performance-curves.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Performance curves\n",
      "\n",
      "In this notebook we will show how to compute performance curves (ROC and PR curves to be specific) given only positive and unlabeled data.\n",
      "\n",
      "We will show several results:\n",
      "- the true curves rank, assuming all labels are known\n",
      "- the curves that would be obtained by treating the unlabeled set as negative\n",
      "- bounds on the performance curves given a correct estimate of the fraction of positives in the unlabeled set\n",
      "- bounds on the performance curves given an interval estimate of the fraction of positives in the unlabeled set that is obtained by peeking at the labels of 300 unlabeled instances.\n",
      "\n",
      "This notebook is intended to enable you to easily change the configuration of experiments, so feel free to make modifications where you see fit to see their effect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random\n",
      "import operator as op\n",
      "import optunity.metrics\n",
      "import semisup_metrics as ss\n",
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\n",
      "import pickle\n",
      "import csv\n",
      "import util\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Create or load data set\n",
      "Generate simulated data or load the results of an experiment in an existing paper. Feel free to configure the code below as you please."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# fraction of positives/negatives that are known\n",
      "# known_neg_frac == 0 implies PU learning\n",
      "known_pos_frac = 0.1\n",
      "known_neg_frac = 0.0\n",
      "\n",
      "# load results from the paper?\n",
      "# http://www.sciencedirect.com/science/article/pii/S0925231215001174\n",
      "use_paper_data = True\n",
      "dataset = 'covtype'\n",
      "#dataset = 'sensit'\n",
      "\n",
      "# generate a simulated data set (requires use_paper_data = False)\n",
      "# number of instances per class\n",
      "# the number of unlabeled instances depends on these settings + known_X_frac\n",
      "\n",
      "# if we use a lot of data, computation times are a little long\n",
      "# but the resulting estimates become excellent, which corroborates consistency\n",
      "# num_pos = 20000\n",
      "# num_neg = 100000 \n",
      "\n",
      "# if you simulate a smaller data set you can see some effects better\n",
      "# but estimated bounds will be much wider\n",
      "# because the ECDF confidence interval becomes large\n",
      "num_pos = 2000  \n",
      "num_neg = 10000 \n",
      "distid = 2  # can be 1, 2 or 3, these correspond to certain curves in ROC space\n",
      "\n",
      "# generate rankings and label vectors and compute corresponding beta\n",
      "# beta is based on known_pos_frac, known_neg_frac and the number of pos and negs\n",
      "# labels is a list of {True, False, None}, where None indicates unlabeled\n",
      "# true_labels is a list of {True, False}\n",
      "if use_paper_data:\n",
      "    labels, true_labels, decision_values, beta = util.load_dataset(dataset, \n",
      "                                                                   known_pos_frac,\n",
      "                                                                   known_neg_frac)\n",
      "else:\n",
      "    labels, true_labels, decision_values, beta = util.simulate_data(distid, num_pos, num_neg,\n",
      "                                                                    known_pos_frac,\n",
      "                                                                    known_neg_frac)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data set characteristics"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Known parameters:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('total number of instances: \\t %d' % len(labels))\n",
      "print('number of known positives: \\t %d' % len(filter(lambda x: x == True, labels)))\n",
      "print('number of known negatives: \\t %d' % len(filter(lambda x: x == False, labels)))\n",
      "print('number of unlabeled instances: \\t %d' % len(filter(lambda x: x == None, labels)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total number of instances: \t 40000\n",
        "number of known positives: \t 2000\n",
        "number of known negatives: \t 0\n",
        "number of unlabeled instances: \t 38000\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unknown parameters:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('number of latent positives: \\t %d' % len(filter(lambda x: x[0] == None and x[1] == True, zip(labels, true_labels))))\n",
      "print('number of latent negatives: \\t %d' % len(filter(lambda x: x[0] == None and x[1] == False, zip(labels, true_labels))))\n",
      "print('beta: \\t %1.4f' % beta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "number of latent positives: \t 18000\n",
        "number of latent negatives: \t 20000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "beta: \t 0.4737\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Estimate beta\n",
      "\n",
      "This step can be avoided if sufficient domain knowledge exist to guesstimate beta, or when using data-driven approaches as mentioned in the paper. \n",
      "\n",
      "In this notebook we use a point estimate you can provide (\\hat{beta} in the paper). Change this parameter to see its effect in the figures later on. Additionally, we will perform Bayesian inference on beta by peeking at the true label of some unlabeled instances, as described in Section 6.3."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "betahat = beta\n",
      "\n",
      "print('true value of beta\\t%1.4f' % beta)\n",
      "print('point estimate of beta\\t%1.4f' % betahat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "true value of beta\t0.4737\n",
        "point estimate of beta\t0.4737\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively, estimate beta by peeking at the latent labels of a few unlabeled instances. This corresponds to Section 6.3 in the manuscript."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# determine the latent labels (requires manual labeling in practice)\n",
      "latent_labels = [true_label for label, true_label in zip(labels, true_labels) if label is None]\n",
      "\n",
      "# we will peek at 300 labels to estimate beta based on a 95% credible interval\n",
      "num_peeks = 300\n",
      "credible_interval_length = 0.95\n",
      "\n",
      "# peek at the true label of a subset of unlabeled instances\n",
      "unlabeled_ranks = [idx for idx, lab in enumerate(labels) if lab == None]\n",
      "sample = np.random.choice(unlabeled_ranks, num_peeks, replace=False)\n",
      "sample_labels = [true_labels[i] for i in sample]\n",
      "npos = sum(sample_labels)\n",
      "nneg = sample.size - npos\n",
      "\n",
      "# compute interval based on the percentile function of the posterior\n",
      "beta_interval_ppf = ss.estimate_beta_by_labeling(npos, nneg, credible_interval_length, HPD=False)\n",
      "print('Credible interval via PPF: %1.4f <= beta <= %1.4f.' % (beta_interval_ppf.lower, beta_interval_ppf.upper))\n",
      "print(\"Width of credible interval based on PPF: %1.5f.\\n\" % (beta_interval_ppf.upper - beta_interval_ppf.lower))\n",
      "\n",
      "# compute interval based on the highest posterior density region (shorter)\n",
      "beta_interval_hpd = ss.estimate_beta_by_labeling(npos, nneg, credible_interval_length, HPD=True)\n",
      "print('Credible interval via HPD: %1.4f <= beta <= %1.4f.' % (beta_interval_hpd.lower, beta_interval_hpd.upper))\n",
      "print(\"Width of credible interval based on HPD: %1.5f.\" % (beta_interval_hpd.upper - beta_interval_hpd.lower))\n",
      "\n",
      "# continue with beta based on HPD, because this is the shortest credible interval\n",
      "# note that the coverage of both intervals is equal to credible_interval_length\n",
      "beta_interval = beta_interval_hpd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Credible interval via PPF: 0.4372 <= beta <= 0.5497.\n",
        "Width of credible interval based on PPF: 0.11251.\n",
        "\n",
        "Credible interval via HPD: 0.4372 <= beta <= 0.5497.\n",
        "Width of credible interval based on HPD: 0.11251.\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 1. Compute cumulative rank distribution of known positives"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sort the labels in descending order of corresponding decision values\n",
      "sort_labels, sort_dv, sort_true_labels = zip(*sorted(zip(labels, decision_values, true_labels),\n",
      "                                                     key=op.itemgetter(1), reverse=True))\n",
      "\n",
      "# ranks of the known positives\n",
      "known_pos_ranks = [idx for idx, lab in enumerate(sort_labels) if lab]\n",
      "\n",
      "# compute rank ECDF of known positives\n",
      "known_pos_ecdf = ss.compute_ecdf_curve(known_pos_ranks)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we determine a confidence interval on the rank CDF of known positives. We can do this in several ways, our code provides a bootstrap approach and a method based on the Dvoretzky\u2013Kiefer\u2013Wolfowitz (DKW) inequality. Feel free to experiment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ci_width = 0.95      # width of the confidence band on ECDF to be used\n",
      "use_bootstrap = True # use bootstrap to compute confidence band\n",
      "nboot = 2000         # number of bootstrap iterations to use, not used if use_bootstrap = False\n",
      "\n",
      "if use_bootstrap:\n",
      "    cdf_bounds = ss.bootstrap_ecdf_bounds(labels, decision_values, nboot=nboot, ci_width=ci_width)\n",
      "else:\n",
      "    cdf_bounds = ss.dkw_bounds(labels, decision_values, ci_width=ci_width)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For reference, we will also compute the rank ECDF of latent positives. In practical applications this is impossible, as the latent positives are by definition not known."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "latent_positives = map(lambda x, y: x == True and y == None, true_labels, labels)\n",
      "sort_lps, _ = zip(*sorted(zip(latent_positives, decision_values),\n",
      "                          key=op.itemgetter(1), reverse=True))\n",
      "latent_pos_ranks = [idx for idx, lab in enumerate(sort_lps) if lab]\n",
      "latent_pos_ecdf = ss.compute_ecdf_curve(latent_pos_ranks)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the rank CDFs of known and latent positives. It may occur that the rank CDF of latent positives is not within the confidence interval of known positives, in which case the corresponding bounds on performance will not be strict."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# convenience plot functions\n",
      "def plot_proxy():\n",
      "    p = plt.Rectangle((0, 0), 0, 0, color='blue', alpha=0.4)\n",
      "    ax = plt.gca()\n",
      "    ax.add_patch(p)\n",
      "    return p\n",
      "\n",
      "def fix_plot_shape(fig):\n",
      "    ax = fig.add_subplot(111, aspect='equal')\n",
      "    axes = fig.gca()\n",
      "    axes.set_xlim([0,1])\n",
      "    axes.set_ylim([0,1])\n",
      "\n",
      "xs = list(range(len(labels)))\n",
      "plt.figure(1)\n",
      "plt.fill_between(xs, list(map(cdf_bounds.lower, xs)), list(map(cdf_bounds.upper, xs)), \n",
      "                 color='blue', alpha=0.4)\n",
      "plt.plot(*zip(*known_pos_ecdf), color='black', linestyle='dashed', linewidth=2)\n",
      "plt.plot(*zip(*latent_pos_ecdf), color='black', linewidth=2)\n",
      "plot_proxy()\n",
      "plt.xlabel('rank')\n",
      "plt.ylabel('TPR')\n",
      "plt.legend(['known positives', 'latent positives', 'expected region'], loc=4)\n",
      "plt.title('Rank CDF')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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srGw4fx4uX1Z9NiZNkhLoouapiuc4ypMEjhroyhWV/N67V2237dz5WvmP3Nws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\nRERERERERERERAL+C3OsQE76kRIWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5b9d4db4d0>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 2. Compute contingency tables for each rank\n",
      "These tables are computed based on estimate of beta and the rank CDF of known positives. We will show the results for betahat and a the Bayesian credible interval on beta."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# first, compute contingency tables based on the point estimate betahat\n",
      "# presorted = True is a computational shortcut\n",
      "# we can use this because we already sorted by decision values earlier\n",
      "tables_point = ss.compute_contingency_tables(labels=sort_labels, decision_values=sort_dv,\n",
      "                                             reference_lb=cdf_bounds.lower,\n",
      "                                             reference_ub=cdf_bounds.upper,\n",
      "                                             beta=betahat, presorted=True)\n",
      "\n",
      "# second, compute contingency tables based on the credible interval \n",
      "# we start with a convenience function for readability\n",
      "compute_tables = lambda beta: ss.compute_contingency_tables(labels=sort_labels, decision_values=sort_dv,\n",
      "                                                   reference_lb=cdf_bounds.lower,\n",
      "                                                   reference_ub=cdf_bounds.upper,\n",
      "                                                   beta=beta, \n",
      "                                                   presorted=True)\n",
      "\n",
      "# tables based on lower bound on beta, only lower bound tables are to be used\n",
      "tables_interval_lb = compute_tables(beta_interval.lower)\n",
      "# tables based on upper bound on beta, only upper bound tables are to be used\n",
      "tables_interval_ub = compute_tables(beta_interval.upper)\n",
      "# merge into a single variable\n",
      "# ss._lb_ub is a collections.namedtuple with fields 'lower' and 'upper'\n",
      "tables_interval = ss._lb_ub(lower=tables_interval_lb.lower, upper=tables_interval_ub.upper)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 3. Compute and plot performance estimates based on the contingency tables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 3.1 ROC curves\n",
      "\n",
      "Start off with the easy stuff: the true ROC curve (unknown in practice), and the curve we obtain by assuming beta=0."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute the true ROC curve (we use Optunity's ROC function)\n",
      "_, roc_true = optunity.metrics.roc_auc(true_labels, decision_values, return_curve=True)\n",
      "# compute the ROC curve that would be obtained by treating all unlabeled as negative\n",
      "_, roc_neg = optunity.metrics.roc_auc(labels, decision_values, return_curve=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compute bounds based on the proposed method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# we can directly use the contingency tables we already computed anyways\n",
      "roc_bounds = lambda tables: ss._lb_ub(lower=ss.roc_from_cts(tables.lower),\n",
      "                                      upper=ss.roc_from_cts(tables.upper))\n",
      "roc_bounds_point = roc_bounds(tables_point)\n",
      "roc_bounds_interval = roc_bounds(tables_interval)\n",
      "\n",
      "# an alternative without all these intermediate steps would be:\n",
      "# roc_bounds_point = ss.roc_bounds(labels, decision_values, beta=betahat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, what if we would compute bounds on the labeled instances and the ones we peeked at to estimate beta? The indices of the random sample of unlabeled data we peeked at is in sample."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# labels and decision values of peeked instances in sample_labels and sample_decision_values\n",
      "sample_decision_values = [decision_values[i] for i in sample]\n",
      "\n",
      "# labels and decision values of known instances before peeking\n",
      "filtered = filter(lambda x: x[0] is not None, zip(labels, decision_values))\n",
      "apriori_known_labels = map(op.itemgetter(0), filtered)\n",
      "apriori_known_dvs = map(op.itemgetter(1), filtered)\n",
      "\n",
      "# all known labels and decision values after peeking\n",
      "all_known_labels = apriori_known_labels + sample_labels\n",
      "all_known_dvs = apriori_known_dvs + sample_decision_values\n",
      "\n",
      "# data statistics\n",
      "print('total number of known positives after peeking:\\t%d' % sum(all_known_labels))\n",
      "print('total number of known negatives after peeking:\\t%d' % (len(all_known_labels) - sum(all_known_labels)))\n",
      "\n",
      "# compute the resulting ROC curve\n",
      "_, roc_peek = optunity.metrics.roc_auc(all_known_labels, all_known_dvs, return_curve=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total number of known positives after peeking:\t2148\n",
        "total number of known negatives after peeking:\t152\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the resulting curves"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# convenience function for plot legend\n",
      "def plot_proxy2():\n",
      "    p = plt.Rectangle((0, 0), 0, 0, color='none', \n",
      "                      edgecolor='red', hatch='xxx', alpha=0.8)\n",
      "    ax = plt.gca()\n",
      "    ax.add_patch(p)\n",
      "    return p\n",
      "\n",
      "xs = [float(x) / 100 for x in range(101)]\n",
      "roc_point_up = ss.zoh(*zip(*roc_bounds_point.upper))\n",
      "roc_point_lo = ss.zoh(*zip(*roc_bounds_point.lower))\n",
      "roc_interval_up = ss.zoh(*zip(*roc_bounds_interval.upper))\n",
      "roc_interval_lo = ss.zoh(*zip(*roc_bounds_interval.lower))\n",
      "fig = plt.figure(2)\n",
      "fix_plot_shape(fig)\n",
      "plt.plot(*zip(*roc_true), color='black', linewidth=2)\n",
      "plt.fill_between(xs, list(map(roc_point_lo, xs)), list(map(roc_point_up, xs)), color='blue', alpha=0.4)\n",
      "plt.fill_between(xs, list(map(roc_interval_lo, xs)), list(map(roc_interval_up, xs)), \n",
      "                 color='none', edgecolor='red', alpha=0.8, hatch='xxx')\n",
      "plt.plot(*zip(*roc_neg), color='black', linestyle='dashed')\n",
      "plt.plot(*zip(*roc_peek), color='red', linestyle='solid', linewidth=2)\n",
      "plot_proxy()\n",
      "plot_proxy2()\n",
      "plt.xlabel('FPR')\n",
      "plt.ylabel('TPR')\n",
      "plt.legend(['true curve', 'beta=0', 'after labeling',\n",
      "            'expected region via betahat', 'expected region via interval'],\n",
      "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
      "plt.title('Receiver Operating Characteristic curve')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qqlp2XatlEOX6vI/z0F5Kzm7d1ItBuXL/qaknT56kWrVqHD16FA8Pj6LoPY1G\no/nPaEWtyR8RZXf++Wf45x/l5WU2w+TJyq6bzwb3WVmwfy8cPKguS0+HwHhoKFmUTYzhwd/eBGA9\nBoYhxGZcwausL/2N9jzp6s3ZQYu4GNg0b5FQS66jowRvcxwDGsRQJ2EHxgn/gyZN1Brshg1vqNmt\nW7emdevWN1SGpvQIDAxk3rx51p2sNJpbHa2oNXmTmak8of/5RwX8OH5cKW2DQY1Wa9S4dmp79mxE\nIGFICL81DOXKXUH4+IBfbAS11/THGB+Nc8YVkoGXgfkGA3c37MKA2sEM3/cde3pM4xzQwjK1fbis\n8gSvdCaCRmEhrLs/lCb7l9D1mwE4errgVNETuwv+UL8+LFyonNg0dzxX7/9cWAIDA5k/f751D+ui\nJCQkhHnz5gEwZMgQpkyZUuR1aG5ftKLWXMvp02rnKScnFTJzwgSYPj1HMYeG5tihIZdNeucO2H1P\nKD12hLC98vvs3vYDFTaE0sCyvOoP4FUPP9o5ujCn92d4lfVVNuce06w2513dQ7nn6xBSHgul4wPg\n+0EITH2OZxZ+hAx/FGOXd8HX97rXPF9NWFgYu3btYsyYMTdUjub2wGAwFMv2nLNnz2bt2rXs27cP\ngI4dO1KtWjWGZ5uKNJrbhBIPkH5HEhcnsmSJSIcOIu+8I9KkiUhQUM7OVLaEh6u0oCAx7QqXU6dE\nNm0SeeMNkRkzRCYPXCjP2DnKQcsGGRkgs6o2ltdfDpMvvjDLqrHhct4/SM77B8mqseEye7bI7Nki\ns2aJjB0rsvKNcMlqrMqXmTOVTD/9VCTNTEhIkCFDhkjVqlXl+++/L5Iyb1e4BTflCAwMlMmTJ0u9\nevXEy8tLnn76aUmzbKDy3XffSaNGjcTT01Puvfde2bdvn4iI9OvXT4xGozg7O0vZsmVl2rRpIiLy\nxBNPSMWKFcXDw0PatGkjBw4cuG55WrVqJV9++aX1eP78+dKyZcsiaKnmdqKA35oeUd/RHD6s7M8x\nMWpq++JFaN5chfa8cAHWrs3zsjNnwHwavNMgPQ1WLYAT3mA0gqdnAn8sfpYndy/nDUv+WFdfNo/4\nBmPtttTMRxQRZXu+eBHuuw8e9AG7H7MgMRl++gk++0wtq7pBvvvuO0aOHMmjjz7K/v37cXd3v+Ey\nNTcXIsKyZcvYuHEjLi4udOnShffee4/u3bszePBgvv/+e5o2bcqSJUvo2rUrR44cYcmSJWzdupV5\n8+blmvqGFAfkAAAgAElEQVTu3LkzCxcuxNHRkdGjR9O3b1/+/PNPAKZMmUJo9qzSVRgMBuLj4wGI\njIykUaNG1rSGDRty4MCBYuwBjaZ0KO2XnduPdetE7r9fDYEbNRL55huRrCyVFh6uRrDh4bm/i0hY\nmMjMp8PlaGAH+eyZcJkzPFxianeQb8bslmd7fyYzHJwl3TKKvmK0l733DZGTtYNzjZqz93he+nK4\nfD4kp6wvQi/JqTnrRQYPFqlTR21dOWGCSHJykTT5888/lxo1asivv/5aJOXdCXADI+oJEybk2k40\n+zNhwoRC5c8v378RGBgos2fPth7/8MMPUqNGDRk5cqS89dZbufLWqVNHfv/9d+t12Vtc5kVCQoIY\nDAZJTEy8Lnns7Ozk8OHD1uMjR46IwWC4rjI0tz8F/NZuGUq7D28P4uNFfvlF5PXXRTp2FDl6VJ0v\nQDHbpu+aFS6fDgyXk3U65FK8nwz+SqY5OEucRUGbQPbXbieLp8bmUsyrxobLqrHhElWzg3w6KFw+\n+khk82aRsyt/F1O9BiL33Sfy0ksia9eKnDolYjYXafMTEhIkJSWlSMu83eEWnfr+4YcfrMf79+8X\nZ2dneeSRR8TFxUU8PT2tH1dXV1m+fLn1OltFbTKZJCQkRGrUqCHu7u7i6ekpRqNRjh8/fl3yeHh4\nyO7du63Hu3fvFjc3txtspeZ2o4Dfmp76viM4fRq+/FLtWGUwQL9+8M03KgY3KCex0NA810EDnK4Y\nxN42oTR6ezhPOcJWyzrm9LRkzi8cRJ8/V3GXJe8peycO9Z/L8ZZ9rdfHBQSxq3sorZcOJyMTNj01\nmwdHBFG7NhhOnYTJ70PPHspxrUKFYusGT0/PYitbc3MRExOT63ulSpXw9/dn3LhxjB07Ns9rrvYU\n/+qrr1i3bh1hYWEEBARw6dIlvL29rQ5nkyZNYvLkyfmWlZiodnerX78+e/fupWlTteTwr7/+okGD\nBjfcRs2dg94093YmJQU++ggGDlTLrVxdwc0NHnkkR0kXwKVLaqvozz6D2DNQxjEnbE7inlU0eK08\n71qU9OkyrsT6BFLGrx6JfnXzLC/LBPZ28GRPZW42pKfB6NEweDBMnFhkSlpEuHjxYpGUpbn1EBE+\n++wzTp8+TXx8PO+//z69evViyJAhfPHFF+zatQsRISUlhfXr15OcnAxAhQoVOHbsmLWc5ORkypQp\ng7e3NykpKdco+LFjx5KUlJTnJ1tJAwwYMIDp06cTGxvL6dOnmT59OoMGDSqRvtBoSpLSnZO4Fdmz\nR+Shh5T39qZNhZratk3fvyhcxo8XmThR5JsxOVPXK0O2y3pXH0mxTHNfMhglrFkvOVmnnXVqOzuv\nrU06unYH+XxIuMRtsNS1e7eyP48bV6RT3PHx8dKtWzcZNGhQkZV5J8MtOvU9ZcoUqVevnnh6esqg\nQYMkNTVVRER++uknadasmXh6eoqfn588+eSTkpSUJCIia9euFX9/f/H09JQPP/xQkpOT5bHHHhM3\nNzcJDAyUxYsXi9FolGPHjl23TKNHjxZvb2/x9vaWkJCQIm2v5vaggN9ascf67gR8DNgBc4GrXSR9\ngaVARdQ0/AfAwjzKsbRDUyjS0qBjRzXF3bRpgbG3gWvST6+LIPXFECKeDMXBAWts7cT0JJp89hgN\n09Ro4VfvAC73+Zymv0y/Zr/n5t+GsPNxFdv73rUhbGgfSuuXgri73FlYsACWLoV69dTGHTe4Hjqb\nHTt20KtXLx5//HGmTJlCmTJliqTcOxkd61ujKRlKaz9qO+Aw8ABwGtgN9AYO2uSZCJQBxqCU9mGg\nApB1VVn6oXA9zJwJf/2l9oOGa2zOgFLWedikU1LURliVz0bQabVK39p7Jk6bP6fDziU4AqcNRsLu\nG8zDMXuAnNjbaWlqVZeIur7rD8NxIo3Ux/viWzYNp4N/qv0n770XHnpILQXLJwzp9WA2m5k+fTrT\npk1jzpw5PPbYYzdcpkahFbVGUzKU1qYczYGjQJTleDnwGLkV9RkgOzCzO3CRa5W05no4dgzWrIEx\nY3IUdSExmeD775UudXW1nExLpvGMhwm8cgmA5R6VOPtyGP4ZKbA0J7JSerraIOOhh9TGVT5RUOG3\nRIyuLuBngvr3wIhBEBiYsyd1EbF+/XpWrVrFrl27CAgIKNKyNRqNprQpzhH1E8BDwFDLcT+gBfCC\nTR4jsAmoDbgBTwI/5lGWfnsvDPv3w5tvwv33qyAh+Uxt5zX1fWlMKCuPB3HiBAQRQatvXiHB2ZO6\n+9Zhh3rjWnjvM1TpP4fyJ/dap8MBmq0KYU2rUO57IYgmTSzlDx6snMPmzoWqVYu12SKCyWTCvghG\n55rc6BG1RlMylNaIujC/4rHAXiAYqAH8DDQCkq7OOHHiROv34OBggoODi0DE24SsLDV9vWIF9Omj\nll7ZKuYCYnMDnBgRinloCIaHQmnmkUm7BQNwuhRLpYwUTMDnji5ULV+HJsHPgo2SjgsIIiEBTrcK\npd/fIXhJKGzPgGHDoHJlpaSrVCn25hsMBq2ki4jNmzezefPm0hZDo9HYUJwj6pYoG3Qny/EYwExu\nh7IfgPeBbZbjMCAECL+qLP32nh+RkfDuu2BnB3//DQ4OhbZJi8Aff6gtphtlhvPI4l64XjqFvWUD\njZ+BjyrfzQOv/Ergxahc+0GfLB/EuXPg5wddu0JAXAT076/mwB9/HN56C/Rezrc8ekSt0ZQMpTWi\nDgdqAYFALPAUypnMlkMoZ7NtKCeyOsDxYpTp9sBkgu3bYdUqOHAAXn4ZypWDESMKdfnlyxC5XZmw\nY2LgHsNftF/1LB5xag3pYQy8ihBV7yGGj1hFmTKucDEKUNMk585BkrPakrpxY7A7dgQ+/FCtzR4/\nXm2LWcR26Gz2798PoANGaDQaTRHxMMqT+yhqRA0w3PIB5en9HfAX8DfQJ59ySnxN203L8eMi3buL\ndOmiQm1euVLoEKDm3eESuTRcjlbrIJ8PDpfP3jojkfcNFjMGEZAUB2d5yWAUe5A29R+Wzz/PuCYE\n6Oxh4XKmfgdJ3WopPyNDpH17ka++Ut+LkcOHD0ulSpVkxYoVxVqPJgduwXXUGs2tSAG/tWJfR11U\nWNpxh7N6tQoT9uCDsGEDTJ2qzhfCWcw8OZR1p4PYsQOapG3joa8G4pJ4BoeMKwgGfvFvQq+YCOKB\nR5v15rPEc4T3UOVn26TPVFLT3a+1i8D9fUv5P/+sduFasKBYmx4VFUWbNm2YOHEizzzzTLHWpclB\nT31rNCVDQVPftwql+6pzM7B1q4o0dvKkOrbZD/rf9ouW8HD5+WeRN0LMsnHwckn09hexRBZLc/KQ\nF4N6WncsevzxyfnuFz1unApyZi2/cWORmjVFDh0q1qafOnVKqlevLjNnzizWejTXwm06oh43bpz4\n+vqKn59fsZS/YMECuf/++wuVd8KECdKvX7//VI/ttdHR0VK2bFkxF/FmNpqSoYDfmo71fUtw7JiK\nhT116n/yoj5yBMJ+EXrtfpWO83rhFh/DpfK1SChXk9cdnfg0YiUGg5H+/b+kU6c3rtmcACAxUa2t\nvvfeq04+/HCR7BOdHxkZGXTs2JHhw4fz3HPPFVs9mjuHmJgYpk+fzqFDh4iNjWXhwoW0bt261OTJ\n6/f2X6719/cnKSnphsrT3JzoNS03KzExMHkynDqlNO1zz0FDS2yY7Knt2bPVcR5T32mjQvj18dkk\nJUKTN0bztLcPtfeuxGTnwL6Or+J7fCcv+vizZvsi7DHw0uOTqXX/ECAnBOiWfqr8e74OIaFTKA+E\nBFGmjKX+ESOgUiV49dVi7QZHR0cWLVpEs2bNirUezZ1DTEwMPj4++Pj4FEl5WVlZN7Q8UG7AhHAj\n12puHfSI+mbkwAF4+mlo3Ro+/VStR163TilIW/tzUFDOFpUhIdb0zFdDWHJ3KHsI4lS5xhi93C1K\n2pEdPabhe2KXVUkbjfa83D2UUZEb8Y2OsCrpXd1DifULYrc5iP39QxkYGaKWYEVEqHXSLi7wySdQ\nApHAtJLWXC9TpkyhZs2auLu7U79+fdasWQPAL7/8woMPPkhsbCxubm706tWLkSNHsn37dtzc3PD2\n9gYgPT2d1157jYCAACpWrMjIkSNJS0sD1FrzKlWqMHXqVPz8/Bg8ePC/yjNq1Cj8/f3x8PCgadOm\nbN261ZpmMBhIS0ujV69euLu7ExQUxL59+6zpsbGx9OjRg/Lly1O9enVmzJiRZx1RUVEYjUbMZjOg\n4k2MHz+e+++/H3d3dx566KFcu8otXryYgIAAfH19ee+99wgMDCQsLOw6e1qjyaG0zQclx+HDIq1b\ni/z2W+7zhbRJm5oEyYrR4fLuuyJzZmXJ4ZYDREAy7ctIQrlacq5qE+nWaqAAYjTay/Dhq6ye3bY2\n6XfeERk/XmTHDpGsLBHZvFmkenWR2rVF2rUTiYwske7QlC78Vxu1xQfihj//kZUrV8qZM2dERGTF\nihXi6uoqZ8+eFRGRzZs3S5UqVax5Fy5ceI09+aWXXpLHHntMEhISJCkpSbp06SJjxowREZFff/1V\n7O3t5Y033pCMjAzrzly2XG2jXrp0qcTHx4vJZJIPP/xQKlasKOnp6SKi7MwODg6yatUqycrKkg8+\n+ECqVasmWVlZYjKZpEmTJvLuu+9KZmamHD9+XKpXry4bNmywXpttoz5x4oQYDAYxmUwiItK2bVup\nWbOm/PPPP5KamirBwcHyxhtviIjIgQMHpGzZsrJt2zbJyMiQ1157TRwcHCQsLOw/97nmxijgt6ZH\n1Dcdn3+uvLrbtPlPlycmQlwcVPDJpN38ftTesZjMMq788dQnZDi58d7l09aR9NChK2jSpHuu6wWI\njYWKFWHUKGjRAuyOHoa334aePWH+fPjxR7jrriJo7NWyJ/LndcYn12jy4oknnqBixYoAPPnkk9Sq\nVYudO3cC104X53X85ZdfMn36dDw9PSlbtixjxoxh+fLl1jxGo5G3334bBwcHnJyc/lWevn374uXl\nhdFo5JVXXiE9PZ3Dhw9b05s2bUr37t2xs7PjlVdeIS0tje3bt7N7927i4uJ48803sbe3p1q1agwZ\nMiSXLPlhMBh4+umnqVmzJk5OTjz55JPs3bsXgG+++YauXbty77334uDgwDvvvKNt2zcx2kZ9M3H+\nPOzeraKLPfzwtcutCrBJExJCwpTZLFsGj219HcM2A5UPbyLDyY0/en5EjV3LGF7lbtac3IM9Bl7u\nNomaFiWdPd29vutskpKhz18heI4Mxc47CDZuVJHP3npLvUAUE9HR0TzyyCN07dqVxo0bF1s9mhKi\nlG2nixcv5qOPPiIqKgqA5OTkXNO+BXHhwgWuXLlCkE10PxGxTikDlCtXDkdHx0LL88EHHzB//nxi\nY2MxGAwkJiYSFxdnTa9i4yRqMBioUqWKNW9sbCxeXl7WdJPJRJtCvshnv6wAODs7k5ycDKjpdNs6\nnZ2di8xmryl6tKK+mVi1Ch57DDp0KDA2d36xu38+FkRcAFyIbUHjDVPIKFOWbU/NoNbOJbxZpSFr\nwj5WNuluk3gxcgO76rYHoNk3Iay+NxRj3SC6dAafi5byg4Ph99/VKLpWrWJrdmJiIp07d2bgwIGM\nHj262OrR3BlER0czbNgwNm3aRKtWrTAYDDRu3Dhfx6urR5K+vr44OzsTGRmJn59foa4piC1btjBt\n2jQ2bdpE/fr1AfD29s4lz8mTJ63fzWYzp06donLlytjZ2VGtWjWOHDlyw3LYUqlSpVwj+tTU1EK/\nyGhKHq2obxbS01VAky+/VA5aoaF57hcN5DiQ2aSfqRTE3lVQ0/cSdbfNBSDVrTwNfp3Bp/cOYvGK\nUQA888xSajZ7il1129N66XAEWNFuNs1HBNGsGRiNQJVG0KgRbN4MX32ldsEqJkwmE3379uW+++7j\n9ddfL7Z6NHcOKSkpGAwGfH19MZvNLF682Bp6Ni8qVqzIqVOnyMzMxMHBAaPRyNChQ3nppZeYOXMm\n5cqV4/Tp0xw4cIAH/8OsUlJSEvb29vj6+pKRkcGUKVNITEzMlSciIoLVq1fTpUsXPv30U5ycnGjZ\nsiUAbm5uTJ06lRdeeAFHR0cOHjxIWloaTZs2/Vev7/zSe/ToQatWrdi+fTtBQUFMnDhRe5DfxGgb\n9c3CTz9B3br/2Yv6l1/A2RmCNkzCOTmOuKqNyXD25HhmGh+tGYuImc6dx9Os2VPWawTIyICWrZQt\n2mhEBfIePlxtSr1qVbEqaYBx48aRnJzMzJkztY1MUyTUq1ePV199lVatWlGxYkX279/P/fffnyuP\n7b3Wvn176tevT8WKFSlfvjwAoaGh1KxZk5YtW+Lh4UHHjh1zjWr/7V41GAzWPJ06daJTp07Url2b\nwMBAnJ2d8ff3z5W3W7durFixAm9vb7766iu+/fZb7OzssLOz4/vvv2fv3r1Ur16dcuXKMWzYMKui\nt60nL7muTss+rl+/PjNmzKBXr15UqlQJNzc3ypcvT5kyZf69gzWafCg1T7wSISVFpGNHkb171XEh\nY3dnp6e06iCfDgqXr949Jln2jiIgZwOayZJXN0sVn2oCSLPabWXWLFNO7O46HWTGoHDZNC1czNll\n7d8v8uCDIvPni1g8R4ubH3/8UeLi4kqkLs31w20amUyTm6SkJLG3t5eoqKjSFuWOpYDf2i1Dafdh\n8TJjhki9eoVWzLbp6ekii14Ml6haHeRk3Q4iIMnuFWXlmF3SsGEXAaSqb3U5WKutrBobLqvGhktM\nHaXYv/vOsvQqPFykWTOR++8X+f330ukDzU0JWlHftqxbt05SUlIkOTlZhg8fLk2aNCltke5oCvit\naRt1qXPyJKxZo4KHXIdNOjv9jz/gcNkgAlr0ou3SoYjBwG8D5zN/71r27fsOFxcvhr+0kcgrl6z7\nSS9vP5u7BwbRtq1lN8qyZcHJCT74AJo3L8HGazSa0mLdunUMGDAAEaFZs2aFWvKlKR20oi5NzGYV\nv7t/f7BZflFYzp2DsDCoVNFMw/nTAbjiVpGwk3/x44/vYzAYGTp0BeXK1YDoCABMZvD1JUdJAyxa\npF4CtJLWaO4YvvzyS7788svSFkNTCLQzWWmybBkkJSknsux10rNn54QDzcZ2HbUlPXNnBP/7n3Ig\na/XjeLzOHiS1bDnmdnuPWWvHAfDEEx9Sr17HXLG7v3lgNl22hmDYYyn/7FnYsgW6dSv25ppMJh3Q\nRKPRaK6TW8XN1jKFfxtx4ACMHAljx6op53/ZT/rq9ItDQljeOJSmCRtpvmYcBoQfen/GgI1TuXgx\nmifc/ej13DoMBoM1dne0bxCZmfBqcAR2Yy1lrlgBPj6qjmJERBg1ahSHDh1iw4YN2sP7FkHvR63R\nlAwF7Ud9qzwtb6+Hwq5dKtLXiRPg7n6tTRqUss7DJh0XB3v3wsGlEQz4vifuF09gAMIfHkvfo1s5\n8s/vBAY2Z/KTH9Fh+YsAbOk3m7iAIKKj4fHHoWlTS/lDhkBysgpqkk9gh6Ji2rRpLFq0iK1bt+Lp\n6VmsdWmKDq2oNZqSoSBFrW3UJUlCgtpXOltjzp17XZdv3Ai//QZ2dvBI3I9WJX3w/qG8duUSR/75\nHQ8PP0aOXI3j5TO5rj1/Hry94e67LSdMJrh0CTp3LnYlvWzZMmbMmMEff/yhlbRGo9FcJ1pRlxQm\nE4wbB9WqQe/e8Oab/xq72zY95rlQft0VREAABP3wDk3XT8AARLYeznf//MZvZw9hb+/IiBHfUvPy\nmdz7SS8PIa1bKI88b9lPetMmtb91u3bqxaEYCQsL46WXXmLTpk25YgtrNBqNpnBoZ7KS4rPPID5e\nuVu/+WaB+0lfvd90yvhQTK+FUD8tgqbr36bpd0pJ7+76Lgtb9uPN80cBGNFpLM3tHKw26biAII56\nBPFH11Ce3BOC57EICA+HZ59V9vEvv1Qu4MWI0Whk5cqVNGjQoFjr0WhuZ4KDg5k3b16J1PXII4+w\nZMmSEqkrm8mTJzN06ND/dG1J9s3EiRPp379/idRlix5RlwRbtqg43gkJSklexzrprCxYFRVE2gOh\n9F7cg7Lx0RiAXY+9z6aW/fhiUlOyzFk82qw34/d9B/u+s9qkAS5fhq7Dg7BPsZSfkqK8zJ9/3hIz\ntHhp165dsdehuTn45BNlYikuypdXW6/eakRFRVG9enWysrIw/sff3NWhQouTH374oUTqsWXMmDH/\n+dob6Zvg4GD69+/P4MGDC13Xf2XhwoXMmzePLVu2XPe1WlEXN9HR8M47MGwYfPjhdV0qAt99B4cO\nQY9Ta3CLjwZgf7vn2dlhFLM+aENS0gXq1u3AgA6jYNlzua6/ckX5qtWqBey1nMzKgoEDS0RJa+4s\nzp//z6HqC0V0dPGVXRKUlPOdyWTCzs6uROq61blexVtaDpT6aV2cpKTAa6/BQw/BvHnXtU5awiP4\n+WfYuRM6xC6myQ/vA/B3+xdxj41k6cxHiYnZg69vdd7oNIZWa8axpd9stvSbTfNvQ/CNjuDCBWWG\ntttrKX/CBKhSBR55pJQ6RKMpGWJjY+nRowfly5enevXqzJgxA4D4+HiqVq3K999/D6h9qmvWrMnS\npUsBGDRoECNGjODBBx/E3d2d4OBgYmJirOUeOnSIjh074uPjQ926dVm5cqU1LTU1lVdffZXAwEA8\nPT1p06YNaWlp1r2jPT09cXNzY+fOnQDMnz+fevXq4e3tTadOnXLV8/PPP1O3bl08PT154YUXEJF8\nlcTEiRN54okn6N+/Px4eHixatIjLly8zePBgKlWqRJUqVXjrrbes+2mbzWZeffVVypUrR/Xq1Zk5\ncyZGo9GabjuVLCK89957BAYGUqFCBQYOHGjdECQqKgqj0cjixYsJCAigXLlyTJo0KU8Zd+7ciZ+f\nX642rF69mkaNGlnbYDul3LNnT/z8/PD09KRt27ZERkYW8N+Go0eP0qJFCzw8POjWrRsJCQnWtB07\ndnDvvffi5eXFPffcw2+//QaoDYG2bNnC888/j5ubGy++qFbJjBo1Cn9/fzw8PGjatClbt261lmUw\nGMjIyGDgwIG4u7vToEEDImye5VOmTKFmzZq4u7tTv3591qxZA8DBgwcZOXIk27dvx83NDW9v7wLb\nczVaURcX6ekwerTyqP7pp+uySae9Hcq5p0M4/HUEzbO20ebrkRgQ/u7wEtuf+oQXvSqz68hmXMqU\n5a3uoXT4abLVJh0XEMSu7qE0WxWC/4UIGmbalL9/P/TqBcW0Q05aWhq//vprsZSt0RQWs9lMly5d\naNy4MbGxsYSFhfHxxx+zceNGvL29mT9/PkOHDuXChQu8/PLLNGnShH79+lmvX7ZsGePHjycuLo57\n7rmHvn37Amr7zI4dO9KvXz8uXLjA8uXLefbZZzl48CAAr732Gn/++Sfbt28nPj6eqVOnYjQarVOd\nly9fJikpiRYtWrB27VomT57M6tWriYuLo3Xr1vTu3RuAuLg4evTowaRJk7h48SI1atRg27ZtBY7+\n1q1bR8+ePbl8+TJ9+vRh0KBBODo6cuzYMf788082btzIXMsqkzlz5vDTTz/x119/sWfPHtasWZPv\nLlsLFixg0aJFbN68mePHj5OcnMzzzz+fq+5t27Zx5MgRwsLCeOeddzh06NA18rVo0QJXV1fCwsJy\n9XN2315N586dOXr0KBcuXKBJkyb55gP1MrF48WIWLFjAmTNnsLe3tyrd06dP8+ijjzJ+/HgSEhL4\n4IMP6NGjBxcvXuT999+ndevWfPbZZyQlJfHpp58C0Lx5c/766y8SEhLo06cPPXv2JCMjw1rXunXr\n6N27N5cvX6Zr1665+qNmzZps3bqVxMREJkyYQL9+/Th37hx33XUXX3zxBa1atSIpKYn4+Ph823Mr\nU9Lx0W+MlBSRoUNFqlcXadIk9wYb2YSHiwQFqY9NelycyAcfiMwaEi7n/YPkStlyIiAX/erJ3Jmp\n0q/fHAHEzmgn35SvJef9g2TV2HCZPVusn08+Efl0YLhcrm0pf8cOkXnz1GYexbRTVUZGhjz66KPS\nt2/fYilfUzpwHZtyjB0rue7Dov6MHVs4mXfs2CH+/v65zk2aNEmefvpp6/ELL7wgDRo0kCpVqkh8\nfLz1/MCBA6V3797W4+TkZLGzs5OTJ0/K8uXLpXXr1rnKHTZsmLz99ttiMpnE2dlZ9u3bd408J06c\nEIPBICabHek6deok8+bNsx6bTCZxcXGR6OhoWbRokbRq1SpXGVWqVMmV35YJEyZI27Ztrcdnz56V\nMmXKSGpqqvXcsmXLpF27diIi0q5dO5kzZ4417ZdffsklX3BwsLWu9u3by6xZs6x5Dx8+LA4ODmIy\nmaztOn36tDW9efPmsnz58jzlfPPNN+WZZ54REZHExERxdXWVmJgYaxv69euX53UJCQliMBgkMTEx\nz/Tg4GAZM2aM9TgyMlIcHR3FZDLJlClTpH///rnyP/TQQ7Jo0SLrtXPnzs2z3Gy8vLys/9cJEyZI\nx44drWkHDhwQZ2fnfK+95557ZO3atSIismDBArn//vvzzVvAb02PqIuclBR48UWwtwdPT5uA2v/O\nlSuwZAmkpSnHGYfUyzgnX8BstOfXZ5ay/+hWli0bCcCwTmNo4+R+TRnnzyuftY4dwc0NyMyE995T\nUVKWLlVRyIoYk8nEgAEDMBgMLFiwoMjL12iuh+joaGJjY/Hy8rJ+Jk+ezHkbT7ehQ4dy4MABBg0a\nhJdNnH2DwZBrGaGrqyve3t7ExsYSHR3Nzp07c5W7bNkyzp07x8WLF0lLS6NGjRqFlnHUqFHWcnws\nv8vTp09z5syZa5YyVq1atcDybPNHR0eTmZmJn5+ftfwRI0Zw4cIFAM6cOZOrvIKWTZ45c4YAG8cD\nf39/srKyOHfunPVcxYoVrd9dXFxISUnJs6w+ffrw7bffkpGRwbfffktQUFCe7TKZTLzxxhvUrFkT\nD5wFgKUAACAASURBVA8PqlWrhsFgIC4uLl85bcvx9/cnMzOTuLg4oqOjWblyZa7/2bZt2zh79qw1\n/9UzFR988AH16tXD09MTLy8vLl++nKvuChUq5GpvWlqa1WywePFiGjdubK1r//79XLx4MV+5C4t2\nJitKspW0iwtERsKcOep8IdZJmyaF8s2hIBISoFFWBC1XvkKZ1EsAJPkEcOr8UWYvHYrZbKJbywGM\nPb7duk46eznWCe8gjEYYdX8Ebu+FwBdfwEcfqc02Xnzxul4aCouIMGLECM6fP8/69etxcHAo8jo0\nmuvB39+fatWqceTIkTzTTSYTw4YNY8CAAXz22WcMGjTIqmBFhJMnT1rzJicnEx8fT+XKlfH396dt\n27Zs3LjxmjLNZjNOTk4cPXqUhg0b5krLa8ra39+ft956yzrdbcs///yTS4arZbqaq72eq1atSpky\nZbh48WKeXuZ+fn65yiuo7EqVKhEVFWU9jomJwd7engoVKuSyqReGu+66i4CAAH788UeWLVtGnz59\n8sy3bNky1q1bR1hYGAEBAVy6dAlvb+8CHblsZYmJicHBwYFy5crh7+9P//79mZP9LL6Kq/83W7Zs\nYdq0aWzatIn69esD/Gvd2URHRzNs2DA2bdpEq1atMBgMNG7c2HrtjXiM6xF1UZGWpoKIODsrJT11\naqFt0oSGcmlECJd/jaBRVgTNV43GbOeAc3IcZ2vcx+peM/lw4QBSUy/Tok47Pkk4dY1NuvmqEBz/\njqB/fYuSDg2FqCg1sn/uuWJR0vD/9u48Lspqf+D4ZxgWAXFhUwTBULvmWo5SphkumVuZpKbmXi5l\nLlevTVp23a7d8Wdp3UoxSytzS63MLC2XXNNArTT3BRVwQXFhh5nz++OBYREQlWEc/b5fr3k585xn\nzpwHhC/PWb5Hm5Cxf/9+vvvuO8qVK2eTzxDiVoSFheHl5cWMGTNITU3FbDazf/9+oqKiAJg+fTp6\nvZ4FCxYwbtw4+vXrZ70jAm150vbt28nIyGDixIk0a9aMwMBAOnXqxJEjR1i0aBGZmZlkZmby+++/\nc+jQIZycnBg0aBBjxowhPj4es9nMzp07ycjIwM/PDycnJ44fP279jGHDhjF9+nTrJKmrV69aJ6Z1\n7NiRAwcO8M0335CVlcUHH3yQ7w6woIJBJCAggHbt2jFmzBiuX7+OxWLh+PHjbNmyBYAePXrw/vvv\nExcXx5UrVzCZTEUGkV69ejFr1ixOnTpFUlISEyZMoGfPnsUuMysuqPXu3ZvZs2ezdetWunfvXug5\nSUlJuLm54e3tTXJyMhMmTCiyvpzPW7RoEQcPHiQlJYW3336b7t27o9Pp6NOnD99//z3r16/HbDaT\nlpbG5s2biY2NBbS747zfl+vXr+Ps7Iyvry8ZGRlMmTLFOnnuZpKTk9HpdPj6+mKxWFiwYAH79++3\nllepUoWzZ8+SmZlZovrykkBdWkwmbb30zp25QTpH3nXSQ4fmv7sGYnwNLGlk4oWNQ3li0VBOPRJB\n0KENZLiV5+e+nzBt7VTOZKbxsKsHy5KvEPX8DOs6aYCEEAPfPW6i346hVJ+aXb+vr3ZHPWWKFqxt\nJCIigrVr11K+fHmbfYZwDP7+2hIqWz38/UvWDicnJ9asWcO+ffsIDQ3Fz8+PIUOGcO3aNaKjo5k1\naxZffPEFOp0Oo9GITqfDlL0Bjk6no3fv3kyePBkfHx/27t1rnRHu5eXF+vXrWbp0KYGBgQQEBDB+\n/HjrRKOZM2fSoEEDmjZtio+PD+PHj0cphYeHB2+++SbNmzencuXK7N69m+eeew6j0UjPnj2pWLEi\nDRo0YN26dQD4+vry9ddf88Ybb+Dr68uxY8do0aJFkddb2DriL774goyMDOus8u7du1uD/eDBg2nX\nrh0NGzbEYDDQqVMn9Hp9ocF30KBB9O3bl5YtWxIaGoqHh4d1Bn3OZxfWnqL06tWLLVu20KZNm3wz\nn/NeQ79+/QgJCSEwMJD69etb706Lu/5+/foxYMAAAgICyMjIsE4MCwoK4rvvvmP69On4+/sTHBzM\nu+++a/1jYtSoUaxYsQJvb29Gjx5N+/btad++PQ8++CA1atTA3d2d4ODgYr/WOa/r1q3L2LFjadas\nGVWrVmX//v35vm9t2rShXr16VK1aFf+S/mfO+YxbOtt+VEm6Huxm7drcbA96/S1tspGWBv/7H1Q5\nG02Hb7XyxIC6PLjrS/Z2mMCopAS2bp2Hj1cVNleoQhW9S76EJgBnz0JjFc2za4fipAOmToWPP9Y2\n3ejSpSy+AuIedb9tyjFw4ECCgoKYOnWqvZtSZn788UdeeeWVfF3couzJphy2dOIE/Pe/WiKRnE02\nSjAmjcmE5REDa9dC+cPRtN6em5u706y2APySeo2tW+fhonflc+9gjrw4hyOQL0VofDw0zIzmmV1G\nnOZFwvnzWvqm//xHgrQQt+he/OOjoLS0NDZu3Ei7du04f/48kydPJiIiwt7NEsWQQH0njh6FYcO0\nrSI/+SQ3MOeMSRe1n7TJhDIa2drRROxf0HWnkd3Pa4FXZ85Cn5UGwHu/ztFO969F+otzrHfRuyNM\nhK0y8n1zE3V9oesuI/qZJm0c+oMP4J134Pnny/RLIcS9oCxTddqLUopJkybRs2dP3N3d6dy5M1Om\nTLF3s0QxHOV/5N3XzXbwoLYLVkoKLFlS4q5u0G6+t70fTa2ZQ3F1hW15urK9z/xBt2kPc1LnRKiy\n8HJ5PzqM/DFfV3dmJliionlxy1AqVUK7k46J0cakJ0+GZs1scsnx8fFs3bqVHj162KR+cfe537q+\nhbCX4rq+ZTLZ7UhLg7Fjc5Np34IrV2DBAjhwAFxdb/yu+BzT0tXtVBYedyvP5Mr51xkqpY1JP94M\nKldGG5Peswc++0x72ChIJyUl0blzZw4fPmyT+oUQQhROur5vx/z52h3skiXa6xKOSV+qYWDuXPA/\nG02XnUa2FVgHnRBiIHmTNlvxsJOel4et4jdP73zlsbHQqkI0jZcb0UVmj0mPHQvLl2t5vG0gKyuL\nXr160ahRI9566y2bfIYQQojC2brruz0wG9AD8wFTIeeEA7MAFyAh+3VBd0832/Hj0LkzfPghtGmj\nHcu7NhqKDNw/hps4exY6/JobeAF8Y6IJW2VkWo0wXvvpHeoDX3V6m+RnJ+crX9/ahJsb9NxnRP9/\nJqhXD156CZ55RsvhbQNKKV577TWOHDnC2rVrJaHJfUa6voUoG8V1fdsyUOuBw0BbIBb4HegFHMxz\nTiVgO/A0cBbwRQvWBd0dvxSysuCFF+DRR7UNN/IqZkwaIHZ1NGroUNxcuWF5FUDCtk95/8uXOQ9k\nOjnz+QdJWFy0zTOU0saku/44FB9fcPk0Eho10nbmqlgRJk2yWUKT999/n/nz57Nt2zYqVqxok88Q\ndy8J1EKUDXuNUYcBx4BTQCawFCi4Xqg3sBItSEPhQfru8c47Ws7sVq1u6W1ms5YLxbmILWKvXInj\n/1YZaZr9+mpgA2uQBq2XPfQB8PMHF2e0yD1tmvbvxIk2C9IArVu35ocffpAgLYQQdmLLQB0I5E0i\nezb7WF61AW9gExAF9OVu9e23sG0bLFwI48ffdD/pvOWHF0fTZIWRHf3z7xcNkJmZzqcftOdK8iUi\nKmjJ7V1TLlvLL16Epvpo2m00ov8ku/5Bg+DYMW39tg2zjgE0aNAgX2YeIUTZy7tHtK117NiRL7/8\nskw+K8c777zD4MGDb+u99mjv7XJycuLEiRO3/D5b/pYvSb+YC9AYaAN4ADuB34CjNmzXrTt6FN59\nF774Ah54oETrpHOOJSVBuX8b2dXNxPUC66B3df0vc9ZO40jsX/hWqMrT3tXh2jn+avNPwlYZ+e05\nExnnoOMxI7rZ2fXv3w/e3lp73N3t9AUR4kZNmzblwoUL1pzKObnfc57r9VqX0u2WBwQE8Pvvv9vh\nyu7MqVOnCA0NJSsrq9gc2cUpy/Xda9euLZPPyWv8+PG3/d5baW94eDh9+/blpZdeuu3PswdbBupY\nIO/aourkdnHnOIPW3Z2a/dgCNKKQQD1p0iTr8/DwcMLDw0u1sUXKyNDuoF9/XQvSkD93N9w4Jp2n\nPCMRfm4bia52/tzcuyNMHJvTlQ2JZ3B1dmP4sJVUfTccpdNxtFl/ztdqQbMFQ/H0ALdl2fUnJ8Nb\nb8Hbb0OerdaEKC2bN29m8+bNt/XeCxcu4OfnB2gbFOTsaBQcHIynp2e+c2+nPO82lY6orMb0zWaz\n9Y8ekd+d/rFjsVhu+4+tO2HLT4xC69quAbgCLwCrC5zzHdACbeKZB/Ao8HdhlU2aNMn6KLMgDVqm\nr/LltZnetygtTVtq7et7Y9muw5uYkKiNDIx82kjXvavQmzO5HNiADI9KJCdrswq8vLLfkJGhjUc3\naQKtW9/+9RQjJSWF5cuX26Ru4RjCw8Pz/aw5qri4OJ5//nn8/f0JDQ21biRx+fJlqlevzpo1awAt\nP0CtWrWsG28MGDCAYcOG0a5dOypUqEB4eHi+LRQPHTrEU089hY+PD3Xq1LHueAWQmprK2LFjqVGj\nBpUqVaJly5akpaXRsmVLACpVqoSXlxe7du0C4LPPPrNumtG+fft8n/Pzzz9Tp04dKlWqxIgRI1BK\nFRnoJ02aRLdu3ejbty8VK1bk888/5+rVq7z00ktUq1aNoKAgJk6caN0hzGKxMHbsWPz8/AgNDeXD\nDz/EycnJWp63m10pxbRp06hRowZVqlShf//+1t2kTp06hZOTE1988QUhISH4+fkxffr0Qtu4a9cu\nAgIC8l3DN998Q6NGjazX0Ldv7shn9+7dCQgIoFKlSjz55JPWXcYKk7e9CxcupEWLFowbNw5vb29C\nQ0P56aefAG2nv61bt/Laa6/h5eXFyJEjb/o9HTBgAK+88gqdOnWifPnyzJw5k4CAgHy7reW9jt27\nd9OsWTMqV65MtWrVGDFixG3tllXWOqDN/D4G5PRtDM1+5PgXcAD4CxhZRD2qzF29qtT8+Uq1bKk9\noqJyy6KilGrTRvs37/Ns1zZHqfMN26j/DYhSX46OUmfqtFErJ0SpyEilIiOVmvJipHLTOSlAvVOv\ng8p0cVdKmxqmfn0xUn32WpQ6/kAbFbcmu/7wcKV69lTq9deVSk+3yeVmZGSozp07q759+yqLxWKT\nzxCOh6KHsG44Nzg4WBkMBlWnTh3l5eWl6tSpk++5wWC4o/Lg4OAStdlsNqvGjRurqVOnqszMTHXi\nxAkVGhqq1q1bp5RSav369apq1arqwoUL6uWXX1bdu3e3vrd///7Ky8tLbd26VaWnp6tRo0apFi1a\nKKWUSkpKUkFBQWrhwoXKbDarvXv3Kl9fX/X3338rpZR69dVXVatWrVRcXJwym81q586dKj09XZ06\ndUrpdDplNputn/Ptt9+qWrVqqUOHDimz2aymTZumHn/8caWUUhcvXlReXl5q5cqVKisrS82aNUs5\nOzurTz/9tNDr/fe//61cXFzUd999p5RSKjU1VT333HNq2LBhKiUlRV24cEGFhYWpyMhIpZRSc+bM\nUXXr1lWxsbEqMTFRtWnTRjk5OVnbFx4ebv2sTz/9VNWqVUudPHlSJSUlqYiICNW3b1+llFInT55U\nOp1ODRkyRKWlpak//vhDubm5qYMHDxbazpo1a6qff/7Z+rpbt27KZDJZr6FPnz7WsgULFqikpCSV\nkZGhRo8erR5++OEiv99527tgwQLl4uKi5s+frywWi5ozZ46qVq1aoeeW5Hvav39/VbFiRbVjxw6l\nlFJpaWnFXkd0dLTatWuXMpvN6tSpU+qhhx5Ss2fPtp6r0+nU8ePHC72OYn7WHEaR36RSZ7Fo0bR5\nc6XeflupkydvGpjzHotfE6WOh7ZRcwdHqTlztKpWTsgN1jNf+kp5OelVIKjNvjWtATrdrbza1He+\nWvBalDpZq426tD67frNZqRde0IJ0VpaNLtmiBgwYoDp06KAyMjJs8hnCMXELgTowMLBUA3PB8sDA\nwBK1+bfffrshqE+fPl0NHDjQ+nrEiBGqfv36KigoSF2+fNl6vH///qpXr17W10lJSUqv16szZ86o\npUuXqieeeCJfvUOGDFGTJ09WZrNZubu7qz///POG9uQEtLyBun379vkChtlsVh4eHiomJkZ9/vnn\nqlmzZvnqCAoKKjZQP/nkk9bX586dU25ubio1NdV6bPHixapVq1ZKKaVatWql5s2bZy375Zdf8rUv\nbzBr3bq1mjNnjvXcw4cPKxcXF2U2m63XFRsbay0PCwtTS5cuLbSdb731lho0aJBSSqlr164pT09P\ndfr0aes15A3UeSUmJiqdTqeuXbtWaHnBQF2rVi1rWXJystLpdOr8+fPWc+fPn28tL+57qpT2/6F/\n//4lvo6CZs2apbp27Wp9fbuBWjKT5ZWRARMmaDOqV6yAqtosbGrUKNGYdPqAoZgvwfYekejqGqwL\n4nLGpKsvHMDw+IO8rMxMdXLGM+E4mW6eRD0zmXM1W9BiyXBqZYD+k0i8n8qu/6eftFyj06drW2ja\nwBtvvMHBgwfZsGGDJDQRty01NZXExMQbxpw9PT0JDAwscky6pOUlHaOOiYkhLi6OypUrW4+ZzWZr\nFzRoezJ/+OGHvPnmm/nO0+l0BOXJ8Ofp6Ym3tzdxcXHExMSwa9eufOdnZWXRr18/Ll26RFpaGjVr\n1ixxG0eNGsXYsWPzHY+NjSU+Pj5fGwCqV8+fSrigvOfHxMSQmZlJQECA9ZjFYrGu3oiPj89XX8HP\nyis+Pp6QkBDr6+DgYLKysjh//rz1WNWc35OAh4cHycnJhdbVu3dvHn/8cebMmcOqVaswGAyFXpfZ\nbObNN99kxYoVXLx4EScnJ3Q6HQkJCXhZxwKLVrA9oA1x5OwBnXecurjvac65Bb8+xV3HkSNHGDNm\nDNHR0aSkpJCVlUWTJk1u2uabkUCd1+jRsG4dfPllbpAuodhYIEFbLeXpqc2My+tK0iW+On+Yn5SZ\nRgCWLE4+EsGOHrNJ9q6Ob0w0mZng4QHeOT9fycnaZtUzZtgsSH/88cesXr2abdu23TChRwhHFBwc\nzAMPPMCRI0cKLTebzQwZMoR+/frx0UcfMWDAAGuAVUpx5kzuqtKkpCQuX75MYGAgwcHBPPnkk6xf\nv/6GOi0WC+XKlePYsWM0bNgwX1lhE5iCg4OZOHEivXr1uqHs6NGj+dpQsE0FFZwRXr16ddzc3Lh0\n6VKhE58CAgLy1Vdc3dWqVcu3T/Xp06dxdnamSpUq+cbUS+Khhx4iJCSEH3/8kcWLF9O7d+9Cz1u8\neDGrV69mw4YNhISEcOXKFby9vUtlMl7B70Vx39OiFHcdr7zyCgaDgWXLluHp6cns2bNZuXLlHbdb\nNuXIkZCgJTNZtEibVX0L66QvrosmfbSRTT0j2d4v/zppgIqHNlHho86sNGfSCMhwLsf2HrP5edhK\na5BuutLIdx0jtbXSOfV/9pmWBa1BA5td9lNPPcW6devw8fGx2WeI+4O7uzvBwcHExsbmu6tKTk4m\nNjaW4ODgOyp3L+FyxLCwMLy8vJgxYwapqamYzWb2799PVFQUANOnT0ev17NgwQLGjRtHv3798k0O\nWrt2Ldu3bycjI4OJEyfSrFkzAgMD6dSpE0eOHGHRokVkZmaSmZnJ77//zqFDh3BycmLQoEGMGTOG\n+Ph4zGYzO3fuJCMjAz8/P5ycnDh+/Lj1M4YNG8b06dOtk6SuXr1qncTUsWNHDhw4wDfffENWVhYf\nfPAB586dK/J6CwawgIAA2rVrx5gxY7h+/ToWi4Xjx4+zZcsWAHr06MH7779PXFwcV65cwWQyFTkb\nulevXsyaNYtTp06RlJTEhAkT6NmzZ7Ezn4sLqL1792b27Nls3bqV7t27F3pOUlISbm5ueHt7k5yc\nzIQJE4qs71ZVqVIl3/ehc+fORX5Pi7uWoq4jKSkJLy8vPDw8OHToEHPmzCmVdkugzrFhAzz1lLb7\nVM466Ojo/Hm8DYbcpVfZ5dc2RZM03MjWziZSHjJYu7lzgrX/oU089MHTdDNnkgHsbDOaH//5CyF/\nfo9vTLQ1j/f3zU38o7eBiq2z6x8xAr7+WvvXhmrXri0JTUSpCAgIICUlhQoVKnDx4kXOnTvHuXPn\nuHjxIhUqVCAlJeWOyvN25RbHycmJNWvWsG/fPkJDQ/Hz82PIkCFcu3aN6OhoZs2axRdffIFOp8No\nNKLT6TBl50TQ6XT07t2byZMn4+Pjw969e60zwr28vFi/fj1Lly4lMDCQgIAAxo8fT0ZGBgAzZ86k\nQYMGNG3aFB8fH8aPH49SCg8PD958802aN29O5cqV2b17N8899xxGo5GePXtSsWJFGjRowLp16wDw\n9fXl66+/5o033sDX15djx47RokWLIq+3sDXWX3zxBRkZGdZZ5d27d7cG+8GDB9OuXTsaNmyIwWCg\nU6dO6PX6QoPvoEGD6Nu3Ly1btiQ0NBQPDw/rDPqczy6sPUXp1asXW7ZsoU2bNnh7exd6Df369SMk\nJITAwEDq169Ps2bNSrysqrCvRd7Xo0aNYsWKFXh7ezN69GjKly9f7Pe0qPXrRV3HzJkzWbx4MRUq\nVGDIkCH07Nkz3/tvd3mY7EedY9AgbYOL5s211zfJ3Z1TfuUKLGsdia5J/nLfmGieXDiQ9HMHqWbJ\nIh4d3w5Zjt7QzVr+xCKt/jXPRnK1poFXX9WGo8nMhIgIrT3PPWfLqxaiWPdbru+BAwcSFBTE1KlT\n7d2UMvPjjz/yyiuv5OviFmVP9qO+mbg4OH0awsJu6W1mCySngHchvcZeCSdxPfc31SxZHALm9l9g\nDdJ5KQUpydCjR3aQBvjkE6hZE7oUTI1+Zy5fvlxmSReEcET3w89HWloaa9euJSsri9jYWCZPnkxE\nRIS9myWKIYEaYP16qFsXcmY832RMOqd8z9BIVneKpNm3+ceka0SvpOX8nnhZzOwEfvCrSaPA+tby\nnO7uTT0jWdY6kt5/GqkWH61F7e+/h5UrS32zjQMHDtCwYUPrOJ0Q4kZlmarTXpRSTJo0CW9vbxo3\nbky9evWYMmWKvZsliuEo/yNt181mNmtbV54+DTkD/0XsJ503t3fGVBP//dmAtzdUi9cC7+4Irbz5\nnK5USTzDL8C7LYcxuMXL+crDVhlZ18rEKR8DTz8NzVyj0Y8dDUFBWrCePBn+8Y9Su8Tk5GSaNGnC\nuHHjGDRoUKnVK+5991vXtxD2Yq/9qEuTbX4pHDsGU6ZAhQrQrx+8+qp2vJgxaQDzx5FsTTHwyy+Q\nMw8rZ8xZKcXapAsMSDzLTO8aeE47il7vnG9MetXTkWQ2NPDCC+Dnh/ZHQv/+0Lu3NlZeykuxhgwZ\nQmpqqsPsMCPuHhKohSgbxQXq+3cd9fbt8O9/w/Dh2oStPXtK9LaMTPhuFex1gmrVbixfmJSAOVHb\ne6RJ0x4c0ef/EmdmaptfdRyorbfm9Gl45RUYORK6dr3Tq7rB119/zcaNG9lTwusTQghxd7mdMWod\n2gYbjis2Ft58U9sqsmtXLUiXYEw67f1IPn88kiYrjDTRRVsnf+WMOS9p/wYTr+dm7PFwr5Sv/NuO\n2jrriF1GPA9Fa5tNv/oqvPyyTYK0Uoq5c+eyZMkSKlSoUOr1CyGEsK/ywFjgY+BVtKDeFW13q4K7\nYNlaoblRb0tampY7u2HDEuXuzvv811+VevPN/Lm7c54vfX2HCgpqpAC1yE/L4f1X+HBr+cIRUeq/\n/9X2+rButNG5s7bxhw3JBhviTlBE/mFnZ+dr2WXykIc8SuGR/TNVqOLGqFcB14CdQDu0/aTT0Ha4\n2lfM+2wh+3dGKZg7F44f1yaQDRumHbvJmDSRkSTXMTBzJvj4aMuo8o45b+0TyYc7P2fTpv/h51eT\ntY260OSX90iqWI3UigH80j2Sv90NvPJKdne5UtC3r5ZDfOrUUp3dLURpKm7cTAhRNoobo64F5CSt\nnQ/EAyHcmMbacSQna5ttLFwIeZLKl8Rvv2kTxK1rnfP4fvdXbNr0P5ycnJnUYTy11v2fVpAdgC9f\nhudH5hnT/u03baPqyZMlSAshhChWcYHaXOB5LI4cpAG++QaaNtWCdM6YNBS9HCu7PGOMkSMPmqjy\nsFaeM+a8tU8k2w6sY+F3b1Ie+KZOa9p8ORidUmS5uLO95/+47BlMp2+NBA01Adn1z56tjUvbaKMN\nIYQQ9wczcD3PIyvP8yL70m3kzgfbMjKUattWqRUrSjwmnfO2r9+IUidC849Jr5wQpUaP/kXp9S6q\nI6hEJ2elQJl1enXVO0R9O26bioxUasIEpf5amKfOZcuUeuwxpTIz7/yaCtizZ48aNmxYqdcr7l9o\n42dCCDsq7o763rrd+/FHOHUK3nmnyP2kC8vtvXEj7HUy4NTTlG9Meq+TnlVzurDInElPAEsWma4e\nJHmHsGnQlySEGMjIADc3qPWCAepn13/1qrZ227l0V8YdO3aMTp068cEHH5RqvUIIIeyruGjhDgwD\nagJ/AZ+i3VU7loMH4fPPYevW3BShJbRnD2zaBCEhwNnc49dTr3JmXg/2pifjDWS6enDwiSEEHNli\nHXO2WODsWWjfHsqVy3njdW3xdClvtHHu3Dmefvpp3n77bbp1uzGfuBBCCMdVXKD+HMgAtgEdgbrA\nqLJoVKnJWR8dHq7NAsvJzHWTMWllNLKvp4mvjxsIDIQqZ3PHpJVSbHu/HXNTEikHxDz0FAdbvUb9\njR+wte88AAxfG1nd3ETjDgYeewz49VctqcmDD8K0aVDCfXVL4urVq7Rv357+/fszLGcWuxBCiPvC\nX3meOwN77dUQbmeM+tw5pVq3Vuqzz25pTDotTanN70apIyFt1LLX849JR0Yq1af3x+pXbYGVOviP\n1mrl+N/zlf/vf0p9NChKJTXLU3/dukpNnqxVXsrGjBmjhg8fLuulhU0gY9RC2F1xa4P2Ao8UifyI\nzQAAIABJREFU87osZf/OKKH0dC1n9q5dUKlSidZJYzAQGwtLl8KVK9AoK5onF+eOSSeEGIiLO8DF\nqQ/zkSWLa27lyfCtidI7W8tBywjavj20cM+uPzUVAgK0XbFK8U46R2pqKq6uruhlBrmwAVlHLYT9\nFZdCtBH5Z303wH6zvkvObNbSg3p6QsWKJX7bhQswfz5kZUH16uBU4CuTkZHKmrnP845FG6Y/2PEt\nVIE83qmpWixu2jT7gFLaHw3Dh9skSAO4u7tLkBZCiHtYcWPUf2C/O+jboxTMmKHl8j5/HuZpY8Y3\nG5PO+peRdQ+bcKtioHLl/OukAZqufJ1+rh6MO3+YCsCZWi0I/Hu9tTxnC8soZaB7d3Dbn13/q6/C\n6tXw7LNl/ZUQQghxj7h3ds+yWOC992DnTm129cyZuYHZZLphP+mcwJ2RAWtbmGj+lZF9vUxwPTfw\n5nRnTwlpwqH1M3geMOv0OCvFzudnWMt3R5hovNxI2rMmGmYCE4wwaZLWhrFjSy2xiVKKzMxMXAtL\njyaEEOKeVNzY01ngvSLOUdllZaX4Mer0dHjrLVi1Sttbev78Eo1JZ2bCsmVw6BA0Vvlzd+cE4aNH\nt/Lee60Za8liBpDuXokf/vmLtRy0rSuJjmZw9FBcXdDyiX/zDZQvD+PHl8oXwGw2M2zYMPz8/Jg+\nfXqp1CnEzcgYtRD2d7OEJ15l1ZDbdvWqdtcK2ph0wcHlIpjNsHKltsw6OBg4feM5iYlniYzshsWS\nxchyFSDtGmnlfW44LzYWujcH1z+zD/z6q7bxx+ef3941FZCZmcmAAQOIj49n1qxZpVKnEEIIx1Bc\noD4HTC6rhtyW06dh1ChtfXJUFHzyiXb8JmPSGI3sfs7EH7EGatQAv9P5x6TDVhnZ+dx0Znz9T65f\nv0C/KnUIOn+INE8fNr70Vb6u8dhYeNQ5mocXZ9f/xx/w/vvw7bdaWrI7ZDab6du3L1evXuWHH37A\n3UaT0oQQQjgee66bLujGBZ4Wi1KdOik1Y8YtrZNWSqkjS6PU0ZA2avkbN66TjozU9pt+06+WApR3\neT91ubyfUqD2tH/DWn6mThs1d3CUWvZ6lMoKz65/+3Ytn/iff5bKGlaLxaIGDx6sWrVqpVJTU0ul\nTiFuBbKOWgi7K+6Oum2ZteJ2HDsGhw9DfLw2u7uEubvPn4cvDxh4qJuJtotvHJMG2O/myYzLWl/4\nfDdPKiaexaJz4mBLLfNXQoiBNS1MRPw0FB9f0M+bCydPap/z3nvQoEGpXGJGRgaVKlXiu+++o5w1\nD6kQQoj7SXGB+lKZteJ2bNumzfS+xf2cd+zQJmEX1SttsZhZuHAgmeYMenn68FRWBk6WLE41epYk\nnxDMZjhzBpoFogVpZda6ukGbxBYScocXlsvNzY0ZM2aUWn1CCCEcT8lmXt2NVq/WZnpHRmrjz9HR\nuWV5x6TzlKenw759UDc1d0x6a59IwlYZ8Y3R3r9hw/ucPPkbVZ3d6DBkec6sV2LrtCUzE2Ji4JnA\naDpvNaKf8xHUrKmNkX/2WakGaSGEEMKR5B84S0xU6tFHc3Nn32RMOufY8eVR6sOBhY9Jn6nTRs0f\n+ZMq5+qhADWhx2y1eswmpUAlV6iqzjzYWn3QP0pFz8tTv8mk1OjRSpnNZTZmKERZQsaohbA7R1kf\nmf07I9vatbBhA7z7bu6xQtZJ5xMdTUK3oWRmws7++cekQctGtuL9p1mSfImmtVvy8r9+JXxBPx78\n7UuiO05kh38X+m4bSsWKoIuM1JZfLVumLcEqX75ULnLLli00adIEDw+PUqlPiDsl66iFsD/H7Pre\nsgVatLiltyQlQXpa0UnCjsUdYEnyJVzQ0a/NaFxSrxIavQKAjcEDqFNHW6ats1i0sejly2HWrFIL\n0hs2bKBbt26cPHmyVOoTQghxb3C8QJ2VBT/8kD9AFjEmnbfcPM7Idx0j2VZgTBrA51QUy5eNBKDj\nY314bvNHhH0zHufMVI6FtOGRGom0XW9E99FHEBQEXl7wxRfZmVLu3NWrV+nfvz9LliyhXr16pVKn\nEEKIe4OjdGnldn1/9ZXW9X3+fKG5u4HcwJ1dbv6XkYUPmbhW24CnZ+6mG7sjtPLzCwfwatx+vLz8\nmTr1KA+c2UenWW3QW7KIfnkOjU+sQDfDpNV78KC2BOsWZ5sXZ8SIEaSmpjJ//vxSq1OI0iBd30LY\nn6035WgPzEZLRzofMBVxXlNgJ9ADWFVkbRcuwIIF8OmnkJBQ9Jh0gXXUm7pHcjrFQKCnVpwQYmB3\nhIknFg0lSymapF0H4Nlnp+DuXoGqx7ejt2SR4VaeR6I/QffJPG1f6+XLtT8USjFI79q1ixUrVnDg\nwIFSq1MIIcS9w5Zd33rgQ7RgXRfoBTxUxHkm4Cdu9pf7rFnw/PO3tAwqNU27CQ4IKLx8ZfJl4i7H\n4Ov7AM2bD8I5LYkG67VJavqgAJycdNp67WnT4JVXoEqVEn92SWzYsIH33nsPb2/vUq1XCCHEvcGW\ngToMOAacAjKBpUCXQs4bAawALhZb219/wf79MHBgicakMRrJ+iiSpeGRdNlhxP9MbnlO1/emXh8x\nzZIJQM/H+qPXu1Bv80e4p1zCXL4i+qWLtfqHD4dr16Br1zv5ehRqwoQJ9OrVq9TrFUIIcW+wZdd3\nIHAmz+uzwKOFnNMFaI3W/V30ms2jR7U76QMHbhyTLmK/6RNeBo5VhIrdTfnGpHOef396D+evxFLN\nO5ixR3/lj2PbafTTfwFQ06ZBkyZafU2awGOPlXhnLiGEEKK02DJQlyRRwmzgjexzdRTX9Z2QoM32\n/u23m45J55T/9oU2OTzBJ3dMGrTc3heqP8yPkd0A6BhhYo9/bdpGdqNc6hWuV38Ir5HDtbrSsvvO\np0y51esXQggh7pgtA3UsUD3P6+pod9V5GdC6xAF8gQ5o3eSrC1Y2aelSuHIF0tMJj4oivGBCkwIS\nE7U9O6pXL7x8//4fuXTpFL6+oRgMPeDMXsola+nN1bNdcieMbdkC9eqBr2+xnyfEvWDz5s1s3rzZ\n3s0QQpQRZ+A4UANwBfZR+GSyHAuAiCLKlBo4UKm5c4tNEZo3heie+VFq4sT8KUJXTsjd1tJQq4UC\nVETEDLVyQpSKq9lcWdCpLL2rsrRsmVv/yJFK/fBDqaRjNJvN6rXXXlPHjx8vlfqEsDUkhagQdmfL\nQdcs4DVgHfA3sAw4CAzNftyalBQtG1lON3fOBLK8a6YNBjAYME83UfkdIw+lROdbM50QYtC2qGw9\nij3HtuGsd6Fz9UcIW2UkMbABOhSXW3ZB9957Wp0bN0JUFLRqVSpfkBkzZvDHH38QGBhYKvUJIYQQ\ndwul2rdX6ty53D/1o6KUMhi0R967a6Wd9vFLUepCsEFdCDbk24AjMlKp9u3HK0A97+GtLgQb1JqR\nP6l0Ny+lQF3/5metku3blQoNVeo//ymVO5OTJ08qHx8fdeLEiVKpT4iygNxRC2F3jjONOTERSrjW\nODERVBG/XrKyMti+/VMABnj5AVBv00e4pl/nSotOlH+urTaB7IMPICJCu7MuBaNGjWL06NE88MAD\npVKfEEKI+4OtM5OVHmdncHHRnuddRw03LNdK3RbN0xu1/aaBfF3fe/eu4vr1C9RxK0/6oEXsj9tP\nq88HYtG7UPGz2VoX+6BBWk7v//636F08bsGaNWs4ePAgy5cvv+O6hBBC3F8cJ1BfuZKb1OQm66gD\nZhv5sbOJzOytLHdH5K6j3rHu/wB4Inw4l4Ib0+KrV7Q6Aquhi4+DN4xQp462HKsUgjSAXq9n3rx5\nuLm5lUp9Qggh7h+OkmxfqRdfhEOHtFdF7Deds476yxaRJIYaKFcut9g3Jhr/Bf14Iv5vyrm489//\nO0eDP7+n9Wd9SPMNpNyqJdqddP/+MGGCJDcRAtmUQ4i7geNEowoVSnSaRcH161DYzevn17UspS3r\nd8DdvYJ1q0vz4FcgM1PrXh83ToK0EEKIu4bjRKTNm2+a25vISBLfieTpjUb8TufP7V1/xb9YnJkC\nwNjEs/jGRJOerpV7pibAP/8JzzxTeIQXQggh7MRxAnW/ftZ10sWto04IMbCutTYm7RuTu456dq0W\npKQnExrajKTeHxO2yohL4nmt7h9+gIYNoW1b+16jEEIIUYDjTCYLC8t9XkRub4CLF+FcYP7c3lte\nnMsPX2nPW7YcRkKIge3PmOj0cUft/e3aabtzNW9eas3dtWsX9evXx9PTs9TqFEIIcf9xnDtqH58S\nnXb2LHh45D92LP4Ap0/vwdPTmyZNegCQlKQNSQMQFwcPPwylFFSvX7/OM888w5kzZ25+shBCCFEM\nxwnU8fG5z4vZjzo2FkIuad3dW/tEsrVPJHu/GQ/A448PxMWlHL4x0YT/aCSlWXZX944dEB5eak39\n+OOPadu2LXXq1Cm1OoUQQtyfHKfre8YM8NMyiRW1jjrzPybc/4YnduQmODGbM1mTngRA5wces45Z\nf9/WRN8MLUMZ5cpBy5al0syLFy/y3nvvsXHjxlKpTwghxP3NUdZHKhUVVeiYtFV0NJkvDeXCBdg1\nMJKE7GQnBw/+wuzZTxHk8wB7PLUUpFtejGSvrjFTlz2I7vgx7W5606ZSaKSie/fuhIaGMmPGjDuu\nTwh7k3XUQtif49xRl4A568Zje/euAuDRf7SCs38AWirvOm5/a0HaywuefLJUPn/79u0cPHiQRYsW\nlUp9QgghhOME6mJye+eMWZ8cH8nGDdAlO13oheqPsHfvNwC8FPeXNfd3s6VGnP5RW3tvaCg88kip\nNLFFixZs376dcnlTogkhhBB3wHECdTG5vXOexyYauBgMuwO0ddRfhPXm2rVzBDmXI6XXx1zK7g7/\nKdzE0GXZe0zrdFC/fqk1s1KlSqVWlxBCCOE4gTrvmHQR66gvL9cSiyVU09ZRn/1fJwAebhzBpRpN\nrG9P8gpAn3xdSxWamgqy9aQQQoi7lOMszyqBxERwddWeK6X4ISURgMf+0dp6jsUCtU6s1164u2vr\npyW3txBCiLuU40SoInJ7511HfeWKdkftGxNN+SXDOW3OoJKnD312L7ZuwJGSAk2OLdHqefzxO5pI\nZrFYOHbs2J1clRBCCFEsxwnUReT2zukGV0YjXkeiCYjT1knPD2wIQENDN6Kfn2HN/e158HeCjmQv\nxfL11XJ836aPPvqIIUOGlMbVCSGEEA5NqagopQwG7REVpQpK3hKlzgYY1IVgg1o5IUpVq1ZPAWrU\nqHUqMlKplROi1IVggzrvU0cpUCokRKmWLZW6cuWGukri8OHDysfHRx05cuS23i+EIwCUvX/4hbjf\nOc5ksptITc19fvHqOeLiDlCuXAUefDDcetxsAc/Ma9qLxx6DjAyoWPGWP0spxauvvsrEiROpXbv2\nHbZcCCGEKJpjdX0Xsx+1+2Qjqztqub1TVr0OwIMPPomzs6s1bejKpyK1ddOgRfYnnritpvz888+c\nOXOG4cOH3+lVCSGEEMVynEBdYEy64Jh17EgTsVW1/ahX+2rBuLF/LWuQ3tnFxMWgRygfc0Crb/9+\n6NjxtpoyZcoU/vOf/+DsfM90SAghhLhLOU6kuck66ovpBnT7tW7pP2P/BKDv/p9ocGQLW/tE8rer\ngVZVDqJLTAR/f20S2YMP3lZTVq5cib+//51ekRBCCHFTjhOob+LSJW0N9aVLp7h8+TTl3StSz8Xd\nWp6VBfWv7dBe+PtDly5aVrLbUKVKldJoshBCCHFTjhOoo6NvyO2dN/e37gkTbu4GDhzYDEALvSvb\n+84DIGyVkfPNTZQ/sV07PykJOnQo4wsQQgghbp3jBOpCcnvnzf3dsLeRa51NbNy/FoAqj75o3epy\nd4SJdouNuJiPaufXqgVyVyyEEMIBOE6gLiS3t5XBwE/hJp5bMZTZ5w4BULlBJ2vxheoG/mjYl5qr\nB2jpQnv2LMOGCyGEELfPcWZ9FyM9XRuDVkpxMFNbUB0U1MhanpEBDx9Zpr2oWBFq1rzF+tPp1asX\nqXkXawshhBBlwHECdTHrqNN3RPP0RiMrO79NkrLgr3flgcunreUBf63jgUM/aXfTDRpAcPAtffSX\nX35JYmIi7u7uNz9ZCCGEKEW3N+257CkVFXXjZLLsMeu00UYW1DHxp/Np5s6N4OHQZnzv6sHuCK28\n1ZzuVE48Cc89B+fPw+bNudts3URWVhZ16tThs88+o2XLlra4NiHuWjptZYSj/J4Q4p7kOGPUxayj\nPjc+krh9Bs7u+x4A/1pPsLtJD55YNBSUBde07LShPXrAsmUlDtIAK1asoGrVqjxxm1nMhBBCiDvh\nOIG6GGlp2j7Tp079DkBw8CPWMreUK3imXiK1Vn3cAwNvqdvbYrEwffp0TCZTzp2FEEIIUaYcZ4y6\nmP2o/d81Uv1CFKdO7QagsasHYauMbO0TSaa7FwApbbvA6dO3FKhPnjxJ1apVad++faleihBCCFFS\njnKbqFSbNkWuo/5+cjQVF4zkyZgdVPCozP7qj/D78zO46l+LAf+sjEWnJ/PRFpRr0kDbiKN7dzte\nihCOQ8aohbA/x7mjzhmTHjo0X5BWCv7QG1jZQNtg4zGLhd+fn0FCiIGqx3egU4qz1cLI+M9M+Pln\nCAmx51UIIYQQt6QsAnV74BBwFDAWUv4i8AfwJ7AdaHgrlSclaeuoT5zXdsV6xM3TWlb12DYAYoJa\nUK4c2mJrCdRCCCEciK0DtR74EC1Y1wV6AQ8VOOcE0BItQE8F5hVaUxHrqBMSoFp8NKf/WgOAW8cJ\nhK0y4hsTTZXsQJ1SoSquE/4F3t7g51fa1yiEEELYjK0DdRhwDDgFZAJLgS4FztkJXM1+vgsIKrSm\nIvajTt4STbOfx7I/PRknJ2d8mw1gd4SJsBXjqHLiNwDqH/sWhg+H0FAt6clNKKVu41KFEEKI0mfr\nQB0InMnz+mz2saK8BKwttKSIddTVpgxlQf3nsCgLDzwQhpubJwkhBo491ge9OYNM53Ls6fMeeHmV\nqNt7//79PP300yW4NCGEEML2bL2O+lZuTVsBg4DmhRVOmjTJ+jw8PJxwL23ZVUYGHDsfBcCDD7ay\nnlM+Ufv7IMvFHS8vICbmpoHaYrEwcuRInn322VtothD3js2bN7N582Z7N0MIUYYeA37K83o8hU8o\na4jWRV6riHqUiopSVlFRSrVpo9K2R6kPB0ap+m5eClCjR/+iIiOVWjkhSl0KqKsUqEO1OqrLjdso\n9fLLSq1Zo4ozd+5cFRYWprKysoo9T4j7Bbf2x7YQwgZs3fUdBdQGagCuwAvA6gLnBAOrgD5owbpw\nORPI8uT5TggxcMonlAPpSbigI8ylHL4x0YStMnKiSQ8AUtx9uDhmOmzZAg8/XGT1Z86c4a233uKz\nzz5Dr9ffwSULIYQQpcfWXd9ZwGvAOrQZ4J8CB4HsjaWJBN4GKgNzso9lok1Cy6+Q/agT/oBTp7ag\nUNSq/ghtl40CYGufSCrHacu1dEA5D70WpAMLHx5XSjF06FBGjRpFvXr17viihRBCiNJSFrm+f8x+\n5BWZ5/nL2Y9bdvo0nD27CYD6IU3g9J5Cz6u4ZxM89VSxdQ0ePJjOnTvfTjOEEEIIm3GcTTly1lHn\nPDeZiIkxcPr0ZgC6xUSxte8nAIStMnLVvzYAaW4V8Ph1LXz+aZFV63Q6unbtatPmCyGEELfDcQJ1\nnrShmEyYxxlJCRhPXNwfuOmcsPT6kIQQrXx3hIlOs9oCYHZ2Q6+zwAMP2KvlQgghxG1znFzfBdZR\nx48yUXntEABqVX+EazUftxZfqVoHl/QkFNDo+EqcesgmHEIIIRyT4wTqAuLjYWfGdQDqhxjylVU9\nuhUnSxaZzh64lXeF1q3t0UQhhBDijjlOoC6wH3XV2UZ+dq8AaOPTvjG55bV2fwXAybqdcK5ZA+rU\nuaG6Dz/8kG+//damTRZCCCHulOME6jzrqM3jjCxu/AZnLx3HxaUc5p4fWjfi8I2JpsY+LQB7NgxF\n17oV6PJvpxsTE8OkSZNo0KCBPa5ECCGEKDHHmkyWvY46fmIkv395EoDQ0Me5WrMZuyNMPLFoKE5Z\n6bimJ5Hm6oWfLgGeyL/kSinFsGHDGDt2LDVr1izzyxBCCCFuhePcUecRFwcxMdr66X/8o1W+MreU\nKwCcr98Gt5ij0LRpvvIlS5YQFxfHv/71r7JprBBCCHEHHOeOOs866oAXjcRdPAFogTonbejWPpG0\n+OoVyl85S/nAilCzBri5WatISEhgzJgxrF69GhcXF3tchRBCCHFLHOeOOnsddcpDBr5q/Dpxl0/i\n5lIOg5OesFVGdkeYuOYbiu+ZPVh0eiod3gVPPJGviqSkJN5++23Cwm7MUCqEEELcjRwnUGevo46J\ngV2piQA8pneh9ZLX2B1hIiG4Mc2XjsDJYiaudkv0vt7QokW+KmrUqMGrr75a5k0XQgghbpfjBOps\n+/ZBbKw2Pt3Czct6vOm3b1J791eku3iS2aUbhIaCv7+9mimEEEKUCscZo46OJqOBgUOH4OxxbY8P\nzy7T2BrUkFafvkjl84exOOlZ3nUJL+z6AGZOt3ODhRBCiDvnOHfURiPnf4xG//d3xF8+jYebJ5Ue\n64PnlVgqXTgKwK42Ewi9/ieutUNumO0thBBCOCLHCdQmE15jh6JbPwKAh+p3ouqZfbT5pCc6ZeHv\nJ4YQ8uf3NP5rIUyYAEBmZiavv/46KSkpdmy4EEIIcfscJlCbzZCSChvStXXSDRt2puH6/8M5M5XD\nzQZw4PHBuKVf0zbgCA0FYOrUqfz111+4u7vbs+lCCCHEbXOYMeqMMUaWtH6X7Yvb4gS0rFgNl/Rk\nAC5VfxjD8tdR1YJwe/UlAHbs2MG8efPYu3cvugIpRIUQQghH4TB31Fs6mthjuUqWJYvagQ1p+9M7\nuKZeBeDBHQvYX/t53B+pAzVrcv36dfr27cucOXMICAiwc8uFEEKI2+c4gTrZQHz8BgBqPfwcuyNM\nVI79C4B9Dw/kweS9eA56AYBRo0bRqlUrunbtarf2CiGEEKXBYbq+nZ3h8OGNANSp0xqnzDRcMrSu\n77TkTKrr4+DJJ7FYLNSqVYsRI0bYs7lCCCFEqXCYO+rAS+uJi9uPi4s7TfWutPxyME4WM+d96tLq\nxAI8+0aAXo+TkxMTJkzAy8vr5pUKIYQQdzmHCdQpq/4JQL3qD9P8u7dwsmQBcLlTXzxCq0KvXvZs\nnhBCCGETDhOol1fUJoX1uHyGNC8/Kl04SnJ5f/5hPoDun6PB09POLRRCCCFKn6OsW1LlXD3IyEjh\nvEclfFOukKV3JeHl8VRNO0XWvHk4u7rau41C3HOylzY6yu8JIe5JDnNHnZaRwjK38vimXMGic2JL\n28n4n/yNqA4deLRZM8xms72bKIQQQpQ6hwnU/kC39CTMzq581+4jmh1cSPqzz9Dn3//GaDSi1+vt\n3UQhhBCi1DnM8qycju2U8v64O2Xg2r41E2JiaNCgAT169LBr24QQQghbcZhA7ZbzJMuM4fwP7B33\nBp/36sWff/5pz2YJIYQQNuUwXd/zs/9NdymPvnNHxk+fzpQpU/D397dru4QQQghbcpTZnEoBKZ6+\nXPauRbUNi9hxPp5HH30UFxcXe7dNiHuWzPoWwv4cpuv7qs6JLOfylPOviFPtmrSoXdPeTRJCCCFs\nzmG6vscFNQSdHn3/PvZuihBCCFFmHCZQZ169SFpFfyr16mDvpgghhBBlxmG6vlWVR6BhKDpfH3s3\nRQghhCgzDnNH7Z+ezHtZ51FK2bspQgghRJmxdaBuDxwCjgLGIs75ILv8D+CRoio6cfkAVyu758xC\nFUIIIe4LtgzUeuBDtGBdF+gFPFTgnI5ALaA2MASYU1Rlv6RfY9LUqbZpqQ1s3rzZ3k24JY7WXpA2\nCyHuD7YM1GHAMeAUkAksBboUOOdZ4PPs57uASkCVwirr3eFZgoKCbNJQW3C0X8iO1l6QNgsh7g+2\nDNSBwJk8r89mH7vZOYVG48lz3y/VxgkhhBCOwJaBuqSzvgoOOhf6Pr+AqnfWGiGEEELk8xjwU57X\n47lxQtlcoGee14covOv7GFoAl4c85FG2j2MIIe5ZzsBxoAbaLpX7KHwy2drs548Bv5VV44QQQggB\nHYDDaH+Vj88+NjT7kePD7PI/gMZl2johhBBCCCGEEOJeUWoJUsrIzdr7Ilo7/wS2Aw3LrmlFKsnX\nGKApkAVElEWjilGS9oYDe4H9wOYyaVXxbtZmX7T5G/vQ2jygzFpWuM+A88BfxZxzN/3cCSHsRI/W\nBV4DcOHmY9qPYt8x7ZK0txlQMft5e+w/Bl+SNuectxFYAzxfVo0roh03a28l4AC5y/p8y6pxRShJ\nmycB72Q/9wUuYd+8+0+gBd+iAvXd9HMnxH3nbsr1XaoJUspASdq7E7ia/XwXRawRL0MlaTPACGAF\ncLHMWla4krS3N7ASbQ0+QEJZNa4IJWlzPFAh+3kFtECdVUbtK8xWILGY8rvp506I+87dFKhLNUFK\nGShJe/N6idy7Ensp6de4C7npXFUZtKsoJWlvbcAb2AREAX3LpmlFKkmbPwHqAXFoXcmjyqZpt+1u\n+rkT4r5zN21zWdKAUKIEKWXgVj63FTAIaG6jtpRUSdo8G3gj+1wdN369y1JJ2uuCtlqgDeCB1ovx\nG9p4qj2UpM0T0LrEw4GawM9AI+C67Zp1x+6Wnzsh7jt3U6COBarneV2d3O7Mos4Jyj5mDyVpL2gT\nyD5BG6MurnuxLJSkzQa07lrQxk87oHXhrrZ5625UkvaeQevuTs1+bEELevYK1CVp8+PAf7KfHwdO\nAv9A6xG4G91NP3dCCDtytAQpJWlvMNp45WNl2rKilaTNeS3AvrO+S9LeOsAvaJO4PNAmRNUtuybe\noCRtfg/4d/bzKmiB3LuM2leUGpRsMpm9f+6EEHbmaAlSbtbe+WgThfZmP3aXdQMLUZKTWTUlAAAB\nVUlEQVSvcQ57B2ooWXv/hTbz+y9gZJm2rnA3a7Mv8D3a/+G/0CbE2dMStPHyDLQeikHc3T93Qggh\nhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBC2JqZ3HXie4EQtNSYV7Nf/w28nX1uwePT\nyrapQgghxP2nsPzU4WgJPUDLFnYEbRvFJ/McLwccREtZKoQQogh30+5Z4t6UAkQDtQocT0NLrxla\n5i0SQggHIoFa3Cl3cru9VxZS7oOWH3o/+Xdg8kbbu/lvWzdQCCGEuJ8V1fV9BdiDtiPUkALH9wHJ\nwLu2b54QQghxf7vZGHVRx2ugbe9YvZDzhBBCZJOub2Evp4D3gYl2bocQQtzVnO3dAOHwVBHHSnJ8\nLtqM8CC0PZmFEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEvfw/\nIyM1Rnnj+5sAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5ba196a150>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Including the resulting ROC curve based on the peeked data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 3.2 PR curves"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# we can directly use the contingency tables we already computed anyways\n",
      "pr_bounds = lambda tables: ss._lb_ub(lower=ss.pr_from_cts(tables.lower),\n",
      "                                      upper=ss.pr_from_cts(tables.upper))\n",
      "pr_bounds_point = pr_bounds(tables_point)\n",
      "pr_bounds_interval = pr_bounds(tables_interval)\n",
      "\n",
      "# an alternative without all these intermediate steps would be:\n",
      "# roc_bounds_point = ss.roc_bounds(labels, decision_values, beta=betahat)\n",
      "\n",
      "# compute the true ROC curve (we use Optunity's ROC function)\n",
      "_, pr_true = optunity.metrics.pr_auc(true_labels, decision_values, return_curve=True)\n",
      "# compute the ROC curve that would be obtained by treating all unlabeled as negative\n",
      "_, pr_neg = optunity.metrics.pr_auc(labels, decision_values, return_curve=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# PR curve based on all known labels after labeling 300 unlabeled instances\n",
      "# we compute this by constructing the PR curve with weighted instances\n",
      "# the weighting is used to fix the empirical class contributions to our estimate of beta\n",
      "\n",
      "# compute the weight\n",
      "npos_prior = len(filter(lambda x: x == True, labels))\n",
      "neg_weight = float(npos + npos_prior) / npos\n",
      "print(\"Normalizing weight for negatives: %1.3f\" % neg_weight)\n",
      "\n",
      "all_known_labels, all_known_dvs\n",
      "all_known_labels_sorted, _ = zip(*sorted(zip(all_known_labels, all_known_dvs),\n",
      "                                         key=op.itemgetter(1), reverse=True))\n",
      "known_after_labeling_cts = ss.compute_labeled_cts(all_known_labels_sorted)\n",
      "\n",
      "# weigh contingency tables\n",
      "weighted_cts = map(lambda ct: ss.ContingencyTable(TP=ct.TP, FN=ct.FN,\n",
      "                                               FP=ct.FP * neg_weight,\n",
      "                                               TN=ct.TN * neg_weight),\n",
      "                   known_after_labeling_cts)\n",
      "pr_after_labeling = ss.pr_from_cts(weighted_cts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Normalizing weight for negatives: 14.514\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pr_point_up = ss.zoh(*zip(*pr_bounds_point.upper))\n",
      "pr_point_lo = ss.zoh(*zip(*pr_bounds_point.lower))\n",
      "pr_interval_up = ss.zoh(*zip(*pr_bounds_interval.upper))\n",
      "pr_interval_lo = ss.zoh(*zip(*pr_bounds_interval.lower))\n",
      "fig = plt.figure(3)\n",
      "fix_plot_shape(fig)\n",
      "plt.plot(*zip(*pr_true), color='black', linewidth=2)\n",
      "plt.plot(*zip(*pr_neg), color='black', linestyle='dashed')\n",
      "plt.fill_between(xs, list(map(pr_point_lo, xs)), list(map(pr_point_up, xs)), color='blue', alpha=0.4)\n",
      "plt.fill_between(xs, list(map(pr_interval_lo, xs)), list(map(pr_interval_up, xs)), \n",
      "                 color='none', edgecolor='red', alpha=0.8, hatch='xxx')\n",
      "plt.plot(*zip(*pr_after_labeling), color='red', linestyle='solid', linewidth=2)\n",
      "plot_proxy()\n",
      "plot_proxy2()\n",
      "plt.xlabel('Recall')\n",
      "plt.ylabel('Precision')\n",
      "plt.legend(['true curve', 'beta=0', 'after labeling',\n",
      "            'expected region via betahat', 'expected region via interval'], \n",
      "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
      "plt.title('Precision-Recall curve')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xt/eCXPFZ54Y8Pl4tbfaISC0/YKGnVi3o3FnJ830ddlgYDB6s1qg1bKh8Eq+9\nBm3bar7sx6CwKurRo0cTmPR9+f3333njjTdo3bo1ZcuWZWwmudH9/Pz45ptvzIp68eLFTJ06ld9/\n/x1vb29u375N8eLFOX36NH5+fkyZMoWpU6dmWJdOpzMr4saNG9O/f3+zjzokJISQkBB2796d25eu\nUYjJSlFb5W1XHgOTCcnBe0XVrTMBCK/SFq8jG3LUlI2VLTVqdKRGjY6YTCYuXTrEpT2LiNj1Hbvj\norh66yJXQ78nNPR7AGxti1G+1DPUvHEBG52Oa5tmkOBSFktLaywtrRExUeTWJbbfvoxRhPBNX3DD\nyoa7d//l7t1/iYq6RtTdqyQaEwBw+CIAe+cyODqWwsmpFM7OZahWzJUKxgRKJuXczitSDD5SUaaM\n8seXKwcp3G/5i4WFGlW/8YZy1s+ZAzNmKHN5585Qp87D69Ao9IgIc+bM4fnnn8fOzo6PP/6Yl19+\nmc6dO9O5c2eeffZZ6taty71799i2bRvNmzfH3t6ekiVLcubMGbOijo6OxtbWluLFixMTE5NOwY8d\nOzZTpZ+SPn36MGPGDNq3b4+IMGPGDEaMGPFErl1DIz+Rc41flXVdQ7IdQlRAYhxLyda+36UKK5qT\n5U4ZyX8K2iO/eNeRAa3fkbp1XxE3N1/zMq/H3Wyti4iFziLLc0q5eEo3Rw95rf14GTfufzJr1r1H\nXs71uPKvvlIhum9vLoDLuR7Ir10T+eQTFaJ04kSRO3eewMKKpxcK6fKsadOmSeXKlcXZ2Vn69esn\n9+/fFxGRDRs2SN26dcXZ2Vk8PDykR48eEhUVJSIia9euFS8vL3F2dpbPP/9coqOjpVOnTuLg4CA+\nPj6yaNEisbCwkDNnzuS4T++9954UL15cihcvLkFBQbl6vRpPB1k8a0/c9N0W+BKwBL4BpqeRuwFL\ngFKo0f1nwMIM6pGTLQcT+sxAYmvUz9SnmtL0DXC06RCiXH2pv2YMkLw8K7d9ur4/v8XPNTtz0bYY\niYnxFIk8i8ffv3Ku0rMYTYl4Ht/ClcptiC3uhYWFJQ53rlDl6EZuNRmMUzFXmu+Yz/munxDl3xiT\nyYjt8S14rh3PzoZ9uBV9A+vQhWx2KMnxiMPExaWehGKhs8DHugjuvvVx829K+fLNaFTEnoZrxuWJ\nT/vmTWi7LQiP76djWS+PfNKPIp80SS3vWrdOrbFr2lTNHM8s/JsGUDhN3xoahZH88lFbAieAZ4HL\nwH7gFeBTv8rKAAAgAElEQVRYinMmAbbAGJTSPgGUBBLT1CUnWg1lzzP9ia1eD3j4OmqTzpJbpatg\nFReNU+RZIPU66vzy+T6O3GhM5PLlfzh9eicX//6V66d2cDYxlrSLk+zt3Wjg35TBlw/TpIgDe3rP\nf6L9+zkgGLsmel58EcyrUgqCzzoj+d27YDCoJV7HjqkQpS1bJjnaNdKiKWoNjbwhv3zU9YDTwPmk\n/R+BTqRW1FeA6kmfHYEbpFfSCpMpR5OCrvnWxzIxjsIzX+7hWFpa4eVVCy+vWriVa0TTJYHEionl\nbd7liJi4ePEAhw79wrVrp9h0cDWbAGcLS6qtHY+vvgfPPBNA8eJeud4vDw84clkt3ercGWrVyvUm\ncg9HR2jVSgV079ULhgxREWrGjAGv3L83GhoaGo/Lk1TUZYCLKfYvAWlTIC0AtgARgAPQI7PKdAlx\n5slkKdcBA6nMtA+wvn+H7f2/p+TpnTT++a1UsszKpzXtFhZ5jwfy+j3p2vVT7hl+Jnz1GFbodFyK\nPMuOIxvYkTShrmTJCtQsU52u/57g9x5fYW/nmCv9o8t0LpXU8+OPKmpbwzVB6IKVPFPTdH7LlyyB\nxEQ1W7xnT5W16/59NUNu8mQ1IU1DQ0Mjn3mSw82uKB/14KT9XihF/UaKc8ajTN5vAeWAP4EaQFSa\numREyYpcc6+C0dmVbhfCsExhzs1oHfXad/7i3/JNKXP0Dzp8pQKfZLWOOpVPduV77Ov6Sb6vY84N\n+dWrxwnfGUJ46EJ2xt/nfnxyii2dzgJvbz21PKrQ8/Lf0DMYnU73WO0bTVDrxyCO95tOy3f0ySlC\nC5rPOq185EgYOlStvR43Dl5+Gd5//z9nEt+2bRvbtm0z70+ePBk007eGxhMnv3zUDVA+6LZJ+2MA\nE6knlP0GfAzsStrfDAQBhjR1yan6PXE+9z+kSNFMfabPf94Cm6TJVg/80R4nttJxhlpuEelZE7Gw\nzNLnanPvFk6RZ4ly9WbZlPPp5FBwfNY5lTdcPIQD8TEsqdiSsKvHOHNmN8akJWEA3lY2vFTMFd9e\n87Go/vwjt/9Xz2D+sVFKumdPFXq1wPqsM5J/9RXMm6fWndWrp0bWN2+qaGh+ftCsGVgnLZMzGp/q\nddqaj1pDI2/ILx+1ASgP+KBM2y+hJpOl5Dhqstku1CSyisDZDGsT00NHN3fc/Sl69yp/9V5gPhZr\n727+bBf1L/ecSmdaXmdKNE88c7hxIcu2CiNWOh11be2JbTKIFt564uJiOHVqB8eO/cmBvT9wIepf\nPrlzBeZ0pGLFljRuPJDatbthbZ2zCF86nVLOt24pnfjaa2paf6GhSBHlcJ85U6XWjI9XJvI//lAK\nukwZeOYZOHNGBVhp0wa6d1fHNDQ0NHKZJ6moE4HhwEbUDPAQ1ESyB+HCgoEpwHfAIVTc8feAm+lq\nAmyib7L7uckkevpm7jPt8w2gTLP3nTyI9NZzq0xVcx0Xq7TjaIvXMy6/8j1i7d0yvJCC5pN+XHn9\nFe8Q6V0HQ6cPqVq1LS0c3NFfPMi3tSew9e917Dv6BydObOXEia0sX/42ras9T9C/J3PcPt56RGDL\np2G8fCAIi/z2SedUrsy+yfIVK9T+m2+qshMnKsU9c6aaRffaayoO+VM8wtbQ0Mh7CosDTk7X7s5f\nrT8kwa9ijn22D9ZXH2zzHvu6Ts+w/L/lGqFf/2GqRrPt035MecOf3sRobcfmwT8RZ+/6yPVfLaPn\n5k2VQrPZb+nld93LUWXrbOr+MiHVNaat3+7ENi7/MJRgEc5fOwmo9drVa3SiTZt3qG9lm6P+1Vga\nRPjw6bQcVYB80rktnzBBKfL4eHjrLahY0ZxEpjCjmb41NPKGpyPWt/4ldrb5kASfzPNFpySl3D1c\nZV76O+BtTjbsS5Nlw9jf6SMarFCp7PZ3+oiAb17G9n7q/I3ZjQ2eXbnOmIhYWqWSW9+/g/P10+Zy\nKYOyZLf+ba8Ec8hKj5UVVKkCx49DiYthdPotkEQj/N58GtWub6X27tnYxKZOBHDdS59p/U0WD2Fv\nXAzT3bwJPb4Fk0mtnKtYsRU967zE0B3zs9W/7a8GYxA9Hh6qfxUqgOe/YVi8VkB80rklNxph8WIV\nVOXWLWjfXo2yixalsPK0Kurx48cTHByMtbU1ERERuV7/woULCQkJYceOHQ89d9KkSZw5c4bFixfn\nuJ2UZcPDw6lSpQp379598H/TKEQ8HfmoRXKejzoNFsYEun1Uk1JndtEq5FVzvTU3TsP2/h0uVHue\nq34Nc6GzqdEZE+g3wpHBr1tTddOXqi8JsRS7GZ5KSYPKdR0eDneySKxT9NZlfA6sAhFMAlevQquW\nwpgxylX61lsq57WlxFMy4SID13SkwZYp2MTe5VKlgHT1Of17guc/b4ndnavmY8VuhlP86jE6XjvB\ntBovMG1aOO3ajaNIEUdOnNjC+z8E8sK/JwiNTTtBPz0WFmoOlskEO3YovbZoEdyNgvgEFd/1qcDS\nEvr1UyPrkSPh669VMJW//srvnmmkIDw8nBkzZnD8+HEiIiJYuHAhTZs2zbf+PI5STVnWy8uLqKgo\nTUk/hRQaRW0Zfz/TfNQ1fwyi2PHM8y0/oMyJ5OVbxe5cYUevYM7U6UHpk9tJsCnGzp5fY7RODimZ\nG/mi93WeSvuZbbFJUmiNlr+N94HVtJ/ZlqLR1zFZpPZnliwJ/aqF0WZzEMc9WuIeHkared1xuxCG\nzmTkme1f02u0J7V/n0Jk8fKsbvEVgb93otWzFtjWqgyAw77NtJ3fBffIE1jfuIZFXCwJ9Zuw+t3d\nfN1lE8ee6WxuL66oCwEhPSl9chu93/Og9LHNdPy0GW3mdcEq4T4ATZYNp9ztCF588SOmTr3AS00D\ncbKwYk9cNJ2unWTR7A7oDv/+0PtTrJiah6UnjFZ/BPFDs2C+qRPMxVeDuLs1j/JZ55X8iy/gp59U\ngpDBg2HtWjQKBuHh4bi6uuLq6por9SUmZhyjKbs8jmWiMFs1NJ4+5JJfU1kz+FdZPtogp30CZPFb\nBpk3T2TcOJHFb6ljmSWVSJus48H2zawYiXIpKwJys2RFWTnWINe89Gb54yat+HHycbnj5puuXaOF\npQjIteIVZOEbhlSyxL0GkSZNRFq2THU83KOeXHWrkq6uhDJeqY+9/rqIpWXyfpcuIkuWiAQEiGm/\nQa6uN8gtz/T1pN0SLW1S7V+sFCC7un8hZ2p3k4sVW8niUdukY8fJYm1tJ4AUs7CU3q3elB+DQnOc\n9OOb1wxyvnyARG8vgEk9ckP+668qKcjSpSKXLoncvv0YofvzFgphUg4RkalTp0q5cuXEwcFBKleu\nLKtXrxYRkT///FPs7OzEwsJC7O3t5aWXXpIiRYqIpaWl2Nvbi4uLi4iIxMbGyqhRo8TLy0tKliwp\nQ4cONSf22Lp1q5QpU0amT58upUqVkj59+qRr/7vvvpMmTZqY9998800pW7asODo6il6vlx07dphl\nkyZNkm7duslLL70kDg4OUrt2bTl06JBZfvnyZenSpYu4u7uLr6+vzJw50yybOHGi9OrVS0REzp07\nJzqdToxGo4iING/eXCZMmCCNGzcWBwcHadOmjURGRprLfv/99+Ll5SWurq7y4Ycfire3t2zatOmx\n773Go5HFs1ZokLPPtJNrHtXkqqdevhtukM8/FwkKEvn5Z5HISJHZ/ZWSvealT6UEslLU+174QATk\numcNWTl6r1zz0ssd12TFmrKOB0o8o/ozkq995y+5X9RFBORfn7rp2j5WuYsc3XNHEhPT9K9cOREX\nl3Tnm5KUu9HS+qFKVkCkTZv0ykSvF9HrxbTgG/N52xu8m7odKysJrTVU5n98LdXxyDLVzJ/P1nxR\nDrYeJQJyx7GU1KrxorRJkn1sYSmvd5ggCz65Imdqd5O/W43I1v2bH2iQq2X1cqucXlaNM8isWer4\nxo0isbGp+5/qujK4vgIpX79exN9fKez69UW6dxeZP18p7gIMj6qos/Mdzc72iCxfvlyuXLkiIiI/\n/fSTFCtWTK5evSoiItu2bRNPT0/zuQsXLkylVEVE3nrrLenUqZPcunVLoqKipGPHjjJmzBgRUYra\nyspKRo8eLfHx8WYFnpK0inrJkiVy8+ZNMRqN8vnnn0upUqUkLi5ORJSytba2lpUrV0piYqJ89tln\n4uvrK4mJiWI0GqV27dry4YcfSkJCgpw9e1b8/Pxk48aN5rJZKWp/f385deqU3L9/X1q0aCGjR48W\nEZEjR46Ivb297Nq1S+Lj4+Wdd94Ra2tr2bx58yPfc43HI4tnrfCYvh84Mk2iYku//bbyxXbtCq6u\nUKIkGE05q7LmhmkAhL70FSSZoI1WmSRgzgGlj22iw5fPUuTeLS5U78i6kVtTyXfVGUGx31fwTH3H\n9Ct5zpxRE5GScuI+QIdAiRJYVKuS+vwFC9SSoAcULap8oxs3pp8A9aCuWjXh77+5dPg2JRd+gjHs\noBJ4eKCrVg330YM4G+Weqozr5X/Mn30PrqHGn58D4Hj3Klsj/mFjkmysyUjj9R/S6z0P/P63gmpb\nvsIqLoaH4eqqfNj37kN0NCQkQFSU8mnPmQP//vvQKgo2JUuq+OIODjBrlop+dvs29O0LI0aozF6a\nGTPX6NatG6VKqdX7PXr0oHz58uzduxdIby7OaH/BggXMmDEDZ2dn7O3tGTNmDD/++KP5HAsLCyZP\nnoy1tTVFspGBrWfPnri4uGBhYcHIkSOJi4vjxIkTZnmdOnXo0qULlpaWjBw5ktjYWEJDQ9m/fz+R\nkZGMHz8eKysrfH19GTRoUKq+ZIZOp6N///74+/tTpEgRevTowcGD6llfsWIFL7zwAo0aNcLa2poP\nPvhA820XYAqNoi4Sc5OdnT7ll/bB1F0RhO5/YZQqleS2DlM+3dXPZewzzgzr+Hucrd2VBFt7s0/1\nQIcJ6c7LyietMyamkp+v2Yn6q0djmRjPkRbD+OO11ThfPU5kGZV7ZFPj96kshyl7/X8Zd8rGBsqX\nh2nT4Lvvko/r9fDbb/DNN9CoEQQEQGQkDBqkkkvY2qrP27eryUwP86nGx+NZxYmKFcFSElV9v/4K\nCxZQbn4QA2qGcaVEdXMVt0pVyvQ+Ol0/k2r/VSDlT9eWb3tRdUkg95xK4R4eRtvZHTL06Yf2DWZP\nv2BabgzCOzIMBwcoWxZcz4cRPSyIK5MKsE86J/IxY1QAlXffhfXrwccHBgxQYUuflolnuTWmfkQW\nLVpErVq1cHFxwcXFhcOHD3Pjxo1slb1+/Tr37t1Dr9eby7dr147IyEjzOe7u7tjYZP+l/rPPPqNy\n5co4Ozvj4uLCnTt3UtXn6elp/qzT6fD09CQiIoLw8HAiIiLM/XBxcWHq1Klcu3YtW+0+eFkBsLOz\nIzpaRW6MiIhI1aadnV2u+ew1/rvIOf9nZcFHV2XcOJETS9P7BG9tMsjYscpcuuRtg5z2TfaJZvYz\nYNJZyMbAlal8pj9PPGyWrxyzP3OfdMVkH3JEucaycqxBtvUJEZNOp0zCrr6pyq8YY5Dx40UWLhTl\nh07ZfweH5H4dPpzaz7lhg0irVvnic434db/8/NIKOePTSlaMMcjKMfvl4jOtZf2bG1Jd/3XPGrIx\ncKV5/3DTIfKLR+VkeQb3Pqc+/0VvGWTSJJF//827689T+b59Itu3izz3nMjff+fMZvYEoRD6qM+f\nPy+2traya9cuMZlMIiJSs2ZNCQkJERFlus7K9G00GqVo0aISERGRYf1py2dEStP3X3/9JSVKlJDD\nhw+b5S4uLmYz88SJE6VBgwap2vfw8JCdO3dKaGiolC9fPtN2Jk2alKnpu0WLFuZrTtunyZMny6uv\nvmqW3bt3T2xsbDTTdz6SxbP2RCOT5SomC0uwsECnA8t6eqgwPdU6Vme9Hvd/lIk0vpieqIDpdFkS\nmGpR2r5OH1Nv7TjzflxRZ2r9PiXVOmCTpbVZ3nRJIOh0hHb7nPZfteGvXgs4X7sLkV61SSziaD4v\n1qEE7hcMNP1hqGrnxSlcqtwm1TriAzo9z1SEHj3A0kavgmU86P+mTWpNVseOamQMqeVp1/Hq9Xki\n9wgMpLMRtgYGY7ijx9kZIt/6Q12zvRu2adZ5L5gbjyTdP7cLYZAUaMYNuA04p/xfdJme6TrxSG99\nOvl9bz22N+Hbb6FTJz3lP56OVT7fnyciv3cPpk5V67G1CGePRExMDDqdDjc3N0wmE4sWLeLw4cOZ\nnl+qVCkuXbpEQkIC1tbWWFhYMHjwYN566y1mz56Nu7s7ly9f5siRI7Rp0ybH/YmKisLKygo3Nzfi\n4+OZNm0ad++mXn8ZFhbG6tWr6dixIzNnzqRIkSI0aNAAAAcHBz755BPeeOMNbGxsOHbsGLGxsdSp\nU+ehs74zk3ft2pWGDRsSGhqKXq9n0qRJ2gzyAkyhMX3rxGRenuXgkPE5er3KUjhggDKZGo3q+IbX\n1rB54FIOth+b6vwYR490dZgskt9dbO7fARFemNGCIjE3aRPcFYBav0/B51Dychufg2tosvQ1AEK7\nz+BguzHJ9YnK5aDXK8tmhtYyS0vo1i1ZSRcgrCxVuubXXlMhsMPDk+9rWiTFSw5gXve+t9PHTBi4\nlPaOyWa4oO/68PXdf4lIjM+ksvSmz+LFVX6MxYvVOuzbt5VP+9atR7++Asdzz4GzM2TDB6mRMZUr\nV2bUqFE0bNiQUqVKcfjwYZo0aZLqnJT+2FatWlGlShVKlSpFiRIlAJg+fTr+/v40aNAAJycnWrdu\nzcmTJzMsnxE6nc58Ttu2bWnbti0VKlTAx8cHOzs7vFLkPtfpdLz44ov89NNPFC9enB9++IFVq1Zh\naWmJpaUl69at4+DBg/j5+eHu7s6QIUPMij5lOxn1K63swX6VKlWYNWsWL7/8MqVLl8bBwYESJUpg\nWwB/gzQKD3LBp6ks+OSmjBsncn9nxqbF6GiRq1dFxGCQO3UDZM6AZNPpd8MNMnu2pDK/ZmR6XTA7\n1iy/VKGlhLUfn6rMpoFLldk8A3Puns7TUplu5w81yNxBBrlTTy2NMlMQTa/ZkMfFKUv8zH4GOe+f\n8+Vqi8cdMN+rYsrMI4DUs3OWwc8FyaefXJUV4/4nJ+r3Mp+3+r3dGdZ/oYK6v7P7G+SUT4Asedsg\nO3ao/79pf8G8f9mW//qrSOXKIl99pWaLR0dnaTJ7klAITd8aOScqKkqsrKzk/Pnz+d2V/yxZPGuF\nBvm3ZFVZ/sY2CR6SvR++axsMMm6c+mFfPtogJ70D5OtBBtncf5EYLazkt2G/ZqpYHiiJu67ekmBd\nJJUyTrCyFQE5+OzIVMfvFveWb4cZZMFQ5R+f1c8gP/wgcv16xv17Ij/8W7aIfPGFSMOGyXKTSWTv\n3lxt/15j5TMeN07k66+zv878t2HrzPdrfIf3pXbtrmJlZSslQEaC/J3By88vI7dmq/4L5QNk7kCl\nuM+XD5DwNQVI8T6KfNkykZAQkaFDRUaMUP/HfABNUT+1/PLLLxITEyPR0dESGBgotWvXzu8u/afJ\n4lkrPLG+w8s2wsZ4D52lJSVWPzz2srGmno8+And3ZRr1uxVGs6WB2FhnPzZ4Zlyo9jwbh/3CkKHK\ntBvjXJrvO6+l+5ahWFvBiZHBeHfRUyplbscnGXv6xg21xCcsDJo0gRMnVCzRihXhhx/gwgXo3Vst\n28ql9uOr6dm4EXbtUpOWS1x8eGzyZt8PxO3yIQB+mBqO+/n9+O/8Bu+jG7EUtbYuEvgRlXYNYPXb\nm7leqRW+YStotngwtvdv81fPeRxvFpiu/gftb+gczFE7PQ0bQtWqyqPgdiEM2zcLWGzw7Mjj46FP\nHxWatG1b8pqnNda3BgwePJgVK1YgItStW5e5c+dSvnz5/O7Wf5b8ykedq+jEhJjA+uFLFgHl9vX3\nh4sX1fwcvR74IeftRruUJaGIPS5XjgGQYGXH7uajQafj11HbqLplJt93+JlauoO4uoKFDurX59ES\nMCcmqsXD8+apzBUlSkC1aiqTRWacOaMWlLdvDyEhSivduAFffQWHD0P//mr97rvvKqeuo2PmdeUA\nGxvo0EENe0NDITsLO1LGau85JtlHZ7KwJMK/GfcjzzMrIZaQxFiGJyUP6fxFAGcdS+F3NzkOebMf\nhqZT1CkpVgy8yyrdt3+/OlbuNrwSVyCnAWSNjQ28/z68/jrUrasWnGto5AILFixgwYIF+d0NjacI\nue5aUYL77pS9c/aryE579yp7QWSkyMCByRGhUpgRw8JERo0S+XaYQUytlB9z6aiH+1RTml7XvfWn\nHG/Y17y/e8xaOe+vTNvjxomMHy+y9B2DJLZ4BNNnYqLImjUir70mUrWqMllPmKD8kkuXisyYIdKn\nj7reKlVEtm1LLr9/vzrv2WdFfvvt4XaVf/8VefNNkQYNVF3r16fvX2ioCgWWA9Ot0Sjy15fK3D93\noEHmDlThXOcOSo4uZr6/Y/ani3a2u/sMWffmxlT3/0SFFulM4LfS7OckROnKscqnPrOfQTZ8bJDb\ndQPk0lpDsjW5IJq+08qrVhXp2FHk+++T/Cl5A5rpW0MjT8jiWSs0yCWPOjL+3Vg5vPGSSPXqIhUr\nioweLdKsmciQIUqhPSDpx+76BoN8+rJBburVD9+6dSKTJz/8hz3lOuufRxvklHdLue5VW25/s1xE\n1DroqAYBcvwHg0T8apDElo/ww9uwociLL4r06yeyapVIWJhITEzG/8HISJGPP1b1TJwoMmmSyDPP\niHTtKnLsWM6+DZGRIt98I1KpknIwb92qlEDnziKNG6v7OWNGjhVL4l6DXL8ucvasyLkVBrlZO0CC\nhxhkzgCDhFdIvr8XKwVIopWtXPWpm+U69bvFVQzz6w4l5P0iDmKbRlF/WLKCzBu2LkeT2ebOFfno\nI5G5Aw1ypmwzOdWot8QMf7dgKuaM1lkbDCIffCDSooX6P+YBaIpaQyNPyOJZK0Q+6jL1WdBnJ4F6\nA2U2fa/WC61cCV26KBt3+/YqstYD025YGBIYSOR1sF0YjGNLPceOKZetl1fW+Z4r7vqWJj8M5Uap\nKsQbLYl4Pxj9EH3qZa2P45MMC1Pm6hEjVP8tsrlK7uJFVfbcObWEp1cvsLZ+eLmMOHxYZXW6eVMt\n7u7YUZnZr11TZtZWrWDZske7viS5aXAgMfdgabNgIjz0WFio0KAWFuBxJYwX1gViYQmhfR+ez/uo\nnRPDPqiBS8I9IPmLW8XajmfqvUr5ZoF4eemxSJFhreniIVjHReEYeY7dL33FuVpd8Dm0Fp8Dq/E8\n+ocKywpsnbwdz1eaUaIE2NmBjUWiWuf89ddQqlTB8lmDCkEaEaHWWz9hNB+1hkbe8HT4qE0m0Omw\nv3NJ5UqsXl1tD6hbF7ZtgxdeSC4DuLmDLkl3p5zcZTRBojE5psStW3Dnjlqna2o4gIvFa9Dyx0Bc\nXcGzHpBbsSeOH4fRo1UaxDp1cla2bFm15QZVq8KWLWpRtL198nFvb6WgBg9WN+QxfNoWFuBgDz17\nwl8xat/bG1xcoNgJsNmjmrgcARals37nKFHCH0vHEnDjPAANKrbin5PbOJJwn6u7QuiyK4RrNsVY\nXrsLnYp70fTS37he/hsLk0pB2GTZMBr/OBxdknKRFM9D0Q2rWRZViwrnNlLx5C88c3Y9RWJuKqGd\n3SNf/xNj0CD1YrVnDyQFxdDQ0NDIbySiRHUZN9Yk8Z98IfLdd+ntBhs3igwfrj7v2iVSr14606LJ\nJDJlisjSUWq51qpxyqd6yjtAlo4yyKlTIqtXq3XCp32VHzNXTZtnz6oQkVu2PEEDSi5x7ZpIz54i\n/fsrU+sTMu0a9ykz+Vd9MvBppzFd3/R4JsUa9+YS2mGiHE8RqlRA4jIJF/tgad35as+LocMEuezf\nNJUsMZOsZMbOXcTYKkDidhskJkb55AuEaVyvF2nfXuTkyVz7l2cEmulbQyNPyOJZKzTIDScftYa6\nf3+RP/9Mf5X37im/7/r1yn9dt65IQoKSpfix+3OaQY57BsieOUpxR0eLhK82iLFV8g9jTKMAufZ7\nLv+wNmig/L8pJ3EVdOLi1JtNs2Yi1aqJ7N79xBTP7boBMrOvQeYHqmAmGfmcz9Tqkqx0U6xvN+os\nUynXSzoLma6zkFpJAVW+AflIp5Pm/o1l8HNBssOvYbpJgyaQ65415e9Wb8oV3wbm46H6YTJnQNIE\nuYEGWTh4p9zxqS4CcnTYbFm/XiR8TervT54p7mXL1IvfkCEimcSlflzQFHWBoHnz5vLNN9/kSVvt\n2rWTRYsW5UlbD5gyZYoMGjTokcrm5b1JmVY0t8niWSs8PupLJWthbWNBiaLRsGYNVMogm9Pw4Spz\n1Ntvwz//wKhRUKuWkiX5/GJj4dDrwdR7TU+qaHtP0qe4d69aHjVpUrr0lYWCkydVrsn165V9esmS\nJ+KTjesfyP17sLpdMKcc9NjbJ69Gcj0fRquFfSh+9ai5yNVyjThdrydn9d1pvGw4PgfXcNfdj639\nFxNRujInT/7F0aN/cPToRq5cOZqqOXf3cnxk786Qc3v4s/sXxJWuSv3VowHlE39xaj0sxMTmgT9w\ntXwzKm+bS+Vtc7GJu2s2nwN8OD6OWJMNfpH76PX7q9gk3kP3yy/p3RpPcp31rFnKd/PRR+Q2OfFR\nf/WVmuLwpChRQk3rKGycP38ePz8/EhMTzXMockrLli3p3bs3AwYMyOXeFX4e5960aNGC3r17M3Dg\nwGydP3nyZE6fPs3ixYtz3NbChQsJCQlhx44dGcqfCh816LCyFPXDlCI9WyqGDlU/kH37wuzZSkE+\nUNQXL4LJRJEiFmqdc168oty9q3699u6Fzz9XfvTCSIUK6jp69FAvPwsWgK+vCr6di9jaqK1fXzjv\nqjJ2njoFOh2YIuG+FOGOQxmOVXyREx1GEVfa11z20HPv4fgg3aZOh41NUapWbUvVqklBQv5Zz72l\nw64hupYAACAASURBVNgae5ctJiPXr58h8PoZAgGWv42nmx8t7t+lnm0xdDcuYJEUgCUgpGeWfX7r\n6wpc9W9K2b/XYXv/NgDRc7/HbkGdvMmpYWMDQ4ZAu3YqqLxH+vj1ecW1a2oOwpPiwoUnV3dekPbF\n5klhNBqx1BK6ZIuc5uDOq/9hWgpNUg7buDsc6f+pUtIpJz+lpGpVFcFJlxR1JClRPHv3wsiRStE8\nqXzD772nlNjw4Wqyz5AhamKbjQ389FPhVdIpadxYTUDz9YVOnZT1QiTX8zXrRgfhezOMfv3ggw/g\no85hvHYuiBJr5iOr11LBdJz4qze5eFElCYkLDaPOiozzhYOaAd5+0xd4DV1J37f+5LB3Hab2/Y6O\nHSfj798Ea0sbLkWeZUlMJG/evMAbSclXHhBnZcPtYsUJaz+e9W9u4FKlALPM4cYFyu9dQpEkJQ1g\nuziEb14L45df4M7ZGzBlirp3YWEqeEluf/9OnlSz8h7hLf9pJSIigq5du1KiRAn8/PyYNWsWADdv\n3qRs2bKsW7cOgOjoaPz9/VmyZAkA/fr1Y+jQobRp0wZHR0datGhBeHi4ud7jx4/TunVrXF1dqVSp\nEsuXLzfL7t+/z6hRo/Dx8cHZ2ZlmzZoRGxtLs2bNAHB2dsbBwYG9Sb9L3377LZUrV6Z48eK0bds2\nVTt//vknlSpVwtnZmTfeeAMRyVRJTJo0iW7dutG7d2+cnJz4/vvvuXPnDgMHDqR06dJ4enoyYcIE\nTCb18mkymRg1ahTu7u74+fkxe/ZsLCwszPIWLVoQEhICKMX00Ucf4ePjQ8mSJenbt685Icj58+ex\nsLBg0aJFeHt74+7uzpQpUzLs4969e/Hw8Eh1DatXr6ZGjRrma+jdu7dZ1r17dzw8PHB2dqZ58+Yc\nPXo0XZ0pOX36NPXr18fJyYkXX3yRWyky9ezZs4dGjRrh4uJCzZo12b59OwDjxo1jx44dDB8+HAcH\nB958800ARowYgZeXF05OTtSpU4edO3ea69LpdMTHx9O3b18cHR2pWrUqYSmexWnTpuHv74+joyNV\nqlRhzZo1ABw7dozXXnuN0NBQHBwcKJ7Lg5yCglzwqCdbvzqUer10VsTGqkAh27eL1KqlfMTvvadk\nue0zbNVK5O23RTp1Enn9dRVY5KefRG7ceHzHRUHl1CmRl18WGTYsX/JlG1sGSMxfBondZZCo+ipB\nx+jRKgDN7P4GOZeDpCGnK7SUqX2/k27dPpNatbqIczFXqQxyGaQbiG2Sr9vJyUOqVesg3RoPlN1O\nHmLUWchVn3pyq0R52Ri4IpXP+7arr1x1ryImZShP3hwdn8z92bRJpGVLkZs3c/XfTA581A/ywT+p\nbezY7PXZaDRK7dq15cMPP5SEhAQ5e/as+Pn5ycaNG0VE5I8//pBSpUrJtWvXZNCgQdK9e3dz2b59\n+4qDg4Ps2LFD4uLiZMSIEeYcztHR0eLp6SkLFy4Uo9EoBw4cEDc3Nzl69KiIiLz++uvSsmVLiYiI\nEKPRKKGhoRIXFyfnz59PlSdaRGTNmjXi7+8vx48fF6PRKB999JE0atRIRESuX78uDg4OsnLlSklM\nTJQvvvhCrKysUuWWTsnEiRPF2tpa1q5dKyIi/2/vzuOirvMHjr+G+xDkEBFBMLVSUzsoy7LE3MxW\nu7NVyyNN0y2zdIvU3Oxyw21X7TJrzdVcf9q5W62aZmu6ZSZuZppmmqICggeKXALD+/fHB4YBBhgP\nZhh5Px+PeTjf+X7m+33PjMN7vp+zsLBQ7rjjDhk7dqwUFBRIdna2dO/eXebNmyciInPnzpXOnTtL\nenq65OTkSJ8+fcTLy8vhOtbz58+XDh06yN69eyUvL0/uuusuGTp0qIhUrn89ZswYKSoqkh9++EH8\n/f1lRy1zO7Rv315W2/UvuueeeyQlJcX2GuzbfhcsWCB5eXlSXFwsjz32mFx22WW1ft69evWS2NhY\n2b59u+Tn58vdd99tO9bBgwclMjJSVqxYISIiq1evlsjISDlSPg9B9TW7RUQWL14sx44dE6vVKn/5\ny1+kVatWcurUKVucAQEBsmLFCikrK5PJkydXWUv8/fffl8zMTBERWbZsmQQHB8uhQ4dEpOa659XV\n8V3zGLK7TS/Z+My/nf+2iogMGSJy0UUiAweK/OMf5g9axZeloudsxYxm1Tnan5cn8t57ZpIR+/1T\npphz5eY6H9v5IC/PJOvRo80PI3tn8v6exf7cXDNnzK5d5jfEwkdT5WBMomTFJ1ZJ0vbJOjs+UbId\n7H/zzTJ5fdw/5fXItvJQSEvp3OYKCQgIsa32ZX/r7Bsod/QYLpMmfeWw13gZFtkf073q4w31/rz4\nosjzz5/TBTzwwET97bffSnx8fJXHZsyYIQ888IBte/z48dKlSxeJi4uTY3Y/boYPHy6DBw+2befl\n5Ym3t7ccOHBAli5dKtdff32V444ZM0aeffZZsVqtEhgYKFu3bq0RT0VCs0/U/fr1q5IgrFarBAUF\nSVpamixcuFB69OhR5RhxcXF1JupevXrZtg8dOiT+/v5SWFhoe2zJkiXSu3dvERHp3bu3vPXWW7Z9\nX3zxRZX47JPXjTfeKHPnzrWV/fnnn8XX11esVqvtdaWnp9v2d+/eXZYuXeowzqefflpGjhwpIiK5\nubkSHBws+/fvt72G2jpp5eTkiMVikdxa/r4mJSXJ5MmTbds//fST+Pn5idVqlZdeesn2w6LCzTff\nLAsXLrQ9t76OaOHh4bbP9ZlnnpGbbrrJtm/79u0SGBhY63Mvu+wy2w+oBQsWnHGi9pg2arF4EXTs\nIHSqpX3akb59zdjqnBxT7f3BB2Zu7NOdeN5qhSVL4O9/N2O3Fy6EoCDTBu3lBdu3wzvv1L5Q9vkq\nONi8J1Onmk5yMTFmjHuzZuY9Ky6uZQHucy8kBK64onI77l4o+jfkF5im2yxvKK/ZIza27mNZLBZa\nhcdxfXAkA4MjWX//PLLbXM6RI7+yf///2L//fxzatZZf9m3ip5JCftqwEDYs5B/+IWSeOgnAjm63\n0TpzO8X+IXw39A2av3oroXmZ/Hj70+z+GDoXQnurWe/7nHnkEXj0UVPV/tRTuKaRvPFJS0sjIyOD\n8PBw22NWq9VWBQ1mQYrXXnuNqVOnVilnsViIs+sDExwcTEREBBkZGaSlpbFx48Yq5UtLSxk2bBhH\njx6lqKiI9u3bOx3jhAkTmDRpUpXH09PTyczMrBIDQJt65k+wL5+WlkZJSQkxdv0VysrKbGtgZ2Zm\nVjle9XPZy8zMJMGu40F8fDylpaVkZWXZHmtlN0FFUFAQ+fn5Do81ZMgQrr32WubOnctHH31EYmKi\nw9dltVqZOnUqH3zwAYcPH8bLywuLxcKRI0cIqeVvrP1x4uPjKSkp4ciRI6SlpfH+++/z6aef2vaX\nlpZyo12n3urt1C+//DLvvPMOGRkZWCwWcnNzOXLkiG1/dHR0lddbVFREWVmZrRlg1qxZ7Nu3DzBN\nK0ePHnUY8+nwmETtbS0m4Fg6xCbWX7hCjx6m2/DAgWYmkyuvhNRUk2Ar2vzA3E9JqexJa98mmJFh\nVi9KSoI33jCzoJWWmp5O+fmm98xFFzXOiTFcwd8fXn7ZTDmWlgaHDkFenvnxEhZmfhSNH296Jtu/\nv08+ad5Pb++63384o/0BzyQTsGwe/oUwbFIyu69LIahnIvv3w85/bOaqDcmsuXceeXnQe0kyK3un\ncCQhkRYtICZjM1d9mMzKu+aBwA3vJfPdPSl4XZBIy5Yd6BfVnu5pqXz9xH/56cD/yFiZwgovb9KP\n7rP1UfTa+gkXt7mc7hf1YtSy8Ry56DpC//cBmcRwbPVmfFYk89aN82jVCm5+JBn/2Sn4XH0OXv/r\nr5uFWB57DJ55Blq0aJCPvTGLj4/nggsuYNeuXQ73W61WxowZw7Bhw3j99dcZMWKELcGKCAcOHLCV\nzcvL49ixY8TGxhIfH0+vXr1YtWpVjWOWlZUREBDA7t276WY/EROOOyzFx8czbdo0Bg8eXGPfL7/8\nUiWG6jFVZ7FYqpyjTZs2+Pv7c/ToUYe9zGNiYqocr65jt27d2pZ0APbv34+Pjw/R0dFV2tSd0alT\nJxISElixYgVLlixhyJAhDsstWbKETz75hDVr1pCQkMDx48eJiIiosyOXfSz79+/H19eXqKgo4uPj\nGTp0KG+99ZbD51X/bNavX8+f//xnvvzySy4pXwypvnNXSEtLY8yYMXz55Zf06NEDi8XC5Zdfbnvu\n6XZcs+cxncmCC44Qsv+n+i+H7HXoYJYGvLu8c9CVV8Lnn1f+YevWzaw01b696fy1aVPlH8GUFNON\ndc4cePFFM1tXhw7mOD4+0KeP6Sx26aVNN0nb8/U170/PnuY9nzQJVq6E3r1NMh82zCSPu+6CIUNM\nLceUKWamtuefr+wgZf/+JyaaW0rKGe8P7JlIyBspXP5/yVyct5mbIjYz/KdkPu2Zwt6IRCL7JnLy\n6RSGbU+md+hmfLdu5tIlyazolUJBx0SKuybyv9+lkLgsGet3mynbZJL4d3elcKJ9D2KTHuaWcR/z\nbVR73vj9vxh9czK9gyPx8vZlx4HvWbhmNjf8uoH/bjGdSgKPfM/NXz7J3t+MZsB3f+SK95JZ0DGF\nA/cls2neZk58eZavf+dOOHLE/J8cNMjUeDSxqT67d+9OSEgIM2fOpLCwEKvVyrZt20hNTQVgxowZ\neHt7s2DBAp544gmGDRtm60gFsHz5cr7++muKi4uZNm0aPXr0IDY2lv79+7Nr1y4WL15MSUkJJSUl\nbNq0iZ07d+Ll5cXIkSOZOHEimZmZWK1WNmzYQHFxMVFRUXh5ebFnzx7bOcaOHcuMGTNsnaROnDhh\n65j229/+lu3bt/Pxxx9TWlrKK6+8wqFDh6hN9SQSExND3759mThxIidPnqSsrIw9e/awbt06AO69\n917mzJlDRkYGx48fJyUlpdYkMnjwYNsVYl5eHlOmTGHQoEF1DjOrK6kNGTKE2bNns379egYOHOiw\nTF5eHv7+/kRERJCfn8+UKVNqPV7F+RYvXsyOHTsoKCjgj3/8IwMHDsRisXD//ffz6aefsmrVKqxW\nK0VFRaxdu5b09HTAXB3bfy4nT57Ex8eHFi1aUFxczHPPPWfrPFef/Px8LBYLLVq0oKysjAULFrBt\n2zbb/ujoaA4ePEhJSYlTx/NEsjuul+THdhApb5g/I4cPi7Rvb1be2rjRTBbx0EOm/XrQIJEOHUTa\ntTOrVC1cKNK/v8ju3Wd+PmXk5Zn38x//EPn+e9PJrqTEvLcTJ5pVoT74wKVt2gUF1Zpyy/dbr0iU\n3LWpNZp5SzemyqluiXL8wkR5c7RZOe3ll2tv8549+4SMHr1MuncfIoGBzeUvdm3UWd5+VdqsP5n4\npSz5g2lTT49JlKOrztHrP3BAZOhQkbffrvWjqQ+n0UY9e7ZpR26o2+zZzsedkZEhgwcPllatWkl4\neLj06NFD1qxZI6mpqRIeHi579uwREdM2fN1118mMGTNERGTEiBEyduxYuemmm6RZs2bSq1cv2bdv\nn+24P//8s/Tv31+ioqIkMjJS+vTpIz/88IOImE5cjz32mMTGxkrz5s2lV69eUlTed+OPf/yjREVF\nSVhYmGwsX/nv3Xffla5du0poaKi0adNGRo0aZTvPypUr5aKLLpLmzZvLI4884rDTU4Xp06fXaIc9\nceKEjBs3TuLi4qR58+Zy+eWXy7Jly0REpLS0VB5//HGJjIyUdu3ayaxZs8TX19f2XPtzlZWVyXPP\nPSdt2rSRqKgoGTp0qBw/flxETNu7fSe06s91ZP/+/eLl5SUDBgyo9TXk5eXJ7bffLiEhIdK2bVtZ\ntGiReHl52T6z6pKSkmTKlCnSvXt3CQ0Nldtuu02O2nXk3bhxo/Tq1UsiIiIkKipKBgwYIAcOHBAR\nkQ0bNshFF10k4eHhMmHCBLFarTJy5EgJDQ2VmJgYmTlzplxwwQWyZs0ah+919fdg6tSpEhERIS1a\ntJCJEydWeT+Ki4ulf//+tjiqq+O75jFkb0wPk6jt/lOckeuvNytQ/eY3ZqnICmVlZoWiRx4xvcXv\nvffsfhQo561aJdKzp5lRzkWJ+mz2F/43Vf73P5E5c8wCbn/9a92d015//ZR81blvleScYXd/3W3P\n256f0foKWTIptUbfvDOO//Bh84Oz/A/N6aKJzUw2YsQIefrpp90dhkstX75cEhIS3B1Gk1fHd81j\nSE6zODnS87azfzdefNEsEbllS+1lTpyo2YtZNawffjDDvAYOFOnc2VxhV3DBcK8z2V9WZgYAvD3W\nzA2/5A+1DwfLaNdD9nW7VTb1HC1zwuOkRUi0LVFnYpHPA8OkIDjC9tiamXbJ+mzjf/99854uW2Zq\nN04DTSxRDx8+/LxP1IWFhfLvf/9bSkpK5ODBg3L11VfL448/7u6wmrw6vmseQ9JbdJWMgY+e/buR\nmSlSSxWKcrP8fDOf+Jw5ZlGVu+82tR+dOolMnWoSzRdfiKxb16gSd0lSH/nqr6ny5z+bMN8YZeYG\nf+2BVHnnYceJe9/FN9a6eIiAbW7xxY+buefPOv5ly8w8Ar17i/zzn05/JDSxRD1ixAiZNm2au8No\nUAUFBXLVVVdJSEiItGzZUkaOHCknT550d1hNXh3fNc+Z63t/dCLefX9D60UvuTsW5QpWq+lZn5pq\nhsJ5e5vZtzIzzTzuXbrAZ5+ZtPb00zByJFUmb3fTetEFBWZUmveWzfg+8hB5+bCs9zyy2yTSsmXl\nUp4t0jZzx0vX2JbhfLd5DN+dyOTV8sM/eNMfmLHzS8qssKHH49x8QxFB40dVvsYzjX/fPtNxMiWl\ncnrdOuh61Eq5xvkx17eA5ZwOOlWNmre3GZvtaBGTw4fhX/8yC1sHBcEnn5jhYKNHw/Hjptezm6bo\nCwoyN0KAAAgIgCH3wcYSs3y01Wp+WwQXwtG4S7FYS1k3fD4F8VfgveMLmNMXgOLVL7PNx58bRLjz\nw6HwIVhPZOE9berZBdi2rVkc5g9/MHMD2I0JVUqpsyHpkV0kY/Qf3V07oRqj4mKRv/3NTOE6dqyZ\nxvWii0QWL24UVeMV90tLRXJyRHYvS5Vf2vaRpU/UbNMuaNai9vW0/QJlxw6Rov9uMp0izya+Ll1E\nRoyodxYzmljVt1LuUsd3rcH1A3YCvwDJtZRJAr4HtgFraykjx4Nba6JWzvvqK5F+/cxc5H/5i1mf\nfOZMM8bHDXOTV9+/fVGqPPmkyKuvirz3VGWyTrukn5RhkbToi+UZvyC5olqy/unCWyu3r7zyzOPb\nuNEM3frsszrfRjRRK+USdXzXGrSN2hv4GfgNkA5sAgYDO+zKhAFfAzcDB4EWwBFqkozILnjdPoDo\n+X9qwJDVeaWwENavh9WrzeQ1MTGwbZv599VXzcQ1v/xi2r5//NFMbuPvD2+9Vdmme+KEmW3t8GEz\nYQucszbtL7+Eb74x1eHhv25m0H8ewmKB9UPe4MgF3cnO3s2rr95CVvbu2l9jRTvxmbRZb99uJqZ5\n//1ap7/VNmqlXMNdbdTdgd3AvvLtpcDtVE3UQ4APMUkaHCfpSj6+5zRAdZ4LDDTzvfftW/nYqVNm\nJrS77zZTnbZqVTnNZliYScozZ5rt7GyTCFu2NNOjnjxpsmpp6TkJz74Jfst8KF5VPjW6l+mL0bJl\nB5588hueeukaXjryKwCZoa0I9g0g9Oi+sw/gkkvghhvgzTfhiSfO/nhKKY9zD/C23fb9YOvUWmEW\n8BrwHyAVGIpjciI4RjIfe8ndtRPqfFBWJrJtm0j5DEtVHDwo8u23ZgmunJzKNtzCQpENG0TGjTMT\nszz/vCkrcs6qxr95LVXmDDNLdH4wuXI41z/+sF4uDwgVQOKjOsj+Vh0rZzX7RCRr+Vmc//hx095d\ny7wCaNV3o9CrV696V3k6V2655RZZtGiRS85VYcaMGfLggw+e0XPdEe+Zslgstc6wVsd3rUHdTf2J\n+jXgGyAQiAR2AY6WtpKMyC6S+eRfXfy2KuXADz+ITJ4skpRkOrBdffU5m0BlyxaRj55OlV8S+sii\nCZWdzf7+2BfSqlVHAeTjoHBbol44dJVkRZQn7i+/PLPzX365yIABIgUFNV4qp5Gor7zySomPj5fY\n2FiJjIyU2NjYKvfj4+PPav+VFW3yHsbRMpenq76pOZVzXPmDx5EzTdQNWfWdDtivYdaGyiruCgcw\n1d2F5bd1wKWYzmdVzCw6ivc3q2g2/QRJSUkkJSU1SNBK1atbN3OzWuGLL0xV+RdfmO2LLjLrbb70\nkhmvbLHUbDOuWEijWpuxBbPGy6WXJpJ5dQo3jn4IH1/4eug8TiUkMmHC58yceR3zcg5yR/mhhr1r\nV61/440mfddy/FrP//bbZrjbq6+ytnt31q5de0ZvS3Z2NlFRUYBZoKBiRaP4+HiCg4OrlD2T/dnZ\n2WcUV2MhLmrTt1qteDfRJU7rczYrWAG25SxdrSHPmIq5Om4L+AG/Az6pVuZfQE9Mx7Mg4GrgJ0cH\nm9isNU/0HsD06dM1SavGwdsbbr4ZPvrIDJ5++2244w646ioYNcq0aefkmHHdpykmBsIjzOqhFU3i\nERHxPPro52wJDLOVK6ve9+S//zXZ/ptvTu+ETzwB69aRlJ/P9OnTbTdPlZGRwd13303Lli1p164d\nr75qKvOOHTtGmzZt+OyzzwCzUlOHDh1YvHgxACNGjGDs2LH07duX0NBQkpKSqiyhuHPnTm666SYi\nIyPp2LGjbcUrgMLCQiZNmkTbtm0JCwvjhhtuoKioyLYOdlhYGCEhIWzcuBGAd955h86dOxMREUG/\nfv2qnGf16tV07NiRsLAwxo8fj4jUmuinT5/OPffcw9ChQ2nevDkLFy7kxIkTjBo1itatWxMXF8e0\nadNsK4SVlZUxadIkoqKiaNeuHa+99hpeXl62/UlJScyfPx8wPy5eeOEF2rZtS3R0NMOHD7etJrVv\n3z7bGswJCQlERUUxY8YMhzFu3LiRmJiYKq/h448/5tJLL7W9hqFDK1s+Bw4cSExMDGFhYfTq1cu2\nypgj9vH+/e9/p2fPnjzxxBNERETQrl07Vq5cCcDUqVNZv349jzzyCCEhITz66KP1fqYjRoxg3Lhx\n9O/fn2bNmvHyyy8TExNTZbU1+9fx3Xff0aNHD8LDw2ndujXjx4932WpZPYHVmKvcveW3X5187i2Y\nnt+7gcnljz1UfqvwB2A78CPwaC3HkYzILnJo+lzX1VEodTbKykS2bxf5059EunUTuf9+szBGWpqZ\nJtXJqun/vW3mEX/tgVSZOdO0Wc984F3p4+UjN4K0i4ivfSrS022z3rtX5JZbRD75xFaU06j6jo+P\nl8TEROnYsaOEhIRIx44dq9xPTEw8q/3x8fFOvfVWq1WuuOIKef7556WkpER+/fVXadeunXz++eci\nIrJq1Spp1aqVZGdny4MPPigDBw60PXf48OESEhIi69evl1OnTsmECROkZ8+eImJWdYqLi5O///3v\nYrVa5fvvv5cWLVrITz/9JCIiv//976V3796SkZEhVqtVNmzYIKdOnZJ9+/bVqPr+5z//KR06dJCd\nO3eK1WqVF154Qa699loRETl8+LCEhITIhx9+KKWlpTJr1izx8fGpter7mWeeEV9fX/nXv/4lImYu\n7zvuuEPGjh0rBQUFkp2dLd27d5d58+aJiMjcuXOlc+fOkp6eLjk5OdKnT58qK0DZV7PPnz9fOnTo\nIHv37pW8vDy56667bKtHVVTpjxkzRoqKiuSHH34Qf39/2bFjh8M427dvL6tXr7Zt33PPPZKSkmJ7\nDffff79t34IFCyQvL0+Ki4vlsccek8suu6zWz9s+3gULFoivr6/87W9/k7KyMpk7d660bt3aYVln\nPtPhw4dL8+bN5ZtvvhERkaKiojpfx+bNm2Xjxo1itVpl37590qlTJ5ltt+xbQ7ZR/1yecKMxw6cq\nbq4kuUHRcuj5t2r9sJRqtAoLRT79VGTMGDO2u0MHkfIvtojU26ZcvCFV8nr0kbkPpsqSSabN+s2H\nP5PY2K4CyEwff8eJ2snjV3ns00/NZDEffywip5eoY2Njz2lirr4/NjbWqbf722+/rZHUZ8yYIQ88\n8IBte/z48dKlSxeJi4uTY8eO2R4fPny4DB482Ladl5cn3t7ecuDAAVm6dKlcf/31VY47ZswYefbZ\nZ8VqtUpgYKBs3bq1RjyO2qj79etXJWFYrVYJCgqStLQ0WbhwofTo0aPKMeLi4upM1L169bJtHzp0\nSPz9/aWwsND22JIlS6R3794iItK7d295663Kv6VffPFFlfjsk9mNN94oc+dWXiD9/PPP4uvrK1ar\n1fa60tPTbfu7d+8uS5cudRjn008/LSNHjhQRkdzcXAkODpb9+/fbXoN9oraXk5MjFotFcnNzHe6v\nnqg7dOhg25efny8Wi0WysrJsZe3bqOv6TEXM/4fhw4c7/TqqmzVrltx555227YZsoz4OrDj93Hpu\n5QVG4a1TiCpPFBAAAwaYG0B6upnu9LLLzNCxetqUfa9JxPfVFIYNe4hjx+DbEfOwXJDIExdez9tv\n/44nt69ks5cPt4e2IskvgpjsreaJP/0Ea9bAo4/C1Vc732b917/CG29UjtF2UmFhITk5OTXanIOD\ng4mNja21TdrZ/c62UaelpZGRkUF4eLjtMavVaquCBhg9ejSvvfYaU6dOrVLOYrEQFxdX5dwRERFk\nZGSQlpbGxo0bq5QvLS1l2LBhHD16lKKiItq3b+90jBMmTGDSpElVHk9PTyczM7NKDABt2rShLvbl\n09LSKCkpISYmxvZYWVkZ8fHxAGRmZlY5XvVz2cvMzCQhIcG2HR8fT2lpKVlZWbbHWrVqZbsfFBRE\nfn6+w2MNGTKEa6+9lrlz5/LRRx+RmJjo8HVZrVamTp3KBx98wOHDh/Hy8sJisXDkyBFCahnvc+Yw\nvQAAHAVJREFUb696PGCaOFq2bAlUbaeu6zOtKFv9/anrdezatYuJEyeyefNmCgoKKC0t5corr6w3\n5vo4k6j/A/wZ+Ag4Zff4/8767KfDAhZfz5maXKlaxcbCK6/A738PW7ZAcLBp765HUCCcCoasLLC0\ngcDAUB5++FOWLZvAsq/eYNnxg0wJtfJixRMuuaTyyRs31pwEpTatWpmx1ePGnfZLawzi4+O54IIL\n2LVrl8P9VquVMWPGMGzYMF5//XVGjBhhS7AiwoEDB2xl8/LyOHbsGLGxscTHx9OrVy9WrVpV45hl\nZWUEBASwe/duunXrVmWfow5M8fHxTJs2jcGDB9fY98svv1SJoXpM1VkslirnaNOmDf7+/hw9etRh\nx6eYmJgqx6vr2K1bt2bfvn227f379+Pj40N0dHSVNnVndOrUiYSEBFasWMGSJUsYMmSIw3JLlizh\nk08+Yc2aNSQkJHD8+HEiIiLOSWe86p9FXZ9pbep6HePGjSMxMZFly5YRHBzM7Nmz+fDDD886bmc6\nk10DXAnMAP5id3Op4ILDTv0xU8ojdOhgrlpjY83ELO++C/fea652k5PNTGIVNm82j82bR9CieQzc\nnIz3ls3s2wclJT6Mv/YBnml5IRYszMjNtD3tlF8z8lvEVx5n3rx6j2/bn5192ok6MDCQ+Ph40tPT\nq1xV5efnk56eTnx8/FntDwwMdCqO7t27ExISwsyZMyksLMRqtbJt2zZSU1MBmDFjBt7e3ixYsIAn\nnniCYcOGVekctHz5cr7++muKi4uZNm0aPXr0IDY2lv79+7Nr1y4WL15MSUkJJSUlbNq0iZ07d+Ll\n5cXIkSOZOHEimZmZWK1WNmzYQHFxMVFRUXh5ebFnzx7bOcaOHcuMGTNsnaROnDhh68T029/+lu3b\nt/Pxxx9TWlrKK6+8wqFDh2p9vdUTWExMDH379mXixImcPHmSsrIy9uzZw7p16wC49957mTNnDhkZ\nGRw/fpyUlJRae0MPHjyYWbNmsW/fPvLy8pgyZQqDBg2qs+dzXQl1yJAhzJ49m/Xr1zNw4ECHZfLy\n8vD39yciIoL8/HymTJlS6/FOV3R0dJXPYcCAAbV+pnW9ltpeR15eHiEhIQQFBbFz507mzp17TuJ2\nJlEnAb0d3FwqPyhKE7U6v3ToAPfdZ5bofO89WLcOdu+GGTMqk2lFEk1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       "text": [
        "<matplotlib.figure.Figure at 0x7f5ba1644150>"
       ]
      }
     ],
     "prompt_number": 36
    }
   ],
   "metadata": {}
  }
 ]
}