Discrete_Random_Variables.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Discrete Random Variable**\n",
    "\n",
    "A **random variable** is a real-valued function of a probabilistic sample space. It is **discrete** if it's range is *finite* or countably infinite, i.e. if a one-to-one correspondance can be created between it's range and the positive integers.\n",
    "\n",
    "A discrete random variable has an associated **probability mass function** (PMF) (aka probability distribution function) that gives the probability of each range value for the random variable. If *x* is any real number, the **probability mass** of *x* is the probability of the event $\\left\\{X=x\\right\\}\\hspace{1pt}$ consisting of all outcomes that give rise to the value *x* for *X* and is denoted\n",
    "\n",
    "$$p_X\\left(x\\right) = P\\left(\\left\\{X=x\\right\\}\\right)$$\n",
    "\n",
    "The PMF of a random variable *X* can be calculated as follows:\n",
    "\n",
    "For each possible value *x* of *X*:\n",
    "\n",
    "1. Collect all possible disjoint events in $\\Omega\\hspace{1pt}$ that give rise to the event $\\left\\{X=x\\right\\}\\hspace{1pt}$\n",
    "\n",
    "2. Add their probabilities to obtain $p_X\\left(x\\right)$\n",
    "\n",
    "3. Repeat for all *x*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Functions of Random Variables**\n",
    "\n",
    "If $Y=g\\left(X\\right)\\hspace{1pt}$ is a function of a random variable *X*, then *Y* is also a random variable. If *X* is discrete with PMF $p_X\\hspace{1pt}$, then *Y* is also discrete and its PMF is \n",
    "\n",
    "$$p_Y\\left(y\\right) = \\sum_{\\{x \\hspace{1pt}\\vert \\hspace{1pt} g\\left(x\\right)=y\\}} p_x\\left(x\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expectation (Mean)**\n",
    "\n",
    "The **expected** value, or mean, of a random variable *X* with PMF $p_X\\hspace{1pt}$ is defined as\n",
    "\n",
    "$$E\\left[X\\right] = \\sum_x x p_X\\left(x\\right)$$\n",
    "\n",
    "Note that the expectation is well-defined only if \n",
    "\n",
    "$$\\sum_x \\left| x \\right| p_X \\left(x\\right) \\lt \\infty$$\n",
    "\n",
    "This fails to hold for certain distributions. For example, consider a power law PMF of the form $p_X\\left(x\\right) = \\frac{1}{x^{\\alpha+1}}\\hspace{1pt}$ with $\\alpha\\le1$ for $x$ any positive integer. Then the expected value,$\\sum_{n=1}^{\\infty}\\frac{1}{x^{\\alpha}}$ is a divergent <a href=https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#p-series>p-series</a>.\n",
    "\n",
    "**Expected Value of Functions of Random Variables**\n",
    "\n",
    "Let *X* be a random variable with PMF $p_X\\hspace{1pt}$ and let $g\\left(X\\right)\\hspace{1pt}$ be a function of *X*. Then the expected value of the random variable $Y=g\\left(X\\right)\\hspace{1pt}$ is \n",
    "\n",
    "$$E\\left[Y\\right]=E\\left[g\\left(X\\right)\\right] = \\sum_x g\\left(x\\right) p_X \\left(x\\right)$$\n",
    "\n",
    "**Note** that unless $g\\left(X\\right)\\hspace{1pt}$ is a linear function, it is **not** generally true that $E\\left[g\\left(X\\right)\\right] = g\\left(E\\left[X\\right]\\right)\\hspace{1pt}$. This is illustrated in the following example.\n",
    "\n",
    "*Example*\n",
    "Problem 21 page 123 of [1]. Assume you toss a fair coin until the first tails appears at say toss *n* and that you receive $2^n\\hspace{1pt}$ dollars as a reward. What is the expected about of your winnings? How much would you pay to play the game?\n",
    "\n",
    "Let the RV *X* be the amount you receive as a reward. Let the RV *N* be the number of tosses up to an including the first tail. Then we have $X=g\\left(N\\right)=2^N\\hspace{1pt}$. We know that *N* can be represented as a geometric random variable with PMF, with $p=\\frac{1}{2}$ assuming a fair coin\n",
    "\n",
    "$$P_N\\left(n\\right) = \\left(\\frac{1}{2}\\right)^n$$\n",
    "\n",
    "with expected value\n",
    "\n",
    "$$E\\left[N\\right] = \\sum_{n=1}^{\\infty}n\\left(\\frac{1}{2}\\right)^n = \\frac{1}{p} = 2$$\n",
    "\n",
    "and it is *tempting, but wrong*, to argue that the expected reward is $2^{E\\left[N\\right]}=2^2=4\\hspace{1pt}$. But such an argument assumes that \n",
    "\n",
    "$$E\\left[g\\left(N\\right)\\right]=E\\left[2^N\\right]=2^{E\\left[N\\right]}=g\\left(E\\left[N\\right]\\right)$$\n",
    "\n",
    "which is not true. Consider again the RV X. It takes on values $2^0, 2^1, 2^2, \\ldots\\hspace{1pt}$, i.e. values $2^n\\hspace{1pt}$ for any integer *n*. Noting that a particular outcome occurs with the same probability as obtaining the first tails on the $n^{th}$ toss, the expected value is \n",
    "\n",
    "$$E\\left[X\\right] = \\sum_{k=0}^{\\infty}2^k 2^{-k} = \\infty$$\n",
    "\n",
    "So it is argued that the expected, or mean payout is infinite, implying that one should pay **any** amount to play this game. However, it is **more accurate to state that the expected value is undefined** and so too is the variance. Several researchers have presented alternative risk assesments for determining a fair *entrance* fee for this game - try a quick Google search. Below are simulated outcomes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max payout = 16384\n"
     ]
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAABEMAAAGqCAYAAADgL4oPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XtcVHX+x/H3ICje76CCRSqKGJKlZq4Whphp3s1C13s3\n",
       "rdbcMv11xW5S1ratRWlRke1mZqVWxpq6WGulrZqWaFLeuCilpnlHYH5/fAXEK5eZOXN5PR8PHmfm\n",
       "zMw5nxmpYd7z/X6+NrvdbhcAAAAAAICP8LO6AAAAAAAAAFciDAEAAAAAAD6FMAQAAAAAAPgUwhAA\n",
       "AAAAAOBTCEMAAAAAAIBPIQwBAAAAAAA+5aJhSGZmpnr06KF27drp8ssv1z/+8Q9J0v79+xUXF6fW\n",
       "rVurV69eOnDgQPFjZsyYofDwcEVERGjp0qXF+9euXauoqCiFh4dr0qRJxftPnDihW265ReHh4erS\n",
       "pYt27tzpyOcIAABQKePGjVNwcLCioqKK902ZMkVt27ZVdHS0Bg8erIMHD1pYIQAAKI+LhiEBAQF6\n",
       "8cUXtWnTJn377bd65ZVXtHnzZiUmJiouLk5bt25VbGysEhMTJUnp6el6//33lZ6ertTUVE2cOFF2\n",
       "u12SNGHCBCUnJysjI0MZGRlKTU2VJCUnJ6thw4bKyMjQ5MmTNXXqVCc+ZQAAgPIZO3Zs8d8tRXr1\n",
       "6qVNmzZpw4YNat26tWbMmGFRdQAAoLwuGoY0adJEV1xxhSSpVq1aatu2rbKzs7V48WKNHj1akjR6\n",
       "9GgtXLhQkrRo0SLFx8crICBAYWFhatWqlVavXq3du3fr0KFD6ty5syRp1KhRxY85/VhDhgzR8uXL\n",
       "Hf9MAQAAKqh79+6qX79+qX1xcXHy8zN/Sl199dXKysqyojQAAFAB/uW5844dO7R+/XpdffXVys3N\n",
       "VXBwsCQpODhYubm5kqScnBx16dKl+DGhoaHKzs5WQECAQkNDi/eHhIQoOztbkpSdna3mzZubgvz9\n",
       "VbduXe3fv18NGjQovr/NZqvgUwQAAEWKRmvCsd58803Fx8eftZ+/XwAAqBxn/e1S5gaqhw8f1pAh\n",
       "Q/TSSy+pdu3apW6z2WwuebO32+382O16/PHHLa/BHX54HXgteC14HXgtyvcD53j66adVtWpVDR8+\n",
       "/Jy3W/3v7ms//DfPa+4rP7zuvOa+8ONMZQpDTp48qSFDhmjkyJEaOHCgJDMaZM+ePZKk3bt3Kygo\n",
       "SJIZ8ZGZmVn82KysLIWGhiokJKTU8NGi/UWP2bVrlyQpPz9fBw8eLDUqBAAAwB29/fbbWrJkif75\n",
       "z39aXQoAACiHi4Yhdrtd48ePV2RkpO67777i/f3791dKSookKSUlpTgk6d+/v+bNm6e8vDxt375d\n",
       "GRkZ6ty5s5o0aaI6depo9erVstvtmjt3rgYMGHDWsRYsWKDY2FiHP1EAAABHSk1N1cyZM7Vo0SIF\n",
       "BgZaXQ4AACiHi/YMWbVqld599121b99eHTp0kGSWzp02bZqGDRum5ORkhYWFaf78+ZKkyMhIDRs2\n",
       "TJGRkfL391dSUlLxFJqkpCSNGTNGx44dU58+fdS7d29J0vjx4zVy5EiFh4erYcOGmjdvnrOer1eI\n",
       "iYmxugS3wOtQgteiBK+FwetQgtcCjhAfH6+VK1dq7969at68uaZPn64ZM2YoLy9PcXFxkqRrrrlG\n",
       "SUlJFlcK/pt3PV5za/C6ux6vuXex2Z09EcdBbDab0+cMAQDgzXgvdT1ecwAAKs6Z76NlbqAKAAAA\n",
       "AADgDQhDAAAAAACATyEMAQAAAAAAPoUwBAAAAAAA+BTCEAAAAAAA4FMIQwAAAAAAgE8hDAEAAAAA\n",
       "AD6FMAQAAAAAAPgUwhAAAAAAAOBTCEMAAAAAAIBPIQwBAAAAAAA+hTAEAAAAAAD4FMIQAAAAAADg\n",
       "UwhDAAAAAACATyEMAQAAAAAAPoUwBAAAAAAA+BTCEAAAAAAA4FMIQwAAAAAAgE8hDAEAAAAAAD6F\n",
       "MAQAAAAAAPgUwhAAAAAAAOBTCEMAAAAAAIBPIQwBAAAAAAA+hTAEAAAAAAD4FMIQAAAAAADgUwhD\n",
       "AAAAAACATyEMAQAAAAAAPoUwBAAAAAAA+BTCEAAAAAAA4FMIQwAAAAAAgE8hDAEAAAAAAD6FMAQA\n",
       "AAAAAPgUwhAAAAAAAOBTCEMAAAAAAIBPIQwBAAAAAAA+hTAEAAAAAAD4FMIQAAAAAADgUwhDAAAA\n",
       "AACATyEMAQAAAAAHWLNGWrLE6ioAlAVhCAAAAAA4wOzZUt++0rvvWl0JgIshDAEAAAAABwgJkYYN\n",
       "k6ZNk1JSrK4GwIUQhgAAAACAg7RrJy1fbgKRxYutrgbA+RCGAAAAAIADtWkjffKJdOut0gsvWF0N\n",
       "gHMhDAEAAAAAB7DbSy537CilpkoPPCC9/nrJbU8/LX3xhTX1AShBGAIAAAAADmKzlVy+9lpp82bp\n",
       "jjskPz/pp5+kJ5+UevWS5syxrkYAhCEAAAAA4DQREVJ2tnTnneZy7drS449LDz4oJSdbXR3guwhD\n",
       "AAAAAMCJmjWTXntNWrJE+uMPafhw6bvvTCjCMryANfytLgAAAAAAvMHpPUPO5cYbpcxMKSjIXF+6\n",
       "VOrZU/rsM2nZMjON5vhx6cgRKTzc+fUCvoyRIQAAAADgIKf3DDmXoiBEkiIjTZPV1FRp717p8sul\n",
       "kBCpdWvTdBWA8xCGAJAk/f7775oy5SHdfPMYvfbaHNkv9tUGAAAAKq19e+mbb8yokIkTzb6kJNNo\n",
       "9eWXra0N8GZMkwGgI0eO6Kqruis7u6vy8rpryZLZ2rRpq2bNet7q0gAAALxeRITZPvKIabTauLHU\n",
       "u7cUGyvt2SM98YRZjQaA4/CfFAClpqbqt9+ClZc3R9J4HT2aqtdee1knT560ujQAAACP4YiBtY0b\n",
       "m+1ll0mrVkkrV0rx8VJ+fvmPNWGC6UcC4GyEIQBOhR61T9tTQ3a7VFBQYFVJAAAAHuliPUPKo2lT\n",
       "01j10CFp9GipvH+avfaadNNNZjWbffscVxfgDQhDACg2NlZVq/5Pfn4vSFqlwMARuvHGAQoMDLS6\n",
       "NAAAAJ9WrZr04YfS7t3SHXdI27aV/bEREWZkyPXXS127muV8ARiEIQDUuHFjffvtfxQbu0oREfdr\n",
       "3LgwzZ//ttVlAQAAQFL16tLixdLWrVLLllKfPma0yMXY7Wa6zdy50rBhUufOUkCAOU5hofPrBtwZ\n",
       "YQgASVJ4eLiWLv1Imzd/q1deeUHVq1e3uiQAAACP4szF+GrVklaskBYskH77TbrqKumXXy5ej81m\n",
       "fp58Ulq3TvrTn6Q2baQqVaRNm0pqfvttM5Jk/37p66+d9zycoSzBEHAmwhAAAAAAcBBH9gw5U0CA\n",
       "NGSIme4yebIUE2OW5D2fojCkSIcOUlqaWcp33Djp8svNKjVbtkiZmeZYrVubwOSee6QTJ5z3XBxl\n",
       "/36pTh2zEg+9/1EehCEAAAAXMG7cOAUHBysqKqp43/79+xUXF6fWrVurV69eOnDggIUVAvBFEyaY\n",
       "0R49ephVZ87lzDCkSJcuUnKytGiRmXJz3XXSY4+ZAOTxx6WxY6WcHKlbN7O0rzs7ftw8x/XrzTSg\n",
       "C4VDwOkIQwAAAC5g7NixSk1NLbUvMTFRcXFx2rp1q2JjY5WYmGhRdYDvOXbMfACGNGaM9MYbUv/+\n",
       "pknq4cOlb7fbzciP8+nf3zRYfe89c33wYOnee6U33zRNW/v1k6KipPbtTQNXd9WkifTppyYg6tZN\n",
       "eucd505ZgncgDAEAALiA7t27q379+qX2LV68WKNHj5YkjR49WgsXLrSiNMAnTZtmGor+8IPVlZzN\n",
       "ig/gffpIa9ZI//mPVLu26QtSpLCwbNN2rr/e1N6jR8k+m82MFnnoIfNaN2smPfOM4+uvrKLX3GYz\n",
       "q+0sW2bq9POTUlLO/W+yb590113S0aOurRXuxd/qAgAAADxNbm6ugoODJUnBwcHKzc09730TEhKK\n",
       "L8fExCgmJsbJ1QHerWpVs23fXvr2W+nqq62t50zO7BlyPi1bmuDjxRelG26Q/v53acSI80+TKY/J\n",
       "k81PcrL04IMmSHjuOdOA1R2c+Ryjo6WNG83ollmzpNdfN+HItdeW3GfZMmn2bNM/5e23zbQhuIe0\n",
       "tDSlpaW55Fw2u90zBhDZbDZ5SKkAALgl3ksrbseOHerXr59+OPVVdP369fX7778X396gQQPt37//\n",
       "rMfxmgOO88Yb0u23mwai110nNW0q3X23aQbaooXV1Rn/93+mmef//Z91NXz/vXTjjSW9PrZtM8vr\n",
       "OsL+/eb1T0uTHn7Y9CyxIvw5XVaWCTOyss6+7eRJ6bXXTJ1DhpgQp3Ztaf586YMPzHLD994r3Xqr\n",
       "lJgoBQa6vn5cmDPfR5kmAwAAUE7BwcHac+qTxu7duxUUFGRxRYD327fPbD/80IwGGDrUrCDSsaP0\n",
       "66/W1uZOrrjCjJjp1s1cr1nTccdu0EBavty87k8/LTVsKH3yiTRqlAlKnnjCLPvrShf6nBwQYMKO\n",
       "H380fWY6dpQWL5YKCszIlptvltLTTZDSpo0JTfLyXFc7rEUYAgAAUE79+/dXSkqKJCklJUUDBw60\n",
       "uCLA+/n5Sfffbz7MDhli9t1zjzRwoJkm8ssv1tYnuU/Tzksvlb76ykydcXRW6+dnQoOjR6XYWNOE\n",
       "de5cE4w8/rg539VXmxEprlCWqUBBQdJbb0kJCdKAAdLw4Sa8kUzA88EHZtTInDkmMDlzdZ6jR805\n",
       "qlSRaBHlPQhDAAAALiA+Pl5du3bVTz/9pObNm+utt97StGnT9MUXX6h169ZasWKFpk2bZnWZgNcr\n",
       "+tDbr58UEmL22Wxm+sywYVKvXlJmpukBsXWrdXVaPW3kdM6spXp1EyLk5EgrVpggYfJkszrNH3+Y\n",
       "ZW5PZcZOV9bnGR9vVtwZOVLq3r3042+5Rdq1yzToHTFCiokxwcmqVaYPiWRGkgwaJP35z9LevQ5/\n",
       "GnAxeoYAAOAjeC91PV5zwHGee858AH3uuXPf/uSTpsnnzp3mek6O6SviStOmSfXqma2v++EHExwU\n",
       "jdjZssVMRXG0nTtNsLFrl+OOmZdnlud9+mlpxw6zb+lSKS5OOnJEevRRE/TcfrtZbadOnZLHHjhg\n",
       "VvT5+Wdp3DjJnyVLKoWeIQAAAABwAY8+alY7kcw3/1deKe3ebW1NviwqyoQC/fqZaUzdujlniokj\n",
       "Vsw5U9Wq0m23Sdu3m+k0r70m9expbqtZU/rb36TVq02vmssvN9O2ipZ6jo01P3feaV6Djz92n+lT\n",
       "KI0wBAAAAIBXmDjRjEBISTFTHJo1M6MTXPVhlA+9pdWpY3q8/Pyz9Pnn0l/+Yvq+HD/u2PM4czpQ\n",
       "/fom2DjzHK1ameV733xT+ugjMy2od28TAE2dKuXmmqWOH3nE9FmZO5ffD3dDGAIAAADA7ZX1g2Sb\n",
       "NuaD66uvSnfcYUYjDBhgplPcc4907Jhz63SnniHupGNHaf16ae1a029k7lzHHNfqgKFnT1PDzp1S\n",
       "8+Zm3/jxpmlr795mqeMnnpBmzJBuuEHauNHaelGCMAQAAACARyhP0GCzSbNnS3v2mOVfw8KkV14x\n",
       "I0Xy851WIi6gYUMpLU2aP98sx2uzmYarleGMaTIVERQkvf66qSc8vGR/QICZwrVhgwlHbrjBBCgb\n",
       "NlhXK4wyhSHjxo1TcHCwoqKiivclJCQoNDRUHTp0UIcOHfT5558X3zZjxgyFh4crIiJCS5cuLd6/\n",
       "du1aRUVFKTw8XJMmTSref+LECd1yyy0KDw9Xly5dtLOo6xEAAAAAVEJwsFlidtAgE4jYbNLYsQQi\n",
       "Vrr5ZjNV5uGHzWid6OjKLY3sDmHIxQQESH/9q2nIOnSoacZ6773SwYNWV+a7yhSGjB07VqmpqaX2\n",
       "2Ww2/fWvf9X69eu1fv163XjjjZKk9PR0vf/++0pPT1dqaqomTpxY3P11woQJSk5OVkZGhjIyMoqP\n",
       "mZycrIYNGyojI0OTJ0/W1KlTHfkcAQAAAHi4ykyHsNlMX4dffpE+/NCsNDNypON7V6DsqlWTnnrK\n",
       "TJvx8zPTm+6+26zWUh5WT5Mpr2rVpLvukjZvlk6cMD1JnnnGrGAD1ypTGNK9e3fVr1//rP3nWuJm\n",
       "0aJFio+PV0BAgMLCwtSqVSutXr1au3fv1qFDh9S5c2dJ0qhRo7TwVDvhxYsXa/To0ZKkIUOGaPny\n",
       "5RV+QgAAAAC8U2VHAPj5STVqSIsWSb//Lv35z1JBgWNqkzzvg7k7aNDA9BJJT5c2bTK9RYpWZjlx\n",
       "Qtq2rWT0xLFjJsD6y1/MSi75+e4zTaa8GjaU5swx02W++Ubq0MFs7XZGLblKpVY9njVrlt555x11\n",
       "7NhRL7zwgurVq6ecnBx16dKl+D6hoaHKzs5WQECAQkNDi/eHhIQoOztbkpSdna3mp7rN+Pv7q27d\n",
       "utq/f78aNGhQ6nwJCQnFl2NiYhQTE1OZ8gEA8GppaWlKS0uzugwAcDu1aplApFs3M3Vm61bT1NMR\n",
       "PPGDuTto3dr0E3nnHen666WEBGnlSumDD8ztzz8vPfCAdNVVZjTJrFlmf58+JtjyVFFRZsWdBQuk\n",
       "rl1L9k+aZFaiadTIutq8XYXDkAkTJuixxx6TJD366KO6//77lZyc7LDCzuX0MAQAAFzYmV8cTJ8+\n",
       "3bpiAKCSHD3qolo1acWKkkBk1SqzXCqsNWqUWaa2Rw/T/Pahh0wAMmSIVLOmGRny1FPSddeZ0SEJ\n",
       "CZJ/pb7it57NZvqo7Nsn/ec/pr/IokVm6tB990lTpkiBgVZX6X0q/GsTFBRUfPm2225Tv379JJkR\n",
       "H5mZmcW3ZWVlKTQ0VCEhIcrKyjprf9Fjdu3apWbNmik/P18HDx48a1QIAAAAAN/m6FEXtWubKRqD\n",
       "B5sVQL78Uure3bHnQPlFRJi+LitWmNDD39+M/igsNNNqTp8aM3iwtbU6UoMGJvSRpP79TRA0ZYp0\n",
       "+eXSiy9KN93EyCNHqvDSurt37y6+/PHHHxevNNO/f3/NmzdPeXl52r59uzIyMtS5c2c1adJEderU\n",
       "0erVq2W32zV37lwNGDCg+DEpKSmSpAULFig2NrYyzwkAAAAAysTPT1q4UHr2WWnAAOnrryt+LHqG\n",
       "OI7NJsXGloz6qFfPhAVFt/mCli1N49+kJBOK9OkjvfyyGRGDyivTyJD4+HitXLlSe/fuVfPmzTV9\n",
       "+nSlpaXp+++/l81m02WXXabZs2dLkiIjIzVs2DBFRkbK399fSUlJsp36bU1KStKYMWN07Ngx9enT\n",
       "R71795YkjR8/XiNHjlR4eLgaNmyoefPmOenpAgAAAMDZHnzQLPE6cKD0ySfS1VdX7Di+8kEdrtOr\n",
       "l7RxowlC7r3X/Nxxh/Tkk9JpEzZQTjb7uZaEcUM2m+2cq9cAAICy4b3U9XjNAcd55hnp0CFpxgzn\n",
       "nmfJEmnMGOn1181IkfKYMsV8OJ0yxSmlAZJMw9/EROmtt6Rrr5XefNOMIvFGznwfrfA0GQAAAABw\n",
       "JVeMuujTR3rvPTNCZOZM558PKK/WrU0AsmuXdMMNZhTTtGkmLETZEYYAAAAAwGliY6XMTGnOHHP5\n",
       "o4/K9jgGgsGVmjc3TVY3bjQr77RoIf3lL9Jp65bgAghDAAAAALg9VwcNoaFmud3sbLPCR3i4tHLl\n",
       "xR9HzxC4WrNm0ttvS0uXmt+/6Ghp0iRp+3YpLU366iurK3RPhCEAAAAAPIKrg4agIGnLFmnzZunn\n",
       "n6WYGLPcK+COOnSQXnpJ+vFHKTBQatVK6tHD9BXp18/sRwnCEAAAAAC4gIgIMzJl5Uozbea556yu\n",
       "CDi/pk3NUtEHDpgpXvv2ST17mt/dZs2kK66Q5s+XCgqsrtRahCEAAAAA3J479OO49lozdWbqVKlJ\n",
       "E+nw4dK3u0ONQJHataVBg6QGDcy0ma1bpZEjpRo1pKefljp2lGbPlho3NuFIYaHVFbsWYQgAAAAA\n",
       "j+AO/Ti6dpW2bTPftvfpc/YKHu5QI3AudeuaESNffy19/71pvjpxorR3rxntFBEhJSf7zogRwhAA\n",
       "AAAAKIfLLpNOnJDatZO6dZN27LC6IqB8bDbp5pulvDzp5Enpu++kV181jVivvFL697+9f6QTYQgA\n",
       "AAAAt+duH8z8/KSkJGnMGDPd4LHHpNdft7oqoHyqVJH8/U04Ehsrffml+V2eNMmMFHniCbMazcGD\n",
       "VlfqeIQhAAAAADyCu01BsdmkyZPNt+hPPmmmzPha3wV4F5vNLCX944/Sa69JGRmmV079+mYqTXa2\n",
       "1RU6DmEIAAAAAFTCVVdJf/xhVu+YPNnqaoDK8/c3y/LOnWtGZW3cKL33nhQaKt19t5SVZXWFlUcY\n",
       "AgAAAACVVLu2aVDp7291JYDjXX65tH699OuvZjWa9u2l0aNNI1ZPRRgCAAAAwO25W88QwBc1bizN\n",
       "nGmW6Y2MlG66SapWzez74w+rqysfwhAAAAAAHsHdeoYAvqpRI2nqVNNTZMYMacMGqWVLs1TvkiWe\n",
       "EV4ShgAAAAAAgHKrXl3661+ld9+VvvlGOnxY6tvXjBp59lnp2LHS9z9yxH2CEsIQAAAAAG7PXT5A\n",
       "ATi3Vq2kd96RCgqk2bOlNWuk8HBp1iwzrWb7dqlWLaldO9OYNT9f2rVLWrtWWrBAOnHCtfUShgAA\n",
       "AADwCEyTAdyfn59ZjvfDD6WPPjI/bdpIUVFSSIj08svS669LERHSpZdKHTtKN98stWhhRpPs3++a\n",
       "Oul1DAAAAAAAHK5zZ+k//zGjRT74QDp6VLr+evPz3/9Ky5dL/fqZUCQrS3r+ebN8b3S0NH68c2uz\n",
       "2e2eMeDMZrPJQ0oFAMAt8V7qerzmgOMkJJipMtOnW10JAGc6cEBatUp69VXps8+c9z7KNBkAAAAA\n",
       "HoFpMoD3q1fPNGH99FPnnocwBAAAAAAA+BTCEAAAAAAA4FMIQwAAAAC4PdrvAHAkwhAAAAAAHoGe\n",
       "IQAchTAEAAAAAAD4FMIQAAAAAG6PaTIAHIkwBAAAAIBHYJoMAEchDAEAAAAAAD6FMAQAAACA22Oa\n",
       "DABHIgwBAAAA4BGYJgPAUQhDAAAAAACATyEMAQAAAAAAPoUwBAAAAIDbo2cIAEciDAEAAADgEegZ\n",
       "AsBRCEMAAAAAAIBPIQwBAAAA4PaYJgPAkQhDAAAAAHgEpskAcBTCEAAAAAAA4FMIQwAAAAC4PabJ\n",
       "AHAkwhAAAAAAHoFpMgAchTAEAAAAAAD4FMIQAAAAAG6PaTIAHIkwBAAAAIBHYJoMAEchDAEAAAAA\n",
       "AD6FMAQAAKCCZsyYoXbt2ikqKkrDhw/XiRMnrC4JAACUAWEIAABABezYsUOvv/661q1bpx9++EEF\n",
       "BQWaN2+e1WUBXoueIQAcyd/qAgAAADxRnTp1FBAQoKNHj6pKlSo6evSoQkJCrC4L8Gr0DAHgKIQh\n",
       "AAAAFdCgQQPdf//9uuSSS1S9enXdcMMN6tmz51n3S0hIKL4cExOjmJgY1xUJAIAHSUtLU1pamkvO\n",
       "ZbPbPWPAmc1mk4eUCgCAW+K91LF++eUX9evXT1999ZXq1q2rm2++WUOHDtWIESOK78NrDjjO1KlS\n",
       "/frStGlWVwLAVZz5PkrPEAAAgAr43//+p65du6phw4by9/fX4MGD9fXXX1tdFuDVmCYDwFEIQwAA\n",
       "ACogIiJC3377rY4dOya73a5ly5YpMjLS6rIAAEAZEIYAAABUQHR0tEaNGqWOHTuqffv2kqQ77rjD\n",
       "4qoA78WMMwCORM8QAAB8BO+lrsdrDjjOgw9KjRqZLQDfQM8QAAAAAAAAByEMAQAAAAAAPoUwBAAA\n",
       "AIDbY8YZAEciDAEAAADgEVhaF4CjEIYAAAAAAACfQhgCAAAAwO0xTQaAIxGGAAAAAPAITJMB4CiE\n",
       "IQAAAAAAwKcQhgAAAABwe0yTAeBIhCEAAAAAPALTZAA4CmEIAAAAAADwKYQhAAAAHuC226TPPrO6\n",
       "CgAAvIO/1QUAAADg4pKTpSVLpJwcqysBrEHPEACOxMgQAAAAD5GXZ3UFgLXoGQLAUQhDAAAAPICf\n",
       "n7Rvn9VVAADgHQhDAAAAPECjRlZXAFiLaTIAHIkwBAAAwAOEhJjtiRPW1gFYiWkyABylTGHIuHHj\n",
       "FBwcrKioqOJ9+/fvV1xcnFq3bq1evXrpwIEDxbfNmDFD4eHhioiI0NKlS4v3r127VlFRUQoPD9ek\n",
       "SZOK9584cUK33HKLwsPD1aVLF+3cudMRzw0AAMBrtGhhtjRQBQCg8soUhowdO1apqaml9iUmJiou\n",
       "Lk5bt25VbGysEhMTJUnp6el6//33lZ6ertTUVE2cOFH2U2PaJkyYoOTkZGVkZCgjI6P4mMnJyWrY\n",
       "sKEyMjI0efJkTZ061ZHPEQAAwOMVTRHIzra2DsAqTJMB4EhlCkO6d++u+vXrl9q3ePFijR49WpI0\n",
       "evRoLVy4UJK0aNEixcfHKyAgQGFhYWrVqpVWr16t3bt369ChQ+rcubMkadSoUcWPOf1YQ4YM0fLl\n",
       "yx3z7AAAALxM9+5WVwBYh2kyABzFv6IPzM3NVXBwsCQpODhYubm5kqScnBx16dKl+H6hoaHKzs5W\n",
       "QECAQkNDi/eHhIQo+9RXG9nZ2WrevLkpyN9fdevW1f79+9WgQYNS50xISCi+HBMTo5iYmIqWDwCA\n",
       "10tLS1NaWprVZQAAALidCochp7PZbLK5IKY9PQwBAAAXduYXB9OnT7euGDhE1apSXp506JBUu7bV\n",
       "1QCuxTQZAI5U4dVkgoODtWfPHknS7t27FRQUJMmM+MjMzCy+X1ZWlkJDQxUSEqKsrKyz9hc9Zteu\n",
       "XZKk/Px8HTx48KxRIQAAAL7uX/+SwsOl0/6kAnwK02QAOEqFw5D+/fsrJSVFkpSSkqKBAwcW7583\n",
       "b57y8vK0fft2ZWRkqHPnzmrSpInq1Kmj1atXy263a+7cuRowYMBZx1qwYIFiY2Mr+7wAAAC8UkaG\n",
       "9MADVlcBAIBnK9M0mfj4eK1cuVJ79+5V8+bN9cQTT2jatGkaNmyYkpOTFRYWpvnz50uSIiMjNWzY\n",
       "MEVGRsrf319JSUnFU2iSkpI0ZswYHTt2TH369FHv3r0lSePHj9fIkSMVHh6uhg0bat68eU56ugAA\n",
       "AJ6voMD+i6XmAAAgAElEQVTqCgAA8Gw2u90zZt/ZbDZ5SKkAALgl3ktdz5Gv+eDB0ogR0r590po1\n",
       "0htvOOSwgMf4y1+kli2lSZOsrgSAqzjzb5cKT5MBAACAa9ls0iWXSKdarQE+h54hAByFMAQAAMCD\n",
       "XHKJtHGj1VUAAODZCEMAAAA8yGWXSbm50vHjVlcCuBaz/AA4EmEIAACAB6leXWrVStqxw+pKANdj\n",
       "mgwARyEMAQAA8DAtWkjbtlldhWOsWsU3/gAA1yMMAQAA8DD79kkzZlhdhWN06yZ9+aXVVcATEJoB\n",
       "cCTCEAAAAA9w+gfBHTuk//7XslIc7tlnzfSHRYusrgTujmkyAByFMAQAAMBDFH0QXLZMatfO2loc\n",
       "ad06sx04kG//AQCuQRgCAADgYVq1kjZtktLTHX/sggLpX/9y/HEv5J57zLZxY6bMAABcgzAEAADA\n",
       "w9SqZbbOGB2SmyuNGCFlZzv+2Odz771Sr17S9OnSiy+67rzwLIwaAuBIhCEAAAAoVvSB89VXXXeu\n",
       "unWlf/9bGjXK9EL5+WfnnxueiZ4hAByFMAQAAMAD/f67VKWKdOyY4475zTclU2Seflr6/HPHHbss\n",
       "ataU7rpLCg+Xjhxx7bkBAL6FMAQAAMAD1atn+nuMHCllZjrmmF27Sg8+WHK9Tx/HHPd8zjXtYfJk\n",
       "s50yxbnnhudhmgwARyIMAQAA8ADn+yD44YfSoEGOP1+bNmabkeH4Y5/uzGkPDRtKX31lpuns2uXc\n",
       "c8PzME0GgKMQhgAAAHiIMz8Idu9utj/84Jjjt25ttnfdJW3ZIo0fL332mWOOfS7nC3i6dZOGD5cu\n",
       "vVQqLHTe+QEAvoswBAAAwEMtXWq2eXmOOV5BgQlBkpLM9b59TRhSUOCY45/Jbj//N/3vvGO2LVs6\n",
       "59zwPEyTAeBIhCEAAAAeKjCw5PLJk5U/Xn6+VK1aSUDRs6e0bJnUtGnlj30+5wtDqlSRcnKkHTuk\n",
       "qCjnnR+ehWkyAByFMAQAAMCDFX1b/vXXlT9Wfr4JIYrUrm22v/1mpqv897+OHSVysW/6mzY1PVF+\n",
       "/NFMndm713HnBgD4NsIQAAAAD9e1q/TddxV77K5dJQFHQYHk71/69jffNNt//tP0KHn33YrXeS4X\n",
       "+6Z/8GBp3Tpp1Sqz5G5RgLJxo3T8uGNrAQD4DsIQAAAADzdqlJSeXrHHXnqpdOed5nJ+/tlhyNix\n",
       "0kMPmXNI0pgx0oQJF29sesklUlbWhe9T1h4QHTqY59e4sZSaavZFR0v33Ve2x8OzHDwoPfCAtHt3\n",
       "6f30DAHgSIQhAAAAHuBCHwQ7dDCjJyoqOVnat+/cYYgk9e9f+vprr5npNL/8Unq/zSalpEhffill\n",
       "Zko33VRy25Qp0j/+IW3bdvZjyqJtW2nGDBPMFDWMnT3bPP6FF8p2DHiGbdvMv2mzZlL9+tLnn5eE\n",
       "b/QMAeAohCEALHPgwAENGvRnBQW10BVXdNfatWutLgkA3Nr5PghGRUk//SSdOFH+Y9aoYbZvv312\n",
       "z5AinTqZ7YEDpXuTPPXU2fd99FHpuuvM5Q0bTANWSXr+eWnSJLM6zIoVZl95v+kfPFhq0sSco0oV\n",
       "6bbbzP4HHjDNVuE9rrhC+uIL6YYbpD59zL/37NnOW9kIgO8hDAFgmZtuukVLltTQb7/9Wxs23K4e\n",
       "Pfooh79mAaDcqleXWrWSNm0q/2OvukoaOtQECocPn3tkiJ+fCS7q1pWuuaZk/9tvS0eOlFwPCjIj\n",
       "Qk6/PTHx7NEgsbEV+6bfZjM9TF55xXwonjNH2r5duvde6Y47mEbhLYr+HXv2lObNM6OWPv/cBGnN\n",
       "m1tbGwDvQRgCwBJHjhzR6tVfKi8vSVK4pFGSumvlypUWVwYAnqmiU2XsdumWW0qunysMOdPx46bx\n",
       "aqtW0scfS3FxJqSoVq3kPu++K8XHS2vWSIsXSxER5lzJyeb2xYsrFl40bSrdc4+5bLNJYWFmSsW2\n",
       "bdKiReU/HtzT6SFZgwZS797Szz+fPWULACqKMASAJapWrXrq0m+ntnbZ7TmqVauWVSUBgEfr1Em6\n",
       "/XbzITImpnyPDQ6WPvjAXD7XNJkzVatmvqFPSJDee89MhRk/Xjp0yHxgvfFG6dZbpapVTa+QyZOl\n",
       "LVvMY8eNM6HFxIlmWk9FekA8+qg0fXrJ9YAAadYsc55jx8p/PLgXRvgAcAXCEACWCAgI0MMPP6Ka\n",
       "Na+XlKjAwMFq2dKmG264werSAMAjdelScrk8g+yKPngOGWJGc/iV46/DAQOkJUvM5WuvNT1FAgPN\n",
       "vqJQ5cEHz35cv35mpZB69SrW56RmTemxx0rvi42VOnaUnnuu/MeD+6FRKgBnK8NASABwjoSEhxUd\n",
       "Hakvv/xal1xyre66667TRowAAE53sW/Lo6NLXz950oyYKAubzfyMGFG+mk4fzPfww2YVmTPDlGrV\n",
       "pM2bpdq1S5/vt9/MUrmO9MIL0pVXSsOHS+Hhjj02AMC7EIYAsNSgQYM0aNAgq8sAAI9woW/Li7Lk\n",
       "KVOkzz6TfvjBBANF/vY3M1pj0qTSj6vslISjR81KMT17Si+/LDVqdPZ9IiLO3teokfT99yV1O8Il\n",
       "l5ipO7fcIq1eXfYwCO6FaTIAXIFpMgAAAF7i8GGzess110jfflv6tmefle677+zH2O2Vm5JQvbrp\n",
       "4eHnJ919d/kCiOhoqW3bip/7XO6+2/RAef55xx4XrsU0GQDORhgCAADgJWrWNKFEly5nhyHXXmu2\n",
       "5/rW3Zs+eNps0quvmpEwo0aZKToAAJyJMAQAAMDLnCsMufRSsz1z+VlvnJIQFmYaqc6dK0VGSk8+\n",
       "aXVFKA9v/J0E4H4IQwAAACrowIEDGjp0qNq2bavIyEh9e2YCYZG2baXcXGnfvpJ9RR8wBw0yIydO\n",
       "3+9NI0OKjBkjpaSYHiqPPcYIEU/jjb+TANwLYQgAAEAFTZo0SX369NHmzZu1ceNGtXV0A4wKqlLF\n",
       "hByjRpkPlYWF5nqPHub2iRNL398bP3jabOb5P/ecaewaGSlt2yYdO2ZuW7fO6gpxPowMAeAKhCEA\n",
       "AAAVcPDgQX311VcaN26cJMnf319169Z12vnK+wHx0CFpyRJzOT3dPP7660vfXpHjeqIJE6QbbzRh\n",
       "UIcOZt/Qoabh7M6dZgv34o0BHQD3wtK6AAAAFbB9+3Y1btxYY8eO1YYNG3TVVVfppZdeUo0aNUrd\n",
       "LyEhofhyTEyMYmJiKnzO8nxAPHbMrPQiSV99ZUKPmjWlPXuk+HgpLU3q16/8x/VEfn4mGBo3Tnrr\n",
       "LenOO6X9+81SvFFRUo0a0qefmhE1AADrpKWlKS0tzSXnIgwBAACogPz8fK1bt04vv/yyOnXqpPvu\n",
       "u0+JiYl64oknSt3v9DDElQIDTdjxySfSggXS5ZebUCA4WOrdW0pNNbf7wsiQIm++aUaB3HijWV2n\n",
       "QQPpyy+lpk2l6dOlM/7pYBFf+p0EUNqZXxpMnz7daeciDAEAAKiA0NBQhYaGqlOnTpKkoUOHKjEx\n",
       "0eKqSlu8WMrLMyMfDh2SWrY0+/v0MSMiDh6UvvvO+0eGnG7+/JLLdrv07rtSt27SNdeY0TQzZ1pX\n",
       "G0r40u8kAGvQMwQAAKACmjRpoubNm2vr1q2SpGXLlqldu3YWV3W2qlWlgoLSoUdRmR9/bLbHj1tT\n",
       "mzv485/NUrwLFkgvvijNnm11RWBkCABXIAwBAACooFmzZmnEiBGKjo7Wxo0b9dBDD1ld0jk99pjZ\n",
       "rl1rtjab9M470tGj5npYmCVluZU//UnaskVKSJAefljautWESLAGI0MAOBthCAAAQAVFR0fru+++\n",
       "04YNG/TRRx85dTWZyiiact2kScm+W2812379TCNRSK1aSf/+t/TMM1KbNlJcXElg5K0YhQHAVxGG\n",
       "AAAAeIDKfmj97bfSDUIDAszWRU37PUb79lJ+vvTzz6bZ7KBBpu+KN2ra1DTV/eAD6eRJq6spQUAD\n",
       "wBUIQwAAADxEZaYONGpk+oecbuFCac6cytXkjapUMc1m5841q/Lcfbd3fkAPCDDLDQ8bZn43Zs1y\n",
       "n+CHaTIAnI0wBAAAwEcNGFAyXQZn8/c3q82sWVMy1cibNGgg3XOP6Y2yYoVpqNumjVmFyMrwxxuD\n",
       "JwDuhzAEAAAAOI/ataUvvpDef1969lmrq3Esu92MwPDzk3r0MIHIG29IDzwg3XijtG2bdbUxMgSA\n",
       "sxGGAAAAABcQFCQtXy69/ro0aVLZRi68+qoZVVJk714zHeXdd92rKeuZoUNsrLRxo9Sli3T11dLk\n",
       "yaZ/imRCoYcfljZtcn2dAOBohCEAAADARTRrJn35pfSPf5iRFOvWXfj+f/ubNHKk9N575vq335pG\n",
       "pSNHSjVrmqWNrXa+UCcw0CwxvHq1VKOGdM010pgxUq9eZqWdyy+X7r9fOnTItXUBgCMRhgAAAABl\n",
       "0KyZdOSIWXHmqqukF14w+8/VdDQ6Wnr8cWn4cCkyUjp+XOrbV0pPN0HI6NGmSWv//tLOna59HkWK\n",
       "psmcT4sW0tNPm+kzu3aZfb/+an727pXatpWef96sSvP449IffziuNqbJAHA2whAAAAAPwLfl7qFG\n",
       "DWnDBul//zNTYWw2qVo1acoUE3gUKSw0ocmhQ1Lr1tLNN5sgpW1bMzpk+3bzuE8+kTp2NMezQllC\n",
       "h6goE4jY7VLjxuYnJcWMdJkzR9qzxyzbXLeumUaUm1vy2G++MaNiinqT2GxSu3ZSdvb5z8fvOgBX\n",
       "IAwBAADwEHxb7j6uukpaudJcjo42IySiokr6aRQWmg//tWpJH35oQoLExJLHh4WZUSJ2u5ScLHXq\n",
       "JAUHmyatrgoDKnuea66RfvrJhDx2u/T55+Y1adJEGjxYysiQunY195PMFKPhw81zj4w0v8/Tpplj\n",
       "7Ntnmrf+/ru5L7/rAJzN3+oCAAAAAE8UElISKNjt0ltvSVdcId1wgxkl4nfqa8cqVaS///38x+nf\n",
       "34wU+fvfTTjw/vvSK6+UhAjOcrFpMmVhs5nRMpLUu7f52bxZGj/e9BYJDDS9Vpo2lUJDzVK+kplq\n",
       "88gjpjlrRETJ8e65x1wvCkUAwFkYGQIAAABUks0mjRsnpaZKS5aY1Wf8yvGXdliYCUOOHzfTarp2\n",
       "NaNFiqaYvPiilJ/vnLodrW1b6euvpR07zDK97dqZIOR0QUFmis2CBdLBg+a+q1ebcKRjR6lfP8fX\n",
       "BQCns9ntnjErz2azyUNKBQDALfFe6nqOfM379pUmTjRbuDe7XVq2zIzsqFWrYsc4dsw0JZ05s2Rf\n",
       "q1bS/PlShw6OqTMy0vT9aNfOMccDAEdz5t8ujAwBAAAAHMhmk+LiKh6ESFL16tJzz5keHGvXSidP\n",
       "SgMGSFde6dhleenNAcBXEYYAAAAAburaa00A4u9vmrRu2mRGjNhs0t13S089ZRqQFjlxwkw7KQsG\n",
       "igHwZYQhAAAAHoAPrpDM1JaNG6Xrr5eSkqRHHzUNR/v3l3JypNdek+rVM6NILtaE1BENVAHAUxGG\n",
       "AAAAeAg+uEKSatc2DVrtdvOTkyNVrSq1bCndd5903XWmIWnbtmZ1mhMnzn8sfqcA+CrCEAAAAMCD\n",
       "NW1qVmXZvl2KipISEqQNG6RPP5U++cSszpKaevboIkYbAfBl/lYXAAAAAKDymjQxU2iKdOwo/fij\n",
       "NHeudO+9ZuTIzJkmMJGYJgPAtzEyBAAAAPBSNps0apSUni717Gl6jdx1l5lak5FBGALAdxGGAAAA\n",
       "AF4uIEB64AHp++9NABISYvYHB1tbFwBYhTAEAADAjQ0fLn3wgdVVwFuEhEivvipt2SLl5kp161pd\n",
       "EQBYg54hAAAAbuy996SlS6VOnayuBN6kTRurKwAAazEyBAAAwM3t22e29HcAAMAxCEMAAADcWLdu\n",
       "ZltQYG0dAAB4E6bJAAAAuKHCQunAAalBA3P9l1+srQcAAG/CyBAAAAA3lJIiNWwo2e3m+rZt1tYD\n",
       "AIA3IQwBAABwQ4WFZpufb20dAAB4I8IQAAAAN9SsmdlmZEjXXGMu791rXT0AAHgTwhAAAAA3tGWL\n",
       "2f78s/Tgg+Zy69bW1QMAgDehgSoAAICbKSyU/vrXkutVq5b0DgEAAJVX6ZEhYWFhat++vTp06KDO\n",
       "nTtLkvbv36+4uDi1bt1avXr10oEDB4rvP2PGDIWHhysiIkJLly4t3r927VpFRUUpPDxckyZNqmxZ\n",
       "AAAAHuvZZ0tf37/fmjoAAPBWlQ5DbDab0tLStH79eq1Zs0aSlJiYqLi4OG3dulWxsbFKTEyUJKWn\n",
       "p+v9999Xenq6UlNTNXHiRNlPfc0xYcIEJScnKyMjQxkZGUpNTa1saQAAAB7p4EGzbdHCbL/7zrpa\n",
       "AADwRg7pGWI/Y9zm4sWLNXr0aEnS6NGjtXDhQknSokWLFB8fr4CAAIWFhalVq1ZavXq1du/erUOH\n",
       "DhWPLBk1alTxYwAAAHxNWJjZvvGG9I9/SDNnWloOAABep9I9Q2w2m3r27KkqVarozjvv1O23367c\n",
       "3FwFBwdLkoKDg5WbmytJysnJUZcuXYofGxoaquzsbAUEBCg0NLR4f0hIiLKzs886V0JCQvHlmJgY\n",
       "xcTEVLZ8AAC8VlpamtLS0qwuA+W0bJk0YYK53KaN1KOHtfUAAOCNKh2GrFq1Sk2bNtVvv/2muLg4\n",
       "RURElLrdZrPJZrNV9jSSSochAADgws784mD69OnWFYMyO3bMbC+7rGR5XQAA4FiVnibTtGlTSVLj\n",
       "xo01aNAgrVmzRsHBwdqzZ48kaffu3QoKCpJkRnxkZmYWPzYrK0uhoaEKCQlRVlZWqf0hISGVLQ0A\n",
       "AMDjNGxottu3W1sHAADerFJhyNGjR3Xo0CFJ0pEjR7R06VJFRUWpf//+SklJkSSlpKRo4MCBkqT+\n",
       "/ftr3rx5ysvL0/bt25WRkaHOnTurSZMmqlOnjlavXi273a65c+cWPwYAAAAAAMCRKjVNJjc3V4MG\n",
       "DZIk5efna8SIEerVq5c6duyoYcOGKTk5WWFhYZo/f74kKTIyUsOGDVNkZKT8/f2VlJRUPIUmKSlJ\n",
       "Y8aM0bFjx9SnTx/17t27kk8NAADA89jt0pVXSl98YXUlAAB4L5v9zKVg3JTNZjtr1RoAAFB2vJe6\n",
       "Xnlfc7td+u9/pWnTpFWrnFgYAAAewJl/uzhkaV0AAABUXlyc1Lev5KDe8wAA4DwqvZoMAAAAHGP5\n",
       "crMlDAEAwLkYGQIAAOBmCEMAAHAuwhAAAAA3QxgCAIBzEYYAAAC4mQMHrK4AAADvRhgCAADgJlq1\n",
       "MtstW6ytAwAAb0cYAvg4ltl0L/x7AL6t6H8BeXnW1gEAgLcjDAF81KJFi9SgQYj8/auqc+frtXv3\n",
       "bqtL8mnLly9XcPBl8vcPUPv2XbVjxw6rSwJgkZYtra4AAADvRxgC+KD09HQNH367fv/9AxUWHta6\n",
       "dVerX794q8vyWZmZmRow4Fb9+uvrKiw8ok2bBig2tj+jRAAf1bev1RUAAOD9CEMAH7Rq1SpJfSV1\n",
       "lVRNBQVPav36VTp58qTFlfmmNWvWqEqVrpJ6SqqmwsIHlZ2dqX379lldGgAXs9ule++Vjh61uhIA\n",
       "ALwbYQjggxo3biw/v3RJBaf2pCswsLb8/f2tLMtnNW7cWIWFWyWdOLVnhwoL81S7dm0rywJgEZtN\n",
       "ql7d6ioAAPBuhCGAD+rXr586dmykWrW6KzBwgqpX76U5c16WzWazujSf1L17d8XGdlCtWl0VGDhB\n",
       "NWp019/+9ryqVatmdWkAAACAV7LZPWRSus1mY/484ED5+flauHCh9uzZo65du+rKK6+0uiSfVlhY\n",
       "qE8++USZmZnq2LGjunTpYnVJ8EK8l7peeV/zFi2kL76giSoAAJJz/3YhDAEAwEfwXup6FQlDli0z\n",
       "WwAAfJ0z/3ZhmgwAAAAAAPAphCEAAABugoE7AAC4BmEIAACAG6GXNQAAzkcYAgAA4CYYGQIAgGsQ\n",
       "hgAAAFRCQUGBOnTooH79+jnkeIwMAQDA+QhDAAAAKuGll15SZGSkbBVMMY4fl376ycFFAQCACyIM\n",
       "AQAAqKCsrCwtWbJEt912W4WX/qteXYqIMJeZJgMAgGv4W10AAACAp5o8ebJmzpypP/7447z3SUhI\n",
       "KL4cExOjmJiYCx6TaTIAAF+VlpamtLQ0l5yLMAQAAKACPv30UwUFBalDhw4X/MPt9DDk119N2HH6\n",
       "CJAbb5Q+/1zKz3derQAAeIIzvzSYPn26087FNBkAAIAK+Prrr7V48WJddtllio+P14oVKzRq1KgL\n",
       "PubEibP3tW9vtllZTJMBAMBVCEMAAAAq4JlnnlFmZqa2b9+uefPm6frrr9c777xzwcdUq2a2p4ci\n",
       "RQHIjh1myzQZAACcjzAEAADAAcqymkxR8LF+fcm+wkKz3bnTCUUBAIBzIgwBAACopOuuu06LFy8u\n",
       "8/2fe67kst1uRozs2ME0GQAAXIUwBAAAwEWKwo4tW0r2FRaaaTNFfVaZJgMAgPMRhgAAALjY5s0l\n",
       "lwsLpfBwc5mRIQAAuAZhCAAAgIsUhR29epXeN368ubxnDyNDAABwBcIQAAAAFykKQxo0KNlXWChV\n",
       "r24uFxS4viYAAHwRYQgAAICTHTsmDR9ecv2zz0ouFxZKfn7SI4+4vi4AAHwVYQgAAICTZWdL771X\n",
       "MjLk0KGS2+x2E4Z06WKuM00GAADnIwwBAABwspo1zfbXX6V69cxSukXByObNUn6+1KmTuV5YaE2N\n",
       "AAD4Epvd7hl9y202mzykVAAA3BLvpa5X9Jrv2SM1bWr2NWsm5eRIublSUJAZCdK0qdl36aXShg0m\n",
       "MAEAwNc5828XRoYAAAC4UNE0mOnTS/a1aGG2O3cShAAA4AqEIQAAAE52+pdaRWFIUQAiSY8+6tp6\n",
       "AADwdYQhAAAATnbmCN/77isJRUJCpMhI19cEAIAvIwwBAABwsjNHhjRpIu3eXXKbH3+RAQDgUv5W\n",
       "FwCgRGpqqv797+Vq0qSxJky4S3Xq1LG6JK+Qk5OjOXPe0OHDRzV06EB1KVq/EgAskJcn1a0rTZsm\n",
       "zZxpVo9hOV0AAFyLMARwE7NmJWnatJk6evQOVau2QXPm/EkbNnyjWrVqWV2aR8vOzlb79lfrjz8G\n",
       "KD8/WElJA/TBB2+qb9++VpcGwIecPjLkyBFp48bStxGGAADgWiytC7iJ2rUb6fDh/0qKkCTVrHmT\n",
       "Xn55qMaMGWNpXZ7u4Ycf1bPP/qGCgpdO7flMERFPaPPm1ZbWBViB91LXK3rNMzOlSy4p2f/bb1Lj\n",
       "xlJBgVlWd8MGM3UGAACUYGldwMvZ7XYdP35EUrPifQUFzXTkyBHrivISf/xxRAUFzU7b00yHDx+2\n",
       "rB4AkKRGjcz28ccZGQIAgBUIQwA3YLPZ1LfvIAUG3i7pJ0kL5Of3sXr16mV1aR5v6NABqlHjJUnL\n",
       "Jf2oGjUmafjwwVaXBcDHHD167v1PPSUdP04YAgCAqxGGAG7in/98XTffXE/BwX0VGfm8UlM/Unh4\n",
       "uNVlebzrrrtOKSmz1KLFA2radIgmTOiup59+3OqyAPiYe+89e1/PnmZ76BBhCAAArkbPEAAAfATv\n",
       "pa5X9JpfcYXpC1LEbpfuvltKSjLX9+yRgoOtqREAAHdFzxAAAAAPdnoQUiQoqORyUQ8RAADgGoQh\n",
       "AAAALnL0qPTRR+byAw9IK1ZIhw9LVapYWxcAAL6GaTIAAPgI3ktdr+g1v/JKaf16Mz0GAACUDdNk\n",
       "AAAAPFinTlZXAAAATkcYAgAA4GSXXipNm2Z1FQAAoAhhCAAAgJPZ7SyfCwCAOyEMAQAAcDLCEAAA\n",
       "3AthCAAAgJMRhgAA4F4IQwAAAJyMMAQAAPfib3UBcI3vvvtOO3fuVHR0tMLDw60up1hWVpZWr16t\n",
       "Ro0a6dprr5WNvxSBC/rxxx+1ZcsWtWnTRlFRUVaXA6CMCEMAAHAvjAzxAffdN1UxMUM1fvw/dcUV\n",
       "f9K//vWe1SVJklauXKm2ba/UuHHv6KabJqh//1tVWFhodVmA23r++ZfUuXOcxo//p7p0uUHPPfei\n",
       "1SUBKCPCEAAA3IvNbrfbrS6iLGw2mzykVLeybt06de8+UEePbpRUT9KPCgz8k37/PVeBgYGW1hYS\n",
       "0lo5OX+X1EdSnmrV6qa33npQQ4cOtbQuwB3l5OSoZcvLdfz4BknNJWUpMDBaGRkbFBoaanV58BC8\n",
       "l7pe0Wv++OMmDElIsLoiAAA8hzP/dmFkiJfbtWuX/P2jZYIQSbpcNlug9u3bZ2VZkqRff90l6bpT\n",
       "16oqL6+Ldu3aZWVJgNvKyclR1aqXygQhkhSqqlXDlJ2dbWVZAMqIkSEAALgXwhAvFx0drfz8byWt\n",
       "P7XnPdWqFagmTZpYWZYkKSqqs/z8/i7JLmmn/P0XqVOnTlaXBbil8PBwFRZmS1p2as9yFRZmqnXr\n",
       "1laWBaAMliyRjh0jDAEAwJ0Qhni5yy67TCkpr6l69R6qVq2hgoL+T0uXLlKVKlWsLk0LF76rFi0+\n",
       "ULVqDRQQEKmnnrpf3bt3t7oswC3VrVtXn3wyX3Xr/lmBgY1Up85wLVo0T/Xr17e6NAAX0bev9M47\n",
       "hCEAALgTeob4iJMnT+r3339Xo0aN5OfnPhmY3W7X3r17VadOHVWrVs3qcgC3V1BQoL1796pRo0Zu\n",
       "EWrCs/Be6npmlTS7atWSpk6VHnnE6ooAAPAczvzbhaV1fURAQICCgoKsLuMsNptNjRs3troMwGNU\n",
       "qVJFwcHBVpcB4P/bu/Pwqup73+OfkHlECEMgYTIJhJAwlMla9cFSBLkCVhQpLU7QAUuv0/Fy63XA\n",
       "ayFQT09bj9XH0+JQvBeotIp6ISK2cYQoMggkaBKSkAlQICGBzPneP7KzTSBMIdk7Yb1fz7MfyBq/\n",
       "v+9eK7/f/mavtS5SRYVUV+ftKAAAQJPO8xUBdFoNDQ3as2ePdu7cqdraWm+H4zFff/21tm3bppKS\n",
       "Em+H4lEVFRX69NNPlZOT49U4qqur9fnnn2vfvn0e+Ut2Tk6O0tPTVV5e3uH78qbS0lKlp6crPz/f\n",
       "280Qa58AAB4xSURBVKFcsqZjNSsry9uhABfk73/3dgQAAKAJxRCcU2Vlpa65Zqq++92bdd118zRy\n",
       "5Hc7xZNoOtrrr7+hwYMTNG3arxQbm6Q///lFb4fkEbt379agQQmaMmWRkpOv1qJFD3jlK/XFxcVK\n",
       "SPiOrr/+Lk2YMF3Tpt3SYYU4M9Mvf/mQkpOv1g033KvBg4dr9+7dHbIvb/v44481cOAwTZ36SyUk\n",
       "jNXjj//G2yG12b59+zRkSKKmTPmFRo26VgsXLubyD3R6VVXejgAAADThniE4p0cffVK/+90eVVWt\n",
       "k9RN/v7/XXPmVOnVV//s7dA6THl5uaKiBunUqc2SxknKUnDwd7V//w4NHDjQ2+F1qLi40crJeVDS\n",
       "HZLKFBp6tf72t6c1ffp0j8YxffptevfdBNXVPSWpRsHBM7R8+XTdf/997b6vTZs26bbbHtLJk1sl\n",
       "dZe0Wlde+e/Kybm8CiJmpl69BujYsf+SNF3SEYWEjNc///k3TZw40dvhXbTExAnKzPyZpIWSyhUa\n",
       "eo1effVJ3Xzzzd4OrVOjL/W8pnuGSNKAARJPkAcA4MJ15NiFb4bgnHbuzFRV1Q8l+UryUW3tbH3x\n",
       "xX5vh9WhCgsL5evbS42FEEmKV0BAotcvG/GE/Pz9kma7fuqu2tofKDMz0+Nx7Nu3X3V1TXEEqLJy\n",
       "hnbu7Jg49u/fr9raH6ixECJJs115uLycPHlSJ04cVWMhRJL6qFu3a7R/f9ds64EDzY/VcFVX39Bl\n",
       "2wLnqK72dgQAAKAJxZDL0JEjR5SZmanqNo66GhoalJ2drfz8fI0dm6jg4PWSaiWZ/P1f1JVX9lfd\n",
       "BdwFrqKiQhkZGSorK2tTHM1VV1crMzNTR44cueRtnc+AAQNUX39UUrpryn5VV+9zP/mmKzh58qQy\n",
       "MjJUWlp6UesNGZIoaZ3rp+Py939HI0aMkNR4D5XMzExVub7nbWY6cOCADhw40O7V2uTkRPn5rVPj\n",
       "X1OrFBLyhkaNGqbMzEwdPHhQGRkZ7Xa5VmJiovz9N0s6JqlO0h81YEDcWZcvKyvTvn37tGfPHuXm\n",
       "5l5025vOi9LSUuXm5uqzzz5TRkZGm8/X09XW1mrbtm364IMP3O+VJIWGhuqKK3pLelNSmaT3VV+f\n",
       "psTExHbZ7+mOHz+ujIwMnTx5stXpp06duqTtx8Ulysen6VgtU0DARoWFhen999933H1+0HVQDAEA\n",
       "oBOxLqILhepVjzyy1AIDu1tYWJz17TvEMjMzL2r9Y8eO2ahRV1tISIwFBfW2adNusWuumWrBwTHm\n",
       "69vbfHzCLCRkkMXFjbLi4uKzbuedd96x0NBICw8fasHBV9iaNWvb3KbMzEzr23eIhYXFWUBAhD3y\n",
       "yNI2b+tCvfnmWxYaGmkRESMtMDDcwsJ6W3h4vAUGRlhKyr93+P4vxb/+9S8LD+9t4eFDLSiou61a\n",
       "9fIFr7tnzx7r1WuARUQkWVBQpN133/+whoYGe+qpFRYYGGFhYXHWq9cAS09Pt2uvnWrBwVEWHBxl\n",
       "11471U6ePNlubSgpKbHY2JEWFjbUgoP72XXX3WC9ew+y4OAYk4ItIGCQBQZG2O9//5/tsr/7719i\n",
       "gYE9zMenh0m9LSCgh82de7fV19e3WG7t2nUWFNTdfH0jTbrCAgL62HXXTbNTp05d0H6azouwsDjr\n",
       "1i3CunXrblKQdesWbb17D7J9+/ZdUjvy8vLsiiv6mxRkUj8LDOxh27dvd8/funWrBQdfYVKwSf3N\n",
       "3z/CUlNTL2mfrfnLX16yoKDuFh4+1MLDe1taWtoZ0yMi+tj777/f5n1kZmZanz6DLSIiyQIDe1h4\n",
       "eJT5+ESY1Ne6dQuze+99wBoaGtqjOZcV+lLPk2SSmWQWGOjtaAAA6Fo6cuzSZUZFDODOb8uWLRYa\n",
       "GmvSEZMqTHrS4uPHWEFBgRUXF1/QB4N58xZaQMAvTKo3qdJCQm6wp55abg8++KAFBY03qdykMvP1\n",
       "/YVNnjyz1W2Ul5dbSEhPkz4wqcGkty0wMMK+/PJLKysrs5ycHKuurm6xztdff215eXlWV1d3xvaG\n",
       "DRtrPj7PuwaThy00NNa2bNly1jaUlJTYwYMHraamxg4cOGDHjh07b7tbc+zYMdu+fbtFRcWa9H9c\n",
       "+y+0kJAYS09Pb3Wdmpoay8nJsdLS0rNu99ChQ5afn3/GB+0LlZOTYx9++KG7+FBWVmbZ2dlWXV1t\n",
       "VVVVFhHRx6TNJtWYtNmCgnpaTk7OBW//5MmTtmPHDsvPzzczs48++shCQgaaVOzKwUsWHh5lQUFz\n",
       "TKo1qdaCgubYAw/8z4tuS0NDg/v4PF1NTY3t3r3bvvrqK4uNHWXSf5k00KT1rjjyLCSkn+3atcvM\n",
       "zI4cOWJ5eXmt5vX48eOWk5NjtbW17mm1tbV24MABy8nJsezsbLvqqsnm6/uQ65itsODg79qyZcvc\n",
       "x09RUZGFhESadLdJc11tr7GgoFvt3/7tEfvmm28sNze31WPYzKyiosLCwnqZ9L5JD5l0jUlDTMo3\n",
       "KcOkx+zKK5MvOofNJSVNMKmPSQddOVpjPXpEm1njefnxxx9bcHCkSbtc8z+00NBIKy8vP+s2T5w4\n",
       "YdnZ2VZVVeWedq7jPDs724KDe5u037WPdyw8vJdt2rTJNf1L1/RU69697xm/Cy7GqVOnbMeOHTZp\n",
       "0n8zKd6kFNe2j1tg4HD7+9//3uZtX67oSz2veTGE9AMAcHEohhgDuLP55ptvrKioyBoaGuyxxx4z\n",
       "f/9fmrTOpCtM6mdSmPn797TAwJ42ffqt7g8etbW1lp+fb2VlZVZQUOD+wBcXN9akj12DtqMmLTY/\n",
       "vwjz8+tp0m9NetmkCJMGmBRiGzdutD179lh6erqVlZVZbm6uXX/9jSb1N+mESeNNCjGpl+sv4MEW\n",
       "GBhl3bv3tbfeestKS0tt/vyFFhAQbsHB/WzYsO+c8cHY19ffpFPuYoSf3222YsUK9/yysjLLz8+3\n",
       "yspKmzXrRxYY2MMCAnpaQECkhYTEWEBAuD366P++oFx+8sknduLECfe0yspK69bNz/UBudr1AfzH\n",
       "9vzzz1teXl6LD4i7d++2Pn0GWWjoQAsMDLc//OHZFtuvq6uzuXPvNn//cAsK6mVjxlxzRqGmqS2t\n",
       "faCuqamxCROuc/3Vv7d16xZqP/vZIgsMDLfQ0IHWq9cAe/vtty0kJMb1QTTO9T742/TpM9wFp1On\n",
       "TtmBAwfss88+s9raWqupqbG8vDyrqKhoEWt+fr6dOHHCnn/+eQsOXthsMH/SdQxsaDZtg33ve9PP\n",
       "mtuGhgb78ssvbdeuXe62lZeX2/e+d4MFBfW2wMAedtNNc6ympsbq6+tt7969tnfvXquvr7f6+nrz\n",
       "8enmKvKFufZ3xKQSCwubY6tXr7Z77rnXAgIiLDi4n40YMcEOHz5slZWVlpeXZ0888RsLCAiz0NAB\n",
       "1q/flfbhhx/a7t27LSZmmPn5RZrkbz4+3V1t2uva/lcm9TNf3z7m7x9iv/714/b6669bePjVJk0z\n",
       "6S3XcuUmvWD9+sWbv3+4BQf3t7i4UVZYWOjOa1FRkRUUFNjevXstPDzepCdM6mHSApN+aFJPk0JN\n",
       "ijQpwJ577gV3zg4dOmSHDx8+4zhqem9OFxAQZtKPm71PuSb52Qsv/NmCgiIsKKiPScktPpiFhcXZ\n",
       "e++912qx9C9/edF1fA2yHj36W3p6uu3du9f69BlsoaEDLSAgzJYu/Y0dOXLEvc5bb71l3btPa7aP\n",
       "F00KMH//HiZ9r8W+Q0L6uYtuFRUVlp+fb0eOHLHCwkJ3UevIkSNWUlJi1dXVlpeX16II2HSu9Os3\n",
       "1JW/4mbb/1/2xBNPnPWYdCr6Us9rXgwZP97b0QAA0LV05NilUz1NJjU1Vffff7/q6+u1cOFCLVmy\n",
       "xD2PO+A3qqysVGRkpCorKyUFSWq6J4C/Gu/rES2pVNJASXmSpkjaIyn3LFv89i73jdvrJumnkv6v\n",
       "pK9d056Q9IikUZKyJS2Q9EdJgZLq1XifBbnWNUmjJWVKGitpr6R/k/SYpGBJlZL8XOt0k9QgKVZS\n",
       "iCvO1oRKmiVpvaSa0+Y1batp/0mSvnCt81NJ/+mK8Xx8z7FcsKR5kladZxshkhZL+u05lomRVNiG\n",
       "GKTG9gVL+rmk/3BNC5f0S0krmi0XKCnKNe8rnZmzpvfhYvSXNFzSe822MVPSZknHL2D9gFbiCJQ0\n",
       "SdKHkk6dNv30C+tD1HgMPiUpXo3HVXOJajwHWnsCTG9JN6nxmK5WYx5D1HhufCxpkKQBktLUmNvf\n",
       "utp3g6S3XXE3nWshajzGhkl6R1LTPWyulJQsacN52u0rqY+kvpLCJG2XFKHGXP7ltHVby4PU8pxt\n",
       "zl+N50N3V7x5zeaFqvHY/A/XMt+X9P/OsY8mYWp8j94+bVv3SVqulr+DmguXdIukV9SYM1PjMRcu\n",
       "6VpJG8/SptPzdbb4Tj9XwtSY1/mSnmy1JePHj9fWrVvl6+vb6nynoC/1vOZPk8nKkuLOfksiAABw\n",
       "mo4cu3SaYkh9fb2GDRumLVu2KDo6WuPHj9eaNWs0fPhwSQzgJOmll17SPffccxFrtPYBtK3O96Gp\n",
       "teUuZJ2zfbBri6aCUGd1vmLH+bTn+9kZXOgxdT7NC2LeiKM9j2G0v3DXv7WS/FRRcUihoaHeDMir\n",
       "6Es9r3kxJCNDcg1rAADABXDEo3U//fRTxcXFafDgwfL399fcuXO1YcPpf2V1tosrhEjt+8H5Qj8s\n",
       "Vp/l/2fTngd2Zy6ESJdWCJEur0KI1D6FEOnSCiHSpcfBB8vOK0KN3yo7LukbSUmKiOjh3ZDgaBUV\n",
       "3o4AAAA08fN2AE2Kioo0YMAA988xMTFKT09vsczSpUvd/580aZImTZrkoegAAF2Pr6RFrn8bL51r\n",
       "aMjwbkgelpaWprS0NG+HAZcrr/R2BAAAoEmnKYY0fo303JoXQwAAOLcGSamSrnb9f6Mu/n45Xdvp\n",
       "fzh48snW76kCz4iM9HYEAACgSae5TCY6OloFBQXunwsKChQTE+PFiDqfu+66y9shAEAXUqbGm8aO\n",
       "UeNNbzcrJ2e/d0MCAABAp9BpiiHjxo1TVlaW8vLyVFNTo3Xr1mnmzJneDqtTeemll/Taa695OwwA\n",
       "6EJOStolX99cnThRpCu5TgFeMGyYlJnp7SgAAEBzneYyGT8/Pz377LOaOnWq6uvrtWDBAveTZPCt\n",
       "W2+9lScBAADQhdBtAwDQ+XSaR+ueD48DBADg0tCXep6Pj4+GDjW9+WbjN0QAAMCFc8SjdQEAAC5H\n",
       "X33l7QgAAMDpKIYAAAB0sIYGb0cAAACaoxgCAADQwerrvR0BAABojmIIAABAB6us9HYEAACgOYoh\n",
       "AAAAbVRQUKDrr79eI0aMUFJSkp555plWl+MBeQAAdC48TQYAAIegL21/hw4d0qFDhzR69GhVVFRo\n",
       "7NixeuONNzTcVf3w8fGRZDxeFwCANuBpMgAAAJ1QVFSURo8eLUkKCwvT8OHDVVxc3GKZQYO8ERkA\n",
       "ADgXP28HAAAAcDnIy8vTzp07NXHixBbT8/OXaunSxv9PmjRJkyZN8nhsAAB0BWlpaUpLS/PIvrhM\n",
       "BgAAh6Av7TgVFRWaNGmSHn30Ud18883u6VwmAwBA23GZDAAAQCdVW1ur2bNn6yc/+UmLQggAAOi8\n",
       "+GYIAAAOQV/a/sxMd955pyIjI/X73//+jPl8MwQAgLbryLELxRAAAByCvrT9ffTRR7ruuus0cuRI\n",
       "V+FDSklJ0bRp0yRRDAEA4FJQDBEDOAAALhV9qedRDAEAoO24ZwgAAAAAAEA7oRgCAAAAAAAchWII\n",
       "AAAAAABwFIohAAAAAADAUSiGAAAAAAAAR6EYAgAAAAAAHIViCAAAAAAAcBSKIQAAAAAAwFEohgAA\n",
       "AAAAAEehGAIAAAAAAByFYggAAEAH6sZoCwCATofuGQAAoAOtXOntCAAAwOl8zMy8HcSF8PHxURcJ\n",
       "FQCATom+1PPIOQAAbdeR/SjfDAEAAAAAAI5CMQQAAAAAADgKxRAAAAAAAOAoFEMAAAAAAICjUAwB\n",
       "AAAAAACOQjEEAAAAAAA4CsUQAAAAAADgKBRDAAAAAACAo1AMAQAAAAAAjkIxBAAAAAAAOArFEAAA\n",
       "AAAA4CgUQwAAAAAAgKNQDAEAAAAAAI5CMQQAAAAAADgKxRAAAAAAAOAoFEMAAAAAAICjUAwBAAAA\n",
       "AACOQjEEAAAAAAA4CsUQAAAAAADgKBRDAAAAAACAo1AMAQAAAAAAjkIxBAAAAAAAOArFEAAAAAAA\n",
       "4CgUQwAAAAAAgKNQDAEAAAAAAI5CMQQAAAAAADgKxRAAAAAAAOAoFEMAAAAAAICjUAwBAAAAAACO\n",
       "QjEEAAAAAAA4CsUQAAAAAADgKBRDAAAAAACAo1AMAQAAAAAAjkIxBAAAAAAAOArFEAAAAAAA4CgU\n",
       "QwAAAAAAgKNQDAEAAAAAAI5CMQQAAAAAADgKxRAAAAAAAOAoFEMAAAAAAICjUAwBAAAAAACOQjEE\n",
       "AAAAAAA4CsUQAAAAAADgKBRDuqC0tDRvh9ApkIdvkYtvkYtG5OFb5AJwFs55zyPn3kHePY+cX17a\n",
       "XAxZunSpYmJiNGbMGI0ZM0abNm1yz0tJSVF8fLwSEhK0efNm9/TPP/9cycnJio+P13333eeeXl1d\n",
       "rdtvv13x8fG66qqrlJ+f39awHIGTsBF5+Ba5+Ba5aEQevkUu0JFSU1OVkJCg+Ph4rVy50tvhQJzz\n",
       "3kDOvYO8ex45v7y0uRji4+OjBx98UDt37tTOnTt14403SpIyMjK0bt06ZWRkKDU1Vffee6/MTJK0\n",
       "aNEirVq1SllZWcrKylJqaqokadWqVYqMjFRWVpYeeOABLVmypB2aBgAA0HHq6+u1ePFipaamKiMj\n",
       "Q2vWrFFmZqa3wwIAABfgki6TaSpyNLdhwwb96Ec/kr+/vwYPHqy4uDilp6erpKRE5eXlmjBhgiTp\n",
       "jjvu0BtvvCFJevPNN3XnnXdKkmbPnq333nvvUsICAADocJ9++qni4uI0ePBg+fv7a+7cudqwYYO3\n",
       "wwIAABfC2mjp0qU2aNAgGzlypN1zzz12/PhxMzNbvHixvfrqq+7lFixYYOvXr7ft27fbD37wA/f0\n",
       "Dz74wG666SYzM0tKSrKioiL3vNjYWDt69GiL/UnixYsXL168eF3iC+3ntddes4ULF7p/Xr16tS1e\n",
       "vLjFMt5+v3nx4sWLF6+u/uoofjqHKVOm6NChQ2dMX7ZsmRYtWqTHH39ckvTYY4/poYce0qpVq861\n",
       "uUtirXwLBQAAwFt8fHzOuwzjFwAAOqdzFkPefffdC9rIwoULNWPGDElSdHS0CgoK3PMKCwsVExOj\n",
       "6OhoFRYWnjG9aZ2DBw+qf//+qqurU1lZmXr27HnRjQEAAPCU08c8BQUF7rENAADo3Np8z5CSkhL3\n",
       "/19//XUlJydLkmbOnKm1a9eqpqZGubm5ysrK0oQJExQVFaWIiAilp6fLzLR69WrNmjXLvc4rr7wi\n",
       "SVq/fr0mT558KW0CAADocOPGjVNWVpby8vJUU1OjdevWaebMmd4OCwAAXIBzfjPkXJYsWaJdu3bJ\n",
       "x8dHQ4YM0QsvvCBJSkxM1Jw5c5SYmCg/Pz8999xz7q+RPvfcc7rrrrtUWVmp6dOna9q0aZKkBQsW\n",
       "aP78+YqPj1dkZKTWrl3bDk0DAADoOH5+fnr22Wc1depU1dfXa8GCBRo+fLi3wwIAABegzd8M+etf\n",
       "/6ovvvhCu3fv1htvvKG+ffu65z3yyCPKzs7W/v37NXXqVPf0sWPHas+ePcrOztYzzzzjnh4YGKhB\n",
       "gwbJz89PlZWVevDBB1VWVuaen5KSovj4eCUkJGjz5s3u6Z9//rmSk5MVHx+v++67zz29urpat99+\n",
       "u+Lj43XVVVcpPz+/rc3sdFJTU5WQkKD4+HitXLnS2+G0u4KCAl1//fUaMWKEkpKS3MfJsWPHNGXK\n",
       "FA0dOlQ33HCDSktL3etc7PHRldTX12vMmDHuy9CcmofS0lLdeuutGj58uBITE5Wenu7YXKSkpGjE\n",
       "iBFKTk7WvHnzVF1d7Yhc3HPPPerbt6/7W4hS+54PXanfaC0XDz/8sIYPH65Ro0bplltuoQ/1oBtv\n",
       "vFFffvmlsrOz9etf/7rFvMu9z/Ykxgfew1jEsxjzeJ5Tx1ae1inHch12a9aLtHnzZquvrzczsyVL\n",
       "ltiSJUvMzGzfvn02atQoq6mpsdzcXIuNjbWGhgYzMxs/frylp6ebmdmNN95omzZtMjOzP/3pT7Zo\n",
       "0SIzM1u7dq3dfvvtnm5Oh6irq7PY2FjLzc21mpoaGzVqlGVkZHg7rHZVUlJiO3fuNDOz8vJyGzp0\n",
       "qGVkZNjDDz9sK1euNDOzFStWXNLx0ZX87ne/s3nz5tmMGTPMzBybhzvuuMNWrVplZma1tbVWWlrq\n",
       "yFzk5ubakCFDrKqqyszM5syZYy+//LIjcvHBBx/Yjh07LCkpyT2tPdvdlfqN1nJBH9r5OKHP9iTG\n",
       "B97DWMSzGPN4lpPHVp7WGcdynaYY0tw//vEP+/GPf2xmZsuXL7cVK1a4502dOtW2bt1qxcXFlpCQ\n",
       "4J6+Zs0a+/nPf+5eZtu2bWbW+EukV69eHoy+43zyySc2depU988pKSmWkpLixYg63qxZs+zdd9+1\n",
       "YcOG2aFDh8yscUA0bNgwM2vb8dFVFBQU2OTJk+2f//yn+zHUTsxDaWmpDRky5IzpTszF0aNHbejQ\n",
       "oXbs2DGrra21m266yTZv3uyYXOTm5rboQNuz3V2t3zg9F83Rh3YOTuyzPcnJ4wNPYiziWYx5PM/p\n",
       "YytP62xjuTZfJtORXnzxRU2fPl2SVFxc3OLO7DExMSoqKjpjenR0tIqKiiRJRUVFGjBggKTG63m7\n",
       "d++uY8eOebAFHaN5u6Rvc3G5ysvL086dOzVx4kQdPnzYfSlW3759dfjwYUltOz66igceeEBPP/20\n",
       "unX79jR1Yh5yc3PVu3dv3X333frOd76jn/70pzp58qQjc9GzZ0899NBDGjhwoPr3768rrrhCU6ZM\n",
       "cWQupPY9Hy6nfoM+tHNwWp/tSU4fH3gSYxHPYszjeYytvMvbYzmPFkOmTJmi5OTkM15vvfWWe5ll\n",
       "y5YpICBA8+bN82RoXULTjWidoKKiQrNnz9Yf//hHhYeHt5jn4+Nz2efi7bffVp8+fTRmzBiZWavL\n",
       "OCEPklRXV6cdO3bo3nvv1Y4dOxQaGqoVK1a0WMYpucjJydEf/vAH5eXlqbi4WBUVFXr11VdbLOOU\n",
       "XJzOqe0+HX1o58Hx2DGcPj7wJMYinseYx/MYW3Ue3shzm58m0xbvvvvuOee//PLL2rhxo9577z33\n",
       "tOjoaBUUFLh/LiwsVExMjKKjo1VYWHjG9KZ1Dh48qP79+6uurk5lZWXq2bNnO7fG807PRUFBQYvK\n",
       "2OWitrZWs2fP1vz583XzzTdLaqwUHjp0SFFRUSopKVGfPn0kXdzxER0d7dmGXIJPPvlEb775pjZu\n",
       "3KiqqiqdOHFC8+fPd1wepMZKcExMjMaPHy9JuvXWW5WSkqKoqCjH5WL79u26+uqrFRkZKUm65ZZb\n",
       "tHXrVkfmQmqf3wuXU79BH9q5OKXP9iTGB57FWMTzGPN4HmMr7/L2WK7TXCaTmpqqp59+Whs2bFBQ\n",
       "UJB7+syZM7V27VrV1NQoNzdXWVlZmjBhgqKiohQREaH09HSZmVavXq1Zs2a513nllVckSevXr9fk\n",
       "yZO90qb2Nm7cOGVlZSkvL081NTVat26dZs6c6e2w2pWZacGCBUpMTNT999/vnt78PX3llVfcg6CL\n",
       "OT6a1ukKli9froKCAuXm5mrt2rX6/ve/r9WrVzsuD5IUFRWlAQMG6KuvvpIkbdmyRSNGjNCMGTMc\n",
       "l4uEhARt27ZNlZWVMjNt2bJFiYmJjsyF1D6/Fy6XfoM+tPNxQp/tSYwPPI+xiOcx5vE8xlbe5fWx\n",
       "3MXe9KSjxMXF2cCBA2306NE2evRo951gzcyWLVtmsbGxNmzYMEtNTXVP3759uyUlJVlsbKz96le/\n",
       "ck+vqqqy2267zeLi4mzixImWm5vryaZ0qI0bN9rQoUMtNjbWli9f7u1w2t2HH35oPj4+NmrUKPex\n",
       "sGnTJjt69KhNnjzZ4uPjbcqUKXb8+HH3Ohd7fHQ1aWlp7ju4OzUPu3btsnHjxtnIkSPthz/8oZWW\n",
       "ljo2FytXrrTExERLSkqyO+64w2pqahyRi7lz51q/fv3M39/fYmJi7MUXX2zXdnelfuP0XKxatYo+\n",
       "tJO63PtsT2J84F2MRTyHMY/nOXVs5WmdcSznY3aWiwABAAAAAAAuQ53mMhkAAAAAAABPoBgCAAAA\n",
       "AAAchWIIAAAAAABwFIohAAAAAADAUSiGAAAAAAAAR6EYAgAAAAAAHOX/AxpPX/Q/3/EAAAAAAElF\n",
       "TkSuQmCC\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "games = 10000\n",
    "p = 0.5 #use a fair coin\n",
    "\n",
    "def playGame(p, n=0):\n",
    "    r = numpy.random.rand()\n",
    "    if r<=p: return n\n",
    "    else: return playGame(p,n+1)\n",
    "    \n",
    "payouts = [2**playGame(p=p, n=0) for i in range(games)]\n",
    "cumAvg = numpy.cumsum(payouts)\n",
    "cumAvg = [cumAvg[i]/float((i+1)) for i in range(games)]\n",
    "\n",
    "f,axarr = pyplot.subplots(1,2)\n",
    "f.subplots_adjust(right=2.5)\n",
    "f.subplots_adjust(top=1.5)\n",
    "axarr[0].scatter(range(games),payouts)\n",
    "axarr[1].plot(cumAvg)\n",
    "\n",
    "print \"Max payout = {0}\".format(max(payouts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Higher Order Moments**\n",
    "\n",
    "The expected value is special case of the more general notion of the $n^{th}$ **moment** of a random variable $X$, defined as\n",
    "\n",
    "$$E\\left[X\\right] = \\sum_x x^n p_X\\left(x\\right)$$\n",
    "\n",
    "where again this is only well defined if \n",
    "\n",
    "$$\\sum_x \\left| x^n \\right| p_X \\left(x\\right) \\lt \\infty$$\n",
    "\n",
    "As with the mean, this condition can fail for certain distributions. Consider the power law PMF described previously. All moments, *m*, such that $m\\ge\\alpha\\hspace{1pt}$ fail to satisfy this condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variance**\n",
    "\n",
    "The **variance** of a random variable, denoted $var\\left(X\\right)\\hspace{1pt}$ is defined as the expected value of the random variable $\\left(X - E\\left[X\\right]\\right)^2\\hspace{1pt}$ and the following identities hold\n",
    "\n",
    "$$\\begin{eqnarray}var\\left(X\\right) &=& E\\left[\\left(X-E\\left[X\\right]\\right)^2\\right] \\cr\n",
    "        &=& \\sum_x\\left(x-E\\left[X\\right]\\right)^2 p_X\\left(x\\right) \\cr\n",
    "        &=& E\\left[X^2\\right] - \\left(E\\left[X\\right]\\right)^2\n",
    "\\end{eqnarray}$$\n",
    "\n",
    "The variance is a measure of the expected value of the square of difference between an arbitrary observation of a RV and the mean of that RV.  \n",
    "\n",
    "The **standard deviation**, $\\sigma_X\\hspace{1pt}$, is defined as the square root of the variance.\n",
    "\n",
    "**Linear Function of a Random Variable**\n",
    "\n",
    "Let *X* be a random variable and let $Y=aX+b\\hspace{1pt}$ for scalars *a* and *b*. Then\n",
    "\n",
    "$$E\\left[Y\\right] = a E\\left[X\\right] + b$$\n",
    "\n",
    "and \n",
    "\n",
    "$$var\\left(Y\\right) = a^2var\\left(X\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Joint PMFs of Multiple Random Variables**\n",
    "\n",
    "Consider two discrete random variables *X* and *Y*. The probabilities of the pairs $\\left(x,y\\right)\\hspace{1pt}$ that the *X* and *Y* can take are described by the **joint PMF** denoted $p_{X,Y}$\n",
    "\n",
    "$$p_{X,Y}\\left(x,y\\right) = P\\left(X=x,Y=y\\right)$$\n",
    "\n",
    "From the joint PMF, the PMF of *X* or *Y* can be obtained as\n",
    "\n",
    "$$p_X\\left(x\\right) = \\sum_y p_{X,Y}\\left(x,y\\right) \\quad p_Y\\left(y\\right) = \\sum_x p_{X,Y}\\left(x,y\\right)$$\n",
    "\n",
    "where here $p_X\\hspace{1pt}$ and $p_Y\\hspace{1pt}$ are referred to as the **marginal PMFs**, though their meaning and values are exactly the same as the standard PMF of the single variables $X$ and $Y$. The term *marginal* simply distinguishes them from the full joint PMF.\n",
    "\n",
    "Naturally, these notions can be extended to any number of discrete random variables $X_1, \\ldots, X_n\\hspace{1pt}$ with joint PMF\n",
    "\n",
    "$$p_{X_1,\\ldots,X_n}\\left(x_1,\\ldots,x_n\\right) = P\\left(X_1=x_1,\\ldots,X_n=x_n\\right)$$\n",
    "\n",
    "For any $X_i\\hspace{1pt}$ let $X_1, \\ldots, X_{n-1}$ be the remaining random variables from $X_1, \\ldots, X_n$ the PMF of $X_i\\hspace{1pt}$ is \n",
    "\n",
    "$$p_{X_i}\\left(x\\right) = \\sum_{x_1}\\ldots\\sum_{x_{n-1}}p_{X_1\\ldots,X_n}\\left(x_1,\\ldots,x_{n-1}\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Functions of Multiple Random Variables**\n",
    "A function $Z=g\\left(X,Y\\right)\\hspace{1pt}$ of the random variables *X* and *Y* is a random varibale with PMF\n",
    "\n",
    "$$p_Z\\left(z\\right) = \\sum_{\\left\\{ \\left(x,y\\right) \\vert g\\left(x,y\\right)=z\\right\\}} p_{X,Y}\\left(x,y\\right)$$\n",
    "\n",
    "The expected value of *Z* is\n",
    "\n",
    "$$E\\left[g\\left(X,Y\\right)\\right] = \\sum_x\\sum_y g\\left(x,y\\right) p_{X,Y}\\left(x,y\\right) $$\n",
    "\n",
    "These notions can be extended to any number of discrete random variables. Let $\\bar{X_s} = \\left\\{X_1,\\ldots,X_n\\right\\}\\hspace{1pt}$ be a set of discrete random variables with joint PMF $p_{\\bar{X_s}}\\hspace{1pt}$. Let *Z* be the random variable defined by $Z=g\\left(\\bar{X_s}\\right)\\hspace{1pt}$, then *Z* has PMF\n",
    "\n",
    "$$p_Z(z) = \\sum_{\\left\\{\\left(x_1,\\ldots,x_n\\right) \\hspace{2pt}\\vert \\hspace{2pt} g\\left(x_1,\\ldots,x_n\\right)=z\\right\\}} p_{\\bar{X_s}}\\left(x_1,\\ldots, x_n\\right)$$\n",
    "\n",
    "and the expected value of *Z* is\n",
    "\n",
    "$$E\\left[Z\\right] = E\\left[g\\left(\\bar{X_s}\\right)\\right] = \\sum_{x_1}\\ldots\\sum_{x_n}g\\left(x_1,\\ldots,x_n\\right)p_{\\bar{X_s\n",
    "}}\\left(x_1,\\ldots,x_n\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conditioning a RV on another RV**\n",
    "\n",
    "Let *X* and *Y* be two random variables. The **conditional PMF** of *X* given *Y* is \n",
    "\n",
    "$$p_{X\\vert Y} \\left(x \\vert y \\right) = \n",
    "\\frac {P\\left( X=x,Y=y \\right)} {P\\left( Y=y \\right)} = \n",
    "\\frac{P \\left( \\left\\{ X=x \\right\\} \\cap \\left\\{ Y=y \\right\\} \\right)} {P\\left( \\left\\{Y=y\\right\\} \\right)}\n",
    "= \\frac{p_{X,Y}\\left(x,y\\right)}{p_Y\\left(y\\right)}$$\n",
    "\n",
    "The conditional probability is itself a valid probability model and satisfies\n",
    "\n",
    "$$\\sum_x p_{X\\vert Y} \\left(x\\vert y\\right) = 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conditional Expectation**\n",
    "\n",
    "Let *X* and *Y* be random variables. The conditional expectation of *X* given *Y=y* is \n",
    "\n",
    "$$E\\left[X\\vert Y =y\\right] = \\sum_x x p_{X \\vert Y}\\left(x \\vert y\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Total Expectation Theorem**\n",
    "If $A_1,\\ldots,A_n\\hspace{1pt}$ is a disjoint partition of the sample space with $P\\left(A_i\\right)>0$ for all *i* then\n",
    "\n",
    "$$E[X] = \\sum_i^n P\\left(A_i\\right) E\\left[X\\vert A_i \\right]$$\n",
    "\n",
    "In words, this states that expected value of *X* is a weighted average of the expected values of *X* under the events $A_i\\hspace{1pt}$ where the weights are the probability of the events $A_i\\hspace{1pt}$ provided they form a partition of the sample space.\n",
    "\n",
    "For any event *B* with $P\\left(A_i \\cap B\\right) > 0 \\hspace{1pt}$ for all *i*, we have\n",
    "\n",
    "$$E\\left[X\\vert B \\right] = \\sum_{i=1}^n P \\left( A_i \\vert B \\right) E \\left[X \\vert A_i \\cap B \\right]$$\n",
    "\n",
    "where this has a similar interpretation as a weighted average of the expected values of *X* under the events  $A_i \\cap B\\hspace{1pt}$. Finally, we also have\n",
    "\n",
    "$$ E \\left[X \\right] = \\sum_y p_Y\\left( y \\right) E\\left[X \\vert Y=y \\right]$$\n",
    "\n",
    "which can also be intrepreted as stating that the expected value of *X* is a weighted average of the conditional expectation of *X* conditioned on *Y* where the weights are the PMF of *Y*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**\n",
    "\n",
    "Problem 33 page 128 of [1]. \n",
    "\n",
    "A coin that has probability of heads equal to *p* is tossed successively and independently until a head or tails comes twice in a row. Find the exepcted value of the number of tosses.\n",
    "\n",
    "As shown in the text, the *total expectation theorem* can be used to obtain the solution\n",
    "\n",
    "$$E\\left[X\\right] = \\frac{2+pq}{1-pq}$$\n",
    "\n",
    "where $q=1-p\\hspace{1pt}$. \n",
    "\n",
    "In particular, note that the expected value is bounded, $2\\le E\\left[X\\right]\\le 3\\hspace{1pt}$. This is observed in the simulations below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAABCUAAAGqCAYAAAA81v44AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8FHX+P/DXbMlmNySBkNAj0gRCCwgiRQxi4eRs2EVE\n",
       "71SaZ/nhFWygX793Fh6e7VSs+LV7nl2UAyUiIk2MYKEFkBZKgARI2Z3Zmd8fn0x2N43dZHZndvf1\n",
       "fDzySNmSyW422Xnt6/MeSdM0DUREREREREREMWYzewOIiIiIiIiIKDkxlCAiIiIiIiIiUzCUICIi\n",
       "IiIiIiJTMJQgIiIiIiIiIlMwlCAiIiIiIiIiUzCUICIiIiIiIiJTnDCU+Mc//oF+/fphwIABuOaa\n",
       "a+D1emOxXUREREQhqqurMXz4cOTn5yMvLw+zZ8+ud57S0lKMHz8e+fn56N+/PxYsWBD7DSUiIqKw\n",
       "NRlK7NixAy+88ALWrVuHDRs2wO/34+23347VthERERHVSk1NxdKlS1FUVIT169dj6dKlWL58ech5\n",
       "nn76aQwePBhFRUUoLCzErFmzoCiKSVtMREREJ9JkKJGRkQGn04nKykooioLKykp07tw5VttGRERE\n",
       "FMLj8QAAfD4f/H4/srKyQk7v2LEjjh49CgA4evQo2rZtC4fDEfPtJCIiovA0+V86KysLs2bNwkkn\n",
       "nQS3243zzjsPZ599du3pkiRFfQOJiIgSnaZpZm9C3FBVFUOGDEFxcTGmT5+OvLy8kNNvuukmnHXW\n",
       "WejUqROOHTuGd999t9518PkLERFRyxj53KXJpkRxcTEef/xx7NixA3v37sXx48fxxhtv1NsYvsX2\n",
       "bc6cOaZvQ7K98TbnbZ4sb7zdw3z76CNo48cbcl0UGZvNhqKiIuzevRvLli1DYWFhyOl///vfkZ+f\n",
       "j71796KoqAgzZ87EsWPH6l2P6b9DSfbGvy283ZPljbc5b/NkeDP8f3tTJ65duxYjR46srT5OnDgR\n",
       "K1asMHwjiIiI4orfL97INJmZmZgwYQLWrl0b8vUVK1bg8ssvBwD06NED3bp1w6ZNm8zYRCIiIgpD\n",
       "k6FEnz59sHLlSlRVVUHTNCxZsqReTZKIiCjpMJQwRWlpKcrKygAAVVVVWLx4MQYPHhxynj59+mDJ\n",
       "kiUAgP3792PTpk3o3r17zLeViIiIwtPkTIlBgwbhuuuuw9ChQ2Gz2TBkyBDcfPPNsdo2akRBQYHZ\n",
       "m5B0eJvHHm9zc/B2DxNDCVOUlJRgypQpUFUVqqpi8uTJGDduHObPnw8AmDp1Ku666y7ccMMNGDRo\n",
       "EFRVxSOPPFJvGCbFHv+2mIO3e+zxNo893ubxT9JasChEkqSorCkhIiKytDffBJ59FvjmmxZfFf+X\n",
       "xh5vcyIiouYz+v9ok8s3iIiIqAFsShAREREZgqEEERFRpBhKEBERERmCoQQREVGkGEoQERERGYKh\n",
       "BBERUaQYShAREREZgqEEERFRpBhKEBERERmCoQQREVGkGEoQERERGYKhBBERUaQYShAREREZgqEE\n",
       "ERFRpBhKEBERERmCoQQREVGkGEoQERERGYKhBBERUaQYShAREREZgqEEERFRpBhKEBERERmCoQQR\n",
       "EVGkGEoQERERGYKhBBERUaQYShAREREZgqEEERFRpBhKEBERERmCoQQREVGkGEoQERERGYKhBBER\n",
       "UaQYShAREREZgqEEERFRpBhKEBERERmCoQQREVGkGEoQERERGYKhBBERUaQYShAREREZgqEEERFR\n",
       "pBSFoQQRERGRARhKEBERRUoPJFTV3O0gIiIiinMMJYiIiCKlhxJsSxARERG1CEMJIiKiSDGUICIi\n",
       "IjIEQwkiIqJI6WGEopi7HdR8zz8PaJrZW0FERJT0GEoQERFFik2J+Dd1KvDTT2ZvBRERUdJjKEFE\n",
       "RBQphhKJQZbN3gIiIqKkx1CCiIgoUgwliIiIiAzBUIKIiChSDCUSA2dKEBERmY6hBBERUaQYShAR\n",
       "EREZgqEEERFRpBhKEBERERmCoQQREVGkGEokBi7fICIiMh1DCSIiokgxlCAiIiIyBEMJIiKiSDGU\n",
       "SAxsShAREZmOoQQREVGkGEoQERERGYKhBBERUaQYShAREREZgqEEERFRpBhKmKK6uhrDhw9Hfn4+\n",
       "8vLyMHv27AbPV1hYiMGDB6N///4oKCiI7UYSERFRRBxmbwAREVHcYShhitTUVCxduhQejweKomD0\n",
       "6NFYvnw5Ro8eXXuesrIyzJw5E4sWLUKXLl1QWlra+BVypgQREZHp2JQgIiKKFEMJ03g8HgCAz+eD\n",
       "3+9HVlZWyOlvvvkmLr30UnTp0gUAkJ2dHfNtJCIiovCxKUFERBQpvx9wuRhKmEBVVQwZMgTFxcWY\n",
       "Pn068vLyQk7fsmULZFnG2LFjcezYMdx2222YPHlyveuZCwAvvAAsXIiCggIu8yAiImpEYWEhCgsL\n",
       "o3b9kqY1v7soSRJacHEiIqL4NGAA8NtvwMKFQNDSgebg/9LmKS8vx3nnnYeHHnooJFC45ZZbsG7d\n",
       "Onz55ZeorKzEiBEj8Nlnn6FXr16155EkCRoArFwJDB8e820nIiKKZ0Y/d+HyDSIiokj5/UBKCpsS\n",
       "JsrMzMSECROwdu3akK/n5ubi3HPPhdvtRtu2bTFmzBj8+OOPJm0lERERnQhDCSIiokgxlDBFaWkp\n",
       "ysrKAABVVVVYvHgxBg8eHHKeiy66CMuXL4ff70dlZSVWrVpVb4kHERERWQdnShAREUWKoYQpSkpK\n",
       "MGXKFKiqClVVMXnyZIwbNw7z588HAEydOhV9+vTB+PHjMXDgQNhsNtx0002NhxJcNkNERGQ6zpQg\n",
       "IiKKVLdugNMJPPkkMH58i66K/0tjr3amxHffAaefbvbmEBERxRXOlCAiIjIbmxKJgWEQERGR6RhK\n",
       "EBERRYqhBBEREZEhGEoQERFFiqEEERERkSEYShAREUWKoURi4PINIiIi0zGUICIiihRDCSIiIiJD\n",
       "MJQgIiKKFEOJxMCmBBERkekYShAREUWKoQQRERGRIRhKEBERRYqhBBEREZEhGEoQERFFiqFEYuDy\n",
       "DSIiItMxlCAiIooUQwkiIiIiQzCUICIiioSmAaoKOJ0MJeIdmxJERESmYyhBREQUCVUFJAlwOBhK\n",
       "EBEREbUQQwkiIqJI+P2A3S7eGEoQERERtUiTocSmTZswePDg2rfMzEw8+eSTsdo2IiIi62EoQURE\n",
       "RGQYR1Mn9u7dGz/88AMAQFVVdO7cGZdccklMNoyIiMiSGEokDs6UICIiMl3YyzeWLFmCHj16IDc3\n",
       "N5rbQ0REZG0MJYiIiIgM02RTItjbb7+Na665pt7X586dW/txQUEBCgoKjNguigGf34cHlz2IB8Y+\n",
       "ENkFvV7g738H7r8/OhtGxnr4YeDmm4E2bczeEmsrLQUWLADuvNO0Tfh408fI9mRjZO7IwBfnzgX+\n",
       "+lfA7TZtu6iOFoYShYWFKCwsNH67iIiIiOKQpGkn7i76fD507twZv/zyC3JycgIXliSEcXGyqAMV\n",
       "B9DrqV4o/1t5ZBcsKQEGDBA7cWR9eXnAG28AgwebvSXWtnIlMGMGsG6daZtwy8Jb0K11N8waOSvw\n",
       "xXbtgO+/B9hSs46DB4G+fYHp08VhQe+7r0VXx/+lsSdJEjQAKCwEzjzT5K0hIiKKL0Y/dwlr+cbn\n",
       "n3+OU089NSSQoPinqAp8fl8zLqiIN4oPvL/CY4Hbyef3QVHrbIPPZ/p2UR1cvkFERERkmLBCibfe\n",
       "egtXX311tLeFYsyv+psXSvj9fCIeT2RZvFHTZNn032uf3we/VmcbfD7Tt4vqYCiRONhQISIiMt0J\n",
       "Q4mKigosWbIEEydOjMX2UAwpqgJVU+FXI3xSbYFXlCkCDCXCI8um/16zKREnGEoQERERGeaEgy7T\n",
       "0tJQytkBCUnf+fH5fXDbIhiix1AivvD+Co8Fbqd6oYTeSuL9Zy0MJYiIiIgME/YhQSnx6DXxiJdw\n",
       "cPlGfGFTIjxWXL6h3298vFkLQ4nEweUbREREpmMokcSCmxKRXVART+RUNQpbRYazQAMgLljgdqrX\n",
       "lPDVPDZ5/1kLQwkiIiIiwzCUSGItCiWC35O1sSkRHivOlGAoYU0MJYiIiIgMw1AiiekDLpu1fCP4\n",
       "PVmbBRoAcUFRTP+d9vl9oYNn9VCCjzVrYSiROLh8g4iIyHQMJZIYmxJJQNPYlAgXmxIULoYSRERE\n",
       "RIZhKJHEWjToMvg9WZc+94M7tSdmlaaExqaE5TGUSBxsShAREZmOoUQSY1MiCegNCTYlToxNCQoX\n",
       "QwkiIiIiwzCUSGIMJZIA76vwWWD2BkOJOMFQgoiIiMgwDCWSGAddJgE2JcIny6b/TnPQZZxgKEFE\n",
       "RERkGIYSSYxNiSTA+yp8iiJmcOhzOEzApkScYCiRODhTgoiIyHQMJZIYQ4kkwKZE+PTbyMSdTIYS\n",
       "cYKhROJgKEFERGQ6hhJJjEffSAIMkMKn30YmhxI8+kYcYChBREREZBiGEkmMTYkkwKZE+PTbyMTf\n",
       "azYl4gRDCSIiIiLDMJRIYhx0mQQYIIXP5KaEpmmQVZmDLuMBQwnTVFdXY/jw4cjPz0deXh5mz57d\n",
       "6HnXrFkDh8OB999/P4ZbSERERJFymL0BZB42JZIAmxLhM7kpIavi+7MpEQcYSpgmNTUVS5cuhcfj\n",
       "gaIoGD16NJYvX47Ro0eHnM/v9+Ovf/0rxo8fD62puRGcKUFERGQ6NiWSGEOJJMD7Knwm31b645Ch\n",
       "RBxQFIYSJvJ4PAAAn88Hv9+PrKyseud56qmncNlllyEnJ6fpK2MoQUREZDo2JZIYB10mATYlwmfy\n",
       "0Tf0xyEHXcYBNiVMpaoqhgwZguLiYkyfPh15eXkhp+/ZswcfffQRvvrqK6xZswaSJDV4PXMB4PXX\n",
       "ge++Q0FBAQoKCqK96URERHGpsLAQhYWFUbt+hhJJjE2JJMD7KnxsSlC4GEqYymazoaioCOXl5Tjv\n",
       "vPNQWFgYEijcfvvteOihhyBJEjRNa3T5xlwAuPZa4LzzYrHZREREcatueH///fcbev0MJZIYB10m\n",
       "ATYlwmdyU8KreMW356BL6/P7AYeDoYTJMjMzMWHCBKxduzbkidL333+Pq666CgBQWlqKzz//HE6n\n",
       "ExdeeKFJW0pERERN4UyJJFbblFDZlEhYFjjMZdww+bZiUyKOsClhmtLSUpSVlQEAqqqqsHjxYgwe\n",
       "PDjkPNu2bcP27duxfft2XHbZZXj22WcbDyQ4U4KIiMh0bEokMS7fSAL6fcSmxIlx+QaFi6GEaUpK\n",
       "SjBlyhSoqgpVVTF58mSMGzcO8+fPBwBMnTrV5C0kIiKiSDGUSGIcdJkE2JQIHwddUrgYSphmwIAB\n",
       "WLduXb2vNxZGvPLKK9HeJCIiImohLt9IYoqqwOP0sCmRyNiUCJ8FmhIepye0KeH1Ah4PH2tWw1Ai\n",
       "cXD5BhERkekYSiQxPZTQB+yFf0GGEnFDlsWOE0OJE7PATIl6oYTPx1DCihhKEBERERmGoUQS86v+\n",
       "5jUluHwjfigK4HZzpzYc+m1k4vINj9NT/+gbHg8fa1bDUCJxsClBRERkOoYSSUzRFLgdbi7fSGSy\n",
       "LEIJNiVOzAJNCbfDXb8pwVDJehhKEBERERmGoUQSY1MiCbApET5FASTJ/KZE3UGXbEpYD0MJIiIi\n",
       "IsMwlEhiHHSZBNiUCJ8sA6mpnClBJ8ZQInFw+QYREZHpGEokMUVV4HZy+UZCY1MifIpieijhdnL5\n",
       "RlzQQwmHg6EEERERUQsxlEhifo3LNxIemxLh05sSZi/f4KBL62NTgoiIiMgwDCWSmKK2YNClJPHV\n",
       "23jApkT4rNCU4KDL+MBQgoiIiMgwDCWSWIsGXbpcfDIeD9iUCJ9VmhIcdGl9waEEA6P4xpkSRERE\n",
       "pmMokcRaNOjSxFeUKQJsSoTPAk0JDrqME2xKJA6GEkRERKZjKJHEWjTo0uXijlI8YFMifPptxUGX\n",
       "dCIMJYiIiIgMw1AiibVo0CWXb8QHNiXCpzclTFy+4Xa4oWoqNP3VWy7fsCaGEkRERESGYSiRxBRV\n",
       "gcfB5RsJjU2J8OkzJcxqSqg+uOwu2CV7YK4El29YE0MJIiIiIsMwlEhiXL6RBNiUCJ8FZkqk2FNg\n",
       "t9kDSzi4fMOaGEokDs6UICIiMh1DiSTGo28kATYlwmeBo2+k2FPgsDngV+s0JfhYsxaGEomDoQQR\n",
       "EZHpGEokMUVV4HawKZHQ2JQIn8m3VW1TQmJTwvKCQwlV5Y4tERERUQswlEhiHHSZBNiUCI+midvI\n",
       "xN/rkKZE3ZkSfKxZix5KSJJ4U1Wzt4iIiIgobjGUSGL6TAlZlQPT/sO6IAddxg2TD3MZN/x+wGYD\n",
       "UlJMb0o4bI7QpgQHXVqPHkoAXMJBRERE1EIMJZKYoipw2Bxw2pyQ1QheSefyjfgRfJhLVswbpyiA\n",
       "wyF2MM1evqEPutQ0Lt+wKoYSiYN/F4mIiEzHUCKJ+VU/HDYHUuwpkS3h4PKN+CHLgNMpdri5Y9u4\n",
       "4NvJCss3VH8gKHE6+VizGoYSRERERIZhKJHEFFWBXbJHHkqwKRE/9B1bh4NzJZoSfDuZ3ZTQB136\n",
       "fGI5iYntDWoEQwkiIiIiwzCUSGL68g2GEglMbwA4nby/mqLfThZYvlE7U0IPJdhysR6GEomDyzeI\n",
       "iIhMx1Aiifm1Fizf0OcUkLUpSiCUYFOiccFNCSss39D8oaEEH2vWwlCCiIiIyDAMJZKYoiqw27h8\n",
       "I6HJsunLEuKCBWZv1Bt0yeUb1sVQInGwKUFERGQ6hhJJjIMukwCbEuEJPvqGFZoSKpsSlsZQgoiI\n",
       "iMgwDCWSWItmSqSm8tXbeBDclGAo0TgLNSU4UyIOMJQgIiIiMgxDiSTGo28kgeCmBO+vxgU3Jcxe\n",
       "vsGjb1gfQ4nEweUbREREpmMokcRaNOiSyzfiA5sS4QluSlhh+QYHXVobQwkiIiIiwzjM3gAyDwdd\n",
       "JgE2JcITfPQNk24nr+KtM+hSY1PCqhhKEBERERmGoUQS46DLJMCmRHj0poSlBl362ZSwKoYSRERE\n",
       "RIZhKJHEOOgyCbApER4LNCXqD7pUOejSqhhKJA7OlCAiIjIdQ4kkxkGXSYBNifAENyUsM+hS4fIN\n",
       "q2IokTgYShAREZmOgy6TGAddJgE2JcKj304mLZXQNI2DLuMJQwkiIiIiwzCUSGJcvpEE2JQIT/Dt\n",
       "ZMLvtV/zQ5Ik2G32oOUbPhH+cfmG9TCUICIiIjLMCUOJsrIyXHbZZejbty/y8vKwcuXKWGwXxYB+\n",
       "9A2Xw8XlG4mKTYnw6LeTSUslfH4fXHYXAAQdfcPH5RtWxVDCNNXV1Rg+fDjy8/ORl5eH2bNn1zvP\n",
       "G2+8gUGDBmHgwIEYNWoU1q9fb8KWEhERUbhOOFPitttuw/nnn4/33nsPiqKgoqIiFttFMcCjbyQB\n",
       "NiXCE3w7mfB7rS/dABB09I2aUMJmE+veVVV8TOZjKGGa1NRULF26FB6PB4qiYPTo0Vi+fDlGjx5d\n",
       "e57u3btj2bJlyMzMxBdffIGbb7658RdUOFOCiIjIdE2GEuXl5fjmm2/w6quvijM7HMjMzIzJhlH0\n",
       "NWvQpb5zlJLCV2/jAZsS4QmeKWFSU0IPJWoHXXq94nEmSYEdX4YS1sBQwlQejwcA4PP54Pf7kZWV\n",
       "FXL6iBEjaj8ePnw4du/e3fiVqWpUtpGIiIjC12QosX37duTk5OCGG27Ajz/+iFNPPRVPPPFE7RMC\n",
       "AJg7d27txwUFBSgoKDBu615+GRg9GjjlFOOukwAAqqZCgwabZIsslNCfjBv0ivJ3u77D/or9uLjP\n",
       "xS2+rnoqK4FHHwXmzIn8cvPmAffdZ/w2xZos49FV/8RtkoqUFjYlyqrL8Nza5/C30X8zaOMsRG9K\n",
       "RHEHc+5c4K9/Bdzumi/s3w+8+SZwxx31mxLBgy6BwOPN6YzKtgWbUzgHd42+Cy6HK+rfqyXuXXov\n",
       "7htzH5z26N8m9bQwlCgsLERhYaHx25UkVFXFkCFDUFxcjOnTpyMvL6/R87700ks4//zzGzxtLgC8\n",
       "9x6wcaPxz1+IiIgSSLSfuzT5spuiKFi3bh1mzJiBdevWIS0tDQ899FDIeebOnVv7Zvg/9A8+ALgW\n",
       "NCr0pRuSJEUWSiiKoQMBv9v9Hb7Y+kWLr6dB+/YB8+dHfrmSkuZdzmo0DfD78cpPr+G45mvx/fVb\n",
       "2W9YULTAmG2zGv2QoFFsSjz+uMgham3aBLz+OoD6yzdCZkoAMW1wPLHyCRyuOhyT79US//zunzjq\n",
       "PWrON29hKFFQUBDyv5MiY7PZUFRUhN27d2PZsmWNPklaunQpXn75ZTz88MMNnj4XwNwrrojO8xci\n",
       "IqIEEu3nLk2GEl26dEGXLl0wbNgwAMBll12GdevWGb4RjVIUVs6jRF+6AQApthR4/d4wL6iIJ+EG\n",
       "Dd9TVAWVcmWLr6dBvmbuiCs1O4Txrua+UjQ/VLvU4pkSiqqIneVEpIdtURoqqShAeXmdq/b5RCsH\n",
       "dZZv1B10CcR02GWlXBkX97OiKpHNwjESl29YQmZmJiZMmIC1a9fWO239+vW46aab8PHHH6NNmzYm\n",
       "bB0RERGFq8lQokOHDsjNzcXmzZsBAEuWLEG/fv1ismEAxE4Uh/NFhV8TTQkAkS/fMHAgoOyXUaVU\n",
       "tfh6GuTzNe/3R5YTI5SoefVfVmX4HbYW79TKqgxZTdDHY3BTIgo7mGVlgW9Ty+cDqsTvfpODLoGY\n",
       "DeD0q/64uZ9lVWYokYRKS0tRVvOAqqqqwuLFizF48OCQ8+zcuRMTJ07E66+/jp49ezZ9hRx0SURE\n",
       "ZLoTHn3jqaeewqRJk+Dz+dCjRw+88sorsdgugaFE1OiHAwUiDCUMbkrIqowqmaFEVNS8+i/7Zfht\n",
       "thY/lmS/DNmfoI9Hg5cl1XW4ZjVEOKFE7aBLnw/IyBDnjVFTQg8IrX4/q5oKVVMZSiShkpISTJky\n",
       "BaqqQlVVTJ48GePGjcP8miV3U6dOxQMPPIAjR45g+vTpAACn04nVq1ebudlERETUhBOGEoMGDcKa\n",
       "NWtisS31cflG1OgzJQBzmxKKqkS3KZHMyzdqXv1XVMWQpkRCL9/QmxJR2sHUQ4l6yzcaa0o0Nugy\n",
       "yvSA0Or3s759DCWSz4ABAxpcRjp16tTaj1988UW8+OKL4V0hmxJERESms/bx5diUiBpFVZoXShj8\n",
       "irJlmxKqGv87GnpTQpXht6HlTYk4qfU3i4WaEmYOuqxtSlj8ftabHAwlqMUYShAREZnO2qEEmxJR\n",
       "EzLo0sTlG1FvSqhq5Meh13+ueG9LBDUlFDYlmhblo2802pSo+RtnlUGXbEqEiaEEERERkWGsHUqw\n",
       "KRE1lhp0Gc2mBBD5zpz+OxfvoYSiiEGXfhl+W8uPvpEUMyWivHyjXlMCAKqqLDPoMl5mSuhNDoYS\n",
       "1GJsShAREZnO2qEEmxJRY5XlG1FvSgCRb2ciNSUcYimAYpfYlGhKlJsShw6J9/WaEkCDoYRpyzfY\n",
       "lAgPQwkiIiIiw1g7lGBTImqS5ugbQOS/QwnUlNBqDgmq2A1oSqgy/JofWiK+shjclIjlTAmgXihh\n",
       "l+xQNJOWb3CmRHgYSiSORPx7RkREFGesHUqwKRE1LT76hv5EvIVP6NiUiKKapgQAMejSgKZE8PuE\n",
       "EtyUiOXRNwBrLd9gUyI8DCUSB0MJIiIi01k7lGBTImpaPOjSZgMkKfIhknXEZKZEUjclRCghG3H0\n",
       "jZpXp63+KnqzxODoGy5XBE0JswZdcqZEeBhKEBERERnG2qEEmxJR0+JBl4Ahr94qqgK/5o/OThCb\n",
       "EtBqdpwUmzEzJYLfJxS9KRHFQZft2kXQlNDYlGiKqU0JTRNhLEOJxMCmBBERkemsHUqwKRE1LR50\n",
       "CRjyqrL+imdUlnCwKQHNIXacZDsMmSkBWP9V9GaJQVOiffvwj75h2qBLzpQ4MVUVLTFJEp8zlCAi\n",
       "IiJqEWuHEmxKRE2LB10ChlTK9Vc8o7KEg00JqA69KYEWhxJJ05SIUigRblPCbjNx+QabEicWvHQD\n",
       "YCgR79iUICIiMp21Qwk2JaKmxYMuAUMq5fornmxKREFwU8KmtbzVkugzJaI06FJVgfJyICcn/KaE\n",
       "aYMuOVPixBhKJBaGEkRERKazdijBpkTUtHjQJcCmhNXJMlS7HkqATYmm6EcqicIyifJyID0dSE0N\n",
       "sylhgUGXVr+PTW1KBP8NBBhKEBEREbWQdUMJreaVXTYlooIzJZqQQE0JtXamhAFNiUSfKRGl5RuH\n",
       "DwNZWeLq6zUl3G5rzZSQOVPihNiUSCxsShAREZnOuqGE/iSPTYmosNLRNwA2JaJClqHaxUNcljQ2\n",
       "JZoS3JQweAczOJSo15TIzLTW0TfYlDix4L+BAEOJZHPgALB2rdlbQURElFAcJz6LSfQdKDYlosIq\n",
       "gy5lvwy3w82mRDQoClSHCCV8RsyUUJNgpoStJqdV1cDHLXTokAglHI4GmhKtW1tu0KXb4bZ8G6Z2\n",
       "poTKpgS1ULhNiddeA44dA2bOjOxyREREdELWDSX0J+BsSkSFVQZdKqqCDFcGmxLRENyU4EyJpulN\n",
       "CSCwk2lQKNGspoSJgy4zXBmWv49Nb0owlEgc4YYL06YBlZXR3RYiIqIkZd3lG2xKRJWVZkpkpmay\n",
       "KRENsgx/TSjhk1Tjjr5h8VfRm0U/JChg+PwGPZRosCmRmQlUVlpqpkRmaqbl2zCcKUGGUdXwzqf/\n",
       "fSAiIiLDWTeUYFMiqoKPvqEv4/CrYTyxjsLRN9JT0qPblIg0lEiUpoSi1IYSso0zJZoUHLYZvFSi\n",
       "yUGXDTQlzD76RnpKuuXvYx4SlAwTblNCDyW6dYvethARESUp64YSbEpEVfCgSyCCtoTByzdkv4wM\n",
       "VwYq5SjUYr1e8T7SnblEakrUzJTw2gxoSiTyTIm6TQkDdzKDmxKNLd/w+r0hTQnNr4hXcPWd3xgt\n",
       "36iUK5HhyrD8fayHJl7FG/tvzlAisYQTSvj9QGmp+DgrS7z3mvC7R0RElKCsH0qwKREVwYMugQhC\n",
       "iWg0JVzp0Vu+Ybc3rylht8f/k05FgWqTAAA+A4++kZDLNwxelhQs4qaEzQ5Nb0lI4v6L5aDLdFe6\n",
       "5e9j2S8QzgkSAAAgAElEQVTDLtnZlKCWCyeU2Lkz8LG+3OPii6OzPUREREnIuqGE/gScTYmoCB50\n",
       "CZjYlFDl6A66TEtrXlMiLS0hmhJKzfINr4EzJaxe7W+W4KaEwTuZ4TQl6s6UsMlKYOkGwEGXdSiq\n",
       "grSUNIYS1HLhzJRwuQIf6/f1F19EZ3uIiIiSkHVDCS7fiKrgQZdAhE0JIwdd+mUxUyJaTQmPp3mD\n",
       "Lj2e+A8lFAX+mn0nWVKNa0pYvNrfLFFuSrRtG35TwmFzQPLJ9UOJWDUlUtItfx/LqgyP08NQglou\n",
       "3OUbDX1cXGz89hARESUh64YSHHQZVcGDLgFzl29kuDKiF0o0pymhKAnXlKi2+Q2bKWH1V9GbpW5T\n",
       "IkpH3winKWGXapYcBYcSMRx0GTdNCSebEmSAcEIJVQVyc8WDuKoKOPdc8fX//MeYbVi0KPR3ioiI\n",
       "KMlYN5SQ5ebNA6CwWGbQpSpH9+gbSd6UUOwS7JJdLN9o4WNJX8dv9XkDzVK3KRGF5RuRNCVMW76h\n",
       "NyUsfh/LfjYlyCDhLN/Q7/PWrcUD+sEHxdfLy1v+/X/4ARg/XmxHWVnLr4+IiCgOWTeUUBTA7WZT\n",
       "IkrqLt9w2V2mLN9gUyKKZBl+G+B2ug2ZKaGoCtxOt+VfRW+WukffMOjvjqYBR44Abdo0cLVeb0go\n",
       "4bKLdesilJBD17HHavlGPDUlOFOCjBDu8g27XTxey8rEAxoADh5s/vf1+4HqavEHQvfLL82/PiIi\n",
       "ojhm3VBClkUowaZEVFjl6BuyXxZH32BTwng1TQm3w41qyd/ypoQqw+1wW37eQLMEh20GLpU4elT8\n",
       "GXM6Izv6Rr2ZEjFYvqFpGryKF61SWln+PuZMCTJMuMs39KYEELj/jx4N//u88gowY0bg87/9Tfxx\n",
       "GDcu8LWffgr/+oiIiBKIdUMJNiWiyipH31BUJbqDLpO8KaHUNCV8UstnSiRVU8KgnUx96YZ+teEe\n",
       "fcMu+2O+fKNaqUaKPQUp9hTL38ecKUGGOVEooWnAe++Jj08/Xby324F58wIhRTjmzweefTbwf2Xd\n",
       "utDTr7sO+Pnn8K+PiIgogVg3lGBTIqqsMOjSr/ohSRLSUtLYlIgGRYFsq2lKwICmhL+mKWHxeQPN\n",
       "EqWjbwSHEiFNCU1rctClVHemRAyaElVKFdxON5x2p+XvYzYlyDAnmikhy8A99wCbNwM9e4qv2WzA\n",
       "SSeFv3yjpARYtUp8fOWVwLFjwK+/Bk5/7DHg6quBwsLwmhtEREQJxrqhBJsSUWWFQZf6XAu3w82m\n",
       "RDQENSW8bEo0re7RN6LdlNDDvbS0hpsSSuwHXVbJVXA73HDYHJa/jzlTggxzohAg+O/mKaeI93Y7\n",
       "0K4dsG1beN8j+HxZWcDAgSKoAICJE4E77gDOOANYvx546qnwt52IiChBWDeUYFMiquoOuoyoKWHQ\n",
       "K8qyKsNpc8LtdLMpEQ2KAtkOEfpICmdKNCXWTQmfT4QOqamAzwdZ9p746BuxakrYnJa/j3n0DTJM\n",
       "Q6HE5s0iIABCH3etWon3djvQpw+wc2d43+NPfxLvc3LEHIrrrw+c9v774n1amnh/223hXefPPwP/\n",
       "8z/hnZeIiMjirBtKsCkRVVZYvsGmRJTJMhSbJpoSYFOiUZoW2gAycKlEo00JPZSQJMDlgs0bOuiy\n",
       "3kyJWCzfiLemBGdKkBEaCiVGjwYGDRIfBz/u9KUefr94YJeXB77WVOPihx/E++HDxXyKJ58Un19+\n",
       "ObBoUeB8L78s3q9eDSxZ0vR2z5sH3HcfsHUrl3wQEVHcs24owaZEVFlh+Ybsl+G0R7kpkZbWvKZE\n",
       "IoQSigKfraYpAQOaEok6U0JvSUiS+DxKgy4bbEoAgNsNuzd0+YbDhEGXnCkRJoYSiaWhmRLBh+MN\n",
       "DiVOO028b9NGPKDT0kQwAYg5E/rHdd1+OzB3LvDqq+Lzw4eBW28F3n0XOPfcwPluuEH8Pg0fDpxz\n",
       "TuPbvHYtsGCB+LhXL+CJJ0JP1zTrBhWqGttt0zRx6FUiIrI064YSbEpElRUOCRrVpoSqim3zeNiU\n",
       "cLoho2an6URD3ZqQsE0JWQ4EbYDhyzfatm3gaoNCCc3thtMXCAntkh02NiWaxKYEGaahHeTU1MDH\n",
       "igJ07CjO5/Hgq21f4i/f3CdOa9sWOHQocN7duxv+HtXVYumGnlACwDPPNHze4N+l4GGYda8PALKz\n",
       "xfvly0WzQv/7npIivp/V/PyzeLzYbMD+/dH7PkuWAEVFQHGx+F5ut/je770n7sfiYuuGNkREScq6\n",
       "oYQsiycGisJ/HlFghUOCRnWmhCyLJ2YhL09HcNkEmSnhs2mBORDNuS2CJOxMCUUJDLkEojbosvGm\n",
       "RCoyVCekmqaGw+aAQzGxKREnMyU46JIMEU4oERRajn99PB5d8aj45Ngx4NNPA2HAvn31r+v110WD\n",
       "Qm9fvPaaeD97dsPbc/vtgY/z8oAjR+qf57PPxB+WX38VAzP/8x/RrDj5ZOCll8Q2Hzokts/pBN58\n",
       "s+HvFUsvvgj07x/4vEMHYM0aMb8DEH8sm/tcb9MmYNo04PvvxVKZc84BBg8OHC1FksT3vvxyID1d\n",
       "fN1mA0aMaFFQzxfNiIiMY91QQp8+zyd8UWGFQZdRbUroO33N2cYEakrINUffUNSa+60FoQSbEpGr\n",
       "G0o01JRQU1OR4Q98f3H0jQZCCTYlaimqUrt8Q4t1aM1QIrE0tFPqdgc+rhNK5OXkiYtpKlBaKo6c\n",
       "oT829+ypf12TJwNvvRUIJSZOFLMjHnig4e355z9Dd86D2xUAUFEBPPSQ+OOSnS127nW7dgE33ig+\n",
       "HjUKyMgQ23bddQ1/r+aaPRv4978ju8xNN4n3v/0G/PKL+Pi004DevcWhVdu2FctWwuX3i/PPnw8U\n",
       "FIj3Q4cCQ4aI0+fMAWbNErelqormxMaN4vZLTxfLZn75BTjrLHF/VFcDX34pAowbbgC6dweuuQb4\n",
       "xz9EoNLQ74nTKYaW2u3AH/4gfh/4IhoRUbNYN5TQdxRauCNFDWto0KXX7w3jgsYt39BnSqQ6UiH7\n",
       "ZfhVA5/Y6zt9zW1KJEIoEdyU8Mt19oojVztTwuKvokesoaZElAZdhjQlanZS1FQX0tXA97fb7LAr\n",
       "auyXbyhV8Dg9cTNTwmV3wW6zw6/FOBBgKGGq6upqDB8+HPn5+cjLy8PsRhoHt956K3r16oVBgwbh\n",
       "B33QZEMibEqc1lnMlTjqPRo4jx44vPuuCB30o3IE78jq5/F4xE7vibzwQuDj228XO8vHjgWaFA8+\n",
       "GDj92WfFnAndqFHA734nPj7jjMAOvM/XvJ3mw4eBqqAXDh56CLjiCnFde/ee+PL6ZTduBE46Cejb\n",
       "V+zA/+lP4udq106cvmYNcO+99S//7rvifPpbbq64T1avFg2JfftEa2TlSnFbbNkiZnjMmxe4jkGD\n",
       "RACiaeIIKIsWiTAkKwv44x9FEHX22eK8CxYA27eLMOmuu0Sg0qdP4P788MPADKJXXxVfX7xYLJmx\n",
       "2cRpTqe4jVatEmFV796hS32IiCiEdUMJfUehhTtS1DArDLrUmxKSJCHVkYpqxcBhVC1tSiTC8g1Z\n",
       "hiypbEqcSENNCYN2Mg8dCqcp4UKGP7CTKwZdqrFfviGL5Rvx0pRw2Bzh/90yUt1QIgb3DQWkpqZi\n",
       "6dKlKCoqwvr167F06VIsX7485DwLFy7E1q1bsWXLFjz//POYPn1641fY0E56cFNi1Sqxk1tDf2wc\n",
       "qToCTJkSernVq4EPPgDOP198fvx48IaH9fPVuvFG4NGaZSL6IMuMDPGqPRC6FGLaNODUUwMDLpcv\n",
       "B+6+W+wsL1sW2LZZs8ROc2MtjYb4/aLF4PGIHXA9YOjcWSyR6NxZNA70IZ/l5aJxcNVVYtnIzz+L\n",
       "7dFDAV3btuIoJN6aF0NGjRLLUB58UOzUf/ih2H6XC7jyytBt2r0buOgi8X3eekvcP336iOBl2rTA\n",
       "so0TSUkR33PjRvH56NFAZWVgOGZFhVhesn+/+Pm7dwceewy4+WZx/qeeEgHHli0iiLrlFmDYMBFO\n",
       "aJpok5x+OtCli7ie7GzgjTeAV14J//YnIkoSjhOfxSRsSkSVFZZv6DMlALHEoEqpQlpKWrOvLwSb\n",
       "EoAs15kpkdri+8vtcKO8upEJ8/FKlkObElFavlGvKREUSqTXWb7R4EyJGDQl3I74mSnhtDtr/255\n",
       "nJ7YfXM2JUzn8Yj72+fzwe/3I6vOEoePP/4YU2oCg+HDh6OsrAz79+9H+/bt61/ZiZoS+mE6a+jN\n",
       "nCPVR9BtwYLAETUA8co7IHbEAeDrrwOnBT+ew3XnnWLHdvXq+qeVlJz48vqr+ZWVYjv1cGbOHNFw\n",
       "eO65hi+3f78IZjIyxKv9uuuvD9wen34qQgkA6Ncv9PIXXAB88gnwzjvi80ceaTwocDpD74PPPxct\n",
       "j0suCXxt7dpA6KL/TEaRpECDIpjebOnVS7xfvFjM7Jg1S3z+3nvApZeKj9PTxfunnqp//UuXiiUi\n",
       "jz8uftZrrxVf/8MfxBFYHn/c+J+JiCgOsSmRpKx09A2g5rCVRg67DG5KRBpKJEpTQlHgk0QoYVhT\n",
       "wpGATYk69Wyjlkpomggl2rQRnzc26NKfmoJWQU0Ju2SHw4zlG3LgkKBWv49lVbZOUyIG9w2FUlUV\n",
       "+fn5aN++PcaOHYu8vLyQ0/fs2YPc3Nzaz7t06YLdDRwZYy6AOV99hfTz0nHjkzcGTqgJJS546wKo\n",
       "WW1CLhPSlGjK7bcDF14Y+Pzo0cbP25TCwvpf+9e/gEmTwr8Ot1s0CP71L+Dhh8XX5s8PhCh1degA\n",
       "ZGaKZQfvvy9mUmRmitOWLRNzMvLzxQ7100/Xn3vxySehn//lL6JlEI7x48Ufz9//Xny+erUIJABz\n",
       "d95zckRzYtcu8fdbDyROZOxY8Yf/1luBGTOAFStEa+Lss0VTxOUS/38eeww4cAD473/F+Y4fj//n\n",
       "IESUUAoLCzF37tzaN6NZN5RgUyKqLHH0jZpXO4FAU8IwwU2JSHcYEqgp4bWJ5RuGzZRwJuBMiYaa\n",
       "Ega88l1RIa5Wf9G1sUOCKq4UpPkDf4ptkg1OP6BGYZuaUilX1g66tPpMCUVV4LQ5rRNKsCkRUzab\n",
       "DUVFRdi9ezeWLVuGwgZ23OsOQJUa2KGdC+Du0SNxfORxvHTkpcAJNcs3Pt38KY5fPAEYOLD2JH32\n",
       "0bYj20KvrO426Esu9FfG24SGG2Fzu8USh61bA8szZswIvDofiRkzRECg3zYzZoj3ZWWBeQ3z5wfO\n",
       "36WLeD9rljiP1yte9deXldx2GzBzplinpm+bqoq5Gnv3isfFn/4kzhs8kDMc//mPWBIxbFjkP2c0\n",
       "dekS+v8iHA5HIFAZMUK0LxYvFktE5s0TAzpnzQLatwfOO0/MxUhPF4GFPrsjEqtWifkjREQGKigo\n",
       "SOJQgk2JqGlo0KXZTYlKubLZ11UPmxKAooiZEgY3Jay+wxqxuk0Jg5ZKBC/dABpvSiguJ9KCmhKS\n",
       "JMHll6A5jW9vNCXelm9YqinBUMIUmZmZmDBhAtYGD3kE0LlzZ+zatav28927d6Nz584NX4nWwFEV\n",
       "apLEFAWoliuxNv0YpPvFTqWiKkh1pGLvsZoBj0uWiPd12wK68nLx+6EPUWyOlBSgR4/mX74h330n\n",
       "liD88ENoYDJtmnivhwlAIJRJSRFzHBpaBqOTJBEodOwo5lc8+aRoXAQf6jQcKSlioGUic7lEg2Ll\n",
       "ShE8FBeLZojfL8KY3Fxg4UJxO156KfD//h9w5pniNnY4xIDOO+4QX//gA9F8ufZaMcciIwMYN07M\n",
       "3yAiigPWnSmhL99gUyIqrDDost5MiWgs30j2poSkItWRCr/mh+Z0Qmrmjq2maZBVGamOVMtX+yNW\n",
       "tylh0E5m3VCi8aaEE2nVoa/ipqo2qClO2IMvHO1Bl0oVOrTqEDeDLoNnSsQUQwlTlZaWwuFwoHXr\n",
       "1qiqqsLixYsxZ86ckPNceOGFePrpp3HVVVdh5cqVaN26dcPzJABoDR3qsWaeQPGTQOU/jmFL+fba\n",
       "kxRVwdBOQ1HurZmtM26cODpEXp54dXv4cLFD+P774vQNG8ROpdUMHw6ccorYqe3bV7QbFAX4+GMR\n",
       "VLhcYgZFuMsumtKpU8uvIxl07x64vfU5IhUVIij67rvA79Q114jnKMFHaPnnPwMf/+lP4r6bNEm0\n",
       "Mk4+WcwV2blTDCCdMkUMFlWU5jd4iIgMZt1QQpbFq9VsSkSFYYMuK5vfbqg3UyIayzea25Rwu8Xl\n",
       "ojFYK1YUBT5JhdPuFLezw97sgE/VVNgkG1wOl+VfRY9YFJsSbdsGPm+sKSG7HPAcD91pSVUlqI46\n",
       "R3iIxUwJhztuDgnKpkRyKikpwZQpU6CqKlRVxeTJkzFu3DjMr1l2MHXqVJx//vlYuHAhevbsibS0\n",
       "NLzS1NEOGmpK1NyfXY4CWz56H6lBDz2/5ke7tHY4VBV0eMfLLxfvd+wQj+tHHgnsQGZktOCnjSJJ\n",
       "Eofg1GdFXHGFaEQ89FDgPH37mrNtFJCWBrz2mvhYX8ahPyeZP1/8rkqSOILIunUiXEqrGRi+bp04\n",
       "Osk114jDmvbuLZbvvP124Pq7dBENi1deAa6+OnY/VwxpmobdR3cjNzMX7/3yHoZ3Ho7czARv4ViJ\n",
       "/jx64ULgiy/E0Xp69BDLwbKzxd+ds84SR/KRJHH+H34QYa7fL5Y5ZWSII/IsXSqOktOpk5g/c+yY\n",
       "uI6MDNE42rVLBMGjRolWUWUl8NVXotE2dqz4+9ynj3gOlp4ODBhg9q1DQawbSrApEVVWGHRZb6aE\n",
       "lZoSwUfuaM7UdCuQZVTb/HDaRCihOhywN/P+0ncCnTbrD0GMWENNiSgs32isKSGnOOBRQoMvlyrB\n",
       "74ztMMUqJb4OCcqZEslpwIABWLduXb2vT506NeTzp59+Oqzr09QG1usHteR6/fd71Bx/AZ9t/gyK\n",
       "qqBzemfsOban/uX0B/z2mmbFpZeKYZBRctx3HAOeHYAdZTtw4M4DyEnLiewKMjLEfIg//9n45SEU\n",
       "kd/KfsOKXStw9YDGgwENwNbDWwEAvdr2ql3GUa1Uw97nFFT1zEWGKw2HKg/hubXP4bbTb8OiQSkY\n",
       "fLgY3dt0h6ZpkGbNEv/zbDax43fLLSKY+stfxCFcX3hB7Cw++ihwxhlix08PrlqgSq7Chxs/xJX9\n",
       "r4RNCq85tKl0E97Y8AbuOuMucVQqW2S7LMe8x3Dv0nvxzJpnIKsyOrbqiJLjJWiV0goD2g3A1sNb\n",
       "cbDyIK4bdB2eHP8kMlNb/nMmFUUBiopEqNW1K1BaKv4Gbt8OfPaZaJDZbGLmTHq6CBCGDhUBqNMp\n",
       "livJsgjd9MMrjx0r/qcuWRL439q7t7juc84Rh+Ndu1aEE9Oni/Pk5AD79olWUEoKvN4KHF2xBFnX\n",
       "boZNVuAdPQKunXsgHTgAbNok/u6lpAB79kBuk4Fj7VrDI0uwuVw43qc73mt/GIezPcjpMRBdTuoH\n",
       "d1pr9MzqiQxXBtKcafXmE9V9kTemvF5xmOGOHcWrYAsWiNs/NVV8TdPEAN1evUTrqmNHoF070ZrK\n",
       "zhYBZqtWIiwaNEgszWvTRoQ6aWkxb/lZN5TQB12yKREVVhh0qe9YABZqSmhaYKcjJSVk5zHuKAq8\n",
       "8NeGCVoLmhL6fRUPQxAj1lBTIgrLNxptSqTY4a7zJ87ll6A6jd+mptQ2JThTomkMJRJLQ02JRpbu\n",
       "/f4tcUSIe8fci2W/LUNZdRlap7ZGpVyJ9355D4uKF+HNDW9iZ84fkAuInbwo/v9475f3sKNsBwCg\n",
       "3bx2UO9TGxzo2aQ77xRvLeTz+2CX7CEvdlB9j698HHcsugOPnvMoUh2pOK/HeeiR1QOzv5yNt356\n",
       "Cyt2r8CEXhMw9uSxcDlctZf7oeQH3PjJjVhXEgjkRnQZgU+v+RSnv3g6thzeUu973bP0nnpfe/Xi\n",
       "V7GrfBeeWPUEFl27CINXrhQnbNkimhIdOwbOvHy5WO4BAGPGiJ3JmTNP/EMuXAhMmIAjXbJRfspJ\n",
       "yEUG/u/YMjw0UsU1ba5BjicHT5//NBYVL4LL7sKo3FE4v9f5kCQJZdVlOLn1ydh8aDNu+uQmfLPz\n",
       "G8xf+D8oTwXuPedBVClVKPeW44JTLsC5Pc4FABz1HsWd/70TfbP7Ykf5DlT4KrCxdCO+3fVt7SZt\n",
       "umUTyqvL0bV1V+ws34l5K+ahfav2OL3z6fi+5HsMem4Q7hlzD0bmjkReTl5jP1lyKC0Vgdf27eI5\n",
       "sc0mZpP897/QAEg7d4rlRIcCbTEtNRXw+aB27ABb+VEoY0aj+pnHkT54OJCZCd+BfdjUqhopGW3Q\n",
       "vU332hckdYfLSrDk3YexZ+UiHPaWofiF8WjVPhddMrrA5/ch05WJXUd3Icu9Ec4L2+CYz4GU6/+M\n",
       "lLQMbD60Ge+uew1DurZFlqctPtvyGQAgf1J/eJVq7Pf9jPSUdOR3cMPjHIn+7frjmO8Ylmz5L+zf\n",
       "r0O/A0BVxxykVlSj88ZluOibLHQ7aofryAdwVvmwvbMHR6or0apMw7JTMnB4QA9859iHMnihdGyH\n",
       "11I2YljXEchJy0Gb1DY4q9tZsEk27D++H2kpaRjScQgGtBuATYc2YVPpJpze5XR0TO+IFHud/w37\n",
       "94sVAh5P6HMMnf5/ST8yj9MpluB5vcBpp4lw6OBB4P77RUBRUiKux+EQTarNm8X9WlQknpwWF4sW\n",
       "SmmpCDFsNvHY9fnE4az1faAxY0RoNGYM0K2bOJ+mRWXf3LqhBJsSUWXY8o2WNCVqXn0HLNSU0H8+\n",
       "SQo8IONVzUwJffmG1oL7S98JjIfDRUasoaNvRKEpoQfOqgrYgkIJX4od7jp/4lyqBH+sl2/EW1OC\n",
       "MyXICA3NlDjB3/0cTw5+Lf0Vp794OjbeshEzF87EgqIFtad/8LvuuHX8oqgH2rcsvAUAcH/B/ZhT\n",
       "OAebDm1Cn+w+Uf2ewVRNxciXRuKG/Bsw7bNp6JTeCbvv2B1xMFK4oxBjXx2LgpML8NV1X0UerFjM\n",
       "1zu+RlpKGooPF+P1Da/juoHX4dtd36Lg5ALcsegOAMCfF/+53uXev+J9THx3Ip5eHWj5XJ9/PYZ1\n",
       "GoaZC0UYMHPYTFzY+0Lct/Q+rCtZh7aPiDWC/3vW/+KkzJPw5KonMSJ3BO4bcx+WbFuCy/IuQ1l1\n",
       "GZ5e/TTat2qPf678J4r2FcHj9GDI80Mwvud4zDtnHvJ65kFauxbav/8NacMG4J57xO/vZ58B06bB\n",
       "K/nhuuUW4KOPgAceAD7/HBg5UgzVfOcdcfSZt94K+XlWpZZC3XMY72ar6HEcKH6tDfZ1SEeVpOCW\n",
       "H6/EyWWA1w502PAsNspA3kHgZK+4rK8dsOwAoKWnQ6o5ksjm5+7FPWM1HO7fo/Y2OqvbWSjaV4Tu\n",
       "bbpjzd41yM3IxRdbv8ApbU/BfWfeh3vOuKfeDnC7tHZ4+7K3Q7728aaP8eiKRzHt02nI9mRjeJfh\n",
       "mDJoCi7uc3HYzY5o0zQNkiyLQACAf/2POPzZv2Hv2h3u/3yEar8Xb+Tb8GI/H1pVKeg65gKodjv2\n",
       "+8ux59gejD+QgX4lfpxx0a3oMXYiUr5YLGbh9OkDVFdj6zvPIvXuOeiy9zi8qU74unZB6sEjcB4u\n",
       "Q1m6E1vSZfzYAcg583x0n/kY1MoKnHL2lVhS8i0uf/1CaAB8DjEAWMIitNr+LfKr8jG001D8c2Vg\n",
       "5kl6Sjq6tu6KbUe24Xc9f4f//PofpDpS0b9df5x77USMOWkM8n3HcaDiAHaU78DO8p1ol9YOu47u\n",
       "Qll1GdJd6fA4PdhauQfZyEbf7L5YfOMy/LDvB+w5tgd3nXEXRuaODLntvt/7PdbvX4+y6jL8fPBn\n",
       "bD28FWf1PBs3Xv42Tm59cu3vSIWvAmkpaYELer3os24dFEWG3LkDct58Bukrv8HpSnekKBrsa0rw\n",
       "wsG2kO1bUN75MMpaObC2+0/4enh7OI8exzf2PXCkpWP4Z0U4pxjoXAFsswH/zQL25uVi6C4FLlcr\n",
       "ZG3biyFbKwAAqgRs7Z0Db6oTFaoXHY+q2O+oRt/dXrhlDQ6/huq2mbAfr0Rpn5PwybO3o0ytxDc7\n",
       "v8HWwwpKjvwVuWourhh4BTpndIZX8UIZ1A3ZnmEY0H4AerTpAbfTDa/ihc/vw+Gqw9h0aBNyM3KR\n",
       "7clGTloOdhzcgk4VNjj37od08CDw6qvA/fdDqxkgrUmAraGWYQtZN5QIbkowlDCcFY6+EbJ8wypN\n",
       "Cf33Doj/UEJRUG3z14YJLW5K1IQbVn8VPWJ1mxIGLt/Izg79mv7nzBUUSngbaEqk+CUojhgv36hp\n",
       "SuihhKZplt054EwJMkrdQ4cCaPDvfru0djhQcQAAMLTTUADApkObACAkkACA37TDwLnnGraN+mFI\n",
       "67YQLuh9AX7f6/eYNHASth3ZhjGvjMG+O/fFZCfquO840v8hDku6as8qsX2SHYOeG4Q/Dv4jbl90\n",
       "O67qfxXeujSwo6rPJqrr8n+LmRyFOwox8LmB2DB9Q8jpL657ERf3uRjZnux6l4224L+DessBAMb3\n",
       "HI9JAybhL4v/gpLjJcjvkI9TO56KRcWLsPto6BEvPt38KQDgiVVPYESXEfj2D9/C5/dB1VRsOrQJ\n",
       "cwvnwmFz4JK+l0Cbo8Gv+nHXV3fhkW8fwS8Hf6n9/fLd46t9zqS3BH4o+QEp9hT0a9cPAHDtwGtr\n",
       "v++V/a8EALT1tMWcAjEMduqpU+Hz++ByuLD/+H7cu/Re9H+2P7q36Y6eWT2xcvdKZLXNwmflV+FA\n",
       "xQEMO6cAkx49FR9t+ghX3Xgxrv/vAZw3YkSDt1W5C9iUDbx1dgd0nfoXTB06DW6nGyOqjqDcWw7b\n",
       "QRmdpk0Ddu7Ewg/TIFVUiFeFKyuhDB4Ee0F/+C+9DNu+eg+dKgEs/gZSdjZw3XXAmWei59df493b\n",
       "bwf+XQzfjGn4+Lyu+I+vCBP7TsRj5z6GdFedw+QqCmAPbzfnwt4X4sLeF+JQ5SE89O1DKD5cjGmf\n",
       "TtS/pzgAACAASURBVMOl716K9mnt0b9dfxz1HoXD5sC0odPQL6cfVE3FsM6RHbK2wleBwh2FGNB+\n",
       "ACRIobMtDh8G/H7I112LfVkpyPjqW/zauy20vD5I3XsQhzaswtlBRyL+qrcTv7STkLF6Ocr7peDQ\n",
       "qMGYsjMLUz5ehyrNh3YvfwIA2JllR2paJrJKtuLHvlnwf3YjUkpuwBG3BLdfQqpPBLM9Aawq6IXX\n",
       "/nEmytpl4PPti7G/ogIHKoCLep+PoZ2GYuzJY0Wj57fH4df8+PWJ2yCrMv447I+4v+B+tEtrB6/f\n",
       "C7/qhyRJWLFrBQp3FOLuM+7Gg2c9CEAsVSraV4QUewr2HNuDO0feiW6tu6F9qyaO6hOGM7qe0ehp\n",
       "p3Y6Fad2OvWE1xESSABi4O+IEXBA7DDn3dPAcrwtW2D/8kukdu+O9keOoPfChZh0x7uBWRieCmAf\n",
       "UL3gJaSe1A3VWzdiyP690L5djoPt7SKo6z8Iy4YNw47e7ZDm1ZCxbBUOHtiOLp36YO2va9EzNx+7\n",
       "Ro/BKv9OrN6yFMXpCo56j6J7m+5I2b8WqY5U/K7n75CXk4cUewr2H9+Pb3d9i1+3/YrjvuPomN4R\n",
       "xYeL8cvBX1DuLUevrF74cf+PtT/CwPYDUa1Uo+RYCQDgmO8Y2qW1Q7VSjRxPDrLPz0b1uW2w80Ap\n",
       "xnYcAXdGW2w/uBn4U1E4d03YrBtK6E0JLt+ICiscfSNk0KWVmhL6q+bxHkrIMrwQMyWcNifUFuzY\n",
       "6kdKSYqZEgYtlTh0SDTrgumFB1dIU8KGVDl0x8jlB1RnnaZEDI6+4Xa6IUkS7JJd/I2QrPkvgjMl\n",
       "yDBhNCVevef3GNCuCl9u/xLn9jgXQzoOAQB0bNWx/mUBlFWXGbqJYxaMQY4nBx9e9WHI14v2FWHG\n",
       "0BkAgMkDJ+PVH1+F/QE7vv3DtxjRZYRhoeL3e7/HKW1PCdnp0wOJcd3G4cvtX+Lhsx/G2JPH4rQX\n",
       "T8Pti8ThP9/+6W3MOXMO+mT3wTe/fYMxC8bgp+k/1e5AA8CbG95EaWUpDv3lEMqqy9DjyR741+p/\n",
       "YdLASXDYHLXf56ZPbsIbE9/A1f2vjklYqmkabv3iVjy9+mlc1f8q7D66G8t3LgcgQqkvtn6BL7Z+\n",
       "AQC4st+VeOfnd1C0L/AE/fubv0eVXIV+7fpB0zS0Tm2Ncm85Wqe2BoDapRn5HfLr3a92mx0Pn/0w\n",
       "Hj77YQCAV/GGLOUINrjj4Ih+LkmSaq+rfav2eP6C5/H4+Mcx9dOpeH3967g+/3r8fOBn9HumX8jl\n",
       "Hjn7Eby+4XWM77EeV70yAQekSvz801L0PAyUZLuwzePFY+c+hhnDZuC0Otvaxt0GbdxtgNYQh5QF\n",
       "IJWViSGENUdm0f/T2AH0uvjiBrfdlp8vjiyyYQNSLroIlz3zGy4DxLDOMZXin+uECeJ/6zXXiIp5\n",
       "27bin7HNBkyeLE7v108cqveuu4D+/cXypdatgUWL0HbiRDx6zqMAxO/AOz+/g0xXJvYd34cth7dg\n",
       "R9kO/HXJXzFy9T54ZKC0U2vcNGwazho1Cb6cLGwv+RX/9+vbuHjgFeiY3hF9s/ti9pezUaVUYVTu\n",
       "KEx552q4/ECvQ8BVPwE9UzvC2bEL2mwvwagVIsxyAlg8GBglA5sVGZmrS1AJBbkTLsLe867GBzml\n",
       "AIB+7frhtpMLapfUBjdC0gFRz5cknLRvnxj+2LkzTv29WIJW8usalGY6sfnQZjy/5GGs3r8OM8bM\n",
       "wv+ePw/Da67j4Zrb4NfSX9E3u2/t427USaNqv48e1HicntqvBW/H+J7jMb7n+JD7sWvrrujaumuD\n",
       "93Fc6tVLvOmuvFIMjq2oEL+TBw8CGRlI7dABAJA6dixSa87aGkDQJTFG/+D0Gxr8VnkAbjinfsuq\n",
       "IZf0vaTBrx/1HsXK3SuR4crAsE7DQsJuTdOw6+gutE5tjdLKUngVL475jsHn90H2yxjeZXjIfS39\n",
       "ydi/xdZ8xgkEXrHm8o2osMSgy+BDgrIpYTxFQbXkrx0QpTpb1pTQrycpZkpEYfkGEFT8Cgolqp02\n",
       "ZNQJJVJUCYoz6BXFGDYlANQegcO04U0nwJkSZBQNdZoSP/4IfPJJyJeud3yKy9yXAQAWFy+Gy+HC\n",
       "pAGTsOHAhnpNi4fPfhir96w2bvs0DSt2rQAgGhO3fnErnlnzDD688kNsLN2I/A75AIBx3cfhkj6X\n",
       "4IONH2DUy6Ow4g8rMCK34Ve0IzX0haG4ot8VyHJnoVvrbqhWqtG9TXfccfoduGnITSE7zOV/K8cN\n",
       "H92A9399H3eOvBN9/9UXa25agzELxNPtGQtnoHBKISRJwpJtSzDp/UkAgCx3FrLcWVh38zqc+/q5\n",
       "uOXzW2qv84JTLsAnmz/BpPcnYdL7k2qHem49vBU9s3oa8jMGk+4PPNEe2mko3v4pUPXX5gTu78NV\n",
       "h5HmTIPL4cLbl72NKrkKqqbCYXM0GCLogUSkGgskjOJxevDaJa/htUteq/3a9iPbkZaShs2HNuOY\n",
       "9xh+1+t3+POo0J2haqUav5X9hp5ZPSOfJdK6tXiLlM0mBvLt2CHW0v/jH2Lne/du4LffAsMVNU0M\n",
       "/duyRRyF5OSTxbr5l18WQ/0AYMQI4MgRcX3lNYf4TUkRy1MGDoR01lm4qqIbsODfIrzw5ANFgD91\n",
       "GuzvzoUmSZC0MgAP1bwB7QAMB/DOqa/ju7Yahv4mY9ZuFe0rgIOtn4e3Jq/U0tLg79kdyvotOOIp\n",
       "x4/Du+KZhfdjm60cN/SfjBs6DYIkSejdwE1Qd6pH3eUptfThtd27i6U2QTr2HYaOAAZ0yselA65o\n",
       "9OaWJKnJGRsZLoseXchsNpsY7glY7rC7Ga6M2qZVXZIk4aTMk2rPF2vWfMYJsCkRZVYZdBnSlIhG\n",
       "KMGmBJx2J5x2J1SbrUUzJfTrSfimhEE7mQ2FErV5R/DyDacEly/01doUP+rPlIhRUwKA5edKcKYE\n",
       "GWXdnrVA0HNG+dtlaOgpfquUVgACIcbfx/0do14eVbucrWhqEfLn5yMvJw///uXfLdomRVXw+ZbP\n",
       "0b1N95AlC0OeH4L1+9cDAC5+R7yaHNxemD16Nj7Y+AFG5o7E6xteDwklmrsc65vfvgEAvPvzu/VO\n",
       "O7fHufV2mDNcGXjtktdw9xl3o1dWL8xbMQ/DXhAV90N/OYS2j7SF7QEbKu6qwDmvnQMA2DhzY+3l\n",
       "B3ccjAt7X4iXf3gZADD3zLm1Sw/2HN2DYS8MQ7t57WrPn+pIReVdlYa1J+78rxj62TWzK1668CWM\n",
       "6z4Oas0wVH35ji7LHfoHXv/7mQi6tekGQCxbakyqIxW9sxvabY4RlwuYOzfyyx05IkKIk08Wn+/d\n",
       "CyxaJJoUH30k5mls3CiGfpaUiNBi2TLxtUGDYLfbge++g3T66eJ/eWUlju0qRkpGG9i2bIHzeBWu\n",
       "/Ppr4IcfoBzaAPnvdwMlB5HTv784BGXXrpA8HjicTjgAdKx5I0p21g0l2JSIKksMuqwzU+Jw1eFm\n",
       "X1c9bEoAioIqKdBwUB22Zj+W9DX8STFTwuEQawFb6IRNiVZiJ6faKcEl1w8llFgPugxuSlj8CByc\n",
       "KUFGWbN7NdBffPziV/Pw0yd/xuMAzvyjHV+/5EdlTUKR4wk93Gb7tPbYf3w/jvuOI9OViUEdBmHj\n",
       "zI1Id6Vj7d61KDlWgo7p4e1qlFWX4deDv+Lhbx+GTbKh+Ehxbfig6922d+3Xpgyagld/fLXe9Qzt\n",
       "NBRfTPoCOWk5GPr8UEw9dSoGth+INXvW4LQXT8ONQ27ECxe8ENHts7F0I/Jy8nD3GXejb3ZfTHhz\n",
       "Au4+427c8vkt6JXVq8HLeJye2iUupX8uRb9n+qH41mKkpaTh+5u/x6nPn4q0v4u120f/drTeLIC5\n",
       "Z86F2+HG0+eHHta1c0Zn7Pl/e2B7QLTIxp48Fkt3LMW4/xuHL6/7stnBRNfHu2LmsJm4/+v7USlX\n",
       "Yt458zBr5Kza0/U5GB1adWjW9ZPFtGkT+up1p07ADTV1+UsvBSZOFEtL9CMRXHONGH7ekJQUICUF\n",
       "6a1r5hV07S7e1yxB0WcRENGJWfexwqZEVFlh0GVIU8Lo5RteL5sSsgyvFDxTovlNCX0Nf1LMlDBw\n",
       "0GU4TYlKJ+Dyhe7UilAi6ElQLJZvxFtTomamhFfxxvab+/2hR1VgKBHXgnc1LrngL7ixUnxcbRP3\n",
       "aUmGDYCKDFcGUh2pqFZEYOlyuJCWkobdR3fXrrHtnd27dijllsNbwg4lHvvuMfzPsv8JGaZZV/tW\n",
       "7WsHa04eOBnbjmyrFxxKkoTzep4HQDQ6Bj03CBV3VeC0F08DIAZGXnDKBTjqPYrcjFy0cbdBx1Yd\n",
       "kZMWGrjo7v7q/7N35vGO1GW6f2rLdvac3je2Zu9uugVENmlEQBEFBBwXFlERRhz3cYHrFXAGx2VE\n",
       "kEHwul3tkQFx7rCIiIiNCIgioIIKCEI3NHTTJ33WLLXeP36ppFJbKklVpZLzfj+f8znnJJWqSi1J\n",
       "/Z563ue9BPdvuR9nrT0L71z7TgDAto+zdP2LXh2gNSRYyOLLn3i59v+rlr4K5UvKWPW1VdhV2uUM\n",
       "JwSwcmSlQ5Cwvkfls+x9i7yIx3c8jrXfWAv+ch5nrzsb33jTNzBRmqhZkP14cOuDOOI7zNb+qbs/\n",
       "BQA4ca8TGwQJYh7CccDAAHDmmd1eE4KYVyRXlCCnRKQkIeiyIVMiyqDLTpwSlZgHPGFRDW+rGHWn\n",
       "hNZB9w2zhr9vMyUiCLosFFjGlhW3TImSCKTs5RuqEX/5hkumRFIxXVbklCA6hbdEQowX6/9Uqrt4\n",
       "SGGyBQdWa/vUxFO1aRbmFuLETSfi5dn6oFvgBZy8z8nYWdwZeB0WD7DUebsg8bYD34abnrgJBy89\n",
       "GD8680e49clbcfSqo7Hvgn2xcfeNvsKheW6YjoRPH/VpPPTCQzjlv05pmO6IlUfg/vfc3/DYZZsv\n",
       "w6X3Xlr7/11r3xX4vQQhLabx1AefwlRlqq3XW69d1ixag/vfcz+O/M6R+MEff4Af/PEHDdPuObYn\n",
       "3rfhffjo4R9FRszg7mfvxq1P3oqdxZ244XHWGeSfXv1PeMead2DRwCLsld+r/TdGEARBtE1yRQly\n",
       "SkRKEoIuI3VKWMs35qNToiqumLX3kiBBF7jOnBL9nCkRctBlqXooZ20lxm5OiZJoQJIblydpQClG\n",
       "p4RhGD3nlKDyDSIMOI9W63J1F49zAwCmMafM4Udn/qjBmbMgtwBPF552vHb30d2xdWpr4HVICSnH\n",
       "Y4+8/xFsWLoB560/D2sWrcGigUV436veV3te4AXfcMHCJwu48CcXYtMfNwEAjlx5JL5w3Bdw9v87\n",
       "G5v+uAm7jeyG56eexwNbH3C06rz8V5c3zCuKVpwjmRGMZEZCmdcRK4+A8TkDO+Z2YPFX6m0F37X2\n",
       "XfjPP/0nLr7nYlx8z8WO160YXoFnPvSM6/YnCIIg4iW5ogQ5JSIlCUGX1kyJnJQL3ykxMNC5U6JX\n",
       "RYmquGLNgtAEypRwxe6UCGGQ6Va6Abg7JYqigVTFLkoYmInRKaHoCniOr30mJDlTwjAMypQgQsMr\n",
       "hUAWAIyOQhgeBjCNO/92J6447oqGacwWkP923L81PD6cHsaVv7kS564/F7ImY0FuQcOg305RKSKf\n",
       "zWPf8X3x4AsP4sJDLqy1erS30wvKQGoA3z3lu1g+tBz3bbmvNp/rT74eb93vrTht/9OwZWoLTtx0\n",
       "Im7+881424Esgf+JHU9AN3QUPllgGRDbfo9Dlh3S1jrEzaKBRQ3dMQBg01s3wTAMPPLSI7ji11fg\n",
       "0GWH4pNHfhKyJiMjZjzmRBAEQcRNckUJckpEShKCLlVDhchF2H1jbIycEpYsCI0yJdyJwCnhJUq4\n",
       "ZkqIBkSbUyKlAarAubwwGkpKqaH3dJKdEuZdXZ7jSZQgOsbLKaHwAP7yF1Zffp17wOFlGy/DJ+/+\n",
       "ZMO5AwDvWPMOXHHfFRj7Yj1Mb+KTE45uDWZHjKJSxPsPfj++cNwXGsT6ThF5Ef/2+kbBJCflav3r\n",
       "V42swvmvOh9f+83XcMq+p+CtN70Vdzx9BwBgLMvWPay2ot2E4zgcvOxg/PhtP649RoIEQRBEsvCW\n",
       "7rsNOSUiJQlBl/buG4nMlOhVUcJ0SmhWpwRHmRJuuDklIhIl3JwSc6IOqdy4TSVVhxJj+UZJredJ\n",
       "AMnOlLBm0aT4FGSdRAmifayZEorliogDgCVLgMWsHGBWnnW8dnV+NQA4RIkDFx7omNZsrfmxn30M\n",
       "M5UZqLoK/nIeW6e2oqgWkRPZPMISJILygUM/gAdfeBCZf83UBIk3rn5jrOtAEARBEE2dErvvvjuG\n",
       "h4chCAIkScJvf/vbONaLnBIRk4Sgy4ZMiSicEtaWoIbh3dKpYaX6zSkh17IgNJ4yJVxxc0rEWL4x\n",
       "J+jMKWE5RkXVgCJZRkgRl2+UlHqeBJBsp4QpkAHsc2tWcQ4WI8VNlND14J8xRKKo7TEDkCx5s2XL\n",
       "R8J+C/bD2kVrHa9dNLAIgFOU4DgOaxatweM7Hq89duqNp2JAGsCcMofj9zwemsHO51VfW4XV+dW4\n",
       "8OALQ3k/rZIRM/j+qd/HOf9zDu477z4csfII31ITgiAIgoiCpqIEx3HYvHkz8m5X2FFCTolIsZdv\n",
       "pIV07OUbDd03onJK8Dz70fXGgYTnSvWJU6La5lLR52oOB1XswCnRz5kS9pagIZRKTEwEL9+oQIUu\n",
       "8BAqFSDDLMWSZkCJs3zD7pRIcKaEKZABLYipYWIXJTiO/QT9jCEShVm+cf4jjY9vH6z//fg/Pg7O\n",
       "RXDyEiWAurPiqQ8+he889h3826//DXPKHADgpB+e1DDt3wp/8w2tjJqzDzobZx90dteWTxAEQRCB\n",
       "5HDD8Ci6jBJySkSKvfuGeWe06b6OqvtGVE4JoDVhq1+cElXxqCFTgm9flLDOJ6m2/raxCm1A7OUb\n",
       "siZDy6TqLTsAiKpeS/8Pa538cHNKJHU/mwIZkBBRAqASjh7GlBquu73x8VP3O7X2t8ALru4BP1Hi\n",
       "lrffgrfs+xaszq/GF477QtP1eM+G9wRfaYIgCILoMwI5JV7/+tdDEARccMEFOP/88xuev/TSS2t/\n",
       "b9y4ERsXLgQefhg499zO1mweOCXe/u/X4qIT3oij1+4Ry/L+4z+At7wFWLnS2X2D4zhWR64r/u2x\n",
       "Iuq+EZlTAmhN2LLeNU+4KDFTmcHVD12NS157ifNJ0ylhyYJQBaPtgW3DfBJq628bRQEGLbdFQyrf\n",
       "GBtzPu7mlJA1GVq6KkqMjQGGAVEznEGXUZZvuGRKtLyfP/tZ9pPy+fy4+WZgt92AQw9tc03rAhnQ\n",
       "G6LExb+4GJ8/9vMNIvDmzZuxefPmCFeSCIqZKcHb9PiT9z656WuH08MA4OqiWLd4HW55+y21/286\n",
       "4yasHFmJodQQ1nxjDQDgiQ88AcMwkBJStXkRBEEQxHykqShx//33Y+nSpXjllVdw/PHHY7/99sPR\n",
       "Rx9de94qSgAANm0CbrwxHFGiz50SP9m6CXs8tig2UeKGG4DVq5koYQ+6BOoX+L6ixHxwSvRI+caW\n",
       "qS349qPfdhclVBWGKNayQyRBgsornTklBKk2sNJ0rat241CxOyVC6r6xh8tp7eWU0DPpulNCVaHx\n",
       "HFTDMsiN2ClRVIoNTom2yjeuvhq46CIWDujFT38KbNjQkShhz5RIuijxpfu/hE8f9emGQefGjRux\n",
       "cePG2v+XXXZZFGtKBMCr+0aQXAVTjHALwbRz5oFn1v7+4Vt/iHf+9ztxwMIDgq0kQRAEQfQ5Tb91\n",
       "ly5dCgBYuHAhTjvttOZBl7LMrsg7xRwo9LFTQhYKmKyEsK0CUizWx9j2oEsg4AV+mE4JW6ZEUSm2\n",
       "PS8H88ApIWuy9/5SFEASIXACOI6rOiXQvlPCYpnvO7eEPVMiBCt+oQCMjzsf93JK6NlMXZSQZagi\n",
       "XwvCq70w6qBLscOgS1lufr4EmaYJicuUADyPGU3XoBlauJ9tRKh4RZMGDXu85o3X4Lg9jmtpmUeu\n",
       "OhLjWZcPCIIgCIKYp/h+6xaLRczMzAAA5ubmcNddd2HtWmcCdQNhiRLzwCmhiAVMyfGJEqVSfTxg\n",
       "D7oEAl7ghxh0aXdKlNVyePkl88Ap4StKqCoMQawN3iRegsqj40wJALUyn74hIqeEb6ZEpdIgShhW\n",
       "p4QsQ5OERlGAr35U6zqioKQ2Zkq01RI0JlGilzIlzPMk1NI0IlTsZRu1xwOKEhe9+iIMpYdaWuaq\n",
       "kVXY+cmdLb2GIAiCIPoZ3/KN7du347TTTgMAqKqKd73rXTjhhBP85ximU0KS+tYpoesGjEx3RQm7\n",
       "/b7pBb7Z9s4cIHVoKbdmSvAcj5SQQlktNwyO2kaWgXSa/d2uUyKdZvaShNLMKaFLQk1IEHkRCs8B\n",
       "lc4yJYCqwNHvTomIRAkvp4Th4pRwbGNzvfwyG9qkY6eEprHPh7icEj2SKWGuW6ilaUSodFK+QRAE\n",
       "QRBEOPiKEnvssQcee+yx1uYoy8CuXewCle/gS90MuuxTp8S2iRmA1zCtxC9K6IYODpzjoqvpBb61\n",
       "dAPo2FJud2tkxazjjm3bhOWUmJzsfF0iorlTQqgLCUIITgnBInAktDNDW7g5JUIo32il+4aRzTY6\n",
       "JUQBmm5bhwhLOBxOiVYzJUyhIQ6nRA9lStRECXJKJBazfOP3S4GDX7I87hJeSRAEQRBENIR/K0CW\n",
       "mSAxPd3ZfPrcKfHcdiZGzGrxixJuLgkgwAW+NeQS6NwpYcmUAKphl2FdvFOmBAxRaBQSOum+YbHM\n",
       "t9WZIcnYnRIRlm80OCWqTh5Zk4FMNrhTIgI6dkrEKEr0UqYEOSWSj+mU0KpXQ38+aj986vXAK3Ov\n",
       "dG+lCIIgCGKeEY0oAXRewtHnTonnd3RXlLDnSQABRYkQa++9nBKhME8yJTRDc95RBwBVhS6KDSUX\n",
       "isCFkikh8mJ/Z0p0OPivVNhhMzDgfM7LKYGcRZSoVJyZEkAoYokXHWdKxOmU6KFMCXJKJB8zU2Io\n",
       "OwoA+N07j8GXjgJ2lijzgSAIgiDiIrmiRJ87JV4sFIC5BbGJEqrKfmSZJcK3JUqEXL5hzZQAyCnR\n",
       "Kua+chUIFAW6yDcKCVwHTon5lCnR4XFtuiTc3N9emRJcNucs3zBiLt/oJacEZUoQIcGBuSX2/xsr\n",
       "1eOq+1bkmnZMJwiCIAgiJKITJSYm2p+HrtczKWq3FvuLF3dNAIW9MWd0sJ1awDLeYeUbXDLKNxLn\n",
       "lDAdOkDPiBKu+0xVodsyJRTKlHAnZKeEV+kG4O2UcIgSbk6JGMs3KFPCB3JK9BX5EnDwtvr/i0aW\n",
       "45Blh+C4PVtr80kQBEEQRPuEfysgDKeE6ZLguL4t39gxXQAm9kZpxaOxLM8qSmhGMpwS1jueQEKc\n",
       "EuaxB/S2KKEo0AW+oSWowuuA2l5LSWv+x7zIlAjBKeGGKAKaXO1UUR3YypoMPtcoSuiS2NWgy8Q7\n",
       "JShTggiJN/yN/ZgcfviZ+N2qi7u3QgRBEAQxD4nGKcHznYkS1rvVfVq+sbNYAGaWw4ARy100u1Mi\n",
       "CZkSjvINckq0RFOnhMjX9rPIi5A7dEpY59XXmRIdHtfNnBJaWWHHVrW+g4kSA42ihBhzpoTdKUGZ\n",
       "Et6QU6Jv+fxrAW7x4m6vBkEQBEHMO6IRJRYvDscpAfStU2JXqYAhcRwZI49CKfpcCUf5RgK6bziC\n",
       "Lskp0RKBnBK83SnRfvcN67z62ikRYfmGKAJGxXJswhQlBm3lGy5OhSjLN3rNKUGZEkQE/HY5XEsb\n",
       "CYIgCIKIlmhEiSVLyCnRhCm5gLF0Hmk9flEiMUGX9pagUTklWskl6SOnhOZwShjhOSX6LVMi5PKN\n",
       "8XH35yTJXZQQBgad5RtxBl32WKZEV8s37OIsQE6JPoE3AJ4L/7KIIAiCIAh/kilKzAOnxKxWwIKB\n",
       "PFJal5wSHkGXFbXiPZOInRI5KRfOxbthsDdqHkOt2N77yCmh8ZZMCUGCzHXglLAMBPsyUyKm8g27\n",
       "U8IwDCZK2Ms3yCnhifVzIy2mu+OUEG2iLjkl+gISJQiCIAiiOyRTlJgHTomiUcDike6IEkkJunRt\n",
       "CRrGxbumsVwTU0AhpwREXkSF09s+l6x1/H2ZKWEv34go6NLulNAMDTzHOzIljC44JXJSrr6eSXZK\n",
       "WBxWVL5BhIlgwLW0kSAIgiCIaEmmKDEPnBIVvoDl+TxEpTtOiVCCLs0LccNoa50cmRJiSJkS1tIN\n",
       "oH+dEnozpwRny5Qw2j6XrHX8fZkpEaNTwt4ONCWkgGwWKBbZRLIMXXLZxlEGXaqN5Ru94pToGVGC\n",
       "yjd6gptPv9H1u5EgCIIgiGhJpigxD5wSiljAqoXdEyVCCbrkOOZIaPPurSNTIiynhF2UmK9OCYEL\n",
       "zymhKfMnUyLCoEu7U6JBlLCWb6RiLt9QGss3Et19w+KwEjgBmq5BN9prddsW5JToG4xqB5z6A+0J\n",
       "7ARBEARBdEYyRYk+d0rougE9XcDui8fAV/IolOMRJbLZkIMugY4s5a5OiShEiVaErV5ySjTLlBC4\n",
       "0DIlVF2dX5kSEZVv2DMlvEQJQ5Kg6TGWb8ThlNA0QNdDbQnKcRxSQipekaxFUSI0BxgROoZNk8Cr\n",
       "X92V9SAIgiCI+U60LUHbvevQ506JndNFQBexYDQDoTIem1NiZCTk8g2gI0u5I1MiqvKNVoStPnJK\n",
       "qDanRJnTKFPCDXtL0A7LJCYm/J0SnNJclEAq5vINu1MiikyJoG6KJlhLiYAulHC0KEqMZEbIKREi\n",
       "W7duxbHHHosDDzwQa9aswdVXX+2YZufOnXjDG96A9evXY82aNfje977nOi+HU2KPPSJYY4IgCIIg\n",
       "mhGNKDE0BKTTwMxMe/Poc6fEM9smIMh5pFIAV85jojgR+TJLJWB0tHn3jZbKN4COLOUOp0RU5Rvz\n",
       "2SlhyYHo2Clhzafot/INe1ZKlOUbXpkSDd03XESJqLtv2JwSoZdvhCRKWEuJgOSLEqOZUXJKSDqP\n",
       "+QAAIABJREFUhIgkSbjyyivxxBNP4De/+Q3+4z/+A3/5y18aprnmmmuwYcMGPPbYY9i8eTM+/vGP\n",
       "Q3U5dwzebpUgCIIgCKIbRCNKpFLA+Hj7JRx97pTY8koBkjrOxiWl+DIlTKeEZ/cNPlULT3Ql5PIN\n",
       "R6YEOSVaopkoofAhOiVsmRJ9V75hd0q0e0wrLK9yeNj9eVEM6JSQpNi7b9gzJUIv3wjTKSH0kFMi\n",
       "TU6JMFmyZAnWr18PABgcHMT++++Pbdu2NUyzdOlSTE9PAwCmp6cxPj4O0f7dBbBcJIIgCIIguk74\n",
       "MdPmgDCfZ6LE7ru3Pg/rIKEPnRIvTBSQMZhTwohZlJid9Q+6nKxMes+EnBKJQtZkiLzoHXTJI7JM\n",
       "ib4q3wjRKbFrFzA25j3WkSSAk2VgqEmmhFv5RkROCVVXoRlag0DYVvmGKDYXJZpNEwBrKRGQbFGi\n",
       "olYwkhnBzuLOmFZufvHcc8/h0UcfxWGHHdbw+Pnnn4/Xve51WLZsGWZmZnDTTTe5vv5f5Pr5tLH6\n",
       "QxAEQRCEk82bN2Pz5s2RzT96UaIdrAPDPnRKbNtVwABfFSXm4hUlCoVkBF0ahhFdS9BKZd44JQZT\n",
       "g6ioFeeTigJFQG2gGWamRF+2BA3JKeFXumHOOlimRCq2oMuSwko3OIuS0lbQ5eBgc1Gi2TQBcMuU\n",
       "qGgu50BUtOKU0JlTYuvU1phWbv4wOzuLM844A1dddRUGBwcbnrviiiuwfv16bN68Gc888wyOP/54\n",
       "/OEPf8DQ0FDDdJfGuL4EQRAE0cts3LgRGzdurP1/2WWXhTr/6Mo3OhElrAPDPnRK7JgpYEhkooQW\n",
       "kyhRLCYr6FIzNAic0DAQykpZFJViy/NyME+cEhW1gsHUoHfQpaV8Q+IlVDoQJawDwb5sCermlGgj\n",
       "qLdQYJVrXtiDLitqxVOUiCvosqQ2lm4AbbYEDSpKVDoTEHrJKUFBl9GgKApOP/10nHXWWTj11FMd\n",
       "zz/wwAM488wzAQB77bUX9thjDzz55JNxryZBEARBEAFJpijR506JV2YLGEkxUUItDqKiVdzvdoeI\n",
       "vftGt4Mu7Z03gAhbgrbqlDCPPfO9JlQUM50S3pkS9fINkRdRgtpRp5SawNGPLUGtTgmeZ/UXut7y\n",
       "rAI5JdQALUHdRImIyjdMp0TDerbrlPATHCqVyJwSiRYl0iMUdBkihmHgve99Lw444AB85CMfcZ1m\n",
       "v/32w9133w0A2L59O5588knsueeeca4mQRAEQRAtEH75hmmdJ6eEJ4VSAQtyC9iN+AqHfDaPXeVd\n",
       "WDK4JLJlmqJEpeITdBlj+YabWyMrRRR02apTwvoeTbeEW0hal/EVJVQVKm80CAkVTu/MKWEROPo6\n",
       "UwKoH9f2wWcTmokSni1BTVFEUQBZBpdKQTNs3YuiKt9wc0q0mikRRHCQZSa+GEZb29ak17pvLMot\n",
       "IqdEiNx///3YtGkT1q1bhw0bNgBg5RpbtmwBAFxwwQW4+OKLcd555+Gggw6Cruv40pe+hLzfiUkQ\n",
       "BEEQRFeJNlNi+/b25tHnTokpuYD9F+1TG+/ms6yEIw5RouaU8Ai6jM0pYeu8AUTslAhqGbffNTd3\n",
       "Ui7X+XqFTFOnhCNTogOnRL9mSpgDSftxbZZKWI+jAARxSghuTgmOq7slZBlI5XrTKdFMlEin6+dU\n",
       "Nus9rQ89130jQ06JMDnqqKOgN3ExLViwALfddltMa0QQBEEQRKeEW75hGLV2duSU8GZGLWDxcN4h\n",
       "SkRJQ0vQBARd9pxTIoHURAm3Nq6qCoVHg5BQNss32shK6NtMCTeXBOA5yGxGIKeEmygB2ESJdHxB\n",
       "l3FmSqRSHZ9TvZYpMZgaZB1O7PuTIAiCIAiCABC2KGHeSRcEypTwoWgUsGysLkqMZ8djFSWSEHTZ\n",
       "E5kSQOJFiaHUkE+mhGEruVDbHmw3ZErwElSjT4RC+/42afO4npho0ykBNIgSXDodX9BlWE6JoaFY\n",
       "RIley5RIC+nw2h0T0XHJJd1eA4IgCIKYt4QrSlgHg2E5JQSBBc61ETqXVCp8ASvGu+eUSELQJTkl\n",
       "OkfWZAylPUQJVYXMGxA5WzilJLUl8jkyJeaDU6KN4zqIU4IP6JSIrXwjjEyJoKJEOs1+OnFK9Fim\n",
       "REpIhdfumIiOD36w22tAEARBEPOW8EWJdJr9nc+z24btYHVKcFxkdwi7hSwUsNsiJkooChMlJopt\n",
       "bquANJRvJCDo0i9TwmijvKCBeeSU8O++YXdKKO07W/Q+7b7h55SIoHxDFAFBaxQl0mL1M9MiSvDp\n",
       "NDQjpvKNODMlwnJK9FCmREpIkVOCIAiCIAjCh+icEuPj4TglgLbv7iYVPT2BvZaOg+PYWxtJ5VEo\n",
       "R++UGB5m182y6l6+kRbTsZZv2NdBEiRw4Drv7NCJU8J+7PWqKGE6JezhlJ04JXibwNEPeDkl2jyu\n",
       "AzkltOZOiVjLNyhTIjiGwX5421cnOSV6H47r9hoQBEEQxLwlOlFibIxdobdz19vqlAD6yilRmGYX\n",
       "pvlhNghIpYBhKZ7yjWyWLa+idL/7hv1up0koJRydOCXsx17SRQnJxynBGc5wyhBEpL7qvuHllIio\n",
       "fMPNKeEqSsRZvtGLToluZUpoGhMk7ANYckr0PiRKEARBEETXiE6UyGbZhVqx2Pp8+tgp8ezLBfBy\n",
       "fdSSSgFDYryihKwko3zDbR1yUq7zi3c3UWIeOiUqvO4suaBMiUbsIpRJROUbkhRMlODTme5232gn\n",
       "UyIup4QtJDd2UcIuzALklCAIgiAIguiA6EQJoP2wS/tAoY/agm7ZUYCkNooSg0IXnBIJCLq0Z0oA\n",
       "COfi3a18o12nRIehfFHSNFOCq2dK1AaZHWRKmPur7zIlQirf0DRgZgYYHfWeRhQBMYFOiZyUa1zP\n",
       "hDslula+0a4oQU6J5ENOCYIgCILoGskUJewDhT5qC7p1ooCMHq8ooets12Qy1fGAmgCnhEumBIBw\n",
       "Lt6tgatAXzolDMOArMkYSA0EckrUBpkdOCWs8+qrTAmv8o0Wj+vJSRYma48bsCJJgKBbRAldRoq3\n",
       "iBLFYt0pEVfQpeos30h6pkRXyzfIKdGfkChBEARBEF0jmaJEHzsltu0qIMc1ihI5LlpRolxmY3SO\n",
       "qzsl2hIlQgy69MyUiMop0UpL0B7IlNAMDTzHIytmPZ0SMqc3uBs6zZSwui7IKeGkWemGOVtRr4tm\n",
       "nuUbmUy8QZc9lCnR1Zag5JToX0iUIAiCIIiukUxRoo+dEtunCxgU4xUlzNINc3lJCLp0awkKhOiU\n",
       "6KQlaA84JczBjuc+U1VUuLpTgufYqW604ZQwDAOaodVKfuZFpkQbx3UQUUKSqqJEgEyJWIMueyhT\n",
       "oqstQckpQRAEQRAEETrJFCX62CnxymwBo6lGUSJtjKCoFCMb6NlFiSSUb9jrwk3IKRGMpqKE6ZSw\n",
       "DN4kQYIhtj6wNfcVV72TOG8yJVo8ricmWnBKNBElhHQ23qDLXnJKdLMlKDkl+grD6o4gpwRBEARB\n",
       "dI1kihJ97JQolAoYyzaKEorCYTQzisnyZCTLdIoS3Q+6tCfom5BTIhhBnBJlrlF8EnkRRhvnkn0Q\n",
       "2FeZEl4tQSMq35AkQDJ6wCnRTqaE+SHjJZz0S0tQckr0DYZVh2infTlBEARBEKGQTFGij50SU5UC\n",
       "Fgw0ihKyDOSz0ZVwWEWJdJqJEm4uBYmXYs2USJxTQtfZb+ugo1dFCVumBMD2r9HGwNY+CJT4Fges\n",
       "ScbtmAYiK98QRSZKGFJzp0S3MyVaLt9oJjjM00yJtJgmp0RCKeeH6/9E4EIiCIIgCCIY0YsSExOt\n",
       "z8d+97KPnBLTagGLh91FiYlSG9sqAHanhOJRviHwAjhwTtu4SZjdN5KYKeFm5e9hUaLMaQ1uFJEX\n",
       "oUtC604J2yCw78o3vJwSLR7XQUQJjgNSkKGJTUSJTDa+7hsemRItl2/EJEr0YqZETsyRKJFAdqzb\n",
       "C0Ofqf5DogRBEARBdI1kOiXsg8M+ckrM6RNYNtY9p4Rf+QbQ5AI/xPKNRDol3EIPe1WUUFVUbOUb\n",
       "ktCBU8ImbvRN+UbMTgkAyHAVqLyHKDE3BxgGBCkVX/mGi1OC53johg7d0IPNJE6nRI9mShSVYgwr\n",
       "SLQGh1mzezSJEgRBEATRNaIVJcbHwynf6COnRJkrYOX4eO3/bogSiubulACaXOCH6ZRIYqZEPzol\n",
       "eJtTQmzDKWEbBPZdS9AYnRIAkOZkaF6ixNQUkEpB5MX4gi5dnBIcx7W2n+N2SvRApoRhGOxzjpco\n",
       "UyKhPDf1HACgeNN/AsuXd3dlCIIgCGIeQ06JmFHEAlYtjNcpUSwCuVx9eYrm7lIAAjgl+jlTot+c\n",
       "EtAcYoIu8B1nSvRdS1Cv7hsROSXSkL2dEpOTNVEirkyJolJ0OCWAFsMuKVPCIUpYu9ZQpkQymSiy\n",
       "kkn1LSdT9w2CIAiC6CLJFCX62CmhpQrYY4mLKJGJ0SmhqhD47pZveGZKiFkU1Q5tzuSUABQFJbdM\n",
       "iXacEvMxU6LN8g2LCcqTFOcjSlSdEgInxFu+ITlFicBtQQ2jvh0pU6KGdd+SU4IgCIIgCMKbZIoS\n",
       "feqUmJ6rAIKMRaMDtcfma/mGp1NCIqdEEII5JVSHmNC2U2K+ZUpEWL6RggyFC1C+EWfQpZtTgpeC\n",
       "7WdTkOA4ypSw0CBKkFMi0bgJ5ARBEARBxEe0okQuxy7USi1ejPWpU+K57bvAV/Lg+bpN1Lw+H8+N\n",
       "xyZKqHr3gy49MyVEypQIgq8oYRiAqqIMZ9mFLvKUKWHFL1MiovKNlBHAKcH3kFPCer5RpkQNckok\n",
       "H6P6Vex2/BMEQRAEER/RihIcx67Sd+1qbT596pR4fkcBotI4aumGU0Ilp4THSvWeU0ISJMiaDMMw\n",
       "6k9qGsDzUFwyJTShdVFiXmZKeHRT8ELXWRzE6GjzaSXIkJGwoMtOMiViFiV6JVOCnBIEQRAEQRDB\n",
       "iFaUANor4ehTp8TWnQWk9e6LEoqHIADEF3TplynRVadEj4kSPMc772hX34fdjSLyIhMlWtxf8zJT\n",
       "osXjemoKGBx01zfs+DolNA1Isf0KoLElZwRBl7qhQ9ZkZMSM47lEOyWSlinhIhiRU4IgCIIgCCIY\n",
       "yRQl+tQpsW1XATmu+6KEqnU/6DKxTokeK98AXPZZVdSzb2NJkNoq35iXmRItHtdBSzcAH6eEtUUO\n",
       "4CzhiKB8o6yWkRbT4Fw6DwTOlIhRlDAMA5qhNZSfJUKUcHFKVLQKOSUIgiAIgiACkExRok+dEi9P\n",
       "FTAoJECU0LtfvkFOic7wFSWqop59G4u8CI3nWndKzNdMiRaO68CihGEgZchQwJbpcEoAtWPXUcIR\n",
       "QfmGV+mGufykOSWsbTZNEiNK2M4rckoQBEEQBEEEIx5RYmKitfn0qVPildkCRlLuosRIegTTlWln\n",
       "HXkIuAVd+okSFa3iPqMQyze81iEn5cgpEYC2nBK8BK1dp8R8y5Ro8bgOLEqoKlROhKKxj95mokSD\n",
       "KBBB+YZXyCWQzEwJu0AGAGkhnQxRgjIlCIIgCIIg2oKcEjGysziBsYy7KCHwAobTw5gsT4a+3J7q\n",
       "vhHGxbubKKFprCuF70r1mVPCJVNCbccpMR8zJaIq35BZO1Bz1g2iRDpdb6sJQOCiL9/oRaeE3WGV\n",
       "GKcEZUoQBEEQBEG0RTJFiT51SkxWClg4MN7wmPX6PKoSDrsooRndL9/wzJQI4+LdrQtMkLvMPeyU\n",
       "aHC3VEU9R9mFIEETOMqUsOLWcQWIrnxDZiGX5i5oECU4DshkGss3jIjLN9QSclLO9bkkZkq4iZk9\n",
       "IUqQU4IgCIIgCMKT6EWJ8XFySlSZUQpYNOzulABiFCX07gddemZKhHHxXqk4j8MgokSfOSXcyi7a\n",
       "ckr0e6ZEnEGXsgzVyykBsBM1xqDLkuJdvpFUp4RdzPQtOQubNkWJjJhBRa00tu4lCIIgCIIgAPSS\n",
       "U6IPRIk5vYClowkQJRLglLCXBJh07JTQNPf1DHIMuQ1QEypKVNRK00wJR9kFL0Ft1ylhFzd0tT8G\n",
       "WCE6JcbHm08HWYYqMKeEbujOQbZFlIgl6FL1Lt+INFOi0p6I4CZm9oJTgud4pIQUymo5jrUkCIIg\n",
       "CILoKZIpStgHCn1SvlHiCliR9xYlxnPjMYkS/kGXvk6JEIMuI8mUUBT2Ju0tDoO4bdwGqAkVJWTd\n",
       "3ylhVPeT1REjCRJUHm1lSlj3FcdxEDihsbSgV/FySkQVdGkp3zAHrQ3tOG2iRORBl1E4JbwEB9PB\n",
       "1GH5hptTIumiBEAlHARBEARBEF4kU5SwDxT6pHxDEQpYtTAJTokEBF26pOgDITgl3I5BIJiw5eWU\n",
       "aPOubpQ0675hSKJj+4q82LZTwm1efdGBw8spEWX5Bs/KNxylG0Bj+UYcQZd+TokEZkq4iZmSIEHW\n",
       "5HicO52IEhR2mTgW5hbi2pOu7fZqEARBEMS8J1xRwq2Wn5wSNdRUAbsvcYoS5pg3LlFCT0D5hluK\n",
       "vrl8VVfbb43qJUr0m1OiSaaEIQjOwRvfplPCxTLfNx04/JwSLRzXExPBRQlNaHRKNGAv34g66DIM\n",
       "p4T1c9/rfNH1+vkVcktQnuODr2unkFOir5B4EUuHlnZ7NYg+YPt24Nlnu70WBEEQvUtynRJ9FnRZ\n",
       "LCuAWMSKBcMNjzc4JTJ5FMoxOCWQgKBLj0wJjuM6u3iPwinRa6KEqsIQRYeQwJwSCMUpEfguetLx\n",
       "agkaYfmGJgR0SsQRdBlXpoS5nc2WpyG2BAViLOEgp0RfoXNM1CLi489/BlavBn7/e+dzug488wz7\n",
       "u1IB7rwz3nULgqq6dxf/xCeAvfYCXvMa4De/iX+9CIIgep3oRYmhIaBcbu0i1J5d0AdOied3TIKT\n",
       "R8HzjVkH3SjfSIxTwiVTAujw4p2cEtVMCd4pJAgSFA4dZ0oAfVa+4dV9I6KWoC05JaIOumzilAit\n",
       "fCNoiUcTvMTMnhAlyCmRPAyDRImYOfJIJjwccghwxBHAq18NXHcdMDPDTqPVq4HbbgPuvht44xuZ\n",
       "jnnZZfXXn3oq8J731L/GLrqICQKG4S4WmMzOBl9HwwCmp+vze+kl4HvfA97xDnaJIAjAl77EPsZm\n",
       "Z9nn/223MRGF44DDD2fdnYOKEzMz/utOEAQxH3AfmdrQNA2HHHIIVqxYgdtuu817QrcBIccBY2PA\n",
       "rl3A4sXB1qoPnRLPby9AVJyjlq6IEuh+0KVXpgTQ4cX7PHJKpIU0ACAtpB2ihC6KrkJCaE6Jfirf\n",
       "6NApYRjs421sLMDEsgy9mVMizfZrLEGXTTIlAgddVtcZ6bS3KNFsmgB4iZm9IErkpByKSjHqNex7\n",
       "tm7dinPOOQc7duwAx3F4//vfjw996EOO6TZv3oyPfvSjUBQFCxYswObNmx3TGCCnRFzMzQGDg+zv\n",
       "6Wng178GTjqJ/f+73wH/+I/s75tvBt7yFvb3G97ABvqXXgocdBBzT9xyC3tuaAj48IeBa6uRIP/+\n",
       "7+z33nsDX/8664b0wANMTHj6aacoMTAAXHklczYIAhNGDj2UleJ99KPe72P9euBVrwI+9Sn2Y+XE\n",
       "E9nPU08B3/0uE1UuuAC48ELg3nuBN70JWLCg8TUvvQQsW8b+/u53mUAxM8NeF6ijE0EQRJ8QSJS4\n",
       "6qqrcMABB2BmZsZ/Qq8BYT7PPulbESX6zCmxZWcBaa25KDFRnAh1uYbhLkr4BV16XjiHWL7hZcMG\n",
       "yCkRhGblG7rg4pTgJSi8EUqmROC76EnHzykRcDvNzLC7Ym6HnQNZhibWnRKmsFQj7qDLZk6JsMo3\n",
       "wnJKeIiZvSBKUPlGOEiShCuvvBLr16/H7OwsDj74YBx//PHYf//9a9NMTk7ioosuws9+9jOsWLEC\n",
       "O3fu9JgbOSXi4JVXgEWL2N8XXsgEhTe+kX12lkrAzp3AAQcAX/sacPrpwI9/DPzrvwJf/jLw058C\n",
       "v/0tcNhh9fmZzrSrr2biwtNPs2kfeAB46CEmZth5+9uZabdSARYuBH72M+D97/de5yeeAK6/ni3j\n",
       "M58BPvQh9tFlOuK+9S3gG98AikVg40ZgxYr6a/fZB/jCF4APfIC9ny9+sf7ciSeydbn+eiaCfP3r\n",
       "wFFHAR/7GBMiXnmFiRSXXMKmlyTgc59jQs3atW1tfoIgiJ6gqSjxwgsv4I477sAll1yCr371q/4T\n",
       "W++GWWklV8IwnAOFPnBKvDAxgSznFCWsNw2jcErIMtt85nU0EyW8yzccd92thFi+4VYSYEJOieY0\n",
       "K9/QRcFVSJB5o+Vzyc0yH/guetLxc0oEPK4Dl24AzCkhBsuUiCXoUi1hNDPq+lxgN0yMokRPZ0pQ\n",
       "+UYoLFmyBEuWLAEADA4OYv/998e2bdsaRIkf/vCHOP3007GiOlJcYL89XYWcEvHwv/83+z07y0QE\n",
       "k8FB9rNwYWP5wlvfyn5MXv1q4L//mxlvTz2VPaaqTLxYswZYuhSwXp4+9RRzrt14Ixvoi6KzSzjA\n",
       "BJEXXmBOtz33dLoYrrqK/bjBcUx08GPlSiaoTE6y97dtG/DudwPnnceef+IJ4OijgV/+kn2EvOlN\n",
       "TDgZGgKeew7405+ARx4BvvMd4H/9L1a2kssBf/878OKLwEc+ArztbfWbTm4YBlvX7duBO+4ATjkF\n",
       "GB0FeMthXy6za1G3bUQQBBEXTUWJj370o/jyl7+M6elp1+cvvfTS2t8bZ2aw0c8p4cPjOx7Hoy89\n",
       "irMPfAf7tOR5fPvb7AN7n5icEtf89hr87JmfNTy2dHApvvnmb/q/8PrrgeOPZ99qHrw8VcAgbxu5\n",
       "XHstBvZ4I2R5DwBVp0QpgFPi2mvZt9duuzWd1OqSANh4wGhSvlHRPFpghli+4VYSYPLuzZNQD9kK\n",
       "LFnf8nzbcUr8+wP/jrPWnYXFVafE3Bzwla+wuxOdWM0BMM/m3Fzdp9oBX/wi8L73MUtn06BLT6cE\n",
       "XPfXL37BQsaOP965XDfLvN9d9CvuuwIXHXoRRjIj3m/mjjvYbSYrqRTw7W+zKyYP7vzbnUgJKbxu\n",
       "j9d5z9trebkcu6VV5fP3fh6fkSsQvbpveBzX//zPwF//Wv9/etrFZnv77cDICPsAs1IVJUynhEOY\n",
       "Gxxktgu0Vr7xP3/9HywaWIQjVh7h+rwXRaWIpYPu3Qf8wkx//OcfY8XwChy24rCWRIkb/nQD/vvh\n",
       "7+P7xWm87YY3AwAGpAF8/7TvOwUaF/wyJZ59XsbP/qv5QKEjWhQlMmKm9r/VKbF582bXcgKiNZ57\n",
       "7jk8+uijOMx6Gx3A008/DUVRcOyxx2JmZgYf/vCHcfbZZztef83ftyNz9SY8MPYANm7ciI2Wzwci\n",
       "GJrGciIOOoiVQGzaBPzqVyxzwSxpu+UW4LTTGgWJVjnttMb/BYENyN3YZx/2+4Mf9J9nNsvKPaLG\n",
       "/EobG2OlKl6YHZMBYI892M9b3sLKV55/nokZv/wly+PI5ZiL493vBvbbj12v/MM/MGFBVdnvf/1X\n",
       "9vjatUzgsHLSScA99zBBAgBe+1rgmGOAT3+azdvEy0xIEMT8I+prF9+Pmttvvx2LFi3Chg0bPFfC\n",
       "Kkrg2mu9yzd27fJdkYe3PYzbnroNZ+97Zu3O5Y9/zK7R94nJKXHLk7fgtatei/XVwbBmaDjjpjNw\n",
       "/cnXg/OTkG+6iZWm+IgS0+VZZMXBxgc3bcLQ2xfVRImx7BimylPQDd3/7s1//RcTJAKIEsWiU5TQ\n",
       "Oe/uG8PpYUxX3AWoULtvuJQEmLzl/glMv/kp4JCWZ9uWU+IHf/wBDlpyEBZXnRIvvsgurj73OdQH\n",
       "grreeGshKPfey25RhCBKXH89cOyxAUQJRYEmOluC1p0Szu1wzz3eooSiK44yA7+76N965Ft4095v\n",
       "wkFLDvJ+M5s3s9tS1tth//RPwNatvqLE3c/eDUmQWhclfv5zhyhx3e+vw0fLe2LQzSnhc1xv2sQE\n",
       "ImuGxO672yb62c/YjvIQJVQVKKvlhkErAOYTrrrNWum+ceff7sSK4RUtixJTlSlPp4Rfm807/nYH\n",
       "9snv07Iocdezd2HVgtVI63fj/a9i3ulz/uccFEoFLBlc0nR9/TIl/vCEjP/elCxRYjhd77ZkdUrY\n",
       "B8CXWZP8iEDMzs7ijDPOwFVXXYXBwcbvVkVR8Mgjj+AXv/gFisUiDj/8cLzmNa/B3rYR6JkLgZEP\n",
       "nYUT9johzlXvC0olViohSez3Qw8B37Tcv/nWt5jL4OabWW7CN5vc2yH82W039j1t5/bbgR/+ELj4\n",
       "YlYCMjHR+BH8gQ8AGzawspBPf5p9xcoyK3W58EImSixdCvzlL+w+wVe/yu6jAOyreHKSCU5HHME6\n",
       "p6xcCSxZwgJGHd97RNcxnTEAu6abm2POGzuKUu908/LL7LiZmwNOPrkF5ycx74j62sVXlHjggQdw\n",
       "66234o477kC5XMb09DTOOeccfP/733d/gdeAcHy8aflGUSmyLAOLhb5YZD8YjscpUVSK2Lj7Rhy9\n",
       "W+NAQtEV/7t4tRX1mUQuISPYPHaFAtKzhdoXiMiLGEwNYroy7TlQCLo8E3enhHf5hm8JScjdN7zW\n",
       "YWROxcTsVMvzBOBdQuQjbBWVInvPVadEw+Y1Wxgqivt8m1Estt4S14NCob5ebWVKCBIUzj1Tolhk\n",
       "X2BuqLqKwVTjRb9fpkTtXPajWGRpYW9+c/2xyy9vfh4pRWhyGyUMxWL9lpBlXroiu98G8jmui0V2\n",
       "98pHO2ETuQmZsgxdSkNRqnkO9pBJS+5OK903asdwixRKBeSz7lcgfi1Bi0qx3r5Yluu31pqIEkWl\n",
       "iBP3PQG8cg3evM/JAMdhJD0SOADSL1OiMCmHdap5Q5kSiUBRFJx++uk466yzcKrp57ewcuVKLFiw\n",
       "ANlsFtlsFq997Wvxhz/8wSFKAAAH8qy3w//9v/VwSoCJEocfzr5HZmbYHfwPf5g997GPOUsjiHA4\n",
       "+WT2U6kA998PTE2xQeX4OBPOly9vnH7VKvZ79erGx486Cjj/fODRR5nT5Ygj2GB1n30FM5BhAAAg\n",
       "AElEQVRYqcg997CWp6tXs24o113HsjEOPpiV0GzYwByEP/oR8K53sWkNg300ZmzaO9E5ssz20/bt\n",
       "7PL0//0/1mb3xReZIymVqt8LXryYXa88+SQzcC5fzkqASiV243d8nDmGJIm5ixYsYMfO7ruzLJcz\n",
       "z2THDc97X2IT3UdVWYnY0FD9GOg1fEWJK664AldccQUA4N5778VXvvIVb0EC8A+6bHK1WFJK7ILN\n",
       "EjZYKrEf5ONxSriFvmUldiHpK0rUVtSbolJCxj4AKRQgWUQJoC4K+IoSAZZnndRqxUulAIPzDrr0\n",
       "FSXCdEr4ZEoMzanQ5lro32WlDadESS2x91wVxByb1xxotfNJXCqFIkqoKrvYMNeruVOC98iU0F3P\n",
       "pVLJW5RwGwj6ZUqU1FLz2nm7Wgaw/5sc1yW1hFm5jWOjVGJXbdaHlBIMWW65+4bbqgdZHgBAlmFU\n",
       "nRJFpegZMgm0FnRZO4ZbxE+U8HNKlBTL8mS5rtA0ESXYZ2yObXNFAVKp2mdsEPwyJQrTCRclKFMi\n",
       "FAzDwHvf+14ccMAB+MhHPuI6zSmnnIIPfvCD0DQNlUoFDz30ED72sY+5TuvrgiQ8MRuevPnNzLyZ\n",
       "y7FTwDxFbr6ZGQUfecS/mwURDuk08LoWDYRubNjAfqzsu2/jvD/zGTb4vfZaZhT+2tfYgNec9otf\n",
       "ZMeDeY/h0ENZkKkoAiecwER9a4aFYTBn9L77stDTqSng9a9nAyv76amqzHmzcmXz92IYzA0wMcHm\n",
       "bb2RcNddLO8jn2df1atWscH7q17VeM1sZ+dOlvExPs7mMTnJ3qeZbbLXXuz6gOfZ4H7nThZ6evjh\n",
       "7L1s3sycJrrO3qf5nvbem22fkRHmilm9molCg4PMofLAA+xr9KWXWLnOH/7ASkc3bGDTrFvHsltW\n",
       "rWIlQsPDLDB12TIWBHvPPWyb5nJsX83Nsf9HbFW2c3PMNVMoAFu2AA8/XO9KMzjIcmHyefa6Aw9k\n",
       "fx9yCFu/LVvYflVV9r6np9n2GRtjRvING9hrKhUWDJvPs+3idgnmtT913f0ruFcoFuvnysAA28/P\n",
       "PFPP/nvySeZq2raNHScAqz5+9lmWlbPbbmz7TU2x4yGTYft0fBx48MF6h6NikU1bKjERyhQPFy9m\n",
       "+/iZZ1imzZ//zLbrypVsuuGquXPhQrbPt21jy5IkJjpu28aOMU1zd+B0SkuVYk2/vP1EiSee8H1p\n",
       "bSBjcUrUBocxZUq4tcfLiuxCcgQ+9fEBRALHvA2DiRLT7qLEnmPepSCtihIOpwSXYKdEqYS0rEEr\n",
       "hixK+DglagMsVQVyOZSqh2Ft/NFJ2GVIosTkZH12QACnBN9a9w0/UcJtIOiXKVETGP1oV5RQ2ht8\n",
       "o1Sqb0QAuqGjolVguIWbAq6DTIA9pKoBFGg/UUJimRJ+7TiB1oIuS0oJFdUjC8YHX6eET6ZEgwjS\n",
       "QvlGSa0Kv+Z0qVTtMzYIfpkSk1VRwmpfDR1ySnSd+++/H5s2bcK6deuwoTp6uuKKK7BlyxYAwAUX\n",
       "XID99tsPb3jDG7Bu3TrwPI/zzz8fBxxwgOv8KOgyOI8+Wh+wKQobfH7yk43TWE+PY45hP0T/sXw5\n",
       "y6ww2bGDffYuXsy+/mSZ/b9jBxtM/fSn7Brjyivr2Ref+hQrJ3ngAXbnfmCADZj23ZcNzvbaC/j4\n",
       "x9kA9thjWa7GmjVseYcdxgZOq1axLioHWapFf/lLVj70wx/WH+N55gY55BDgj38E7r6bCSUbNrD1\n",
       "/Nzn2CWIpgHHHccG30NDLGA1k2HTlkrstXvuyQZ8o6PA2WcDjz/OzostW9h7efllNkj8+99Z15kX\n",
       "X6w//853svnyPPtKLxSYyPDCC2yZ27ez4dIXv8je28gIsP/+rBJ05UqWM6IobF1OPtndhWKvFl67\n",
       "trFzyx57eO/XgQG2jUze9z7gmmvY8iYm2Pt56SXmwnjySfbeH3uMDVjXrGH7YfVqth83bGDvU9fZ\n",
       "+3vkEebm4XnmqNm1i22Tgw9myx0erl8a/vSnbLp8nu3/rVvZsVQssgybN7yBrcuiReyYO+AANphf\n",
       "saIz0eKFF4Af/ICJK6tXs32Uz7MfM/OlUGDOlJ072XvQdbbee+3F3seqVexyc9cuZtCdm2P76aWX\n",
       "mPi2227s/9lZ9v41jR3Lr7zC3ttzz7FwX1lmrz/1VOCss9g+fPll9vjSpfXLqFKJiQzr1tVLqnS9\n",
       "nn22axfb9n/+M6tkHhtjx8A738nWWRTZfJ97jglJPM+298AA6xa0eDE7X8fHmaj04ovsNS+91FAR\n",
       "HQqBRYljjjkGx/h9u2iat4QVxCmh+jglYsqU8HNK+L+wuUhQVksYt178z8wAmgbRQ5TodHnWSe2i\n",
       "BDjv0ommTomQgi49MyWqfjO9ONfyPAF06JTga04JoG5tS4IoYc7CS5Qoq5bSBNMp4ZIpMce5d9/w\n",
       "dUq4dd/wyJTQdA2KrkTqlGhblLDsB3N7GUprTglztZsOem0iSI2qKKGq/u04gdaCLktq+KJEM6dE\n",
       "TQhrRZQwS1Ys07XslPDIlJiclaFp7KPVVPtDp0NRYqrSZlkaUeOoo46C7vVhZeETn/gEPvGJTzSd\n",
       "jso3mlOpuA9+/vmf418XIpmYLV8B9h1pfr2PjrISkJNPrj8/M8MG7z//ORMEzjyTdRZZvZp9t3Ic\n",
       "G5g/+SRz3Dz3HHNXAGwQdd99rHRB09jA641vZAOtbJaVMPA8G8hdfz1wzjns2FUUFrj64IPsDvR3\n",
       "vwuce67zu3zLFpYb9de/soHuunVMEHjhBXY9ODTEhLb5ZLASRfa+zTvje+3Ffh/SQu7bAQcwl4yd\n",
       "V15h++TZZ+v7cGaGZfkfdRTbHzMzTAQzBasHHwTuvJMNsl94gYlVzzzDBBxZZgPutWvZwH75cjbd\n",
       "9u3MMTIywkSDF19kYs+BB7Lj6PHH2bFz112sdGn9eiY87NjB1rNSYQKBYbB1ftvb2LoceCBb5sKF\n",
       "7HgtFtm6DQzUS6hyOXa8LFnCuuhY9fHpaXZccVwwQ7aXQ+jAAxv/5/nG5Rx5pP98163zf96K6a4x\n",
       "A4XDJLxM3aoV1/VMDVq+kWCnhP8LA4gSWgm5lGXe1e0hTMUvShi8d9DlWHYMu0q73MM2Qyzf8HRK\n",
       "VLeLETAzw0GLTgnDMCxOiVFAknpSlGgIJ1VVaDznkSmht+eUcOu+4XIX3TxXEumUsOyH2vp5RYt7\n",
       "HNeBSjdclldDlmGkgjklWgm6LCklTJZdRBAfDMNAoVTAWHbM9XmJl1BU3c/DktqmKKFONjolEPAz\n",
       "topfpsTOWTa/QiGhooSUxctzL0e0YkS7UPkGy4NYv57duf7KV5wfib/6Vf3vc89leRK/+938GpgR\n",
       "4TE0xO7Annii9zRr1rCf009n/7/8MnNcvPa17P9/+If6tBdfzDqIvfQSK8m47DJ2J9mKJAFnnMF+\n",
       "/Fi1is2PiIeFC+uCkxtug/CTTnK6QQoFJgDMzjKB4+GHmbPrwQfZPNauZW6bcpmVIOyxBztebryR\n",
       "DeDXrmXH1I03NskLg/dlQDtYr1UoqyNMUcJrMAiQUwJARSthwEWU4GMWJdJpAD7lGyIvYiA1gJnK\n",
       "jLOlY4jlG56ZEqYoUQpZlPAQtmRNhgGj6pQYcDglAHQuSkxOdvwp1kyUcGZKcK4lF5WIMyXMcyXp\n",
       "Tona+imKt1PC5bgORZRowSnREHRpDnxd6hPa2S6z8iwyYsYzL6eZU6J21z9up4RHpsT0XF2UiCwV\n",
       "vkVRwtq1hso3iCTy+98Dr3kNu+v58MPsDuJNN7Fwyq99rXFaw2C/v/e92FeTmOcsWVKvsbeTybA7\n",
       "6wArNyDmH2bHkKEhVkJykE/zt07p5UyLpBNeMWWnokSvOiUMI5BIIOslDKRtosSCBeCq28W8nm0q\n",
       "SmhavYgoAPZBlCQB4FXw8D6rXNfBMGJ1SgR9fw5adEqY+9bafSN0UQJwt/K3QEuihKpCc+u+wUuo\n",
       "8N7lG16bvJVMiTicErPybOP7DUKpxHxy1ffe1CnRpHwj0PLMYkMr1eMzkFPCHnTJ80yMcFGPTAeJ\n",
       "YY4aAuBXugH4d98ILVMCLTolfDIlZuZkLFgQWrMbdyjosu+Y7+Ub997Lfj/8MPt9880sAM8qSKxf\n",
       "z2zSBEEQBBEV8YkSExO+L7c7JRrG+jE4JVRdhaZrjruGTe/iKUo95cQH2ShhMGMZgExMsLjdiYmG\n",
       "6/h8No+Jks+2MtsatilKcJwB8BoMvUVRQtfZgIi3HTJhZ0qYx4mtfWNgWnRKmPu21n0jKlGiyfHf\n",
       "jFadEirPuZZcyNA8B9teh1QrmRJxOCUAtO6WsIlD5nw4L6dEGOUb1nhtE1kGTKeEWkJO8o75dnUq\n",
       "eIklagmKrmBOCZ7F0kyUaOaUKCpFls2RkEyJmaJsfqRGh1+5DwVd9hwGN7/LN4pFVmd97rksnf+h\n",
       "h5hF/p572PNPPskO60cfdbaWJAiCIIgwiUeUGBlhhT4+woLplDBkGRDFWnB9XE4J00ptv0BpehfP\n",
       "MYJ1RzFKGMrYnBJ77w0UCg5RwnfAFXB51smtgyjd0AGdh6p473rXdXAr3QDC775RKECTBHClCEQJ\n",
       "D6dESkgxIag64AhdlDDjejugUGCzCe6UcM+U8Cvf8HVKtJopEZUoUW3P25YokUrVRqy1waGmRVe+\n",
       "4bbfZRlIV50SSovdN/zWq7pdJorBR+QTpQl/p0ST7hu1/RCnU8JDzEwJKcyWZfMjNTrIKdF3BHFK\n",
       "PPNMvXTBpFx2ao69xGOPsTC2665jgXDHHst+770361pw660syMx+H4IgCIIgoiAeUYLnWXKIj4Xd\n",
       "vFiT5aLzbnUMTgkvK3XTu3hBRQmUMGJtflwosFsPhoFhqRSbKKHqKmAIvmPs8ey4063hVroBtF2+\n",
       "4ZcpUVw4Cj5sp4RX+YZSwrKhZcz6HpVTYtmyjkdKExNsNoGdEgLcMyW4NpwS7WRKRFW+odb3V0vY\n",
       "9oP5ecOrHmJbGE4Jt/1uL9/wyZRwBF36rVcb26VTp0RteTE6JbzKN3gjBQgyli9PsChBTolEEsQp\n",
       "sXo1S2K3ct55LFitFzBbXL/0Uv2x++5jlyCXXw584AON07/jHcCb3xzvOhIEQRDzm3hECaBproR5\n",
       "sVYpzTnvVsfolLATllNC5UoYztqcEuPjQD6PRWIhNlFCMzRAF33H2N12SpQWjYMvtykCtFq+oZYw\n",
       "lhmDwAnQ5HI0TokQRkqmhhXUKaG4dd/gJVS4Np0SrWZKROiUWD60vD1RwrIfzM8bTo3QKeG232UZ\n",
       "XNoSdNnMKaEHd0q0ul0KpQLGs+Oez3tlSuiGjopWaVmU0CUmZKWEVNtOCa/yDV1JITckB4kv6gxy\n",
       "SvQdzZwSZpbC8883Pj45ydwTp55af2zrVvb7+uuZC6GFiJdI2L6dVV2mUuyjY9myehXmQw8xQeKz\n",
       "n+3uOhIEQRAEEKcoMT7uL0qYTonKXF86JTSuhJEBmyiRzwP5PBYK8YkSqq6CM9oQJVoMBGyGZ6ZE\n",
       "oQB5yQIIlZBFCR+nRFbKIp/NQy67uHSAxIkSuqE3iDqu3Td4uJZcVOLKlIjQKbF8OARRoplTopOg\n",
       "S8NgTa09nBJcQKdE0EwJRVNgwMDiwcWxOCXKahlpIY0FuQUtiRKqyNdL5EJuCarJKWQHEy5KkFMi\n",
       "kfz1r5xvv/XNm9lve1aJ2XLwlltYfEyxyNoJ/uQnwIUXsv+3bIlklZuiquxzyqtbgWEA//mfwGGH\n",
       "xbteBEEQBOFF4pwSspdTImpRImKnhM6XMJJzFyUW8HGLEv7lG56iREjlG7qhQzd08JzL4VcoQFm6\n",
       "GGKMTomsyEQJpVLsCaeEoilICama7djVKeGRKVHmNF+nhNudvdAzJcxBeybT+HgTUULTNSiagqWD\n",
       "S1sTJRSFLXPxYodTgtf08IMuy2V2zLi1gmjBKeHovuGxXuYxPJ4dD1WU8MqUsAp5rYkSXP39htwS\n",
       "VK2kkBlIlihR0SrklOgB/vQnDk8/7f382Wez33ZRwjrgF4R6NvPJJ9cfNztaxM0DD9TX56672N/3\n",
       "3w88+CD7KLz8cvbcfvt1Z/0IgiAIwk5yRInqhbU1U6I2RomjfMMjCT+QUyLAHV5dKGF00F2UGHcR\n",
       "JTxb+wVcnn1yE03X2nNKhFi+YQ4sXGt5CwVoy5ZAlNvc3204JXJSDvlsHqpcdh57QPuihNlCJiRR\n",
       "YsUKNjv7HVj37hvOTAlWvuF0Sqgqu9MnCO7an5urxS9ToukdYXPQbk9Qa3Jcl9UyMmKm5cF3bYda\n",
       "3Frm542g6S0d14FECXMit8+8qigR1CkRJOjSegzH4ZSwCnmtiBKKyNXfb8hOCbWcQiaXLFGCnBK9\n",
       "gSgE677xwgvM/WCWOygK8J731J+/9NLG6T/yEeB3vwtnHVvlxhvZ75tvBo4/HkingSOOAF7zGvb4\n",
       "Zz9b/8wnCIIgiCSQHFFCKTks9Pl8jOUbHnctAzklaivqja8ogbookRJSyIgZzMqzHS3POrnDKYHu\n",
       "OiW8wuoAAIUCjOXLIVVCFiX8nBLVu75qpVRzSjRs4nZFCUVh28dyh75dWhIlVBWKR/mGm1PCPEa8\n",
       "NAG3/A+vvIGSys7jpueM28i+iShhCofjuTZEiVyu4TPI/LzxdEp0Ur5hLs+tZE2WwWcCOiUCBl1a\n",
       "j+FCOUSnhNc+NkWQjIsoYbra7KKqLEMWonNKyKUUUt0WJXS94X1TpkRvIInBRInbbwcefxz4l39h\n",
       "u7lcBtavrz//9a+z37vtBvzmN0wM+OIXWYbDgw+2v36//z3w61+7P2cYwM9/Xi8TueAC1ink2mtZ\n",
       "eOXpp3vPdx53QiUIgiASSHJEiepgRpGLzoFhTE4Jt7uWOSkXiigBsYT8kLsoMWYRJYAmJRwdihKa\n",
       "kRCnhFvnDQAoFMCtWAEpRqdEVsxiPDcOTak4BTGgfVHC7455C+g6az23dGkrTgnDvXwDqnNQ20SU\n",
       "cOuU4lm+UR3sN3UX5ZyuJORy/qKEvWwgKB5OiXxmDKJmeHff8HBKuK266/Lc9nul0ppTIkDQZe0Y\n",
       "Drl8w69EJytl6+KQ9ZzjOPdyO1mGLKDuRrOcU00/Yy14CZpyKYVUpouiBMexH12vr5OLU6KoFCNc\n",
       "OaIdxICiBFBvAbpzJ3DNNUwwOO64xmmee45lNRxySP2xd72LCRpB+NWv2Gn+6KMsz+K884CjjwZ+\n",
       "+lPntN/6FnDCCUwIeeEF4JvfZJ1CAODznw/8tgiCIAii63jcrm6DIKKET+GmOZhRZhqdEs8/j+47\n",
       "JZoNsPJ54OWXPSeRFQ3gNOTS1YGdYbAr57ExJkoY7qLEbqO7eS/PXuDqs3p2pwSP7gZdelmwIctA\n",
       "uQxx8TJwcusdPWrz8HJKzM05HjYHWMPpYeiVSrhOiZBEiakpYGgIGBwMLkooHi1B/ZwSgtCCU8Kr\n",
       "fCNip0RD2UBQXPZDSSlhYWoMKg+IbrcMO3VKmMuzn6ctOCWCBl02OCVCzpTwK9FxLd8A6ueL9TFZ\n",
       "hjzIe5dvtOKUcBE0y8UUJIsoYRgR3Qn2EiWAupBVfd7VKaGUYBhGoDaURDw0c0qccw47pm6/nQkO\n",
       "ALBoEft91FHAypXAL37hfJ05DQD8/e/A2rXAzAz7HLfz7LPMeXHrrcAf/8gOo1e9qnGak04Cdu1i\n",
       "3dVNvvzl+t8rV9b/vvFG9vFDEARBEL1CIpwSmq5B1VWMZEbcLfRddEo0tdwGcC4UZkqAmgXPVy9+\n",
       "iswNgkwGGB/HqB6fUyIJ5RteFmzs2gXk80gPjSIl687ng9CmUyKfyUNX5UQ6JUxTjTlmD1a+4eKU\n",
       "4CVUDIXdzbXc0W3qlHDJlPBrCRrIKdGOKNGpU8IqSqglLEyPQeM9BiSdBF02yZTgM8GcEgInQDUC\n",
       "lG/YRYKABHJKeOxjz6BLwP18kWXIvOFdvtFhpkR5LgUhLSOTYad6MSpDQhBRoor9PBV5ESIvNp6r\n",
       "RNdx09qtCAJzIwBMXLDy+tcDJ57Ibp7cfHNdtDApFpnzweT973fO3zCAvfYCDjwQ+MxngBtu8F6X\n",
       "M85o/P/pp4F3vxvYtq3+Xr7wBbZOBEEQBNFLxCtKeNzdNy9ys2IWSqUeNjgywq6/NU50r1MOkY6d\n",
       "Ej6DqV2zJXCaZd4TE/XbGPk8RrUJhygxUfJwQnRavqFrTZ0SY5kxZ9hmiOUbnpkS1e2SHhxFRmlz\n",
       "X3eQKWHIcnROiYDOFjeCiBIVrVJ/gaJAdgm6FHkRqqE5tkVbmRK85Bwww1K+EbFTwvP88FueTZRY\n",
       "II1A9Qq5izDoshWnRKDyjTacEoZhYKI0gbHMmOc0fm1fG/ZDQFGiIhjhOCVcBM3STApiis2vw9PN\n",
       "nw5ECYByJZJIs/INXWdOtQ9/2Ck67L47+71qFctv2M1mbsxmWemFyQ03NF7G7L8/cMwxzmWawsSJ\n",
       "J7KciKkp4OqrmSPjX/6lPt0RRwDve1+9tE9RgE9/ml07EQRBEEQvkQinhHmRm5WyUOW6U6I2UKrw\n",
       "LKlfb/PueQA6ckoMDbG/PUpMJmdL4K2iRKHA6tsBIJ/HsNqiU2JsjLVUDCDStFO+kRbTSAmpxrBN\n",
       "r/INc7+0sG88MyWqo+/M8Fj4ooSXU8Iy0DVUJRqnxOgou6ps8/htxynhlSmhaIqjBKDtTIledkoo\n",
       "JYxLI1C9PgHDKt9wESWEbPBMiUDlG204JYpKEQInNF2+X6ZEq06JMq937pTwEDSLMynwFlEislyJ\n",
       "gKKEKSYJfOO01IEjeQQRJXieBQ3/5CftLePvf6+HVd54Yz2C5K9/Be67jz2+dSvLjwCAt7+dfb3f\n",
       "eSdw3XXA8DDwwQ8Cr3sd65xhvv7ll+uXH/YOywRBEATRSyRDlLA4JTRbW8baOCXiXImOnBJ+IzoA\n",
       "u2aL4HWXkEugPVEil2Pb2mxE7oO7KOFfvgHA2eHAq3yD4zxDAb3wzJQwRYnBUaQ1wGhnEN+qU8Iy\n",
       "oOMUNRqnhCiyQmIzJa1FWhYlFAUVznAVElRddQQRttt9w+suetROieH0MObkOVdRxHd5IyPA9DSg\n",
       "aSipJYxLw1C8WuKFUb4xNsZKkqzioSyDz6agqEbz7htc6903JooT3u2ELTQr3QBCyJSwYooSEWVK\n",
       "zM2kwIvJESXcXBIAOSWSyGWfdY7mP/Yx4C9/YX9bRYnp6faWsfvuwJFHsr/f8Q73aVasAL7zHe97\n",
       "DRzHOm3ss0/9sWefZYIFQRAEQfQ6yRAlrE6JShkQRRSLtoFSxLkSRbXoLkoEcUo0ESWmiiUIPqLE\n",
       "oGwTJTJNRIkmy7NibkcTzdAgcP5OCcBFGPEq3wBaLuHwzJSobhdeECELQHl2MvA8a1QqrTslqgM6\n",
       "qGq4Tgnrxu9gpGQXJSpq+5kSit6GU8IrU8LjLno+m/fvMmA/KE0COiV4jsdoZhST5YDHhzXJc3gY\n",
       "mJxk4ok0DIXzGAGEUb6RSrHblzMz9edkGWKW7S+RFx130htWgRehGcG7b2SlLDiOCzToLZQKGM+N\n",
       "+07j1/Y1K2UxlBqCLJdgAI0DdQ9RosRpkWVKzE2lYAishCnRogQ5JRKFAWD6bweyvy0fBVdeyQQC\n",
       "oFGU6JR77qn//b3vsdadf/lL4GpM8Dxw773MsXHXXewx0ylBEARBEL1MfKLE2FjtLqWdolKsOyUs\n",
       "bRljd0q4lW80a+PmUE+cTBdLEI0WRIlmTglzeQHS3Np1SjjWwcspAbQcdumZKWHZLmWJQ3lmV+B5\n",
       "1mjRKVFUirW7vryq1QSxfN6yeTt1SgAdjZTMCBJRZBelc5VKU6eEzOve4ZQ2p4T1EHY7pNz2l99d\n",
       "9LHMGMpq2fuOfTOnhMfrzH0FNDlHHC90ikNFpYi8OASZ91hHj2PaS09ptrwaZtCl4V+6ATDrfxCn\n",
       "hPn5CQTfLkGcEq7lI6iLIBzHYbE05jzfvEQJu1OiwkSEVlplegmaM1MpQCCnBNE+9ssL09h2ww3A\n",
       "K6/URYmvfpV9RLUTcXXssaz84sUXgXPPBf7xH4H99mut9GLJEtaJ4/WvB77+dXZpRRAEQRC9Tnyi\n",
       "hCAwSd/Fwm7asrNiFrpcdmZKxOCUMNfBjtnGzfuFzZ0L06USRHiIEoODkPQK1Ll6UGFgUSLA7RW3\n",
       "oMtEOCV8MiWACEQJv+4bVacEr2kwRAnlMrvQC618AwjFKQGw2c0UAzglOPdMCVVXW3ZKuO0vv0yJ\n",
       "gdQAUkIKZdWjvMhLlDBVFw/x0ZrB0JIo4bIfSmoJI8IAVB7OMElzXTp1SliWV0OWIeaqooRP6QbQ\n",
       "YtBli2JN0PINv0wJAFgkjUKXbJ8LFsGhRqWCEqd6OyUCugfcBLJKBVArKWjoAVGCnBKJ5Y9/bPz/\n",
       "//yfxr+XLWN/p9OdLefyy+vz6gSOYzkTfHhXcQRBEATRNeITJQDPq0VzYJiVstAUOXFOiU7LN2ZK\n",
       "JUichyjBcZhL58FP1QfgUYoSqq62J0p4BV0CnqGAXriVAwBoCACtSDzk2TYyGNrpviFmkZNyEDVg\n",
       "sqwglQIGBmyihH2QFQTrxh8fD02UmCs3DngEToBhGPUBrKKgwunuQoLudEoEKd8Imilhuhl8zxu/\n",
       "kb3PcW3NYHBknvjhJkooJeQgQRU4d/EkjKBLwLnfzaBLNHdKtBR0GaNTwupY8RQlXJwSRd6jfKPZ\n",
       "Z6wFN4Fs1y5gOJeuCXOJFiXIKZFYDj3U+VipxAb9X/pS/WulzWgggiAIgiB8SIYoYXVKVHrYKeFR\n",
       "TjFbKSHlJUoAKGXzEKbq28V3YBGgXMTE7KIqWa7hVV2FwHe3fMMtOBFAw3aRUwIqYYoSTZwSHMdB\n",
       "MjhsLxadmzdhTonZUuOAh+O4RreEqkLmde+Si3acEkEzJSwCo+d5064oEbJTIgMRuuCRwRBG0KW5\n",
       "PGt/StMpgeZOiZaCLqNwSvhlSlSXt0AcgSravka8RAlOdQ26TAkpaLrmKoDYcRPICgVgZDDVG6IE\n",
       "OSV6ilyONU9asqT+2CuvdG99CIIgCKJfCU+U8AoYtOLjlMhJOWSlLHSLUyKXs0iyQIQAACAASURB\n",
       "VIz1k+yUMFfUYzA1W/YXJcq5RlHC9y6wubxcrqkoYU7KWTqemUGXzW785zN5FMrRlG+4tZgE4BAl\n",
       "5Jk2gi7bdEoAQErn8PLctHPzJkyUsDslAFsJh+mUcBESVF2F4eKU8DuEW8qUsDhP2nZKeIh77Qy+\n",
       "HcuzOCUyEKEJgvsgMeLyDZUrBnJKBAq6bEeUKBeQz3SQKVFd94XCUHBRAoqrU4LjuMAlHG4CWaEA\n",
       "jA71iChBTomeo1Cof/UddBBw+OHdXR+CIAiC6EeS45SoBl0aity7TgkPkWBOLiEt+IgSA+MQp+vb\n",
       "ZSwzhkKp4B4U2EL5htsAipVvJN8poaZFqHNt9F/zEyV8nBIAIOrA9tJM4p0SxUoTUUJVIbt03+A4\n",
       "DgInOM4lv0NKN1hbVnuXCM9MCaV+LofulLCUbzhEMz+8nBKGAF3kvZ0SmuZIs+tIlNA0QNchZQSo\n",
       "QZwSAYMuoyrf8M2UMMtoxCEoItc4gYcoMccprk4JIHgJh5ugaRclOqiUag45JeYFuVzj/6bb8LHH\n",
       "gDPPjH99CIIgCKLfSYYoYWlppytKojIl0kIaqq66h+EBgUSCYhNRojKQR2q2vl3MtoeuF+kdihKa\n",
       "rkHkuxt06ZspUd0uSlqCMjvjnKYZfuUbTZwSomZgR2kqkaJENWojmCihKKhAc3WjiLwIQxACZ0p4\n",
       "dUrxypSolWL53RHuZvlGdcRaUqqihJdTguNYMbmuB15114ms+11RgFQKosRB44JlSrQadDmeDZa1\n",
       "MVGc6Kz7RnXdx4UhyPYxupco4eGUAIKHXboJmoUCkB8hpwQRHnvvDWzcWP+/03BLgiAIgiD8iV+U\n",
       "sNZXVzEHGzkpB9icEjUbfZecEhzHISNmmg+wfMopikoJGasoYfZ4rCIP5pGabdwu+WweE0XntgrF\n",
       "KdGOKBFi0KWnU8KyXbS0BK0YoijRzClhGBA1A6+UIxQlXI79ZhgGC/Iz276ZokRaaLxKTovpBqdE\n",
       "xSVTAmBigiEJrk4Jt0PYq1OKX6ZETspF75TwOj+aLc/ilEhDhC4J3ue2W6hkJ6JE9diUJEDlgnXf\n",
       "6GbQZZBMiTFhABX7GD2ddhUlZniLU8I2TWCnhIugOTHhFCXaONWCQU6JeYGuA+vW1f9fuLB760IQ\n",
       "BEEQ84FwRYlmtxOaOSXELAxFTZRTAmhyFy+ASOCYt80poQ7lkZ5r3C6eg4sQRAkxYNBlw6AvxPIN\n",
       "10wJRQHm5oDhYba4dAra3GzgedZoNejSHGBpGnSew87yJLJZ1je+Uqm6990GWUEIwSkxM8NmYdqH\n",
       "s1mgJAfJlNBc3SgiL0JvxSnhEiwINMmUkBLslMjnYVSdEmmdh+HllAAcx7VhsGMik2lteXZRgucB\n",
       "Qyghk/CgyyBOiTF+AGW+0U3i5ZSYNSodOyXcnDuFAjA+Sk4JIjx0nXUwB4Ann6z/TRAEQRBENCSj\n",
       "fMNi+YaqJCpTAmhyFy+ASFC2ztucxlK0qg7nkSnGI0poRvfLN1ydEpOTLOa82nRdz6ShF+cCzxMA\n",
       "GzW2GnRpDrBUFboooFAqIJtlq5FKAeUyulq+YdOvgokSqooy5+GU4CUYNoHG75ByCxYE3DMlDMNA\n",
       "Ra0gI2ZicUq0LUpMTEDkRQi6DkMS/Z0SluO6XGaHAt/sU9NPlEinwXGAkCkhK+S854EWgi4jbAmq\n",
       "6Ioj28b6WTnC54KLEpA7zpRwc+4UCsDCfP34zzLjU5COya0ThlOCRInE8vjj7LemsbbQALDPPt1b\n",
       "H4IgCIKYLyRHlKiG46GLTomc5D5I6NQpUdZKyKWqF+P2USYAbSSPbCk+p4QkBBclagOSEMs3XDMl\n",
       "bNvFaEeUMNfRbdTo45RgZUMKdFHArvJEbZvVNnGCRIlcDigrQTIlvMsudIEPHHTZSqZEWS0jJaTA\n",
       "c3zCnRITbD6KAgii97nt0Tq11eXZnRIAwKdsOTNuiw9avqHWP7vy2TwmSs1rFwqlAsZz477T8BwP\n",
       "nuNrYae15VlEkBEugxJnW0cPUWImDKeER0tQqyjBcRG6Jah8o6/59rfZb00DTjkF2Ly5q6tDEARB\n",
       "EPOGeEUJj1h0a9Alp3qIEnE4JbzKNzp1SmglDKargoeHKJGLUZQIUr7hCNuMuvuGXZTIZmCU3FtD\n",
       "euJ3DLocP6quQjeqrTOrgsakXIhGlBgbY+EQbh1VfHBzSjQVJVQVZY/yjVqmRCtOCRdxw60zg/Uc\n",
       "SrJTgpuYYPNRVX+nhOCevdHq8lxFiXQJKb5J+UYr3Tda2C4lpQTd0JtmWgA++7n62mEug2JAUWIa\n",
       "5XCcEi4tQReNW45/JFiUoPKNRFMus9+qysq0jjmmu+tDEARBEPOF5DklqoPDrmRKeJVvdOiUkPUS\n",
       "BnycEsZYHrlKAFHCMNhVU6fdNwI4JRzrEGb3DbdMCYdTovn7c+B3DLocP+Y+5ziOPSdKmFYiEiVS\n",
       "KXaVO9NaeGdbokQ1U8LN4dCyU8IjU8LtLr71HIraKTGaGcV0Zdq7K47X8sbGwE1NIydkAEUBJzZx\n",
       "SliO645ECVtpEZ8qIcU1d0oE7r7RgoNkV3kX8tk8O+6b4Lmfq8sb4tKY42yfy/bzpfreZ/RyZJkS\n",
       "C/ICdEOvba/EihLklEgUhu0UuO46YHbW3xhIEARBEET4JEOUsDgleD+nRESihG7okDUZGdE9wc7z\n",
       "Lp6msauXVKqpKDGY8RclBt1EibJtW1UqbDvwfIflG82dErV1MAc4YQZdug10rX0vgUDvz0GLTokG\n",
       "d4yiAJKIWTUiUQLwdAr5YWvUgmwWqKjNnRIlj/INiZegiy06JTwcF/ZMiTidEgIvYDg9jKnKlPt8\n",
       "vJYnitBzWSxU0+x4kKRonRKZDBvdzM01HJ9cqoR0M6dE0KBLy3YZkAagaArKatlzvkHyJEw893N1\n",
       "eTlDQpHTGtfTfr5oGsDzmNNDckq4ZEqMj3NICamaqyOxogQ5JRLPhg0kShAEQRBE3MQrSpgWdt1W\n",
       "o2xxSnCqBhXsakCS4infKKtlpMW0551Dz7t45uCD4/xFCaOEIR9RAvk8BpUATgnrYKeDoMsgmRKO\n",
       "dQg56LJZpgSXy4Irew+sXGnTKcFWSgUvpTGrRyhKtDFScnNKNBUl/j97bx5syXWXCX65Z9713byv\n",
       "Fm1WaTEOLZZl2o3Cg6IpG5rFIHDbmoFu3EF3O7DHTUyHe7oJhi1CwuAxzQQOmzEQgUED2EEPbUyb\n",
       "ZgvowYJBjdvCWGgsxGK7Siqpllfv5t1zX+aPvHnvycyT23v3vVfC54tQqOrec/OcPHkyK3/f+X7f\n",
       "z/PggK6UkAQJAd/MU6JuSdDjVEoADVI4Mv35Oz2ccWOSk5Oko1VKAJvrniElpDpKiTpGl8S8cBwH\n",
       "XdMxtsaFx21CShRe51V/vOchkiVM7MmmQfZ+WZ136n7bsqeErqfvgRuBlMiW7QVi8sX0GqalMRwr\n",
       "vvhFRkowMDAwMDAcN46XlJCk2KkvI2FPXlYlQYIUAmbA5QPDI0zfKEvdAEp28WqSBD4sdLViUoIf\n",
       "9KEEZur8joqU8EMfsngAUmKbRpc088QcKdEGZzm1jwng0EoJXpJgRlsmJYgqK9siJWi7sOuALAyB\n",
       "MIQNipkoVukbDZUSdUuC5pQS2yYlMma0jUgJ4jq4/Q5OOeKKlJDLq28cVClBu+6Z9I06pEQto8vM\n",
       "86tqXhopJQqu8/o6uC54RU33V0RKkPfbljwlPA8wzbiSMElKHECUVA/bUEqw9I0bHoyUYGBgYGBg\n",
       "OF4cLykBUAMz8mVViQQsvDAfGB6hUqLM5BIAWlKrXCmRGmgePmehV0JKyAqHubATl8Vc4ShJCfGE\n",
       "0zeo5omZeeFbbfDOFkmJGkoJTlbgRzYkdVNa8EZUSpSSEqu3aT8qUErwEgKBa+QpUbckaEopUZW+\n",
       "0Sooh9lqlSslGgTfqf6I6+D22zhlx2qRUlKCkr5RNOyy/mikBEQLErZkdNlQQTIyR82UEsR1jqIo\n",
       "fd/UJCUiWV6Xi6W1KXzGZpAlNJNKwhx34yklWEnQVy7K/rljYGBgYGBg2D5uDFKCeMmVIx4zGilx\n",
       "kkqJIil6A1Ki3yohJWRgJqbn5cjSN8IA8kkbXRZ5ShDzIrQ6EOyGRMAhlRKcKEKJBoAaS99fkaSE\n",
       "5wGSVJp2EYr84ZUSlJKgKaXEUaRveNtJ37B7LQwtbqWOkbebvhFF9UgJqWb6RoXRZRAG8AIvlSqw\n",
       "VaVE5jq7gQuRFyHwq4jNdSEoWg2lhARFVMBzPLXNQT0lyPvjlUBK1CVfGIpx6dIlvOlNb8J9992H\n",
       "+++/Hx/+8IcL2z799NMQRRGf/OQnG/XBlBIMDAwMDAzHi5MhJUaj1EcppUTIY+EHN5RSonDXtyZJ\n",
       "EHAW+u1Vu6xzIeJpm/DpeRlqQ4zM9Dz9fUnfoHpKZOZFaHcgOFskJWooJSBJkAMdgRKf85GQEpm1\n",
       "XwUaKeGFNZQSJWRCwDdQShzUU6LonqEF7SQK1nUURbB9O2VGq2t6/h7JIgji665sgnazq2FgI/YR\n",
       "kbecvuF5cXBKBq4FpIQYHT59I5kT0g+nkpSwD+4pkXtWui5EtZW+DhRSIpSkNPFL85SoICUSgmZN\n",
       "bCD92MiSEg1vtXqoS0pQ7lGAGV1uA5Ik4YMf/CCee+45fOYzn8FHPvIRPP/887l2QRDgB37gB/DN\n",
       "3/zNiBqWYi7j4BkYGBgYGBi2jxtQKcFh7lFIiVewUiIUCFKiQCkx4Y9HKeGHPiSxfvrGyFq92R9H\n",
       "9Q1iXsR2F5LT8HoftvqGKEL2hwikDCkhSfGxG77YbkspkS1K4kc1lBIlaReBsFFKhGF8aqoan2YQ\n",
       "pEUvB/aUKLpnaEE7iYJ17QQOZEFOBaS1lBK2HZ8cEbSbXRUDM4yVErJavHN9kOobtEYHTd+oUX2D\n",
       "RqgOW8Mj85TIPStdF7LWrlRKhJKYHidNKVGhICiqvPFKUkqwkqCHx9mzZ/Hggw8CADqdDu655x5c\n",
       "vnw51+5nfuZn8Oijj+LUqVOVx/zjPwZ+8Rc3f3ddRkowMDAwMDAcJ7b3z+6WPCXkkMPM9Y9VKWF6\n",
       "ZrVS4hCkRCSYGHTKSYkx0vPSkloIoiAtWd9S9Y0DKSWOufqG1O4BTsPrvQWlhOjp8MQMKSEIcRnW\n",
       "Jttnvh+3l4jz1HXguecanRJNKVFKSlQpJXgJPuEpYduxiCCJ2ZNz7nTivx/GU4JaZcA0yyP7gnWd\n",
       "Td0A4vV5YXKh+FgA9SZYdGX0RyHg+xCqjC6bpm8UkRKjEXDrrev1GYkWhBpKCWr1DeLmpRGqukop\n",
       "J0zgMCVBaUoJWe2k+ysiJQ6plCirvAHcWKSE4zuQW0wpcdS4ePEiPv/5z+Ohhx5Kff7yyy/jU5/6\n",
       "FP7oj/4ITz/9dGFlrU/sAcBj+MQngHb7PIDz6+/47W3ZMDAwMDAwvOLx5JNP4sknnzyy498QpITp\n",
       "mesXVinksAiOWSnhVyglRA371n7+CzLAKiMlRCtNSpBb34inzciQEuvSfva4mJQwy0vL0eK/OH2j\n",
       "nlJiqA3T6RtFEVlTpUSN6htSuwfO3SIpkQQSYbh+20yRUSulBO/ocIQNKbGe4iSIqktKkOViEzSM\n",
       "lKIobj4YbD6rrZQIrMK0C1IpkV0jyTknpMShPCWqUp5oKLiPyGdEAl3T8bkrnys+FkC9CWZtEcOl\n",
       "D3geBFmF6U3ov82s6yo+pbCRrgN/93ep9RkJ1ekbdYwuaYSqrul4ae+lwuMaloGhNiz8nkQ2hYSq\n",
       "lGh1K5USgSRAIwm65H5cBfl1SmXSyEzycXojkRJMKXH0WCwWePTRR/GhD30IneSBtcJ73/tefOAD\n",
       "HwDHcYiiqDB949HTwG/sPYZ/82+A//7f098V8BgMDAwMDAxfkTh//jzOnz+//vvjjz++1eMfPykx\n",
       "HAIvv5z6iNwFlUIOc+94lRK0XVgSmqTBmh1MKeEHISC42OmscuELlBKjKP8WnSgVbu7eXLu/ouEl\n",
       "CKIAsqScvFKCDJiDAJjNYhv9FeRuH3DrHxNA9RpMiK2Vv0CKjFopJThHh83FKSupKU4CrVrlF1Au\n",
       "468J04yHrG5sFA6vlBAkBDzW91J2mNlldShPiSp1EQ1FSglKmkKt9A1Kf7OWiHMLL1ZKyMp2jS5r\n",
       "pm9EggU+PLzRJY1QrfLaaJq+UeUpoWg1SAlRgEb4gaTaaVqtUpk0MvNGVUqUlgRlSolDw/M8vP3t\n",
       "b8c73vEOvPWtb819/7nPfQ7f9V3fBQDY39/H7/3e70GSJHz7t3879XgcB5w+Hf/5a74G+Oxnj2zo\n",
       "DAwMDAwMDBRsR6AYRfHLpZQPXnLIvC2GUQgn2JSKE0Ng7lNIiRNWShw0fWOysAFfAc9zgOPE89Ru\n",
       "p9rIMrAfFpMSTforGl4CP/ShSCdrdJmTYU+nQK+XetmXO30oblj7mACqSYkMsZUio1ZKCVg6LGTS\n",
       "N4DmZpe0yR8OG0VKFP4KmgYEoJASvAw3rOcp4RPVN6pIiUN5SmxRKUFLU0gpeYpA6W/S4tGZO7FS\n",
       "QikJEg9idFl03Uej1PoMaygl6hhdFqW1bMtToo5SQmv3apASfJ74JdrVqb7RxFOi04kP3bSqcCUO\n",
       "SUpIvIQwCvPXlaE2oijCO9/5Ttx7771473vfS23z5S9/GRcuXMCFCxfw6KOP4ud+7ucKCQkgJiW+\n",
       "4RuAq1ebWwcxMDAwMDAwHB7bUUokAWudJMwMKWH7NhRhUypOCoFF4K3f61U1frGMJAncSSolDlh9\n",
       "Yzy3wAWrNuNxfP4ZXagsA3thPmA9KlKi08DoMkVKbMnoMifDpkTfSncHnLdlUiJDbNGUEtFShxnF\n",
       "vg+aBly7tmq8DVKi4fZtESkRcnSlxMydAb6PqMpTgvfrKyUKyA2e4xFGIcIoXN+7lm+hK3fj49zA\n",
       "Solxi0NrbgO+D7HVzOjy7Nny7uoqJcIaSonaRpcUpcQ2S4JWeUpoLb2SlPBFPk/8kqREHaVEA08J\n",
       "jos/H49rXLMmOCQpwXHcOoWjq3S3OLCvHDz11FP42Mc+hgceeACvf/3rAQDvf//78eKLLwIA3v3u\n",
       "dx/ouBwHnDkDPP301obKwMDAwMDAUBPbISXqpm4AucDM8iy0pI0kPlZKeGuVPM/Hh/YjEdKNqJRI\n",
       "BqooccCbeWmdLAlSghZlIj6/635NpUTSXxK8RVFh8is1fSMMoKj1lBItqQU/9OOyg1tM38jJsCnz\n",
       "onYG4LyGW1ZNlRLkdV8pJYKljmUYz3mrtWWlxGAQn2vJNSPRlJQgPSUETqCau4m8GJMShFKCzEih\n",
       "pW/QyA2O49ZqiWQslmfhdCvWQLek1pErJQ5KShgaoM0twPMgKZ3jMbrMkhJ8zfQNmtElOaaGSgk3\n",
       "cGH7Njpyh/o9bQxVSolWe6eSlPC2pZSgeErQSAlgM+03EikBbFI4GClxMDz88MMIw/qE9RNPPFHZ\n",
       "hvlHMDAwMDAwnCy2k75xGFIis/MmBlFKKQHE7/ged8KeElUBFsfFsg7bTjWZLCzwFaSEJAF7gY6o\n",
       "iVJCFHNO/GXDSxCnb9RTSqzNNq3x9pUSQrlSQuvp0DwgavDyWYuUIJUS5HVfKSX8uY5FcETpG6oa\n",
       "X7MKg9IEo9EBSAnfRyQKVCIBWBlUNvCUoEnmE2QrcJCmi7XK6NLQQCkx0AYYW2OEUckaofQ3UkOo\n",
       "MzMmJcpKgm4rfYNCSgS8Bc4/vNFlU6VEopIoqkaQRdZTImes6bpotwfVpITAHV4pQfE3qUNKbBXb\n",
       "ICWY2eUNg4T2Jm+HN77xRIbCwMDAwMDwFY2TJyUyO29CEGEeunlSIrzBPSUAakA1NYnSfwWkBMcB\n",
       "c5GilFBLSImC/sqGB8RGl5IoIgzriRvWAc42lRJZGTZlXkRZRcgBnlMvgAdwuPSNlVLCm+mYeUdE\n",
       "SgCNIqUipUTElyslIlEoJxIErranBE0ynyBbgYOcz8LAa4tKCZEX0ZbbmDvz4uNR+pvDRSCJwHgM\n",
       "SW0V79ATQWadoRc20rRYHTOdArK8mrMQkV/uwVPL6JJCqPaUHkzPzJVsBZqlbiRjKLrGANZKiak9\n",
       "3ZBDVKUEd2ilRJP0DeAISIkoiv8rSlNsqJRguHFAkhI/8RMnNw4GBgYGBoavVBw/KUFK2EFTSoRY\n",
       "hE4uUHJxhEqJKlKirmkfpUznzCQM7QpICQBYyDXSN2j1GxuSErEEWoQs1+N41mPYotFlHU8JALAk\n",
       "wJo1iCoOY3S5Ukq4Ex1T98YlJWQZgOCCj/KkhOM7a0+JQiKBl+ALaKaUoHhKAPkKHOR8JoFXrhTf\n",
       "FpUSQI0UDkp/lm/B2+kCe3uQlII0E2B7SonE4ODqVUCWYXkxURkE5WqFWkaXlGcXx3GxisQe547Z\n",
       "lJTIeUpkSRDXhaBq6MgdTO1p/BmFlHAFHFopcdD0ja0hCGJCokhlwpQSr1iQl/Trvg44wjLsDAwM\n",
       "DAwMDBQcPymhqnFwuFgAyO+A8kGE5XErJarSNw6hlJhZBClB0+Mnh5L7cVlMYhdU13SMLKK03wGU\n",
       "EtkKln7oQ+CF2jH2egxbTN/IybAL5sWRODiLSe3jHlYpEYki7ImOsX3EpMSouFwjCRopwXEABBeB\n",
       "W6yUCEWhnEjgovpKiQJPCSBfgYOcT5EXwXN8rmxoZWQvy/FayqwnmlICoNwjWdBICc+Cv9MDrl2D\n",
       "pLRg+3aePAGoRpcHIiWAFClheiaESKt8nNUyuix4dhWRNUehlIAsp69DESlxWKVEZi0mlYT7/dXh\n",
       "KKREzVutHspSNwCmlHgFgyQleD4mJhgYGBgYGBiOD8dPSgCpLazsDqgQhFhEeVLCCY9WKUGabWbR\n",
       "SCmRIQnmlgUR1UoJUREQdXvAZBOEl3pKFPRXNjwgNroUV0qJRhU4tpi+kasMUTAvjsTDPmKlxPq6\n",
       "+z5CQQLv9rFwF/BD/4ZUSgAoJyV8PyYlCtI3JEGK0ze24ClRtYtO3RGuiuw5jrqut62UCHd2gL09\n",
       "8LIMSZDgBJTakdsyugTSSgk/JiqrHmcCLyCIgjRhkh1TwbNrW6RE1lOCppRISIl1f0eplCDW4mSS\n",
       "riR8LEqJbZASTClxw4EZXTIwMDAwMJwsTp6UyCklQiwjSvrGUSsljshTYm5bkLlqUkKWgaCffose\n",
       "toYHJiWCIJ4uRUl/nhACjUmJLaZv5MpMFpESsgB3Pq19XDhOc6VEEmB5HnyIaGk8dtQdTOzJDUFK\n",
       "DIfpz6IoAgQXvpMmClKeEgJfqG4QeREe30ApUeIpUbWLTt0RrhPZ00iJEqVEY1LCsxAOB8D+PiCK\n",
       "xUHittI3gFz6hohqpQTP8evSq4VjKkg9G2rDY1VKpJ5VFFLC4aNSUkIVVTiBU2paml2L2cfGOoVp\n",
       "hRuWlGBKiRsOjJRgYGBgYGA4WZw8KUEGhlEEPghhRnbqvb7VOnqlxKGrbwCZGpIxFo4FmSdIiWyU\n",
       "uQKNlDiMUsK240yZ7MuWH/oQuPrpG+vgZsvVN+ooJVxZgLtsQEocxFMiCZR8Hz4nQdM2834jkBLZ\n",
       "aQmiAIh4uE76WqSVEmJh+obES/BKqm9kl3CZpwRtF53ctT+QUgI4FqUEp+uxr40kFQeJ207fmEzW\n",
       "SgkJ1UoJgJLCQUvfaEDWGJYBXT2Ep0RJ+kYpKSGEpekbPMdDERTYfrp6EYnsWsw+TplSgoGBgYGB\n",
       "gYHhlYmTISWGQ7pSYiU9dzOkhKYBTvDKVEoss6REiVLC726PlCiKjYLo5NM3cp4SBWSNp4jwFrPa\n",
       "xz2QpwSplIjEoycliLVfBdpycXwHXCjnLnvKU0LgKpQS4daUErmAlUzf2KZSoqEioKw/y7PA6av1\n",
       "VqWU2Fb6RrK+V0oJqYZSAlhV4IiIe4uSvtHUU2LYohOjRf1vI33D5kO6UsLZKBuqUjiynhI0pYQb\n",
       "vgJICaaUuOHAlBIMDAwMDAwnixtLKbEy6fMiKxco2cHJKiWoZnh1SAnXgirUIyXcXjpg7cpd2L69\n",
       "2f3bAilxEKPLk1JK+IoEf1lS7jGLQyolPNz4Sgk3iCtvFJISvo9AKPGUSJQSNUmJUqVEtiRohtzb\n",
       "qlJim+kbvgV+eGp1EseolAA2SgmuVU8pwR+BUqKhp0Rdo8sUKeE46wpLcJyYlChRSgDVZpdZTwkq\n",
       "KUEoJRrwf/VQRUoQhFGVUsL0GpQ6ZjhyMFKCgYGBgYHhZHHypEQmMIQgwkOelDhJpQTP8ZAFOS8t\n",
       "rkESmK4FVVhJ2itICa+TDlg5jsNAHWBsjWv3VzS0BDeC0WVdTwlf3jIpUaGUcAlSYmSO8qSEQzFD\n",
       "LMJJkRKeh7DCU8LlwtpGl2XVN3K76EetlNhW+oZnQdw9vTqJY1JKkKSEF/vM1FZKhAdTStCqkhzE\n",
       "U6KqJChkGbpKXAdBiKO8ZJyuC4srUEqQpESVUqKGp8SJp2+s7qtKpQRL37ihwEgJBgYGBgaGk8XJ\n",
       "kxKZwDCSRPgUUsI6QaUEULCLV4MkSB27gpRw2vm36FTQtSWlxEkbXaaUEmEIjMfAYJBrF6gSAnNR\n",
       "+7iHVkoUpG9EEY5dKWFZ8dRkD+EGLgSUkxKByJeqG9ymSokS1cUrVSkhnTqzOokSpQSxrqNou0oJ\n",
       "mavnKZE1mswZXTacl5E1aqaUyKph6iglgPT94rqw+GA7Sgm+vlLihk3fqFH+lOF4wUgJBgYGBgaG\n",
       "k8XJkxLkS7XnAaIIn6Okb3gnp5QACna36pASybE9DzDNuIYdBbIM2MdESjQxujyK9I2Up8R8DrTb\n",
       "VMIjUBQEy2Xt4x5aKRER6Ru2AVGMa9Z7Ho6dlBiP46bZl+VKUsL3Kz0lXL6BUqKmp0QURa8IpYQf\n",
       "+gijEGKSvlGmlCDWtefFa6GIlyvqbzPQjFKCr6eUqDS6PICnRGOlRFNPCSBPSnD+4ZUSdTwlCFKi\n",
       "14sfuVv7Z4OREn9vwUgJBgYGBgaGk8XJkxJ+Jn1DkhDwBUqJoyIljlApYQcWWrIWO+/v7BS+/cgy\n",
       "YGtHT0rcEEaXZKBboh4JNQWhtUVSokwp4Xlww7RSAiCm+CCkRKuV/7wmjEqHLQAAIABJREFUKVE0\n",
       "LbWUEgJfqm5wG5QEresp4YUeeC6dNrJtpQRZ2SNBLVKCuA7JNecS48kqpcRqXddSSVD62ww0o5Tg\n",
       "6yslSo0uT8BTInUdapISJucfu6cEx8WP3Mmk5slWYZtGlyx944YCIyUYGBgYGBhOFqWkhG3beOih\n",
       "h/Dggw/i3nvvxQ/+4A/SGzrO1tI3IIoIaaSEd4TpGzWUEi2pdSClhBNYaMtaafANxNNnqseklFgZ\n",
       "XdaxSOjKXVi+hdD3tmp0uQ50y0gJVUVkNjCEa6CUCKMQbuBCFdXVoHy4oVRMSijKsSolRqNiUkLk\n",
       "qowuiz0lJEGCi6CRp0QRwUHuotPuoUKlBC1oJ0EprVtUfaOpUmL9vEkmt8pTgpinqmHT+tsMdNWf\n",
       "osDyLCh1lRJVRpcNlBJe4GHpLtFT6GotGqhKCfI6rJ79dUiJHKmUISWoz1hy/A09JYAtp3DUJCWi\n",
       "KMr75hBoSS2mlLjBwEgJBgYGBgaGk0WpGFlVVXz6059Gq9WC7/t4+OGH8ad/+qd4+OGH0w0PopQY\n",
       "xSZs2bx+TpILSIkjTN+oo5SoI0XXtPV5JViTEkVR5gqyDCxVPff7lGHdCRhdJmabgeeA32JJ0HVw\n",
       "UTYvmgpYWyQlCKWE7dtQRAVc8jbqeXCCLSslaBdA02KziIqt9zKlRCkpEXrwBa4wIIrTN5opJQoJ\n",
       "DmIXnXYPbd1TgnKPDtQBDMtAFEWba1nS3/p5k0xuVfWNgyglqtI35hYUoYFSoszosoFSYmJPsKPu\n",
       "gOfqC+So1Tdo6RvIGGtmSIml4tVL32jgKZF9dBSREqO83+fBUJOUSAgJ6npEwX3BcCKIGBnBwMDA\n",
       "wMBwQ6Dy7bS12h50XRdBEECnRkrbM7rkJAmRmCclzCNSSkRRVM9TIvsiGUXxLqGqpgeaCabcyEJb\n",
       "qaeUWColSomEkJGIYPMYjC6TMfius1Wjy/Xue9m8lJwfFQ2UErlr7vtwypQSTUkJ06RfAI6rtX1b\n",
       "RkpInJKbFkVUCKVEsaeExEtwuAZKiZIdX9JTokgpkSt9WDQvqR8WeEpQ7lFFVCALMhZugSFqkVJC\n",
       "0+J7t4FS4lCkRKcTH2+VvqEK9atvlBpdFhCqfaWPuTNPERpNUzeS/nPVN5LrEIbrlLuBFlcJCqMw\n",
       "/o5UFrku5nDz48yoj6qC9SpPCUVQbgilRFnqBlBNvjAcP5hSgoGBgYGB4WRRZduGMAzx1V/91fjS\n",
       "l76E97znPbj33ntT3z/22GPAn/0ZMJvh/JNP4tS9p/D05afxLx78F8XH3NER7o0ghBFVKQHRgqJs\n",
       "2sekhIjI8/DPP/kOTJ1po5OMIuDS82fwl+/7aO47J3Ag8iIEvuRlE5QXSduOA1We4HWopISJrqoB\n",
       "xohaYSKBogALma6UeO76c/RgpyRoL4r9SKNLf+kAP/I+4Md/vHBcyRgCb69x+sZP/iTwp3+a/uzO\n",
       "OwHvloynRGZePvhB4Du/E4DWAoxx6dhIXB5dhOLPMSxqQCglcsEcoZQYakM8t/ccHvm1R3D5PPA/\n",
       "/zHwL5//Iv7HpyboPPPM5jeiCPzczwFnz+b7Kolir6shxJe+iMEttxSey2evfxqTXRvAt6Q+dwMX\n",
       "krBSSkwmwDvfCbguemGAj315BkRPwD//2tKUC1uIgC9/GXjkEfzkXwH3/m/AdXEfL373t0H7hz9c\n",
       "rJSYTICf/Vngh34onk6hQCnxEz8BfN/3lfqw/Ph//H0okoTvf/vX5wfZQCkBbNREXaWb/3LV3+/+\n",
       "bpx+0X8N8bzZ3QUUpVwpYdvkYai4Mr+Cf/27/xp+6OMX9i/iR/7wf8G1v2zh373x3+H8ufNxI46L\n",
       "+1PVOH1D6NXi8WhGl57t4//8IPBv/22xUkLgBfzvfyLhn/zytyBS44fpxJ5g2ErfHb/+68Cv/mr6\n",
       "t5oG/MqvxJwNtfoGmW4nywDHQRZkCKGG67MZzvR3ckqJBRooJb785fjkwjDV/FvGF/B1vgn8/CMA\n",
       "gA+80Mag86sA4rUuCzIcP52TRlNKPPlP34ivfeL/gaQW5+P8yl/+Cv7TX/2n1Gf3XgnwAUFAEr/+\n",
       "7d8C3//9m2G+5aKA2+cBtHeUkxKXLmj4b799CY/9f48VtmE4XjBSgoGBgYGB4WRRSUrwPI9nnnkG\n",
       "0+kU3/RN34Qnn3wS58+fX3//2GOPAR/4QBywnD+PX/jcL+A3//o3S0mJqatBCzi4hgXTM9MlQQUJ\n",
       "EDyEUQCBi4NgTQNMV0LgOfitv/ktfPxtH290ktMZ8M//+m1YWD+LjpZ+WSwLdkhoYmbXlxb1U4Ip\n",
       "L7LQ1TTgRQMYFobLkGVgIQ6A6TR+y12RHbqmY2yNi0mJAs+F6TQ2ecuCNLoU9y4DP/VTwPveV/pW\n",
       "pms6Qv/lxkaXv/ZrwL/6V8Add8R/dxzge74HEH804ymRmZcnngDuuQfQWi1wq6CwDszRVVz0r+J/\n",
       "KGpAKCVMz8wpJSw/Vkrcrd+NT37nJ+H4Dr74fwNv+Ubg+W//z/jluy/j+/7huza/+eEfBp5/vjEp\n",
       "cYGfQr74DAYPfV3huTy7/AOguwCVlOBlmHMAX/wi8OyzwE//NKLQxy/8+h/gLd/1U/jb3lWIe39A\n",
       "Pa4kSHjxtAp84hOA6+LjnwPu+qfAy5/6IVi//Unc+o9+OLWkUp4Sf/3XwM///JqUKPSU+NmfBf7x\n",
       "Py4lJT7xl78HmVdqkxK560UguUfO7ZzLf7m6T3/nd+L74S13Es+b//pfgXPnoF2gKDqA1LouE3g8\n",
       "d/05XBhfwPve9D4Mwv8X/9M/+B78X9d+H09efHJDSgDAk08Ct94K69lmSoms0aVjBnjiiThuTz0/\n",
       "M/hf/xvwD77/7Vieu3n92Z2DO1Ntfud3gLvvBt785s1n73oX8PLLwF13xcqaQk8JQpkURYA70/E3\n",
       "L4xx5gEKKcFRlBKynHp+rZ+xzzwDXL8OZDyMnnn+NzG2Ddz/+nciDIF/9Nv/EjveNQC3AgB6Sg8z\n",
       "Z5b6ja7HlWwSBJ6L8//xM7j6+F/j7Fd9NXXeAOBTf/MpvPb0a/HGW9+4/uz/+Mh3w+dehYTu+9zn\n",
       "4n/2/v2/j//+qt8XcOW/BPjM0+WkRGf8RtzD/zQee+xr1p89/vjjhe0Zjh6MlGBgYGBgYDhZVJIS\n",
       "Cfr9Pr71W78Vf/7nf54iJQCkXk4Nyyg3ngNgjDmoGIK/YOSqb4SCBPgqbN9GW24DiIOBpSsidByc\n",
       "bp/GI695pP4ZAvibvwFgD3Dx6hj333Em9V2RLDyLnGN6TeWCz61ICUrwTUKWAScQY5n3bLZmFIba\n",
       "MJ7PhkqJIvk/mb7BT4342plmXJazAMPWENHKhJSKgvQNwwC+4zuA22+P/x5FwD/7Z0AUZJQSt96a\n",
       "+51hALdpbXB2DTfOFboLD19QSrwtSKVElozyPNgrpQTHcfjGu74RAPChBfDVbWD8ahO/IfwGvu8R\n",
       "Yu098USxNrxUKRFguHe59FymjoFuJ5+SkEjDLQtx3+fOAY88AjGK8J+fCRB927dh8YVfg7RfknKB\n",
       "APimbwIA/O57gB95C/CFv/oPeM0XrpR7SiQXZoVCT4lVO62nYWxnlC6reZm5BiReARWaFgel5M9K\n",
       "fF+GrWHxM2fVn2GsrDzI+/01r4m7EzUsPEr6R830DcMy8Orhq+PnkhviG1/7HXheHONL4y+lG676\n",
       "szwLqqjBrukpkU3fiDx/fRkKn1+2DcGy8eadB4HXPFR4fMMA3v52gFzWt9wSf37XXfn+U9eBeO4v\n",
       "lwDMIV68bgC4I0VKRK6LReTULwlqGDEr+Uj6Of+3g+cwsSfANzyC2QS4xt+E3ZmBhJSg+WgMh+lb\n",
       "dHr1BegA5ldeKCUlDMvAN9z5DXjzHRu25pdVHT4XrUkJwwDuu48Y5jUB3lMB9scu5G4xKRHOzuLV\n",
       "LQqRyXBiYKQEAwMDAwPDyaLUU2J/fx+TVT01y7Lwh3/4h3j961+fb0iSEnYNUsIADOiYv2CkS/15\n",
       "HkJOBB+kd1g1DVg6EkLPbZwTnfQHS8fFvfy4miglUru+NDt+GikBC/1WPU8J10UuCXr9ok3rj1Kl\n",
       "IEEZKZFU3xCmxqZxCXRNR+S5jdM3smNI7BSqPCWS2Fdot8E79XwcojDEjhnimlRCYpCeEtlgzvdh\n",
       "+1LhFFOrPJQlrBdEsWEU4qrswbt+rfR8Zr4BV8gf2w1cKCQpsZo7juPWu9pV5pSpne/Vsromu5Cm\n",
       "i3JPCcOIo89V2Raqp4RlxSkPhkGvMrCal0VoYO4XzF1R+kaJUqIOKWEY9Pu9sOoDsa6rSIn1c2nV\n",
       "sGxMydo7aPWNhJSIogi2b9OfX4k84ADeJeSylgRpfY390EcYhZv1QD73V8/Yl5IfkqSE4yCQhHyK\n",
       "XFFJ0IKHF+kpYRirdDfas7LgXABgduUiAMC89lLZtFD9NwZyDz4XbdpkhykI0KQAxrRcKVHxTwHD\n",
       "CYCREgwMDAwMDCeLUlLiypUrePOb34wHH3wQDz30EB555BF8/ddT5NZNlRIrUsJ8yUjvvPk+AkEC\n",
       "H6ZVCYlSIjokKXFpn0JKHLFSIuC3SEpsQSmRVN9QFECc1SQlVB1R4DdK33Cc+L9OJ910oEfp0n6Z\n",
       "gVpW/J9hAEKrA8GuR0pYsxECHrgeFRgeApVKCcsXC6d4W6TE1J7C0IBgdJ3yow3M0IDNFZASYp6U\n",
       "ADbVB6rKeKZ2vlfDvCzZ0GZmtVICWAe8VE8JY7OmyqpvWJEBM6pHSkRRVKqUKCQAoigmSEhSgnK/\n",
       "F3pKEOu6Finh+7EcQ5LKSYnV2jto9Y3ID2BZwHhuQxZkejUNo969XUVKkOslIYbWVSUopMSVSZ6U\n",
       "CF0bnKIih4akhB9t0r4MI19CeaANMLbHiKINcZC9RRfXLgEA7AqlEo2U2JG68CpICXVFSihigQqI\n",
       "9juGEwcjJRgYGBgYGE4Wpekbr33ta/EXf/EX1UfJkBJjO3ZhLyo9ZxiACh3KZQPWbUSQ4HkIIMak\n",
       "REYpsXAkRL53KFLiMuUF/VBKiRokQchb6LdvHFKCNLqU6pISmg74Jc7zFKXEeBz3n33Z0/UQPPjN\n",
       "2sgMlNzgFV/VBZx6ZWCnly8g0FBOiElSqVLC8iTsHDEpYVgGDA2Vc25zBpYUgqUOKVGqlCB2vomY\n",
       "HZeEJVoLB6oar8PE1iRFcJCB7tmzdE8JkpSQdtP3DBG0O4IBISpJ3yDWtRd64Dm+8JwKCQDCjHad\n",
       "vkG53wurPjRQSpxpn9k04rhKpURLqqmUoBhdJmO6sl9CqG6JlCCVNUXlQNfdWDr2kmdKRinBy5Rr\n",
       "TUnfuLK4Ahj2xoiGgBd46MiddX9hK33/yYIMVVQxd+foKb3cuQCAde3leOj7V8vnhUZKiF143IZM\n",
       "NAzgda8jGggCFCnAeFatlHjDG0q7ZzhmMFKCgYGBgYHhZFG/YH0ZMqREGIU5wzESiVLCu5ZXSvi8\n",
       "BIGmlLBj6X3WPb4Okhfmq7P8C/pRKyVCwcJO5+CkRF/tY+EuECwX21FKEEaX0qIBKdFQKVHU/87Q\n",
       "A8+JhQ3JWEpsdyHVJCXmV1+AUUVKZEuCZpUSXkOlRDZhPUEYxhdTze8OJ6QEPymvIOOK9PQGN3Ch\n",
       "SBVKiYoynkmQ6zgxT8PzwEVhjt7SB8fFlWASf1GqUmL1f6qnRJlSggjafYmengIgt66rSvbqqg7D\n",
       "phyLuEePRSlBNCrzuUjO56BGl8mYro5KCNUapEQU0e9TclnTlBJrUEiJfZNCSrgO+C0oJUiFlWEA\n",
       "bi9//2Xv0ywp4V6/AgAI9vfpkwLA9m14gYe2lPbZ2ZE6cLGpCEJTSihigMmcpW8wMDAwMDAwMDTB\n",
       "kZAS5P9pSEiJ4LqRftFdKSVE5JUSc1sC5wcHV0qYQ1yf05USa0+LEhxUKREJFgaHICV4jkdf7WM5\n",
       "29+60aXSgJTggrCR0aVh0H09B0MfAqR0wwJSQur0ILk1NO6Ic8QrSYlMSdDUdfd9mJ5UOMU9pQfL\n",
       "t9YqAwDFSgnbjiN7yvZbQkpIk2LSDgAC2cDUiRVHJNzAhUaSEsQk11JKkDvfqyUcRREucBPsmCGi\n",
       "MEwtq5ynBPF/qqdESilBv2f8IESkjBEqNUmJktQNoEQpseovCOIqCUWeEoVKiQZGl8PWMNWoUikh\n",
       "10/fyBpd8qu/XxuVPLtqkBKLRcybyZn4uchToo5SYpycM0k4OA4EhTJ5ZUaXlIeHH6bTN8J+/v6r\n",
       "IiX8/b34D0amTiiBsTXGsDXcpKms0Be7cLEhiHLDXJES04XDSIlXGJhSgoGBgYGB4WRxJKTEbmu3\n",
       "kpRwVtLbrFLC4yRIyCslFrYIzvehq83f5kYjoMXpGFHGVBXwrMdwAFIiDCNAsqB3tXgQdUmJUfqF\n",
       "Wdd0LKbbIyUSo0vFNIDd3XqkRMP0jaL++wMPXLQKmJOt2sEg9btkSHK7D8ktqaZBwN67jEVHbqaU\n",
       "IHd9K5QSHMdhoA7S1SQo1yo+eHEEa1gGgp0elBm9lCsALCwXEGx0lS6mdlpR4QYuVHk7nhLJME3P\n",
       "hCfxcAVgMb6WWlYpgmM0Sq0X0lNiXZqSuIBFSonLozngawAXwJhR1m9TpUQFKTEex8Vslktg4TRQ\n",
       "SjQ1uiQa7ag7mNiTHKmUnE9LPrjRJR/62N0Fro8r0jd2d+nrk2hCu0eLPCVyZVkzpERH0DF1KaSE\n",
       "60JQa5ASDY0uaaRgFSkRGSPstznw4wltSuJjU1I3AKAvtuFgcy1oSglZCDBdMqXEKw2MlGBgYGBg\n",
       "YDhZbJ2UGJkjvFp/NUZm8cvwaARIZ3Xw07xSwk9ICYpSgg/CAyslzvR0jCkS76qAZz2GA6RvLCwX\n",
       "CEXIPID5HOj3C49fpJQA4hdts4FSwnXjzfpuN99PYnQpy4C2HAGvfnVp4JL0z4UVSolM+kYRB9Mf\n",
       "+OCiVcC8WMQnriip3yVDkrt9KG4+qKPBvX4N4c4ORlbJuWSUEikyyvexdIuVEkA8D6l1XaSUKIlg\n",
       "R9YI3ZvOoU0Lxlf48hUDnKNjqA1z5+MGLrSElMhMMqmUKErfSO18r4ZpWAaG2hDTloDp5S+nlRJZ\n",
       "TwliveT8BkRtcwFLlBIXrhoQnCF4R8eXr1Lm7wBKCerzhqi8sbsbExPjBYWUKFNK1EjfGFmjHCkh\n",
       "8iI6cidHKiXn026glMgaXXJhgFe/Grg+KZkX4joUoegeJbm21DXOqkzI5/4IuEXXMQ8opITnNVdK\n",
       "0Iwuiao9oxEgnKITuCQp0e/HFZaTxxNnGLhytl2qVFpfzwx6UhtOtLloufkTBMh8gLnpQuaLSYkK\n",
       "fprhBMBICQYGBgYGhpPFVkkJy7MQRAFu699WqZRo36pDnF2HyIubUnG+Dy8SIfN5pcTcEiH4Bycl\n",
       "bh3qmHn5wOUolRLjhRXvCE8mQK9XrDRANSlhzYzapEQiPqC9aJHpG5plVAYuSf9CEDVO36C9eHd3\n",
       "PHAhvfJG8lEyJKWzA8WrR0qEo+sQdk8dSilhusVKCYCyI38AUsKwDAxvuRudRfE2+Qt7BiRvSPUl\n",
       "SJESJZ4SRekbKXNKgpTQNR2LjozFlRdz6RspTwlivaRUFz6RvrEiLoqUEi/sjSAHQ0j+EC9SyvRu\n",
       "WymRyOyHQ2CyoKRvlHlKHFApUTYuy4tJibqeEtn0DSHy4ymeViglKu7tpkqJnB9HRilx7owOM1o9\n",
       "YwnCgXM9iBolzaRIKVEQtWc9JaSz1UoJQYgfvavK1hAnM0xvO12qVCpSSvSEjVIiimJTXkLkFatY\n",
       "ogCy6oKP6KREGMZjSf2OgYGBgYGBgeErHFslJcb2GLoW7/BWkRL9O3So1n7ObNCDFJMSRJAgikDI\n",
       "ixDCCLra/G3OMIBzZ3Usw2NQSth2/MaKmJTgg2o/CaCalHAWk0akBM3PAUhX39BsA7j77kpSoq/2\n",
       "IYaAT5TDS6FB+kZvx0cUSIWNDAO46674hV9uD2orJWAYUE7fDMMyUiUBU6hQSixqKCW2QUqcue0e\n",
       "9M3itJRL+waUUKcGtW7ooqVUV98oVEqQ5pQZUsLsqjD3Xsqlb6Q8JYj1Qt1FJ9oUKSVeNgxokQ4l\n",
       "1HFptB2lRBUpoevxf9NlA6VEjfSNKIpgWAYG6qA+KeFbaCv1lBLZ6hshJ0CEj7vuAox5hdFlxb1d\n",
       "h5RIKWtKlBKGAdx9iw6HzyslOM+DqNQgJSQNgbmMicN2O9c86ymh3pS//4baMKeaIc9Hni7h33kO\n",
       "rblNnxQUkxJdsQU7iudiPqf4cQgCEATo9F0goJMSs1l8akX8LsPJoOifDAYGBgYGBobjwVZJieRl\n",
       "rszkDYhfEE+9RkfLNnJlGb1IhMJrML30TpbW4uDzgC71Gg/PMICvuk2HzR2xpwTPx4HvqnTBZIuk\n",
       "hDunkBKSFG+91SQEgHT1jbZTj5TgOR5CBEz8fIlKAI2qb3T6HqKgXClx+nT84u5hAK2ezyX4yRTy\n",
       "qbNQBAULt2ScRSVBPQ+m01Ap0WrF550lhipIibNn74YcAM6SLiG/PDbQ4gpIiWBFSph5P47aSglK\n",
       "+oau6bB7LTh7V3LpGyIvxutsOgXuvJNudEkqJVasksYrVCLvysRAm9fR4nRcHm9PKZEjoyikxMxq\n",
       "qJSoSN8wPRMCJ8THrElKmJ6JtnKw6huzpQABIU6fiqipKGtsiZRIKWsqlBL33qHDl/KkBO/5kLQ8\n",
       "yUBTSkizBb2WMPKeEu3bCpQSmTQ98ny0mQXpq+5FZ+GiCIWkhLAhJahztyIlWj0XoU8nJcoIY4bj\n",
       "R2T38YUvUDkwBgYGBgYGhmPE0ZEStBJ9KxgGcNP9Q3S9cU4p4UYSVCG/c6lpgHcIUuK+O3RqCcKt\n",
       "KiWSga4CqunSAh9qtd5Ey0iJoTaEt5zn++M4qlqijJRYG11KUUxK3HVXJSmBKIIYAoZbUMaygVKi\n",
       "0/MR+eVKiSSAXFidWKHhFu9qJpAnc0i7Z8oJMVIpkb3uvo+F01ApwXHxQMfj9I+q0jfau5i0eEyv\n",
       "XqS2uTo10BGKSYm2IkOwFrEXB+HHkVJKFBhdkuaUWVLC3+nC288bXUqCFBMS3S5w6hTV6DKllDhz\n",
       "Bmi1oNk+lcjbmxvoSjq6oo5rlDK9TZUSmqSB5/g8sUAhJeb2dpUSqQC2BikRhAHcwEVHUespJTJG\n",
       "l8aYQwAew50gVn2UKSXuvDPOFQjpaqOie3QwiJd0FGWUNRVKidferSNUjNjgN3mghSF4P4BcUymh\n",
       "TJeFDy9yXRsG0L29On0DSD9S2wsHO/e/Af1lsVLJsAyqoXJH1GCF7rr/QlKi6yL0ikkJ5idxA8Hp\n",
       "4au+6qQHwcDAwMDAwHDsSokkF/e21+nYCSZ5pUQoQs2qEgCoWgifBwZip9HQgiCWzL72bmIXj0Bu\n",
       "968AtZQSQJqUMC0I0XaUEj6NlMj0l6CouyiKEEZhvLMbLhHwEnDzzdWkRBgi4ADDHtO/b6CUaHc9\n",
       "hDVJifGEhyUi9tOogDozoZ6+qZyUyColMoTYoo5SIku20VI4KkgJXdMxa4uYXXmB2ub6wkBfLlFK\n",
       "qDI6roEoM3dk9Y2DeEoEgx2Eo326pwR5YUilRHYXnWinzWwqkbe/NLCj6OjLOq4vCkgJc6OUqkMc\n",
       "Uq87hZRYOttVSjQlJWzfhiqqkCSuvlIiTJehDDgRej/AzKxQSpw+DXQ68QOwoAntHpXlODVhPi9Q\n",
       "wyTIkBJ33KYCgYS9yXLzQPM8BJIITa7nKaHNrcJnZdZTYnBrO76f7Q1pWUVK9JY+Tt/3Bqg+4Fp0\n",
       "RVWRUkLjFLgI4AVeOSnRcRG4jJRgYGBgYGBgYKiLYyclklzcwa1tSJGHXrjZ6YXnwYkktKRWnpTo\n",
       "z+AJgFjTYiDBdBobnZ27qQ/IC9huenuydvpGXaVEq7WO6GaWBfGgpAQhRdc1HaG5PDQpEUQBBE4A\n",
       "x3FoOwbmkk4PqrPwfYQCVx7sN1BKBB6RvpFRkGRjX1viYC8KyBACrbmN1plbD6eUsBsqJYADkxLL\n",
       "jgLz2iVqm5FpYKDq0FU6KaEIMs7KBqKdAlIi9Jp5StirIGwQqz6IJbzJ46eQEtld9JbUSrWTp3P4\n",
       "ob8JqpMSnbaBoaZjQDk/APEDwnHWO/x17tG6pISZjJNAafWNLSslksCeWIqlyBpdJqTEsO/Hqo8y\n",
       "pYRefn+XPZaSn1HVMAkypISuA4Kr48JVY/NAc10EkkAnTyhKCW1mlysleGlTSVjPK5Vocz4cxu3D\n",
       "wEffjjC4+S5MNA7TKxfp81JASvBhCEGUMLEnpaSE2nEROIyUeKWAVd5gYGBgYGA4eRw7KZG8lHE8\n",
       "h7HYw8AkgiffhxuIeQIAgNQzEPI8am0vUvoTBR6c08cL19L16WunbxxAKTG3LEhoSEok25SLzS6e\n",
       "rumILPPQpESSugEALdvATNTj34ch1TBz80MfIc8XB/sN0jdkNVZKeB69UTaWcmQeznySP1AG3YWH\n",
       "7tnbD6yUiDwPti+mjetQg5RIIh4SNUgJu9eCtXeZ2mbiGNhtFysl5BUpEfTppERSYYWGMk8JYfcU\n",
       "hPGE7ilRpJQIMvNJtOPG47QKYdXh1DVwqqNjt61j6lCuFc/HaSmrHfBtKiVox0pSApJzWeOQ6RtD\n",
       "bZhT1iTkDbEUS5E1ujQMIOIFDLp+rPqgzYvnxUqTXq+SlCjKKkuWdR1PCcuKOVRNAyRfx4vX06SE\n",
       "L/J08oSilGgvnGKlxGotLhaEyWTm/itTSsyvv4ylBIiyinlbwuzKRfq8FJASCAIIkgLDMspJibYL\n",
       "j5ESDAwMDAwMDAy1sX1SQq1HSgDAVO5AXxBlMj0PTiihRZFTi10DASX4rQJZXU70dFy8Rtm53KZS\n",
       "giQlbAsy12pGSgC5QIJWbpDWX4JCpUQYrINVzTIwFfRiX4TUDwNEQgkp0SB9I4h8iJwYd1eHlJB4\n",
       "uIsCLwsCfTNA/+Y7DqyUiDwfoiblds22qZSIoghje4yBOoDb78C7fpU6zJln4HS3nJQ4IxnwenlS\n",
       "wvEdeIF3IE8J6dQZSNMF3VMiuTC9HrCMKyRkd9FbgRArHDqd9bxf6beaAAAgAElEQVSkVAirDheB\n",
       "gTN9HWd6OmZ+wbUiBnFYpUTyDNB1wAnox6KmcBxB+kZyLk2UEqTRpWEAkSBi0A9gZpULCZJalcm9\n",
       "PcqXQk6OVamUINUwBaTEmmjmADXS8dIoo5QQ+dpKie7CzaUlJUjWYmrclGdlESkxvXIBs3b8/Ft2\n",
       "ZSwLlEplpIRUg5RQNBeexUgJBgYGBgYGBoa6ODGlBADM1Tb6C2IIngcnENFW8koJvm0gFIQDKyUA\n",
       "QA51XNrP71welVJiYVuQuIZKCYD6os3bznaUElxMAmmWgQmvU/vL/9BHJAi1lRKeF8etvV6+qRd6\n",
       "68AiO1DXjTfHu93NkFxZgDsvJyXs+RhCCLT6u4fylBDUfCC/TVJi7s5j6b4gIdjpwd+/Th3mMhzh\n",
       "pp1yUuKUYMDrHFApkfGUGJkj6JoO9fTNUKcm3VMiiex5HtjZASaT3C56x/Q20WlCSlCUEmZk4OaB\n",
       "jpt2dJiUMr0A0qTEFpUSbkQ/FjWF4wiMLpNzqa2UyBpdGvG4uqoPDxZkjjYo4r46ZPpGSg1TkL5B\n",
       "HqfFryqqEKSEV5OUEHkRQ5tDsEN5cGCzFstIiYE6yFViSZosrr6IRSe+x61uC3aBUqmMlBBltZKU\n",
       "kDUXDiMlXjFg6RsMDAwMDAwnjyMhJWgvhgnIl7JFS0NvTrwR+D6sQEJHye9acq0RAqHmm3xBf1o0\n",
       "xMuZF3TTM49MKbF0LCi8lpZrFCBHShC7m7qmQ9gCKZGUAwUAZWlgzA83/ZWREkGASCwhJTJKickk\n",
       "3qjlKasr3sUXqaREdoPXMABXEeEt6UZ9CaZXLmLS4sHxfHnllzJPCc+DpOUDeXJ6h9qQTkpkd6JN\n",
       "M/YWySAV7Og6YNB3sC3OwC16OSmxKxhwOmntfR1PCYETEEYhwihMKSWG2hCtM7ehtbDX5xxFUd5T\n",
       "Yj12I+cp0Zm7uTaaSJT3NeMUJIc3cNtQxy06vUwvgJxSIusDkUUhKdFqpUgJL9qyUsKO547sjxzT\n",
       "yExf4wMpJcK8UoILA6gdC5F3tKRESg2TvQ4UUqIr6NibZ9I3BK5W+gYAnLJFuDtd6piStVhGSmiS\n",
       "BoETUiWlkybWtZdhduNxuP0O3AKlkmEZGLYoeS1BAFnW1qRELvVlRUpIqgvHZKTEUeHSpUt405ve\n",
       "hPvuuw/3338/PvzhD+fafPzjH8frXvc6PPDAA/jar/1aPPvssycwUgYGBgYGBoa62CopMbLiHVdF\n",
       "VKAICubuPNeUjM+XHQ09sonnwfHFmJTI7lpqBkIhb6hYBfIlsCPouDKhyKkbKCXWREsdUsK1oAiH\n",
       "V0rsqDsQHR+BQnnRbaiUWJMSixHGIAKXAol3/EMfnChiZBW0yRhdlnEwfuhDFldKiUzDbCw1GgF+\n",
       "DVJiduUi5qsdUFogmBpnkVLCj9M3ssgqJXLHbqCUSBQJAMANd8EbdK8MTzDwqlMVpAQ3gt1qrpTg\n",
       "OG5NJmTTN7pnX4XuwlufM2mMSgt0c54SCztPSkiZ9I1WC75k4PYzOm4/rcMVC64V4bZZ5x7VNT2/\n",
       "PilKCZ9roJTIGF1SeKbUNT0KpUTW6HI0ArjVuOS2hcCmzAt5XxWQElEUNxsM6P0m919KDZMl8pLn\n",
       "PtFdX1lVVCFICVfk6KQSjZRweDi9NnVMiadE6rFBeXZl5z1p4uxdhtOPjx0Megiu71H7sHwLXZlC\n",
       "jAQBJEnFyBrRn3ErUkJUXNhLRkocFSRJwgc/+EE899xz+MxnPoOPfOQjeP7551Nt7rzzTvzJn/wJ\n",
       "nn32Wfzoj/4o3vWudxUejyklGBgYGBgYTh5bV0okO0zDFmVXGWlztWVHQWdGlNNYKSW6Wn7XMlQN\n",
       "hJx0IKVE0l9PypcgzEmSCyAJEniOX7+g1yElTNeCugVSQuRFdAIBCzHI/5BCShSRAqTRpbwwMEpI\n",
       "CZpZY+qHPiCItdM3yk7XCz0oYhxYZBuORptrlQzJU6S4HGoJzGsvYdmJq7hQ1QwJSpQSnO9BbpUr\n",
       "JfpqHwt3kQoSm5AS5P0h7Z6GOKWTLb5s4I6zQ+iajrE9TimOElJCjwyYGp2UKPOUADaBbpaU2Ln5\n",
       "TgzMEKoSqyhS5AZ5Iw2HwGiUr8wwNXMXMJX2ZFkIVRWhYuDOszruvGmIQK6ZvnFAT4lQ1TCdxsH3\n",
       "cAiEfAOlxFGkbzRUStCMLjkpHpfcsuDTSInstaLc26YZn16BH2uxp0RB+sa6u+ScyfQNgaOTStLq\n",
       "eU6s76HFwe7RVTF1PCUAOilhGIB3fQ/eKjUk0nVEFKWSYRkYqIOYiMsio5QoIiUE2YW1oJMSNURz\n",
       "DBU4e/YsHnzwQQBAp9PBPffcg8uX06k4b3zjG9Hv9wEADz30EF566aVjHycDAwMDAwNDfdC3U5si\n",
       "k74BbF4Mz+2cSzU1DOCmm+I/m30ZvTkRcK4qIHRVDdY8HSAEsoFQkA+klLjzzvjPA1XHyDyYUgLY\n",
       "7KbKglxPKeGZUMXDkxIA0A54TDkX/ZL+EhS56pNGl9LcwCh6TWF/6R8G4CWpdvpG2en6oQ9FkmCM\n",
       "olxDmuo8UGRguaAfbAV77zLQjwOZA3lKhCG4MISsCbmfkNPLczz6ah8Te4Ld1m56oCQsC7j55tyx\n",
       "yPtDOXUTMF3m2pi2B4gmbt3tQVgFczNnhr4aX/mElFAiA6bSXCkBxASbF3iwLEBQLQRmgJbUAie3\n",
       "YQFQRQOWtZsmN6hKid2Up4Q6W1YqJWahAAQyem0FHU0GBAezpYNeW0kPMmt0eUBPCSvS0O3G8WK/\n",
       "D0Qi3YehUClxCKPLgTZYk0pJkJtVSkRR+U4tzeiSk+JxiaoFz6yRvvHMM6VNaNB14LnnNmuFHPsa\n",
       "rgvs7KSOtdvR8aXJ36WVEgLopBLHbYiJVdkb3QTMrkodU6GnxKW0YWWWEE9u0cjYBwY7cdf6LvBX\n",
       "z+XnpchPAohNLGuQErzswpozpcRx4OLFi/j85z+Phx56qLDNL/7iL+Itb3kL9btPTqf428cfA8cB\n",
       "58+fx/nz549opAwMDAwMDK9sPPnkk3jyySeP7PhHTkpkYRjAfffFf172RJy+TpAMvg/Lk3C6ld+1\n",
       "9CUDIScfSCnxhjfEfx62dPyd8Xep7+sqJYD4xdr0zDhANKtLdFqehY6obUwWSpAjJa5dS33f9jns\n",
       "w8araP2Zm/zpMpNJMlgVZwb2w/pGl5wklwf7dZUSgQdVFjHfs+KghJhDKilxWgbMclLC3b8K9GO5\n",
       "dd3qG6ZnbgIs30coiNBa+ehQXvFgvh+fZnL8SlKiQCmR3B/a2VvBZYg3AHhhbwLO3YEgcKnzyZIS\n",
       "rcDAvlSglCjxlAA2SgnTBEJ5DF3T10HzpMVDci/ANHfzSomcp8RNKaWEPF3k8m80sZdSSlxzfAhu\n",
       "3IbnOXCOjovXxnjgzrPpQZKKoxq+L1SFjGliHmibtcgFgOjAXqjoZOLe5N5OT1S8rn0/5iYkypSm\n",
       "gtjMM0EWZKiiirk7R0+Jb8iEDOP52HMlDONYtgjZ9A3DAHg5HhevmnCXB/OUqENKJEaXlUqJK5tj\n",
       "ne0NMfdHGVIiKiaVknYrUmLHCnG9Qw/oSU+Js8lyKVBKkKk8g0H8CIYxBm67DQAg7p4GN/mz/LxU\n",
       "khKtalJCdLGcy1TCqYgwZmiOxWKBRx99FB/60IfQ6XSobT796U/jl37pl/DUU09Rv39bv4/vfvyx\n",
       "IxwlAwMDAwPD3w9kyfvHH398q8c/fPpGEABhCBcBbN9e5+KWkRLJy5y5I6C7JEgGz4Pli+i387uW\n",
       "nmgg5JRDeUqc7uqYeYdUSpCVBGhJ5kQwZfsWdkM+LpEolvM/VUoJ1QMMzs7/kMi9B+KX750duskk\n",
       "WX1DmBnYD+qTErxYopRokL7hhz40WYJzJd+IFkuFioLQzCsKSAT7+wh24qC9tlKCJKN8H5EgUS8n\n",
       "x6WnOHf8A5ISnbOvQmeRJ9heuGZA9Dbzku3P8R3Igoyeb2BOIyXCGkoJXoIXxkqJQE4HYYuOBNF5\n",
       "AZaFNLlR4ikRhEG8tiazXJuW1EopJfYcD5K/6U/ydLywR7leW6q+MfM2pITt2+B8FeNxnnxqSa3C\n",
       "9I3kctIUDWVKCdq4yHORamSj0dI3+FX6BidZsBdHS0oInIAgChBFUaGnBHmsmwc6zCidvuEUKSWA\n",
       "uJ3jrP/aXwZYFJASiadE0/QNUQTabYA3phB3TwEAlNNnoczyz5VKUkLZkBI5nnlFSgScCz6SSa4Y\n",
       "QKyKof6OoTE8z8Pb3/52vOMd78Bb3/pWaptnn30W3/u934vf+q3fwqBg0ssIQQYGBgYGBobjw+FJ\n",
       "iZX0dmxPUrm4dUiJZY9Hd7l5IYXvw/Qk7LTzSgmXX5ESh6i+cbavY5kpQdhUKZEy7atQStiBhVNe\n",
       "WEuvW01KRNiPKMF5Jn2jLNggq2/wEwN7fk1SIgggSAqm9hRhFOa/b5C+4YUeVEWEv1dOSgwGK8m1\n",
       "qiDKvt1nYYwAPX7pTNYdrfJLEgVGUQTbtzcBlufFSomCZVBaFrQJKWEb0NX4BHs3nUNvmSfYXtw3\n",
       "oATFpESilOi6BqbC4T0lPDEdhC27KiT7JbqnRFYpsfKUSHbQOUqbbEnQq44HNdr0p1DK9ALIp28c\n",
       "0FNi6m5ICcu3wIcadamXpW8U3erAAUgJ4lzqmF2S6RtJUCsoq/tNsmDNj5aU4Dhus15KPCWSY906\n",
       "1GHzxoZscBw4fFitlAAAz4Pqhlio9H+WyHLCTUiJpJk0WUA6FUsstNO3QpvnSd4qUkJV2thfGnQ/\n",
       "jhUp4QYuOpqcm/bFAlDVtSiE4YCIogjvfOc7ce+99+K9730vtc2LL76It73tbfjYxz6Gu+++u/hY\n",
       "YC6XDAwMDAwMNwIOn75BSd0A6pESiz6HrkW8GHoeLFeMSYlMgGBzBgLsHEopcYuuw8IWlRJFpMTK\n",
       "J8MJLez6/lZICdkNcD2ipDE0ICVIo8tGpITvgxMEdOQOpvYUAy2z68TzccQUhgDPwzCA17ymeAxt\n",
       "VUK4TyclktQeRVmlTsgqBKuclODHE+D2cwBi4ojjOHoZyVX6hhM4EHlxPRfwfYS8dDBSotsFbDsl\n",
       "QS9TStx/6n4AQO/UrQg8wLNNSOpmnJcNAxpXQUrwEtqugQl/eE8JV0jft3avBWF5OSYsEnIjijb1\n",
       "WoG0UiL0NjvoFFZJE9QUkXfNddAmxq1xOi6Pj04pMbEJUsKzIEYFpESJ0WXRrW55FoIo2KwzSsNs\n",
       "WklWKVH1OBP4jVJisYjvC14UVuoeC+bo4KREWRoB6Y+5VtbUUErcflqHJ6aVEjYfYVCmlEgefOMx\n",
       "Fm0JVkBRhKGgJCjFyFNX85VYdB1QxxaE07HXS+fsbeAW6cofQH1SgvqMJUiJXiuel1W2SHxs5iex\n",
       "FTz11FP42Mc+hgceeACvf/3rAQDvf//78eKLLwIA3v3ud+PHfuzHMB6P8Z73vAdAXLHjs5/97ImN\n",
       "mYGBgYGBgaEcR0dKqDquLa/lmqdJiQh9hwg4fR9LT8JOJx8gWDAQRDc1VkqQbue37epw+bxSglqu\n",
       "joK1UiKKykmJvbjUnBtaGNYkJRIZaRAAQjaQCAIIYYR9f0bvb7b5vFQpQRhdwjBw1dPjvOcaSgmI\n",
       "4jrwy5ESwEYtsSIlyjwlWqoIbmwAtxYrJYD4z56oQcgYeWYhTeaIds9sfrcaZ+66rramc9fc8xDw\n",
       "B1RKcFw80PEYOLMaQ430DZ4XYGgccPUF7J67Z93m8mSEDl9OSihuCHAcFkG6j6aeEpYVk32JegMA\n",
       "vJ0uxOW1tFJiNovPJzFVWHtKpJUSqQuoqoAkoR+IaU8Jz0KXSDvpCDquTg+vlGhJLfihD9u3oYrq\n",
       "uj/DSislJG57SomxnfbjODKlRBgrJdbTuxpXyFtYTijPLqrkKG1wUBUgkz9ropS446yOUM6SEjWV\n",
       "EoaBZVfJX4cVmqRvZL2DdB3oXHLAnYlZgv5Nd4CjKJUMu4qU6GBsG7i9ipRoy7kqy4yU2A4efvhh\n",
       "hCFFsUfgox/9KD760Y8e04gYGBgYGBgYDovDp280UEpkc2pnvQg77oaUiDwPlidh0EkHCFEUwYwM\n",
       "+JHWSCkRhmmPyXNndPjSZkyJq3yZ1J3EWinhunFgQEtIJYIpN7Iw9Nzab6Lr9/Ps7p9tI5AlGPa4\n",
       "tD+gWikh8iJgWeAAeGIrns4aSgmIYmGZVwAps8uqMbQ1CcI0v1VLIyVcQYuVCCVQZkuop2/a/K7I\n",
       "V2K1NZ0LrnwfwUGVEslAyfmrQUoAwKwtYnb1hVSb6wsDPbmClJgtYWl6tuhKSilRtqZJTwkLIwy1\n",
       "zXUIdvoQF9fTnhK0C7NK3/CCAqXEqp1ucWlPCc9Cnzi/PqVML4DGSgmO4+ISqhZxj1gWRmZaKSHz\n",
       "DZQSqzVdq/LGqr9apEQDpQRpNJkiJXwfPmdhPq5QSshyTBDN54VNaFDVuBvTRP46J6CQEnpXA7gI\n",
       "EzckSImg3FOCICXMjpq/DitQS4J2u/G8E+wO7R4dDoG+6aF30+0AgN6Z29B2Ad9NP1uqlRItLLwZ\n",
       "BjqlPDNJSnTy6RuMlGBgYGBgYGBgoONYSQnTRCoXd6Z5aIUOPDN+oQydOPhtKxps3177AszdOSRO\n",
       "hR81q74xm8UGZ4nH5O1ndhApU/hBvMtSZweWxFopUZZkTgRTXmRhYNvNSYnBIJZ4JL4IloVALah+\n",
       "0TR9gxPWjdb91SElBKHcRJIwu6zylGhrIuRFuacEVsNy+BY4q5yUaM1taGdu2fyuaJyEUiIVXHke\n",
       "Aq6mUkItICXIbdGapMSyo2B59cVUm5FpYKBm7iM7Q0pMl7BbxaREsqNcBFIpYUaZIEzXIc+NtFKi\n",
       "gJTI7aBT2g3MKKWUuB4sU/0NtHyZXgCNlRLrubLS5ND+Mq2UUIUGSomK9I26pMTI3KwNcu3VUUqQ\n",
       "Rpfr6V2Ny4OFWVX6BkC9v+sEyNkKHHWUEjzPgXd0XJqaa1LC4oLaSgmrR7kOK3ihB4ET02aRHBf/\n",
       "Zbwho2j3/2AQYmBF6J89F49TEDFTOUwzpGAVKcGLEjS+i+6paf57gpTYYaQEAwMDAwMDA0NtHCsp\n",
       "kX0pswIbE7GLyYX4hTJwPPCKBJ7jIQkSnCA2wTQsA11RhxvW2Fos6U+VRcDt4NJe/EJZZweWxFop\n",
       "UZOU8GGh71jNSQlNi19wE4NHy0KkqocmJdZGl1lSotPZ+CJQf5hO36CCMLusIkY6moSWYyDcqSYl\n",
       "bLTBVyglOgsX3bO3b373ClFKWD0N1t7lVJuJY2DYKldKSNMF3E6FUqIkfYP0lFiE6THxw1OQF5O0\n",
       "p0SRUiLrNUBpt2MGKVJiL1rgVGfTZrelY+IcXilBmytYFvbmaaWEJpaQEjSlREn6Rm2lBEEqkWuv\n",
       "rlIiMbrMpm+4oYXpfmZgQRCrIvp9YhCHIyXKPCVcTobjxI+QBJKv46UZQUo0UEo4vXapUsJ3JPB8\n",
       "Zpoz50dVSnSuwhEBpd1bfzZri5hduZhqV0VKQBDQ4nS0hpRFRJISPUZKMDAwMDAwMDDUxeFJCceJ\n",
       "SQn7AKSEb2Eq9jB/IW4Xuj54Jd7hJXcuDctAT9LhhjW2Fkv6AwDRG+LCNWPd/1EqJXzOQs9qRkqs\n",
       "q+ORL9qr/railODTSgnHQdoXgfrD5kqJIhO9ONAVcVY2YKrVpIQVtcHbBWTJCv1lgN5N5za/O4BS\n",
       "wkc9pQQ1haUGKRFFUS7gcfsduNevptrNPAOnu1WkxAxeb1islAjrKyUWfnpM0qnTUObzcqXEzg4w\n",
       "m0GMuPUOeodTgOUS6G2CPug6essglb5hcHOc6W2ORSvTC2BrSolrs7RSoiVvN32DTH1pWhK0llKC\n",
       "pyslIs+DHVgYX88MbDKJrwGZWrYFpYQbuHADd+PXAQCOg7kjQ9fT5VKVUMdL8yXguggcGw4fFZNk\n",
       "WVJip1PqKTGbivlx1yAl+vIFjNV0ut2iI2N57VLqs9w1JbEiJZRwCHVQTkoMGCnBwMDAwMDAwFAb\n",
       "W1NKjMx0bvqwNcw5oI9G6WDV8iwslB0sL61ICceDoMQvr2SQYFgG+ooO5wBKiWxwLAc6Xtwz1v0f\n",
       "pVIi4Cx0rGVzpQSQIyU4rZWbz2x/QNrYM4u10eWqUaq/4RA5Z7b1DzdKCeoYgPXubRDEaTPkRi2J\n",
       "JC/8jDjCnDA89P24ugD5u+EQMIMOBKeYlHCtBVQf6A5v3vxOG6Yk82uUKCV8rr5SIjcHNUiJpbeE\n",
       "xEtQRGX9WbDTQ3B9L9VuERi4qU/cR0T1hiAMEEQBBGMCv7cdT4mZlyYl1FO3QJubeU8J8kYSBKDX\n",
       "g7y04QUeTM/ErivFMnqeeKQMh+guvZRSwhCmuEXfHOvmwRDLsHxdN1FKrK/Nyoz26lRbD93yLLQV\n",
       "jbrMC9M3SpQSI3O0mbtw5aGgqqk2ZUaXtZUSK6PL9fNTFOH7DniOx3Iupo+RfcgC1AoVZc+J9dhX\n",
       "WUmSIGHuzKGIysbUEwBcF1NTznXX5nW8PJ8DrgvPWiKUxPTvSGRICX+nS1VKRFGEIAowNQpICeKi\n",
       "0kiJHvcCxlq6FqfVa8G69lLqszpKCdHTIXYpi4ggJfR+npSoM+cMDAwMDAwMDF+J2A4poSi5l7mB\n",
       "OoBhGWtfCICulDC1AayX47e3yPMhFCglBooOZwtKCS3S8bJxPEqJgLfQWs5rv4kqSjEpwbfbtZUS\n",
       "RSqF7M53VRnSzQ9jrw+qn0KC1a4ybaOWhBd6EDkRu7yBMVH6cjyON+DJmFbXgYXfhViilJheuYhJ\n",
       "iwNH/DArmU+N8ZBKiYOmb9CCnWgwQGTspz6zOQO3EOuF9CTwQg+KoIAbjxH286SEIiiNPSUmbnpc\n",
       "rTO3ojO3V+kbBUqJ1TnL49la1n/a5qltOgs3vmdWQftEmuC24abdLboOiyte10EYwA99yIKcb5NB\n",
       "6tp4HsBxuD6RUkqJrrpFpQSpDrPt+AbOBN+HVUoUGV26tglN1LCzkxE4FVyrwyolZs4sTwy5Lia2\n",
       "kjtOR9Bx2VoArgvfXiKUS4yEyYfeaAS/36OSEokfznjMVSolWlILYRSmSKaW/xImcpowcvttOHtp\n",
       "pVKKaMpiRUrwjg6+Xa6UGO4wpcQrAgVcGQMDAwMDA8Px4sg8JTRJg8AJML1NdY0cKeFZcNpDuFdX\n",
       "pITjQVDpSgld0+EEh/OUAIC2oOPK9HiUEqFgQV3Mi1mCDMqUEmKri7E1RhhlSqFtw+gy21/uh/XT\n",
       "N6pevJNdfB0GRtg0LIql5k4Xolt8zWdXLmLWTgc9B/GU8LAlT4mCcrHUHdjhLrjxJPWRwxu4/TQ9\n",
       "fcMN3Dg4NwxEg8N5SlhuHA2PM2lX3bOvQnfpQRSB/7+9M/+V5DrL/1NrV/Xe1XebzZ7B37Edb2MH\n",
       "B0sRAkFiQkRsCLEQRCQIELJArEII5Q/ACwhBEPkFxBKCRPg1QrHlRCGKIbFR4jEIB4GdzMSzz9zu\n",
       "21vty/n+UN19u/bq7nvvJM77kaJ4+lZXnTq19DnPed73Ne2MnBLTc5aHk3n4RtfkUrepja3wmZlO\n",
       "2l1pD3csnN8dmxpcIVuUmF2rzJX2BRZdJfOQp4Wmm66JZnWJRJc8DwQBTIMV55TIeCes65TISnTp\n",
       "OAZUSU0+tocgSki8FIoScQHXcTDQ5cR+2nIX163RVJQwwfJEiZhTIui0U8M3FitvJF6nsfObVWJZ\n",
       "7HfVvYa9WIlgr92Ev7vvVPICDxNngpaSYfOaihIwNTA1X5TY6KSLEiV/CgiCIAiCIL6vODRRAkgO\n",
       "yNOcEl5zA/7NcCWYeR5EJd0p0a1qsPz1nRJNUcPN8YpOiSVFCSaYkMfDAwnf4KtVVKUqxna0tN86\n",
       "iS4znRmJL5ZPdFk02ZnlO2j5fdzyikWJodWEZGfP3PQbl6A3KpHPcnNKeB5Mx0g4JVxWzinRVtoY\n",
       "WsOoOLTYdxnlYtOeD3FjC+JgFPnMl/s4vb3gOFL3HUeLogS0nOobJXJK6KYLVU22q3X8DFq6D1UF\n",
       "Jqab65QQB6N5qUjNQuo26tiau4uYqiKQ+/iBnf3tzuxo8OQcUWIJ4TBy3afH29vbr9RgeiZaWaJE\n",
       "mlOC4wBBgDXtjzgriRIrOCXSEl06tgVVXE2UMM3wka5G5+jJti84JcbOONUpsZciSnRUDbfsQZhA\n",
       "1pyASeVFCaZ1Up0Ss3s69f2S8u6K93vFvIG+0IxsEzqV9sMwBtYALaUFnsv4WZyKEv5Eg592zwoC\n",
       "EARwPBubnQo5Jb4H4MgqQRAEQRDfFdxeUcI1wdobYL2pU8JxIajpTonNehfWATgl2oqGXb03P/5S\n",
       "ToklwzcgmhCGgwMRJaCq6ZPtJZ0Sa4VvFIkSZZ0SvIS608cNt1iU2NObkHKcEtbNq7Aa+ckF58wm\n",
       "mbaedEqwck4JkRdRl+sYWgslARdj9ktW3gCAyuYOKsPJ/N+O64PJI5za3F+pVUQFkiBBd/WIKMFt\n",
       "rJdTwrA8KDUHlmehITfmf6u2NyEGQKs2gGF5+zkl0kSJ4WjulGgbQeo2ylCfC3nBNN+C1tzvnxMb\n",
       "TUDSYVix2XnMKVGGhCihqFDV0JEAhM97u65iMAijSSKHS3NKAIAowta9tUWJWRjbKjkl0sI33DWc\n",
       "Ent74S1bZD6Z3daSkO2U6E+SosRGTcPA7QOyjGA8Dl9sWcRECWhatlOCl9LfLyk5M+LvAFnfRY9F\n",
       "HRBctwtuIfYlN58EMBclnGGGu4fjAI6D69rY3qDwDYIgCIIgiLLcdqeE2N0CN5hu43mQFpwSs9CP\n",
       "vhlWJLC85ZwSaYnFuqqGPeuQnRKGAcvxAPjg+v39pdoCMkUCwyglSsySTLbb6ftPq75x1OEbru+i\n",
       "4jIIgYsbk9r888y51KSFiuNn7s+5dR1Oqx75rEg8sc1JwinhlHRKpO4/RUCKk/Z8qNsnoI73y51+\n",
       "58YAnNOELEVdFrPjLYoSQo4oUSanhG65qLT20FE6kdAIjucxqPLYrF2EYbmRxKjRRmkQ9obznBKt\n",
       "DFGiMtTnQp4ryeCdmFtE4MHZbXznZjSM5SCcEp6kJt43NfDrPbgAACAASURBVFlFrRY+J5HDpTkl\n",
       "gHASaqwuSiiiApEX5+8ywzUOpPqGa5vLOSUWEkGWnRxHnBJ2ulOiN06KEttNDWMvFCXYZDlRgtc2\n",
       "0p0S/npOCXmyh5uehoUURxC7UadSWVHC2tNgpeVBAUInhetgqysnEqqSKEEQBEEQBJHOgYgSgSSl\n",
       "xuLmiRJe4CFgAaStTYij6TauC3HRKbEQvrHd1GB66zslNhdKEB6mU6I/NlE3VHCKkj8oX2Bdp8Rw\n",
       "CDQa2Ukm59U3psHNpUWJAwzf8AIPdcOFXdPQ39ufDGfNpXaHbchObFl7cX+7t+B18u+7CJIEO8Up\n",
       "4ZR0SqTuf0VRorFzJ+oTe/7vizf6EJxk56WJEuJWfvhGYU4Jy4PU6qFbTQa5j+sSNtSLMGwvN6cE\n",
       "vzecOyVaupe6jTQcz4U8W5QgecnzE10N37mRfl+v45RIEyVSJ/IocEoYq4dvxNtluqtX34g4JVxr\n",
       "ZafEsqKExEsYOelOid1RUpQ41tagBzNRYgKuEg2vihAXJTY2CnNKrCJKiMMhhvwmJvvGJMibO5CH\n",
       "+vzfZUUJfXd6fmkIAnzPQasuz9PLAGGqmSX0aYIgCIIgiO8rDkSUcESkxuLmiRIzQUA51kVFD7fh\n",
       "PBdSdSGnxEL4xlZDgxOI8O31ckrsNDVM/MPPKbE3MtDVK0stja0rSpQRBNZJdNlRO9iz9iIVVeaU\n",
       "dUoELqpjC25Dixwuay51o9+G4qYcb/7FXmKkXySeOJaedEoER++UaB47jaa+7wK5tNtHJSgnSkjb\n",
       "6aKE5VkIWJAdF49womvYLsRG+iRMr1egyZf3nRKZosQeeI7HxJmgPnHTRYnBaC7kmbwIJeX8KoGG\n",
       "t3czRIk1nBKOEBMlpoJAqiiR45Sw13BKxNs1E0aAkk6JaaLL2aR2ZafEGqJEnlMiTZQ42Z06CWQZ\n",
       "3EQHJ5cQJXwfGI8hdTKcEmvmlJCHY5iV7chmoVNpIfSthCjh+AICXcPQTX+/sKkoIQtS4rXA89k/\n",
       "G8TtIeeXhSAIgiCII+RARAmbD1IHc7mixFQQUE9oUGfbeB6kqVOiKlXnK2Y9s4duVQMnSfCs9ZwS\n",
       "xzUNBguPt2ilLkMpp4QkATyP4XCETV1eT5SY+X/zRAlFCb8UBIWTjXiiy2WdErIgQxEVjJ1xcpsl\n",
       "nBK1sY2gXSxKqCpg+h2oOaIE398Dp21EPqtJNbi+C8uzkl+QJDh27Lp7HuxgDadEswlMJqF4Mw21\n",
       "iZMqSmydQsNm8N3wIlzp96GwcqKEfCxdlDBcAxIv5VarkHgJpu1BqKdPwqxmFV3pCkzbg8SJ6Uu8\n",
       "0/tlVpmhPnHSQzwGwzB0wTBg8DyqXPJ4KjRcTagEYRjUOk4Jm0s6JapSdWmnhJPilHD8WD6OAlGi\n",
       "Zy7ksVnWKcF8mGaYskBVMXVK2EfnlMjJKXFzkBQl7tjU4IpTUULXwVWipTgjzF5C01rCqlJfPqdE\n",
       "liixUBZYGRnwlOORzWrbp8L7dkoZUUK3BLQr+WFsEuMh8EKkWRS6QRAEQRAEkc2BiBJWnihhZYgS\n",
       "0xXQ+h0a6s6+U0KeOSVSSoJykgjPXM8pcWpDgyMkrdRlKOWUAABVxaQ/wIYhrS5KpCRPTBUlOA6o\n",
       "VADLKiUIrJPoEoiVXVykZKJL13dRndhAt1soSgBAtdmG4gGBnz57E4djiBtbkc9mJQH3zL2UL4hw\n",
       "bSN63V0Xjr+GU4Lnw0Qee3tLOSUESca4wmF08xIA4Nqwj7qQL0rUg3B5Xe3WMkWJvHwSQDjRNW0X\n",
       "fC19Eua06mjhBkzbRc1BOHtWYhPL6f0yq8xQHVvpqhIDmGkApokJz6EuJo9X4zVcH67vlGjIDZie\n",
       "Cdd3w+/GRQk3J3wjyykhiqk5JfbMWD6OEk4Jxhgsz1q6+oYXxJ4rUYTnLFF9o9MJP586nFZySsSr\n",
       "bzAGOA5uDaTEvs7sTKtTyDJ43QBfRpSYNmrRIbfIujklqmMbaJyKbBY6lfbfK2VEibFZnFtH5eRE\n",
       "s0iUIAiCIAiCyOZARAmD81d2SjRPa2hNwyn4wINcm+aUmK5cMsbQN/voKB1AkuCXFCWyYnhPb01X\n",
       "8RC1UpehlFMCAFQV+mCArikcfPiGlTIYnuWxKCFKVHyEB6nVlg7fAHJCI5YI31BHBoSNYqcEAGhd\n",
       "EaYIWJNB8o8AKkMdla2d5Pey2pnmlHBdWOs4JYD9/jPN1FqLWROeUU3A6NpFAMDNcR9NKV+U0Cw+\n",
       "nLxVOZgmIon75k6JnMobwDSnhOMBanqb/E4LLXYLluOhZaYksFw43/kq+thMbsdxYFoH6ih8ZiYc\n",
       "0JaT+2pKGm5OMkSJqbuhDBzHoaOEIUYwTRioJnNKZIVvZDklBAGumRQlEtcz47oD+9fP9m1IghQm\n",
       "m0U5p8Qs0WXk+RCEUJQo65RQ1fD5NIzMTdJQ1bBKCc/Caxy5Dr4P8Dx294RkiFynDgg2fFGCYJgQ\n",
       "lhElpPTrkJtTotUCxuOwTVPiz2hDdyG274j0VWvnTjQtNhc8+2YfmpIvSkwMARv1DvbMvWhZ4ClM\n",
       "4KFw4fNHogRBEARBEEQ5DkiU8DJFiZ4xtS2b4ZhxNm6frVo2T7VQZ2P4jg8+xSlhuAYEToAqqeBk\n",
       "CZ5dLnxjMgkNBPEca2d2NLDKHoKALS1KVKVqaaeEORiia/IHLkrM+jN+PJhmapGERfzAD1cGNQ3g\n",
       "uOxwkcQX/blTIrMN0/CNXi80eWThBR7UkQl5p6QooQGmxMEapbgeAKhjE+rWyeT3Fizz8XYmnBKe\n",
       "B8svL0p01W5y34uiRMqOemYv9RmZ1CuYXP9OuI3RR7uS8hwp+6LEhgmg24UghF3u7LvPw9AOoNAp\n",
       "IfESLMcFUzImYZ0OWl4fpuOmJ7BcON9ZvgFlZKRux2ld1CYOAsPAiGfopPRBZ6FM75yZKOEYS7mZ\n",
       "5venaUIPsp0S8Vs91ylh+gm9IQwpW7jRSzgl4q6Psk4JP/Cjz7YownPt9HPJegksvE+K3hMzOC7c\n",
       "LvCmOSUWr8O06lLavnieA2drcHgBomFBUHKu36Io0e3uv2NjzHJKpLad50NhYqG856IowYIAHT1A\n",
       "deMHIn0lygp0GRhdfxtAKEqkJX6d4/sY6QI2NQk1uYaRPUpuw/NQeHJKEARBEARBLMOBiBI6XHTV\n",
       "5GBu0eo/HXNi7naerloKsoAx18TwOwNwcaeEZ0ZWJDlZhG+Vc0rMjhenpkqAp+LK7ni18I2STglz\n",
       "OMSGza0uSlSroRhgmsgN35geb+aUKBIEmguTzMjxWq1wJTVtlrQQvpHZhiXCN5ShDvmYhsEgXIkF\n",
       "kClmdLuALXKwM5wS9YmDxvE7k9+rZoSZSNI8SeCMwHFh+2IiQmHG0k6JjPCNtGfEbCgwrl8BAOxZ\n",
       "6ZOi2bk4vgPNxLyD4+2aiRJ5lTeAcKJrOR6CSrpTgu9uouXuwXI8NCde9oXp9eY5JSqDSep2XLeL\n",
       "HVuCq48w5n1s1ZPbbNS6GNix/hTFafnWlASLOcyvjWli4quRJs3eOYuRUTMqQgWu784rXSy2w7VK\n",
       "OiWyRImpqBTPj1E2p8TMKTE/F1GEP80pETmXIAhL8KSVeFjYcJkJcihKTN0wYlSUYLIMwwhfHXEk\n",
       "T4MFDpJhQ1BynC5p4RsZTgkBUkTYTjR04aIu/vYYw134PNDZ0hLXfVATMbx2AUC2cDjH9zE2QmdI\n",
       "1nuQCQLUFKdEWSGIOGqyc+8QBEEQBHF0HIgoMeGcwvCN+EDYcI25HXgodjG62IcQuFDqC9U33Kgo\n",
       "wcsS/JJOibyBt+BouHijv1L4xixpX5ZVO9xQhTMeoWuxfJUgRkQkmC1TzvIUVKvZ+RyqVcAwSoVv\n",
       "NBaqJCSO126HCecSXzy48A0v8FCZhm/U6+EcCsh3SlgSD3ucLkq0dA+tY2eS38sRT1wruvrumR4C\n",
       "QQKf8TRMuzd/3yVEidSkku06nFvXAAAjp4/tRobjyOzB8R10DBYRJRbbJfACeI4vdkoIoVPCl9Pb\n",
       "JG1soemMYTkuGnpKVQ0gnPgOBpAgQLdGEPWM2ammYceR4U1GGPMetlLOb2uhTG8EVYU7SUmwmMNc\n",
       "jDIMjFw18c7JyinBcVy6W0IQ4KbklEhcz4wEp0C2U0KSylffiIdv+Gk5JYZDoF6fC4jRRmirixKu\n",
       "FOaUiDklmCSj09kXmhep+F2Y4FAxHYiVEk6J6ax9/o6N4fouEIgRYTvr/ICoo2t49QKGVT71uk/q\n",
       "MiYLTokiUWKkF4gSfHb4xhI/BQRBEARBEN9XHIwoweylRYnFAfpE1jC51AcfeKjUp04Jad8pMVs9\n",
       "5isigpIlQfNWpmRfw9u3wklC2Xh1YLlEl64+hmazpZbHIiIBkJjolnFK5IZvMD9blFg8XuKLfimn\n",
       "ROD6GAzSF2pnuIGLymgCaNr8cL4PjEahJhJH0wBLFODow8TfPMdCzQEamyeS38vJKeE5VuS6u4ab\n",
       "PpGbUsopMVuJTrk3Ziu/aZNrr92Et3sTADDx+9hp5eeUaBv7OR6q1Wi7gNAtUZRTQuRF2K4HV0yf\n",
       "hFW2j6Np6bBdD/UsUUIUgVoNHVcANxjCr9fnwlW08Rq2HBGePsZYdHC8k9zXsdZ+md4IqgpXH63s\n",
       "lBg65UuCAhl5JUQRrpWsvrGMU2ImlMSdEqXDN1isqo0owvMcVKUq2u3w2fF95KsNC3Eey0yQu13A\n",
       "tcVUp4QvJCtvzKhyGmY9KS7hlJB4CQwsFCEWcAMXCJJJNSMNjYkSs2d0fP07GNfk1OtuNlWYN0On\n",
       "UhlRYlgkSggcKpyYaBKFb3x3Qj4JgiAIgvju4EBEiTFWECUWBuimqsF6+xYYOKi1sEmpTomKhMBZ\n",
       "3ymhMA2Xe8lJQhHLJLr0jDE0y/+uEiW8wENNd+YzktKiRNwpkZZsUxBgjD3Uarnze3iBB3moR0SJ\n",
       "4RBoNDLntLBEEc4kGb89vP4dDBUOvJA84Mwyn0CS4DnRFWvX9AAxeyK/bvhG7mSn0wHrT/OucD0c\n",
       "T7mAi6JEy9i/p+LtAqaiREH4hsRLsD0XjpAeLqJun0DTsmB7LhpjO3eiu2HxkIZj+J0Ul8R0m01L\n",
       "hGdMMBEdnOwm93VC02Bx6fe1r09WFiUGVrIkaJZTAsjIKyEI8LLCN5RyokSeU2LVRJeBE+aUEITw\n",
       "2RkOUSxKrOiU8Jz08I08UaIuaDCmWVglpZZ9gJgowXFcagUOL/AAP0eUiF3UulyH7duwPRvGjcsw\n",
       "GpXU6243a7CnTqVSTolJvigR8DwU7DslZjksSJQgCIIgCILI5kBEiSGzUgdzVakKn/mhuJDjlHBq\n",
       "GtzLNxDw+2UZF50Ss30LSzgl8gaBNV7D1UFvqXKDwHJOicCYQLMzVpkzKBIlOmpnXlowfrxSTonA\n",
       "R33iHJpTYjL0C0/X9V1Ig3FElCiaS1mCCE9PihKjaxcxqqUrIHnt9G0rFr7hAtKaTokVRQlO64Kb\n",
       "Juiz+T7u2MgXJZp6sShRpiSo7Xqw+fR2NXbuRNtyYLseagWiRNfk0NR9sE6KzWW6zabFwdcn0GUT\n",
       "d2wm93VqQ4PNZ4gSxmS5RJfKVDQzTezFRYlVnRL2ek6JuSixqlMiSDolfM+d72t+PockSrh2mNci\n",
       "Hr7hcdmiREvWYCBMGLOMKAEsiL8LuL6LwBNLixLzssDWHqyb12A1q6nXfeZUCliAoTVEW8m4j4HQ\n",
       "KVEgSuSFb5AoQRAEQRAEkc7BiBKBmTq5WRwY5jklvKYGdv0GPG6/AkKaU0KoSGAH4JRoiBpujpZ3\n",
       "SsiCDD/wwczs+PGw8SqYqaNtHawooYgKJEGC7uqJ45V1StQXJplLOSVKiBL6wCs8XS/wIA2XEyVM\n",
       "QYQ7GSf+pt+4BL1eSflWfviGP11lnrfJ8sJl6wzik/+OGpadjIhDK4oSwsYWhEEouHhSH3duF4kS\n",
       "bqEoUVgSdOqUMJGe2K957DTapg/bc1Gb5IsSmoVI8s3UbUwOgTGBrpg4s5Pc7vS2Bl9OFyUCQ1/J\n",
       "KcFMEz1DjYQSreSUEEX46ya6XMMpsZjoclGUCFxnvq9lRAnHASwrTD1RBk0DXGs/+fAcx4GbI0p0\n",
       "FA06wqShkrqkKJHhlAjc8k4JYL/f3d0bcNuN1OvOOm2wXg9Da4i6XM8X9Hwfg3GBU2IhfINECYIg\n",
       "CIIgiHIciCgxCIzMSdds8JbnlGAdDfzuTXhIOiV6Zm9ukxYVEcxZ3ynRrmjYNZKThCJmyfCCnKR2\n",
       "YeNVwDLQtqz1RYleLzLhSR0MlxUlmIfqeL9NK4dvZCS61IfFooQbuBAHo+VECV6GbyRFCfPGFZjN\n",
       "/IlggoXKBfPTs1xwSzglZEGGIioYOwttSrlWM/JECXlzB/JwAs8PwCoDnNlJJuRQRRWMsXDiVEKU\n",
       "KOWU8E040NGsNBN/b3SPQ3UBzxlDHefcw5qGjhmKElxWkgJNQ8dksMdjmHKArXZygnrndhtMHsFx\n",
       "Y5UvZqLEkiVB+2Yf3tiEI6qRiiozp0SnE95zCcNRmlNCEODb64sSPbO3klMiK9Elc52VnBJ7e+F/\n",
       "piaLzPiaY+2XaZ7jOHByRImNmgYDoeIiqzkKSFmnRODCc8s7JYD9eyHo3YLfbqW/3qZOpcLQDSAq\n",
       "SmSEhzGeRAmCIAiCIIhlOSBRQl9elFgYoHNdDVL/BlwUOCUUCcxd3ynRrWrYS7FTl0EV1VJOCc42\n",
       "0DSt/KyPMYqcEkC2KBEYJvb28g/nBz6qqzglSoZv6KPi8A24LnjTAprN0qKEARm+Pkn8zbl1HU4r\n",
       "fRV2GaeEb3ngcpwSihL206x8aer+V3RKqFvHoY5MXNkdAW4NipwUFGaOo+v69Uj4zco5JQQJk+AW\n",
       "qnwbPJd8BXA8j4HKQbCuoDoqECUMBs0My4hmbdM2AhiDASzUwPPJ2bAsCeCcBi7diiUzVVUww1jJ\n",
       "KeEMTQj1/e8xxmB5YcWKSgWoVIBJ7JZKc0qwaQLXeLnYZUSJmajUN/srOSXSEl0GnruSU2LZybGm\n",
       "AbaR7pSwWbYosdXQYHArihIZTgnfWc0pMdv3bJNFMUrc2ISwN1pelMjMKcGhAgrfIAiCIAiCWIa1\n",
       "RQnmOBgEZmYsbq4oMR3kClsalFG6U2JxsCgqIljR0uKUvEHgRk3D0FneKTFrF4zinBL1yRABz+dv\n",
       "F2MdUcLeM1Gt5kYhhHHhY/PQnBLGuNgpoY4t+O0mwHFLiRKBoSf+5u3ehNdOrvTntlMUwZyoU8K3\n",
       "XPApYsAMjgsnsZaVs/8VRYnazh2oTWxcuN6H6GR3nqZquD65HsnxsI5TQuduoi5kH2+oSqiY16CO\n",
       "jdyL0zYCaGY4ucvapqX7sMcjOGhkHk9wwzK9EVQVsJYTDhedElJj/3u2b0PkRQi8MGtW4lZPc0oE\n",
       "nABV8hLOgmVEiZmodGV0ZXmnRFaiyxVzSqwiSlhmulPCDrJFiWNtDQYfnpysZl/3ZXJKeM5qTgl+\n",
       "MATf3YSqhs9yxPU0dSqVFSX2RiVEialTol4HbDv8H4kSBEEQBEEQ2awtSrimDqGiZE6EyoRvyDsa\n",
       "anqxU0KsllhanJI3CNyZliBc1SkBq1iU0IZD6NWcWOoU1hElzL5ZOOj1mY/qKqJEilMikWxTFGGM\n",
       "i50S9YmDYJoUsawooQdKqijBej2wDGtIrlNiIR4fAHzbA1fJdxcUJrvMEyWsWKWGBZo7d6Kpe3j7\n",
       "Vh+SX0aUsApFiTI5JUz+BppS9vHGNRmqexPKyCwUJTYtAZyWHb7R0F14+hiekC4gAftleiOooQC4\n",
       "ilPCH5uQWvvfm4VuLDQrKUqkOCV8TkS1EgsrwXKixKxdV8ZXVnNKpCS6ZEfolLD0dKeEmSNKnNA0\n",
       "mEL4cqlUC0QJy8JiLeEsp4Rrr+aUkAZjSJtbqZspW8ehjo1SokTg+TAdAY1GkVMiFL44LjzetWvh\n",
       "da6Wrz5NHBGsbBwTQRAEQRCHyvqihKWjkrMSpqkaekYPvV52+IZ6XEPTugmX5TslJKXE0uKUvMH3\n",
       "8Y4Gg63ulOBMq1CU2BiPYNRKZpObkhAJZoXuY6JEz+gljmftFYsSXuBBHRaIEr1eyhf3E10qYihA\n",
       "JZJtiiLMUbFToj5xEGid+eGKRIlaDTCgwNeNxN+4vX5mLoNmpQnTM+H4TuTzQBAg+SwycfftfKcE\n",
       "kC5KRK5Duw2MRoCuJ+6NnpGeUBIA2sfPoG0yXLp1EyorFiXUBZFgHaeEJdxES84+nl6vom73UBnp\n",
       "uRPdluFj0+Zzt6lPHMAywKTsygYq03A5fu+pKjjLWtop0TN6CAwTlfaCKOFFn/W0Wz3dKSGiKkeV\n",
       "Ay/wMHEmaCkLZVDLihIrVN/wAg+uGz4Lsy8yz4s4JXo9IPGSjTQgfNjyNsn6mqmnOyVML1uUuGNT\n",
       "gynaAAClyCmxu4vFWsJZOSUcq8ApEbugs7wP6siAsnkcQPhKXdystn0K9bFdSpTwHR/VphCKDdM8\n",
       "IYlteA4V7D9/mgZ861tYKo8HQRAEQRDE9xtrixKeZUCttTL/3lW76FvhCt3i/HFREKjfoaHt7cJh\n",
       "+U4JqSqBW8IpkZV7746NLix+dacEZxWLEluTCcxazmA8hUyRwLIwC2rPDN8YmJnnO8MLPCgjI1uU\n",
       "mIkgiS/uh29ktkEQYE28wjY0Ju7c3TA7XN614jjAlRS4YzPxN3EwgrixnfE9Dh2lgz1zL/K5L3Ko\n",
       "cnLks8DxICzplOiq3WgfCALQaITLoinhG91q+gmKsgJdAq5f+1/U+OzO61a76A2uQXQ8oNlMbRNQ\n",
       "PqeEK+2iXcmehFn1OraNUfiPrCXebhct3UPX4rMvYL0O0Qug6AZ4OTvhSV3o4toweV9zlr2UcNhS\n",
       "Wpg4EzDDhKplOyXSbvVUpwSEhCixZ+6hrcTycZQRJUbLOyUEToDrh8/VfFIrCIDrzfc1P5e8B2m6\n",
       "0SpOCXOS7pTQPTnzcD9wTIMth/FOSpFT4vr1SLuznBKOuZxTolsNn9Hq2EJ151TqZs0TZ9DQvdxn\n",
       "dIbv+Gi0hMi+4wQcB5mLihJvvUWhGwRBEARBEHmsLUr4tpkrSpRJdNk80wUPlumUmA0WJVUE5xU7\n",
       "JRgL5/JZSR/v3NbgSrfg+i4qQnpJySxqvAIuYPnJG1QV2xMDdjO7X9JIFSWuXQv/wIeXaibyxI/n\n",
       "joqdEsxxINjOfFK7SvgGkCFKiCJMvTh8ozHZrx4x01yKVm8DWYU/SYoS8lCHvHks83tp7fR4DlXE\n",
       "RAnbBV9Z3imR6INuF7hyZamcEgAwrIvYu/FGbjiFpmrgBkPYzep8drqOUwIcQycjpAQA3HYLZ/cA\n",
       "p5Xj9tE0NCceugayLyDHwWgo2BpZkHL6oClpuDlO3te8ZS8lHPIcj7bSBjMnqGr5TokyOSU8ToQi\n",
       "R8M3Uq9ngSjRrXYT4RtlnRJ+EHuuRBHM95bLKaGqQBBgdKNYvFykXgc8N90pYbjZTomTGy04kguP\n",
       "B9RKQaLLwSDS7qycErYpZre90wGGw0g22pmboTFx0Ni5M/wsdt3bO6FTqaffygyxmhG4PhrtUJTo\n",
       "KJ3UMDafxzx8AwhfCW++ma0VEQRBEARBEAcgSgS2BbWWbcvWVA27kz5sOxzgzlh0SrTuDL/vQprP\n",
       "fVVRxcSZIGDBfu6JmgT4xU4JwwgXE7PmCKe3O2DVW1BEBdySntp2IMNX5Hwvrqpi07DhNbP7JY1U\n",
       "keDmzciJZDklvHGxKFEZGXCatXnbl0p0WUKUsPXi8I2W7oFbECWKwjcAIKhUwXQr8bk6NqFun8j8\n",
       "XqooIXCoclFBiTkeBGWFnBJxcSjlegHFosSkLsMavJnrXNAUDZoJ2M39PCXr5JQAgI2clWG/3cHZ\n",
       "HuAWiBIN3UXHZLkX0GpWsaUzVOrZx2tXNPSM5H0tWM7SIVaaqoFzdNQ21s8p4UFEVYq+c1YRJTRV\n",
       "w039ZqQNZXNKeIGXECXgecvllJgmOLCv9Zdatec4oKakOyUmTrYowfMcXKbCEZAvKslTgXBRlMhw\n",
       "SthGjlNi5lQa7ldwmT3/LSNA6/iZ+WEWr7ukVGFIwI3rbxXnlFgQJSpiBRWhgokTLeES8IC8IEpo\n",
       "WihKkFOCIAiCIAgim/Wrb9g2agWixM1xPxFTu+iUEBURQ7QQLKzwSoIEgRPCCcZsEl0VwfvFTomi\n",
       "SW67rgBOdenJDgA0mQS/wOo/m5z47fLlQIEUkaDRSKgrWaKErxeLEsrIgL1QQjNxvFYrzIvgxxL7\n",
       "lQzfcEqIEk3DA6ZJETsdYG+v2CkBpQrOtBMf1ycO6tunMr+W7pQAVMRECdeFeBBOidlJLClKmA0F\n",
       "bHIR3Wq+U0Izo86FtZwSCKvQZMFrG/h/fcBt5Vjvp/ki2kaQewFnQkqtkVGhA9MyvSkOIMF2lg6x\n",
       "0lQNomOivrmCUyIevsHC6huLrCRKTFfhl3VKCLwAn8WeK0EAF8sp0e8xFNYE1jR4N5cTJQCgpiad\n",
       "EoEVhm+0csxgHqqhKJH3nk0TJVKcEpbrwnPFiLCdIHZRNVXD7u4lCAFQbW2kbQIAGFUF9C6/uZQo\n",
       "Mdt//B3gc4AMCt8gCIIgCIJYhgMoCWqjXs+fTO0ayYFwPMnkUNQQxGLhVUmNDBTlmgSuhFOiTNy0\n",
       "4GiQ+RVEiUCCW1KUWHYkmhAJZunbS4gSQRlRYmxGJrWJ4wlCGNqxsNoIoHT4hm0Uh2+0jAB8d2N+\n",
       "fEUB3n47v6s4tQbeSooSTd1D89jpzO+ltdMVABXRSfvKTokDEiXsZg2ydRWbBc+RZgJue18kWCen\n",
       "BABsNrKPJ21t4a49wM0ouQoA6HRCYcjwcifDs3uuqW1lbrNZ1zBykve1ZLsrOSUkz0Jja0mnRFr4\n",
       "BkQo0vrhG7Ptl3VKCJyAAAE62kKYgCgCvh9xSji9cfgwyXLGnsINg97yokS9mnRKGEMHkOVFrTJB\n",
       "wNXgCGFy3ExKOiXGugdVlvKTRaaIEoNrFzCo8uCm4W9p131clzG+9p1CUYJ5PpqdAlEixSkxS3RJ\n",
       "EARBEARBpLO2KME5Luo5K66aGq6AJkSJWJLJiawhFut0KAAAEelJREFUEKKTRVWMiRJVEUKwvlMC\n",
       "ACRPg8StJkp4cjlRYjb5LktCJABKixIwi0UJdWRE7PiZx4uP2ks4JZggwDG93IVaAGjrQaRfNA2w\n",
       "7fwFXrFWh2DFqmj4HpoWQ2saK55GqlOCY0lRwnUhqofjlLA9G47voCZll4d12010bA87rWJRwmvt\n",
       "iwTrOiW2c0QJdXsHigf4eaJEpQJPEmBXxIhoFceb7qO7mZ6UFJiW6Q2S97XoeCs5JWTPRmtnSadE\n",
       "SviGywQoRU4JxsqLEks6JTiOAwceHW1fGPE5DnzAIAvhhL7TAfhBH6zoBaBp4PrLixKNqgiRkyDw\n",
       "++8Ac+CAV3IEEABMrMMRkB8iV1KUGOku1AI3U5ooUdMdjOtS1ibhuTQU1HW3UJRAGVGCA+SFn9XZ\n",
       "+41ECYIgCIIgiGzWFyVcF42cWHFN1TB0ip0SpqIhEPKdEpW6BD44GKeEwjSIbHlRou6LcCs5y4PA\n",
       "fHIibh6dKMFZxaJEdWzBXZjUlhYl4k4JJdkGJxBREXxUcvKGMsbQMRmEmCjRaOTnDZUadYixho5u\n",
       "XMKkwkGQsidGaXkfHAFQYqIEPA+iejhOiT1rLxKClAbrtKGZYanavHPRTMDvFIsSZXNKbOeIIM3j\n",
       "JwEAfic/WatRr2BSz5+czoSNne2dzG1OaBpMFhO6FAWy4+evtKfQldsQWYD29v7NuLJTgolQxJhT\n",
       "woqJEo4TPh85toFVnRIAwDMR7c5+Gxw+gAxhfk9JEnBc6SPIuZ5hIzQIoxVEiZoECdF3pTl0IKj5\n",
       "150XGnCFgp+YkuEbE8NDtcDNFL+ozUoTGyYHvV7J2gQAYLVq0EwUOyV8Hy0tX5TwUpwSsdMjCIIg\n",
       "CIIgYqwtSvCuh2Yje/LdkBtwAwstLTqpjDsl7JoGVuCUqNQOzilR5TUIK4gSDV+AI5cTJSpb2SvD\n",
       "aZQVJXa/uZs4nmCXEyW8Bfv/Uk6JgvAN0xFRV/NnWF7gQTMBbiEVvaYVX6tKqwEptqQ8vHYBw2r+\n",
       "dUgN3+AYFBYTJVwXkpK/CjsYfHklUaIodCP8XheaCZzaKCFKtPdFglWdEtxUlNlp5ogSJ8JcHV4r\n",
       "P1mr0VCgN/Ir2ASdNhwBOLWTnVPi1IYGW4j25xe//SZqHh8tvVmCbaEJSxCgdfeFoNWdEiIUscAp\n",
       "UeCSAFZ3SgAAx0S0tP02OPAhs2if3FHvw8lxvoSN0CBPikWJL3/5y5F/N2oixJgoYY0ciNV8UUKs\n",
       "NFcTJVKcEhPDRa3gGY1fVJ7jccqvw2pWszYBAHitBjQT6KgFNq8SooTPARKJEt8zcFgu0TWxHvF3\n",
       "C3E0UL8fPdTnRw/1+fc+uSPGS5cu4cd+7Mdw//3344EHHsBf/MVfJLYRXB+tZvZkg+M4qFwH1e5e\n",
       "5PO4U8JtamAFTgmlcXBOiYaggfeXFyVqPg9bKidKVI8dvCihiir8b/vRlURVheCWdEq0V3BKlAjf\n",
       "MGwBdaVYlOhaXOTilBElqu0mKm5035PrlwpX6NPa6fAMCmLXz/MgVfNXYXd3o6JEaklATQtLty7Y\n",
       "PsqIEuLGJjQTuHOrWJQIFuJcVs0pwbzw73mJNdvTagVOo0CUaKowG/nPEdM6MEXg9E728e7c0uBJ\n",
       "0Wv1r//3v6j7y+umm1wdJi9GSxCv6JRwA+FgRYkVnBJgAlrt/Q1teKjERImT1T6sgvvMb2uo2f1Z\n",
       "ReBM4j/srYYEPoienz12INXynz9ZacLlD8YpoZseagVuprSLetJTI3l00q570Gljx5Hn4TBZcEEJ\n",
       "pwTHEuEbi/9PrE+ZcQkA/PZv/zbOnj2Lc+fO4fz580fcSiINmjTcHqjfjx7q86OH+vx7n9wRoyRJ\n",
       "+LM/+zO88cYbeOWVV/CpT30K//M//xPZRvR8tJvZCewAoBJoUNqxlfWYU4K1NTCx2CkhsoNxSrQq\n",
       "GuCuIEp4PGy5YHVlOkFpnDi21L7LiBIcx0GV1OhgWFUhecWiRG3iRFbaVw7fSBmM646IWiVWtSOG\n",
       "G7joGGxpUaKhJUUJ8+ZlmM3iiWBClOACVIKoKMF7LqSCnBKSFBUAVEmFwAkwXGPhgNNrtRCqUUaU\n",
       "kDZ2oJlhqdos6nIdXYsD04pFiSKnhO+Gf28r2YJDc/sUAgBWLX/12GqokZXoNIJ2F6YInNzIng2f\n",
       "2emAVfbg+cH8M4/nUPOWFyWaXhWmyEV0giynxKKmlOaUcJiISjx844idEghENNv7bbDhQ4qJEscq\n",
       "feg5JWWBMETumNxHkU4Qp1UXEwKuPXEgF4gSarUFp8gpIQihkFfglNAtF/Xqck4JADjmKJEQpNSq\n",
       "x1oXx9x8tw8QihLtbkyUsOJOCQaJkVPiMCkzLvn85z+Pt956C2+++Sb+6q/+Cr/+679+m1pLEARB\n",
       "EEQZckeMOzs7ePjhhwEA9Xod73rXu3D16tXINqLHCkUJ0dUgNnuRz+JOCXQ1QIyuhFWlamTwrzal\n",
       "AxMlNFUDW1GUsKT8gbZXCWPgm6eWFyXseJGJmCgBhIP2nrnfn0ytQvbNwiSTtYkdyUmQebxe9Fql\n",
       "OSUWjw8AuiWiVilwSrg2Gg6wWEewjCjR3OpA8aITQ/vm9XmpySw0VUPPiLbT4QMosQkdfA9SrSAP\n",
       "g5QUABL9kHKtyogSXOs4ujqPZi17YsRxHLZtKdJZ1epqOSV8VwJntyOJC+Pwgog9hYOTk8QWAKxm\n",
       "tfA62MoGTJEHz2eLeVVFAtwqruyO5p95Aoeqt7y9WtGrsCQuWoI45pSYaUfGgqZUlaqJFfowV8r6\n",
       "Tom6XIfIiwmnRHlRYsEpwSVFiW2pj5GYf61GkoZtqZe7TRrtppQQcF3dgdzIFyVq9TZcrkBIAMIX\n",
       "0eJ9nXIdDMubVwHJJOXdte2IkSy6aa83YWMDO3bBvhGKEp2N2Hsw9n5xeUAip8ShUmZc8rnPfQ6/\n",
       "9Eu/BAB47LHHMBgMcOPGjSNvK0EQBEEQ5eBYxH+ezcWLF/GjP/qjeOONN1CfFovPzapOEARBEEQp\n",
       "Sv4UEwukjUsA4IknnsAnPvEJvPe97wUAvP/978fzzz+PH/zBH5xvQ+MXgiAIgliPgxy7lFjGAiaT\n",
       "CZ566il88pOfjPzw0yCKIAiCIIijJmtcMiM+PomLEDR+IQiCIIjvHgqji13XxUc+8hH84i/+In7m\n",
       "Z37mKNpEEARBEASRStG45MSJE7h06dL835cvX8aJEyeOsokEQRAEQSxBrijBGMOv/uqv4r777sPv\n",
       "/u7vHlWbCIIgCIIgEpQZlzz55JP4h3/4BwDAK6+8gna7je3t5aphEQRBEARxdOTmlPi3f/s3/MiP\n",
       "/AgeeuihufXx2WefxU/+5E8eWQMJgiAIgiCA9HHJM888g7fffhsA8PTTTwMAfvM3fxMvvvgiarUa\n",
       "/u7v/g7vfve7b1ubCYIgCILIJ9cp8cM//MMIggCvv/46zp8/j/Pnz88FiRdffBH33nsvzp49i+ef\n",
       "f/5IGvv9SFZN9n6/j8cffxx33303fuInfgKDweA2t/Sdh+/7eOSRR/DEE08AoD4/bAaDAZ566im8\n",
       "613vwn333YdXX32V+vyQefbZZ3H//ffjwQcfxEc/+lHYtk19fgj8yq/8Cra3t/Hggw/OP8vr52ef\n",
       "fRZnz57Fvffei5deeul2NPm7lrRxyQc/+EE8/fTTc0ECAP7yL/8Sb731Fv7zP/8zIUjQ+OXgOKh7\n",
       "+xvf+AYefPBBnD17Fr/zO79zpOfwvcYq40Lq9/WwLAuPPfYYHn74Ydx33334xCc+AYD6/KhYZjxO\n",
       "/b4+p0+fxkMPPYRHHnkEP/RDPwTgiPqcrYDneeyuu+5iFy5cYI7jsHPnzrFvfvObq+yKKODatWvs\n",
       "/PnzjDHGxuMxu/vuu9k3v/lN9gd/8Afs+eefZ4wx9txzz7E//MM/vJ3NfEfyp3/6p+yjH/0oe+KJ\n",
       "JxhjjPr8kPn4xz/O/uZv/oYxxpjrumwwGFCfHyIXLlxgZ86cYZZlMcYY+7mf+zn293//99Tnh8BX\n",
       "vvIV9tprr7EHHnhg/llWP7/xxhvs3LlzzHEcduHCBXbXXXcx3/dvS7vfidD45WBZ994OgoAxxth7\n",
       "3vMe9uqrrzLGGPvgBz/IXnjhhSM+k+8dlh0XUr8fDLquM8bC8cljjz3GXn75ZerzI6LseJz6/WA4\n",
       "ffo06/V6kc+Oos9XEiW++tWvsg984APzfz/77LPs2WefXWVXxJL89E//NPvCF77A7rnnHnb9+nXG\n",
       "WPgDdc8999zmlr2zuHTpEnvf+97HvvSlL7EPfehDjDFGfX6IDAYDdubMmcTn1OeHR6/XY3fffTfr\n",
       "9/vMdV32oQ99iL300kvU54fEhQsXIhO3rH5+5pln2HPPPTff7gMf+AD72te+drSNfQdD45eDZ917\n",
       "++rVq+zee++df/5P//RP7Omnnz6i1n/vUzQupH4/WHRdZ48++ij77//+b+rzI2CZ8Tj1+8Fw+vRp\n",
       "tru7G/nsKPq8sPpGGleuXMGpU6fm/z558iSuXLmyyq6IJbh48SLOnz+Pxx57DDdu3Jgn7tre3saN\n",
       "Gzduc+veWfze7/0e/uRP/gQ8v/+IUJ8fHhcuXMDm5iZ++Zd/Ge9+97vxa7/2a9B1nfr8ENE0Db//\n",
       "+7+PO+64A8ePH0e73cbjjz9OfX5EZPXz1atXcfLkyfl29Pt6sND45fBZ9t6Of37ixAm6JiUpMy6k\n",
       "fj8YgiDAww8/jO3t7Xn4DPX54bPMeJz6/WDgOA7vf//78eijj+Kv//qvARxNn68kSsTrfROHz2Qy\n",
       "wUc+8hF88pOfRKPRiPyN4zi6JgfIv/zLv2BrawuPPPJIZi176vODxfM8vPbaa/iN3/gNvPbaa6jV\n",
       "anjuueci21CfHyzf+ta38Od//ue4ePEirl69islkgn/8x3+MbEN9fjQU9TNdg4OD+vJooXfI4UHj\n",
       "wqOF53m8/vrruHz5Mr7yla/gX//1XyN/pz4/eGg8fnv493//d5w/fx4vvPACPvWpT+Hll1+O/P2w\n",
       "+nwlUSJeA/zSpUsRNYQ4WGY12T/2sY/Na7Jvb2/j+vXrAIBr165ha2vrdjbxHcVXv/pVfO5zn8OZ\n",
       "M2fwC7/wC/jSl76Ej33sY9Tnh8jJkydx8uRJvOc97wEAPPXUU3jttdews7NDfX5IfP3rX8d73/te\n",
       "dLtdiKKIn/3Zn8XXvvY16vMjIut9Ev99vXz5Mk6cOHFb2vhOhMYvh88y9/bJkydx4sQJXL58OfI5\n",
       "3fP5LDMupH4/WFqtFn7qp34K3/jGN6jPD5llx+PU7wfDsWPHAACbm5v48Ic/jP/4j/84kj5fSZR4\n",
       "9NFH8eabb+LixYtwHAf//M//jCeffHKVXREFsIya7E8++SQ+/elPAwA+/elPz3+UiPV55plncOnS\n",
       "JVy4cAGf/exn8eM//uP4zGc+Q31+iOzs7ODUqVP4v//7PwDAF7/4Rdx///144oknqM8PiXvvvRev\n",
       "vPIKTNMEYwxf/OIXcd9991GfHxFZ75Mnn3wSn/3sZ+E4Di5cuIA333xznv2aWB8avxw+y97bOzs7\n",
       "aDabePXVV8EYw2c+8xl67+Sw7LiQ+n19dnd359UGTNPEF77wBTzyyCPU54fMsuNx6vf1MQwD4/EY\n",
       "AKDrOl566SU8+OCDR9PnqybB+PznP8/uvvtudtddd7Fnnnlm1d0QBbz88suM4zh27tw59vDDD7OH\n",
       "H36YvfDCC6zX67H3ve997OzZs+zxxx9ne3t7t7up70i+/OUvz7P9Up8fLq+//jp79NFH2UMPPcQ+\n",
       "/OEPs8FgQH1+yDz//PPsvvvuYw888AD7+Mc/zhzHoT4/BH7+53+eHTt2jEmSxE6ePMn+9m//Nref\n",
       "/+iP/ojddddd7J577mEvvvjibWz5OxMavxwcB3Vvf/3rX2cPPPAAu+uuu9hv/dZv3Y5T+Z5hlXEh\n",
       "9ft6/Nd//Rd75JFH2Llz59iDDz7I/viP/5gxlj8upD4/WMqOx6nf1+Pb3/42O3fuHDt37hy7//77\n",
       "57+RR9HnHGMZQToEQRAEQRAEQRAEQRCHyErhGwRBEARBEARBEARBEOtCogRBEARBEARBEARBELcF\n",
       "EiUIgiAIgiAIgiAIgrgtkChBEARBEARBEARBEMRtgUQJgiAIgiAIgiAIgiBuCyRKEARBEARBEARB\n",
       "EARxW/j/VrQp4i/WUGgAAAAASUVORK5CYII=\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pValues = [0.2*(i+1) for i in range(3)]\n",
    "numGames = 5000\n",
    "\n",
    "def playGame(p, count = 0, lastToss = -1):\n",
    "    heads = numpy.random.rand()<=p\n",
    "    if lastToss == -1: return playGame(p,count+1, heads)\n",
    "    if (lastToss and heads) or (not lastToss and not heads): return count + 1\n",
    "    else: return playGame(p, count+1, heads)\n",
    "    \n",
    "rslts = []\n",
    "for p in pValues:\n",
    "    rslt = []\n",
    "    for g in range(numGames):\n",
    "        rslt.append(playGame(p))\n",
    "    rslts.append(rslt)\n",
    "\n",
    "cumAvgs = []\n",
    "for r in rslts:\n",
    "    cumSum = numpy.cumsum(r)\n",
    "    cumAvgs.append([cumSum[i]/float((i+1)) for i in range(numGames)])\n",
    "\n",
    "f,axarr = pyplot.subplots(1,2)\n",
    "f.subplots_adjust(right=2.5)\n",
    "f.subplots_adjust(top=1.5)\n",
    "for r in rslts: axarr[0].plot(range(min(100,numGames)),r[0:min(100,numGames)])\n",
    "for ca in cumAvgs: axarr[1].plot(range(numGames), ca)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Independence of Random Variables**\n",
    "\n",
    "Two random variables *X* and *Y* are **independent** if\n",
    "\n",
    "$$p_{X,Y} \\left(x,y\\right) = p_X \\left(x\\right) p_Y \\left(y\\right) \\quad \\forall \\hspace{2pt} x,y$$\n",
    "\n",
    "which is equivalent to requiring that the events $\\left\\{X=x\\right\\}\\hspace{1pt}$ and $\\left\\{Y=y\\right\\}\\hspace{1pt}$ are independent **for all** combinations of *x* and *y*. This concept can be extended to any number of random variables, that is the set of random variables $X_1,\\ldots,X_n\\hspace{1pt}$ are independent if\n",
    "\n",
    "$$P_{X_1,\\ldots,X_n} \\left(x_1,\\ldots,x_n\\right) = p_{X_1}\\left(x_1\\right) \\ldots p_{X_n}\\left(x_n\\right) \\quad \\forall \\hspace{2pt} x_1,\\ldots,x_n$$\n",
    "\n",
    "Notice that unlike the case of independent **events** we do not explicitly require the sub-conditions of independence of all the different combinations of the random variables. In fact, these conditions are embedded in the given condition because it must hold for all $x_1,\\ldots,x_n\\hspace{1pt}$.\n",
    "\n",
    "*X* and *Y* are said to **conditionally independent** given an event *A* if\n",
    "\n",
    "$$p_{X,Y \\vert A} \\left(x,y\\right) = p_{X\\vert A}\\left(x\\right) p_{Y \\vert A}\\left(y\\right) \\quad \\forall \\hspace{2pt} x,y$$\n",
    "\n",
    "If $X_1,\\ldots,X_n$ are independent\n",
    "\n",
    "$$var\\left(X_1 + \\ldots + X_n\\right) = var\\left(X_1\\right) + \\ldots var\\left(X_n\\right)$$\n",
    "\n",
    "i.e. the variance of the sum of **independent** random variables is equal to the sum of the variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "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": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}