YZQKFFqvb\n",
       "AucDa3u7ReodQHwCwXp0diMS92M+fgnav035OvAR4OlknPbf1LARcJeZfdfMLjSzb5vZymj/TXru\n",
       "fi/wb8BNFAHX/e5+Ftp3U80w91crznH3p4AHzGyNXhsfdeClmvuTmJmtQhGhH+LuD6XTvMg31f6b\n",
       "hMxsT+BOd7+I7s6LAe2/SW4msB1F8cR2FK3BP57OoP03OZnZJsAHKYqh1gNWMbO3pvNo300tE7G/\n",
       "Rh141emAVSaAmS1PEXQd7+6Lwug7zGydMH1d4M4wvqyT3FvC+DnZ+NLOc2Wodgb2MrMbgBOAl5vZ\n",
       "8Wj/TRW3ALe4+wXh8ykUgdjt2n+T3g7A79z9npC78SPgRWjfTTXDOFfekiyzQVjXTGC1kDNaadSB\n",
       "V6sDVjNbgaLi2Wkj3qb0YWYGfAe40t2PSCadRlFRlPC+KBm/r5mtYGYbAZsBf3T324EHQ4ssA96W\n",
       "LCMj4u6fdPe57r4RsC/wK3d/G9p/U0L43W82s83DqN2AK4DT0f6b7K4G5pvZSuE33w24Eu27qWYY\n",
       "58qflKxrH+DsvltvoEXBqylazV0HfKLJ1gx6Ve6Tl1DUDboYuCi89gDWAH4J/Bn4BbB6sswnwz68\n",
       "GnhVMn574LIw7ZsT/d2WtRewC+1Wjdp/U+QFvAC4ALiEItdkNe2/qfECPkoRKF9GUal6ee27yfui\n",
       "KBW4FXiSoi7WgcPcX8As4GTgWuAPwLx+aVIHqiIiIiINGXkHqiIiIiJSUOAlIiIi0hAFXiIiIiIN\n",
       "UeAlIiIi0hAFXiIiIiINUeAlIiIi0hAFXiIiIiINUeAlIiIi0pD/D4oa4VYD9VuwAAAAAElFTkSu\n",
       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a109e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm0JVV5sPHnpbtphmYQwWZqRAMoGEYRkE+ljQShVTDG\n",
       "KM5Bl/JpCCjGGSMaFaMxolEQFRBxQIOGwAqKohKjURwYRIEgjgwyfA6IEBXk/f6offpWV5/p3ntO\n",
       "nXtvP7+1ap2qXbuqdtWue+57du2qisxEkiRJ47fepAsgSZK0rjDwkiRJaomBlyRJUksMvCRJklpi\n",
       "4CVJktQSAy9JkqSW9A28ImKDiLg0Iq6IiKsj4qQe+d4TET+IiCsjYu/xFFWSJGl+W9xvZmb+LiIe\n",
       "m5l3R8Ri4KsR8ajM/GonT0SsAnbKzJ0jYn/gVOCA8RZbkiRp/hl4qTEz7y6j6wOLgF82shwOnFXy\n",
       "XgpsHhHLR1lISZKkhWBg4BUR60XEFcCtwJcz8+pGlu2AG2rTNwLbj66IkiRJC8MwLV73ZeZeVMHU\n",
       "YyJiZZds0VxsBGWTJElaUPr28arLzDsi4j+AfYFLarNuAlbUprcvaWuICIMxSZI0b2Rms2Fp1voG\n",
       "XhGxJXBvZv46IjYE/hx4YyPb+cAxwDkRcQDw68y8tdv6xrEDGr+IODEzT5x0OTQz1t/8Zv3NX9bd\n",
       "/DauBqNBLV7bAGdFxHpUlyXPzswvRsTRAJl5WmZeGBGrIuJ64C7gqHEUVJIkab4b9DiJq4B9uqSf\n",
       "1pg+ZsTlkiRJWnB8cr2GccmkC6BZuWTSBdCsXDLpAmjGLpl0ATT3RGY7fd4jIu3jJUmS5oNxxS22\n",
       "eEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXE\n",
       "wEuSJKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKkl\n",
       "Bl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEkt\n",
       "MfCSJElqiYGXJElSSwy8JEmSWtI38IqIFRHx5Yj4fkR8LyKO7ZJnZUTcERGXl+GE8RVXkiRp/lo8\n",
       "YP49wMsy84qIWAZ8JyK+kJnXNPL9Z2YePp4iSpIkLQx9W7wy85bMvKKM/xa4Bti2S9YYQ9kkSZIW\n",
       "lKH7eEXEjsDewKWNWQkcGBFXRsSFEbHb6IonSZK0cAy61AhAucx4LnBcafmquwxYkZl3R8RhwHnA\n",
       "LqMtpiRJ0vw3MPCKiCXAp4GPZuZ5zfmZeWdt/LMRcUpEbJGZv+yyrhNrk5dk5iUzKrUkSdIIRcRK\n",
       "YOXYt5OZ/QoRwFnALzLzZT3yLAduy8yMiP2AT2Xmjl3yZWbaF0ySJM1544pbBrV4/R/g2cB3I+Ly\n",
       "kvZaYAeAzDwNeCrw4oi4F7gbOHLUhZQkSVoI+rZ4jXRDtnhJkqR5Ylxxi0+ulyRJaomBlyRJUksM\n",
       "vCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi\n",
       "4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQS\n",
       "Ay9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSW\n",
       "GHhJkiS1xMBLkiSpJX0Dr4hYERFfjojvR8T3IuLYHvneExE/iIgrI2Lv8RRVkiRpfls8YP49wMsy\n",
       "84qIWAZ8JyK+kJnXdDJExCpgp8zcOSL2B04FDhhfkSVJkuanvi1emXlLZl5Rxn8LXANs28h2OHBW\n",
       "yXMpsHlELB9DWSVJkua1oft4RcSOwN7ApY1Z2wE31KZvBLafbcEkSZIWmqECr3KZ8VzguNLytVaW\n",
       "xnTOtmCSJEkLzaA+XkTEEuDTwEcz87wuWW4CVtSmty9p3dZ1Ym3yksy8ZOiSSpIkjUlErARWjn07\n",
       "mb0bpyIiqPpv/SIzX9YjzyrgmMxcFREHACdn5lqd6yMiM7PZMiZJkjTnjCtuGRR4PQr4CvBdpi4f\n",
       "vhbYASAzTyv53gscCtwFHJWZl3VZl4GXJEmaFyYSeI10QwZekiRpnhhX3OKT6yVJklpi4CVJktQS\n",
       "Ay9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSW\n",
       "GHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJmrMi\n",
       "2DKCAyP8rpK0MPhlJmku+znwNeDDEy6HJI2EgZekOSeCRRHsDCwuSc+ZZHmkuSKCT0SQEav/NjTP\n",
       "GHhpnVG+rH4bwQXTXG6vCJaPq1zq6rnAdZMuhDRTJUD66wgePiDf0AFUBDsAR5bJeyLYdTZl1GQY\n",
       "eGnBiWD3CO5XAq2dS1qW2RsDT5zmKi8Hbolgox7biwhiiHItmeZ210nlOD+llrRdSbfVS/NC6ZN4\n",
       "JHAm8O0IHtAlz/rle+meCBb1WM/7Iri9lvTTRparI3hQBF+PYL0Izo/gqAjWH9W+aPQMvLQQfRf4\n",
       "ZRl/RwTLmhmGDYIaAdXuPbJ9Drgpgo/3Wc9zgD94eaC30rK4AriLWnCcyc1l9CMTKZg0fX9sTH8P\n",
       "IIK/imDTknZobf6fNFcQwRnAS4AtI3hE47toz9r4j4ADyjafBJxBFfBpjjLw0oISsUZLCcARwJ1l\n",
       "fFNg+zL+90OsK4B31ZKWl/QPR1SBQQS7AIcA2wDPqH2pNnWChpd32c7WtoYBVcviz2rTF9bG3wQQ\n",
       "wdJWS6R1WmnNzgj2meEqdiifW5Xvk08Bd5SWrhVUN4/cCLy006IewdJynh9VW8/psLrV7F2ZfBfY\n",
       "sM9292rsx34Rq7/7NGEGXlpoPl0b/5v6jEzuzOQmqub6rYZY1zLguNr0M0sfi+fB6n5izUsIdzRX\n",
       "EsHGtcluAdbPqVrDhilTqyLYLIIzIthmDOt+decxEV0u1b6TqtXrAQCZvAG4BnjIqMsh9bF/+fzO\n",
       "oIwlSNuxBFD3ArtlcgNTl803bizyXqrW3d8CLwaeVdJ/V4aOr1J9Z10OkMnx5fN3wBtq+T5QG98t\n",
       "giURfCCCY4BLgRsG7YPaYeClBaP2z/s1wJJMTqFqqgd4WC3rP0KVt/Sz6NVx/vja+JeBpzPVsZUI\n",
       "Ngd2BL7fKMfGtfGPUX2xAvwVsF8j7yG1yVMjOCKCDXqUZxKeQfXL++ZBGacjgi2Bk4DtIzgYeF2Z\n",
       "9Tngs8DZmWTmGv1bFgNvHmU5+pTv2baurdsieCTw9WkscijwY2BX4LpMrgHI5N9q8//QWOYE4OIy\n",
       "/nc9+oq+jupHyFo/fjJ5E7AIWJrJ0ZkEcHiZfSbwQuBfavt0Xa/+ZGpRlm+3cQ/VptrZlsPCHiB3\n",
       "hty8S/pZkAn5JwOWPwLyXsiAvLYsc0T5TMgX18YT8q8hH95IS8idyucPy3q3q81bDrleI/8u5fN9\n",
       "kMdBXtaY/6vyeTvkskkf57JP19bKt+kI13tql+OZA5Y5t+TbCDL65FsEudMsyjZUeRwW9lA7Dz5d\n",
       "Pi+CfGuf/M+pLXNhj3Ul5AMhTyjji8p0Qn4IcvdavjPLslFL22+aZe82nDzpYztfhnHFLbZ4aT66\n",
       "Dvg2VC1GpQ/GV6keQQBw04Dlb6X6lbgtU5euzqvNP6U2vlMmHwaur6V9rny+qaS/BCBzje1uT7kb\n",
       "D3hKVr9Ef1SmXwKcDOxdy78S2LyMbwncOUc64l9N1QIF8IoI9ozgzHLnaEZwRcTq/ZyOp89gmVPL\n",
       "513A/23OLK2XXwD+AvjBDNZPxBqXqunWOhDBAyN40EzWr3npo+XzEOA1ja4DdfVz4pONeR8qn9dk\n",
       "8tNM3pxJZPLHTH5a1r0z1Y1BdwJnUb6HMlffkU0m3xyyzN9uTNe/045jgSl3dD54mLvL54T5Hjk6\n",
       "rHtDvTWiy6+5Q4dYfuMBvwg7w+Fdtnsi5NJGvp1reZZD3gj5gTLvu93K3mxVgXxYl3mPaPm4BuTB\n",
       "kFuU6aeUcjwL8nLIk3sdqyHWvVVtfO+y3IvK532Q+9aP45D1FrV594N8fkn/Yy3PEdPY/+fVlvt8\n",
       "+dyqzNuts77y+b+NZc8p6VdM+u/DYfYDU63XJ0Bu0Djv3tIl/9Zl3tmQT4Vc3Jjfacla0WN7O9TW\n",
       "/5gu85dD7jGN8q9HdWVgWZf19CzHXB9Ys/UvIL9cPo8qab+H3Gd02yPHsR9RVj52EZGZOT+iUc1p\n",
       "tWdyLQV+35i9JJN7p7EOgMdTdWb9T2ALqr6Pv8nknj7Lb8xU363FmVO3jzfWTebUr7DOvEwigoOo\n",
       "OuCeWn6p3VeybU31i/mMzMGPUCjL7pHJlYPyDljPXpQOvMCJZYDqJoODgXOgZ/+zTTJXH4/O+t5Y\n",
       "lnkgVavZm6huPnhnr2WGKGP92P4wk526pK+hHOsdgGWZXD3EurfL5OYy/USqc+PiXstR9aP5YG16\n",
       "j0yuGrArmoNKnT+Kqn/UzpRzNIIXUPXP+ghwLXBo5tQztSL4S+BcYHkmt/VY918Cn8nsfq7Wzr/1\n",
       "euWZrXIzyx9hze+l+SKCE4B/KJOHMnX1oe6uTJZFsCfw63o9TX97Y4pbhoj4zqC6NHNVj/krqb5M\n",
       "Ly/DCW1Gjg6jHSCXj3h923VaJiAfBLl0luur95s6rnx2WmZyGus5ZbrL9FjPNl3SPlYr45umsa63\n",
       "dFpoyrJfG2KZpZDPKPm3mOW+XNirNavW4pOQB5V6eEWvVq+Sp19r4rtmWMYjar/aE3J9yKfXpjt9\n",
       "0n7Vbbt91rtpyfO+Wlq/8g8aDpnh/m0P+cnZ1KPDjM//vUrd/Qzyesh/65Ln2Fodb19L/wfId89y\n",
       "+0Gfvosj3M9O+Z836WM+g7KfOcTf3ltq+/mt2W2PHMt+DLHhR1P1RekXeJ0/qR1wGOHJMNWB/MAR\n",
       "rrPzx/CI8vnqWa7v8T0Cg4MgPzzNdQXkhmM4jksgN5nlOl4B+Y0y/gDI99C49FnmvbV2LL45orrq\n",
       "DO+HfECZd7+SdmOX5f69zFvaZ13N4X6zLOvTuqzzYshl5VzbkDUvS3SGXbusa3PIY8r8TWvpH60t\n",
       "9zvIlWX8e13W+2KqS6G/qaV9iqrz9EZD7tNRtWVfO+rz0mHg8f9IOfZnUV1a37dLniW1OtobchvI\n",
       "Pcv0mye9D0Pu56LaPpzUmBfd/kbKvPcP87cLuS3kFowhkKTqAnAU5H91+RvcAvKNkD8teTvpz4Jc\n",
       "b2bbI8dSB0NufMcBgdcFk9oBhxGeDFN9XD4+gnWt6PEP9w0Dluv8g+/6B0sVeH2/vs5JH7cx1UXn\n",
       "Tqq/q+3rjbX5AfmoxrH93xls51mQ+0H+a1nHRVStWR+A3LiRd3m3eqHqS1IPgncs08dCPhHySZCL\n",
       "60HKCI7PDo1973oe1MtWGzZv5Omkn95I7/TzubHzxU11J+qeJcjavPMPoLbMIyD/vss2Fw+xT/X8\n",
       "p076HByivI9lyKByPgxUfRiv7nWe1PJtVvJ9oFFnL5j0PkxjX9/WKPv7S/rujfRNSvoSyN/W0hf1\n",
       "WXfz3N94RGXuBIwH1LbzWcgtIT9T0k4q6SsbZXjHzLZJjuX4D7nxfoHXQcAvgCupnjS9W5s74DDC\n",
       "k4HsnKTvG8G66i0xP27+AZR/7s1/7PV/zlv2K+Okj1ULddH5AvzX2jG5s8w7qMuX25f6BB8HUl16\n",
       "ewrkYyCP7rL80AFCl/UvrdcLUy0392/k2wlygxEeo/qX64P75Hso1a/w5r6+izVbMC6bQRkWdfsH\n",
       "TRVwNrd3f8qjMLocm3o5vjHXz3HI1831v8VS70+bRv6kenTMwP2C/I9G3X6LFi4TjvDYBORfNvbh\n",
       "T3t8J/wp5Dsbaa/v/A2V9R3QOae7LL9WS/0My/yl+v8GyPfSaJVs/B2tMcxsm8xouYHrHXLj/QKv\n",
       "TYCNyvhhwHW9doCpDrsnAisnffKta0P5Q3tAn/m3Q74b8lKq5vYZ9Rli7buAdmtMb10bX1KW2bRs\n",
       "t5N+QGOdG9bm7T/pY9lSfa2q7fOr+32h1I7pk7usp1eQ1Ry6/mgasqz3lXVsCPnJtv4hT2dbVC1U\n",
       "vfb9csjdR1y2t0H+W59tvqCW9+CSFlQtSfW6XcyIWg1msS/rUfU/C9YO/A+bZNlqZXw15MW16e/M\n",
       "4NzYl6rl/1UD8t+/tv+Pm/S+z7JeD27UZ2e4pEvaQ7ukPbjPOf5D+jz7bBrl7Gz3lCHydrb9VKou\n",
       "CT+vpfUNjssVvHqcMtT5M+39GW6newdeXfL+GFjrH7YtXpMfyonXtQMoVSflhNyndpK+fYbb6fwy\n",
       "eTzVrf2LGn+M9eGBZZnOr69/Kp+3Qb6GqUs8nYeP3jPp49hifdVbADfrcuxeDfmkkrfTn+nUxjo2\n",
       "7HPs68Os+qdQteTU1/elSR+/HuX8Yrf9H/M2+53/y6genPlCyKsbdZnluJ4y7jIOsQ/dyn54bfx5\n",
       "Ey7f8Y1jVj+GA/txzuQ8gLxg0vUywuN3ce14vbGWvl8t/bCS9obGefCJPuf3K7odI6of4z0vV3bJ\n",
       "33k47cCbsyitlrXpZivY7cNvl7HU77Ab79fitRxWP5ZiP+Anbe6Aw5AVPfWP+/Qe8zsn5eLGSTr0\n",
       "H0dzXY20p0E+rssf5uWN6TMhr2mk/RDyu2X815M+li3X2+pjWcbPhvwK5C5d8j6r5Dme6k6/BzF1\n",
       "d19QtWh2grhOH7xLIXccZVnLMKPOrC0d081Y847MGbf0TWObT6ht7zFdzvuEvLvL8Ty/Nv+RJb31\n",
       "S1o9/qmu0foxou0spWp12r3bOd5jmZd0Kdv1XdK2LvmfRWlBpHpq/Hmd755Jn5uTGqgujX+aLv0v\n",
       "Ie9u/k2X6U/TO+j6I9Xl6E5LfP2Ze1uVtKH6XZXvrrdCnjiN/EsGnMMP7DJ/K8iby/jjIV8+scAL\n",
       "+ATVe9r+QPWSzecDRwNHl/l/A3wPuAL4b+CAHusZyw5M8+TaFvLpky5Hy/u8iCro6VwKOqOkH0p5\n",
       "IB+1XwRlOpjqINztD7Hn3SplvQn5+B7zN6f0x2HNJuDOsDO9+xok5fU868pQ/hENFRhAvqDXceuR\n",
       "fzEjDJBqX7JdtzfXhvIPfmR9zobY3iaN6WY9vb0x/84uee4tnyN7SOSQZb8e8mW1cryG0h+Q6sfA\n",
       "z0a0nQ819nezkn4EPV6XU8vb7SHE729Md1rCXtesg0mfj3N1oPoBt3UjbSnVZcpOS2Pnkvq+9XOz\n",
       "dryzlvbk6RxzyLtK/ufOcj+aXQ0+Rnl8EtUdyJ302qVXxnJetFh549mBaR741X98ky5LC/t6f6pf\n",
       "gt2+jI6un/hM3YW2Z235xfU8JW3j8gf3AshrG3k3pNbvYcgy/m3JfxLkX7Dmr6Jf9wgivM2+/zHt\n",
       "dswe2eL2Hwn57Ekfh/kw1OrnMqonpG/YmF9vtfkA5D216eNaLOdSqsdpLKHqkrC8MX8fyCtHsJ0t\n",
       "upy7V3X5h/nkkn87pp7bdmpJe0ot336s3YL/77Xx+nrXehq9w1B1Fkx1B+n6CB3IWxv/R+rPOVzB\n",
       "gLuxa3nXembiDMt8Rm2dj6f7Y2cMvEZ4knQO6LSeIUR1O/xJ4yjTCPet00n9EMhdmbo756v1L+su\n",
       "J9eDIT/YLVgqwdDqQLXLsmdA/g3k6WX6ts68IcvcCfi6dhymCuY2ZOpVMcdP+jjP9YGqtXAPqgc6\n",
       "duppzl72W5cHqs6/f91nfucl7PeHfEitPo+GPKfFcl7a72+6FsD8qJa2Za28nR9mx5d5SyDX77Ke\n",
       "zj/Eb5XPziXAbl0UXtqY3qS2nk5Xhc731lLITXr/c829J30uLOSBqf65u5fp/4D8TKMOjqnl37+k\n",
       "LaO6oSMZcct0bbsvY83Hv1xZPh9anbf0PO9nM6xTrwyqvZLhhcCuwPHAQZl8JYJ/Ar6QyUV9lntC\n",
       "Jhe2U9r+IlgKbJDJHWW6WZHHA/9cm942k58PerVKl+108r8NePWQxXt0Jl8dlKm86ubITD4xRN6l\n",
       "mWu9Hkh9RLBBJr+bdDk0exFsAPxvGR5J1bVjw3HVbwT7AXsBp0P1Cq5u3w+1/J3viVcAq6i+ey6o\n",
       "ZbmVqj/wVlSPHXoE8MhMvhHBJpncGcEHgYcCB2fy+wjeT9WtBaquLuv32n6zbBFslMndjbRfUL0S\n",
       "rO+yGq3yovnV51AEdwJ/DryS6oX2/fwM2GEcdRTBbVTnI52yrZ1nQq8MGl2EOZ7IcZpR7k+6/eJp\n",
       "RMBn94mO3znpfSjleVatTIsaZew2LK8tu4zqrpRda/Pvg1zZY1vd1vdNph7w2RwumfTxcXBYiAPV\n",
       "89iWlfFbIN9U/g6PYUQ3SNS21fy77vvCdqbuOpvu0Hnd1VfK55Nr62y+peJQploBO8P109in9cox\n",
       "W+PS5aTrdV0YKHeAQj63fC4t6RdRe3xKl+EXkBeNqUx71LazQ/c8jOX8WNdavO4CjgU+VJLOBw4H\n",
       "Hgd8sZZ1UyCBXYAVwHlU0fmRwL6Z43mB6SClhehFwPsbs54BPVuNjs3kX2axza8BB5bJv6d6MfTJ\n",
       "ZXop1S/wuq0zuXWm25M0WI+W671yhi9Kj+A44AXA7nR/+fDA1rUI3gH8XSN5Max+aX291er/AVt2\n",
       "Wc1jM7mkts7PUFpFsrRIjOpl0vUX1s90HRpOvdULurZQvp/q9YS7dVn8+ZmcOaZy7QN8N3OqbGvO\n",
       "t8Vr2Ch2ObW+BrX0jag6iAbkaUw9cbceXXdeAfGaLpH3Sc20FvblCV3K0W34IlXH2z8r058rn9uO\n",
       "oAyrO0/2mP88qjsRHwd5YVvnk4PDujyw5kOI68O0bxxi6gXhzaHTuvSHaaxrCVV/qs9T+nFRvd7p\n",
       "7VQd8zvfo82HLCdVv61ur6R6GC088sNhvAPV+0yTHne8lzwryvmyGeQ7Sv6eb6UYf5nJcax3wbV4\n",
       "RXAYVR+CLYFHAedldV15B+Brmaxo5D8KOAO4JpPdevyS/HPg61StPXWnUvVBWEzV+vP7zNG1hvXr\n",
       "jwXsUYa3AjvAGr8I3we8JP0lJy1Yte+HZwIfL+OvBO4Azs3kl0OsY33gR8B2jVkfzeQ5oyrrgDJs\n",
       "DfxjJs9rY3uajHLFJjK5b9JlGda44pYFFXhFsCfwVOCEkvRe4Jgy/jmqy2B7d1lus5zqpP5s4Gzg\n",
       "Pqom959n8r0yr9fBOho4DfjbTN47on2JUobbgc+Uz3uBlZk8tpbvDOAosMlcWldFsC1wUy3pKmDv\n",
       "TP5Y5gfVpbk/1pZZQnX5D6ouA53AZ4tMTht/qaW5zcBr4PpZDtwyINsXMjlkFtvYE/hxJr+J4EWw\n",
       "1pfTuzN56UzX39jWscC7GdCPobTknQi8sP6lKmndEsFWwG1dZl1IdadhxzKqQKv+fbFJ5lot+tI6\n",
       "bVxxy3qjXuEEPbA2/vLa+CqmOorebzYbyOTKTH5Txj9Qkn9Vy9K1g950lSDy3WU7fSPjTH6WyfMN\n",
       "uqR1Wya3l1bv5s03qxrTv6V6y0jHUoMuqT0LKfC6FKrLbZn8M3AI8JZMPkv1xXMxg58ZMl0PYeo5\n",
       "IJcBW0WwuDTrz0gEz2Sq5e7QWZZP0rrnJV3Sms/V2x+4HNglc/XlRkktWBCXGmu3qt6Uyfbj2MYQ\n",
       "ZTgEeB3wGJh+f6sITgZ+B7yqJL05k9ePtJCS1lkRXAD8HNgJeCzVgylvmGyppLlrXHHL4lGvsE0R\n",
       "PJoqUHlCSdp5gsW5iRJ0AUSwbybfHrRQrXXsuMYsn4UlaWQyedKkyyBp/l9q/ApTQddXMtd6mGeb\n",
       "bi6f15XPU6FqjYtg42bmCLLcJXkf1YNJ614PfGxcBZUkSZMxby811h77APAw4CfZeDdX2yLYOpNb\n",
       "IvgVsDmwiKk7h/6Fqnl/D6r+Fgd2WcU2mQPvzJQkSWPm4yTWWt/cfd1DBOsBdwIbDchaD8z2y+Rb\n",
       "Yy2YJEkaio+TqIlg3zJ67kQL0kN5Mu/FA7KtKPmWA4sMuiRJWvjmZeBF9XR6MvmrSRekjzvK56bA\n",
       "tsBzmTreJ2VyI0Amt82nVyhIkqSZm5eXGstlxtszecAo1jcOEewFXN68FBrBVpncPqFiSZKkIazT\n",
       "fbwiWJLJPWV8E+A3+IoLSZI0JutsH68IHgL8IYIDItgOOBnAoEuSJM03c/oBqhFsClxbJr9emzUn\n",
       "O9VLkiT1M2dbvCI4jKkO6nc0Zj+35eJIkiTN2pwLvCKICL4NXFhLfk/53K+8BHuST6iXJEmakTnX\n",
       "ub68bPqiMnkCcBbVexDJpJ3CSpKkddqC7VwfwW4RnBXB+uWF0S8H/ht4bCZvyeTGTNKgS5IkzXcT\n",
       "bfGKYAPoetnwaZn8aysFkyRJalhwLV4RPBPYtcfsz7ZZFkmSpDZMJPCK4DXAx4DLgDNLOf4M2Kh0\n",
       "nvcZXZIkacFp/TlepR/XW2tJN5f+W19uuyySJEltmsQDVF9fPtcD9gB+PIEySJIkta71zvXlBdc3\n",
       "Z7JdKxuWJEmapol1ro+IMyLi1oi4qk+e90TEDyLiyojYu3c+ti6j+8ygrJIkSfPaMJ3rzwQO7TUz\n",
       "IlYBO2XmzsCLgFP7rOsfgW9ncuu0SilJkrQADAy8MvO/gF/1yXI41dPlycxLgc0jYnmPvM8FHjzd\n",
       "QkqSJC0Eo3icxHbADbXpG4Hte+R9B7DVCLYpSZI074zqrsZm57OuPfYzeeWItidJkjTvjCLwuglY\n",
       "UZvevqStJSJOrE1ekpmXjGD7kiRJsxIRK4GVY9/OMI+TiIgdgQsyc/cu81YBx2Tmqog4ADg5Mw/o\n",
       "km8st2VKkiSN2rjiloEtXhHxCeAgYMuIuAF4A7AEIDNPy8wLI2JVRFwP3AUcNepCSpIkLQStP0C1\n",
       "lY1JkiTNwsQeoCpJkqTRMPCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuS\n",
       "JKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6S\n",
       "JEktMfAsLOXrAAAHeUlEQVSSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuS\n",
       "JKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLVkYOAVEYdGxLUR\n",
       "8YOIeFWX+Ssj4o6IuLwMJ4ynqJIkSfPb4n4zI2IR8F7gYOAm4FsRcX5mXtPI+p+ZefiYyihJkrQg\n",
       "DGrx2g+4PjN/kpn3AOcAR3TJFyMvmSRJ0gIzKPDaDrihNn1jSatL4MCIuDIiLoyI3UZZQEmSpIWi\n",
       "76VGqqBqkMuAFZl5d0QcBpwH7DLrkkmSJC0wgwKvm4AVtekVVK1eq2XmnbXxz0bEKRGxRWb+srmy\n",
       "iDixNnlJZl4y7RJLkiSNWESsBFaOfTuZvRu1ImIx8D/A44CbgW8Cz6h3ro+I5cBtmZkRsR/wqczc\n",
       "scu6MjPtCyZJkua8ccUtfVu8MvPeiDgGuAhYBJyemddExNFl/mnAU4EXR8S9wN3AkaMupCRJ0kLQ\n",
       "t8VrpBuyxUuSJM0T44pbfHK9JElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6S\n",
       "JEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCS\n",
       "JElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGX\n",
       "JElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqycDAKyIOjYhr\n",
       "I+IHEfGqHnneU+ZfGRF7j76YkiRJ81/fwCsiFgHvBQ4FdgOeERG7NvKsAnbKzJ2BFwGnjqmsmpCI\n",
       "WDnpMmjmrL/5zfqbv6w7dTOoxWs/4PrM/Elm3gOcAxzRyHM4cBZAZl4KbB4Ry0deUk3SykkXQLOy\n",
       "ctIF0KysnHQBNGMrJ10AzT2DAq/tgBtq0zeWtEF5tp990SRJkhaWQYFXDrmemOFykiRJ64zFA+bf\n",
       "BKyoTa+gatHql2f7kraWiDAgm6ci4g2TLoNmzvqb36y/+cu6U9OgwOvbwM4RsSNwM/B04BmNPOcD\n",
       "xwDnRMQBwK8z89bmijKz2SomSZK0TukbeGXmvRFxDHARsAg4PTOviYijy/zTMvPCiFgVEdcDdwFH\n",
       "jb3UkiRJ81BkevVPkiSpDWN/cv0wD2BVuyJiRUR8OSK+HxHfi4hjS/oWEfGFiLguIj4fEZvXlnlN\n",
       "qcNrI+KQWvrDI+KqMu/dk9ifdVVELIqIyyPigjJt/c0TEbF5RJwbEddExNURsb/1Nz+Uuvh+Oe4f\n",
       "j4il1t3cFRFnRMStEXFVLW1k9VXq/5Ml/RsR8cCBhcrMsQ1UlyevB3YElgBXALuOc5sOQ9XL1sBe\n",
       "ZXwZ8D/ArsDbgVeW9FcBbyvju5W6W1Lq8nqmWku/CexXxi8EDp30/q0rA3A88DHg/DJt/c2TgerZ\n",
       "h88v44uBzay/uT+U4/8jYGmZ/iTwPOtu7g7Ao4G9gatqaSOrL+AlwCll/OnAOYPKNO4Wr2EewKqW\n",
       "ZeYtmXlFGf8tcA3V89hWPwy3fD65jB8BfCIz78nMn1CdjPtHxDbAJpn5zZLvI7VlNEYRsT2wCvgQ\n",
       "U49zsf7mgYjYDHh0Zp4BVV/azLwD628++A1wD7BRRCwGNqK68cy6m6My87+AXzWSR1lf9XV9Gnjc\n",
       "oDKNO/Aa5gGsmqByx+rewKXA8py6I/VWoPMGgm1Z8zEinXpspt+E9duWdwGvAO6rpVl/88ODgNsj\n",
       "4syIuCwiPhgRG2P9zXmZ+UvgncDPqAKuX2fmF7Du5ptR1tfqOCcz7wXuiIgt+m183IGXPffnsIhY\n",
       "RhWhH5eZd9bnZdVuav3NQRHxROC2zLyctR9eDFh/c9xiYB+qyxP7UN0N/up6ButvboqIPwFeSnUZ\n",
       "altgWUQ8u57HuptfJlFf4w68hnkAqyYgIpZQBV1nZ+Z5JfnWiNi6zN8GuK2kd3tI7o0lfftGeteH\n",
       "52qkDgQOj4gfA58A/iwizsb6my9uBG7MzG+V6XOpArFbrL85b1/gvzPzF6V14zPAI7Hu5ptRfFfe\n",
       "WFtmh7KuxcBmpWW0p3EHXqsfwBoR61N1PDt/zNvUABERwOnA1Zl5cm3W+VQdRSmf59XSj4yI9SPi\n",
       "QcDOwDcz8xbgN+WOrACeU1tGY5KZr83MFZn5IOBI4EuZ+Rysv3mhHPcbImKXknQw8H3gAqy/ue5a\n",
       "4ICI2LAc84OBq7Hu5ptRfFf+e5d1PRX44sCtt3BHwWFUd81dD7ymzbsZHHrWyaOo+gZdAVxehkOB\n",
       "LYCLgeuAzwOb15Z5banDa4HH19IfDlxV5r1n0vu2rg3AQUzd1Wj9zZMB2BP4FnAlVavJZtbf/BiA\n",
       "V1IFyldRdapeYt3N3YHqqsDNwB+o+mIdNcr6ApYCnwJ+AHwD2HFQmXyAqiRJUkvG/gBVSZIkVQy8\n",
       "JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqyf8Hp1p7e+uGy68AAAAA\n",
       "SUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1084fd9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHUZJREFUeJzt3XuYXVWZ5/HvSxJuAblqCEkwIKBA2xpFCIgahUFIt8EL\n",
       "KGo7Dk4rjyODgq2IYyvtdKuN3S0iypPHAQVULsqIOEaFRkLTrXInhqvQogYwQUFucod3/li74HBy\n",
       "qk6lcs6qOpXv53n2k7P3XmfvdWpVqn619tprR2YiSZKk/ltvvCsgSZK0rjB4SZIkVWLwkiRJqsTg\n",
       "JUmSVInBS5IkqRKDlyRJUiUjBq+I2DAiLouIayPihoj47DDlToyIWyJiWUTM609VJUmSBtvUkXZm\n",
       "5iMR8drMfCgipgL/HhH7ZOa/D5WJiIXAjpm5U0TsCZwMzO9vtSVJkgZP10uNmflQ83J9YApwT1uR\n",
       "RcBpTdnLgM0jYkYvKylJkjQZdA1eEbFeRFwLrAIuzswb2orMAla0rN8OzO5dFSVJkiaH0fR4PZWZ\n",
       "L6WEqVdHxIIOxaL9bT2omyRJ0qQy4hivVpl5X0T8ANgdWNqy6w5gTsv67Gbbs0SEYUySJA2MzGzv\n",
       "WFprIwaviNgaeCIz742IjYD/AvxdW7HzgSOAsyJiPnBvZq7qdLx+fAD1X0Qcl5nHjXc9NDa232Cz\n",
       "/QaXbTfY+tVh1K3HayZwWkSsR7kseUZmXhQRhwNk5uLMXBIRCyPiVuBPwGH9qKgkSdKg6zadxHLg\n",
       "ZR22L25bP6LH9ZIkSZp0nLleo7F0vCugtbJ0vCugtbJ0vCugMVs63hXQxBOZdca8R0Q6xkuSJA2C\n",
       "fuUWe7wkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmS\n",
       "KjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi\n",
       "8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAl\n",
       "SZJUicFLkiSpEoOXJElSJSMGr4iYExEXR8T1EXFdRBzZocyCiLgvIq5plk/0r7qSJEmDa2qX/Y8D\n",
       "R2XmtRGxCXBVRFyYmTe2lbskMxf1p4qSJEmTw4g9Xpm5MjOvbV4/CNwIbNuhaPShbpIkSZPKqMd4\n",
       "RcRcYB5wWduuBPaOiGURsSQidu1d9SRJkiaPbpcaAWguM34H+GDT89XqamBOZj4UEQcC5wE797aa\n",
       "kiRJg69r8IqIacC5wDcy87z2/Zn5QMvrH0bEVyJiy8y8p8OxjmtZXZqZS8dUa0mSpB6KiAXAgr6f\n",
       "JzNHqkQApwF3Z+ZRw5SZAdyVmRkRewDnZObcDuUyMx0LJkmSJrx+5ZZuPV6vBP4K+EVEXNNs+ziw\n",
       "HUBmLgYOBt4fEU8ADwGH9rqSkiRJk8GIPV49PZE9XpIkaUD0K7c4c70kSVIlBi9JkqRKDF6SJEmV\n",
       "GLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4\n",
       "SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIk\n",
       "SarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJU\n",
       "yYjBKyLmRMTFEXF9RFwXEUcOU+7EiLglIpZFxLz+VFWSJGmwTe2y/3HgqMy8NiI2Aa6KiAsz88ah\n",
       "AhGxENgxM3eKiD2Bk4H5/auyJEnSYBqxxyszV2bmtc3rB4EbgW3bii0CTmvKXAZsHhEz+lBXSZKk\n",
       "gTbqMV4RMReYB1zWtmsWsKJl/XZg9tpWTJIkabIZVfBqLjN+B/hg0/O1WpG29VzbikmSJE023cZ4\n",
       "ERHTgHOBb2TmeR2K3AHMaVmf3WzrdKzjWlaXZubSUddUkiSpTyJiAbCg7+fJHL5zKiKCMn7r7sw8\n",
       "apgyC4EjMnNhRMwHTsjM1QbXR0RmZnvPmCRJ0oTTr9zSLXjtA/wb8AueuXz4cWA7gMxc3JQ7CTgA\n",
       "+BNwWGZe3eFYBi9JkjQQxiV49fREBi9JkjQg+pVbnLlekiSpEoOXJElSJQYvSZKkSgxekiRJlRi8\n",
       "JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmS\n",
       "JFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmq\n",
       "xOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVEnX\n",
       "4BURp0bEqohYPsz+BRFxX0Rc0yyf6H01JUmSBt/UUZT5GvAl4PQRylySmYt6UyVJkqTJqWuPV2Ze\n",
       "CvyxS7HoTXUkSZImr16M8Upg74hYFhFLImLXHhxTkqSnRbB7BJ+OYPsIpkewSwTPb/Z9L4LPj3cd\n",
       "J6IIpkawfsv69Nb1NTiOY8J7ZDSXGru5GpiTmQ9FxIHAecDOnQpGxHEtq0szc2kPzi9J6oEIIpOs\n",
       "eL71gA2AxzN5osP+7YFftW3+27YyXwEWNa9/mMlP+lTdnopgG8rvyz2BG4BPZ3J2BNMyeTyCANbP\n",
       "5NG1OMdRwL80r38JfBn4IvBABGcDv8wcObBGsD+wO/CxCN4NnDf0PRLBJsDZwPGZXDLWek4UEbEA\n",
       "WND382R2/z8WEXOB72fmi0dR9jbg5Zl5T9v2zEwvSUrSBBDBLsB/pYzh/R3wTuAM4B7gAOAq4HLg\n",
       "5cC5wDsyeWwtz/lc4A+ZZAQfB/5hDd7+34HTgJnAW4BbgPcBBwH/DOwF7N2UnZ7JQ2tT136JYGPg\n",
       "vcAJIxR7imeuSH0WeKDZdjFwWya/73KOGcBlUHoE2/yUZ75OrV6aybK240yB1QNx43jgox2OfQhw\n",
       "V6cgPWj6llsys+sCzAWWD7NvBs8EuD2AXw9TLkdzLhcXF5d1ZYGcBrkd5JGQB0HO6tN5ZkN+DnK7\n",
       "Zn0OZI5huQryuZBzm2NuAbkh5HshXwT5Z5DRdu6NII8Z4ZhLR9j3WcgpI3yurSE/Brk+5BTIVzbv\n",
       "exjySsid1/Lr9lzIN0BObT5re/3e15TbDfLgLnXdscP7FzVfv4D8SLPt+y37V3Rpj281x94Q8tuQ\n",
       "j7btX9hy/imQGzSvt2i+Bw5pK38f5N3N69Nbtn8NcgPIf4BcCXl/y77tIJd3qNulkIdCHjre/8/G\n",
       "3v5kX447ihOfCdwJPAasAN4DHA4c3uz/AHAdcC0l7c6v+QFcXFxcBnGBPGGYX6YfW8vjrg/5Jsi/\n",
       "b453wTDn+VfImZBLIL/U/OJv/ojOT0KeCfm8Zn3bLgGgffkM5A8gf9q2/diW1wf06es6G/KRlvOc\n",
       "QlsYbCk7jRJ6p0PuAvn5ZvvGkF8e5rNdN8qvwSdbXt/b8vo2yOeswefZvanfzOaz/abtPFdDPtm2\n",
       "7VeQG67BOaZ0OMbQMmOY96zXYdtOkI/x7PA4tLwBcodmGXXdxvf/KNmX4w76B3BxcXGpsTThY1fI\n",
       "11F6eKYzQg/HMMfYBvL4tl9I+zT7ngf5oWbb37a8ZwPIvSCfQ+k1Geqt+jrkHyHnt5Q9ephfoOdC\n",
       "zoL8PORTzba5Y/garN8cZ4emLmdCfhFyS8i3tAWr1mU3yGmV2yso4a+1Hi+GvGmUwSkp4XUm5I8g\n",
       "L28NTM3xvw55J+Q1kDO6HOu2TmFlLT/jcS3HfxHk1LU41haQm7asb76m399tx9ufEj535JletNbl\n",
       "nTW/H8b2Gch+HHdUY7x6wTFeksZLBFMyebJ5fS7w58B/AO8G3gYsy+TmEd6/A/CfXU5zSCbfGeb9\n",
       "syhXDe5q2fzaTJZ2KPth4J+6nKuTzwMfaV4fCGwEfA+YksnjYzjemEQwjWZcUGa9gfrDiWAecA6w\n",
       "4zBF5gHXNK/fCOwAXA/8LJMHxnC+KZTxWG8FLslkZXMTQd/aofZNEWuquVFgL2Ar4K9pboZoPEoZ\n",
       "K3ZNJpeOQ/WG1a/cYvCSNClFcCTwBmC/EYpdC7y0eX0KsDXlTrP/B9wNfBt4E2Wg82nAEuA+4CJ4\n",
       "+pfopyi/rN/dctwzgSMyuSeCkyhDMobsmcnlXer+RuC7zepK4NDm/I9QBpavoAS56U1d5zdl35rJ\n",
       "t0c69roqgs0ogfTCTO4e7/qs6yL4LPCxDrtmAfsAN2fbYP/aDF6S1EHz1/QbKMHnTuBI4OuUO/aG\n",
       "nEPpgfgd8I+UQLV1Jr9o7rR7B+Uus6uBl7Wd4lvAFZmr34XW2tMQwb7Af6P0oOzWVnQRsAVwcSYr\n",
       "xvpZh9P0qLwk8+meG2kgNHOKvYXyR8RXOxR5J+WPjE0y+XrFqhm8JGlIBLOBT1KmPZjTbL6bcilj\n",
       "yDuAszN5qnnPqC7HRLAp8FrKPIeXZ3L7GOr3QuCwpg7vnGiXUKSJqPkjam/KH0DHUHqTW30L+HAm\n",
       "K4d5/xzg/cD1mXxz6JhjvQxr8JI0MJpxPhsBDwFLKfNAfTlHOQ9UBPMpP4C/ACykXE77QiZHR3A0\n",
       "Zd6mVttn8usINgc+AXwpk9/05MNIGhdNT+5JwBRKb/LQjPu/Bb4C3Ab8DNgYeDurB7W/4Znxkltk\n",
       "cm9z3K2Ah4GHRwplBi9JY9bPwbfNpYKngJ0ol/h2BjYfpvjemfyswzGmAhsC28Lwg9zbbDDaICdp\n",
       "8EWwM3AsJYR1clsmO0TwCuB04EVt+5dSwlunCWShBLjHnrkRx+AlaQ003fZQBmc/j/IX4lPAEcAy\n",
       "4HXAfS13+61ROGuO/13KzOHtHgbOAqYBRwO7Uh5V8pJm/3LgRODfgN9TZktv9RHgJ5SxUpdk8tsI\n",
       "DqOMvzpppDsQJU1+EUyn/IF3KHApZT7Rx1vvHI3geZSbYXah3Ll6JeXxR1B+Fh0MvJLys7DVcuAR\n",
       "iFcYvKR1XNMz9F3gL5tNP6AMGl8IY76b7SpKL9WmlB84Q48GS+AvKGOndgReAHyGEt6+CPzPptwl\n",
       "lEuCmcn5I9R9CuXS43AP6J3enPuKoXFZktRvzc+macDrKXdU/k2zB4OXNKBaep9eQ/kr7XuZZBOk\n",
       "DqJMD/AI5dlqSyiX3Z7M5JHmQbTPp0xRMBSKllDC1khWUcLT3EwejWAjePrZa5tSfsgk8GnKdAgX\n",
       "Afs27z2F8my8kTwA7JTJqi7lVtNcnnwO5QHImwJbZa7W6yVJ48ZLjdIEFsFc4BOZ/HUE67X22ETw\n",
       "TuAbPTrVLcBeQ/MQNX+p7UuZpqBfkzNOp1w63IwycP1NwD6Z3NmP80nSRGDwknqg6Xl6KeV248ci\n",
       "eAElTNwM/LzTTOKjOOZelOeUtjsEuJUytmAx8GVKD89MypxRv6dMwnks5TJeUnq+TqbcrfNWyriF\n",
       "6yhjE87xEpwk1WHwksao6bF5FeUy3fGjeMvumVzVdoyhweHDzYL+KPBmypirL1IGc+7f7PtuJm8e\n",
       "Q9UlSeOkX7llvV4fUOqnCDaO4GsRfD6C6RHMj+B5EUQEMyOYGsGbI9gtgqUR3AY8CPyQErpOBV7Y\n",
       "csjFwIaZBKVHCuDKCP4zghdFcHQESXl2237ABS3vfZhy593MTDbMZEl5/ikfyuT1lOcBvsXQJUka\n",
       "Yo+XJpwIdsvk+maSu7nABpQHFM+jBKg1cSVlWoPFlMnynhzF+d9OmSG51T9lPv0AYknSJOelRq0T\n",
       "IjiV8qiVkWxHmZdqNnADsA1lQr0fA1sCZ1OmR7gqkyfWoi7PBx4d7vEUkqTJy+ClgRTBn1NmM9+a\n",
       "8ky9S4FD2qcgiGAHSq8WwHsolwSXUh50/CRlGoZNMjs+RFWSpJ4yeGngNIPaH6TMJ3U1cOAo3rZX\n",
       "Jj/va8UkSeqiX7llaq8PqHVDBNsAb6TczXcu5YHIh1KmSRiytPl35tCjaJqHnv4j5RExe1LmhloA\n",
       "HJvJ52rUXZKk8WKPl0Ylgudkcn8EC4CLuxS/ijJ1wyrgwEyu73f9JEnqJXu8VE3TK3Us8Pdt24c8\n",
       "TJm9/EIggFnAKyizp/vYF0mShmGPl54lgr2B/2jZdFfz7+GUhzP/ApjnDOqSpMnMHi/1VfOw5vdQ\n",
       "5rv6A7BNhzmvDM6SJK0Fg9c6rhkk/7uWTVdS7izsOtGoJElaMwavPohgS8qdehsCOwGnZ3LbCOVn\n",
       "Atu2Px+wnyLYAvgasEOz6Qzg6Ez+UKsOkiStaxzj1SPN4222At5FGZg+pUOx4zM5pim/CNi1KTc0\n",
       "iP1SykShZJIRzAK+CawEvprJRW3nnALkSOOtIghgc+D+oV6sZtstwAsoA+W3yuThsXxuSZImIydQ\n",
       "rSCCGJpvqm37epTnBT4KTM/kgQg2Bo4EtgA+2vaWK4BXA08BTwAnAh9o2X8vJQwNuaopc9owVbsJ\n",
       "eBFlcPvRlEfk/KytzLHArcB84MPDHOe3zft2A/4MmOolRUmSVmfw6qGmp2gKJXz8L+ANwLRm903A\n",
       "LymX4W4Abh7FIS8BPgP8ZKRnA0ZwCHA68BPKswXvB55o6YnaijKwfTFwPXB3ZnlYcwQ/ojx/cPvm\n",
       "cA8CPwBWAAdTHibd6mbghc3r/YGHKHcmzmjWX53JpaP4bJIkrXMMXmt0LqZTLqEFJay8BDiZ0mP1\n",
       "MKuHlD9RLumdCyzh2ZcJHwQWAo9RHsC8NbA3cB5wARC1plZoLhE+lxLWVpsvK4INM3lkFMdZz+kg\n",
       "JEkansFrVOfgvcDnKAGp3VOU8PUBymNtTqBcemOYy4s7ALPsFZIkad1j8Brx2GxE6YHan3L57n2U\n",
       "2dQvAP400h2FkiRJ7ZxAtYMI3gq8AzgI+CGwZSZ/HN9aSZIkdbZetwIRcWpErIqI5SOUOTEibomI\n",
       "ZRExr7dVHDpHqWsEh0TwuwgSOBvYDPgS8BeGLkmSNJF1DV6Uu/sOGG5nRCwEdszMnSiX+E5e00pE\n",
       "EBFsEsF6ETw3ghdHcFEEObQATzb/foMy0P0MYG4mr83kyE7jtCRJkiaSrpcaM/PSiJg7QpFFNPNP\n",
       "ZeZlEbF5RMzIzFXDvaEZuH4vZWb3beDpGdt/T7lrb8illDsQVwFHUOafuiiT33SrtyRJ0kTTizFe\n",
       "syhzSQ25HZhNCUvPEsG/AEd1OMbvgP2A1wG/AK4YZib1y9a6tpIkSeOkV4Pr20f9D3fZ7yjgR8D7\n",
       "KZcLHwemZLKy2X9Dj+ojSZI04fQieN0BzGlZn91s63S6/w1PPkWZtX1pZi7twfklSZLWSkQsABb0\n",
       "/TyjmcerGeP1/cx8cYd9C4EjMnNhRMwHTsjM+R3KTZhHBkmSJI1k3ObxiogzgdcAW0fECuBTNM81\n",
       "zMzFmbkkIhZGxK2UR+8c1utKSpIkTQaTYuZ6SZKkXupXbhnNPF6SJEnqAYOXJElSJQYvSZKkSgxe\n",
       "kiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJ\n",
       "kioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRV\n",
       "YvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqqRr\n",
       "8IqIAyLipoi4JSKO6bB/QUTcFxHXNMsn+lNVSZKkwTZ1pJ0RMQU4CdgPuAO4IiLOz8wb24pekpmL\n",
       "+lRHSZKkSaFbj9cewK2Z+evMfBw4CzioQ7noec0kSZImmW7BaxawomX99mZbqwT2johlEbEkInbt\n",
       "ZQUlSZImixEvNVJCVTdXA3My86GIOBA4D9h5rWsmSZI0yXQLXncAc1rW51B6vZ6WmQ+0vP5hRHwl\n",
       "IrbMzHvaDxYRx7WsLs3MpWtcY0mSpB6LiAXAgr6fJ3P4Tq2ImArcDOwL3AlcDry9dXB9RMwA7srM\n",
       "jIg9gHMyc26HY2VmOhZMkiRNeP3KLSP2eGXmExFxBPBjYApwSmbeGBGHN/sXAwcD74+IJ4CHgEN7\n",
       "XUlJkqTJYMQer56eyB4vSZI0IPqVW5y5XpIkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmS\n",
       "JFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmq\n",
       "xOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInB\n",
       "S5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklRJ1+AVEQdExE0R\n",
       "cUtEHDNMmROb/csiYl7vqylJkjT4RgxeETEFOAk4ANgVeHtE7NJWZiGwY2buBLwPOLlPddU4iYgF\n",
       "410HjZ3tN9hsv8Fl26mTbj1eewC3ZuavM/Nx4CzgoLYyi4DTADLzMmDziJjR85pqPC0Y7wporSwY\n",
       "7wporSwY7wpozBaMdwU08XQLXrOAFS3rtzfbupWZvfZVkyRJmly6Ba8c5XFijO+TJElaZ0ztsv8O\n",
       "YE7L+hxKj9ZIZWY321YTEQayARURnxrvOmjsbL/BZvsNLttO7boFryuBnSJiLnAn8Dbg7W1lzgeO\n",
       "AM6KiPnAvZm5qv1AmdneKyZJkrROGTF4ZeYTEXEE8GNgCnBKZt4YEYc3+xdn5pKIWBgRtwJ/Ag7r\n",
       "e60lSZIGUGR69U+SJKmGvs9cP5oJWFVXRMyJiIsj4vqIuC4ijmy2bxkRF0bELyPigojYvOU9xzZt\n",
       "eFNE7N+y/eURsbzZ98Xx+DzrqoiYEhHXRMT3m3Xbb0BExOYR8Z2IuDEiboiIPW2/wdC0xfXN1/1b\n",
       "EbGBbTdxRcSpEbEqIpa3bOtZezXtf3az/ecR8fyulcrMvi2Uy5O3AnOBacC1wC79PKfLqNplG+Cl\n",
       "zetNgJuBXYDjgY82248BPte83rVpu2lNW97KM72llwN7NK+XAAeM9+dbVxbgaOCbwPnNuu03IAtl\n",
       "7sP3NK+nApvZfhN/ab7+vwI2aNbPBt5t203cBXgVMA9Y3rKtZ+0F/A/gK83rtwFndatTv3u8RjMB\n",
       "qyrLzJWZeW3z+kHgRsp8bE9Phtv8+8bm9UHAmZn5eGb+mvLNuGdEzAQ2zczLm3Knt7xHfRQRs4GF\n",
       "wP/hmelcbL8BEBGbAa/KzFOhjKXNzPuw/QbB/cDjwMYRMRXYmHLjmW03QWXmpcAf2zb3sr1aj3Uu\n",
       "sG+3OvU7eI1mAlaNo+aO1XnAZcCMfOaO1FXA0BMItuXZ04gMtWP79juwfWv5AvAR4KmWbbbfYNge\n",
       "+H1EfC0iro6Ir0bEdGy/CS8z7wH+GfgtJXDdm5kXYtsNml6219M5JzOfAO6LiC1HOnm/g5cj9yew\n",
       "iNiEktA/mJkPtO7L0m9q+01AEfGXwF2ZeQ2rT14M2H4T3FTgZZTLEy+j3A3+sdYCtt/EFBEvAD5E\n",
       "uQy1LbBJRPxVaxnbbrCMR3v1O3iNZgJWjYOImEYJXWdk5nnN5lURsU2zfyZwV7O90yS5tzfbZ7dt\n",
       "7zh5rnpqb2BRRNwGnAm8LiLOwPYbFLcDt2fmFc36dyhBbKXtN+HtDvw0M+9uejf+L7AXtt2g6cXP\n",
       "yttb3rNdc6ypwGZNz+iw+h28np6ANSLWpww8O7/P51QXERHAKcANmXlCy67zKQNFaf49r2X7oRGx\n",
       "fkRsD+wEXJ6ZK4H7mzuyAnhXy3vUJ5n58cyck5nbA4cCP8nMd2H7DYTm674iInZuNu0HXA98H9tv\n",
       "orsJmB8RGzVf8/2AG7DtBk0vflZ+r8OxDgYu6nr2CncUHEi5a+5W4NiadzO4DNsm+1DGBl0LXNMs\n",
       "BwBbAv8K/BK4ANi85T0fb9rwJuD1LdtfDixv9p043p9tXVuA1/DMXY2234AswEuAK4BllF6TzWy/\n",
       "wViAj1KC8nLKoOpptt3EXShXBe4EHqOMxTqsl+0FbACcA9wC/ByY261OTqAqSZJUSd8nUJUkSVJh\n",
       "8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIq+f+rRc5Rp18KSwAAAABJ\n",
       "RU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e11c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# euler-maruyama method\n",
    "# plot by variable steps\n",
    "# average _ 100 times\n",
    "# Brownian paramator (p) = 1 \n",
    "\n",
    "import pylab\n",
    "from random import normalvariate as norm\n",
    "from random import seed\n",
    "from math import sqrt\n",
    "\n",
    "x = np.arange(0,time, 1)\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "time = 10000\n",
    "average_num = 100\n",
    "p = 1\n",
    "\n",
    "for num, j in enumerate(steps):\n",
    "    step = j\n",
    "    y_all = [] \n",
    "    for l in range(average_num):\n",
    "        y_num = [0] * (time)\n",
    "        value = 1\n",
    "        y_num[0] = value\n",
    "        for i in range(time - 1):\n",
    "            update_value = value + step * (2 - value) * value + p * sqrt(step) * value * norm(0, 1)\n",
    "            y_num[i + 1] = update_value\n",
    "            value = update_value\n",
    "        y_all.append(y_num)\n",
    "    y = np.array(y_all)\n",
    "    np.reshape(y, (average_num, time))\n",
    "    y_ave = [np.average(y[:, k]) for k in range(time) ]\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_ave)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHQ1JREFUeJzt3Xm8HGWd7/HPLzkhAYKEGBKWBEEWBccFdCDiQhxQIGrU\n",
       "GUbQ0TsXF1AHF3RcRy7o9c7izLigV4zjBo4D7gwoXMWReHV8CYwQZFUyow7BS1BZROMCw+/+UU97\n",
       "Kk2f0yc53c9Z+Lxfr3p11VNPVT1dT3X191RVOpGZSJIkafjmTHUDJEmSHigMXpIkSZUYvCRJkiox\n",
       "eEmSJFVi8JIkSarE4CVJklTJuMErIhZExGURsT4iro+Ivxqj3pkRcVNEXB0RBw+nqZIkSTPbyHgz\n",
       "M/PXEfGUzNwcESPANyPiiZn5zU6diFgN7JeZ+0fEYcBZwMrhNluSJGnm6XurMTM3l9HtgLnA7V1V\n",
       "1gBnl7qXAYsiYtkgGylJkjQb9A1eETEnItYDm4BLM/P6rip7Aje3pjcCywfXREmSpNlhIle87svM\n",
       "x9CEqSdHxKoe1aJ7sQG0TZIkaVYZ9xmvtsy8KyK+BDwOWNeadQuwojW9vJRtISIMY5IkacbIzO4L\n",
       "S5M2bvCKiCXAvZl5Z0RsDzwVeFtXtQuAU4DzImIlcGdmbuq1vmG8AQ1fRJyRmWdMdTu0bey/mc3+\n",
       "m7nsu5ltWBeM+l3x2h04OyLm0NyW/ERm/ktEnAyQmWsz86KIWB0RG4BfAicOo6GSJEkzXb+fk7gG\n",
       "OKRH+dqu6VMG3C5JkqRZx1+u10Ssm+oGaFLWTXUDNCnrproB2mbrproBmn4is84z7xGRPuMlSZJm\n",
       "gmHlFq94SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmS\n",
       "JFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmq\n",
       "xOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInB\n",
       "S5IkqRKDlyRJUiUGL0mSpErGDV4RsSIiLo2I6yLi2oh4VY86qyLiroi4qgxvHV5zJUmSZq6RPvPv\n",
       "AU7NzPURsRD4TkRckpk3dNX7emauGU4TJUmSZodxr3hl5q2Zub6M/wK4AdijR9UYQtskSZJmlQk/\n",
       "4xURewMHA5d1zUrg8Ii4OiIuioiDBtc8SZKk2aPfrUYAym3GzwKvLle+2q4EVmTm5og4FjgfOGCw\n",
       "zZQkSZr5+gaviJgHfA74x8w8v3t+Zt7dGr84Ij4QEYsz8/Ye6zqjNbkuM9dtU6slSZIGKCJWAauG\n",
       "vp3MHK8RAZwN/CwzTx2jzjLgtszMiDgU+HRm7t2jXmamz4JJkqRpb1i5pd8VrycALwC+GxFXlbK3\n",
       "AHsBZOZa4Djg5RFxL7AZOGHQjZQkSZoNxr3iNdANecVLkiTNEMPKLf5yvSRJUiUGL0mSpEoMXpIk\n",
       "SZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIq\n",
       "MXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLw\n",
       "kiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJ\n",
       "klTJuMErIlZExKURcV1EXBsRrxqj3pkRcVNEXB0RBw+nqZIkSTPbSJ/59wCnZub6iFgIfCciLsnM\n",
       "GzoVImI1sF9m7h8RhwFnASuH12RJkqSZadwrXpl5a2auL+O/AG4A9uiqtgY4u9S5DFgUEcu2phER\n",
       "7DCROhFUuZoWQURM/9uwERwRwfwBr3OHCE6L4GmDXG+fbX4mgqMjWDrG/OUTOUYmsJ2jInhoazoi\n",
       "WDKB5d4bwXZbua35rfH3tbcTwUgEH4rgbRH83dast7YIto9gx6luRz8RbD/J5UfKsb9Tj3k7RPDr\n",
       "CBb2mLckgp0ns+0e64wI5ranB7n+qVI+f/fbhwNY766DXmdZ76IIXjWMNg9TOV53KeNztvb4mQnf\n",
       "fZMRwfzu834Ej4hgz2qNyMwJDcDewI+AhV3lFwKHt6a/Cjy2x/IJuT3kNyET8hjIgPyTMr0b5KMh\n",
       "vwB5NuRcyN1Gl8/TILM1PQ/yHMi9WmXbtcZ3hVwK+UnIfbZsSybka1rrWQq5vDX/jFLnAMh3QL6p\n",
       "9z7Jw8t7eiXkLyB3GKPefMi3QI5AHlXe80sgV5T5UV47++K60qYvlGVWttY1B/K1Zd8l5LsgHw/5\n",
       "KMh9S52dx2jH9pDHtqYD8imQj2qVXd9pQ5neA/JqyM9AHgT5Isi9IZdAfgPypNayT4F8YRnfrbWN\n",
       "R0AeVqYPgFwAOaerP7LTv6VPXly286Qyb22Z92jIfco6lpT3f22Z907I70M+EvLBkM+A3KvUe2x7\n",
       "O2V4VXl9PuRDyv7p9MVSyN3L/k/Il5byEcgLIA8ty/9t+/iDPB1ydVnmRMg/am3vRZBvh1zb1Y6D\n",
       "S93ocax+DfIzPfrytZAfgjyhtd+eCvksms/SK0qfPQbyEprP3V6l/QtL/bld69wdcl6Pz0pCvgly\n",
       "p1b5WsjXlHmPKWW7QN5Zyo6HPLVrXQG5Sxl/XKm3R9f8p0O+DPJ/QJ5byheUfb1nq+4LaD5Le0J+\n",
       "udXOXSHfDPmwVvsvhTwO8s/HPr/lWa11HF/a8rQy74JS/tauZfYt5b9tHX+vK+Mvhjy69ElCvrp1\n",
       "LvgJ5Bchd6A51hd1+qNs98qyzJcg31bG/6q814e0jtEFZbiGcj5rte3BZZlFZZvR7s8x9sEfQj68\n",
       "qz8Scsey7aU054PTeiw7F/Kw0r5dKOegsv2X0pz/kubz8Q7I/SH/W9lHCfmQUv+VrWPkeWXecTTn\n",
       "vaWl/BGl/IU054OEPLC04UE0x/+hkDt2tfGFkLfSfE6Xd449yEMgzy1tfQXk9yAfDnlx65hYPdax\n",
       "U9bxx5DPLnXnQz4U8smQD2rVORpyQRlfRvOZWgB5PuQRZX8/FPK5kBd2jouu7RwHuQbyp5CnlGV+\n",
       "n+Y7ay7kc9p9THM+P6scq/dBPqEs8xzIjTSf1ztpzu3B6PnqY5A3dI6bVh8fyv3PEe+CfF/pr0eV\n",
       "/btT6xg9vlX3EbS+TyF3gjyytOfgsu92LO1d1jmvltefQf6Y1vd8Vzt2gty1Tz89jOYcnDTH8/Zd\n",
       "57mPdvZdU07Pz8pkh4lVgoXAvwHP7jHvQuAJremvAof0qJeQv9d6g93D68YoP758EDrTD4P8xx71\n",
       "vt4a36/H/P3KgXVpq+xb3W0onXBxj+Wv6Grr4WPMS5oP8PPLATjW++0MnW29ZIz5t5bXh5fXz5fX\n",
       "d4xR/09b47eMUecoRk9qneH9pd392ttr+CTkP0yg3hsnUGevbWzDIIcnj1H+EchP9Ci/hxKAJjnc\n",
       "1xq/nSYwdabXQH68jP9Hj2X/dYLb+GaPsgfRfLG1y/alCYpb1G2dTLvXceg2vucNNF/YY33+n9s1\n",
       "fdJWrPuuccrfDHkqzbnl+HHW8aWu6YeV1y8yGtyz1TdJ84XVa12LIe/dxv000WER5IoJ1Pt7RoNj\n",
       "0vyR1xn/Lk1gH+v8kTQBayeaP/oG1fbOH56X0/sPpWTs4/w5Y5R/vvTTp7vKr9uG9l0K+Z+Qry/T\n",
       "L96GdYy3T3sNzyivV0L+0yT27d2t8Qt6zP8ITdjqtewVNN+dP2+VfQJyfldo6R7e3Rq/pKvuGyDv\n",
       "mEC7X1peuz83nc/Ymq7yX9J8v53I6Hf9xZBvhfzLMbbxhR5lx0EuGFbwKn8FjS0i5gFfBC7OzPf0\n",
       "mP9BYF1mnlembwSOyMxNXfUSTm+VrCrDUNwBzaVWSQP1QeBlU92IKeA5ZUvnASdMdSNUzYE0jxpN\n",
       "xt1w/1v508u6MnS8jcwc/K3+Ple6AjgHePc4dVYDF5XxlcC3x6jXTpPdf320h59NItX3Grqvak10\n",
       "uHwr65/dZ/7nWuNfH6feZZA3seVf0P2Gv6H5C7YzvS1/zbWH6Jq+szV+wATXcU95/c0A+vDY1n47\n",
       "fZx6/05z+bi7/FPl9eE0V6Yua817+wS2v6pr+jSav4i25j18gN5XajtDrytRWzt8ki1vmX22M17+\n",
       "2tywLesty3YfE0lzNeHIrrK309zSmex76R5+OM68v+D+V51/2aPee/psY/E48940wXb+zx5lS7qm\n",
       "n87o7cRew1+Wff57NI8wjFXvfX3a/cwB7Pfzy+v3y+ttY9T7M8hNPfrpV4xetW/35bWt6Q+Ps/2X\n",
       "jVH+fwfw3jrDh2huyyfk/ymv60sfdW5zTXRdby6vX4VcR3OF7J9L2eZWve47DhMdvktzvB/bVd4+\n",
       "L+87xrK9js1ew+tobr1uTbuey5Z3gbZmOJHmsaF22ae2cV0THbqvlGVp/wKa799SRv1bjcATgfuA\n",
       "9cBVZTgWOBk4uVXv/cAG4Gp63GbsCl7709wr7pzIHsnoh3oBzQl+Ps3zQrtDHji6jnxtqbcr5BGl\n",
       "bB6jX2j7MvpMxFc6XxhdH5xXQu5cOvrxNM8GHAt5JqPPE72ztLFzm+EQRgPh/HKgPJMtw858yCfS\n",
       "nGQvoblU35m305b7Ih9Mc2tmYY/OX9CqN7+09bQyr3NyeDLNiat7vZ3bkUtpbjncVvbNQ0u7Xszo\n",
       "sxcvoLn8+hi2DKcHd+2vx7WmO5eLD6F5ZuMn5WA9qZQlzfNNB5Z623W9lxsZDYVL2u+1q/330TyL\n",
       "tG+rn3eHfHAZ36HMfz6tQNBazzxGbzefQ3Mbrfu5hO0g/4DRy+X7lD7/Is0XwZzSxmPLNn7a3kZX\n",
       "GPlRef106dulbPnB3tz1Ht9bjrXDIL9S6uxOc/l8O5ovglU0J9PVpc5fMPol8BvIl3Stc6Q1vTPl\n",
       "+Zay7neW8V1pLsOfyuhzeruy5a22P6f5THamn9dab6fsFZCv7NoPn4R8aKtsaXkvh5W+7zzbslt5\n",
       "/yvZ8lZd5wv245DPLHV3pAlynWegOrc4b6a5Jf0otnwGZT6t53pozhfPKPtjRenfJYx+0Z9K6wuw\n",
       "te92KeWd54eeXN7jxjK9Pc2trTWljZ0/qg7ocWz8rzK9kuaZphWttr4D8r/TfCEeTXM+OOj+585c\n",
       "TBPW/obmM7HFfi6vIzTPXyXk51rzO7dqFpX3dRLN5+NFNM85zS3vZ79S/1GM/tE3r5Qt62pPp8++\n",
       "V9o+p+t9v6BsY26r/CDIv+vx+Qm2fARlFaNB9fdLG5PmvPHeVr39aW6N/XFZ97cgH9n5/JfXzm3q\n",
       "J5X3tSvNufD1NKH1qZTPUZnfOQYe3dmvrbb+CPIbZXwR5A8Y/S5aVt7HHuV9b+D+55tFlGcru8of\n",
       "RPM5ObpMdwLVo2nOJZtpnofcl+b26/Zdy+/eXm9XXzyjzD8I8rOlrBNoVrSWP72UfQ3yyK71H9ja\n",
       "5539s0c5Xl8E+beQJ7bqdx7TeC7N9/rJNH8EdW6xPoHm1t7tPfbFfJrP6a405993lfpJ830XNOeT\n",
       "D5SyP6N5LmyE5ntobin/E5rb4GtpzjftP2pXMnoeXcSWFyk6341zy/u+aFjBq++txkFpbjXm6kwu\n",
       "bqaZA8zL5DflXxL9Vyabt23d7AQszeTfIxgBDsjk+m1YTwBfA47K5L+65j0IWJjJj7difX8I3JfJ\n",
       "+X3qbQc8Hbgik43j1BsBTs7kf0+0DRNsZwDLgN9kckcp+2vgxkw+Xqb3AP5fJtt8wESwGNicya/H\n",
       "qXMksCmTa7ey/Ttl8vNtbdtklX+FNieTe7rKlwB3Z/KbMZbbGdhxa46rrWzXbsBPM7m3T73dgT0y\n",
       "+c44dY4GnpM5dbcaI/gw8P5M1g9wnYszuX0Syx8BvCezzr+67tOW04APZvKTMh3AQzL54VasYw6w\n",
       "Qya/GGP+YmBJJt8fQJPHakN0zjURHJLJlWV8F5pz6l1D2Oa87s9vn/pLM7lt0O0YpvIvlP8ok3O6\n",
       "yhN4aiZf7bHMOuAIYMFY57Gu+ttn8qvW9HbQnH8yuW9y72DrleN590xuGafOEzL51/uXR+YQbjXW\n",
       "Dl5PyuSbVTYoSZL6imBkrD/Oyk/jHJXJlyo3a8oNK3j1+wHVQftV/yqSJKmW8a6Il6tcD7jQNUy1\n",
       "fyjtt5W3J0mSNG0YvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKqgav\n",
       "7v+GR5Ik6YGk9hUvSZKkByyDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJ\n",
       "klSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSp\n",
       "EoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKukbvCLioxGxKSKuGWP+qoi4KyKuKsNbB99MSZKkmW9k\n",
       "AnU+BrwPOGecOl/PzDWDaZIkSdLs1PeKV2Z+A7ijT7UYTHMkSZJmr0E845XA4RFxdURcFBEHDWCd\n",
       "kiRJs85EbjX2cyWwIjM3R8SxwPnAAb0qRsQZrcl1mbluANuXJEmalIhYBawa+nYycyKN2Ru4MDMf\n",
       "OYG6PwAem5m3d5VnZnpLUpIkTXvDyi2TvtUYEcsiIsr4oTRh7vY+i0mSJD3g9L3VGBHnAkcASyLi\n",
       "ZuB0YB5AZq4FjgNeHhH3ApuBE4bXXEmSpJlrQrcaB7IhbzVKkqQZYtreapQkSdLEGLwkSZIqMXhJ\n",
       "kiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJ\n",
       "qsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJ\n",
       "wUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOX\n",
       "JElSJX2DV0R8NCI2RcQ149Q5MyJuioirI+LgwTZRkiRpdpjIFa+PAceMNTMiVgP7Zeb+wEnAWQNq\n",
       "myRJ0qzSN3hl5jeAO8apsgY4u9S9DFgUEcsG0zxJkqTZYxDPeO0J3Nya3ggsH8B6JUmSZpVBPVwf\n",
       "XdM5oPVKkiTNGiMDWMctwIrW9PJSdj8RcUZrcl1mrhvA9iVJkiYlIlYBq4a+ncz+F6ciYm/gwsx8\n",
       "ZI95q4FTMnN1RKwE3pOZK3vUy8zsvjImSZI07Qwrt/S94hUR5wJHAEsi4mbgdGAeQGauzcyLImJ1\n",
       "RGwAfgmcOOhGSpIkzQYTuuI1kA15xUuSJM0Qw8ot/nK9JElSJQYvSZKkSgxekiRJlRi8JEmSKjF4\n",
       "SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIk\n",
       "SarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJU\n",
       "icFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVEnf4BURx0TE\n",
       "jRFxU0S8scf8VRFxV0RcVYa3DqepkiRJM9vIeDMjYi7wfuAo4Bbgioi4IDNv6Kr69cxcM6Q2SpIk\n",
       "zQr9rngdCmzIzB9m5j3AecCzetSLgbdMkiRplukXvPYEbm5NbyxlbQkcHhFXR8RFEXHQIBsoSZI0\n",
       "W4x7q5EmVPVzJbAiMzdHxLHA+cABk26ZJEnSLNMveN0CrGhNr6C56vU7mXl3a/ziiPhARCzOzNu7\n",
       "VxYRZ7Qm12Xmuq1usSRJ0oBFxCpg1dC3kzn2Ra2IGAG+BxwJ/Bi4HHhe++H6iFgG3JaZGRGHAp/O\n",
       "zL17rCsz02fBJEnStDes3DLuFa/MvDciTgG+DMwFPpKZN0TEyWX+WuA44OURcS+wGThh0I2UJEma\n",
       "Dca94jXQDXnFS5IkzRDDyi3+cr0kSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAl\n",
       "SZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5Ik\n",
       "qRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIl\n",
       "Bi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpkr7BKyKOiYgbI+KmiHjj\n",
       "GHXOLPOvjoiDB99MSZKkmW/c4BURc4H3A8cABwHPi4gDu+qsBvbLzP2Bk4CzhtRWTZGIWDXVbdC2\n",
       "s/9mNvtv5rLv1Eu/K16HAhsy84eZeQ9wHvCsrjprgLMBMvMyYFFELBt4SzWVVk11AzQpq6a6AZqU\n",
       "VVPdAG2zVVPdAE0//YLXnsDNremNpaxfneWTb5okSdLs0i945QTXE9u4nCRJ0gPGSJ/5twArWtMr\n",
       "aK5ojVdneSm7n4gwkM1QEXH6VLdB287+m9nsv5nLvlO3fsHr34D9I2Jv4MfA8cDzuupcAJwCnBcR\n",
       "K4E7M3NT94oys/uqmCRJ0gPKuMErM++NiFOALwNzgY9k5g0RcXKZvzYzL4qI1RGxAfglcOLQWy1J\n",
       "kjQDRaZ3/yRJkmoY+i/XT+QHWFVXRKyIiEsj4rqIuDYiXlXKF0fEJRHx/Yj4SkQsai3z5tKHN0bE\n",
       "01rlj42Ia8q8907F+3mgioi5EXFVRFxYpu2/GSIiFkXEZyPihoi4PiIOs/9mhtIX15X9/k8RMd++\n",
       "m74i4qMRsSkirmmVDay/Sv9/qpR/OyIe0rdRmTm0geb25AZgb2AesB44cJjbdJhQv+wGPKaMLwS+\n",
       "BxwIvBN4Qyl/I/DXZfyg0nfzSl9uYPRq6eXAoWX8IuCYqX5/D5QBeC3wSeCCMm3/zZCB5rcPX1TG\n",
       "R4Cd7b/pP5T9/x/A/DL9KeBP7bvpOwBPAg4GrmmVDay/gFcAHyjjxwPn9WvTsK94TeQHWFVZZt6a\n",
       "mevL+C+AG2h+j+13P4ZbXp9dxp8FnJuZ92TmD2kOxsMiYndgp8y8vNQ7p7WMhigilgOrgQ8z+nMu\n",
       "9t8MEBE7A0/KzI9C8yxtZt6F/TcT/By4B9ghIkaAHWj+4Zl9N01l5jeAO7qKB9lf7XV9DjiyX5uG\n",
       "Hbwm8gOsmkLlX6weDFwGLMvRf5G6Cej8DwR7sOXPiHT6sbv8FuzfWt4NvB64r1Vm/80M+wA/iYiP\n",
       "RcSVEfEPEbEj9t+0l5m3A38P/CdN4LozMy/BvptpBtlfv8s5mXkvcFdELB5v48MOXj65P41FxEKa\n",
       "hP7qzLy7PS+b66b23zQUEc8AbsvMq7j/jxcD9t80NwIcQnN74hCafw3+pnYF+296ioh9gdfQ3Iba\n",
       "A1gYES9o17HvZpap6K9hB6+J/ACrpkBEzKMJXZ/IzPNL8aaI2K3M3x24rZT3+pHcjaV8eVd5zx/P\n",
       "1UAdDqyJiB8A5wJ/EBGfwP6bKTYCGzPzijL9WZogdqv9N+09DvhWZv6sXN34PPB47LuZZhDnyo2t\n",
       "ZfYq6xoBdi5XRsc07OD1ux9gjYjtaB48u2DI21QfERHAR4DrM/M9rVkX0DwoSnk9v1V+QkRsFxH7\n",
       "APsDl2fmrcDPy7/ICuCFrWU0JJn5lsxckZn7ACcAX8vMF2L/zQhlv98cEQeUoqOA64ALsf+muxuB\n",
       "lRGxfdnnRwHXY9/NNIM4V/5zj3UdB/xL361X+BcFx9L8q7kNwJtr/msGhzH75Ik0zwatB64qwzHA\n",
       "YuCrwPeBrwCLWsu8pfThjcDRrfLHAteUeWdO9Xt7oA3AEYz+q0b7b4YMwKOBK4Craa6a7Gz/zYwB\n",
       "eANNUL6G5qHqefbd9B1o7gr8GPgtzbNYJw6yv4D5wKeBm4BvA3v3a5M/oCpJklTJ0H9AVZIkSQ2D\n",
       "lyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklTJ/wfsIl42ucMisgAAAABJ\n",
       "RU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109620b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHFFJREFUeJzt3Xu0ZGV55/Hv01cbGmku2gLd2sglCio2KiCiHBURehk0\n",
       "EzIioyIZI4Mh3uMtRjCJ0TUZb8QRmSgEjaIORoSIgyi0o8sRL3RjA43QURIapDEiKGIiyDN/7PfQ\n",
       "m6LOqeo+VW+dy/ez1l5nX97a+9373bXrV2/tqhOZiSRJkoZv3qgrIEmSNFcYvCRJkioxeEmSJFVi\n",
       "8JIkSarE4CVJklSJwUuSJKmSSYNXRDwsIq6MiPURcV1EvGeCcmdGxI0RcXVErB5OVSVJkma2BZMt\n",
       "zMx/j4hnZ+Y9EbEA+GZEHJGZ3xwvExFrgH0zc7+IOBQ4CzhsuNWWJEmaeXp+1JiZ95TRRcB84I6O\n",
       "IscB55WyVwLLImL5ICspSZI0G/QMXhExLyLWA1uAKzLzuo4iewE3t6Y3AysGV0VJkqTZoZ8er/sz\n",
       "88k0YepZETHWpVh0PmwAdZMkSZpVJr3Hqy0z74qILwFPBda2Ft0CrGxNryjzHiQiDGOSJGnGyMzO\n",
       "jqUpmzR4RcTuwH2ZeWdELAGeB7yro9hFwGnAZyLiMODOzNzSbX3D2AENX0SckZlnjLoe2j6238xm\n",
       "+81ctt3MNqwOo149XnsA50XEPJqPJT+ZmV+LiFMAMvPszLwkItZExCbgV8DJw6ioJEnSTNfr5yQ2\n",
       "AAd3mX92x/RpA66XJEnSrOMv16sfa0ddAU3J2lFXQFOydtQV0HZbO+oKaPqJzDr3vEdEeo+XJEma\n",
       "CYaVW+zxkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIk\n",
       "SarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJU\n",
       "icFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKD\n",
       "lyRJUiUGL0mSpEoMXpIkSZVMGrwiYmVEXBER10bENRHxmi5lxiLirohYV4Z3DK+6kiRJM9eCHsvv\n",
       "BV6fmesjYinw/Yi4LDM3dpT7emYeN5wqSpIkzQ6T9nhl5m2Zub6M3w1sBPbsUjSGUDdJkqRZpe97\n",
       "vCJiFbAauLJjUQKHR8TVEXFJRBwwuOpJkiTNHr0+agSgfMx4AfDa0vPVdhWwMjPviYhjgQuB/Qdb\n",
       "TUmSpJmvZ/CKiIXA54F/yMwLO5dn5i9b41+OiI9ExK6ZeUeXdZ3RmlybmWu3q9aSJEkDFBFjwNjQ\n",
       "t5OZk1UigPOAn2Xm6ycosxy4PTMzIg4BPpeZq7qUy8z0XjBJkjTtDSu39OrxegbwUuAHEbGuzHs7\n",
       "8GiAzDwbOB44NSLuA+4BThh0JSVJkmaDSXu8Brohe7wkSdIMMazc4i/XS5IkVWLwkiRJqsTgJUmS\n",
       "VInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkS\n",
       "g5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYv\n",
       "SZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIk\n",
       "SZVMGrwiYmVEXBER10bENRHxmgnKnRkRN0bE1RGxejhVlSRJmtkW9Fh+L/D6zFwfEUuB70fEZZm5\n",
       "cbxARKwB9s3M/SLiUOAs4LDhVVmSJGlmmrTHKzNvy8z1ZfxuYCOwZ0ex44DzSpkrgWURsXwIdZ2R\n",
       "InhYBAdFcEIEO4y6PoMWQYy6DpKmrwgigh3L30URPd/wqyWC90aQEfzzqOuiwej7Hq+IWAWsBq7s\n",
       "WLQXcHNrejOwYqoV27pdIoKFZfzhEfx+GX90ORkzgg9FcHoZf0cE8yKYX8rNH1RdetRzQWv8MRG8\n",
       "P4JDgV8D64Hzgc3bG1TKcdg1gh0HU+O+t/u0clxXRXB3BD+L4DXlOCdwfwT79rNfZR+eHsGuA67j\n",
       "kb2OSwQHR3BOGV8cwYIIVkxU7wj+JoKdeqzz4RE8e/trPjURPCeCldtQvp82ekQEi3qUWRHB727D\n",
       "dhdFcEsEh0fw6H4f12Odj+jcnwj+vHVNyAhOKn//qfPFPoKdyjClNw4RHF2eG++KYLeprKu1zgUl\n",
       "qDyytS8/H8S6W9vYL4IDW9O7RrBPa3rxADd3I3A3cD/wH8C9EfxJBGu35fo83oYRzC/tv13X9gj2\n",
       "ieAVEfxZBEvKdWnn7VzXwlKf+RG8OILHRbCy17Wjj/XuUM6B5wFvKbMfG8EuHeUOjeCvIh76Wh7B\n",
       "0gh2rvUauC26PHdf2z4fez02greX58Wry3n0+XK8VkWwf/nbM9+U41O/8yAzew7AUuB7wIu6LLsY\n",
       "eEZr+qvAwV3KZT/basrmPMjHQv4KMstwHuQvW9P9DFH+XtWx/k+X+Sf2qMdCyN+H/CDkLpA7Qb6z\n",
       "PPZayDHI90A+v4+6HNwavwvy/ZB/APleyP9X5p9UtvusMv0TyCMgn9llfVdBPhdyh1Z9d5/smPZ7\n",
       "/FuP2WEbj/eTuqxjX8iTIZdAvqtVdiPk5ZALW2UfC3kS5JIe9YoJjvnKLmXnQ36xVeYNXR73ibLd\n",
       "l0ywX9+EfGNr+pUTlPs25BmQF5c2a+/bXpCLIddA7l7OpdWQb5ms3Tr3u/zdB3Jll+3fBLlzKXME\n",
       "5NGQV9I8b44vZe4cr1c5jp8q63oC5LLxdXXZ9i6QX6A55zeWcqeUZU8r5+rDOh6zN+R+Exyrw0sb\n",
       "LoM8BPKaLsdsXmt8ZdnvVa11/LRd5x7DRaV8Qn60Y9lHIXdsbSch17fKP7F17F/UYzt/CPlfIC8t\n",
       "09dAzu84Lu9slf/T1vyJjtX48Eaaa9KBrXP73ePHc5LzZgnkn0M+GnJRxzov48HPjy9Bvq+M/4bm\n",
       "urXDROtubWMR5N/QnNNRhldA3t2xvV93TK/p89wfL78P5Odb0w95Tep4HTm4tc+nQf51j2O8juY6\n",
       "NL+s4yjIc8qys8s6V0AeSHN+b+mxvqeW9Swo0xshv9VR5lWQx1LO93IOda5nHuTmMv46yJ0hT+go\n",
       "s1frdesHHcv+J+TRE1xLnwy5qsdxXAv58ta8j9G8Pv8nyLdBboLcjeb6txsPfh4H5B7lfHhTq04b\n",
       "IU9vTd9S9mt+63EHQf4xzfXsRMjv9DjencOlkEe06nIizTm6CPKRpcwrO+q6EPLNzTIeci0cxNDH\n",
       "Cc9C4FLgdRMs/yhwQmv6emB5l3IJnNEaxiZp6LWTHMi3lb+/hVzQugDtXhp8ooZ5DU1Q6Zz/Vpon\n",
       "0BdpXqTeWBp/Wxq3c/gXmgvE6o79eukU1/tPkyy7vzV+IORTy/EItj5Bjy7HISFfAPm98ZOulDuv\n",
       "tY4vtcbn01ywng35CMgnQb6u9bgLW2VPbu3vH3Sp56c6pq8rJ3pnufWQ34e8lSakXs7WC0/n8KYJ\n",
       "5v+PKRzrC/ooc12P5VeXNruyj3WdDvmY9rwJXnimMtxa/t5Ac+GZ7HzqNXwL8t8h/7LP8qfSPLc+\n",
       "OaB9+d9d5r2UrQFpIeS5NAH3wC5lX9ExPdG51Wv4Y5oL+apJypzURzte1TH9Vppr0iKaN0Cv77M+\n",
       "/1j+Xtaj3ImQn21NX8+DA03n8HrKi3Op0870DqHjw8WUEFQe/2qa8+cLrTLrKIGtdazGX4Cf1WWd\n",
       "7bq+mSbQvba0xRaa69/GCeqTNIHhRJoX+6S5Fk71fPwdmmvj79KE0PFlR23nOi+E/DjkLuU47DZB\n",
       "mRPL+NdLuc5w+y+t8f1L282jua7/tLXsBsjn0Tw3PgT59i7be9ME7THV4ZxtLL9v2dcPQD6D5o3h\n",
       "Wpo3Pf+ZB4LTA8P7If+t93qvSDi9NVA/eAEBfAL4wCRl1gCXlPHDgG9PUK6vHaDpAUjIz9G8swjI\n",
       "5ZDPgVzU9441BzppAsPxHQf4EzQh5NIeDXEIzbvd8eByC+QB5YR9OM3FaA+ad5Pzt6FuR0A+DvKF\n",
       "NO9G9y7z31q2c1aZnkfTC3AoHb1ANO9enw65YQhPgvawtM99WtDxuPFevC+XJ0LS9Iy0L6wHdTzm\n",
       "Iro/2bsNf9+x/ae1lt3fUXZ1q44nddRhMc3Feh7NBWkx5CNbywPyYZReKcgdaS5e0eUYLC3nw240\n",
       "F992Hf6otO9Ya97zIY+cZB8nu2B/gea5ciLk75TtP7y1/G6aHpSg6cV5einT+WL5NZrnx/gL9njP\n",
       "0pdbZW4v7bk75N9BvpyHhuWjIH/YMe+fIf+1fTxbL9zX0byzPxfyv5Vj8Rc0b6jGH/8VyO+W8Z/Q\n",
       "BPFrIBeX9Tyb5jnY87kH+TLIx4y/gLXqcThb34wk5BXlOO5E89yc17FPl3Vr+9a5cjLkp1vzuvVe\n",
       "vK61vB0+NtLRa9ix/mtLuVtbj3kHvXvKkuaF9D1l/NSO5+2jOrazuLU/Z/Hga8yZk2zjT2jC73iI\n",
       "fWGPNgmaXqT/00f9301z3T2QrS+6C2nCfz/Xi31oemme2a0erfEdaULYx0tb/y+2hvmPlXWdRNND\n",
       "9XOa5/sjJtnH9vF6HE0ge2dHmd158Jve8yZZ37JyjO+E/GFr/p4d+3tQl+fcRMfmKX0cv6Mgv9qa\n",
       "PpHmercTTfB5Bc2bx8dCfoStIWc89J1N81x7Glt7lx9B81rYPr6dnS6/R9MzdQHNa17Q52tteVxn\n",
       "SPyvbP1k4/Ky7509kEnTaRCjCl5H0Hwuvx5YV4ZjgVOAU1rlPgxsAq6my8eMpUzPHaB50UvIDQPf\n",
       "0a0HdPfWvHnlyXUpWz9+Gf94c69hHPBhDTQXpfEu3QtoegZ/VvblL8vy9TQX73k076J3gPyz1rE5\n",
       "taxrCc2LXtcXmEnqsITmo7QHTuA+HrMLTS/lK1rzxnvqguZCu2ep87xtqROt7u4RtckDL2B9lH0B\n",
       "TQ/d+Lv8zh6Lp5XnR0A+cYr1Gv+o/aNTXM8yOl60Z+pQLup9v3nahvXu2NGOH+pSZh5NUJ/0dgCa\n",
       "j80+PcGyvcq2nlnWt0v5+6A3O9u5D0HzRrW9HydBHkfzgr54qseOpqcl2foxZ9J8PJaQZ/R47ONo\n",
       "3qQ/FfIfyrFImp6202gFzRGcVwtowvhDPgWa4nqXQO7UMe9zZb9fPsFjltK8GfoU5P8tZf+6o8xf\n",
       "QZ5P09mxX5d1HAT5t1M9p0bQDn3Vt5zrD9s6TQ6jPiVpDl9EZGZOehNbBO8D3pA5nJvdIliSya+H\n",
       "sW49WARPAO7I5NZR12UmiuYLJU/K5PsRLMjkvgGvf34mvx3kOtXdMNpvVCI4Grghk5tGXZfJRBCZ\n",
       "1Hlx06zVT27ZrvVOl+AVwcOBq4B3Z3JulUpJkiR1MReC1y3AnsPq7ZIkSerXsILXdPpfjXsAJ426\n",
       "EpIkScMyLXq8yv1AG4CFs+VeCEmSNHPN9h6v44EzDV2SJGk2G3mPV/n21m+A52RyRZXKSJIkTWI2\n",
       "93j9EYChS5IkzXbTIXg9D/z5CEmSNPtNh+C1N3D2qCshSZI0bCO9xyuCHYB/A3bJ5D+qVESSJKmH\n",
       "2XqP1wHAjYYuSZI0F4w6eD0BuGbEdZAkSapi1MHrYOAHI66DJElSFaMOXocC3xpxHSRJkqoY2c31\n",
       "5YdT7wSWZ3J3lUpIkiT1YTbeXH8gcJOhS5IkzRWjDF6rgXUj3L4kSVJVowxe+wCbRrh9SZKkqkYZ\n",
       "vPYGfjzC7UuSJFVl8JIkSapklMFrFQYvSZI0h4wkeEWwBNgVuHUU25ckSRqFUfV4PQa4OZPfjmj7\n",
       "kiRJ1Y0qeO0N/GhE25YkSRqJUQYv7++SJElzyqiC1yrgphFtW5IkaSRGFbz2AjaPaNuSJEkjMarg\n",
       "tSd+o1GSJM0xowxePxnRtiVJkkZiVMFrD+zxkiRJc0z14BXBTsB84Be1ty1JkjRKo+jx2gO4NZMc\n",
       "wbYlSZJGpmfwiohzImJLRGyYYPlYRNwVEevK8I4eq/T+LkmSNCct6KPMucDfAp+YpMzXM/O4Prfp\n",
       "NxolSdKc1LPHKzO/Afy8R7HYhm16Y70kSZqTBnGPVwKHR8TVEXFJRBzQo7w9XpIkaU7q56PGXq4C\n",
       "VmbmPRFxLHAhsH+3ghFxBrzyaPjRDRGXj2Xm2gFsX5IkaUoiYgwYG/p2Mnt/uTAiVgEXZ+YT+yj7\n",
       "Y+ApmXlHx/zMzIhgLfAXmVy+XTWWJEkasvHcMuj1TvmjxohYHhFRxg+hCXN3TPKQRwG3TXW7kiRJ\n",
       "M03Pjxoj4nzgSGD3iLgZOB1YCJCZZwPHA6dGxH3APcAJPVa5HIOXJEmag/r6qHEgG4pIyCU0v1i/\n",
       "2B9QlSRJ09W0/ahxGz0S2GLokiRJc1Ht4PUoYEvlbUqSJE0Lo+jxur3yNiVJkqaF2sFrV+Bnlbcp\n",
       "SZI0LRi8JEmSKqkdvHYDJvuNL0mSpFlrFD1eBi9JkjQnGbwkSZIqMXhJkiRVMop7vLy5XpIkzUn2\n",
       "eEmSJFVi8JIkSaqkdvBaCtxVeZuSJEnTQu3gdWcm91fepiRJ0rRQO3j5MaMkSZqzDF6SJEmVGLwk\n",
       "SZIqqR28/A0vSZI0Z9njJUmSVInBS5IkqRKDlyRJUiXe4yVJklSJPV6SJEmVGLwkSZIqMXhJkiRV\n",
       "YvCSJEmqpPo/ya68PUmSpGmjavDK5P6a25MkSZpOavd4SZIkzVkGL0mSpEoMXpIkSZX0DF4RcU5E\n",
       "bImIDZOUOTMiboyIqyNi9WCrKEmSNDv00+N1LnDMRAsjYg2wb2buB7wKOGtAdZMkSZpVegavzPwG\n",
       "8PNJihwHnFfKXgksi4jlg6meJEnS7DGIe7z2Am5uTW8GVgxgvZIkSbPKoG6uj47pHNB6JUmSZo0F\n",
       "A1jHLcDK1vSKMu8hIuKM1uTazFw7gO1LkiRNSUSMAWND305m786piFgFXJyZT+yybA1wWmauiYjD\n",
       "gA9m5mFdymVmdvaMSZIkTTvDyi09e7wi4nzgSGD3iLgZOB1YCJCZZ2fmJRGxJiI2Ab8CTh50JSVJ\n",
       "kmaDvnq8BrIhe7wkSdIMMazc4i/XS5IkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoM\n",
       "XpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwk\n",
       "SZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIk\n",
       "VWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZX0DF4RcUxEXB8RN0bEW7osH4uI\n",
       "uyJiXRneMZyqSpIkzWwLJlsYEfOBDwNHAbcA342IizJzY0fRr2fmcUOqoyRJ0qzQq8frEGBTZt6U\n",
       "mfcCnwFe2KVcDLxmkiRJs0yv4LUXcHNrenOZ15bA4RFxdURcEhEHDLKCkiRJs8WkHzXShKpergJW\n",
       "ZuY9EXEscCGw/5RrJkmSNMv0Cl63ACtb0ytper0ekJm/bI1/OSI+EhG7ZuYdnSuLiDNak2szc+02\n",
       "11iSJGnAImIMGBv6djIn7tSKiAXAD4HnArcC3wFe0r65PiKWA7dnZkbEIcDnMnNVl3VlZnovmCRJ\n",
       "mvaGlVsm7fHKzPsi4jTgUmA+8PHM3BgRp5TlZwPHA6dGxH3APcAJg66kJEnSbDBpj9dAN2SPlyRJ\n",
       "miGGlVv85XpJkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYv\n",
       "SZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIk\n",
       "SZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIq\n",
       "MXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJT2DV0QcExHXR8SNEfGWCcqcWZZfHRGrB19N\n",
       "SZKkmW/S4BUR84EPA8cABwAviYjHd5RZA+ybmfsBrwLOGlJdNSIRMTbqOmj72X4zm+03c9l26qZX\n",
       "j9chwKbMvCkz7wU+A7ywo8xxwHkAmXklsCwilg+8phqlsVFXQFMyNuoKaErGRl0BbbexUVdA00+v\n",
       "4LUXcHNrenOZ16vMiqlXTZIkaXbpFbyyz/XEdj5OkiRpzljQY/ktwMrW9EqaHq3Jyqwo8x4iIgxk\n",
       "M1REnD7qOmj72X4zm+03c9l26tQreH0P2C8iVgG3Ai8GXtJR5iLgNOAzEXEYcGdmbulcUWZ29opJ\n",
       "kiTNKZMGr8y8LyJOAy4F5gMfz8yNEXFKWX52Zl4SEWsiYhPwK+DkoddakiRpBopMP/2TJEmqYei/\n",
       "XN/PD7CqrohYGRFXRMS1EXFNRLymzN81Ii6LiBsi4isRsaz1mLeVNrw+Io5uzX9KRGwoyz40iv2Z\n",
       "qyJifkSsi4iLy7TtN0NExLKIuCAiNkbEdRFxqO03M5S2uLYc909HxGLbbvqKiHMiYktEbGjNG1h7\n",
       "lfb/bJn/7Yh4TM9KZebQBpqPJzcBq4CFwHrg8cPcpkNf7fIo4MllfCnwQ+DxwH8H3lzmvwV4bxk/\n",
       "oLTdwtKWm9jaW/od4JAyfglwzKj3b64MwBuATwEXlWnbb4YMNL99+IdlfAGws+03/Ydy/H8ELC7T\n",
       "nwVOsu2m7wA8E1gNbGjNG1h7Aa8GPlLGXwx8pledht3j1c8PsKqyzLwtM9eX8buBjTS/x/bAj+GW\n",
       "vy8q4y8Ezs/MezPzJpqT8dCI2APYKTO/U8p9ovUYDVFErADWAB9j68+52H4zQETsDDwzM8+B5l7a\n",
       "zLwL228m+AVwL7BDRCwAdqD54pltN01l5jeAn3fMHmR7tdf1eeC5veo07ODVzw+waoTKN1ZXA1cC\n",
       "y3PrN1K3AOP/gWBPHvwzIuPt2Dn/FmzfWj4A/Clwf2ue7Tcz7A38NCLOjYirIuLvImJHbL9pLzPv\n",
       "AN4H/CtN4LozMy/DtptpBtleD+SczLwPuCsidp1s48MOXt65P41FxFKahP7azPxle1k2/aa23zQU\n",
       "ES8Abs/MdTz0x4sB22+aWwAcTPPxxME03wZ/a7uA7Tc9RcQ+wOtoPobaE1gaES9tl7HtZpZRtNew\n",
       "g1c/P8CqEYiIhTSh65OZeWGZvSUiHlWW7wHcXuZ3+5HczWX+io75XX88VwN1OHBcRPwYOB94TkR8\n",
       "EttvptgMbM7M75bpC2iC2G2237T3VOBbmfmz0rvxj8DTse1mmkFcKze3HvPosq4FwM6lZ3RCww5e\n",
       "D/wAa0Qsornx7KIhb1M9REQAHweuy8wPthZdRHOjKOXvha35J0TEoojYG9gP+E5m3gb8onwjK4CX\n",
       "tR6jIcnMt2fmyszcGzgBuDwzX4btNyOU435zROxfZh0FXAtcjO033V0PHBYRS8oxPwq4DttuphnE\n",
       "tfKLXdZ1PPC1nluv8I2CY2m+NbcJeFvNbzM4TNgmR9DcG7QeWFeGY4Bdga8CNwBfAZa1HvP20obX\n",
       "A89vzX8KsKEsO3PU+zbXBuBItn6r0fabIQNwEPBd4GqaXpOdbb+ZMQBvpgnKG2huql5o203fgeZT\n",
       "gVuB39Dci3XyINsLWAx8DrgR+Dawqled/AFVSZKkSob+A6qSJElqGLwkSZIqMXhJkiRVYvCSJEmq\n",
       "xOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSv4/JqS0vBUWD+MAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109686710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHbRJREFUeJzt3Xu4JHV95/H3h5kBFJABBQRmBOViIKs4iDDihUmiCY5Z\n",
       "cBM2wV1dQ/IkxISYmDzRjWtWcttskk1WTdSQRI0xCWDQJWggioYxoBEUmBG5CCiGOwjDfURm4Lt/\n",
       "/Oo4h8OZcwamu/r0Oe/X8/Rzuququ75dv+qqT/+quk6qCkmSJA3fdqMuQJIkaaEweEmSJPXE4CVJ\n",
       "ktQTg5ckSVJPDF6SJEk9MXhJkiT1ZMbglWTHJBcnWZvkqiS/v4Xp3pvkuiTrkqwYTqmSJEnjbfFM\n",
       "I6vq4SQ/UFUbkiwGLkry8qq6aGKaJKuBA6vqoCRHAR8AVg63bEmSpPEz66HGqtrQ3d0eWASsnzLJ\n",
       "ccBHumkvBpYm2WuQRUqSJM0HswavJNslWQvcAVxQVVdNmWRf4KZJj28Glg2uREmSpPlha3q8Hquq\n",
       "F9HC1CuTrJpmskx92gBqkyRJmldmPMdrsqq6L8k/AUcAayaNugVYPunxsm7Y4yQxjEmSpLFRVVM7\n",
       "lrbZjMErybOATVV1b5KnAa8GfmvKZOcApwBnJFkJ3FtVd0z3esN4Axq+JKdW1amjrkNPje033my/\n",
       "8WXbjbdhdRjN1uO1N/CRJNvRDkt+tKo+l+RkgKo6rarOTbI6yfXAQ8BJwyhUkiRp3M12OYkrgMOn\n",
       "GX7alMenDLguSZKkeccr12trrBl1Adoma0ZdgLbJmlEXoKdszagL0NyTqn7OeU9SnuMlSZLGwbBy\n",
       "iz1ekiRJPTF4SZIk9cTgJUmS1BODlyRJUk8MXpIkST0xeEmSJPXE4CVJktQTg5ckSVJPDF6SJEk9\n",
       "MXhJkiT1xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9cTgJUmS1BODlyRJUk8MXpIkST0xeEmSJPXE\n",
       "4CVJktQTg5ckSVJPDF6SJEk9MXhJkiT1xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9cTgJUmS1BOD\n",
       "lyRJUk8MXpIkST0xeEmSJPVkxuCVZHmSC5JcmeRrSd4yzTSrktyX5PLu9s7hlStJkjS+Fs8yfiPw\n",
       "1qpam2Rn4NIk51fV1VOm+3xVHTecEiVJkuaHGXu8qur2qlrb3X8QuBrYZ5pJM4TaJEmS5pWtPscr\n",
       "yf7ACuDiKaMKODrJuiTnJjl0cOVJkiTNH7MdagSgO8x4FvDLXc/XZJcBy6tqQ5LXAGcDBw+2TEmS\n",
       "pPE3a/BKsgT4OPC3VXX21PFV9cCk++cleX+S3atq/TSvdeqkh2uqas1TqlqSJGmAkqwCVg19PlU1\n",
       "UxEBPgLcXVVv3cI0ewF3VlUlORL4WFXtP810VVWeCyZJkua8YeWW2Xq8Xga8Afhqksu7Ye8AngNQ\n",
       "VacBJwBvTrIJ2ACcOOgiJUmS5oMZe7wGOiN7vCRJ0pgYVm7xyvWSJEk9MXhJkiT1xOAlSZLUE4OX\n",
       "JElSTwxekiRJPTF4SZIk9cTgJUmS1BODlyRJUk8MXpIkST0xeEmSJPXE4CVJktQTg5ckSVJPDF6S\n",
       "JEk9MXhJkiT1xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9cTgJUmS1BODlyRJUk8MXpIkST0xeEmS\n",
       "JPXE4CVJktQTg5ckSVJPDF6SJEk9MXhJkiT1xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9cTgJUmS\n",
       "1JMZg1eS5UkuSHJlkq8lecsWpntvkuuSrEuyYjilSpIkjbfFs4zfCLy1qtYm2Rm4NMn5VXX1xARJ\n",
       "VgMHVtVBSY4CPgCsHF7JkiRJ42nGHq+qur2q1nb3HwSuBvaZMtlxwEe6aS4GlibZawi1SpLUu4Rd\n",
       "Eg5KWD7qWjT+Zuvx+p4k+wMrgIunjNoXuGnS45uBZcAd21ibJGmEEl4IFPDNKh4adT1bIyG0fdCu\n",
       "wA8Dl3SjVgA7Av8K7AVcBewN3AYcDRwI3Ag8oxt+IHAIsB54IRCgEtYDXwAuB+4H7gXW0Toyrqvi\n",
       "kaG/SY21rQpe3WHGs4Bf7nq+njDJlMe1rYVJc0m3Md+b1uP7auAW4FO0je4S2kZ+x+7xpu5p36lq\n",
       "n4Xu+bsDD3WvcS+wU/e8fWmfoc8B+wMPAq8ADqLtQJ4GfKub7jBgKXADcF/3GmcDr6Rt/A8FDgC+\n",
       "CFwDvBxYBXwHuBbYD3ikq2EjcC5wa1fPPsCLu+n+Dri6iu9s67IbNwnb05bFEcBfAJcBG2g76yu7\n",
       "23LgOcBLacvufto68Q3gKNpy3p620/4qrZ3uZPO2cg/aDn5P4HbaunMt8B5g7cR609UTYHEVG5/i\n",
       "+3ka8H3AT9HWjbuAx4C/Ai6r4uFJ83kJ8DrgcOBHJr3MIwl30ELLF7r3swj4F2AtbZ3/D8AutPXu\n",
       "JcAPAHd3y/IlwP8DdqCtt7d1z1lBWzePoX1pX9Utjxto6/0BwDNpy/Yy4MRufs+htcldwPNpy/Xp\n",
       "wLe79zphLfCurt4Lu9f6Q+DLwMFdfc8DrgfuobXDv9E+I+cA76O15xuq+GbCdrTP5kraZ3X7bllN\n",
       "nNu8MeF9XT1Lu2lvBK7o3jvd9B+iBcLLJrf1ZAlLgOO75XVTt8wepu239wO+2d3fp6vjmio2JbwI\n",
       "OJa2vj4AnEk7WgXwLOBngGd373U9rb3STb8H8MkqPj+pjnTL+K4q7uo+H9Dab89umT823ftIeHq3\n",
       "bK6kbfsyEUy73sNbuvdy+0La1qRq5oyUZAltB3NeVb17mvF/DqypqjO6x9cAx1TVHVOmK+C3Jg1a\n",
       "U1Vrtq18LVQJu1Vxz8ROCXgUWDR555SwlLbBuIy2oVwG/EfaBv15wM7Av9M2TktoG+dbu78H0DaU\n",
       "99ACzWtoG7graAFoMW3HOZMNtA3sq2gb/D1oG6upX3i+TduBHNI9fpi2c7sV+Drtm/cG2o757u41\n",
       "VtJC2wu74QfTvsHfRdu4HkULcKcD19F2ig/SNoAAP0rb8B9MC2s70DaC36XtMN40qb77uvne0M3r\n",
       "27SNNrSAdxitx+BPu9oPA86q4sZZlg8JuwMPTLRbt2Pbg9aez6PtjBdVtV71rr13pm3M/+3JhJGE\n",
       "XYATaDuAjbQ2OZi23L9Aa5dfoK0fD9GW1X20ZbqOFm4PpbXJpV0dO9FC8a60ndgLumV1CG25/2NX\n",
       "6wtpO7/J6+uDtKB7DW3Zfj/wTlooup0WSJazeT37evfaj3W3f6e11760oPAIbZ15fnc7nRb2f4y2\n",
       "o/0q8OFuutfTQvmE73TvG9q69qvAp4FbqtjYtcuraevdEbQd/d209WiX7nm30dahI7r3fn03zV20\n",
       "9eM6WkB9IW39Sfc+ruqWyde7Zfhot1zvoq1ry2kh7+Du76do69kzujoe7F57E23dv5MWEr4DkLCI\n",
       "tsOf+EL0OAk7bWtvXkKqqITDaZ+d3Wjbittp6/MBtLZZQmvnZwLP7Wo/nxYkNwIvoq1bRdvm7NQN\n",
       "34XH+0b3mkVb5ktp6+NdtHY8r5v3dsBqWkiccHtX27/S1otjadvGr9GW/6uBz9LaZE/aOg9tHbmH\n",
       "zacb3d29D2jrzL/SAuIuXd2P0sL39t3tEdq29mLaNnFifZt47U93y2MT7bN3B239eD5wUTe//9ZN\n",
       "c05X37Kups9V8ejEiyXs1D33oG7Q07tldUm3TIr22dhQxYZu+mXw178LXzkcHt0E118Fn31dVU3t\n",
       "WNpmMwavJKGdv3V3Vb11C9OsBk6pqtVJVgLvrqonnFyfpIbxBjS+JjZWU4YtmvwB6oZtR/uAP5/2\n",
       "QXsD8FraxvYg2gds4nzFi2k7wu+jhY3baT1V93T3vwp8grYx26Mb/jzaDnbi2/LRtA3Bn3SvP9Er\n",
       "9QdV3Duprt1pH+Dv0HaAYfPGZCNwCu0Dv5jWK3UVbYfzXdrG6e4pPRvPom1c2NK34L50vSRF27Hu\n",
       "RgsezwR+kNYOu9I29htoy/xw2k5jEW3juy/tG/mi7nkX0ZbN0bSdxkO0Xo4Ja2nLaf/u74600DWx\n",
       "Q4HWVrtNKfUq4Eu0nfM3aBv213avsYS2rO+nteNu3XzP78Y/RFtv9qLtTDYBHwM+UcW6J7vMBqEL\n",
       "Cc/s6j2IFq6+QlvOL6Mtz11o6/z30Wq/graD3IG2Lt9Oe6970nZSH6ziwi3Mb+KztSdtefz7k1n3\n",
       "uiD8/bRlfGcVD0/3udYTdcvuGFqv6T608H0rrX0LuLKKf5sy/RKAKh5JWAxUFY9O+kKyH3BjFfdP\n",
       "mdd+tHXovtkOhXZfWFfRgtJSWqC+iBae9qB9Lnekfeau7e5PHAnYj7Yu3NQN/6cqbknYlfbZ3gM4\n",
       "snvNC2lfEM/saj+Rtg5PrPvfpYXTq2nh8EHgo7TtzNG07fUDtCBP9/7W0XpXJ77c3sbmnr9dp3m7\n",
       "D9O23xPbla8Ap3Y1HgY5fhTB6+W0FPtVNh8+fActnVNVp3XT/RltwTwEnFRVl03zWgavBS5hT+A/\n",
       "03Z2rwR+nBZW/pnN32wOoB3muoH2oX8B7cM50cPySdo6+Xe0ELa+im8kPIMWdo6n9SL8C+2QwQbg\n",
       "GVXc1cNbVKc7THI47Zvty2jt9m1aO+9I6xU7nBain0bbWD4duGBqT1m3U9mTtj5A60mpbtiP03b8\n",
       "K2jrzIO0b/sTPTL70ALZeuDaqaFe0tzXbQNSxWNbGPds4I204Po12pfv+6Z8sZ3oTf8uLYTdSNvm\n",
       "HNDd3zA1lA4rt8x6qHFgMzJ4jZVuJZ349vRowm60rv6daN/InkY7cfVztG8rzwQ+Q9up7kj7Nr4f\n",
       "7QTU1d34o2mHE66ldSVfSutOXkU7NPMx2rep19B2qqF9K/pqFbcM+z1LkjTB4KWh6A4pvRL4IVpQ\n",
       "2p0WrI7qJnmYdgjmMdqhvd1pXcyLgY/TAth2tB7PCZfTDpE8rxu/I6379rNbc96PJEmjZvDSNuu6\n",
       "ZA+lBa1fpB2i+S6tl+k82rkyO9K6bT9F67JdSut9uruKO0dQtiRJvTN46UnrgtYzgJ8HTqaFrJ2B\n",
       "NbSTmb8AXDLdcXNJkhYyg5eeoAtWL6L9IuMY2i/OLqb1WB1K+1XfEtov6iYu+HeBQUuSpJkZvBa4\n",
       "7joji2m/5jqUdnHDn+juf5kWqqBdzPFm2i+8LgQe2tL1ayRJ0vQMXgtUwvG067y8hc3XiLqKduHK\n",
       "fwLOH5d/5SFJ0rgYVm7Z6v/VqH4k7EW70vQuwG/STnb/E9olFi4Cdqhiw+gqlCRJT5U9XnNAwmHA\n",
       "r9D+jccOtPOxbqOdm3WmhwolSeqXPV7zUPd/vd5Gu8Do+2gnyH/Zk98lSZqfDF4jkLAM+CPaf65/\n",
       "D/CzVTww2qokSdKwGbx60P27nR+h/d/BI2j/aueLwAuquGeUtUmSpP54jteQJRxJOyn+n2n/wPMS\n",
       "4ItVXDPSwiRJ0hZ5jtcYSjgZ+G3gF6v4y1HXI0mSRsvgNWAJK4FfA5YBBwArq/jmaKuSJElzwXaj\n",
       "LmA+SFiccHDCGcBZwKW0nq7nGbokSdIEe7y2QcJi4H8BP9MN+gvgp73AqSRJmo7B6ylI2Bt4K+36\n",
       "W98GXlTFTaOtSpIkzXUGrycp4RW0XyheB/w68NkqNo62KkmSNA4MXk9CwsuBTwA/VcU/jLoeSZI0\n",
       "Xjy5fislHEcLXf/V0CVJkp4Ke7xm0Z1A/0fAjwHHVfGlEZckSZLGlMFrBglLgNOA/YAVVawfcUmS\n",
       "JGmMeahxGglLEt4G3AA8G3idoUuSJG0re7ymSNgB+DiwPXAccHkV/fxDS0mSNK8ZvCZJ2IUWuu4B\n",
       "/pOXiZAkSYPkocZOwn7AF4Abab9cNHRJkqSBMngBCQcCFwKnAz9bxaYRlyRJkuahBR+8El5F6+n6\n",
       "3Sp+3/O5JEnSsCzoc7wSXgv8NfATVVww4nIkSdI8l6p+OniSVFWll5lthYQX0g4vvs7QJUmSJhtW\n",
       "blmQPV4JewBfAn7R0CVJkvqy4M7xSngJcCnwt7TDjJIkSb2YNXgl+VCSO5JcsYXxq5Lcl+Ty7vbO\n",
       "wZc5GN2vF88Ffg042RPpJUlSn7bmUOOHgT8F/maGaT5fVccNpqThSDgIOB/4zSr+YdT1SJKkhWfW\n",
       "Hq+qupB2JfeZzJmT5qeTcDjweeB3qvjzUdcjSZIWpkGc41XA0UnWJTk3yaEDeM2BSXgBcB7wS1V8\n",
       "cNT1SJKkhWsQv2q8DFheVRuSvAY4Gzh4ugmTnDrp4ZqqWjOA+W9RwnLgU8Dbqvj4MOclSZLGV5JV\n",
       "wKqhz2drruOVZH/gk1X1gq2Y9gbgxVW1fsrwXq/jlfAc2iUj/k8Vf9LXfCVJ0vgbVm7Z5kONSfZK\n",
       "ku7+kbQwt36Wpw1VwjOBzwDvM3RJkqS5YtZDjUlOB44BnpXkJuBdwBKAqjoNOAF4c5JNwAbgxOGV\n",
       "O7uE7Wi/wDyvit8bZS2SJEmTzat/GZSwG3AasC+wqoqNw5yfJEman+bsoca5ImEp7eKoG4AfNnRJ\n",
       "kqS5Zl70eCUsof2a8jbg56p4bBjzkSRJC4M9XluQEPjeRVHfbOiSJElz1SCu4zVq/wU4GniJhxcl\n",
       "SdJcNtbBK+EHgPfQzul6cNT1SJIkzWRsDzUmvBQ4E3h9FZeNuh5JkqTZjGXw6i4b8ffAyVWcP+p6\n",
       "JEmStsbY/aqxO5n+TOD2Kt6y7ZVJkiQ93rB+1TiO53j9PPB84E2jLkSSJOnJGKser4TDgM8CL6vi\n",
       "2sFUJkmS9HgL/jpeCTvTDjG+1dAlSZLG0dj0eCX8NVBVnDS4qiRJkp5oQZ/jlfBGYCVwxKhrkSRJ\n",
       "eqrmfPBKOAp4L7DKi6RKkqRxNqfP8UrYEfgw8AtVrBt1PZIkSdtiTp/jlfA3tHD4xir6KVSSJC14\n",
       "C+4cr4QTgZcChxm6JEnSfDAne7wS9gbWAquruHS4lUmSJD3egrmOV8J2wIeA0wxdkiRpPplzwQv4\n",
       "OWA34HdGXYgkSdIgzalDjQnPAS6lXTriyl4KkyRJmmLeH2pMWAz8A/AHhi5JkjQfzZngBfwP4H7g\n",
       "j0ddiCRJ0jDMictJJKwE3gys8NIRkiRpvhp5j1fC9rRfMf5SFbeNuh5JkqRhGXnwAn4f+AZw1qgL\n",
       "kSRJGqaRHmpMeC1wAh5ilCRJC8DIglfCXsAHgROqWD+qOiRJkvoykut4JQQ4E7ihirf3UoAkSdJW\n",
       "mm//JPtngEOAN41o/pIkSb3rvccr4fnARcArq7i6l5lLkiQ9CSO7cn2SDyW5I8kVM0zz3iTXJVmX\n",
       "ZMWWp2M74K+A3zZ0SZKkhWZrLifxYeDYLY1Msho4sKoOov2D6w/M8FpvBhYB738yRUqSJM0Hswav\n",
       "qroQuGeGSY4DPtJNezGwNMleW5j2VOCkKh59knVKkiSNvUFcQHVf4KZJj28Glm1h2t+u4usDmKck\n",
       "SdLYGdSV66eefLalM/bfN6D5SZIkjZ1BXE7iFmD5pMfLumHTyP/M5oi2pqrWDGD+kiRJ2yTJKmDV\n",
       "0OezNZeTSLI/8MmqesE041YDp1TV6iQrgXdX1cppphvKzzIlSZIGbWQXUE1yOnAM8KwkNwHvApYA\n",
       "VNVpVXVuktVJrgceAk4adJGSJEnzwUj+ZZAkSdJcNrILqEqSJGkwDF6SJEk9MXhJkiT1xOAlSZLU\n",
       "E4OXJElSTwxekiRJPTF4SZIk9cTgJUmS1BODlyRJUk8MXpIkST0xeEmSJPXE4CVJktQTg5ckSVJP\n",
       "DF6SJEk9MXhJkiT1xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9cTgJUmS1BODlyRJUk8MXpIkST0x\n",
       "eEmSJPXE4CVJktQTg5ckSVJPDF6SJEk9MXhJkiT1xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9WTW\n",
       "4JXk2CTXJLkuydunGb8qyX1JLu9u7xxOqZIkSeNt8UwjkywC/gx4FXAL8OUk51TV1VMm/XxVHTek\n",
       "GiVJkuaF2Xq8jgSur6pvVdVG4Azg+Gmmy8ArkyRJmmdmC177AjdNenxzN2yyAo5Osi7JuUkOHWSB\n",
       "kiRJ88WMhxppoWo2lwHLq2pDktcAZwMHb3NlkiRJ88xswesWYPmkx8tpvV7fU1UPTLp/XpL3J9m9\n",
       "qtZPfbEkp056uKaq1jzpiiVJkgYsySpg1dDnU7XlTq0ki4GvAz8E3ApcArx+8sn1SfYC7qyqSnIk\n",
       "8LGq2n+a16qq8lwwSZI05w0rt8zY41VVm5KcAnwaWAR8sKquTnJyN/404ATgzUk2ARuAEwddpCRJ\n",
       "0nwwY4/XQGdkj5ckSRoTw8otXrlekiSpJwYvSZKknhi8JEmSemLwkiRJ6onBS5IkqScGL0mSpJ4Y\n",
       "vCRJknpi8JIkSeqJwUuSJKknBi9JkqSeGLwkSZJ6YvCSJEnqicFLkiSpJwYvSZKknhi8JEmSemLw\n",
       "kiRJ6onBS5IkqScGL0mSpJ4YvCRJknpi8JIkSeqJwUuSJKknBi9JkqSeGLwkSZJ6YvCSJEnqicFL\n",
       "kiSpJwYvSZKknhi8JEmSemLwkiRJ6onBS5IkqScGL0mSpJ4YvCRJknpi8JIkSerJrMErybFJrkly\n",
       "XZK3b2Ga93bj1yVZMfgyJUmSxt+MwSvJIuDPgGOBQ4HXJzlkyjSrgQOr6iDg54APDKlWjUiSVaOu\n",
       "QU+d7TfebL/xZdtpOrP1eB0JXF9V36qqjcAZwPFTpjkO+AhAVV0MLE2y18Ar1SitGnUB2iarRl2A\n",
       "tsmqURegp2zVqAvQ3DNb8NoXuGnS45u7YbNNs2zbS5MkSZpfZgtetZWvk6f4PEmSpAVj8SzjbwGW\n",
       "T3q8nNajNdM0y7phT5DEQDamkrxr1DXoqbP9xpvtN75sO001W/D6CnBQkv2BW4GfBF4/ZZpzgFOA\n",
       "M5KsBO6tqjumvlBVTe0VkyRJWlBmDF5VtSnJKcCngUXAB6vq6iQnd+NPq6pzk6xOcj3wEHDS0KuW\n",
       "JEkaQ6ny6J8kSVIfhn7l+q25AKv6lWR5kguSXJnka0ne0g3fPcn5Sa5N8pkkSyc95ze6NrwmyQ9P\n",
       "Gv7iJFd0494zivezUCVZlOTyJJ/sHtt+YyLJ0iRnJbk6yVVJjrL9xkPXFld2y/3vk+xg281dST6U\n",
       "5I4kV0waNrD26tr/zG74l5LsN2tRVTW0G+3w5PXA/sASYC1wyDDn6W2r2uXZwIu6+zsDXwcOAf4Q\n",
       "eFs3/O3A/+7uH9q13ZKuLa9nc2/pJcCR3f1zgWNH/f4Wyg34VeDvgHO6x7bfmNxo1z786e7+YmBX\n",
       "22/u37rl/01gh+7xmcCbbLu5ewNeAawArpg0bGDtBfwC8P7u/k8CZ8xW07B7vLbmAqzqWVXdXlVr\n",
       "u/sPAlfTrsf2vYvhdn9f190/Hji9qjZW1bdoK+NRSfYGdqmqS7rp/mbSczRESZYBq4G/YvPlXGy/\n",
       "MZBkV+AVVfUhaOfSVtV92H7j4H5gI/D0JIuBp9N+eGbbzVFVdSFwz5TBg2yvya/1ceCHZqtp2MFr\n",
       "ay7AqhHqfrG6ArgY2Ks2/yL1DmDiPxDsw+MvIzLRjlOH34Lt25f/C/w68NikYbbfeHgu8O0kH05y\n",
       "WZK/TLITtt+cV1XrgT8GbqQFrnur6nxsu3EzyPb6Xs6pqk3AfUl2n2nmww5enrk/hyXZmZbQf7mq\n",
       "Hpg8rlq/qe03ByX5UeDOqrqcJ168GLD95rjFwOG0wxOH034N/t8nT2D7zU1JDgB+hXYYah9g5yRv\n",
       "mDyNbTdeRtFeww5eW3MBVo1AkiW00PXRqjq7G3xHkmd34/cG7uyGT3eR3Ju74cumDJ/24rkaqKOB\n",
       "45LcAJwO/GCSj2L7jYubgZur6svd47NoQex222/OOwL4YlXd3fVufAJ4KbbduBnEtvLmSc95Tvda\n",
       "i4Fdu57RLRp28PreBViTbE878eycIc9Ts0gS4IPAVVX17kmjzqGdKEr39+xJw09Msn2S5wIHAZdU\n",
       "1e3A/d0vsgK8cdJzNCRV9Y6qWl5VzwVOBP6lqt6I7TcWuuV+U5KDu0GvAq4EPontN9ddA6xM8rRu\n",
       "mb8KuArbbtwMYlv5j9O81gnA52adew+/KHgN7Vdz1wO/0eevGbxtsU1eTjs3aC1weXc7Ftgd+Cxw\n",
       "LfAZYOmk57yja8NrgB+ZNPzFwBXduPeO+r0ttBtwDJt/1Wj7jckNOAz4MrCO1muyq+03HjfgbbSg\n",
       "fAXtpOoltt3cvdGOCtwKPEI7F+ukQbYXsAPwMeA64EvA/rPV5AVUJUmSejL0C6hKkiSpMXhJkiT1\n",
       "xOAlSZLUE4OXJElSTwxekiRJPTF4SZIk9cTgJUmS1BODlyRJUk/+P1AvOSQLygIDAAAAAElFTkSu\n",
       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1097b8910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAGtBJREFUeJzt3X2sXdWZ3/Hvg81LeDWOiTH2NRdiDCEwDUkENE0aTyed\n",
       "gqci/SPSEGlGLf2jUSqUNKN20olGCpVatapUNUOjRKhNRiTThomSEUM0jCbpNJ5mVA3JhHdjAwaM\n",
       "X/ALYGwM5sXA0z+efbjHl8u9Bp+zzj3X34+0tc/Ze99z1mEh66e1nr12ZCaSJEkavhNG3QBJkqTj\n",
       "hcFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmSGpk1eEXEKRFxV0TcGxEPRcR/fJvrbo6IRyPi\n",
       "voi4YjhNlSRJGm+LZzuZmS9HxK9m5qGIWAz8dUR8PDP/undNRKwH1mTmRRFxFfBN4OrhNluSJGn8\n",
       "zDnVmJmHupcnAYuAfdMuuQ64tbv2LmBJRCwfZCMlSZIWgjmDV0ScEBH3AnuAn2bmQ9MuWQls73u/\n",
       "A1g1uCZKkiQtDEcz4vVGZn6IClN/PyLWzXBZTP+zAbRNkiRpQZm1xqtfZh6IiD8DPgps6Du1E5jo\n",
       "e7+qO3aEiDCMSZKksZGZ0weWjtmswSsilgGvZeb+iHgP8A+BfzftsjuAG4HbIuJqYH9m7pnp84bx\n",
       "AzR8EXFTZt406nbo3bH/xpv9N77su/E2rAGjuUa8VgC3RsQJ1LTkdzPzLyPicwCZeUtm3hkR6yNi\n",
       "C/AicMMwGipJkjTu5lpO4gHgwzMcv2Xa+xsH3C5JkqQFx5XrdTQ2jLoBOiYbRt0AHZMNo26A3rUN\n",
       "o26A5p/IbFPzHhFpjZckSRoHw8otjnhJkiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKk\n",
       "RgxekiRJjRi8JEmSGjF4SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0Y\n",
       "vCRJkhoxeEmSJDVi8JIkSWrE4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJ\n",
       "kiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKkRmYNXhExERE/jYiNEfFgRHxhhmvWRcSB\n",
       "iLin235/eM2VJEkaX4vnOH8Y+FJm3hsRpwO/jIifZOamadf9VWZeN5wmSpIkLQyzjnhl5u7MvLd7\n",
       "/QKwCThvhktjCG2TJElaUI66xisiJoErgLumnUrgYxFxX0TcGRGXDq55kiRJC8dcU40AdNOMPwC+\n",
       "2I189bsbmMjMQxFxLXA7sHawzZQkSRp/cwaviDgR+CHwR5l5+/TzmXmw7/WfR8Q3ImJpZu6b4bNu\n",
       "6nu7ITM3vKtWS5IkDVBErAPWDf17MnO2RgRwK/BsZn7pba5ZDuzNzIyIK4HvZ+bkDNdlZloLJkmS\n",
       "5r1h5Za5Rrz+HvBbwP0RcU937CvAaoDMvAX4DPD5iHgNOARcP+hGSpIkLQSzjngN9Isc8ZIkSWNi\n",
       "WLnFleslSZIaMXhJkiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmS\n",
       "GjF4SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi\n",
       "8JIkSWrE4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAl\n",
       "SZLUiMFLkiSpEYOXJElSIwYvSZKkRmYNXhExERE/jYiNEfFgRHzhba67OSIejYj7IuKK4TRVkiRp\n",
       "vC2e4/xh4EuZeW9EnA78MiJ+kpmbehdExHpgTWZeFBFXAd8Erh5ekyVJksbTrCNembk7M+/tXr8A\n",
       "bALOm3bZdcCt3TV3AUsiYvkQ2ipJkjTWjrrGKyImgSuAu6adWgls73u/A1h1rA2TJElaaI4qeHXT\n",
       "jD8AvtiNfL3lkmnv81gbJkmStNDMVeNFRJwI/BD4o8y8fYZLdgITfe9Xdcdm+qyb+t5uyMwNR91S\n",
       "SZKkIYmIdcC6oX9P5tsPTkVEUPVbz2bml97mmvXAjZm5PiKuBr6WmW8pro+IzMzpI2OSJEnzzrBy\n",
       "y1zB6+PA/wXuZ2r68CvAaoDMvKW77uvANcCLwA2ZefcMn2XwkiRJY2EkwWugX2TwkiRJY2JYucWV\n",
       "6yVJkhoxeEmSJDVi8JIkSWrE4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJ\n",
       "kiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSI4tH3QBJkqRhiiCA9wBLgbO6/dnA+4BVwHJgWbed\n",
       "1W3DaUtmDuuzj/yiiMzMaPJlkiRpwYngBOA04AwqPAVwMpBUkDoXuKg7diawEpgEzgdOAfYB+4Hn\n",
       "utd7gKeA3cAzwLPd8YMQjw4jtxi8JEnSyHWjUmcC51Fh6WJgNbAGWAEsoYLVIuBF4GkqcL1MBbD9\n",
       "VJB6tDv2PLAT2ApsA/ZlctShZ1i5xeAlSZKGogtTS6iRp+nbku6yFVTYOg94nRqB2kEFqMeBLd2x\n",
       "/cDeTJ5r0/bh5BZrvCRJ0qwiWExN8QGcSo1EnQqcSNVOLadGo1ZS03qnMRWoDlPBaWff9gAVpOje\n",
       "PwXsyuRgg58zUo54SZJ0nIvgbOD91LTe6VRguoCa8pvs3r9CTem9TE3fvUiFqlepGqldVIB6sju3\n",
       "C3hqXMOUU42SJOkd6YrRT6UKz1dQwer87vW5VKBaQd3N15vWO8hUbVRv257Jq00bP2IGL0mSjiMR\n",
       "LKKWNTiVmso7ozv1GnAOtRTCOVRoWk3dzXcCdUffGdTI1XuAl4AD1KjUI1Sh+S6mRqh2AdsyeaXF\n",
       "7xoXBi9JksZQVx+1hKm1o3r7JdSU3FIqWJ1JjUatBd5Lha4XqOD0VPf6DeAk6o6+3hIIz3TnN1PF\n",
       "6a9Qo1YvAIcyeaPBz1xwDF6SJM0TEZwOTFAjTZdSwWl6sOrtT+PItaN6++e7c89RyyA8T41GPUwF\n",
       "qwOZvNbsR+kI3tUoSdIQdEsenAtcSBWYn06Fpt4incuYWoDzRGo06hQqJG2ngtIO4AmODFa9/UFH\n",
       "ndTjiJckacHpwtQZ1LTdSqrW6WSqkPwSKlCt6M6dQ4Wkx6jwdAjYS41A7aem8p7sjh+mwtSz72Qx\n",
       "To0fpxolScelrsh8CVOrl/cKzhdToelCasRqGVPF5suoZQ6eoO7Ke4mqfXoaeIgKU7up2qi9FpZr\n",
       "OoOXJGnsdSNRp1MBqX97X7etpGqnelN9vefyvUAtcbCfukPvJeruvmeoZRB2UaHqmd4+k5db/S4t\n",
       "PAYvSdK81K0VdQa1nMF5HBmmpgesc6g7857u2/b27XsLcO6jwtaLwP5MXm/3iySDlySpsS5QncPU\n",
       "iubLqMLy91IjUu+lVjdfTdU/baWKzXtB6ulpr58Gns7kxZa/Q3o3DF6SpGMWwSnUHXqTVGDqPZy4\n",
       "NxrVq586k6qnOkAFqkeoEPUsXXF5t98GPJ7J4YY/Qxo6g5ckaVYRnEGFqglq2u+j1IjUCmo9qVOo\n",
       "gvQdVGB6jKmVy3ujUweo0avnqSk+i851XBpZ8IqIbwO/AezNzMtnOL8O+FOquBHgh5n572e4zuAl\n",
       "SccggtOoILWKKkJfA3yYClvnA0nVR22nnrl3DzVStZsanXoZeMFlEKS5jTJ4fYIqcPzOLMHrdzLz\n",
       "ujk+x+AlSTOI4ERqVKpXP3UuU3f3XUKFquXU4p1bqWC1gwpZv6SWTHgykxdat11aqEa2cn1m/iwi\n",
       "Jue4zEAlSbOI4Cymaqt6+95inpcwVTf1LDVCtZMarbqTGr3aAzzvaJU03gbxyKAEPhYR91H/UPzr\n",
       "zHxoAJ8rSfNKtwbV2VQR+lJquYSTqX8HlzJVoN5bwPPMbjuPqdGqJ/v29wJ/ADzonX7S8WEQwetu\n",
       "YCIzD0XEtcDt1CMa3iIibup7uyEzNwzg+yVpYLpwtZqqn1pLjU6tAi6jllV4nSpEf44amXqVGvV/\n",
       "llq8cyvwi+71QapIfRc+Ykaa17rSqXVD/56juauxm2r80Uw1XjNc+wTwkczcN+24NV6S5oUITqfq\n",
       "pyaoQHUxVbQ+SY1OPU9N822hbhzaCWwCHslk/wiaLKmxkdV4zSUillN3PGZEXEmFuX1z/Z0kDUsE\n",
       "Sziynqp/m6QeWbOdClQPAPdTo/VPALsyOdC80ZKOC3MGr4j4HvBJYFlEbAe+StUqkJm3AJ8BPh8R\n",
       "r1Frv1w/vOZKOt51U4HncGSQmv76BKbqqHrbXX2v92byRtuWS5ILqEqaR7p1qlYAi6jlEyaoeqsL\n",
       "qeUVLqCC1SGODFVbp71/znoqScfClesljb0IzqTqqT7E1HIKK6i7A3urq++iCtj3UNOB26hgtYOa\n",
       "CtzqelWShs3gJWne6hYA7T3vr7fw5wpq1Gp5d241cBpVtH4/8Ch1V+BT1F2CO4Hdmbzeuv2SNJ3B\n",
       "S9JI9NVUXdBt51LTfWuZClhLqBDVC1A7qEC1m3r+3y5qCvAZg5WkcWDwkjRwEZxEBacLqAVAl1Hr\n",
       "Vy3tjk9228vUNN8TVIjaRo1cbeveG6gkLSjzdjkJSfNTBIuphT+XUtN851PTgOdTo1aT3f5pKlA9\n",
       "Qy0K2lu/ajc1SvVEJs83br4kLUgGL2kMddN/51KjU6uAU7v9RLefpEax9lIrqm+jQtRO4D5qGvBJ\n",
       "YFsmrzVuviQdt5xqlOaZbvqvd5ffuX37VdQja1Z12yHgMSpAHaLqqrZ3+yeBLZm80rr9krQQWOMl\n",
       "LQBdqFpFTfn19muoQNULWWdR03+7qOm+3d3rnVTQ2gFsz+Rg6/ZL0vHC4CXNc9303xnUtN9p1KKf\n",
       "07e11NTfDipI7aSeBbiFCle9hylbqC5JI2TwkuaJbs2qD1IjVR+gFgP9IFVXdRh4CXiRClTTt4ct\n",
       "VJek+c/gJTXUTQmuoUap1nTbxcAl1JTgI922mVoM9AHg8UwOjaTBkqSBMnhJA9JNCS7jyFqrVd2x\n",
       "1VS91WqqUP1xaoX1x6iQtRnYmcnh9i2XJLVi8JLegW46cDU1QnUxFax604ET1HRgr86qt3+GWnbh\n",
       "ceCxTF5u3nBJ0rxg8JL6RLCIClCrqTqrS6iFQc+h7gycoArVHwE2UeFqExWqtvmQZUnSbAxeOm5E\n",
       "cAK1jtUkcCbwXqamAy+g6q0uoO4OfBJ4mApVW6kFQ/dQq627hpUk6V0xeGlB6eqs3kfVU11MjVZd\n",
       "TIWqS6kFQbcC+6nH2GynpgO3UksvbLGQXZI0LAYvjaUIzmTqbsBLmbpDcA3wClW0/ggVqHrPCNzo\n",
       "kguSpFEyeGle6h7EfD4VqtZSo1jnUbVXlwOnUFOBDwMbqTsEt1DF68+Nos2SJM1lWLnFh2RrTt20\n",
       "4HnAZX3bWqqAfSU1DfgQNWK1u3vdO7YnkzbpXpKkec4RL/WK2VcyVch+IVXYfj5Vg3U58CrwYLdt\n",
       "pEawtgNP+ngbSdJC41Sjjkk3anU2NVJ1KbWm1YVUsFoDHKCK2J8DnqCWXXiSqr26P5On27dakqTR\n",
       "MHjpqERwMhWsLuLIYPURIKkaq4e6bQtV3L4lk4MjabAkSfOQwUtv6qYGJ6hwtZYKVpNU4FpN9zDm\n",
       "bv9Yt787k2dG0V5JksaNwes41D325kJqOYb+7VeAF5h6UPMWalpwI/Wg5pdG0mBJkhYIg9cC1beQ\n",
       "6PRwdTE1erWTqeUYetsDjl5JkjQ8Bq8xFsFJ1LTgBd3+/UytdbUGeIO3hquHqdorH3sjSVJjBq8x\n",
       "EMHZVJ1Vr9ZqklqKYS2wjbpbcEu37ei2LcA+17qSJGn+MHjNE124mqSC1VqmHodzCXAS3VQgVXO1\n",
       "rXu90borSZLGh8Groa7uagU1WtXbLqWmCBdRa1vtoArbN/dtex25kiRp/Bm8hqALWMuokavLmApZ\n",
       "lwGvU6NVD3b7jdS04DOGK0mSFjaD17v+XhZRhezv77bVVIH7B7v3r1KLivYC1oPUXYN7WrdVkiTN\n",
       "DyMLXhHxbeA3gL2ZefnbXHMzcC1wCPhnmXnPDNcMNXhFcAo1Hfgr1KjVKqbqr/ZRC4k+Rk0TPkE3\n",
       "gpXJ/mG1SZIkjadh5ZbFR3HNHwL/DfjOTCcjYj2wJjMvioirgG8CVw+uib3vYTG13tXybnsfNXp1\n",
       "ORW2JqmRq/upkatfUjVYD2VyaNDtkSRJeqfmDF6Z+bOImJzlkuuAW7tr74qIJRGxPDPf8VRdF64m\n",
       "mXoUTm+/lpoufBbYA+zt9juBO4D/AGzO5NV3+p2SJEmtHM2I11xWAtv73u+gpvlmDF7dcwZXMnO4\n",
       "Oh/YzdSjcB4F/qzbP5nJ4QG0V5IkaSQGEbwAps+Bzlg4FsHdVNDqPWfw0W7/s+71Y5m8PKA2SZIk\n",
       "zSuDCF47gYm+96u6YzO47G9hx4/hwMvAhszcMIDvlyRJOiYRsQ5YN/TvOZrlJLoarx/NdFdjV1x/\n",
       "Y2auj4irga9l5luK6+fjOl6SJEkzGdldjRHxPeCTwLKI2A58FTgRIDNvycw7I2J9RGwBXgRuGHQj\n",
       "JUmSFoIFv4CqJEnSOzWs3HLCoD9QkiRJMzN4SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMG\n",
       "L0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6S\n",
       "JEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmS\n",
       "GjF4SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEbmDF4RcU1EbI6IRyPiyzOcXxcR\n",
       "ByLinm77/eE0VZIkabwtnu1kRCwCvg58CtgJ/CIi7sjMTdMu/avMvG5IbZQkSVoQ5hrxuhLYkplb\n",
       "M/MwcBvw6Rmui4G3TJIkaYGZK3itBLb3vd/RHeuXwMci4r6IuDMiLh1kAyVJkhaKWacaqVA1l7uB\n",
       "icw8FBHXArcDa4+5ZZIkSQvMXMFrJzDR936CGvV6U2Ye7Hv95xHxjYhYmpn7pn9YRNzU93ZDZm54\n",
       "xy2WJEkasIhYB6wb+vdkvv2gVkQsBh4Gfg14Cvg58Nn+4vqIWA7szcyMiCuB72fm5AyflZlpLZgk\n",
       "SZr3hpVbZh3xyszXIuJG4C+ARcC3MnNTRHyuO38L8Bng8xHxGnAIuH7QjZQkSVoIZh3xGugXOeIl\n",
       "SZLGxLByiyvXS5IkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhox\n",
       "eEmSJDVi8JIkSWrE4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCS\n",
       "JElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmSGjF4SZIkNWLwkiRJasTgJUmS\n",
       "1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhqZM3hFxDURsTkiHo2IL7/NNTd35++LiCsG\n",
       "30xJkqTxN2vwiohFwNeBa4BLgc9GxAemXbMeWJOZFwH/AvjmkNqqEYmIdaNug949+2+82X/jy77T\n",
       "TOYa8boS2JKZWzPzMHAb8Olp11wH3AqQmXcBSyJi+cBbqlFaN+oG6JisG3UDdEzWjboBetfWjboB\n",
       "mn/mCl4rge1973d0x+a6ZtWxN02SJGlhmSt45VF+TrzLv5MkSTpuLJ7j/E5gou/9BDWiNds1q7pj\n",
       "bxERBrIxFRFfHXUb9O7Zf+PN/htf9p2mmyt4/S1wUURMAk8Bvwl8dto1dwA3ArdFxNXA/szcM/2D\n",
       "MnP6qJgkSdJxZdbglZmvRcSNwF8Ai4BvZeamiPhcd/6WzLwzItZHxBbgReCGobdakiRpDEWms3+S\n",
       "JEktDH3l+qNZgFVtRcRERPw0IjZGxIMR8YXu+NKI+ElEPBIRP46IJX1/83tdH26OiF/vO/6RiHig\n",
       "O/cHo/g9x6uIWBQR90TEj7r39t+YiIglEfGDiNgUEQ9FxFX233jo+mJj99/9f0XEyfbd/BUR346I\n",
       "PRHxQN+xgfVX1/9/3B3/m4g4f85GZebQNmp6cgswCZwI3At8YJjf6XZU/XIu8KHu9enAw8AHgP8M\n",
       "/G53/MvAf+peX9r13YldX25harT058CV3es7gWtG/fuOlw34HeB/And07+2/MdmotQ//efd6MXCW\n",
       "/Tf/t+6//+PAyd37Pwb+qX03fzfgE8AVwAN9xwbWX8C/BL7Rvf5N4La52jTsEa+jWYBVjWXm7sy8\n",
       "t3v9ArCJWo/tzcVwu/0/6V5/GvheZh7OzK3U/4xXRcQK4IzM/Hl33Xf6/kZDFBGrgPXA/2BqORf7\n",
       "bwxExFnAJzLz21C1tJl5APtvHDwPHAZOjYjFwKnUjWf23TyVmT8Dnpt2eJD91f9ZPwR+ba42DTt4\n",
       "Hc0CrBqh7o7VK4C7gOU5dUfqHqD3BILzOHIZkV4/Tj++E/u3lf8K/Bvgjb5j9t94uAB4OiL+MCLu\n",
       "joj/HhGnYf/Ne5m5D/gvwDYqcO3PzJ9g342bQfbXmzknM18DDkTE0tm+fNjBy8r9eSwiTqcS+hcz\n",
       "82D/uaxxU/tvHoqIfwzszcx7eOvixYD9N88tBj5MTU98mLob/N/2X2D/zU8R8X7gX1HTUOcBp0fE\n",
       "b/VfY9+Nl1H017CD19EswKoRiIgTqdD13cy8vTu8JyLO7c6vAPZ2x2daJHdHd3zVtOMzLp6rgfoY\n",
       "cF1EPAF8D/gHEfFd7L9xsQPYkZm/6N7/gApiu+2/ee+jwP/LzGe70Y0/Af4u9t24GcS/lTv6/mZ1\n",
       "91mLgbO6kdG3Nezg9eYCrBFxElV4dseQv1NziIgAvgU8lJlf6zt1B1UoSre/ve/49RFxUkRcAFwE\n",
       "/DwzdwPPd3dkBfDbfX+jIcnMr2TmRGZeAFwP/J/M/G3sv7HQ/XffHhFru0OfAjYCP8L+m+82A1dH\n",
       "xHu6/+afAh7Cvhs3g/i38k9n+KzPAH8557c3uKPgWuquuS3A77W8m8Htbfvk41Rt0L3APd12DbAU\n",
       "+N/AI8CPgSV9f/OVrg83A/+o7/hHgAe6czeP+rcdbxvwSabuarT/xmQD/g7wC+A+atTkLPtvPDbg\n",
       "d6mg/ABVVH2ifTd/N2pW4CngVaoW64ZB9hdwMvB94FHgb4DJudrkAqqSJEmNDH0BVUmSJBWDlyRJ\n",
       "UiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE4CVJktTI/wfRGbu6mYl49QAAAABJRU5E\n",
       "rkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a806690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# choose the paramator of Brownian\n",
    "# Brownian paramator (p) = 0.1\n",
    "\n",
    "import pylab\n",
    "from random import normalvariate as norm\n",
    "from random import seed\n",
    "from math import sqrt\n",
    "\n",
    "x = np.arange(0,time, 1)\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "time = 10000\n",
    "average_num = 100\n",
    "p = 0.1\n",
    "\n",
    "for num, j in enumerate(steps):\n",
    "    step = j\n",
    "    y_all = [] \n",
    "    for l in range(average_num):\n",
    "        y_num = [0] * (time)\n",
    "        value = 1\n",
    "        y_num[0] = value\n",
    "        for i in range(time - 1):\n",
    "            update_value = value + step * (2 - value) * value + p * sqrt(step) * value * norm(0, 1)\n",
    "            y_num[i + 1] = update_value\n",
    "            value = update_value\n",
    "        y_all.append(y_num)\n",
    "    y = np.array(y_all)\n",
    "    np.reshape(y, (average_num, time))\n",
    "    y_ave = [np.average(y[:, k]) for k in range(time) ]\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_ave)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xe4JFWZx/Hfy8ww5AFEBhgGBxAFlIyABBmiA0pwJaqI\n",
       "uCuoIAomFF3BBQyrgkiQVUAQJQiKqBgQGERFVJJEAQXJSYJKEAbe/aNO3T733Erdt7vu3Jnv53nq\n",
       "6QqnTp2uqq5661T1KXN3AQAAYPAWGOsCAAAAzC8IvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMAL\n",
       "AACgJZWBl5ktZGZXm9n1ZnaLmX2uJN3xZnaHmd1gZusNpqgAAADj28Sqie7+nJlt5e7PmNlESb82\n",
       "s83d/dd5GjPbUdIr3X01M9tY0smSNhlssQEAAMaf2luN7v5M6F1Q0gRJjydJdpZ0Rkh7taQlzWxq\n",
       "PwsJAAAwL6gNvMxsATO7XtLDki5391uSJNMk3RsN3ydpxf4VEQAAYN7QpMbrJXdfV1kw9QYzm1mQ\n",
       "zNLZ+lA2AACAeUrlM14xd3/KzH4iaUNJs6NJ90uaHg2vGMYNY2YEYwAAYNxw97RiadQqAy8zW0bS\n",
       "HHd/0swWlrSdpCOTZBdJOkjSOWa2iaQn3f3hovwG8QUweGZ2hLsfMdblQG/YfuMb22/8YtuNb4Oq\n",
       "MKqr8Vpe0hlmtoCy25LfdvdLzewASXL3U9z9YjPb0czulPS0pP0GUVAAAIDxrq45iRslrV8w/pRk\n",
       "+KA+lwsAAGCeQ8v1aGL2WBcAozJ7rAuAUZk91gVAz2aPdQEw9zH3dp55NzPnGS8AADAeDCpuocYL\n",
       "AACgJQReAAAALSHwAgAAaAmBFwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQRe\n",
       "AAAALSHwAgAAaAmBFwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHw\n",
       "AgAAaAmBFwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHwAgAAaAmB\n",
       "FwAAQEsIvAAAAFpC4AUAANCSysDLzKab2eVmdrOZ3WRmBxekmWlmT5nZdaH71OCKCwAAMH5NrJn+\n",
       "gqRD3P16M1tM0jVmdom735qku8Lddx5MEQEAAOYNlTVe7v6Qu18f+v8l6VZJKxQktQGUDQAAYJ7S\n",
       "+BkvM5shaT1JVyeTXNKmZnaDmV1sZmv2r3gAAADzjrpbjZKkcJvxfEkfDDVfsWslTXf3Z8xsB0kX\n",
       "SnpVf4sJAAAw/tUGXmY2SdIFks5y9wvT6e7+z6j/p2Z2kpkt7e6PF+R1RDQ4291n91RqAACAPjKz\n",
       "mZJmDnw57l5VCJN0hqS/u/shJWmmSnrE3d3MNpJ0nrvPKEjn7s6zYAAAYK43qLilrsZrM0nvkPQn\n",
       "M7sujPukpJUkyd1PkbSbpPeZ2RxJz0jaq9+FBAAAmBdU1nj1dUHUeAEAgHFiUHELLdcDAAC0hMAL\n",
       "AACgJQReAAAALSHwAgAAaAmBFwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQRe\n",
       "AAAALSHwAgAAaAmBFwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHw\n",
       "AgAAaAmBFwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHwAgAAaAmB\n",
       "FwAAQEsIvAC0zkybmWmRsS4HALSNwAvAWPi1pA+PdSEAoG2VgZeZTTezy83sZjO7ycwOLkl3vJnd\n",
       "YWY3mNl6gykqgHkMNV4A5jt1NV4vSDrE3V8jaRNJB5rZGnECM9tR0ivdfTVJ+0s6eSAlBTCvsbEu\n",
       "ANCUmU400/pjXQ6Mf5WBl7s/5O7Xh/5/SbpV0gpJsp0lnRHSXC1pSTObOoCyYj5ipiXMdLyZvjzW\n",
       "ZRmPzGRmWnasy1GDRx0wnrxf0tvHuhAY/xof+MxshqT1JF2dTJom6d5o+D5JK462YBh74eQ9qWTa\n",
       "0WZ6TTS8iZkW7uPi95b0AUmH9jHP+clbJT081oWoQY3XfMBMvzLTjLEuR5+8NNYFwPjXKPAys8Uk\n",
       "nS/pg6Hma0SSZNh7KYyZFjLT5ILxZqa9esmzZDmL9yuvBsvavK1lDcAHJT1fMu2Tkv4rGr4qpJeZ\n",
       "3ExbjnLZT+U9ZtrWTIuNMr9xz0w/NdP0hsnn9touicBrfrGFpNePdSH65CNjXYDxykx7xxfrybS3\n",
       "mWnigJe/hJkOGeQymqoNvMxskqQLJJ3l7hcWJLlfGnYyWDGMK8rriKibWZDkN5KuKBi/vKSz68ra\n",
       "hX+Yaac+5lfITAtKurJBuulm+tagy9ODYT8SM001G1a7uWGSfsGofx0z7Zpm2MUtsDh4v0TSexvM\n",
       "01goxzL9zLMFsyS9tmHayqDGTF9s+6LATEslz8iMy1uNZlqu5eV9wGzEIx6tM9P2Znpjr7M3yH/9\n",
       "Nr6nmfYy0zaDXs7cLPwWV21pWSeb6XWSvqvsAj2d/nZJ35G0TkUehdPMNMlMS5pl5wszLW6mZc10\n",
       "q5muSo7xO0r6SnVZbWYWn0w40uw1p9R/u97U/avRJJ0q6RZ3P64k2UWS3hnSbyLpSXcvvMXh7kdE\n",
       "3eyCJOtL2rioKJ0yaQUz/T70/7eZVqn6DhWG/cDNdLCZyr5jJTMtVlKLtkKYbnlXksV2kvbtZdnd\n",
       "MNM9ZppipovM9J5o/Fp169FM0yT9QcNvI6cn7nh/epOkHxRktZea3QJLq/RfaDDPEDPtYKYlQv/E\n",
       "gnX/FkmPhukLmunlDfJ0M61Rl64XZQeWAi+F9J80056hf8miLGvy+aikgyrKM4h/HB4t6Roz5c+A\n",
       "NjrJht/XQgMoT9fMNFPSg33I58/59mvgeA2vXY7zWa1iGTPMtHYv5Svxs9DFy2i6XZrUbl6jPlxg\n",
       "h8cgqp4zPlvST5N51gifR5qp9X/mm2kBs1YvRM6QdGddIjNNM9Pho1zWe9V5Nq7oPHlW+JxTkcf1\n",
       "Zlo9Kdvmyu7ILB6G/1tZPPKwpNWV/SHwsGiW2vXr7rPd/QjpxQelm/evS9+ruoJsJukdkrYys+tC\n",
       "t4OZHWBmB4SCXizpr2Z2p6RTlD2A2G8TJclMEyStK+l1YSc9UtJ+o8kz8jF1bpVNqwiSivxT0j8K\n",
       "xt8VPheQ9HNJv8gnmGmymbYMzz709bkBMz1kpt2TcVOU1UwuJ2knDW9D6U+qr5nbVqq9zbWpmfYI\n",
       "/UO3KMN3zW8hfzcav6iF58LMdK6ZTorySm9Xl93yLHOxsn1XyoK2PZLpS0X9n5P0SMN8X91lOZq6\n",
       "3mxYmcrk++XRoZOkJ8yycoVaiU8Vzjjyeb0R+3gIUpeX9HSzYndlQvjcKnzuaVZ4oRWXZ2Vlv68b\n",
       "B1CedFkLm+l9BeMvimq5plTMf7GZjmy4uFdJ2rqL4o0IhMMx8Pbw25aZVg7HyNxdkm6I0k8PNQIr\n",
       "5TUBZnpZF2XIg/4bwudikp5NyuRmnYuzKJgYca4x0/+aaZNk9KQkzbS6fSRKu3zo/aSkXWqSp7+F\n",
       "W8K+9t+SDqyY7+aGZVkrBFOLmOmiMG5jK38O9hxJ1zXJO1rGa+NgLWzbzRrOvmjDdPtIOirk/1ga\n",
       "/HShKqhqmmZyuAibaqbDpKFay/xcfqSkmck8Hw4XICtJQ8F10V01mWkrM705DA62dQZ3b6XLFpWO\n",
       "88UlnxgNe5ZsRLo3hmnbS75D6D80fB5dkP5QyWeH/qWSaRPy5Uh+jeQXpssO/W9u/t1Ky50vZ1rU\n",
       "/8Yw7X3RuHcWzd/7unaX/IRk3Blh/CppeSvK/39h2oZRWb1onnh6Qdprw/D5yfi7w/DXwudjUX67\n",
       "J3n9V8X3XUvyKQXr4LCo//Bk+jvC+FmS/6jJ+g/pdy4Yv5/kB0p+avTdTpZ864bba4GQ98sr0uT7\n",
       "7ZujstwV9b8+9F8ahj+QbJ/PF2yv85L18TfJr4/W+TskXzT0T2zyXWq+50khr32jZWxTM88mUdor\n",
       "0/Uv+bGSb9Jg2VMlf3VNmm3Dci5M1o1LvkvVbyWadlvDdeGS3xANryn56hVpRyxT8oXDtJdF6X5Y\n",
       "Nl8Y/n74vC4aF+9Tm9eUOf79viwMW5JmrWj4iDDuiWichc4lP1PyP0l+WrxPR2mvqljf60p+Yshr\n",
       "sXw/DZ8HlMxzbNH6DOPWaLB9XfJ31GzbJUK6nSTfOPRPCp8fl/xLkp+WpH+poEwbSv71aHjRqD8/\n",
       "HuwbjTsr2jYflfyoum3ZYD89PMrTJd+tyf5dtt+U7Mf5tH1q8rhL8p9E6W8Ln69Kl5F0q0p+T1UZ\n",
       "wjJeiL7r37O0ql1HvXR9z7B8xcklfz76kvkP76sFG2Dpig23SzL8uYoN+aaCnXmRZP4X0h0x9B+q\n",
       "mpON5JMVnURqdriXov5XqxNsuEIQ0L917R7/YMO4O8L41dLyVpQ/D7zen3wXK8uj6EfWxfg48Lo1\n",
       "mXZ3zfc9NRp+WcFyPhlNX1qdwKvyx1iwnDcl+9IMyf9V8t3Oj9J+XvKrVXBwUecEumLFsvM0b03W\n",
       "XR4UbxHGXxyGD062z7/D+EmSTwn994Rpy5ZtP8l/GT7XUnZiWinK87WSr9vFfnlCyOu9Uf5b1cyz\n",
       "cVKe05LpLvkXo+ETJf9mQT6XhbSfqFjWzILtuHoY3lnyt1b8Vm4M055Nxv9Y8g9VLOdkyR8O/c9V\n",
       "7Hd5eRaVfK/Qv1SYtlyyT7wqGf5VNJyX8+6CvF3y/Wr2/zj91DC8rOTXRmk+FqW5J54njLtanQCw\n",
       "8NgQ0k1JxyXlOS5M/5CyIMzV+e2XBV7xslZNxr82mraUsuBldWVBzgLRtHMlv1/yPUuWkV9oHi75\n",
       "FqF/8fB5TMH3LDwGSX5FGD8tSrdI6F8oDH+0ZD/5Z9l6S9Mm45dIhk9K9o9dy/JM5jtd8u8UrPP0\n",
       "O8bTro7Gv0byVUJ/fM7/U8E+85qyfSl050v+WFkZSsryiexTpetwNF3fMyzfEMq/0Hbh85CqHbDg\n",
       "R5F3n0+Gvzh8Of7lghWfH6DWjn/MyY46ol9Z4HGY5Gsny1grTP9bkte3FNVy1OwMcXdg+Fwlmndt\n",
       "hStJZT/e4yR/S5OdP6Q5Kxn3dBi/ZsV6X1HyhaPx+VXoj5PyTq7ZdnH38pLxK5aMP7Esv2hZb9Hw\n",
       "q7+hZYXhWdG4ZcLnYQ3KunWyziaGz7hGYYdo+olh3JNJPvmV88+itPG+8ljYr/L9bfWkvKsqBA/R\n",
       "PrBkmP42ye+L0l8ZPvOa1Ac1/PeVf4fnwvBx0bz/F6a9p8E+Omy/UXQiCsN7SL5p6F9Y8sUK9suv\n",
       "FuQ7M+R1sORbSv5KySeH9L+W/IdJ+gsK9vUvJdvIC5b9qyiPL0v+gYI0WybL+qrkz6jgN1Dym8u7\n",
       "B9PxFWnj7sWK33O+nveL+lcI01ZJ8y1Yzo7h85/RuC+WpF+toAyrJfktIvlKJcu8Pxp+NF0HDfa1\n",
       "fPsvm86blOnKmnzWq9lOaZnWjaa9Ler/Xw0/Xl0YPk+s2l6h2zx85sehL5csOx23lORPhfH3qVPD\n",
       "tUSYntfw/XdBPqtE/ZOV/R4n5ttVyYVpNP/W+baNxn09jEtr3N+k6MKyZp9Nt0taQ5p3tyi7sMgv\n",
       "Jh8Mab4XpbmpIL91k+F/F6R5vGg9V2y3D2efKkw72q7vGZZviKHA60Ph84x0JYThvGboNWFn3avm\n",
       "x+WSzwrzL14y/baof0QgULGj/CZ8np5soB0qyvLjkGaBijSlXbIu1g7930rS/TRK9ynJFy/Ygb4i\n",
       "+W/zHT2a951R/6kFO9yZ0birSsq5QtS/asmPK++26WUdNFg3ruxAEX+3w8P0zaNxec3ix5SdKBaq\n",
       "WPZu0TKmh3HTkjJtH6W5IIx7LMnn1PB5eZT2+ZJlLqukxkzy/wmfy0Tj/ho+39VwvR0ZPhctSy/5\n",
       "58M8pXlG3VpR/+aKfkfJcq9SuHWrLHB5hTq1dccV5LuFols8oTuvap+K1ml+Mvijkv284KB6aZLP\n",
       "owVptitY3t9LyrF9+PxdUVkL9tXpki9T81spPMgn63nfaN/Ib5v9jzq3t4q2SW2Xpg/Dxypc5BXM\n",
       "8+d0u0Xp7g+fkxVdlBSsk7h7sSCvusDrayV5xd12yvbXsttR+0j+UOiPH6l4e5Lu2wXznij5f0i+\n",
       "QCjPk5JvVJC/qxO4nRhNmxTmywOseB3dkeSTH2OmSL6ZQo225MeE9PFx8E3JvHdq+KMtyxet12j6\n",
       "kmH48GhcfhzZIUyLv8eCST5/jfMvWG8TFW77J+PT39pjku+m4RcLRd1/NdgP0m7psE3KgsDQqXDf\n",
       "G23X9wxLF6ShwCvfYKenGy7054HXq7tckWcriuQrugfScclKnxj1x4HHFSHdHurczinrJqtzT7/b\n",
       "bi/JFwz964Vl/iBJk1fr5z+2HcPwBMlX7nJ56Tq7tMFBe52ofwfJD6hIu3WDMlRtj7jbXcODhPdK\n",
       "/rlo+NNh3tcVzPuRhsvPr+j+EIbzK/18e25b8EN9uCSvq2pONmVdfjtis4ppTddb1W/iS8nJvGn3\n",
       "sDq1yHUn+UfVCSBPbLqMmjxNWQ1Ofhsnvy19aJTmREXPfqlz2ybvni44kV9XsKz8BFi2jV2dZ1Dj\n",
       "7i2Sv6Hme/6xYNwBUXm21/CLxvUq8oovhurWX9k6LZr/Co2sUSjrJiTDSyfDSzYtV0i3XDRuwYLt\n",
       "1c33+0XJ+POj/viCrWp7x/uYa3iw9YUkzc/D56rhMw4wdw7fIw9UvcF3W0nDn8O8WfINJD86Grdj\n",
       "wXwfjfqnpstLlnmDhp8HXZ3jyO7KLl7jWqgvKHtWb1uNDHCXKCjL5IppY9EtPT8EXnl3dtT/AXV+\n",
       "tHngtW2XK88LNnrTLj7oxCe2YdWaYePc0yC/L6pzld9Ll98WWVvy9ZU9VDgsTShLftt0N2U/hia3\n",
       "jOq6S1VwOzbp9oj636XO7ZiiLn1Gp7YL3+3XDdIeqE7tkEv+mTDvJgVpD+22HKHLr8LybRLXeOVp\n",
       "RgTzUbd8DyeJo8LnmX3YnqdXTDsulO2dPeQbX2X+pibtC+HzG13uA6P97t+ItlVaq/iswi2tHk/k\n",
       "/ejK1tszoTwndZHX2qMsy/ol6/92dWrO67rpyfDyyfCDku/dMK//VMEFQbStrGE+dd3Po/4jupw3\n",
       "rwU7t0Ha9NnkvEsrGBao2RfTCwhXUluo4sDr1Kh/6MI5LGvPgnn2SIbjbXueCs5JXXSjOTcOoiuq\n",
       "fQudBhJ4jWUDhktE/R9U56+k+V/cf6Huvac+SaG4oc9PRP1Frez+u0F+01T/d+YqecOkc5S1bTOj\n",
       "JN2Z4fN7ytovOWoUy8xtLenJmjTnRv2nS5WvCvpdtwUwG2omoc6MZNn5/lz0mqOmf7NOLR0+twif\n",
       "edMmcdMPVX+Dvsas6zc55M0t7NPlfEXeVTFtwaT5gW58I+rftCZt/nfvttviipuMSd+4sZCk50Lz\n",
       "B7/qc3tXTZW11L2wmY6SRjZtUWG0b+MY1mZRaBNJklZT81bn03bZHkiGl1PUnEyNb0r6fDrSTI+G\n",
       "5iX61QTP9lH/zC7nzRuM/o8GaV9XMn7pZHhOzfHiDQXjmjTV8O6o/7K8x7K2K89Rdv6InZsM3xP1\n",
       "767RvXWi12NOU902PbReD8fo0RnDGq9uutkN0z09imU07W5skKbuoc+6Lr8636csTYjQ754Lrhbm\n",
       "pu6ysF7eOsBl5LcHvjfAZbTd9fKMxKC7mcnwfT3kcaayW8WPqr7W5t4x+I5FDwr32h0yyvmL/i3W\n",
       "bVd0y3U0Xdlxv+ljA+Oh++4A8iyrXetn9+Ao5t11LljvDTvNczVe3diyYbpBtLadahKtr1+fpFLe\n",
       "uN2Zlal6r0FIX3TeRDcNWDZtjLSJ5yR9pmHarUIr7uf3cfmp6aGV+d0GuIy2xfvRpyX9bwvL/FrN\n",
       "9PStCL1cJU+UdLukZVRfa7NizfRBSGs7RmO0++NafShDWQPA3ygZX6essc429s+29PrmlSptvA7p\n",
       "b6OY94Ae5vlrw3SjfqtEpFHDvb0Yy8CrqKX38aDslTGnR/1NA6Jeb43mqm7xVWnU+nLim12kfbGH\n",
       "/MusI2WviGroh31cdpETJF0/4GU09X1lgcVoxUHQ0eq+qr4X36+Z/j/J8FKSHu9yGQN96e4oPSYN\n",
       "tbTeD3W3e8uM9hgUK3vdT5NbYUWqXvszr+j1GF6lquX9ftlY2esEezGrYFxdLHJxw7xHcws09VAf\n",
       "8xpmbnnGq87Jkk6Senpn1HMV087oIb8y/xn15+u1LmAYbc1Qk3V4esG4Z3pY1hzVv0Zm3yhtqqzG\n",
       "oerHe6C7bpd0d81yY0XPQIwHB/cwz/+5N36FUZNnE89yl0uDf97BXbO7nGWyuq8hGkTg1WsQkYpf\n",
       "2dKP4DnX5LVTsX7WEJRJn6+LfUfSiX1aThs1Pf3cVpIG8mxhW+f1pkHjp+sShONOlSbHL2n4RWNR\n",
       "ZcEvG+aT5tVXbQdev+1xvgfddaCyd+oVeWcyHL9QNj+wxNWb+yq7lRE/cDgqJTvORjWzNX1f1ggN\n",
       "Hga8JXwW1SwUPXxe55fKXiydG1HV7D50a7Tohdbx7c37o/7C9woG54R8b1NWQzAvu6PL9Eu46+cl\n",
       "04r2u90l7VyTZ36RcllFmrJlpkpf3tyDpgfdVL8e4j02fP5K3V0wVonfcVj3Z5bG3Ifn5V5bA/DP\n",
       "LrIvu3hKH8xOfVbDH5T/etR/jPvQy9rz33jR8aPMD6L+BUtTdRxWn6RS+tB5marv0M3Ll99cMe2G\n",
       "iml1/tAw3SeUvae3yNsa5rF3w3RVmgZBQ/uiu94j6dvJ9D92scyHu0jblbYDr/Tfalc1nO95aVhw\n",
       "k96mvKQofbBL6C6Ixt3krt+4l/4zJv03TlNVV3av0chnlRZQ988rNPnRPqXOc2bxd8mj/Q26XKbc\n",
       "dbv7sPVcVZM4Jxzwh+6RJ4FpXLtTdVKNT05VB8xerkzeJenX0fBN4bPpv67K/LTH+coC6atVEAi5\n",
       "Dzth/jmZNuKg6q4fqf7ZvkdD2ssr0jR5ROA2d93ZIN3Pov6qFwRX7Wux9LbZaP/pl8v3w23ch78U\n",
       "usLkgnFfjvrj2rs3SVq1l4JJ+oCS7d8Nd/2qh9kOUeeftysr+1d4WhN4bbSMfyXTF1CnNiIODJcJ\n",
       "n1ur+d2IL0k6IvTf2yB9fgeg6ne+a8n4m6RGL0HfVNmLussU1ZoV3dY6TcMD4/Qiep2KZdQ9DnFO\n",
       "yfj3J8MXq3On4+/JtPtK8rhPWdnzuxnfVVb7XBZv3BY+q/4dGgdBx1WkS+8ypRdfdXdtcn9rUAvX\n",
       "s7YDr/SHUbQTFwUFcZS6uLLq2dUUVqL7iJ02PqE+466L3Ds7jXvnoFDiSHVq0Y4tSVNUe/flgnHr\n",
       "SFrZXbe467OSPhRNM2VNQTR1joafrMq8S50rrn+r88xVftXZ5EC9k4qr7vMaqn9r+F+xdwqf10Zl\n",
       "TJ/1elGS3PX96Ep8jqQnSsoQB1RVz6W9KHV9AjlP0rei4TOUHSju7jKf1K3hs9vbXLerc6tW6jQN\n",
       "8gaVnwhyG9ZMlyS5V97aPkoaakKgSnrC2j18xn9oaForMHTSddf6kn5Skq7q9t4hFemKgp86ec1j\n",
       "fAvoOUlyH5H/N9QJQKTs2ZUdQ9p4381/G19R5yQTH48eU+/PRd6n+mdRZinbR+Jjz6kaeTFzvbJa\n",
       "+KIA/e/q/AYfCreKvyDpgXCCyv/Y9DFlz7jm+2R+wowDrPiCt6hG7kWNvJgqvKh112/ddaSkBd0b\n",
       "PbuaL7v0GOhe+pzose7128ldV0k6vmL6FRr5vOK0gnT/KelKZUH5v5QFQelFyLdKFlP2TG5+oRsH\n",
       "dEP7hbtOjsZfJukv6qyzE5K8Do364+f7jg1lz8u2irteLAlkjlenhj4N5L4U9Q/dYXHXIerELo8m\n",
       "86TLyI9p+fetu9vzS0mvdi9twqkv2g680h9PvPybpKGg6NI4kXtn2F3/ctffwhV14cnWXXdFg5XP\n",
       "MyVV8XnQ96w6B/GywCu+5ZAvb8RBxF1/ch92Mv+eOrdrngi1E0tWlTHKa2/32qu689x1YVSb95I6\n",
       "P5y85uQZZQHG3Sr3e/eh9B+PxufLfzSpAXsilHEDd30wjMtr3fLbTg9q+C3D14eam8KDYHKQywPJ\n",
       "PG387Npd7iP++bpJ1P+uZNrDoebiNHV+iN9yH3aLWpLeWlSuyCPqnCA2UPac38SCsjfxXHSrVsqe\n",
       "a9zXXc+HdfRGda4IZ8czhhqFvN+izzU1vP2d2FnJ8AlJYJFvsxnxb8RdF2p4jeUFkqa6a3d1am3i\n",
       "E+ADkt6uzgH/10qubKP8y45HdxWM+7CyoCc+UVyZpEkPynl53hj6i/59/GAoU/wv3qJ85K79FdUs\n",
       "hFu/8S2mCyTtqc5J9llJ00N/HmTnF5V1twQ/q+wEldaMzVDxn3lmx+Vy1zXu+mo0fX93fSGZ50fu\n",
       "ekbDv++3wufTYT+8SOHC1l2H5QGm+9D33shd/45Osvn4eNs+q+rbOI9reCC6uWqe74uWL3W2b5E8\n",
       "3yZtBe4uaUK0f+bH0bWUtVl2lLKLz6eV/KknrJe7GywjT/+Shl9U/zaMd3f91V2Lu+tUjdzWny3J\n",
       "8llJeyTjjlHn4js/Zvws2S/iMm3jrqfVqeVOt0G+TSe7623qBF/5/p6v61tV7Bh3fTCqvc+PEfld\n",
       "nbhm8N/KalcPDGXzsF3Katbz80N+xyf/I0tle47u2i48VzxYLbfjlb/YM+/id0rdkjWZ4VLWKvHQ\n",
       "S23L8/SVJH8+aXV272j4/Ul6U2gZOBl/VbRsl/wd6rx6J219Oe9+oM4rD74W5v1skuaxirIvr+L3\n",
       "RG0h+S8Llnd0QVpX9tqKvGXwA5JluLLW/Ock3+9AZa/AmVqwnLxbPKRfNV5n6rQ8nb5mwQq+Y74O\n",
       "VwrDy0q+bEG6q0O6w+IyJGnylrl3UvYqnd2itAtH2zcft6Syd7BN0sh3l70+yXti1P/h5PudJfmx\n",
       "yXfN36rwA3VeW5O/pPmEZF2n3dUl4/P5n5f8iYr9xhVaWi4YP+K3ovBOxWg4f/XRpmXrOslzWpq/\n",
       "5O8Pwxtpn9ryAAATk0lEQVQm6V+ZLMvVafcs39cuj6YfIPmV0fB3knVyvLKXc+e/sx+q07p4vE8+\n",
       "rvDuRXXeuvCs5JdFef1U2StsLOyX90RlvCVKd1H0PWeEcRM0/AX2w9aZsveAHhV9z2uT9ZK3Cj85\n",
       "Wk6+/26c/FYKuyS/+J2XKyh6hUxUvlmSr1GwTa8ryC/f5w+Pv5/kn4uGf1e2TybrZZdo+El12tb7\n",
       "fJTvMeq8Fi1+s8PNCi9oVuflzIsn+Zeul5BmY3WOA/mrePaI06vz4viidX10NG2zZNn7Vnz3vE22\n",
       "B6Jxfy0rc7I+1ojmyc97P6xYx3G3evjMW5b/SfjcO00fhvM2vnbK9/eC33e6fy8Q9tcjkmXvVHSs\n",
       "kXyPMLy05E9IPqFg3/1SyfdbOSrDwdGyti5Jv19SprxV/nfn2zoMx+eGPcPneRr+KqWC/UkjxvWj\n",
       "63uG5Tum4i+fvzB4VvSl3y35EdEKPbdsZVTtkMnwng3njQOvXRVO5NH0ReJlhO47YdwOCsGERr6X\n",
       "8PLm68dd8kdC/0Ia/oqGlYq+a+gWCGXeryDPSyRfpGo9Kjtp5Hl9RPKdlb18dkSAGtIfmaznbau2\n",
       "Uch3hZrvvo4KXsabpMkPMFuWbfOKcfmLuv+sEKhXlGWi5K8ombag5BuE/s8oCwDz7WRh/DHRvrSy\n",
       "OieY/LUeeTDwIWVBRf6y+MWrypV8v9Xr9v8GecxQ9gLrEyS/rSTdW6PvtXv0vd5bfJDKXtmVLGeX\n",
       "ZPhXFeVaVPJvKjtYu8JLvKPtsoDCi5OT+VaI97Ew75OK3rdXsy72j/a7Q6PvOa3ke/6l6boO6fOL\n",
       "BlPntV75BcyMaN+KXz1zmrKAcxvJt0ryi9/huaQ676r06Du9oaQsL5f85QXjr1QIpKO8822/nMJ7\n",
       "FhvsV7tHw1PUOXYuq05DvX8omHeWogsKhcCraB+Pu4qynKYsWFgtmveYJE3+rswPxOszSr9+suxd\n",
       "K5a3fkF5n0rKe320jeILn5dF8+TB/g8q1nHcTVK44A7rLH/R+1uS9HkFRR545fvQt6N0J4f+V0u+\n",
       "TsGy8yBlhkKAW1K+bSrWU34sPrLBvrRDVP7NKtK+FK97Zee9VaPh+DVMh0v+5iR96f40TwRe4Usu\n",
       "Eq387aIvPStZmS9T9vLRtzfLf/iKU/aiz1Uazvtpya9pugxlB8ipFXkNHcSbr58R5Z9UvjOU7ygl\n",
       "eT9WllbD32E4o0FeuyXlNMlfWZH+EhW84LbBOvZkfP6S2Y8kaU+sWo9h3FZh/MtVEwT20ml4bchC\n",
       "6X4n+d/UqcX8cbL+lg3jJzdclku+TN3+M4DvOCvPX1mA9KaCNKsXHNB2jYaPUKgBq1lWXnN8cI9l\n",
       "fY+Sq/OKtH/R8PcUWjL9FQXzXKyKWsmC9BtG627nsJwFJV8sSVd5kZSkzcu8uDqB6t/CtK1VcuHU\n",
       "sLw/72VfUlZbs1JNmqEgoCbdRwt+x3HA8XVFNSkN8lssTa9OTd8kdV50nQeKm2r4HYn1u12nSXn3\n",
       "V3beuy1Me5myWth9C/a5YxRdYJbk+VYldzjC9Pzdj7PCcP5i9XXDcN5qfH48/VqU7ztrvs9BdfuF\n",
       "srtQIwKyaLopOycs1+U6fF1Fmgck/3uDvC4KvzuLf3uS31n2u5tnAq/wRfOaoW2iFbv26PL3SxS9\n",
       "wHgw38GPbbDjTSnbiDXzueTPFowr2BmG1lmjZSi75VaYVtlJdPuQ35QGee3Uy0G5y/Xgkr+QjM+v\n",
       "BDeIxm0s+aIF8/9HMm7nQZa5wXeaoOzVNa6setujafn+0vOJMuRj3ZyIesy/8kJGWdAZv5jaFa68\n",
       "e1iWK7oF3EMee0X70p9r0i7V5e9pITWsoQzpF1a4wldWc/fGknSlF1sFaV8b0i7cTdkblnd9yd8z\n",
       "oP3IJT+rQboFlVxghHnfHD6P7nO58n2gb78hFdzW7dP6K80zOk5+PJknDbymS/4VhVq9MK4u8Hp3\n",
       "28dRdS5GRtTARWmmqmEg1+16HVTgNVYtO+f/CHxJ2as6nnXvulXqYdy13ahLVe9TKv/nVS5/aPEv\n",
       "Xea9sNT476vbKvv3xf11CYO7VdKujGcPT/5CzVv87aUNsF6k5XlWktx1TT7CvfDfV6/TyKYJmjZH\n",
       "MBDuejF6GXX6B5P84eRRvfTXXa7+vjGgKP/K13a46zkNb9LhQxrZ1EvTZY22Ber4X1B1jcw+KWlX\n",
       "L/832zDhezbepzz7I8dnQv8clbeFlv+5YYcG2eYPIverQdchnv3Bqe6f3706S9VNLeRleF4j2+77\n",
       "owZULnc9of62ei5lb4TYus953qDqZiSK2uL7hzp/isofzn/Qfdi/EuN5y/TS8PZo5ce00nbR3PvS\n",
       "3taikqb0IZ9GxiTwctdzlu3i97g3Dh7GXAhSKlu+DSdZqct3p4WDeZERbVS561IzrarmDQ1uq/79\n",
       "g/U3GtkoXT+toqwpj2FtvIUfV+2B0b2wgbzLVPyaijblTRscKnX+ReSuZ8202NgUabC85N9SLS37\n",
       "Kmt4Gg2B3qBfNdW0HE1P/vlx4UX1/s7W1rlrn1HM+zpJarpdx5q7TlP2z+l+ulvVgdcjyv75N3Qc\n",
       "dB8WUCwbxqUB+zqqf5Xcper9vZu9yss50NeYefZv3tYCy/DwZAsLMnN3Hyc/mdEJrcqvONqgMuQz\n",
       "x721WiYMiJlWUtYo33zxG5gbhN/PV92HtV81TzDTCpLunx/3p7Bdj3Hv6RVy45qZFpG0sPuIxkyb\n",
       "zr+xpN+Nl/3GTKbsztgM91G9mLvH5Q8mbpmbXyI7nk1271uE3q/XnmAMuese9f9WBuqNmxr1LlW9\n",
       "JQPzqD7UzPxeDRtcnhu4y0MN58AeoxgLBF4D0Mega/M+5QPMj66QKl9/NG656x8ikEeXwu3sa2oT\n",
       "zl1OUkkjxuMVtxoBAOOGmb4o6TT3odcvAQMxqLiFwAsAACAxqLil7Xc1AgAAzLcIvAAAAFpC4AUA\n",
       "ANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALakNvMzsNDN72MxuLJk+08yeMrPrQvep/hcTAABg\n",
       "/GvyyqDTJX1N0pkVaa5w9537UyQAAIB5U22Nl7tfKemJmmS0SA8AAFCjH894uaRNzewGM7vYzNbs\n",
       "Q54AAADznCa3GutcK2m6uz9jZjtIulDSq4oSmtkR0eBsd5/dh+UDAACMipnNlDRz4Mtp8pJsM5sh\n",
       "6UfuvlaDtHdJ2sDdH0/G85JsAAAwLsy1L8k2s6lmZqF/I2XB3OM1swEAAMx3am81mtnZkraUtIyZ\n",
       "3SvpM5ImSZK7nyJpN0nvM7M5kp6RtNfgigsAADB+NbrV2JcFcasRAACME3PtrUYAAAA0Q+AFAADQ\n",
       "EgIvAACAlhB4AQAAtITACwAAoCUEXgAAAC0h8AIAAGgJgRcAAEBLCLwAAABaQuAFAADQEgIvAACA\n",
       "lhB4AQAAtITACwAAoCUEXgAAAC0h8AIAAGgJgRcAAEBLCLwAAABaQuAFAADQEgIvAACAlhB4AQAA\n",
       "tITACwAAoCUEXgAAAC0h8AIAAGgJgRcAAEBLCLwAAABaQuAFAADQEgIvAACAlhB4AQAAtITACwAA\n",
       "oCUEXgAAAC0h8AIAAGhJbeBlZqeZ2cNmdmNFmuPN7A4zu8HM1utvEQEAAOYNTWq8Tpc0q2yime0o\n",
       "6ZXuvpqk/SWd3KeyAQAAzFNqAy93v1LSExVJdpZ0Rkh7taQlzWxqf4oHAAAw7+jHM17TJN0bDd8n\n",
       "acU+5AsAADBP6dfD9ZYMe5/yBQAAmGdM7EMe90uaHg2vGMaNYGZHRIOz3X12H5YPAAAwKmY2U9LM\n",
       "gS/Hvb5yysxmSPqRu69VMG1HSQe5+45mtomk49x9k4J07u5pzRgAAMBcZ1BxS22Nl5mdLWlLScuY\n",
       "2b2SPiNpkiS5+ynufrGZ7Whmd0p6WtJ+/S4kAADAvKBRjVdfFkSNFwAAGCcGFbfQcj0AAEBLCLwA\n",
       "AABaQuAFAADQEgIvAACAlhB4AQAAtITACwAAoCUEXgAAAC0h8AIAAGgJgRcAAEBLCLwAAABaQuAF\n",
       "AADQEgIvAACAlhB4AQAAtITACwAAoCUEXgAAAC0h8AIAAGgJgRcAAEBLCLwAAABaQuAFAADQEgIv\n",
       "AACAlhB4AQAAtITACwAAoCUEXgAAAC0h8AIAAGgJgRcAAEBLCLwAAABaQuAFAADQEgIvAACAlhB4\n",
       "AQAAtITACwAAoCUEXgAAAC2pDbzMbJaZ3WZmd5jZxwumzzSzp8zsutB9ajBFBQAAGN8mVk00swmS\n",
       "TpC0raT7Jf3BzC5y91uTpFe4+84DKiMAAMA8oa7GayNJd7r73e7+gqRzJO1SkM76XjIAAIB5TF3g\n",
       "NU3SvdHwfWFczCVtamY3mNnFZrZmPwsIAAAwr6i81agsqKpzraTp7v6Mme0g6UJJrxp1yQAAAOYx\n",
       "dYHX/ZKmR8PTldV6DXH3f0b9PzWzk8xsaXd/PM3MzI6IBme7++yuSwwAANBnZjZT0syBL8e9vFLL\n",
       "zCZK+rOkbSQ9IOn3kvaOH643s6mSHnF3N7ONJJ3n7jMK8nJ351kwAAAw1xtU3FJZ4+Xuc8zsIEk/\n",
       "lzRB0qnufquZHRCmnyJpN0nvM7M5kp6RtFe/CwkAADAvqKzx6uuCqPECAADjxKDiFlquBwAAaAmB\n",
       "FwAAQEsIvAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHwAgAAaAmBFwAAQEsI\n",
       "vAAAAFpC4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHwAgAAaAmBFwAAQEsIvAAAAFpC\n",
       "4AUAANASAi8AAICWEHgBAAC0hMALAACgJQReAAAALSHwAgAAaAmBFwAAQEsIvAAAAFpC4AUAANAS\n",
       "Ai8AAICWEHgBAAC0hMALAACgJQReAAAALakNvMxslpndZmZ3mNnHS9IcH6bfYGbr9b+YAAAA419l\n",
       "4GVmEySdIGmWpDUl7W1mayRpdpT0SndfTdL+kk4eUFkxRsxs5liXAb1j+41vbL/xi22HInU1XhtJ\n",
       "utPd73b3FySdI2mXJM3Oks6QJHe/WtKSZja17yXFWJo51gXAqMwc6wJgVGaOdQHQs5ljXQDMfeoC\n",
       "r2mS7o2G7wvj6tKsOPqiAQAAzFvqAi9vmI/1OB8AAMB8Y2LN9PslTY+Gpyur0apKs2IYN4KZEZCN\n",
       "U2b2mbEuA3rH9hvf2H7jF9sOqbrA64+SVjOzGZIekLSnpL2TNBdJOkjSOWa2iaQn3f3hNCN3T2vF\n",
       "AAAA5iuVgZe7zzGzgyT9XNIESae6+61mdkCYfoq7X2xmO5rZnZKelrTfwEsNAAAwDpk7d/8AAADa\n",
       "MPCW65s0wIp2mdl0M7vczG42s5vM7OAwfmkzu8TMbjezX5jZktE8nwjb8DYz2z4av4GZ3RimfXUs\n",
       "vs/8yswmmNl1ZvajMMz2GyfMbEkzO9/MbjWzW8xsY7bf+BC2xc1hvX/XzCaz7eZeZnaamT1sZjdG\n",
       "4/q2vcL2PzeM/52ZvaK2UO4+sE7Z7ck7Jc2QNEnS9ZLWGOQy6Rptl+UkrRv6F5P0Z0lrSPqipI+F\n",
       "8R+X9PnQv2bYdpPCtrxTndrS30vaKPRfLGnWWH+/+aWTdKik70i6KAyz/cZJp6ztw3eH/omSprD9\n",
       "5v4urP+/Spochs+VtC/bbu7tJG0haT1JN0bj+ra9JL1f0kmhf09J59SVadA1Xk0aYEXL3P0hd78+\n",
       "9P9L0q3K2mMbagw3fO4a+neRdLa7v+DudyvbGTc2s+UlLe7uvw/pzozmwQCZ2YqSdpT0TXWac2H7\n",
       "jQNmNkXSFu5+mpQ9S+vuT4ntNx78Q9ILkhYxs4mSFlH2xzO23VzK3a+U9EQyup/bK87rAknb1JVp\n",
       "0IFXkwZYMYbCP1bXk3S1pKne+Ufqw5LyNxCsoOHNiOTbMR1/v9i+bTlW0kclvRSNY/uNDytLetTM\n",
       "Tjeza83sG2a2qNh+cz13f1zSlyXdoyzgetLdLxHbbrzp5/YainPcfY6kp8xs6aqFDzrw4sn9uZiZ\n",
       "LaYsQv+gu/8znuZZvSnbby5kZm+W9Ii7X6eRjRdLYvvN5SZKWl/Z7Yn1lf0b/LA4Adtv7mRmq0r6\n",
       "kLLbUCtIWszM3hGnYduNL2OxvQYdeDVpgBVjwMwmKQu6vu3uF4bRD5vZcmH68pIeCeOLGsm9L4xf\n",
       "MRlf2Hgu+mpTSTub2V2Szpa0tZl9W2y/8eI+Sfe5+x/C8PnKArGH2H5zvQ0l/dbd/x5qN74v6fVi\n",
       "2403/ThW3hfNs1LIa6KkKaFmtNSgA6+hBljNbEFlD55dNOBlooaZmaRTJd3i7sdFky5S9qCowueF\n",
       "0fi9zGxBM1tZ0mqSfu/uD0n6R/hHlknaJ5oHA+Lun3T36e6+sqS9JF3m7vuI7TcuhPV+r5m9Koza\n",
       "VtLNkn4ktt/c7jZJm5jZwmGdbyvpFrHtxpt+HCt/WJDXbpIurV16C/8o2EHZv+bulPSJNv/NQFe6\n",
       "TTZX9mzQ9ZKuC90sSUtL+qWk2yX9QtKS0TyfDNvwNklvjMZvIOnGMO34sf5u81snaUt1/tXI9hsn\n",
       "naR1JP1B0g3Kak2msP3GRyfpY8oC5RuVPVQ9iW0393bK7go8IOl5Zc9i7dfP7SVpsqTzJN0h6XeS\n",
       "ZtSViQZUAQAAWjLwBlQBAACQIfACAABoCYEXAABASwi8AAAAWkLgBQAA0BICLwAAgJYQeAEAALSE\n",
       "wAsAAKAl/w/Gb/TcFaGDbgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ab260d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm8JFV58PHfw8ywLwOKCDIyRkAlouICiBJHxQUSURN8\n",
       "A3k1rtGY4BqXRE1Ao9EYjZEoinFFo6gYFSMuuOCrIUGjQBBRQVEBIy4oCriAPu8ffZp7bt3q5d7b\n",
       "XX3vzO/7+dSnu6pOnXNq6eqnT52qjsxEkiRJ07fVrCsgSZK0pTDwkiRJ6oiBlyRJUkcMvCRJkjpi\n",
       "4CVJktQRAy9JkqSODA28ImLbiDg3Is6PiK9ExEsHpDspIi6JiAsi4qDpVFWSJGl1WztsZmb+IiLu\n",
       "m5nXR8Ra4HMRce/M/Fw/TUQcBeybmftFxCHA64BDp1ttSZKk1WfkpcbMvL683RpYA1zdSHI08LaS\n",
       "9lxgfUTsMclKSpIkbQ5GBl4RsVVEnA9cBXw6M7/SSHIr4PJq/Apg78lVUZIkafMwTovXbzLzLvSC\n",
       "qd+JiE0tyaK52ATqJkmStFkZ2serlpnXRMSHgbsDZ1ezrgQ2VON7l2nzRITBmCRJWjUys9mwtGxD\n",
       "A6+IuDlwY2b+JCK2Ax4AvLCR7AzgeOC0iDgU+ElmXtWW3zRWQNMXESdm5omzroeWxv23urn/Vi/3\n",
       "3eo2rQajUS1eewJvi4it6F2WfHtmfjIingSQmadk5pkRcVREXApcBzx2GhWVJEla7UY9TuJC4K4t\n",
       "009pjB8/4XpJkiRtdnxyvcZx9qwroGU5e9YV0LKcPesKaMnOnnUFtPJEZjd93iMi7eMlSZJWg2nF\n",
       "LbZ4SZIkdcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIk\n",
       "dcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIkdcTAS5Ik\n",
       "qSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIkdcTAS5IkqSMGXpIk\n",
       "SR0x8JIkSeqIgZckSVJHDLwkSZI6MjTwiogNEfHpiLgoIr4cEU9tSbMpIq6JiPPK8ILpVVeSJGn1\n",
       "Wjti/g3AMzLz/IjYEfhiRJyVmRc30n0mM4+eThUlSZI2D0NbvDLze5l5fnl/LXAxsFdL0phC3SRJ\n",
       "kjYrY/fxioiNwEHAuY1ZCRwWERdExJkRccDkqidJkrT5GHWpEYBymfF04Gml5av2JWBDZl4fEUcC\n",
       "HwD2n2w1JUmSVr+RgVdErAPeB7wjMz/QnJ+ZP6vefyQiTo6I3TLz6pa8TqxGz87Ms5dUa0mSpAmK\n",
       "iE3ApqmXk5nDKhHA24AfZeYzBqTZA/h+ZmZEHAy8JzM3tqTLzLQvmCRJWvGmFbeMavG6F/BI4H8i\n",
       "4rwy7XnArQEy8xTgGODJEXEjcD1w7KQrKUmStDkY2uI10YJs8ZIkSavEtOIWn1wvSZLUEQMvSZKk\n",
       "jhh4SZIkdcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIk\n",
       "dcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIkdcTAS5Ik\n",
       "qSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIkdcTAS5IkqSMGXpIk\n",
       "SR0x8JIkSeqIgZckaUki2CqCAyN4wKzrIq0WQwOviNgQEZ+OiIsi4ssR8dQB6U6KiEsi4oKIOGg6\n",
       "VZUkLVcE20Zwdnl/6whOXkZ27wb+B/j4JOombQkiMwfPjLglcMvMPD8idgS+CDwsMy+u0hwFHJ+Z\n",
       "R0XEIcCrM/PQlrwyM2PyqyBJGlcE/ZP+GuBPgNdnsqRzc5UXS81DWqmmFbcMbfHKzO9l5vnl/bXA\n",
       "xcBejWRHA28rac4F1kfEHpOuqCRpeSLYpho9FLhhVnWRtlRj9/GKiI3AQcC5jVm3Ai6vxq8A9l5u\n",
       "xbZ0EbwqgqNmXQ9JixPBDrOuQ18EBzQm7Vq93xr49TLy3qW83QP4dQRrl5rXalL6te06OuXKEEGW\n",
       "4TWzrot6xgq8ymXG04GnlZavBUka44OvX64CEewZwWkR3HaG1Xg68NxZFR7B2gi2n1X5K1U5gTVb\n",
       "fbWClS/KV3VU1nbAtRE8JYK7d1HmkLpsBVwUwc2rya8vr58CtqOcqyNY01h2uzGCi9PL69XMXbbc\n",
       "EnwCuDqCW06zkAjWNfbdcv35BPPSMowMvCJiHfA+4B2Z+YGWJFcCG6rxvcu0trxOrIZNS6hvV/4M\n",
       "+EPgnTOux8Wjk0zNq4DrZlj+ilMFolMJvEpH5/dMI+8t3O7A0yPYfZKZlh8nRzcm98dPAr4w49av\n",
       "Py2v766mPbS8bg+cCdyvjO/YWPY0egHVMD8HyOTGMn5yBA9cWlVXlfuW1/+dVgERfA74FfCDZeaz\n",
       "zehU6ouITb34ZIeXRGzzt9MqZ9RdjQG8CfhKZv7TgGRnAH9c0h8K/CQzr2pLmJknVsPZS6/25EWw\n",
       "WwQPKqPHl9dmM/2gZb8bwfMnWJf+fpll4HPcDMueqAgigiNapt8YwdsXkVX/i/sLk6nZAt8GHjGl\n",
       "vLdIEezGXEvM0yac/V8AH6zK2oqF+++KCZe5GL9fXu/XmP5rev27AB5dXputW7ceI/+HAD8q799c\n",
       "XnePYN1iKrmaNAPp0gK+7YTLuDVwrwlld9/q/bKCuHFEcKtJXikqXW7+ZlL5jdKLS/JFcN3z4Jcv\n",
       "mFY5o1q87gU8ErhvRJxXhiMj4kkR8aRS0TOBb0bEpcAp9FqLVqNnAx8tH6L1ZVrzV+AgewIvnmBd\n",
       "Di6vD6zvGurYLFvbJu0JwFn15ZTy5bCG3vHdn3bvciId9LnYtUr7lmlVdlIieHIE+8+6HjP2TKD/\n",
       "y/X5EZO58y6CHYHdyvv1EdwNuD3wB42kv5xEeUt0//J6fTXt34GHw4KW1Zc3xj8Bg/urRdB/bNBH\n",
       "ADJ5PPAx4B+Z3+d3c7NPy7TdJlzGy+qRCO6x2Awi2D6CA+n14+vbPYKNy6zbKJ8DLp1gfk8HXjjB\n",
       "/IYq37dL7vc4rlF3NX4uM7fKzLtk5kFl+EhmnpKZp1Tpjs/MfTPzzpn5pUlUrNnnoAP9A/TnXRUY\n",
       "wZ0jeGvLrP4vxjuWdLfpqk6Ve086wwjuGMGnl7DcOL++h3lDea0vibdddrp9eT2kUf5W5Xi8RTX5\n",
       "MeMUHME7FnH58Ptlmeblq6U6mRn2E1whtmuM/+eoBSL40wiOHJHsGOA55f3FwH8Df1TNv6a8ns4Y\n",
       "Ivir+jiJYENprVuu9wLbR3B4OYY3Ab9gYYv2BY3xfsf5zwzItx8cPKaa9iB6n5Ghd7WX/mP7Dq/2\n",
       "itW2bq+PYNdJBfUsfCbaqc0EVYf520ZwiwiO69/cEMHD6F0t+R9gX+bv28smVMcFIrgEphPYRbDn\n",
       "NPJtlDHpAHqgFfnk+gieADf1G2jO6x9wrZczS5oNJc3GEeWsK+neAXytMfvrTDZyb5a9I71LII+O\n",
       "6P1qrBzYGP9m/4ugBAFbs0QRvKL8Eho3/c5LLavFG4BNEeN3wo3gfODbEwrED67eP5zy5Vg6RMPc\n",
       "rfXNyy4fpXc8fqylfjuM6IT8fxn/8mE/sPtg28wIzmlrAS2XUm8Z0fqlsG1J8/5yrJ8ewX4RPGMV\n",
       "f/ktRv88cp/yesighJXX0ev/BEAEe8TcHXx99bbud7Ludze4bSbrgacCTx5VWASfAP6OcpyU1tjv\n",
       "MHcZb9Gq46Tfofr36F0a3RHYPpPfAHct817N/FYx4KbLRXcbUMQ5wFWZS2odeAVwyRKWm6d0D7lo\n",
       "ufks0q5As6/zQ+j1h/tNBB+dQBm7Mdfq8gN6rZSD3A+4il5/5Bsi2MDcsQ697jJnMYXv+gjWRPDw\n",
       "CHYqk/at5o17tWhY/jerRtcPTDg59eftl5QfwlORmZ0MvaLGTZtPhEzIXRvT9yzT+8NzGvMT8r7V\n",
       "/F+OKOedVdoPNfI+G/KHI5Y/CPKsapmrFrGOdVk5bF6dBvIfmukby0ZzHPIekIdDbih5XVrm7Twg\n",
       "jzWQvypp7zW5Y6B9fcdcZv0Sy9ymyuPJA7bxz0u6fy3jV4/YH7tD/ryeN6DsW1bLBOTWkLuPeUz8\n",
       "ZWPe8dW8TZB3LdMPGHEcnQ558xHH1NaDjoVl7u97Qm4z6XwXWYcXQZ7Q3FeQt4Hccdh+qMYvg/xi\n",
       "mX4m5K2rbfg1yF+37QPIn41zrLfsjzst9nPSyG+rxnH3Fsj3Qb68THtoI/2Ly3a6EPKfW47F+5Vp\n",
       "20BuKO//gYXn3++NU2/IM0q6ZwzaB2Ou56Eln/0Xmw/kHSEPXuQyayD/B/IKyH8c9pla4vqcAPnA\n",
       "ks93hnyuo5r3zUb5j4L8m8a055Tljinj25XxtZD3WUZ9H1DyuxRy30aZr1hqvlX+d6ry+8Zy8xtR\n",
       "1laN+p/Sm86S9+fQ8qa5MvNXbPwVKAdP2wF3VmPjvKt8GNZB7r3YD0Ej7XXl9XzIYyF/G/JGqkCm\n",
       "TLuyGn/tUj90g5ajFyS1fqDLutbjF5ZlDof83QHb7OED8uofaH8C+VzIZ1fL3BLy+/0P9gQP7rr8\n",
       "N0A+CHKvMZe59RLKO7ta/p8hv1JOWv3A/sxGnX5evf8tyH1KPv9UTT+m2nbHVdMf3VL+/ar5D4N8\n",
       "YWNfv6rMe0YZ/1FVt+Z+bD226X3xtx1H9xpyHPWHU0vaN7aUtw5yq2p80QFUKeOt5f05Vbm7Vmn+\n",
       "DXLtpI6xKt/rq/L+tkw7qIzvU16/27JcfQJ+COQNI7bh0xrjT6/y2qtluz4Z8mnV+B4j8l/0tumX\n",
       "Wx0jQ89R9D7/dZr+l+gfNPLpB5jPg/wy5GMb+ewyqIwRx/LhS9zHdx+2XgOW+YvFLlMt+7jG9njk\n",
       "gH12syWsS/OL/wWQrx9wLvidIcfLYyFf15j2uLLc71fT9oP8fHkfS6jvWgZ/tyTkT4csuyPk9mOU\n",
       "8fo6z6UcIwOOvbePOP7fBXmH3jwmUu6Cekwj0/YVHn8FmP/r/s3V9K80T3LV+6sHHAAbRuyEenge\n",
       "878UEvLrkC+BfErzAIB8c7Xsj1s+IB+FfHhLubdpKftOzA+s+l/a7xhycGfbelTlHDJs2ZbhMHpf\n",
       "Tu8p652QX5jQAf9nJb+/ayn3j4cs962S5piWeQNPGJAPbpTxvvL699W0J0P+dTV+LuS1jeXu0Bjf\n",
       "a8Cx098XT4F8QyPN9ZB/DHlSGT+0mUcZvxby3mXa50Ycq637HvJu9H6Btu3f5q/0fyl59H90bE85\n",
       "IZbxDzfK36saPwjybZRfz2XazpDb0gta69bk2zbK3VTSry/jD2orY5nHW13eS4dsxzc0ltt5jM9J\n",
       "f9iD0gJdDYdWefW/TLdqKX+nMr7/kH35i/L6O4tc9/556Wll/M7N46aR/gUD1u/Q6v32LfOf25LX\n",
       "T8q8rQfU7RYt+bwE8j8gH1Ol2wD5iBHruWnYelXptoF8yIBtfChjBreQzyzL/M2AY+0vy+uLyvSd\n",
       "ynYbmT/zW8cT8pFl+t821w3y/iXNd1vW5/GQH2hMO7osd7+W9Al57iKOrbPKOp0w4rPxosb2X1+N\n",
       "fwPynCGf236r6ksbef72kHrdlnIVYEiamxpnqmnbNcrYdv4yDDyuljNMPMPBKz3+CkB+stoQH6mm\n",
       "f6Ka/qMRO77fEnDvIeUkVUsR5J0HfKCaQ0D+eWNa/4RzaHP5lnIPLvPq9fndRn6H0rtEsHNZpu1D\n",
       "lpAPbU4r6WNA+lHD61umtX4Z0msZvBRyz5Z5x0E+tSz/SOZaDgbV66OQz2rJ52eN9Xo8vZbHfrN5\n",
       "65cS84P3ZK5Z/JRq2i1L2n7r0Dch7zJi+2w95NiI/n5qpPkH5l/KPpnel/IPq2nvLa/ryutX6Z0o\n",
       "HsT8y6X10PyVPGportvbBqzLA6r3wVyT/+9Qgt1q/qNGfF4+2bIvHlbSP7qaVh936yB3Y8gXAiO+\n",
       "0Brl/fmQOr68TN+ulHmfcbdnWe7cxvRm94j+9Me3lP9Lej/2vtEy79vV+yfS+3w8DvK2Y5w/b6pf\n",
       "23q3pH9vo+z+sJbeD4aEvLJlfuu5FfIqymerZd4BLfnUP8a2Yv6l3HtArhuQ18Ma+SxoOWP++eYp\n",
       "LWUn1Q+MIdu0/qxt05j3VOZalfpXZXav0g+9alCO5br17teQu5R5d4T8ciP9K+kFL/U6fKcxfhy9\n",
       "80xC3nPEZ7R5rOxKafFpTO//ULrzoHzoBdbPhvyHarlT6jKqtKcP2MYH02uR+/cyfkyzns1jb9Cx\n",
       "Xc2/E1WLJb3vrr9gfmPOOxcux8A8lzNMPMPBKz7eClQflJc0DwzIz9L4ldMyHFle71NNuyfkcdUO\n",
       "2Lb6YNyxSrd9oy6Dyvg/jfEDGjv1HVStDi3r+AjIT5f3h1D1jaiGQwbU5TND6vU5eifz+zP/g19/\n",
       "6f/+kOX7efTf9+v1VsiDGvXZUC83YB+2fsBZGLTWQ/+L/YH0vpTmzWtJ/wdVmf9J+cXC3BdG0mtJ\n",
       "3I75lxK/WNV322r6+pYyFqzniG3YrPPQVsuW7XOnxvTmr+HmcDLkF4bMv4Jey2Hd1+vF9E7WP6DX\n",
       "cjVo2ds3xs+l1yesP75pjG3yxJZpB9Lyo6Ea7ltv75bP0LWQPxgw72Ylj3fTa6VYU82rvzT+k/Kl\n",
       "S69/07Bt3GxtP6Est1MZf9mAutTLDAqUL2ukPagxfkLzGGnkv2vZJ/eopp01oB6nttTxcZCXN+r0\n",
       "1Wr+9ZD/r6XeGwes8w/K/D1Y+GP2MHr9R59F4xw/7Pgpy+7V2Jetn59GefuNWcaeJf0taLkMRnVJ\n",
       "eMT316eHlPG4lvT98/SXmOsa8XfV/H5r8T4jPmfbM9eqn5AbmQs09xv1GS3z1tI7X53WcpzdtUr/\n",
       "J9X7Q6iuGpS0n6mXb263RtnfKuWugXx/mVZfwvx75p/311Xvdy77d02j/Cx1unl13PSXGXRlLGlp\n",
       "pd2SAq/9y0bYq95IZd415UD8HuSbxvjQNTdsfwf+nNI3o6S7jqplrVr+zxrLP5TeL42P1nmOOqip\n",
       "LjUMOBDr/i/fp9cStsugZYaU89Tq/cur91tDvgLypLL8qdVBfEd6HUabeb2GhX0Yng15XVsdGnUd\n",
       "1PG03yH9rgPm94f1zPUx659Ekl5H8WbaY0ue/UDr6/RaxJ5J+fVZ5tcf3gVf2I1jZGvmB9L9D3K9\n",
       "z7Yp2/S+w/ZJmXfsiPVtpt+pMf3F5bXZx7F5HL2zMe8N5fWJVZoo23fcy9B3b5nW/7HyecgHDjn+\n",
       "+10Bflle96HXh7I//1H0WkeGlb+mZV/VJ9/mzSS/Te9zetGA80tbX9BnVe/fTO/L4FsDtvEH6/Ey\n",
       "bV+qS66Nef9b5fOgEfs9KTe+NLbnuQPqsmNLXmv7+37YOWdAXe9V8rwj1ZdQlfcXmGut/9Mh+fTT\n",
       "/1fLtmquQ9uPzubwsmrZyyD3b5Rzz+r9v9AL7rYpaR7Rkt9/l9d5l5UbeT4Pcoe2Y3vENlzQ77cx\n",
       "/KJKe11j3hvL64eqNPWl2Z2qujwPcoeyT7Il7Q7MnYfr7jP9LiR3p9ea+KQy3m9MOI7y/VYtc/iA\n",
       "dflMlea3IG9T3ve7S9yK+efdnZvbsgwbIE8cUEb/JqL+/Je1pOmfZ77N/HND0vtRXV9iHfQD687t\n",
       "+5Oh+3upw8QzHHxADl8BepHr9lTRdtlxzQ3Ub9E4sDH9gS15Npd9RXm9ht6lvY+NrvdNv577dfpl\n",
       "ld/XG2mblx36w/6NdB+py2b+ZcZBzepJabKmFxi0/Xp+LNWlOXontR+15LUn5Keq8V0b+ZxbPjC3\n",
       "bimjOZwD+ZsR270/9FuzblfGz6b90uarG+PNmwra0r+oMe3vIJ8/oF4nDTpWWqYfUY7NtQy5c2pQ\n",
       "3YYcx/2h7l/T9qXbzKsfJF/WrDO9k18//YHV/juxpb63G1Kn/nAx5HMa066l16r8MXpByEOH5Nfs\n",
       "zxPM74z+IXpfVM0WvgXrXcpYW17/sJp/uzL+8sZynxywn3Yr8z/F/B8q/eHfIF9SpX9pow5vajtO\n",
       "hhwXbZeJm9Muq/b5OdWyr2pZNimX11nYdy6Zu/z2unHrOMY69PP+6zJ+JuPfnZtt86rxgwesYz28\n",
       "kMYXaln2HMg/Ku+PaSzzvDK93zrzhPL6VXo/AAb1s6zz+FaZdmo17R4jtlWzz1DbcBXtl+supNda\n",
       "dIsqvzpw+Rm9Hwa/YO7OxDUsDJLfVN73f8BtNaS+927U4UWQH6+2R9v69H8s7TQgz7rO9dWNpzf3\n",
       "YxnOb5k28NhZ5PC5xviRA9Lt074ujP1ZX9RnahqZLmUFysq/ruz4+oO5Jy23KTP3y3UHer94FnS0\n",
       "ZvBdJ1+n90vo9NH1vukgek3Lzt+rkXbQbfvvZ37L2Gshn1qNH9E8yAZsn/c3pv02c3dvHUAvOGj9\n",
       "pT7Getb9evodrEf1E3sgLY+3qOafSHXprpq/TaOcm0P+UbXcW6v3Owz40D2MuX5vV7KwH1Ey+HLL\n",
       "kQO275I/ZP192Bg2NPL/fci31yeFQWUz/5fZVcx12O23oPQ7O5/RWO7gfl7M3WV2YEt9my0/zx+x\n",
       "rz/fGL+E3t0/H2HuEsG8obHNX1vGm3dkvZS5L4jWL63GNnwk5IfHqPcNIz5L5zC/m8G8Og1ZdifI\n",
       "2y3h+OhfqvxeGf85veB5H8pdcGX+uxrLndFSv+votRJ8tGVev1X4uKUey4M+G5C7LWGZpHSsrvZ9\n",
       "/aNvnB93zS/PZO4c0n9UwqaWNHeid144mbmWwOaP5foy+9bNPJrrMua6f7ulLhePsZ6vHJDfi1vS\n",
       "tt5YVOZtqsaH3o3M/MtwSe+S83eqda9bDN9Xr8ci9v+g4aIR89c08vxNNe+aMcvoD/0uOndm7qpa\n",
       "fxjyI4Kx9vmiP1PTyHQpK1A2wE19cKrp9Ydh72r6Wsj3jshz45Ad8RTKszrG+CCtZWGn4qTll0SZ\n",
       "Xt9t+e16nZi7pv/KRv4LWuwa+d6JlhMfvVveT67G5x2Qi9tH+SYWPuNnQ2Od62FnepcNz2ss82nI\n",
       "+1fjOzKgs21jud808j+4mvf1avrxZVr/7p5/HVC/5nOGPlKmHzZgvy1qe7Xk0W/afyaD7+ranrn+\n",
       "Im+tyn5CI9065vc9e2mZfhhzdwE+DXKPljLqu+j2H1CPZt+zQ+m1ot6V3iWnZl+3fZnfQnQRg1t4\n",
       "6+O9P75jVXb9zJ+Xl7r07zpbcPmsTG+2ev6C3t23Q8sfsO5JudzMwn6ESUs/qEkM9FrLnzFk/oEs\n",
       "7GIwqEXoWUPW/SUTrvetWGSwyVzfqv5zpt5BuUzUSNcPoM6hd77ut+b1W0t/2Fi3fhDSv/zVvwJy\n",
       "UMt2uD+9vmknljSPhnxAS133GbIt+3c1fwvy/y5i/fs/ZJ/FXP+xQWXcaYz8xj22l/JoiLbgPlnY\n",
       "tSOouomMyPNT1XI/ZeHNcFuXz3TzUvP9B+XP/FbCfsDev8IztNWcuRs4bsH8Vrcdhq8HQ9dzyZ+p\n",
       "aWS62BVgYX+T5hd5f3pr0+YYB2zdX6h/QLyO6pbXReTX73e2oNWkKq9/6fDUxnp9uXr//MWWPWb9\n",
       "DqW6Dj7BfP+eubtkbmTuBNnvA1S36H0F8o5LKKPZB6buSLuRxpcWvdbOeru+kfmXHG7TUkbrM3bo\n",
       "BR0L+hNNa6D3S7Pf4nfHQWVTmv0hvzalerwD8r8HzLupf1cZr585dbPq/U3HNL3b34+g+oJj8A+U\n",
       "pP2RBBvpPXdt2In0BbS3+PTrsaAjc6Ps/63GX1vOC/1LKG/s6jgYY//0f6i9gd4X5CPo3SFcX6Ju\n",
       "PgLlhFnXu9S99QpAS7p9aLlzmt4X/RH07oy9hvKMtOocdF3Ldjqa+ef7ZEB/v2rZZp/KnZl7NER/\n",
       "+K0JbI9Bx/K+i1z2y8utSyPvDw+p22WNc8AO9fiQPNcyv5vCvJszWrZ9vx9fP+Be0Oe6zP8bSqBK\n",
       "o1sO82+eSuZf0n8l1bMgx1mHXjpGplnSNp9GpotdAeY/bT5ptI5U0wdeqx6S9xHlIOh3cK5bR562\n",
       "hPzOgrx8yPxdywmjf6fRoDt3tl1s2Yus5+0Z8tyTZeZdt6jUfe22Kie+ZEjz7Yi8b2pVGTN9/1lD\n",
       "Py0f4p0Ws/xKH5h79tfQZ9RMqew19J4JVPc56e/r5mXoaxaZ9670WgOGPYut2f9k3ombAXdjjlH2\n",
       "OloeRVGdG548zjrM6HjYnfLMwDL0g/c/Zu5y9/tmXc9qOzf3z9jPjCp5HFYt2+9c/tlh+5qFN6E8\n",
       "Z4xy+ml/XMabx/eui6n3gDLW0uvM/sYq37FaEst35EPKMu9fbl0aea+n90Pw3xvrnFRPxq/SX0v1\n",
       "IPEh+f5elc8O1ftfNtIlVWsi1SOZlrAuSenOUW23hLxbI91HGCOY3mwDLxY+W+ijzZMx5RLOMg+u\n",
       "/g6oTwaPXEI+27L4v6dY0Eehq+3ezb69ab2eXb1fdJBc8jqhLD9WfxLm/kZqxbRSTHjbvmolHS+N\n",
       "wGcNvb41e9HyLLdJlleG79Lr23dAmdfvuFuf4Dcuo6ztqfpersShGRAM2F4T69814f2XkH+/yOXv\n",
       "11xXqn+kGLBM3dLx72OWs57eIx32rabV9V7S+WzUdlnCcn9L41FDE6zTzZi7I/xwepd/r6XX73rB\n",
       "DUlj5Nf/UX5kNe0+LOy7davmd/4y1mGb8hlZ8l9Rzc+PRe+jcYbSb2n6IiIzc8G/t0dwLPCuMro2\n",
       "W/50NYLtgf0zOX8ydbnpD2SPyOSTk8hzzHLfD2wN/GUmF3ZV7rSVP/l+MHAZcBuATBbs6zHzWgvs\n",
       "mskPxky/DfAL4MxMfncpZa5kERwC/EUm/2fWdYG5z85S9+8Syns58GzgLsDXMvlFNe9o4IOZRAQn\n",
       "AZ/N5L1d1GuWqvPX/pnL/7PpaSp1vQTYr0xaVJ3LH9ifCmzM5B5l2n2As2HwcRjBo8pyW2Uu/GP5\n",
       "Mcs+CXgK8JhM3raUPIbkvQNwQya/mmS+kxLBRuCLwPb0/lS9m0BhhRkUtyw73xUQeL0XOIbel8s/\n",
       "dlMX/ghZWXl9AAANWklEQVQ4ATgok+u7KHNzF8F3gT3L6IGZfLnDshN4fCZv7qrMLVUEXwDu3mHg\n",
       "tb6U94kB89e0/VjbnHUd/C5HBD+n96PsAuDHwM6Z/GyZea4BbgT+M5PDll/LgeU8HPg34K6ZnDet\n",
       "claiCLYGfgmr4zibls058Fo1JxENFsEfAKdD9/uyHEP7ZvKNLsvdEkXwX8Ahfl5npxzvX8/kdrOu\n",
       "yygRxDRaSyI4DXhCJtdOOu+qjAcAHwe2zewFIVsSv5unF3itnXSGixHBAeXtw2ZZD03ETuX1hV0X\n",
       "vCWfGGbgcGCrWVdCfH/WFRjHtC5RZXLsNPJt+Gl5XZGXAzvyqllXYHM008AL2Lm8fnumtdAkXFRe\n",
       "XzvTWmiqMrlh1nUQJwOfmnUlNneZnAtb7o86f9BOz8wuNUawO70TyOHAnltq5z1JkrTybI6XGl9N\n",
       "r1P91JqjJUmSVpJZ9tXY4jorSpKkLdssA6/HlNdHzbAOkiRJnZllH68EzsnkXp1UQJIkaUzT6uM1\n",
       "yxavbwCPm2H5kiRJnZpl4LUe+NEMy5ckSerULAOvHWF6Tx2WJElaaWYSeEWwjt6jLLyzUZIkbTFm\n",
       "1eJ1ALDG53dJkqQtyawCr5fOqFxJkqSZmVXg9UPgrBmVLUmSNBOzCrwexdyfKkuSJG0RZhV4/Qr4\n",
       "8IzKliRJmomRgVdEvDkiroqICwfM3xQR10TEeWV4wfD8WANsDWy3tCpLkiStTmvHSPMW4J+BU4ek\n",
       "+UxmHj1mmXuX1/8YM70kSdJmYWSLV2Z+FvjxiGSL+S+j9/by5epFLCNJkrTqTaKPVwKHRcQFEXFm\n",
       "RBwwIv09JlCmJEnSqjPOpcZRvgRsyMzrI+JI4APA/m0JI+JEeO418I3zIk7flJlnT6B8SZKkZYmI\n",
       "TcCmqZeTOfrh8RGxEfhQZh44RtrLgLtl5tWN6ZmZEcGngRdn8smlVVmSJGm6+nHLpPNd9qXGiNgj\n",
       "IqK8P5heMDes/9Z6RvcZkyRJ2uyMvNQYEe8C7gPcPCIuB04A1gFk5inAMcCTI+JG4Hrg2BFZ7gJc\n",
       "s5xKS5IkrUZjXWqcSEFzlxp/BNw+kx90UrAkSdIirdhLjYsRwS7AbtjiJUmStkBd/2XQ7QEy+VXH\n",
       "5UqSJM1c14HXLsAnOi5TkiRpReg68FqPlxklSdIWahYtXj/puExJkqQVYRaBly1ekiRpi9R14LUr\n",
       "Bl6SJGkL1XXgtTv4/C5JkrRl6jrwujkGXpIkaQs1i8Drhx2XKUmStCLM4nES/kG2JEnaInUdeB0I\n",
       "/KzjMiVJklaETv8kGxJgbSa/7qRQSZKkJdgs/iQb+IlBlyRJ2lJ1HXj9qOPyJEmSVoyuA6+rOy5P\n",
       "kiRpxTDwkiRJ6oiXGiVJkjpii5ckSVJHDLwkSZI64qVGSZKkjtjiJUmS1BEDL0mSpI54qVGSJKkj\n",
       "tnhJkiR1xMBLkiSpI53/SXbH5UmSJK0YnQZemfy6y/IkSZJWkq5bvCRJkrZYBl6SJEkdMfCSJEnq\n",
       "yMjAKyLeHBFXRcSFQ9KcFBGXRMQFEXHQZKsoSZK0eRinxestwIMHzYyIo4B9M3M/4InA6yZUN0mS\n",
       "pM3KyMArMz8L/HhIkqOBt5W05wLrI2KPyVRPkiRp8zGJPl63Ai6vxq8A9p5AvpIkSZuVSXWuj8Z4\n",
       "TihfSZKkzcbaCeRxJbChGt+7TFsgIk6sRs/OzLMnUL4kSdKyRMQmYNPUy8kc3TgVERuBD2XmgS3z\n",
       "jgKOz8yjIuJQ4J8y89CWdJmZzZYxSZKkFWdaccvIFq+IeBdwH+DmEXE5cAKwDiAzT8nMMyPiqIi4\n",
       "FLgOeOykKylJkrQ5GKvFayIF2eIlSZJWiWnFLT65XpIkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwk\n",
       "SZI6YuAlSZLUEQMvSZKkjhh4SZIkdcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAl\n",
       "SZLUEQMvSZKkjhh4SZIkdcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMv\n",
       "SZKkjhh4SZIkdcTAS5IkqSMGXpIkSR0x8JIkSeqIgZckSVJHDLwkSZI6YuAlSZLUEQMvSZKkjowM\n",
       "vCLiwRHx1Yi4JCKe2zJ/U0RcExHnleEF06mqJEnS6rZ22MyIWAO8BjgCuBL4QkSckZkXN5J+JjOP\n",
       "nlIdJUmSNgujWrwOBi7NzG9l5g3AacBDW9LFxGsmSZK0mRkVeN0KuLwav6JMqyVwWERcEBFnRsQB\n",
       "k6ygJEnS5mLopUZ6QdUoXwI2ZOb1EXEk8AFg/2XXTJIkaTMzKvC6EthQjW+g1+p1k8z8WfX+IxFx\n",
       "ckTslplXNzOLiBOr0bMz8+xF11iSJGnCImITsGnq5WQObtSKiLXA14D7A98FPg8cV3euj4g9gO9n\n",
       "ZkbEwcB7MnNjS16ZmfYFkyRJK9604pahLV6ZeWNEHA98DFgDvCkzL46IJ5X5pwDHAE+OiBuB64Fj\n",
       "J11JSZKkzcHQFq+JFmSLlyRJWiWmFbf45HpJkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiB\n",
       "lyRJUkcMvCRJkjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiBlyRJUkcM\n",
       "vCRJkjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiBlyRJUkcMvCRJkjpi\n",
       "4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiBlyRJUkcMvCRJkjpi4CVJktSR\n",
       "kYFXRDw4Ir4aEZdExHMHpDmpzL8gIg6afDUlSZJWv6GBV0SsAV4DPBg4ADguIu7QSHMUsG9m7gc8\n",
       "EXjdlOqqGYmITbOug5bO/be6uf9WL/ed2oxq8ToYuDQzv5WZNwCnAQ9tpDkaeBtAZp4LrI+IPSZe\n",
       "U83SpllXQMuyadYV0LJsmnUFtGSbZl0BrTyjAq9bAZdX41eUaaPS7L38qkmSJG1eRgVeOWY+scTl\n",
       "JEmSthhrR8y/EthQjW+g16I1LM3eZdoCEWFAtkpFxAmzroOWzv23urn/Vi/3nZpGBV7/DewXERuB\n",
       "7wJ/CBzXSHMGcDxwWkQcCvwkM69qZpSZzVYxSZKkLcrQwCszb4yI44GPAWuAN2XmxRHxpDL/lMw8\n",
       "MyKOiohLgeuAx0691pIkSatQZHr1T5IkqQtTf3L9OA9gVbciYkNEfDoiLoqIL0fEU8v03SLirIj4\n",
       "ekR8PCLWV8v8VdmHX42IB1bT7xYRF5Z5r57F+mypImJNRJwXER8q4+6/VSIi1kfE6RFxcUR8JSIO\n",
       "cf+tDmVfXFS2+zsjYhv33coVEW+OiKsi4sJq2sT2V9n/7y7T/ysi9hlZqcyc2kDv8uSlwEZgHXA+\n",
       "cIdplukw1n65JXCX8n5H4GvAHYCXA88p058LvKy8P6Dsu3VlX17KXGvp54GDy/szgQfPev22lAF4\n",
       "JvCvwBll3P23SgZ6zz58XHm/FtjF/bfyh7L9vwlsU8bfDTzafbdyB+Bw4CDgwmraxPYX8GfAyeX9\n",
       "HwKnjarTtFu8xnkAqzqWmd/LzPPL+2uBi+k9j+2mh+GW14eV9w8F3pWZN2Tmt+gdjIdExJ7ATpn5\n",
       "+ZLu1GoZTVFE7A0cBbyRuce5uP9WgYjYBTg8M98Mvb60mXkN7r/V4KfADcD2EbEW2J7ejWfuuxUq\n",
       "Mz8L/LgxeZL7q87rfcD9R9Vp2oHXOA9g1QyVO1YPAs4F9si5O1KvAvr/QLAX8x8j0t+PzelX4v7t\n",
       "yquAZwO/qaa5/1aH2wA/iIi3RMSXIuJfImIH3H8rXmZeDbwS+A69gOsnmXkW7rvVZpL766Y4JzNv\n",
       "BK6JiN2GFT7twMue+ytYROxIL0J/Wmb+rJ6XvXZT998KFBG/B3w/M89j4cOLAfffCrcWuCu9yxN3\n",
       "pXc3+F/WCdx/K1NE3BZ4Or3LUHsBO0bEI+s07rvVZRb7a9qB1zgPYNUMRMQ6ekHX2zPzA2XyVRFx\n",
       "yzJ/T+D7ZXrbQ3KvKNP3bkxvfXiuJuow4OiIuAx4F3C/iHg77r/V4grgisz8Qhk/nV4g9j3334p3\n",
       "d+CczPxRad34N+CeuO9Wm0mcK6+olrl1yWstsEtpGR1o2oHXTQ9gjYit6XU8O2PKZWqEiAjgTcBX\n",
       "MvOfqlln0OsoSnn9QDX92IjYOiJuA+wHfD4zvwf8tNyRFcCjqmU0JZn5vMzckJm3AY4FPpWZj8L9\n",
       "tyqU7X55ROxfJh0BXAR8CPffSvdV4NCI2K5s8yOAr+C+W20mca78YEtexwCfHFl6B3cUHEnvrrlL\n",
       "gb/q8m4Gh4H75N70+gadD5xXhgcDuwGfAL4OfBxYXy3zvLIPvwo8qJp+N+DCMu+kWa/bljYA92Hu\n",
       "rkb33yoZgDsDXwAuoNdqsov7b3UMwHPoBcoX0utUvc59t3IHelcFvgv8il5frMdOcn8B2wDvAS4B\n",
       "/gvYOKpOPkBVkiSpI1N/gKokSZJ6DLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIkdcTAS5IkqSMGXpIk\n",
       "SR0x8JIkSerI/wcl2RjS9H5VUAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10adc7b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JFV5+PHvOxu7ICLrDI7CoIBEBxQRQUZBhTEZNaJC\n",
       "giZEAxFxIVHchfxcEzUSQkSSqD8kBqJoEAQjBBkUE8eFRVYFBWUJowFlG6OMvPmjzmVqir63753p\n",
       "ru6+9/t5nnpu16nTVW/1qdv99qnTVZGZSJIkqf9mDToASZKkmcLES5IkqSUmXpIkSS0x8ZIkSWqJ\n",
       "iZckSVJLTLwkSZJaMmHiFREbRsSKiLgyIq6LiA+OU+/kiLgxIq6KiMX9CVWSJGm0zZloYWb+b0Q8\n",
       "JzNXRcQc4LKI2C8zLxurExFLgZ0zc1FEPAM4Fdinv2FLkiSNnq6nGjNzVXk4D5gN3N2osgw4vdRd\n",
       "AWwREdv0MkhJkqTpoGviFRGzIuJKYCVwSWZe16iyA3Brbf42YH7vQpQkSZoeJtPj9VBmPpUqmXp2\n",
       "RCzpUC2aT+tBbJIkSdPKhGO86jLznog4H3gasLy26HZgQW1+filbS0SYjEmSpJGRmc2OpfU2YeIV\n",
       "EVsBqzPzlxGxEfA84C8b1c4FjgXOioh9gF9m5spO6+vHDqj/IuLEzDxx0HFo3dh+o832G1223Wjr\n",
       "V4dRtx6v7YDTI2IW1WnJMzLz4og4GiAzT8vMCyJiaUTcBDwAHNmPQCVJkkZdt8tJXA3s2aH8tMb8\n",
       "sT2OS5IkadrxyvWajOWDDkDrZfmgA9B6WT7oALTOlg86AA2fyGxnzHtEpGO8JEnSKOhX3mKPlyRJ\n",
       "UktMvCRJklpi4iVJktQSEy9JkqSWmHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUktMvCRJ\n",
       "klpi4iVJktQSEy9JkqSWmHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUktMvCRJklpi4iVJ\n",
       "ktQSEy9JkqSWmHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUktMvCRJklpi4iVJktQSEy9J\n",
       "kqSWmHhJkiS1xMRLkiSpJRMmXhGxICIuiYhrI+KaiHhDhzpLIuKeiLiiTO/qX7iSJEmja06X5Q8C\n",
       "x2XmlRGxKfC9iLgoM69v1Ls0M5f1J0RJkqTpYcIer8y8MzOvLI/vB64Htu9QNfoQmyRJ0rQy6TFe\n",
       "EbEQWAysaCxKYN+IuCoiLoiI3XoXniRJ0vTR7VQjAOU049nAG0vPV93lwILMXBURhwDnALv0NkxJ\n",
       "kqTR1zXxioi5wBeAf87Mc5rLM/O+2uOvRMTHI2LLzLy7w7pOrM0uz8zl6xS1JElSD0XEEmBJ37eT\n",
       "mRMFEcDpwF2Zedw4dbYBfpaZGRF7A5/LzIUd6mVmOhZMkiQNvX7lLd16vJ4FHAF8PyKuKGXvAHYE\n",
       "yMzTgEOB10bEamAVcFivg5QkSZoOJuzx6umG7PGSJEkjol95i1eulyRJaomJlyRJUktMvCRJklpi\n",
       "4iVJktQSEy9JkqSWmHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUktMvCRJklpi4iVJktQS\n",
       "Ey9JkqSWmHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUktMvCRJklpi4iVJktQSEy9JkqSW\n",
       "mHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUktMvCRJklpi4iVJktQSEy9JkqSWmHhJkiS1\n",
       "xMRLkiSpJRMmXhGxICIuiYhrI+KaiHjDOPVOjogbI+KqiFjcn1AlSZJG25wuyx8EjsvMKyNiU+B7\n",
       "EXFRZl4/ViEilgI7Z+aiiHgGcCqwT/9CliRJGk0T9nhl5p2ZeWV5fD9wPbB9o9oy4PRSZwWwRURs\n",
       "04dYJXURwXMiuCGCvQcdiyTpkSY9xisiFgKLgRWNRTsAt9bmbwPmr29gkqYmgo8BXwOeCKyIYLMB\n",
       "hyRJaphU4lVOM54NvLH0fD2iSmM+1zcwaTqIICM4I2Ldf8gSQUTw5AjOj2DTxrLzI3hrBAm8qRQf\n",
       "UP7eG8FPIth4XbctjZIITorgeYOOQ5pIZE6cI0XEXODLwFcy86QOyz8BLM/Ms8r8DcABmbmyUS+B\n",
       "v6wVLc/M5esXvjR4EWwN7JbJ8kb5HKpxkmPmZa41P9n13wwsrBV9EjgOeAJwZa38vzOroQARHAp8\n",
       "vrbsyWX7V5TlkekXJE0PEewIvBM4qhRtksmqAYakERQRS4AltaITMrPZsbT+25ko8YqIoBq/dVdm\n",
       "HjdOnaXAsZm5NCL2AU7KzEcMro+I7McOSG2J4FnAf2aSEewC/Bg4EviHUmUL4IFMVkewCdDsHb4s\n",
       "k/2nuM1dgB+U2YuBA8vjO4Fta1W3y+TODs//e+CYWtFrqX4AM7a+NwNnAbtn8tupxKbJiWBLYHUm\n",
       "9w46lukogj2B75XZy4D9gPdl8u7BRaXpoF95S7fTH88CjgCeExFXlOmQiDg6Io4GyMwLgB9HxE3A\n",
       "aaz9Ji9NCxFsSPWm/lAEX6RKhk5kTdIF8EvgwQjez5qk6wPARuXx6ils71Hl9OFY0rV7JgcBnyvz\n",
       "Y0nXUZlEp6QLIJPXAS+rFZ1ae3wgcAXVmLC9JhvbTFZO+342Yq3XtJu7gHsiOLtfcXUSwQYRnB7B\n",
       "vRHs1+a22xLBDqxJujYvX2z+EHhXBP88uMikCWRmK1O1qXa25eTU6wnyryBznGm7ccrfW3v+c0rZ\n",
       "FmX+1DL/77U6e0GeD7kt5F/U1rO0EctWpXyXKe7DE8fWBzkbckWZ/ynkRwf9Go/CBPmhWrs8FTIg\n",
       "N4TcCXJOqROQW0JuCnk85LWN4+JTkDs12j0hNyrzG/cgzk7H4wfGYpwuE+Svyr69tlY2a2yfBx2f\n",
       "02hP/cpbRn4HnIZ7qr0JPgFy1jo8/1Hlg+ySsp5T6x8mLcQfkFuX7X0IcjfI10MeW8qOKPXmQD6u\n",
       "fAjfD3nVOK9Dp2lXyN/pUL6iD/vzB5BzG/v3nrK9Rw/6eBnWCXJ7yN0naMOxaZPa45/XHm/Toe6f\n",
       "lL8Plb9vK+2RkLt3iWejUu+xjfIPQn69sZ1VjfkjO6yvfvxtOujXe5Jt8pIS79M7LNugtj+vLmUB\n",
       "eWCjTR9V2uyFkC8e9D45Dc9UHS9kX9bd3k70ZwechnuCfFPjTf+YKTz3RZP4oFsy0QdFeQPeZB1j\n",
       "P7KxrSknjo313dxY399A/gjytpKsJeRZteU7tNRGm5ft/XTQx8uwTSU52qrebqX8LZM4Nh/xBQFy\n",
       "B8h/n6DuS8vfr3WJ61Wl3ufLfKde13m1+i+AfGc9GSntvrBR3soXmvVoj7EYT+8WK+SvxxLPMv83\n",
       "tee/vsPrdceg9286TVRfNq4sr+1qyFsgX9qoE+X/a+tJrnMWZHQom9/j2Det4mbc42u91t9eI/Rn\n",
       "B5yGd4J89AQfMLO7PPelzTdFqm+454wlQKzdo7Bx+XtcbR2zG+t47CRi3rB8OB7QeO5ze/SaPB3y\n",
       "aZB/VGI+sLaNg0qdpw2grQ4rMewz6ONmAPse1E79lbKPQn65w3H7mLJ8HuTOtfqbQf5jqfMaql7S\n",
       "Z0E+F/KFjXXXj8vHluNg2w7b+mM6JPvlg+bqWr3XNZ738S77O97/5J715GTQ7dIh7md1eo26PGdR\n",
       "qffycfb5O435Uwe9n8M+lWP9JV3qbDXBcbYl5JM7lL9/Etu+BfL82vyxjXUcXf7eDfk+yJd3WMdc\n",
       "yCMg3wx5L+S5kH9RW/78Nesj+/IattdY/dkBp+GcqE69nVsO4AMhLyv/sM1/tm1K/VmQp5SyPy9/\n",
       "V1N9a9ppnG0c2GF9Y9NOkJ8YZ9m4SV+HuvN6/dpMsM2BneKhSj5WQH4Y8nepEsN3Q24w6GNpgphn\n",
       "lzh/fz3Xs6z5Id7hOPhVj2OfT+N0IlVCnuVDYa3tN+qdVMrf1qj3HsiFk9j2jpD715734bH/Mdac\n",
       "6kyq3tdOiV9M9D/Uo2Px59R6fHm4ByIT8tmQe3SKbZx11V+jqJU9u9R5FGtO3f6iy/o+WOptCbn5\n",
       "II//Nqfyv7YI8r7aa9lxvGDj9X4J1ReLQ5l4uMXY1PF0b2mz+vjK/5rEusam11J9piwr6/nROPUW\n",
       "Qb6sNv9lEy+nFtoon0OjG3eceodTfWuYTW28UFkWrH3q4oIOz//9Sf7DPHESsWxG1RuWkN/ttJ5S\n",
       "r/mN90/Lh88HIZ9E9W16z9o/9YmQZ7T0us/v5wfZFOLo9C00IfccdGwdYl3UIc6OiWs5VsdO4b6j\n",
       "w/Lxjr8/LMfIm5rHeR/362Xlg6o5Jmzb8r/1zDL/a9ZOKj63Dtt6EuP0Aje2vQfVKcks/xe/KI8v\n",
       "htysD6/B5rVtfxpyP8h/KPN7rcP6xn68cEKXetuWfevY1uX1fqjx2rycIf5yMonXZkvI4xtlH4L8\n",
       "CVWy9BjIOyf4H5lbnjMfcu9aOyXlxyKNdT+2tvxsqnF2z4N8cWO9T6V8FpX/h6NK+T0dYgiqsyub\n",
       "UQ3b2K0c20/rUPcj5e/1kD+k6t16eod6B+MYL6f+tk3OhnxFOeAOG6dO85vj/lTdvkktWYO8oFbn\n",
       "SMZJKCB3Kf+o9XV+k2osSkLuNoX4N4Y8j+pbcbB2T9icRt23T/AmkpDfH3R7DPhY+ADVDxjO6fQG\n",
       "N+j4anGOxXR87fGfdKi3B+SZ47T1U1gzGP5JkNfUlp3f9j51iP0VrD0uqT7tUOqM9SIv7PG2t4T8\n",
       "Ypf/lYeTPqofz2zCOL3TU9juvAm289J1XOecsfaeRN37IC+l+uXvktqH9GzWfHlb3ojr/kEfK+v4\n",
       "ugTkfzT25cEubX0UVQ/hsi71pvzr2XIMNddzWu3xnaXe+WV+SbftUCV6n2ms85IO9Z5YW/70NeVk\n",
       "X1779hq5Pzvg1Iu2WftbXCnbkDW/DLqczh/E9WkD1pwiTKZweQK6/IJrHfcpGCdRgDwI8rgO+/Aj\n",
       "/GVf8zXcmjUDZJ8/wFh2LDH8FPJvy+Ox02Obs/YlG7Yu5fVftl1I1fNVb+/vQX5/7Jgvz7kY8p2D\n",
       "fu0b+75rI+5lLW1308Z2nwt5DFUP4DZUvcafH+f9YMqnzRvba/5/3sN69DpONh7W7rHpNH2otMd9\n",
       "VL0y/1LKR+YyHVRnLLol0/VE5GQ6JK2QZ3R67nrGNrscV51iWqcfSdWOrY9O1Fbl/W7W2mWs1/6M\n",
       "N3W9ZVCveOX64RBBUF1h/aFM7im32vhJWbwIuJHqNjdzOzz9z4BDgG2AfYCbgcd3qDc7k4d6HXuv\n",
       "RbAV8FtgZ+CvMnnugEMaWhGcAqzK5PgBbPuVwGea5Zlr7hEbwVFUF3AG+EEmT4rgcmBxKdsxk1tr\n",
       "9Y8GPtFpXcMqgj8GLsl8+P+1jW0+Fbg7k59OUOdOqveEuguBl2dyT63ez4EjM/lyh3XU34dekMmF\n",
       "ETwNuDqTX6/vfkxFuXDxvcCjgCcBN9QWr3WHiPIe8vMyO3TvexFsDjwFuBT4FdU+XUf1Xj9mf2Ar\n",
       "4A7gucApmdxfLvh7RyZvmGD9O5Q6PU8kItgH+C/gs8AxOYA7P/QrbzHxmubK7TReBvwt1b39vtmp\n",
       "3tgHT3nTqfsE1dXTP9bpw6ncDuVI4CPADZns2rvoNSwieAbwrTJ7O7Agk4xgTubkr8g/he09Cbge\n",
       "2Jjq1kbPBP4NeAXVVft/kbn2LZnKsfgG4IR6+XhJVQSvp/qC8fFM/rfX+zCTlER2D6o7ObwK+Iuy\n",
       "aFOqu59cBlwD/P9Mjuzw/I+U57wqkzNaCXocETwmk7umUP9bwDPK7F7A97O6bdgfUx2/n6BKat6U\n",
       "yVm9jneCuJr3iq17DVWc32krnlFk4qV1EsEq1tyyZjwXZvKC2nPOouoVWzr2DS6C2em9/Ga0Dkn5\n",
       "pcABVN+o/xB4+1S+8UewMfA7mQ8ndJ228w6q2y69B/hIJr+axHqPgIc/vIeuF2ImiODtVO3WyRuB\n",
       "m6gSsYOA7YH3As/O5BvtRNhbEVwD7F5mT6K6QX2nL7kLMrltHdb/cA/tZHpny5eQevJ4HnAB5ZZh\n",
       "o9DDOwxMvDRlEcwFfkP1IfTKUnwZ8Ozy+EDg0cDXpvINTzNXBIuBQ6kSoqa/zuStk1jHm4EP14pm\n",
       "AUuperg2ovpAvobqg2Ls1OacqST+ESwCHtNM6tSeCN5A1dM+5nDgzAmeskEmv+lvVP0TwcHAVxrF\n",
       "f0aVMF1AdYx/MpPXTHG9F1ElqHWzmqf3InhsJj9v9E4fXbb521Jna2CTTG6eSgwzlYmXpqx0db81\n",
       "k10jmOU3f/VKBB8G7gS2pkqOfgjsAvw7cDCwJ9VpvJ9ksrL2vEWl7kRuz2R+7Vv7ezN5T+/3Qv0W\n",
       "we7ArWPjcyJ4NLAd1bjKL5VqpwCfyOTawUTZO+X03n3AhsAemVwz9t4bwTuBHYDXARuO13sbwYZU\n",
       "465WUY2d+0JZtDvVGKy/K/PHZHJqBLOoErsXUI3RHRu/tSSTS3u+kzOIiZcmLYJNgSuo3tzsVlYr\n",
       "OpyKHHNUJv9Y6vwamAf8KXAW1YdU0+MmGsyt6SGCd1El1TPi/SmClwJn14oe0WtV6nX6P5pT67Wq\n",
       "9xg/GvhFh/p3ZbLVeoY84/Urb5nV6xWqXRHMjyBr06upPsx2pvrV4ZzBRqgZZOxXoc8vf8fGsvxD\n",
       "BKdE8E2qpGvzTP6pDI4/BHgTVe/YEqpv8SZdM0Am75spSVdxbmP+oQjeEsHXI7gugvsj+H8dnrd/\n",
       "/TR7Jh+h+j+CNUnXx4D5wDuBfUy6hps9XiMogkOBHwFXAudTfXg1fSmTF7camNRQLl9SP8V9ceYj\n",
       "xqtIM0IEBwIvAn4JvHu8erVfmcd4l2qI4F+oxs3ZQ9wnnmoUABE8Hfh2o/jVVKdtfk31rWcj4Mej\n",
       "PFBV00sEn6Eas3L8IK7HIw2bCPYGVpTZq6kuvfF24DuZ/HgSz98AOC6TD/UvypnNxGsGK70GNwNf\n",
       "phqYWefAY0kaQWUw/m/7cQFSrT8Trxksgt9j7fEBT6bqpt43kx0HE5UkSdOXg+unsQjmRvC+cZY9\n",
       "jyrpOp3qmiwLMrk2k8NMuiRJGi32ePVJBDtRJUnLu9TbAB6+Xcn2VNdF+i6P/DXiSF9cUJKkUWKP\n",
       "1wgp5+1vAi6JICLYq7bsJeVaRmMXyqvfI+4Oql8qNpOuZ5p0SZI0+ky8eqScLty33Hj3+7VF/wx8\n",
       "d+w6W8AXgXnlJsBjVy6+jOpGst8DXghsVH5OvBPe9kSSpGnDU409Ms7Vhv8HOl7I7vPAy8rj/TI7\n",
       "3kxVkiQNiKcaByyCWRHMi2CjDssOKA+Xl78vBDYBtgVOoBrrFcC88vfrpd4BJl2SJM0c9nhNQgRz\n",
       "Ya0xVpsAZLKqfmXuTGIyN6OOYB7VDUwv7FfMkiRp3dnjNSARXA6PGNj+APBABJsA/1bKNgPolnSV\n",
       "Or8x6ZIkaeYx8ZpABFsDi8vsceU04bbAeaXsfqr7blFu+CtJkjQuE6+JHQR8Fdgwk5MAMlmZyTJg\n",
       "WalzC76OkiRpEkwYxhHBK4DPAndlVtfdqsvkvEwik8d7ny1JkjQZDq7vIILTgKOAX1NdR+uBAYck\n",
       "SZJa1K+8pXmF9BkvgjOBw8rsRvZmSZKkXvFUY1Fu7bMjVdL17nIa0aRLkiT1TNfEKyI+FRErI+Lq\n",
       "cZYviYh7IuKKMr2r92H2TwSvL1edfwj4CXB5Ju8bcFiSJGkamsypxk8Dfwd8ZoI6l2bmsgmWD6UI\n",
       "Hgec3Cj++0HEIkmSpr+uPV6Z+Q3gF12qjcSg+Q7+q/w9ApgHzMrkUwOMR5IkTWO9GFyfwL4RcRVw\n",
       "O/DmzLyuB+vtqwjeDGwH7JjJrYOOR5IkTX+9SLwuBxZk5qqIOAQ4B9ilU8WIOLE2uzwzl/dg+1MW\n",
       "wYuBDwOYdEmSpIhYAizp+3Ymcx2viFgInJeZe0yi7s3AXpl5d6N8aK7jVQbTAzwqk/sGGowkSRo6\n",
       "Q3uT7IjYJiKiPN6bKpm7u8vTWlcuF/HnEdxUiuaadEmSpDZ1PdUYEWcCBwBbRcStwAnAXIDMPA04\n",
       "FHhtRKwGVrHm4qNDIYIA9gO+Xiv+ViarBxSSJEmaoab1LYMi2AP4fq1oMbBJJt9sMw5JkjRavGXQ\n",
       "ujm49nj7TP57YJFIkqQZb9r1eEXwFOB/gF8BdwGvAa7JZEW/ty1JkqaHfuUt0yLxKuO4Hhpn8UaZ\n",
       "/G8/titJkqanof1V45AY796Ki026JEnSsBjpMV4RzAYuAp4DfC2TAwcckiRJ0rhG+lRjBBcBBwE/\n",
       "zmSnXq5bkiTNXJ5qbIhgS6qk6/dNuiRJ0igYyR6vMpj+s0Bkcngv1ilJkjTG63itbSlwOLDXoAOR\n",
       "JEmarJE71Vh6u94PvDqTywcdjyRJ0mSN1KnGxvW6Ns7kV+sfmSRJ0tocXF8ZuybX9iZdkiRp1IxE\n",
       "4hXBrhHcAcwDjvOei5IkaRSNxKnGCL4ELMOLpEqSpBbM2Hs1RrARsAo4NJMv9D4ySZKktc3IxCuC\n",
       "zYB7ATLpyw22JUmSmmbc4PoI5lKSLuDxg4xFkiSpF4Yy8Ypga+CuMrtzJrcMMBxJkqSeGNYr168s\n",
       "f1+YyY8GGokkSVKPDF3iFcHN5eGCTG4baDCSJEk9NFSnGstg+oXAQSZdkiRpuhmqxAt4FXBNJhcP\n",
       "OhBJkqReG5pTjeU+jMcArxt0LJIkSf0wTD1epwG7AZcOOhBJkqR+GIrEK4J9gT8Ffi+Tdq7oKkmS\n",
       "1LKBJ14RPA/4JvDVTL486HgkSZL6ZaCJVwSLgAuB92Ry8CBjkSRJ6rdB93i9DPhuJu8dcBySJEl9\n",
       "N7BfNUZwBPB+YMmgYpAkSWpTZLYzlr1+l+8IFgI3AzcAuzmgXpIkDZN63tJLg+rxOga4OZNdB7R9\n",
       "SZKk1nUd4xURn4qIlRFx9QR1To6IGyPiqohYPPH6COCPgN+deriSJEmjazKD6z8N4//iMCKWAjtn\n",
       "5iLgKODU8esyuyzfOpPrphirJEnSSOt6qjEzvxERCyeosgw4vdRdERFbRMQ2mbmyQ90fAk+g+jWj\n",
       "JEnSjNKLy0nsANxam78NmD9O3ScALwe+0IPtSpIkjZReDa5vjvof71eKf5DJ53u0TUmSpJHSi8Tr\n",
       "dmBBbX5+KesgnhjBiWVmeWYu78H2JUmS1ktELKGFa4tO6jpeZYzXeZm5R4dlS4FjM3NpROwDnJSZ\n",
       "+3So15frYUiSJPXawK7jFRFnAgcAW0XErcAJwFyAzDwtMy+IiKURcRPwAHBkr4OUJEmaDgZy5XpJ\n",
       "kqRh1q+8ZdA3yZYkSZoxTLwkSZJaYuIlSZLUEhMvSZKklph4SZIktcTES5IkqSUmXpIkSS0x8ZIk\n",
       "SWqJiZckSVJLTLwkSZJaYuIlSZLUEhMvSZKklph4SZIktcTES5IkqSUmXpIkSS0x8ZIkSWqJiZck\n",
       "SVJLTLwkSZJaYuIlSZLUEhMvSZKklph4SZIktcTES5IkqSUmXpIkSS0x8ZIkSWqJiZckSVJLTLwk\n",
       "SZJaYuIlSZLUEhMvSZKklph4SZIktcTES5IkqSUmXpIkSS3pmnhFxMERcUNE3BgRb+2wfElE3BMR\n",
       "V5TpXf0JVZIkabTNmWhhRMwGTgEOAm4HvhMR52bm9Y2ql2bmsj7FKEmSNC106/HaG7gpM2/JzAeB\n",
       "s4AXdagXPY9MkiRpmumWeO0A3Fqbv62U1SWwb0RcFREXRMRuvQxQkiRpupjwVCNVUtXN5cCCzFwV\n",
       "EYcA5wC7rHdkkiRJ00y3xOt2YEFtfgFVr9fDMvO+2uOvRMTHI2LLzLy7ubKIOLE2uzwzl085YkmS\n",
       "pB6LiCXAkr5vJ3P8Tq2ImAP8ADgQuAP4NnB4fXB9RGwD/CwzMyL2Bj6XmQs7rCsz07FgkiRp6PUr\n",
       "b5mwxyszV0fEscBXgdnAJzPz+og4uiw/DTgUeG1ErAZWAYf1OkhJkqTpYMIer55uyB4vSZI0IvqV\n",
       "t3jlekmSpJaYeEmSJLXExEuSJKklJl6SJEktMfGSJElqiYmXJElSS0y8JEmSWmLiJUmS1BITL0mS\n",
       "pJaYeEmSJLXExEuSJKklJl6SJEktMfGSJElqiYmXJElSS0y8JEmSWmLiJUmS1BITL0mSpJaYeEmS\n",
       "JLXExEuSJKklJl6SJEktMfGSJElqiYmXJElSS0y8JEmSWmLiJUmS1BITL0mSpJaYeEmSJLXExEuS\n",
       "JKklJl6SJEktMfGSJElqiYmXJElSS0y8JEmSWmLiJUmS1JKuiVdEHBwRN0TEjRHx1nHqnFyWXxUR\n",
       "i3sfpiRJ0uibMPGKiNnAKcDBwG7A4RGxa6POUmDnzFwEHAWc2qdYNSARsWTQMWjd2X6jzfYbXbad\n",
       "OunW47U3cFNm3pKZDwJnAS9q1FkGnA6QmSuALSJim55HqkFaMugAtF6WDDoArZclgw5A62zJoAPQ\n",
       "8OmWeO0A3Fqbv62Udaszf/1DkyRJml66JV45yfXEOj5PkiRpxpjTZfntwILa/AKqHq2J6swvZY8Q\n",
       "ESZkIyoiThh0DFp3tt9os/1Gl22npm6J13eBRRGxELgDeAVweKPOucCxwFkRsQ/wy8xc2VxRZjZ7\n",
       "xSRJkmaUCROvzFwdEccCXwVmA5/MzOsj4uiy/LTMvCAilkbETcADwJF9j1qSJGkERaZn/yRJktrQ\n",
       "9yvXT+YCrGpXRCyIiEsi4tqIuCYi3lDKt4yIiyLihxFxYURsUXvO20sb3hARz6+V7xURV5dlfzuI\n",
       "/ZmpImJ2RFwREeeVedtvRETEFhFxdkRcHxHXRcQzbL/RUNri2vK6/0tEbGDbDa+I+FRErIyIq2tl\n",
       "PWuv0v7/Wsq/FRGP6xpUZvZtojo9eROwEJgLXAns2s9tOk2qXbYFnloebwr8ANgV+Gvg+FL+VuBD\n",
       "5fFupe3mlra8iTW9pd8G9i6PLwAOHvT+zZQJ+HPgs8C5Zd72G5GJ6tqHf1IezwE2t/2Gfyqv/4+B\n",
       "Dcr8vwJ/ZNsN7wTsDywGrq6V9ay9gGOAj5fHrwDO6hZTv3u8JnMBVrUsM+/MzCvL4/uB66mux/bw\n",
       "xXDL3xeXxy8CzszMBzPzFqqD8RkRsR2wWWZ+u9T7TO056qOImA8sBf6JNZdzsf1GQERsDuyfmZ+C\n",
       "aixtZt62YCkCAAACjklEQVSD7TcK7gUeBDaOiDnAxlQ/PLPthlRmfgP4RaO4l+1VX9cXgAO7xdTv\n",
       "xGsyF2DVAJVfrC4GVgDb5JpfpK4Exu5AsD1rX0ZkrB2b5bdj+7blY8BbgIdqZbbfaHg88POI+HRE\n",
       "XB4R/xgRm2D7Db3MvBv4KPBTqoTrl5l5EbbdqOllez2c52TmauCeiNhyoo33O/Fy5P4Qi4hNqTL0\n",
       "N2bmffVlWfWb2n5DKCJ+F/hZZl7BIy9eDNh+Q24OsCfV6Yk9qX4N/rZ6BdtvOEXETsCbqE5DbQ9s\n",
       "GhFH1OvYdqNlEO3V78RrMhdg1QBExFyqpOuMzDynFK+MiG3L8u2An5XyThfJva2Uz2+Ud7x4rnpq\n",
       "X2BZRNwMnAk8NyLOwPYbFbcBt2Xmd8r82VSJ2J2239B7GvCfmXlX6d34IvBMbLtR04v3yttqz9mx\n",
       "rGsOsHnpGR1XvxOvhy/AGhHzqAaendvnbaqLiAjgk8B1mXlSbdG5VANFKX/PqZUfFhHzIuLxwCLg\n",
       "25l5J3Bv+UVWAK+sPUd9kpnvyMwFmfl44DDga5n5Smy/kVBe91sjYpdSdBBwLXAett+wuwHYJyI2\n",
       "Kq/5QcB12HajphfvlV/qsK5DgYu7br2FXxQcQvWruZuAt7f5awancdtkP6qxQVcCV5TpYGBL4D+A\n",
       "HwIXAlvUnvOO0oY3AC+ole8FXF2WnTzofZtpE3AAa37VaPuNyAQ8BfgOcBVVr8nmtt9oTMDxVIny\n",
       "1VSDqufadsM7UZ0VuAP4DdVYrCN72V7ABsDngBuBbwELu8XkBVQlSZJa0vcLqEqSJKli4iVJktQS\n",
       "Ey9JkqSWmHhJkiS1xMRLkiSpJSZekiRJLTHxkiRJaomJlyRJUkv+D4f3mJsv9VoLAAAAAElFTkSu\n",
       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae55d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHONJREFUeJzt3XuUXWWZ5/HvkwsIAgkIRiCB0AIC3gARooJGAYVoxx6b\n",
       "1eKMzqjdo2PLeBtHbZq1xGX36hnn5tC2NqtbbdQRRHAQES+oBGTUoJCES8IlAkpAwv0SLprIM388\n",
       "O3AsKlVFUuetOpXvZ62zcs7e+5zzVm0uv7zvs58dmYkkSZL6b9pED0CSJGlrYfCSJElqxOAlSZLU\n",
       "iMFLkiSpEYOXJElSIwYvSZKkRkYMXhHxjIhYGhHLI2JlRPzdJo47LSJujIgVEXFIf4YqSZI02GaM\n",
       "tDMzH4uIV2fmIxExA7gsIo7MzMs2HhMRi4B9M3O/iDgC+BywoL/DliRJGjyjLjVm5iPd022A6cC9\n",
       "Qw5ZDJzRHbsUmB0Rc8ZzkJIkSVPBqMErIqZFxHJgLXBxZq4ccsiewK09r9cAc8dviJIkSVPDWGa8\n",
       "Hs/Mg6kw9cqIWDjMYTH0beMwNkmSpCllxBqvXpn5QER8GzgMWNKz6zZgXs/rud22PxARhjFJkjQw\n",
       "MnPoxNIWGzF4RcSuwIbMvD8itgOOBT4x5LDzgZOAsyJiAXB/Zq4d7vP68QOo/yLi1Mw8daLHoc3j\n",
       "+Rtsnr/B5bkbbP2aMBptxmt34IyImEYtS345M38YEe8GyMzTM/PCiFgUEauBh4F39GOgkiRJg260\n",
       "dhJXA4cOs/30Ia9PGudxSZIkTTl2rtdYLJnoAWiLLJnoAWiLLJnoAWizLZnoAWjyicw2Ne8RkdZ4\n",
       "SZKkQdCv3OKMlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE4CVJktSIwUuSJKkR\n",
       "g5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYv\n",
       "SZKkRgxekiRJjRi8JEmSGjF4SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIk\n",
       "SY0YvCRJkhoxeEmSJDVi8JIkSWpkxOAVEfMi4uKIuDYiromI9w1zzMKIeCAilnWPU/o3XEmSpME1\n",
       "Y5T964EPZubyiNgBuCIiLsrMVUOOuyQzF/dniJIkSVPDiDNemXlHZi7vnq8DVgF7DHNo9GFskiRJ\n",
       "U8qYa7wiYj5wCLB0yK4EXh4RKyLiwog4aPyGJ0mSNHWMttQIQLfMeA7w/m7mq9eVwLzMfCQijgfO\n",
       "A/Yf32FKkiQNvlGDV0TMBM4FvpKZ5w3dn5kP9Tz/TkR8NiJ2ycx7h/msU3teLsnMJZs1akmSpHEU\n",
       "EQuBhX3/nswcaRABnAHck5kf3MQxc4A7MzMj4nDg7MycP8xxmZnWgkmSpEmvX7lltBmvVwBvBa6K\n",
       "iGXdtpOBvQAy83TgBOA9EbEBeAQ4cbwHKUmSNBWMOOM1rl/kjJckSRoQ/cotdq6XJElqxOAlSZLU\n",
       "iMFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmSGjF4SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGD\n",
       "lyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE4CVJktSIwUuSJKkRg5ckSVIjBi9J\n",
       "kqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKkRgxekiRJ\n",
       "jRi8JEmSGhkxeEXEvIi4OCKujYhrIuJ9mzjutIi4MSJWRMQh/RmqJEnSYJsxyv71wAczc3lE7ABc\n",
       "EREXZeaqjQdExCJg38zcLyKOAD4HLOjfkCVJkgbTiDNemXlHZi7vnq8DVgF7DDlsMXBGd8xSYHZE\n",
       "zOnDWCVJkgbamGu8ImI+cAiwdMiuPYFbe16vAeZu6cAkSZKmmjEFr26Z8Rzg/d3M11MOGfI6t3Rg\n",
       "kiRJU81oNV5ExEzgXOArmXneMIfcBszreT232zbcZ53a83JJZi4Z80glSZL6JCIWAgv7/j2Zm56c\n",
       "ioig6rfuycwPbuKYRcBJmbkoIhYAn87MpxTXR0Rm5tCZMUmSpEmnX7lltOB1JHApcBVPLh+eDOwF\n",
       "kJmnd8d9BjgOeBh4R2ZeOcxnGbwkSdJAmJDgNa5fZPCSJEkDol+5xc71kiRJjRi8JEmSGjF4SZIk\n",
       "NWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE\n",
       "4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAlSZLUyIyJ\n",
       "HoAkSdJEiGAe8FbgceDHwAPAAcCGfn2nwUuSJE1ZEfwR8OfAM4C7gH8GjgA+DewLPAjsNORtv+/X\n",
       "eFxqlCRJTUXwjO7P7SOYHsGs7vX+EcyJePr5JILZEewdwbYR7BrB6yO4BPglNYt1CLCYCl+nA7cC\n",
       "B2cyK5PIJIBp3fO+TUw54yVJkvouggOANwF/270euv8+akJoYwg7A3gZ8F+B3wIvAM4DZndv+T4w\n",
       "E3gV8H7g9cN87a3A+zM5red7ngGsz3zqrFYmubk/31hFZt+/o74oIjMzRj9SkiQNkggCeC2wM7Ab\n",
       "cA+wHjgVuBbYATgeuAr4CfAx4GSqrupnwHbAAuACKkydAjwH+FNgSbfvPuC5w3z9SuD87rjLqCXF\n",
       "x4HHMnl083+m/uQWg5ckSfoDEewFrAOmA3tmsjyCXagANB04GLieCkfHUrNQRwJrqJB1DbA/VSt1\n",
       "NfB/gW9kcucWjms6sE0mj0bwXGCnTJZtyWdu+rv6k1tcapQkaSsWwR7AK4ETqav6HgLeO+SYjW4H\n",
       "9gCuAF7SbbsG+B7wukwe6edYu+XBR7vnv+znd/WLwUuSpM0UwXZU/RHwB/VBLwauHq6OqIWujunN\n",
       "1NV7/wjckMlj3ZLgXGpJ8LXAUVTB+UPAT6klwqCC2IHAxcCvqdmrbTK5IoJpmTzeFcBni7qoqcSl\n",
       "RkmSRhDBzsDHqQLuZVT90EpgPhVcNmUdcC4Vcr4N/ALYE7gkkwe7z32MCmx/RBWVXwU8ArwCWJrJ\n",
       "+iFjCeA/UHVRu3ebf0fVVS2mlv52poLfvcAuQ8b0MPDMIduOzuRHo/watjrWeEmStnoRRO8MSwR7\n",
       "Ap+hwstnqWLt/0a1Dvgd8CxqGey7wIpM7h3yebOA11DLZaupZbTfUAXepwOHAc/vDj+ZukruTcC2\n",
       "3bb3UQHnSKqeaadu25uoAPT6bjy9bgNWAceM4Ue+hwpn21Dhaqj/B7y02/9d4AfdcQGcvHHGLYLD\n",
       "gXcCfw/cDUzP5PYxfP9Wy+AlSZrSItgR+BC1zLUPFaY+RgWoP6MKuBcBlwL3U/VIbwNupoLMop6P\n",
       "e293/MHUTNDGoPQ4Y+th+dvuPacA3wCuG48lte5nPIu64u+vqeadv6PCUAKvA/YCvtqN/eFuHM+i\n",
       "guHhVBuFtUMCaLjkN74mLHhFxBeoxH5nZr5wmP0LgW8CN3Wbzs3MvxnmOIOXJE1hXc3PR4AfUbMw\n",
       "/54KDL8CzqCW2nak2gq8Cvg8FY5eDSyklsCuoWZxrgD2ptoJHECFrE8AN1JX0R1EtRb420w+333/\n",
       "zsDsTG7exPiOppb6LqOW9g4F1mTy1e7WMQdToWYxNWN0TiaPj8svRwNnIoPXUdQ69ZdGCF4fyszF\n",
       "o3yOwUuSBlwEO1HLaI9RNUafoIqvtwV25cnmlvd1j2XU8ts8KkBd3217afeex6hQtoJaIvvi0Jkc\n",
       "aNPYUuo1Ye0kMvPHETF/lMMMVJI0SUQwg5o9ehG1FHcPddPfG4CvjuVKuwjmA58E/pi62u1uaplr\n",
       "XnfIzd32D1OBayW1bHbxeIYkA5emmvFoJ5HAyyNiBVUw+OHMXDkOnytJU1rXpHJXKsRsoP4SO2No\n",
       "AfgYPmd7qkXAbtQVb8cCc6g6qHXUFXX7UHVS/xDBZVRh99eoZbf5wBuoGwZfQRWTz6Y6jM/sPiOp\n",
       "IvGbGOdwJW1NxiN4XQnMy8xHIuJ46j5K+w93YESc2vNySWYuGYfvl6RJr2tSeSDVMuA51LLbf9zE\n",
       "sadQV8St5slAtTcVoL5D9Vz6J2o26oHuM6Fmpe6naqsuHDqz1S3bvYZqVbA71XLgAGom7CLgEur/\n",
       "CzcAH8/k1i3/yaXB0JVOLez794zlqsZuqfFbw9V4DXPszcBLMnPIJbvWeEkaHBFst/E+bxFsS91L\n",
       "7mBq5uej3evLqSvetqHC1FzgL6h7xq2l+jHNoQLS87qPvpaaRbqUunLtUipYTQfuoIrJX9p93vO7\n",
       "45NaxnseT7YgWELdPHh76qq4bzsLJY2fSXvLoIiYQ13xmBFxOBXmntY0uSRNBt2S3ceAdwFzIvgV\n",
       "FXrm9xy2Gvg5NTv0cip4PUq1H3iAalg5n5qFOhRYSrU2+OkIt1O5o+f52d1jpHHaOkAaUKMGr4g4\n",
       "k7rsd9eIuJXq3jsTIDNPB04A3hMRG6i/3Z3Yv+FK2ppFsB9VB7U91eF7BnBQJsu7/bsA0zK5u3u9\n",
       "A7WcdhhVv3Q/FaQOAn7Y7TsGuIUKSTtTS26nUGUUz6ZqV39JBavHJ0PgmQxjkLR5bKAqaVLp6pA2\n",
       "Xj23AxV4PkwFo5FcSgWpaVSvqPXUXxJvodoa/ISaefo29ZfE7amgdSVVYH458GAm94zrDyRpINm5\n",
       "XtKUE8HuwGnUjNRXqMaVe1M1Uz8Bjqbql/4R+O/wxC1OdqJqoIIKVSdQV+H9C3AXsICapboL+K0z\n",
       "RJKeLoOXpOa6YLSAujvFLKpI/FBqVuly4ALqKqD9qEaYh1KNMG+iissfpu5995dU9/Ltqdmm9wHL\n",
       "qWL0r3ef9Xyqm/g3gDPtGC5pIhm8JDXRLfUtpNoVPHfI7uuoGqlvUt3L96dmlS6hCsrXU40776Zm\n",
       "pQ7ree+5VM3UddQVgRcA12+sz5KkycTgJakvNl4hF8FB1BV9J1BX6X0S+By1nPcc4O5M1vW8bwaQ\n",
       "Y+mCLkmDxuAlaYtE8ALgS9SS4XXAomEOO5NqZXC+S32StmYGL0lPS8/Vga+gmnoeCHyA6nq+jqq/\n",
       "eibVlmFb4KZMHpqY0UrS5DJpG6hKaq8LVbtSS4DPoG4Rs1f3+sXdYWupf8cvAT4ILM9kbfvRSpI2\n",
       "csZLmkARbANsk8m67rY0u1FNPh/u6q5mUK0VHqUC1nuBVwPHU7VX91C3ktmRWkb8IVUQf1X359m9\n",
       "dVmSpLFxqVEacF2IeibVDHQx1T1946zzvdStZnpdR93AGOp+fbtRQesCYA3wGeuwJKk/XGqUJpFu\n",
       "qW/apq7o625VsyfwLOAI4HHg3VSdFcBfA9+iaq3mUMuGK6g2DLsAL6I6tl9PzWy9hloqvKpPP5Ik\n",
       "qQFnvKROBM8G3gLcCZxHBZ+N/4LMB15L3e/vQOD1Q95+BdUE9FnAIVRD0ew+60HgGuCL1FLgY85U\n",
       "SdLk5lKjNI66Zb8/pTqnv5Dqmn7YCG95lCpSfyawFPgpdW/AF1D1VAup29vcSM1e/c9M7u3T8CVJ\n",
       "fWbwksZBBG8DTqVujvwbagbrPCpUfT2TuyKYBryOqrHanipuX5XJYxMyaElScwYvaRO6jutQASmo\n",
       "ZcGjqcL0HagaK4DbqBmrS4EPZHJz25FKkgaFwUtbrQhm8eSNmaHuD3hT9+fbu30bXUV1Zj8fuJgq\n",
       "at8X+D7VjmFlJg83GbgkaWB5VaOmrG5p771Ue4XHqXqrfYDfUQ1Bp1NX/+1GzVbdT7VjuJwqWD+O\n",
       "uo9gm79FSJK0mZzxUlMRzKRaIzwOHAvMA07sdn+KClu3APdRVwM+DCz1KkBJUksuNWog9dwv8M3U\n",
       "kuDzqUA1E/gVcA7wnUxumLBBSpI0hMFLA6ELWscCjwFHAv8K2Bv4OrVM+PNMbpq4EUqSNDqDlyal\n",
       "7l6DOwJ/TC0Zvq7b9WvgF8BXgAsyWT8xI5Qk6emzuF7NdbNXM4ANVGH7gcCfUN3YNwAvpjq9T6N6\n",
       "Xn0O+LfAfQYtSZKeyuCljQFrL6rP1e5U76u/6B47AeuB3wM3UPcQPAPYjmpAuht1lWF6VaEkSSMz\n",
       "eG2lIphLzV4dDPx5t/m31OzVTOoGzscBV1I3bb4rkw0TMFRJkqYMa7ymmG72ahuqwP3vqD5Ys6kr\n",
       "CW8C7gBeRnVw/y6wAlgJnAvMyuTeCKZn8vsJGL4kSZOCxfUaVgR7UkuCv6c6sx9LtW+4GfhPVIH7\n",
       "jlQT0t2BZ1M3cr46k0cmYsySJE12Bi8RwbZU49EDqasI/033/AZgCVVrdRfwxUzumaBhSpI08Axe\n",
       "W4FumfANwM7AnwGvBx6lbpdzFzxxM+i1wAVUr6x/yGRV+9FKkjR1GbwGTHf/waSuFnwhVbT+C+Be\n",
       "YI9u2/OAbak6rG2ohqO7Ab8EPgtcA9wOHEa1bjgbWO3tcyRJ6i+D1wTpGoRu6A07EU9cDXoQ8E7g\n",
       "WcDdwHzqSsFe66gZqhnUTNZOVB+sK6glwulU+4Y1wNXAOQYrSZImlsGrge4Gzu8CjgaeS/WsAniA\n",
       "moVaB+xPzVAB3APcSnVnn0b1wbqdqrW6BZgF3NbbhiGCmTYXlSRpcjN4bdF3M43qRfVs4AXUzNSL\n",
       "qKv95lDB6ijgEWAZ8A1qme8OKkjNAvahWjDMAH5ANQw1QEmSNAVNWPCKiC9QRd53ZuYLN3HMacDx\n",
       "VHB5e2YuG+aYJsGrWwY8CngF8GEqND3Q/bmW6ll1LVWsfg3VYmE6cBnVQHSlHdglSdq6TeS9Gr8I\n",
       "/D3wpeF2RsQiYN/M3C8ijqDu17dg/IY4su5KwIVU/6pnUy0W1gIXUfVXS4DtqSU/A5UkSZowowav\n",
       "zPxxRMwf4ZDF1L37yMylETE7IuZk5tqxDqIrYM9M1kewK7A3tQS4O3Uz5gOoGqp13b7fUPcK3Bc4\n",
       "lJpp+ybwK+D5mdw05CvuHetYJEmS+mU87tW4J1VgvtEaYC416zSsCPalWie8BXgl1XE9u9krqKB0\n",
       "MxWuVlN1VwdQVwU+ShWv30+FrU8CK7yPoCRJmuzG6ybZQ9dAh13Si+BTwDFUb6tfA/8CvJ1qr7Az\n",
       "tUR5USa/HadxSZIkTRrjEbxuA+b1vJ7bbRvGv34F3LIKLr8Afv+jzFzSs/Nuqhu7JElSUxGxkKoZ\n",
       "7+/3jKWdRFfj9a3hrmrsiutPysxFEbEA+HRmPqW4fhD6eEmSJMEEXtUYEWcCrwJ2jYhbgY8DMwEy\n",
       "8/TMvDAiFkXEauBh4B3jPUhJkqSpYKtooCpJkvR09Cu3TBvvD5QkSdLwDF6SJEmNGLwkSZIaMXhJ\n",
       "kiQ1YvCSJElqxOAlSZLUiMFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmSGjF4SZIkNWLwkiRJ\n",
       "asTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE4CVJktSI\n",
       "wUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAlSZLUiMFLkiSpkVGD\n",
       "V0QcFxHXRcSNEfHRYfYvjIgHImJZ9zilP0OVJEkabDNG2hkR04HPAMcAtwE/j4jzM3PVkEMvyczF\n",
       "fRqjJEnSlDDajNfhwOrMvCUz1wNnAW8c5rgY95FJkiRNMaMFrz2BW3ter+m29Urg5RGxIiIujIiD\n",
       "xnOAkiRJU8WIS41UqBrNlcC8zHwkIo4HzgP23+KRSZIkTTGjBa/bgHk9r+dRs15PyMyHep5/JyI+\n",
       "GxG7ZOa9Qz8sIk7tebkkM5c87RFLkiSNs4hYCCzs+/dkbnpSKyJmANcDRwO3A5cDb+ktro+IOcCd\n",
       "mZkRcThwdmbOH+azMjOtBZMkSZNev3LLiDNembkhIk4CvgdMBz6fmasi4t3d/tOBE4D3RMQG4BHg\n",
       "xPEepCRJ0lQw4ozXuH6RM16SJGlA9Cu32LlekiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmSGjF4\n",
       "SZIkNWLwkiRJasTgJUmS1IjBS5IkqRGDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIk\n",
       "SWrE4CVJktSIwUuSJKkRg5ckSVIjBi9JkqRGDF6SJEmNGLwkSZIaMXhJkiQ1YvCSJElqxOAlSZLU\n",
       "iMFLkiSpEYOXJElSIwYvSZKkRgxekiRJjRi8JEmSGjF4SZIkNWLwkiRJasTgJUmS1MiowSsijouI\n",
       "6yLixoj46CaOOa3bvyIiDhn/YUqSJA2+EYNXREwHPgMcBxwEvCUiDhxyzCJg38zcD3gX8Lk+jVUT\n",
       "JCIWTvQYtPk8f4PN8ze4PHcazmgzXocDqzPzlsxcD5wFvHHIMYuBMwAycykwOyLmjPtINZEWTvQA\n",
       "tEUWTvQAtEUWTvQAtNkWTvQANPmMFrz2BG7teb2m2zbaMXO3fGiSJElTy2jBK8f4ObGZ75MkSdpq\n",
       "zBhl/23AvJ7X86gZrZGOmdtte4qIMJANqIj4+ESPQZvP8zfYPH+Dy3OnoUYLXr8A9ouI+cDtwJuB\n",
       "tww55nzgJOCsiFgA3J+Za4d+UGYOnRWTJEnaqowYvDJzQ0ScBHwPmA58PjNXRcS7u/2nZ+aFEbEo\n",
       "IlYDDwPv6PuoJUmSBlBkuvonSZLUQt8714+lAavaioh5EXFxRFwbEddExPu67btExEURcUNEfD8i\n",
       "Zve856+6c3hdRLy2Z/tLIuLqbt//noifZ2sVEdMjYllEfKt77fkbEBExOyLOiYhVEbEyIo7w/A2G\n",
       "7lxc2/3evxoR23ruJq+I+EJErI2Iq3u2jdv56s7/17rtP4uIvUcdVGb27UEtT64G5gMzgeXAgf38\n",
       "Th9jOi/PAQ7unu8AXA8cCHwK+Ei3/aPAf+meH9Sdu5nduVzNk7OllwOHd88vBI6b6J9va3kAHwL+\n",
       "D3B+99rzNyAPqvfhO7vnM4BZnr/J/+h+/zcB23avvwb8O8/d5H0ARwGHAFf3bBu38wX8JfDZ7vmb\n",
       "gbNGG1O/Z7zG0oBVjWXmHZm5vHu+DlhF9WN7ohlu9+efdM/fCJyZmesz8xbqH8YjImJ3YMfMvLw7\n",
       "7ks971EfRcRcYBHwzzzZzsXzNwAiYhZwVGZ+AaqWNjMfwPM3CB4E1gPbR8QMYHvqwjPP3SSVmT8G\n",
       "7huyeTzPV+9nnQscPdqY+h28xtKAVROou2L1EGApMCefvCJ1LbDxDgR78IdtRDaex6Hbb8Pz28r/\n",
       "Av4z8HjPNs/fYNgHuCsivhgRV0bEP0XEM/H8TXqZeS/wP4BfU4Hr/sy8CM/doBnP8/VEzsnMDcAD\n",
       "EbHLSF/e7+Bl5f4kFhE7UAn9/Zn5UO++rHlTz98kFBFvAO7MzGU8tXkx4Pmb5GYAh1LLE4dSV4N/\n",
       "rPcAz9/kFBHPBT5ALUPtAewQEW/tPcZzN1gm4nz1O3iNpQGrJkBEzKRC15cz87xu89qIeE63f3fg\n",
       "zm77cE1y13Tb5w7ZPmzzXI2rlwOLI+Jm4EzgNRHxZTx/g2INsCYzf969PocKYnd4/ia9w4CfZOY9\n",
       "3ezGN4CX4bkbNOPx38o1Pe/Zq/usGcCsbmZ0k/odvJ5owBoR21CFZ+f3+Ts1iogI4PPAysz8dM+u\n",
       "86lCUbo/z+vZfmJEbBMR+wD7AZdn5h3Ag90VWQG8rec96pPMPDkz52XmPsCJwI8y8214/gZC93u/\n",
       "NSL27zYdA1wLfAvP32R3HbAgIrbrfufHACvx3A2a8fhv5TeH+awTgB+O+u0Nrig4nrpqbjXwVy2v\n",
       "ZvCxyXNyJFUbtBxY1j2OA3YBfgDcAHwfmN3znpO7c3gd8Lqe7S8Bru72nTbRP9vW9gBexZNXNXr+\n",
       "BuQBvBj4ObCCmjWZ5fkbjAfwESooX00VVc/03E3eB7UqcDvwO6oW6x3jeb6AbYGzgRuBnwHzRxuT\n",
       "DVQlSZIa6XsDVUmSJBWDlyRJUiMGL0mSpEYMXpIkSY0YvCRJkhoxeEmSJDVi8JIkSWrE4CVJktTI\n",
       "/wceyIe3JyW1gQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aec99d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# choose the paramator of Brownian\n",
    "# Brownian paramator (p) = 0.5\n",
    "\n",
    "import pylab\n",
    "from random import normalvariate as norm\n",
    "from random import seed\n",
    "from math import sqrt\n",
    "\n",
    "x = np.arange(0,time, 1)\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "time = 10000\n",
    "average_num = 100\n",
    "p = 0.5\n",
    "\n",
    "for num, j in enumerate(steps):\n",
    "    step = j\n",
    "    y_all = [] \n",
    "    for l in range(average_num):\n",
    "        y_num = [0] * (time)\n",
    "        value = 1\n",
    "        y_num[0] = value\n",
    "        for i in range(time - 1):\n",
    "            update_value = value + step * (2 - value) * value + p * sqrt(step) * value * norm(0, 1)\n",
    "            y_num[i + 1] = update_value\n",
    "            value = update_value\n",
    "        y_all.append(y_num)\n",
    "    y = np.array(y_all)\n",
    "    np.reshape(y, (average_num, time))\n",
    "    y_ave = [np.average(y[:, k]) for k in range(time) ]\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_ave)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAlQAAAEUCAYAAADtKKjYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAF/tJREFUeJzt3XuUJnV95/H3BxjwlkiQLCIMjiuXI/ESFhcIl9gYjTC7\n",
       "op5lQbKeKLsaw4bgkt0cXeMGcs4mRrMaFomKCAFDoiIoEjN4gTBeTgIY7pcRIStHQB2CXAIMEQa/\n",
       "+0fVME1Pdz/dU91dz/P0+3VOnX6qnt/z1LdPner5zK9+9atUFZIkSdp62/RdgCRJ0qgzUEmSJHVk\n",
       "oJIkSerIQCVJktSRgUqSJKkjA5UkSVJHswaqJM9IclWS65PcmuT9M7Q7PcntSW5Ist/ilCpJkjSc\n",
       "tpvtzar6lySHV9WGJNsB30pyaFV9a1ObJKuBPatqryQHAh8DDlrcsiVJkobHwEt+VbWhfbk9sC1w\n",
       "/5QmRwHntW2vAnZMsstCFilJkjTMBgaqJNskuR5YD1xRVbdOabIbcNek9buB3ReuREmSpOE2lx6q\n",
       "n1bVL9KEpF9OMjFNs0z92ALUJkmSNBJmHUM1WVU9lORvgFcCaye9dQ+wctL67u22p0liyJIkSSOj\n",
       "qqZ2GM1o1kCVZGdgY1U9mOSZwGuBP5jS7BLgROAzSQ4CHqyq9V0L0/BIcmpVndp3Hdo6Hr/R5vEb\n",
       "XR670TbfjqBBPVS7Aucl2Ybm8uBfVNXlSd4JUFVnVtWaJKuT3AE8Chy/NYVLkiSNqkHTJtwE/Jtp\n",
       "tp85Zf3EBa5LkiRpZDhTuuZibd8FqJO1fRegTtb2XYC22tq+C9DSSdXSjBVPUo6hkiRJo2C+ucUe\n",
       "KkmSpI4MVJIkSR0ZqCRJkjoyUEmSJHVkoJIkSerIQCVJktSRgUqSJKkjA5UkSVJHBipJkqSODFSS\n",
       "JEkdGagkSZI6MlBJkiR1ZKCSJEnqyEAlSZLUkYFKkiSpIwOVJElSRwYqSZKkjgxUkiRJHRmoJEmS\n",
       "OjJQSZIkdWSgkiRJ6shAJUmS1JGBSpIkqSMDlSRJUkcGKkmSpI4MVJIkSR0ZqCRJkjoyUEmSJHVk\n",
       "oJIkSerIQCVJktTRrIEqycokVyS5JcnNSU6aps1EkoeSXNcu71u8ciVJkobPdgPefwI4uaquT/Ic\n",
       "4JokX6uqdVPafb2qjlqcEiVJkobbrD1UVfWjqrq+ff0IsA54wTRNswi1SZIkjYQ5j6FKsgrYD7hq\n",
       "ylsFHJzkhiRrkuy7cOVJkiQNv0GX/ABoL/ddCLyr7ama7FpgZVVtSHIkcDGw98KWKUmSNLwGBqok\n",
       "K4CLgPOr6uKp71fVw5NeX5rko0l2qqr7p/muUyetrq2qtVtVtSRJ0gJKMgFMbPXnq2q2Lw9wHvDj\n",
       "qjp5hja7APdWVSU5ALigqlZN066qyrFWkiRp6M03twzqoToEeAtwY5Lr2m3vBfYAqKozgaOBE5Js\n",
       "BDYAb5531ZIkSSNs1h6qBd2RPVSSJGlEzDe3OFO6JElSRwYqSZKkjgxUkiRJHRmoJEmSOjJQSZIk\n",
       "dWSgkiRJ6shAJUmS1JGBSpIkqSMDlSRJUkcGKkmSpI4MVJIkSR0ZqCRJkjoyUEmSJHVkoJIkSerI\n",
       "QCVJktSRgUqSJKkjA5UkSVJHBipJkqSODFSSJEkdGagkSZI6MlBJkiR1ZKCSJEnqyEAlSZLUkYFK\n",
       "kiSpIwOVJElSRwYqSZKkjgxUkiRJHRmoJEmSOjJQSZIkdWSgkiRJ6shAJUmS1NGsgSrJyiRXJLkl\n",
       "yc1JTpqh3elJbk9yQ5L9FqdUSZKk4bTdgPefAE6uquuTPAe4JsnXqmrdpgZJVgN7VtVeSQ4EPgYc\n",
       "tHglS5IkDZdZe6iq6kdVdX37+hFgHfCCKc2OAs5r21wF7Jhkl0WoVZIkaSjNeQxVklXAfsBVU97a\n",
       "Dbhr0vrdwO5dC5MkSRoVcwpU7eW+C4F3tT1VWzSZsl5dC5MkSRoVg8ZQkWQFcBFwflVdPE2Te4CV\n",
       "k9Z3b7dN912nTlpdW1Vr51ypJEnSIkkyAUxs9eerZu5MShKa8VE/rqqTZ2izGjixqlYnOQg4raq2\n",
       "GJSepKpqak+WJEnS0JlvbhkUqA4FvgHcyObLeO8F9gCoqjPbdmcARwCPAsdX1bVdC5MkSerLggaq\n",
       "hWSgkiRJo2K+ucWZ0iVJkjoyUEmSJHVkoJIkSerIQCVJktSRgUqSJKkjA5UkSVJHBipJkqSODFSS\n",
       "JEkdGagkSZI6MlBJkiR1ZKCSJEnqyEAlSZLUkYFKkiSpIwOVJElSRwYqSZKkjgxUkiRJHRmoJEmS\n",
       "OjJQSZIkdWSgkiRJ6shAJUmS1JGBSpIkqSMDlSRJUkcGKkmSpI4MVJIkSR0ZqCRJkjoyUEmSJHVk\n",
       "oJIkSerIQCVJktSRgUqSJKkjA5UkSVJHBipJkqSODFSSJEkdDQxUSc5Jsj7JTTO8P5HkoSTXtcv7\n",
       "Fr5MSZKk4bXdHNr8OfAR4FOztPl6VR21MCVJkiSNloE9VFX1TeCBAc2yMOVIkiSNnoUYQ1XAwUlu\n",
       "SLImyb4L8J2SJEkjYy6X/Aa5FlhZVRuSHAlcDOw9XcMkp05aXVtVaxdg/5IkSZ0kmQAmtvrzVTWX\n",
       "nawC/rqqXjaHtt8D9q+q+6dsr6ry0qAkSRp6880tnS/5JdklSdrXB9CEtPsHfEySJGlsDLzkl+TT\n",
       "wKuAnZPcBZwCrACoqjOBo4ETkmwENgBvXrxyJUmShs+cLvktyI685CdJkkbEkl/ykyRJWu4MVJIk\n",
       "SR0ZqCRJkjoyUEmSJHVkoJIkSerIQCVJktSRgUqSJKkjA5UkSVJHBipJkqSODFSSJEkdGagkSZI6\n",
       "MlBJkiR1ZKCSJEnqaLu+C9DWSdiG5vitaH9uBzxcxeO9FiZJ0jJkoFpkCSuAPYGXtssvAM9lcwja\n",
       "tKwYsD51G8ATwMZJy5MJHwf+rIr1S/DrSZIkDFQLpu0xeiGbg9OmZW/gbuDmdrkQuJ8mAE0NRHNe\n",
       "r+Kn09SwN3AysC7h88CfVnHL4vzGkiRpk1TV0uwoqarKkuxsESUE2JXNvU2bgtO+wINsDk6blnVV\n",
       "bFjiGncGTgD+K3A98CHg8iqW5mBLkjTi5ptbDFSzSNiJLXucXgo8CdzE04PTrVU82FOp00p4BvBr\n",
       "wO/Q1Pxh4NOOs5IkaXYGqo4Sfhb4LZoenh3Zssfp5iru7a/C+Wt71V5HE6x+ATgDOLOK+3stTJKk\n",
       "IWWg2koJPwecBJwIfBX4AHDTuF0mS3g5TbA6Cvgr4LQq7ui3KkmShst8c8uyn4cqYeeEPwTuoBlU\n",
       "fnAV/6mKG8ctTAG0v9fbaC5dPgT8fcLnEw5te7IkSdI8LdtAlfD8hD8BbgOeB+xfxX+u4vaeS1sS\n",
       "Vfygit8DVgGXA+cCVyYck3j3pyRJ87HsAlXC7gmnA7cCOwCvqOI3q7iz38r6UcWjVfwZsA/wx8Bv\n",
       "A3cknJzwM/1WJ0nSaFg2gSphVTvp5Y3A48C+VZxUxd09lzYUqniyii9UcRhwDHAQcGfCnySs7Lk8\n",
       "SZKG2tgHqoQ9E84BrqGZUHOfKv5HFT/qubShVcXVVRwL7A9sC9yQcEXCbyb8q57LkyRp6IztXX4J\n",
       "LwF+j2a6gDOA06t4YKn2P07a+ayOoOm5Wg18G7gA+EIV9/VZmyRJi2HZT5uQ8ArgfcAvA6fRPNfu\n",
       "nxd7v8tFwrOAI4FjacLq37M5XBlYJUljYdkGqoRXAv8L+Lc0j1r5eBWPLtb+BAnPBv49Tc/Va4Bv\n",
       "AZ8FvljFQ33WJklSF8suUCUcTBOkXgp8EPhkFY8t9H40u/aOwNfThKvDgbU0PVeXVPFwj6VJkjRv\n",
       "Yx+oErYHDqEZy3Mk8Gya2/3PreInXb9f3SU8l2Ym9mOBw2jmuboA+FIVj/RZmyRJczGWgSphN5rw\n",
       "tBp4NfBdYE27XFPFkwtWqBZU+0ifN9L0XB1M81ifzwJrqtjQZ22SJM1kwQNVknOAfwfcW1Uvm6HN\n",
       "6TSBZwPwtqq6rkthCSuAX2JziNqd5h/iNcBXRu3hxGokPA94E024OgD4Cs0jfx7bimUD8MQ4Ph5I\n",
       "ktS/xQhUhwGPAJ+aLlAlWQ2cWFWrkxwI/N+qOmi+hSXsSnNr/pHAa4H/RxOgLgWurmLjXH8pDb+E\n",
       "n6e5LLgr8MwBy7Nm2L4NMweu+4E7p1nuM4RJkgZZlEt+SVYBfz1DoPo4cEVVfbZd/w7wqqpaP1th\n",
       "CdsCB7J5LNS/Br5GE6K+7MSbGqR95uBMIeznaR52vWrKsgPTB61Ni4FLkjTvQLUQD8HdDbhr0vrd\n",
       "NJfo1k9t2M6y/TqaEPWrbds1wH8DrqziiQWoR8tE22v5cLvMSTtgfmrQ+qVJr3dIDFySpPlZiEAF\n",
       "MDXBzfQPzndp7vi6FPhdn6OnpdbOj3Vju2xhDoGrEi6huWvx8ioeX+SSJUkjYCEC1T3wtIfn7t5u\n",
       "m8b2H4Ennmzb7AlloNJQmUPgWgn8B5rZ+M9P+CLwOQxXkjTSkkwAE1v9+QUYQzV5UPpBwGlbMyhd\n",
       "GjWTwtUxwD7AxWwOV16+lqQRthh3+X0aeBWwM824qFOAFQBVdWbb5gyaO/QeBY6vqmu7FiaNkjZc\n",
       "HU0TrvaCp/VcGa4kacSM5cSe0ihJ2IPN4WpPNvdc/a3hSpJGg4FKGiIJL6QJV/+RzeHqAuAKw5Uk\n",
       "DS8DlTSkJoWrY4AXA1+g6bkyXEnSkDFQSSMgYRWbw9WLaMLVn1axrs+6JEmN+eaWbRazGEnTq+LO\n",
       "Kv5PFQfQPNfw+8A3Es5qHwYuSRohBiqpZ1V8r4r/DewN/Bi4MeH9CTv2XJokaY4MVNKQqOKBKt4D\n",
       "vILmWYTfTfjvCc/ouTRJ0gAGKmnIVHF3FW+nmbH3MOC2hLe2DxSXJA0hB6VLQy7hEOCDwM8C7wHW\n",
       "+IBmSVpc3uUnjaGEAK8H/hj4J+DdVVzZb1WSNL68y08aQ1VUFZcALwfOAz6XcFHCPj2XJknCQCWN\n",
       "lCo2VnEOzcOYrwa+lfDxhF17Lk2SljUDlTSCqthQxQdogtXDwM0Jf5jw3J5Lk6RlyUAljbAq7q/i\n",
       "d4H9gBfQTLVwcsIOPZcmScuKgUoaA1V8v4rjgV8BDqeZauEtiee4JC0F7/KTxlDCYcAHgGcDJ1Tx\n",
       "dz2XJEkjxWkTJAFPTbVwNPBR4LgqLuu5JEkaGQYqSU/T9lZdBLytijV91yNJo8B5qCQ9TRXfBI4C\n",
       "zk14Q9/1SNI42q7vAiQtviquTDgS+JuE7av4XN81SdI4MVBJy0QV1yS8Dvhywooq/qrvmiRpXBio\n",
       "pGWkihsSXgN8te2pOrfvmiRpHBiopGWmilsSXg1c1oaqT/RdkySNOgOVtAxVcVvC4cDlbag6o++a\n",
       "JGmUGaikZaqKOxJeBfxtwg5VfKjvmiRpVBmopGWsijvbUHV5G6r+qO+aJGkUGaikZa6Kuyb1VG0P\n",
       "/EEVSzPjrySNCQOVJKr4YcIEcBmwQ8J7DVWSNHfOlC4JgCrWA4cDRwAfap8FKEmaAwOVpKdUcR/w\n",
       "auBQ4COJfyMkaS78Yynpaap4AHgtsB9wpqFKkgbzD6WkLVTxEM2lv72BP0/YtueSJGmoDQxUSY5I\n",
       "8p0ktyd59zTvTyR5KMl17fK+xSlV0lKq4mFgNbAbcH7Cip5LkqShlaqZb+RJsi1wG/Aa4B7g28Bx\n",
       "VbVuUpsJ4Heq6qhZd5RUVTnIVRoxCc8EPg9sAI6r4vGeS5KkRTff3DKoh+oA4I6qurOqngA+A7xh\n",
       "uv3Oo0ZJI6SKx4A30kyzcmHCDj2XJElDZ1Cg2g24a9L63e22yQo4OMkNSdYk2XchC5TUvyp+AhwN\n",
       "/AT4YttrJUlqDZrYcy4T+10LrKyqDUmOBC6mGcgqaYxU8UTCccB5wJcSjqri0ant2vmrdgCetZVL\n",
       "Ab/f3m0oSSNhUKC6B1g5aX0lTS/VU6rq4UmvL03y0SQ7VdX9U78syamTVtdW1dp5VyypN1VsTPh1\n",
       "4JPAjQkPMH0oepxmzNV8lvvan28Ajgc+vGS/mKRlrx0TPrHVnx8wKH07mkHpvwL8ALiaLQel7wLc\n",
       "W1WV5ADggqpaNc13OShdGhPt3FQHABvZMhg9VsWTHb77EOBs4CU+/kZSX+abW2btoaqqjUlOBL4C\n",
       "bAucXVXrkryzff9MmnEVJyTZ9If1zVtdvaSRUMVPgSsX6ev/DvgpzWzt31ykfUjSgpq1h2pBd2QP\n",
       "laQ5SjgZ2K+KX++7FknL03xzi4FK0tBJeB7wj8CLHJwuqQ8LPQ+VJC25Kn4MrAHe0nctkjQXBipJ\n",
       "w+os4B3tNAySNNQMVJKG1VrgmcCBPdchSQMZqCQNpXbKhLOAd/RdiyQN4qB0SUMrYRfgO8ALq/jn\n",
       "vuuRtHw4KF3S2KhiPXAZ8Gt91yJJszFQSRp2XvaTNPQMVJKG3WXATgn7912IJM3EQCVpqLWPufkk\n",
       "9lJJGmIOSpc09BJeANwM7FHFI33XI2n8OShd0tip4gc0D0o+tu9aJGk6BipJo+ITeNlP0pAyUEka\n",
       "FV8Gdkt4ed+FSNJUBipJI6GKJ4FzsJdK0hByULqkkZGwB3AtsLKKx/quR9L4clC6pLFVxfeBq4Gj\n",
       "+65FkiYzUEkaNWcBv9F3EZI0mYFK0qj5EvDihJf0XYgkbWKgkjRSqngCOBd4e8+lSNJTHJQuaeQk\n",
       "vBi4Eti9ip/0XY+k8eOgdEljr4p/BK4H3tR3LZIEBipJo+ssnJNK0pDwkp+kkZSwA3AXcHAVd/Rd\n",
       "j6Tx4iU/SctCO3bqPBycLmkI2EMlaWQl7AN8Hdijisf7rkfS+LCHStKyUcVtwG3A6/uuRdLyZqCS\n",
       "NOo+gYPTJfXMS36SRlrCM4C7gVdWcWfP5UgaE17yk7SsVPEvwF8C/6XvWiQtX/ZQSRp5CS8Fvgys\n",
       "qmJj3/VIGn32UEladqq4Gfg+cGTftUhangYGqiRHJPlOktuTvHuGNqe379+QZL+FL1OSBjoL+I2+\n",
       "i5C0PM0aqJJsC5wBHAHsCxyX5CVT2qwG9qyqvWj+mH1skWpVT5JM9F2Dtt4yOn4XAAcn7N53IQtp\n",
       "GR2/seOxW14G9VAdANxRVXdW1RPAZ4A3TGlzFM1sxVTVVcCOSXZZ8ErVp4m+C1AnE30XsBSqeBT4\n",
       "LHB837UssIm+C9BWm+i7AC2dQYFqN5pnZW1yd7ttUJux+h+ipJFxFvD2hG37LkTS8jIoUM31FsCp\n",
       "o+CX5tZBSZqkiuuAe4HX9l2LpOVluwHv3wOsnLS+kqYHarY2u7fbtpDEoDWikpzSdw3aesvw+F2a\n",
       "MZqkZRkev7HhsVs+BgWqfwD2SrIK+AFwLHDclDaXACcCn0lyEPBgVa2f+kXOQSVJksbVrIGqqjYm\n",
       "ORH4CrAtcHZVrUvyzvb9M6tqTZLVSe4AHmX8BoRKkiTNaslmSpckSRpXiz5T+lwmBtXwSnJnkhuT\n",
       "XJfk6r7r0eySnJNkfZKbJm3bKcnXknw3yVeT7NhnjZreDMfu1CR3t+ffdUmO6LNGzSzJyiRXJLkl\n",
       "yc1JTmq3e/4NuVmO3bzOv0XtoWonBr0NeA3NQPVvA8dV1bpF26kWVJLvAftX1f1916LBkhwGPAJ8\n",
       "qqpe1m77IHBfVX2w/U/Nz1XVe/qsU1ua4didAjxcVR/utTgNlOT5wPOr6vokzwGuAd5IMwzG82+I\n",
       "zXLsjmEe599i91DNZWJQDT9vKBgRVfVN4IEpm5+afLf9+cYlLUpzMsOxA8+/kVBVP6qq69vXjwDr\n",
       "aOZp9PwbcrMcO5jH+bfYgWouE4NquBVwWZJ/SPKOvovRVtll0p236wGfZDBafrt9TurZXi4aDe2d\n",
       "8fsBV+H5N1ImHbsr201zPv8WO1A54n30HVJV+wFHAr/VXpbQiKrmGr/n5ej4GPAi4BeBHwIf6rcc\n",
       "DdJeMroIeFdVPTz5Pc+/4dYeuwtpjt0jzPP8W+xANZeJQTXEquqH7c9/Ar5AcxlXo2V9O0aAJLvS\n",
       "zCSuEVBV91YL+CSef0MtyQqaMPUXVXVxu9nzbwRMOnbnbzp28z3/FjtQPTUxaJLtaSYGvWSR96kF\n",
       "kuRZSX6mff1s4FeBm2b/lIbQJcBb29dvBS6epa2GSPsP8CZvwvNvaCUJcDZwa1WdNuktz78hN9Ox\n",
       "m+/5t+jzUCU5EjiNzRODvn9Rd6gFk+RFNL1S0EwC+5cev+GW5NPAq4CdacZr/D7wReACYA/gTuCY\n",
       "qnqwrxo1vWmO3SnABM3lhgK+B7xzuidRqH9JDgW+AdzI5st6/xO4Gs+/oTbDsXsvzZNh5nz+ObGn\n",
       "JElSR4s+sackSdK4M1BJkiR1ZKCSJEnqyEAlSZLUkYFKkiSpIwOVJElSRwYqSZKkjgxUkiRJHf1/\n",
       "461t1oburzgAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b4ebbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xe8JFWZ//HPwwQEBhjHwBKGIEFlVQSUZGAUFJhVwF1Z\n",
       "wRVdDLBiWrOyKuCuqz+ziLoY14xxWURMCKOyKqKSJAkqEhRUwhAHGHx+f5xzuk+fruqu27e77r0z\n",
       "3/fr1a/urqquOl3xqZPK3B0RERERmbx1ZjoBIiIiImsLBV4iIiIiLVHgJSIiItISBV4iIiIiLVHg\n",
       "JSIiItISBV4iIiIiLRkYeJnZ/czsHDM738wuMbO310x3gpldYWYXmNnOk0mqiIiIyNw2f9BId19l\n",
       "Zk9y9zvNbD5wtpk93t3PTtOY2XJgO3ff3sx2Bz4C7DHZZIuIiIjMPUOLGt39zvhxITAPuKmY5EDg\n",
       "03Hac4DFZrbJOBMpIiIisiYYGniZ2Tpmdj5wA3CWu19STLI5cE32/Vpgi/ElUURERGTN0CTH66/u\n",
       "/mhCMPVEM1tWMZmVPxtD2kRERETWKAPreOXcfaWZfRN4DLAiG3UdsDT7vkUc1sPMFIyJiIjInOHu\n",
       "ZcbStA0MvMzsgcBqd7/FzNYDngIcX0x2KvBS4GQz2wO4xd1vqJrfJP6ATJ6ZHefux810OmQ02n5z\n",
       "m7bf3KVtN7dNKsNoWI7XpsCnzWwdQrHkZ939+2Z2FIC7n+Tup5vZcjO7ErgDOGISCRURERGZ64Z1\n",
       "J3ERsEvF8JOK7y8dc7pERERE1jjquV6aWDHTCZBpWTHTCZBpWTHTCZCRrZjpBMjsY+7t1Hk3M1cd\n",
       "LxEREZkLJhW3KMdLREREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUKvERERERaosBL\n",
       "REREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUKvERERERa\n",
       "osBLREREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUKvERE\n",
       "RERaosBLREREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUKvERERERaosBLREREpCUK\n",
       "vERERERaMjDwMrOlZnaWmV1sZr8ys5dXTLPMzFaa2Xnx9abJJVdERERk7po/ZPy9wCvd/XwzWwT8\n",
       "wsy+5+6XFtP9wN0PnEwSRURERNYMA3O83P16dz8/fr4duBTYrGJSm0DaRERERNYojet4mdnWwM7A\n",
       "OcUoB/YyswvM7HQz23F8yRMRERFZcwwragQgFjN+FXhFzPnK/RJY6u53mtkBwCnADuNNpoiIiMjc\n",
       "NzTwMrMFwNeAz7n7KeV4d78t+/wtM/uwmS1x95sq5nVc9nWFu68YKdUiIiIiY2Rmy4BlE1+Ouw9K\n",
       "hAGfBm5091fWTLMJ8Cd3dzPbDfiyu29dMZ27u+qCiYiIyKw3qbhlWI7X44DnABea2Xlx2DHAlgDu\n",
       "fhLwTODFZrYauBM4dNyJFBEREVkTDMzxGuuClOMlIiIic8Sk4hb1XC8iIiLSEgVeIiIiIi1R4CUi\n",
       "IiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R\n",
       "4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIi\n",
       "Ii1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVe\n",
       "IiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSEgVeIiIiIi1R4CUiIiLSkoGBl5ktNbOzzOxiM/uV\n",
       "mb28ZroTzOwKM7vAzHaeTFJFRERE5rb5Q8bfC7zS3c83s0XAL8zse+5+aZrAzJYD27n79ma2O/AR\n",
       "YI/JJVlERERkbhqY4+Xu17v7+fHz7cClwGbFZAcCn47TnAMsNrNNJpBWERERkTmtcR0vM9sa2Bk4\n",
       "pxi1OXBN9v1aYIvpJkxERERkTdMo8IrFjF8FXhFzvvomKb77dBMmIiIisqYZVscLM1sAfA34nLuf\n",
       "UjHJdcDS7PsWcVjVvI7Lvq5w9xWNUyoiIiIyIWa2DFg28eW412dOmZkR6m/d6O6vrJlmOfBSd19u\n",
       "ZnsA73f3vsr1ZubuXuaMiYiIiMw6k4pbhgVejwd+CFxIt/jwGGBLAHc/KU53IrA/cAdwhLv/smJe\n",
       "CrxERERkTpiRwGusC1LgJSIiInPEpOIW9VwvIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAl\n",
       "IiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiIt\n",
       "UeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIi\n",
       "IiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIF\n",
       "XiIiIiItUeAlIiIi0hIFXiIiIiItUeAlIiIi0hIFXiIiIiItGRp4mdknzewGM7uoZvwyM1tpZufF\n",
       "15vGn0wRERGRuW9+g2k+BXwQ+MyAaX7g7geOJ0kiIiIia6ahOV7u/iPg5iGT2XiSIyIiIrLmGkcd\n",
       "Lwf2MrMLzOx0M9txDPMUERERWeM0KWoc5pfAUne/08wOAE4Bdqia0MyOy76ucPcVY1i+iIiIyLSY\n",
       "2TJg2cSX4+5NErM18A13f2SDaX8H7OruNxXD3d1VJCkiIiKz3qTilmkXNZrZJmZm8fNuhGDupiE/\n",
       "ExEREVnrDC1qNLMvAnsDDzSza4BjgQUA7n4S8EzgxWa2GrgTOHRyyRURERGZuxoVNY5lQSpqFBER\n",
       "kTli1hY1ioiIiEgzCrxEREREWqLAS0RERKQlCrxEREREWqLAS0RERKQlCrxEREREWqLAS0RERKQl\n",
       "CrxEREREWqLAS0RERKQlCrxEREREWqLAS0RERKQlCrxEREREWqLAS0RERKQlCrxEREREWtJq4GWG\n",
       "m3Fcm8sUERERmS3M3dtZkJlDWJY71spCRUREREZgZu7uY49XVNQoIiIi0hIFXiIiIiItUeAlIiIi\n",
       "0hIFXiIiIiItUeAlIiIi0pIZCbzMWD4TyxURERGZSTPSnQSoSwkRkdnADAd2duf8mU6LyGyi7iRE\n",
       "RGRSHjrTCRBZW8y5wMuM/cx4/0ynQ0RkDXLvTCdAZG3RduB1Yvpg1qyo0YyNzXhwNujbwCvGnTAR\n",
       "kZwZZsYRTc9Vc1H23/46owkRWYu0HXhdkH1+Y8PfnA78YQJpmTgzFpux7kynQ0ZjxjpmfMaMDWY6\n",
       "LdIeM+aZcTiwAPgkrNHbf2F813lKpCVtB177ZZ/fNmhCM+5vxj8BOwHzJpqqybkZ+K+ZToSMbDFw\n",
       "OPD2mU6ITI4Z/2HGv2SDHg58Blgvfp+XTbttmzlgZvzJjL0nuIj7xfc1ObgUmVXaDrz+MoVpfwJ8\n",
       "jpoTghlvNeOvZmw3lpRNzj+bsclMJ0JGslF8f/DAqWYpMxbNdBrmiH8DXpl9T4HWZ+P7/GzclcAB\n",
       "bSQqehCw5wTn/6T4vuEElyFzkBm7mnH/+NnNeOpMp2kczHhc9nk7s87NR2vaDrzeEruRuBU6G7Pu\n",
       "TqunlY0ZjyjG7wEYcMXYUzlevwOuN+NhbS7UjIPN+H2by1wDbRnfWz8wpysGXbetyfWTxmwHM5bH\n",
       "9fWaOOzR8X1+MW3bQcok6189Pr5vasbfTHA5Mvf8HDg3O4fsMspMYgD3hfElazRmPCAGj2ebdYrY\n",
       "rwD+o+20tBp4ufPn+PHYbPBDGv78IjO2yL7vNZ5UTdw28X29gVON3//QDRxmTKygPCdzjIAfxPc5\n",
       "F3jRrbuzxcCp1mJmbGnGadmgbxJyOZ8Tvy+N7/Pj9CkAO7mdFHZMsrPFVH/29cAfJ7gcaYkZ3zZj\n",
       "02nOY4/4cVu6gf+o8cI/AIeZ8YDppGkM/gP4Tvx8txnrx887t52QoSvSzD5pZjeY2UUDpjnBzK4w\n",
       "swvMrMmfODr7fGHNNJ+vGPb87PPE6iSMI/vRjM2LQY+dzvzmsOcBN8x0Iqbp6plOwAgWxPfdZzQV\n",
       "s9svgL8rhlVVMk8B11cmm5xa75zgvN8zwXnLzNiP6V9vflIx7DEjzitV2Zjpm8AyNkmB17fbTkiT\n",
       "CPZTwP51I81sObCdu28PHAl8pME8r2swze0Vw45v8LtxuIIhlf8buLb4ftI05zdXPQrArCdonmv+\n",
       "bNZ6juV0HRLfXz+jqZjdqhrtVG3nFHgdPMG0SA0z9i3ryZqxkRnbz1Sa5oBJ9Mv2jBF/95LivXVm\n",
       "rEP/TWg61m8142qz9p7cMDTwcvcfEVrn1TkQ+HSc9hxgsZkNq0zeJICqy3H6dTnAjBc3mN9UvWrU\n",
       "H9Z1IWHGE0ZPzpS12gWHGYtq/ncKAD7UZnrG7BjgY+Oe6YSLYD8Y32+Z4DKmLRb3PXr4lBNxX8Ww\n",
       "QYHXlMTuSEauzpEqNq9NzPhHM1YUg79Hdv4w4xJgJRXXgrVdtr+NtM9OSCotu34G01B17U3H+gJC\n",
       "tYKdzNrpQWEcdbw2B67Jvl/L8CzFHwwZD/X9ylQdbB9uML8eZjzYbHB2rNnId7jH1gz/4YjzG0Xb\n",
       "9ZL+QrcVGBD6Q6K7L9yvGPdjM77cUtqm4574/k8TmPcNWT2DsSm6H9h33PMfs58B583QsquKkC+t\n",
       "GFZ7ETPj0NhIqKrC/ZdgWnfRrV88pxMojsmXoLL7jAUxkD2X0N3HnGbGg8wmUrdoSXwf+3mlqYqe\n",
       "Bn4R3/fIpjnMjJ3aSxXfrRi2cXx/Yjas0xLcjAMnlZhxHWRly6mBlUHde8cXleaTusDhjimka5AT\n",
       "CSf9QfYbMr7OjFQijBeAdOCtV4w7yIwfjTDPt5jx1QaTrkv/894+WDVhtCfd3LDZ7P8mMdOsovZY\n",
       "izDN2Jrem5YLaiadLWayq5VTGk7XdxectfRKxS9V57AnAI804xgz/rnJgsxY16xTl6by7jse59Pu\n",
       "26vm7v6F053vKMzYxoy/HTLZfYxez2jaxpwbchLwyzHOLzk0vk8i8Lpp2ARmbEZ/TwPpmr0kG/YF\n",
       "4L1jStewNL2XbmOjXLr+59ehDeNvFgD/O6k0jSPwuo5u6x8IJ6DKOlxmdlx6wXHH0V0ZO5gxP2tJ\n",
       "AeHicVD8/Jxs+KqKWZ8d5o+bNS4Ssvib3dMBFU96eUW7qqKIJlp//EZ2x52i+PKCfjDdpuNTcTyh\n",
       "VUoTZSvKSRQBj40ZO9W1/skurLtNaPEpOOppJBLTNJ0uIH5Hbz9Ts71hwCUzuOy3NpjmcmDz4twE\n",
       "3dyofyy+59J2fFvDZUEoGj7XjC0J+8jtwF0V0+3YcH6D5De3qTFQq8esGU+K598fAL/Khpc5zBPL\n",
       "fZiC1WZja2E6qdzMFBxNoj5VZT+cZvzSjA1jPbyq8+m6MV1fK4a3laO7rPmkX/m82SuuhkXHw3GT\n",
       "Ss9YAq9TgecCmNkewC3uXtmKzd2P676OO96dewlR//cJEXDekuJ+hEh54zguSRXkziOcfN4AXJh1\n",
       "7tb0ji1VPvwp3Zytw+nN5Zpu4NWkEUElMz4So+6mUs5B3zaNF/Ky9VZTf4rz+HWqixMD1E4z/CxQ\n",
       "WDxoRtNtKToVsWXqRkMmO5+ieDSTbgo6gZHZWBtIpMBrkRnfNOMtWZrKPuum6kHx/SfMYJFDQ305\n",
       "cmYsjTdRW1X9II77zQTT9H26zc5vJdRhLVt57VHU0asKlvPxqxsuOx0jvweOIBR9VFW7GDk4N+Pd\n",
       "ZvyRLEB379QJva1i+oPNJhbAn0lYN0uL4S+Oy37khJY705ruDwBY834g0/bbdcxFZSug9nq0MyFo\n",
       "vgT4MfTk6EM4hy6kP3huq4/B8jr+CKqrFACHPBE+sBRuf8KMBl5m9kXCynyomV1jZs83s6PM7CgA\n",
       "dz8d+K2ZXUnIPj16wOyqpE77Ul2adCHfEbjbnVuLosmHEbKbn+TOpfF3R5MVWZh175wGyHOl0kFQ\n",
       "tgSZbuCV3yG8hNAT/0Bm7BxbAP4LTKlybToo5sd6Gh7nty0ht+tBdT8c4nfxfXu6OWZ/S28gNyyg\n",
       "+vf43mZl4SvIijrNeHRNUUZd2v85vt+ZDTuy6cIbFAWl7O3TgOX0ZndP94ZoXULXB28A9hnjXfok\n",
       "3F0xLAXwV0FvvSPrdnz4kLpGLCN4R/F9BXAYYT9fTffYyXPbf0gI0JKqoozclC60Uao7e1/FTct0\n",
       "Llq7E867qXuMj2bjqurbPZ7+wGjS0g3PS1tebluWDBqZVRnBjHuASxvmhOclHY8aMW1VzmbwPr4l\n",
       "4T+lafJz/fqEG/imfXaOW76u/8Gdi2umy/uxG6V0qLEmrRoPc/fN3H2huy9190+6+0nuflI2zUvd\n",
       "fTt338ndp1puvVl8zzfqPxECqapiRdz5hTsr49dUkS8v+x9WVyAtI7k1vpePWJlu4PVdQq7dEkLL\n",
       "0Mo7BjMWxrt4I+QAfiKOOq1q+ux3i8w6RYtp/W1M6LQ1BQzrUp39O2i+O2Rf8wtG2l/eHKdLdR7S\n",
       "wV73SKir4nvqiHJSxXel/G75PHqLMtJJrK7eRnrG5llTXWic9wob3Cpt2/ieOthdnaVpukXV6xLu\n",
       "fO8cNJEZT5lOZepYTPTzUX8fXRfntTBLSxlQ3Zc1QsiP2+dOc9nJn4vvZ7pzszuX0Lv/lzdmG2ef\n",
       "h9XVqzyXVchz8u4Avkw4dyyGnvqw0wm8yvWbcrveTszhLuw6jWWNKt2I3zpwqhpmvM6My82a33Ca\n",
       "sWN+bjJjvRQAmXUr9E+xJKJqOetT3YAgd6NZp2FMWl6TEoNH0q1TNY4brsWEwOlDVFy/BtR7y+s5\n",
       "b0Q4j5aN6p6Q3UhNRNxWecCXrqmXx/fjsnHldfIaJmSmW7DkDoFQ54pu8U++49RVdE/1H/qyVeOB\n",
       "VFf8lUe9PzHjGYQK97kdiu+pJ/bKk6wZr4q5Kmlneqs7i9y5mXDSrjtg0wYvD6zH1uVWxDRcTPdE\n",
       "nZb5BcLz5FYSAo35A5ZbNd+H0d0poTf4vCcGB6m1Z0pveoj0A4vZnUVoVVdWJP/PpumZps2h9uTQ\n",
       "V5RY453QqHFBLt1pLrTwmIqTYmB9QjbNVcVvjO56mlIl3rhP5nVznk44LjybpupY/y6jF0EDPI3s\n",
       "omzGghhA3ZjfsWfj1zfrBJpJCmY+RvdEd272m1T3KAWq+Ql95BzUIh3n5uPcQ3FJVHXjkeS5QPvm\n",
       "x2rFPje0W494Edo2G/RFQiOUe4AlZnyN7joaGniZ8XWzyhbfWxffUzP/hVQ/PmVZxbxfU3ceHJPd\n",
       "4j6bF0X/Efj7Ih1117B9CefvVFVisRn/PWSZFwPnZN9PAm6Mn/O6iNN9Buob0gcb/DzV8hFO+5qx\n",
       "mxmHWHWDNIA30T2nTbuusTsr3bmLsA9WXUfq9oH8OH0S4dg5xKyvW6GRq+PUMeM2C3XGt6C3Bexy\n",
       "905An1pappvTqkcPTi6X191beYVFVQ13H/C6fzHtm8B3LIadEKe9Mv9tNu+vjLDcnvkUv3t71fCK\n",
       "eT6vGHcQ+Kk1v9sz/ua9TdIQf/Oy4r8+vuK354LvVgzbYPB28kdl81xS/PYI8EXZ9wdW/O9dwedn\n",
       "w/cAPzp+fkwc/u1s+nmT2d/cwVfEzxtly1se39Owa2p+f122Hp4waFtU/PauOP0zwA+v2pYV2+pm\n",
       "8A3i592n+F/vVzG//wXfNPu+foNjYJsR1nH+n74PfmEcvkvF9CvKdQj+njj9ncVxm15p/72nYtwb\n",
       "p7F/XBLn8Z/g68fPe4MfWUx3fbHMlRXr7SLwM+PnB9dsk282SNODKuZd93pZk+O4ap8F/1gxr3lx\n",
       "+KkV22dh1XzisCeMuv7jPPYY8h/3rhi2Jfhbsu/r1sz7x9k064A/adjxW7E//6Bmn9xvGv/5C+A3\n",
       "ZvN60IC0HFGx7L5zSfG7T4N/K07z+mmk87fgD8m+bxjnuUExXdV1x8H3z6b5K/hL83QP+x8D1skW\n",
       "Q6axON2iIj2/LqbbDvwT4G+N4/8L/N39/4PG6ZvKazbkeG1bN8K9t+NWd/7Dva8VVLpDq2sdlRcH\n",
       "pIq5TVvpfa9i2BsqhlUpe96/h/oy8tRL/isbzhuyu/14p13VVcTd9BcrfCGug7o7lfviPA36OrZ8\n",
       "K725DJtW1Dv4Od0mzRDuiM6Kn4+J73nu5dh6tDdjT+vtIX9vC32x5RVTU9l9yq0rnzCQnEK3fkkn\n",
       "B7BhPYs07/UpOuK1+ofCL6a7f0w1+72qAv2B7j11Fja20Chi0Lw3HjCuiSfSLd79RcX4vQHMenJG\n",
       "0/pZL44rWzqloqYFZn31Ln46elI7d8L/5s6dwMeBc9x76jtBf3cXD6T/7vgiusWVadun3IHD43uT\n",
       "znKn0sprWK5o33nVQuekG5LVpwVw7+Rq3x6n2ycbPaiByj0DxjVR9Vga6D7GaAP6u1xYRW8uSc/+\n",
       "bNbJncvX9y5U5P6Y8Q6znhy0y+PwlAu8a/z+tOKnT2V0h9Fb52hQruEzR5j/H+h2geMj/D5ZSO/2\n",
       "TTnTRxbH7xE1v9/BQiOZ5YTc2aon0TSWnXeHdfGUnmZQdhXV04+XO1e68wJC6QCE1t/TWV9TMuOB\n",
       "lzu/JTzQedTf/4lQTPE3xB70G3gMzfoDe0rdiJjdW/U8yaSc/+2EFmxV6/xJDdJSavJIiK0IQcfX\n",
       "6PaZkrKv6+oLpINtEb2VhyF0FZIHDj+mW0cvl/fndYd7pwXJM8z61ml5oZuO99GtH5f8D73FBymI\n",
       "SgFpXZ9ri+ieLPJ6JqsHBS/W23ngLfQHr4Oe95fm26jSuBkPi8Ung1ouvii+r0e4aA3qxNdjvcFR\n",
       "W0I2DRzy+Zcn5O8U3/P9tLy5mHa/Su7hZOvOi9yH18Py0BK7fFTN7Vla0kX1rXH61KCmSf9TC+iv\n",
       "l1fVlQTAAQOCeOgPSPYidE5a9l2W12NJ//8Ms04xS18nx1lwPEqDgSZSl0CLCM/Re1M27m7gjOz7\n",
       "wljE/ZRYn+useJHOA89za9L6enq7XUg3+qkeUFo338imuYDqm9xR9QVeWTH4KMHKfKobrDQW66Zu\n",
       "Tu81Jn02wiPUUhWAuuvIBwjBzDfj9+nW6003/H81Y5cBN8Bnx/eyk926dZKKsj/AiPUJRzHjgVd0\n",
       "CP11tI6awu9vIzwUtJNDZtYJCKrK0OcTLm7HNZl5zCEqexn+MvDsbJryYlxe0G8h1K1oWmF/WOdy\n",
       "TQKvLQiBzQZ0cwfSAfC8Ict9QcW4M+m9aC4i1EFJ0lMF3mTWqadX3rGWOQg3QcgFSXVkzNjWjNqH\n",
       "sg+Q+mYblLuQ7mbXIxxoda2L8sArX9frUNPxroWOL/PckPWgp14XhAtm2TQ8db+S6tqU/aHVOZiw\n",
       "HasuwOlC/9/xPR0Hu8e0VgVJHyQcS02eLNExoJ5NnfUtPGvvLfTnejw5vqcAcVCF4sY5RLEe3Hbx\n",
       "c9o3p5NzkVtFN2foPAt9w43SomwBYV/IL+xX1Uz7VHpzlkvluknH6aPoXaf5TW8eeKbzZ7opzC9c\n",
       "KWd05FZzNfsfwPvcOzdHdxD27TwYXUX3eLmJcB5/Pr05Gm+hX2rYU+6rq8zY3kL3OHnP6htC33F6\n",
       "BCG3racSthnLp1HfbeuKYb+N7/9YV8cXalvmbUC4xrydKdTtrUlTJ8cr5or+hf6GaN+ivlFVbuTu\n",
       "SOI2S3Xt3k7ITa87dusaU7y/ZvirgD3cuYPu/0195I39MXHJrAi83LnPveeu4k0VWf6DpOKKG7Nh\n",
       "KTt6T/qtSzgQ30r/BryacJd1DvRkce5j1n/XZN3HCpUB3rnF91voVvYuo/W+Oxt3Xp0to6p372GB\n",
       "V36nvAX9LbfeV/O7pw0Y/2RCNxe5PNchP6E/B8C9s85SsJJOuDfHNKWHqt8fOq1QngE8woxdatI4\n",
       "TGU/coS73tRtw16EE9QDzCp72F9E7BMnK4pJ6h51kW/z6wknvnsJxdPpJHgK/X3IlIFTmWtXJ+0D\n",
       "ZW7KZu6hqC+u/+vpL3qqylVL+9nQ3BnrfZpB0043028WERp/HE99rnLK1agqjtqLsD81CrzMOJpw\n",
       "cUhBceqQeSp3uO+ie6NWPgf1bnr/xx8IjVx6zgFmndzHOg8htHLN5zUoV2lQjkjnuIwXrnQ+eCDd\n",
       "7fsGd16R/eaN2ed/pFe+rlPg9cmqBceguuoRSrl9aoanoOMrhONiA0IAtgOhtendhPX9ScL/X0i3\n",
       "BXK6nh1XMd/0eLglMcckvzHel/5GJs+qmMcdhK5fygYL32RwEDzIt4dPUmlRvJnoXEvMeBbhWDyK\n",
       "EKwOazhUO+/4Xl5jPkO3S511svf0Hwa1wu/sKwOCyTR+tRkrzLgsDsr7NUznqKpGIFBT/O1e3ULR\n",
       "nZvcOyUid8Vh6fx85aB0TsesCLxK7p06T1NVBhd1HgjcE4sZzijGHerOAYSOWG+lm2X/LqqLNt5m\n",
       "xu/o9rIPgHvfMyXzVk2dO5F4pzSP3t7GS2XrFhiec3Yn3Z3wEYSLwb8O+U2V8sRQXjzSPvQ6BufU\n",
       "pFyG7Qjb6e8JJ7CdYmCZ1tdSQhEAVLQqHWJY/auzs8+fopt9XdVX0IZMr17CGYTtvB6huHU1oUn2\n",
       "77Np9orvfUFQw+K+dGLs6R+uqNsFYf/5ejGsKvD6fcWwOvn+Xj4qqk/M4Uh1Vl4/aNpoUIeRFxOC\n",
       "yflmbGw2tG7ki6HTLUB+QW0SeKVc9He7c3z8/GN611VV0fM/0a3nluqFfjQt38ITM8rzb8pxyS94\n",
       "g1pDnmzVrRahd/ueSO+5MeVU9XSW6qGLnlT08qqsuBFgHeu21OwEVTXF7qfQf+NZKoPmdD5LF+W7\n",
       "CDdy6xOOnyvcQ7AW6ye/gBCA5csvc5dz74rvFxK2S8qlMapzVavOr3XFvjD1orROEWfDeqOlrQjX\n",
       "qLzuWqrW8FtCkDhqlYGUe1v+31voBrBp/3oIcJc7RijKrlPXtc3NEOrmWffZjfMI9UHTeaVqH6ur\n",
       "mzudFvPUXSpsAAAfL0lEQVQfp7cO2cTio9kYeL19+CR9UjFlZR0NC72Yfz070R1GzDqPB3G+46ec\n",
       "spsJO++wLOR1CVmzlXd/mfwinp8Uz47LuIJwR0GRHqjeTsPuKM+nt7L+HQw+cdQZ1lv74+L7sFya\n",
       "9PSB+wjr9o+EYq+n0dt9xbF07zSGPWy9VK63skiwNpCqOPnlRY0QGgZUdisRL/75XdyL6HYfcj+6\n",
       "6/0l0M1hcO/k5lQVCTR53meZ+/ieyqmKbWjGSwj7YJkz+JRsmmH7V/5/F1RdPIpheYXcJpWGywrs\n",
       "+Yn2LkJO0Dxgf4YXy+cn7sdmn5sUkSwl3FTk0x5GuClIRcMvr/jdk+jm6uQXpJPj+0+BJ8c6dal4\n",
       "9TfAye49F9Nn0tsf3WPo7ci3L7fRjMPprTv5TCrqagGnlwPce+okplKIN9LbnUCek7K9hW508kB8\n",
       "V4YH4ymI+zyh5/NUlSNt57sJx05Z1Ji7h95zaZlLt4RublhS1adhVeBVdWOyinDDVqU8FoFOtYmq\n",
       "6gx5YPd/1v9IqkFSUVhdsPdausW0A5kxr+JYXw8qc/rzxm7rxZvDY+kGf6cTSjD6AmD3ynPvJnTX\n",
       "w1nAN8x662bFc0jV9plSdYgm3LnTvafIumnfe1M22wKvI6Gvn48mUq7MPRVBC4Qd4hl0O6uEmouw\n",
       "e6cs+i7CDjgs8KptlVnMN79Q5TtSKk5bTWjdWJUrVXUA5ZH9UYSLeroA7URorZGffO9gtB3pXkKL\n",
       "u4NrxqeTXVVQlypW4s5NhOJLIxS53kG4aEJva7pv0a2X9C6mpiwie22Wjk8xOAfr+OJ7T+Dlztvp\n",
       "zzVKdi++30NYbwvpVmofJE9XOhENrDhuodf2npOUO6+p2f9vLr6fSLiwrKK+rt/m+RczXhDrOj7J\n",
       "jMfRvQj/hHDRSSffd9DN+cyDx6n2KfTu4ntqHZgquK8mBOarY/oGFTvmOaepCP/D7sNzyN25w513\n",
       "5cGQO6s99AeUigHrHqSeKuHX1W9ZRDhuv2/GvxAChfxBxBfExkOdoDMWIZdFnaXPFN+r6r08zr22\n",
       "/liSciDeR2+Qk5+PTiYE/O/MhjXZ1mn/fo0757tzEbC+e+fBxKsI58kH0L//JqmleF2R0O30N9Yo\n",
       "HUD3PASh8+3f0K0CkbuPWE0g3VSY9ZReVDUSu5KQM7lT0RgiD2r2pP/pCVVSPbvLCMFoGTClm+CV\n",
       "cfz6ZnzO+p97iYX+BecTzrVlzu9iqjMS8ul+TDdnbF3oFNsdTfe8m6Tz2+OK4fcSbtrSNtqQ/oyX\n",
       "46luzPAIs8p6W2XA/AJGy/k7jYobk3GZVYGXOx9zn3qHavFEDN36AXsVk6QTYP44o5XFNJfTe2eV\n",
       "Aq9RH7UzSB54pZ6ir3bn1+58oGL6H5lVDgfAnY+68+GsXtg17tyV1a+CigO1ppigLNq4PBZBlMFD\n",
       "qnz/oJiGu+g/gMuD4AbCXc4GhIOx7zl9hE4jp91aLabph8CO7jzNnecPme+bi+9ljhfufDF+LOvd\n",
       "lPUKUqeX2xKKM6uC0jwHKG+4kU7A+zJY2cR9kKpik00Jj+QqL9LJsemDGT8hZMNDaGCRF9n2nJzc\n",
       "eSPd9fYv8ffPo77eXenMOJ983b/bnRX05hztRagwm7bpYQPmeWPFsLo6jlOR1mtaB2dVTVTkYOXW\n",
       "o7u99yRc8PIgI52P0vntzGx5lzE9g4K3C+i98N5Db3c4S+iet1L9mx3MOg14Bj6zNXoZgHsn1zCd\n",
       "Q5LUFc4G1BcJp6LGymoX7tzr3teKs0p+Hfwz3eP11GK6X9HNPT7aQmff+bFfd3P6AEIJRL5Pn0pv\n",
       "ILK3GZvVNFRJxV93AxvHm/i76a9r+oT4vpJwY/tsQpF31aPq/kI4xp9TMW4jqtd5eVOXcmJ7riPu\n",
       "PevkG3T3hzITI5UKpHrWiymq7FB/njucrPTAjIfGnPw3EupuPy+m5ZPFftWIO0+vqC40NrMq8Jqm\n",
       "hVkluboWcXmfSuVOsB+9lfhWEQ78Z0wxHVvSH/GX8sDr08BJRY5Ykncz8XLrbz7+DopcIXes6P/s\n",
       "x3H4PXTrAKSL4O8qlpnXL/mOe+duMr+r/DxUPg+zzFEqc4juoltMcgdZLkZhSncoZmxqNQ/TzSpK\n",
       "wtRaYXUq1xceCX0H5JnF93UI6/HVhLvpFLR2Gkm4h2Agbq983aZ1WBablLYuvg8qVkh9FeWPg9ks\n",
       "W9YhdC/yqUgqLyoaVAzS1xVKtv+lY+y/s9FlnUoIx972hJPlQfTmUH2cbpCUn69SMXQKxnpOrmZs\n",
       "ECsfv4rqHMcmxYzDrCDsC/8PuL87TwZek42vbBxi3X6Q8nPQcwnbNN/nUmXf1DXNvfG7U/1onyZS\n",
       "8fag3L4vkwXKcXkLCd1MHELI5Uoth/NHHJU5v33MeLyFbh+GdaGzipCL9iiGFzXmuZ3D+nmqcj7d\n",
       "G69VdIvy8pb2L4s5pGlbnEhNP3IW+sv7vHV7ly/3g11iTmZZFWIrujer29JtWZpa+Jp7JyC6m/p6\n",
       "kLdTrDPrf9YnZN10WO+THDak+txXdsmQiuVqu79x58CsyLKMN+5l+Lm+7E0Awr65EMKjnGLu42V0\n",
       "nzyzFd1MmNlpEr2yVvcoO5keYIf0Xlv1uqVpj7kD5nFfzfCBPTln0x2SDTsB/F8bpuEM8POy7zs1\n",
       "+A9npP8K/tr4u6XZPKyY/s5s3Keq0hI/Pzab7poirR+pScuRxTy2HLCOHfzWhtv7h3H6e8D/GD+/\n",
       "vWK6XxTzfzj4z7Lvm8Tp5oGvLtdNHLcN+O+y71W9jT+g+H5wnLayF/Bi3aWnBbyz5r+eE9djT4/R\n",
       "Q9bP9nG6q7PfHAP+jYp1My++v6PBceB0e+nvSQf4d8D/oeL3+bo5A/zVg47j4vsHs33n3mK++4I/\n",
       "q0jzC7PxL2q6vpq+COeZdSqGf7fq2KpYFydXrM+3lcda/L4cfNvs+w+y3xyaDX9IHHYToffuS7Lp\n",
       "fk32ZIoB/+u1dHvx/vaAfeB/KoZtE99vq5l3Pu0zBqTh37LptqyZ5jvgB4Bfm037OPAnk/WwPmT/\n",
       "Ta+fxPcFxfDdwR834D/0vLJzhBOe5FA5zYB5peNjUUzLDYRj8mjw52a/+332m/XjsJ+AXxY/lz3K\n",
       "/3TIcl8bh78a/A/gH65Y34fU7Qd127kYdkDFumqybRz8dvC3VQy/je7xll5fiPN+4PSPccZyrihf\n",
       "a1KOV4c7Tjcbsox8p9M7d7pDSeutLI+u64m5tNK6z3x8GYN7tc5bT+1Db4ecTVplXUg3F+tDhCKa\n",
       "/M6lU9E5tlrK74zeWswrv0vO++c6Jp/IvbZ7gbJ4t/xe5lQOq+CdpKzuBe5s6iEX6Y0V012Vf3Hn\n",
       "Und2o7sdd4l9MC0itKTyinncAZ3clBVUNCN37yvaWicOH9bT91Ue6sIdS329sN0IOVRvIDz4e2jO\n",
       "jXunovof6HaK+1Doaf34QkKL3vsIOalNu1qoa6F4E6H4KX/u4QfprcO0n3ttgwAq1v+r6bZELc9d\n",
       "exPq0uTFyXlOQ5N+76YknkP7ihHdeWrcB6v2n1xVlwWV/Za5c7p7T+5S3ov/F7MWiKkByEkeimvz\n",
       "St/7uHMh/c9ULeUV6ev22ZugUx8rl863fcV/Fd3x1NWNg956YnU5XisJ5/M812SBO2e693Rg/RTC\n",
       "8bQvvT3x58v4r7jN8v3kZHfOcR+YzippH3zywKmCcv9/IYA7t3soKt3EQ3dLH/beagGr6HbGvJGF\n",
       "vgsfTLfoulxnu1voK/HbNfUhX2Oh78t3E6ohVG33yyuGQfP+9H5EKCb/e5r1MZa3qN/AnX8j5Gjm\n",
       "RaeL6C/JuAzAfSy52hOxRgZe0YmEk3Qqtig78hxFPo87KB7S696oJ+dVhAqfp9GthDxoJxxUUbXJ\n",
       "xfG1xJONh1YbP6H3oMpbO21M94D9untfUWSnvpv3tnhpWmk/XYhSB4d5dvZR2fipGlrEEZ0X3x9L\n",
       "b92G1PT9dEJw0le/K5P6x1lIuNjXNWHP10mTysb7QedRViuBN5vxZjPeY9bX+/35hH6HdibUK1ne\n",
       "YP7ENKc6FA+Fnvo157l3iu2atIh6OmE91j11YjWhfkbej96dMRjZFfhb7281NZA797h36iCWTwBI\n",
       "xSbrmnWKjfJK03kdvs8ye30q+/yK2qnCBTpv+Xl1vGlIRTOp6LVzAfbYl1HFjUFpJd2GEakeZn4u\n",
       "+BKhUcCg7bdRvDlZYtYpAirrWA66MObXprrAazWhekgeePXd/LpzhjvrufN9d26jW6coXw9VFfRf\n",
       "V7Pc8qbuuPie6ic3aZGclPWmmlSyh3BdS61mlxD2hYfQ/U9VT2ZZRjjPVHUq/gDoeRJL3+PyYtC+\n",
       "Of0NyqoCr4eTdTAef3+7O3/nzv80vFb2rUcPrQ4/Xgwub1b+vcG8Z9YkstHazLJrtmx38HcMyvId\n",
       "8Lv8lR70+QLwA8FfHr+vajK/OM88+/lh8f0xA6Y/aUD26/wR18f6Vesi+74p+IK69VGxfv69anzF\n",
       "758XpzkwG/bKOOyF4Odn8/xKfF88le00ZLp1iQ8xLoaXWeivrZsX4YG7XrFdPgf+ZvDb43R/l41b\n",
       "UKZ1SDpfVMz7/cXvL2i6Dxe/O61YX5VF3HGbfKhi/Z5VtVzwncD3ISs6qtlfPzfK/tpku2ev59QM\n",
       "Pwb8keCPHGcaxpTmvv0X/P4jzC8vylkWx287wr7ydPBvEIpzHxCHnZDN+2bwg+gWa9a9ngm+X/y8\n",
       "Sd1/rUnDr7Jp+4pz4zRXxvH3NplnxXq7NFvGY7JxN5EVtdccH/l/2QB8R/BLp7KNB007jf1ozzh+\n",
       "acW4VPS+TcW4W8CvyL4/ccCyH1j89tFjOB42zz5vXfUfs9+kh6v/dZR1N7X0Mdb5pdeanOOVO5je\n",
       "VjwbUP+omFzqDuFSD830PwSs684n3DmVbm7R+726GX+VlP18Gd1chdoect05Ks6777mQ3uyuoUpf\n",
       "DlWs8Jrm+0f3yqKZI+lvqg7dnti/C9U9BEcpR6XT7YN7p+L0AnrvslK/X88z41tm036AM+7c7V5Z\n",
       "Kfnr9D54950V06R5pNyrI4vhz3Hn34nFo+58k7jNatblIGX/PG7G/bPipFEe1fIg+otF6/bZrQit\n",
       "trbK9wu6Fcd7WgS6c4GH3ISRn7k6Db+hN0exLjfrve5c5D7So6jG6R8qhvUVL7rXdqEwiMf3T3ho\n",
       "BQqjVcK/lZCr4XRzfh+SjV8M3OvercZRc/5bQrcF8PUV4wdJ/Z3lx1wp5bwMy8Grk58/O+dEd5a4\n",
       "dzq9rdJTydy901XPw8z6csrfAJ3W0FWqcv0GdQQ7TJpfVce7qcFEXmF9HUIDrc9Cz3NmB+1/+Xo7\n",
       "253zp5rIzNUA3u3N4ELvdnNybDZdnsuY1v9VzFFrReDloW+Y9F/f56HIrcmJLbVo3DTOx723ns7d\n",
       "xftUPIzYcsx9YO/USXlAV7U6aSSeyMrs4aEnaA/dfTwvG5Tq96TO7A6m/+Gk+e/Tye3CitEL3Hkt\n",
       "ocPKO+jWRXo/ocjoZcPS13CaqnTdR9Fv1ajce4pL6+o+DHtMSNl1yL8SgvyyP6jfTSFdf/FuFw2p\n",
       "p/7KlqB06xxeRXe/OIxuf1JV9edKr64Y1ujh31NwKOE5fcOOnz28wQOw2+De3xece+f8MeimpU5e\n",
       "3JeKZjp1ktw754lBgURpA8JxvA7dagllC7qq+pfl9WQrRn+QdpNqFOnGdxPCI95+MWDaKqvp1pWb\n",
       "Siu4/Hy/QzGsLKL/IeH4fTKh5WrZ4/qW9Hd/NJ19NbWWvo2wjfJ5/7/4vj5hX9s0nq+upr/eX119\n",
       "LghFv1cCG7p3urAY1Q+g0xsB9AZ8+TUvD1DTuq46/10yzfS0Yq0IvKLUU/2rhk2YSSeN59eMTyel\n",
       "qoeyNtGXizVAfrCvYup3kD18ivVranwnzuu6+H6Xe2Xdgtxi98oe4C+J87jWnUUemk3/PBs/6LmN\n",
       "VwAPde/UJRnFKL36J0fWDK8LvIZ13FnV4WZVv15l44Sm/lK8l35eDnDnZHdu8FABucmNRj7N5YTc\n",
       "0LoOaEfizpc89NV23JBJp/IopDYsJuzPX6P3wljVp9Iwef3QVOm4zHn8HIMf51K6Kr6vym4kys4q\n",
       "07ZcRLency+mOYb+a8wJhD6shjVEapIzmXcM+kT6O+gcZrU7/xf36bp6ZFXSueIA7zZcqQuWbnPn\n",
       "T+6c5c5n3Xsew5TOmeW6KJ/lOsg3iu+dm5B4o5X/r3RT/Ajgt97tQ+0YitxwH9AQyENdy+29ujf6\n",
       "KXHnue6d7moeSW+Dk1Pp1uXM12/6XOa0XUj1499mn0mUX7ZZVjqFsuT7ge8zYhl05e/A58fxd05h\n",
       "fp0uFYh1dRr+LjXv3pxQB+tBY1gne066jHya6cvrHLy+YvxmhObjV1PT5HwKy1pVrIeDhuwT+euI\n",
       "muleAn5lMWzfYduO0E3BmVXbJnt9AHzjEf/rvnEem9SMX1gsq7JrgCHL2Dn7/aoW9pVGdWpm6wv8\n",
       "N+DrjuO/j3N9Nh2ejb9hXNsC/K3DfjPqfybUIT16xHVzUFzuE7Nhi2r+c1+XIgP+x7Xgf0tNnbZi\n",
       "+kPjb+Zly3pWzbR99evydQa+YjYfM4Ruf9bJvqcuN1496TRPKm5Za3K83Fnl3im+morNB/wu5RpV\n",
       "NQuvS8dHCUVnf2FqdXXSndVKD3Wwmj4QfFBaqu46p3JnPGl5nYPy2X0QOrA8m1BHZrpFST139O6V\n",
       "TeWTMou7std0dz7k3vMf8NDCauC2i8dmbVN0D3for3AfOccrdelQl46yTlr5vLuh3DmPbgutYY+4\n",
       "GZey2f9HK6eahdzZ1pvlJFZp8uzLtryYUKfpNxXjptoZ9XsY/gQHGKFOlDuHuNc+YHyYlKtfPumk\n",
       "3M+/6964pfYuwN7uXOz1ddp65g2c4aHk4uPAo92rz93u3EB/p8+5Mqd1VrX69dDtT75OUq7e1tmw\n",
       "npzE2W6tCbxG5V5/0YgXSHPvy+4d5td0y9SbBgwfJTwuYtrZu4O49/dLNUtU9W+0fTZu1IsWAN6t\n",
       "TDuobkOSenlOAcx/1k04Ac8ePslQdwDUneArLhYbVU03jIe+1H7E8Dpt43Ad/RfqV1PRLH5N487X\n",
       "qH781iSsQ7cbnKq0fN2dZ9NbdJXqT5WP4BnInZUNb5bb2L9yKfDq1Iv10NfW5nSfzPArqKxSUclD\n",
       "dy5VwWrd9De5h4fau/Mi96Hbv646BPQ2LNrFnec2TcdM8G41mXTj+GT3vrpzs5oCr5mRd1y5T+1U\n",
       "mRjkNe3UciomGsiNyWX0P2cybx22IeN7knyTSrafiu/vA/BuC7JJKHO1ThvDPH/D4D6iIORcpGB0\n",
       "s0ETDuLOE917npE6Ee5s4aF/oO8TH7fkod+gpw756RrBnUcTcgCadmY56nLcfXgjAPeeeoJnAFs1\n",
       "zMmZanrMnW+Ne75DpGcPVj1X+Ajgq+480p2PtZimYWrPj8WN1jjq/rbhcOCEuP3PmunETJXFcszJ\n",
       "L8jM3b1plwtrPLPOzr5XTZFfW+l4LuFhqx8BbvFZ1Ntvto7eC/zRnXdn4y6m+0w1gHWmkK1ft7wD\n",
       "CTkk6/iQRgIxbc91n1y2fPb/c9P+nyOk4VXuY3modCvMWAQc5QN6xZfB4nb/pTu7TnMeAOv7CA8q\n",
       "nq3iMxhPdx+pW5cZEXu2v4FQZWN7CEFrNj5tq/k+noZXa4RJxS0KvGZItqNv5D561xBrAzOOBea5\n",
       "d1uPmnEpWRN3b96P2rjS5MBLplFPpOkyeszA/7S43NaCPZl5ad+bzv42jnnI+JixBHDiUyu821+W\n",
       "tlWNScUtKmqcYQq6GrmJ8AidfH8t+xWaCaN0cjkVpwH/nX1v8uy3sUoNcdpersy4vah+tMxU6Nw2\n",
       "i8R6YTe789M86IoeQ3gEmrRgovUBZKBNmN4Du9cmqU7JEho8FLol8yZRZyXnztMBzPgD8Oe5WJdB\n",
       "5qYxVX/YAjhgDPORCXOfcuezMg0qapRZz4xHEDpUfLZ7ePxGVgy3P3CPghIRERkn1fGStZoZFwAe\n",
       "W2+lwOu0lCskIiIyTpOKW1TUKHNFpwVRqvBN6CNKRERkzlCOl8wJWdHiLoQHwf6elrtWEBGRtYda\n",
       "NcraLj0s9WDiQ48VdImIyFwzNPAys/3N7DIzu8LMXl8xfpmZrTSz8+LrTZNJqqzlXhTf3zJwKhER\n",
       "kVlsYB0vM5sHnEh4/tl1wLlmdqq7X1pM+gN3P3BCaRTBnZXWm+F74wwlRUREZGTDcrx2A65096vc\n",
       "/V7gZOCgiulUd0va8Ofs8+4zlgoREZERDQu8NoeeB6JeG4flHNjLzC4ws9PNbEdEJiN/sPMNM5YK\n",
       "ERGREQ3rTqJJ5eVfAkvd/U4zOwA4Bdhh2ikT6ffN7PPAh1iLiIjMRsMCr+uApdn3pYRcrw53vy37\n",
       "/C0z+7CZLXH3m8qZmdlx2dcV7r5iyimWtZY7t5qxK/ALtWgUEZFxMrNlwLKJL2dQP15mNh+4HNgH\n",
       "+APwM+CwvHK9mW0C/Mnd3cx2A77s7ltXzEv9eMm0xQdlL3fntJlOi4iIrLlmpOd6d19tZi8FvgPM\n",
       "Az7h7pea2VFx/EnAM4EXm9lq4E7g0HEnUiSJD6ZW0CUiInOSeq4XERERKajnehEREZE5ToGXiIiI\n",
       "SEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGX\n",
       "iIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0\n",
       "RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImI\n",
       "iIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEsUeImIiIi0RIGXiIiISEuG\n",
       "Bl5mtr+ZXWZmV5jZ62umOSGOv8DMdh5/MkVERETmvoGBl5nNA04E9gd2BA4zs4cX0ywHtnP37YEj\n",
       "gY9MKK0yQ8xs2UynQUan7Te3afvNXdp2UmVYjtduwJXufpW73wucDBxUTHMg8GkAdz8HWGxmm4w9\n",
       "pTKTls10AmRals10AmRals10AmRky2Y6ATL7DAu8Ngeuyb5fG4cNm2aL6SdNREREZM0yLPDyhvOx\n",
       "EX8nIiIistaYP2T8dcDS7PtSQo7WoGm2iMP6mJkCsjnKzI6d6TTI6LT95jZtv7lL205KwwKvnwPb\n",
       "m9nWwB+AZwGHFdOcCrwUONnM9gBucfcbyhm5e5krJiIiIrJWGRh4uftqM3sp8B1gHvAJd7/UzI6K\n",
       "409y99PNbLmZXQncARwx8VSLiIiIzEHmrtI/ERERkTZMvOf6Jh2wSrvMbKmZnWVmF5vZr8zs5XH4\n",
       "EjP7npn92sy+a2aLs9+8MW7Dy8zsqdnwXc3sojjuAzPxf9ZWZjbPzM4zs2/E79p+c4SZLTazr5rZ\n",
       "pWZ2iZntru03N8RtcXFc718ws3W17WYvM/ukmd1gZhdlw8a2veL2/1Ic/lMz22pootx9Yi9C8eSV\n",
       "wNbAAuB84OGTXKZejbbL3wCPjp8XAZcDDwfeCbwuDn898I74ece47RbEbXkl3dzSnwG7xc+nA/vP\n",
       "9P9bW17Aq4DPA6fG79p+c+RF6Pvw+fHzfGBjbb/Z/4rr/7fAuvH7l4DnadvN3hfwBGBn4KJs2Ni2\n",
       "F3A08OH4+VnAycPSNOkcryYdsErL3P16dz8/fr4duJTQH1unM9z4fnD8fBDwRXe/192vIuyMu5vZ\n",
       "psCG7v6zON1nst/IBJnZFsBy4ON0u3PR9psDzGxj4Anu/kkIdWndfSXafnPBrcC9wPpmNh9Yn9Dw\n",
       "TNtulnL3HwE3F4PHub3yeX0N2GdYmiYdeDXpgFVmUGyxujNwDrCJd1uk3gCkJxBsRm83Imk7lsOv\n",
       "Q9u3Le8DXgv8NRum7Tc3bAP82cw+ZWa/NLOPmdkGaPvNeu5+E/Ae4GpCwHWLu38Pbbu5ZpzbqxPn\n",
       "uPtqYKWZLRm08EkHXqq5P4uZ2SJChP4Kd78tH+ch31TbbxYys6cBf3L38+jvvBjQ9pvl5gO7EIon\n",
       "diG0Bn9DPoG23+xkZtsC/0oohtoMWGRmz8mn0babW2Zie0068GrSAavMADNbQAi6Puvup8TBN5jZ\n",
       "38TxmwJ/isOrOsm9Ng7fohhe2XmujNVewIFm9jvgi8CTzeyzaPvNFdcC17r7ufH7VwmB2PXafrPe\n",
       "Y4Afu/uNMXfj68CeaNvNNeM4V16b/WbLOK/5wMYxZ7TWpAOvTgesZraQUPHs1AkvU4YwMwM+AVzi\n",
       "7u/PRp1KqChKfD8lG36omS00s22A7YGfufv1wK2xRZYBh2e/kQlx92Pcfam7bwMcCpzp7oej7Tcn\n",
       "xPV+jZntEAftC1wMfANtv9nuMmAPM1svrvN9gUvQtptrxnGu/N+KeT0T+P7QpbfQouAAQqu5K4E3\n",
       "ttmaQa/abfJ4Qt2g84Hz4mt/YAlwBvBr4LvA4uw3x8RteBmwXzZ8V+CiOO6Emf5va9sL2Jtuq0Zt\n",
       "vznyAnYCzgUuIOSabKztNzdewOsIgfJFhErVC7TtZu+LUCrwB+AeQl2sI8a5vYB1gS8DVwA/BbYe\n",
       "liZ1oCoiIiLSkol3oCoiIiIigQIvERERkZYo8BIRERFpiQIvERERkZYo8BIRERFpiQIvERERkZYo\n",
       "8BIRERFpiQIvERERkZb8f1+G7Jqa1IVJAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10adb9d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JFV5+PHvOzMMi+yiyDKAyiAQEVAEZNFxh1FBI1Hc\n",
       "xSQuEReMSvSniNFE4x40Ki4YxAUXFCVi3EfcQBQYUQEhRsMiiCCooMLI+/ujTs+tW9Pbvbe77jLf\n",
       "z/PU012nTlWdqlO3+72nTp2OzESSJEnjt2i2CyBJkrS+MPCSJElqiYGXJElSSwy8JEmSWmLgJUmS\n",
       "1BIDL0mSpJb0DbwiYqOIOC8iLoqIn0bEG3rkOykiLo+I1RGx73iKKkmSNL8t6bcwM/8UEQ/OzFsj\n",
       "Ygnw7Yg4JDO/3ckTESuBXTNzeUQcALwHOHC8xZYkSZp/Bt5qzMxby9ulwGLgxkaWI4BTS97zgC0j\n",
       "YttRFlKSJGkhGBh4RcSiiLgIuA74Rmb+tJFlB+DK2vxVwI6jK6IkSdLCMEyL1x2ZuQ9VMPXAiFjR\n",
       "JVs0VxtB2SRJkhaUvn286jLz5oj4ArAfsKq26GpgWW1+x5I2SUQYjEmSpHkjM5sNSzPWN/CKiG2A\n",
       "NZl5U0RsDDwceG0j2+eBY4HTI+JA4KbMvK7b9sZxABq/iDgxM0+c7XJoeqy/+c36m7+su/ltXA1G\n",
       "g1q8tgNOjYhFVLclT8vMr0XEcwAy8+TMPDsiVkbEFcAtwDHjKKgkSdJ8N2g4iYuB+3ZJP7kxf+yI\n",
       "yyVJkrTgOHK9hrFqtgugGVk12wXQjKya7QJo2lbNdgE090RmO33eIyLt4yVJkuaDccUttnhJkiS1\n",
       "xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSp\n",
       "JQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJ\n",
       "LTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJ\n",
       "aomBlyRJUksMvCRJklrSN/CKiGUR8Y2I+ElE/DgiXtglz4qIuDkiLizTq8ZXXEmSpPlryYDltwPH\n",
       "ZeZFEbEp8MOI+EpmXtLI983MPGI8RZQkSVoY+rZ4Zea1mXlRef8H4BJg+y5ZYwxlkyRJWlCG7uMV\n",
       "EbsA+wLnNRYlcFBErI6IsyNiz9EVT5IkaeEYdKsRgHKb8dPAi0rLV90FwLLMvDUiDgfOBHYbbTEl\n",
       "SZLmv4GBV0RsAJwBfCQzz2wuz8zf195/MSLeHRFbZ+aNXbZ1Ym12VWaumlapJUmSRigiVgArxr6f\n",
       "zOxXiABOBW7IzON65NkW+HVmZkTsD3wyM3fpki8z075gkiRpzhtX3DKoxetg4KnAjyLiwpL2SmAn\n",
       "gMw8GTgKeF5ErAFuBY4edSElSZIWgr4tXiPdkS1ekiRpnhhX3OLI9ZIkSS0x8JIkSWqJgZckSVJL\n",
       "DLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJa\n",
       "YuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLU\n",
       "EgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKk\n",
       "lhh4SZIktaRv4BURyyLiGxHxk4j4cUS8sEe+kyLi8ohYHRH7jqeokiRJ89uSActvB47LzIsiYlPg\n",
       "hxHxlcy8pJMhIlYCu2bm8og4AHgPcOD4iixJkjQ/9W3xysxrM/Oi8v4PwCXA9o1sRwCnljznAVtG\n",
       "xLZjKKskSdK8NnQfr4jYBdgXOK+xaAfgytr8VcCOMy2YJEnSQjNU4FVuM34aeFFp+VonS2M+Z1ow\n",
       "SZKkhWZQHy8iYgPgDOAjmXlmlyxXA8tq8zuWtG7bOrE2uyozVw1dUkmSpDGJiBXAirHvJ7N341RE\n",
       "BFX/rRsy87geeVYCx2bmyog4EHhHZq7TuT4iMjObLWOSJElzzrjilkGB1yHAOcCPmLh9+EpgJ4DM\n",
       "PLnkexdwGHALcExmXtBlWwZekiRpXpiVwGukOzLwkiRJ88S44hZHrpckSWqJgZckSVJLDLwkSZJa\n",
       "YuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLU\n",
       "EgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKk\n",
       "lhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIk\n",
       "tcTAS5IkqSUGXpIkSS0ZGHhFxCkRcV1EXNxj+YqIuDkiLizTq0ZfTEmSpPlvyRB5PgS8E/hwnzzf\n",
       "zMwjRlMkSZKkhWlgi1dmfgv47YBsMZriSJIkLVyj6OOVwEERsToizo6IPUewTUmSpAVnmFuNg1wA\n",
       "LMvMWyPicOBMYLduGSPixNrsqsxcNYL9S5IkzUhErABWjH0/mTlMYXYBzsrMvYbI+7/A/TLzxkZ6\n",
       "Zqa3JCVJ0pw3rrhlxrcaI2LbiIjyfn+qYO7GAatJkiStdwbeaoyIjwMPAraJiCuB1wAbAGTmycBR\n",
       "wPMiYg1wK3D0+IorSZI0fw11q3EkO/JWoyRJmifm7K1GSZIkDcfAS5IkqSUGXpIkSS0x8JIkSWqJ\n",
       "gZckSVJLDLwaIrh/BI5DJkmSRs7Aa10nA1vNdiEkSdLC4zheDREkQCZzvqySJGk8HMerZRFsN9tl\n",
       "kCRJC4uB17ouLa/bz2opJEnSgmPgta47U/3m5A6zXRBJkrSwGHjVRBBUHes/Buw8y8WRJEkLjIHX\n",
       "ZFsAfwR+Duw4y2WRJEkLzLwLvCI4KmJ05Y7gQRFkBJsA3wM2A34DvDyC145qP5IkSfMu8AI+Bfxl\n",
       "hNtbVV4PAnYv7zcrrydE2PIlSZJGY16N4xXB1sANnfmZjrUVwR2wzjYOBW4Hzi3z12dy15nsR5Ik\n",
       "zS/rxTheEdxlQAvTqxr57zTN/dxcBkrtnNBVtcWXZ3IeVfAFcJfp7EOSJKlpTgVewK+BKyPYorkg\n",
       "ghOA44Av15KnPMhp2fbmtaTfAT/qzGRyXXldOtVtS5Ik9TNnAq8Itq3N7t4lS6ej+0XAYeX9wRFr\n",
       "+2MRwUYRvGTArk5ozN+PRktazV5lu0cO2ObIRRARbNr2fiVJ0vjMmT5eEexNFVR1vAb4d+BNwLNr\n",
       "6V/J5BGd31TsyCQieDDwdWBxJnd02UfA5PR+/cQi2BD4E3BbJhvW0nem6vt1a691ZyqCY4BTgEWZ\n",
       "tFNJkiQJWD/6eB0HXAv8c5l/LXATk4MugBd3W7kEYl8vs28uQVbTy8rrkcAzgBf1K1Amfwa+CHyr\n",
       "tp83A78Abum3bqNsW0ewzxTy70MVdAE8fNj1JEnS3DYnAq8IfkYVCN0NuKBHthsyiUx+WubvBPyk\n",
       "R96XAE/pkv5v5fX6TD6cyUlDFO9tpYwPiODDwD/Wyv2CMgbYbmV+aZm/LILX17ZxEXBhv51EsGft\n",
       "1uKptUVfiuCtQ5RTkiTNcXPiVmPttuHpwHuAb3bL1+u2YATnAgeU2b8Ai8v7JZkTY35FcCnVU4p3\n",
       "raf3LzeHAufUkj4GPLmR7fxM9o9gB+CqWvp+mfywc3wDbmsm8D/AcqpWv0n9zmY6dIYkSRregrzV\n",
       "GMExETytzP4B+Gwm51C1Zm1L9ZTjHcBXmWit6ubt5fVvM1nCxO3KNRE8MoLNSmDzs5JnKgOw/rIx\n",
       "/zDgeY20+5fX/26k/6AEYwBEsHF9YQTLIvhRBL8pSfekOt5XAa9o5I3SmnboFMouSZLmkFlr8Spj\n",
       "cP2hlmVGncgjWJbJlbX5m2DtsBT7AT8o75+QyaemuO1mud4EvHyItKb9gF9m8psItgR+2yfva4BP\n",
       "AJeW+WOBd4GtX5IkjduCaPEqA6Quj2A74F/qy2b65F496Cq2rr1/Yu39qmnuov4E4ztr7w8qr52g\n",
       "6+lU53V5Y/3vUAV/15f5QS1Xb4dJx/SuoUsqSZLmpLZvNX6B6nbfNUx+ovCNo95RGU6ic5vvZbX0\n",
       "67uv0dfxwOHAHsDumVxV2+a5jbxfzCQzuaKRfnBjfg/g6vJ+T5g0ZteiTH5fhqvYh8ZvU5bbjncu\n",
       "w11ogYpghx5P50qS5qm2A6+7NeZfQNVi9Lpx7CyTa2DSk4v3nuZ23pTJOZlcmsllJe0t5SnLBA6p\n",
       "Zb+p9r7T9+u7wEc7iREsp+qz9uqyjUsyuYUq+Nq53vqXyerSb2074JiSvBnwG+A/pnM8mvsieBbV\n",
       "gxoOJyJJC0jbgdeyxvzpmXxvnAORZvIi4GbgDZk9h5+Y6T6+QzUGGZmsqaX/gKq17AlUQWbHz8rr\n",
       "1bU0Mrklk//rsY9rgdPKbCeA3WPGhZ9lEewTwd1HvM2NI/h6BAeX29sZMelnouaDD5bXLWe1FKxt\n",
       "Yf1/tr5pVCLYOWJSd5BRb3+TiLX/+EpzStuB1x9Lx/CXAisy1z7NN27bAP9vnDvIZLtund5La9nV\n",
       "mfy2y/KvTHEfnVuO7y2vG8OkJx4fNuWCz6IInkI1vtnPI0Z6LT4JeDBV0Pvrkray7PPgiHVaXuey\n",
       "4zpvIjiw1HNGsEE9UwTblfQp/37pEO4JvB64zxi2rTkggvuO+G9wkF8AN0RUP8s2Bi8Fvj+mbUsz\n",
       "0nbg9SqATN6a2X2srnHIZM0c+tmdvcvrzjMo04PL674RPJqqRQ2mGMjNAR+ovb9rc2EEiyLYsd8G\n",
       "Itgmgns2kjv96R5TS/t4ef028KsINpyrLTi1/9Svh7XBVlA9OdtxW8SkfoOd1tznltaEHHTupqAz\n",
       "DMp7I3jgiLapueWHwK0Ra8dAbEu33+WdkQhewMRv+9bT3x7BlyPYddT7lKZiYOAVEadExHURcXGf\n",
       "PCdFxOURsToi9u2zueaYWOudTH5U+nV1vaU4hE4/r05LzllUA88CVRP7TMrXss8ycUvtJxHsFMGD\n",
       "ItiqpB0OXBmx9qegJinByPWwzoMMz+qRv/4k6QnAHbPxA+hD+Ex5PbCWdgvrPgn77Qj2juAzsPac\n",
       "nQD8Z3l/7HQLEMH2EWuD4c4toQPx6doFJ4Kl5e2GMNFVoiWbDs4yZWv79UbwvdrxvZiqz+TlZdlr\n",
       "I+j3fSWNxTAtXh8CDuu1MCJWArtm5nKq31V8T59t/WJKpVM3nyivZzfSby6vb4ngSS2WZyaOpPot\n",
       "zHcAN1IF5qtg7S3ow8vrg3s8wXlMfSaCTSPWDlPytdqiTgBT/wWCV5bXM7sVLILFEew0xDGMQ6el\n",
       "qj6cSKfV6ahG3ouAxzXSVpTX4yPWvp+qq4HrIrgHk4dg2SuCbUtr5AmzeI40Oo+tz7TUIvTn8nrK\n",
       "mFueDwQOiWD7emIE11L9k9LrJ+qksRkYeGXmt+g/0OcRlN8WzMzzgC0jYtseeX/WI11DyuSPVLec\n",
       "3g3cubaoM27Y84CPlc7lD5tuv6/S5+OacfX7KNvdhCpwuAAmfdgviuBjwPNraZOuqah+1/KDtfnX\n",
       "UA1Q2wmo1n6ZZHLegLJkl8DuVOCXEePpG1gCu0Xlv+7Plta+RRFrA+gdM7m99Atc+zRuJmf02eze\n",
       "XdKm/CRvo1Ny5/h/XUu7lmqIk9dSnaPnRnBoRO9/0DSndf6Z64xFOK5+VwBE8EaY9Pd25155a+ts\n",
       "FNH310v6+UcmP8h0MbXPk4ixtLpJvWUZdKrfBOwCXNxj2VnAQbX5rwL365Ivh9mX0/ATZEBmdWoT\n",
       "yD915hvTLpDfnOK26+svHUPZTy7b3gjyyNq+ft/Y9/0g/wD5hLLeYsj3Q/5TWX52Le8JjfPxD5Bf\n",
       "Ku8/B/lRyNW1dU+qrfsVyMW18n2hvq0xHP8vIT/RONZP9ton5Gsg31Lefx3yuZDPhDyxccy/LfPP\n",
       "nE75Ie8P+ZYu19BJkEshL+txjXWmJZD7QMZs/32sbxPkwyFfMY31zix/U9vV6nHXMZazs48Hltc9\n",
       "B+RfNOy1DLlXyfvPPa7Pg7ulz3bdOc3NaVxxy7A7HxR4HVyb/ypw37YOYH2fII+D3Km837N8kDyt\n",
       "x4fOAyAPGGKb94D8VX29MZT7LZCnl/cra/ta1PxArM1vCrlT45he3uU4Bx5jrRyH1dZ7LOQTIDdr\n",
       "bO9eIzzuT0FeMSB4eeE0trtReV3KRJD6trK9xUNu464l/58b5Xkf5NYlz5a19Of3OYYXzPbfxkKa\n",
       "IDeB3GpAntvLud8K8qQht/uAzmdGmR97MNL42/425IoB+V9YK9ceA/K+s+TbvMzvUFt3i8bnyyYG\n",
       "Xk79prkceL0XOLo2fymwbbcDAE6sTStm+6QuxKl8STYDh/r0pwHrL+qx3r8Pse91vuCpWp02aKQd\n",
       "CPnlWoAQVC1R/1rL8wHIo8v71aUMn+9SrqUlIOu0Fr1sGufstEYg8e7yuqa2n38sr7tRtfrsPs36\n",
       "6RdwjfxLoGzzzkPm3a9Wjjf3Kk9J/2qptwf0OI6B14vTlOqx05K5aZ88X27UwT1qy5Y2/w5rdZmQ\n",
       "9+lyDSwaw3EshrwDcpsy/9myr+sgl/RY5+21Mp3dZ9tLm9cs5AZd0uqB34WQ1812/TrNjYmqf2w9\n",
       "Tsmx7GfIwvQLvFYCZ5f3BwLn9sg3lgNw6lVneTDkQT2+FO/SZ70DavkC8rZhAoLygZqQW9bStihp\n",
       "x5X5zRvluM8UjqfbcTy4S7mnfIsLckWP7S+C/Jcey26D/Ktp7KtngFLmTxnxdZCQ67RAN/Ishdwd\n",
       "8vGQV3fK1Sfwuhvkxl2O6avl9cv14+ikzfbfxHyeSmDSOc8blLQDqbXGQp7e5fraoPxtXgN5Sa/r\n",
       "sUv9JuRNYziOnSB/VZu/tlbW93XJf3KXY+r6Nw55a1m+sssxHt2Y79y23x7ymmkcx79B7j/b18V8\n",
       "nCA3hnwrpRV9Lk+zFnhRjX90DXAb1VNWzwKeAzynluddVI/0r6bLbcZxHoDToPrL93YLHPrk/+t6\n",
       "nsZ6K/us12nSfzPkPiXtySXtKdRaUGrTxlM4jjfU1rvTGM5Ts2yXlvRlPQKvhPzkFPfxnC7beHRt\n",
       "+X2mck6mcFwfHJDnG7XydG4zLqPqq3XwEPvYgur2dJSg63jIqyD3pWqN7Gz7EMjtemzjQMhd2vzb\n",
       "mE8TVb++znncm4luBUl1i3y38v79jevrN82/e8i/KfN/7HV91NbZfITH8Ojm5w/k3zXKu7hHOZ4F\n",
       "+aLy/ndl2Z1q+VY0t11b9ntq/3xQ3S5f0tkG5K3l/VC35Ovlmu3rYj5OkDfU6nX72S5P/7Iyljqe\n",
       "9wfgNOi85+GND7b/g7yoT/5OvgeV+UNrH9Tv6bPepNa1knZMj4DlU1P90KLqtD22DzuqjskXUXVi\n",
       "TyZuhXQeYNgacpvy/ofl9UODylx7/6we5+KRY67/zn4267LsgVR9BCeVaQT7fHqPY61fGzt3vkAb\n",
       "5Vw+zvMx3yaqALjTB/JjtfP04B7n9wXl9VU9lj+qS9o6LeCjvB5q2zyxuU2qFrndmXiYZbuS/k2q\n",
       "gHLt5xGTu0F0/tHr9D28tMx/ZIplCqouBVuX9RfVlh0M+Ywu+d8xzs+ihTxBPqbHdTny29rTKFvn\n",
       "O2bpRBpjqeMWD2o8B+A06LznYshH1i7wR0CuLsvOg3xyI39CvqnLdjrrb9hl2SN6fLme2OOPbGPI\n",
       "h03jWO7FNPpwTXEfm0Ee0mf5XcvrYyG/W/5Y17n1UfsjfmTj/L2/TE+DPJoxtN41ylH/go6S9nGq\n",
       "1qhmvbxyRPu8c49670wfZiIQPYTJrWJr2vi7mMGxda3vMe0rGudt2wHnNaluGx/A5BaxhLygzzq9\n",
       "+laNLLigenq5s791+lQx0dH9AVStUM0y7lHydR4A+UN5vS9Vv7T3QJ5LravDFMr229p+9q2lX988\n",
       "/kYd/A/kJiOs7w0g7z3b13iP6/C/RnHdM/HE9GXlc6BzLlvtE1q+S/ZvpN1cyrLfRBo5lv23d6Dj\n",
       "OQCnqdbD2sepH1peTyvpf8XEMAvrdOCtfYEf0UjfuPbH84HaF/r5kB+iGvags/z5DHHraj5MTO6E\n",
       "nF2Wf6i2vB74/s0slLWz73fXvjhurZcf8ql0Caqnub/mAxpP6vJF+sva+2an8LENZTDD43pRrYxj\n",
       "D77K3+Ska4zJrUBJ1S+vW9CwtH4+qYLbl9XSFte322P/nSeGuwZmUzyWfy3bOrvXuYO8suS5qnGM\n",
       "D6mv01j2uNr7Z0+zbDfVr9WStnVjP53pez3St6qd87tPYd+Ly+srats6oI3ra8jyLamVa8a3Bctx\n",
       "nlXe1/8p/HnLx9UJshaVv4X6Pznfn8hHjmX/7R3oeA7AaTp1kfUPjJuYeGJv0Afx+VTjQ21X+yBd\n",
       "+0Va8jT/S39M+eAc+sNoPkw0Wh/6nN/mNPQDBSMs61Zl391aPZ5El6fdRrDPl1AbJqD2Qddvemft\n",
       "fdeHdGa5zutlXTZE/m0owzQ00vdliI7FVK2BV0PeBfKwRl0mE8PIdIKojRrrfxLymY205zMxjMtD\n",
       "GDDsR9lu85+tezDFIJ2JPmo7D3l+O9PHBuT7aO39tIYwqa3/NsgT+pRl2Onj07ym6lPfB2JavObv\n",
       "UivTa2a4rW0gT4H8+zJ/77LdHzc/Q8d8TN1a5C9pzF8NeScDL6cR1sWkL7h1pj7rnd1nvbvW8tXT\n",
       "d5jt4x3jefyPcox31N6fXzv2vRrnYqy3FQeUtVvfije0uP9FVK2szUFjJ113w1yHs3T+ljbK+2YG\n",
       "tEow8UReZ5iSSX3qSp6eT8ZCHgV5Rpf0ThnqrUBjaSGp7etRZb4zjt463REGbOckyN8Pua+kGk9v\n",
       "xyHy1aeNplKmLtt7FlVL9Rv67COp+p/1GqB1Stdul3UvKq+fZQQtjSOo/90b5ZtWX6za5+MttWtp\n",
       "MdUt4kPKsscxolb3PuUIGg+cNKbG5xND1+WUytFeBY7nAJymUxc9h5no+0QdE7cnm9NzG/m2grwY\n",
       "8tWzfawtnMsdepyTpWX546ke5R/p04rTKGd94NORPak2zbI0B8F9DBO3XB4+1S+vlsr8tVKu+n/L\n",
       "PZ/yLev0+/JOJm7Ddx1tHvJYyP/okr47LT0NRu0fiTLfGfz3jFqeRVS3028s87+DPKixnfMgHzfE\n",
       "/jq35R/VJ89GVC3O/1nyXgx5txkc4wqq2/CPpPoFi06Xiy8y0aL2xObnJNWDR9MOvJh8Gy8hX1vS\n",
       "vlPmXz6C+uv8rR1aSwuqhy/qv9SxOeRDuqz/KKqxzr5dK2fPIB/y9SX/slraLo3j3K+xzn6N5VP+\n",
       "9YUhzsO9qAK95lO0zakxBiZD1eWUyzOOjXY/8PEcgNNM6iQ3Z+KR8vcPuU7notyAqmPryEZ1n69T\n",
       "lz/e9852mfqUtetwDrNUluj2Ic5EH7FOp/uR/3LCDOo4IHcs78/pk/8uXa6LnlOPbbyeWf7nhYnW\n",
       "iGTyeHfnUD1p2Bnc+H2dYKGW5wPlfO1NNUzJULfZyxfxsL+2kJBfHNGx1vvU/WdJ2xByi/L+AZCX\n",
       "97k2bmHi6cy9hrj2O+stpXZngIl/cIf69YE++9i1to//raV3+uHWB9j9UbfrEPIMqtbKenmP7LG/\n",
       "+gMUnWl3JsYG7ExbNdbbisnj1CXkR8rrjJ92ZOKnqY6nutXZ2ccqqhauzlAsDy/5a/2WWeecjORa\n",
       "G8dGux/8eA7Aaab1kkH1BNSwH3RX9fqiWJ+n8gHdGfF+6PGAnHqez+YH+MA+VWMsSycAPL5L+e5K\n",
       "NWxKNNbpjIe3F+R/Q74a8ufly3kbqtas+vE9ost+P0DpDzPLdbFbo6wv7lI/vTqd1/tCjvzWGdVP\n",
       "m43kljmTW4VPm8J6W1G1qCyrXSuXDlhn7W9G9lh+Pn0C+x5l+HR5fwdVP7ybGnXRGSLn4kb6bbVA\n",
       "p94K1vnZuO+W+c4t85N7lKFb/deHlvlCv+8OqvEem+v3bVUe4rx06891Tvm8XvuPH40HyljbSkfP\n",
       "8s6oXOPYaPcTMJ4DcGp3KhfsyB6hXkhT+UJt/anFhTh1+bB8/CyW5fjmFwbr3mKut1isHQ5hwHZf\n",
       "BnlWr7wlfVpP6o2xPs5j3Qdo+k1/N8y5mEG5FjGi/m2N45p2kEjVBywh79/jHG5Wy7POz+uVvJ+b\n",
       "yjlj4pc7/qa2nw+W185DNf8K+dMB9fWGsr36U507N4+hy/579Xm7jKplKYepJ6rx/ZrbuAtVq9v9\n",
       "u5WBqlXtL122tUmPMu025Dm9p4GXk5PTejMxMUxCp89Pt5+TuUdZ9uQxlqNzu+b0LsvqH+a31NK/\n",
       "WNKGarFgYhy85WU+mPjZnlntj1cr44FUfRW3LPM3UD0R2+yvl0wMalofRf+Js30MQx7n6pkGiVRP\n",
       "fq8NDvoFOn228YwpBl7dBsZNyOf1KEOvAZ07ZX5StzLW6vSvamn7UwbFphrkd2Oqlt7/KmmX0+jz\n",
       "N+BYOmV5eJfyNX927lO1982neputsI+kCniXDl8WZnQt9Nxuexf0eA7Ayclp4U0l+Hglk1sh7sHE\n",
       "cAor6x+qY9j/No0P7XV+l4+J2xinQH6mlv7pkt5zIN4u2+rsZxuqvlNjOa4x1dXzqDqEb0LtFxKo\n",
       "+qjNm+MoZf7mCAKvDWr1eXyfwOvQPtvoXPcDH8qhegrz+z328ZSS53W1tH8u238r1c+YdYKXd5XX\n",
       "vSBfCvm2PuV6CeTy2jprg7xa3no/x72ncP6O6dRBl+NZ0+d8JlUL6N5Ug3f/uKTdMP26ZCzXbrm/\n",
       "OX4RkZkZrexM0oIRwdOBU4GnAB/tke1ewH2ApZl8LIJFwN6ZXDjNfT4HeG8t6c6Z3Ngj78OBLwOL\n",
       "gDuA64GVmfxgCvvrfBDfCmzSSc9k3n5mRrA5cDPwx8yJY5rLItgG2DyTn89wOw8FvjogW89rqmwj\n",
       "gddlckIEi4E3AOdk8l8RLM7kLxFsBvyuseobgX+Cieun/D28Erg8k0809rMY2DqT62vX4fuA1Zm8\n",
       "u0u5/ggidVMVAAAK10lEQVRs1KXIR2VyRpdjAFiUydDBRgSLMrkjgoOBbw+7HvBM4CDg2WX+2cCp\n",
       "mdw2hW3UyjGeuGXRqDcoSSP2UarAa8cuy55eXi8DPgV8tHzYvwS4IIJdprnPetC1vN8XJBNfDEeW\n",
       "17uU8kxF57O4E6CcCGw8xW3MKZn8DrgzsOtsl2VYmfxmpkFX2c7XuiSvLIHQXYH7DrimOl4dwX7A\n",
       "R4CXAWdFcB6wJoK9mRx0fa68rgaWlKlTnjsyeX0z6CrL/pLJ9WX2HcAXqP6J+WmPMv19l7T3AZ/t\n",
       "kv5E4N5TCbo65S2v3ynnbIva4qXAUeX9n4HbgZ3K/AYwaV/nTjfoGidbvCTNeRF8GHhamf1sJn9d\n",
       "W3Y+sF+PVa/IZPkU97Uh8KfO/DCtTiXY+x2w+bDrdNnG44DPUH2xfSiTv0x1G5o7IngJVevLS4GV\n",
       "wIcz+cMU1n8s3YOZXrak+ufkskzWTKWstX2uAF4H7A7cJ5Nfdclzb+DiMntEJmdNZ1/TKNvdgIdn\n",
       "clqZ3yKTm2vLPwE8obHaVpncNP19jiduMfCSNOfVb/11C2oiCKrbH7c2Fn08kyfX8jwe+EznP+oe\n",
       "+3oJ8FaqVqglmdw+RPk6H6RfB96byacGHpTURwRLqVp0OpYDJwGHd8ne97blFPZ5D+B/ymzP24MR\n",
       "HAu8k+p2/o9mut9RiOCpUAVlVIHj9pl8Y2bbNPCStB4rwc2pmTyzT54VwLbA5VSB2Dsy2b+2PsAD\n",
       "Mjm3x/oHAd+BqbVa1ba9ceZEa5k0U/V+UsBxVP8UbALsBZxHl75VM9jX2mBv0PUfwXKqFuV2gogB\n",
       "ItiY6h+vGzLZZjTbHE/csmRwFkmafcMEQpms6rwvHY/vH8ERwLJatn4dvbecZvE2BJ5u0KUxuCfV\n",
       "bb8E3hbBO0qL7fdhtA9fZHJbDLnFTC4f5b5nKpM/RrBPJqtnuyyD2OIlacGqtRbUXUzVWnA68LeZ\n",
       "E7cnI7gG2I7q6ciBtxilhaY8kHJrJr+e7bLMNp9qlKSpe2eXtL3K69HAOQARPDKCF1IFXa816NL6\n",
       "KpNfGHSNly1ekhasMkbRGqpxtl4BbMW64ysdDnyxNr91Jr9tp4SS5io710vSNJTgKztPMpZBMv8I\n",
       "7E/1FGLTlAZ7lLQwGXhJ0ohFsAZYDBxK1TL2o3qfL0nrLwMvSRqxCA4BvgVsOBdHuJY0ewy8JEmS\n",
       "WuJTjZIkSfOcgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0ZGHhF\n",
       "xGERcWlEXB4Rx3dZviIibo6IC8v0qvEUVZIkaX5b0m9hRCwG3gU8DLgaOD8iPp+ZlzSyfjMzjxhT\n",
       "GSVJkhaEQS1e+wNXZOYvMvN24HTgyC75/CkgSZKkAQYFXjsAV9bmryppdQkcFBGrI+LsiNhzlAWU\n",
       "JElaKPreaqQKqga5AFiWmbdGxOHAmcBuMy6ZJEnSAjMo8LoaWFabX0bV6rVWZv6+9v6LEfHuiNg6\n",
       "M29sbiwiTqzNrsrMVVMusSRJ0ohFxApgxdj3k9m7USsilgCXAQ8FrgG+Dzyp3rk+IrYFfp2ZGRH7\n",
       "A5/MzF26bCsz075gkiRpzhtX3NK3xSsz10TEscCXgMXABzPzkoh4Tll+MnAU8LyIWAPcChw96kJK\n",
       "kiQtBH1bvEa6I1u8JEnSPDGuuMWR6yVJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJ\n",
       "LTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJ\n",
       "aomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJ\n",
       "UksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksGBl4R\n",
       "cVhEXBoRl0fE8T3ynFSWr46IfUdfTEmSpPmvb+AVEYuBdwGHAXsCT4qIPRp5VgK7ZuZy4NnAe8ZU\n",
       "Vs2SiFgx22XQ9Fl/85v1N39Zd+pmUIvX/sAVmfmLzLwdOB04spHnCOBUgMw8D9gyIrYdeUk1m1bM\n",
       "dgE0IytmuwCakRWzXQBN24rZLoDmnkGB1w7AlbX5q0raoDw7zrxokiRJC8ugwCuH3E5Mcz1JkqT1\n",
       "xpIBy68GltXml1G1aPXLs2NJW0dEGJDNUxHxmtkug6bP+pvfrL/5y7pT06DA6wfA8ojYBbgGeCLw\n",
       "pEaezwPHAqdHxIHATZl5XXNDmdlsFZMkSVqv9A28MnNNRBwLfAlYDHwwMy+JiOeU5Sdn5tkRsTIi\n",
       "rgBuAY4Ze6klSZLmocj07p8kSVIbxj5y/TADsKpdEbEsIr4RET+JiB9HxAtL+tYR8ZWI+FlEfDki\n",
       "tqyt84pSh5dGxCNq6feLiIvLsn+fjeNZX0XE4oi4MCLOKvPW3zwREVtGxKcj4pKI+GlEHGD9zQ+l\n",
       "Ln5SzvvHImJD627uiohTIuK6iLi4ljay+ir1/4mSfm5E7DywUJk5tonq9uQVwC7ABsBFwB7j3KfT\n",
       "UPVyN2Cf8n5T4DJgD+BNwMtL+vHAG8v7PUvdbVDq8gomWku/D+xf3p8NHDbbx7e+TMBLgI8Cny/z\n",
       "1t88majGPnxWeb8E2ML6m/tTOf8/BzYs858AnmHdzd0JOBTYF7i4ljay+gL+AXh3ef9E4PRBZRp3\n",
       "i9cwA7CqZZl5bWZeVN7/AbiEajy2tYPhltfHlvdHAh/PzNsz8xdUF+MBEbEdsFlmfr/k+3BtHY1R\n",
       "ROwIrAQ+wMRwLtbfPBARWwCHZuYpUPWlzcybsf7mg98BtwObRMQSYBOqB8+suzkqM78F/LaRPMr6\n",
       "qm/rDOChg8o07sBrmAFYNYvKE6v7AucB2+bEE6nXAZ1fINieycOIdOqxmX411m9b3g68DLijlmb9\n",
       "zQ93B66PiA9FxAUR8f6IuBPW35yXmTcCbwX+jyrguikzv4J1N9+Msr7WxjmZuQa4OSK27rfzcQde\n",
       "9tyfwyJiU6oI/UWZ+fv6sqzaTa2/OSgiHg38OjMvZN3BiwHrb45bAtyX6vbEfameBv+negbrb26K\n",
       "iHsCL6a6DbU9sGlEPLWex7qbX2ajvsYdeA0zAKtmQURsQBV0nZaZZ5bk6yLibmX5dsCvS3q3QXKv\n",
       "Kuk7NtK7Dp6rkToIOCIi/hf4OPCQiDgN62++uAq4KjPPL/OfpgrErrX+5rz9gO9m5g2ldeMzwAOw\n",
       "7uabUXxWXlVbZ6eyrSXAFqVltKdxB15rB2CNiKVUHc8+P+Z9aoCICOCDwE8z8x21RZ+n6ihKeT2z\n",
       "ln50RCyNiLsDy4HvZ+a1wO/KE1kBPK22jsYkM1+Zmcsy8+7A0cDXM/NpWH/zQjnvV0bEbiXpYcBP\n",
       "gLOw/ua6S4EDI2Ljcs4fBvwU626+GcVn5ee6bOso4GsD997CEwWHUz01dwXwijafZnDqWSeHUPUN\n",
       "ugi4sEyHAVsDXwV+BnwZ2LK2zitLHV4KPLKWfj/g4rLspNk+tvVtAh7ExFON1t88mYC9gfOB1VSt\n",
       "JltYf/NjAl5OFShfTNWpegPrbu5OVHcFrgFuo+qLdcwo6wvYEPgkcDlwLrDLoDI5gKokSVJLxj6A\n",
       "qiRJkioGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIkteT/A27RYAUi\n",
       "w9tbAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aafdfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHnBJREFUeJzt3Xm4ZFV57/Hv23TTDI00hJluaBRQUKOAAirKEVGh1cYo\n",
       "ChiMolGDIgSvBgfuBXJzJU5RwahoRAkOYNQgPMEIKo1TAiiDyCREVAZpjAwqXBTwzR97ne5NdZ1T\n",
       "p7urVp06/f08z3pO7b1X7b2qVlWdX609VGQmkiRJGrxZw26AJEnS2sLgJUmSVInBS5IkqRKDlyRJ\n",
       "UiUGL0mSpEoMXpIkSZVMGrwiYr2IuCQiroyIayPi5AnqnRIRN0bEVRGx22CaKkmSNNpmT7YwMx+I\n",
       "iGdn5v0RMRv4bkTsk5nfHa8TEYuBHTNzp4jYC/gYsPdgmy1JkjR6eu5qzMz7y811gXWAuzqqLAHO\n",
       "KHUvAeZHxJb9bKQkSdJM0DN4RcSsiLgSWAZclJnXdlTZFrilNX0rsKB/TZQkSZoZpjLi9cfMfDJN\n",
       "mHpWRIx1qRadd+tD2yRJkmaUSY/xasvMeyPi34CnAEtbi24DFramF5R5jxARhjFJkjQyMrNzYGmN\n",
       "TRq8ImIz4KHMvCci1geeC5zUUe1c4CjgrIjYG7gnM5d1W98gHoAGLyJOzMwTh90OrR77b7TZf6PL\n",
       "vhttgxow6jXitTVwRkTMotkteWZmfjMi3gCQmadl5vkRsTgibgLuA44YREMlSZJGXa/LSVwN7N5l\n",
       "/mkd00f1uV2SJEkzjleu11QsHXYDtEaWDrsBWiNLh90Arbalw26App/IrHPMe0Skx3hJkqRRMKjc\n",
       "4oiXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUG\n",
       "L0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6S\n",
       "JEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmS\n",
       "KjF4SZIkVWLwkiRJqmTS4BURCyPiooi4JiJ+HBFHd6kzFhH3RsQVpRw/uOZKkiSNrtk9lj8IHJuZ\n",
       "V0bEPOCHEXFhZl7XUe/izFwymCZKkiTNDJOOeGXmHZl5Zbn9O+A6YJsuVWMAbZMkSZpRpnyMV0Qs\n",
       "AnYDLulYlMDTI+KqiDg/InbtX/MkSZJmjl67GgEouxm/BBxTRr7aLgcWZub9EXEgcA6wc3+bKUmS\n",
       "NPp6Bq+ImAN8GfhsZp7TuTwzf9u6/bWI+GhEbJqZd3VZ14mtyaWZuXS1Wi1JktRHETEGjA18O5k5\n",
       "WSMCOAP4dWYeO0GdLYE7MzMjYk/gi5m5qEu9zEyPBZMkSdPeoHJLrxGvZwCHAz+KiCvKvHcC2wFk\n",
       "5mnAwcCREfEQcD9waL8bKUmSNBNMOuLV1w054iVJkkbEoHKLV66XJEmqxOAlSZJUicFLkiSpEoOX\n",
       "JElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mS\n",
       "pEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmV\n",
       "GLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKpk0\n",
       "eEXEwoi4KCKuiYgfR8TRE9Q7JSJujIirImK3wTRVkiRptM3usfxB4NjMvDIi5gE/jIgLM/O68QoR\n",
       "sRjYMTN3ioi9gI8Bew+uyZIkSaNp0hGvzLwjM68st38HXAds01FtCXBGqXMJMD8ithxAWyVJkkba\n",
       "lI/xiohFwG7AJR2LtgVuaU3fCixY04ZJkiTNNFMKXmU345eAY8rI10pVOqZzTRsmSZI00/Q6xouI\n",
       "mAN8GfhsZp7TpcptwMLW9IIyr9u6TmxNLs3MpVNuqSRJ0oBExBgwNvDtZE48OBURQXP81q8z89gJ\n",
       "6iwGjsrMxRGxN/ChzFzp4PqIyMzsHBmTJEmadgaVW3oFr32AbwM/YsXuw3cC2wFk5mml3keAA4D7\n",
       "gCMy8/Iu6zJ4SZKkkTCU4NXXDRm8JEnSiBhUbvHK9ZIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJ\n",
       "klSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSp\n",
       "EoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUG\n",
       "L0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKegav\n",
       "iDg9IpZFxNUTLB+LiHsj4opSju9/MyVJkkbf7CnU+TRwKvDPk9S5ODOX9KdJkiRJM1PPEa/M/A5w\n",
       "d49q0Z/mSJIkzVz9OMYrgadHxFURcX5E7NqHdUqSJM04U9nV2MvlwMLMvD8iDgTOAXbuVjEiTmxN\n",
       "Ls3MpX3YviRJ0hqJiDFgbODbycypNGYRcF5mPnEKdW8G9sjMuzrmZ2a6S1KSJE17g8ota7yrMSK2\n",
       "jIgot/ekCXN39bibJEnSWqfnrsaI+AKwL7BZRNwCnADMAcjM04CDgSMj4iHgfuDQwTVXkiRpdE1p\n",
       "V2NfNuSuRkmSNCKm7a5GSZIkTY3BS5IkqRKDlyRJUiUGL0mSNG1EEBEz9xdxDF6SJGlaKIHrj8Dt\n",
       "w27LoBi8JEnSUEWwKIJZNKELYKsIXjXMNg2KwUuSJA1NBIcANwMPl1lj5e9nhtGeQTN4SVplEWwZ\n",
       "wf7Dboek0RbBu4GzWrP+I5OLgSeW5RsMpWED5AVUNdIimA1smMm9w27L2iCCrWl+ueLnZdbjgesz\n",
       "l+8ekDTDRbAQ2DeTz67BOtYFfl8mzwNelrl8erzOeEA5CfhE5uCO+yrHlq3bboMXUNVaK4JDIzgp\n",
       "gtdEkBGcH8E6ETwKeBC4J4IdW/WfPn5GTATzZ/LZMYMUwdwIZkXwjAjuieB8mgNef96qdg3wcAS7\n",
       "DqeVkgYtgj0ieFE523BL4J+AM8vn8Xj52/L3r8vfz0fws9Y6xuvtGcFmwKvHl2WypDN0FW8uf08A\n",
       "biuf+YN4fFsDNwEPlP8tfxrBvoPYFjjipQGK4CnALZksW4X7HAJsBHwRVnkU60s0vx067hTgaIBM\n",
       "w9eqKB+ud0yw+EM0gXcD4E2t+bMyqfOBImmgIngpzWfqRG4Dtp3Cqg4DLgB+3WXZGcARk31uRPB8\n",
       "4DfA98usFwFfy+ThEo42B/49k9+V+nNpjhWLTB7ssr6tgR2ArwAHlbqXTbB1BpFbDF4aiAiOB/5v\n",
       "mXxWJt+ZpO5BwDk9Vvl3wPGZRARLgA8Cjwb2Ap4N/H2r7reA/Tru/5JM/nUVHsJaK4Ix4KKO2QuA\n",
       "Q4FtMvlfHfUfQ/NtEWBhJrcOvJFSn0Uwq3OXeRlh+RXNLqi14v9XObPwRTzyM/ky4Kmt6V/QHIP1\n",
       "FuD9wHY0o99voTkr8eayjn2BnVr3mwu8GDi7TG+eyX9PsV3PAb7RmvVLYOuOar8v2wD4ceby48RO\n",
       "Bn4KnAn8/0k28xzgm62tDiR4kZlVSrOpOtuy1C2Qz4HMUv6rdXu8XNzlPhtAPrZL3YR8X/n7Wsij\n",
       "INftsf1ZkBtDbgRZvkzkhpDnQm7TWu+l5W8M+zmb5LFsBPkByMUd87eCfE/rsey0GuueB7lhx7yA\n",
       "fCrknDK9S2sbJ6/Cur/aut+94+trLX8s5NKyvR0gdx72c22xjBfIzcpr90Md809qva5PnOC+z2zV\n",
       "+TrkEa1lr4ZcrzW9EeRpkC+DnNWa/2XIw4f9PJS2nNx6PButwv126fxshdyita6/a80PyHVWo22v\n",
       "7fL/4vkT/B9JyGMgfzTBsse3bm/T2kZCPq65TQ7kOa7XmYN5AJbhlwle1GeVZZu05v0L5GFd6v6i\n",
       "hKf9xj+k2h9KfWjf3I7tvWuIz9WFkBeUYPh9yCWQc8uydTvauTvkPpN8qDy+84NuFfroJMg3TrDe\n",
       "B8fbtIqPbUnHesaD76JJHsNLII+F3HjYr2PL2lnKe7H9mvwD5JMgL4c8r7xX7u7y2r0f8ruTvLbb\n",
       "ZaPyvu+27Mmt26dUeLxPg/w25PZlevzL6T6Qvym3/wNy0z5tbw5dQlkf1rkJ5CYd8/eDnE3zJXOi\n",
       "vnhaq/6ukHtMvB1yIH1Q78U9mAdgGWSf5ea9/iGWwJSQu5Xpzej4JgP5mi4v/n8tf1f5H/waPJ49\n",
       "W9u9vZ8fBFPc/iYTfBB0ll27zPsZ5K9YMbo3Pv80yP9N8017PVrhrbXd9jfCK3pseynl294aPM4X\n",
       "T7Du81q3b52gzssnWOefsGI0cy7kZZC7D/s9YhlMKa/jKp8NrdfeXjRfFjpfk7uXeu+c5H0z/tr8\n",
       "Ec0XqvH5n+tSdz/I+zrmfRjy463pwyD/FPKB8r6fvQaPbwfIheV2dGx3/gSPZ4Nhvwb60K97Q34e\n",
       "cscyvRUdI/G910EOpG31noTBPADLoPor3916Ez6h/OM7DvIvWnWW/4Od4jq3hdxtmG/q8sHTfmzf\n",
       "r7Td+TTfMhPyhvJ3H8gXdHzgbVnqHwx5KuRNdOweLMs367hft/J6mm+Gv4D8VJf+fRx9HFns0sbP\n",
       "lHZcMP7B37F8Ds3IwjM62v3z8qEZpY17tpYd31F312G9lix9fa28pN2Xrf49qvy9j1XYvU4z6rHD\n",
       "JMuD5ovAZWX9B7SWrQP5JpqRoeWhqixbD3JHyKPL67fr7jKaEZ5tW21JyLNYsUt/E8gxyEPKsud2\n",
       "CUXdyq6t9k96CEaX5/IRnzMd0+O7S08b9mthOhWDl6ViX+Vzy5vwXFb+ZpY0u6i+2Jp+6bDbvBqP\n",
       "8YOt9v8D5J2QV0K+v3y4Hg75vYk+3GhGnZ4EeT1lVJBm1+DygFDmzaI5Zmt8/gFd1jWX1fhGWz58\n",
       "Xw35FB45SnZolz6b0of0kPtk1gRt71ZOLH9/ONE/P8v0L+U13N5dty3dR53GyysgL4Z8fI/1Xt1x\n",
       "vy/wyAD1ltayg4b8HOzGihGz8VHru2i+sGzR5Tl4c+s5m/B9TRMM/7HjvldDvqIs3wPyE5BLhv06\n",
       "mK7F4GXpc38sH0X4Jc3oSueb+5ZSb13Ih8q850Eua9X53rAfRx+eh6n8k38zzbfgx/DI3WXt0jkS\n",
       "kzTHSYzfvgfyrQN+LLNYcYzcPMivlW0vHuR2B/A4xncRjD93+7Pim/5rIcfK7W1bdVZpt/Fk/7DW\n",
       "oN0b0ozedZ5YcCrN7uBV2s1R+TnfaJABFnJTVhzL+LeUg5khnzjJ+25DmlHbR9GcjNOtznEloCw/\n",
       "cYRHjpBOVo6G3GvYz/0qPIeTjYhtArlZq177pKKjIN8G+exhP4ZRKwYvSx/7YqXdW53lRxP9Iysf\n",
       "hk+E3GLYj6NPz8UsyO1pdgesWz7ok+a4tPf1eJ6SlUdotijrbc/79bAf50wtref/RpqRwxtaz/v4\n",
       "cYfbQx5Es+vo2TzyBI9zae3CohklmOi1vyPNCMEH6Tjbi+b4oHafP1zm/7g176945Jls4/OndEwd\n",
       "zRlaSbPreF3IO2iO/fsm5Lwe951Ds7t73ngbaA4f+E6X13RfQykrn9zSWT5Y6o2PGD9xgvXsCvks\n",
       "yMVTeF8uD+N0DyynMoIjpR2PpdvZfD+FfG9r+lXDbvMoF4OXpctzmrNovt3t26Pe+CUeLul4k65D\n",
       "cyzCwZDr0+w6m7bfyof4PL+eFaN+W3VZPv4Ns70rY3167A6x9K1/3jrFf8Ttsqxj+khWjJSc3LH+\n",
       "jWl2QXeuY2eaY+WunGAbXy9/n0prl09Z546TtO09rHxa/gk9Hs/pkO9qvc8Xtpb9+RSej7tYcUbb\n",
       "eHkj5HPXsG/26LKtz0L+rtz+Kl2OYZziuoPm2KTtOtZ/Mz2C6CgXmhA9tzX9aMhv0BwbOf4c/ITW\n",
       "JRIsq/tckwNZ76g/gFEokPtSjuFhxanD20/xvltDHsiKb2/rlzdZ54fZJ8vyWTTf7LenGaLv+sE+\n",
       "7OfEYulnoRnBSMpuyDLvo63X/NGQZ5Qw8b7W+2miy3VsTrN77Kkd89ejOSuts/7nO/4Zjn/JubZM\n",
       "t0+GGL/sxvU0u68nCkOvo9kFOH480oUlbIyHsN3L/budNdyt/LDLvD/reB6fysqhdLy8sNSZRRM2\n",
       "DymfZ+1dvo+mOUPvPR33fTTN7rAtB9T/j6LLCRxrW6EZxXwHIziaNx3LoHKLV64fgAjmA9+m/Lr6\n",
       "BH5J87MFDwHPyOTbEbwc2DGTd5f1nAT8n1L/9zRXY/9ex3reAjy/lIkcBpwPzMsB/sioNEwTXHl8\n",
       "c+DuTB6a5H6zgRcCuwMnAv8GHNBR7WTgpCy/JxfBFjQ/mxTAw9nxI+3lt+h+RfMD7ve35p9Lc0Vv\n",
       "gC0y+VVr2abA3TTv5a91bP/uTDad6HEDp9JcTfz9wOOAjwPvKp8rrwPOGd/W+G+XZk76My2zaH55\n",
       "YnvgzyeqNwWvzuSMNbi/NDSDyi1rZfCKYCOa3376QCZv7fO612PlnyT4MHBMa3on4MZy++PAX3VZ\n",
       "1aXAnuX2PGh+hwr4DPCXwJxMHmht90Jgf+DdwL/Q/AD6D4FdMrl+NR+OtNaJYBua36G7gOank94z\n",
       "WUhZxXWvD5wOHJPJnZPU24Lmffwsmh8T/txk4XHQIpgDvA34f2XW04AjgNeX6cOBx9D8dMyxwBhN\n",
       "ID2/bkul/jF49a0dPBr4r9ash4B/AC6k+T2q+Zn8fDXX/SbgI2Xy+WWdG2YuD03tuvvA8t8v/CTw\n",
       "OuA84L2t+R/P5MhS/wXAIcDr24FL0sxURqYWZXLzsNsyLoJoh9ASJLfL5IYhNksaCIPXGm+fDWmG\n",
       "448osx5H88vq35zgLusBS4G9gc8Dr6AJVUfRfBN9GfAAcGgmX43gCcDV5b6bZXb9JfbONu1AM3L1\n",
       "k475c4H5wG/buykkSVIdBq/V2iYLaI6LehzwjjL7AZpRqD+WOrsDTwBeCiyhGU5/3+puM9eSX7CX\n",
       "JGkmM3it0rbYjOa4qle0Zr8R+NZUhsTL/T8FvB24AZYf8/Fc4GLgB+X23bB8t9+ngTe6G1CSpNFn\n",
       "8Jrydgh4xJlNe1AONO/XAbJdtjkX+MOg1i9JkuoaVG6Z1e8V1hbBkyPICJ4XwTzgo2XRps3lMrg8\n",
       "kx8MMhRl8ntDlyRJ6mX2sBuwqsqI1uY0I1njpyr/FPh6q9q+mdxdu22SJEmTmZbBK4JXAl+muVbM\n",
       "2cCfAM+juZ7VVzqqH5jJv0dwHPAwcBcrLscgSZI0bfQ8xisiTgdeANyZmV2vxB4RpwAHAvcDr87M\n",
       "K7rU6bmvtFyk77+BR/Vo99E0B7afncmDPepKkiStkmEe4/VpVv75jOUiYjGwY2buRHMV449NdeMR\n",
       "HB7BfhHMimBH4A80oetImpGuP6MZlZtFc3X3lwEbZHJqJp81dEmSpFEypbMaI2IRcF63Ea+I+Dhw\n",
       "UWaeXaavB/bNzGUd9TIzI4K3A7sBL59gc9tn8otVehSSJEl9NJ3PatwWuKU1fSuwoFvF8jM5J7Mi\n",
       "dD0NeCxwO/CqchaioUuSJM1I/Tq4vjMRTjSM9h2aXYaf6Lj8wrZ9aockSdK01Y/gdRuwsDW9oMzr\n",
       "4i8uhTO3Bk6IYGlmLu3D9iVJktZIRIwBYwPfTh+O8VoMHJWZiyNib+BDmbl3l3pD/ZFsSZKkqRpU\n",
       "buk54hURXwD2BTaLiFuAE4A5AJl5WmaeHxGLI+Im4D7giH43UpIkaSaYcb/VKEmStKam81mNkiRJ\n",
       "mgKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuSJKkSg5ckSVIl\n",
       "Bi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxe\n",
       "kiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJ\n",
       "kioxeEmSJFVi8JIkSaqkZ/CKiAMi4vqIuDEijuuyfCwi7o2IK0o5fjBNlSRJGm2zJ1sYEesAHwH2\n",
       "B24DLouIczPzuo6qF2fmkgG1UZIkaUboNeK1J3BTZv4sMx8EzgIO6lIv+t4ySZKkGaZX8NoWuKU1\n",
       "fWuZ15bA0yPiqog4PyJ27WcDJUmSZopJdzXShKpeLgcWZub9EXEgcA6w8xq3TJIkaYbpFbxuAxa2\n",
       "phfSjHotl5m/bd3+WkR8NCI2zcy7OlcWESe2Jpdm5tJVbrEkSVKfRcQYMDbw7WROPKgVEbOBG4Dn\n",
       "ALcDlwKHtQ+uj4gtgTszMyNiT+CLmbmoy7oyMz0WTJIkTXuDyi2Tjnhl5kMRcRTwdWAd4FOZeV1E\n",
       "vKEsPw04GDgyIh4C7gcO7XcjJUmSZoJJR7z6uiFHvCRJ0ogYVG7xyvWSJEmVGLwkSZIqMXhJkiRV\n",
       "YvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTg\n",
       "JUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuS\n",
       "JKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElS\n",
       "JQYvSZKkSnoGr4g4ICKuj4gbI+K4CeqcUpZfFRG79b+ZkiRJo2/S4BUR6wAfAQ4AdgUOi4hdOuos\n",
       "BnbMzJ2A1wMfG1BbNSQRMTbsNmj12X+jzf4bXfaduuk14rUncFNm/iwzHwTOAg7qqLMEOAMgMy8B\n",
       "5kfEln1vqYZpbNgN0BoZG3YDtEbGht0ArbaxYTdA00+v4LUtcEtr+tYyr1edBWveNEmSpJmlV/DK\n",
       "Ka4nVvN+kiRJa43ZPZbfBixsTS+kGdGarM6CMm8lEWEgG1ERccKw26DVZ/+NNvtvdNl36tQreP0A\n",
       "2CkiFgG3A4cAh3XUORc4CjgrIvYG7snMZZ0ryszOUTFJkqS1yqTBKzMfioijgK8D6wCfyszrIuIN\n",
       "ZflpmXl+RCyOiJuA+4AjBt5qSZKkERSZ7v2TJEmqYeBXrp/KBVhVV0QsjIiLIuKaiPhxRBxd5m8a\n",
       "ERdGxE8i4oKImN+6zztKH14fEc9rzd8jIq4uyz48jMeztoqIdSLiiog4r0zbfyMiIuZHxJci4rqI\n",
       "uDYi9rL/RkPpi2vK8/75iJhr301fEXF6RCyLiKtb8/rWX6X/zy7z/zMitu/ZqMwcWKHZPXkTsAiY\n",
       "A1wJ7DLIbVqm1C9bAU8ut+cBNwC7AO8F/qbMPw74+3J719J3c0pf3sSK0dJLgT3L7fOBA4b9+NaW\n",
       "ArwF+Bxwbpm2/0ak0Fz78DXl9mxgY/tv+pfy/P8UmFumzwZeZd9N3wI8E9gNuLo1r2/9BbwR+Gi5\n",
       "fQhwVq82DXrEayoXYFVlmXlHZl5Zbv8OuI7memzLL4Zb/r643D4I+EJmPpiZP6N5Me4VEVsDG2Xm\n",
       "paXeP7fuowGKiAXAYuCfWHE5F/tvBETExsAzM/N0aI6lzcx7sf9GwW+AB4ENImI2sAHNiWf23TSV\n",
       "md8B7u6Y3c/+aq/ry8BzerVp0MFrKhdg1RCVM1Z3Ay4BtswVZ6QuA8Z/gWAbHnkZkfF+7Jx/G/Zv\n",
       "LR8E3gb8sTXP/hsNOwC/iohPR8TlEfHJiNgQ+2/ay8y7gA8Av6AJXPdk5oXYd6Omn/21POdk5kPA\n",
       "vRGx6WQbH3Tw8sj9aSwi5tEk9GMy87ftZdmMm9p/01BEvBC4MzOvYOWLFwP23zQ3G9idZvfE7jRn\n",
       "g7+9XcH+m54i4jHAX9PshtoGmBcRh7fr2HejZRj9NejgNZULsGoIImIOTeg6MzPPKbOXRcRWZfnW\n",
       "wJ1lfreL5N5a5i/omN/14rnqq6cDSyLiZuALwH4RcSb236i4Fbg1My8r01+iCWJ32H/T3lOA72fm\n",
       "r8voxleAp2HfjZp+fFbe2rrPdmVds4GNy8johAYdvJZfgDUi1qU58OzcAW9TPUREAJ8Crs3MD7UW\n",
       "nUtzoCjl7zmt+YdGxLoRsQOwE3BpZt4B/KackRXAK1v30YBk5jszc2Fm7gAcCnwrM1+J/TcSyvN+\n",
       "S0TsXGbtD1wDnIf9N91dD+wdEeuX53x/4Frsu1HTj8/Kr3ZZ18HAN3tuvcIZBQfSnDV3E/COmmcz\n",
       "WCbsk31ojg26EriilAOATYFvAD8BLgDmt+7zztKH1wPPb83fA7i6LDtl2I9tbSvAvqw4q9H+G5EC\n",
       "PAm4DLiKZtRkY/tvNArwNzRB+Wqag6rn2HfTt9DsFbgd+APNsVhH9LO/gLnAF4Ebgf8EFvVqkxdQ\n",
       "lSRJqmTgF1CVJElSw+AlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVfI/\n",
       "tMFf0vFEJRYAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a97d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# choose the paramator of Brownian\n",
    "# Brownian paramator (p) = 1.5\n",
    "\n",
    "import pylab\n",
    "from random import normalvariate as norm\n",
    "from random import seed\n",
    "from math import sqrt\n",
    "\n",
    "x = np.arange(0,time, 1)\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "time = 10000\n",
    "average_num = 100\n",
    "p = 1.5\n",
    "\n",
    "for num, j in enumerate(steps):\n",
    "    step = j\n",
    "    y_all = [] \n",
    "    for l in range(average_num):\n",
    "        y_num = [0] * (time)\n",
    "        value = 1\n",
    "        y_num[0] = value\n",
    "        for i in range(time - 1):\n",
    "            update_value = value + step * (2 - value) * value + p * sqrt(step) * value * norm(0, 1)\n",
    "            y_num[i + 1] = update_value\n",
    "            value = update_value\n",
    "        y_all.append(y_num)\n",
    "    y = np.array(y_all)\n",
    "    np.reshape(y, (average_num, time))\n",
    "    y_ave = [np.average(y[:, k]) for k in range(time) ]\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_ave)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAlQAAAEUCAYAAADtKKjYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAGZdJREFUeJzt3XuUZWV95vHvA423gCIxdATatEY0okBgGGThhdLoBFsH\n",
       "NONEHU0UEyQoomiMEXXBOC5NNIk3xHSiKMQIGjQtaHtBpfGOF6Dl0qiMig2EBm1BLnEE+c0f+7Rd\n",
       "VFdXdfU+p/Y+Vd/PWrX6XPY552HTdfo57373e1JVSJIkafvt0HUASZKkcWehkiRJaslCJUmS1JKF\n",
       "SpIkqSULlSRJUksWKkmSpJZmLFRJ7pXkwiSXJLkiyZu3st07k3w/ydokB4wmqiRJUj8tmenOqvpF\n",
       "kidU1e1JlgBfTvLYqvrypm2SrAAeWlV7J3k08B7gkNHGliRJ6o9ZD/lV1e2Di/cAdgQ2TtnkCOD0\n",
       "wbYXArsmWTrMkJIkSX02a6FKskOSS4ANwPlVdcWUTfYE1k+6fg2w1/AiSpIk9du2jFDdVVW/T1OS\n",
       "Hp9kYprNMvVhQ8gmSZI0FmacQzVZVd2c5JPAQcCaSXddCyybdH2vwW13k8SSJUmSxkZVTR0w2qoZ\n",
       "C1WSBwB3VtVNSe4NPBn431M2Owc4DjgrySHATVW1oW2wxSLJyVV1ctc5+sR9Mj33y/TcL9Nzv2zJ\n",
       "fTI998v05joQNNsI1QOB05PsQHN48F+q6vNJjgGoqpVVtTrJiiRXAbcBR21PcEmSpHE127IJlwIH\n",
       "TnP7yinXjxtyLkmSpLHhSundW9N1gB5a03WAnlrTdYCeWtN1gJ5a03WAHlrTdYCeWtN1gIUgVfMz\n",
       "VzxJOYdKkiSNg7n2FkeoJEmSWrJQSZIktWShkiRJaslCJUmS1JKFSpIkqSULlSRJUksWKkmSpJYs\n",
       "VJIkSS1ZqCRJklqyUEmSJLVkoZIkSWrJQiVJktSShUqSJKklC5UkSVJLFipJkqSWLFSSJEktWagk\n",
       "SZJaslBJkiS1ZKGSJElqyUIlSZLUkoVKkiSpJQuVJElSSxYqSZKklixUkiRJLVmoJEmSWrJQSZIk\n",
       "tWShkiRJaslCJUmS1JKFSpIkqSULlSRJUkszFqoky5Kcn+TyJJclOX6abSaS3Jzk4sHP60YXV5Ik\n",
       "qX+WzHL/HcAJVXVJkp2Bbyc5r6rWTdnugqo6YjQRJUmS+m3GEaqqur6qLhlcvhVYB+wxzaYZQTZJ\n",
       "kqSxsM1zqJIsBw4ALpxyVwGHJlmbZHWSfYYXT5Ikqf9mO+QHwOBw39nAywYjVZNdBCyrqtuTPAVY\n",
       "BTxsuDElSZL6a9ZClWQn4KPAB6tq1dT7q+qWSZc/leTUJLtV1cZpnuvkSVfXVNWa7UotSZI0REkm\n",
       "gIntfnxVzfTkAU4HflpVJ2xlm6XADVVVSQ4GPlJVy6fZrqrKuVaSJKn35tpbZhuhegzwPOA7SS4e\n",
       "3HYi8CCAqloJPBM4NsmdwO3As+ecWpIkaYzNOEI11BdyhEqSJI2JufYWV0qXJElqyUIlSZLUkoVK\n",
       "kiSpJQuVJElSSxYqSZKklixUkiRJLVmoJEmSWrJQSZIktWShkiRJaslCJUmS1JKFSpIkqSULlSRJ\n",
       "UksWKkmSpJYsVJIkSS1ZqCRJklqyUEmSJLVkoZIkSWrJQiVJktSShUqSJKklC5UkSVJLFipJkqSW\n",
       "LFSSJEktWagkSZJaslBJkiS1ZKGSJElqyUIlSZLUkoVKkiSpJQuVJElSSxYqSZKklixUkiRJLVmo\n",
       "JEmSWpqxUCVZluT8JJcnuSzJ8VvZ7p1Jvp9kbZIDRhNVkiSpn5bMcv8dwAlVdUmSnYFvJzmvqtZt\n",
       "2iDJCuChVbV3kkcD7wEOGV1kSZKkfplxhKqqrq+qSwaXbwXWAXtM2ewI4PTBNhcCuyZZOoKskiRJ\n",
       "vbTNc6iSLAcOAC6ccteewPpJ168B9mobTJIkaVxsU6EaHO47G3jZYKRqi02mXK+2wSRJksbFbHOo\n",
       "SLIT8FHgg1W1appNrgWWTbq+1+C26Z7r5ElX11TVmm1OKkmSNCJJJoCJ7X581dYHk5KEZn7UT6vq\n",
       "hK1sswI4rqpWJDkEeHtVbTEpPUlV1dSRLEmSpN6Za2+ZrVA9Fvgi8B02H8Y7EXgQQFWtHGx3CnA4\n",
       "cBtwVFVd1DaYJElSV4ZaqIbJQiVJksbFXHuLK6VLkiS1ZKGSJElqyUIlSZLUkoVKkiSpJQuVJElS\n",
       "SxYqSZKklixUkiRJLVmoJEmSWrJQSZIktWShkiRJaslCJUmS1JKFSpIkqSULlSRJUksWKkmSpJYs\n",
       "VJIkSS1ZqCRJklqyUEmSJLVkoZIkSWrJQiVJktSShUqSJKklC5UkSVJLFipJkqSWLFSSJEktWagk\n",
       "SZJaslBJkiS1ZKGSJElqyUIlSZLUkoVKkiSpJQuVJElSSxYqSZKklixUkiRJLVmoJEmSWpq1UCU5\n",
       "LcmGJJdu5f6JJDcnuXjw87rhx5QkSeqvJduwzfuBdwFnzLDNBVV1xHAiSZIkjZdZR6iq6kvAz2bZ\n",
       "LMOJI0mSNH6GMYeqgEOTrE2yOsk+Q3hOSZKksbEth/xmcxGwrKpuT/IUYBXwsOk2THLypKtrqmrN\n",
       "EF5fkiSplSQTwMR2P76qtuVFlgPnVtW+27DtD4H/UlUbp9xeVeWhQUmS1Htz7S2tD/klWZokg8sH\n",
       "05S0jbM8TJIkacGY9ZBfkjOBw4AHJFkPnATsBFBVK4FnAscmuRO4HXj26OJKkiT1zzYd8hvKC3nI\n",
       "T5IkjYl5P+QnSZK02FmoJEmSWrJQSZIktWShkiRJaslCJUmS1JKFSpIkqSULlSRJUksWKkmSpJYs\n",
       "VJIkSS1ZqCRJklqyUEmSJLVkoVrEEpKwb8LrEj6SsF/XmSRJGkcWqkUmYUnCYQn/AFwFnAv8FvAN\n",
       "4PMJr01Y0mlISZLGTKpqfl5ojt/arOFJ+A3gvwFHAk8F1gMfH/ysraIG2z0IeC9wf+AFVVzeTWJJ\n",
       "kro1195ioVqgEnYHngY8HZgAvgmsAs6p4uoZHhfgaOBNwFuBv6/izpEHliSpRyxUi1jC3jSjUEcC\n",
       "+wGfpRmFWl3Fxjk+13LgfcBv0IxWXTnctJIk9ZeFahFJ2AE4iGYU6khgN+AcmhL1hSp+MYTn/wvg\n",
       "DcCbgbdX8atWoSVJGgMWqgUu4Z7AE9g8EnUzzaG8jwPfqOKuEbzmQ4DTgJ2Ao6r43rBfQ5KkPrFQ\n",
       "LUAJuwIraArUHwKXM5hUXsV35ynDDsBLgJOA/wO8axTlTZKkPrBQLRAJy9g8CvVo4AKaEnVuFRs6\n",
       "zPVQ4APAXcALq7iqqyySJI2KhWpMDc6u25emQD0dWA58gqZEfbaKW7tLd3cJOwLHA68FTgZOdbRK\n",
       "krSQWKjGyGABzceyeSQqNAVqFfDlvi9XkPBwmtGqX9CMVv2w20SSJA2HharnEh5Is8jm4cCTgavZ\n",
       "XKIu3bTI5rgYjFadALwaeD2wctz+GyRJmspC1TMJ9wAOpSlQhwO/A3wO+DTwmSqu6TDe0CQ8Ajid\n",
       "5qzDP59p8VBJkvrOQtUDCQ+mORvvcJolDr7LoEABF/b9UN72GhzC/EvglcCJwHsdrZIkjSMLVQcS\n",
       "7g0cxuZRqPvTlKdPA+dVcWOH8eZdwqNo5lb9BDi6ivXdJpIkaW4sVPNgcEbe77G5QB0KXExToD4N\n",
       "XLLYz3pL2IlmXtXLgL8CPuBolSRpXFioRiThvsAfsLlEhc0F6vNV3NxhvN5K2J9mtOo6mtGq67pN\n",
       "JEnS7CxUQzJYGXx/NheoA4GvsblErXPEZdsMJuafCLyYZn7VB913kqQ+s1C1kPAAmiUN/nDwczOb\n",
       "C9QFVdzeYbyxl3AgzWjVD4Fjqri+20SSJE3PQjUHg7PSDmbzKNTDgTVsXtLgB92lW5gGX+78euBo\n",
       "4OXAWV2PVg3mez0IeDDwkMGfmy7/B/CCKn7WXUJJ0nwbeqFKchrwVOCGqtp3K9u8E3gKcDvwgqq6\n",
       "uG2wURgcelrG5jPyngSsZ/Mo1Feq+GV3CRePhINo1q26Eji2ihtG+FoBlrJlWdp0eQ+aOV4/nPTz\n",
       "g8Gf/5NmtHJFFT8aVUZJUr+MolA9DrgVOGO6QpVkBXBcVa1I8mjgHVV1SNtgczFYrXt3mn8Y9wD2\n",
       "nHR58s+uwAbgq2wehXKSdEcS7gWcBBwFvLSKf2vxXPdl+rL0EJrvRbyNzSVpamn6cRV3zPDcx9Oc\n",
       "sXhkFd/a3oySpPExkkN+SZYD526lUP0jcH5VfXhw/UrgsKra0CZY8xgC7MbWS9Km23YHNtKMMlw7\n",
       "+HPqz7XAT6r41VwyaPQSHk0zWrUWeEkVP5lmm3vQrDK/tdJ0L7YsSpsu/6iKW1pmfDrwTzTfWfiJ\n",
       "Ns8lSeq/ufaWJUN4zT3hbgs3XgPsRTMStFUJuzBzSdoDeCDNYcSp5ehy4LxJ16+faYRB/VbFhQkH\n",
       "AG8ALk14C7ALdy9OS2lK8eSi9O+TLt84yrlYVaxKuA5YlfDGKk4d1WtJksbPMAoVNGsyTTbtP2wJ\n",
       "57O5LO3A5tGkTX9eTbM0wa/LUxX/OaSM6rHB/+dXJfw7zYT164CvAP9CU5rWd/2VPVV8I+GxwOrB\n",
       "1wu9erEv4CpJagyjUF1LM9F7k70Gt03jv/4YNl4ON94Ct32m6ldrhvD6WkCq+CrNHLdequIHCYcC\n",
       "HwfOSvjTKn7RdS5JUjtJJoCJ7X78EOZQTZ6Ufgjw9vmelC7Nt8GE+g/QfIA4soqfdptIkjRMozjL\n",
       "70yaZQYeQDMv6iRgJ4CqWjnY5hSaZQhuA46qqovaBpP6brCa/puAPwKeUsX/7TiSJGlIXNhTmmcJ\n",
       "xwAnA8+o4usdx5EkDcFce8sOowwjLQZVrAT+DDg34Y+6ziNJmn8WKmkIqlhNs6L6OxNe3nUeSdL8\n",
       "8pCfNEQJvwOsBj4HvMKFZCVpPHnIT+pQFVcDjwH2BT6acJ+OI0mS5oGFShqyKm6iOev158D5Cbt3\n",
       "HEmSNGIWKmkEqvgl8HyaL+H+WsLDO44kSRqhYX31jKQpBt8teFLC1cAXE55ZxZe6ziVJGj5HqKQR\n",
       "q+I04Hk0c6qe1XUeSdLweZafNE8S9gM+AbwbeMtgBEuS1EOulC71WMKewCeBrwPHVXFnx5EkSdNw\n",
       "2QSpx6q4Fng8sBz4eMLO3SaSJA2DhUqaZ1X8HPjvwHXABQkP7DiSJKklC5XUgSruAF4EfIxmWYVH\n",
       "dhxJktSCc6ikjiU8F3gb8OwqvtB1HkmSc6iksVPFvwJ/DJyZ8Cdd55EkzZ0jVFJPJOxDcwbgacAb\n",
       "XVZBkrrjsgnSGEv4bZq1qr4DHDOYayVJmmce8pPGWBXXAxPAbwGfTLhvt4kkSdvCQiX1TBW3As8A\n",
       "vg98OWGvjiNJkmZhoZJ6aLCC+nHAGTTLKvx+x5EkSTNwDpXUcwl/DJwCPKuK87vOI0mLgZPSpQUo\n",
       "4cnA+4FHVHFL13kkaaGzUEkLVMLpwA1VvKrrLJK00FmopAUqYSlwGTBRxeVd55GkhcxlE6QFqooN\n",
       "wBuAUxL8cCJJPWKhksbLe4BdgWd3HUSStJmH/KQxk3Ao8G80E9R/3nUeSVqInEMlLQIJpwE/q+KV\n",
       "XWeRpIXIQiUtAgm700xQf2IVl3WdR5IWGielS4tAFTcAJwPvdoK6JHXPQiWNr5XALsBzuw4iSYvd\n",
       "rIUqyeFJrkzy/SSvnub+iSQ3J7l48PO60USVNFkVvwJeDLwl4X5d55GkxWzGOVRJdgS+CzwJuBb4\n",
       "JvCcqlo3aZsJ4BVVdcSML+QcKmkkEt4L3FrFy7vOIkkLxbDnUB0MXFVVP6qqO4CzgCOne905ZJQ0\n",
       "XK8B/lfC/l0HkaTFarZCtSewftL1awa3TVbAoUnWJlmdZJ9hBpQ0sypuBF6PE9QlqTOzFaptWVPh\n",
       "ImBZVe0PvAtY1TqVpLl6L3BP4E+6DiJJi9GSWe6/Flg26foymlGqX6uqWyZd/lSSU5PsVlUbpz5Z\n",
       "kpMnXV1TVWvmnFjSFqr4VcKLgXMSzqnipq4zSdI4GcwJn9jux88yKX0JzaT0PwCuA77BlpPSlwI3\n",
       "VFUlORj4SFUtn+a5nJQujVjCSuD/VXF811kkaZzNtbfMOEJVVXcmOQ74DLAj8L6qWpfkmMH9K4Fn\n",
       "AscmuRO4Hb+0VerSicAVCadVcUnXYSRpsfCrZ6QFJuFo4AXA46q4q+M4kjSW/OoZSe+jGX1+ftdB\n",
       "JGmxcIRKWoASDgI+ATyiip91nUeSxs1ce4uFSlqgEk4FqoqXdJ1FksaNhUoSAAm7AVcAT63i213n\n",
       "kaRx4hwqSQBUsZHmrL93J/6uS9Io+SYrLWwfoPnGg6M6ziFJC5qH/KQFLuFA4FM0E9S3+AYDSdKW\n",
       "nEMlaQsJpwA7VnFs11kkaRxYqCRtIeH+wDrgaVV8q+s8ktR3TkqXtIXBWlR/DZyasGPXeSRpobFQ\n",
       "SYvHGcAdwJ91HUSSFhoP+UmLSML+wGeBR1bxk67zSFJfOYdK0owS3gHcu4oXdZ1FkvrKQiVpRgm7\n",
       "0qyg/owqLuw6jyT1kZPSJc2oipuAV9OsoO4EdUkaAguVtDh9EPhP4Oiug0jSQuAhP2mRStgP+BzN\n",
       "BPUbu84jSX3iHCpJ2yzhbcAuVfx511kkqU8sVJK2WcL9aFZQ/x9VfK3rPJLUF05Kl7TNqrgZeBWu\n",
       "oC5JrVioJH0IuBn4i66DSNK48pCfJBIeCayhmaB+Q8dxJKlzzqGStF0S/g74zSqO6jqLJHXNQiVp\n",
       "uyTsQjNB/VlVfKXrPJLUJSelS9ouVdwC/CXNCupLus4jSePEQiVpsg8DG4Fjuw4iSePEQ36S7iZh\n",
       "H+AC4FFVbOg6jyR1wUN+klqp4grg/cBbu84iSePCESpJW0jYmWaC+nOr+GLXeSRpvjlCJam1Km4F\n",
       "XkEzQX2nrvNIUt9ZqCRtzdnA9cBLug4iSX3nIT9JW5Xwe8CXgX2r+I+u80jSfBn6Ib8khye5Msn3\n",
       "k7x6K9u8c3D/2iQHzCWwpP6q4krgn3GCuiTNaMZClWRH4BTgcGAf4DlJHjFlmxXAQ6tqb+BFwHtG\n",
       "lHVBSjLRdYa+cZ9Mr8P98kbg8QmHdfT6M/Lvy/TcL1tyn0zP/TIcs41QHQxcVVU/qqo7gLOAI6ds\n",
       "cwRwOkBVXQjsmmTp0JMuXBNdB+ihia4D9NREFy9axW3ACfR3gvpE1wF6aqLrAD000XWAnproOsBC\n",
       "MFuh2hNYP+n6NYPbZttmr/bRJPXIx4BrgZd2HUSS+mi2QrWtM9anTtqan5nukuZFFUVTpk5MtvhQ\n",
       "JUmL3oxn+SU5BDi5qg4fXH8NcFdV/e2kbf4RWFNVZw2uXwkcVlUbpjyXJUuSJI2NuZzlN9s3yn8L\n",
       "2DvJcuA64FnAc6Zscw5wHHDWoIDdNLVMzTWUJEnSOJmxUFXVnUmOAz4D7Ai8r6rWJTlmcP/Kqlqd\n",
       "ZEWSq4DbgKNGnlqSJKlH5m1hT0mSpIVq5F89sy0Lgy42SZYlOT/J5UkuS3J815n6JMmOSS5Ocm7X\n",
       "Wfoiya5Jzk6yLskVg8Pri1qS1wx+hy5N8qEk9+w6UxeSnJZkQ5JLJ922W5LzknwvyWeT7Nplxi5s\n",
       "Zb+8dfA7tDbJx5Lcr8uMXZhuv0y675VJ7kqyWxfZurK1fZLkpYO/L5cl+dutPX6TkRaqbVkYdJG6\n",
       "Azihqh4JHAK8xP1yNy8DrsCzRSd7B7C6qh4B7Aes6zhPpwbzOo8GDqyqfWmmJDy7y0wdej/Ne+xk\n",
       "fw2cV1UPAz4/uL7YTLdfPgs8sqr2B74HvGbeU3Vvuv1CkmXAk4Gr5z1R97bYJ0meQLPO5n5V9Sjg\n",
       "72Z7klGPUG3LwqCLTlVdX1WXDC7fSvOP4x7dpuqHJHsBK4D3suVyHIvS4FP046rqNGjmNlbVzR3H\n",
       "6trPaT6Y3CfJEuA+NOtkLTpV9SXgZ1Nu/vWCy4M/nz6voXpguv1SVedV1V2DqxeyCNdM3MrfF4B/\n",
       "AP5qnuP0wlb2ybHAmwfdhaq6cbbnGXWh2paFQRe1wSftA2h+uQVvA14F3DXbhovIg4Ebk7w/yUVJ\n",
       "/jnJfboO1aWq2gj8PfBjmjOQb6qqz3WbqleWTjrbegPgt1ds6YXA6q5D9EGSI4Frquo7XWfpkb2B\n",
       "xyf5epI1SQ6a7QGjLlQesplBkp2Bs4GXDUaqFrUkTwNuqKqLcXRqsiXAgcCpVXUgzdm0i/EQzq8l\n",
       "+V3g5cBymtHdnZM8t9NQPVXNmUe+F0+S5LXAL6vqQ11n6drgw9mJwEmTb+4oTp8sAe5fVYfQfMj/\n",
       "yGwPGHWhuhZYNun6MppRqkUvyU7AR4EPVtWqrvP0xKHAEUl+CJwJPDHJGR1n6oNraD49fnNw/Wya\n",
       "grWYHQR8tap+WlV30nw1zqEdZ+qTDUl+GyDJA4EbOs7TG0leQDOtwALe+F2aDyZrB++9ewHfTrJ7\n",
       "p6m6dw3N+wqD9967kvzmTA8YdaH69cKgSe5BszDoOSN+zd5LEuB9wBVV9fau8/RFVZ1YVcuq6sE0\n",
       "E4y/UFV/2nWurlXV9cD6JA8b3PQk4PIOI/XBlcAhSe49+H16Es2JDGqcAzx/cPn5gB/aaM46pxlt\n",
       "OLKqftF1nj6oqkuramlVPXjw3nsNzckei72ErwKeCDB4771HVf10pgeMtFANPjluWhj0CuDDVbWo\n",
       "z04aeAzwPOAJg+UBLh78ouvuPEyx2UuBf02yluYsvzd1nKdTVbUWOIPmQ9umeR//1F2i7iQ5E/gq\n",
       "8PAk65McBfwN8OQk36P5R+FvuszYhWn2ywuBdwE7A+cN3ndP7TRkBybtl4dN+vsy2aJ7393KPjkN\n",
       "eMhgKYUzgVk/3LuwpyRJUksjX9hTkiRpobNQSZIktWShkiRJaslCJUmS1JKFSpIkqSULlSRJUksW\n",
       "KkmSpJYsVJIkSS39f5mNYbqb1TPMAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a86e510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4LVV5oPH3g8sMckGU8SrIFDHKFJmcrnECIpgYB4wY\n",
       "IXGkaYgmjq2CHWMSbeMUNWjEGAfUqI1ocEDjjdq24AA0CijYahhaNDIoIATC13/UqnvWqbOHc+7d\n",
       "u845976/56mnqlatWrV21R6+vWpVVWQmkiRJmr5NFrsCkiRJGwsDL0mSpJ4YeEmSJPXEwEuSJKkn\n",
       "Bl6SJEk9MfCSJEnqycjAKyK2jIgLI+KSiLg8Iv5ySL63RcRVEXFpRBw8napKkiQtbytGLczMOyLi\n",
       "0Zl5e0SsAL4WEQ/PzK+1eSLiWGCfzNw3Ig4H3gUcMd1qS5IkLT9jTzVm5u1lcnNgU+DGTpbjgfeX\n",
       "vBcCKyNi50lWUpIkaUMwNvCKiE0i4hLgBuDLmXl5J8vuwDXV/LXAHpOroiRJ0oZhPi1e92TmQTTB\n",
       "1CMjYvWAbNFdbQJ1kyRJ2qCM7ONVy8xbIuKfgd8C1lSLrgNWVfN7lLRZIsJgTJIkLRuZ2W1YWm8j\n",
       "A6+I2Am4OzNvjoitgMcBr+1kOw84FfhIRBwB3JyZNwwqbxovQNMXEWdm5pmLXQ+tG4/f8ubxW748\n",
       "dsvbtBqMxrV47Qq8PyI2oTkt+YHM/FJEPB8gM8/KzPMj4tiIuBq4DTh5GhWVJEla7sbdTuIy4JAB\n",
       "6Wd15k+dcL0kSZI2ON65XvOxZrEroPWyZrEroPWyZrEroHW2ZrEroKUnMvvp8x4RaR8vSZK0HEwr\n",
       "brHFS5IkqScGXpIkST0x8JIkSeqJgZckSVJPDLwkSZJ6YuAlSZLUEwMvSZKknhh4SZIk9cTAS5Ik\n",
       "qScGXpIkST0x8JIkSeqJgZckSVJPDLwkSZJ6YuAlSZLUEwMvSZKknhh4SZIk9cTAS5IkqScGXpIk\n",
       "ST0x8JIkSeqJgZckSVJPDLwkSZJ6YuAlSZLUEwMvSZKknhh4SZIk9cTAS5IkqScGXpIkST0x8JIk\n",
       "SeqJgZckSVJPDLwkSZJ6YuAlSZLUk5GBV0SsiogvR8T3IuK7EXHagDyrI+KWiLi4DK+aXnUlSZKW\n",
       "rxVjlt8FvCgzL4mIbYFvR8QFmXlFJ9+/Zubx06miJEnShmFki1dm/jQzLynTtwJXALsNyBpTqJsk\n",
       "SdIGZd59vCJiT+Bg4MLOogSOiohLI+L8iDhgctWTJEnacIw71QhAOc34ceD00vJV+w6wKjNvj4hj\n",
       "gHOB/SZbTUmSpOVvbOAVEZsBnwA+mJnndpdn5q+q6c9GxDsjYsfMvHFAWWdWs2syc8061VqSJGmC\n",
       "ImI1sHrq28nMUZUI4P3ALzLzRUPy7Az8LDMzIg4DPpaZew7Il5lpXzBJkrTkTStuGdfi9TDgROD/\n",
       "RMTFJe2VwP0AMvMs4CnACyPibuB24IRJV1KSJGlDMLLFa6IbssVLkiQtE9OKW7xzvSRJUk8MvCRJ\n",
       "knpi4CVJktQTAy9JkqSeGHhJkiT1xMBLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk8MvCRJknpi4CVJ\n",
       "ktQTAy9JkqSeGHhJkiT1xMBLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk8MvCRJknpi4CVJktQTAy9J\n",
       "kqSeGHhJkiT1xMBLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk8MvCRJknpi4CVJktQTAy9JkqSeGHhJ\n",
       "kiT1xMBLkiSpJwZekiRJPRkZeEXEqoj4ckR8LyK+GxGnDcn3toi4KiIujYiDp1NVSZKk5W3FmOV3\n",
       "AS/KzEsiYlvg2xFxQWZe0WaIiGOBfTJz34g4HHgXcMT0qixJkrQ8jWzxysyfZuYlZfpW4Apgt062\n",
       "44H3lzwXAisjYucp1FWSJGlZm3cfr4jYEzgYuLCzaHfgmmr+WmCP9a2YJEnShmZegVc5zfhx4PTS\n",
       "8jUnS2c+17dikiRJG5pxfbyIiM2ATwAfzMxzB2S5DlhVze9R0gaVdWY1uyYz18y7ppIkSVMSEauB\n",
       "1VPfTubwxqmICJr+W7/IzBcNyXMscGpmHhsRRwBvycw5nesjIjOz2zImSZK05EwrbhkXeD0c+Arw\n",
       "f5g5ffhK4H4AmXlWyfe3wNHAbcDJmfmdAWUZeEmSpGVhUQKviW7IwEuSJC0T04pbvHO9JElSTwy8\n",
       "JEmSemLgJUmS1BMDL0mSpJ4YeEmSJPXEwEuSJKknBl6SJEk9MfCSJEnqiYGXJElSTwy8JEmSemLg\n",
       "JUmS1BMDL0mSpJ4YeEmSJPXEwEuSJKknBl6SJEk9MfCSJEnqiYGXJElSTwy8JEmSemLgJUmS1BMD\n",
       "L0mSpJ4YeEmSJPXEwEuSJKknBl6SJEk9MfCSJEnqiYGXJElSTwy8JEmSemLgJUmS1BMDL0mSpJ4Y\n",
       "eEmSJPXEwEuSJKknBl6SJEk9MfCSJEnqydjAKyLOjogbIuKyIctXR8QtEXFxGV41+WpKkiQtfyvm\n",
       "ked9wNuBfxyR518z8/jJVEmSJGnDNLbFKzO/Ctw0JltMpjqSJEkbrkn08UrgqIi4NCLOj4gDJlCm\n",
       "JEnSBmc+pxrH+Q6wKjNvj4hjgHOB/QZljIgzq9k1mblmAtuXJElaLxGxGlg99e1k5nwqsyfw6cx8\n",
       "8Dzy/gg4NDNv7KRnZnpKUpIkLXnTilvW+1RjROwcEVGmD6MJ5m4cs5okSdJGZ+ypxog4B3gUsFNE\n",
       "XAOcAWwGkJlnAU8BXhgRdwO3AydMr7qSJEnL17xONU5kQ55qlCRJy8SSPdUoSZKk+THwkiRJ6omB\n",
       "lyRJUk8MvCRJknpi4CVJktQTAy9JkqSeGHhJkiT1xMBLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk8M\n",
       "vCRJknpi4CVJktQTAy9JkqSeGHhJkiT1xMBLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk8MvCRJknpi\n",
       "4CVJktQTAy9JkqSeGHhJkiT1xMBLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk96DbwiOKzP7UmSJC0l\n",
       "kZn9bCgiIckketmgJEnSOoqIzMyJxyyeapQkSepJ74FXhC1ekiRp4zQ28IqIsyPihoi4bESet0XE\n",
       "VRFxaUQcPKbI/RZcS0mSpA3AfFq83gccPWxhRBwL7JOZ+wLPA941prwr5189SZKkDcfYwCszvwrc\n",
       "NCLL8cD7S94LgZURsfO4ciM4MIJ+evZLkiQtAZPo47U7cE01fy2wx6gVItgbuGgC25YkSVo2JtW5\n",
       "vtthflxL1m8Dm09o25IkScvCigmUcR2wqprfo6QNcGYZf+0YeBWwegKblyRJWj8RsZoeApNJBF7n\n",
       "AacCH4mII4CbM/OGwVnPbCcuBX5vAtuWJElab5m5BljTzkfEGdPYztg710fEOcCjgJ2AG4AzgM1K\n",
       "Jc8qef6W5srH24CTM/M7A8rJIWcgN8/krvV4DZIkSRM1rTvX9/3IoEOAblC2VyY/7qUSkiRJ87BB\n",
       "PDIok4sHJP+6zzpIkiQtlqXwrMbHLXYFJEmS+tDrqcbMjEE3Tc30+Y2SJGnp2CBONUqSJG3MFiPw\n",
       "mvM4oQg+uwj1kCRJ6tVinGrcAbixu9zTjZIkaanYkE41tvfsekedGMGmi1AXSZKk3ixG4HV3Gb+h\n",
       "k/74visiSZLUp8Vs8erev2uLvisiSZLUp94Dr0z+E7gFuAm4vlr0077rIkmS1KdFuZ1EJiszuRs4\n",
       "qUrebDHqIkmS1JfFvo/X3dX05otWC0mSpB4sduC1TzU9p8UrgjMi+G6P9ZEkSZqaxQ687qim17Z4\n",
       "RfDWCH4MrAYe1HOdJEmSpmKxA69PVdN1i9cjgfvD3Oc6SpIkLVeLGnhl8stqtg68DmqzAETwit4q\n",
       "JUmSNCWL3eJV225AWtvi9fo+KyJJkjQNSynwmvPwbOzfJUmSNiBLKfDaoZpuT0HushgVkSRJmoal\n",
       "Enj9Cti6mm+vdvxgmxCxtt+XJEnSsrRUAq+LgW0GpNfPc3xsT3WRJEmaiqUQeK0E3s7swKvtVH9X\n",
       "nRbB/hGc3FvNJEmSJmjRA69MbgFuY3Z/rv/sjFtXAmf3US9JkqRJW/TAq1gBHBXBFmW+fYbjpp18\n",
       "n+6vSpIkSZO1VAKvm8t4/zJuA6/u8xvvAogg+qiUJEnSJC2JwCuTr5bJS8u4Dbw2r7IFM1c+PqyP\n",
       "ekmSJE3Skgi8ahFsxUzg1d7b6w5gC+DaMj/oLveSJElL2pILvIAdmelUf3wZ3wIczkwL2Iq+KyVJ\n",
       "krS+lmLgdS3w4Gr+D2huOXEc8Icl7fGjCohg8whOn071JEmS1k1k5vhck9hQRGbm0E7xEQyryP2B\n",
       "y5l7g9UtM7lzSFmHAN/OtBO+JElauHFxy7paSi1eXxmSfgNw+4D010fwtCHr/HpIuiRJ0qIZG3hF\n",
       "xNERcWVEXBURLxuwfHVE3BIRF5fhVetSkUweNST9TuAnAxa9GHjNkOLubuq2pAJLSZK0kRvZST0i\n",
       "NgX+luY5idcB34yI8zLzik7Wf83M4+cUsH7ezcxVjKcBXy/TJwAfKdPdO9u32oBrSwa3lkmSJPVu\n",
       "3NWBhwFXZ+aPASLiI8CTgG7gNY2+VKdkrg2svlGlXw58n+Zmq/cMWbe98erWGHhJkqQlYtypuN2B\n",
       "a6r5a0taLYGjIuLSiDg/Ig5Yj/q8Z22hM0EXmSQzwdRdzPTh2ntIOe19vrZaj7pIkiRN1LjAaz6X\n",
       "PH4HWJWZBwJvB85dj/q8AHjGwIokdwObZHIlM6cY17Z4RXB0BKeUWQMvSZK05Iw71XgdsKqaX8VM\n",
       "vysAMvNX1fRnI+KdEbFjZt7YLSwizqxm12TmmtllcU8EH6UJ5uYoLV8A9yrjT1WLP9tsg3OYCbx2\n",
       "Bn4w8JVJkiQVEbEaWD317Yy6j1dErKDpT/UY4HrgIuAZdef6iNgZ+FlmZkQcBnwsM/ccUNbE7odR\n",
       "3fPrQ5mcWNJup2nh2pWmA/6bAbyXlyRJWqhFuY9XZt4NnAp8nqZT+0cz84qIeH5EPL9kewpwWURc\n",
       "AryFJujpy5bVdHtacTNK0DVfEfwsglMnVitJkqQBlsyd6xdW1toWr/Mz+Z1O2r7AVW3e+bR4lXU/\n",
       "nMkzy/xmmdw1ibpKkqTlZ2O4c/1CbEfTsnZsxNqrHW8t43XtUH8XQASPB/5j/aonSZI017IMvDK5\n",
       "FbipzLanNtvnNr5pvuVEsF0E7cUBzy7jx5Rl269vPSVJkmrLMvAqfl7Gd5TxdWX8uDK+GCCC80aU\n",
       "cR9g207aS8v45gg2Xd9KSpIktZZt4JXJxcA/AZtH8FjgIdXinwD/XKaPA4hgvwh27hQz7tztiyZR\n",
       "V0mSJFjGgVdxG7A5cEEn/VdUjzWKIGhui/HTCJ5W5dtiTPl9XqEpSZI2cMs98LqTwcHTrcA51fyx\n",
       "1fTzASJ4IPAHVfpFA8qZdWVjBA+J4Kh1q6okSdrYjbtz/VL3/CHpt2aSMXMi8TPVsvZO/B8H6udK\n",
       "to8f+glw/zL9yU65X6TpF+ZNWSVJ0oIt9xav2i+BV5fpUZ3i9+2MW20wtcWAtNa891cE20asvVJS\n",
       "kiRp2Qdel1XTO2TyujL9gHmsu1ln/vAI/gLYpUrbBtZ2zP8hcO8y/+BBBUbwpOpGrs8D/mEe9ZAk\n",
       "SRuJ5R54nVnG12WuPVUI5dYS5a71p3VXilj7kO2uV5bxNsArgK3L/PeZHcwNa8l6aCl/E0rrW+nY\n",
       "394zLCOau+NLkqSNz3IPvLYr49076f9ZTX+wjI+p0l5WTf8Z8MJ65Uxup7kycsch2/3TIeltK9qL\n",
       "gZVluj11eUinPpIkaSOz3AOvLw9JrwOv9garF1Zpu7UTmbwpk78bUMYRwB9FNHeyHyeCI5m5+eob\n",
       "q0XbdcaSJGkjtawDr0z+bcii+rTjndX4z8v0lmW8w4ji20cP/fmIPABEcCDw9SGL/7qMb6nye1Xk\n",
       "hEWwMoJPLXY9JEkaZVkHXpX6VOGdwCXtTOn79Srg15m8BrgaeBjwyUxuHlDW58t6bRlHdpY/C6Dz\n",
       "OKFLqulzO/lPLuNtqrTnRLBLBFdFeHf8CXkQcPxiV0KSpFE2hMDrm8C/VvMrmTnlB0Amf5G59mrD\n",
       "22nu5fWLTjkPAXbL5OgR23o0M8+I3AIggq06ef5LZ/4H5XTlI4EflLR3A/8P2AdYPWJ7kiRpA7Lc\n",
       "b6BKJod15u8Ylrdon+n4ns56lw3IW7sK+N/MPFT7daW16hlVng9mcn0Er6Z5jNGjaTrof3FEuXeP\n",
       "2a7mZ8vxWZamchVsZM7qmyhJ2gBtCC1e6ySTb84j20PL+HOZ7JfJnZlrW8raU4Tto4l+Afx9Kft1\n",
       "mVxIc1PXQxit22KmdbOcT9meBfwogk0j5nUPOqk3EewfMeeG05LW0UYbeM1HJt/KJDJn3YpiWN6d\n",
       "Mmed8oTm7vjjroqcVXYED4xgv2p+iwj+ptwD7PR5V74nERwcMeuZl4tlOQewR9Gc/n4u8MPuwgju\n",
       "G8H/7L1WUuNK4DuLXQlpQ7ExBl5vA14y4TIvGJLebe06m/F31b+c5oatrRcy05rzloVXbToiiAju\n",
       "Q7M/PzRk+airRiftEWW73ScSzFJalV6xxK4sbZ8Z+gCYc+EGNC1iv9trjaTZNsbfCmkqNroPUyan\n",
       "Z/I/1rOY13bmvzUk36wfy0z+OJMfLXBbb15g/omJ4D4jnjf5DOBnNA8Nr9dp75H2feDGKVav3uZ2\n",
       "zNy8duWovMALgNcDB3bKeH3ErBvrTqpuJ5Y+XMOW71PNbtkZt1YhLa6tx2eRNB8bXeA1IX/dmX/N\n",
       "oEyZ3ARcX2brW158rs4XwebddasWmTWd9EcupKIDyr0ogt+eZ/ZnMPx5k78q4/2rsvekPK6JuQ8h\n",
       "n5gINongYxHctyTVp2uHPW2gdUMZP6+T/gqaJw7U29l13Wu51geAPUYsv6qafnIZd3/kDp1APXoT\n",
       "weYRPHqx66HRItgqonn+7Dzz/+Y06yNtLAy81kEmvy7PgdwB+FbmyCsTDwFOq++OX/qMfaDM3szg\n",
       "u9q39/36lzJur97s9iNbqIcCT5pn3lFX2f1HPVPu3L99N1N9Si+CwyJ41aDCIjglYmzQ1NoZeCpw\n",
       "Q2lN+mi1bE6LVwRPi1j78PMd1iYHZ0bwG1XWzat1Arg+gntFsH0Ej51n3erttq/9uAjeFDG79XLA\n",
       "6c720VfP6eT5YZnetJzCHRXILaoIHkFzL71/GZe3Wufkctpa/foC8O8LyP9b06qItDEx8FoPmdyc\n",
       "ufbKx2F5bsjk7QMWnURzemwl8PQq/bYybgOElTR90i5tM0RwvyqQoEpfFcFJ86j6fG8j0j5nkgh+\n",
       "p3Tw/3Q5PfaCTt4daW630bZ8zSkDeDnDnwTwDobf/b/r+mr6gGr6q3RO00WwLU1g9pcR7E1zDzVo\n",
       "AoMzgD+qstdB2xll/EOa4PiCCJ5blbtv2R+jbmPRvvYtaVrT/qRzddgL564ClGMfwdbAfwX2Lulb\n",
       "0bSKXTNim4tt7fGNmHXsRzkb+MZ0qqMRHj4uQwQPrGbvmkYlyufoimmULS1FBl6LJJN7qpaywwFK\n",
       "YNC2dP1bCXB2BG7MnNXC9BOaG7BS1tu9PLbopcD7yhfZg7rbjOC/lck5pzaHaAOAHYD3lrQnAk9h\n",
       "bmfvpzFzZWHdb6l+buW4e22N7Bg/RBu8XEzT0rJFaRW6o3RSb4Op+wL3r9b7WBm/OGLtQ8//HZof\n",
       "AmYCr52qdd5dTbfb3Y3h2v3xqCrthLKNx9IEmwD/XC3/CvCSEnQ9H3hrtWwbmMjpz6kop8zr1/qt\n",
       "kr4iYu1p1O467TFftvdh28CdV01/cNKFl/6ZwKyWZy0B5XdkbN++CN4YMfdsh4Yz8Fp8/5eZH97f\n",
       "6Sx7KnBvZjqpD2o5g+bL8RLg1Cpt/wge0+k/9royfg7z054W/DDN6b1WfWr0lDL+wyqtvsqz7k82\n",
       "8JYP1Yd77D2sIubso3b7T6AEXsCDy3iHkg5NK9+gzvObwtqLLXaKmNN/b5i2L9uo1sP2de1epbXr\n",
       "1acLj6um2z58ewF/0ynvr1janZy7X75tn6DDgU9ErG3NrX2ijHu5EGNjFMFbI8Y/c3aI9k9Ujsy1\n",
       "7n7ZTsznR16TEcE7IvirEcvbls5th+Wp/BnMvpG5RjPwWnwPAF5eOrmeAvyYmbvZv57mR7m9aeus\n",
       "+3jFzM02B92k9aU0d8w/YdBGo3lO5FvLv5pxt1bolv/KMn52Ju8CXj1i3QOq/jv3Kdt+T8SsU7Qj\n",
       "T9d2vHVQYiY/Zybwak/L/pxyU1uaU4aPH1JmfTPd+nFT/6+bsdL+YGwzIs9eZdzuvwuAh0TwQaov\n",
       "tPI4q3sxc0oR4LsDyjuJ6nmUEbwsgoNGbH+k0jJ406irLhdozyHpbWvW1hEcH8Hbq222QeesfR3B\n",
       "ke1p3AjeWfoQrrPSn29et5Epn4mXl/F8W4fHlfmICe7nhTqNwTcYns9TMy6iaU0OWNsqPxEDTkXf\n",
       "FsERZdkZET57dYpOYfAf0VZ7odF8W6LfFME20dx38pnls3Pg+NU2UpnZy9Bsqp9tLacBMgcMp3fm\n",
       "txqR/8md+TsG5PnNEdvK5tDMqtPrSvqvRq0DuVPJf+yQ5ZeX8amQD+ssO6va3vEl7Stj9lV0yriu\n",
       "jK8sy9eMqW87PKma/n4Z/8OAfM8dkLZ32dZLyvxxCzy24/b9FvNcr8136Xq8915QyjhmAu/j+1V1\n",
       "e3D92iB/b9jrHrEfEvL0avp961CngNy5KuOueayzW6ee91nH/fEmyMM7r+eh1fxeVJ/rBZR7XHdf\n",
       "dZafXi+H3Ld6LSsGvT9HlLVZyXMD5DfL9MfmUcfdIXcbcCy27aS9rrOvE/LYqm5fHfI+227Etncp\n",
       "6+65vu/pDXkYdewhD4D8dH08RpSz34jvqLMmVd/F208M3EfrXe5yfwHLfYB8SOfN+jDI7SGfOeQH\n",
       "aZMRb/RflDyDvtCeUsZnD1l3O5qA5JQq7Q7Ib1fzB0D+sFsvyHtVeT5QxltDPqJMnzRgex+s1v+D\n",
       "kvbtzmt9VGc79yn5Pge5A+QKyJdCblKWD9svv19NPxdy1YA876/nq21+pv2ir5af3Fl3C8jNqn3/\n",
       "2jH1aYfzII8c8J54cZXn5+V1Di1nwPoPhzxtxHtua8j/MaaMbRb4Pn5OKeu6zmv/yoi6d1/XfmXd\n",
       "Nqj9y6qsT6/DZ6v9U7L5sNfZyd8N7JMSaK/Dttduj5nP7CHd5ZC/XGC5rx71Oqpyj2DuH5E/G/Q9\n",
       "MqKs80ueuyHvX5UzMhiFvA3y1k5a+x2wzYDPxhur6d+ttnV+tf6mzHxXfnjIdreHfGp3XzvM2U9P\n",
       "GPG5P7xzbM4fU9ao77e3rEPdVpTxLpCPGLD8lZBvWM/Xn5AHzi8vc/bRRI5Bfwd7Oi9gQxiYaVn5\n",
       "jU76sA/HdpB7d97kp1bL2y/VLw74MATkZQPSXzUg7UbISzo/Iu0/od07dXo0TWC0NeSuVfq5kH9d\n",
       "lfkSOq+rLG//UT+rSv9Muy3IZ5Ufk4TcZch+/F/VdvaBPKCk161I29AEbd3XugklUBxxnIZ9wVxR\n",
       "ldGmHVTGL6AJdreBPLSz3ktHbGvTkueFY7Y958uNmR/c6KQfP6ycTr6D27ov4D38hs775A9H1Lkd\n",
       "3l7GTy/jQzuv9Y00P8Tt/ArI+46owxMg71/Nn1bWe+Sg1zlg/a+O2zcL2B8J+fky3b7fzhj0Xlpg\n",
       "uWe1+2LAskF/KGa9VyCvpvkOWNXdPs0flBdB7ljmby15fqvMv7wqK0bUsVvuptV672RugLtZNV3/\n",
       "6TinKuOEKv3zVfrukPtW2/2bMj5qXY7bxjBU+/GmTvpJkP8+4H3z2gFl7AL538Z9xhdYr/asSP09\n",
       "umm1fMf1+UyWMr6wkDIMvDbCgaYVZuhpoOrN+ZAhy7ca9EFg5tTggyF3HffhKcOWZd0tIY9fwGv4\n",
       "aVXGMZAfqub3Yaa1a86HtfoSuHY+H+byZfD3g/JQTqt19t0f05yKOaGkBeS957G/2+HRnfk/rabb\n",
       "uu/aKWMvyJXt/l/g+6Et+6Bq+uxOnp2qZYfSBCvbQj5/zPHdvaxfl31hVW59KnHPAXVrW0KPGrK/\n",
       "VtKcfrsEcn/IS+sv1zJ+BeQFnfV+Xk1/dczxT8hzq/l/GvRah6zbDVoGtjh31vkcA1pWmB1YbMZM\n",
       "wDssiF5J82OzzzzeA+eWdeb8+aA5pT/o2H4c8u+Y3XXgRMjvUFqmaAKu7vdE9/N4TP3er9J3gHxy\n",
       "97iX6WcOqdPaYz9kn7TDs8t7+m+rtGsGvMfaH+VPlPETBuyfPRbyeet7oPmD+NtUfx6msI3Hdvbv\n",
       "M4Z8Xod+Zpg5nTuf4XWQ10A+dh51G1bG/em0jnfWe1pJfy2j/xDcZ1gZw9dhXvkWfBz6e1NN5wVs\n",
       "zEP5st58TJ4tmfkxPrukBdWP54A3erc/1jofO5qm4fqL+DkDtjfrh47S8kf176Qa/mEd67ES8qn1\n",
       "flmHMh5Y1WNPZv+Tr4cfrO9+G7L9R1KCXsgvlW18ssz/R5n/9JA6DRsOK+OLB7wX/teQdY4seber\n",
       "6tYuq/sjfrdK77a+zXpvzbOud4/ap53yuqfk31NNrxyw7k3V8i067933jtje60e8R5KZU+/t8OfV\n",
       "9Jy+kWOOf3d/vLyzvO2z95Qqz/cgfwPyawPW/zDkPQP2VTKkdQHy81WebZj9eT6Eqn8f5PPGHdMR\n",
       "r+3bY9Y9ubPeNwbkWVmV//CS9poFfuZ2Lus9YJKf5SHbuqFs62sTKm8l5O910ub03x1xDOqh/Q25\n",
       "14Bl7R/OF1ZpcwLuajuvgnz7PN7f9fCjzvyxQ9b70oj98eNufUrdnzx8HUZ+Jtf52Ez7zTTtF+Aw\n",
       "3/2fCbnXkGV1U/+DStoO5UO2KwN+qBaw3U0hr2JuZ9vuB+uRkPeu5runSa8u43XqczPB/XhfqtM8\n",
       "kNfT9IV5WlXXk8r4o1OuS7udx4/50qqH9rTe70EeSXPauv4hnU8ZD2PmH+gDmGm17Haefm9Jf/aA\n",
       "ur8M8uvV/Kur8j/L3E7u9TDnXy1zT+PWrTMXMrvFLmlaAf+C0mm/Tq/KfEDnS/qzlNOvnbI2GfG+\n",
       "Hja8nAEvYUZCAAAK5ElEQVSB+4DXtQVN4PSlAWW0n4mflP11FU2weC+aAPwxzLRUH1ny/rpa/yya\n",
       "H/vdB5R9TxmfNOS7ZNjwySHp76Bp8Ry2306C/O80f7YeMM99+eExy3/GzGnToft4zGesDY7/dMjy\n",
       "FTQtir8/YvnQVpgh+/WiCX0/nFnKO7tKu7mk3VBt7zhm94MdNLSf8Tl/hku5V9L0pWz/bB0xpJxb\n",
       "quk/hHxcmf7jeRzv7vDEIe+TOY0RzG6Fbs9G/Mmg9wXN9+DDmmkW9H6Z97EZf/A4GriS5plyLxuS\n",
       "521l+aXAwUPyTOUFOMzzQJM7jFm+aR/1qLb3RJrTHTdAvqtKf3PnQ3S/atlmi70fR7yeLUt92xao\n",
       "VYy4+mpC29yps6/a4XRmWsDqYWAAzdxWyG1p+tSN+tL7ZRkfS3Ma6G8GlBsL+NFZG4RUae22tmD2\n",
       "P+i9q/JfydxWpXb4Ub19yAcN2We/2d12tc6HaH6sPlvl756u+QLNafM1VVp9UcEpdK7s7Lzup1bL\n",
       "nkcTpCRNv7n/3tnW65l9pWJ3ePyQ/bsF5Lvb/VE+Z4NOr3aDwT0HlLX9mPfGZ2lOLyXNBTrtNuuu\n",
       "Dz+Yx3tiK8afquwOr6O50u7mKm1lnWeBn7H6T83+A5YPLbfzev+gSj8T8n9W8zsyt4/toyG3Lst3\n",
       "Y4GnSUuZ9VXZ94Z8RjX/zwOOdTucW8o4csjypAlaPgN5Yme77TpzurnMY7iG5tTyQTSfsUHdYDZh\n",
       "9p+s3ynjP2Z2MHkoMxdy3NPJP+x7M2lOuX+8TB+4KIEXzc0lr6a5P89mNDfpfGAnz7HA+WX6cOAb\n",
       "Q8qaygtwmP4ArO53e9l+COZ15clSGVhAoDHBbe5B88P/5E76QTR9qRK+nAy5IKGqd7vP31/SNqE5\n",
       "dbQNTZ+ObotSd5hzBdI6vJatOvMPrstlJrjNMn9Spw7fZPZVwi8Zsp0nDXkNc67WY0R/lrL8nAHL\n",
       "tqP5UXsQ1Q8mYzr5D9+3X26nT2SmT9Sw244s6P3XfT0lrQ2shl5cwcwP7Dllvm49eAEzpy/f3Flv\n",
       "ZNeIMXU8huYCirdVaXfR/EAfVx8/Ov15ytAGHr9bv/fHbPvcav3jhtSrHZ5aPksraK4O/GR17JLm\n",
       "AoH6s/ZfaS5G+maV9qkB5d5Jc9ubcXXdlOFdOV5STe/NTFBSt1A+sVPeJsz9k5F0TnGPqM/+NC1f\n",
       "B9D8mWvXHxbQfWhAGdvSBEr7Q25fpc+6cn/EMem24rdXTX59SB06AwM/q+s7jNlxHAl8rpp/OdDp\n",
       "V8DfAU+v5q8Edh5Q1lRegMP0B+DMfreXu6zLF7TDwH25+XyOH01Qc7955Gv/Ld7EzD/DN477UZjg\n",
       "63lw58vxyjKuO3ufQHNqcWgrLs0VWQdDvrWsv9uQfO0P5ceYaSG4E3J1WV63GnyOciXtiO3uwZD+\n",
       "hc2xyi+UulXBxQPPorR+DKjbvcv0falO3S1gf25CuSpwQsfnaazD/cnGlHlvqoteSp3fTRVADVlv\n",
       "ViBS0v53dbzavph/XgUZ9e102qFd57s0QfVezFzI8Ctm99vrDGckTcA87ke+PUW3KXOvWK+Ht3Tf\n",
       "15SAk+aUejf/gZ35zTvrtgH8TSP24+0lT3v6fvV6HMu6D2jbFzFoWkZ/c4Flfbms/9BO+vcG7IcH\n",
       "dPI8tXzGnlnml1Tg9RTgPdX8icDbO3k+DVRXMvFF4NABZU3lBThMf+g78HJYHsevBAq9t0oyc9PG\n",
       "15Qv7e2nvL2x5dOc1tl2wtvdGnJLP3/rvR/XtkTTtEaNurdcd/hMWW/ghSadbdQ3E/0e5HFw7ze0\n",
       "7yGaCzz+neY2PQcxc6XmF0fUfUuaflCv7Wz7RJpbrVzeSb+OuS3He5Zlj5vAvtyRnlv1x9Rnzp8r\n",
       "mguG3lHtkzfOs6wtmLkp+L2aMbm+dRw0jHrOHDDv53N1Hzkz3/UkLVPZPLj90rEZJ7/dHzD7O+eW\n",
       "KW9vbPmZvGcK270dIMY90EsjZc78HmVyN/DICDYFdsvkmvK4tj8CvgF8rc5frfewCPYFjqB5z38/\n",
       "kzs72+i+L4n4xaFl+S3Ac8vQOpXZz9cdVPc7aB41dgFwRgT3onlm6zNonn37T8D7aJ5Le202j07r\n",
       "lvHjbr3WVebSeqZqJv85IO0imkdd/ZcFlnUnzWPnyJx5hug0lH8BQxZGHEHzb+voMv8K4J7M/Osq\n",
       "z98BazLzI2X+SuBRmXlDpyyDMUmStGxk5sT/+oxr8foWsG9E7AlcDzydJtKunUcTtX+kBGo3d4Mu\n",
       "mE7lJUmSlpORgVdm3h0RpwKfp7nC8b2ZeUVEPL8sPyszz4+IYyPiauA24OSp11qSJGkZGnmqUZIk\n",
       "SZOzybQ3EBFHR8SVEXFVRLxs2tvTeBGxKiK+HBHfi4jvRsRpJX3HiLggIn4QEV+IiJXVOq8ox/DK\n",
       "iHh8lX5oRFxWlr11MV7PxioiNo2IiyPi02Xe47dMRMTKiPh4RFwREZdHxOEev+WhHIvvlf3+4YjY\n",
       "wmO3dEXE2RFxQ0RcVqVN7HiV4//Rkv6NiLj/2EpN91LP8Tdgdeh/AHYBDirT2wLfBx4IvAF4aUl/\n",
       "GfBXZfqAcuw2K8fyamZaSy8CDivT5wNHL/br21gG4MXAh4DzyrzHb5kMwPuBPyrTK4DtPX5Lfyj7\n",
       "//8C5XmefBR4tsdu6Q7AI4CDgcuqtIkdL+AU4J1l+unAR8bVadotXocBV2fmjzPzLuAjwJOmvE2N\n",
       "kZk/zcxLyvStwBXA7sDxND8IlPHvluknAedk5l2Z+WOaN+PhEbErsF1mXlTy/WO1jqYoIvageWrE\n",
       "3zNzqbjHbxmIiO2BR2Tm2dD0pc3MW/D4LQe/BO4Cto6IFcDWNBeeeeyWqMz8KnBTJ3mSx6su6xPA\n",
       "Y8bVadqB1+7ANdX8tSVNS0S5YvVg4EKaJw60V6TeAOxcpnejOXat9jh206/D49uXNwMvAe6p0jx+\n",
       "y8NewM8j4n0R8Z2IeE9EbIPHb8nLzBuBNwH/RhNw3ZyZF+CxW24mebzWxjmZeTdwS0TsOGrj0w68\n",
       "7Lm/hEXEtjQR+umZ+at6WTbtph6/JSgingj8LDMvZsiNET1+S9oK4BCa0xOH0FwN/vI6g8dvaYqI\n",
       "vYE/oTkNtRuwbUScWOfx2C0vi3G8ph14XQesquZXMTtq1CKJiM1ogq4PZOa5JfmGiNilLN8V+FlJ\n",
       "7x7HPWiO43Vluk6/bpr1FgBHAcdHxI+Ac4DfjogP4PFbLq4Frs3Mb5b5j9MEYj/1+C15vwV8PTN/\n",
       "UVo3PknzTGOP3fIyie/Ka6t17lfKWgFsX1pGh5p24LX2BqwRsTlNx7PzprxNjRERAbwXuDwz31It\n",
       "Oo+moyhlfG6VfkJEbB4RewH7Ahdl5k+BX5YrsgJ4VrWOpiQzX5mZqzJzL+AE4F8y81l4/JaFst+v\n",
       "iYj9StJjge/RPPfW47e0XQkcERFblX3+WOByPHbLzSS+Kz81oKynAF8au/Uerig4huaquauBV/R5\n",
       "NYPD0GPycJq+QZcAF5fhaGBHmoec/wD4ArCyWueV5RheCTyhSj8UuKwse9tiv7aNbQAexcxVjR6/\n",
       "ZTIABwLfpHnu3ydprmr0+C2DAXgpTaB8GU2n6s08dkt3oDkrcD3wHzR9sU6e5PECtgA+BlxF87zP\n",
       "PcfVyRuoSpIk9WTqN1CVJElSw8BLkiSpJwZekiRJPTHwkiRJ6omBlyRJUk8MvCRJknpi4CVJktQT\n",
       "Ay9JkqSe/H/diY8K7LoUnwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10636ced0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm8JFV58PHfAzPDIruswsiwiaAQEQRE1HGB4GiIqET0\n",
       "jYlocIui6OtOlKhvXteohKCYCKLkdQkCaiSKCyOgQpBNVhkiyKLsgsBoAHneP+r0vXVr+nb3zL1d\n",
       "fe+d3/fzqU9VnTpVdbqrb/dzzzl1KjITSZIkDd8aoy6AJEnS6sLAS5IkqSUGXpIkSS0x8JIkSWqJ\n",
       "gZckSVJLDLwkSZJa0jPwioi1I+KCiLg0Iq6KiP87Sb5jI2JZRFwWEXsMp6iSJEmz27xeGzPzDxHx\n",
       "rMxcHhHzgPMiYv/MPK+TJyKWADtm5k4RsQ/wGWDf4RZbkiRp9unb1JiZy8viAmBN4O5GloOBk0ve\n",
       "C4CNImKL6SykJEnSXNA38IqINSLiUuA24OzMvKqRZWvgptr6zcA201dESZKkuWGQGq9HMvNJVMHU\n",
       "MyJicZds0dxtGsomSZI0p/Ts41WXmfdGxLeBvYCltU23AAtr69uUtAkiwmBMkiTNGpnZrFiasp6B\n",
       "V0RsCjycmfdExDrAAcDfN7J9E3gj8JWI2Be4JzNv63a8YbwADV9EHJOZx4y6HFo1Xr/Zzes3e3nt\n",
       "ZrdhVRj1q/HaCjg5Itagapb8Umb+ICJeC5CZJ2TmmRGxJCKuAx4ADh9GQSVJkma7fsNJXA48uUv6\n",
       "CY31N05zuSRJkuYcR67XIJaOugCakqWjLoCmZOmoC6BVtnTUBdDME5nt9HmPiLSPlyRJmg2GFbdY\n",
       "4yVJktQSAy9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQS\n",
       "Ay9JkqSWGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSW\n",
       "GHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJaomBlyRJUksMvCRJklpi4CVJktQSAy9JkqSWGHhJkiS1\n",
       "xMBLkiSpJQZekiRJLTHwkiRJaknPwCsiFkbE2RFxZURcERFHdsmzOCLujYhLynT08IorSZI0e83r\n",
       "s/0h4KjMvDQi1gMuiojvZebVjXw/ysyDh1NESZKkuaFnjVdm3pqZl5bl+4Grgcd0yRpDKJskSdKc\n",
       "MnAfr4hYBOwBXNDYlMB+EXFZRJwZEbtOX/EkSZLmjn5NjQCUZsZTgTeXmq+6i4GFmbk8Ip4HnAE8\n",
       "bnqLKUmSNPv1DbwiYj7wdeCUzDyjuT0z76st/2dEHB8Rm2Tm3V2OdUxtdWlmLl2lUkuSJE2jiFgM\n",
       "LB76eTKzVyECOBm4KzOPmiTPFsDtmZkRsTfwtcxc1CVfZqZ9wSRJ0ow3rLilX43X04C/BH4eEZeU\n",
       "tPcAjwXIzBOAlwCvj4iHgeXAYdNdSEmSpLmgZ43XtJ7IGi9JkjRLDCtuceR6SZKklhh4SZIktcTA\n",
       "S5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUG\n",
       "XpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x\n",
       "8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJ\n",
       "gZckSVJLDLwkSZJa0jPwioiFEXF2RFwZEVdExJGT5Ds2IpZFxGURscdwiipJkjS7zeuz/SHgqMy8\n",
       "NCLWAy6KiO9l5tWdDBGxBNgxM3eKiH2AzwD7Dq/IkiRJs1PPGq/MvDUzLy3L9wNXA49pZDsYOLnk\n",
       "uQDYKCK2GEJZJUmSZrWB+3hFxCJgD+CCxqatgZtq6zcD20y1YJIkSXPNQIFXaWY8FXhzqflaIUtj\n",
       "PadaMEmSpLmmXx8vImI+8HXglMw8o0uWW4CFtfVtSlq3Yx1TW12amUsHLqkkSdKQRMRiYPHQz5M5\n",
       "eeVURARV/627MvOoSfIsAd6YmUsiYl/gU5m5Quf6iMjMbNaMSZIkzTjDilv6BV77A+cAP2e8+fA9\n",
       "wGMBMvOEku844CDgAeDwzLy4y7EMvCRJ0qwwksBrWk9k4CVJkmaJYcUtjlwvSZLUEgMvSZKklhh4\n",
       "SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTA\n",
       "S5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUG\n",
       "XpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x\n",
       "8JIkSWqJgZckSVJLDLwkSZJa0jfwiogTI+K2iLh8ku2LI+LeiLikTEdPfzElSZJmv3kD5DkJ+Cfg\n",
       "iz3y/CgzD56eIkmSJM1NfWu8MvNc4Ld9ssX0FEeSJGnumo4+XgnsFxGXRcSZEbHrNBxTkiRpzhmk\n",
       "qbGfi4GFmbk8Ip4HnAE8rlvGiDimtro0M5dOw/klSZKmJCIWA4uHfp7MHKQwi4BvZeZuA+S9Htgz\n",
       "M+9upGdm2iQpSZJmvGHFLVNuaoyILSIiyvLeVMHc3X12kyRJWu30bWqMiC8DzwQ2jYibgPcD8wEy\n",
       "8wTgJcDrI+JhYDlw2PCKK0mSNHsN1NQ4LSeyqVGSJM0SM7apUZIkSYMx8JIkSWqJgZckSVJLDLwk\n",
       "SZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAl\n",
       "SZLUEgMvSZKklszqwCuC0yL4k1GXQ5IkaRCzNvCK4AnAIcAzR10WSZKkQczawAv42zK/f6SlkCRJ\n",
       "GtBsDrweLvN5Iy2FJEnSgGZz4PWmMn9aBBuMtCSSJEkDmJWBVwRvrq3+FXBvSX9pBG8bTakkSZJ6\n",
       "i8xs50QRmZnROw/bAkdkcnSfPDc00zOJCG4EFmbS8zySJEm9DBK3rIqZVuN1A/DeiJ7l2qK2/PHG\n",
       "toUAEQZekiRp5pkxgVcEe9ZW9y5pG0XwrEYgtVFt+Qu1/despT9qKIWUJEmaghkTeAG715Z/X+bL\n",
       "gB8CTwGIYF3gu7V8VwHbluULgNvK8obDK6YkSdKqmUmB12drywvKfNMy7wySOiGgyiQzubGs7sl4\n",
       "M6SBlyRJmnFmUuDVCbZ+BawXwS61bR8t87eX+b0woWmyaSzwiuCQCO6btlJKkiStopkUeH2lzLcF\n",
       "/pGqGXFMeSbjc8vqrplcXNu8pLb8B+AnEXw4ggXAacB6wymyJEnS4GbSqO/3Aa8DFgE7AE8q6bsB\n",
       "lwOHlWUy+XVj32tqy2uX+TuB5Z3EEoQ9Fzg3c9VqwCJYBDxSa96UJEkaWOs1XhF8NYIPd9n0KOAB\n",
       "4FbgRSXtl5lcQdXJ/l2THTOT68vi6Y1N760t/w/wbeBzXcq0VgQZMRa0TeZ6qqZQInhUBJ/uk1+S\n",
       "JGnMKJoa/4KqNqppXaoaqnuAB4GHYKyfVz3/ayY57lrAocDLamkLuuQ7LILHdFbKKPgHlNVXRrB9\n",
       "BDtHcGAtzwsi+F+19Z1K2Y6cpCySJEkrGFVT420AZaDU7TO5jvEar4eBdQAyebDk/2Vt3+vpopM3\n",
       "gm8McP5bgIhgf+BTtfTP1DNF8JFM3gWcDGxS23Qt8NSSZ2EmNw1wTkmStJrrW+MVESdGxG0RcXmP\n",
       "PMdGxLKIuCwi9pg8H+eUxS0i2BA4ClgWwXyqGq8HqGq8mv67tnxdr/Jmjo0B1rEGVW1YsywJnNvr\n",
       "WMD/LvMV9gc2LnP7e0mSpIEM0tR4EnDQZBsjYgmwY2buRNUM+JnJ8gK71pYPpnrANVRNi08D/kh5\n",
       "4DVQD+AeKPNFmSs+p7GLhzsLZayvB3tl7qEzGn63kfA/0lmIYJtVPL4kSVqN9A28MvNc4Lc9shxM\n",
       "1RRHZl4AbBQRW0yS99HA4WX5i0wcrR7gIqpmxS9mcul4GUiqJslf9StvyT+f6k7Ipr8AntBn96O6\n",
       "HbLM3w+cWpZ3q23vV3MmSZI0LZ3rt4YJfZxuhp41QFdT1Wx1fLvMM5MHM7kvk79u7lS7c3EgmexO\n",
       "Feh11iOTf8/kKqpA8cdlUyf4+2SZ30tNBFsCAbwrkw9kcijw9bL5d2W+qDHgqyRJ0gqm667GaKxn\n",
       "11xAJhfAhAdanzHJMaYsk7snSX9lJvsDa2RyObAd8Dbg6ZTau5pNgRsYD7YAPl/mR9TSroqoHu4t\n",
       "SZLUzXQEXrcAC2vr25S0LuZ/MCKOgad9GZZ2Eptjb7WmNGGSyQ2lL9h5mTxSNj8BOA94PNWgrvVm\n",
       "zvvL/F7KA7yLtwy3xJIkaRgiYnFEHNOZhnaezEkrp+qFWQR8KzN367JtCfDGzFwSEfsCn8rMfbvk\n",
       "y8yM8XW2BtbL5BcR7A48lMnVq/5Spk8Ee2ZyUQSnAy+Eqqmytn0P4GLgaZn8pNwhSTNfyXstcGHm\n",
       "+DhgkiRpZmvGLdOl7zheEfFl4JnAphFxE1UH8/kAmXlCZp4ZEUsi4jqquw8Pn/xo4zLHa8Uy+fmq\n",
       "FH5YMrmoLN45SZbOXZadoS9+A2wFEMG8zOquyjJMxk5lMvCSJGk1N1CN17ScaEiR4zDVarKensl5\n",
       "tfR1qIaTeEsmj0SwOdUNA3cAe2RyWcn3Kkp/sGZNmCRJmrmGFbeM4pFBs8m/AdSDrrL++0yO7PQH\n",
       "y+T2TO4CzgY2q2W9o7MQwYsjeHELZZYkSTOUgVdvX1vJ/M9k4nMlNwZOKcunAqdGWPMlSdLqysCr\n",
       "t+8AL1qJ/GsCz62tb8qK/cTWnWqh2hLBolGXQZKkucTAq4cyoOvKDHfRfDTRo4G7GmnrT61U7ShB\n",
       "1/XlmZqSJGkaGHhNr4MAIlgjgn2o+nvdycRHCp0TwaYR7b/3EWQEOwyQLxh/FmXf/JIkaTAGXtOr\n",
       "83zJfwTOpxrZ/k7gWbU8O1F1un97mwWLYO2yeF0EC7psXxTB08vqK6meawmMDa0hSZKmyMBrGmWO\n",
       "PUz8zbXkuzL5I1XAVdf244U2ri13az48CTinLB83/OJIkrT6MfAavvsAMrmukb4ynfanQ73W7U0R\n",
       "bAFjzaKfp3pEEqU27Pz6jhFs2lopJUmawwy8pt9Hy/w04LfAFbVtK9RyRXBkBC9ooVwP15b/Dri1\n",
       "BFR/BF7F+Phj/wM8uyz/rMzvQJIkTZmB1/RbVuZLM9kkkz90NmRyIeM1T3eX+adpp2nv1V3S9u+R\n",
       "/3WZEx4ALkmSpsjAa/p1nt940yTbf0R1p+AmEVxS0rYdeqngwDKv9+/auFtGgExOKIvPgRWaSSVJ\n",
       "0iow8Jp+88v8rG4bM8lMfllWn9RJrz0XcpiWZfK72nMjT6xt2xL4dVnepZZ+BbCj/bwkSZo6A6/p\n",
       "dzpwUCbLV3bHCOb12Z5TDNA+2iXtfGCXTG4D3g2QyTW17Z0m0TZq5SRJmtMMvKZZJn/I5LuruPuk\n",
       "tUr1ZzxG8NaVCcAiWJOqc/3JteQjy3zfTqCVyRdrtWGUtIeBC4DNBzjPhRGsN2i5JEla3Rh4zSyP\n",
       "7pZYgqxHakmfKOm79ztgBAuBhcBtmTxU29R5dNHLByjXPsCZEVwewV6TnGc9YC/g7AGOJ0nSasnA\n",
       "a3R2pOrcXu/g3jXw6uGDvTZGsB1wI3A9sHVj8yllvtYA51la5k8EvjVJns6jhfYqNWySJKnBwGtE\n",
       "MvnvTO7J5B5g55J8YjNfBItrq/XxtG6i/92GB/U4/43AvwL/PkBxL6gtbxnB40vZtoxgzfIg7Utr\n",
       "eeyIL0lSFwZeM0Am15bFHQAi+E6tD9dny/wk4DCqZsO/LekPlfxRmhSbjq8tf6HLeY/I5IEBinhs\n",
       "Y/0tpZnzN8BXGB9Co8N+XpIkdRGZbYxiABGRmRn9c66eIriOKvB6AlU/qc2BRcB7gB0zeU4j/18D\n",
       "LwH+CcY686+ROd7pPqIaOT9z7OHXUynfnsA1wP0DZL8r01ovSdLsNay4xRqvmaPTLHgl43cQ3gC8\n",
       "BjijS/6dgRfAhDsolzTy3F72n7JMLiq1Y7/pke2lZb6yfdUkSVotGHjNEOUh2pdMsvnWLmkndUn7\n",
       "j85CBJsAjwNumXrpJtiaLn3RitupnlFJBI+a5vNKkjTrGXjNIJk8ubb657Xl33XJu4yqxmu9+thb\n",
       "EWMj559e8q2w7xTLmFR9zHYGjqDqSP+JsvlHVP3QAJ4xneeVJGkusI/XDBPBXcDhVMM2vJSqufGC\n",
       "et+tSfZbD7gPeHYmZ3c65zcHRB2GCNYGNi93ShLB94GPZPK9YZ9b0twUwZaZXWv7pVYMK24x8JpD\n",
       "SrD1JuAy4Bxg/0x+PKJyAKyZOWHgV0kaSPke2Tpz7BmyUqvsXK9BnEV1l+M5Zf0nIywLwJ+O+PyS\n",
       "ZqHaIMzrjrQg0hAYeM0td9ZX+jVPDlFnlPwzI3hMebj3E0ZUFkmzT+eRZt6koznHwGtueSXwA+AA\n",
       "YMGoCtFoGvhZmV8xirKMUgk6j4zgNxEsG3V5pFlkwzJfv2cuaRYy8JpDMnkok+dm8v3GA7FHYavG\n",
       "/Af1jRF8qNwQMJf9BfBpYEuqZ3NKGszflflWPXNJs5CBl4bl9tryMcBzIvgzgAi2At4LnD+CcrXp\n",
       "4VEXQJqldivzr3USIthyRGWRppWBl4ai3M34ybJ6XJm/JYK9GH8o+BMieGUE50SwMIJ1Wi/ocNXH\n",
       "ZSNi6jcbRPCu2l2j0pwSwUYRfBDYu5a2TQm6flOGrpFmNYeTUCsiuBHGHuT9CuD5VIOtfguqmrBi\n",
       "XiZ/bLl4XUWwFtXjm54N3JPJN3rk3bE8fYAIngR8nkbgBVMfV63N8dmktjX+qXgl8IVGlsdn8ovW\n",
       "CqTV2siGk4iIgyLimohYFhHv7LJ9cUTcGxGXlOno6S6k5oRLa8sfohrx/jImBl0AB3bbOWKs6aEV\n",
       "pTn0D8CNVF/+Z9RucW/m3Q9YVntM0tvoEnRNoSwblPmatTRrqzXX3dcl7QsRPLb1kkjTqOeXd0Ss\n",
       "SdVMdBCwK/CyiNilS9YfZeYeZfrQEMqp2e+9teVtgfuB5mfpVmB5c8dS8/TzCP5+eMVbwUFd0jaN\n",
       "YEEEBzTSX13mnYeD1weN3ZhqeI0Xwdgo/wOL4CnAvWW1/izPA/wB0lwSwQsaSUuBlzfS9gV+1UqB\n",
       "pCHp91/z3sB1mXlDZj4EfIWJzxDssNlDPWVyOVUTY8ehjA95sQ3VeD0XUAUqYyLYCXhPWX1fRPVZ\n",
       "i2C/CP67lm+TiLHAZ0oi2J3uDwI/lSrIOiuCw2vpryrzX0WwJzCvrN+ZyT1leI3OA8y3WMnibF3K\n",
       "dAhMqPX7DvhIJs0pi8p8XWB+Jndn8uURlkcain6B19bATbX1mxkfHLMjgf0i4rKIODMidp3OAmru\n",
       "yOQU4IPAFZk8TDXUwqcyuSWT5cADwCkR7AoQwbOBa4H31Q7zSGlm+zGwfQTbRfA64HLKALIRRBm0\n",
       "9RkRbBHBRyMGG84hgqdSNYF2sz9wfFk+MYJtS9+1up9RBVf/ATym9tofAi5i5QOvg8v8tC7bHFxS\n",
       "c8mBwHGZ/L58P3TsC/wf4G9HUyxpevULvAbpeX8xsDAz/4TqcTVnTLlUmrMyeV9mVXOTyVsyOaq2\n",
       "+RKqYOLK0sm2PvbXM2rL9c73xwKfoQQ5EcwHXle2/Yiq+fLtwH8OWMR/qy0fQlV7tRZ0bea8gfEb\n",
       "Br5f5j8DngMc3WUstVspgVcEG5Sy9nN4j23Nf4L6iuDpEWy+svtJ0y2Cnco/SG+N4CCq/p7zmvky\n",
       "uSCTozM5ntKc36n5lmajnnc1RsS+wDGZeVBZfzfwSGZ+pMc+1wN7ZubdjfRk4o/X0sxcOoWya46J\n",
       "YGPg7kk2b5bJnQMMpfBqqjsKVzDInYC14/8ykx0a254GnAd8gIm1cADrUN2peWpZ3zSTuyY59jZU\n",
       "tcd3ZE4eBJW+bX9oJK8LvINqbDSAh4CPZI4NONlTKcOxmbx5kPzSsERwMvBXZfWXwPbAbpm9n3Lh\n",
       "Z1jDEhGLgcW1pPeP4q7GnwE7RcSiiFgAvBT4Zj1DRGwREaXfTexNFcx1/fHMzGNq09KpF19zSSa/\n",
       "BZp3zn6/bOs8h/KJZf7CLoe4mPGga4Wa1zJWWNc/ogiWlH5UHa/tku0nwK6ZvL+RfkQmf6BqKu28\n",
       "lruY3M1lvtlkGUo/s9PLaucRTNtk8nsm9u2aDxwdwfPLfuuWgK2X3/fZLg1V+Tus3xyyPfDZfkFX\n",
       "zZGO6aXplplL63HKsM7TM/DKzIeBNwLfBa4CvpqZV0fEayOi88P0EuDyiLgU+BTV2EzSKsnko6Vm\n",
       "alvgkEwOqNdUZXJlJlHG1Pp6Sf4h1ee0PoRDJzi6hPG+Vjcy8Y7DutMZ70e1TuZY02G9bJnJ1WX1\n",
       "g8C2pSz/WrZ/h6ombOfmvsUKgVbEpM2FlwHPK8s7AjtkcktZ/ymsMLzGxuWH6AHgD90CzAi2KYsP\n",
       "TnJOaSg6zeoRfDqC44G3UtUsfLKW7SsDHq7zt/37yYZ4kWYyB1DVnBHBE6k62a+ZySMR7Ex1Z+Fd\n",
       "XZoo18usaqgi+BxwRGfDMAcnjWAXqn9iOk7PrIaaaOTrlHfnTK6d5Fh/pKrlu4YqUPtYbfMOwHbA\n",
       "g5mcW24u6Dyo+9OZvGVqr0QaTKmN/Y/M6qaXxubNgDvK8qLM/kNFRLAcxp5y8dHMFWrJNQIRbAjc\n",
       "A6xbauZXZt8A3g38KnNCP9uRGtkAqtJskckVpQbqkbL+i1qTX3N8ub8CKENQHEFLajVmHYc0a6ci\n",
       "uKgsvnyyoKvYCNiPqn/MxxrbtqNqpj2n/Ngtq2+LGLspoKsItoxgrwjeGdG12XXaRPCB0rS6qvu/\n",
       "wWanGe15ABHs39xQuhBsRlWDfFNz+ySeX1u+fdJcmrII1mh0weilU6P/lAGOe1jjEXHrUN25ekoE\n",
       "P1nJYs46Bl5aXXwA2LxWm3V8BNvCWN8xqDq9b9hCWY6kGkpjo7K+fWdDBOsx3mTas+klk/vKnZP3\n",
       "Nzb9lKqptps3UQ1RcWOfO8MuBS4EPgx8tlc5piKCTYG/A94Qwc4RrLuS++8J/DPwiWGUT9NiuzI/\n",
       "t5H+QqiCr3K382TdACbI5Ozyd/wBcBDhIdsGOK3XHdgR7FoGle78c/foxvb55e7V+pA4XwaWR4wN\n",
       "l7NBbdtTp6HcM5qBl1YLmTyUOdak8ZdlfkMty5ZlPLHftVCWfypDaXRGpL8uguMjeAm1x6RkDvww\n",
       "7M7YYp1m0mVMcmcnE2u+NmhujGCzUkO2RSN9kKEvVkVnOJHXUjWZfnyQnSI4IYJ/proBCGDLCB4/\n",
       "hPJpFZSx9P6hfJaW1DYdTRXQ/59ezz4d0O5U/8RoGjVqjzv9Qrv2RS21VlcCZ9WST2vUbr60zA+J\n",
       "4MJGc/Pby3zCP7wR4w9Jn4sMvLQ6+lFj/bhMbhtJSarR+gFeD/x7J3Fl+pmVvmpbMd7v5Z7a5t2o\n",
       "vjQXlWbY79a2LYKx5oTO+Zo/ZBeW+Vcj+Mde5YiYOKBrBI8u/+m+uMdu72ms97oblAj2KIuvAd5Q\n",
       "2/QiWKEZV6PzCFWfnabTMtk7k+l4pu+HwTG9huD3EWNPEfhxmS8qg1U3B22eLEA6N4J9S5/Wt9bS\n",
       "92rk6wRoG1INMN053wXMYQZeWu1kcjPjg7Bun8mbRliWfafpOLeWIS2gekh3J/2KTH7d6LS8AVWQ\n",
       "9+wIvkP1XjxS/hM9Gjgbxsq1H9XjiQ4Bjorg8RE8MYLXl6DqwAjWKvveH8GzaufpNOM+v/QZu63U\n",
       "qNW/d/4JJtxBWu+/M0EEhwEXd+mg/eZanlejkZqkv90CYP0ufRxXWebYj/MjEby7dO7WKir/gHXu\n",
       "yD6g0ez/BKq+pF9q7Fb/e92/sf5TqkBqD7r7XTnv16n+kdozk/0pXRvmdECd5R75YU/Vqdo5l5NT\n",
       "vwlyO8iEnD8DyrJlKUtn2rGFc/5z45z1aXHJ89gy/5seeRPyS7XlI8s+WzXynN1YL3dU512Qb4B8\n",
       "a23bfpCvhNwAch7kUyB/Osm5z6m9phshzx319ZwJU+f97ZPn55AvnqbzHQK5Tll+abk2+0KuP+TX\n",
       "Wf8sXDfq972la/vi6ud0qO9lQi4r85Ma6a8t83XK/LOQx9WOc2yXY+3ZWD8Mct1G2s/K/muU9b8Z\n",
       "/XvNtL/PWb3c2f0CnJzmwgQZkGu0eL6Xdfly/G2Zb9nIu6BP4NXtOH9dlp83SZ4ty2tOyD8vyzt1\n",
       "yfdgl7Q7IN8NuSnkvFo539rtBwlys3K+/UZ9nVu6tn8zyA9z7f3cYhXPs1nZ/4TasY6gCqS/1NJr\n",
       "fUrjs9E34Kx9pjcb9bWapGyP7gSxfa7b4atw7E0n+57p8ff8mj5/75/uc6xnl7SPQd5X3vvOP15H\n",
       "1vK9tbH/d0Z/LchhHNemRmkGKH+PA93VNU3n+zKwJtUjiHaj6kS7dVb9wG5t5H0wqz5nr6glX86K\n",
       "Txno2Aj4AtWjjP6TWt+1mt9QHq+UyTfK61/WJV+9U//LgQ0y2SyT/5vV3XD1hyl/HaDcrVp3eznf\n",
       "jyM4vNacMqeUYTWeBtVjqBpNus289Rsr3r+Kp+x0mn9NLe1zVHeZ3rJi9umXyYWMDzQM453BJ1Xe\n",
       "l1MoQ1GUJvMVxtJrUwSbl3J8nqqJfnm547eeZ42ICeNjHVDSJ9xF2McdwB/LmIed465d+nT9okv+\n",
       "7zN+13S3O46/wcQ+XB2bUO5uzOSHZf72TNYv3ydZ8tX7o95RW34b8Ke9homJGLsrfNpEMK+NJk4D\n",
       "L2k1lckjmfw+q35gt2SyvE/+U6geGL5WJrtn8lGqL9ezgLWpArlTGX++ZGdsrs4jjDbOiTcNdPux\n",
       "27PM6yPzv77Mb8wcv+uzS/k6/dhuiOC8CBZErPBMzROBayJYf7LjDEMpS5Zph/57DHTMeRET7j79\n",
       "ZyY+D3erHj8iu9QPtYpFOLTHthNX8ZgrLZPv1D5Xp/fMXHkZpey1/oL7RvQP2oaoc1PLq2ppd0Sw\n",
       "bQTbR3BeKzEJAAAMBklEQVQocD6MBSLvAO6M4KQyHwvSJrvmEXyttvq52vLvgOsZf+LGP9S2HUj1\n",
       "mMAjshoUdXFJ7wwR8r8yx/rLjsnkt5ncnf1vEur009uJKhju6Nyp/Qa6iOo5n7/tc+yBlL/JbSKY\n",
       "R/Xs21P77TNls73KzsnJaWZNlD4okI8u659sNn3Vmhc26XGcrSCfQdXn45hBmpGY2N/ssB7NI1e2\n",
       "+H68BPJva+f+IOR203Dcd5bj7cR4v5tzIH9SO9edjX0OLe/pI/X3Y4BzbV5vooL8905zF+TOnddT\n",
       "1p8zos/dSZM1N0IeBfmmsvzfPT4Xkza7Qj4f8uWQa5bP9A+nsezNcnT6V93SZdtpkK9rpP2gHOeZ\n",
       "Zf2VkGdCfg7y6ZCP6nKcI1mxK8CC8ve2PeSHupRzTaapX+BKvCcrNI2Wz3lSdVFYZ5DvhknOcUy3\n",
       "z8H4dvr+bazSedv7oxjOC3BycprZU/ky37yR9mjI3YZwrq27fJE+F/LxjHfm/dcy/01Lr79Tjl/W\n",
       "ln8KufYA++7Z+SGg6sP2d+XH5k8gT+7yWn8+2Y9IoyxJ1Rfs+LK8F+SCkmc9av2fIDep7fMOxvvv\n",
       "JeQTR/35qpXzRaVMv4D8Xkl7Sbcf1sb049ry/ZMce9danjtqy0umodydvo671I670SRlfULZ50+7\n",
       "XecBXus+kLt3Sb8R8pFRX8PG+/KhWvmiln5PLf2HZf6uVTj+QZO9T+N5yFUpe99zt/cmDucFODk5\n",
       "OXWm8iP2bMjjypfo4xrbt2f8bqzOtEOfY67BxE7860OuOWB51mica/vG+jP77N/J9y+Qf2zsu7yx\n",
       "/ona8gG15fXK+7JDlx/qZvnq0xv6/Ig/a9TXu8u1r5eveWdtfdoT8nvls7Ax5CnlPU4aATHjNxF0\n",
       "m744xTJvWA8uqGoPH1+21WujlkOe2eWz8UfIhWX5432uV1L+AWq8pseVc69SrVFL1/P0knZoj9f2\n",
       "/1bi2G+HfF/Z78O1YxzX+duo8pFTfR1dz9/emzicF+Dk5OTUnGo/ol1/TKiaYDpftm+B3LDHsd5f\n",
       "C1TWqu23sMc+QTUUxvUl706MD7ewW+0Yd0yyf72Wqde0qLY8v7a8Rjn/3WX9Wsjzy/KbIV9XO1e3\n",
       "O1yb02WN9ffMtB/q8lru7vEa1u+8lkn2Hbu2tbT6Hb0vZ2JN06c6AU8t//aQP6ME5pD/QDW8wnzI\n",
       "jzBe67p+2d4JJFa4M7C2vesdoqVsa5Tl+uvcCfLbkE+GfBPkE6lqj/6isf8etHgn9Spezz+rva56\n",
       "IP1FJjbfT7hu9WvaJa3e7Pq6xrZ5kP8DuTbkRQZeTk5OTgNO5Qv0qX3yHN380oY8kGp4i1dDnkVV\n",
       "m3BqyfMdyOc0vuzvobpF/hLIa8sxlgzwg7At5NtqeY6GfBIrjnfUb4rGcT/AxGbCZv7bu5RlLcjF\n",
       "ZftFVH3A6n3lspH3MaO+vj2u6TrlGn27Vv7NIG8s29emRxNv4736K8aD1XMaeZ5FVZPYybspvWvY\n",
       "uk1XlPkXmOJ4gpCvKMd64aivwRCu6QbltR3V/NxT1Qo+o5a+cW2/62vpr5rkGq9Qc12uSxnnkBzG\n",
       "ayqFH76IyMycuyPRSpp1yq34d/bNONFrqe4CO6tfxuKpmZzf5dwbA3f32O/yTHYvZfwYcHhJfz6w\n",
       "LLsPv9E8R/MLfp9M/muSvM8AbsscH1ag3LK/PJMH+51rpolgwcqWO4IFwP8003OSu/MieBJwCfBc\n",
       "Jj6BYWVslY0hXFZF+ZzcnTnwM15njdrn+OdUf08r3IEdwUNUd+iuSXWHZnN4jI9TPYGjc1fxTzJ5\n",
       "Wpfj3A1sXNYYRtxi4CVptVYert3zUTaZRO3Lf34mD0fwY6pHKn0MeDHVQ76XAF8Dnkg1RMDN9UBm\n",
       "kvM3v4T/ATi62w9oBLEyP6wRvI3qEVEfyC63/WtFEXyaakiUd5SkdTMnjJ/VzP8A42NcHQrcSBUA\n",
       "PEIVoC8HDs3k5Ag+TjXkxXkl/zyvS38RHAh8F/hC5tg/IM083wT+rJG8gGqcuvfW0i4H9sscG5+s\n",
       "eZzO39cxEMcYeEnSEESwDvA+qh/EE6meWfljqoBsnW7/YU9ynIOA763Mj2kEe1GNdXYecGpmz/Gx\n",
       "1JIINgcWZPVs1175lgDfBi7NnPS5hJqiCNbIHoNMl3G49mE8qP2XzGpw38Y/N4dn8oUex9kZ2C2T\n",
       "U4cVtxh4SZKkOaHUKr6NKmh+qKR1BnHeFPj1oLXGBl6SJEktGVbc4iODJEmSWmLgJUmS1BIDL0mS\n",
       "pJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmS\n",
       "JLXEwEuSJKklfQOviDgoIq6JiGUR8c5J8hxbtl8WEXtMfzElSZJmv56BV0SsCRwHHATsCrwsInZp\n",
       "5FkC7JiZOwGvAT4zpLJqRCJi8ajLoFXn9ZvdvH6zl9dO3fSr8dobuC4zb8jMh4CvAH/eyHMwcDJA\n",
       "Zl4AbBQRW0x7STVKi0ddAE3J4lEXQFOyeNQF0CpbPOoCaObpF3htDdxUW7+5pPXLs83UiyZJkjS3\n",
       "9Au8csDjxCruJ0mStNqY12f7LcDC2vpCqhqtXnm2KWkriAgDslkqIt4/6jJo1Xn9Zjev3+zltVNT\n",
       "v8DrZ8BOEbEI+DXwUuBljTzfBN4IfCUi9gXuyczbmgfKzGatmCRJ0mqlZ+CVmQ9HxBuB7wJrAp/P\n",
       "zKsj4rVl+wmZeWZELImI64AHgMOHXmpJkqRZKDJt/ZMkSWrD0EeuH2QAVrUrIhZGxNkRcWVEXBER\n",
       "R5b0TSLiexFxbUScFREb1fZ5d7mG10TEgbX0PSPi8rLt06N4PauriFgzIi6JiG+Vda/fLBERG0XE\n",
       "qRFxdURcFRH7eP1mh3Itrizv+/+LiLW8djNXRJwYEbdFxOW1tGm7XuX6f7Wknx8R2/YtVGYObaJq\n",
       "nrwOWATMBy4FdhnmOZ0Gui5bAk8qy+sBvwB2AT4KvKOkvxP4cFnetVy7+eVaXsd4bel/AXuX5TOB\n",
       "g0b9+laXCXgr8G/AN8u612+WTFRjH76qLM8DNvT6zfypvP+/BNYq618F/tprN3Mn4OnAHsDltbRp\n",
       "u17AG4Djy/JLga/0K9Owa7wGGYBVLcvMWzPz0rJ8P3A11XhsY4PhlvkLy/KfA1/OzIcy8waqD+M+\n",
       "EbEVsH5m/lfJ98XaPhqiiNgGWAL8K+PDuXj9ZoGI2BB4emaeCFVf2sy8F6/fbPA74CFg3YiYB6xL\n",
       "deOZ126Gysxzgd82kqfzetWP9XXgOf3KNOzAa5ABWDVC5Y7VPYALgC1y/I7U24DOEwgew8RhRDrX\n",
       "sZl+C17ftnwSeDvwSC3N6zc7bAfcEREnRcTFEfEvEfEovH4zXmbeDXwCuJEq4LonM7+H1262mc7r\n",
       "NRbnZObDwL0RsUmvkw878LLn/gwWEetRRehvzsz76tuyqjf1+s1AEfEC4PbMvIQVBy8GvH4z3Dzg\n",
       "yVTNE0+muhv8XfUMXr+ZKSJ2AN5C1Qz1GGC9iPjLeh6v3ewyius17MBrkAFYNQIRMZ8q6PpSZp5R\n",
       "km+LiC3L9q2A20t6t0Fyby7p2zTSuw6eq2m1H3BwRFwPfBl4dkR8Ca/fbHEzcHNmXljWT6UKxG71\n",
       "+s14ewE/ycy7Su3GacBT8drNNtPxXXlzbZ/HlmPNAzYsNaOTGnbgNTYAa0QsoOp49s0hn1N9REQA\n",
       "nweuysxP1TZ9k6qjKGV+Ri39sIhYEBHbATsB/5WZtwK/K3dkBfCK2j4aksx8T2YuzMztgMOAH2bm\n",
       "K/D6zQrlfb8pIh5Xkp4LXAl8C6/fTHcNsG9ErFPe8+cCV+G1m22m47vyG12O9RLgB33P3sIdBc+j\n",
       "umvuOuDdbd7N4DTpNdmfqm/QpcAlZToI2AT4PnAtcBawUW2f95RreA3wp7X0PYHLy7ZjR/3aVrcJ\n",
       "eCbjdzV6/WbJBPwJcCFwGVWtyYZev9kxAe+gCpQvp+pUPd9rN3MnqlaBXwMPUvXFOnw6rxewFvA1\n",
       "YBlwPrCoX5kcQFWSJKklQx9AVZIkSRUDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGX\n",
       "JElSSwy8JEmSWvL/ARMpLYF/3fT/AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ae3f110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm8JGV97/HPbzYEQYaRRZbBER0UFHWAACLIuERhYuAa\n",
       "UTFXQ1BfGg3XhURE44K5SbyJ90ZFNJAbMAQVNKIEDCSiMkSvskSYcYBBIUJkETBssrgw8rt/1NMz\n",
       "NT19Tp+Z0/2c02c+79erXt1V9VTV0119ur/nqaqnIjORJEnS8M2a6gpIkiRtLgxekiRJlRi8JEmS\n",
       "KjF4SZIkVWLwkiRJqsTgJUmSVMm4wSsiHhcRV0TEioi4PiI+Mka5UyLixohYGRFLhlNVSZKk0TZn\n",
       "vJmZ+YuIeGFmPhIRc4BvR8QhmfntTpmIWAY8LTMXR8SBwN8ABw232pIkSaOn76HGzHykPJ0HzAbu\n",
       "7SpyJHBWKXsFMD8idhpkJSVJkmaCvsErImZFxArgLuDSzLy+q8iuwK2t8duA3QZXRUmSpJlhIi1e\n",
       "j2Xmc2nC1AsiYmmPYtG92ADqJkmSNKOMe45XW2Y+EBH/DOwPLG/Nuh1Y2BrfrUxbT0QYxiRJ0sjI\n",
       "zO6GpUkbN3hFxPbAmsy8PyK2BH4T+HBXsQuA44FzI+Ig4P7MvKvX+obxAjR8EXFyZp481fXQpnH/\n",
       "jTb33+hy3422YTUY9Wvx2hk4KyJm0RyWPDszvxERbwHIzNMz86KIWBYRNwEPA8cNo6KSJEmjrl93\n",
       "EquAfXtMP71r/PgB10uSJGnGsed6TcTyqa6AJmX5VFdAk7J8qiugTbZ8qiug6Scy65zzHhHpOV6S\n",
       "JGkUDCu32OIlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTg\n",
       "JUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJwUuS\n",
       "JKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElS\n",
       "JQYvSZKkSgxekiRJlRi8JEmSKhk3eEXEwoi4NCKui4hrI+LtPcosjYgHIuKaMrx/eNWVJEkaXXP6\n",
       "zH8UeFdmroiIrYHvRcQlmbm6q9xlmXnkcKooSZI0M4zb4pWZd2bmivL8IWA1sEuPojGEukmSJM0o\n",
       "Ez7HKyIWAUuAK7pmJXBwRKyMiIsiYu/BVU+SJGnm6HeoEYBymPFLwDtKy1fb1cDCzHwkIo4Azgf2\n",
       "HGw1JUmSRl/f4BURc4HzgM9m5vnd8zPzwdbziyPi0xGxIDPv7bGuk1ujyzNz+SbVWpIkaYAiYimw\n",
       "dOjbyczxKhHAWcA9mfmuMcrsBNydmRkRBwBfzMxFPcplZnoumCRJmvaGlVv6tXg9H3gd8P2IuKZM\n",
       "ex+wO0Bmng4cDbw1ItYAjwDHDLqSkiRJM8G4LV4D3ZAtXpIkaUQMK7fYc70kSVIlBi9JkqRKDF6S\n",
       "JEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmS\n",
       "KjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi\n",
       "8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAl\n",
       "SZJUybjBKyIWRsSlEXFdRFwbEW8fo9wpEXFjRKyMiCXDqaokSdJom9Nn/qPAuzJzRURsDXwvIi7J\n",
       "zNWdAhGxDHhaZi6OiAOBvwEOGl6VJUmSRtO4LV6ZeWdmrijPHwJWA7t0FTsSOKuUuQKYHxE7DaGu\n",
       "kiRJI23C53hFxCJgCXBF16xdgVtb47cBu022YpIkSTPNhIJXOcz4JeAdpeVrgyJd4znZikmSJM00\n",
       "/c7xIiLmAucBn83M83sUuR1Y2BrfrUzrta6TW6PLM3P5hGsqSZI0JBGxFFg69O1kjt04FRFBc/7W\n",
       "PZn5rjHKLAOOz8xlEXEQ8PHM3ODk+ojIzOxuGZMkSZp2hpVb+gWvQ4B/A77PusOH7wN2B8jM00u5\n",
       "U4HDgYeB4zLz6h7rMnhJkqSRMCXBa6AbMnhJkqQRMazcYs/1kiRJlRi8JEmSKjF4SZIkVWLwkiRJ\n",
       "qsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJklSJ\n",
       "wUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOX\n",
       "JElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mS\n",
       "pEr6Bq+IODMi7oqIVWPMXxoRD0TENWV4/+CrKUmSNPrmTKDMZ4BPAv8wTpnLMvPIwVRJkiRpZurb\n",
       "4pWZ3wLu61MsBlMdSZKkmWsQ53glcHBErIyIiyJi7wGsU5IkacaZyKHGfq4GFmbmIxFxBHA+sGev\n",
       "ghFxcmt0eWYuH8D2JUmSJiUilgJLh76dzJxIZRYBF2bmPhMoezOwX2be2zU9M9NDkpIkadobVm6Z\n",
       "9KHGiNgpIqI8P4AmzN3bZzFJkqTNTt9DjRFxDnAYsH1E3Ap8CJgLkJmnA0cDb42INcAjwDHDq64k\n",
       "SdLomtChxoFsyEONkiRpREzbQ42SJEmaGIOXJElSJQYvSZKkSgxekiRJlRi8JEmSKjF4SZIkVWLw\n",
       "kiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi8JIkSarE4CVJ\n",
       "klSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEkCInhZBIcNdRuZOcz1\n",
       "r9tQRGZmVNmYJEnSRoogATKJYeUWW7wkTUoEx0Sw/1TXQ5ImI4J5redPH9Z2DF6SNkkEh0RwHnAO\n",
       "cFUEcyKICL4UwQunun6StJF+2Xp+w7A2YvCStFEi2CWC3YBvAb/TmnUt8BjwSuCbEbwogoE100cw\n",
       "K4JTxpi3XQR7DGpbkjZbFw57A57j1UME8zO5f6rrIU0XJUA91mPWecD1wAda024CntYaX5DJfQOo\n",
       "w+7AfwLPAa7PZE0Ej6P5B/IhIIDtMrk/grnADsBTgMsz+fVkty9p5orgWcAq4Fk0rV2zIX7pOV5D\n",
       "Ug6PrI7gqnJi3X0R7DzV9ZKmg3Lew+/1mpfJ0Zl8ENiyTPpqJouB5wN/WabdG8E2ETx5klXZvTyu\n",
       "BL4fwTHAz4GHYW3L2o/K4xnA7cC3gTURzJnktiXNUOV3fxVAJtdl8utMfjWs7W32wau84Y8Bz4D1\n",
       "ThC+I4I/m5pa1RfBvAi26po2O4I3RfCpQR4ymklKaN8rgl9GsE2fstP27y2C50WQZYgybccy+5fA\n",
       "3wOfBhYAuwGfAvbtLJ/JL4C9gGPL+HcyOQn4zVLkZ8AtEezU2mZErFtHmTYngg9GrA1ynelHsf5h\n",
       "zb1ozi1ruxnYLoIPA6/vmveJCJ7Z/52QNFNFsFX5jtujNa3923ZdlXpsrocaexw6ORH4Gs1hkgXA\n",
       "j8v0RZn8Z+XqVRHBfsAa4FHWfeBeDhwMfB94HM0PLtBcXttjHYuB1wF/3vkPoby3xwGPZHJumbYl\n",
       "sE0mdw/r9QxaBNtn8l99ynwXOKgz3lyCzPbAMZmcGsFLgX8FXgD8G/DZzA1CwZTrXELdw2HAZeX5\n",
       "rpncsQnrPg14SxldAbwjk3+L4DeAK4G/Bk4AlgKn0jT1n82G4Qmav9GPAU8EDgf+CFgMfA+YBzzQ\n",
       "VffVsN5n7ijgwswxX6+kGah8L/+0M975PYvgt4ELgFdm8uX1lxlSbsnMcQfgTOAuYNU4ZU4BbqQ5\n",
       "BLBkjDLZb1vDHCAXQT4K+TBkQn6uPI5ZL8jlkCsgXwAZk9j2nM62IA+a4vfhz0o93tuq03jDI5An\n",
       "l+fbtKbvDBmt8cPL+nfss753TuXrH+d92aZ8Rl4LuR3kV0t97y+P8yD3gfwZ5BZlmSdAPgR5d+vz\n",
       "dMIE3tNtIbeb6tfceu2/X+q1xRj1vQ9ypwFs542tdR4F+YMJfgbbw3P6bON3O5/V1rStIVe11vHx\n",
       "8vjCqX7vHRwcNm3ofA9vRPkvdn2XfBvyxPFywLByywQqy6HAkrGCF7AMuKg8PxC4fFNfAORukM+D\n",
       "fA3klyEX9go8kLO7xl/a9YYuKdP3KeNHQN7Z40v8jD71OaBV9nbIeZv4Aen1A7Ia8pmQsyp8QPeH\n",
       "/C3WD07dw+6QR5bnh0O+HPJtkFuVdVzeY5kHWs//vpS7ooxfP862Xg75Q8gTNuI1PA7yM5CHDOH9\n",
       "iXHq2ms4AfKpkO+GXNFnPyfkb5bHz3VN3wPyK5Av2oi6vrws+9GJfvFA7gD53DH+ljqv/ZLWtPnl\n",
       "/T6tzNtnQO/zjpCf7noPOuHr3Na099KE2XllmSMGtP1XQ17ctf37er0vDg4O03eAPLj8/T5pjPnz\n",
       "IPcuz58N+QGaRpf3l++37u/og3uvhxxK/Sf2Ilk0TvA6DXhNa/wGYIP/jicYvHr9aL27/DhsAXkZ\n",
       "TQtUQh7Kxv/HvA1N69McyCf3+8KFnEsTPjpf1j+CfGWZNwvyJMgtO+sp9ey0kOwDeWVr2w+VHd79\n",
       "w5NluZ1b210AuceAPqBzemxvF8h/gfwdyBsgfz6B9fxpWfbuHu/7K7vGV5RlFtL8R/H6Mj67R11O\n",
       "6rPdN3YvM8A/3idAPhFyZdc2boHck6alZBeafwa6g0JnuLS1vi3bdSz7e07XNnv9AzCh1wS5uMey\n",
       "e27k39VXIf+iPN8S8tbO8zGWHXgogVzSqs/jW9Nnl8/Z0IIQ44fsnl/iDg4OUzt0/Y5c0vqbfUWZ\n",
       "tn/7ewPyD8r8/SH/qVX+t8v8HVrTxvwHdjoHrwuBg1vjXwf2G+sFlC++V0AubL1JT6EJKfdBvgTy\n",
       "+WX6MeWNuXGcL8vO8JyyzDyaUJGQHys/ng9C/sUkd3y7Dk+iOVTS3v4FkN/vmva98nh0j/UthDyj\n",
       "zP9Kedyna/m3TbLOc3u8T8+cxPqeWh7n0xyWOxRyqzJ01v8orRDZYx2dIPjv7dcJ+cmucotpWija\n",
       "df9UeVzZrtNYfziQh5X6ZPnj+1vI3y71fX3Xuu9inBAD+RyasP34sq87y23UIbiy7be3ln9PeVwG\n",
       "eTTNf3Jzxlh2bdiCPL48Pw3yvPJ8g+VoWpH7/e18dzKfs038LO3IFB12p2lp3gFye5qQ3f1+LKGr\n",
       "JRryhZA3Q86dijo7OGyuA+tOdUmalvvO885RlQN7/A3/ose0r3etdwvIp4+/bXIor2liL7xv8Hp+\n",
       "a/zrwL69XgDkP3a9Ec+D/FZr/FU93vTHWvPfTNMCMQvyE5Cvrrjzt2n9SP6k63U81jX+1NbzXfqs\n",
       "9/N9fhSfAfmd1vjOkKfQhLReh46+UX5M2oe1nlXpPZo9wXLzOmW7Xut55T3+jda0f+latl+I2Njh\n",
       "25Cns/HnC+zCgM5Xg3xHj3p9jXWHeTstQQm5Q2u5P+xa5pwe6z67zHsn5Joe2zmv1t/QdBxo/jnZ\n",
       "eYzPxrHlvX96a9rJU11nB4fNaRjjb3MW5L59vtuP7xr/vY3fNjmM1zShqxojYhFwYWbu02PeacDy\n",
       "zCxXr8UNwGGZeVdXuYQPlbGf/QSO3Lm5iAmAc4Fjs0e/GRHMp7ki6q8zebRvZYcsggXAPWV0x8zm\n",
       "KokIzqLp1PEvy/gfAS/N5GV91jeL5irKNcB9wFWZHFD6HZrI612cyU1lXWcAb+ia/8FM/ufEXl19\n",
       "ESwD3gG8dIwiT8jkwVb5fWiuuJyo19Bc+DELmA1cUaa/CXgoky9sdKUHrHwGOh18Xk7rKskuKzN5\n",
       "bmu57YB7y2jnKsC1nZVG8Argy8DLM/nnrm0uBDKT2wb2QkZYBE/K5M7S5cS1YxS7H7g4k9+tWDVp\n",
       "s1W6n7kT2Al4LfBxYI9Mbi7zOwHmd2h+P18M3EHT9c08mquf9wW+Cfwyc/yrmSNiKa1gAnwop+Kq\n",
       "xhLMFjGxk+sPYpyT62kOo+xYUuwWkH8C+eKpTtSbkMDPgXzJENY7r2t8f5qrEIPmEFevJtWkOebd\n",
       "PpfrA+Vxo1pxpnqgOSz8R5BXQ+41TrnOVYW70pwEvn1puXg25NZl3oRa36bLAHk+5AvK81msO/zc\n",
       "Gf68z/KdCyfuojkUfGZn2al+baM4QL6q6/2/meYUiex8xga0nYA8dIpf6+xBviaHzW8on6EJXyS0\n",
       "Ees9drzvMJrzVD81vNfFmNuezNC3xSsizqHpD2d7mm4lPgTMLTU6vZQ5laZPnYeB4zLz6h7ryZxG\n",
       "/XiNugi2BrYGftKenuv6Jtkic70bfmrElNvhPCdzbStdv/J/DHy0a/Iumet/RrTpOv9hZ48+7TZi\n",
       "HZ3bkryRpnf/7YFDMvl/A6nk2NtdlMktXdNOBf6wNel3MzfomLZ7PefT9Ic2P3O9ftO0mYrgf9B0\n",
       "K/Vc4Bc0RzA+n7n26NCmrjeBn2eu37l3LcPKLZttB6ozSQTHA59kAl+amrlKx7XX0NzLEGBOeo/C\n",
       "gYrgn2la+a8Dvgq8N3Ntb/+zMvl1BDsAfwtcmclHupYf7xSC52fynQHXdxuawyydu3K8H/gCMB/4\n",
       "B5o7AHR7APgE8OHM9e/PGcEuNLdi6nge8EAmqwdZb42O1u9Pt4szWdaj/E7Aw5k8NIF1J7Ask4sn\n",
       "X9ONZ/CSNCERLAFWZNo7+zBE8G7gr1qTTgYS+DBwCetuk9Qxq7MvIniQpqX6icBTgUNozs/7CfCm\n",
       "TM4aYD3b5w6O5V5gR5rbQL2IpsPsbt8u9Ww7nuYuAx0bnEeomS2CLWhuQt8J3Sey/t8F0LQOR3AT\n",
       "cATwCDTnlbaOzswBIss53BG8neZzeD7NOVuzpuq7zOAlSdNEBK8Cng5jXrhyIPAVYJfWtDcBfwe8\n",
       "IpPzu9b3AeBPaS4CmQU8G/gP4IjcxAtAIvgs8N9pTkj+GM0t0m5tFXlmJtf3WO4I4KJxVv0RmrDZ\n",
       "PpXhfwMnZ/LwptRVo6G07B4BPI2mVbTjqZn8qNzfNWk+w3eWeb+guf1cL3NoLiwD2BvWfh5/QPP3\n",
       "dU5O4cUsBi9JmmYieBbNYZYraILTLsBWmc2VtxG8GTi9vUyv88Mi2Jbmqsle9srkhh7LvAm4PHPD\n",
       "qzAjeB7wHeDjmbyrNX1rmvP+ftjndQXNPVuvAnYGnpjJ1RHMz2zqGcFq4BmlXOcQ6b8Ar87Wlcga\n",
       "bRFsRXNY+jSaFt1uJ2ZucG5pZ9leAePNNIfi+5ny+9oavCRpRJUb9B5B82PS80s3ghWsOz/vbppD\n",
       "gB2nZ/IHJRA9gaY1oHPRxewe52L9ANiTIV5cUQ5lzqU5nNl93trHgZ9m8hfD2LaGJ4KTaG5Gfx1N\n",
       "a1W3fwReRfOPxhd6tZq21vUEmvNOnwv8iqZrh+9l8quynY/Q9AX6M5rW2c/TdIn0C2D3zPVaaKsz\n",
       "eEnSDFaCTLbOB9sSWAysLEXeBryTJlB13E7TX+D1ERxN86N4AXAksF8mG1xhPsT6B82Vbce3Jr+M\n",
       "JoBdE0F43uH0FsGLgG/QnPv3UVh7cciXac5LvBj4aHfQn8T29gVWZfJoacG9IJO7B7HuQTB4SdJm\n",
       "KIJ50LNrmAOAz9GEs3tpOmLuuC2ThRWqt4HSmfQBNJ1ebtejyGWZLC2HPZ+SyaqqFRTQBOXuIBzB\n",
       "d2k6nO4c4rsgk6OqV26aGFZumTXoFUqSBiebO3rMpQlZ0FzlFZlcBfxxmdYJXU8EfmOqQhdAJsdm\n",
       "shewZIwih0XwNOCDwPdLlxeqJIJPRnAH8FgEWYI9EfwWTSfo76G5MATguCmq5oxmi5ckjbgIfgRc\n",
       "ncnRU12XtgieQdO9xgKa4Phz2OA2VSdludWahqccCj6KdaGqp8l0DjzTeKhRktRT+VFlFM6himAv\n",
       "mnvr/RnNuWgX0Nzn9plTWrEZKIJPA2+lOW/rHuDVtA5D9+g6ZKtMfl69otOUwUuSNKN09eT/AppO\n",
       "WU/I5BtTV6uJi2A2TUe4NwILae4+MKm7h2zsRQitrkg+k8kbWtO3oblasO3vgDe3119C+6uBS6fT\n",
       "ie3TgcFLkjQj9ejv6QqaTmirtMCU8HEGcHYml/aYP690gdC588B49sjk5l7bKLeXmtXrqsAIFgI/\n",
       "LqM7ZvLTUq8Y7yrCCH5Kc79PgDMzeWOZ3nlPt6fpBf6yTN7fp+5q8eR6SdJM1emdfMvyeGB5vKec\n",
       "AN7u04wI5kYwK4ItInh8BBHBHmOtvMx/XQTXRrA0gq+U9Wa5t+ZjNCeSfzNi7X0tO8tuAfwygrPp\n",
       "HbougvWC1o8iOK1rHYspJ7MDvy7bPbE8fq1M/3Frkbsj2Bt4CPj5WBcgRLCAJljtAJwEvKHzukqR\n",
       "/TK5J5NDDV3Thy1ekqRpI4JdaQLObJpOPLstoemUs5ezaA67PRH4L5pbz9wOfAjYr8+mjy3LQ9Nv\n",
       "1avL9p/eKvPvNF1lbNvpwb9V7wD2YV2/a3fS9OL/rQi+BLyyz/ahuaLwi7BhixnlnoUR7AzcAdwC\n",
       "PAjs07rv4WeA3y/lD8pc28muNoGHGiVJm5UIDgL2YF1XGr3cCTxpAqu7iOZ2Ne+luSn5x2j6QFsB\n",
       "LMjkvoi1ga3bwcCfAK/rDlxj1LvXD+tbaO5ZeDZNOHw7zSHV79K0Wt3b6jx3EU34eg9NmHsdsIrm\n",
       "RuY3s37L2+MzeaRfnbTxDF6SpM1aBC+huV/gmkzmtqY/mybYvI0mIP0XcC3NobqVsHHdJERwJs2h\n",
       "x6OBL2/K1aLlxPuLgJdu7PbL8jvS9PqfEbwP+PPW7COB1wDnZvLVja2bJsbgJUna7EVwDPCNTH46\n",
       "wfL7AI8rHc5WVc47OyFzvdsoTWZd/wH2tVWLwUuSJKkSr2qUJEkacQYvSZKkSgxekiRJlRi8JEmS\n",
       "KjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi\n",
       "8JIkSaqkb/CKiMMj4oaIuDEi3tNj/tKIeCAirinD+4dTVUmSpNE2Z7yZETEbOBV4CXA7cFVEXJCZ\n",
       "q7uKXpaZRw6pjpIkSTNCvxavA4CbMvOWzHwUOBc4qke5GHjNJEmSZph+wWtX4NbW+G1lWlsCB0fE\n",
       "yoi4KCL2HmQFJUmSZopxDzXShKp+rgYWZuYjEXEEcD6w56RrJkmSNMP0C163Awtb4wtpWr3WyswH\n",
       "W88vjohPR8SCzLy3e2URcXJrdHlmLt/oGkuSJA1YRCwFlg59O5ljN2pFxBzgB8CLgTuAK4HXtk+u\n",
       "j4idgLszMyPiAOCLmbmox7oyMz0XTJIkTXvDyi3jtnhl5pqIOB74V2A2cEZmro6It5T5pwNHA2+N\n",
       "iDXAI8Axg66kJEnSTDBui9dAN2SLlyRJGhHDyi32XC9JklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6S\n",
       "JEmVGLwkSZIqMXhJkiRVYvCSJEmqxOAlSZJUicFLkiSpEoOXJElSJQYvSZKkSgxekiRJlRi8JEmS\n",
       "KjF4SZIkVWLwkiRJqsTgJUmSVInBS5IkqRKDlyRJUiUGL0mSpEoMXpIkSZUYvCRJkioxeEmSJFVi\n",
       "8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmVGLwkSZIqMXhJkiRVYvCSJEmqpG/w\n",
       "iojDI+KGiLgxIt4zRplTyvyVEbFk8NWUJEkafeMGr4iYDZwKHA7sDbw2IvbqKrMMeFpmLgbeDPzN\n",
       "kOqqKRIRS6e6Dtp07r/R5v4bXe479dKvxesA4KbMvCUzHwXOBY7qKnMkcBZAZl4BzI+InQZeU02l\n",
       "pVNdAU3K0qmugCZl6VRXQJts6VRXQNNPv+C1K3Bra/y2Mq1fmd0mXzVJkqSZpV/wygmuJzZxOUmS\n",
       "pM3GnD7zbwcWtsYX0rRojVdmtzJtAxFhIBtREfGhqa6DNp37b7S5/0aX+07d+gWvfwcWR8Qi4A7g\n",
       "NcBru8pcABwPnBsRBwH3Z+Zd3SvKzO5WMUmSpM3KuMErM9dExPHAvwKzgTMyc3VEvKXMPz0zL4qI\n",
       "ZRFxE/AwcNzQay1JkjSCItOjf5IkSTUMvef6iXTAqroiYmFEXBoR10XEtRHx9jJ9QURcEhE/jIiv\n",
       "RcT81jLvLfvwhoh4aWv6fhGxqsz7xFS8ns1VRMyOiGsi4sIy7v4bERExPyK+FBGrI+L6iDjQ/Tca\n",
       "yr64rrzvn4+ILdx301dEnBkRd0XEqta0ge2vsv+/UKZfHhFP7lupzBzaQHN48iZgETAXWAHsNcxt\n",
       "OkxovzwJeG55vjXwA2Av4K+AE8v09wD/qzzfu+y7uWVf3sS61tIrgQPK84uAw6f69W0uA3AC8Dng\n",
       "gjLu/huRgabvwzeU53OAbd1/038o7/+PgC3K+BeAY91303cADgWWAKta0wa2v4C3AZ8uz18DnNuv\n",
       "TsNu8ZpIB6yqLDPvzMwV5flDwGqa/tjWdoZbHv9beX4UcE5mPpqZt9B8GA+MiJ2BbTLzylLuH1rL\n",
       "aIgiYjdgGfB3rOvOxf03AiJiW+DQzDwTmnNpM/MB3H+j4GfAo8BWETEH2IrmwjP33TSVmd8C7uua\n",
       "PMj91V7XecCL+9Vp2MFrIh2wagqVK1aXAFcAO+W6K1LvAjp3INiF9bsR6ezH7um34/6t5WPAu4HH\n",
       "WtPcf6PhKcBPI+IzEXF1RPzfiHg87r9pLzPvBf4P8GOawHV/Zl6C+27UDHJ/rc05mbkGeCAiFoy3\n",
       "8WEHL8/cn8YiYmuahP6OzHywPS+bdlP33zQUES8H7s7Ma9iw82LA/TfNzQH2pTk8sS/N1eAntQu4\n",
       "/6aniHgq8E6aw1C7AFtHxOvaZdx3o2Uq9tewg9dEOmDVFIiIuTSh6+zMPL9MvisinlTm7wzcXab3\n",
       "6iT3tjJ9t67pPTvP1UAdDBwZETcD5wAvioizcf+NituA2zLzqjL+JZogdqf7b9rbH/hOZt5TWje+\n",
       "DDwP991HDOP/AAABUUlEQVSoGcR35W2tZXYv65oDbFtaRsc07OC1tgPWiJhHc+LZBUPepvqIiADO\n",
       "AK7PzI+3Zl1Ac6Io5fH81vRjImJeRDwFWAxcmZl3Aj8rV2QF8PrWMhqSzHxfZi7MzKcAxwDfzMzX\n",
       "4/4bCeV9vzUi9iyTXgJcB1yI+2+6uwE4KCK2LO/5S4Drcd+NmkF8V/5Tj3UdDXyj79YrXFFwBM1V\n",
       "czcB7615NYPDmPvkEJpzg1YA15ThcGAB8HXgh8DXgPmtZd5X9uENwMta0/cDVpV5p0z1a9vcBuAw\n",
       "1l3V6P4bkQF4DnAVsJKm1WRb999oDMCJNEF5Fc1J1XPdd9N3oDkqcAfwK5pzsY4b5P4CtgC+CNwI\n",
       "XA4s6lcnO1CVJEmqZOgdqEqSJKlh8JIkSarE4CVJklSJwUuSJKkSg5ckSVIlBi9JkqRKDF6SJEmV\n",
       "GLwkSZIq+f+WplspmqNSrAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a7b1d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# choose the paramator of Brownian\n",
    "# Brownian paramator (p) = 1.75\n",
    "\n",
    "import pylab\n",
    "from random import normalvariate as norm\n",
    "from random import seed\n",
    "from math import sqrt\n",
    "\n",
    "x = np.arange(0,time, 1)\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "time = 10000\n",
    "average_num = 100\n",
    "p = 2\n",
    "\n",
    "for num, j in enumerate(steps):\n",
    "    step = j\n",
    "    y_all = [] \n",
    "    for l in range(average_num):\n",
    "        y_num = [0] * (time)\n",
    "        value = 1\n",
    "        y_num[0] = value\n",
    "        for i in range(time - 1):\n",
    "            update_value = value + step * (2 - value) * value + p * sqrt(step) * value * norm(0, 1)\n",
    "            y_num[i + 1] = update_value\n",
    "            value = update_value\n",
    "        y_all.append(y_num)\n",
    "    y = np.array(y_all)\n",
    "    np.reshape(y, (average_num, time))\n",
    "    y_ave = [np.average(y[:, k]) for k in range(time) ]\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_ave)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAlQAAAEUCAYAAADtKKjYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAGsxJREFUeJzt3XuUZXV55vHvAw0ahhhkVOTSilFALl5aCfQChdKRCaCg\n",
       "E80IK4kOJt4SvJBZjopORJdRTDLKECMBuQTEgAQNiqIElQY0ob0ADUorMAuVxtAgCHJRgfDOH3sD\n",
       "RVHdVdX7VO1z6nw/a9XqOufsU+dZe1VXPfXbe78nVYUkSZI23EZ9B5AkSRp1FipJkqSOLFSSJEkd\n",
       "WagkSZI6slBJkiR1ZKGSJEnqaL2FKsljk6xMckWSq5N8eB3bHZvk2iSrkiybn6iSJEnDacn6Hqyq\n",
       "XyV5UVXdk2QJ8I0kL6iqbzy4TZIDgWdU1Q5J9gSOA5bPb2xJkqThMeMhv6q6p/10U2Bj4LYpmxwM\n",
       "nNpuuxLYIslWgwwpSZI0zGYsVEk2SnIFsBa4sKqunrLJtsANk26vAbYbXERJkqThNpsVqgeq6rk0\n",
       "JWmfJBPTbJapTxtANkmSpJGw3nOoJquqO5J8CdgdWDHpoRuBpZNub9fe9whJLFmSJGlkVNXUBaN1\n",
       "Wm+hSvIE4P6quj3JbwD7Ae+fstkXgMOBM5MsB26vqrVdg42LJEdV1VF95xgm7pPpuV+m536Znvvl\n",
       "0dwn03O/TG+uC0EzrVBtDZyaZCOaw4OfqqqvJXkjQFUdX1XnJTkwyXXA3cBhGxJckiRpVM00NuEq\n",
       "4HnT3H/8lNuHDziXJEnSyHBSev9W9B1gCK3oO8CQWtF3gCG1ou8AQ2pF3wGG0Iq+AwypFX0HWAxS\n",
       "tTDniicpz6GSJEmjYK69xRUqSZKkjixUkiRJHVmoJEmSOrJQSZIkdWShkiRJ6shCJUmS1JGFSpIk\n",
       "qSMLlSRJUkcWKkmSpI4sVJIkSR1ZqCRJkjqyUEmSJHVkoZIkSerIQiVJktSRhUqSJKkjC5UkSVJH\n",
       "FipJkqSOLFSSJEkdWagkSZI6slBJkiR1ZKGSJEnqyEIlSZLUkYVKkiSpIwuVJElSRxYqSZKkjixU\n",
       "kiRJHVmoJEmSOrJQSZIkdWShkiRJ6shCJUmS1NF6C1WSpUkuTPL9JN9L8tZptplIckeSy9uP985f\n",
       "XEmSpOGzZIbH7wOOqKorkmwOfDfJBVW1esp2F1XVwfMTUZIkabitd4Wqqm6qqivaz+8CVgPbTLNp\n",
       "5iGbJEnSSJj1OVRJtgeWASunPFTAXklWJTkvyS6DiydJkjT8ZjrkB0B7uO9s4G3tStVklwFLq+qe\n",
       "JAcA5wA7DjamJEnS8JqxUCXZBPgscHpVnTP18aq6c9LnX07yiSRbVtVt03ytoybdXFFVKzYotSRJ\n",
       "0gAlmQAmNvj5VbW+Lx7gVODWqjpiHdtsBdxcVZVkD+Csqtp+mu2qqjzXSpIkDb259paZVqj2Bv4Q\n",
       "uDLJ5e19RwJPAaiq44FXAW9Ocj9wD3DInFNLkiSNsPWuUA30hVyhkiRJI2KuvcVJ6ZIkSR1ZqCRJ\n",
       "kjqyUEmSJHVkoZIkSerIQiVJktSRhUqSJKkjC5UkSVJHFipJkqSOLFSSJEkdWagkSZI6slBJkiR1\n",
       "ZKGSJEnqyEIlSZLUkYVKkiSpIwuVJElSRxYqSZKkjixUkiRJHVmoJEmSOrJQSZIkdWShkiRJ6shC\n",
       "JUmS1JGFSpIkqSMLlSRJUkcWKkmSpI4sVJIkSR1ZqCRJkjqyUEmSJHVkoZIkSerIQiVJktSRhUqS\n",
       "JKkjC5UkSVJH6y1USZYmuTDJ95N8L8lb17HdsUmuTbIqybL5iSpJkjSclszw+H3AEVV1RZLNge8m\n",
       "uaCqVj+4QZIDgWdU1Q5J9gSOA5bPX2RJkqThst4Vqqq6qaquaD+/C1gNbDNls4OBU9ttVgJbJNlq\n",
       "HrJKkiQNpVmfQ5Vke2AZsHLKQ9sCN0y6vQbYrmswSZKkUTGrQtUe7jsbeFu7UvWoTabcrq7BJEmS\n",
       "RsVM51CRZBPgs8DpVXXONJvcCCyddHu79r7pvtZRk26uqKoVs04qSZI0T5JMABMb/PyqdS8mJQnN\n",
       "+VG3VtUR69jmQODwqjowyXLgmKp61EnpSaqqpq5kSZIkDZ259paZCtULgIuBK3n4MN6RwFMAqur4\n",
       "druPA/sDdwOHVdVlXYNJkiT1ZaCFapAsVJIkaVTMtbc4KV2SJKkjC5UkSVJHFipJkqSOLFSSJEkd\n",
       "WagkSZI6slBJkiR1ZKGSJEnqyEIlSZLUkYVKkiSpIwuVJElSRxYqSZKkjixUkiRJHVmoJEmSOrJQ\n",
       "SZIkdWShkiRJ6shCJUmS1JGFSpIkqSMLlSRJUkcWKkmSpI4sVJIkSR1ZqCRJkjqyUEmSJHVkoZIk\n",
       "SerIQiVJktSRhUqSJKkjC5UkSVJHFipJkqSOLFSSJEkdWagkSZI6slBJkiR1ZKGSJEnqyEIlSZLU\n",
       "0YyFKsnJSdYmuWodj08kuSPJ5e3HewcfU5IkaXjNZoXqFGD/Gba5qKqWtR8fHEAuLaCEnRM+kLBn\n",
       "QvrOI0nSqJmxUFXVJcDPZ9jMX8IjKGGbhBOAi4EtgU8DqxIOT3h8v+kkSRodgziHqoC9kqxKcl6S\n",
       "XQbwNTWPEh6X8EHgKuB2YMcqDgd2BN4O7A1cn3BawgtdtZIkaf2WDOBrXAYsrap7khwAnEPzi/lR\n",
       "khw16eaKqloxgNfXLCVsCrwBeC9wPrCsip88+HgVDwBfB76e8ATgNcAJ7XM/CZxWxc8WPLgkSfMs\n",
       "yQQwscHPr6rZvMj2wLlV9axZbHs98Pyqum3K/VVVrnT0oF1hehXwYeA64J1VrJrDc/emKWIHA18B\n",
       "Pglc2BYwSZIWnbn2ls4rVEm2Am6uqkqyB01Ju22m52lhJOwL/BWwCfCmKr46l+dXUcA3gG+051X9\n",
       "AfAxYLOEE4F/qOKmAceWJGmkzLhCleQMYF/gCcBa4H00v5ypquOT/BnwZuB+4B7gz6vq0mm+jitU\n",
       "CyhhV+BoYDeaQ3xnDGpFqV212gN4PfBKmsOEnwQuqOI/BvEakiT1aa69ZVaH/AbBQrUwErYF3k9z\n",
       "eO5o4O+q+PU8vt7jgENoDgk+ETgROKWKNfP1mpIkzbe59hYnpS8SCb+V8JfAlcDPaK7c++h8limA\n",
       "Kn5RxQlV7A68AtgauDLh3ISDk4Fc+CBJ0lBzhWrEtVfuvQl4D3Ae8BdV3NBzpv8E/HeaQ4JPBU4G\n",
       "TqriR33mkiRptlyhGhMJSXg1sJpmkv1+VRzWd5kCqOLuKk6pYi/gd4HHAd9JOD/hVW0JlCRp0XCF\n",
       "agQlTNBcubcx8I4qvt5vopklPJbmBPbXA88ETgVOrOLaXoNJkjQNT0pfxBJ2oznRfFfgSOAzozgL\n",
       "KmEn4E9oBodeTTM89J+r+FWvwSRJalmoFqGE7Wiu3HsZzXDO4+b7ZPOF0B76eznNqtUy4HTgk1Vc\n",
       "3WswSdLY8xyqRaS9cu9DwCrgZmCnKo5ZDGUKoIp7q/inKv4rsCfNHLOvJnwr4cMJ+7djGSRJGmqu\n",
       "UA2hhMfQXLl3JPAlmiv3xmKuUztmYR+aYbL7AL9Dc+L9RcDFwCVV/Ly/hJKkceAhvxGWsBHNuIEP\n",
       "0ZSId1VxVb+p+tWWyz14uGQtB67n4YJ1cRU395dQkrQYWahGVMKLaK7cg+bKvRU9xhlaCZsAz+Ph\n",
       "gvUC4Kc05eoimoJ1Y38JJUmLgYVqxCQ8C/gIsBPNIb5/GsUr9/qSsDHwbB4+RLgPcDuTChbwo/ZN\n",
       "niVJmhUL1RBr31R4a2Dn9mNv4MXAXwJ/X8W9PcZbFNrDprvw8ArWvsC9PFyuLgKutWBJktbHQjUE\n",
       "2lWT7Xm4OO3S/vtMml/uq2nmL30POL2KO/pJuvi1JXYHHl7B2hfYhPb8K5qCdbWrgpKkySxUC6g9\n",
       "YXoHHlmadm7vu4WmNK2e/FHFrf2kFTxUsJ7KIwvWFsAlPLyKtaqK/+gtpCSpdxaqeZDwmzSrS5NL\n",
       "087AU4Af8eji9MMq7uolrOYsYVseOaphG+CbNAXrnCqu6TGeJKkHFqoOEp7Io1ebdga2BH7IlNUm\n",
       "4DrPe1p8Ep4EvBCYoBlj8ZJxH18hSePGQjVjDgIsZfritDHTHKYDfuw5NuMp4RDgr4G9q/hJ33kk\n",
       "SQvDQrXO12dTmveMe09713TFaa1Xf2mqhLcDbwBeUMVtfeeRJM2/ufaWJfMZZhi0V9wdCnwAuAZ4\n",
       "WRWX9ZtKo6SKYxK2Ac5NeEkVv+w7kyRpuCzaFar20N5BNDOe7gTeXcVFC/X6Wlza+VanAb8JvLKK\n",
       "+3uOJEmaRx7yAxImaN4Pb3OaQ3xf9FCeumoPG3+R5r0E3+T3lCQtXnPtLRvNZ5iFlvD8hPOBk4C/\n",
       "A5ZVca6/+DQI7RWdrwR2B/53z3EkSUNkURSqhJ0SzgLOBT4P7FzFpx3OqEGr4k7gQOC1Ca/vO48k\n",
       "aTiMdKFKWJpwIvAN4DJghyo+4Wwozacq1gL7Ax9IOLjvPJKk/o1koUp4YsJHgSuAm4Edqzi6irt7\n",
       "jqYxUcW1wMHASQl79Z1HktSvkSpUCY9LOIpmZtSmwK5VHFnFz/tNpnFUxbeBPwI+l/DMvvNIkvoz\n",
       "EoUq4bEJRwDXAk8H9qji8Cpu6jmaxlwVXwHeCXylnVUlSRpDQz3YM2EJ8FrgfcDl+J5qGkJVnJqw\n",
       "NfDlhH2quKPvTJKkhTWUc6jaoZyvBD4I/DtwZBX/Np/5pC7a79ljgd2A/av4dc+RJEkdjPRgz/aX\n",
       "0n40QzkBjgQucI6URkH7NkdnAgUc4htqS9LoGtlClbAc+DCwNfBe4LMWKY2ahMcCXwFWAW/3e1iS\n",
       "RtPAJ6UnOTnJ2iTrPHcpybFJrk2yKsmy2b5481x2S/g8cBZwOrBbFWf7i0ijqIpfAa8AXgy8o+c4\n",
       "kqQFMpur/E6hGWI4rSQHAs+oqh2ANwDHzeaFE56WcBrwNWAFzSypk3zTWY26Km6n+T/zpwl/1Hce\n",
       "SdL8m7FQVdUlsN45TwcDp7bbrgS2SLLVujZOeHLCx4FvA/+PZrr5x9q/7KVFoYobgQOAv0n43b7z\n",
       "SJLm1yDmUG0L3DDp9hpgu+k2TPgQ8H3gXpr323t/Fb8YQAZp6FSxGvg94FMJu/edR5I0fwY1h2rq\n",
       "SVvrOv/pScBzqx5RwKRFq4pvtm+i/IV2RtV1fWeSJA3eIArVjcDSSbe3a++bRtYAf5ymfq2oqhUD\n",
       "eH1pqFXx+YQn00xT37t9c2VJ0hBJMgFMbPDzZzM2Icn2wLlV9axpHjsQOLyqDkyyHDimqpZPs92c\n",
       "Lj+UFpuE9wMvBSaquKvvPJKkdRv4HKokZwD7Ak8A1tK8DcwmAFV1fLvNx2muarobOKyqLusaTFps\n",
       "2sG1JwBPAQ6q4t6eI0mS1mFkB3tK46B9f8rPAbcDr3XemiQNp4EP9pQ0OO2ctUOAZ9C8M4AkaRGw\n",
       "UEkLrIp7gIOAVyS8re88kqTuBjU2QdIcVHFrO/Dzmwn/XsVZfWeSJG04C5XUkyp+nPBS4IKEW6q4\n",
       "sO9MkqQN4yE/qUdVrAJeDXwm4Tl955EkbRgLldSzdmXqcOBLCU/tO48kae485CcNgSrOaqepn99O\n",
       "U7+170ySpNlzhUoaElUcC3we+GLCZn3nkSTNnoM9pSGSsBHwD8AWwO+1c6skSQvMwZ7SCKviAeCP\n",
       "gccAx7VvVyNJGnIWKmnIVHEf8CpgGc17Z0qShpwnpUtDqIo72xlVDw7+PL7vTJKkdbNQSUOqirUJ\n",
       "+wOXJKyt4py+M0mSpmehkoZYFdclHAR8OeH2Klb0nUmS9GieQyUNuSq+AxxKM039qIRN+s4kSXok\n",
       "C5U0Aqr4Ks1J6stpzqvaqedIkqRJLFTSiKjip8ABNHOqvpnwp45VkKTh4GBPaQS1K1SfAm4DXteW\n",
       "LUnSgDjYUxoDVfwQ2Bu4FLg84fd7jiRJY80VKmnEJexJs1q1EnhLFbf3HEmSRp4rVNKYqWIlzQnr\n",
       "dwKrEl7UcyRJGjuuUEmLSMIBwInAmcB7qvhVz5EkaSS5QiWNsSq+DDwHeCrwnYTn9hxJksaChUpa\n",
       "ZKr4GfD7wEeACxLembBxz7EkaVHzkJ+0iCU8FTgV2Bh4TRXX9xxJkkaCh/wkPaSKHwMvBs4BvpXw\n",
       "OoeBStLguUIljYmEZwGnA9cDb6ji5p4jSdLQcoVK0rSquArYA/ghzXiFg3qOJEmLhitU0hhK2Ifm\n",
       "3KoLgD+v4q6eI0nSUHGFStKMqriYZrzCJsAVCXv1HEmSRporVNKYS/hvwHE0A0E/UMW9PUeSpN4N\n",
       "fIUqyf5JfpDk2iTvnObxiSR3JLm8/XjvXENL6k8V/ww8t/34t4Rdeo4kSSNnvYUqycbAx4H9gV2A\n",
       "Q5PsPM2mF1XVsvbjg/OQU9I8quIm4CDgeODihLcmnhIgSbM10w/MPYDrqupHVXUfzfuDvXya7TyU\n",
       "J424KqqKE4DlwKHA+Qnb9RxLkkbCTIVqW+CGSbfXtPdNVsBeSVYlOS+JhwukEVbFdcALgYuAyxIO\n",
       "7TmSJA29mQrVbM5YvwxYWlXPAf6WZiKzpBFWxf1VfBA4APiLhDMSHt93LkkaVktmePxGYOmk20tp\n",
       "VqkeUlV3Tvr8y0k+kWTLqrpt6hdLctSkmyuqasWcE0taMFV8N+H5wNHAlQmHVfHVvnNJ0qAlmQAm\n",
       "Nvj56xubkGQJzVTl/wL8FPgWcGhVrZ60zVbAzVVVSfYAzqqq7af5Wo5NkEZYwn7AycDngHdV8cue\n",
       "I0nSvBno2ISquh84HDgfuBr4TFWtTvLGJG9sN3sVcFWSK4BjgEM2LLqkYVbFBTTDQHcGjug5jiQN\n",
       "FQd7SpqTdhDon1Tx0r6zSNJ88a1nJM23lcCeieNSJOlBFipJc1LFT4FfAr/ddxZJGhYWKkkb4lKa\n",
       "AaCSJCxUkjbMSmDPvkNI0rCwUEnaEBYqSZrEq/wkzVnCZsAtwJZV/LrvPJI0aF7lJ2neVXEPzdDf\n",
       "ZX1nkaRhYKGStKE87CdJLQuVpA1loZKkloVK0oZydIIktSxUkjbUNcDjE57YdxBJ6puFStIGqeIB\n",
       "4Nt42E+SLFSSOrkUC5UkWagkdbISz6OSJAd7Stpw7flT19IM+Hyg7zySNCgO9pS0YKq4BbgV2Knv\n",
       "LJLUJwuVpK4cnyBp7FmoJHXlgE9JY89CJakrC5WksedJ6ZI6SXgMcBvwpCru7juPJA2CJ6VLWlBV\n",
       "/Bq4Cnh+31kkqS8WKkmD4GE/SWPNQiVpECxUksaahUrSIDg6QdJYs1BJGoTrgcckbNt3EEnqg4VK\n",
       "UmdVFB72kzTGLFSSBuVSLFSSxpSFStKgrMTzqCSNKQd7ShqIhC2AG4DHV3F/33kkqQsHe0rqRRW3\n",
       "A2uAXfvOIkkLzUIlaZAcnyBpLFmoJA2SV/pJGkszFqok+yf5QZJrk7xzHdsc2z6+KsmywceUNCIs\n",
       "VJLG0noLVZKNgY8D+wO7AIcm2XnKNgcCz6iqHYA3AMfNU9ZFKclE3xmGjftkeiOyX64CnpLwWwv1\n",
       "giOyXxac++XR3CfTc78MxkwrVHsA11XVj6rqPuBM4OVTtjkYOBWgqlYCWyTZauBJF6+JvgMMoYm+\n",
       "Awypib4DzKS9uu9y4HcW8GUnFvC1RslE3wGG0ETfAYbURN8BFoOZCtW2NJdBP2hNe99M22zXPZqk\n",
       "EeVhP0ljZ6ZCNdshVVPnNCzMcCtJw8iJ6ZLGznoHeyZZDhxVVfu3t98NPFBVH5m0zd8DK6rqzPb2\n",
       "D4B9q2rtlK9lyZIkSSNjLoM9l8zw+HeAHZJsD/wUeDVw6JRtvgAcDpzZFrDbp5apuYaSJEkaJest\n",
       "VFV1f5LDgfOBjYGTqmp1kje2jx9fVeclOTDJdcDdwGHznlqSJGmILNh7+UmSJC1W8z4pfTaDQcdN\n",
       "kqVJLkzy/STfS/LWvjMNkyQbJ7k8ybl9ZxkWSbZIcnaS1Umubg+vj7Uk727/D12V5B+TPKbvTH1I\n",
       "cnKStUmumnTflkkuSHJNkn9JskWfGfuwjv3y1+3/oVVJPpdkwealDYvp9sukx/5nkgeSbNlHtr6s\n",
       "a58keUv7/fK9JB9Z1/MfNK+FajaDQcfUfcARVbUrzfue/Zn75RHeBlyNV4tO9n+B86pqZ+DZwOqe\n",
       "8/SqPa/z9cDzqupZNKckHNJnph6dQvMzdrJ3ARdU1Y7A19rb42a6/fIvwK5V9RzgGuDdC56qf9Pt\n",
       "F5IsBfYDfrzgifr3qH2S5EU0czafXVW7AX8z0xeZ7xWq2QwGHTtVdVNVXdF+fhfNL8dt+k01HJJs\n",
       "BxwInMijx3GMpfav6BdW1cnQnNtYVXf0HKtvv6D5w2SzJEuAzYAb+43Uj6q6BPj5lLsfGrjc/vuK\n",
       "BQ01BKbbL1V1QVU90N5cyRjOTFzH9wvAR4H/tcBxhsI69smbgQ+33YWqumWmrzPfhWo2g0HHWvuX\n",
       "9jKa/9yCjwHvAB6YacMx8jTgliSnJLksySeTbNZ3qD5V1W3A/wF+QnMF8u1V9dV+Uw2VrSZdbb0W\n",
       "8N0rHu11wHl9hxgGSV4OrKmqK/vOMkR2APZJcmmSFUl2n+kJ812oPGSzHkk2B84G3tauVI21JC8D\n",
       "bq6qy3F1arIlwPOAT1TV82iuph3HQzgPSfJ04O3A9jSru5sn+YNeQw2paq488mfxJEneA9xbVf/Y\n",
       "d5a+tX+cHQm8b/LdPcUZJkuAx1fVcpo/8s+a6QnzXahuBJZOur2UZpVq7CXZBPgscHpVndN3niGx\n",
       "F3BwkuuBM4AXJzmt50zDYA3NX4/fbm+fTVOwxtnuwL9W1a1VdT/wOZrvHzXWJnkyQJKtgZt7zjM0\n",
       "kvwPmtMKLOCNp9P8YbKq/dm7HfDdJE/qNVX/1tD8XKH92ftAkv+8vifMd6F6aDBokk1pBoN+YZ5f\n",
       "c+glCXAScHVVHdN3nmFRVUdW1dKqehrNCcZfr6rX9J2rb1V1E3BDkh3bu14CfL/HSMPgB8DyJL/R\n",
       "/n96Cc2FDGp8AXht+/lrAf9oo7nqnGa14eVV9au+8wyDqrqqqraqqqe1P3vX0FzsMe4l/BzgxQDt\n",
       "z95Nq+rW9T1hXgtV+5fjg4NBrwY+U1VjfXVSa2/gD4EXteMBLm//o+uRPEzxsLcAn06yiuYqvw/1\n",
       "nKdXVbUKOI3mj7YHz/s4ob9E/UlyBvCvwE5JbkhyGHA0sF+Sa2h+KRzdZ8Y+TLNfXgf8LbA5cEH7\n",
       "c/cTvYbswaT9suOk75fJxu7n7jr2ycnAb7ejFM4AZvzj3sGekiRJHc37YE9JkqTFzkIlSZLUkYVK\n",
       "kiSpIwuVJElSRxYqSZKkjixUkiRJHVmoJEmSOrJQSZIkdfT/AQOyAWlDVWEOAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10964ec10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm4JFV5+PHvOzMMiyAjiqwjo4IKBhVRQBQdFRVGf7gr\n",
       "Jm64L0SDccNoRKMxmmjclbgQogZcgxJBEWVUXHBhEdlRURgDCAoquIC8vz/q9Ny6NdXd98501+17\n",
       "5/t5nnq6llPnnKrq5e1Tp6oiM5EkSdL4LZrrCkiSJG0sDLwkSZI6YuAlSZLUEQMvSZKkjhh4SZIk\n",
       "dcTAS5IkqSMDA6+I2CwizoiIsyPi/Ih4S590746ISyLinIjYazxVlSRJmt+WDFqYmX+MiAdn5o0R\n",
       "sQQ4PSIekJmn99JExCpg18zcLSL2BT4A7DfeakuSJM0/Q081ZuaNZXQpsBj4dSPJIcCxJe0ZwLKI\n",
       "2G6UlZQkSVoIhgZeEbEoIs4GrgJOy8zzG0l2Ai6vTV8B7Dy6KkqSJC0MM2nxuiUz70UVTD0wIla2\n",
       "JIvmaiOomyRJ0oIysI9XXWZeHxFfBO4DrK4tWgMsr03vXOZNExEGY5Ikad7IzGbD0gYbGHhFxO2A\n",
       "mzPzuojYHHgY8IZGsi8AhwPHR8R+wHWZeVVbfuPYAI1fRByVmUfNdT20fjx+85vHb/7y2M1v42ow\n",
       "GtbitQNwbEQsojot+bHM/GpEPB8gM4/OzJMiYlVEXArcABw2jopKkiTNd8NuJ3EucO+W+Uc3pg8f\n",
       "cb0kSZIWHO9cr5lYPdcV0AZZPdcV0AZZPdcV0HpbPdcV0OSJzG76vEdE2sdLkiTNB+OKW2zxkiRJ\n",
       "6oiBlyRJUkcMvCRJkjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiBlyRJ\n",
       "UkcMvCRJkjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiBlyRJUkcMvCRJ\n",
       "kjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJHTHwkiRJ6oiBlyRJUkcMvCRJkjpi4CVJ\n",
       "ktQRAy9JkqSOGHhJkiR1ZGDgFRHLI+K0iDgvIn4cES9pSbMyIq6PiLPK8NrxVVeSJGn+WjJk+U3A\n",
       "EZl5dkRsCfwwIr6SmRc00n09Mw8ZTxUlSZIWhoEtXpl5ZWaeXcZ/D1wA7NiSNMZQN0mSpAVlxn28\n",
       "ImIFsBdwRmNRAvtHxDkRcVJE7DG66kmSJC0cw041AlBOM34GeGlp+ao7E1iemTdGxMHACcBdRltN\n",
       "SZKk+W9o4BURmwCfBT6emSc0l2fm72rjJ0fE+yNim8z8dUteR9UmV2fm6vWqtSRJ0ghFxEpg5djL\n",
       "ycxBlQjgWODazDyiT5rtgKszMyNiH+BTmbmiJV1mpn3BJEnSxBtX3DKsxev+wFOBH0XEWWXea4A7\n",
       "AGTm0cATgBdGxM3AjcCho66kJEnSQjCwxWukBdniJUmS5olxxS3euV6SJKkjBl6SJEkdMfCSJEnq\n",
       "iIGXJElSRwy8JEmSOmLgJUmS1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElS\n",
       "Rwy8JEmSOmLgJUmS1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElSRwy8JEmS\n",
       "OmLgJUmS1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElSRwy8JEmSOmLgJUmS\n",
       "1BEDL0mSpI4MDLwiYnlEnBYR50XEjyPiJX3SvTsiLomIcyJir/FUVZIkaX5bMmT5TcARmXl2RGwJ\n",
       "/DAivpKZF/QSRMQqYNfM3C0i9gU+AOw3vipLkiTNTwNbvDLzysw8u4z/HrgA2LGR7BDg2JLmDGBZ\n",
       "RGw3hrpKkiTNazPu4xURK4C9gDMai3YCLq9NXwHsvKEVkyRJWmhmFHiV04yfAV5aWr7WSdKYzg2t\n",
       "mCRJ0kIzrI8XEbEJ8Fng45l5QkuSNcDy2vTOZV5bXkfVJldn5uoZ11SSJGlMImIlsHLs5WT2b5yK\n",
       "iKDqv3VtZh7RJ80q4PDMXBUR+wHvzMx1OtdHRGZms2VMkiRp4owrbhkWeD0A+AbwI6ZOH74GuANA\n",
       "Zh5d0r0XOAi4ATgsM89sycvAS5IkzQtzEniNtCADL0mSNE+MK27xzvWSJEkdMfCSJEnqiIGXJElS\n",
       "Rwy8JEmSOmLgJUmS1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElSRwy8JEmS\n",
       "OmLgJUmS1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElSRwy8JEmSOmLgJUmS\n",
       "1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElSRwy8JEmSOmLgJUmS1BEDL0mS\n",
       "pI4YeEmSJHXEwEuSJKkjQwOviPhoRFwVEef2Wb4yIq6PiLPK8NrRV1OSJGn+WzKDNMcA7wH+a0Ca\n",
       "r2fmIaOpkiRJ0sI0tMUrM78J/GZIshhNdSRJkhauUfTxSmD/iDgnIk6KiD1GkKckSdKCM5NTjcOc\n",
       "CSzPzBsj4mDgBOAubQkj4qja5OrMXD2C8iVJkjZIRKwEVo69nMycSWVWACdm5p4zSPszYO/M/HVj\n",
       "fmampyQlSdLEG1fcssGnGiNiu4iIMr4PVTD36yGrSZIkbXSGnmqMiOOABwG3i4jLgdcDmwBk5tHA\n",
       "E4AXRsTNwI3AoeOrriRJ0vw1o1ONIynIU42SJGmemNhTjZIkSZoZAy9JkqSOGHhJkiR1xMBLkiSp\n",
       "IwZekiRJHTHwkiRJ6oiBlyRJUkcMvCRJkjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpIwZekiRJ\n",
       "HTHwkiRJ6oiBlyRJUkcMvCRJkjpi4CVJktQRAy9JkqSOGHhJkiR1xMBLkiSpI50GXhHs0mV5kiRJ\n",
       "k6TrFq9lHZcnSZI0MSIzuykoIiFvArbJ5PedFCpJkrQeIiIzM0adb9ctXpsA7+q4TEmSpInQdYsX\n",
       "AJmMPIKUJEkalYXS4iVJkrTRmpPAK4Ld56JcSZKkuTRXLV7nR7DTHJUtSZI0J+byVOOSOSxbkiSp\n",
       "c3MZeNnBXpIkbVTsXC9JktSRoYFXRHw0Iq6KiHMHpHl3RFwSEedExF6jraIkSdLCMJMWr2OAg/ot\n",
       "jIhVwK6ZuRvwPOADMyx76xmmkyRJWhCGBl6Z+U3gNwOSHAIcW9KeASyLiO36pD21Nn72TCspSZK0\n",
       "EIyij9dOwOW16SuAnfuk/cYIypMkSZqXRtW5vnmFYr/nEL1pROVJkiTNO6O4l9YaYHlteucyr0W8\n",
       "Hl55HWy+DFZSDZIkSXMrIlbSQWAyo4dkR8QK4MTM3LNl2Srg8MxcFRH7Ae/MzP1a0mVmRgSLgL+A\n",
       "D8uWJEmTaVwPyR7a4hURxwEPAm4XEZcDrwc2AcjMozPzpIhYFRGXAjcAhw3KL5NbwnBLkiRthGbU\n",
       "4jWSgmqRY0TVB8wWL0mSNInG1eLlneslSZI6YuAlSZLUEQMvSZKkjsxV4LUc+HMEd5+j8iVJkjo3\n",
       "V4HXTcBS4MdzVL4kSVLn5irwurk3EkFGcOIc1UOSJKkzc3U7ia2B6+rLvbWEJEmaFAvtdhI3zVG5\n",
       "kiRJc2bOTzVKkiRtLCYm8Ipg8VxURJIkqStzEnhlckvL7M06r4gkSVKH5uwGqi2d6Tedk4pIkiR1\n",
       "ZBLuXH9KebXFS5IkLWiTEHidVl7XzGktJEmSxmxO7uM1NY9FmdwSQYL38pIkSZNhod3HC1i3k30E\n",
       "L4xgk7mqjyRJ0jjNaYvX1DLqlbh/Jt/upFKSJEktFmSLVx+vmusKSJIkjcMkBl5L5roCkiRJ4zAp\n",
       "gdena+P28ZIkSQvSRARemTypNrl0zioiSZI0RhMReDX8Ya4rIEmSNA4TcVVjtXzalY0XZLJHB9WS\n",
       "JElax7iuapzUwMubqUqSpDmzMd1OQpIkaUGa1MDrN3NdAUmSpFGb1MDLW0pIkqQFZ1IDry2HJYhg\n",
       "VQQP7qIykiRJozCpneuvzeR2g/Or0tsJX5IkjdqC71xfAqhHl8mb29JE8LAIFjfmPXDcdZMkSRqF\n",
       "iQm8ihvL63YRZD3IiuBfgFOAAxrrfL2rykmSJG2IoYFXRBwUERdGxCUR8aqW5Ssj4vqIOKsMr92A\n",
       "+jQfkH3v2niv7E0iuNUGlCFJkjQnmoHONBGxGHgvcCCwBvh+RHwhMy9oJP16Zh4ygvpsPoP6LQHu\n",
       "NIKyJEmSOjWsxWsf4NLMvCwzbwKOZ6ofVt2oOp+dCNyvNr0ZQATLavO2KIMkSdK8Mizw2gm4vDZ9\n",
       "RZlXl8D+EXFORJwUEev9jMVMbs7ku8DOZVYv4KrfNmJ/4Lv19SImrq+aJEnSOgaeagRmcq+JM4Hl\n",
       "mXljRBwMnADcZUMqlcmaCL4I3KalHi9rWWUHqlOhkiRJE2tY4LUGWF6bXk7V6rVWZv6uNn5yRLw/\n",
       "IrbJzF83M4uIo2qTqzNz9YCyLwaWRbAr8KQh9dxsyHJJkqS+ImIlsHLs5Qy6gWpELAEuAh4K/BL4\n",
       "HvCUeuf6iNgOuDozMyL2AT6VmSta8prVjcgieB2wlKr17EnAtcB7gKNKkp8Du5Txe2Ry7kzzliRJ\n",
       "GmRcN1Ad2OKVmTdHxOHAl4HFwEcy84KIeH5ZfjTwBOCFEXEz1X24Dh1R3a4D7lqbPgH4v9r0VUwF\n",
       "Xt5eQpIkTbxhpxrJzJOBkxvzjq6Nvw943+irxm+AXYFHlOnfAdfXlu9Tlp/CDJ7tKEmSNNcm+WrA\n",
       "65gKuqDqYP/b2vSVmfyE6irLf+iyYpIkSetjkgOv3zemL2J6i1fvKsZNgZURQzvgz1oE949gn1Hn\n",
       "K0mSNk6THHjd2Jh+MPDnMn4NsKqx/JNjqMPpwLfGkK8kSdoIzafA6xNMtYIdnsnVZfwpY67H0H5w\n",
       "kiRJMzHJgVevbj8qr1/K5MIyfWIt3aWd1kqSJGk9TXLg9ZPy+jDgw5ncBJDJPTOntYY1W8aGimBR\n",
       "xLRnQvbmvyyCzSLYI2LqQdwR7DXbMiRJkpomOfD6Q3m9JpPnDkh3Q28kov+jiiK4bQQRwRbAR4Fv\n",
       "tyR7O3Bv4DymAj+AwyPW1keSJGm9TGzglcktmUQmtwxJWm/xOmBAumuAR1IFXM8AiKDtjrQPaZn3\n",
       "FEb0WKIIFkeweBR5SZKk+WViA69ZqAdercFRLcA6BrhzbdFDy/KXR7BdmffIliw239BK1pwKfH2E\n",
       "+UmSpHliIQRe9VOA7+2T5lnl9XZA/eHdN5fXfwU+Xcb/sr4ViWCrCL7fpyWtZyVw//UtQ5IkzV/z\n",
       "PvCawalIgA/Xxu9QGz8tYu10b180g6K1d8WP4KQh5TwQuA8+O1KSJLWY94EXQCYBVQAWwVkRLIng\n",
       "0AhuHcEeQ1b/eXmtB1yXMBWs/bE2/+CIgfus9wxL+3BJkqaJ4FER035TtBGKzOymoIjMzEGn4DYw\n",
       "fxYzdepwQyXVA7j/RPVIovoVjptnrvvBiWAJVLe8AG6fya/61DNhbbAoSdpIRPBm4DV+/88P44pb\n",
       "FkSLF0DmwL5ZN8O0lq/XwMBnMAbwu0zWZPJTpu+nflc3Prs2fptBdV1fEWwSwXkR7FmmPxbBK8ZR\n",
       "liRp5Ay4tHACryGWABeX8dMyeUsm3wc+30hXv6Lxt72RTOrNgs/rU8aK2vhj2hKM4DYS+1IFkL27\n",
       "+T8VeP4G5ilJ6oaBlzae5xCWFrHmm/7R5XVP4FzgZ7X0f+qT1Z595m9VG/9RnzQ/HFLNYR7XG4lY\n",
       "2wdtuz5pJUmTxcBLG02LVz9XAmTyY6q+WxcAf90n7enldW1AFsEOEdy93D7ixWX2F4Fb98njnhtY\n",
       "3yNq471Tm1uWusz6SsoIdip90yiPSloQgXgE10bw93NdD0lq2Nh/c8XCexOc1mf+xX3m7wzcFqDW\n",
       "Yf43bQkzOQA4BfhebfYvgR8Df67N+y1w2EwqG8FrI7jPTNIOyedFwO/XY9UrgIvK+FXABze0LhNi\n",
       "G6rTstJYRXCriJHeYFkLmy1eWliBVyYPobqVw25Uwc/u5bFDd+2T/i+Z026oClVwtXefIi6jPaha\n",
       "AnyL6oHeB5VhrQgO613NWJv3COCfgJcP2qbywO7tInh4nyS/AnYoaVeW11s3y2vJ95Qyen4E21O1\n",
       "0t1r0DqTKoItI7iqMfuJc1IZbWy+RvtzXzUPRbBpxLRuI6O2qJSzIM4uaP0smNtJdKF+K4gIDgC+\n",
       "0UhyL+BLwPb1y4UjuAj6PsD7qky2r6VdCjwlk2NrZZ5CdZqyX3+utwGvLOP/Bvwf1QO/75Q51W+t\n",
       "5Lct1b3JehcPXAmcCayqJXtM5joXHqyjnGJ9TCb/MyxtSf8Q4EmZvGAm6WcqghXAz3r73Ft2CCCC\n",
       "u1Hd2qX5OR1lGb0v0GWZXD+uctSNCD4NHJxZdeEYcd5LmeqqslXmep2lUIe8ncRk+CCsvTqxLZC6\n",
       "mvYWsV8MyHO7kue9ypf4Y4D/LAFSz2LgujL+ZUoLV832tfGXUwVdAG/pzSytZjuXOr6vsW496AJ4\n",
       "cG29Z0f0vdBgW+Bz/fqXlT5ku9ZmncR4rsLs9VPbNIJNxpC/5qdP091zUT/QUTkar90Z35NH3lob\n",
       "32VMZWgeMPCanRdT3SR1G6YenP2h2vJrqFqnbmnc4b7+z+a3NESwO3BWmfxkeb06gqeU8Vtg7enS\n",
       "J2RWFwXU3IF234vgzAh2oWrZurzM73Xy/0qf9dbUxvcHlvZJt7y87tZn+f9SPQWgZ1OACE4urVRr\n",
       "RXBTBHfsk88wvS/K7aiexzlUBDHkmZqapyLYsZya/6sR57tVBBnBspbFW0fwhd7pfs1b4zwF9He1\n",
       "8X63JdJGwMBrFspzIX8C7Ai8p8x7HtXzGcnkppLml1R3vieCHZl+X6/6l3YvKDm0T5H/XV4vA64F\n",
       "9qs1T59TS7eS6f+m6mXtVdavu0d57Rd43FAbH9QX4Qfl9awI3tSyfCdovX/ZQcDjG/OWMP2ZmgOV\n",
       "q0mPLJO9CxR+DtNaCgf5NFWAvOlMy5wEEfyidwPdjVXEVJ/NCB4fwfElIMpyOmcNVcvwqPVab+9c\n",
       "yq7/SO8D/D+q57/uPuTRYp2KYB8DwhmbybN/pQ0yMV8O88jVwNll/G/K65kw7ZTaWcC9y2mvaTdT\n",
       "LTdj3b1M9q6Q/MchZW5B1Vp0UW3egVSnHP+3TG9W+jTtX0vzuiH5fqll3p8opyIj+CzlTv3N1qGW\n",
       "U3r/0LK8FwTdHMGBjfSX1dL28u77b7NeXgRPorqa9J/LuvWAbVvgO6XM1sCyBFu9wO9R/cqcUMuB\n",
       "/ea6Ek2jOMVbAqf7DkmzGXBhxNo+iJ8BnlxL8tGWdTboey6CpRFsydQzWJdFVMFXTb2l9XyYqCdK\n",
       "fIXaFd8RrIrguSVA3CaCg+ewbpNmLC1eLd9Fl7QmnCARfCii750CtAEMvGav3t/pdKiCqcxpz3O8\n",
       "AjiO6suu3p+Kkv5Cqh+MdX4kimsb038D3JK5tp8XmVxTTjn2AocPlfnfGVL/U8vrmkzeztQPxFPL\n",
       "6xlQXSlIdcPWu5X5zX+Cz2hmXC6t36ZMNn+Ynsv0Z14+tvzQbsHUY5g+O6Def45Ye7Vo/fFMNzTS\n",
       "nQrcr9T3taVeh8bU/cr+lal7ssH0e6PNF+v1BIQIrqsdn5Epx/DPEX2vBp5JHr0fprc25t+z9E3s\n",
       "6d3y5JDyHm1quz3LoyNYPKCv4qB6PZLqM/8bplp/TwUuHbLq7kOWDypz0YhbYpv3Ffwi8B9Uf1he\n",
       "RNX3sl7+0oi1f2oGimDrGHIF9SQp74OhfxLKe3qU6o+R+wxwVQRPjuCnIy5nJEr3l+eALaXjYOA1\n",
       "e/VnQl7eJ02vH9dty+uXqFqn1vbFyuSJmXwNpv143LW0Wq0AXlbmvbq89rsp65uAazI5rzbvEOCx\n",
       "ZfyTjfS9lqdeC9XNpT6fKGW/q8zv9bfqnZak8QPY69vW66vwYar+bb2g8Z8a5a5han/AVGvhB5k6\n",
       "/Xp7BrtzaRGp31qj3z2UlgJvLOPHMdWv7RCm/zjff0iZEyNibV1nHXiVVp+tgb0jOKFl+bQ+bxG8\n",
       "o3b6bthx6bVs9k499/pDnRPBFhHcLmJo37vefdce3Jh/NnBCCer/nekB/+9a8mn2fwT4HFU/wKWl\n",
       "Pr1L+m8f0bd/ZM9zyusS+t8b7tkt827qjURweMTw+8qVU4K3ovps/nFAus1KAHFgOT6vH5Z3bd36\n",
       "qfhbKJ+fRpD1aOBImFGQfklZf0Mfh9aVo4ET6zMiuGvE2vdS73uieQHThjqyNr4NcABwPHDHmMxb\n",
       "S5wyPInWW5bmmnEPVVHdlDXe7cgVkI8akubjkAl5cXl914C0UdJkY/5SyEf2Wz7Dum5ZXrMMz4Nc\n",
       "BblJLc2tIPdqrJd9hmPK8iX1OkH+XT1dmffeMn1DeT0R8i998j1k0DbW9sHLyj5prn8c5Btq03vX\n",
       "xrcor/tCbg35+9qyvy+vW6/Hvt0ectcRvJ+eBvkDyJhB2itLfY+YRf73g3wP5G2bx6jtmPd5D+wx\n",
       "pIx62kvKvMPK9Cshfw55xUzzaJl/LuRrB7wve8MtkF/ss+wu/dbrU5/dIPeAvHEG5a5omfdhyP0h\n",
       "nzGonFp5qxvv54R85IDPwtBtKOmX1tLdobHeasij65+Bxmdnt0Zeb4B8W5/jtuWGfhYa+X4H8gF9\n",
       "lj0V8sT1zPe3Le+xZ5ZtuHVtex5Qll0E+adZlnHv5ndDLd97QD6ufOZ78944yn03ov0/9L21MQzj\n",
       "ilvm/QZM4gC5K+S7am/eTYekPxnyLwOW7wC51QbUZwnkklmk/+SAH5m/rY1/t6R/SZ+0n6cK7PaE\n",
       "vL7Me3X5UeqX/wEt9dmqLHtzI+3h5XU5jQC1Jd9DIL9Sm34q5IvK+C61sjYr8w4esH/etL5fSpBP\n",
       "oQr+FpXpr5W8Tp7Bur26v2EW5X2krNM8RpvW0mzd3J6W/Xca5OmQmzXy/2YzbWP9/xy2ryAfW0t/\n",
       "LbUgtMw7E/LdA94zK8p+PLJl2WPK618PWP/fBuzrXw9YrzcEVQC9F+STy7xv99kvb4F87IDyEvKa\n",
       "2vibqT6/K2vvzXWGAfv2mf3Wgby8Nn6nkv7VtXmHtNWxT73vub7fTy11XlTyfDfku1uWnzpom/vk\n",
       "eb/Gtr8D8sFl2bPKvN2oAu0vUf1xuFst/Ra1vALyFeVY7tPnWJ7fb98x9b3VGz4+i+1YArnfqPb1\n",
       "kP2flO/4xvJXQ/5onHWYlMHAa54NTAUCN891Xdaj7nctdf+P8iPwQqb+ha/zZQ+5ZZ8v9k3K8i3q\n",
       "61D9I0zaA7ZHt9Rn15Z0X4PcvJHu/N4XIVWw2u8HZ/vaOgl5IFXLzErIO83gx2zoD16f9W5TW/c5\n",
       "Zd43avOGBegXzbZcyPf32Qd3qKXZt/klO2DfXVRLc7s+aeqtMk+u17mM/4SqZeppfcp6ywzq0fY+\n",
       "/Nfa/J0gFzMgWOmTx62Zev/3hge3rLNlc91aHvfpU85B5fXrjfRLhtTv+eV13wFpWltMqT67Q7e/\n",
       "DJsM2C9Pb5lX/9y/rsx7GeTi9fjO2ao+PmjbKAHjLPJuO3719+QHy/RDIG9iqpW+PuxYy2/7xrL7\n",
       "lX1369p79uwyHlQtvslUK9rDGut/Zxbb8vjZbPv6DJCfLfU6ipYAi/KnYpx1mJTBwGseDlT/su8w\n",
       "1/UY0bY0T6c0g57mF9Vlbctb8u0FSNvV1t2+kebUlvzvOoM699J+qe3HpE+96y0V+w/Jd53t6ZN+\n",
       "J8jNqU6FDfrhe3hJfzuqH/+dGvn872zKLev8Uy3/s2rj+9TSPA3yh5A/a2zjx9vqWUtTX/48qpbb\n",
       "QdvXdpqsvk92Ka/fHHB8/hZyU6aCqifW0r6zpLl2wDF+eu/Hq7lNJc91tqGRR+9UdVC1mvxDyz7v\n",
       "F5D2hpMa6Xut4y8dst7by+ufavPeUV5bT/WxbhBxGtUfgH6t1L3hmPJ6G9b9E9Nrrb1zY/4HyuuO\n",
       "bXVpqVvzD9UPyvx/b8z/Ym2d5c334QzKefGA7bxHbfw1VC2uV7ake2jJ61V98vlCY/rbJX39/XTH\n",
       "Pu/Jvl1RWral3jr8nJmuN5uBqbMTz6T6k9QMfHvlP24c5U/SYODlMNFD+SB+td+XIlXLywuG5PGK\n",
       "sv6Da/P+sfklN4s63ZeqT9h9a+t/tZHm6c38a8O1TO8Ptwvk7WdSF6afykvIPwz5ocuyrTsw/RTQ\n",
       "9iWPxWX60nq55Ufi2QPqcXUtr80b5W0K+T+Qn2Dq9OlzqYKKm6laHu5YtvmNkM+G/BVVwPU9yP9u\n",
       "fgHPYBv7De9hqkXwp7192Ehzp+aPQHOfQ/6M2mmhRp12HlLPa1rmnVDSH0dpmaAREPepy92oApFL\n",
       "aA/EllC1jK1tBS3r3YvpLXfN4aSSbnnZ/3uVbd61Vvbu5Ri+tWX9Xiv03Wvzmv3nHtnYR/XTvFf2\n",
       "9iNVC9HqljIeSKPf6IDvjObQr6X6irLsSbV5u5T9+8Qh5bxyBu+/71C1on+H6j1fX/aj8rp4Bvn0\n",
       "hlNbtnFprU6HNJYtaqn3Oq1bkK9vrPfBIdu+M+TjZ/qd2ajz2v5+jeXfqqVZ5/NI1cp9zWzKbMnj\n",
       "AW37pOvBwMthoofyAV9M1Yl5uw3I57Tygf4vpp8m2ZmqVSXXM99ePls25vf6MzyuzxfoN6l+xPbr\n",
       "s7zt3+BP6+X1+RGpT68pX/j9vsSXMdVysRVVULQp5CltX4ylHvUWjb0g9y3zd4Q8tqWM50N+mun9\n",
       "4JrbtnXLeh9v2f5ry369E+TrmN5vqDc0T4EuK+vXg4Be0H0oQ07DDjn2i2n0q4J8H+TDqZ0Gbxk+\n",
       "wAguoKjtl98NKOvzLXVuayH8Vp+8r4Rc0Xiv94YDS16bNtZ7Zu391Uv78pbPTG/YtlZW/WKF5mfj\n",
       "/Lb3ZKPsB9bStwW8sxpq+faC9ZW1eW9spG97P76vnhdV/60s74/en5JmkLn/kHr1tvHIPt+X/wP5\n",
       "0Fr6RbXl963XZ8AxSRr9Lku6XheGC+p5UwWvtxnwOen1v92c6afAT6+l+2xt/sNb8jmmcUx67+XD\n",
       "IJ864D2oYrgEAAAJ+0lEQVQRvdeS9z3W87MWzPKCqbZ9WM1n4Pt4vb8PhleIg4ALqS4bflWfNO8u\n",
       "y88BWv/pGHg5zGSgvYP0P9aWD736r0++MWxdqk62X6U67Vnvx/GpPl94N1L9GC2jOmWxxwx/KHYs\n",
       "5R1B1cl/OY0rQ/sNZb2E/Fhj2eGNbVnnR6mxL3rLvwx5DlUryRG1+R/rs4+adVrUWP4wyD1b1juw\n",
       "9yNECcypgqznMv3ihts0y+jgPXerWnkfhtx2DGXcuxznZv+godtI9eP/OKoLM9a5SAby7AHvmb6t\n",
       "QfXPBORzSvr6hQ314OjVZd4vGvn/iukB+X/WxhdTtd79rOzjpVQXCzynluYpfd5bQdVv6oyWbVrN\n",
       "9NOtCXnbkscLavNuorqa9xiqQOoR1H7MG+sfWl6fPuTzkuU93ms5rJ8uvSelRboxDOzzNuDY9YZe\n",
       "Wb1g7CCqFqHeKeqH1PLajHX7yPXW6bXWX9iyfae3vR8beSyiChaT6cHsX5XXHajeq728VjH9Qol+\n",
       "30dblWOTZfrf6mnLe+xhs/isPaqsfzBDWs3KtvdONz9k3eWM5ftnyAawmOpGgSuATajuqbN7I80q\n",
       "oDR/sy+wzlUQ49wAh/EPwMpuy8vbQH6/fBi277LsRj3qVzX1htMppwxalv1LbfyfmWq9S6ofrCuH\n",
       "lJdUp/GeV8abV9Tt0afc3rBjI6+9qi/DdY8f1amOFzbmrf3CHlDHrUu+T4R80Jj2+w5M3Y7iQx0e\n",
       "7/W+cniW5TwS8qPlh3Dn4ekHf/5Y94q93vDiEdW3fro9mB589TqUn06t/1UZ6qfxz2+pX7OVL6iC\n",
       "yN1q8zZn+m0ekiqI652+PbMl39+0zLt/y3ZtSwmKqFqm30r/ixR6+dy5ZdltKFeAUp2ee8JU+uNP\n",
       "ncH+bWtJHjTs2VKvu88yj3rr2ssay15SW/YYpq76rA/bzrCcl7fMuyO10/VUV7/3W7/eIv0nyFsN\n",
       "2ZeLGuu/b0j6ixvpD6O66nSz8tnLsXwHDPnA3w/4Um361cCrG2k+CDy5Nn0hsM6pJgOv+TsAR811\n",
       "HeZu23NLqk7Pt29ZdmDLF8VBVD+EvS/0hBzp/mPq1NAOtJ/K/Gh5jdkev34/PHO073dlPa6QW2jD\n",
       "TI8ftY7fHRyb1h9AyG1Yt19m/Yro3mm7vrdr6ZNva4t1+aFtXnF9WAkW6hfVbND7mqolacUs0i+q\n",
       "hll99nYoAc0BVH+CFrHulazPaaxzrwFBS68/3CNa9n9StSb2Lhb5A9Xp47bAcs9GvpeV+Y+HvHBA\n",
       "+c2heYXts6iunGxLu7LP/N4tQIKq1W8TqjMSz2Hq9HBzqF8x2zu1e0qftL3hj5C3mqvA6wnAh2rT\n",
       "TwXe00hzIrB/bfpUYO+WvMayAQ7jHzbmwGv4vsntqToZb0t109g5CVyoWk+Oour/lZCrPH4LY5jl\n",
       "j/ciai1Uc1fnvBvVbRqiDPcZc3lBewf1ZbMJmOby2A3Yts0Gfa+UAOTNlH5tJaBZ549iLX1b69it\n",
       "N6B+u1P9AXxbLb9eH7GLmN5V5Bzab9fxbKo/rHtTWjypThUm1dmDV9TSDru33sVUp47rXT/aTgEn\n",
       "Vd++RzF1G6Fzmda1hBzH+2LYowpyyPKe5jO9ZrqeNK9l9bzM3mNqDp/DelwNHFUGbaQyuYV1n6s6\n",
       "F/W4EHhBbdYP+qUdUXlJy+9OVs+3vW7dNeaPzP6PjyrLT6f2/NnMvs8A7i0/D4gIlmRWj4zbwPpd\n",
       "UEZfWYa6uzbS9h7JRASLM6c9gq+Z78kw7TFmHwNOoHr02eeAd1A9Gu8E4DFUj2J6fSa/r62zlKrB\n",
       "6I1Uj7k7CziGqvvUxeXzsjZ5bb1FwJ0Y08PMe6ci2hdG7EcVsR9Upo8EbsnMt9bSfBBYnZnHl+kL\n",
       "gQdl5lWNvAzGJEnSvJGZQx8WP1vDWrx+AOwWESuAXwJPBp7SSPMFqn/6x5dA7bpm0AXjqbwkSdJ8\n",
       "MjDwysybI+Jw4MtUVzh+JDMviIjnl+VHZ+ZJEbEqIi4FbgAOG3utJUmS5qGBpxolSZI0OovGXUBE\n",
       "HBQRF0bEJRHxqnGXp+EiYnlEnBYR50XEjyPiJWX+NhHxlYi4OCJOiYhltXWOLMfwwoh4eG3+3hFx\n",
       "bln2rrnYno1VRCyOiLMi4sQy7fGbJyJiWUR8JiIuiIjzI2Jfj9/8UI7FeWW//3dEbOqxm1wR8dGI\n",
       "uCoizq3NG9nxKsf/k2X+dyNil6GVGvOltENvwOrQ/QBsD9yrjG8JXATsDrwNeGWZ/yrgX8r4HuXY\n",
       "bVKO5aVMtZZ+D9injJ8EHDTX27exDMDLgE8AXyjTHr95MgDHAs8q40uortTy+E34UPb/T4FNy/Qn\n",
       "gWd47CZ3AA4A9gLOrc0b2fECXgS8v4w/GTh+WJ3G3eK1D3BpZl6WmTcBxwOPHnOZGiIzr8zMs8v4\n",
       "74ELgJ2AQ6h+ECivjynjjwaOy8ybMvMyqjfjvhGxA7BVZn6vpPuv2joao4jYmeqpER9m6jJoj988\n",
       "EBFbAwdk5keh6kubmdfj8ZsPfgvcBGwREUuALaguPPPYTajM/Cbwm8bsUR6vel6fBR46rE7jDrx2\n",
       "Ai6vTV9R5mlClCtW9wLOoHriQO+K1KuA7cr4jlTHrqd3HJvz1+Dx7cq/A69g+j2bPH7zwx2BX0XE\n",
       "MRFxZkR8KCJuhcdv4mXmr4G3A7+gCriuy8yv4LGbb0Z5vNbGOZl5M3B9RGwzqPBxB1723J9gEbEl\n",
       "VYT+0sz8XX1ZVu2mHr8JFBGPAq7OzLNY9+bFgMdvwi0B7k11euLeVFeDv7qewOM3mSLizsDfUZ2G\n",
       "2hHYMiKeWk/jsZtf5uJ4jTvwWgMsr00vZ3rUqDkSEZtQBV0fy8wTyuyrImL7snwH4Ooyv3kcd6Y6\n",
       "jmvKeH3+mnHWWwDsDxwSET8DjgMeEhEfw+M3X1wBXJGZ3y/Tn6EKxK70+E28+wDfzsxrS+vG56ie\n",
       "aeyxm19G8V15RW2dO5S8lgBbl5bRvsYdeK29AWtELKXqePaFMZepISIigI8A52fmO2uLvkDVUZTy\n",
       "ekJt/qERsTQi7gjsBnwvM68EfluuyArgabV1NCaZ+ZrMXJ6ZdwQOBb6WmU/D4zcvlP1+eUTcpcw6\n",
       "EDiP6rm3Hr/JdiGwX0RsXvb5gcD5eOzmm1F8V36+Ja8nAF8dWnoHVxQcTHXV3KXAkV1ezeDQ95g8\n",
       "gKpv0NlUz646CziI6llXpwIXA6cAy2rrvKYcwwuBR9Tm7w2cW5a9e663bWMbgAcxdVWjx2+eDMA9\n",
       "ge8D51C1mmzt8ZsfA9XzCM8r+/1YqivgPHYTOlCdFfgl8GeqvliHjfJ4AZsCn6J6ruN3gRXD6uQN\n",
       "VCVJkjoy9huoSpIkqWLgJUmS1BEDL0mSpI4YeEmSJHXEwEuSJKkjBl6SJEkdMfCSJEnqiIGXJElS\n",
       "R/4/LNQhkIEtiVoAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10967a850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmYJEWZ+PHvOxc3MyLKOQoIKAjI4SIiyoCKMLjouqyA\n",
       "x4/FCw9EcddzPViPVfdSkQVRV0RdFU9ARRGVwRsPbhgVPHYB5VAZEBABfX9/ZNR0dk5Vd3V3VfYx\n",
       "38/z5FOZkZGRUZXV3W9HREZGZiJJkqThmzfdFZAkSVpbGHhJkiS1xMBLkiSpJQZekiRJLTHwkiRJ\n",
       "aomBlyRJUkvGDLwiYt2IuCgiLo2IqyPi7T3ynRQR10TEZRGxx3CqKkmSNLstGGtnZt4dEQdk5l0R\n",
       "sQD4dkTsl5nf7uSJiOXA9pm5Q0Q8CjgV2Ge41ZYkSZp9xu1qzMy7yuoiYD7w+0aWw4AzSt6LgCUR\n",
       "sdkgKylJkjQXjBt4RcS8iLgUuAm4IDOvbmTZCriutn09sPXgqihJkjQ39NPi9ZfM3J0qmHpcRCzr\n",
       "ki2ahw2gbpIkSXPKmGO86jLztoj4EvBIYEVt1w3A0tr21iVtlIgwGJMkSbNGZjYblqZszMArIjYF\n",
       "7svMVRGxHvBE4J8b2c4BjgM+GRH7AKsy86Zu5Q3jDWj4IuLEzDxxuuuhyfH6zW5ev9nLaze7DavB\n",
       "aLwWry2AMyJiHlW35Ecz8+sRcSxAZp6WmedGxPKIuBa4EzhmGBWVJEma7cabTuIKYM8u6ac1to8b\n",
       "cL0kSZLmHGeuVz9WTHcFNCUrprsCmpIV010BTdqK6a6AZp7IbGfMe0SkY7wkSdJsMKy4xRYvSZKk\n",
       "lhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIk\n",
       "tcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5Ik\n",
       "qSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJaYuAlSZLUEgMvSZKklhh4SZIktcTAS5IkqSUGXpIk\n",
       "SS0x8JIkSWqJgZckSVJLxgy8ImJpRFwQEVdFxJURcXyXPMsi4raIuKQsrx9edSVJkmavBePsvxc4\n",
       "ITMvjYgNgR9HxPmZubKR78LMPGw4VZQkSZobxmzxyswbM/PSsn4HsBLYskvWGELdJEmS5pS+x3hF\n",
       "xDbAHsBFjV0J7BsRl0XEuRGx8+CqJ0mSNHeM19UIQOlm/AzwstLyVXcxsDQz74qIQ4CzgB0HW01J\n",
       "kqTZb9zAKyIWAp8FPpaZZzX3Z+YfautfjohTImKTzPx9l7JOrG2uyMwVk6q1JEnSAEXEMmDZ0M+T\n",
       "mWNVIoAzgN9l5gk98mwG3JyZGRF7A5/KzG265MvMdCyYJEma8YYVt4zX4vUY4FnA5RFxSUl7HfAg\n",
       "gMw8DTgceFFE3AfcBRw56EpKkiTNBWO2eA30RLZ4SZKkWWJYcYsz10uSJLXEwEuSJKklBl6SJEkt\n",
       "MfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElq\n",
       "iYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGXJElS\n",
       "Swy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmS\n",
       "WmLgJUmS1JIxA6+IWBoRF0TEVRFxZUQc3yPfSRFxTURcFhF7DKeqkiRJs9uCcfbfC5yQmZdGxIbA\n",
       "jyPi/Mxc2ckQEcuB7TNzh4h4FHAqsM/wqixJkjQ7jdnilZk3ZualZf0OYCWwZSPbYcAZJc9FwJKI\n",
       "2GwIdZUkSZrV+h7jFRHbAHsAFzV2bQVcV9u+Hth6qhWTJEmaa/oKvEo342eAl5WWrzWyNLZzqhWT\n",
       "JEmaa8Yb40VELAQ+C3wsM8/qkuUGYGlte+uS1q2sE2ubKzJzRd81lSRJGpKIWAYsG/p5Mns3TkVE\n",
       "UI3f+l1mntAjz3LguMxcHhH7AO/OzDUG10dEZmazZUySJGnGGVbcMl7gtR/wTeByRroPXwc8CCAz\n",
       "Tyv5TgYOBu4EjsnMi7uUZeAlSZJmhWkJvAZ6IgMvSZI0SwwrbnHmekmSpJYYeEmSJLXEwEuSJKkl\n",
       "Bl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEkt\n",
       "MfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElq\n",
       "iYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGXJElS\n",
       "Swy8JEmSWmLgJUmS1JJxA6+I+FBE3BQRV/TYvywibouIS8ry+sFXU5IkafZb0Eee04H3Ah8ZI8+F\n",
       "mXnYYKokSZI0N43b4pWZ3wJuHSdbDKY6kiRJc9cgxnglsG9EXBYR50bEzgMoU5Ikac7pp6txPBcD\n",
       "SzPzrog4BDgL2LFbxog4sba5IjNXDOD8kiRJUxIRy4BlQz9PZvZTmW2AL2Tmrn3k/SWwV2b+vpGe\n",
       "mWmXpCRJmvGGFbdMuasxIjaLiCjre1MFc78f5zBJkqS1zrhdjRHxCWB/YNOIuA54E7AQIDNPAw4H\n",
       "XhQR9wF3AUcOr7qSJEmzV19djQM5kV2NkiRplpixXY2SJEnqj4GXJElSSwy8JEmSWmLgJUmS1BID\n",
       "L0mSpJYYeEmSJLXEwEuSJKklBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWjLrAq8IHjHddZAkSZqM\n",
       "WRd4AZdG8MrproQkSdJEzarAK4KXlNW7prUikiRJkzDjA68ILo5g0wgOAk4uyfOns06SJEmTsWC6\n",
       "KzCWCALYAzgP2LO2a6PpqZEkSdLkzfQWryXltR50/RbYcBrqIkmSNCUzusULOLuxfR7wJWDHaaiL\n",
       "JEnSlMzYFq8IdgIe20g+FLiDRldjBOu3VS9JkqTJmrGBF3B1eb0P+ClAJn+mCrxWdzVG8HTgztZr\n",
       "J0mSNEEzOfDqOA84Gvh82f4Do8d4nQkQwaKW6yVJkjQhM32MF8BfZ5LA08r2Gl2NxRLg5tZqJUmS\n",
       "NEEzvsWrBF11dwD7ljFgAH8pr97pKEmSZrQZ1eIVwUbAbsAfx8h2R3ndP4K/YyR4dG4vSZI0o017\n",
       "4BXB/YB1gMXAT0ry6eX15C6HrCqv9wD/XEs/O4KHZXL3UCoqSZI0RZHZ7Mkb0okiMjNjzfQ1uhI7\n",
       "7spkg+5l8VXgXOCZwCNru56YydemXFlJkrRW6xW3TNW0jvEaZ/6tP4+x74fA3wNXAs+rpT9gANWS\n",
       "JEkaiukeXL/bGPtOGGPfw4FHUAVf9few3gDqJEmSNBTTFnhFcCTwvTGynDHGvqNq6xsCR5T1/+5x\n",
       "rq0juDyC506slpIkSYMzbWO8uoztOgh4FvAq4C+Z3DJ2eauPX5jJfRHcAywE1s3kT428rwLeWTYf\n",
       "XI75+eTfjSRJmsvm1BivCJ7RSLomk/MzOTqTm8YLuuoyua+sHlde746g+UG9s7a+FLg2gu0mVmtJ\n",
       "kqSpGTfwiogPRcRNEXHFGHlOiohrIuKyiNhj7PJYD/ifWtLPMtmx/yqv9uvG9lm19cW18zWnzPh2\n",
       "eV06iXNKkiRNWj8tXqcDB/faGRHLge0zcwfgBcCp45R3bG19d+DRfdShmz2BvTobmaMeF3RrxOpW\n",
       "rq1r6ffU1p12QpIktaqvMV4RsQ3whczctcu+9wEXZGZ5WHX8BNg/M29q5EvIbYBflaQlmdw2lcqv\n",
       "WZc1xo0to5qW4ltUd0keBBzS2Zm5RpekJEnSjB7jtRVwXW37eka3MtX9qrx+aNBBV7EIeGltewWw\n",
       "LfCpTN7NSNB1OqXLMYItu4wJkyRJGrhBDa5vBi7jNaOdO6Dzjj5pci9rTkPxEeCvG2nfAJZEcH/g\n",
       "BuCMCDaNYP4w6iVJkgSDeVbjDYweqL51SevixPJ6yj4Rt/wuM1cM4PxNd3VJO768LqcK+n4A7MLI\n",
       "QPv/BW6hmsri34ZQJ0mSNINFxDKqIUrDPc8AxngtB47LzOURsQ/w7szcp0u+LA1hB2Vy/lQrPnZ9\n",
       "2RW4mJHAclkmF9b2r0f3AO3kzFFdlZIkaS00rDFe47Z4RcQngP2BTSPiOuBNVBOVkpmnZea5EbE8\n",
       "Iq4F7gSO6VVWW4PZM7kigt2ouhQ3Z2RsWWf/H6N7TfbqmipJkjQA0zZzfTvnZDGwijK7fWNf1zfu\n",
       "nY6SJGkm39U4Y5U7J7dvBl3Fft2OieB7ETxnuDWTJElrozkdeAGM8UzGO8rryY30fRj9EG5JkqSB\n",
       "mNNdjeOJYF4mfynzeC2gNrO9XY6SJK297Gocgkz+Ul6zzAHW8V/TVCVJkjSHrdWB1xg2mu4KSJKk\n",
       "ucfAa7R9qabD2Hi6KyJJkuYeA6+aTL5H9dzJKQVeETwjYtTzKyVJkgy8urgdWBzBGyLYcJJlLKP3\n",
       "g8IlSdJaysBrTauoZrB/M/C5TmIEb4lgrwg26XVgBPMieBJUg/YlSZLq1urpJLqJYD6MTLiaSUSw\n",
       "LvDHelqX404AHgUcAbwPeCGwbiZ/GnqlJUnSQE3bsxrXNpn8OYJ7Kc+j7PZooQi2y+QXjeQTGRkb\n",
       "tn55fVsEdwKXZHLWkKosSZJmCVu8uojgkcD2wBuBnbrlabZ6RXAz8ICyeStwv8Yh8zK7Px9SkiTN\n",
       "LE6g2qJMfgRcRBV0ndLnYXfX1ptBF8Czp1ovSZI0u9nV2EMmv4wqzn0xcCnwGeBC4FfAxV0OGW8s\n",
       "184DrJ4kSZqFDLz688NM3gYQwQZU001Ep+swgodSdU2O5Y/j7JckSXOcY7zGEMEWwK+p3Z1YHqj9\n",
       "O2DnTG4saXcAG9QO/Xvgt8DZwPxa+lnAMzINwiRJmskc4zUNMvlNJlGfEqK0cl0PbF7LWg+6npLJ\n",
       "GZl8KZMFwIdr+55KbbB+BM+NYI/h1F6SJM00Bl6T8xtgywgeWOb96tgmk3PqGTM5BnhkLakePX8Q\n",
       "+MjwqilJkmYSA6/JuRH4EnATI5Otfg/4v26ZM/kxsF7ZfFsED6vt3mVYlZQkSTOLgdfk3Ngl7TFj\n",
       "zdOVyd3AbcCTgBeVsWIA3x5C/SRJ0gxk4DU5j24m9Dk56uLyehgjz3PcL4KfD6pikiRp5jLwmpwX\n",
       "UHUtrjPB4z5WXrdppG831QpJkqSZz+kkpqjzLMduD87ukncd4Fpg6y67faSQJEkzhNNJzFyPBR7X\n",
       "T8ZM/pTJ0rL5khKsLQPuZeQ5j5IkaY6yxWsaRLAYuL02830Ch2Zy7vTWbDgieBTV+105A+qyB9VN\n",
       "DrtlctZ010eSNDMNK24x8JoBIribarzYu4F3ZHLTNFdpoEpgeUsmD5zmetwP+D3VVCCHAvtTPXdz\n",
       "w85TCCRJAgOvOa0zTqyjn/Fis8lExsEN4dynACszeW8EF0P3JwXMtc9ckjQ1jvGa295c36jN8TVr\n",
       "RfCEiP7GvkXwnGbwOaA6rAO8CDipPGGg5+OZIsgI1h90HSRJqjPwmhlOBA6obW80TfUYiAhOBs4H\n",
       "vlyS7hnnkJ3LcQsGXJX9a+v3Nfatx5quHPD5JUkaxcBrBiiD7C8EPlWSHj+N1ZmSCHYAXlI2149g\n",
       "EbCo7Ns3giMieH7jsH8ory8ccHXO65L2EOBx5UkCH6aa3qNj2wGfX5KkURzjNcO0PR6qdGtukcmv\n",
       "B1TeJ4Aj+8j6WeCNwEpGZvE/PZPnDKIepS6/BDagNlVHr881glOBFzrWS5IE0zjGKyIOjoifRMQ1\n",
       "EfHqLvuXRcRtEXFJWV4/6EquZU7rrERwRwQbDvl8fwXcMIiCIvhbqqDrVGDXcbL/LXAVI0HXZTC4\n",
       "ux4j2ILqCQFPqyU/ZoxDXleOG3R3pyRJq40ZeEXEfOBk4GCqcThHRcROXbJemJl7lOWtQ6jn2uQ1\n",
       "ABF8mKq15sAhD7a/XznfW8oA80dNoazPlNc7gGtq6f8ObD/OsW8DDi11GEQA1mnBu47qez4/k+/2\n",
       "ypzJrcBNDDD4kySpabwWr72BazPzV5l5L/BJ4Cld8tk9MyCZrCqrR5fXs2mM+YpgnQguj+CofsuN\n",
       "YPcI1u2ya/fy2mmp3G0i9S3lZgTH15LfmsmfgCeW7V9mjnoQeKflqTN31keAL9b2T2kes3I3Y8f1\n",
       "mWTm6pa1sWxG9U+GJElDMV7gtRVVi0HH9SWtLoF9I+KyiDg3InYeZAXXUs9sbK8ObCPYHbibqivv\n",
       "42WahDFF8J/AJdB1ZvzNGtvdWjR7lTuvlAvwnvL62kxuB8jka6WeHyj7HkTVive9sv3VTnomf2yU\n",
       "/eYIHt5vXRreWV6fnMmfJ3jsyyd5TkmSxjVe4NXPyPuLgaWZ+QjgveBjWKYqk49nEmWg96eB+wNE\n",
       "8ABGAp2OTXqVU5uX6oTyekBpnVoUwRvKeKYnwagB7TtMoKpfaWz/JpN3NN7LlZncW9avy+Suchfn\n",
       "xpmrW/U63ZBH1A59A5Of3uGW8vqdCR73cRg/kJUkabLGG0h8A6x+qDNl/fp6hsz8Q239yxFxSkRs\n",
       "kpm/bxYWESfWNldk5ooJ13jt8xtgqwjWA27usn8JI4FG050Ro4KZjuOpJm3dmGrs3g+oArjjgUWl\n",
       "FW2jWrfnahHVlA+ZvI+RrsT9qbroPtzneyKTzvdmI+DOkvapCM5snO9+ZfzVRATw9m71H8fbgSsi\n",
       "eH8mL5jgsZKkWSwilgHLhn6esaaTiIgFwE+pxhj9muoP9FGZubKWZzPg5szMiNgb+FRmbtOlLKeT\n",
       "mIQI3gr8U5dduwEfAl6SyQ+6HHc7oydiPRB4NnBMl7LmZZIRvIzqeZF1m2byu1q5zS/MLplcNf47\n",
       "6U8EGwN/oJpU9o3A4Zl8dgLHbwS8D7gok5MmeO6NoOompRrz9vY+x4ZJkuaYaZlOIjPvA46jmojy\n",
       "auDMzFwZEcdGxLEl2+HAFRFxKdUf7X7mcFL/Nm5svxA4L5MrgFuppkwYpdNiVUu6LZMLyhxZhzfz\n",
       "l64/YCTAqvlt6Z6cH8EHu+z/aR/voW+Z3F4Gw78JOAd4bgQPmkARPwOeARN/6HWtFQ7grVTBnyRJ\n",
       "A+MEqjNcCaLeBbwUeH8mx9b2dS7eQzP5WQQ/Y/QYrXm1oKpzzDxgz0x+FMGOwM2dLrkybUWnhef1\n",
       "VMHHWI7IXD3b/sBFcCxV61XfE8pGcBbVnbcHZXL+JM65Lowa6L+EqutycSb/O9HyJEmzkw/JXkuV\n",
       "u/JeBhxaD7oaflqClFED45tBV0n7SyY/Kus/q4+DKvm3A/bL5G1Udzyu0UJG1RJ0yDCDruKXnZXx\n",
       "5jKLYMsI3snIdCffn8wJy6OEoOrmBFhF1bL4q8mUVxfBjuUGiVZFcFWEd2tK0kxgi9csFsEGVJOV\n",
       "1r2HKlBbrxZETPU8nS/JO4E3dO5SHLYSpHwF2BPGbvVqjD1bt8wjNpVzb0XjRpJ6uREsHO9ziGAh\n",
       "1Xxsny5Jq4DMHPw/POWz+lMmt0fwH1R3q/4dVVfwn6G9x1BJ0lxgi5fWkMmdwOJa0t9k8nJgyaCC\n",
       "ruKQcr7XtBV0lfPdkslene0Ijix3dxLBphFs3uWwq6cadJVz3wBsWTZvK68/Kef+FnBPBFtF8C8l\n",
       "ACaCLSJ4WK2Yf6Caw2xVWapsg5mZf7UI7kd1x+ttJQB9BfBwqnGZE53HTJozyu+Jbw64zPkRxJCf\n",
       "KKI5zMBrlutMVlr8uKTd1iP7ZM/xlWluLelMW/EJ4K6yvhL4TQS7RnBobf9fDeqkmfymrP4XcDqw\n",
       "TQls9ivp1wOvBe4od2N+GVgZwTERvIHez6vsNsXHVPT1fNQInjDg8xLB1j2mLJF6iuDBEYP7We1S\n",
       "/vwI9qaaauexESwoQdiEf49FsFEEPygt2AD3Uc2n6B3PmhS7GueA8stk10wun+66DEsEb6aaVHUs\n",
       "8wc9/UN52PbvgIfCmJ/v1VRzojWdSjVn2m/qiYMKZCN4DdX8Y3UvBk6pbT8cVk/5sWSygXkEe1G1\n",
       "3F2XyT0lbRXVjQf93vywKfDNzK6f1bSLYNdyx7CGqDM0YFj/0HWZ9mZbqjGjX8tc/Y9cv2U9C/ho\n",
       "t312389tdjWqpzL9wpwNuoo3AesCX+ux/63DmHMrk99kck/5Y/zJkvxgqoeL71v7xdsrkHhlJjfC\n",
       "6mdVHgrVH4ayTPpnMILjGAm6lpTXXajuBL2cqqt0g0yuZuQxSt8Yo7yzIzi5kXZaBKsi+CLwI+Ba\n",
       "4E8RPDqCR1O6uiN4aaObtZeTgJ0iVte3fq6LIyY299pElS6ig7s9aiuC64HLa0980JBFcGlLpzqw\n",
       "vD4hYsJB/3N67YjRz4Wd0SLYIGJCTybRsGT5qz3spTpVO+dymdsLZEJ+AXKDsv7+aa7PPqUeT4T8\n",
       "eFlPyGtreRZBbgX5kNr+hHzLFM771VLGsrK9oI/PLSeyv1HX5vLdLmk79VOH+nkg/x3yH2v7juxy\n",
       "3P+UfSum8Hk9sNv5y771avuunM7v01xfys/thfXrADlvvO/OOGXuVF4XQO5Wu5aH9PjuPnCc8uZB\n",
       "PqiU1+34pZA3QG47ibpGKf/VkI9t8XPv1P3Q6f4OzJZlWHHLrH8DLi4zaSm/VDfpFeT0+EX+vHHK\n",
       "fBBkdEn/BeTJE6jb08r5ntVI3x/yuFp91qm9l7ECr4Rc1SXtzEb5j4R8MuQOjXwvh7xfj3KPbZTR\n",
       "NWCa4LW5bozAa7uS/nPI907392i2LGN8z98AuWSsY2rBdEJ+erxrC7m4W+BQC64+2/gOXUH1z84v\n",
       "enzHdofcoMt59qh9r08rr6eW11dAPqD2Pk6YxGd2DeTdU/0+T/ZalWXDAZe9CPLHpewfDan+G0Bu\n",
       "2tbnVZ2ToVyfWf8GXFxm4gL5gG7BUtkXkAshtxgvoIC8pew/rJH+8pJ+8ATqVG/V+TxVC1CzBS4h\n",
       "39usV6lzJyBbt7Z/F8hXdinjo5DfhvyXWtp/ltede/whTMhnldcP1Oq91VQCL8iHMjrAO7b84dsM\n",
       "8i2Q8yEvq/1hzea1qx27cIrfizFbJWf6ArlxbX37xrU7rKTXW33/C3K9kr4Fo4P5LRrHJ+TikneD\n",
       "8roY8u1U/7A8o5F3Ucnzw27fpVo969/Xwxv5bqrlmw+5a6+yIHesXz+qID0hH1y2j4X89z4+w2b5\n",
       "U/pOTeDandfts27keSpdWpzHKHNPuv8zuc8Q6t8pe4f2vu/kUMqd7W/AxWU2L1RdFqsDgsa+g2v7\n",
       "Vpa0DSGPgvxVSZ8/wfNtPEbQswvk1Y20n/coZ2fIa8r6PMglpV6PHqP8+h+xbufeh+q/2ntL2t9D\n",
       "bs5Il2pC3kOPgLZRvw16nP+lZf95jPyHXl86f5gfA3nSGO/jvvL66Ql89nuXY/aDfHNj3y6Q2/U4\n",
       "bt/p/p6Weryt/oevx+fyvi5pX2ck4FpeXk8qaZuP8Rl/vMv3sb68FvIYyO830q+BPL5R94R8Se38\n",
       "neW7tZ+rXuc5qcfn0e2floRcv0f+RZCP75L/xJau388a5/1clzyrf0Z7lLFnyXN07fv82i7v6eiS\n",
       "fxm11jWqYPsMyN9DPmICdd+oXn5733mGcq5WKj/MN+DiMheWxi+tfXv8Qr+7sb3FJM+1VS1wSKrW\n",
       "s04Lw+MgLy/pG1FaFSZYfrNlor7sXvKsRxWwJeRjGsev0+W4PzG61WpLqpas+zeO3b38sn9+j/Mv\n",
       "K/ku7LJv3S7XYtylz89kHlUA0q2MvWrrb6kdcwAj3cNrdIm18J3ciaq1aF6XOh9aW38+5NmN/c1A\n",
       "5om9PjPIH5X0FX183r0+w8MhX0z1j0W3bvmlVIHeZpDnNI6dB/nS2vbZ9NEVR++u+MN65G/m24mR\n",
       "n+mdIG+CPJBG4Ab5GsijpngtO920G0P+ba/vLtU/Nj2/0436v7jHz887qX5e96zt+0rZVw98z55A\n",
       "/TvH/FV53aSdnwF6fhZTKreNyg/zDbi4zIWFqom/2y/xHXr84cspnm8h1X+d/9hl33zIZ0+x/AdQ\n",
       "jXV7IOQhkzj+2sb7fc5YnwPVQOcvdNn/Daruy3dQa1mgCj7/le7dLfXA8U6qLqR6S8UfIS+AfH3Z\n",
       "HnPcCeTDIJ/b4/p2WxaW4+pprxvid+9gyLfXtgPy2eW8t9fqcF2zrrVj9q+lv6+kHUXVMtJ8f6c2\n",
       "zr8hI12Mi7rk3662vqDk+3+NPOtO8D0vgnxSOfZfa+VMaOwTVetNp2v1IMjfUbW4PbFL3s45VnW+\n",
       "M1QD7Lt9B6L2s5iQt9e+t1vUylwf8ojGeT4Gef9yHXcoec5pXK/X1n52Ot+3A2rn/2k9f+1cPb+3\n",
       "tXwv6ZHn9l7HjPMZL6jnh/wO5JOH9fMw+tz0VccJl9tG5Yf5Blxc5spSfnF3fil9rPEL+O9q+w6n\n",
       "5UGm0/R51H9Jb1LSvs5Ii1xn6RW07jiFc+9Cjy6jWp6F5TxfnMD7OL68HtWlvo8rrzcyOtC7FfIX\n",
       "Q/qM6+PtPgN58xh/XIPR3WsrG2V1bZVjpJXjHMiD+qjTQqoge7y7dG+byB/wLsc3xybtPIDP8x21\n",
       "8naopW9W0p4HuWfjmFf1+Lz3gty2rP+5y3dpn8b2OoyM47yyW5m1c3Za6zotiL1a7xY38ifk67rk\n",
       "W9al7IR8K+SmXfIfCHlhn5/pgeWYzu+AD0K+oP69g9x8OD8fTOq7NW65wyi0zTfg4rI2LbQ0EHcm\n",
       "LCX4eEWPfZvRGPdRWzaE3LKlOn6ynPNpdO/iWlyr18oeZWxeWz+68V4WMbpL5/UTqFvnD+APG+l7\n",
       "lNdFjO5ybi5X1dbf0Cj3i5RB833W5VDIjYbw+X+qHlBM4vjOnZBPGlB9ltQ+s+uoxjQ9oZbW64ab\n",
       "AxhpzWteh06Aec0Y1yqp7hL94hj73904Z33fN8rrVl2Oe05tfTkj/3Ak5NIe7+f5VGMoO4HbyyC/\n",
       "CfmV8jPxYMgb+vxM3wL5wdr2FeXcnVbDS6byHWica9PR2wyk3DXOM4xCu7+h4bwBFxeXtXeBfGb5\n",
       "JTxvms6f5eDFAAAIqklEQVR/fO2PUHaCmrJvd8g3Ud0I0Vf9GN1a8KxaevOP4fKSfjZVN98mkCfX\n",
       "/3BQm76jllZvJekMjv4bRrq8PgL5slr+A0s5E7qJo+VrMKVrz4D/maEar9Wt5bDvO/0g31M77oJG\n",
       "Oe+qrX+eqjvyRshfN/K9mmoc5P+V67qwcY6vNetY0h8GeQfkv3V5D51uyUMg3ziVa9b8bvbI1+kO\n",
       "rneFP6WkvY5qDsBO3S6aZF2C6g7dQ5v1GVbc4iODJGkKIlgAox4evxuwBXBe2X5aJp+fQHmPBn6R\n",
       "yU21tA2B9wNH1bIeBHy1SxFPAz5X274L2ATYieoZg03rUj2B4IBMzuy3nuqtzGh/dy3pM8DTM9d4\n",
       "lNFYZSwENgNupHrY/ZnAG4GfUj2p4qDO9YrgO8C+5dDHl+WNmfy5j/N06vScTE5v7HssrH7I+AaZ\n",
       "q5+VO2URXAs8BLg1k03Gqdt+mXynS/oVjH4m7ryJfMalrJOBl9SSNsrkjmrfcOIWAy9JGoAItgV+\n",
       "0Ui+Gdiynz+AfZ7jBuBc4Hl9HvJ44OuNtGdSPdx9F4D0eYNDE8H8QV37cc7TCfSeksk5Ezz2K8CT\n",
       "puN7EMGZwNPLZucZs/fLZFUEy4ALgO0y+WXjuCcy8k/HN4EDqILTEzJ59wTr0AyCDszkgmqfz2qU\n",
       "pBmr/HF4SNm8laqFYLNB/uHNZKtMng/8U0l6CbAB8HFgfeBtJX0/YNtMvgH8c62IHTL5OFVrGfR+\n",
       "xqgGoI2gq5znT1UP1sSCruLpVM+enQ5H19ZPKa+HRRDAVlSjoX655mGrW+HuAY7Kkef0viuCvfs5\n",
       "cQSb1oKubWqB5zci2Lj/tzBxtnhJ0ixUHjR+20S7VmrHz8shPFhemqgItqdqmV1F1VXfcXMmm/VZ\n",
       "xqbALWVzQa+gN4LPAy8FruukdYKu0s3/3ZL8AYjn2+IlSQIgk1WTDbrK8QZdmhEyuTaTB1N1GdYt\n",
       "n0AZv2WkJfi+CN4bwboAEewaQZYWrqcyEnQ9A9izVsb3gOeXzc7rwNniJUmSZoQIdgMekclHJ3n8\n",
       "j4C9+sj6zNLt3q2MdYErILZ3cL0kSdIYIlgMPAlG3aW7A/Dzid1Z6l2NkiRJfYng+8CZmbxrcscb\n",
       "eEmSJLXC6SQkSZJmOQMvSZKklhh4SZIktcTAS5IkqSUGXpIkSS0x8JIkSWqJgZckSVJLDLwkSZJa\n",
       "Mm7gFREHR8RPIuKaiHh1jzwnlf2XRcQeg6+mJEnS7Ddm4BUR84GTgYOBnYGjImKnRp7lwPaZuQPw\n",
       "AuDUIdVV0yQilk13HTR5Xr/Zzes3e3nt1M14LV57A9dm5q8y817gk8BTGnkOA84AyMyLgCURsdnA\n",
       "a6rptGy6K6ApWTbdFdCULJvuCmjSlk13BTTzjBd4bQVcV9u+vqSNl2frqVdNkiRpbhkv8Or3CdrN\n",
       "h0i28+RtSZKkWWTBOPtvAJbWtpdStWiNlWfrkraGiDAgm6Ui4k3TXQdNntdvdvP6zV5eOzWNF3j9\n",
       "CNghIrYBfg0cARzVyHMOcBzwyYjYB1iVmTc1C8rMZquYJEnSWmXMwCsz74uI44DzgPnAf2fmyog4\n",
       "tuw/LTPPjYjlEXEtcCdwzNBrLUmSNAtFpr1/kiRJbRj6zPX9TMCqdkXE0oi4ICKuiogrI+L4kr5J\n",
       "RJwfET+LiK9GxJLaMa8t1/AnEXFQLX2viLii7HvPdLyftVVEzI+ISyLiC2Xb6zdLRMSSiPhMRKyM\n",
       "iKsj4lFev9mhXIuryuf+8YhYx2s3c0XEhyLipoi4opY2sOtVrv+ZJf37EfHgcSuVmUNbqLonrwW2\n",
       "ARYClwI7DfOcLn1dl82B3cv6hsBPgZ2AfwVeVdJfDbyjrO9crt3Cci2vZaS19AfA3mX9XODg6X5/\n",
       "a8sCvAL4H+Ccsu31myUL1dyHzynrC4DFXr+Zv5TP/xfAOmX7TOBor93MXYDHAnsAV9TSBna9gBcD\n",
       "p5T1I4BPjlenYbd49TMBq1qWmTdm5qVl/Q5gJdV8bKsnwy2vTy3rTwE+kZn3ZuavqL6Mj4qILYCN\n",
       "MvMHJd9HasdoiCJia2A58EFGpnPx+s0CEbEYeGxmfgiqsbSZeRtev9ngduBeYP2IWACsT3Xjmddu\n",
       "hsrMbwG3NpIHeb3qZX0WePx4dRp24NXPBKyaRuWO1T2Ai4DNcuSO1JuAzhMItmT0NCKd69hMvwGv\n",
       "b1veBbwS+Estzes3O2wL3BIRp0fExRHxgYjYAK/fjJeZvwf+A/g/qoBrVWaej9duthnk9Vod52Tm\n",
       "fcBtEbHJWCcfduDlyP0ZLCI2pIrQX5aZf6jvy6rd1Os3A0XEk4GbM/MS1py8GPD6zXALgD2puif2\n",
       "pLob/DX1DF6/mSkiHgK8nKobaktgw4h4Vj2P1252mY7rNezAq58JWDUNImIhVdD10cw8qyTfFBGb\n",
       "l/1bADeX9G6T5F5f0rdupHedPFcDtS9wWET8EvgEcGBEfBSv32xxPXB9Zv6wbH+GKhC70es34z0S\n",
       "+G5m/q60bnwOeDReu9lmEL8rr68d86BS1gJgcWkZ7WnYgdfqCVgjYhHVwLNzhnxOjSMiAvhv4OrM\n",
       "fHdt1zlUA0Upr2fV0o+MiEURsS2wA/CDzLwRuL3ckRXAs2vHaEgy83WZuTQztwWOBL6Rmc/G6zcr\n",
       "lM/9uojYsSQ9AbgK+AJev5nuJ8A+EbFe+cyfAFyN1262GcTvyrO7lHU48PVxz97CHQWHUN01dy3w\n",
       "2jbvZnDpeU32oxobdClwSVkOBjYBvgb8DPgqsKR2zOvKNfwJ8KRa+l7AFWXfSdP93ta2Bdifkbsa\n",
       "vX6zZAEeAfwQuIyq1WSx1292LMCrqALlK6gGVS/02s3chapX4NfAPVRjsY4Z5PUC1gE+BVwDfB/Y\n",
       "Zrw6OYGqJElSS4Y+gaokSZIqBl6SJEktMfCSJElqiYGXJElSSwy8JEmSWmLgJUmS1BIDL0mSpJYY\n",
       "eEmSJLXk/wPld/Ij7ov6PwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a877b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEUCAYAAAD6CjgRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm8HGWd7/HPLysBhIhAWBKIsqi4sgiMggZUBqKvuAwj\n",
       "y8VRXEcnF7erLG64XXdlkIuDDiqigisI1zhuEBQc4gIBxICgooRdkUURBfKbP+o5SaXTffok6a4+\n",
       "ffJ5v171Ol1PPVX1dFf16W8/tXRkJpIkSeq/SYNugCRJ0obC4CVJktQQg5ckSVJDDF6SJEkNMXhJ\n",
       "kiQ1xOAlSZLUkFGDV0RsFBFLImJpRPwyIt7fod7JEXFdRFwREbv3p6mSJEnDbcpoEzPz/og4IDPv\n",
       "i4gpwMURsV9mXjxSJyLmAztn5i4RsQ/wSWDf/jZbkiRp+HQ91JiZ95WH04DJwJ0tVRYAZ5S6S4CZ\n",
       "ETGrl42UJEmaCLoGr4iYFBFLgduACzPzly1VtgdurI0vB2b3romSJEkTw1h6vFZk5pOpwtTTI2Je\n",
       "m2rROlsP2iZJkjShjHqOV11m3h0R3wL2AhbXJt0EzKmNzy5lq4kIw5gkSRoamdnasbTeRg1eEbEl\n",
       "8GBm3hURM4BnA+9qqXYesBA4OyL2Be7KzNvaLa8fT0D9FxEnZuaJg26H1o3bb7i5/YaX22649avD\n",
       "qFuP17bAGRExieqw5JmZ+YOIeDVAZp6WmYsiYn5EXA/8BTi6Hw2VJEkadt1uJ3EVsEeb8tNaxhf2\n",
       "uF2SJEkTjneu11gsHnQDtF4WD7oBWi+LB90ArbPFg26Axp/IbOac94hIz/GSJEnDoF+5xR4vSZKk\n",
       "hhi8JEmSGmLwkiRJaojBS5IkqSEGL0mSpIYYvCRJkhpi8JIkSWqIwUuSJKkhBi9JkqSGGLwkSZIa\n",
       "YvCSJElqiMFLkiSpIQYvSZKkhhi8JEmSGmLwkiRJaojBS5IkqSEGL0mSpIYYvCRJkhpi8JIkSWqI\n",
       "wUuSJKkhBi9JkqSGGLwkSZIaYvCSJElqiMFLkiSpIQYvSZKkhhi8JEmSGmLwkiRJaojBS5IkqSEG\n",
       "L0mSpIYYvCRJkhoyavCKiDkRcWFEXB0Rv4iIY9rUmRcRd0fE5WV4W/+aK0mSNLymdJn+APCGzFwa\n",
       "EZsCP4+I72XmspZ6F2Xmgv40UZIkaWIYtccrM2/NzKXl8Z+BZcB2bapGH9omSZI0oYz5HK+ImAvs\n",
       "DixpmZTAUyPiiohYFBG79a55kiRJE0e3Q40AlMOMXwNeV3q+6i4D5mTmfRFxCHAusGtvmylJkjT8\n",
       "ugaviJgKfB34Qmae2zo9M++tPf52RJwaEVtk5p1tlnVibXRxZi5ep1ZLkiT1UETMA+b1fT2ZOVoj\n",
       "AjgD+GNmvqFDnVnA7ZmZEbE38JXMnNumXmam54JJkqRxr1+5pVuP19OAo4ArI+LyUnYCsANAZp4G\n",
       "HAq8JiIeBO4DDu91IyVJkiaCUXu8eroie7wkSdKQ6Fdu8c71kiRJDTF4SZIkNcTgJUmS1BCDlyRJ\n",
       "UkMMXpIkSQ0xeEmSJDXE4CVJktQQg5ckSVJDDF6SJEkNMXhJkiQ1xOAlSZLUEIOXJElSQwxekiRJ\n",
       "DTF4SZIkNcTgJUmS1BCDlyRJUkMMXpIkSQ0xeEmSJDXE4CVJktQQg5ckSVJDDF6SJEkNMXhJkiQ1\n",
       "xOAlSZLUEIOXJElSQwxekiRJDTF4SZIkNcTgJUmS1BCDlyRJUkMMXpIkSQ0xeEmSJDXE4CVJktSQ\n",
       "UYNXRMyJiAsj4uqI+EVEHNOh3skRcV1EXBERu/enqZIkScNtSpfpDwBvyMylEbEp8POI+F5mLhup\n",
       "EBHzgZ0zc5eI2Af4JLBv/5osSZI0nEbt8crMWzNzaXn8Z2AZsF1LtQXAGaXOEmBmRMzqQ1slSZKG\n",
       "2pjP8YqIucDuwJKWSdsDN9bGlwOz17dhkiRJE82Yglc5zPg14HWl52uNKi3jub4NkyRJmmi6neNF\n",
       "REwFvg58ITPPbVPlJmBObXx2KWu3rBNro4szc/GYWypJktQnETEPmNf39WR27pyKiKA6f+uPmfmG\n",
       "DnXmAwszc35E7AuclJlrnFwfEZmZrT1jkiRJ406/cku34LUf8EPgSlYdPjwB2AEgM08r9U4BDgb+\n",
       "AhydmZe1WZbBS5IkDYWBBK+ersjgJUmShkS/cot3rpckSWqIwUuSJKkhBi9JkqSGGLwkSZIaYvCS\n",
       "JElqiMFLkiSpIQYvSZKkhhi8JEmSGmLwkiRJaojBS5IkqSEGL0mSpIYYvCRJkhpi8JIkSWqIwUuS\n",
       "JKkhBi9JkqSGGLwkSZIaYvCSJElqiMFLkiSpIQYvSZKkhhi8JEmSGmLwkiRJaojBS5IkqSEGL0mS\n",
       "pIYYvCRJkhpi8JIkSWqIwUuSJKkhBi9JkqSGGLwkSZIaYvCSJElqiMFLkiSpIQYvSZKkhhi8JEmS\n",
       "GtI1eEXEZyLitoi4qsP0eRFxd0RcXoa39b6ZkiRJw2/KGOp8FvgE8PlR6lyUmQt60yRJkqSJqWuP\n",
       "V2b+CPhTl2rRm+ZIkiRNXL04xyuBp0bEFRGxKCJ268EyJUmSJpyxHGrs5jJgTmbeFxGHAOcCu7ar\n",
       "GBEn1kYXZ+biHqxfkiRpvUTEPGBe39eTmWNpzFzg/Mx8whjq/hbYMzPvbCnPzPSQpCRJGvf6lVvW\n",
       "+1BjRMyKiCiP96YKc3d2mU2SJGmD0/VQY0ScBTwD2DIibgTeCUwFyMzTgEOB10TEg8B9wOH9a64k\n",
       "SdLwGtOhxp6syEONkiRpSIzbQ42SJEkaG4OXJElSQwxekiRJDTF4SZIkNcTgJUmS1BCDlyRJUkMM\n",
       "XpIkSQ0xeEmSJDXE4CVJktQQg5ckSVJDDF6SJEkNMXhJkiQ1xOAlSZLUEIOXJElSQwxekiRJDTF4\n",
       "qaMI9oxgowgeHcHzB90eSZKGncFLbUXwEuBnwF+Ba4BzIpjRpl403TZNPBFsGkFGsM8odTZqsk1a\n",
       "XQTPjWC7QbdDGnYGrw1cBFuXD7yR4bsRbAx8rk31uyOICF4fweQIjgNWRPD4dqFMWgvPKX8vLfvW\n",
       "RgARzI3gmgheBvw1gt17sbIIHhXBw7vUmVreE6/sxTongPOBNw26EdKwi8xsZkURmZn2jowzEayA\n",
       "jr1WRwJXAg8H3g4c1GVxzwe+ncnfa8ufBCwB9spctZ4IdgHuzuT29Wi+JoAIdgRuaDPpAuDANuXT\n",
       "gYcyeajLcicDD9aKHpPJtWXayD++/TK5pMP8RwFnltFHZrZt44RXerV3Aq4DPpjJcQNuktSIfuUW\n",
       "e7w2YBFMpwpd9wJzgLPq0zM5K5OrM7k4k3/ssJhn1B6fC/wtgq1qZQ8Be5X1/d8IpkdwGPAr4La1\n",
       "bO/M0htXL5ttb9vwimAWq0LXo1smt4auhcBfgL8Bl3ZY3sMj+GgEs6n2x7prItirFroALm6zjK0j\n",
       "uIUqdH24FB9Umz57pIe4Zb4ZEezWrl1DbgVV6AL4p0E2RJoIDF4boHK4cBbwzVK0VSbLMzmy9Eod\n",
       "C2zZZtZJwNbAHuXvrEx+WOb5GHBjqXd7+WD6ehl/GXALcDxwP3B2rS1Zer86tfXGCN5ZRn8O/KUc\n",
       "ApoRwdllnVdGrPGhrXGu9KTcWkZ/mMmvgE2o9r1PAZR9679KndOApeXxXhF8MoInR/CZCJ5dwtad\n",
       "wBup9ovnAouAxwJ/LvP9tNaEj5Z2vKB2qP1Eqi8E25Q6Hwc+CcyszTeynxPBhRFMiuBRwH3A1aWn\n",
       "bUKI4Nm10TOBnSPYdVDtkSYCDzVOQBFsA9yWyRobN4JDga/Wiv6eyfQervsQqg+7lUYOMdZ6CH4J\n",
       "PIHqnJH5pWwz4EnAJcAzMllceuTuX8smPCKTO0dp3yQguh2mUv9F8Hbg3WV0i0z+VJs2HdixhLH6\n",
       "PJsCT4T2hweL44APwGr73kyqMPfPwA+oQlky+v41LZMHyoUmbwYeRxXgNqX6MvGZDvO9mKq3bXom\n",
       "fxxl+eNaCcYryuikzJW9fDdmssMY5n8+8P8zVzvcKw0NDzUOqdK79JxyCGRKj5a3bQRfjGCzNtPf\n",
       "TtW7dH4ZPz2Cl5Zv8ytYPXQB7L2+bWrxX8ChVCdL/z/gKSMTMokyPC6TFZk8h1UnVd8D/IjqH/2F\n",
       "EewPa5z/dS1wSm38a8Bkqg/REX8sz7XTm+UkWHUOmgYjgpNYFbqm1kMXQCZ/aw1dpfzPmfwYmEJt\n",
       "3wJ+WKvzQarerP1qZXdl8iJgK+CgTO7P5G+s6gl7FXBHeXx42U8fKOPXUoUuqEIXwDeAzVua97Xy\n",
       "90yq4PWHsi/27ItNw2aVv4+pfYk7HpgTwSvLc3tdu/daCWjnABc11FZpeGRmI0O1qmbWNYgB8lDI\n",
       "V7cp3w8ya8Mr12HZ/wq5V3n8s5blPalWb0bLtE7D9iOPB/26lXaP1tbXQy6H3LbUDci3QT6rzXK+\n",
       "UJtvYSk7CnI65DzIv9amP6U235NL2V8H/VpM9KFsv4W17bDbei5vS8jJ5fHNkI9ey/nnQO5dHs+E\n",
       "/ABktNSZWtq6bev7BvIppWykDc9usw+vsa/2+zVez/kfBvn00vYbWqbtOMp79eOlTv3/0F2D3ucc\n",
       "HNZ16FduGfonMB4GyI/X/tEc1zLtT6X8V2sbdiCnjPJP7q76P7yWaVtBfq42fgvkMyEvhnxFWfbz\n",
       "IQ8a9GtX2jKpfCBPL//0Ly7tXrCWy9mozHdH+XtSl1C3H+QNLWVPhzx20K/JRBogX1he20e0vNZT\n",
       "Bt22dXgu/wZ5Spc6y2rvw/8NeW6D7ZtT1n0q5Gshf7yW82/dso3WaDvVl8y/tXtPlel7Qj4EuXkp\n",
       "3w5yf2pfEh0chmHoV27xHK/1FMFZwOFl9GeUK/iKXamu3jsok+9FsGep8yHgs1SHS26nulrrs5n8\n",
       "tiwzSr09asu6A1ZeLTgV2Bh4EXAUq19ZeFYmR5bl7JDJ73v0VBsVQWSueY7aGOedBG3P4fpEJsdE\n",
       "8EbKidU1DwN+TXXRAMDrMjl5Xdav1UVwGaxx/62NsjrUN6FFsD2wHNgy+3y+V8s5WXXfzlx5LmW3\n",
       "ZTzEqlNQ9gYuy1HOhyzrPB54X634L8B5mRzZeuUncABw0bq+t6Um9S23DHtyHGwazr3LN7olpcdm\n",
       "WqdvgbV5RuuBScgdIH/Xaf4O7Rip+/JBvybjZYB8U3lNJpdv8Zu1TJ8L+WvIxZC/K2WPb9kWx0JO\n",
       "Xcv1ngb5RsgnDvo1GA8D5OPKa3l1+bto0G0awGswsj/9c/l7RI+XfwjkhyBvLct/a22dn6s9/nCX\n",
       "5Yz0lr1jHdtxUW1d7y1lz+rwf26vHjzvHSFPGPT2dZi4Q79yy9A/gfVvV06BPLFTyIHclOoQ1iMh\n",
       "b4J8aSmfW/snslHLPFHqJ+SnWqbNhVwA+aXa/F9p84/p3SU0TB/0azSsA+TG6zhftGyLC6jO/fl+\n",
       "+SDZqsN8u7TMdwXlnKOyzA9Cng+5DdV5Q48f9GvU59d/5NyoHBkfdJsG9Drs3q/wUZZfX+ZZpSxq\n",
       "0/+70/+3Wp2X1JYxeT3aEuULy7a1so2oDjPvDHllbT2bj2F5by5192iznpHl7D3obewwMQeDV8/b\n",
       "kwH51Tb/DL9KdXLoFMhXdfiH+bba4559eFKd33QN5DmQkwb9Gm3IA+SBkG/osP3rw8vKvhKQvy9l\n",
       "3x/DfCPDo9ayXTPK36mQ0xp6LWZC7tBh2iaQi8pzeU/tPTWn9hxfOOjtOeiBVRe0/FPL9u/6/4Oq\n",
       "J/2JkJu2mbZpbZ87bZRlHFTqzW0zrX4u6al9fh2ml2CWkBd1qfuUltdqs9q0D7RM26if7XbYMAeD\n",
       "V8/bk9fW3rSfK9/KlnT4cDyzhKEzWsqfO+jn4dD3/WRy2dYPjDFIvbXMN401D10m5PEt43+HPHAM\n",
       "7dgE8tIyzxGQ9458kPf4+U6l6p24szz3f6i1dYs29bu9HucPehuOx6EWxEbCWMcvWrV6v2spnzUy\n",
       "bYzrXKMu5JG15b+CDr25fXj+P6vvU1RfOu+k1ttWa9c7yt+rWb1n7sesGWSTIbxow2F8DgavNZaX\n",
       "x0LeQ3VVWr1b/alUV9S8FfLFkDPbzPuY8gZ9QZtp9Uvdj6XlcBXVFXiHM4ZucoeJNYzsZ5AvgPxf\n",
       "rOptqA87tcyzA+TOLWWPL/vZgtp8by771ch46y0NRgs32/Xguc2A3GwMQep6yP1q84yUbwn5B8j7\n",
       "Id838kE+6G02ngfIfWuv3392qPPBltf/AcjTy/43UvamMa7vtbV5pkEeUxu/o+HnXn/vHFB7fHTL\n",
       "8z2HqkfuNW32xWllWR9rKf9Sy2fCdMgnD3p7OwzfMLDgRXV35tuAq0apczLVb3ldAezeyycw8u2l\n",
       "vFEvpzpZd6OWN9prqS5X7vRh8ZSyjJdShbJRvyVSXQY+Y9Ab3WE4hhKuDliH+YJVXwLaDc+C/A+q\n",
       "iwAS8l9Y1UNxQnlP3EQ5WZvqxP4LIN9CORdxDG14NOSubdb95drjd0L+oGX6caO9j6h6ztbrflIb\n",
       "wtDymr60lM2gOlR7SSn/Ne17TxPymWuxrvohxQNrj9/PAA7VQX5xlH0/qd0Kg9UPXf+gw3PbCvIj\n",
       "tfdHlP3w56VsVqkbVD1nnj/rMOowyOC1P9Wl4G2DF9VPviwqj/cBLl3bJ1D++U9vKZtce6Ot6PDG\n",
       "3IzqJPR62Y3lA+txVOffjJT/qfZ4KQ2dH+Pg0G2gOswysm8+gVHukdRm3qPK9As6vEd+Tedzg67p\n",
       "MM925QNrEi3nBFFdNFK/Ue3bB/36DfvAmhdztA7TS72ZtbJTIT+3Duvah9rJ9gy4J6js7/eUfXEn\n",
       "yOsg30v1BWOTlroHlPdKx0BP9/Myn1h7/LFBb3uH8T0M9FAjMHeU4PUfwGG18WuAWe2eQAlKn4Xc\n",
       "pirL2ZAn194Ir6O6S3u7oHU/Vc/CyGGMF5dlBNW5AdnuDcnqXdpfoHzrcXAYzwOr7qa/vOzz8zvU\n",
       "m97yPvlUm/fOMVTnbZ1HdR7j1lS3vKjXeS8dTqDvsN4dqb4w2avVm+29Xcv2uLiEj7W6+GKM61oZ\n",
       "9Af9vPvw3Cax+heZlV8QWsZHzpHcctBt7sN+tEmHaftBPqI2vj/k0YNu83ge+hW8xnQD1YiYC5yf\n",
       "mU9oM+184P2Z+eMy/n3g2Mz8eUu9pPM9864AfgK8sqX85Zkdf4hWEhDBwcC3gRmZ3F9uarkR1Y12\n",
       "byuP27kZmAPsDPw+c61/kFw9FMHDqX5/cn4mr29gXVMyV/4+5YRUblp9XybLIvg/wIeBdwGnUr03\n",
       "PpDJ8WNc1q5Uv9t5MfB74J2ZXN+flq+d8p6/her3NR/KXPW7wOWG0rsCy0rRQ1Tv+yuBLUvZhzI5\n",
       "trkWD4d+3UC1V8HrA5l5SRn/PvCWzLyspd5I8Ho7sBPwdOBO4B2ZfLuqwzbA1plcuR7PSVIRwQzg\n",
       "vjJ6FPALYGkZPzCTCwfSMKlhJZw8KbPa/yP4CPAmYFJm9eEUwSHA5pmc3Wb+DwFvrhVdQ3V3/3cD\n",
       "x2by9x62dadMft1h2iSqD9OrqH68/UKqXwSomwVMBh5FFRS7yiQimEX1o/XL17XtwyKCpwHbATdn\n",
       "ckkEm1P9wP3zVu0P/QleU7pX6eomqvQ8YnYpa2PvM+GyafDQ74CXZ+bi+tRMbgVu7UGbJAGZ/BWI\n",
       "CLbO5HaACOZQnWXQ4X0qTTzlw3RpregtVMFrRVQfrbOBRQAR3JvJt0YqRnAsVej6KPAH4LnA04B7\n",
       "SpXlEZyTyW8iWACcAhxDFY5+l8mDY21nBPsC/x3BEzL5RSmbA+wLfAe4u2WWlaGrhKek6s1r9TBg\n",
       "GrALcGmt/rbAzfWfd4rgXZmcONY2D5vWn7KK4HDgbFgMfPqSiG9cAJMntZ25F+vvQY/XfGBhZs6P\n",
       "iH2BkzJz3zb1+pIcJUlaF6WHa1FL8chv7r4beEfLtJ0z+XXL72I+RNW7BO17nwBOz+QVLevenir8\n",
       "nZ/J90vZy4DTS5XXUh0SHc1epb2bAJtkckcExwD/XqvzwkzOGW0hbX5Tc8RLMzmjSxuGRtluZwAv\n",
       "LkXnAQvaVC37QDCQQ40RcRbVjzBvSZWi30l17giZeVqpcwpwMNWPox7depix1DF4SZLGnQhOpPps\n",
       "+zDwCapzuOo+RNXT9P7aYcldgN8Bj6Q67Hg7sHWp/w6q4FZ3SybblXnfQXWu2Yh3A1+l6iGDqldt\n",
       "S9r7MvAN4NpMrmjzXCYDszK5ufMzXmOeLYBdMllSxs8GDiuTJ2e2/fH1oVJelwOB7wILgU9msiKC\n",
       "J1KdZ34SVRCuHTIeUPDq2YoMXpKkIVB6Rj4C3Ls2h9wi+Dfg063ne7X0KJ1C9cEPVRC4oGUxxwBn\n",
       "AXcA3wNelMldZTmbZ65xqLEvIphd2nZYJpc3sc5+iuBuYDOqwPXaUertD7wQWAgxxeAlSdKQiWAn\n",
       "WOMKyOdksiiCvYDdqA6BPXvksON4EMFpwKuAjTL526Dbsz4iuA+YAWxczn0dwzwDvKqxJysyeEmS\n",
       "NmARPALYEfjNSC/WeDZyoj/wdeAc4Fvjvd0R7AG8B1iYyW9L2Q1Ur/t2mdwy9mUZvCRJUoMieB9w\n",
       "Qr0sk3H7Wd5yWPcWYNva+Mpbh4xtWf3JLX27XFKSJA2997YWRLBrBBnBLhFMimBaGSaX6Y1niwge\n",
       "Vgtdh5a/I6FrCfCvaxO6+skeL0mS1FEE00YuGIjgVqobtHbyAOXOB1RXfb4qk+/2sW2TqG7psVK5\n",
       "P9ljgUdkju0Gsu2XbY+XJElqWMtVmkeVv5cAX2xTfWrt8Y7Ad8rtM3qu9LCt9lNHI4dBM1m2PqGr\n",
       "n+zxkiRJYxbBVKrfhFxRHk+nuv/VYVT38/wp1e+OHgocUWbr+ZWREfyC6meTKOu7src/3eTJ9ZIk\n",
       "acjUzr3aE7i7/juUETyTqpfsKqqfM7qJ6qT4v2aufgixZZmzgRvL6JTR6q57uw1ekiRpyETwDKof\n",
       "Qqw7gOonljr5fCYvabOsBcA3R8b7eYWl53hJkqShk8lF5eGSWvGFtb8HUv0+4kdr0/8lgt0iOLJc\n",
       "Qbljua/YN2t15vet0X1kj5ckSeqrEpouq10d+S7gwUze01JvErA58BtgZofFbZ3JHf1sb9UWDzVK\n",
       "kqQNQPm9zJcAy6h+t3LkvLADM0c9RNnDNhi8JEnSBqj0hE3O5IHm1tmf3DKl1wuUJEnqpUxWACsG\n",
       "3Y5e8OR6SZKkhhi8JEmSGmLwkiRJaojBS5IkqSEGL0mSpIYYvCRJkhpi8JIkSWqIwUuSJKkhBi9J\n",
       "kqSGGLwkSZIaYvCSJElqiMFLkiSpIQYvSZKkhhi8JEmSGmLwkiRJaojBS5IkqSEGL0mSpIZ0DV4R\n",
       "cXBEXBMR10XEsW2mz4uIuyPi8jK8rT9NlSRJGm5TRpsYEZOBU4BnATcBP42I8zJzWUvVizJzQZ/a\n",
       "KEmSNCF06/HaG7g+M2/IzAeAs4HntakXPW+ZJEnSBNMteG0P3FgbX17K6hJ4akRcERGLImK3XjZQ\n",
       "kiRpohj1UCNVqOrmMmBOZt4XEYcA5wK7rnfLJEmSJphuwesmYE5tfA5Vr9dKmXlv7fG3I+LUiNgi\n",
       "M+9sXVhEnFgbXZyZi9e6xZIkST0WEfOAeX1fT2bnTq2ImAJcCzwTuBn4CXBE/eT6iJgF3J6ZGRF7\n",
       "A1/JzLltlpWZ6blgkiRp3OtXbhm1xyszH4yIhcB3gMnA6Zm5LCJeXaafBhwKvCYiHgTuAw7vdSMl\n",
       "SZImglF7vHq6Inu8JEnSkOhXbvHO9ZIkSQ0xeEmSJDXE4CVJktQQg5ckSVJDDF6SJEkNMXhJkiQ1\n",
       "xOAlSZLUEIOXJElSQwxekiRJDTF4SZIkNcTgJUmS1BCDlyRJUkMMXpIkSQ0xeEmSJDXE4CVJktQQ\n",
       "g5ckSVJDDF6SJEkNMXhJkiQ1xOAlSZLUEIOXJElSQwxekiRJDTF4SZIkNcTgJUmS1BCDlyRJUkMM\n",
       "XpIkSQ0xeEmSJDXE4CVJktQQg5ckSVJDDF6SJEkNMXhJkiQ1xOAlSZLUEIOXJElSQ7oGr4g4OCKu\n",
       "iYjrIuLYDnVOLtOviIjde99MSZKk4Tdq8IqIycApwMHAbsAREfHYljrzgZ0zcxfgVcAn+9RWDUhE\n",
       "zBt0G7Tu3H7Dze03vNx2aqdbj9fewPWZeUNmPgCcDTyvpc4C4AyAzFwCzIyIWT1vqQZp3qAboPUy\n",
       "b9AN0HqZN+gGaJ3NG3QDNP50C17bAzfWxpeXsm51Zq9/0yRJkiaWbsErx7icWMf5JEmSNhhTuky/\n",
       "CZhTG59D1aM1Wp3ZpWwNEWEgG1IR8c5Bt0Hrzu033Nx+w8ttp1bdgtfPgF0iYi5wM3AYcERLnfOA\n",
       "hcDZEbEvcFdm3ta6oMxs7RWTJEnaoIwavDLzwYhYCHwHmAycnpnLIuLVZfppmbkoIuZHxPXAX4Cj\n",
       "+95qSZKkIRSZHv2TJElqQt/vXD+WG7CqWRExJyIujIirI+IXEXFMKd8iIr4XEb+KiO9GxMzaPMeX\n",
       "bXhNRBxUK98zIq4q0/59EM9nQxURkyPi8og4v4y7/YZERMyMiK9FxLKI+GVE7OP2Gw5lW1xdXvcv\n",
       "RcR0t934FRGfiYjbIuKqWlnPtlfZ/l8u5ZdGxI5dG5WZfRuoDk9eD8wFpgJLgcf2c50OY9ou2wBP\n",
       "Lo83Ba4FHgt8CHhLKT8W+EB5vFvZdlPLtryeVb2lPwH2Lo8XAQcP+vltKAPwRuCLwHll3O03JAPV\n",
       "vQ9fVh5PATZ3+43/obz+vwGml/EvAy9x243fAdgf2B24qlbWs+0FvBY4tTw+DDi7W5v63eM1lhuw\n",
       "qmGZeWtmLi2P/wwso7of28qb4Za/zy+PnweclZkPZOYNVDvjPhGxLfCwzPxJqff52jzqo4iYDcwH\n",
       "/pNVt3Nx+w2BiNgc2D8zPwPVubSZeTduv2FwD/AAsHFETAE2prrwzG03TmXmj4A/tRT3cnvVl/V1\n",
       "4Jnd2tTv4DWWG7BqgMoVq7sDS4BZueqK1NuAkV8g2I7VbyMysh1by2/C7duUjwNvBlbUytx+w+GR\n",
       "wB0R8dmIuCwiPh0Rm+D2G/cy807go8DvqQLXXZn5Pdx2w6aX22tlzsnMB4G7I2KL0Vbe7+Dlmfvj\n",
       "WERsSpUGLtWJAAAB9klEQVTQX5eZ99anZdVv6vYbhyLiucDtmXk5a968GHD7jXNTgD2oDk/sQXU1\n",
       "+HH1Cm6/8SkidgJeT3UYajtg04g4ql7HbTdcBrG9+h28xnIDVg1AREylCl1nZua5pfi2iNimTN8W\n",
       "uL2Ut7tJ7vJSPrulvO3Nc9VTTwUWRMRvgbOAAyPiTNx+w2I5sDwzf1rGv0YVxG51+417ewE/zsw/\n",
       "lt6NbwD/gNtu2PTif+Xy2jw7lGVNATYvPaMd9Tt4rbwBa0RMozrx7Lw+r1NdREQApwO/zMyTapPO\n",
       "ozpRlPL33Fr54RExLSIeCewC/CQzbwXuKVdkBfDi2jzqk8w8ITPnZOYjgcOBCzLzxbj9hkJ53W+M\n",
       "iF1L0bOAq4HzcfuNd9cA+0bEjPKaPwv4JW67YdOL/5XfbLOsQ4EfdF17A1cUHEJ11dz1wPFNXs3g\n",
       "0HGb7Ed1btBS4PIyHAxsAXwf+BXwXWBmbZ4Tyja8BvjHWvmewFVl2smDfm4b2gA8g1VXNbr9hmQA\n",
       "ngT8FLiCqtdkc7ffcAzAW6iC8lVUJ1VPdduN34HqqMDNwN+pzsU6upfbC5gOfAW4DrgUmNutTd5A\n",
       "VZIkqSF9v4GqJEmSKgYvSZKkhhi8JEmSGmLwkiRJaojBS5IkqSEGL0mSpIYYvCRJkhpi8JIkSWrI\n",
       "/wAJQKNu9TdE2AAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b5ba550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# choose the paramator of Brownian\n",
    "# Brownian paramator (p) = 2\n",
    "\n",
    "import pylab\n",
    "from random import normalvariate as norm\n",
    "from random import seed\n",
    "from math import sqrt\n",
    "\n",
    "x = np.arange(0,time, 1)\n",
    "steps = [0.1, 0.01, 0.001, 0.0001]\n",
    "time = 10000\n",
    "average_num = 100\n",
    "p = 2\n",
    "\n",
    "for num, j in enumerate(steps):\n",
    "    step = j\n",
    "    y_all = [] \n",
    "    for l in range(average_num):\n",
    "        y_num = [0] * (time)\n",
    "        value = 1\n",
    "        y_num[0] = value\n",
    "        for i in range(time - 1):\n",
    "            update_value = value + step * (2 - value) * value + p * sqrt(step) * value * norm(0, 1)\n",
    "            y_num[i + 1] = update_value\n",
    "            value = update_value\n",
    "        y_all.append(y_num)\n",
    "    y = np.array(y_all)\n",
    "    np.reshape(y, (average_num, time))\n",
    "    y_ave = [np.average(y[:, k]) for k in range(time) ]\n",
    "    fig = plt.figure(figsize=(10, 20)) # horizontal, vertical\n",
    "    plt.subplot(4, 1, num+1)\n",
    "    plt.plot(x, y_ave)\n",
    "    plt.ylim(0,3)"
   ]
  },
  {
   "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
}