04_Gaussians.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
       "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
       "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
       "\n",
       "    div.cell{\n",
       "        width: 850px;\n",
       "        margin-left: 0% !important;\n",
       "        margin-right: auto;\n",
       "    }\n",
       "    div.text_cell code {\n",
       "        background: transparent;\n",
       "        color: #000000;\n",
       "        font-weight: 600;\n",
       "        font-size: 11pt;\n",
       "        font-style: bold;\n",
       "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
       "   }\n",
       "    h1 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "\t}\n",
       "\t\n",
       "    div.input_area {\n",
       "        background: #F6F6F9;\n",
       "        border: 1px solid #586e75;\n",
       "    }\n",
       "\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 30pt;\n",
       "        line-height: 100%;\n",
       "        color:#c76c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 1em;\n",
       "        display: block;\n",
       "        white-space: wrap;\n",
       "    } \n",
       "    h2 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h2 {\n",
       "        font-weight: 200;\n",
       "        font-size: 20pt;\n",
       "        font-style: italic;\n",
       "        line-height: 100%;\n",
       "        color:#c76c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 1.5em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    } \n",
       "    h3 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h3 {\n",
       "        font-weight: 300;\n",
       "        font-size: 18pt;\n",
       "        line-height: 100%;\n",
       "        color:#d77c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 2em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    h4 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h4 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color:#d77c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    h5 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-style: normal;\n",
       "        color: #1d3b84;\n",
       "        font-size: 16pt;\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 1.5em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    div.text_cell_render{\n",
       "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
       "        line-height: 135%;\n",
       "        font-size: 125%;\n",
       "        width:750px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "        text-align:justify;\n",
       "        text-justify:inter-word;\n",
       "    }\n",
       "    div.output_subarea.output_text.output_pyout {\n",
       "        overflow-x: auto;\n",
       "        overflow-y: scroll;\n",
       "        max-height: 50000px;\n",
       "    }\n",
       "    div.output_subarea.output_stream.output_stdout.output_text {\n",
       "        overflow-x: auto;\n",
       "        overflow-y: scroll;\n",
       "        max-height: 50000px;\n",
       "    }\n",
       "    code{\n",
       "      font-size: 70%;\n",
       "    }\n",
       "    .rendered_html code{\n",
       "    background-color: transparent;\n",
       "    }\n",
       "    ul{\n",
       "        margin: 2em;\n",
       "    }\n",
       "    ul li{\n",
       "        padding-left: 0.5em; \n",
       "        margin-bottom: 0.5em; \n",
       "        margin-top: 0.5em; \n",
       "    }\n",
       "    ul li li{\n",
       "        padding-left: 0.2em; \n",
       "        margin-bottom: 0.2em; \n",
       "        margin-top: 0.2em; \n",
       "    }\n",
       "    ol{\n",
       "        margin: 2em;\n",
       "    }\n",
       "    ol li{\n",
       "        padding-left: 0.5em; \n",
       "        margin-bottom: 0.5em; \n",
       "        margin-top: 0.5em; \n",
       "    }\n",
       "    ul li{\n",
       "        padding-left: 0.5em; \n",
       "        margin-bottom: 0.5em; \n",
       "        margin-top: 0.2em; \n",
       "    }\n",
       "    a:link{\n",
       "       font-weight: bold;\n",
       "       color:#447adb;\n",
       "    }\n",
       "    a:visited{\n",
       "       font-weight: bold;\n",
       "       color: #1d3b84;\n",
       "    }\n",
       "    a:hover{\n",
       "       font-weight: bold;\n",
       "       color: #1d3b84;\n",
       "    }\n",
       "    a:focus{\n",
       "       font-weight: bold;\n",
       "       color:#447adb;\n",
       "    }\n",
       "    a:active{\n",
       "       font-weight: bold;\n",
       "       color:#447adb;\n",
       "    }\n",
       "    .rendered_html :link {\n",
       "       text-decoration: underline; \n",
       "    }\n",
       "    .rendered_html :hover {\n",
       "       text-decoration: none; \n",
       "    }\n",
       "    .rendered_html :visited {\n",
       "      text-decoration: none;\n",
       "    }\n",
       "    .rendered_html :focus {\n",
       "      text-decoration: none;\n",
       "    }\n",
       "    .rendered_html :active {\n",
       "      text-decoration: none;\n",
       "    }\n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    } \n",
       "    hr {\n",
       "      color: #f3f3f3;\n",
       "      background-color: #f3f3f3;\n",
       "      height: 1px;\n",
       "    }\n",
       "    blockquote{\n",
       "      display:block;\n",
       "      background: #fcfcfc;\n",
       "      border-left: 5px solid #c76c0c;\n",
       "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "      width:680px;\n",
       "      padding: 10px 10px 10px 10px;\n",
       "      text-align:justify;\n",
       "      text-justify:inter-word;\n",
       "      }\n",
       "      blockquote p {\n",
       "        margin-bottom: 0;\n",
       "        line-height: 125%;\n",
       "        font-size: 100%;\n",
       "      }\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "from __future__ import division, print_function\n",
    "import matplotlib.pyplot as plt\n",
    "import book_format\n",
    "book_format.load_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last chapter ended by discussing some of the drawbacks of the Discrete Bayesian filter. For many tracking and filtering problems our desire is to have a filter that is *unimodal* and *continuous*. That is, we want to model our system using floating point math (continuous) and to have only one belief represented (unimodal). For example, we want to say an aircraft is at (12.34, -95.54, 2389.5) where that is latitude, longitude, and altitude. We do not want our filter to tell us \"it *might be* at (1.65, -78.01, 2100.45) or it *might be* at (34.36, -98.23, 2543.79).\" That doesn't match our physical intuition of how the world works, and as we discussed, it can be prohibitively expensive to compute the multimodal case. \n",
    "\n",
    ">So we desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is very computationally efficient to calculate. As you might guess from the chapter name, Gaussian distributions provide all of these features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean, Variance, and Standard Deviations\n",
    "\n",
    "### Random Variables\n",
    "\n",
    "To understand Gaussians we first need to understand a few simple mathematical definitions and computations.\n",
    "\n",
    "To understand Gaussians we first need to understand a few simple mathematical computations. We start with a *random variable* x. Maybe x is the height of the students in a class in meters. We call $x$ *random* because the height of one student does not depend on the height of another student - each is independent. For a specific classrom perhaps the heights are\n",
    "\n",
    "$$x= [1.8, 2.0, 1.7, 1.9, 1.6]$$\n",
    "\n",
    "Another example of a random variable would be the result of a coin toss. Each coin toss is independent from all other tosses. Rolling a die would be another example of a random variable.\n",
    "\n",
    "The coin toss and die roll are examples of *discrete random variables*. That is, the outcome of any given event comes from a discrete set of values. The roll of a six sided die can never produce a value of 7 or 3.24, for example. In contrast, the student heights are continuous; they can take on any value (within biological limits, naturally). For example, heights of 1.7, 1.71, 1.711, 1.7111, 1.71111,.... are all possible. Do not confuse the *measurement* of the random variable with the actual value. If we can only measure the height of a person to 0.1 meters we would only record values from 0.1, 0.2, 0.3...2.7, or 27 discrete choices. Nonetheless the heights can vary between any arbitrary real value between those ranges, and so it is continuous. \n",
    "\n",
    "### The Mean of a Random Variable\n",
    "\n",
    "We want to know the *average* height of the students. Another word for *average* is the *mean*.  We compute the mean by summing the values and dividing by the number of values. In this case we have\n",
    "\n",
    "$$mean = (1.8 + 2.0 + 1.7 + 1.9 + 1.6)/5 = 1.8$$\n",
    "\n",
    "In statistics we normally use the symbol $\\mu$ to denote the mean, so we could write \n",
    "\n",
    "$$\\mu_x = 1.8$$\n",
    "\n",
    "where the subscript *x* denotes that this is the mean for the vector $\\mathbf{x}$. We can formalize this computation with the equation\n",
    "\n",
    "$$ \\mu_x = \\frac{1}{n}\\sum^n_{i=1} x_i$$\n",
    "\n",
    "NumPy has the function `numpy.mean()` which computes the mean for you."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x= [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "print(np.mean(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Deviation of a Random Variable\n",
    "\n",
    "The computation above tells us the average height of the students, but it doesn't tell us everything we might want to know. For example, suppose a second class has students with these heights:\n",
    "\n",
    "$$y = [2.2, 1.5, 2.3, 1.7, 1.3]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = [2.2, 1.5, 2.3, 1.7, 1.3]\n",
    "np.mean(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the mean of these heights is also 1.8 m, but notice that there is a much greater amount of variation in the heights in this class. Finally, suppose a third class has heights\n",
    "\n",
    "$$ z = [1.8, 1.8, 1.8, 1.8, 1.8]$$\n",
    "\n",
    "In this third class the average height is again 1.8 m, but here there is no variation in the height between students at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to be able to specify how much *variation* there is between the heights of the students. You can imagine a number of reasons for this. Perhaps a school district needs to order 5,000 desks, and they want to be sure they buy sizes that accommodate the range of heights of the students. \n",
    "\n",
    "Statistics has formalized this concept of measuring variation into the notion of *standard deviation* and *variance*:\n",
    "\n",
    "**The standard deviation is defined as the square root of the average of the squared differences from the mean.**\n",
    "\n",
    "That's a mouthful; as an equation this is stated as\n",
    "\n",
    "$$\\sigma = \\sqrt{\\frac{1}{N}\\sum_{i=1}^N(x_i - \\mu)^2}$$\n",
    "\n",
    "where $\\sigma$ is the notation for the standard deviation.\n",
    "\n",
    "\n",
    "If this is the first time you have seen this it may not have a lot of meaning for you. But let's just work through that with the data from three classes to be sure we understand the formula. We just subtract the mean of x from each value of x, square it, take the average of those, and then take the square root of the result.  The mean of $[1.8, 2.0, 1.7, 1.9, 1.6]$ is 1.8, so we compute the standard deviation as\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_x &=\\sqrt{\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0^2 + 0.2^2 + (-0.1)^2 + 0.1^2 + (-0.2)^2}{5}} \\\\\n",
    "&= \\sqrt{\\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5}} \\\\\n",
    "&= \\sqrt{0.02} \\\\\n",
    "\\sigma_x&= 0.1414\n",
    "\\end{aligned}$$\n",
    "\n",
    "We use the symbol $\\sigma$ to denote the standard deviation.\n",
    "\n",
    "We can verify this computation with the NumPy method `std()` which computes the standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1414\n"
     ]
    }
   ],
   "source": [
    "print('{:.4f}'.format(np.std(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does this number *mean* (no pun intended)? *How much* in \"how much do the heights vary\" is not a mathematical term. We will be able to define it much more precisely once we introduce the concept of a Gaussian in the next section. For now I'll say that for many things in nature, including the height of people, 68% of all values lie within one standard deviation of the mean. In other words we can conclude that for a random class 68% of the students will have heights between 1.66 (1.8-0.1414) meters and 1.94 (1.8+0.1414) meters. \n",
    "\n",
    "We can look at this in a plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAvIAAAGHCAYAAADSnLajAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X10VPWdx/HPTHhKIgwhbAKEp+BCxBAeQogQQEAkK0sX\n",
       "1sozBwgrUD2AEJfasmIBBbFQ6QolETwYU1q34NENtYsVUpCHgm0iBiki6EYiLiaUkISSFVyTu39Y\n",
       "psQ8MBMyufld3q9zck7mzvfOfIcvyfnkzm/udVmWZQkAAACAUdx2NwAAAADAfwR5AAAAwEAEeQAA\n",
       "AMBABHkAAADAQAR5AAAAwEAEeQAAAMBABHkAAADAQLYF+bVr12rQoEHyeDyKiIjQ+PHjdfLkyZvu\n",
       "d+LECY0YMUIhISHq3LmznnnmmUboFgAAAGhabAvyBw4c0MKFC3X06FHt27dPzZo10/3336+SkpJa\n",
       "97l8+bLGjBmjjh07Kjc3Vy+88ILWr1+vDRs2NGLnAAAAgP1cTeXKruXl5fJ4PNq1a5fGjRtXY016\n",
       "erqWLVumoqIitWzZUpK0Zs0apaen6/PPP2/MdgEAAABbNZk18pcvX1ZlZaXCwsJqrTl69KiGDx/u\n",
       "DfGSlJycrPPnz6ugoKAx2gQAAACahCYT5BcvXqwBAwZoyJAhtdYUFhYqMjKyyrbrtwsLCwPaHwAA\n",
       "ANCUNLO7AUl6/PHHdeTIER0+fFgul6vWurru+7aysrKGaA0AAACwhcfjqfN+24N8amqqdu7cqf37\n",
       "96t79+511nbo0KHakfeioiLvfQAAAMDtwtalNYsXL9aOHTu0b98+9erV66b1Q4YM0aFDh3Tt2jXv\n",
       "tr179yoqKkrdunULZKsAAABAk2LbWWsWLFigX/ziF8rKylLv3r2921u3bq3Q0FBJ0rJly5STk6Ps\n",
       "7GxJ33wgNiYmRiNHjtTy5ct1+vRpzZkzRytXrlRqamqVx79xac3N3pZA05WbmytJSkhIsLkT+MvX\n",
       "pXBN5MRZ8AM/l87BLJ2DWTqHPxnWtiPy6enpunLlikaPHq1OnTp5v55//nlvTWFhofLz872327Rp\n",
       "o7179+r8+fNKSEjQokWLtHTp0mohHgAAAHA629bIV1ZW3rQmIyOj2rY+ffrowIEDgWgJAAAAMEaT\n",
       "Of0kAAAAAN8R5AEAAAADEeQBAAAAA9l+HvnG8O2TZ9R2kozaTrJBvZ31CcrJyW1C/VBf33rJv7PT\n",
       "NLX+qafemfVVz3Bifz/UU099aWnNdTXhiDwAAABgoNviiPy3VVT8qZZ7+lDfBOs9nvO17GNG/9TX\n",
       "zZz+qb9e7/Gcr2Ffc/qnnnon1lf9ubS/H+pvvd4Xt2WQDwo6Uss9Nf9DUm9vffPm7yooqLDJ9EN9\n",
       "fetrZk7/1F+vb9787F+/L/SpPtD9UE899frWz6X9/VB/6/W+sO3KroFW9apYO2zsBLfi7NmzkqTu\n",
       "3bvb2gf853J9z6c6y9oS4E7Q0Pi5dA5m6RzM0jnKyqZ4v2+yV3YFAAAAUH8EeQAAAMBABHkAAADA\n",
       "QAR5AAAAwEC35VlrAAC4HfEhdMBZOCIPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiI\n",
       "IA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIgg\n",
       "DwAAABiIIA8AAAAYqJndDQA3crm+51OdZW0JcCcAAABNG0fkAQAAAAMR5AEAAAADEeQBAAAAAxHk\n",
       "AQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQB\n",
       "AAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAzWzuwEAQNPmcn3PpzrL2hLgTgAAN+KIPAAAAGAggjwA\n",
       "AABgIII8AAAAYCCCPAAAAGCg2+LDri7X/Cq3LWurT3XU21Ff0z4uG/uhvqHqJauW7Wb0f3vX3/h9\n",
       "zT+PkiVXDXc1jf6pr+GeWrbz+5Z66u2uLy0tq7GuJhyRBwAAAAx0WxyR/7aKiiTqDar39zGaWv/U\n",
       "U++ken81tf6pb9j9mlr/t3P9//1fh79u69Ek+qH+1ut94bIsq7b314xWVva3tyXatvVUua+2V1zT\n",
       "28LU219f01u9llXz2/iN0Q/1vtW7qhXU/EBNtX/qa95e19IaO/qh3r/6v/1c1r205tvRoKn0T33t\n",
       "9bm5uZKkhISEJtEP9fWvv3FpjcfjUV1uiyPyvv6p4u+fNNQ3fH318GdvP9Q3XH1DBcDaUB+4et9+\n",
       "Ll3Vwl+g+qH+1utr/3lsmMennnrq619f5vsSedbIAwAAACYiyAMAAAAGIsgDAAAABiLIAwAAAAYi\n",
       "yAMAAAAGIsgDAAAABiLIAwAAAAa6Lc4jDwAA4CS+XnfFodf9xF9xRB4AAAAwEEEeAAAAMBBBHgAA\n",
       "ADAQQR4AAAAwEEEeAAAAMBBBHgAAADAQQR4AAAAwEEEeAAAAMBBBHgAAADCQrUH+4MGDGj9+vDp3\n",
       "7iy3263MzMw668+ePSu3213ta8+ePY3UMQAAANA0NLPzycvLy9W3b1/Nnj1bs2bN8vlyw2+//bb6\n",
       "9evnvR0WFhaoFgEAAIAmydYgP3bsWI0dO1aSlJKS4vN+7dq1U0RERIC6AgAAAJo+I9fIf/e731Vk\n",
       "ZKSGDRum119/3e52AAAAgEZnVJBv3bq1nn/+eb322mt66623NHr0aE2ZMkW//OUv7W4NAAAAaFS2\n",
       "Lq3xV3h4uFJTU7234+PjVVxcrHXr1mnGjBm17pebm9sY7aERMVPnYJbOwSydg1k6B7M0T8+ePX2u\n",
       "NeqIfE0GDRqkjz/+2O42AAAAgEZl1BH5muTl5alTp0511iQkJDRSN2gszNQ5mKVzMEvnYJbOwSzN\n",
       "U1ZW5nOt7aefvH40vbKyUgUFBcrLy1N4eLi6dOmiZcuWKScnR9nZ2ZKkzMxMtWjRQv3795fb7dab\n",
       "b76ptLQ0rVu3zs6XAQAAADQ6W4N8Tk6O7rvvPkmSy+XSihUrtGLFCqWkpOjll19WYWGh8vPzvfUu\n",
       "l0urV69WQUGBgoKCFBMTo4yMDE2fPt2ulwAAAADYwmVZlmV3E4Fw49sSHo/Hxk7gD18vCubQ/7aO\n",
       "wiydg1k6B7N0DmbpXP5kWOM/7AoAAADcjgjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAAgIEI8gAA\n",
       "AICBCPIAAACAgQjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAA\n",
       "gIEI8gAAAICBCPIAAACAgQjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAAgIEI8gAAAICBCPIAAACA\n",
       "gQjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAAgIEI8gAAAICB\n",
       "CPIAAACAgQjyAAAAgIEI8gAAAICBCPIAAACAgQjyAAAAgIGa+VpoWZY++OADnTp1ShcvXpTL5VL7\n",
       "9u3Vu3dvxcXFyeVyBbJPAAAAADe4aZDft2+fMjIy9Otf/1p/+ctfaqxp3bq1/umf/klz5szR6NGj\n",
       "G7xJAAAAAFXVGuTfeustPfXUUzp27Jj69OmjuXPnKj4+Xj169FBYWJgsy1JJSYk+/fRTvffee9q7\n",
       "d6/GjBmj+Ph4rV69Wg888EBjvg4AAADgtuKyLMuq6Y6QkBDNmzdPjzzyiHr37u3Tg506dUrp6ena\n",
       "tm2bysvLG7RRf5WVlXm/93g8NnYCf/i6RKuW/7ZoQpilczBL52CWzsEsncufDFtrkP/zn/+sv/u7\n",
       "v6tXA7eyb0MhyJuJX0zOwSydg1k6B7N0DmbpXP5k2FrPWnMrQdzuEA8AAAA4HaefBAAAAAzkc5C3\n",
       "LEsZGRkaPny4oqKiFBISouDgYAUHB3u/DwkJCWSvAAAAAP7K5/PIf//739eGDRvUuXNnJSYm1rhm\n",
       "h3PJAwAAAI2j1g+7flu7du00bNgwZWVlye1u+ity+LCrmfjwjnMwS+dgls7BLJ2DWTpXg3zYtSbj\n",
       "xo0zIsQDAAAATudzKv/Od76jgwcPBrIXAAAAAD7yeWlNSUmJxo0bp7i4OD388MPq0qWLgoKCqtVF\n",
       "REQ0eJP1wdIaM/FWoXMwS+dgls7BLJ2DWTqXPxnW5w+7hoaGKikpSRs2bNBLL71UY43L5VJFRYWv\n",
       "DwkAAACgnnwO8gsWLNC2bds0ZMgQzloDAAAA2MznpTVt27bVhAkTlJmZGeieGgRLa8zEW4XOwSyd\n",
       "g1k6B7N0DmbpXAE5a03z5s01ePDg+ncFAAAAoMH4HOSnTZumX//614HsBQAAAICPfF4j/9BDD2nJ\n",
       "kiX6h3/4B/3Lv/yLunbtWuNZaxITExu0QQAAAADV+bxG3pcLQTWls9awRt5MrPlzDmbpHMzSOZil\n",
       "czBL5wrI6Sdffvnl+ncEAAAAoEH5fETeNByRNxNHGJyDWToHs3QOZukczNK5AnLWGgAAAABNR61B\n",
       "fsWKFbp06ZLfD3jp0iWtWLHilpoCAAAAULdag3xWVpa6du2qOXPm6K233tK1a9dqfZBr165p9+7d\n",
       "SklJUbdu3bRr166ANAsAAADgG7WukbcsS//xH/+h9evX6/jx4woKClJsbKx69OihsLAwWZalkpIS\n",
       "5efn68MPP1RFRYXi4+O1dOlSTZ06tbFfRzWskTcTa/6cg1k6B7N0DmbpHMzSufzJsD592PX9999X\n",
       "VlaWjhw5oo8++kjFxcVyuVxq3769evfuraFDh2rChAnq27fvrXffQAjyZuIXk3MwS+dgls7BLJ2D\n",
       "WTpXgwd5ExHkzcQvJudgls7BLJ2DWToHs3QuzloDAAAAOBxBHgAAADAQQR4AAAAwEEEeAAAAMBBB\n",
       "HgAAADAQQR4AAAAwkM9BftSoUfrd735X6/379+/Xfffd1yBNAQAAAKibz0H+wIEDKioqqvX+oqIi\n",
       "vfPOOw3REwAAAICbaLClNf/zP/+j0NDQhno4AAAAAHVoVtedu3bt0q5du7xXBdu6dauys7Or1V26\n",
       "dEnZ2dm65557/HrygwcP6ic/+YmOHTum8+fPKyMjQ7Nnz65znxMnTmjhwoXKyclRu3bt9L3vfU9P\n",
       "PfWUX88LAAAAmK7OIH/y5Ent3LnTexngP/zhD3rvvfeq1LhcLoWGhmrUqFH66U9/6teTl5eXq2/f\n",
       "vpo9e7ZmzZp108sNX758WWPGjNHIkSOVm5urU6dOac6cOQoNDdXjjz/u13MDAAAAJnNZ1w+334Tb\n",
       "7db27ds1Y8aMgDTSunVrbd68WbNmzaq1Jj09XcuWLVNRUZFatmwpSVqzZo3S09P1+eefV6ktKyvz\n",
       "fu/xeALSMxrezf6Yu87H/7awEbN0DmbpHMzSOZilc/mTYX1eI19ZWRmwEO+ro0ePavjw4d4QL0nJ\n",
       "yck6f/68CgoKbOwMAAAAaFx1Lq2pzZUrV1RSUlLjX3ldu3a95aZqU1hYWO3xIyMjvfd169atxv1y\n",
       "c3MD1hPswUydg1k6B7N0DmbpHMzSPD179vS51ucg/+WXX2rVqlXatm2biouLa6xxuVyqqKjw+cn9\n",
       "5evbSAAAAIDT+RzkFyxYoFdeeUUPPvighg0bprCwsED2VaMOHTqosLCwyrbr57bv0KFDrfslJCQE\n",
       "tC80PmbqHMzSOZilczBL52CW5rlxjfzN+Bzk33jjDc2dO1dbt26tV1MNYciQIfrBD36ga9euedfJ\n",
       "7927V1FRUbUuqwEAAACcyOcPu7pcLg0cOLBBn7y8vFx5eXnKy8tTZWWlCgoKlJeXp3PnzkmSli1b\n",
       "pvvvv99bP336dIWEhCglJUUnT57UG2+8oR//+MecehIAAAC3HZ+D/IQJE2q8GNStyMnJUXx8vOLj\n",
       "43X16lWtWLFC8fHxWrFihaRvPsCan5/vrW/Tpo327t2r8+fPKyEhQYsWLdLSpUuVmpraoH0BAAAA\n",
       "TV2t55G/cOFCldulpaWaOnWq4uPjNW/ePHXt2lVBQUHV9ouIiAhMp37iPPJm4ry4zsEsnYNZOgez\n",
       "dA5m6Vz+ZNhag7zb7fPB+r89WIDPWuMPgryZ+MXkHMzSOZilczBL52CWzuVPhq31w64/+tGP/H5i\n",
       "Tg8JAAAANI5aj8ibjiPyZuIIg3MwS+dgls7BLJ2DWTqXPxnW//UzAAAAAGzn83nkV61aVedffy6X\n",
       "S61atVLnzp117733KioqqkEaBAAAAFCdz0tr/Pnwa1BQkObOnavNmzfX60OzDYGlNWbirULnYJbO\n",
       "wSydg1k6B7N0roAsrfnss88UFxenlJQUvffeeyotLVVpaalyc3M1e/Zs9evXT6dOndKxY8c0Y8YM\n",
       "bdmyRWvWrKn/qwAAAABQK5+PyE+YMEHBwcH61a9+VeP9U6ZM0bVr15SVlSVJ+sd//Ed98sknOnPm\n",
       "TMN16weOyJuJIwzOwSydg1k6B7N0DmbpXAE5Ir9//36NHDmy1vtHjBih3/3ud97bY8eOVUFBga8P\n",
       "DwAAAMAPPgf5Fi1a6OjRo7Xe/4c//EEtW7b03v766691xx133Fp3AAAAAGrkc5CfPn26tm/frsWL\n",
       "F+v06dP6+uuv9fXXX+ujjz7SY489pu3bt2vatGne+v379+vuu+8OSNMAAADA7c7n00/++Mc/VlFR\n",
       "kTZt2qRNmzZ512ZdX3v10EMPad26dZKkq1evauDAgRo6dGgAWgYAAADg95Vdjx07pt/+9rfe9e/d\n",
       "unXTAw88oPj4+IA0WF982NVMfHjHOZilczBL52CWzsEsncufDOt3kDcFQd5M/GJyDmbpHMzSOZil\n",
       "czBL5wrIWWsAAAAANB21rpGPjo6Wy+XS6dOn1bx5c+/tmv6yu77d5XIpPz8/oA0DAAAAqCPIjxgx\n",
       "Qi6Xy/vWzYgRI276YL6+zQMAAADg1rBGHk0Ka/6cg1k6B7N0DmbpHMzSuVgjDwAAADicX0H+4sWL\n",
       "evLJJ5WUlKSePXt6r/RaXFysVatW6dSpUwFpEgAAAEBVPl8Q6uzZsxo6dKguXbqkPn366L//+7/1\n",
       "5ZdfSpLCw8O1Y8cOXbhwQZs3bw5YswAAAAC+4XOQf+KJJ2RZlk6ePKk2bdooIiKiyv3jx4/Xrl27\n",
       "GrxBAAAAANX5vLQmOztbCxcuVI8ePWq8Pzo6WufOnWuwxgAAAADUzucgf/XqVbVr167W+0tLS+V2\n",
       "89lZAAAAoDH4nLxjY2P1zjvv1Hr/rl27FB8f3xA9AQAAALgJn9fIp6amaubMmerTp48mT54sSfr6\n",
       "66916tQpPf3003r33XeVlZUVsEYBAAAA/I1fF4R67rnn9NRTT6mioqLK9qCgID333HP613/91wZv\n",
       "sL64IJSZuMCFczBL52CWzsEsnYNZOpc/GdbvK7t+9tlneuONN3TmzBlVVlbqzjvv1MSJExUdHV2/\n",
       "bgOEIG8mfjE5B7N0DmbpHMzSOZilcwU0yJuCIG8mfjE5B7N0DmbpHMzSOZilc/mTYX1eI3+jK1eu\n",
       "qKSkpMb/HF27dq3PQwIAAADwg89B/ssvv9SqVau0bds2FRcX11jjcrmqrZ8HAAAA0PB8DvILFizQ\n",
       "K6+8ogcffFDDhg1TWFhYIPsCAAAAUAef18i3bdtWkydP1tatWwPdU4NgjbyZWPPnHMzSOZilczBL\n",
       "52CWzuVPhvX5glAul0sDBw6sf1cAAAAAGozPQX7ChAnKzs4OZC8AAAAAfFTr0poLFy5UuV1aWqqp\n",
       "U6cqPj5e8+bNU9euXRUUFFRtv4iIiMB06ieW1piJtwqdg1k6B7N0DmbpHMzSuRrkPPJut88H6//2\n",
       "YE3orDUEeTPxi8k5mKVzMEvnYJbOwSydq0HOI/+jH/3I7yf29T8VAAAAgFvDlV3RpHCEwTmYpXMw\n",
       "S+dgls7BLJ0rIGetAQAAANB0EOQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEA\n",
       "AAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAA\n",
       "AAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAA\n",
       "AxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAAD\n",
       "EeQBAAAAA9ke5NPS0hQdHa3g4GAlJCTo8OHDtdaePXtWbre72teePXsasWMAAADAfrYG+R07dmjJ\n",
       "kiVavny58vLylJSUpLFjx+rcuXN17vf222+rsLDQ+zVq1KhG6hgAAABoGmwN8hs2bNCcOXP08MMP\n",
       "KyYmRhs3blTHjh2Vnp5e537t2rVTRESE96t58+aN1DEAAADQNNgW5L/66isdO3ZMycnJVbYnJyfr\n",
       "yJEjde773e9+V5GRkRo2bJhef/31QLYJAAAANEm2BfmLFy+qoqJCkZGRVbZHRESosLCwxn1at26t\n",
       "559/Xq+99preeustjR49WlOmTNEvf/nLxmgZAAAAaDKa2d2AP8LDw5Wamuq9HR8fr+LiYq1bt04z\n",
       "Zsyodb/c3NzGaA+NiJk6B7N0DmbpHMzSOZileXr27OlzrW1H5Nu3b6+goCAVFRVV2V5UVKSOHTv6\n",
       "/DiDBg3Sxx9/3NDtAQAAAE2ay7Isy64nHzx4sPr166ctW7Z4t/Xq1UuTJk3SmjVrfHqM1NRUvfnm\n",
       "m/rkk0+qbC8rK/N+7/F4GqZhBJzL5fKpzsb/tvARs3QOZukczNI5mKVz+ZNhbV1a8/jjj2vmzJlK\n",
       "TExUUlKSXnzxRRUWFuqRRx6RJC1btkw5OTnKzs6WJGVmZqpFixbq37+/3G633nzzTaWlpWndunV2\n",
       "vgwAAACg0dka5CdPnqzi4mKtXr1aX3zxheLi4rR792516dJFklRYWKj8/Hxvvcvl0urVq1VQUKCg\n",
       "oCDFxMQoIyND06dPt+slAAAAALawdWlNILG0xky8VegczNI5mKVzMEvnYJbO5U+GtfWCUAAAAADq\n",
       "hyAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiI\n",
       "IA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIgg\n",
       "DwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAP\n",
       "AAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8A\n",
       "AAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAA\n",
       "ABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAA\n",
       "GIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAY\n",
       "iCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGIggDwAAABiI\n",
       "IA8AAAAYiCAPAAAAGIggDwAAABiIIA8AAAAYiCAPAAAAGMj2IJ+Wlqbo6GgFBwcrISFBhw8frrP+\n",
       "xIkTGjFihEJCQtS5c2c988wzjdQpAAAA0HTYGuR37NihJUuWaPny5crLy1NSUpLGjh2rc+fO1Vh/\n",
       "+fJljRkzRh07dlRubq5eeOEFrV+/Xhs2bGjkzgEAAAB7uSzLsux68nvuuUf9+/fXli1bvNt69eql\n",
       "iRMn6tlnn61Wn56ermXLlqmoqEgtW7aUJK1Zs0bp6en6/PPPq9SWlZV5v/d4PAF6BWhoLpfLpzob\n",
       "/9vCR8zSOZilczBL52CWzuVPhrXtiPxXX32lY8eOKTk5ucr25ORkHTlypMZ9jh49quHDh3tD/PX6\n",
       "8+fPq6CgIKD9AgAAAE2JbUH+4sWLqqioUGRkZJXtERERKiwsrHGfwsLCavXXb9e2DwAAAOBEzexu\n",
       "wB++vo30bTe+RYGmrbS01Kc6Ztr0MUvnYJbOwSydg1lCsvGIfPv27RUUFKSioqIq24uKitSxY8ca\n",
       "9+nQoUO1I+/X9+/QoUNgGgUAAACaINuCfIsWLTRw4EDt2bOnyva9e/cqKSmpxn2GDBmiQ4cO6dq1\n",
       "a1Xqo6Ki1K1bt4D2CwAAADQltp61ZufOnZo5c6bS0tKUlJSkF198URkZGTp58qS6dOmiZcuWKScn\n",
       "R9nZ2ZK+Of1kTEyMRo4cqeXLl+v06dOaM2eOVq5cqdTUVLteBgAAANDobF0jP3nyZBUXF2v16tX6\n",
       "4osvFBcXp927d6tLly6SvvkAa35+vre+TZs22rt3rxYsWKCEhAS1a9dOS5cuJcQDAADgtmPrEXkA\n",
       "AAAA9WPrlV0DJS0tTdHR0QoODlZCQoIOHz5sd0vw08GDBzV+/Hh17txZbrdbmZmZdreEelq7dq0G\n",
       "DRokj8ejiIgIjR8/XidPnrS7LdTD5s2b1a9fP3k8Hnk8HiUlJWn37t12t4VbtHbtWrndbi1atMju\n",
       "VuCnlStXyu12V/nq1KmT3W2hnr744gvNnj1bERERCg4OVmxsrA4ePFjnPo4L8jt27NCSJUu0fPly\n",
       "5eXlKSkpSWPHjtW5c+fsbg1+KC8vV9++ffXCCy8oODi43qcehf0OHDighQsX6ujRo9q3b5+aNWum\n",
       "+++/XyUlJXa3Bj916dJF69at0/vvv6/33ntP9913n/75n/9Zx48ft7s11NO7776rl156SX379uX3\n",
       "rKHuuusuFRYWer9OnDhhd0uoh9LSUg0dOlQul0u7d+/WRx99pJ/97GeKiIiocz/HLa2555571L9/\n",
       "f23ZssW7rVevXpo4caKeffZZGztDfbVu3VqbN2/WrFmz7G4FDaC8vFwej0e7du3SuHHj7G4Htyg8\n",
       "PFzPPfec5s2bZ3cr8FNZWZkGDhyobdu2aeXKlYqLi9PGjRvtbgt+WLlypV5//XXCuwP827/9mw4d\n",
       "OqRDhw4j7qTzAAAKF0lEQVT5tZ+jjsh/9dVXOnbsmJKTk6tsT05O1pEjR2zqCsCNLl++rMrKSoWF\n",
       "hdndCm5BRUWFfvWrX+nq1au699577W4H9TB//nxNmjRJI0aMkMOO6d1W8vPzFRUVpR49emjatGn6\n",
       "9NNP7W4J9ZCVlaXExERNmTJFkZGRGjBggDZv3nzT/RwV5C9evKiKigpFRkZW2R4REVHtQlIA7LF4\n",
       "8WINGDBAQ4YMsbsV1MOJEyd0xx13qFWrVpo/f7527typmJgYu9uCn1566SXl5+dr9erVkup/5XTY\n",
       "a/DgwcrMzNTbb7+tl156SYWFhUpKStKlS5fsbg1+ys/PV1pamv7+7/9ee/bs0eLFi/XDH/7wpmHe\n",
       "1tNPAri9PP744zpy5IgOHz5McDDUXXfdpQ8++EBlZWV67bXXNHXqVO3fv18JCQl2twYfnT59Wk8+\n",
       "+aQOHz6soKAgSZJlWRyVN9ADDzzg/b5Pnz4aMmSIoqOjlZmZyam5DVNZWanExEStWbNGktSvXz99\n",
       "/PHH2rx5sxYsWFDrfo4K8u3bt1dQUJCKioqqbC8qKlLHjh1t6gqAJKWmpmrnzp3av3+/unfvbnc7\n",
       "qKfmzZurR48ekqQBAwYoJydHmzdvVkZGhs2dwVdHjx7VxYsXFRsb691WUVGhQ4cOacuWLSovL1fz\n",
       "5s1t7BD1FRISotjYWH3yySd2twI/derUSXfffXeVbXfddZc+++yzOvdz1NKaFi1aaODAgdqzZ0+V\n",
       "7Xv37lVSUpJNXQFYvHixduzYoX379qlXr152t4MGVFFRocrKSrvbgB8efPBB/elPf9Lx48d1/Phx\n",
       "5eXlKSEhQdOmTVNeXh4h3mBXr17VqVOnOHhpoKFDh+qjjz6qsu3MmTM3PfDlqCPy0jdv3c+cOVOJ\n",
       "iYlKSkrSiy++qMLCQj3yyCN2twY/lJeX6+OPP5b0zdtNBQUFysvLU3h4uPfKvzDDggUL9Itf/EJZ\n",
       "WVnyeDzez6u0bt1aoaGhNncHf/zwhz/Ud77zHXXu3Fl/+ctf9Oqrr+rAgQP67W9/a3dr8MP16wDc\n",
       "KCQkRGFhYdWOCKJpW7p0qcaPH68uXbrowoULeuaZZ/Tll19q9uzZdrcGP6WmpiopKUnPPvusJk+e\n",
       "rPfff1+bNm3S2rVr697RcqC0tDSre/fuVsuWLa2EhATr0KFDdrcEP+3fv99yuVyWy+Wy3G639/s5\n",
       "c+bY3Rr89O0ZXv9atWqV3a3BTykpKVa3bt2sli1bWhEREdaYMWOsPXv22N0WGsDIkSOtRYsW2d0G\n",
       "/DR16lSrU6dOVosWLayoqChr4sSJ1qlTp+xuC/X0X//1X1a/fv2sVq1aWTExMdamTZtuuo/jziMP\n",
       "AAAA3A4ctUYeAAAAuF0Q5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR\n",
       "5AEA9ZKSkqLo6Gi72wCA2xZBHgAc7NVXX9ULL7wQsMd3uVwBe2xJ+vDDD7Vy5UoVFBQE9HkAwEQE\n",
       "eQBwsFdffVX//u//HrDHD/TFwT/88EM9/fTTBHkAqAFBHgAcLtBHzRtDoP9gAAATEeQBwGBXrlzR\n",
       "0qVLFR0drVatWikiIkKjRo3SoUOHNHLkSO3evVtnz56V2+32fknSO++8I7fbrYMHD1Z5vOu1mZmZ\n",
       "VbZnZWWpT58+Cg4OVlxcnP7zP/+zxn4sy9KmTZsUFxen4OBgRUZGau7cuSouLq5S1717d40dO1aH\n",
       "Dx9WYmKigoODdeedd2r79u3emldeeUWTJ0+WJI0aNcrb/89//vNb/ncDACdoZncDAID6e/TRR/Xa\n",
       "a69p4cKFio2N1aVLl/THP/5RH3zwgZYvX64nnnhCn3/+ud/La248ir9nzx499NBDio2N1dq1a3Xp\n",
       "0iU9/PDDioqKqna0/9FHH9XLL7+slJQUPfbYY/rss8+0adMm/fGPf1ROTo5atmzpffxPP/1UkyZN\n",
       "0ty5czVnzhxt27ZNKSkpGjhwoO6++26NGDFCjz32mDZu3Kgnn3xSvXv3liQlJSXd4r8aADgDQR4A\n",
       "DPab3/xG8+fP109+8pMa7+/UqZNKS0s1ffr0ej/HD37wA3Xo0EG///3v1bp1a0nfHCEfPXq0unfv\n",
       "7q07cuSItm7dqu3bt2vGjBne7Q888ICGDx+un//855o3b56kb47cnzlzRgcPHtSwYcMkSZMmTVKX\n",
       "Ll2UkZGh9evXKzo6WsOGDdPGjRs1ZswY3XvvvfV+DQDgRCytAQCDtW3bVu+++67Onz8fkMf/4osv\n",
       "dPz4cc2cOdMb4qVvgnxsbGyV2p07d+qOO+5QcnKyLl686P2KiYlRRESE9u/fX6U+JibGG+IlqX37\n",
       "9oqJidGnn34akNcCAE5DkAcAg61fv14nT55U165dNWjQID311FM6c+ZMgz3+9bPF9OzZs9p93952\n",
       "5swZXblyRZGRkYqIiKjydeHCBf35z3+uUt+1a9dqj9m2bVuVlJQ0WP8A4GQsrQEAg02cOFHDhw/X\n",
       "rl27tGfPHm3cuFHr1q3TK6+8omnTptW6X21nsqmoqKh3L5WVlQoPD9eOHTtqvD8sLKzK7aCgoBrr\n",
       "OEMNAPiGIA8AhouMjNT8+fM1f/58lZWVafDgwVqxYoWmTZtWa2C/HqpLS0urbP/2+dq7desmSTUe\n",
       "5f/2tjvvvFPZ2dm65557FBoaWu/XcyMnnDoTAAKFpTUAYKjKykqVlZVV2ebxeNS9e3fv9tDQ0BqX\n",
       "qnTr1k1BQUE6cOBAle1paWlVbnfs2FH9+/fX9u3bdfnyZe/2ffv26cMPP6xSO3XqVFVWVurpp5+u\n",
       "9nwVFRXV/mjwxfU/CC5duuT3vgDgdByRBwBDXb58WVFRUZo4caL69u2rNm3a6Pe//73efvttLVq0\n",
       "SJI0aNAg7dy5U0uWLFFiYqLcbremTp0qj8ejSZMmadOmTXK5XOrRo4d+85vfVFvHLklr167VuHHj\n",
       "NGzYMKWkpKi0tFQ/+9nPFBsbqytXrnjrhg8frgULFmj9+vX64IMPlJycrJYtW+qTTz7R66+/rmee\n",
       "eUazZs266eu6cWlNfHy8goKCtHbtWpWUlCg4OFiDBw+ucrYcALhtWQAAI3311VfWE088YQ0YMMBq\n",
       "27atFRoaasXFxVkbNmywKioqLMuyrP/93/+1Zs+ebYWHh1tut9tyu93e/S9evGhNnDjRCg0NtcLD\n",
       "w61HH33UOnnypOVyuazMzMwqz/XGG29Yd999t9WqVSurT58+VlZWlpWSkmJFR0dX6+vll1+2EhMT\n",
       "rZCQEKtNmzZWXFyc9f3vf986d+6ct6Z79+7W2LFjq+07cuRIa9SoUVW2ZWRkWD179rSaNWtmud3u\n",
       "ar0BwO3KZVl8qggAAAAwDWvkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAMR5AEAAAADEeQBAAAA\n",
       "AxHkAQAAAAMR5AEAAAADEeQBAAAAAxHkAQAAAAP9P3lqIgAYgrVHAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48093bde10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_height_std(x, lw=10):\n",
    "    m = np.mean(x)\n",
    "    s = np.std(x)\n",
    "\n",
    "    for i, height in enumerate(x):\n",
    "        plt.plot([i+1, i+1], [0, height], color='k', lw=lw)\n",
    "    plt.xlim(0,len(x)+1)\n",
    "    plt.axhline(m-s, ls='--')\n",
    "    plt.axhline(m+s, ls='--')\n",
    "    plt.fill_between((0, len(x)+1), m-s, m+s, \n",
    "                     facecolor='yellow', alpha=0.4)\n",
    "    plt.xlabel('student')\n",
    "    plt.ylabel('height (m)')\n",
    "    plt.show()\n",
    "    \n",
    "x= [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "plot_height_std(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For only 5 students we obviously will not get exactly 68% within one standard deviation (normally denoted as $1\\sigma$), but we do see that 3 out of 5 students are within $1\\sigma$, or 60%, which is as close as you can get to 68% with only 5 samples. I haven't yet introduced enough math or Python for you to fully understand the next bit of code, but let's look at the results for a class with 100 students."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAvQAAAGHCAYAAADfgsbkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X10U3WCxvEnaXkpCBHBlkqBFg92eBdoUQsIqHTs4uJR\n",
       "fIGyYhmR0S0IZR1dEAUUZYS1u4AUxZFSGVyBIwujqyMgCDLgTBGrDgjoIAUHW5ZCy5YVHNq7fzhE\n",
       "YpM0KXn7pd/POT2nufd3732S3tw+vb1JbJZlWQIAAABgJHu4AwAAAABoOAo9AAAAYDAKPQAAAGAw\n",
       "Cj0AAABgMAo9AAAAYDAKPQAAAGAwCj0AAABgsLAW+nnz5ik9PV0Oh0Px8fEaOXKk9u7d63WZw4cP\n",
       "y2631/nauHFjiFIDAAAAkSOshX7btm2aNGmSdu3apS1btig2Nla33HKLTp06Ve+y7733nsrKypxf\n",
       "w4YNC0FiAAAAILLYIumTYs+cOSOHw6ENGzZoxIgRbsccPnxYXbp0UXFxsfr37x/ihAAAAEBkiahr\n",
       "6E+fPq3a2lq1adOm3rF33nmnEhISNGjQIL355pshSAcAAABEnog6Q3/PPffoL3/5i3bv3i2bzeZ2\n",
       "TEVFhV577TUNHDhQsbGx2rBhg5599lkVFRVp7NixIU4MAAAAhFfEFPpp06ZpzZo12rFjh5KTk/1a\n",
       "dtKkSfrwww/16aefOqdVVVUFOCEAAAAQOg6Hw6dxEXHJTV5enlavXq0tW7b4XeYlKT09XV9++WXg\n",
       "gwEAAAARLjbcAaZMmaK1a9dq69atuuaaaxq0jpKSEl111VUBTgYAAABEvrAW+tzcXP32t7/V+vXr\n",
       "5XA4VFZWJklq1aqVWrZsKUmaPn26iouLtXnzZklSUVGRmjZtqmuvvVZ2u11vvfWWCgoKNH/+fI/b\n",
       "8fXfFWg8du/eLUlKS0sLcxJEIvYP1Id9BN6wf6A+3vaRhlw2HtZCv3TpUtlsNt18880u02fPnq2n\n",
       "nnpKklRWVqZDhw4559lsNs2dO1elpaWKiYlRamqqCgsLlZ2dHdLsAAAAQCQIa6Gvra2td0xhYaHL\n",
       "7XHjxmncuHHBigQAAAAYJSJeFAsAAACgYSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAA\n",
       "AIDBKPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAA\n",
       "gMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACA\n",
       "wSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAAAIDB\n",
       "KPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo9AAAAIDBKPQAAACAwSj0AAAAgMEo\n",
       "9AAAAIDBKPQAAACAwSj0AAAAgMFiwx0AAADTpKenS5IsywpzEgDgDD0AAABgNAo9AAAAYDAKPQAA\n",
       "AGAwCj0AAABgMAo9AAAAYDAKPQAAAGAwCj0AAABgMAo9AAAAYDAKPQAAUchms8lms4U7BoAQoNAD\n",
       "AIKCQgkAoUGhBwAAAAxGoQcAAEBY8J+8wKDQAwAk8YsViDY8pxuPsBX6efPmKT09XQ6HQ/Hx8Ro5\n",
       "cqT27t1b73Kff/65hgwZohYtWigpKUnPPPNMCNICAAAAkSlshX7btm2aNGmSdu3apS1btig2Nla3\n",
       "3HKLTp065XGZ06dPa/jw4UpMTNTu3bu1cOFCLViwQPn5+SFMDgAAAESO2HBt+Pe//73L7ZUrV8rh\n",
       "cGjnzp0aMWKE22VWrVqls2fPqqioSM2aNVP37t21f/9+5efna9q0aaGIDQAAAESUiLmG/vTp06qt\n",
       "rVWbNm08jtm1a5cGDx6sZs2aOadlZmbq2LFjKi0tDUVMAAAAIKJETKGfMmWK+vbtqxtuuMHjmLKy\n",
       "MiUkJLhMu3C7rKwsqPlMwItfAAAAGp+wXXJzsWnTpmnnzp3asWOH10La0LK6e/fuhkYzUmO7v5eC\n",
       "xyr6paenS5KKi4v9Xrax7h+Bvt/R/DiacN9MyBitIuWxj5Qc3piQMRjc3e+uXbv6vZ6wF/q8vDyt\n",
       "WbNGW7duVXJystex7du3r3Mmvry83DkPAAAAaGxslmVZ4dr4lClTtHbtWm3dulWpqan1jn/ppZf0\n",
       "+OOP6/jx487r6J977jktXbpUR48edRlbVVXl/N7hcAQ2eIS68B+MMP5IjXHhL+K0tLQwJ0GwNeR5\n",
       "0Vj3j0AfQ6L5mGTCfTMhY7QKxjGkIT9PE/YBEzIGg7d9pCEdNmxn6HNzc/Xb3/5W69evl8PhcJ55\n",
       "b9WqlVq2bClJmj59uoqLi7V582ZJUnZ2tubMmaOcnBzNnDlTBw4c0PPPP6/Zs2d73dZPr9TxtM94\n",
       "uqLHlPGS5XY5U/KHdvyPT6DIyMP4YI33xJT8Zo+3JLlfkRn5TT/eRu/jH/nj04Kw/rr7XP3rd10m\n",
       "ch6f6Bnv7g+SS11/ZaX7cd6E7UWxS5cuVXV1tW6++WZdddVVzq8XXnjBOaasrEyHDh1y3m7durU2\n",
       "bdqkY8eOKS0tTZMnT9ajjz6qvLy8cNwFAAAAIOzCdoa+tra23jGFhYV1pvXs2VPbtm27pG3X1PzZ\n",
       "w5yeHsfHxvaSJJ0//7lP4/1dP+MZz/jgjPe8nOf1OxzH3Cxjxv0NxPgfpgXu8Xe/TOTc32ge73mZ\n",
       "yMh/4XfrhTPJ4c7TmMa79prw54mE4+2Fs+2uXc+39fub3/X3jPffX74I+4tiwyEmZqeHOe4f0IvH\n",
       "uy5b/3h/1894xjM+sOM9L+d5/U2aHP7792U+jfcnjwnjf5gWuMff/TKRc3+jebznZSItv3uR9nhG\n",
       "4/hAPt9N71eelwt8ftffM5de6MP6othgcn1BwepLXp/N9ktJkmW9fMnrChYTMgZaQ+/z4cOHJane\n",
       "d1ZCcIRyX23ItoKxf5jw/GxoRk/Lhfo+R/p+FWqRktFbjkjJGGiRcgwx4bEPRo5AH8uCsS1v+0hV\n",
       "1b3O7yP+RbEAAODSREopi2Y8xoHB4+gqJWWepMA9HhHzSbEAAAAA/EehhxFstl86/7oHAEQ/jvuA\n",
       "7yj0AABAEiUakYX90XcUegBAvfjFCgCRi0IPAAFC6QUAhAOFHh5RTgAAgK/oDeFDoQeCjAMcgGjA\n",
       "sQyIXLwPfZDxvqsAADQugX6PcaA+nKGPQJwFAerieQEAgHucoUejxNkTAEC04GoAcIYeMJC3s9WN\n",
       "8Ux2Y7zPDcVjBQDRh0IPAIhq/BGD+rCPmIefmSsKPaIWT3YAANAYUOgRcFwOAgAAEDoUegAAAPiE\n",
       "E3ORiUIPAAAAGIxCDwBhxhmv8OGxBxANKPRoEH4JuuLxAEKD5xqiGfs3GopCD4BfIgAQIhxvEQx8\n",
       "UiyAiBEpn3bIJwkDAEzCGXogQnEWJzJFys8lUnIAAMKPQg8AAC4Jf2Aimpmwf1PoAQAAAINR6C/S\n",
       "0L/ATPjLDQCAaMDvXKAuCj0AAABgMAp9I8EZDcBMPHcRDOxXQHRpdIWegxgAAACiSaMr9AAAAEA0\n",
       "odADYRTN/zGK5vsGAEAkodADACJKpPwxGCk5AKA+FPow4pcFAKA+/K4AUJ/YcAcIBZtt4kW3Jkqy\n",
       "eRhp/X38T6Zay+pZ70SX5eoff3EWSfJ1vPf1Nzx/Q8b/eJ/9W7/nx79heVwf+/rHX5zDff4ff3Fa\n",
       "btcj2WRZL7tLWuex/4H7X8TByu9+fP3r95Q/cvYf78+Xhj3+btYSpue7v/kj7XjlPn+gn+8/5vAv\n",
       "f+CPV6Yfbz3lj6zjlff8kXC88vz7IhjHq4Y8/g19vnsfH/n5G9avAn+8bdj4ysoqDzk84ww9AAAA\n",
       "YLBGcYbenZqajAaN9WU5d2O8LedPlksd35D89S3jbx5/lzE9v7/LBDt/qMc3JH8gny/+Lhdpz3d/\n",
       "lwvEzzfQ+U0+3vq7TKQ9H4O9TKQdb8NxvArkeH+X43gb3fn9YbMsy9N1BUarqvrx3xWXX+74yVyb\n",
       "3N1t9/8+kixLsv195sXLeRv/45gfl/Nl/MXLeLrkw9NPLND5f7pMoPKH6vEPZf4flvE8/uIcPy7j\n",
       "PU+w8rvbf7zlb8j+dnEOf/I35Pny43KBe/xD+Xz/cbnA7j91t1H/+GDlN/l425D8btcSpPGBzh9p\n",
       "xyt/j7ehPF5dvFygjrehfPwj5XgV6uOtt/VHSv6LL7lxOH7aYd1rFGfo3T2A7rn/Qda3Xnc/zPpy\n",
       "uGbx78DkWejy+7KM5wOB7+Pry+Nr9p+uPxj5A1VcfMnTkPwN/cXv6/r9GR/K/P4e6OvLE6zne6CK\n",
       "V315Qpk/0M/3i9cZ7uNVQx9/X4Urf6Qcry5ezj3/j1cmHG8D/fg39Plev8jOH+gTo6E+3lb5fwk9\n",
       "19ADAAAAJqPQAwAQQDabrZ6zywAQWBR6AIgyFEoAaFwo9AAAICrwxywaKwo9AAAAYDAKPQAAAGAw\n",
       "Cj0AAABgMAo9AAAAYDAKPQAAAGAwCr1heAU/Qo19DsHAfgUAgUOhB9BglDIAgEmi9fcWhR4AgBCJ\n",
       "1jIBILxifR1oWZY+++wzffHFFzpx4oRsNpvatWunbt26qVevXhygAAAAgDCot9Bv2bJFhYWF+t3v\n",
       "fqf//d//dTumVatW+sd//EeNHz9eN998c8BDAgAAAHDPY6F/99139eSTT2rPnj3q2bOnJkyYoH79\n",
       "+qlLly5q06aNLMvSqVOn9PXXX+vjjz/Wpk2bNHz4cPXr109z587VrbfeGsr7AQAAgAC4cNWFZVlh\n",
       "TgJfeSz0o0aN0oMPPqiVK1eqW7duHleQkZGhsWPHSpK++OILLV26VKNGjdKZM2cCnxZRjQMIAACA\n",
       "/zy+KLa0tFQLFy70WuZ/qlu3blq0aJEOHz7s0/jt27dr5MiRSkpKkt1uV1FRkdfxhw8flt1ur/O1\n",
       "ceNGnzMCAAAA0cTjGforr7yywSv1ddkzZ86od+/euv/++zVu3DifX1j73nvvqU+fPs7bbdq0aVBO\n",
       "AAAiAf+hBHApfH6Xm2DIyspSVlaWJCknJ8fn5a644grFx8cHKRUAAABgDp/fh96yLBUWFmrw4MHq\n",
       "0KGDWrRoobi4OMXFxTm/b9GiRTCzOt15551KSEjQoEGD9Oabb4ZkmwAAAEAk8vkM/a9+9Svl5+cr\n",
       "KSlJAwYMkMPhqDMm2O9F36pVK73wwgsaOHCgYmNjtWHDBt17770qKipyvjAXAAAAaEx8LvTLly/X\n",
       "bbfdpvXr18tuD88HzLZt21Z5eXnO2/369VNFRYXmz5/vtdDv3r3bp2mRNo8cvs8jh+/zIiWHt3mh\n",
       "zhHKbZn+WJmcMVJyeJtHDt/nRUoOb/PI4fu8SMnhbV6ottW1a1eP4z3xq5mPGDEibGXek/T0dH35\n",
       "5ZfhjgEAAACEhc3y8SX148aNU01NjVatWhWUIK1atdKSJUs0btw4v5bLy8vTW2+9pa+++splelVV\n",
       "lfP7iy8P8vZOApEyjxzmZYyUHGT0b54nkfJ4eJsXKTlMyBgpOUzIGCk5yBhdOcjo3zxPHdYbny+5\n",
       "WbhwoUaMGKFf/vKXeuCBB9SxY0fFxMTUGefPu8+cOXPGeXa9trZWpaWlKikpUdu2bdWxY0dNnz5d\n",
       "xcXF2rx5sySpqKhITZs21bXXXiu73a633npLBQUFmj9/vs/bBAAAAKKJz4W+ZcuWysjIUH5+vl55\n",
       "5RW3Y2w2m2pqanzeeHFxsW666SbnsrNmzdKsWbOUk5Oj5cuXq6ysTIcOHXJZ/9y5c1VaWqqYmBil\n",
       "pqaqsLBQ2dnZPm8TAAAAiCY+F/rc3Fy9+uqruuGGGwL2LjdDhw5VbW2tx/mFhYUut8eNG+f3JTkA\n",
       "AABANPO50K9du1b33XefioqKgpkHAAAAgB98fsuaJk2a6Prrrw9mFgAAAAB+8rnQjxkzRr/73e+C\n",
       "mQUAAACAn3y+5GbUqFGaOnWqfv7zn+sXv/iFOnXq5PZdbgYMGBDQgAAAAAA887nQDxs2zPn9pk2b\n",
       "3I7x911uACCcGvIe9QAARBqfC/3y5cuDmQMAAABAA/hc6HNycoIYAwAAAEBD+PyiWAAAAACRx2Oh\n",
       "nzVrlk6ePOn3Ck+ePKlZs2ZdUigAAAAAvvFY6NevX69OnTpp/Pjxevfdd3Xu3DmPKzl37pzeeecd\n",
       "5eTkqHPnztqwYUNQwgIAAABw5fEa+pKSEv3nf/6nFixYoKKiIsXExKhHjx7q0qWL2rRpI8uydOrU\n",
       "KR06dEj79u1TTU2N+vXrp1deeUWjR48O5X0AAAAAGi2Phd5msyk7O1vZ2dn65JNPtH79eu3cuVPF\n",
       "xcWqqKiQzWZTu3bt1K1bN9111126/fbb1bt371BmBwAAABo9n97lpm/fvurbt2+wswAAAADwE+9y\n",
       "AwAAABiMQg8AAAAYjEIPAAAAGIxCDwAAABiMQg8AAAAYjEIPAAAAGMznQj9s2DC9//77Hudv3bpV\n",
       "N910U0BCAQAAAPCNz4V+27ZtKi8v9zi/vLxcH3zwQSAyAQAAAPBRwC65+etf/6qWLVsGanUAAAAA\n",
       "fOD1k2I3bNigDRs2yLIsSdKyZcu0efPmOuNOnjypzZs367rrrgtOSgAAAABueS30e/fu1Zo1a2Sz\n",
       "2SRJf/zjH/Xxxx+7jLHZbGrZsqWGDRumf//3fw9eUgAAAAB1eC30M2bM0IwZMyRJdrtdv/nNbzR2\n",
       "7NiQBAMAAABQP6+F/mK1tbXBzAEAAACgAXwu9Berrq7WqVOnnNfWX6xTp06XHAoAAACAb3wu9N99\n",
       "953mzJmjV199VRUVFW7H2Gw21dTUBCwcAAAAAO98LvS5ublasWKF7rjjDg0aNEht2rQJZi4AAAAA\n",
       "PvC50K9bt04TJkzQsmXLgpkHAAAAgB98/mApm82m/v37BzMLAAAAAD/5XOhvv/12tx8qBQAAACB8\n",
       "PF5yc/z4cZfbM2bM0OjRozVhwgQ9+OCD6tSpk2JiYuosFx8fH/iUAAAAANzyWOjbt2/vdnpJSYmW\n",
       "L1/udh7vcgMAAACElsdC/9RTT/m9MpvNdklhAAAAAPjHY6GfPXt2CGMAAAAAaAifXxQLAAAAIPL4\n",
       "/D70c+bM8XpJjc1mU/PmzZWUlKQbb7xRHTp0CEhAAAAAAJ75Veh9FRMTowkTJmjJkiWy2/knAAAA\n",
       "ABAsPrftI0eOqFevXsrJydHHH3+syspKVVZWavfu3br//vvVp08fffHFF9qzZ4/Gjh2rl19+Wc8+\n",
       "+2wwswMAAACNns2yLMuXgbfffrvi4uL0xhtvuJ1/77336ty5c1q/fr0k6R/+4R/01Vdf6eDBg4FL\n",
       "64eqqirn9w6Hw/n9hcuG3N3tSJlHDvMyRkoOMkZXDjJGVw4TMkZKDjJGVw4y+jfPU4f1xucz9Fu3\n",
       "btXQoUM9zh8yZIjef/995+2srCyVlpb6unoAAAAADeBzoW/atKl27drlcf4f//hHNWvWzHn7/Pnz\n",
       "uuyyyy4tHQAAAACvfC702dnZWrlypaZMmaIDBw7o/PnzOn/+vPbv369HHnlEK1eu1JgxY5zjt27d\n",
       "qu7duwclNAAAAIAf+PwuN88//7zKy8u1ePFiLV68uM61P6NGjdL8+fMlSWfPnlX//v01cODAIEQG\n",
       "AAAAcIHPL4q9YM+ePfr973/vvD6+c+fOuvXWW9WvX7+gBGwoXhQbPTlMyBgpOcgYXTnIGF05TMgY\n",
       "KTnIGF05yBj8F8X6fIb+gn79+kVceQcAAAAaKz71CQAAADCYxzP0KSkpstlsOnDggJo0aeK87enf\n",
       "BpZlyWaz6dChQ0ENDAAAAOBHHgv9kCFDZLPZnNf4DBkypN6VXRgLAAAAIDQ8FvoVK1Z4vQ0AAAAg\n",
       "/LiGHgAAADCYX4X+xIkTeuKJJ5SRkaGuXbs6Pzm2oqJCc+bM0RdffBGUkAAAAADc8/ltKw8fPqyB\n",
       "Awfq5MmT6tmzp/7yl7/ou+++kyS1bdtWq1ev1vHjx7VkyZKghQUAAADgyucz9I899pgsy9LevXv1\n",
       "7rvv1pk/cuRIbdmyxa+Nb9++XSNHjlRSUpLsdruKiorqXebzzz/XkCFD1KJFCyUlJemZZ57xa5sA\n",
       "AABANPG50G/evFmTJk1Sly5d3M5PSUnR0aNH/dr4mTNn1Lt3by1cuFBxcXH1vkvO6dOnNXz4cCUm\n",
       "Jmr37t1auHChFixYoPz8fL+2CwAAAEQLny+5OXv2rK644gqP8ysrK2W3+/ca26ysLGVlZUmScnJy\n",
       "6h2/atUqnT17VkVFRWrWrJm6d++u/fv3Kz8/X9OmTfNr2wAAAEA08LmB9+jRQx988IHH+Rs2bFC/\n",
       "fv0CkcmjXbt2afDgwWrWrJlzWmZmpo4dO6bS0tKgbhsAAACIRD4X+ry8PK1du1Zz587VyZMnJUnn\n",
       "z5/XF198oTFjxuijjz4K+lnysrIyJSQkuEy7cLusrCyo2wYAAAAikc+X3GRnZ+vIkSN68skn9dRT\n",
       "T0mSbr31VklSTEyMFixYoJEjRwYn5d819JNod+/e7dO0SJtHDt/nkcP3eZGSw9s8cvg+L1JyeJtH\n",
       "Dt/nkcP3eZGSw9s8cvg+L1JyeJsXqm117drV43hPfC70kvSv//qvys7O1rp163Tw4EHV1tbq6quv\n",
       "1l133aWUlBS/N+6v9u3b1zkTX15e7pwHAAAANDY2y7KscIeQpFatWmnJkiUaN26cxzEvvfSSHn/8\n",
       "cR0/ftx5Hf1zzz2npUuX1nmHnaqqKuf3DofD+f2Fs/zu7nakzCOHeRkjJQcZoysHGaMrhwkZIyUH\n",
       "GaMrBxn9m+epw3rj39vS/F11dbWOHj2qI0eO1Pnyx5kzZ1RSUqKSkhLV1taqtLRUJSUlznI+ffp0\n",
       "3XLLLc7x2dnZatGihXJycrR3716tW7dOzz//PO9wAwAAgEbL50tuvvvuO82ZM0evvvqqKioq3I6x\n",
       "2WyqqanxeePFxcW66aabnMvOmjVLs2bNUk5OjpYvX66ysjIdOnTIOb5169batGmTcnNzlZaWpiuu\n",
       "uEKPPvqo8vLyfN4mAAAAEE18LvS5ublasWKF7rjjDg0aNEht2rS55I0PHTpUtbW1HucXFhbWmdaz\n",
       "Z09t27btkrcNAAAARAOfC/26des0YcIELVu2LJh5AAAAAPjB52vobTab+vfvH8wsAAAAAPzkc6G/\n",
       "/fbbtXnz5mBmAQAAAOAnj5fcHD9+3OX2jBkzNHr0aE2YMEEPPvigOnXqpJiYmDrLxcfHBz4lAAAA\n",
       "ALc8FnpPH9RUUlKi5cuXu53n77vcAAAAALg0Hgv9U0895ffKLrxJPgAAAIDQ8FjoZ8+eHcIYAAAA\n",
       "ABqiQZ8UCwAAACAyUOgBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegB\n",
       "AAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEA\n",
       "AACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAA\n",
       "AINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAA\n",
       "g1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACD\n",
       "UegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAINR6AEAAACDUegBAAAAg1HoAQAAAIOF\n",
       "vdAXFBQoJSVFcXFxSktL044dOzyOPXz4sOx2e52vjRs3hjAxAAAAEDnCWuhXr16tqVOnaubMmSop\n",
       "KVFGRoaysrJ09OhRr8u99957Kisrc34NGzYsRIkBAACAyBLWQp+fn6/x48frgQceUGpqqhYtWqTE\n",
       "xEQtXbrU63JXXHGF4uPjnV9NmjQJUWIAAAAgsoSt0H///ffas2ePMjMzXaZnZmZq586dXpe98847\n",
       "lZCQoEGDBunNN98MZkwAAAAgooWt0J84cUI1NTVKSEhwmR4fH6+ysjK3y7Rq1UovvPCC1q5dq3ff\n",
       "fVc333yz7r33Xq1atSoUkQEAAICIExvuAP5o27at8vLynLf79euniooKzZ8/X2PHjvW43O7du32a\n",
       "FmnzyOH7PHL4Pi9ScnibRw7f50VKDm/zyOH7PHL4Pi9ScnibRw7f50VKDm/zQrWtrl27ehzvSdjO\n",
       "0Ldr104xMTEqLy93mV5eXq7ExESf15Oenq4vv/wy0PEAAAAAI9gsy7LCtfHrr79effr00csvv+yc\n",
       "ds011+juu+/Ws88+69M68vLy9NZbb+mrr75ymV5VVeX83uFwOL+32WySJHd3O1LmkcO8jJGSg4zR\n",
       "lYOM0ZXDhIyRkoOM0ZWDjP7N89RhvQnrJTfTpk3TfffdpwEDBigjI0MvvfSSysrK9NBDD0mSpk+f\n",
       "ruLiYm3evFmSVFRUpKZNm+raa6+V3W7XW2+9pYKCAs2fPz+cdwMAAAAIm7AW+nvuuUcVFRWaO3eu\n",
       "vv32W/Xq1UvvvPOOOnbsKEkqKyvToUOHnONtNpvmzp2r0tJSxcTEKDU1VYWFhcrOzg7XXQAAAADC\n",
       "KqyX3AQTl9xETw4TMkZKDjJGVw4yRlcOEzJGSg4yRlcOMgb/kpuwfrAUAAAAgEtDoQcAAAAMRqEH\n",
       "AAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcA\n",
       "AAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAA\n",
       "AAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAA\n",
       "DEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAM\n",
       "RqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxG\n",
       "oQcAAAC1B2AsAAAP6ElEQVQMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAxGoQcA\n",
       "AAAMRqEHAAAADEahBwAAAAxGoQcAAAAMRqEHAAAADEahBwAAAAwW9kJfUFCglJQUxcXFKS0tTTt2\n",
       "7PA6/vPPP9eQIUPUokULJSUl6ZlnnglRUgAAACDyhLXQr169WlOnTtXMmTNVUlKijIwMZWVl6ejR\n",
       "o27Hnz59WsOHD1diYqJ2796thQsXasGCBcrPzw9xcgAAACAyhLXQ5+fna/z48XrggQeUmpqqRYsW\n",
       "KTExUUuXLnU7ftWqVTp79qyKiorUvXt3jRo1So8//jiFHgAAAI1W2Ar9999/rz179igzM9NlemZm\n",
       "pnbu3Ol2mV27dmnw4MFq1qyZy/hjx46ptLQ0qHkBAACASBS2Qn/ixAnV1NQoISHBZXp8fLzKysrc\n",
       "LlNWVlZn/IXbnpYBAAAAopnNsiwrHBs+duyYkpKStH37dg0aNMg5/emnn9brr7+u/fv311nm5z//\n",
       "uTp27Kjf/OY3zmlHjhxRcnKydu3apeuuu845vaqqKrh3AAAAAAgih8Ph07iwnaFv166dYmJiVF5e\n",
       "7jK9vLxciYmJbpdp3759nTPxF5Zv3759cIICAAAAESxshb5p06bq37+/Nm7c6DJ906ZNysjIcLvM\n",
       "DTfcoA8//FDnzp1zGd+hQwd17tw5qHkBAACASBS2S24kac2aNbrvvvtUUFCgjIwMvfTSSyosLNTe\n",
       "vXvVsWNHTZ8+XcXFxdq8ebOkH962MjU1VUOHDtXMmTN14MABjR8/XrNnz1ZeXl647gYAAAAQNrHh\n",
       "3Pg999yjiooKzZ07V99++6169eqld955Rx07dpT0wwtdDx065BzfunVrbdq0Sbm5uUpLS9MVV1yh\n",
       "Rx99lDIPAACARiusZ+gBAAAAXJqwfrBUsBQUFCglJUVxcXFKS0vTjh07wh0JYTBv3jylp6fL4XAo\n",
       "Pj5eI0eO1N69e+uMmz17tjp06KAWLVpo2LBh2rdvXxjSItzmzZsnu92uyZMnu0xn/2jcvv32W91/\n",
       "//2Kj49XXFycevTooe3bt7uMYR9pnM6fP68ZM2aoS5cuiouLU5cuXfTkk0+qpqbGZRz7R+Oxfft2\n",
       "jRw5UklJSbLb7SoqKqozpr794dy5c5o8ebKuvPJKXXbZZbr99tv117/+td5tR12hX716taZOnaqZ\n",
       "M2eqpKREGRkZysrK0tGjR8MdDSG2bds2TZo0Sbt27dKWLVsUGxurW265RadOnXKOef7555Wfn68X\n",
       "X3xRxcXFio+P1/Dhw1VdXR3G5Ai1jz76SK+88op69+4tm83mnM7+0bhVVlZq4MCBstlseuedd7R/\n",
       "/369+OKLio+Pd45hH2m8nnvuOb388stavHixDhw4oIULF6qgoEDz5s1zjmH/aFzOnDmj3r17a+HC\n",
       "hYqLi3P5fSL5tj9MnTpV69at0xtvvKEPP/xQp0+f1m233aba2lrvG7eizIABA6yJEye6TOvatas1\n",
       "ffr0MCVCpKiurrZiYmKst99+27Isy6qtrbXat29vPffcc84x3333ndWqVSvr5ZdfDldMhFhlZaV1\n",
       "9dVXWx988IE1dOhQa/LkyZZlsX/AsqZPn24NGjTI43z2kcbttttus3JyclymjRs3zrrtttssy2L/\n",
       "aOwuu+wyq6ioyHnbl/2hsrLSatq0qfX66687xxw9etSy2+3We++953V7UXWG/vvvv9eePXuUmZnp\n",
       "Mj0zM1M7d+4MUypEitOnT6u2tlZt2rSRJH399dcqLy932V+aN2+uG2+8kf2lEZk4caLuvvtuDRky\n",
       "RNZFLyli/8D69es1YMAA3XvvvUpISFDfvn21ZMkS53z2kcYtKytLW7Zs0YEDByRJ+/bt09atWzVi\n",
       "xAhJ7B9w5cv+8PHHH+tvf/uby5ikpCR169at3n0mrO9yE2gnTpxQTU2NEhISXKbHx8fX+UAqND5T\n",
       "pkxR3759dcMNN0iSc59wt78cO3Ys5PkQeq+88ooOHTqk119/XZJc/j3K/oFDhw6poKBA06ZN04wZ\n",
       "M/TJJ584X2ORm5vLPtLI/fM//7O++eYbdevWTbGxsTp//rxmzpyphx56SBLHELjyZX8oKytTTEyM\n",
       "2rZt6zImISGhzgex/lRUFXrAk2nTpmnnzp3asWNHnWva3PFlDMx24MABPfHEE9qxY4diYmIkSZZl\n",
       "uZyl94T9o3Gora3VgAED9Oyzz0qS+vTpoy+//FJLlixRbm6u12XZR6LfokWLVFhYqDfeeEM9evTQ\n",
       "J598oilTpig5OVm/+MUvvC7L/oGLBWJ/iKpLbtq1a6eYmJg6f8WUl5crMTExTKkQbnl5eVq9erW2\n",
       "bNmi5ORk5/T27dtLktv95cI8RK9du3bpxIkT6tGjh5o0aaImTZpo+/btKigoUNOmTdWuXTtJ7B+N\n",
       "2VVXXaXu3bu7TPvZz36mI0eOSOIY0tg9++yzmjFjhu655x716NFD//RP/6Rp06Y5XxTL/oGL+bI/\n",
       "tG/fXjU1NaqoqHAZU1ZWVu8+E1WFvmnTpurfv782btzoMn3Tpk3KyMgIUyqE05QpU5xl/pprrnGZ\n",
       "l5KSovbt27vsL2fPntWOHTvYXxqBO+64Q3/+85/16aef6tNPP1VJSYnS0tI0ZswYlZSUqGvXruwf\n",
       "jdzAgQO1f/9+l2kHDx50nhjgGNK4WZYlu921Rtntdud/+dg/cDFf9of+/furSZMmLmO++eYb7d+/\n",
       "v959Jmb27Nmzg5I8TFq3bq1Zs2bpqquuUlxcnObOnasdO3aosLBQDocj3PEQQrm5uXrttde0du1a\n",
       "JSUlqbq6WtXV1bLZbGratKlsNptqamr061//WqmpqaqpqdG0adNUXl6uZcuWqWnTpuG+Cwii5s2b\n",
       "68orr3R+xcfHa9WqVercubPuv/9+9g+oc+fOmjNnjmJiYpSYmKj3339fM2fO1PTp05Wens4+0sh9\n",
       "+eWXWrFihX72s5+pSZMm2rp1q5544gmNHj1amZmZ7B+N0JkzZ7Rv3z6VlZXp1VdfVa9eveRwOPS3\n",
       "v/1NDoej3v2hefPm+vbbb7VkyRL16dNHVVVVeuihh3T55Zfr+eef935pTuDeoCdyFBQUWMnJyVaz\n",
       "Zs2stLQ068MPPwx3JISBzWaz7Ha7ZbPZXL7mzJnjMm727NlWYmKi1bx5c2vo0KHW3r17w5QY4Xbx\n",
       "21ZewP7RuP33f/+31adPH6t58+ZWamqqtXjx4jpj2Ecap+rqautf/uVfrOTkZCsuLs7q0qWL9cQT\n",
       "T1jnzp1zGcf+0Xhs3brV2TUu7h/jx493jqlvfzh37pw1efJkq23btlaLFi2skSNHWt98802927ZZ\n",
       "lg+vAAMAAAAQkaLqGnoAAACgsaHQAwAAAAaj0AMAAAAGo9ADAAAABqPQAwAAAAaj0AMAAAAGo9AD\n",
       "AAAABqPQAwAaJCcnRykpKeGOAQCNHoUeAKLY66+/roULFwZt/V4/ijwA9u3bp9mzZ6u0tDSo2wEA\n",
       "k1HoASCKvf766/qP//iPoK0/2B82vm/fPj399NMUegDwgkIPAFEu2GfRQyHYfzgAgMko9ABgsOrq\n",
       "aj366KNKSUlR8+bNFR8fr2HDhunDDz/U0KFD9c477+jw4cOy2+3OL0n64IMPZLfbtX37dpf1XRhb\n",
       "VFTkMn39+vXq2bOn4uLi1KtXL/3Xf/2X2zyWZWnx4sXq1auX4uLilJCQoAkTJqiiosJlXHJysrKy\n",
       "srRjxw4NGDBAcXFxuvrqq7Vy5UrnmBUrVuiee+6RJA0bNsyZ/7XXXrvkxw0AoklsuAMAABru4Ycf\n",
       "1tq1azVp0iT16NFDJ0+e1J/+9Cd99tlnmjlzph577DF98803fl92c/FZ/Y0bN2rUqFHq0aOH5s2b\n",
       "p5MnT+qBBx5Qhw4d6pz9f/jhh7V8+XLl5OTokUce0ZEjR7R48WL96U9/UnFxsZo1a+Zc/9dff627\n",
       "775bEyZM0Pjx4/Xqq68qJydH/fv3V/fu3TVkyBA98sgjWrRokZ544gl169ZNkpSRkXGJjxoARBcK\n",
       "PQAY7O2339bEiRP1b//2b27nX3XVVaqsrFR2dnaDt/H444+rffv2+sMf/qBWrVpJ+uGM+c0336zk\n",
       "5GTnuJ07d2rZsmVauXKlxo4d65x+6623avDgwXrttdf04IMPSvrhTP7Bgwe1fft2DRo0SJJ09913\n",
       "q2PHjiosLNSCBQuUkpKiQYMGadGiRRo+fLhuvPHGBt8HAIhmXHIDAAa7/PLL9dFHH+nYsWNBWf+3\n",
       "336rTz/9VPfdd5+zzEs/FPoePXq4jF2zZo0uu+wyZWZm6sSJE86v1NRUxcfHa+vWrS7jU1NTnWVe\n",
       "ktq1a6fU1FR9/fXXQbkvABCtKPQAYLAFCxZo79696tSpk9LT0/Xkk0/q4MGDAVv/hXeX6dq1a515\n",
       "P5128OBBVVdXKyEhQfHx8S5fx48f1//8z/+4jO/UqVOddV5++eU6depUwPIDQGPAJTcAYLC77rpL\n",
       "gwcP1oYNG7Rx40YtWrRI8+fP14oVKzRmzBiPy3l655uampoGZ6mtrVXbtm21evVqt/PbtGnjcjsm\n",
       "JsbtON7RBgD8Q6EHAMMlJCRo4sSJmjhxoqqqqnT99ddr1qxZGjNmjMfifqFcV1ZWukz/6fu9d+7c\n",
       "WZLcnvX/6bSrr75amzdv1nXXXaeWLVs2+P5cLBrechMAgo1LbgDAULW1taqqqnKZ5nA4lJyc7Jze\n",
       "smVLt5ewdO7cWTExMdq2bZvL9IKCApfbiYmJuvbaa7Vy5UqdPn3aOX3Lli3at2+fy9jRo0ertrZW\n",
       "Tz/9dJ3t1dTU1PnjwRcX/jA4efKk38sCQGPBGXoAMNTp06fVoUMH3XXXXerdu7dat26tP/zhD3rv\n",
       "vfc0efJkSVJ6errWrFmjqVOnasCAAbLb7Ro9erQcDofuvvtuLV68WDabTV26dNHbb79d5zp3SZo3\n",
       "b55GjBihQYMGKScnR5WVlXrxxRfVo0cPVVdXO8cNHjxYubm5WrBggT777DNlZmaqWbNm+uqrr/Tm\n",
       "m2/qmWee0bhx4+q9XxdfctOvXz/FxMRo3rx5OnXqlOLi4nT99de7vLsOADR6FgDASN9//7312GOP\n",
       "WX379rUuv/xyq2XLllavXr2s/Px8q6amxrIsy/q///s/6/7777fatm1r2e12y263O5c/ceKEdddd\n",
       "d1ktW7a02rZtaz388MPW3r17LZvNZhUVFblsa926dVb37t2t5s2bWz179rTWr19v5eTkWCkpKXVy\n",
       "LV++3BowYIDVokULq3Xr1lavXr2sX/3qV9bRo0edY5KTk62srKw6yw4dOtQaNmyYy7TCwkKra9eu\n",
       "VmxsrGW32+tkA4DGzmZZvPoIAAAAMBXX0AMAAAAGo9ADAAAABqPQAwAAAAaj0AMAAAAGo9ADAAAA\n",
       "BqPQAwAAAAaj0AMAAAAGo9ADAAAABqPQAwAAAAaj0AMAAAAG+3+osh/QQO4yfwAAAABJRU5ErkJg\n",
       "gg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48244e0b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean of x = 1.826\n",
      "std of x = 0.140\n"
     ]
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "x = [1.8 + .1414*randn() for i in range(100)]\n",
    "plot_height_std(x, lw=2)\n",
    "\n",
    "print('mean of x = {:.3f}'.format(np.mean(x)))\n",
    "print('std of x = {:.3f}'.format(np.std(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see by eye that roughly 68% of the heights lie within $1\\sigma$ of the mean 1.8."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll discuss this in greater depth soon. For now let's compute the standard deviation for \n",
    "\n",
    "$$y = [2.2, 1.5, 2.3, 1.7, 1.3]$$\n",
    "\n",
    "The mean of y is $\\mu=1.8$ m, so \n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_y &=\\sqrt{\\frac{(2.2-1.8)^2 + (1.5-1.8)^2 + (2.3-1.8)^2 + (1.7-1.8)^2 + (1.3-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0.4^2 + (-0.3)^2 + 0.5^2 + (-0.1)^2 + (-0.5)^2}{5}} \\\\\n",
    "&= \\sqrt{\\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5}} \\\\\n",
    "&= \\sqrt{0.152} \\\\\n",
    "\\sigma_y&= 0.39 \\ m\n",
    "\\end{aligned}$$\n",
    "\n",
    "We will verify that with NumPy with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3899 m\n"
     ]
    }
   ],
   "source": [
    "print('{:.4f} m'.format(np.std(y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This corresponds with what we would expect. There is more variation in the heights for y, and the standard deviation is larger.\n",
    "\n",
    "Finally, let's compute the standard deviation for \n",
    "\n",
    "$$ z = [1.8, 1.8, 1.8, 1.8, 1.8]$$\n",
    "\n",
    "There is no variation in the values, so we would expect the standard deviation to be zero. We show this to be true with\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_z &=\\sqrt{\\frac{(1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (183-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0+0+0+0+0}{5}} \\\\\n",
    "\\sigma_Z&= 0.0 \\ m\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance of a Random Variable\n",
    "Finally, the *variance* is defined as the square of the standard deviation. Some texts define this in the opposite way, which gives the definitions\n",
    "\n",
    "* **The variance is the average of the squared differences from the mean.**\n",
    "\n",
    "* **The standard deviation is the square root of the variance.**\n",
    "\n",
    "Both ways of thinking about it are equivalent. We use the notation $\\sigma^2$ for the variance, and the equation for the variance is\n",
    "\n",
    "\n",
    "$$\\sigma^2 = \\frac{1}{N}\\sum_{i=1}^N(x_i - \\mu)^2$$\n",
    "\n",
    "\n",
    "To make sure we understand this let's compute the variance for $x$:\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_x^2 &=\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5} \\\\\n",
    "&= \\frac{0^2 + 0.2^2 + (-0.1)^2 + 0.1^2 + (-0.2)^2}{5} \\\\\n",
    "&= \\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5} \\\\\n",
    "&=0.02\n",
    "\\end{aligned}$$\n",
    "\n",
    "We previously computed $\\sigma_x=0.1414$, and indeed the square of 0.1414 is 0.02. We can verify this computation with the NumPy function `numpy.var`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VAR(x) = 0.02 m\n"
     ]
    }
   ],
   "source": [
    "print('VAR(x) = {:.2f} m'.format(np.var(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many texts alternatively use *VAR(x)* to denote the variance of x, and I opted to use that here just to expose you to that convention."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why the Square of the Differences\n",
    "\n",
    "As an aside, why are we taking the *square* of the difference? I could go into a lot of math, but let's just look at this in a simple way. Here is a chart of the values of x plotted against the mean for $x=[3,-3,3,-3]$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAhkAAAELCAYAAAB07JSGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAADZJJREFUeJzt3VuIVXX7wPFnT6aNJTuZMgrH6qVJIsrSUdALKdJoSiSI\n",
       "oqAjUWQHTC+iC6OiqOgEFWp0U5EEaYGUyVSQKWGEUwQdKaKDYSM11XaULHPv96rhNW365//3NHvb\n",
       "5wPSPs3vWbBazHfWXnum0mg0GgEAUFjbSG8AAHBgEhkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCk\n",
       "KBoZS5cujSlTpkS1Wo1qtRqzZs2KtWvXlhwBALSISslfxvXiiy/GmDFjoqurK+r1ejz11FNx//33\n",
       "x6ZNm2LKlCmlxgAALaBoZOxLR0dH3HfffXHNNddkjgEAmsyorIV3794dq1atip07d8bs2bOzxgAA\n",
       "Tap4ZLz//vsxc+bM+OWXX6K9vT1WrlwZkydPLj0GAGhyxd8u2bVrV2zevDlqtVqsWrUqHnvssVi3\n",
       "bl10d3dHREStVis5DgBoAtVqda/H0q/JmDt3bkycODGefPLJiBAZAHAg2ldkpP+ejN27d0e9Xs8e\n",
       "AwA0maLXZNx6660xb968mDhxYgwODsazzz4b69evj97e3n2+fl/Vwz+nUqnscT/5pBb/R319fRER\n",
       "Q28xMnIcI83H8dFc/urdiaKRsXXr1rj00kujv78/qtVqTJkyJXp7e2Pu3LklxwAALaBoZPx+3QUA\n",
       "gL9dAgCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqR\n",
       "AQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqRAQCk\n",
       "EBkAQAqRAQCkEBkAQAqRAQCkKBoZ9957b0yfPj2q1WpMmDAh5s+fHx9++GHJEQBAiygaGevXr48b\n",
       "b7wx3nrrrXj99ddj1KhRMWfOnPjxxx9LjgEAWsCokov19vbucf+ZZ56JarUaGzdujPPOO6/kKACg\n",
       "yaVek7Ft27ao1+sxfvz4zDEAQBNKjYyFCxfG6aefHjNnzswcAwA0oaJvl/yvxYsXx8aNG+PNN9+M\n",
       "SqWyz9f09fVljWc/2B/Nxf5oPvZJ87AvmkNXV9ewz6dExqJFi2LlypWxbt26OO644zJGAABNrtJo\n",
       "NBolF1y4cGGsWrUq1q1bF5MnT97r+VqtNnS7Wq2WHM3f9MczTIX/V2A//f4TWnd39whvCY6R5uP4\n",
       "aC5/9T296JmMG264IVasWBGrV6+OarUa/f39ERExbty4OPTQQ0uOAgCaXNELP5cvXx7bt2+Ps846\n",
       "K4455pihfw899FDJMQBACyh6JqNer5dcDgBoYf52CQCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClE\n",
       "BgCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQ\n",
       "QmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQQmQAAClEBgCQomhkbNiwIebPnx8T\n",
       "J06Mtra2ePrpp0suDwC0kKKRsWPHjjj11FPjkUceifb29qhUKiWXBwBayKiSi/X09ERPT09ERFx5\n",
       "5ZUllwYAWoxrMgCAFEXPZPxdfX19IzmeP7A/mov90Xzsk+ZhXzSHrq6uYZ93JgMASDGiZzK6u7tH\n",
       "cjx/YH80h99/QrM/mo99MvIcH82lVqsN+7wzGQBAiqJnMnbs2BGfffZZRETU6/X46quv4r333ouO\n",
       "jo7o7OwsOQoAaHJFz2Rs2rQppk6dGlOnTo2dO3fG7bffHlOnTo3bb7+95BgAoAUUPZNxxhlnRL1e\n",
       "L7kkANCiXJMBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQ\n",
       "GQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBACpEBAKQQGQBA\n",
       "CpEBAKQQGQBACpEBAKQQGQBACpEBAKQoHhnLli2L448/Ptrb26O7uzvefPPN0iMAgBZQNDKee+65\n",
       "uPnmm2PJkiXx3nvvxaxZs6Knpyc2b95ccgwA0AKKRsbDDz8cV111VVx99dUxefLkePTRR+Poo4+O\n",
       "5cuXlxwDALSAUaUW+vXXX+Pdd9+NW265ZY/Hzz777Ni4ceM+v6ZSKTWd/dPY45790Sy6R3oDGOIY\n",
       "aT6Oj2by00/DP1/sTMb3338fu3fvjqOOOmqPxydMmBD9/f2lxgAALcKnSwCAFMUi44gjjoiDDjoo\n",
       "tm7dusfjW7dujaOPPrrUGACgRRS7JmP06NExbdq0ePXVV+OCCy4Yevy1116LCy+8cJ9f02js82H+\n",
       "QX19fRER0d3tfc5mUPnDm/4NB8mIc4w0D8dH86nVhn++WGRERCxevDguu+yymDFjRsyaNSsef/zx\n",
       "6O/vj+uuu67kGACgBRSNjIsuuigGBgbi7rvvjm+//TZOOeWUWLt2bXR2dpYcAwC0gKKRERGxYMGC\n",
       "WLBgQellAYAW49MlAEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZ\n",
       "AEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZAEAKkQEApBAZAEAK\n",
       "kQEApBAZAEAKkQEApBAZAEAKkQEApBAZAECKYpHxxBNPxJlnnhmHH354tLW1xddff11qaQCgBRWL\n",
       "jJ9//jnOOeecuPPOO0stCQC0sFGlFlq4cGFERPT19ZVaEgBoYa7JAABSFDuTsT+c9Wge9kVzsl+a\n",
       "h33RfOyTkdfV1TXs88OeyViyZEm0tbUN+2/Dhg1FNxgAODBUGo1G48+eHBgYiIGBgWEX6OzsjPb2\n",
       "9qH7fX19MWPGjPjyyy9j0qRJe72+VqsN3a5Wq/uzzRT0+08C3d3dI7wlRERUKpU97g9zePIPcYw0\n",
       "D8dH8/mr7+nDvl3S0dERHR0d5bcKADjgFbsmo7+/P/r7++PTTz+NiIgPP/wwfvjhhzj22GNj/Pjx\n",
       "pcYAAC2i2KdLHn/88Zg6dWpceumlUalU4rzzzotp06bFSy+9VGoEANBCikXGHXfcEfV6Per1euze\n",
       "vXvov5dffnmpEQBAC/F7MgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEghMgCAFCID\n",
       "AEghMgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEgh\n",
       "MgCAFCIDAEghMgCAFCIDAEghMgCAFCIDAEhRJDJ+/PHHuOmmm+Kkk06KsWPHxqRJk+L666+PH374\n",
       "ocTyAEALKhIZW7ZsiS1btsQDDzwQH3zwQaxYsSI2bNgQl1xySYnlAYAWNKrEIieffHK88MILQ/f/\n",
       "85//xAMPPBDz5s2L7du3x2GHHVZiDADQQtKuyajVajFmzJgYO3Zs1ggAoImlRMZPP/0Ut912W1x7\n",
       "7bXR1ubaUgD4N6o0Go3Gnz25ZMmSuOeee4Zd4I033ojZs2cP3d++fXv09PTEwQcfHL29vTF69Og9\n",
       "Xl+r1YZuf/bZZ/u73XBAmj59+h73N23aNEJbAs3H8dF8urq6hm5Xq9W9nh/2moxFixbF5ZdfPuyA\n",
       "zs7Oodvbt2+Pc889N9ra2mLNmjV7BQYA8O8x7JmMv2NwcDB6enqiUqlEb29vHHrooft83f+eydhX\n",
       "9fDP6uvri4iI7u7uEd4SIiIqlcoe9wsdnvw/OEaah+Oj+fzV9/Qiny4ZHByMs88+OwYHB2P16tUx\n",
       "ODgYg4ODERHR0dERBx98cIkxAEALKRIZ77zzTrz99ttRqVTixBNPHHq8UqnEunXr9rhmAwD4dygS\n",
       "GWeccUbU6/USSwEABwifLwUAUogMACCFyAAAUogMACCFyAAAUogMACCFyAAAUogMACCFyAAAUogM\n",
       "ACCFyAAAUogMACCFyAAAUogMACCFyAAAUogMACCFyAAAUogMACCFyAAAUogMACCFyAAAUogMACCF\n",
       "yAAAUogMACCFyAAAUogMACCFyAAAUogMACCFyAAAUhSLjGuuuSZOOOGEGDt2bEyYMCHOP//8+Pjj\n",
       "j0stDwC0mGKRMX369Hj66afjk08+iVdeeSUajUbMmTMnfvvtt1IjAIAWMqrUQtdee+3Q7UmTJsVd\n",
       "d90Vp512WnzxxRfR1dVVagwA0CJSrsnYsWNHPPnkk9HV1RXHH398xggAoMkVjYxly5bFuHHjYty4\n",
       "cbFmzZp4+eWXY9SoYidLAIAWUmk0Go0/e3LJkiVxzz33DLvAG2+8EbNnz46IiG3btsV3330XW7Zs\n",
       "iQcffDA++uijePfdd2PcuHFDr6/VaoU2HQBoFtVqda/Hho2MgYGBGBgYGHbRzs7OaG9v3+vxXbt2\n",
       "xfjx42Pp0qVxxRVXDD0uMgDgwLOvyBj2vYyOjo7o6OjYr2H1ej0ajUbU6/X9+noAoLUVuWDi888/\n",
       "j+effz7mzp0bRxxxRHzzzTdx3333xSGHHBLz5s3b47X7Kh0A4MBT5MLPMWPGxPr166Onpye6urri\n",
       "4osvjmq1Gm+99VYceeSRJUYAAC1m2GsyAAD2l79dAgCkEBkAQAqRAQCkEBkAQAqRAQCkEBkAQAqR\n",
       "AQCkEBkAQAqRAQCk+C9H4O5405jIdgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f480904db38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with book_format.figsize(8,4):\n",
    "    x = [3,-3,3,-3]\n",
    "    m = np.average(x)\n",
    "    for i in range(len(x)):\n",
    "        plt.plot([i,i], [m,x[i]], color='k')\n",
    "    plt.axhline(m)\n",
    "    plt.xlim(-1, len(x))\n",
    "    plt.tick_params(axis='x', labelbottom='off')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we didn't take the square of the differences the signs would cancel everything out:\n",
    "\n",
    "$$\\frac{(3-0) + (-3-0) + (3-0) + (-3-0)}{4} = 0$$\n",
    "\n",
    "This is clearly incorrect, as there is more than 0 variance in the data. \n",
    "\n",
    "Maybe we can use the absolute value? We can see by inspection that the result is $12/4=3$ which is certainly correct - each value varies by 3 from the mean. But what if we change $x=[6, -2, -3, 1]$? In this case we get $12/4=3$. $x$ is clearly more spread out than in the last example, but we get the same variance, so this cannot be correct. If we use the correct formula we get a variance of 3.5, which correctly reflects the larger variatin in $x$.\n",
    "\n",
    "This is clearly not a proof of correctness; indeed, Gauss recognized that is is somewhat arbitrary. If the variable is distributed normally we can prove that the variance is computed by this function. If there are outliers, meaning values that are not normally distributed, than squaring the difference gives disproportinate weight to that term. For example, let's see what happens if we have $x = [1,-1,1,-2,3,2,100]$. I'll use NumPy's `var()` method to compute the variance for me."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance of x = 1210.69\n"
     ]
    }
   ],
   "source": [
    "x=[1,-1,1,-2,3,2,100]\n",
    "print('Variance of x = {:.2f}'.format(np.var(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is this *correct*? You tell me. Without the outlier of 100 we get $\\sigma^2=2.89$, which accurately reflects how $x$ absent the outlier is varying. The one outlier swamps the computation. I will not continue down this path; if you are interested you might want to look at the work that James Berger has done on this problem. For Kalman filters, which assume Gaussian distributions, we can prove that squaring the terms produces optimal results. More about that soon."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to learn about Gaussians. Let's remind ourselves of the motivation for this chapter.\n",
    "\n",
    ">We desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is very computationally efficient to calculate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we go into the math, lets just look at a graph of a Gaussian distribution to get a sense of what we are talking about."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAtcAAAGHCAYAAAB76H43AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdUVOe+PvBnZuhtBJSiKFgQe0FQsYEC9t6jxph6TDUa\n",
       "b3K8N7+TZk4STTwnyVUTU5REY0GNJlZQEBsqqNhBFAEVBhWRXmfm94f3jNnSBAfemeH5rMVazrP3\n",
       "MA87RL4O+91bptVqtSAiIiIioqcmF12AiIiIiMhUcLgmIiIiItITDtdERERERHrC4ZqIiIiISE84\n",
       "XBMRERER6QmHayIiIiIiPeFwTURERESkJzUO1ytXrkTPnj2hVCqhVCoxYMAA7Nmzp8ZPeOHCBQQG\n",
       "BsLGxgYeHh745JNP9FqYiIiIiMhQmdW0sXXr1li2bBm8vb2h0Wiwbt06TJw4EXFxcejZs2el/fPy\n",
       "8hAaGoqgoCDEx8fjypUreP7552Fra4tFixY12BdBRERERGQIZHW9Q6OzszM+//xzvPzyy5W2rV69\n",
       "GkuWLEFWVhYsLS0BAJ9++ilWr16NW7du6acxEREREZGBeuJzrtVqNTZt2oSSkhIMGTKkyn1iY2Mx\n",
       "ePBg3WANAMOHD0dGRgbS0tKevi0RERERkQGr8bQQ4OE51AEBASgtLYW1tTW2bNkCHx+fKvdVqVRo\n",
       "06aNJHN1ddVt8/T01ENlIiIiIiLDVOtw3alTJ5w/fx65ubkIDw/HzJkzER0dDT8/v0r7ymSyOr14\n",
       "bm5unfYnIiIiIjIkSqVS8rjW4drc3Bzt2rUDAPTu3RtxcXFYuXIl1q5dW2lfNzc3qFQqSZaVlaXb\n",
       "RkRERERkyup8nWu1Wg2NRlPltoCAABw5cgSlpaW6LDIyEq1ateIpIURERERk8mp85/rvf/87xo4d\n",
       "Cw8PD+Tn5+O3335DTEwM9u3bBwBYsmQJ4uLicODAAQDArFmz8NFHH2HevHl4//33kZSUhC+++AIf\n",
       "fvhhrUUef0u9ocTHxwNAlae1UM147OqHx63+eOzqj8eu/njs6o/Hrv547OpH1HGr6dTmGofrrKws\n",
       "zJkzByqVCkqlEj179sS+ffsQGhoK4OEixZSUFN3+Dg4OiIyMxOuvvw4/Pz84OTlh8eLFWLhwoZ6+\n",
       "FCIiIiIiw1XjcF3VedW1be/WrRtiYmKerhURERERkRGq8znXRERERERUNQ7XRERERER6wuGaiIiI\n",
       "iEhPOFwTEREREekJh2siIiIiIj3hcE1EREREpCccromIiIiI9ITDNRERERGRnnC4JiIiIiLSEw7X\n",
       "RERERER6wuGaiIiIiEhPOFwTEREREemJmegCRET09IpLi5Bf9ADFpQUoKi3E7ZxrAACbVDmsLW1g\n",
       "Y2kHW2sH2FrZQyaTCW5LRGS6OFwTERmRCnU5bt9NRXpWMtLvXIfq/k3cy1WhsDivyv0PXpY+trSw\n",
       "RnOlG1wdW6G1Swe0cW2PNi4dYGlh3QjtiYhMH4drIiIDdz/vDi6nnsGVtDO4evM8SstL6v25SsuK\n",
       "cfvuDdy+ewNnrh4FACjkZmjr7oNObXqhW7u+aNncU1/ViYiaHA7XREQGqKikAGeTj+HUlWjcyExs\n",
       "0NdSaypw7fYlXLt9CbtiN8DduQ36dByMPj5D4Kx0bdDXJiIyNRyuiYgMSHrWNUSf/QMJ145Dra54\n",
       "4ucp5GZQ2jrCxtoeNha2KCgoAgDYO9ihuLQIRSX5yCvMQVlFaa2fKzM7HbtiN2BX7AZ08fRFYO9x\n",
       "8GnTE3IZ18ATEdWGwzURkWBarRYXb8Qh6sxOXL99qdb97W2aoX3LLmjt2gGtW7SDi2NLNLNzhlyu\n",
       "0O0THx8PAPDz85O8Tl5RDu49yMStuzeQnnUNqZlJuJubWe1rXU47g8tpZ+Di2ArDfCegX+dhUCj4\n",
       "o4OIqDr8G5KISBCtVouk9HPYdXw90u9cq3Hftu6d0K2tPzp79UbL5l71ehdZJpNBaesEpa0T2rfq\n",
       "qsuzc7OQmJ6A89dPIik9ARqtptJz7+TcxqaDqxAZvw0j+86AX6dAKP4yzBMR0UMcromIBEjPuoY/\n",
       "jobh6q0L1e7TQukOv85B8O8UiOZKtwbr4qx0xcDuIzCw+wjkF+UiIfkYTl6JRnpWcqV9s3OzsCHy\n",
       "G0TGb8PkIS+gi1efButFRGSMOFwTETWiopIC7Dq+Hscu7IcW2ir36ejRHUN9J6Czl2+jn+dsb6PE\n",
       "4J6jMbjnaNzITMLhhF04e+04NBq1ZL87Obfx3c5P0K1dX0we8kKDDv9ERMaEwzURUSPQarWISzyE\n",
       "nUfWIb84t8p9erbvjxH9psOjRbtGble1tu4+aOvug/H5zyEibitiL0VWGrIvppxCYtpZDPefilC/\n",
       "KTwfm4iaPP4tSETUwPIKc7DxwEpcSo2vcrtP654YO2AOPN28G7nZk3G0b44Zw+YjpM8k7Du5Gaeu\n",
       "REveda9Ql2PPiY04n3ISc0IX8DrZRNSkcbgmImpAZ5OPY0vUahSW5Ffa1kLpjilBL6OLl6+AZnXn\n",
       "rHTF7OFvYUivMQg/tAapmUmS7bfupGD5xncwqv9MhPSZJLl6CRFRU8HhmoioAZSWlyA8+nucuhJd\n",
       "aZuZwhyh/lMR0mcSzM0sBLR7Oq1d2uPtaZ8hPjGm0mkuak0Fdh1fj6T0c5g7ciGUtk4CmxIRNT4O\n",
       "10REepZ1/xZ+3rMMmdnplba1c++M2cPfQotm7gKa6Y9cJkffzkPRxasPth5ao7uV+n8k37qAZRsW\n",
       "Yu7IRfBp01NQSyKixsfbbRER6dGZq0fx5abFlQZrhdwM4wbOxVtTlxr9YP1XdtYOmDdqMZ4f/V+w\n",
       "tXaQbMsvzsWq3z/E3pObq7x2NhGRKeI710REeqDRarDr2HocOL290jZXJw/MG7kYrVp4NX6xRtLb\n",
       "eyDat+yCX/atkFy7Wwst9p7YiIx7qZgzfAEsza0EtiQianh855qI6CmVlhXjp12fVzlY+/kEYvHM\n",
       "L016sP4PB1tHvDbpQ4zqNxMyyCTbzl2Lxb/Dl+B+3l1B7YiIGgeHayKip5CTfxf/Dl+CCymnJLlC\n",
       "YYYZw17FsyPeblLv1srlCozqPxOvT/6o0mkit+/ewFebFiNNVfnOj0REpoLDNRFRPWVmp2PF5vdw\n",
       "+16qJHewccTbU/+Jgd1HQCaTVf1kE9exdQ8snrkcLZ2l17zOL87Ft9vex+XUM4KaERE1LA7XRET1\n",
       "cCMzEV+H/zdyC+9L8lYt2uKdmcvg6dZRUDPD4ezgioXTP0f3dn0leVlFKdb8+SlOXo4S1IyIqOFw\n",
       "uCYiqqPLqWewcvsHKCotkOQ92vfD21P/CUf7FoKaGR5LC2u8OPbvCOkzWZJrNGpsiPwGB0//LqgZ\n",
       "EVHD4NVCiIjq4HTSYfwa8TU0GrUkH9R9JKYGvcy7ElZBLpNj/KC5aGbvjG2HfpTcOn3n0TCUV5Rh\n",
       "ZL8ZAhsSEekPh2sioicUl3gI6/d/LRkOAWBkvxkPr5DRRM+vflJDeo6BvY0jftm/Amp1hS7fc2Ij\n",
       "KtQVGBMwi8eQiIweh2sioidQ1WAtgwxTgl7CkJ5jBDYzLr29B8DO2h5r/vgUpeUlujwiLhwV6jJM\n",
       "GDSPAzYRGTWec01EVIuqBmu5TI65IxdysK4Hb4/ueHXih7CysJHkUWd2Yvvhn6DVaqt5JhGR4eNw\n",
       "TURUg+oG6+dGLUYfnyECmxm3di074fVJH8Ha0laSxyTswq7j6wW1IiJ6ehyuiYiqce5aLNZHfFPl\n",
       "YN3be4DAZqbB080bb0z+BLZW9pI8Mn4bIuK2CmpFRPR0OFwTEVUhKf0c1u37ClqtRpdxsNa/1i7t\n",
       "8OaUT2Dz2IC96/h6xCTsEtSKiKj+OFwTET0mVXUVP+z6THJFi4eD9TscrBtAy+ZeeG3iB7C0sJbk\n",
       "22J+xIlLBwW1IiKqHw7XRER/kZmdju92foKyv1zJAgCeCXkDvb0HCmpl+tq4dsD88e/D3MxCkm88\n",
       "uBIXUk4JakVEVHccromI/s/9vLtY9fuHKCrJl+STBr+Afl2GCWrVdLRv1RUvjV0CheLRVWK1Wg3W\n",
       "7f0SaaqrApsRET05DtdERACKSwvx/R+fILfwviQf7j8NQ33HC2rV9HT27I15IxdDJnv046m8ogzf\n",
       "/bEUdx9kCmxGRPRkah2uP/vsM/j7+0OpVMLFxQXjx4/HpUuXanxOamoq5HJ5pY+IiAi9FSci0he1\n",
       "ugI/716GzOx0ST6o+0iMCZglqFXT1bNDf0wLekWSFRbnYfWOj5BflCuoFRHRk6l1uI6JicEbb7yB\n",
       "2NhYREVFwczMDCEhIcjJyan1k+/fvx8qlUr3MXToUL2UJiLSF61Wi81Rq5F085wk79m+P6YGvcy7\n",
       "BQoyqMdIDPefKsnu5aqw5o+lKCsvFdSKiKh2td7+fN++fZLHv/76K5RKJY4fP44xY2q+M5mTkxNc\n",
       "XFyeriERUQOKiNuKE5elV6TwcvPBsyMXQi5XCGpFADAmYDYeFGTj1JVoXZaWlYwNkd9g3qjF/IcP\n",
       "ERmkOp9znZeXB41GA0dHx1r3nTx5MlxdXTFo0CBs27atXgWJiBrKmatHsTt2gyRzdnDFy+OWwMLM\n",
       "UlAr+g+ZTIaZwa/Bp3VPSX42+Rj2n9oiqBURUc3qPFwvWLAAvXv3RkBAQLX72Nvb46uvvkJ4eDj2\n",
       "7t2L4OBgzJgxAxs2bKj2OUREjenmnevYEPmNJLOxtMP8Cf8P9jbNBLWix5kpzPHCmPfg7txGku85\n",
       "sREJyccFtSIiqp5Mq9Vqa9/toUWLFmHLli04evQovLy86vRCb7zxBo4cOYJz5x6d15ib+2hhSnJy\n",
       "cp0+HxFRfRWXFWL3uZ9QVJany+QyOUK6zoab0lNgM6pOfkkO9pz7GaUVxbrMTG6OEd2fg7Odm8Bm\n",
       "RNQUeXt76/6sVCol2574neuFCxdi8+bNiIqKqvNgDQD+/v4coIlIOLVGjZikrZLBGgD6tR/NwdqA\n",
       "2Vs5IqjTVMkl+io05Yi+shnFZQUCmxERSdW6oBF4eCpIeHg4oqOj0bFjx3q9UEJCAlq2bFntdj8/\n",
       "v3p93rqKj49v1NczJTx29cPjVn8Ncew2R32HO3k3JdmQnmMwNeglvb2GITDN7zs/OLo6YNPBlbqk\n",
       "qCwfcTf34s0pS2FuZq6XVzHNY9c4eOzqj8eufkQdt7+effG4Wofr119/HevXr8eOHTugVCqhUqkA\n",
       "PDyv2tbWFgCwZMkSxMXF4cCBAwCAsLAwWFhYoFevXpDL5fjzzz+xatUqLFu2TB9fDxFRvRw9vw/H\n",
       "LkivgOTt0R2TBj8vqBHV1YBuocjMTkNMwi5dlqpKwu+Hf8L0YfMFNiMieqjW4Xr16tWQyWQIDg6W\n",
       "5B9++CH+8Y9/AABUKhVSUlJ022QyGZYuXYq0tDQoFAr4+Phg7dq1mDWLN2MgIjFSMhKxNeYHSebk\n",
       "4ILnR/+X5HbbZPgmDn4eWTm3kZh2VpcdvbAPXu4+6NuZ91MgIrFq/Ymi0Whq/SRr166VPJ47dy7m\n",
       "zp1b/1ZERHqUX5SLtXuXQ6NR6zILcyu8PPa/YWftILAZ1YdCrsC8ke9g+aZ3kJ2bpcs3H1yNVs29\n",
       "0KpFW4HtiKipq/Ol+IiIjIlGo8Yv+1YgtyBbks8JfQutWniJKUVPzcbKDi+OeQ/mCgtdVq4uw4+7\n",
       "P0dRCRc4EpE4HK6JyKTtO7ml0q3Ng/tMRC/vAYIakb54tGhX6Tzr7Nws/Brxb2i0tf/WlYioIXC4\n",
       "JiKTdTn1TKU7+bVv2QVjA+YIakT61q/LMAzsNkKSXboRj8g43hWYiMTgcE1EJul+3l38uv9f0OLR\n",
       "fbLsrZWYN2oxFzCamMmBL6GNq7ck23NiI5JvXRTUiIiaMg7XRGRyKtTlWLt3OQpL8nWZTCbHc6MW\n",
       "Q2nnJLAZNQRzM3O8MPpd2FrZ6zKtVoNf9q1AQXFeDc8kItI/DtdEZHJ2x/6GNNVVSTYmYBY6tu4u\n",
       "qBE1NCeHFpg7cpEkyy28jw0R30Cr1VbzLCIi/eNwTUQmJTEtAQdP/y7Junr5IcRvsqBG1Fg6e/ZG\n",
       "SB/pf+dLqfE4dPZPQY2IqCnicE1EJiO/KBfrI76WZEo7Z8wZ/hbkMv511xSMCZgFLzcfSfbHsV+Q\n",
       "nnVNUCMiamr404aITIJWq8WGyG+QV5Sjy2SQYe6It2HLG8U0GQqFGZ4btQjWlra6TK2pwNq9y1Fc\n",
       "WiiwGRE1FRyuicgkxCTswuXU05JseN+p8PbgedZNjbODK2aFvCHJsnOzsCXqO0GNiKgp4XBNREbv\n",
       "1t0U7DwWJsm83H0wst9MQY1ItJ4dAjCoxyhJdvrqEcQnxghqRERNBYdrIjJqpeUlWLf3K6jVFbrM\n",
       "2sIGz41cBIVcIbAZiTZp8PNo2dxLkoVHf4/7eXfEFCKiJoHDNREZtd8P/4w7Obcl2Yzg1+Ds4Cqo\n",
       "ERkKczMLPDdyEcwU5rqsuKwI6yO+hkajFtiMiEwZh2siMlqXbsTj+MUISda/awh8Ow4S1IgMjbtz\n",
       "G0wY9Jwku3b7EqLP/iGoERGZOg7XRGSUCovzsPHASknm0qwlpgS+JKgRGarBPUfDp01PSbbr+Abc\n",
       "upsiqBERmTIO10RkdLRaLTZHfye57J5cJsezI96GpbmVwGZkiOQyOeaELoDNX26PrtZU4Jd9/0JZ\n",
       "RanAZkRkijhcE5HROZ10GAnJxyXZcP9p8HTrKKgRGTqlnRNmDHtVkqnu38Sfx34V1IiITBWHayIy\n",
       "Kjn59xB+aI0k83BphxF9pwlqRMait/cA9Os8TJLFJOxCUvo5QY2IyBRxuCYio6HVavHbgW8ld9oz\n",
       "U5jj2eELoVCYCWxGxmJy4EuVriTz24H/RXFpkaBGRGRqOFwTkdE4en5vpXcZxw14Fu7OrQU1ImNj\n",
       "bWmDZ0e8DRlkuiwn/y52Hl0rsBURmRIO10RkFO7k3MaOo+skWQePbgjsPVZMITJa7Vp2xlDf8ZLs\n",
       "+MVIXEk7K6gREZkSDtdEZPA0GjXWR3yD8ooyXWZpYY05oW9BLuNfY1R3owNmwcWxlSTbeOB/Jacc\n",
       "ERHVB38qEZHBi0nYjVRVkiSbGvgSnBxcBDUiY2dhZonZoW9B9pd/nD0oyMbvR3h6CBE9HQ7XRGTQ\n",
       "8orvY1fseknWrV1f9H3sqg9EddXW3QfDfCdIshOXDuB2zjVBjYjIFHC4JiKDpdVqEXttl+R0EGtL\n",
       "W8wYNh8ymayGZxI9mdH9n4Grk4ckO35tN8oqSgQ1IiJjx+GaiAzWVdUZZOWlS7LJQ16E0tZJUCMy\n",
       "NeZmFpjz2OkhxWX5iLsRIbAVERkzDtdEZJDu593B6dSDkqyzpy/6dh4qqBGZKk+3jgjpM0mSXb9z\n",
       "HpduxAtqRETGjMM1ERkcrVaLTQdXoUIjvTrIjGGv8nQQahAj+82Eu3MbSbY5ajVvLkNEdcbhmogM\n",
       "zsnLUUhMT5BkEwfNg5NDC0GNyNSZm5lj9mOXdnxQkI1dx9fX8Cwioso4XBORQcktuI/fD/8kybw9\n",
       "uiOgW6igRtRUtHHtgKGPXT3k6Pm9SMm4IqgRERkjDtdEZDC0Wu3DX8WXPfpVvJncHDODX+PNYqhR\n",
       "jOo3E/ZWjrrHWmix8cBKlFeUC2xFRMaEP62IyGCcuXoEF2/ESbLenkPRopm7oEbU1FiYWyKg/RhJ\n",
       "lpVzCxFx4YIaEZGx4XBNRAahsDgPW2N+lGQt7D3g4+4nqBE1VW7NvNDBtZcki4zfhox7qWIKEZFR\n",
       "4XBNRAZhx5F1KCzO0z02U5hjQIexPB2EhOjjFQwHm0enh2g0amw8sBIajVpgKyIyBvypRUTCXb15\n",
       "ASevREmyEX2nQ2nTXFAjauoszawxbegrkiwtKxkx53YLakRExoLDNREJVV5Rhs1RqyWZu3MbBPeZ\n",
       "KKgR0UM9OwSgR/v+kmz38Q3Izs0S1IiIjAGHayISKiIuHHcfZEiyGcNeg5nCXFAjokemBb0Cawsb\n",
       "3eOyilJsjloNrVYrsBURGTIO10QkTGZ2Og7E/y7JBnYfiXYtOwlqRCSltHPChMHPS7LE9ATEJR4S\n",
       "U4iIDB6HayISQqPVYNPBVVBrKnSZg60jxg2cI7AVUWUBXUPQwaObJNtxZB0KS/IFNSIiQ8bhmoiE\n",
       "iL0YiRuZiZJsSuDLsLG0E9SIqGoymQwzHztVqaA4F38c/UVgKyIyVByuiajR5Rbexx9HwyRZt7b+\n",
       "6NUhQFAjopq5OLbEcP+pkiz2UiSu374sqBERGSoO10TU6LbF/Ci5xbmFuRWmBr0CmUwmsBVRzYL7\n",
       "TIaLYytJtiX6O1SoeWt0InqEwzURNaqLKXFISD4uycYEzIKTQwtBjYiejLmZOWYMmy/JMrPTEX32\n",
       "T0GNiMgQcbgmokZTWlaM8ENrJFkblw4I7DlGUCOiuvH26I6+nYdKsn0nN/Ha10SkU+Nw/dlnn8Hf\n",
       "3x9KpRIuLi4YP348Ll26VOsnvXDhAgIDA2FjYwMPDw988skneitMRMZr36nNyMm/q3ssl8kxI/g1\n",
       "yOUKga2I6mbi4OdhY2Wve1xeUYbwQ2t47WsiAlDLcB0TE4M33ngDsbGxiIqKgpmZGUJCQpCTk1Pt\n",
       "c/Ly8hAaGgp3d3fEx8fj66+/xvLly7FixQq9lyci46G6f7PSr8+Deo9Ha5d2ghoR1Y+dtQMmDHpO\n",
       "kl1OPY2Ea7GCGhGRITGraeO+ffskj3/99VcolUocP34cY8ZU/WvcDRs2oKSkBGFhYbC0tESXLl2Q\n",
       "mJiIFStWYNGiRfprTkRGQ6vVYmv0Gmg0al3WzM4Zo/rNENiKqP76dwnGqctRuJ7x6Goh22N+RKc2\n",
       "vWBtaVPDM4nI1NXpnOu8vDxoNBo4OjpWu09sbCwGDx4MS0tLXTZ8+HBkZGQgLS2t/k2JyGidTT6G\n",
       "q7cuSLJJQ16EpYW1oEZET0cmk2H6sFehkD96jyq38D52x24Q2IqIDEGdhusFCxagd+/eCAio/lq0\n",
       "KpUKrq6ukuw/j1UqVT0qEpExKykrxu+Hf5ZkPm168prWZPTcnVsjuM9ESXbk3B6kZ10T1IiIDIFM\n",
       "+4QrMBYtWoQtW7bg6NGj8PLyqna/ESNGoHXr1vjxxx91WXp6Ory8vBAbG4t+/frp8tzcXN2fk5OT\n",
       "61GfiAxd/I0DuJxxQvdYLpNjXK+/QWnjLLAVkX5UqMvxR8L3KCh5oMucbN0wuucLkMt4QS4iU+Xt\n",
       "7a37s1KplGx7ov/zFy5ciM2bNyMqKqrGwRoA3NzcKr1DnZWVpdtGRE3Hg6K7uJJ5SpJ1adWfgzWZ\n",
       "DDOFOfq1GyXJ7heqcFV1RlAjIhKtxgWNwMNTQcLDwxEdHY2OHTvW+gkDAgLw3nvvobS0VHfedWRk\n",
       "JFq1agVPT89qn+fn51eH2vUXHx/fqK9nSnjs6qepHjetVov/3f4PaLUaXeZo1xzPjX8LluZWT/Q5\n",
       "muqx0wceu/qr67Hzgx9yKm7izNWjuuzCrcOYEDwT9jbNGqSjoeL3Xf3x2NWPqOP217MvHlfjO9ev\n",
       "v/461q1bhw0bNkCpVEKlUkGlUqGwsFC3z5IlSxASEqJ7PGvWLNjY2GDevHm4dOkStm/fji+++IJX\n",
       "CiFqYs5cPYrkSosYX3jiwZrImEwc/Lzke7u4rAg7j4YJbEREotQ4XK9evRoFBQUIDg5Gy5YtdR9f\n",
       "ffWVbh+VSoWUlBTdYwcHB0RGRiIjIwN+fn548803sXjxYixcuLDhvgoiMiglZcXYcWStJOvUphd6\n",
       "chEjmahmds4Y1f8ZSXbqSjSu375czTOIyFTVeFqIRqOpaTMAYO3atZWybt26ISYmpv6tiMio7Tu5\n",
       "GbmF93WPFXIzTA16GTKZTGArooYV2HMMTl4+iMzsdF0WHv09/mvWCih4F1KiJoNLmYlIrzKz03Eo\n",
       "QXonxuA+E+Hi2EpQI6LGoVCYYdrQv0myjOw0HD63W1AjIhKBwzUR6Y1Wq0X4IemdGB3tmiPUf6rA\n",
       "VkSNp0OrrvDvFCTJ9pzYKPlNDhGZNg7XRKQ3Z64ewbVbFyXZ5MAXuYiRmpQJg56DlcWjW6CXlhVj\n",
       "x5F14goRUaPicE1EelFcWoTfH1/E6NkbPdr3F9SISAwHW0eMCZglyU4nHcbVmxeqeQYRmRIO10Sk\n",
       "F/tPbUZeYY7usUJhhqmBXMRITdOgHqPQqkVbSRZ+6Huo1RWCGhFRY+FwTURPLeNeGg6dfWwRo+9E\n",
       "uDi2FNSISCyFXIHpjy1uzLp/q9JiXyIyPRyuieipaLVabD20Bpq/3onRvgUXMVKT19a9E/p3CZZk\n",
       "e09uRk7+PUGNiKgxcLgmoqdyOukwrt2+JMkmD+EiRiIAGDdwLmws7XSPy8pL8PuRnwU2IqKGxuGa\n",
       "iOqtuLSo0lUQOnv6okf7fmIKERkYexslxg6YI8kSko/jStpZQY2IqKFxuCaiett3chPyiqSLGKcE\n",
       "vsRFjER/MaBbKNq4dJBk2w79gPKKckGNiKghcbgmonrJuJeGmIRdkizYdxIXMRI9Ri5XYNrQv0GG\n",
       "R//ovPMgA9FndghsRUQNhcM1EdWZ7k6Mjy1iHM5FjERV8nTzxoBuwyXZ/rhw3M+7I6gRETUUDtdE\n",
       "VGfxSYdx/bFFjFMCX4SFuaWgRkSGb+zAObC1stc9Lq8ow/bDXNxIZGo4XBNRnRSXFmHnY4sYu3j6\n",
       "ons7LmIkqomtlT3GD5wryc5fP4HLqacFNSKihsDhmojqZG9VixiDeCdGoifRr2swPN06SrJth37k\n",
       "4kYiE8LhmoieWMa9VBx+bBFjSJ9JaNHMXVAjIuMil8kx/bHFjXdzMxHFxY1EJoPDNRE9Ea1Wi/Bo\n",
       "6SJGJ/sWCPXjIkaiumjt0h4De4yUZBFc3EhkMjhcE9ETiU+KwfWMy5JscuBLXMRIVA9jA2bD1tpB\n",
       "95iLG4lMB4drIqpVcWkhdh4Jk2RdvPqge7u+ghoRGTcbKzsubiQyURyuiahWe0/wToxE+tavyzAu\n",
       "biQyQRyuiahGt++m4vC53ZIspM9kLmIkekpc3EhkmjhcE1G1Ht6J8XvpIkYHF4T6TRHYish0cHEj\n",
       "kenhcE1E1YpPikFKxhVJNoWLGIn0iosbiUwLh2siqlJxaSF2PHYnxq5efujW1l9MISITxcWNRKaF\n",
       "wzURVWknNRNVAAAgAElEQVTPiY3IL3qge2ymMMfkwBe5iJGoAXBxI5Hp4HBNRJXcvnsDh8/tkWRc\n",
       "xEjUcLi4kch0cLgmIomHixjXQPvYIsYQ/8kCWxGZvuoWN2bnZQlqRET1weGaiCTiEg9VvYjRjIsY\n",
       "iRpaVYsbf+fiRiKjwuGaiHSKSguw8/FFjG39eCdGokZS9eLGk1zcSGREOFwTkc7eE5uQX5yre2ym\n",
       "MMeUwJcENiJqeri4kci4cbgmIgDVLGL0m4zmSjdBjYiaJi5uJDJuHK6J6OEixmjpIkZnB1eE+HER\n",
       "I5EIXNxIZLw4XBPRw0WMmVzESGRIuLiRyDhxuCZq4qpbxNitHe/ESCQSFzcSGScO10RN3J7YjVzE\n",
       "SGSg+nUZBi83H0nGxY1Eho3DNVETdutuCo6c3yvJQv2mcBEjkYGQy+SYNvQVLm4kMiIcromaKI1W\n",
       "g63RP0gXMSpdEew3SWArInocFzcSGRcO10RNVNyVyosYpwa+zEWMRAaIixuJjAeHa6ImqKi0ADuP\n",
       "hkmybm390bWtn6BGRFQTLm4kMh4cromaoD2xv6HgL4sYzRUWXMRIZOCqWty49dAPKK8oE9SIiKrC\n",
       "4ZqoiXm4iHGfJAvxnwJnpaugRkT0JKpa3HgvV8XFjUQGhsM1UROi0WqwJfr7SosYQ/pwESORMah6\n",
       "ceNWLm4kMiAcromakJOXo5CamSTJpga+DHMzC0GNiKiuuLiRyLBxuCZqIgpL8vHHsV8kWfd2fbmI\n",
       "kcjIcHEjkWGrdbg+fPgwxo8fDw8PD8jlcoSFhdW4f2pqKuRyeaWPiIgIvZUmorrbdWw9CovzdI/N\n",
       "zSwwOfBFgY2IqL64uJHIcNU6XBcWFqJHjx74+uuvYW1tDZlMVttTAAD79++HSqXSfQwdOvSpyxJR\n",
       "/aSpknH8ovQfuMP9p8HZgYsYiYwRFzcSGa5ah+tRo0Zh6dKlmDJlCuTyJz+LxMnJCS4uLroPc3Pz\n",
       "pypKRPWj0agRHv09tNDqMpdmLTHMd6LAVkT0tLi4kcgwNdg515MnT4arqysGDRqEbdu2NdTLEFEt\n",
       "jl+MRPqda5JsatArMDfjP3iJjB0XNxIZHplWq9XWvttD9vb2WLlyJebOnVvtPtnZ2fjll18wcOBA\n",
       "mJmZYefOnfj0008RFhaG2bNnS/bNzX10E4vk5OR61CeimpSUF2LHmdUoqyjRZZ7OnRHYaYrAVkSk\n",
       "T8lZCYi9tkuSBXeZiVaOHQQ1IjJ93t7euj8rlUrJNjN9v5izszMWLlyoe+zr64vs7GwsW7as0nBN\n",
       "RA3rTGqUZLA2k5vDr22owEZEpG8dXHoiOess7uXf1mWnUvZjfG8vKOR6/zFPRLVolP/r/P398fPP\n",
       "Nf+ays+vcS4HFh8f36ivZ0p47OpH1HFLyUjEtWPnJNmYAbMQ2GdYo/Z4Gvyeqz8eu/ozxmPn5umE\n",
       "Lzcu1q2tyC/JwQOkY4Tf9EbtYYzHzlDw2NWPqOP217MvHtco17lOSEhAy5YtG+OliAiAWqNGePR3\n",
       "kszNqTWCeo0T1IiIGhIXNxIZjie6FF9CQgISEhKg0WiQlpaGhIQE3Lx5EwCwZMkShISE6PYPCwvD\n",
       "xo0bceXKFSQlJeHLL7/EqlWr8OabbzbcV0FEEkfP78Xte6mSbNrQV6BQ8FfERKaKixuJDEOtw3Vc\n",
       "XBx8fX3h6+uLkpISfPDBB/D19cUHH3wAAFCpVEhJSdHtL5PJsHTpUvj7+6Nv377YsmUL1q5diwUL\n",
       "FjTcV0FEOnmFOdgd+5sk6+MzBN4e3QU1IqLGwDs3EhmGWt/GCgoKgkajqXb72rVrJY/nzp1b49VE\n",
       "iKhh7Ti6DiVlRbrHVhY2mDh4nrhCRNRo+nUZhtiLkUhVJemyrYd+wJI53WFuZiGwGVHT0SjnXBNR\n",
       "40i+dRHxiTGSbHT/Z6C0dRLUiIgaE+/cSCQeh2siE6FWV2DroTWSrGVzLwzuOVpQIyISgYsbicTi\n",
       "cE1kIg4l7EJmdrokmz70b1DIFYIaEZEoXNxIJA6HayITcD/vLvae2CjJ+nUehnYtOwtqREQicXEj\n",
       "kTgcrolMwLaYH1BWUap7bG1pi/GDuLCYqCnr12UYvNx8JNnWQz+gvKJMUCOipoHDNZGRO3/9JC6k\n",
       "nJJk4wfOhb1NM0GNiMgQcHEjkRgcromMWGlZMbYd+kGSebn7IKBbqKBGRGRIqlzceGor7j7IFNSI\n",
       "yPRxuCYyYntObEROwT3dY7lMjhlDX4Vcxv+1ieihSosb1WUIj/4eWq1WYCsi08WfwERG6tbdFMQk\n",
       "7JJkQ33Ho1ULLzGFiMgg2VjZYeKgeZIsMT0BZ64eEVOIyMRxuCYyQhqNGpsProZG++juqU72LTCy\n",
       "30yBrYjIUPXtPBQdPLpJsu0xP6GopEBQIyLTxeGayAgduxiBtKxkSTY16BVYmlsJakREhkwmk2HG\n",
       "sFehUJjpsvziXPxx7BeBrYhME4drIiOTV5iDXcd+lWQ92/dHt3b+ghoRkTFwdWyF4X5TJdnxixFI\n",
       "ybgiqBGRaeJwTWRkth/+GcVlRbrHluZWmBz4ksBGRGQsQvymwKVZS0m2OWo1KtTlghoRmR4O10RG\n",
       "5Era2UqLkEYHzIKjfXNBjYjImJibmWNG8KuSLDM7HVFndgpqRGR6OFwTGYmyilJsif5Oknm0aIch\n",
       "PccIakRExsjbozv6dR4myfaf3MJrXxPpCYdrIiMRGbcV2blZuscy/N8CJblCYCsiMkYTBs+DrZW9\n",
       "7jGvfU2kPxyuiYxAxr00HIj/XZIN7jkKnm7eghoRkTGzs3bAxMHPSzJe+5pIPzhcExk4jUaNjQdX\n",
       "Qq2p0GUOto4YEzBbYCsiMna89jVRw+BwTWTgjpzfizTVVUk2JfBlWFvaCmpERKaA174mahgcrokM\n",
       "2P28u/jz+HpJ1qN9P/TqECCoERGZkuqufX399iVBjYiMH4drIgOl1WqxJfo7lJWX6DIrCxtMDXoF\n",
       "MplMYDMiMiVVXft644GVKK8oE9SIyLhxuCYyUGeuHsXl1NOSbMKg59DMzllQIyIyRQ+vff2aJLvz\n",
       "IAP7T20R1IjIuHG4JjJAhcV52BbzoyRr37ILArqFCmpERKbM26MbBnQbLskOxG/HrbspghoRGS8O\n",
       "10QG6Pcja1FQnKt7rFCYYWbwa5DL+L8sETWMCYOeg9LWSfdYo9XgtwP/C7VGLbAVkfHhT2oiA5OY\n",
       "loBTV6Il2ci+0+Hq5CGoERE1BdaWtpg+bL4ku3UnBdG8NTpRnXC4JjIgpeUl2By1WpK5O7dBcJ9J\n",
       "ghoRUVPSvV1f9PYeKMn2ntiEOzkZghoRGR8O10QGZO+JjcjOk97i/JmQN2CmMBfYioiakimBL8Pm\n",
       "sVujbzq4EhqtRmArIuPB4ZrIQKRnXUP02T8l2ZBeY+Dl1lFQIyJqihxsm2HykBck2bXblxB7MVJQ\n",
       "IyLjwuGayABUqMuxIfIbaP/yzpCjfQuM5S3OiUgA/05B6OTZW5LtPBqGBwXZghoRGQ8O10QGYP+p\n",
       "cGRmp0uyGcPmw9LCWlAjImrKZDIZZg57FRbmVrqspKwIW6K+g1arFdiMyPBxuCYS7Oad64iM2yrJ\n",
       "+nYeii5efQQ1IiICnBxcMG7AHEl28UYcziYfE9SIyDhwuCYS6OHpIN9KFgo52Dpi8pAXBbYiInpo\n",
       "cI9R8HL3kWThh9Ygv+iBoEZEho/DNZFAEXFbkXEvVZLNGPYqbKzsxBQiIvoLuVyBZ4LfgEJhpssK\n",
       "i/OwJfp7nh5CVA0O10SC3LqbgojHTgfx8wlE93Z9BTUiIqrM3bk1RvWdIcnOXYvFmatHBTUiMmwc\n",
       "rokEUKsrsCHiG2j+clthe5tmmBLI00GIyPAE+01GG5cOkiz80BrkFeYIakRkuDhcEwkQEb8Ntyud\n",
       "DjIfttYOYgoREdVAIVdg9vAFktNDikrysTlqNU8PIXoMh2uiRnb77g3sP7VFkvXpOBg92vcX1IiI\n",
       "qHbuzq0xpv8sSXYh5RTikw4LakRkmDhcEzUitbri4dVB/no6iLUSU4JeFtiKiOjJDPOdAM/H7hq7\n",
       "7dAPyC24L6gRkeHhcE3UiCLit+HW3RRJNn3YfNjxdBAiMgJyuQJzQt+CmcJclxWVFmBT1CqeHkL0\n",
       "fzhcEzWS9Kxr2H9ysyTr7T0QPTsECGpERFR3rk4eGDtgtiS7dCMecYmHxBQiMjAcrokaQYW6HL/u\n",
       "/7fkZjH21kpMDXpFYCsiovoJ6jUObd07SbJth35AUWmeoEZEhoPDNVEjOJsWjaycW5JsZsjrsLdR\n",
       "CmpERFR/crkCs0PfhLmZhS4rLivC8Wu7eHoINXkcrokaWOaDG7iSeUqS9e8SzJvFEJFRc3FshXED\n",
       "npVkGQ9SkKSKF9SIyDDUOlwfPnwY48ePh4eHB+RyOcLCwmr9pBcuXEBgYCBsbGzg4eGBTz75RC9l\n",
       "iYxNcWkhjiX/KcmcHFwwaQhvFkNExm9IrzHo0KqrJDudehCq+zcFNSISr9bhurCwED169MDXX38N\n",
       "a2tryGSyGvfPy8tDaGgo3N3dER8fj6+//hrLly/HihUr9FaayFhsi/kRRWWPzkGUQYbZoW/B2tJG\n",
       "YCsiIv2Qy+SYM3wBrCwe/Z2m1lTgl/3/QoW6XGAzInFqHa5HjRqFpUuXYsqUKZDLaz+LZMOGDSgp\n",
       "KUFYWBi6dOmCKVOm4L333uNwTU3OuWuxOHUlWpIN9R0Pb49ughoREemfk4MLpj52rf5bd1Kw7+SW\n",
       "ap5BZNr0fs51bGwsBg8eDEtLS102fPhwZGRkIC0tTd8vR2SQ8gofYFPUaknm7twGYwJmV/MMIiLj\n",
       "5d8pCL06DJBkkfHbkJKRKKgRkTh6H65VKhVcXV0l2X8eq1Qqfb8ckcHRarX47cC3KCx+dDrIw1+d\n",
       "vi1ZWU9EZCpkMhlmDJsPa3M7XabVavBrxL9QUlYssBlR4zPT9yes7Zzs6sTHN+7q4sZ+PVPCY1ez\n",
       "KxlxuJx6WpL1bD0EWen3kZXOWwTXB7/n6o/Hrv547OpuoPc4HLi8Ufc4OzcLa7Z9jgHe4wS2Mi78\n",
       "vqufxj5u3t7e1W7T+zvXbm5uld6hzsrK0m0jMmU5hVk4nXpAkrWw90BXjwHVPIOIyHS0dGyPTu7+\n",
       "kuzanXNIz+bpIdR06P2d64CAALz33nsoLS3VnXcdGRmJVq1awdPTs9rn+fn56btKlf7zL5vGej1T\n",
       "wmNXs7KKUny5MQwarVqXWVnYYFDHCZDL5Dxu9cDvufrjsas/Hrv6i4+Ph6/nMOSUZEpunBWXuh/D\n",
       "Bo5CMztnge0MG7/v6kfUccvNza122xNdii8hIQEJCQnQaDRIS0tDQkICbt58eA3LJUuWICQkRLf/\n",
       "rFmzYGNjg3nz5uHSpUvYvn07vvjiCyxatEgPXwqR4dp5JKzStV1nDJsPeytHQY2IiBqfmcIcc0cu\n",
       "hFyu0GWFJfn4Zf+/oNGoa3gmkWmodbiOi4uDr68vfH19UVJSgg8++AC+vr744IMPADxcpJiSkqLb\n",
       "38HBAZGRkcjIyICfnx/efPNNLF68GAsXLmy4r4JIsAspp3Dk/B5J1rfzUPTxGSKoERGROK1d2mNM\n",
       "/1mS7Nqti4iM3yaoEVHjqfW0kKCgIGg0mmq3r127tlLWrVs3xMTEPF0zIiORW3Afv0V+K8mcla6Y\n",
       "GvSKoEZEROIF+01C0s1zuHrzvC7be2ITvD26o13LzgKbETUsvS9oJGpKNFoN1kd8jcKSfF0mlysw\n",
       "b+Q7sLKwFtiMiEgsuUyOZ0e8DVtrB12m0WoQtm8FikoKBDYjalgcromeQvSZnUi6eU6Sje7/DDzd\n",
       "OgpqRERkOJS2TpgT+pYky8m/i40HV0Kr1QpqRdSwOFwT1dONzET8eXy9JOvg0Q0hfSYJakREZHi6\n",
       "tvVDUO/xkuzctVgcvxghqBFRw+JwTVQPhSX5WLfnS8nKdxtLOzw7/G3JCnkiIgLGDXgWHi7tJNn2\n",
       "mJ+QmZ0uqBFRw+FwTVRH/znPOqfgniSfFfomHO2bC2pFRGS4zM3MMW/kO7Awt9Jl5eoyrNv7JcrK\n",
       "SwU2I9I/DtdEdRR95g9cuiG9zerQ3uPRo30/QY2IiAyfi2MrTB/6N0mWmZ2O8OjvBTUiahgcronq\n",
       "ICUjEX8e+0WSebp1xLiBzwpqRERkPPw7BcHPJ1CSnbwShdhLBwQ1ItI/DtdET6iwOA9he7+ERvvo\n",
       "uu82lnZ4ftRimCnMBTYjIjIOMpkM04fNh6ujhyTfGr0Gt+/eENSKSL84XBM9gYfnWX9T6Tzr2cPf\n",
       "gpODi6BWRETGx8rCGi+MeRcWZpa6rFxdhp93L0NxaaHAZkT6weGa6AlEnd6BS6nS86yH+U5A93Z9\n",
       "BTUiIjJe7s5tMH3YfEl2NzcTv0V+y+tfk9HjcE1Ui+RbF7DrsetZe7n5YNwAnmdNRFRffTsPxcBu\n",
       "IyTZuesncCjhT0GNiPSDwzVRDXLy72HtnsrnWc8btRgKhZnAZkRExm9y4IuVrn+982gYUjISBTUi\n",
       "enocromqUV5Rjp93f4GC4lxJ/uyIt+Hk0EJQKyIi02FuZoEXRr8LawsbXabRqLFu73LkFz0Q2Iyo\n",
       "/jhcE1VjW8wPSMtKlmSj+s1E17Z+ghoREZme5ko3zB6+QJI9KMjG2j3LoVZXCGpFVH8cromqEHsx\n",
       "EscvRkiyrl5+GNFvuqBGRESmq0f7fgjuM1GSXbt9Cb8fWSuoEVH9cbgmekyaKhnhh9ZIsuZKNzw7\n",
       "4m3IZfxfhoioIYwd8Cy8PbpLssPnduPk5YOCGhHVDycFor/IL8rFz7u/QIW6XJdZmFnixTF/h42V\n",
       "ncBmRESmTSFXYN6oxXC0l65p2Rz1HdJUydU8i8jwcLgm+j8V6nL8vGdZpRvFPBPyOlq18BJTioio\n",
       "CbG3UeKlsUtgbmahyyrU5fhx9+fIK+QCRzIOHK6JAGi1Wmw9tAbXb1+S5EG9xqGPzxBBrYiImp7W\n",
       "Lu3wTPDrkiy3IBtr9yyT/FaRyFBxuCbCw/P6jl+MlGQdPLphwqDnBDUiImq6/DoFYmjv8ZLsesZl\n",
       "bIv5iXdwJIPH4ZqavMS0BPx++GdJ5qx0xYuj3+WNYoiIBBk/6Dl0bN1Dkh27sA+Hz+0W1IjoyXC4\n",
       "pibtTs5trN27XHIHRksLa7wy7n9ga+0gsBkRUdOmkCvw/KjFcHJwkeTbD/+My6mnBbUiqh2Ha2qy\n",
       "ikoLsOaPT1FcWqjLZJDhuRGL4O7cRmAzIiICAFtrB7wy7r9haW6ly7RaDdbu/RIZ99IENiOqHodr\n",
       "apLU6gqs2/Ml7jzIkOTjBj6Lbu38BbUiIqLHtWzuhXmjFkP2l/sMlJYVY82fn/IW6WSQOFxTk6PV\n",
       "ahF+6HskpidIcv9OQQjuM0lQKyIiqk7Xtn6YOHieJLufdwc/7voc5RVlYkoRVYPDNTU5kfHbKl0Z\n",
       "xMvNBzODX4NMJhPUioiIahLUaxwGdhshyW5kJmLjwZW8gggZFA7X1KScTjqMXcfXSzInB5dKNy0g\n",
       "IiLDIpPJMDXo5UpXEIlPjMGeExsFtSKqjMM1NRnXbl/C+shvJJm1pS3mT/h/cLBtJqgVERE9KYXC\n",
       "DC+MfhcuzVpK8v2ntuDYhf2CWhFJcbimJiHr/i38+OdnUKsrdJlCboaXxi6Bm1Nrgc2IiKgubKzs\n",
       "8Mr492FrZS/Jt0R/j4spcYJaET3C4ZpMXn7RA3y38xMUlRZI8lmhb8Lbo5ugVkREVF8uji3xyvj/\n",
       "gbni0el8Dy/RtxypqqsCmxFxuCYTV1xahNU7PkZ2XpYkHxMwG/6dAgW1IiKip9XWvROeG/WO5BJ9\n",
       "5RVl+P6PpbiTk1HDM4kaFodrMlnlFWX4Ydc/cetuiiTv3zUEw/2nCmpFRET60qN9P0wNelmSFRbn\n",
       "4budH/Ma2CQMh2sySWqNGmH7vsK1WxcleSfP3pgxdD4vuUdEZCIG9xiFUL8pkuxergqrd34suQMv\n",
       "UWPhcE0mR6vVYnPUapy/flKSe7n54MUx70GhMBPUjIiIGsLYAXPg3ylIkt26k4I1f3yKsvJSMaWo\n",
       "yeJwTSbnz2O/4sSlA5LMzak1/jbhfViaWwlqRUREDUUmk+GZkNfh06anJL+ecRk/7/4CFepyQc2o\n",
       "KeJwTSYl6swOHDi9XZI52rfAqxM/qHTZJiIiMh1mCnO8NObv8HLzkeSX087g1/3/hkajFtSMmhoO\n",
       "12Qyjpzbgx1H1kkyO2slXp/0IRztm4spRUREjcbSwhrzJ/w/tHT2lORnk49hc9R3vE06NQoO12QS\n",
       "jl+MRPihNZLsP3/Juji2EtSKiIgam42VHV6b9CFaKN0leeylSOw8uo4DNjU4Dtdk9E5dicbmg6sk\n",
       "mbnCAi+PXYI2rh0EtSIiIlEcbB3x+uSP0MzOWZJHndmJ3bG/ccCmBsXhmozamatHsSHyW2jx6C9K\n",
       "hcIML479Ozq27iGwGRERieTk4ILXJ30EO2ulJI+IC8eeExywqeFwuCajde5aLH7ZtwJarUaXyeUK\n",
       "vDD6XXTx8hXYjIiIDIGrkwdenfgBrC1sJPn+U+HYc2IjB2xqEByuySidv34S6/Z+Bc1fB2uZHPNG\n",
       "voPu7foKbEZERIaktUs7vDbpoyoG7C3Ye2KToFZkyjhck9E5c/Uoft6zDGpNhS6TyeR4dsRC9PIe\n",
       "ILAZEREZIk83b7w26UNYPTZg7zu1GXtObBTUikwVh2syKqeuRCNs3wrJ9UplkGF26Jvo4zNYYDMi\n",
       "IjJknm4d8XpVA/bJzVzkSHr1RMP1qlWr0LZtW1hbW8PPzw9Hjx6tdt/U1FTI5fJKHxEREXorTU3T\n",
       "sQv7sSHiG8k51jLI8EzIG+jbeajAZkREZAw83TpW+Q72/lNb8Pvhnzlgk17UOlxv3rwZb7/9Nt5/\n",
       "/30kJCRgwIABGDVqFG7evFnj8/bv3w+VSqX7GDqUww/VX0zCLmyOWi25KohcJsezI95G/67BApsR\n",
       "EZEx8XLriFcnfgBLC2tJfijhT2w8uJJ3cqSnVutwvWLFCjz//PN48cUX4ePjg2+++Qbu7u5YvXp1\n",
       "jc9zcnKCi4uL7sPc3FxvpalpORC/HdtifpRkCrkZ5o1aDL9OgYJaERGRsWrr7oPXJ30Ea0tbSX7i\n",
       "0gGE7VuBCnW5oGZkCmocrsvKynDmzBkMHz5ckg8fPhzHjx+v8RNPnjwZrq6uGDRoELZt2/b0TanJ\n",
       "0Wg12HFkLf449oskVyjM8OKY97h4kYiI6s3LrSPemvIp7B+7DvbZ5GP4cdfnKKsoFdSMjF2Nw/W9\n",
       "e/egVqvh6uoqyV1cXKBSqap8jr29Pb766iuEh4dj7969CA4OxowZM7Bhwwb9tSaTp1ZXYH3E14g6\n",
       "s1OSm5tZ4JVx/4Nu7fwFNSMiIlPRqoUXFkz7Jxztmkvyy6mn8d2Oj1FcWiioGRkzmbaGs/czMjLg\n",
       "4eGBw4cPY9CgQbr8448/xm+//YbExMQnepE33ngDR44cwblz5yR5bm6u7s/Jycl17U4mqlxdhpjE\n",
       "bch4cF2SmyssMLTzdLgpvcQUIyIik1RQmovIixuQX3JfkjezcUFwl5mwtXQQ1IwMlbe3t+7PSqX0\n",
       "tx81vnPdvHlzKBQKZGVlSfKsrCy4u7s/cQF/f38Oz/RESsqLEHlxfaXB2srcFsO7PcvBmoiI9M7O\n",
       "UomR3eeimY2LJH9QdAd7z69FTuEdQc3IGJnVtNHCwgJ9+vRBREQEpkyZossjIyMxbdq0J36RhIQE\n",
       "tGzZssZ9/Pz8nvjzPY34+PhGfT1T0tDHLjsvC6t3fIx7BRmS3FnpitcmfogWzZ78H3SGhN9z9cdj\n",
       "V388dvXHY1d/xn7sfH374Ps/liI1M0mXFZXl48Dl9Xhx7BJ0bN29wV7b2I+dKKKO21/PvnhcrVcL\n",
       "WbRoEdatW4effvoJV65cwYIFC6BSqTB//nwAwJIlSxASEqLbPywsDBs3bsSVK1eQlJSEL7/8EqtW\n",
       "rcKbb76phy+FTNWNzER8teld3Mm5Lck9WrTDwmlfGO1gTURExsPWyh5vTPoYPdr3k+TFZUVYvfMj\n",
       "nE46LKgZGZMa37kGgOnTpyM7OxtLly5FZmYmunfvjj179qB169YAAJVKhZSUFN3+MpkMS5cuRVpa\n",
       "GhQKBXx8fLB27VrMmjWr4b4KMmqnkw5jQ+S3lS591NGjO14cuwTWljbVPJOIiEi/LMwt8cLod7E1\n",
       "5kccPb9Xl6vVFQjbtwLZeXcQ6jcFMplMYEsyZLUO1wDw6quv4tVXX61y29q1ayWP586di7lz5z59\n",
       "MzJ5Wq0W+05uxt6Tmypt8+04CLNDF8DcjNdHJyKixiWXKzAt6BU42rfAn49dDnbX8fVQZd/EMyGv\n",
       "w9zMQlBDMmRPNFwT6Vt5RRl+O/C/Vf6KbUTfaRjV/xnIZbWetURERNQgZDIZQv0mo5mdM36L/BZq\n",
       "TYVuW3xSDO4+yMBL45ZAaesksCUZIk4v1OgeFGTj223/r9JgrVCYYc7wBRgTMJuDNRERGQT/ToF4\n",
       "deI/Kt3NMS0rGV9u+i+kZ10T1IwMFScYalTXb1/C8o3vIFWVJMkfLiL5CH07DxXUjIiIqGodW/fA\n",
       "OzOWw8WxlSTPLcjG1+H/jdNJRwQ1I0PE4ZoahVarRUzCLny7/R/IL3og2ebi2AqLZixD+1ZdBbUj\n",
       "IiKqmYtjSyya8QU6e/pK8nJ1GcL2fYXth3+GWl1RzbOpKeFwTQ2urLwUv0b8G9tifoRGo5Zs6+TZ\n",
       "G4um81J7RERk+Gws7fC38f+Dob3HV9p26Owf+Gbb+3hQkC2gGRkSDtfUoO4+yMS/wv+O+MSYSttG\n",
       "9J2G+ePfh42VnYBmREREdSeXKzBpyAuYHfomFArpdSFuZCZi2W+LkJR+TlA7MgQcrqnBxCfGYNlv\n",
       "C3H77g1JbmlhjZfGLnm4cFGuENSOiIio/vp1CcaCqf+Eo11zSV5QnItVOz5CxKlwaLQaQe1IJA7X\n",
       "pHel5SXYEPktftn/L5SWl0i2uTp5YPHMLyvd/YqIiMjYeLl1xLuzVlQ6D1ur1WBX7AZ8t+Nj5Bbe\n",
       "F26vCSsAACAASURBVNSOROFwTXp1++4NLN/4Dk5ePlhpW68OA/DOjOVwfWy1NRERkbGytXbA3ya8\n",
       "j1H9n4EM0rs2JqYn4PMNb+NCyilB7UgE3kSG9EKj1eDIuT3YeTSs0m3MzRTmmDTkBQzqPpK3iyUi\n",
       "IpMjl8kxqt8MeLl1xC/7VqCwJF+3rbA4Dz/8+U8M6j4SEwc/DwtzS4FNqTHwnWt6avfz7mDV9g+w\n",
       "LebHSoO1q5MH3pmxHIN7jOJgTUREJq2zZ2+8O2tFlZeWPXphH5Zvege37qYIaEaNicM11ZtWq0Xs\n",
       "pQP4bMMCXL11odL2/l1DsHjml2jVwqvxyxEREQngaN8Cb07+GGOrWLSfdf8Wvtr0Lvae3MxrYpsw\n",
       "nhZC9ZJbeB+bDq7CpRvxlbZZWlhj5rBX0cdniIBmREREYsnlCgzvOw0+bXril33/wt3cTN02taYC\n",
       "e09sxPlrsZgV+hZau7QT2JQaAt+5pjrRarU4efkgPlu/oMrBuqNHdyyZ/TUHayIiavI8/+9qIv27\n",
       "BFfadvteKr7a/F/YHbsB5RXlVTybjBXfuaYnllecjRPX90CVm1Zpm7mZBSYMmodBPUZCLuO/2YiI\n",
       "iICHv82dFfomurb1w5ao75BfnKvbptGosf9UOM5fP4lerYahhb2HwKakLxyuqVblFeU4cHo79p/d\n",
       "Ao1WXWl7W/dOmB36FlwcWwpoR0REZPh6dghA+1ZdsS3mR5xOOizZlpmdjszsdfB27Y3OXTvC1tpB\n",
       "UEvSBw7XVKPkWxexJeo7ZOXcqrTNXGGB0QHPYGjv8bzTIhERUS3srB3w3MhF8O04CJujViOvMEey\n",
       "PTnrLJb++gYmDHwOfbsM5W+CjRSHa6rS/bw72HF0HRKSj1e53adNT0wfOh8tmrk3cjMiIiLj1r1d\n",
       "X7Rv2QXbD/+EU1eiJdsKi/Pw24FvEXspEtOHzucVt4wQh2uSKC0vwcH433Hw9O8oV5dV2m5lboNp\n",
       "w/4GP58hvG41ERFRPdlY2WHO8AXw7xSE8ENrcCfntmT7jcxELNu4CAFdgzG6/yw42DoKakp1xeGa\n",
       "ADy8w+LZq0ex82gYHhRkV7lPB5de6OMVDP9Ogxu5HRERkWnyadMT7836N9bvWoXzN49ArXl0/Wut\n",
       "VoPjFyNxOukIQvymYKjveFiY8Q6Pho7DdROn1WqRmJ6AP4//ilt3qr5rlIdLO0wNfBn3MwobuR0R\n",
       "EZHpMzczR3ePgWjbvCuu5pzCxZRTku2l5SXYHbsBxy7sw7iBz6KPzxCej23AOFw3Yamqq/jz2K9I\n",
       "ruLuigBgb63E2IHPol+XYZDL5LifUfm61kRERKQfdlbN8Mq4/8bFlDjsOLIWdx5kSLY/KMjGr/v/\n",
       "jYOnd2B0/2fQvV1fnqJpgDhcN0EZ99L+f3v3Hhdlmf4P/PPMcJ5hYDgN52EQBBFFEVREBVJrMxPT\n",
       "b6iVu6CpmWnlbu3Xrb6Juq1mmWbhbmVKRm5a/XJTtGRR1MQDungAQY6DnM8gyMmZ+/cHMes0nIOZ\n",
       "Aa736zUvnXuuZ+Z6Lke9uOee+0H8xa9wI+dSp4/zeQYInTgPjwZGwNTYTMvZEUIIISObr3sgxkgn\n",
       "4vzNkzh56Ws0Nt9Te7y4Mh+fHfsbXO08MDfoGYyRTqQmW49Qcz2C3C3P+WWz+otdxkzwnIZ5Qc/R\n",
       "ntWEEEKIDvH5BgiZMA+BY0Lx0+VvkHT9GBSKB2oxBeXZ+PvRzZA5eGPu1KUY7TKemmw9QM31CJBX\n",
       "koEfLx9Bev7VLmO8XSdg3rTn4Crx0GJmhBBCCOmOmbEQC2a0XwH5+IU4XLtzHgxMLSavJAMf/7+3\n",
       "IZV4YnbAIowbNZnWZOsQNdfDlJIpkSH/DxKvfo87XaypBgCpxBNPBi/DaJfxWsyOEEIIIX1hY2GP\n",
       "Pzz+R8wJ/B+cuHgI1zv5FFpeloV9x7fBTuyE2ZMWIsB7Jgz4hjrIdmSj5nqYaX3Qgiu3z+BM6g8o\n",
       "q9a8qmIHF7tReGzy0xjnPoU+QiKEEEKGCEcbKVbM+1/cLc9BfPIhpOVrbjZQXlOErxL2IP7iV5jh\n",
       "9wSmjZ1Nl1TXImquh4m6hmqcv3kS52+eRGNTfZdxbg5e+N3kCIyR+lNTTQghhAxRLnajsDr8TeSV\n",
       "ZOLUlW9wK++KRkxtQxV++PkLnLz4T0zynokQvyfgZCvTQbYjCzXXQ5hSqUBGwXVcuPUjbuVegZIp\n",
       "u4z1dB6HxyZHwNPZl5pqQgghZJiQOXhh1fw3UFwpR8LV73At85xGP9CmaMXFtARcTEvAKKexmOk3\n",
       "F76yyTA0oCUjg4Ga6yGorrEaF9P+jeRbP6H6XkWXcTyOh4mewQidOB9Se08tZkgIIYQQbXK0keL3\n",
       "j72KJ4KewelrR5F8KwFtilaNuJyiNOQUpUFgKkKgVwimjp0NRxupDjIevqi5HiLaHrTiVl4KUjLO\n",
       "IC0vpdtZalNjAab5PoqZfnMhNrfVYpaEEEII0SVrkQT/E7oKj09ZggtpCTh/4wRqOpmIa2yqx5nU\n",
       "H3Am9QdIJZ6YOnY2/EfPoOtbDABqrvWYkimRU5SOlIwkpGb9jKbW+93GO1i7InjcY5gy5hEYG5lq\n",
       "KUtCCCGE6BuBqQhzAhbiEf9w3Mq9jKTrx5FdeKvTWHlZFuRlWfju7D6MlQVg0uiZ8HHzh6GBkZaz\n",
       "Hh6oudYzjDEUlGUhNTsZ1zLPoaahstt4Q74RJo4OxjTfxyBz8KL11IQQQghR4fP48PMIgp9HEIoq\n",
       "8nHh1k9IyUxCU0ujRmzbg1akZl1AatYFmBiZYfyoKZjkNROjXcaDz+PrIPuhiZprPaBQKpBbnI7r\n",
       "2RdxI+ciahuqejxGYuWMYN/HEDgmFAITcy1kSQghhJChzMnWDU+HrUL4jD/gRvZFXExL6PJaGM2t\n",
       "93H59mlcvn0aAlMRfGWBGOc+Gd6uE2BkaKzlzIcWaq51pKmlEXfu3kBa/lXczL3c7fZ5HYSmFpjk\n",
       "NQMBXiFwlXjQLDUhhBBC+szIwBgB3iEI8A5BZV0pLqUn4vLt052uzQba12dfSv83LqX/G4YGRvBy\n",
       "nYBx7pPhKwuAuZmllrPXf9RcawljDMWV+UjPv4Z0+TXklWRAqVT0eJyRgTHGj5qKAO8QeLn60ccy\n",
       "hBBCCBkwNhb2eCLoGTw+dQnyS+7g2p2z+M+dn3Gvqa7T+LYHrbiVexm3ci+DAwcXu1Hwlk6Al+sE\n",
       "yBy86IqQoOZ60DDGUFlXiuzCW8gquoWsuzdR11jdq2ONDIzh4zYJfh5T4SsLpC8nEkIIIWRQ8Tge\n",
       "3B294e7ojadmrkB24S1cvXMO17OTO12fDQAMDAXl2Sgoz8ZPV76BkaEJPJ18f2m2/SARO4/IT9mp\n",
       "uR4gjDFU1ZchuzANWYU3kV14q8cvIz7M1FiAce6TMX7UVHhLJ8DIgNYzEUIIIUT7+Dw+vFz94OXq\n",
       "h8VhLyC7KA03cy/jZs6lbnub1rZmpOWnqC7JLjS1gLvjGIxy9MEoJx842cpGxCfw1Fz3U3NrEwrK\n",
       "spFfmon80juQl2R2+RFKVyRiZ4xx84eP1B8ezmPpoxRCCCGE6BU+30DVaC8KeR6FFXm4mXsJN3Mv\n",
       "o6gir9tjG5rqcCOnfbMGADA2NIGbgxfcHX0glXjAxc4D5mYW2jgNraLmuhdaWptQVClHUUUuCivy\n",
       "IC/LQklVAVg3F3LpjJGBMUa7jFc11NYWkkHKmBBCCCFkYHEcBxc7d7jYuWPu1KWob6xB5t3ryCy4\n",
       "jgx5Kurv13R7fEtbMzIL2uM7WJnbwlXiCReJxy8N9yiYGgsG+1QGFTXXD2GMobahEiVVBSisyEPR\n",
       "L7eK2hIwsD4/nyHfCDIHL3g4+8LT2ReuktEwNKDZaUIIIYQMfSKBGIHeoQj0DgVjDCVVcmQUpCKj\n",
       "4Dryim+jpa25x+eovleB6nsVSM2+oBqzFkngYCOFo7UUjjZSOFhLYSd2HDJLSkZkc61QKlBafRdl\n",
       "1YUorS5EWU0hyqoLUVZThNZevBG6YmRgDFd7T3g6+cLTZRykEk+6uhEhhBBChj2O4+Bo4wZHGzc8\n",
       "4r8ACqUCRRV5yClOR25ROnKKb6Ohl8tnq+rLUFVfhlu5l1VjfL4B7MXOqkbbTuwEW0sHtD1ogaGe\n",
       "fU9t2DbX95sbUFVfhsq6MlTVlaKqvhxVdaUoKpejoaUOLLlvSzo6Yyd2gpv9aLjZe8HNYTQcrKVD\n",
       "5qcqQgghhJDBwufx4SrxgKvEA2ET54MxhvLaYuQWpUNeloWC8mwUV8p7tS0xACgUD1BUmY+iynyN\n",
       "x0wNhfg5Xwo7S0fYWjrA2kICK3NbiM3tYG5mofUdS4Zkc93S2oTaxmrUNVSh9pdbXUM16hqrUH2v\n",
       "AlV1ZV1uG9MfHDjYWjrA2c4dTjYyONnKILX3pCsjEkIIIYT0AsdxkIidIBE7Ich3DoD2PbOLK/Mh\n",
       "L8vG3bL2Lf1Kqwv7/J22prYG5BSlIacoTeMxQ74RxOY2EItsYS2yg9jcDlYiW1gIrCASiCESiGFq\n",
       "JBjQBrxXzXVMTAx27NiB0tJSjB07Frt27cL06dO7jL958yZeeuklXLlyBVZWVli9ejXeeuutbl/j\n",
       "fksDGu7Xo6GpHg1Nte2/3q9DQ1M97jXVoeF+HWob25vo5tb7fTvLPjAxMoPEyhlONm5wspXB2VYG\n",
       "R2sp7TVNCCGEEDKADA2MILUfDan9aNVY64MWlFbdRUmVHMWVchRXyVFSWdDjlyW70qZoRXltMcpr\n",
       "i7vOg2+karRFAjEsBGKIzMQwF4ghNBX9crOAwNS8V414j831119/jVdeeQV79+7F9OnT8fHHH+Px\n",
       "xx9Heno6XFxcNOLr6+sxZ84chIaGIiUlBbdv30ZUVBQEAgE2bNjQ5ev879+f6ymVAWUhsILEyhn2\n",
       "Vs6QiJ0hsWq/iczEI3LDc0IIIYQQXTMyMFYtJ3lYQ1M9iivlKK8pQnltMSpq2hvmyrrSPs90/1qb\n",
       "olW1zrsnPB4fQhMRXovY1WVMj831zp07ERUVhRUrVgAAPvzwQ5w8eRJ79+7FO++8oxEfFxeH5uZm\n",
       "xMbGwtjYGD4+PsjIyMDOnTu7ba4HmgHfENYiCaxFdrC2sIe1hQTWIgnKiqogNLbEtKnBWsuFEEII\n",
       "IYT0n9BUhNEu4zDaZZza+OXLl9DQUgeJsxXKa4pRUVeCmvoKVN8rR/W9CrS0Ng1oHkqlAo3N97qN\n",
       "6ba5bm1txbVr1/D666+rjT/66KO4cOFCp8ckJydjxowZMDY2Vot/6623IJfLIZVKe5t/l/h8A1gI\n",
       "rGApsIaF0AoWQmtYCq1gIbCGpdAaNhb2MBdYgsfxNI5NqU35za9PCCGEEEJ0j8fjQ2RqhbGyAIyV\n",
       "qT/GGENTS2N7o11fgZp7FaiuL0dNQyXqG2tUt9YHLX16TaGpqNvHu22uKysroVAoIJGoX+zEzs4O\n",
       "paWlnR5TWloKV1dXtbGO40tLS7tsro0MjCE0s4DQ1AJCUxHMTS0gNBP9cr99TCSwgqXQGgJT804b\n",
       "Z0IIIYQQQoD2L1GamQhhZiKEs617pzGMMTS33kd9Yw3qGmtQ31iN+vvtTfe9+3VobPrl+4DN7b+2\n",
       "tjVD8Fua6/6eSH+89dwnvYpTtgH32rqfju+Op6cnAKCurm+XKidUu/6iuvUf1a7/qHb9R7XrP6pd\n",
       "/1Ht+meg6mbCN4eJyBwSkWvPwT3odvrXxsYGfD4fZWXqC7zLysrg4ODQ6TH29vYas9odx9vb2/+W\n",
       "XAkhhBBCCNFr3TbXRkZGmDRpEn766Se18VOnTmHatGmdHhMUFIRz586hpaVFLd7JyWlA1lsTQggh\n",
       "hBCirzjGGOsu4PDhw1i2bBliYmIwbdo0/P3vf8f+/fuRlpYGFxcXbNy4EVeuXEFCQgKA9q34vLy8\n",
       "EBoaijfffBOZmZmIiorCpk2b8Oqrr2rlpAghhBBCCNGFHtdcR0REoKqqClu3bkVJSQnGjRuH+Ph4\n",
       "1R7XpaWlyM3NVcWLRCKcOnUKa9euRUBAAKysrPCnP/2JGmtCCCGEEDLs9ThzTQghhBBCCOmdYbWf\n",
       "3dmzZzF//nw4OzuDx+MhNja218dmZWXB3Nwc5ubmg5ih/upr7fLz88Hj8TRuv16fP9z19z23a9cu\n",
       "eHt7w8TEBI6Ojti4ceMgZ6p/+lq7TZs2dfqe4/F4qKys1FLW+qE/77v4+HhMnToVIpEItra2WLBg\n",
       "AbKysrSQrX7pT+0OHz6MCRMmQCAQwM3NDe+9954WMtU/f/vb3xAYGAgLCwvY2dlh/vz5SEtL6/G4\n",
       "mzdvIiQkBGZmZnB2dsaWLVu0kK1+6U/tWlpaEBkZCT8/PxgZGSEsLExL2eqX/tTuzJkzCA8Ph6Oj\n",
       "IwQCAfz8/LB//34tZTzMmuvGxkaMHz8eu3fvhqmpaa+3BWxtbcWSJUsQEhIyYi993t/a/fjjjygt\n",
       "LVXdRtpf/v7UbcOGDdi7dy927NiBjIwMnDhxAiEhIVrIVr/0tXavvfaa2nutpKQEISEhCAsLg42N\n",
       "jZay1g99rV12djYWLFiA0NBQpKamIiEhAc3NzZg7d66WMtYffa3diRMn8Oyzz+KFF15AWloaYmJi\n",
       "8MEHH+Djjz/WUsb6IykpCS+99BKSk5ORmJgIAwMDzJ49GzU1NV0eU19fjzlz5sDBwQEpKSnYvXs3\n",
       "duzYgZ07d2oxc93rT+0UCgVMTU2xbt06PPHEEyO2P+lP7ZKTk+Hn54dvv/0WaWlpWLNmDVatWoVD\n",
       "hw5pJ2k2TAmFQhYbG9ur2FdeeYUtX76cHThwgAmFwkHOTP/1pnZ5eXmM4ziWkpKipaz0X2/qlpGR\n",
       "wQwNDVlGRoaWshoa+vL3tUNBQQHj8/ns0KFDg5TV0NCb2h05coTx+XymVCpVY4mJiYzjOFZVVTXY\n",
       "Keqt3tRu6dKlbOHChWpje/bsYS4uLoOZ2pDQ0NDA+Hw+O3bsWJcxMTExzMLCgjU3N6vGtm7dypyc\n",
       "nLSRot7qTe0etnbtWhYaGjrIWQ0Nfa1dh4iICLZo0aJBykrdsJq57o/jx4/j+PHj2LNnDxgtP++z\n",
       "hQsXQiKRYPr06fj22291nY7eO3r0KNzd3REfHw93d3fIZDJERkaioqJC16kNOfv27YOVlRUWLVqk\n",
       "61T0XnBwMIRCIT799FMoFArcu3cPBw4cwOTJk2FlZaXr9PRaa2srjI2N1cZMTExQWFiIgoICHWWl\n",
       "H+rr66FUKiEWi7uMSU5OxowZM9Rq+Oijj6K4uBhyuVwbaeql3tSOdK6/taurq9Pav3cjurkuLi7G\n",
       "qlWrEBcXBzMzM12nM6SYm5vj/fffx5EjR3DixAnMmjULixcvRlxcnK5T02u5ubmQy+U4fPgwvvji\n",
       "Cxw8eBAZGRl48skn6Ye7PlAoFPj888+xbNkyGBoa6jodvefg4ID4+Hi8+eabMDExgaWlJdLS0vDD\n",
       "Dz/oOjW999hjj+Ho0aM4deoUlEol7ty5g/fffx8AUFJSouPsdOvll1/GxIkTERQU1GVMaWkpJBKJ\n",
       "2ljH/V9fcG4k6U3tSOf6U7tjx44hMTERq1atGsTM/mvAL38+lCxbtgxr1qxBYGCgrlMZcqytrdW2\n",
       "V/T390dVVRXeffddPPvsszrMTL8plUq0tLTg4MGD8PDwAAAcPHgQXl5eSElJofdiL508eRKFhYVY\n",
       "uXKlrlMZEnJzc7FgwQJERUXhmWeeQX19Pf7v//4PERERSExMHLFrOXtj5cqVyMnJQXh4ONra2mBh\n",
       "YYH169ervmA7Um3YsAEXLlzA+fPnu33/0HtLU29rRzT1p3Y///wznn32WezZswcBAQGDnGG7kfsv\n",
       "A4DTp08jOjoahoaGMDQ0xPPPP4/GxkYYGhris88+03V6Q05gYOCI3H2gLxwcHGBgYKBqrAHAw8MD\n",
       "fD5/xH/E3BeffPIJgoOD4e3tretUhoR//OMfcHFxwfbt2+Hn54cZM2bgyy+/RFJSEpKTk3Wdnt7b\n",
       "tm0bGhsbUVBQgNLSUtUPwe7u7jrOTDdeffVVfP3110hMTISbm1u3sfb29hoz1GVlZarHRpq+1I6o\n",
       "60/tzp8/j7lz52LLli1YvXr14Cb4kBE9c33r1i21+99//z3++te/4sqVK3B0dNRRVkNXamoq1a0H\n",
       "06dPx4MHD5Cbm6v6jzk3NxcKhQJSqVTH2Q0NxcXFiI+Px759+3SdypDBGNOYZe24r1QqdZHSkMNx\n",
       "HBwcHAAAhw4dwrRp02Btba3jrLTv5ZdfxpEjR3D69GmMHj26x/igoCD8+c9/RktLi2rd9alTp+Dk\n",
       "5DTi/s3ra+3If/WndmfPnsW8efOwefNmrF+/fpAzVDesZq4bGxuRmpqK1NRUKJVKyOVypKam4u7d\n",
       "uwCAjRs3Yvbs2ap4Hx8ftZujoyN4PB58fHxgaWmpq9PQib7WLjY2FocOHcLt27eRmZmJ9957DzEx\n",
       "MVi3bp2uTkEn+lq32bNnw9/fH8uXL0dqair+85//YPny5Zg6darWPq7SF32tXYfPP/8cQqEQERER\n",
       "2k5Zb/S1dvPnz8e1a9ewZcsWZGVl4dq1a4iKioKrqysmTZqkq9PQib7WrqqqCnv37sXt27eRmpqK\n",
       "l19+Gd9++y127dqlq1PQmbVr1+LAgQOIi4uDhYWFalvMxsZGVcyv6/fMM8/AzMwMkZGRSEtLw3ff\n",
       "fYft27djw4YNujgFnelP7QAgPT0dqampqKysRENDA65fv47U1FRtp69T/andmTNn8Pjjj2PNmjVY\n",
       "unSp6hitbR6glT1JtOT06dOM4zjGcRzj8Xiq30dFRTHGGIuMjGQymazL4/fv38/Mzc21la5e6Wvt\n",
       "YmNjmY+PDxMIBEwkErHAwEAWFxenq/R1pj/vuZKSEvb0008zc3NzZmdnx5577jlWXl6ui/R1qj+1\n",
       "UyqVTCaTsbVr1+oiZb3Rn9odOXKETZo0iQmFQmZnZ8fCw8PZ7du3dZG+TvW1dpWVlSwoKIgJhUIm\n",
       "EAjYnDlz2OXLl3WVvk79umYdt+joaFVMZ++9mzdvspkzZzITExPm6OjINm/erO3Uda6/tXNzc9N4\n",
       "v/J4PG2nr1P9qV1kZGSnx3TXAw5ozozRFgWEEEIIIYQMhGG1LIQQQgghhBBdouaaEEIIIYSQAULN\n",
       "NSGEEEIIIQOEmmtCCCGEEEIGCDXXhBBCCCGEDBBqrgkhhBBCCBkg1FwTQgghhBAyQKi5JoQQLQkN\n",
       "DUVYWJiu09CayMhIyGSyfh27adMm8Hg8lJeXD3BWhBAyuKi5JoSMCOnp6ViyZAlkMhlMTU3h5OSE\n",
       "0NBQREdHq8XFxMQgNjZ2UHLgOA4cxw3Kc3e4cOECoqOjUVdX16v4AwcOgMfj4fLly50+Pm/evH43\n",
       "yNo4XwB45513cPTo0UF/HUII6Q1qrgkhw15ycjL8/f2RkpKC5cuX4+OPP8aaNWtgaWmJ7du3q8XG\n",
       "xMTgwIEDg5KHNi6I29fmujf62yB/+umnyMzMHLA8ukLNNSFEnxjoOgFCCBlsW7duhbm5Oa5cuQKx\n",
       "WKz2WEVFhY6yGlzaaOR7YmCgnf9iOI7Ti/MlhBCAZq4JISNATk4OfHx8NBprALC1tVX93s3NDenp\n",
       "6UhKSgKPxwOPx1MtiehYPlFQUKB2/JkzZ8Dj8XD27Fm18U8++QSjRo2CmZkZpkyZgnPnznWaW0tL\n",
       "C6Kjo+Hp6QkTExM4Oztjw4YNaGpqUovj8XhYs2YNvv/+e/j6+sLExAS+vr748ccfVTGbNm3C66+/\n",
       "DgCQyWSqc/h1bgPhq6++QmBgIMzMzGBlZYWIiAjk5+erxXS25rqpqQnr16+HjY0NRCIRwsPDUVhY\n",
       "CB6Pp7FEBwBqa2sRGRkJsVgMS0tLLF++XK02PB4PjY2NiI2NVZ3vSFrXTgjRPzRzTQgZ9mQyGc6f\n",
       "P48bN25g/PjxXcbt3r0b69atg7m5Od544w0AgFAo7PPr7du3Dy+88AKCg4Px6quvIj8/HwsWLIBY\n",
       "LIarq6sqjjGGp556CmfPnsWqVavg4+OD9PR0xMTEIC0tTa1xBtqXt/zwww948cUXIRQK8eGHH2LR\n",
       "okUoKCiAlZUVFi1ahKysLBw6dAi7du2CjY0NAMDb27vHnGtra1FZWakx3tbWpjG2bds2vPHGG3j6\n",
       "6aexYsUKVFdX46OPPkJwcDCuX7+uel1Ac0lJZGQkjhw5gmXLliEoKAhnzpzBE0880WksACxZsgSj\n",
       "Ro3Ctm3bcPXqVXz22Wews7PDtm3bAAAHDx7E888/jylTpmDVqlUAAIlE0uP5EkLIoGGEEDLMJSYm\n",
       "Mj6fz/h8Pps8eTL74x//yI4fP86am5s1YseOHcvCwsI0xvfv3884jmNyuVxt/PTp04zjOJaUlMQY\n",
       "Y6y1tZXZ2dkxf39/1tbWpor7/PPPGcdxas8dFxfHeDweO3v2rNpzxsXFMY7j2E8//aQa4ziOGRsb\n",
       "s5ycHNXYjRs3GMdx7KOPPlKN7dixo9M8u9JxXt3dZDKZKl4ulzMDAwO2ZcsWtefJyclhJiYm7C9/\n",
       "+Ytq7A9/+ANzc3NT3b969SrjOI6tX79e7dioqCjGcRyLjo5Wjb399tuM4zi2YsUKtdiFCxcyGxsb\n",
       "tTGhUMiioqJ6db6EEDLYaFkIIWTYCwsLw7lz5zBv3jykpaVh586dmDdvHiQSyYB/eTElJQUVFRVY\n",
       "uXKl2prj3//+97C0tFSLPXz4MEaPHg0fHx9UVlaqbjNnzgTHcTh9+rTGebi7u6vujxs3DiKRCHl5\n",
       "eb857z179iAhIUHtdurUKUyZMkUt7rvvvoNCoUBERIRaziKRCL6+vho5P+zkyZMAgBdffFFtfN26\n",
       "dV0es3LlSrX706dPR1VVFRoaGvp6ioQQohW0LIQQMiIEBQXh+++/h0KhQFpaGo4dO4YdO3Zg+fLl\n",
       "kEqlA7ZOVy6XAwA8PT3Vxvl8vsb64zt37iAzM1Nt3XcHjuM0vmz58JKSDmKxGDU1Nb81bQQGBmLy\n",
       "5Mka4x988AHKysrUcga6XmoyatSoLl9DLpeD4ziNmO6O+fU5d6ybr6mp6deSHUIIGWzUXBNCfbfL\n",
       "cAAABFhJREFURhQ+n4/x48dj/PjxCAoKwqxZs/Dll1/22Fx3tR2dQqHo9WuzX+1ooVQqMXbsWOze\n",
       "vbvTeEdHR43ce/O8g0mpVAJon4XubDcQU1PTAX09fThnQgjpC2quCSEjVmBgIACgpKRENdZVE90x\n",
       "Y1pbW6s2m9oxU91BKpUCaJ/hnTVrlmr8wYMHyMvLw8SJE1VjHh4euHr1Kh555JHfeCb/NdgXbfHw\n",
       "8AAAuLi4YMyYMX06ViqVgjGG7OxstZnv7Ozs35STNi5UQwghvUVrrgkhw15iYmKnM53x8fEA1Jc4\n",
       "CAQCVFdXa8R2LF1ISkpSjSkUCnzyySdqcYGBgbC1tcWnn36qttPGF198oXFhl8WLF6OsrAx79+7V\n",
       "eL2WlpZ+rSsWCAQA0Ok5DIRFixaBz+dj8+bNnT5eVVWldv/hxvd3v/sdgPYL9Txsz549vymnrv7M\n",
       "CCFEF2jmmhAy7K1fvx6NjY146qmn4O3tDaVSiWvXruHgwYOwsbHBK6+8oooNDAxETEwMNm/eDE9P\n",
       "TwiFQjz55JMYO3Yspk6dio0bN6K6uhpisRj//Oc/NZaFGBgYYOvWrVi9ejXCwsKwePFi5Ofn48CB\n",
       "A3B3d1dr8p977jl88803WLt2LZKSkhAcHAzGGDIzM3HkyBF88803mDlzZrfn9usfGjpm4zdu3Iil\n",
       "S5fCyMgIs2bN6nRdd289/BoymQzbtm3Da6+9BrlcjvDwcFhaWiIvLw//+te/sHjxYrz99tudHuvv\n",
       "749Fixbho48+Ql1dHaZMmYKkpCTVOu7+zkAHBAQgISEB77//PpycnCCRSGiva0KI7uhqmxJCCNGW\n",
       "kydPspUrVzIfHx8mEomYsbExc3d3ZytXrmT5+flqseXl5Sw8PJxZWFhobEOXm5vL5syZw0xMTJiD\n",
       "gwN78803WUJCAuPxeKqt+Drs3buXubu7MxMTEzZ58mR2/vx5FhoaqrHN34MHD9h7773Hxo0bx0xM\n",
       "TJhYLGYBAQFs06ZNrLq6WhXHcRxbs2aNxrm5ublpbEO3bds25urqyvh8fqe5PWz//v2Mx+OxS5cu\n",
       "dfr4vHnz1GrQ4ejRoywkJISZm5szgUDAvL292YsvvsjS09NVMZGRkRrH3r9/n7300kvM2tqaCYVC\n",
       "Fh4ezjIyMhjHcezdd99VxW3atInxeDxWVlbWab4PbzWYlZXFHnnkESYUCjW2OySEEG3jGKNvhRBC\n",
       "CNGd1NRU+Pv7Iy4uDkuXLtV1OoQQ8pvQmmtCCCFa09zcrDG2a9cu8Pn8HpfAEELIUEBrrgkhhGjN\n",
       "9u3bcfXqVYSFhcHAwAAnTpzAyZMnsXr1ajg5Oek6PUII+c1oWQghhBCtSUhIQHR0NNLT09HQ0ACp\n",
       "VIply5bhjTfeAI9HH6YSQoY+aq4JIYQQQggZIDRNQAghhBBCyACh5poQQgghhJABQs01IYQQQggh\n",
       "A4Saa0IIIYQQQgYINdeEEEIIIYQMEGquCSGEEEIIGSD/H4ZilxP8LCf0AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48038424a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from stats import plot_gaussian\n",
    "\n",
    "plot_gaussian(mean=1.8, variance=0.1414**2, xlabel='Student Height')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probably this is immediately recognizable to you as a 'bell curve'. This curve is ubiquitous because under real world conditions most observations are distributed in such a manner. In fact, this is the bell curve the student heights given earlier. \n",
    "\n",
    "This curve is not unique to heights - a vast amount of natural phenomena exhibits this sort of distribution, including the sensors that we use in filtering problems. As we will see, it also has all the attributes that we are looking for - it represents a unimodal belief or value as a probability, it is continuous, and it is computationally efficient. We will soon discover that it also other desirable qualities that we do not yet recognize we need."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nomenclature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A bit of nomenclature before we continue - this chart depicts the *probability density* of of a *random variable* having any value between ($-\\infty..\\infty)$. What does that mean? Imagine we take an infinite number of infinitely precise measurements of the speed of automobiles on a section of highway. We could then plot the results by showing the relative number of cars going at any given speed. If the average was 120 kph, it might look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAukAAAGHCAYAAAAN0sy8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlYVOfdPvB7ZmBYVFBkFRBcMe4CKouIG7gkalwwBqPR\n",
       "mlhTa1zqm7z29W1rkzT1TWpi0mhMYtUk7kvihgquiOCCBhfcRRGFQUEEZIeZ3x/+GH0EQRR4Zpj7\n",
       "c11eV+eec4YbegJfhvOco9DpdDoQEREREZHBUMouQEREREREIg7pREREREQGhkM6EREREZGB4ZBO\n",
       "RERERGRgOKQTERERERkYDulERERERAaGQzoRERERkYF5riF96dKlaNWqFaysrODr64uYmJgqtz93\n",
       "7hyCg4NhbW0NNzc3fPTRR8LzW7duRWhoKBwdHWFjYwM/Pz/s2LFD2GbVqlVQKpXCP5VKheLi4hp+\n",
       "ikRERERExqXaIX3Dhg2YPXs2FixYgISEBAQEBGDo0KFISUmpdPucnByEhITAxcUF8fHxWLJkCT77\n",
       "7DMsXrxYv010dDQGDRqEiIgIJCQkYNiwYRg1alSF4d/a2hrp6enQaDTQaDRIS0uDWq1+yU+ZiIiI\n",
       "iMiwKaq742jv3r3RvXt3LF++XJ+1b98eY8eOxT/+8Y8K2y9btgzz589Heno6LCwsAACffPIJli1b\n",
       "htu3b1f5cYKCgvD5558DePRO+syZM5Gbm/tCnxgRERERkbGq8p304uJinD59GqGhoUIeGhqK2NjY\n",
       "SveJi4tDUFCQfkAv3z41NRXJycnP/Fg5OTmws7MTsoKCAnh6esLd3R3Dhw9HQkJCtZ8QEREREZGx\n",
       "q3JIz8jIQFlZGZycnITc0dERGo2m0n00Gk2F7csfP2ufb775BqmpqZg4caI+69ChA1auXInt27dj\n",
       "3bp1sLS0RGBgIK5du1b9Z0VEREREZMTMavsFFQpFjbbfsmULPvjgA2zcuBHu7u763M/PD35+fvrH\n",
       "AQEB6NGjB77++mssWbJEn2dnZ798aSIiIiIiSWxtbStkVb6Tbm9vD5VKhfT0dCFPT0+Hi4tLpfs4\n",
       "OztXeMe8fH9nZ2ch37x5MyZNmoSffvoJr776apXllUolvL29cfXq1Sq3IyIiIiIydlUO6Wq1Gj4+\n",
       "PoiMjBTyqKgoBAQEVLqPv78/jhw5gqKiImF7V1dXeHh46LONGzdi0qRJWL16NUaPHl1tUZ1OhzNn\n",
       "zqBFixbVbktEREREZMyqPd1l7ty5mDhxInr16oWAgAB8++230Gg0mD59OgBg/vz5OHnyJPbt2wcA\n",
       "CA8Px8KFCzF58mQsWLAAly9fxqJFi/C3v/1N/5rr16/HxIkTsXjxYvTp00f/zrtardYvHl24cCH8\n",
       "/f3Rtm1b5OTk4KuvvkJiYiK+++67Z3at7E8F9Pzi4+MBAL6+vpKbkGw8FqgcjwUqx2OByvFYqB3V\n",
       "nbJd7ZA+btw4ZGZm4uOPP0ZaWhq6dOmCiIgI/fnjGo0GSUlJ+u1tbGwQFRWFGTNmwNfXF3Z2dpg3\n",
       "bx7mzJmj32b58uXQarWYNWsWZs2apc/79euHAwcO6ItPmzYNGo0Gtra28Pb2RnR0NA8IIiIiImrw\n",
       "qr1OuqF78rcQvpP+cvibMZXjsUDleCxQOR4LVI7HQu2oboat9o6jRERERERUvzikExEREREZGA7p\n",
       "REREREQGhkM6EREREZGB4ZBORERERGRgOKQTERERERkYDulERERERAaGQzoRERERkYHhkE5ERERE\n",
       "ZGA4pBMRERERGRgO6UREREREBoZDOhERERGRgeGQTkRERERkYMxkFyAiIrly8x/gbtYdZGRrkJlz\n",
       "F3kFucgveojC4nw8ePAAAPBbWiSsLBrB2qIxmjRqBntbJ9jbOsOxmSsszC0lfwZERA0Ph3QiIhOi\n",
       "0+mQlpmMi8m/4UbaJdxKv4YHDzOr3e9OVuW5QqGEs50bWjq1Q1vXjvBq2R1NGzev5dZERKaHQzoR\n",
       "UQNXpi3D5VtnkHD1KC4m/4bsvPu19to6nRZpmbeQlnkLxy/sBwC4NG+Jrm384OMVBGc791r7WERE\n",
       "poRDOhFRA3Xn3k0cv3gApy5HIzf/Qb193PKhfe+JjXC194Rvh37w6zQQjSyb1FsHIiJjxyGdiKgB\n",
       "0eq0uHjzNA6e3oYrt8891z4qlRmc7dzhYOuC5rZOsG1kB2vLxrBUWyPpehIAoFVrT+QXPkReYS4e\n",
       "PMxAxgMN7j5IRUa2psrXvpNxE3diViHi2Fr07NAPfbu9ihb2Hi/9eRIRNXQc0omIGgCtTotTl48g\n",
       "8uQmpN+/XeW2anNLtHfrgg4e3eHp7IUW9h4wU5lXum1xlgoA0K2tb6XP5xc+RMrd67ieegGXb51B\n",
       "suYKtDpthe1KSosRez4Ssecj0blVTwzzfxNuDq1r+FkSEZkODulEREZMp9Ph/I2T2BW7BqmZyc/c\n",
       "zkJthR5tA+Dj1RetW3SEuVnlQ3lNWVs2hlfLbvBq2Q3D/N5EfuFDnL1+HKeuRONKyjnoKhnYz984\n",
       "ifM3TqJbW38M8wuHS3Oet05E9DQO6URERurOvRvYdOg7JKVefOY2bV07IbDLEHRp0wtqM4s672Rt\n",
       "2Rh+nQbCr9NA5OQ9wPGLBxBzJgJZDzMqbHvmWhzOXT+OoG7DMNRvPKwtGtd5PyIiY8EhnYjIyBQU\n",
       "5WP3sXU4fGZXpe9UKxVK9GjfB/17jEBLp7YSGj5i06gpQnxHY4D3SJy9fhwHTv+KZM0VYRutTovD\n",
       "CTtx6vIRDA+ciN4dB0Cp4H32iIg4pBMRGZGz149h48HlyMmreOFyBRTw8eqLoX7j4dDURUK7yqmU\n",
       "KvRoF4Dubf1x4eYp7Dq2FrfvJgnbPCzIxrp9/8aJiwcxIWQm7G2dJbUlIjIMHNKJiIxAQVEethz+\n",
       "AScuHqz0+Y6ePhgeMBGuDp71W6wGFAoFOrXyRUdPH5y5FodtMauRmZMubHP9TiL+uWY2RgZOQmDX\n",
       "IXxXnYhMFod0IiIDdyXlHNZELqn0vG47G0eMCX4HXVr3ktDsxSgUCnRvF4COrXxw4NSviDq5BSVl\n",
       "xfrni0sKsenQdzhz/RgmDp4N20Z2EtsSEcnBIZ2IyEBptWXYc2Ij9h7fCB10wnNKpQqDfEYhtGcY\n",
       "1OZ1vyC0LqjNLDCk9xvo+Uo/bDjwLS4l/yY8fyXlLP5vzRxMGjIXXi27SWpJRCQH/45IRGSAcvMf\n",
       "YNmvf8ee4xsqDOguzVviT298htcC3jLaAf1JzW2c8N7Iv2D8wBmwUFsJz+UWZGPpL3/Drrg1KNOW\n",
       "SWpIRFT/+E46EZGBuZF2Gf+J+D9kP8wUcgUUGOAzEsP8wmFuppbUrm4oFAoEdA5Bh5bdsSbqK1x9\n",
       "4m6pOuiw98QmJGuuYvLQebC25KUaiajh4zvpREQGJP7SYXy9ZUGFAb2JlS1mjF6IkX0mN7gB/Ul2\n",
       "Ng6YMepvGNp7PBRQCM9dupWAxRs+QHrWHUntiIjqD4d0IiIDoNVpsStuDX7c+wVKy0qE59q06IgP\n",
       "wr9Ae/euktrVL6VShaF+4zFj9EI0sW4qPHf3QSoWr/8vXLh5WlI7IqL6wSGdiEiyktJirNr9Ofae\n",
       "2FThuYE+r+OPYz6CbWPTu8JJe/eu+DD8C3i6eAl5QXE+vtv+MeLOR0lqRkRU9zikExFJVFCUj2+3\n",
       "fYSEq7FCrlKZ4a3QWRjZZzJUSpWkdvLZNGqGmaM/Rq9X+gu5VqfFuv3fPFpYq9M9Y28iIuPFIZ2I\n",
       "SJLc/Af4eusCYZEk8Oj88/fHVBxMTZW5mTkmhLyP14OmQPHUzY0ijq3DxgPfQssrvxBRA8OruxAR\n",
       "SZCZnY6lv/wN97LThNzJzg3vjfwL7GwcJTUzTAqFAgO8R8Le1gmrdy8Wbn509Pxe5BXl4u3Bc6FS\n",
       "8ccaETUMfCediKiepd+/jS82/XeFAd3T2Quzx/6DA3oVurbxw4zRC2FtIV6GMeFqLP4T8X8oKS15\n",
       "xp5ERMaFQzoRUT1Kv38bX2/5X+TkZQl5B48emDF6IRpZ2UhqZjxat3gFs8I+RbPG9kJ+LukEVuz6\n",
       "J0pKi5+xJxGR8eCQTkRUT/QDer44oPu0D8K04X+GhbmlpGbGx6W5O2aFfQp7W2chv3DzFL7b/gmK\n",
       "S4okNSMiqh0c0omI6kH6/dv4asuCCgN6QOcQTBwyB2Yqc0nNjJedjQPeH/sJHJu5CvnllDP4bvvH\n",
       "fEediIwah3Qiojp2N+sOvtqyALn5D4Q8oHMoxg14D0oFvxW/qKaNm+P9MZ/ApXlLIb9y+xxWRnyG\n",
       "srJSSc2IiF4OfzIQEdWhrNx7+GbrXysM6IGdB2PcgOkc0GuBTaOmmDnmY7g6tBLy8zdO4qfIL3l5\n",
       "RiIySvzpQERUR3Lzs7H0l4XIepgh5IGdByNswO85oNeixlY2mDFqIZzt3IX89JUYrN+/FFqdVlIz\n",
       "IqIXw58QRER14NGdRP+O9KzbQu7XcSAH9DrS2MoGM0YvrLCY9NiF/fg1eiXvTEpERoU/JYiIallJ\n",
       "aTG+3/kPpNy9LuTd2vpj/MA/cECvQ7aN7PDH0X+vcHnGQwk7cOD0NkmtiIhqjj8piIhqkVanxU97\n",
       "v8S12+eF3Mu9GyYNngulUiWpmemws3HEjNEL0cS6qZBvi1mFU5ejJbUiIqoZDulERLVox9EfkXAt\n",
       "Vsg8nNvjndf+G+ZmvMxifXFs5oo/vP43WKqthfznyK9wJeWcpFZERM+PQzoRUS05cnY39p/6Vcic\n",
       "7dwxfcQCWKitJLUyXa4Onnjntf+GSmmmz8q0pfhh56dIzbgprxgR0XPgkE5EVAsSb8Rj86HvhczG\n",
       "uhmmj/xfNLKykdSK2rt3xYSQmUJWWJyPb7d9hOy8+5JaERFVj0M6EdFLSrmbhJW7P4fuicv8qc0s\n",
       "MG3E/8DOxlFiMwIA3w7BGBE4ScgePMzEDzv/ybuSEpHB4pBORPQScvKy8P2OT1BcUqjPFAolJg+d\n",
       "h5ZObSU2oycN9BmFvt2GCVmy5grW7fuGl2YkIoPEIZ2I6AWVlJZgxa5FePAwU8jHBr+Dzq17SmpF\n",
       "lVEoFBjVdype8fAW8vjLhxEVv0VSKyKiZ+OQTkT0AnQ6HTYdWo4baZeEvF/34Qh66h1bMgwqpQqT\n",
       "h/4JTs3chHxn7M84e/24pFZERJXjkE5E9AKOnI3AscR9QubVshtGBk2WU4iei5VFI0wb8T+wtmgs\n",
       "5D/u/QJ37t2Q1IqIqCIO6URENXQl5Sy2Hl4hZA62Lpgy9L+g4s2KDJ5DUxf87tUPhBtLFZcU4vud\n",
       "nyKvMFdiMyKixzikExHVQGZ2Ov4T8Rm0T1zJxUJthXeG/xnWlo2r2JMMSXv3rhgb/K6Q3c+5ix/3\n",
       "fCH8f0tEJAuHdCKi51RSWowVuxYh/4l3WxVQYNLgOXBp7i6xGb2IPl2HoE/XoUJ2Mfk09hzfIKkR\n",
       "EdFjzzWkL126FK1atYKVlRV8fX0RExNT5fbnzp1DcHAwrK2t4ebmho8++kh4fuvWrQgNDYWjoyNs\n",
       "bGzg5+eHHTt2VHidLVu2oGPHjrC0tESnTp3w66+/VtiGiKi+bDn8PW7fSxKyYf7h6NK6l6RG9LJG\n",
       "9/0dPF28hGzP8Q1IvBEvqRER0SPVDukbNmzA7NmzsWDBAiQkJCAgIABDhw5FSkpKpdvn5OQgJCQE\n",
       "Li4uiI+Px5IlS/DZZ59h8eLF+m2io6MxaNAgREREICEhAcOGDcOoUaOE4T8uLg7jx4/HxIkTcebM\n",
       "GUyYMAFhYWE4ceJELXzaREQ1c/zCAcSejxKybm38ENpzrKRGVBvMVOb43bAP0MTKVsh/3PsFMrI1\n",
       "kloREQEKXTV3cejduze6d++O5cuX67P27dtj7Nix+Mc//lFh+2XLlmH+/PlIT0+HhYUFAOCTTz7B\n",
       "smXLcPv27So/TlBQED7//HMAwBtvvIEHDx5g7969+m1CQkLg4OCAtWvX6rPs7Gz9/7a1Fb/JUs3E\n",
       "xz9658jX11dyE5KNx4IoNeMm/rXhA+HulA5NW2De+M9hZWEtsVndM5Vj4ertc/hm61+F89FdHVph\n",
       "zrh/Qm1mIbGZ4TCVY4Gqx2OhdlQ3w1b5TnpxcTFOnz6N0NBQIQ8NDUVsbGyl+8TFxSEoKEg/oJdv\n",
       "n5qaiuTk5Gd+rJycHNjZ2ekfHzt2rEYfl4ioLhQU5WPFrv8TBnRzMzV+N+yDBj+gm5J2bl0wPHCi\n",
       "kN25dwObD34nqRERmboqh/SMjAyUlZXByclJyB0dHaHRVP5nQI1GU2H78sfP2uebb75BamoqJk58\n",
       "/A3yWa/zrNcgIqptOp0O6/b9G/cepAr5uP7T4ergKacU1ZkB3q+jWxs/ITt2YT/iLx2W1IiITJlZ\n",
       "bb+gQqGo0fZbtmzBBx98gI0bN8Ld/eWujlD+5xd6Ofw6UjlTPxYupZ1EQpL417u2Tt2hyrcxua+N\n",
       "qXy+r9gH4UbqVeQUZOqztVHfIOdeEWys7KrY03SYyrFA1eOx8HLatWtX5fNVvpNub28PlUqF9PR0\n",
       "IU9PT4eLi0ul+zg7O1d4t7t8f2dnZyHfvHkzJk2ahJ9++gmvvvrqc73O069BRFQX7uelI/6GeEdR\n",
       "u0bO6N16iKRGVB/UZhYI9hoNpeLxjY5KtcWIvrwVZdpSic2IyNRU+U66Wq2Gj48PIiMjMWbMGH0e\n",
       "FRWFsLCwSvfx9/fHhx9+iKKiIv156VFRUXB1dYWHh4d+u40bN2Ly5Mn48ccfMXr06EpfJyoqCvPm\n",
       "zRM+bmBg4DP7cgHDy+FCECpn6sdCUUkhPl+3ClpdmT6zVFtjxti/wqFp5W9QNFSmeixYNlNi08HH\n",
       "F0y4n6dBSv45jO33bhV7NWymeixQRTwWaseTC0crU+0lGOfOnYtVq1ZhxYoVuHjxImbNmgWNRoPp\n",
       "06cDAObPn49Bgwbptw8PD4e1tTUmT56MxMREbN26FYsWLcLcuXP126xfvx4TJkzAokWL0KdPH2g0\n",
       "Gmg0Gty/f1+/zaxZs3DgwAEsWrQIly5dwqeffopDhw5h9uzZNf4iEBHVxC/RK5CeJV6NavzAP5jc\n",
       "gG7K+nQZgm5t/YUs+swunL1+TFIjIjI11Q7p48aNw5dffomPP/4YPXr0QGxsLCIiIvTnj2s0GiQl\n",
       "Pb65h42NDaKiopCamgpfX1/MnDkT8+bNw5w5c/TbLF++HFqtFrNmzUKLFi30/8aOfXy9YX9/f6xf\n",
       "vx6rVq1Ct27d8PPPP2Pjxo3o2bNnbX7+RESC364erXA9dL+OA+Hdvo+kRiSDQqHAm4NmwM7GUcjX\n",
       "RH2N+zl3JbUiIlNS7XXSDR2vk157+OcrKmeqx8L9nLtYtGY2Corz9ZljM1f815v/goW5pcRm8pjq\n",
       "sVAuWXMFX2yaD6328alPbVw7Yebov0OpVFWxZ8Nj6scCPcZjoXa81HXSiYhMRZm2DKv3LBYGdJXK\n",
       "DG8P+ZPJDugEeDi3x/AA8frp1+8kYv/pbZIaEZGp4JBORARgz/ENuJF2SchGBE6Cu2NrSY3IUPT3\n",
       "HoEOHj2ELCJuLVLuXpfUiIhMAYd0IjJ5N9IuIfLkZiHr6OmDft2HS2pEhkSpUGLCoJloZNlEn5Vp\n",
       "S/Hjni9QXFIksRkRNWQc0onIpBWVFOLnvUug02n1mY11M0wImVnjm7NRw2Xb2A7jB/5ByNKzbmP7\n",
       "0dWSGhFRQ8chnYhM2rYjq3AvO03IwkNmool1U0mNyFB1a+sPv44DhSz6TAQu3DwlqRERNWQc0onI\n",
       "ZF1M/g0x5/YIWZ8uQ9DR01tSIzJ0o4PfQXNbJyFbG/Vv5OZXfVMSIqKa4pBORCYprzAXa6K+EjIH\n",
       "WxeMDJospxAZBUu1FSYNngOF4vGPz5z8LKzf/w2M/IrGRGRgOKQTkUnadPA75ORl6R8rFEq8NXg2\n",
       "L7dI1Wrl0gGDe4YJ2bmkEzh56ZCcQkTUIHFIJyKTc+ryEZy+ckTIQnzHoJWLl6RGZGwG9wqDh3N7\n",
       "Idty+Ac8eJgpqRERNTQc0onIpDx4mIlNB5cLmZtDawzpPU5SIzJGKpUZJobOgrlKrc8KivKwfv9S\n",
       "nvZCRLWCQzoRmQydToe1+/6N/KKH+sxMZY6Jg2fDTGUusRkZI8dmrngt4C0hu3DzFI5fOCCpERE1\n",
       "JBzSichkHEvch0vJvwnZawET4NK8paRGZOyCu7+K1i1eEbKt0SuQlXtPUiMiaig4pBORScjKzcAv\n",
       "R1YKWVvXTujXY4SkRtQQKJUqTAh5H+Zmj097KSzOx7p9vNoLEb0cDulE1ODpdDpsOLAMhcX5+kxt\n",
       "ZoHwkJlQKvhtkF6OQ1MXjAicJGSXbiUgLjFKUiMiagj404mIGryTlw5VuCvk8MCJsLd1ltSIGpqg\n",
       "bsPQ1rWTkP0S/R/cz7krqRERGTsO6UTUoOXkZWHr4RVC1trlFQR1GyapETVESoUS4SEzoX7iOvtF\n",
       "JYVYG/U1tDqtxGZEZKw4pBNRg6XT6bDx4HLhai7mKjXCQ/7I01yo1tnbOmPkU6e9XLl9DscS90lq\n",
       "RETGjD+liKjB+u3qUZy9fkzIhvmHw7GZq6RG1NAFdh2C9m5dhGzbkVXIfnhfUiMiMlYc0omoQcrN\n",
       "z8bmQ98LmYdTO/TvMVxSIzIFSoUSb4b8UTjtpaA4H5sOLefVXoioRjikE1GDtPXwD3hYkK1/rFKZ\n",
       "Pbqai1IlsRWZguY2TnjNf4KQnb1+HAnX4iQ1IiJjxCGdiBqcs9eP49SVI0I2pNcbvGkR1Zu+3YbB\n",
       "w7m9kG0+9B3yCnMlNSIiY8MhnYgalPyih9h48Fshc3VohUE+oyQ1IlOkVKoQPuiPUCnN9Flu/gP8\n",
       "emSVvFJEZFQ4pBNRg7Ij5ifk5GXpHz+6I+RMqFRmVexFVPtcmrdEiO8YITt+YT8u3zojqRERGRMO\n",
       "6UTUYFy/cwFHz+8VskE+o+Hm0FpSIzJ1IT3HwsnOTcjW71+KopJCSY2IyFhwSCeiBqGktATrDywV\n",
       "MoemLTC4V5ikRkSAuZk5wgf9EQoo9FlmTjoi4tZKbEVExoBDOhE1CPtPbUX6/dtCNn7gezA3U0tq\n",
       "RPRIK5cOFe5weyhhJ5I1VyU1IiJjwCGdiIxeetYd7D25Scj8Og5Eu6duKkMky/CAt9CsiYP+sU6n\n",
       "xbp9/0ZZWanEVkRkyDikE5FR0+l02LB/qTDsNLayxcigyfJKET3FQm2FNwa8J2Spmck48Nt2SY2I\n",
       "yNBxSCcio3bswn5cu5MoZKP7/g6NLJtIakRUuY6e3vDtECxke46vR2Z2uqRGRGTIOKQTkdHKyXuA\n",
       "bU9dd7qDRw/4ePWVU4ioGqP7ToX1E79AlpQWY9Oh76DT6SS2IiJDxCGdiIzWL9ErkF/0UP/Y3EyN\n",
       "N/pPh0KhqGIvInkaW9lgZJ+3hezCzVNIuBYrqRERGSoO6URklC7cPI1TV44I2TC/N9Hc1klSI6Ln\n",
       "49dxINq06ChkWw7/gIKiPEmNiMgQcUgnIqNTVFKIjQe/FTJXh1bo12OEpEZEz0+hUGDcgPegUj6+\n",
       "C25OXhZ2xa2R2IqIDA2HdCIyOnuOb8D9nLv6xwqFEuMH/AEqpUpiK6Ln59LcHQN9RgnZkTO7ee10\n",
       "ItLjkE5ERkVzPwUHn7psXd9uw+Dh3E5SI6IXE9prLOxtnfWPddBh/YGlKNOWSWxFRIaCQzoRGQ2d\n",
       "TodNB7+D9okhpmnj5njVf4LEVkQvRm1mgbD+vxeyO/duIDphl6RGRGRIOKQTkdE4fSUGV2+fE7JR\n",
       "fafCUm0lqRHRy3nFowd82gcJ2a5ja5GVe09SIyIyFBzSicgoFBYX4Jcj/xEyr5bd0L2tv6RGRLVj\n",
       "VN/fwUptrX9cXFKILYd/kNiIiAwBh3QiMgp7jq9HTl6W/rFKaYax/abxmuhk9GwaNcPwwElCdvb6\n",
       "cZy9flxSIyIyBBzSicjgpWYk49BvO4RsgPdIODVzldSIqHYFdAmFp7OXkG059D2KSgolNSIi2Tik\n",
       "E5FB0+l02HzoO2h1Wn3WrLE9QnuFSWxFVLuUCiXeGPAelIrHP5azHmYg8sQmia2ISCYO6URk0E5d\n",
       "jsa1O4lCNjp4KizMLSU1Iqobrg6e6NdjuJAdOL0N6fdvS2pERDJxSCcig1VQlI9fj6wSsg4ePdC1\n",
       "jZ+cQkR1bEjv8bBtZKd/XKYtxaZD30Gn00lsRUQycEgnIoO1+/h65OQ/sVhUZYaxwe9ysSg1WJZq\n",
       "K4zq+zshu5JyFr9dPSqpERHJwiGdiAxSasZNRCfsFLKB3qPg2KyFpEZE9aNHu0B4uXcTsl+i/4PC\n",
       "4gJJjYhIBg7pRGRw9HcWfWKxqF0TB4T2HCuxFVH9UCgUGNt/GlRKM32WnXcfu4+tk9iKiOobh3Qi\n",
       "Mjjxlw/jeuoFIRsd/A7U5haSGhHVL6dmrhjgPVLIDifsRGrGTTmFiKjecUgnIoNSUJRXYbFoR08f\n",
       "dGndS04hIklCe4WhWRMH/WOtTotNB7mIlMhUcEgnIoMScWwdcvMf6B+bqcwxJvgdLhYlk2Nhbokx\n",
       "wVOF7HrqBZy8dEhOISKqVxzSichg3Ll3A9FnIoRskM9oODR1kdSISK4urXujo6ePkG07sgr5RQ8l\n",
       "NSKi+sIhnYgMwuM/5T+xWNTGEYN6jpbYikguhUKBMcHvwExlrs9yC7KxK3atxFZEVB84pBORQTh5\n",
       "8RCS0i4K2Zjgd6A242JRMm0OTV0Q4jtGyGLO7UHK3euSGhFRfeCQTkTS5Rc9xLaY1ULWqZUvF4sS\n",
       "/X+DfEfD3tZZ/1in02LjweXCZUqJqGHhkE5E0kXErcXDgmz94/LFokT0iLmZGmP7vStkyZorOJa4\n",
       "T1IjIqprHNKJSKqUu0k4cnaPkIX4jhHeNSSiR5ci7drGT8i2H/0JDwtyJDUiorr0XEP60qVL0apV\n",
       "K1hZWcHX1xcxMTFVbn/u3DkEBwfD2toabm5u+Oijj4TnNRoNwsPD8corr8DMzAxTpkyp8BqrVq2C\n",
       "UqkU/qlUKhQXF9fg0yMiQ6bVabHp0HJhsWhzWycM9B0lsRWR4Rrdd6qwTiO/MBc7jv4ksRER1ZVq\n",
       "h/QNGzZg9uzZWLBgARISEhAQEIChQ4ciJSWl0u1zcnIQEhICFxcXxMfHY8mSJfjss8+wePFi/TZF\n",
       "RUVwcHDEyTNUAAAgAElEQVTA/Pnz0bt372de/9ja2hrp6enQaDTQaDRIS0uDWq1+wU+ViAzNiQsH\n",
       "cTPtspCNDX6Xi0WJnsHOxgGDe40TsrjEKNx46r8jIjJ+1Q7pixcvxpQpUzB16lR4eXnhq6++gouL\n",
       "C5YtW1bp9mvWrEFhYSFWr16Njh07YsyYMfjwww+FId3DwwNLlizBpEmTYGdn98yPrVAo4ODgAEdH\n",
       "R/0/ImoY8gsfYttRcbFo59a90KmVr6RGRMahv/cIODZzFbJNh5ZDqy2T1IiI6kKVQ3pxcTFOnz6N\n",
       "0NBQIQ8NDUVsbGyl+8TFxSEoKAgWFhbC9qmpqUhOTq5RuYKCAnh6esLd3R3Dhw9HQkJCjfYnIsO1\n",
       "M24N8p44l9ZcpcaYvlOr2IOIgEcLq8P6TROy23eTEHs+SlIjIqoLVQ7pGRkZKCsrg5OTk5A7OjpC\n",
       "o9FUuo9Go6mwffnjZ+1TmQ4dOmDlypXYvn071q1bB0tLSwQGBuLatWvP/RpEZJhupV/D0acWi4b2\n",
       "Govmtk7P2IOInuTVsht6tAsUsp2xPyM3P/sZexCRsTGr7Rd81vnlNeXn5wc/v8er2AMCAtCjRw98\n",
       "/fXXWLJkSaX7xMfH18rHNnX8OlK5ujgWdDoddp9dBR10+qyJZTM0RUseewaM/98Ynta2PjinPIFS\n",
       "bQmAR/cbWLntCwS0e61OPy6PBSrHY+HltGvXrsrnq3wn3d7eHiqVCunp6UKenp4OFxeXSvdxdnau\n",
       "8I55+f7Ozi9+STWlUglvb29cvXr1hV+DiOS7djcBGQ/vCFmv1kOgUtb6ewZEDVojCxt0de8rZNfu\n",
       "JuBe7m1JjYioNlX5U1GtVsPHxweRkZEYM+bxLYmjoqIQFhZW6T7+/v748MMPUVRUpD8vPSoqCq6u\n",
       "rvDw8HjhojqdDmfOnIG3t/czt/H15YKzl1H+GzG/jlRXx0JeYS62nBL/Eta1jR9GhrxRqx+Hag+/\n",
       "Lxi27j264c7ay0i//3gwP5cWjXnBn0GpVNXqx+KxQOV4LNSO7OyqT0+r9uouc+fOxapVq7BixQpc\n",
       "vHgRs2bNgkajwfTp0wEA8+fPx6BBg/Tbh4eHw9raGpMnT0ZiYiK2bt2KRYsWYe7cucLrJiQkICEh\n",
       "AdnZ2cjMzERCQgIuXLigf37hwoWIjIxEUlISEhISMHXqVCQmJuo/LhEZn51Hf0ZeYa7+sbmZGqP7\n",
       "/k5iIyLjVuki0ntJOHpur6RGRFRbqv378rhx45CZmYmPP/4YaWlp6NKlCyIiIuDu7g7g0WLQpKQk\n",
       "/fY2NjaIiorCjBkz4OvrCzs7O8ybNw9z5swRXrf8HXGFQgGdTocdO3bA09NT/1rZ2dmYNm0aNBoN\n",
       "bG1t4e3tjejoaP7WRmSkkjVXEXs+UsgG9wyDnQ0vrUr0Mtq7d4V3+yCcvnJEn+2MW4Pu7QLQxLqp\n",
       "xGZE9DKe6yTQ9957D++9916lz61cubJC1rlzZxw+fLjK19RqtVU+v3jxYuHa6kRkvLTaMmw6uFxY\n",
       "LOrQtAX6e78usRVRw/F60GQk3jiJopJCAEBBUR62H/0JE0JmSm5GRC+q2tNdiIheVlziPty6K14+\n",
       "dWy/d2FuZi6pEVHD0rRxcwz1Gy9kxy/sR1LqJUmNiOhlcUgnojr1sCAHO2J/FrJubf3xikcPSY2I\n",
       "Gqbgbq/B2c5dyHgnUiLjxSGdiOrUztifkP/EYlG1mQVGBXGxKFFtU6nMENZfXER6594NxHARKZFR\n",
       "4pBORHXmpuYK4s7vE7LBvcbBzsZBUiOihq2dWxf4tA8Ssl2xPyM3/4GkRkT0ojikE1GdqGyxqGMz\n",
       "V/T3HiGxFVHD93rQFFiYW+ofFxTnY3vMjxIbEdGL4JBORHUi9nwUUu5eF7KwftNgpuJiUaK6ZNvY\n",
       "DkP93hSy4xcPICn1oqRGRPQiOKQTUa3Lzc/GzqcWi/ZoFwivlt0kNSIyLcHdXoVL85ZCtungcpRx\n",
       "ESmR0eCQTkS1bkfsT8gveqh/rDa3xOtBUyQ2IjItKpUZxj51J9I7GTcRc3a3pEZEVFMc0omoVt1I\n",
       "u4xjieJi0aG930CzJvaSGhGZpnZuneHrFSxku+LWIiePi0iJjAGHdCKqNeWLRZ/kZOeG4O6vSWpE\n",
       "ZNpGBr0NC7WV/nFhcT62H10tsRERPS8O6URUa46e24vb95KEjItFieSxbWSHYU8tIj1x8SCu30mU\n",
       "1IiInheHdCKqFbn5D7Azbo2QebcPQnv3rpIaEREA9O32Klo09xCyTQe/4yJSIgPHIZ2IasX2mB9R\n",
       "UJSnf2xhbonXgybLK0REAACVUoWxT92JNDUzmYtIiQwch3QiemlJqRdx/OIBIRvqNx5NGzeX1IiI\n",
       "ntTWtRN8O1S2iDRLUiMiqg6HdCJ6KWWVLBZ1tnNHcDcuFiUyJK/3mQxLtbX+cWFxPrbFcBEpkaHi\n",
       "kE5ELyXm7G7cybgpZGH9p0GlMpNTiIgqZdOoWYVFpCcvHcI1LiIlMkgc0onoheXkPcCuuLVC5uPV\n",
       "F+3cukhqRERVCeo2rJJFpMtRVlYqqRERPQuHdCJ6YduPrkZhcb7+sYXaCq/3mSyvEBFVSaVUIeyp\n",
       "RaRpmbcQfTZCUiMiehYO6UT0Qq7fuYATFw8K2bDeb8K2sZ2kRkT0PNq4dkKvV/oLWcSxdcjOuy+p\n",
       "ERFVhkM6EdVYZYtFWzT3QN/ur0pqREQ1MSLwbWERaVFxAbYd4SJSIkPCIZ2Iaiw6YRdSM5OFbGz/\n",
       "aVApVZIaEVFN2DRqilf9w4Us/vJhXL19XlIjInoah3QiqpHsh/cRcXydkPXs0A9tXTtJakREL6JP\n",
       "16FwtfcUss2HvuMiUiIDwSGdiGrklyMrUVRcoH9spbbGSC4WJTI6jxaR/l7I0jJvIfoMF5ESGQIO\n",
       "6UT03C7fOoPTV44I2asBE2DTqKmkRkT0Mlq3eKXiItLj65D9kItIiWTjkE5Ez6W0rASbD30vZG4O\n",
       "rdGnyxBJjYioNowIfBtWTy0i/TVmlbxCRASAQzoRPaeDp7cjPeu2kIX1/z2UXCxKZNRsGjXFqwET\n",
       "hOzU5WhcvX1OUiMiAjikE9FzuJ9zD3tPbBQy/04haOXiJakREdWmwC5D4OrQSsg2HeQiUiKZOKQT\n",
       "UbW2Rq9AcWmR/rG1ZRMMD5wosRER1SaVUoWwfuIiUs39FBw+s1NSIyLikE5EVbpw8xTOXj8mZCMC\n",
       "J6KxlY2kRkRUF1q36IDeHQcK2e5j6/HgYaakRkSmjUM6ET1TSWlxhcWiHs7t4ddpkKRGRFSXRgRO\n",
       "hJVFI/3jopJC/HpklbxCRCaMQzoRPdO++K3IyNboHysUSozr/3soFfzWQdQQNbFuitf8xUWkp68c\n",
       "wZUULiIlqm/8SUtElcotuI+o+C1C1qfLELg7tpHUiIjqQ2CXwXBzaC1kmw4th1ZbJqkRkWnikE5E\n",
       "Feh0Opy4EYnSshJ91sTKFq8GhEtsRUT1QVnJnUjT79/GxbQTkhoRmSYO6URUQcr9y7iTdU3IRgZN\n",
       "hrVFY0mNiKg+tXLxgt9Ti0jP3IpGXlGOpEZEpodDOhEJikoKcSIpUsjatOiInh36ySlERFIMD5wk\n",
       "LCIt1Zbg1M19EhsRmRYO6UQk2HtiE/KLH79bplQoEdZ/GhQKhcRWRFTfmljb4rWAt4TsZsYFXL51\n",
       "RlIjItPCIZ2I9NIyU3Dw9DYhC+7+GlrYe8opRERSBXYOhZujuIh086HvhfUqRFQ3OKQTEQBAq9Ni\n",
       "44FlKNM+vg24bSM7DPV7U2IrIpJJqVRhXP/pQpaedRuHftshqRGR6eCQTkQAgOMXDuB66gUhGx08\n",
       "FZZqK0mNiMgQeDq3h3+nECHbc2IjsnLvSWpEZBo4pBMRcvOzsS1mtZC5NmuD7m0DJDUiIkMyPHAi\n",
       "1GaW+sfFJYXYGv0fiY2IGj4O6USEbTGrkF+Yq3+sUpqhV+shXCxKRACAxlY28PboL2RnrsXhfNJJ\n",
       "SY2IGj4O6UQm7urtczhx8aCQdXUPQhPLZpIaEZEhauvUA80btxCyTYe+Q1FxgaRGRA0bh3QiE1ZS\n",
       "WoIN+5cJmUvzlujUwk9SIyIyVEqFEv5thkGpeDw6ZOXew+7j6yW2Imq4OKQTmbB9p7bi7oNUIXtj\n",
       "wB+gVKokNSIiQ2bX2Bn9egwXskO/7UDK3SRJjYgaLg7pRCbqblYqok5uFrKAziFo3aKDpEZEZAyG\n",
       "9h6PZk0c9I+1Oi027F8KrbZMYiuihodDOpEJ0ul02HjwW+GGJI2tbDE8cJLEVkRkDCzUVgjrN03I\n",
       "bt29hiNnd0tqRNQwcUgnMkHxl6NxJeWskI3qOwWNLJtIakRExqRz654VLtG6M24NsnIzJDUiang4\n",
       "pBOZmPzCh/j1qesbt3fvCl+vYEmNiMgYjQl+BxZP3OysqLgAWw//ILERUcPCIZ3IxGw/+iNyC7L1\n",
       "j1UqM4zr/3teE52IasS2sR2GB0wUsjPXj+Fc0glJjYgaFg7pRCYkKfUiYs9HClmo71g4NnOV1IiI\n",
       "jFmfLoPh4dxeyDYdXI5CXjud6KVxSCcyESWlJVi37xshc2zaAoN8x0hqRETGTqlUYfyA94Rrpz94\n",
       "mImIY+sktiJqGDikE5mIyJObkJ51W8jGDXgP5mbmkhoRUUPg6tAK/b1HCNnhhJ24lX5NUiOihoFD\n",
       "OpEJSM24iaj4LULm3ykE7d27SGpERA3JkN7jYffEtdN1Oi3WH1iKMl47neiFcUgnauC02jKse+pG\n",
       "IzbWzTCyz9sSWxFRQ2JhbolxA6YL2e27STj023ZJjYiM33MN6UuXLkWrVq1gZWUFX19fxMTEVLn9\n",
       "uXPnEBwcDGtra7i5ueGjjz4SntdoNAgPD8crr7wCMzMzTJkypdLX2bJlCzp27AhLS0t06tQJv/76\n",
       "63N+WkRU7sjZ3UjWXBGysf3ehbVlY0mNiKgh6ujpgx7tAoUsIm4d7malSmpEZNyqHdI3bNiA2bNn\n",
       "Y8GCBUhISEBAQACGDh2KlJSUSrfPyclBSEgIXFxcEB8fjyVLluCzzz7D4sWL9dsUFRXBwcEB8+fP\n",
       "R+/evSu99FtcXBzGjx+PiRMn4syZM5gwYQLCwsJw4gQv7UT0vO7n3MWO2J+FrGsbP3RvF/CMPYiI\n",
       "XtyY4HdhbfH4DYCSsmKs3/8NtDqtxFZExqnaIX3x4sWYMmUKpk6dCi8vL3z11VdwcXHBsmXLKt1+\n",
       "zZo1KCwsxOrVq9GxY0eMGTMGH374oTCke3h4YMmSJZg0aRLs7OwqfZ0vv/wSAwYMwPz58+Hl5YU/\n",
       "//nP6NevH7788ssX/FSJTItOp8PGA9+iuKRQn1mqrSvczpuIqLbYNGqK0cFThezanUTEnY+S1IjI\n",
       "eFU5pBcXF+P06dMIDQ0V8tDQUMTGxla6T1xcHIKCgmBhYSFsn5qaiuTk5OcuduzYsRp9XCISxV+O\n",
       "xoXk00I2ss/bsG1c+S/GRES1oWeHfujg0UPItsWsRlZuhqRGRMapyiE9IyMDZWVlcHJyEnJHR0do\n",
       "NJpK99FoNBW2L3/8rH1q8jo1eQ0iU5Wbn13h9txtXDvBv3OIpEZEZCoUCgXGD3gPanNLfVZYnI+N\n",
       "B7+FTqeT2IzIuJjV9gvKvLV4fHy8tI/dkPDraPxirvyKvMJc/WOlQoUuTn1x+tTpKvaqiMcCleOx\n",
       "QOWe91jo5haMkzf26h8n3ojH5j0/opVDp7qqRvWM3xdeTrt27ap8vsp30u3t7aFSqZCeni7k6enp\n",
       "cHFxqXQfZ2fnCu92l+/v7OxcbeHqXqcmr0Fkiu5kXUfSvfNC1q1lX9hYNZfUiIhMkZeLDxyauAnZ\n",
       "iaS9KCzJl9SIyLhU+U66Wq2Gj48PIiMjMWbM41uHR0VFISwsrNJ9/P398eGHH6KoqEh/XnpUVBRc\n",
       "XV3h4eHx3MX8/f0RFRWFefPmCR83MDDwmfv4+vo+9+tTReW/EfPraLwKivKxY81yIWth74lJw2dA\n",
       "pXr+P5zxWKByPBao3IscCy3buGDR2jkoKysFABSV5iMp5xQmDZ5TJx2pfvD7Qu3Izs6u8vlqr+4y\n",
       "d+5crFq1CitWrMDFixcxa9YsaDQaTJ/+6KYF8+fPx6BBg/Tbh4eHw9raGpMnT0ZiYiK2bt2KRYsW\n",
       "Ye7cucLrJiQkICEhAdnZ2cjMzERCQgIuXLigf37WrFk4cOAAFi1ahEuXLuHTTz/FoUOHMHv27Bp9\n",
       "AYhMybaYVcjKvad/rFAo8ebAmg3oRES1xdnOHUN6vSFk8ZcOI/EGT5Mgqk61P7nHjRuHzMxMfPzx\n",
       "x0hLS0OXLl0QEREBd3d3AI8WeCYlJem3t7GxQVRUFGbMmAFfX1/Y2dlh3rx5mDNH/K3Z29sbwKNz\n",
       "2HU6HXbs2AFPT0/9a/n7+2P9+vVYsGAB/vKXv6Bt27bYuHEjevbsWWufPFFDcvnWGcSejxSy/j2G\n",
       "w8O56nPeiIjq0iCfUfjt6lGkZtzUZxsPfIv/fusrWFlYyytGZOAUOiNfav3knwpsbW0lNjF+/POV\n",
       "8SosLsCnP78vvIvu2MwVH4QvhtrMooo9K8djgcrxWKByL3Ms3Eq/hn9t+AC6J25qFNh5MN4Y+F6t\n",
       "9aP6w+8LtaO6Gbba012IyPA9ugbxE6e5QIEJITNfaEAnIqptLZ3aYoD3CCE7en4vLiUnSGpEZPg4\n",
       "pBMZucu3zuDouT1C1t97BFq5dJDUiIiooqF+b8KhaQshW7fv3ygoypPUiMiwcUgnMmKFxQVYt+/f\n",
       "QubYtAWG+YdLakREVDm1mQUmhLwPBR7fTyXrYQZ+ObJSYisiw8UhnciIbY9ZjftPneYSztNciMhA\n",
       "tW7RAf29RwrZscR9uHDzlKRGRIaLQzqRkbqSchYxT53m0q/HcLRu8YqkRkRE1Rvm/yacmok3OVq3\n",
       "7xvkFz6U1IjIMHFIJzJCRcUFWPvUaS4OTVvgVf8JkhoRET0ftZkF3gp9HwrF4xEkO+8+tkavkNiK\n",
       "yPBwSCcyQttiVuN+zl39YwUUCB/0R6jNeZoLERk+D+f2GOQzSshOXDyIc0knJDUiMjwc0omMzIWb\n",
       "pyuc5hLc/TW0ce0oqRERUc0N6T0eLs1bCtmG/cuQV5AjqRGRYeGQTmRE8gpysHbf10LmYOuC1wLe\n",
       "ktSIiOjFmJuZY0LI+1A+cdpLTn4WNh/+QWIrIsPBIZ3ISOh0Omw8uBw5eVn6TKFQ4q3Bs3maCxEZ\n",
       "pZZObRHSc6yQnbocjYSrsZIaERkODulERuLU5Wj8dvWokIX2HINWLl6SGhERvbzBvcLQwt5TyNYf\n",
       "WIbsh/flFCIyEBzSiYxAVm4GNh36TsjcHFpjcK9xkhoREdUOM5U53gp9HyqlmT7LL8zFmn1fQ6fT\n",
       "SWxGJBeHdCIDp9VpsTbqa+HW2WYqc0wcPAdmKnOJzYiIaoebQ2sM83tTyC4l/4YjZyMkNSKSj0M6\n",
       "kYGLObsbl1POCNnwgIlwae4uqRERUe0b6PM62rQQr1K17chqaO6nSGpEJBeHdCIDlp51B9tiVgtZ\n",
       "W7fOCO7xmqRGRER1Q6lU4a3Bs2ChttJnJWXF+HHvFygtK5HYjEgODulEBqq0rAQ/7fkCJaXF+sxS\n",
       "bY23nrpkGRFRQ9Hcxglh/aYJ2e27SdhzfIOkRkTy8Cc9kYGKiFuHW3evCdmY4HdgZ+MoqRERUd3r\n",
       "2aEfurcNELKo+K1ISr0oqRGRHBzSiQzQ5VtnsP/UL0LWrY0fer3SX1IjIqL6oVAo8MaA6bBp1Eyf\n",
       "6XRa/LT3SxQU5UtsRlS/OKQTGZiHBTn4OXIJdHh86THbxs0xfuAfoFAoJDYjIqofjaxsMCHkfSHL\n",
       "zEnHlsPfS2pEVP84pBMZEJ1Oh3X7/o3svMc38VBAgYmhs9HIykZiMyKi+vWKRw8EdxcXyZ+4eBAn\n",
       "Lx2W1IiofnFIJzIgR8/txbmkE0I2yHc02rt3kdSIiEie4YET4dK8pZBtPLAM9x6kSWpEVH84pBMZ\n",
       "iLTMFPwS/R8h83BqV+EGH0REpkJtZoG3h/wJ5iq1PisqKcTq3f/iZRmpweOQTmQASkqLsXr35ygp\n",
       "e3y5RQtzS0waMhcqlVkVexIRNWwt7D3wet8pQnbr7jXsjP1ZUiOi+sEhncgAbD/6I1Izk4UsrP/v\n",
       "4dDURVIjIiLD0afLEHRt4ydkB05vw4WbpyQ1Iqp7HNKJJDt7/RgOJ+wUMh+vvujZoZ+cQkREBkah\n",
       "UODNQTPQrLG9kP8c+ZWw0J6oIeGQTiRRZnY61kR+JWR2No4Y1//3vNwiEdETGlk2waQhc6F44o7L\n",
       "Dwuy8dPeL6HVaSU2I6obHNKJJCktK8HK3Z+joPjxzTmUShXeHvInWFk0ktiMiMgwtXHtiKG93xCy\n",
       "Kylnse/kFkmNiOoOh3QiSbbFrMat9KtCNiJwElq5eElqRERk+EJ7jkVbt85CtuvYOly9fU5SI6K6\n",
       "wSGdSIKEq7EVzkPv0roX+vcYIakREZFxUCpVmDR4DhpZNtFnOp0Wq3b/i+enU4PCIZ2ont17kIa1\n",
       "+/4tZHZNHDAh5H2eh05E9ByaNm6OiYNnC1lu/gOs3v0vlGnLJLUiql0c0onqUUlpMVbu/gyFT5yH\n",
       "rlKaYcqw/4K1ZWOJzYiIjEtHTx+E9gwTsmt3ErErbq2kRkS1i0M6UT369cgq3L6bJGQj+7wND+f2\n",
       "khoRERmvYX7j0d6ti5Dti9+C80knJTUiqj0c0onqSfylwzhyNkLIurXxQ3D31yQ1IiIybkqlCpOG\n",
       "/Ak2jZoJ+U+RXyIzO11SK6LawSGdqB7cuXcT6/Z/I2TNbZzwZsgfeR46EdFLsGnUFFOGzoPyieun\n",
       "FxTl4T8R/4eS0hKJzYheDod0ojqWX/gQP+z6FCWlxfrMTGX+6Dx0C56HTkT0stq4dsLwwElClnL3\n",
       "OrZGr5DUiOjlcUgnqkNanRY/7llc4c+uYf1/j5ZObSW1IiJqeAZ4j0TXNr2F7Oi5PYg7HyWpEdHL\n",
       "4ZBOVIf2HNuAC8mnhSyw82D4dxokqRERUcOkUCgQHjITzW2dhHzjoeW4kXZZUiuiF8chnaiOnEs6\n",
       "gT0nNgiZh3N7jA5+R1IjIqKGzdqiMd559b9hbqbWZ2VlpfjPrkW80REZHQ7pRHXgblYqftr7pZA1\n",
       "sbLF74Z9AHMzc0mtiIgaPleHVggfNFPIsvPuY8WuRVxISkaFQzpRLSsoysP3O/8h3LBIqVBi8rD/\n",
       "QrMm9hKbERGZBh+vIAz0eV3IbqZdxpbD30tqRFRzHNKJapFWW4bVu/+F9Pu3hXxk0GS0c+ssqRUR\n",
       "kekZHjARHVp2F7LY85E4em6vpEZENcMhnagWbT/6Y4WFoj5efdGv+3BJjYiITJNSqcLbQ/9UYSHp\n",
       "5kPf4/qdC5JaET0/DulEteRY4n4cOL1NyFo6tcObg2bwhkVERBI0smyCd1+bD7W5pT4r05bih13/\n",
       "REa2RmIzoupxSCeqBUmpF7HhwDIhs21k9+iHg5mFpFZERNTC3hMTQt4XsryCHHy3/RMUFOVJakVU\n",
       "PQ7pRC/pfs5d/LDznyjTluozc5Ua7w7/M2wb20lsRkREANCjXQCG9HpDyDT3U7By9+co05ZJakVU\n",
       "NQ7pRC+hqLgA3+/4Bx4WZAt5eMhM3lGUiMiADPUbD+/2fYTsUvJv+CV6haRGRFXjkE70gsq0ZVi5\n",
       "+3Pcybgp5IN7hcHHK0hOKSIiqlT5HUk9nNoJefSZCESf2SWpFdGzcUgnegE6nQ6bDi7HhZunhLxr\n",
       "Gz8M9XtTUisiIqqK2swC7w7/M5o1Fu9ZseXwCly4efoZexHJwSGd6AXsi9+K2PORQubm2BoTQ2dB\n",
       "qeB/VkREhsqmUTNMG7EAFk9c8UWn02Ll7s9w+16SxGZEIk4TRDV06nI0dsT+JGTNmjjg9yMWwEJt\n",
       "JakVERE9L1cHT7w95E9Q4PHlcYuKC/Dtto9wP+euxGZEj3FIJ6qBa3cS8XPUV0JmpbbG9JH/C9tG\n",
       "vJILEZGx6Ny6J14PmiJkOXlZWLbt78grzJXUiugxDulEzyn9/m38sONTlJU9vtSiSmmGqa/Nh0vz\n",
       "lhKbERHRi+jXYziCu78mZOn3b+P77f9AcWmRpFZEj3BIJ3oODx5mYumvC5Ff9FDIw0P+iPbuXSS1\n",
       "IiKil6FQKDCq7+/QvV2AkCelXcRPe76AltdQJ4k4pBNVI68wF0t/+Ruycu8J+av+4ejZoZ+cUkRE\n",
       "VCuUCiUmhs5GG9dOQn7m+jFsjV4BnU4nqRmZOg7pRFUoX0ikuZ8i5H6dBiG0Z5ikVkREVJvMzdR4\n",
       "t5JTF6PPRCDy5GZJrcjUPdeQvnTpUrRq1QpWVlbw9fVFTExMldufO3cOwcHBsLa2hpubGz766KMK\n",
       "2xw+fBg+Pj6wsrJCmzZtsHz5cuH5VatWQalUCv9UKhWKi4tr8OkRvbjSshKs2LUIyZorQt61TW+8\n",
       "MeA9KBSKZ+xJRETGxtqy8aOLADRuLuS74tbwZkckRbVD+oYNGzB79mwsWLAACQkJCAgIwNChQ5GS\n",
       "klLp9jk5OQgJCYGLiwvi4+OxZMkSfPbZZ1i8eLF+mxs3bmDYsGHo06cPEhISMH/+fMycORNbt24V\n",
       "Xsva2hrp6enQaDTQaDRIS0uDWq1+yU+ZqHpabRl+jlyCS7cShLytW2e8PeRPUClVkpoREVFdadbE\n",
       "Ae+N/F9Yqa2FfPOh73Hi4kFJrchUVTukL168GFOmTMHUqVPh5eWFr776Ci4uLli2bFml269ZswaF\n",
       "hYVYvXo1OnbsiDFjxuDDDz8UhvRvv/0Wbm5uWLJkCby8vPDOO+/g7bffxueffy68lkKhgIODAxwd\n",
       "HfX/iOqaTqfD5sM/4PQV8S9Gbo6t8e5rf4a5GX9RJCJqqFrYe2LaiAUVvtevifoaZ64dk9SKTFGV\n",
       "Q3pxcTFOnz6N0NBQIQ8NDUVsbGyl+8TFxSEoKAgWFhbC9qmpqUhOTtZvU9lrxsfHo6zs8UrqgoIC\n",
       "eHp6wt3dHcOHD0dCgviuJlFt0+l02H50NWLO7hZyh6Yt8N7Iv8DKwvoZexIRUUPRxrUj3nltPlRK\n",
       "MypgP4kAACAASURBVH2m02mxas/nuJTMWYTqR5VDekZGBsrKyuDk5CTkjo6O0Gg0le6j0WgqbF/+\n",
       "uHyf9PT0SrcpLS1FRkYGAKBDhw5YuXIltm/fjnXr1sHS0hKBgYG4du1aDT49opqJOLYW+0/9KmS2\n",
       "jezwh1F/RRPrppJaERFRfXvFowfeHjIXCsXjUamsrBQ/7PwUSamXJDYjU2FW/SY1U1uL6fz8/ODn\n",
       "56d/HBAQgB49euDrr7/GkiVLKt0nPj6+Vj62qTPVr+PZlCNIuHVYyNRmVghuH4YbV1JwA5Wvw2jI\n",
       "TPVYoIp4LFA50zoW1PBvMwyx13bqk+LSInyz9a8I6RQO+yauErvJZ1rHQu1r165dlc9X+U66vb09\n",
       "VCoV0tPThTw9PR0uLi6V7uPs7FzhXfby/Z2dnavcxszMDPb29pUXVSrh7e2Nq1evVlWZ6IWcvx1b\n",
       "cUBXWSKkUziaWjtIakVERLK1deqOnq3EU3RLyooQlbgWGbmpklqRKajynXS1Wg0fHx9ERkZizJgx\n",
       "+jwqKgphYZVfI9rf3x8ffvghioqK9OelR0VFwdXVFR4eHvptfvnlF2G/qKgo9OzZEypV5VfN0Ol0\n",
       "OHPmDLy9vZ/Z19fXt6pPh6pR/huxqX0dD57ejtPJB4TMQm2FP45aCA/n9pJayWWqxwJVxGOBypny\n",
       "seALX9gfb47dx9bps5KyIhy8tB5/GLUQHs5VvyPa0JjysVCbsrOzq3y+2qu7zJ07F6tWrcKKFStw\n",
       "8eJFzJo1CxqNBtOnTwcAzJ8/H4MGDdJvHx4eDmtra0yePBmJiYnYunUrFi1ahLlz5+q3mT59Ou7c\n",
       "uYM5c+bg4sWL+OGHH7B69WrMmzdPv83ChQsRGRmJpKQkJCQkYOrUqUhMTNR/XKLacDhhJ3458h8h\n",
       "U5tb4r2RfzXZAZ2IiCoa0mscBvcS36AsKM7H0l/+ilvpXC9Hta/ac9LHjRuHzMxMfPzxx0hLS0OX\n",
       "Ll0QEREBd3d3AI8WgyYlJem3t7GxQVRUFGbMmAFfX1/Y2dlh3rx5mDNnjn4bT09PREREYM6cOVi2\n",
       "bBlcXV3x9ddfY9SoUfptsrOzMW3aNGg0Gtja2sLb2xvR0dH8rY1qzf5Tv2JbzCohMzdTY/rI/0Xr\n",
       "Fh3klCIiIoOkUCgwzC8cOh0QeXKTPi8ozsc3W/+CGaP/jpZObSU2pIZGodPpdLJLvIwn/1Rga2sr\n",
       "sYnxM5U/X+l0Ouw9sRERT/zZEgDMVWpMG/E/8GrZTVIzw2EqxwJVj8cCleOx8IhOp8OuuDWIPLlZ\n",
       "yK0sGuEPr5vGX2F5LNSO6mbYak93IWpIdDoddsb+v/buOzyqKv0D+HcmdTLpZdI7IaQREAgtAUIT\n",
       "lAWkI6AgrqhYKAuoKz+wAZIFAUF0dUVWRUFBUCzUCCGhl0AIPY1Aeps0UmbO7w/MrOOkASGT8v08\n",
       "D0/IOe+98x7mkOedm3PP/arWAv3Zv73OAp2IiOolkUjweO8pGNJ9rFZ7eUUp1u/4P1xLv6CnzKit\n",
       "YZFO7YYQAj8c/hz7Tm3Xajc2MsXzoxcjwLOrnjIjIqLWRCKRYESfqTqFekXVHXy88x1cTObWhPTg\n",
       "WKRTu6AWamyL/gS/n/tJq93U2Awvjl4KP7cQPWVGREStUU2hPrSH9s2kVapKfLp7Oc5cPaKnzKit\n",
       "aPKHGRG1NFXVVfhq7xqcvRar1W5mYo4Xn1jKG32IiOi+3C3Up8DUWIYfY/+raVerVdj86ypUVJaj\n",
       "d/AQPWZIrRmLdGrTyivK8J/dy3H1L2sEzWVWmP3EW3B18NJPYkRE1GYM7j4GpsZm+C76Ewjc3Y9D\n",
       "QOCbAxtQXlmGgY+M0nOG1BpxuQu1WcrSAny4/U2dAt1KbotXxr3LAp2IiJpMeOdhmPboHEgl2qXV\n",
       "zphN+OHw51ALtZ4yo9aKRTq1STmFGfjgu9eQnpOk1a6wccXcCSvgZOuup8yIiKit6t6pP2aOeA2G\n",
       "BkZa7dFnf8QXv/4LVdWVesqMWiMW6dTmpGVdx5ptryGvKEur3dOpI+aMXw5bS4WeMiMiorYuxCcM\n",
       "s0a+CRMjU632c9fisOGHJSi9U6ynzKi1YZFObUr89WNY9/0/UVxepNUe6PkIXhrzNsxllnrKjIiI\n",
       "2gt/j1C8On4ZLOU2Wu1Jty9hzbbXkafMquNIov9hkU5tghAC+0/twOc/v4/K6gqtvrCASPz9b2/o\n",
       "XNUgIiJ6WNwcfDBvwvtwtHXTas8qSMcHW19DWtZ1PWVGrQWLdGr1qlVV+Gb/evwY+1/NXfU1BnUb\n",
       "jSlDXoGBATcyIiKi5mVrqcDc8Svg6xqk1a4sK8Da797A6SsxesqMWgMW6dSqld4pxkc738KxxANa\n",
       "7VKpASYOfAGjwqdDIpHoKTsiImrvzEzN8eLoJejq11ervUpVic2/rcLuuK+48wvVipcXqdXKyEvD\n",
       "Zz8tR05Rhla7zNgMzzy+CP4eoXrKjIiI6H+MDI3x9PD5sLV0wIHTO7X69p78Hhl5aZj26FyYGsv0\n",
       "lCG1RLySTq3S2WuxWLV1oU6Bbm/lhHkTV7JAJyKiFkUqkWJU+PRal2BeSDqBD7Yt0tmVjNo3FunU\n",
       "qqjUKuyM+QKbfolCZdUdrT5fl0DMm7hS5yYdIiKilqJn4EC8MvZdWJhZa7Vn5KUh6tt/IDHltJ4y\n",
       "o5aGRTq1GsVlRfjoh6U4eGanTl+vwEF48Ym3uMUiERG1eN7OnfCPSVFwc/DRai+7U4yPd72Dn49+\n",
       "DbVapafsqKVgkU6tQkrmVfzrm/m4ln5Bq91AaoiJA1/A5MEvwcjQqI6jiYiIWhYbCwe8On4Zuvj1\n",
       "0enbc+I7fLTzLRSXFeohM2opWKRTi6YWahw4/QPWfPc6CkpytfqszO3wyrj30DfkUe7gQkRErY6J\n",
       "kSlmDF+AkX2fgkSiXZJdvXkeK7+Zj6Tbl/WUHekbi3RqsZSlhfh41zvYdWSzzq/9OrgGYcGkVfB2\n",
       "9tdTdkRERA9OIpFgcPcxeGnM2zrr1ItK8rBu+z+x9+T3XP7SDrFIpxbpcuo5vL9lDi6nntXpG9B1\n",
       "JGY/8RYs5da1HElERNT6+LkFY+GTq3UefKRWq7A77ius3/F/KCjO0VN2pA8s0qlFqVZV4ccj/8XG\n",
       "WtbimZla4NkRr2NMv2f4BFEiImpzrOS2eGnM2xjcbYxO3/VbF7Hi6zk4ey1WD5mRPrDSoRbjVk4y\n",
       "vty7FrdzU3T6fF0C8dSwubCxcGj+xIiIiJqJgdQAI8OfgrdLJ2zZ9yFK7xRr+sorSrHplygkBpzG\n",
       "2AF/58OP2jgW6aR3KrUK+0/twG/Ht0Klrtbqk0ikeLTHeDzacwIMpAZ6ypCIiKh5hfiE4bUpa/HV\n",
       "vrW4khav1Xf80kFcu5WAyYNm8+F9bRiLdNKrzPyb+GrvOqRlXdPps5Lb4qlhc+HnFqKHzIiIiPTL\n",
       "ytwWL4xegkNnd+PHuP9Cpfrfhax8ZTY2/LAEfYKHYlT4dMhMzPSYKT0MLNJJL1Sqahw8+yN+PfYN\n",
       "qlVVOv3d/ftj7IBnITe10EN2RERELYNUIkXkIyPh5x6Mzb+tRlZ+ulZ/XMJeJKacxqRBsxHo9Yie\n",
       "sqSHgUU6NbvkjCvYeuAj3M5L1emTyywxMfL5Wh/uQERE1F65OfhgwaRV+CnuSxw+9zMEhKavsCQP\n",
       "H+96Gz0DBmJ0xHTI+fTtNoFFOjWb8opS/BT7JWIv7NH64VIj1LcXJgx8XmefWCIiIgKMjUwwtv+z\n",
       "6OrXF1v2fYjswtta/ccvHURC8kmM7PsUegYNglTCTfxaMxbp9NAJIXD2Wix2HPoPlGUFOv1mphYY\n",
       "238muvv355NDiYiIGuDjEoCFUz7Ar8e+wcEzP0IItaav9E4xvjmwAUcT92NC5Cy4OfjoMVN6ECzS\n",
       "6aFKz0nCjkP/wfVbF2vt79FpAEZHzICFmVUzZ0ZERNR6GRuaYFT4dHTp0Adf7/sQmfk3tfpTMq4g\n",
       "6pt/oF/oY3is12TITOR6ypTuF4t0eiiKy4rw89GvcfTifq1P+DUcrJwxYeDz3DqKiIjoAXg6dcSC\n",
       "yasRfXYX9pzYhqrqSk2fEGocOrcbZ67EYHivyegdPITbGbciLNKpSVWrqhAT/yt+O/4tyivLdPoN\n",
       "pIYY3P0JDOkxDsaGJnrIkIiIqG0xMjTC0B7j0M0/AtsP/QcJSSe0+ovLi7At+mMcjv8Zo8KfRqBX\n",
       "Ny4vbQVYpFOTUAs1Tl+JwS9HtyBPmVVrTCfPrhjT7xk42bo3c3ZERERtn52lI5772xu4kHQC2w99\n",
       "hnxltlZ/Zv5NfPLju/B3D8XoiBlwdfDST6LUKCzS6YEIIXAx+RR2x31V65aKAOBg7YIx/Z7hJ3ci\n",
       "IqJmEOITBn/3UOw/tQMHzvygtQQGAK7cjMfKLXPxiH8EhvecCIWNq54ypfqwSKf7dv3WReyO/QpJ\n",
       "GZdq7Tc1NsOwnhPRL/QxGBoYNXN2RERE7ZexkQke6z0ZfUKG4ue4r3HiUrTW9scCAqevHMbZq0fQ\n",
       "IyASw8ImwM7KUY8Z01+xSKd7IoTAlbR47Dn5HW7UsWOLVGqAPsFDMbznRO55TkREpEfW5naYMvQV\n",
       "9OsyAjtjNuFa+gWtfrVQ43jiAZy8/Dt6Bw7GkB7jYGvpoKds6c9YpFOjCCGQkHwSe098h9Ssa7XG\n",
       "SCBBN/9+GN5rEhysnZs5QyIiIqqLu8IHL415GwnJJ7E77itk5KVp9avVKsQm7MHRxP3o7t8Pg7qN\n",
       "gbMd7yHTJxbpVC+VqhpnrsXi4OkfcCs3pc64IO/uGNF7Km9CISIiaqEkEglCfMIQ5N0dZ6/G4tfj\n",
       "3yK74JZWjFqtwolL0ThxKRohPmEY3H0svJ399ZRx+8YinWpVeqcYcRf24vD5X1BUkldnXCePLhjW\n",
       "cyJ8XAKaMTsiIiK6X1KJFN38I9DFrw9OXzmMX49/i7wi3Z3ZLiSdwIWkE/B1DcKALn9DsE8P7rPe\n",
       "jFikk5aisjxsi/4EJxIPorK6os64YJ8wPNpjHDydOjZjdkRERNRUDKQGCAuIRLeOEThx+XccOLUD\n",
       "2YW3deJu3LqIG7cuwsbCARGdh8O0yh6mRmZ6yLh9YZFOqKquwvkbx7DnwvfIUta+jSJwd815F78+\n",
       "GNpjHFwdvJsxQyIiInpYDAwM0TtoMHoGROL8jePYd2o7bmbf0IkrKM7Bj7H/hYHUEN72wXD0sIG7\n",
       "wlcPGbcPLNLbseyCW4hL2Ifjlw6itFxZZ5yxoQl6Bg5C/y4joLBxacYMiYiIqLlIpQbo4tcHoR16\n",
       "4+rN89h/ageu3IzXiVOpq3E9+xyivjkHVwdv9AochO6d+kNuaqGHrNsuFuntTHlFKc5dP4qTl3/H\n",
       "9fSEemOtzO3QL/Rx9Akewv94RERE7YREIoG/Ryj8PUJxKycZh+J/xunLh1GlqtSJvZWTjO2HPsOu\n",
       "I5vR2bcXegcNhp97CKQSqR4yb1tYpLcD1aoqJKacwanLh5CQfBLVqqp6432cAxDeeRi6+vWFgQGn\n",
       "CBERUXvl6uCNJwe/hFF9n0Lcxf04cv5XFBTn6MRVq6pw5moMzlyNgbW5HR7pGI5HOkbAXeHLp43f\n",
       "J1ZgbZRKVY3rty7i3LU4nL0eh7I7xfXGy0zk8LQNREenRzC43/BmypKIiIhaA7nMEkO6j8HAR0Zh\n",
       "175vcC3rHG4XJkEItU5sYUkeDp7ZhYNndsHB2kVTsHPf9XvDIr0NqayuwJW0eMRfP4qEpJMoqyhp\n",
       "8Bgf5wD0CRmKLn59cP7chQbjiYiIqP0ykBrAw64TPOw6wdffCycuReNY4v5at3AEgJzC29hzYhv2\n",
       "nNgGZzsPhPj0RIhPGNwdfbkkpgEs0ls5ZWkhLqWewcWUU0hMOYPKqjsNHmNn5Yju/v3RvVN/ONq4\n",
       "NkOWRERE1NbYWNjj0bDxGNJjLG7cuoijF/fj/PVjdW7hnJGXhoy8NOw9+R2s5LYI9glDiE8Y/NxC\n",
       "YGRo1MzZt3ws0lsZlVqF1MyrSEw5g8TU00jPTmrUcXJTC3TtGI4enfrDy8mf68OIiIioSUglUvi5\n",
       "hcDPLQQVA+8gIekkTl+NwaWUM1Cpq2s9pqg0H7EXfkPshd9gbGQKP7dgdPLogk4eXaCwcWWdAhbp\n",
       "LZ5aqJGZl4Zr6Qm4np6Aa+kJjVrGAgBmphYI8QlDqG8vdPLsAkMDfkolIiKih8fEyBTd/CPQzT8C\n",
       "ZXdKEH/jGM5cjcHVmxdqXb8OAJVVd3Ax+RQuJp8CANiY28PfIxSdPLuio3tnmMssm3MILQaL9Bbm\n",
       "r0X59VsXUdrATZ9/ZiW3RWiHXujs2xu+roF8fC8RERHphZmpOXoHDUbvoMEoKVciMeU0Ltw4jktp\n",
       "5+pdnltQkotjiQdwLPEAAMDR1g2+LoHwcQmAr2sgbC0U7eJKO4t0PSspVyI18ypSMq8gJeMqUrOu\n",
       "4U5l2T2dw0PRAQFejyDIuzs8HDvwRgwiIiJqUcxllggLiERYQCSqqitx9eZ5XEg6joSkU1CWFdR7\n",
       "bFZ+OrLy0xGXsBcAYG1uBx+XQHg7+8PD0Q9uDt4wMjRujmE0Kxbpzai0XIlbuSlIz0lGenYSUjOv\n",
       "Iqco457PY2ZqgQCPLgjwegQBnl1hYWb9ELIlIiIianpGhsYI8u6OIO/uEAMFMvJScTntHC6nxeNG\n",
       "+sVaH5r0Z4UleZo92YG7T0p1tvOAp2MHuCs6wMPRDy52Hq3+WS+tO/sWSq1WIU+Zjdu5qUjPScKt\n",
       "nGTcyklGQUnufZ1PZmwGX9cgdHALhp9bMFztvSDlMhYiIiJq5SQSCVzsveBi74WBj4xGVXUlkm5f\n",
       "wuW0c7iSFo9buSl1rmWvoVarNLUWsA8AYGhgBCdbdzjbecDF3hPOdp5wsfeEldy21SyVYZH+ACqr\n",
       "KpBdeAtZ+enIzE9HVsHdX8dkF96GSlX73cyNYWZiDm/nTvBzD0YH12C4OXizKCciIqI2z8jQGP4e\n",
       "ofD3CAUAlFeUISXzCm7cSsSN24lIzbza4JPTgbtPQE3PSUJ6jvYueGYm5nC284CTnQcU1i5Q2LjA\n",
       "wdoZdpaOLe7Ke8vKpoURQqC4rAh5yizkFWUiT5mNvKJM5CqzkF+UhYLiXAiIB3oNqUQKF3sveDl1\n",
       "hJezP7ycOsLB2qXVfMojIiIielhkJmYI8OyKAM+uAICq6irczL6B5IxLSM26hptZN5CnrP1BSrUp\n",
       "qyjBjdt3C/4/k0qksLN0hIONCxTWLrC3doadpQI2Fg6wtVTA1FjWpONqjHZbpAshUF5RisKSPBSV\n",
       "5t/9WpL3x9d85BdnI68oq84N+e+HVGoAZ1t3uDp4w9XBG+4KX7grfGFiZNpkr0FERETUVhkZGsHH\n",
       "pRN8XDpp2krKlbiZfQNpWdeQlnUdaVnXUVSaf0/nVQs1cooykFOUgUSc1uk3MzGHjaUDbP8o2m0s\n",
       "7v7dUm4LK7kNLOU2TX7zaqOK9I8++ghRUVHIzMxEUFAQ1qxZg/Dw8DrjL1y4gJdeegknT56Era0t\n",
       "Zs2ahcWLF2vFHDp0CPPmzUNiYiJcXFywcOFCzJo1Sytm+/btWLx4MZKSkuDr64v33nsPo0ePrvN1\n",
       "1UKNsjslKCkvQkm5EiVld78Wlxeh9I82ZVkhikryUVSS16QF+F9ZyKzgaOsGVwdvuP1RlDvauPOJ\n",
       "WkRERERNyFxmqXW1HQCKy4qQkZeK27mpuJ2XqnnaaWOezF6bsooSlOWU/LHuvXYyEzks5TawMrOB\n",
       "pdwWlnIbWMqtYWFmDXOZFeSmFjCXWcFcZgljI5MGX7PBIn3r1q2YM2cONm7ciPDwcGzYsAHDhw9H\n",
       "YmIi3N3ddeKVSiWGDBmCAQMG4NSpU7h06RJmzJgBuVyOefPmAQCSk5Px2GOP4dlnn8WWLVsQExOD\n",
       "F198EQ4ODhgzZgwA4OjRo5g0aRLefvttjBkzBtu3b8f48eMRGxuLsLCwWnOd++G4Bm8uaEoSSGBr\n",
       "pYCjjRucbN3gaOMGR9u7f+SmFs2WBxERERH9j4WZFSzMOqOje2dNm1qokf/Hxh45hbeRU3gb2QW3\n",
       "kV14G8rS+reBbIzyilKUV5QiKz+9wVhjQxMsnvrvemMaLNJXr16NGTNmYObMmQCAdevW4bfffsPG\n",
       "jRuxbNkynfivv/4ad+7cwebNm2FiYoLAwEBcvnwZq1ev1hTpH3/8Mdzc3LB27VoAgL+/P44fP45/\n",
       "/etfmiJ9zZo1GDhwIF5//XUAwBtvvIHo6GisWbMGW7ZsqTXXh1GgmxiZws7KCXaWCs1Xeysn2Fo6\n",
       "ws5KAWPDhj8JEREREZF+SSVS2Fs5wd7KSafvTmU5cgoz/ijcbyFPmY0CZTbyi3NQUJwLlfr+NwSp\n",
       "TWNWc9RbpFdWVuLMmTNYuHChVvvQoUMRFxdX6zFHjx5FREQETExMtOIXL16M1NRUeHp64ujRoxg6\n",
       "dKjOOTdv3gyVSgUDAwMcO3YMr7zyik7Mhg0bGhxUYxkZGsPa3B5W5rawltvd/WpuByu5LWws7GFn\n",
       "5QS5qQVv4iQiIiJqw0yNZXBX+MBd4aPTpxZqKEsLkK/MQUFxNvKVOcgvzkFRSR6UpQUoKitAcWkB\n",
       "1E18sbjeIj03NxcqlQqOjo5a7QqFApmZmbUek5mZCQ8PD622muMzMzPh6emJrKwsnXM6Ojqiuroa\n",
       "ubm5cHR0RGZmZq0xdb1uDZmx2d11P2aWMJdZweKPtT/mMiuY/9FmJb9bjMtM5CzAiYiIiKhOUokU\n",
       "1uZ2sDa3A9Cp1hi1UKO0XHm3aC8tgLK0AMrSfCjLCv53n+SdYpSUF6G0vLhRV+abfHcXfRa970zf\n",
       "3OjYqgoVqiqUDzGb1sfPzw8AUFRUpOdMSN84F6gG5wLV4FygGpwLdZHA3NgW5sa2cLV58LNJ6+u0\n",
       "t7eHgYEBsrK095/MysqCs7Nzrcc4OTnpXO2uOd7JyaneGENDQ9jb29cbU3MOIiIiIqK2qt4i3djY\n",
       "GN26dcPevXu12vft24c+ffrUekzv3r0RExODiooKrXhXV1d4enpqYvbt26dzzh49esDAwKDemL59\n",
       "+zZyaERERERErZRowNatW4WxsbH47LPPRGJionjllVeEhYWFSEtLE0II8dprr4lBgwZp4ouKioST\n",
       "k5OYNGmSSEhIENu3bxeWlpZi9erVmpjk5GQhl8vFnDlzRGJiovj000+FsbGx2LFjhyYmLi5OGBoa\n",
       "ihUrVohLly6JZcuWCSMjI3HixImGUiYiIiIiatUkQogGn2u/ceNGrFy5EhkZGQgJCcEHH3ygeZjR\n",
       "jBkzcOjQISQlJWniExISMHv2bJw4cQK2trZ4/vnndR5mdPjwYcydOxcXL16Eq6srFi1ahOeee04r\n",
       "Zvv27XjzzTeRlJSEDh06NPgwIyIiIiKitqBRRToRERERETWfetekU9tTXV2NN954Az4+PpDJZPDx\n",
       "8cHixYuhUqm04pYuXQpXV1eYmZkhMjISiYmJesqYmsrhw4cxcuRIuLm5QSqVYvNm3d2QGnrfKyoq\n",
       "8PLLL8PBwQHm5uYYNWoUbt261VxDoCZS31yorq7GokWLEBoaCnNzc7i4uGDKlCm4efOm1jk4F9qG\n",
       "xvxcqDFr1ixIpVKsWrVKq51zoW1ozFy4evUqxowZAxsbG8jlcnTr1g2XL1/W9HMuNC0W6e3MsmXL\n",
       "8Mknn+DDDz/ElStXsHbtWnz00UdYvny5Jub999/H6tWrsX79epw8eRIKhQJDhgxBSUmJHjOnB1Va\n",
       "WorOnTtj7dq1kMlkOtulNuZ9nzNnDnbs2IFvv/0WMTExUCqVGDFiBNTqpn/aLz089c2F0tJSnD17\n",
       "Fm+++SbOnj2LXbt24ebNmxg2bJjWh3nOhbahoZ8LNb7//nucPHkSLi4uOjGcC21DQ3MhOTkZffv2\n",
       "ha+vL6Kjo3Hx4kW89957MDc318RwLjQx/S6Jp+Y2YsQIMX36dK22p556SowYMUIIIYRarRZOTk5i\n",
       "2bJlmv7y8nJhYWEhPvnkk2bNlR4ec3NzsXnzZs33jXnfCwsLhbGxsdiyZYsm5ubNm0IqlYo9e/Y0\n",
       "X/LUpP46F2qTmJgoJBKJSEhIEEJwLrRVdc2FlJQU4erqKi5fviy8vLzEqlWrNH2cC21TbXNh8uTJ\n",
       "YurUqXUew7nQ9HglvZ0ZPnw4Dh48iCtXrgAAEhMTER0djccffxzA3U/KWVlZGDp0qOYYU1NT9OvX\n",
       "D3FxcXrJmR6+xrzvp0+fRlVVlVaMm5sbAgICODfauJoHltjY3H06B+dC+1FdXY3Jkydj8eLF8Pf3\n",
       "1+nnXGgf1Go1du/ejYCAAAwbNgwKhQJhYWHYtm2bJoZzoemxSG9nXnzxRUyZMgUBAQEwNjZGcHAw\n",
       "pk+fjueffx4ANA+QcnR01DpOoVDoPFyK2o7GvO+ZmZkwMDCAnZ2dVoyjo6POA8+o7aisrMT8+fMx\n",
       "cuRIuLi4AOBcaE+WLFkChUKBWbNm1drPudA+ZGdno6SkBMuWLcOwYcOwf/9+TJ48GVOmTMEvv/wC\n",
       "gHPhYTDUdwLUvNatW4dNmzbh22+/RVBQEM6ePYtXX30VXl5eeOaZZ+o9tq61itS28X1vv6qrqzF1\n",
       "6lQolUrs3r1b3+lQM/v999+xefNmnDt3TqtdcFO4dqdmTfno0aMxZ84cAEDnzp1x6tQprF+/Ho89\n",
       "9pg+02uzeCW9nXnvvffwxhtvYMKECQgKCsLUqVMxb948zY2jTk5OAKDzqTcrK0vTR21PY953Jycn\n",
       "qFQq5OXlacVkZmZybrRBNcscEhIScODAAc1SF4Bzob04dOgQMjIy4OzsDCMjIxgZGSE1NRWLFi2C\n",
       "h4cHAM6F9sLe3h6GhoYIDAzUau/UqRPS0tIAcC48DCzS2xkhBKRS7bddKpVqrox4e3vDyckJe/fu\n",
       "1fTfuXMHR44cQZ8+fZo1V2o+jXnfu3XrBiMjI62Y9PR0XL58mXOjjamqqsLEiRORkJCA6OhoKBQK\n",
       "rX7OhfbhxRdfxIULFxAfH4/4+HicO3cOLi4umDdvHg4cOACAc6G9MDY2Ro8ePbS2WwTubsnor118\n",
       "bAAACm5JREFU5eUFgHPhYeByl3Zm9OjRWLFiBby9vREYGIizZ8/igw8+wNNPPw3g7tKGOXPmYNmy\n",
       "ZejUqRP8/Pzw7rvvwsLCAk8++aSes6cHUVpaimvXrgG4+6vL1NRUnDt3DnZ2dnB3d2/wfbeyssLM\n",
       "mTOxcOFCKBQK2NraYt68eQgNDcXgwYP1OTS6R/XNBRcXF4wfPx6nTp3CTz/9BCGE5r4Ea2trmJqa\n",
       "ci60IQ39XHBwcNCKNzIygpOTE/z8/ADw50Jb0tBcWLhwISZMmICIiAhERkYiOjoaW7duxa5duwBw\n",
       "LjwU+t1chppbSUmJmD9/vvDy8hIymUz4+PiIf/7zn6KiokIrbunSpcLZ2VmYmpqKAQMGiIsXL+op\n",
       "Y2oq0dHRQiKRCIlEIqRSqebvM2bM0MQ09L5XVFSIl19+WdjZ2QkzMzMxcuRIkZ6e3txDoQdU31xI\n",
       "SUnRaa/58+ct2TgX2obG/Fz4s79uwSgE50Jb0Zi58MUXX4iOHTsKmUwmQkNDxbfffqt1Ds6FpiUR\n",
       "gneAEBERERG1JFyTTkRERETUwrBIJyIiIiJqYVikExERERG1MCzSiYiIiIhaGBbpREREREQtDIt0\n",
       "IiIiIqIWhkU6EREREVELwyKdiIjqNX36dHh7e+u0l5aWwsnJCZs2bdK0LV26FFKpFNnZ2U3y2ikp\n",
       "KZBKpXj//fcbjF2wYAF69erVJK9LRKRvLNKJiKhBEolEp23t2rUwMTHBtGnT9PL6fzV//nzEx8fj\n",
       "p59+euj5EBE9bCzSiYioQX99OHVVVRXWrFmDZ555BoaGhnrKSpuTkxNGjhyJqKgofadCRPTAWKQT\n",
       "EdE92717N3JzczFhwgR9p6Jl4sSJOHLkCK5fv67vVIiIHgiLdCKiZlRSUoJ//OMf8Pb2hqmpKRQK\n",
       "BSIjIxETEwMAGDBgAAICAhAfH4+IiAjI5XJ4enpi1apVOucSQuDDDz9ESEgIZDIZHB0d8eyzzyIv\n",
       "L08ndu/evejfvz8sLCxgYWGB4cOHIz4+Xidu586dCA4OhkwmQ0hICH744Ydax7Fz5064uLggICCg\n",
       "wTHfvn0bgYGB6NixI9LT0+95nDVj/fTTT+Hr6wtTU1OEhYXh1KlTOnGDBg2CRCLBzp07G8yLiKgl\n",
       "Y5FORNSMXnjhBaxfvx5jx47Fxo0bsWjRIigUCpw/f14TU1RUhGHDhqFz586IioqCv78/FixYgJUr\n",
       "V+qca/78+ejduzfWrVuH5557Dt9//z0iIyNRUVGhiduyZQuGDx8OMzMzrFixAkuXLkVSUhIiIiJw\n",
       "5coVTdzevXsxduxYSKVSLF++HE888QRmzpyJ06dP66wJj4uLQ/fu3Rscb2pqKvr16wepVIqYmBi4\n",
       "ubkBuLvGvLHjBICtW7ciKioKL7zwAt59912kpKRgzJgxqK6u1oqzsrKCr68vYmNjG8yNiKhFE0RE\n",
       "1Gysra3Fyy+/XGd///79hUQiEStWrNC0qVQqERkZKeRyuSgqKhJCCBEbGyskEon46quvtI4/cuSI\n",
       "kEgk4t///rcQQoiSkhJhY2MjZs6cqRVXUFAgFAqFePLJJzVtXbp0ES4uLkKpVGraDh48KCQSifD2\n",
       "9ta0VVVVCalUKubOnauT/5IlS4REIhFZWVni2rVrwsPDQ3Tt2lXk5ube1ziTk5OFRCIRDg4OorCw\n",
       "UBP7448/ColEInbv3q2Tw9ChQ0XHjh112omIWhNeSSciakbW1tY4duwYbt++XWeMgYEBZs+erfle\n",
       "KpVi9uzZKCsrw++//w4A2LZtG8zNzTF06FDk5uZq/vj7+0OhUCA6OhoAsG/fPhQWFmLy5MlacdXV\n",
       "1QgPD9fEZWRkID4+HtOmTYOFhYXmtSMjIxEUFKSVX35+PoQQsLGxqXMMiYmJ6NevH5ydnREdHQ07\n",
       "O7t7GmdNXjXGjh0LKysrzffh4eEAgOTkZJ3z2tjYIDc3t87ciIhag5ZxSz4RUTsRFRWFp59+Gh4e\n",
       "HujatSuGDRuGadOmoWPHjpoYR0dHmJubax3n5+cH4O6+4QBw9epVlJSUwNHRsdbXycnJ0cQBwJAh\n",
       "Q2qNMzAwAHB3WcqfX+evr33u3DmddvGXHV/+bOTIkVAoFNi/f7/OWGrUN86afGp4eHhofV/zAaGg\n",
       "oKDWvKRSXoMiotaNRToRUTMaN24cIiIisGvXLuzduxfr1q3DypUr8cUXX2Dy5MmNPo9arYadnR22\n",
       "bt1aa39NEatWqwEAmzdvhqur64MPAICdnR0kEkmtBXKN8ePHY9OmTfjiiy/w0ksvPfBr1nyY+Kva\n",
       "PigUFBTA3t7+gV+TiEifWKQTETUzR0dHPPfcc3juuedQVFSEXr16YcmSJZoiPTMzE8XFxVrLTmqu\n",
       "iHt5eQEAfH19sX//fvTs2RNyubzO1+rQoQMAwN7eHgMHDqwzztPTU+t1/uyvbQYGBvDz80NSUlKd\n",
       "51u+fDlMTU3x6quvwtzcHNOnT9eJacw470dycjJCQkLu+3giopaAvw8kImomarUaRUVFWm1WVlbw\n",
       "8vLSaler1diwYYPO92ZmZoiMjAQATJo0CWq1Gm+//bbO66hUKhQWFgIAHn30UVhbW2PZsmWoqqrS\n",
       "ia1ZFuPs7IwuXbrgyy+/hFKp1PQfPHgQiYmJOsf17du31i0Q/2zDhg2YNm0a/v73v+O7776r9d+j\n",
       "oXHeq6KiIiQlJaFPnz73dTwRUUvBK+lERM1EqVTC1dUV48aNQ+fOnWFpaYnY2Fjs2bMHL7/8sibO\n",
       "yckJa9euRVpaGoKCgrBz504cOnQIy5cv11x1joiIwOzZsxEVFYXz589j6NChMDExwfXr17F9+3a8\n",
       "8847eOqpp2BhYYGPP/4YU6ZMQdeuXTF58mQoFAqkpaXht99+Q3BwMDZt2gTg7tXvxx9/HOHh4Zg+\n",
       "fToKCwuxfv16BAUFoaSkRGsso0aNwqZNm5CYmIjAwMA6x/z555+jpKQEU6dOhVwux2OPPXZP47xX\n",
       "+/fvhxACo0aNuq/jiYhaDL3uLUNE1I5UVlaKhQsXiq5duwpra2shl8tFSEiIWL16tVCpVEKIu1sT\n",
       "BgQEiPPnz4uIiAghk8mEh4eHiIqKqvWcn3/+uQgLCxNmZmbC0tJShISEiAULFoibN29qxcXExIjh\n",
       "w4cLGxsbIZPJRIcOHcTTTz8tjh07phW3Y8cOERgYKExNTUVwcLDYuXOnmD59utYWjEIIUV1dLRwd\n",
       "HcWSJUu02pcuXSqkUqnIysrSGvfw4cOFmZmZiI6Ovqdx1mzB+P777+uMXSKRiLfeekurbcKECSI8\n",
       "PLzWfysiotZEIkQ9t+cTEVGzGjBgALKzs2tdYtLSrFixAhs3bsSNGzdgaHhvv5h9GOPMyMiAj48P\n",
       "tm7dipEjRzbZeYmI9IFr0omI6L68+uqrqKysxJdffqnvVAAAq1evRmhoKAt0ImoTuCadiKiFaS2/\n",
       "4JTJZMjIyLjv45t6nFFRUU16PiIifeKVdCKiFkQikUAikeg7jYeuvYyTiOh+cU06EREREVELwyvp\n",
       "REREREQtDIt0IiIiIqIWhkU6EREREVELwyKdiIiIiKiFYZFORERERNTCsEgnIiIiImph/h/PU7LW\n",
       "90ccRAAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4809011c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian(mean=120, variance=17**2, xlabel='speed(kph)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The y-axis depicts the *probability density* - the relative amount of cars that are going the speed at the corresponding x-axis.\n",
    "\n",
    "You may object that human heights or automobile speeds cannot be less than zero, let alone $-\\infty$. This is true, but this is a common limitation of mathematical modeling. \"The map is not the territory\" is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above very closely models the distribution of the measured automobile speeds, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. \n",
    "\n",
    "You will see these distributions called *Gaussian distributions*, *normal distributions*, and *bell curves*. Bell curve is ambiguous because there are other distributions which also look bell shaped but are not Gaussian distributions, so we will not use it further in this book. But *Gaussian* and *normal* both mean the same thing, and are used interchangeably. I will use both throughout this book as different sources will use either term, and so I want you to be used to seeing both. Finally, as in this paragraph, it is typical to shorten the name and just talk about a *Gaussian* or *normal* - these are both typical shortcut names for the *Gaussian distribution*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So let us explore how Gaussians work. A Gaussian is a *continuous probability distribution* that is completely described with two parameters, the mean ($\\mu$) and the variance ($\\sigma^2$). It is defined as:\n",
    "$$ \n",
    "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 }\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in `stats.py` with the function `gaussian(x, mean, var)`.\n",
    "\n",
    "> **Optional:** Let's remind ourselves how to look at a function stored in a file by using the *%load* magic. If you type *%load -s gaussian stats.py* into a code cell and then press CTRL-Enter, the notebook will create a new input cell and load the function into it.\n",
    "\n",
    "    %load -s gaussian stats.py\n",
    "    \n",
    "    def gaussian(x, mean, var):\n",
    "        \"\"\"returns normal distribution for x given a \n",
    "        gaussian with the specified mean and variance. \n",
    "        \"\"\"\n",
    "        return np.exp((-0.5*(x-mean)**2)/var) / \\\n",
    "                         np.sqrt(_two_pi*var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><p><p><p>We will plot a Gaussian with a mean of 22 $(\\mu=22)$, with a variance of 4 $(\\sigma^2=4)$, and then discuss what this means. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAuAAAAGHCAYAAADxx+d2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdYVGfePvB7ClVAkSZgR8GOCqIi2MXeW9RoLElWk5io\n",
       "m7K+mze7+2625GeSNTGJpqoxGjWKLWLBggJWJKBiF0FEQECk15n5/ZHNmEcQEYFnyv25Lv8495zD\n",
       "3GQCfBnOeY5Cp9PpQEREREREDUIpuwARERERkTnhAE5ERERE1IA4gBMRERERNSAO4EREREREDYgD\n",
       "OBERERFRA+IATkRERETUgDiAExERERE1oBoN4F988QXatGkDGxsb+Pv7Iyoq6rH7RkREYPz48fDw\n",
       "8ECjRo3g6+uLtWvXVtrv2LFj8PPzg42NDby8vPDll1/W/rMgIiIiIjISTxzAt2zZgiVLluDdd99F\n",
       "XFwcAgMDMXLkSKSkpFS5/8mTJ+Hr64vt27cjISEBixYtwssvv4wff/xRv8+tW7cwatQoBAUFIS4u\n",
       "DsuXL8fixYsRGhpad58ZEREREZEBUjzpTpi9e/dG9+7dhXeovb29MWXKFPzzn/+s0ZNMnz4dGo0G\n",
       "27ZtAwC888472LlzJ65evarf56WXXkJCQgJOnDhRm8+DiIiIiMgoVPsOeFlZGWJjYxESEiLkISEh\n",
       "TzUo5+bmomnTpvrtkydPVvkxY2JioNFoavxxiYiIiIiMjbq6B7OysqDRaODm5ibkrq6uSE9Pr9ET\n",
       "/Pzzzzhy5IgwsGdkZFT6mG5ubqioqEBWVlalx4iIiIiITEW1A/izio6OxqxZs7Bq1Sr4+/s/9fG5\n",
       "ubn10IqIiIiIqGE0bty4UlbtKSjOzs5QqVTIyMgQ8oyMDLi7u1f7ZFFRURg1ahT+/ve/4w9/+IPw\n",
       "WLNmzSq9g56RkQG1Wg1nZ+dqPy4RERERkTGrdgC3tLSEn58fDh48KOTh4eEIDAx87HHHjx/HqFGj\n",
       "8Le//Q2vv/56pcf79u2L8PDwSh+zV69eUKlUT9OfiIiIiMioPPEUlGXLlmH27NkICAhAYGAg1qxZ\n",
       "g/T0dCxcuBAAsHz5cpw9exaHDh0C8Os64KNHj8Zrr72GGTNm6N/pVqlUcHFxAQAsXLgQn332GZYu\n",
       "XYqXX34Z0dHRWL9+PTZv3vzYHlW9ff97MTExAFCrU11ILr52xouvnTx3s5IReX4fzl6JQFl5yVMf\n",
       "v2rJTmF78coJT/0xrC1t4ecdjAE9xqBZ0xZPfTzVHr/2jBtfP+NV09fuSadRP3EAnzZtGrKzs/H+\n",
       "++8jLS0NXbt2RVhYGFq0+PWbbXp6OhITE/X7r1+/HiUlJVixYgVWrFihz1u3bq3fr3Xr1ggLC8PS\n",
       "pUuxevVqeHp6YtWqVZg4ceKT6hARmS2dTodrKedx4OxPuHHn4hP3V6ss4OHcGi1cveDu1AJODm5w\n",
       "tHeBnY0DVi0R933/xbXIL3qA3ML7yMhJRcb9O7iTeQt37t2EVqet8uOXlBUh+uIBRF88gE6t/TDE\n",
       "byLaN+9SF58qEZFJe+I64DL9/rcHvgNuuvjaGS++dg3nRmoC9p7chJupCdXu5+7UEp3b9EKHlt3R\n",
       "xr0DLNQWVe6nUIjbj/tJUFpegqS0q7icHIsLN88gMzet2uf3aemLsYGz0dKtXbX70bPh155x4+tn\n",
       "vGrzDnhVM2y9roJCRETP5l5OKkKPfYtLybGP3adxo6bo03kIenoHw92pZZ0+v5WFNXxa+sKnpS/G\n",
       "B81FWvZtnLl8FGevRCC/6EGl/a/ejsfV2/HwbdcX4/rNgUuT6i/YJyIyRxzAiYgMUGlZMQ6c3Yaj\n",
       "sbug0VZUuU87z84I9h2Nbm0DoFLV/7dzhUIBD+dWmBA8F2MDn8f5xNM4ErsLyenXKu0bf+MkEm7F\n",
       "YFivKRjqN+mx78QTEZkjDuBERAYm4VYMthxZjQcF2VU+3qFVD4zqMwOtm3k3cLOHVCo1erTvh+7t\n",
       "ApF49zL2ntpU6bz0Ck059p36ETFXjmHaoD/Ap6WvpLZERIaFAzgRkYEoLi3Czsi1OJkQXuXjXh6d\n",
       "MCbweXh5dmrgZo+nUCjg5dkJiyf9HVdvx2PPiQ1IuXdT2CfzwV18vuMv6O87CuP6vQBLCytJbYmI\n",
       "DAMHcCIiA3D9zkVsPPgJ7udnVnqscaOmmBA8Dz29g6B49OpJA6FQKNChVXf4tPTF2SsR2Bm5DgXF\n",
       "4jJcx+PDcPX2ecwevoQXaRKRWeMATkQkkVanRfjZbQg7tRm6R5b7UyqUGNRzHEYETIeVpY2khk9H\n",
       "oVAgoOMgdGnTC3uiN+DExYPQ4eESKxk5d/Dx1ncwrt9sDOox3mB/oSAiqk8cwImIJCkozsOGAytx\n",
       "uYoVTtwcm+P5kNfRSuJ53s/C1toO04csQq+OA7Hh4Epk52boH9NqNdgZuQ5Jadcwc9hiWBvJLxdE\n",
       "RHWl2lvRExFR/Ui5dxMrNi2rNHwroMCgHuPw1syPjHb4/r22Hh3xzsyV6NN5aKXH4m6cwEeb30Ja\n",
       "doqEZkRE8nAAJyJqYPE3TuGTn/4HOQVZQt7I2h4LJ7yHif3nw1JtOhcqWlvaYObQ1/DimD/BxqqR\n",
       "8Nivp6S8jUtJj1/nnIjI1HAAJyJqIDqdDuExofh2779RVlEqPNba3Qdvz/wYHVv1kNSu/nXz6oO3\n",
       "ZnwET+fWQl5aVoyvdr+PqPP75RQjImpgHMCJiBqARqvBj4c/x57o7ys9NqD7GLwx+R9wtHeR0Kxh\n",
       "OTduhqXTP0BAx0FCrtVpsfXoGuyMXAutViOpHRFRw+BFmERE9aysohTr932EC4lnhFypVGHqwJfR\n",
       "r+twSc3ksFRbYdaw1+Hp0gY7j68VVkk5ErsLDwruY3bIGw1yd08iIhn43Y2IqB4Vlxbi6z3/xI3U\n",
       "BCG3sWqE+aPeNtu7QyoUv15s6uTghu/3fyyckhN7LRKlZcWYN/otkzoXnojoNzwFhYionuQX5WLV\n",
       "9v+tNHw3tXfBsmkfmO3w/XvdvHrj9Sn/gEMjRyFPSIrB6p3/h+LSIknNiIjqDwdwIqJ6kF+Ui89D\n",
       "38OdzEQhd3dqiSXT/g23ps0lNTM8Ld3aYem0f8O5cTMhv5magM9D30NRaYGkZkRE9YMDOBFRHSso\n",
       "zsPnoe/hbnaykLd298HrU/6BJnZOkpoZLicHNyyZ+i94OLUS8tv3bmD1jr+huLRQUjMiorrHAZyI\n",
       "qA4VFOfhsyqGb5+Wvnh14t/QyNpeUjPD59DIEYunvI/WzXyEPDnjOlbv+j+UlBVLakZEVLc4gBMR\n",
       "1ZHC3975zkoScp+Wvnhp7P/AysJaTjEj0sjaHq9O/CvaenQU8qS0q1iz6/9QyiGciEwAB3AiojpQ\n",
       "WlaMNbv+jtRHh+8Wvw7fXM2j5qwsbbBw/Hto7S6+E5549zK+3P1+pZsYEREZGw7gRETPqLyiHN/s\n",
       "/TeSM64LuXeLbhy+a8na0gaLxr+HVm7thfxGagLW7fsIGt6sh4iMGAdwIqJnoNVq8MPBlbh6O17I\n",
       "2zfvipfH/hmWFhy+a8vGqhEWTfwLWrh6CfnFxDPYemQNdDrdY44kIjJsHMCJiGpJp9NhW8TX+OV6\n",
       "tJC3cPX69Z1vDt/PzNbKDq9M/CvcnVoK+cmEcISd2iSpFRHRs+EATkRUS/vPbEXUhf1C5trEAwvH\n",
       "vwdrSxtJrUxPI2t7LJrwFzjauwj5gTM/4Xh8mKRWRES1xwGciKgWzl45hn2nfhSyxnZOeGXiX2Fv\n",
       "21hSK9PVxM4Jr0z4C2wfWcZxe8TXOH/zlKRWRES1wwGciOgp3Uy9hE2HVgmZrZUdXpnwFzR1cJXU\n",
       "yvS5NW2OheP/V7ioVQcdvt//H6TcS6zmSCIiw8IBnIjoKWQ+SMM3P/8LGk2FPlOp1Hhp7P9UOk+Z\n",
       "6l7rZt6YP/ptKBUPf3yVVZTiqz3/QG7BfYnNiIhqjgM4EVENFZUU4Mtdf0dhSb6Qzxy6GF6enSS1\n",
       "Mj+dWvthysCXhSy3IBtf7fkHysq5RjgRGT4O4ERENaDRavDd3g9w78FdIR/Rezp6dRggqZX5Cuo2\n",
       "AgO7jxWylHs3seHgSmh1WkmtiIhqhgM4EVEN7Ipaj2t3LgiZn09/jOz9nKRGNCF4Ljq39hey+Bsn\n",
       "sf/0FkmNiIhqhgM4EdETnL1yDBG/7Baytu4dMXPoa1AoFJJakVKpwgsj/wgPp1ZCvv/0FlxIPCOp\n",
       "FRHRk3EAJyKqRsq9RGw+9LmQNbFzwvzR78BCbSmpFf3G2tIGL4/7M+xtxKUfNxxYiXs5qZJaERFV\n",
       "jwM4EdFjFBTn4duf/4VyTZk+U6sssGD0n+DQqInEZvR7TR1cMXfUW8LKKCVlRfjm53+jpKxYYjMi\n",
       "oqpxACciqoJWq8G6fR/ifn6mkE8fvBCtmrWX1Ioep33zLpgQPE/I0u+nYFP4Kuh0OkmtiIiqxgGc\n",
       "iKgK+09vxbWU80LW33cUencaIqkRPcmA7mPg59NfyOJunMCR2J2SGhERVY0DOBHRI64kx+HAma1C\n",
       "5uXZGROD50tqRDWhUCgwY8ir8HRuLeR7ojfgVtoVOaWIiKrAAZyI6HdyC+7j+wP/gQ4PT1uwt22C\n",
       "eSPfhEqlltiMasLSwgoLxvwJtlZ2+kyr02Ldvo8q3UCJiEgWDuBERP+l0Wqwbv9HKCjO1WcKhRIv\n",
       "jFgGh0aOEpvR03Bu3AyzQl4Xspz8TGw8+CnPBycig8ABnIjov/ad2oybqQlCNqL3dHi36CapEdVW\n",
       "17YBGNRjnJBdvHUWRx9Zz52ISAYO4EREAC4n/4Lws9uEzKeFL4b3miKpET2rsf1mo5WbuGLN7ujv\n",
       "kZR+TVIjIqJfcQAnIrOXV/gAPxxYKZz37WDriNnDl0KpVElsRs9CrbLA3FFvwsaqkT7TajVYF7YC\n",
       "RSUFEpsRkbnjAE5EZk2n02HToVXIf/S875F/5M12TICTgxtmDVssZPfzM7HlyGqeD05E0nAAJyKz\n",
       "Fnk+DJeSzgnZiN7T0b55F0mNqK518+qDAd3HCNkv16Nx9kqEnEJEZPY4gBOR2UrLvo2dkeuErK17\n",
       "R4TwvG+TMz7oBTR3aStkP0V8hezcDEmNiMiccQAnIrNUXlGG9fs/RoWmXJ9ZW9pi9oglUPG8b5Oj\n",
       "VllgzoilsFBZ6rPSsmJsOLASGq1GYjMiMkccwInILO058QPuZiUJ2dRBf4CTg5ucQlTvmjVtgfHB\n",
       "c4UsMe0yDsVsl1OIiMwWB3AiMjuXk39BxCPrQfv59EevDgMkNaKGEtxtJDq19hOyfac2I5lLExJR\n",
       "A+IATkRmpai0AJsOfSZkTe1dMHXQy5IaUUNSKBSYOXQx7Gwa6zOtTovvD6xEaXmJxGZEZE44gBOR\n",
       "WQk99i1yC7L12wqFErOHL4GtlZ3EVtSQHBo1wYyhrwpZ5oO72BP9vaRGRGRuOIATkdm4kHgGZy4f\n",
       "FbIhPSfAy7OzpEYkS9e2AejXZbiQHY8Pw7WUC5IaEZE54QBORGahsDgPmw9/IWTuTi0xss8MSY1I\n",
       "tgn958GpsXjR7aZDq1BaViypERGZCw7gRGQWtkV8jfyiB/ptpUKJWcNeh4XaQmIrksnKwhqzhr0u\n",
       "ZPfz7mFX1HpJjYjIXHAAJyKTF3f9BM5dixSykF5T0dKtnaRGZCjaeXaudJfMqAv7cfV2vKRGRGQO\n",
       "OIATkUnLL3qALUfXCJmnSxuEBPBul/SrsYGz4dLYXch+PPQZSngqChHVEw7gRGSydDodth5Zg8Li\n",
       "PH2mUqrx/LA3oFbx1BP6laWFFWaFvA4FFPrsfn4mdkWuk1eKiEwaB3AiMllxN04g/uYpIRvRezo8\n",
       "XVrLKUQGq61HRwzsMVbIoi8ewJXkOEmNiMiUcQAnIpNUWJKPbUe/ErKWru0w1H+SpEZk6EYHzoJr\n",
       "Ew8h+/Hw51wVhYjqHAdwIjJJuyLXIb84V7+tUqoxK+R1qJQqia3IkFmq/3sqiuLhj8ac/EzsPblJ\n",
       "YisiMkUcwInI5Fy9HY9Tlw4L2bBek+Hu1FJSIzIWbdw7YOAjq6Ici/sZSenXJDUiIlPEAZyITEpZ\n",
       "eSk2HxFvuOPWtDmG+XPVE6qZUX1nwsnh4Q16dNBh86HPUaEpl9iKiEwJB3AiMin7Tv+I7NwM/bYC\n",
       "Cswc+hpvuEM1ZmVhjemDFwnZ3exkHD63U1IjIjI1HMCJyGSk3LuJI7G7hSzYdyTauHeQ1IiMVYdW\n",
       "3RHQcZCQ7T+zBRn370hqRESmhAM4EZkEjaYCmw59Bp1Oq88c7ZwxJnC2xFZkzCYGz4OdTWP9tkZT\n",
       "gc2Hv4D2d/+PERHVBgdwIjIJR37ZjdTMW0I2bfBCWFvaSGpExq6RjQMmD1ggZDfvXsLJi+GSGhGR\n",
       "qeAATkRGL/NBGvaf2ixkft7B6NzGX1IjMhU9vYPRqVVPIdsVtR4PCrIlNSIiU8ABnIiMmk6nw9aj\n",
       "a1CuKdNnttb2mPTIO5dEtaFQKDBt8EJYWljrs5KyIoQe/1ZiKyIydhzAicio/XI9GldvxwvZpP7z\n",
       "YW/bRFIjMjVNHVwxNvB5IYu7fgKXkmIlNSIiY8cBnIiMVnFp5XcivZt3Ra8OA+UUIpMV3G0kWrh6\n",
       "CdlPEV+irKJUUiMiMmYcwInIaIWd2oS8whz9tkqpxtRBf4BCoZDYikyRUqnC9MGLoMDD/7eyczMQ\n",
       "fna7xFZEZKw4gBORUUq5dxPH48OEbIjfRLg1bS6pEZm6lm7tENRtpJAdOheKjJxUSY2IyFhxACci\n",
       "o6PVarD1yBphzW8nBzeEBPB281S/RgfOFK4v0Ggq8NORNdDpdBJbEZGx4QBOREbnxMVwJGdcF7Ip\n",
       "A1+CpdpKUiMyF7ZWdpjUf76QXbtzAeeuHpfUiIiMUY0G8C+++AJt2rSBjY0N/P39ERUV9dh9S0tL\n",
       "MXfuXPj6+sLS0hKDBg2qtE9ERASUSmWlf9euXav9Z0JEZiGv8AH2nNggZL5efbjmNzWYnt7B8G7R\n",
       "Tch2RK5FUWmBpEZEZGyeOIBv2bIFS5Yswbvvvou4uDgEBgZi5MiRSElJqXJ/jUYDGxsbLF68GKNH\n",
       "j672YqhLly4hPT1d/69du3a1/0yIyCzsjFqL4tJC/balhTXX/KYGpVAoMG3QH6BSqfVZftED/Hxi\n",
       "o8RWRGRMnjiAf/zxx5g3bx4WLFgAHx8ffPrpp3B3d8fq1aur3N/W1harV6/Giy++CE9Pz2rPi3Nx\n",
       "cYGrq6v+n1LJM2KI6PGupVxAzJVjQjaqzww42rtIakTmytXRE8P8JgtZ9Pn9SE6//pgjiIgeqnbi\n",
       "LSsrQ2xsLEJCQoQ8JCQEJ06ceOYn9/f3h4eHB4YOHYqIiIhn/nhEZLoqNOX46eiXQubh3BoDuo+R\n",
       "1IjM3bBek+HcuJl+Wwcdfor4CtrfXRxMRFSVagfwrKwsaDQauLm5CbmrqyvS09Nr/aQeHh5Ys2YN\n",
       "QkNDERoaCh8fHwwZMqTac8uJyLxF/LIHGTl3hGzaoIVQKVWSGpG5s1BbYuqgPwjZ7YzrOJ1wWFIj\n",
       "IjIW6ifvUve8vb3h7e2t3+7Tpw+SkpKwYsUKBAUFVXlMTExMjT52Tfcjw8PXznjV92tXVJqHsNgf\n",
       "haydW3fcv1uA+3f5/03tiBet8uuv9lo6dcDt7Cv67dBja6EtsIaV2qben5uvm3Hj62e8nvTatW/f\n",
       "vtrHq30H3NnZGSqVChkZGUKekZEBd3f3GlasmYCAAFy/znPniKiyc0mHUaEt129bqq3Rs9VgiY2I\n",
       "HvJvPRQq5cP3s0orihB/m8sSEtHjVfsOuKWlJfz8/HDw4EFMnvzwYpPw8HBMnTq1TovExcXBw8Pj\n",
       "sY/7+1e/xNhvv4k8aT8yPHztjFdDvHY3UxNwKzpByMYHzUGQb/96e05zxK+/Z1NikY2wUw//SnM1\n",
       "/RzGD5oFT5fW9fJ8/L5p3Pj6Ga+avna5ubnVPv7EZUeWLVuGdevW4dtvv8Xly5fxxhtvID09HQsX\n",
       "LgQALF++HEOHDhWOuXTpEuLi4pCVlYWCggLEx8cjLi5O//jKlSuxa9cuXL9+HQkJCVi+fDl27dqF\n",
       "11577Ul1iMiMaLQa/BTxtZB5OrdGv67DJTUiqtoQv4lwavzweimdTottEV/xDplEVKUnngM+bdo0\n",
       "ZGdn4/3330daWhq6du2KsLAwtGjRAgCQnp6OxMRE4ZjRo0cjOTkZwK/rpfbo0QMKhQIajQYAUF5e\n",
       "jrfeegt37tyBjY0NunTpgrCwMIwYMaKuPz8iMmLRFw7gblaSkE0Z+DKUvPCSDIyF2hKT+i/A13v+\n",
       "qc9u3r2E2GuR8PPhX2uISFSjizAXLVqERYsWVfnY2rVrK2W3bt2q9uO99dZbeOutt2ry1ERkpgqK\n",
       "8xB2cpOQ+fsMgJdnJ0mNiKrXpU0vdGrth0tJ5/TZzsh16NymF6wt6/+CTCIyHrzzDREZpJ9P/CDc\n",
       "2tvKwhrjg16Q2IioegqFApP6LxDukJlbeB8HzmyV2IqIDBEHcCIyOLczbuDkxXAhGx4wDY3tmkpq\n",
       "RFQzro4eGNxjvJD9uoZ9qqRGRGSIOIATkUHR6rTYFvE1dHh48ZprEw8M7DFWYiuimgsJmIomdk76\n",
       "bY22AtsjvuYFmUSkxwGciAzK2csRSEq/KmSTBrwItcpCUiOip2NlYY0JwfOE7MrtOFxIPC2pEREZ\n",
       "Gg7gRGQwiksLsTv6eyHr0jYAnVr3lNSIqHZ6tO+H9s27Clno8e9QVlEqqRERGRIO4ERkMPaf3oL8\n",
       "ogf6bbXKApP6z5fYiKh2FAoFJg94EUrFwx+z9/Pu4WjsbomtiMhQcAAnIoNwLycVx+L3CtkQv4lw\n",
       "btxMUiOiZ+Ph3ArBvqOELDxmOx4UZEtqRESGggM4ERmEnVHrodVq9NuOds4Y5j9ZYiOiZzey93No\n",
       "ZG2v3y4rL8Ge6A0SGxGRIeAATkTSXUs5j4uJZ4RsXNALsLSwktSIqG7YWtthVN+ZQnb2SgSS0q9J\n",
       "akREhoADOBFJpdVqEHr8OyFr3cwHPb2DJDUiqluBXULg7tRSyEKPfctlCYnMGAdwIpLq9KUjuJuV\n",
       "JGQT+8+HQqGQU4iojqmUKkzqv0DIktKvIubqcUmNiEg2DuBEJE1JWTF+PrlRyPy8g9HG3UdSI6L6\n",
       "4dPSF13bBgjZ7ujvUVpeIqkREcnEAZyIpDkUs11YdtBCZYmx/eZIbERUfyYEz4NKqdZv5xZk43DM\n",
       "DomNiEgWDuBEJMX9vHs4ErtLyAb1HI+mDi6SGhHVL5cm7hjYY4yQHT63A/fzMiU1IiJZOIATkRS7\n",
       "ozegQlOu33awdcQw/0kSGxHVv5Be02Bv01i/Xa4pq3T3VyIyfRzAiajB3Uq7gthrkUI2OnAWrCxt\n",
       "JDUiahg2VrYYE/i8kMVei8TN1EuSGhGRDBzAiahB6XS6SssOerq0Qe+OgyQ1ImpYvTsNRnOXtkIW\n",
       "evxbaHVaSY2IqKFxACeiBhV7LRLJj9yEZGLwfCiVKkmNiBqWUqnC5AHisoQp927izKWjkhoRUUPj\n",
       "AE5EDaasohS7o8TzXbu2DYB3i66SGhHJ4eXZGd3bBwrZzyd+QElZsaRGRNSQOIATUYM5GrsbOQVZ\n",
       "+m2VUo3xQXPlFSKSaHzQC1CrLPTbeUU5OHh2m8RGRNRQOIATUYPILbyP8JjtQhbsOwqujh6SGhHJ\n",
       "5eTghsE9JwjZ0V92ITs3Q1IjImooHMCJqEHsPbERZb+765+ttT1GBEyT2IhIvmH+k+DQyFG/rdFU\n",
       "cFlCIjPAAZyI6t2dzEScvnREyEb2ng5baztJjYgMg5WlDcYGzhayX65HI/HuFUmNiKghcAAnonql\n",
       "0+mw4/ha6KDTZ26OzRHUdYTEVkSGo1fHgWjuKi5LuIPLEhKZNA7gRFSvLiSewfU7F4RsQvBcqFRq\n",
       "SY2IDItSocTE4PlClpxxHb9ci5LUiIjqGwdwIqo3FZpy7IpcJ2Q+LX3RqbWfnEJEBqp98y7o5tVH\n",
       "yHZHb0BZRamkRkRUnziAE1G9iYzfh8zcNP224r/v9CkUComtiAzTuH5zoFI+/MtQTn4mIn7ZI7ER\n",
       "EdUXDuBEVC8Ki/Ow/8wWIQvsPAwezq0kNSIybK6OHgj2HSVk4We3Ia/wgaRGRFRfOIATUb3Yd3oL\n",
       "iksL9dtWljYY1XeGxEZEhm9EwDTYWtvrt0vLSxB2apPERkRUHziAE1Gdy7h/B1Hn9wlZSK+psLdt\n",
       "IqkRkXGwtbbDyN7ThexkwiHczUqSU4iI6gUHcCKqczsj1wlLqDV1cMXA7mMkNiIyHkFdR8C1ycM7\n",
       "xOp0WuyIXAudTlfNUURkTDiAE1GdupIch4SkGCEbH/QCLNSWkhoRGReVSo3xwXOF7OrteFxOjpVT\n",
       "iIjqHAdwIqozGq0GOyK/E7K2Hh3RvV2gpEZExqlLm15o37yrkO2IXAuNViOpERHVJQ7gRFRnTiUc\n",
       "Qlr2bSHjsoNET0+hUGBC8Dwo8PBrJ+P+HZy4eFBiKyKqKxzAiahOFJcWYe9JcbWGXh0GolWz9pIa\n",
       "ERm3Fq5tEdBpsJCFnfpRWF2IiIwTB3AiqhPhZ7ehoDhXv22htsSYwOclNiIyfmP6zoKl2kq/XVic\n",
       "h4Nnt0lsRER1gQM4ET2z7NwMHI3bLWRDek6Eo72zpEZEpqGxXVMM8Z8kZBFxe5BfkiOpERHVBQ7g\n",
       "RPTMdkWvh0ZTod9u3KgphvhPlNiIyHQM7jkeje2c9NsaTQVik45KbEREz4oDOBE9k4y824i7fkLI\n",
       "xgQ+DysLa0mNiEyLlYU1xj5yOldy9iXcy0uR1IiInhUHcCKqNZ1Oh5hb4ULWwtULvToOlFOIyET5\n",
       "dxiA5q5thSzmVrhwwysiMh4cwImo1m5lXkR2QZqQTeo/H0oFv7UQ1SWlQomJwfOFLKvgLmKvRkpq\n",
       "RETPgj8liahWyspLEZt8RMh82/WFl2dnSY2ITFv75l3QzauPkO2J3oCyilJJjYiotjiAE1GtHI7d\n",
       "iaKyfP22SqXGuH5zJDYiMn3jg16ASqnWb+cUZCEidnc1RxCRIeIATkRP7UFBNg7HhArZAN8xcGni\n",
       "LqkRkXlwaeKO/r6jhCw8ZjvyCrksIZEx4QBORE/t5xM/CH/2bmTjgOEBUyU2IjIfwwOmwVJto98u\n",
       "LS9B2Km5N3vwAAAgAElEQVRN1RxBRIaGAzgRPZXbGTdw5rK4BvGoPjNgY9VIUiMi82JrbQffFv2F\n",
       "7GTCYaRmJskpRERPjQM4EdWYTqfDjsi1QtbE1gWBXUIkNSIyTz7NesLBuql+W6fTYmfkWuh0Oomt\n",
       "iKimOIATUY2dv3kKN1MThMyv9VColCpJjYjMk1Kpgl+boUJ2NSUel5LOSWpERE+DAzgR1Uh5RTl2\n",
       "Rq0TMo8mXvB09JJTiMjMNXdsD+/mXYVsR+RaaDQVkhoRUU1xACeiGjkevxfZuRn6baVCCf9H3oEj\n",
       "ooajUCgwsf98KKDQZ/dyUhF1Yb/EVkRUExzAieiJ8otyceDMViEL7DocTWxdJDUiIgDwdGmDPp3F\n",
       "X4T3nd6CopICSY2IqCY4gBPRE+079SNKyor02zaWthjVZ4bERkT0m9F9Z8LKwlq/XVSSj/2nt0hs\n",
       "RERPwgGciKqVln0b0RcPCtnw3tNgZ+MgqRER/Z5DI0cM858sZMfPh+FeTqqkRkT0JBzAiahaOyPX\n",
       "QafT6redGzdDcLfREhsR0aMG9hwHR/uHp4RptRrsjFovsRERVYcDOBE91qWkWFxOjhWy8UFzYaG2\n",
       "kNSIiKpiqbbCuH5zhOxi4hlcSzkvqRERVYcDOBFVSaPVYOcjN91p59kZ3bx6S2pERNXp6R2E1u4+\n",
       "Qrbj+HfQajWSGhHR43AAJ6IqnbhwAOn3U/TbCvx3yTOFopqjiEgWhUKBicHzhSw1KwmnLx2R1IiI\n",
       "HocDOBFVUlRagLBTPwpZQMdBaOHKm+4QGbI27j7w8w4Wsp9PbkRJWbGkRkRUFQ7gRFTJgdNbUViS\n",
       "r9+2VFthTODzEhsRUU2N7TcHFipL/XZ+0QMcitkusRERPYoDOBEJ7uXcxfH4MCEb1msyGts1ldSI\n",
       "iJ5GUwcXDOo5XsiOxO7C/bx7khoR0aM4gBORYFfUOmi0FfptRzvnSj/MiciwDfOfBAdbR/12haYc\n",
       "e6I3SGxERL/HAZyI9K6lnMeFxDNCNi5oDizVVpIaEVFtWFnaYHTgLCE7dy0St9KuSmpERL/HAZyI\n",
       "APx6447Q498JWetmPuj5yAVdRGQcenccBE+XNkK24/h30Ol0khoR0W84gBMRAODUpcO4m5UkZJMG\n",
       "LOCyg0RGSqlUVVqWMCn9KmKvRUpqRES/4QBORCguLcLeExuFzN9nAFo385bUiIjqgneLrujaNkDI\n",
       "dkd9j7KKUkmNiAjgAE5EAMLPbkN+ca5+20JtibH9uOwgkSkYHzQXKqVav51TkIWjsbslNiIiDuBE\n",
       "Zi4rNx1H48QfxkP8JsLR3kVSIyKqS66OHgj2HSVk4THbkVeYI6kREXEAJzJzu6LWQ6N5uOxg40ZN\n",
       "McRvosRGRFTXRgRMQyNre/12WXkJfj65sZojiKg+cQAnMmM3UhMQf+OkkI3tNxtWFtaSGhFRfbC1\n",
       "tsPIPs8J2emEw7iTmSipEZF54wBOZKa0Wg1Cj30rZC3d2sO/wwBJjYioPvXrMhxujs312zrosOP4\n",
       "Wi5LSCQBB3AiM3XmckSld78m9V8ApYLfFohMkUqlxoTguUJ2/c6FSjffIqL6x5+0RGaopKwYP5/4\n",
       "Qch6egehrUcHSY2IqCF0au0Hn5a+QrYrch0qNOWSGhGZpxoN4F988QXatGkDGxsb+Pv7Iyoq6rH7\n",
       "lpaWYu7cufD19YWlpSUGDRpU5X7Hjh2Dn58fbGxs4OXlhS+//LJ2nwERPbVDMaHIK3q4AoJaZYFx\n",
       "/eZIbEREDUGhUGBi8HwofveXrszcNETG75PYisj8PHEA37JlC5YsWYJ3330XcXFxCAwMxMiRI5GS\n",
       "klLl/hqNBjY2Nli8eDFGjx5d5V30bt26hVGjRiEoKAhxcXFYvnw5Fi9ejNDQ0Gf/jIioWvfz7uFI\n",
       "7E4hG9xzApo6uEpqREQNycO5FQI7DxOy/ac3I78o9zFHEFFde+IA/vHHH2PevHlYsGABfHx88Omn\n",
       "n8Ld3R2rV6+ucn9bW1usXr0aL774Ijw9Pau8uGPNmjVo3rw5PvnkE/j4+ODFF1/ECy+8gA8//PDZ\n",
       "PyMiqtbu6O+FPzc72DpimP8kiY2IqKGN6jsD1pa2+u3isiLsPflDNUcQUV2qdgAvKytDbGwsQkJC\n",
       "hDwkJAQnTpyo9ZOePHmyyo8ZExMDjUZT649LRNW7mXoJsdfEU8jGBD4PK0sbSY2ISAZ72yYY0Xua\n",
       "kJ28eAgp97gsIVFDUFf3YFZWFjQaDdzc3ITc1dUV6enptX7SjIyMSh/Tzc0NFRUVyMrKqvQYAMTE\n",
       "xNToY9d0PzI8fO3ql1anRVj8d0LWtFEzqIocnvm/PV87Y+QvbPE1NE7P8ro10rrDwcYJecXZAH5d\n",
       "lnD93v9geJc5VZ4+SnWPX3fG60mvXfv27at9nKugEJmJGxlxuF8o/uLcq00If9ASmSmVUoVebcRz\n",
       "we/lpSAp65KkRkTmo9p3wJ2dnaFSqZCRkSHkGRkZcHd3r/WTNmvWrNI76BkZGVCr1XB2dq7yGH9/\n",
       "/yrz3/z2m8iT9iPDw9eu/hWVFGB77KdC1tM7GKOHPNu533ztTAdfQ+NSV197/vBHetENJCQ9fDfv\n",
       "wt3jGDd0Ou+IW4/4vdN41fS1y82t/qLmat8Bt7S0hJ+fHw4ePCjk4eHhCAwMrEnPKvXt2xfh4eGV\n",
       "PmavXr2gUqlq/XGJqGr7Tm9GYXGefttCbYnxQVx2kIiAif3nQaV8+H7cg4JsHIrhqmRE9emJp6As\n",
       "W7YM69atw7fffovLly/jjTfeQHp6OhYuXAgAWL58OYYOHSocc+nSJcTFxSErKwsFBQWIj49HXFyc\n",
       "/vGFCxciNTUVS5cuxeXLl/HNN99g/fr1ePPNN+v40yOitOzbiIwPE7KQXlPgaO8iqRERGRJXR08M\n",
       "6D5GyI6c24nsvIzHHEFEz6raU1AAYNq0acjOzsb777+PtLQ0dO3aFWFhYWjRogUAID09HYmJ4lXT\n",
       "o0ePRnJyMoBfF/3v0aMHFAqFfoWT1q1bIywsDEuXLsXq1avh6emJVatWYeLEiXX9+RGZNZ1Oh9Bj\n",
       "30Kr0+qzpg6uGNRzvMRWRGRohgdMw9krEcgvegAAKNeUYWfkOiwY/Y7kZkSm6YkDOAAsWrQIixYt\n",
       "qvKxtWvXVspu3br1xI/Zv39/nDt3riZPT0S1dCHxNK6mxAvZxOB5sFRbSWpERIbIxsoWYwNnY9Oh\n",
       "Vfos/sZJXEu5AO8WXSU2IzJNXAWFyESVV5Rhx3HxF2TvFt3QzauPpEZEZMgCOg1CSzdx6bTtx76G\n",
       "Rsv7cxDVNQ7gRCbqSOwu4RxOpUKJyQNe5LKDRFSl375H/F5a9m1EXzggqRGR6eIATmSCcvKzEH52\n",
       "m5AFdRsJd6eWkhoRkTFo4+6DXh0GClnYyU3CKkpE9Ow4gBOZoN1R61FWUarfbmRtj1F9ZkhsRETG\n",
       "Yly/ObD83RrgRaUFCDu1WWIjItPDAZzIxNxMvYRz1yKFbEzg87C1tpPUiIiMSWO7pgjpNUXIoi7s\n",
       "x92sJDmFiEwQB3AiE6LVarD92DdC5unSBn07D33MEURElQ3qMQ5Ojd302zqdFtsivoZOp5PYish0\n",
       "cAAnMiEnEw7hTqa4Lv+UAS9CqeQdZomo5izUlpgYPF/IbqQm4NzV45IaEZkWDuBEJqKgOA97ojcI\n",
       "WU/vYHh5dpbUiIiMWde2AejQqoeQ7Yxah+LSIkmNiEwHB3AiE7EnegOKSgv025YW1hgfNEdiIyIy\n",
       "ZgqFAlMGvASV6uE9+/IKc7D/NC/IJHpWHMCJTMCttKs4mRAuZCMCpsHR3kVSIyIyBa6OHhjSc6KQ\n",
       "HYv7GXezkiU1IjINHMCJjJxWq8FPEV8KmZtjcwzsMVZSIyIyJSG9pgi/zGt1WmyL+IoXZBI9Aw7g\n",
       "REYu+uJB3Ln3yIWXA1+CWmUhqRERmRJLCytM6r9AyHhBJtGz4QBOZMTyix7g5xM/CFlP7yD4tPSV\n",
       "1IiITFE3r97o2KqnkPGCTKLa4wBOZMR2R29AcWmhftvSwhoTgudJbEREpkihUGDygBd5QSZRHeEA\n",
       "TmSkEu9ewelLh4VsZO/n0MTOSVIjIjJlvCCTqO5wACcyQpoqLrxs1rQFBnYfI6kREZkDXpBJVDc4\n",
       "gBMZoegL+5GaeUvIpg56WfjzMBFRXeMFmUR1gwM4kZHJK3yAvSc2CpmfT3+0b95VUiMiMie8IJPo\n",
       "2XEAJzIyu6PXo7js4Q86K0sbTAiaK68QEZmVx12QuffkxmqOIqLf4wBOZESu37mAM5ePCtmo3jPQ\n",
       "2K6ppEZEZI5cHT0w1E+8IDMyPgy3M25IakRkXDiAExmJ8opybDmyRsjcnVqiv+8oSY2IyJwN6zUF\n",
       "To3d9Ns66LD5yBfQaDUSWxEZBw7gREbi8LlQ3MtJFbLpgxfxwksiksJSbYWpA/8gZHfuJSIyPkxS\n",
       "IyLjwQGcyAjcy7mLg2e3CVlgl2Fo69FRUiMiIqBT657o0b6fkO09uRE5+VmSGhEZBw7gRAZOp9Nh\n",
       "69E1qNCU6zN7m8YY22+OxFZERL+aNGABrC1t9dul5SUIPfaNxEZEho8DOJGBi7l6DNdSzgvZhP7z\n",
       "0cjaXlIjIqKHGjdqijGBzwtZ/M1TuJh4VlIjIsPHAZzIgBWW5GPH8bVC5tPCF/4+/SU1IiKqLKjr\n",
       "cLR0ay9kP0V8hdLyEkmNiAwbB3AiA7Y76nsUFOfqt9UqC0wbvBAKhUJiKyIikVKpwvTBi6BQPBwr\n",
       "cvIzsf/0ZomtiAwXB3AiA3UzNQEnE8KFbHjAVLg0cZfUiIjo8Vq4tsWA7mOE7GjsbqRmJskpRGTA\n",
       "OIATGaAKTeU1v90cm2Nwz4mPOYKISL7RfWagiZ2Tflur02LL0dXQ6rQSWxEZHg7gRAboyLmdSL+f\n",
       "ImTThyyChdpCUiMioiezsrTBlIEvCVlS2lVEnd8vqRGRYeIATmRg7uWkYv+ZrULWu9MQtPPsLKkR\n",
       "EVHNdfPqgy5tA4RsT/T3uJ+XKakRkeHhAE5kQLQ6LX489Lmw5ncja3uMD3pBYisioqczdeDLsLK0\n",
       "0W+Xlpdg65HV0Ol0ElsRGQ4O4EQGJPrCAdy8e0nIJg14EXY2DpIaERE9PUd7Z4zvJ75xcCk5FjFX\n",
       "j0tqRGRYOIATGYic/Ezsjv5eyDq19uOa30RklAK7hsDrkVPnQo99g/yi3MccQWQ+OIATGQCdToet\n",
       "R75EaVmxPrOysMa0QVzzm4iMk1KhxIwhr0CtenjxeGFJPm9TTwQO4EQG4dzV40hIihGycf3moKmD\n",
       "i6RGRETPztXREyN7Pydk565F8jb1ZPY4gBNJll+Ui+2PvCPU1qMj+nUbIakREVHdGdxzPDxd2gjZ\n",
       "1qNrUFxaJKkRkXwcwIkkCz3+LQpL8vXbapUFZgx9DUoFvzyJyPipVGrMfOR72oOCbOx55JoXInPC\n",
       "n/BEEl1MPItzj6wKMLL3c3Bz9JTUiIio7rVw9cLgnhOELOrCftxITZDUiEguDuBEkhSXFmLrUfF2\n",
       "854ubTC453hJjYiI6s+IPtPh0sRDyH489DnKykslNSKShwM4kSShx7/Dg4Js/bZSocTMoa9BpVJL\n",
       "bEVEVD8s1VZ4bsgrQpb54C5+PrlRUiMieTiAE0lwMfEsTl86LGSD/SaihauXpEZERPWvffMu6Ndl\n",
       "uJAd+2UPbvJUFDIzHMCJGlhhST42H/lCyNydWlZaqouIyBSND56LpvYPl1jVQYeN4atQWl4isRVR\n",
       "w+IATtTAtkd8g7zCHP22UqHErGGvw0JtUc1RRESmwdrSBjOHvS5kWbnpXBWFzAoHcKIGFH/jFGKu\n",
       "HhOyYb2moKVbO0mNiIganneLrujvO0rIjseH4VrKeUmNiBoWB3CiBlJQnIetR1YLmadzawwPmCqp\n",
       "ERGRPGP7zYFz42ZCtil8FUrKiiU1Imo4HMCJGsjWo2uQX5yr31YqVXg+5A2oVTz1hIjMj5WFNWYN\n",
       "WwwFFPrsfn4mdkauldiKqGFwACdqALHXohB3/YSQjQiYVun2zERE5sTLszMG9BgrZCcuHsTl5F8k\n",
       "NSJqGBzAiepZXmEOfjr6pZC1cPXCMP/JkhoRERmOMYGz4FrpBj2foai0QFIjovrHAZyoHul0vy6v\n",
       "VViSr89UKjWeD3mDN9whIsKvN+iZFfIGFIqHI8mDgmz8dOTLao4iMm4cwInqUeT5fbicHCtko3rP\n",
       "gLtTS0mNiIgMTxt3HwzpOUHIzl2LRMyVY485gsi4cQAnqifp91OwK3KdkLX16IghfhOqPoCIyIyN\n",
       "7DMDns6thWzr0S9xP++enEJE9YgDOFE9qNCU4/v9/0G5pkyfWVnaYPbwJVAqVRKbEREZJgu1BeaM\n",
       "WCasDFVSVoQNBz+BVquR2Iyo7nEAJ6oHYSd/xJ3MRCGbOvBlODm4SWpERGT43J1aYnzQC0J2MzUB\n",
       "h8/tlNSIqH5wACeqY9fvXMDhczuErKd3EHp1GCinEBGREQn2HYUOrXoI2d5Tm3A744akRkR1jwM4\n",
       "UR0qKi3ADwc+gQ46fdbEzgnTBi2EQqGo5kgiIgIApUKJWcMWo5G1vT7TajX4/sB/UFZeKrEZUd3h\n",
       "AE5Uh3468iVyCrL02woo8HzIEtha20lsRURkXBo3aornhrwqZPdyUnmXTDIZHMCJ6sjZKxE4dy1S\n",
       "yAb1HA/vFl0lNSIiMl6+7fqgT+ehQhZ1YT8uJJ6R1Iio7nAAJ6oD93JSseXIGiHzdG6N0X1nSWpE\n",
       "RGT8JvdfAOfGzYRsY/gq5ORnSmpEVDc4gBM9o/KKMqzd9yHKykv0mYXKEnNGLIOF2qKaI4mIqDpW\n",
       "ljaYM2IZlL+7S2ZRST7W7/8YGi5NSEaMAzjRM9oVtQ6pmbeEbNKABbzbJRFRHWjdzBujA58XssS7\n",
       "l7H/9GZJjYieHQdwomcQf+MUjseHCVmP9v0Q2CVEUiMiItMzxG9CpaUJD57Zhqu34yU1Ino2HMCJ\n",
       "aul+3j1sOrRKyJwau+G5Ia9wyUEiojqkVCgxO+QNONg66jMddNhwYCXyCh9IbEZUOxzAiWpBo6nA\n",
       "uv0fobi0UJ+plGrMHfEmbKwaSWxGRGSa7G2bYPbwJVDg4RsceUU5+OHgSmh1WonNiJ4eB3CiWth7\n",
       "6kckpV0VsrH9ZqNVs/aSGhERmT6flr4ICZgiZFdux+FwzI7HHEFkmDiAEz2lC4lncChmu5B1bu2P\n",
       "QT3GSWpERGQ+RvR+Dl4enYTs55Mbcf3OBUmNiJ4eB3Cip5D5IA0/HFgpZI3tnDAr5HWe901E1ABU\n",
       "ShXmjFgG29/dql6n02Ldvo+QW3BfYjOimuMATlRDZRWl+G7vByguK9JnSoUSc0csg52Ng8RmRETm\n",
       "xdHeGbND3hCy/KIHWBu2AhpNhaRWRDXHAZyoBnQ6HX468iVSs5KEfHzQXHh5dpZTiojIjHVu44/h\n",
       "AdOELDHtMnZFfy+pEVHNcQAnqoGTCeE4ffmIkHVvF4iBPcZKakRERCN7T0eHlt2FLOKX3Yi9FiWp\n",
       "EVHNcAAneoLbGTfwU8RXQubq6ImZwxbzvG8iIomU/z0f3NHOWch/PPQZ0u+nSGpF9GQ1GsC/+OIL\n",
       "tGnTBjY2NvD390dUVPW/WV64cAEDBgyAra0tmjdvjr///e/C4xEREVAqlZX+Xbt2rfafCVE9KCzJ\n",
       "x3d7PxDOKbS0sMaC0X+CtaWNxGZERAQAdjYOmD/6bahUan1WWl6Cb/d+gJKyYonNiB7viQP4li1b\n",
       "sGTJErz77ruIi4tDYGAgRo4ciZSUqn+zzMvLw7Bhw+Du7o6YmBh88sknWLFiBT7++ONK+166dAnp\n",
       "6en6f+3atXv2z4iojmi0GqwL+xD38zOFfMaQV+Du1EJSKyIielSrZt6Y3P9FIcu4fwc/HPyEN+kh\n",
       "g/TEAfzjjz/GvHnzsGDBAvj4+ODTTz+Fu7s7Vq9eXeX+GzduRElJCdavX49OnTph8uTJeOedd6oc\n",
       "wF1cXODq6qr/p1TyjBgyHLsi1+FqSryQ9fcdDT+f/pIaERHR4/TrOhy9OgwUsvM3T+HA6a1yChFV\n",
       "o9qJt6ysDLGxsQgJCRHykJAQnDhxospjTp48ieDgYFhZWQn73717F8nJycK+/v7+8PDwwNChQxER\n",
       "EVHLT4Go7p2+dBgRcXuErK17R0wIniunEBERVUuhUGD64EXwdGkj5PtOb0b8jZOSWhFVrdoBPCsr\n",
       "CxqNBm5ubkLu6uqK9PT0Ko9JT0+vtP9v278d4+HhgTVr1iA0NBShoaHw8fHBkCFDnnhuOVFDuJV2\n",
       "FZuPiH/haWLnhPmj34FaZSGpFRERPYmlhRVeGrMcjR65N8OGg5/g7iPLyBLJpH7yLk+nJqtCeHt7\n",
       "w9vbW7/dp08fJCUlYcWKFQgKCqrymJiYmBo9f033I8NjCK9dUWke9sZ/J1x0qVKq0c9rAq5dviGx\n",
       "mWEzhNeOnpa/sMXX0DjxdatakNd4HEzYCN1/z/8uKy/BZ9v+ilG+82FtYSu53UN8/YzXk1679u3b\n",
       "V/t4te+AOzs7Q6VSISMjQ8gzMjLg7u5e5THNmjWr9O74b8c3a9bssc8VEBCA69evV1uWqD5VaMpx\n",
       "9Mo2FJcXCHlguzFwsqv6/3ciIjI8bo1bIaDNcCErKH2A41e3Q6vVSGpF9FC174BbWlrCz88PBw8e\n",
       "xOTJk/V5eHg4pk6dWuUxffv2xTvvvIPS0lL9eeDh4eHw9PREq1atHvtccXFx8PDweOzj/v7+j30M\n",
       "ePibyJP2I8NjCK+dTqfDhoMrkV1wV8iH+k/GuH6zJbUyfIbw2lHd4GtoXPi192T+8If6sBbRFw/o\n",
       "s/TcZCQXxmPqoJclNuPrZ8xq+trl5uZW+/gTlx1ZtmwZ1q1bh2+//RaXL1/GG2+8gfT0dCxcuBAA\n",
       "sHz5cgwdOlS//8yZM2Fra4u5c+ciISEBoaGh+OCDD7Bs2TL9PitXrsSuXbtw/fp1JCQkYPny5di1\n",
       "axdee+21J9Uhqhf7z2xFzJVjQta5tT/G9J0pqRERET2ryQNfhJdHJyGLPB+GY3E/S2pE9KsnngM+\n",
       "bdo0ZGdn4/3330daWhq6du2KsLAwtGjx6zrI6enpSExM1O/v4OCA8PBwvPrqq/D390fTpk3x5ptv\n",
       "YunSpfp9ysvL8dZbb+HOnTuwsbFBly5dEBYWhhEjRtTDp0hUvbNXIrDv1I9C5uroiTkjlkKpVElq\n",
       "RUREz0qtssD80W/jwx/fRE5Blj4PPfYtmjq4omvbAIntyJwpdDqdTnaJx/n92/eNGzeudl/+Ocd4\n",
       "yXztbqQm4PMdfxEuurS1tseyaR/A1fHxp0TRr/h1Z7wevV7ecH8SUFX4tfd0UjNvYeVPy1FaXqLP\n",
       "LNVWeH3KP9DSreFvAsjXz3jV5hSUqmZY3vmGzNa9nFR88/O/xRVPVGq8NOZPHL6JiEyIp0sbzB35\n",
       "JhSKh2NPWUUpvtrzD+Q8crdjoobAAZzMUkFxHr7c9T6KSvKFfNbQxfDy7CypFRER1ZfObfwxZYB4\n",
       "u/q8whx8uet9FJcWSWpF5ooDOJmd8ooyfLPnX8jMTRPyUX1mwL/DAEmtiIiovgX7jsKgHuOE7G52\n",
       "Mtbt+xAaLk9IDYgDOJkVrVaD7/d/jMS0y0Ie0HEQhgdMk9SKiIgayvigF9DNq4+QXU6OxebDX8CA\n",
       "L4sjE8MBnMyGTqfDT0e/QvzNU0LernkXPDfklRrdxZWIiIybUqnCnOFL0dJNvFPh6UuHsSd6g6RW\n",
       "ZG44gJPZ2Hdqs3BDBgBwc2yOF0f/CWqVhaRWRETU0CwtrPDy2P9BUwdXIT90LhRHY3dLakXmhAM4\n",
       "mYXI+DDsP7NFyJrYOeGViX+BrbWdpFZERCSLQyNHvDLhL2hk4yDkOyK/w9krEXJKkdngAE4mL/Za\n",
       "FLZFfC1kttb2WDThr3C0d5HUioiIZHN19MSi8e/BysJayDeGr8KlpHOSWpE54ABOJu3q7XhsOLAS\n",
       "Ojy8sMZCbYk/jPsz3J1aSGxGRESGoKVbO7w4ZjlUyoc3B9dqNfhu7//DrbSrEpuRKeMATiYr8e5l\n",
       "fP3zv6DRPrzRjlKhxPxRb6ONeweJzYiIyJD4tPTF7OFLoMDDi/HLKkqxZtf/4U5mosRmZKo4gJNJ\n",
       "Sk6/jtW7/g9lv7vtMADMHLYYndvw1r9ERCTq6R2EyQPFG/UUlxbi89C/IC37tqRWZKo4gJPJuZOZ\n",
       "iNU7/4bSsmIhnxA8DwEdB0lqRUREhq6/72iMCJguZIUl+fgs9D3cy0mV1IpMEQdwMilp2bfx+Y6/\n",
       "oqi0QMhH952JwT3HS2pFRETGYmSf5yrdLTO/6AFWhb6HrNx0Sa3I1HAAJ5NxLycVn4W+h8LiPCEP\n",
       "6TWFd7kkIqIaUSgUmBA8D0HdRgp5bkE2Ptv+v7iflympGZkSDuBkEjIfpOGz0PeQX/RAyAf1GIfR\n",
       "fWdJakVERMZIoVBgysCX0KfzUCG/n5+Jz0L/Fw8KsiU1I1PBAZyMXkZOKj7d9udK3xCDuo3EhOB5\n",
       "vMU8ERE9NaVCiecGL4K/zwAhz8pNxyfb/gf38+5JakamgAM4GbW7Wcn4dNufkVt4X8j7dB6KKQNf\n",
       "4vBNRES1plSqMCvkdXRvFyjk2bkZ+GTbn5H5IE1SMzJ2HMDJaKXcS8Sq7e9WOu0koOMgPDd4EZQK\n",
       "/u9NRETPRqVU4YURy9DNq7eQ5+Rn4tNtf0YGV0ehWuCEQkYpOf06Pgv9XxSW5At5387DMHPYYiiV\n",
       "KknNiIjI1KhUaswb+RZ6egcJeW7hfXy67c+4m5UsqRkZKw7gZHQS717GZzveQ3FpoZD39x2F6UP4\n",
       "zjcREdU9lUqNOcOXVrqfRH7RA6za/i5S7vGOmVRznFTIqCTcisHnO/5S6SY7g3uOx+QBL3H4JiKi\n",
       "eqNUqjBz2GL07TxMyAtL8rFq+7u4fueipGZkbDitkNE4c/kovt7zT5RXlAl5SK+pGB80lxdcEhFR\n",
       "vVMqlJg+ZBH6+44S8pKyIqze+TfE3zgpqRkZEw7gZBSOxO7EDwc/gVanFfLRfWdiTOAsDt9ERNRg\n",
       "lO0Qd+gAAB33SURBVAolJg94CYN7ThDyCk05vgtbgajz+yU1I2Ohll2AqDo6nQ67o9fj8LmdQq7A\n",
       "rzdJCH7kHQgiIqKGoFAoMD7oBTSytseeExv0uU6nxdaja5Bf9AAjek/nG0RUJQ7gZLDKK8rx4+HP\n",
       "EHPlmJCrlGrMHr6k0tXoREREDUmhUGBYr8mwt22CzYc/F/5Ku+/0ZuQXPcCUgS9xZS6qhAM4GaTC\n",
       "4jx8s/cD3ExNEHIrC2u8OGY5fFr6SmpGREQk6tN5CBrZ2GNd2Ico1zy8Tinqwn7k5GfhhZF/hLWl\n",
       "jcSGZGh4DjgZnMwHafh4658qDd92No2xePL7HL6JiMjgdG0bgFcn/Q22VnZCnpAUg5Vb/4T7eZmS\n",
       "mpEh4gBOBuVm6iV8vOVtZD64K+QuTTywdNq/0dKtnaRmRERE1Wvr0RFvTP0nGts5Cfnd7GR8tOUt\n",
       "JKVfk9SMDA0HcDIYpy8dwWc73qt0d0svz85YNu3fcGniLqkZERFRzbg7tcQfp/8/NHdtK+T5RQ+w\n",
       "atu7iL0WJakZGRIO4CSdVqvBmcQD2Bj+KTSaCuEx/w4D8MqEv6KRjYOkdkRERE+niZ0T3pjyT/h6\n",
       "9RHyck0Z1u37EHG3j0Gn00lqR4aAAzhJlV+Ui/CETbiSdrbSYyP7zMDskCWwUFtIaEZERFR7VhbW\n",
       "mDf6bQz1n1zpsfMpkThyeQuKSgokNCNDwAGcpEm5l4gPN7+JjLxkIbdQWWLO8KUYyfVTiYjIiCkV\n",
       "SozrNxuzhi2GSikuPJeacwMfbn4TqZlJcsqRVBzAqcHpdDqcTDiElVv/hJx88apwR3sXLJn2L/h3\n",
       "GCCpHRERUd3q3WkIXp30N9jZNBbyrNx0fLz1bZx95H4XZPo4gFODKi0vwcbwT/Hjoc+EtVIBoF3z\n",
       "LnjzuQ/RwtVLUjsiIqL60c6zM96a8SFaubUX8vKKMmw48B9si/gaFZpySe2ooXEApwaTln0bH25+\n",
       "E2cuH630WAf3Xnh1wl9hb9u4iiOJiIiMn6O9C16f8k+0d+tR6bHj8Xvxn61/QuaDNAnNqKFxAKd6\n",
       "p9PpcPrSYXy0+S1k3L8jPGaptkK/9uMQ0HY4VCremJWIiEybhdoCfduNRt92Y6BWiYsMpNy7if+3\n",
       "aSnOXomQU44aDAdwqleFJflYu28FNoavQllFqfBYs6Yt8MfnPoSXazdJ7YiIiORo79YdS6b+C472\n",
       "LkJeWl6CDQdW4oeDn6CkrFhSO6pvHMCp3lxJjsO/f3gDcddPVHosoOMg/PG5FXB3aiGhGRERkXwt\n",
       "3drh7Zkfo9sj64UDwJnLR7Fi0zLczrghoRnVNw7gVOfKKkrx/9u786gmz3wP4N+EHcIeQtjDjoDg\n",
       "hgpuWJeiTr1dpnasdnq9bUev2utSR+1pPWPPtMx00and7Jy5Z2a4tb1i29tarXbcEEWQgooKyCL7\n",
       "lrAKBhAkee8fSlokLFZMWL6fc3KM7/Pk5ZfzM/r15eF5v07+b3zy7U40tzb2GDMzMcez81/GyoUb\n",
       "YGFmaaQKiYiIhgcbS1u8sGQbls1dAzMT8x5jdc012J24Fd+nfc4f0BxluOiWhlS56jr2HdsDZWNF\n",
       "rzFPFz/8Nm4T5E686k1ERNRNJBJhZkQc/NzHIeGHXahpKNeNaQUt/vXjl7hanIGVC/8Lni5+/ZyJ\n",
       "RgpeAach0Xm7AwdT/oldiVt7hW8RRFgw5SlsfuZthm8iIqI+uEt98Moz72LG+LheY9X1pXhv/+9x\n",
       "ND0RGk2XEaqjocQr4PTACiquYv/Jj1HfrOw15mQnw3MLN8LfI9QIlREREY0s5mYWeOaRNQhTTMb+\n",
       "U5+gpbVJN6bVanD0/P/ialE6fjNvLbxdA4xYKT0IBnD6xdo61PguJQGp2cf1jk8dNxdPzXkJVhbW\n",
       "Bq6MiIhoZAv3i8Kr7h/g6+T/RuY9d8qsrCvGrsStmBWxCEuiV/Df2RGIAZzumyAIyMxPxsGzCWhp\n",
       "a+o17iiRYtkjaxDmO8UI1REREY0ONpa2+O2jmzAhIBqJJ/fiZnuzbkwQtDhz+XtkXU/FU3NexISA\n",
       "GIhEIiNWS/eDAZzuS2VdMb46/TcUV1/TOz4rYjEem/EcLM2tDFwZERHR6BThPx1+7qH4+vTfcKHg\n",
       "bI+xltYm/OPIuwj1mYSnYl+Ci4Obkaqk+8EAToPSdkuN79O+QMrVHyAI2l7jMkcPLJ+3jmu9iYiI\n",
       "HgKJlR2eX/QKosbNxZen/4qGZlWP8dyyi8jf9zJiJ/wKC6OehpWFjZEqpcFgAKd+aTRdSM0+hiPp\n",
       "+9Ha3tJr3MTEFPMnP4GFUU/DzNRczxmIiIhoqIQqJuHVlR/g2I9f4eSFb6DR/rQjikbThZMXvkV6\n",
       "bhKWRD+L6LD5EItNjFgt9YUBnPQSBAGXr6fhUOo+1N2o1jsnTDEFT855gd/uIiIiMiBzUwv8KmYF\n",
       "JgfPxoFTe1FUndtjXN3ejMRTe3H28hE8Mfs/EOwdaaRKqS8M4NRLUVUODqb8D0qV+XrHne1d8dTs\n",
       "FxHuF2XgyoiIiKibm7MX/uvXbyEj7zQOpe5Ds7qhx3h1Qxk+/uYPCPKKwK9iVkIhDzJSpXQvBnDS\n",
       "qagtwtHz+5FdkqF33MzUHAujfo1HJj3O5SZERETDgEgkwtRxcxEZEI2TF77ByQvf4HZXZ485BRVX\n",
       "sDtxK8L9pmLJ9Gfh4aIwTrGkwwBOKFddxw/piX0Gb5FIjOiweVg0bTnsJU4Gro6IiIgGYmFmicXT\n",
       "lyM6bAEOpX7Wa+9wAMgu/hE5xRmYFDQTcdN/A1dHDyNUSgAD+JhWpizED+mJyCnN7HPOeL+peGzG\n",
       "c7yFPBER0QjgaCvFbx/dhDmRS3Do3GcoqLzaY1yAgAsFZ3GxIAWRAdFYEPUUvGT+Rqp27GIAH2ME\n",
       "QUBeeRZOXfgW+RWX+5yncAvGv814ntsKEhERjUA+8iCsf+qPyC+/jMNpn6NMWdBjXICArOupyLqe\n",
       "ihCfiVgY9Wv4u4fyZj4GwgA+RnRpbuNC/lkkXTyI6oayPucp5MFYNP03CPGewA8hERHRCBfsHYkg\n",
       "rwhkl2Tg+7QvUF1f2mtOXtkl5JVdgq9bCGInPoYI/+kw4faFDxUD+Ch3s60Z53NO4Mzl79Hc2tjn\n",
       "PIVbMBZNY/AmIiIabUQiEcb7TUWY7xRkFabieObXqKor6TWvpCYPJTV5cJRIMTNyMWLCF8DG0tYI\n",
       "FY9+DOCjkCAIKKnJR8qVo7h0/Rw0mq4+5/q7h+LRqcsQ7B3J4E1ERDSKiUViTAqaiYmBM3Ct7CKO\n",
       "/fgVimuu9ZrXpK7HoXP/gx/S9yMqJBazIhbBw8XXCBWPXgzgo0h7RysuFqTg7JWjer/F1E0kEiMy\n",
       "YDrmTXocPtwTlIiIaEwRiUQIVUxGqGIyiqpycCzja1wru9hr3u2uTqRmH0Nq9jF4ywIQHb4Ak4Jm\n",
       "wcrC2ghVjy4M4COcVqtBfsUV/Jh7CleK0nFb09nnXHNTC0wPm4/YiY9Bai83YJVEREQ0HPl7hOE/\n",
       "PcJQ01CO5KzDyMg73WsfcQAor72O8lPX8c2Zv2NS0ExMD1sAX7dgfvf8F2IAH6FqGirw47VTyMxL\n",
       "7ndtNwBI7eWYGRGHaaHzuJaLiIiIenFz9sZv5q3FYzErkZpzAimXj6BJXd9rXmdXB87nnsT53JNw\n",
       "tnPF5ODZmBw8G27O3K74fjCAjyCqpipkFZ7DpcLUfpeYAHeWmYT7TsHMiEUI9o6EWCQ2TJFEREQ0\n",
       "YtlY2WHBlCfxyKR/w9WidKRmH0N++WUIEHrNbWhR4VjGlziW8SU8XHwxJXg2JgXNhKOtixEqH1kY\n",
       "wIc5VWMlLhWeQ1Zhar/bB3ZzsnXB1HGPIDp8Pj8ARERE9IuYiE0wITAGEwJj0NCiwvmcO1e9m9UN\n",
       "eudX1ZWgqq4EB1MS4OMaiAj/6YjwnwZXJ08DVz4yMIAPMxpNF4prriGnJBM5JRegaqoc8DUWZpaY\n",
       "EBCDqaGPwN8jlFe7iYiIaMg427liSfSziJv2DPLKLuF87knklGSiS3Nb7/wyVSHKVIU4lPoZXB09\n",
       "EeE/DRH+0+DlGsCMchcD+DBws+0GrpVdQk5JJvLKLqG9s23A14hEYgR5jkfUuFhEBkTDwszSAJUS\n",
       "ERHRWGUiNkGY7xSE+U5Be0crrhSdR2beGRRUXoUgaPW+RtVUieOZlTie+TUkVvYI8Z6AEJ8JCPGe\n",
       "CDsbBwO/g+GDAdwI2jrUKKrKRUHFFRRUXEFNQ/mgXicSiRHoGY6JgTMQ4T8NttZj9w8uERERGY+V\n",
       "hQ2mhc7DtNB5aG5txMWCFFwsSOl1y/ufU7c3IzM/GZn5yQAATxc/hPhMRJDnePi6h4ypi4kM4AbQ\n",
       "dkuNUmU+rlflorDiCspri/r8n+K9xGITBHqEY0JgDCL8p8PW2v4hV0tEREQ0ePY2Tpg7cSnmTlyK\n",
       "G+oGXC1Kx5XidBRWZkOr1fT5usq6YlTWFeNE5tcQi03gLQtAgEcYAjzD4Os2blTvN84APsQEQUDt\n",
       "jWqUVOfpbumqbKy4r3NIrOwRqpiEMN8pCPGeACsLm4dULREREdHQcZA4Y1bkYsyKXIy2W2rklF7A\n",
       "1aJ05JVn4VY/S2y1Wg1KlfkoVebjxIX/g0gkhqeLL3zdguHtGgiFPAguDu6jZt9xBvAHoBW0aGhW\n",
       "oaK2CJW1d/4XV15bhLZbN+/rPCKI4CXzxzjFRIT5RsGbP6RAREREI5y1pQRRIXMQFTIHGk0XSpUF\n",
       "yCu/hGull1BRW6R3a8NugqBFRW0RKmqLfjqfhQTergHwkQfB2zUAni6+cJBIR2QoZwAfpI7Odigb\n",
       "K6FsrEBVXQkq7n7bpKOz/RedT+7khSCvCAR5jUeARzisLSVDXDERERHR8GBiYgp/j1D4e4RiSfQK\n",
       "qNtbkF+ehYKKq7helYO6G9UDnqOtQ4288izklWfpjllb2sJd6gMPqQLuUgU8pAq4OXvDzNT8Yb6d\n",
       "B8YAfo+2DjVUjZVQNlRA2VihC91NN+t+8TlFEMHN2RsKt2AEeIQhyCsCdjaOQ1g1ERER0cghsbLT\n",
       "3UUTAJrVjbhelXP3kQ1V48DbMANA262buF6ZjeuV2bpjYpEYUgc3yBw94OroofvV1dEDNlZ2D+X9\n",
       "3K8xF8C1ghYtrU1oaFaivvtx46fnrfe5fEQfS3NrKORB8HULga9bCHzkgVzHTURERNQHe4kTJgfP\n",
       "wuTgWQDubNFcqixAmbIQZcoClKsKB7VNM3An69U2VaG2qQrZ94zZWNrC1dETLg5ucLJ3hbOdDM52\n",
       "MjjZyWBv4wSx2GSI35l+oyqAC4KA1vYW3FA34Ia6AU036+8+r8eNu8+bbtbjtqZzyL6mlYUNPF38\n",
       "4CXzg6eLHzxlfpA5uBusgURERESjja21A8b7TcV4v6kA7oTquqZqlKkKUaosQGVdMarry9B5+9Z9\n",
       "nbf11k0U11xDcc21XmMmYlM42krhbOcKJzsZnOxcYGfjBPvuh8QJgiAMyZrzQQXwTz75BO+++y6U\n",
       "SiXCwsLw/vvvY+bMmX3Ov3r1KtavX4+MjAw4OTlh9erV2LFjR485ycnJ2Lx5M3Jzc+Hu7o6tW7di\n",
       "9erVfZ5T1ViJlrYbULc342ZbM9RtzbjZdgM32+88r2tSoq3zJjSpXYN86/dHJBJDai+H3MkTbs7e\n",
       "d0O3P5zsZCNy8T8RERHRSCEWieHq5AlXJ09MHTcXwE+bYVTVlaC6vgxV9SWoqi9FY0vtL/oaGm2X\n",
       "bkVE33WYwNpcgrPFbrpQbmtlD4m1PSRW9rC9+6u5qP8tFAcM4ImJidi4cSP27t2LmTNn4uOPP8ai\n",
       "RYuQm5sLLy+vXvNbWlqwYMECxMbGIjMzE9euXcOqVatgY2ODzZs3AwBKSkqwePFivPjii/jiiy9w\n",
       "9uxZrF27Fi4uLnjyySf11vHWZ+sHKnVImJiYwsXeDXInrzsPZy/InTzh4uA+7Bf0ExEREY0VYpEY\n",
       "Lg5ucHFww4TAGN3x9o421N2ohqqpErVNVVA13lmOUnujGl2a2w/0NbWCBuqOZqhrmvud98d/T+h3\n",
       "fMAAvnv3bqxatQovvPACAOCDDz7ADz/8gL179yI+Pr7X/M8//xy3bt1CQkICLCwsEBoairy8POze\n",
       "vVsXwD/99FN4enpiz549AIDg4GCkp6fjvffe6zOADyUrCxtI7eWQ2svhfPfX7oeDxHDrf4iIiIho\n",
       "aFlZWMPbNQDergE9jmu1GjTdrIeqqQoNzUo0tNSisaUWDS0qNLbUDsnPAQ5WvwG8s7MTFy9exNat\n",
       "W3scX7hwIVJTU/W+Ji0tDbNmzYKFhUWP+Tt27EBZWRl8fHyQlpaGhQsX9jpnQkICNBoNTEx+eQA2\n",
       "N7OEo0QKB4nznYftneeOtt3HpNzyj4iIiGiMEYtN4GzvCmd7V73j7R1taLpZi4aWWjQ0q9Dc2oBm\n",
       "dROaWxt1j1+6/fS9+g3g9fX10Gg0cHXtWahMJoNSqX99jFKphLe3d49j3a9XKpXw8fGBSqXqdU5X\n",
       "V1d0dXWhvr6+1xgAONu7wtbaAbZ319fYWjvcXWvjAFtre5QVV8La3BbR02ZwTTYRERER3RcrC2tY\n",
       "WdzZT7wvaefPof22Gp4KdzS3NqKltfGnn09sb4G6rRnq9v6XpwAPYReUhxV+Nz7xTr/jssg7ob+l\n",
       "peWhfH16eAIDAwEAzc0D/4Gl4YW9G7lu3Oj5e7ZwZOFnb2Rj/0au0HHhuueudt79zOxfv/c7l0ql\n",
       "MDExgUql6nFcpVLBzc1N72vkcnmvq+Pdr5fL5f3OMTU1hVQqvb93QEREREQ0gvQbwM3NzTF58mQc\n",
       "O3asx/Hjx48jJiZG72uio6Nx9uxZdHR09Jjv4eEBHx8f3Zzjx4/3OmdUVNQDrf8mIiIiIhruRIIg\n",
       "CP1NOHDgAJ577jl88skniImJwaeffop//OMfyMnJgZeXF1599VVkZGTgxIkTAO4sAQkODkZsbCxe\n",
       "f/115OfnY9WqVdi5cyc2bdoEACgtLUV4eDheeukl/O53v8O5c+ewbt067N+/H0888cTDf9dERERE\n",
       "REYy4BrwZcuWoaGhAW+++SZqamowfvx4HDlyRLcHuFKpRHFxsW6+nZ0djh8/jnXr1mHKlClwcnLC\n",
       "li1bdOEbABQKBY4cOYJNmzZh79698PDwwIcffsjwTURERESj3oBXwImIiIiIaOj0uwZ8uDlz5gyW\n",
       "Ll0KT09PiMViJCT0vstQQUEBnnzySTg6OsLGxgaTJ09GXl6eEaqlnxuody0tLVi7di28vLxgbW2N\n",
       "kJAQvP/++0aqlu71pz/9CVFRUbC3t4dMJsPSpUuRk5PTa97OnTvh4eEBa2trzJ07F7m5uUaoln5u\n",
       "oN51dXVh27ZtiIyMhEQigbu7O1asWIGKigojVk3dBvvZ67Z69WqIxWLs2rXLgFWSPoPtHXPL8DSY\n",
       "/j1IdhlRAby1tRURERHYs2cPrKysem15WFJSghkzZsDf3x9JSUnIycnBW2+9BYmEN94xtoF6t3Hj\n",
       "RvzrX//Cvn37kJeXh9deew3bt2/Hvn37jFQx/VxycjLWr1+PtLQ0nDp1Cqamppg/fz6ampp0c95+\n",
       "+23s3r0bH330ETIyMiCTybBgwQKo1WojVk4D9a61tRWXLl3C66+/jkuXLuHgwYOoqKhAXFwcNBqN\n",
       "kaunwXz2un311VfIyMiAu7s774cxDAymd8wtw9dg+vdA2UUYoSQSiZCQkNDj2PLly4WVK1caqSIa\n",
       "LH29Cw8PF3bu3Nnj2Jw5c4SXX37ZkKXRIKnVasHExEQ4fPiwIAiCoNVqBblcLsTHx+vmtLe3C7a2\n",
       "tsJf//pXY5VJetzbO31yc3MFkUgkZGdnG7AyGoy++ldaWip4eHgIeXl5gkKhEHbt2mWkCqkv+nrH\n",
       "3DJy6Ovfg2SXEXUFvD9arRaHDx/GuHHjEBcXB5lMhqlTp+LAgQPGLo0GYdGiRfjuu+9QWVkJAEhN\n",
       "TUVWVhbi4uKMXBnp09LSAq1WC0dHRwB3ruKoVCosXLhQN8fS0hKzZ89GamqqscokPe7tnT7dNwfp\n",
       "bw4Zh77+dXV1Yfny5dixYweCg4ONWB31597eMbeMLPo+ew+SXUZNAK+trYVarUZ8fDzi4uJw4sQJ\n",
       "LF++HCtWrMCRI0eMXR4N4O2330ZoaCi8vb1hbm6O2NhYvPPOO1i8eLGxSyM9NmzYgIkTJyI6OhoA\n",
       "dDfWcnV17TFPJpP1uukWGde9vbtXZ2cnXnnlFSxduhTu7u4Gro4Goq9/f/jDHyCTybB69WojVkYD\n",
       "ubd3zC0ji77P3oNklyG/Fb2xaLVaAMDjjz+OjRs3AgAiIiKQmZmJjz76iEFumNuyZQvS09Nx6NAh\n",
       "+Pj4IDk5Ga+88gp8fHzw6KOPGrs8+pnNmzcjNTUVKSkpg1pnyrWow8dAvevq6sLKlSvR0tKCw4cP\n",
       "G6FC6o++/p0+fRoJCQnIysrqMVfgBmfDir7eMbeMHH393fkg2WXUBHCpVApTU1OEhob2OB4SEoLE\n",
       "xEQjVUWD0draij179uCbb77BkiVLAADh4eHIysrCe++9xwA+jGzatAkHDhxAUlISFAqF7rhcLgcA\n",
       "qFQqeHp66o6rVCrdGBlXX73r1r2MIScnB6dPn+byk2Gmr/4lJyejpqYGbm5uumMajQbbtm3Dnj17\n",
       "UF5eboRq6ef66h1zy8jQV/8eNLuMmiUo5ubmiIqK6rV1T0FBgd5/bGj4EAQBgiBALO75x1EsFvMq\n",
       "zjCyYcMGJCYm4tSpUwgKCuox5uvrC7lcjmPHjumO3bp1CykpKYiJiTF0qXSP/noHALdv38YzzzyD\n",
       "7OxsJCUlQSaTGaFK6kt//Vu7di2uXr2Ky5cv4/Lly8jKyoK7uzs2b96MkydPGqli6tZf75hbhr/+\n",
       "+veg2WVEXQFvbW1FYWEhgDvfuikrK0NWVhacnZ3h5eWFrVu3YtmyZZg1axbmzp2LpKQkJCYm4uDB\n",
       "g0aunAbq3bx587B9+3ZIJBJ4e3sjOTkZn332Gd59910jV04AsG7dOuzbtw/ffvst7O3tdeu6bW1t\n",
       "YWNjA5FIhI0bNyI+Ph4hISEIDAzEm2++CVtbWzz77LNGrn5sG6h3Go0GTz/9NDIzM3Ho0CEIgqCb\n",
       "4+DgAEtLS2OWP+YN1D8XFxe4uLj0eI2ZmRnkcjkCAwONUTLdNVDvADC3DGMD9U8ikTxYdhmy/VkM\n",
       "ICkpSRCJRIJIJBLEYrHu+apVq3Rz/vnPfwpBQUGClZWVEBkZKezfv9+IFVO3gXpXW1srvPDCC4Kn\n",
       "p6dgZWUljBs3jttoDSP39q378cYbb/SYt3PnTsHNzU2wtLQUYmNjhZycHCNVTN0G6l1JSUmfc+7d\n",
       "LpQMb7CfvZ/jNoTDw2B7x9wyPA2mfw+SXXgreiIiIiIiAxo1a8CJiIiIiEYCBnAiIiIiIgNiACci\n",
       "IiIiMiAGcCIiIiIiA2IAJyIiIiIyIAZwIiIiIiIDYgAnIiIiIjIgBnAiIiIiIgMaUbeiJyKiwUtP\n",
       "T8d3330HExMTrF+/HjKZbMDXHD16FAkJCejs7IStrS0sLS2xZs0ayOVyxMfH48MPPzRA5UREoxsD\n",
       "OBHRKFRaWoqkpCS89dZb6OjowO9//3t88MEHfc5vaGjAypUrAQB79+6FQqHQjW3ZsgVHjx7FqlWr\n",
       "HnbZRERjApegEBGNQunp6XjssccAABYWFggICEBtba3euXV1dYiOjoZUKsXRo0d7hG8A2L59O/Lz\n",
       "8zF//vyHXTYR0ZjAAE5ENApNmzYNhw8fBgB0dnaivLxc7xIUQRDw9NNPQywW4+9//7vec0mlUoSG\n",
       "hmLChAkPtWYiorGCS1CIiEYhhUKB2bNn47XXXoNYLMa2bdv0zvviiy9w5swZfPnllzAzM+vzfM8/\n",
       "//zDKpWIaMwRCYIgGLsIIiIyjpkzZ6KwsBA1NTUQi/lNUSIiQ+DftkREY9Tt27eRlpaG2bNnM3wT\n",
       "ERkQ/8YlIhqjGhoaIAgC/Pz8+p13+vRpwxRERDRGMIATEY1RUqm033XfANDa2opz584ZqCIiorGB\n",
       "AZyIaIwyNTXF448/3u8V7j//+c9Ys2aN4YoiIhoDGMCJiMawv/zlL6iurkZ8fHyP442Njdi+fTuW\n",
       "LVsGZ2dnI1VHRDQ6cRcUIqIxrr6+Hm+88QZyc3Ph5eUFiUQCmUyGDRs2wN7e3tjlERGNOgzgRERE\n",
       "REQGxCUoREREREQGxABORERERGRADOBERERERAbEAE5EREREZEAM4EREREREBsQATkRERERkQAzg\n",
       "REREREQGxABORERERGRADOBERERERAbEAE5EREREZEAM4EREREREBvT/+fVCElMvLrQAAAAASUVO\n",
       "RK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4808fdaa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from stats import gaussian, norm_cdf\n",
    "plot_gaussian(22, 4, mean_line=True, xlabel='$^{\\circ}C$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what does this curve *mean*? Assume for a moment that we have a thermometer, which reads 22$\\,^{\\circ}C$. No thermometer is perfectly accurate, and so we normally expect that thermometer will read $\\pm$ that temperature by some amount each time we read it. Furthermore, a theorem called  **Central Limit Theorem** states that if we make many measurements that the measurements will be normally distributed. So, when we look at this chart we can *sort of* think of it as representing the probability of the thermometer reading a particular value given the actual temperature of 22$^{\\circ}C$. However, that is not quite accurate mathematically. \n",
    "\n",
    "Recall that we said that the distribution is *continuous*. Think of an infinitely long straight line - what is the probability that a point you pick randomly is at, say, 2.0. Clearly 0%, as there is an infinite number of choices to choose from. The same is true for normal distributions; in the graph above the probability of being *exactly* 22$^{\\circ}C$ is 0% because there are an infinite number of values the reading can take.\n",
    "\n",
    "So what then is this curve? It is something we call the *probability density function.* Later we will delve into this in greater detail; for now just understand that the area under the curve at any region gives you the probability of those values. So, for example, if you compute the area under the curve between 20 and 22 the result will be the probability of the temperature reading being between those two temperatures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So how do you compute the probability, or area under the curve? Well, you integrate the equation for the Gaussian \n",
    "\n",
    "$$ \\int^{x_1}_{x_0}  \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 } dx$$\n",
    "\n",
    "I wrote `stats.norm_cdf` which computes the integral for you. So, for example, we can compute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of value in range 21.5 to 22.5 is 19.74%\n",
      "Probability of value in range 23.5 to 24.5 is 12.10%\n"
     ]
    }
   ],
   "source": [
    "print('Probability of value in range 21.5 to 22.5 is {:.2f}%'.format(\n",
    "      norm_cdf((21.5, 22.5), 22,4)*100))\n",
    "print('Probability of value in range 23.5 to 24.5 is {:.2f}%'.format(\n",
    "      norm_cdf((23.5, 24.5), 22,4)*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the mean ($\\mu$) is what it sounds like - the average of all possible probabilities. Because of the symmetric shape of the curve it is also the tallest part of the curve. The thermometer reads $22^{\\circ}C$, so that is what we used for the mean.  \n",
    "\n",
    "> *Important*: I will repeat what I wrote at the top of this section: \"A Gaussian...is completely described with two parameters\"\n",
    "\n",
    "The standard notation for a normal distribution for a random variable $X$ is $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$. This means I can express the temperature reading of our thermometer as\n",
    "\n",
    "$$temp = \\mathcal{N}(22,4)$$\n",
    "\n",
    "This is an **extremely important** result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the distribution of measurements for over any range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this is a probability density distribution it is required that the area under the curve always equals one. This should be intuitively clear - the area under the curve represents all possible occurrences, which must sum to one. We can prove this ourselves with a bit of code. (If you are mathematically inclined, integrate the Gaussian equation from $-\\infty$ to $\\infty$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(norm_cdf((-1e8, 1e8), mu=0, var=4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This leads to an important insight. If the variance is small the curve will be narrow. this is because the variance is a measure of *how much* the samples vary from the mean. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n",
    "\n",
    "Let's look at that graphically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAt8AAAFwCAYAAABgqBdiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XtcVHXeB/DPmYGB4X4TBEVDQ8syL6AWumrlg+uuWY8X\n",
       "pFxdybVHaitTq7VHu7pdLG2zRH1aL2WWuGr1tGmrpGZEWxpReUsNr8GAIAx3BmbO8wcPg+fMMAzD\n",
       "HGYGPu/Xi9f6+805Z35zZOXLt+/5/gRRFEUQEREREZHiVK5eABERERFRd8Hgm4iIiIiokzD4JiIi\n",
       "IiLqJAy+iYiIiIg6CYNvIiIiIqJOwuCbiIiIiKiTMPgmIiIiIuokdgXfGRkZiIuLg1arRWJiIrKz\n",
       "s20ev2PHDgwdOhT+/v647rrr8NprrzllsUREREREnqzN4DszMxMLFy7EsmXLkJeXh6SkJEyaNAmX\n",
       "Ll2yevzevXsxa9YsLFiwAMePH0dGRgZef/11rF271umLJyIiIiLyJEJbO1yOGjUKQ4cOxYYNG8xz\n",
       "AwYMwPTp0/Hiiy9aHH/fffehvr4eu3btMs+99dZbWLlyJS5evOjEpRMREREReRabmW+DwYDc3Fwk\n",
       "JydL5pOTk5GTk9PqOT4+PpI5X19fXL58mcE3EREREXVrNoPvkpISGI1GREVFSeYjIyOh0+msnjNx\n",
       "4kR8/PHH2L9/P0wmE06fPo1Vq1YBAAoLC520bCIiIiIiz+Pl7AvOnz8fv/zyC+6++240NDQgODgY\n",
       "jzzyCJ599lmoVNJYX6/XO/vtiYiIiIg6TXBwcLuOt5n5joiIgFqtRlFRkWS+qKgI0dHRrZ738ssv\n",
       "o7q6GhcvXoROp8OIESMAAP369WvX4oiIiIiIuhKbwbdGo0FCQgL27dsnmd+/fz+SkpJsXlgQBERH\n",
       "R8PLywsffPABkpKSEB4e3vEVExERERF5qDbLThYtWoTZs2dj5MiRSEpKwvr166HT6bBgwQIAwNKl\n",
       "S3HkyBFkZWUBAEpLS7Fjxw6MHz8e9fX12Lx5M3bt2oUvvvjC5vu0N2VPrTt69CgAIDEx0cUr6Vp4\n",
       "X5XB+6oMT7ivuquXsHb3M9BXXzXPDYsfjdkTF8JL7e3ClbXOE+6rp+K9VQbvqzI6UjrdZvCdkpKC\n",
       "0tJSrFixAoWFhRg8eDD27NmD2NhYAIBOp0N+fr7knK1bt+KJJ56AKIpISkrCoUOH+JdORERmuquX\n",
       "8MbO/0Z1bYVk/vszX8HQWI/5k5dCpVK7aHVERMqx64HL9PR0pKenW31t8+bNknF4eHirbQiJiIgA\n",
       "YMfBDRaBd7Pj547iyKlDGDXozk5eFRGR8uzaXp6IiMhZSvQ6nL18TDLno9FKxv8+caAzl0RE1GkY\n",
       "fBMRUaf67ufDkvF1PQdiSeprkrlffj2OqxVXOnNZRESdgsE3ERF1GlEUceSU9AH8ETeOR1RoL/Tt\n",
       "OUAyLw/SiYi6AgbfRETUaS4V/4Lisl/NY5VKjeHxowEAI24YJzn26M9fQBTFTl0fEZHSnL7DJRER\n",
       "UWuOyrLeg/oOh782CEBTm8HdX2yESTQBAApLL6Kg5Dx69Yjr9HUSXUsURRgMBo/8ZbBv374AgLq6\n",
       "OhevxHNoNBqLXdmdicE3ERF1ClEUkXsmWzKXeE22O9AvBDf0HYYT578zz313OpvBN7mUyWRCfX09\n",
       "NBoN1GrPa3/p6+vr6iV4FFEUUVdXBx8fH8UCcJadEBFRpyjR61BRXWYea7x8cHO/EZJjEgb+RjLO\n",
       "//VEp6yNqDUGgwG+vr4eGXhT+wmCAF9fXxgMBsXeg8E3ERF1ivO6nyXjvj0HQOPlI5m7vtdNkvGl\n",
       "4l/QaGxQfG1EtgiC4OolUCdS+u+bwTcREXWK84WnJeO46IEWx4QG9kBwQLh53GA04Ncr55VeGhFR\n",
       "p2HwTUREneKc7pRkLG8t2Ow62bw8Y05E5MkYfBMRkeIMDfUokGWwr+tpmfkGLDPi5wsZfBNR18Hg\n",
       "m4iIFHep+Ky5hSAARAT3RKBfsNVj5UH5ed1pq8cRUdcniiJWrlyJfv36QavVYvDgwdi2bZtd5x45\n",
       "cgR//vOfcdNNNyEgIAB9+/bFzJkzcebMGYVXbRtbDRIRkeLOybLXrWW9AaB3ZD+oVGqYTEYAQGlF\n",
       "ESqqyxHkH6LoGonI/Tz11FN45ZVXMH/+fIwcORIfffQRZs+eDUEQcN9999k895VXXsHXX3+NGTNm\n",
       "4JZbbkFhYSHeeustDB8+HF9//TVuvvnmTvoUUgy+iYhIcfLs9XVWHrZspvHyQe8e/XCxqCU7dV73\n",
       "M27pP0qx9RGR81VXV8Pf39/h83/99VesWrUK6enpWLt2LQBg3rx5GDduHB5//HHMnDnTZgvIxYsX\n",
       "Y8SIEfDyagl3Z86cicGDB+PFF1/E+++/7/DaOoJlJ0REpChRFC3qtuUPVcpZPnTJ0hMiZ9q5cydU\n",
       "KhUOHDhg8dp7770HlUqFw4cP48cff0RaWhr69+8PrVaLHj164N5778WlS5ck52zZsgUqlQoHDx7E\n",
       "I488gqioKAQGBnZojR9//DEaGxuRnp4umU9PT0dhYSGys7NbObPJbbfdJgm8AeD666/HoEGDcPLk\n",
       "yQ6trSOY+SYiIkWVV5WgoqZlcx1vLw16RVxn85y46IE4/MOn5vEFBt9ETjV58mQEBgYiMzMTd9xx\n",
       "h+S1zMxM9OrVC2PHjsWqVatw+vRpzJ07FzExMTh79izWr1+Pb7/9FseOHYNWq5Wc+/DDDyMsLAzL\n",
       "ly+HXq8H0PQLeGlpqV3rCgoKgkajAQB8//338PX1tSgPGTGiaXOuvLw8jBs3zuIatoiiiKKiItx4\n",
       "443tOs+ZGHwTEZGiCkulGbJeEXFQq23/+ImNvF4y1pVedPq6iJTwyBv3KHr9NY9+5JTr+Pr6YsqU\n",
       "Kdi9ezcyMjLM5Rvl5eXYt28fHnroIQDAgw8+iMWLF0vOnTJlCkaPHo3du3dj1qxZktcCAwNx6NAh\n",
       "ydbsFy5cQL9+/exa15YtWzBnzhwAQGFhIaKioiyOiY6OBgAUFBTY+WlbbNu2DQUFBXjuuefafa6z\n",
       "MPgmIiJF6a5Kg++e4bFtnhMeHAUvtbd5d8vKWj2qaisQoA1SZI1E3VFqaiq2bduGrKwsTJw4EQDw\n",
       "4YcfoqGhAampqQAgyWxXVVWhvr4e8fHxCAkJQW5urkXwPX/+fEngDTQFy1lZWXatadCgQeY/19bW\n",
       "wsfHx+IYX19f8+vtcerUKTz00EO47bbbcP/997frXGdi8E1ERIqyCL7D2g6+1So1IkN7oaDkvHmu\n",
       "6OolBMi2nycix02cOBGhoaHYvn27Ofjevn074uLiMHLkSABAWVkZ/vKXv2Dnzp0oKyuTnN9cVnKt\n",
       "/v37W8z5+PhYlLbYQ6vVoq6uzmK+eU5e8mKLTqfD73//e4SGhmLXrl2KbyFvC4NvIiJSVNHVy5Kx\n",
       "PcF383HXBt+6q5fRn8E3kdN4eXlh6tSp2LlzJ95++22Ul5fj4MGDWLJkifmYlJQU5OTkYMmSJRg2\n",
       "bJj5IcrU1FSYTCaLa1oLiE0mE4qLi+1aU0hIiDmzHR0djc8//9zimMLCQgBATEyMXdfU6/WYNGkS\n",
       "Kioq8OWXX6Jnz552nacUBt9ERKQYURStZL5723VulOw4+XWI3JGzarI7S2pqKjZu3Ii9e/eioKAA\n",
       "jY2N5pKTsrIyfP7553juueewfPly8zl1dXW4evWq3e9x8eJFh2q+hw0bho0bN+Knn37C4MGDzcd8\n",
       "8803AIChQ4e2eb26ujrcddddOHv2LLKysnDDDTfYvW6lMPgmIiLFVNSUoba+2jzWePsiJDDCrnPl\n",
       "GXIG30TON378eERFRSEzMxMFBQW48cYbccsttwCA+SFMeYb79ddfhyiKdr+HozXfd999Nx577DGs\n",
       "W7cOGRkZAJp+oV+/fj2io6MxZswY87GlpaW4cuUK+vbta86+G41GzJw5E9988w0+/vhjjBrlHnsF\n",
       "MPgmIiLF6GSdTnqG9oZKsG+LCcvg+3IrRxKRo9RqNaZPn45Nmzahvr4eTz/9tPm1oKAgjB8/HitX\n",
       "roTBYECfPn2QnZ2Nw4cPIzw83O4A3NGa7169emHhwoV49dVXYTQaMWLECHz88cfIzs7Gu+++K9lg\n",
       "580338Tzzz+PgwcPmtsPLl68GJ988gnuuusulJSU4L333pNc/w9/+EO71+QMDL6JiEgxRWWyem87\n",
       "Op006xHSU7LNvL6qFLX1NdD6+Dl1jUTdXWpqKtauXQtBEMwlJ83ef/99PProo9iwYQMaGhowbtw4\n",
       "HDhwABMmTLB4aFGJhxhffvllhIWFYcOGDXjnnXcQHx+Pd9991yJwFgTB/NXshx9+gCAI+OSTT/DJ\n",
       "J59YHM/gm4iIuhx55jsq1L56bwDwUnujR3C0JIAvKrvc5u6YRNQ+o0ePtvrwJAD07NkTmZmZFvPn\n",
       "zp2TjOfOnYu5c+c6fW2CIODJJ5/Ek08+afO4Z555Bs8884xk7uDBg05fjzNwe3kiIlKMIz2+JcfL\n",
       "H7osZd03EXk2u4LvjIwMxMXFQavVIjExEdnZ2TaP37NnD2699VYEBQWhR48euOeee3DmzBmnLJiI\n",
       "iDyHvE7b3jaD5uPD+dAlEXUtbQbfmZmZWLhwIZYtW4a8vDwkJSVh0qRJuHTJ+j+AZ8+exT333IPx\n",
       "48cjLy8PWVlZqKurw+9+9zunL56IiNxXVW0FqmpbNuHwUnsjPCiyXdeQB+vynuFERJ6mzeB79erV\n",
       "SEtLw7x58zBw4ECsWbMG0dHRWLdundXj8/LyYDKZ8NJLL6Ffv34YMmQInnzySfzyyy/t6glJRESe\n",
       "rUiWpY4M7QWVSt3K0dax1zcRdTU2g2+DwYDc3FwkJydL5pOTk5GTk2P1nNGjRyMgIABvv/02jEYj\n",
       "KisrsWXLFowcORJhYWHOWzkREbm1K+U6yTgqtFe7rxEpO+dq5RU0Ghs6tC4iIleyGXyXlJTAaDQi\n",
       "KipKMh8ZGQmdTmf1nOjoaOzZswfLli2Dr68vQkJCcPz4cYsWL0RE1LWVVkh/TkQEt39LZ42XD4L9\n",
       "WxI3omhCWWVJh9dGROQqTm81mJ+fj3vuuQdpaWm47777UFFRgaeffhopKSk4cOBAqz0gjx496uyl\n",
       "dHu8p8rgfVUG76syXHlfT+efkIyryuocWo+P2h9AS9ni10cOIya0f0eX1yH8flWOu93bvn37wtfX\n",
       "19XLoE5WWVmJY8eOtfp6fHy8w9e2GXxHRERArVajqKhIMl9UVITo6Gir52zYsAGxsbF45ZVXzHPv\n",
       "vfceYmNj8fXXXyMpKcnhxRIRkeeorCuXjAN8Qxy6ToBPCIrRUustvy4RkSexGXxrNBokJCRg3759\n",
       "mDZtmnl+//79mDFjhtVzRFGESiWtZmket9bAHQASExPtXjTZ1pw14D11Lt5XZfC+KsMd7uvu3Dcl\n",
       "49EjxyGsnd1OAOCK8RfkX/nJPPYP8XHZ53KH+9pVueu9raurc/USyAUCAwNtfi/q9fpWX2tLm91O\n",
       "Fi1ahC1btmDjxo04efIkHn30Ueh0OixYsAAAsHTpUkyYMMF8/JQpU5Cbm4sXXngBZ86cQW5uLtLS\n",
       "0tCnTx8kJCQ4vFAiIvIcdYZaSZtBlUqNkIBwh64VESx97qhUb/2ZIyIiT9BmzXdKSgpKS0uxYsUK\n",
       "FBYWYvDgwdizZw9iY5t6r+p0OuTn55uPHzNmDDIzM/Hyyy9j5cqV8PPzw2233YbPPvsMWq1WuU9C\n",
       "RERuo1QvLVcMD4xsd5tB87lB0gc1SyqKWjmSiMj92fXAZXp6OtLT062+tnnzZou56dOnY/r06R1b\n",
       "GREReSx5p5NwWfa6PSwz30UQRbHVB/iJiNyZXdvLExERtUeJXh58t7/NYLNAvxBovHzM4zpDDarr\n",
       "Kh2+HhGRKzH4JiIipyuRlZ040uO7mSAIFplz1n0TdQ8vvvgi7rnnHvTq1QsqlarVSgxPwuCbiIic\n",
       "Tl7zLS8daS955lwe3BNR17Rs2TJ888035s4jXaHczOmb7BAREckz0x2p+QaAiCBmvok8TXV1Nfz9\n",
       "/Tt0jXPnzqFv374AYNHK2lN1jU9BRERuw2QyorSyWDIXHtTRzLf0fHY8IeqYnTt3QqVS4cCBAxav\n",
       "vffee1CpVDh8+DB+/PFHpKWloX///tBqtejRowfuvfdeXLp0SXLOli1boFKpcPDgQTzyyCOIiopC\n",
       "YGBgh9fZHHh3Jcx8ExGRU5VXXYXR2Gge+/sGQuvTseyXvGZc/kAnEbXP5MmTERgYiMzMTNxxxx2S\n",
       "1zIzM9GrVy+MHTsWq1atwunTpzF37lzExMTg7NmzWL9+Pb799lscO3bMoo30ww8/jLCwMCxfvty8\n",
       "EY0oiigtLbVrXUFBQdBoNM75kG6KwTcRETmVvM1gRx62bO0a8ppyInehGi0qen3TV86pefb19cWU\n",
       "KVOwe/duZGRkQK1u6sNfXl6Offv24aGHHgIAPPjgg1i8eLHk3ClTpmD06NHYvXs3Zs2aJXktMDAQ\n",
       "hw4dkpSIXLhwAf369bNrXVu2bMGcOXM68tHcHoNvIiJyKvnDkB1pM9hMvi19eWUJGhob4O3l3eFr\n",
       "E3VXqamp2LZtG7KysjBx4kQAwIcffoiGhgakpqYCgCSzXVVVhfr6esTHxyMkJAS5ubkWwff8+fMt\n",
       "arOjo6ORlZVl15oGDRrUkY/kERh8ExGRU12tkNd7R7ZypP28vTQI9g+DvvoqAECEiPKqEvQIie7w\n",
       "tYm6q4kTJyI0NBTbt283B9/bt29HXFwcRo4cCQAoKyvDX/7yF+zcuRNlZWWS85vLSq7Vv39/izkf\n",
       "Hx+L0pbujME3ERE5VXlliWQcGtjDKdcNDexhDr4BMPgm6iAvLy9MnToVO3fuxNtvv43y8nIcPHgQ\n",
       "S5YsMR+TkpKCnJwcLFmyBMOGDTM/RJmamgqTyWRxTXkNOACYTCYUFxdbzFsTEhICX19fBz+RZ2Dw\n",
       "TURETlVWeUUyDg2McMp1QwMjcF738zXvU2LjaCLXcFZNdmdJTU3Fxo0bsXfvXhQUFKCxsdFcclJW\n",
       "VobPP/8czz33HJYvX24+p66uDlevXm3tkhYuXrzImu9rMPgmIiKnkgfFzsx8S9/nSitHEpG9xo8f\n",
       "j6ioKGRmZqKgoAA33ngjbrnlFgAwP4Qpz3C//vrrEEX7HyxlzbcUg28iInIaURRRVqVU8C3NoDP4\n",
       "Juo4tVqN6dOnY9OmTaivr8fTTz9tfi0oKAjjx4/HypUrYTAY0KdPH2RnZ+Pw4cMIDw+3OwDvSM33\n",
       "1q1bceHCBfP4u+++w4oVKwAAc+bMQZ8+fRy6risx+CYiIqepqtWj0dhgHms1ftD6+Dnl2pbBt319\n",
       "g4nIttTUVKxduxaCIJhLTpq9//77ePTRR7FhwwY0NDRg3LhxOHDgACZMmGCx1bsSW79v2rQJX3zx\n",
       "hfn6R48exZEjRyAIAsaOHcvgm4iIujd5yUmIk+q9AZadECll9OjRVh+eBICePXsiMzPTYv7cuXOS\n",
       "8dy5czF37lynr+3gwYNOv6arcXt5IiJyGsuHLZ1TcmLtWmWVV9pVd0pE5A4YfBMRkdNcVTD49vcN\n",
       "hLdXy7bT9Q11qK2vdtr1iYg6A4NvIiJyGsse384rOxEEAaEB8rpvthskIs/C4JuIiJxGqTaDrV2P\n",
       "dd9E5GkYfBMRkdMotcFOa9dj8E1EnobBNxEROY1l5tvZwbc8882yEyLyLAy+iYjIKRoaG1BRU2Ye\n",
       "CxAQ4h/u1PeQty5k5puIPA2DbyIicgp9tXTTm6CAMKjVzt1OIkye+a5i5puIPAuDbyIicgql672t\n",
       "XZNlJ0TkaRh8ExGRU1jUewc4P/iWl53oq0phNBmd/j5EREqxK/jOyMhAXFwctFotEhMTkZ2d3eqx\n",
       "zz77LFQqldWvkhJmKIiIuiold7dspvHygb82yDw2iSZUVF91+vsQESmlzeA7MzMTCxcuxLJly5CX\n",
       "l4ekpCRMmjQJly5dsnr8448/Dp1OZ/4qLCzEuHHjcPvttyMiwvlZECIicg9Kdzpp7bosPSEiT9Jm\n",
       "8L169WqkpaVh3rx5GDhwINasWYPo6GisW7fO6vH+/v6IjIw0fxkMBnz55ZeYP3++0xdPRETuo7xK\n",
       "+sBliAJlJ9auK39fIuoazp8/32o1xY4dO1y9PIfZfAzdYDAgNzcXTzzxhGQ+OTkZOTk5dr3Bxo0b\n",
       "ERYWhmnTpjm+SiIicnt6i+A7TJH3CfGXXldfxbIToq4sNTUVkydPlszdeuutLlpNx9kMvktKSmA0\n",
       "GhEVFSWZj4yMhE6na/PiRqMRmzZtwuzZs+Ht7d2xlRIRkVsrl9VeBwc4t8d3a9eVtzgkIvdQXV0N\n",
       "f3//Dl9n6NChuO+++5ywIvfg3AasMp999hkuX75sV8nJ0aNHlVxKt8R7qgzeV2Xwviqjs+6r0dSI\n",
       "6toK81iAgNMnf4FKOOf09yq7UiEZ51880+nfP/x+VY673du+ffvC19fX1ctwup07dyIlJQVZWVm4\n",
       "4447JK+99957mDNnDg4dOoSQkBC8/vrrOHz4MAoKChAQEIAJEyZg5cqViI2NNZ+zZcsW3H///fj8\n",
       "88/x4YcfIjMzE1euXIHJZOrwWkVRRHV1Nby9vaHRaDp8PXtUVlbi2LFjrb4eHx/v8LVtBt8RERFQ\n",
       "q9UoKiqSzBcVFSE6OrrNi//P//wPRo8ejRtuuMHhBRIRkfurMVRKxr6aAKgEZbrZ+vkE2nxvImrb\n",
       "5MmTERgYiMzMTIvgOzMzE7169cLYsWOxatUqnD59GnPnzkVMTAzOnj2L9evX49tvv8WxY8eg1Wol\n",
       "5z788MMICwvD8uXLodfrATQFz6Wl9v0XqqCgIIsA+69//SuWLl0KQRAwfPhwrFixAhMnTuzAp3ct\n",
       "m8G3RqNBQkIC9u3bJ6nZ3r9/P2bMmGHzwgUFBdizZw82btxo10ISExPtOo7a1pw14D11Lt5XZfC+\n",
       "KqOz7+svvx4HvmsZ9wjtqdh7665GIev4++axEYZO+5z8flWOu97burq6dh0fFxen0EqanDvnnP+a\n",
       "5OvriylTpmD37t3IyMiAWq0GAJSXl2Pfvn146KGHAAAPPvggFi9eLDl3ypQpGD16NHbv3o1Zs2ZJ\n",
       "XgsMDMShQ4egUrX88n3hwgX069fPrnVt2bIFc+bMAQCo1WokJydj6tSp6NWrF3755ResXr0av//9\n",
       "77F7925MmTLF4c/flsDAQJvfi82/WDiizbKTRYsWYfbs2Rg5ciSSkpKwfv166HQ6LFiwAACwdOlS\n",
       "HDlyBFlZWZLzNm3ahICAAKSkpDi8OCIi8gzlsoceQxSq9waAYH95zfdViKIIQRAUe0+irig1NRXb\n",
       "tm1DVlaWOZP84YcfoqGhAampqQAgyWxXVVWhvr4e8fHxCAkJQW5urkXwPX/+fEngDQDR0dEWcWJr\n",
       "Bg0aZP5zbGwsPvvsM8nrs2fPxqBBg7B48WJFg28ltRl8p6SkoLS0FCtWrEBhYSEGDx6MPXv2mOt8\n",
       "dDod8vPzJeeIoohNmzZh1qxZXbJOioiIpOQPPSrV6QQAtD5+8PH2RX1DU0ay0diA6rpKBFyz+Q4R\n",
       "tW3ixIkIDQ3F9u3bzcH39u3bERcXh5EjRwIAysrK8Je//AU7d+5EWVmZ5Hxr2d/+/ftbzPn4+FiU\n",
       "tjgqNDQUaWlpePnll3Hx4kX06dPHKdftTHY9cJmeno709HSrr23evNliThAEi4CciIi6LnnmW56d\n",
       "drbggHAUl/1qHuurShl8E7WTl5cXpk6dip07d+Ltt99GeXk5Dh48iCVLlpiPSUlJQU5ODpYsWYJh\n",
       "w4YhMLDpmYvU1FSrD1PKa8ABwGQyobi42K41hYSEtJm47d27NwDg6tWrXTf4JiIiskXe4ztYwcw3\n",
       "0NTr+9rgu7yqFL16KFtrS2QPZ9Vkd5bU1FRs3LgRe/fuRUFBARobG80lJ2VlZfj888/x3HPPYfny\n",
       "5eZz6urqcPWq/f31L1686FDNd2uaE7w9evSwew3uhME3ERF1mHyjGyVrvgEgRLbFvL6aG+0QOWL8\n",
       "+PGIiopCZmYmCgoKcOONN+KWW24BAPNDmPIM9+uvvw5RFO1+D0drvktKShARIf3/+q+//opNmzbh\n",
       "pptuQq9evexegzth8E1ERB1WXlUiGSu1wY75+rJdLssrudEOkSPUajWmT5+OTZs2ob6+Hk8//bT5\n",
       "taCgIIwfPx4rV66EwWBAnz59kJ2djcOHDyM8PNzuANzRmu/HH38c+fn5uPPOOxEdHY3z589jw4YN\n",
       "qKmpwZo1a9p9PXehTBNWIiLqNkyiCfpq6YNY8i3gnU0e3Jdzl0sih6WmpqK2thaiKJpLTpq9//77\n",
       "mDx5MjZs2IAnnngCer0eBw4cQEBAgEWHIWd3HJo4cSIEQcDatWvx0EMP4e9//zvGjRuHnJwc3H77\n",
       "7U59r87EzDcREXVIdW0FjKZG89hX4wcfjeVDV84k76YiL3shIvuNHj261Z0oe/bsiczMTIt5eW37\n",
       "3LlzMXfuXKeuKzU11eKXga6AmW8iIuoQi04nCj9sCVjp9V3FzDcReQYG30RE1CHywFfphy2tvUc5\n",
       "H7gkIg/B4JuIiDqkXB58K9zjGwAC/YKhElp+hNXUVcLQWK/4+xIRdRSDbyIi6hD57pZKdzoBAJVK\n",
       "jSD/UOk6WPdNRB6AwTcREXWIK2q+m95HVnrCum8i8gAMvomIqENcUfMNWLYz5EOXROQJGHwTEVGH\n",
       "yHeXlG+AoxR55lvea5yIyB0x+CYiog6pkAW9nRZ8y96ngh1PSCHt2UqdqC0MvomIyGENjQ2orqs0\n",
       "jwUICPAL7pT3tnjgkplvUoBKpWp1AxrqmoxGo9N367wWg28iInJYZY004A3wC4Zape6U95ZnvuXl\n",
       "L0TO4O3tDYPBAKPRyAx4NyCKIgwGAzQajWLvwe3liYjIYfJsc2eVnACWXVXk5S9EziAIAnx9fdHQ\n",
       "0ICGhgZXL6fdKiub/stUYGCgi1fiOXx8fBTNfDP4JiIih8kDXnkpiJIsy06uQhRFRX9oUvckCIKi\n",
       "mVAlHTt2DACQmJjo4pVQM5adEBGRw+QPOXZm8O3nEwAvtbd5bGioQ52httPen4jIEQy+iYjIYa4s\n",
       "OxEEwbJkxtluAAAgAElEQVTjSQ1LT4jIvTH4JiIih7ky823t/bjFPBG5OwbfRETkMMse350bfLPj\n",
       "CRF5GgbfRETkMH2N/IHLzis7AdjxhIg8D4NvIiJyWEWVfGv5Ti478bPseEJE5M4YfBMRkUOMJiOq\n",
       "aiskc4F+IZ26BsvMN4NvInJvDL6JiMghlTXlENGy45+/NkjS+q8zWNZ8s+yEiNwbg28iInKIxcOW\n",
       "fp1bcgJYdjuRl8EQEbkbu4LvjIwMxMXFQavVIjExEdnZ2W2e87e//Q033HADfH19ERMTg6VLl3Z4\n",
       "sURE5D7k9dVBAZ37sCVgvduJKIqtHE1E5Hptbi+fmZmJhQsXYt26dRgzZgzWrl2LSZMm4cSJE4iN\n",
       "jbV6zqJFi/Dpp5/itddew+DBg6HX61FYWOj0xRMRkeu4Q+Zb6+MPb7UGDUYDAMDQWI86Qy20Pn6d\n",
       "vhYiInu0GXyvXr0aaWlpmDdvHgBgzZo1+Oyzz7Bu3Tq8+OKLFsf//PPPeOutt/DTTz9h4MCB5vkh\n",
       "Q4Y4cdlERORqFpnvTu50AjTtchnkH4rSiiLzXEX1VQbfROS2bJadGAwG5ObmIjk5WTKfnJyMnJwc\n",
       "q+d8/PHH6NevH/bs2YN+/fohLi4Oc+fOxZUrV5y3aiIicjl55tsVwTfAjXaIyLPYDL5LSkpgNBoR\n",
       "FRUlmY+MjIROp7N6Tn5+Pi5cuIAdO3bg3XffxdatW3Hq1CncddddrMMjIupC5EGuPAjuLEEB8l7f\n",
       "7HhCRO6rzbKT9jKZTKivr8fWrVtx/fXXAwC2bt2KgQMH4ujRoxgxYoTV844ePerspXR7vKfK4H1V\n",
       "Bu+rMpS8r7riXyXjgktFaNR3/t9jXVWDZHz81I8QqvwVfU9+vyqH91YZvK/OFR8f7/C5NjPfERER\n",
       "UKvVKCoqkswXFRUhOjra6jnR0dHw8vIyB94AcP3110OtVuPixYsOL5SIiNxLTUOVZKzVBLhkHX6a\n",
       "QMm41lDpknUQEdnDZuZbo9EgISEB+/btw7Rp08zz+/fvx4wZM6yeM2bMGDQ2NiI/Px/9+vUD0FSK\n",
       "YjQa0bdv31bfKzEx0ZH1kxXNv93ynjoX76syeF+VofR9NZmM2JpTLZkbc+s4eHtpFHk/m2vxr0Tu\n",
       "hQPmsTZQo9jn5vercnhvlcH7qgy9Xu/wuW32+V60aBG2bNmCjRs34uTJk3j00Ueh0+mwYMECAMDS\n",
       "pUsxYcIE8/ETJkzA8OHDcf/99yMvLw/ff/897r//ftx66638iyci6iKqaisgiibz2M8nwCWBN2Dl\n",
       "gUtutENEbqzNmu+UlBSUlpZixYoVKCwsxODBg7Fnzx5zj2+dTof8/Hzz8YIg4J///CceeeQRjB07\n",
       "FlqtFsnJyVi9erVyn4KIiDqV/KFGV3U6aXpvdjshIs9h1wOX6enpSE9Pt/ra5s2bLeZ69uyJHTt2\n",
       "dGxlRETktircoMd3s2BZt5OK6jKIoghBEFy0IiKi1tm1vTwREdG15JlvV7UZBACtpmmXy2ZNu1zW\n",
       "uGw9RES2MPgmIqJ2c6fMtyAIVnp9s/SEiNwTg28iImo3d9ndspk88y5fHxGRu2DwTURE7VZR4z5l\n",
       "J4Bl8M/MNxG5KwbfRETUbvJ2fsFulvlmu0EiclcMvomIqN0sy05cm/lm2QkReQoG30RE1C6iKKKi\n",
       "plwy5+qab5adEJGnYPBNRETtUl1XCaOp0Tz20Wjh4+3rwhVZKTth8E1EborBNxERtYtlvbdrS04A\n",
       "IDiAZSdE5BkYfBMRUbvIO524uuTE2hr01VchiqKLVkNE1DoG30RE1C7yDXaC/VwffGs1/vD2atnl\n",
       "sqHRgFpDtQtXRERkHYNvIiJqF4ut5QNcX3YiCAI7nhCRR2DwTURE7eJOW8tfy6L0hL2+icgNMfgm\n",
       "IqJ2kWe+g9yg7ARgxxMi8gwMvomIqF3cbYOdZiw7ISJPwOCbiIjaRZ5Rdoeab4Ab7RCRZ2DwTURE\n",
       "dhNF0TLz7S5lJwEsOyEi98fgm4iI7FZbX41GY4N5rPHyga9G68IVtWDZCRF5AgbfRERkN4uHLf1D\n",
       "IQiCi1YjxQcuicgTMPgmIiK7WWyw4yYPWwKWNd8VVWXc5ZKI3A6DbyIisps8m+wuPb4BwFfjB42X\n",
       "j3ncYOQul0Tkfhh8ExGR3SzbDLpP8G1tl0t9Feu+ici9MPgmIiK7yYNvdyo7AayUnrDum4jcDINv\n",
       "IiKymzuXnQBsN0hE7o/BNxER2c39M9/y4JtlJ0TkXuwOvjMyMhAXFwetVovExERkZ2e3euz58+eh\n",
       "Uqksvvbt2+eURRMRkWu4c803AASz7ISI3JxdwXdmZiYWLlyIZcuWIS8vD0lJSZg0aRIuXbpk87x/\n",
       "/etf0Ol05q/bb7/dKYsmIqLOJ4oi9DWelvlm8E1E7sWu4Hv16tVIS0vDvHnzMHDgQKxZswbR0dFY\n",
       "t26dzfPCwsIQGRlp/vL29nbKoomIqPPVGWphaKgzj73U3tD6+LtwRZYsdrlktxMicjNtBt8GgwG5\n",
       "ublITk6WzCcnJyMnJ8fmuVOnTkVUVBTGjBmDXbt2dWylRETkUhU17ru7ZTN52Qkz30TkbtoMvktK\n",
       "SmA0GhEVFSWZj4yMhE6ns3pOYGAgVq1ahX/84x/Yu3cv7rzzTsycORPbtm1zzqqJiKjTyeun3a3e\n",
       "G7AsO6mo5i6XRORevJS4aHh4OB577DHzePjw4SgtLcXKlSsxa9Ysq+ccPXpUiaV0a7ynyuB9VQbv\n",
       "qzKceV/PXTkmGZsMgtv9vYmiCC+VNxpNDQCadrnM+SYbPl5ap76Pu33uroT3Vhm8r84VHx/v8Llt\n",
       "Zr4jIiKgVqtRVFQkmS8qKkJ0dLTdbzRixAicOXOm/SskIiK3UGOokoy1mgAXraR1giBYrKtWtm4i\n",
       "IldqM/Ot0WiQkJCAffv2Ydq0aeb5/fv3Y8aMGXa/UV5eHmJiYlp9PTEx0e5rkW3Nv93ynjoX76sy\n",
       "eF+VocR9vVz7E3C+ZRx/3UC3/Hv76nwMKn9tqU+PvS4GA/sMccq1+f2qHN5bZfC+KkOv1zt8rl1l\n",
       "J4sWLcLs2bMxcuRIJCUlYf369dDpdFiwYAEAYOnSpThy5AiysrIAAO+88w40Gg2GDh0KlUqFTz75\n",
       "BBkZGVi5cqXDCyUiIteSb1gjr692F/KOJ3zokojciV3Bd0pKCkpLS7FixQoUFhZi8ODB2LNnD2Jj\n",
       "YwEAOp0O+fn55uMFQcCKFStw4cIFqNVqDBw4EJs3b8Z9992nzKcgIiLFyYNY+Vbu7kL+IKi+isE3\n",
       "EbkPux+4TE9PR3p6utXXNm/eLBnPmTMHc+bM6djKiIjIrVjsbunnft1OACu9vmvY65uI3Ifd28sT\n",
       "EVH35u5byzez6PXNzDcRuREG30RE1Kb6hjrUGWrMY7XKC/7aQBeuqHXcYp6I3BmDbyIiapNlyUkI\n",
       "VIJ7/giR16LL105E5Eru+S8nERG5FU/Y3bKZtW4n3OWSiNwFg28iImqTvM2gu3Y6AQBfjRYab1/z\n",
       "uNHYgJp6brRDRO6BwTcREbWpvKpUMg72D3fRSuxj0fGEpSdE5CYYfBMRUZvkZSfyjiLuhh1PiMhd\n",
       "MfgmIqI2yYNXdy47AdjxhIjcF4NvIiJqk8Xulm5fdiLNfLPshIjcBYNvIiJqk6dlvuXrY+abiNwF\n",
       "g28iIrJJFEUrmW/3Dr6D/GQ13wy+ichNMPgmIiKb6gw1MDTWm8feXhpoffxduKK2caMdInJXDL6J\n",
       "iMimcnnJiX8YBEFw0WrsY22jHSIid8Dgm4iIbLJsM+jeJSeA9W4n3OWSiNwBg28iIrLJot7bzR+2\n",
       "BJp2ufS5ZpdLo7GRu1wSkVtg8E1ERDZZdDrxgMw3YKX0hBvtEJEbYPBNREQ26atlW8t7QOYbAILk\n",
       "u1yy7puI3ACDbyIisqmrZL7Z8YSI3AGDbyIiskkvC1qDA9x7d8tm3GiHiNwRg28iIrJJXyUrO/GQ\n",
       "zLe87ETetYWIyBUYfBMRUatMogn6Glnm20OCb8te3yw7ISLXY/BNREStqq6tgMlkNI+1Pv7QePu4\n",
       "cEX2s9brm4jI1Rh8ExFRq6ztbukpguVlJ2w1SERugME3ERG1yhN3t2xmkfmuKeMul0Tkcgy+iYio\n",
       "VZ64u2UzX40WPhqteWw0NqKmrtKFKyIiYvBNREQ2eGqP72bBftxoh4jci13Bd0ZGBuLi4qDVapGY\n",
       "mIjs7Gy7Ln7mzBkEBgYiMDCwQ4skIiLX8NTdLZsFWfT6ZscTInKtNoPvzMxMLFy4EMuWLUNeXh6S\n",
       "kpIwadIkXLp0yeZ5BoMBqampGDduHARBcNqCiYio8+irPLPNYDPLXS6Z+SYi12oz+F69ejXS0tIw\n",
       "b948DBw4EGvWrEF0dDTWrVtn87wnn3wSQ4cOxYwZM/iACxGRh7Ks+faM3S2byTueyMtoiIg6m83g\n",
       "22AwIDc3F8nJyZL55ORk5OTktHrep59+ik8//RRvvvkmA28iIg9mubtlaCtHuid5x5OKGpadEJFr\n",
       "edl6saSkBEajEVFRUZL5yMhI6HQ6q+cUFBTggQcewEcffQQ/Pz/nrZSIiDqV0diIylq9eSxAQJBf\n",
       "x4PvwhIRn38HfPE9cPYycKUMqK4DwoOBqFBg6ADg9uHAmFsAX5+OlS1a7HLJzDcRuZjN4NsRs2fP\n",
       "Rnp6OkaMGNGu844ePerspXR7vKfK4H1VBu+rMjpyX6vr9ZKxj7cfvv8+z6FrmUzA1yeDsDM7Ejkn\n",
       "gyCKlkH1hf/P6ez9N/DSu0CgthF3jSrF9N8Uo3eEwaH31emLJeNfiy855XuN36/K4b1VBu+rc8XH\n",
       "xzt8rs3gOyIiAmq1GkVFRZL5oqIiREdHWz3n4MGDOHz4MJ577jkAgCiKMJlM8Pb2xrp16/CnP/3J\n",
       "4cUSEVHnqTFUScZ+Gsc6Vx0774dVu/vg+AX/dp1XWeuF9w9FYfsXkZg25goemFSAYH9j2ydeQ77m\n",
       "WtlnIiLqbDaDb41Gg4SEBOzbtw/Tpk0zz+/fvx8zZsywes6xY8ck448++gh//etfceTIEcTExLT6\n",
       "XomJie1ZN9nQ/Nst76lz8b4qg/dVGc64rz+cbQB+bBlH9+jdruvV1IlYtAb4n48dXgIAwCQK+MeX\n",
       "kfj8h0hkLAFS7rS/FKXeUIuPcjPM47qGaiQkJDjchYvfr8rhvVUG76sy9Hp92we1os2yk0WLFmH2\n",
       "7NkYOXIkkpKSsH79euh0OixYsAAAsHTpUhw5cgRZWVkAgEGDBknO//bbb6FSqSzmiYjIvVl2OrG/\n",
       "3vvEOREzlwPHz1l/fWg88LskIOlmoHck4O8LlFYApy8Bh3KBj78ESmU/265WAKlPAwdzRax+BNDa\n",
       "UQ/u8/+7XNYbagEARlMjqusqEaANsvuzEBE5U5vBd0pKCkpLS7FixQoUFhZi8ODB2LNnD2JjYwEA\n",
       "Op0O+fn5Nq/BPt9ERJ7HcndL+9oM7v1aRMpyoLrW8rV7xgJP/gEYOcjyZ0N/NM3/YSLw1iIR27OA\n",
       "FVuA/ALpNTZ8BOT+DPzzVRE9Qtv++RLsH4Ziw6/mcUX1VQbfROQydu1wmZ6ejnPnzqGurg5HjhzB\n",
       "mDFjzK9t3rzZZvA9d+5cVFRUdHylRETUqSwz321vsPPOHhFTnrQMvAfEAllrgN0vCRh1k9BmUsbX\n",
       "R8Dc3ws49h6w4gFA4y19/chJYEw6kP9r2+1sLTqecJdLInIhu4JvIiLqfiwz37aD7w0fiUj7K2CU\n",
       "PRM5+7fA0U3AHQnt/6+gvj4CnvqjgJwNwPW9pa+duQSMfRD45bLtADyIG+0QkRth8E1ERFa1J/P9\n",
       "zh4R6a9K5wQBeGMh8M5yAQF+HSs/HD5QwNFNwJ2yZ8YKSoAJjwIXda0H4NxinojcCYNvIiKyynJ3\n",
       "S+vB94dfiJj3knRO4w1kvgA8PMN5z/wE+Qv49DXgvv+Qzl/QNQXgV8qsB+AsOyEid8Lgm4iILNQ3\n",
       "1KHWUGMeq1Ve8LfykOJ3p0T84bmmTXSaeXsBu18Ept/u/IftNd4C3n26qZTlWmcvA9OeAuoNlgG4\n",
       "RdkJM99E5EIMvomIyEKFLDsc5B8KlSD9kXG5WMSUJ4Da+pY5tRp4/1ngd0nKdblSqQRsXArMuEM6\n",
       "n/0j8MArTZu7XUteLiP/bEREnYnBNxERWbCo95aVbtQbREx7CiiUVqYgYwkwTYGMt5yXl4CtTwO3\n",
       "D5fOb/0M+FumdM6y7ISZbyJyHQbfRERkwbLeW1q6seStpnZ/11p0LzB/Suft66DxFvCPvza1MbzW\n",
       "kxlAzk8t2W952UlFdZlFdpyIqLMw+CYiIgu2Op3s+FzE2l3S4yePBl5J74yVSYUFCfjkVSA4oGWu\n",
       "0di0E2ZJeVOA7ePtC1+Nn/n15l0uiYhcgcE3ERFZKJf1wg76/9KNCzoRD7wiPfa6aOCdZYBa7Zrd\n",
       "jONjBWxZJp27XAzMf7ml/lteelJeVdJZyyMikmDwTUREFsorpcFpaGAEjEYRf3wBqKhumdd4A/9Y\n",
       "AYQGuSbwbnb3bwQsvlc69/GXwKZ/Nv05JCBc8lp5paxYnYiokzD4JiIiC2WyzHBIQARWbwcO50mP\n",
       "W/kQkHCDawPvZi8uAEYNks4tfKNpB8yQwAjJvPzzERF1FgbfRERkQZ75Li6LwvK3pcckjwT+PK0T\n",
       "F9UGb6+mHuB+vi1z1bXA/S8CwX7S4Fv++YiIOguDbyIikjAaGyW9sE0mFR5/MxyGhpZjQgOBTU81\n",
       "9dx2J/GxAlY/Ip378gfgcN4QyVx5FctOiMg1GHwTEZGEvroMIlpa8Z25+J/493FpkL12CRDTw70C\n",
       "72bzpwCTbpXOrds9AFU1LXXfLDshIldh8E1ERBLXdgKprI7AF9/PkLw+ZQww887OXpX9BEHAuseB\n",
       "AG3LXHWdGodyHzCPWXZCRK7C4JuIiCTKrglMv8ybB0ODj3kc5N+U9RYE98x6N+vTU8BLsr7j5wtG\n",
       "4nxBAoCmshNutENErsDgm4iIJJoz3xcKhyP/V2n9xisPAr3ctNxELv0/gaTB0rkv8+6H0eiFRmMD\n",
       "qmorXLMwIurWGHwTEZFEWWUJGo3eOPz9nyTzowY11VN7CpVKwFuLANU1P+n0VTH4/nTTh+BGO0Tk\n",
       "Cgy+iYhIoryqFHk/T4G+Kto8p1I1lZu4W3eTtgwdIOCBu6VzR0/MQFVNuKS8hoioszD4JiIiiUu6\n",
       "enx3StrAe8E9wPCBnhV4N3thPhAW1DJuNPriqx/+yHaDROQSDL6JiEjik6/GoqGxpVVIWJAJL8x3\n",
       "4YI6KDxYwIoHpHNnLv0G2T/wRyARdT7+y0NERGa5PzfghzO/kcwtTwNCgzwz691s/hRgQKz0Acv1\n",
       "Hw5HYyM7nhBR52LwTUREAABRFLF4jQmiqDbPhQXp8OBUz/9RoVYLePr+Isnc5eIe2LLHRQsiom7L\n",
       "8/9FJSIip9j7NfBFnkYyd/fYvfD28uysd7M7ErUY2PeQZO7ZjUBNHbPfRNR5GHwTEREaGkUseUs6\n",
       "1zvyR9w2+IprFqSA0IAI3Dr4PahVBvNcQQnwxg4XLoqIuh27g++MjAzExcVBq9UiMTER2dnZrR57\n",
       "4sQJ3H777ejZsye0Wi369++P//7v/0ZDQ4NTFk1ERM719v8Cpy5cO2PC6CGbERYY4aolOZ2PRovI\n",
       "0DrcEv+pZP6V94BSPbPfRNQ57Aq+MzMzsXDhQixbtgx5eXlISkrCpEmTcOnSJavH+/j4IC0tDfv3\n",
       "78fp06fxt7/9DRs3bsRTTz3l1MUTEVHHVdeKeH6TdO7GuAPoEXoeIYHhrlmUQkICwpFw4y74eFeZ\n",
       "5yqqgRffdeGiiKhbsSv4Xr16NdLS0jBv3jwMHDgQa9asQXR0NNatW2f1+P79+2POnDkYPHgwYmNj\n",
       "cdddd+G+++7DV1995dTFExFRx725Eyguaxl7qesw6ub3AQAhAV0n8w00lZ74aqqRcOMuyfzaXcD5\n",
       "Qma/iUh5bQbfBoMBubm5SE5OlswnJycjJyfHrjc5e/Ys/vWvf1lcg4iIXKu8UsTKbdK5IQP+iQBt\n",
       "UzQeFhTpglUpJ/T/P88t1+9BgLZlh0tDA/DM3121KiLqTtoMvktKSmA0GhEVFSWZj4yMhE6ns3lu\n",
       "UlIStFotBgwYgFGjRuHZZ5/t0GKJiMi5XvsAKK9sGftoqjFs4EfmcVhgDxesSjnNn8fLy2DO7jd7\n",
       "71/AD2eY/SYiZXkpefEdO3agqqoKeXl5ePzxx/HEE09g5cqVVo89evSokkvplnhPlcH7qgzeV2XY\n",
       "uq+lFV54/YObAbT09R42cDd8NdUAAJWgxs8nzkIQukarQQAoL2mp9R7Y9wscO5uCorKeAABRBB55\n",
       "rRyr5v/S5nX4/aoc3ltl8L46V3x8vMPntpn5joiIgFqtRlGRdHOCoqIiREdH2zy3d+/euOGGG5Ca\n",
       "moqXX34Zb7zxBoxGo8OLJSIi53knqydqDS2Bd4h/PYZc0wkkwCe4SwXeQNNnaqZSmTA+QVr7/eWx\n",
       "EJy44NfZyyKibqTNzLdGo0FCQgL27duHadOmmef379+PGTNm2P1GRqMRJpMJJpMJarXa4vXExES7\n",
       "r0W2Nf92y3vqXLyvyuB9VUZb9/WiTsRu2WM7D/ynDjWGevM4OjK2y/296Kv6Ye9PW8zj2J5f49ab\n",
       "HsK/j7cck5lzIz6dZv2XDn6/Kof3Vhm8r8rQ6/UOn2tXt5NFixZhy5Yt2LhxI06ePIlHH30UOp0O\n",
       "CxYsAAAsXboUEyZMMB+/detW7Ny5E6dOnUJ+fj527NiBp556CjNnzoS3t7fDiyUiIud4fnPTQ4bN\n",
       "YqOAOxNPSI4JC+xaD1sCQKB/CNTqlrxTnaEaT/2xXnLM3n8DXx9j7TcRKcOumu+UlBSUlpZixYoV\n",
       "KCwsxODBg7Fnzx7ExsYCAHQ6HfLz883He3t746WXXsKZM2cgiiL69u2LP//5z3jssceU+RRERGS3\n",
       "Xy6LeGevdO6Z+4GqWulD9F2t0wkAqAQVwgJ64Iq+0Dw3bIAOY27pi+wfW4575m1g3xsuWCARdXl2\n",
       "P3CZnp6O9PR0q69t3rxZMk5NTUVqamrHVkZERIp4cStw7eM3A2KBOb8F3vmXdCv5sKCu1emkWWiQ\n",
       "NPi+WlmM5+f3xR0PtxyTdRQ4nCdi7NCuVfNORK5n9/byRETk+c4ViNgqy3ovTwO8vARcrSiWzHe1\n",
       "NoPN5Bn9ssorGD9cwO3Dpcc983dAFFl+QkTOxeCbiKgbefk9oPGarHd8LDDzzqY/X62UZr5Du2DN\n",
       "N2D5S0XzLx3P/Ul63BffAwdzO2tVRNRdMPgmIuomLupEbPlUOvfUnKasd31DHaprK8zzKpUawQFh\n",
       "nbzCziHPfF+taPqlY8wQAckjpcc+/Taz30TkXAy+iYi6iVe2AQ2NLeN+McCs5KY/NwegzUICwqFW\n",
       "WbaF7Qosgu9rMv7y7HfOT8Dn3JuEiJyIwTcRUTdwuVjExk+kc0/9sSnrDQBlld2j3htovewEAEbd\n",
       "JOB3t0mPf34Ts99E5DwMvomIuoGV26R9vfv2BGb/tmUsz3x3xTaDzYIDwqESWn78VdXqYWho6fX9\n",
       "9P3S47N/ZO03ETkPg28ioi6usETE2/8rnVs6B/D2ammjJ3/YsitusNNMrVIjJCBcMld2zecfOUjA\n",
       "pFul5zy3kdlvInIOBt9ERF3cq+8D9YaWcWwU8MdJ0mPkbQZDu2iP72ahssx+qezzy7PfX/4AHGL2\n",
       "m4icgME3EVEXVnRVxIaPpHNP/gHw0Ug3j7najWq+AcvPVybL/I+6ScBv5dnvTUqvioi6AwbfRERd\n",
       "2KoPgNqWcmb06gHMm2x5XKm+SDLuyjXfgOXnK9HrLI55Ok06PpwHfHcmQMllEVE3wOCbiKiLKqvy\n",
       "QsZu6dwTsyyz3vUNdaisKTePVYKqy2e+I4J7SsbyXz4A4NabLft+//2zGCWXRUTdAINvIqIu6v2D\n",
       "kaipaxn3DAf+NMXyuFJZ1jc0qAfUai+FV+da8uDbWuYbsKz9/u5sIHLPMvtNRI5j8E1E1AWVV6vx\n",
       "jy+lpRWP3wdofQSLY+WBpzww7YoiQiyDb2vdTJIGC/iPEdK5tz+LVnJpRNTFMfgmIuqCth+KQk19\n",
       "yw6VkaHAf91j/ViL4Duo6wffQX6h8PbSmMd1hhpU11VaPdYi+30mCIfz2HaQiBzD4JuIqIspqxCR\n",
       "eVia9V58L+Dna5n1BoASWb2zPCvcFQmCYKXu23rpyehbBExIlM49z84nROQgBt9ERF3MG/8Aquta\n",
       "st4RIUD6f7Z+fHcsOwGAcDvrvgHL7PeB74Avmf0mIgcw+CYi6kL0VSLe2CGdW5QKBPhZz3oDQGl5\n",
       "9wy+7X3oEgDGDBFwpzz7vVmJVRFRV8fgm4ioC3lzJ6CvahmHBQEPTW39eKPJiFLZBjvyjHBXFREc\n",
       "JRmXlLcefAOWfb8/Pwpk/8DsNxG1D4NvIqIuorJaxOvbpXMLZwKB/q1nvcurSmAyGc3jAG0wfDVa\n",
       "pZboViwy3xWWvb6v9ZuhAhLjKyRzrP0movZi8E1E1EWs3Q2UXdOwI1DbiIen2z5Hnu3tLiUnQPvK\n",
       "Tpr96beFknHWUeCrH5n9JiL7MfgmIuoCqmpErPpAOpc6rhjBAa1nvYHu+7Al0LTFvCC0/BjUV5XC\n",
       "0Fhv85zh11chgdlvIuoABt9ERF1AxodAqb5l7O9rxMxxxa2f8P/k26p3p+DbS+2N0IBwydzVirbv\n",
       "2XxZ9nv/EeDrY8x+E5F9GHwTEXm46loRq96Xzs0cW4wgP6P1E64hz3yHyx5C7Oos2g228dAl0JT9\n",
       "HjdMOsfsNxHZi8E3EZGHW/chcKW8ZRzoB9w73vbDg826c9kJ4FjdNwA8I+v7/a9vgH8z+01EdmDw\n",
       "TUTkwWrqRLwmy3r/eToQ7N921lsURcvguxvsbnktR4Pv8cMFjB0qnWPfbyKyB4NvIiIPtuEjoLis\n",
       "ZRygbdpUxx6VNXrUGWrMY423L4L8Qp28QvcWERItGReXF9h9rjz7/dm/gW+OM/tNRLbZHXxnZGQg\n",
       "LrWCDaAAACAASURBVC4OWq0WiYmJyM7ObvXYQ4cO4e6770ZMTAz8/f0xZMgQbN7MlAARkTPV1ot4\n",
       "VZb1fmgaEB5su8NJs+LyXyXjyJAYCIJ953YVUaExknFx2a+tHGlp/HDgN0Okc6z9JqK22BV8Z2Zm\n",
       "YuHChVi2bBny8vKQlJSESZMm4dKlS1aP//rrrzFkyBDs2rULx48fR3p6Oh544AF88MEHVo8nIqL2\n",
       "+5+PAV1py9hfCyy+1/7zi65elowjQ3s5aWWeIyIkGgJafuEoq7jSZrvBZoIg4GlZ9nvvv4FvTzD7\n",
       "TUStsyv4Xr16NdLS0jBv3jwMHDgQa9asQXR0NNatW2f1+KVLl+L555/Hbbfdhuuuuw4LFizA1KlT\n",
       "sWvXLqcunoiou6qrF7HyPencg1OBiBD7M9fyLG9UNwy+NV4+CA3qYR6LEHGlrNDGGVJ3JABjbpHO\n",
       "MftNRLa0GXwbDAbk5uYiOTlZMp+cnIycnBy730iv1yMsLKz9KyQiIgtv/y9QeE3W28+3fVlvACgu\n",
       "k9Y3d8fMN2D5ueXlOLZYy37v+Ro4cpLZbyKyrs3gu6SkBEajEVFR0t6vkZGR0Onseyr8n//8Jw4c\n",
       "OIAHHnjAsVUSEZFZXb2IV2RZ7wX/CUSGtq9eW5757q7Btzzj3566bwC4MxEYzew3EdnJS+k3+Oqr\n",
       "rzBr1iy8+eabSExMbPW4o0ePKr2Ubof3VBm8r8rgfbXfzi97oKCkj3ns423Cfwz6CUePNloc29p9\n",
       "NZoaLdrqXT6nQ9HFq85drAeoq5C2ZTx59keEq/rZPEd+X1NHB+KrHweYx5/mAO/uPoFBfWrkp1Ib\n",
       "+G+BMnhfnSs+Pt7hc9vMfEdERECtVqOoSLphQ1FREaKjo1s5q0l2djZ+97vf4YUXXsB//dd/ObxI\n",
       "IiJqYmgUsCVL2pt66ugrCA+yDLxtqawrg4iW0gg/TSC81RqnrNHTBGmlJZH62tJWjmzdyIGVGHxd\n",
       "lWRu479s/4wkou6pzcy3RqNBQkIC9u3bh2nTppnn9+/fjxkzZrR63uHDhzF58mQ8//zzeOSRR9pc\n",
       "iK2sOLVP82+3vKfOxfuqDN7X9snYLaL4mt0sfTXAqkVR6BkuDcjbuq8/nP038H3LODaqX7f9Oyiv\n",
       "isP+49vM4ypDORISEqy2XbR1X199RMRvF7WMvzwWAiEgAQk3dK/2jY7ivwXK4H1Vhl6vd/hcu7qd\n",
       "LFq0CFu2bMHGjRtx8uRJPProo9DpdFiwYAGApu4mEyZMMB9/6NAhTJo0Cenp6bj33nuh0+mg0+lw\n",
       "5coVhxdKRNTd1dSJ+OsW6dwDdwM9w9sf3LHeu0Wwfxh8vH3N43pDLSpqymycYd1/jARuvUk69wK3\n",
       "uCAiGbuC75SUFPztb3/DihUrMGzYMOTk5GDPnj2IjY0FAOh0OuTn55uPf+edd1BXV4dXX30V0dHR\n",
       "iImJQUxMDEaNGqXMpyAi6gbWfSjtcKL1Af4y27FrWQbfMa0c2fUJgoAeHdhs59rrPDNPOve/2UDu\n",
       "z+x8QkQt7N7hMj09HefOnUNdXR2OHDmCMWPGmF/bvHmzJPjevHkzjEYjTCaT5OvaY4iIyH6V1ZYd\n",
       "Tv483bGsNwAUyXe37MaZbwCICpF3PLF/m/lrJY8ERg2SzjH7TUTXUrzbCRERddwb/wBKrqn1DvQD\n",
       "npjl2LVEUUTx1c7ZYMdoNKK6uhrV1dWoqqoyfxkMBphMJoiiKEnSAICPjw+0Wi18fX3N/+vr64vA\n",
       "wEAEBgZarcXuqMiw3pKxfPdPezVlv0X8bnHL3MdfAt+fFjFsAGu/iYjBNxGR2yurELHqA+ncY6lA\n",
       "eLBjwVxVbQVq6ls6c3h7aRASGNGuaxiNRhQWFuLChQsoLCxEcXGx+evKlSu4cuUKSkpKUF1d7dAa\n",
       "W+Pt7Y2wsDCEhYUhPDzc/BUTE4PY2Fj07t0bvXv3RlBQULuuK//lo8iBspNmE0cBIwcB355omXth\n",
       "M7D7JYcvSURdCINvIiI3t2o7oL+mi11oIPDYTMevV1h6UTKODO0FlWC9ClGv1+PkyZM4ffo0Lly4\n",
       "gPPnz+PChQu4dOkSDAaD44twUENDA4qKiiza38oFBQWhd+/e6Nu3LwYMGID4+HgMGDAA1113Hby9\n",
       "vS2OlwffOtk9ag9BEPB0mojJj7fMfXQYyDstYiiz30TdHoNvIiI3Vlwm4o0d0rnHZwHBAY4HcYWl\n",
       "FyTjmPC+EEUR58+fx/Hjx3Hy5EmcOnUKp06dQkGBY7XPrlZRUYETJ07gxIkT2Lt3r3ne29sbcXFx\n",
       "GDBgAG6++WYMGTIEN998MyJDe0MlqGASm0pfyqpKUFNfBT+fAIfef9JtwIgbgSMnW+Ze2AzsYvab\n",
       "qNtj8E1E5MZeeheorm0ZR4YCD0/v2DULSi6god6I8qIalP1fe/cdFtWVPnD8ewcYOogUEWmKClhQ\n",
       "A1iwYgC7azeiZnVNWxM3pmw2xSSmuZtkkzW70SS7+W3iSowlkWiIBVSwgBqwFxTFBiogRZq0mbm/\n",
       "PyaMDF0EBvR8nuc+eA/nzrxzvMx958y559y8w9V9Mfzjtf+Rl3fv0+s1hpWVFZaWlrqf1tbWKJVK\n",
       "FAqFbpMkCYVCgSzLlJWVUVpaSmlpKSUlJbotPz+f0tLS+4qloqKClJQUUlJSiIqKArQ91V5eXkhW\n",
       "pZh2kLHrbIGNozk3s6/h1aVXA49YO0mSeOsPMpOq9H5H7tPOfPKIt+j9FoSHmUi+BUEQ2qjLN2RW\n",
       "b9Yve+1xsDS/9+Tt9u3bHD58mISEBH6J3kJORtUFIjLqPK4+HTt2xMPDA1dXV5ycnGpsjo6OWFtb\n",
       "o1A0emKtBt25c4fc3FxycnLIzc0lNzeXrKwsrl+/TlpaGunp6aSnp9/TkBhZlrl48aJembFSQVr8\n",
       "K4wLmcigQYPo06dPrcNV6jN+CAT4QNK5u2V/WQ3RK+UWuWlUEIT2QSTfgiAIbdSyf0NFlVXj3TvB\n",
       "079r3LElJSUkJyezc+dODh06xJkzZ5Dle59v2tjYGC8vL3x8fOjevTuenp54eHjg4eFxzzc1NgcL\n",
       "CwssLCxwdXWts45GoyEnJ4dr165x4cIFLly4QEpKChcuXGhwrHglVbmGk0fOcPLIGQDMzc3x9/fH\n",
       "09OT/v3717kCZlWSJPHuk/ozn+xOguhftTdlCoLwcBLJtyAIQhuUlCzzfYx+2XtPgZlp7QmfLMtc\n",
       "unSJ2NhY4uLiOHToEGq1+p6e08rKCj8/P3r16oWPjw++vr54eXlhamra1JdhEAqFAkdHRxwdHfH3\n",
       "99f7XX5+PhcuXODMmTOcPHmSkydPkpqa2uAHk5KSEg4cOMCBAweIiIjg448/ZsSIEYwYMYKhQ4di\n",
       "Z2dX63FjBsGjAdqku9KrqyEkQMbISPR+C8LDSCTfgiAIbYwsy/xltX5Zv+4wN0y/rKysjIMHD7Jn\n",
       "zx7i4uJIS0u7p+exsjPF3cuFedOeZMCAAfTo0QMjI6P7jL5ts7W1JSAggICAAF1ZYWEhp0+f5uDh\n",
       "eDZFRZB7o4jykvo/uGRmZrJp0yY2bdqEJEkMGDCA0NBQQkND8fLy0tWTJIm//VEmsMrKlycuwnfR\n",
       "8Pi4Zn95giC0AyL5FgRBaGN2HILYo/plHy4GhULizp07xMXFsWPHDmJjYykqKqr9QWrh4+ODS1d7\n",
       "Co2v07GLJUozY4b5jWNW8JxmfgXti7W1NUOGDGHQ4EHcVCZRWl5CUW4ZOelFdDbtxbEjx7l161ad\n",
       "x8uyzNGjRzl69CgffvghXbt2JSwsjNDQUO0QFR8jwkNl1lX5JuOt/8Cs0XKd32QIgvDgEsm3IAhC\n",
       "G6JWy7z6hX7Z6P4FFN/YwzPP7GTv3r2NnvHD2dmZkJAQBg8ezODBg7G3t+ebbR9z7MLdhN3F3qM5\n",
       "w2/XFJKCzvYeXMk4j7W9Gdb2Zjw9+Sl6efpz6dIl4uPj2bp1K6dPn6asrKzOx7l8+TJfffUVX331\n",
       "FQ4ODowdO5YZgyfwQ2wA5SrtNwvXMuHzH+Hl8NZ6dYIgtBUi+RYEQWhD1u6AU6kgaQqwKN2BZcl2\n",
       "rkYn8OK2igaPVSqVDBo0iODgYBwcHOjcubPe8AqAG9Xn+HYQyXdVLg7uXMk4r9u/kXON3l0D8PLy\n",
       "wsvLi169elFRUYEsy+zbt499+/aRnJxc5+NlZ2cTERFBREQEXS2dyGI8d8wnUGYygBX/U/CHiTId\n",
       "bUTvtyA8TETyLQiC0Ebk3i7lrY9jccjdgkVpLBLa6fJU9Rzj4OBAaGgoo0ePJigoCAsLCwCSkpJq\n",
       "1K1QVXArT3/RnM727s0W/4Ogc7VvAm5mX61Rx8TEhICAAIKCgnj11Ve5efMmu3btIiYmhkOHDlFR\n",
       "UfsHpdLiLGz4Fpvib1EZdaa4YAIv/nUC36zoJ6YeFISHiEi+BUEQDEij0XD48GF++uknIrdsx6is\n",
       "EMsGjnFxcWHs2LGMHTuWRx55pNE3SWbmpelWcASws3bE3LShZ3u4VP8moPo3BbXp3Lkz8+fPZ/78\n",
       "+RQUFLB3715iYmKIi4ujsLCw1mOM1TexLf6aveu/Zug+D2bPmsq0adNwc3NrltchCELbJZJvQRAE\n",
       "Azh37hybN2/m559/JiOj4UVuPD09GTduHGPHjqVv375N6ilNz7qsty/Ge9dUvU0yctOoUJVjYqxs\n",
       "1PE2NjZMmjSJSZMmUVZWxv79+4mKimLXrl0UFxfXeszNG1dZuXIlK1euJDAwkOnTpzNu3DiDzKMu\n",
       "CELLE8m3IAhCKykoKGDr1q1s2rSJkydPNljf1dWdKVMmM2HCBLy9ve97aMK1LP1VHN06edVR8+Fl\n",
       "aW5DRxsncguyANBo1NzIvoKHc897fixTU1NCQkIICQmhtLSUuLg4oqKiiI7ZTUV57TfNJiYmkpiY\n",
       "yNtvv82YMWOYNm0aQ4cOxdhYXK4F4UEh/poFQRBakEaj4eDBg2zatIkdO3bUO0sGgFphT7H5BF5c\n",
       "/Dte/+OAZh0LnJapn3y7O3Vvtsd+kLg7ddcl3wDXMi82KfmuyszMTDdUqLi4mNGP7+HK2SjMS+N0\n",
       "Y/urKisrY+vWrWzduhUnJyemTp3K7Nmz6dq1633FIQiC4YnkWxAEoQWkp6fzww8/8MMPP3D9+vX6\n",
       "KyssKDINpdj8d5SaDmVwHxNee4ZmTbxV6grSs/WHnbh3Esl3bdw6def4xQTd/rVqH1rul6WlJV9/\n",
       "NJFHFk5ErsjHouQXLO9EYlZxpNb6WVlZuqkLBw0axOzZsxk3bhxmZmbNGpcgCK1DJN+CIAjNpKys\n",
       "jB07drBp0ybi4+PrrStJEkOHDsXabTpfxYYiKyx0v/vsBe2COs3pZs411Oq786Z0sLLHxrL2JdEf\n",
       "dh7VPpRUH67THPp6STwzRWbVj7YUWYZTZBmOtdFlXgj9iV07N9f5ge3w4cMcPnyYt99+mylTpvDY\n",
       "Y4/Rq1evZo9PEISWI5JvQRCE+3Tp0iXWrVvHjz/+yO3bt+ut6+bmxowZM5g+fTrG5i74hoOsuPv7\n",
       "hRMh0Lf5p52r3nsrer3r5urUTW8/IzedsopSTE2at6f5nSdg/S7IydfuF6q7kqJ6gX37lvLrr78S\n",
       "GRnJtm3bal3FtLCwkLVr17J27Vr8/PyYPXs2kyZNwtraulljFASh+YnkWxAEoQnKy8uJjo7m+++/\n",
       "JyEhod66ZmZmjBs3jpkzZzJo0CAUCm22PXe5zO0qM9HZWMKKp1sm3urJt5sY710nC1MrHDu4cOu2\n",
       "dk50WdaQnnUJry7N28Pc0UbivSdlFv/9btn6XfD4OImxv61Kunz5crZt28b69etrnbsd4OTJk5w8\n",
       "eZL333+fCRMmEB4eTv/+/cXc4YLQRonkWxAE4R6kpaWxfv16NmzYQE5OTr11+/fvz8yZM5k4cWKN\n",
       "aeO2H5T5Pka//lt/gE4dWyZhupZ5QW9f9HzXz71Td13yDdoPL82dfAM8ORn+sxWOpdwtW/x3OLVW\n",
       "xtJcwtzcnOnTpzN9+nRSU1PZsGEDmzdvrvXcKykp0d1n4Ovry7x585g8eTJWVlbNHrcgCE2naLiK\n",
       "IAjCw02lUhETE8PChQsZOXIkq1evrjPx7tChA4sWLWLnzp1ERkYSHh5eI/EuuqPf2wkwoCf8aUbL\n",
       "xF+uKuNmzjW9MncnMc1gfarPBNMS474BjIwkvnoFFFWuxlduwtv/V7Oul5cXr7/+OgkJCaxatYoR\n",
       "I0bU2budnJzMG2+8wZAhQ3jzzTdJTk5ukfgFQbh3oudbEAShDhkZGWzYsIH169c3uBBOQEAAc+fO\n",
       "Zdy4cZiamtZb962v4WqVh1Mo4N9/AWPjlun1vn7rit7KlvY2nbA0Fwu41Me92hzo1adpbE4BvhJ/\n",
       "mimzcsPdspUbYE6IjL9PzXNCqVQyfvx4xo8fr5tVZ9OmTdy4caNG3aKiIiIiIoiIiOCRRx5h7ty5\n",
       "TJgwocFzVBCEliOSb0EQhCo0Gg379+9n3bp17N69G7VaXWdda2trpk6dSnh4ON7e3o16/KRkmX9u\n",
       "0i9bOptak6zmcjUjRW9fDDlpmKtjNyRJgfzbh5as2zcoLq19qfjm8O4TsDkOrmVq9zUaeOpDOPwf\n",
       "ud4PZa6urixdupQlS5awb98+vvvuO2JjY9FoNDXqHj16lKNHj/Lee+8xY8YMwsPDxbzhgmAAjR52\n",
       "snr1arp27Yq5uTkBAQEcOHCgzrplZWUsWLCAfv36oVQqCQ4ObpZgBUEQWkp2djZffvklo0aNYsGC\n",
       "BURHR9eZePv5+fG3v/2NQ4cO8c477zQ68a5QyTz1oTaxquThDO8sao5XULfUG2f19j2ce7TsEz4A\n",
       "TJXmdLZ31yu7dKPlhm5YWUisflm/7FgKrNzYuOONjIwIDg7m66+/Zt++fTz33HM4OjrWWvf27dt8\n",
       "/fXXjB49mnnz5rF9+3YqKiru8xUIgtBYjUq+N2zYwNKlS1m2bBnHjx8nKCiIcePGkZaWVmt9tVqN\n",
       "ubk5S5YsYcKECeKOa0EQ2iRZljl06BBLliwhKCiIDz/8sM73NXNzc2bPns2WLVvYsmULs2fPxsLC\n",
       "ota6dfnoOziuf98jq18GS/OWe4+UZZnU6/rJd/cufVrs+R4k3avdYFm9HZvb+CCJx0L0y97+Gs5f\n",
       "le/pcbp06cJLL71EfHw8q1atYujQoXXWjY+PZ/HixQwbNoxPP/201qErgiA0r0Yl359++ikLFy5k\n",
       "0aJFeHt7889//pPOnTvzxRdf1FrfwsKCL774gieeeIIuXbogy/f2xiEIgtCSbt++zX//+19CQkKY\n",
       "M2cOUVFRdfb8eXt78+6773Lo0CH+9re/4efn16TnPHJO5p1qN9HNCYVxQ1q2cyIr7zpFJfm6fVMT\n",
       "M7o4iqEGjeHVpbfefur1My3+nP94HjpUmaq7pAwef0/7rcm9MjExYfz48URERLB7924WLVqEra1t\n",
       "rXWzsrL417/+xfDhw3niiSeIi4urd8iVIAhN12DyXV5eztGjRwkLC9MrDwsLa3BuW0EQhLZClmWO\n",
       "Hj3KSy+9xODBg3nvvfe4dOlSrXWVSiVTp07lhx9+YPv27cyfP7/GjCX34k6pzPx3QVUll3HoAJ/+\n",
       "qckP2WgXqyWMXV18MVIYtfwTPwC8XPR7vtOyUqlQl7foc3bqKPHpEv2yxGR4/9v7e9xu3bqxbNky\n",
       "Dh06xCeffMIjjzxSaz2NRsPu3btZuHAho0aNYvXq1dy6dev+nlwQBD0NJt/Z2dmo1Wo6deqkV+7k\n",
       "5NTg3f+CIAiGVrkS4Lhx45g+fTqbN2+mrKys1rqenp688cYbHDp0iE8//RR/f/9mGTb3l9Vw7qp+\n",
       "2X9ebbk5vauqOeSkdx01hepsLO1wsuui29fIGm4Vprf48/5+PEwdoV+24n9w6PT9f4tsZmbGtGnT\n",
       "+PHHH/nll1+YO3culpaWtdZNT0/n448/JigoiMWLFxMfH1/rjZyCINybNjPbSV0rdwlNJ9q0ZYh2\n",
       "bRnN3a6pqanExMRw4MCBOpNt0N6oNnDgQEJDQ+nTpw+SJJGamtpscRxMtmHVj/o3OE4enE0X86u0\n",
       "9KkkyzJnLx/VK1MVGolz+B7YKp3I4rpuPzP/Gi4durV4G/5xjBH7jvcmp8AEALUaZr1RSsQryViY\n",
       "Nl8CPGXKFMaMGcP+/fuJjo7m6tWrNeqoVCq2b9/O9u3bcXZ2JiQkhFGjRtU5hOV+ifOzZYh2bV49\n",
       "ejT9xvUGk28HBweMjIzIzMzUK8/MzKRz585NfmJBEITmVlpaSnx8PDExMQ0m0I6OjoSEhBAcHIyd\n",
       "nV2LxHO72Ij31nnolXWxL+OFqbXf1NncisvyuVN+d3o8I4Ux9lbifftedLJx50LmMd1+VsG1emo3\n",
       "nw5Wat6cc4WlX929wKdnm7Ey0pXXH2veGMzNzQkLCyM0NJQLFy4QHR1NQkJCrfdBZGRkEBERwfr1\n",
       "6xk0aBChoaH06tVLTKwgCPegweRbqVTi7+9PdHQ006dP15XHxMQwc+bMZgskICCg2R7rYVf56Va0\n",
       "afMS7doymqNdz507x7p16/jpp58oLKx7LmaFQsGjjz5KeHg4w4cPx8io5cY+azQy01+H7IKqzw8b\n",
       "V5gypE/t422bU1JSEpkF+r2YXV18GDRwcIs/94OkW4EHBy5s0e3fKryOWqNqlXYMCIDzt2S+2Hy3\n",
       "7KeDjsyd4Mj04JZJdgMDAwkPDycvL4/Nmzezbt26Wu+NUKlUxMfHEx8fj5eXF3PmzGH69Ol06NCh\n",
       "yc8t3mNbhmjXlpGfn99wpTo0atjJiy++yPz58xk4cCBBQUF8+eWXZGRk8MwzzwDw2muvkZiYyK5d\n",
       "u3THnD17lvLycrKzsykqKuLEiRPIskz//v2bHKwgCEKlkpIStm3bxvfff8+RI0fqrevs7Mzs2bOZ\n",
       "PXt2q31j99F3sGW/ftlr82FIn9brIbx5+4refncXMd77XnW0caSjtSO5hdqbDjWymqyCNKB1PsR8\n",
       "/CzsSYLzVTq7/7ACeneT8fFouXPJzs6ORYsW8Yc//IHDhw/z/fff1zkfeGpqKu+//z4fffQREyZM\n",
       "IDw8vNnulxCEB1Gjku9Zs2aRk5PD+++/z82bN+nbty/btm3Dzc0N0H4NVf2T8YQJE3RjxyRJYsCA\n",
       "AUiSJKYuEgShyWRZ5vTp02zcuJEtW7bU28stSRIjRowgPDyc0aNHY2zcere47EqUWfZv/bJAX3jr\n",
       "D60WArIsc+O2/tCbHm59Wy+AB0hPNz8Ond2t27+e13JLzVdnYSax9i2Zoc9AhUpbVngHpr+uXf3S\n",
       "yqJlE1xJkhg8eDCDBw/mrbfe4ocffmD9+vVcuXKlRt3y8nIiIyOJjIzE29ub2bNnM2XKlBYb1iUI\n",
       "7ZUkG3AS7qpd9i1148bDSHzF1DJEu7aMxrRrfn4+P/30Exs3buTs2foXOrG3t2f27Nk89thjug6C\n",
       "1nQtQyZgEWTfvlvW0QaOfAMezq3XE7g9dgvbT36j2zdXWrDiqf9hZNRm7rNvN45fSOC/2z7S7duY\n",
       "2/P+U/9XzxHNb/Vmmec+0S+bNRq+f5dW72HWaDQkJCSwbt06YmJiUKlUddZVKpWEhYUxc+ZMhg4d\n",
       "Wu9QL/Ee2zJEu7aM+8lhxbuwIAhtkkaj4fDhw2zYsIHt27dTXl7//MpBQUHMmTOHsLAwlEplK0Wp\n",
       "r6xcZuYy/cRbkmDd8tZNvKFm76y3R3+ReDeRt3s/FAojNBrtN7cFJTncun0Txw6td/PqH6fC4TOw\n",
       "dsfdso17YFBveOGxVgsD0N47MWzYMIYNG8atW7fYtGkT33//PenpNadhLC8vJyoqiqioKFxcXJgx\n",
       "YwYzZ87E1dW1dYMWhDakUStcCoIgtJaMjAxWrVpFcHAw4eHhbNmypc7E297enieffJJdu3bx3Xff\n",
       "MXHiRIMl3rIss+Qf2gVRqnr3SQgb1PpjX6/n6iffvT1Fr1dTmZta1lhw5+yV+u8zaG6SJPHFn8Gv\n",
       "u375K6sh7qjhVpF2dHRk8eLF7N27l2+//ZawsLA6e7dv3LjBP//5T4YPH868efPYunUrpaWlrRyx\n",
       "IBie6AYRBMHgSkpK2Lx5M5GRkcTHx1PfaDiFQsHIkSOZNWsWo0ePNliyXd3H6+Drrfplk4Zqb7Js\n",
       "bfnFueQU39Qr8/Vo+RlWHmS9PP25kH5Kt3/myhFG9p/YqjFYmEn8+IF2WFN+kbZMrdaO/z7wpYyv\n",
       "p+FucKz8uxw5ciQZGRn8+OOPbNq0qdZ5wwHdTCk2NjZMnjyZGTNmIMuyuElTeCiI5FsQBINQq9Uc\n",
       "OnSI//znPxw6dKjehXAA3NzcmDlzJjNmzGhzawysi5Z5dbV+mVcXWPMmKBStn0ycvaK/sI57px7Y\n",
       "WDZ9CjgBenf1Z8uBb3X7F9NPU1ZRiqmJWavG4eWqvQFz8it3y/IKYdyLkPCVjIuj4ZNXZ2dnnn32\n",
       "WRYvXszhw4fZtGkT27Ztq7WXu6CggIiICCIiInBxcWHEiBE4OzuLYSnCA00MOxEEoVVduHCBDz/8\n",
       "kGHDhjFv3jz27t1bZ+KtVCqZPHkyERERxMXFsWTJkjaXeO85IrPwA/0yG0vY/FfoYG2YROjM5US9\n",
       "/d6e/gaJ40HSyc4Ve5tOun2VuoLz144bJJaJQyXefVK/7FomTPwzFBQbbghKdZUzpXzyySccPnyY\n",
       "Dz74oN7phm/cuMH69esZPnw4M2fOZN26dfc1l7IgtFWi51sQhBZ369YtoqKiiIyM5NSpUw3W79On\n",
       "D9OmTWPq1Kn3tWhHSzuVKjPttbtTwAGYGEPkX6Gvl2ES7ztlRZypNh65l0i+75skSfTu6s++E9t0\n",
       "ZUfO78fPyzCLFr3xe23CXXWo0/ELMPMNiPq7jImx4XvAq7KxsSE8PJzw8HDOnz/Ppk2biIyMJDc3\n",
       "t9b6SUlJJCUl8c477zB69GimTJnCqFGjMDU1beXIBaH5ieRbEIQWkZeXx44dO/jll184ePAgGo2m\n",
       "3vrOzs5MmTKFqVOn0rNnz1aKsuku35AZ/xIUFOuXf/MGBPsbLvE5fuEgavXdTwMOts64d+peCw6v\n",
       "/AAAIABJREFUzxFCYw3oMUwv+T59KZGSsjuYm1q0eiySJLH6JZmb2fBLwt3ymERYtAK+eUPGyKht\n",
       "JeCVvL29WbZsGa+88gp79uxh8+bNxMXF1bqAT3l5OTt27GDHjh3Y2toyYcIEJk2aRGBgYIuuUCsI\n",
       "LUkk34IgNJuCggJiYmKIioriwIED9c7/C2Bubk5gYCAjR47k97//fbu5mKamy4z+E1y/pV/+t8UQ\n",
       "HmbYhCfp/F69/QDvkeImtmbS1cUHK1Nbisq0QyEq1OWcTD3IoF6PGiQeY2OJ9e/KBD8HSefulkfs\n",
       "1P5sywk4aIeVjR07lrFjx5KXl8fq1avZv38/58+fr7V+fn4+69atY926dTg4ODBu3DgmTJhAQEBA\n",
       "u3nvEAQQybcgCPepqKiI2NhYoqKiiIuLa3A+bkmSCAoKYurUqYwdO5bkZO3cfO3l4nkhTWb0kpqJ\n",
       "9+Jp8Odww8RUKa8wm9T0M3plAT4jDBTNg0chKejq2IdT6fG6sqRz+wyWfANYmktE/V0m6Cm4dONu\n",
       "ecROUGtgzTIZ4zY2BKU2dnZ2jBkzhjFjxuDo6MiWLVuIjIysdSVNgOzsbNauXcvatWtxcnLSJeL+\n",
       "/v4oFOJ2NqFtE8m3IAj3LCcnh127drFz507i4+MbTLgBfH19mTRpElOmTGlzN0021vmr2sT7Zo5+\n",
       "eXgofLa09VcarO5oyn5k7t5wZ2/VGSe7LgaM6MFTPflOST9FfnEutpYdDRaTk53Ezn/IBC+B9Ky7\n",
       "5d/HaKciXPt22xsDXh8PDw/+9Kc/sWTJEo4fP05kZCRRUVHk5eXVWj8rK4s1a9awZs0anJ2dGTt2\n",
       "LGFhYQQGBmJsLNIcoe0RZ6UgCI2Snp5OTEwMO3bsICkpqcEx3ABeXl5MmjSJiRMn4uXl1QpRtpzT\n",
       "l2TClkJGtcR7/lj47+sY/Ot9WZb5NTlWr6yrYx8DRfPg6mDhiJ1lJ/KKMwGQZQ2JyXGEBEwzaFxe\n",
       "rhJxn2s/HF7LvFu+cQ+o1BDxtoyZaftJwEH7YXbAgAEMGDCAZcuWsW/fPn755Rd27dpFUVFRrcdk\n",
       "ZGTw7bff8u2332Jra8vo0aMJCwtj+PDhWFpatvIrEITaieRbEIRaaTQazpw5Q2xsLDExMZw+fbpR\n",
       "x7m7uzNx4kQmTpyIj4+PwXuDm8OOQzKz34TCO/rlCybAf/5i+MQbICXtJDdzrun2JSS6OvQ2YEQP\n",
       "rm6OfTlSfDfD3X9yO8GP/A4jhWGHTnXrIhG3SpuAX6myxtLmvRDyPET+VcbRzvDnalMolUpCQkII\n",
       "CQmhrKxMLxEvLi6u9Zj8/HwiIyOJjIxEqVQybNgwQkNDefTRR3F0dGzlVyAId4nkWxAEncLCQg4c\n",
       "OEBsbCxxcXHcunWr4YPQfk0cFhbGxIkT6du37wORcFda9aPM8yuhekf/oknw1SuGWUSnNrHH9JfX\n",
       "dLf3wVxpZaBoHmxeTn6cTNtHhVo73Cqv8BYnLh7kkZ7DDBwZeHaWiP2tB/xylTHgCadg8FPw80cy\n",
       "vbq2jXO2qUxNTQkNDSU0NJTS0lK9RPzOnTu1HlNeXs6ePXvYs2cPkiTh5+fHqFGjGDlyJH5+fu3m\n",
       "nhPhwSCSb0F4iMmyTGpqKrGxscTGxpKYmNjgDCWVfH19GTNmDGFhYQ9MD3dVKpXMi/+Cz3+o+bvF\n",
       "0+CfL7SdxDszN52z1eb29nUZaKBoHnxmJhYE+o4i4XS0rizu2M9tIvkG8HDWDkEZ8wKcq7K6++Ub\n",
       "EPQ0bHpfJnRg2zh375eZmRlhYWGEhYVRWlrK3r17iYmJYc+ePXWOEZdlmRMnTnDixAk+++wz7Ozs\n",
       "GDFiBCNHjmT48OE4ODi08qsQHjYi+RaEh0xWVhbx8fG6LSMjo1HHSZKEv7+/LuF2d3dv4UgN52a2\n",
       "zOPvwe4k/XJJgk+WwPOzDH9zZVVxx6P09j069cDRWizP3ZJGDZikl3xfyTjP5Zvn6drZ24BR3eXW\n",
       "SSL+S5lZb+qfxwXFMP5lePcJmVfmto0hU83FzMxMN2OKSqUiKSmJXbt2ER0dTVpaWp3H5eXlsWXL\n",
       "FrZs2YIkSfTt25cRI0YwdOhQBgwYIBb2EZqdSL4F4QFXWFjI4cOHdcn2hQsXGn2spaUlw4cPZ9So\n",
       "UYwePfqhGCf58wGZRX+F7Nv65ZbmsG45TBrWtpKV3IJb/Hp2j17ZqAGTkQvbVpwPGueObvh6PELy\n",
       "1aO6sp2HN/DMlLcMGJU+OxuJbZ/IPPuJ/kqYajW88RXsSoT/vSXTxfHBO1eMjY0ZPHgwgwcP5o03\n",
       "3uDcuXPExMQ0eP+KLMucPHmSkydP8vnnn2NqakpAQABBQUEMGTKEvn37ihlUhPsmziBBeMDcvn2b\n",
       "xMRE3Xbq1CnUanWjj+/WrRvBwcEEBwcTGBiIUqlswWjbjtIymT+vglU/1vydqxNs/RD692x7Scov\n",
       "B7/TjT0GsLNyoH/3IRw7dtyAUT0cggdM1ku+z149yvlrJ/B272fAqPSZGEt89YqMtzu8sgrkuzNR\n",
       "EnsU+j0O//e6zO+Gt71zu7lIkoSvry++vr786U9/Iisri7179xIXF8eBAwcoKCio89iysjJdxwWA\n",
       "lZUVAwcOJCgoiEGDBuHj4yOSceGeiTNGENq569evk5SUpEu2U1JS7ul4MzMzBg4cqOvd9vDwaKFI\n",
       "2669x2Se/TucvVLzd6MGwHfLobND20tO0rJSSTwXp1c2dtBsjIzEW3tr8Hbvh5dLL1JvnNWV/bT/\n",
       "G/485xMUBp75pCpJknhpDvh4yCx4H3Ly7/4utwCmvgq/Hyfz4bPaOcMfdE5OTsycOZOZM2eiUqk4\n",
       "duwYcXFx7N27lzNnztR7bFFRke7GTQALCwsGDBiAv78//v7+DBgwAGtr69Z4GUI7Jt6hBaEdKSkp\n",
       "4fTp07qbhY4ePcqNGzcaPrAKhUKBn58fQ4cOZdiwYQ/1mMaMHJlXVt1djrsqIyN4ZxH8ZV7bHBcr\n",
       "yzKR+7/RK3Ox92BQr9EGiujhI0kSU4Yv4JMNr+jKrmdf4dfkOAb3Ntyql3WZECRxfI3M79+DPfr3\n",
       "57JmO2w5AB88LfPU5LZ5zrcEY2NjAgMDCQwM5M9//jO3bt1i3759JCQkcPDgQW7evFnv8Xfu3NHr\n",
       "GVcoFHh7e+Pv709AQAD9+vXDw8OjTd0jIhieSL4FoY1SqVRcuHBBl2ifOHGClJSUexpCUql79+4E\n",
       "BQUxdOhQBg8ejI2NTQtE3H6UV8h8+RO89R/tDWjVdXXRju8e1LvtXjDjT+3kYrr+2NXfDV/Qpnpc\n",
       "HwYezj3x7zmcIyn7dWU/7f8Gb/d+2Fm3vVkzujhKRK+U+XgdvPlv7QI8lW4XwrN/h2+i4LMXZIb0\n",
       "abvnf0txdHRk+vTpTJ8+HVmWuXLlCgcPHtQl47m5ufUer9FoSE5OJjk5mYiICABsbGzo27cvfn5+\n",
       "+Pn50bdvX1xcXERC/hATybcgtAHFxcWcO3eO5ORkzp49y9mzZzl//jylpaX3/FiV4xsDAwMJCAhg\n",
       "4MCBODk5tUDU7U95hcy322DFGv1VAKtaMAFWPg82lm33wpiZm07k/v/qlfm498fXY4CBInq4TRo6\n",
       "nxOph1CpKwC4U1bEd9GfsXjaOygkhYGjq0mhkPjLPBjtL/OHD+DMZf3fJ52DoU/D2MEyyxfBwF5t\n",
       "92+hJUmSRNeuXenatSvh4eFoNBpSUlI4ePAghw4d4siRI+Tk5DT4OAUFBXq94wD29vb4+fnRu3dv\n",
       "fHx88PHxwdPTU8w3/pAQybcgtCKVSsW1a9e4ePEiKSkpnD17luTkZK5evYpc9U6oe6BUKvHz82Pg\n",
       "wIEEBgbyyCOPPPQ929WVlcus3QEr/qe/8l9Vft1h1Usw1K9tJxrlFWWs2fEpFaq7N1mampgxa/Qz\n",
       "Bozq4dbRxomJQXP5af+3urKU9FPsTookNHC64QJrQKCvxNFvZT7bCO/8F4pL9H+/45B2Gz9E5s2F\n",
       "bfuboNagUCh0ifLChQt1PeNHjhwhKSmJI0eOcPHixUY9Vk5Ojm59hUpmZmb07NlT9xy+vr74+PjQ\n",
       "oUOHlnpJgoGI5FsQWkBZWRmXL1/m4sWLetvly5cpLy9v+AHq4enpSb9+/XRb7969H9ox2w25fEPm\n",
       "qy3w36iaUwdWsraAd56A56aDsXHbTi7UahXfbP+Y9FuX9MpnjHoKB1tnA0UlgHZ6x7NXjpKSdlJX\n",
       "9nPCWuysHQjwGWnAyOpnYizxcjg8FiLz0r9g056adbYd1G6BvjLPTIXZj4KFWdv+W2kNVXvGZ8yY\n",
       "AWjnDD969ChHjhzh+PHjnD59msLCwkY9XmlpqW6aw6ocHBzw8vKiW7dueHl56TYXFxfRU95OieRb\n",
       "EJqopKSEa9eucfXqVa5cucLVq1d1240bN9BUX4+8Cezt7fUSbT8/P+zs7Joh+gfXnVKZbQdhzTZt\n",
       "wlDXFwpKE3hyMrz+eNucyaQ6jUbN97tXceay/so/A3oMZaBvsIGiEiopJAXzwp7nbxHPc6esSFce\n",
       "EfNPzE0t6d01wIDRNczVSWLDe/DMFJm3vob4kzXrJCZrt5f/BY+Pk5kbBv4+bWvBKUOzs7Pj0Ucf\n",
       "5dFHtTfcajQarly5wsmTJzl16hQnT57kzJkzlJSUNPBId2VnZ5Odnc3hw4f1yk1NTXXJv7u7O+7u\n",
       "7ri5ueHu7o6LiwsmJibN+tqE5iOSb0GoQ0FBATdu3NBtR44cITs7m9LSUtLT0xu9MmRjSJKEp6cn\n",
       "vXr1olevXvj6+tKrVy+cnJzEha0R7pTKbD+o7bWLSoA79QyVV5rAoknw2nxtwtEelJTd4X87P62R\n",
       "eLvYezD70T+Kc6SN6GBlz+/HvcS/t36AWqMCtB+a/hP1V2aOeoqhfccYOMKGBftL7HtEZncSLP8/\n",
       "SDhVs05eIXy2Ubt1dYEZwTIzg0UiXhuFQkG3bt3o1q0bU6ZMAbTDD1NTUzl16hTnzp3T3e/T0M2c\n",
       "1ZWVlemOr+15O3fujLu7O+bm5nTq1IkbN27QpUsXnJ2dcXJyEsm5AUlyUweaNoP8/LuTjdra2hoq\n",
       "jAdOUpL2Ah0Q0LZ7WgylvLyc7Oxsbt26pbdlZmZy8+ZNXbLd2K8K75W9vT09evSge/fuuoUfvL29\n",
       "sbCwaJHna+uacr6q1TLHUiAmUbtKX/wpKK+o/xhbK/j9OHhpjnbp7fbiWuZFvov5JzdzrumVd7Rx\n",
       "4oVZf8PWsmOtx4n3gZbRmHY9cn4f/9vxD2T0L69BfcL43bAFmJu2j791WZbZlQgrN8COw3V/i1Sp\n",
       "U0cICYCQQO12rytnPsznrCzLZGdn62ZKqUyqU1NTqaho4M2tCSRJwsHBgc6dO9OpUyecnZ11W2WZ\n",
       "o6MjVlZW4gNVHe4nh21Uz/fq1av5+OOPycjIoHfv3qxcuZJhw4bVWf/UqVM899xzJCYm0rFjR55+\n",
       "+mnefPPNewpMEBqroqKC27dvc/v2bfLy8vS23NzcGol2Xl5eq8Tl4uJC9+7d6dGjB15eXrqEW9w8\n",
       "c+8yc2V+PQu/ntV+7f1rsnZatMZ4xBv+OBUeCwFL8/ZzESm8c5voxB/Yd2Ibsqw/hMnWsiOLpyyv\n",
       "M/EWDMvfewR3SovYFPdvvfKE09GcuZzE5GG/55GewzBq49NCSpJE6EAIHQip6Xfvn8itY0HIzFz4\n",
       "Llq7AXh1kRnUCwJ7wcBe0L8HmJu2n7/B1iRJEo6Ojjg6OjJixAhduUqlIj09ndTUVN126dIlLl68\n",
       "yO3bddzI0giyLOuuifVRKpU4ODjg4OCAvb19ja2y3NbWFltbW5GsN1KDyfeGDRtYunQpX3zxBcOG\n",
       "DWPVqlWMGzeOs2fP4ubmVqN+QUEBoaGhjBo1iqSkJJKTk1m4cCGWlpa8+OKLLfIihPatoqKCwsJC\n",
       "CgsLKSoqorCwkIKCghplVbeqiXZL9VA3RKFQ0KVLFzw8PPQ2T09P3N3dMTMzM0hc7VVZucy1TLh8\n",
       "Ay5e105/dva37dY9XmNcnWD6KAgPg4B29FW4RtZw5WYKicmx/Jocq7dsfCU3Jy+enPQ6HazsDRCh\n",
       "0FjD+43HxrIja3f+g3JVma48vziXtTv/wbaD6xjebzwDegxtk/OBV+flKvHRs/DuEzI/7YdNu2Hb\n",
       "ISir5/7x1OvabV2Mdl+h0CbkvTzB97fN0xk8O4NL228CgzA2NsbT0xNPT0/dOPJKubm5pKamcu3a\n",
       "Nd2WlpZGWloaWVlZzfL85eXlum+DG8PIyAgbGxtsbW2xsbGhQ4cOusS8srxys7S01NusrKywsLBA\n",
       "qVQ2S+xtWYPDTgYNGkT//v356quvdGU9e/ZkxowZrFixokb9L774gtdee43MzEzdDAwffPABX3zx\n",
       "Benp6Xp1xbCTlnE/X93JskxFRQXl5eW1bmVlZbWWl5aWcufOHd3PkpISSkpKGlVWVlbWcGAGoFQq\n",
       "cXFxoUuXLri4uADau86DgoJwcXHB1dX1oXiTaCpZlikt1/ZQ5xdrx4lm5UFGDmTkan9m5cLFa0Vk\n",
       "5im5VaBs8Gvt+nh2ht8Nh5mjYXBv7VzGbV25qoyMnDSu37pM6o2zpKSd5HZR3fMGB/iM5LHRi1Ga\n",
       "NDy7zcP8FX5Lutd2Tb91if/+8hHZ+XXfI+LRqQfdXfvg6eyNk10XHGydMTFu++NxC4tlfo6HH2K1\n",
       "w7+KGn8PYQ3GRuBoW0bnjuX06W5NJ3tw7KDdHDrc/XdHG7Ayf3hW4GyqkpIS0tPTuXbtGgkJCWRm\n",
       "ZlJWVkZGRgYZGRlkZ2cbOsQ6KZVKLC0tsbCwwMrKSpecW1hYYGZmhqmpKWZmZrrN3Ny8RlnVzdTU\n",
       "FFNTU5RKJSYmJjU2IyOjJnXQ3E8OW2/yXV5ejqWlJevXr2f69LtzlT733HOcPn2auLi4Gsc8/vjj\n",
       "5OXl8fPPP+vKEhMTGTRoEJcvX8bDw6NZAm9tl9MyWPfjbmRZgyzLVTYNGo32p6yRkZHRaDS6ehqN\n",
       "Bn6rq6msU6WuXLWssj7olWvku/XUajUajRq1WoVG9281GrUatUb7s7i4EI1Gg6lSqS1Xq+7W+61O\n",
       "5U+1WoVarUJVUY5KVYFaVdHk+abbDUnC0qoDVjYdsba1x8rGDkubjlhZd8S2oxM2dp2wtXPEwqqD\n",
       "7g9SltF9eHR1ddU9VH1Npf87/Yoytf+hazR1P2C9/yt1/FKWpRrjTqvGp9FIqNQSKjWoNKBWV+5L\n",
       "qDUSajV6+yqVRGmFRFm5gtJyBWXlEqW6fysoLZe4U2pEUYmCgmIjVOqWW2DE2kLFoN6FDOlTwJA+\n",
       "Bbh1atoUjo093+tqx9qo1BWUV5RRXlFKuaqcclUZFRVl3CkrIr84V7sV5VJ0J79Rj9vRxolZwU/T\n",
       "y9O/0TGI5LtlNKVdy1VlRP/6A7uPROpuxKyPhISdjSMOts5YmdtgYWqFhZk1FmaWmBgpMTYywdjY\n",
       "RPvzt61yMR/te5aE9q1LQpKk395tpEb8rukqVHD8ghn7T5hz4IQFJy6Yota0XIJsptRgZa7BwkzG\n",
       "0lyDpZkGS3MZSzMNZkoZE+O7m9JERmksY2JMtX0ZhULbI6+QZBQSSAowUmj/rVCA9Fu5kUL7u8p6\n",
       "2uN+O6aWl1m9rHoVSZLrr1DrMfXv13XMpcvaqUm7de2me16VqoKCvBzycm9xO/cWt/O0P/Nzs3/b\n",
       "z6YwP5eKivubGrc9kCQJIyNjjIyNMTI2wdjY+Ld9E4x/+2lkbISxkQlGxsYEDh7CB2+90nJjvrOz\n",
       "s1Gr1XTq1Emv3MnJqc6ZHjIyMnB3d9crqzw+IyNDL/luT37Zc4KvP1tm6DCEWshIaBQd0EgdUCvs\n",
       "0Cjs0Cgq/90BtZEjaoXjbz+d0CjsQDLWJqy3f9saxbPFXoNQPyOjMuxtrtHJ/gKdOl6gU8cUOljf\n",
       "RJJk8oph2+GGH6M9srN2JHjAZIL6hDWqt1tom5TGpkwMmstA32B2H4nk13OxqNV1J+EyMrkFWeQW\n",
       "NM/QgdYW1A8CeyvJvt2NjJyeZOV2JzO3BwXFzTcXfeWHfvIbriu41lHere5DlICDjCTfwUiTg0KT\n",
       "g5E6++6/NTkYabIxUmv3FZoCFHI+Cvk+vv4wEFmWUakqUKkqgIbjv1Fgxwdv3d9zNvtUg0399Fz1\n",
       "E0RbNH/KYOZPOW7oMIRmccfQAQhN0um3re6bvR9UJXdKKaGe+RNr0aNHD6Dtv7e2N/fTrqYKS8YH\n",
       "zmN84LzmDqudqONOTaGN6/Db5mXoQNqM+31frfc7YQcHB4yMjMjMzNQrz8zMpHPnzrUe4+zsXKNX\n",
       "vPJ4Z2exApsgCIIgCILw8Ko3+VYqlfj7+xMdHa1XHhMTQ1BQUK3HDBkyhP379+vdRBcTE6ObFUIQ\n",
       "BEEQBEEQHlYNznayceNG5s+fz+rVqwkKCuLLL7/km2++4cyZM7i5ufHaa6+RmJjIrl27AO1Ug97e\n",
       "3owaNYply5Zx/vx5Fi5cyPLly3nhhRda5UUJgiAIgiAIQlvU4JjvWbNmkZOTw/vvv8/Nmzfp27cv\n",
       "27Zt083xnZGRwaVLl3T1bWxsiImJ4dlnnyUgIICOHTvy8ssvi8RbEARBEARBeOgZdHl5QRAEQRAE\n",
       "QXiYtNwkvL/Zt28fkydPxtXVFYVCwZo1a+qs+/TTT6NQKPjkk09aOqx2rzHtmpKSwrRp07Czs8PS\n",
       "0hJ/f3/OnTtngGjbj4bataCggMWLF+Pm5oaFhQU+Pj6sXLnSQNG2H3/9618JDAzE1tYWJycnJk+e\n",
       "zJkzZ2rUW758OV26dMHCwoLg4GDOnj1rgGjbl4baVqVS8Ze//IV+/fphZWWFi4sLc+fOJS0tzYBR\n",
       "t22NPV8riWtX4zW2bcX16940pl3F9everVq1in79+ulW5QwKCmLbtm16dZpy3Wrx5Lu4uBg/Pz8+\n",
       "++wzzM3N65yK8IcffiAxMREXF5d2sxS0ITXUrpcvX2bo0KF4eXkRGxvLmTNn+OCDD7CysjJQxO1D\n",
       "Q+26dOlSdu7cSUREBOfOneONN97g1VdfJSIiwkARtw979+7lueee4+DBg+zZswdjY2NCQkLIy8vT\n",
       "1fnwww/59NNP+fzzz0lMTMTJyYnQ0FCKiooMGHnb11DbFhcXc+zYMZYtW8axY8fYsmULaWlpjB07\n",
       "FrVabeDo26bGnK+VxLXr3jSmbcX16941pl3F9eveubm58dFHH3Hs2DGOHDnC6NGjmTJlCidOnADu\n",
       "47oltyIrKyt5zZo1NcqvXLkid+nSRT537pzs6ekpf/LJJ60ZVrtXW7vOmTNHnjdvnoEiejDU1q59\n",
       "+vSRly9frlc2cuRIecmSJa0ZWrtXVFQkGxkZyVFRUbIsy7JGo5GdnZ3lFStW6OqUlJTI1tbW8ldf\n",
       "fWWoMNul6m1bm7Nnz8qSJMmnT59uxcjar7raVFy77l9tbSuuX/evtnYV16/m0bFjR/nf//73fV23\n",
       "WrznuyEqlYo5c+bw5ptv4u3tbehwHggajYaoqCh8fX0ZO3YsTk5ODBw4kI0bNxo6tHZv3LhxbN26\n",
       "VbfUfEJCAsePH2fs2LEGjqx9KSgoQKPRYGdnB2h7ujIzMwkLC9PVMTMzY8SIESQkJBgqzHapetvW\n",
       "pnKBiPrqCHfV1qbi2tU8qretuH41j9rOWXH9uj9qtZr169dTWlrKiBEj7uu6ZfDk++2338bJyYmn\n",
       "n37a0KE8MLKysigqKmLFihWMHTuWXbt2MWfOHObOnVtjrJJwbz788EN69eqFu7s7SqWSUaNG8dFH\n",
       "HzF+/HhDh9auPP/88wwYMIAhQ4YA6Bbm6tSpk149JyenGot2CfWr3rbVlZeX89JLLzF58mRcXFxa\n",
       "Obr2qbY2Fdeu5lG9bcX1q3nUds6K61fTnDp1CisrK8zMzHjqqafYuHEj3t7e93Xdavbl5e9FXFwc\n",
       "a9as4fhx/WXbZTEBy33RaDQATJkyhaVLlwLg5+dHUlISn3/+ufhDuw8vv/wyhw8f5ueff8bDw4O9\n",
       "e/fy0ksv4eHhwZgxYwwdXrvw4osvkpCQwIEDBxo1RlaMo228htpWpVIxb948CgoKiIqKMkCE7U9t\n",
       "bSquXc2jtrYV16/7V9f7gLh+NY2Pjw8nT54kPz+fTZs28dhjjxEbG1vvMQ1et1p2ZIy+6mNoly9f\n",
       "LisUCtnY2Fi3SZIkGxkZyW5ubq0ZWrtWvV3LyspkExMT+YMPPtCr9+6778q9e/du7fDarertWjmG\n",
       "buvWrXr1nnjiCTkkJKS1w2uXli5dKru4uMjnz5/XK09NTZUlSZKTkpL0ysePHy8vWLCgNUNst+pq\n",
       "20oVFRXyjBkzZF9fXzkzM7OVo2uf6mpTce26f3W1rbh+3Z+62lVcv5pPSEiIvGDBAvnSpUtNvm4Z\n",
       "dNjJ4sWLOXXqFCdOnODEiRMcP34cFxcXXnzxRXbv3m3I0No1pVJJYGBgjWmZUlJS8PT0NExQDwBZ\n",
       "lpFlGYVC/89GoVCIHq9GeP7559mwYQN79uyhZ8+eer/r2rUrzs7OREdH68pKS0s5cOAAQUFBrR1q\n",
       "u1Nf2wJUVFQwe/ZsTp8+TWxsLE5OTgaIsn2pr03Ftev+1Ne24vrVdPW1q7h+NR+1Wo1Go7mv61aL\n",
       "DzspLi7mwoULgPbrpKtXr3L8+HHs7e1xc3PD0dFRr76JiQnOzs706NGjpUNr1xpq11deeYVZs2Yx\n",
       "fPhwgoODiY2NZcOGDWzZssXAkbdtDbXro48+yquvvoqVlRXu7u7s3buXtWvX8vHHHxs48rbt2Wef\n",
       "JSIigp9++glbW1vdeDhra2ssLS2RJImlS5eyYsUKfHx86NGjB++//z7W1taEh4cbOPq2raG2VavV\n",
       "zJw5k6SkJH7++WdkWdbV6dChA2ZmZoYMv01qqE0dHR3FtauJGmpbQFy/mqChdrWyshLXryZ49dVX\n",
       "mThxIq6urhQWFrJu3Tr27t3Ljh07AJp+3WqRPvkqYmNjZUmSZEmSZIVCofv3woULa60vpmtqnMa0\n",
       "67fffiv37NlTNjc3l/v16yevX7/egBG3Dw21a1ZWlrxo0SLZ1dVVNjc3l319fcX52giJfDJXAAAA\n",
       "3ElEQVTV27Nye+edd/TqLV++XO7cubNsZmYmjxo1Sj5z5oyBIm4/Gmrby5cv11mntqlfhcafr1WJ\n",
       "a1fjNLZtxfXr3jSmXcX1694tWLBA9vDwkE1NTWUnJyc5NDRUjo6O1qvTlOuWWF5eEARBEARBEFqJ\n",
       "wacaFARBEARBEISHhUi+BUEQBEEQBKGViORbEARBEARBEFqJSL4FQRAEQRAEoZWI5FsQBEEQBEEQ\n",
       "WolIvgVBEARBEAShlYjkWxAEQRAEQRBaiUi+BUEQBEEQBKGViORbEARBEARBEFrJ/wNSXhNZX5VT\n",
       "4AAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4809060d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "    \n",
    "xs = np.arange(15, 30, 0.05)\n",
    "plt.plot(xs, gaussian(xs, 23, 0.2), label='var=0.2')\n",
    "plt.plot(xs, gaussian(xs, 23, 1), label='var=1')\n",
    "plt.plot(xs, gaussian(xs, 23, 5), label='var=5')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what is this telling us? The blue gaussian is very narrow. It is saying that we believe $x=23$, and that we are very sure about that. In contrast, the red gaussian also believes that $x=23$, but we are much less sure about that. Our believe that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out - we think it is quite likely that $x=20$ or $x=26$, for example. The blue gaussian has almost completely eliminated $22$ or $24$ as possible value - their probability is almost $0\\%$, whereas the red curve considers them nearly as likely as $23$.\n",
    "\n",
    "If we think back to the thermometer, we can consider these three curves as representing the readings from three different thermometers. The blue curve represents a very accurate thermometer, and the black one represents a fairly inaccurate one. Green of course represents one in between the two others. Note the very powerful property the Gaussian distribution affords us - we can entirely represent both the reading and the error of a thermometer with only two numbers - the mean and the variance.\n",
    "\n",
    "It is worth spending a few words on standard deviation now. The standard deviation is a measure of how much variation from the mean exists. For Gaussian distributions, 68% of all the data falls within one standard deviation($1\\sigma$) of the mean, 95% falls within two standard deviations ($2\\sigma$), and 99.7% within three ($3\\sigma$). This is often called the 68-95-99.7 rule. So if you were told that the average test score in a class was 71 with a standard deviation of 9.4, you could conclude that 95% of the students received a score between 52.2 and 89.8 if the distribution is normal (that is calculated with $71 \\pm (2 * 9.4)$). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following graph depicts the relationship between the standard deviation and the normal distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAv4AAAGGCAYAAAAD/IWIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Wd8VHWixvFnZlJIAom0hN57kRZ670V6EVRQsa9617be\n",
       "VXf37t3du0VXd9fewYKA0rv0EkLvVXpvCQSSkIS0OfcFuwOHgLQk/ym/7yvPMwk+fDTk4eTMOQ7L\n",
       "siwBAAAA8GtO0wUAAAAAFDyGPwAAABAAGP4AAABAAGD4AwAAAAEg6EYvJCcnF2YPAAAAAPkkKioq\n",
       "T8YZfwAAACAAMPwBAACAAHDDS32udr0fFQDAtTZs2CBJio2NNdwEP4f/Tr6B/04AbtfNLtXnjD8A\n",
       "AAAQABj+AAAAQABg+AMAAAABgOEPAAAABACGPwAAABAAGP4AAABAAGD4AwAAAAGA4Q8AAAAEAIY/\n",
       "AAAAEAAY/gAAAEAAYPgDAAAAAYDhDwAAAAQAhj8AAAAQABj+AAAAQABg+AMAAAABgOEPAAAABACG\n",
       "PwAAABAAGP4AAABAAGD4AwAAAAGA4Q8AAAAEAIY/AAAAEAAY/gAAAEAAYPgDAAAAAYDhDwAAAAQA\n",
       "hj8AAAAQABj+AAAAQABg+AMAAAABgOEPAAAABACGPwAAABAAGP4AAABAAGD4AwAAAAGA4Q8AAAAE\n",
       "AIY/AAAAEAAY/gAAAEAAYPgDAAAAAYDhDwAAAAQAhj8AAAAQAIJMFwAAFKzc3BylZiTrUla6MrMy\n",
       "dPLCQUnS4dORCg0OU5GQMBULj1KQK9hwUwBAQWL4A4AfychM1/4TO3Tk9F6dTjquM+eP6+yF08p1\n",
       "5+T52EU7x3v+2elwqlRUGUWXqKCY4uVVOaamalZsqIgixQqzPgCgADH8AcCHWZalE2cPaev+1dpz\n",
       "dJuOntknt+W+7V/HbbmVcOGkEi6c1I5/Zw45VCG6mmpVvFeNarRW5Ziacjgc+fsbAAAUGoY/APig\n",
       "5ItJ2rBnudbvXqaT547c8ue9/+J02/F//WvgDT/WkqVjCQd0LOGAFm+cpuh7yql53U6KrdNRJSNj\n",
       "7rg7AMAMhj8A+JATiYe0aMNUbdoXL+s2zuwXDYtSeGhEnjy6eHllZKYpNf3CTX+NhAsnNWf1eM1Z\n",
       "PV4Nq7VQt9ghqlq29m31BwCY47Asy7reC8nJyZ5/joqKKrRCAHzXhg0bJEmxsbGGm/if/Sd2auH6\n",
       "Kdp9ZNNNPzamRAXVrnivKkbXUMy/r9kP+/fov/ZKnf98B7iUlaGE8yd05vxxHUs4qL3Htunk2cM3\n",
       "/XfVKF9f3WKHqG7lJlwGlM/4egJwu2623znjDwBe7Mz5E5oeN1Y7D2244cc4HE7VrdRYTWq1U51K\n",
       "jRVVtMRt/3uKhISpUkwNVYqpoeZ1OkmSUtMvaO+xbdq8L147D2287huE95/Yqf0ndqpmhYYa1GG0\n",
       "KpSudtv/bgBA4WD4A4AXSruUqh/Xfq+4bfPkdude92PKlKio1vW7q1nt9oqMKJ7vHYqF36NmtTuo\n",
       "We0OSstI0aa9K7V65yIdTzyY52P3Hd+uv49/RS3rd1Xf1g8VSB8AwN1h+AOAF7EsS5v3xWvSss+U\n",
       "lpFy3Y+pWraOusUOVv2qsXI6Cuc5jBFhkWrfqI/a3dtbe49t06INU7Xn2Fbbx1iytGbnIm3eF69B\n",
       "7R9T6/rduPwHALwIwx8AvERq+gX9sPRTbd2/+rqvVy1bR/3bjlL18vULudkVDodDtSs1Uu1KjXT0\n",
       "zH7NWvWt9hy1/wUgMytDExd/qC374jWi63MqEVnaUFsAwNV4cy+AfMObEe/cln2r9P2Sj5V2KTXP\n",
       "ayWKlVb/do+oSc22d30G/UZv7r1TlmVp1+GNmhY3VgnnT+R5PTQkTEM6PKGW9bpw9v828fUE4Hbx\n",
       "5l4A8GLZOdmasXKsVmydm+c1lytIvVrcry5NByo4KMRAu5tzOByqXzVWdSo11optczVn1XfKysn0\n",
       "vJ6ZlaHxi97X/hM7NKzz0woNLmKwLQAENoY/ABiSlJKgMXP/rqNn9uV5rVJMTT3U/b9UtmQlA81u\n",
       "n8sVpM5N+qthtRYav/B97T+x0/b6ut1LdSzhgB7r89+KKVHBUEsACGyF864wAIDNrsOb9Nb4l/OM\n",
       "fpcrSP3ajNJL9//NZ0b/1UpFldHzQ/6koZ2eUkhQqO21U+eO6u8Tf6XN++INtQOAwMYZfwAoZCu2\n",
       "ztWU5V/kefJuichoPdbnv1UppoahZvnD6XCqQ6M+qlWxocbMeUunk455XsvKvqSxc/+uhNYn1aP5\n",
       "UK77B4BCxBl/ACgkbneupiz/QpOXfZZn9Deo1kL//cA/fH70X61MiYp6ZcTfFVunY57X5qz+Tt8t\n",
       "fE85udkGmgFAYOKMPwAUgsysDH394z+049B6W+6QQ/3ajlLXZoP88ux3aHARjerxoqqXq6fJyz63\n",
       "Pf133e6lSkpJ0ON9X1NEkWIGWwJAYOCMPwAUsPRLF/Xh9P/NM/pDgovoiX6vq1vsYL8c/f/hcDjU\n",
       "tmFPPTvofxUeWtT22v4TO/Xe5N8oJe28oXYAEDgY/gBQgFLTL+j9Kb/V4VN7bHlU0ZJ6Yehf1LBa\n",
       "C0PNCl/NCg308vA3VTqqrC0/de6o3p30hpJSEgw1A4DAwPAHgAJyPjVR7056QyfOHrbl5UtX1SvD\n",
       "31LF6GpmihkUXby8Xhr+pqqVq2vLE5NP6V+TXteZ6zwEDACQPxj+AFAAziWf0b8mvaGECydtefVy\n",
       "9fTLIf+ne4qWNNTMvKJhkXp20P+qfhX7E2kvXDyndye9oZNnjxhqBgD+jeEPAPksKSVR70/9nc6n\n",
       "JtryupWb6hcDf6+w0AhDzbxHSFCoHu/7azWp2daWX8xI1ofTfs+ZfwAoAAx/AMhHyReT9OHU/8lz\n",
       "vXqjGq31ZL/XFRIceoPPDDxBrmA90utltarfzZanpl/QB1N+p8QLpww1AwD/xPAHgHySmn5BH0z9\n",
       "HyUm2wdrs1rt9WjvXynIFWyomfdyOl16oOtzan9vH1uenJakD67zFygAwJ1j+ANAPkjPvKgPp/2v\n",
       "zpw/bssb1WitkT1flMvpMtTM+zkcDg3p9IRa1+9uy8+nXr5kilt9AkD+YPgDwF3KzsnS57P+qpPX\n",
       "3L2nQdXmeqTXy4z+W+B0ODW86y/Uom5nW34u+Yw+nvFHZWSmG2oGAP6D4Q8Ad8HtztU38/+pAyd2\n",
       "2vK6lZtqdJ//5vKe2+B0OPVgt+fVtFZ7W34i8ZC+nPM3ZedkG2oGAP6B4Q8Ad8iyLE1Z/qW27l9t\n",
       "y6uWraPH7/u1goMY/bfL6XRpVI8XVK9KM1u+99g2fbfwPbktt6FmAOD7GP4AcIcWbpiiuG1zbVlM\n",
       "iQp6qv9vuHvPXXC5gjS6z6uqHFPTlm/aG6fpcV+ZKQUAfoDhDwB3YPO+eM1eNc6WRRUtqV8M+L0i\n",
       "ihQz1Mp/hAYX0dMDfqfoe8rZ8mWbZyp++3xDrQDAtzH8AeA2HT2zX+MWvGvLwkLC9YsB/6MSkaUN\n",
       "tfI/RcMi9YuBv1dkeHFbPmnpp9pzdKuhVgDguxj+AHAbzqee1Wez/qzsnCxP5nIG6Yl+r6tcqcoG\n",
       "m/mnklExenrA7xQSdOXSKbfl1pi5bymBp/sCwG1h+APALcrMvqTPZ/0lz33l7+/yjGpWaGiolf+r\n",
       "GF1No3q+ZMsyMtP06cw/K+1SqqFWAOB7GP4AcAssy9L4he/reOJBW96l6UC1rt/NUKvA0ahGK/Vr\n",
       "M8qWJV44qa/mvi23O9dQKwDwLQx/ALgFSzbN0OZ98basQbUW6t921A0+A/mtW+zgPA/42nNsq2av\n",
       "Hm+oEQD4FoY/ANzE3mPbNDP+G1tWrmRlPdzzJTl5Km+hcTgcGt7lWVUrW9eWL9owRVv2rTLUCgB8\n",
       "B8MfAH5GUkqixs57W9ZVD44KC43Q431fU5GQMIPNAlNwULBG3/eqIiPsd/r5buF7Op10zFArAPAN\n",
       "DH8AuIHsnCyNmfOm0jJSPJlDDj3S62WVvqeswWaBLSqihB7r82u5nEGeLDP7kr6Y/TdlZKYbbAYA\n",
       "3o3hDwA3MG3FGB1N2G/LercaoXpVmhlqhP+oVq6OBnd4zJYlnD+hiYs/lGVZhloBgHdj+APAdWza\n",
       "u1Irt/9oyxpUa6EeLYYZaoRrtbu3t1rW7WLLNu+Lz/PfDQBwGcMfAK6ReOGUJiz+0JaViiqjUT1e\n",
       "kNPBH5vewuFwaFiXp1W+dFVbPnXFlzqWcPAGnwUAgYvvYABwleycLI2d+3dlZmV4MpcrSKP7vKqw\n",
       "0AiDzXA9IUGhGt37VYUGF/Fkubk5+mru37neHwCuwfAHgKtMj/sqz0O6BrV/TBWjqxtqhJuJLl5O\n",
       "I7o+Z8sSk0/p+yUfcb0/AFyF4Q8A/7btwBrFbZtryxrXaKP29/Y21Ai3qlnt9mrboKct27R3pdbs\n",
       "XGSoEQB4H4Y/AEhKvpikCYvs1/WXjIrRA92ek8PhMNQKt2NQx8dUvlQVWzZl+RdKOH/CTCEA8DIM\n",
       "fwABz2259e2CfyntUqonczpdGt2b6/p9SUhQqEb3eVUhQaGeLCsnU9/8+E/l5GYbbAYA3oHhDyDg\n",
       "Lds8U3uPbbNl97V+SJViahhqhDsVXby8hnR8wpYdTdiveWsmGmoEAN6D4Q8goB1LOKhZ8eNsWc0K\n",
       "DdW12UBDjXC3WtXvpkbVW9myRRumat/x7YYaAYB3YPgDCFhZOZn6Zv4/lOvO8WThoUU1kvv1+zSH\n",
       "w6ER3Z5TVNGSnsySpW/n/0vpmRcNNgMAs/jOBiBgzV71nc4kHbdlI7o+q+LFShlqhPwSUaSYRvV4\n",
       "QQ5deWP2hYvnNHX5lwZbAYBZDH8AAWnf8R1avnmWLWtZr6sa12xjqBHyW62K96rLNZdsrdu9VNsO\n",
       "rDHUCADMYvgDCDiXsjL03cL3ZOnKw51KFCutwR0eN9gKBaFPqwdVtmQlWzZx8cdKTb9gqBEAmMPw\n",
       "BxBwpq0Yo6SUBFv2UI9fKiw03FAjFJTgoGCN7PGinE6XJ7uYkazvl3zCU30BBByGP4CAsvPQBq3e\n",
       "udCWdWrcTzUrNDTUCAWtYnQ19W453JZtO7BG639aZqYQABjC8AcQMDIy0zRx8Ue2LKZ4BfVtO9JQ\n",
       "IxSWbrFDVDmmpi2bsvwLpaSdN9QIAAofwx9AwJix8mslpyV5jp0Op0b2eMH2pFf4J5fTpZE9XlCw\n",
       "K8STZWSmadKyzwy2AoDCxfAHEBD2Hd+uVTsW2LIuzQapcpmaN/gM+JuYEhV0X5sHbdnW/au1df9q\n",
       "Q40AoHAx/AH4vazsTE1cZL/EJ/qecnmu+4b/69i4nypdc8nPpKWfKf0SD/YC4P8Y/gD83ry1E5SY\n",
       "fMqWPdDteQUHhdzgM+CvXE6XHuz2nO0uPynp5zU9bqzBVgBQOBj+APza0TP7tWTTTFvW7t7eql6+\n",
       "nqFGMK1cqSrqETvUlq3ZtVh7jm411AgACgfDH4Dfys3N0fhFH8iy3J6seNFS6tdmlMFW8Abdmw9V\n",
       "mRIVbdmExR8qM/uSoUYAUPAY/gD81qKN03Ty7GFbdn+XZ3hQFxQcFKwHuj0nhxyeLCklQXNWfWew\n",
       "FQAULIY/AL90OumYflz3vS2LrdNR9avGGmoEb1O1bB11aHyfLVu+ZbYOndpjqBEAFCyGPwC/47bc\n",
       "mrDoQ+Xm5niyiLBIDe7wuMFW8EZ9Wz+kEpHRnmNLliYs+kDZOdkGWwFAwWD4A/A7K7fN06FTP9my\n",
       "oR2fVNGwSEON4K1CQ8I0osuztux00jEt3DDZUCMAKDgMfwB+JSklUTPjv7VlDao2V9Na7Qw1grer\n",
       "U7mxWtbrassWrp+iU+eOGmoEAAWD4Q/Ar0xd8aWyrrozS5GQcA3r/LQcDsfPfBYC3aD2oxUZXtxz\n",
       "nOvO0Q9LPpFlWQZbAUD+YvgD8Bs7D23QtgNrbFn/tg+reLFShhrBV4QXKaqhnZ60ZQdO7tK63UsN\n",
       "NQKA/MfwB+AXsrIzNWnZZ7ascplaatOwh6FG8DWNarRWvSrNbNmMlV8r7VKqoUYAkL8Y/gD8woL1\n",
       "k5WUkuA5djicur/zM3I6+GMOt8bhcGhopycV7ArxZBczkjU7fpzBVgCQf/iOCMDnnTl/Qos3TrNl\n",
       "HRr1UcXoaoYawVeViiqj7s2H2LJVOxbo8Om9hhoBQP5h+APwaZZladLST5XrvnLP/siI4urT6kGD\n",
       "reDLujYbrNL3lPMcW7L0w5JP5HbnGmwFAHeP4Q/Ap23aG6e9x7bZssEdHldYaLihRvB1wUHBur/z\n",
       "07bseOJBxW2bZ6gRAOQPhj8An5WRmaZpK8bastoVG6lJzbaGGsFf1K7USE1rtbdlc1aPV3JakqFG\n",
       "AHD3GP4AfNac1eOVkn7ec+xyBWlY56e4Zz/yxaD2oxUaEuY5vpSVrunX/EUTAHwJwx+ATzqWcCDP\n",
       "pRfdmg1WdPHyhhrB30QVLaH7rnmvyMa9cdpzdKuhRgBwdxj+AHyO23L/+6mqbk9WMiomz91YgLvV\n",
       "vlEflS9d1ZZNWvaZsnOyDTUCgDvH8Afgc1bvWKgjZ/bZsmGdnlJIUKihRvBXLqdL93d+xpYlnD+h\n",
       "JZumG2oEAHeO4Q/Ap6RlpGjWKvsDlRpVb5XniatAfqlatrbaNOhuyxasn6SklERDjQDgzjD8AfiU\n",
       "OWsmKP1Squc4JLiIBnd83GAjBIJ+bR9WRFik5zg7J0sz47822AgAbh/DH4DPOJF4WPHb59uyns2H\n",
       "qXix0oYaIVBEFCmmfm1G2rJNe1dq3/EdhhoBwO1j+APwCZZlacryz21v6C0VVUadmvQ32AqBpFW9\n",
       "rqoQXc2WTVn+hXJ5oi8AH8HwB+ATNu+L1/4TO23Z4A6PKzgo2FAjBBqn06WhHZ+0ZSfPHtaqa34K\n",
       "BQDeiuEPwOtlZl/SjLivbFm9yk1Vv2qsmUIIWNXK1VVsnY62bM7q8UrLSDHUCABuHcMfgNdbtGGq\n",
       "zl886zl2OYM0qOPjPKEXRgxo+4hCgot4jtMzL2rOmgkGGwHArWH4A/Bq55LPaPHGabasU5O+iuEJ\n",
       "vTAkqmgJ9Wxxvy2L3z5fJxIPGWoEALeG4Q/Aq02LG6uc3CtPSY0ML64eze//mc8ACl6nxv1UOqqs\n",
       "59iy3Jq8/AtZlmWwFQD8PIY/AK/105Et2nZgjS3r13aUwkLDDTUCLgsOCs7z/IgDJ3Zq8754Q40A\n",
       "4OYY/gC8Um5ujqas+MKWVS5TS83rdjJTCLhG/aqxeZ4YPT1urDKzLxlqBAA/j+EPwCut2DZXZ5KO\n",
       "27KhHZ+U08EfW/Aegzs8JpczyHN84eI5Ldow1WAjALgxvoMC8Dqp6Rc0b81EW9aqXldVLlPTUCPg\n",
       "+qKLl1enJn1t2eKN03Qu+YyhRgBwYwx/AF5n3pqJupSV7jkuEhKuvm1GGWwE3FiP5vcrMry45zgn\n",
       "N1sz4r822AgAro/hD8CrnDp3TPE7FtiyXi2HKzLiHkONgJ8XFhqu/u0etmVb9q3SgRO7DDUCgOtj\n",
       "+APwKjNWfiXLcnuOS0eVVYdGfQw2Am4utk5HVYquYcumrRgj91X/LwOAaQx/AF5jz9Gt2nV4oy3r\n",
       "3+5hBbmCDTUCbo3T4dSgDqNt2dGE/drw03JDjQAgL4Y/AK/gdudqWtxYW1a9XD3dW72VoUbA7ale\n",
       "vr4a12hjy2atGsftPQF4DYY/AK+wdtcSnTx72JYNbD9aDofDTCHgDvRv97Bcriu390y+eE5LNk43\n",
       "2AgArmD4AzAuMytDc1aPt2WxtTty+074nFJRZdSpcT9btnjjNF24eM5QIwC4guEPwLjFG6crJf28\n",
       "5zjYFaK+bUYabATcuR7Nh6poWJTnOCsnU7NXjTPYCAAuY/gDMOrCxXNavGmaLevUpJ9KRJY21Ai4\n",
       "O2GhEerT6gFbtm73Uh09s99QIwC4jOEPwKjZq8YpOyfLc1wsLErdYocYbATcvdYNuqtsyUq2bNqK\n",
       "MbIsy1AjAGD4AzDoWMJBrd+9zJb1af2gwkLDzRQC8onL6dLA9vbbex44uUtb96821AgAGP4ADLEs\n",
       "S9PjxsrSlTOgZUpUVKv63Qy2AvJP3cpNVK9KM1s2I/5rZedkG2oEINAx/AEYsePQeu07vt2WDWz/\n",
       "qFxOl6FGQP4b2P5ROR1XvtWeSz6jFVvnGGwEIJAx/AEUutzcHM2I+8qW1a7USHUrNzVTCCggZUpU\n",
       "VNuGvWzZ/HU/KDU92VAjAIGM4Q+g0MXvmK+ECyc9xw6HU4N4WBf8VO9WIxQWcuV9K5ey0jVvzQSD\n",
       "jQAEKoY/gEKVnnlR89ZMtGWt6nVVuVJVzBQCCljRsEj1bDnclsXvWKBT544aagQgUDH8ARSqhesn\n",
       "K+1Squc4JLiI7mv9oMFGQMHr0KiPSkeV9RxbllvT4sYabAQgEDH8ARSac8lntGzLbFvWrdkgRUYU\n",
       "N9QIKBxBrmANaP+ILfvpyGbtOrzRUCMAgYjhD6DQzIz/Rrm5OZ7jqKIl1aXpQIONgMLTsFpL1Shf\n",
       "35ZNixurXHeuoUYAAg3DH0ChOHTqJ23eF2/L+rUZqZDgUEONgMLlcDg0qMPjcujKm9jPJB3Xqu3z\n",
       "DbYCEEgY/gAKnGVZmrbCfj1zhehqiq3T0VAjwIyK0dXUol4XWzZ37URlZKYZagQgkDD8ARS4zfvi\n",
       "dfj0Hls2qP1o24ONgEDRt81DCgku4jlOy0jRwvVTDDYCECj4rgugQGXnZGlm/De2rEG1FqpZoaGh\n",
       "RoBZUREl1LXZIFu2bMssnUs5Y6gRgEDB8AdQoFZsnaOklATPsdPp0oB2j/zMZwD+r0vTAYqKKOE5\n",
       "zsnN1uz4cQYbAQgEDH8ABSY1PVnz102yZe0a9lJM8fKGGgHeITS4iPq2eciWbdwbpyOn9xpqBCAQ\n",
       "MPwBFJgf136vS1npnuOwkHD1uuYJpkCgal6nk8pf88TqaSvGyrIsM4UA+D2GP4ACcSbpuOK3/2jL\n",
       "erS4X0XDIg01AryL0+nSwPajbdnBU7u1df9qQ40A+DuGP4ACMWPl13Jbbs9xycgYdWh0n8FGgPep\n",
       "XamR6leJtWUz479RTm62oUYA/BnDH0C+23tsm3YcWm/L+rd7WMFBwYYaAd5rQPtHbLe2PZt8WnFb\n",
       "5xlsBMBfMfwB5Cu35da0OPvDuqqWraPGNdoYagR4tzIlKqpNgx62bP66H5SZnWGoEQB/xfAHkK8O\n",
       "JmzXicRDtmxg+9FyOByGGgHer3erEQoNCfMcp2de1LZjcQYbAfBHDH8A+SY7N0ubjy6zZU1rtVPV\n",
       "srXNFAJ8RLHwe9Qjdqgt23N6g1Iykgw1AuCPGP4A8s2uE2uUkZXqOQ5yBatf21EGGwG+o1OTfipe\n",
       "rLTn2G25tenIEoONAPgbhj+AfJF8MUk7T9hvQ9ixcV+VjIwx1AjwLcFBIerXZqQtO3ruJx04sctQ\n",
       "IwD+huEPIF/MWf2dctxXbkEYERapHs2H/sxnALhW09rtVSmmpi2bHjfWdmtcALhTDH8Ad+1E4iGt\n",
       "3WW/JKF3yxEKC40w1AjwTU6HU4PaP2rLjpzZp817V5opBMCvBJkuAMC3WZalaXFj9d6F6bb8nw0m\n",
       "G2oE+Lbq5evr/QszbFmJ+NK6t3orBQeFGGoFwB9wxh/AXdl1eKP2HtuWJ3e5OK8A5Jek1EQt2zLb\n",
       "dA0APo7hD+CO5bpzNX3lV6ZrAAFh4frJSk1PNl0DgA9j+AO4Y6t2LNCZpOOmawAB4VJWuuatnWi6\n",
       "BgAfxvAHcEcyMtM0bw0jBChMq7bP1+mkY6ZrAPBRDH8Ad2Th+im6mMFlB0BhcltuzVj5tekaAHwU\n",
       "wx/AbTuXckbLtswyXQMISDsPbbjuG+oB4GYY/gBu2+z4ccrJvfKwrsiI4gbbAP6vWtm6tuNpPNQL\n",
       "wB1g+AO4LYdP79XGvXG27L7WDxlqAwSGgR1G245PJB7S+t3LzJQB4LMY/gBumWVZmrZijC0rX6qK\n",
       "WtbtbKgREBiqlKmlprXa27LZq79TVnamoUYAfBHDH8At27J/tQ6d+smWDWw/Wk6ny1AjIHD0azPS\n",
       "9mC85IvntGTT9J/5DACwY/gDuCXZOdmaGW+/m0j9KrGqXamRoUZAYCkZFaNOjfvaskUbpyk5LclQ\n",
       "IwC+huEP4JbEbZurc8lnPMdOh1MD2j9isBEQeLo3H6qIIsU8x1nZlzR39QSDjQD4EoY/gJtKy0jR\n",
       "/HU/2LI2DXuqTImKhhoBgSk8tKh6txphy9bsWqyTZw+bKQTApzD8AdzUj+t+UEZmmue4SEi4ercc\n",
       "8TOfAaCgtG3QU9HFy3uOLcut6XFfmSsEwGcw/AH8rITzJxS3bZ4t6958qIqFRxlqBAQ2lytIA9rZ\n",
       "L7P76egW7Tq8yVAjAL6C4Q/gZ82M/0Zud67nuESx0nneYAigcDWo2lw1KjSwZTNWfqXcq75WAeBa\n",
       "DH8AN7Tv+A5tO7DWlvVrO0rBQSGGGgGQJIfDoUHtR8shhyc7de6o1uxcZLAVAG/H8AdwXW53bp6H\n",
       "dVW+zkOEAJhRMbq6mtftZMvmrpmgS1kZZgoB8HoMfwDXtW73Mh1PPGjLBrUfLYfDcYPPAFDY7mv9\n",
       "kIJdV34Cl5p+QYs3TjXYCIA3Y/gDyCMzK0OzV42zZU1qtlW1cnUNNQJwPcWLlVLnpgNs2ZJNM3Q+\n",
       "9ayhRgC8GcMfQB6LNk5VSvp5z3GQK1j92z1ssBGAG+kWO1jFwu/xHGfnZGnO6u8MNgLgrRj+AGyS\n",
       "UhK1ZOMMW9apSX+VjIwx1AjAzykSEqY+rR6wZet2L9WxhAOGGgHwVgx/ADazVn2r7Nwsz3GxsCh1\n",
       "jx1isBGAm2lVv5vKlqxky6bFjZVlWYYaAfBGDH8AHodP79XGPSts2X1tRiosNNxQIwC3wuV0aUC7\n",
       "R23Z/uM7tOPQejOFAHglhj8ASZJlWZq64ktbVr5UFbWq18VQIwC3o16VpqpTqbEtmxH3lXJzcww1\n",
       "AuBtGP4AJEmb9q7U4VN7bNmgDo/J6XQZagTgdg1s/6gcjivf2hMunFT8jvkGGwHwJgx/AMrKydTM\n",
       "lV/bsgbVWqhWxXsNNQJwJ8qVqqJW9brasnlrJio986KhRgC8CcMfgJZumqnzF6/c99vpdGlgu0cM\n",
       "NgJwp+5eIoDJAAAgAElEQVRr/aBCgot4jtMupWrh+skGGwHwFgx/IMAlpyVp4YYptqzDvX0UXby8\n",
       "oUYA7kZkRHF1azbIli3bMlvnUs4YagTAWzD8gQA3Z9V3ysq+5DkOL1JMvVoON9gIwN3q0nSgoiJK\n",
       "eI5zc3M0K/5bg40AeAOGPxDAjiUc1NpdS2xZn1YjFF6kqKFGAPJDSHCo+rZ5yJZt2rtSB0/uNtQI\n",
       "gDdg+AMByrIsTYsbI0tXHvATU7yC2jboabAVgPzSvG5nVShdzZZNWf6F3JbbUCMApjH8gQC1/eBa\n",
       "7T++w5YNbP+oXK4gQ40A5Cenw6lBHR6zZccSDmj97qWGGgEwjeEPBKCc3GzNiLPfvrNOpcaqV6WZ\n",
       "oUYACkLNCg3UuEYbWzYrfpwuZWUYagTAJIY/EIBWbJ2rxORTnmOHw6mB7UfL4XAYbAWgIAxo/4iC\n",
       "XMGe45T081rA7T2BgMTwBwLMxYwUzV/7vS1r06CHypWqbKgRgIJUMjJGXZsNtGVLN89Q4oVTN/gM\n",
       "AP6K4Q8EmLlrJigjK91zXCQkXH1aPWCwEYCC1q3Z4Dy395xxzdO6Afg/hj8QQE4kHlb89vm2rGeL\n",
       "YSoWHmWoEYDCEBoSpv7tHrZl2w6s0d5j2ww1AmACwx8IEJZlacryz2VddSu/UlFl1KFRX4OtABSW\n",
       "ZrU7qHKZWrZs6vIvlevONdQIQGFj+AMBYvO+eO0/sdOWDerwmIKDgm/wGQD8idPh1JCOT9iyk+eO\n",
       "aNWOBYYaAShsDH8gAGRlZ2pG3Fe2rG7lpmpQtbmZQgCMqFKmlprX6WTL5q4er/RLF80UAlCoGP5A\n",
       "AFi0YarOXzzrOXY6XRrc8XFu3wkEoH5tRykkuIjnOO1SquatnWiwEYDCwvAH/Ny5lDNavHGaLevU\n",
       "uK9iipc31AiASfcULanusUNsWdy2eTqddMxQIwCFheEP+LnpcV8pOzfLc1ws/B71bDHcYCMApnVu\n",
       "2l8lIqM9x253rqYs/0KWZRlsBaCgMfwBP7b32DZt3b/alvVvO0phoeGGGgHwBiFBoRrY7lFbtufo\n",
       "Vm07sMZMIQCFguEP+Kncf5/Bu1rlmJpqXrezoUYAvEmjGq1Vq0JDWzZ1xRhlZWcaagSgoDH8AT+1\n",
       "cts8nTp31JYN6fSknA6+7AFIDodDQzo9JafT5cnOpyZq4YYpBlsBKEgsAMAPpaYna+6aCbasZd0u\n",
       "qnLNw3sABLayJSuqU2P7Q/wWb5ymxAunDDUCUJAY/oAfmrt6vDIy0zzHoSFh6td2lMFGALxVzxbD\n",
       "FRle3HOck5utaSvGGGwEoKAw/AE/c/TM/jxP4uzVYrgiI4rf4DMABLKw0HANaP+ILdtxaL12Htpg\n",
       "qBGAgsLwB/yI23Jr0tJPZenKLfmi7ymnjo3vM9gKgLeLrd1R1crVtWVTln+h7JysG3wGAF/E8Af8\n",
       "yOodC3XkzD5bNrjjEwpyBRtqBMAXOBwODe30pBxXvfn/bPJpLdk0w2ArAPmN4Q/4iYsZKZq1apwt\n",
       "a1S9lepVaWqoEQBfUqF0NbVr2MuWLVg/SUkpiYYaAchvDH/AT8yM/0bpl1I9xyFBoRrc8XGDjQD4\n",
       "mj6tH1BEWKTnODsnS9PjxhpsBCA/MfwBP3Do1E9as3ORLevZcriKFyttqBEAXxRRpJj6tbHfAWzL\n",
       "/lXac3SroUYA8hPDH/Bxbneuflj6qS2LKVFBnZv0M9QIgC9rVb+rKsXUtGWTl32unNxsQ40A5BeG\n",
       "P+DjVm7/UScSD9myYZ2e5g29AO6I0+HUsE5PySGHJztz/riWbJxusBWA/MDwB3xYStoFzVn1nS1r\n",
       "Vqu9alVsaKgRAH9QuUxNtarfzZbNXzdJZ5NPG2oEID8w/AEfNmPlV8rISvcch4aEaWCH0QYbAfAX\n",
       "/duOsr/RNzdLk5Z+JsuyfuazAHgzhj/go/af2Kn1Py2zZX1aPaCoiBJmCgHwKxFhkRrY7lFbtvvI\n",
       "Jm3Zv9pMIQB3jeEP+KDc3BxNuuYNveVKVlaHRjyhF0D+aVG3s2qUr2/Lpi7/QhmZ6Tf4DADejOEP\n",
       "+KDlW2fr1LmjtmxY56flcroMNQLgjxwOh+7v8oxcziBPlpyWpLlrxhtsBeBOMfwBH3Mu5Yzmrp5g\n",
       "y1rU7azq5esZagTAn5UpUVFdmw20ZSu2ztWxhAOGGgG4Uwx/wIdYlqVJSz5VVk6mJwsLjdCAdo8Y\n",
       "bAXA3/VoPkwlI2M8x5bl1vdLPpHbnWuwFYDbxfAHfMjmffHadWSTLRvQ7lEVC7/HUCMAgSAkOFRD\n",
       "Oz1py46e2af47fMNNQJwJxj+gI9Iv3RRU5Z9bsuql6+vVvW7GmoEIJDUrxqrxjXa2LJZq8YpOS3J\n",
       "UCMAt4vhD/iImfFfKzUj2XPscgVpRJdfyOngyxhA4Rjc8XGFBhfxHF/KSte0FWMNNgJwO1gMgA/Y\n",
       "f2KnVu1YaMt6xA5VTIkKhhoBCET3FC2p+1o/ZMs27Y3T7iObDTUCcDsY/oCXy87J1sTFH9mymOIV\n",
       "1C12iKFGAAJZ+0Z9VKF0NVv2/ZKPlZmVYagRgFvF8Ae83KINU5Rw/oQtG971FwoOCjbUCEAgczld\n",
       "Gt7lGTnk8GRJKQmas5p7+wPejuEPeLHTSce0YMNkW9a6fvc8T9IEgMJUuUwtdWzc15Yt3zJbh07t\n",
       "MdQIwK1g+ANeym259f3ij5Wbm+PJioXfwz37AXiF+9o8pBKR0Z5jS5YmLPpA2TnZBlsB+DkMf8BL\n",
       "rdm5WAdO7rJlQzo+ofAiRQ01AoArQoOLaESXZ23Z6aRjWnjNTykBeA+GP+CFktOSNGPlV7asXuWm\n",
       "alKzrZlCAHAddSo3Vsu6XWzZwvVTdPLsEUONAPwchj/gZSzL0vdLPlFGZponCwkK1bAuT8vhcPzM\n",
       "ZwJA4RvYYbTt6eG57hxNWPyh3O5cg60AXA/DH/AyG/es0I6D62xZn9YPqmRkjKFGAHBjEUWKaVin\n",
       "p2zZkdN7tXzrHEONANwIwx/wIilp5zV5+Re2rEqZ2up0zd0zAMCbNK7ZRvdWb2XL5qz6TueSzxhq\n",
       "BOB6GP6Al7AsSz8s/UTpl1I9WZArWA92f15Op8tgMwC4uWGdn1JYSLjnOCsnUxMXfyTLsgy2AnA1\n",
       "hj/gJTbtXaltB9basj6tHlCZEhUNNQKAWxcVUUID24+2ZXuObdXaXUsMNQJwLYY/4AVS0y9o8rLP\n",
       "bFnlmJrq3HSAoUYAcPta1e+mWhUa2rJpcWN0PvWsoUYArsbwB7zApKWfKe2qS3xcriA92P2XcnGJ\n",
       "DwAf4nA4NKLbcwoOCvFkGZlpmrD4Qy75AbwAwx8wbPO+eG3Zv8qW9Wn5gMqW5BIfeI9Tp07pkUce\n",
       "UXR0tMLCwlS/fn2tWLHC83pKSoqeffZZVaxYUeHh4apTp47+9a9/2X6Nl19+WSVLllSlSpU0fvx4\n",
       "22uzZs1S+/btC+X3goJVKqqM+rYZact+OrJZq3YsMNQIwH8EmS4ABLLU9GT9sPRTW1Ypuoa6NBto\n",
       "qBGQ14ULF9S2bVt16NBBc+fOVenSpXXw4EFFR0d7PubFF1/U8uXLNW7cOFWtWlXLly/Xk08+qVKl\n",
       "SmnkyJGaNWuWJkyYoIULF2rv3r167LHH1LNnT5UsWVKpqal6+eWXNWvWLIO/S+Snjo37avuBtdp/\n",
       "YqcnmxY3VrUq3qvS95Q12AwIbJzxBwyavOwzpWWkeI4vX+LzX1ziA6/y1ltvqXz58vrqq68UGxur\n",
       "ypUrq3PnzqpTp47nY9avX6+HH35YHTt2VKVKlTRq1Ci1atVK69ZdfibF7t271alTJzVt2lQjRoxQ\n",
       "ZGSkDh8+LEl64403NGrUKNuvB9/mdDj1UPdfKjS4iCfLyr6k8Qvf58FegEEMf8CQLftWafO+eFvW\n",
       "q8VwlStV2VAj4PqmT5+uFi1aaPjw4YqJiVGTJk304Ycf2j6md+/emjlzpo4fPy5JWrVqlbZs2aJe\n",
       "vXpJkho3bqwNGzbowoUL2rBhgzIyMlSjRg2tWbNGy5Yt0xtvvFHovy8UrJJRMRrU4TFbduDkLi3b\n",
       "wk92AFMY/oAByWlJ+n7Jx7asQnQ1dWs2yFAj4MYOHjyojz76SDVq1NCCBQv0wgsv6LXXXrON/zff\n",
       "fFP16tVTpUqVFBISok6dOumtt95Snz59JEk9evTQyJEj1bx5cz322GP65ptvFB4erqefflqffvqp\n",
       "vvzyS9WrV0+xsbFavXq1qd8q8lnr+t1Vr3JTWzZ71Xc6de6ooUZAYHNYN3ibfXJysuefo6KiCq0Q\n",
       "4O8sy9LHM/6on45s9mQuZ5B+NeJtlS9dxVyxu+T4g8N2bP2eO3h4I4f9P5Nu5UYrISEhatGihVau\n",
       "XOnJfvOb32jatGnatWuXJOmVV17RrFmz9M9//lOVK1fW8uXL9dprr2ny5Mnq2bPndX/dP//5zzpx\n",
       "4oR+8YtfqHv37tq6dau2bdumxx57TIcOHVJQUOC+Dc2fvp6SLybpr+N+qfTMi56sQnQ1vXL/W3K5\n",
       "Ave/MVAQbrbfOeMPFLK4bXNto1+6/KAuXx798G/lypVTvXr1bFmdOnV09Ojls7ZpaWl699139c47\n",
       "7+i+++5TgwYN9Nxzz2nEiBF6++23r/tr7t27V2PGjNGbb76ppUuXqmPHjoqJiVH37t2VmZmpPXv2\n",
       "FPjvC4UjqmgJDev8lC07nnBQC9ZPNtQICFwMf6AQnTp3TDPivrZl1cvVU1fu4gMv1rZtW/3000+2\n",
       "bO/evapSpYqkyz/FsixLTqf9W4rT6bzuvdsty9JTTz2ld955R8WKFZNlWcrKyvK8lp2drdxc3gDq\n",
       "T5rWaq/GNdvYsvnrJ+nomf2GGgGBieEPFJKc3Gx9M/8fys7N8mRFQsI1sucLcnIXH3ixl156SWvW\n",
       "rNFf/vIX7d+/X5MmTdL777+v5557TpJUtGhRde3aVa+99pqWL1+uQ4cO6auvvtK3336rQYPyvm/l\n",
       "yy+/VMmSJTVw4OW/8LZr105LlixRfHy8PvroI4WEhKh27dqF+ntEwXI4HLq/8zMqFn6PJ3O7czVu\n",
       "wbvKzsn6mc8EkJ+4xh8oJDNXfqNFG6faslE9X1TzOp3MFMpn/nRNsj+7k2v8JWnu3Ll64403tGfP\n",
       "HlWuXFnPP/+8nn/+ec/riYmJev311zV//nydO3dOVapU0RNPPKGXX37Z9uucOXNGrVq10qpVq1S2\n",
       "7JX7uf/tb3/TP/7xD0VGRuqjjz5Sjx497vj36A/89etp+8F1+nzWX2xZx8Z9NaTjE4YaAf7lZvud\n",
       "4Q8Ugn3Hd+iDKb+TpStfbk1rtdMjvV6R49ol5qP8daj4mzsd/ihc/vz19N2C97R29xJb9nT/36p+\n",
       "1VhDjQD/wZt7AcPSMy9q3IJ3baP/nqIldX/nZ/xm9APArRrc8XGVKFbalo1b+J6S05IMNQICB8Mf\n",
       "KGCTl36u86mJtmxkjxcUXqSooUYAYE5YaIQe7vWKnI4rEyQtI0Xj5r8rt+U22Azwfwx/oABt3BOn\n",
       "DXuW27LOTfqrVsV7DTUCAPOqlauj3q1G2LI9x7ZqycbphhoBgYHhDxSQpJQE/bD0E1tWrmRl9W0z\n",
       "0lAjAPAe3WOHqEb5+rZs9urvdOT0PkONAP/H8AcKQE5utsbOe1sZmWmezOUK0sO9XlJwUIjBZgDg\n",
       "HZxOl0b1fEnhRYp5Mrc7V1//+I4yMtMNNgP8F8MfKACz4r/VkdN7bVn/Ng+rXKkqZgoBgBcqXqyU\n",
       "Huz2nC07m3xak5Z9aqgR4N8Y/kA+235wnZZunmnL6leNVccmfQ018hKrV0uvvSZlZppuAngHy5J+\n",
       "+1tp8eKAvq/qvdVbqV3DXrZsw0/LtW73UkONAP/F8AfyUVJKgr5b8J4tK160lEZ2/6XtDhYBZfVq\n",
       "6eWXpWPHpL/8RQoNNd0I8A4Oh/SnP0kZGZe/RgL4LwADO4xW2ZKVbNmkpZ8q8cIpQ40A/8QDvIB8\n",
       "kpObrXcn/8Z2iY/T6dILQ/+sqmXrGGxWOPI8cKjVj9K0aVLTplK/fpIzQP/i42ViytiPz5w20wPX\n",
       "sCxp4UJp5UqpZ085tg+xv+xHD/C6kZNnj+idia8qOzfLk1WMrq4Xh/1NwUHBBpsBvuNm+z2oMMsA\n",
       "/mz2qnF5ruvv12ZUQIz+6/r8cykrS6peXZrOLfq8xeBrg6kmWuC6MjKkxETps8+klgq4n8mXK1VZ\n",
       "AzuM1qSlV67vP5ZwQFNXfKnhXZ4x2AzwHwx/IB9sP7hOSzbNsGX1q8aqc9P+hhp5gcmTpYSEyyMm\n",
       "J0d66impZEnTrQLeJ8/ajz/+hZkeuEpKyuWvk5QU6b33pAoVpD8E5lO92zXspT1Ht2jbgbWeLH77\n",
       "j6patrZa1O1ssBngHxj+wF3iuv6fER19+c2LCQnSxx9LLpf06qtSEH/0ALIs6Z//lC5cuPwX4woV\n",
       "TDcyzuFw6MFu/6UTZw/rXPIZT/794o9VvlQVlS9d1WA7wPcF+CoB7s5/7tefnnnRkzkdTj3S+1eK\n",
       "CIs02MzL/OcvAM88c/kNjQAue+QR6Y9/ZPRfJbxIUT1+368V7LryzJPs3Cx9OedN25+1AG4fwx+4\n",
       "CzNXfpP3uv62o1StXIBe138zxYtfPusP4PJfgrn87boqlK6m+7s8bcvOJp/WuAXvyW25DbUCfB/D\n",
       "H7hD63Yv1bIts2xZ/Sqx6tx0gKFGAOA/WtbrqjYNetiyHQfXafGGaYYaAb6P4Q/cgaNn9mvi4o9s\n",
       "2T1FS2pkD67rB4D8MqTjE6oYXd2WzV79nfYc3WqoEeDbWCjAbUpJu6AvZv9VObnZnizIFawn+r7O\n",
       "df0AkI+Cg0L0+H2/VniRYp7Mstz6+sd/6HzqWYPNAN/E8AduQ25ujsbOfUsXLp6z5SO6PqtKMTUM\n",
       "tQIA/1UiMloP93xJDl25McDFjGSNnft32wkYADfH8Aduw9QVY3Tg5C5b1qlxP+4vDQAFqF6VpurV\n",
       "crgtO3x6j6Ys+8JQI8A3MfyBW7R6x0LFbZtry2pVaKgB7R81UwgAAkjPlverXuWmtix+x3zFbZtn\n",
       "qBHgexj+wC04dGqPflj2qS0rUay0Hu3zqlxObk8JAAXN6XBqVK+XVDIyxpZPWf6F9h7bbqgV4FsY\n",
       "/sBNJKcl6cs5f1Nubo4nCw4K0RP9XldR3swLAIUmokgxPdnvdYUEF/Fkbneuxs59S2eTTxtsBvgG\n",
       "hj/wM7JzLj8tMiXtvC1/qPsvVaF0NUOtACBwlStVRQ/3fNGWpV1K1eez/qKMzHRDrQDfwPAHbsCy\n",
       "LI1f9IEOn9pjy7s1G6ymtdoZagUAuLd6K93X+kFbdurcUX09723lunMNtQK8H8MfuIEf136vjXtW\n",
       "2LI6lZuob5uHDDUCAPxHj+bD1LhmG1u268gmTVvxpaFGgPdj+APXsf6n5Zq3dqItiy5eXo/2ekVO\n",
       "3swLAMY5HA6N7P6CKkXbn6GyYutcLd8y21ArwLsx/IFrHDixS+MXvW/LIooU09P9f6vwIkUNtQIA\n",
       "XCskOFRP9n9DxYuWsuVTV4zRzkMbDLUCvBfDH7jKmfMn9MXsv9ru4ONyBemJvq+r9D1lDTYDAFxP\n",
       "VEQJPdX/twq96k4/luXW2Hlv6+iZ/QabAd6H4Q/8W0raeX08/Q9Ku5Rqyx/q9l+qXr6eoVYAgJsp\n",
       "X7qKHu39KzkcV2ZNVvYlfTrjT9zmE7gKwx+QdCkrQ5/M+JOSUhJsee+WIxRbp6OhVgCAW1W/aqyG\n",
       "dHzClqVmJOvj6X9UanqyoVaAd2H4I+Dl5uZozJw3dTzxoC1vVb+berUcbqgVAOB2dWjUR12bDbJl\n",
       "iRdO6rNZf1ZWdqahVoD3YPgjoLktt75b9L5+OrrFlter0kzDOz8jh8NhqBkA4E70aztKsbXtP6k9\n",
       "cnqvxs79u+39W0AgYvgjYFmWpanLv9SGn5bb8krRNTS696/kcgUZagYAuFNOh1MPdn9etSrea8t3\n",
       "Ht6gcQvfk9tyG2oGmMfwR8D6ce33WrF1ji0rGRWjpwf8VqEhYYZaAQDuVpArWI/f95rKl6piyzfu\n",
       "WaGpy7+QZVlmigGGMfwRkJZvmZ3nAV2R4cX17MD/VbHwewy1AgDkl7DQcD0z8H9UMirGlq/YOjfP\n",
       "n/9AoGD4I+Cs3bVEU5Z/YcvCQiP07KDfc69+APAjUREl9NygPygyorgt/3Ht91q6aaahVoA5DH8E\n",
       "lI174jR+0Qe2LCQoVM8M+J3KXfMjYQCA7ysVVUbPDvxfhYfan7w+LW6M4rbONdQKMIPhj4Cxdf9q\n",
       "fTv/n7KuemOXyxmkx/u+pqpl6xhsBgAoSOVKVdbTA36nkKBQWz5p2WdavWOhoVZA4WP4IyDsOLhe\n",
       "X817x3Y3B6fDqUd7v6K6lZsYbAYAKAxVy9bWk/3eUJAr2JZPXPyR1v+0zEwpoJAx/OH3dh7aoC/n\n",
       "vqlc95X7NzscTo3q+ZIa1WhtsBkAoDDVrtRIT/R9TS7nlds1W7I0bsF7Wn/NrZ0Bf8Twh1/bfnCd\n",
       "vpj9tzwPbXmw2/NqVru9oVYAAFPqVWmm0X1eldPp8mSW5da4Be9q3e6lBpsBBY/hD7+1df8ajZnz\n",
       "lu1MvyQN7/ILtazXxVArAIBp91ZvqUd6vSyH48oMsiy3vlvwntbuWmywGVCwGP7wS5v3rdLYeX+/\n",
       "7uhv27CnoVYAAG/RpGZbPdLrZTmvHv+yNH7hB1rFG37hp4Ju/iGAb1m7a4nGL/rAdvcehxwa3vVZ\n",
       "tWnQ3WAzAIA3aVqrnRwOp77+8R253bmSLo//iYs/VGZ2hjo36W+4IZC/GP7wK8u3zM7zcC6HHHqg\n",
       "2/NqVb+roVYAAG/VpGYbOR1OjZ33d8/4l6RpK8boUma6erUcLofDYbAhkH+41Ad+wbIszV/3Q97R\n",
       "73DqoR6/ZPQDAG6oUY1Wevy+X8vlsp8Pnbd2oqatGGO7FTTgyxj+8Hluy61pcWM1Z/V4W+5yBumx\n",
       "Pq+qRd3OhpoBAHxFw2ot9Ez/vA/5WrZllsYvfD/P3eEAX8Twh0/LzsnWNz/+U8s2z7TlwUEheqr/\n",
       "b7hPPwDgltWu1EjPDf6DwkIjbPm63Uv1+ay/KDMrw1AzIH8w/OGzMjLT9MmMP2rT3jhbXiQkXM8N\n",
       "+gNP5AUA3LaqZevol0P+T8XComz5riOb9P6U3yk1/YKhZsDdY/jDJ124eE7vTf6N9h3fbssjw4vr\n",
       "l0P/T9XK1TXUDADg68qXrqoXhv1VJSNjbPnRhP361w+vK/HCKUPNgLvD8IfPOZZwUO9MfFUnzh62\n",
       "5dH3lNNLw/+mCqWrmSkGAPAb0cXL6aX7835PSUw+pXe+/28dOLHTUDPgzjH84VO2H1yndye9ruS0\n",
       "JFteuUwtvXj/3/KcnQEA4E5FRhTXL4f+WbUrNbLl6ZdS9cG032v9T8vMFAPuEMMfPsGyLC3ZNENf\n",
       "zPqrsnIyba81qNpczw/+o4qGRRpqBwDwV0VCwvR0/98qtk5HW56bm6Nv5/9Lc1aP53af8Bk8wAte\n",
       "LzsnS98v+Vjrdi/N81qnxv00sP2jcjpdBpoBAAJBkCtYo3q8qNL3lNO8NRNsr81f94NOnTuqkT1e\n",
       "UJGQMEMNgVvDGX94tf+8iffa0e90ODWs89Ma3PFxRj8AoMA5HA71bjlcj/R6WUGuYNtr2w6s0T9/\n",
       "+DVv+oXXY/jDax08uVt/n/CKjpzZZ8uLhITr6QG/U/t7extqBgAIVM1qd9Dzg/+kotfc7vPUuaN6\n",
       "e+KvtPvIZkPNgJtj+MPrWJalpZtm6r0pv81zv+To4uX1yvC3uEc/AMCYauXq6Fcj3s5zx5+MzDR9\n",
       "Mv2PmrtmgtzuXEPtgBtj+MOrZGSmaczctzQtbkyePzTrV4nVK8PfUkyJCobaAQBwWYnI0npx2F/V\n",
       "rFZ7W27J0o9rv9cnM/6k1PRkQ+2A62P4w2scTzyotyf8Slv3r87zWo/mQ/Vkv9fzPEYdAABTQoJD\n",
       "9XCvlzWg3aNyOOyT6qejW/TWhJd18ORuQ+2AvLirD4yzLEvLt8zWjPivlZubY3stLCRcI3u+qIbV\n",
       "WhhqBwDAjTkcDnVtNlAVo6vp63nvKDXjyln+5Ivn9O7k36h3y+Hq0XwoN6OAcZzxh1Gp6Rf06cz/\n",
       "09QVX+YZ/RWiq+nVB//B6AcAeL1aFe/Vfz/4T1UrV9eWW5Zbc9dM0PtT/0fnUxMNtQMuY/jDmJ2H\n",
       "NujN717SrsMb87zWpkEPvTTsbyoVVcZAMwAAbl9U0RL6r8F/UtdmA/O8duDETr353UvatHelgWbA\n",
       "ZVzqg0J3KStD0+PGaNWOhXleCwsJ14huz6lJzbYGmgEAcHdcriANaPeoala4V98teNd26U965kV9\n",
       "Ne9tbTuwRsM6PaUInjiPQsYZfxSq/Sd26s3vXrzu6K9ato5+/dC/GP0AAJ9Xr0pT/fqhf6lOpcZ5\n",
       "Xtu0d6X+Ou4F7Ty0wUAzBDLO+KNQZGSma1b8N1q5/cc8rzkdTvVoPkw9W94vF298AgD4iciI4npm\n",
       "4P9o2eaZmrVqnO29bCnp5/XpzP9TbJ2OGtzhcRXl7D8KAcMfBW7HwfX6YeknunDxXJ7XoouX16ge\n",
       "L6hymVoGmgEAULCcDqe6NB2oOpWaaNyCd3U88aDt9Q0/LddPR7ZoSMcn1LRWOzkcDkNNEQgclmVZ\n",
       "13shOfnKNWlRUVHX+xDgZ124eE7TVozR5n3x1329Y+O+6td2lEKCQgu5GQqC4w/2b1bW76/7RwsM\n",
       "u3ZTXP87AEzj68k/5eRma/66SVq4frLcljvP6/WqNNPQTk9yYwvcsZvtd874I9/lunO1YssczV0z\n",
       "XpnZl/K8XjqqrEZ0e041KzQw0A4AADOCXMG6r/WDalithcYv+kAnzx62vb7r8Eb99dvt6t58iLo2\n",
       "G6zgoGAzReG3OOOPfLXv+A5NWf5Fnj/MpCs/7uzVajhn+f0QZyh9A2f8fQNfT/4vNzdHizZO04/r\n",
       "vs/zHBvp8kmywR0fV/2qsQbawVdxxh+F4lzyGU1f+ZW27l993dcrRFfTA12fU8Xo6oXcDAAA7+Ny\n",
       "BZoQFvMAAA4hSURBVKlni2FqVKOVJi7+SAdP7ra9nph8Sp/O/D/VrdxUA9uPVtmSFQ01hT9h+OOu\n",
       "ZGSmaeGGqVq6ecZ1z1iEhYTrvjYj1a5hTx5VDgDANcqUqKgXhv5F63Yv1YyVX+viVff9l6TdRzZp\n",
       "z9EtandvL/Vscb+Khd9jqCn8AcMfdyQ7J0tx2+ZpwfrJSr+Uet2Pia3TUQPbjVZkBH9IAQBwIw6H\n",
       "Qy3rdVHDai00e9U4xW+fL0tXLu9yW26t2DpXa3YtUafG/dSl2QCFhxY12Bi+imv8cVty3blav3uZ\n",
       "5q2dqPOpidf9mErRNTS44xOqVq5OIbeDSVyT7Bu4xt838PUU2I4lHNTUFV/qwImd1309LDRCXZsO\n",
       "VMfGfRUaElbI7eDNbrbfGf64JbnuXG3cs0Lz1/6gxORT1/2YyIji6t/2YcXW6Sing4dCBxqGim9g\n",
       "+PsGvp5gWZa27l+t6Su/UlJKwnU/plhYlLo3H6q2DXsqOCikkBvCG/HmXtyV7JxsbdyzQgs3TFHi\n",
       "hZPX/ZjQkDB1bTpQnZv058wDAAD5wOFwqHHNNqpfNVbx2+dr4frJSr3m+v/UjGRNXfGllmyaru6x\n",
       "Q9SyXleFBHPXPNwYZ/xxXemZFxW/fYGWb5mllLTz1/0YlzNI7e7tpR7Nh6lYOP+PBDrOUPoGzvj7\n",
       "Br6ecK3MrAwt3zJbizdNV0Zm2nU/JiIsUu3/v717iWnrysMA/vn6hbGx8QNMMBQM5e3EaSCPyaRk\n",
       "GqbVzEQz08W0lVppdrPrYhZdV6MomhWrquss2kXVLhJVjZQoVdOg0ExGCSQpkASTYkMwYIxt/MIY\n",
       "P+4s7DBJgxOTYBzj7ydZ9r0+Nn+Ejvnu9Tn37Psj3tz3J/5fLlMc6kNb4g95MXT7O1wbv7Tp4lsA\n",
       "IAhSHO46gXcO/Q1GrXmHK6RXFYNKaWDwLw3sT5TLajyCyyPf4srt77Ce4/+0XKrA4e4TeOvAX1FT\n",
       "vWeHK6RiYvCnvMx5p3F55FuMTg0jnU5t2kaQCDjU9RbeOfQelxOnpzColAYG/9LA/kTPE15dwfc3\n",
       "z2L45wtIphKbtpFAgn2th3Gi910013VA8usPANp1GPwpp3hiDaOOYVwbv4SZRUfOdgqZEr+xvY3f\n",
       "7f8zjDqe4afNMaiUBgb/0sD+RPkKRvwYun0eP41dRGx9NWc7i6kZR23voK/zOFRK9Q5WSDuJwZ+e\n",
       "8nBpGv8Zv4Qbk0OIr8dytquqrEa//SSO7fsD1BVVO1ghlSIGldLA4F8a2J9oq9bWY7g2fglDt75D\n",
       "ILKcs51cpsCB9jdx1PY2vwXYhRj8CUBmhd1bUz/h2tglzC49eGbbWr0FJw68i4Odx3l5MMobg0pp\n",
       "YPAvDexP9KJSqSRGp37C5ZFzcC+7ntl2j/G1zLcAHf1Qq7Q7UyAVFIN/GVtPxDHuvIFRxzDuukZy\n",
       "jgF8pKPRjv79J9Fj7eN1+GnLGFRKA4N/aWB/opcliiImZ+9g6PZ53J0ZhSimc7YVBCk6X9uPA+3H\n",
       "sLflMFTKyh2slLYTr+NfZhLJBO7P3sLo5FWMOW/knPH/SFVlNY50D+BIz+8585+IiGiXkEgk6Gza\n",
       "j86m/QiEl3H97g+4Pv79psOA0ukU7rpGcNc1AplUjp7mXhzo6EePtRcKGdcF2E14xn8XWFuPYXL2\n",
       "Nsanb+Dn6f/mvL7vIxJI0Nn0Bo7a3obNehBSKY//6OXxDGVp4Bn/0sD+RIWQTqdwb+YWro1fwoTz\n",
       "JtLP+BYAAJTyCtisB2FrOYSupjdQWaHZoUrpRfGM/y7lXVnAhPMmJpw38cA9gVQ6+dzXmHR16O3o\n",
       "x5GeAV5/n4iIqMwIghQ91j70WPsQjPhx/e4PuDk5BI9/btP28cQaRhxXMeK4CkEioKW+Cz3Wg7BZ\n",
       "+1Crt3BicAniGf8SEU+sYXr+HiZn72DCeROewOad9Nd0GiMOtP0WvR39aKxtZSelguEZytLAM/6l\n",
       "gf2JdoooiljwzWBk8ipGHcPwhTx5vc6kq0OPtQ+dr+1HS3035wW8Iji5t0StJ+NwLUxiam4MUw/H\n",
       "MeOZyuusPgBoVDrsbzuK3vZjsNZ3caIu7QgGldLA4F8a2J+oGERRxKxnCiOOYdxyDCMY9ef1OkEi\n",
       "oLG2FW0Ne9HWuBct9V1QyisKXC1thsG/RERjIcx4puBacOCBexyuRcdzr8LzuJrqevRY+2Cz9qHV\n",
       "0gOpIC1gtURPY1ApDQz+pYH9iYotLabhnL+fGVbsuokF32zerxUEKZrMbXjd0oPmPR1oMrdDq64u\n",
       "YLX0CMf4v4KSqQTcXhdmPA64FhyYWXTAG1zY0nsIghSv13ejx3oQPdZe1OotBaqWiIiIyo0gEdBq\n",
       "6UarpRt/OfZ3+IIeTLhuYsI5Asfcz0ilco9CSKdTcC7ch3Ph/sY+g7YWzXXtaDK3o3lPOxpqWrhW\n",
       "UBEw+BfY6loE7mUn3F4X3MsuuJedWPQ93NLZ/EdqdHvQ1mhDe6MdXU1vcMltIiIi2hFGnRn99pPo\n",
       "t59EfD2GyYd3cH/2DqbmxnJODn6cP7QEf2gJo45hAIBUkKHO0ABLjRX1piZYTFbUm5pRVclRJoXE\n",
       "4L9NVuMRLAXm4fHPYSngxrxvBvNe1zOXzX4eg7Y2M16uwYa2hr3QV5m2sWIiIiKirVMqVNjXegT7\n",
       "Wo8AAELRAKbmxjPzEufG4V2Zf+57pNLJ7AlR1xP7tWp99iCgCbV6C8z6Bpj19VxZeJsw+G9BLL4K\n",
       "f8gDX8iD5aAHSwE3PAE3lgJuhFdXXuq9BYmAPaYmNGe/AnvdYoNRx0tuEhER0atNq9ajt+NN9Ha8\n",
       "CQAIhJfxwD2BmcVJuBYcmFt2Ip1O5fVeoWgAoWgA92ZGn9ivVmlhrrag1mCBWW+BSVcHg9YMo64W\n",
       "lUquL5AvBv+stJhGZDWIlYgPKxEfghEf/GEvfCEP/MEl+EIeRNfC2/bzdBojms1tmUkvde1orG3l\n",
       "DHgiIiIqefoqEw52HsfBzuMAMlcqnFtyYmbRkZ3fOAl/2Lul94zGQpiOhTC9cO+p51RKNYxaMwza\n",
       "Whi1tTBoa6FTG6DTGKFTG6BVV0MmlW/L71bqdnXwF0URsXgU4VgQkdUVRGIhhFeDCMeCiMaCCK2u\n",
       "IBjxZ4J+1J/30ehWCIIUdfoG1JuaYalpztybrJzdTkRERGVBIVOipb4TLfWdG/sisRDml13ZOZBO\n",
       "uJddWPQ/fOak4Vxi8SjmvNOY807nbFOl0kGrMUCnNqBaY4BWbUC1xghtpR5qlRYalRZqVRVUCvWu\n",
       "XvOoJIJ/MpVALB5FLB7Favb+ie21SGZ7PYroWhiRbLiPxEIFCfObkQoymKrrYNY3ZMekWWCpaYZZ\n",
       "3wi5jEeZRERERI9oVFq0N+5De+O+jX2pVBKegBvuZReWAnPw+N3wBObgXVl4oYuiPC4cy2RDt9f5\n",
       "zHaCRIC6ogpqlXbjXqOqQmVFZlulVEOlrESFInN79FilqIRCXvHKHzS8cPBPp1NIppJIphKb3J7e\n",
       "n0iuI55YQzyxhvVEPHufuW3sS65hfX0tc/9Ym5f9Y28XqSCDoaoGBl0tjFozaqrrYdZbUKu3wKgz\n",
       "89r5RERERC9IKpWh3tSEelPTE/vT6RT8Ye/G3EpvYB6+UGYYtj+0tK05MS2mNw4StkoiEVChUEGV\n",
       "PShQKCqglFVALldCIVNCIVNAIVdCsdk+eQUUMiXkMiUUciXkUjlkT9xkG48FQfrCBxh5Bf9/nfnH\n",
       "U2E+LaZf6Ae+yiqVGug0BlRrTNBpDNBrTDDqzE+MFxMY7omIiIh2jCBIYdLVwaSrQ3dz7xPPpcU0\n",
       "wtEV+LIXX/EFPdm5mn4Eo5lbZDUIEYVfBE8U0xsjUgpJAglkUjmk2YOBf77377zXc8or+G91Asar\n",
       "RCmvgKZShypVNTQqbfaxDppKHTQqXXaslxHVGiMUcmWxyyUiIiKiPAkSATqNATqNAS31XZu2SaWS\n",
       "CK0GEIwGsgcE/z8wCEUDiK6FM7dYCPHE2g7/BlsnQkQitY5Eah1A5puGfElEcfMF2x9f8peIiIiI\n",
       "iEqHTvf0Ymj5HyIQEREREVHJYvAnIiIiIioDOYf6EBERERHR7sEz/kREREREZYDBn4iIiIioDDD4\n",
       "ExERERGVAQZ/IiIiIqIywOBPRERERFQGGPyJiMrI6dOncebMmY3tDz/8ENevXy9iRUREtFMY/ImI\n",
       "ysi5c+fQ29sLAEgmk7hw4QJsNluRqyIiop3A4E9EBTE4OAi73Y6qqipoNBp0dXXho48+KnZZZS0Q\n",
       "CMDtdsNutwMAbty4gc7OTmg0miJXRr/G/kNEhSArdgFEtPt88sknaGhowJ07d7C4uAi73Y6xsTHI\n",
       "ZPzIKaahoSEcP358Y/vKlSsYGBiAz+eD0WgsYmX0OPYfIioUfooQUd4+//xz/PLLLzmf7+vrg91u\n",
       "x8jICAYHBwEAdXV1EEURgUAANTU1O1UqbeLy5cuwWq0AgFQqhbNnz+L06dP46quv8PHHHxe5OgKA\n",
       "8fFx9h8iKhgGfyLKWz7hcHBwECdPntzYnpychMlkYmh5Bfz444/o7u7Gl19+iXg8jg8++ADDw8Mb\n",
       "Y/6p+C5evMj+Q0QFw+BPRNuqpqYG4XB4Y/vUqVP47LPPilgRAYDX60U4HMbXX39d7FLoGdh/iKiQ\n",
       "JKIoisUugoh2j1QqhVOnTsFqtcLpdKK/vx8DAwPFLqvsffPNNzh//jy++OKLYpdCz8D+Q0SFxOBP\n",
       "RFQGPv30U9hsNrz//vvFLoWIiIqEwZ+IiIiIqAzwOv5ERERERGWAwZ+IiIiIqAww+BMRERERlQEG\n",
       "fyIiIiKiMsDgT0RERERUBhj8iYiIiIjKAIM/EREREVEZ+B/H1tUZSdQuawAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4800f56470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from gaussian_internal import display_stddev_plot\n",
    "display_stddev_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> An equivalent formation for a Gaussian is $\\mathcal{N}(\\mu,1/\\tau)$ where $\\mu$ is the *mean* and $tau$ the *precision*. Here $1/\\tau = \\sigma^2$; it is the reciprocal of the variance. While we do not use this formulation in this book, it underscores that the variance is a measure of how precise our data is. A small variance yields large precision - our measurement is very precise. Conversely, a large variance yields low precision - our belief is spread out across a large area. You should become comfortable with thinking about Gaussians in these equivalent forms. Gaussians reflect our *belief* about a measurement, they express the *precision* of the measurement, and they express how much *variance* there is in the measurements. These are all different ways of stating the same fact.</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interactive Gaussians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For those that are reading this in IPython Notebook, here is an interactive version of the Gaussian plots. Use the sliders to modify $\\mu$ and $\\sigma^2$. Adjusting $\\mu$ will move the graph to the left and right because you are adjusting the mean, and adjusting $\\sigma^2$ will make the bell curve thicker and thinner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAxoAAAGNCAYAAACWvAeAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8FHX+x/H3ZtMhoScECBB6CzW0AII0KQqIgnKeBbEQ\n",
       "z4rth6fniZz1jrOC3olgRVAUlCZBOgElhhB6gAgESIOEBELq7v7+QHOOCU2HTJJ9PR8PH6efmVne\n",
       "uXmQ5L07M1+by+VyCQAAAABM5GF1AAAAAABVD0UDAAAAgOkoGgAAAABMR9EAAAAAYDqKBgAAAADT\n",
       "UTQAAAAAmI6iAQAAAMB0Fy0a69ev16hRo9SoUSN5eHjogw8+uOiL7tixQ/3795e/v78aNWqk559/\n",
       "3pSwAAAAACqHixaN3NxcdezYUa+//rr8/Pxks9kuuH9OTo6GDBmikJAQxcbG6vXXX9err76qGTNm\n",
       "mBYaAAAAQMVmu5yVwQMCAvT222/rtttuO+8+s2bN0tSpU5WWliYfHx9J0j/+8Q/NmjVLR48e/eOJ\n",
       "AQAAAFR4pt+jsXnzZvXr16+kZEjS0KFDdfz4cR0+fNjsPw4AAABABeRp9gumpqaqcePGhllwcHDJ\n",
       "tiZNmpTMs7Ozzf7jAQAAAFxhNWrUuOg+pn+icbF7OAAAAABUfaYXjfr16ys1NdUwS0tLK9kGAAAA\n",
       "oOoz/dKp3r1768knn1RBQUHJfRrR0dFq2LCh4bKp37qUj19Q+cXGxkqSIiIiLE6C8sI5d0+cd/fD\n",
       "OXc/nHP3c7m3PVzS423j4+MVHx8vp9Opw4cPKz4+XsnJyZKkqVOnavDgwSX7/+lPf5K/v7/uuOMO\n",
       "7dq1S19++aVefvllTZky5TK/FAAAAACV1UWLxtatW9W1a1d17dpV+fn5evbZZ9W1a1c9++yzks7d\n",
       "4J2UlFSyf2BgoKKjo3X8+HFFRETogQce0GOPPaZHHnnkyn0VAAAAACqUi146NWDAADmdzvNunzNn\n",
       "TqlZhw4dtG7duj+WDAAAAEClZfrN4AAAAABA0QAAAABgOooGAAAAANNRNAAAAACYjqIBAAAAwHQU\n",
       "DQAAAACmo2gAAAAAMB1FAwAAAIDpKBoAAAAATEfRAAAAAGA6igYAAAAA01E0AAAAAJiOogEAAADA\n",
       "dBQNAAAAAKajaAAAAAAwHUUDAAAAgOkoGgAAAABMR9EAAAAAYDqKBgAAAADTUTQAAAAAmI6iAQAA\n",
       "AMB0FA0AAAAApqNoAAAAADAdRQMAAACA6SgaAAAAAExH0QAAAABgOooGAAAAANNRNAAAAACYjqIB\n",
       "AAAAwHQUDQAAAACmo2gAAAAAMB1FAwAAAIDpKBoAAAAATEfRAAAAAGA6igYAAAAA01E0AAAAAJiO\n",
       "ogEAAADAdBQNAAAAAKajaAAAAAAwHUUDAAAAgOkoGgAAAABMR9EAAAAAYDqKBgAAAADTUTQAAAAA\n",
       "mI6iAQAAAMB0FA0AAAAApqNoAAAAADAdRQMAAACA6SgaAAAAAExH0QAAAABgOooGAAAAANNRNAAA\n",
       "AACYjqIBAAAAwHQUDQAAAACmo2gAAAAAMB1FAwAAAIDpKBoAAAAATEfRAAAAAGA6igYAAAAA01E0\n",
       "AAAAAJiOogEAAADAdJdUNGbOnKmwsDD5+fkpIiJCGzduvOD+y5YtU69evRQYGKh69eppzJgx2r9/\n",
       "vymBAQAAAFR8Fy0a8+fP18MPP6ynn35a8fHxioyM1PDhw5WcnFzm/gcOHNCYMWM0YMAAxcfHa9Wq\n",
       "VcrPz9eIESNMDw8AAACgYrpo0ZgxY4YmTpyoSZMmqXXr1nrjjTcUEhKiWbNmlbl/fHy8nE6nXnzx\n",
       "RTVr1kydOnXSk08+qYMHDyozM9P0LwAAAABAxXPBolFYWKi4uDgNHTrUMB86dKhiYmLKPKZPnz6q\n",
       "Xr26/vvf/8rhcOj06dOaO3euevToodq1a5uXHAAAAECFZXO5XK7zbTx+/LgaNWqk9evXq2/fviXz\n",
       "adOm6dNPP9XevXvLPC4mJkZjxoxRVlaWnE6nunTpouXLl6tevXqG/bKzs0v+nXs4AAAAgIqrZcuW\n",
       "Jf9eo0aNi+5v+lOnkpKSNGbMGE2cOFGxsbFau3atAgICNH78eF2g0wAAAACoQjwvtLFu3bqy2+1K\n",
       "S0szzNPS0hQSElLmMe+++65CQ0P18ssvl8w+/vhjhYaGavPmzYqMjCzzuIiIiMvNjkooNjZWEufb\n",
       "nXDO3RPn3f1wzt0P59z9/PpqpEtxwU80vL291a1bN61cudIwj46OPm9hcLlc8vAwvuwv/+10Oi8r\n",
       "HAAAAIDK6aKXTk2ZMkVz587V7NmztWfPHj300ENKTU3V5MmTJUlTp07V4MGDS/YfNWqU4uLi9Pzz\n",
       "z2v//v2Ki4vTxIkT1bhxY3Xr1u3KfSUAAAAAKowLXjolSePHj9fJkyc1ffp0paSkKDw8XMuWLVNo\n",
       "aKgkKTU1VUlJSSX79+3bV/Pnz9dLL72kV155Rf7+/urdu7dWrFghPz+/K/eVAAAAAKgwLlo0JCkq\n",
       "KkpRUVFlbpszZ06p2Y033qgbb7zxjyUDAAAAUGmZ/tQpAAAAAKBoAAAAADAdRQMAAACA6SgaAAAA\n",
       "AExH0QAAAABgOooGAAAAANNRNAAAAACYjqIBAAAAwHQUDQAAAACmo2gAAAAAMB1FAwAAAIDpKBoA\n",
       "AAAATEfRAAAAAGA6igYAAAAA01E0AAAAAJiOogEAAADAdBQNAAAAAKajaAAAAAAwHUUDAAAAgOko\n",
       "GgAAAABMR9EAAAAAYDqKBgAAAADTUTQAAAAAmI6iAQAAAMB0FA0AAAAApqNoAAAAADAdRQMAAACA\n",
       "6SgaAAAAAExH0QAAAABgOooGAAAAANNRNAAAAACYjqIBAAAAwHQUDQAAAACmo2gAAAAAMB1FAwAA\n",
       "AIDpKBoAAAAATEfRAAAAAGA6igYAAAAA01E0AAAAAJiOogEAAADAdBQNAAAAAKajaAAAAAAwHUUD\n",
       "AAAAgOkoGgAAAABMR9EAAAAAYDqKBgAAAADTUTQAAAAAmI6iAQAAAMB0FA0AAAAApqNoAAAAADAd\n",
       "RQMAAACA6SgaAAAAAExH0QAAAABgOooGAAAAANNRNAAAAACYjqIBAAAAwHQUDQAAAACmo2gAAAAA\n",
       "MB1FAwAAAIDpKBoAAAAATEfRAAAAAGC6SyoaM2fOVFhYmPz8/BQREaGNGzde9JjXXntNbdq0ka+v\n",
       "rxo0aKCpU6f+4bAAAAAAKgfPi+0wf/58Pfzww5o1a5b69u2rt99+W8OHD9fu3bsVGhpa5jFTpkzR\n",
       "0qVL9c9//lPh4eHKzs5WSkqK6eEBAAAAVEwXLRozZszQxIkTNWnSJEnSG2+8oRUrVmjWrFl64YUX\n",
       "Su2/b98+vfXWW9qxY4dat25dMu/UqZOJsQEAAABUZBe8dKqwsFBxcXEaOnSoYT506FDFxMSUeczi\n",
       "xYvVrFkzLVu2TM2aNVNYWJjuuOMOZWRkmJcaAAAAQIV2wU80Tpw4IYfDoeDgYMM8KChIqampZR6T\n",
       "lJSkw4cPa8GCBfrwww8lSY899piuu+46bd68WTabrczjYmNjf09+VFKcb/fDOXdPnHf3wzl3P5xz\n",
       "99GyZcvL2v+il05dLqfTqYKCAn300Udq0aKFJOmjjz5S69atFRsbq+7du5v9RwIAAACoYC5YNOrW\n",
       "rSu73a60tDTDPC0tTSEhIWUeExISIk9Pz5KSIUktWrSQ3W7XkSNHzls0IiIiLjc7KqFf3vXgfLsP\n",
       "zrl74ry7H865++Gcu5/s7OzL2v+C92h4e3urW7duWrlypWEeHR2tyMjIMo/p27eviouLlZSUVDJL\n",
       "SkqSw+FQkyZNLiscAAAAgMrpoutoTJkyRXPnztXs2bO1Z88ePfTQQ0pNTdXkyZMlSVOnTtXgwYNL\n",
       "9h88eLC6du2qO++8U/Hx8dq2bZvuvPNO9erVi8YLAAAAuImL3qMxfvx4nTx5UtOnT1dKSorCw8O1\n",
       "bNmykjU0UlNTDZ9e2Gw2LVmyRA8++KCuuuoq+fn5aejQoZoxY8aV+yoAAAAAVCiXdDN4VFSUoqKi\n",
       "ytw2Z86cUrP69etrwYIFfywZAAAAgErropdOAQAAAMDlomgAAAAAMB1FAwAAAIDpKBoAAAAATEfR\n",
       "AAAAAGA6igYAAAAA01E0AAAAAJiOogEAAADAdBQNAAAAAKajaAAAAAAwHUUDAAAAgOkoGgAAAABM\n",
       "R9EAAAAAYDqKBgAAAADTUTQAAAAAmI6iAQAAAMB0FA0AAAAApqNoAAAAADAdRQMAAACA6SgaAAAA\n",
       "AExH0QAAAABgOooGAAAAANN5Wh0AAFA5FRUXKut0hjJzMpR5OkNZp9N1MiddWTkZyshMlY+Xv3Zm\n",
       "rFPtgHqqHRik2oH1VCvg3P/6ePlaHR8AcIVRNAAA5+V0OpSUslcpJw7/XCYySspEztmsCx+cn6mM\n",
       "00fL3FTNL/BcAQmop1qBQaoTGKSgWg3VomEHeXl6XYGvBABQ3igaAAADl8ulYyd+0tY9a/Vj4gbl\n",
       "5F6kUPwOuXk5ys3LUXL6QcPcz6eaurTso+5t+iusQVt52LjCFwAqK4oGAECSlHU6Q7F71yt23zql\n",
       "nDxiSYa8glzF7FypmJ0rVTswSBGt+6t7m/4Krt3IkjwAgN+PogEAbiyvIFfxBzZr6961Onh0l1xy\n",
       "XfKxNtlUo3pt1Q4I+tU9GOfuxzh6KEX5RbmqF1JbmTnpyjydrszTGcrMSdepMyfldDou+vqZOela\n",
       "ufVzrdz6uRoHtVBEm/7q2qqfAqvV/CNfMgCgnFA0AMDNOBzF2n04TrF712ln0lYVOQovuL+Pl6/a\n",
       "h0UoqFZD1QkMKrmhu2b1OvK0l30/RW7GuSIR0T6i1Dan06Hs3MyfC8i5m8lPnErRzkOxys3LKfP1\n",
       "jqQf0JH0A1q0YY7aNO6s7m0HKLxZT3l7+VzmVw8AKC8UDQBwE3kFZxUdu1Cbd0Wf9xf6X3jYPNSm\n",
       "SRd1bzNA4c16mPoLvYeHXbUCzn360fxXc4ejWHuPxGvr3rXacfCHMguQ0+XU7sNx2n04Tj5evopo\n",
       "3V/De92swGq1TMsHADAHRQMAqjiny6kfdq/RNzEf6fTZUxfct3FwS3Vv019dW/VVgH/5XqJkt3uq\n",
       "fViE2odFKK/grBIObtbWPWu1/+jOMi/pKijK16ad3yo2cb2G9Riv/p2vPe8nLACA8kfRAIAq7KeU\n",
       "fVq47j0dSdt/3n3qBAYrok1/RbTpr+BaDcsx3fn5+firZ7tB6tlukLJOn9CP+9Zr6961Zd6kXlCY\n",
       "p8UbP1DMzmiNvepOtQ8rfbkWAKD8UTQAoArKPpOprzd9qK1715a53d+nurq06nvuMbIhbWSz2co3\n",
       "4GWoFVBXgyPGanDEWB3L+Elb967Tj/vWKzs307Bfxqnjevfr6WrXpKuu7z+pwpQmAHBXFA0AqEKK\n",
       "iou0dtvX+nbr5yosyi+13cvurUHdrtegiOsr5ercDeuFqWG9MF3X51ZtTFiuZVvmKa8g17DP7sNx\n",
       "2vvxdvXvNFLDet4kP59qFqUFAPdG0QCAKsDlcmnnT1v11fr3dSI7tcx9OreI1Oh+t6tOYHA5pzOf\n",
       "3cOu/p2vVbfWV2np5k8Vs3OlXC5nyXan06E1275W7N51ujbyz+rZfhCL/wFAOaNoAEAll5qZrC/X\n",
       "zdbeI/Flbg+p01g39L9brULDyznZlVfdL1A3DZysvuHX6It17+ngsV2G7afzsjXvu7e1cccK3dD/\n",
       "bjVr0MaipADgfigaAFBJ5RWc1fIt87Q+YVmZC+D5+wZoZK8Jigy/RnYPuwUJy0/DemF68Ibp2rZ/\n",
       "kxZvmKusMycM25PTD+q1z/9PEa37a3S/21WjWm2LkgKA+6BoAEAldPzEIc1e+ooyTh0vtc1m81Df\n",
       "8GEa0etmVfMLtCCdNWw2m7q26qsOYd216scv9V3sV6XW4ojdt077jsTr9uGPVclPeACgIqFoAEAl\n",
       "s3XvWn323UwVFZde0K5lo3Dd0H+SGtRtWv7BKghvLx+N6DVBvdoN0qKNcxW/P8aw/XRett7+6lld\n",
       "G/lnDe52fYV+4hYAVGYUDQCoJIqKi/TVhve1MWF5qW21A+ppTL+J6tSiN784/6x2YJDuHPGE9h/d\n",
       "oYXrZuv4iUMl21wup77Z9KEOp+7TLUMe5MlUAHAF8AgOAKgEsk5n6I2Ffy2zZPRuP0RP3fqWOreM\n",
       "pGSUoWWjcD0x4V8a1vMm2WT8/yfh4Pf657zHdCzjkDXhAKAKo2gAQAW393C8Xvl0ig6nJhrmnnYv\n",
       "TRh8vyYM/ou8vXwsSlc5eHjYNaLXBN07+hn5+wYYtmVkp2jGgif0w541FqUDgKqJogEAFZTT5dS3\n",
       "P3yuWYueU27+acO2OoHBemT8y+rdfrBF6Sqndk276vEJ/1RoUHPDvKi4UB+vfF3zV7+jouIii9IB\n",
       "QNVC0QCACuhs/hn99+sXtHTzJ3LJZdjWvmmEHp/wL4UGNbMoXeVWJzBYD497UZEdhpbatmnHCr3+\n",
       "xVPKzEm3IBkAVC0UDQCoYJLTk/TqvEe161CsYW6TTSN736K7Rz0lf9/qFqWrGrw8vXXzoPt0y5AH\n",
       "5GX3Nmw7krZfr8x7VHsOb7MoHQBUDRQNAKhANu9apX8veFInc9IM82p+gYoa86yu6TFOHja+dZul\n",
       "Z7tBeuSml1S3Rn3D/Gz+ab2zaJqWfz9fTpfTonQAULnx0woAKoBiR5HmrXpb81a9pWKH8R6BJsEt\n",
       "9cSEf6lNk84WpavaGtVrpscm/FMdwrob5i65tHzLPP1n8XTlFeRalA4AKi+KBgBYrLCoQO9986I2\n",
       "74outa1fxxF68MYXVCugngXJ3Ie/T3Xddd1UXRd5q2y/+cRo9+E4vbnwGZ0+m21ROgConCgaAGCh\n",
       "swVnNHPR37X7cJxh7uXprVuveUTjrr5HXp5eFqVzLx42Dw3pfoPuG/OsqvvVMGw7mpH0803iGRal\n",
       "A4DKh6IBABbJyT2lNxc+o6TjewzzOjWC9ehNr6h7m/4WJXNvrRt30uMT/qUmwS0N8/SsY3r986lK\n",
       "yzpmUTIAqFwoGgBggcycDL3+xVM6lvGTYd6gblM9Mu4lNajb1JpgkCTVCqir+294Xm0aG++LyTpz\n",
       "Qq9//pSS05MsSgYAlQdFAwDKWVrmUb32+f8p49RxwzwspI0evHG6AqvVsigZfs3Hy1d3X/dXdW4R\n",
       "aZifycvWmwuf1sFjuyxKBgCVA0UDAMpRcvpBvfbFUzp15qRh3qZJF913/d/l78P6GBWJl6eX7hj+\n",
       "qHr9ZgX2/MKzmvnVc9r1U+x5jgQAUDQAoJwcOLZLbyx8Wrl5OYZ555aRuue6p+Tj5WtRMlyIh4dd\n",
       "Ewb9RQO7jjHMixyF+u+SF/Xjvg0WJQOAis3T6gAA4A52/RSr95e+oiJHoWHeu/0Q3TRwsjw87BYl\n",
       "w6Ww2Wwa3fd2+ftW15KYj0vmTqdDH66YobyCXPXtOMzChABQ8VA0AOAKi927Th9HvyGn02GYD+o2\n",
       "RqP63C6bzWZRMlwOm82mod1vlJ9PNX2x5j9yySXp3MJ+C9a8o7yCXA3pfoPFKQGg4qBoAMAVtCFh\n",
       "ueGX0l9cF3krv5RWUv06Dpe/TzV9tPJ1Q3n8JuYjnS04o1F9bqM8AoAoGgBwRbhcLkVv/UJLNn9i\n",
       "mNtk07ir7+Uym0quW+ur5OvtX+pyuO9+/Ep5BWc0/mouhwMAbgYHAJO5XC59E/NxqZLh4WHXbcOm\n",
       "UDKqiPZhEYq6/ln5evsb5jE7o/Xht6/J8ZtL5QDA3VA0AMBkK35YoFWxCw0zL7u37r52qrq17mdR\n",
       "KlwJLRq21wM3PK/qfjUM87jEDZq36i05XU6LkgGA9SgaAGCi1XGLtHzLPMPM19tf913/rNqHRViU\n",
       "CldSaFBzPTTuBdWqXtcw/2HPGn2x9r9yuVznORIAqrZLKhozZ85UWFiY/Pz8FBERoY0bN17Si+/f\n",
       "v18BAQEKCAj4QyEBoDLYmLBCizbMNcz8vP11/9hpat6wvTWhUC6CazXUQ+NeUO2Aeob5xoTl+nrT\n",
       "B5QNAG7pokVj/vz5evjhh/X0008rPj5ekZGRGj58uJKTky94XGFhoW6++Wb179+fp28AqPJ+2LNG\n",
       "n6951zDz9vLVvaP/psbBLSxKhfJUOzBIfxk7TYHVahnm3/24SCt+WGBRKgCwzkWLxowZMzRx4kRN\n",
       "mjRJrVu31htvvKGQkBDNmjXrgsc9+eST6ty5s8aNG8c7OQCqtPj9Mfok+k3DI2w97V6657qn1KxB\n",
       "GwuTobzVqxmiv1w/TdV8jZ/kL98yT6vjFlmUCgCsccGiUVhYqLi4OA0dOtQwHzp0qGJiYs573NKl\n",
       "S7V06VK9+eablAwAVdqun2L1wYoZcv3qpl+7h6cmjXxSrUI7WpgMVgmpE6r7rn9Ofr95GtWiDXO1\n",
       "MWGFRakAoPxdcB2NEydOyOFwKDg42DAPCgpSampqmcccP35c99xzjxYtWiR/f/8y9ylLbGzsJe+L\n",
       "yo/z7X6q4jlPPXVI3+35TA5nccnMJpv6thytvJNS7Mmq9zVfrqp43i/VgNbjFb3rExU7i0pmC9a8\n",
       "o2NHj6t5UNUtoe58zt0V59x9tGzZ8rL2N/2pU7feequioqLUvXt3s18aACqMjJyjWr1nvqFkSFJk\n",
       "y+vUpG5bi1KhIqkX2EgD294ku4fxPb2Y/d/o8Ik9FqUCgPJzwU806tatK7vdrrS0NMM8LS1NISEh\n",
       "ZR6zZs0arV+/Xs8995ykcwtXOZ1OeXl5adasWbrrrrvKPC4igsc+uoNf3vXgfLuPqnjOk9OT9PnC\n",
       "GYZ3qiVp3NX3ql/H4Ralqliq4nn/fSIU1ryp3lvyUkkpdcmljfsXq03rtlXqkcecc/fDOXc/2dnZ\n",
       "l7X/BT/R8Pb2Vrdu3bRy5UrDPDo6WpGRkWUes3PnTm3fvr3kn2nTpsnPz0/bt2/XjTfeeFnhAKCi\n",
       "STmZrJmL/q68wrOG+ei+d1AyUKb2YRG6bdgU2Wz/+5HrcBbr/aWvKDF5h4XJAODKuuilU1OmTNHc\n",
       "uXM1e/Zs7dmzRw899JBSU1M1efJkSdLUqVM1ePDgkv3btWtn+KdBgwby8PBQu3btVLNmzSv3lQDA\n",
       "FZZxKkVvf/U35eblGObDe96sQd3GWJQKlUGXlpG6ZcgDhlmRo1D/+eYf+illr0WpAODKuuClU5I0\n",
       "fvx4nTx5UtOnT1dKSorCw8O1bNkyhYaGSpJSU1OVlJR0wddgHQ0AlV3W6Qy9/eXflJObZZgP7DpG\n",
       "w3reZFEqVCY92l6twqICLVjzTsmssChf7yyapvtvmK7QoGYWpgMA813SzeBRUVH66aeflJ+fr61b\n",
       "t6pv374l2+bMmXPBonHHHXcoJyfnvNsBoKI7ffaU3v7yWWWezjDM+4QP0+i+t/NmCi5Z347DNKbf\n",
       "HYZZXuFZzVz0d6VmXnghXACobEx/6hQAVCUFhXl6d/F0pZ86bph3bzNA466+h5KByzaw6xgN73mz\n",
       "YZabl6NZi6Yp+0ymRakAwHwUDQA4D4ejWO8ve1VH0g8Y5p1bROpPQx6Qh41vofh9hvW8SQO7Gu/r\n",
       "yTqdoVmLpymvINeiVABgLn5KAkAZXC6XPvtupvYcjjPM2zTurNuGPSK7h92iZKgKbDabRve9XZEd\n",
       "hhrmx08c0ntLXlJRcdF5jgSAyoOiAQBlWLr5U32/Z7VhFhrUXHeOfFKedi+LUqEqsdlsGnf1verQ\n",
       "rIdhvv/oDn0S/YacLqdFyQDAHBQNAPiNDQnLtXLr54ZZncBg3TvqGfl6+1mUClWR3cOuO4Y9qqb1\n",
       "WxvmcYkb9PXGDyxKBQDmoGgAwK8kHNyiL9b+1zCr5heoqDHPKrAaawHBfN5ePrpn1F8VVLOBYb46\n",
       "brHWxH1tUSoA+OMoGgDws6Tje/TB8hly/eqSFW9PH00e9bSCajW4wJHAH1P9lzLrX8sw/2rD+4pL\n",
       "3GhRKgD4YygaACApNTNZ//n6HypyFJbMPGwemjjicTWp38rCZHAXdWoE697Rz8jHy9cw/2jla0pM\n",
       "3mFRKgD4/SgaANxe9plMzVo0TWcLzhjm4wdGqX1YhEWp4I5Cg5pp0sj/k8evnmrmcBTrvSUv6viJ\n",
       "Q9YFA4DfgaIBwK3lFZzVO4unKes3q34P7zVBkR2GWJQK7qxNk866ZcgDhll+4VnNWjRNmTkZ5zkK\n",
       "ACoeigYAt1XsKNLspS/p2G/eKY7sMETDeoy3JhSgcyvPj+pzm2GWnZupdxZPU27+aYtSAcDloWgA\n",
       "cEtOl1OfRL+pxOQEw7xDWHeNu3qybDabRcmAcwZ1u15XdRppmKVmJuu/37ygouLC8xwFABUHRQOA\n",
       "W/pm04f6cd96w6xJ/Va6Y/hjrPqNCsFms2nsVXeqc4tIwzzp+B59+O2/5XQ6LEoGAJeGogHA7azd\n",
       "9o2++3GRYRZUs4HuHfW0vL18LEoFlObhYdet1zys5g3aGebbD2zWl+tny+VyWZQMAC6OogHArWw/\n",
       "sEVfrX/fMAvwr6moMc+qul+gRamA8/Py9Nbd1z2l+rVDDfP125dpzTYW9ANQcVE0ALiNQ6mJ+nDF\n",
       "DLn0v3eBfbx8NXn0M6pTI9jCZMCF+ftWV9SYv6lG9TqG+eINcxW/P8aiVABwYRQNAG7hRHZqmQvy\n",
       "3TnySYUGNbcwGXBpagXUU9ToZ+Tr7V8yc8mlj759TT+l7LUwGQCUjaIBoMrLzT+tdxY/rzN52Yb5\n",
       "TQOj1LZJF4tSAZevQd2mmjTyScOCfkWOQv3nmxeUcSrFwmQAUBpFA0CVVlRcpPe+eVHpWccM86Hd\n",
       "x6k3C/KhEmrduJNuHnifYZabl6N3Fj+v3Lwci1IBQGkUDQBVltPl1KfRb+jg8d2GebfWV2lk7z9Z\n",
       "lAr443q1H6RrfrOoZMap4/rvkhdZYwNAhUHRAFBlLdv8qX5M3GCYNW/YXn8a/AAL8qHSG9FrgiLa\n",
       "9DfMko7v0SfRb8rpclqUCgD+h6IBoEqK2RmtlVu/MMyCajXUXdf+n7w8vSxKBZjHZrNpwqD71aJR\n",
       "B8M8LnGDlsR8YlEqAPgfigaAKmfP4W1asHqWYVbdr4Ymj35G1XwDLEoFmM/L00t3jfw/BddqZJiv\n",
       "il2oTTsqi5b9AAAgAElEQVS+tSgVAJxD0QBQpRzL+EnvL3vFcOmIl6e37h31V9WtUd/CZMCV4e9b\n",
       "XZNHP6MAvxqG+edr3tXuQ3EWpQIAigaAKuTUmZN65+vpKijMK5nZZNNt10xRk/qtLEwGXFl1agTr\n",
       "nlFPy8vTu2TmdDk1Z9krOpqRZGEyAO6MogGgSsgrOKt3Fz+v7DMnDfMxV01Upxa9LEoFlJ8m9Vvq\n",
       "9mGPyqb/PeigoChf7y6erqzTJyxMBsBdUTQAVHoOR7HmLH9Vx04cMsz7d75WV3cZZU0owAIdm/fU\n",
       "2P6TDLPs3Ey9+/V05RWctSgVAHdF0QBQqblcLn2+9l3tPbzNMO/QrIeu7zfRolSAdfp3vlYDOl9n\n",
       "mB0/cUhzlr8qh6PYolQA3BFFA0Cltir2S8XsjDbMGge10O3DpsjDw25RKsBaY/rdoY7Nexpmew9v\n",
       "0/w178jlclmUCoC7oWgAqLRi967TNzEfGWa1A+rpnlF/lY+Xr0WpAOt5eNjPPQQhuKVhvmXXKq3c\n",
       "+rlFqQC4G4oGgEpp/9Ed+iT6TcPMz9tf947+mwKr1bIoFVBxeHv56J5Rf1WdwGDDfOnmT/XDnjUW\n",
       "pQLgTigaACqdlJNH9N43L8rh/N/15na7p+66bqpC6oRamAyoWAL8a2ry6Gfk71PdMP901Vvad2S7\n",
       "RakAuAuKBoBKJTs3U+8sfl55hcYn6Nwy+AG1bBRuUSqg4gqu3Uh3X/eUPO1eJTOn06HZS1/W8ROH\n",
       "LUwGoKqjaACoNAoK835eEyDDML8u8lZFtOlvUSqg4mvesJ3+PPQhwyy/8KzeWTxNp36z9gwAmIWi\n",
       "AaBScDgdmrPs1VKrHPfpcI0GR4y1KBVQeXRt1Vej+95hmJ06c1LvLn5e+YV51oQCUKVRNABUeC6X\n",
       "S5+veUe7D8cZ5u2adtONV98jm812niMB/NrArqPVr+MIw+zYiUN6f+nLrLEBwHQUDQAVXnTswlJr\n",
       "ZTQKaqaJwx+TnbUygEtms9l0Q/9J6hDW3TDfeyRe81fPYo0NAKaiaACo0LbuXaclMR8bZrUD6mny\n",
       "qGfk4+1nUSqg8vLwsOv24Y+q8W/X2Nj9nb79YYFFqQBURRQNABVWYvIOffrbtTJ8qrFWBvAH+Xj5\n",
       "6p7rSq+xsWzLPH2/e7VFqQBUNRQNABVSyskjmr2kjLUyrmWtDMAMgdVqavKYv8nfN8Awn/fd26yx\n",
       "AcAUFA0AFc6F18roYFEqoOoJrtVQd1879TxrbByyLhiAKoGiAaBCyWetDKBcnX+NjeeVdfqERakA\n",
       "VAUUDQAVhsNRXPZaGeHDWCsDuIK6tuqrMf3uMMxOnTmpd7+erryCXGtCAaj0KBoAKgSny6lPVr2p\n",
       "Pb9ZK6N90wjdOOBu1soArrCru4zWVZ2Ma2wcP3FI//3mBRUVF1qUCkBlRtEAUCF8vfEDxe5dZ5iF\n",
       "BjXXHcMfZa0MoBzYbDaNvWqSOjTrYZgfOLZLH6yYIafTYVEyAJUVRQOA5b778SutjltsmNWpEax7\n",
       "Rz3NWhlAOfLwsOuOYY+qaUhrwzzh4BYtWPMuC/oBuCwUDQCW+n73ai3e+IFhFuBfU/eN+TtrZQAW\n",
       "8Pby0b2jnlb92sbHSMfsXKllW+ZZlApAZUTRAGCZnUlbNW/VW4aZj7efJo/+m+rVDLEoFYBqvgGK\n",
       "GvOsalWva5h/+8MCrd++1KJUACobigYASyQd36s5y1+V0+Usmdntnrr72qcUGtTMwmQAJKlWQF1F\n",
       "Xf9sqQX9Fq59T3GJGy1KBaAyoWgAKHcpJ4/oP19PNzzJxiabbr9milqFhluYDMCv1a8dqsmjn5G3\n",
       "p0/JzCWXPvr2NVYPB3BRFA0A5SozJ0MzFz2nswVnDPNxV9+rzi0jLUoF4Hya1m+lO0c+IY9fPf3N\n",
       "4SzWe0te1JG0AxYmA1DRUTQAlJszeTmauejvyj5z0jAf3vNm9e04zKJUAC6mXdNuumXIA4ZZQVG+\n",
       "3ln8vNKzjluUCkBFR9EAUC4KCvP07uLnlZ51zDDv23G4hvW8yaJUAC5V9zYDNKbfRMPsTF72z28e\n",
       "ZFqUCkBFRtEAcMU5nA7NXvaKDqftN8w7t4jUjf3vYtVvoJIY2HW0BnW73jDLzEnXrEXPqbA436JU\n",
       "ACoqigaAK8rlcilm/9fae3ibYd6qUbhuveYRw3XfACq+UX1uU8+2Aw2z4ycPa/We+Sp2FFmUCkBF\n",
       "RNEAcMW4XC7F/hStn07sMswbBTXTpGunysvTy6JkAH4vm82mmwf/Re3DIgzz9JxkbUhcJIfTYVEy\n",
       "ABUNRQPAFfPtDwu0J+UHw6xujfqaPOpv8vPxtygVgD/K7mHXxOGPq1lIW8M8OXOf5q16y7A+DgD3\n",
       "RdEAcEWsiv1Sy7bMM8wC/Wvpvuv/rsBqNS1KBcAs3l4+umfUXxVSp7Fh/sOeNVqw+h25XC6LkgGo\n",
       "KCgaAEy3dts3+nrTh4aZr7e/Jo95RnVr1LcoFQCz+ftWV9SYZ1UroJ5hHrNzpRaue4+yAbg5igYA\n",
       "U21MWKEv1882zDw9vDR59N/UqF4zi1IBuFJqVq+j+8dOk59XdcN8/falWrzxA8oG4MYoGgBMs3nX\n",
       "Ki1Y845hZvfw1MB2N6tZgzYWpQJwpdWrGaKhHf4sX69qhvnquEVauvlTi1IBsNolF42ZM2cqLCxM\n",
       "fn5+ioiI0MaNG8+779q1azV69Gg1aNBA1apVU6dOnTRnzhxTAgOomLbuXavPVr1tmHnavXR12/Gq\n",
       "X6OJRakAlJca/nU1pP0tquYbYJiv3Pq5Vnw/36JUAKx0SUVj/vz5evjhh/X0008rPj5ekZGRGj58\n",
       "uJKTk8vcf/PmzerUqZMWLlyoXbt2KSoqSvfcc4/mzZtX5v4AKre4xI36eOUbcul/l0jYPTw1aeST\n",
       "alCTy6UAd1GrWpDuu/45+fkYP9lYtmWeVsV+aVEqAFa5pKIxY8YMTZw4UZMmTVLr1q31xhtvKCQk\n",
       "RLNmzSpz/6lTp2ratGnq3bu3mjZtqsmTJ2vs2LFauHChqeEBWC/h4BZ9uGKGXL96nKWHh10TRzxe\n",
       "6jn7AKq+0KBmum/Ms/Lx9jPMv970odZs+9qiVACscNGiUVhYqLi4OA0dOtQwHzp0qGJiYi75D8rO\n",
       "zlbt2rUvPyGACmvXT7Gas+yfhmfm22weun3YFHVs3tPCZACs1KR+K0WNflbeXr6G+Vfr39eGhOUW\n",
       "pQJQ3jwvtsOJEyfkcDgUHBxsmAcFBSk1NfWS/pAlS5Zo9erVFywmsbGxl/RaqBo435Xf8ayDWr1n\n",
       "gZwu4yrAfVqOkiPbp9Q55py7J867+/n1OR/Qepy+2z1PDmdxyezzNe/qaPJRtQzuYkU8XAH8PXcf\n",
       "LVu2vKz9r/hTpzZt2qRbbrlFb775piIiuIwCqApSsw9pzd7PS5WMyBbXqlm9DhalAlDR1K/RRFe3\n",
       "HS8Pm90w33xgqQ6mJ1iUCkB5uegnGnXr1pXdbldaWpphnpaWppCQkAseu3HjRo0cOVLPP/+87r33\n",
       "3gvuSwlxD7+868H5rrySju/RZz98YXiHUpJuGhilPuHXlNqfc+6eOO/u5/znPELNmzfTe0teMnzf\n",
       "iDmwRC1btFLXVn3LMSXMxN9z95OdnX1Z+1/0Ew1vb29169ZNK1euNMyjo6MVGRl53uPWr1+vESNG\n",
       "6LnnntODDz54WaEAVEyHUxM1a/E0FRblG+Y39L+rzJIBAJLUPixCE0c8Lg+P/32y4XI59eGKGdp+\n",
       "YIuFyQBcSZd06dSUKVM0d+5czZ49W3v27NFDDz2k1NRUTZ48WdK5p0wNHjy4ZP+1a9dq+PDhioqK\n",
       "0oQJE5SamqrU1FRlZGRcma8CwBV38Nhuvf3V31VQmGeYj+57h/p3vtaiVAAqi47Ne+r2YVNks/3v\n",
       "Vw+ny6k5y19VXOL51+YCUHld9NIpSRo/frxOnjyp6dOnKyUlReHh4Vq2bJlCQ0MlSampqUpKSirZ\n",
       "/4MPPlB+fr5effVVvfrqqyXzpk2bGvYDUDnsPhSn2UtfUlFxoWE+svctGtRtjEWpAFQ2XVr2kcNR\n",
       "rI++fa1k3R2n06EPlv9L+YV5iuwwxOKEAMx0SUVDkqKiohQVFVXmtt+u+j1nzhxWAgeqiG37N+nD\n",
       "Ff8udU/GNT3G65oe4yxKBaCyimjTX8WOYs1b9VZJ2XDJpc++e1v5hbka2JU3L4Cq4pKLBgD3s3nX\n",
       "Kn323UzDYnySdG3knzUk4gaLUgGo7Hq1HyS73a5PVr5hWIdn0Ya5yivI1Yhef5LNZrMwIQAzUDQA\n",
       "lGlN3Nf6asP7pebjBtyjfp1GWJAIQFXSvc0A+Xr7a86yV1XsKCqZf/vD58oryNXY/nfJw3bFn8IP\n",
       "4AribzAAA5fLpWWb55UqGR42D916zcOUDACmCW/WQ5NHP1NqBfH125fpk5VvyOF0nOdIAJUBRQNA\n",
       "CafLqS/Xz9aKH+Yb5na7p+4c+aS6txlgTTAAVVar0I66f+w0+ftUN8y37l2rOcteKfUQCgCVB0UD\n",
       "gCTJ4XTo0+g3tS5+iWHu7eWryaOeUcfmPS1KBqCqa1q/lR688R8K9K9lmCcc/F7vfj291GO1AVQO\n",
       "FA0AKiou0pxlr+qHPWsMc3+f6rp/7DS1btzJomQA3EWDuk300LgXVDswyDBPTE7Q21/9Xbn5py1K\n",
       "BuD3omgAbq6gKF//+Wa6Eg4aV+cN8K+pB26Yrqb1W1mUDIC7qVczRA+Pe1HBtRsZ5odS9+nNL55W\n",
       "Tm6WRckA/B4UDcCNnc0/o7e/elb7jmw3zGsH1NPD415Uw3pNrQkGwG3VrF5HD934gkKDmhvmx08e\n",
       "1uufP6XMnHSLkgG4XBQNwE1l52bqzYVP61DKPsM8uFYjPTTuRdWrGWJRMgDurrpfoO4f+7yaN2xv\n",
       "mGdkp+jfn09Vyslki5IBuBwUDcANJacn6V+fPa5jJw4Z5o2CmunBG/+hWgF1rQkGAD/z8/FX1Ji/\n",
       "qV3TboZ59pmT+veCJ7X7UJxFyQBcKooG4Ga2H9is1z+fqlNnThrmzRu00wNjn1eAfw2LkgGAkben\n",
       "j+669v/UtVVfwzy/8Kze/Xq61sUvkcvlsigdgIthZXDATbhcLq3c+oWWbv6k1LZ2TbvpzhFPyNvL\n",
       "x4JkAHB+nnYv3XbNI/Lzqa5NO1aUzF0upxaue0+pJ5N144C7ZbfzKw1Q0fC3EnADRcWFmrfqbcXu\n",
       "W1dq24DO12l0vztk97BbkAwALs7Dw67xV9+roJoNtGjDHLn0v08xNu38VhmnjmviyCdUzTfAwpQA\n",
       "fotLp4AqLic3S28ufKZUyfDwsOumgVEa238SJQNAhWez2XR111G6Z9Rf5ePtZ9iWeHSHZnz2hNIy\n",
       "j1qUDkBZKBpAFXY049xN34dSjU+W8vcN0H1j/q4+4ddYlAwAfp/2YRGaMv5l1QkMNswzslM0Y/4T\n",
       "2ns43qJkAH6LogFUUQkHt+i1BVOVdeaEYR5cq5EevekVtQoNtygZAPwxIXUaa8pNr6hZg7aGeV7h\n",
       "Wb2zeJrWb19mUTIAv0bRAKoYl8ul6K0LNXvJyyosLjBsa9O4sx656SXWyABQ6QX419Bfrp+mnu0G\n",
       "GeZOl1NfrP2PFqx5Vw5HsUXpAEjcDA5UKUXFhfrsu5naundtqW1XdRqp66+6k/sxAFQZXp5e+tPg\n",
       "+1W/dqi+3viB4SbxjQnLlZ51THeOeEL+vtUtTAm4Lz7RAKqInNxTevPLZ0qVDA+bh8ZfPfnc4x8p\n",
       "GQCqGJvNpkHdxuiu66bKx8vXsC0xOUEz5j+h9KxjFqUD3BtFA6gC9h/dqVc/e1SHUow3ffv5VFPU\n",
       "mGfVt+Mwi5IBQPkIb9ZDj4x/SbUD6hnm6aeO65+fPa64xI0WJQPcF0UDqMQcToeWbv5Uby18Rtm/\n",
       "Wek7qGYDPXrTK2rduJNF6QCgfDWo21SP3vyqwkLaGOb5hWc1d/k/9emqt1RQlG9ROsD9UDSASioz\n",
       "J11vfPFXffvDAsN1yZLUKrSjptz0ioJqNbQoHQBYI8C/pu4f+7x6tL261LYtu1bp1XmP6mhGkgXJ\n",
       "APdD0QAqoW37N+nlTx7WTyl7S20b1O16RY3+Gzc/AnBbXp5eumXIg7qh/12y243PvUnPOqZ/zX9C\n",
       "6+KXyOVynecVAJiBp04BlUhBUb6+XDdbm3dFl9oW6F9Lfx76kNo06WxBMgCoWGw2m/p3vlbNG7bT\n",
       "3OX/MtwQ7nAUa+G697T3cLz+NOQBBfjXsDApUHXxiQZQSRzL+En/nPdYmSWjXZOuevKWf1MyAOA3\n",
       "GtVrpscn/Eu92g8utW3XoVi9/OnD2ndkuwXJgKqPTzSACs7lcmn99qVatHFuqcWn7B6eGtX3NvXv\n",
       "fK08bLxvAABl8fHy1Z8G3682jTvrs+9mKr/wbMm2nNwszfzq7xocMVYjek0odakVgN+Pv01ABXYm\n",
       "L0efRr+pnT9tLbUtqGYD3T78UYUGNbcgGQBUPl1b9VWT4Jb6YMUMHUr93+PAXXIpOnahEo/u0O3D\n",
       "pqhujfoWpgSqDt4CBSqoxOQEvfTJQ2WWjJ7tBunxCf+iZADAZapTI1gP3fgPDe0+TjbZDNsOpybq\n",
       "5U8f0Y/71luUDqha+EQDqGDOFpzRkphPtClhRanH1vp6++umgVHq1rqfRekAoPKz2z11beQtahXa\n",
       "UR99+29l52aWbCsozNMHK2Zo+4EtGtt/kmpWr2NhUqByo2gAFYTL5VJc4kZ9tf595ZzNKrW9af3W\n",
       "un3YFNWpEWxBOgCoelqFhuvJW17Tp6ve0s6kHwzb4g/EaM+Rbbq29y3q13G4PDzsFqUEKi+KBlAB\n",
       "ZJxK0YI175T55BObbBrS/QYN73kzNykCgMmq+wXq7munakPCci3aMEfFjqKSbQWFeVq47j19v2e1\n",
       "bh54nxoHt7AwKVD58FsLYKGi4iKt+vFLRW/9wvDD7Rd1a9TXzYP+olah4RakAwD3YLPZdFWnEWre\n",
       "oJ3mrXpLR9IPGLYfTU/Svz57XP06DdfI3rfIz6eaRUmByoWiAVgkMTlBC1a/o/RTx0tts9s9NaTb\n",
       "DRrS/QZ5eXpbkA4A3E/Dek015aaXtXHHt1oS87HhMbguubR++zLF79+ssf0nqUvLPrLZbBd4NQAU\n",
       "DaCcnT57Sl9tmKPYvevK3N6qUbjGDZys4FoNyzkZAMDDw66rOo1Qp+a99NWG9xWXuNGwPedsluYu\n",
       "/6e27P5O4wbco3o1QyxKClR8FA2gnDhdTm3eGa2vN32ovILcUtur+9XQ9VdNVETr/rxLBgAWq1G9\n",
       "tu4Y/ph6thukBWve0cnsNMP2vYe36cWPH9Q1PcZpYNfr5eXpZVFSoOKiaADlIDk9SZ+vfVeHUvaV\n",
       "ub1Ph2t0XZ9b5e9bvZyTAQAupG2TLpr65zcUvXWhVsV+KYezuGRbsaNISzd/qq1712ncgHvUunEn\n",
       "C5MCFQ9FA7iCUjOTtWzLPMXvjylze4M6TXTToCiFhbQp52QAgEvl7emjkb3/pIjWV2n+mnd04OhO\n",
       "w/b0rGN6+6tn1apRuEZG3sL3dOBnFA3gCsg4laLl33+mH/dtkMvlLLXd29NHI3pPUP9O1/LIWgCo\n",
       "JIJrN9IDY5/X1r1rtWjDXJ3JyzZsTzy6Q4kL/k/tmnbTiF4TeBwu3B6/4QAmyszJ0Lc/LND3u7+T\n",
       "s4yCIUnhzXrohv53q3ZgvXJOBwD4o2w2m3q0vVrtwyL0zaYPFbMzutQ+uw/9qN2HflTH5r00otcE\n",
       "NajbxIKkgPUoGoAJss9kauXWLxSza6UcjuIy92lUr5mujbxF7Zp2K+d0AACzVfMN0M2D/qJe7Ydo\n",
       "acwn2pdcesHVhINbtOPg9+raqq+G97pZQTxNEG6GogH8AafPntKq2C+1MWGFihyFZe4TUqexRvSa\n",
       "oI7Ne/E0KQCoYprWb6W/jH1O+4/u0NKYT5WUssew3SWXfkzcoLj9m9SjzQAN63mT6tQItigtUL4o\n",
       "GsDvcDb/jFbHLdLa+CUqLMovc596NRtoRK+b1aVlH3l42Ms5IQCgPLVsFK6Hxr2gvUfitTTmk1Kr\n",
       "i7tcTn2/Z7W27lun3u2HaGj3G1UroK5FaYHyQdEALkN61jFtSFiu73evNqwY+2u1A+ppWM+b1b3t\n",
       "ANkpGADgNmw2m9o26aI2jTtr509btXTzpzp+4pBhH6fToU07Vuj73d+pW6t+6tdpBDeNo8qiaAAX\n",
       "4XQ6tOvQj9qwfZn2Hok/7341qtXW0B7j1Lv9YHnaWbgJANyVzWZTeLMeah8Wofj9MVq2ZZ7Ss44Z\n",
       "9il2FOn7Pav1/Z7ValK/lfp1HK4uLfvIy9PbotSA+SgawHmcycvR5l2rtClhuTJPZ5x3vwC/Ghrc\n",
       "/Qb1Cb9G3p4+5ZgQAFCRedg81LVVX3Vq0Vs/7luv5Vs+08mctFL7HU5N1OHURH21YY4i2w9Rn/Bh\n",
       "PJkQVQJFA/iNw6n7tSFhmeISN6rYUXTe/ar71dDVXUbpqk4j5OPtV44JAQCVid3Drh5tr1a3Vv30\n",
       "/Z7VWrn1C2XmpJfaLzcvR9GxC7Xqx68U3qy7+nUcoVahHXmQCCotigYgqai4UNv2b9KG7ct0OG3/\n",
       "BfdtWr+1+nUaoc4tIuXlySVSAIBLY7d7KrLDUPVqN+jcJbkJy7X38LZS+7lcTiUc/F4JB79XcK1G\n",
       "6ttxmHq0HSg/H38LUgO/H0UDbsvpcupwaqK2JW7S1n3rlJuXc959veze6tq6n/p1HM5NewCAP8TD\n",
       "w67wZj0U3qyH0rOOaWPCuZvD88p4yEha1lEtXPeevon5WF1b9VXXln3VMjSch42gUqBowK24XC4d\n",
       "Sk1U/P5Nit8fo6wzJy64f53AYPXtOFy92g1UNb/AckoJAHAXQbUaamz/SRoZeYti967ThoTlpZ5U\n",
       "JUmFRfnasmuVtuxapWq+AerUope6tOyrFo06UDpQYVE0UOW5XC4dSduvbfs3adv+GGVd4MbuX7Rt\n",
       "0lVXdRqhtk26sAYGAOCK8/HyVZ/waxTZYaiSju/WhoTlij+wWU6no9S+ufmnFbMzWjE7o1XNL1Cd\n",
       "m/dWl1Z91KJhe35moUKhaKBKcrlcSk4/qG37N2rb/pgyb7r7LT+faurZbpD6hg9TUK0G5ZASAAAj\n",
       "m82m5g3bq3nD9srOzVTMjpXatPNb5eRmlbl/bl6ONu38Vpt2fqsAvxrq1OJc6WjeoB2lA5ajaKDK\n",
       "KCwuUNKxPdqXHK/4/ZvLfITgb3l7+qh9WIS6tOyjdk27yduLx9MCACqGGtVqa3ivmzW0+41KPLpD\n",
       "2xI3KuHg9zpbcKbM/U/nZWvjjhXauGOFAvxrqlPzXmrbtKtaNGwvP59q5ZweoGigEnM4HTqSdkCJ\n",
       "yQlKTE5QUsoeORzFFz3Oy9Nb7ZtGqEurc+XCx8u3HNICAPD72O2eatuki9o26aLxAycrMTlB2xI3\n",
       "KeHgljJvIJek02dPlZQOm81DjYNbqHVoR7UK7aSwkNYsDIhyQdFApeFyuZSamazE5ATtS07QgaM7\n",
       "lX+eb7C/5WX3VruwburSso/aN+3GuhcAgErJ0+6ldk27qV3TbrrJEaV9R7Zr2/5N2nHw+/OWDtfP\n",
       "T1k8nJqolVu/kJfdW80atFWrxp3UOrSjGtUL4zIrXBEUDVRYTpdTJ06lKOn43pJPLXLOln2Nall+\n",
       "+WbcpWUfdQiLoFwAAKoUT7uX2odFqH1YhIqKi7TvSPy50pH0wwXfiCtyFGpf8nbtS96ubyT5+1RX\n",
       "y0Yd1Cq0o5o1aKf6dUJ5khVMQdFAheByuXQiO1VH0g4oOf2gjqQf0NH0pEv+xOIXdQKD1Sq0o1o3\n",
       "7qR2TbvJl3IBAHADXp5e6tCsuzo0615SOvYlb1dicoJSTh654LFnC85o+8Et2n5wy8+v5a2G9cLU\n",
       "OKi5QoNaqHFwCwXXasinHrhsFA2Uu19KRXL6wXPFIu2AkjOSlFeQe9mvVd2vhlqFhqtVaEe1Cu2o\n",
       "ujXqX4HEAABUHr8uHZKUnZupxOQd564OOLL9omtIFRUX6lDKPh1K2Vcy8/b0UaN6zRQa3FyhQc3V\n",
       "OLiFnC6nPGweV/RrQeVG0cAV43Q6lHX6hNKyjin9538OHNmrzNxUFcbk/67X9PbyVYuG7c99ahHa\n",
       "USF1m/BNDgCAC6hRrba6t+mv7m36y+VyKeNUSsmnHfuP7tTZ/NMXfY3C4gIlpexRUsqekpmnh7dq\n",
       "Vw/W/lPfK6hWQwXVaqDgWg1VJzBYdju/YoKiAROcLTij9KzjJWXil2KRcSpFxY6iP/Tafj7VFBrU\n",
       "XM0atFXr0E5qUr+lPO1eJiUHAMC92Gw2BdVqoKBaDdSv43A5nQ4dzfhJickJOnhst46kH9Dps6cu\n",
       "6bWKnYVKz0lW+q5kw9zDw666NeorqFZDBddqoKCaDX8uIg1V3S9QNpvtSnxpqIAoGrggp9Oh7Nws\n",
       "nTpzQlmnT+jUmRM6dfqkss6c0KnTJ5SZk67Tedmm/Fl+3v4KDWr+88ey564JrRMYzDckAACuEA8P\n",
       "uxoHn/uZOzhirFwul7JzM3++Z/KAktMO6kj6/7d37zFRXXkcwL93nswwMLxEFFGkq6VMKWFFtqC1\n",
       "3Vab2hJi04jSkChtah/YUIjpg4IhEaG1iTY2QAw1QB/GatKQJktIyRZtXTRiS1oX0FZp7bY6sFh5\n",
       "MzPM3Lt/DEwZRW23c+dS+H6SyZ175hzmSybo/O49596LGP4d/9eLostz8PHf171m1JsQZo5EqCkC\n",
       "IaYIhARFINQUjtAg93NzYBgPKM4iLDTmKIfTjuHRQQyPDWB47Nft4MgvuDbU5ykkBkeuQZREn7+/\n",
       "XhvgmeMZE/kXxETegYiQKE6DIiIiUpAgCAgxhSPEFI577vgbAPfaymtDffhP70X8p/eC58ItI79h\n",
       "ytX1Ru3DGO0dxk+93dO/PwQEGUM8BUhIUARCTOEwGYJhMpi9tjptAA9GznC/qdCoqqrCW2+9BavV\n",
       "CovFgrfffhurV6++af+zZ89i+/btaGtrQ1hYGJ599lmUlJT4LDS5iZIIu8MGm2MEY/ZR2Bzux+Tz\n",
       "UWcAgB8AAAsCSURBVPsIRiYLidEpBYVtCI7x/2+NxO8VGBDkOV0aGRqNoatjMBsi8Pf71rGoICIi\n",
       "+hMQBAFhwfMQFjwPSX+5F4C7+Dj+r3+if/S/CI4wes5g9F67/LsuRX89CRIGR69hcPQafuz57pZ9\n",
       "tWodTIZgBBqCrytEgmEIMMGgMyJAZ4RBb0SALtC91RsRoDXwClp+cttC46OPPsJLL72E6upqrF69\n",
       "GpWVlVi/fj06OzsRExNzQ//BwUGsW7cODzzwAM6cOYOuri7k5uYiMDAQhYWFsvwSM5EkSXCJTjhd\n",
       "Tjhd4xh3OuB0jXv2nS4HHON2OJz2KVsbHE4HHOM2jHu1u1+zjY/BZh/FmGMUNvsIbI4xSJCU/lWh\n",
       "VmkQERKF+aHRXvMw54cuRKAh2KvvmTNnAIBFBhER0Z+YIAgwBYTAFBCClL+meL02Zh9xr93svzyl\n",
       "APkZvf2XMe50+CzDuMuBa8N9t72K1nT0OgMMOiMM+kDodQYE6IzQa/TQaQOg0+ih07ofWo0eem3A\n",
       "xNa9r5vop9VooVFPPjTQqHVe+zzb8hsKjb179yI3NxdPP/00AGD//v1oampCdXU1ysvLb+j/4Ycf\n",
       "wmazob6+Hnq9HgkJCTh37hz27t17y0Lj6wsnIUkSJEiQJPeXZ0kSJ9rcz91t0sRD9PQVJdHTV5wc\n",
       "M9lnok2URIiiC5IkQhRFrzZREiFd1+YSXXCJTq/nLtHl/ZprymueAmIc4xPb2SLQEOyeSxkU4dmG\n",
       "TMynnNznjX2IiIgIcF/IZUnUMiyJWubVLkoiBoZ/+XXN5+T6z6E+XBu+iv6hPgyN9vvlIKrdMQa7\n",
       "Ywz9w1dlew+1WgOtp/jQQKPWQq3SQKVSQa3SQK1Su/fVaqgFNdQqNVTqKe0qFdSCGsKUrUqYeKhU\n",
       "UAlqqFQqCFPaJp8LggqCIEAQhIl9AQKEKe3ufjqtHn9dfvNZSn/ULQsNh8OBr776Ci+//LJX+8MP\n",
       "P4zW1tZpx5w8eRL33Xcf9Hq9V/+SkhJcunQJS5YsmXbcwX+8+Xuz0x+gUqmnne8YZAxxL8gyRUxs\n",
       "w6HV6JSOS0RERH9yKkHlPkgZFHHTPk7XOAZGfnEXHxMFyODILxgZG7phXelMP6jrcrkPRM9kZlO4\n",
       "coVGX18fXC4X5s+f79UeGRkJq9U67Rir1YrFixd7tU2Ot1qtNy00dm2t/82hyX9GR8YAjPns5y1b\n",
       "5j66MTDgmytV0czHz3xu4uc+9/Azn3vk+sw1CECEaREiTIt8+nNpenL+zfp8ojznoxERERER0S0L\n",
       "jYiICKjVavT09Hi19/T0YMGCBdOOiYqKuuFsx+T4qKioP5KViIiIiIj+JG45dUqn02HFihX49NNP\n",
       "8cQTT3jam5ubsXHjxmnHpKWl4ZVXXoHdbves02hubkZ0dPQN06bMZvMfzU9ERERERDPQbadOFRYW\n",
       "oq6uDgcPHkRXVxfy8/NhtVrx3HPPAQBee+01rF271tP/ySefhNFoxNatW9HR0YGPP/4Yb7755py6\n",
       "tC0RERER0Vx328vbZmVl4erVqygrK8OVK1eQmJiIxsZGzz00rFYrurt/vbtjcHAwmpubkZeXh5SU\n",
       "FISFhWHHjh0oKCiQ77cgIiIiIqIZRZAmb1pBRERERETkI36/PXNFRQVWrlwJs9mMyMhIZGZmoqOj\n",
       "w98xyM8qKyuRlJQEs9kMs9mM9PR0NDY2Kh2L/KiiogIqlQovvvii0lFIJqWlpe6bSE15LFy4UOlY\n",
       "JLMrV65gy5YtiIyMhMFggMViweeff650LJJRbGzsDX/rKpUKGRkZSkcjmTidThQVFSEuLg4GgwFx\n",
       "cXEoKSmBy+W65bjbTp3ytePHj2P79u1YuXIlRFHEzp07sXbtWnR2diI0NNTfcchPYmJisGfPHixb\n",
       "tgyiKKKurg4bNmxAW1sbkpKSlI5HMjt16hRqampwzz338BLYs1x8fDyOHTvm2Ver1cqFIdn19/dj\n",
       "1apVWLNmDRobGzFv3jx0d3cjMjJS6Wgkoy+//NLrC+bly5exYsUKbNq0ScFUJKfy8nIcOHAA7733\n",
       "HhITE/H1119j69at0Ov1KC4uvuk4vxcaTU1NXvvvv/8+zGYzWltb8dhjj/k7DvlJZmam135ZWRmq\n",
       "q6tx+vRpFhqz3MDAAHJyclBbW4vS0lKl45DM1Go1v2TOIXv27EF0dDTq6uo8bTe7MS/NHuHh4V77\n",
       "NTU1MJvNyMrKUigRya2trQ2ZmZme7+qLFy9GRkYGTp8+fctxfp86db3BwUGIosizGXOIy+XC4cOH\n",
       "YbPZsGbNGqXjkMy2bduGjRs34v777weXhM1+3d3diI6ORlxcHLKzs/H9998rHYlk1NDQgNTUVGza\n",
       "tAnz589HcnIyKisrlY5FfiRJEg4ePIicnBzPbQ1o9lm/fj0+++wznD9/HgDQ2dmJlpYWPProo7cc\n",
       "5/czGtfLz89HcnIy0tLSlI5CMjt79izS0tJgt9thMBhw5MgR3HnnnUrHIhnV1NSgu7sbhw4dAgBO\n",
       "m5rl7r33XtTX1yM+Ph49PT0oKytDeno6Ojo6EBYWpnQ8kkF3dzeqqqpQWFiIoqIitLe3e9Zh5eXl\n",
       "KZyO/KG5uRk//PADnnnmGaWjkIxeeOEF/PTTT7jrrrug0WjgdDpRXFzsud3FzShaaBQWFqK1tRUn\n",
       "TpzgF5A5ID4+Ht988w0GBgZw9OhRbN68GS0tLUhJSVE6Gsng/PnzeP3113HixAnPPH1JknhWYxZ7\n",
       "5JFHPM/vvvtupKWlYenSpaivr+clzmcpURSRmpqK3bt3AwCSkpLw3XffobKykoXGHFFTU4PU1FQk\n",
       "JiYqHYVktH//ftTW1uLw4cOwWCxob29Hfn4+YmNj8dRTT910nGKFRkFBAY4cOYKWlhbExsYqFYP8\n",
       "SKvVIi4uDgCQnJyMtrY2VFZWora2VuFkJIeTJ0+ir68PFovF0+ZyufDFF1/gwIEDGBkZgVarVTAh\n",
       "yc1oNMJiseDChQtKRyGZLFy4EAkJCV5t8fHx+PHHHxVKRP7U29uLTz75BFVVVUpHIZnt3r0bxcXF\n",
       "nnU4FosFly5dQkVFxcwrNPLz83H06FG0tLRg+fLlSkSgGcDlckEURaVjkEwef/xxpKamevYlSUJu\n",
       "bi6WL1+OoqIiFhlzgM1mQ1dXFx588EGlo5BMVq1ahXPnznm1ffvttzyAOEfU1dUhICAA2dnZSkch\n",
       "mUmSBJXKe2m3SqW67SwFvxcaeXl5+OCDD9DQ0ACz2Qyr1QoACAoKQmBgoL/jkJ+8+uqryMjIwKJF\n",
       "izA0NIRDhw7h+PHjN1yFjGaPyXumTGU0GhEaGnrDEVCaHXbs2IHMzEzExMSgt7cXu3btwtjYGLZs\n",
       "2aJ0NJJJQUEB0tPTUV5ejqysLLS3t+Odd95BRUWF0tFIZpIk4d1338XmzZthNBqVjkMy27BhA954\n",
       "4w0sXboUCQkJaG9vx759+27777vfC43q6moIgoCHHnrIq720tBQ7d+70dxzyk56eHuTk5MBqtcJs\n",
       "NiMpKQlNTU1Yt26d0tHIjwRB4HqsWeznn39GdnY2+vr6MG/ePKSlpeHUqVOIiYlROhrJJCUlBQ0N\n",
       "DSgqKsKuXbuwZMkSlJWV4fnnn1c6Gsns2LFjuHjxoudiHzS77du3D8HBwcjLy0NPTw8WLFiAbdu2\n",
       "3fa7uyBxZSYREREREfmY4vfRICIiIiKi2YeFBhERERER+RwLDSIiIiIi8jkWGkRERERE5HMsNIiI\n",
       "iIiIyOdYaBARERERkc+x0CAiIiIiIp9joUFERERERD73Px0L4HlryPN+AAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f480928b6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from IPython.html.widgets import interact, interactive, fixed\n",
    "import IPython.html.widgets as widgets\n",
    "\n",
    "def plt_g(mu,variance):\n",
    "    xs = np.arange(2, 8, 0.1)\n",
    "    ys = gaussian (xs, mu, variance)\n",
    "    plt.plot(xs, ys)\n",
    "    plt.ylim((0, 1))\n",
    "    plt.show()\n",
    "\n",
    "interact (plt_g, mu=(0, 10), \n",
    "          variance=widgets.FloatSliderWidget(value=0.6, min=0.2, max=4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if you are reading this in an IPython Notebook, here is an animation of a Gaussian. First, the mean is being shifted to the right. Then the mean is centered at $\\mu=5$ and the variance is modified.\n",
    "\n",
    "<img src='animations/04_gaussian_animate.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting Exponentials (Optional)\n",
    "\n",
    "Where does the shape of the Gaussian come from? Recall the equation for the Gaussian:\n",
    "\n",
    "$$ f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 }$$\n",
    "\n",
    "$\\mu$ and $\\sigma$ are constants, so a simplified form of this equation is\n",
    "\n",
    "$$ \n",
    "f(x, \\mu, \\sigma) = c_1 * e^{-c_2{(x-\\mu)^2} }\n",
    "$$\n",
    "\n",
    "Let's just simplify it further by assuming the constants are one(not true for Gaussians, but the general shape will be the same) and the mean is zero.\n",
    "\n",
    "$$ \n",
    "f(x)=e^{-x^2}\n",
    "$$\n",
    "\n",
    "Raising a value to a negative power is the same as the reciprocal of the value raised to a positive power. I.e.\n",
    "\n",
    "$$e^{-x^2} = \\frac{1}{e^{x^2}}$$\n",
    "\n",
    "\n",
    "Let's plot this in stages. Here is $e^{x^2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAy4AAAGaCAYAAADpdxfhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xt0VfWd///XPrmSCwkJOQkkCqEGiahUQSFxhCLhYgUj\n",
       "TqdoNKjFwrQ0I2XNSsX6FaqIxXEwUtQFtAiFXwb1W8Y6rQMpxSqQWLmqlZtyEQPkJIQQCIaQy+f3\n",
       "B1+27gRIIgfOSc7zsRZr+fnszz7nvfNZS/Lisz97W8YYIwAAAADwYy5fFwAAAAAArSG4AAAAAPB7\n",
       "BBcAAAAAfo/gAgAAAMDvEVwAAAAA+D2CCwAAAAC/R3ABAFxRI0eOVN++fdXU1OTrUtqlqalJ/fv3\n",
       "17Bhw3xdCgAEJIILAOCKeeedd/TXv/5VM2fOlMvl3b+CFi9eLJfLJZfLpV/96letjt+4caMef/xx\n",
       "DR48WImJiQoLC1OvXr2Um5urjz/+uMV4l8ulWbNmaf369Xrrrbe8WjsAoHUWL6AEAFwpN910k6qq\n",
       "qrR//35ZluW1z12+fLkefvhhdevWTVFRUTp48KCee+45/eIXv7jgOUlJSTp69KiGDBmiQYMGKTw8\n",
       "XFu2bNFf//pXBQcH680331R2dnaL89LS0hQWFqZ//OMfXqsfANA6VlwAAFdEcXGxPvroI+Xk5Hg1\n",
       "tLzxxht65JFHlJKSovXr12vjxo3q37+/ZsyYoYKCggueN336dB08eFAbNmxQQUGBfv3rX+svf/mL\n",
       "li1bpoaGBv34xz9WfX19i/MeeOAB7dixQ+vXr/faNQAAWkdwAYBObOvWrbrvvvvUs2dPhYWFqWfP\n",
       "npo4caL27t1rj5k2bZpcLpf+7d/+rcX5r7/+ulwul2677TY1NDRIkg4cOCCXy6Xhw4fr0KFDeuCB\n",
       "B5SQkKCIiAjdcssteuONN85by+9+9ztJ0n333efoP378uFJTUxUWFqYPP/zQccwYo7vuuksul0uv\n",
       "vPJKi89866239MADDyg9PV3FxcVKT09XcnKy1q9fr9tuu03Tp0/Xq6++et568vPz1bNnzxb9ubm5\n",
       "uuaaa1RZWXneVZVz9Z+7HgDAFWIAAJ3SihUrTHBwsImKijI5OTnmF7/4hbn33ntNcHCwiY2NNdu3\n",
       "bzfGGHPmzBlzyy23GMuyzH//93/b53/++eema9euJj4+3hw8eNDu379/v7EsywwYMMD07t3b3Hzz\n",
       "zebxxx83kydPNrGxscayLPPiiy+2qOeqq64yMTEx563173//uwkNDTW9e/c2VVVVdv/zzz9vLMsy\n",
       "P/jBD1qc8+c//9mEhYWZf/qnf3Kcc05tba25++67jcvlMr/73e/a/oMzxlx33XXGsizz8ccfn/d4\n",
       "fHy8SU5ObtdnAgAuDcEFADqhzz77zISFhZlrrrnGHD582HHsb3/7mwkODjYDBw60+/bt22diY2NN\n",
       "t27dzIEDB0xdXZ0ZOHCgcblc5o9//KPj/HPBxbIsc9999zmO7d2718TGxpqwsDDzxRdf2P0HDhww\n",
       "lmWZESNGXLDmefPmGcuyzPjx440xxnzwwQcmJCTE9OnTx1RXVzvG1tXVmblz55rnn3/enD59+oKf\n",
       "2djYaF566SUze/Zsc/z48QuO+6aSkhJjWZa5+uqrTVNT03nHjBkzxliWZT777LM2fSYA4NIRXACg\n",
       "E5o+fbqxLMv8z//8z3mPjx8/3liWZXbs2GH3/eEPfzCWZZnBgwebqVOnGsuyzLRp01qcey64hISE\n",
       "mAMHDrQ4/sQTTxjLssyzzz5r961bt85YlmUeeuihi9Z99913G8uyzNNPP2169+5twsLCzIcfftjG\n",
       "q750FRUV5pprrjEul8v84Q9/uOC4Rx991FiWZYqKiq5YbQAQ6IJ9fasaAMD7Nm7cKEl67733tHnz\n",
       "5hbHPR6PJGnnzp1KT0+XJN17772aOnWqXn75ZX344YcaNGiQ/uM//uOC33H11VerV69eLfqHDh2q\n",
       "5557Ttu3b7f7KioqJElxcXEXrXvp0qW66aabNHPmTEnSf/7nf+qWW2656DneUl1dre9///vau3ev\n",
       "fvnLX+ree++94Nj4+HhJUnl5+RWpDQAgEVwAoBOqrKyUdPYX/wuxLEunTp1y9P3gBz/Qyy+/LEn6\n",
       "6U9/quDgC/81kZiYeNH+6upqx3dJZzfbX0y3bt00fPhwLVu2TNHR0Zo0adJFx3tLVVWVRo8erc2b\n",
       "N2vGjBl65plnLjr+3Mszvfl0NADAxfFUMQDohGJiYmRZlo4dO6ampqbz/mlsbFRubq59TlVVlR56\n",
       "6CGFhoYqOjpa+fn5Onz48AW/49yqzYX6Y2Ji7L7u3btLko4dO3bRuletWqVly5YpISFBJ0+e1L/+\n",
       "67+2+Zq/raNHj+qOO+7Q5s2b9atf/UrPPvtsq+ecu46EhITLXR4A4P8huABAJ5SZmSljjN5///02\n",
       "n/PII4/o4MGDeuGFF7R48WIdPXpU999/v7260NzBgwf1xRdftOh/7733JJ192eQ5ffr0kSSVlpZe\n",
       "8Pv379+vH/3oR+rWrZs2bdqkO++8UytXrtTixYvbfA3tdeTIEQ0bNkwff/yx5s6dq//zf/5Pm847\n",
       "dOiQpK+vCwBwBfh6kw0AwPt2795tP1Vs165dLY7X19ebdevW2e0XX3zR8UQvY4yZPHmysSzLPPnk\n",
       "k45zv/lUsQkTJjievPX555+bmJiYFk8VM+bij0M+90hml8tl3nrrLWOMMUePHjXJyckmIiLCfPLJ\n",
       "J+3/IbTi4MGD5pprrjGWZZnf/OY37TqXxyEDwJVnGdPKDccAgA5p5cqVeuSRR9TQ0KAxY8YoLS1N\n",
       "jY2N+vLLL7Vx40bV19fr2LFj2rx5s2677Tb17NlT27dvt2/xOn36tG699Vbt2LFDRUVFuuOOOySd\n",
       "fQFlnz59dOONN6q6ulpxcXEaOXKkjh07pjfeeEMnT57UvHnz9NhjjznqefTRR7VkyRJt27ZNAwYM\n",
       "cBybPn26CgoKlJeXp5deesnuf//99zVixAj17dtXmzZtUkREhNd+Pqmpqfriiy90/fXX65//+Z/P\n",
       "u/9m/PjxLWrduXOn+vfvr4ceekivvfaa1+oBALSitWRTX19vZsyYYVJTU014eLhJTU01Tz75pGlo\n",
       "aHCMmzlzpunZs6fp0qWL+d73vmc+/fRTx/HTp0+bn/3sZ6Z79+4mMjLS3H333aa0tNQx5tixY+bB\n",
       "Bx80MTExJiYmxuTm5rb5ufsAgJZ27NhhHn30UZOammrCwsJMt27dzHXXXWd+9KMfmT//+c+murra\n",
       "9OnTx4SGhpqSkpIW5+/cudNERkaaHj16GI/HY4z5esVl+PDh5tChQ+aBBx4wCQkJpkuXLmbQoEHm\n",
       "9ddfP28txcXFxrIs8/jjjzv63377bWNZlrn55pvNmTNnWpz3q1/9yrhcLvPII4944SfyNcuyjMvl\n",
       "Mi6Xy15B+uYfl8tlli1b1uK8p556yliWZdavX+/VegAAF9fqisvTTz+tl156Sb///e91ww036KOP\n",
       "PtLDDz+sn//853ryySclSXPnztWzzz6rZcuWqW/fvnr66ae1YcMG7d69W1FRUZKkn/zkJ3r77bf1\n",
       "+9//XnFxcZo+fbqOHz+uLVu2yOU6u9XmzjvvVGlpqX7729/KGKNHH31Uffr00dtvv32Z4xsAoK3O\n",
       "rbh873vf07p169p17s0336zKykrt37/f/n9/R2KMUVpamrp06aJPPvnE1+UAQGBpLdmMHTvWPPzw\n",
       "w46+iRMnmrFjxxpjjGlqajJJSUlmzpw59vHa2loTHR1tFi5caIwx5vjx4yY0NNQUFhbaY7788kvj\n",
       "crnMmjVrjDFn/1XQsixTXFxsj9mwYYOxLMvs3r37W+YyAIC3fXPFpb3eeecdY1mWWb58+WWo7PJ7\n",
       "/fXXjWVZ9j4cAMCV0+o/d915551at26ddu/eLUnasWOH3n33Xd11112Szj4FxuPxaNSoUfY54eHh\n",
       "Gjp0qIqLiyVJW7ZsUX19vWNMSkqK0tPTVVJSIkkqKSlRVFSUMjIy7DGZmZmKjIy0xwAAOrY777xT\n",
       "WVlZeuaZZ1p9p4u/aWpq0tNPP62hQ4cqOzvb1+UAQMBp9QWUP/3pT1VaWqr09HQFBweroaFBTz75\n",
       "pP1s/bKyMkktX0Tmdrvt5/+XlZUpKCjIftPwOYmJifb5ZWVlLZ6Hb1mW3G63PUZyvtAMAHDlnThx\n",
       "QpLU0NDwrf6f/Oabbzo+pyPZuHGjJP4uAoBv65vv+GqvVoPL/Pnz9dprr2nlypXq37+/tm3bpsce\n",
       "e0y9e/fWj370o4ue29obhTvav7YBAKRevXqpqqrK12UAAAJMq7eKPfvss3riiSf0wx/+UP3799eD\n",
       "Dz6o6dOn67nnnpMkJSUlSWr5BmWPx2MfS0pKUmNjoyorKy86pqKiwnHcGKPy8nJ7DAAAAIDA1OqK\n",
       "izGmxZNfXC6XvVqSmpqqpKQkFRUVaeDAgZLOPvt/w4YNeuGFFyRJAwcOVEhIiIqKinT//fdLOvv2\n",
       "5F27dikzM1OSlJGRoZqaGpWUlNj7XEpKSnTq1Cl7THOXstSEjmPz5s2SpEGDBvm4ElxJzHvgYc4D\n",
       "D3MeeJjzwOSt22tbDS733HOPfv3rXys1NVXXXXedtm3bphdffFEPPfSQpLO3g02bNk1z5sxRv379\n",
       "lJaWptmzZys6Olo5OTmSzgaMSZMmKT8/X263234c8oABA5SVlSVJSk9P15gxYzRlyhQtWrRIxhhN\n",
       "mTJF48aNU1pamlcuFgAAAEDH1GpwefHFF9W1a1dNnTpVHo9HPXr00OTJk/XUU0/ZY/Lz81VbW6up\n",
       "U6eqqqpKQ4YMUVFRkSIjI+0xBQUFCg4O1oQJE1RbW6usrCytWLHCsQ+msLBQeXl5Gj16tCQpOztb\n",
       "CxYs8Ob1AgAAAOiAWn0Bpb/55lITt4oFBpaVAxPzHniY88DDnAce5jwweev394732mIAAAAAAYfg\n",
       "AgAAAMDvEVwAAAAA+D2CCwAAAAC/R3ABAAAA4PcILgAAAAD8HsEFAAAAgN8juAAAAADwewQXAAAA\n",
       "AH6P4AIAAADA7wX7ugAAAAAAnceHO9+VJMV3TVRcV7dcCvHK5xJcAAAAAHjN/36wUpUnPHb7mYeX\n",
       "eeVzuVUMAAAAgFc0NjWqquboZflsggsAAAAAr6iuOaampka7HdUlxmufTXABAAAA4BXfvEVMkuK6\n",
       "ur322QQXAAAAAF5x7ES5ox3XNcFrn01wAQAAAOAVzYNLfNdEr302wQUAAACAV3CrGAAAAAC/x4oL\n",
       "AAAAAL/XMriw4gIAAADAjzQ2NqiqptLR143N+QAAAAD8yfGaShnTZLe7RnRTaHCY1z6f4AIAAADg\n",
       "klW2eBSy924TkwguAAAAALzgcj5RTCK4AAAAAPCCy7kxXyK4AAAAAPCC5sGFFRcAAAAAfqf5rWLe\n",
       "fIeLRHABAAAA4AWsuAAAAADwaw2N9aquOWa3LVnqFu29d7hIBBcAAAAAl6jq5FEZGbvdNSpOIcEh\n",
       "Xv0OggsAAACAS1JZ3Wx/S7R3bxOTCC4AAAAALlGLjfkx3t2YLxFcAAAAAFyio9VHHG2CCwAAAAC/\n",
       "c7TZrWLdY5K8/h2tBpfevXvL5XK1+DN27FhJkjFGs2bNUnJysiIiIjR8+HDt2LHD8Rl1dXXKy8tT\n",
       "QkKCoqKilJ2drUOHDjnGVFVVKTc3V7GxsYqNjdXEiRNVXV3txUsFAAAAcDk03+Pik+CyZcsWlZWV\n",
       "2X+2bt0qy7I0YcIESdLzzz+vefPmacGCBdq0aZPcbrdGjhypmpoa+zOmTZumVatWaeXKlVq/fr1O\n",
       "nDihsWPHqqmpyR6Tk5Oj7du3a82aNVq9erW2bt2q3Nxcr18wAAAAAO8xxuhodZmj73IEl+DWBsTH\n",
       "xzvaixcvVkxMjH74wx/KGKOCggLNmDFD48ePlyQtW7ZMbrdbhYWFmjx5sqqrq7VkyRItXbpUI0aM\n",
       "kCQtX75cvXr10tq1azVq1Cjt3LlTa9as0caNGzV48GBJ0sKFC3X77bdrz5496tu3r7evGwAAAIAX\n",
       "fHX6pE6f+cpuhwaHKToi1uvf0649LsYY/e53v9ODDz6osLAw7d+/Xx6PR6NGjbLHhIeHa+jQoSou\n",
       "LpZ0dsWmvr7eMSYlJUXp6ekqKSmRJJWUlCgqKkoZGRn2mMzMTEVGRtpjAAAAAPif5qst8TGJsizL\n",
       "69/T6orLN/3lL3/RgQMH9OMf/1iSVFZ2tsjEROdTA9xutw4fPmyPCQoKarFyk5iYaJ9fVlamhATn\n",
       "mzUty5Lb7bbHnM/mzZvbUz46OOY7MDHvgYc5DzzMeeBhzjuX/RWfOtpBJtwxx2lpaV75nnatuCxe\n",
       "vFi33nqrbrjhhlbHtpayjDEXPQ4AAADA/508XeVoR4d5/zYxqR0rLuXl5Xr77bf1yiuv2H1JSWc3\n",
       "3Xg8HqWkpNj9Ho/HPpaUlKTGxkZVVlY6Vl08Ho+GDRtmj6moqHB8nzFG5eXl9uecz6BBg9paPjqw\n",
       "c4md+Q4szHvgYc4DD3MeeJjzzmlPlXNrR/9rB2jQgK/n2FtPCm7zisvSpUsVHh6u+++/3+5LTU1V\n",
       "UlKSioqK7L7Tp09rw4YNyszMlCQNHDhQISEhjjGlpaXatWuXPSYjI0M1NTWO/SwlJSU6deqUPQYA\n",
       "AACA/2mxx6Wr918+KbVxxcUYo9/+9re67777FBERYfdblqVp06Zpzpw56tevn9LS0jR79mxFR0cr\n",
       "JydHkhQTE6NJkyYpPz9fbrdbcXFxmj59ugYMGKCsrCxJUnp6usaMGaMpU6Zo0aJFMsZoypQpGjdu\n",
       "nNfuiQMAAADgfS3e4RLb47J8T5uCy9/+9jft3btXhYWFLY7l5+ertrZWU6dOVVVVlYYMGaKioiJF\n",
       "RkbaYwoKChQcHKwJEyaotrZWWVlZWrFihWMfTGFhofLy8jR69GhJUnZ2thYsWHCp1wcAAADgMqlv\n",
       "qNfxmkq7bclSXLT7snxXm4LL8OHD1djYeMHjM2fO1MyZMy94PDQ0VPPnz9f8+fMvOCY2NlbLly9v\n",
       "SzkAAAAA/MCxk+Uy+vqhW7FR8QoJDrks39Wup4oBAAAAwDlHjx9xtONjLs/+FongAgAAAOBbqjzR\n",
       "bH9LzIWfCHypCC4AAAAAvpWjx5s9UYzgAgAAAMDfHGXFBQAAAIC/a77HpTt7XAAAAAD4kybT1OLl\n",
       "kwmxPS/b9xFcAAAAALTb8ZOVamist9sR4dGKCI+6bN9HcAEAAADQbhXHDzvaCbE9Luv3EVwAAAAA\n",
       "tFtFs/0tBBcAAAAAfudodbPgEkNwAQAAAOBnyllxAQAAAODvWu5xuXxPFJMILgAAAADaqamp8TyP\n",
       "QmbFBQAAAIAfOV5TqcbGBrsdeZkfhSwRXAAAAAC0U8snil3e28QkggsAAACAdiq/wu9wkQguAAAA\n",
       "ANrpaLMVl+4EFwAAAAD+pvmtYm6CCwAAAAB/wx4XAAAAAH6tqalRR084H4XcPTbpsn8vwQUAAABA\n",
       "m1XVHHU+CrlLV0WEXd5HIUsEFwAAAADtUFHV7DaxmMu/v0UiuAAAAABoh/Ljhxxtd7fLv79FIrgA\n",
       "AAAAaIfyqubBJfmKfC/BBQAAAECbeY45g0siwQUAAACAv2HFBQAAAIBfq6s/raqao3bbslzqzuZ8\n",
       "AAAAAP6k4vhhRzuua4JCgkOuyHcTXAAAAAC0SXmVM7gkxl6Z28QkggsAAACANvL4aH+LRHABAAAA\n",
       "0Ea+2pgvEVwAAAAAtBHBBQAAAIBfM8a0CC5X6h0uEsEFAAAAQBucOFWluvrTdjssJFxdI7tdse9v\n",
       "U3A5cuSIHnroIbndbnXp0kX9+/fX+++/7xgza9YsJScnKyIiQsOHD9eOHTscx+vq6pSXl6eEhARF\n",
       "RUUpOztbhw45E1tVVZVyc3MVGxur2NhYTZw4UdXV1Zd4iQAAAAAu1fk25luWdcW+v9Xgcvz4cd12\n",
       "222yLEvvvPOOdu3apQULFsjtdttj5s6dq3nz5mnBggXatGmT3G63Ro4cqZqaGnvMtGnTtGrVKq1c\n",
       "uVLr16/XiRMnNHbsWDU1NdljcnJytH37dq1Zs0arV6/W1q1blZub6+VLBgAAANBevtzfIknBrQ14\n",
       "/vnnlZycrKVLl9p9vXr1sv/bGKOCggLNmDFD48ePlyQtW7ZMbrdbhYWFmjx5sqqrq7VkyRItXbpU\n",
       "I0aMkCQtX75cvXr10tq1azVq1Cjt3LlTa9as0caNGzV48GBJ0sKFC3X77bdrz5496tu3rzevGwAA\n",
       "AEA7+Dq4tLri8tZbb+nWW2/VhAkTlJiYqJtuukkvv/yyfXz//v3yeDwaNWqU3RceHq6hQ4equLhY\n",
       "krRlyxbV19c7xqSkpCg9PV0lJSWSpJKSEkVFRSkjI8Mek5mZqcjISHsMAAAAAN9ofqvYldyYL7Vh\n",
       "xWXfvn165ZVXNH36dD3xxBPatm2b8vLyJElTp05VWVmZJCkxMdFxntvt1uHDZ9+sWVZWpqCgIMXH\n",
       "xzvGJCYm2ueXlZUpISHBcdyyLLndbntMc5s3b27LNaKTYL4DE/MeeJjzwMOcBx7mvGP6smyvo330\n",
       "SLU2n2h9LtPS0rzy/a0Gl6amJt1666169tlnJUkDBgzQZ599ppdffllTp0696LmtbdYxxrSjVAAA\n",
       "AAC+UN94RjV1Xz80y5KlruFxV7SGVoNLz549dd111zn6+vXrp4MHD0qSkpKSJEkej0cpKSn2GI/H\n",
       "Yx9LSkpSY2OjKisrHasuHo9Hw4YNs8dUVFQ4vscYo/Lycvtzmhs0aFCrF4iO79y/yjDfgYV5DzzM\n",
       "eeBhzgMPc95xfVm+V/rg63Z8TKKGDM648Anf4K2nBLe6x+W2227Trl27HH179uxR7969JUmpqalK\n",
       "SkpSUVGRffz06dPasGGDMjMzJUkDBw5USEiIY0xpaal27dplj8nIyFBNTY1jP0tJSYlOnTpljwEA\n",
       "AABw5ZUd+9LRToq76orX0OqKy89//nNlZmZqzpw5+uEPf6ht27bpN7/5jZ577jlJZ28HmzZtmubM\n",
       "maN+/fopLS1Ns2fPVnR0tHJyciRJMTExmjRpkvLz8+V2uxUXF6fp06drwIABysrKkiSlp6drzJgx\n",
       "mjJlihYtWiRjjKZMmaJx48Z57b44AAAAAO3nOVbqaCfGpVxg5OXTanAZNGiQ3nrrLT3xxBN65pln\n",
       "1KtXL82ePVs/+clP7DH5+fmqra3V1KlTVVVVpSFDhqioqEiRkZH2mIKCAgUHB2vChAmqra1VVlaW\n",
       "VqxY4dgHU1hYqLy8PI0ePVqSlJ2drQULFnjzegEAAAC0U4dYcZGk73//+/r+979/0TEzZ87UzJkz\n",
       "L3g8NDRU8+fP1/z58y84JjY2VsuXL29LSQAAAACukLJmKy5JPlhxaXWPCwAAAIDAVd9Qr6PHjzj6\n",
       "En2w4kJwAQAAAHBBFccPq8k02e3YqHiFh3a54nUQXAAAAABckKeq+W1iV361RSK4AAAAALiIskrf\n",
       "b8yXCC4AAAAALqL5iosvHoUsEVwAAAAAXAQrLgAAAAD8WmNTo8qPH3b0+eJRyBLBBQAAAMAFVFZ7\n",
       "1NBYb7eju8QosktXn9RCcAEAAABwXmXHnLeJ+Wp/i0RwAQAAAHABRyoPOto94nv5qBKCCwAAAIAL\n",
       "OFL5haPdI/5qH1VCcAEAAABwAS1XXAguAAAAAPxIQ2O9PFWHHH09uhNcAAAAAPiR8qpDampqtNux\n",
       "UfGKCIvyWT0EFwAAAAAt+NPGfIngAgAAAOA8mgeXnj68TUwiuAAAAAA4j8OsuAAAAADwd0eO+s+j\n",
       "kCWCCwAAAIBm6s7UqvKEx25blkuJcSk+rIjgAgAAAKCZsmNfOtoJMUkKDQ7zUTVnEVwAAAAAOBz2\n",
       "s9vEJIILAAAAgGb87VHIEsEFAAAAQDMtgkt3ggsAAAAAP2KM0aGjBxx9PblVDAAAAIA/OfFVlWpq\n",
       "q+12SHCoEmJ7+LCiswguAAAAAGyHKg442j3ie8nlCvJNMd9AcAEAAABga36bWHL33j6pozmCCwAA\n",
       "AADb4Yr9jnZyQm/fFNIMwQUAAACAjRUXAAAAAH6tvuGMyqsOOfp6ElwAAAAA+JMjlQfVZJrsdlxX\n",
       "t7qERfqwoq8RXAAAAABI8t/bxCSCCwAAAID/53CL4JLqm0LOg+ACAAAAQJJ0yE+fKCa1IbjMmjVL\n",
       "LpfL8adnz54txiQnJysiIkLDhw/Xjh07HMfr6uqUl5enhIQERUVFKTs7W4cOOTf9VFVVKTc3V7Gx\n",
       "sYqNjdXEiRNVXV0tAAAAAJefMabFrWL+sjFfauOKS79+/VRWVmb/+eSTT+xjc+fO1bx587RgwQJt\n",
       "2rRJbrdbI0eOVE1NjT1m2rRpWrVqlVauXKn169frxIkTGjt2rJqavt74k5OTo+3bt2vNmjVavXq1\n",
       "tm7dqtzcXC9eKgAAAIALqTpZodq6U3Y7LCRc8TGJPqzIKbgtg4KCguR2u1v0G2NUUFCgGTNmaPz4\n",
       "8ZKkZcuWye12q7CwUJMnT1Z1dbWWLFmipUuXasSIEZKk5cuXq1evXlq7dq1GjRqlnTt3as2aNdq4\n",
       "caMGDx4sSVq4cKFuv/127dmzR3379vXW9QIAAAA4j/Ottrgs/9lZ0qZK9u3bp+TkZPXp00f333+/\n",
       "9u8/e+/b/v375fF4NGrUKHtseHi4hg4dquLiYknSli1bVF9f7xiTkpKi9PR0lZSUSJJKSkoUFRWl\n",
       "jIwMe0xmZqYiIyPtMQAAAAAuny/L9zraKQl9fFTJ+bW64jJkyBAtW7ZM/fr1k8fj0ezZs5WZmalP\n",
       "P/1UZWVlkqTEROcSktvt1uHDhyVJZWVlCgoKUnx8vGNMYmKifX5ZWZkSEhIcxy3Lktvttsecz+bN\n",
       "m9twiegsmO/AxLwHHuY88DDngYc590//2LPV0W78yuWVuUpLS7vkz5DaEFzGjBlj//f111+vjIwM\n",
       "paamatmyZfZtXedjWdZFP9cY044yAQAAAFxOx045Fwzionr4qJLza9Mel2+KiIhQ//799fnnn+ue\n",
       "e+6RJHk8HqWkpNhjPB6PkpKSJElJSUlqbGxUZWWlY9XF4/Fo2LBh9piKigrH9xhjVF5ebn/O+Qwa\n",
       "NKi95aNmWrvEAAAgAElEQVQDOpf0me/AwrwHHuY88DDngYc5918nTh3XVxtP2u2goGCN+KfRCgpq\n",
       "d1xowVtPCm73bpvTp09r586d6tGjh1JTU5WUlKSioiLH8Q0bNigzM1OSNHDgQIWEhDjGlJaWateu\n",
       "XfaYjIwM1dTUOPazlJSU6NSpU/YYAAAAAJdHaYVzf0tyfG+vhBZvarWaf//3f9fdd9+tq666SuXl\n",
       "5XrmmWdUW1urhx56SNLZRx3PmTNH/fr1U1pammbPnq3o6Gjl5ORIkmJiYjRp0iTl5+fL7XYrLi5O\n",
       "06dP14ABA5SVlSVJSk9P15gxYzRlyhQtWrRIxhhNmTJF48aN89o9cQAAAADO78vyfY52itu/NuZL\n",
       "bQguhw4d0v3336+jR48qISFBGRkZ+uCDD3TVVVdJkvLz81VbW6upU6eqqqpKQ4YMUVFRkSIjI+3P\n",
       "KCgoUHBwsCZMmKDa2lplZWVpxYoVjn0whYWFysvL0+jRoyVJ2dnZWrBggbevFwAAAEAzpc2eKHaV\n",
       "+zs+quTCWg0u//Vf/9Xqh8ycOVMzZ8684PHQ0FDNnz9f8+fPv+CY2NhYLV++vNXvAgAAAOBdX1Y0\n",
       "W3Hxs0chS99ijwsAAACAzuPU6ZM6dqLcbrssl3p27+XDis6P4AIAAAAEsNJm+1uS4q9WSHCoj6q5\n",
       "MIILAAAAEMBKm90m5o/7WySCCwAAABDQvmyxMd//9rdIBBcAAAAgoH3pcQYXf9yYLxFcAAAAgIB1\n",
       "6vRJVVQfsdsuy6XkhFQfVnRhBBcAAAAgQB30fO5oJ8VfrbCQcB9Vc3EEFwAAACBANQ8uVyde46NK\n",
       "WkdwAQAAAALUQc9njnavxDQfVdI6ggsAAAAQoL5oFlxYcQEAAADgV47XVOrEqSq7HRwUop7xvXxY\n",
       "0cURXAAAAIAA1Pw2sZSEPgoKCvZRNa0juAAAAAABqCNtzJcILgAAAEBA+qKs4+xvkQguAAAAQMAx\n",
       "xuhguXPFxZ+fKCYRXAAAAICAU3H8iGrrTtnt8NAIJXTr6cOKWkdwAQAAAALMF549jvbV7u/IZfl3\n",
       "NPDv6gAAAAB43YEjzuDSK6mvjyppO4ILAAAAEGD2l+1ytHv3uNZHlbQdwQUAAAAIIHX1p3W44oCj\n",
       "r3cSwQUAAACAH/myfK+aTJPd7h6TpOiIGB9W1DYEFwAAACCA7D+y29HuCLeJSQQXAAAAIKAcONJs\n",
       "f0sHuE1MIrgAAAAAAcMYowNlzieKpbLiAgAAAMCfHDtRrpNfHbfbIcGh6tm9t+8KageCCwAAABAg\n",
       "9je7TezqxDQFuYJ8VE37EFwAAACAANHiNrEOsr9FIrgAAAAAAeNAB32imERwAQAAAAJC3ZlalVbs\n",
       "c/R1lCeKSQQXAAAAICAcKNvjePGkO7anukbG+rCi9iG4AAAAAAFg7+Edjnafnuk+quTbIbgAAAAA\n",
       "AWDf4Z2Odp+e1/mokm+H4AIAAAB0co2NDS2eKNapV1yee+45uVwu5eXlOfpnzZql5ORkRUREaPjw\n",
       "4dqxw7kMVVdXp7y8PCUkJCgqKkrZ2dk6dOiQY0xVVZVyc3MVGxur2NhYTZw4UdXV1d/ysgAAAACc\n",
       "c+joAZ2pP223o7vEKCG2hw8rar82B5cPPvhAixcv1o033ijLsuz+uXPnat68eVqwYIE2bdokt9ut\n",
       "kSNHqqamxh4zbdo0rVq1SitXrtT69et14sQJjR07Vk1NX28OysnJ0fbt27VmzRqtXr1aW7duVW5u\n",
       "rpcuEwAAAAhcew8129+SfJ3jd/qOoE3Bpbq6Wg8++KBee+01devWze43xqigoEAzZszQ+PHj1b9/\n",
       "fy1btkwnT55UYWGhfe6SJUv0wgsvaMSIEbrpppu0fPlyffzxx1q7dq0kaefOnVqzZo0WLVqkwYMH\n",
       "a8iQIVq4cKH+9Kc/ac+ePeetCQAAAEDb7OvgG/OlNgaXyZMn61/+5V80bNgwGWPs/v3798vj8WjU\n",
       "qFF2X3h4uIYOHari4mJJ0pYtW1RfX+8Yk5KSovT0dJWUlEiSSkpKFBUVpYyMDHtMZmamIiMj7TEA\n",
       "AAAA2s8Y02Jj/nc62MZ8SQpubcDixYu1b98+ewXlm0tKZWVlkqTExETHOW63W4cPH7bHBAUFKT4+\n",
       "3jEmMTHRPr+srEwJCQmO45Zlye1222MAAAAAtF/F8SM6Wfv13vHQkHAlJ6T6sKJv56LBZffu3frl\n",
       "L3+pDRs2KCgoSNLZxPbNVZcLae2eubZ8Rms2b958yZ+BjoP5DkzMe+BhzgMPcx54mPMr6zPPNkc7\n",
       "LiJJ27Zuu8Bo70tLS/PK51z0VrGSkhIdPXpU/fv3V0hIiEJCQvT+++/rlVdeUWhoqLp37y5J8ng8\n",
       "jvM8Ho+SkpIkSUlJSWpsbFRlZeVFx1RUVDiOG2NUXl5ujwEAAADQfp7qLxztpJhePqrk0lx0xWX8\n",
       "+PG69dZb7bYxRo888oj69u2rJ554QmlpaUpKSlJRUZEGDhwoSTp9+rQ2bNigF154QZI0cOBAhYSE\n",
       "qKioSPfff78kqbS0VLt27VJmZqYkKSMjQzU1NSopKbH3uZSUlOjUqVP2mPMZNGjQJVw6Oopz/yrD\n",
       "fAcW5j3wMOeBhzkPPMz5lWeM0dsfveroG3brKH0nuf8Vq8Fbrzi5aHCJiYlRTEyMoy8iIkLdunXT\n",
       "dded3dAzbdo0zZkzR/369VNaWppmz56t6Oho5eTk2J8xadIk5efny+12Ky4uTtOnT9eAAQOUlZUl\n",
       "SUpPT9eYMWM0ZcoULVq0SMYYTZkyRePGjfPa0hIAAAAQaI5Wl+l4zdd3PoUEherqxL4+rOjba3Vz\n",
       "fnOWZTn2r+Tn56u2tlZTp05VVVWVhgwZoqKiIkVGRtpjCgoKFBwcrAkTJqi2tlZZWVlasWKF43MK\n",
       "CwuVl5en0aNHS5Kys7O1YMGCS7k2AAAAIKB9XvoPRzu1x7UKCQ7xUTWXpt3B5d13323RN3PmTM2c\n",
       "OfOC54SGhmr+/PmaP3/+BcfExsZq+fLl7S0HAAAAwAV8dsgZXK5Jud5HlVy6Nr3HBQAAAEDHYoxp\n",
       "seKSlnKDj6q5dAQXAAAAoBNqsb8lOFRXJ3bc/eMEFwAAAKATarm/pV+H3d8iEVwAAACATqn5/pa0\n",
       "Dry/RSK4AAAAAJ2OMUafffmJo++aK/julsuB4AIAAAB0Mp6qUlWfOma3Q4PD1CupY76/5RyCCwAA\n",
       "ANDJ7D74kaN9TXJ/BQd13P0tEsEFAAAA6HR2f/mxo9336gE+qsR7CC4AAABAJ9LY1KjPSp37W669\n",
       "iuACAAAAwI8c9HymujO1dju6S4x6dL/ahxV5B8EFAAAA6ER2Ndvf0veqG+WyOv6v/R3/CgAAAADY\n",
       "9jQPLp1gf4tEcAEAAAA6jboztdpfttvR1xn2t0gEFwAAAKDT+PzQp2pqarTbCbE9Fdc1wYcVeQ/B\n",
       "BQAAAOgkdn6x1dG+9qobfVSJ9xFcAAAAgE5i54FtjnZ675t9VIn3EVwAAACATqDi+BFVVB+x20Gu\n",
       "YPVNucGHFXkXwQUAAADoBHZ+4Vxt+U7PdIWFdvFRNd5HcAEAAAA6gZ0HnPtbOtNtYhLBBQAAAOjw\n",
       "6hvO6LPSTxx96b0ILgAAAAD8yL7DO3Wmoc5ux0TFq0f81T6syPsILgAAAEAH1/wxyOm9bpJlWT6q\n",
       "5vIguAAAAAAd3KcHtjja13Wy28QkggsAAADQoVUcPyLPsVK77XIFqe/VnefFk+cQXAAAAIAO7B/7\n",
       "Nzna3+l5nSLConxUzeVDcAEAAAA6sE/3OYPL9am3+KiSy4vgAgAAAHRQtXWn9PnhHY6+/qmDfFTN\n",
       "5UVwAQAAADqonV9sU1NTo912d0uWu1tPH1Z0+RBcAAAAgA6q+f6WznqbmERwAQAAADqkxqZG7Tjg\n",
       "fH9LZ71NTCK4AAAAAB3SgSO79NXpk3Y7IixKfXqm+7Ciy4vgAgAAAHRAH+39u6Od3vtmBbmCfFTN\n",
       "5UdwAQAAADoYY4w+3vuBo+/G7wz2UTVXBsEFAAAA6GBKK/br2Ilyux0cFKLret3sw4ouv1aDy8sv\n",
       "v6wBAwYoJiZGMTExyszM1DvvvOMYM2vWLCUnJysiIkLDhw/Xjh3OZ0nX1dUpLy9PCQkJioqKUnZ2\n",
       "tg4dOuQYU1VVpdzcXMXGxio2NlYTJ05UdXW1Fy4RAAAA6Fw+3lviaPfrdZPCQrv4qJoro9XgctVV\n",
       "V+n555/Xtm3btGXLFt1xxx2655579NFHH0mS5s6dq3nz5mnBggXatGmT3G63Ro4cqZqaGvszpk2b\n",
       "plWrVmnlypVav369Tpw4obFjx6qpqckek5OTo+3bt2vNmjVavXq1tm7dqtzc3MtwyQAAAEDH9nGz\n",
       "/S0DOvltYpIU3NqAu+++29GePXu2Xn31VX344Ye68cYbVVBQoBkzZmj8+PGSpGXLlsntdquwsFCT\n",
       "J09WdXW1lixZoqVLl2rEiBGSpOXLl6tXr15au3atRo0apZ07d2rNmjXauHGjBg8++0NfuHChbr/9\n",
       "du3Zs0d9+/b19nUDAAAAHVJ51SEdqTxot12Wq1O/v+Wcdu1xaWxs1MqVK3X69GkNHTpU+/fvl8fj\n",
       "0ahRo+wx4eHhGjp0qIqLiyVJW7ZsUX19vWNMSkqK0tPTVVJydomrpKREUVFRysjIsMdkZmYqMjLS\n",
       "HgMAAACg5dPErkm5XpFduvqomiun1RUXSfrkk0+UkZGhuro6denSRW+88YauvfZaO5wkJiY6xrvd\n",
       "bh0+fFiSVFZWpqCgIMXHxzvGJCYmqqyszB6TkJDgOG5Zltxutz3mfDZv3tyW8tFJMN+BiXkPPMx5\n",
       "4GHOAw9zfmmKP1rraMeG9PTrn2laWppXPqdNwaVfv376+OOPVV1drTfffFP33Xef3n333YueY1nW\n",
       "RY8bY9peJQAAAACdPF2lyprDjr6r4wJjW0WbgktISIj69OkjSbrpppu0adMmvfzyy3rqqackSR6P\n",
       "RykpKfZ4j8ejpKQkSVJSUpIaGxtVWVnpWHXxeDwaNmyYPaaiosLxncYYlZeX259zPoMGDWpL+ejg\n",
       "zv0LAvMdWJj3wMOcBx7mPPAw55fuL5tXOdp9eqZr6G13+KiatvHWk4K/1XtcGhsb1dTUpNTUVCUl\n",
       "JamoqMg+dvr0aW3YsEGZmZmSpIEDByokJMQxprS0VLt27bLHZGRkqKamxrGfpaSkRKdOnbLHAAAA\n",
       "AIFu22cbHO2b+/6Tjyq58lpdcXn88cc1duxYpaSk6OTJkyosLNR7772n1atXSzr7qOM5c+aoX79+\n",
       "SktL0+zZsxUdHa2cnBxJUkxMjCZNmqT8/Hy53W7FxcVp+vTpGjBggLKysiRJ6enpGjNmjKZMmaJF\n",
       "ixbJGKMpU6Zo3LhxXrsnDgAAAOjIKo4fUWn5PrttydKAazIuckbn0mpw8Xg8evDBB1VWVqaYmBgN\n",
       "GDBAq1ev1siRIyVJ+fn5qq2t1dSpU1VVVaUhQ4aoqKhIkZGR9mcUFBQoODhYEyZMUG1trbKysrRi\n",
       "xQrHPpjCwkLl5eVp9OjRkqTs7GwtWLDA29cLAAAAdEjb9jhXW76T0l8xkXE+qubKazW4vPbaa61+\n",
       "yMyZMzVz5swLHg8NDdX8+fM1f/78C46JjY3V8uXLW/0uAAAAIBBt/Wyjo31T2m0+qsQ3vtUeFwAA\n",
       "AABXjudYqQ4fPWC3Lcul7wbQbWISwQUAAADwe5t3v+9op6Vcr+iIWB9V4xsEFwAAAMCPGWO0edd7\n",
       "jr6BfW/3UTW+Q3ABAAAA/Nj+I7tVecJjt4ODQvTdtMB7ZQjBBQAAAPBjm3f9zdG+vs8t6hIWef7B\n",
       "nRjBBQAAAPBTDY31LZ4mdku/7/mmGB8juAAAAAB+aucX2/TV6ZN2OyI8Wum9bvJhRb5DcAEAAAD8\n",
       "1KZmt4ndnHabgoNCfFOMjxFcAAAAAD906vRJfbLvQ0ffoAC9TUwiuAAAAAB+acvu99XY2GC3u8ck\n",
       "KbXHtT6syLcILgAAAIAf+uDTvzraQ64bIcuyfFSN7xFcAAAAAD9TWrFPpRX77LZluXRL+nAfVuR7\n",
       "BBcAAADAz/x9xzpHu9/V31W36O4+qsY/EFwAAAAAP1LfUK9Nu95z9A2+7g4fVeM/CC4AAACAH/lk\n",
       "399bvLvlhj6DfViRfyC4AAAAAH5k4ydrHO1B1w5VSHBgvrvlmwguAAAAgJ/wVB3SZ6WfOPoyrx/l\n",
       "o2r8C8EFAAAA8BPFzVZb+vRIV8/uvXxUjX8huAAAAAB+oL7hjP6+811HX+YNrLacQ3ABAAAA/MD2\n",
       "z4tbbMr/blqmDyvyLwQXAAAAwA9s+Hi1oz04fbhCg8N8VI3/IbgAAAAAPnbQ87n2H9nl6Mu8YbSP\n",
       "qvFPBBcAAADAx97/6M+O9rVXD1Bit2QfVeOfCC4AAACAD5386ri27Fnv6Bs2YKyPqvFfBBcAAADA\n",
       "h4r/UaTGxga73T0mSdelDvRhRf6J4AIAAAD4SGNjg9Z//L+OvtsHfF8ui1/Tm+MnAgAAAPjI1s82\n",
       "6sSpKrsdGhKuIdeN8GFF/ovgAgAAAPiAMUbrtr7l6Ls1fbi6hEX6qCL/RnABAAAAfGDPlx/rUMV+\n",
       "u23J0ve+O86HFfk3ggsAAADgA3/d8t+O9o3fGSx3t54+qsb/EVwAAACAK+xQxQHtOrjd0XfHwHt8\n",
       "VE3HQHABAAAArrDme1v69EhXao9+PqqmYyC4AAAAAFfQ0eoybdn9vqOP1ZbWEVwAAACAK2jt5lVq\n",
       "Mk12O7Fbiq7vc4sPK+oYWg0uzz33nG655RbFxMTI7Xbr7rvv1qefftpi3KxZs5ScnKyIiAgNHz5c\n",
       "O3bscByvq6tTXl6eEhISFBUVpezsbB06dMgxpqqqSrm5uYqNjVVsbKwmTpyo6urqS7xEAAAAwD9U\n",
       "nTyqv+9c5+gbecs/88LJNmj1J/Tee+/pZz/7mUpKSrRu3ToFBwcrKytLVVVfvyhn7ty5mjdvnhYs\n",
       "WKBNmzbJ7XZr5MiRqqmpscdMmzZNq1at0sqVK7V+/XqdOHFCY8eOVVPT12kzJydH27dv15o1a7R6\n",
       "9Wpt3bpVubm5Xr5kAAAAwDfWbX1LjY0Ndju+a6IGXjvUhxV1HMGtDVi9erWjvXz5csXExKi4uFh3\n",
       "3XWXjDEqKCjQjBkzNH78eEnSsmXL5Ha7VVhYqMmTJ6u6ulpLlizR0qVLNWLECPtzevXqpbVr12rU\n",
       "qFHauXOn1qxZo40bN2rw4MGSpIULF+r222/Xnj171LdvX29fOwAAAHDFnPzquIr/UeToyxp0r4Jc\n",
       "QT6qqGNp95rUiRMn1NTUpG7dukmS9u/fL4/Ho1GjRtljwsPDNXToUBUXF0uStmzZovr6eseYlJQU\n",
       "paenq6SkRJJUUlKiqKgoZWRk2GMyMzMVGRlpjwEAAAA6qrWbV6m+4YzdjomK163pd/iwoo6l1RWX\n",
       "5h577DHddNNNdsAoKyuTJCUmJjrGud1uHT582B4TFBSk+Ph4x5jExET7/LKyMiUkJDiOW5Ylt9tt\n",
       "j2lu8+bN7S0fHRjzHZiY98DDnAce5jzwBOKcf1V3Uu9/9I6jr2/CQH20/SMfVXTlpKWleeVz2hVc\n",
       "pk+fruLiYm3YsEGWZbU6vrUxxpj2fD0AAADQIX1SulGNTV/vbYkIjVbfpJt9WFHH0+bg8vOf/1xv\n",
       "vPGG3n33XfXu3dvuT0pKkiR5PB6lpKTY/R6Pxz6WlJSkxsZGVVZWOlZdPB6Phg0bZo+pqKhwfKcx\n",
       "RuXl5fbnNDdo0KC2lo8O7Ny/yjDfgYV5DzzMeeBhzgNPoM75sRPl+v9Ktjv6xt72gAbfOMRHFV1Z\n",
       "3npKcJv2uDz22GN6/fXXtW7duhab5FNTU5WUlKSioq83Gp0+fVobNmxQZmamJGngwIEKCQlxjCkt\n",
       "LdWuXbvsMRkZGaqpqXHsZykpKdGpU6fsMQAAAEBHs+bDNx2rLXFd3RrSf4QPK+qYWl1xmTp1qlas\n",
       "WKG33npLMTEx9n6T6OhoRUZGyrIsTZs2TXPmzFG/fv2Ulpam2bNnKzo6Wjk5OZKkmJgYTZo0Sfn5\n",
       "+XK73YqLi9P06dM1YMAAZWVlSZLS09M1ZswYTZkyRYsWLZIxRlOmTNG4ceO8dl8cAAAAcCWVHftS\n",
       "H+z4q6Nv9K0/VHBQiI8q6rhaDS6vvvqqLMuyH2N8zqxZs/TUU09JkvLz81VbW6upU6eqqqpKQ4YM\n",
       "UVFRkSIjI+3xBQUFCg4O1oQJE1RbW6usrCytWLHCsQ+msLBQeXl5Gj16tCQpOztbCxYs8MqFAgAA\n",
       "AFfa/2xcLmO+fm9hQmxP3Zo+3IcVdVytBpdvviDyYmbOnKmZM2de8HhoaKjmz5+v+fPnX3BMbGys\n",
       "li9f3qbvAwAAAPzZ3kM79Mm+Dx194zIf5L0t31K73+MCAAAA4OKMMfrjhmWOvt5J12rANRkXOAOt\n",
       "IbgAAAAAXrb982IdKNvt6Mv+p4lteqUIzo/gAgAAAHjRmYY6/XH9Ukff9X1u1XeS+/umoE6C4AIA\n",
       "AAB40btb/6hjJ79+P6HLFaTs2yb6sKLOgeACAAAAeMnxmkr9ZdMfHH1Db/y+EuNSLnAG2orgAgAA\n",
       "AHjJ2xt+rzMNdXY7MjxaYwZP8GFFnQfBBQAAAPCCz0o/0ebd7zn67sp4QBHhUT6qqHMhuAAAAACX\n",
       "qKGxXm+8u9DR17N7b2VcP9JHFXU+BBcAAADgEr279W15jpU6+n44/F952aQXEVwAAACAS1B5wqPV\n",
       "H77u6BvSP0t9evbzUUWdE8EFAAAA+JaMMVr511dU33DG7osMj+bxx5cBwQUAAAD4lj7cuU67D37k\n",
       "6Lv7tomK7NLVRxV1XgQXAAAA4Fs4capK//3+a46+tJQbNKR/lo8q6twILgAAAEA7GWP05rsL9VVd\n",
       "jd0XEhyq+0b8VJZl+bCyzovgAgAAALTT5t3v6aO9Hzj67srIUUJsDx9V1PkRXAAAAIB2qDpZof/7\n",
       "7iJH39WJaRr23XE+qigwEFwAAACANmoyTSr8ywLVnvnK7gsJClXuqMd4Z8tlRnABAAAA2ui9bX/S\n",
       "7i+dTxEbd1uuEuNSfFRR4CC4AAAAAG3wZflevb3x946+tJQbNPS7d/moosBCcAEAAABaUXemVkv/\n",
       "9z/V2NRg93UJi9QDI/9NLotfqa8EfsoAAADARRhj9ObfFqni+GFH/30jpiqua4KPqgo8BBcAAADg\n",
       "Ior/UaQPd77r6Mu8fpRuSsv0UUWBieACAAAAXMBBz+f6v+8tdvQlxV2le4dO8lFFgYvgAgAAAJzH\n",
       "qdoTWvLO82ps/HpfS2hIuH50V75CQ8J8WFlgIrgAAAAAzTQ2Nui1d/5Dx06UO/rvHzFVSXFX+aiq\n",
       "wEZwAQAAAJp5a8NS7Sn9xNE3dMBdGnjt7T6qCAQXAAAA4BuK//EXvbf9T46+Pj3Tdc/tD/umIEgi\n",
       "uAAAAAC2HQe26I11rzr6ukV116S7fqHgoBAfVQWJ4AIAAABIOvsEsSXv/IeaTJPdFxIcqkfHPaHo\n",
       "iFgfVgaJ4AIAAADoaHWZFv7xGZ2pP233WbI0cfTPdZW7jw8rwzkEFwAAAAS0k19V69W3ntbJ2mpH\n",
       "/73DJmnANRk+qgrNEVwAAAAQsM7U12nR/zyriuOHHf0jBo7XsO+O9VFVOB+CCwAAAAJSfcMZ/e7P\n",
       "c/VF2R5H/6Brh2ncbbk+qgoXQnABAABAwKlvqNfv/jxXO7/Y6ujvm3KDckb+TC6LX5P9Tasz8v77\n",
       "7+vuu+9WSkqKXC6Xli1b1mLMrFmzlJycrIiICA0fPlw7duxwHK+rq1NeXp4SEhIUFRWl7OxsHTp0\n",
       "yDGmqqpKubm5io2NVWxsrCZOnKjqaud9hgAAAMClOhtafq0dB7Y4+nt2761JYx/nscd+qtXgcurU\n",
       "Kd1444166aWX1KVLF1mW5Tg+d+5czZs3TwsWLNCmTZvkdrs1cuRI1dTU2GOmTZumVatWaeXKlVq/\n",
       "fr1OnDihsWPHqqnp60fN5eTkaPv27VqzZo1Wr16trVu3KjeXJToAAAB4T31DvZb8eW6L0JIUd5V+\n",
       "es8sdQmL9FFlaE1wawPuvPNO3XnnnZKkhx9+2HHMGKOCggLNmDFD48ePlyQtW7ZMbrdbhYWFmjx5\n",
       "sqqrq7VkyRItXbpUI0aMkCQtX75cvXr10tq1azVq1Cjt3LlTa9as0caNGzV48GBJ0sKFC3X77bdr\n",
       "z5496tu3rzevGQAAAAGovqFeS96Zq08PbHb0J8al6Gf3PqOukbyrxZ9d0s17+/fvl8fj0ahRo+y+\n",
       "8PBwDR06VMXFxZKkLVu2qL6+3jEmJSVF6enpKikpkSSVlJQoKipKGRlfP24uMzNTkZGR9hgAAADg\n",
       "26o7U6vFf5qjT/c3Cy3dUpRHaOkQWl1xuZiysjJJUmJioqPf7Xbr8OHD9pigoCDFx8c7xiQmJtrn\n",
       "l5WVKSEh4f9v796Dm6zXPIB/00LSW5Je07S0QCstIHdpkVYuAgVl94gcvMDR9Zw6zojjjcvOIM66\n",
       "6xxlcQZGFlZBZR1HzhGWymHdWR1YiwOrRVCoFIsWELm10Ca90Gtobu/72z/apo1NSy9p8ib9fmZK\n",
       "kvf3vL88ya/PTB7yvm/dxlUqFQwGgyvGk+Li4h7HKPhwvYcnrvvwwzUffrjmw4+v17zVbsHR8/tR\n",
       "11Lltl0XHoe54x7BL+cv+zSf4SYjI8Mr8wyqcenNb8+F+S0hxFA9NRERERERAKDZWo+vft6HZmu9\n",
       "23ZdeByWTP4HRKi1fsqM+mtQjYvRaAQAmM1mpKSkuLabzWbXmNFohCRJqKurc/vWxWw2Y/78+a6Y\n",
       "mpoat7mFEKiurnbN40lWVtZg0qcA0fG/Mlzv4YXrPvxwzYcfrvnw4+s1r6i+jM/++x00W92vVJti\n",
       "SMdzy/6Fh4f5iLeuFDyoc1zS0tJgNBpRWFjo2ma1WnH8+HHk5uYCAGbOnImRI0e6xdy4cQMXLlxw\n",
       "xeTk5KClpcXtfJaTJ0/CYrG4YoiIiIiI+qrs2hn8+9/+Cc2t7h+ax4+ehpcf+Vc2LQHojt+4WCwW\n",
       "XHFXvPQAABDxSURBVLp0CQAgyzKuX7+Os2fPIi4uDqmpqVi7di02b96MCRMmICMjA5s2bYJWq8UT\n",
       "TzwBANDr9XjmmWewYcMGGAwGxMbGYv369Zg2bRry8vIAABMnTsSDDz6I1atXY/fu3RBCYPXq1Xjo\n",
       "oYe8dkwcEREREQU/IQS++uEzfHHiEwghu41ljZ+PJxa/yL/TEqDu2LicPn0aCxcuBNB23srrr7+O\n",
       "119/Hfn5+fjoo4+wYcMGtLa24oUXXkB9fT1mz56NwsJCREZ2XgN7+/btGDFiBFauXInW1lbk5eXh\n",
       "k08+cTsPZt++fXjppZfwwAMPAAAefvhhvPvuu95+vUREREQUpGwOK/YdeQcll77tNrbwnuVYNueP\n",
       "CFEN6oAj8iOVCLCz5LseI6fX6/2YCfkKj4Eenrjuww/XfPjhmg8/Q7nmdY1m/McXb6Gy9prbdpUq\n",
       "BMvn5mPBjGVef07qG299fh+yq4oREREREflC2bUz+MuX/4bb1ma37RGaKPxp6T9i4pgZfsqMvImN\n",
       "CxEREREFJIfTjs+//Sv+7+zn3caS48bgmd9tREJ0kh8yo6HAxoWIiIiIAk5VXQX+8r9v4+ZvDg0D\n",
       "gOnjcvHk4pegUYf7PjEaMmxciIiIiChgCCHw7bkv8dk3H8Eh2d3GVKoQ/C7nSeRlrbjjH0OnwMPG\n",
       "hYiIiIgCwq2mahQcfR/nr5/pNharM+CPD6xHevIEP2RGvsDGhYiIiIgUTZYlFJUexucnPoHdYe02\n",
       "PjNzLh5f+BzCNZEe9qZgwcaFiIiIiBSrqq4c//nVTlwzXew2phkZhscWrEb2hPt5aNgwwMaFiIiI\n",
       "iBTHam9F4akDOFbyP5BkZ7fxcaMm4Q95L/KqYcMIGxciIiIiUgxZyDhVdgyfn/grmm83dBsPU0dg\n",
       "+dx8zJ6UhxBViB8yJH9h40JEREREinCl8jwOfv0hKqovexyfete9eOz+1dBHxfo4M1ICNi5ERERE\n",
       "5FeVtddw6Lv9KL38ncdxfVQcVsx7BtPH5fBclmGMjQsRERER+UV1/U0c/m4/zvxyHAKi2/jIUDUW\n",
       "zlyOvKwV0IwM80OGpCRsXIiIiIjIp2oaqnDk9N9w6vwxyEL2GDMj4z48POdPiNUZfJwdKRUbFyIi\n",
       "IiLyidrmSvx88yTKv73g8RsWABidmIHlc/MxbtQkH2dHSsfGhYiIiIiGjBACF8rP4qvi/8KlG+d6\n",
       "jEuOH4u/z3kCk9OyeR4LecTGhYiIiIi8rtVmwanzx1BUehjV9Td7jDPEjMLfzf4Dpmfk8vLG1Cs2\n",
       "LkRERETkNTdrrqKo9DCKL3wNu9PWY9yo+LFYOPP3uCdzDkJDQn2YIQUqNi5ERERENCiW1ib88EsR\n",
       "TpUdQ3n1r73GGvVj8PsF+ZgwejoPCaN+YeNCRERERP3mlBw4f70Ep84fw09XTkOSnT3GhoSEYvq4\n",
       "HBjDMhGvTcbEMTN8mCkFCzYuRERERNQnkuTExYpSlFz6FqWXv0OrzdJrvD4qDvdNXoKcyYuhj4xF\n",
       "cXGxjzKlYMTGhYiIiIh6ZHfa8Et5KUqvfI/Sy9/jtrW513gVVMhMnYr7pjyAKXfdy/NXyGvYuBAR\n",
       "ERGRmyZLPX66Woyfrp7GxfKzcDjtd9wnIToZ905cgOyJ9yNGm+CDLGm4YeNCRERENMzZ7K24XFmG\n",
       "i+U/4mJFKSprr/Vpv8gwLaaNy8GsiQuRljSeJ9vTkGLjQkRERDTMSJIT5dW/uhqVa1UXez25vquI\n",
       "MC2m3TUbMzLuQ0bqFB4KRj7DxoWIiIgoyFmszbhWdRFXqy7gSuV5XDdf6tPhXx1iouIxKT0bU9Jn\n",
       "ITNlCkJD+RGSfI+/dURERERBxCk5YLpVgQrzZVw1XcTVygsw19/o1xwqqJCaOA6T07IwOT0bo+LT\n",
       "eBgY+R0bFyIiIqIAZXfaUFV7HRXVV3Cj5jIqqq+gsu46JKlvh311laBPQuboaRifOhUZqVMQGaYd\n",
       "goyJBo6NCxEREZHCSZIT1Q1VMN0qR1VdOUx1Fai6VY6a+krIQh7QnNqIaGSkTMH41KnIHD0VcbpE\n",
       "L2dN5F1sXIiIiIgUQAiBJks9ahqrUNNQhdqGtlvTrQpUN1RClqUBz61ShSA5bjTSkiciLWkC0pMm\n",
       "IFZn4OFfFFDYuBARERH5iMNpR31zLeqba1DbaEJtYxVqGkyobahCbaMJdqfNK8+jj4pDakI6Ug13\n",
       "IT15IkYnZiBcE+GVuYn8hY0LERERkRdIkhNNtxvQ0FKH+uYaNLTUupqUtttatLQ2ev1543SJSDGk\n",
       "IzUhHSmGu5CSkA5dZLTXn4fI39i4EBEREfVAliVYrC2wWJvQfLsBTZYGNFnq0XS7Hs23G9BouYVm\n",
       "SwMab9fD0to0pLnoI2NhjEtFUuxoGONGwxibCmNcCiI0UUP6vERKwcaFiIiIgp4sZNjsVljtFrTa\n",
       "bqPV1oKW1mZYrM2wtDa5blusHffbHrfaLBAQPsszTB2BhOgkJEQnIV6fhIRoIxKik2GMS2WDQsMe\n",
       "GxciIiJSJCEEnJIDNocVdocVNoet/bbjcWtbE2K/DavN0n57G612C1ptlvb7bWNWe6tPG5CeqFQh\n",
       "0EfGIEabgFhtAhKikxEfbXQ1KlHhOp4wT9QDxTUuu3btwtatW2EymTBp0iRs374dc+bM8XdaRERE\n",
       "BECSJTiddjgkBxxOO5w93DokB5ySHQ5n563DaXON2x02VJlvwik58H3F57C3NyV2hw02hxU2Z9t9\n",
       "McBL/fqDCipEheugi4pFjDYBMVHxiNF2/CQgOioe+qhYhIaE+jtVooCkqMaloKAAa9euxXvvvYc5\n",
       "c+Zg586dWLp0KcrKypCamurv9IiIiHokhIAQMmQhQ5bbb4XUdl+WIYQMSZa6xEhdYqXOfdq3u8X3\n",
       "GiNDkp2QZQlOyQlJdkKSnJBkCZLsgCRJcMpOyLKzfVxqH+8a52yLaY91G2uPdUgOOJ32Af/NkF7d\n",
       "8v6U3hShiUJkmBZREXroImOgi4iBLjK6/TbGtS0qXIfQUEV9tCIKKiohhP+/N2137733Yvr06fjg\n",
       "gw9c2zIzM/Hoo49i8+bNAIDGxs6rcVQ3l/c6X99eWd9evrffpr7O5+2vtfv+OpTzvvz6668AgHHj\n",
       "xnXGKfh96ftb4t33uO/viHLWtodIAMCVK1cAAOnp6YOarz/vS9c5O+8L15oKCNcCu/37m/1cv5+i\n",
       "62+q5/nb5uwyv2tO9/lF5453nF90TjC4+bu89l7nd3tNnfN7zFMICMht40J2vV9CCNTW1UIIgdjY\n",
       "2M4xIbdl7XrcGf/b/fsd6/a4Y//OxxACMjpjOx93bVDaG4j2hoKUTT1CgzBNBMLVkQjXRCIyXIuo\n",
       "MB0iw7WIDNMhMlzX1qCEa133I8K0/IbEi4qLiwEAWVlZfs6EfKnr53e9Xj/geRTz3wJ2ux1nzpzB\n",
       "hg0b3LYvWbIEJ06c8LjPOwf/2RepkUIcPe/vDMgfin7xdwbka9dq/Z0BKUlo6AhoRoRBPVID9ci2\n",
       "W83IcGhGaKBWh7U3IREIU0cgXBPZfttxv20sXN02zm9DiAKbYiq4trYWkiQhMTHRbbvBYIDJZPK4\n",
       "z5v5e3yRGhEREQUwp12gxW7xdxoEICMjA4D7/8AT9VWIvxMgIiIiIiK6E8U0LvHx8QgNDYXZbHbb\n",
       "bjabkZSU5KesiIiIiIhICRRzqJharcbMmTNRWFiIRx55xLX9yJEjeOyxx1yPB3NCDxERERERBSbF\n",
       "NC4AsH79ejz11FOYNWsWcnNz8f7778NkMuG5557zd2pERERERORHimpcHn/8cdTV1WHTpk2oqqrC\n",
       "lClTcOjQIf4NFyIiIiKiYU5Rf8eFiIiIiIjIE8WcnN/Vrl27kJaWhvDwcGRlZeH48eO9xp87dw7z\n",
       "589HREQEUlJS8Oabb/ooU/KW/qz5tWvXEBIS0u2nsLDQhxnTYHzzzTdYtmwZUlJSEBISgj177nxp\n",
       "c9Z5YOvvmrPOA99bb72F7Oxs6PV6GAwGLFu2DD///PMd92OtB66BrDlrPfDt3LkT06ZNg16vh16v\n",
       "R25uLg4dOtTrPgOtc8U1LgUFBVi7di1ee+01nD17Frm5uVi6dCkqKio8xjc1NWHx4sVISkpCcXEx\n",
       "duzYga1bt2Lbtm0+zpwGqr9r3uHLL7+EyWRy/SxYsMBHGdNgWSwWTJ06FTt27EB4eDhUKlWv8azz\n",
       "wNffNe/AOg9cX3/9NV588UWcPHkSR48exYgRI5CXl4f6+voe92GtB7aBrHkH1nrgSk1NxZYtW1BS\n",
       "UoIffvgBCxcuxPLly/Hjjz96jB9UnQuFmTVrlnj22WfdtmVkZIhXX33VY/yuXbuEXq8XVqvVtW3T\n",
       "pk1i1KhRQ5oneU9/1/zq1atCpVKJ4uJiX6RHQywqKkrs2bOn1xjWeXDpy5qzzoNPS0uLCA0NFV98\n",
       "8UWPMaz14NKXNWetB6fY2Fixe/duj2ODqXNFfeNit9tx5swZLFmyxG37kiVLcOLECY/7nDx5EnPn\n",
       "zoVGo3GLr6ysxPXr14c0Xxq8gax5hxUrViAxMRFz5szBwYMHhzJN8jPW+fDFOg8eTU1NkGUZMTEx\n",
       "Pcaw1oNLX9a8A2s9OEiShP3798NqtWLevHkeYwZT54pqXGprayFJEhITE922GwwGmEwmj/uYTKZu\n",
       "8R2Pe9qHlGMga67VavH222/jwIEDOHz4MBYtWoSVK1di7969vkiZ/IB1PvywzoPPmjVrMGPGDOTk\n",
       "5PQYw1oPLn1Zc9Z6cDh37hyioqIQFhaGZ599Fp9++inGjx/vMXYwda6oyyEPRF+Pk6bgERcXh3Xr\n",
       "1rke33PPPairq8OWLVvw5JNP+jEzGiqs8+GHdR5c1q9fjxMnTuD48eO91jNrPXj0dc1Z68FhwoQJ\n",
       "KC0tRWNjIw4cOIBVq1bh2LFjyMrK6hY7mDpX1Dcu8fHxCA0NhdlsdttuNpuRlJTkcR+j0ditO+vY\n",
       "32g0Dk2i5DUDWXNPsrOzcenSJW+nRwrBOieAdR6o1q1bh4KCAhw9ehRjx47tNZa1Hhz6s+aesNYD\n",
       "z8iRI5Geno4ZM2Zg8+bNmD17Nnbu3OkxdjB1rqjGRa1WY+bMmd0ugXfkyBHk5uZ63CcnJwdFRUWw\n",
       "2Wxu8aNGjcKYMWOGNF8avIGsuSdnz55FcnKyt9MjhWCdE8A6D0Rr1qxxfYDNzMy8YzxrPfD1d809\n",
       "Ya0HPkmSIMuyx7FB1bnXLh/gJQUFBUKtVosPP/xQlJWViZdffllotVpRXl4uhBBi48aNYtGiRa74\n",
       "xsZGYTQaxapVq8RPP/0kDh48KHQ6ndi2bZu/XgL1U3/X/OOPPxb79u0TZWVl4sKFC2Lr1q1CrVaL\n",
       "7du3++slUD+1tLSIkpISUVJSIiIiIsQbb7whSkpKWOdBrL9rzjoPfM8//7zQ6XTi6NGjoqqqyvXT\n",
       "0tLiimGtB5eBrDlrPfC98soroqioSFy9elWUlpaKjRs3ipCQEFFYWCiE8G6dK65xEaLtMmljx44V\n",
       "Go1GZGVliaKiItdYfn6+SEtLc4s/d+6cmDdvnggLCxPJycnijTfe8HXKNEj9WfM9e/aIu+++W0RG\n",
       "RgqdTieys7PF3r17/ZE2DdCxY8eESqUSKpVKhISEuO4//fTTQgjWeTDq75qzzgPfb9e64+fPf/6z\n",
       "K4a1HlwGsuas9cCXn58vxowZIzQajTAYDGLx4sWupqVj3Ft1rhJCCG9+NURERERERORtijrHhYiI\n",
       "iIiIyBM2LkREREREpHhsXIiIiIiISPHYuBARERERkeKxcSEiIiIiIsVj40JERERERIrHxoWIiIiI\n",
       "iBSPjQsRERERESne/wN8nGNQWDoh4wAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48092abe48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 3, 0.01)\n",
    "plt.plot(x, np.exp(x**2))\n",
    "plt.title('exp(x^2)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As x gets larger the value of $e^{x^2}$ grows exponentially (hence the name *exponential function*). If we take the reciprocal of a rapidly increasing number the result should approach, but never reach 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAyAAAAGaCAYAAAD3vidSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd0FGXfxvFrN40khF5MKIHQQYFAKEakKB0pAiKIIiAi\n",
       "qI8I6AMojwiiqChiA0URBEWKIB0FpBMEYghKR0KPiZQQatruvH/4Eh0TmiSZbPb7OYdz9HfP7F7J\n",
       "0C529x6bYRiGAAAAACAH2K0OAAAAAMB9UEAAAAAA5BgKCAAAAIAcQwEBAAAAkGMoIAAAAAByDAUE\n",
       "AAAAQI6hgAAAMmjRooUqV64sp9NpdRRLzZkzR3a7XWvXrrU6CgDkGRQQAIDJ8uXL9eOPP2rUqFGy\n",
       "2//6YyItLU3vv/+++vTpo9q1a8vb21t2u12ffvrpTT3u0KFDZbfbdfz48SzJefbsWdWqVUt2u13l\n",
       "ypXTsWPHbnj81KlT1aVLF1WuXFn+/v4qWLCgGjZsqA8++EBpaWkZzunWrZtq1KihF154Qdw2CwCy\n",
       "ho0bEQIA/i40NFQJCQk6fPiwbDZb+vzcuXMqUqSIbDabSpYsKS8vLx0/flyffPKJ+vfvf8PHDQkJ\n",
       "UdGiRbV9+/bbzpiYmKj7779fUVFRqlWrlnbu3KkKFSpo/fr1CgoKyvScTz75RE8//bRKliypZs2a\n",
       "qXz58jp16pQWL16sP/74Q40aNdLq1avl7e1tOm/mzJl6/PHHNXfuXHXt2vW2swOAu+MVEABAuoiI\n",
       "CO3cuVOPPPKIqXxIkr+/v1asWKHY2FjFxsaqT58+N/24O3bs0JEjR9S5c+fbznjx4kW1adNGUVFR\n",
       "Gjp0qHbs2KF3331XMTExuu+++xQfH5/peVWqVNGiRYsUGxurWbNm6fXXX9eUKVN08OBB1a5dW5s2\n",
       "bdLHH3+c4bzOnTvLz89PkydPvu3sAAAKCABYLioqSt27d1dQUJB8fHwUFBSkXr166dChQ+nHPP/8\n",
       "87Lb7XruuecynH/1cwr33HNP+tuIjhw5IrvdrmbNmunkyZPq2bOnihcvLj8/P9WrV09z587NNMvU\n",
       "qVMlSd27d8+w5uXlpVatWqlkyZK3/DV+9913kpReQCZOnCi73a6OHTtmOHbz5s3y8vJSpUqVdOHC\n",
       "BdPa5cuX1a5dO23btk3vvPOOxo8fL0kaPHiwZs6cqcOHD6t58+Y6c+ZMhsdt1qyZ2rdvn6FYBQQE\n",
       "6MUXX5QkrVu3LsN5/v7+euCBB7R27VodPnz4lr92AIAZBQQALPT111+rQYMGWrZsmZo1a6bBgwfr\n",
       "7rvv1jfffKOwsDDt3LlTkjR+/HiFhYXpo48+0sKFC9PPP3TokPr3768iRYpo9uzZ8vT0ND1+QkKC\n",
       "GjVqpH379qlfv3567LHH9Ntvv6l79+6aOHFihjyrVq1SgQIFVLNmzSz9OhcsWKCqVauqSpUqkv4s\n",
       "VB07dtSSJUtMOc6ePasePXrI09NTc+bMUUBAQPpaUlKSOnbsqK1bt2rGjBkaMmSI6TkeeeQRLVmy\n",
       "REeOHFHz5s117ty5m8539fv2z+/fVY0aNZL05/cHAHCbDACAJQ4ePGj4+PgYFStWNGJjY01r69at\n",
       "Mzw9PY26deumz2JiYoxChQoZhQsXNo4cOWIkJycbdevWNex2u7Fo0SLT+YcPHzZsNpths9mM7t27\n",
       "m9YOHTpkFCpUyPDx8TGOHj2aPj9y5Ihhs9mM+++//6byjxo1yrDZbMann3563eMOHDhg2Gw24+WX\n",
       "XzbNExISjHLlyhne3t7Gtm3bDMMwjPbt2xs2m814//33MzzO+vXrjdGjRxvr1q277vP9/PPPxujR\n",
       "o43Fixff1NdhGIbRqlUrw2azGVOmTMl0/aeffjJsNpvx6KOP3vRjAgAyxysgAGCRyZMnKyUlRe+9\n",
       "954CAwNNa02aNFH79u0VFRWlvXv3SpLKly+vqVOn6ty5c3r44Yc1ZMgQRUVF6bnnnlOHDh0yfQ5P\n",
       "T0+9+eabpllISIiefvpppaSk6Kuvvkqfx8TESJJKly6dlV+m5s+fL0kZPv9RqFAhzZ49W4ZhqHv3\n",
       "7ho9erSWLl2qTp06ZfpWs8aNG+uVV15RkyZNrvt8derU0SuvvKL27dvfVL6JEydq5cqVqlOnjvr2\n",
       "7ZvpMVe/J1e/RwCAfy/z15oBANlu8+bNkqT169crMjIyw/rVD1Pv3btX1apVk/TnX+KfeeYZffzx\n",
       "x9q2bZvCwsLSPweRmbJlyyo4ODjDvHHjxho3bpyio6PTZ6dOnZIkFSlS5N9/UZn47rvvFBwcrDp1\n",
       "6mRYa9CggcaNG6cXX3xRo0ePVnBwsKZNm5alz389X3/9tYYOHapSpUppwYIF8vDwyPS4okWLSpL+\n",
       "+OOPHMsGAHkVBQQALHL1g9LvvvvuNY+x2Wy6dOmSada1a9f03Zqefvrpa35uQdI1PzB+dZ6YmGh6\n",
       "LklZer+LEydOKDIyMtNXNK7q1KmThg8fLofDoccff1wFCxbMsue/nhkzZqhPnz4qU6aM1qxZo7Jl\n",
       "y17z2Ks3ZPznB9gBALeOt2ABgEUKFiwom82ms2fPyul0ZvrD4XDoscceSz8nISFBjz/+uLy9vRUQ\n",
       "EKD//ve/io2NveZzXGtL2qvzv/9lv1ixYpL+/CB4Vvnuu+9kGMY1t99NSUlR9+7d5XA4VLRoUb39\n",
       "9tv65Zdfsuz5r2XKlCnq3bu3ypcvrw0bNigkJOS6x1/9nhQvXjzbswFAXkcBAQCLhIeHyzAMbdiw\n",
       "4abP6dOnj44dO6Z33nlHn332mU6fPq0ePXqk/wv9Px07dkxHjx7NMF+/fr2kP286eNXVv4SfOHHi\n",
       "Vr6M61qwYIFKlCihe++9N9P1F198UT///LOGDBmiRYsWKTU1Vd26dcvwqk9Wev/99zVgwABVrlxZ\n",
       "GzZsuO4rH1edPHlSkm5YVAAAN0YBAQCLPPvss/L29tbQoUO1f//+DOtpaWlau3Zt+v9PnDhRixcv\n",
       "VqdOnfTss8+qW7duevLJJ7Vx40aNGjUq0+dIS0vTsGHDTG+rOnTokCZNmiRvb2/17NkzfR4cHKzS\n",
       "pUvr559/zpKv7/Tp09q4cWOm9/qQpIULF+rDDz9UvXr19Oabbyo8PFxjxozRgQMHNHDgwCzJ8E/j\n",
       "xo3T4MGDVaNGDW3YsOGad03/p23btknSDT8ADwC4MZuRlW/2BQDcktmzZ6tPnz5KS0tT69atValS\n",
       "JTkcDh0/flybN29Wamqqzp49q8jISN1zzz0KCgpSdHR0+lunkpKSVL9+fe3Zs0crV67UfffdJ+nP\n",
       "GxGGhISoZs2aSkxMVJEiRdSiRQudPXtWc+fO1YULFzRhwgQNGjTIlKdfv3764osvtGPHDtWqVStD\n",
       "3jfffFP79u2TJEVHR+uXX35Rw4YNVblyZUlStWrVNGzYMEnSF198oX79+mn58uVq3bq16XGOHj2q\n",
       "0NBQGYahHTt2qFy5culrrVq10qpVqzR16tRbutv6jXz55Zfq06ePbDabnn766fQPlv9d4cKFM3xP\n",
       "JOnhhx/Wt99+q0OHDpmyAgD+hRvt07t+/Xqjffv2RqlSpQybzWZMnz79hnv7/vLLL0bjxo0NX19f\n",
       "o1SpUsaYMWNua69gAMjL9uzZY/Tr188oX7684ePjYxQuXNioXr260bdvX2PZsmVGYmKiERISYnh7\n",
       "extbtmzJcP7evXsNf39/IzAw0IiPjzcM46/7gDRr1sw4efKk0bNnT6N48eKGr6+vERYWZsyZMyfT\n",
       "LBEREYbNZjOGDx+e6XrTpk0Nm81m2O1204+rs2bNmqUf265dO6NQoUJGamqq6TFSU1ONhg0bGna7\n",
       "3Zg3b16G54iPjzcCAwON/PnzG3v37r3p7+ONvPrqq+k5r94j5Z8/ypcvn+G8ixcvGv7+/jd9fxQA\n",
       "wPXd8BWQFStWaPPmzQoNDVWvXr00efJk9erV65rHnz9/XpUrV1bTpk31yiuvaO/everTp49effXV\n",
       "DHetBQBkj6uvgDRt2lRr1qy5pXPr1KmjM2fO6PDhw7Lb/907dS9cuKDixYura9eupnuNuKIZM2ao\n",
       "d+/emjdvnrp06WJ1HABweTf8k6VNmzYaO3asunTpclN/EH399ddKSkrSl19+qerVq6tLly4aNmyY\n",
       "JkyYkCWBAQDZ6/XXX9fx48c1a9asf/0Yy5cvV2pq6jV3v3IVTqdT48ePV2hoKOUDALJIln8IfcuW\n",
       "Lbr33nvl4+OTPmvZsqViY2Mz3YkFAJC7tGnTRs2bN9drr732r+8J8vDDD8vhcLh8AZk3b5727Nmj\n",
       "d955x+ooAJBnZPmNCOPi4jJsaXj1hldxcXGmO/L+/QZYAICsc/78eUl/7oL1b36vnTdvnulx3FXr\n",
       "1q3T7wHCn1kA8JfbuWlslhcQ7hILANYLDg5WQkKC1TEAAMggy9+CdccddyguLs40u3rH3TvuuCOr\n",
       "nw4AAACAC8nyV0DuvvtuDRs2TMnJyemfA1m1apVKlSplevvVPx05tUepaSlKdaTqctIFXbySqAuX\n",
       "E3XxcqLOXz6n04lxSkq5/K8y2Wx2hQRV010h9VWzQgMVK0gRskpkZKQkKSwszOIkyClcc/fEdXc/\n",
       "XHP3wzV3P1n1VtQbFpBLly7p4MGDkv7cDeTo0aOKjo5W0aJFVaZMGY0YMULbt2/X6tWrJUmPPPKI\n",
       "Ro8erd69e2vkyJHav3+/3nrrLb366qvXfZ5aFe++7rphGLp45bxOJ/6uU+d+1x8JJ3X8jxgd/+OQ\n",
       "Ll65/jfDMJw6dHK3Dp3crYUbpymoaLBqVmiosKpNVKLwzd0FFwAAAMDtu2EB2b59e/qddW02m0aN\n",
       "GqVRo0apd+/e+uKLLxQXF6eYmJj04wsUKKBVq1bpmWeeUVhYmIoUKaIXXnhBgwcPvq2gNptNAX4F\n",
       "FeBXUOUDq6bPDcPQuYundfyPQzoad1AHT+7SsbiDchrOaz5W7Jmjij1zVN9vm6Nyd1RRvWpNVady\n",
       "I/nnC7itjAAAAACu74YFpGnTpnI6r/2X+WnTpmWY3XnnnVq/fv3tJbtJNptNhQOKq3BAcdWs0FCS\n",
       "lJRyRTGxe3Tg+K/adyxasaePXPP8I3H7dSRuvxasn6o7y4epUc02qlymJh+mBwAAALJBln8GJDfI\n",
       "5+2r6uXqqnq5upKkM4nx+iVmq36N2aZDJ/fIyOTVEYczTTsP/aSdh35SycKldW+tNqpXtZl8ffxy\n",
       "Oj4AAACQZ+XJAvJPRQuWVLPQDmoW2kGXrpzXzkNbtX3fOh06uTvT4+MTTujbdZ9pyeaZql/tPjWr\n",
       "04EPrgMAAABZwC0KyN/5+xZQ+J0tFH5nC505H6/Ifeu1be86nToXm+HY5NQkbfxluTb9+r3qVG6k\n",
       "FmGdFVSsXM6HBgAAAPIItysgf1e0QEm1qt9NLes9pEOxe7Rx53LtPPSTnE6H6TjDcOrn/Rv08/4N\n",
       "qlEuTC3qdVVIUNVrPCoAAACAa3HrAnKVzWZTxVI1VLFUDSVePKuIXSu1edcPOn8p412Edx+J1O4j\n",
       "kaoWXEcPhPdUmRIVLEgMAAAAuCYKyD8UzF9EbRp2V8t6XfXzgY1aHblAcWePZzhu79Eo7T0apdqV\n",
       "wtWu4SMqWaS0BWkBAAAA10IBuQYPD0/Vr9ZMYVWbaFfMdq2KnK+jcQcyHBd9MEI7f/tJ9as10wN3\n",
       "91TB/EUsSAsAAAC4BgrIDdhtdtWs0EB3hdTXwRO7tGLr7Ay7ZxmGU1v3/KgdBzerRVgXNavTQd6e\n",
       "PhYlBgAAAHIvCshNstlsqlzmLlUqfaf2HYvWkoiZOvFHjOmYlNQkLdvytbbsWqmO9/ZW7Yrh3NAQ\n",
       "AAAA+BsKyC2y2WyqFhyqqmVrK/q3LVq+ZZbiE06Yjjl74ZSmLR+vCqVq6KGm/RVULNiitAAAAEDu\n",
       "Yrc6gKuy2WwKrRSu4Y++r27NBsg/X0CGYw6d3K23vxmixZtnKiU12YKUAAAAQO5CAblNHnYPNarZ\n",
       "Wv97fLKa1m4vu93DtO50OrQ6cr7GffWc9hyJsiglAAAAkDtQQLKIX7786tzkCY3o+b6qBdfJsH7m\n",
       "fLw+WTRG01e8owuXz1mQEAAAALAeBSSLlSxSWgM6/k9PtBumgvmLZliPOrBJb3z1nHYc3GxBOgAA\n",
       "AMBaFJBsYLPZVKvi3Xrp0Q/VpPYDssm8E9alK+c1bfl4TVs+XhevnLcoJQAAAJDzKCDZyNfHT12a\n",
       "9NPQ7uNVunhIhvUdBzdr3Mz/aOdvP1mQDgAAAMh5FJAcULZkRQ3tPl4PhD8qD7t55+MLVxI1ddmb\n",
       "+nrlB0pKuWJRQgAAACBnUEByiIfdQy3rddWLPd5R6RIZXw3ZuneNxs8aoqNxBy1IBwAAAOQMCkgO\n",
       "CypWTkO7va22DXtk2LL3VOLvem/ecK2KXCCn4bQoIQAAAJB9KCAW8PDwVOsGD+uF7uNVskhp05rT\n",
       "6dCSzTP08YJRSrx41qKEAAAAQPaggFiodPEQvdj9Xd1zV+sMawdP/Kq3Zw3W/mM7LUgGAAAAZA8K\n",
       "iMW8vXz08H0D1O+B4fLLF2Bau3AlUZMWjtYP2+byliwAAADkCRSQXKJmhYYa3nOiKpe+yzQ3DKeW\n",
       "bZmlTxeN5Z4hAAAAcHkUkFykUP6ievrBV9W6wcMZbl6492jU/++SdcCidAAAAMDto4DkMna7h9o2\n",
       "7KEBnV6Rv28B01rCxdN6/9uXtXXPGovSAQAAALeHApJLVQsO1X97TFD5wKqmeZojVV+v+kDz138u\n",
       "hyPNonQAAADAv0MBycUKBxTTc13Gqmlohwxr66OXatLC0bpwOdGCZAAAAMC/QwHJ5Tw8PNW5cV/1\n",
       "ajVYXh7eprWDJ37Vu7Nf0MlThy1KBwAAANwaCoiLCKvaRM93G6fCAcVN87MXTum9eSP0a8w2i5IB\n",
       "AAAAN48C4kLKlKigF7qPV8VSNUzzlNQkfb5knNZGLZZhGBalAwAAAG6MAuJiAvwK6ZkHR6txrbam\n",
       "uSFD3238QnPWTObD6QAAAMi1KCAuyMPDU12b9tdDTfvLbjNfwohdK/XJotd0OfmiRekAAACAa6OA\n",
       "uLB7a7XVUx3/p3zefqb5/uM79f68l5Rw4bRFyQAAAIDMUUBcXLXgUA3u9qaKFChhmv9+5pjemztM\n",
       "v585ZlEyAAAAICMKSB4QWLSshj78tsoFVjHNz108o4nzRujQyT0WJQMAAADMKCB5RIBfIT3beYxq\n",
       "Vmhoml9JvqSPvxulnb9tsSgZAAAA8BcKSB7i7emjvm1fVKO7WpvmaY5UfbHsbW38ZYVFyQAAAIA/\n",
       "UUDyGLvdQw81e0rt7u5pmhsyNG/tp1oa8TX3CgEAAIBlKCB5kM1mU6v6D6lH82czbNO7cvs8zVr9\n",
       "kRxOh0XpAAAA4M4oIHnY3TWa68n2L8nL09s037rnR01f8Y7SHKkWJQMAAIC7ooDkcTXKh+k/XcbK\n",
       "P1+Aab7zty36fMk4paQlW5QMAAAA7ogC4gbK3VH5z3uFBBQ3zfccjdInC8coKeWKRckAAADgbigg\n",
       "bqJE4VIa9NAbKlEoyDT/7eRufbzgFV1KumBRMgAAALgTCogbKRxQXM91fUNBxcqZ5kfjD+rD+f/T\n",
       "+UvnrAkGAAAAt0EBcTMF/AvpP11eU3DJSqZ57Okj+uDbl5Rw4ZRFyQAAAOAOKCBuyD9fgJ7pPEYV\n",
       "S9Uwzf84F6v3572kU+d+tygZAAAA8joKiJvK5+2rAR1fUfXgOqb52Qun9MH8kZQQAAAAZAsKiBvz\n",
       "9vJRv/YjVKvi3aZ54sUzlBAAAABkCwqIm/P08FLvNi+ofrVmpjklBAAAANmBAgJ52D30SPNn1aDa\n",
       "faY5JQQAAABZjQICSZLd7qEezZ+hhAAAACBbUUCQjhICAACA7EYBgQklBAAAANmJAoIMKCEAAADI\n",
       "LhQQZOp6JeTjBa9wx3QAAAD8KxQQXNO1SsjZC6f00YJROn8pwaJkAAAAcFUUEFzX1RISVrWJaX7q\n",
       "XKw+/m6ULl05b1EyAAAAuCIKCG7IbvdQzxbPZbhj+u9njmnSwtG6knzJomQAAABwNRQQ3BQPu4ce\n",
       "bz1E1cvVNc2P/3FIny4aq+TUJIuSAQAAwJVQQHDTPD281Lfdf1W59F2meczve/XZkjeUmpZiUTIA\n",
       "AAC4CgoIbom3p4+ebP+SygdWNc0PHP9FXyx7W2mOVIuSAQAAwBXcVAGZNGmSypcvL19fX4WFhWnT\n",
       "pk3XPX758uVq2LChChQooOLFi6tTp046ePBglgSG9Xy8fTWg4/9UukSIab77SKRm/PCenE6HRckA\n",
       "AACQ292wgMyZM0fPP/+8Ro4cqejoaIWHh6tNmzY6fvx4psf/9ttv6tSpk5o2baro6GitXr1aSUlJ\n",
       "atu2bZaHh3V8ffz1dKdXFVi0rGkefTBC89ZOkWEYFiUDAABAbnbDAjJhwgT16dNHTzzxhKpUqaIP\n",
       "PvhAgYGBmjx5cqbHR0dHy+l0aty4cQoJCVGtWrU0bNgwHTp0SGfPns3yLwDWye9bQM88OFrFCwWZ\n",
       "5pt3/aBlW2ZZlAoAAAC52XULSEpKiqKiotSyZUvTvGXLloqIiMj0nHvuuUf58+fXZ599JofDoQsX\n",
       "Lmj69OmqX7++ihQpknXJkSsU8C+sZx4crUL5i5rmK7fP09qoxRalAgAAQG5lM67zXpnY2FiVLl1a\n",
       "GzZsUKNGjdLnY8aM0axZs7Rv375Mz4uIiFCnTp2UkJAgp9Op0NBQrVixQsWLFzcdl5iYmP7ffEbE\n",
       "tZ27fFo//PqlktOumOb3VOqgCiVqWpQKAAAAWaVSpUrp/12wYMF//ThZvgtWTEyMOnXqpD59+igy\n",
       "MlLr1q1TQECAunXrxucC8rBCfsV0f/Xu8rR7meYRB5fo+NkDFqUCAABAbuN5vcVixYrJw8ND8fHx\n",
       "pnl8fLwCAwMzPefTTz9VmTJl9NZbb6XPvvrqK5UpU0ZbtmxReHh4pueFhYXdanbkOmEqX6GcPln8\n",
       "mhyONEmSIUObDizUwAdHqWKpGoqMjPzzSK632+Cauyeuu/vhmrsfrrn7+fu7l27HdV8B8fb2Vt26\n",
       "dbVy5UrTfNWqVdcsEoZhyG43P+zV/3c6nbeTFS6gStlaerzVENlsf/0cSHWkaMri13XiVIyFyQAA\n",
       "AJAb3PAtWEOGDNH06dM1depU7d27V4MGDVJcXJwGDBggSRoxYoSaN2+efnyHDh0UFRWl1157TQcP\n",
       "HlRUVJT69OmjsmXLqm7dutn3lSDXqF0pXA/fN8A0S0q5rMnfjdaFK+yEBgAA4M5uWEC6deumiRMn\n",
       "auzYsQoNDVVERISWL1+uMmXKSJLi4uIUE/PXv2w3atRIc+bM0aJFi1SnTh21adNG+fLl0/fffy9f\n",
       "X9/s+0qQq4Tf2VLtwx8zzS5cSdTqPd8oKfWSRakAAABgtet+BuSqgQMHauDAgZmuTZs2LcOsa9eu\n",
       "6tq16+0lg8trHtZZl5LOa03UovTZhaQErdkzR/XCGsjHK5+F6QAAAGCFLN8FC7jKZrOpY6PeCqva\n",
       "xDQ/fTFW05e/I4fTYVEyAAAAWIUCgmxls9n0SPNnVaVMLdN895FIzVv7CVszAwAAuBkKCLKdp4eX\n",
       "+rYbplLFy5vmEbtW6fttcy1KBQAAACtQQJAjfH38NKDj/+TvY75r5oqfvtGW3astSgUAAICcRgFB\n",
       "jinoX0TNq/eQt6d5N7Q5P07S7sORFqUCAABATqKAIEcV9Cum+6p1k5eHd/rMaTg1bfl4HY07aGEy\n",
       "AAAA5AQKCHJciQJl1Kv1ENlkS5+lpCXr08Vjderc7xYmAwAAQHajgMAStSo2VJemT5pmF68k6pOF\n",
       "Y3ThcqJFqQAAAJDdKCCwTONabdU8rItpdirxd326eKySU5MsSgUAAIDsRAGBpdqHP5rhRoXH4g9q\n",
       "xvcT5ORGhQAAAHkOBQSWutaNCn+N2aZFm760KBUAAACyCwUElrt6o8KgYuVM87U7FmvjzuXWhAIA\n",
       "AEC2oIAgV/D18dNTHUaqoH8R0/zb9Z9zjxAAAIA8hAKCXKNwQDH17/CyvL3ypc8Mw6npK97RyVOH\n",
       "LUwGAACArEIBQa5SpkQF9W49VDbbXz81k1OT9MnisTp38YyFyQAAAJAVKCDIde4MqafOjfuaZokX\n",
       "z/y5PW/KFYtSAQAAICtQQJArNan9gJrUfsA0O3nqsKaveJfteQEAAFwYBQS51oP39tGd5euZZruP\n",
       "RGrBhi8sSgQAAIDbRQFBrmW3e+jx1kNUuniIab5h5zKtj15qUSoAAADcDgoIcjUfb1891WGkCuUv\n",
       "apovWD9Vv8ZssygVAAAA/i0KCHK9gvmL6KkOI+Xz9+15ZejLFe/q+B+HLEwGAACAW0UBgUsoVby8\n",
       "+rR90bQ9b0pasqYseUOJl85amAwAAAC3ggICl1G9XF11bfqkaZZ48Yw+WzJOKWnJFqUCAADAraCA\n",
       "wKXcW7ONmtZub5odiz+oWas+lGEYFqUCAADAzaKAwOV0vLe3qgfXMc2iDmzS91vnWJQIAAAAN4sC\n",
       "ApfjYffQ422G6o4iZUzzFVtnK+rAJotSAQAA4GZQQOCSfH381b/Dy/L3LWCaf73yAx2NO2BRKgAA\n",
       "ANwIBQQuq1jBO9Sv3TB52D3TZ6mOFH22ZJwSLpy2MBkAAACuhQICl1ahVA11v3+gaXb+coI+W/KG\n",
       "klOTLEoFAACAa6GAwOU1qH6/7q/7oGl24lSMvvphopyG06JUAAAAyAwFBHlC+/BHdWdIfdNs56Gf\n",
       "tHzLLIsSAQAAIDMUEOQJdruHHm81WKWKlTPNV27/Vtv3rbMkEwAAADKigCDP8PH21ZPtX1aAb0HT\n",
       "fNbqj3T4930WpQIAAMDfUUCQpxQpUFz92r8kTw+v9JnDkabPl4zT2fN/WJgMAAAAEgUEeVD5wCp6\n",
       "pPmzptmFK4masvh1JaVcsSgVAAAAJAoI8qiwqk3Uqv5DplnsmaOa8f0EOZ0Oi1IBAACAAoI8q03D\n",
       "HqpdMdw023V4u5axMxYAAIBlKCDIs+w2ux5tOUhlSlQwzVdFztfP+zdYlAoAAMC9UUCQp3l7+ajf\n",
       "AyNUwK+waT5r1Uc6Fv+bRakAAADcFwUEeV7hgGJ64oHh8vDwTJ+lOlL02dJxOn8pwcJkAAAA7ocC\n",
       "ArdQPrA99svBAAAgAElEQVSKut/3tGmWePGMPl/6plLTUi1KBQAA4H4oIHAbDarfp/vqdDTNjsTt\n",
       "19w1k2UYhkWpAAAA3AsFBG6lwz29VDU41DTbuneN1u1YYlEiAAAA90IBgVux2z3Uu81QlSgUZJov\n",
       "3DRde4/usCgVAACA+6CAwO34+eTXkx1elq+3X/rMMJyavny8/kg4aWEyAACAvI8CArdUsnApPd5m\n",
       "qGy2v34JXEm5rClL3tDl5IsWJgMAAMjbKCBwW9XL1VXHRr1Msz8STurLFRPkdDosSgUAAJC3UUDg\n",
       "1pqFdlT9as1Ms71Ho7R480yLEgEAAORtFBC4NZvNpofvG6jgOyqb5muiFmrb3rUWpQIAAMi7KCBw\n",
       "e16e3ur3wHAV9C9imn/z48c6/Pt+i1IBAADkTRQQQFJB/yLq98AIeXl4p88cjjRNXfqmzl08Y2Ey\n",
       "AACAvIUCAvy/4DsqqUfzZ0yz85cT9PnSN5WSlmxRKgAAgLyFAgL8TVjVJmpet7Npdiz+oGavniTD\n",
       "MCxKBQAAkHdQQIB/eCC8p2qUCzPNIvev148/f2dRIgAAgLyDAgL8g93uoV6th6hkkdKm+ZLNM7X7\n",
       "cKRFqQAAAPIGCgiQCV8fP/Vv/7L8fPKnzwwZmv79u4o7e9zCZAAAAK6NAgJcQ/FCgerT9kXZbX/9\n",
       "MklOuaIpi1/XpaQLFiYDAABwXRQQ4DqqlK2lBxv3Nc1OJ8Zp+vJ35HA6LEoFAADguiggwA00rtVO\n",
       "DWs0N832H9+pRRunWxMIAADAhVFAgBuw2Wx6qOlTKh9Y1TRfF71EW3avtigVAACAa6KAADfBy9NL\n",
       "T7QbrkL5i5rmc9d8opjYfRalAgAAcD03VUAmTZqk8uXLy9fXV2FhYdq0adMNz5k4caKqVq2qfPny\n",
       "KSgoSCNGjLjtsICVCvgX0pPtX5KXp3f6zOFM09RlbyrhwikLkwEAALiOGxaQOXPm6Pnnn9fIkSMV\n",
       "HR2t8PBwtWnTRsePX3sr0iFDhmjy5MkaP3689u3bpxUrVqhJkyZZGhywQpkSFdSzxXOm2YXL5/TZ\n",
       "0nFKSU22KBUAAIDruGEBmTBhgvr06aMnnnhCVapU0QcffKDAwEBNnjw50+P379+vjz76SIsXL1b7\n",
       "9u1Vrlw51apVS61bt87y8IAV6lRupJb1uppmJ/6I0azVH8kwDItSAQAAuIbrFpCUlBRFRUWpZcuW\n",
       "pnnLli0VERGR6TmLFi1SSEiIli9frpCQEJUvX169e/fWqVO8RQV5R9u7H9Gd5euZZlEHNmpV5HyL\n",
       "EgEAALgGz+stnj59Wg6HQyVLljTNS5Qoobi4uEzPiYmJ0dGjRzV37lzNmDFDkvTCCy+offv22rJl\n",
       "i2w2W6bnRUZG/pv8cFF54XrfWaKpjscdVuKV0+mzpRFf6VJCisoUqWxhstwpL1xz3Dquu/vhmrsf\n",
       "rrn7qFSpUpY8TpbvguV0OpWcnKyZM2eqUaNGatSokWbOnKlt27bxExR5irenj+6r1k3envlM800H\n",
       "FurcZV7xAwAAyMx1XwEpVqyYPDw8FB8fb5rHx8crMDAw03MCAwPl6empihUrps8qVqwoDw8PHTt2\n",
       "TPXq1cv0vLCwsFvNDhd0tYTmpesdFFxSkxeOltNwSpJSHSmKiFmkod3Hyz9fgMXprJcXrzlujOvu\n",
       "frjm7odr7n4SExOz5HGu+wqIt7e36tatq5UrV5rmq1atUnh4eKbnNGrUSGlpaYqJiUmfxcTEyOFw\n",
       "KDg4OAsiA7lLlbK19GDjvqbZ6cQ4TV/+jhxOh0WpAAAAcqcbvgVryJAhmj59uqZOnaq9e/dq0KBB\n",
       "iouL04ABAyRJI0aMUPPmzdOPb968uerUqaO+ffsqOjpaO3bsUN++fdWwYUMaMvKsxrXa6e4aLUyz\n",
       "/cd3auHGaRYlAgAAyJ1uWEC6deumiRMnauzYsQoNDVVERISWL1+uMmXKSJLi4uJMr3bYbDYtXbpU\n",
       "JUqUUOPGjdW6dWuVLVtWixYtyr6vArCYzWbTQ836KySwmmm+PnqptuxebVEqAACA3Oe6nwG5auDA\n",
       "gRo4cGCma9OmZfwX3jvuuENz5869vWSAi/H08FLfdsP07uwXlHDxr52x5q75RCULl1JIULXrnA0A\n",
       "AOAesnwXLMCdFfAvpH7tX5KXp3f6zOFM09Slb+rseXbGAgAAoIAAWaxMiRD1bPGcaXbhSqI+XzpO\n",
       "KanJFqUCAADIHSggQDaoU7mRWtZ7yDQ7cSpGs1Z/KMMwLEoFAABgPQoIkE3a3t1Dd4XUN82iDmzS\n",
       "qu3fWpQIAADAehQQIJvYbXY91mqwAouWNc2XbZmlX2O2WZQKAADAWhQQIBvl8/ZVvwdGyO9vd0Q3\n",
       "ZGjG9xP0+5ljFiYDAACwBgUEyGbFCwWqb9sXZbf99cstOTVJU5a8rktXzluYDAAAIOdRQIAcULlM\n",
       "TXVu8oRpdiYxXtNWvCOH02FRKgAAgJxHAQFyyL012+ruGi1MswPHf9HCjRlv5gkAAJBXUUCAHGKz\n",
       "2fRQs/4Z7oi+PnqptuxaZVEqAACAnEUBAXKQp4eXnmg3TIXzFzPN5679VDGxey1KBQAAkHMoIEAO\n",
       "C/ArpCc7vCQvT+/0mcOZpqlL39TZ86csTAYAAJD9KCCABUoXD9GjLQeZZheuJOrzpeOUkppsUSoA\n",
       "AIDsRwEBLBJa6R61qv+QaXbiVIy+XvWBDMOwKBUAAED2ooAAFmrTsIfuCqlvmu04uFkrt39rUSIA\n",
       "AIDsRQEBLGS32fVYq8EKLFrWNF+25Wv9cmirRakAAACyDwUEsFg+b1892f4l+eULMM1n/vCeYk8f\n",
       "tSgVAABA9qCAALlAsYJ3qG/bF2W3/fVLMjk1SZ8tfUOXrpy3MBkAAEDWooAAuUTlMjXVuUk/0+xM\n",
       "Yry+WD5eDkeaRakAAACyFgUEyEXurdlG4Xe2MM0OnvhV3677jJ2xAABAnkABAXIRm82mrk37KySo\n",
       "mmm+edcP2rBzmUWpAAAAsg4FBMhlPD289ES74SpSoIRpvmDDF9pzJMqiVAAAAFmDAgLkQgF+BdW/\n",
       "/cvy8cqXPjMMp6aveEe/nzluYTIAAIDbQwEBcqmgYsHq3eYF2WRLnyWlXNaUJWN1kZ2xAACAi6KA\n",
       "ALlYjfJh6nhvb9PsTGK8pi57S2mOVGtCAQAA3AYKCJDLNQvtoLtrmHfGOnRyt+au+YSdsQAAgMuh\n",
       "gAC5nM1m00PN+qtiqRqm+U97ftTaHYssSgUAAPDvUEAAF/DnzljDVKzgHab5oo1falfMdotSAQAA\n",
       "3DoKCOAi/H0LqH+Hl5XP2y99ZsjQl9+/q9jTR6wLBgAAcAsoIIALuaNIGfVp+6Jstr9+6SanJmnK\n",
       "4td14fI5C5MBAADcHAoI4GKqBYeqc+O+ptnZC6f0+dI3lZrGzlgAACB3o4AALqhxrXZqdFdr0+zw\n",
       "7/s0+8eP2RkLAADkahQQwAXZbDZ1adJPlcvUNM2371un1ZELLEoFAABwYxQQwEV5eHiqb9v/qkSh\n",
       "INN8ScRM7fxti0WpAAAAro8CArgwv3z51b/Dy/L18TfNZ/zwno7GHbQoFQAAwLVRQAAXV6JwKfVt\n",
       "+1/Z/7YzVmpaij5b8obOnj9lYTIAAICMKCBAHlClbC11u2+AaXb+coI+XfyariRftigVAABARhQQ\n",
       "II8Iv7Ol7q/byTT7/cwxTVsxXg6nw6JUAAAAZhQQIA9pf08v1arQ0DTbd3SHvl33GdvzAgCAXIEC\n",
       "AuQhdptdj7UarLIlK5nmm3/9Xmt3LLYoFQAAwF8oIEAe4+3lo/7tX1LhgOKm+aKN0/XLoZ8sSgUA\n",
       "APAnCgiQBxXwL6ynOoxUPm+/9JkhQzO+f0/H4n+zMBkAAHB3FBAgjwoqFqw+bV80bc+bkpasKYtf\n",
       "Z3teAABgGQoIkIdVCw7VQ82eMs3OX07QlMVj2Z4XAABYggIC5HH33NVK99Uxb88be+aopq94h+15\n",
       "AQBAjqOAAG6gQ6NeqvmP7Xn3Ho3St2unsD0vAADIURQQwA3YbXb1ajVYZUtUNM037/pBqyLnW5QK\n",
       "AAC4IwoI4Ca8vXzUv8PLGbbnXRrxlbbvW29RKgAA4G4oIIAbKeBfWAM6/k++f9ueV5JmrfpQB47/\n",
       "YlEqAADgTigggJsJLFpW/dqPkIeHZ/rM4UzT50vfVOzpoxYmAwAA7oACArihSqXv0qMtnjPNklIu\n",
       "65NFY3Tu4hmLUgEAAHdAAQHcVN0qjdX+nl6m2bmLZ/Tpote4RwgAAMg2FBDAjTWv+6Aa3dXaNDt5\n",
       "+oi+WP6WHI40i1IBAIC8jAICuDGbzaYuTZ/UneXrmeb7j+3U7B8ncY8QAACQ5SgggJvzsHvo8TZD\n",
       "FVyykmm+de8ardg626JUAAAgr6KAAJCPVz717/CyihYsaZp/v3WOtuxebVEqAACQF1FAAEiSAvwK\n",
       "aWDHUfLPF2Caz/lxkvYcibIoFQAAyGsoIADSlSgcpP4dXpaXh3f6zGk49cWyt3Qk7oCFyQAAQF5B\n",
       "AQFgUj6wqnq1HiKbbOmzlLRkfbroNcWfPWFhMgAAkBdQQABkUKtiQ3Vp+qRpdinpgiYtHM2NCgEA\n",
       "wG25qQIyadIklS9fXr6+vgoLC9OmTZtu6sEPHjyogIAABQQE3PhgALlK41pt1ar+Q6ZZwoVTmrxw\n",
       "tC4nXbQoFQAAcHU3LCBz5szR888/r5EjRyo6Olrh4eFq06aNjh8/ft3zUlJS1L17dzVp0kQ2m+26\n",
       "xwLIndo2fER312hhmv1+5pimLHldKWnJFqUCAACu7IYFZMKECerTp4+eeOIJValSRR988IECAwM1\n",
       "efLk6543bNgw1a5dWw899BA3MwNclM1mU7f7BqhmhQameUzsXk1f8a4cTodFyQAAgKu6bgFJSUlR\n",
       "VFSUWrZsaZq3bNlSERER1zxv2bJlWrZsmT788EPKB+DiPOwe6tV6iCoEVTfNd8Vs05w1k/k1DgAA\n",
       "bonn9RZPnz4th8OhkiXNNycrUaKE4uLiMj0nNjZW/fv318KFC+Xn53fTQSIjI2/6WLg+rrfrqVem\n",
       "rc6cO61zl/9In/20e7UuJV5RaHCzG57PNXdPXHf3wzV3P1xz91GpUqUseZws3wXrscce08CBA1Wv\n",
       "Xr2sfmgAFvL2zKfm1XvI36egaf7ric3aG7vdolQAAMDVXPcVkGLFisnDw0Px8fGmeXx8vAIDAzM9\n",
       "Z+3atdqwYYNGjx4tSTIMQ06nU15eXpo8ebL69euX6XlhYWH/Jj9czNV/JeF6u64q1Str4tzhupR0\n",
       "IX0WeXilalS9S3UqN8pwPNfcPXHd3Q/X3P1wzd1PYmJiljzOdV8B8fb2Vt26dbVy5UrTfNWqVQoP\n",
       "D8/0nF27dmnnzp3pP8aMGSNfX1/t3LlTXbt2zZLQAKxTsnApDej4P3l7+qTPDBma+cNE7TsabWEy\n",
       "AADgCm74FqwhQ4Zo+vTpmjp1qvbu3atBgwYpLi5OAwYMkCSNGDFCzZs3Tz++evXqph9BQUGy2+2q\n",
       "Xr26ChUqlH1fCYAcE3xHZT3xwHDZ7R7pM4czTZ8vHaeY2H0WJgMAALndDQtIt27dNHHiRI0dO1ah\n",
       "oaGKiIjQ8uXLVaZMGUlSXFycYmJirvsY3AcEyHuqBYeqZ4vnTLOUtGR9umiMTpy6/u8JAADAfd3U\n",
       "h9AHDhyow4cPKykpSdu3b1ejRn+9z3vatGnXLSC9e/fW+fPnbz8pgFynXtUm6tz4CdPsSsplTfpu\n",
       "tOITTlqUCgAA5GZZvgsWAPfSNLS92jTsYZpdvJKoSQtG6ez5UxalAgAAuRUFBMBta12/m5qGdjDN\n",
       "Ei6e1sffjdKVlIsWpQIAALkRBQTAbbPZbHrw3j5qWKO5aX7qXKxW756l5LQrFiUDAAC5DQUEQJaw\n",
       "2Wzqft9AhVa6xzRPuPyHftwzW8kplBAAAEABAZCF7HYPPdbqeVUPrmOan75wUp8teUOpaSkWJQMA\n",
       "ALkFBQRAlvL08FLfdsNUIai6aX7gxK+atuIdORxpFiUDAAC5AQUEQJbz9vJR/w4jVaZEBdN8V8w2\n",
       "fb3qQzkNp0XJAACA1SggALKFr4+fBnYapYK+xUzzyP3rNXfNJzIMw6JkAADAShQQANkmv28Btajx\n",
       "iPL7FDLNI3at1Pz1n1FCAABwQxQQANnKz6eAWtzZUwX8C5vmG3Yu18KN0yghAAC4GQoIgGwXkK+w\n",
       "nu08RgG+BU3ztTsWa2nEV5QQAADcCAUEQI64o0gZPdN5jPzzBZjmqyLn6/utcyxKBQAAchoFBECO\n",
       "CSoWrGc6j5afT37TfMXW2Vq5/VuLUgEAgJxEAQGQo0oXD9HTD76qfN5+pvnSiK+0JmqhRakAAEBO\n",
       "oYAAyHFlS1bUwE6j5OOVzzRfuHG61kcvtSgVAADICRQQAJYoH1hFAzr+T96ePqb5/PWfU0IAAMjD\n",
       "KCAALFOhVA317zBSXh7epvn89Z9r3Y4lFqUCAADZiQICwFKVy9ylfu1HyNPDyzRfsGGq1kYttigV\n",
       "AADILhQQAJarFhyqJ9u/lOGVkO82fqE1UYssSgUAALIDBQRArnCtErJw4zT9+DO7YwEAkFdQQADk\n",
       "GlWDa6t/h5fl5WkuIYs2TdfqyAUWpQIAAFmJAgIgV6lStpae6jAyQwlZvHmGVm2fb1EqAACQVSgg\n",
       "AHKdymVqZrpF75KImfp+6xwZhmFRMgAAcLsoIABypUql79JTmZSQ5T99oyURX1FCAABwURQQALlW\n",
       "pdJ3akCnV+T9jzumr46crwUbpsppOC1KBgAA/i0KCIBcrWKpGnq606vK5+1nmq+PXqrZP06S0+mw\n",
       "KBkAAPg3KCAAcr2QoKp6tvMY+eULMM1/2r1aM1e+L4cjzaJkAADgVlFAALiEsiUr6rkurynAr5Bp\n",
       "/vP+DZq2YrxS01ItSgYAAG4FBQSAywgqVk6Dur6uQvmLmua/HNqqz5eOU0pqskXJAADAzaKAAHAp\n",
       "JQqX0qCH3lDRgiVN871Ho/TJojG6knzZomQAAOBmUEAAuJyiBUpqUNc3VLJwadP8t5O79eGCkbpw\n",
       "+ZxFyQAAwI1QQAC4pEL5i+q5rmNVqlg50/zEHzGaOO8lnTkfb00wAABwXRQQAC4rwK+Q/tNlrMoF\n",
       "VjHNT52L1cS5I/T7mWMWJQMAANdCAQHg0vzy5dczD45WteA6pnnipbN6f95LOvz7PouSAQCAzFBA\n",
       "ALg8H698erL9CNWpfK9pfjn5oj5eMEp7j+6wKBkAAPgnCgiAPMHTw0u9Wg/WvTXbmuYpacmasvh1\n",
       "/bx/o0XJAADA31FAAOQZdptdXZs+qdYNHjbNHc40zfh+gtZHL7UoGQAAuIoCAiBPsdlsatuwh7o2\n",
       "fdI0N2Ro/vrPtXDjdDkNp0XpAAAABQRAntS4Vjv1ajVYdruHab4maqFmfD9BqWmpFiUDAMC9UUAA\n",
       "5FlhVZvoqQ4j5e2VzzSPOrBJkxe+qstJFy1KBgCA+6KAAMjTqgWHalDX1xXgV8g0/+3kbr3/7Us6\n",
       "e/6URckAAHBPFBAAeV6ZEhU05OG3VKJwKdP89zPH9N7cYTp56rBFyQAAcD8UEABuoWiBkhrc7U2F\n",
       "BFYzzRMvndXEb1/S/mM7LUoGAIB7oYAAcBv++QL0TOfRqlXxbtM8OeWKJi8ao4hdqyxKBgCA+6CA\n",
       "AHArXp7e6tPmBTWp/YBp7nQ6NPvHj7Vw4zQ5nQ6L0gEAkPdRQAC4HbvdQ12a9NOD9/bNsLYmapE+\n",
       "X/aWklOuWJAMAIC8jwICwG01q9NBT7QbJi9Pb9N8V8w2Tfz2JSVcOG1RMgAA8i4KCAC3Vqvi3RrU\n",
       "9Q0V8C9smp88dVjvznlRx+J/sygZAAB5EwUEgNsrW7Kihj48XqWLh5jm5y8l6P1vX9KOgxEWJQMA\n",
       "IO+hgACApMIBxTSo6+u6K6S+aZ6alqJpy9/W91vnyGk4LUoHAEDeQQEBgP/n4+2rJx4Yrvvrdsqw\n",
       "tvynbzRt2dt8OB0AgNtEAQGAv7Hb7OrYqLd63P+M7HYP09rOQz9pwtxhOnXud4vSAQDg+iggAJCJ\n",
       "u+9soWcefFX++QJM89/PHNO7s1/UvqPRFiUDAMC1UUAA4Boqlb5LL/R4R6WKlTPNLydf1ORFY/Tj\n",
       "zwtlGIY14QAAcFEUEAC4jqIFSur5bm+qTuVGprlhOLVo03TN/GGiUtKSLUoHAIDroYAAwA34eOXT\n",
       "462Hqv09vWSTzbQWuX+9Js4doTOJ8RalAwDAtVBAAOAm2Gw2tQjrrKc6jpSvt59p7cSpGL39zRDt\n",
       "itluUToAAFwHBQQAbkH1cnU1tPt4lSxS2jS/knxJU5a8riWbZ8rhdFiUDgCA3I8CAgC3qEThUhrS\n",
       "7W3VrNAgw9qqyPma9N2rOn/pnAXJAADI/SggAPAv+Pr46Yl2w9WxUW/ZbebfSg+e+FVvfzNYh07u\n",
       "sSgdAAC5FwUEAP4lm82m++t20rNdXlMBv8KmtfOXEvTh/JFaE7WIrXoBAPibmy4gkyZNUvny5eXr\n",
       "66uwsDBt2rTpmseuW7dOHTt2VFBQkPz9/VWrVi1NmzYtSwIDQG5TsVQN/feRCapY+k7T3Gk4tXDj\n",
       "NH2+dJwuXTlvUToAAHKXmyogc+bM0fPPP6+RI0cqOjpa4eHhatOmjY4fP57p8Vu2bFGtWrU0f/58\n",
       "7d69WwMHDlT//v31zTffZGl4AMgtCvgX1jMPjlbzsC4Z1n6N2aa3Zg3Wbyd3W5AMAIDcxWbcxHsD\n",
       "GjRooNq1a+vTTz9Nn1WuXFldu3bVG2+8cVNP9PDDD8vhcOjbb79NnyUmJqb/d8GCBW8lN1xUZGSk\n",
       "JCksLMziJMgp7njNf43Zpq9+mKgrKZdNc5vNrlb1H1Kr+t3kYfewKF3OcMfr7u645u6Ha+5+surv\n",
       "7jd8BSQlJUVRUVFq2bKlad6yZUtFRETc9BMlJiaqSJEit54QAFzMXSH19eIjExRcspJpbhhOfb91\n",
       "jj6a/z8lXDhlUToAAKx1w1dAYmNjVbp0aW3YsEGNGjVKn48ZM0azZs3Svn37bvgkS5cuVefOnRUR\n",
       "EWFqyX9vUQcPHvw3+QEg13I4HYo+tk67T27JsObt6avwig+obNEqFiQDAODWVar01z+sZesrILdr\n",
       "8+bN6tmzpz788ENeogPgVjzsHqpb7n41r95D+bz8TWspaVe0bt88bT20QmmOVIsSAgCQ8zxvdECx\n",
       "YsXk4eGh+Ph40zw+Pl6BgYHXPXfTpk1q166dXnvtNT311FPXPZZy4h54v6j74ZpLUpiahrfSVysn\n",
       "at+xaNPK/riflZAcp8daPq/gOypd43zXw3V3P1xz98M1dz9/f/fS7bjhKyDe3t6qW7euVq5caZqv\n",
       "WrVK4eHh1zxvw4YNatu2rUaPHq3nnnvu9pMCgAsr4F9IAzq9og739JL9Hx9A/yPhpN6bO0wrts6R\n",
       "w+mwKCEAADnjpt6CNWTIEE2fPl1Tp07V3r17NWjQIMXFxWnAgAGSpBEjRqh58+bpx69bt05t2rTR\n",
       "wIED1aNHD8XFxSkuLk6nTvGhSwDuy26zq3lYZz3/0DgVLVjStOY0nFrx0zeaOHe4/kg4aVFCAACy\n",
       "300VkG7dumnixIkaO3asQkNDFRERoeXLl6tMmTKSpLi4OMXExKQf/+WXXyopKUnjx49XYGCggoKC\n",
       "FBQUpAYNGmTPVwEALqTcHZU17JGJurtGiwxrR+MP6q1Zg7Vx53LuoA4AyJNu6j4g2YX7gLgf3i/q\n",
       "frjm1/drzDbNXv2xLlzJ+L7aqsGheqT5syqUv6gFyW4P1939cM3dD9fc/eTYfUAAANnnrpD6Gv7o\n",
       "B6pZIeMrxPuO7tAbM/+jiF2reDUEAJBnUEAAwGIBfgX1RLvh6tniP/Lx9jWtJaVc1uwfP9ak717V\n",
       "mfPx13gEAABcBwUEAHIBm82mBtXv1/CeE1WhVI0M6/uP79S4rwZpw85lchpOCxICAJA1KCAAkIsU\n",
       "LVBS/+nymro06SdvTx/TWkpqkr5d95k++PZldsoCALgsCggA5DJ2m11Naj+g4Y++r8ql78qwHhO7\n",
       "V299PVirIxfI4UizICEAAP8eBQQAcqliBe/QM53HqPv9T2f4bEiqI0WLN8/Q+G+G6vDv+yxKCADA\n",
       "raOAAEAuZrPZFH5nS7306AeqXq5uhvXYM0f13tzhmv3jJF1OumhBQgAAbg0FBABcQOGA4nqqw0g9\n",
       "2nKQ/HzyZ1iP2LVSY2c8o+371rFlLwAgV6OAAICLsNlsql+tmV7u9ZHqVW2aYf3ilUTN/GGiPlrw\n",
       "iuL5kDoAIJeigACAiwnwK6THWj2vZzuPUYlCQRnWD574VW9+PUhLNs9UcsoVCxICAHBtFBAAcFGV\n",
       "y9TUsJ7vq23DHvL08DKtORxpWhU5n7dlAQByHQoIALgwL08vtW7wsEY8+oGqlK2VYT3x0lnN/GGi\n",
       "3ps3XMfif7MgIQAAZhQQAMgDihcK1NOdXtXjrYeqgH/hDOtHft+vd2e/qFmrPtT5S+csSAgAwJ8o\n",
       "IACQR9hsNtWtcq/+12uSWoR1kYeHp2ndkKGf9vyo12YM1I8/f6fUtBSLkgIA3BkFBADyGB9vX7W/\n",
       "5zG99OiHuiukfob15JQrWrTpS70+4xlt37deTsNpQUoAgLuigABAHlW8UKCebP+SBnYapZJFSmdY\n",
       "P3vhlGb+8J7e+eYF7T+204KEAAB3RAEBgDyuWnCohj8yUQ827itfb78M6ydOxejj70Zp8sIxOnnq\n",
       "SM4HBAC4Fc8bHwIAcHUeHp5qFtpB9f6vvbsPjqLM8wD+7Z63zGQyk9fJ+6uEBAKEQIIkhiDy4qIu\n",
       "667lymldHdzeqaWWKGeterfWlS/n1kJJ6V6BdZa7R7aWPZHVWl0XENwgEBMNgQAhLwjkFZLJG2GS\n",
       "SSZvM31/TDISMiEvzGQyk++nqu2m+/f0PO1Tv4JfdffTqffiy5KPUXj+MKy2oVExVfVnUF1fhhUL\n",
       "1mDjys0I1hk81FsiIvJlvANCRDSHaNU6PLL6X/Dv//jfWDY/d8xxCRK+qyrAm/nP4ONj/wOT+boH\n",
       "esQ4QqQAABVtSURBVElERL6MBQgR0RwUFhiJLRtfwr89tgN3RaeNOW61DaHw/CG8sfdpfHri9+ju\n",
       "5dS9RETkGixAiIjmsPiI+Xj+kbfw5I//w+mL6oPWAXxd9jle/9+n8HnhH9Bj6fJAL4mIyJfwHRAi\n",
       "ojlOEAQsSsrCgoRlOFX1NQ6X7Mf1rtZRMQND/fjq9Kc4WX4I9y59CPcu/TH81ToP9ZiIiLwZCxAi\n",
       "IgIAyEQZVqatRWZqHr6rLMDhko9hMneMiukfsODLkgM4VvZX5C6+H2syfgK9NthDPSYiIm/EAoSI\n",
       "iEaRyxS4Z/H9WLFgDYouHMGRU38e8w7IwGAfCs58huPn/oaVC9dh3fKfIkQf7qEeExGRN2EBQkRE\n",
       "TinkSqxe+hCy09bj5PmD+Kr0U/T0dY+KsVqH8E35YRRfOILM1NVYn/mI03dJiIiIRrAAISKi21Iq\n",
       "VFi7/Ke4Z/GP8E35lzh25jN09XaOirFJNpRUHcOpqq+RlpSFaE0KDLo4D/WYiIhmMxYgREQ0KX5K\n",
       "NdYufxh56Q/g28q/4++ln+J6d9uoGAkSLtSU4AJKEKKNhKizYOm8HMhk/OuGiIjs+DcCERFNiUKu\n",
       "xKolG5GTth6lF0/gaOknaO28Niauw9yM/MO78Ln2D8hb+hByFq2HWuXvgR4TEdFswgKEiIimRSaT\n",
       "4+6F9yErdTXOXfkOR0v/jKutNWPiOs3t+KxwLw5/9xFWpq1D7pKNCA+K9kCPiYhoNmABQkREd0QU\n",
       "ZchIzsHSedm4fK0Cx8o+x4WakjFx/YN9OH72Cxw/+wVSYtORu2QjFiVlQSbKPNBrIiLyFBYgRETk\n",
       "EoIgIDlmEZJjFqHg5JeobCpBbXs5BocGxsRebDyHi43nEKQNRc7i+5Gdth46/0AP9JqIiGaa6OkO\n",
       "EBGR79GpQ7Dyro14/Z8/xIPZTyBA47y46DS342/F+/Cfv/8X5B96B983lsMm2Wa4t0RENJN4B4SI\n",
       "iNxGq9bh/hWP4r5lD+Ps5SIUnj+E2ubqMXFW2xBOf38Sp78/iRB9OFYuXIe7F96HQG2IB3pNRETu\n",
       "xAKEiIjcTiFXICt1NbJSV6OxtQaF5w+h9OJxp49ndZha8LfifTj47f9hQXwGstPWIS0xE3KZwgM9\n",
       "JyIiV2MBQkREMyrWkIR/WPcsfpL7T/iuqgCF5w+j7UbTmDhJsqGy7jQq605Dq9YjK3U1MlPvRUxY\n",
       "IgRB8EDPiYjIFViAEBGRR2j8tFiTsQmrlz6ES43lKK74CueuFMNqHRoTa7aYcKzscxwr+xwRwbHI\n",
       "TF2NzJQ8BOsMHug5ERHdCRYgRETkUaIgIiUuHSlx6eixdKH04gkUV3yFpvY6p/HG6434ouiP+KLo\n",
       "j7grOg1ZqauxdF4ONH7ame04ERFNCwsQIiKaNfzVOqxe+hDy0h9EY+sVFFd8hdMXT6BvoNdp/JVr\n",
       "FbhyrQIHvv4AqXFLkZF8DxYlZUGjYjFCRDRbsQAhIqJZRxAExIXPQ1z4PPx01VaU15SgtPo4qurP\n",
       "OJ2m12odQkVtKSpqSyET5UiNW4qlyTlYfNcKFiNERLMMCxAiIprVlAoVlqeswvKUVejuNaHsUiFK\n",
       "q0+gznjRabzVNoSKulJU1JVC9nc5UuLSkT4vG4sSM8f9HgkREc0cFiBEROQ1AjR65KU/iLz0B9F2\n",
       "oxml1cdRevGE01m0AHsxMjKTlgABCZEpWJS0AkuSVsAQFM3ZtIiIPIAFCBEReaWwwEhsXLkZP7r7\n",
       "MVxrr8XZS0Uou1Q0bjEiQUJtczVqm6vx12/+gLDAKCxOysKipBVIjEyFTJTN8BUQEc1NLECIiMir\n",
       "CYKAmLAkxIQl4cHsJ9DUXo+zl79B2aUitHZeG7dd240mFJz5DAVnPoNaqcH8uHQsjF+G1PgMBAWE\n",
       "zuAVEBHNLSxAiIjIZwiCgOiwBESHJeCBlY+juaMe5y5/i/LaElxtrRm3nWWgF+cuF+Pc5WIAQGRI\n",
       "HBbEL8PChGVIjFwAhZxfYScichUWIERE5JMEQUBUaAKiQhOwceVmdHa34ULNKZTXlODS1Quw2sZ+\n",
       "8HBEc0cDmjsaUHDmL1DIlUiKXIDkmEVIjl2CuPB5fFyLiOgOsAAhIqI5ISggDKvSH8Cq9Adg6e9F\n",
       "dUMZyq+UoKqhDD2WrnHbDQ4N4GLjOVxsPAcU74NK4Ye7otOQHLMYyTGLEBOWCJEFCRHRpLEAISKi\n",
       "OUet0iAj+R5kJN8Dm82KxtYaVNWfQVV9GeqM30Ny8q2REf2DfY6Ztezn8se86DTMi16EpKhURIcl\n",
       "Qi7jI1tERONhAUJERHOaKMoQH5GM+Ihk/Ojux9DbZ0Z1w1lU1ZehuuEsTOaO27a39PegvKYE5TUl\n",
       "AACFTIm48HlIjExFYlQqEiNToVXrZuJSiIi8AgsQIiKim2j8tFg2PxfL5udCkiS03WjGpavl9qWx\n",
       "HN0W023bD1oHcKWpEleaKgH7TRIYAqOGC5IFSIiYj/DgGL5HQkRzFgsQIiKicQiCAENQFAxBUbhn\n",
       "8f2QJAnG6424dLUc3zeW4/LVC+jtN094ntYbTWi90YTvqgoAAAq5EjFhSYgLn4dYw12INcxDeFAU\n",
       "3yUhojmBBQgREdEkCYKAyJA4RIbEIS/9QdgkG6611eHytQv2jxw2VcPUc33C8wwODTg+ijhCqfBD\n",
       "bFiSvSAJn4dYQxLCAqN4p4SIfA4LECIiomkSBRGxhiTEGpKwJmMTJElCZ3cbapurUdNkLzCutdfd\n",
       "9qX2EQODfT88ujVMLlMgIjgWUaHx9iXEPq2wzj/QnZdFRORWLECIiIhcRBAEBOsMCNYZsDwlDwDQ\n",
       "P2BBfcsl1DRVoa75Ihpar8A8wXskI4asg7jaVoOrbaM/oqhV64eLkgREBsciPDgG4cEx8PcLcPk1\n",
       "ERG5GgsQIiIiN1Ip1ZgfuwTzY5cAACRJwg1zOxparqCx9QoaWi+jseUyevq6J31Os8WE7xvP4/vG\n",
       "86P2a9V6hAdFIzw4GoagGEQExyA8KAZBAaF8v4SIZg0WIERERDNIEAQEBYQhKCAM6fNWAoDj0a2G\n",
       "lstoaL2Cq61X0NRej67ezimd22wxwWwxjXqMC7BPDRwaGIFQ/fASGOnYDtYZ+J4JEc0oFiBEREQe\n",
       "dvOjW0uTcxz7u3tvoKm9Hk0d9fZ1ex2MHY0YtA5M6fyD1gE0dzSguaNhzDFREBGsMzgKkhB9uKNA\n",
       "Cg4IQ4B/IERBvONrJCIawQKEiIholgrQBCIlLhApcemOfTabFW0mI5ra69DUXo+WzqtovX4NrTea\n",
       "MGQdnPJv2CQb2k1GtJuMTo/LRDkCA0IcBcnNxUmQLgxB2lAoFappXyMRzT0sQIiIiLyIKMrs73kE\n",
       "RSMj+R7HfpvNio6uVrR2XkNL51W0XB9ed15Dj6Vr2r9ntQ2hw9SCDlPLuDFqlT+UohpqpRZVHYXQ\n",
       "+QdB7x/sWOu19m2lnIUKEbEAISIi8gmiKENYYCTCAiORlpg56pjZ0mW/y3GjGW0mIzpMRrTfMKLN\n",
       "1Izu3ht3/NuW/h5Y0AOTpR1GU924cWqVP3T+QdBpgqBV66BV6+1rjd6xHTC8rfHT8tEvIh/FAoSI\n",
       "iMjH2f+xr0NCxPwxx/oHLGg3tQw/htWMzu42XO9uR2dXKzq72yf1pffJsvT3wNLfg5brVyeMFQQR\n",
       "/n4BCNDo4a/WwV+lhdpPC41KC42z9fC2n0rDwoVolmMBQkRENIeplGpEhyUgOizB6fG+AQs6u9uG\n",
       "l3ZcHy5M7IVKG0zmDtgm8aHFqZIkm2NWr6kQIECt8ofazx/+qgCo/fzhp9QML+pbttWj9qtu+rNc\n",
       "pnD5NRGR3aQKkD179mDnzp0wGo1IS0vDu+++i9zc3HHjy8vL8dxzz+HUqVMIDg7GU089hddee81l\n",
       "nSYiIqKZ4adUIzIkDpEhcU6P22xWmC3d+PZUIXoHzAiPCoGp5zq6ejpHr3tvwGazur2/EiT09pvR\n",
       "229GB8Z/b2UicpkCKqUaKrkKSoWffZErh7dVUA7vVylUUMhVUCn8hvcNx49sy+3xcpkCcpkCCrkS\n",
       "CpkCcrmS0x/TnDVhAbJ//3688MILeP/995Gbm4vdu3dj48aNqKysRGxs7Jj4rq4urF+/Hvfeey9K\n",
       "S0tRVVWFrVu3wt/fH9u3b3fLRRAREZFniKIMOv9ABGsjEAwgc1Gm0zibZEOPpRtdPdfR3Wu/s9Ft\n",
       "MaHH0mXf7jXBbOmyL703YBnondkLucWQdRBDlkH0uPE3REGEXK60FyYyBeRyBRQy5Q9rx37lqLVM\n",
       "JodcJodMlEMUZZCLcshko7dlogwyx7bzP8tlcog3bTvON3wuUZBBFEWIgghBENz4f4LmmgkLkF27\n",
       "dmHr1q34xS9+AQD47W9/i8OHD+P999/H22+/PSZ+37596OvrQ35+PlQqFRYuXIjq6mrs2rWLBQgR\n",
       "EdEcJQoiAjR6BGj0k4ofsg4OFyQmmHu70NtvhqW/B719ZvT2d6O3rwe9fd3o7e+x3/Hos9/16B+w\n",
       "uPlKXMcm2TAw2IeBwT5Pd2VCAoThokSEMFyU2GwSREHAX8pUEEQRMscxe5yjeBFFyASZo539mMyx\n",
       "LYgiZKIMwsifBREC7O8BCYJgX2BfQxAgCgIEiMDwMVEQ7D0UhLFtb94vAALEW84jDJ9HvOU8t7S9\n",
       "6ZwAbirIhB/+O3IMAn6o14QxxZsw/Dsj7cac66b4iWPHaTfR794Se9vfFQCZqEBSVCpc5bYFyMDA\n",
       "AM6cOYNf/vKXo/Zv2LABRUVFTtsUFxdj1apVUKlUo+Jfe+011NfXIz4+3gXdJiIiIl8mlykQqA1B\n",
       "oDZkSu2s1iH09vfA0m9GT58Zln4z+gYsw0sv+ofXfTetf9j3w353vNfizSRIsNqGYAWAW56k6xv0\n",
       "7N0qcr8ATSD+61/3uux8ty1A2tvbYbVaER4ePmq/wWCA0ej8g0VGoxFxcaOfEx1pbzQaxy1ATKap\n",
       "vWRG3ik5ORkAx3su4ZjPTRz3uWe2jblK1EKl0QIaT/eEyDe4MrddPk8dnxEkIiIiIqLx3LYACQ0N\n",
       "hUwmQ0vL6FkkWlpaEBkZ6bRNRETEmLsjI+0jIiLupK9EREREROTlbvsIllKpxPLly3HkyBE88sgj\n",
       "jv1Hjx7Fo48+6rRNdnY2Xn75ZfT39zveAzl69Ciio6PHPH6l10/uRTQiIiIiIvINEz6CtX37duzd\n",
       "uxe/+93vUFVVhW3btsFoNOLpp58GALz66qtYt26dI/7xxx+HRqPBli1bUFFRgU8//RS/+c1vOAMW\n",
       "ERERERFNPA3vz3/+c3R0dOCtt95Cc3MzFi9ejIMHDzq+AWI0GlFTU+OI1+l0OHr0KJ599llkZmYi\n",
       "ODgYL730El588UX3XQUREREREXkFQZIkydOdICIiIiKiucHls2Ddas+ePUhMTIRarUZmZiYKCwtv\n",
       "G19eXo7Vq1dDo9EgJiYGb775pru7SC42lTGvq6uzf6joluXIkSMz2GOarhMnTmDTpk2IiYmBKIrI\n",
       "z8+fsA1z3PtNddyZ597v17/+NbKysqDX62EwGLBp0yZUVFRM2I757r2mM+bMde+2e/dupKenQ6/X\n",
       "Q6/XIycnBwcPHrxtm+nmuFsLkP379+OFF17Ar371K5w9exY5OTnYuHEjGhsbncZ3dXVh/fr1iIyM\n",
       "RGlpKd577z3s3LkTu3btcmc3yYWmOuYjvvzySxiNRseyZs2aGeox3Ymenh4sWbIE7733HtRq9YTT\n",
       "cDPHfcNUx30E89x7HT9+HM899xyKi4tRUFAAuVyOdevWobOzc9w2zHfvNp0xH8Fc906xsbHYsWMH\n",
       "ysrKcPr0adx33314+OGHce7cOafxd5TjkhutWLFCevLJJ0ftS05Oll599VWn8Xv27JH0er3U19fn\n",
       "2PfWW29J0dHR7uwmudBUx7y2tlYSBEEqLS2die6RG2m1Wik/P/+2Mcxx3zOZcWee+x6z2SzJZDLp\n",
       "iy++GDeG+e5bJjPmzHXfExwcLH3wwQdOj91JjrvtDsjAwADOnDmDDRs2jNq/YcMGFBUVOW1TXFyM\n",
       "VatWOabvHYlvampCfX29u7pKLjKdMR/xs5/9DOHh4cjNzcUnn3zizm6SBzHH5zbmue/o6uqCzWZD\n",
       "UFDQuDHMd98ymTEfwVz3flarFR999BH6+vqQl5fnNOZOctxtBUh7ezusVivCw8NH7TcYDGM+VDjC\n",
       "aDSOiR/583htaPaYzpgHBATgnXfewYEDB3Do0CGsXbsWjz32GPbt2zcTXaYZxhyfm5jnvmfbtm3I\n",
       "yMhAdnb2uDHMd98ymTFnrnu/8vJyaLVa+Pn54cknn8THH3+MlJQUp7F3kuMTTsM7kyb7HDH5jpCQ\n",
       "kFFTNC9btgwdHR3YsWMHnnjiCQ/2jNyBOT43Mc99y/bt21FUVITCwsLb5jTz3XdMdsyZ694vNTUV\n",
       "58+fh8lkwoEDB7B582YcO3YMmZmZY2LvJMfddgckNDQUMpkMLS0to/a3tLQgMjLSaZuIiIgxFdNI\n",
       "+4iICPd0lFxmOmPuTFZWFi5duuTq7tEswBynEcxz7/Tiiy9i//79KCgoQEJCwm1jme++YSpj7gxz\n",
       "3bsoFAokJSUhIyMDb7/9NlauXIndu3c7jb2THHdbAaJUKrF8+fIxU68dPXoUOTk5TttkZ2fj5MmT\n",
       "6O/vHxUfHR2N+Ph4d3WVXGQ6Y+7M2bNnERUV5eru0SzAHKcRzHPvs23bNsc/ROfPnz9hPPPd+011\n",
       "zJ1hrns3q9UKm83m9Ngd5bjLXpN3Yv/+/ZJSqZQ+/PBDqbKyUnr++eelgIAAqaGhQZIkSXrllVek\n",
       "tWvXOuJNJpMUEREhbd68Wbpw4YL0ySefSDqdTtq1a5c7u0kuNNUx37t3r/SnP/1JqqyslKqrq6Wd\n",
       "O3dKSqVSevfddz11CTQFZrNZKisrk8rKyiSNRiO98cYbUllZGXPcx0113Jnn3u+ZZ56RdDqdVFBQ\n",
       "IDU3NzsWs9nsiGG++5bpjDlz3bu9/PLL0smTJ6Xa2lrp/Pnz0iuvvCKJoigdOXJEkiTX5rhbCxBJ\n",
       "sk/RlZCQIKlUKikzM1M6efKk49iWLVukxMTEUfHl5eVSXl6e5OfnJ0VFRUlvvPGGu7tILjaVMc/P\n",
       "z5cWLlwo+fv7SzqdTsrKypL27dvniW7TNBw7dkwSBEESBEESRdGxvXXrVkmSmOO+aqrjzjz3freO\n",
       "9cjy+uuvO2KY775lOmPOXPduW7ZskeLj4yWVSiUZDAZp/fr1juJj5LirclyQJEly5a0aIiIiIiKi\n",
       "8bj1S+hEREREREQ3YwFCREREREQzhgUIERERERHNGBYgREREREQ0Y1iAEBERERHRjGEBQkRERERE\n",
       "M4YFCBERERERzRgWIERERERENGP+H+6pG+1HBqllAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4809123e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, 1/np.exp(x**2))\n",
    "plt.title('exp(1/x^2)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know that $1/e^x = e^{-x}$, so we can equivalently calculate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAyAAAAGaCAYAAAD3vidSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmcjXX/x/H3dWYzw5ixm2Hs+74MSbIUMsqSLW2yJao7\n",
       "pbpRSqQoJXfdUUmUEorshIQYYRqjrE3GFmbsM7bZzrl+f/Rr6rpnbJmZa86c1/Px8HjU53tdZ97H\n",
       "ZfB2zvlehmmapgAAAAAgFzjsDgAAAADAc1BAAAAAAOQaCggAAACAXEMBAQAAAJBrKCAAAAAAcg0F\n",
       "BAAAAECuoYAAAK5bu3btVK1aNblcLrujZKshQ4aoaNGiOnPmjN1RACDfo4AAAK7L8uXL9d1332n0\n",
       "6NFyOHLvj4+ffvpJwcHBcjgcioiIUGpq6lWPj42N1Ztvvqm2bduqXLly8vPzU8mSJRUREaElS5Zk\n",
       "ec6LL76oS5cuaezYsTnxFAAAf2NwI0IAwPVo2LChzp49qwMHDsgwjFz5mj///LPatGmjpKQk1apV\n",
       "S7/88os6deqk+fPny9vbO8tzevfurXnz5qlGjRpq0aKFSpQoobi4OH3zzTdKTU3Vc889pzfffDPT\n",
       "eQMGDNDnn3+uAwcOKDQ0NKefGgB4LF4BAQBcU2RkpHbs2KEHHngg18rHnj171LZtW126dElz5sxR\n",
       "VFSUevbsqSVLlqh3795yOp1ZntehQwdFRUVp9+7d+uijj/Taa6/pyy+/1E8//aTChQvrrbfe0vbt\n",
       "2zOd9/DDDystLU3Tp0/P6acGAB6NAgIAeVR0dLR69+6t0NBQ+fn5KTQ0VH369NH+/fszjnn66afl\n",
       "cDj01FNPZTp/7ty5cjgcuu2225Seni5JOnjwoBwOh9q0aaOjR4/qwQcfVIkSJRQQEKAmTZpo3rx5\n",
       "WWb58y/lvXv3vqHn0LVrVzkcDk2aNCnT2htvvCGHw6FevXplWouNjdWdd96ptLQ0rVy5Ut27d5eP\n",
       "j4/mzJmjJ598UgsWLFCfPn2U1Yv4ffv2VaNGjTLNa9eurfvuu0+StG7dukzrrVu3VqlSpSggAJDT\n",
       "TABAnvP555+b3t7eZqFChcwHHnjAHD58uNmtWzfT29vbDA4ONmNiYkzTNM3U1FSzSZMmpmEY5jff\n",
       "fJNx/m+//WYWLlzYLFasmHn48OGM+YEDB0zDMMz69eubFSpUMBs1amSOGDHCHDRokBkcHGwahmG+\n",
       "8847mfKEhYWZQUFBN/w8zp49a1aoUMH09fU1t27dmjGPjIw0vb29zcqVK5tJSUmWc+Li4sywsDAz\n",
       "NDTU3LFjR5aPO27cONMwDLNv3743lOfxxx83DcMw33333SzXu3XrZhqGYe7bt++GHhcAcP0oIACQ\n",
       "x8TGxpp+fn5mlSpVzGPHjlnW1q1bZ3p7e5uNGzfOmMXFxZnBwcFmkSJFzIMHD5opKSlm48aNTYfD\n",
       "YS5atMhy/p8FxDAMs3fv3pa1/fv3m8HBwaafn5956NChjPnBgwdNwzDMO++88x89ny1btpi+vr5m\n",
       "xYoVzXPnzplnzpwxy5UrZ/r5+ZlRUVGZjv/000/NsWPHmgcPHrzq486fP98cM2aM+fPPP19XjnPn\n",
       "zpmlSpUyvb29zb1792Z5zIQJE0zDMMxp06Zd12MCAG4cb8ECgDxm6tSpSk1N1TvvvKOQkBDLWqtW\n",
       "rdSpUydFR0drz549kqSKFStq+vTpOnfunO677z4NGzZM0dHReuqpp9S5c+csv4a3t7cmTJhgmVWq\n",
       "VEmPP/64UlNT9fnnn2fM4+LiJElly5b9R8+nadOmGj9+vA4ePKj+/furf//+OnLkiN544w01btw4\n",
       "0/F9+vTRSy+9pPLly1/1cbt166aXX35ZdevWvWYGl8ulfv366cSJExoyZIiqV6+e5XF/PscDBw5c\n",
       "xzMDAPwTWW8hAgCwzaZNmyRJ69evV1RUVKb1hIQESX98SLtmzZqS/vjL+BNPPKH3339fW7duVXh4\n",
       "uCZOnHjFr1GuXLks/4LfsmVLjR8/XjExMRmzkydPSpKKFi2a6fiDBw9q5syZlplhGBo9erRlNmzY\n",
       "MK1bt07ffPONJKlz584aOnToFfNlJ9M09fjjj2vhwoVq06ZNlp9H+VOxYsUkSSdOnMiVbADgiSgg\n",
       "AJDHnD59WpL09ttvX/EYwzB08eJFy6xHjx56//33JUmPP/74FbeplaRSpUpddZ6YmGj5WpKy/MD3\n",
       "wYMHM907I6sCIkndu3fX0qVLJSlXy8fgwYM1bdo0tW3bVosXL77qz8ufN1jMrZ2+AMAT8RYsAMhj\n",
       "goKCZBiGzpw5I5fLleUPp9Ophx9+OOOcs2fP6pFHHpGvr68CAwP173//W8eOHbvi1/jzVZQrzYOC\n",
       "gjJmxYsXl6Qs7xLeunXrLLP9rwMHDmjo0KEKCgqSt7e3Bg8erAsXLlzfT8g/5HQ61bdvX02bNk0R\n",
       "ERFaunSpChQocNVz/nyOJUqUyNFsAODJKCAAkMc0b95cpmlqw4YN131Ov379dPjwYb311luaNm2a\n",
       "Tp06pfvvvz/jX/T/1+HDh3Xo0KFM8/Xr10v646aDf6pUqZIk6ffff7+Rp5EhNTVVvXr10vnz5/XZ\n",
       "Z59p3Lhxio2N1eDBg//R412PtLQ0PfDAA5o1a5a6du2qRYsWydfX95rnHT16VNJfzxkAkAPs/Qw8\n",
       "AOB/7du3L2MXrKx2a0pLSzPXrl2b8f/vvPOOaRiGee+992bMBg0aZBqGYY4aNcpy7t93wbrvvvtM\n",
       "l8uVsfbbb7+ZQUFBmXbBMs1/vg2vaZrm0KFDTcMwzKeffjpj1qFDB9MwDPPjjz/+R495NcnJyWan\n",
       "Tp0ydvpyOp3Xfe6f2/DGxsZmey4AwB8M08ziTb0AAFvNmTNH/fr1U3p6ujp06KCqVavK6XTqyJEj\n",
       "2rRpk9LS0nTmzBlFRUXptttuU2hoqGJiYjLeOpWcnKymTZtq9+7dWrVqle644w5Jf3xmo1KlSqpX\n",
       "r54SExNVtGhRtWvXTmfOnNG8efN0/vx5TZo0KdNnNAYOHKhPPvlE27dvV/369a/7eSxatEj33nuv\n",
       "wsPDFRkZmfH5i5MnT6pBgwY6d+6ctm3bplq1amXTz9wfrwZ9+umnCgoK0r/+9S85HJlf7G/YsKG6\n",
       "dOlimZmmqdDQUBUoUIBdsAAgJ12roaxfv97s1KmTWaZMGdMwDHPmzJnXbDU///yz2bJlS9Pf398s\n",
       "U6aMOXbs2JuvSgDgYXbv3m0OHDjQrFixounn52cWKVLErFWrltm/f39z2bJlZmJiolmpUiXT19fX\n",
       "3Lx5c6bz9+zZYxYsWNAMCQkxExISTNP86xWQNm3amEePHjUffPBBs0SJEqa/v78ZHh5uzp07N8ss\n",
       "kZGRpmEY5ogRI647/6FDh8yiRYuaQUFB5v79+zOtf//996aXl5dZp04d89KlS9f9uNfSunVr0+Fw\n",
       "mA6HI+PVnr//cDgcZr9+/TKdt3btWtMwDPPVV1/NtiwAgMyu+QrIihUrtGnTJjVs2FB9+vTR1KlT\n",
       "1adPnysen5SUpGrVqql169Z6+eWXtWfPHvXr10+vvPKKhg0blu0FCgBw/f58BaR169Zau3btDZ3b\n",
       "qFEjnT59WgcOHMjyVQV3179/f82ePVsHDhzIdP8VAED2ueafIBERERo3bpy6d+9+XX/gfPHFF0pO\n",
       "Ttann36qWrVqqXv37ho+fPhV910HAOR9r732mo4cOaLZs2fbHSXb/fm8hgwZQvkAgByW7f+EtXnz\n",
       "Zt1+++3y8/PLmLVv317Hjh3LcscVAIB7iIiIUNu2bfXqq69meU8Qd/b666+rYMGCevnll+2OAgD5\n",
       "XrbfiDA+Pl7lypWzzP68sVV8fLzlzrt/v9EVACDnJSUlSZLS09P/0e/BX331leVx8osJEyZowoQJ\n",
       "kvizCQCux9/vF3Wjsr2AcPdYAMi7ypcvr7Nnz9odAwDgwbL9LVilS5dWfHy8ZfbnnXVLly6d3V8O\n",
       "AAAAgBvJ9ldAbr31Vg0fPlwpKSkZnwNZvXq1ypQpY3n71f86eHK30tJTleZM06Xk87pwOVHnLyXq\n",
       "wqVEJV06p1OJ8UpOvfSPMhmGQ5VCa6pupaaqV/kWFQ+iCNklKipKkhQeHm5zEuQWrrln4rp7Hq65\n",
       "5+Gae57seovqNQvIxYsXFRsbK0lyuVw6dOiQYmJiVKxYMYWFhWnkyJHatm2b1qxZI0l64IEHNGbM\n",
       "GPXt21ejRo3Svn379MYbb+iVV1656tepX+XWq66bpqkLl5N0KvG4Tp47rhNnj+rIiTgdObFfFy5f\n",
       "/SfDNF3af3SX9h/dpYU/zFBosfKqV7mZwmu0Uskiodf6KQAAAACQTa5ZQLZt25ZxB13DMDR69GiN\n",
       "Hj1affv21SeffKL4+HjFxcVlHF+4cGGtXr1aTzzxhMLDw1W0aFE999xzeuaZZ24qqGEYCgwIUmBA\n",
       "kCqG1MiYm6apcxdO6ciJ/ToUH6vYozt1OD5WLtN1xcc6dvqQjp0+pJVb56pC6epqUrO1GlVroYIF\n",
       "Am8qIwAAAICru2YBad26tVyuK/9lfsaMGZlmderU0fr1628u2XUyDENFAkuoSGAJ1avcTJKUnHpZ\n",
       "ccd269cjv2jv4RgdO3XwiucfjN+ng/H7tGD9dNWpGK4W9SJULaweH6YHAAAAckC2fwYkLyjg669a\n",
       "FRqrVoXGkqTTiQn6OW6Lfonbqv1Hd8vM4tURpytdO/b/qB37f1SpImV1e/0INanRRv5+AbkdHwAA\n",
       "AMi38mUB+V/FgkqpTcPOatOwsy5eTtKO/Vu0be867T+6K8vjE87+rq/XTdOSTbPUtOYdatOoMx9c\n",
       "BwAAALKBRxSQvyvoX1jN67RT8zrtdDopQVF712vrnnU6ee5YpmNT0pL1w8/LtfGXlWpUrYXahXdT\n",
       "aPEKuR8aAAAAyCc8roD8XbHCpXRX015q36Sn9h/brR92LNeO/T/K5XJajjNNl37at0E/7dug2hXC\n",
       "1a5JD1UKrXGFRwUAAABwJR5dQP5kGIaqlKmtKmVqK/HCGUXuXKVNO79V0sXMdwvedTBKuw5GqWb5\n",
       "Rrqn+YMKK1nZhsQAAACAe6KA/I+gQkUV0ay32jfpoZ9+/UFrohYo/syRTMftORStPYei1aBqc93d\n",
       "7AGVKlrWhrQAAACAe6GAXIGXl7ea1myj8BqttDNum1ZHzdeh+F8zHRcTG6kdv/2opjXb6J5bH1RQ\n",
       "oaI2pAUAAADcAwXkGhyGQ/Uq36K6lZoq9vedWrFlTqbds0zTpS27v9P22E1qF95dbRp1lq+3n02J\n",
       "AQAAgLyLAnKdDMNQtbC6qlq2jvYejtGSyFn6/USc5ZjUtGQt2/yFNu9cpS6391WDKs25oSEAAADw\n",
       "NxSQG2QYhmqWb6ga5Roo5rfNWr55thLO/m455sz5k5qxfKIql6mtnq0HKbR4eZvSAgAAAHmLw+4A\n",
       "7sowDDWs2lwjHvqPerUZrIIFAjMds//oLr355TAt3jRLqWkpNqQEAAAA8hYKyE3ycnipRb0OeumR\n",
       "qWrdoJMcDi/Lusvl1Jqo+Rr/+VPafTDappQAAABA3kABySYBBQqpW6sBGvngf1SzfKNM66eTEvTB\n",
       "orGaueItnb90zoaEAAAAgP0oINmsVNGyGtzlJQ24e7iCChXLtB7960a9/vlT2h67yYZ0AAAAgL0o\n",
       "IDnAMAzVr3KrXnjoPbVqcI8MWXfCung5STOWT9SM5RN14XKSTSkBAACA3EcByUH+fgHq3mqgnu09\n",
       "UWVLVMq0vj12k8bP+pd2/PajDekAAACA3EcByQXlSlXRs70n6p7mD8nLYd35+PzlRE1fNkFfrHpX\n",
       "yamXbUoIAAAA5A4KSC7xcnipfZMeev7+t1S2ZOZXQ7bsWauJs4fpUHysDekAAACA3EEByWWhxSvo\n",
       "2V5vqmOz+zNt2Xsy8bje+WqEVkctkMt02ZQQAAAAyDkUEBt4eXmrwy336bneE1WqaFnLmsvl1JJN\n",
       "n+n9BaOVeOGMTQkBAACAnEEBsVHZEpX0fO+3dVvdDpnWYn//RW/Ofkb7Du+wIRkAAACQMyggNvP1\n",
       "8dN9dwzWwHtGKKBAoGXt/OVETVk4Rt9uncdbsgAAAJAvUEDyiHqVm2nEg5NVrWxdy9w0XVq2ebY+\n",
       "XDSOe4YAAADA7VFA8pDgQsX0+L2vqMMt92W6eeGeQ9H/v0vWrzalAwAAAG4eBSSPcTi81LHZ/Rrc\n",
       "9WUV9C9sWTt74ZT+8/WL2rJ7rU3pAAAAgJtDAcmjapZvqH/fP0kVQ2pY5unONH2x+l3NX/+xnM50\n",
       "m9IBAAAA/wwFJA8rElhcT3Ufp9YNO2daWx+zVFMWjtH5S4k2JAMAAAD+GQpIHufl5a1uLfurz13P\n",
       "yMfL17IW+/svenvOczp68oBN6QAAAIAbQwFxE+E1WunpXuNVJLCEZX7m/Em989VI/RK31aZkAAAA\n",
       "wPWjgLiRsJKV9VzviapSprZlnpqWrI+XjNf30YtlmqZN6QAAAIBro4C4mcCAYD1x7xi1rN/RMjdl\n",
       "6psfPtHctVP5cDoAAADyLAqIG/Ly8laP1oPUs/UgOQzrJYzcuUofLHpVl1Iu2JQOAAAAuDIKiBu7\n",
       "vX5HPdblJRXwDbDM9x3Zof989YLOnj9lUzIAAAAgaxQQN1ezfEM902uCihYuaZkfP31Y78wbruOn\n",
       "D9uUDAAAAMiMApIPhBQrp2fve1MVQqpb5ucunNbkr0Zq/9HdNiUDAAAArCgg+URgQLCe7DZW9So3\n",
       "s8wvp1zU+9+M1o7fNtuUDAAAAPgLBSQf8fX2U/+Oz6tF3Q6WebozTZ8se1M//LzCpmQAAADAHygg\n",
       "+YzD4aWebR7T3bc+aJmbMvXV9x9qaeQX3CsEAAAAtqGA5EOGYeiupj11f9snM23Tu2rbV5q95r9y\n",
       "upw2pQMAAIAno4DkY7fWbqtHO70gH29fy3zL7u80c8VbSnem2ZQMAAAAnooCks/Vrhiuf3Ufp4IF\n",
       "Ai3zHb9t1sdLxis1PcWmZAAAAPBEFBAPUKF0tT/uFRJYwjLffShaHywcq+TUyzYlAwAAgKehgHiI\n",
       "kkXKaGjP11UyONQy/+3oLr2/4GVdTD5vUzIAAAB4EgqIBykSWEJP9XhdocUrWOaHEmL13vyXlHTx\n",
       "nD3BAAAA4DEoIB6mcMFg/av7qypfqqplfuzUQb379Qs6e/6kTckAAADgCSggHqhggUA90W2sqpSp\n",
       "bZmfOHdM//nqBZ08d9ymZAAAAMjvKCAeqoCvvwZ3eVm1yjeyzM+cP6l354+ihAAAACBHUEA8mK+P\n",
       "nwZ2Gqn6VW61zBMvnKaEAAAAIEdQQDyct5eP+kY8p6Y121jmlBAAAADkBAoI5OXw0gNtn9QtNe+w\n",
       "zCkhAAAAyG4UEEiSHA4v3d/2CUoIAAAAchQFBBkoIQAAAMhpFBBYUEIAAACQkyggyIQSAgAAgJxC\n",
       "AUGWrlZC3l/wMndMBwAAwD9CAcEVXamEnDl/Uv9dMFpJF8/alAwAAADuigKCq/qzhITXaGWZnzx3\n",
       "TO9/M1oXLyfZlAwAAADuiAKCa3I4vPRgu6cy3TH9+OnDmrJwjC6nXLQpGQAAANwNBQTXxcvhpUc6\n",
       "DFOtCo0t8yMn9uvDReOUkpZsUzIAAAC4EwoIrpu3l4/63/1vVStb1zKPO75H05a8rrT0VJuSAQAA\n",
       "wF1QQHBDfL399GinF1QxpIZl/uuRn/XJsjeV7kyzKRkAAADcwXUVkClTpqhixYry9/dXeHi4Nm7c\n",
       "eNXjly9frmbNmqlw4cIqUaKEunbtqtjY2GwJDPv5+fprcJeXVLZkJct818EoffbtO3K5nDYlAwAA\n",
       "QF53zQIyd+5cPf300xo1apRiYmLUvHlzRURE6MiRI1ke/9tvv6lr165q3bq1YmJitGbNGiUnJ6tj\n",
       "x47ZHh728fcrqMe7vqKQYuUs85jYSH31/UcyTdOmZAAAAMjLrllAJk2apH79+mnAgAGqXr263n33\n",
       "XYWEhGjq1KlZHh8TEyOXy6Xx48erUqVKql+/voYPH679+/frzJkz2f4EYJ9C/oX1xL1jVCI41DLf\n",
       "tPNbLds826ZUAAAAyMuuWkBSU1MVHR2t9u3bW+bt27dXZGRklufcdtttKlSokKZNmyan06nz589r\n",
       "5syZatq0qYoWLZp9yZEnFC5YRE/cO0bBhYpZ5qu2faXvoxfblAoAAAB5lWFe5b0yx44dU9myZbVh\n",
       "wwa1aNEiYz527FjNnj1be/fuzfK8yMhIde3aVWfPnpXL5VLDhg21YsUKlShRwnJcYmJixn/zGRH3\n",
       "du7SKX37y6dKSb9smd9WtbMql6xnUyoAAABkl6pVq2b8d1BQ0D9+nGzfBSsuLk5du3ZVv379FBUV\n",
       "pXXr1ikwMFC9evXicwH5WHBAcd1Zq7e8HT6WeWTsEh0586tNqQAAAJDXeF9tsXjx4vLy8lJCQoJl\n",
       "npCQoJCQkCzP+fDDDxUWFqY33ngjY/b5558rLCxMmzdvVvPmzbM8Lzw8/EazI88JV8XKFfTB4lfl\n",
       "dKZLkkyZ2vjrQg25d7SqlKmtqKioP47kensMrrln4rp7Hq655+Gae56/v3vpZlz1FRBfX181btxY\n",
       "q1atssxXr159xSJhmqYcDuvD/vn/LpfrZrLCDVQvV1+P3DVMhvHXr4E0Z6o+Wvyafj8ZZ2MyAAAA\n",
       "5AXXfAvWsGHDNHPmTE2fPl179uzR0KFDFR8fr8GDB0uSRo4cqbZt22Yc37lzZ0VHR+vVV19VbGys\n",
       "oqOj1a9fP5UrV06NGzfOuWeCPKNB1ea6747Bllly6iVN/WaMzl9mJzQAAABPds0C0qtXL02ePFnj\n",
       "xo1Tw4YNFRkZqeXLlyssLEySFB8fr7i4v/5lu0WLFpo7d64WLVqkRo0aKSIiQgUKFNDKlSvl7++f\n",
       "c88EeUrzOu3VqfnDltn5y4las/tLJaddtCkVAAAA7HbVz4D8aciQIRoyZEiWazNmzMg069Gjh3r0\n",
       "6HFzyeD22oZ308XkJK2NXpQxO598Vmt3z1WT8Fvk51PAxnQAAACwQ7bvggX8yTAMdWnRV+E1Wlnm\n",
       "py4c08zlb8npctqUDAAAAHahgCBHGYahB9o+qeph9S3zXQej9NX3H7A1MwAAgIehgCDHeXv5qP/d\n",
       "w1WmREXLPHLnaq3cOs+mVAAAALADBQS5wt8vQIO7vKSCfta7Zq748Utt3rXGplQAAADIbRQQ5Jqg\n",
       "gkXVttb98vW27oY297sp2nUgyqZUAAAAyE0UEOSqoIDiuqNmL/l4+WbMXKZLM5ZP1KH4WBuTAQAA\n",
       "IDdQQJDrShYOU58Ow2TIyJilpqfow8XjdPLccRuTAQAAIKdRQGCL+lWaqXvrRy2zC5cT9cHCsTp/\n",
       "KdGmVAAAAMhpFBDYpmX9jmob3t0yO5l4XB8uHqeUtGSbUgEAACAnUUBgq07NH8p0o8LDCbH6bOUk\n",
       "ubhRIQAAQL5DAYGtrnSjwl/itmrRxk9tSgUAAICcQgGB7f68UWFo8QqW+ffbF+uHHcvtCQUAAIAc\n",
       "QQFBnuDvF6DHOo9SUMGilvnX6z/mHiEAAAD5CAUEeUaRwOIa1PlF+foUyJiZpkszV7yloycP2JgM\n",
       "AAAA2YUCgjwlrGRl9e3wrAzjr1+aKWnJ+mDxOJ27cNrGZAAAAMgOFBDkOXUqNVG3lv0ts8QLp//Y\n",
       "njf1sk2pAAAAkB0oIMiTWjW4R60a3GOZHT15QDNXvM32vAAAAG6MAoI8697b+6lOxSaW2a6DUVqw\n",
       "4RObEgEAAOBmUUCQZzkcXnqkwzCVLVHJMt+wY5nWxyy1KRUAAABuBgUEeZqfr78e6zxKwYWKWeYL\n",
       "1k/XL3FbbUoFAACAf4oCgjwvqFBRPdZ5lPz+vj2vTH264m0dObHfxmQAAAC4URQQuIUyJSqqX8fn\n",
       "Ldvzpqan6KMlryvx4hkbkwEAAOBGUEDgNmpVaKwerR+1zBIvnNa0JeOVmp5iUyoAAADcCAoI3Mrt\n",
       "9SLUukEny+xwQqxmr35PpmnalAoAAADXiwICt9Pl9r6qVb6RZRb960at3DLXpkQAAAC4XhQQuB0v\n",
       "h5ceiXhWpYuGWeYrtsxR9K8bbUoFAACA60EBgVvy9yuoQZ1fVEH/wpb5F6ve1aH4X21KBQAAgGuh\n",
       "gMBtFQ8qrYF3D5eXwztjluZM1bQl43X2/CkbkwEAAOBKKCBwa5XL1FbvO4dYZkmXzmrakteVkpZs\n",
       "UyoAAABcCQUEbu+WWnfqzsb3Wma/n4zT599Olst02ZQKAAAAWaGAIF/o1Pwh1anU1DLbsf9HLd88\n",
       "26ZEAAAAyAoFBPmCw+GlR+56RmWKV7DMV237Wtv2rrMlEwAAADKjgCDf8PP116OdXlSgf5BlPnvN\n",
       "f3Xg+F6bUgEAAODvKCDIV4oWLqGBnV6Qt5dPxszpTNfHS8brTNIJG5MBAABAooAgH6oYUl0PtH3S\n",
       "Mjt/OVEfLX5NyamXbUoFAAAAiQKCfCq8Rivd1bSnZXbs9CF9tnKSXC6nTakAAABAAUG+FdHsfjWo\n",
       "0twy23lgm5axMxYAAIBtKCDItxyGQw+1H6qwkpUt89VR8/XTvg02pQIAAPBsFBDka74+fhp4z0gV\n",
       "Dihimc9e/V8dTvjNplQAAACeiwKCfK9IYHENuGeEvLy8M2ZpzlRNWzpeSRfP2pgMAADA81BA4BEq\n",
       "hlRX7zset8wSL5zWx0snKC09zaZUAAAAnocCAo9xS607dEejLpbZwfh9mrd2qkzTtCkVAACAZ6GA\n",
       "wKN0vq2PapRvaJlt2bNW67YvsSkRAACAZ6GAwKM4HF7qG/GsSgaHWuYLN87UnkPbbUoFAADgOSgg\n",
       "8DgBfoX0aOcX5e8bkDEzTZdmLp+oE2eP2pgMAAAg/6OAwCOVKlJGj0Q8K8P461vgcuolfbTkdV1K\n",
       "uWBjMgAAgPyNAgKPVatCY3Vp0ccyO3H2qD5dMUkul9OmVAAAAPkbBQQerU3DLmpas41ltudQtBZv\n",
       "mmVTIgAAgPyNAgKPZhiG7rtjiMqXrmaZr41eqK17vrcpFQAAQP5FAYHH8/H21cB7RiioYFHL/Mvv\n",
       "3teB4/tsSgUAAJA/UUAASUEFi2rgPSPl4+WbMXM60zV96QSdu3DaxmQAAAD5CwUE+H/lS1fV/W2f\n",
       "sMySLp2s4hrLAAAgAElEQVTVx0snKDU9xaZUAAAA+QsFBPib8Bqt1LZxN8vscEKs5qyZItM0bUoF\n",
       "AACQf1BAgP9xT/MHVbtCuGUWtW+9vvvpG5sSAQAA5B8UEOB/OBxe6tNhmEoVLWuZL9k0S7sORNmU\n",
       "CgAAIH+ggABZ8PcL0KBOLyrAr1DGzJSpmSvfVvyZIzYmAwAAcG8UEOAKSgSHqF/H5+Uw/vo2SUm9\n",
       "rI8Wv6aLyedtTAYAAOC+KCDAVVQvV1/3tuxvmZ1KjNfM5W/J6XLalAoAAMB9UUCAa2hZ/241q93W\n",
       "Mtt3ZIcW/TDTnkAAAABujAICXINhGOrZ+jFVDKlhma+LWaLNu9bYlAoAAMA9UUCA6+Dj7aMBd49Q\n",
       "cKFilvm8tR8o7them1IBAAC4n+sqIFOmTFHFihXl7++v8PBwbdy48ZrnTJ48WTVq1FCBAgUUGhqq\n",
       "kSNH3nRYwE6FCwbr0U4vyMfbN2PmdKVr+rIJOnv+pI3JAAAA3Mc1C8jcuXP19NNPa9SoUYqJiVHz\n",
       "5s0VERGhI0euvBXpsGHDNHXqVE2cOFF79+7VihUr1KpVq2wNDtghrGRlPdjuKcvs/KVzmrZ0vFLT\n",
       "UmxKBQAA4D6uWUAmTZqkfv36acCAAapevbreffddhYSEaOrUqVkev2/fPv33v//V4sWL1alTJ1Wo\n",
       "UEH169dXhw4dsj08YIdG1VqofZMeltnvJ+I0e81/ZZqmTakAAADcw1ULSGpqqqKjo9W+fXvLvH37\n",
       "9oqMjMzynEWLFqlSpUpavny5KlWqpIoVK6pv3746eZK3qCD/6HjrA6pTsYllFv3rD1odNd+mRAAA\n",
       "AO7B+2qLp06dktPpVKlSpSzzkiVLKj4+Pstz4uLidOjQIc2bN0+fffaZJOm5555Tp06dtHnzZhmG\n",
       "keV5UVFR/yQ/3FR+uN51SrbWkfgDSrx8KmO2NPJzXTybqrCi1WxMljflh2uOG8d19zxcc8/DNfcc\n",
       "VatWzZbHyfZdsFwul1JSUjRr1iy1aNFCLVq00KxZs7R161Z+gSJf8fX20x01e8nXu4BlvvHXhTp3\n",
       "iVf8AAAAsnLVV0CKFy8uLy8vJSQkWOYJCQkKCQnJ8pyQkBB5e3urSpUqGbMqVarIy8tLhw8fVpMm\n",
       "TbI8Lzw8/Eazww39WULz0/UOLV9KUxeOkct0SZLSnKmKjFukZ3tPVMECgTans19+vOa4Nq675+Ga\n",
       "ex6uuedJTEzMlse56isgvr6+aty4sVatWmWZr169Ws2bN8/ynBYtWig9PV1xcXEZs7i4ODmdTpUv\n",
       "Xz4bIgN5S/Vy9XVvy/6W2anEeM1c/pacLqdNqQAAAPKma74Fa9iwYZo5c6amT5+uPXv2aOjQoYqP\n",
       "j9fgwYMlSSNHjlTbtm0zjm/btq0aNWqk/v37KyYmRtu3b1f//v3VrFkzGjLyrZb179attdtZZvuO\n",
       "7NDCH2bYlAgAACBvumYB6dWrlyZPnqxx48apYcOGioyM1PLlyxUWFiZJio+Pt7zaYRiGli5dqpIl\n",
       "S6ply5bq0KGDypUrp0WLFuXcswBsZhiGerYZpEohNS3z9TFLtXnXGptSAQAA5D1X/QzIn4YMGaIh\n",
       "Q4ZkuTZjRuZ/4S1durTmzZt3c8kAN+Pt5aP+dw/X23Oe09kLf+2MNW/tBypVpIwqhda8ytkAAACe\n",
       "Idt3wQI8WeGCwRrY6QX5ePtmzJyudE1fOkFnktgZCwAAgAICZLOwkpX0YLunLLPzlxP18dLxSk1L\n",
       "sSkVAABA3kABAXJAo2ot1L5JT8vs95Nxmr3mPZmmaVMqAAAA+1FAgBzS8db7VbdSU8ss+teNWr3t\n",
       "a5sSAQAA2I8CAuQQh+HQw3c9o5Bi5SzzZZtn65e4rTalAgAAsBcFBMhBBXz9NfCekQr42x3RTZn6\n",
       "bOUkHT992MZkAAAA9qCAADmsRHCI+nd8Xg7jr2+3lLRkfbTkNV28nGRjMgAAgNxHAQFyQbWweurW\n",
       "aoBldjoxQTNWvCWny2lTKgAAgNxHAQFyye31OurW2u0ss1+P/KyFP2S+mScAAEB+RQEBcolhGOrZ\n",
       "ZlCmO6Kvj1mqzTtX25QKAAAgd1FAgFzk7eWjAXcPV5FCxS3zed9/qLhje2xKBQAAkHsoIEAuCwwI\n",
       "1qOdX5CPt2/GzOlK1/SlE3Qm6aSNyQAAAHIeBQSwQdkSlfRQ+6GW2fnLifp46XilpqXYlAoAACDn\n",
       "UUAAmzSsepvuatrTMvv9ZJy+WP2uTNO0KRUAAEDOooAANopodr/qVmpqmW2P3aRV2762KREAAEDO\n",
       "ooAANnIYDj181zMKKVbOMl+2+Qv9vH+LTakAAAByDgUEsFkBX3892ukFBRQItMxnffuOjp06ZFMq\n",
       "AACAnEEBAfKA4kGl1b/j83IYf31LpqQla9rS13XxcpKNyQAAALIXBQTII6qF1VO3VgMts9OJCfpk\n",
       "+UQ5nek2pQIAAMheFBAgD7m9XoSa12lnmcX+/ou+XjeNnbEAAEC+QAEB8hDDMNSj9SBVCq1pmW/a\n",
       "+a027FhmUyoAAIDsQwEB8hhvLx8NuHuEihYuaZkv2PCJdh+MtikVAABA9qCAAHlQYECQBnV6UX4+\n",
       "BTJmpunSzBVv6fjpIzYmAwAAuDkUECCPCi1eXn0jnpMhI2OWnHpJHy0ZpwvsjAUAANwUBQTIw2pX\n",
       "DFeX2/taZqcTEzR92RtKd6bZEwoAAOAmUECAPK5Nw866tbZ1Z6z9R3dp3toP2BkLAAC4HQoIkMcZ\n",
       "hqGebQapSpnalvmPu7/T99sX2ZQKAADgn6GAAG7gj52xhqt4UGnLfNEPn2pn3DabUgEAANw4Cgjg\n",
       "Jgr6F9agzi+qgG9AxsyUqU9Xvq1jpw7aFwwAAOAGUEAAN1K6aJj6dXxehvHXt25KWrI+Wvyazl86\n",
       "Z2MyAACA60MBAdxMzfIN1a1lf8vszPmT+njpBKWlszMWAADI2ygggBtqWf9utajbwTI7cHyv5nz3\n",
       "PjtjAQCAPI0CArghwzDUvdVAVQurZ5lv27tOa6IW2JQKAADg2igggJvy8vJW/47/VsngUMt8SeQs\n",
       "7fhts02pAAAAro4CArixgAKFNKjzi/L3K2iZf/btOzoUH2tTKgAAgCujgABurmSRMurf8d9y/G1n\n",
       "rLT0VE1b8rrOJJ20MRkAAEBmFBAgH6herr563THYMku6dFYfLn5Vl1Mu2ZQKAAAgMwoIkE80r9Ne\n",
       "dzbuapkdP31YM1ZMlNPltCkVAACAFQUEyEc63dZH9Ss3s8z2Htqur9dNY3teAACQJ1BAgHzEYTj0\n",
       "8F3PqFypqpb5pl9W6vvti21KBQAA8BcKCJDP+Pr4aVCnF1QksIRlvuiHmfp5/482pQIAAPgDBQTI\n",
       "hwoXLKLHOo9SAd+AjJkpU5+tfEeHE36zMRkAAPB0FBAgnwotXl79Oj5v2Z43NT1FHy1+je15AQCA\n",
       "bSggQD5Ws3xD9WzzmGWWdOmsPlo8ju15AQCALSggQD53W927dEcj6/a8x04f0swVb7E9LwAAyHUU\n",
       "EMADdG7RR/X+Z3vePYei9fX3H7E9LwAAyFUUEMADOAyH+tz1jMqVrGKZb9r5rVZHzbcpFQAA8EQU\n",
       "EMBD+Pr4aVDnFzNtz7s08nNt27veplQAAMDTUEAAD1K4YBEN7vKS/P+2Pa8kzV79nn498rNNqQAA\n",
       "gCehgAAeJqRYOQ3sNFJeXt4ZM6crXR8vnaBjpw7ZmAwAAHgCCgjggaqWrauH2j1lmSWnXtIHi8bq\n",
       "3IXTNqUCAACegAICeKjG1Vuq0219LLNzF07rw0Wvco8QAACQYygggAdr2/hetajbwTI7euqgPln+\n",
       "hpzOdJtSAQCA/IwCAngwwzDUvfWjqlOxiWW+7/AOzfluCvcIAQAA2Y4CAng4L4eXHol4VuVLVbXM\n",
       "t+xZqxVb5tiUCgAA5FcUEADy8ymgQZ1fVLGgUpb5yi1ztXnXGptSAQCA/IgCAkCSFBgQrCFdRqtg\n",
       "gUDLfO53U7T7YLRNqQAAQH5DAQGQoWSRUA3q/KJ8vHwzZi7TpU+WvaGD8b/amAwAAOQXFBAAFhVD\n",
       "aqhPh2EyZGTMUtNT9OGiV5Vw5ncbkwEAgPyAAgIgk/pVmql760cts4vJ5zVl4RhuVAgAAG7KdRWQ\n",
       "KVOmqGLFivL391d4eLg2btx4XQ8eGxurwMBABQYGXvtgAHlKy/oddVfTnpbZ2fMnNXXhGF1KvmBT\n",
       "KgAA4O6uWUDmzp2rp59+WqNGjVJMTIyaN2+uiIgIHTly5Krnpaamqnfv3mrVqpUMw7jqsQDypo7N\n",
       "HtCttdtZZsdPH9ZHS15TanqKTakAAIA7u2YBmTRpkvr166cBAwaoevXqevfddxUSEqKpU6de9bzh\n",
       "w4erQYMG6tmzJzczA9yUYRjqdcdg1at8i2Ued2yPZq54W06X06ZkAADAXV21gKSmpio6Olrt27e3\n",
       "zNu3b6/IyMgrnrds2TItW7ZM7733HuUDcHNeDi/16TBMlUNrWeY747Zq7tqpfI8DAIAb4n21xVOn\n",
       "TsnpdKpUKevNyUqWLKn4+Pgszzl27JgGDRqkhQsXKiAg4LqDREVFXfexcH9cb/fTJKyjTp87pXOX\n",
       "TmTMfty1RhcTL6th+TbXPJ9r7pm47p6Ha+55uOaeo2rVqtnyONm+C9bDDz+sIUOGqEmTJtn90ABs\n",
       "5OtdQG1r3a+CfkGW+S+/b9KeY9tsSgUAANzNVV8BKV68uLy8vJSQkGCZJyQkKCQkJMtzvv/+e23Y\n",
       "sEFjxoyRJJmmKZfLJR8fH02dOlUDBw7M8rzw8PB/kh9u5s9/JeF6u6/qtapp8rwRuph8PmMWdWCV\n",
       "ateoq0bVWmQ6nmvumbjunodr7nm45p4nMTExWx7nqq+A+Pr6qnHjxlq1apVlvnr1ajVv3jzLc3bu\n",
       "3KkdO3Zk/Bg7dqz8/f21Y8cO9ejRI1tCA7BPqSJlNLjLS/L19suYmTI169vJ2nsoxsZkAADAHVzz\n",
       "LVjDhg3TzJkzNX36dO3Zs0dDhw5VfHy8Bg8eLEkaOXKk2rZtm3F8rVq1LD9CQ0PlcDhUq1YtBQcH\n",
       "59wzAZBrypeupgH3jJDD4ZUxc7rS9fHS8Yo7ttfGZAAAIK+7ZgHp1auXJk+erHHjxqlhw4aKjIzU\n",
       "8uXLFRYWJkmKj49XXFzcVR+D+4AA+U/N8g31YLunLLPU9BR9uGisfj959d8TAACA57quD6EPGTJE\n",
       "Bw4cUHJysrZt26YWLf56n/eMGTOuWkD69u2rpKSkm08KIM9pUqOVurUcYJldTr2kKd+MUcLZozal\n",
       "AgAAeVm274IFwLO0bthJEc3ut8wuXE7UlAWjdSbppE2pAABAXkUBAXDTOjTtpdYNO1tmZy+c0vvf\n",
       "jNbl1As2pQIAAHkRBQTATTMMQ/fe3k/Nare1zE+eO6Y1u2YrJf2yTckAAEBeQwEBkC0Mw1DvO4ao\n",
       "YdXbLPOzl07ou91zlJJKCQEAABQQANnI4fDSw3c9rVrlG1nmp84f1bQlrystPdWmZAAAIK+ggADI\n",
       "Vt5ePup/93BVDq1lmf/6+y+aseItOZ3pNiUDAAB5AQUEQLbz9fHToM6jFFaysmW+M26rvlj9nlym\n",
       "y6ZkAADAbhQQADnC3y9AQ7qOVpB/ccs8at96zVv7gUzTtCkZAACwEwUEQI4p5F9Y7Wo/oEJ+wZZ5\n",
       "5M5Vmr9+GiUEAAAPRAEBkKMC/AqrXZ0HVbhgEct8w47lWvjDDEoIAAAehgICIMcFFiiiJ7uNVaB/\n",
       "kGX+/fbFWhr5OSUEAAAPQgEBkCtKFw3TE93GqmCBQMt8ddR8rdwy16ZUAAAgt1FAAOSa0OLl9US3\n",
       "MQrwK2SZr9gyR6u2fW1TKgAAkJsoIAByVdkSlfT4va+ogG+AZb408nOtjV5oUyoAAJBbKCAAcl25\n",
       "UlU0pOto+fkUsMwX/jBT62OW2pQKAADkBgoIAFtUDKmuwV1ekq+3n2U+f/3HlBAAAPIxCggA21Qu\n",
       "U1uDOo+Sj5evZT5//cdat32JTakAAEBOooAAsFW1sLoa2GmkvL18LPMFG6br++jFNqUCAAA5hQIC\n",
       "wHY1yzfUo51eyPRKyDc/fKK10YtsSgUAAHICBQRAnnClErLwhxn67id2xwIAIL+ggADIM2qUb6BB\n",
       "nV+Uj7e1hCzaOFNrohbYlAoAAGQnCgiAPKV6ufp6rPOoTCVk8abPtHrbfJtSAQCA7EIBAZDnVAur\n",
       "l+UWvUsiZ2nllrkyTdOmZAAA4GZRQADkSVXL1tVjWZSQ5T9+qSWRn1NCAABwUxQQAHlW1bJ1NLjr\n",
       "y/L9nzumr4marwUbpstlumxKBgAA/ikKCIA8rUqZ2nq86ysq4Btgma+PWao5302Ry+W0KRkAAPgn\n",
       "KCAA8rxKoTX0ZLexCigQaJn/uGuNZq36j5zOdJuSAQCAG0UBAeAWypWqoqe6v6rAgGDL/Kd9GzRj\n",
       "xUSlpafZlAwAANwICggAtxFavIKG9nhNwYWKWeY/79+ij5eOV2paik3JAADA9aKAAHArJYuU0dCe\n",
       "r6tYUCnLfM+haH2waKwup1yyKRkAALgeFBAAbqdY4VIa2uN1lSpS1jL/7eguvbdglM5fOmdTMgAA\n",
       "cC0UEABuKbhQMT3VY5zKFK9gmf9+Ik6Tv3pBp5MS7AkGAACuigICwG0FBgTrX93HqUJIdcv85Llj\n",
       "mjxvpI6fPmxTMgAAcCUUEABuLaBAIT1x7xjVLN/IMk+8eEb/+eoFHTi+16ZkAAAgKxQQAG7Pz6eA\n",
       "Hu00Uo2q3W6ZX0q5oPcXjNaeQ9ttSgYAAP4XBQRAvuDt5aM+HZ7R7fU6Wuap6Sn6aPFr+mnfDzYl\n",
       "AwAAf0cBAZBvOAyHerR+VB1uuc8yd7rS9dnKSVofs9SmZAAA4E8UEAD5imEY6tjsfvVo/ahlbsrU\n",
       "/PUfa+EPM+UyXTalAwAAFBAA+VLL+nerz13PyOHwsszXRi/UZysnKS09zaZkAAB4NgoIgHwrvEYr\n",
       "PdZ5lHx9Cljm0b9u1NSFr+hS8gWbkgEA4LkoIADytZrlG2poj9cUGBBsmf92dJf+8/ULOpN00qZk\n",
       "AAB4JgoIgHwvrGRlDbvvDZUsUsYyP376sN6ZN1xHTx6wKRkAAJ6HAgLAIxQrXErP9JqgSiE1LfPE\n",
       "i2c0+esXtO/wDpuSAQDgWSggADxGwQKBeqLbGNWvcqtlnpJ6WVMXjVXkztU2JQMAwHNQQAB4FB9v\n",
       "X/WLeE6tGtxjmbtcTs357n0t/GGGXC6nTekAAMj/KCAAPI7D4aXurQbq3tv7Z1pbG71IHy97Qymp\n",
       "l21IBgBA/kcBAeCx2jTqrAF3D5ePt69lvjNuqyZ//YLOnj9lUzIAAPIvCggAj1a/yq0a2uN1FS5Y\n",
       "xDI/evKA3p77vA4n/GZTMgAA8icKCACPV65UFT1730SVLVHJMk+6eFb/+foFbY+NtCkZAAD5DwUE\n",
       "ACQVCSyuoT1eU91KTS3ztPRUzVj+plZumSuX6bIpHQAA+QcFBAD+n5+vvwbcM0J3Nu6aaW35j19q\n",
       "xrI3+XA6AAA3iQICAH/jMBzq0qKv7r/zCTkcXpa1Hft/1KR5w3Xy3HGb0gEA4P4oIACQhVvrtNMT\n",
       "976iggUCLfPjpw/r7TnPa++hGJuSAQDg3iggAHAFVcvW1XP3v6UyxStY5pdSLmjqorH67qeFMk3T\n",
       "nnAAALgpCggAXEWxwqX0dK8JalSthWVumi4t2jhTs76drNT0FJvSAQDgfiggAHANfj4F9EiHZ9Xp\n",
       "tj4yZFjWovat1+R5I3U6McGmdAAAuBcKCABcB8Mw1C68mx7rMkr+vgGWtd9PxunNL4dpZ9w2m9IB\n",
       "AOA+KCAAcANqVWisZ3tPVKmiZS3zyykX9dGS17Rk0yw5XU6b0gEAkPdRQADgBpUsUkbDer2pepVv\n",
       "ybS2Omq+pnzzipIunrMhGQAAeR8FBAD+AX+/AA24e4S6tOgrh2H9rTT291/05pfPaP/R3TalAwAg\n",
       "76KAAMA/ZBiG7mzcVU92f1WFA4pY1pIuntV780dpbfQituoFAOBvrruATJkyRRUrVpS/v7/Cw8O1\n",
       "cePGKx67bt06denSRaGhoSpYsKDq16+vGTNmZEtgAMhrqpSprX8/MElVytaxzF2mSwt/mKGPl47X\n",
       "xctJNqUDACBvua4CMnfuXD399NMaNWqUYmJi1Lx5c0VEROjIkSNZHr9582bVr19f8+fP165duzRk\n",
       "yBANGjRIX375ZbaGB4C8onDBInri3jFqG94909ovcVv1xuxn9NvRXTYkAwAgbzHM63hvwC233KIG\n",
       "DRroww8/zJhVq1ZNPXr00Ouvv35dX+i+++6T0+nU119/nTFLTEzM+O+goKAbyQ03FRUVJUkKDw+3\n",
       "OQlyiyde81/iturzbyfrcuoly9wwHLqraU/d1bSXvBxeNqXLHZ543T0d19zzcM09T3b93f2ar4Ck\n",
       "pqYqOjpa7du3t8zbt2+vyMjI6/5CiYmJKlq06I0nBAA3U7dSUz3/wCSVL1XVMjdNl1Zumav/zn9J\n",
       "Z8+ftCkdAAD2uuYrIMeOHVPZsmW1YcMGtWjRImM+duxYzZ49W3v37r3mF1m6dKm6deumyMhIS0v+\n",
       "e4uKjY39J/kBIM9yupyKObxOu45uzrTm6+2v5lXuUbli1W1IBgDAjata9a9/WMvRV0Bu1qZNm/Tg\n",
       "gw/qvffe4yU6AB7Fy+GlxhXuVNta96uAT0HLWmr6Za3b+5W27F+hdGeaTQkBAMh93tc6oHjx4vLy\n",
       "8lJCQoJlnpCQoJCQkKueu3HjRt1999169dVX9dhjj131WMqJZ+D9op6Hay5J4Wrd/C59vmqy9h6O\n",
       "sazsi/9JZ1Pi9XD7p1W+dNUrnO9+uO6eh2vuebjmnufv7166Gdd8BcTX11eNGzfWqlWrLPPVq1er\n",
       "efPmVzxvw4YN6tixo8aMGaOnnnrq5pMCgBsrXDBYg7u+rM639ZHjfz6AfuLsUb0zb7hWbJkrp8tp\n",
       "U0IAAHLHdb0Fa9iwYZo5c6amT5+uPXv2aOjQoYqPj9fgwYMlSSNHjlTbtm0zjl+3bp0iIiI0ZMgQ\n",
       "3X///YqPj1d8fLxOnuRDlwA8l8NwqG14Nz3dc7yKBZWyrLlMl1b8+KUmzxuhE2eP2pQQAICcd10F\n",
       "pFevXpo8ebLGjRunhg0bKjIyUsuXL1dYWJgkKT4+XnFxcRnHf/rpp0pOTtbEiRMVEhKi0NBQhYaG\n",
       "6pZbbsmZZwEAbqRC6Woa/sBk3Vq7Xaa1QwmxemP2M/phx3LuoA4AyJeu6z4gOYX7gHge3i/qebjm\n",
       "V/dL3FbNWfO+zl/O/L7aGuUb6oG2Tyq4UDEbkt0crrvn4Zp7Hq6558m1+4AAAHJO3UpNNeKhd1Wv\n",
       "cuZXiPce2q7XZ/1LkTtX82oIACDfoIAAgM0CA4I04O4RerDdv+Tn629ZS069pDnfva8p37yi00kJ\n",
       "V3gEAADcBwUEAPIAwzB0S607NeLByapcpnam9X1Hdmj850O1YccyuUyXDQkBAMgeFBAAyEOKFS6l\n",
       "f3V/Vd1bDZSvt59lLTUtWV+vm6Z3v36RnbIAAG6LAgIAeYzDcKhVg3s04qH/qFrZupnW447t0Rtf\n",
       "PKM1UQvkdKbbkBAAgH+OAgIAeVTxoNJ6ottY9b7z8UyfDUlzpmrxps808ctndeD4XpsSAgBw4ygg\n",
       "AJCHGYah5nXa64WH3lWtCo0zrR87fUjvzBuhOd9N0aXkCzYkBADgxlBAAMANFAksocc6j9JD7Ycq\n",
       "wK9QpvXInas07rMntG3vOrbsBQDkaRQQAHAThmGoac02erHPf9WkRutM6xcuJ2rWt5P13wUvK4EP\n",
       "qQMA8igKCAC4mcCAYD1819N6sttYlQwOzbQe+/svmvDFUC3ZNEspqZdtSAgAwJVRQADATVULq6fh\n",
       "D/5HHZvdL28vH8ua05mu1VHzeVsWACDPoYAAgBvz8fZRh1vu08iH3lX1cvUzrSdePKNZ307WO1+N\n",
       "0OGE32xICACAFQUEAPKBEsEherzrK3qkw7MqXLBIpvWDx/fp7TnPa/bq95R08ZwNCQEA+AMFBADy\n",
       "CcMw1Lj67XqpzxS1C+8uLy9vy7opUz/u/k6vfjZE3/30jdLSU21KCgDwZBQQAMhn/Hz91em2h/XC\n",
       "Q++pbqWmmdZTUi9r0cZP9dpnT2jb3vVymS4bUgIAPBUFBADyqRLBIXq00wsa0nW0ShUtm2n9zPmT\n",
       "mvXtO3rry+e07/AOGxICADwRBQQA8rma5RtqxAOTdW/L/vL3Dci0/vvJOL3/zWhNXThWR08ezP2A\n",
       "AACP4n3tQwAA7s7Ly1ttGnZWkxqt9e3Wedr480o5XemWY/YcitbeQ9vVtGYbRTTrraKFS9qUFgCQ\n",
       "n/EKCAB4kEL+hdW91UC98PB7alStRaZ1U6a27FmrVz99XPO+/1CJF87YkBIAkJ9RQADAA5UIDlHf\n",
       "iOf07H1vqnKZ2pnWna50bfx5hcbOHKwFGz7R+Uts3QsAyB4UEADwYOVLV9NT3cdpUKcXs/ygepoz\n",
       "Veu2L9aYGY9p8cbPdPFykg0pAQD5CZ8BAQAPZxiG6lRqopoVGmnbnnVauXWuziSdsByTmp6iNT8t\n",
       "0A+/rFDrBveodYNOKuhf2KbEAAB3RgEBAEiSvBxealb7ToXXaKktu9dq5dZ5Srxw2nJMSuplfbv1\n",
       "K32/fYla1L1LbRp2UVChojYlBgC4IwoIAMDC28tHt9W9S01rtlHkzlVate3/2rvX2CjOcw/g/5m9\n",
       "edfrXV/X92ts7GDAGGyCHS5JwLQkESdtlIaTfDhwek5aNVFJUNUkUqOjpDmpGhSURIJIUXqEq9IT\n",
       "SomaHEoITk25xE6IwYDxhQC+gr2+Ya+99vq2+54Pa28wXl/Ztb32/ydNZph53tl38uoRPJqZd/46\n",
       "5h2QgcE+FF74FKcu/R1rl27G5tU/QogxfI56TEREvoQFCBERuaVSqrFx5ePISc/DmcvH8GXJJ+jp\n",
       "6x4VY7cP4auy4yi+cgJZaRuRl/Wk23dJiIiIRrAAISKiCalVGmxa/SM8uPyH+KrsC5y88Cm6ejtG\n",
       "xb48M0gAABQJSURBVDiEA+cqT+Lbyn8iPSkb0bpUmAxxc9RjIiKaz1iAEBHRlPiptdi0+glsyHgU\n",
       "X1f8A/8o+QS3u1tHxQgIXKk+hys4hxB9JGSDDSuTc6FQ8K8bIiJy4t8IREQ0LSqlGutXbEVueh5K\n",
       "rp5GQckRtHTcGhPXbm1C/vG9+Ez/R2xY+Thyl+VBq/Gfgx4TEdF8wgKEiIhmRKFQ4oGljyA7bSMu\n",
       "3fgGBSV/xc2W6jFxHdY2fHr2AI5/8zHWpm/GuhVbER4UPQc9JiKi+YAFCBER3RNZViAzJRcrk3Nw\n",
       "/VY5TpZ+hivV58bE9Q/24dTFozh18ShSYzOwbsVWLEvKhkJWzEGviYhorrAAISIij5AkCSkxy5AS\n",
       "swyFZ75AReM51LSVYXBoYEzs1YZLuNpwCUH6UOQu/wFy0vNg8A+cg14TEdFsk+e6A0REtPAYtCFY\n",
       "e99WvP7vH+GxnGcRoHNfXHRY2/D34oP4r//5D+R//g6+ayiDQzhmubdERDSbeAeEiIi8Rq814Adr\n",
       "nsIjq57AxetFOHv5c9Q0VY2JszuGcP67Mzj/3RmEGMOxdulmPLD0EQTqQ+ag10RE5E0sQIiIyOtU\n",
       "ShWy0zYiO20jGlqqcfby5yi5esrt41ntlmb8vfggjn39v7g/PhM56ZuRnpgFpUI1Bz0nIiJPYwFC\n",
       "RESzKtaUhH/d/Dz+Zd2/4ZvKQpy9fBytnY1j4oRwoKL2PCpqz0OvNSI7bSOy0h5CTFgiJEmag54T\n",
       "EZEnsAAhIqI5ofPT4+HMbdi48nFcayhDcfmXuHSjGHb70JhYq82Ck6Wf4WTpZ4gIjkVW2kZkpW5A\n",
       "sME0Bz0nIqJ7wQKEiIjmlCzJSI3LQGpcBnpsXSi5ehrF5V+isa3Wbbz5dgOOFv0JR4v+hPui05Gd\n",
       "thErk3Oh89PPbseJiGhGWIAQEdG84a81YOPKx7Eh4zE0tNxAcfmXOH/1NPoGet3G37hVjhu3ynH4\n",
       "nx8iLW4lMlMexLKkbOg0LEaIiOYrFiBERDTvSJKEuPBkxIUn40frd6Ks+hxKqk6hsu6C22l67fYh\n",
       "lNeUoLymBApZibS4lViZkovl961hMUJENM+wACEionlNrdJgdep6rE5dj+5eC0qvnUVJ1WnUmq+6\n",
       "jbc7hlBeW4Ly2hIo/qFEalwGMpJzsCwxa9zvkRAR0exhAUJERD4jQGfEhozHsCHjMbR2NqGk6hRK\n",
       "rp52O4sW4CxGRmbSkiAhITIVy5LWYEXSGpiCojmbFhHRHGABQkREPiksMBJb127HDx94GrfaanDx\n",
       "WhFKrxWNW4wICNQ0VaGmqQr/99UfERYYheVJ2ViWtAaJkWlQyIpZvgIiosWJBQgREfk0SZIQE5aE\n",
       "mLAkPJbzLBrb6nDx+lcovVaElo5b47Zr7WxE4YVPUXjhU2jVOiyJy8DS+FVIi89EUEDoLF4BEdHi\n",
       "wgKEiIgWDEmSEB2WgOiwBDy69hk0tdfh0vWvUVZzDjdbqsdtZxvoxaXrxbh0vRgAEBkSh/vjV2Fp\n",
       "wiokRt4PlZJfYSci8hQWIEREtCBJkoSo0AREhSZg69rt6OhuxZXqb1FWfQ7Xbl6B3TH2g4cjmtrr\n",
       "0dRej8ILf4NKqUZS5P1IiVmGlNgViAtP5uNaRET3gAUIEREtCkEBYVif8SjWZzwKW38vqupLUXbj\n",
       "HCrrS9Fj6xq33eDQAK42XMLVhktA8UFoVH64LzodKTHLkRKzDDFhiZBZkBARTRkLECIiWnS0Gh0y\n",
       "Ux5EZsqDcDjsaGipRmXdBVTWlaLW/B2Em2+NjOgf7HPNrOU8lz+So9ORHL0MSVFpiA5LhFLBR7aI\n",
       "iMbDAoSIiBY1WVYgPiIF8REp+OEDT6O3z4qq+ouorCtFVf1FWKztE7a39fegrPocyqrPAQBUCjXi\n",
       "wpORGJmGxKg0JEamQa81zMalEBH5BBYgREREd9D56bFqyTqsWrIOQgi0djbh2s0y59JQhm6bZcL2\n",
       "g/YB3GiswI3GCsB5kwSmwKjhguR+JEQsQXhwDN8jIaJFiwUIERHROCRJgikoCqagKDy4/AcQQsB8\n",
       "uwHXbpbhu4YyXL95Bb391knP09LZiJbORnxTWQgAUCnViAlLQlx4MmJN9yHWlIzwoCi+S0JEiwIL\n",
       "ECIioimSJAmRIXGIDInDhozH4BAO3GqtxfVbV5wfOWysgqXn9qTnGRwacH0UcYRa5YfYsCRnQRKe\n",
       "jFhTEsICo3inhIgWHBYgREREMyRLMmJNSYg1JeHhzG0QQqCjuxU1TVWobnQWGLfaaid8qX3EwGDf\n",
       "949uDVMqVIgIjkVUaLxzCXFOK2zwD/TmZREReRULECIiIg+RJAnBBhOCDSasTt0AAOgfsKGu+Rqq\n",
       "GytR23QV9S03YJ3kPZIRQ/ZB3Gytxs3W0R9R1GuNw0VJAiKDYxEeHIPw4Bj4+wV4/JqIiDyNBQgR\n",
       "EZEXadRaLIldgSWxKwAAQgh0WttQ33wDDS03UN9yHQ3N19HT1z3lc1ptFnzXcBnfNVwetV+vNSI8\n",
       "KBrhwdEwBcUgIjgG4UExCAoI5fslRDRvsAAhIiKaRZIkISggDEEBYchIXgsArke36puvo77lBm62\n",
       "3EBjWx26ejumdW6rzQKrzTLqMS7AOTVwaGAEQo3DS2CkazvYYOJ7JkQ0q1iAEBERzbE7H91amZLr\n",
       "2t/d24nGtjo0ttc51221MLc3YNA+MK3zD9oH0NRej6b2+jHHZElGsMHkKkhCjOGuAik4IAwB/oGQ\n",
       "Jfmer5GIaAQLECIionkqQBeI1LhApMZluPY5HHa0WsxobKtFY1sdmjtuouX2LbR0NmLIPjjt33AI\n",
       "B9osZrRZzG6PK2QlAgNCXAXJncVJkCEMQfpQqFWaGV8jES0+LECIiIh8iCwrnO95BEUjM+VB136H\n",
       "w472rha0dNxCc8dNNN8eXnfcQo+ta8a/Z3cMod3SjHZL87gxWo0/1LIWWrUele1nYfAPgtE/2LU2\n",
       "6p3baiULFSJiAUJERLQgyLICYYGRCAuMRHpi1qhjVluX8y5HZxNaLWa0W8xo6zSj1dKE7t7Oe/5t\n",
       "W38PbOiBxdYGs6V23Ditxh8G/yAYdEHQaw3Qa43Otc7o2g4Y3tb56fnoF9ECxQKEiIhogXP+Y9+A\n",
       "hIglY471D9jQZmkefgyrCR3drbjd3YaOrhZ0dLdN6UvvU2Xr74GtvwfNt29OGitJMvz9AhCgM8Jf\n",
       "a4C/Rg+tnx46jR46d+vhbT+NjoUL0TzHAoSIiGgR06i1iA5LQHRYgtvjfQM2dHS3Di9tuD1cmDgL\n",
       "lVZYrO1wTOFDi9MlhMM1q9d0SJCg1fhD6+cPf00AtH7+8FPrhhftXdvaUfs1d/xZqVB5/JqIyGlK\n",
       "Bcj+/fuxZ88emM1mpKen491338W6devGjS8rK8MLL7yAb7/9FsHBwfjZz36G1157zWOdJiIiotnh\n",
       "p9YiMiQOkSFxbo87HHZYbd34+tuz6B2wIjwqBJae2+jq6Ri97u2Ew2H3en8FBHr7rejtt6Id47+3\n",
       "MhmlQgWNWguNUgO1ys+5KNXD2xqoh/drVBqolBpoVH7D+4bjR7aVznilQgWlQgWVUg2VQgWlUs3p\n",
       "j2nRmrQAOXToEF588UV88MEHWLduHfbt24etW7eioqICsbGxY+K7urqQl5eHhx56CCUlJaisrMTO\n",
       "nTvh7++P3bt3e+UiiIiIaG7IsgIG/0AE6yMQDCBrWZbbOIdwoMfWja6e2+judd7Z6LZZ0GPrcm73\n",
       "WmC1dTmX3k7YBnpn90LuMmQfxJBtED1e/A1ZkqFUqp2FiUIFpVIFlUL9/dq1Xz1qrVAooVQooZCV\n",
       "kGUFlLISCsXobYWsgMK17f7PSoUS8h3brvMNn0uWFJBlGbIkQ5IkL/6foMVm0gJk79692LlzJ376\n",
       "058CAN5//30cP34cH3zwAd56660x8QcPHkRfXx/y8/Oh0WiwdOlSVFVVYe/evSxAiIiIFilZkhGg\n",
       "MyJAZ5xS/JB9cLggscDa24Xefits/T3o7bOit78bvX096O3rRm9/j/OOR5/zrkf/gM3LV+I5DuHA\n",
       "wGAfBgb75rork5IgDRclMqThosThEJAlCX8r1UCSZShcx5xxruJFlqGQFK52zmMK17Yky1DICkgj\n",
       "f5ZkSHC+ByRJknOBcw1JgixJkCADw8dkSXL2UJLGtr1zvwRIkO86jzR8Hvmu89zV9o5zArijIJO+\n",
       "/+/IMUj4vl6TxhRv0vDvjLQbc6474iePHafdZL97V+yEvysBClmFpKg0eMqEBcjAwAAuXLiAX//6\n",
       "16P2b9myBUVFRW7bFBcXY/369dBoNKPiX3vtNdTV1SE+Pt4D3SYiIqKFTKlQIVAfgkB9yLTa2e1D\n",
       "6O3vga3fip4+K2z9VvQN2IaXXvQPr/vuWH+/7/v93nivxZcJCNgdQ7ADwF1P0vUNzu3dKvK+AF0g\n",
       "/vs/D3jsfBMWIG1tbbDb7QgPDx+132QywWx2/8Eis9mMuLjRz4mOtDebzeMWIBbL9F4yI9+UkpIC\n",
       "gOO9mHDMFyeO++Iz38ZcI+uh0ekB3Vz3hGhh8GRue3yeOj4jSERERERE45mwAAkNDYVCoUBz8+hZ\n",
       "JJqbmxEZGem2TURExJi7IyPtIyIi7qWvRERERETk4yZ8BEutVmP16tU4ceIEnnzySdf+goICPPXU\n",
       "U27b5OTk4OWXX0Z/f7/rPZCCggJER0ePefzKaJzai2hERERERLQwTPoI1u7du3HgwAH84Q9/QGVl\n",
       "JXbt2gWz2Yyf//znAIBXX30VmzdvdsU/88wz0Ol02LFjB8rLy/HJJ5/g97//PWfAIiIiIiKiyafh\n",
       "/clPfoL29na8+eabaGpqwvLly3Hs2DHXN0DMZjOqq6td8QaDAQUFBXj++eeRlZWF4OBg/OpXv8JL\n",
       "L73kvasgIiIiIiKfIAkhxFx3goiIiIiIFgePz4J1t/379yMxMRFarRZZWVk4e/bshPFlZWXYuHEj\n",
       "dDodYmJi8Nvf/tbbXSQPm86Y19bWOj9UdNdy4sSJWewxzdTp06exbds2xMTEQJZl5OfnT9qGOe77\n",
       "pjvuzHPf97vf/Q7Z2dkwGo0wmUzYtm0bysvLJ23HfPddMxlz5rpv27dvHzIyMmA0GmE0GpGbm4tj\n",
       "x45N2GamOe7VAuTQoUN48cUX8Zvf/AYXL15Ebm4utm7dioaGBrfxXV1dyMvLQ2RkJEpKSvDee+9h\n",
       "z5492Lt3rze7SR403TEf8cUXX8BsNruWhx9+eJZ6TPeip6cHK1aswHvvvQetVjvpNNzM8YVhuuM+\n",
       "gnnuu06dOoUXXngBxcXFKCwshFKpxObNm9HR0TFuG+a7b5vJmI9grvum2NhYvP322ygtLcX58+fx\n",
       "yCOP4IknnsClS5fcxt9TjgsvWrNmjXjuuedG7UtJSRGvvvqq2/j9+/cLo9Eo+vr6XPvefPNNER0d\n",
       "7c1ukgdNd8xramqEJEmipKRkNrpHXqTX60V+fv6EMczxhWcq4848X3isVqtQKBTi6NGj48Yw3xeW\n",
       "qYw5c33hCQ4OFh9++KHbY/eS4167AzIwMIALFy5gy5Yto/Zv2bIFRUVFbtsUFxdj/fr1rul7R+Ib\n",
       "GxtRV1fnra6Sh8xkzEf8+Mc/Rnh4ONatW4cjR454s5s0h5jjixvzfOHo6uqCw+FAUFDQuDHM94Vl\n",
       "KmM+grnu++x2Oz7++GP09fVhw4YNbmPuJce9VoC0tbXBbrcjPDx81H6TyTTmQ4UjzGbzmPiRP4/X\n",
       "huaPmYx5QEAA3nnnHRw+fBiff/45Nm3ahKeffhoHDx6cjS7TLGOOL07M84Vn165dyMzMRE5Ozrgx\n",
       "zPeFZSpjzlz3fWVlZdDr9fDz88Nzzz2Hv/zlL0hNTXUbey85Puk0vLNpqs8R08IREhIyaormVatW\n",
       "ob29HW+//TaeffbZOewZeQNzfHFini8su3fvRlFREc6ePTthTjPfF46pjjlz3felpaXh8uXLsFgs\n",
       "OHz4MLZv346TJ08iKytrTOy95LjX7oCEhoZCoVCgubl51P7m5mZERka6bRMRETGmYhppHxER4Z2O\n",
       "ksfMZMzdyc7OxrVr1zzdPZoHmOM0gnnum1566SUcOnQIhYWFSEhImDCW+b4wTGfM3WGu+xaVSoWk\n",
       "pCRkZmbirbfewtq1a7Fv3z63sfeS414rQNRqNVavXj1m6rWCggLk5ua6bZOTk4MzZ86gv79/VHx0\n",
       "dDTi4+O91VXykJmMuTsXL15EVFSUp7tH8wBznEYwz33Prl27XP8QXbJkyaTxzHffN90xd4e57tvs\n",
       "djscDofbY/eU4x57Td6NQ4cOCbVaLT766CNRUVEhfvnLX4qAgABRX18vhBDilVdeEZs2bXLFWywW\n",
       "ERERIbZv3y6uXLkijhw5IgwGg9i7d683u0keNN0xP3DggPjzn/8sKioqRFVVldizZ49Qq9Xi3Xff\n",
       "natLoGmwWq2itLRUlJaWCp1OJ9544w1RWlrKHF/gpjvuzHPf94tf/EIYDAZRWFgompqaXIvVanXF\n",
       "MN8XlpmMOXPdt7388svizJkzoqamRly+fFm88sorQpZlceLECSGEZ3PcqwWIEM4puhISEoRGoxFZ\n",
       "WVnizJkzrmM7duwQiYmJo+LLysrEhg0bhJ+fn4iKihJvvPGGt7tIHjadMc/PzxdLly4V/v7+wmAw\n",
       "iOzsbHHw4MG56DbNwMmTJ4UkSUKSJCHLsmt7586dQgjm+EI13XFnnvu+u8d6ZHn99dddMcz3hWUm\n",
       "Y85c9207duwQ8fHxQqPRCJPJJPLy8lzFx8hxT+W4JIQQnrxVQ0RERERENB6vfgmdiIiIiIjoTixA\n",
       "iIiIiIho1rAAISIiIiKiWcMChIiIiIiIZg0LECIiIiIimjUsQIiIiIiIaNawACEiIiIiolnDAoSI\n",
       "iIiIiGbN/wNdf7Zt9OdzAwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4800d89dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, np.exp(-x**2))\n",
    "plt.title('exp(-x^2)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final piece of the puzzle is to plot the values for -x as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAxkAAAGaCAYAAABjWI6gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Wl4lFWe//9PVTYSyEIgQMKasC8BQsIWgiwCEhVFcaG1\n",
       "tUUdR9qZ1vHX/7G9xunFtqe1u0e97Bmdadt2bRVtW1FAZF9C2EIIYQkQCGFPWAIJa5aq+//AsfBO\n",
       "QgiQ5NTyfl2XD8636q58ihKSb859znFYlmUJAAAAAJqI03QAAAAAAP6FJgMAAABAk6LJAAAAANCk\n",
       "aDIAAAAANCmaDAAAAABNiiYDAAAAQJOiyQAANNrkyZPVp08fud1u01Ga1OzZsxUbG6uysjLTUQDA\n",
       "L9BkAAAaZcGCBVq6dKl+8YtfyOlsuW8fmzZtUkxMjJxOpzIzM1VVVdXg8wsLC/W73/1OkyZNUrdu\n",
       "3RQWFqYOHTooMzNTX331Vb3X/Nu//ZvOnz+v559/vjneAgAEHAeH8QEAGiMlJUWnTp3Svn375HA4\n",
       "WuRr5ufna8KECaqoqNCAAQO0detWTZs2TZ999pmCg4PrvWbmzJn65JNP1K9fP2VkZCguLk5FRUX6\n",
       "/PPPVVVVpZ/+9Kf63e9+V+e6Rx55RB988IH27dunhISE5n5rAODXmMkAAFxRdna2tmzZovvuu6/F\n",
       "GoyCggJNmjRJ58+f18cff6ycnBzdfffd+uqrrzRz5ky5XK56r5s6dapycnK0Y8cO/elPf9JvfvMb\n",
       "ffTRR9q0aZOioqL0hz/8QZs3b65z3QMPPKDq6mq99dZbzf3WAMDv0WQAgJfKzc3VzJkzlZCQoLCw\n",
       "MCUkJOjBBx/U3r17Pc956qmn5HQ69ZOf/KTO9XPmzJHT6dSYMWNUU1MjSSouLpbT6dSECRN0+PBh\n",
       "3X///YqLi1NERISGDx+uTz75pN4s3/3gPXPmzKt6D9OnT5fT6dTLL79c57GXXnpJTqdT99xzT53H\n",
       "CgsLdeONN6q6uloLFy7UjBkzFBISoo8//lj/9E//pL///e968MEHVd9k/EMPPaRhw4bVqQ8cOFD3\n",
       "3nuvJGnFihV1Hh8/frw6duxIkwEATcECAHidDz74wAoODrbatGlj3XfffdYzzzxj3XnnnVZwcLAV\n",
       "ExNj5eXlWZZlWVVVVdbw4cMth8Nhff75557r9+zZY0VFRVnt2rWzDhw44Knv27fPcjgc1pAhQ6we\n",
       "PXpYw4YNs372s59Zjz32mBUTE2M5HA7rlVdeqZOna9euVnR09FW/j1OnTlk9evSwQkNDrQ0bNnjq\n",
       "2dnZVnBwsNWzZ0+roqLCdk1RUZHVtWtXKyEhwdqyZUu9r/vCCy9YDofDeuihh64qz49//GPL4XBY\n",
       "r732Wr2P33nnnZbD4bB27dp1Va8LALCjyQAAL1NYWGiFhYVZvXr1so4cOWJ7bMWKFVZwcLCVmprq\n",
       "qRUVFVkxMTFW27ZtreLiYquystJKTU21nE6nNXfuXNv13zUZDofDmjlzpu2xvXv3WjExMVZYWJi1\n",
       "f/9+T724uNhyOBzWjTfeeE3vZ/369VZoaKiVmJhonT592iorK7O6detmhYWFWTk5OXWe/+6771rP\n",
       "P/+8VVxc3ODrfvbZZ9avfvUrKz8/v1E5Tp8+bXXs2NEKDg62du7cWe9zXnzxRcvhcFhvvvlmo14T\n",
       "AFA/bpcCAC/zxhtvqKqqSq+88ori4+Ntj40bN07Tpk1Tbm6uCgoKJEmJiYl66623dPr0ad177716\n",
       "+umnlZubq5/85Ce67bbb6v0awcHBevHFF221pKQk/fjHP1ZVVZU++OADT72oqEiS1KVLl2t6PyNG\n",
       "jNBvf/tbFRcX6+GHH9bDDz+sgwcP6qWXXlJqamqd5z/44IP693//d3Xv3r3B173zzjv185//XMnJ\n",
       "yVfM4Ha7NWvWLB07dkyzZ89W3759633ed+9x3759jXhnAIDLqX9rDgCAMWvWrJEkrVy5Ujk5OXUe\n",
       "Ly0tlfTtwuj+/ftL+vYH7ieeeEL//d//rQ0bNigtLU2///3vL/s1unXrVu8P8TfccIN++9vfKi8v\n",
       "z1M7fvy4JCk2NrbO84uLi/XOO+/Yag6HQ7/4xS9staefflorVqzQ559/Lkm67bbb9OSTT142X1Oy\n",
       "LEs//vGP9cUXX2jChAn1rg/5Trt27SRJx44da5FsAOCvaDIAwMucPHlSkvSf//mfl32Ow+HQuXPn\n",
       "bLW77rpL//3f/y1J+vGPf3zZLV4lqWPHjg3Wy8vLbV9LUr2LrIuLi+ucLVFfkyFJM2bM0Lx58ySp\n",
       "RRuMxx9/XG+++aYmTZqkL7/8ssE/l+8OGWypHbQAwF9xuxQAeJno6Gg5HA6VlZXJ7XbX+5/L5dID\n",
       "DzzguebUqVP60Y9+pNDQUEVGRupf//VfdeTIkct+je9mQy5Xj46O9tTat28vSfWehj1+/Ph6s9W2\n",
       "b98+Pfnkk4qOjlZwcLAef/xxnT17tnF/INfI5XLpoYce0ptvvqnMzEzNmzdPrVq1avCa795jXFxc\n",
       "s2YDAH9HkwEAXiY9PV2WZWnVqlWNvmbWrFk6cOCA/vCHP+jNN9/UiRMn9IMf/MDzm/naDhw4oP37\n",
       "99epr1y5UtK3B+99JykpSZJ06NChq3kbHlVVVbrnnnt05swZvffee3rhhRdUWFioxx9//JperzGq\n",
       "q6t133336f3339f06dM1d+5chYaGXvG6w4cPS7r0ngEA18jsunMAQG27du3y7C5V3y5I1dXV1rJl\n",
       "yzzjV155xXI4HNYdd9zhqT322GOWw+GwnnvuOdu1399d6t5777XcbrfnsT179ljR0dF1dpeyrGvf\n",
       "wtayLOvJJ5+0HA6H9dRTT3lqU6dOtRwOh/XnP//5ml6zIRcvXrSmTZvm2UHL5XI1+trvtrAtLCxs\n",
       "8lwAEEgcllXPTbYAAKM+/vhjzZo1SzU1NZo6dap69+4tl8ulgwcPas2aNaqurlZZWZlycnI0ZswY\n",
       "JSQkKC8vz3Ob08WLFzVixAjt2LFDixYt0sSJEyV9u4YiKSlJgwcPVnl5uWJjYzV58mSVlZXpk08+\n",
       "0ZkzZ/Tyyy/XWTPx6KOP6i9/+Ys2b96sIUOGNPp9zJ07V3fccYfS0tKUnZ3tWQ9x/PhxDR06VKdP\n",
       "n9bGjRs1YMCAJvqT+3ZW591331V0dLT++Z//WU5n3Un7lJQU3X777baaZVlKSEhQq1at2F0KAK7X\n",
       "lbqQlStXWtOmTbM6d+5sORwO65133rli55Kfn2/dcMMNVnh4uNW5c2fr+eefv/52CAACzI4dO6xH\n",
       "H33USkxMtMLCwqy2bdtaAwYMsB5++GFr/vz5Vnl5uZWUlGSFhoZaa9eurXN9QUGB1bp1ays+Pt4q\n",
       "LS21LOvSTMaECROsw4cPW/fff78VFxdnhYeHW2lpadacOXPqzZKdnW05HA7rZz/7WaPz79+/34qN\n",
       "jbWio6OtvXv31nl8+fLlVlBQkDVo0CDr/PnzjX7dKxk/frzldDotp9PpmbX5/n9Op9OaNWtWneuW\n",
       "LVtmORwO69e//nWTZQGAQHXFmYyvv/5aa9asUUpKih588EG98cYbevDBBy/7/IqKCvXp00fjx4/X\n",
       "z3/+cxUUFGjWrFn65S9/qaeffrrJmyQAQON9N5Mxfvx4LVu27KquHTZsmE6ePKl9+/bVOzvg6x5+\n",
       "+GF9+OGH2rdvX53zSQAAV+eK3yUyMzP1wgsvaMaMGY36pvLXv/5VFy9e1LvvvqsBAwZoxowZeuaZ\n",
       "ZxrclxwA4P1+85vf6ODBg/rwww9NR2ly372v2bNn02AAQBNo8l9FrV27VmPHjlVYWJinNmXKFB05\n",
       "cqTenUwAAL4hMzNTkyZN0q9//et6z8zwZf/xH/+h1q1b6+c//7npKADgF5r8ML6SkhJ169bNVvvu\n",
       "cKeSkhLbCbPfP+wJAND8KioqJEk1NTXX9G/wp59+ansdf/Hiiy/qxRdflMT3JgBojO+fp1SfJm8y\n",
       "OCUVALxX9+7dderUKdMxAAB+rslvl+rUqZNKSkpste9OkO3UqVNTfzkAAAAAXqbJZzJGjx6tZ555\n",
       "RpWVlZ51GYsXL1bnzp1tt0rVdqUpF/iHnJwcSVJaWprhJGgpfOa+63zlWX215gNlb/1Gli6/BiMy\n",
       "IkaJ8X0V36674mLiFR7WWsVF++Vy16hztwSVVZTq6MkDKi7ZrbKKYw1+zcE9R2nGuEfVNrJ9U78d\n",
       "NDP+rgcePvPAczW3k16xyTh37pwKCwslSW63W/v371deXp7atWunrl276tlnn9XGjRu1ZMkSSdJ9\n",
       "992nX/3qV3rooYf03HPPadeuXXrppZf0y1/+8treDQCgxeXuztJnK/+sM+dP1/t4dJt2GjVgogb3\n",
       "HKXOcYlyOuwT45Vl347T+l364cOyLB07dVhbizZo3Y6lOnbqcJ3Xzd+7TrsO5OmW0ffrhqG31Hld\n",
       "AIBvuGKTsXHjRs9JsQ6HQ7/4xS/0i1/8Qg899JD+8pe/qKSkREVFRZ7nR0VFafHixXriiSeUlpam\n",
       "2NhY/fSnP9W//Mu/NN+7AAA0icqqC/p0xZ+0oWB5vY937dBTN424WwMThyvIGXRVr+1wONQxtos6\n",
       "xnbRjal3aM/hbVq08W/adWCLPUP1Rf191VvaUbxJP5zylKJax1zz+wEAmHHFJmP8+PFyu92Xffzt\n",
       "t9+uUxs0aJBWrlx5fckAAC3q8PFivb3gdzp2+kidx+JiEnR7xo+UnDSiSTb4cDgc6t0lWb27JGvP\n",
       "4e2au/od7S8ttD1n54E8vfThU/rR1KfVp+vg6/6aAICWwzw0AEBbizbolU9/VqfBCAoKVubImfrZ\n",
       "/a9qcM+RzbKDYK/OA/Uv97you8c/plahEbbHzpw/rdc//6Wy8hc2+dcFADSfJl/4DQDwHZZlafnm\n",
       "uZq7+t06i7s7xXbVQ5n/TwntezR7DqczSGOH3KxBSSP03sKXtffIDs9jbsutT5b/j0pPHdIdY2fJ\n",
       "eZW3aQEAWh4zGQAQoCzL0pdr3tUXq9+p02CMHjhZP535hxZpML6vbWR7/dOMX2vqyHvlkH3WZGXe\n",
       "PL33zSuqcVW3aCYAwNVjJgMAApDbcuvT5X/Smq3225CcDqfuHPeobhhys6FkUpAzSDeP+oG6xCXp\n",
       "vW9eUVX1Rc9jubuzdLHqgh6+5V8VGhxmLCMAoGHMZABAgHFbbn20+L/qNBitQiP0j7f/u9EG4/sG\n",
       "9xypp+7+D8W0aWer7yjepD99+RtV11QZSgYAuBKaDAAIIJZl6W8r3tT6gmW2eutWkfrnGb9W/+4p\n",
       "hpLVr0tckp66+7eKi4631XcfzNdf5v+OW6cAwEvRZABAgPh2DcZ7ysr/2laPbh2rn9z1H+raoaeh\n",
       "ZA2LjeqgJ+/+D8W362arby/O0XvfvCKX22UoGQDgcmgyACBArNj8lZZu+txWi4poq5/c9RvFt+tq\n",
       "KFXjRLVuq5/MeKFOo5FXmK3PVv5ZlmVd5koAgAk0GQAQAPIKs/XFavvhqa1bReqJO3+luJj4y1zl\n",
       "XVqHR+mJO35V59aprPyvtXzzXEOpAAD1ockAAD+37+guvf/Nq7ZtasNCw/XjO35ZZ2bA20W1bqsn\n",
       "7nxebdu0t9W/WP2ONhdmG0oFAKiNJgMA/Fj5uTK9Ne9FVbsu7cTkdAbpkZuf8do1GFcSGxWnf7z9\n",
       "3+ucDv7Bold16HiRoVQAgO+jyQAAP1Xjqtbb83+vivOnbPV7J85Wv+5DDaVqGgntu+uRW56xnf5d\n",
       "XVOlP3/1W529UGEwGQBAoskAAL/1xeq3VXS0wFablDZDowdOMpSoafXtNkT3Tpxtq5WdOa53Fvye\n",
       "HacAwDCaDADwQxt3rtCqLQtstX7dU3Tr6PsMJWoeowdOqnN44O5DW7Vg7YeGEgEAJJoMAPA7h48X\n",
       "6+Olr9tqsVEd9KOb/sV2e5G/uGPsw+rZeaCttiTn79p1YIuhRAAAmgwA8CNV1ZV6Z+EfVF1zaaF3\n",
       "SFCoHrnlGbUOjzKYrPkEBQXr4Zv/P0W3jvXULFl6/5tXdeb8aYPJACBw0WQAgB+Zm/WuSssO2Wr3\n",
       "TPxHn91JqrEiI2L0wE3/IoccnlrF+VP6YNFrcltug8kAIDDRZACAn9i+L0er8+3rMEYOuFEjB9xo\n",
       "KFHL6tM1WVNG3G2rFezP1YrNXxpKBACBiyYDAPzAmfOn9eHiP9pq7aM76a5xjxpKZMbUkfcqKaG/\n",
       "rfbVmg908BjnZwBAS6LJAAAfZ1mWPlz8XzpzodxTczqcenDq0woLDTeYrOUFOYP04E1PKyKsjafm\n",
       "ctfow8WvqcZVbTAZAAQWmgwA8HHrti/R9uIcW+2mkfeqR6c+hhKZFRsVpx9MesJWO3yiWIs3fmYo\n",
       "EQAEHpoMAPBh5WfL9MXqt221xPh+mjL8LkOJvMOQXqOV1necrfbNxk91+Pg+Q4kAILDQZACAj7Is\n",
       "S5+u+F9dqDrvqYUGh+mBm55SkB+eh3G1Zox7RJERMZ6x2+3SB4tfk8tVYzAVAAQGmgwA8FF5e9Yq\n",
       "f+96W+2W9PvVPrqToUTepXV4lO6d+Litdvj4Pi3K4bYpAGhuNBkA4IPOXTyjv634k63WvVMfjRty\n",
       "i6FE3mlwz1FK7TPWVlu04VOVlB00lAgAAgNNBgD4oC9WvW07zTrIGaz7Jv2TnNwmVceM8f+gyPBo\n",
       "z9jlrtEny/9XlmUZTAUA/o0mAwB8TOGhbVpfsMxWmzL8LsW362YokXdrEx6lGeP/wVbbc2ibcnat\n",
       "NJQIAPwfTQYA+BCXq6bObVLx7bpp8vAZhhL5hpTeY9Sv21Bb7YtVb+t85VlDiQDAv9FkAIAPWbVl\n",
       "gY6ePGCr3TtxtoKDQgwl8g0Oh0N3T/hH25/TmQvlmpf9V4OpAMB/0WQAgI8oP1emBes/stVG9J+g\n",
       "pIT+hhL5lriYeE1Ku9NWW5O/UPtLCg0lAgD/RZMBAD5ibta7qqy64BmHh0botjE/MpjI90xOm6G4\n",
       "6HjP2JKlT5f/r9yW22AqAPA/NBkA4AP2Ht6unJ32hco3j75PUa1jLnMF6hMSHKq7Jjxmqx04tqfO\n",
       "ny0A4PrQZACAl3O7XfrbijdttYT2PZQxONNQIt/Wv3uKhvQabat9teZ92ywRAOD60GQAgJdbX7Bc\n",
       "h08U22p3j/8HBXEmxjW7PeNHCgoK9ozLz5VpyabPDSYCAP9CkwEAXqyy6oLmr7XvgJTa9wb17DzQ\n",
       "UCL/0D66kyak3G6rLdv0hcoqjhtKBAD+hSYDALzY0twvVHHulGccHBSiaekPGEzkPyanzVBkxKU1\n",
       "LdWuKn215j2DiQDAf9BkAICXKj9bpmWbvrDVxqfcptioOEOJ/Et4WIRuHX2/rbZp92oVHdlpKBEA\n",
       "+A+aDADwUvPW/lVVNZWecZvwaE1O42TvpjRywER1jku01b7MeleWZRlKBAD+gSYDALzQoeNF2rBj\n",
       "ma2WOWqmwsMiDCXyT05nkO684WFbrehogbbt22goEQD4B5oMAPBCX2a9J0uXfpveMbaL0gdNMZjI\n",
       "f/XukqyBPdJstXnZH8jtdhlKBAC+jyYDALxM4aGt2nkgz1abnvEQW9Y2o2ljfiiHHJ7x0ZMHtHHn\n",
       "CnOBAMDH0WQAgBexLEtfZX9gq/XqPFADeqQaShQYEtr30PD+4221BWs/UnVNlZlAAODjaDIAwIts\n",
       "27dRxUd32WrTxjwgh8NxmSvQVG4e9QPbAX2nzp7Q6vwFBhMBgO+iyQAAL+G23JqfbT94b1DicCXG\n",
       "9zOUKLDERnXQ2ORMW23Rxs90vvKsoUQA4LtoMgDAS+TuWq0jJ/d7xg45dGv6/Q1cgaY2ZcTdCgsN\n",
       "94zPXzyjFblfGUwEAL6JJgMAvIDLVaMF6z6y1VL73qCE9j3MBApQbcKjdOOw6bba8rwvde7iGUOJ\n",
       "AMA30WQAgBdYt2OpTpSXeMZOZ5AyR800mChwjU+5Ta1bRXrGlVUXtDx3rsFEAOB7aDIAwLAaV7UW\n",
       "bfybrTZ64GTFxcQbShTYWoWG68bUO2y1FXnzdPZChaFEAOB7aDIAwLANBct16sxxzzg4KEQ3jbjb\n",
       "YCKMHXKz2oRHe8ZV1Re1dNPnBhMBgG+hyQAAg1yumjqzGOmDJiumTTtDiSBJYSGtNCntTltt9ZYF\n",
       "qjh32lAiAPAtNBkAYNCGguUqqzjmGQcFBevG1DsbuAItJSN5qqIi2nrGVTWVWrrp7wYTAYDvoMkA\n",
       "AEPqm8UYPXCy2ka2N5QI3xcaEqbJw2fYaln5C1Vx7pShRADgO2gyAMCQjTtX6mRFqWcc5AzWJGYx\n",
       "vEr6oCmK/t6ta9WuKi3fzE5TAHAlNBkAYIDL7dKijZ/aaqMG3KjYqDhDiVCfkOBQTa69NiN/oc6x\n",
       "0xQANIgmAwAMyNm50nYuRpAzuM6tOfAOowZOUmREjGdcVX1RK/PmG0wEAN6PJgMAWpjL7dKiDfZZ\n",
       "jJEDJig2qoOhRGhIaHCYJg673VZbuWWeLlSeN5QIALwfTQYAtLDc3at1vPyoZ+x0Bmny8LsMJsKV\n",
       "jEmeqoiwNp7xhcpzysr/2mAiAPBuNBkA0ILclltLcuzboI7oP0HtojoaSoTGaBUarnEp02y15Zu/\n",
       "VFV1paFEAODdaDIAoAVt35ejoycPeMYOh1OT01iL4QvGDblFYaHhnvHZC+XK3rbIYCIA8F40GQDQ\n",
       "QizL0uKcz2y1Yb3HKC4m3lAiXI2IVm00dvDNttrS3C9UXVNtKBEAeC+aDABoIXuP7FDx0V222qQ0\n",
       "zsXwJRNSpikkONQzLj97UhsKlhlMBADeqVFNxuuvv67ExESFh4crLS1NWVlZDT5/wYIFGjVqlKKi\n",
       "ohQXF6fp06ersLCwSQIDgK9astE+izGg+zB1jks0lAbXIjIiRumDpthqS3L+LpfbZSgRAHinKzYZ\n",
       "c+bM0VNPPaXnnntOeXl5Sk9PV2Zmpg4ePFjv8/fs2aPp06dr/PjxysvL05IlS3Tx4kXdfPPN9T4f\n",
       "AALB4eP7tGN/rq3GuRi+aeKw6QpyBnvGJytKlVe4xmAiAPA+V2wyXn75Zc2aNUuPPPKI+vbtq9de\n",
       "e03x8fF644036n1+Xl6e3G63fvvb3yopKUlDhgzRM888o71796qsrKzJ3wAA+ILFtXaUSozvp6SE\n",
       "AYbS4Hq0jWyvkQMm2GpLN30hy7IMJQIA79Ngk1FVVaXc3FxNmWKfGp4yZYqys7PrvWbMmDFq06aN\n",
       "3nzzTblcLp05c0bvvPOORowYodjY2KZLDgA+4vjpo9pc6zfdk9LulMPhMJQI12vCsOly6NLnd+h4\n",
       "kXYfzDeYCAC8S3BDD544cUIul0sdO9r3b+/QoYNKSkrqvSY+Pl4LFizQ9OnT9cQTT8jtdislJUVf\n",
       "f93woUU5OTlXGR2+jM878ATyZ75u7wJZltszjomI08WTDuWU+f+fiT9/7l1i++hg2aWF/J8vf1eT\n",
       "Bt5nMJF38OfPHPXjMw8cvXv3bvRzm3x3qaKiIk2fPl2zZs1STk6OVqxYocjISN1zzz1MJQMIOBeq\n",
       "zmpP6RZbbVDndGYx/MDAzqNs4yOni1R2rtRQGgDwLg3OZLRv315BQUEqLbX/o1laWqr4+Pr3df/f\n",
       "//1fde3aVS+99JKn9sEHH6hr165au3at0tPT670uLS3tarPDB3332w4+78AR6J/5V2vel9u6tPNQ\n",
       "bGScZtz0gIKCGvzn1+cFxueept0nNqjoaIGnUnJxt6aMu8VgJnMC4zPH9/GZB57y8vJGP7fBmYzQ\n",
       "0FClpqZq0SL7iaaLFy++bLNgWZacTvvLfjd2u931XQIAfqmy+qLWbP3GVpsw7Ha/bzACycTU6bZx\n",
       "7u4slVUcN5QGALzHFW+Xevrpp/XOO+/orbfeUkFBgZ588kmVlJTo8ccflyQ9++yzmjRpkuf5t912\n",
       "m3Jzc/XrX/9ahYWFys3N1axZs9StWzelpqY23zsBAC+zfscyna886xlHtIrUqIGTGrgCvmZQ0nB1\n",
       "aNvZM3a7XVqR95XBRADgHa7YZNxzzz169dVX9cILLyglJUXZ2dlasGCBunbtKkkqKSlRUVGR5/kZ\n",
       "GRmaM2eO5s6dq2HDhikzM1OtWrXSwoULFR4e3nzvBAC8iNvt0srN9h82M5JvUlhIK0OJ0BycDqcm\n",
       "DrPPZqzdtsjWXAJAIGrUnP3s2bM1e/bseh97++2369Tuuusu3XXXXdeXDAB82LZ9OTpeftQzDnIG\n",
       "a+xgDiX1R8P7jdP8tX/VmfOnJf3fbXL533DYIoCA1uS7SwEApOWbv7SNU/uOVXQbzgryRyHBoRo3\n",
       "9FZbbWXePFXXVBtKBADm0WQAQBM7ULpHew9vt9UmpNxmKA1aQkbyVIV+71a4ivOnlLt7tcFEAGAW\n",
       "TQYANLHluXNt4z5dB6tzXKKhNGgJEa3aaHStRf0r8r7ifCgAAYsmAwCa0Kkzx7W5cI2tNnHY7YbS\n",
       "oCWNG3qrHLp0yOLh4/u0p9aMFgAECpoMAGhCK/Pmy21dOhOoY2wX9eueYjARWkr76E5K7jnCVlvJ\n",
       "drYAAhRNBgA0kYtVF5S9zX546YSU2+R08E9toBhfa+3N1r0bdPz00cs8GwD8F9/5AKCJrNu+RBer\n",
       "znvGbcKjldZvnMFEaGk9EwaoS1ySZ2zJ0qot8w0mAgAzaDIAoAm46jnpOWPwVIUGhxlKBBMcDofG\n",
       "p0yz1dbtWKoLlecvcwUA+CeaDABoAvl716us4phnHBwUorGDMw0mgikpvTMUGRHjGVdWXdC67UsM\n",
       "JgKAlkeTAQBNYEWtw/eG9xtv+0ETgSMkuG6DuXLLPLndLkOJAKDl0WQAwHU6ULpH+47utNVq3zKD\n",
       "wDIm+SYFB4V4xmUVx7S1aKPBRADQsmgyAOA61V7Y27fbEMW362YoDbxBZESM0vreYKvVXrMDAP6M\n",
       "JgMArsOZ86e1afdqW23ckFsNpYE3qT2btffwdh08ttdQGgBoWTQZAHAdsrctkstV4xm3j+6kAYmp\n",
       "BhPBWyS076E+XQfbais2M5sBIDDQZADANXK5apSVv9BWGzv4Zg7fg8f4ofbZjNzdWSo/V2YoDQC0\n",
       "HL4TAsA12rJ3ne0HxtCQVho5cKLBRPA2AxJTFRcd7xm73DVak/+NwUQA0DJoMgDgGq3Mm2cbj+g/\n",
       "QRFhbQywLX36AAAgAElEQVSlgTdyOpwal2Jfo5O9bZFqXNWGEgFAy6DJAIBrUN+2tTcMudlQGniz\n",
       "Ef0nKiw03DOuOH9KW/asNZgIAJofTQYAXIP6tq3tFNvVUBp4s1ah4RrZf4KttmrLAkNpAKBl0GQA\n",
       "wFVi21pcrbGD7bNc+47uZDtbAH6NJgMArlL2tsW2bWvbRXfUgB7DDCaCt+sY20V9uw6x1VYzmwHA\n",
       "j9FkAMBV+Hbb2q9ttRsG3yKnM8hQIviKsbXW7GzatVrnLlQYSgMAzYsmAwCuAtvW4loNSkxT28g4\n",
       "z7jaVaV1O5YaTAQAzYcmAwCuwqo8+4LvEf3Gs20tGsXpDFLG4ExbbXX+13K7XYYSAUDzockAgEY6\n",
       "dLxIRUcLbLWxQ24xlAa+aPTASQoOCvGMyyqOaXvxJoOJAKB50GQAQCNl5S+0jft0Haz4dmxbi8Zr\n",
       "Ex6l1D5jbTUWgAPwRzQZANAIFyrPK2fXKlttbK1bX4DGqL0AfOeBPJWeOmwoDQA0D5oMAGiEjTtX\n",
       "qKr6omcc3TpWg5JGGEwEX9WtYy/16NTXVqu9YxkA+DqaDAC4AsuytGar/Vap9EFTFMS2tbhGtWcz\n",
       "1u9YpotVFwylAYCmR5MBAFew98gOHT15wDN2OpwaPWiywUTwdUN7pSsyPNozvlh1Xht3rjAXCACa\n",
       "GE0GAFxB7QXfyUkjFNOmnaE08AchwSFKT55iq63eskCWZRlKBABNiyYDABpQce60tuxZa6vVPusA\n",
       "uBbpg26S03Hp23BJ2UEVHtpmMBEANB2aDABowLodS+Ry13jGcTEJ6t012WAi+Iu2ke01uOcoW23V\n",
       "lvmXeTYA+BaaDAC4DLfbpeyt39hqGclTbb99Bq5H7QXgW4s26NSZE4bSAEDT4TslAFxGwf7NKjtz\n",
       "3DMOCQrViAETDCaCv+nVeaDi23XzjC3LrbXbFhtMBABNgyYDAC5jda2zC4b1yVDrVpGG0sAfORwO\n",
       "ZSRPtdWyty+Sy1VzmSsAwDfQZABAPU6Wl6qgONdWyxg89TLPBq5dWr/xCg1p5RlXnDulrUUbDCYC\n",
       "gOtHkwEA9VizbZEsXdpOtEuHJHXr2NtgIvir8LAIDe87zlbLqnX4IwD4GpoMAKiluqZa67YvsdUy\n",
       "kjPlcDgMJYK/qz1Ltvtgvo6dOmwoDQBcP5oMAKglf+9anb1Q7hmHh0Yote9Yg4ng7zrHJapHfF9b\n",
       "LavWzmYA4EtoMgCgltoLvkcMmKiw790zDzSH2gvAN+xYpqrqSkNpAOD60GQAwPccOVGsoiMFttqY\n",
       "5JsMpUEgSek9xrZ72fnKs8rdnWUwEQBcO5oMAPie2reo9OoySJ1iuxpKg0ASEhyqUQNvtNVYAA7A\n",
       "V9FkAMD/qay6oI07V9hqtW9hAZpT+iD7rNmB0kIdKN1jKA0AXDuaDAD4Pzm7Vqmy6oJnHBkRo8E9\n",
       "RxpMhEATFxOvft1TbDVmMwD4IpoMAJBkWVadBd/pgyYrOCjEUCIEqtqzZ5t2rdL5yrOG0gDAtaHJ\n",
       "AABJ+47u0pETxZ6xw+FU+qAp5gIhYA1MTFNMm3aecXVNlTYWrDAXCACuAU0GAEjK2mqfxRiYmKa2\n",
       "kXGG0iCQBTmD6jS4WVsXyrKsy1wBAN6HJgNAwDt7oUKbC9fYaiz4hkmjB02W0xnkGZeWHdKew9sM\n",
       "JgKAq0OTASDgrd+xVC5XjWfcLrqj+nUfajARAl1061gNTrJvOpCVzwJwAL6DJgNAQHNb7jq794wZ\n",
       "dJOcDv55hFkZg+2zaVv2rlPFuVOG0gDA1eG7KICAtnN/nk6Wl3rGwUEhGjVwksFEwLd6d0lWh7ad\n",
       "PWO326W125cYTAQAjUeTASCg1Z7FGNo7XW3CowylAS5xOBx11gZlb/1GbrfLUCIAaDyaDAABq6zi\n",
       "uLbvy7HVMpIzDaUB6hoxYIJCgkM941NnT2h78SaDiQCgcWgyAASstdsXybLcnnFC+x5KjO9rMBFg\n",
       "FxHWRql9xtpqLAAH4AtoMgAEpBpXtdZus9/fnpE8VQ6Hw1AioH4Zg+2zazv3b9aJ8hJDaQCgcWgy\n",
       "AASk/L3rVXH+0k49YaHhSus3zmAioH7dOvZStw69PGNLltZs/cZgIgC4MpoMAAGp9oLv4f3Gq1Vo\n",
       "uKE0QMPG1NrOdt2OpaquqTaUBgCujCYDQMApKTuoPYfspydzwje8WWqfsQoPa+0Zn7tQobw92QYT\n",
       "AUDDaDIABJzat5okJfRXQvvuhtIAVxYaEqYR/SfYamtYAA7Ai9FkAAgoldUXtWHHMluNWQz4gtr/\n",
       "nxYdLdCRE8VmwgDAFTSqyXj99deVmJio8PBwpaWlKSsr64rXvPrqq+rXr59atWqlhIQEPfvss9cd\n",
       "FgCu16Zdq3Wh6rxn3CY8WkN6pRtMBDROx9gu6t0l2VZjO1sA3uqKTcacOXP01FNP6bnnnlNeXp7S\n",
       "09OVmZmpgwcPXvaap59+Wm+88YZ+//vfa+fOnfr66681bhy7tgAwy7IsZW392lYbNXCSQoJDDCUC\n",
       "rk5GrQXgG3eu0MWqC4bSAMDlXbHJePnllzVr1iw98sgj6tu3r1577TXFx8frjTfeqPf5u3bt0n/9\n",
       "13/pyy+/1LRp09SjRw8NGTJEU6dyOwIAsw6UFurQsSLP2CGHxiRPMZgIuDqDk0YqKqKtZ1xZfVE5\n",
       "O1caTAQA9WuwyaiqqlJubq6mTLF/E54yZYqys+vf1WLu3LlKSkrSggULlJSUpMTERD300EM6fvx4\n",
       "06UGgGtQ+9aS/j2GqV1UR0NpgKsXFBSs0YMm2WpZWxfKsixDiQCgfsENPXjixAm5XC517Gj/Jtyh\n",
       "QweVlNR/2mhRUZH279+vTz75RO+9954k6ac//ammTZumtWvXXvY03ZycnGvJDx/F5x14TH/mldUX\n",
       "lLNrla3WKbyX8Vz+jj/fptfG3UkOOWTp28biyIlifb38C3WI6mo42bf4zAMPn3ng6N27d6Of2+S7\n",
       "S7ndblVWVur9999XRkaGMjIy9P7772vDhg38TwjAmL3H8uVy13jGrcOildC2p8FEwLVpHRatzrH2\n",
       "b/S7SzYZSgMA9WtwJqN9+/YKCgpSaWmprV5aWqr4+Ph6r4mPj1dwcLB69erlqfXq1UtBQUE6cOCA\n",
       "hg8fXu91aWlpV5sdPui7RpPPO3B4w2futtz6evtfbLUJw27ViOEjDCXyf97wufuziPZO/c/c5z3j\n",
       "/WU79ejAPmoTHmUsE5954OEzDzzl5eWNfm6DMxmhoaFKTU3VokWLbPXFixcrPb3+LR8zMjJUU1Oj\n",
       "oqJLiyuLiorkcrnUvTuHXQFoeYUHt+r46SOecZAzWKMGTjaYCLg+/boPVbvoS7cyu1w1Wr9jqcFE\n",
       "AGB3xdulnn76ab3zzjt66623VFBQoCeffFIlJSV6/PHHJUnPPvusJk26tAht0qRJGjZsmB5++GHl\n",
       "5eVp8+bNevjhhzVq1Cg6XQBGZOXbt60d0mu0olrHGEoDXD+nw6kxg26y1dZs/UZuy20oEQDYXbHJ\n",
       "uOeee/Tqq6/qhRdeUEpKirKzs7VgwQJ17frtArOSkhLbrIXD4dC8efPUoUMH3XDDDZo6daq6deum\n",
       "uXPnNt+7AIDLOH32pLYWbbDVap81APiikQNuVFDQpbueT5SXaNeBLQYTAcAlDa7J+M7s2bM1e/bs\n",
       "eh97++2369Q6deqkTz755PqSAUATWLttse23u/HtuqlnwgCDiYCmERkRrZReY5Sz69I5GVn5X6t/\n",
       "9xSDqQDgW02+uxQAeAuXq0bZ2+xrysYk33TZrbQBX1N7Vm7bvhydOsO5VADMo8kA4Le27duo8nNl\n",
       "nnFocJiG9xtvLhDQxBLj+ymhfQ/P2LLcyt622FwgAPg/NBkA/FbtE77T+o1TeFhrQ2mApudwOJSR\n",
       "bJ/NWLttsVyumstcAQAtgyYDgF86duqIdh20L4JlwTf8UVq/cQoLaeUZV5w/pfyi9QYTAQBNBgA/\n",
       "tWarfRajR6e+6hKXZCgN0HxahYbXuQ2w9iweALQ0mgwAfqeqplLrdyyz1ZjFgD+r/f934aGtKi07\n",
       "ZCgNANBkAPBDm3dn6XzlWc84olWkUnqPMZgIaF4J7XsoKb6/rZa1ldkMAObQZADwO7VvFRk1YKJC\n",
       "gkMNpQFaxphasxkbCparqrrSUBoAgY4mA4BfOVC6R/tLC221McncKgX/N7RXulqHR3nGFyrPadPu\n",
       "1QYTAQhkNBkA/EpW/te2cb/uKYqLiTeUBmg5IcEhGjXgRlttDQvAARhCkwHAb5y/eLbOb27HDs40\n",
       "lAZoeWOSb5JDl060P3Bsjw6U7jGYCECgoskA4DfWFyxTdU2VZ9w2Mk4De6QaTAS0rPbRndSve4qt\n",
       "Vnt2DwBaAk0GAL/gttx1FnyPGTRFTmeQoUSAGbW3s920e7XOXzx7mWcDQPOgyQDgFwoPbtXx00c8\n",
       "4yBnsEYNnGwwEWDGwB6patumvWdcXVOlDQXLDSYCEIhoMgD4hdW1bgkZ2mu0olrHGEoDmON0Bik9\n",
       "eYqttmbrN7Isy1AiAIGIJgOAzzt15oS2Fm2w1TjhG4Fs9MDJtlsFS08dUuGhbQYTAQg0NBkAfF72\n",
       "tkWyLLdnHN+um5ISBhhMBJgV1bqtBvccaatlbWUBOICWQ5MBwKfVuKq1dttiWy1jcKYcDsdlrgAC\n",
       "Q0ayffvm/L3rVX6uzFAaAIGGJgOAT8vfu14V5095xmEhrTS833hzgQAv0bvLIHVs28UzdrtdWrd9\n",
       "icFEAAIJTQYAn5a11b5t7fD+E9QqNNxQGsB7OBwOjUm+yVbL3rpIbrfLUCIAgYQmA4DPOnryoPbU\n",
       "WsyakcyCb+A7IwZMUEhwqGd86uwJbS/eZDARgEBBkwHAZ62ptZC1Z+eBSmjf3VAawPtEhLVRap+x\n",
       "tlrtQysBoDnQZADwSZVVF7S+1gFjYwdnXubZQODKqPX3Yuf+zTpRXmIoDYBAQZMBwCfl7FqlyqoL\n",
       "nnFkREydLTsBSN069lK3Dr08Y0uW1mz9xmAiAIGAJgOAz7Esq84J3+mDJis4KMRQIsC7jal1OOW6\n",
       "HUtVXVNlKA2AQECTAcDn7Du6U0dOFHvGDodT6YOmmAsEeLnUPmMVHtbaMz53oUKbC9cYTATA39Fk\n",
       "APA5tReuDkpMU9vIOENpAO8XGhKmEf0n2GqrtywwlAZAIKDJAOBTzpw/rc177L+Brb2wFUBdtTdG\n",
       "2F9aqP0luw2lAeDvaDIA+JS12xbL5arxjOOi49W32xCDiQDf0KFtZ/XvPsxWW8VsBoBmQpMBwGe4\n",
       "3K46J3yPGTxVTgf/lAGNccOQm23j3MIsnTl/2lAaAP6M78wAfEb+3vU6ffakZxwaHKZRA280mAjw\n",
       "Lf17DFO76I6esctVo+xtiw0mAuCvaDIA+IxVW+bbxsP7jVdEWBtDaQDf43Q4NXawfTYja+tCudwu\n",
       "Q4kA+CuaDAA+4fDxYu09vN1WG1vr1g8AVzZqwI0KDQ7zjMvPnlT+3vUGEwHwRzQZAHxC7VmM3l2S\n",
       "ldC+u6E0gO+KaNVGaf3G2Wqra/39AoDrRZMBwOudu3hGObtW2mo3DLnFUBrA99VeAL7n8HYdPl5s\n",
       "JgwAv0STAcDrrdu+RNU1VZ5x28g4DUoabjAR4NsS2vdQr84DbbXV+WxnC6Dp0GQA8Gput0ur87+2\n",
       "1TIGZyrIGWQoEeAfxtaaDczZuVLnL541lAaAv6HJAODVtu3LUVnFMc84JChU6QMnGUwE+IfBPUcq\n",
       "pk07z7iqplLrdiw1mAiAP6HJAODVai/4Tu07Vq3DowylAfxHkDNIY5Kn2mqr8xfIbbkNJQLgT2gy\n",
       "AHitoycPavfBfFvthqEs+AaaSvqgyQoKCvaMT5aXqqA412AiAP6CJgOA16q9rWZSQn91iUsylAbw\n",
       "P5ERMRrWO8NWW7WFBeAArh9NBgCvdKHynDbsXGGrsW0t0PRq/70q2J+rY6cOG0oDwF/QZADwSut2\n",
       "LFVV9UXPOLpNOw3pOcpgIsA/de/UW9079rbVau/oBgBXiyYDgNdxW25lbam1bW3yTbZ7xwE0nbG1\n",
       "Dudbt2OpLlSeN5QGgD+gyQDgdQqKc3W8/KhnHBQUrPRBUwwmAvxbSu8MRYZHe8aVVRe0nu1sAVwH\n",
       "mgwAXqf2wtNhvTMUGRFjKA3g/0KCQ5QxONNWW7llntxul6FEAHwdTQYAr1JSdlAF++1baLLgG2h+\n",
       "Y5Kn1tnOdtu+HIOJAPgymgwAXmXF5q9s4x6d+qp7p96XeTaAphLVOkZpfW6w1VbkfXWZZwNAw2gy\n",
       "AHiNsxcqtLFgha02PmWamTBAABqXcqttvOfQNh06XmQoDQBfRpMBwGus2fqNql1VnnHbyDgN6TXa\n",
       "YCIgsHSJS1KvLoNstZWb5xlKA8CX0WQA8Ao1rmqtzrcv+L5hyC0KcgYZSgQEpvFD7bOHObtXqeLc\n",
       "KUNpAPgqmgwAXiF3d5btB5nQkFYaPWiSwURAYBqUmKZ20R09Y5erRllbFxpMBMAX0WQAMM6yrDoL\n",
       "vkcNuFERYW0MJQICl9MZpHFD7Gsz1uQvVHVN1WWuAIC6aDIAGLfn8Hbb4lKHHBo39NYGrgDQnEYN\n",
       "nKRWoRGe8ZkL5crdvdpgIgC+hiYDgHEra22TOShpuOJi4g2lAdAqNFyjBtpvV1yx+StZlmUoEQBf\n",
       "Q5MBwKjjp49q694Nthrb1gLmjRtyixyOSz8mHD5RrD2HtxlMBMCX0GQAMGrVlvmydOm3o53jEtWr\n",
       "86AGrgDQEtpFd1Ry0ghbbflmDucD0Dg0GQCMuVB5Tuu2L7HVJqTcJofDYSgRgO+rPau4vWijjp06\n",
       "bCgNAF9CkwHAmLXbF6uy+qJnHBXRVsP6ZBhMBOD7eiYMUJe4JM/YksVsBoBGockAYITL7dLKvPm2\n",
       "2tghmQoOCjGUCEBtDodDE4fdbqtt2LFMZ86fNpQIgK9oVJPx+uuvKzExUeHh4UpLS1NWVlajXryw\n",
       "sFCRkZGKjIy8rpAA/E9eYbZOnTnuGYcEhWpM8lSDiQDUJ6X3GLVt094zrnZVaXX+1wYTAfAFV2wy\n",
       "5syZo6eeekrPPfec8vLylJ6erszMTB08eLDB66qqqjRz5kyNGzeO+6sB2FiWpaWbPrfVhvcfrzbh\n",
       "UYYSAbicoKBgjU+5zVZbvWWBqqorDSUC4Auu2GS8/PLLmjVrlh555BH17dtXr732muLj4/XGG280\n",
       "eN0zzzyjoUOH6u6772ZfbQA2uw/m1zl8r/YtGQC8x+hBkxX+vcP5zl08o/U7lhpMBMDbNdhkVFVV\n",
       "KTc3V1OmTLHVp0yZouzs7MteN3/+fM2fP19//OMfaTAA1FF7FiO550h1aNvZUBoAV9IqNLzO7YzL\n",
       "N38pt9tlKBEAbxfc0IMnTpyQy+VSx44dbfUOHTqopKSk3muOHDmixx57TF988YUiIiLqfU59cnJy\n",
       "Gv1c+D4+78Dz3WdedrZEOw/k2R7rHNGP/yf8FJ+r/4hxdJXT4ZTbckuSTpSX6PNFH6p7+/625/GZ\n",
       "Bx4+88DRu3fvRj+3yXeXeuCBBzR79mwNHz68qV8agB/YfmSdbdwhqqvioroYSgOgsSLCIpUYZz8o\n",
       "c/vhddyxAKBeDc5ktG/fXkFBQSotLbXVS0tLFR8fX+81y5cv16pVq/SrX/1K0rcLPN1ut0JCQvTG\n",
       "G2/o0Ucfrfe6tLS0a8kPH/Pdbzv4vAPH9z/zsopj+iB7h+3x28c9oOQk/n/wN/xd90+dEzvotx/8\n",
       "xDM+cfawYhNaq2fnAXzmAYjPPPCUl5c3+rkNzmSEhoYqNTVVixYtstUXL16s9PT0eq/Ztm2btmzZ\n",
       "4vnv+eefV3h4uLZs2aK77rqr0cEA+J/lm7/03GohSR3bdtHARL45Ab4ivl03DeiRaqstzf3CUBoA\n",
       "3qzBmQxJevrpp/XAAw9oxIgRSk9P1//8z/+opKREjz/+uCTp2Wef1caNG7VkyRJJ0oABA2zXb9iw\n",
       "QU6ns04dQGA5d/GM1m5fYqtNTJ0up4MzQQFfMnHYdO0o3uQZbyvaoNKyQwYTAfBGV2wy7rnnHp08\n",
       "eVIvvPCCjh49quTkZC1YsEBdu3aVJJWUlKioqKjB1+CcDABZ+QtVVX3RM45q3VZpfccZTATgWvTu\n",
       "MkhdO/TUwWN7PbXlm+eqV/RIg6kAeJtG/Qpx9uzZ2rdvny5evKiNGzcqIyPD89jbb7/dYJPx0EMP\n",
       "qaKi4vqTAvBZLneNVuXNs9XGDZ2mkOAQQ4kAXCuHw6GJw6bbahsKVuhC1VlDiQB4I+5TANDs9h7L\n",
       "15kLlxaLhYWGa0zylAauAODNhvZOV2xUB8+4xlWtgiMbDCYC4G1oMgA0K7fl1vbD9m1rxwyaooiw\n",
       "NoYSAbheQc4gTUi5zVbbVZKjqpqLl7kCQKChyQDQrA6e3KUzF8s8Y6czSOOGTjOYCEBTGD1wslqH\n",
       "R3nG1a4q7TrKoWwAvkWTAaDZWJalrYfW2GppfW9Q28j2hhIBaCqhIWGaUOsXBjuObFBVdaWhRAC8\n",
       "CU0GgGZTsH+zys6V2Go3pt5hKA2AppYxJFNhoeGecWXNea3dvthgIgDegiYDQLNZtPFT23hwz1GK\n",
       "b9fNUBoATS0irI3GDr7ZVlu26QvVuKoNJQLgLWgyADSLPYe3q+hIga02ZfhdhtIAaC7jh05TSFCo\n",
       "Z3zq7Anl7FxlMBEAb0CTAaBZLNr4N9u4X/cUdevYy1AaAM0lqnWMRg2cZKst2fR3ud0uQ4kAeAOa\n",
       "DABN7kDpHu3cv9lWu4lZDMBv3Zg6XQ7HpR8pjp06rC171xtMBMA0mgwATa72LEaHqK7q2XmgoTQA\n",
       "mltsVAclxQ2y1Rbn/E2WZRlKBMA0mgwATeroyQPK32s/fC+5S4ahNABaysDO6bbxoWNFKtifaygN\n",
       "ANNoMgA0qcUbP7ON27WOV0JMkqE0AFpKTER7dWvXz1b7ev0cZjOAAEWTAaDJHD99VJt2r7bVBnUd\n",
       "I4fDYSgRgJaU3GWMbby/ZLd2HsgzlAaASTQZAJrM4o1/k2W5PeNOsV3VLbavwUQAWlK7NvEalDjc\n",
       "VlvIbAYQkGgyADSJE+Ul2lCw3FabPHwGsxhAgJk68l7beN/Rndp9MN9QGgCm0GQAaBKLNnwq9/dm\n",
       "MTrEJGhYn7EGEwEwoVvHXhrYI81W+3r9x8xmAAGGJgPAdTt++midWYybRt6jIGeQoUQATJo68h7b\n",
       "uOhIgQoPbTWUBoAJNBkArtuijX+rM4uRyiwGELC6d+qj/t2H2Wpfr59jKA0AE2gyAFyX46ePamOd\n",
       "WYx75WQWAwhotddm7D28ndkMIIDQZAC4LvWtxUjtw+F7QKBLjO+rft2G2moL139iKA2AlkaTAeCa\n",
       "HT99VBt3rrDVmMUA8J2pI2faxoWHtqrw0DZDaQC0JJoMANeszixG287MYgDwSErop75dh9hq89f+\n",
       "lZ2mgABAkwHgmtQ3izF1xD3MYgCwyRz1A9u46EiBCvZvNpQGQEuhyQBwTRas+6jOLMYwZjEA1JKU\n",
       "0E8DeqTaasxmAP6PJgPAVTt8vFi5u1bbasxiALicW0bfZxsfPLZX+XvXGUoDoCXQZAC4avPX/lWW\n",
       "Lv0WMqFddw3ry7kYAOrXtUNPDek12labv/ZDud0uQ4kANDeaDABXpejITm3bt9FWuyX9fjkd/HMC\n",
       "4PJuHnWfHHJ4xiVlB7Vp9+oGrgDgy/ipAECjWZalednv22o94vtqUOJwQ4kA+Ir4dl2V1m+crbZg\n",
       "3UdyuWoMJQLQnGgyADTazgN52nN4u602Lf2Hcjgcl7kCAC7JHDXTtnbrZHmp1u1YajARgOZCkwGg\n",
       "Ub6dxfjAVuvXbah6d0k2lAiAr2kf3UmjB0yy1RZu+ETVNVWGEgFoLjQZABply561Onhsr612a/oP\n",
       "DaUB4KumjLhbwUEhnnH52ZNanb/AYCIAzYEmA8AVudwuzV/7oa02pNdodevYy1AiAL6qbWR7ZQzO\n",
       "tNW+2fCpzl08YygRgOZAkwHgijYULFfpqUOescPhrLPvPQA01pThd6lVaIRnfKHynBZv/MxgIgBN\n",
       "jSYDQIMqqy9q/tq/2moj+k9Qp9iuhhIB8HVtwqM0OW2GrbZyyzydrCg1lAhAU6PJANCgZblzVXHu\n",
       "lGccHBSizJEzDSYC4A/GpdyqmDbtPGOXq6bObZkAfBdNBoDLqjh3Sks3fW6rjU+5TbFRcYYSAfAX\n",
       "ocFhdW67zNm5UgePFRlKBKAp0WQAuKwF6z5SVfVFz7h1eJQmp91pMBEAfzK833gltOtuq83NekeW\n",
       "ZRlKBKCp0GQAqNfRkwe0dvsSWy1z5EyFh7U2lAiAv3E6g3Rbxo9std0H87XzQJ6hRACaCk0GgHrN\n",
       "zXpXluX2jDvEJGjMoCkGEwHwR/27p6hP18G22tysd+V2uwwlAtAUaDIA1LHrwBbtKN5kq92W8aCC\n",
       "goINJQLgrxwOh26vNZtx5ESx1u9YZigRgKZAkwHAxu126YvVb9tqPRMGKDlppKFEAPxd1w49ldZ3\n",
       "nK02L/sDXag8ZygRgOtFkwHAZkPBCh0+UWyrTR/7kBwOh5lAAALCrek/VEhQqGd85kK5vtnwqcFE\n",
       "AK4HTQYAjwuV5/TVmvdstdQ+Y9W9Ux9DiQAEitioON2YdoettjJvno6dOmwoEYDrQZMBwGPh+jk6\n",
       "c6HcMw4JCtWtY35oMBGAQDIp9U77AX3uGn1e6/ZNAL6BJgOAJKmk7KBWbplvq92YdofaRXU0lAhA\n",
       "oAkNCdPtGQ/Zatv35WhHca6ZQACuGU0GAFmWpc9W/Nm2ZWTbyDhNSuXgPQAta1ifDCXF97fVPl/1\n",
       "F7lcNYYSAbgWNBkAtLVovXYd3GKrTR87S6EhYYYSAQhUDodDd457RA5d2myi9NQhrcpfYDAVgKtF\n",
       "kwEEuKqaSv191V9stT5dkjW012hDiQAEum4de2nkwBtttYXrPtaZ86cNJQJwtWgygAC3bNMXKqs4\n",
       "5hk7HU7dOe5RtqwFYNSto3+osNBwz/hC1XnNzXrXYCIAV4MmAwhgZRXHtTjnM1tt7JCbldC+u6FE\n",
       "AMAxsc8AACAASURBVPCtqNYxmjriXlttQ8Fy7Tm83VAiAFeDJgMIYJ+tfFPVNVWecevwKGWOmmkw\n",
       "EQBcMn7orYpv181W+2TZ/6jGVW0oEYDGoskAAlT+3nXaWrTBVpuW/oAiwtoYSgQAdkFBwbpnwj/a\n",
       "aiVlB7U890tDiQA0Fk0GEIAuVl3QpyvetNV6xPfVqFoLLQHAtJ6dB2rkgFqLwDfM0cmKUkOJADQG\n",
       "TQYQgOav/avKz570jJ3OIM2cOFtOB/8kAPA+t2f8SBGtIj3j6poqfbbizwYTAbgSfqIAAsyB0j1a\n",
       "tcW+3/zElNuV0L6HmUAAcAVtwqN025gHbbVt+zYqf+96Q4kAXAlNBhBAXG6XPl72uizL7anFRnXQ\n",
       "1JH3NnAVAJg3auCN6hHf11b7bMWbqqy6YCgRgIbQZAABZPWWBTp0rMhWu2fCP3KyNwCv53Q4de8E\n",
       "+22dp86e0Ly1fzWYCsDl0GQAAeLUmeOaX+ub8bA+GRrQI9VQIgC4Op3jemh8yjRbbVXefBUdKTCU\n",
       "CMDl0GQAAcCyLH209HVVVl/01MJDI3THDQ8bTAUAVy9z1A/ULqqjZ2zJ0oeL/6iqmkqDqQDURpMB\n",
       "BIB1O5Zq5/7NttqtYx5QdOtYQ4kA4NqEhbTSDyY9YasdO31EC9fNMZQIQH1oMgA/d+rMcX2+6i+2\n",
       "Ws/OAzUm+SZDiQDg+vTpOljpg6bYaktzv9D+kkJDiQDU1ugm4/XXX1diYqLCw8OVlpamrKysyz53\n",
       "xYoVuv3225WQkKDWrVtryJAhevvtt5skMIDG++42qYtV5z210OAw3TfpnzgTA4BPuz3jR4pp084z\n",
       "tiy3PlzyR9W4qg2mAvCdRv2UMWfOHD311FN67rnnlJeXp/T0dGVmZurgwYP1Pn/t2rUaMmSIPvvs\n",
       "M23fvl2zZ8/WY489po8++qhJwwNoWH23SU0b84DiYuINJQKAphEe1lr3Tpxtqx09eUCLNv7NUCIA\n",
       "39eoJuPll1/WrFmz9Mgjj6hv37567bXXFB8frzfeeKPe5z/77LN6/vnnNXr0aPXo0UOPP/647rzz\n",
       "Tn322WdNGh7A5V3uNqmxQ242lAgAmtbAxDSN6D/BVlu08W86dLzoMlcAaClXbDKqqqqUm5urKVPs\n",
       "9z5OmTJF2dnZjf5C5eXlio1lkSnQErhNCkCguOOGhxUZEeMZu90uvbfwFXabAgwLvtITTpw4IZfL\n",
       "pY4dO9rqHTp0UElJSaO+yLx587Rs2bIGm5KcnJxGvRb8A59389pdklvnNqkhXcdr/57D2q/DRjLx\n",
       "mQcmPvfAY+IzT+02SSt2XrpNqqTsoN76+39qeNKUBq5CU+HveeDo3bt3o5/b7L/SXLNmje6//379\n",
       "8Y9/VFpaWnN/OSDglZ8/qZx9i221jlHd1C+ev38A/FO3dv3+//buPC6qev8f+OvMDDNsAwzLILuo\n",
       "uIZL4kaaS8gVNfNmZpZ1s8U0LdO6df3dvH299bPFe225X+1W14yumltlpaiQKai4oaKGgDuKMIis\n",
       "wzIwzJzvHyB1AhSN4Qzwej4e85jhfT6HXjYi8545n88HXfV9JbX03MPIKTovUyIiuuUnGd7e3lAq\n",
       "lcjLy5PU8/Ly4Od388mj+/btw4QJE/Dmm2/iueeeu+lYNiAdw413O/h820aNxYz3N/4FNdZfVldR\n",
       "Ozhi1h8XyTbZm895x8TnveOR+znvE94b761bgILSX16vHM7agUXDP4SLk5ssmdo7uZ9zan0lJSXN\n",
       "HnvLTzLUajUGDhyI+Ph4ST0hIQGRkZFNnpeUlITx48djyZIlePHFF5sdiIju3PaD63HlmvSduykj\n",
       "n+FqUkTU7jlpnPH4H16C8Kt5Z6XlRVi/ayVEUZQxGVHH1KzLpRYuXIgvvvgCq1atQnp6OubPnw+D\n",
       "wYDZs2cDqF1NKioqqn78nj17EBMTgzlz5mD69OkwGAwwGAzIz8+3zZ+CiHDuahp+TPlGUuvXbRiG\n",
       "9r5PpkRERK2ri38vRA+aIqmdOH8Qh9N/kikRUcd1y8ulAODhhx9GQUEB3nrrLeTm5iI8PBxxcXEI\n",
       "CgoCABgMBly48MtycbGxsTCZTFi2bBmWLVtWX+/cubNkHBG1jHKTEf/d+QFE/PJunbuLJx4ZMweC\n",
       "IMiYjIiodY0bPA3pl47j8rVz9bXNez5DF//e/FSXqBU1e+L3nDlzcPHiRZhMJhw5cgTDhw+vP7Z6\n",
       "9WpJ87B69WpYLBZYrVbJjQ0GUcsTRRFrE/6FIqP0k8IZ0fN5HTIRdThKpQpPjFsAtUpTX6sym/B5\n",
       "3Hsw11TLmIyoY+GC+URt3J7jP+DnC4cltdEDJqFHcD+ZEhERyUuvC8Af731KUruafxHfJK6SKRFR\n",
       "x8Mmg6gNyzKcwff7v5TUgn3DcP89j8uUiIjIPkTeFY3+YdIFavb/vBMpGYkyJSLqWNhkELVRFaYy\n",
       "rI5bBou1pr7mpHbGzJhXoFI6yJiMiEh+giBg+n1z4eMunYex/qePkVeYLVMqoo6DTQZRG2QVrViT\n",
       "8BEKfzMP49GxL8LL3VemVERE9sVJ44KZE/4seeOlum5+RrW5SsZkRO0fmwyiNijhyOYG8zBG9p+I\n",
       "ft2GypSIiMg+Bfp0wZSRz0hquQWXsWnPpzIlIuoY2GQQtTGnLx1F3IGvJLVgfTdMuudPMiUiIrJv\n",
       "kXdFY2CPeyW1Q6d3Yf+pnTIlImr/2GQQtSH5xbmI3bFcsh+Gi6MWT014FQ4qzsMgImqMIAh4ZMwc\n",
       "+OoCJfXNez7DhZx0mVIRtW9sMojaiCqzCau2voPKqvL6miAo8GTMK/B008uYjIjI/mnUTpg5/s+S\n",
       "/TMs1hqs2vYuiozXZUxG1D6xySBqA6yiFWvjP0JOQZakPumex7kfBhFRM/l7h+Cx6PmSmrGiGKu2\n",
       "voPqGk4EJ2pJbDKI2oDtB79C6rlkSW1A2D0Yc/dkmRIREbVNA8IiET1oqqR2+do5rN+1EqIoNnEW\n",
       "Ed0uNhlEdu5IRiJ2Ht4kqfl5BePRqHkQBEGmVEREbdf4YdPRJzRCUkvJSET8kc0yJSJqf9hkENmx\n",
       "CzkZWPfjvyQ1Vyd3zJr0V2jUTjKlIiJq2xSCAk/8YQH0ugBJfduBtTiamSRTKqL2hU0GkZ0qKMnD\n",
       "f7a+DYvllx29VUoHPDNxEbzcuOEeEdHv4aRxwaz7/x+cNa6S+pqEj3D+6mmZUhG1H2wyiOyQsaIE\n",
       "K7csQVlliaQ+PWoeuvj3lCkVEVH7otcF4Jn7F0GpUNXXLJYa/Gfr28gvzpUxGVHbxyaDyM5UmU34\n",
       "9Pu3kF+cI6n/YfDDGNRzpEypiIjap24BfTA9aq6kVm4y4uMtS1BaXixTKqK2j00GkR2xWC34Iu4f\n",
       "yMo7K6kP7D4CMUMfkSkVEVH7NrjXaIwbMk1Su15iwMffLZHsTUREzccmg8hOiKKIDbtWIu1SiqTe\n",
       "I6gfHot+EQqBP65ERLYSM+QRDOo5SlK7mn8Rn219G+aaanlCEbVhfNVCZAdEUcS3SZ/j4OldknqA\n",
       "TyiemvAaVEoHmZIREXUMgiBgetRc9Aq5W1I/l/0zYncsh9VqkSkZUdvEJoPIDsQd/Ap7Un+Q1Dzd\n",
       "9JjzwN/gpHGWKRURUceiUjrgqQmvIqRTd0n95PmDWPfj/8IqWmVKRtT2sMkgkllCyjfYeXijpObq\n",
       "5I45k9+Am4tOplRERB2TxsERsye9Dl/PQEn9cPpubNj1MRsNomZik0Eko8TUrfhh/5eSmrPGFXP/\n",
       "uAS+v9kkioiIWoeLkxuen/w/0Gl9JPUDaQnYvOcziKIoUzKitoNNBpFMdh//Hl8n/kdS0zg4Ys7k\n",
       "vyHAp7M8oYiICACg03pj3oN/h7uLp6S+7+R2fJv0ORsNoltgk0Ekg11Hv8W3SZ9Lag4qNZ57YHGD\n",
       "a4GJiEgePh5+mDflTWidPST1Pak/4OvEz3jpFNFNsMkgamXxhzfhu32xkpqDUo1nJi5Ct4A+MqUi\n",
       "IqLG+OoCMO/Bv8PFyU1STzoRh/U/ruCqU0RNYJNB1EpEUcTW5LXYemCtpO6gUmPWpL+iV8gAmZIR\n",
       "EdHN+HkFY94fl8DFUSupHzy9C//d+QEslhqZkhHZLzYZRK3AarVg40//RvyRTZK62sERsx9YjB7B\n",
       "/WRKRkREzRHgE4oXprzV4NKpo2f24vO491BdUyVTMiL7xCaDyMbMNWas3v4P7P95p6SucXDEnAf+\n",
       "hrDAcJmSERHR7fD3DsH8h/4/PFy9JPVTFw5j5Tf/g3KTUaZkRPaHTQaRDVVWleOT7/6OE+cOSOrO\n",
       "jlrMffDv6BrQW6ZkRER0J/S6AMyfuhRe7r6S+oXcdHywaREKS/NlSkZkX9hkENlIQWkePti0CGey\n",
       "T0nqHq5eeGnqUnTmKlJERG2Sl5sv5j+0FH5ewZJ6XmE23t/4Gq7mX5QpGZH9YJNBZAOXDGewfP2r\n",
       "yC24LKn76gLx0tR30MkzSKZkRETUEjxcvTB/6lJ0/c2qgCXlhXh/0yKcPH9IpmRE9oFNBlELO352\n",
       "P/61+XUYK0sk9ZBO3TF/6lJ4uvk0cSYREbUlzhpXPD/5DfTvFimpV5tNWLX1HSSkfMNN+6jDYpNB\n",
       "1EKsVgt+2P9frI5bBrOlWnKsf1gkXpjyJlx/s846ERG1bQ4qNZ6MeRkj+0+U1EWI+GH/l1ib8BHM\n",
       "NdVNnE3UfqnkDkDUHpSbjIjdsRwZWccbHIse9BDGD3sUCoE9PRFRe6RQKDFl5DPQe/jj68T/SHYC\n",
       "P5y+GzkFWXh6/GsNJosTtWd81UP0O2XnX8A/vnqlQYOhVKjwaNQLmBg5gw0GEVEHMKLfeMyZ/Aac\n",
       "NC6Seva1C1j21ctIu5giUzKi1sdXPkR3SBRFJJ2Iw/INr6GgNE9yzM1ZhxemvIWhfe6TKR0REcmh\n",
       "R3A/vDztPeg9/CX1iqoyfPL9W9h2YC0sVotM6YhaD5sMojtQYSrDqm3vYvOeT1FjMUuOhfr1xJ8f\n",
       "/Se6+PeUKR0REclJrwvAy48sQ9+uQxoc23l4Ez7a/FdcLzHIkIyo9bDJILpN566m4d11C3Dy/MEG\n",
       "x4aHj8MLU96Eu4unDMmIiMheOGlc8PSEv2DSPU9A+M0lsxdzM/DuugU4nL6bq09Ru8WJ30TNVF1T\n",
       "ha3Ja5F4/AeIkP5S0Kid8MiYORjY416Z0hERkb0RBAFREQ8ipFMYvtj+TxgriuuPVVVXYk38h0i7\n",
       "mIJpY+bA2dFVxqRELY9NBlEzZBnOYk38h8grym5wLFjfDX+KeRk+Hn4yJCMiInsXFhiO1x79AF/9\n",
       "+L9IuySd/H387H5cyM3Aw6OfQ3iXwTIlJGp5bDKIbsJUXYm4A+uQeGIbxF8tSXjD6AGTcP89j0Ol\n",
       "dJAhHRERtRVuLh6YNemv2HdqB7bsXS3ZO6OkrACf/bAU/btFYsqoZ3jJLbULbDKIGiGKIk6eP4Sv\n",
       "Ez9DcVlBg+OeWh88Fv0iwgLDZUhHRERtkSAIGNE3BmGBd+HLHe8jO/+C5HjquWRkXk7FAyNmYlif\n",
       "KAiCIFNSot+PTQbRbxSWXsOmPZ82uZ555F1jMXnEU3BUO7VyMiIiag86eQZh4bR3sePQBvyY8o1k\n",
       "877K6gqs37UCRzL2YMrIpxHo00XGpER3jk0GUR1TdSV2Hf0WPx3bIvkY+wZPNz0eHv0cenceKEM6\n",
       "IiJqT1RKB0yMnIH+YZFY/+NKXL52TnL8/NU0LFv3Mob2icKEYY/BzcVDpqREd4ZNBnV4FqsFh07v\n",
       "wrYD6yQrf9ygUCgxZsADGDdkGtQOGhkSEhFRexXo0wULpr2LpNRt2HZgLaprquqPiRBxIC0Bx87u\n",
       "wx8GTcXI/vfDQcU5gNQ2sMmgDksURZy+dBTf7/8SuQWXGx0T6tcT08bMgb93SCunIyKijkKpUGL0\n",
       "3ZPQt+sQbNr9CU5nHZMcr6quxPf7v8S+UzswbvA0DOo1CkqFUqa0RM3DJoM6HFEUkZ51DNsPbUCW\n",
       "4UyjY7RO7pgQOQND+9wHhcA9K4mIyPa83H3x3AOLcfrSUXyb9DmuFedIjheWXsO6H/+FhJSvMW7I\n",
       "NAzsPhwKNhtkp9hkUIdx45OL7Yc24HLe2UbHOCjVGH33A4iKeJATu4mIqNUJgoA+oRHoGdwfe09u\n",
       "x/ZD61FZVS4Zk1+cg//ufB/xRzZh3OBp6B8WyU82yO6wyaB2z2KpwfGz+7H7+Pe4cu18o2MECBjU\n",
       "axQmDHsMOq13KyckIiKSUipVGDXgfkT0HIkdh9Zj/6l4WKw1kjF5hdmI3fFPbE1eg1ED7sfQ3vdB\n",
       "wzfIyE6wyaB2q9xkRPKpeCSdjENJI3td3HBX6CDEDJ2OID2XCSQiIvvi6uSGh0bNwpi7J2Pn4U04\n",
       "dHqXZMlbACgozcPXif/B9oPrMbzvONzbbwLcXHQyJSaqxSaD2p0r1y4g+ed4HEnfLVml47fCuwzG\n",
       "uCHTEKTv2orpiIiIbp+nmx7To+YiKuJB7Dy8EUcyEiH+ptmoqCpD/JHN+PHot+jbZQjuCf8DwoLC\n",
       "ObeQZMEmg9qFiqoyHM3ciwNpCci+duGmY/t2HYpxQx7mBkdERNTm+Hj4YUb0fIwd9BB+OroFhzN2\n",
       "w2KRXkZltVqQei4ZqeeS4ePuh8jwaAzuNQZaZ3eZUlNHxCaD2iyLpQYZl1Nx9MxenDh3oNEN9G5Q\n",
       "qzQY3HsMRvWfCL0uoBVTEhERtTxfXQCmR83FhGGPIulEHPad3I6KqrIG4/JLcvHdvlj8kLwGvYIH\n",
       "IKLnvQjvMoT7PpHNscmgNsVqteB8zmkczdyL1HMHUGEy3nS8u6sX7u03AZF3jYWLo7aVUhIREbUO\n",
       "NxcdJkY+hrGDpuBg2o/Ye3I7rhVdbTDOarUg7VIK0i6lQO3giH5dh+Lu7sPRPagfN/gjm2CTQXav\n",
       "2lyFzCsncOrCYaRdTGl0V+5fEyCgV8gADLtrLO4KHQSlkn/NiYiofdM4OGJk/4m4t98EnLv6M/af\n",
       "iseJcwcarEgFANVmE45k7MGRjD3QODiid+eB6Nt1KHp3vhtOGhcZ0lN7xFdfZHdEUcT1EgPOXDmJ\n",
       "tIspyLx8AmZL05dC3aDT+mBonygM7T0GOq1PKyQlIiKyL4IgICwwHGGB4TBWFOPQ6Z9wKP0n5BVm\n",
       "Nzq+ymzC8bP7cfzsfigVKnQL6IMewf3QM6Q//L07c9I43TE2GWQXSsuLkHnlJM7U3YqM+c06z9lR\n",
       "i/7dhuHu7iPQLaA3dz4lIiKqo3X2QFTEg7hv4B+RnX8RRzMTcTRzL0rKCxsdb7HWIPPKCWReOYHv\n",
       "938JVyf32oYjuB+6B/XlG3h0W9hkUKsTRRG5BZdxMTcTlwyZuJib0eQ7LI3RqJ0Q3mUwBnYfgR7B\n",
       "/aBS8lpSIiKipgiCgCB9FwTpu2DSPU/g3NU0HD+bjFPnD6G0oqjJ88oqS3A0MwlHM5MA1F4xEOrX\n",
       "E6F+PdDFvxesopWfdFCT2GSQTYmiiMLSa7h6/SKyr13EiTOHcd2YA3Ny0/tXNEan9UF4l0G4K3Qw\n",
       "ugX2YWNBRER0BxQKJboH9UX3oL6YOnoWsgxncfL8QZw8fwj5xTk3PbfImI8iYz6OndkLAFApHOCt\n",
       "9Ud25SkE+NQ2MXoPf15VQADYZFALKjcZca3oKgwFV3D1+iVczb+InOuXUFldcdvfS6V0QBf/Xuge\n",
       "1Bd9OkfA3zsEgiDYIDUREVHHpBAUCPXrgVC/Hph0zxPIL85F5uVUZF45gTNXTsF0i9/fNVYzDCVZ\n",
       "MBzLqq+pVRr4e3dGoE8oOnkFw1cXgE6eQXBz0fH3eAfDJoNuS1V1JQqN+cgvzkFeUQ6uFV2tv5Xf\n",
       "YjnZmxEEBYL1XevfXQn17wm1imt4ExERtQZBEKDX+UOv88eIfuNhsVqQZTiLjMvHcebKSVzOO4ca\n",
       "i/mW36e6pgqXDLWXQ/+ao9oZvroA+HoGQq8LgN7DH17uvvB008NZ48oGpB1ik0H1zDXVMFYUo6S8\n",
       "CKXlhSgszUeh8RqKjPl1j/NvuS9FczlrXNG5U3d09uuBzp16IKRTGJfNIyIishNKhRJd/Huii39P\n",
       "jB86HeYaM7Lzz+NCTgYu5qbjQk4GyipLmv39TNUVyMo7i6y8sw2OadRO8NLq4en2y83dxRPurp5w\n",
       "c9bB3UUHjdqpJf941Aqa1WSsXLkSy5Ytg8FgQJ8+ffDBBx9g+PDhTY4/deoU5s2bhyNHjsDT0xPP\n",
       "PfccFi9e3GKh6dZEUUS12YRyUxkqqoyoMJXV3qrKUF5phLGiGKUVxSitKIKxvPa+sqrcJlkc1c4I\n",
       "8AlFgHdn1JQr4KMNxJgR0XzXgoiIqI1wUDnUTfruCWAyRFHE7n0JKCjLhUYr4Er+eWTnX0R5Zelt\n",
       "f++q6krkFGQhpyCryTEaB0e4uXjCzaW26dA6e8DFUQsXRy2c6+9d4eKkhYujGzQOjnydIbNbNhkb\n",
       "NmzASy+9hI8//hjDhw/HihUrEBMTg9OnTyMoKKjB+NLSUowdOxajRo1CSkoK0tPTMXPmTLi4uGDh\n",
       "woU2+UO0dRarBTU11aixmGG2mGvva8ww11ShymxCtdmEKrMJpupKVJkra7+urq1VmStRVV1Ze9xc\n",
       "iUpTOSqqahuKxjbgsSWV0gE+Hn7Qe/jDzzsEgT6hCPAOhaebvv4HPSUlBQD4g09ERNSGCYIANydP\n",
       "uDl5IiIiAkDtG5zFZQXIzr+A3OtZyCu6irzCbOQVZaPKbPpd/70qswn5xTm3nJx+g1KhgrOjK5w1\n",
       "rtConeDo4AiN2qnucd292gma3zx2UKlrb0o1HFQOUCnVv9RUaig5qb3ZbtlkLF++HDNnzsTTTz8N\n",
       "APjoo4+wY8cOfPzxx1i6dGmD8WvXroXJZEJsbCw0Gg169+6NjIwMLF++/KZNRublEwAAq2gFUPsX\n",
       "Vfz1Y4gQRRGou6+tQTpGtEKs/ap+DCDCKopAM8eLogiraIHFaoHVaoHVapV+LVpra1YLLGITY6zW\n",
       "unEW1Fhr6huIGksNzJa6xzXm+qbiRqa2QKFQQufqDS83fe01lXU3X10AdFpvrihBRETUQQmCAJ3W\n",
       "GzqtN8K7DK6vi6KIkvLC+oYjr/AqCkoMKDBeQ2HpNZhrbr3h7u2yWGtgrCiGsaK4Rb+vQlBAVd+I\n",
       "OMBBqYZK5QClQgWFQgll3a32sepXj5V1YxT1daVSBYVQ97VSCUFQQBAUUAgCBAi1jxUKCIIAAXX3\n",
       "glA3ToCibnzt41/qAgQoFMr6x/X1ujd4BdTdC7++FyRvAAu/+vqX44BeG9zs/1c3bTKqq6tx7Ngx\n",
       "vPrqq5J6dHQ0kpOTGz3nwIEDGDFiBDQajWT84sWLkZWVhZCQkEbPW/HtG80OTbYhCApond3h5qyD\n",
       "m7MHdFof6Nx84Kn1gaebHjqtD9xddGwkiIiIqNkEQYCHqxc8XL3QI7if5JgoiiirLEFh6TUU1N2K\n",
       "jPkoLS9CaXkRSsoLUVpRBIulda/OaIpVtKK67iqTjujNJ2ObPfamTcb169dhsVjg6+srqev1ehgM\n",
       "hkbPMRgMCA6Wdjk3zjcYDE02GbcTmmRiBYzGst/1LcLCwgAAJSXNnyxGbRuf846Jz3vHw+e842m5\n",
       "51yAh5MvPJx80dX31qOpbWjxbRp5rT0RERERUcd20ybD29sbSqUSeXl5knpeXh78/PwaPadTp04N\n",
       "PuW4cX6nTp1+T1YiIiIiImoDbnq5lFqtxsCBAxEfH48pU6bU1xMSEjB16tRGzxk2bBhee+01VFVV\n",
       "1c/LSEhIQEBAQINLpdzd3X9vfiIiIiIisjO3vFxq4cKF+OKLL7Bq1Sqkp6dj/vz5MBgMmD17NgBg\n",
       "0aJFiIqKqh//6KOPwtnZGU8++STS0tLwzTff4N133+XytUREREREHcQtl7B9+OGHUVBQgLfeegu5\n",
       "ubkIDw9HXFxc/R4ZBoMBFy5cqB/v5uaGhIQEzJ07FxEREfD09MQrr7yCBQsW2O5PQUREREREdkMQ\n",
       "azeTICIiIiIiahEtvrrUnXr22WfRrVs3ODs7Q6/XY/LkyUhPT5c7FtlIUVERXnjhBfTq1QvOzs4I\n",
       "Dg7G888/j8LCQrmjkQ19+umnGD16NDw8PKBQKHD58mW5I5ENrFy5EqGhoXByckJERAT27dsndySy\n",
       "oaSkJEyaNAmBgYFQKBSIjeWS9O3d22+/jUGDBsHd3R16vR6TJk1CWlqa3LHIhlasWIF+/frB3d0d\n",
       "7u7uiIyMRFxc3E3PsZsmY9CgQYiNjUVGRgZ27twJURQRFRWFmhr72HyFWlZOTg5ycnKwbNky/Pzz\n",
       "z1izZg2SkpIwffp0uaORDVVWVmLcuHFYsmSJ3FHIRjZs2ICXXnoJr7/+OlJTUxEZGYmYmBhcuXJF\n",
       "7mhkI+Xl5ejbty8+/PBDODk5cSn7DiAxMRHz5s3DgQMH8NNPP0GlUiEqKgpFRUVyRyMbCQoKwnvv\n",
       "vYfjx4/j6NGjGDNmDCZPnowTJ040eY7dXi518uRJ9O/fH5mZmfWbvVD7tn37dkycOBElJSVwdXWV\n",
       "Ow7ZUEpKCgYPHoxLly412LyT2rYhQ4agf//++OSTT+pr3bt3x0MPPYSlS5fKmIxag1arxYoVK/DE\n",
       "E0/IHYVaUXl5Odzd3fHdd99hwoQJcsehVuLl5YV33nkHzz77bKPH7eaTjF8rLy/H6tWrERYWhtDQ\n",
       "ULnjUCspKSmBRqOBs7Oz3FGI6A5UV1fj2LFjiI6OltSjo6ORnJwsUyoisrXS0lJYrVbodDq5o1Ar\n",
       "sFgsWL9+PUwmE+69994mx9lVk7Fy5UpotVpotVps3boV27Ztg0p1ywWwqB0oLi7G4sWLMWvWLCgU\n",
       "dvXXkoia6fr167BYLPD19ZXU9Xp9g01aiaj9mD9/PgYMGIBhw4bJHYVs6NSpU3B1dYWjoyNmzZqF\n",
       "jRs3okePHk2Ot+mruddffx0KheKmt6SkpPrxM2bMQGpqKhITE9G7d2/ExMTAaDTaMiK1sNt9zgGg\n",
       "rKwM999/f/31ftS23MlzTkRE7cPChQuRnJyMr7/+mvNx2rmePXvi5MmTOHz4MObNm4dHHnkEQeiT\n",
       "FgAAAqNJREFUKSkpTY636ZyMgoICFBQU3HRMUFAQnJycGtTNZjN0Oh1WrFiBP/3pT7aKSC3sdp/z\n",
       "srIyjB8/HoIgYPv27bxUqg26k59zzslon6qrq+Hi4oL169djypQp9fW5c+fi9OnT2L17t4zpqDVw\n",
       "TkbHsmDBAmzcuBG7d+9G9+7d5Y5DrWzs2LEIDAzE6tWrGz1u02uRvLy84OXldUfnWq1WiKIIq9Xa\n",
       "wqnIlm7nOTcajYiJiWGD0cb9np9zal/UajUGDhyI+Ph4SZORkJCAqVOnypiMiFra/PnzsWnTJjYY\n",
       "HZjFYrnp63S7mPBw/vx5bN68GWPHjoW3tzeys7PxzjvvwNHRERMnTpQ7HtmA0WhEdHQ0jEYjtmzZ\n",
       "AqPRWH9pnJeXFxwcHGROSLZgMBhgMBhw5swZAEBaWhoKCwsREhLCCYPtxMKFC/H4449j8ODBiIyM\n",
       "xL///W8YDAbMnj1b7mhkI+Xl5Th79iyA2jcIs7KykJqaCi8vLwQFBcmcjmxh7ty5WLNmDbZs2QJ3\n",
       "d/f6OVdarRYuLi4ypyNb+Mtf/oKJEyciMDAQRqMR69atQ2JiInbs2NH0SaIduHLlihgTEyPq9XpR\n",
       "rVaLQUFB4owZM8TMzEy5o5GN7N69WxQEQVQoFKIgCPU3hUIhJiYmyh2PbOSNN96QPNc37mNjY+WO\n",
       "Ri1o5cqVYufOnUWNRiNGRESIe/fulTsS2dCNf89/+2/6zJkz5Y5GNtLY729BEMQlS5bIHY1s5Mkn\n",
       "nxRDQkJEjUYj6vV6cezYsWJ8fPxNz7HbfTKIiIiIiKht4lqhRERERETUothkEBERERFRi2KTQURE\n",
       "RERELYpNBhERERERtSg2GURERERE1KLYZBARERERUYtik0FERERERC2KTQYREREREbWo/wNKVNRj\n",
       "kUo0rwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f48090deb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-3, 3, 0.01)\n",
    "plt.plot(x, np.exp(-x**2))\n",
    "plt.title('exp(-x^2)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And with this we have the shape of the Gaussian. The Gaussian equation has different constants, and hence a somewhat different shape, but both are 'bell curves', as seen below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAxkAAAGNCAYAAAB9i7yDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XtUVOe9P/73nuF+F0EEFRRRkKtcROUiahQ1iYnNvZe0\n",
       "SZPTNqenbZpfz8rJ75fvatOmJ6enXTlpTk9sv21O0iRNT9K0NfEu3kFQQEQugiJ4VxBEucPAzP79\n",
       "4WGGZw8gl5nZc3m/1upafT7M3vuDQ3Q+PM/neSRZlmUQERERERFZiEbtBIiIiIiIyLmwyCAiIiIi\n",
       "IotikUFERERERBbFIoOIiIiIiCyKRQYREREREVkUiwwiIiIiIrIoFhlERERERGRR9ywyjh49ioce\n",
       "eghz586FRqPBH//4x3vetLq6Gnl5efDx8cHcuXPxs5/9zCLJEhERERGR/btnkdHT04Pk5GT8+te/\n",
       "hre3NyRJGvf1nZ2dWL9+PcLDw1FeXo5f//rX+OUvf4k333zTYkkTEREREZH9kiZz4re/vz/+67/+\n",
       "C1//+tfHfM3WrVvxyiuvoKWlBZ6engCAn//859i6dSuuXr06/YyJiIiIiMiuWbwno6SkBLm5ucYC\n",
       "AwDy8/Nx/fp1XLp0ydKPIyIiIiIiO+Nm6Rs2NzcjMjJSiIWFhRm/FhUVZYx3dHRY+vFERERERGRl\n",
       "gYGB437d4jMZ9+rZICIiIiIi52bxImP27Nlobm4WYi0tLcavERERERGRc7P4cqmVK1fi5ZdfxsDA\n",
       "gLEvo6CgAHPmzBGWSinda8qFnEN5eTkAICMjQ+VMyFb4njuu3oFubD/2EYqr90KGuEfI7c4I7Ch6\n",
       "FR3d4ZO+r5dHJ+7P/jdEhNaZfS154Qo8mvc8ZviHTDlvUgf/W3c9fM9dz2RaHSa0hW1lZSUqKyth\n",
       "MBhw6dIlVFZW4sqVKwCAV155BevWrTO+/itf+Qp8fHzwzDPPoLa2Fn/729/wi1/8Ai+99NIUvhUi\n",
       "IlJDxbki/PyDf8Kx6j2jFBhz8PfDb5gVGO5uwJfXA39+Dfj9D+rx78+dx7e3AL7e4r37dQH44uhP\n",
       "cO1mgtlzqxqP418//CccPrUdBtlg8e+LiIhs455FRllZGdLS0pCWlob+/n78+Mc/RlpaGn784x8D\n",
       "uNvM3dTUZHx9QEAACgoKcP36dWRkZOB73/sefvSjH+GHP/yh9b4LIiKyiAFdHz7a92u8v/tX6Oq9\n",
       "Y/Z1P+90FJx4E739AUI8Kwk4/QHwp59IeHKdhJToHqxO7sDWf5Zw7n+Ah3PF+wzpPbDvxGvw9thk\n",
       "nsNgP/529F38dttP0dljngMREdm/ey6XWr16NQyGsX+b9N5775nFEhMTceTIkellRkRENnWt9SLe\n",
       "2/XvuHnnutnXQoMisCHzGbzw78tw87b4tWceAH77z4CH++gbf4SHSPjbGzJe+2/gp/9tivf0afHx\n",
       "3m/hLz/Pw7Hqd3GppUG4rv5yJX7x8Yv4xsaXsHhe8rS/PyIish2LN34TEZHjqW4qxX/85V/MCgyt\n",
       "1g2blj+Ff/nqW9j612U4dU687vmHgHdfGbvAGCZJEn7ynIQ3XhDj11qBf3knFt975N/w+OpvwcvD\n",
       "R/h6V+8dvPP3n6Coas+UvzciIrI9FhlERC5MlmUcrNiGP2x/A7rBfuFrs4Pn4Z+f+hU2rXgKfz/i\n",
       "jj/uFq/dsgrY+qPJbV3+8tckvPikGDtaCfzqzxrkptyPV772NhZGxAtfN8gGfHrot/jrkT/AYNBP\n",
       "6vsjIiJ1sMggInJRsizji2N/xLbC982au1cmrMePnvoVIkLmo/mWjH/8lXhtXBTw/quAVjv5s5H+\n",
       "/R+BNWli7LX/Bk43yJjhH4J/evRn2Lj8SUgQ732kcgc+2PsfGNIPTvqZRERkWywyiIhc0N3Zgd/h\n",
       "wMltQlwjafDY6m/hy+u+Cw/3u9uQ//DXQHun6TUe7sAnPwMCfKd2+Kqbm4SPXwNCgkyxwSHg+TcA\n",
       "vV6GVqPF/Su+jOce/Bd4uHsJ11acK8IfdvwbdEMDU3o2ERHZBosMIiIXY5AN+HPBb3CsWuxz8PLw\n",
       "wbcf/j9YlXK/MXa0UsYnB8Trf/oPQNLCqRUYw8KCJbzzIzF28izwh+2mcfLC5Xjx8X9FkN9M4XVn\n",
       "Lp7E//3i5xgc0k0rByIish4WGURELkSWZXx2+Pc4UXdQiPt6+eN7j/4MS6JSjbGhIRnf/w/x+rRY\n",
       "4P95yjK5PLZGwmNrxNj/+1vgVodp6dbc0Gi8+PgbCA0Uz+Q4d6UK/73z37l0iojITrHIICJyEXd7\n",
       "MD5AUZXYwR3oG4zvP/avmDdroRD//Xag6rx4j1+/OLU+jLG8+X3xsL7bXcAvPhJfExwwCz94/F8R\n",
       "PjNSiNdeLMcHe/8DejaDExHZHRYZREQu4vCp7Thw8u9CLMBnBr7/2M8RPnOeEO/pk/GTP4jXfzUf\n",
       "yE62XIEBAHNnSfj/viHGfvMZcK1VbEQP8J2B7z/6ulmhUdlQjL8e+QNkWXw9ERGpi0UGEZELqGwo\n",
       "xrZC8fBUXy9/fPeR1xAaFG72+q1/B1pHHLbt4wX82z9aJ7cfPAFEhJjG/Trg9ffNX+frHYDvfuk1\n",
       "s6VTRVW7cejU59ZJjoiIpoRFBhGRk7tw4yw+3PuWsE2tp4c3/vFLPzGbGQDuzmL88k9i7AdPAHNC\n",
       "LTuLMczbU8Krz4ixd7cDjVfNZycCfGfgu4/8FDP8QoT4tsL3caqh2Cr5ERHR5LHIICJyYh097Xh3\n",
       "x79hUG/aiUmj0eK5+18268EYppzF8PMGXrJQs/dYntsMREeYxkN64F8/HP21wQGh+PbD/8fsdPCP\n",
       "9r2Fq61NVsySiIgmikUGEZGTGtIP4r2dv0Rn720h/uTaFxAXtXTUa3r7zWcxvvc4MDPQOrMYw9zd\n",
       "JLz2vBj7017gRtvovRYRIVF47oGXodFojbHBIR3+sP0NdPd1jnoNERHZDosMIiInta3wPTTdqBNi\n",
       "6zIexcqEdWNe8+Ee289iDHvyPnE2QzcIvP2XsV8fG5mCJ9e+IMTau1rx/q5fcscpIiKVscggInJC\n",
       "ZfWHcfT0LiEWF5WKB1d+ZcxrDAYZv/5UjL3wiPVnMYa5uUn4oaKg+e02oKtn7J2jViasEw4PBIBz\n",
       "V6uxq+Rja6RIREQTxCKDiMjJXGu9iP858I4QCw6YhW9s+KGwvEhpXylQf8k01mqB7z1mrSxH9+wD\n",
       "wMxA07ijWzwFfDRfyv0mFs5JEGL7y/+Gs5dPWyFDIiKaCBYZRERORDc4gPf3/AqDQ6ZGb3etB557\n",
       "4GX4egeMe+1bn4jjx9fcPcfClny8JPzjI2LsPz+7O8syFq3WDd+8/58R6BtsjMmQ8eHet9DVe2fM\n",
       "64iIyHpYZBAROZHPi/6IlvarQuyJtd8ecyepYbVNMvaVirEXn7R0dhPzT48Cnh6m8cUbwN4T41/j\n",
       "7xOEpzf8EBJMRVFn7218tO9tGGSDlTIlIqKxsMggInIStRfKUVgl9mEsj78Py+Pvu+e1v90mjrOS\n",
       "gMx4285iDAudIeHJtWLsd9tGf+1Ii+clIT/zcSFWd6kCh099YcHsiIhoIlhkEBE5ga7eO/i44D+F\n",
       "WEjgbDyW9/wYV5j0Dcj40z4xZuteDKVvf0kc7ygGLjePvWRq2MblTyI6YokQ237sI1y5yfMziIhs\n",
       "iUUGEZGDk2UZHxf8Bl19HcaYRtLg6xtfgqeH9z2v/+wQcKfLNA4JArasskamE7ciAUiJMY0Nhns3\n",
       "gAOAVqPF1ze8BB9PP2NMbxjCxwVvY0g/aIVMiYhoNCwyiIgc3PHa/ai9WC7ENix/EvNnL57Q9X9Q\n",
       "rCb6+ibA00OdpVLDJEnCt7eIsT9sBwaH7j2bERwQii+v+64Qu9Z2EQVlf7VkikRENA4WGUREDqyj\n",
       "ux3bCt8TYgvC45C/bGLrneovyShU7PT6/GZLZTc9X82/exjgsOZbMGtOH0tKzEpkxOYJsb1lf8G1\n",
       "1gsWzJCIiMbCIoOIyEHJsoy/HP4d+nS9xpiHmyee3vAitOOchzHSu4olSDnJQFyUurMYw/x9JTyp\n",
       "OJz8g90Tv/7RvOfg7xNkHBsMenxU8Db0+iELZUhERGNhkUFE5KAqz5egqlHc2/WBrK8iJHD2hK7X\n",
       "62V8rGj4fv4hS2VnGd/YJI6/KAJud957yRQA+HoH4Mm13xFi11ovYF85l00REVkbiwwiIgfU09+F\n",
       "zw7/XyEWNXsx8lIemPA9DlUAN26Zxn7ewGNrLJWhZWQnA9ERpvGADvj04MSvT164AumLc4XYvtK/\n",
       "oLn9ioUyJCKi0bDIICJyQNuOviecZq3VuOEr6/4JmgkukwKAP+0Vx4+uvnvitj2RJAlPK2YzJrNk\n",
       "CgAeXf0P8PcONI71hiF8euh3kOWJzYgQEdHkscggInIwDVdrcKJO/HV+/rLHED4zcsL36O2X8dfD\n",
       "YuyrGyyQnBU8rcirpAZouDLxAsHPOwCPrv4HIXb+ag3Kzx6xRHpERDQKFhlERA5Erx8yWyYVPjMS\n",
       "65c9Oqn7fFEEdPeNvAewJs0SGVpe9BwJuSli7M8Fk7tH6qJsxEUuFWLbjr6H3oHuaWZHRESjYZFB\n",
       "RORAjp7ehRu3LguxJ9e+ADet+6Tuo1wq9dR6QKu1r6VSIylnWT49MLnrJUnC42u+Lfw5dfV1YEfx\n",
       "nyyQHRERKbHIICJyEB097dh14s9CLHPJGkRHLJnUfdo7ZewVN6XC1+x0qdSwR/IA7Yh2kzMXgZqm\n",
       "yfVUhAaFY13GI0LsWNUeXGpusECGREQ0EosMIiIH8XnRHzGgM61x8vbwwUPZ35j0fb4oBIb0pnFs\n",
       "JLB0kSUytJ6QIAnrMsTYJ/snf5/1GY8iNDDcOJYh4y+HfgeDbJhmhkRENBKLDCIiB9B4rRbl9WKj\n",
       "8v0rv4IA36AxrhibsuH7sTV3lxPZuyfuE8efHsSkd4hyd/PAY2u+JcQu3zxv9mdLRETTwyKDiMjO\n",
       "GQx6fHb490IsImQ+cpI3jXHF2Dq6ZRSUiTF7OxtjLF9aBbi7mcYNV4BT5yZ/nyVRqUiJWSnEth/7\n",
       "UJglIiKi6WGRQURk507UHcK1totC7PHV/wDtJM7EGLbjGKAbNI1j5gLJMdNM0EaC/CVsXC7GJnMw\n",
       "30gP53wDWq2pYunoacf+k3+fRnZERDQSiwwiIjs2oOvDzhJxB6T02FVYOCdhSvdTLpV6dLVjLJUa\n",
       "plwy9fnRqd0nJHA21qQ+LMQOntyG9s7WKWZGREQjscggIrJjByq2obPntnHspnXH5qynp3Svrh4Z\n",
       "u4+LMUdZKjXswWxxydTZy0D9pamd3L0+41H4+5h6Wgb1Omw/9sF0UyQiIrDIICKyWx3d7Th4cpsQ\n",
       "W536EIIDQqd0v10lwIDONJ4fDqTFTidD2wv0k8wODdw2xdkMb08fPLjyq0Ls5LlCNF2vn2J2REQ0\n",
       "jEUGEZGd2lHyJ+iGBoxjP+9ArM+Y3MneIzn6UqlhD68Sx1MtMgBgefxazAldIMS+KPrjpHetIiIi\n",
       "EYsMIiI7dLW1CaVnxK7mTSuegrenz5Tu1z8gY1eJGHO0pVLDHsoRx6VngGutUysKNBotHln1TSHW\n",
       "dKMONRfKxriCiIgmgkUGEZEd+qLoA8gwfXAOC56LrMT8Kd/v4Emgt980nhMKLJvcQeF2Y06ohMx4\n",
       "MfZF0dTvt2huEhLmiyf97Sj+CAaDfowriIjoXlhkEBHZmYar1ai/XCnEtuQ8M6Uta4dtPyaOH8wG\n",
       "NBrHWyo17OFccTzVXaaGbc7+GiSY/jxu3LqMsvrD07spEZELY5FBRGRHZFnG9uKPhFjMnATEz0+f\n",
       "1j13FouxzdlTvp1d+FKeOD54ErjTNfU+ioiQ+Vi2ZLUQ21XyZwwO6Ua/gIiIxsUig4jIjtRcKMPF\n",
       "G2eF2Obsp6fVoF3ZAFy9aRp7ewJrpl6z2IW4KAmxkabxkB5m2/NO1v0rviwc0He7uw2FVbumd1Mi\n",
       "IhfFIoOIyE4YZAN2FosH7yUuWIYF4XHTuu8OxVKp9csAb0/HXSo1TLnL1BeF07tfcMAs5CZtEmL7\n",
       "yv6K3oHu6d2YiMgFscggIrITFWcLcf3WJeNYgoQHs746zhUToywyHnTwpVLDlLtM7SsFhoamt/Vs\n",
       "fubj8PTwNo57+7twuGL7tO5JROSKWGQQEdkBvX4Iu47/WYilx65CRMj8ad33RpuMsjox9kDWtG5p\n",
       "N5bHA8EBpvHtLuDEmend0887APelbRFihyq/QE9/1/RuTETkYlhkEBHZgeNnDqCto9k41mi02LTi\n",
       "qWnfV9nwvWwJEB7i+EulAECrlbBxuRhTngUyFatTH4Kvl79xPKDrw6GKz6d/YyIiF8Iig4hIZUP6\n",
       "Qewr+0yIrUxYj9Cg8Gnf21mXSg3btFIc7yoe/XWT4eXhjfvSvyTEDlfuQHdf5/RvTkTkIlhkEBGp\n",
       "rLTuEG53tRrHblp3bMh8fNr37R+Qsb9cjDn61rVKG5YDIzfeOn1+6qd/j5Sbcj/8vAONY91gPw6c\n",
       "/Pu070tE5CpYZBARqUivHzKbxchKXI8gv5nTvndRlfkp3ymLpn1buxISJGG54vTv3RZYMuXp7oV1\n",
       "GY8IscLTu9DZc2f6NycicgEsMoiIVFRadwjtnaZDLLRaN9yX/sg4V0zc3hPiOH85pnXehr1SLpmy\n",
       "RJEBADlJGxHgM8M41g0N4MDJv1nm5kRETo5FBhGRSkabxViZsB4z/EMscv99peJ4Q6ZFbmt37lcU\n",
       "GQVlgG5w+kumPNw9sX7Zo0KsqGoPOntuT/veRETOjkUGEZFKyuqP4FZni3Gs1bhhnYVmMa63yqhu\n",
       "NI01GmDdMovc2u6kLgbCgk3j7r67S8UsISsxH4Ejlq4N6nU4dIo7TRER3QuLDCIiFegNeuwr+4sQ\n",
       "WxF/H4IDQi1yf+UsxrI4IDjA+ZZKAYBGI2HTCjFmia1sAcDdzQPrlb0ZVXvQw52miIjGxSKDiEgF\n",
       "5fVHhHMxtBo3s6U506EsMvKXj/46Z6HsyygoHf11U7EiYR38fYKMY91gP45U7rTcA4iInBCLDCIi\n",
       "G9Mb9NhXKs5iLI9fg+CAWZa5v15GQZkY2+DkRcZ9GeJWttWNQPOt6fdlAICHmyfWpj0sxI6c3oG+\n",
       "gV6L3J+IyBmxyCAisrGKc4Vo7bhhHGs0Wqxf9pgF7w/c6jCNA/2AzCUWu71dCg6QkBEnxpRnhExH\n",
       "dtJG+Hj6Gcd9Az0oqtptuQcQETkZFhlERDZkkA3YXy5ug5q5ZA1mBoRZ7BnKrWvXZQBubs7ZjzGS\n",
       "srF9vwWXTHl5eCMvdbMQO3TqC+gGByz3ECIiJ8Iig4jIhmovlOPGrcvGsSRpsD7Dcr0YALBPUWQ4\n",
       "+1KpYesVRUZBGSDLllkyBQB5KQ/A08PbOO7u60BxzT6L3Z+IyJmwyCAishFZllFQ/lchlrYoG6FB\n",
       "4RZ7Rke3jJJaMeYqRcbKRMDHyzS+cQs4c8Fy9/fx8kNu8v1C7EDFNgwODVruIUREToJFBhGRjTRe\n",
       "P4OLN84KsXUZljkXY9jBk4BebxovmQ/MC3P+pVIA4OkhIW+pGFM2wE/XmtTNcHfzMI47um+htO6g\n",
       "ZR9CROQEJlRkvPPOO1iwYAG8vb2RkZGBoqKicV+/a9curFixAgEBAQgNDcWWLVvQ0NBgkYSJiBzV\n",
       "/jJxFiM+Kg1zQhdY9BnKfox8Jz3leyxmfRkWLjL8fYKQlZgvPqP8b9Ab9GNcQUTkmu5ZZHzyySd4\n",
       "8cUX8eqrr6KyshJZWVnYtGkTrly5Murrz58/jy1btmD16tWorKzE/v370d/fj/vvv3/U1xMRuYJr\n",
       "rRdw5lKFELPkuRjDDih2VHKVpVLD1iuKqiOVgG7Qcn0ZALA2bQu0Gjfj+FZnCyobjln0GUREju6e\n",
       "Rcabb76JZ599Fs899xxiY2Px9ttvIzw8HFu3bh319ZWVlTAYDHjjjTcQHR2NlJQUvPzyy2hsbER7\n",
       "e7vFvwEiIkdQoNhRakF4HKIj4i36jEvNMhqvmcbubkBuikUfYfcSFgDhM03jnj6gpMayz5jhH4Ll\n",
       "8WuE2IGT2yzaZE5E5OjGLTJ0Oh0qKiqQny9ODefn56O4uHjUa7Kzs+Hn54ff//730Ov16Orqwvvv\n",
       "v4/MzEwEBwdbLnMiIgfReucGTil+070u4xFIkmV7JQ6eFMcrEwFfb9foxxgmSZLZkilL92UAwJq0\n",
       "LZBg+rO92tqEc1eqLP8gIiIH5TbeF9va2qDX6xEWJu7fPmvWLDQ3N496TXh4OHbt2oUtW7bgu9/9\n",
       "LgwGA1JTU7F79/iHFpWXW/DUJLJ7fL9djyu/58cbd0GWDcZxkE8o+m9JKG+37J/JZ/vmAzD9Gj92\n",
       "9nWUl98Y8/W2oMb7vjAkGICp1+Xzwz3YklZv8efMDV6MK+2mRv6/H/oj1iV8xeLPcTSu/N+6q+J7\n",
       "7joWLVo04ddafHeppqYmbNmyBc8++yzKy8tx+PBh+Pv744knnuBUMhG5nD5dN863nBZiiXOyLD6L\n",
       "IctA2Tl/IZaxuMuiz3AUmYs7hXHdZR909mot/pyEOSuE8fU7TWjvabH4c4iIHNG4MxkhISHQarVo\n",
       "aRH/0mxpaUF4+Oj7uv/ud7/DvHnz8Itf/MIY++ijjzBv3jyUlJQgKytr1OsyMjImmzs5oOHfdvD9\n",
       "dh2u/p5vP/YhDLJp56Fg/1A8uuFpaLXj/vU7afWXZLSN+Gzt4wV845FYeLirs1xK7fc98X0ZNU13\n",
       "/79BlnBbvxRrMyz9Z5GBc22laLpRZ4w0959Dft4DFn6OY1D7PSfb43vuejo6Oib82nFnMjw8PJCe\n",
       "no59+8QTTQsKCsYsFmRZhkYj3nZ4bDAYRruEiMgpDQz241j1XiG2Ju1hixcYgHk/Rm4KVCsw7MF9\n",
       "is88hypGf910rU3fIowrzhWhvbPVOg8jInIg91wu9dJLL+H999/Hu+++i7q6OvzgBz9Ac3MzvvOd\n",
       "7wAAXnnlFaxbt874+oceeggVFRX42c9+hoaGBlRUVODZZ59FZGQk0tPTrfedEBHZmRNnDqJ3oNs4\n",
       "9vHyx4qEdeNcMXUHFUui17r4X7fK7/+wlYqMxOhlmDVjjnFsMOhxuHK7dR5GRORA7llkPPHEE3jr\n",
       "rbfw+uuvIzU1FcXFxdi1axfmzZsHAGhubkZTU5Px9Tk5Ofjkk0/w+eefIy0tDZs2bYKXlxf27NkD\n",
       "b29v630nRER2xGDQ48gp8cNmTtIGeLp7WeFZstlv6l29yFi1FBg5qX7mItDSbvm+QI2kwdo0cTaj\n",
       "pGafUFwSEbmiCTV+v/DCC7hw4QL6+/tRVlaGnJwc49fee+89ocgAgMceewzl5eXo6upCS0sLtm3b\n",
       "hri4OMtmTkRkx2oulKO1w7Szk1bjhtxk6xxKWtkA3B7R4x3kDyyd+AYgTinQT0LaYjF25JR1nrUs\n",
       "Lg/+PkHG8cBgP45V7R3nCiIi52fx3aWIiAg4dOoLYZwem4tAP+ucFaTsx1iTCmi1rtuPMWx1mji2\n",
       "Vl+Gu5sH8pY+KMSOVO7A4NCgdR5IROQAWGQQEVnY5ZbzaLxWK8TWpD5ktecdUhYZLr5UatgaRZFh\n",
       "rb4MAMhJ2giPEUvhOntvo+JcofUeSERk51hkEBFZ2KGKz4Xx4nnJmBO6YIxXT49uUMZR8RgOl+/H\n",
       "GJaTDGhHHI9x9jJwvdU65zX5ePlhpaKp/3Dldp4PRUQui0UGEZEF3e5qxamGY0JsbdrDVnteWR3Q\n",
       "02caz54JLJlvtcc5FH9fCcsU7YCHrdSXAQB5Sx+EBNMytWutF3BeMaNFROQqWGQQEVnQkcqdMMim\n",
       "M4HCguciLirVas9T9mOsTYPFTxN3ZLbqywCAkMDZSFqYKcSOcDtbInJRLDKIiCykX9eH4hrx8NI1\n",
       "qQ9BI1nvr9qjleJY+aHa1dmyLwMAVit6b6obS9F658YYryYicl4sMoiILOR47X7063qNYz/vQGTE\n",
       "5VntebpBGcXVYoxFhigrCXAfccB64zXgSov1+iQWRsRjbmi0cSxDxtHTO632PCIie8Uig4jIAvSj\n",
       "nPSck7wRHm6eVntmeT3QN2Aah88EFs4Z+/WuyNdbQma8GLPmkilJkrA6dbMQO37mAPoGese4gojI\n",
       "ObHIICKygKrGE2jvvGkcu2ndkZu8yarPVB4ul5fKfozRrFa0xFh7yVTqohzxcD5dH47X7rfuQ4mI\n",
       "7AyLDCIiCzisOHxvWdxq4YOmNSj7MVYtterjHJby3BBrzmQAgLubeYF55PQOGAx66z6YiMiOsMgg\n",
       "Ipqmyy3nceFGvRBTLpmxtKEhGceqxFie9TaxcmgrEwEPd9P4UjNw4bp1z6/ITtoAN63poe2dN1Hd\n",
       "VGbVZxIR2RMWGURE06Rs7I2NTEH4zEirPvNUA9A94nyMWTOAuCirPtJheXtKWJkoxgpPj/5aS/H3\n",
       "CUJG7CohpuzZISJyZiwyiIimoav3Dk6eKxRieSkPWv25yn6MVUvZjzGe3BRxrFxqZg3K2azGa7W4\n",
       "crPR+g8mIrIDLDKIiKahuGYf9Poh4zgkcDbiF6SPc4VlsB9jcpR/PtaeyQCAiJD5WDwvWYgdPsXZ\n",
       "DCJyDSwyiIimSK8fQlHVHiGWm3y/VQ/fu/tc2exDMvsxxrcyEXDTmsYNV4AbbdbtywCA1UvF2YyK\n",
       "c0Xo6Gm3+nOJiNTGIoOIaIpONx4XPjB6uHthecJaqz+3qhHo6DaNgwOAhAVWf6xD8/WWkB4rxmwx\n",
       "mxG/IB2hgeHGsd4whGNVe63/YCIilbHIICKaoiOVO4Rx5pI18PH0s/5zFf0YuSmARsN+jHvJVWHJ\n",
       "lEbSIC9V7NEprtmHIf2g9R9ORKQiFhlERFMw2ra1q1Lut8mz2Y8xNWr0ZQBA5pK18PTwNo47e2/j\n",
       "9PkS2zyciEglLDKIiKZgtG1rZwfPs/pzDQb2Y0xVdhIwcgOu6kagvdP6fRleHt5YvmSNEDt6epfV\n",
       "n0tEpCYWGUREk6TWtrUAcOYicKvDNA70A1JibPJohzcjQELyQtNYlmF2oKG15CaLs1wXbtRzO1si\n",
       "cmosMoiIJqm4pkDYtnZmYBji56fZ5NnKfoycZECrZT/GRCn7MmxxXgYAhAXPRew88bCOQs5mEJET\n",
       "Y5FBRDQGAmxdAAAgAElEQVQJd7et3S3EViU/AI1GO8YVlsV+jOlRqy8DAHIVPTsnzxaip6/TdgkQ\n",
       "EdkQiwwioklQa9taAJBl2azIYD/G5ChP/j55FujutX5fBgAkLsjADP9Q43hQr8PxMwds8mwiIltj\n",
       "kUFENAlHK8WG78y41TbZthYAzl8FWkac4+brDaQutsmjnUZYsITFI/rz9XqgpMY2z9ZotMhJ3iTE\n",
       "Cqt2w2DQ2yYBIiIbYpFBRDRBV1ub0HSjTojlpjxgs+cXKZqUVyYA7m7sx5gstfoyAGBlwjq4ad2N\n",
       "4/bOm6i9eNJ2CRAR2QiLDCKiCSqq2iOMF89LRvhM629ba3q+OM5OGf11ND5lX4byz9Wa/LwDkL44\n",
       "V4ixAZyInBGLDCKiCegb6EX52aNCLFex9MXaihUfhnOSbfp4p6EsMo7XAgM62/RlAOYN4PWXK9Fy\n",
       "+5rNnk9EZAssMoiIJqCs/jB0g/3GcaBvMBKjM232/NbbMs5eNo21WmB5vM0e71SiZkuIDDONB3RA\n",
       "Wd3Yr7e0yLAYzJ8dK8SUO5YRETk6FhlERPcgyzKOVYtLpbIS86G10ba1AHCsWhwvjQH8fNiPMVXK\n",
       "2Qxb9mUA5rMZJ84cRL+uz7ZJEBFZEYsMIqJ7aLx+BjdumaYRNJIGKxPX2zQHs34MLpWaFmXzty3P\n",
       "ywCApTFZ8PcONI77db0oqz9s2ySIiKyIRQYR0T0oG76TojMR5DfTpjmY9WOw6XtalOdllNQAer3t\n",
       "+jLc3dyRlZQvxApP74Is2y4HIiJrYpFBRDSOzp47OH2+RIgpzzqwtt5+GSfPirHsJJum4HRiI4GZ\n",
       "pokEdPYANU22zSErcQM0kumf4eb2K2i4aqNDO4iIrIxFBhHROI6f2Q+9Ycg4Dg2KwKJ5tv2EX1YH\n",
       "DJpSQHQEEB7CfozpkCTJrFCz5Va2ADDDPwTJC1cIsaOnd47xaiIix8Iig4hoDAaDHsXVe4VYTtJG\n",
       "4bfPtqD88Mutay1D2ddSXD3666xJ2QBe3VSK211ttk+EiMjCWGQQEY2h7tIptHe1GsfuWg9kxq+x\n",
       "eR7KfgwewmcZyr4WW89kAEDMnASEz4w0jmXZgJKaAtsnQkRkYSwyiIjGUKg4uyBtcQ58vfxtmoNe\n",
       "L6NYsUyf/RiWkbYY8PIwja+0AJebbdt4LUkScpI2CrHi2n3Q64fGuIKIyDGwyCAiGsWtjhbUXawQ\n",
       "YjnJG8d4tfXUXgA6uk3j4AAgLsrmaTglTw8Jy5aIMTVmMzLiVsPD3cs47uy5jeqmUtsnQkRkQSwy\n",
       "iIhGcaxmH2SYfqs9d1Y0IsMW2TwPs/MxkgCNhk3flqLsy1AeemgL3p4+WBabJ8SKFIc/EhE5GhYZ\n",
       "REQKg0ODOF67X4jlJG2CJNn+wz37MaxL2UR/TIWZjLt5iLNk565U4ebta+okQ0RkASwyiIgUqhpL\n",
       "0N3XYRx7e/ggPTZXlVxGm8kgy1mZCIysHasbgTtdtj8Qb07oAswPjxViRYqdzYiIHAmLDCIiBWXD\n",
       "d2b8WniOWDNvK1daZFxuMY09PYCMOJun4dRmBEhIjDaNZfnu6d9qUDaAl545CN3ggDrJEBFNE4sM\n",
       "IqIRrrddRNP1OiGWnbRBlVyU/QHL4u42K5NlZal8KN+w1EXZwu5lvQPdqDhXpE4yRETTxCKDiGgE\n",
       "5RKVmLmJmB08T51cTovjLB7CZxXKvgw1DuUDAHc3D6xIuE+IsQGciBwViwwiov81oOtDWf1hIaZc\n",
       "wmJLyiZknvRtHcpD+U7UArpB2/dlAEBWojhrdrmlAZdbzquSCxHRdLDIICL6X+Vnj2JA12cc+/sE\n",
       "IXnhclVy6eiWUdUoxpTLesgyIsOAubNM434dUHFWnVxCg8IRF5UqxDibQUSOiEUGEREAWZbNGr6z\n",
       "EtfDTeuuSj7Ha+82IQ9LWAAEB7AfwxokSTLbtUutvgzAfPbs5Nmj6B3oHuPVRET2iUUGERGACzfO\n",
       "4nrbReNYkjTISsxXLR/2Y9iW2aF8KhYZCQsyEOQ30zgeHNKhrO6wegkREU0BiwwiIgBF1eIsRsKC\n",
       "DMzwD1UpG/Zj2JrZoXzVd2e31KDVaM0K3KLqParlQ0Q0FSwyiMjldfd14lTDMSGmZsP34JCME2fE\n",
       "GIsM60paCPj7mMZtd4Bzl9XLZ2Xiemg0WuO4pf0qzl9T6QAPIqIpYJFBRC7vxJkD0OuHjOOZgWGI\n",
       "i1qqWj6nzgF9I85giwgB5oerlo5L0GoluzkvAwACfYORHC1uOlBUxQZwInIcLDKIyKUZZIPZ7j3Z\n",
       "iRugkdT761H54TY7+W5zMlmXsshQsy8DAHKSxdm0043H0dlzW6VsiIgmh0UGEbm0+kuVuNXRYhy7\n",
       "ad2xImGdihkBxxRN38qmZLIO5ZI0NWcyAGDR3CTMmjHHODYY9Cip3a9iRkREE8cig4hcmnIWY+mi\n",
       "LPh5B6iUzd1mY+WHW/Zj2EZmPOBmaoPA+atAS7t6zdaSJJn1BhVX74XBoFcpIyKiiWORQUQuq72z\n",
       "FbUXyoVYTtImlbK56/xVoPWOaeznDSQvVC8fV+LrLSEtVoypvWQqM34N3N08jOPb3W2ovXhSxYyI\n",
       "iCaGRQYRuayS2n2QZYNxHBEyHwvCY8e5wvqUsxgrEgA3N/Zj2IpyaZraS6Z8PP2QvjhXiLEBnIgc\n",
       "AYsMInJJQ/pBlNSI69tzkjaq3mBt1vSdok4erkp58rfaMxkAkJMszq7VXzqFto5mlbIhIpoYFhlE\n",
       "5JKqGk+gs9e0U4+nhzcy4vJUzOguZdM3+zFsSzmTUXEO6OlT9xC8yLAYRM6KMY5lyDhWvVfFjIiI\n",
       "7o1FBhG5JGXD97K41fDy8FYpm7tab8s4d8U01mqB5fHq5eOKwoIlLJpnGuv1QOmZsV9vK9mK7WyP\n",
       "nzmAwaFBlbIhIro3FhlE5HKa26/g/FXx9GQ1T/gedqxaHC+NAfx82I9ha8rZjMLTo7/OltIX58Lb\n",
       "09c47unrROX5YhUzIiIaH4sMInI5yqUm0RFLEBESpVI2JqMdwke2p+zLKK4e/XW25OHuicwla4TY\n",
       "MTaAE5EdY5FBRC5lYLAfpWcOCjF7mMUARunHYNO3KpR9MCU1gF6vbl8GYP5z2nSjDtfbLqqTDBHR\n",
       "PUyoyHjnnXewYMECeHt7IyMjA0VFRfe85q233kJcXBy8vLwQERGBV155ZdrJEhFN18mzhejT9RrH\n",
       "ft6BSInJUjGju3r7ZVScE2PK36iTbSyOBEKCTOOuXqC6Ub18hoUFz8WiueIPBbezJSJ7dc8i45NP\n",
       "PsGLL76IV199FZWVlcjKysKmTZtw5cqVMa956aWXsHXrVvzyl79EfX09du/ejbw89XdtISLXJssy\n",
       "iqp3C7EVCevg7uauUkYmZXXA4JBpHB0BhIewH0MNkiSZzWaofV7GsBxFA3hZ/WH06/pUyoaIaGz3\n",
       "LDLefPNNPPvss3juuecQGxuLt99+G+Hh4di6deuorz979ix+85vf4IsvvsDmzZsxf/58pKSkYONG\n",
       "+1iOQESu63JLA67ebDKOJUjITspXMSMT5YdYbl2rriw7PC8DAJKjlyPAZ4ZxPDDYj/L6IypmREQ0\n",
       "unGLDJ1Oh4qKCuTni/8I5+fno7h49F0tPv/8c0RHR2PXrl2Ijo7GggUL8Mwzz6C1tdVyWRMRTYFy\n",
       "acmS+WmYGRCmUjYi5YdYHsKnrtFmMmRZ/b4MrdYNKxPXCbGi6j12kRsR0Uhu432xra0Ner0eYWHi\n",
       "P8KzZs1Cc/Pop402NTXh0qVL+PTTT/HBBx8AAH70ox9h8+bNKCkpGfM03fLy8qnkTw6K77frUfs9\n",
       "HxjsQ/nZo0JstneM6nkBgN4AFJ1Owci/koM0tSgv71cvKQuxhz/fqZCHJHi6L8XA4N3fxV1rBXYU\n",
       "VCM8WKdyZoCfYTYkSJBxt7C43nYRuw9tw6yAefe40jYc9T2nqeN77joWLVo04ddafHcpg8GAgYEB\n",
       "fPjhh8jJyUFOTg4+/PBDlJaW8oeQiFTTeLMKeoOp6cHXMxARMxaqmJFJ0w1vdPeZCowAnyFEzXL8\n",
       "AsORubvJiI/sEWKnm/xUykbk6xmIOcHiP/Tnmk+qlA0R0ejGnckICQmBVqtFS0uLEG9paUF4ePio\n",
       "14SHh8PNzQ0xMTHGWExMDLRaLS5fvoxly5aNel1GRsZkcycHNFxo8v12HfbwnhtkA3bX/rcQW5P2\n",
       "IDKXZaqUkaj0srjUJS/VDZmZjv3fiD2879O1MVvGqRG7Sl3vXoCMjGj1EhrBJ0SD337+U+P4Uns9\n",
       "nk9YDD/vANVycob3nCaH77nr6ejomPBrx53J8PDwQHp6Ovbt2yfECwoKkJU1+paPOTk5GBoaQlOT\n",
       "qbmyqakJer0eUVHqH3ZFRK6n4Uo1Wu9cN461GjesSFivYkaiYvZj2CVlX4a9NH8DQFzUUswMNC1l\n",
       "1uuHcOLMARUzIiIS3XO51EsvvYT3338f7777Lurq6vCDH/wAzc3N+M53vgMAeOWVV7BunakJbd26\n",
       "dUhLS8M3v/lNVFZW4tSpU/jmN7+JFStWsNIlIlUUVYnb1qbErESAb9AYr7Y97ixln1YmAiPbCGua\n",
       "gNud9tFgrZE0yE7cIMSOVe+FQTaolBERkeieRcYTTzyBt956C6+//jpSU1NRXFyMXbt2Yd68uw1m\n",
       "zc3NwqyFJEnYsWMHZs2ahVWrVmHjxo2IjIzE559/br3vgohoDHe6b6G6qVSIKc8aUNPlZhmXR6xI\n",
       "9fQA0mPVy4dMgvwlJI5YHSXLd0//thfL4++DVmta9dzW0Yyzl0+PcwURke2M25Mx7IUXXsALL7ww\n",
       "6tfee+89s9js2bPx6aefTi8zIiILKKkpEH67Gz4zEgsj4lXMSHSsWhwviwM8PXgIn73IThZP+z5W\n",
       "Ddyv/gHxAAB/n0CkxmSj/KzpnIyiqt1YEpWqYlZERHdZfHcpIiJ7odcPobhG7CnLTtow5lbaajA7\n",
       "H4NLpeyKPfdlAOazcjUXynG7i+dSEZH6WGQQkdOquVCGjp5249jDzRPL4larl9AolB9ac9j0bVeU\n",
       "RV/pGUA3aB99GQCwIDwOESHzjWNZNqC4pkC9hIiI/heLDCJyWsoTvjPi8uDt6atSNuY6umVUNYqx\n",
       "lYnq5EKjiwwD5s4yjft1QMVZ9fJRkiQJOUnibEZJTQH0+qExriAisg0WGUTklG7evo6zV8QmWHtq\n",
       "+AbuNhHLI34pHj8fCA6wn6Vc9L8f4hWzGcrdwNSWEZcHT3cv47iz9zaqmk6omBEREYsMInJSx6rF\n",
       "WYz5s2MxN9Q+DlIbZrZ1LZdK2aWsJHFsb30ZXh7eZssAlbN4RES2xiKDiJyObmgAJ84cFGL2NosB\n",
       "sB/DUZg1f1cDsmw/fRmA+c93w9VqtLRfVSkbIiIWGUTkhE6dK0LvQLdx7OPlj9RF2SpmZE43KONE\n",
       "rRjjIXz2KWkh4O9jGrfdAc5dVi+f0USEzEd0+BIhVlTN2QwiUg+LDCJyOsqlIivi18LdzUOlbEZX\n",
       "cfZuE/GwOaFA1Gz18qGxabWSWUO+vfVlAEC2YjajtO4QdIMDKmVDRK6ORQYROZXLLedxqaVBiGUn\n",
       "2d9SKbN+jGTY1fkdJFJuZWtvfRkAsDQmC77eAcZx30APTp4rVDEjInJlLDKIyKkUVe0WxnFRqQgN\n",
       "Clcpm7HxED7HMlpfhr1xd3PHivj7hNgxNoATkUpYZBCR0+jt7zb7zW1u8iaVshmbLMujzmSQ/cqM\n",
       "B9y0pnHDFaCl3b6av4H/PdEephmxyzfP43LLeRUzIiJXxSKDiJzGibqDGBwyNTrM8A9Fwvx0FTMa\n",
       "3dnLwK0O0zjA925zMdkvX28JqYvFmD0umQoJnI24qFQhppzdIyKyBRYZROQUDLLBrOE7OzEfGo12\n",
       "jCvUUySeEYispLvNxWTflEva7LH5GzDfzvbkuUL09neP8WoiIutgkUFETqHhSjVa71w3jrUaN6xI\n",
       "WK9iRmNjP4ZjUi5pK7bDvgwASJifjhl+Icbx4JAOpXWHVMyIiFwRiwwicgqFiiUhS2NWIsA3SKVs\n",
       "xsd+DMekLAYrzgI9ffbXl6HRaJGVlC/EjlXvtbsDBInIubHIICKHd7urDdVNpULMHk/4BoAbbTIa\n",
       "r5nG7m7AsiVjv57sR1iwhJi5pvGQHig9o14+41mZsF5YKthy+yoartaomBERuRoWGUTk8Ipr9kGW\n",
       "DcZx+MxIREfEq5jR2JRbn6bHAj5e7MdwFI6wlS0ABPjOQPLC5UKsqJoN4ERkOywyiMihDekHUVJT\n",
       "IMRykjfZ7cF2yqZv9mM4lqwkcWyPO0wNy0kSt2+uajyBjp52lbIhIlfDIoOIHFpV4wl09t42jj3d\n",
       "vbAsbrV6Cd2DWT9Gijp50NQo36/iakCvt89eh0VzExE2w7S+y2DQ43jtfhUzIiJXwiKDiBxaUbW4\n",
       "be2yJWvg5eGtUjbj6+qRUdkgxrIS1cmFpiY2EpgZaBp39QLVjerlMx5JkpCdtEGIFVfvg8GgVykj\n",
       "InIlLDKIyGHduHUF5xXNrDlJ9tnwDQDHawGDqXUEcVFA6Az7XNZFo5MkyWH6MgAgM34N3N08jOPb\n",
       "3W2ovXhSxYyIyFWwyCAih3VM0ci6cE4CIkKiVMrm3pRLpdiP4ZgcqS/Dx9MP6YtzhZjy0EoiImtg\n",
       "kUFEDmlA14cTigPGcpM3jfFq+6D8MMrzMRyTsi/DXk/+Hpaj+O+i/tIptHU0q5QNEbkKFhlE5JDK\n",
       "zx7FgK7POPb3CTLbstOeDA7JOF4rxlhkOKa0xYCXaQUSrt4ELjfbZ/M3AESGxSByVoxxLEPGseq9\n",
       "KmZERK6ARQYRORxZls1O+M5KXA83rbtKGd1bZQPQ228az54JRM9RLx+aOk8PyewARXufzchWHE55\n",
       "/MwBDA7pVMqGiFwBiwwicjgXbtTjettF41iSNMhKzFcvoQlQno+Rkwy7PcuD7k3ZT2PvRUb64lx4\n",
       "e/oaxz19nTjVcEzFjIjI2bHIICKHo2xcTVyQgRn+oSplMzHKfgw2fTs25VK3YjveYQoAPNw9kblk\n",
       "jRArPL1LpWyIyBWwyCAih9LVewenzou/gVU2ttobWZbND+FjkeHQVirON6luBO502W9fBmC+McKl\n",
       "lgZcaj6nUjZE5OxYZBCRQympKYBeP2QchwaGIzbSvo/NPn8VuGk6lBy+3kBKzNivJ/s3I0BCYrRp\n",
       "LMtASc3Yr7cHs2bMwZKoNCF2lLMZRGQlLDKIyGHoDXqzE76zkzdCI9n3X2XKWYyVCYCbG/sxHJ2j\n",
       "9WUAwKqU+4VxRUMRunrvqJQNETkz+/6XmYhohKrGE7jTfcs49nDzxIqE+1TMaGLMDuGz74kXmiBH\n",
       "68sAgCXz0zAzMMw41uuHUFxToGJGROSsWGQQkcM4enqnMF4Wtxo+nn4qZTNxo+0sRY5POZNxohYY\n",
       "0Nl3X4ZG0iA3WZzNKKreA71Br1JGROSsWGQQkUO41noRjdfE0+xyFUs/7NGNNhkNV0xjNy2wPF69\n",
       "fMhyomYDc2eZxv06oLxevXwmakX8ffBw8zSOO7pvoarxhIoZEZEzYpFBRA5BOYuxaG4SIkKiVMpm\n",
       "4o5WiuP0WMDPh/0YzkCSJKxSLH07ckqdXCbDx8sPGXF5QqxQ8d8XEdF0scggIrvX09+F8rNHhNiq\n",
       "lAdUymZyjiqWSq1KVScPsg7l+1l4evTX2RtlA/j5a7W41npRnWSIyCmxyCAiu3e8dj8Gh3TG8Qz/\n",
       "UCRGL1Mxo4krVMxkrFqqTh5kHcr381gVMDRk330ZABARMh8xcxKEWGEVt7MlIsthkUFEds1g0KOw\n",
       "arcQy0neBK1Gq1JGE9d2R0ZNk2ksSWz6djaxkcCsGaZxdx9wqkG9fCYjVzEbWF5/BL393SplQ0TO\n",
       "hkUGEdm1mgvlaO+8aRy7az2QlbBOxYwmTrl17dJFQKAf+zGciSRJZrMZyj4ce5W8cDmC/GYax7qh\n",
       "ARw/c0DFjIjImbDIICK7pmz4To/Nha93gErZTI7yw2Yuz8dwSsr39agDNH8DgFajRXbSRiFWWLUL\n",
       "BtmgUkZE5ExYZBCR3bpx6wrOXRGnA1YtdYyGb8C8yMhj07dTUr6vhVWAwWD/fRkAkJW4Hlqtm3F8\n",
       "q6MFdRcrVMyIiJwFiwwislvKbTWjI5Zgbmi0StlMTke3jErF2nz2YzinxGggyN80vtMFVDeql89k\n",
       "+PsEIW1RjhA7epoN4EQ0fSwyiMgu9Q30oLT+sBBzlG1rAaC4GjCMWHUSPx8IncF+DGek0UjIVRSQ\n",
       "jtKXAZj/d1V3qQI3b19TKRsichYsMojILh0/cwC6wX7jONBvJlIWrlAxo8k5oty6lkulnJqjnpcB\n",
       "AFGzFyEqbJEQU+7oRkQ0WSwyiMjuGGQDik4rtq1N2iCsHbd3PB/DtYy2w5QsO0ZfBgDkKg7nO37m\n",
       "APoGelXKhoicAYsMIrI7dRcr0NpxwzjWat2QlZivYkaT09Mno6xOjK3izlJOLXUR4OdtGt+8DZy9\n",
       "rF4+k5W6KAf+3oHG8YCuDye4nS0RTQOLDCKyO8rG07RFOfD3CVIpm8k7XgsM6U3jmLlARCj7MZyZ\n",
       "m5uEbEVfxhEH2coWANzd3JGTvEmIHTm9AwaDfowriIjGxyKDiOxKc/sV1F0St9B0pIZvYJTzMbhU\n",
       "yiUoz8tQLpmzd9lJG822s625UK5iRkTkyFhkEJFdOXxquzCePzsWUbMXjfFq+2R2PgaLDJegPC/j\n",
       "iIP1ZQT4BiFj8Sohdrhy+xivJiIaH4sMIrIb3X2dKKs7LMRWp25WJ5kpGtDJOF4rxtj07Roy4gAv\n",
       "D9P4Witw4bp6+UxFXuqDwvj81RpcbW1SKRsicmQsMojIbhyr3otBvc44nuEfipSYlSpmNHlldcCA\n",
       "6VvAvDAgarZ6+ZDteHpIWJEgxhzpvAwAmBsajZi5iULsyKkdKmVDRI6MRQYR2YUh/SAKq8SG71Up\n",
       "D0Cr0aqU0dQoz8fIWwpIEpu+XYXyvIyjDnRexrDVS8XZw/JzR9HZc1ulbIjIUbHIICK7UHGuSPgg\n",
       "4+HuhZWJ61TMaGqUzb5s+nYtZudlONAOU8MSF2RgZmCYcazXD6Goeo+KGRGRI2KRQUSqk2XZrOF7\n",
       "Rfx98PH0UymjqRkaknGsWozxfAzXsiIBcB9xZmTTdeDqTcdp/gYAjUaLvBSxN+NY1R4MDunGuIKI\n",
       "yByLDCJS3flrtUJzqQQJeUsfHOcK+1ReD/T0mcZhwcDiSPXyIdvz8ZKwbIkYO+yAsxkrEtbBy8PH\n",
       "OO7q60DFuUIVMyIiR8Mig4hUd0SxTWZi9DKEBoWrlM3UHTwpjteksR/DFa1OE8fKnwtH4OXhjRUJ\n",
       "4nLFw6e2O9SWvESkLhYZRKSq1js3UN1YKsQcbdvaYYfFMwTNPmySa1ijeN+VPxeOIi/lAUiS6WPC\n",
       "tbaLOH+tRsWMiMiRsMggIlUdPb0TMky/HZ0TugAxcxLHucI+DehkFFWJsbXp6uRC6spKAjzcTeOL\n",
       "N4AL1x1vBmBmYBiSojOF2KFTPJyPiCaGRQYRqaZvoAfHa/cLsTWpDznkEqMTZ4D+EX2xc2cBC+eo\n",
       "lw+px9tTQpaiTj7koLMZylnF2qYy3Lx9TaVsiMiRsMggItWU1BZgYLDfOA7wmYG0xTkqZjR1ynX3\n",
       "a9mP4dKUS+UOOWBfBgAsjIjH3NBo41iGzNkMIpoQFhlEpAq9QY8jlTuFWG7KJrhp3ce4wr6xH4NG\n",
       "Ui6VO1QBh2yaliQJa9MeFmKlZw6iq/eOShkRkaOYUJHxzjvvYMGCBfD29kZGRgaKioomdPOGhgb4\n",
       "+/vD399/WkkSkfOpbCjG7a5W49hd64HspI0qZjR1vf0yShT9sGvYj+HSMuMBHy/T+HobcO6yevlM\n",
       "R+qibMzwCzGOB/U6FFbtVjEjInIE9ywyPvnkE7z44ot49dVXUVlZiaysLGzatAlXrlwZ9zqdToen\n",
       "nnoKeXl5XDJARAJZlnHg5N+F2LIlq+HnHaBSRtNTXA0MDpnGC+cAUbP5954r83CXkJMsxhy1L0Or\n",
       "dcPq1IeEWOHpXdANDqiUERE5gnsWGW+++SaeffZZPPfcc4iNjcXbb7+N8PBwbN26ddzrXn75ZSxd\n",
       "uhSPP/64Q04RE5H1nLtSZXb4nnJJhiNR9mNwqRQB5rNZjlpkAMDKxPXwHnE4X09/F06cOaBiRkRk\n",
       "78YtMnQ6HSoqKpCfny/E8/PzUVxcPOZ1O3fuxM6dO/Gf//mfLDCIyIxyFiNp4XLMmuG4WzEpm3q5\n",
       "dS0B5udlHKoADAbH/DfRy8PbbDnjoVNfwGDQq5QREdk7t/G+2NbWBr1ej7CwMCE+a9YsNDc3j3rN\n",
       "9evX8a1vfQvbtm2Dj4/PqK8ZTXl5+YRfS46P77frGX7P27ubUX+5UvjaHJ84h/2Z6O7XoLx+KQDT\n",
       "8qgZmtMoLx8a+yIX4qjvqyUY9ICv11L09GsBAG13gE931CImov8eV9qnIGkeNJIGBtkAAGjraMbf\n",
       "932MqJAlwutc+T13VXzPXceiRYsm/FqL7y719NNP44UXXsCyZcssfWsicgK1148L41kB8xAaMFel\n",
       "bKavstEPeoOpwFgQ1oeQQBYYBLhpgdSFXUKs/Jxj9h0BgI+nPxaEigeA1F47zhULRDSqcWcyQkJC\n",
       "oNVq0dLSIsRbWloQHh4+6jWHDh3C0aNH8dprrwG42+BpMBjg7u6OrVu34vnnnx/1uoyMjKnkTw5m\n",
       "+LcdfL9dx8j3vL3zJj4qPiN8/eG8p5EU7bg/D/9zXPyAtTHbmz/f4H/rw750XkZRrWnc2DYPGRmR\n",
       "6iU0TXMWzMIbH33fOG7rvobgCF8snBPP99wF8T13PR0dHRN+7bgzGR4eHkhPT8e+ffuEeEFBAbKy\n",
       "ska9pqamBqdPnzb+76c//Sm8vb1x+vRpPPbYYxNOjIicz6FTXxiXWgBA2Iy5SFjg2P84mfVjsOmb\n",
       "RlD2ZRw+Bej1jvub//CZkYifLzYdHajYplI2RGTPxp3JAICXXnoJTz/9NDIzM5GVlYXf/va3aG5u\n",
       "xrA8JGsAACAASURBVHe+8x0AwCuvvIKysjLs378fABAfHy9cX1paCo1GYxYnItfS09+Fktr9Qmxt\n",
       "+hZoJMc9E7S9U0ZlgxjLS1UnF7JPyTFAcADQ3nl33NENVDYA6XHq5jUda9O24MxFU3Vd01SKlvar\n",
       "KmZERPbonv+6P/HEE3jrrbfw+uuvIzU1FcXFxdi1axfmzZsHAGhubkZTU9O49+A5GURUVLUHukFT\n",
       "w2uA7wxkxOapmNH0HTkFjFyOnhIDhATx7zsy0Wgks9kM5ZbHjmbR3ETMm7VQiB069blK2RCRvZrQ\n",
       "rxBfeOEFXLhwAf39/SgrK0NOTo7xa++99964RcYzzzyDzs7O6WdKRA5LbxjC0codQixv6Wa4u7mr\n",
       "lJFl8HwMmgjlz4WjFxmSJGFt2hYhVlp3GH26bpUyIiJ75LjrFIjIYTTerEJXn6lZzNPDG9lJ+eNc\n",
       "4Rj2l4ljno9Bo7lP0XZ0tBIY0DluXwYALF2UheCAWcbxkH4QdddLVcyIiOwNiwwisiqDbEDtNXHb\n",
       "2uzEfPh4+qmUkWVcbpZx9rJp7KYFVrMfg0YRGwnMCTWN+waA4mr18rEErUaLNakPCbGzzeXQDTnm\n",
       "GSBEZHksMojIqq7cOouu/nbjWKPRIm/pZhUzsowCxSzGykTA35f9GGROkiSszxRj+5zgl/4rE9bD\n",
       "19t07segXoezN3goGxHdxSKDiKxGlmVUXz0mxDJiV2GGf4hKGVmOcqnUOp4/SuNYr/j5UP78OCIP\n",
       "d0+sUfzC4Mz1UugGB1TKiIjsCYsMIrKaukun0N7TLMTuS/+SStlYjsEg44CieVf5IZJoJGVfRsU5\n",
       "4FaHY/dlAEBOyiZ4engbxwNDvSipLVAxIyKyFywyiMhq9pX9RRgnL1yB8JmOe9rxsMoGoO2OaRzo\n",
       "B2Q48LkHZH2zZkhYusg0lmXggBOsLPLx9ENu8v1C7ODJbRjSD6qUERHZCxYZRGQV56/Voul6nRDL\n",
       "X/aYStlYlnI9/do0wM2N/Rg0PuWSOmVfj6NavXQz3LUexvHt7jaU1x9VMSMisgcsMojIKvaVfSaM\n",
       "46JSERkWo1I2lmXWj5E5+uuIRhqtL0OWHX/JVIBvEFYkrBNi+0/+DQaDXqWMiMgesMggIou73HIe\n",
       "9ZdOCbENTjKL0dsvo6hKjLEfgyYiJwXwNP3CH5eagfNX1cvHku5L3wJJMn2kuHn7Gk43nlAxIyJS\n",
       "G4sMIrI45SzGrIB5WDgnQaVsLKvwNKAbsdx8fjiwcI56+ZDj8PaUkJssxpxlyVRwwCxEhyYKsYLy\n",
       "z5xipoaIpoZFBhFZ1I1bl1HVKB6+lzQ3R6VsLE/5oXB95t1zEIgmQnlehjNsZTssYU6WML56swl1\n",
       "lypUyoaI1MYig4gsqqDsr8J4pm84IoKiVcrG8pQfCrlUiiZD+fNy8CQwNOQcv+0P8glB5Exxm7Xd\n",
       "Jz7hbAaRi2KRQUQW03rnBk6eKxRiifOyneY3/c23ZFSdN40lCVibrl4+5HiSY4DQINO4swcorRv7\n",
       "9Y4maW62ML7UfA71lytVyoaI1MQig4gspqDsM8iywTieHTwPkcGxKmZkWcqlUhlxQHCAcxRQZBsa\n",
       "jWS2la1yS2RHNtMvHIkLxG9wD2cziFwSiwwisoi2jmaU1h0SYuuXPeo0sxgAsEdsNTFbX080Ecol\n",
       "U8qfK0e3cfmTwvjCjXqcu1I1xquJyFmxyCAii9hX+hcYRsxizAqKQNriXBUzsiy9XsZexY6cm1ao\n",
       "kws5to2Kn5uyOqD1tvP8pj8yLAYJ8zOE2O4T/8PZDCIXwyKDiKat9c4Ns1mMDcufgFajVSkjyyut\n",
       "A9o7TeMZ/sDyePXyIcc1e6aE1MWmsSwDe51oyRQAbFz+hDBuul6HhqvVKmVDRGpgkUFE07av7DOz\n",
       "WYx0J5rFAIDdJeI4PxNwc3OepWBkW5tWiuM9JaO/zlFFzV6MJVFpQmz3iU9UyoaI1MAig4impfXO\n",
       "DZSZzWI8CY0TzWIA5uvmlUteiCZDudRub+ndJXnORNmb0XitlrMZRC6ERQYRTctovRjpi53n8D0A\n",
       "aGmXUV4vxlhk0HQsjweC/E3jWx0w+xlzdAvCYxEXuVSI7TnxqUrZEJGtscggoilrvXMDZfWHhZgz\n",
       "zmIoG77TY4GwYC6Voqlzc5OQr9hlapeTLZkCgI3LnxLGDVer0XC1RqVsiMiWWGQQ0ZSZzWLMmON0\n",
       "sxgAl0qRdSh/jpxtK1sAiI6IQ+y8FCG2s+RP3GmKyAWwyCCiKRltFmNj5hNON4uh18tmh6Upm3aJ\n",
       "pkJZZJTXO9dWtsM2rfiyMG66Xoe6S6dUyoaIbIVFBhFNya7jfzabxUhzwlkM5da1wQHcupYsY/ZM\n",
       "CWmxprEzbmUL3J3NiJ+fLsQ4m0Hk/FhkENGkXWu9iIqzhULMGWcxAGBXsTjOzwS0WvZjkGUoZzOU\n",
       "WyU7iwdWfkUYX7nZiKpGJ1wfRkRGLDKIaNJ2lvwJMky/hYyYGYW0WOc6F2MY+zHImsy2sj3hfFvZ\n",
       "AsC8WQuREiOuM9xZ8jEMBr1KGRGRtbHIIKJJabpej5oLZULsgayvQiM5318nzbdknDwrxjYsVycX\n",
       "ck7KrWzbO4ETZ9TLx5ruX/EVSDDNAja3X8HJc4XjXEFEjsz5PhUQkdXIsowdxR8KsfnhsUhcsGyM\n",
       "KxzbjmPiOCOOW9eSZbm5SdiQKca2F6mTi7WFz5yHjLg8Ibbr+J+h1w+plBERWROLDCKasPrLlTh/\n",
       "rVaIbc76GiTJOT94Kz/sbXa+vnayA8qfK2ctMgBg04qnhN6tWx0tOH7mgIoZEZG1sMggogm5O4vx\n",
       "kRCLi1yKRXOTVMrIunr7ZRSIq8LwsHO2nZDKNq0A3EbsmXDmInD+qvP1ZQBASOBsrIxfJ8T2lH6K\n",
       "wSGdShkRkbWwyCCiCTl9vgRXbjYKsQezvqZSNta3vwzoH/G5J2o2kLRQvXzIec0IkLBqqRj7woln\n",
       "M/IzH4eb1t047ui+hcKqXSpmRETWwCKDiO5Jb9BjZ8nHQiwlZiUiw2JUysj6Pv//27vv+Cjq9IHj\n",
       "n9nd9F4IJCH03pHQQToSQUCQZsFyShEURU/lTs+fnqcottMDzgbiKR1FpEdapBO69N4TQjrp2Z3f\n",
       "H0sSJgUCZDOb7PN+vfa1O8/MbB4ddneemW8ppqlUZW0WJvTnSE2m/LwC6dIiQhNbs3MRaZmpOmUk\n",
       "hLAFKTKEELe188gGYhMv5i8riqHIuPeVidmssrzQSd5A6Y8hbOihztrlzQcgPrlyNpkC6Nv2EVyd\n",
       "3fOXM7LSiNy1RMeMhBBlTYoMIcQtZeVksmLbT5pYu8Y9qOYfplNGtrfzCMQlFSx7e1CkOYsQZalO\n",
       "qEKzOgXLZjOsqsRz1Xm6edMnfKgmtmn/cuJTYnXKSAhR1qTIEELc0vo9v5KSlpi/bDI6EdF+pI4Z\n",
       "2d6yQkP3P9gRnJ2kqZSwLUdqMgXQrfUAfD0D8pfN5twizTKFEBWXFBlCiBKlpCWybvcvmlj31gPx\n",
       "966iU0blQ4auFXooPHrZ6u2QlV15m0w5m1yKNLuMPrqJC1dP65SREKIsSZEhhCjRyu3zyM7JzF/2\n",
       "cPOmT/gQHTOyvZMXVQ6fLVg2GaGfzPItykF4I6hWcGGf1HTYuFe/fMpD20bdCQmoqYn9uvl7VLXy\n",
       "FldCOAopMoQQxboSf55th37XxCLaj8TNxUOnjMpH4aFD729lHWJUCFszGBQGFOoAXpmHsgUwGIwM\n",
       "7PKkJnb8wgGOnt+nU0ZCiLIiRYYQoli/bp6Dqlryl4N8Q+jcrK+OGZUPaSol9FR4FLPfNoPFUrmv\n",
       "6jeu2ZoGYS00sV83z8FiMeuUkRCiLEiRIYQo4tj5/Rw+u1sTG9hlNEajSaeMykdsgsof+7UxGbpW\n",
       "lKde4eDuWrB88SrsOqJfPuVBURQGFbqbcfnaWXYcXq9TRkKIsiBFhhBCw2Ixs/SP2ZpY3ZAmNK9T\n",
       "+TsmLI0CS8HNG1rVh9oh0lRKlB83F4UHO2pjizfok0t5CguqS3jDbprY8q0/kpGVplNGQoh7JUWG\n",
       "EEJj55GNXLp2VhMb3PUph5jt+ueN2uWhPXRJQzi4od21y0s24hAdoQd0ehwno3P+cmpGMmt2LtIx\n",
       "IyHEvZAiQwiRLyMrjd+2/KCJtWnQlZrVGuiUUfmJT1ZZv0cbK3yyJ0R56N8JXAvOtTl7BfYc0y+f\n",
       "8uLvXYVe4Q9rYpv2Ledq4iWdMhJC3AspMoQQ+VbvWEBqRnL+spPRmQGdH9cxo/KzbLN1luU8TWtD\n",
       "o5qV/+6NsD+e7goRHbSxRQ7QZAqgd5sh2gn6LLn8Uqj5phCiYpAiQwgBQEzCBTbtX6GJ9Qp/mADv\n",
       "qjplVL6WFDqJG9JdlzSEAIo21VuywTGaTDk7uTCoy1Oa2KEz0Rw+u6f4HYQQdkuKDCEEqqqyZOO3\n",
       "miEj/byq0LtN5Z54L0/ydZXIXdrYI9IfQ+hoQGdwdipYPnUJ9p/QL5/ydF+DLtQJbqyJ/RI1C7M5\n",
       "V6eMhBB3Q4oMIQQHT+/g2AXt2K2Duz6Ns5OLThmVr9+2QM5N5y/1w6BZHf3yEcLbQ+GBdtrY4o26\n",
       "pFLuFEVhSLe/oFDQXDE28SJRB1bqmJUQ4k5JkSGEg8vOzeLnqFmaWIPqzWlVr2MJe1Q+hUeVGtIN\n",
       "hxhNS9i3wk2mFq93jCZTADWq1qN9016a2Ort80lNT9IpIyHEnZIiQwgHt373UhJSruYvGxQDQ7o9\n",
       "6zAn2cnXVVZt18akqZSwBwO7gNNN818evwB/ntYvn/I2oOPjuDi75S9nZKfz6+Y5OmYkhLgTUmQI\n",
       "4cASUuKIjF6iiXVt+SAhgTV1yqj8/bIJsrILluuEwH0N9ctHiDy+Xgp92mpjixxoEmxvD1/6tRuh\n",
       "ie08soGTlw7plJEQ4k5IkSGEA1uy6RtycgvOsD3cvInoMFLHjMrf/N+1yyP7SFMpYT8KN5lauM5x\n",
       "mkwBdG81gOCAGprYwvX/Jdeco1NGQojSkiJDCAd14NR2Dp7eqYk91OkJ3F08dcqo/F1NVFm3Wxsb\n",
       "1VufXIQozqCuRZtMOcLEfHmMRhPDe4zVxGISLrBhzzKdMhJClJYUGUI4oMzsDBZt/EYTqxXckA6F\n",
       "OlpWdovWayfga14XmtaRuxjCfvh7F52Y76e1+uSil7qhTWnfpFAn8J0LiE+J1SkjIURpSJEhhANa\n",
       "se0nkq/H5y8bDEZG9hyPQXGsr4QiTaXkLoawQ6P6aJcX/A5ms+M0mQIY1OVJ3F298pdzcrNZsvFb\n",
       "HTMSQtyOY51RCCE4H3uSqP3a8eZ7th5ESGAtfRLSyfkYlS0HtDEpMoQ9eqgLeBYMssSVeNi4V798\n",
       "9ODp5s3AzqM1sT/P7OLAqR06ZSSEuB0pMoRwIGaLmfnrZ6CqlvyYv3cQ/dqPuMVeldP8ddrlDk2h\n",
       "dog0lRL2x91V4eFu2tjcSH1y0VOHpr2oFawd+m3Jxm/Iys7QKSMhxK1IkSGEA/lj/0ouXtUOtD+8\n",
       "x1iHmdn7ZvMKtWsf2af47YSwB4/21S4v2QCZWY7VZMqgGBjRQ9usM/H6NZZv+0nHrIQQJZEiQwgH\n",
       "kZgax4pCP8b3NehCk1ptdMpIP/uOq+w/WbBsMMAwmYBP2LFebSDIr2A5JQ1WbtMvH72EVqlF99YP\n",
       "aWJR+1Zw+vIRnTISQpREigwhHICqqsxbN4OsnMz8mJuzOw/f/4yOWelnzirtct92EBwoTaWE/TKZ\n",
       "FIYXGvztxzX65KK3iA6jCPCumr+sojI38kuyc7N0zEoIUZgUGUI4gO2H13H0nLan6IDOT+Dj4a9T\n",
       "RvrJyVWZW6ip1OgIfXIR4k48WqhJ3/ItEJfoWE2mAFycXBnVe4ImdjXpMqu3L9ApIyFEcaTIEKKS\n",
       "S0yN45eoWZpY3dCmdG7+gE4Z6WvVNohLKlj28bROeCaEvWvfFBreNPl1rtnx5szI0yCsBZ2aaTuq\n",
       "rNuzlHMxJ3TKSAhRWKmLjBkzZlC7dm3c3NwIDw9n8+bNJW67ceNGBg0aREhICB4eHrRs2ZLZs2eX\n",
       "ScJCiNLLayaVmZ2eH3M2ufBo74kONydGnh8KNZUa3gvcXKSplLB/iqLw5IPa2PcrrZ9zRzSoy5P4\n",
       "egbkL6uqhbm/f0muOUfHrIQQeUp1lrFgwQJeeukl3nzzTfbt20enTp2IiIjgwoULxW6/bds2WrZs\n",
       "yZIlSzh06BDjx49nzJgxzJs3r0yTF0LcWnHNpB7q/ARVfIN1ykhf8ckqv23Rxp6UplKiAhndzzpQ\n",
       "QZ4DJ2Hvcf3y0ZObiwcjeo7XxK7En2ftrsU6ZSSEuFmpioxPP/2Up59+mr/85S80bNiQL774guDg\n",
       "YGbOnFns9lOmTOHdd9+lY8eO1KpVi3HjxjFkyBCWLFlSpskLIUpWUjOpri0fLGGPym9eJOTkFizX\n",
       "D4OOzfTLR4g7FVJF4YF22tjsFfrkYg+a1g6nXWPt0HBrdy3mYtzpEvYQQpSX2xYZ2dnZ7Nmzh759\n",
       "tW0f+/bty9atW0v9h5KTk/H3d7xOpkLoQZpJFe977UTnjI6wNkERoiJ5qr92eV4kZGU7ZpMpgIfv\n",
       "fwYvd9/8ZYvFzA+rP5PRpoTQmel2G1y7dg2z2UzVqlU18aCgIGJiYkr1R5YvX8769etvWZRER0eX\n",
       "6r1E5SDH27aOx+wp0kyqZVh3zp28xDku6ZKT3sf8yAV39hxrnL+sKCotgw8SHS3tt21J7+NeGYW6\n",
       "K3i7tyAl3foTnpACn805Re/WSbfZs3zocczb1OjNxqMFzaRiEi7w3c+f0LZO31vsJcqKfM4dR/36\n",
       "9Uu9rc0vaW7ZsoXHHnuML7/8kvDwcFv/OSEcXnJ6PNFnIjWxqt41aBTs2J+/pVsDNcsdGqVQzV8K\n",
       "DFHxOJtU+oUnaGLLtgeWsLVjqBHQiLpBLTSxI1d2cjnxlE4ZCSFueycjMDAQo9FIbGysJh4bG0tw\n",
       "8K07j27evJn+/fvzz3/+k7Fjx95yWylAHEPe1Q453raRa87hs4VvkGspOHl2dnJlzMNTdOvsbQ/H\n",
       "PDVNJVJ7Y4e/jvaRf4c2ZA/HvTJ73VtlYVTB8o5jPvgHt6FOqH7N//Q+5k2bN+GjuS8Tn1JwvrLz\n",
       "3GqmdPk3Hm7euuRU2el9zEX5S05OLvW2t72T4ezsTJs2bVi7VjsYd2RkJJ06dSpxv6ioKB588EHe\n",
       "eecdXnzxxVInJIS4e6u2z+fCVe2Vu6HdnnXY0aTyzPsdrmcULAcHQP+Sv76EsHutGyiENypYVlX4\n",
       "epl++dgDNxd3nnjgJZSb+p2lpCUyf90Mhx3mVwg9laq51OTJk/n+++/57rvvOHLkCJMmTSImJoZx\n",
       "48YB1tGkevfunb/9xo0biYiIYPz48YwaNYqYmBhiYmKIi4uzzX+FEIKTlw7xe/TPmljLeh3p0KSX\n",
       "ThnZj69/1S4/MwCcTNLhW1Rs4x7WLs9a7tgdwAHqhDSmb9uhmtj+U9vZeWS9ThkJ4bhKVWQMHz6c\n",
       "zz//nPfee4/WrVuzdetWVq5cSVhYGAAxMTGcPl0wXNycOXPIzMxk2rRpBAcHExISQkhICO3bt7fN\n",
       "f4UQDi4tM5X/rfkclYITDB8Pf0b2HO/woyftPqqy51jBsqLAswP1y0eIsjKyt3XG+jzXkmDJRt3S\n",
       "sRv92o2gRlA9TWzxxm+IS7qiU0ZCOKZSd/weP348Z86cITMzk127dtGlS5f8dbNnz9YUGbNnz8Zs\n",
       "NmOxWDSPm7cRQpQNVVX5KfJLElO1dwof7ztJ2iEDXxW6i9GvPdSs5tiFl6gc3F0VRheaTPKrpfrk\n",
       "Yk+MRhOj+72Ms8klP5aVk8mslR+Rk5utY2ZCOBbHHTBfiEpi497f+PP0Tk2sR+uBNKzRUqeM7Edi\n",
       "ispcbXcyxgzWJxchbGFcoX/Pf+yHP087dpMpgCC/UB6+/xlN7FLcGX7e9J1OGQnheKTIEKICOxdz\n",
       "nGVbftDEalStz0Odn9ApI/vy7W+QnlmwHFoF+nfULx8hylrjWgrdWmtjM3/RJxd706lZX1rV147w\n",
       "sOXPNUQf3aRTRkI4FikyhKig0jOvM3vlNMyW3PyYm7M7T0e8isnopGNm9iE3V2X6Em3s+SFgkg7f\n",
       "opIpfDfjh1WQlCp3MxRFYVSvCVTx0Y6uN3/9TGITLuqUlRCOQ4oMISogi2rhx8gvSCjUD+PRPi8S\n",
       "4FNVp6zsy69/wPmbpvdxdYYxg/TLRwhbebibdVjmPGkZ8I2DD2ebx83Fg6f7/1Vz4SX7Rv+M7Jws\n",
       "HTMTovKTIkOICihy1+Ii/TC6tRpAy3oddMrI/nyxSLv82AMQ4CN3MUTl4+ykMEE7aiv/WQI5uXI3\n",
       "A6B6lToM7fasJnYl/jyLNn6tU0ZCOAYpMoSoYA6f3c3KbfM0sRpB9RjY+UmdMrI/e4+r/LFfG3tx\n",
       "mD65CFEexg4Gt4LBlLgQK8PZ3qxTs760aXi/Jrbj8Dq2HFyjU0ZCVH5SZAhRgcQlXWHO6k8182F4\n",
       "uHrxTP/XcDJJP4w8XyzULvdsA83ryl0MUXkF+Cg80U8b+3wBMtP1DYqiMLLneKr6VdfEF2/8htOX\n",
       "j+iUlRCVmxQZQlQQWTmZfLd8KhlZafkxRTHwVMSr+HsH6ZiZfbkQqzI3UhuTuxjCEbw0Qru88zBs\n",
       "+1OfXOyRi7MbTz/4V838GWZLLt+t+JDE1Gs6ZiZE5SRFhhAVgEW18NPaL7gcf04TH9j5CZkPo5BP\n",
       "50NOwYBb1KsO/TuVvL0QlUWjmgoPFhqi+ZO5+uRir0ICa/JY30maWGp6Et8tn0p2rnQEF6IsSZEh\n",
       "RAWwavs89p3cqom1rt+ZnvfJzHI3u5akFhlV56+PgdEoTaWEYyh8N+OXKDh8RppM3ax1/U70bau9\n",
       "vXn+6knmr5shzcuEKENSZAhh53Yd3cSandqhkoIDavBo74koipw83+w/S7ST7wUHwOh+JW8vRGXT\n",
       "Kxzua6iNTf2fPrnYswc7jqJp7XBNLProJtbuWqxTRkJUPlJkCGHHTl8+ytzfv9TEPN18GDPw77g4\n",
       "u+mUlX26nq7yZaFha18eCS7OUogJx6EoClOe0Mbm/Q6nL8kV+psZFAOjH3iZIL9QTXzFtp/YfSxK\n",
       "p6yEqFykyBDCTsUnx/Lt8g8wmws6GJiMTjw7YAoB3jLhXmHfLIPE1IJlXy8YK5PvCQf0cDdoXKtg\n",
       "2WyGD3/SLR275ebiwZiH/oa7i6cm/mPkF5y6dFinrISoPKTIEMIOpaYnM2PpO1zPSNbER/WeSJ2Q\n",
       "RjplZb8yslQ+LtTBdcIQ8PKQuxjC8RgMClNGa2NzVsKlOLmbUViQXyjPPjQFo8GUHzObc/l2+QfE\n",
       "JV3RMTMhKj4pMoSwM1k5mXy97D3iki5r4g+0G07bRt10ysq+zfwFrsQXLLu5yLC1wrGN7AV1QgqW\n",
       "s3PgI7mbUax6oU0Z1XuCJpaWmcrMpe+QkpakU1ZCVHxSZAhhR8wWM9+v/JhzsSc08TYNuhLRYaRO\n",
       "Wdm36+lqkY6tE4ZCFT+5iyEcl8mk8Nrj2thXS+F8jNzNKE67xj3o1147NNe15Bhm/vqOZm4iIUTp\n",
       "SZEhhJ1QVZUF62Zw6Gy0Jt4wrCWP9X0RgyIf1+J8uRiu3XSx0dMNXntMv3yEsBdPRkDYTd23snPg\n",
       "3dn65WPvItqPpG2j7prYpbgzfLP8A3Jys/VJSogKTM5ahLADqqryS9Qsth9ep4mHVqnNM/1fx2R0\n",
       "0ikz+5aUqjKtUF+MScMh0FfuYgjh4qzw9jPa2JxVcOyc3M0ojqIojOo9gcY179PET178kzmrP8Vi\n",
       "MeuUmRAVkxQZQtiBldvnsXHfb5qYv3cQ4wf9AzcXd52ysn+fLYCkQiNKvTJKv3yEsDej+0HDGgXL\n",
       "ZjO8/a1++dg7k9GJZ/q/Rs1qDTTxA6e2M/f3/2BRLTplJkTFI0WGEDqLjP6ZNTsXamKebj6MH/w2\n",
       "3h5+OmVl/65cU/l0vjY2eST4esldDCHymEwK7z6njS1cD3uPy92Mkrg4uTJu4JtU9a+uie88soEF\n",
       "62ZKoSFEKUmRIYSONu1bzm9bftDE3F08mfDwO1QtNEmU0HrrG0jLKFgO8IFJMqKUEEUM7Q6ttRfm\n",
       "eWOGtZmmKJ6HmzfPD/4//LyqaOLbDkWyeOM38v9OiFKQIkMInWzYu4wlm7TtFlycXBk/+B+EVqml\n",
       "T1IVxP4TKrNXaGP/9xeZF0OI4hgMCu+N0cYid8HyLfrkU1H4eQUycci7+Hj4a+KbD6zil6hZUmgI\n",
       "cRtSZAihg3W7f+GXqFmamJPJmbGD3irSFlhoqarKK1/Czb/vjWrCGJndW4gS9esAPdtoY698CVnZ\n",
       "cqJ8K1V8g5k49J94uftq4hv3/caSTd9I0ykhbkGKDCHK2dqdi/h18xxNzMnozLMDplAvtKlOWVUc\n",
       "K7bC+t3a2McTwckkdzGEKImiKHw2CQw3/eqfvAhfLNIvp4qiql8oE4e8i4ebtyYetX8l83+fLqNO\n",
       "CVECKTKEKCeqqrJ8608s36addtfJ5MyYgX+ncc3WOmVWcWRmqUz+Qhvr0xYiOuqTjxAVSfO6SpE7\n",
       "fu99D7EJcjfjdoIDajDx4XfwcPXSxLcfXsf/1nyO2ZyrU2ZC2C8pMoQoBxaLmYXr/8vaXdrLhs5O\n",
       "rowb9BYNa7TUKbOK5f0frFdf8xgM8PEL1qu0Qojbe/dZ61DPeVLTrZ3Axe2FVqnNC0PfK9J0avfx\n",
       "P5i18iOyc7N0ykwI+yRFhhA2lpObw+xVH7PlzzWauIuTK+MH/YP61ZvrlFnFcvScyoc/amNjB1uv\n",
       "zgohSifQt/gJ+tbvlrsZpRESWJNJj/wLX88ATfzg6Z3M+Pn/SMtMLWFPIRyPFBlC2FBGVhpf/fou\n",
       "+09u08TdXb2YMORd6oY20SmzikVVVZ6fBjk3tUioFgDvj9UvJyEqqueHQNPa2tjYDyEjSwqN0gjy\n",
       "C2XSsPcJ8KmqiZ++coTPF00hISVOp8yEsC9SZAhhI/EpsXy+aArHLx7UxH09A3hp2PvUklGkQPHs\n",
       "NAAAHSJJREFUSu1/q2HjXm3ssxfBx1PuYghxp5xMCl+/ATe3Mjx1Cd6dVfI+QivAuyqTHnmf4IAa\n",
       "mnhswkU+W/g6l+LO6JSZEPZDigwhbOBszHE+nf8aV+LPa+JV/arz0rCpVPMP0ymziudynMrL/9bG\n",
       "+raD4b30yUeIyqBjM4XxD2tjH8+zzkEjSsfXM4BJw96nbqFRAZPTEvhs0RQOnNqhU2ZC2AcpMoQo\n",
       "Y3tPbOHLxW+SmpGsides1oBJw97H37tKCXuKwlRV5dmpkHhTM2cXZ5j+inT2FuJevT8OQm/6OjKb\n",
       "4el/ydwZd8LdxZPnB79Nq3qdNPHsnEy+Wz6VyOifZdI+4bCkyBCijFgsZn7b8j9mr5xGjjlbs65V\n",
       "/U68MPSfeBYaZ13c2jfLYPV2bezdZ6FudSkwhLhX3h4K01/RxvadgH98q08+FZWTyZmnIl6hW6sB\n",
       "mriKym9bfuCnyC/Iyc0uYW8hKi8pMoQoA2mZqfx32XtERi8psq5v20d4KuJVnE0uOmRWcZ26aJ3Z\n",
       "+2ZdW8LkkfrkI0RlNLCrwqg+2tjHc2HjHrn6ficMBiNDuz3LsO5jMCjaU6udRzbw2aI3iE+O1Sk7\n",
       "IfQhRYYQ9+hi3Gk+nvcqR89peyYbDSYe7f0CAzo9XuRHR9xado7KE+9CWkZBzMMNZv8djEa5iyFE\n",
       "WfrPZAi7aaAkVYUn34OkVCk07lTXlg8yfvDbuLl4aOIXr55m2rxXOHQmWqfMhCh/cuYjxF1SVZWo\n",
       "/Sv5dMHrxKdor1B5u/vxwtD36NBUeiffjddnwPZD2tinL0KdUCkwhChrft4K3/9dO9rUhVh4birS\n",
       "n+AuNKzRkldGfESQb4gmnp51na+WvceKbT9htph1yk6I8iNFhhB3IT3zOt+t+JDFG78m15yjWVc7\n",
       "uBF/ffQT6oQ00im7im3JBpV/L9TGBnSGZx/SJx8hHEGPNgqvjNLGlmyET+bpkk6FF+QXyisjp9Gi\n",
       "bvsi69bsXMQXi//OteQYHTITovxIkSHEHTp56RAfzn2ZA6e2F1nXpXk/Xhj6T3w8/HXIrOI7eVHl\n",
       "Lx9oYzWqWptJyWhSQtjWP5+D1oWm73ljJmyQ2cDvipuLB3/p/wYDO49GKdRk9syVo3w492V2Htkg\n",
       "d4tEpSVFhhCllJ2bxc9Rs/hy8ZskpmpndHVxduPJfpMZ3nMcJqOTThlWbMnXVR5+A1LSCmJOJlj4\n",
       "HgT4SIEhhK25OCss/hf4eRXELBYY+Q+4eFVOhO+Goij0Dh/CxCHv4OXuq1mXlZ3Bj2v/zferPiY9\n",
       "87pOGQphO1JkCFEK52JOMG3uK2zcuwwV7Y9tjaB6vDbqU9o0vF+n7Cq+3FyVEW/BoUKT5H48Edo1\n",
       "kQJDiPJSO0Thx7e1/TPikmDga5CaJoXG3apfvTmvP/o5TWuFF1m398QWPvhpEgdP79QhMyFsR4oM\n",
       "IW4hMzuDnzd9x6cLXyc28WKR9T1aD+Sl4R9QxTdYh+wqB1VVefFzWFvo93VEL5j4iD45CeHIIjoq\n",
       "vP2MNrbvBIz4h/WCgLg73h6+jBn4d4b1GIuTyVmzLvl6PN/89j6zVnxEclqCThkKUbZMeicghD1S\n",
       "VZUDp3awZNM3JF2PL7Le36sKj/V9kfrVm+uQXeXy2QL47y/aWPsmMEv6YQihmzefgj3HYNnmgtjq\n",
       "7fD8J/DVa6p8Nu+Soih0bRFB/erN+GH1Z1yMO61Zv+/kVo6d38egrk/TsWlv+f8sKjS5kyFEIQkp\n",
       "V/n6t3/x3YqpxRYYnZr14Y3Hv5ACowx8u0zl1UIT7tWoCks/BDcX+XEVQi8Gg8JP/wdtGmrj3y6D\n",
       "d2bpklKlUs0/jMkjPqRv20eKzKOUkZ3O/HXT+WLJm0WKECEqErmTIcQNmdkZrNv9C+v3LCUnN7vI\n",
       "en/vIIb3GEuTWm10yK7ymRepMvYjbczLHX6bBlX9pcAQQm8ebgq/TVPpOAbO3TTa6ruzwMmk8vcn\n",
       "5XN6L0xGJwZ0epxW9Tsx//cZnL96UrP+1KVDTJv7Ch2a9qZ/x8fw9vAt4Z2EsE9SZAiHZ7aY2XF4\n",
       "HSu2zSU1PanIeoPBSM/Wg+jXfgTOTi46ZFj5/LxRZfQ/rTML53F2giXvQ/O6cuIihL2oFqCw8hOV\n",
       "zuMgKbUg/tbX1kLjtcfk83qvqlepw8sjPiRq3wpWbPuJ7Nys/HUqKtsORbLnxGYeaDuMbq0ewskk\n",
       "IxiKikGKDOGwVFXl8NndLNvyA1fizxe7Te3gRozoOZ6QwJrlnF3lNWeldS4Mi6UgZjLCovegd1s5\n",
       "YRHC3jSupbDyY5UHXobU9IL4GzOsHcGnjJb+U/fKaDDS476BtKjbnkUbvuLwuT2a9VnZGSzb8gOb\n",
       "D66mX7sRtG3cHaPBqFO2QpSOFBnC4aiqypFze1i1YwHnYo4Xu42Xmw/9Oz1Oh6a9irSXFXfvi0Uq\n",
       "L32ujSkK/O8f8FAXOUkRwl51aKaw4mOViFcgLaMg/ubXEJsIn70oo06VhQCfqowd9BaHz+7ml6hZ\n",
       "XE26rFmfkHKVub9/SWT0Evq1H0GbBl0wSLEh7JQUGcJh5N25WLVjAedjTxS7jZPRmR73DaJ3+BBc\n",
       "nd3KOcPKy2KBv/1XZer/tHGDAb6bAiN6S4EhhL3r0lJh+TSVB1+BjIIWPXy5COISYWKEgrNJio17\n",
       "pSgKTWuH06hGK/44sIpVO+aTkZWm2SYu6TL/W/MZa3ctol+7EbSq30nubAi7I0WGqPTM5lz2ntjC\n",
       "hr3LuHD1VLHbKCi0bdyd/h0fw88rsJwzrNzSMg28/WNtog5q485O8NPbMLSHFBhCVBTdWius+lRl\n",
       "0OuQfNMk1fN/h8OnGjD16eK/Y8WdMxpNdG/9EOGNurF6x3y2HFyL2ZKr2SY24SJzVn/C8q0/0r31\n",
       "Q3Ro0gsXuUAm7ISiqqpulx2Sk5PzX/v4+OiVhihH0dHRAISHF531tKylZaay9eBaog6sJLmYoWjz\n",
       "NKvdlogOowgLqmPznBzN6Usq/Salc/KKuybu7gq/fAB92kmBUVmV52ddlL8DJ1X6TYaYQl+tVXyy\n",
       "+fUjZzo0k892WUtIucqanYvYcXgdFtVS7DbuLp50adGP+1v2x9vDz+Y5yefc8dzJubsUGaJclccX\n",
       "0oWrp9n651p2HdmgGaWjsOZ12tGv/QjCguraLBdHNv93lXEfQYr2Lj9V/WHpVGjfVE5CKjM5+aj8\n",
       "zl5R6fcyHL+gjTs7wUcTYOJQ63wbomzFJV1hzc6F7Dq6CbWEYsNgMNKiTns6N3+A+mHNbda3UD7n\n",
       "jkeKDGG3bPWFlJ51nd3H/mDboUguXr315EUt6nagX/vhVK8idy5s4Xq6youfw/criq5r3cBaYIRV\n",
       "lROPyk5OPhxDQorKo2/D2p1F1z3QHmb9DYID5fNuC7GJl1i/eyk7j27AbM4tcbsqPsF0at6Xdo17\n",
       "4uVetuda8jl3PFJkCLtVll9IZnMuR8/vY/fxP9h/cluxE+jlcTa50K5JT7q3GkCQX+g9/21RvJVb\n",
       "VZ7/GM7HFl03rKf1hMPDTU44HIGcfDgOs1nlb1/BtJ+KrgvwgU9fhMcfkGFubSUlLZGo/SvZfGAV\n",
       "6VnXS9zOYDDSuEZrwhvdT/M67ctk3if5nDueOzl3l47fokKxWMycunyY3cf+YN/JbaRnpt5yex/P\n",
       "AO5v2Z9Ozfrg4epVTlk6nivXVF79D8yLLLrO2WRh0uCLTH2phpxkCFEJGY0KHz4Pvk6n+GBBDa5n\n",
       "FJxaxCfDk/+03tmc8apKw5ryHVDWvD38GNDpMfq0Hcr2Q7/zx4FVXE28VGQ7i8XMobPRHDobjbOT\n",
       "Ky3rduC+Bl1oENZSJvgTNiFFhrB72TlZHLuwn4Ond3LoTHSxs3LfTEGhcc3WdGzWh2a122I0yj9z\n",
       "W0nLUPlkHkybqx07P0+jmvDmiKM0CM1AUWRCQyEqsz6tE2lWM41Pfm1O1D7tug17oOWT8PwQlb+N\n",
       "hkBfKTbKmouTK91aDeD+lv05eelPthxcy/6T24qMSAWQnZPJrqMb2XV0Iy5OrjSp1YYWdTvQpNZ9\n",
       "uLl46JC9qIzk7EvYHVVVuZYcw/ELBzh0Jppj5/eTYy65KVQeP68qdGjamw5NeuLnVaUcMnVcmVkq\n",
       "s1bABz/Apbii6w0GeGkEvPMXOHKomOpDCFEpBftns+4L+GQ+vP0tZN301Z2dA58vgFnL4a+Pqbzw\n",
       "CHh7SLFR1hRFoX715tSv3pzU9CR2HF7PjiPriU24WOz2WTmZ7D2xhb0ntmA0mKgX2pSGNVrSqGYr\n",
       "QgJryYS04q5JkSHsQkpaIscuHOD4jUdiajFnrsVwd/WiVb2O3NegK/VCm8jMpzaWkqby3W/w8Vy4\n",
       "UsKowK3qw9evQ3hjOXkQwhEZjQqvPQZDuqlM/KRop/CUNHjra+v3yPNDVCYNhyA/+b6wBS93X3qH\n",
       "D6FXm4e5GHeG3cc2sfvYHySnJRS7vdmSy7EL+zl2YT/LtvyAp5uPteCo0ZIGYS3kAp64I1JkiHKn\n",
       "qipX4s9z5soxzsYc48yVoyVeYSmOi7Mbzeu0o02DrjSs0RKTUdqS2trBUyozfoYf1xTfLAog0Bfe\n",
       "fgbGDAInk5wwCOHo6lW3Tty3YB28PgMuFBoQIvm69W7op/NhWA+V5wZCl5bSQdwWFEUhLKgOYUF1\n",
       "GNh5NCcvHWLvia0cPLWDlPTEEve7npHM7mNR7D4WBVhbDNQObkTt4IbUCWmMRbXInQ5RIhldStiU\n",
       "qqokpFzl0rUzXLx6hv3Hd3It9TI55pLnryiOn1cVmtdpS7Pa7ahXvakUFuUgNkFl0XrrTL5bD5a8\n",
       "nYszvDgM/jYafDyLnhzI6COOSY6747nVMc/MUpn+M7w/BxJvMV5Ho5rwdH/raHS1gqXYsDWLauFc\n",
       "zAkOnNrOgVM7iEu6fEf7mwxOBHqF0KRuK0KrWIuYIN8QaVVQickQtkIXaZmpXE28REz8BS5dO8ul\n",
       "uDNcvnaWjOz0O34vk9GJOiGNaRDWgqa1wgkJrClXt8rBmcsqq7bDL5usHTUtxc/zBFhn7R73MLwy\n",
       "8tbj4MvJpmOS4+54SnPME1NUvlwMXy62jjx1K20bwyM94KEu0LCG3OGwNVVViUu6wrHz+zh2YT/H\n",
       "Lxwk8y5+v51NLoQE1qJ6ldpUC6hBVb9QqvmH4e3hJ8ewEpAiQ9hMVnYGCalxxCVdJjbxMlcTL+U/\n",
       "0m4znOytKIqBGkF1aRDWggZhLagd0ghn072P4S1uLTZBZetB2LQXVm8vOnNvcUIC4dmBMGEIVClF\n",
       "O2o52XRMctwdz50c87QMlW9/gy8WwZlSXDwPqwp92lofnVtA9SA5WbU1s8XMuZgTHD2/l+MXDnA+\n",
       "9iS55py7fj9XZ3eq+oVS1b86QX6hBPmGEOBTFX/vINxdPKUAqSCkyBB3JSc3m9T0JJLTEklJSyAh\n",
       "JY6E1KskpsbdeB1323kpSsvdxZNa1RpQK7ghtao1pGa1+jJsno0lpaocPAUHTsGuw7DlIJwqOpR6\n",
       "iXrcB88PgYFd76zPhZxsOiY57o7nbo65xaKyLhq+WQZLoyDXXLr9QqtAh6bQoRnc1wCa1SndRQ9x\n",
       "93Jyc7gYd4rTl49y5soRTl8+yvWM29yOKiUXZzcCvILw9y54+Hj44+Ppj7e7Hz4efrg4u5XJ3xL3\n",
       "pswn45sxYwbTpk0jJiaGpk2b8vnnn9OlS5cStz948CATJ05k165d+Pv7M3bsWN56661Spi/Kgqqq\n",
       "ZOdkkpZ5nfSsVNIzr1sfWddJy0glNT2JlPQkUtITSU2zPmdkpdkkF1dnd0Kr1CY0sBa5aQaqeFWn\n",
       "Z9e+ctXCBrKyVc5esRYPpy7B6ctw8iIcPFX8LNy307IejOgNI3pB7RA5XkKIsmUwKPRpB33aQUy8\n",
       "ysL1sGg9bDlw6/0uxcGSjdZHnqr+Ks3qQONaUCfE+qgdArWDwdNdvr/ulZPJ6Uan70bAYFRVZcPm\n",
       "SOKvX8HFS+FC3Ckuxp0hLSPljt87KzuDy/HnuBx/rsRtXJxc8fbwx9vDWnR4ufvi4eqFh6sX7vnP\n",
       "nni4eeHh6o2Lk6ucZ+jstkXGggULeOmll5g5cyZdunRh+vTpREREcPjwYcLCwopsn5KSQp8+feje\n",
       "vTvR0dEcOXKEp59+Gg8PDyZPnmyT/4iKzmwxk5ubTa45hxxzjvU5N4ec3CyycjLJzskkKyeTzOwM\n",
       "snIyrMvZ1lhWTgZZ2RnW9TkZZGSmkZ5lLSiKm4DHlkxGJ6r4BhPkG0JwYE2qV6lNaGBt/L2D8j/o\n",
       "eVe65INfOtk5KompkJRq7SyZdN36HJ9sHUL2SjzExMOVa9bXcUlwL/cmTUZrU4R+HWBgF2hcS46T\n",
       "EKJ8VAtQeHGYdSCJS3EqP2+EVdutzTkzSjFWSGyC9bEuuui6QF+V0ECo6g/V/KFqwI1nf/DzAl8v\n",
       "8PUEHw/razcX+Z26HUVR8Hbzx9vNP//ulaqqJF2P52Lcaa5cO0ds4iViEy4Sm3iRrJzMe/p7WTmZ\n",
       "xCVdLnXndKPBhLurJ+4unrg4u+Hq5IqLs9uN1zeend1wKfTayeRsfRidcTI5YTI6F8RMzhilU3up\n",
       "3ba5VPv27WnVqhVfffVVfqxBgwY88sgjvP/++0W2nzlzJlOmTCE2NhYXF2ub+n/961/MnDmTixe1\n",
       "w5TefMvl9z3Wy6wWrD1NLRZAtb5WUVGx/uNVVRXUG8uAmreNRc3fDvK2s+5joWCfvDMwS9573bS9\n",
       "9WEdbcGimrFYLKiqBYtqwWyxoFosWLBgsag3XptvxNX8fVSL5cZrFYvFgtlixmzOsT5bzOSaczFb\n",
       "cjHfeM41m1GxgFr8l1nJB6eEL78yeh+1hPdRFCNebt54ufvi6xWIr2cAvp6B+HoG4unmjcFgKPQ+\n",
       "2v1PnDgBQL169Uv4u8VnWVL+JW5/p/E7fH+LxXpbP9cMObkFrws/iluXlW39wczMgvQs6+v0zJue\n",
       "s63PKWml+2G9FyYjtG4AHZvB/a2gd9uynxxLms04JjnujsdWxzwzS2XLQet8G1sPQvRR7SR/tuBk\n",
       "Ah9P8HIHN2frQBduLgUPd1dwdbGuc3G2bm8yFvNsBJPpxvNNrw0GUBQwKNbnUr82WH+1i319h1/d\n",
       "d7J5Se995MgRABo3bnzL7VXVOhxuQspVElKvkpASR/L1eGvz7PSEO+jrcWdX0ZQ73L40DIoBo9EJ\n",
       "k8kJk8GEyWDCaDJhUEwYDAbreoMRxWDAqBgxGIwYFAMGg9EaVxSMBpM1ZryxTjFiNBpQMIBisB5z\n",
       "FBTFgKIo1gfW1yjWfqwKCgZFgRvbGBQFxbrSus5wY3vrO+W/Dzci1hfKTU9KQTxvKe9A5q1XoGfL\n",
       "oPxt7qm5VHZ2Nnv27OG1117TxPv27cvWrVuL3Wfbtm107do1v8DI2/6tt97i3Llz1KxZs9j9hr1Z\n",
       "/EmnqGzkOOvFZLSO0NKiHjSva23P3LYxeLjJ1TohhP1ydVHoFQ69btQu2Tkq+0/Ctj8h+gj8eRqO\n",
       "nCvbwiMnF64lWR/iVhrffpN8Pjcech5QkSWuLH1zuFsWGdeuXcNsNlO1alVNPCgoiJiYmGL3iYmJ\n",
       "oUaNGppY3v4xMTElFhl3krQQomzkZkOyja8I1q9v/UG5+c6lqPzkuDue8jzmDUKsjyf72vxPCSHu\n",
       "UplP0yhtGIUQQgghhHBstywyAgMDMRqNxMZqh6WJjY0lODi42H2qVatW5C5H3v7VqlW7l1yFEEII\n",
       "IYQQFcAtm0s5OzvTpk0b1q5dy9ChQ/PjkZGRDBs2rNh9OnbsyOuvv05WVlZ+v4zIyEhCQ0OLNJWS\n",
       "uTGEEEIIIYSofG7bXGry5Ml8//33fPfddxw5coRJkyYRExPDuHHjAJgyZQq9e/fO3/7RRx/F3d2d\n",
       "p556ikOHDvHzzz/z4YcfyvC1QgghhBBCOIjbzpMxfPhw4uPjee+997hy5QrNmzdn5cqV+XNkxMTE\n",
       "cPr06fztvb29iYyMZMKECYSHh+Pv78+rr77Kyy+/bLv/CiGEEEIIIYTduO08GUIIIYQQQghxJ8p8\n",
       "dKm79dxzz1GvXj3c3d0JCgpi8ODB+ZO8iMonMTGRF154gcaNG+Pu7k6NGjV4/vnnSUhI0Ds1YUNf\n",
       "f/01PXr0wNfXF4PBwPnz5/VOSdjAjBkzqF27Nm5uboSHh7N582a9UxI2FBUVxcCBA6levToGg4E5\n",
       "c+bonZKwsQ8++IC2bdvi4+NDUFAQAwcO5NChQ3qnJWxo+vTptGzZEh8fH3x8fOjUqRMrV6685T52\n",
       "U2S0bduWOXPmcPToUdasWYOqqvTu3Zvc3Fy9UxM2cPnyZS5fvsy0adP4888/+fHHH4mKimLUqFF6\n",
       "pyZsKCMjg379+vHOO+/onYqwkQULFvDSSy/x5ptvsm/fPjp16kRERAQXLlzQOzVhI2lpabRo0YJ/\n",
       "//vfuLm5yVD2DmDTpk1MnDiRbdu2sX79ekwmE7179yYxMVHv1ISNhIWF8dFHH7F37152795Nz549\n",
       "GTx4MPv37y9xH7ttLnXgwAFatWrFsWPH8if4EZXbqlWrGDBgAMnJyXh6euqdjrCh6Oho2rVrx9mz\n",
       "Z4tM3ikqtvbt29OqVSu++uqr/FiDBg145JFHeP/993XMTJQHLy8vpk+fzujRo/VORZSjtLQ0fHx8\n",
       "+PXXX+nfv7/e6YhyEhAQwNSpU3nuueeKXW83dzJulpaWxuzZs6lfvz61a9fWOx1RTpKTk3FxccHd\n",
       "3V3vVIQQdyE7O5s9e/bQt692Gua+ffuydetWnbISQthaSkoKFosFPz8/vVMR5cBsNjN//nwyMzO5\n",
       "//77S9zOroqMGTNm4OXlhZeXF8uXL2fFihWYTLcdAEtUAklJSbz11luMGTMGg8Gu/lkKIUrp2rVr\n",
       "mM1mqlatqokHBQUVmaRVCFF5TJo0idatW9OxY0e9UxE2dPDgQTw9PXF1dWXMmDEsXLiQhg0blri9\n",
       "Tc/m3nzzTQwGwy0fUVFR+ds//vjj7Nu3j02bNtGkSRMiIiJITU21ZYqijN3pMQe4fv06Dz30UH57\n",
       "P1Gx3M0xF0IIUTlMnjyZrVu3smTJEumPU8k1atSIAwcOsHPnTiZOnMjIkSOJjo4ucXub9smIj48n\n",
       "Pj7+ltuEhYXh5uZWJJ6Tk4Ofnx/Tp0/nySeftFWKoozd6TG/fv06Dz74IIqisGrVKmkqVQHdzedc\n",
       "+mRUTtnZ2Xh4eDB//nyGDh2aH58wYQKHDx9mw4YNOmYnyoP0yXAsL7/8MgsXLmTDhg00aNBA73RE\n",
       "OevTpw/Vq1dn9uzZxa63aVukgIAAAgIC7mpfi8WCqqpYLJYyzkrY0p0c89TUVCIiIqTAqODu5XMu\n",
       "KhdnZ2fatGnD2rVrNUVGZGQkw4YN0zEzIURZmzRpEosWLZICw4GZzeZbnqfbRYeHU6dOsXjxYvr0\n",
       "6UNgYCAXL15k6tSpuLq6MmDAAL3TEzaQmppK3759SU1NZenSpaSmpuY3jQsICMDJyUnnDIUtxMTE\n",
       "EBMTw/HjxwE4dOgQCQkJ1KxZUzoMVhKTJ0/miSeeoF27dnTq1In//ve/xMTEMG7cOL1TEzaSlpbG\n",
       "iRMnAOsFwnPnzrFv3z4CAgIICwvTOTthCxMmTODHH39k6dKl+Pj45Pe58vLywsPDQ+fshC288cYb\n",
       "DBgwgOrVq5OamsrcuXPZtGkTq1evLnkn1Q5cuHBBjYiIUIOCglRnZ2c1LCxMffzxx9Vjx47pnZqw\n",
       "kQ0bNqiKoqgGg0FVFCX/YTAY1E2bNumdnrCRt99+W3Os857nzJmjd2qiDM2YMUOtVauW6uLiooaH\n",
       "h6t//PGH3ikJG8r7Pi/8nf7000/rnZqwkeJ+vxVFUd955x29UxM28tRTT6k1a9ZUXVxc1KCgILVP\n",
       "nz7q2rVrb7mP3c6TIYQQQgghhKiYZKxQIYQQQgghRJmSIkMIIYQQQghRpqTIEEIIIYQQQpQpKTKE\n",
       "EEIIIYQQZUqKDCGEEEIIIUSZkiJDCCGEEEIIUaakyBBCCCGEEEKUKSkyhBBCCCGEEGXq/wE4RteP\n",
       "CD61GQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f480913f7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-3, 3, 0.01)\n",
    "plt.plot(x, np.exp(-x**2))\n",
    "plot_gaussian(mean=0, variance=0.16, xlim=(-3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computational Properties of the Gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall how our discrete Bayesian filter worked. We had a vector implemented as a NumPy array representing our belief at a certain moment in time. When we performed another measurement using the `update()` function we had to multiply probabilities together, and when we performed the motion step using the `predict()` function we had to shift and add probabilities. I've promised you that the Kalman filter uses essentially the same process, and that  it uses Gaussians instead of histograms, so you might reasonable expect that we will be multiplying, adding, and shifting Gaussians in the Kalman filter.\n",
    "\n",
    "A typical textbook would directly launch into a multi-page proof of the behavior of Gaussians under these operations, but I don't see the value in that right now. I think the math will be much more intuitive and clear if we just start developing a Kalman filter using Gaussians. I will provide the equations for multiplying and shifting Gaussians at the appropriate time. You will then be able to develop a physical intuition for what these operations do, rather than be forced to digest a lot of fairly abstract math.\n",
    "\n",
    "The key point, which I will only assert for now, is that all the operations are very simple, and that they preserve the properties of the Gaussian. This is somewhat remarkable, in that the Gaussian is a nonlinear function, and typically if you multiply a nonlinear equation with itself you end up with a different equation. For example, the shape of `sin(x)sin(x)` is very different from `sin(x)`. But the result of multiplying two Gaussians is yet another Gaussian. This is a fundamental property, and a key reason why Kalman filters are computationally feasible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing Probabilities with scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this chapter I have used custom code for computing Gaussians, plotting, and so on. I chose to do that to give you a chance to look at the code and see how these functions are implemented.  However, Python comes with \"batteries included\" as the saying goes, and it comes with a wide range of statistics functions in the module `scipy.stats`. I find the performance of some of the functions rather slow (the scipy.stats documentation contains a warning to this effect), but this is offset by the fact that this is standard code available to everyone, and it is well tested. So let's walk through how to use scipy.stats to compute various things.\n",
    "\n",
    "The scipy.stats module contains a number of objects which you can use to compute attributes of various probability distributions. The full documentation for this module is here: http://http://docs.scipy.org/doc/scipy/reference/stats.html. However, we will focus on the  norm variable, which implements the normal distribution. Let's look at some code that uses `scipy.stats.norm` to compute a Gaussian, and compare its value to the value returned by the `gaussian()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.131146572034\n",
      "0.131146572034\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "print(norm(2, 3).pdf(1.5))\n",
    "print(gaussian(x=1.5, mean=2, var=3*3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The call `norm(2,3)` creates what scipy calls a 'frozen' distribution - it creates and returns an object with a mean of 2 and a standard deviation of 3. You can then use this object multiple times to get the probability density of various values, like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probability density of 1.5 is 0.1311\n",
      "probability density of 2.5 is also 0.1311\n",
      "whereas probability density of 2 is 0.1330\n"
     ]
    }
   ],
   "source": [
    "n23 = norm(2,3)\n",
    "print('probability density of 1.5 is %.4f' % n23.pdf(1.5))\n",
    "print('probability density of 2.5 is also %.4f' % n23.pdf(2.5))\n",
    "print('whereas probability density of 2 is %.4f' % n23.pdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we look at the documentation for `scipy.stats.norm` <a href=\"http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor\">here</a>[1] we see that there are many other functions that norm provides.\n",
    "\n",
    "For example, we can generate $n$ samples from the distribution with the `rvs()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.27260045  4.2238164  -2.42780752  1.88734677  8.10098857  6.17644384\n",
      "  2.94186917 -1.4252601   2.73244031  2.65367357  1.35429458  1.26983037\n",
      "  4.86749902 -0.23136419  2.56313679]\n"
     ]
    }
   ],
   "source": [
    "print(n23.rvs(size=15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get the *cumulative distribution function (CDF)*, which is the probability that a randomly drawn value from the distribution is less than or equal to $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    }
   ],
   "source": [
    "# probability that a random value is less than the mean 2\n",
    "print(n23.cdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can get various properties of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance is 9.0\n",
      "standard deviation is 3.0\n",
      "mean is 2.0\n"
     ]
    }
   ],
   "source": [
    "print('variance is', n23.var())\n",
    "print('standard deviation is', n23.std())\n",
    "print('mean is', n23.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other functions available, and if you are interested I urge you to peruse the documentation. I find the documentation to be excessively terse, but with a bit of googling you can find out what a function does and some examples of how to use it. Most of this functionality is not of immediate interest to the book, so I will leave the topic in your hands to explore. The <a href=\"http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\">SciPy tutorial</a> [2] is quite approachable, and I suggest starting there. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fat Tails"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Earlier I spoke very briefly about the *central limit theorem*, which states that under certain conditions the arithmetic sum of **any** independent random variables will be normally distributed, regardless of how the random variables are distributed. This is extremely important for (at least) two reasons. First, nature is full of distributions which are not normal, but when we apply the central limit theorem over large populations we end up with normal distributions. Second, Gaussians are mathematically *tractable*. We will see this more as we develop the Kalman filter theory, but there are very nice closed form solutions for operations on Gaussians that allow us to use them analytically.\n",
    "\n",
    "However, a key part of the proof is \"under certain conditions\". These conditions often do not hold for the physical world. The resulting distributions are called *fat tailed*. Let's consider a trivial example. We think of things like test scores as being normally distributed. If you have ever had a professor 'grade on a curve' you have been subject to this assumption. But of course test scores cannot follow a normal distribution. This is because the distribution assigns a nonzero probability distribution for *any* value, no matter how far from the mean. So, for example, say your mean is 90 and the standard deviation is 13. The normal distribution assumes that there is a large chance of somebody getting a 90, and a small chance of somebody getting a 40. However, it also implies that there is a tiny chance of somebody getting a -10, or of 150. It assumes that there is a infinitesimal chance of getting a score of -1e300, or 4e50. In other words, the *tails* of the distribution are infinite. \n",
    "\n",
    "But for a test we know this is not true. You cannot get less than 0, or more than 100. Let's plot this using a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8lfWd//33yclCEhIgZN8DhH01QQTBrYBFOm2ty1it\n",
       "Fsb2Lox1UOpth8fttDOjd2e8dRi1Fuqv9YfW6oij3La2aIlVEQSRiGFLgEBCFpITkgBZIOvJ+f3h\n",
       "cPC6EpKQnOQ6y+v5ePSPzzfXOfkcrrbJO9d3sblcLpcAAAAAwMsEWd0AAAAAAPSEsAIAAADAKxFW\n",
       "AAAAAHglwgoAAAAAr0RYAQAAAOCVCCsAAAAAvBJhBQAAAIBX6ndY2bBhg7KyshQeHq7c3Fzt3Lnz\n",
       "ste2tbVpxYoVmjVrlkJDQ3XjjTd2u2bLli1aunSp4uPjFR0drWuuuUbvvPPOwD4FAAAAAL/Tr7Cy\n",
       "efNmPfTQQ3rsscdUUFCgBQsWaNmyZaqoqOjxeqfTqfDwcD344INavny5bDZbt2s+/vhjLV68WFu3\n",
       "blVBQYFuueUW3Xrrrb2GIAAAAACBw9afE+znzZun2bNn64UXXnCPTZw4Ubfffrt+8Ytf9PraH//4\n",
       "xzp8+LA+/PDDPpuZN2+eFi1apKeffrofrQMAAADwZ30+WWlvb9e+ffu0dOlSw/jSpUu1a9cujzbT\n",
       "2NiomJgYj74nAAAAAN8U3NcFdXV1cjqdSkhIMIzHx8fL4XB4rJFf/epXqqqq0r333msYb2ho8Nj3\n",
       "AAAAADA8Ro0aNej36DOsDIe33npLjz76qN544w2lpaVZ3Q4AAAAAL9DnNLDY2FjZ7XbV1NQYxmtq\n",
       "apSUlDToBt58803dd999euWVV7R8+fJBvx8AAAAA/9Dnk5XQ0FDl5ORo27Ztuu2229zjeXl5uuOO\n",
       "Owb1zd944w2tWLFCv/vd7/Sd73ynz+s98SgJ3i8/P1+SlJuba3EnGC7c88DDPQ9M3PfAwz0PPJ5e\n",
       "wtGvaWBr167Vvffeq6uvvloLFizQr3/9azkcDq1atUqStG7dOu3du1fvv/+++zWFhYVqb29XXV2d\n",
       "mpubtX//frlcLs2ePVuS9Prrr+vee+/V+vXrtXDhQvf6l9DQUBbZAwAAAOhfWLnzzjtVX1+vJ554\n",
       "QtXV1ZoxY4a2bt3qXl/icDhUUlJieM3y5ctVVlYmSbLZbJozZ45sNpucTqck6YUXXlBXV5fWrFmj\n",
       "NWvWuF93ww036IMPPvDIhwMAAADgu/q9wH716tVavXp1j1/btGlTt7HS0tJe368/564AAAAACFz9\n",
       "OsEeAAAAAIYbYQUAAACAVyKsAAAAAPBKhBUAAAAAXomwAgAAAMArEVYAAAAAeCXCCgAAAACvRFgB\n",
       "AAAA4JUIKwAAAAC8EmEFAAAAgFcirAAAAADwSoQVAAAAAF6JsAIAAADAKxFWAAAAAHglwgoAAAAA\n",
       "r0RYAQAAAOCVCCsAAAAAvBJhBQAAAIBXIqwAAAAA8EqEFQAAAABeKdjqBgAAgcHlcqm48pAOlXym\n",
       "I6UH1Ons1J6Kd5QWN16zJlyj9IRs2Ww2q9sEAHgRwgoAYMgdLd+vLR+/qOr6csN4XfMpHS3fr/c/\n",
       "36LMpEm6/fofKj1hgkVdAgC8DWEFADBknM5O/f87/rc+3r+1z2tPVh/Vf7z+f+uW+d/Vkrm3K8jG\n",
       "TGUACHSEFQDAkGjvaNNv/vQLHS3f3+/XuOTSn3e/ppqzp3TPkn+QPcg+hB0CALwdYQUA4HEdnR36\n",
       "zTu/0NEKY1CxyaZZ2fM1KihJEaFRik0eo/wj21VUts9wXf6R7ZJL+t7Na3jCAgABjLACAPC4t7b/\n",
       "pltQGRMVpxXLfqKspMnKz8+XJOVOztXcyder8OTneuUvz+h8a5P7+vyj2xUTHa9vLLhnWHsHAHgP\n",
       "/lwFAPCoTw7+RbsObTOMJcdm6pG7nlJW0uQeXzM1M0c/uespjYmKM4xv2/vf2n/80yHrFQDg3Qgr\n",
       "AACPqao7qTc/+o1hbOyoBD1w678oKmJ0r6+NHZWoB297XFHhowzjr//1V2o8f9bjvQIAvB9hBQDg\n",
       "Ec4up17Le17Ork73WGjICP3wG+sUFTGql1deEjsqUfd/Y53sQZdmKZ9vbdJ/vf8ruVwuj/cMAPBu\n",
       "hBUAgEd89MU7Kj993DD23a89oOTYzCt6n3HJk7XsmrsMY4dP5iv/6PbBtggA8DGEFQDAoJ1tqtXW\n",
       "T18zjM2esEA5kxYN6P0W59zabX3LH3f+Tm3tLQPuEQDgewgrAIBB+/Pu19TR2e6uI8JG6vYbfjjg\n",
       "9wsKsn95zor90nSwhvNnlJf/1qD6BAD4FsIKAGBQTtWWam/RR4axv7n2XkVHjhnU+8aPSdaNs79p\n",
       "GPtg3x9U31gzqPcFAPgOwgoAYFD+sPNluXRp8XtiTJqumbbYI++99Oo7FB1xKfR0OjuUt/dNj7w3\n",
       "AMD7EVYAAANWUnVER8oLDGPfWvh92YPsHnn/EaHhWm46FPLTwg94ugIAAYKwAgAYMPNTjgkp0zQ1\n",
       "M8ej3+PqKTcqdlSiu+7qcvJ0BQACBGEFADAglbUlOnwy3zD29Xl/K5vN5tHvYw+y6+ar7zCMfVr4\n",
       "gc421Xr0+wAAvA9hBQAwINtMTzcyEycpO3XGkHyv3Mk3dHu68vH+rUPyvQAA3oOwAgC4YmcaT2v/\n",
       "8U8NY0vn3u7xpyoX2YPs+lrOrYaxXYe2ce4KAPg5wgoA4IrtPPCeXK4ud500Nl3TsnKH9HvOnXKD\n",
       "IkdEueuWtvPaU/TBkH5PAIC1CCsAgCvS3tmmXYfzDGPXzVo+ZE9VLgoNDtPCmV83jG3/4k/q+kpo\n",
       "AgD4F8IKAOCKfH50hy60Nrnr8LBI5U6+fli+98KZy2QPunSqfW1DtY6VHxiW7w0AGH6EFQDAFfnk\n",
       "wHuGev60xQoLGTEs33tUZIzmZF9rGNt1eNuwfG8AwPAjrAAA+q2q7qTKTx931zbZtHDmsmHtYcGM\n",
       "pYb6wIk9ajx/blh7AAAMD8IKAKDfPi00LmifmD7TsKXwcBifPFXxY1LcdVeXU5+x0B4A/BJhBQDQ\n",
       "L05np/KPbDeMXTP1a8Peh81m04Lpxqcruw/lyeVyDXsvAIChRVgBAPTL4ZP5am5pcNfhoRGaMX6e\n",
       "Jb1cPeVG2e3GhfZlNcWW9AIAGDqEFQBAv5ingF016TqFBodZ0svI8GhNzzSe65J/5CNLegEADB3C\n",
       "CgCgT43nz6mwNN8wZsUUsK/KnXyDof782E45nZ3WNAMAGBL9CisbNmxQVlaWwsPDlZubq507d172\n",
       "2ra2Nq1YsUKzZs1SaGiobrzxxh6v2759u3JychQeHq7x48frhRdeGNgnAAAMuS+KdxoOX0wam670\n",
       "hAkWdiRNzcxReFikuz7f0qgj5QUWdgQA8LQ+w8rmzZv10EMP6bHHHlNBQYEWLFigZcuWqaKiosfr\n",
       "nU6nwsPD9eCDD2r58p5PNC4tLdUtt9yihQsXqqCgQOvWrdODDz6oLVu2DP4TAQA8bt8x4x+p5k6+\n",
       "YchPrO9LSHCI5mQvMIyZNwAAAPi2PsPK+vXrtXLlSt1///2aNGmSnnvuOSUlJWnjxo09Xh8REaGN\n",
       "GzfqBz/4gVJSUnrcneXXv/61UlNT9eyzz2rSpEn6wQ9+oO9///t6+umnB/+JAAAedbapVqXVRwxj\n",
       "V01caFE3RuapYAdK9qi1vcWaZgAAHtdrWGlvb9e+ffu0dKlxi8ilS5dq165dA/6mu3fv7vE98/Pz\n",
       "5XQ6B/y+AADP+6L4E0OdmThJMdHxFnVjNC55isZExbnrjs52HTjxqYUdAQA8Kbi3L9bV1cnpdCoh\n",
       "IcEwHh8fL4fDMeBvWlNT0+09ExIS1NnZqbq6um5fuyg/P7/Hcfgn7nfg4Z57px37txnq2PB0j90r\n",
       "T7xPSnS2zjbVuuuP8t9V0PmoQb8vhg7/Ww883PPAkZ2d7dH3YzcwAMBlNbWeVX1zlWEsc+wUi7rp\n",
       "WUbsVENddfaEOjrbLOoGAOBJvT5ZiY2Nld1uV01NjWG8pqZGSUlJA/6miYmJ3Z7M1NTUKDg4WLGx\n",
       "sZd9XW5u7mW/Bv9x8a8v3O/AwT33Xnl73zLU45On6rprbxr0+3rynrtcLn1a+o7qG7/8WdXlcios\n",
       "xqWrJvLfJ2/D/9YDD/c88DQ0NPR90RXo9clKaGiocnJytG2bcQpAXl6eFixYcJlX9W3+/PnKy8vr\n",
       "9p5z586V3W4f8PsCADzri+PG9SpzvGRh/VfZbDbNmjDfMFZwfODrKgEA3qPPaWBr167VSy+9pBdf\n",
       "fFFFRUVas2aNHA6HVq1aJUlat26dFi9ebHhNYWGhCgoKVFdXp+bmZu3fv18FBZf2vl+1apVOnTql\n",
       "hx9+WEVFRfrtb3+rl19+WY888oiHPx4AYKDONNaq8nSJu7bJptmmUOAtzGGl8OQ+tTMVDAB8Xq/T\n",
       "wCTpzjvvVH19vZ544glVV1drxowZ2rp1q9LS0iRJDodDJSUlhtcsX75cZWVlkr78i9ecOXNks9nc\n",
       "O31lZmZq69atevjhh7Vx40alpKTol7/8pW699VZPfz4AwAAdKv3MUGclTVZ05BiLuuldRmK2Ro0c\n",
       "q4bmeklSe0erjpR9oZnjr7G4MwDAYPQZViRp9erVWr16dY9f27RpU7ex0tLSPt/zuuuu0+eff96f\n",
       "bw8AsMCBE3sM9YzxV1vUSd+CbEGaNf4afbz/z+6xguO7CSsA4OPYDQwA0M2F1mYdP3XYMDZj3DyL\n",
       "uukf81SwwyV75XR2WtQNAMATCCsAgG4On/xcXV2XDulNiElV/JhkCzvq2/jkKRoZPspdt7Rf0Imq\n",
       "Igs7AgAMFmEFANDNwRLjFLCZXv5URZKCguyamnmVYexw6V6LugEAeAJhBQBg0NHZoaKT+wxjM8Z7\n",
       "f1iRpOlZcw31oVJOzQYAX0ZYAQAYFFceVFtHq7uOjhyj9IQJFnbUf5PSZ8sedGnvmNpzVTp99pSF\n",
       "HQEABoOwAgAwKDxp3KlxetZcBdl848dFeFiEJqRMM4zxdAUAfJdv/PQBAAwb8xSwqZk5FnUyMNOy\n",
       "cg31IdatAIDPIqwAANxqz1WrtqHaXduDgjUxbaaFHV05c1gpOVWoC23NFnUDABgMwgoAwM08BWx8\n",
       "8hSNCA23qJuBiRudpISYVHfd5epS0ckvLOwIADBQhBUAgJt5CtgUH5sCdtF009OVorJ9l7kSAODN\n",
       "CCsAAElSe2ebiisPGcbM55b4iikZxpB1pLxALpfLom4AAANFWAEASJKOVx5Wh7PdXY8ZGavEmDQL\n",
       "Oxq4rKTJCg0Oc9eN58+qur7Mwo4AAANBWAEASOo+VWpK5lWy2WwWdTM4IcEhyk6dYRg7Ul5gUTcA\n",
       "gIEirAAAJPW0ZbFvTgG7aHLGbENdVMYiewDwNYQVAIDqGhw6fa7KXQcF2ZWd6ltbFptNyZhjqE+c\n",
       "KlR7R5tF3QAABoKwAgDo9lRlXPIUhYdFWNSNZ8SNTlZMVJy77nR26ERVoYUdAQCuFGEFAKCjFfsN\n",
       "9ZQM354CJkk2m02TTU9XmAoGAL6FsAIAAa6ry6niioOGscnpsy9ztW8xTwU7yiJ7APAphBUACHAV\n",
       "p0+opf2Cu44cEaWUuEzrGvKg7LQZCrJd+lFXXV+us011FnYEALgShBUACHBHy41TwMy/4PuyiLCR\n",
       "ykicaBhjC2MA8B3+8dMIADBgxyoOGOpJabMs6mRomNetmMMZAMB7EVYAIIC1d7TpRHWRYWximm9v\n",
       "WWw2Od0YvoorD8rlclnUDQDgShBWACCAlVQVyensdNcx0fGKHZVoYUeelx4/QWEhI9x104Vzcpyp\n",
       "sLAjAEB/EVYAIID1NAXMZrNZ1M3QsNuDNT5lmmHM/LkBAN6JsAIAAcx8voq/TQG7aGLaDENdXHnw\n",
       "MlcCALwJYQUAAtT51iZVni4xjJl/qfcX2anGEFZceUhdXU6LugEA9BdhBQACVHHFQbl0aaF5Smym\n",
       "oiJGW9jR0EmJy1RE2Eh33dJ2XpW1pRZ2BADoD8IKAASobutV0v1ry+KvCrIFKTt1umGMqWAA4P0I\n",
       "KwAQoIpPHTLU2an+OQXsIvN6nGMVhBUA8HaEFQAIQI3nz6nmTKW7ttmCNC55qoUdDT1zWDlRVahO\n",
       "Z4dF3QAA+oOwAgAB6ETVYUOdFj9e4WERFnUzPOLHpCg6coy7bu9oVXnNcQs7AgD0hbACAAGouNI4\n",
       "BWyC6RwSf2Sz2TQx1TwVjPNWAMCbEVYAIACdOGV8smJefO6vsk1bMx9jkT0AeDXCCgAEmKYL51Rd\n",
       "X+6uv1yvMsXCjobPRNMmAmXVx9TRyboVAPBWhBUACDDHTxUa6tS4LIWHRVrUzfCKiY7X6JFj3XWH\n",
       "s10Vp1m3AgDeirACAAHmRLctiwNjCpj05bqV8ab1OcdNU+IAAN6DsAIAAca8uN78y7u/M28mQFgB\n",
       "AO9FWAGAANLc0mhcryKbxqf49/kqZuawUlpVJGeX06JuAAC9IawAQAAx7wKWEpeliLCRFnVjjfgx\n",
       "KYoKH+Wu2zpaVXm6xMKOAACXQ1gBgABinvI0IYDWq1zU07oV8yGZAADvQFgBgAASiIdB9sQ89c28\n",
       "QxoAwDsQVgAgQJxvbVJ1XZm7DsT1KhdNSDE+USo5VaguV5dF3QAALoewAgAB4sSpQrnkctfJsRmK\n",
       "HBFlYUfWSYpNN5wtc6GtWdV15b28AgBgBcIKAASIkqoiQx2I61UuCrIFaXyy8akS61YAwPsQVgAg\n",
       "QJRUG8PKuOQpFnXiHSakms5bqSSsAIC3IawAQADo6GxXxekThrGspMkWdeMdxiebdgQ7dVgul+sy\n",
       "VwMArEBYAYAAUHH6hJzOTncdExWn0SPHWtiR9VLjxyksZIS7bmpp0OlzVRZ2BAAwI6wAQAAwr1cJ\n",
       "9KcqkmQPsivLNBXuuGlrZwCAtQgrABAASquPGGrzL+mBaoJpkb051AEArNWvsLJhwwZlZWUpPDxc\n",
       "ubm52rlzZ6/XHzx4UNdff70iIiKUmpqqxx9/vNs1r7zyimbNmqXIyEglJSXp3nvvVU1NzcA+BQDg\n",
       "slwul0qrjxrGxiXzZEWSxqUQVgDAm/UZVjZv3qyHHnpIjz32mAoKCrRgwQItW7ZMFRUVPV7f2Nio\n",
       "JUuWKCkpSfn5+Xr22Wf11FNPaf369e5rtm/frhUrVujv/u7vVFhYqLfffltFRUW65557PPfJAACS\n",
       "pNpz1WpuaXDXYSEjlDQ2w8KOvEd6wgTZg4LddX1jjRqaz1jYEQDgq/oMK+vXr9fKlSt1//33a9Kk\n",
       "SXruueeUlJSkjRs39nj9q6++qtbWVr388suaOnWqbrvtNv30pz81hJW9e/cqLS1Na9asUUZGhubN\n",
       "m6cHHnhAe/bs8dwnAwBIkkpNWxZnJk6SPchuUTfeJTQ4TGnx4w1j5i2eAQDW6TWstLe3a9++fVq6\n",
       "dKlhfOnSpdq1a1ePr9m9e7cWLVqksLAww/VVVVUqKyuTJC1ZskS1tbX605/+JJfLpbq6Or3++uta\n",
       "vnz5YD8PAMCkpMq8XoUpYF9lnhLHVDAA8B7BvX2xrq5OTqdTCQkJhvH4+Hg5HI4eX+NwOJSenm4Y\n",
       "u/h6h8OhjIwMzZo1S7///e/13e9+V21tbers7NSSJUv00ksv9dpsfn5+X58HfoT7HXi450OjsOQL\n",
       "Q93ZFOQ1/9be0EfXhVBDfaj4c2VEzraom8DgDfcdw4t7Hjiys7M9+n4e3w3MZrP1ec2nn36qFStW\n",
       "6J//+Z+1b98+vffee3I4HPrRj37k6XYAIKC1dbSooaXOXdtkU2xUqoUdeZ8407/HmfMOdTjbLeoG\n",
       "APBVvT5ZiY2Nld1u77ZLV01NjZKSknp8TWJiYrenLhdfn5iYKEn6z//8Ty1evFg/+clPJEnTp09X\n",
       "ZGSkFi1apH/7t39TcnJyj++dm5vbj48EX3fxry/c78DBPR86h0uNf81Mjs3QgmuutaibS7ztnm8v\n",
       "3uw+ENIll2KSIjUpfZbFXfkfb7vvGHrc88DT0NDQ90VXoNcnK6GhocrJydG2bdsM43l5eVqwYEGP\n",
       "r5k/f7527NihtrY2w/UpKSnKyPhy9xmXy6WgIOO3vlh3dXVd+acAAPSo2/kqHAbZI/O5MyWmfzcA\n",
       "gDX6nAa2du1avfTSS3rxxRdVVFSkNWvWyOFwaNWqVZKkdevWafHixe7r7777bkVERGjFihU6fPiw\n",
       "tmzZoieffFJr1651X/Ptb39bf/jDH/TrX/9aJSUl+uSTT/QP//APysnJUWoq0xMAwFO6nVzPYZA9\n",
       "GmcOK1WFFnUCAPiqXqeBSdKdd96p+vp6PfHEE6qurtaMGTO0detWpaWlSfpy0XxJSYn7+ujoaOXl\n",
       "5emBBx5Qbm6uYmJi9Mgjj+jhhx92X3P33XeroaFBzz//vH7yk59o9OjRuummm/Tkk08OwUcEgMDk\n",
       "dHaqrKbYMMZhkD0zh5WT1Ufl7HKyxTMAWKzPsCJJq1ev1urVq3v82qZNm7qNTZ8+Xdu3bx/wewIA\n",
       "Bq+ytlQdnZcWikdHjlFMVLyFHXmv+NHJigyP1vmWRklSW0erqurKlBY/zuLOACCweXw3MACAdzAf\n",
       "bjguaUq/dmwMRDabTeNM63nMh2kCAIYfYQUA/FS3xfVMAevVuOSphprDIQHAeoQVAPBDLpdLpaaT\n",
       "681PDmBkXs9zoqpILpfLom4AABJhBQD80pmm02o4f8ZdhwSHKjWO9Re9SY0brxD7pdPsG5rrdbap\n",
       "1sKOAACEFQDwQ+anKukJ2bLb+7WnSsAKCQ5ResIEwxhTwQDAWoQVAPBD5kMNmQLWP93PWyGsAICV\n",
       "CCsA4IdKTb9km38JR8+6hRVOsgcASxFWAMDPtLRdUFV9uWEsM2mSRd34lizTE6jqujJdaGu2qBsA\n",
       "AGEFAPxMmeOYXK4ud50Qk6rIEVEWduQ7IkaMVNLYdHftkksnq49Z2BEABDbCCgD4mZ4Og0T/mf+9\n",
       "WLcCANYhrACAn+l2GCSL66+I+fBM878nAGD4EFYAwI90dTl10mGctmQ+7BC9My+yL3Mck9PZaVE3\n",
       "ABDYCCsA4Eeq68vV1t7iriPDoxU3OtnCjnzP2OgERUWMdtftnW06VXfSuoYAIIARVgDAj5jXV2Ql\n",
       "TZbNZrOoG99ks9m6nUvDuhUAsAZhBQD8CIdBekaWaSoY61YAwBqEFQDwI+ZfqjkMcmDMmxKUVB+R\n",
       "y+WyqBsACFyEFQDwEw3NZ3Sm8bS7ttuDlRY/3sKOfFda/DiF2EPddUNzvc421VrYEQAEJsIKAPgJ\n",
       "8/kqafHjFRIcepmr0Ztge4jSEyYYxpgKBgDDj7ACAH6itMq8XoUpYINhXrdSUkVYAYDhRlgBAD9h\n",
       "XlzPYZCDk5U0yVCbn1wBAIYeYQUA/EB7R5sqa0sMY4SVwTHvpFZVV6bWr5xhAwAYeoQVAPADZTXF\n",
       "6upyuuvYUYmKjhzdyyvQl8jwaCWMSXXXLleXyhzHLOwIAAIPYQUA/ECp6dBCtiz2jG5TwTgcEgCG\n",
       "FWEFAPxAafVRQ80UMM/otsiedSsAMKwIKwDg47pcXd221SWseIb5CdVJxzHDdDsAwNAirACAj6s5\n",
       "c0oX2prddXhYpBLHplnYkf+IH52syBFR7rqtvUXV9eUWdgQAgYWwAgA+rttTlcRJCrLxf++eYLPZ\n",
       "uj2lYt0KAAwffpoBgI8zL67PSmYKmCeZ162Y1wcBAIYOYQUAfFz3wyDZCcyTzOetsMgeAIYPYQUA\n",
       "fFjThQbVnqty10G2IGUkZlvYkf9JSxgve1Cwuz7TeFoNzWcs7AgAAgdhBQB8mHm9SkpclsJCRljU\n",
       "jX8KDQ5TWvx4wxhPVwBgeBBWAMCHlVZzGORwGGdaB1RadeQyVwIAPImwAgA+rLSKwyCHg3kdkHmd\n",
       "EABgaBBWAMBHdXR2qPz0ccMYYWVomP9dK2tL1N7RZlE3ABA4CCsA4KMqa0+o09nhrsdExWlMVKyF\n",
       "Hfmv6MjRih2V6K67upwqqym2sCMACAyEFQDwUSWmdRPmLXbhWeb1QObzbQAAnkdYAQAfZV5cz2GQ\n",
       "Q6vbSfasWwGAIUdYAQAf5HK5uu1IxWGQQ8scVkqrj6jL1WVRNwAQGAgrAOCD6hocamppcNehISOU\n",
       "HJthYUf+L3FsmsLDIt11S9t51Zw5ZWFHAOD/CCsA4INKTOslMhMnyh5kt6ibwBBkC1JW4iTDmHkq\n",
       "HgDAswgrAOCDzCfXj2MK2LAwrwsyh0YAgGcRVgDAB5nDCovrh4d5XVBp9dHLXAkA8ATCCgD4mAut\n",
       "zaquL3fXNtmUmTjRwo4CR0ZitoJsl3501p6rUtOFcxZ2BAD+jbACAD7mpMP41/yk2AzDwm8MnbCQ\n",
       "EUqJyzKMmZ9yAQA8h7ACAD7GfBikeUtdDC3z4ZDm+wEA8BzCCgD4mG6L61mvMqx6Om8FADA0CCsA\n",
       "4EOczk6VOY4ZxtgJbHiZw0r56ePq6Gy3qBsA8G+EFQDwIafqTqq9s81dR0eMUUx0vIUdBZ4xUbEa\n",
       "ExXnrp3OTlWcPmFhRwDgv/oVVjZs2KCsrCyFh4crNzdXO3fu7PX6gwcP6vrrr1dERIRSU1P1+OOP\n",
       "d7umvb1dP/vZzzRu3DiNGDFCGRkZ+uUvfzmwTwEAAaKnLYttNptF3QSucUwFA4Bh0WdY2bx5sx56\n",
       "6CE99thjKigo0IIFC7Rs2TJVVFT0eH1jY6OWLFmipKQk5efn69lnn9VTTz2l9evXG6676667tG3b\n",
       "Nv3mN7/RsWPH9Oabb2rmzJme+VQA4KfMhxAyBcwaWd0W2XM4JAAMheC+Lli/fr1Wrlyp+++/X5L0\n",
       "3HPP6b333tPGjRv1i1/8otv1r776qlpbW/Xyyy8rLCxMU6dO1ZEjR7R+/XqtXbtWkrRt2zZ98MEH\n",
       "KikpUUxMjCQpPT3dk58LAPyOy+VSCYdBeoXui+yPyuVy8ZQLADys1ycr7e3t2rdvn5YuXWoYX7p0\n",
       "qXbt2tXja3bv3q1FixYpLCzMcH1VVZXKysokSW+//bbmzp2rp59+WmlpaZo4caLWrFmj8+fPD/bz\n",
       "AIDfOttUp4bmencdYg9VqunMDwyP5NgMhYWMcNfNLQ2qPVdlYUcA4J96DSt1dXVyOp1KSEgwjMfH\n",
       "x8vhcPRvQyYBAAAgAElEQVT4GofD0e36i/XF15SUlGjnzp06ePCgtmzZoueff17vvfeeVqxYMdDP\n",
       "AQB+r7TaONUoPTFbwfYQi7oJbPYguzITJxnGWLcCAJ7X5zSwK9WfR+BdXV0KCgrSa6+9pqioKEnS\n",
       "888/r5tvvlm1tbWKi4vr8XX5+fke7RXejfsdeLjnvdtz4mNDHa5RPv9v5sv9hynaUO85sEP2C6Ms\n",
       "6sa3+PJ9x8BwzwNHdna2R9+v1ycrsbGxstvtqqmpMYzX1NQoKSmpx9ckJiZ2e+py8fWJiYmSpKSk\n",
       "JCUnJ7uDiiRNnvzl/N/y8vIr/AgAEBhONxk3NomPTrOoE0hSfFSqoa5trLSoEwDwX70+WQkNDVVO\n",
       "To62bdum2267zT2el5enO+64o8fXzJ8/Xz/96U/V1tbmXreSl5enlJQUZWRkSJIWLlyoN998U+fP\n",
       "n1dkZKQk6dixLw85u3hNT3Jzc6/go8FXXfzrC/c7cHDP+9bSdkGv7Ko1jC257huKHBF1mVd4N3+4\n",
       "5y1tU/XXos1yubokSQ0tdZoyfZLP3pPh4A/3HVeGex54GhoaPPp+fW5dvHbtWr300kt68cUXVVRU\n",
       "pDVr1sjhcGjVqlWSpHXr1mnx4sXu6++++25FRERoxYoVOnz4sLZs2aInn3zSvRPYxWvGjh2rlStX\n",
       "qrCwUJ988onWrFmjO+64Q7GxsR79gADgD046jrp/KZakhJhUfim2WHhYhJLHGneyPFl91KJuAMA/\n",
       "9blm5c4771R9fb2eeOIJVVdXa8aMGdq6davS0r6cfuBwOFRSUuK+Pjo6Wnl5eXrggQeUm5urmJgY\n",
       "PfLII3r44Yfd10RGRur999/Xgw8+qLlz52rMmDG69dZb9e///u9D8BEBwPeVVhkXb49P5nwVb5CV\n",
       "PEWn6k6665KqIk3L4i/IAOAp/Vpgv3r1aq1evbrHr23atKnb2PTp07V9+/Ze33PixIn6y1/+0p9v\n",
       "DwABr8S0E1gWh0F6haykydp54F13bT4HBwAwOH1OAwMAWMvZ5dRJxzHD2DierHiFcaZDOcsdxXI6\n",
       "Oy3qBgD8D2EFALzcqdpStXe0uuuoiNGKHZVoYUe4KCYqXqMiY9x1h7NdlbUlvbwCAHAlCCsA4OXM\n",
       "hw2OS5rcrzOtMPRsNpuykoxPV0qqmAoGAJ5CWAEAL3eiqtBQZzEFzKtkmaaCcZI9AHgOYQUAvJjL\n",
       "5WInMC83zrTZQUl1kVwul0XdAIB/IawAgBc703haDefPuOuQ4FClxo2zsCOYpcZlKSQ41F03nj+r\n",
       "M42nLewIAPwHYQUAvJh5y+KMhGzZ7f3adR7DxG4PVkZCtmHMfN8AAANDWAEAL2ZerD0ueapFnaA3\n",
       "5q2kzVP3AAADQ1gBAC9WYlpcbz7XA96h245gLLIHAI8grACAl7rQ2ixHfYW7tsmmzKRJFnaEyzHf\n",
       "l+q6MrW0nbeoGwDwH4QVAPBSpdVH5NKlXaWSxqYrImykhR3hciJHRCkxJs1du+TSSccxCzsCAP9A\n",
       "WAEAL2U+r4PzVbybeYoe61YAYPAIKwDgpUqqjDtKsV7Fu2X1cN4KAGBwCCsA4IU6nR0qcxQbxsw7\n",
       "TsG7mBfZn3Qck7PLaVE3AOAfCCsA4IUqa0vV4Wx316MiYxQTFW9hR+hL3OgkjQwf5a7bO1pVVVdm\n",
       "YUcA4PsIKwDghcxbFmclT5bNZrOoG/SHzWbrvm6FqWAAMCiEFQDwQubDIMdzGKRP6HbeCovsAWBQ\n",
       "CCsA4GVcLpdKTYvrzb8EwzuZF9mbd3QDAFwZwgoAeJnac9Vqamlw16EhI5QSl2VhR+ivtPjxCraH\n",
       "uOuzTbU621RnYUcA4NsIKwDgZcxbFmcmZMseZLeoG1yJkOAQpcdPMIzxdAUABo6wAgBe5sSpw4Z6\n",
       "fMo0izrBQGQlTzLU5vAJAOg/wgoAeJnjVYQVX8a6FQDwHMIKAHiRs011qm+ocdf2oGBlJk60sCNc\n",
       "KfNmCKdqS9XW3mJRNwDg2wgrAOBFzFPA0hMmKDQkzKJuMBBREaMUNzrZXXe5ulRWU2xhRwDguwgr\n",
       "AOBFTpwyHgbJFDDfNC7JfDgkU8EAYCAIKwDgRczrVSakcBikL8pKNq5b4XBIABgYwgoAeImmC+dU\n",
       "c6bSXdtsQd0Wa8M3jEs2Plk5WX1EXV1Oi7oBAN9FWAEAL2He4jY1LkvhYREWdYPBiB+ToogRUe66\n",
       "pf2CqurLLOwIAHwTYQUAvMRxzlfxG0G2II03TQU7Xnn4MlcDAC6HsAIAXsK8uJ71Kr5tQsp0Q338\n",
       "1CGLOgEA30VYAQAv0NJ2XqdqSw1j45IJK75sQqo5rBSqy9VlUTcA4JsIKwDgBUqqiuSSy10njU3X\n",
       "yPBoCzvCYKXEZig89NKaowutTaquK7ewIwDwPYQVAPAC3c5X4amKzwsKsndbd8RUMAC4MoQVAPAC\n",
       "LK73TxNSTWGlkrACAFeCsAIAFmvraFX56eOGsQmEFb/QbZF9FetWAOBKEFYAwGInq48aDgyMG5Wk\n",
       "USNjLOwInpIal6URX1m3cr6lUY76Cgs7AgDfQlgBAIt1W6/ClsV+IyjI3m39kXnKHwDg8ggrAGCx\n",
       "YtOia8KKf+m2hTHrVgCg3wgrAGCh9s42nXQcNYyZf7mFbzOvPzp+6rBcLtdlrgYAfBVhBQAsVFp1\n",
       "RE5np7seG52gsdEJFnYET0uNH6ew0HB33dzSIMeZSgs7AgDfQVgBAAsVVx401Nk8VfE79iC7xidN\n",
       "MYwdN913AEDPCCsAYKFj5rCSNtOiTjCUuq1bYZE9APQLYQUALNLa3qJyR7FhbGLqDIu6wVDqaZE9\n",
       "61YAoG+EFQCwSInpgMD40cmcr+Kn0uLGKSxkhLtuamnQ6bOnLOwIAHwDYQUALNJtvQpTwPyW3R6s\n",
       "rGTjuhXzFEAAQHeEFQCwyLEKFtcHkuwU4/0triCsAEBfCCsAYIELrc2qrC01jBFW/NtE05OzY5UH\n",
       "DdMAAQDdEVYAwAJfHgx46RfVpLHpiooYbWFHGGpp8eMUHhbpri+0NumUKbACAIwIKwBgge7nq7AL\n",
       "mL8LCrJ3u8/HKg5Y1A0A+IZ+hZUNGzYoKytL4eHhys3N1c6dO3u9/uDBg7r++usVERGh1NRUPf74\n",
       "45e9dufOnQoODtaMGfygBhA4iisPGeqJafx/YCAwTwU7SlgBgF71GVY2b96shx56SI899pgKCgq0\n",
       "YMECLVu2TBUVFT1e39jYqCVLligpKUn5+fl69tln9dRTT2n9+vXdrj179qzuu+8+LV68WDabbfCf\n",
       "BgB8QNOFBlXVnXTXNtk0IYX1KoFgkimslJwqVEdnh0XdAID36zOsrF+/XitXrtT999+vSZMm6bnn\n",
       "nlNSUpI2btzY4/WvvvqqWltb9fLLL2vq1Km67bbb9NOf/rTHsHL//fdr5cqVmj9/PodjAQgY5tPL\n",
       "U+KzFDFipEXdYDjFj0nRqMhLZ+m0d7bppOOohR0BgHfrNay0t7dr3759Wrp0qWF86dKl2rVrV4+v\n",
       "2b17txYtWqSwsDDD9VVVVSorK3OPbdiwQbW1tXrssccIKgACytHyAkPNqfWBw2azaVL6LMMY61YA\n",
       "4PKCe/tiXV2dnE6nEhISDOPx8fFyOBw9vsbhcCg9Pd0wdvH1DodDGRkZOnjwoP71X/9Ve/bsuaLp\n",
       "X/n5+f2+Fr6P+x14AuWeHyj+zFDbWiMC5rObBeLnDumMMtT7inYpIWSiRd1YIxDve6DjngeO7Oxs\n",
       "j76fx3cD6yt8tLW16W//9m/19NNPKyMjw9PfHgC8WlPLGTW3nXPXQTa7EqLTe3kF/E3SqExDXdd0\n",
       "Su2dbdY0AwBertcnK7GxsbLb7aqpqTGM19TUKCkpqcfXJCYmdnvqcvH1iYmJqq6u1pEjR7Ry5Uqt\n",
       "XLlSktTV1SWXy6WQkBC9++67Wrx4cY/vnZub279PBZ928a8v3O/AEUj3fMeBdw31hJSpumbefIu6\n",
       "sU4g3fOefHziLZ0+e0qS5JJL0fGhmj7O//8tAv2+ByLueeBpaGjw6Pv1+mQlNDRUOTk52rZtm2E8\n",
       "Ly9PCxYs6PE18+fP144dO9TW1ma4PiUlRRkZGUpNTdWhQ4e0f/9+939WrVqlCRMmaP/+/Zo/P/B+\n",
       "aAMIHEfL9xvqSRlzLOoEVpqUxroVAOiPPqeBrV27Vi+99JJefPFFFRUVac2aNXI4HFq1apUkad26\n",
       "dYYnIXfffbciIiK0YsUKHT58WFu2bNGTTz6ptWvXSpKCg4M1depUw3/i4uIUFhamqVOnKjIyssc+\n",
       "AMDXObuc3X4pnWxabI3AYD5vhbACAD3rdRqYJN15552qr6/XE088oerqas2YMUNbt25VWlqapC8X\n",
       "zZeUlLivj46OVl5enh544AHl5uYqJiZGjzzyiB5++OHLfg+bzcY5KwD8XnlNsVrbL7jryPBopcRl\n",
       "WdgRrJKdOl02W5Bcri5JUlV9mRrPn1N05GiLOwMA79JnWJGk1atXa/Xq1T1+bdOmTd3Gpk+fru3b\n",
       "t/e7iZ///Of6+c9/3u/rAcAXHTFPAUubpSCbx/c5gQ+IGDFSafHjVV5T7B47WlGguZNvsK4pAPBC\n",
       "/JQEgGFytMx4vor5vA0Elsnpsw11UdkXFnUCAN6LsAIAw6Cl7UK3k8pZrxLYppg2VzhSVqCu/5kW\n",
       "BgD4EmEFAIZBceVBwy+iCWNSNSYqzsKOYLXMxIkaERrhrptbGlR5uqSXVwBA4CGsAMAw6LZlMU9V\n",
       "Ap7dHqxJpl3BmAoGAEaEFQAYBkfKWa+C7qZkXmWojxBWAMCAsAIAQ+xM42nVnqty10FBdmWnzrCw\n",
       "I3iLyenGdSul1UfU0nbeom4AwPsQVgBgiBWe3GeosxInaURouEXdwJvERMcpISbVXXe5ujggEgC+\n",
       "grACAEOs8OTnhnpqZo5FncAbTckwTgUrKtt3mSsBIPAQVgBgCHV0tnf7S/lU0zoFBDbzFsZFZQVy\n",
       "uVwWdQMA3oWwAgBD6Pipw2rvbHPXoyJjlBybaV1D8DrjU6YqxB7qrs821armbKWFHQGA9yCsAMAQ\n",
       "6mkKmM1ms6gbeKPQ4DBNSJ1uGCs6ya5gACARVgBgSBWZFtezXgU9mZwx21CzbgUAvkRYAYAhUnuu\n",
       "Wqe/smWxPShYE02HAAKSNNW0yP74qcNq62i1qBsA8B6EFQAYIuYpYOOTpyg8LMKibuDN4sekKCY6\n",
       "3l13Ojt0tHy/hR0BgHcgrADAEDGfrzI1iylg6JnNZtP0rLmGsUOley3qBgC8B2EFAIZAe0ebiisP\n",
       "GsZYr4LeTMvKNdSFpZ+ry9VlUTcA4B0IKwAwBI5VHFCns8Ndx0THK2FMai+vQKCbkDJdYSEj3HXj\n",
       "hbOqqDlhYUcAYD3CCgAMgUOlnxlqtixGX0KCQzTZdEAkU8EABDrCCgB4WJerS4dK8g1jM8ZdbVE3\n",
       "8CXmdSuHS/MvcyUABAbCCgB4WJmjWI0XzrrrsNBwTUiZ3ssrgC9NzbxKNl16AldZW6KzTXUWdgQA\n",
       "1iKsAICHHSoxTgGbkjFHIcEhFnUDXxIVMVoZSRMNYzxdARDICCsA4GEHTWFlxrh5FnUCX8RUMAC4\n",
       "hLACAB5Ue65ajjMV7jrIFqRpbFmMKzDdtIXxsYoDnGYPIGARVgDAgw6W7DHUE1KmKWLESIu6gS9K\n",
       "GpthOM2+w9muI2VfWNgRAFiHsAIAHnTwhHEK2HR2AcMVstlsmmmaOlhwfLdF3QCAtQgrAOAhzS2N\n",
       "Kqk+YhibMZ6wgis3a8I1hvpwab46OjsuczUA+C/CCgB4yOHSvXK5utx1cmymxkYnWNgRfFVW0mRF\n",
       "RYx2163tF1RcecDCjgDAGoQVAPAQ81SdGePmXuZKoHdBQfZuU8H2H//Uom4AwDqEFQDwgJa28zpS\n",
       "XmAYmz1hgUXdwB/MNE0FO1CyR11dTou6AQBrEFYAwAMOle6V09npruNGJSk5NtO6huDzslOnKzws\n",
       "0l2fb2nUiaoiCzsCgOFHWAEAD/iieJehnp29QDabzaJu4A+C7SHdDog8cIKpYAACC2EFAAappe1C\n",
       "t3MwZmdfa1E38CfmXcH2H98tl8tlUTcAMPwIKwAwSIdL96rTeWlb2bGjEpQal2VhR/AXk9PnKDQ4\n",
       "zF2fa67XSccxCzsCgOFFWAGAQSo4bpwCNmfCtUwBg0eEhoRpamaOYeyLYzst6gYAhh9hBQAGobW9\n",
       "RYUn9xnGZmezCxg856qJCw31vuKd7AoGIGAQVgBgEA6X5humgMVExystfryFHcHfTM3KUVhouLtu\n",
       "PH9WJ6oKLewIAIYPYQUABmHfsR2Geg67gMHDQoPDuh0Q+fnRHZe5GgD8C2EFAAbofGtTtylgc7IX\n",
       "XuZqYODMU8EKju82PNEDAH9FWAGAASoo3iVn16WDIONHJzMFDENicvpsRYyIctcXWpt0tHy/hR0B\n",
       "wPAgrADAAOUf2W6ocydfzxQwDAm7PVizJ8w3jH1+jKlgAPwfYQUABuBM4+lui5xzJl1nUTcIBDmT\n",
       "Fhnqgyf2qL2zzaJuAGB4EFYAYADyj35sqDMTJyludJJF3SAQjE+equjIMe66raNVh0r2WtgRAAw9\n",
       "wgoAXCGXy6XPTWEld/L1FnWDQBEUZNdVpg0cPiv60KJuAGB4EFYA4ApV1Z1UdX25uw6yBWlO9rUW\n",
       "doRAcfXUGw11UdkXajh/xqJuAGDoEVYA4ArtNS2sn5wxR1ERoyzqBoEkNW6cUmIz3bXL1dVtowcA\n",
       "8CeEFQC4Ak5np/aapt7MZQoYhtHVU28y1HsKP5DL5bKoGwAYWoQVALgCh0/mq6mlwV2PCI3QDNPp\n",
       "4sBQyp10nYKC7O7acaZC5TXHLewIAIYOYQUArsDuw+8b6pxJ1yk0JMyibhCIoiJGa1pmjmFsT+Ff\n",
       "LeoGAIYWYQUA+ulcc70KT+4zjM2fttiibhDI5pmmgn1+bIc6Otst6gYAhk6/w8qGDRuUlZWl8PBw\n",
       "5ebmaufOnb1ef/DgQV1//fWKiIhQamqqHn/8ccPXt2zZoqVLlyo+Pl7R0dG65ppr9M477wzsUwDA\n",
       "MPis8AO5XF3uOjk2U2nx4y3sCIFqamaOIkdEueuWtvM6WPKZhR0BwNDoV1jZvHmzHnroIT322GMq\n",
       "KCjQggULtGzZMlVUVPR4fWNjo5YsWaKkpCTl5+fr2Wef1VNPPaX169e7r/n444+1ePFibd26VQUF\n",
       "Bbrlllt066239hmCAMAKXa4u7S40TgGbP22xbDabRR0hkAXbQ7qd7fPJwb9Y1A0ADJ1+hZX169dr\n",
       "5cqVuv/++zVp0iQ999xzSkpK0saNG3u8/tVXX1Vra6tefvllTZ06Vbfddpt++tOfGsLKM888o0cf\n",
       "fVS5ubkaN26cfvaznyknJ0dvv/22Zz4ZAHjQ8crDqm+ocdc9/bIIDCfzFMTiyoOqOVNpUTcAMDT6\n",
       "DCvt7e3at2+fli5dahhfunSpdu3a1eNrdu/erUWLFiksLMxwfVVVlcrKyi77vRobGxUTE9Pf3gFg\n",
       "2Ow+nGeoZ42/xjANBxhuybGZGpc0xTC28+B7FnUDAEMjuK8L6urq5HQ6lZCQYBiPj4+Xw+Ho8TUO\n",
       "h0Pp6emGsYuvdzgcysjI6PaaX/3qV6qqqtK999572V7y8/P7ahd+hPsdeLz1nre0N+uLY58YxmJC\n",
       "0r22X1/Cv+HgJI+cqBIVuevdB99XyohpCraHWNhV37jvgYd7Hjiys7M9+n5DshvYlc7hfuutt/To\n",
       "o4/qtddeU1pa2lC0BAADVlzzhbpcTncdNWKMEkdlWtcQ8D8yYqcoLDjCXbc7W3Wy7rCFHQGAZ/X5\n",
       "ZCU2NlZ2u101NTWG8ZqaGiUlJfX4msTExG5PXS6+PjEx0TD+5ptv6vvf/75eeeUVLV++vNdecnNz\n",
       "+2oXfuDiX1+434HDm++509mpPxRsMIwtvvpWzZ0z16KO/IM333Nf42g/or9+fmm9Z2XTUd21/AcW\n",
       "dnR53PfAwz0PPA0NDX1fdAX6fLISGhqqnJwcbdu2zTCel5enBQsW9Pia+fPna8eOHWprazNcn5KS\n",
       "YpgC9sYbb+i+++7Tyy+/rO985zsD/QwAMGT2n/hUDefPuOvQ4LBuZ1wAVlow/WZDXV5TzIn2APxG\n",
       "v6aBrV27Vi+99JJefPFFFRUVac2aNXI4HFq1apUkad26dVq8+NKuJHfffbciIiK0YsUKHT58WFu2\n",
       "bNGTTz6ptWvXuq95/fXXdc899+jJJ5/UwoUL5XA45HA4dObMmW7fHwCssmP/VkM9d8qNiggbaVE3\n",
       "QHdxo5M0OWOOYcz831sA8FX9Cit33nmnnnnmGT3xxBOaM2eOdu3apa1bt7rXlzgcDpWUlLivj46O\n",
       "Vl5enqqqqpSbm6sHH3xQjzzyiB5++GH3NS+88IK6urq0Zs0aJScnu/9z++23e/gjAsDAnKot1Ymq\n",
       "QsPYdbNusagb4PIWzvi6oc4/+rHhiSAA+Ko+16xctHr1aq1evbrHr23atKnb2PTp07V9+/bLvt+H\n",
       "H37Y328NAJbYvv/Phnpi6gwljU2/zNWAdaZn5Sp2VKLqGr5cL+rs6tSO/Vv1jQXfs7gzABicIdkN\n",
       "DAB8XdOFc/r8yMeGsetm974JCGCVoCC7bpjzTcPYzgPvqa2j1aKOAMAzCCsA0IPtBX9Wh7PdXcdE\n",
       "xWlaFjuAwXvNm3qTYT3VhbZm7Sn8q4UdAcDgEVYAwKS1vUU7DhgXKN941bdkD7Jb1BHQt7CQEVo4\n",
       "07h25cMv/qiuLudlXgEA3o+wAgAmuw/lqaXtvLuOGBGla6Yt7uUVgHdYNOsW2e2XlqPWN9ToYMln\n",
       "FnYEAINDWAGAr+h0dujDL/5gGLtu5i0KCxlhUUdA/42KjFHuxOsMY3n5W+RyuSzqCAAGh7ACAF+R\n",
       "f+RjnWuud9chwaFaxHbF8CE3XvUtQ11eU6yisi8s6gYABoewAgD/w+ns1F/2vmEYu2bqYkVFjLKo\n",
       "I+DKJcdmaMa4qw1j7+3ZzNMVAD6JsAIA/2Pvke2qb6hx10FBdt2U861eXgF4p5uvvtNQn3Qc1bGK\n",
       "AxZ1AwADR1gBAP3PU5XPzE9Vvqax0QkWdQQMXHrCBE3LzDWMvbvndZ6uAPA5hBUAkPRZ0Yeqb7z0\n",
       "VMUeFKylc2+3sCNgcG6eZ3y6UlJVpKPl+y3qBgAGhrACIOB1dHb0+FQlJjreoo6AwctMnKjJGXMM\n",
       "Y3/c9Tt1ubos6ggArhxhBUDA23ngXZ1pqnXX9qBgLeGpCvzA8mvuNtSVp0tUULzLom4A4MoRVgAE\n",
       "tAutzd2eqlw7Y6liouMs6gjwnIzEbM2esMAw9uddr8rp7LSoIwC4MoQVAAEtL/8tXWhrdtdhoeG6\n",
       "+eq/tbAjwLO+seAeBdku/bivbajWrkPbLOwIAPqPsAIgYJ1prNX2gj8ZxpbkfIdzVeBX4sek6Jpp\n",
       "iw1jWz/9L11obb7MKwDAexBWAASst3duUqezw12PiozRDXO+aWFHwNBYNu8uhQaHuevzrU16d8/r\n",
       "FnYEAP1DWAEQkI6W7++20PiW+XcrNCTsMq8AfNeokTFaMvc2w9iO/VtVXV9uUUcA0D+EFQABp9PZ\n",
       "oTc/+o1hLD1+guZNudGijoChd+NV3zJsx93l6tJb23/LQZEAvBphBUDA+eiLd1RzttJd22TTHTf+\n",
       "XwoKslvYFTC0QoPDdOuivzOMHas4oH3HdljUEQD0jbACIKDUNTj03p7NhrFrpi1WRuJEizoChs/M\n",
       "8fM0MW2mYezN7b9Vc0ujRR0BQO8IKwAChsvl0n+9/yu1d7a5xyLCRupvrr3Xwq6A4WOz2XTHjT+S\n",
       "3R7sHjvf0qi3d2yysCsAuDzCCoCAsevQNhVXHjSMfWvh9zUyPNqijoDhlzAmRV83nSX0WdGHKir7\n",
       "wqKOAODyCCsAAsKZxlq9vfMlw9iktFndzp8AAsHXcr6t5LEZhrHX3n9e51ubLOoIAHpGWAHg97q6\n",
       "nHpl2zNqa29xj4WGjNBdi/9eNpvNws4AawTbQ/TdxQ/Ipkv//W9ortfmDzayOxgAr0JYAeD3tu19\n",
       "UydOHTaMffPaezU2OsGijgDrZSRO1NdybjWMFRTv0t4jH1nTEAD0gLACwK+VVB3ptvvX5PTZWjhz\n",
       "mUUdAd7jlvnfVWrcOMPYf3/0v3T67CmLOgIAI8IKAL/VdKFBL7/7tLpcXe6xkeGj9L2laxRk4//+\n",
       "gGB7iO77+sMKsYe6x9raW/Tin59UW0erhZ0BwJf4aQ3ALzm7nNr07lM621xnGL9nyYOKjhxjUVeA\n",
       "90mMSdO3F60wjFXXl+v1v25g/QoAyxFWAPilP+x8WccrDxnGbpjzTU3LyrWoI8B7LZy5TDkTFxnG\n",
       "Pj/6sT4qeMeijgDgS4QVAH5n96E8ffTFHw1jE1Kn61vX3mdRR4B3s9lsuutrf6/EmDTD+Nsfb9LB\n",
       "ks8s6goACCsA/Ezhyc+1+YONhrExI2O1ctkjhlO7ARiFhYbr/m/8o8JCw91jLrn08rv/ofKa4xZ2\n",
       "BiCQEVYA+I3ymuP631ufMiyoD7GH6v5v/KOiIkZb2BngGxLGpGjlskdk+8oGFO2dbfpff/x/VXuu\n",
       "2sLOAAQqwgoAv1BVd1Ib3/4XtX9lByObbLrv62uVnjDBws4A3zI1M0e33/BDw1jjhbN6fsvPdKbx\n",
       "tEVdAQhUhBUAPq+6vlzPb/m5zrc2GcZvu+GHmjXhGou6AnzXopnLdNNV3zKMnW2q1fNbfqaG5jMW\n",
       "dQUgEBFWAPi0U7Wlev6tf1JzS4NhfHHOd3TdrFss6grwfd9c+H3Nm3KTYayuwaFn3lynugaHRV0B\n",
       "CDSEFQA+q7jykJ598/9RkymoXD/7G/qba++1qCvAPwTZgvTdxQ9oTva1hvH6hho989/rVF1fblFn\n",
       "AAIJYQWAT/qieJc2vv0vam2/YBhfNPMWfee6+2Wz2SzqDPAfQUF23Xfzw5ox7mrDeOP5s3rmv9fp\n",
       "aPl+izoDECgIKwB8SperS3/e/Zo2bf3/1OnsMHzt+tnf0O03/JCgAniQ3R6sv7vlUeVOut4w3tJ2\n",
       "XmKTAEQAAA+oSURBVBvf/hftOPCuRZ0BCAQcOgDAZ1xobdbv857ToR4OqfubBfdqce53CCrAELDb\n",
       "g/W9m9coPCxSOw5sdY93ubr03x++oHJHsW6/4YeGM1oAwBMIKwB8wvFTh/XKe/+ps811hvGgILvu\n",
       "uunvdc20r1nUGRAYgmxBuv2GH2pMVKze+eQVueRyf21P0QcqdRzVimU/UWrcOAu7BOBvCCsAvFpb\n",
       "R6ve/fR1ffjFH+X6ymGPkjQyfJTuX/6oxqdMs6g7ILDYbDYtzv2O4sek6Hd/+U/DuUanz57Sf2x+\n",
       "VMvm3aWvXfVt2e38igFg8FizAsBrFZ78XP/2+3/QB/ve7hZU0uLH65G7niaoABaYOX6e1t7570qI\n",
       "STWMO52d+tOu3+up//qJSquPWtQdAH/Cnz0AeB3HmQr9adfvdeDEnh6/ftNV39Y3FtyjYHvIMHcG\n",
       "4KLk2Ew9ctfTemv7b/Xp4fcNX6uqL9Mzb/yjrp5yo5Zd813FRMdZ1CUAX0dYAeA1zjTW6r3PNmtP\n",
       "4QfdnqRI0uiRY/XdxT/WlIw5FnQHwCwsZITuXvxjTU6frTc+fEEXWpvcX3PJpT1FH+jzYzt03axb\n",
       "tDj3Ngs7BeCrCCsALHfmfI0KT+3W73cXqavL2e3rNluQrpt1i5bPv0cj2G0I8DpXTVyo7NQZenvH\n",
       "Ju098pHha53ODn2w7w/aeeA9TUrM1ZyMG61pEoBPIqwAsER7Z5v2H/9Unx5+X8WVBy97XXpCtu68\n",
       "8UdKT5gwjN0BuFJREaN0780P6eopN+rNj36jmrOVhq+3d7bJ2dVpUXcAfBVhBcCw6XR26FjFQe0/\n",
       "vlsFxZ+oxXT6/FfFj07W8gXf0+wJ8zk7BfAhk9Jn6R+/96w+K/xAW/e8robmekmSPShYU5LnWdwd\n",
       "AF9DWAEwpM4116u48qAKT+7T4dJ8tfYSUCQpfkyKvnbVt3X1lBvZ+hTwUfYgu+ZPX6Kcyddp54H3\n",
       "9OG+P2hK5lWKDIu2ujUAPobfBAB4jNPZKceZCpXXHFdZTbGOVx7S6XNV/XptfHSavnnd9zR93FwF\n",
       "2dhVHfAHocFhuumqb2nRzFvU3tmqokNsZwzgyvQrrGzYsEFPPfWUHA6Hpk2bpmeeeUYLFy687PUH\n",
       "Dx7Uj3/8Y+3du1cxMTH60Y9+pH/6p38yXLN9+3atXbtWhYWFSk5O1qOPPqof/ehHg/s0AIZFR2eH\n",
       "6hocOn32lE6fq1Lt2VOqPlOhU7Wl6nR29Pt9RoaP0tVTbtBIV6JGR8Rp5vjcIewagFVCgkMUEsxW\n",
       "4wCuXJ9hZfPmzXrooYe0ceNGLVy48P+0d/8xTV57GMCfvkUorI45tS0/HB3Mi8oYd2GSONziEmVz\n",
       "Y5i5TcYgGzCXEA1B0MyhmGAusrEsJIDo3Eak+2HMkrHNbGSjV5m6qQsg/yA/9F51gtJuegUs2Ja2\n",
       "5/6x2dxeWEFk2r57PkkDnPd7Xt6TpyUe+/Yc1NbWYuXKlejs7MS8efPG1A8NDWHFihVYtmwZWltb\n",
       "0dXVhZycHNx1110oKioCAJw7dw5PP/001q5di3379uHo0aNYt24d5s6di9WrV0//KIloQk6nAyM2\n",
       "C0asFgxbLRixXsOw9RqGhq9iwHIFg8NXMGD5DwYsl3FtZHDcpYUnY2ZwKOJjkvBQzBL8bV48ApQz\n",
       "0NraOs2jISIiIjmYcLJSWVmJnJwcvPbaawCA6upqfPvtt9i9ezfKy8vH1H/66aewWq0wGAwICgrC\n",
       "okWL0N3djcrKSvdk5b333kNkZCSqqqoAALGxsfjpp5/w7rvvep2sXDD/y+NnIYSXK//jY157TfWc\n",
       "3rp57Sf3MXg54x/0u3T13wCArp+V03K+349Osd/Ufp/wmtDUzgkIOF1OuFxOOH9/uMb96oDL5YJL\n",
       "/Pa9w+mAfdQGu8OGUYcNtlErRkftsDtssI9aYXfYcN0+Apv9+pSueSKSpIRe+zfMn/cgFtz3d9wf\n",
       "tgCSdHPZEhER0V+T18mK3W7HyZMn8cYbb3i0p6Sk4NixY+P2OX78OB577DEEBQV51G/btg0///wz\n",
       "oqKicPz4caSkpIw5p8FggNPphFI5/j9k3t2/aVKDInn4Z+edvgKaitC77sU87QOYp4lBlHY+YsIX\n",
       "Ioh7oxAREdEUeJ2sXL58GU6nE1qt1qNdo9HAZDKN28dkMuG+++7zaLvR32QyISoqCmazecw5tVot\n",
       "HA4HLl++PObYDf/INngfDRH5HOt1O6zX7V5r5s+fDwAYHBy8HZdEPoCZ/zUx978eZk63atqX3OF+\n",
       "CERERERENB28TlbmzJkDpVIJs9ns0W42mxEWFjZuH51ON+Zdlxv9dTqd15qAgADMmTPn5kZARERE\n",
       "RESy5PU2sMDAQCQmJqKpqQnPP/+8u91oNOLFF18ct8+SJUuwefNm2Gw29+dWjEYjIiIiEBUV5a75\n",
       "4osvPPoZjUYsXrx4zOdVQkNDb35URERERETk9ya8DayoqAj19fWoq6tDV1cXCgoKYDKZkJeXBwAo\n",
       "Li7G8uXL3fUvv/wyQkJCkJ2djVOnTqGhoQEVFRXulcAAIC8vDxcvXkRhYSG6urrw4YcfwmAwYNMm\n",
       "foCeiIiIiIh+M+HSxWvWrMGVK1dQVlaG/v5+xMfHo7Gx0b3HislkwtmzZ931d999N4xGI9avX49H\n",
       "HnkE9957LzZt2oTCwkJ3jV6vR2NjIwoLC7F7925ERESgpqYGzz333J8wRCIiIiIi8kcKMdVNJoiI\n",
       "iIiIiP5E074a2FT19/fj1VdfhUajQXBwMOLi4nDkyBGPmtLSUkRERCAkJARPPPEEOju5EYe/0uv1\n",
       "kCRpzCM1NRXAb5sjMm95cTgc2LJlC6KjoxEcHIzo6Ghs27YNTqfTo465y8+1a9ewYcMG6PV6hISE\n",
       "IDk5Ga2trR41zN1/HTlyBGlpaYiMjIQkSTAYxm4zMFG+NpsN+fn5mDt3LtRqNVatWoWLFy/eriHQ\n",
       "TZoo84aGBjz55JPQaDSQJAmHDx8ecw5m7l+8Ze5wOLB582YkJCRArVYjPDwcmZmZ6O3t9TjHVDP3\n",
       "icnKwMAAkpOToVAo0NjYiO7ubuzcuRMajcZdU1FRgcrKSuzcuRMtLS3QaDRYsWIFLBbLHbxymqq2\n",
       "tjaYTCb34+TJk1AoFEhPTwcAvPPOO8xbZsrLy7Fnzx7U1NSgp6cHVVVV2LVrF9566y13DV/n8rR2\n",
       "7VoYjUZ89NFH6OjoQEpKCpYvX45Lly4BYO7+bnh4GA899BCqqqoQHBw8ZguDyeS7YcMGNDQ0YP/+\n",
       "/Th69CiGhoaQmpoKl8t1u4dDkzBR5iMjI1i6dCkqKysBjL+tBTP3L94yHx4eRnt7O0pKStDe3o6v\n",
       "vvoKvb29eOqppzz+Q3LKmQsfUFxcLJYuXfqHx10ul9DpdKK8vNzddv36dTFz5kyxZ8+e23GJ9Ccr\n",
       "KysTs2bNElarlXnLVGpqqsjOzvZoe+WVV0RqaqoQgq9zuRoZGREBAQHiwIEDHu2JiYmipKRECCGY\n",
       "u4yo1WphMBjcP0/mdT0wMCACAwPFvn373DW9vb1CkiTx3Xff3b6Lpyn5/8z/16+//ioUCoU4fPiw\n",
       "Rzsz92/eMr+hs7NTKBQK0dHRIYS4tcx94p2VL7/8EklJSUhPT4dWq8XDDz+M2tpa9/Fz587BbDYj\n",
       "JSXF3aZSqfD444/j2LFjd+KSaRoJIVBXV4esrCwEBQUxb5lauXIlDh06hJ6eHgBAZ2cnmpub8cwz\n",
       "zwDg61yuHA4HnE6neyn7G1QqFX788UfmLnOTybetrQ2jo6MeNZGRkVi4cCGfAzLFzOVvcHAQADBr\n",
       "1iwAt5a5T0xWzp49i127duGBBx5AU1MTCgoK8Oabb7onLDc2kNRqtR79NBrNmM0lyf8YjUacP38e\n",
       "r7/+OgDmLVfr1q1DZmYmFi5ciMDAQDz44IPIzs52L4PO3OVp5syZWLJkCcrKynDp0iU4nU588skn\n",
       "OHHiBPr7+5m7zE0mX5PJBKVSidmzZ3vUaLXaMZtSkzwwc3mz2+3YuHEj0tLSEB4eDuDWMp9w6eLb\n",
       "weVyISkpCTt27AAAJCQk4MyZM6itrcX69eu99h3vPkjyLx988AGSkpIQHx8/YS3z9l/V1dXYu3cv\n",
       "9u/fj7i4OLS3t6OgoAB6vR65uble+zJ3//bxxx8jNzcXkZGRUCqVSExMREZGBtra2rz2Y+7yxnyJ\n",
       "5MfhcCArKwtDQ0P4+uuvp+WcPvHOSnh4OBYtWuTRtmDBAly4cAEAoNPpAGDMzMtsNruPkX/65Zdf\n",
       "cODAAfe7KgDzlqsdO3Zgy5YtWLNmDeLi4pCVlYWioiL3B+yZu3xFR0fj+++/x/DwMPr6+nDixAnY\n",
       "7XbExMQwd5mbTL46nQ5OpxNXrlzxqDGZTHwOyBQzlyeHw4GMjAx0dHTg4MGD7lvAgFvL3CcmK8nJ\n",
       "yeju7vZoO336NPR6PQDg/vvvh06nQ1NTk/u41WrFDz/8gEcfffR2XipNs/r6eqhUKmRkZLjbmLc8\n",
       "CSEgSZ5/ciRJgvh9qyfmLn/BwcHQarW4evUqmpqasGrVKuYuc5PJNzExETNmzPCo6evrQ3d3N58D\n",
       "MsXM5Wd0dBTp6eno6OhAc3Ozx4q+wK1lriwtLS39My76ZkRFRWH79u1QKpUICwvDwYMHUVJSguLi\n",
       "YixevBgKhQJOpxNvv/02YmNj4XQ6UVRUBLPZjPfffx+BgYF3egg0BUII5Obm4tlnn8Xq1avd7cxb\n",
       "ns6cOYP6+nosWLAAM2bMQHNzM7Zu3YqXXnoJKSkpzF3GmpqacPr0aQQEBKC1tRWZmZkIDw9HdXU1\n",
       "JEli7n5ueHgYnZ2dMJlMqKurQ3x8PEJDQzE6OorQ0NAJ81WpVOjv70dtbS0SEhIwODiIvLw83HPP\n",
       "PaioqODtYj5oosyvXr2Knp4eXLhwAQaDAcnJyZAkCQqFAmq1mpn7IW+Zq9VqvPDCC2hpacHnn38O\n",
       "tVoNi8UCi8WCgIAABAQE3Frmt7Z42fT55ptvREJCglCpVCI2NlbU1NSMqSktLRVhYWFCpVKJZcuW\n",
       "iVOnTt2BK6XpcujQISFJkmhpaRn3OPOWF4vFIjZu3Cj0er0IDg4W0dHRYuvWrcJms3nUMXf5+eyz\n",
       "z0RMTIwICgoSYWFhIj8/XwwNDXnUMHf/1dzcLBQKhVAoFEKSJPf3OTk57pqJ8rXZbCI/P1/Mnj1b\n",
       "hISEiLS0NNHX13e7h0KTNFHme/fuHff49u3b3edg5v7FW+bnz58f037j8b9LHE81c4UQv9+DQURE\n",
       "RERE5EN84jMrRERERERE/4+TFSIiIiIi8kmcrBARERERkU/iZIWIiIiIiHwSJytEREREROSTOFkh\n",
       "IiIiIiKfxMkKERERERH5JE5WiIiIiIjIJ/0XkMJRB/+WilkAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4800f56208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(10,100, 0.05)\n",
    "plt.plot(xs, [gaussian(x, 90, 13) for x in xs], label='var=0.2')\n",
    "plt.xlim((60,120))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the problem with this chart is that the area under the drawn curve cannot equal 1, so it is not a probability distribution. What actually happens is that a few more students get scores nearer the upper end of the range (for example), and that tail becomes 'fat'. Also, the test is probably not able to perfectly distinguish incredibly minute differences in skill in the students, so the distribution to the left of the mean is also probably a bit bunched up in places. The resulting distribution is called a *fat tail distribution*.\n",
    "\n",
    "We are not going to be applying Kalman filters to grades of student papers, but we are using physical sensors to measure the world. The errors in sensor's measurements are rarely truly Gaussian. And, of course, the signal itself will have time dependent correlations. For example, consider a sensor mounted on a helicopter. The rotating blades cause vibrations in the air frame, which will cause small deviations in the flight path. This deviation will be related to the frequency of the vibration, hence the values at t and t+1 are not *independent*. The vibration will effect sensors such as the INS. No physical object can react instantly to changes, so the INS will somewhat lag the vibrations in a perhaps quite complex way, and so the noise introduced by the vibration will be anything but independent. \n",
    "\n",
    "It is far too early to be talking about the difficulties that this presents to the Kalman filter designer. It is worth keeping in the back of your mind the fact that the Kalman filter math is based on a somewhat idealized model of the world.  For now I will present a bit of code that I will be using later in the book to form fat tail distributions to simulate various processes and sensors. This distribution is called the student's t distribution. \n",
    "\n",
    "Let's say I want to model a sensor that has some noise in the output. For simplicity, let's say the signal is a constant 10, and the standard deviation of the noise is 2. We can use the function `numpy.random.randn()` to get a random number with a mean of 0 and a standard deviation of 1. So I could simulate this sensor with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "\n",
    "def sense():\n",
    "    return 10 + randn()*2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot that signal and see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAyIAAAGNCAYAAADtmMVMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXl4XMWV6I8k23gBzGrAGLNM2IkZhJJ58/K+ecw338xA\n",
       "5n2ME4aXlxcGMm+GIQkZcIAACSQGYgg7yNhmscG2vBvvNsa7LdnyprYl25IsedFq7fvSWlrdfd8f\n",
       "rdt9l6p7q+6tu3Tr/PIRq+9SdW7tp+rUqTRJkiRAEARBEARBEARxkXSvBUAQBEEQBEEQZOSBigiC\n",
       "IAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6D\n",
       "igiCIAiCIAiCIK5jqIjk5eXBww8/DFOmTIH09HRYvHix6n53dzf86le/ghtuuAHGjx8Pd9xxB3z8\n",
       "8ceOCowgCIIgCIIgSPIzyuhmMBiEadOmwRNPPAGPP/44pKWlqe7PmDEDcnNzYenSpXDzzTdDbm4u\n",
       "PPnkk3DVVVfBY4895qjgCIIgCIIgCIIkL2msJ6tfcsklMHfuXHj88cfj17773e/Cv/zLv8DMmTPj\n",
       "1x544AGYNm0azJ49W7y0CIIgCIIgCIKkBLb2iDz00EOwadMmuHDhAgAAHDx4EIqKiuDBBx8UIhyC\n",
       "IAiCIAiCIKmJoWmWGe+88w48/vjjMHXqVBg1KhbUnDlz4Ic//KHu2a6uLjtRIQiCIAiCIAjiARMn\n",
       "TnQkXFuKyAsvvABHjhyBzZs3w4033gi5ubnw/PPPw4033gj/+I//KEpGBEEQBEEQBEFSDMuKSDAY\n",
       "hOzsbFi/fj380z/9EwAA3HPPPVBUVATvv/8+KiIIgiAIgiAIglCxrIhIkgSSJEF6unqbSXp6Opjt\n",
       "f3dqeQcZeQQCAQAAyMrK8lgSJJXAcoU4BZYtxAmwXCFO4Ma2ClP3vWfPngUAgGg0CtXV1VBUVARX\n",
       "Xnkl3HDDDfB3f/d38PLLL8PFF18MU6dOhdzcXFiyZAm89957jguOIAiCIAiCIEjyYug1q6CgADIz\n",
       "MyEzMxMGBgZg5syZkJmZGXfXu2zZMvirv/oreOyxx+Duu++Gd999F2bNmgVPP/20K8IjCIIgCIIg\n",
       "CJKcGK6IPPDAAxCNRqn3r776aliwYIFwoRAEQRAEQRAESW1snSOCIAiCIAiCIAhiBVREEARBEARB\n",
       "EARxHVREEARBEMTndAc7oKbpnNdiIAiCCAUVEQRBEATxOUt2fAzvr3zBazEQBEGEgooIgiAIgvgc\n",
       "ycBxDIIgSLKCigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6D\n",
       "igiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiC\n",
       "IK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiCIAiCIK6DigiCIAiC\n",
       "IElPzvaPIP/Udq/FQBCEA1REEARBEARJegJluXCoeKfXYiAIwgEqIgiCIAiCpBSnKo5CVIp6LQaC\n",
       "ICagIoIgCOJz5q1/DVo6G7wWA0GShvmb34ILzRWOxnGoeCf0DfQ6GgeCpDqoiCAIgvicspoiOHeh\n",
       "2GsxEARRsGL3XAiU53ktBoIkNaiIIAiCIAiCIAjiOqiIIAiCJAGS1wIgCIIgiGBQEUEQBEEQBLFA\n",
       "mtcCIEiSg4oIgiAIgiCIBXClEkHsgYoIgiAIgvidNJx7RxAk9UBFBEEQBEH8joRz77ykuaC8oXqI\n",
       "IPZARQRBEARBEARBRhCz17wClQ3lXouBigiCIAiCIIgl0GQOSVLO1ZXA6arjXouBigiCIEhygKY5\n",
       "COI70GQOSWIkH/QrqIggCIIgiN/BmXc2MJ0QJKlARQRBECQpwAHWiAZn3v0JKj4IYgtDRSQvLw8e\n",
       "fvhhmDJlCqSnp8PixYt1z5w5cwZ+/OMfw+WXXw4TJkyA+++/H8rKyhwTGEEQZGSCA1EE4QOVBATx\n",
       "O4aKSDAYhGnTpkF2djaMGzdO5wqvsrISfvCDH8Bf/MVfwN69e6GkpATefPNNuPjiix0VGjFGkiRo\n",
       "aKvxWgwEQRAE8RBU3hHE74wyuvnQQw/BQw89BAAAP//5z3X3X3nlFXjwwQfhvffei1+76aabhAqI\n",
       "GNM32AtpkAbjLpoQv1bfWg3vLJ8Bs5/d4KFkiAiCAz3QPxiEqyZe67UoCIIgCIKkFN4r65b3iESj\n",
       "UdiyZQvceeed8OCDD8KkSZPg+9//PqxevVqkfIgJby99Fj5Y9aLqWjgy5JE0iGgWbn0P3lj0CwAA\n",
       "2LB/Efzxy3/3WCIEQTwB9yJYANMMQfyO4YqIEc3NzdDb2wtvvfUWzJo1C959913YvXs3/OxnP4OL\n",
       "L74YfvjDH1LfDQQCVqNFNHT2tkF6WoYqTVt76gFgZKVzqn5rW0cLAMS+7+TZAujsbUvZb/UjrGk9\n",
       "FAlBODIE48ZMMH/YIlVVVTBmAPM+VeCtx93d3ZbeG2kEg8F4GpWWlkJTTbuj8dVU10Ag5J88wfKB\n",
       "8FBf32BYZm699VbHZbCsiESjUQAAmD59OsyYMQMAAKZNmwaBQADmzJljqIggTuP9UhuCjCTyytdC\n",
       "Xcd5ePwHr3otCoIgCIIkDZYVkauuugpGjRoFd911l+r6HXfcAatWrTJ8Nysry2q0iIacfIC0tDRV\n",
       "mlY3XgpbT46MdJY1+VT91r1nV0Bbb+z7cs+vhtae1P1WP8FbrnaVL+V6npecfIAbb7wRsr6LeZ/s\n",
       "WG2zDldvhMYurP9G5OQDTJgwAbKysiAnH+Cuu+6CGybd4mh8N954I2RN8z5PUr0vRMSTkw9w3XXX\n",
       "GZaZrq4ux+WwvEdkzJgx8L3vfU/nqvfMmTO4YR1BkJGFC2c8aL0WIgiCIEiyY+q+t6ioCIqKiiAa\n",
       "jUJ1dTUUFRVBbW0tAAC8+OKLsGrVKpg/fz6cO3cO5s+fD6tWrYKnn37aFeGtEomE4VxdiddiiAPH\n",
       "JylLmiJz0zCjRzQSHmg3skFFlIlUTaXWrkZ4Jnu612IgiHAMFZGCggLIzMyEzMxMGBgYgJkzZ0Jm\n",
       "ZibMnDkTAAD++Z//Gb744gt4//33Ydq0aTB37lxYsmRJ3OWvXzlx/jDMXvOKK3F9uOolKKsucjYS\n",
       "HJ+kLBJmblKA+YQ4DiqiTKRqKrV1NXktAoI4guEekQceeCC+KZ3GE088AU888YRQoZwmEo24FldV\n",
       "YzmUVh2DO278S9fiRFITHOx6T0tnA/xp8S/xjB4kaegOdkJGejpMGHep16K4jhuLSGgyiSD2sLxH\n",
       "BPEvOFxFEGfo7G0jXkezOcSvvL7wP+HjNb/3WgxPSKVFJFR4EGfwvpKgIuIG2ID4EjdXxpDUBler\n",
       "EL8yFAlBT5/znm946e3v9loEU6LYRyCI46AikoKg2sPGbz55BJo76r0Ww1EOnNyWWo4ZPAZnJRFe\n",
       "Cspyob27xX5AKVb2fv/F4xB0WBmxk2TB/m6Y8ckj4oRhoKWzAeaum+lqnAjiNaiIpCA4N8tOcMD/\n",
       "s3J2WL33M9h0IMdrMTwhGo3A+yt/67UYpnQHO2AoPOS1GIhDLNn+Eew6ts5+QDbsjPyqwoSjYa9F\n",
       "oDI4NOB6nGcvnILy2hOuxwsQ88qFnvkQL0BFBPE94cgQDIb6vRbDE9DkxzrhaBhqms56LYYpry74\n",
       "N9h8cInXYiBISuBXpcs+zn7ZG4t+AaVVxxyNA/EfflA+URFBfM/K3fPgt5/+1KHQU7fbkkFlxv/0\n",
       "9HV6LQLiIOjMAEkGvFgFQpARqojgwCyZSPV9HFaRJAk6egTYniPMODac9MGsVCqz8cBiqKg/7bUY\n",
       "9kixPSJ+BydwkJFIb383bD28wtU4R6giklqkeoOZ6t9nleLKApj51ZNei+FfsNggw+w+th72n/zW\n",
       "azEQxNf4wUwH8ZaSygBsO7LK1ThHqCLi7swSzmP5l2T2gtQ/GPRaBGG8s2wGRCL+3bhqBnbgIwdJ\n",
       "kiAqGR/0q0VIM2OnjCVxO2eHVDKJG6FZiIwARqgiYs5QOOS1CIZ8uPolqG0+DwD6xjblBkWp9j1u\n",
       "kwTpV9daJd4+2ZGOOxaoJEmpV88QJpZs/xjeyvm112IgPiGZJ7MQRN+Lud+voSJCoLe/G56f+7+9\n",
       "FsOQqoZyOFN7EgCSx3Spo6cl+e203SY5stafOJh2ews3wrOzfyQsPMxm5xE1O17RcBqaO3HfGiIe\n",
       "nNxARiKoiBAIoecIR1i2YzZ8/PXvbIczEOqH5o46ARL512wuHBmC4ECPkLCwaxPPhZZKr0VAkgoB\n",
       "LU0Kzrw7ZTrV1dvuSLhWaetu8loEBPEtqIggvkc7kF6X9yXMynnaE1ncYn3eQvjd5/+qHr+k+GxZ\n",
       "sqzskbArO8twDGdLkxevzXf8ulfCqTr/52XPOhKuFULhQXh94VNMzxqXE3/mIYLYBRURJOlw8nDD\n",
       "vsFeXwz42nuaY38IEAW7L3E4NaD0vsQhvscH7VKy0CdoNVkEPP2J0bNeK7NIiuKDdgUVERfABkQs\n",
       "Ts6cv/zZY3D8zAHHwmeFZQaTtVx538yw4ddZWwTxA2cunPJaBNuEhgYhFB50NhJVu2ijTUmWhlMo\n",
       "I/KjEQVe6CUjVBFJ9cqW6t8nEn1H1RX0l30xDT+s3CAIgrDy/soX4OPV9vcJsuNGGyluAsXOpKUk\n",
       "SdA70ClMFmSE4IOJ8hGqiCAsvLHoFxCODHkthk5FFzlzTm74fTDAF9k4JInCksx7RBAEMaexvRbq\n",
       "26rjv3EVVI2dyaWGrkpYd2yOQGmQEYEPxgcjVBFJlcaP9h1ivq+1q9HR/RhWwQErwoIz5YRSt2xH\n",
       "xRfAoZJdSX0ApCeIavZ90HFvzl8C5+pKmJ/3a4/nSB31Qf44gVkeDjlt8oYgDjFCFZFUgdbgplZD\n",
       "PBIVD5aBA+498g6vZ3JX7JqDLoSTCNHlZWdgLeQWbhYapmu4qij4oI3k+F5s01MDSZKEud93Gj+M\n",
       "r0aoIuJ9wgslRWeAEGNSbY+I14N7FuRxgheNtx86DAR8YVONpCap1qaPVI6U7om530eYGKGKSKqA\n",
       "HaITeNUXSJIEfYO94sNNkgFsssiJIIgNFIpcMkw+8FLfWg39g32JCzYV1+W75sCWg0ttSoW4SbI4\n",
       "vCHhRT88QhURtxs/h+PDGTrBeDMgPnn+MLz82WPMz+Myvn9wo/FOxUGbCArPHoT27havxTDG67rq\n",
       "dfxKnJ7p8fhb3172LGw8sMhWGCWVgfjfh0t2wYFT2wEnHpFUZUQoIl297VDbXOG1GM6R4su5ukFe\n",
       "in5uV7Aj/jcqGf7GC6UAV4zILNz6Lmw7usprMRAL+LlM25FN5W1yuH/mMbv6fNMsy3HbAU3DRiLe\n",
       "5/mIUEQWfvsevLfiOa/FQHyI3wf8fu6oRZMcM/4xGUdSviQFDAMoL8tXMpRsxBqkvE1PSwyteFoK\n",
       "v/dHbtA30OtLb50iqG48A4dKdnkthu8YEYpINBrVXMFBBDN+bBgdFsm7WSFlvD5Md4dJ6sG9zTKD\n",
       "M5HIiEHQHhGWOuNV95WWph9asbRv1G8aQe3DzK/+A+ZteN1rMRxh/f6FsGIXnvWiZUQoIl4jqjEs\n",
       "qQzAV1vfNX1OaJvlxwbQhyL5kZ6+2Cm7ST3AF4gkSb4a8Ld1NTkex9HTe2Hxtx84Hg8r89a/BjuO\n",
       "fi08XP/kqov4cZKIBUF18NnZP4I6ExfWXlV31YqILIRNYZJhteSZ7OkQjUZshTE4NADt3c2CJPIG\n",
       "ak75qKHyk9I7QhUR/1doEgVluVB09qDXYriPo/VCXxa8ayvSCH8l4JVrKByyJU2qESjPhWdn/0hI\n",
       "WHbNfFo6G+D1RU8JkcWIwyW74NiZ/Y7Hw0pZTREUnvOmDfNyIOdI3DznUyRpn6fkcMlumJXztOpa\n",
       "W7fzyrwV0tKtDa2SQdkwQ8RkD06eOU9xZYHXIsRJaUXkmezpjrhD9RvOjtPTYOvhFVDfWuVkLIgl\n",
       "kr/TchRNh9jUfkFc0DZrnWozK3Ok/HGOmO6cIW38tBqGxOCpR2U1RdDcUae6FhoyPk3cq3F9uso0\n",
       "S1L8vzG2yqjPlJhIJAyN7bVei8FEVIpCd7DT0TjKa05AVNJuE/COboVzHK9JaUUEACibnrBD4mHb\n",
       "kVXD7gO9IZVmR95eNoOtwSN0KmZrN6HwICqMhtjvqGkzlnZLqGNlHAffSIpAqnmh4VXfupYqWE6w\n",
       "va9sKIcjpbsdFkwvmXqzOr0Onq8rgcMlguTzWV0/WLwD3lryX16LwcSRkt3w6oKfOxrH3PUzoaqx\n",
       "3NE4kpWUV0RGwqyxG1+YCkv7zDjYoNe3VvHNEilkMZNqV8E6eHvZDGuCpTApMxOuGfCwmHGkzLcL\n",
       "IC0tDfYc3+CReasD7afPZsCtYLdfiQyvLBaePQCHCd6I1uYugGU7P7EVhxWIdZNQF9fkLoDluxLy\n",
       "Gddp5/NbZGsxODQgMDRn6env8loEz/BDFzHKawGchlyxk78BVyK6HOUWbYEN+xeprvmpzxM5e+z1\n",
       "d1U3noUpk26BjPQM22GFwhQzBR80NH5ARF6nxf+1G5hGqWAJT9NjoJKRgLVN2LB/EVw98Tr4y1v/\n",
       "u43IkjDdfdR+u4lXE2jpyj0i8l51O16zWPC6M9OQCvtdRiJetG4jYEVEPFEpCoVcs2puV0h7Ram6\n",
       "6SxEomHNVe8aFUnnftnh+Fysih+s+i0Unc2Px6zDwxmy9u5mqGupcjQOFZpOOBwZstUxK9+UJAm6\n",
       "etsth6UPW2wZcarMpZJZI5IasJTIhrYafd0ntIXyE8pnlcqHV+U/DYdW4OWY4UztSQj2dzM/P6Is\n",
       "PnR430eM0NrClvB7jm8gXm9orYaFDG50zSgoy4UvNr1pOxw38HJ2o0FjypRqjUY4olX6FN9oOBA3\n",
       "Lsd2O+F5G16Hd5Z7Z+r13JxHYV/RZiFhnak9CYedthW3gRSNwjvLfyM+XB90MimHhbYQJ4f5+PPS\n",
       "Z6C2+bztcJw+p4SGckVEroPHzxxw1lzJgryh8CD0cgzYefCyzM9Z90fYengl8/NW2snqxjN0K4Qk\n",
       "xotsS0pFpLmjHirqyxyPR2ueJJpjZbm2XKhpK3pPX9dw45navZ5Q0yxfpJX8PX6QJYHbK1Gknqu5\n",
       "Xe0lZ9Wez+BQ8U7uoPsHg5bFIqErNzbNdYYiQ6ZnIuhkYOnpUQ/Rg1qBp7CmPotnubippJeumQlf\n",
       "pJJnuG1YuiMbTpw7ZD0eBz5x+c5P4PdfPC4kLL3iphb4mezpjik9MmtzF8CZ2lOx2B0uEh+sehHy\n",
       "ir4h30ziNsZ3pll5eXnw8MMPw5QpUyA9PR0WL15Mffapp56C9PR0+OAD5w/PWrDlz/Dx1y8zPeuP\n",
       "gSYZ0Rn+yvwnhhWb1Bp9uJ6DDtuAM7VRTB9t/JBc9pN5Vlwre/6pbZB3civbu5LsNlPk9ztUGq24\n",
       "5mVyWesfd5FOwjV7bbF+7yvcHPPCmIx7RJIQbZ6S+nJSTvijvXOv1zpdXRgb4FsY/Hb0tGquiDsD\n",
       "hJRfwYEe1kAskVu0BfJPbeN+TytrVIoyKcJ6E/ZhsI3gwlARCQaDMG3aNMjOzoZx48ZRZx3WrFkD\n",
       "BQUFMHnyZP9tUEoDQpvgMxkF4tgyq5d7RBwN3U8HGvqr8XK9Qyc23mJk8FfK6vG7fHYI9nfDil1z\n",
       "vRbDNuvyvoSymhMW3/a2z3Gr/Q5HhuCZ7OmGz7CXdY4naQM/H3T1hl8hYMD66YbXYcfRr22HYxdd\n",
       "f0E8ldf5lk5Ev7WzYA08N+dRAdIkIz47Wf2hhx6CWbNmwSOPPKL2AqGguroaZsyYAStWrIDRo0c7\n",
       "IqQdQkODws0yRA3QeMNxq00ldlpeKpgpN7tgnpZWBg7aLIqXryRKv7Yu85OSraRNzrYPrYjjGNq8\n",
       "slK7aJM+F1oq4Fh57DR1P+R8RUMZHCrhN6fjgasttdWWSY63hc0ddb49MdwM5X63SDQCfQPWDxRm\n",
       "yVGyT0wfaB9Jgoi0autugm1HVjkStlc0tNXYC8BvE/I+x9YekXA4DD/96U/hD3/4A9x+++2iZDKF\n",
       "Z9Vl/ua3CCcq+6F75sctqZWdejK4CB0M90M0GvFaDAHYa7xEZ5Xckew5vtF0llMEkWgEXl/0lOqa\n",
       "qG+iLqEnEaxJsWbffFi8bdhENgnqrxBS6DNn5TwNH6580WsxbPPt4ZXw8uePmTxFb/P0XrMIz8i3\n",
       "fDzwM+xDueT25zceLd0LWw+viP+WP9ezPEmhtsAb3M83W+eIzJw5EyZNmgRPPfWU+cMKAoGAnWih\n",
       "r6+POZzmjnpdvJXNlYbv9w526d5R0h5sYo4fAKCxsYn4bFdXF1c47e1tqudra4cVLEmKX6uqqoSO\n",
       "ph6ucHXxtLXF/y4sLAQAgOYm8jfw0N1jTS5ZMZLf6+joUP1edeQDONd0Au6+/r9xy1RaWgINE9R2\n",
       "snV1F2x/q0xnXwtcOu5K1Um75eXl0NWY8J5SWVkFGX0BqGmoBoDYd8nfqCzrwWAw/jcAQGVzhep3\n",
       "Y2Oj6nfvQOwE977+fkvfMzAYk/HE6aOqcLXk5M+C//vfXoJRGfZWRItOFOniaWlt0cXb19fH9D2h\n",
       "cEz+Y4Fjqus8aaF9trUn1p60tanropxWrGF39rWqnu9kaAtqamogMJS4X1paCs21nbrnent742H1\n",
       "BhN/e0Vt2zmVDKz5x0Nbe5tpmHKeDQwMWI7/3PnzMDgY85TDEwapDzB6fzA0SL2vbAfNZJAHwaGh\n",
       "IUfLQHVbGdxwxW3xAwYDgQCcqypTyasQKn7txIkiGDfmYmKY5eVlqnayXVPnABJ1or4h0c/LZR4A\n",
       "IDrscMPKt/f0tzO9W1VVCaP61c801NfH3+sPJSwyKisrIT14Sfy3dixT3Vgdv6eMNxwJQ1nZaao8\n",
       "TU1NMGniVCZ5lfT0qvvkyopKSOsl5weN+vp6VRjHjx+DjPRRUFNfq5OnuLgYasc3moY5ZKO8yn1n\n",
       "c7O+76BxoS42lop/w5kDqt806urqiM/U1dUZvu9leyxT3VgFALFxg1Keqkb1+PjWW291XBbLKyL7\n",
       "9u2DxYsXw4IFC1TX/TaDbkkr99k3mCHell+ZZuI8Og0O9VmUxjzuvkFnvXFYZVPh53CuqUhQaP4t\n",
       "l0MRAW4MndsigqQ6Pm+zvZgbbuyqgiUH3XEPn1u2Blq61ZYHtmfEBWSpO+ZB7hlNJxNm2T8Y7oeo\n",
       "g840eMZFyWxGlgpYXhHJzc2FhoYGuO666+LXIpEIvPTSS5CdnQ01NXQbu6ysLKvRAgDAzrLx0NVv\n",
       "Hk5OfsyfdySqjlcqC8KBswArjrwLL/yf9+G6K6eq3mvvboZ1x+iy1rVUwpYitu/IyQe47tpric8e\n",
       "qd0MDZ3s6VHSkgtVrbHnc/IBbrhhChyrit279Y5bAPIBbrzxJrjm8uth2ynr6Vzath8qWmJ/33vv\n",
       "vfB1AcC1115jO99y8mcBAL9cS4bP+5PfO9G0G2raYr9lrX3SNZO4w83JB7j77rth8lU3qa5NnjzZ\n",
       "9reqwrv+Osi6Lyv++/bbb4dbp9wT/33TTTdB1t1Z0HeiGY5WxL6reDivx40fDx19sWv7zq6Etl59\n",
       "OZZ/1w0UQ2l94ndbdxOsOwYwftw4S9+ztfgi6BkAuOLKK6GylZ5vOfkA9977l3DphMu441CHcS+s\n",
       "CSTiyckHuOrqq1Tx5uQDjJ8wnul7+geDsPIIQOb9mbBEcf4oy7tyudI+W9N0DraeBLjyyiuhoiVx\n",
       "X04r5fND4RAUns2H79/5t7rwG9trYVNhoi5PnDgR6g3agpx8gKlTp0LWvYm0ueuuu2DqNd/RPXug\n",
       "ci00d8fC2nNmObQH7be5drioIgp7yxLfOn48W/6xkpMfK6NGYebkx/LsfDPA2LFjTeNv7qiD1Xs+\n",
       "g18/8idVGN/5i7+AU/V5EBxkT9OcfIBrr7su/jytbCmfzxiVobufo2gHc/IBatrK4JJJo+H2qfcS\n",
       "wzlc0gVQHPt7zJgxltJ8y8FlAADwv/77zwyfy8kHuOOO2+H6q2+BFUdiMpZ3HILzzaCrv5CWFv+G\n",
       "e++9Fy6dcDkxvNtuvw1uu2Fa/NrptgOqOqesE42hMige1oMunnAxtA47Z0pPTweIAoy5PAL33JwF\n",
       "6ekZzN/e0tkA648b53NOPsDNN98EWXepv/E6RR/SHeyEr4e99N98882QdWfi2d3lS6FDUT8HT7XB\n",
       "4eHjU5TfOSpjFNx5553w7Um9PDn5ANdccw1Iw4tHN9xyLVxzxRSmbzxQsRZaehJl6uZbboasO/jK\n",
       "SUv4HJyoBci6/35YehAgMzMTRo8ao+rPZDnvueeeuGzPZE+Hf/4fT8Df3f8j3feMGj3KUnnNyQe4\n",
       "7PLLoLoN4JpJ7GOCDqkajlerZQUwz/vrr7+e+Ey7VAWF1YSyD+bhuoVc1q65Rj22CxW3w+HzsfHa\n",
       "7Gc3xC13nMTyisivfvUrOHXqFJw4cQJOnDgBRUVFMHnyZHjuuedg9253Dg6zfphMTFMeCoegvrWK\n",
       "cN9YOxa2AsEZjNHjM7/6D2uBamjtUi+byt/q5UqXLr2FyuLvmRCVdCZTTLRkcSPnhJgDx89wVEhs\n",
       "62T12LsRwoGRbnCm9iQs3ZFNvKedgcOT1W0iuH06e6EYzlw4JTRMHlhnaKsazzgqx46Cr2FHgTWP\n",
       "THabBJ37XoNGxqx/WrDlz1DddM6mRMlBe08L+8O645DstLeGQRPRuw+2xjPZ06E72GFBAmfAFRY+\n",
       "TN33FhUVQVFREUSjUaiuroaioiKora2Fq6++Gu666674f3fffTeMHj0arr32WldsygAA1uctdChk\n",
       "0bt+nS+UIpY4a5rOwRuLfqGuRJLqH8eRJAkKzx40f5DAoZJd8OqCfxMskXus3Tdfd02V7pydRNI1\n",
       "hvGyJmkv2SIcNfcHbxffDvg9nEDo7G2DYH93fHAj2nshL3J98KJW8Mbp2/LEg7gDkxyWwWnE5KX8\n",
       "Jc9kT4fT1YX02Bw6k4g5LPl7CWmvL9fi4u0PWTP9BgDL5YSWblbrbyQacd3xjh9aGkNFpKCgADIz\n",
       "MyEzMxPSxPOEAAAgAElEQVQGBgZg5syZkJmZCTNnznRLPkN6+vQbNbWYD8a8PB/DvAgoC6XTkg4O\n",
       "DVDvuZVKnb1tsHDru5q4tb5OydKcryshzIrw43TFpM3s2R18UN33JglEd8MCOsio2yfE+wgvVzL/\n",
       "+OW/w5z1ib5i7jrn+g2er/QiRXYG1sJQ2LpCbCUf3R+Dp2l+sQhA/y6/7Df1ixxKGttqVb952/q+\n",
       "gV4IKs4cO1yyi+v9E+cO6T0pMhxA6QpW8ssnefxmztOw6FvnDwU3wovybrhH5IEHHuDqxCsrK20L\n",
       "xIfVRswnyglDhs/45BF488nFcMn4iW4IRLgiUe44A9NsAG0WgrECvfbVkyrbbz/ig7lEwxNyWTlf\n",
       "VwK9/T1w73fMPZrJp4Ar89GWMuVme8obl05rTA3TrFB4ENLT0uMe1JSDnc7eNtprSYOdTrp/MAij\n",
       "R1nfR2UHT1aBbGpCosvunLV/gPtu+wE89g/PssXPnNf671S2mSK+gyUMntR+b+XzMDQUgqsuuxYA\n",
       "+M/NqB322BiLmBwzS/470ez5QaWw2me2djVCxMaKyMHiHTD5qpvgpmtvsxyGF9g6R8RrjBoKo+VB\n",
       "86JqfN9tTV92Q8qCaG1WHhy6NWMQJpz3oG2Eic6VOORr72mBupaY0kxsLF2eEWDuqDSyMks5/D2d\n",
       "vW3w4eqX2AWLx2M9PXK2fQRffvO27fiGwiEIR6zNKIuqE5UN5dAVbBcSlrUy5ocu1pg3Fv4Cvtzy\n",
       "jgcxM6RNGrtpltfnUnhpVml976Uad76BvU4MRUJQUnXM/EHRMrhQbdMgLR7NZxvfgLwT3xg+39Hd\n",
       "At19HZbzSGUKrm3L/N9M6fGFCZ99Vu6eB5vyc7wWg5ukU0RaOhvi2rtheZcrh0mHb6XDEXeyOhv0\n",
       "xoJ2XaC9J8Fu30nMNhafqjgKJ88fth2P0Z4a2reuy/vKkp37zoI13O8QG0abe0Rqms5BVUO55ffd\n",
       "gvSZb+Y8DV9sfgsAvJPro9UvwZLtH5NvEkTyejDrBd19HVDfVm3+oAmSJEE4MsRkfis/LxK/meNY\n",
       "a3+tlb8X5v5EtQfBan1jK//WN6A7j2wN4LUcMuz5cKb2JFfIvN8oSfpZe20YpPzX6yx+SVv/YLvX\n",
       "8Lze8JN0isi3R1YmfhiuiMj/uteA88Ium/MKBx3n4li87UPIP7Vddc1sWbK5o05I3FY6uX2Fm6CS\n",
       "YyAv09PvjPs7s1Jqt5HnM82yX2cSWaIwzRq+qFzF8gLT1RibplkiO2Rlfjnpp58Xnm/8+OvfwXNz\n",
       "HoVX5v/cOYGskoQdPS9dvdZW/rqU5ncMisirC35O9ZxUUhmArYdWEO8pIuG668wkhnUvm6JKkgSS\n",
       "q9Mzqv6Tms8jbyLG74TCg1Bec0J9cTgvB0L9EBzo8UCqJFRElBh2bJLRIMp8COcn+CdWxTUATs5Y\n",
       "HCvP0ykiUYJplhox35ZoSNOgrqWKw8Ure3oUns0nXp+95hXYc3yj4bvxcpvkgx6e8iNB1Pgdwzpt\n",
       "FLf9NFy95zPV76RZ7fC4+Fgd+FU2lHE9L7qdSpr8NcDtb0hLS4M3l/w6/judFr+mTRsI9RMf239y\n",
       "K2w7uioRPrEsEfJd+ZhGhl6OSaHEvIgP22CHz4p8Y9EvdH2zEqO9w1x1kepz3odpngIcKd0DcxUO\n",
       "RJR8tvEN+OOCf3dZohhJrYgY4aclP/vdAfuMQ2yALdI0y9l0HIqEVL/DJgpBeQ39lHKuQa9ipvid\n",
       "5TPgcCn72TcDoX7K+TNqFm59j3qvqlGxssKZxpvzl0Deia2WVmeSAv9U3TgtnQ2q39p6QS577DVf\n",
       "N0slCH+0g36QQSA+UlJYJeFVCMWUG7Y4x4waIyAu7zBT+Iz6UMsliRCkxjDKasgAENs0bWTeFSWZ\n",
       "ZmlkEllLehVOLwBiXr+0bXJnfGXNvfamjDYe8VEbocKgLLZ3N+vGY26R3IqIFBsU5mz7iP9FQ9z1\n",
       "mlXfWg052+nf4OXsnNyIOqWQhDUuLc1Ms6gVn9fGVfP8UDikvEl/T5Jg66Hl8PayGVzxcSNnOSHv\n",
       "dwbWwpp9X8D+k1tNgoi9K3JlwAniZYuwH0mIxxmBny3nht0G260aLcqUkQsPZjPrW+3vS6Fx8vwR\n",
       "7/crUM8r8C+s/RbPaeeEWGy8awJjnpuXDTG5ZJSe3CuPssxGh0QayM3kTZXBURBryvz+i8ehQeGy\n",
       "OGf7R/Cnxb9UPUOb6WeBtxTtCqwDAICK+tPkB+y0F06O90SWIYF4rojM/OpJCA1Z89IhgQSN7bUQ\n",
       "KM/V37O1ydqd5l2O5cS5QxAo03+DjD8OpnMmTVQKAABETE2zxMDkcY2CcLt7o4ZHwMniLAQHemwd\n",
       "OEc/G4WdKMlDG+lP1obaYtqdqjhqOrgosnjopoyfB5DJCIvCdURe9eTcRL1gy5/V+xi8VkqSAEmS\n",
       "OPotxvS05AHTPlZiqG+rZnK0YFl6wplRwg/CM5mQo75gYkI7FA7B+bpSbnEGFAcWDgzSDy/knTQ4\n",
       "Vp7H7WkqGT1TAZDzxA+r5p4rIh09LRAc6DZ/cBj1qd9GCaieZXWbI6V74PiZA0zPmhYEl/UQ5aBS\n",
       "cnizq3ZQz75Xw2a8Ng65Gz1qtOkzpo2h8rZrAxt6QXpj0S9g9tpXeV9zBFXSeFCB529+C4KD9hwM\n",
       "RKMRax75jBTkZBkA+9UswQbyJ7mVA32DvUzPaVP6mezpcPZCsVhhLOanH/bZ2JnEY217SN958vxh\n",
       "WLpjdiwcFwpNb3837D+z3vmIhmGZjFu99zPi9YPFOyB7ze9jP3zQpp2nrWrYwUsrFoh5yJTPcHom\n",
       "e3p85cawTnoos+eKiB0kMPInJS89ku6aJbj9DFm2czYs3/lJLDTGTXt0adjlMWo8n8mebjhrQhLH\n",
       "iWbC6GAzq4f58LZnCQWL78WoFI0f1mYYvg9mGfTQZeofDEJHdwv5cZc/hTbg9meakpnxySOG+5m8\n",
       "H6Kpae1qFGfe5IPBBSs7CtbA6wuf4nvJpQ77TO1J03N/SClNXB2yIbMkRdUH2FFRx8GqiLhdXDp6\n",
       "Wl3xxkbytKdNE1ElaXCI/awxAGttaVP7BTh74RQAsCkiNE+DyklAJ9p0eQzBWv78YXEilvdXvgBr\n",
       "chfEf7d01pu+42UqJLUiYohh+U7c9HT/BXMl5JDRpFXnnVVNnHbN9Zohr331ZCJ8TRq4ZpplmPbG\n",
       "Hzsqg2Fzpc0E83PjGJWihuXo2dk/hu7gsFkCRzokwlTaY1H+5sKFkQ5BtrbuZqFRrM1dAP0GJgl2\n",
       "yF7zCry97FlYsWsurN77Ode7hpMHHrava/Z9AT19xitbZ2tPQVt3k+66VmovdKuSykD83B8r0dvp\n",
       "21bsmpOowwCwas+nXO9LIOni33hgMfVpFqx8DemdpvYLbGZTkvYPqyj2vOmcXDgDuxMDOto+cuG3\n",
       "78Mna/8Qu0dQROTnRXyT+a4b+hPhYXNvt1aQI5EwVDWecSUuHpSTzoktQeYrIl6svPtCEbH63cb+\n",
       "uZNnVo6GXCB4+xPeLy+tOgZbD62A1q5G3b11uV8Oh8kX6rz1r8UPntRiNJtipIiYDsI4RLS68gLA\n",
       "1sHbaUh9h+ZzZ8z+MRws3qF7bN6G12H1ns9AkqLQ0cM+CE90YOp/AcDWSeYJtUad1sH+bli1m39g\n",
       "5QZyPJFIGNq69ANkUh0VEu/wLOWhkp1wgrD/paQyQOyghsJD8JtPHlFf9IFJDgBA3omtcK7OxEzJ\n",
       "iqg+WvFxMqV7+jrif49KH2UhBLV0u4/ZNB0SVK6aO9114OBFWy8kRoNyzmvaPBQ2OYeJCTt7iZzj\n",
       "6Om98OGqF4WFZ3cSsn74vC1eT46keBd/+4EtWVjxhSJiGcnAOMsPnYVZhTDdRjA8MHPoU2SFYGdg\n",
       "HWw7ugpW7p6reybupYpTiLKaIiirppumxNGEa2Q6dvT0HnownE1vbdM5VpF0MDUUpntEFLNkpDhI\n",
       "p9KafqPzJocyJDOesupCOHn+iOF7A6F+6OhpId/UeM8CADhXV2JVRCrn609DfjHdRz4AiOnMDMuA\n",
       "cfh7CzfB64v0JkM8YilPx+Zh7Jjxumufb5oF7YQVHpIbT+13i5tZHln4YY+FTHpGBjS01bJviObY\n",
       "rC58oC4R/4yzdnhyjTWgpJo0chBlbhLTxCCZDlLbW54Vc7bn5HLnVv0ZMjvs1mX6Q/QJW2WK6A4t\n",
       "JSSXWX8uiqRTRFQbqQ1XRLR/qEKh/K0nHBmCzza8wSoeF2YNnFNLZEPhIThx7jDMmP1jOSKh4ZdW\n",
       "HRcanhPI54aYpfHSHdnQN5DYOCpJEtNo0DRvGWRkCYcP7zvUpTs+hpkK0zwlpBUR9f0Yng7PNHm/\n",
       "cvc86qN2SgDNgxnPbNmavV8wP6uOhBIH4bJIE8JIJEy1dW/tajRdxVy5e55upc6sflPlp9Zxcv13\n",
       "3JzBYyVuVPoo+PPS/4JAeR77S8ze7azJRAuizWzV0EZaNrTVwIpd+gk74/gSf7o1OLYaC3M5Vjyn\n",
       "jSsqRWDLwWWqa7Klg840zfsuScCckw8+gsLR03sBgNynKg8L9ZqkU0RUBZmklEsSzF03E3YUrDEK\n",
       "RfXrTO1JOFSyi3j//ZW/hdJqvoH1eVGzuCSbebNXTO6fuXAKnp/7KDQrNi+xDHZ5qtpnG9kVN224\n",
       "fmiYlBw9vRdqm88rrkj0E4OVTznwHayDvqgU1cjsHr0aD3jasqU9mEr1rMnMed9AD5csQgeHlKDk\n",
       "gwiFxRQ3xxQ3YBlNOTCub6BX5z47JkIUagxWDE2hKjLG3/T1vi/gt/P+D/HeG4t+AQcNTnoGiHnj\n",
       "yTthfLYOr0wJjHP42dk/gu5gh+EzNHr6uqBd6yhCCGm6v3r6OuPedEjUtVQRr2dkxEyzSOUlHgfX\n",
       "Vkb+GiO3f0dKd8Ox8v3U54ImHsdYJ3dIMhaeyYdDJTvZ3ifEY6dNcnuFTCcpY/z9A0HYUfB1/Hck\n",
       "GqGacjmx2sQfpr109bM3w6U7smN/aM6N+eOX+hPUR/Q5IgD2NFJt5dx6eAWU156AwrNsrnMBYh3g\n",
       "il1ziPdYTtDWkr3mlZhsCSmJz5mfV2FlNo8ymzwcFtUsxgwfVzYAECyfwUqbBMDWcFmXJ9jfHZ/J\n",
       "UIfIFmZJZQDeW/F84j0H8o4mi850Q6dpGodq+ojXcKWlddMs2qCDaTAiPzP8L62Defnzx2DZzpiL\n",
       "0W7FfoDWrkZ4f+UL+mBZOypaGpmkXZPJWSBGJgdWEdn5WpVv3vqZ8NpC8iqhaN5f+Vt4e/lvqPcH\n",
       "QuSVON49IhKAKr9pHpRiz/LV+GU7P4n31/F9lJRnReSu3ebTicG2abllHVQZPsdgcaKgoGwf8dnX\n",
       "Fv6n+twNEVavRmnq97GKGaKaJEIyyOWG5LlUfwCye/hCEeHBzDTrQkuFfJMtPABIT7OeDGdqT8Fv\n",
       "P/2pyVO0jtnsrWGPVVRTFfcLTHNHvWpgG41GhJ5qbEcppaVHadWxeCOp3QBcUnWMOxYWGc3zhn6/\n",
       "lbBJmQf6rKVe8JbOBiEHNNpSdobflTT/CkMXnHn41CzWZD4pn43MtdixP7RiebKtuxneXf4cc5hO\n",
       "QpN344FFguMxmyIyGegJLp99Ng4S5SU0NABdBu7TaW1BBoPLciO2Hl5JvSeivitDUOadvZCJIzkd\n",
       "BWX7YPvR1fRQlGZMglY1dO2ONg0dGIybKT80z2pG5U0EdhzPiIBUfv2zuytG3KyZIJgfVnQ8UUSU\n",
       "B6zYQZuADW21UFIZiN3jaILSNIoIz7tVjeUwGOo3fCY40Av5RmYFtOgElg/Z/7fdKjIr51eqA7MK\n",
       "z+bD28uetR6gJfeuxmjNf5bvnANLtn8MwYEe3QbgncMmfMo8N4+HSRPhQP2w6CX4xLfphfrT4l/C\n",
       "MR6773igjOYNXAnBaIpokD5dwXbdYMpRhZ2QDiSPYryIXiZv6Wwgm6tKUmLyhkEqL9h9bIPpM1dN\n",
       "vJY73PKaE9xmt6I5U3vKYJWabT8kDWJumbQtNBOaURmcXrM09aJHYbZmtT4qRZfDsObUg4+dBWvg\n",
       "SCndUUp5zQn45tByprBEDvoiAicB3RuM8itMews3kd8dRuu1L+ryBK1Refti81sm2wScQy1XXBWh\n",
       "v0BYQXdrstuzFZHG9lrhYRYqTjKPz64SE1KdGVbMrxQRmT4SKM/l9sMeC3q4U6BEQRqsSJJEbFTm\n",
       "rPujQUR8coUUG0rlzaXfHlnlqWatjHnehteIzyg7WflQQt7VMInRG0wyeVqhbb50+xviTrNsRPuH\n",
       "Bf8PAmW5coi2ZdKizXurMdCUzXh41G0WFpSBtDQ4WLwdthxcqo+PI7GJUdvUTZbvmgOb85cYRMCG\n",
       "FcVtreLAL77IxClkeSe2CAvLkPjR8GbmwGRFJD09gyUS6h1tWyKqbSGZZvGWhQVb/hw/fFgdduzf\n",
       "bUdXwVZGRcNZlCt5aXC4ZBd9ElBAGTVuGwzuGUSt7Wvoc7CJO+cumLjg1r3MV7ZsT/wZRFdccdTa\n",
       "RJ9DsB09gKZZXFi3E+RfKrXiClMepKdb3COiu8tZYZbuyCas1lgrZKVVxwwbpm8Pr2B37aiSRnyh\n",
       "b2q/oPJZL8eh3GSeedv/AACAtPRYFeDqvJi2iJjkrQ+WQ2Vk+22WvKjWHNwkf0c4ojYHY+lgSHeN\n",
       "32Yj2M+3qV0IhPy0tTFVhNW7orynp5EHklbq377CzfDC3J+oru05vtHgDXoch0t2Qf7wCpJZHXRz\n",
       "M6WdsQm9HTSfFPMamuz8e0Qk5rLFXk+cSauT549A4dl8k6iN91sRIZnsaAuWjT1nvKep62QZ/h9R\n",
       "Ll1smntGchvcqm46yyidCf7pPoWPYbzaNO5lS+ShIiJix5KmABCWbq2Fq7/06YbXrYdnsVeLn2ou\n",
       "C8TYaMmNytHTe003gLLS0dsaN3kyMmNqar8gJD4Spnk6LMtQOEQ8xVdpgifLLSuJqm/Svae2OWZZ\n",
       "RWHJqWeypzM8JZ6Wzgau55UNY/uwGYn2+77Y9Cb5ZYYym1A/jFYxvYUmU99AD0Qi5EM4bX2FhTbj\n",
       "d5//K3xzKOE2U5lv6enkMmslrasayyEUHlRd27B/oa9m/hyFUqbl1J7xySN6H/1gr1xb0Wl5B5cA\n",
       "RntErBxoqJCFob/ffWw98ZR7FmjfZdMfkj4cjnop70dkUbT6TDx9OeOGUdGvsYTP+OmnKo5aFEgM\n",
       "bvcefppUpJE4HNvcNMuLzf6+WBExculphGWN3WW0e1DimM2aW6xSvN8ubJkcJHhzya/thWFxNZgF\n",
       "UiUk5o3O1znJ1tIYP5U/LbPXvsr1vPF5PbF79W01tmQCUCS72RYRxh4xYeqlzU+Wt9niGBwagE35\n",
       "OeKUJ4KpiVJxNOpHggM9UNVwhniP3gbxCEfa6Zj4c/G2D1neiHO+rpT5WVZIYfT0dZKf5RhUJg6X\n",
       "ZUuwfor3KdEMmOxP5EVSKSKJ9MmwdLK6IlyGldCNBxbDYZUbfYuoJiTF0G7V26RGCl35GS6DkYh+\n",
       "JWpnYB1zuG7A2u6ePH+YPVCeiSoLZ5yI4vONsxImpPoITcTx01iAlIfey+eZIqJMDq2rUWYvPpJk\n",
       "YGttlLhplL+dgRaDWfY75kVIIErZLInp4retU5yoG9/syGmaJVHK3B++/HfNCgen2R0DrGeD6MqL\n",
       "NjJbaU5JJ0PljRUxKyL69/nDO9t4HI5V0TeoKunoaWV6rrWrESRJgk35S1T7rEjIikMkGoE/Lf5l\n",
       "4rqF9srIM6CVtLbaHvX0d6l+61ysO3BOwmCoH16Z/3NNPDYDtSonIdnsirLrmH6waqhgme0RUW1W\n",
       "Tzwrlx9W5c20iCj7DaYQjcu+E724myuzpHTdrHR56xqKb3ahb7bmzMT9VfOSqgAcP0M+EsLO+Ky3\n",
       "vxu6g+SJEtvw7pWRa5HL59UAeLkiQvnYQyW7Eid+8wZJmAohF1hnViKo0DLWcEN94v6flz5jHI4C\n",
       "kkmSe9hPN8M+1Ch8Q5vV2L0jpxUDy+HHaft3jNG/o3VR6EfzIqsQBwCaneVmp6Gz4CfF+9SFfCip\n",
       "Oxj/bZSfRecOEl0mF2tMFN5Y9AsorzkBuwJr4UJLpWH88RSnzKAyIT+alkY3JzRI66gUhaFw4vwH\n",
       "4d7ceLPZQvzESS0XitfuwHpuU7WhcEhl0mVZ34knrHpzM4B5u0SbBKyz5NBFadpE/5gVO8lneFmL\n",
       "CaimkiLgyZKEqanifcoeEbNw+0N9fI4lBKhmxZUFifgHg9A3kDAfU5Yj3nbB6T0QvH0v8yQkYx/X\n",
       "09epWoWVQNLtrZT5ePXL8IbGk6eRPFYPTY2bohuaZsUfthSHHXxhmqVk5W6yBx8ShiYjAs5GEIbF\n",
       "jJUPNByQD8piCMfo4CgarBXXzFWipdlV7jfUDAzZO+QsjWA7b/YdRg1v32AvvJnza5blLsWf3g+8\n",
       "SbR3N3sUs6j0cC9dg4ynvg8OGZvSxMsepYyV1xTB7z7/V6a44oNPSYItir0j6vjobD20Ap6f+6g+\n",
       "PEEzk9q9b2dqT1oOy3FU1pnm33zk9B6dKYdZWm3Yvwj+8OX/YxDAOdSb1RNl8DS3m2PNCqmB/BUN\n",
       "/K78jU54F4UTzTK1rWcYzLdp2mO78qUBu2I1e+2r1P07jvRfyjB5wzd5vL61CqLRCFxoqYAT5w7x\n",
       "y6aLTx3hK/N/rnA5HIO2V7e7r1O3305JadUxCIUHIRqNQFSKwqsL/g0aLJhBJ+qfv5xjyPhOEeFC\n",
       "ApATtrmjnjhro5wdIZ3lwTvrFBzoUdk2s1QR2jN2Dr1jRTtoJjYadqJRNRjWgmhsr2U0x9NHEKjc\n",
       "af6aQSbzDrbN3Pe2dzdDU8cFWwM00qnWLCTkcmbQ8trC/9R51eGNiZgumpUQ+8e4ODdoE7fSZaLs\n",
       "Uj6ysr6MWemRCRsN2gwSu6GtmiseehTGK76mG3VFw9Tm218p1e9NItlmJd6h7WXhlsLGypV5+TYw\n",
       "jxLiMjZ2tgolAtvhazE6iJAsgrEMRAckRg2aFW9cDHIwBsL8aEc3+x4ZsxK0Lu9LkydiVDee1Sk/\n",
       "DW21qgMMScdAmJXht5fNgEB5Hqzc/Sl8+c077OlAyUchkzFKFPJ8tvFPECjLhbeXzYCvvnkXAMDU\n",
       "rNcI4mSyPPcVn2hyHw/3iLBXgsb2WniZMAuonEn5+OvfqTZJkRLT1EUfA98cWm7d/7wGU/e92tsO\n",
       "NMSJgw6toRSxtavRUhhvLfkvOF6+31r8Ws9i5If0lwzT3vgeky9uhxwRWAlTAknIIaLt3c3xmUhn\n",
       "lGhJ8693eG1aJ5cxnRxmZY902+AdY0cEw/8ymD16TURy8XRlxnaY+2A1NyYrXcovZbmKRiNcK/Vz\n",
       "1v3BCZGIGB9EqE4rq+5yDc2YEqNAppC8Qn+Se+JPW4qvQXn8YNVv4fONs+K/z9eVwp+X/pfqwFjS\n",
       "/gqWtjs0NMhdF6hPm4Uj0b8zSnBSQAqvsb0WKhvKjOPRcILHaQCIN73lISlWRC40V0Af5yyg0cyr\n",
       "6bs0zVeSrLmmM4lXdvNHeJE/Ls736lqq+EOneJGycsK6nE/Ld81RLV8Ohvq57SG5UouQJzQf+ir3\n",
       "vTbLUOIBpmAsQYu7qd3ElTNHw3yweEfs7AiBCldCDRGbOH4YK+8/+S0AmK/6xMcllE7BdAJHUm4N\n",
       "sdexlFcXDQcpqf5lyR75tPb2nhaIRB1wb6yBZ5UoFBqA4ooC8wchkV8lVce4ZdKaB6/cPc/wIF/R\n",
       "tvNeDiwAEmV5/f6Fuo2+tLz3WGRD1uz9QniY9to6MSaSRizf+Ulsf4OiwXome7prEzV9g73xuGTz\n",
       "0u5gu+1G/WTFEf5voK6ImLxm8ATLBMrK3fOI8UelKISGBmHmV0/Ct4dXmgjB/q1eVMGkUESMMjLu\n",
       "+lhrk0qcBSeGwCxHd7BDtymZBfpm9Ng/gfJcxoC0s6PcohBEYD94ivi+zQZBPnAxHBmC4+X745+Y\n",
       "s/0jeHXBv2niIgQgqOdqbK+BGZ88Qryn8gwGbB38JsFOA0TY4YruPCptrrBoiX+jZHxAHv/mQoHf\n",
       "bTEftCYg9Yybf3XfaqG4a8vrt4dXxu2MjcrV0PAhlfIz6/O+Yo6zrSth8nj09D7m94ywZCxFqKsd\n",
       "va3wxWbKuTeU99bsUwxCmd2Iqn+erj4ORWcPqq4p81cvq2ICxG4ZZrY+4Yunq7cdevq6DJ/hsWk3\n",
       "tGJiDsU6kiTFbfa1aRFTdvmlMPqmuEmyhew1PLiVVcx4mUtMkChdQh8u3Q1HSvdQxTtTewpatROp\n",
       "HGXIrFyTVqHMXFbL+aZ1WiBJUnyysay6kLtO0Z+3378onYKwjmnyir6BF+b9BDp6WuBcXYnhs7LH\n",
       "TVJ72NOvXlUaWaZZHPXZ0iCM2xzHHO3ycjQaoc72mcnCIo/5AX7mUTsDY8S8bbaiUHQT7aWtmlOZ\n",
       "P92lWH0xL24Gpi7D76o8dLlA3olv2M/j4VTezisaueW7PlHdYz1kUvGC0cMAEOucdwbWckjoAjbr\n",
       "muwWVQ5mX9Fmw+dpplmmh2kqslYuD1pl5tsjK+HAyW3E8IkM52Hh2Xzo6euEonNKb2LmkDZj1rdW\n",
       "xVdNWJ53Gtrhoqwus0l4bd5Hwq5E2pZj5sIn4eOvf0eJSOz3Hzi1TWh4Kobr26mKI/DC3J84F48G\n",
       "nrGN9lmS62YafQO98Ez2dNUECG1C58VPf6r6feDUtoTDHA17CzfCkdLdajkF5jtJRlZHRNryklu0\n",
       "RT3ZyGAVp/RiR1VDFPli9Vyfr7a+w/F0TGLl/hmzND8czyP91xadPch+ZIZDJMeKCCWRxo4Zr3xI\n",
       "/Y4N0ywaYY3SsejbD2DbkVWm71mOVfuin9etBSPCrCAqRaG3v5st/Y1m4lSySCb6FaPplrDZmBhr\n",
       "9s2HgtN7DSUolc1LOOsB7TAvllDYnpFn4/w3cBMFzeyPjlXfrYk/5c3PpLLDk+bK93k3ygOQ3am+\n",
       "u+J5qkvL/kF3DgNkQenC1AwmxyAKBhjNT0+ePwIDg2IOLtSWhS+3vA0HixMOP3jb3Wg0AsG4wpvE\n",
       "DLH5RSYAACAASURBVOdVu8GmbP42W/+XPlqN2aNFtAP2orMHYcP+hfHfuUVbAEBziKjqFc7cM9w3\n",
       "xheUEWmE8CTJbD6LfFe7MseS5iovdgYm+zJaJU4Zm5Kjp/eqJj8a29Qmmyt3z4UFW95WXdOew6Q6\n",
       "pJax76Tl8qnzRx13q2xEUigiUUUiMyeWoWmW0XI4HW2HWt10lk0Up2bGbJQbK4clkaITqUmnQSKt\n",
       "WPNZ0/WrfuWf3Aa//+Jxyps2VlcEKEmlFmzOaaze+3nsD5Pzalg4WLwDNh1gLxsidQfVwE3xt9my\n",
       "Mz1A8uXOXrYDCDmCjEPbQ8a+mVpd/vXWmPbKXtwEgGsmli8ObXsXjvK5FB9l5RTvxOYazQ0HOlfG\n",
       "+t/b3wX7CukrXznbPtS4riWHu2DLnyGfazUgDVbt+YzsEUqTmSfOH45PYMRu81doklUA90qpx8gm\n",
       "QGbjAZ7SFDd6Unzrku0fq5T5+CQrQ3oYyUZK74p6xeZm0zIrLj+4xjt2LQ4Jn8UcpHyGi83+3EpZ\n",
       "r9OcI6UN42DxTt05VFpMV8cJ0L515Z55nk50e6aIlNeehAaNFkg7udKoktJcjhHfiIdjrfRrG1z+\n",
       "WU6aPJTbbiztS+ZyKB8F9sdtQV6S1UccidIVoe4++myjUYdrds/KYDDIajZFk8VApgPDG6G1tHZS\n",
       "vJgZNDg7CtZwLfnzwlKmtemv9JICoC8bh4p3Jg79hNhMs/ZAKSVWvN6x1sX5m98ivx8vpzbNGq14\n",
       "zVLw2cY31FIwVWZrdUWGtCKizcNF337AEJsVbIZGep2jAdyYT98rpjU/tTsMSNiZS5B/aptqBpjU\n",
       "ZllxvBIKD+r2b5lORvlM6WBFV7YliNe/UHhQ5UaW+D7lerfKDNi6aZYZxEGnoMGmLAmxn+aoc7Rn\n",
       "4+aZJmeXkQPlG8+wYrbXl+rkiCBSPG/izkv00+QZJhMySkWE/VvsT1Y6gWeKSKAsF5bs+Eh1rZCi\n",
       "iMgFICpFmZUVkjkXqSCRDkaiFShtw9MVbCc+JwqaHDR75sR7yl8MrmZtyGO0gbW8uggOFTOc86GO\n",
       "JPYvY3sZNZhp3n70a764GTGcmaLk2e/n/9wRWShSAADA3PUzud/kV7Joy9XqP+pbq+BI6R6Tg8jI\n",
       "YQXKjJ05nK4uVA26th1ZBa8o05uhgD+TPV11crASXreJJMwGLVqoZ8LY7DDi+zIIHSANZdqyKNTa\n",
       "MkQ86VpTzI6fsea+2wyj79O6G3fDNLC68SyEwgNyhIbP8tbFt5b+mut5eaKC55Ts83WlKpMfAEq6\n",
       "SZLvTS21s9I8vPLFE7Bs52zGp9XpcPzM/ngfnnA/Lx5i+dHkifxM3omtXGGzWoOYQikjyn5C7zpY\n",
       "stQO6h0acVpzUPWQxPiUX6a4MLp7srMQGqq6ymqaZVC9la4x3MbCGriDUFJJbtDauppUmWP1hF/l\n",
       "IXaLvn2f+T3LDatFt29+ZenObCgo2wf/8b9eNnyutPo4lFYfh7++5++ZwlVWLPJMCx275iPM71ks\n",
       "A9yNnvZ9hmeE2Hg6tDr73soXyANSBQkTTM40FiTz4NAAjB97seraQKgfPlr9Mtx47W22wmZdPY2b\n",
       "JnLOXLKWS9Lp6GYoZ86z17yijVkvC0iqplxrltba1WhYFmjfYsWEwsiZiJFSTIvL7uC6pCoA4UGA\n",
       "v7rlQX0e2JytTriBNzLhMYbn/CPW/Q2ku1pPkS2dDdT3mzvqYPSoMYZxWOGd5b/RXdPuBwTVr8Tv\n",
       "waEBaGitZopHm6S1TecV98SMAkhtv7mZmfXyFvceass2ihHONOLv23m9MOrvABi3NfTVFEIdMsk3\n",
       "WeFJT1euiLB+M6VdY4jXSUxXRPLy8uDhhx+GKVOmQHp6OixenFhqDofD8NJLL8G9994LF198MUye\n",
       "PBl+9rOfQW0t3Ve6Em1FoFUMyXD2ziBhKReNDzGiY9WWkFp8TQen6jc7GV0HK8XsoGw0NnyfWjFj\n",
       "8gyG+lWHR1rl4nETKTEAR6VgMPXhfIb09Cdr/2Bwlw3aSpbTM4fMK17A3znZMR98Jns6vLv8OUU/\n",
       "Iyn+nx1qu2Fh8V13hcUJBlPI7CsQAHSvWbR6IZ9W3D9A2OhNnLBmG0QCWLNFNmLQomcZK2zKX8L8\n",
       "LHPecrl8ZLwGxnVPmJmupGznZJsSUe+zp8u+4c3TMrsCdHPQWTlPw8yvnmQO20lETPYoZ87lv+X6\n",
       "eL6+lPiOGaTyoZ7Yk59LQJoMEFHOHPeaJSh+HrfSsYAlCA706JxsyFUiQjqckIq6feergvJkVbru\n",
       "mh18vVk9GAzCtGnTIDs7G8aNG6cq3MFgEAoLC+HVV1+FwsJC2LhxI9TW1sKDDz7ImSnDUM3XYpW1\n",
       "ucPkQDbCO6prDNn9TPZ0aGwnF1Cr2XTZhCuI180qgrZsnWfctKt878tvGNzCMQ62RI+XLxozVnNF\n",
       "33CaYVkkzhftnkBvGwdtiZ1ELku0GXCaC1fDLxDYXi7b+Ql8tDq2shdb8deYLtBOQnYc8kd2KFZz\n",
       "lVQ3xkwlaprPMYXOoxgxuShXoOvQPCyOIZ7TsIkOTsQLT1UyLVI2fPCk68QnCEl9rdmr/mmj1BgY\n",
       "qOj6SVbUTypXR7VnHRmZofLvETEe3okof8RWiqevshKpZHL2Ge+Cukl/Io87Q5EQ/O7zf4UPVr1I\n",
       "jDBKaycZTMl4LCak4RVms/wlYTiZ7qHbO9Mveeihh2DWrFnwyCOPqJaCAAAmTpwIO3bsgEcffRRu\n",
       "vfVW+N73vgeff/45nD59GsrKzO2q2Q8mi6E7hIriZUf1kuqScWGQD2aqbChnkouVSVdMsfimgNkJ\n",
       "j/1DW4a45Euc2gUAgEMlnHtRDKC5FY3hYW01gXfASIJvVkQyKKL8ZVe7r4QVs5VKo3pfcHqvYg8I\n",
       "YVaRSxIBSABfbH4LGimTFGcoCnFVI1ub1Tc4vA+GY0Vkb+Em6j2aa2DVuTwCVqYAADYaHBKqfGMo\n",
       "HBJwFglljw5APO36BntVvvxZia8wWWzetedZzdvwmuk7WpM83j0BJGTxabbxflU1bMF3ABoAgO4M\n",
       "DlV6OZhItLM/VDjQwPF9UuLpoXBIfbAfAEBammF4pMlcWntjdcZ/Vs7TAEBfyZXi+Uy5z5IiHIkW\n",
       "N81KUyrNjCvtBpvVvVwREb5HpKsrNpi//PLLud+lm2bRB9OJk9U175A1EUNemf8EANBth6MMA6R4\n",
       "R68g3UPbOy0spiZmpllOofR/ZsUbB5cHEk1YSne65puTE7PJ9a1VqgZf9ExfYunWpW6ds6zSPGzV\n",
       "NJ2Djh4+N7mJjZv8xlnk8Mxn/ZWDAgkIM20e1N3iiqNwxaWTZKEcIR4sQ3kNawcHDHwtu5T2gOyv\n",
       "f2+60ZMEb1K//NljAAAw+9kNXO/JM5n6sqZ7kCjcnxb9kis+EoVn8+G7t3yfLAcrjJ4H/XiwIwld\n",
       "32h5BWSYtDQ4enovLN2RrbpMct+bveYV+N4d/5M3BkPatCeeO4CI875kPlz9EmSkZZg+pyxPa/bN\n",
       "Fxa/Xdp7yKvVLCjHuGYKAck0i7VwUve+UQKw7RmWEaGKSCgUgueffx4efvhhmDx5sunzwb6EPXMg\n",
       "EICOjsQs2jPZ0+HxH7wKAAA19eTZwUgkCiUlpcN/a13r6pWX3t5eCAQCpnI1N5ML1NpddA9Rcrgb\n",
       "j3+mu9fZ0al6xiwMmd6BTuo9AKDuxTlTrp4dVb5bXa3eYHehthaCQbVdeWsbeQBZdEJtAsCSlrTn\n",
       "AoEADA6qZy3r6urgotGxMtDT06N7t65ObZoXCARUFai9neyul+TpR1nWzGQuV6RnVVVVvCHIO7gH\n",
       "tp5cBP2hRMdy+rTyXAA2qqurYWyInJYD/THTkmPHjjOHV1lZqQ5jQG2eMhQKEfMkEonEn2XJ286O\n",
       "Tjh5nnygp7xnYXTGRcT7yvCPH48pgeVnYulcXFwC4TB9dUdbj9vb24gynzx5MhbeKfIqAun5iy+6\n",
       "THXt+PFYusurZJEI/wqjMp7z589T7ynjC4VCqt8kTp8+Dc21nbrrPT3qyRDSRE5ra2zv2GCIYeUg\n",
       "LY046AwEAjAY1s8ChkJqxUVbz80oKqKbGhUUFBA70+iwKXBfXx90BpstDX6PBQKQnh4bCFU2x0wG\n",
       "6+vVm6grKirieaOUCSBWzi4Zp26jSGkvy9/Xp56xbm9LeGG87rJboLEhEXd9fSLcDsI5OKo2vqpK\n",
       "d39gcAACgUC8X+zp6YYLw/2Hsj5VNifajtJSvSlwR2eiL9N6glO2fYWFhdDUFBsIn7tQrAunX/Pt\n",
       "9Y0XAACgoaFe96wRNTU1EAgHVGmlhMdEPBAIQE1jTfzvlp4LqvtdXV1QB4lr2vzT1uWhUEinhAAk\n",
       "ZvEDgQCEhmJlqbmjDg6d3EOUSaaiImHGWlOj7vu7OtWH3QHEJlQDgQBcaD8HBZU7ht+rgcBQIszu\n",
       "bnXfWEUoO0Z0dOjbn2CQ7H2QRHt7e/wbSV7MIuFwfHJbpqWlRTdmUdIXVI8r4++1kvfLNjYmFDbW\n",
       "MY2ShuGyV15OXpUeHByEquoq1TW5bsgMhYdgy+41AAAwMGC8h668vBy6m0JQX5eoKyxj2w+X/R6u\n",
       "v/w7xHvhcDhenqurE+Ntt05cF6aIhMNheOyxx6C7uxu2bNli/gIAiPJWwP4OW+dEi693UF/Z9c/o\n",
       "K6bVWVUrnel1E2/WHSAmrDA5PbFl4jXLa1/XAACnag9A90BswLA28AlMuOhSl2K28+3s73IaZpky\n",
       "FDEfhOpnr8WsiFjBvM65UwZZvFtVtpTAFROuZTBNM7jH8DlpYGweYR6jG2lmvwyopIynqbnsG47P\n",
       "o4dJSOB0C17zWfqeOAxJwbZiYRaQYcnierO6jX8CRzSSFIX2XoVCo98kwhce0zNiVo5I78r9/qFz\n",
       "W6B/iFU5EFBXOYJg69L1D7UHKWdk8QUjBEn3h5qoFIHyBuMDjAeG+mBH8VKueHlXo6paS2Hs6Alc\n",
       "77iFEHco4XAYfvrTn0JxcTHs3r2b2Sxrwvjx8b+zsrLgiiuuVN3PysqCrKwsmDKFvMciPSMD7r77\n",
       "7tjfmv0rpCwaP2ECZGVlmcp1zaRJxOvjFfJqycrKgptvvYFop3/F5VfEn1H+RwpD+d+0705T3dNy\n",
       "ww036K41dFXC4YpvVNfuuOvW+N833nij6t6UG6bA+Anq77rqyqtInwj33nuv6vfoy9j2JJC+Nysr\n",
       "Cy66SD1bfv3118flu3TipfHnZApr9qmen3B1Bihr/xVXsJsDXnbZZYb3lTLffvvt8euyEiIzbqw6\n",
       "7baepK+a0Zh641RquRw7Lrah/1gd+8nKN998szqMi9ROAUaPGUPMk4yMDBg7bhwAAOwqM/c2dPnl\n",
       "xmlohDLu1Uc/BACA66ZcAwAAd999N4waRZ8jueTiSyA6oQcy78+ErKwsuPLKK3VhAgBMmxarP/d8\n",
       "97vEcG6/Sz07dM8998D999+vupZ5332q3+kZ5qYDWpRy3XLLLdR7AAD3ZcbiGzc2lg+ZmZnUcEvr\n",
       "DxPz8ZJLL1H9JnVYcpqNGTPaTHzIoHxzVlYW3PeX9+mujxmjdrU6ZjSf69V77/1L6j05z+X/vjtt\n",
       "uP3PiLX/E8ZPsGwuMu5KKR7uLcN16LrrrlM9c8stt+i+r2cgtrp60eVpurwgezOKyTpuuK7JXHVV\n",
       "ot299NJL4FpF3BUtxs4ylPFecbXeG+HYseMgKysrnjYTJkyAKcP9x4Tx4+PfrWw77rrrLl04cruZ\n",
       "lZWlK5vK5++77z5qPwoAMG6c1lFJDG16mzF1aqztvJbyHq3skrh88gQ413wCAGLfd8edd6juXzpx\n",
       "oqrP1X6DNu/HjDauW1lZWTAqI9HOjdeUB22Yt9ySyJupU9V9/2UT9W2xBLHyPFohx9SpN6jCvPRS\n",
       "9UTaoXPqsYMZpD5g3AT9d1Dfv+Iy6ngIAGDU6NFw6UR1eVbWExLjFOO0u797Vzz8q64mv3fdtYmy\n",
       "YyQLjeuuvRYAAG5TjBOUBAe7dYrTtcPvkBg71jj9brvtNsjKyoKpNyTGchMmjGcb215zDfH6qIwM\n",
       "mDAh5rpeW7bcwLYiMjQ0BD/5yU+guLgY9u7dC5MMGh8zqDsTaGqzkY0q5/MiKDp3kHzD4mSd1RkS\n",
       "0j4VEWjl+fKbt22Fp131UJ0uyuAR4tMNr6v9FTg280rPQNmUw2nKatg949hxOSvnSX0bm498kSzZ\n",
       "/pH5Q8Ms3ZFt6pr6XcI5AUpW7KbPZMt4tganOXmXBilvm9rM3acn3PeyiEKui21dTQ7VOaO9B+rV\n",
       "Xauu2Eks2MLSntFlW7l7LlM8TN5ubCSrUZokvKUl0tHq4XTOeL6y2lmSZeEpn8q9oduProbPN85i\n",
       "isMOpHNZRMFi329/g7LNc0QsfLL5XtFE2X7ps/9ryaGESHlIGLowZ8ySNNVmdft4uZPZ1DQrGAzC\n",
       "2bOxhioajUJ1dTUUFRXBlVdeCZMnT4ZHH30UAoEAbN68GSRJgsbGmOZ32WWXwdix5FmPOIqEbGir\n",
       "geLKAsqD5smsX0XVv8NaYES3N1Yru7Jhmrfhdcvxmx84xZouzg7LlKtJ7GlmVSYxrWWGS4qIa7jU\n",
       "GhkN+iTOk3NpZUW5KZQEsaM2i9d2HWB7n3VWf/+JrTrTy55+czOexBkQ5vLQZPl0w+vwm5/o3YOz\n",
       "nndkBW0bFD+lPIlIY1QyhULciG0cPynblfs9jPoN645FvDO//WzjG/G/j5Xvtz+hx1CH+wcT+xlE\n",
       "K/X3fuevh+UQGqwpVr8jZgIq6a7pPaLyhe/euUXsch04xW7hQENlBcR5oK0Wr43eTadmCgoKIDMz\n",
       "EzIzM2FgYABmzpwJmZmZMHPmTLhw4QJs2rQJGhoa4P7774fJkyfH/1u9ejWXIKt2fwqDFJ/vLN6q\n",
       "WM7CcNJ7x7Yjq6Clk7zRjtSR855LUVZdqA+XsYUx9V7EnCzW0s/IN7oSpYMB+cvMfOS7fUK6FtGH\n",
       "vYnBZIDhkhRGGB+IaSz/oHbwafJB1JO6NS/uPb6R+V0ejpQmNqGahjd8Pz3uWcmYtbkLYH0evzlg\n",
       "XA9hqD8XjyPvg3KqNTUc4EoSPJM9Xd+mKdwRi5SLmF82PQXR9v9oy2P+yW9txaOkpatBVeeioN83\n",
       "+KdFv4RvDi4zDEc1OLdRN4T3xZQ8sToJSOqzYzLzu+9lf5xdedPJRxDrqol08x9R2O1LVFYkjPXK\n",
       "60GznphEc9b90dVYrZRtmnItgeSJh0gZ0xWRBx54gOiBSsboHg8ZGQaiGCy7ij4cyipbD68wKBjq\n",
       "69FoRHFSt/N8qDuAJwEpac8xHpzISs72jyCLwTVhNBpJNLbD+Wp0hgEAuNQq0StoRrpwD9gqRMzm\n",
       "aOsGfS6Sz5e4V4eSXWgmH4LIi/bwv/KaE460I8t2zuZ+x8phVVSMVocZPveyCVfSXYEylIGowDSV\n",
       "zS76Bnrg8ksSNt88KzwChHA+CpCgn+UcCA4OnNyWUEAJ39DSpfY8Zaozm9wUeegcNRjJxXwHZ8dq\n",
       "PO2pzm2tn0bnFvMiDfSfYSW5ufslTaa6t4JiD6VZOGu/dfT0Xuo9X5+s7haGiogoGMun5cEIbVaG\n",
       "sfXK2faR6lAcrwZ6NJtKkjjXXG7tsMaNBxZDa5d6A1dUSpjKyGlm7rfF2xbY6T0iTpi5dPW2UQ80\n",
       "E+kX3irc/YjFBrSnT+Phjvjt5iutdqCu1gjMB2IMHAca0gN2v+7Jq+OlVezurP1IfyioH/A4XPdU\n",
       "AxcBeeff09ETCK2vmqC0k7Bad8b8wYtOT8IEhCbPaprP657hgrhyxE9DW43BwZh8pll207Gd8/wr\n",
       "r1DvEbFZdhRpqh2XuYG3ioji40dlmHtvsR0dY2ZdaLE240pfDxletTGpQIHyXHjx058qOll3Gvp2\n",
       "k02/CfTyxA9e42T3sfW6a5MunxLPo/jg0sw1qSJNi85SnAWQ3mN+0hghplmiD0HUBkcI/rSvB3Ls\n",
       "6VFQtk/YwV1p4PzY2ix4+b7sU1/EYI9Ug46d2T8cob3wmd7mjcPgcbmT3HxwCRSU5cLB4p2qd1q7\n",
       "Gg0PwGVF7uTrWqu43qMdhqvl64KPdO3ukdLdXHHxkp6WHm9fWdLIXC/SKOleHmLowQSKNg1/88kj\n",
       "NsMTa+oWNy4wmKjpM9lHZ00Y/u9gNd8GYChbtsfkfO3H7mN8B5qawTKx9ur8f1O1NYMhAXvlhqPN\n",
       "LWI9fkMcvlkRGWXBxCVWcSlHq5NfYAq3qoF8MI3dxjVxSrYxi7d9YCseFhlkNh5YZKsxEtnhZCg3\n",
       "X8VXRIwrZVO3+96dVHi/gJCSsJarJds/hoqG2BkEdO8oPGXU2RUQLzD6Aje+TmQavrfiufjfx8rz\n",
       "dHHQ9hlapbSK4P/fYND73ornxUTMOZgLhc3P60lPT0+shIlYEbGRr8LrlUvmcsoGX/SKkNkA2NgU\n",
       "jnTXm7bLSt5S37CgYOrjj4VxquKoXWl8Q3dfB/QpHB3oVvc5iZVsH+8RcRRFIbPifSgcGaK7zCVg\n",
       "t3iRTv5ki1fR+LPkNaNrTbeX0MizLuJO3ow5cpFXRIZxqG7Uc8500vCy8jqBfOovC+EI2zkyvFgd\n",
       "pLDORnPh+AqJBOnpGQauNp0VwI+KlrWBjIvfYTAAbWw3d53sBFsZ3BinpaXHU0nIINpOEJT4exk8\n",
       "vvFgebM6w3ukDf92EK/Y+K9uUzGSVdBnBPu7ideVOT177aswdjT7OSheEHe9rjANFGma5QW+Mc0y\n",
       "3JxpoBU3d9TFgmLJCKcT29SMKMokRxQkiEpRqKwvM3wu7wTf4UN2mb/pLd01kY2dUqlJY1wRsUp7\n",
       "d7PhfWYlzwd7KrToN6cTFEgBrfvgkDOb+piLFPOeL464NU/P3/yW9gHhKM1SXR88MB2tTnP5KLHJ\n",
       "69AnqVYrhMdB+WafDu76B803tmekZ8TbWEmK2u4OtZNQ+cXblTeN36Vcj5va+RFJ7czD1MsVZ6E0\n",
       "m9TjOWfJLUT1z7S0IoVvlu7ymFCmuuksdf+JlnMXig2OkfAX246uEhoeblYHILb7wYGemJtGhhaT\n",
       "pdJ7NvsXXw5nfVyCyvoyWL7rEweF4od4yB3jR7F04Or8Ydsj4hRvLPoF03P+U0MI52OQ0t6nAyoA\n",
       "gAvN51X+9b3kfH2p4BA5Byci2izeg18F48dVF3O8lZk3dpZmMj1N8GZ1ze/DJbs4XhacvgbKssjw\n",
       "VGHbcitm+3HTd70qwVbKFs87vHm6YtccKK85Qb3vBwctSiytqtre6zeSV0QUkLSxzzfOgplf/Yfx\n",
       "i3H3fQ4IxYnZYTHS8FIuy8mgo5zyIiZ6+ZfxOZYZCUlKpIyfmgbDMy981ogBAJe5oh+pbDBeCZR5\n",
       "fdFTqt9CZnRMCvRQRLD5l9cKoYUzmuKXQQKmFkDweQp0WVzCh3WeBeUBaCLMiozyya3cqKg/Dc9k\n",
       "T3dpjwjA+v2JM3tEmiXbDc+zgSTxYHWBsqSJCS8cGTKOJMkRkuIeJoNv9oiQtNL4ychMsxNiGwUr\n",
       "mGnWrB2sJEkwZrTJqfQ+gTXduc+bGU7LdB90+kYmcH7cI6JNa+ZGirMzd+rbWZfRmfF6sG+C4yUo\n",
       "jXA68TBMnbwP6qApKWZf78TAUmn+zPJ9Ww+vNHnCbELNSFER8321LTbdz1JgKfFm7RTvN4puT/cV\n",
       "blI7gHELS1lrtEdEc89C+BGH9jN6AalchYYGbLuPHrmmWSaNIdO+bs2/xtFJqlOORUPLyOPDrjLl\n",
       "htnM3agkSY4flCcKZnN+5sGlvFldTsskGATZxOkhTweze2ZOkmGACgCVFC94OtLSHJ9ZJA3OtDt6\n",
       "jH5ajNTaPUFYWd9w/g0b4flcsaWhcjXO8A2GK8EmQYjeP2FGRf1poeGR0O29MzXN4vxGB9rTY+X7\n",
       "Vb9FK9jEPRwW8jZKkYsUfqCc3dWvzFdb3yVenzrpO9xh+ZV9hZu9FsEyvjHNIsJTMVn2IEiSpVOO\n",
       "RSF79Xlzya8Nn5OkqO/sFmkwr4hwznIny/eLkLNvoAcOlzh7hoAWPw+lRK+IsO618mJGyOs9Gnbj\n",
       "d2JM3tnb7g9Bkgrzsqs6AE1Sm9XxbhIvPHsQ/NSKyC68tYTDRiY59vB61UyFkSxu96VW0sXDtEz3\n",
       "YtXIAYqZ3RMTkMDTiUXf5ABpEMA2MBjeCO6HRtFE3PdWPAfNHfWmwUgSozcaC6zfv1BsgIxiKk9N\n",
       "pwal+G7ZjMBLdcTYrjSGiMHr1sMrhDom8EVdsIFXHfzgUD9TnovGqAQ5v0JjQ+ljdb7B+Q2tXQ0W\n",
       "RHF1TcRmyOL31fDS0dsKGw8sjv9euXsu1/sLt75rL81FfZ5JOJGoQJMcTZ6Y1R3uyTdugRSy+KjN\n",
       "tyIJVf60NMe/7OJxlzocgzvYcawigeTpWMs3ighJG2vquGD6mpPeFngxO8egs7cN5q2faRqOBBLM\n",
       "yvmVKLFUiB5osaYp7x6RxDki3lWPeRte9yxuOzhyngYBx3LGI0Wks7cNlmz/2PV4JdXf/hlQeIUf\n",
       "ZpppMpyqOKo7ET1ZEL3iZ5xPxo4MRJVzx+qLAK9ZQQGnlp+uLrT1fmdvG0Td3h/hg/rLw+hRF3kt\n",
       "gueEI0OetrveKiLKzeoGj23Oz6He42qIfFBBkrUTo8FaeFk2i6ny0uFzRFiobTbfCFleS3cL6BXV\n",
       "jWdMnxFzjojYU6xlvByMN7WbT37YQVdfNL87e1oN7wuXh+GZKsM9Nt7P7rtJ4dl8r0Ug4olZoZ18\n",
       "FVUmXCxb2piEO8ghKD8tneYWFGb0CD4kUokoE2paWiaHgXZqIN5VPTu+3qzOFoYjjyKMsA4aeQfs\n",
       "fvRGlerwKhYsipoVhHvN8hF1rVWG999eNsMdQYZhGUzZNW/hbXf9sCLiNY6kgPDVZYMVDwmYzJCd\n",
       "k8AedS2Vrsdtq89zyEzSCqLjwFXi1MfXplkscJ2ZgB2ceBjTdOmObL5wfeA0azDkzMnhiAkpXE33\n",
       "FW7SXTMq4jRvMsKwZeYvMQ0S+GeOvSsA8hk2qAyZszZ3geH9spoi6r2kTF3tHhHRX0E6k4PV7pu+\n",
       "MwAAIABJREFU5b9nKSrGaxZWN3ZSsW3yjSLixgw4atbiEVoplJvVcUXEWXzcmPnhTCC3MBvKO93p\n",
       "uNIm+risadkVWOd8JEmUHkacPH/E+sspkAa+mqhiTU+fJnvfYC/xuivjgBQoi8mOp4qI0rTDjT3J\n",
       "qIiIx6k0LSjb50i4SAw/1wUvZfNfuvhNHgWMHXiU8xu8HBdIhL9EU1izj0EQzvgZOlB3p3aM5RdW\n",
       "z1wsLF1BC26lOUjGyTeixBay5Fh5Hv0mKgopj6eKiOudPpZn4YjMQ4kQnuoQLmRE4OXSc3t3s+tx\n",
       "Grrv9XEnLMX/z+xBTkXEBw21j5OdSPINYcXgZllp7Wp0LS6noK08iMQP9ZeH5JI2NfHRKG+kNqXJ\n",
       "jZ8HSkhyYrlMJckhmEokybgjTIWN+9y56emSiD/aM0cGcy7Wj2QbjPoBOysirKm9/ehqsZ4BSWVK\n",
       "ZB1KwjbdeVKvbvlGEcE9IsmJWEUE88c1fJzUqNwm8PsekY7eVvOHkig/JZBgKDwE9SbezZIRP5n+\n",
       "dPa2eS1CSsFTjwcc3tsiurY72nqkpTkdA8KAbxQRdzaJYIETjug01QXnn84TcYeRtFnd1Jbe4bRg\n",
       "Od/HiA9XvWj6TFJNAEkAuUWbYV/RZq8lEU59W7V7kbmU5Sml0NgYA527UMz8rOPnReA4C+FklNcC\n",
       "uAlWD/HYHWSkpaXHB1s4E+4eTh5yZRfezc3JTOHZfBP3vT5Wylhdi3LvEfEOCSQIhQc9lCAuCB8M\n",
       "g9jzdSXWZEFcgZSDTvSJmwwOiPYbHT0t0OHgIdADg0Ecd/gA36yIuDHvPbJmWt3BbiXWbkbXKja4\n",
       "HuIMkhSFr/d+4bUYZEZQx9DV2+6p+1434J+s8Pab/WDCVNFwmuv5Aye/dUgSxDUIyuS6vC+FRzMq\n",
       "Xdz8M6muJNMKaLOAk+vdJhX6BC2+UURSMXFHAnYbHa0iYtdUBGFn/8mtXotAxGpb4P3wkZ/tBV9D\n",
       "yOBE+2Tq1KlwfoKnfYEkQRpukLVNSpTbFCU9PcPR8DHnEV58o4jkF293PA6sIOKxO2hIS1cXwc0H\n",
       "l2gewEHBSGMkrVwaKSEAANFo8qdFMuWnBICKCOIK8za8rvrt1kpchkBFpLuvQ38RJ5URTnyjiLgC\n",
       "VhDxCDbNQtzBD+YnNEbSHhEzapvPeS0CFdZZ72TKzdg3+bduJAto4WBOWXWhJ/FmZIgzzTpTe1J3\n",
       "DVfDnKW4osBrEYQzokaBWEHEYzdFlbOPpM5r0GTGGLGIn2d9cRATZ+mObK9FsE0yrYgAoBoigsqG\n",
       "Mq9FSD5cKngZAveIEEmy5rs7SFjV8TFuWA+5zYhSRJKtgiQDdgcZZisixRVHbYWPkPHzOQm8s6kX\n",
       "jR7rkCSIEd19nY6E6/UeEV8r6UnCom/f91qEpMOtVWq0QlDz7ZGVXosw4hlRJRJXRMTT2tVo631l\n",
       "o4j5gwDwl4O04TK05/hGJ8RBKESjEUfC9bIdkEDytdkikrq4tTeprbvJ0fCTbQUU8Z4RpYgg/sPP\n",
       "51kg3sB7dobcfR8u2SVeGMR1nD752ZDYbnXv4keQJAenExFeRpYigrbn/sYH2fP9O//WaxEQH5QD\n",
       "xDs2e33gGvYTCOIaTq/QIP5nRCki2L0gZtx5431eizDisWqahTPZiF0kkPx9mj2C+Bze9nt93kKH\n",
       "JEGShRGmiKAq4mfW7//KaxEQHyDxnp2BCggiiDO1J1ERQRAEcRFDRSQvLw8efvhhmDJlCqSnp8Pi\n",
       "xYt1z7z22mtw/fXXw/jx4+Fv//ZvobS01DFh7YK+zREzogxl5K/v/nsXJBm5RIFvICjygC4E4VaE\n",
       "EQRJgOMshBNDRSQYDMK0adMgOzsbxo0bp/Pq8M4778CHH34Ic+bMgYKCApg0aRL8/d//PfT29joq\n",
       "NII4h3kjiicvO8uF5gqu59NREUEEgisiCGIdVEMQXgwVkYceeghmzZoFjzzyCKSnqx+VJAk+/vhj\n",
       "+N3vfgc/+tGP4O6774bFixdDT08PLF++3FGhrYJu5RAz2FbNsKn1E6OcPqALGVGgIoJ4Qcq4jcYV\n",
       "EYQTy3tEKisroampCf7hH/4hfm3s2LHwN3/zN3Dw4EEhwonGU7eQSMqA7ay/QNMsRCR4KjiCWOf/\n",
       "s/fmcVYU58L/0+fMmX3fN5iFmWGGGRhmOGwDsomAbALKKhJQgwsiYoxRiQETFZOYmOjVXJPcJJJc\n",
       "rzG5ud77yevNzSe/+CZXJW8k7kvQCO6AoGyyCTP9++OcPqeXqu6q7urlnHm++UTmdFdXPV1VXetT\n",
       "z4NncRFebE9E9u+PObKrqqrSXK+srEzcCxq4I4JYwbIjgg1tsEioZuEMMS1prBnuaXonTx/3ND0E\n",
       "SSuwHUY4ccVqFurQI6nK3r17LcMcOnjIA0kQVs6cPgMAaIwiXSmO1Hia3smTJzxND0EAAE6dSg+N\n",
       "jXP9/Vzhjxw+7JIkSKpgeyJSXV0NAAAHDmid0Rw4cCBxD0FSDbbdDhzwBokQnhFBBMJiOQ9BEDF8\n",
       "egIdGg52bE9EmpqaoLq6Gn7/+98nrp0+fRqefvpp6OvrEyIcgnhNY0ODZZiy8nIPJEFYyc/LAwDc\n",
       "iU1X6uvqPE0vMyviaXoIAgCQk5vrtwhCCIX42uHPzhxxSRIkVTBdSjxx4gS89dZbAAAwMDAA7777\n",
       "Lrz44otQVlYGQ4YMgRtuuAHuvvtuaG9vh9bWVrjzzjuhoKAAVq1a5YnwCCIaXAtNPWTdv0h6se/T\n",
       "9z1ND1X8EARBvMN0R+S5556D3t5e6O3thdOnT8PWrVuht7cXtm7dCgAAN998M2zevBk2bNgAY8eO\n",
       "hQMHDsDvf/97yIuvUCJI6sEwCMGBimeU5DPsPsXLA41RpCd/2/1nT9NDh4YIYh/sHRFeTHdEpk2b\n",
       "BgMWjfLWrVsTExMESXXQalawaB0yEv76xlOmYbA8EJEc/gyNUSDekzaKpbhQh3DiitUsBElVUC0j\n",
       "9cCJCIIgKQ+ecUMGKTgRQRAVqN4TLJgmhjgPQRAECQR5OYV+i4CkGDgRQRAVTMZ7cdcEQTwnJGF3\n",
       "hSBBp6mm3W8RkBQjbVr2hHdlBHEETjJEUFVSLyQeFrUrVM0aJKDqCoKkAP60x0OrWn1JF3FO2kxE\n",
       "pPQ56oX4CB5WF4OneYQ7VFRKCir8FgFBkEHEwSP7fEm3pa7Tl3QR56TNRATnIYhn4LjXko8Pf+i3\n",
       "CAgATtIQBPGU9z9+25d0g7JhmhXJ9luElCNtJiKh9HkVxEcGGA6r445IsMDSCD54vgNBEDcJypoL\n",
       "niHlJ216BymUNq+C+Miw2hHWgbCh8Q426wGui5GqBGXSjO0zoqava5bfIrhKRXEt9zN21ctHNPTa\n",
       "eg5xB96JyJTueS5JkjqkTe+QEY74LQKSBpQUVEBmRpZpmGAM7bxnaGWL3yIQoQ22w2Gyv9a5E1a6\n",
       "KU6gCEpdxR0RRE26n+msKRvK/1B6Z8mggUWrQk1teaM7gqQQadM7RHAigghACoqiaQCpLK3zWwQh\n",
       "ZEVy/BZh0KFMRPJziqj3rCggPCsCkkyIu6R7O5vu74fQMfNFVl06xENJUoe0mYgcPfGp3yIg6YJl\n",
       "JxKUdWZv8WNVOyiqRanO7HFL4fwxi3xLX6k7lSValZXZ45bCovPWMcWRn+vOhOHK+be4Ei9iQpoP\n",
       "1FNhx+fqi77mtwhpCX+PhX1c2kxEEEQEEljvkJN0QAeDaqAUUPWafZ+8R7zuxWDgqoVfdT0NR8Tr\n",
       "ajiUAZGwucqhm0hxP0/6MqkoroVMtDKDpBnKjkg4RFYPDQIjGvFsCQ3WxRESZjsiuFNGJpgjixRg\n",
       "Ws9Cv0VAXIJ3wF1ZUgfz+1a7JE1wSLVGlLqbIvA1gm4hRckDv8tO1G7amOFThMSjJbXqdToQSrG2\n",
       "xC5RV+or4jZetpde9SGzxy3zJB074ETEJnj4cvCiH+DWVzRBdmauT9KIh7ZCPVgGD4h4Eu2lrg6x\n",
       "dPjKYU4JJBg+pFu0aOmuJRRQrDP9inmprzKHqqWpiZPd9LYhowRKIo7crHy/RaCCo2mbhOKqBkia\n",
       "wTIqSfO+hZYDUoo1F16oZvm908COv3LSzfcylFJ8xdC9QV2qlOHgorq03m8RbGOnXUiFcyVmzJu4\n",
       "ym8RhOGkXecdG/Ja2UpHUmtkYYLXE4Mw2sUPHFZmd1mxaoRIA6LyoiohaQcZXwbdAVd9ShX8HuKE\n",
       "4hLo5WCRS/29pcy8D3EOobBHNI7xQRCA65Z8gyu8om7Do3YTpInI5mXf5H4mI5wJkXCmC9KwIbJt\n",
       "cNLX8ZbjwEC/7bREM6btPF/STZvR9MJJl3maXlAP7g5mRHRSUvx/vE8FdTvWDrTOM13qvLp8b139\n",
       "QPJ6mryfmqCcYaHtiPB0+G4N1FJnVwsJ+6SJUFZYaeu5VFXNKs4vs/egj5+SyKbOtbaGEG//wDlX\n",
       "0iIkzhDGnwJMo55X8tQevF8NIuIBVh9jQAZ3bkHbKg6l4S5gTVnSrns6DkiDMhGhnREBkCy/N+07\n",
       "iC+j9Cv14MPyrQWqXOwKE4zPjxu7bWG6LOY4eQ+znDuve67hWn9/cHZE/CI9ak0c1o+H5dCO1Yw4\n",
       "XT44v/nyyu/6LYIWG0dEAtVhCoC2ihck1QERtNWP1PxOz4lIclLp5+psYiKimxix5LlWNcuNMkq/\n",
       "ck8PglMudtu+VN0RsYMkpU8b6ug9KM/WlTdCSUGF4fo5j3ZEgtx/p9VomrXyiPhYcEdEDFkR/3wb\n",
       "0Aju5+oN8gB5R8SPTsbNbryhuk3zO5RezSEABGdBVlm4sSVPUF4C8RRSe+PfQJcv3YScHDuS7338\n",
       "D6403MTeoJVdrXlGr3/OVd2GN+8iHvkgY9uFRNUsR0ggsZvUZWnMLMLgjogogjXslxhURdJ9ZERT\n",
       "zUr3Op8uq3nrF2xJ/giKalZIwI6IS8XDIsPkURe6k7jHLJ223m8RUhLepiFxWN0FWTzB5rfG2oYu\n",
       "Om+tvQQ8wlFfRzU7Sb4xsXOm/bRE41MXmD4jC4l9Nidi1peKfkQKcov9FsEAqeFqb+ixFdfYjmkO\n",
       "pYlhVT9kWfbNugQAQE3ZUF/STcU6T4LWWabLRCQvpzDxt5mXXy+h1x2GVVSfJ1MSSL7LIIwUrOOj\n",
       "W/r8FgGCfEgkSDUzyOo/PHjZF6AriHSaiIC3qlleV54Fk9Z4mp6f8DZmfS3z4aqFX4WRzeNgZvRi\n",
       "11OXAaC8uEb1iLeNb2FuiafpKfgzUPeum02XHR+148mBxG6Cz35EEqpZuh0Rhmc1R9X9eA+X0pw/\n",
       "8VJX4k0XlLJWl/nLb/8/X2XhxQtjEW6cQ7EzoZBASpvFHCcTKrNng54/qJrlEAkkg4nIiuJaclgR\n",
       "ExGPBy0Z4QznkaTIqh5v6ZTm10BnU1RY+pEMC1voevWSNFkFssLuQN0vj6685ZIuOz6aLygg33zy\n",
       "sLrxnrUmZPKhcEhAO2hI31yAhqpWVyYjRXZNpA4SlO/XTn8t2ggKHlZnQEqfxRxHnzttx93EVbAX\n",
       "MJ0RQfO9zpAk4xY/zbeIiIFja32X4zi8hqdJ7B42wTU51BArPufHIPLTkSQJrl70NdMw+s7Fq85G\n",
       "rZK1de3DnqSpxu5A3Un+eGl+lqcRdnvS4sQUufo9gjIMUhaJDDsinFazMlw52GkuwxcX3OpCmoMb\n",
       "vu+av4WvLW/gCl9TNtRcdTm4mlkuYdN8r2ApkMFB2kxEAIyz8arSelpAx2nlZjtf5c0IRyDaPpUp\n",
       "rIjJE8+AcK5HagOk97LjUFAkRXl8K5Ve7YgkvNZKAGU+eHK3GjRSV8MCsipvSfz9tq59GGZ1mTtI\n",
       "dWNlXiOKk2fV5eRj3n9l1X2Jv1vqOimh+CYilruVNrDqDtwu68EI06Rf4gjrkBm9F0GhyUQkKDsi\n",
       "LQFeAI2pZqXLkNKFOkeJ0rtdCLSaxcV3Njxu6zl9gdIyNSQks8UUWGJwGTAC9G14igQMDYNPY7uM\n",
       "DG/M/NEIun6rU5R2oTCv1LpaBjorVDsinBORZdOvdkWO9qGjAQBg776/a0NI2nAkFk1el/jbnR0R\n",
       "C1wr6xSZoPuMnXZHfJHZjFHwQsCKGdcIjY+G7aY+YO1ibnaBreec9HUBy4IEQZULIKATETurXpJk\n",
       "PCiVn0tWb0g5r64gZhCYHclhT8/PHAha5uvwS+9XxFmLYbUjLMMsn3EN0TKX5WpXqux8xDEsXMTf\n",
       "T8R8q5JyPs0L1PIPAJ/VrMI8sYYQNi+7BwDM6o51Zne3TIiHlFyZiFg6rw16g8RBKr1L4oyIHZlt\n",
       "fMRmrZfdNsFui1hX3sgenyvtro3Jn2R/R2QegwZGbXkjdLdM5JPJljRkJnXNZkuT+4xIgMAzIk4x\n",
       "nhGhDtwEZLao1WF9NLVlfLqtrFSW1NFV1Uh4VCGJqlmcjZnvK/UeJV+httTlIpNGzoZegnli610C\n",
       "bQglDifdpJeTvoSVHgEFun7hV50KY/9RBzsiI5vHQWejOMMPysQhFCJ/07zfrjtnc6xkSIEBRFpi\n",
       "/7C6+huoq2gSJgs/Ntsvl/s0J5YXzdpHFm2T0a1Gc8ylhZW25fGKUS2s52YlKCtkV50OUuvilyxp\n",
       "NBEhrXA6mJla6cMzyFNX3gilBRUMIZO0N/S4Yho4P7uQa+XEzQqpPYhLOiPiIywdgCyDH2oVSn3O\n",
       "ycqzHYeTgb1kVS919SvVrFCFEjsiznVpszKzHcniyHykgzMikiRBXo49dQYzWczqAs9A041FB6so\n",
       "Q4xpjuuYzpUurWi+uOA2rnjSHVumZFVlNqV7HlMqrPH5CqHS2GnTrZ6x/b4MzxXllRofs5eaJXbN\n",
       "+Ts5F/bJsQMaX04KXu+IGN4hKHWYQGqNFEyQgL2gvWpUvnLp9yAr00odim3yZAWp4uuT4RyS2JKD\n",
       "hdu/8FAyFUIyfjf6Vqm7PQVZfN7llDsSfG3tP8PK86+zH7kD4bMiWVzhQxRLSTzUuLBDSK1fPNam\n",
       "GOvolfNvYRNKKBzv4aYUkkq9ZhCoKxQSBlh2GNk8Tkg8M3ovot6bPW6ZkDREU1VC2LXn7A/Wzb1Z\n",
       "+7iAOmZ7P0SA2tTMMUuS8VG+6LYhoxynw4xJedhdxHGrzz9/zCJbz2VGsohaASx8eHAv3wMuvfsd\n",
       "l/9Ym4yABXi3SJuJCAAwZ6KV6s8tl35PY/HFTlqKLr5VQ6T3DyKBBNWlQwjJmad35byvQH1FM/U+\n",
       "b2PsryUH/wYn7Pkkqf4SK+/03oXUe+VF1ZCTlSs0PVYmdl4A2ZnsaYvYEWmuaXccBzPxb5VlR9Ja\n",
       "mScWoqyw2qlUjtB6Vjdvi0Qbzohlp/mOCNduiGvtQnqeEVl03jrqvXkTV3koCTvXLPqaauAdr6+c\n",
       "g/keneoPcxUzS8euQ0NbT4FWFh8Gh3ZStDNmmNGrTBTce8fMSHJ3Oszhjy3b4a6239ipNmg1yykS\n",
       "/xBy3dwvE+/XljcSD+vyMLSqBQCsV4MNh7QkCTYvuwfGGGbj9rY81fGyrEyzHGbmJSMcgSGVw9TC\n",
       "qMQKmGoWA6wr/MOHdkNv22SuuFfP2mRHJAP3XP0LIfGoMZajObRzAZ7BWZFc8VBsW8VBrBwA1uM5\n",
       "d95f+Ze/LhQ48KXCg2UZOSwL2rm/dHd2t/HiOx09r+SPF/lkaZrcZiVQ72bYRW34wokRjOk9qgUu\n",
       "lwyLyAN8xjG84Ip5X0n8vXGJ/TrpeJDu866w35omZqTNRITHhvWEzpkAQNkG5khPBHp9fwkAsiLZ\n",
       "BpWufCvVK5BMO0xWaZUVA9GVdmhlbGJ2x+U/Zuj4ff5gLM33sjll83MllZa2ozMi3AeL4zsLKWJN\n",
       "a/KoCxNtgyj8sKtPLyfzclB8FIist8r7mx1Wz4qQVx4HCPKa1UH7TljFDEJpoSKRLBM/Kt4iul0v\n",
       "yS+n3jPbPTXVFIjLKM6ZqYB3thlFc227PeekqnJSn9lycn6USw5b9USC/oF+vicSCxXu9ZXqesiT\n",
       "TIp0Wxrah46Ge6/9pe3n/Rp6Oe4lz507B7fddhs0NzdDTk4ONDc3w+233w79/XwV0i7tDT2Jv2dG\n",
       "2VYfRjT2Ok+YscAyM/j06mkDF6YDylb2Bxm+LJGWg0iUFGg7LjEODf3AOi9lkG13piSdX1IjQd/B\n",
       "cicPzWIdVt+pOas0fGi3UAtMbjNr7CWwaibj+RvLFltiC+YhAxZ18aJJX4j9IVRopT2hm+8dOWw8\n",
       "8Q7vt1NZUgcAAKNbjFZ5nOE8P0TtdOpxy8oiKzkmjn2VakQ6JzUg01bOjXld4dAUtohBbqD7JMbP\n",
       "RL0Y4GSM7TgnNOXhdb76uTjIe4OfkBSCTM6znFpSVDXr7rvvhocffhgeeOAB2L17N3z/+9+Hhx56\n",
       "CLZv3y5CPkuGxlVFJEliVoMJx01KerFVdRWHGc9wKAMaqluJ95w2hBKwqWYlJkICs0YCSdP4SNqb\n",
       "pAcCDc+ugt0diOuWfJ1w1ZgxuSYDASfyUM93UL6ZeRNXwXVLvg53XvnTxLWyoiq46qKvmqY4n8F+\n",
       "fBBhN4xhr4l19r1TnrUc2LunmmW2IxKSQlBCsi5ow+IXAP83580GLSGSVFxy1WGWNcnJpzHUwMA5\n",
       "AABYMuUK6vPKRPS8URfaFY8L83oT8E6JAfV4x9Jqlo33lQCgvJjvTJyVMQsRBEYlyQs5OCd5dh0+\n",
       "isbxROS5556DhQsXwrx582Do0KGwYMECmD9/Pvz1r38VIZ8rZGZkwfarfu4oDtYPldVB2KSu2XDf\n",
       "xl/btphirePKGE9iBVPsR0OLTfSOyETBqjVEWMcPsrlO7+U66y52oO0CUuuDjdUzTbyUsmmoaoOQ\n",
       "FIKwSnVAmczod8HUjB9xPptAQvGuY+Kpy27b0vfjTEJCNcvGhIwsLz0/E3WedwKTpofVecmkqMgB\n",
       "AHx55XfIN0wtKCn/GsMU5sbOM5qpGiV2xAKQ/U4Gs6R6bGlNj6MOs37X6l1Jy7MmpjNMyk1HA23G\n",
       "Zx1O3nnKkZSvTtU0yWH9q+C15Q0wd8JKoixemt93nNKFF14If/zjH2H37t0AAPD666/DU089BXPn\n",
       "znUsHBs2Zu6SBHmOZ4Lm6Yru8q0/IIZ8YBAqmY7gj0Mtv8Ws3UmjL8Lpn1XDwNrwyyDD3AkrqTqb\n",
       "JMdOvBTkFhOvOy093pX89obRhDhig4ycTAd+Tygdz+SRc2zHmcT9DoBWl3nMSo6yffZBD+uARRyJ\n",
       "1kTxJ6IbeJp9a6SyN28aYjen9SzgEdEaZmuM4nJu0XlrbT87v2+1reduvfT7xPK4f9MTkEGxqGZW\n",
       "fmZtCE3VOGbyWUG2TAPA2n+LGNUssdj5ph1rRSh+qDJzYcPiOxzFRaLWgYEf2pvxOAZ0ko4eWZah\n",
       "s3GM4LSNqfP6HrKThgKxPQVJuxut1lzx0NiMfa8tca699lr44IMPoKOjAzIyMuDcuXPw1a9+Fa6+\n",
       "+mrbce7atYs57L59HwEAwLvvvgtZZ7TP0eJ5+aWXITerAI6cPGg7/RdeeIF4fWzTLHhu7+/hwIED\n",
       "lvEMDAwkwhw8eFAT/uBBrWy739xtGtff//4GHDl6hHr/2PHjTA3Z0aNHAQDg5ZdfsgwLAFCUUw5H\n",
       "Tx0yDTMgD8DBj2Pvs2vXLjjXfzZx76WXjOl8+umnTGknkbjqjBnPP/+8ZZhjx47BPnlf4vcnn3xC\n",
       "TP/YsWPw/PPkegJArmd79+6F0AnyJHn//v2GZ1555RWY2bkK/vDao5rrz1Pq52cnPqPKo5brw48+\n",
       "JF4/dvwY9Rk9r7/2OnyYe8A0zZcs6tmbb71JvK7/PkgMUCy4vPfeewAQazvUcvPUIeUM3Ftv/cNw\n",
       "b/7oLybq9auvvkp8ft++/YZrn585k/j77NnkN3L82GcwrLIb3v6Y7Zt87bXXDNc+/PBDOHP2lOVz\n",
       "+/I/gUOHzL9nVl5//TUIh2JqsK+9GpNJ3xm++dab8NnBc/D552cMz/f3x9R3lHI5cfIkvP7a69T0\n",
       "9u2LfZOH952CvKwiOHHmKJOcr76qza8ZHcvhj28kFw/+9re/wcGPP7aMR0lfz4nPTsDLr7xsuP7O\n",
       "u+8Qw+/atQs+IHx/JE6dMpbpycNnE/Hoeffdd6n39r71PhTmlBna8127dlH7ypMnT1JlU+rh2/94\n",
       "2yjHe+8AQPJbVHj55ZfhrXf+DgAAr7wS+3Zofa1Ce+kk+Cs8pZFXzd49dL8OpXnV8OmJ/fDO3ncS\n",
       "eVmeXwuHPvtIE47WntL49NPDCVnOnT1nuG/V1pxUles//hFrY8Y0zqT2Myy8//4HAAAgQQa8/NIr\n",
       "pmFffOFF6j3a4tDhfafgs8+s+xf12Gj//lg7+PbbxjoCAJAdLgCAAwAAcOrkSTgs08c4Slxqdu3a\n",
       "BQePJ7+lN954w1I+gFieVxc1aq69+dabzIuQjSXd8O6BtzTXPjvxGbz5prY/O37kBNOYg8a87ivg\n",
       "/7z0L4nfR44eSeStfmylfPua9I8f14w3NP2qhxvojqc8999/P/z0pz+Fxx57DF544QXYsWMHPPjg\n",
       "g/CTn/xEhHzMcK0WCFjeoEVRUVBvKwl9Bef2+8GgXuCGakZpntgVixj8uect/Dm5YPR6AemS86W2\n",
       "mO4/xgCj4PTVTPayEeGh3OxJdzHPqMKcUsiOkK0Cqb8JUdvuk1oXaNLLzyLvhJkTe6eKgnoYNcSe\n",
       "sy4SWRnkfJBBvSMSr088KidEzSx6flYU1EFTRRdz/LQoczK1CwGuOcRL/SMipt+4Wb7lZNLPtu0/\n",
       "+o4hJi8hKwQ6l2HKcHumfEW1IcmyclbxyvIE+kbyoGi17bTzs7YsNJSx+b9yOiYr5SgLWlp0q58p\n",
       "pJp11113wW233QbLli2Dzs5OWL16Ndx4442mh9VryxtN44xG2S3t1NTEdB0bGhsNz9HiGd09GqLR\n",
       "KHR2kjutaDRqKUNvL9ny1qiR3QAAUFVVZRlPKBRK3K+oqEiEj0ajUFGhPbw5vG24qTztHe1QVEQ3\n",
       "z1dYVAiFhVYmgCERx8iRIy3DAgCUlpVZhgmFQlBVFdN/j0aj0DsmmXejRxtVesoY4tR1ENHFAAAg\n",
       "AElEQVSjzjsn9Pb2UstWIb+gAGprkypg5WXlxHQLCgoSMo0aabSCRXqmqamJ+h41NTWG9xw5ciQx\n",
       "7Jhe8rZyXp61Q8JoNAqNDY3E67Q6Rsr/7lHdEI1GIT+PPujo7jaWv5q21jbi9cpK6/MUtHMuDUNj\n",
       "KgQ1NbUaeXnq0C2XfRe2XfFDaG1tMdyLRqMwenSsHRg1qpv4fE2NsQPJykrq6GdmJlVhykrLIBqN\n",
       "wtIZV6nC0i2jjOwytmv1dfVQWRWbIBUUFEDbsA5DmI4RIyAajUJ5BeHguIocnVnWSCRCDNc5YgSM\n",
       "HBWr993dsXzQd3rD24ZDNBqFzEzj+4RCsbBKeeTl5UHnCLqfo9Eje2HzqjshGo1CVia7c8auLm1b\n",
       "N2KENm+i0ShUMNQ3pS/Sk5efB6NGGb//hsZGYvhoNApDh7CpueTkGr/nlpaWRDyGNBsaqPei0Sjk\n",
       "EuKL9ZVk88N5Jt92V7wPaWvTfsPDh3TDsgvXaeRRGDWqG8IZMfW9rq5Ymj09PWBGNBqF+zc9ofmt\n",
       "fr/mZvpCTW68PWxqboLs7Oz4OxnVxtR9FgulpSUJWTIiGQY5rNoYdTm0tsYM2AwZMoT4XGFBAVPf\n",
       "rrTpmZmZlu1cTw/9fW9YcTfxejQahfx8a+MpytgIAKA2/s0odVZPcVFywSUnNxdKiukLMNXVxjY1\n",
       "Go3C9MkXwPeu/w0AAHR0GNs9Ei0tLYZxwPC24UxqmlNHzyfmbX5efuJbWDo91pZXVlZCL6WvZkGf\n",
       "TnFxceKafmw1ZIjRXUVhYaEmDnW/On/SpbCg7zLbsvHgeCIiy7Khww+FQqamF29c/k2oKrXvw0ON\n",
       "YqqssZo8YFHICKs7S/em4YrNarcXuyYzWhL57nW/AoD4TJ5lNVK270QqHGLT9FOvKpAdGvKWj73y\n",
       "XD7jGrjj8h9DY41uksedvHv1qbF6OMG5pXMunLDS1KSoCGeELOdMbPv7Y3jOcpfQQbFlZeZAbpZZ\n",
       "p6tYg+GI1CLs2PapHJEZSXhZl+23gJIUgm9e86h1QCV8Ih/4Patr22z/EG11R6/y4YShHA5GAcS/\n",
       "i+mZZkqorMwcUzmUsYNibtqpzL6b742/h6KSXF/BsIMty+INxggq+wwO7+TsUFblBcls5+C13ZSp\n",
       "jlhVESqW4GRZFjp8cKpJo/7dPnQ0XDD2YiFyWeF4tLFo0SK455574Mknn4R33nkH/uM//gPuu+8+\n",
       "WLx4MfWZzIwsIZ3M/ZuegOk9F8Etl34Pasu1Kytfv+JfNL+VATlAcnDgzMgD+eFIBvtKHG+l+fY1\n",
       "/5b42zjxIseVyGdJ4ppasNrwV79DJCOTaK44Foa2/cd6MYa6HJ0SCoWhpKAcblz2Taa0E+jzhpJX\n",
       "6slcUT7/Lo+C2bdCLSfKeyihi/JKTA/2UweOglWzHAyJLUNYTaZZJ85OYJmMkawVWeVzRoZJ+2mz\n",
       "YXNy2JRKXBRlIEA6Lkmjq3ksfGXVfcTwZUVVhgO3mrg58sBYT5O/J3EYRWA5SA/AVu9YB2ArZm5g\n",
       "CucaplazQvF/Y2GY/YEk2jRjbeExN8rUVpGaCLJOIHO6NM6e+xwAAG5e9V2u50QMxr9//X+ozFs7\n",
       "S1OsirfFgk1QTO/GcTRkdGEB3FBONDcJQPbdo38+ZR0a3nfffbB8+XLYsGEDjBgxAm666SZYv349\n",
       "3HXXXeYPCrKhHsmIEFW9ik0Hfs5z22qGzZQCpxhqb+vGCmS+48H7EdhxxCcB6+BOJQtnzbczgeVZ\n",
       "DWGJX58zdFO5yZDZqrIzjZuQ70rDz7e4ngxdXlTN7JdEgZZnPDKw7KrY7WRFdM6mdVVXDHY9GtPl\n",
       "tJDf4v1MLZHRJsbq64T4ww5WOhVngnoUPWPaGRGrYqyraFLFpQ2vn0iLnli21Y+E5TPsG11RoLW9\n",
       "rDXYrO32ysQmrT/IMMlzYh+lD6NfkZWSZxnLi2pgZvRiTYhLL9jIKDFw7dypSyMUNn7rIgZorH2A\n",
       "PkEr315OJxZ2mDdxFZMwJIe7PF+D+urscUtZRDOFPR9kcqEzbcWz57UMYne+TN0XMJ25M9dWcQvH\n",
       "rVheXh7ce++9sHfvXjh58iS8/fbbcOedd2p0nEnY9TjthKGVMT1EMYMY8sBEWOFZ+gXhT4dlJUMm\n",
       "/MVD25CRcM2irYbrPPnil13tiZ0XQEgKGdLvaDDXD6ateouo4ayrT1fM09ulT77D3AkrobzIuPsR\n",
       "MimT0kLzcwIssAySrErayepbBeGd1YTjAw5j3hm564s/syUDvS573/6JaHNJbyMBQHaEPMiycmho\n",
       "VgN45VW3yaNbJib+7mwy18d3q8OdOnq+6f16E7WqwDhhs8Bs8qrU/ZBuZ8Ss7ksgJco9khGBhZMu\n",
       "M9xnhWvgD8m2JpNgqpi3T4q2T4VuVR0EAOhpmwx3XP5jrnh4UYzlOMX0bWUZelqTzqPNVM2KTXxI\n",
       "Aai1U8zz99pF26CndZJpGBZ42hTxvtQkQ/qix8FtQ4xn0RJpAdmKZBDw7li8Dj+ca03tiXUMSvVi\n",
       "rWjtQ40HamkrpNZNLQ17XoT16dIoJXkuFiGNLuFQKAwdDbrDhSbbf0SHhoI7YapTSWb1M/PnvBo0\n",
       "mKXT3UK3Sz8gDyTzXDkDJKttGsUYPqQbyopiB5pb6ynGChjeNcTjxM7ujohFjR8zfArcsOwe0zSV\n",
       "FXSr8ivOL+P2O6TEyWY5TPmXbyWNFzfbXNJ7lhRWQFL1grLiqeQTe0rx/0qGp9S664vOWwcLJq0B\n",
       "AICivFLm2DPCEShTHEsylJ2Shh1YVbmCjNmOiKFvYGoPCCokmt0B9/OF+JUwptvVNBYAAEY2j4Mr\n",
       "5n1Fcy8khUydu9JwuusViU+slEEvm7YGRz47KhKLBde4HCQ/VWmDgDpNXPTQxUsa7pB2JNV3vcK3\n",
       "iYhCVYmYGbzCivOvNbmbmH5zxZml0+E2PWzm0aCUR1Vk+/odsGTqlUwD78Rgxc5MndXxl0Y1iz8Z\n",
       "Y3x0assbYYRTx0T6D5rV1LKI1Q5ZtqcmpxJJlgcSDsnUsus79cmj5sDWtQ9bxMswEYnXTRaHSLZX\n",
       "neJy0BwD5mTmWq6IKnJadfT682Y82DWDbHZ3COcB5QQu7kKT3jM3K181KY3ldWt9l0HdCoCiqm8x\n",
       "cdJXRbuqWeo6+NU1D0JutrXlH1pMJLIph7PNikMTWmifIrZ/Mt8R0e6ESCDB1NHzYfJIuqEVCUKu\n",
       "1lM9JLVXskdtNmrLGw3GT2y9jZxUDVLnHzEo7yKmkDogE/8Uj+BdCcZvibBOF5eGoDLHnDgtISO8\n",
       "4+Lyoup4EmbvZ79eu41vExFl1WPhZPsrSrzYWXkE4PvOElZidNdJEwcnB39HNY9nfjYvpxAiGRHL\n",
       "97jvul8n/rarE0+DridN2BERWD63XPo95uds9/cuTj6tykw/SVZQ5+GALENBbhFsX79DG8aG3Cxl\n",
       "kxzgM9Qhh1mXTTsrQXg3/YRUGbiyWgjr67qATzhgzGPSQMPkuWF1ZFOqVs+q65KpR2yzQrHY2SBE\n",
       "BgCxyV5TTTv0tE2Gvq5ZxgAkOD9Q2kFmyzorUX9YYhX6a2v/GdZeeBPxXmVxDYxu6YN1c79MiNif\n",
       "IcLcCRTdf0pLZDb5S9aJeP0OheDiqVearm7Hjjo686nlCozlkZ9TqDV+YoGiLm6ROAAA1Ng0JpGY\n",
       "bHFY6bHKc9YxEWvZ6cMpBjxoT29b90NGCbxhXMf05A471872ADH0sLqYmWGeM1HxxOlp+XAcghX/\n",
       "dkRcypO2IaOgs9HCD0CifdSWWmP1cNh0CemQPYewhIowZ9xy8qq8A9uexpUoPqtYJNRxmllU0qbK\n",
       "+A4afSyL7T/hnTAtZ2jXdduVehnl2HkSxawubRDGslLFYsoxGY82nXuv/SVd7Uz9fLwByssp1Mnk\n",
       "Tgdv1AmnwzvIGD4k5o9CMUXLM5nSm1VMysnWDLYNMfoEsUqfZwLOWu9lecB81Zh6WD2p8iJCxWVK\n",
       "99xYvCbxJc33SrB52T0waeRs7X1O1Sya6sB3NjwOOVnWPnLMZGS9bhaPXgW2vKiasMMSK5+szBy4\n",
       "fN7NRN13zcorlxTmlBVWQtTEDLSZiicJ2llJNUqZtVhNoGOhidZ9PCFhrIu0cuzSZIg6gU+mqOTf\n",
       "8KFkn0TcSTp83qxX496doaiwVlpYWCvhVDW3orHa6KeNp8xXzrwORrf2xR903p7YnjOYdguEeq3r\n",
       "+7Q7PjZlsEHanREpL6qGqy4ympAFsN7izM8pJK42Gg4Ycco+d+JKbh1zXpgGFhx+RGzJYLrKSrlO\n",
       "tKTCm67LGOYhMpQWVsL50cXx2xQJGLLyiwtuNX9IlqnxKD50iKjyVaZ07LYaGg7VLDbdZnulNzBg\n",
       "fKfZ45apYqUP9JOD49hlJzrYtFUm/SDCDN5BDund2RDb5nY1jQOA2Lta+Qmh5zH93cntrLqjNF/Q\n",
       "8GMdfdvlPyJe15YxQ51waRTQUtcJa2ZvFhYfi6U15V0WTV5Lvaf+zTZhYYdlJViSJGiobqWaWWct\n",
       "D2I4hyvRPHVhWKXxsLLhO2LapbW4r7HAZz8eqp8hymJx4rYno2RSH0IPyb17AfSqoZSZk6qj71dI\n",
       "7WlZkc5Rq087sf5NRHzZJpJ0/+pvk6/TVq2ndM8jpMBekA6+XyJFDKvjfqB/F8t3E/4xMK+3Uq5a\n",
       "rHpT5yHkOl6Qq/YOay1bwpqL2cRDL5Pqb/UK40WTvqAKw5/PLE/oD6sXF5A79xuW3mO7QxkY6Ddc\n",
       "i3Cbdo4PkgU4b6SmYHOSY1Y2dleMRTS5NGekVhMN2nkh0+J3KHDiacs6Zn8V0MvD0wsdHIxXcGKi\n",
       "mQRJhXfW2EsAgH+3S3lmmd5ksqS9L5R4HWusHg6rLtgI29b90NF0nXdcY/Y2PW2ToXvYBENbsFlv\n",
       "hEOVZlu1tQd4p7s7siwLX0jWtx+KjHrV42k9C4WY8dUjgwxfWv4tmBm9OHGFhFne2XEtIFPMBHc1\n",
       "jTU6WnYIqW4uPu9yoWnYxUfVLP/01Vj8PqiZM3655ndZYZXyACl2+4I5ZOn0q2D5jGuo993YhdLk\n",
       "pUknQQtHesLMrKw9WK1jaVfKE9cph9WtvEbT8pvJsy4hjuk9FzE/p4lDNXBVb+/bOiPCssKv225f\n",
       "PWsT3Lj8W+Sw3BLE6JeNE5HRrZMS5zhIYtJ35ew3g9aqWdaUFVYm1JysKM4vg5Y6o21+FtR1qbSw\n",
       "0iQkG2oHaTlZJn5NwN6uk9lXK8X/JwJhzY3AZotUr2ZGl1g+d8NSiqU4h9C6a9IZkfl9qwFAPWiL\n",
       "/8u4O2j+TbnTv5YVVUFICjGpmrlBG8FK4Rfm3AhXzL/FqLZE8dnDDNOGiHkg1uEbKZ5CghU7Wpnr\n",
       "nWAOqxsB8yZeypY4Jw3VbZrFXD7NeZZMZd8tGzVsPNdZo0R0FopzepSFCaXd0O7bejeW9V01Sz1L\n",
       "U6+ujBk+xfT55GSAHf0KjT6baYWo/0jWzKFvbXMN7gQPuCMZmVCQW2Qd0ATPzSoT88DdD0CZCLCu\n",
       "XukHUcnn7Mmp+dg5VOoiZt60DYkk46W/p5h81g+iFZ8SyvecmZFFUU0krwaxQNoRqSyphRXn0z1N\n",
       "61dvzdSGSN8B0dkk1bO9+SRVTUY4ApdMW68tDUq2fP2Kf4Exw6fYt8QTJzODvrvGWiTqurvqguto\n",
       "ibJFpmPW2KVEi2g0bSxnTamJvoUrsOSJ+WINjSGVzR6prcTIYFLNYnFsmnTaZzApKqggJnZqjU18\n",
       "ccFt5IBO1JNt5r2ZhUGjqX5n+cH2vKhJvjaeqpJ6mN6zQB0g/g95R2R6z0JLS44iOdd/1iADLzxP\n",
       "yQ7S0ZMZyTbdlRkwqdf5Oe4eHbDCd9Us6kqZVWPgpOzoujRMKJ34yObxBn8LVLGCYLHAJxEywhFo\n",
       "qetK6N9qD2Iac8ztmXhteQNXeKuOlHqfkN/5OUUwadSc5LNWK082C01rNYt2RsROPhufmavzsrvx\n",
       "kjvh9i/8gCkt7rKOB49kZCXs4wMAZGfqDyob46V6i2derecvC9cGhTbaE/WkyfYukOp1ivPLE5dy\n",
       "s/KJi0MstutJzIwuIZopdkud0G5ot6JlGyp6v4ij3/miWc1qru2ASEbs+0wYazKJN7k4aL4jYud7\n",
       "on0pI5vHccdF4uZV302mZbOfN/serb5VyxQZRRrXMd1wTfGLonD+mEWQZ2Le2qq/yssp0CwIKaVp\n",
       "UI9VFolCoYRvKy84e+5z0/tODFsQQwgcF9577WPaHT1dgrSzourAfjlS9X1HZERjUqdRXZhujplF\n",
       "2eMePrQbNl78DUpc3qI3lUiC6f0cHY4y8tU1D8FNK++Fruax8A2SPwZiX+qTehvrwTjFMRRDB6vn\n",
       "/DGLmC2SXbNoK1w26wbHdYl+WF3MoC43S9sxFeeXGd6R2lBbiEDr2MOhMHznuscTv791zaPaaAnv\n",
       "lvBvorvHqgo4nODYVB/XhBHnW8oRv8F2TRSSpPn+nZ6LuX/TE4kyVrz5kg4Z2/XmSx5ia7dArBY0\n",
       "1GFN03KU72Im88YgDNs98etqnwNuN536ySZNlemGpdtVA04uHRdCeYh5KXX9HzVsfPyaM66Yd4ul\n",
       "qi1Lv2umuii6SGnfyupZm5Jh4kFmRi/WtO8XTlgZL1e+nFNUQWkO9JJuD/RaK+xv39c1C/JyCrnk\n",
       "ShDvZ9Q7IkomFOYKOnsrSaDPNxlk7wb/uiIjm4EXts3Mhe9nREKhMMVnhbGiD61qdZSkZBg5ajNa\n",
       "WcFxmAjzdT4/IpYhDFdo9uu9pLKk1tB5Of3w6sobdVd41zwtBia6+wbVLF26POZ7ZVnWDaj095N/\n",
       "dzT0xG3HO1uJp1t28mnCJ0AGOwe2qapZjHrh+TmF0NGgPQyqz9tVOssp9rf33SsbGWSh8c8ev4x6\n",
       "j3mF2GA9idI1WVjKsgPtAL6TeMxhsOLEscKqrnMSSC4ZgiFrMJj6EVH+TfS7ZjsdioELCWjlmknx\n",
       "mWQFKbYr5+utFSbRt9tfopxvAzC+km3VLIa8SV6wlQRTWnpys/Ng67ofwpY1D8aTjj3LW8e+ptsh\n",
       "N8rE8r0bGTUsaW66sqQ2YSiBF+VtzvWfSyYd/7ekoBxGt/ZBfaVxwqn4ABIxmbjn6l9ArW5sI1JV\n",
       "Xr8opHZVkTzXKSw5LnxXzQIwriLq75MjsJOqdtZdUlCuUekgNaqjW/o4U9DO6BNYvI+ovqOyJHm4\n",
       "a5juUCtvpR7fMUOITGaQVbPM2bDk67or9jKPtTG18hDOa/xA8yxDr+J0YEE192qn1bHbUsUfmzp6\n",
       "PvkGJ7INE7ZhQznG0q6raIL1C7bYkkPNtYu2qWK2Hnzp4XOExV8n1JM3kZbCEoMTgkyFucWwZMoV\n",
       "1pHo67hVVsiybk7i/6TaDG6fJAzvs35hzEw9a/tAOnNjBknfXN8WhsMMfkR4EpWMOyLKz29c8RPL\n",
       "xyeNnGO4ljzRZ6+ONFS32XqOBwkkmDWWbA3K6SDXjvne5IQDICcrF0oLKhN3lFh5oC/2KItByhkh\n",
       "/nZTJMpERvNNSRJcPvfm2DlHnViks3Y8ashuWo81mO9lSkoi/OU+vqtmAZALaGgVi8dRPj45uj+R\n",
       "IkBsB8TK9nM+71YfR+m5UdDVpUMSOwbKoWEe1OVy6azrLbc6Wb1Bk4hZCiF8nLrf29ZpbfO79YHQ\n",
       "4g1JIVg39+bkhYRqVnIDmQTRppoPDSxVNctGTjpd4V885XK488qfxeWSufsbJR6rHRHiBJfi6T0k\n",
       "haCreSzxnjFefZzJKySP0SyvpyyALJl6BczoXRR/zoV6oqqQdn2nEDtTk0FJKBSGaerDqQ7SUXPw\n",
       "6D5hcTl5zt7nzBKvekBADq+oNctqC3KEgbzCRZPXsosI5EGSvt6ETHZEVELF/8s2ADbdHbCIo7m2\n",
       "nXCVc7AnemxoMgKUAaC+shk6m6IJdTEjFvnm4flT0d0XrQdVHNd63VtqnI9K1vWWZSJxw9Lt9Odd\n",
       "VOLXLyQMH2r0MaPHzIiJm/g4ETHn/DGLCQ85K7QzZ08BgPZjEj0jTa4OOo2IdwXNeC0rk38iYoiX\n",
       "oymwY0eb+Jq6MiktrDCoxKjJyTRafEh4OWVO1CQ4SNCjik/fePAfuOZTL3HaWOm9WSfFsLMj4kgU\n",
       "CEkhKMxL+lFR8u6WS79PeYL87jGVNT70OyKedHIMeVxSEDv03dHQQy0rEWgWf3zcQSCmbVgFJ4Vx\n",
       "qczUayme1AqxfU6/andQAoCm2naY1rPQcbzq+qL8bVTNYveszhRGApBA/526WCYBMCJz88rvwqSR\n",
       "s+kr6Xr1L/1KN2d9YspPnapOsniSOyXE+Dizk7ZTkrCsZXW+iy85LpK72oRrotK2Uf2svM4DxM7w\n",
       "6Y8atNaPtDTbPr3XnosAp/g2EZnYOROi7VNjPxg7RacDskh8tseqE+46qve2tgzBs9VCUxVij8KK\n",
       "7paJmt9fmHMjbOa0Yc9juk4TSvd+xFm8ybsmN5fNTa8mflqpsejC5yqmapk8+loGcYztA3xekOjw\n",
       "6BmhdQAJ8L3rf0NQ8SLHqyZE2RExw7bXdV3HbQbRyZxFxSDV3faGHvNnmK1m8U/URUOMU47dSfzU\n",
       "DIZM4hIgHsmClysJxTGzfqPn7LkzGhlys/JhyRR2R2XjO2bAhsV3GG8Q2q+KEu0giGciQvvGp/Us\n",
       "TKiNSRAyOWbJsGhDbHP5ysVzE/Zx6iqa4OqLbodRwybA2PZpiev6iRkL5sYbtD9L8svh/k1PcKYg\n",
       "Jo8MKqIy3yKfXSkMZt5N+mr+9o09vNd1LUzpA5VvS+sU2LvFKt8mInMnrIQ1s+n+OGhcMe8W+4la\n",
       "mQwWgqT6ryppkwr37WsfY3JWZZ6qZpuHGGblTJqtfxW6Z2lyJzxyxitwRXEtlBZWWMevh7XzZlBV\n",
       "UKNZzWP91imy6K0qJeOWiPedUF/ZJCwuKwyOGk0ySlEfsj/opKz2MTxHMh5gZ0WfdljdFWTzNGgp\n",
       "53Hac79pxb3QFTdDSjprRxTKRC4rSM8p38PU0QsMzl/t4ueOjUqIxJ8TO2dSBmusK6R87zO6pQ+u\n",
       "WxK3yGjRfp04fVyVCn++1ZQ3aBydKpCS1XtiNt0Ft1BdjQWRYMmUyxMrsZJEmCSr235b9cJdG5yi\n",
       "CEkhGNE4Bq6cfwvMUK1MO/4W4u260r6z7KgkFuv0tyRF40PQREQ/MOZ+V60cOZnmjlUBANYv2ALj\n",
       "R1iff2XZueVBAkIf6/GOnOWiqk8EUyoTultiVhLsfAjWzzivFDz1VGkQsiLZLk+OYtSUDTFYZdDT\n",
       "UN1G8MngDhXF1cTr5IZRsz8qBsbVF8PZgsQgU/mX/By5vhnddSncv+kJsilIl9oqng7ua2v/mfsZ\n",
       "bVqkqzLDByPDtYu3Jj1GM6SfFcmGpprhhuu9bZMtnxWF3Y46NyvfMOA1i2toVQsUxp2YWqmZapzH\n",
       "2mxvzJ4bUtkMsykHbrmhqWZxWCVkTsqNtsUElrFHOJwBbUOM3rZJjGweByvO3wAXTlgpdgJHEFR/\n",
       "OL2kwMbikwkSSJCTmZs4IyACXvVrnm+3OO4byy4spVVSUKEx0ax/qpFwmF4GGZbPuCb+ty5Nw8Ia\n",
       "STB9L0VeYNWzdPp6+MKcL9ED6OK10k6xrs+x+3dcHjtHOq5jmmV8Xc1juT5zursHWhrGGCg3DDuM\n",
       "xkTEdP5W1r3sGFcRScpNRJxg5lmSCkPBqB2ruaXP6pXH9vl9q+GbV/+r4brecoiI+jq/7zLmT5y7\n",
       "g9WooRgiM33UGJytMTSIwGKmk0XdwKWZCE9dVc4xiB6pschQW96YPITK8A1/+9rHoKd1kuG60X8L\n",
       "PW1WtT37DszY66C5IyqNNBZ3WVWz6JCec2KwgpoOUz1j3up0eD/Y5GTlQV/XBXChoN0oBatd5bYh\n",
       "o5gmIrQqMXPMEoPDPJAkCIczYMOSpKqY9b6KfYjfOWO12rzsm0xGdZy23jlZubBlzT9R79OMEPR1\n",
       "zdL8pi6YmbQvvH3nkMphMGb4eaq4zd+eptrHnmexkEo9tJrYsLbXmlAmr8x9PkeVf/du+KV2B5m1\n",
       "KnK2sevm3pzoD3kWoLzclQ7ERIT1da0sbVlHwFdphla1wgiTQ9IkaB+C+4cgrVWzmGLRWV1R5F5H\n",
       "8Uni5K2k2D489b4mL1XhWHT9S1SHsoyWQfmkpqlm6Z0wJeNPBBQDY3my6vl+Yc6NMGb4FLBTes42\n",
       "pglXLRq7kgLzw3W2JGE4l6IKbHpbbXdeg67M9KZHeSYw/aQ0SJ2WzzsirLC8O+8EXVT7yuwk0Uka\n",
       "qT3v4YaWjwsnr4HCvBJNmCBkDevgUm10w09I3wrJ+tiw2hGJexoIr2s4lK6zIMXafFm1F4r2hVbZ\n",
       "2QOo6tYEKGfReGTNjGTD0ErtpDUzI8tRe3rx1CuZwuVmJdXV7DoWdptATETsIEo1yyyWm1Z8m9ms\n",
       "pwKXmo4DM4V6WHXLeSt+YtDtkuoY2bZ27N8OyuHb7MwcuHX1A9Q4v3f9b6C1vstwfXrckoyS7RT1\n",
       "VwNZejPIioDxBwo4OyS1vxo/vv8xw6dAdmaOTatZ4iRW5z9pcHr/piegpmyIa+mbwfr9aTzxupTW\n",
       "uQHKZEeHZYuoyuPCvFLiuQAreUg6xtoJgT/4dcBYlDNEi0R8YXrPQrgq7quEDsshX/YXcKufEc3y\n",
       "GdcYHPV6hd0ziVWlcfUuIfWU7XvLysyGLZfRd3Pycwrhvo3/LkAeNrxZ5Tem8a1rHoUFky5j8I9H\n",
       "v9/XdYHmt8bUMKtkPlohMyM1vnpBuOk8xm80uqpmuwzCGnpBK5CMkzF942sYoKrQv6PyaGFeqeZ6\n",
       "NqN549njtJ6j9bWIZnKVNjgqK6qCm1bcqxHOrFNzq9baaZRt+2RgOAsSJFgHtswTEd3ra/LD4lBk\n",
       "/0C/8T4RK9WsGFmZORDJiNhy4hiyKn+bqoa2fEzEo7lq4VdN2zX1M43VxrNDAAB3XvlTy/RJdDZF\n",
       "GUPaMJ7hMzlZeYb3c3tn3/SAsGRc5XccN4mAF5AIs/xq1N+jMlmhedq2k/9KnM4/NIwAACAASURB\n",
       "VJUlddA2xOjLIhwKG2qV22M1rnqs2Qax0WdK9g2s0Ni67uG4VoMNYUiXiQvC3n0HqTURUeVLXjaf\n",
       "dRkAcsaKqBrdLROTJls5YElbvyJ1/SV3WT9kZopOtNUEF1YYkrswdjdCdfERsuP2L/wgaT5aj+6d\n",
       "MiM688AJ6yMxjLb1rZ18KbrF/f2xQaZyGNxLrBpjXk/MqQaTfwOD2p32N20iYqhynG26Oh2SahZx\n",
       "d9dSNSumC/6FOTcmUuGF1H6IGJw62dFgnQxkRrIhI4PgLVyChIoQb55UWh02FcDY9mkuG1pgyXt7\n",
       "k0cAti6CvfydKIf6s967edk9yYUnQTgxEmBYSVe1G9dffCf5Ib01TXZTlIm/vrrmQcM5JiUeu19/\n",
       "V9M4aNFpP9y9foe1eXcd9jRs2CgrJBvlIcLYJ5UVVjEvKhfEjZnEoo+r2scPr5vh5S4zi1vUwHHH\n",
       "5T+GTJ2zFjbMVbPszgDXzNkM73/8Nnz730ysRZBgqHT6TtaOLwQ1NDvSVtAGbRlMnnXt0dc1K+ED\n",
       "g7cLMS9LiXBwmT0VvfleNStnXgdt9SPhjp9dxbSyFokPjMwHxS4dVrdoyASY5Fc9Zr7iok+rVLA1\n",
       "HttYvC/NvwRPW2KVpf2Wqlls+s7KVTuLOAqkzo/7rIaNdvZLy78FhXklHLtDZAb62Z+3epNvX/Nv\n",
       "jmRhpaOhV+NQlZeywir45NgB7udYJuqVJXUsMVkHMakS6rN4Tta9WFekRbe2dpyvCkX1vW1b90PD\n",
       "jor6fametT1SiW2p64Taiib28PWdMKFTa7Y8P6fQ0kO4lwexuc4SCd6F+O51v9KY2A7F9x6MxlyS\n",
       "u45uyWJGIHZEChKrUWyUFJTbctJmy2oWI0Mqh9ne3heO6QFwcpGzzJC1SUhw04p7YcGky7ie06Aq\n",
       "j1HDJhhudzZFYZXi+4TwTgv67KVNN9PrvHGqLh2ScE7JUttysvIsD5m7tUWakcE/ibS9qmj5mPYd\n",
       "t8XNMTpNP6EXbU8oy0eGVrXA/ZueIAxKdSuIxhNJTMlN61nIvLpnqp4EIKRjEaHDT57fKqog5Pgb\n",
       "qtugpKBCW/42iq9fNp+I8DQBRhUZn098Evjexn+HsRYmTelYv4+pQ0MfsoPUViauEQo3VdW1ebJW\n",
       "3faUFlbaWogIh8KwbV2yTdY4R3WyS5U4BB8jJysv7oyT0boVpfy4S9VkC5tmwIL21mJ33pypdOr9\n",
       "/LCMcRS/VG6Ol/UEYiIyK3oxfOPKn1h+XU63iszM1PW2TdZ4M7VDIeeEygx1fVl83uXQUNUa/8WQ\n",
       "ByYViDZYsdMgD61qgZwsawdCLGhWwAmy9HXNMhzWok2qaLAOMoQ1JII+ZLeaA1NnZBQaqltdOVDq\n",
       "7WFjbefHA00VS7TetiLckimXE00Rk+pWT9vkpL8VAvpv3M68m9R+8B/YNjvgbIEqQFFeKWy65G7L\n",
       "1NRtlDxA6gP4MsJgclbHrLGXcMXnJqFQmLs9qyiqgejwqQmfXU5xaqLcc+eWKTo5sYvGTLNJOLXD\n",
       "YrU/GRFtd6rmeMpNZGlnRJQNEZBg/YLbAMB8vCyaQExEwuEMKMordb02mlWatRfexG0hy01ys5Kr\n",
       "FtN7F0LEliqaEVFnREQM1iOqsxcXjL0Ytl/1cwAgV4OOhh5Ycf4GgxR0zPb6ncme8FBr8+AaLy11\n",
       "nUInuQp2JiJTuufB96//jZD0syLZQuIxw9QClI0zIqfPnGRKl6t/opjf5CUcCif9rZBkEtDAWqlm\n",
       "ec2wuhGWYS6IJicGVjsiGjg/ViX0/L7VXM/5jb6u3r72B7BmzmaoLh2iCkNXR7WGYSLC+MHUlDVA\n",
       "I8FZqWnq8XJktTYlwhKe73DUXbO8N1iMjFNX3sS0cGvVxno/kOevv8IXmWywZvZmmDUu3o65op5I\n",
       "uj7IdkSYcVxp7T/fXNMhPCWzwcYFYy+Brese5kozGTE9XrtnRKzgbVDu3/SERo8zJIUc6a67QW/b\n",
       "ecTrA4x66qIGaDN6L3JF7c/6sJu4hkhf1++4/McaZ2Bu9UdLplxhcrCTv0UvK6pO2L43h3648yur\n",
       "vqeTwijH0ulXwepZm7jlo8UXF4ItnJklOwELGU4GH3YmaBHVAXWrb9fObl99RbNlGD8na57vKBjS\n",
       "FxdXfk4h3Ljsm3YlYQp1Nh0mIvFvbOaYJTBzzBKmsHq+s+FxlSNbLZIkJc7HuWEEgKWJaB86Gory\n",
       "S60DamNO/HXl/FuYnqCpYzk7Zs9HtH2qEHPRIY4h/+C1muVye+lE5+2qi2LWq6ztqpPhteIQyYgw\n",
       "VTyiapSXVrMorDTsXnAg+APQe791Ws36Rs6i3lM6/faGHhitU6lZPWsTjB9xPumxQYA2140dHFuZ\n",
       "85Zde8Nog3llJ+W/etb1TJNCs4FnXUWj5fOt9V0wrmO6Sfz8aeuvhkJhWD1rE0TCbLutRXmlKhXR\n",
       "JH5ZI7Kis3FMQt9ZYYCgmqV8s5suuQvybZw9/NKKb3OFbyhvh+qiRu507OL2RIRmMZKnXogb9NDP\n",
       "iCj5EA5nqEIbw589d0aQLNZkCNJ0oLFw8hpYOHmNaRhaeyFKC8MMJ3Xz2sXbLA+lm6E+l2q6UKAW\n",
       "kckJrm2RXIeW3yQnv14ungRrIuIyZJ03PjN0NWUNHKGTDKkcBnU6axB26qu6wd667mGYNXYp1/Om\n",
       "hwt5sBCedztTdJVX92uTRs6OHwhny/Hkx2iUqii/DGb0LtKFU6cbe+baRVsNpgrHdUwP3K6PGlHn\n",
       "fezgh64tW5+iDZQRjhjNORPIzy6EiZ3aM023XZZ0wmnlRsQN9O2fJEkwrmM6LJl6heb63AkroL7S\n",
       "uMq/bd0P4dILNroqo8jMqC1vSOg7Kyw//xpjkvF/h9V16q6zyZJoUxllH1bZDbO6Ukt9i0j8de+J\n",
       "q9TSgzk7N+Qcbdz3Xfdr09ARB4NbHm677AG4nNNIjGg6G6PQTTAUw4LS/w2pHAa5WfzO9cxxVh+y\n",
       "KWq/duRU199Lpq1PLBCJPqyekRFxffDPM/HzsktOKfO9TvOlMFe8nj0X+pJ12OmWFVZBRphQhCbx\n",
       "Lpi0Bl5++/8BQExH/8zZ045koNHVNBYum72ZObx6INo2tBs6Gnstn7GdfYxOfVLuIJoNJCkEsjwA\n",
       "37jyJ65+Hz5rh3hOOJwBK2eqdwXNzUk7gbXjY+3kCnKLYURDL3zw8R7N9TCprbGBs+/KWV611HVC\n",
       "S10n/OPD1xyIkGqV2bm8ynkuW6/O8FCIYYHM/iBNMU7BJvz1l9wJ/f39sO2nX9RcnzNuOfzppd/C\n",
       "qTMnbMqhRX0GhxtdnhrejbGgFE0PJyydcRVcMn098Z61byN3+tjpvYugu2Wi5tp3NjzOvMtDk2ts\n",
       "+1QoL6qGv77xlGMZ1dAsZ4rOHx7VUy8Pq6fURMQpM8YsMticZoXmaTTVqCqpg4qiGjh4dJ+jiZ1V\n",
       "o54ZyYKxNIeBFoRDYccOvDoae+DSC67XXJOsOiRd4Vp1fKR4/NbHtktRnlHXVmwjGMR88VImSewK\n",
       "k53IOB7xvB4zJueFuoglLue94IeFUFVaD3dc/mPTMKUFFXD+mMWG6yxFm5ddAFvX2jwTaQmfcRF1\n",
       "W6hu4+dOXAmv7n0OPji4h/SYt8TroDKAXXXBRtj53P/6IkpICglrSkXV9EhGxGC63bTtMPumbbaF\n",
       "oVCY+TxpIimX+6Sgjk8GlWpWOBSGglwO5zIqgll89vDz4CQdfpmaatohJ0Leas3MyILxI2YQ77F+\n",
       "i5YD8XSqFD4TtN2nqsK4EzIBZbzx4m9AcX6Z84gcwvfdO3txs7N0RDkUVw8W6aq9BAsjoJ2zKKzV\n",
       "cdnqBe3gskIoFIbzuucySmVE8b/kBPPxJKGceZudgFaVkoJyqCx0sMMSMII0RjG1zSlYTJb3FuG3\n",
       "hUmWwboj0lLX6ZqqUPogwmZ3PA6xS7QC42KjqaYdlo67wb0EAjY49pqG6ja/RTAicNBo1iiHQ+Ka\n",
       "xtb6kcLiUuDtqCVJgtWzNsHh44eYwztBbyBCJFmZOXDm81OuxZ+AqgTOptoZFKZ0z/PpW5Z0//qN\n",
       "czmWT78GvvNLf891AIBrk+esSDbBTL4TLLQK4u9Rrzs/G3LJuqcY2N7JS1gX8nhUs7x0aBioicg1\n",
       "i7aaB/BzYCiJb1R967h4sjGe58aKLlZ2dfRezsTV8L5RUAceouhtmwx1FU1w1w5yx1RaUAFtQ7uZ\n",
       "4rJunK0rZW/bZI2lE1bs6k97hVf1qDi/jHlnxrlMJs+TipojOdH5RYqvvrIZRjSOIT+QYgsUmZEs\n",
       "aK3vMlwf1zEd/vrGU1xnFezkvd/qICaO1blpqDZajUsnJEkyOA52E2VcofdpVZBbBLdc+n3P5DDD\n",
       "7/orkrHt0yCTWb01xSYi+/btg1tuuQX++7//G44fPw7Nzc3wgx/8AKZMmcIVj5VfgyBt1wnBt3mI\n",
       "rPlXDM5eJjsraWXLNTUdyfCHKdbjJcIZET6JfCcUCkF/v8nEz6QsLpywkqr+psf5NCTmdNQOtHrO\n",
       "Mqhyb5Lgjdms2rIG+OiTd7mfE6EmQ8NMNcuPD4jkWPPmld+lhqe2myblqH4mKAsYq2dtsu2rBsD4\n",
       "HkF5Lzo25OP8NsuLqvnTQFQkv5PacjYLpWJTJeFdvf7CnC/B0ROfuhb/2Papts/uuonjiciRI0dg\n",
       "0qRJMGXKFHjyySehoqIC9uzZA5WVlSLkCwxBaWRFDNEvvWAjHDtxBB79Q9KcqNXgX8SKNg29xQi3\n",
       "p5usKxyknZk0mwrDrZd+PxDvFLQzIu6QOu84tn0ajG7pg5seWm4dmID5N5bMBzsqGLaN5SX+SMZw\n",
       "3ZKvc1sD87ov0H8b4VAG9A+c81QGJgK+ckxSSxG5GDe6pQ86m6LC4ktlhg/tht3vveS3GB7AV3+s\n",
       "+rna8gbLCRipbXW6a6Nv0zYsvsNTdU7HE5FvfetbUFdXBz/72c8S1xoavJvJeka8nERu0/k1uVF0\n",
       "1tUTESrx99V/QO72Of4M2PRlmzrDRi2sDuoAACpL6swDiCpoHwcptJXb8uJgrF46zhnGlXi+KCUm\n",
       "fylOyM3KT54lCfYY1nWGVrXCewfeYgr7xQW3Wn+3AUAS2GfOGruUyWKaWX0XWcVIOx8hj5wFpwIb\n",
       "Ft8B139/kQ0txuA1BHqJRJ4ftILVuJLohbzhjCrXonD85TzxxBMwbtw4WL58OVRVVUFPTw88+OCD\n",
       "ImTzBC9XYlNyYOvDSnWqrI4HfAFQDCZlUVooctfTuzLPzc6H+zc9waYbnyaFnElx8OUHSpVqqG5L\n",
       "DFLb6kdBbXkj2+KMzTJxfafVwbM3rfg28wAnL7swpVSARCy4ze+71FJ121IOQd/y/Zue8HygNnjw\n",
       "v++fPHIO8UyVwpDKYbbj5q2DI5vHwT1X/8J2eqmC46ndnj174KGHHoIbb7wRbrvtNnjhhRdg48aY\n",
       "990NG8iHXHft2mUrrVOnTtl+lvbcO4f2MMmkbIW//NLLkJtl7R37wIEDhjhPnTwJAAD1Ja3wweG3\n",
       "4OzZs9zvc+Douxp53/voPYP8J+PpWMU9MJBUPdqzZw/Ix43e0M+di733Ky+/rLn+0ksvQXYk6Yn7\n",
       "jTfegIMfHGN+DzP27t0LoRN8HshZ8vGDjz4AAICPD3xMDL9/v7bMjhw+bIj77OefJ36fOHPUcF9k\n",
       "PthlQB7QyGT3mwEAOHryEDGOy/q2wNH9p2HXfra4le+HJssbb7yh+c0q84cffmgZ/oMPP0iEWTr2\n",
       "BjjzaQh2HWaLf6C/31H+qTly8mBCjn0ffZS4/vHBg9xpqL/xgwc/TvwdS+eQJtyi3msg60wJNY13\n",
       "97+jeZ4G7f6rr74K7+fu11x78cUXITuSSwz//gfvAwDA0aNHE3G2Fo+H1uLx8Itnt1vK0n+un0le\n",
       "PUpZHj92PHFt9+7dcOzA51zxHDlyhJj+Bx98ALsgeU3dB5w8Y2wT9M8rqqD663v27IGBY8mJZKyN\n",
       "OcolsygGVOqqR48d08h6+vRpze9En/lKrO8Q9R3pUcf7zjvvQOSUNp297+wFgNhZVn3406dPm8sm\n",
       "y8xyf/rpp669o57Pz8TqrAi57fLeR++bywAAH39sHAepefOtN+Gzg0k1w8OHj3iWh2pOnjyZSLe5\n",
       "MAq7X/9HUqYjZJlkWYZ//CMWTn3/vffeh13ndiUWVNX3Pvj0LcM1Xkjj4Pfffx929duP8+SZ41S5\n",
       "WlvdN9DgeEdkYGAAxowZA3fddRd0d3fD2rVr4frrr0+pXRHPiM+Gu+r7bEchcr1gRO14X9K1TCsg\n",
       "OyLWK3Ck1Y30WEFPQjFVyrmyEw5lwJpJzr342kG9IpuTmR8MKygqGdyWpjCnzKIu+5UfNr9zn4uv\n",
       "NL/aJfOiAaiXHOjrVPClJ/kRCUZfw4//cotuRkvyqqCuxP5ugzPE5WcQupdUw/GOSG1tLYwYMUJz\n",
       "rb29Hd577z3qM9Eo24GuHc9of+fk5DA/q4+D9lzozdPw593WMp09dxb+dSdAd3c3FOUbvVDr06yq\n",
       "qjLE+Yfdv4DDJwDmzlgMv3vlEYhkZnK/z1sfZMPvX03Ke+LF/fDcXq38/9+b/wqHT1i/UzQahcef\n",
       "KoSnX/5vaG5uhjHDjeH//W8ZcOYcwKhRo+DfVZPl7u7RCediO54B6OjoEHK4acczAE1NjRAdwZYv\n",
       "ygyeJR+VvKqqrjaE3/EMQE1N8vqOZwDWLbwRTp75LLEVu+MZ0JTZqTMn4d933a95pnd0FCpLaplk\n",
       "d4OCyjsgI5wBw+o6Les+Cwc+/QD+8wVncVix45lYm/G7V5LXWNP7VH4HXnjXPPxh+V143iKMHqVe\n",
       "hcJhYe/+0aF34b/iefnx2bfg5diCIlRWGtsKK37/Rg4cPRWL6+1ju+DN/cn32//p+/BfL8TCZedk\n",
       "W8Z95pVP4C9vk/NH3QbT7nd1dWm8GO94BmD82AlUnf4j8B48/y5AYVGRIc5/+0sYBvr7TWX+9a4M\n",
       "+PwcX3nueAYgHC/LZ999Ag7ENyja2tq41Gzqmx+AyuJaCIW+ZIi/vr5e0xao+4DDxw/Br3WLjXr5\n",
       "//UvEkC/9vqOZwCam5uhty0Z74gRI1z102JG/0A//OJZgOsvuQuqSuoSOuw7ngHI1vXPSp85auQo\n",
       "+I+/iW1DDsMaOPDp+/DXN57S5HljQwNEu7T519jYCDv/AVBXWwevfKCV43evZcOx0/S6LUkSk9w7\n",
       "ngEoLS1ztZ1U89tXsgDOaOVWr2azyu2Eky8dgL/uoZfrjmcAKioqTO+3tbZBe8NoAHC3j6GhtG+0\n",
       "seWOZwBKS0qJ4wVJkmDYsGHwJ9X4ccczAEOHDoVodxR+sVMCWda+V/YeGf74hv133fGMUdYdzwAM\n",
       "GTIEoj328+/oZ5/Cr3eR5Tp61P3dV8cTkUmTJsHf//53zbU333wTGhsbnUZtwM+VctFuRC6eeiUU\n",
       "5plPaEiUCdXLZ9fftVpFFuoa0f/FHgAAyMnKMzVjmpOVq7H4de+1v3T9gK8Vqaq7bPfbtvL27JSg\n",
       "Lm4xH0L34VvSW8FLJ8zOFbHutDm2cBOAJde68ibIySKr3iVxr/JdEF0C//XMz/ke8j/bhGHVbwek\n",
       "CzVlRu+iYDrN5YDsIDCNKppHOJ6IbN68Gfr6+uDuu++GZcuWwQsvvAAPPPAAbN++XYR8acvU0fNt\n",
       "PVdaWKnp6MsKndn7T3Zq5k2Xp4f6fXJo6BS/JyGu4Nmgx179ig6fCl1N48wDBWDgBqAbQLroRiQv\n",
       "O3m+Koi+lxxLFJDyHIwk1uMYysDtukeSoJi0MBHvu9y2Uom10ohZDVh03lqvxLBk6ugF9JsmBcu7\n",
       "KBCERYQg4viMSDQahSeeeAIef/xxGDlyJNx+++1w5513wjXXXCNCvsAQFD8ierqax8J3r/uV7eeD\n",
       "+GH4Yd0mKzMHmmraLQMGL7fSA7tlLkkSw8psMHBrMq+vkwW5xcnFiqBsL6oxkwk/MAZSI5Mk58ML\n",
       "U/S16DsbfgUdDT0mAhnzLYBfhxBSo4YEgxENvabe5M3Gfrzjp1DI+dkykjyOx3E+VxghBpHnzp0L\n",
       "c+fOFRGVKb6u7sULOogTkoxwxPaz3S0T4U8v/tbGk26WhcsraYSP9tvX/JurafrFqpkbHT1fnF8G\n",
       "DVXuW81wE0dfbAAn6gDA9In0dc2CmrKh7svCidN23GmJ+NOGx975yyu/Cwfec89zsleQclB/JiiS\n",
       "EYGtax/2RqB4embYKvWgfv+pQhAXQgTCa1I6LGAiQiIoBn7s4p1nFiSQH2VLXaeQeLIzjaZ/7RKU\n",
       "jyqIk05enK6UZEWy4Usrvi1IGoSMO/VsxfnXMoUz+946GnrhjXefN4/A68Gaw/TcW9CylmtIZTN1\n",
       "IrLpkrthYKDfOpUANktbLvsnyCbsTJYVVcEnRw/4IFESpbRZncMhrASwIroAt/qVaVzo9JJE4HOl\n",
       "JL8crl20LfbDzw0Rwl/phJ2D8wrbr/o5m3M4Rty3OpWeZZjKBGXy6QdBVI9UuGbR16Cxerh5IN6y\n",
       "U8ITnmOZ/Ad1gcCsGIvyy2D1rE2mzzdWt0FzbYdgqQSTdJeuuVxVWg9FDvoQL5jYdQHceeVP/RYD\n",
       "SSEqimqgbQjdAAzvxMKtHZFUJ/A7IpmR7IR5NzvMGrsUfv+c/TMUQgnogOPeDb+EzAz7B63Vh2Od\n",
       "4qbFHWXAF9BiGOQEcyIS1EGvSII8EXIDt8o0OzOPei8khWBcx3Qh6QShTvLIkCuwf3BCSApBYV6J\n",
       "9uIgXgDxgiAay+Dh9rU/ML3Pf1hdwNp/GrbXgZ+IOGV+36WmB5GY4Sj8ovwyGEZSeQpoo2c2CQmm\n",
       "xAgLVaX10Jji5hHTi+TX5HQwKbKDd7wbxdsxxsPnZufbS87WU+6yde3DrpuSThLEHKCjN3OetqTh\n",
       "AHEw4KT1I54RMakHvGdK9LQ39MAwF3ZN/V7cSKmJiN3Ot1SA7w2loFjamm9c8S+O03PCiIZe11c5\n",
       "AzqnsmBwdRRbLvsnv0VgRpYBIuFMONv/ud+ieI6tTiBIHyCnLFO750FBbjH0tE4y3mRotwrySuDE\n",
       "6eNcabqNmb+htCSlmlJ6/bxywW1w4vQxD2UZbASonXIBr61mXbtoq6Png0pKTURSHo9WTBZMugwW\n",
       "TLpMSFwp1d8ww/pW6fn2wUSGjIyIKxMRJ5PylKgBKbYSm5WZAxM7Z9p+fuPF34D+/nP8D5LMtwZp\n",
       "QodwMXnkHCjSq1pxUlNmfraRZ5HA71VlDSnWJviJk5zi7VvCocAfy/YFnIgwImSHATu9QCDKmzwi\n",
       "DlmWg9WRu0B5UQ30tp0nPN6MkM/NuMffie0zaWnS/vrZLCU0AwLwrZYWVlg6Bl583uUw3OSwccpi\n",
       "lf0BqesBEcMUJyLynvnIyyl0kFr6MugnImG/O/GAIxP+Iv9OP9DChTdMG70Ahla1pvzBRisyI1mw\n",
       "9sIvGW/YGFmqc2ruxFUQbZ9qXzCnpMJoI4Ux7tr4PwlIFab3LoTjJ4/4LUZagrWQnAdmk/SivNLB\n",
       "cV6Kk9QahbvQ4Y1sHgs3Lv+WnyIgHsHTcGJj4R1Lpl7htwhUcrLolpAcIXBZOzszB4ZWtQiLz09G\n",
       "NPTCZ6eOupoGDqBEgLloALNk0EHaEVE0KfKyC+Dzc2e8FiklSamJiBtzgFAojJaFTEhL/ymochVI\n",
       "gqDuoWZJdCP0jO5xPZ1gvTUBDwW8fN7Nrqeh7kdSTf3yinm3QLXFuQZEIKlVPZKkWL1OSSSJ2H5k\n",
       "Z8Yce9686ruDQXFECCk1EUH8JH2+KGyig01pQYXfIgAAQH5WkSdO2gI/GLb69IMuv4JOzmsXbYPW\n",
       "+i6fhLFHd8sEX9NPTV9M9oS9cPwKyAhHBMsyuEhrdVtZNuyIbFv3QyiJ919Bd/AZJHAi4iGp+FGm\n",
       "nsTWBH7gN0hRvo9tl/9IcMxY3q6SYvqqSm1w4igXSX8unLDCbxFskRnJhghOoDyhoqhaY7pbhKsI\n",
       "f0A/IkgKkoqTqhRbxkMGDf76EbH8ltPls0mxCVOQCZoaJZJky2X/FJzFtnT+5iQJ8nIKYevah/2W\n",
       "xDF5OQViHH/bJLUmIoGo1PZlwMYbQegMxu9j9rilMGb4FL/FcEZQBj2MZGflup7G0ulXQUeD++eL\n",
       "EGtys/Nh/Ijz/RbDM0oKyr1JKMW+e4ROOBSGFedv8C39lJqIeNGBuElK7iKkEcmBLjagiL8oNXDe\n",
       "xEttPS+yLXE8AQzEAhE7qy7YCBdNXutqGueNutDV+BF2wqEwXHrBRtfTGYwLKVakVsuA+EXKTES2\n",
       "rnsYMjOy/RYDSQPSxdQpgohg0CyQxFdwc7PyITcr32dheAhg+eBquK/gpCcABGQBZtn0q2F0a5/f\n",
       "YjgiZSYiZYVV1oE8YNB02ib0tE6y7904AIwaNt72s9gBpB44ZnIZzGAEQUgEZLBuRkFukd8iOGLy\n",
       "qDl+i+CYwE9EwuHAizjoWDf3y36L4Bs4EUVE4PQwqZf1ECffiB6sEUg6tAvfuPInkJNp02ktLsAI\n",
       "I9Cj/FtXPwA5KX4uJF0ISWG/RXBMYCyJIEiAGN3SB6c/P+W3GEiKUFJQQfQoPdjB/iX1QF8fwSDQ\n",
       "E5GaNPMgGw4FOrtNKcovhZtW3IvnKxAkzSjILYILokuo9yuKa2Dvvr97KBESZO4Q7ucHSVdQgwBh\n",
       "IXVHxinIFxfcBqfOfOa3GLbBSQiCBAQP+/cV518LF0/9oncJIhqyM1ErAEECRwqcf0kVcCLCi4O6\n",
       "V1JQ7p2Nb8QV0kEvFkF4yAhHIMPEU3NBTmof9gwyd1z+YyjOL/NbDARBENfAiQhiymWzNsGpMyf8\n",
       "FiMw4FZzKhLEyWMQZeLn/k1P+C1CWoMLV0gqk9ZnMPBMkDBwIoKY0tkU9VsEZLCADTszOCFGECTI\n",
       "3L1+B+SgWiHCAE5EOMEBQOqCVk0CDurcIgiCWBIEFWGr/jQ/p9AjSZBUByciyKChp3WyY8tlQegA\n",
       "EAThB79dBBFHS10nNNW0+y2GL4SkEERMzs0hfOBEBBk05GTlwvgRM/wW/S3mHQAADixJREFUA0Gc\n",
       "g7tH3OBuNuImmZFsz9IKQl2uKq2Hzcvu8VsMX9iy5kEIoS8dYeBEBEGQYICqcwiCpCC3rn4AStGw\n",
       "wKChorjGbxHSCpyIcDBzzBIoyC32WwzER4KwEpW2uLTKH0SVnOBJhCCIXbx2vhzENg1B7IITEQ4W\n",
       "Tl7jtwgIgiA4HUYQBEHSAlRyQxAOcCUKQVIT/HYRBEGCB05EEAQJBnhGhB08rI4gCIKkATgRQRAk\n",
       "GODgGkEQBEEGFTgRQRAkvQniRgvu/ngOGppAEAQJHkInItu3b4dQKAQbN24UGS2CIIMBHJwzg4Nq\n",
       "BBnEYFuJpBHCJiJ/+ctf4Ec/+hGMGjUKJPxIEARBkACBh9WRtAHVWJE0QshE5OjRo7B69Wr46U9/\n",
       "CiUlJSKiRBAESVtwUIwgCIIggvyIrF+/HpYuXQpTp04FGWfqCILY4JKpV8LJMyf8FsMTnKpWYSuL\n",
       "IIMY1DpB0gjHE5Ef/ehHsGfPHnj00UcBAJjUsnbt2uU0WQTR4FWdOvP551h/XSMPciFPeP6+/9H7\n",
       "AGCvjrhV1h9++KGj+M9+/rmj5wcj/f39gcqvIMmCpBanT58GAHIdwnqFiKS1tdX1NBxNRHbv3g1b\n",
       "tmyBp59+GsLhMAAAyLKMuyIIggQGVINCEARBkGDiaCKyc+dOOHToEHR2diau9ff3w//+7//Cww8/\n",
       "DCdOnIBIJGJ4LhqNOkkWQRIoqz9e1KkdzwBkZWZi/U0xPnthHzy3l6+OuF2vDsvvwgvv2o//P1/K\n",
       "BPgc21JWyurugYxwJgypbPZbFE/bLCQ9+e/XsuH4aW0dwnqFuMHRo0ddT8PRRGTx4sUwbty4xG9Z\n",
       "lmHdunXQ1tYGt912G3ESgiAI4iUdjb0w8oNX/BZDi1Mdb9x15qKppt1vERAEQRACjiYiRUVFUFRU\n",
       "pLmWm5sLJSUlMGLECEeCIQiCiKCqpA6+uOA2v8UQSlNtO+z75D2/xUAQBEEQRwixmqVGkiT0I4Ig\n",
       "CGJCcX6po+fXXngT7oogyCAFR1hIOiF8IvLUU0+JjhJBECStiA6fCl1NY20/H5JCOBpBkEEKLkEg\n",
       "6YQwz+oIgiAIG5IkQU5Wnt9iIAiCIIiv4EQEQRAEQRAkRcDNUCSdwIkIgiAIgiAIgiCegxMRBOEB\n",
       "DTEgCIIgPlJaWImOWpG0QfhhdQRJa9BSEYIgCOIjV8y/Bc71n/VbDAQRAk5EEARBEARBUoSsSDZk\n",
       "RbL9FgNBhICqWQiCIAiCIAiCeA5ORBAEQRAEQRAE8RyciCAID3hYHUEQBEEQRAg4EUEQBEEQBEEQ\n",
       "xHNwIoIgPKDVLARBEARBECHgRARBEARBEARBEM/BiQiC8IBnRBAEQRAEQYSAExEEQRAEQRAEQTwH\n",
       "JyIIgiAIgiAIgngOTkQQhAc8rI4gCIIgCCIEnIggCIIgCIIgCOI5OBFBEB7wsDqCIAiCIIgQcCKC\n",
       "IAiCIAiCIIjn4EQEQRAEQRAEQRDPwYkIgnCQEcrwWwQEQRAEQZC0AEdVCMLIlsv+CTIjWX6LgSAI\n",
       "giAIkhbgRARBGKkqrfdbBARBEARBkLQBVbMQBEEQBEEQBPEcnIggCIIgCIIgCOI5OBFBEARBEARB\n",
       "EMRzcCKCIAiCIAiCIIjn4EQEQRAEQRAEQRDPwYkIgiAIgiAIgiCegxMRBEEQBEEQBEE8ByciCIIg\n",
       "CIIgCIJ4Dk5EEARBEARBEATxHJyIIAiCIAiCIAjiOTgRQRAEQRAEQRDEcxxPRLZv3w5jx46FoqIi\n",
       "qKyshIULF8Jrr70mQjYEQRAEQRAEQdIUxxORP/3pT3DdddfBzp074Y9//CNkZGTAzJkz4fDhwyLk\n",
       "QxAEQRAEQRAkDclwGsHvfvc7ze+f//znUFRUBM8++yzMmzfPafQIgiAIgiAIgqQhws+IHDt2DAYG\n",
       "BqCkpER01AiCIAiCIAiCpAmSLMuyyAiXLVsGb7/9NuzatQskSUpcP3r0qMhkEARBEARBEATxgKKi\n",
       "IlfidayapebGG2+EZ599Fp5++mnNJARBEARBEARBEESNsInI5s2b4fHHH4ennnoKGhsbRUWLIAiC\n",
       "IAiCIEgaIkQ1a9OmTfCrX/0KnnrqKRg+fLgIuRAEQRAEQRAESWMc74hs2LABfvGLX8ATTzwBRUVF\n",
       "sH//fgAAKCgogLy8PMcCIgiCIAiCIAiSfjjeEQmFQiBJEuij2bZtG3zta19zJByCIAiCIAiCIOmJ\n",
       "cKtZCIIgCIIgCIIgVgj3I0LioYcegqamJsjJyYFoNApPP/20F8kiKcCf//xnWLhwIdTX10MoFIJH\n",
       "HnnEEGbbtm1QV1cHubm5MH36dHj99dc198+cOQMbN26EiooKyM/Ph4suugg+/PBDTZjDhw/DZZdd\n",
       "BsXFxVBcXAxr1qxBk9JpzPbt22Hs2LFQVFQElZWVsHDhQnjttdcM4bBuIbw8+OCD0N3dDUVFRVBU\n",
       "VAR9fX3w5JNPasJgvUKcsn37dgiFQrBx40bNdaxbCC/btm2DUCik+X9tba0hjG/1SnaZxx57TI5E\n",
       "IvKPf/xj+e9//7u8ceNGOT8/X37vvffcThpJAZ588kl5y5Yt8q9//Ws5NzdXfuSRRzT377nnHrmg\n",
       "oED+zW9+I7/66qvysmXL5NraWvn48eOJMFdffbVcW1sr/+EPf5Cff/55edq0afLo0aPl/v7+RJg5\n",
       "c+bIXV1d8l/+8hd5586dcmdnp7xgwQLP3hPxltmzZ8s/+9nP5Ndee01+5ZVX5MWLF8vV1dXyp59+\n",
       "mgiDdQuxw3/+53/Kv/vd7+S3335bfuutt+QtW7bIkUhEfvHFF2VZxnqFOGfnzp1yU1OT3N3dLW/c\n",
       "uDFxHesWYoetW7fKHR0d8oEDBxL/P3ToUOK+3/XK9YnIuHHj5PXr12uutba2yrfeeqvbSSMpRn5+\n",
       "vmYiMjAwIFdXV8t333134tqpU6fkgoIC+eGHH5ZlWZaPHDkiZ2Zmyo8++mgizPvvvy+HQiH5f/7n\n",
       "f2RZluXXX39dliRJfvbZZxNhnn76aVmSJHn37t1uvxYSAD777DM5HA7Lv/3tb2VZxrqFiKW0tFT+\n",
       "4Q9/iPUKccyRI0fkYcOGyf/3//5fedq0aYmJCNYtxC5bt26Vu7q6iPeCUK9cVc36/PPP4fnnn4dZ\n",
       "s2Zprs+aNQueffZZN5NG0oC9e/fCgQMHNPUnOzsbpkyZkqg/f/vb3+Ds2bOaMPX19dDR0QE7d+4E\n",
       "AICdO3dCfn4+TJw4MRGmr68P8vLyEmGQ9ObYsWMwMDAAJSUlAIB1CxFDf38/PPbYY3D69GmYMmUK\n",
       "1ivEMevXr4elS5fC1KlTNUaAsG4hTtizZw/U1dVBc3MzrFy5Evbu3QsAwahXQj2r6zl06BD09/dD\n",
       "VVWV5nplZWXCzC+C0FDqCKn+fPTRR4kw4XAYysrKNGGqqqoSz+/fvx8qKio09yVJwno4iNi0aRP0\n",
       "9PQkGkmsW4gTXnnlFZg4cSKcOXMGcnJy4PHHH4fhw4cnOm6sV4gdfvSjH8GePXvg0UcfBYBYmStg\n",
       "m4XYZcKECfDII49Ae3s7HDhwAO68807o6+uD1157LRD1ytWJCIK4hbqBJiGjMTgkzo033gjPPvss\n",
       "PP3005b1BgDrFmJNe3s7vPzyy3D06FH41a9+BStWrICnnnrK9BmsV4gZu3fvhi1btsDTTz8N4XAY\n",
       "AGJ1gqVeYN1CzJgzZ07i766uLpg4cSI0NTXBI488AuPHj6c+51W9clU1q7y8HMLhMBw4cEBz/cCB\n",
       "A1BTU+Nm0kgaUF1dDQBArD/Kverqaujv74dPPvnENMzBgwc192VZho8//jgRBklPNm/eDL/85S/h\n",
       "j3/8IzQ2NiauY91CnBCJRKC5uRl6enrg7rvvhgkTJsCDDz6Y6NewXiG87Ny5Ew4dOgSdnZ0QiUQg\n",
       "EonAn//8Z3jooYcgMzMTysvLAQDrFuKc3Nxc6Pz/27l3lVaiMIrjewJOJOCkEMQYQS20UQtJGm20\n",
       "sRAhIAgqKGipeCkstFQ7X8DKF7DxASIoEjF2k3iLhWgTsBQhQizMOsXBwTmcxpDM8cj/BwO5fMww\n",
       "sBiyIHv39pr7+/tv8cyqaxGxbdskEgmTTqd9nx8dHZmhoaF6Xho/QFdXl2ltbfXlp1wum7OzMy8/\n",
       "iUTCNDQ0+GaKxaK5u7vzZgYHB02pVPL9TzGbzZrX11dy+IOtra15JaSnp8f3HdlCLb2/v5tKpUKu\n",
       "ULWJiQlzfX1t8vm8yefzJpfLmWQyaWZmZkwulzPd3d1kCzVRLpdNoVAwsVjsezyzvrLyvhoHBwey\n",
       "bVv7+/u6vb3V6uqqmpqa2L4Xkn7vZuS6rlzXVSQS0c7OjlzX9fKxu7uraDSqw8NDXV1daWpqSvF4\n",
       "XKVSyTvH4uKi2tvbfdvKDQwMqFKpeDNjY2Pq7+9XNpvV+fm5+vr6lEqlAr9fBGNpaUmO4+j4+FhP\n",
       "T0/e8Tk3ZAvV2NjYUCaT0ePjoy4vL7W5ualQKKR0Oi2JXKF2hoeHtby87L0nW6jG+vq6Tk9P9fDw\n",
       "oIuLC42PjysajX6b31l1LyKStLe3p87OToXDYSWTSWUymSAui//AycmJLMuSZVkKhULe64WFBW9m\n",
       "a2tLsVhMjY2NGhkZ0c3Nje8cb29vWllZUXNzsyKRiFKplIrFom/m+flZs7OzchxHjuNobm5OLy8v\n",
       "gdwjgvdnnj6O7e1t3xzZwlfNz8+ro6ND4XBYLS0tGh0d9UrIB3KFWvi8fe8HsoWvmp6eVltbm2zb\n",
       "Vjwe1+TkpAqFgm/mX+bKkljFBAAAACBYdV0jAgAAAAB/QxEBAAAAEDiKCAAAAIDAUUQAAAAABI4i\n",
       "AgAAACBwFBEAAAAAgaOIAAAAAAgcRQQAAABA4H4Be+KR25lqlv0AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4800d930b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = [sense() for i in range(5000)]\n",
    "plt.plot(zs, lw=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks like I would expect. The signal is centered around 10. A standard deviation of 2 means that 68% of the measurements will be within $\\pm$ 2 of 10, and 99% will be within $\\pm$ 6 of 10, and that looks like what is happening. \n",
    "\n",
    "Now let's look at a fat tailed distribution. There are many choices, I will use the Student's T distribution. I will not go into the math, but just give you the source code for it and then plot a distribution using it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "\n",
    "def rand_student_t(df, mu=0, std=1):\n",
    "    \"\"\"return random number distributed by student's t distribution with\n",
    "    `df` degrees of freedom with the specified mean and standard deviation.\n",
    "    \"\"\"\n",
    "    x = random.gauss(0, std)\n",
    "    y = 2.0*random.gammavariate(0.5*df, 2.0)\n",
    "    return x / (math.sqrt(y/df)) + mu  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAyIAAAGNCAYAAADtmMVMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvXecHMWZ///0rLIAmWAJgUjGZJ99yHA23H35gQGfffhk\n",
       "OGxjc74DJxzgEBljYyRMNlEkESQQyhJBWUhCOaOc42q1q7hB0ua8O/37Y6Z7OlR1V3We1ef9eoF2\n",
       "Zrqrnq6qrqqn6qnnUVRVVQkAAAAAAAAAIiQVtwAAAAAAAACA4w8oIgAAAAAAAIDIgSICAAAAAAAA\n",
       "iBwoIgAAAAAAAIDIgSICAAAAAAAAiBwoIgAAAAAAAIDIgSICAAAAAAAAiBxHReS5556jK6+8knr1\n",
       "6kW9e/emAQMG0NatW03X3HnnnZRKpUz/XX311aEKDQAAAAAAAMhvHBWRRYsW0T333EMrVqyg+fPn\n",
       "U6dOneiGG26gyspK/RpFUejGG2+k0tJS/b+ZM2eGLjgAAAAAAAAgf+nk9OOsWbNMn0eNGkW9evWi\n",
       "5cuX00033URERKqqUpcuXah3797hSQkAAAAAAADoUEidEampqaF0Ok0nn3yy/p2iKLR06VLq06cP\n",
       "XXTRRXTXXXdRRUVF4IICAAAAAAAAOg6Kqqqq6MU/+9nPaM+ePbRmzRpSFIWIiCZMmEA9e/ak8847\n",
       "j/bu3UuPP/44tbe309q1a6lLly76vdXV1cFLDwAAAAAAAAidXr16BZ6msCLywAMP0MSJE2np0qV0\n",
       "7rnncq87fPgwnXPOOTRhwgS65ZZb9O+hiAAAAAAAAJCfhKGIOJ4R0bj//vtp4sSJtGDBAkclhIio\n",
       "b9++1K9fPyosLAxCPgAAAAAAAEAHxFURGThwIH388ce0YMECuvDCC10TrKiooIMHD1Lfvn2514Sh\n",
       "UYHjkzVr1hAR0RVXXBGzJKCjgbYFwgDtCoQB2hUIi7AtmhwPq9999900YsQIGjNmDPXq1Ut3z1tf\n",
       "X09ERPX19fTQQw/RypUrqbi4mBYuXEgDBgygPn36mMyyAAAAAAAAAMCIoyIydOhQqquro+uvv57O\n",
       "OOMM/b+XX36ZiIgKCgpoy5Yt9OMf/5guuugiuvPOO+mSSy6hFStWUM+ePSN5AAAAAAAAAED+4Wia\n",
       "lU6nHW/u1q2bLdYIAAAAAAAAALghFUcEAAAAAAAAAIIAiggAAAAAAAAgcqCIAAAAAAAAACIHiggA\n",
       "AAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAA\n",
       "ACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCI\n",
       "AAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAA\n",
       "AAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIH\n",
       "iggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAA\n",
       "AAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAg\n",
       "cqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggA\n",
       "AAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAA\n",
       "ACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCI\n",
       "AAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAA\n",
       "AAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACLHURF57rnn6Morr6RevXpR7969acCA\n",
       "AbR161bbdYMHD6YzzzyTevToQddddx1t27YtNIEBAAAAAAAA+Y+jIrJo0SK65557aMWKFTR//nzq\n",
       "1KkT3XDDDVRZWalf88ILL9Arr7xCb775Jq1evZp69+5NN954I9XV1YUuPAAAAAAAACA/cVREZs2a\n",
       "RXfccQddeuml9I1vfINGjRpFFRUVtHz5ciIiUlWVXnvtNXrsscfolltuocsuu4w++ugjqq2tpbFj\n",
       "x0byAAAAAAAAUTBs+vO0vWR93GIA0GGQOiNSU1ND6XSaTj75ZCIi2rt3L5WVldH3v/99/Zpu3brR\n",
       "NddcoysrAAAAAAAdgU17VtL6XUvjFgOADkMnmYsHDhxIl19+OV111VVERFRaWkpERH369DFd17t3\n",
       "bzp06BA3nTVr1sjKCYAjaFMgLNC2QBigXeUvR44cSWz9JVUukL9ccMEFoaYvrIg88MADtHz5clq6\n",
       "dCkpiuJ6vcg1AAAAAAAAgOMTIUXk/vvvp4kTJ9KCBQvo3HPP1b8//fTTiYiorKyM+vXrp39fVlam\n",
       "/8biiiuu8CguAGa01R+0KRA0aFsgDNCu8puRy4hOO+20xNUf2hUIi+rq6lDTdz0jMnDgQJowYQLN\n",
       "nz+fLrzwQtNv5513Hp1++uk0Z84c/bumpiZaunQpXX311cFLCwAAAAAAAOgQOO6I3H333TR69Gia\n",
       "PHky9erVSz8TcuKJJ1LPnj1JURS677776Nlnn6WLL76YLrjgAnr66afpxBNPpNtvvz2SBwAAAAAA\n",
       "AADkH46KyNChQ0lRFLr++utN3w8ePJieeOIJIiJ65JFHqLGxke6++26qrKyk7373uzRnzhzq2bNn\n",
       "eFIDAAAAAAAA8hpHRSSdTgslMmjQIBo0aFAgAgEAAAAAAAA6PlJxRAAAAAAAAAAgCKCIAAAAAAAA\n",
       "ACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCI\n",
       "AAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAA\n",
       "AAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAAAACIH\n",
       "iggAAAAAAAAgcqCIAAAAAAAAACIHiggAAAAAAAAgcqCIAAAAAAB0IGrqK2lL0eq4xQDAFSgiAAAA\n",
       "AAAdiJkrx9F7056JWwwAXIEiAgAAAAAAAIgcKCIAAAAAAB0KNW4BABACiggAAAAAAAAgcqCIAAAA\n",
       "AAAAACIHiggAAAAAAAAgcqCIAAAAAAB0IFQcEQF5AhQRAAAAAAAAQORAEQEAAAAAAABEDhQRAAAA\n",
       "AAAAQORAEQEAAAAAAABEDhQRAAAAAAAAQORAEQEAAABA4lBVlbbuXRO3GACAEIEiAgAAAIDEUVF1\n",
       "iN6d+nTcYthRlLglcEUl+O8F+QEUEQAAAAAkjsROpRGkA4DAgCICAAAAAAAAiBwoIgAAAAAAAIDI\n",
       "gSICAAAAgLxlf3kR3Tvk5rjFSBYwHwN5AhQRAAAAACQPwcl0ZW1FyIIAAMICiggAAAAAAAAJpKW1\n",
       "mdQOvMMFRQQAAAAAySOpbnKTKhfokDz09m20cuvcuMUIDSgiAAAAAEgeSV0FTqpcoMNyrLY8bhFC\n",
       "A4oIAAAAAAAAIHKgiAAAAAAgecAEyjPYs+lYdORNOCgiAAAAAEgeSZ19QUECIDCgiAAAAAAAiJJU\n",
       "BQmAPASKCAAAAACSB3YeAMjScZVfKCIAAAAASB7YeQCgwwNFBAAAAAAAABA5UEQAAJGyo2QD3Tvk\n",
       "5rjFAAAkHZhmAdDhgSICAIiUw0f3xS0CACAfgGmWd1B2IE+AIgIAAAAAIAp2akCI7Ny3kaYs/cj0\n",
       "ndqBFUsoIgAAAAAAonTgSWESaW1riVuESFm4YRrNWzspbjEiA4oIAAAAAABIJA++9TPatOfLuMWI\n",
       "juNMz4UiAgAAAAAQIu3tbXSkujSy/NQONputrK2IWwQQElBEAAAAAABE8XBGZOGGafT3EX8IQRjQ\n",
       "4WA0r46lVpqBIgIAAACAvKH02P54BfBwRqSxuT4EQUCHpCNrHQygiAAAAAAgb3h21P9RQ1Nd3GIA\n",
       "AAIAiggAAIC8oKa+Km4RQEJoT7fHlznc94IOzIGKokiDDrsqIosXL6YBAwZQv379KJVK0UcfmX0b\n",
       "33nnnZRKpUz/XX311aEJDAAA4Pij8OBWenzYnXGLAYAn06yOHAcC8GlubYpbBGkOH43W9NFVEamv\n",
       "r6dvfvObNGTIEOrevTsplpUARVHoxhtvpNLSUv2/mTNnhiYwAAAAd6YtG0XHasrjFiMwGppq4xYB\n",
       "JIrcxN46LwEgKTz89s/p8NF9/hPqwIpsJ7cLfvjDH9IPf/hDIsrsflhRVZW6dOlCvXv3Dlw4AEA8\n",
       "NLc2kaIo1KVT17hFAR75Ys2n1KPbCXT9t2+JWxQAAse4w4DdBpBksIjijO8zIoqi0NKlS6lPnz50\n",
       "0UUX0V133UUVFcePv+dHh95O1XXH4hYDgEB5fsxAeuPTv8UtBvAJJmigoxJUnIzG5gb5m/J8B6a5\n",
       "pTFuEY4rZFtqR4sB44brjogbP/jBD+jWW2+l8847j/bu3UuPP/44fe9736O1a9dSly5dmPesWbPG\n",
       "b7aJobGlgZZ+uZD69Do7blGOa5Lepo7WldLO0jV09dd/FLcoQhytLqPq2spQynX/wYz9adLrTCNf\n",
       "5GRx4MABWkP5K7+RfUf3EFF+14eRjvIcYVLdcISI2GW1ccNG6tH1RCIi2u+jbYxc9jT96J9/R6f0\n",
       "7CN8z5GKCum8DpceJqLw611L/8gRftmNXPY0/fKqxyiVKghVFhY1jcfopO6nSN+3b98+WtOWn+/M\n",
       "zh07qOqwuPJXXV1NROa6O1xaGlmfsbe8yJT/BRdcEGp+vndEbrvtNvrRj35El112Gf3oRz+izz//\n",
       "nHbu3EkzZswIQj4AOgR7K7ZQYdmGuMUAAABgoaX1+NshiGPVvT3dRpPXvR1qHjWNSbRQybMdtIh3\n",
       "/HzviFjp27cv9evXjwoLC7nXXHHFFUFnGxsjlxFdfPFFdP6ZlxERUTrdHssqw/GKprEnvU0daNxC\n",
       "2w4lX06NkcuICgpSnuTdc3Ab7di3gW666nbm77WpQ7SmOPllkeS21drWQgWpAse+ZuQyojP79aNd\n",
       "VSvppu/eTr1OkF+FTBJd9rTRwh3JrA8ZktCuVmydS7NWjqcnfzNM/66q7igpikK9eiannZQdO0BT\n",
       "1tvLauQyom9+65v0lRNOJSKirkVpWuCxbYxcRnThRRfRhWf9k/D1p331q9J5HW7eTlsOhFfv1na1\n",
       "/ehSKqpg5zdyGVH//t+mzp06hyILj5bWZhqzQr4MRi4jOuuss+iKy53vO1BRRCPHPk2vD5zsR8xA\n",
       "sc4RRVhz8HM6WJkrp5HLiE4/vU90fcaOelq6K5e/tkMTFoHHEamoqKCDBw9S3759g046L7jvjVup\n",
       "pa1Z/7z38A7aUYKV8HwgnW6n2oawXrg8tPn0uCqyYP0Umr1qokO6HuUBOg++9TOasvQj9wuJaOXW\n",
       "ubRz/0bTd/VNtbRpz5dhiAbygN0HNlNl3RHTd8+Muof+Meb+mCSSR1XTcYsAEkZrW0vcIgAPCLnv\n",
       "3bBhA23YsIHS6TSVlJTQhg0baP/+/VRfX08PPfQQrVy5koqLi2nhwoU0YMAA6tOnD91yi7ynlnlr\n",
       "J9MrEx/19CA8lm2eTenQAx+ZZ1bpdK6DfHfqM/T25MEh55+fNDTXRRo0x40F66fRX9+/I24xOj55\n",
       "qJMlkdJjBzzfu2DdFBo2/bkApQH5TnNLI9U350+08iD9MMiuuTS3NAY6drW2tdLOfRvdL8xzwjYH\n",
       "S6pvjrDFGjT8t96cLiQEV0Vk9erV1L9/f+rfvz81NTXRoEGDqH///jRo0CAqKCigLVu20I9//GO6\n",
       "6KKL6M4776RLLrmEVqxYQT179pQWZkvRKio+vNPTg/CYMH8oVdYecb8QRE5ra7JWL2rqk2hbCgAb\n",
       "obkTZ2Q2LpbkC0mdZIC4iKZBtLQ20+KN5thoxpX31rZW30rJmh0L6a1Jg3ylETWb9qyMW4TjDH57\n",
       "r6w7QjUNlRHKEiyuZ0SuvfZax0Fr1qxZgQnTUYIS1TZUUbcu3eMWI/l0jOrusCgeK8jVZexxVu8b\n",
       "C1fQpedeEbk9NlFuBdJaJyrlnyICgJGoDlvv3L+RPln4Hl3zrf9g/t5qMMX2Sj66ax02/Xl67d7P\n",
       "KKVIWPiHvJqQ1ClkQsVKDIGfEfFFUluRJE999MfQ0n5v6jO0ZNPnoaUfJV4nukFRVXcU53eAEOt3\n",
       "L6M5qz/xdO/wGS/Q1r2rA5bIzBdrPqONhSu4v4/54nWqNuz45eOOiEZtQxVswSPmWE153CLYyb+5\n",
       "e8cjpm3KfWWF1NzaZPs+qbumCRUrMSRKEYl7YuoVp52coJ9oy97VtHbn4oBTjYe4d8A+WzQc53eA\n",
       "EDOWj6Hpy0fHLYYZw/szbdlImrFirOPl9Y256L75HOjwr+/fSZ8uGuZ+IQiE+qZaGvzhXZHm2dza\n",
       "REeqSx2vCXYXQW4syscdjCDR+g/5QH3B8NL4h+gLjwtDIHkkSxEJaWIaRqex+8BmWrB+auDpxk11\n",
       "3TFasXVuRLnFrHhGmH0+TPyq6o7GlvehI8XMFa6k4Lf2klb76Tz3OFRdh/NcUdHeHrazFzuTF39I\n",
       "fx/xB8dr8qFPNRK1tJEoSwHWwbGaCqk6bWtvCyzvDkGAdRH1InGyFJG4J6YSTFs+miYt/sD9wggr\n",
       "dNX2BXS0psxXGos2zqBxc98MSCJnUjHviFjbW34Na8FSUrqbnhj+m9jyf37MfTTry/Gx5Z8PHKgo\n",
       "ov3ZiLfCmAYn1fB1PrZ2g/wxvK37y/dEWm4L1k2lmSvG0fItcyLziMMag+Popuuba90vighWnQcx\n",
       "Vyk6tCMWr5G55/HelrX3Ly35Pji9P4M//B0VHtzqWaYOBaOc8rLLFiRZikhIPV5UCg7zJYuw9Yye\n",
       "M4TmrpkUWX6+6SBngkSI2wzNjaaW4CY6Xls87P6d+cfYB+jFcQ9wf3drY8auKIwdkeLSXbRow/TA\n",
       "000KL457kPaV7Y4sv5lfjqNZqybQ+Hlv0+YixHyxEqcyHYQifPhoifQ99w65mcorD/nOOzi8GWfx\n",
       "6q4lwbvifkjS6N/QVGfzAhc3iVJEkjIxPVZT7r5SwdI5jus1de/ENaB4VQ5eGvcQtba1St2T9BVo\n",
       "Vlkk420EPEQWWHitTlWDN7f5fOX4Dn92oz2PD/l3PBJiihJwR1l27AA9N/pe7u/VPt3MBzJP0c+I\n",
       "SO6IBLALk48kSfL1u5fRJwvfi1sME4lSRJJimhVodO2olauETHj/Me4BWrV9gdC1SelgRGtqX3kh\n",
       "NSTIdCAYommn63Yt9ex9KlYS8l75I/cM+ew1i4hiqw/Z7ryhuY7KfASe1HCKIr6jZAO1SwbtTcpY\n",
       "y0WgehPzRgYsSNHhHXT46D7/CbnIFcS4e6SqVG53VQ0u747Gu1OfpqPV/kzr85VkKSIJPKze3NrE\n",
       "fNHMaWbl7hCTlWA4UF5E24rXCl0bxW7BgnVTGasAyT4jcu+QmzuczezMFWOpvrGG82vw739lbQU1\n",
       "NtcHnm4i8FFcSd+h6yhMmDeUnhl1j7ebDXU05os3uJe9PXkwbS9e5y2PfCbIw7mBpZQHBFBuh7Jm\n",
       "Zc+PGUhrdy4Rz9rHKJt45dkBEcm37l1Duw9sCV2WJJJoRaQ93R7LYS4jD7/9c5q3drLQtVEN7UWH\n",
       "tlOaswKWlysNUSgi66fY7CL9dGtRdYqBrIwlCSdX15bfGprqqKa+yld2gz74Hb0z5SlfaQRDMG1c\n",
       "vt2xD3h7OSNSXLoLCoxk+Te3NIYkh5lw+/1kTgCjG+uYdtg5Ii6eKM8bNjTX2SxEahuq6R9jc2fV\n",
       "PJ0v9NCPiNV3MvsnUamcnzHKZ4PXLJ22djk7fNF0ZTnK8mcueDA9rAlrWJpzpM1PlfO8MX/dlA63\n",
       "Q5AUnMa2v7x3Ryzv4pufPUFPDP+17zz3Ht5BJaW7fKWRGAU/oEmIl+d5ZcIjjrEdwi4joxKUkNro\n",
       "eCRE5xBpS8e9TuwXgfJ7/ZPH6ckRvzd9l7acL5Oa4wRaaclrAANf/6/EB5xO4mJSohQR6yCbb1tx\n",
       "UU5WeI0pSWUm2uBVEludnbzkQ5q5cpw3WVhfJsQ5QpIwxZDJlk9dYzW1tDZz77G5lA2oo6uprwzM\n",
       "u1NDBzTPEjqszqiLktLdtHv/Zk95JmUQi0sxTKr3uzDrJanPHMZEtKWN38/5JuJ3h/eOyEhRVXfU\n",
       "1ZOVTPvw4zhYbG4Tb1tV1TTtL98Tqwz5SKIUkaR2dyxYL1ISxujErNwKoNr+cMepM0qrafpy23xf\n",
       "MoWF11qJTrHM5MOdoHLEUFXV0aUsCBY/rUHrn96Z+pTueWfk7FfppfEPS6UjezC6I+G1/L0E65T1\n",
       "R9ShEBhMg1a+9hzcRg+9dZv8jdoB7CRMACQQmSuw2rufMclPGdnlZckRfx2ENWZH1b5aWpuptsGf\n",
       "SbQsyVJElHDEyafJedIZNv05mr9O7MyMKE4eYWSoqj1CY754Xfj6JO0exY3XVU/t3Qqlk0xQ9SSy\n",
       "DwlgpXrXvk3SsTHuf+PWcFeOE423Mk9W7IeOQpDvpEI1DZXsXASzCayPcMlQtAVyxzeZvjrw3TBd\n",
       "awssxf3leyI7i+UV7yf7omHX/k1UnDVfHvPF6/TZ4uGR5p8sRSRuAWSwvEjpdDu1tCUhGE+4TXjT\n",
       "ni9p9Y5FgaSlSp4RIcqPNnLvkJupvb0tbjG8oRDTy5Sb0iY8COdDBYZA0aHtXMcbaTVN20vWiyXk\n",
       "MDFoa2/TBxMN1eGTH2J3/5tnsYfCJs8W432hjRvBL37w6tY5H1bft6+skA5W7A1AJu/IKEa1DVWR\n",
       "rLiLZtHY3MB1yGPlxXEP0qxVE31I5Y2a+ioqKbUv4rC6CNGSHTf3TX9CUcakWXYH9s3PnqB3pz5N\n",
       "RETVdf7i1HghUYpIWDb7/le+c83oWE0502591pcT6bF3/8dnPuGRTrcn2KQiplHUV7NwvjmMyNWR\n",
       "oBLNXvWxxPVyK1wy72LQO1YvjnuQZq4QO2NUXnmQmtuCW2U7UsU/5F18eCcNnfykUDpOZVJRdYhe\n",
       "mfCIrzTceGvSIM/3Ht946OMSol3EoXqJ+UcKunzM6TU01dFL4x4SuM3eB740/iF69ePHzNclTYk1\n",
       "yPvX9++k1TsWCt7oy0A0+3/nunv0ndsF4k3l0gjKmYoM4+e9RS9PYJm1xlPPWpk+PuxXNGaOuGVI\n",
       "EkiUImJdbQrV7MMjgz+8i9buXGx7kcqr2FvvXprk5qJVVFlbYfteNpq3kbcmDaZXJ/7Z8/1G3CYy\n",
       "muzuA0W89ct7jpLSXTR9+RhfaSfSlEcQzVROJnJ3EE8bpqmcQgrtL99DW4vXCF3/9Mi7adnuabbv\n",
       "w2irUqaJ0nv8Bk9THqMhG2H1S0lg6rJRNu8+UbBr/2Z6zTrh7KAkZRzOzQvCzaei6hDtKy90lMH8\n",
       "nQuCAq/YNtflCn/9JO/9ZwVyFumT5Q6ri1fasYT2NRq8xUbZcexvw35Nny3+IAiRdHhmhkTudRDH\n",
       "3CVRikiKc0bEqWBKSnfTsZpoG2xjs9lvtqIEqwO/P+1ZmrFirO37B9/6qec0iw5vl7YF98qgD34n\n",
       "dX1QZ0Rk0TpQ607Roo0zaM5qiV2BEJm44J1I7F957TdnTuTSwk2uVfnvq5Rpi48VxAMVRcwgcDI7\n",
       "VW3tLbkP2UfaXLTKs0ws0ul22peHXlbiXtu1trHCA1siiUpsbb+FB7dQ0aHt3Ot1RT20uAkZWtua\n",
       "xc37pOWQlyfpzFgxxhRfiNUvOZ5ZZbmSttaxR02p+PBOT/cREe2t2Mo0F2IhIp3Yey7jvjf7j0Dm\n",
       "MhP6WJRkXp6S41Z1/TGhOg/9CRnP09zSKLYr6JNEKSK2Bi1g9vHyhIfpgxkvOKZq7ECDsd1XhTrl\n",
       "5tYmqm20rzIAM3EPbwvX21e+fRPgQx1KclDD7Lu5fMucyLMurzxEz42+l/nbxsIV9OW2ebbvVZ9n\n",
       "G9xsb1vbWrkysdhctIomSayGGQdnr8pAaDtPAU8GmlsaTeVtSj22TiO4spu75jOpXe76xhrub2t2\n",
       "LBI273MiOQ482BW8v3yPwYbdeyNYu3MJbStea/nWEj4gO6FkTnINk82k7BQRES3ZNYk+Wfhe5gNH\n",
       "Lr64gua1PpqI27wpqWewZPD0BAl97Kq6o9xdwSBJlCJirYsgzT6IiAoPbqX73/xJQKm58/GCdyPL\n",
       "SyNBfaJrxeX0TBnTlODf2LoQlEVbh+vHbWEklWoYWBm/PvrO7Y53l0S022akuHQnN/J854IuzO/D\n",
       "PrvT0FzLlYmFrG2z7ETR2A6DMM3KpRs+L457UNicVHumppZG32aVYVJZe0T/e+qykVRWuV/43sfe\n",
       "+1/ub2HWx1+0fBMwuLw47kH6aNbLROTeLza3NHIDcAq5rpUca6xpxraDFMAYWVlbEcph+1yd8ctm\n",
       "7+EdRMR4DMfijL9t+iGOBYCpy0bRM6PusX1/3JtmaVuh24rXmX9w6wBdXjytko2DgD8Ue7tnyFDf\n",
       "WBtQftERx4rEF2s+Cz8Tx6j3Ibx4Ftv8qrqjfhLzL48Lft33hoGflti5U1dzWtnn86qIiD6ndUCx\n",
       "mnH6xpB8kO9qa1uL+0UGolCOy6sO0aEjxVL37D28I1SzSrnJkbnd1DfW0KAPfpv5Plt+3bv2DFK8\n",
       "UAmyxkuP7ed6kTPnac9V9B3+ZNEw+vuIP/ASdkVxmh6Z2j/nzIrrtMXb++t2X6tD8Fkj1nfY+Pnd\n",
       "qc/QC2PvF1JqZNU1N3KLD/LlE+XuFDcnD/UahCJifHRjeqt3LGQeX9i1fxOVHTtguCm+bZlEKSJa\n",
       "2c1fO4mIxFfwoi8+scZeUFAQshwxEViBZ8px4fqpElkHWNucF0/sgB77+1ybzbG9ZB1tKFwuK52O\n",
       "kw160KgbggnaAAAgAElEQVSk5p5eoGOS7fcdy9ZnR1hdd0w3vezUqTPzGt5ANXDILbR44wxf+Wcw\n",
       "P8O7U5/iXMe+XgSplUqGPROrDjTXjVZaWpvpaI397IVK4Z/rsp8Z5J9DimpFUSGF5qz6mHbt3yR9\n",
       "b5vBLLgt3ZpNz2mya//q3SnsetJYv3s5NTbX05KNM4VkknLzGeAkL4rzPI3NddzfRILjpVL+pkeu\n",
       "h4IDKs+j1WXU0JR71kNHS1zuYOfbYlBgnK0U/AQ01CQQ2JFyzcdoHmf/9d4hN1PpMfEdx6BIjnlj\n",
       "hlGzX6O5az51va6+sSajmMSwuZQoRYQ38Li+rzFociIDYUGqU1TiJJK4tqb9ngPyI3fOo0uuI7fG\n",
       "5Whsrqfh058XTnPqspGe5YmFbPEdOlJMGwtXmn+TeFelvY8M/zXNXzeFiIgKUuxFgLTKdmGtkkr7\n",
       "y8yHxln5uw6NlguqAtuF1fJXaJN+YD64fo83YH+2eDg9+SHDG1UEr3ZBQRL7T4WmrxhDc7Iurnl9\n",
       "xfDpz9PBiuLAc+d5fdPk+HDmP2hj4Ur6WDsn4MLDb/9cOO8o+3Ntks7sA1TzNR4zcL1EdMcil1Q8\n",
       "492TI35PI2e9YvpOVeVra9aqCbbv2H2wOeW0mjYpQs5ISOVa/vaFCWudRaHwWvE0HbUej2aVU1AL\n",
       "AQ7pfLpomLscIZAoRYRPpjAOHSmhYzXl+rdbilYTUYDB1jzDzj+OgTSMZ21uaWRu427a86WvdD3J\n",
       "aijqgxXFFrkyP97/5k+EgvKEqb7yni2tpunw0X20cc9K5u/x4bU0+HU4fv5QGj5DXOFyo7L2iKs5\n",
       "R30T/0Avkf/D6u5YytFhVKptqNbt3WXw6mXOS8/AOyDNdl8abN/juJDDPYgrLsP2kvXSk1m9OvU/\n",
       "2Pdv3LOStu5drX8+UFGk/93a3mKQP/jJRVjrclEeEWnKegoMqk2pqkpb9+aUOJFUNVNx92vZlhtR\n",
       "HsxuaDEvdjnlnfuNf40+pxIQccH6qfTnd3/pfqExb07WnuNfOAS5NM4ZoyG6hfGa+ir7Yp9PcEZE\n",
       "b/xZbxWWF/z5MQPprc8G6de/N+0Z7UbB9OVwdNUp0CsbB9I9B7cKBOhJHu9OfZoeHvoLWrV9vv6d\n",
       "QgrVN9XSsOnPxSgZ0Qtj76PyWvZK7qYicSUpNycI4AVUnTvaWSsnJMrLCgtNOpH3hdlp+Tx68/on\n",
       "f6Waersf9IYm9pkro//73ODOlt7Rvtw6MfAwnrhNLvYbXPXynsclA8/tx+k+aXMCQ1p/fueXtGv/\n",
       "Zv3zhHlDqd7Ls1ng7Wq5CCZ85dDJT9JhFzOW+sYaKTOsgxV79Qmvsa2Nn/e2/q5sO7hSSEqpCYGp\n",
       "3XmfCEVm4ubynrCefcrSEZbfXE0l9L8am+vN5ociOyLS74Tz51AneLa8VX816VA/1qKrljn/6FIE\n",
       "Ri+jQbTEdbuW0uAP7wogJXG8KJhe37u5az4VWuwzFbtT3ca0q5csRcRaQIb+pqLqMBGxJxJulei1\n",
       "kt+f9qyegiuMS4zuQ2ev/oSmLx/tmARrorB44wx687MnbN+/PXmwXiayTFk6Qt9NckMbVMd88Qbt\n",
       "3LfR8dp7h9xsjskRwoTbWpdpTrR4nsey/eW5lUm3VU03SVjkdBpjO81dWyrhJSdKvCzONbc00kNv\n",
       "3Wb/wWO1ayIUHtyambBzApxaOXSkmCbMf8eSChvPSqBw5HhnXhz3oLf8DenLPIPfgUW7u86yM2JM\n",
       "taG5jopLc37wl22ZHci5JqcdkaB6FreinLFirKX/tbRJy/1j5r6hT3hnrhxnukCrt8wYlpzFiCWb\n",
       "Phe8MkiZxTocY38/b+3kwKSxmVYzxBE2zeJIEqkpmyWvnfs30dpdS3gXM++Ryc1ISmLBwLq47IhU\n",
       "oEQ2DdlzQqzzfy+Ne8jRJbZ7ngHWr8h5TOain4eBO4ELoQlTRPgBDZ/66I/8+0JfxbGbJfmpyqaW\n",
       "Rn3rWWPD7uU08PVbbNeu372cuyJXdGibp/znrZ1MC1wOiO85uNW0lZ2RZZn+N6/E29MS5zMifB+0\n",
       "GnPcps2+1Kz29OmiYbSjZINEfk4/eHvwokPbbe0mOBTGX85YZdlYuIKeGZlzB8h6S4J8U7WJwtGa\n",
       "Mlq2eVY2fY4DAq3DDsFuRVXVnFcSS/pOfZOXXqS5tYla28S84hARzV410ZTjhHlD2e6qOeWiKdR/\n",
       "sbiOtSlDls+8BQIZFInDwrmzWdF0Klq9Lto43fR9187dHe6yr+SLmdCIy2PkyQ9/r9fDoSMlVF55\n",
       "MHe9ob5F3czHsVoaVp4iqebOrLLMEFlpepdVLoihex9mrGsriwSccuT2ld3z0sqpouowvTLhUcdr\n",
       "Zd5PuYCGaaZXVG0O88nC922/7SsvpLLKQ/rn1rYWGj/vbeE8eXiZjybqeHsMikrCFJHsv2Q2zXJ3\n",
       "3xuiUIK4Nj7DM7w07kF6abw5WmWZQ8cRB8OmP2/zpGN6RiENPnxkt0GN1+vtzKF93TvkZqptqKJF\n",
       "G6bTkk0CnmgcbFUz3+d2SlrbWmxR3Z147ePHaG4Ero41yV2VHkPRq6pKO/ZtpLLKA/zriSQPq/Np\n",
       "aKpzDTTmH8Zh9Wz689ZO0s2PMtv/v6MRn7+sr7CFOSHWFhGcntTqIEFj2ZbZAUlhtYcn046pTLv2\n",
       "lnsuf3/KuVg9FR7cSkRGhTbzT7Ml766du/Fz0ocz94C4u/ZvlnK6YUzPqKC3Z89EPT9mIL00/mHh\n",
       "9DiZ0MNDf0HTl4+hD2e+SNX19nN4dY01Qm553bCOpyM+f8kuTsCH1bUcnx55N+09vINasi6tWfmY\n",
       "FF+eaa+EfCsZwVelcMirpr7K9AyaV1IWuw9sybQ7h4Uba9vVFJH1u5aadka9yqthN5Dh37Nm52Ld\n",
       "NbYMxvH4aE0ZLd8yh/YcdF/gbWiqox0l69k/doCgjBpR6SSJUkTarB0vwxUqa/RlKQHbitfqZlxB\n",
       "r6ooiuKrhsqrDtlWLNya7mei0ZcDajnu1reclWeZVQwv9WJ7yeW2+E2KiPVWTtnVNlSJSmdMzPXb\n",
       "R9/5b5qomxSJEXZAPiNuu1uOrkeJAu/FtOT2lRWaDkcaB1nnEyLeqbe4Ap2y9CPakj1Dpm3/r9u1\n",
       "hIpLd2VlSgciyMbCFTRq9mvS94354g2p63li8mrQrWplAzX64ZGhv6DyYy4KsEe0x8yZcDhXaCdH\n",
       "ByUGsxSXYw5vfvY3x3zem/oMTV7yoSHp8GcMaTVNzS2NtK9sN63fvYxpfsdTgK3prNw2l4iIG3BQ\n",
       "48ttmbOJ63YtzX0ZwEF/p7GnvPIgvTrxz7Row7SMvAyl2jgJdXJMMkzAO2IQh6mtEhjPzT0+7E6T\n",
       "+3j9eRhiv/Hp47ShcLnzOG65T7NkmfnleBmRA6VFxg21CXshDPnkL653ad4ZWXjq8m1aV8Dvs5Q5\n",
       "b/QkShFZtX0BERE1tTZSbUO1YaFBvmjemfIUlZR6i/bsepDOIo+iKMIr81ZzJ0MijvfJxNpwwrqK\n",
       "de+Qm00HTR0xmi7Z3hsJ28/Q8G7m8PL4h10HRVYKlbUVpvbgbiKS+76tvVUqCnc2YbnrKRMwkhXQ\n",
       "yIjefmW2zl3OdrNSchrgjO+QqqqmDPYc3EoVVZltdM1VJOud45l3+sW68m2CuWKalcfJNEugqFdu\n",
       "m0erdyxk/8jpM5pbm3TlSIYtRattii7fQ5dKC9dP43q5CWNHxGkcaGxpcL1GhE8XDeMEH9UWMnLf\n",
       "sJ/R3RSPtSMyddkoGjr578Jybtm72jw5D2kV9s1PcwrRI0N/YfnVW561DVW0YXdmYjzkY+dJ3zyH\n",
       "1XsZbP2/rZnYn0WrX9HFH1bL27RnJY2eM8TRVLGpJYCgp5Z2bw3qaTzj5fY87el2vTispcIyf2rM\n",
       "euziPeOw6c/T8i1zsmIyFpe5iJu5eiWMhT3juOR2LjhIFm+cQY8P+1WgaT43+v8CTY9HohQRjZLS\n",
       "XfTX9+8wfONmmuV+WL2xuYEqfUW3JlOQKLeJbU29eRVdu37F1i+4MhrZXryORs561TEPVc3YZc5Y\n",
       "MdaQjzOrti+0fXegwhg/QW5Cqncs2gttus05DZFJQ2WteQJtLSd/XVPu7pKy3bRlr9gBfiODPvid\n",
       "aULgFrApDo9Z05aNpC8NXs+c4B5wJPuBP9FJf7nBDlcUY/ntL99DQz75q26eYVVAjMo9vyuI1m5X\n",
       "ex/8Dp722EruLN8yh60cOTQ9hRR6b9oztK+s0HIT+3qVVFq2eTa3XQVyRsTpR57po8+FkEUbpgs7\n",
       "8ihlLCI4y8z/ad2uJbS9ZJ1QvnKo1JI9U+SlbHYd4C9SubXstyYNEljckZeJZwllxUk+mXzTDi6/\n",
       "VVINYyA7zVXbF+iKMgvZeGOsPs496HPuJqfnYV2v56GqNOiD39ryas2asPHYtGclrdbnHTILXWLO\n",
       "SvwQ9njs5Cm1tqGanv7oT0TEKG/BhQXjVcs2z2J6mxS518TxfkbECmuVnfWC8FaVjQ159JzXaJol\n",
       "MFxV3VH93sKDW121Y9EgUUSZ7VAT2UfowrMhtjS82sZqWrNzkWs+q7bPtxxIzTFh/js0du6b5mx0\n",
       "cZwbG2tFldVwc14wxGhPt+ury26edY5Wl9GgD34nmLL9mVi248wOVjB93ovLNEfgTuDi2foMAuuB\n",
       "P94uoFYPNdndN9MEy8O83M3TlFmBdFuUiAanvjy3K+neEpwUEXnzSH5+lXWZlU7hGCW2pMxfhG2a\n",
       "papqIKuZXuOhZFyYM3adHCYQL2bPBaqGXiCoQ/ZG7z/W9/KJ4fK2806ITgh37ttIe7Jna3gUKGyP\n",
       "S2J52K9ZvoW90Ge/VSB96yKbqxze6jCKeGOKoujvZHs2qCt/sYz9vKxgvbL4sXJpbWsRuE8uXVVV\n",
       "qb29jZ4Y/htJaZzyybhYd5J17c7FNGXpCCrP7vKHPS5pddfW3kqLNwqcdY2YWBQR8Uaomv7hwbMP\n",
       "NFZufaPdr/27U56i50bfS0SZ2AW79on7i/dKp4LOzO+9NsSUpSM3prN8yxxauXWux5Tt7DPEQNCr\n",
       "RlXp4bd/rm8vmzs381MVl+6i+9+4lR7ObvG7BXNrbbevtNjKyTjoWtrJJwzF0XxGRK75m56MO+HI\n",
       "XMWbJNk6cR89UFt7q+8o8n7EME54WYNaA0NBk9kh8OZ9hH3IUrc8I6KW1mbBA7Ws/MVkUkk7I2K/\n",
       "/m/Dfp25RujApnwXzWubr338mOu9tsClvMmK5XtWwFOvrNq+wHWw3HNoGz0/eqDnPDTqG2upsdm8\n",
       "Wm2S3XIeQf+oKEzvZU4munrcGFU1zYP3lRXadn6dYLVdY3waXr5Bm7aImCO77lpIeEYTSXTmyrHc\n",
       "30xJWOVweJb563PnARaunyYsiyifLRqu/+22u8BDRHF74M2fUnu63TWoa8YqNlMvpjbjsvMjJJ/l\n",
       "XqfFSGt7nbFiDC3bLOZsY6KoJzg1s2PINsf0hqIQ/f2jP9CE+UO510yY/45+FEG/KQIOHSlxdygT\n",
       "A7EoImk1TdOXj3GNSyGcnosZgEpsLyXWw/Fet/4Ucu/ktbQ7yW7DuqSp+fDWOjCzZZT9efxEcz14\n",
       "ZK8pby2P5tamnA2qKU9z/sZI7CITQZFJmNNk2GR7y6haLyXB2oZnlyl/S8TPJM34jC+Pf5jenDRI\n",
       "8Mbo92Hasm1SUVKUVtMCnb3gdrRTGxZIorGFfaCWd6unyLWq9aN7+bPaRcrDRM3PO55W07Rk0+f6\n",
       "hIvv/c3Z85PI87a1tzL77k8Wvs9cRLBSemy/bedFk3fWlxNc7yfKmA+9M8V6NkM1/CU2+dIOHItM\n",
       "9tOUiyOiqqr8ObEs/LycFwiCQ0ARYeVv+Iq74yfQXzG9WYmaFIu8j9lrygyOED5bPNx+nWq+Xhbj\n",
       "ju7I2c7m2Bns5V5Ze4RGLnuaca0F43vrYN6o52A8t6cn4fycTrE5jMEo29vbhBZHjGjnBPlk5F0u\n",
       "qLCopOptMLghUqGj1WW0xyG8gmtbCWm8Flo8iMFmIxZFpLm1keas/tjR8wBRri6aW53dM/K36MPr\n",
       "kG0vo+Dgz9uG5Zu5OKO9RKt32M24HJ/ZJL+Y7ClDc9EcAaRVc6cWZCkzB1pLOW05kDn0uPfwDlq3\n",
       "03y+waj4WKmoOqwrb1ZHAPa6ED83k5u4sNNj1cn2kvW0necK0IGDR4pdTR9E8VJvpmdRyVY3af2c\n",
       "BNGqbQvoieG/EV6VzRxWl5dJU17HWUwS/WD0OGOE1RysZ6a0RxB5blbbOCaxUq7hx3Odqqbpk4Xv\n",
       "Mydc1jud2F++hx4Zejv395krx9GDb91Gk5eMEJSUzeufPM5NX5QqywFc54mWyryOF72ZafrFcHYS\n",
       "GqZXNKDeOZuMkNgufSZPERFVJ0Tzs8XiCmOiF0CSxiDFs1d9TP8Y+4DQfX4C89nglY3qvNuvYQ08\n",
       "yUvatT0yGpi7Oabcro2qqjQj21fs2u9vYVzzVCYSFsBaxlHHwksasSgiT374eyLKDNKNzfW6eZSd\n",
       "TOEZ7T55FfbJwvfp4wXmVTStg1dIib8esg2P797RW0PUdkRyh8XZD6oYpkROOLrBy956+Og+fRVR\n",
       "M0FhrRz6tXs2rgZrbhytHKjMKETj5r5F01eMcU1TaxNPffRH7kHbwgNbuPe7r2Ro/3A6TEYHNHTy\n",
       "kzR08pPO6VozIL6ZX1zwgwmmqL4pwIHSoQ27vUUib5l2wPZQ1R6aufFDyUHCopDLRAdmvC9ygc60\n",
       "LL136+l02mQ+yLcjdx48D1UUO3oDmvXlBFLVNB06WuIqkzWqu5F9ZVbPiP47ej/9lkjZq2qaW65S\n",
       "517CUGAEktyZnbAZXdOu373c5GFLw/UQtaGPr2+qpS+0OEkOdWBMU1VVk2ldmpPfog3T9eszaTBk\n",
       "8VCe/pbfWKfOc2ltK15LByqKPKbNRngnyCF+iNsZEebYp5r/EDuHZcd60J7lxUs0faLMs2gLkZ8u\n",
       "Gmb6rezYAa73P1YfoTtYypad1QRu6941tH43e1HLyNHqMuE8Rdts7lbsiOhoh3u3layjZZtnC2xN\n",
       "uxfM4o0zxALOZdl7eIfNVm7o5CdpheBhN2tliXZhCudwHq89lbn4x9cm626R0jV5jbbyVtraW2nh\n",
       "hmmMXzQZM3mZzm7YdnmDa8RGs4sxX7DdhOq5Ck8e3GuKtwqtkkrNLU36J2eB2F+n1bTpuRRSpL2m\n",
       "aHTp1JX5/b6yQtvkza1zMZafsMcj07YP53uydJZONvQmBwmqg2LDF4nfMYtPMv4+4g/630fqDppu\n",
       "ddvd0n+zeM2yXpsJhmjfjZCC80iKoghPUq1lbJsIO7ihdnr+zp3ZbdMt/8x3Zoz14YZR3CdH/F7s\n",
       "JkfvPOappvaeKKQwn19ok4BUbv/Ade8ugelVNGQU5qrrxsIVTA9bWnk9MvR22l9un1Qbd0S2FK3W\n",
       "Hco4ta2WVs0LWOYc5KPv5HbeTOOAoV7b2lrN6doWhOyIjinPj7nPJrPXsjamsffwDk9pMNPNPosx\n",
       "WJ+Wk9VLnKrm+l5Wt+5WLsydYuZCpXN6rL7c2j9NWz7K9PloADFZNJ4ZdY/udtgLVllHfP4SfTjz\n",
       "H0Rkf/2NizbC/VYYxLRgH7vXrKkWT1ZGWGYuR6pLbd6Qzj/jUub9TpOGJRs/Z96zrXito7x+SUmu\n",
       "utQ1VvN/VFUqyO6IWAMkunGkutQWqM9tNY7dWWv3iK90iPLsKLsPa4WU7IEr8/OKTuK8rHoZfbIb\n",
       "Bz0Wqks57Ni3wbb7IVNm89ZO1utJq3srL41/iD4WPKxnlELD6qZX8nYbmTJ3L3dxxwpOafmYbHHa\n",
       "hukckkcbdOvEpKnZvlsQlCvJiqpDnr1WGSfaRE47IhYlyvK7piQfqChyNNVQFIWKDu2ge4fcrAeD\n",
       "tOIYZ8HhfdZWFlvbWmjTHvFzPqx60Nyuu0aOFjrArZKxxIx9ktfDyg6Zebrt0JHiQMVoamnQD9Qb\n",
       "25SmiExa/AGZWpGD2NoCoqqqthVxVU3TzJXjTCZORIbFM4YnTh7c+D0W9PbJUYIM0rmmJbIj5m3n\n",
       "JpP3CkYf++HnLzIy0TMzpULkLqPzWKwa/snVxYjPWY5rMnkbxyPrIpnV65qmpIri9iwsC5EpS0eY\n",
       "3tOGpjrTnFQrMZmFJd7Ozp/f+SWt3DpPOB0ZSmy7yVliUEZiV0QcYayyq6TSpxY3ovxDQYbB1NIh\n",
       "G81+1u7kx05wl03ucmMnsttkAuRtAiVvhpHJp7ruqCmAlojXCFZeaetA5zCWeJ0iWjuL58cMpGdG\n",
       "3m3O1uFQrV+2ZFcpeauViqLQ2LlvUmtbq76DJZOvbMwFkUlmEHEc3PBSsqJtQKz43FfTg8D4zrLK\n",
       "niWqW/0rimJ7RlklnrfqOn/dFGGTrpoGs995fSfHaeuUMrKyPOpoaP3rP8Y+QFOWjuALoCi6bfYr\n",
       "Ex4x/yRQm/Zr7AKv372Mhk1/npZs+py+3JYZ1Geu4J8hYdWdFkl7SvZMC3/fzfILa3VYzRkQhXFe\n",
       "xMmt9qIN02nc3Le497a2tdCxmnJ6fsx9ugm1H7aXrKf3pz2byZ8xMVNSGUcWC9ZPtTmP8UJjcz3N\n",
       "+nKCIW5FBs3qIjelCGi2JZqO8HXeRRHJ32R2mf2uW+fulks5Y6moaZaTWZ1pfpDbndrpcD7DWJfW\n",
       "uUDKshgn24e67+6o1NTSaHKuM2/tZJMVz6APf0dvTxqsf9beP5kzIrwybWiuo6LDzmEORBB2ub1/\n",
       "Y+DmgCIkWxHJYq1Q0UikPM+u24rXmlynGd3IbhRYOWtqabC4lpUxhcgVeeGBLVRdd4xaWps9beWq\n",
       "5C3gmYa2I3KwYq+QH22n4/RhRlY3Tao5xZTmnMkIJHIq0zuL+fPKrXNp4oJ36KVsrICiQ9tp9Jwh\n",
       "/vNmwGorFVWHSVVVfSXTJrGbJZnPalu/e5lD2uzEc/E02PDeiTc+1Q4oM0xjQoqsrmEyEXRqF9of\n",
       "3NdasZmGxhHs0oruYEDzJOOwI+L0rjt5RDR5nCPFPgGVmYxb5/2MMtTS/3jBu/o5wlmrnLxq8Z+L\n",
       "dwaBJw8/fWM6CudvrxgtAcws2TiTG1RXQzt4f7SGbavOhl0um/aspM1Fq7h3KaRQe3umf29P59qB\n",
       "eBwRznWcYly+eTaVHtvPVQSd2FbsHHCyqbVRX9Bzq8X95XuYHqD8xOgQgVmuVtNENW0wzbJPotzK\n",
       "zGqtYM7XME8wbY6w+nJ7ftbysSoisrBccFthOQIwzv+aWxotO6UZwY1zj/3lexz7NWu/Yj0HRZR5\n",
       "d4fPeMFV3owI9rwam+vp8y/Hi90fMYlWRGSD5VlhvkyUcfvohxkrxuruGkXJndEw28v/bfivM/6m\n",
       "PY4/1okXrwNnlYU2EdS2oF8YfZ9UXkQGBcTiPStIjC80b1eC5xvderjNm8Ln9kyZNI2mbmO+eN3s\n",
       "Jzxknvroj7SxcAVni1sE+XozDhDGSYQoI2c5uap0l2fU7NfsX/LMq1iHLwXbqpc2Y9spZMijRYq3\n",
       "yjNjxRjauneNKTYEK85EGN6WdNMskVU9AzKTVrMtvXky8I+xD0gdEE23u+/8mXaxhE2ntL85vwmY\n",
       "8fFIq/xoSzKmu9xdGaNJcgKUWw2mu11S9b7DqJCKubvOpTl+3ttCMny88D2as/oTmwmtSCmxrAaM\n",
       "co6ePSS3oOdSjy+Oe5DmrZ1kTy/s+mLpIZaWNHv1x8zzKdqzuvVtpgC2nDRMf6u84H/ZCb1hkdHa\n",
       "N/hZiCUi+mjWK+4XMapyX1kh//Ls9cZ5S8b0MIdbHCbzbzmHQBsLV7hJy2X3gS20xWFRIE7CD+np\n",
       "A/+TW75pVtC4DkDZ/I0mYdodR2vKqF/vr3nMVwy94TvcUFF9mP8j8SZz5om+av5RUDpn3AIwZbJi\n",
       "55VW24ko513K0+RN8DFEd+pMCIrDnJxZnmXF1rl6OTh5P2tsrqeunbv5Xk1yEUcnraZzvxkuct2t\n",
       "8lBXwgvSlNn27pTqRF27dHe+3lUOpnFWVh7xZ9Dqbvaqj22/fS4YF8Mv2u6j23uSVtPUarDHllK6\n",
       "Lbb0RiX2QEVRrsw8+Lxn1YTZOYSLPJSph+bWJurauZstfaf3qqmlUTDIn3E8skqsBDoZ1YMokvcD\n",
       "1EHBi8nSrkX8Nu6MCRTB8i2zqXP2LJL1vCMR6ZM2ZswqD3MLt7qtMchgLWtjLtV1/J1g3s6+SQ7X\n",
       "K+zkWltOkh371tOVF19ru7am3mCuyTit7mnXxlrchneAF+ctl619d0DDFmcp5Hme1j927tTFwURa\n",
       "bhEnc63cgmlaTWeVMMHWYDmXljQSo4hMXep+aF1H1Awqe1ljc0MoJkNeMDYwrWPzapqVaVjRDS7M\n",
       "HRHLX2Gs6LSr7quePJMJrePwU//u92Z+d4oSK4s1iB4rCr21zWwvWacrFy3ZVeacbXTuGR5957/p\n",
       "P777C/rBd27Tv/NWbxyzHdsXKjNehFPL9dqOeJMF47eaAjRo+G+pX++vudablzds4oJ36Tc3Peow\n",
       "eWGtDvMH+LoGB6cVIeB2WH3BuilUWcc+YOmGeTdAIVsJK4qPCYX9PuuOSKFL7J3W9hZ6+O2f05B7\n",
       "7SvWppwsMr468VE6q/f5AhJaJh2GNtLUUu9qOqVxrLbC1bmK0QMPzy1rEIi8r7xza9oii7GeXJ0C\n",
       "ENG6XUsFpbNjlVZEftHFRiL7DrEx/YkL3nFIIqx5SiZdzWMpUWZHmaWIGDEHDM7+60FGq2kWUW5n\n",
       "JTNHtqe5ZudiKinb7Zif1WFL0KVnTU/btXOSSSszx4U2ewO0/Jz7bF3kKSndTS9PeJjOP/My6typ\n",
       "Cz+PPCIxigjbxpy3auSMtZGMmv2qVIX5cdnGQ2vA5sl8psG2trV4N7Nwuc/aeToF+XPPir8jwupo\n",
       "ZFBVlV8GAknyVmmsnYEfjyM8ocIYPIyeuoiINgj4HyfK7R5pzz2FEzDO7qVD7Bna0+3U1tbiuItg\n",
       "rYsCQ7wTsyIehmWoSP1md43amh1XJ3NJyrcZ6xa6yFa84/Y8s37CW4TIHVZny2T1XOg9I/s7qZBF\n",
       "WeX+fe0AACAASURBVPHZTowTYIUUGuVoEpiLyu60AMGalJZXHqKze3/d9B0rjX1Hd1BlfVn2dzNj\n",
       "vniDrv3n/3SUz8g7U54SvjaTYXwLcp8uGkb/3z//yPylmhsbvZh38nBtn/pqvBEPY4MhAecFK8ME\n",
       "3GGHX2T33wta32IN7FjfWCP82NVZ0zQ/5y7NcVwy/5+85ENqZFgTVNcdpeq6o9T31LONKZiuSVm8\n",
       "ZpW6hoLI4OYRzbiLpr3rf3nvDt2LqWMZcMrT2Ge0Wdq669kzA1rspD0HtwZu1RAXiTkjwp7kmv8V\n",
       "xer2t6ruqNSKuFURccv/WG2F6yqWvsJjeE7N5tTrav32kvXuEaQt5eonEjdr+1tVzWXt1DE7xYtx\n",
       "erFFyse0nWxM17YKF55pll927tuoR6x3QiWVdu3fZPN4pP1G5D6geVV8Jy0eTg8P/UUmD0u5aJ+t\n",
       "nez4eTkvPcaVTscdEZffeSiK4jgJUSymL506uQeF9BOpnJcGS+n4dNEwvkejiOeP2uSf915279rT\n",
       "e+KWw+qMzC2Xi098XL2VEVFDS73jNYbE+J0/Q2zWjsN+ji15bVPm3X15/MM2mWXGg7jNrWQ5VlNh\n",
       "OvtERLYzIgcrin3ns9AhrpYpBky27D9Z+B73ev0+RlEbz245mxfl/t5azI8VIzMhDQRFEW5Dr33y\n",
       "FyIKZuFte8k6vbzc4r+lGZ6+NKwT8aWbZwnlzzxfyGDdriX6DqoxlIJTn6QpmrxS3Vy0yn6/jBmX\n",
       "1/uSYRTEJDGKCPvQkb8dEW0LvLmlMdSBfP1u8S1iY+Ncpr00HluIzMGlsAYskZ0QVVWp8OBW2rJ3\n",
       "Nfcap1UiP2+QfUckt+IpCqvT2bFvgymir1eM9fLWpEH0/vRnBQRyP5ypl5g+eqq0YP1UPfCl3cmB\n",
       "GEaPKB9bTAy0ttAsuFrutNLd2tZM5QyvMq5pkuJormK1R+5k2a2pqbcr29YJiLZa9uX2+VRrNZmy\n",
       "tFXee8ea4K/ZsYi7oMGa5NQ31gTjFY6B1h/zlLpuXbp5Ttt0WJ0xu/PTVxlNT3L5GRMXP4PhfpVd\n",
       "E7dKzlrpNdLU0mBzniJlg88qPx8H6WWRjdswfMbzNGz6c/pnlVT9eTUHMC+MdXaaEgiWqrMqR6I8\n",
       "PfJPuSQd2tWkJR9wfzOJFbLXLCsNTXWu3gs1tNhH3s6IWK1UXqOmZrFxwtEMKmQ9/GDFXubikJNM\n",
       "ujUDR7gqRsyQZoezZ1ZElGYrCdZBiChBikiQLUp7UY5UlWY+WyYfsmRMloOpSp6RTxgecKJAUyBy\n",
       "5WPaEiEiomO15fT6J391TMfYuZWU7jbtcPgpeZZd8syV/BgCooyeM0QPbujs8cJZel4MHLf2apyA\n",
       "2ibDpB3SJ9MAMGnxB/pZDUVRqL6pVo9lI9q+jZ5jrK6utTTEFRF+mxcNJmZPVOAHw6NaA2KxA7mx\n",
       "Ey06tN2mOJijwxuzdDfNcoRx/c79G2npJnZgVt9k66aJMbEnIscghW6Yz6rz24BptVnwsOWE+UNN\n",
       "nw9WFJueQSHFta/tdcKpdkEFUFX7jogIc1Z/YvrsuCjjA6MzjQ0+vO8YGTv3Deb3LBeuROx+Tftm\n",
       "Q6GY+WkQuAWe9ZYoP621OxcLJhHOlJGXrlvMCE153XNwq15WQZhmETkHs+bdY6yvsmNyQZy9IhLh\n",
       "XQajqXJYaLs3DU3s8ShpJEYRYa3W8LxsuKFdv3aXh0CFHAa+fotDhuLpaIGx7IR1iNB6hiOk9Dn5\n",
       "bCxcIXSIW3ux29Pt9PKEh2m0IV6DH5d19g5DvJy9Rqc2IlvuTc0Nru09s4qYu+av799hu+ZAeREd\n",
       "qynXnyFnOpcpj32lu2nminGGmByCZNN5efzDjN+yiojo6o7DpM3zYXWX+k0pKVObEDlDtHv/Zm56\n",
       "05ePNsk6ZelHpt8PHS0hIrLt0si2C57DBicnH17QpNLKIYggc/xcMtHPD5QXWX5lTFbVNI23KBki\n",
       "vDD2Pn0XkCijKKZc2kiPrNmZdHA0UgPZdZBp++6uGdg4ef+SwR7ZPCP7Ss7OXioBUw5FUThzC7dy\n",
       "dy7XYwbF+Zvnf8eTbKwJrv1cpxKI+RqRQFvL9gNDpzyl9+/eDqvb/xJtg9YdmN0HMv3x1uI1tKWI\n",
       "b2URFMwgth4WC7SFgE4FwR3N5tVE2bEDVFK6i/787i8DyytM4u8VsjBXqVTTP8KkLZNjIqJGH5ph\n",
       "Q5OgTbEA2ktkgrGlny9oZf2yFhXZUlnDZ7xAo+e8Tm6k1XY6UFFE979xKxERtbXlAgZNWvKhd/m0\n",
       "DiPbeVpXTJ3Q4jyIKAb8H+Vab0tbc8aEzeG2Txe+L7Q9PvjDu2iX3t7MCe4rL7TILShntqGWlNnP\n",
       "smimkKIKHGtCyDtUKYrbardicfcoEkXWza01D6fzWLLmDbxV8haBgFxecJus+8HYPg4eKbbvCnIO\n",
       "8ovutLnhdvhd9zSn8t8KhdhnkYLY2A7Tw6MXc0cn2m2Kqq7Ksm9gjvMxGI7oc4tc3iMYngmNyFgt\n",
       "eD1EzBprrLueiqLQC2Pvo8NHxeOh8QOTivVDLa1NhvOg3k2zlhieRVShOVJdavpstJaQMWnSeHbU\n",
       "/0nfY0Uszg37mk4iOyKir4RDGZoWCZJ8QISSrohoSBTiyq3z9EPVxsH7GCMgmChuW8Z+B44g3SpG\n",
       "HcDKOkFilYWQb/10muoachFMjS42/azeWU2zyjkmAywOH7G7vmXh7O1I3uyO5RTAyMpt8wKpZ+Pq\n",
       "7dFqsQCdTiu+mki8gHT2xPhe2LyiKIqjIpRSCrh5KAwPTn4Y4mCOKDsYBulRSIQwI9S7RQdmteyV\n",
       "2+YFlj+vjpnnHbiH1RUaPWcI6wfvgulZSrzbzDM20aE5phANDMh0ShODBTtrR8SuVHnH6s1JGEbd\n",
       "79i3wSSbNoY1csxA2cmyy9g18KoxDY8WKkaMrmidDu1zUc19k0zbOVaTmQP6DWgtijGGj5GCVJA7\n",
       "ImLPn5TwFTwSo4iwPCp5seMcO/cNGjrpSSIi7uHowOfqAU8KwyC0w+rWgIaMshCZ3KXVtM1lbRBY\n",
       "TWWkCGR5kxc11m+y/tM0mrzxbL2tOHXiWlsQHdC3Fa+1KV1eVriMbC5axZwgam0wpaQS3iWziTyO\n",
       "iBZZPaDSeujtn+t/Hz5SIn2/zE6mGzwly9625Z89GNMscWU8bq9ZtnfdbWJr7VNVNZ7FWq8uOQVx\n",
       "8gLqBO/sQXHpTr3P1xyVNLU0BjAOuO32s77zlucCB09mMhjLVsZEavCHvwskf7/YgjAy2Ll/o+98\n",
       "7P1ccke+xCgiLHgvWVtbq+OExaspRVwEqa1GrfnaO057/iJ2wWk17RpojEddM3+StmXvapowz9sk\n",
       "pkLYjMFpR8RLfSiuJkOyOwesd4nl/tcPWh4yZ2u+WP2p6fMrEx71JcMxzs6O5k1JURSXskumkWTQ\n",
       "JjV8MnUYtPOMltYm2nt4h5gEIXsOEn02T+9uAOXmd3IZpeOTtnQrbStep8c5cisz61hw8EgxPTfa\n",
       "v6mMLJqU05aPCiV90cPpVniKSGtbq/5e5M5TttGxWrGdbN4Y5dbWWGOgyPu5+8Bm2yHzSYvFPIc5\n",
       "YT2HFbUFSD6RTw6QEq2I8NhavIaeC8DOLyh8vwpq+I0mLAXFZpplyEaVmNTwou6KMGPDcMffl22Z\n",
       "TbWN4a0ou3nNkq3bSgEzQll/82mH6PSbLN6vvHK0RgvS5r2tlVUeCEQWK9rCRUYRYV/j0elRhySM\n",
       "lfZXJ/6ZiOJflxN+H1X5thxEqUnlGXN7bWyq1wOsEQms+ifg/WpPt+uCLt7oHMPCiGi7qahiL4R+\n",
       "uX2+6728Ff63Jw+m2Vnval48NvH7PC9pubfPNz79m02JYYdokMeradbxBhSRgGE1fD9nPuIfCs0c\n",
       "rSkL1PQgSpx2RHRPQYKmWV5pT/v3buWHo9Vl3N9UUnUXuaJ8YXHnyUxX0muHk7vVYdOfl0qLh9cd\n",
       "rUDhtDXNRK/02AHaXsKPM5KImVKMaH1tmlRukNB8pu+pZwuff3GOrM5GNKCaEzJ9IduJQXRtuKG5\n",
       "zuIOPbv4xPPnFeLZI1GKS3eGOoF9b9ozzO/rG2uY3xtxqvuKyszE3tj3i7uw9XZGhH2PWPtsNpy5\n",
       "UkkNLOaRyTRLUv6PF8jH4ADhE3+v4AAzNgVIFNYVlcEf3mW7RmRY9Oc7P97J48IN0/g/qnavJ26I\n",
       "DNZRB77KGzgDk7bLpKppPZaKlTxaQDIh7BxAguq6o/T4sF+FYkMf5yrmmaedx/UIZpvUOAZSC2/o\n",
       "lJlcBdUPaAd5/eIWGDAJq7ROC0dOiNZL54IuntIncp7ka2cLjIfG35nyd895aWnI3yPW5loNni8D\n",
       "cwRgsTCQld8tinsUyDjM8cP05aMjyScIgju+HyLJNwNMjoANjbWezIG8IrLKEfbEOgmDGw8vky4h\n",
       "U7YEtbkk4WeS255Oe2pLny4a5jnPINBcXodBKK0sxg49lUpxvLWp9PIEc2ycF8c/xJ00hNnjxGH3\n",
       "HtRBXjez0kLJ3eEkIVovIi7B+Xnwx0E/yi9P9lYP7r9Fy6G1rVk/O8RyRuSVVJ6bZvlyoCOBsczV\n",
       "kJzmBEWid0S0YTDoxqa9HEERZAX7jYS5rWQdbS5aZZJp8pIRgbomNCKiQAi57/VRhnF7jnFi1TZ3\n",
       "u2ArIuXV0hJMQLLYCViJ9NNXfLltnkPA0eMTP2e3WMxd8xnVc9xaRkEqVWB7v9rSbcx+zHHlMsTF\n",
       "D6Msl5zTX/r+D1zcI4fJjBVjY8s7fOKdyPk5Y8FbMPSyiCJqztXS1hz46r9K5rlCkifXQJxE74iE\n",
       "1cRYwdiSQhCRMGsbqkwTsh37NvhOk4eISZWIouBL2XSYFJzQvRfVhXhQ3Y2DR/ZK3yMy4OTjShCL\n",
       "heunUmeRAE+C+B2Yyiuj8k6VH7QFHL9k6rJgI8HLklIUmyJS21BlOefgTpiLH+t3L8vl40Hh6Sh9\n",
       "Q9IY84WYi/OwsI4LxaW7hO8NcsIuY5pVeixY5yOb9qw0OVeBibJ/Vu9YGLcIyVZEwvb1HRRJlM7Y\n",
       "8RijlAeNkzcmHaEdEe8yJHc/JGPuI0sSDnRGyRdrPnW/SBSffQUGNjMdrTxUle1O/FCApiNBkmSz\n",
       "U0fyVe4Eo1jiT8yV6DeDOihOJN4njPj8pcDy5IEdETFUh+WJUbNfi1QWFome8WgFlPSmticJ3oIs\n",
       "GDuL1jAVEaEdEXf8aOVOg3Xcq4NeJnJNLQ0hSHJ84M+bXrADdkcgzL4jCPqc0k/qelX1dg7IRkTz\n",
       "7CSbnTpRIrFaD8TYttdDJPIssl4WnfDiaSssOtpCyfFKohWRfeWFRES0LACXiGGiBUtLEsaVglaJ\n",
       "AHOyjJ37pus1IjbhMqs7dpI7WPvzBgaiBvWVX5zY4ytS12ccefgf9rwqCGecdq5cPnm6s7D7wOa4\n",
       "Rehw+FlkUSn6HRGQLLw4JogK1x558eLFNGDAAOrXrx+lUin66CP7if/BgwfTmWeeST169KDrrruO\n",
       "tm3bFoqwQBzjym6YHYdI8L2wcZoU+D387xessOcXqK+OzZHqUmbQTNnpvlcF4bRefSLJBwAjQS6w\n",
       "wBwq/6hvrKXRc4bELQYXV0Wkvr6evvnNb9KQIUOoe/futo7xhRdeoFdeeYXefPNNWr16NfXu3Ztu\n",
       "vPFGqquLdwJ4PDNh/lCatmyU/rnDdxxOplkxTyyFztCAxBC0l6h8I+/6Ckl5g3JU0twq77XuFzfc\n",
       "Q7IqT76aZoFkEeQCCxZr8o/tJeviFsERV0Xkhz/8IT399NN066236gF1NFRVpddee40ee+wxuuWW\n",
       "W+iyyy6jjz76iGpra2ns2I7sxi/56FHNKRP9tiOT5KE67yZ2IdCr5ylxiyBMe8BeovKPjt1eeWfG\n",
       "ZHcetnqw1+/auZt0XxXHGbd8el+BGEEusGBMA0Hjy1h27969VFZWRt///vf177p160bXXHMNLV8e\n",
       "bKwOIAerszj5hNNikCR8kuxl6nhfYSfKL/OS4/2MSFyTjHP7XuTpPmn3wjHPoU6SnORX1R0LSRJw\n",
       "PBHkAkvcVgZGoBJ1DHzN4EpLS4mIqE8fs91r79699d94nNgNqy5h0tRsNx34SvfTY5AkfJI8za2s\n",
       "rIxbhNhpbQ3PWULQ1NTWxC1CrBQVeY8K7Ycu6gme7is+vFPqet6ErLKyylP+MhQVFdHpXS+Uumdf\n",
       "DDGvWGMHyG/c5mMyFBcXB5aWX8IK1AyiJbSlZLdV0IJUskOY5Duslc0CpaOWeZJVEeDFzr1Lp+4h\n",
       "SOJOklb7jieOl7MQKaUgbhFcaUsn22UzkKc9wLOKcbvEN9LajrZq5ZSe+bfg7EsROf30zAOXlZWZ\n",
       "vi8rK9N/49GzZ08/WQMXOnexR6s+o+8Z0umcclLvIMQJlSSb/vTq1StuEWKna7du0vd06hSP0tyt\n",
       "h7ysHYlzzzs3lnytu+pRs/+Y3M6KF84//+t0ef/LQ8/HL716nhy3CCDLtZcPCCSdk0+Wc3PtREF3\n",
       "mBsnmXPP/HrcIkjjSxE577zz6PTTT6c5c+bo3zU1NdHSpUvp6quvds6YY9d/8olf9SMS0GDsiHTu\n",
       "1EU6mZPyYFCqbYL5U5JhRbJOKsf7mZ66xupY8k3yYkKQKHnwLvz8+rvjFgFkSQX0XgR5RmTF1i8C\n",
       "SwuEgUI3XHFr3EJI4brsWF9fT7t3Z+xU0+k0lZSU0IYNG+jUU0+ls846i+677z569tln6eKLL6YL\n",
       "LriAnn76aTrxxBPp9ttvd0yXp4hYPXMBb1TX2w85diqQV0TyaRKZRA4c2Ru3CLHjZZIZ17T0eHdN\n",
       "OXnJiFjyPR5MsxTKD4Wrcyf7bjqIh6AcsbSn20hRUjA9PQ5QKP+M1V1b+erVq6l///7Uv39/ampq\n",
       "okGDBlH//v1p0KBBRET0yCOP0P3330933303XXnllVRWVkZz5sxxNb1KsqejjkqXTl2l78mHgTPJ\n",
       "VNcdjVuE2PH0rsfU7sqO2YPdgfBJ+gLUuad78+plRFEU9KdAioJUMGeK2tvbqRPO5R435Fs/49r7\n",
       "X3vttZROpymdTlN7e7v+9wcffKBfM2jQIDp06BA1NjbSggUL6NJLL3XPmVdOyTkHZaLvqWfHLYJv\n",
       "vJhm5VuDBt7p0e3EwNIqKMgNemhDwI2kt5Ee3U7w7GLYSNKfE7jzp5sHR5hbMO2lLd1KqYLkO0oA\n",
       "wZDOs1gvsS1D8dwuJskjgxHjxCpfObuPh0NMGDgDpUvn+A9Dn9SDfe7n0nP6C90vsrP2C4Oduejk\n",
       "K4iJHshPkn52IqWkpF0F21HyxAQtH2SMD9H+rFNBZ7rpKmcT9aDycuNAeRE1tzQGklY+EtSh/3xB\n",
       "DdBLWhQku/fvoNzxgwdjyffUXvKeaVIYlALliTuGxi0CfeNrV9DlF/yr/QfBqk4JmAsYzbF458Gs\n",
       "3PeTZw2ihNvuLjv3ilDTD5OrLrsxbhECJ+k7BSJtXoSkPycIjm+cdyX17HaSrzSC6gfrm2oDSScM\n",
       "enb3V0YiBGXilhcoCrXnWWBeKCKiBLhR0/vkM4NLTIJOBR4OIWLgDBj/5dmtSw/fMrAmRKIKg5Ai\n",
       "Yvxb1P7fIJNMKZ3QPX4XyWd+9bzI8rrt+j9GlhfIIPpuOKEox8eh/I6OsDKpHB+Kp99dn2gWO50n\n",
       "cF/t1TcCGeT56XW/l75HISXvvD9CEREkSJOxIAY1L8gEkexzSj8iwsAZNEEMTH7NBBWOiYhoXRcI\n",
       "tF/TjohgN+O1rXXyUB5duwQbMPF7/X8caHpOxNV/hEnSD6sb39sX/jDG8drvX/kToXRA8ugqZDor\n",
       "VocKZ8Gno/G9/jfHLYJvhBfLWPeG2B97GROPVJdCEfFNUg/ZBChXUNv88vmKV/c5fS4IUZLjlyAG\n",
       "Jk87W1YZGHKIyibbfkU7eVP+IQ7gv/vPv9Bt3/tDwKl23AnHRWd/K9T0H739VTr9lGQ7AzErf851\n",
       "3ZW7Y6lE5i3yEsHzXsCMKjDOi3ZNmQUjn/1CDN3KV044NbS0g9o5/sm1d0ne4VyQfhZ3glY2r7z4\n",
       "Wl9pF5fupDTOiPjDrRu4+5YnI5EjTOJa/StQxCeQN13130Tk/CJEaasepemLXx687UXubwr5fxbf\n",
       "bhgVhfaXFTK/F0FEETH6q/fSybe3BxeAy0qfk/tR967O7sVlCSrwWBIJ+z0/47RzE7NyzPOOaGzz\n",
       "XmWN0n1vUsozHzj/jEvpjh88QERiikikOyIxrMv+UdormPgztra1SKbN5hvnXRlIOhpe6+nyC/41\n",
       "cKuRU07KBfX2KlfacEbkO5de71umsEmcIuJGR4i8Hpdphcz2YxfN1a/lRTCeb4nyAJiXVZq4zMoc\n",
       "PWMpCnX2EFjSiO8dEVKovOqQ7XvRybSIIm0cP72091/f9Aj91zW/kb5PBK1zPzvAXb+oVrr//pvh\n",
       "keRjJIgV0kvP/Tb3tyRNmnlt4l8uuU44Dben6X/O91zTuOWaXwvnx5TBR5kmqT5E8Htm7pzTL9Tj\n",
       "xKTJ/ZCvaPmopObG0TwizEWVxuZ6+5cJaG8yu/w2pz+Bi69w/hYnoXZFXPJOEYlrNyHIio1LEZHK\n",
       "V+scrCtEhs8dwaVxGJx6Um/ub4qi0G9uetRX+l7ORJhl4Hwv2B2I7KwZd0REBm6rKck5p19IF/T7\n",
       "hpA8YSicSd159aIUnHzCaT5z9V++P/jObb7TICI6MQbHBN+/8qcm8zSvpXFOnwuJiOgb/a52vfaK\n",
       "i67x5V2R9070dIkVlI8e2f733+/3df+P/+2O3BnQgGdwvt21RzBH/+PNg8xZSioGMpff819/l0o7\n",
       "iDxFkJkb9TWYkaqkBj7+GNMLc1Gg/4X/FlrasiRPEXHZGnVqMD/+tzuCliYUUqkUXXZePO5D8zVW\n",
       "Q9Ave7/eXws0PSNdOnelG779X8zfFFLoBJ/uCgt87ohwR7dsp+e2ui+ys2acMIt08r+44W7T50x9\n",
       "h9MJi3TuvU44RTLN5HWlGpV1R5jfi050gxgLZZPgmRPc7WMi84N/cVeGWHLant+lQHjt66SeX3HN\n",
       "XyOlpELZ1XBzlXrDFex+K0hO63V6oOm1tvsz91EUhbp0yigMxgUUr/ToekLmD5X8m4D6UIxO7CHW\n",
       "3qz9s2xfJjM2xxUY2k1GT4u0+seAxynjUUkPY6DoDuH1375FOu2wiG30PP+MXPR1mUmh00uiFezv\n",
       "/vMv3gUTxE8lppQC+vn1f3K9zq8Jjii33/B//B8dXrK0xVf1v/7TD4ISSUoOL/ToEuwZARtcef0/\n",
       "h98dNV7HqX3rtuPStZOcZxkRxcVXZy67gidQB9Zrurt07vEbF8gjvrsc/dPxJoR+FL6gPB+6tx/7\n",
       "7/f+5Bm5PBye8/6fPe/p/r6nnk3fkFgAyxfvbM0tTb7T0JTEIFrI7Tfeo/99/hmX0v0/e0HoPoUU\n",
       "Oqv3+QFIkMF63uWMU89h52tTRPKhNwt4F0KirdvXJTL3BjXvNO+IyN9/8/+707ygn1QHUAZi62mM\n",
       "Zw36fTWniLgNFtbB8/pvZ1zHvfin8QFKx8BSmddd7t1dp6KkKGUwb+l1wql6tOtvnf9dw3XRdAjf\n",
       "vex6uw00p/Eav7W6iDs96/I3FLy8TA7lF/aryVVDOB6rZGhLt/q6XyEl01lZv892qCwF+LFfvqH/\n",
       "7WTvnyNXwimGKZd1ZdY2uVPIl+ePU5zOkgkUv/XdO6mneYfkgn7/ZLk+vK508K/eDyVd0dU2kX7o\n",
       "a30vcc1NhjRXEZFKxiKBR3tra2dhSeY/vvsL1zS+fuZlUnkqSso0kbz47H/W/z71JPcdBVadPfbL\n",
       "1+n7//JT4ftEV9RlCdIVPhEJm3AGhWgrUkklRVHoPEErhCEDJ9nNZXy0d6sy3/+i/8e8zjqnkp53\n",
       "xKC4BD03kjH5N+Wt5j4HZrVhejb5NMXHouQonLEpIsaBxtjhunVR1lUabVVezP93cBQUuNvJv/p/\n",
       "nzK/T6VSpob/5/9+jXp2t9vuRnnY+mcC7kytDbwt3Wb53Zu8P7/+bveLAibowdAKd9chiDgiAXjN\n",
       "YnVCmmxWReT/bn2K+p56lv5Z9pwW65lVW+RX+zXtPnyh3/uTZ7gTeLezMJ07dWHKY+S3P3rM9Llf\n",
       "7/C8urFM+V6++2Pf6YrWo0iLve9nz9G9P3mGfj/gcf27v90xNJeGZLvneS/y1Sd6vtUsiyZDr6z5\n",
       "4be+fpX59wC67VQqZVbEDYmK1BuvnNzavt8xp4fLGZQwsB0e9kFypmb+sb5DvB0um2mWxLRQUcTD\n",
       "EQZZT0HjZ/cvcHMzQ715mS/ky06mkdgkNmnrEqvdNkUkAJtOEawTV5HJIK8JpVIp03OYTJwiiqVg\n",
       "hefJyXZwylBX7VZFRKBL6szwInL1N/LvgKQV67N/9StncK+TrdVHb3/N9FnGDTNbBnZd6YqIpW17\n",
       "Wf03DoKsjvGb53/H9Nmq2CukUHu7n50fxeQG0fSLSwX8/dfDXAeA7l3NplqnnhTiIMsQpXOnjLLI\n",
       "M7cQStalHq/51k26ACILPV8/8zK68Kxv6p9lz9kYsU6ivnvZDVlRfJyb8DjN5MUFufisb2VFshlr\n",
       "eMrHSEpJmXacrzcEjROZnASyEOKhrK3pB30epCOinykhUffBYuTe3wy8992PaZa1b7/sXL7pX5AL\n",
       "q0Ev0l4itMtvRyVVH4+TYtLWvWuPWHap/BCbImL0zvG1My91uNKM1d6cZUtsfLGD5jc3/ZmI/Hnv\n",
       "SikFQn7ptW/1QViSm666nZGm9wHKvhtlXrEWmaA+e9dI12uYBP1iBW03aZHvXy65jl784zh6+rcj\n",
       "iMhgPxrEwV+fZcGfpKS0P5zvl8yP9a7cfqP5XBLLfEvbEfHi7tj5EZyfgHmgN8Z+3e+gy3NN6Zau\n",
       "5qs/E//CXofs6PSGhQsf3l+s/bo+2EulYpHM43tz3eX/aU2JiHLl6scsj9e3ZxSRXBkYnYyIKSKc\n",
       "SafrjYarsn2kjPcu6/r4E3e+I3yvH57//ehI8slgfsYf8kzzBMaYE7r3on/9p38PQigbX7eYlrQ/\n",
       "LAAAIABJREFUrPFWyq3tSWZF3WpqfMs1v5KQMJuG5FvtacXf4Z2584cP0Q1SZ37NaQVuXaF47zeJ\n",
       "iP7pa98RantJ0lViUUTO6n2+7q/9wdtepKuMnbGr1yzzoGo9MP3cXSPpfI5i0/fUs129hriheQMS\n",
       "Mo+x1PT/ZN0MppTcjsgpJ/WmE7qfpL+MrOjSXrfaZA++fecSZ//2Vjm6Ww58G2XnBe2LwoTuL/+T\n",
       "Oc/g9J6FfkZEUahrl+76IcgTsm5Hg1jJ4XVOJwi7NlWYhWP0H+/kJlab5PAUhF6We0UmavaYNIqu\n",
       "iNx2/R8d72WVhlOeXK9G2XNazGsiOu9nlCGHT0WEZ5LhspjitFgy+Ffv0S3/z3nSITKIPvXbD5jf\n",
       "W1eGr7zkWte03CajXhURq6miloxWrrZ+UKK+uAtDqZRpt994HUtpF8/QnJ9VEWLJ823O2QJ28gJj\n",
       "VQjvUo9u5sXHa771H9xrgx6DeGcjO3fu6npvWk2HtpJuXygUzMdwmdvCYUpJSY9pfSzlJTuRV1Ip\n",
       "oS5RxEsekbbQIvPOWsiKf+ZXzwvBK5i4XFq5JmVnRobYdkS0spItNG3w/O8b7yUi+4FWJ0Vj4E+f\n",
       "pcf/9y0i8h8DQ0Q5sL6gX88qSIpBEbF2oF8x+PzPKSdeq0lyFdLVUUCBfs3F51xO1/UfYM7NUJc9\n",
       "g96VCnoHI+D0nEr69YGTdVOeIA6r89reGaeJmekoCs9ALPedY+koCv39N8Pp33kHX1XVNJEUecdZ\n",
       "wTFZZyPOOPUcoYO/ToMj7zdj+48rGCZLOfAbYIy/Eurcr3TL7niw2sspJ/XmmPcZ/jb9zn6GXj3Z\n",
       "5lvWHZGvnXFJ9nt+y7T2pXYEyjH7ANddPsBkZmZOJbcj8vrAyVJueXPZpIzZ0dm9v04P/+JlUx68\n",
       "M1JiYybnjI1NwXY5iS+Jk2zPWSa1vS3mq+wdNq9ymNv26wMnB5a2CH/9nzeFArKqljq21ZrhC1mX\n",
       "/9a5EW/hwfpOGd9bVh/sbM1hr3+t/9HS/cOAv/GFFkB4YVYhGviTZ33lJYI2bnzlhFPpsV++Lnyf\n",
       "H7Na8UVHPnGNcSxiUUQy3iS8Za036uwLcNVl36fv9RfzYNWj6wmuAZ00rIGItJdVW6XyYqerPXNB\n",
       "KqWbmLVorgcd0iuIKIij8dAlaxhLKSn9pfvTzYNMns+suE3zzzn9Ql2Z1GCvBsuTpBfMSjA7Ijyz\n",
       "C7G0FWKvAMksmH3lhFO58Uxs56kEVnCtJpeKktnRe/WeT0zf9+v9NZsHK66Qbr85BOt0uv8PP37C\n",
       "PX/ytvLKNKPyqIj8+j8eoUdvf5XrPtltQO+SXdHlrRiecdq5tu+CCsbFWxRJ+1hAkJGmW5ceXH/8\n",
       "2nNxd5QEMjrjKzlPkdd86yb6/r/8hM7qfb5+oFdRFPOKtmmj3D0D0cP+ToqdF5MTTTahM1OW57Aq\n",
       "Kn5w6wv9rFyLlH+fU/rpirwTaU4Z9+x2oslN86kn9TE5gvjnr1+tK1c8j3Un9TSPp2F4U1IE4t28\n",
       "du9njskb6+q8vhfb7j+px8kmC5RUqkBorFNI4VrH+OH/b+/Mw6yozvz/1r19by/0Ru/7AjTdDc3S\n",
       "0CzdyL4KyiI7yq4Isrljog4YFRMT14xk0UmCM2NcEsd5njxOYjJZFMH8JhFc0DguTKJGcDCKwRHQ\n",
       "pn5/3Ft1azlVdWq91c338zw89L116pxzT50657znvIv2FNFPxzdGv7KsL9sGVcsgTaDgsJK+ExHp\n",
       "f00nttyV1wgi9RVNNN9CRcBN/bR88SU7eNIlM7Zb5pmqe+pExMioOZHO3YmI3YXAkH6jiYiovG8N\n",
       "U2Czk9+gBusXYFTLRLrhYoUhtlfyQzqOJi3tKuQjQNfCiOFz4M3WpQ2IdjdXiyiKqvfYyEZBidGi\n",
       "WHtyaSRE6eqoGNq0gU6NT0Ss0xARFeeXWZZPRNTK8Q5IVBQlvJKxhDanvaWiuJaqSxu5TkRYE1ZE\n",
       "tstgn+LVVzTRwomXMvMe1zZTc4/5uK5dEBsJHKILl86euVhO/q6iPHY/sKVjTxFaNOkyGpp0254R\n",
       "SQn3hi6MOXqE8TyauPe2S3/ITMd7YNvVNoOdu2xnlvpOmlescBI3a/xQtgqWqdqhIFCrwQIt6IgL\n",
       "eu+BCcr71iQW5fJCKfGfpG6t/H2xWEJFVtl3iFJhES6fexNNHbmAqksajWqh+sRyKKNObu6IhMXm\n",
       "BbfQ2jnXEZF6bFaydvZ1BhsxJP/+rrbphs/cLaxThuuW3637rp8iBh6JIlen+dYVj+m+4xFgnG7m\n",
       "SHlvnM+3aZZu0ufnS9C8Ydy3eVNly8HcoAOc/uJz5vdmAkUqywjtWHGv3Lm+tfkxWjdnR7I+SZQq\n",
       "La5Vsxh14GjvIf1GM1+AzRfdwl2OVcDH4vxyikSiql1V09/pRIfT4J4LOi92tIux4cIbTcrkPY1w\n",
       "j7Ro9bUOJjulgtW7y+k20gxT1SrGc9UJLKY/UmAmUqoDSWWM7a+f9Hj7Du/v3r5oN62dfX3iHg9P\n",
       "RCLyCSxbDdUqW+Vz5nbSmbxnyZSNqmdo1xuQ0QLNlVchjzYoBBLojsv/mSa2X8C8zudRkd0HlcFE\n",
       "lScivCdNwwd0Jf4waCZJzU/KQ9+eirxNmnpUyyTm9/JpkWJpUd63RpWd9P4of1Nfs7g/JiyevMG0\n",
       "HnbxqofwkhA2lW0uMrOQ2orVt6zGfVEUad55qyke43P6YctegjNtc90wWTAyuqekoII5ZirXBcum\n",
       "bqa541YSVxsrjb456qhVFSQiqmUE29ZtnnN4bo1z2AuxMZpjHWbHk3caSI8gIioX2fprZoOS8QDq\n",
       "LcqX+7ILvyoPnoMbRtKOFffo0rN03HV5CgJVlzbIn+MZmbIbToMbknknHtO889aoLq+edbVlmUTq\n",
       "KPY8GC20Kl3oNCr5+sZ/0allERkvPsyo7ms/Eq1VUC8jWLFelPDs/PMcZVtF8a4tH2BZjnkd2KcK\n",
       "o1omSwnM7zcZwCYMm03LpqnjwvC0CzeCoJ+sGKdMyslLpwMt/T7N91pNaSKiAeXD1ffYqSrnQB+P\n",
       "ZckLUNZOrmk+inqtOf9auqDrEvmz1O5FBic4vBscgkCWfUJ/j7qPWU3WvJN7UKpZZsKmIAjUJyvP\n",
       "+BTPTX9XtINWPVhOYvJL1s1JCLSG9decsutPRFJ5t/UbpfO8JGGk8sJ0umKAMjCr10si61gYid89\n",
       "cuB4xrfWudvFSJ2Tdx2jf+aKz9KayKL2Zv3mXkXMM7Nfp7S5qCpp0PUDJ943VdeY458zbG9dctyw\n",
       "bOoV6nGNkcY6uCs/2vY0tQ1xsSR26pnVK9JorG6kHiHS2tnXyZ/tuA70EmX9lLYQkUiU6RGKK8iU\n",
       "2UvK0tmXLyUmtvqKJtV1o04p6aZLA0+20ojT5lstaP/2QP7LycxlCmBfmsSNsGf8npwMzX6so0Dt\n",
       "7l8XnoG6r4Xqj1EO0qnAyplXWtVCzkUpJEjG7la2DWaRZEe3TtGpYmgFEaMTHU0h7K+t7yQitZqH\n",
       "bs/XWKeMmebSC76ii6XChYOdRfaOoFk/TtW5OL+c+ualnF1YnciocmXaDKVORHgFMW2q0oLKRDUt\n",
       "7tMuyIzS57uI9m32G9ibOupaKHX0zYhGM2jplE2qecywTprPyk24gbVD2Ck5noU2FpA2l5QwbpzH\n",
       "sqlX0LaFt1mWpco/5YXGMu2ZL04rbyQiD4PemZTvvQ2hVojWN6qRB0u7cdBSwgafY42N826m1vp2\n",
       "y3wjkWhqA0wQVI4T5DRCRCV4XL/8Llmjw0hgZcKobmlhFRXnl7NVU4UITR+5kKaOVMbSUadxq0pO\n",
       "RFxrgq62Gbr21t7W6WNctPryJutEWozmUsXXRp7fgiLtIRhZGwJS+0QjGYZuRHmOw9wgCBF19GKL\n",
       "TqrtnCzXcbYHQJPFCRH/bopnbWXxYrs9pfqiW21/U1vWn+7f/hR984pHdS7/UmXqv5MGoLwc490D\n",
       "aUAfZCOQkemvt3i0dlTBrHqJcoBV2j9IO7EDqs0nhYQXpASVDKEgM2ZuZMkzwCu9IVk5W1gxbavp\n",
       "dSUjmyfoBELWe5Vh4hXPqPZGXrOG9h/DrdZAlLIXE0igIg6VE0EwV71wirXgbPwcb1z5j6rdbUO7\n",
       "Got3XnJhyhqDzMZDrccfooTno1yTd9oak8UpR5/iJRqJ0rghM6m9aZyscmdSsOrj6plXyZ4dK4pq\n",
       "meOe1ft326U/pDwjgU2ziaB9LoJik0KLWbA6Ca2HJCXavsJ0duKRooOZpzmBURflNbec+fK07jvW\n",
       "M6srG6A6wSRiq60lM0gm0NdbSsn6TYMaRirUVo3e4cT/39j0iOK7VF7rkn1Ya8MTiUTl520ksC6a\n",
       "pFed051WCUQ3r95DOVm5NH7YbJ1GjEBEszuX6zRCVGlcbBLafuaqG0RaPOkybu0UIwcYLFrqhptu\n",
       "2PPitdjtB2nzmuUWN0f0PCi1EQQSOOqcetwjmyfQ7E59kCOzCUSeGBiLIUNBxOooNlletcIOg6US\n",
       "xYvf3qiMXHk69fu+5aJbDa/N6VxB88evZbonNCLCWCRKLvis9XS5i+HYTRRkP/mSOtW2RbdTPENq\n",
       "J/PCRgw8z/DaheNWMQNhqqtnfZRdVVJPF3atJCKiWWOWqQwgtf3WTnDQ5rphzPdI2/6qBb228Y0G\n",
       "d4bXrNSCjbuK1JyMuE0C0fbFd/DfSA7U2EwMwq3a1WzyVi+AbZyICBGVm9HVs66hK+bvYi/8TPL0\n",
       "YqHYUjdcU5y78Yv3fvUztKcukxnPVi/QJZMBRbKIEDH1MKj1lkSUirKdsk1J6MSXaQUd00N7/cXF\n",
       "2oVmMs2A6sHyaZhETmYy3kry2Srz83pusXpWRgbZXPY9FlU988Up/T2MdNNHLaTpHRcx89OpzFnW\n",
       "yhrjeuu9ByoFVMlDk5N1WydD5cfs2Qxu7ND1KfY4pc4jznieYwelyjYrs75ioOE1FlpBqr5iII1s\n",
       "nqD4xt3aNHVqGSHt7zTygJgo1WDM5BDSzOa3XWsftLzfLWkRROSJmohYL4FiFaC/Lidz+7AtXm3F\n",
       "LqCRN49pHQuVyblKdYJR5zNsA01lBjV0yK7+SgsrWXfw1UMwF8jcHO/ds+Unmn6hL5sXKa2ZTcfA\n",
       "2qHcbp/bkqpGSoEwOzmpytGVLZ+tcbtpDT+t8hIEQT7JkZpFKaxZvRqVxXWMPpLIb3rHRdRcN8xc\n",
       "R950Z1l/LTc7n+7a/Djl2FCvM2sBZvm6DUT7qhlexRGR7T047IEUBRKRA/sCxcM+qxw7Sen1yqBI\n",
       "xQWzNhUE/h1HQRBUKkyVxbXUUj/c4ETEGC9sALWLTdM+YbKTbxflM7Qao53KRvm59lydS2qXSrXK\n",
       "m1bv4VZ12zR/J01RqMYYIeW/dOomunnNd1TXdLG7ON1lOyHPzBW8IND0UYt0X+9YcQ+tPp9vZ9sM\n",
       "u4GEnZFqsBrZoNr8nakorjN1uCIhknqjN5bh1NCajdWYqLvOGpo0abSnKMMGdFJBbmpj0+g9LC2o\n",
       "lNVZ6yua5HndvH6WSQyxe5KhLapPZi5daXNzy7i9+X5IUb4zRxJ2SIsgMn/8Gkf3SS4HiQJQzSJB\n",
       "7nFGah4J7w3J9EIkFTTJcBI16YQmaytpAWxodEsJPXZV3U3oaJloel1VTxtvXU6W86j1vAEmR7dO\n",
       "1nzj3ckYSy+WiGg9w6ORJDzI3wlEl865gS694AZmHmYLq4bKZtVn6blWFNVSXZnaML2rbYYmsJWg\n",
       "+Z+Ip01SJ3DqzxLa3WR1/ZwNG/Ig7PKRSe3Du1OjG/yNurTqGTmfbaSNA4H4XTUrg+R5hXUgRIsF\n",
       "gaSapTkRcVJH5iM3Oc3xYnyXFlDXLvtWojiT3+s2aKQS5a66X/PUutnXM08+jDD1jqX6lv19a327\n",
       "pRMNImce8szKdco4A/fCRIldd9Ype3Vpo06AMVINV6KteR3LmQhv/5JOiwxUs1jvUQmnHVZEiFBb\n",
       "v1EcVVAHpJU3Lx2N24zTa7uOLzj6hnWgTmvmj19Ld1z+z57UR8k3r3g09cGgXkpbaKuaS8FddRid\n",
       "InO9k/5qGFkRAhsRYyNFgQQqT+qwZ8VzVAMvj65dXCHJs4JvmaHUo49GMyw7Nt9Ops1dWgsbEaPy\n",
       "U0d7BrtudvqczypwdlHGa9m19vuqa811iRMV5QLKDtqdrGVTE96fJCEpI5pBWy76WiLvZKNGFSci\n",
       "bf1GyfEA9NjZCUnkvW3R7XTlEvXux5hBU5KTqPRs9c/YKGhnXk4hTRt5keo+ooSv9BXTt6jSsnYM\n",
       "5fqZTiT2FxTM+qo8LmkF8MT7YLRT842N/6r6rNWXl9q3UGHYTaQZewR1+1r61qdULA5VvzNoDrWX\n",
       "mtTel+0TEZPFvNUExC2oaGxEnCw27dqIGFeJfc+4IbN030nPTHr+5ici6mtu1IeVgpqRCrHA+MsM\n",
       "bVuVFFQwg7/ZhSWgWC0UzaKU23mmrJbxKjickRbBtI6FtGrmVaZ1UNfHGi5vicl2UTu6YW0isVk6\n",
       "ZWOyQnpjdRkbc/Wm+TtNr9eUNdLssWr1cunZuNUylvrXVI4TtkR6a09afSxUrI1jbwmqNFxjm11B\n",
       "iiP9yObxTHtCo3sntc/VqIPxla/c2BQEgZZO2cSVh9+kXRBhoTw+lnT4lQPUXZuf4PI7XlJQQbes\n",
       "S+ya8niOUNVB0dWNPJAoMdMtXTb1Crpm6Z2UnclvqKSsg3ZRZH2jx+fclHBhTESmg50PxSpz131j\n",
       "5JbUxvhui4gQoYG1Q5NZq3ewPY2uKgs5GTq1QNnNvPyOkKo+RAk983u3PUl3bX5cde/A2qE097xV\n",
       "uuJqy/oZG7cyq6cX9NzsaNpxGKAsX1G4CuXx+u4ND9PYQVO1ORAR0aqZV8nGojNHL2bGEZGY3rHQ\n",
       "crK7aOJ6XYX42iWVpqGi2SQdA8X7aLjpbeg1JaJPq7qeuiRoJmy7sG1EDD/QKk7jT4lFjMCKseS7\n",
       "w1Pf/tWDGd9q7+P73XZORHjb0q/ozayAhnbU4nRdjuP3sHKX3pMpI+bRxOHs+Cx24HnvLr3gBrpw\n",
       "3CWmadj2ieq82xqtjfjlOx1OkpLXPq/6gdIhif55ixTPyKRZY/QOd+zCeg6SjYW0KWadhzUrpm2l\n",
       "G1f+o52qOUbtlpxf+4DIXIiT7Anl1IJARr++vamLLpqwnnlNi3LDqbWBvQ72OxyGFaERRJgTgUEP\n",
       "jGXEuBe9ZgJLZtzEO1Bi9iWixI645bGniRFRbVl/S4OolFGsviR5sWu7s7AbSRrMbln3IFNNjlUM\n",
       "T3RcJ5FxeTlv6Cy6Yv4u3ffKqso7nzYWxbbSqhZuGuHQ4tGYPjoDlTuuSUtOo04bESIUy4jTVUu+\n",
       "YXr7kskbrcvQFmly3G5aZVHaUUv93sLcYg7j80T64U2JYG0NFQMNn9sdGx5Wfc7NztflLw3M8Vim\n",
       "7AJ7yogFps8wHsukass4Oqznpq/nmvOv1TWU9NFMRXHN+dcyv79m6TeTf2kNXN1K4tLviahPRJyo\n",
       "ZrHGNdX0k7qeGc+2VInhcacstSXP+8Q+RXQ2OfOcalUUNFqmUdWEeXxgXD+rBas8Vnu8ALGltimK\n",
       "qZgLyWczYdgcWsgQKu3Xw7rvD+0/lorzzd0Fzxq9xDIfrvdBFuqVAr0+WY7UD22oVaamIP5nWWzi\n",
       "It7tPL5+Dls9WcLKxXNL3XC1qjmrTyXv3TR/J12d3OSVNiZnjV5Kk9rnam9g18W0pmqkNVxEiNDN\n",
       "qxP2TzyvpaovcrxvSs0M6dbc7AK6ePpWmjlmieKauvatDSOojuHe18uA2H4RmhpOS0biVr1Mymfm\n",
       "tcQmEN26/ge0YMI6IiK6MekyMXU5pY7A40lDORi5qyljwrboSMqdi1vX/4CxANF8TrZl37xSmjLC\n",
       "4nhUp7KgZrrCYL+koMI8LxdkxrKopZ5lt5Cq0bIpV9Ct638gf+ZaiNnYoWKpv0kRp8+S+c6naHFd\n",
       "VSUHgpTRz1DaN7GiM/erYqt3mNaAsbBjGftaTYyb5u9UTThWTByW2Ckd3TqZ7tv+b5r6Jsq1OrVI\n",
       "Vlb3VXZmjupHO1nC6xa8gsBebGTm6p4xz/BWwLIJEASqr2iisYOmqgKOrp19vaX6qp0JSmUjorhP\n",
       "MoK2giWIuAkSqbf70eeVciUr1dfXI9tUuSpjdfZ731o1Klkj3lMW76bq+7c/JcdxYjwVx7v2RPae\n",
       "qUiirHrKc9e4tpmm181UxlKF8s/ODRXNXCqZSq5Zeqfpdavn3eVjDAqJ+7c/pTLk1l4z+s08go7+\n",
       "tNpk08qgLaLRDBraf4ziBuPyqksaqCEpIESjGVRcUE6zO5cbBtx0g/LZ2nH6Y3dDiGUDunvDXhoz\n",
       "aKrpGmvhxEvp2mWJTSnleKsu33yTLF2ERhCxj/tGzIpny3Yk5QqXieV9a6ixsoUEQaC7tzzBNbhG\n",
       "GIF4UjhbEEtxNYxOW6TOplTnKMgtUiwUrYu1jWYgv3DcSpWuoukpEyeSG1+7x9DxWGZygGWfErAw\n",
       "T2Gsc6/d1RlYM5S7nlpKC6s05UgDNWm+j1BDpT1Xg8rdLbXTBeedY2TzeN13tlQykn2otb6dbdip\n",
       "yY9r7WCjsysH5qaaNhqY3F3fseIe+urKb1ve3ze3xPS68vlpF/vLpm42dEEs3eOEFdO3qlQ/25u6\n",
       "LCd8ZRXMT7kEVWKlIDKwdijXApD5LrsZoDg6hezRTt6NZiO5wvaKKIeNCC+yB7ZI1HKR6wxjByhO\n",
       "sHciYnyJdVI/bRSfKo9XLJ2yybYAbbRQTNmlFau+VV4jsj5dYQU0ZLFbczJsDmcf5UymHldY1+31\n",
       "MWaQV0bOESFCO9d8z1bePuuTJ4sw35xLjZ/2+hpvzZ2qSwZJaASRlIqLqFjkpa771VCsgeYrl9xH\n",
       "a2Yn1CB4j7Clyefi6dvo/LHLHNdHuYt5OumP3FiiTgoilQM1ErA51m1pJE1zYNJOBRweSIiIZlvE\n",
       "sbDCzdiyaf5O5gnYpvk7NQES1ZOIMrAgC7Pu01I/nO7bltrhT/n61xy91g3XD8qC7g8VSkHkgq6U\n",
       "lzezYI9WxBnuHFP9xLrx6yrsRYf1XD9eUcXSwkrasjARb6asbzVX1HcrYVvpZ17bGvk5hbqJway/\n",
       "zhy9WP7bcSsY5J+fw94VTd2W6uOuvWaZBGJjJDaukyCdiFijVZEyukflRVaqlEjU3jSOWhS2hbwL\n",
       "KNMYNlos8rx83s30lUushWOn6BxBuMyPq404YspIKpOqJCS4D/hpY3KIRKKGfWb9nB00jOWYxDD/\n",
       "xPdLJm+k2y/7kWXZxu+G5a1ERLbiY9WU9rNORIpx2KJPs1SYVdel8dHiUWjVbA1K40ijR+vYxgnj\n",
       "2maaemeTUalm8efvlSc5o80B1aPRPNO4w9htTgmNIMLCbrwCr1BGDJWwWgxJk/OYQVNUpytE9hbG\n",
       "M0YvpvVzdhAR0Y4V9ybvNz8R0cVn0NgNuGkrQ4NwdUUsk0QjGXTr+n9yXA8t5oZuNn63drFv4NSg\n",
       "tb5do4qkKorDfsdq8LanF6T1DJbYtdany8lK9Q3ljnlb4yiugV7yEmZZH65dl0QbKD2fcWE18dkc\n",
       "sL1W2UvdkrhHdYKpEzqYe4Rk1D+mdxh7L+Oul8HvVdZz6ZRNqrhIcrWS/7v1mtVU00bjh2pOHjw8\n",
       "EWHlZH5KnaBvXikNqGEZqicC015h4V2IRTSqVNO16rvmFOYWU2WxtXBshdH45LWRql3VLCPYGwIC\n",
       "1SS9TpUWVumccfhDoo4b592s+nbYgE6d23Ui67EllhG35RhEXxupzbxRsZnTucITLQYlRXnma4bU\n",
       "PrP5iW2f7Hwq6FPEtq+1+ZO13VJ2vmOSj2STaMTSqZs0alQGZSsKkZ4fazOnILeYlk29wvBefcaJ\n",
       "ayxX+8p3y6lL7SBJew1NB0ITIx+e4GjSw7h87k2yDYpRGiKinWu/p3MJy0NmLMtx9G8t8YxMObKu\n",
       "NAEZDe5nDfSPM5M71tJ9+qijfJPP/dufovKiauuEfmFSzeKCcss0jodnDuFC2tWRhEQrGxCeCf+8\n",
       "oeer8uQTxBX/M4rok5VH39z0Y+b9PPYUkpcw8zoo1Xgss/RlYKwuabBho+TtJsa9255U5660EXFb\n",
       "lmoIdL9oVDrvUNasILeI+mv80xueiDh4frGMOM0bv1rlEclN2/C0hSRomRnf3rLuQWpvGue4Hsxy\n",
       "BaWNiI0NCJvY6Q1Gc0Vrfbvaa53grsdGbCwpVAFENe0gqWyyFvtEKWcctnG4YaQ8oZFqepoRQd2o\n",
       "8VLjI0O91zUizR67nIbW6lVmrbFRh5TLRpPcBKoubZCdpLBVPvn7yC3rHtQtztV58eWjMyD3eA5Q\n",
       "5S1oP+sFkW8pY4skiQgR6tKcsPD0kUtmXCkbz7Prk8qjtX6EThVcWa90kXZBREuiOawbv6yv+Y7I\n",
       "JTO205LJlxNRwvhHu+hidcTi/HLDEwCzBzVm0FQLXT7r37Ni2paUlK69X6kvoKyTwaC6ddFt8t+3\n",
       "rHvQdgwVTenqMhntwNWFfXrvWYNvVnKHx45/d56dDfWN6t0cLxaJWUmXihbaVppqWAsAKZ/67h7C\n",
       "xnn/oM1ZUQ/vhpJ6huePRBns+gsk0JaLvkY3XHwfV/5cB2WMttLGHSFK+GXXLsx54ojwYn/CNO+H\n",
       "PKpnytLlWigXUA4Np+MZmSqPSEpPfBGly9vk/9ctv0tttKqAZ+KU3v9oNINpxyI5KmFhZMzLg/Kk\n",
       "yXpc8G9BpOTs2W7m9+VFNardfrP+VllcZ+i5Tb7f4eLasFyW2hzZWzgpY/bYQzR9fme+OK37ztAe\n",
       "S/M/86ILZo1ZSv3L7Nsp2ilaa+NnhrSByfSIqNtEM4alnZK40//3xmkZ5h4yE/9xeSazKF6qX05W\n",
       "H1Pj+eGKjZZ+VS109ZKvy/ezns/2Rbu9dw5lQegEEWUDWHUDsx2R0a2TDXzDG5fnFOvB17pDV5XU\n",
       "M13krp19vclpC7vuhUljWoHM3Rf3BsoL6nQDcHZmH7pv27/Z2jG7fO5N8t9ckVyT/0t7Ib9ZAAAg\n",
       "AElEQVSLDqsFhy1BRSPkmAoZ8v9s1SxlPm4xi4PDNbnwtoGFpzZdtiRSLCNO8ZjedoWZPZ/um44l\n",
       "UzbS7ZftNa6HFBU5Wf+S/HJdWfYXasr0NuwsVGkMt2n5aiCo6+3FidaMUYtp5cwr5c/D+o/RuZqu\n",
       "LetvePJtz2sW+3eObpnE/P7rG/+FOh14L5owbI7uu9qyfhSLGo9DdrqD0Xtwz5afWN57VmQLInaI\n",
       "RKI0YuB5pmliHO9gytbAukz1c7ZuLG2QR4EERzZNPAxu7KDBDdoNLKvVI+cDl9Q8te+a595D+eoz\n",
       "deR8mmqgVWK7yICEb1WZuiLN1cLcYDZP8grQdWUDqK1xlPl8oVFxM6K2TGMDxMpTue4WBLp4xnbK\n",
       "5gga7hUhEERYngJYqdJt158e2k30FI0Wt1avlqeL5sQdNtP7D++Cj5WMSxBJThDSRGEVuMwOEYPy\n",
       "ma2s8d7Fhl9tyg6C6m+pjOAnGV7c1jGekak38ld590o9oTs3/ZimdVxE+reRvUMoj282DNmvW343\n",
       "XXbhjTxVT9XRxBGF3oheKeZ6ffql7s2RSJQaDdRwmHfzBBKTDNvNolEzyMnMdSRsSc44lG1VXzGQ\n",
       "7tpiZsvA3xdZgeeIzGPPSJw96934xEKK0Lxyxna64eJ7ue4xU81iIQgCtVsIQpJ9pRcY97FEXZtq\n",
       "2ujyeTeprxj9DgsPdozCiYh0myvaGo0bMkt2qODnAn/eeWto7riV1gk5FsfezBH8pyrsOnhQBQOG\n",
       "9h/L5b3LbAy7dvm3aNwQc3fVZtiNEK+tSXtTF40eNMVx+XYJgSDSQzA1ZTFvRr86fXlRjUWB7ILr\n",
       "ygc4XkwEIXLYHVDtCE4jBzrRo9UjNXFEiFBedgGHUT9HHXVCBc/JjDTBcWTvcqIy6zP+ugj0yFid\n",
       "S2hzQ6qeWfHspFoB78KD/bXK0FGTprasHxXla088mZI1EZGtmC1EKa9TgqA+wvdisedWlZH3/sWT\n",
       "L3dmS+AAr+wE/cBINUuL/Q0/dfrc7AJLVWC5T/M8Q008hCkj5lnURjT9bA9z1Swl0rtlpj6a/MMW\n",
       "MYaHQiVLp2yU3d07IR2nEymcPxuvNrz82DgTBCFlw6qBJ9ipJjeTK8bzmfa5Zmf24bIJXT3rGlk1\n",
       "mh3k1R/SLojo93hE3fgUy4hzGaeni6BeZaldJP3CiqJaWffZbKdTy9SRC+g+jYGtqhzb9eLYnUzr\n",
       "gKdA99I6rVdSAIhE6PYNey09odiJJ8Bl9yFoJzaBRg4cz9Sp92qsrSsfQJsX3CJ/bqhsptzsAmqu\n",
       "G0bDBkiuLD1QzdJQUVTn6D4jePqimTqNOq8UzPeA22tWCqXLXvX97hbvur5h0AySoBFRCiKKxLxB\n",
       "DM0w/SU2F6hERs9UoPFDz2ecjBgTcege9ubV30m1r433ze9xccygqURE1O3hia1tdKqW4TtBN4ZV\n",
       "V/13/ZKOHqyep+pkMfk3014g2WZlWsPiNKlm2YXnGXvtsY2H+ePXElF61iM7VtxLK2ek1FF5TwEt\n",
       "03Dc99VLvi2fVLJ+e3Vy82Bk83j5hHVax0X247I4xKVTbvfk56ijBY8bMoukF31ye2L34+bV3/Fe\n",
       "cpUmJ0+yCrZTD27soJfeOmB4PczqMTz0hIlKepl5XIQm4BHW1HmbIcWbUaYd3NhhbnTvsl9EhIjs\n",
       "f50oocO/e8NeIkp45dn/6i9d5W+EUfR3GZu/i+f9iGXEadW4myzTKZ8qS9g0e5YlBRV0/MTRZD6p\n",
       "e8cOmka/+H9PJO9XlOVw4jY2oDVvB8n+SWnUeNfmJxzVQUsGhzqRGX6MEdcsvVP2WMhiYM0QWjv7\n",
       "eua10sJKOnHyb/YL9Xmsvnj6Vvr9a//JfSJCoujKrtCe+17FfTzqqOqXgZneKs6InX7DKmL9nBuo\n",
       "tqw/o9zkPGD08+XNa32CScMvpKZkUFUtzXXD6FubH0vVyVw1w/iaebVsEYb5WZ4ruX+zXi13xqhF\n",
       "Np13uKO6tIE+P/OZhzkan4hog2CznG8o72rrN0rn0CMjGjM82fGatAoiLE8mc8etpHc/fJuIiGZ3\n",
       "LieihC/1dGP28nlhrM6D/XHGA0N8XZYsr1mi4u9g8Nw7izoRd/m++Og20CdWtnNd+QC6df0PiDXA\n",
       "6rILYPeHx7B+0/x/oC+7v3RVihsE8rt/sk5EtB9TXxTkFsuCiBGe2GOo3A3xtIC2bwtyHrEMDm8v\n",
       "Fly3/G5drCWJ0sIqVewbI5wIZdp3RGvEzIxXoCAazTC12ZPLsdFPvXwzzcrltWETiSi/T1/m3OwX\n",
       "9RUDDRfiSnjaNTc739SVqRVaNSdtP0ud/KqRTw8thH61rVXi73gs09Q+ihVAdro25g8560t+bVry\n",
       "PCsjuzg/UaozXdB1SWDlOoXPcQ5LNSvtyk62SPuJCItgj+w4yzKoU3vTOBo+wHxycv+yS6oF5nXx\n",
       "DNFYsBg2oJM+/Ph9f8uXyzb7nak2rShooI8//8BRGeyXmEsSISL9zoMRdh7ZgvFr6Y4/H7QcoAty\n",
       "i+jL7i+sM5QFGzt4f8rA5cXOTwSB7t/m7QJLvUmrX+zxOT4wztTrhcKczouppb6dnnruh2T1jFOq\n",
       "Wd7WQ+fFRcGOFfdw2htpVLN47lG8hLeu/wFlZ/axvMcWDpqootiO2qHG/kEzqHztUuOAsSUFxu49\n",
       "vcBR/0jW/5qld1qmSZbCla2ZK1Or97Eov4zu3/4UbbtvPtnZ+0/p/lvU0cC5hd16Vpc2cNbMCien\n",
       "KILrU5Hq0kZ3NlWO5jS7RXifu/KZ23G4YXbN3EUy60bLYgMnRIJIsK0jDRxuhZ61s68zvb5p/k7X\n",
       "x39D+6t3YXhr7Ie4smjSZcEUZIMB5cNo2Zz1fIk96mZSNrwnIjw7ktLgYbRbzJJmJFUEOwJJUAzt\n",
       "P4Y++Ogv9m/0QdAWhAif73YXsMcSdZsrJ4hJwy+kt98/rEntQRBEkxrUVzRRZXEdPfXcDy0n2pRH\n",
       "OHuB6tzA64JZ6iOzxy6np1/QB+y0wk2cEGv4np/dU4fqkkaaxtgJZ6Hsi/ds/amNccreu+dk/nT6\n",
       "dgetcZw4meOrrVJoZ+P/wjmoNZSZEBKL8r2/O1bc41V1bCEEIMCYUd632pVzAV74TtIFCotUEiJB\n",
       "JDhuXPmPtn2LOx08W5Ou9dygVYfI5fB+4BXh6KbeoVvkMf338uxiCzTvvNXUWj/Co5rpy+dpe6fG\n",
       "bH6hXJdUFNXS6llXB1i6MTetesB32ynWBG3mNUtS8xBI4FrQeXZSbFAloxMrUTxLF8/YRn/79ENv\n",
       "yvcAqS2kmEkseripnI54LJPPhaoGXk89pYVVgc4tXAbNBmmcvgm8O/myExjOd04ptLNIOULUq2bZ\n",
       "wfwUxT5eviO7NzwcWP8JjfMbm+T36Uu3XvoD38vpaXbC56QgYuj2NiQU5ZXSQBOd2dLCKq5osUGp\n",
       "uC2YsM5RADBL0uBVg4h3QBdsBnhS/5bbL/sR/fz3j9NzLz/NyJlthJaZjBiv5esb/8Xcq5xdH/bp\n",
       "xq7xOUcaM3UNr+DxmmVEvsrrWuIepZEqL/kW3tuUaGtmpCpxVuym0sLKQNqQFzeqIVcuvsPDmqTg\n",
       "sZMKM811w1wsYByo+Ni2fwp3w9606gFLGyreMdgolfeG4t61qVIIyYxlyR7bfIU3XhiHLSXrrnRj\n",
       "Vl9ToZTDZjRMwso5KYiEncx4Nm1ZeKtJCpHzRCeYhXzfvBLqm5fcmTQMshiOTq8L2maS1svdJ21O\n",
       "eTmFXIHIlCyftpn5fbhcW3vQ59IkgDpC0Z9YR+468w+DwV8pZEpJWEaqVjTXDaM7N2lUlSyCrFmR\n",
       "DjebVkh1crIwk1ytgvRx/Yq7qU+W9e653aCH6cTM45qEv7/Bmb2HH0QiUbp4+lZf8iYiVzLCV1d+\n",
       "OxTrJ76+4OyH+uJEx0cgiPASgsm4JCBXal7vutRXDKQsg938nord3bzspLtdJUZ2I4LBCYZTgcPJ\n",
       "Dojf9hROMKx+SBYoTG9DHHFrsjR9w2io4X0vrd4168VHqpyivFKuQFhBIwtHIRiX9QSlq99DEUWq\n",
       "KTV2WGBEOt/yovwyRxsDEp51Uz7/LfyEY+h0jH1BSgjUZa8ZfMbqpjmY3Me3PgnL4w+lIBLGHbh0\n",
       "o1zg8LZPWpqR8eZctfgOzxeLnuXm1A2wzfuqSxtp94aHVd/pn2MqT+XzLi+qpaVTNtmuo5KVM6+0\n",
       "TqSgKL/UlRvMQAnxeGE1Ud695QnfhT6ncUSIiHate9Dr6njC+WOX0Y/+41u27vF/XgnLtB5eCnKL\n",
       "qdKOpzCV06zg21fqM7nZ+Y5UJSW03hUXjF9HA2rajG8I6LeGYVHuTH7qGe/aggnrXObgx/okfG0X\n",
       "SkEkyL0e7kV9iPafwlMTPuw6BuDC1zgiiTTuYsfo0Rvy8T3JaCRK44bMtF2ehCAINKplku37nNgE\n",
       "YBNBjU4VUNNtdEKIIBh2becBDQ2+sfDwE2by+/S1TpQm0qZCJBp+CA03r95jO8bBwomX0k9/95B6\n",
       "7Hb4LlTYtg/1ph2jkahqc2nyiLmO8jFdh9isapCxYswIY08t6FNEo1snu86nT1ae4bW2xlGWLsSd\n",
       "ChQTh1/ApSoYFkIqiARHVUk9V7otF91Kp878n8+14YNf/8+DV9zupNrDFqIswWRY/7H06f99Ynmn\n",
       "W7SRuEOiYeQSd8+/f9Ugam2w6YksTQ1XVlhl6lSCjUVdRTEEr1DaK8BNz6mpD5h0lFljltHgxlEB\n",
       "VoYPu+pNIonU0TKRfvq7h1yXfe+2J3vMTroh6R8cQoLVZoq75CtnXkUDa+2O7YxiTeamueetsr7f\n",
       "9KpxXyjMLabOwdPM8xYEaqlvp7EW6YIglIJIkK/awNqhXDsDZX2rAqiNNdsX7aba8v6+lpGfk9pt\n",
       "dKM2khXPsSe8BbGg5CjjkhnbiYjouZf/w0021vTCScXtT9q+eLc3FQmAm1bv4Uq3YtpWeuRX3yYi\n",
       "t7vlDhvXoEyBBCrILaZh/dnRonsiFUW1dPRv76albEFe7KR/sZubne+J63he4hlxqjEJVOkJLpvV\n",
       "iQFv2Ibosr7V9PHJ4+muhqek2+2wFfPHr00GgE0Hxj/U6dpMOQf1zSuhFdO2OMrHS0IpiABj+lcP\n",
       "4k7rRJXj9sv2JgM5JRjdMomqSxps50MULnU2IqL549dQS516cnY+oLkfCaHG5A1hWPiZMXbwVHri\n",
       "N9+jL7rPpLsqRKTs8wLdup4VjTvc7alG/Q59deW3k1Gx00hPaj6PiESidP3yu73PWBRTzjYUDcsz\n",
       "t3gRATxsc9ja2ddR99nudFfDU2LRuON7bY/9gZ+e+1deLCMeGvU6t4RSEMECLX3k5RSoPkejGVRX\n",
       "PiDQOkiDi7mDEPsv+JQRrAWKST6m7ns9EERI6zWrN6xg/Hx32e2TYdMNcjq4a8vjtO2++a6esNNx\n",
       "sTC32EWp6cXqF9tpk7AtKoFd0jA+hmwtEsuIU/j8GTonEXvFvjeyIDef0rnR5Ye9mSD/H571Rvhn\n",
       "cNCjmD9+LZ358hQRJdQkTpz8KM01Msfpi+7FABGyOa5H8tWV39a5vw03wQ/+S6ZspLnjVutrEp55\n",
       "yDZ8Akh6dj/DNMGHAdfKiJLKWzq8ZgVeYoJzpQ8FZVCdrvZ0X6oPgkgIY4yEVBDBCs0L0nGydN7Q\n",
       "WfLfWy+61TBWBos+WWEKzGeON4KIum3OlcnHS8LgftIrJg6/gIY3dXmebzwjU2UkzFJ1CSvhr2H6\n",
       "8PqEJ5T9wcUc1ic7n7q7v/CwMmHnHFo3Cal9fR6ifnjuDAA/ZG8hZcwWGkIjiCgXdtgp7h3EY/aO\n",
       "XGeOXkpdbTPov999xTJtT97NldH8iEIpOn0PBuovxlx24VepsbLZ8PrCiZcSEdHfPv1Qd214UxfV\n",
       "lTf5VreeSjhdVKZncOrt757dVt1x8T0erM17d5ueC1y99E6qKq6nnx34V25hOzzrCz9ORELz42RC\n",
       "I4jALsR7etrEFMuIUVF+WbqrwYUXL/O8cato7KCp8ufOwdOo3YcdcRAOhvQb7fjedbOv97AmSUI4\n",
       "IWkxG8Hu3/4UffrZx4HVxYowTvA9HZFSxurK/soztxX0KXJffrrWJehKpthpnoaKgb7Vw298sRGB\n",
       "ahYANgixcOqFGkOf7HzqpwhyKAiCZYCjsBPiRwYkBEk16xwjoL55Lskj0kK9IIAAk6FUHQsR5+LQ\n",
       "a2ehXpRXSg2VDoQSF93OrSDhR48X5PE/PO9TaAQR7CaBdJCXXWB4zXRgR38FvoG+JWHdEvxt1Sfb\n",
       "OMoxcM5dm5+gWIafvpzCp9N+LnP9Ch/cNNvFwfy7a92DPlTEb/zwmhW+Fyk0goiac1G2dwfrCLl3\n",
       "q7t58zJNHbmARg+a4qD08L3M4aA397mgSN/WfUFuMVWV1AdTPgfWLcHfVh0tE6m5dpib6pgiMP7y\n",
       "lZC8av4KIecmYZ5fakp9Dlxpg/C2UniRNv3DpLofUkEEgGCIRjMcxVnACR4bP4VftLk3mLUiO8Bh\n",
       "7yAiRKgg173dQFiJRtxN5/kBqFfZRRTFtKqSpGszLyvTiUvy8Cws/abnxBFxqZrl45wXpo3qUAoi\n",
       "YWqgnk3PbMec0LjxNW6/8qKaAOsBgPeEedeVn/D9hnQIzF9b/0+6YLR2uP2yH1FOlj3VtfamcTSo\n",
       "YYTjMu2jaNeApraSgopgClLwD2u+S32y8q0TAuCCMK2zXZvP79q1iyKRiOpfVVWVF3UD5yg83oXS\n",
       "uTt+//anaED14LSVD4ArpB3mHnDCZF3D8Eym6bQbc3KqqyQvp9B2rIW1s6/z3X1ywmtWgnQ0b0v9\n",
       "cLpv278FWmZJQQVlOzoRCf/77BVBjl1uNh1dG6vjRISflpYW+u1vfyt/jkbdBo8JTwP1ZMLU0ewQ\n",
       "Rh1GAHoNPWhcMKrp2bPdlvf23GjKgEXanmcPENiJiHLicMbgB6317XT/9qfSUnZ53xoaN2SWdUIH\n",
       "hGl95YkgEo1GqazMu/gP4WkeAIAdeqrwGybisSx/C+ghCyszsuLZyb/0vyUvu4D+/vmJYCuUBsK0\n",
       "kPANkXpFfw0CQRAoN6uQTp76JN1VAR4Rj2XS0ikb/ck8RHO1J5FN3nnnHaqurqZ+/frR8uXL6ciR\n",
       "I15kCwDoYfTtBdHh001udj7dtflx3/KPCBH65hWP+pa/39y//Smql4OU6SfT2zfsDbZCSViB94Bz\n",
       "SgoqqLGqJfUF2tWSWW2r6B/WfDfd1QA9gLMhEkRcn4iMHTuW9u7dSy0tLXTs2DG67bbbqKuriw4f\n",
       "PkxFRWwPJX/4wx903/3147fla0dP/NkwHWDzl4/eIiJ1m7355pv0+UfpqpF7hO6YYR84cuQIRT5L\n",
       "HUXz9BW7/ekvH/zF0X3nKqvG3UT//frbvuX/+uuv0/H3PvUtfyPw/NPH8ePHicj4GXx+5qTh9Xff\n",
       "fZf+cDa4Z3f6y8+JiOjQwUOUGcu2SO2+X504ccKTfPzm6NGjRGS/nucPXk9ERAdfPEhERH/84x8p\n",
       "kowKffr0qdD/7nSQk5lP//Pme/Q/9F66qxIILx48SLFo3PN833jjDTpx9LTrfN555x06+6nPJ9wO\n",
       "efXVV+j9Pse40jY1NflaF9eCyKxZKf21trY26uzspMbGRtq7dy9dddVV3PmERzbrmZTkVVFlYWO6\n",
       "q+EZS0ZfRdGIsX/6IPSFQ7RhAADoKQS0cR+LZgZTUJrQ2mb0Di9vAAAtnrvvzcnJocGDB9Nbb71l\n",
       "mKajo0P3XZ8/R+k/X0tce/O9THrmVXY6YMyErsny3w8/T9R/QH8a0q/3teHDzxM19mukjpYOeVfM\n",
       "qK88/Hzqb7v96bNDR+m/jqAfhoGHnydqbW2lBlklx3+s+hbwnzc+PkBvf2j8DD797GN64r/01x9+\n",
       "nqi2rpY62oN7dv93+iQ99nui9uHtpi7IvepXg4cMopOfn6DSwkpX+fjN0TN/olfec/57z3x5mh55\n",
       "IXG/IAj00tGxVFFci/dSw7k2Xj38PNGI9nbKjFufPtrNt7m5hZpq2lzn0z6kg/pXD/KoZt7x8PNE\n",
       "gwa1UnUp3+a1dPrqF54LIqdOnaLXX3+dpkyxH60aAACMwH4o6BEE1FGzM3Mcunnt2ay/4IZ0VwEA\n",
       "S+7a/DjFMrxXG/OKMDm7cG2sfu2119Kzzz5LR44cod///ve0aNEi+vzzz2n16tVe1A+AtJEVP/cm\n",
       "eQB6FhBPzxV6ihtdEBzhWUrrCbMQQhQuD5euT0Tef/99Wr58OR0/fpxKS0ups7OTXnjhBaqtrXWc\n",
       "Z4jaB4SUiOA2Vo01o1omUmNli3VCAMA5j2TDAFsGNU01Q+jgfz9vndAIrAdAwGR5rO4VNqpLGqg4\n",
       "vzzd1ZBxLYj8+Mc/9qIeKmrKGqmjZaLn+Z5rSB5GehvbF+2mhspmrrSXzNhOv/7jU/TXj/5su5xI\n",
       "JEplfats3wcAACBBc90wunnNd9JdDQC4uHX9D6ggl+3xtbew4+J7010FFaFcqeZk5tKqmfwet4Ce\n",
       "q5feSa0NI9JdDV/oXz2IohG+E5HRrZOpqCA8kj8AoLeDExEvCZMuO+j99HYhJIx4bqwOwkGQ3oUA\n",
       "AAAkVbNgywCA73S1Tad4yO0wAB8QRAAAPQKv3TQCAADomSybujndVQAeAUEE9HqmjphHNSW9J9jj\n",
       "ucjtl+2lvJyCdFcD9CDSZTSO8xBvyYhgmQJAbwZvOOj19K8eTP2rB6e7GsAFEEIAi1hGLN1VkIFK\n",
       "lj9Eoxl0//an0l0NAIBPhNJYHQAAALAiO7MPfXOT954bXQGBBAAAuIEgAgAAoMdiZDtUUlARcE0A\n",
       "AADYBapZAAAAehX3bv0pRThdfHuFIP+PExEAAOAFJyIAAAB6FUELIQAAAJwBQQQAAADwChyIAAAA\n",
       "N6ERRHCcDQAAQIXYg6Jqw0gdAABsExpBRKQeNOEAAAAADLCpBgAA/IRGEAEAAABU4JQBAAB6NaER\n",
       "RLCLBAAAoKciKPxmAQAA4CM0gghUswAAAKjoSTYiAAAAbBMaQQQAAADo6UCbDAAA+AmNIALVLAAA\n",
       "ACp60qq+B1UVAADCQmgEkVhGLN1VAAAAECZ6oGoWNtUAAICf0Agi/aoG0Q0X35vuagAAAAAAAAAC\n",
       "IDSCiCAIVFXSkO5qAAAAALaRT0J6kjoZAACkmdAIIgAAAIAKLOoBAKBXA0EEAABAOOmRNiIAAAB4\n",
       "gSACAAAAuAaqWQAAYBcIIgAAAMIJFvUAANCrgSACAAAgnPRI1SwITwAAwAsEEQAAAMAlOLwBAAD7\n",
       "QBABAAAAPEKARAIAANxAEAEAABBOsKgHAIBeDQQRAAAA4aQH2ogAAADgB4IIAAAA4BLITAAAYB8I\n",
       "IgAAAAAAAIDAgSACAAAAAAAACBwIIgAAAAAAAIDAgSACAAAAuCQawXQKAAB2wcgJAAAAuCQSidL9\n",
       "259KdzUAAKBHAUEEAAAAAAAAEDgQRAAAAAAAAACBA0EEAAAAAAAAEDgQRAAAAAAAAACBA0EEAAAA\n",
       "AAAAEDgQRAAAAAAAAACBA0EEAAAAAAAAEDgZ6a4AAAAAwGLc0FnUJzs/3dUAAADgExBEAAAAhJKG\n",
       "ioHUUDEw3dUAAADgE1DNAgAAAAAAAAQOBBEAAAAAAABA4EAQAQAAAAAAAAQOBBEAAAAAAABA4EAQ\n",
       "AQAAAAAAAAQOBBEAAAAAAABA4EAQAQAAAAAAAAQOBBEAAAAAAABA4EAQAQAAAAAAAAQOBBEAAAAA\n",
       "AABA4EAQAQAAAAAAAAQOBBEAAAAAAABA4EAQAQAAAAAAAAQOBBEAAAAAAABA4EAQAQAAAAAAAAQO\n",
       "BBEAAAAAAABA4EAQAQAAAAAAAASOZ4LInj17qLGxkbKzs6mjo4P27dvnVdYAAAAAAACAXoYngshj\n",
       "jz1GV155Jd1000106NAh6urqovPPP5/effddL7IHAAAAAAAA9DI8EUTuvvtuWrt2La1fv56am5vp\n",
       "/vvvp8rKSvrOd77jRfYAAAAAAACAXoZrQeTMmTP04osv0owZM1Tfz5gxg/bv3+82ewAAAAAAAEAv\n",
       "JMNtBsePH6fu7m4qLy9XfV9WVkZHjx5l3nPixAm3xQJARERNTU1EhD4FvAd9C/gB+hXwA/Qr0FOB\n",
       "1ywAAAAAAABA4LgWREpKSigajdKxY8dU3x87dowqKyvdZg8AAAAAAADohbhWzYrH4zRy5Eh65pln\n",
       "aOHChfL3v/zlL2nx4sXy54KCArdFAQAAAAAAAHoJrgURIqKrr76aVq5cSaNHj6auri767ne/S0eP\n",
       "HqWNGzd6kT0AAAAAAACgl+GJILJkyRL66KOP6LbbbqMPPviAhgwZQk8//TTV1tZ6kT0AAAAAAACg\n",
       "lyGIoiimuxIAAAAAAACAc4tAvGbt2bOHGhsbKTs7mzo6Omjfvn1BFAt6CM8++yzNnTuXampqKBKJ\n",
       "0N69e3Vpdu3aRdXV1ZSTk0OTJ0+m1157TXX99OnTtHXrViotLaXc3FyaN28evf/++6o0H3/8Ma1c\n",
       "uZIKCwupsLCQVq1aBVeHvZg77riDRo0aRQUFBVRWVkZz586lw4cP69KhbwE7PPDAAzRs2DAqKCig\n",
       "goIC6urqoqefflqVBn0KuOWOO+6gSCRCW7duVX2PvgXssmvXLopEIqp/VVVVujRp61eizzz66KNi\n",
       "LBYTH3roIfFPf/qTuHXrVjE3N1f8y1/+4nfRoIfw9NNPizfeeKP4k5/8RMzJyRH37t2ruv71r39d\n",
       "zMvLE5988knx1VdfFZcsWSJWVVWJf//73+U0GzduFKuqqsRf/epX4osvvihOmjRJHD58uNjd3S2n\n",
       "mTVrltjW1ia+8MIL4oEDB8TBgweLF154YWC/EwTLzJkzxR/96Efi4cOHxVdeeUVcsGCBWFFRIf7t\n",
       "b3+T06BvAbv8+7//u/jzn/9cfPvtt8U333xTvPHGG8VYLCYeOnRIFEX0KeCeAwcOiI2NjeKwYcPE\n",
       "rVu3yt+jbwEn7Ny5U2xtbRWPHTsm/zt+/Lh8Pd39yndBZPTo0eKGDRtU3zU1NXrwg4cAAAXhSURB\n",
       "VIlf+cpX/C4a9EByc3NVgsjZs2fFiooKcffu3fJ3n3/+uZiXlyd+73vfE0VRFD/55BMxHo+Ljzzy\n",
       "iJzm3XffFSORiPiLX/xCFEVRfO2110RBEMT9+/fLafbt2ycKgiC+8cYbfv8sEAJOnjwpRqNR8Wc/\n",
       "+5koiuhbwDuKiorE73//++hTwDWffPKJ2L9/f/G3v/2tOGnSJFkQQd8CTtm5c6fY1tbGvBaGfuWr\n",
       "ataZM2foxRdfpBkzZqi+nzFjBu3fv9/PokEv4ciRI3Ts2DFVH8rKyqIJEybIfeiPf/wjffHFF6o0\n",
       "NTU11NraSgcOHCAiogMHDlBubi51dnbKabq6uqhPnz5yGtC7+fTTT+ns2bPUt29fIkLfAu7p7u6m\n",
       "Rx99lE6dOkUTJkxAnwKu2bBhAy1evJgmTpxIosKEF30LuOGdd96h6upq6tevHy1fvpyOHDlCROHo\n",
       "V554zTLi+PHj1N3dTeXl5arvy8rK6OjRo34WDXoJUj9h9aG//vWvcppoNErFxcWqNOXl5fL9R48e\n",
       "pdLSUtV1QRDQF88htm/fTu3t7fJAib4FnPLKK69QZ2cnnT59mrKzs+nxxx+n5uZmeeJGnwJOePDB\n",
       "B+mdd96hRx55hIgSz1wC4xVwytixY2nv3r3U0tJCx44do9tuu426urro8OHDoehXvgoiAPiJcpBm\n",
       "IcIhHEhy9dVX0/79+2nfvn2W/YYIfQuY09LSQi+//DKdOHGCnnjiCVq2bBn95je/Mb0HfQqY8cYb\n",
       "b9CNN95I+/bto2g0SkSJPsHTL9C3gBmzZs2S/25ra6POzk5qbGykvXv30pgxYwzvC6pf+aqaVVJS\n",
       "QtFolI4dO6b6/tixY1RZWeln0aCXUFFRQUTE7EPStYqKCuru7qaPPvrINM3//u//qq6Lokgffvih\n",
       "nAb0Tq666ip67LHH6Ne//jU1NDTI36NvAafEYjHq168ftbe30+7du2ns2LH0wAMPyPMa+hSwy4ED\n",
       "B+j48eM0ePBgisViFIvF6Nlnn6U9e/ZQPB6nkpISIkLfAu7JycmhwYMH01tvvRWKMctXQSQej9PI\n",
       "kSPpmWeeUX3/y1/+krq6uvwsGvQSGhsbqaKiQtWHTp06Rfv27ZP70MiRIykWi6nSvPfee/SnP/1J\n",
       "TtPZ2UknT55U6SoeOHCAPvvsM/TFXsz27dtlIWTgwIGqa+hbwCu6u7vp7Nmz6FPAMQsWLKBXX32V\n",
       "XnrpJXrppZfo0KFD1NHRQcuXL6dDhw5RU1MT+hbwhFOnTtHrr79OlZWV4Riz7FjeO+Gxxx4T4/G4\n",
       "+NBDD4mvvfaauG3bNjEvLw/ue4HMyZMnxYMHD4oHDx4Uc3JyxK997WviwYMH5T7yjW98QywoKBCf\n",
       "fPJJ8ZVXXhGXLl0qVldXiydPnpTz2LRpk1hTU6NyLdfe3i6ePXtWTnP++eeLQ4YMEQ8cOCDu379f\n",
       "bGtrE+fOnRv47wXBcMUVV4j5+fnir3/9a/GDDz6Q/yn7DfoWsMuOHTvE5557Tjxy5Ij48ssvizfc\n",
       "cIMYiUTEZ555RhRF9CngHRMnThS3bNkif0bfAk645pprxN/97nfiO++8I77wwgvinDlzxIKCgtCs\n",
       "sXwXRERRFPfs2SM2NDSImZmZYkdHh/jcc88FUSzoIfzmN78RBUEQBUEQI5GI/PfatWvlNLt27RIr\n",
       "KyvFrKwscdKkSeLhw4dVeZw+fVrcunWrWFxcLObk5Ihz584V33vvPVWajz/+WLzkkkvE/Px8MT8/\n",
       "X1y5cqV44sSJQH4jCB5tf5L+3XLLLap06FvADmvWrBHr6+vFzMxMsaysTJw+fboshEigTwEvULrv\n",
       "lUDfAnZZtmyZWFVVJcbjcbG6ulpctGiR+Prrr6vSpLNfCaIIKyYAAAAAAABAsPhqIwIAAAAAAAAA\n",
       "LCCIAAAAAAAAAAIHgggAAAAAAAAgcCCIAAAAAAAAAAIHgggAAAAAAAAgcCCIAAAAAAAAAAIHgggA\n",
       "AAAAAAAgcCCIAAAAAAAAAALn/wMALRXWQKjaIwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4808fdfcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sense_t():\n",
    "    return 10 + rand_student_t(7)*2\n",
    "\n",
    "zs = [sense_t() for i in range(5000)]\n",
    "plt.plot(zs, lw=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the plot that while the output is similar to the normal distribution there are outliers that go far more than 3 standard deviations from the mean. This is what causes the 'fat tail'.\n",
    "\n",
    "It is unlikely that the Student's T distribution is an accurate model of how your sensor (say, a GPS or Doppler) performs, and this is not a book on how to model physical systems. However, it does produce reasonable data to test your filter's performance when presented with real world noise. We will be using distributions like these throughout the rest of the book in our simulations and tests. \n",
    "\n",
    "This is not an idle concern. The Kalman filter equations assume the noise is normally distributed, and perform sub-optimally if this is not true. Designers for mission critical filters, such as the filters on spacecraft, need to master a lot of theory and emperical knowledge about the performance of the sensors on their spacecraft. \n",
    "\n",
    "The code for rand_student_t is included in `filterpy.common`. You may use it with\n",
    "\n",
    "    from filterpy.common import rand_student_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary and Key Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following points **must** be understood by you before we continue:\n",
    "\n",
    "* Normal distributions occur throughout nature\n",
    "* They express a continuous probability distribution\n",
    "* They are completely described by two parameters: the mean ($\\mu$) and variance ($\\sigma^2$)\n",
    "* $\\mu$ is the average of all possible values\n",
    "* The variance $\\sigma^2$ represents how much our measurements vary from the mean\n",
    "* The standard deviation ($\\sigma$) is the square root of the variance ($\\sigma^2$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor\n",
    "\n",
    "[2] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}