Bootstrap.ipynb

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  "name": ""
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "from joblib.parallel import Parallel, delayed"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def bootstrap(data, agg=np.mean, n_bootstraps=10000, seed=None, ci_width=0.95):\n",
      "    data = np.asarray(data)\n",
      "    rng = np.random.RandomState(seed)\n",
      "    n_samples = len(data)\n",
      "    all_aggs = []\n",
      "    for i in range(n_bootstraps):\n",
      "        idx = rng.random_integers(low=0, high=n_samples - 1, size=n_samples)\n",
      "        all_aggs.append(agg(data[idx]))\n",
      "    boostrapped = np.asarray(all_aggs)\n",
      "    boostrapped.sort()\n",
      "    \n",
      "    ci_min = (1 - ci_width) / 2.\n",
      "    ci_max = 1. - ci_min\n",
      "    ci = boostrapped[int(ci_min * n_bootstraps)], boostrapped[int(ci_max * n_bootstraps)]\n",
      "    return boostrapped, ci"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bins = np.linspace(0, 1, 30)\n",
      "data = np.random.uniform(0, 1, size=10)\n",
      "_ = plt.hist(data, bins=bins, alpha=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x3652b90>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "0.47800950435078776"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bootstrapped, ci = bootstrap(data, ci_width=0.99)\n",
      "_ = plt.hist(bootstrapped, bins=bins, alpha=0.5)\n",
      "ci"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "(0.19418497980251903, 0.77660497016829755)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x3771dd0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def unbiased_std(x):\n",
      "    return np.std(x, ddof=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bootstrapped, ci = bootstrap(data, agg=unbiased_std, ci_width=0.99)\n",
      "_ = plt.hist(bootstrapped, bins=bins, alpha=0.5)\n",
      "plt.title(\"Bootstrap distribution for the std dev of a uniform variable\")\n",
      "ci"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(0.19711553043302424, 0.46172529784033078)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pt0P5RERkqy6fI9i8eTP8/f2xZMkSVFdXAwBKS0uh1WqlebRaLYxGo1m7RqOB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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3904e50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Evaluation of the correctness of the bootstrap CI for the mean of a uniform variable"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%time\n",
      "\n",
      "target_ci_width = 0.95\n",
      "\n",
      "\n",
      "def compute_ci_correctness(n_samples, true_value, agg=np.mean, target_ci_width=0.95,\n",
      "                           n_runs = 100):\n",
      "    correctness = []\n",
      "    for i in range(n_runs):\n",
      "        data = np.random.uniform(0, 1, size=n_samples)\n",
      "        _, ci = bootstrap(data, agg=agg, ci_width=target_ci_width,\n",
      "                          n_bootstraps=5000)\n",
      "        correctness.append(float(ci[0] <= true_value <= ci[1]))\n",
      "        \n",
      "    # Look Ma': boostrap CI on the boostrap CI correctness\n",
      "    _, ci_outcomes = bootstrap(correctness, ci_width=0.99,\n",
      "                               n_bootstraps=10000)\n",
      "    return {\n",
      "        'n_samples': n_samples,\n",
      "        'correctness': np.mean(correctness),\n",
      "        'ci_0025_correct': ci_outcomes[0],\n",
      "        'ci_0975_correct': ci_outcomes[1],\n",
      "    }\n",
      "    \n",
      "\n",
      "all_outcomes = Parallel(n_jobs=-1)(delayed(compute_ci_correctness)(\n",
      "    n_samples, 0.5, agg=np.mean, target_ci_width=target_ci_width)\n",
      "    for n_samples in [3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100])\n",
      "    \n",
      "all_outcomes = pd.DataFrame(all_outcomes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 44 ms, sys: 20 ms, total: 64 ms\n",
        "Wall time: 11.8 s\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_outcomes(all_outcomes, target_ci_width):\n",
      "    plt.fill_between(all_outcomes.n_samples.values,\n",
      "                     all_outcomes.ci_0025_correct.values,\n",
      "                     all_outcomes.ci_0975_correct.values,\n",
      "                     alpha=0.2, color='b')\n",
      "    plt.plot(all_outcomes.n_samples, all_outcomes.correctness, 'o-',\n",
      "             alpha=0.8, color='b')\n",
      "    \n",
      "    plt.hlines(target_ci_width,\n",
      "               all_outcomes.n_samples.min(), all_outcomes.n_samples.max(),\n",
      "               linestyles='dotted')\n",
      "    plt.ylim(0.5, 1)\n",
      "    plt.title(\"Correctness of the bootstrap CI interval\")\n",
      "    plt.xlabel(\"Number of source samples\")\n",
      "    plt.ylabel(\"Rate of true value belonging to the CI interval\")\n",
      "    \n",
      "plot_outcomes(all_outcomes, target_ci_width)\n",
      "all_outcomes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>ci_0025_correct</th>\n",
        "      <th>ci_0975_correct</th>\n",
        "      <th>correctness</th>\n",
        "      <th>n_samples</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0 </th>\n",
        "      <td> 0.51</td>\n",
        "      <td> 0.76</td>\n",
        "      <td> 0.64</td>\n",
        "      <td>   3</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1 </th>\n",
        "      <td> 0.67</td>\n",
        "      <td> 0.88</td>\n",
        "      <td> 0.78</td>\n",
        "      <td>   5</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2 </th>\n",
        "      <td> 0.79</td>\n",
        "      <td> 0.95</td>\n",
        "      <td> 0.88</td>\n",
        "      <td>  10</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td>  20</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td> 0.87</td>\n",
        "      <td> 0.99</td>\n",
        "      <td> 0.94</td>\n",
        "      <td>  30</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td>  40</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6 </th>\n",
        "      <td> 0.96</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.99</td>\n",
        "      <td>  50</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7 </th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td>  60</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td> 0.90</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.96</td>\n",
        "      <td>  70</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td>  80</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td>  90</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td> 0.90</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.96</td>\n",
        "      <td> 100</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "    ci_0025_correct  ci_0975_correct  correctness  n_samples\n",
        "0              0.51             0.76         0.64          3\n",
        "1              0.67             0.88         0.78          5\n",
        "2              0.79             0.95         0.88         10\n",
        "3              0.92             1.00         0.97         20\n",
        "4              0.87             0.99         0.94         30\n",
        "5              0.92             1.00         0.97         40\n",
        "6              0.96             1.00         0.99         50\n",
        "7              0.92             1.00         0.97         60\n",
        "8              0.90             1.00         0.96         70\n",
        "9              0.92             1.00         0.97         80\n",
        "10             0.92             1.00         0.97         90\n",
        "11             0.90             1.00         0.96        100"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GZk6Vlbz3pLHqBMRiYM0aYOZM3gzUEjg4yOHmVjceSxoIr7ycH7tOnYCQEPO1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\nIAhCErE4CIIgCEn+AlcXjC4QTfHDAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3900e10>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Evaluation of the correctness of the bootstrap CI for the std deviation of a uniform variable"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "all_outcomes = Parallel(n_jobs=-1)(delayed(compute_ci_correctness)(\n",
      "    n_samples, 1 / np.sqrt(12), target_ci_width=target_ci_width, agg=unbiased_std)\n",
      "    for n_samples in [3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100])\n",
      "    \n",
      "all_outcomes = pd.DataFrame(all_outcomes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_outcomes(all_outcomes, target_ci_width)\n",
      "all_outcomes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>ci_0025_correct</th>\n",
        "      <th>ci_0975_correct</th>\n",
        "      <th>correctness</th>\n",
        "      <th>n_samples</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0 </th>\n",
        "      <td> 0.24</td>\n",
        "      <td> 0.49</td>\n",
        "      <td> 0.36</td>\n",
        "      <td>   3</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1 </th>\n",
        "      <td> 0.50</td>\n",
        "      <td> 0.75</td>\n",
        "      <td> 0.63</td>\n",
        "      <td>   5</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2 </th>\n",
        "      <td> 0.80</td>\n",
        "      <td> 0.96</td>\n",
        "      <td> 0.89</td>\n",
        "      <td>  10</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td> 0.82</td>\n",
        "      <td> 0.97</td>\n",
        "      <td> 0.90</td>\n",
        "      <td>  20</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td> 0.84</td>\n",
        "      <td> 0.98</td>\n",
        "      <td> 0.92</td>\n",
        "      <td>  30</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td> 0.87</td>\n",
        "      <td> 0.99</td>\n",
        "      <td> 0.94</td>\n",
        "      <td>  40</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6 </th>\n",
        "      <td> 0.87</td>\n",
        "      <td> 0.99</td>\n",
        "      <td> 0.94</td>\n",
        "      <td>  50</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7 </th>\n",
        "      <td> 0.83</td>\n",
        "      <td> 0.97</td>\n",
        "      <td> 0.91</td>\n",
        "      <td>  60</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td> 0.89</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.95</td>\n",
        "      <td>  70</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td>  80</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td> 0.85</td>\n",
        "      <td> 0.99</td>\n",
        "      <td> 0.93</td>\n",
        "      <td>  90</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td> 0.92</td>\n",
        "      <td> 1.00</td>\n",
        "      <td> 0.97</td>\n",
        "      <td> 100</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "    ci_0025_correct  ci_0975_correct  correctness  n_samples\n",
        "0              0.24             0.49         0.36          3\n",
        "1              0.50             0.75         0.63          5\n",
        "2              0.80             0.96         0.89         10\n",
        "3              0.82             0.97         0.90         20\n",
        "4              0.84             0.98         0.92         30\n",
        "5              0.87             0.99         0.94         40\n",
        "6              0.87             0.99         0.94         50\n",
        "7              0.83             0.97         0.91         60\n",
        "8              0.89             1.00         0.95         70\n",
        "9              0.92             1.00         0.97         80\n",
        "10             0.85             0.99         0.93         90\n",
        "11             0.92             1.00         0.97        100"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DqcWhshL47TfbFoclS1bjxo15kEh4eysq+Nx7YOBqvPbaPEREUALgnTt8uumv\nv4DHHwcGDza+5LNyveLt2/mxRo60vmlLxng7zOGXMWfwghISh9rRO6306aefAjBvyGpj8fBhY1tg\nOpQ5COnp9rhzh79u3hyqHITgYHtERTW2lZZBQAAwfz4v9bB/P18ToW9fPuVUl0AF9fWK33iDO56t\nCYWCTzPK5fxvHx/T+2RiYmLMmvGtbJutTyXXB71fub+/PwAgyNpWEjeC6mrLi3+vD9o5CHyJUzl8\nfWv+M9C8bk3atOEZyqNGAQcP8g4+IQEYNgxo1Ur/5/StV2wtyOVcFBgDgoKAwEAeqJGaykfV1tSW\n2mCMjxo6d7beAAtzQD4H8I40O9u6bxRdK4IpF5EXi82blGZrlJTwDv/4cT4NMXw4kJen6dyPjk7A\nyZMxetcrtmRkMt5GkQho356PoNQfIjIz+b3VqpVtPETl5/MIPEvPnG8ITJrnYAmYWhzOnuWjh4Zy\nQpqLuuYgNMa8ri1RUcEDF3bsSMWDB6fh6jofjo7c6Vxd/QVmzOiBqVNjrKYDlUq5KNjb88V6/P31\n+0WuXePTk7WNnKyBwkLezi5dbEPohDBpnkNToLTUesI165ODYO55XVvD1ZVPNaWlpaCkZD7y8h75\ncNq0mY/bt1dDJLL86yuRPMrriYjgJTuEfAqhodw3d/eudY2K1Ckq4iPqiIimIQz1Re8toStKSYmh\n0UqHDh3Cyy+/DLlcjmeeeQYLFy7UeL+oqAizZs3CrVu34OzsjHXr1qFz5851ML/+yGT8CcqS51OL\ni3n+wdmztp2DYC0oFDxpy8OD3zvKp21LT9qqruYPQs7OQNeuPErH0PteJOJz9BIJ72StrZJAaSmf\nGYiKsuz/dUtCrzjUN0pJLpdjwYIFOHLkCMRiMbp3746RI0dqLDG6dOlSxMTEYNeuXbh27Rqef/55\nHDlypF7nrSuNuW50bUlp+fmPBOHOHT7X/fjjwEsvNa0cBEtEmbQlEmlOw1iqc7+qiid5urryJLxW\nrYyr42RvzzvXM2d4Z+vh0fC2moLycv5dxcZSuHZd0CsOUqkUeXl56NOnj8b233//HX4GlI48c+YM\nOnTooIp2mjBhQo31p69cuYLXX38dABAWFobMzEwUFBTA14xFex4+fLQYjTnRlfizcuUXiIkB8vNj\n8OABv5lHjuRPbLZYwtlaGT48AWvWfFHDuT9sWM9GtKomFRX8x8ODBya0bFn/6RRHR35fnjrFj+3q\n2jC2mopQfTvLAAAgAElEQVTqaj7a6dmTHqrqit4u5+WXX8ayZctqbPfw8MDLL78sOLLIyclBW7UA\n74CAAKSkpGjsExUVhZ07d6JPnz44c+YMbt++jTt37phVHKqqGqca5r59KSgrmw+plCelVVYCjM0H\nY6vxxhsx6NiRhr+WSkxMDObMsdyV2crL+f3k7c0fLBp6AStnZz6teeoUv0cttdOVSvmIqUcPmn41\nBr3ikJeXh65du9bY3rVrV2RkZAge2JD6S6+//jpeeuklREdHIzIyEtHR0RprRqiTlJSk+jsxMRGJ\niYmCxzcEUxfcY4yvS333Li+hkJvLf06csEdVFX8Sc3GBKgchMNCeSixYAZbo3C8t5U/Kvr7cp2BK\nv4CbGx+NpKRwgbC06RqZjPtGYmOtO0S9riQnJyM5OblBjqVXHIqV9XN1UG3ARL1YLEZ2drbqdXZ2\nNgICAjT2cXd3x7p161Svg4OD0b59e53HUxeHhqSh1o2Wy7mfQNn5K3/u3uXi4+fH8w3EYv7UVVkp\nR1ZWzeNY6rw1YZkwxh9wJBKevNe+PV8i1Rx4e3MfxrlzlpUkp1DwkNWoKOsPva0r2g/OixcvNvpY\nesUhLi4OX331FZ57TnMN3q+//hqxsbGCB46Li8ONGzeQmZkJf39/bNmyBZs2bdLYp6SkBC4uLnBy\ncsLXX3+Nfv36wc3M47+yskdPFrU5iJUow/m0BSAvjx/H35//hIUB/fvzv3U1acwY65i3JiwTpShI\npfyBIyjI+DpQ9aF1a16o8eJFPmKxhAWLCgv5/5/WsyhRR/Qmwd27dw+jR4+Gk5OTSgzOnTuHhw8f\nYteuXQY5pQ8ePKgKZZ09ezbeeOMNrFmzBgAwZ84cnDp1CjNmzIBIJEKXLl2wdu1aeOp47DFVEpxE\nwrNeW7as6SCWywF7+y/Qv38PNGsWo5oWKinh/xBKERCL+ajAz6/u01OUlEbUFfW6R4GBQLt2luEU\nTk8Hbtxo/Cf1ggJ+XcLDKZcBMGGGNGMMx48fx19//QWRSITOnTvj8ccfN9pQYzGVOJSWcqday5aP\nqpYWF/PtykVHWrdejUmT5qnEwNfXcobPRNOivJz7FJR1jywpo58xXmIjO7vxVgi8f5+fOyrKMkYw\nloDJMqRFIhEef/zxRhEEc6AexiqV8h6/qopnUSqfxoKC7DF8eCMZSBB/U17O79U+fSxjpKCNSMSf\n1qureSft42Pe8xcX82m1yEgShoaiSV/GiopHowBlYpNMZh2JTUTTobSUd74JCZYpDErs7PhTu7s7\nn341F+XlfJQfE0P5QA1JkxYH9TDW4cMT4OLyBeTyRzcYdxAnNJ6BRJOnuJjfo/HxljWNpA8HB95J\n29vzTtvUVFVxp3xcHK3N0NAYVJU1MzMT6enpGDhwICorKyGTyeBhxtx5U/kcTpzgTztKgTh+PBUf\nfpiC2FhyEBONT3ExF4TYWOvr+CoquD/PxcV0SXISCR9V9expPaU8zI1Jq7J+9dVX+Prrr/HgwQPc\nvHkTd+7cwbx583D06FGjTmgpMMZvYPW5UbE4BgkJMXj33caziyAAnjjp4cHzCKxteVGAT38ps6jV\nH8AaCpmMi2d8PAmDqRCcVvr888/x+++/q0YKoaGhyM/PN7lhpubhQx4WqE5hofWWIyZsh/v3ec5M\nTIx1CoMST08+3VNUxDvzhkKh4NcoKsr8ju+mhKA4NGvWDM3UxrQymcyg0hiWjq6lQQsL6WYjGhfl\nPRgdbXklKYyhZUveiRcW1nwYMwbGeC5DeDgPLSdMh6A49OvXD++//z4qKytx+PBhjBs3DiNGjDCH\nbSZFlzjcv08jB6LxKCjgSWTdutlW1I1YDHTqxAWivq7DggIgOJj/EKZF0CEtl8uxdu1a/PzzzwCA\nwYMH45lnnjHr6MEUDun0dOD2bc2iXB99BAwYwJ/aiPqhXvPHnHHnCgVfmc3aqnDm5/NOtEsX243T\nv3KFr0dtbBb1/fuPynXY6jVqaGgNaSNITeUO6ebNH217/XXg+ecBtUrjRB3RLu8QGGjeefPqauDS\nJW5DixaW/wSunCZRlnyw5U5PoQDOn+ftrev0bVERdzzHxlKFgrpg0mil33//HYsXL0ZmZiZkf3uV\nRCIRbt26ZdQJLYWyMs0QO8bIIV0f5HLeITPGh/xt2zZOXL6TE08Wy8nh5RwcHc1XpbSuKIUhKIhP\nu9iAK69W7Oz4U39qKr9XDC2lrfxf7daNhMGcCIrD7NmzsWLFCsTExOhda8HakMv5E6b61IMyW9oa\nEo0sCZmMTx+JREBICK+E2dgx+XZ2XJx8fPhURn4+Ly9tSQ5ehYILQ0gIEBpq+8KgxMGBd/IpKTxJ\nTmj6jy+CxUcM1hy5ZY0IioOXlxeefPJJc9hiNh4+rLmNRg11QyrlT38ODrxzE4stq/MF+JRhbCxw\n7x7w1198mykXwDEUpTCEhgIdOjS2NebHyYl/L6dP885ffWpXnYcP+UNcjx700NYY6BWHc+fOAQD6\n9++P1157DU8//bRGSKs1Zw7rWquIwlgNQyLhotCsGV+C0s/P8uf127ThonDjBq8a6uHReEtbyuX8\nXgsPb9oRN82b8xyI06f5iF17tKkckSYkNM46FUQtDunExMRaI5KOHz9uMqO0aWiHdE4Of5JUHykc\nOsSnH6ZNa7DT2BTV1bxUgbMzX0ildWvrnP+9f58vTCORNPzaykLIZPz8nTvzdRgIngmekqIZPKAU\n0JgYLuyE8ZjEIa1ch/TWrVs1lu60BWe09hRIY5QZtgaqqvj1cnXl/6yWstqXsfj48LLXt24BN2/y\ndpmj0qlSGLp2pRXK1GnRgoeOp6byhzU7Oy4MnTuTMDQ2gv/mY8eOrbFt3LhxJjHGXJSW1hzGks9B\nk4oKPpISifjwv29fPlqwZmFQovST9OrFRz8FBfxp1VRIpfwJOTqahEEXbdoAERH8f7CggPthaGTV\n+OgdOVy5cgWXL19GcXExdu7cCcYYRCIRSktLUa1r0t6KKCurOY9JIwdOeTl3ErZowZ/ezD31Yk48\nPXlFz6ws4OpVPmXW0PPbSh9NTAwXV0I3QUH8WkkkQMeOjW0NAdQiDtevX8fevXtRUlKCvXv3qra7\nu7vj66+/NotxpkAq5UN87fnypj5yKC3lfgVfXz71YQlRPebAzo53TL6+PC8iP7/hkucePuRO1e7d\nm/a9ZSihoY1tAaGOYIb0yZMn0atXL3PZo5OGdEiXlQEnT2r+sz58CMybB3zzjW1MmxgKY1wUHj7k\nUUft2zft8seMAbm5XCTs7AxP0tJFdTW/1+LjudgQRGNg0gzpxhaGhkZ93WglyimlpiIM6nWPAgJ4\nSKW11SIyBSIRz9fw8eHTTLm5XCDqmtRXXc19NgkJTWcERtgeFh6h3vBUVtYUgabib5BI+NOsQsFr\n+bRrZ9lrEjcWylINYjEPey0vN9z3UlnJxSEhwXLLdhCEITQ5cSgtrZmGb8v+BuVTrLJaaYcOfAqJ\nMk6F8fXlUVo3bvAKvu7utV+3igru0+rRgxK3COtHUByKi4uxePFi/PrrrwB4ctw777wDTyt9LNIl\nDrY2cqiq4k+wCgXvpDp14k++NHVUdxwdeZilnx8fRRQW8mupPfosL+fXOyGBrjNhGwjOss+aNQse\nHh7Ytm0btm7dCnd3d8ycOdMctjU4jPF/YlscOVRUPIoTd3TkYaiPPQb07s2nkKjDqh/e3vxadujA\nr3N5+aP3ysv5vUXCQNgSgiOHmzdvYufOnarXSUlJiIqKMqlRpkIi4f/EulaAs7aRA2NcEKqq+Gtf\nXx4K6OXVeHWDbB17e15FtVUrXn4lP58/aDg68qgkmqojbAlBcXBxccFvv/2Gvn37AuDrOzTXV0bR\nwtGXu2ctIweFgj+lPnzIBa51a17AzcuLyhmbE3f3R2tG5ObyNZJJkAlbQ1AcvvzyS0ybNg0lJSUA\nAG9vb3z77bcmN8wU6CrVrVykxlJj0eVyHmEklfJ5bn9/Xm7Ay8vyq6HaMso1I2jVQMJWEexePDw8\ncOHCBZU4eHp6Wm3hvfLympnRRUX8SdCSOlqZjAuCTMbtEov5KMHT0zoroRIEYX0IdoljxoxBWlqa\nRnTSuHHjVOs9WBMlJZbrjJZIuHjJ5Tzpql077kfw8Gg6yXkEQVgOgoX3SkpKbKbwnq5IpcZ0Rqvn\nILi4cGdny5Z8JGOrxe4IgrAOmkzhPYWCx/5rjxLMvQIc5SAQBGENNJnCe1VVwC+/8Kkaddat43kA\nAwfW6/C1ogw5ZYzHywcE8N9WGvRFEISVQIX3DKC6WvdUjXI5woaEchAIgrB2LChGx7ToCmMFuM+h\nIRzSlINAEIQtYdI4mEOHDqFTp07o2LEjli9fXuP9wsJCDBkyBN26dUOXLl2wYcMGk9lSWlozXJWx\n+vkclDkSBQU8JNbXly+pOWAAr+rZqhUJA0EQ1ongyOHjjz/WmLcSiUTw9PREbGwsunXrpvdzcrkc\nCxYswJEjRyAWi9G9e3eMHDkS4eHhqn1WrVqF6OhoLFu2DIWFhQgLC8OUKVPgYIKkA13rRpeX89IH\ndSl7QDkIBEE0BQR74XPnzuHs2bMYMWIEGGPYv38/IiMj8eWXX2Ls2LFYuHChzs+dOXMGHTp0QFBQ\nEABgwoQJ2L17t4Y4+Pn54cKFCwCA0tJS+Pj4mEQYAN6hazuADc1xoBwEgiCaGoI9cXZ2NlJTU+H2\nd6zlkiVLMHToUPzyyy+IjY3VKw45OTloq1ZbICAgACkpKRr7PPvss3j88cfh7++PsrIybN26tT5t\n0YtMxjt47SUwa5tSohwEgiCaMoLiUFBQACe1iXNHR0fk5eWhefPmcK4l9EZkQA+6dOlSdOvWDcnJ\nybh58yaeeOIJnD9/Hu4NvFKKrqVBAd0JcGVlXBgoB4EgiKaMoDhMnjwZCQkJGDVqFBhj2Lt3LyZN\nmoSKigpERETo/ZxYLEZ2drbqdXZ2NgICAjT2OXnyJN58800AQEhICIKDg3Ht2jXExcXVOF5SUpLq\n78TERCQmJgqZrqK2MFbtaaXqaqB7d+sr4U0QBJGcnIzk5OQGOZZgEhwA/PHHHzhx4gREIhF69+6t\ns/PWRiaTISwsDEePHoW/vz/i4+OxadMmDZ/DK6+8Ak9PT7z77rvIy8tDbGwsLly4gBZaJVLrmwR3\n5w5w+XLNDv/TT4GePXktfiWFhXyRHKrNTxCEtWPSJDgAiImJgb+/P2QyGUQiEbKyshAYGFj7gR0c\nsGrVKgwePBhyuRyzZ89GeHg41qxZAwCYM2cOFi1ahJkzZyIqKgoKhQL/+c9/aghDQ1BWxqOStNHn\nc9C1L0EQRFNCcOTw2WefYfHixWjVqhXs1WI1L168aHLjlNR35HD6NI800naRzJ8PLF3KE9UA7pco\nKgKeeKIexhIEQVgIJh05rFixAteuXYOPFU/Cl5U9EgAl1dX8R60SOaRSqndEEAQBGJAhHRgYCA/t\nGFArQiLh4aja+QjKSCV1R7VMRr4GgiAIwICRQ3BwMPr3749hw4apQlpFIhFeeeUVkxvXEOirqaQr\nUkkmo5EDQRAEYIA4BAYGIjAwEBKJBBKJRLXoj7Wgb10iXTkONK1EEATBERQH9fwCa6SiQneJC13V\nWBmrWX+JIAiiKaJXHF566SV8+umnGDFiRI33RCIR9uzZY1LDGorSUt2VUQsLgcjImtupiipBEEQt\n4jBt2jQAwKuvvmo2Y0xBWZl+cdCeVmKMchwIgiCAWsQhNjYWAOpUpsLSUK7IpiuvTpfPQSQicSAI\nggAM8DlERkbWSKTw9PRE9+7d8dZbb1l0/oOy4J62/1y5SI8u0SBxIAiCMEAchgwZAgcHB0yaNAmM\nMWzevBmVlZVo3bo1ZsyYgb1795rDTqPQF6lUVMST39SXjpDL+fQTrc9AEARhgDgcOXIEaWlpqtdd\nu3ZFdHQ00tLSEKnLo2tB1CXHQSqlBDiCIAglgs/JcrlcY5GeM2fOQKFQAIDJVm1rKMrKaq4bDeh2\nRlN2NEEQxCMEe/e1a9di5syZKC8vBwC4u7tj7dq1qKiowBtvvGFyA+tDaaluH4IuZzRlRxMEQTxC\nUBy6d++Ov/76CyUlJQC4M1rJ+PHjTWdZA1BWVrMSK8BHDn8vba2CxIEgCOIRguJQXV2NHTt2IDMz\nEzKZDABPgnvnnXdMblx9kMu5Q1rXEp+FhYCu9YooAY4gCIIjKA5PPfUUvLy8EBsbW+ua0ZaGvnWj\nAd3TSgCJA0EQhBJBccjJycFPP/1kDlsaFH3rRjOmu64SQDkOBEEQSgSjlXr16oULFy6Yw5YGRV8Y\nq7Kchq5BEIkDQRAER3Dk8Ntvv2H9+vUIDg5Gs79LlopEIosXjIoK/WGsuqqxAiQOBEEQSgTF4eDB\ngwCgWsOhPms5mxOpVH+pbgpjJQiCqB3BaaWgoCAUFxdjz5492Lt3L0pKShCkHQdqgegTB0qAIwiC\nEEZQHD799FNMmTIFBQUFyMvLw5QpU7By5Upz2FYvZDLDF/khcSAIgtBExATmiSIjI3H69Gm4uroC\nACoqKtCjRw9cvHjRLAYCqFEV1hDOnOGjB23H84oVQO/eQPfuj7Y9eAB07FgzMY4gCMKaMabvVGJQ\nDVI7tUdwOyspW1rbyEF7Wkmh0B29RBAE0VQRdEjPnDkTCQkJePrpp8EYw48//ohZs2aZw7Z6oWvU\nAOiOVgIoUokgCEIdQXF45ZVX0K9fP/z+++8QiUTYsGEDoqOjzWFbvdA1cqiuBiQSwN1dcztjlB1N\nEAShjl5xePDggerv4OBgVYSSSCTCgwcP0ELXMmoWhC5xUEYqaWdO0/KgBEEQmugVh5iYGFVugy4y\nMjJMYlBD8PdyEzXQV1MJIHEgCIJQR684ZGZmmtGMhkUu171dl79BoeCZ1Pb2preLIAjCWhAMPVIo\nFPjuu++wZMkSAEBWVhbOnDljcsPqg76Rg64EOFoelCAIoiaC4jB//nycOnUKGzduBAC4ublh/vz5\nJjesPtQ2rUQJcARBEMIIRiulpKQgLS1NFaHUokULSKVSkxtWH+Ry3Ws56BMHqqtEEAShieDIwcnJ\nCXK1SfyCggKLT4RTKHSv5aDL5yCVAn8nfxMEQRB/I9jLv/DCCxg9ejTy8/OxaNEi9O7dG2+88YY5\nbDMaXSMHmQwoKQG8vGruTzkOBEEQmghOK02ZMgWxsbE4evQoAGD37t0IDw83uWH1QdfIoaiIC4Ou\nNR5IHAiCIDQRFAcAqKyshFwuh0gkQlVVlaltqje6Qll1RSopoRwHgiAITQSnlZYsWYIZM2bgwYMH\nKCwsxMyZM/Hvf//boIMfOnQInTp1QseOHbF8+fIa73/00UeIjo5GdHQ0IiMj4eDggOLi4rq3Qgtd\n0Ur61o0GSBwIgiC0ESzZHRoaigsXLsD57yp2VVVViIqKwvXr12s9sFwuR1hYGI4cOQKxWIzu3btj\n06ZNeqek9u3bhxUrVuDIkSM1jaxj2dk7d4BLlzTF4McfufN53DjNfQsLgUGDdDuwCYIgrBmTluwW\ni8UaU0nV1dUICAgQPPCZM2fQoUMHBAUFwdHRERMmTMDu3bv17r9x40ZMnDjRQLNrRyqtmfGsbwU4\nZ2cSBoIgCG30+hxeeOEFAICnpyc6d+6MQYMGAQAOHz6M+Ph4wQPn5OSgbdu2qtcBAQFISUnRuW9l\nZSV++uknfPHFF3UyXh9Sac0O//59zQV+AEqAIwiC0IdecYiNjYVIJEJcXBxGjRoFgA9REhMTay3I\np8SQfZTs3bsXffr0gZeuOFMjkMl0jxx0JcB5eDTIKQmCIGwKveIwY8aMeh1YLBYjOztb9To7O1vv\ndNTmzZsFp5SSkpJUfycmJiIxMVHvvtojB8Z0V2SlBDiCIGyJ5ORkJCcnN8ixBB3SxiKTyRAWFoaj\nR4/C398f8fHxOh3SJSUlaN++Pe7cuQMXPXM8dXWqpKYClZWPpoyKi4FFiwDtWavCQqBrV8DPr05N\nIwiCsArq45A2KM/BqAM7OGDVqlUYPHgw5HI5Zs+ejfDwcKxZswYAMGfOHADAjz/+iMGDB+sVBmPQ\nHjnQOg4EQRB1w+CRQ2VlJZo3UoW6uqrfiRN8FThl5vOZM8CpU8BLL2nuV1AA9OpFfgeCIGwTk4ay\nnjx5EhEREQgLCwMA/PnnnxZfslsq1VwiVF92NC0PShAEoRtBcXj55Zdx6NAhtPw71Kdbt2745Zdf\nTG5YfdBeP1pXpJISEgeCIIiaGFR7OzAwUOO1g67qdRaEXK4pDrp8DozxfSy8KQRBEI2CYNcYGBiI\nEydOAAAkEglWrlxp0VVZdRXd01VXSSqlRX4IgiD0IThyWL16NT7//HPk5ORALBYjLS0Nn3/+uTls\nMwpdRff0JcBRdjRBEIRuBEcOvr6+qvWjrQHtkUNVFR8luLlpbqflQQmCIPQjKA4zZ87UeK0si7Fu\n3TrTWFRPFArNVeCU/gbtah40rUQQBKEfQXEYNmyYShCqqqqwa9cu+Pv7m9wwY9FeBU5fpBJjQLNm\n5rOLIAjCmhAUh7Fjx2q8njRpEnr37m0yg+qL9vrRtYWx0vKgBEEQujEolFWd69evo6CgwBS2NAi6\nRg66EuAYoxwHgiAIfQiOHNzc3FTTSiKRCK1bt9a55KeloO2Qvn8fiIqquR9lRxMEQehHUBzKy8vN\nYUeDoR3KSmtHEwRB1B294nDu3LlaF+yJiYkxiUH1RXvkoMvnIJdzf4NdnSfVCIIgmgZ6xeHVV1+t\nVRyOHz9uEoPqi0z2yOcgkwGlpYC3t+Y+UiklwBEEQdSGXnFoqNWEzI16RdYHDwAvr5pLhspkNZPi\nCIIgiEcYVHbu4sWLuHLlCqqrq1Xbpk2bZjKj6oO6OOjzN1B2NEEQRO0IikNSUhJ++eUXXLp0CcOG\nDcPBgwfRp08fixUH9XLd+nIcSBwIgiBqR9Alu337dhw5cgR+fn5Yv349zp8/j+LiYnPYZhTqIwdK\ngCMIgjAOQXFwcXGBvb09HBwcUFJSglatWiE7O9scthmF+sjh/n2gRQvd+5E4EARB6EdwWikuLg5F\nRUV49tlnERcXB1dXV/Tq1cscthmFerRSYSEQH697P8pxIAiC0I+gOKxevRoAMHfuXAwePBilpaWI\n0pVybCHIZI9Wd6MEOIIgCOMQnFYaMWIENm7ciIqKCgQHB1u0MADc5yAS8UxpfcuDAiQOBEEQtSEo\nDq+++ip+++03REREYMyYMdi+fbtGSKulIZPxvIbSUsDZuWZZbopUIgiCEEZwWikxMRGJiYmQyWQ4\nfvw4vv76a8yaNQulpaXmsK9OMPaoKqu+aqy0PChBEIQwBiXBVVVVYc+ePdi6dStSU1Mxffp0U9tl\nFMqie6mpqVi/PgX37tljyRI5hg9PUNWCInEgCIIQRlAcxo8fj5SUFAwZMgQLFixAv379YGehFevk\ncuDixVRs3nwad+/Oh0wG3LgBrFnzBebM4cUCpVLA1bWxLSUIgrBsBMVh1qxZ2LhxIxwcDBpkNCoK\nBXDkSAoqK+drRC1VVs7H/v2rERMTA4WC+yIIgiAI/Qj2+EOGDDGHHQ2CXA5IpbzKnkKhWXBPInn0\ngiKVCIIgascy54eMRKEAHBzkqr/VK447OfHtjFF2NEEQhBA2Jw5PPJGA5s2/AGOPymg0b/45hg1L\nAEDLgxIEQRiCoDgoFAp89913WLJkCQAgKysLZ86cMblhxiCXA126xGDOnB5wd18NsfgrhIauxpw5\nPTVWriNxIAiCqB0RY8qcYd3MnTsXdnZ2OHbsGK5evYoHDx5g0KBBOHv2rLlshEgkgoCZAHhuw7lz\nvGTGG28A8+YBgYGP3lcoeHLcgAEmNJYgCMJCMLTv1IWgQzolJQVpaWmIjo4GALRo0QJSqdSok5ka\n9fWjHz6sGZVEy4MSBEEYhuC0kpOTE+RqvW5BQYHF5jkok+AAoLpad+kMEgeCIAhhBHv5F154AaNH\nj0Z+fj4WLVqE3r1744033jCHbXVGWXQP0D1yoLpKBEEQhiE4rTRlyhTExsbi6NGjAIDdu3cjPDzc\n5IYZg1TKcxt4vkPNkFXKjiYIgjAMwZFDVlYWXF1dMWLECIwYMQKurq7Iysoy6OCHDh1Cp06d0LFj\nRyxfvlznPsnJyYiOjkaXLl2QmJhYJ+O1UY4cJBI+paSe56CEchwIgiCEERw5DB06FKK/e9nq6mpk\nZGQgLCwMly5dqvVzcrkcCxYswJEjRyAWi9G9e3eMHDlSY9RRXFyM559/Hj/99BMCAgJQWFhYr8Yo\ny3XrmlJSQuJAEAQhjKA4/PXXXxqvU1NT8fnnnwse+MyZM+jQoQOCgoIAABMmTKgxJbVx40aMGTMG\nAQEBAICW+pZtMxDlyEGXM1oJ5TgQBEEIU+ewo5iYGKSkpAjul5OTg7Zt26peBwQEICcnR2OfGzdu\n4MGDB+jfvz/i4uLw3Xff1dUcDeRyPnKortY/ciBxIAiCEEZw5PDxxx+r/lYoFEhNTYVYLBY8sEjX\nhL8WUqkUqampOHr0KCorK9GzZ0/06NEDHTt2rLFvUlKS6m/lAkTaSCQ0ciAIoumSnJyM5OTkBjmW\noDiUl5c/2tnBAcOHD8eYMWMEDywWi5Gdna16nZ2drZo+UtK2bVu0bNkSLi4ucHFxwWOPPYbz588L\nioM+5HLe+esLY3V21u2kJgiCsAW0H5wXL15s9LFqFQe5XI7S0lKN0YOhxMXF4caNG8jMzIS/vz+2\nbNmCTZs2aezz1FNPYcGCBZDL5Xj48CFSUlLwyiuv1PlcSmQyPmKgBDiCIIj6Uas42Nvb48SJE2CM\nGTRNpHFgBwesWrUKgwcPhlwux+zZsxEeHo41a9YAAObMmYNOnTphyJAh6Nq1K+zs7PDss88iIiLC\n6MZIpbwS68OHusXBw8PoQxMEQTQpDCq8l5ubi3HjxqH53+nFIpEITz/9tFkMVJ5PqHgUY8DPP/Oi\ne3rl36UAABQ2SURBVIcPA7m5gPpS18XFQHAw0L69iY0lCIKwEExaeK+6uho+Pj44duyYxnZzioMh\nqBfdo2klgiCI+iEoDs888wz69Omjse333383mUHGol50T18SHEUqEQRBGIZgnsOLL75o0LbGRnvk\noEscKDuaIAjCMPSOHE6dOoWTJ08iPz8f//3vf1XzVmVlZRolvC0FhYL7HQD94kAjB4IgCMPQKw4S\niUQlBGVlZartHh4e2L59u1mMqwtyuWa5bl1JcCQOBEEQhqFXHPr164d+/fphxowZqvpIloz2yEFd\nHBjjIa4Ogh4WgiAIAjDA52ANwgBwcVCOHLSnlaRSWuSHIAiiLljmep9GoL1+tPrIgcJYCYIg6oZe\ncVi4cCEAYOvWrWYzpj5orx+tPnIgcSAIgqgbesVh//79YIxh2bJl5rTHaLRHDtrTSrQ8KEEQhOHo\nddE++eST8Pb2Rnl5Odzd3TXeE4lEKC0tNblxdUFZVwnQ7ZDWV8KbIAiCqInekcOHH36I4uJiDB06\nFGVlZRo/liYMgKY46MqQpjBWgiAIwxEM7tyzZw/y8vLwxx9/AADi4+PRqlUrkxtWV2QyLg4yGX+t\nHbZK2dEEQRCGIxittHXrVsTHx2Pr1q3YsmUL4uPjsW3bNnPYVieUIwfKjiYIgqg/giOH9957D3/8\n8YdqtFBQUIABAwZg3LhxJjeuLijFobKSxIEgCKK+CI4cGGPw9fVVvfbx8TG6PrgpUU4raTuj5XI+\npWRnMxkdBEEQpkdw5DBkyBAMHjwYkyZNAmMMW7ZswZNPPmkO2+qETMYzpHWFsVKOA0EQRN0QFIcP\nP/wQO3bswIkTJwDw5T1Hjx5tcsPqilTKRUF75CCTAW5ujWcXQRCENWJQKboxY8ZgzJgxpralXiir\nsuoqnUEJcARBEHXDZmbipVLA3r7mtJJMRkX3CIIg6opNiIN2XSXtbGiKVCIIgqgbBolDZWUlrl27\nZmpbjEZo/WhKgCMIgqgbguKwZ88eREdHY/DgwQCAtLQ0jBw50uSG1QWh9aNp5EAQBFE3BMUhKSkJ\nKSkp8Pb2BgBER0fj1q1bJjesLgitH03iQBAEUTcExcHR0RFeXl6aH7KwjDL19aPVfQ5KwSBxIAiC\nqBuCvXznzp3xww8/QCaT4caNG3jhhRfQq1cvc9hmMOojB/VQVopUIgiCMA5Bcfjss89w6dIlNGvW\nDBMnToSHhwdWrFhhDtsMRn39aHWHNK0ARxAEYRyCSXAHDhzA0qVLsXTpUtW2bdu2WVThPblc0+eg\nPnIgcSAIgqg7giMHdVGobVtjom/kQMuDEgRBGIfekcPBgwdx4MAB5OTk4MUXX1RVYi0rK4OjhXl4\ntUNZlSMHhUJ3+W6CIAiidvSKg7+/P2JjY7F7927ExsaqxMHDwwOffPKJ2Qw0hNryHCxMxwiCIKwC\nveIQFRWFqKgoTJo0CU4WnmKsb/1oxig7miAIwhgEHdKZmZlYtGgRLl++jKqqKgCASCSyqEQ4dXFQ\nn1YSiWjkQBAEYQyCDumZM2di7ty5cHBwQHJyMqZPn47JkyebwzaDUa4Cp1AAEonmaIHEgSAIou4I\nikNVVRUGDhwIxhjatWuHpKQk7N+/3xy2GYxy5CCRcDGwt+dC4eDA/yYIgiDqhqA4ODs7Qy6Xo0OH\nDli1ahV27tyJiooKgw5+6NAhdOrUCR07dsTy5ctrvJ+cnAxPT09ER0cjOjoa7733Xt1bAM31o9XD\nWCnHgSAIwjgExWHFihWorKzEypUrcfbsWXz//ff49ttvBQ8sl8uxYMECHDp0CJcvX8amTZtw5cqV\nGvv169cPaWlpSEtLw1tvvWVUI5TiYK3Z0cnJyY1tgkmx5fbZctsAal9TRlAc4uPj4e7ujrZt22LD\nhg3YsWMHbt++LXjgM2fOoEOHDggKCoKjoyMmTJiA3bt319hPGSJbH5TTStrZ0dZSV8nWb1Bbbp8t\ntw2g9jVl9IpDeXk5Pv74Y8yfPx9ffPEFFAoFdu3apSrEJ0ROTg7atm2reh0QEICcnByNfUQiEU6e\nPImoqCgMHToUly9fNqoRukYOlB1NEARhPHpDWadNmwYPDw/07NkTP//8MzZs2ABnZ2ds3LgR3bp1\nEzywSFnPohZiYmKQnZ2N5s2b4+DBgxg1ahSuX79etxZA0+egvkQo5TgQBEEYCdNDZGSk6m+ZTMZ8\nfX1ZZWWlvt1rcOrUKTZ48GDV66VLl7IPPvig1s8EBQWx+/fv19geEhLCANAP/dAP/dBPHX5CQkIM\n7rO10TtysFeLAbW3t4dYLIZLHTy8cXFxuHHjBjIzM+Hv748tW7Zg06ZNGvvk5eWhVatWEIlEOHPm\nDBhjaNGiRY1jpaenG3xegiAIov7oFYcLFy7A3d1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       "text": [
        "<matplotlib.figure.Figure at 0x3791990>"
       ]
      }
     ],
     "prompt_number": 20
    }
   ],
   "metadata": {}
  }
 ]
}