labs/Lab7_Notes.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# special IPython command to prepare the notebook for matplotlib\n",
      "%matplotlib inline \n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import scipy.stats as stats\n",
      "import matplotlib.pyplot as plt\n",
      "import statsmodels.api as sm\n",
      "\n",
      "# To load in the baseball data\n",
      "import requests\n",
      "import StringIO\n",
      "import zipfile\n",
      "\n",
      "# special matplotlib argument for improved plots\n",
      "from matplotlib import rcParams\n",
      "\n",
      "#colorbrewer2 Dark2 qualitative color table\n",
      "dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),\n",
      "                (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),\n",
      "                (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),\n",
      "                (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),\n",
      "                (0.4, 0.6509803921568628, 0.11764705882352941),\n",
      "                (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),\n",
      "                (0.6509803921568628, 0.4627450980392157, 0.11372549019607843)]\n",
      "\n",
      "rcParams['figure.figsize'] = (10, 6)\n",
      "rcParams['figure.dpi'] = 150\n",
      "rcParams['axes.color_cycle'] = dark2_colors\n",
      "rcParams['lines.linewidth'] = 2\n",
      "rcParams['axes.facecolor'] = 'white'\n",
      "rcParams['font.size'] = 14\n",
      "rcParams['patch.edgecolor'] = 'white'\n",
      "rcParams['patch.facecolor'] = dark2_colors[0]\n",
      "rcParams['font.family'] = 'StixGeneral'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Recall from from lab last week 10/10/2014\n",
      "\n",
      "Previously discussed: \n",
      "\n",
      "* Boston Housing data set\n",
      "    * Predict housing prices\n",
      "* Linear regression\n",
      "    * Multiple ways to do this in python: `numpy`, `scipy`, `statsmodels`, `sklearn`"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Today, we will discuss the following:\n",
      "\n",
      "* More linear regression using the `statmodels` python module\n",
      "    * Old Faithful Geyser data set\n",
      "    * Oakland baseball data set\n",
      "\n",
      "<a href=https://raw.githubusercontent.com/cs109/2014/master/labs/Lab7_Notes.ipynb download=Lab7_Notes.ipynb> Download this notebook from Github </a> \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# `statsmodels`\n",
      "\n",
      "[statsmodels](http://statsmodels.sourceforge.net) is python module specifically for estimating statistical models (less machine learning compared to `sklearn`). It can estimate many types of statistical models, but today we will focus on linear regression. \n",
      "\n",
      "### Recap of linear regression and least squares\n",
      "Last week we learned, [linear regression](http://en.wikipedia.org/wiki/Linear_regression) is a method to model the relationship between a set of independent variables $X$ (also knowns as explantory variables, features, predictors) and a dependent variable $Y$.  This method assumes the relationship bewteen each predictor $X$ is linearly related to the dependent variable $Y$.  \n",
      "\n",
      "$$ Y = \\beta_0 + \\beta_1 X + \\epsilon$$\n",
      "\n",
      "On Tuesday in lecture, we learned how to write this model using matrix multiplication \n",
      "\n",
      "$$ Y = \\beta X + \\epsilon$$ \n",
      "\n",
      "where $Y$ has dimensions $n \\times 1$, $X$ has dimensions $n \\times p$ and $\\epsilon$ has dimensions $n \\times 1$.  On Tuesday, we also derived the [least squares](http://en.wikipedia.org/wiki/Least_squares) estimates of the coefficients of a linear model. These estimates minimize the difference between the following: \n",
      "\n",
      "$$ S = \\sum_{i=1}^n r_i = \\sum_{i=1}^n (y_i - (\\beta_0 + \\beta_1 x_i))^2 $$\n",
      "\n",
      "where $n$ is the number of observations.  \n",
      "\n",
      "> The least squares estimates $\\hat{\\beta}_0$ and $\\hat{\\beta}_1$ minimize the sum of the squared residuals $r_i = y_i - (\\beta_0 + \\beta_1 x_i)$ in the model (i.e. makes the difference bewteen the observed $y_i$ and linear model $\\beta_0 + \\beta_1 x_i$ as small as possible). "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Old Faithful Geyser Data Set\n",
      "\n",
      "The [Old Faithful Geyser](https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/faithful.html) data set is a well-known data set that depicts the relationship of the waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA [[webcam]](http://yellowstone.net/webcams/). This data set is found in the base installation of the [R programming language](http://cran.r-project.org).  \n",
      "\n",
      "`faithful` is a data set with 272 observations on 2 variables.\n",
      "\n",
      "Column name| Description \n",
      "--- | --- \n",
      "eruptions | Eruption time (in mins)\n",
      "waiting\t| Waiting time to next eruption (in mins)\n",
      "\n",
      "There is a function in `statsmodels` (or `sm` for short) called `sm.datasets.get_rdataset` which will download and return a data set found in [R](http://cran.r-project.org).  \n",
      "\n",
      "Let's import the `faithful` dataset. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "faithful = sm.datasets.get_rdataset(\"faithful\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's look at the help file\n",
      "# sm.datasets.get_rdataset?\n",
      "# faithful?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "faithful.title"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "'Old Faithful Geyser Data'"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "faithful = faithful.data\n",
      "faithful.head()"
     ],
     "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>eruptions</th>\n",
        "      <th>waiting</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 3.600</td>\n",
        "      <td> 79</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1.800</td>\n",
        "      <td> 54</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 3.333</td>\n",
        "      <td> 74</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 2.283</td>\n",
        "      <td> 62</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 4.533</td>\n",
        "      <td> 85</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "   eruptions  waiting\n",
        "0      3.600       79\n",
        "1      1.800       54\n",
        "2      3.333       74\n",
        "3      2.283       62\n",
        "4      4.533       85"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "faithful.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(272, 2)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Histogram \n",
      "\n",
      "Create a histogram of the time between eruptions. What do you see? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(faithful.waiting)\n",
      "plt.xlabel('Waiting time to next eruption (in mins)')\n",
      "plt.ylabel('Frequency')\n",
      "plt.title('Old Faithful Geyser time between eruption')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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gVGAKsLg0bTEwteUlkiRJykS7HrC+GrAd0T/ta0TzZlHd8Dh37tznXvf09NDT\n09P80kmSJDWot7eX3t7epi2vXSHtk8CHgT7gfqJvWtFawMJabyyGNEmSpFyUK4+OO+64US2vHc2d\nhwDfBx5Kw78GtizNsy3VCwkkSZLGnVaHtFnAEmASMI24b9qWRK3ZnmmeacBk4jYckiRJ41Irmztf\nB5zOwPuf9RO1Zr8E5hC34tgZ2IcIc5IkSeNSK0PaZUQNWj2z0u95Y18USZKkvPnsTkmSpAwZ0iRJ\nkjJkSJMkScqQIU2SJClDhjRJkqQMGdIkSZIyZEiTJEnKkCFNkiQpQ4Y0SZKkDBnSJEmSMmRIkyRJ\nypAhTZIkKUOGNEmSpAxNbHcBcta3bFm7izBq3RPM4ZIkrYgMaYM489Zr+fx1l7S7GCO2zVobcPnM\nj7S7GJIkaQQMaYPo61/G0mV97S7GiD27ApddkqTxzrYwSZKkDBnSJEmSMmRIkyRJypAhTZIkKUOG\nNEmSpAwZ0iRJkjJkSJMkScqQIU2SJClDhjRJkqQMGdIkSZIyZEiTJEnKkCFNkiQpQ4Y0SZKkDBnS\nJEmSMmRIkyRJypAhTZIkKUOGNEmSpAwZ0iRJkjJkSJMkScqQIU2SJClD7QppqwBrtGndkiRJ2Wt1\nSOsCZgHzgZ0K4zcG5gGHAWcBM1pcLkmSpKy0OqQ9H7gSmAr0p3FdwIXA+cBpwInARUB3i8smSZKU\njVaHtIeARaVxewPTgd40fCuwFNi3dcWSJEnKSw4XDuwK3AU8Wxg3H9irPcWRJElqvxxC2hTgsdK4\nxUSTqCRJ0rg0sd0FIGrQlpbG1Q2Pc+fOfe51T08PPT09Y1IoSZKkRvT29tLb29u05eUQ0u4HdiuN\nWwtYWGvmYkiTJEnKRbny6LjjjhvV8nJo7uwFtiyN25bqhQSSJEnjTjtCWmWdXen3tcA9wJ5peBow\nmbgNhyRJ0rjU6ubO9YBDiHukHQD8FbgNmAnMIW7FsTOwD7CkxWWTJEnKRqtD2kPACemn6C7iSQQQ\nTx6QlKGly/qYNMH7TEtSK+Rw4YCkFcSkCd1MPWN2u4sxKosOPrHdRZCkYcnhwgFJkiSVGNIkSZIy\nZEiTJEnKkCFNkiQpQ4Y0SZKkDBnSJEmSMmRIkyRJypAhTZIkKUOGNEmSpAwZ0iRJkjJkSJMkScqQ\nIU2SJClDhjRJksa5pcv62l2EUeuEbSib2O4CSJKk9po0oZupZ8xudzFGZdHBJ7a7CE1nTZokSVKG\nDGmSJEk/PDXyAAAOS0lEQVQZMqRJkiRlyJAmSZKUIUOaJElShgxpkiRJGTKkSZIkZciQJkmSlCFD\nmiRJUoYMaZIkSRkypEmSJGXIkCZJkpQhQ5okSVKGDGmSJEkZMqRJkiRlyJAmSZKUIUOaJElShgxp\nkiRJGTKkSZIkZciQJkmSlCFDmiRJUoYMaZIkSRnKKaRtDMwDDgPOAma0tziSJEntk0tI6wIuBM4H\nTgNOBC4CuttZKMHTt93b7iKMO+7z1nOft577vPXc5yueXELa3sB0oDcN3wosBfZtV4EU/KNuPfd5\n67nPW8993nru8xVPLiFtV+Au4NnCuPnAXu0pjiRJUntNbHcBkinAY6Vxi4GpbSjLc3Z4/lQOnbF7\nO4swKutPfl67iyBJkkaoq90FSL4JbAfsURh3DrAaMLMw7k5gqxaWS5IkaaQWAC8Y6ZtzqUm7H9it\nNG4tYGFp3Ig3VJIkSY3bheWbOxcAb29DWSRJkpR0AX8C9kzD04AHgFXbViJJkqQ2yqW5s5/oezaH\nuBXHzsA+wJJ2FmqcWwd4Cniy3QUZJzYnao7/DlwMPNTW0kiShmsVYCWWbxHseBOAq6heUOBTCcbW\nr4Fl6ee2NM59PvbeDlwDbFEY535vvk2APqrHeOVnW9zfY2034HPAkcD3iX0O7net2LqAWcC9wKsK\n4wc7rjvqmD8CeAR4JbEzridufAtR43YXPpWgWV4GfBZ4afpZH/d5K/QQtWcbFca538fGEcQX6abp\nZxuimwW4v8dSN3FlfuW+nHsAV6TX7vexsRdwEhGMzwIq92PqqICQgfWIW4Uto3pf13rf3xMGmbZC\nHvO7AW8A7iZC2quJprdiE+3twFtbX7SO9D/AUcDWhXHu87HVRTxd45jSePf72JhSGn4D8BXc32Nt\nPWL/rp6GdwCuI05U7vfmez7wF6q32PoMcGZ63TEBITPFkDbY90nD3zW5PHGgbF3gFcAlabiLeCrB\n3fhUgrHQTfRB+wRxwJwLTMInQYy1XYhmn82B84jAdgQe62PlwdLwTOKZwe7vsfUQEQ6+B6wBfJio\ntd8N9/tYeA/xvd2fhi8EDgDejY9fbIXBzpuvoMFjPteQdiRwcmncBsRTCIra/lSCDtEHvBHYkPgD\nfyNwArHPs3sSRAd5GfA4MBvYDzgQ+BrwcjzWx9oEYHfgV0QNm/t7bL2NuGr/fuDnwKW438fKCxh4\n0d19RM3NofhPdyvUeoLSP4njuuFjPperO4sOAc4GnimN7yNSf1GuIXNF1U906l0FOJ6o3XGfj53V\niZrLh9PwDUQz0J3A9qV53e/N9XJif/cRJy2P87E1Bbgy/T6T6j53vzffw0SNTUUlFKxH9PGmNM1Q\n3Fz1vk+6BplWV45/EIcAfyT+E1gCbAb8jPgvYI3SvGsBf21p6caHC4h9+wCwZmma+7x5HiQefVa0\niGjy9FgfW/sSzUDgcT7WJhM1Z58jrmT+MvAdohnU/d585xGPWaz0PXtl+u0/I61xP/WP6478rqlc\nOOBTCVpnCnAj7vOxNo1o7pxUGHcRcb9A9/vYupnqFW8e52NrZ+BvheFuovnnlbjfx8qbiStoTwGO\nI8LZHOJ7vegS4mpPjU7xwoFXUP+47sjvmkpI86kEY2cn4P1U/6v6AtGHBNznY62X+EKFuBniPURI\ndr+PnelUbwEBfreMtbWBR4k+rxD79a9EbbH7feydCpxDhwaEDEwgQlrlPmm1vk8eJI7rjvyuqYQ0\ngC2J/gyHp98va0+ROs6biAOlF/gU8O+Fae7zsTUV+CFx8cA3gdek8e73sXM08KHSOPf32HoVERQ+\nDnyVaq2D+31s7UIE4o3p0IDQZusBnyb6tn6H2Kcw+HHtMS9J0jj3euA3xE2bKwwIK5iuoWeRJEkr\niHWB/YkrOWtdoS9JkiRJkiRJkiRJkiRJkiRJkiRJkiRJkqTlrN3uAjRg3XYXQGolH64qNddRxCNC\nfgO8gHhu4Y1p3GFUn9P5OuIB03MZ/H6FuxBP3ah3V/D9gD+OttBD2Ay4D9h8jNej5a0K3EU8D7DZ\nVgOOJY7NsVxP0deAb4zi/TOBlzapLJKkcegS4OeF4dcTJ8IXleY7ZxjLWgc4ojDcTTxntWJz4D2N\nF3FIHyy8Xhk4Mv0eKxsD+4zh8hvxwaFnaen6jyCOg2b7HrBJC9ZTtEf6GY1TiMfxSJLUsP2BZ4GN\n0vBEotbspMI82wCfHMGyvwCcMarSDe21wJ1jvI6ilYBfAAe1cJ31tHrby3YA/tWC9bwL+FIL1jMW\npjG8f3AkSVrO6sATVEPY2sBi4kHHlabNOQysxXgrcDxRm3E2EewAtkrzbgA8H7gSuJ54qO9EYHsi\n/HURtVHfIR5g/WVgIQMD3UTgi0St2EIiDBxfo/xfB/6R1rEVETY/QdQEdgOfAm4C3gJcDNwL7Aj8\nB/A74Nq0DwDWAD4PfAX4A7BrjfXtSDS1nQccnMZtB5wAfBS4kOpDoYvWBv6L2F+zgduBy1IZB1v3\n/sDTwDxin90O7F1n28t2T+X6IfAToslws1SOrwCnE/t2P6L2dFOiH9VJRLM1aRt/S9SA3gg8SLV2\n9BPpfZ8mnqu4NvABBtY+HQZ8hAjs56Tlr0IcJz8H3kt8Pr8H1qyxDQDXUH3IOUQNWnE9RwK3AG8i\nPs/bqd3cvSXwfeKY+y9iP1+W5v1O2hefSfN2Aa8GPpaGdwKuIB52/4O0Hw4tLHs2cADw30SzbNFC\nYEqdbZMkaVA/Jk7AECfgjxEn39elceXasPuJsAJxUnwTEQA+nt63ZZp2LPDd9Pr5xMl/GdX+pScQ\nJ+e1iBPvU8AWadqhwH+m129I71ujRtn3oBooJgAHpnkrJ/UXAX1U+y99kTihVzqg/5YIQhBNU1PT\n608SJ9darqLabLsGcAfwvML6nihsR9GhwAIi8K4ELKIa6AZb9/FEv8G3EPuiorjtZasTgbDiT8Bx\nRPg4megbuCHw7jS9EtLKy107TavUHB5JPF9xSyLcLCus4w1EmH5vGn478D+F6V8CLk+vX0s8r3H7\nNPz7wvuK1krr2HCQ9WxLfMa7p+HzgM/VWBbEPwTXEoGwm+i/+MU0bVpabnd6fSnwq8J7rwFOI/bh\nPkTgr5TxpsJ8B5TWeTkRVqWO5oUD0tj4AXGy3I4IN18HbgBmER2fbyzN/9o0fUfiZLcWEUzOL83X\nRbU27mHipFf0NPBn4J9EjdCDRG0RwIup1jJVTpR9NcpevJBhGQODCcRJt4s4wUIEqoeAR9Pw7UTt\nEsCbiZB3NFEbOD9t22D2IWoeH0/Dt6Sfd9eY9xnixH5fen0nsb1dddZdCZJfJALU/kQfworBLuLY\nh6i9OTr93ERcCNJP7O8bgQcYGKJqLbeyn65Kv7+RtvfVNd53CbFvK95PhOCKM9L7NiE++8eAm9O0\nv1D97IsqwXHxIOt5OpW5cpzcUmdZEMfDbWl5fUSt6K1p2nxgMtGH7LZS2SvruYbYh38urONJYl9/\nlegL+YPS+x6jdk2n1FEmDj2LpBG4lAgZnyROfn3EyfuLafzc0vxPE7Ui3wP+xuBhYTDl9/VT/Wfs\n10ST2NFEELyMCIKjtazG8ErA+qk8Jy33jsFNJU7sRQsZWPNTT2V7h1r3k0Rt537ElY1LhrHsTYna\nqUa3Zyh9DH4Fb9HGDNw396TfG9WYt/jZF1UuAKkV0AdT75/68jG3rMbrlerMW9RfmP4MsC9Rg/d6\nogbx5sK8T1GtaZU6ljVp0thYAlxA1P6cl8adS9S8bEf0T6tYlahV+QYDT0Qj0T/ItHOIPm1HEzV3\n7xjluobyKNEkO60wblXioonBLCQC0UqFcasQNTTNWvdmRHh+hOhjNxyPAD2lcTuk34Ptdxg6dK9O\ntfZpMAsZuP8qgavevqlVrvvS73r91Ya7nOFMG6nViJrAFxI1zOUa5TWIpm2poxnSpLHzQyKMVZqM\n/kZcxfjT0nwvJGqJJhGdwLckmgS7qf6NVpop/0U0HXWlecvTK78pDFcCwsxUnvOJDv6r1Sn3E0Sz\nYKVGqryOWoGjOG5CGl4K/IyoHXwR0afsy1T7HZXXuT7Rj+4SIhC9M01bGZgBnFnjfeXvsIlp3c8M\nse6jiaa0jxK1nZsXylHc9qLLgZcQ/dk2IpqxK30MK9tc9A+iaXtCmrdcU1a5uGIbqvuqUrP5/ML6\nu6nu+3nA26jWIu0J/IgInPX2RdmDRM3dZqXxxfXUWlY95Xm7CuPK659Qmr94fBaP3fWI2rPFwOEs\nX2s2hQhvkiSNyEosf1XaLJavSVqZaIp8EDiRaBKdT/Rpm0M0S32OqE16IfB34uKBqUTn+D7iRDYF\n+CXRN2obIkAsJTq1TwJeQ9TE/JO4RUgfA6+mq5hE9Lf6eSrDoUSz1X8TJ89Pp/fuR4SJM4kAugvR\n4fwvxFV7m6YyXkE08V5D1CLW8p60/bPT8DTiqs5Pp/LvXuM9axBNlouIMLQTEYx+kKbVW/exVPs4\nTUnr/QPRx6m47dNrrHM/4kKFR9P+mETs618Tfa52K8x7GBE2ryKC1c+AV6Vpy4gbux5LXB25deF9\nl6Xy7EZc9fs0cSVppb/WIan8/5GWsUYqxylEyNszLW8B8U9BrasgjyUuWKgor+cY4jN+JxFIf0tc\nKFG+eGOztH3XpXW+lKip+xHxj8dBaTlHEcfS1USgfCXRR/LvRJ/HdYkrcfuIGt7N0rQPExdn7FtY\n56rEcWwlgySpI3QRtTDF2rM1iVs+qPWKV362wxpEgC3XvK4IjiRCryRJHWEHoqmzeG+2XRj93d81\nMsto/2O2XsHw++PlYnuiBlGSpI4xgeiT9QDRbPUTqjdwVWsdRjTrHUvcGqSdtqX2/edytdfQs0iS\nJEmSJEmSJEmSJEmSJEmSJEmSJEnSSPw/DboZ60FG8dkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109c48810>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This histogram indicates [Old Faithful isn\u2019t as \u201cfaithful\u201d as you might think](http://people.stern.nyu.edu/jsimonof/classes/2301/pdf/geystime.pdf). "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Scatter plot \n",
      "\n",
      "Create a scatter plot of the `waiting` on the x-axis and the `eruptions` on the y-axis. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(faithful.waiting, faithful.eruptions)\n",
      "plt.xlabel('Waiting time to next eruption (in mins)')\n",
      "plt.ylabel('Eruption time (in mins)')\n",
      "plt.title('Old Faithful Geyser')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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meiAiIoWostJqgM2ebcedBT2ZaMRdU2N1115+2X6ZOwWAbjfcfHOkw8Gf/mRT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\n2GG5GVNZmU293XefXbNPn+x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WWXDrrcX134LkXlfR3k5YYPYTsCEwGZgZ9X4p8CvgmiSv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\ngu9Oa6uaR9esUaf46dPVBJoZlK1bp+zac88p6Bo+PPeyJxJ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       "text": [
        "<matplotlib.figure.Figure at 0x10b725910>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Build a linear regression to predict eruption time using `statsmodels`\n",
      "\n",
      "Now let's build a linear regression model for the `faithful` DataFrame, and estimate the next eruption duration if the waiting time since the last eruption has been 75 minutes.\n",
      "\n",
      "$$ Eruptions = \\beta_0 + \\beta_1 * Waiting + \\epsilon $$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = faithful.waiting\n",
      "y = faithful.eruptions\n",
      "model = sm.OLS(y, X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's look at the options in model\n",
      "# model.<tab>"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "results = model.fit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's look at the options in results\n",
      "# results.<tab>"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print results.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:              eruptions   R-squared:                       0.973\n",
        "Model:                            OLS   Adj. R-squared:                  0.973\n",
        "Method:                 Least Squares   F-statistic:                     9621.\n",
        "Date:                Fri, 17 Oct 2014   Prob (F-statistic):          9.97e-214\n",
        "Time:                        10:34:55   Log-Likelihood:                -250.30\n",
        "No. Observations:                 272   AIC:                             502.6\n",
        "Df Residuals:                     271   BIC:                             506.2\n",
        "Df Model:                           1                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "waiting        0.0501      0.001     98.086      0.000         0.049     0.051\n",
        "==============================================================================\n",
        "Omnibus:                       37.012   Durbin-Watson:                   2.835\n",
        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               10.965\n",
        "Skew:                          -0.159   Prob(JB):                      0.00416\n",
        "Kurtosis:                       2.069   Cond. No.                         1.00\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "results.params.values"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([ 0.05012919])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We notice, there is no intercept ($\\beta_0$) fit in this linear model.  To add it, we can use the function `sm.add_constant`.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = sm.add_constant(X)\n",
      "X.head()"
     ],
     "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>const</th>\n",
        "      <th>waiting</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1</td>\n",
        "      <td> 79</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1</td>\n",
        "      <td> 54</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1</td>\n",
        "      <td> 74</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1</td>\n",
        "      <td> 62</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1</td>\n",
        "      <td> 85</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "   const  waiting\n",
        "0      1       79\n",
        "1      1       54\n",
        "2      1       74\n",
        "3      1       62\n",
        "4      1       85"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's fit a linear regression model with an intercept. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "modelW0 = sm.OLS(y, X)\n",
      "resultsW0 = modelW0.fit()\n",
      "print resultsW0.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:              eruptions   R-squared:                       0.811\n",
        "Model:                            OLS   Adj. R-squared:                  0.811\n",
        "Method:                 Least Squares   F-statistic:                     1162.\n",
        "Date:                Fri, 17 Oct 2014   Prob (F-statistic):          8.13e-100\n",
        "Time:                        10:38:10   Log-Likelihood:                -194.51\n",
        "No. Observations:                 272   AIC:                             393.0\n",
        "Df Residuals:                     270   BIC:                             400.2\n",
        "Df Model:                           1                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "const         -1.8740      0.160    -11.702      0.000        -2.189    -1.559\n",
        "waiting        0.0756      0.002     34.089      0.000         0.071     0.080\n",
        "==============================================================================\n",
        "Omnibus:                        4.133   Durbin-Watson:                   2.561\n",
        "Prob(Omnibus):                  0.127   Jarque-Bera (JB):                3.173\n",
        "Skew:                          -0.138   Prob(JB):                        0.205\n",
        "Kurtosis:                       2.548   Cond. No.                         384.\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you want to predict the time to the next eruption using a waiting time of 75, you can directly estimate this using the equation \n",
      "\n",
      "$$ \\hat{y} = \\hat{\\beta}_0 + \\hat{\\beta}_1 * 75 $$ \n",
      "\n",
      "or you can use `results.predict`.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "newX = np.array([1,75])\n",
      "resultsW0.params[0]*newX[0] + resultsW0.params[1] * newX[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "3.7980801099789772"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resultsW0.predict(newX)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "3.7980801099789772"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Based on this linear regression, if the waiting time since the last eruption has been 75 minutes, we expect the next one to last approximately 3.80 minutes."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot the regression line \n",
      "\n",
      "Instead of using `resultsW0.predict(X)`, we can use `resultsW0.fittedvalues` which are the $\\hat{y}$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(faithful.waiting, faithful.eruptions)\n",
      "plt.xlabel('Waiting time to next eruption (in mins)')\n",
      "plt.ylabel('Eruption time (in mins)')\n",
      "plt.title('Old Faithful Geyser')\n",
      "\n",
      "plt.plot(faithful.waiting, resultsW0.fittedvalues, color='blue', linewidth=3)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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s2fB4bCo0aqWVnIMPn8/qq554wurW1lmnZ5YuHLavDTfMfZVffb2thEzWLb+i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\nd/HG+kdQ+Jmu6r8zUSCWQV3Njw3X74UizOEpXddgcgjw9+T+d3QNatM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       "text": [
        "<matplotlib.figure.Figure at 0x10b97fcd0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Residuals, residual sum of squares, mean squared error\n",
      "\n",
      "Recall, we can directly calculate the residuals as \n",
      "\n",
      "$$r_i = y_i - (\\hat{\\beta}_0 + \\hat{\\beta}_1 x_i)$$\n",
      "\n",
      "To calculate the residual sum of squares, \n",
      "\n",
      "$$ S = \\sum_{i=1}^n r_i = \\sum_{i=1}^n (y_i - (\\hat{\\beta}_0 + \\hat{\\beta}_1 x_i))^2 $$\n",
      "\n",
      "where $n$ is the number of observations.  Alternatively, we can simply ask for the residuals using `resultsW0.predict`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resids = faithful.eruptions - resultsW0.predict(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resids = resultsW0.resid"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(faithful.waiting, resids, 'o')\n",
      "plt.hlines(y = 0, xmin=40, xmax = 100)\n",
      "plt.xlabel('Waiting time')\n",
      "plt.ylabel('Residuals')\n",
      "plt.title('Residual Plot')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hOG1UjhxO5cjhqXXfvi/nc7l8rYTxdSfu5RLYLQfWAK8Dx4FTgDqgvrtfErds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\n+z7qbt+Q07kKsVaYK1pzTHyl16Y7Gdu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ZtIsxAdFq4BHg48AldAZ9CR+M/3wcMAATmL0G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\nERERERERERERERERERERERERERGv/X/1RqIiH/MztQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109c80990>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The residual sum of squares: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.sum((faithful.eruptions - resultsW0.predict(X)) ** 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "66.5617757127\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Mean squared error: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.mean((faithful.eruptions - resultsW0.predict(X)) ** 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.244712410708\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Build a linear regression to predict eruption time using least squares \n",
      "\n",
      "Now let's build a linear regression model for the `faithful` DataFrame, but instead of using `statmodels` (or `sklearn`), let's use the least squares estimates of the coefficients for the linear regression model.\n",
      "\n",
      "$$ \\hat{\\beta} = (X^{\\top}X)^{-1} X^{\\top}Y $$ \n",
      "\n",
      "The `numpy` function [`np.dot`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html#numpy.dot) is the dot product (or inner product) of two vectors (or arrays in python).  \n",
      "\n",
      "The `numpy` function [`np.linalg.inv`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.inv.html#numpy.linalg.inv) can be used to compute the inverse of a matrix. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = sm.add_constant(faithful.waiting)\n",
      "y = faithful.eruptions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, compute $X^{\\top}X$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(X.T, X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([[    272,   19284],\n",
        "       [  19284, 1417266]])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, compute the inverse of $X^{\\top}X$ or $(X^{\\top}X)^{-1}$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg.inv(np.dot(X.T, X))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([[  1.04029479e-01,  -1.41547492e-03],\n",
        "       [ -1.41547492e-03,   1.99652136e-05]])"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, compute $\\hat{\\beta} = (X^{\\top}X)^{-1} X^{\\top}Y $"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta = np.linalg.inv(np.dot(X.T, X)).dot(X.T).dot(y)\n",
      "print \"Directly estimating beta:\", beta\n",
      "print \"Estimating beta using statmodels: \", resultsW0.params.values"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Directly estimating beta: [-1.87401599  0.07562795]\n",
        "Estimating beta using statmodels:  [-1.87401599  0.07562795]\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Baseball data from Homework 1\n",
      "\n",
      "Let's return back to the baseball data from [Homework 1](http://nbviewer.ipython.org/github/cs109/2014/blob/master/homework-solutions/HW1-solutions.ipynb). In Problem 1(e), we asked all the students registered in 209 to complete the following problem: \n",
      "\n",
      "> Fit a linear regression to the data from each year and obtain the residuals. Plot the residuals against time to detect a competitive advantage in years 2001-2003 for the Oakland baseball team"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Load baseball data (salaries and wins)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def getZIP(zipFileName):\n",
      "    r = requests.get(zipFileName).content\n",
      "    s = StringIO.StringIO(r)\n",
      "    zf = zipfile.ZipFile(s, 'r') # Read in a list of zipped files\n",
      "    return zf\n",
      "\n",
      "url = 'http://seanlahman.com/files/database/lahman-csv_2014-02-14.zip'\n",
      "zf = getZIP(url)\n",
      "tablenames = zf.namelist()\n",
      "\n",
      "salaries = pd.read_csv(zf.open(tablenames[tablenames.index('Salaries.csv')]))\n",
      "teams = pd.read_csv(zf.open(tablenames[tablenames.index('Teams.csv')]))\n",
      "teams = teams[['yearID', 'teamID', 'W']]\n",
      "\n",
      "totSalaries = salaries.groupby(['yearID','teamID'], as_index=False).sum()\n",
      "joined = pd.merge(totSalaries, teams, how=\"inner\", on=['yearID', 'teamID'])\n",
      "joined.head()"
     ],
     "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>yearID</th>\n",
        "      <th>teamID</th>\n",
        "      <th>salary</th>\n",
        "      <th>W</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1985</td>\n",
        "      <td> ATL</td>\n",
        "      <td> 14807000</td>\n",
        "      <td> 66</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BAL</td>\n",
        "      <td> 11560712</td>\n",
        "      <td> 83</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1985</td>\n",
        "      <td> BOS</td>\n",
        "      <td> 10897560</td>\n",
        "      <td> 81</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1985</td>\n",
        "      <td> CAL</td>\n",
        "      <td> 14427894</td>\n",
        "      <td> 90</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1985</td>\n",
        "      <td> CHA</td>\n",
        "      <td>  9846178</td>\n",
        "      <td> 85</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "   yearID teamID    salary   W\n",
        "0    1985    ATL  14807000  66\n",
        "1    1985    BAL  11560712  83\n",
        "2    1985    BOS  10897560  81\n",
        "3    1985    CAL  14427894  90\n",
        "4    1985    CHA   9846178  85"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For each year, we perform the following: \n",
      "\n",
      "1. Calculate the least squares estimate of the coefficients in a linear regression model where x = salaries (in millions) and y = total wins. \n",
      "2. Calculate the residuals for each team: $$r_i = y_i - \\hat{y}_i$$\n",
      "3. Plot the residuals for each team across time. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "teamName = 'OAK'\n",
      "years = np.arange(1999, 2005)\n",
      "residData = pd.DataFrame()\n",
      "\n",
      "for yr in years: \n",
      "    df = joined[joined['yearID'] == yr]\n",
      "    X = df['salary'].values / 1e6\n",
      "    X = sm.add_constant(X)\n",
      "    y = df['W'].values\n",
      "\n",
      "    # least squares estimates\n",
      "    model = sm.OLS(y, X)\n",
      "    results = model.fit() # fit the linear regression model\n",
      "    beta = results.params # least squares coefficients\n",
      "    yhat = (beta[0] + beta[1]*X[:,1]) # regression line\n",
      "    residData[yr] = results.resid # residuals = y - yhat\n",
      "  \n",
      "residData.index = df['teamID']\n",
      "residData = residData.T\n",
      "residData.index = residData.index.format()\n",
      "\n",
      "residData.plot(title = 'Residuals from least squares estimates across years', figsize = (15, 8),\n",
      "               color=map(lambda x: 'blue' if x=='OAK' else 'gray',df.teamID))\n",
      "plt.xlabel('Year')\n",
      "plt.ylabel('Residuals')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ApAExgCW5uB3wOfA8sBS4yyqlU+omab8HVZV+/fVXFi1axOXLl2nXrh1Tp069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4VEJSYmhvXr1+Pg4DBtd9eZkrs+efKECxcu0Nvbi1KpZMuWLWzfvn1G6nLGkrDo9XrOnj1LYWEh\nMLvZhIUGk8nEw4cPyc3NFVnp8PBwMjMzZ52kDw4O2nSFtTTzmUhWxNHR0SaZdHNzE1mXxsZG6urq\nxpW0RkREEBYWNuF72GQycfPmTXJycjCZTPj5+XH48OGnOusaDAZu375Nfn4+Q0NDYuJ5+eWXiYuL\nmzNJrclkoru7m46ODmGi0tjYSG9v77iEXqVSWWUJLccBNze3RZ+9kCSJmzdvcuXKFSRJIjw8nJdf\nfllkjU0mk5BuTmWbbC+3kVAoFDZJn63NwcGBu3fvUlFRAUzNuGehy//0ej1FRUXcvn2b5uZmwLzu\nWLFiBWlpaePOp2Aukzl+/Dg9PT14eXnx6quvznl/28lCljDLRHFkwCEmJobExETi4+OXbOBTxkK/\nP2cSS5U09vT0EBYWRlBQkJX5lSWqqqooLi5m5cqVREVFTYk0/uAHP/j/2Xvv6LbO+3z8udgAwQGC\ne+9NiBS3KImkqGVrWbIUZTXOOE1P0+Tb9DSt+3PaOKmb2DnpaTO6nJOkSVPb0bQ1bFmUJZKiFkhK\nHOKe4N4LxF739wdz3+ICIDglUTSfc3CIcQlcXNz7vu/zGc+DvXv34ujRo9i1axfOnTu3pv12/D0G\nBwfxzjvvwGAwIDIyEl/5yleAdeR6G7EOYsLFc3uxQBQr/vi4FYAZwEsALjhu7O/vD5PJBJPJBKPR\nyIqqrhdMJhPOnj0LPp8PPz8/CIXCJUnoYvf5fP4TX+RMTEwQomg/uEskEkIUIyIi3E7kIyMjKC8v\nR2dnJ4CFDExBQQHy8/OXtcgUi8UoKSlBfn4+7t+/D6VSSTyP4uPjUVRUhNzcXLL9Uuquo6OjLGlu\nBvYeaCspd1Wr1bh27Rra2toALCjlHTly5IlP3rOzszhz5gxGR0fB5/Nx7NixT0XvLAMOh4PMzEyk\np6ejtrYWVVVVGBgYwO9+9zvExsaitLT0idiLUBRFZNEXK/9lMiz2JNLVzWQyYXJyknVtOYLP58PL\ny4t4i5lMJuKd1dvbS4IwFEUhICBgyZLWubk5vP/++6zS+X379rkts6RpGm1tbbhx4wapLIiNjcX+\n/fvR0tLyRPpmHY3uHfsMFyOHFEURBVK9Xs/K2DIqmPHx8YiLi3vurAsYJUJXhE6tVqOhoYEE9GQy\nGSiKwnvvvcfq9VtPiEQiyGQy+Pn5EYsAdzeBQLCiOSspKYmUYlZVVWFqagrHjh3bcJnD1YLP52P7\n9u3IzMxEX18fqqur0dbWRubcoKAg5OXlIS0tzWXwMSgoCH/6p3+KP/zhDxgaGsKvf/1rnDp1CnFx\ncc/g2ywOq9UKlUpFSk/tPXxFIhGpToiNjd00v+0WPh0oLy+HRqPB7t27F90mKioKUVFRRJNhpaBp\nGk1NTXjttdfwta99DT/5yU8wMjKy5vUNTdOgKApdXV04e/YszGYzEhMT8fLLLzOkcd2wkcOxNvxf\npvH7AE4CsF/RXMFCNvIvHP7PqafRYrGwSORS95fabjklbSvFajKh7kgoh8PB1NQUmbTGx8fJZ4nF\nYiQnJyM1NRVRUVFLRnzHx8dRUVFB6q/5fD7y8/NRUFCwpt4+nU6He/fuobq6mpQ7JSQkoKioaEk/\nLHt1V2bxOTk5ienp6RWXu/r6+qK9vR03b96EyWSCQCBAaWkpsrOzn3imr7e3F+fPn4dOp4NMJsPp\n06cRGBj4RD9zo8NoNOLBgwe4d+8eyYikpKSgpKTkqZo5LxcMsVyqx3I52Z3ForhisRjBwcGIiopC\nbGwsJiYmcO3aNRiNRnh4eODYsWNLli0ODw+jrKyMkEx/f3/s379/3RamjNG9qz5Dd9/d09PTZcbQ\nx8eHLLCtViv6+/tJLyTTY8wgMDCQ9EIuV6BnLaBpGiaTadlCLq5ua4VQKFxWps9isWBwcBA9PT2s\nRX5AQADpU3xapLuzsxMXLlyA0WhEUFAQPvvZzy6r5/Z5xNzcHGpra/Hw4UMi/iSRSEjpqqvvbTab\ncenSJTQ3N4OiKBw4cAC5ubnPNHNuMpnQ1dWFtrY2dHZ2ss5dLy8vJCYmIjk5GREREc9cg2ALTx4r\nyTT+4Ac/eMJ7s4DXX399ze/xk5/8BK+++iq++93v4o033nC7rUqlWlV56vXr1zE2NoYvfelL6O/v\nR0xMDF5//XX8wz/8w6r3m6Io/OM//iMEAgG5NhmBKalUisLCQmCTl6cysCeN/wVAAWCH3ev/C8AT\nwDGH/1uVEM5KYLVaMT8/j9u3b6O+vp51AYWGhiI8PBweHh4somk2mxclomvtD1kOKIqCp6cnZDIZ\nZDIZIZruyKdWq0V1dTUhizweDzk5OSgsLFzXngutVot79+6xeh4TExNRVFS04ggMTdOYm5tzmZ10\nV+7KwNPTEykpKQgJCXmi6q40TePBgwe4ceMGaJpGbGwsXn755ScqsPO8QafT4c6dO6iurobVagVF\nUcjIyEBRUdFzt9BkMktLEcuVZpAEAgGio6MRGRkJX19fUhYrkUjIQlOtVuPWrVvEukUikaC4uBhZ\nWVkrJldms5lFBu3vu/PiFIlEROzKMWCzmozE7Ows6YPs6elhjaFCoRCxsbEkC+nKEoGmaZjNZieS\n5+rGED9HMrjWeUYgELDInV6vJ2TY09MTGRkZkMlkrG2Yfj+BQOD2t9PpdGhubkZjYyMGBwfJ81Kp\nFOnp6di2bdszC05NTEzgvffew8zMDDw8PHD69GmEh4c/k315GjCbzWhqakJ1dTWpjKEoCklJScjL\ny0NERISTuFxFRQVu374NAMjOzsbBgwefKiFjFJTb2trQ3d3NCpT7+/sTIRtHYbwtbH5sVtL41ltv\n4bXXXsOrr76KN9980+22DGkMDAxEUlIS67XR0VG0t7e7JI1f//rX8fOf/5z01h89ehT19fVQqVSr\nDnRSFAXHljx7fBp6GhnYk8Z/A5AOoMju9XcBeOAZkEZ7aLVavPfee05eZAEBAcjOzoZCoViSdNhs\ntmVnOV1tp9PpoNFoSCnukwDTw+JYhrvabKirCVCr1eLu3buoqakh2cKkpCQUFRWti3qofbnr+Pg4\nWltbSf+JO6y23NURTN+D2WzGlStX8PjxYwDAzp07UVJS8qnoX1wN1Go1KisrUVdXB5qmweVykZOT\ng507dz6XghHu4IpYzs3NkdJXe7sKd2DUKmmahlqtJuUriYmJyMvLI2WI9gs+5vy0Wq2LGt27U0Lm\n8/kuSaFcLl/3niZ70qfVaqFSqdDX14ehoSEnkRyGcDGWLgzxW2/SZy/m4oroOW7DXO96vR6XLl0i\nnpr5+fnYu3fvikmCxWJBR0cHGhsb0dnZSeYCPp+PlJQUpKenIzo6ekOMM3q9HufOnUNvby+4XC4O\nHz6MjIyMRbffDD1jNE1jYGAA1dXVaGlpIedfYGAgcnNzkZ6eziotf/z4MS5dugSr1YqYmBicOnXq\niQo5zczMkLLT/v5+1vURFhZGiKJcLn9i+/C8YjOcn8vFZu1pfPfdd/HFL34RX/jCF/D73//e7bbu\nMo2/+93v8JWvfMWJNI6NjaG4uJhFMkdHR6FUKnHx4kW89NJLq9pve9KYk5OD2NhYwgm0Wi1eeOEF\n4FNIGl8D8BkA9rPKRwBUAL7h8H9PlTT+8QNZogUcDodM2AKBAAqFAjk5OevaGzc3N4eWlhY0Nzez\nCKtAIEBiYiISEhIQGhpKBBOWQ0K1Wi0mJiZYJUwcDgc0Ta/7IMHlchcllBwOh5g4M58bHByMtLQ0\nBAQELEpClxvx7Ovrw5UrV4hiZ1ZWFgoLC6HVakm5q/1ieaXlrn5+fpBKpU77U1FRgW3btuHs2bOk\nf/Gll1761Bg7rxVTU1OoqKhAU1MTgIVzvaCgAAUFBRve63MtsFqtKC8vx927dwEsXAv5+fmYnp7G\nwMCA0zW7XDDEkslO1tXVITAwELOzs8syuncsKV2JojFN08R+YbW3tQbIeDzeooTO1fOO26xH5mdo\naAjnz5/H7OwshEIhXnrpJafItTvQNI3+/n40NjaipaWFlCdRFIWYmBgoFAokJSVtyP4yq9WKsrIy\nVFdXA1ggy/v27XMitSaTCZcvX8aBAwdcjqvPI9RqNWpra/Ho0SNicC8Wi5GZmYmcnByiMDowMIAz\nZ85Aq9XCz88Pn/vc5+Dr67su+8CopzNCNvYBVA6Hg5iYGCJk4+npuS6fuVmxRRqff4yOjiIiIgLB\nwcFQqVRux5nVlKf++Mc/xsGDB7Ft2zbynMViQUhICDIzM3H9+vVV7TdFUfjBD36AQ4cOISsry+Xr\n+BSSxh0APgZg33jRDeD/A3DW4f/oV155hagu+vj4ICMjg1zQFRUVAPBEHvf39+Ott96CTqdDYmIi\nfHx8oFQqAQDR0dGIioqCzWZDREQESktLV/z+8/Pz+P3vfw+VSkUyLL29veDxeMRsfmhoCDweb0X7\nr9frQVEUamtriRfYsWPHUFRUhMbGRtA0jZ07d8JoNOLWrVuwWCzIysqCyWTCnTt3YDaboVAoYDQa\nSYlpUlISTCYT6uvrYbFYEB0dDaPRiNbWVpjNZvL7MOIf0dHRa3rMNN739/eDz+cjLS0NAoEAXV1d\nRKSAw+Hgk08+wdTUFKKjo+Hp6Qk+nw9/f38UFxdDIBBAqVSCz+ejtLQUFEWhvLwcWq0WycnJmJqa\nQnl5OdRqNQICAjA7O7vo/iQkJEAul2N0dBReXl7Yu3cvDAYDfvWrX8FoNCIrKwunT59GS0vLup1/\nn5bHjBdfV1cXent7IRQK8eUvfxk5OTm4c+fOM9+/9Xz8wQcf4Pbt20QIx9PTEwqFwmn8KCwsxNDQ\nEN59912oVCqEhoYCYF8vHA4HQ0NDRALfaDQuev5mZGRALpdjcHAQ3t7e2LdvH+RyOerr68HhcFBc\nXAyLxYIbN27AZDIhKyuLWOuYTCakpqbCYDCgpqYGJpMJsbGxMBgMePz4MUwmE0JDQ2G1Wtd0/fN4\nPAwODpLAnEgkQldXFwQCAXJzcyESidDY2AidTofQ0FAMDw8TdWLm/TQaDUJDQ3Hq1CmEhISgsrLy\nqfy+RUVFqK6uxttvvw2bzYbCwkKcPHmSlBAv9f9paWlobGzExYsXodFoyPeZm5tDbGwsXnnlFUil\n0md+/i7ncXt7O8bHx0nFTVFREfbv3w+apvHrX/8aDx8+JJUm/f39kEqlyMvLg4+PD3p7e+Hp6YkD\nBw7Ax8cH9+/ff+bfZyWPb968id7eXqJE2tvbC4qicPDgQeTm5kKlUkGr1WJgYADj4+NErv+zn/3s\nqj7v1q1bGB8fh0wmQ1tbG+rq6gAsXA8CgQAmkwkRERH4/Oc/D6FQ+MyPz9bjjfe4pKRkU5JGAPjz\nP/9zvP322/jv//5vvPLKK06v6/V6NDc3w9/ff0XqqTRN48iRI7h69arTe37729/GL37xC3R0dCA2\nNnbF+0xRFJqbm5GSkoLy8nLU1NRgbGwMBoMBKpUKH330EfApII0cABYA+7Dg00hhwZ/x/wEoB5D0\nx78xABzrtZ56ptEeWq0W77//PpEXz8zMBIfDIYslYKHcMSsrC1lZWUtG8DQaDVpbW9Hc3EwELICF\nKHlCQgJSUlKQkJCwKmNqV0I0qampKCoqgr+//4rfb7mgaZqYQy+nJFej0WBoaIilTMlkGhmRo/UW\nJ6IoymXZrX2Gk8/nw2KxkH5VvV5PTOfdCX+IxWJkZGQgJiYGYWFhz5133EZBX18fbt68iYGBAQAL\nogxFRUXIyMjYECV4awFN06ipqcGNGzdgsVjg4+ODEydOLNr7NT09jU8++YT0H0ulUuTm5kIsFmNw\ncBD9/f0sH1YGTLm1p6cnJBIJyaAxpZ/uxFxWa9DOgMvlLtu2wdVtpRY4NE1jenoanZ2d6Orqgkql\nYo0bEomEiOnExsY+sf5ig8GAy5cvk98qNzcX+/btW/L7aLVaNDU1obGxEcPDw+R5Ly8vpKenQ6FQ\nbHibhsXQ19eHs2fPQqfTQS6XY8+ePbh37x6povHx8SGtGO4gkUhI376Pjw+5L7W4h6MAACAASURB\nVJPJ4OXltaHHhcHBQVRXV6O5uZlk0f39/ZGbm4vExERcuXIFnZ2d4HA4OHLkiNtyXnuYzWb09PSg\nra0NHR0drGPo4eFB/BOZQMwWtuAOmzXTCCyMzYcOHcKDBw/wn//5n/jiF79Ixoy6ujq8+eab+OlP\nf4rp6WkoFAqcPn0a7733Hus9/uM//gPf/OY38Ytf/AJ/8RcLOp2XLl3CrVu38LOf/czpM8vKynDw\n4EF861vfcvn6UqAoCv/7v/+Lubk5zM3NOa09Pw09jf4A/hTAGwB+C+AnANqwQBC/B6AaQC6AXwB4\n6OL/nylp/OMO4M6dOygvLwdN04iIiMCRI0fQ09ODmpoaQn4oikJycjJycnIQGRlJ0uE6nY4QRZVK\nRS5QLpeL+Ph4pKamIiEhYdUlRwaDAffv32f5JSYmJqK4uHhdegefFNRqNe7cuYNHjx6RxV56ejp2\n794NmUzmknjOzMygtraWlN54eXkhMjISXC7XLVld64LYFXp7e0lGwB6BgYHEXiEiIuK5E3l5lqBp\nGl1dXbh58yb5jeVyOUpKSpCSkvJclrJpNBpcvnyZWNtkZGTg4MGDLktwDQYDbt++DaVSCZvNBj6f\nj8LCQuzYscMpkKTRaNDf34+BgQEMDAxgZGSEVeK52Pm5GBYzaF8J6XvWqpC9vb1EkXVubo68RlEU\nwsLCCIkMCgpal30dGRnBuXPnMDMzA6FQiKNHj7otTzebzWhvb0djYyO6urrIXCAQCJCSkgKFQoGo\nqKjn8jx3xOzsLN555x1WcFAqlWLfvn2YmppCSUkJjEYjZmdnMTMzQ272j90FDzkcDry9vV0SSkZw\naCMcR41GQ1RXmf5ckUiEjIwMGAwG1NfXA1ioLmAqYhyh1+vR2dmJtrY2dHV1sYSiGGXF5ORkhIaG\nbmgi/bygYqs8ddPAYrHg7bffxv/8z/9gfHwc0dHR8PLywrZt2/C3f/u3qK+vx7/+67/i4sWLkMvl\neP311/Fnf/Zn4PP5uHDhAn74wx+ioaEBiYmJ+N73vgdfX1987WtfQ2hoKP75n/8ZO3fuJJ81ODiI\nH/7wh3j77bchEAjw4x//GH/5l3+5ov11FMIRCATw8fGBt7c3vL29cfjwYWCTk8a14pmTRgYqlQoX\nLlyARqOBRCLBiRMnEBMTg76+PtTU1KC1tZVcfHK5HMHBwUTUgXmew+EgLi4OqampSExMXFPvlslk\nglKpxL1790jvS2xsLEpKSkg52/OAubk5VFVVoa6uDjabDRRFEfLINOnbbDbU1NTg1q1bMJlMEAqF\n2LdvH7Zv376shYHVal1U8dZdX6her8f09DTUarVTz5X9otzb2xs8Hg/T09NOA7C3tzfx54uIiIC/\nv//WxL4EaJpGc3MzysvLib9dUFAQSktLERsbuyEWg8tBe3s7Ll++DJ1OB5FIhCNHjrgkFVarFQ8f\nPkTFH8vLgQVyuWfPnmX3H5nNZgwNDWFgYAC9vb1oampCdnb2kmSP6fd71qRvPUHTNCYnJ0kWsq+v\nj3X9SqVSQiBjYmJWXB1A0zRqa2tx/fp1WK1WBAUF4dSpUy7702iahkqlIn2KTGCPoijExcVBoVAg\nMTFxVdUlGxVWqxU1NTUoLy9nRcpLS0tRWFiIysrKJRflNE1Do9EsSiiX6vsVCoWLZimZ8fppwmq1\noqWlBdXV1SwF3ICAAGKhlZSUhOPHj0MgEECtVhMhG5VKxTp/g4ODiZCNv7//prluNwq2SOMWnhUo\nikJrayshivbBr8ePH0OhUABbpNEtNgxpBBaihu+//z56enoAALt370ZRURE4HA7Gx8dx69YtdHV1\nsSKkFEUhPDwcmZmZSEpKWnP5otlsRm1tLe7cuUNKUyIjI7Fnzx5ERESs6b2fJWZnZ1FVVYX6+npC\nHhUKBVJSUnD79m1S2pSSkoKDBw8+0Wb+sbExVFdXo7GxkWQpfX19kZeXh23btoHP52NycpJsw0R+\nZTIZ4uPjIRKJMDIygv7+fifbBaFQyMpEhoSEbKoF43rCarWivr4elZWVZJEYGRmJ0tLSDS3rbzKZ\nUFZWhocPF4onYmJicOzYMSf/PCazWlZWRjIykZGROHDgwKoMgh1FvKRSKSIjIxEZGYmoqCj4+fl9\nKheYRqMRPT09JAvpKA4WHh5OSGRAQIDbY2Q0GnHlyhU0NzcDWLBQOHDggBMJmZiYQENDAx4/fsxS\nqQ0JCYFCoUBaWtqmUwsGgJ6eHnz88cfEbiQ2NhYymQy1tbUAFlo8XnzxxTWTNrPZjLm5uUVJ5VI+\nql5eXouSSkcl4vXG8PAwqqur0dTURNYKzOLdw8MDUqmUJWRDURSioqJI6elW9cr6wGazYWpqCsPD\nwxgaGkJvby+mp6chkUgQFRWF0NBQhISEICgoaEOKT60HtkjjxoKr30Ov1+Ojjz5CU1PTp6I8da3Y\nUKQRWBhoqqqqSFOxn58fvLy80NfXx5oAhEIhyzg3MjIS2dnZSE5OXpVSn8ViwaNHj1BVVUXKXMLC\nwlBSUoLo6OhNsxicnZ116Znp4eGBI0eOIDEx8Yl8rs1mQ0dHB6qrq4lABwDExcUhNzcXcXFxi5YO\n1dXVobq6mpTECQQCopxnsVhIGWF/fz+rbA5YWLSGhISwiOR6Wxo87zCbzaipqcGdO3dIJi4hIQF7\n9ux5Zv50i2FoaAgXL17E9PQ0uFwuSktLkZ+f73TujI2NoaysjASgfH19sW/fPiQmJq7qWjYajbh0\n6RLprZNIJE49YxKJhEUilyJImxE0TWN8fJxkIR3tCLy8vAiBjI6OZlWDjI6O4ty5c5ienoZAIMCR\nI0eQlpZGXtdoNHj8+DEaGxuJhx+wUG2gUCigUCjg5+f3dL7oU8bs7CzKysrI+SeTyXDw4EHEx8eD\noig0NTXh0qVLsFgsCAgIcMrKOs7zSz12tw1N07DZbDCbzeTG9KtbLJZltSvw+XzweDzWjcvlLpqR\nX83+WiwWaDQa6PV6l9szllj2li4rOQ4r2ZdPy/s63pYDiqLg5+eHkJAQcgsMDNwUwd4t0rix4Ph7\n9PT04IMPPsD8/Dz4fD6++93vAluk0S02HGk0mUzo6OhATU0N+vv7yfOMimFqaiqSk5Ph4eGB8fFx\n1NbWoqGhgSWcs337dmRlZTllHlzBarWioaEBt2/fJoQjKCgIe/bsWZTIPO/o6enB5cuXnfqSMjIy\nsHv3biJhvh4wGAx49OgRampqMDs7C2BhwZCRkYHc3NxFF3mOJSw2mw3t7e1QKpUskaOEhATk5eUR\nYj83N0cI5MDAAGtxycDPz49FImUy2ab8nVcKpn/3/v37JLubnp6O4uLidZOuXy1sNhvu3LmDyspK\n2Gw2BAQE4MSJE06kVqPRoLy8nPhUikQi7N69G7m5uau2fZiamsKZM2cwMTEBoVCI48ePY3h4GGlp\naejr6yM3x5I+kUjEIpGBgYGfutJpg8GA7u5udHV1oauri+ULyeFwEBkZibi4OBiNRty5cwc2mw2B\ngYE4deoU5HI5TCYT6VPs7u4mE75QKERqaioUCoWT4ftmgtlsxt27d3H37l1YLBbw+Xzs2rULBQUF\nTtnE4eFh/OEPf0BjY+OK+m23sIWnCab1hKIoEnxzXIdSFIWAgAAnIrke1j1PE1ukcWOB+T3MZjNu\n3rxJHBtCQ0Nx4sQJpmVrizS6Ad3f34+QkJBnejGazWZ0dnaiubkZHR0drEilUCgkJYjFxcXYtWuX\n08LLaDSisbERNTU1pGyHoigkJSUhJyfHpfiBzWZDU1MTKioqiFKiv78/SkpKkJSUtCkXITqdDjdu\n3CDiAAEBASgqKiIm14xvZkZGBnbt2rUm8jgxMYHq6mo0NDSwyktzcnKQmZm5ZBmxu76HkZERVFdX\n4/HjxyT7HBAQgNzcXCgUClaE0mAwEEXMgYEBDA4OOkXCPTw8WH2RQUFBz93ktJ7QarWoqqpCbW0t\nrFYrOBwOMjMzUVRU9Ew8yGZmZvD+++8T5df8/HyUlpayFs0WiwUPHjwgNhYURSEnJwdFRUVryiy3\nt7fj/fffh9FohJ+fH06fPg0/Pz+n85OmaczMzEClUhES6Zj1FgqFiIiIICQyODj4U0UiaZrG6Ogo\nyUIODg46Laj8/PxQXFwMHo+H1tZWtLa2koAgh8NBfHw8FAoFEhISNrV6JU3TaG1tRVlZGTmP0tPT\nsXfvXrfBUL1ej7NnzyInJwcAnOYxV/PaUtus9/+YTCZoNBpoNBrMz8873XfnKUpRFKRSKTw9PYlv\nqlgshk6nw+TkJIaGhlhCNh4eHoiMjER0dDSCg4MxMTFBrKAYeHl5IS0tDQkJCSTzvRGP27P4H5qm\nMT8/j5GREYyOjmJ0dBQjIyNObSHAQsA+MDAQFEVhZGSEeGp6enoiPz8fGRkZGBwcxFtvvYXIyEjy\nf0xrCrAwtw8PD2NiYsJpbOByuQgMDERwcDAhkv7+/ht2rh4dHUVwcPAWadxAoCgKXV1duH79OiYm\nJkBRFIqKigiv+DT5NK4W9Pe//33w+XxERUUhOjoa0dHR5MJ/krBYLOjs7ERLSwva29tZA314eDjJ\nKEqlUlRWVuL27dsAFvqXTpw44bJfhTFvZoRzmMnHz88P2dnZ2LZtG4RCIVpaWlBRUUH6nHx9fVFc\nXIzU1NRNuYijaRpNTU34+OOPodPpwOVyUVRUhB07dpABd2pqCrdv38bjx48JeczMzMSuXbuW3eNB\n0zQ6OzuhVCpJWSCw4GuVl5eH+Pj4dT2+Wq0WtbW1qK2tJRkMsViM7du3Iycnx+V+W61WjI6Oor+/\nn9wcywz5fD7CwsIIiQwLC1uTqNLzitnZWVRWVqKhoQE0TYPH4yE3Nxc7d+58YhYL9qBpGo2Njfjo\no49gMpng6emJY8eOsfyZGFGfTz75hCyu4+PjsX///jWVKtI0jYqKCjLuJCcn49ixYys6D2ZnZwmJ\nVKlUJNPOQCAQIDw8nJDIZx28e9ro6+vD+fPnWdlHVwgMDERWVhZSU1M/FaXl4+Pj+Pjjj0kZf2Bg\nIF544QXWQnuzgiEpi/VSLnWuAAsWWz4+PggJCUFYWBirt5LL5YKmaVRWVhKfUQYCgQDbtm1zWwGz\n2TE/P4/h4WHWzZV1i0QiQWhoKCFwfn5+6OjowP3790nFhUwmw86dO5GWlobp6WkMDAxgeHgYBoMB\nHR0dsNlsrKSAQqHA/v374eHhAZPJhNHRUQwPDxMiaa8UzIDH4yEoKIhFJP38/J7pOs5iseD27du4\ne/cuvve9722Rxg0Ee/VUxrM4OTkZISEh9qI4W6TRDWh7+VkGHA4HXl5ekMvlCAoKglwuh0QigUQi\ngVgshkQigUgkWvGFabFY0N3djZaWFrS1tbGa6UNDQ5GamoqUlBSXi/3u7m5cvHgROp0OUqkUL7/8\nMjG9d4X5+Xk8evQIDx8+JIMYl8uFQCAgfVs+Pj4oKiqCQqHYlGQRWFi4fvjhh+jq6gIAREVF4fDh\nw0Q51RGTk5OEPAIL58L27duxa9euRSPcRqMRdXV1qKmpIWqcPB6PTMBP2g+NUc5TKpVE0IexaMnL\ny0N4ePiiQRDGj44hkAMDA5iammJtQ1EUAgMDSTlreHj4skqfNwuY6DzTTyUUCrFjxw7k5+c/MQED\nvV6PDz/8kAiiJCcn4/DhwyzSMDg4iOvXrxO1xICAAOzfv39Vpr+On/3++++js7MTFEWhtLQUO3bs\nWHMgbW5ujhDIvr4+cq0w4PF4LBIZGhq6KbNpNE2jrq4O165dg8VigVQqhUAgcDoe9vD19SW9kJGR\nkZui38kRBoOBGE7TNA2xWIw9e/Zg+/btm3Z+WglmZmbQ1NSE1tZWjIyMsF7j8/mw2WxLehDbC/RY\nrVbi8ygQCFjrkZiYGOTl5SEuLm7THnutVutEEF2RcrFYjJCQEBYx8/LyAkVR0Ov1qK6uhlKpJOsq\nf39/JCYmgsPhYHBwEIODg0sKJzHgcrlITEyEQqGAXC6Hj48PGQONRiMhkMxfV2MGn89HcHAwa3/l\ncvlTqR4bGBjA5cuXCcH9/ve/v0UaNxAcLTfsIZfL8a1vfQvYIo1uQb/xxhurNnsXiUQsIikWi8mN\neSwUCjE9PY2+vj709PSwyhqCg4ORmpqK1NTUZZVCqtVqXLhwAf39/aAoCiUlJdi5c6fbwYCJ+iiV\nStbAJZPJUFRUhLS0tE0Z3bfZbHjw4AEqKipgNpshEomwf/9+ZGRkLGvwnJiYwO3bt9HU1ARgYTBn\nyCNTojg1NYXq6mrU19eTY+vt7Y2cnBxs3759Tdmo1cpyDw4OQqlUoqWlhWSag4ODkZeXh9TU1GUt\nwrVaLUtcx9GjD1gIODhafWzGkmZ7DA8P4+bNmySL7OHhgV27diErK2tdyY19c7pAIMALL7yAbdu2\nkeM7NzeHmzdvksCGh4cHSkpKkJmZueYF3tjYGM6cOYOZmRmIxWK8/PLLLknoesjGz8/Ps0ikYySd\ny+UiLCyMkMiwsLB1J0v2CxpX95d6faXbmkwmXL9+HW1tbU77IhQKkZiYiOTkZHh7e5Njo1KpWPMG\nj8cjxyUyMhLe3t5PZH/X+7svtq3NZkNPTw/q6+thNBqJXUh6ejorKLPc962rq8Px48efe/VYppy5\nra0NbW1txDoDWLg2YmJikJiYiMTEREilUtA0DZ1Ot2iWUq1WL7mAFwgEMJvNZDsPDw9s27YN+fn5\nz6Q0f72g0+kI0WJu9iW6DIRCoRNB9PHxcZrb5ufncf/+fTx8+JDM/R4eHuDz+U4VFQBYpLy3txeZ\nmZkQCASs33QxeHt7w9fXFzKZDL6+vuTGEH9HIrnY5zt+r/XUMjCZTLh58yaqq6sBLBCQo0ePIjIy\ncos0biBQFIX29nb4+vpiaGiIXAsjIyOwWq1b6qnLAM2ooOn1euh0Ouh0OkxMTGBwcBDj4+OYmZlx\n6gFba3OvQCCAVCol/Qj2JNOefNrfZxaDNpsNt27dwt27dwEsqG8eP37cZdmSSqVCeXk5EdQRi8Xw\n9/fH6Ogoa6BjhHM2i9T2yMgIrly5QqKxaWlpOHDgAKRS6Yrfa3x8HLdv3yYZH8YL02w2s1RQo6Ki\nkJubSyKMa8VaF+VqtRo1NTV4+PAhiYB6eHggOzsb2dnZKzoWjEcfk40cHBx06ukQiUROVh+bMUsE\nLEz6N2/eJFldb29vFBcXrzljb7FYcOvWLdy/fx/AgnrxiRMnIJPJACxEmu/evYv79+/DYrGAy+Wi\noKAAO3fuXJfy4aamJly+fBlmsxlBQUE4ffo0CWYZjUb09/ejt7cX/f39aGhoQHx8/LqSCZvNRrIl\nNpvN5RhLUZTTbbX7sIXNCUZoRCaTITw8nJTaBwQEbPismc1mQ39/PyGK9n3BQqEQ8fHxSEpKQlxc\n3IqveavVyrIRYQjl1NQUxsfHl7w2eDwe5HI5AgICnGxEPD09N8yxNRgMTgRxMSLlmJHz9fV1S6Qm\nJydx69YttLe3L9p7yuFwEBwcjPDwcEilUtTW1mJ2dhY8Hg95eXk4e/YsQkNDER4ejsLCQly4cAFm\nsxkRERHw8vJCW1vbshR4gYU+SnsS6evrC4lEAoPBgMnJSXIcXBFkkUhEiCRj/8FkUFeCrq4uXL16\nFXNzc6AoCoWFhSgqKiJKwFtj7sbBYr+H1WrF+Pg4QkJCgC3S6BZLqqcyEuo9PT0k6utYauDr6ws/\nPz9wuVzMzc1hfHycddFzuVxwuVxYLBa3Te7uwBhlM0TSYrEQURORSIS8vDxERERALBZjbm4OSqUS\nKpUKwAJZLCwsRE5ODol4McI5TKSLoigkJiYiJyfnubXYMJlMqKiowIMHD0DTNLy9vXHo0CHEx8ev\n+b2HhoZw9epVlhopRVFITU1FYWEhgoKC1vwZTwJmsxmPHz+GUqkkvzWXy0Vqairy8vKYQWJFsNls\nGB8fZ2UjHSclLpfLsvoIDw/fVP1YNE2jvb0dt27dIuJTfn5+2LNnz6qEpMbHx3Hx4kWMjY05Nafb\nbDbU19ejvLyclE+lpaWhtLR0XZR+bTYbbty4gQcPHgAAtm3bhn379mF0dBS9vb1QqVQYHh7+VEz+\n9r8bc9/Vc8vZFlg4T6xWq1M1C0VRxHaBIb/LfV9G/Y6xd3D8Xfh8PgQCAXn/9fo+67mt1WrF9PQ0\nOZ+5XC7kcjk8PT2d3m+l+8CUHdrrBDDHJSwsjJDIsLCwp9KbvBTMZjO6u7vR3t6O9vZ2EuQDFkgB\n458YHR39xKqCzGYzLl68SDLgTPZyaGgIk5OTS5IYDodDiKQjoZTJZGv2j14MJpPJKdPm2F4BLBBe\nVyWbSxFdg8GAgYEBtLW1ob29nYjb2IMJmDJzHRMwvXfvHm7dukXUrl9++WUEBARgfHwc77zzDtRq\nNXx9fVFSUoIrV67AZDIhNTUVL774Im7dukV8eL28vEjl0vT0NGZmZshfd1VyYrGYEEqJRAKKomAw\nGKBWqzE2Nubyu0gkEpZia0hIyKIZZp1Oh7KyMjQ0NABYqGg6evQoay20RRo3FiiKwi9/+UskJSUh\nKSkJ/v7+Tq9jizS6xYotN2w2G4aHh9HT00Oi7q6IoFgsJnYIjJE2M9kzWU29Xs+6v9hz9n6MK4VA\nIIC3tzerJ9OefGo0GrIwZI6FXC5HdnY2MjIynthgv97o6urChx9+iNnZWVAUhby8PJSUlKy552xm\nZgbV1dWoq6sj2TUej0cmUR6Ph5ycHBQWFm7ociiaptHX1welUskqjQsPD0deXh6Sk5PXFCmem5tj\nieu4Krvx9/dnZSNdlf08b7DZbHj8+DEqKipINDskJASlpaWIiYlZ8v9pmoZSqcQnn3wCq9UKX19f\nHD9+HGFhYQAWsibXr18nZtyhoaE4cOAAwsPD12X/tVotzp8/D5VKBYqiEBMTA6PRiOHhYda4RlEU\nQkNDERUVhaioKNZv97SIB6MEPDAwQOxk7Mdvpvc2MjLSKVCxnH1YL8zNzRE/RSagwCAoKAgvvfTS\nuvl/Wq1WDA4OEkVWe9N2YKHPlemFDA8Pf+atCFarFUqlEpWVlTCZTOByudixYwd27ty5rv3BNpsN\nY2NjRDF6cHCQqITbw8/Pj0Ukn1aZvV6vR0dHB9ra2tDd3c0iuL6+vkhKSkJycjJCQ0Of2hjpKH6V\nnZ2NF154ARwOB6Ojo7h37x5aW1vJ3Mfn8yGRSGCxWFwSEHuIRCKWII89ofT29l7WeWk2m53EYRyv\nL2AhAOEoDuPv77/k/MYoQDOBUKbazBECgQAxMTHkmvLz82P9RvPz8/jggw9IG0Nubi727dvHCuDM\nz8/j3XffxejoKCQSCfbs2YOysjKYTCakpKTgxIkTGBkZwdWrV8k1nZKSgoMHDxISZ7PZMD8/j+np\naXJjCOX09LRT0MQefD4fPj4+JFttNBqhVqsXVYW1J5HBwcHo6+vDtWvXoNVqwePxUFxcjIKCAtA0\nDbVajbm5OczOziIzM3OLNG4gOPY0yuVyMtaEhIQw18gWaXSDFZNGmqYxMDCA5uZmtLS0sBqn7cmE\n/XMRERGIiopCTEzMqmTmbTYbDAaDE7nU6XTQarVob293iq4xGYq1gKIoeHp6IjAwEL6+vouW0kok\nEvD5/GdCALRaLa5fv076uwIDA3HkyBGEhoau+j1pmkZvby+qq6vR3t5OnmcIVlJSEiYmJlBRUUFe\n5/P5yMnJwY4dO9aFPK5Hz9hicEWEvby8kJOTg6ysrHWJvjMRWnurD8eoqFQqJQQyIiLiufbxs1qt\nePjwIW7fvk0WUNHR0SgtLV30XJyfn8elS5fQ3d0NANi+fTsOHDgAgUCAqakplJWVoaOjA8BCCWxp\naSnS0tLW5TqzWCyoq6vDzZs3XS4UKIpCcHAwIYkREREQCoVErKS7uxvf+MY3nunvZTQaMTAwQHoi\nHYkuAEIio6KiEBkZ+cSy3UajES0tLWhsbCQVHsD/Rdq5XC5efPFFZGZmPtFxUq1Wo6urC52dnejp\n6WFVxQiFQsTExBAS+bR71Lq6uvDxxx+TuSoxMRH79+9fdw/UxcZOjUZDgg6Dg4MYHh52mq+FQqFT\nNnK9lKPn5ubQ3t6OtrY2VpAWWAg0MdF/RxLytNHY2IjLly/DarUiNjYWJ0+eJMFjg8FARN8YEs7j\n8ZCamorExERwuVyXPZXuCAxFUUSghyGUXl5eoGkaWq0Wk5OTGB0ddVlCy+FwnGwoAgIClkVCLRYL\nURJnAlGLkV+KohAbG4uSkhK31Tnt7e24fPkydDodJBIJjh07hoSEBNY2zPlpNBpx7tw5dHd3E+JV\nVVUFo9GIpKQknDx5EgCgVCqJNoNQKMSePXuQnZ3tduxljt1ihNJdIoLD4UAoFIKiKBiNRrfZTKFQ\nSJR25+fnMT8/z/qNtoRwNhYoikJrayva2trQ0dHBqmrw9PTEX//1XwNbpNEtlkUaaZrG0NAQIYr2\npXg+Pj5EzCYoKAgmk4mI3qhUKqfIr1AoJAuxmJiYNUU2p6amUFlZSQgTA09PT3zmM59BYGCgS6Lp\nmNV0fLwacLncJXszXb222kUnTdNoaGhAWVkZ9Ho9GXTz8/NXHU03m81obGyEUqkkEUwul4u0tDTk\n5ua6nCxGRkZQUVFBFvd8Ph+5ubnYsWPHmhaoT5I0MjCZTKivr0d1dTVZyPF4PCgUCuTl5a2r6qvF\nYsHIyAirpNXxXBMIBE5WH09KnfRJwWQyQalU4t69e2RiTkpKQklJCet4tra24sqVK9Dr9RCLxTh6\n9CiSkpKg1+tRWVmJmpoaomq4c+dO5Ofnr0kExmq1YmhoiJTY9/X1ORGsoKAgRP3ReigiIsKpymBi\nYgJnzpzB1NQUent7sXfvXpw4cWLDlB2bTCYMDg6S7zc0NOS04PH392eRyNX0OTOwWq3o7u5GY2Mj\n2tvbCQFhMh2jo6OwWq2Qy+U4derUumUXV7J//f39JAvpKuvJEMiwsLAngwVkrgAAIABJREFUFgCY\nnp5GWVkZCbDJ5XIcPHgQcXFxT+Tzljt2MvZDDIkcGBhw2fsVEBBAxqXw8PAl+94Y0DSNiYkJ0p9o\nr3hKURSioqKQlJSExMTEDacnMDAwgDNnzkCr1cLPzw+f+9znWOSesZeqrq4mQS8AiIyMRG5uLpKS\nksj5xBAYe1Eee0Lp6OfqDhKJBDKZjIxVsbGxyw5y6nQ6Qg4HBgZcjg8CgQAcDoeM3QKBADk5OcjP\nz3c7VpjNZty4cQM1NTUAFtRnX3rpJZeBGfvz02q14sMPP0RdXR0AoKCgAHV1dTAYDEhISMCpU6fA\n4/EwOzuLa9eukXVGSEgIDh8+TKrYVgq9Xu9EKKempjA9Pe3SYmQlEAqF8PLyIr6+W6Rx48C+XNhm\ns6Gvrw+tra1ob2+HWq3eEsJZBhYljTRNY2RkBM3NzWhubmYNbN7e3khJSUFqaipCQkLcTiBarRYq\nlYqQSEeJZA8PD0RHRxMSuZySPUf/OA6Hg6ysLGzbtg3Xrl3D0NAQOBwO9u7di/z8/BWRUiarqdfr\nMTIygsbGRvT29rLKMb29vSEWi2E2mwnZXG7jtiOEQuGKiKZEIsH8/Dw+/PBDIkQTExODQ4cOrTpi\nPTs7i5qaGjx69IhMFlKpFNnZ2cjKylrWwnJ4eBgVFRXo7OwEsDDZMORxI/TNuANN0+jq6oJSqWQt\nABh/yYSEhHWPfNM0jampKVZJq2P5GEVRCAoKYll9PC8Kfnq9Hnfv3oVSqSTXxrZt27Bjxw7cv38f\n9fX1ABaErI4ePQqJRIKamhpUVlaSczAzMxN79uxZFbFhyuiZ0vOBgQGX0f6AgADs3r0bMTExbs/T\n1tZWfPDBBzCZTPD394dWq4VOp4O3tzdOnTq1psz+kwIj4MSQSKYH3B5yuZxFIpeykqFpGsPDw2hs\nbERTUxNrgRUZGYnU1FQMDQ2RPp/09HQcOnRoQ/iczs7Okixkb28v63wQiUSIjY1FXFwc4uLi1kSm\nGZhMJlRVVeH+/fuwWq0QCAQoKipCXl7emspkGcVVe9Ek5q/NZgNFUZBKpasS4lKr1SwS6Uo5WiwW\nkyxkWFgYQkNDSXCLpmkMDg4Somg/3/P5fMTFxSEpKQnx8fEbfl6YnZ3Fe++9h/HxcYjFYpw+fdql\nV+bk5CSqq6vR0NBAMtteXl5k/rQPKtlsNkxMTLBUG10dY2BhrcH0BLuDVCp1Kn1ler2npqbIb+mq\n19Hf3x9hYWGgKIq1PhOLxcjPz0dOTs6Sv9P4+DguXLiA8fFxcDgclJaWoqCgYNlzJk3TqKqqQnl5\nOYCFMaOzsxMGgwHx8fH4zGc+Q45FW1sbrl27hvn5+RW34TAeoHNzc6R81PH+cq1BlovNnmmkaRrv\nvPMOfvnLX8JiscDHxwctLS1EfPLs2bP493//d1RWVkIoFOLb3/42Xn/9dYhEIvzyl7/EP/3TP2Fw\ncBBRUVH4u7/7O6SlpeEf/uEfUF5ejq9//ev4r//6L9bn/eIXv8Cbb74Jq9WK119/Hd/4xjdWtL+L\n9ZhqNBpcuXIFn//854Et0ugWLNJI0zTGxsYIUbRfxHp6eiIlJQVpaWlr6jOYm5tDb28vuTEeigy8\nvb0RHR1NbvaLZLVajaqqKjx69IhMjhkZGdi9ezcZJK1WK27cuAGlUglgoQTo2LFja5qgTCYTHj9+\njJqaGpI5pSgKCQkJyMnJQUxMDCwWy5IZTVfPrQUURcHX1xf+/v5LEk3HrCZN0+jv7yc9fsx5EBoa\niry8PKSkpKxqYTM0NISKigriCykQCJCXl4eCgoINv0gAFhYASqUSDQ0NZFEpk8mQm5uLzMzMJ7r4\n1Wg0LL/IkZERpwFOJpOxrD6edSnXUpifn0dVVRUePnzIWhjxeDzs27cP2dnZ6OzsRFlZGVmwREdH\nY//+/SsSV7LZbCzhmv7+fpeCXUajEVqtFlwuF4cPH0ZGRsaS71tRUYGqqioACwI8R44cgV6vx7lz\n5zA0NAQul4sDBw4gOzt7Q/8WFosFw8PDhES6ItIymYxFIplxdXZ2Fo2NjWhsbGQtPv38/KBQKJCe\nng6r1Ypz585hbGwMXC4XL7zwArZv3/5MjwlN02ThbU+uTCYTBgYG0NPTg76+Pqdsj6+vL+lfYiw9\n3BE1++esVismJibQ399Pjq+Pjw9RL3X3v4s9Z//actsuRCIRPD09WTepVOr02B25ZM4Z+7JWV15+\nMpkMPB7PqS9MLBYTIZuYmJjnzl/TaDTi/Pnz6OrqAofDwZEjRxYdM4xGI6lcYcYyLpeL0NBQeHp6\nQq1WY2RkxGWAWS6XsywhgoODCRHS6/WLZilnZ2eXfT5QFAVvb29WllKlUuHevXtkrefp6YkdO3Zg\n+/btSxIxmqZRU1ODsrIyUlHw8ssvrzr719DQgMuXL8NmsyEmJgYjIyPQ6/WIi4vD6dOnWX6N5eXl\nqK6uBk3T8PLywgsvvID4+Hi3hHBubm7JYyUQCODj4wNvb294eXlBrVajp6cHVqsVYrEY+/fvR0hI\nCKvUlclSulKo3cyk0Wq14k/+5E9w7do1XLhwAXv27CGv/fSnP8V3vvMdXLx4EVFRUcjIyMCRI0dw\n6dIl1nv8y7/8C77zne/g5z//Ob75zW8CWCgBZwIt58+fx4kTJ1j/86Mf/QgA8Nprr614n+1JI9Nq\nd/PmTUJytzKNS4NmIl9NTU1oaWlhLQikUimSk5ORlpbm1iB91R/+x2yLPYl0rDVnGvW1Wi25eAFA\noVCgqKho0exaa2srLl26BKPRCB8fH5w8eXLN2QAmilpTU0NMgYGFBQYjnLMSYmSf1VyKcDKD31r6\nNIVCIdk/nU5HFtVMRispKQmhoaEsoikQCFb1uw8MDKCyspJk7oRCISGPyxEXehrlqe5gMBjw6NEj\n1NTUkMlAIBAgIyMDeXl5696H5Aomk8nJ6sORCInFYhaJDA4O3nBWHzabDdevXyceVsACaUxLS8P0\n9DQZsOVyOfbv34/4+PglzznGw82+3NSxN1Eul5NSeC6Xiw8//BBarRbe3t74zGc+s6Ryrl6vx8WL\nF9HV1QWKorBv3z5SuVBRUYFdu3ahrKyMfC+FQoFDhw49NyXFjMcZc/xcEW2RSASKolgBLpFIhLi4\nOMTExEAmk4GmaXR3d5OsslQqRW5uLjw9PVdNilb6P+5e24ygKApcLhccDsfpb0dHB4KCgpb93cVi\n8bLIJZfLBU3TmJubQ09PD5qbmzE8POyyP4zH4yEkJARxcXGIjIxEcHDwc0cYGdhsNpSVlZFAdGFh\nIUpLS50UfaenpzE8PIyhoSH09vZiYmLCJWHw8fFBaGgoiyCuVHBPo9FgYGCAeJm66ndciXKnQCBA\nREQE4uPj4efnR4jTYoFjnU6HS5cukXLRzMxMHDx4cFljn7u5vaenB2fPnoXRaERgYCDm5+eh0+kQ\nExODEydOQKvVkrXQ0NAQ2tvbVySUKJFIyHfz9vYm95m/zHg3NjaGK1euEFup9PR0HDhwwK1eA2Pp\nwpDJyclJHDp0aNOSxh/96Ef4+7//e5fEDgD+5m/+Bjt37sS2bdsQExODL3/5y/jNb37D2ua3v/0t\nvvrVr+K3v/0tvvSlL5HnExMTSTtBfX09IiIiyGu/+c1vQFEUvvKVr6x4nymKwuDgIJqamtDQ0MCa\n1zgcDr73ve8BW6TRLeh/+7d/Y5lKSyQSUnoaERHxVIUemIUgQyBVKpVTVE4kEiEpKYnsn7tBamZm\nBufOncPIyAg4HA7279+P3NzcdSG/Go0GdXV1qK2tJX0gPB4P6enpyMnJWXW0zREmkwm3bt0iUTUf\nHx8cPHgQwcHBbrOZrsjnasD0aq6kfNY+q9nf34/KykqipCYUClFQUIC8vDy3E+WzJo0MbDYb2tvb\noVQq0dfXR55nlIGfpj0Lo4jIZCL7+vqcov5MZJspaX3WsvrT09O4ePEimXwzMjJItQEDHo+HkpIS\nt2V7jPUPQxJVKpXTYkEmkxGSGBUVRcQklEolysrKQNM0oqOjcfLkySX7EMfHx/GHP/wBMzMzkEgk\nOHnyJKKjo8nrFRUVKCoqgtVqxePHj/HRRx/BYrFALpfj0KFD8Pb2XhfCs5zX1vP9NiMoimKRKldE\ny/41iqKIyrder3fKxjILT8afj8vlkv7J4eFhAAulmImJiYiMjFz0s5a7P4vt42Jgzk2dTkfEOebn\n56HRaFiPmeeWu6gVi8Xg8/mkqsb+/zw9PeHt7Q2KojAxMeF0bTLeffYCOxutj3Ep1NbW4qOPPgJN\n04iJiYFCocD4+DhRMl1MeZPP50OtVpPry9PTE1lZWctu/WB6Q+0Fa1wp4QYGBrKsL7y9vWE2m0lW\ncmxsDB0dHYuWwzqCyUw6Kr5qtVpUVVVBq9VCJBLh8OHDSE1NXcYRXICruZ2maZJR7e/vR0VFBYxG\nI3g8HqxW64qIl4+PD8LCwuDj4+NECpcKXFgsFlRVVeHOnTuw2Wzw8vLCoUOHnMR8lovNarmhVqsR\nFhaGoKAgEjhwhEqlQnNzM9LS0hAdHb0i0lhSUoJvf/vbOH78OHbs2IHKykqyNvjd734HAHjllVdW\nvN+O6qnAwvVYUFCAnJwc5vzYIo1uQH//+9+HWCxGcnIyUlNTERUV9cwVHA0GAx48eID79++TyLdY\nLIbBYGBdgBwOB2FhYaSUNSwszGnRabFYUFZWRhq0k5OTcfTo0XWz0rDZbOjo6EBNTQ0hRsCCMXlO\nTg5SUlJWnfnp6OjARx99RExjCwoKUFRUtOxMBpMZVSqVaGlpYVmKxMfHw9/fH0ajkWVt4kg03am+\nuQOT1WRIJDPxMeXIfD4fKSkpyMzMJD2iq81qPi2Mjo5CqVTi8ePHZAHg7++PvLw8KBSKpx5Jp2ma\nTLLMgsKVBHtAQADL6oNZ3D3pfaurq8PHH38Ms9kMLy8vHD58GCMjI7hz547TeSWVSrF7925s376d\nZDQmJydZJNFRoIApZWdIouMi1Gw248qVK0Qoa8eOHSgtLV1yfGtubsalS5dgNpsRFBSE/fv3Q6vV\nYmRkBKOjoxgdHXVaNG9WMISLoqglF28ymQx+fn7g8XguSc96EqeVvLaWc52phmF6Ifv6+ljkmhEm\nmZiYgMlkAkVRyM3NRXFx8XNh12Sz2dySy9nZWczOzq6o18vDwwMSiQQcDgdWqxU6nc6luIiXlxeL\nRAYHBz9zSxRHMBYKTA9id3c3S9DHHp6enqwS05CQEJKZMhqNaGxsRHV1NQnSM37Bubm5rCoopsLE\nXrTGkZAynpvMuB4aGrro+TY/P4/79++jtraWjLvh4eEoLCxESEgIq/TV/r4rUSR7UBQFuVwOuVzu\nsqeSz+eDpmkYjUYYjUYYDAbik+iqfHQ5aw0ej4ewsDBiVcKQQR6Ph7t37xI7raCgIBw+fHhF1WWD\ng4O4fPkymUOzs7Oxd+/eNbWkbFbSeOnSJRw/fhxf/epX8atf/crttiqVasWZxpKSEpSXl+Ov/uqv\n8LOf/Qzf/e538cYbbwBYP9IYGBiIAwcOsILBWz6NS4Pu7Ox8oqa5K4Er5UVG5jk0NBRmsxn9/f0k\nE+nY88Xn8xEREUFIZFBQEFkgNjc34/LlyzCZTJDJZDh16tS6ZQMZTE1NoaamBvX19WSQl0gkyMzM\nRHZ29rKNyDUaDT7++GM0NzcDWDCNPXLkyLL312KxoLm5GUqlkkxwFEUhJSUFeXl5pPF9ue+1HAVa\nRzXa1QyUHA6Hlc10txhczoJ0Lffdva7X69HQ0ICHDx8SEiwSibB9+3bk5uY+0wi6Xq8n6qxM5sMx\ng+Tl5cUikUyv1XpBp9PhypUrZAJnglFVVVVkIZKUlITS0lLMzc3h5s2b5DxlFuEzMzNOC01PT08W\nSZTJZIvuw8zMDM6cOYOxsTHw+XwcO3ZsyWi4yWTChx9+iMbGRrIvZrPZ7WLG8RxhTOeB/+spWynR\neVrkSq1Wo7W1Fa2trazMRUBAAOlTtBfGYQI/KpUKjx8/xuDgoNPxkEgkiIyMJLfAwMANHQhaKUwm\nE3p7e9HZ2Ym2tjYni4KgoCCkpKQgPj7+ufzujAAeI2RjH4RigrSBgYHw8fGB0Wh0yl4u5VfoDhRF\nwcfHh2TMYmNjERAQ8FSP4fz8PEukZnh42OV3YsiAQCBAcXEx0tLSliVSRtM0enp6UF1dzcrQ+Pr6\nwsfHBzqdDmNjY07zp7e3N8kihoeHL8ueaWZmBnfv3kV9fT2ZA2JjY7Fr1y5EREQseVzNZjMmJycx\nMTGBgYEBNDU1kXXZeliaOUIoFLJKR6VSKVpaWkiPNJ/Ph8FgQEREBD7/+c+7JHP2gXZggfiVlpa6\nDeAw1VxM+bGvry+OHj3qUvRopVgJafzBD36w5s9bDl5//fU1v8dPfvITvPrqqywytxjWQhrNZjN2\n7tyJhw8f4pNPPkFxcfGaSeOvfvUr7Nmzh0UW7V/HFml0C3p+fn5dlOLWArPZjNraWty5c4csFCMj\nI1FSUuL2wtXr9ejr6yMk0jHLIhKJiIR+dHQ0OBwOzp8/j9HR0ScqXmEymdDU1ISamhqMjo6S5xnh\nnNjYWJefyWRnbty4AYPBAD6fT8r2lrOon5+fR21tLR4+fEgmOrFYjKysLOTk5CypjLheoGma9Gou\nRjQnJiYwOjrqsqQHWDB1d3VRbzS4mhR4PB5EIhH4fD64XO6Kiet6kmGm12Z8fBzj4+MYHR11yhrw\n+XyEhoayiORq+/K6u7vxwQcfQKPRkD7Wrq4uUrbHZO6ioqIwOztLrt2uri6nkjZG0ZIhisuV+u/q\n6sKFCxdgMBjg6+uL06dPO9mnGI1GjI2Nkezh8PCwSyNrYIFkBwUFEcPsoKAgPHr0CCUlJU77w5TD\n3rhxAzabDRERETh58uSGUb3V6/Vobm5GY2MjBgYGyPNSqRTp6elQKBRuyY5j5QZj8j00NIS+vj4n\nYTORSMQikfaBvOcVarUaN27cQFNTE4D/Cw5MTk6yxgKpVEosPWJiYp5a5nGlpf2M9DxDFO0zTEKh\nEAkJCUhKSkJcXNyS44LVaoVWq3VZBmv/eCW2Bnw+n5QE+/n5wcvLy6nvUiKRrHge12q1TgTR8fwF\nFuZQxwwij8fDuXPn0NfXBx6PhxMnTiA5OXnJz2RaDAYGBtDd3Q2VSuUyixsQEICoqCgyJq9k7h4f\nH8edO3fQ1NREzseoqCgkJyfDw8MDBoOBZP4cs4CO959Elqy/vx+FhYVISEiAv78/q5/QEY6WHEKh\nEEajEeHh4fjCF77gkjiaTCZUVlbi/v37oGkaUqkUBw8eREpKitM50t3djatXr2J2dhYURWHHjh0o\nKipat6qhzUoa33rrLbz22mt49dVX8eabb7rdliGNgYGBSEpKYr02OjqK9vb2RUkjAPT19SEzMxMS\niQQNDQ24evUqgNWTRkZEc7HXsUUa3YJ+4403oFAoUFBQAH9//6f64YzBdlVVFRmsQ0NDSRRgpZOA\nRqNhieo4qllJpVJERkZCo9GQ/rTU1FQcOXLkiahiMuWhtbW1aG5uJtE+mUyG7OxsZGZmkn6zqakp\nXLlyhexXXFwcDh06tKzs5NDQEJRKJUucJzAwEHl5eUhLS9uwAgQ0TaO3txcVFRVkASsSiZCRkYHJ\nyUkUFBSsqIdrOb1fy91uOfc3q8gGA0Zsw574LkZQKYqCWq0m17FQKASPxyPBCx6Ph4CAAPD5fGi1\nWqjVaqfFEo/Hg0QigU6nI9k6X19f4gG7HLJdV1eHBw8eAFggNIcPHwYAQpoZouho/WP/nSMjIxEX\nF0eIoivxg6UW5v39/Th37hw0Gg08PDxw6tSpdYlcrwYWiwWdnZ1obGxER0cHOW/5fD6Sk5OhUChI\nUM0dZmZmcP78eQwPD4PDce4Rp2kaMzMzRFjHlSqpUChEREQEIZEbsSRxMVgsFty/fx9VVVUwm83g\n8XgoLCxEYWEh+Hw+jEYjenp6iC+kPQHhcDgIDw9HfHw8aQ14Uhm05ZBGs9mMrq4utLe3uzS5ZhRP\nGRGp9YbVanUikjMzMxgfH8fMzAw0Gs2KWiM4HI5LAR/mxufzodFoMDk5SYJErvwRhUKhE0FczAbM\narXi6tWrxD5oz5492LlzJ2tbo9GIwcFBImTmSsxMIBDA29ub2Pgw3ychIQFpaWkkq+uK3Nn/VavV\nUKvVq24pcQV70iMWixEYGAgPDw8IhUIIhUKIRCKIRCJyn/krEAhgMpmg0+lYSq+jo6OoqalBdHQ0\neDweMjIykJ+fD7lcvug+OFpyMO8dFhaGL3zhC4sGY8bGxnD16lVSEREXF4cXX3wRMpkMer0eZWVl\n5LcLCgrC0aNH1736bLOWp7777rv44he/+P+z997BbaX31fC5aCQIECDYCRDsVWKX2CSxqa3a7kqU\nVnKdxM5kEsfJZDLj2InjyW7GSZz39fdNHGeyyTr5ZmPv2I5WdaVVWa0KVSgWUEuxF1EkSIoEewMB\not/vD+Z5gotCgiQocTd7ZjDs4MXFvc/zO79yDr7+9a/jgw8+WPF3V6o0/vKXv8S3vvWtFUkj8D/t\nsEePHsWpU6cArJ80rvR+fEkaVwfrPBSampqKXbt2IT4+flNbQux2O1paWvDgwQO6cEdHR6Oqqson\n5URfMTs7yyGR3lpnpFIpqqurN7WyZTAYqHAOec0CgQDbtm2DUCikLSRBQUE4dOgQsrKyVjwPdrsd\nnZ2daGhooCIjDMMgIyMDRUVFm/4e+hOkZaempoYu8BKJBJWVlSgoKNiylQlnGX5CKOfn5/H06VO0\ntrbSyhmZGU5LS0NgYKDfCLA3xcm1fm6z2ahVwBedCDuDYRiaeQSWAzWZTAahULhqxVelUqGwsHDF\nZNPi4iIuXLgArVYLhmGwf//+NfmXbQRETry1tRUdHR30WmQYhop4ZGRk+FxRXq8a9dzcHIdEugp4\nkJECQiJVKtWWI5HEyP3mzZv0+DMzM3Hw4EGvST0i3PTs2TM8e/YMw8PDnGBFJpNxqpAvQ3HXaDSi\nt7cX3d3deP78OUdkLjw8HOnp6cjMzFzVe/llweFwQKfT4fnz5xgaGsL4+LhHu4/1BubEz5LYoZC5\nSplMRlU0VwPLsnj8+DFu374NYPm6SElJobOInrwRAwMDIZVKqbAQAI62gL8qfDweD2Kx2I3QuX70\n9PnU1BRt8xSJRDhy5AhycnI2fF2QRHFdXR215QKW1TJLS0tXbJt1tuQQCoWwWq1QKpX45je/6ZU4\nsiyLJ0+e4M6dOzCZTBAIBMjIyKDxIJ/PR0VFBXbt2rUp684XlTSOjY1RtXayv3nDRtpTnUHmG3fu\n3Invfve7X5LGVwR2cnIS9fX1aGlpoZtITEwMSktL1+3V5w0OhwPt7e24f/8+zfRHRESgqqoKGRkZ\nm7pRkXkcZ2VW19bI4OBgZGZmIikpCfHx8ZvSTuRwOPDs2TNoNBqOkTwAn1rZDAYDmpqa0NTURDdQ\nMk9XWFjo89zkVgSR7q+pqaFEODo6GocPH+ZILn8eYLPZ0NbWhoaGBurtyePxkJWVheLi4lXtHl4l\nzGYzR1xnZGTEo4pxVFQUraY7HA4EBATAbrd79CEDlpMkoaGhdH4nKChoRTJrtVoxMTGByclJSuxI\nkMfn8znZ9416nq4HYrEYu3btQlFRkdeg3+Fw4O7du6itrQWwPMv55ptvblqr4vT0NPVTdO60iI6O\nRk5Ojs+zVwT+9r2dn5+nBHJwcNAtqBYIBFCr1ZRExsbGvlILmenpady8eZMGuOHh4Th8+DCSkpLW\n9DwmkwnPnz+ngjrOCUw+n0/tDlJTUxEWFua3vXBubg49PT3o7u7G4OAgJ2BSqVTIyMhARkYGwsPD\n/fL/NhsGg4HjGfnixQufVX/XEsDz+XxIJBJKokQiERV4Iokmh8OBxcVFLC4uwmAweF331gPS5eEs\nPsXn86mfY3BwMPR6PbRaLb3PhUIhsrOzUVRUhLCwsHXdNw6HAw8ePMCDBw/AsiyUSiVOnjy5YYsp\nlmXR0tKCu3fvwmq1Us0CMhdLXiNJpiQkJNDzLxaLKaEdGBiglhzk/MTExOCb3/zmimvS4uIirl27\nRufsgeUW4LfeemtTr/0vKmkEgO985zt477338P7773skcGQUIiIiYk3qqQ6HA5WVlXjw4AHnd8l8\no0ajcSOZvuJL0rhxsOQEGgwGaDQaaDQa2iIhl8tRXFyMgoKCDbVvsiyLrq4u3Lt3jyqHhYaGorKy\nEtu3b38llSSSxezr6+MImhAwDAOlUknnIdVqtd/aPM1mM+7cuUPnglxbQIhwjrPQh06nQ0NDA9rb\n292UO7Ozsz833nC+gGVZ/PKXv6SqasCyT9L+/ftf2lymv8CyLAYHB9HQ0ICenh76PqvVahQXFyMz\nM3PLVlIJ7HY7tfogD18EL0QiETWKT0hIWPc828LCAm7fvs1pv/YmxBAYGAilUsmZP3QOwlmWhV6v\nx4ULFzA0NASGYbB3715kZWVxTOBXqvpaLBZ88MEHtG01KCgIu3fvdpbsdkN3dzcuX74Ms9mM0NBQ\nnD59GlFRUWs+F55gNBrR3t6O1tZWmmwBlpNg2dnZyM3NdZvp9AVzc3M4f/48RkZGwOPxsH//fupT\n6S/o9XoOiXSdS+fz+YiNjaXXUWxs7EtptzebzXjw4AHq6+tpQqSyshKFhYUbTqQSaylShRwZGeEE\nMiEhIbQKmZiYuKbXy7IsLl26hLCwMPT09HCUPnk8HhISEpCRkYH09PTP3VpqtVppaymZQfSkFu0J\nEokEMpmMkhViG2IymWCxWGCxWNZs7bAaRCIRpFIpJBIJJT6+VPsCAgIgFAqp9UtbWxsaGxtp8pFh\nGIhEIo7YXnFxMYqKijaUjJqbm8OlS5eob+7u3btRVVW1puvdarVifn4eCwsL9OPMzAyeP39O94yN\n6BUQrQCDwcBZ/yUSCXbs2IHg4GB6rp3JZnd3N9WKcEZ+fj4OHDgKA2XMAAAgAElEQVSwabZUX2TS\naDKZcPToUdTX1+Nf//Vf8Y1vfIPu783NzfjJT36Cn/3sZ5iZmUFOTg7OnDmD3/72t5znePfdd/HH\nf/zH+Od//md897vfBbAc65aVlXEq0QRkvvFnP/vZl6TxFYHV6XSIjo6m37BarWhtbUVdXR3NAgcE\nBGDHjh0oLi5e00bDsix6e3tRU1NDBWHkcjkqKiqQm5u7pYLl5uZm6rXmyRuIz+dDrVZTEqlUKtcV\nPHR3d+P69evQ6/Xg8XjYtWsXSktL0dPTA41Gw9nkyVzV4OAgR7QiPT0dRUVFL9Uj8GWjpqYGu3fv\nRm1tLWpra2Gz2SAUClFWVobS0tItZ2DvC+bm5tDY2IjPPvuMbvgymQyFhYUoKChY1TvwVWNpaQla\nrRZPnjxBf3//qpthVFQUFdZRq9U+qcqazWaMjY1x7C2cK43eEBcXhzfeeGNVsZzR0VGcPXsWCwsL\nkEqlOH36NNRq9arH5Yp79+4hLi4O9+7do0RNIpFgz5492LFjh8dAf2ZmBh9++CHGx8chEAhw7Ngx\n5Obmrvl/A8uV7J6eHrS2tqKvr4+eH5FIhG3btiEnJwfx8fHrXmN7enpw+fJlmEwmyOVynDp1CrGx\nset6rrXAYDBwSCQJlAl4PB5UKhUlkWq12q8JM5Zl0draitu3b9NOjvz8fOzbt29FY++NwGg00ipk\nX18fRySGz+cjISGBViFJxcfhcGBubo6qWzp/7O7upkG5UChEamoqMjIykJqaumVtQFiWhc1mozN7\nRqMRY2NjGB8fx9TUFJ1z9ASyD/vLZ1QkEiEgIIAmpmw2GyWVG3lO5xlLT7OXUqnU67VstVpx7949\njm0GsJwYKisrQ15e3oaSKR0dHbh69SrMZjOCg4Nx/Phxt2q6zWajc5OuxJA8fOn48EQaBQIBJBIJ\nWJblzLQzDENf11psX7xBIBAgJCQENpuNVmgFAgFN0BDldlfSud519ItMGoHla+K9997Dr371K0xM\nTCAxMREymQy5ubn4/ve/j6dPn+If//EfcfHiRYSFheHtt9/GH/zBH0AoFOLChQv4u7/7O7S0tCA9\nPR1//dd/jaioKPzt3/4tampq8Hu/93t4++233cYgPvroI8zPz39JGl8R2HfeeQcpKSnUaFYgENA2\njMHBQTx58oTOmZH2utLSUg7RdHvS/55Rcw6oyOJGfNi2IiYnJ3Hu3DlMTk5CIBBQZdWBgQGOCirw\nP1UUQiJXk1fX6/W4ceMGurq6ACy3Br3++uucagPLshgZGUF9fT3HVxFY3hjz8vKwa9euDbeKfN4w\nNzeHW7du0XOnUCjw2muvIS0t7XNJmi0WC1paWtDQ0EATMwKBADk5OSguLl5XVWgzYDKZqDqxVqt1\nC+AJ+Hw+srOzkZSUhLGxMWr14Ur05HI5JZBxcXEICgriKJjqdDqPptXAclsgqRwKBALcv3+fBtd8\nPh+7d+/Grl27VuyIePr0KT7++GPY7XbExsbi9OnTG1Y1ZVkWfX19qKmpoQqxwcHB2LNnDwoKCtyS\nG1arFdevX6cCDDt27MChQ4d8SoKQqnVrays6Oztp4oFhGCQnJ9M5xY0Ej3a7HXfu3EFdXR2AZcXn\n48ePb1omfjUYjUYMDQ3RuUjXdZh0hBASGRcXt+6uGJ1Oh+vXr9P9TqVS4fDhw2vyetsoSAcMqUKS\na4pAJBLRtj5viRSJREIVT5OSkl5Kgs1ms62owrnSR/LwR3AtFArdqncikQgOhwNms5mKcHlS7SY2\nD4SQuxIgPp8PpVJJ1y/SOu2qFDs/P4+enh6qQrsWe4qAgAAOkRSLxZidncXQ0BCtksnlckRERGBk\nZIQeo1gspiMqa7F8slgsuHHjBl2P1Go1cnNzYTKZ3AihL90lfD6fqtsSlXRg2Rv6wIEDUKlUmJ+f\nx/j4OMbHx6k4mS9kU61Wo6CgALGxsVT4p6amhqN6HRgYCLVaDavViunpaY9quOsBuaY8EUrX7zl/\nJET4S2wNfEkaNw6OEM5awOfzOX56hGxarVbMzMzQRUAgEFAVMqFQSH+PENP1fL2ZFUqLxYLr16+j\npaUFAJCXl4cjR47AarVCq9XSmUjXWZygoCCOvQepeJBB7Nu3b8NsNkMkEmHv3r0oLCx0ex3j4+PU\nPJ5k2pw3HIFAgKysLOzcufOlBjJbBf39/bh58ybdiFJSUvDaa699buZxXEFmOBsaGjitGImJiSgu\nLkZqaupLrcaTWUZCEsfGxlZdYHfs2IHKykq3KozVasXo6CinpdWXTDGfz0dkZCSnvTQqKopm4HU6\nHT788EPMzc0hMDAQYWFhNDElFotRVlaGwsJCTqBst9vxySef0HbwHTt24PDhw35NXnnqqpDJZCgr\nK0N+fj7nfxFrnevXr8Nut0OpVOKtt97yOo88OTmJ1tZWtLW1cRQfY2Ji6JyiP2yT5ufnceHCBQwP\nD4NhGOzbtw+7du3aUokZk8nEIZGuXr0MwyA6OppDIlcjvAaDAXfv3sVnn30GYJl07d+/H7m5uS/t\ntVssFkxNTblVDj0JqThDLBYjMjISiYmJiI+PR0RExJrtJ+x2u0ci5+17nn7HX1U+ZxCrjeDgYMjl\ncoSGhiIoKMirYmdAQIBP9zRpD25ra6N7uTfFUalUiujoaKpk6mvyhGVZ1NTU0Lms/Px8FBcXu9mR\nuCrI+noeiZgOwzBYXFzkkK6EhATs2LED6enpEAqFdPbStUI4MTGBoaGhNc2EymQyyGQyyOVy+rnz\n1xKJBFNTU7h48SLGxsbAMAzKy8tRXl7udS9jWRaLi4scEkkqzJ6OjWEYKBQKqNVqREZGor+/n6MP\nERISArFYTLu2srKycPDgQQgEAtqSTD4ajUbqu2qz2cAwDLX/cE5orBfvvPPOl6RxC2Erk8a3ATwD\n8FsA2QAuAggG8AcALvvrgPwAN9JI2gGIxxuZ49mMTWG9YBhmXWRzLSR1YGAADQ0NsNvtUCgUOHLk\nCCIjI+nPjUYjxyPS2dsKWA4YY2JiMDU1RTf+tLQ0HDlyhJMJdDgc6OnpQWNjI7RaLf1+amoqbUF9\n/vw5NBoNh1golUoUFhZi+/btW9ZSYyPwJhtvt9vR1NSEe/fuwWw2g8fjobi4GBUVFZtim/KyMDU1\nhcbGRjx9+pQGMAqFAkVFRcjPz9+U12axWGgArtVqMTo6yllQSSsgEbtxRnJyMg4ePOhWFXU4HJia\nmuK0l46Njfm08ZKqEWlpJdVIgtbWVly9ehU2mw1KpRKnT5+GXC7H4OAg7t69S2dxZDIZKioqkJeX\nB6PRiHPnzmFoaAh8Ph9HjhxBQUHBRk4bAO/XJ8uy6O7u5mTA5XI5ysvLkZubywlqR0dHce7cOczN\nzUEsFqO6uhopKSkAloUbyJyic8u6XC6nfor+tEh69uwZLl26hKWlJQQHB+PUqVOfC/Eps9mM4eFh\nSiI9VbijoqIoiYyPj6fXlMPhgEajQU1NDUwmE11LysvLN62Nk1RfXMmhJ/sHAoVCgYiICISFhYHP\n50Ov19PWTWeEh4cjJSUFOp0O+fn5Xsme6/f9YdHA4/HcCFxAQAAYhoHFYqEB+sLCgseqm0KhgEql\nognm6Ohov615LMtiamqKKpoODQ15tNxxFueam5tzW7N4PB6io6MRGxsLtVoNtVoNmUy2IkFvbW3F\nlStXYLfbkZycjFOnTq2o9Dk5OYnHjx+jo6ODJo6lUikUCgUlf3q9flNUroODg1ckhFKpdMUkJsuy\naGpqwq1bt2Cz2aBQKHDixAm39n9ffUTtdjump6cxMTGBwcFB9PX1udmorQSxWIyjR49i+/btq/6u\n0WjEp59+SiuuYWFhOHr0KBITE2mV2plsevvo+r2/+Iu/+JI0biEwDAOtVovQ0FCadHH9OV4RaXwP\nywQxAEALgM8A/BGAP8MyodwqYP/lX/4Fs7OzKyp/8fl8yOVyKBQKyOVyiMVizMzMQKvVurUVCAQC\npKWlITk5GTweDzabjT6IsqLr196+7+3rrQJCXokUPxHSsFqtHg3fyQIcEhICgUCAqakpjI6O0lYZ\nZxU9hULhRmoXFxfR1dWFrq4uuqERX8OioiKOcM7nHattLFuhOrAZMJlMaG5uRmNjI90gRSIRfY9X\n8rNaDVarlQbYWq0WIyMjnOCDYRioVCoqXBMUFISLFy9S8SpgOTB97bXXkJKSQtVNnQni+Pi4x3tU\nIpFQ38OYmBjExMSAx+NRDzMiqe+K8PBwxMbGYn5+HgMDAwCWs/ZHjhzhVBNJm+idO3fo88hkMhqw\nBgcH4/Tp036by1vt+mRZFp2dnbh//z6tjCsUCpSXlyMnJ4cGX0tLS7h06RKePXsGYFld1Wq1cmZG\nAwICOHOK/ry+XdVdU1JScOLEiS0/X+sNFosFL168oCRyZGTELeEZERGB0NBQ6HQ6muxLTk7GoUOH\n/NK1QConnsihtxY/Ho+HsLAwREREIDw8HOHh4ZQoeksK6vV6Ogf5/Plzuo+sVWiEYRivwiwrefE5\nf87n8zE3N4fR0VH60Ol0HrsLQkJCKDkknoj+JOlWqxUjIyOUJL548cJjnOJM/mJjYzlVROI56qzU\nOj4+7ravBwcH0+chlh2u7cBDQ0M4e/YsjEYjwsPD8bWvfc1tr56ZmUFtbS1aWlro9ZqcnIyioiLI\nZDK3GcLZ2VnMz8+7CcKsF2KxmLaVevO6lEgkXiu5i4uLuHLlCl3H8vLycOjQIY/E31fS6AkmkwkN\nDQ1obGzkeFoC8HoewsPDERkZiaioKPrRm/emVqvFtWvX6J6Xk5ODgwcPrnue+Ys+0/h5A8MwIIUy\noVAIhUJBFd2Dg4NRWloKvCLS+DUAvwHwjwBOA9gGYB7AnwD4Z38dkB/AsixLN7np6Wk0Nzejs7OT\nBn4CgWBNRI3H4yE+Ph4FBQVUNtmfQQ6pfq6HbK70tbfPiRqYM7EjZHirLQY8Hg8ikYhu4v6uvq72\nNTF5f5kYHR3FjRs3Xukc0mbA4XCgt7cXDQ0NbhXo4uJiJCUlrXqubTYbDaC1Wq2bPD3DMIiJiaEk\nkcyDsSyLR48e4d69e/QaF4lEyM/Ph0wmo3OIU1NTHu+BkJAQTntpTEyMx6yeK0wmEyWRJFBzXXtE\nIhG1xFGr1YiOjnZr/ezo6MCNGzdoUCEUCnHs2DFkZ2e/9OvT4XCgo6MD9+/fpx0HoaGhqKioQFZW\nFoDlIP/27duceT2GYZCamoqcnBykp6dvylzawsICR0W2qqrKzZz88w5CIAiJHB4ediORwcHBSE1N\npZVIX8XeWJbF3NycR3LoaWYOWL4WCSF0JockSbheGAwGtLa2oqenB/Pz87Q65awm6Y30iUSiNb3n\n5HU7k0Pn5KczZDKZG0H0d0JCr9dTgjg8PAydTudGIIKDgylBjIuLQ1RU1JrPt9lsxujoKF2bhoeH\n3aqRfD4fMTExHEIaHByMubk5/OY3v8Hk5CTEYjFOnz6N6Oho2tE0ODhInyMoKIh2M/kSexHC51wh\nlEqlmJmZQU9PD0dhlpAYHo+HkJAQWK1WjuXFapBIJG5iPktLS2htbYXZbEZAQACOHj2K7OxsH8/q\n+mC329HR0YHa2lrOTCOx4VgNIpEIkZGRlEQSQikWi2Gz2fD48WM8ePAAdrsdgYGBOHDgAPLz89e8\nNn5JGrcWGIbBv//7v3NG6Jzx34TylZDGvwDwVQDRAI4D6MQyefw7AFtD5WIZrKcLemlpCTU1NdBo\nNGBZFgEBAcjPz0dsbCx0Oh26uro8tnd4AvEWUigUbg9ScdvqYFkWn332GW7cuAG73Y6oqCi89dZb\nUCgUlFwaDAbcv38fHR0dAJY3y9LSUoSHh8NsNqO7uxv9/f0cZTxnSKVSSKVSBAUFISAggBJjX8jv\nVlqU/NUyLBKJKOFYrf2WZVm0tbXh008/pQp7eXl52Ldvn19mvV41yKxra2sr3RDDw8NRXFyMnJwc\nOu9nt9sxMjJCZxI9ka7o6Gg6exsXF+eW4Z+dncWvfvUrThtQQECAx4CQYRiOQA15+Es0ZXBwEB9+\n+CGMRiO9NlyPQygU0gAtLi4O0dHRnAo0MYEGlhVW9+3b90raLh0OB9ra2nD//n0q9iMWi8GyLCfw\nJDPMwcHBOHPmzKYlP/r6+nDp0iUYjUZIpVKcOnUK8fHxm/K/tgKsViseP36Mhw8fwm63g8fjQS6X\nY3Fx0a09U6FQcNpZg4ODMTMz40YOp6amvAb1gYGBlBg6f5TL5Rsm5c7WE6OjoxgZGfE6+yiVSil5\nIUmWtey5LMtiYWHBjSB6CrikUqkbQfT3+utwODA5OYmhoSGaYHJtWWQYBpGRkXRNIMrN/k6GsCyL\n6elpTkXTkwWIWCxGcHAwBAIBpqenvSYUPCEgIMCNELq2j66mHqzVanH16lVOzBYWFobi4mLk5uZS\nguoq6OM6c+lNvdYVDMN4JJfkERsb65fEQX9/P65eveqxZdVZC0IikWD37t3Q6/V0ZtLba5HJZJRA\nSiQSdHZ20oR0XFwcjh49uiahui9J49YCwzCYnZ1FV1cX570leJWkEQBCABgBWABIAIT/93No/XVA\nfoBH0kgwOTmJTz/9lLYciEQi2m7C4/FQUFCA3bt3g2EYzMzM0HaOgYEBn3vPZTIZh0iGhobSz8Vi\n8ZbKeo+NjeHcuXOYmZmBSCTC66+/ju3bt6Orqws3btzA4uIieDwe9uzZg7KyMthsNjx9+hSNjY00\nUCQGvCqVCrOzsxgYGHCbJRMIBIiLi6OiOqSVzxscDgcWFhbQ0tKC5uZmOh/D4/GQlJSEtLQ0hISE\ncIjoeiuvK33tzzkL0mJFht5J22RiYqLX1hKz2YyHDx+irq6OeqtVVFSgqKhoyyr2rgVGoxFPnjyB\nRqOhqnCEXBNxB9cAODIykp63+Ph4jy1YOp0OOp0O7e3tXmer+Hw+oqKi3ARqNmOelohH3bhxAw6H\nA3FxcXjrrbcgkUgwMzND21mHh4e9BssMw2Dnzp0oKSlBd3c3Hj16RAPdtLQ0VFVVragAvRrW02Kl\n1+vR0tICjUbDmYHm8XhIT0/H3r17IRQKce7cOYyMjIDP5+O1116jKs7+gMPhQE1NDR4+fAgASEpK\nQnV19abZSbxqkBnTW7du0T1p+/btOHDgAORyOex2O3Q6Ha3GDw0NrWnGTyqVeiSH/uqwISRpZGQE\nIyMjGB0dxcTEhNtay+fzER0dDaVSid7eXkRFRWF4eHhFBVDycH7v9Xo9dDodRkZGKEH01FIbFBTE\nIYjEcN7fIO3GzsTMlXSJRCK3VtPNnG+3Wq0cVVFnlVHiLbwWewipVIq4uDiEh4dTQkg+bvR1TExM\n4MKFC5iYmADDMEhMTMTExAQlTaQgUFhYuKoqu8PhoEI+Q0NDePToEb02SBu1Xq9fVWVVq9WioqKC\n+oWudazGZDLh1q1baG5uBrA8s/zGG29AKBSivr6e0+JLIJVK8e1vf5v+L4PBwBHdmZiYwMTEhMck\nkLPHL8MwyMzMxN69e1e1dyJ/+yVp3Dpwbk8FltfD5ORkZGZmIi0tjayFW0o9dTeAWj88j7+wImkE\nlluYPv74Y0ocgeUb8I033kBqaqrXv9Pr9WhoaEBTUxNd5MViMcLDw8Hj8TA/P4/5+fkVb6iAgAC3\n6iQhlXK5/JX4PJrNZly9epVWFOVyOQ201Wo1Xn/9dTAM4yZqEhISgsLCQuTn57tVYpytDQYGBjjt\nFsDyeXBWZo2IiPC6WJHZLo1Gw3nPYmJiUFhYiKysrE0TziGiSWslm2Q2zjkgWmkuh8fjQSwWIyQk\nBFFRUVCr1QgLC6OS6bOzs/jkk0/o6w8PD8ehQ4eQnJy8Ka/7ZYHI8ff396OjowMTExNu949cLqee\nU2QuEViuQnoSqPGW9Y6IiEBSUhKdPyT37WbDZrPh2rVrVJCguLgYBw4c8Er6DQYDhoaG0NHRga6u\nLo+Ji5CQEKhUKpjNZmi1WhoYZGVloaqqal0WNr6SRovFgu7ubrS2trrNKUZFRWF6epoGWVFRUais\nrERKSgo+/fRTNDY2Alieqzl69OiG/Qj1ej0uXrwIrVYLhmFQWVmJsrKyLZWY8ycmJydx8+ZN9Pf3\nA1hOoBw+fBhRUVG0YuhcNfQ10RkYGAiVSoWUlBSkpKQgLCzML+eQJHEIORwZGfGYCGIYBhEREZSs\nqVQqTrsluTbXUgkTCoVULMfT63UliKsJwKwX8/PzVKxmeHjY4xwhse6JjY1FXFwcIiMj/bY22e12\nj2TQ+Wtv3ULOINYTpBKo1+tXVGklaqCE9G70NbmK0oSFheHkyZOIiYmB3W5HZ2cnGhsbOZUWX0Yf\nWJZFXV0d7ty5A4fDgfDwcFRXVyMmJob+jt1ux+LiopsyrF6vx+zsLB48eMDpaoiKikJ6ejoyMjIQ\nHR294nXV3d2Na9euYXFxEXw+H+Xl5di9ezdnfzAYDNBoNGhsbOQkTYRCIb71rW9xjtUZDocDs7Oz\nHBXXiYkJr111QqEQSqXSrcXVeZ3+kjRuLTAMgx//+MdQq9VISUlBeno65HI5jYlfphBOAYD/14fn\nSAeg9M/h+AVeSaPBYMCjR4+g0Who1kapVNL2CoZhUFBQgKqqqhWz1BaLBc3Nzaivr6ebslgsxs6d\nO7Fjxw7Y7XbMzs5idnYWMzMzmJubo1XLlbJ1DMMgJCTEY9traGjopmYa7XY7Ll68iM7OTnos5eXl\nUCqVbiqnCQkJKC4uRlpams+bgMFgoARyYGDAzbtOIpFQApmYmOg1Uzc7O4umpiY0NzfTxZMI5/iS\nWdxMEE/KtrY2dHR0cLKTKpUK6enpsNlsmJ2dpeqCvng5MQxD53l4PB5HuTMhIQGHDh3ieGNuZZDq\nIamCDA4OugV1MpkMAoEAs7OzdHMim7BYLMbExATGxsYwMTHhcdbDdQYkNTUVZ86ceSWV2fn5eXz4\n4YcYHR2FQCDA66+/jpycnBX/hgRHN2/ehMPhQHx8PEpKSqic/PDwsNs6wufz4XA4aOY4Ly8PVVVV\nfquUkKRHa2srurq6aKDI4/GQlpaGnJwcpKam0nnx5uZmPHz4kFaPY2JiUFlZCZPJhI8//hhWqxWR\nkZE4ffr0uoWQ+vv7cfHiRRgMBkgkEpw8eXJNYimfJ5hMJjpe4XA4IBQKERMTA4ZhMD097bU1jcfj\nITQ0lFMxDAsLg8PhwIsXLzA4OIjBwUG3dUgqlSI+Pp4+VkrqOUOv11NySNo/Pa1xJOlBCGJMTMya\nEwhLS0vQ6XQ0OTkxMeE1YURsB5RKJdLS0pCenr4parIOhwNjY2OceURXFXIyd+1cGfV15tTT/9Pr\n9SsSQl9aMHk8Hqc91LkySD4GBQWBZVm0t7fj0aNHlKwHBQVhx44diIyMRE9PDzo6OjySCpFIBJVK\nxRHZ8bXt32g04sqVK+jp6QGwLBx26NAhj9fM6OgoGhsb0d7eTveBsLAwFBUVITc3lxNHLSws4PLl\ny1SQbOfOnTh48OCak9Amkwl9fX3o7u7Gs2fPOOuzXC6nBDIuLo7uQ4uLi7hx4waNuUiCfiUFaavV\niqdPn+L27duc/5Gbm4vKykqvFkeusFgstBJJhKdW6kZQKBSUQO7du/dL0riF4FppJCAWgt/73veA\nl0QaAwHcBPCfK/wOD8BJAEf9dUB+gBtpXFpaQm1tLRobG+mNsW3bNlRUVCAyMtLjvGN5eTmKi4tX\nDDQdDge6urpQV1dHfdX4fD5ycnJQWlrqdvOzLAuj0UgJpevDdXNxhVgs5rS6Oj82kiUdHx/Hxx9/\nTDN0zjNTBMSovaioyC8EZW5ujs6p9ff3u21sISEhSEhIQFJSEhISEtyCX5vNho6ODmg0GnrugWV1\ntsLCwpfqBzg1NYW2tja0tbVxyHBYWBiys7ORnZ3tlcwSwSYi7qLT6TAzM+OT6bAzBAIBQkNDERIS\nQjd650dwcPArqWKzLIuJiQlKErVarZvQgkKhoMI1CQkJEAqFtL2OiB5426QUCgWtGo6Pj9OgAlgO\nZr7yla+4yaO/LAwMDOD8+fMwGo0ICQnBmTNnVm0fda1KlpaWYv/+/Zz3zuFwcAjk4OCgR8NnYvdR\nVFSElJSUNc/csCyL8fFxtLS0oL29nXOPqtVq5OTkYPv27V4DP5vNhidPnuDRo0f0b1UqFfLy8lBX\nV0db4o8fP47MzEyfj8vhcODBgwe4f/8+gGUP0Orq6i/ErC/wP6IsU1NTmJiYQE9Pj5sqsCsEAoFb\nO6mvYjTEFoEkcQYHB93Wn6CgIA6JjIqKoiIqzlVET9ehRCLhWE+oVCqfr8WJiQncv38fExMTUCqV\nkMvlmJmZwejoqFviEVjeu6KjoxESEgIejwej0YiJiQm3FnXnGUHy8DYisBKI0JVz5dN17wwICOD8\nH5VK5RNBJnuDqxehXq+nX+v1+lUDeIZhqPWEN0K4mqgXGUupra2liXKZTIZdu3ahoKCAQ7Kmpqbw\n61//GnNzc/S1e6t6EyVpcm7Cw8PdjqO/vx+XLl3C4uIiAgMDcezYMZ8sJwwGA548eYKmpibO6ANR\n7R4fH8fVq1dhMpkQFBSEN998E2lpaas+72qw2WzQarXo7u5GT08PZ90MDAxEamoqAgMD0dbWBpPJ\nBKFQiP3796OwsNDn68/hcOD8+fPo6urifH/79u0oLS1d89y43W5HfX09ampqYLPZ6OiGzWbD1NQU\nZ+350qdxa8GZNDIMQ2dfyXv0smcaUwD0rfBzPoBMAO3+OiA/gJJGk8mE+vp61NfX0wzkSrM/k5OT\nuHXrFq2qhYaG4sCBA0hPT1/xZmZZFsPDw3j8+DEnaE1NTUVpaSkSEhJ8WgxsNhunKun6WM1CxLVK\n6UwwPWXObDYbHjx4gNraWjgcDkgkEiiVSgwODnKyWLGxsXjrrbfWnQ1dDaTlqL+/H1qtFgMDA27E\nIiIigpJI1zm20dFRaDQatLe303Mkl8uxc+dO5Ofnb8ps09y/wzoAACAASURBVMLCAtrb29He3s7x\nnJNKpcjKykJ2djatBBCsZWbMarVCp9NRYYQXL154JJK+toq4mhh7ehAPso2A+IeRhMDg4KBb65Nc\nLqfziOHh4TAYDLS1VKfTeZ1BdFY95vF4yMjIQElJCXQ6He7du8e5ZvLy8nDkyJFX4vdJ2p1u374N\nlmWRnJyMkydPrppVd61KvvHGGz4p9rEsi/n5eUoi+/v7PbYfhYeHc/wiXYNkcn0uLCygra0Nra2t\nnLby0NBQ5OTkrJgE8QSr1YqmpibU1tbSa1ilUoHP51MfytLSUuzbt29VgrO4uIiLFy/SykBFRcWK\nJttbGXa7HTMzM24qpSuJ0RCFRFdy6E9RFLIeO5NIVzLobd0RCAQICQlBSEgIFQwRCASrtvW7fs9s\nNmNpaYmeB0+t/UTV07nFNCwszOO1sLCwwCF2ntRIicAOITGuVhOEzJP7bHh42G3sAlhOZBGxGrVa\n7bFKSxLIroTQuVLozf/RFVKpdEVCuJGEodlsRlNTE+rr6yn5CQsLw+7du5GTk+P1fjUajfjwww8x\nODgIoVBIvQ2dVVpHR0fdOkUCAwMRGxuL2NhYKJVK9Pf3o76+HsCyaEt1dTXHE9oX2O12dHd3o7Gx\nka43zkhJScGbb765oaTTSh63o6Oj6O7uRnd3N8fqCVhOxpSWliIvL29d/7+pqQnXrl1z+358fDxK\nS0uRlpa2pnVhbm4O169fp2MwRLldKBTS1tb9+/d/SRq3EBiGwQcffOC1q+NVC+HIAMid/k4B4P8B\ncMBfB+QHsGazGY2NjaitraWBZFJSEqqqqnzyNHv27Blu3bpFb/DExES89tprPlXYpqenUVdXh5aW\nFrrhxcTEoLS0FNu2bVt3ixzJOnpre12tMkXaG8nDZrOhra2NVjed5xiB5QU6NDQULS0tYFkWSqUS\np06deim+iQ6HA+Pj45REDg4OcrK3zrYKSUlJUKvVEIlEWFpaQnNzM5qammgWms/nY/v27di5cydi\nY2M3FFiZTCZ0dnaira2NYxkREBCAzMxM6jnnbYPeiJcTUfx78eIFfeh0Oo/tmaTqGBAQQOXHfWlR\nEolEXgklqVa6Xr8sy2JmZoaSRK1W63YtBgcHIyEhAREREXQWhhBET7M0AoHAo0ANIRkNDQ3o7u72\nuHG5Gsq/bFgsFly5coXOB5eVlaGysnLVoE2r1eLcuXNrqkquhKWlJbS0tKChocHrXBsRqyCzVDdu\n3IBIJKKEDFg+n9u3b0dubi5UKtWG7h+LxULJI3nfFQoF5ubmwLIs4uLicOrUKa8ttVqtFhcuXMDi\n4iIkEgmqq6uRlJS07uN5WbBarXTG0JkczszMeCUFzgkSIuxBWuvsdrtH0rUSIfNFDMzZkslisdDf\n2QoB4uDgINLT0zmJoaioKBQVFSE7O3vNySGr1UqtJsjDk8BOWFgYgoKCYLPZMDMz47Ze8Xg8jyI8\nJpNpVULoi/VEUFAQJYDBwcFuhFAmk21K273RaKTegeScR0dHY8+ePcjMzPSJhNrtdnz88ce0a2Lf\nvn1UZJD8nLTyEiLprdtKqVRix44diI+P90msxRtaWlpw/fp1TlI8NDQUhYWFyMvLW3fL8mp7u8Ph\ngEajwZ07d2C1WjlKqARqtZq2sa6lZb+npwdnz56lowl8Pp9eW2FhYSgpKUFubq7P9wjLsujq6sLN\nmzeh1+vBMAyKi4tRVVVFrWy2wprwJZZB3g+SPCadH0T06y//8i+BV0Qaf4Blew3X1aIWQJm/DsgP\nYH/605/SwDUuLg579+5ds/S63W5HU1MTampqYDKZfJ53JDAYDGhqauIYtspkMpSUlKCgoMDv84kW\ni4VTlXQmlXNzcz5lLIndAPH3UigUMBqNuHjxIubn5xEQEIDjx48jIyPDr8e+GojtAiGRw8PDnNfD\n4/GgVqspiVQqldBqtdBoNOjt7aW/Fx0djcLCwjUFGTabDb29vWhra8OzZ88oSePz+UhLS0N2djad\n5XrZsNlsGBsboySyv7/fY6YpNDQUKpUKYWFhkEql4PF4tMWJBDNzc3M+KSwSQ2QejweLxQK9Xu82\nR0RM76VSKRXCGB8f9zjPGxgY6OZ/6K1aQDA+Po5r165heHiY832BQIDS0lKUlJS8EiP36elpfPjh\nh5iYmPC57ZJlWTQ2NuKTTz4By7JISkrCyZMn/Xr8xDNxdHQUwPJ5YhjG6/vN5/ORnp6OnJwcpKSk\n+D0otVgsaGxsxOPHj+n1SuZQJRIJTp06hYSEBPr7LMvi4cOHqKmpAcuyiI+Px8mTJzdF2dIZLMuu\niYwZjUbOPbW4uAiDwbCiHQGx4yF+sDabbU0qlS8TpPVJKBTS9c5ut8Nisbglr3g8HqRSKeRyORV5\nE4lEHCsiZ0uipaUltLe3o6+vj3ruZWVlobS0FKGhofQcLSwsoKmpCU+ePKH7qlgspmqZvs50uYJU\nhEhCcGZmxuP9QawXiC1PSEgIDAaD2yyhL2tpYGCgR7sJ569fdqfEwsIC6urq8OTJE46tT1lZGZKT\nk9dM1liWxePHj3H79m0Ay7N3x44d87pfzs/P49GjR/jss8+8xixBQUG0GqlWq6FUKldt9yUt7Q8e\nPADLsoiMjERSUhK6urposlwoFCI3NxdFRUUrzhWuFZOTk7hy5Qod/9m+fTsOHToEAOjt7aXWZc73\nUHh4ODIyMpCRkQGlUrnqeX/x4gX+8z//E3a7HQzDID8/H8+fP6evTSwWo7CwEIWFhT5XNM1mM+7e\nvUvHtmQyGY4cOYKMjIwvNGlkWRa//vWv8Ytf/AI2mw0hISHo7OykVepLly7hypUreP/998Hn8/Gj\nH/0IX/3qV/Hpp5/i7bffxvz8PGpqarB79276nP39/fj5z3+On//85zhw4ADefvtt7Nq1yy/HuxKJ\nJ2spXhFp/D8A3gZQCaAZwDiAQgAZAD7w1wH5Aew777wDlUqFqqoqnwzDV4LRaMT9+/fXPO9IYLVa\n0drairq6OiqlHxAQgIKCAhQXF6+51WI9IPYVn332Gerr69ckvw4sEwWbzUYDvJSUFJSVlSE8PPyV\nWIhYLBbahqfVamkwTCAUCqknWUREBAYHB/H06VMaZAQGBiI3NxeFhYUeM3oOhwNarRZtbW3o6uri\nBH2JiYnIzs5GZmbmpggpbBRTU1O4desWR2XWFUQhTaVS0XYskh0nQa9z8Ds9PY3Z2Vm3luG1QiKR\n0HYyQhDX0la3uLiIe/fuobm5mbNI8ng8BAUF0WqqQCBAdnY2iouLX5pAUG9vLy5evAiz2Yzw8HCc\nOXMG4eHhK/6N1WrFxx9/jNbWVgDA7t27sXfv3k1ptWRZFr29vbh9+zbtoCBtg87nkmEYJCcnIycn\nB+np6RtWN10JZrMZDQ0NqKurc7u29u3bh6KiIqp0TYzC8/PzkZeX52a14wu5W60l0vXhT7udjcDZ\n99XVA9YX31jnh81mowkjkmD0RFLlcjliYmKocMlqgfnCwgKnndXVNkYgEECtVtOZyNjYWAgEAszN\nzeHhw4d4+vQpHA4HFXEqLy9fkQCSmfbGxka6/jMMg7S0NBQVFVFrI28gHRLOraaurYPA8l7N4/Fo\nBdZXiESiFQkhIdFbBTMzM6itreVYO6SkpGDPnj1+8Trt7u7GxYsXYbVaERcXhzNnzrglxkwmE65d\nu4b29uVpp6ysLBw8eBCzs7OcaqRrJwvDMIiOjubMRjrvK7Ozs7h48SIlbaWlpdi7dy8EAgEcDgd6\nenrQ2NjI6R5KSkpCUVHRhrQR7HY7amtr8eDBA9jtdkilUhw9etRj0t1isaCvrw89PT3o7e3lrIdS\nqZRWIBMTE73GnTMzM3jvvffo/Xz8+HHw+XzU1dXRe2QlzQ1vGB0dxccff0zHcL7IM412ux3f/OY3\ncePGDVy4cAF79+6lP/vZz36G733ve7h48SIOHDgAiUSCnTt3UkVwAPi3f/s3/NEf/RHi4uLw9OlT\ntzUsLS0NNTU1UCr9px26WuX3ZaqnuuK7AP7lv//mbQDvABAAaAWwzV8H5AewP/nJT7B//34UFBT4\nLQCbnJzEJ598gufPnwNYrt4cPHjQ555xlmXx7NkzPH78mAZAPB6PDi57k0z2B2ZnZ3HhwgWOYAyw\nPKtYXFyMxMRELCwseJyl/DxYiCwtLWFwcJCSSFcJ9sDAQMTHxyMwMBBjY2MYHx+nP0tKSqLCOePj\n42htbUVHRwennTMmJgbZ2dnIysraUHVjI+2pa8XExARu3rxJWw2Dg4MRERFBq8+ukMvlNHtLKsxD\nQ0PQarVu7Y18Ph9CoRB2u33NCQgAtALhHEA5P4KCgjj3lM1mQ319PR4+fOgW4KpUKlRXV0OhUKC/\nvx8NDQ0cwrwepd+1gGVZ3L9/n4qyZGRk4Pjx46t2EszNzeHs2bMYGxuDUCjEm2++6ZO4w1phMpno\n+zg0NOTmnwosB/RJSUloa2tDYGAg/blQKERSUhJSUlKosMJGWyI9fW2xWLC0tLQlK2ykAkg2ZmeB\nAVcwDIPAwECIxWJIJBKOATipzrk+lpaW0NTURPcEuVyOvXv3Ii0tjRK/9SbllpaWqIKpr0I15ONG\nK916vZ4SyMHBQbc1mSj7Oa+zubm5KC8v9zgvu9La+eLFCzQ2NqKjo4MS/fDwcKqWKRKJYLPZMDw8\njL6+Pmp7sd7rjcfj0YSLp/GAiIgI2va9XoGdl4Xx8XE8evSIo3i6bds27Nmzx+8xiU6nw29/+1vo\n9XqEhITga1/7GiUuw8PDuHDhAubn5yEUCnHkyBHk5uZ6nAWdm5ujBPLFixcYGxtzuyelUilUKhUE\nAgF6e3thtVoRHByMEydOeFVYHh8fR2NjI1pbW2l750q2Ys5wvT5HRkZw5coVOvNaUFCAAwcO+JRo\nttvtGBoaonOQzi27IpEIqampyMjIQEpKitvzGQwGvPvuuzRBfvDgQZSUlGBoaAh1dXUczY2UlBSU\nlpaummABlhPpjY2NuHfvHn74wx9+YUnj3//93+NHP/oRzp8/j+rqaref//mf/znKysrwxhtvgMfj\nobKyEnfv3qU//+Uvf4l3330XGo0G1dXVOH/+POfvy8vL8eDBA78e81Ymje8A+HMApQBiAfwjACGW\nxXA2noryH1iiJBQZGYnXXnvNr3MvrvOOSUlJOHjw4JoqGqOjo6irq+Ms1ImJiSgtLUVKSorfNhiz\n2YwrV65QSWdg+QLKyspCcXGxTwpbdrudk5UeHBxEd3e3T/MYr8pCRK/XU1XWgYEBN2GVoKAgBAQE\nYH5+ngYZrjMGCoWCKp+uVjHyFS+TNALeTcD37NnjNh+5EvkjbWmeAiQej4eIiAjaXhoaGorAwEAs\nLS1xqpXOn6+24QgEAkooiYQ9qfYSZV9iCVNWVuaWeZ2enkZDQwNaWlpoYKhQKOjm768KsclkwqVL\nl2gL9N69e7Fnz55V79/+/n6cP38eS0tLUCgU+MpXvoLIyEi/HJPBYKCB+tDQEMbGxjg/J/PAcXFx\nsFqt6O7uppn74eHhV6Y0uxqIN9xGK22uP+PxeLS9kKxzMzMzXtsTgeVEmbMQDfm4FnJgtVrx6NEj\n1NbWwm63QygUory8HCUlJetqdbdarRgbG+MomXpKDgUEBHBUTDfTn9AZ5Lp89uwZenp63NroeTwe\nVCoVrUTGxcVxKnGrrZ12ux3j4+NoampCV1cXp1LjaX7MG4j1hHOF0PVz5+4aso6SaqUngR2JRMKZ\neXQV2HkVePHiBR4+fEjXLh6Ph5ycHOzevdtv+50n6PV6/Nd//RdGR0cREBCA6upq6HQ63L9/n2on\nVFdXr2mmz2Kx0PlU8l54GtOIiYmhVe6VbE6INoJGo6H7plAopOrxntZqcn1arVbcu3cP9fX1YFkW\nCoUCr7/++rqtgIhFFVFidU5483g8JCYmIj09Henp6fT1mM1mvPvuu5Rs7tq1CwcOLMuOeNLciI6O\nRklJCbKyslbtnltYWIBcLv9CksaFhQXExsYiOjqaM9bkDK1Wi46ODhw9etQraQSAjz76CJcvX8a7\n776LP/zDP6Q/r6qqwr179/x63FuZNALLnoy9AFgAO7DcqnodQNcKf/Oywba3t+P27dv0hk9LS8OB\nAwf8thhudN6RYG5uDg0NDfjss89ocBsREYHS0lJkZ2eve2OZn5/HvXv30NraSi8mPp+PoqIi7Nq1\na8PS9EajEZcvX6YVnezsbCQnJ3PI5au0EHHF7OwsxyNyNdGg5ORklJWVIS4uzq+KhAaDAWKx+KX7\nBVqtVjx+/BiPHj2CzWaDQCBAeno6AgICPLaSrQSxWIywsDDExcUhIyNjzQGQq6+Yp4cvbbABAQEI\nDQ31KtojkUhgNpvR3NyMxsZGuhaIRCLk5uaiuLh43f6AwHIl9+zZs5iZmUFgYCBOnjy5qviOq6pq\namoqTpw44bNXmScsLCxwKjquLXauwbhareYka8h8obNoGMMwlFCRuT7nQJjP50MqlSIkJAQSiYRW\n0dZC6Lz9zGq14sqVKxwxHmA54HvzzTfX3W5stVoxPT3tplI6PT3tlVBIJBKP5HA1e4KVwLIsOjs7\ncevWLbo+5uTkYP/+/T53MRDLFWcvRE+G8a7qomSu+VVUvYhHclNTEw1W1Wo1QkNDqe+qa5u0Uqmk\n121kZKSb/YSrF6EvgaxAIIBMJkNYWBjCw8PdCKFEItnQ+SGq10Txenh42E08h8/nQ6lUctopX4Zd\nDMuy6O/vx6NHj2grpkAgQEFBAXbt2vVSRmWA5XN0+fJlTjIbWG7Pr6qq2vD+6GzRwePxIJFIPFbY\nZTIZRy03Ojqa878dDgeePXuGxsZG9Pf30+8nJCSgqKgI6enpnO6VgYEBXL16FbOzs2AYBiUlJaiq\nqvLrXOrs7Cx6enrQ3d2NoaEhzjWvVCqRkZGB9PR0KBQK/OIXv6D7QXZ2Nk6cOEGvbaPRCI1GA41G\nQ+Oh4OBgFBUVYefOnSsmVr+oQjgfffQRTpw4gW9/+9v4j//4j1V/fyXSePz4ceTn52NsbAwajYZ2\nEf1vJI2esA/AHT88j7/AkkDHuaWNx+Nh586dqKio8JvIhNFoRE1NDZqamui8Y0VFBYqKita08JlM\nJjx58gQNDQ10cZNIJPQG9uV4ie1HXV0duru76ff5fD4KCwuxb98+v2Y3yYD7nTt3wLIs1Go1Tp48\nydl4/GEhQrwHfbEQWQlmsxldXV1oa2vDwMCAT4teSEgIiouLUVBQsO75EzJL9uDBA4yOjoLH40Gh\nUCA8PBxhYWE0eAkPD9808Raj0YjBwUF0dXWhu7vbZ5GGkJAQCIVCWCwWzM3NuQl68Hg8REdH07kn\n0tq6kaBrfn4et27dogEFEc8ggZdIJILVal31/ePz+ZwqAalEOJOqlJQUFBcXr1ngoaOjAx999BGs\nViuio6Nx+vTpVVWFLRYLrl69Sud1ysvLUVlZuab/S1qznEmiq1cdmR2Li4ujWXVf7hUyI0jIoism\nJyfR1taG9vZ2zv8MCQlBVlYWsrKyNjw/OjQ0hAsXLmBhYQFisRj79+9HfX09p7UxMzMTlZWVXiuz\nJpOJkkJCDKempjx6+hHI5XI3Cwsyr+1PjI+P4+bNmzRgj46OxuHDhxEXF+f1b8jsnbMfok6nc1s7\nGYZBREQEJYcqlQqRkZEvPUHlCqPRiMePH3M8kjMzM1FRUcG5XkgbNbmuPbVRrwU8Ho8mkEgVlnRK\n+EMt01eQ989ZpdW1VRdY7oRwrkZGRET4rZ2edJw8evSIzrYFBASgsLAQJSUlm2JJtRo6Ojpw6dIl\n+p6kp6fj9OnTG3rNdrsdd+/exePHjwEsj9+cOHECoaGhMJlMGBkZ4bS1uu5nAoGAQ+ZjY2MpmZ+c\nnERjYyNaWlrodUxsvbZv307Fe4DlDrc33nhjzV6Ja4XRaERvby96enrQ19fHWRNCQ0ORmpqKvr4+\nmhROTEzE1772NU4caLPZ0NrayllnhUIh8vPzUVJS4nFfWwtp/Ju/+ZuNvESf8fbbb2/4OX7605/i\nBz/4Af7qr/4KP/7xj1f9/ZVI4+/8zu9Ao9Fgz549SE1NRVNTEwIDA//XkcYBD98TY3mm8aB/Dscv\nYJ1PoKt4RmBgICoqKlBYWOi3DXWj844Edrsd7e3tqKuro20IQqEQeXl5KCkp8TjrYbPZ0N7ejoaG\nBrdWtG3btuH111/f1I1xaGgI58+fh16vh1gsxokTJ5Camrrq3/nbQsSZVJJssc1mQ19fH9ra2tDb\n28vx+EtNTUV2djZSUlKor+DAwAAGBwfd2jDJoH1hYSGysrJ8DsI7Ozvx8OFDOtcwNDS0YoAoFosp\nmXT+6ItBtzNMJhP6+vrQ2dmJFy9eeMyyOoPP51ORCiJQ41rpJd5tzi2tExMTbouVs7JdbGysz0bW\nZrMZtbW1qKuro+bCaWlp0Gq1WFpaglgsxrFjx7Bt2zY4HA4YDAavlcr5+XmP7UneIBKJEBMTg+Tk\nZFq9JIbXzkGMw+HA7du3UVdXB2C5QnTs2LFVr4eZmRmcPXuWqqqeOHHCJwVics6dSaJr9V4kElGC\nGB8fD6VSue51zZf2aWeVSdfZ34iICOpRuhZrHtcKbGxsLE6dOkXboJx/RkCUBS0WC4ccervWGYZB\naGioGzkMCwvbdEGSpaUl1NTUUDE1sViMffv2IT8/3y1I1uv1GBkZ4VQRPVXeFQoFbS9VKpWIiYnZ\nUsIqS0tLqKurQ0NDA+2iSUtLQ2VlpU+zcmazGcPDw3RWXaPRIDU1FQ6Hw+P5kEqltJKuVqupRQ+B\n0WikLYfOapkrtRxuFkwmE6el1dN4gEgk4lQiY2Nj1zzOQeKJ2tpaSgiCgoJQUlKCwsLCVyLkZrFY\ncOPGDWrDER0djYmJCTgcDiQnJ+PUqVPrOq6pqSlcvHgROp2Oji6s5N/KsiwmJyc5JNKTEJJCoeCQ\nSLlcjtbWVjQ2NnISUQMDA0hOTkZ5eTn27NnzSrqJ+vv70d3djd7eXk5127k9OzIyEr/7u7/rlhBj\nWRZ9fX2oq6ujXR4MwyAzMxOlpaUcq7ovKmn8h3/4B/zwhz/ED37wA/zkJz9Z9fdXI40A8E//9E/4\nsz/7M/z+7/8+3nvvvf91pPH/YLkVlfwNA2AvlknjOX8dkB/AejqB4+PjuHXrFm0zWC+xW+Gfoq+v\nD5988gnN7Kxn3pE818DAAOrq6tDX10e/T25gtVoNvV4PjUbDkR4nCA8Px/Hjxzc900VgMBhw6dIl\nSpr37NmDqqqqDWUNN2IhQlrdLBYL5/eUSiVyc3ORnZ3ttYpgs9nw4sULPH/+HJ2dnW5zQSSjv23b\nNiQlJUGlUnFep91uR1tbGx49ekSvg+DgYOzatQuLi4uoqKight6kPW56ehpTU1NehRlcq5POH4OC\ngjAzM4O2tjb09/djYmJixfZOmUyG2NhYxMTEYGFhAa2trTCbzeDxeCgqKkJFRYXPm7bZbMbo6CiH\nSLpeiwzDIDIykkMknVvkHA4Hnj59inv37lECQnzAiNdhUlISjh8/viYRIovF4tYC6/y1LzY0zvNN\nEokEIyMjmJ+fB8Mw2L17N3bv3r3querr68OFCxdgMpkQFhaGM2fOeFWtY1kW4+PjdB5xcHDQLXlC\nRJ3IIzo62m8VibXO3DocDgwODqK9vR2dnZ2c606lUiErKwvbt29f8X1bWlrC5cuX6QxJaWkp9u3b\nBz6fT32npqam8Pz5c44NgDcIBAKEhYW5kcPQ0NCXHsg5HA40Nzfjzp07WFpaAsMw2LlzJ6qqqiAW\nizlCNYQkeiK9UqnUbQ7xVVjK+AKTyYT6+nrU19fTSk5KSgoqKyt93o9MJhNH2GxiYgIDAwN0Loxh\nGERFRVFCFRcX5/M4g8PhQG9vLxobGzkt0ImJiSgsLHRrOXwZIO3Gzi2tnrxVo6KiOETSW1eHzWZD\nc3MzHj9+TJ9HJpNh165dKCgoeOk2HgQ6nQ4XLlzA9PQ0BAIBDh48iJ07d2J4eBhnz56F0WhEREQE\nvvrVr/qcdGJZFk1NTbh16xa1R6iurl7XbPbS0hKHRI6MjLjtyUKhkFbyiW+wVqvF4uIivv/97/vV\nqmO9cDgcGB4epnOQnrpRqqqqvIr7jI2Noa6uDu3t7XSPVKvVKC0tRXp6Ol2bv2j4zW9+g2984xv4\n+te/jg8+WN0QwhfSCADV1dW4fPkyzp49i3ffffd/FWkMA+A6/MTDcmtqlb8OyA/wSBr/+wdUyMa5\nZH/w4MENGWk7w263Q6PR4P79+3TecceOHaisrFxXG8j4+Djq6+vR2tpKb2CxWAyTyUQvFHLRCAQC\nVFRUoLS09KUHSCzL4tGjR7h3796me6mRuThSlZyZmcHY2BjGxsZWrVACyxsoaXt1nal0tRAxm81o\naWnBkydPaMXQGSKRiAbwZrMZra2tNJMdEhKC3bt3Iy8vD3q9HjqdDvHx8R6vA1J5JWTSmVB6M2df\nDVKpFNHR0UhKSkJsbCyioqLcqhFGoxF3797FkydPACy3Re/btw95eXnr8uSam5vjbLpjY2Nu5Cww\nMJDafAwODtLXFxsbi/z8fNTW1mJmZgZ8Ph/79+9HcXGx3+ewyIzp7OwsOjs70d3dzTnPxDdwNQQG\nBnpUgpXJZOjt7aWtUunp6Th+/DiHZDocDuh0Oo5wjSvhl0gkHJIYGRm5JZUY7XY7nj9/jvb2drcW\n6ISEBGRlZWHbtm2cIOXFixc4f/485ufnIRKJUFRUBJFIxJk59FWdNzExEeXl5YiLi3vpQb8nDA8P\n48aNG1SmPi4uDvn5+TCZTGsSqlGpVAgODt6S77kzPNmnJCUlobKyctUAniibEuEy19ZUgUBAlUjj\n4uKgUqn8IqK2UsthQUHBKyXmer2eU4kcHR1dVWAnNDQUT58+RV1dHd0Hw8LCsGfPHmRnZ7+yVmXS\nLXDnzh04HA5ERkbi5MmTnOru7Owsfvvb32JychJBqjpYJQAAIABJREFUQUE4c+bMil05wHKy+sqV\nKzThlJubi8OHD/tNYI+QeWeBHU9t7gqFAlVVVcjOzvbL//UnSEW1q6sL9fX1nP2FYRjEx8fTOUhX\ne4iFhQU0NjbiyZMn9O8UCgX+9E//9AtJGsfGxhAXF4eYmBhotdpV11xfSeP8/Dzy8/MxOzuLyMhI\njoKtP7CVfRo93cEFAP4/LBPKlwEVgL/CcnWzFMD/BdDh8jteSSOBq5ANsOz/tXfvXr8NpPtr3pEc\n75MnT/Dw4UNOO5jzxZKYmIhjx455bGF9mdBqtbhw4QIWFxcRFBSE6upqJCcnb8r/mp2dRVtbG9ra\n2jitJTKZDElJSYiMjITdbvebhUhAQACampqg0Wg474MrRCIRMjMzsX37doyNjaGrq4sGjzweDxkZ\nGSgoKFjRQ9ThcGB6eho6nQ7Dw8MYGBjA7OyszyqApB3PuSpJPvcUDOl0Oty8eZMa2CqVShw+fJjT\nlrIeEGEIUokcHh72eO6Cg4MhkUhoi3VERAROnjz50nwWgWWZ9MbGRk6GVSqVwmAwgGVZBAcHQ61W\nc/wsfVERDggIQGRkJGQyGXg8HsxmM/W/dCVFMpkMCQkJiIuLQ0JCAkJDQ7c8YXCFxWJBb28vNWsn\n5JvH49HkxeTkJMcXzRucxWjIo7+/n5Lx4OBgKoLC4/GQl5eHsrKydZu8bxR6vR63bt2is6tCoRBB\nQUFuCs4AV6iGVBBflVDNemGxWKDRaFBbW0tbwuPj41FVVeXV38/hcGB0dJSOBAwNDXESNAzDIDY2\nFomJiUhMTKSejpsFk8mEp0+fQqPRUCIvEAiQlZWFoqKiTbXD8hVkHXWejXTt6nBGSEgIysrKkJeX\n90qTKHq9HpcvX6YdXkVFRdi/f7/HaqfJZMKFCxfQ19cHPp+P119/Hbm5uR6f99mzZ/joo49gMBgQ\nGBiIY8eObYplkSsMBgMlkSQxarPZwDAMqqurkZWVtenHsF44HA6cO3eOo3nhjOjoaOoHGRUVRdch\ni8WC5uZm1NfXY25u7gvt0/id73wH7733Ht5//30O8SNYWlpCR0cHdu7c6ZE0vv/++2BZFt/+9rc5\nf0fmG4nllD/hiTTq9Xq0tLTg6dOn+JM/+RPgFZFGT9HqDIAfAfg3/xzOimAANAH4AYDbADIBXAOQ\nCsD5XViVNBIsLS3h/v370Gg0cDgcEIlE2LNnD0pKSvzWwjExMYFbt26ta95xcXERTU1NePLkCQ20\nAwICEBQUxMl4CYVCFBcXo7i4+KWosK2GxcVFXLx4kbb/lJeXo6Kiwi+bl8FgQEdHB9ra2qhZL7A8\nq7F9+3ZkZ2cjNjbW67l1tRBxnaVcybvL2UKEYRifK5vAchAyOzsLmUxGb/CQkBAUFBQgKysLRqMR\nY2Nj/z97bxrVVppejW7NAjHPCBDzPE9iNuAJD7g8lqs7qeopWblJd9bN+laq0umkM/TNTaqz0p3b\nWfd+q75O0l09Vjp2GbvKVcambDObyUwWIGaBGM1khEBoPvcHfd7WkcQsA+Wv9losjCzEkXT0nnc/\nz372xszMDGZmZvD8+fMtFxdasiaRSODj44OVlRXSnVxYWLC7SbV8raxlrrSToFwux2effUZkcqmp\nqThx4oRDOsbWs11sNhsuLi5YXV21IcN8Pp9hsBMcHHxglX+1Wo3W1lY0NzcTUsjlcslnjH4tKIqC\nRqNhSGCfP38OuVxuY7KwFWiHP5rkWzvBurq6HkiXwFGRMDqdjnQK6U7q4uLilgTb0ozGUla6mYx8\nZGQEFRUV0Gg0cHFxQWBgIIaHh8l5lZGRgaKiok1t9R0Fy5D4zs5OTE5O2t1Q0TJtyy7iUTCq2SsM\nBgOePn2KxsZGsgaGhISgtLTUJl6A7nbQncTx8XGbz4e/vz8hiaGhoTbdooOIK6JHTFpbWxljISEh\nIZBKpYiPjz8y7xdtfFdXVweFQrFpMZE22KFlrX5+fgdGIgcHB/HRRx9Bo9HA2dkZFy9eRExMzJa/\nYzab8eDBAxKYXlhYiOPHj5PrucFgwGeffYa2tjYAGyqGS5cuHZjzqzVMJhMaGhrw/vvvIyIiAtev\nX9/RvPphgaIofPzxx2SmFNhwpl5cXGTsfdzd3UkHMjQ0lMxF9vf3IzEx8ZUljVqtFufPn0dzczPe\ne+89vPnmm+Tz0tnZiXfffRf/9m//Bjc3N7i6uiIzM5OciwDw7rvvwmQy4bvf/a7NY9PzjTst/O8U\nNGk0mUwYGhpCZ2cnhoaGyHv02wjCQyGNlwHcdtQf3gNOAfgIgBsAevcxAOCvANyyuN+OSSONhYUF\nPHz4kLSN3d3dcfLkSSQmJjps3tFaFhsREYGysjK7A/jT09NoaWlBb28vIQ5+fn6IjY3F4OAgMcmR\nSCTQ6/WkO8PhcJCSkoK8vLxD19abzWbU1dWR0POwsDBcvXp1T6RWr9ejv78fMpkMIyMjjPDxuLg4\nJCcnIyIiYt8XdJoE2HN63UmEyHZQKBRITU0Fl8uFWq3esfQO2CCYdCZTaGjotrN0dMQATSLp71tJ\n/thsNumq0vNWdDGFzpDby2tsT7Kdnp6OkpISjIyM4N69ezAYDBAIBAgICMDy8rJd0uvl5cUgkS9r\n061Wq3Hjxg1MTk4SYku/92w2G4mJiXZzTnt7e3Hnzh3iQmo2m+1KyujYFb1ej9XV1R2dB66urpvG\ni7i7u0MoFO57rdrNxpz+rFhHWMzPz29pvGSvKioUChEfH4+kpCSEhYXteFOrUqlw8+ZNTE1Ngc1m\no7CwkKgPgI31MDMzE4WFhQ6Tya+srDBmEDczqnFzc4NEIiEEMSAg4EgZ1ewVRqMR7e3taGhoIIXM\noKAglJaWMpQTy8vLhCTaizny8vJCWFgYIiIiEBYWtu3oxkFn3C4uLqKtrQ1dXV2E4Lq4uCArKwuZ\nmZmHWpxdWlpCY2Mjurq6yPoSHR0NqVQKAIxOmHUR1NpgJygoyOGGOEajEVVVVWQzvZeZ9La2NlRW\nVoKiKMTHx+Py5ctYXFxERUUF5ufnwWazcfz4ceTl5R0JOfoPf/hDrK6ugsPh4Etf+tK28UuHCYqi\n8Omnn5KRFGBjljwsLAwDAwMYGBhgfF6dnJwQHR2NgIAAaDQanDx58pUljcDG+fvjH/8Yv/jFLzA3\nN4fw8HC4ubkhNTUVf/EXf4Hu7m78/Oc/x3/8x3+Ay+Xie9/7Hq5fv46Kigr84Ac/AAD8zd/8Df70\nT//U5rGvXr2KW7du2dy+H7BYLDx48ADPnj0j7xubzUZMTAzS09MRGxsLHKHIDWcAxQAqHXAs2+Hv\nAVwDYNn/vwtACeBbFrftmjTSGB0dRVVVFSFlwcHBKCsr27dEj8Zm846lpaUQCASQy+VobW3FxMQE\n+Z24uDikp6dDoVCgpaUFFEXBw8MD58+fR1RU1KZRG9HR0WQhOEy50+joKCoqKrC2tgaRSISrV6/u\nKOiWnpGSyWTo7+9nOJ9GRkYiOTkZsbGxB7YRW11dRWNjI8OMg8/nw2QyOVxuAPzOMjssLAyhoaEO\ns/+nKApqtZpBJHfSnQR+N1sUGRnJcHbdyqFucHAQVVVVRPYVHh6OsrIyuLq64tNPPyXRGgkJCSgv\nLyfPU61WMyRAtAzI+njouS96I7TfzZxSqcSNGzewtrYGNzc3XL9+HWKxGEqlEq2trZDL5eSCSYdF\n00659mS3AQEBjJlE624pRVEMuau9r+3cb4GNAoo1kbSesdyLxI+iKKysrNglh5s51HI4HEa2oY+P\nD2ZmZvDkyRNQFIXAwECUlZVhYmICPT09jMBqFxcXJCQkIDk5GUFBQduuXSaTCVVVVaQzkZKSgpyc\nHDx58oQYKXG5XGRlZaGgoGBX5wddOKEJ4tTU1JaydNqZMisry+FxHYcN2lylvr6enI+BgYEoLS1F\nVFQUNBoNFAoFIYrWc9guLi6kkxgeHn5o8uHdQq/Xo7u7G21tbcSBlC4cSaXSHZ2jjsLz58/R0NCA\n3t5esgYlJiaioKDAroTWciaP/rI3H+/n58eYjdxPbNLc3Bxu3bqFubk5sNlsnDhxAnl5eXt6vJGR\nEdy8eRM6nQ6urq7QaDQwmUzw9vbG1atXj4RsmAZFUXjw4AFaWlrA5XLxe7/3ezva5xwWKIpCZWUl\no0uWlJSEixcvgsPhYGpqCnK5HL29vTb7gldZnvp5BIvForuJ8PX1RXp6OlJSUkgh7iCNcPIAfLDN\n74sAdAA446gD2gL/C0AKgHyL234FwBXARYvb9kwagd+5OT5+/Jiw9uTkZJw4ccJhEgjreUc64Jqu\naAoEAmRkZCA7OxsLCwv49NNPiWtjbm4uSkpK7JKlxcVFNDc3o6uri2ywAwICkJeXh8TExEOT1qjV\nalRUVJDh4uLiYhQVFdmQDYqioFQqIZPJ0NfXx9iUhoSEIDk5GYmJiQdqULCyskLIIk0OuVwug8A4\nOzsjNjYW4eHhcHFxgVKpxMDAgE1g9W4RFBSEvLw84ib6skF3J60J5dzc3KbEmO5OWju7mkwm1NbW\nkrk1b29vnD59GtHR0VAoFLhz5w7UajX4fD7OnTuHlJSULTcWJpMJc3NzDKdWe0Yi7u7ujG5kQEDA\njsgSRVFoa2vDgwcPYDabERYWhmvXrjE6IKurq5DL5ejo6LAbpg5sdJjojllISIhDqvgmkwlqtXpL\nYrmVrJqGi4uLXUJJf2m1WhtyuJWrL5/PZ+Qa0t89PDzI+arVanH37l1SHMjOzsbp06cZ74kjMiBl\nMhnu3r0Lg8EAPz8/XL9+HUajEbW1tZDL5QA2PrdSqRT5+fk2nS16ZsySJG5mVBMQEACTycToxJeU\nlOxpXv2ow2Qyobu7G3V1dWTz6O/vj4KCAvB4PIyNjUGhUNiYhAkEAgZJ9PHx+VzNalqDoiiMjY2h\ntbUVAwMD5LMvFoshlUqRmJj40uYuJyYm0NDQQAxf2Gw2UlJSUFhYCG/v3dlJ0MU4mkRuZbBDF+LE\nYvG2z83axdTLywtXr16FWCze3ZO1gkKhwAcffECutwkJCbh06dKhOcBuBcsOHo/Hw1tvvbUnF9eD\ngiXRpSGRSJCXl0fiOywLlrRE9QvSeLTAYrFw9+5dpKenQywWM9ZZs9lMX5MOhDRyAfw7gJ//9n5f\nwcYs4bTFfSIBhAH4G0cd0Bb4/wAkY6OzSeMDbBBXh5FGGjqdDg0NDWhqaoLJZAKXy0VeXh4KCwsd\n0t2anZ1FTU0Nw0mJw+EgPT0dJ0+ehNFoxP3794mhQkBAAC5cuLCjRVij0aCtrQ2tra1kWN7NzY0E\n1R9GPpPZbEZNTQ3q6+sBbEhWrly5ApFIhOfPn5NNo2VVy9fXF8nJyUhOTj7wyvSLFy9QX1+Prq4u\nuwuki4sL4uLikJCQQDT/1piYmMCDBw8wNTUFAAzbeGBjEysSieDi4gKTyYSVlRW75gZsNhuBgYFI\nS0tDXFzcgUujaFdUWhJFE0iBQLDt7B6bzYZYLEZsbCy8vb0xMDCA7u5uABuFgMuXL+8q088SGo2G\nQSLtWaTTZiOWRNLant9gMOCTTz7Bs2fPAGxIdU6ePAm1Wo2xsTHibEpLy2lYSy1ZLBZSU1ORm5t7\noAY+AOx2Ky0jRlZWVra90FufnzScnZ1tIix8fHy2dfWcmZnBzZs38eLFC/D5fLz22mtbmlXQGZA9\nPT3o7e1lbFh2kgE5NzeHGzduYHFxEXw+H5cuXUJ8fLzNWkubnPj5+WF+fh7T09N2M0e5XC4CAgIY\nRjXT09N4+PAhOba0tDScOHHiSMySOxJmsxnPnj1DbW0t6U55eHiQqJ7NHE5pkhgYGOjQQtdBy1O3\nwvLyMtra2tDZ2UkKm87OzqTQ64g5WoqiMDo6ioaGBlJ443K5yMzMRF5ensMK2EajEdPT00TSqlQq\nba5B9BoeHBwMiUSC4OBghtRUo9Hg448/Jp+vtLQ0nD17dt/7pL6+PnzyySdYX18nhIXH4+Hy5cuI\nj4/f12M7GvT5SVEUPvroI3R3d0MgEOArX/nKvonzy4Q94mgJNzc3xMfHIz4+HiEhIUSB8wVpPDpg\nsVjo7OyEv78/GUsbHR2FXC7HwMAAvv3tbwMHKE91AUDrcf4UG8TNGjUAShx1QFvgrwBcB5Bmcds9\nAGMAvmlxG/XVr34VYWFhADYudGlpaeSCU1NTAwA7/vmTTz5haL9nZ2eRkZGBP/iDPwCbzd7V45nN\nZvziF79Af38/kS8pFAr4+PhALBZDrVZDoVDAw8MD/v7+0Ov1UCqVSE9Pxze/+c1d/z2j0Yif/vSn\n6O3tJa6qk5OTiImJwR/90R/B3d1916/Hfn/+9a9/jfr6ehJGTUu+6M3q3NwcIiIi8Oabb8Lf3//A\nj6+iogJPnz4lRgy0mU94eDhcXV1hNBohkUhw/fp1u+9HdXU1pqamyEXf8vetc8GsH3+nP9OzWj4+\nPpidnYW7uztKS0vh7OxMjr20tPSlvD6VlZWMruvs7Czi4+Nx7NgxdHd3o7a2Fmazedvnk5iYiJCQ\nEExNTcHd3R1nzpyBt7c3uXjt5fjMZjPu3LmD+fl5BAQEYHJykshvLP++s7MzSkpKEBwcjIGBAchk\nMri7u4PL5YLFYsFkMsHV1RUqlYpx/DweD6urq/D390dGRgbq6+sxODgIFxcXZGdnk64LAJSWliIn\nJwfT09PEZe1lvB87/fnYsWNQq9W4f/8+1tbWEBMTA5VKhebmZqytrcHf3x9KpRIeHh5wd3fHiRMn\n4Ovri76+PgiFwl39PYqi4OLiggcPHmB4eBheXl747ne/Cy8vr10dr1KpxAcffIDx8XGy8VIoFMRZ\nNzExkazN9O9XVVXhyZMnhMzS8ziRkZFEKq3X623OR9pteXFxET4+Pnjttdfg5+dHilxxcXGorKwk\nM9oFBQU4e/YsMUw57PfXUT8/fvwYCoUCGo0GS0tLUCgU4HK5RIZt+XoFBQVBpVJBLBbj2rVr4HK5\nL+346NsO+/Wx/NlgMOBnP/sZ5HI5IXFjY2MIDQ3F17/+dUgkEnK+7PTxq6uroVQqodPpMDMzA4VC\nAT6fjy996UvIyckh69nLen7V1dVQq9UIDQ3FxMQEHj16hBcvXth8XtLT0xESEoKhoSGMjo5CLBZD\nIBAQQ6P9HI/BYIBGo0FXVxcUCgWCgoLwzjvvoLa2Frdvb9hq/OEf/iEKCgp2/foexPlpNpuxtLSE\n3t5eTE9Po6ysDFeuXDnU47P+OT8/H8PDw7h58yYmJiZIR5R+f2NiYnD+/HksLS2BxWIxfr+0tPQL\n0niEYClPVSgUmJ2dJXP2y8vLdJH+UGYafwzgzwBYTv1fAPAeAMcM/W2NPAAPsGGEQ2MEwHcA3LC4\nzSGdRmtYd40CAgJQVlZGyOlWWF9fR0dHB9ra2kgnjc/nIz09HVKpFF5eXjCZTKipqcGTJ0+IXMTN\nzQ1vvPHGvitVtBFPU1MTqVqyWCwkJSUhLy/vwGYDNBoN+vr60NnZienp3zWsuVwuUlJSkJKSAolE\ncuAyJpPJRMKQrXOYXF1dScbcVvMrBoMB3d3daGpqspG18Xg8SKVS5OXlQSAQQKPRYGZmBkNDQxgf\nH2fEhdD35/P5MJvN0Ol0u3bbYrFYcHJygrOzM5ydnYn5ikgkIrdZfolEol3LfSYnJ1FZWUneR8tc\nw7i4OJw4cQI8Hg8LCwt4+vQpkXTRFePNIBKJ4O3tzXB1tZY87gZarRZTU1OYmJjA1NQUJicn7RqX\n2INAIEBoaCiJvwgICACLxUKNRcc8KSkJFy5cAJ/Px+LiIlpbW9HV1UU6nh4eHpBKpUhPTz+UDv9B\nQ6fT4e7du2SeMDMzE2fOnNmXdG+nGZBCoRBqtRpTU1Noa2tjFGmswePxyOPweDzk5uYiPz/f5j2i\nc0w7OjpAURScnZ1x8uTJPeWYHmWYzWY0NzfjyZMnmzpCb+dw+r8raF8BeuaZXt/8/f2RnZ2NlJSU\nbddXk8mEnp4eNDQ0kOuBs7Mz8vLykJWVdahrh+UaSnckrRUdljEptLR1L8c8OTmJiooKvHjxAlwu\nF6dOnUJ2djZRdTQ2NuLRo0cANpy9y8vLX2ocy15hMplw8+ZNDAwMQCQS4Wtf+xp8fHwO9ZjW19cx\nODgIuVyOkZERxoiNv78/BAIBidwCNtbFa9eu2Tjebhcm/wUOFiwWC9/73vc2fU8O0z01H8DPsOFY\nqgUQiw1TmrcB/KujDmgLsLCRz/h/AqgGEPfb7xEALB0ZXgpp/O0DQyaT4dGjR8RNMS4uDqdOnbKb\njzg3N4eWlhY8e/aMfEC9vLwglUqRlpZGLromkwlPnjxBbW0tkcLS9xcKhSguLkZ2drZD5mWmp6fR\n1NTEGKYPCwtDfn4+oqKiHL4RMhgMpJszPDxMLqgcDgeenp7kAhkVFYXLly8f2LyiyWTC6Ogonj59\nyjguYIMsJCUlISMjA4GBgVu+JnQ8w9OnT23IiEAgQE5ODnJzc7c0xtBoNBgeHsbAwACGh4cZF2QX\nFxdERUVBIpHA2dkZ/f39GBgY2NSEZK/gcrmEQNojlpYE09nZGU5OTpiYmMCdO3cY5grR0dG4ePEi\nRCIRVlZW8NFHH5GMroyMDJSVlQGAXWdXe7mFNNhsNoNMWn7fiemI2WzG8+fPMTY2hsHBQUxMTGxp\nYCQUCokxRHBwMIKCgmA2m1FRUYGhoSGwWCycPHnSrskDnfvW2tpKihA8Hg+pqanIyck59M3Dy8Ls\n7Cxu3ryJpaUl8Pl8lJeXOzzw2mAwkAzIoaEhxntoWbiwBu0snZiYCLFYDCcnJyiVStTU1BByKRQK\nkZ+fD6lUCh6Ph/b2djx+/JiYluXk5KC4uPiVIf+0w2l3dzcmJydtijkeHh6IiIggRHE7h9MvsDED\n397ejvb2dkK+hUIh0tPTkZ2dbSOtNhgM6OrqQmNjIykou7u7Iz8/H+np6Udydm9+fh43b94kxkBC\nodBuIc7Pz49IWrcz2DGbzaivr0dtbS0oioK/vz+uXLli111eLpfj9u3bMBgMkEgkeOONNw7U52Cn\nMBqN+M1vfoORkRG4urri61//+p5HMfaK1dVV9Pf3Qy6XY2xsjPEZDwkJQVxcHOLj4+Hp6QmKolBT\nU4O6ujpyHxaLhXPnziErK4tx2xek8eiA7jQGBQUhJiYGfn5+0Gq1eP78Oebm5vCVr3wFOET3VDcA\nb2IjI3ENGzmJ9Y46mB0gAsDfAmgFIAXw/wJot7rPSyONNAwGA5qamtDQ0ACDwQA2mw2pVIri4mLw\n+XwMDQ2hpaWFUemOioqCVCq1IWaTk5O4e/cuMRJITU3F6dOnsbq6igcPHpANt6WRiCOI3fLyMlpa\nWtDR0UFIio+PD/Ly8pCSkrKv6p3ZbCadAblcTogAi8VCZGQkkpKSEBcXB4FAgKGhIdy+fRvr6+tw\nc3PD1atXIZFI9v387MFoNGJkZARyuRx9fX02BEUsFuP48eMM6/jNMDMzg+bmZshkMpsF1MnJCbm5\nuZBKpYwNZs0O5nKMRiPGxsaI9bXlXBefz0dkZCRiYmLg7OyMvr4+9Pb2MrIELQ2VaLBYLJIr5OTk\nBC6XC51OB41GA41Gg7W1tX05wLLZbAiFQjILw+VyIRaLMTs7C71eD6FQiPPnz28bYUM7ddpzdt0q\n7kQkEhECaenqur6+DqVSSb7szV/6+fkhLS0NTk5ODMdW67keFosFNpsNk8kEHo+Hs2fPbtttMpvN\nm64FOTk5iIyMPFLdqp2cn/ZAURQ6OjpQWVkJk8kEPz8/vP766w4lx7RRjaWTqbUqgAaLxYK3tzfJ\nGXv06BEx4Tpx4gTy8/MZr/vY2BhqamowPj4OYONzxufziVNqeHg4zp49e+gxRvvF2toaicAYHR21\ncdJksVgQi8VIT09HZGTkkXI43eu5eVgwGo3o6+tDa2srUScBG7I/2nX16dOnRB4ObFzjCwsLkZyc\nfCQNlSiKQnd3N4lIcnd3x5UrVyCRSLC6uspwaZ2ZmbG5pjg7OzNcWmmDnRcvXuD27dvENT4vLw/H\njx/fcg8yMzOD//qv/4JarYanpye+/OUvH+rnc7Pz02Aw4Ne//jXGx8fh7u6Or3/96y89U3J5eRly\nuRxyuZzhxM9isRAWFob4+HjExcVtGoFSW1vLkN0CG3L8EydOgMVifUEajxhYLBZ6e3vBZrOh1Wqx\nvr6O9fV1aLVaaLVaXL16FThCkRvAxoxh17b3Oji8dNJIQ61W4/HjxyQolcvlgsfjkS4Qj8dDWloa\npFKpzQZKp9Ph8ePHxCre09MT5eXliIiIsHwiGBoawoMHD4jkMTIyEqdPn7ZbgdsLtFot2tvb0dLS\nQgiKSCSCVCpFVlbWjit4FEVhcnISMpkMvb29jE13cHAwkpKSkJiYaNcwQqVS4cMPP8Tk5OSmG7u9\nwmAwYHh4mAwF2zNKSUlJwfHjx7c1szCbzRgcHERzczPZYFpCJBIhPz8fWVlZdk0AdrvxoSgKMzMz\nGBgYwODgIMnjBDYWColEgoiICJhMJvT39zMcDH19feHm5obV1VW7Jh8+Pj6QSCSkCiwSiQiJtP5a\nW1vD+vo6VldXsbCwsGN5pzU4HM6OupiWX/TmSa/X2+1MLiwsbBkabwmhUAiz2Qy9Xg8+n4/Lly/b\nDWKmjX9oKdbw8LBdgiIUCkkXcrvMM3uqA29vb+Tk5CA1NfVIZPjtZWOu1+vxySefkGzE9PR0nD17\ndl8dEtop1zILcSujmqCgIHh5eWF1dRUKhQKTk5PkPkKhEHFxcTAYDEQyGxcXh4sXLzLeK4qi0Nvb\ni8rKSrJ2sVgspKSk4Ny5c0fi/dktdDodxsfHMTo6irGxMUa0iSVoRURhYeGR7GwBnz/SaImpqSm0\ntrYycpctN96BgYEoLCxEXFzckcgctAetVotPP/2UGPMlJiaivLx80/XOaDRiZmaGQSStZc9sNhvu\n7u5QqVQwm80QiUS4cuUKYw+0FVZWVvCb3/z8ZIYEAAAgAElEQVQGMzMzEAgEeP311xEZGbm/J7pH\nbHV+6nQ6/OpXv8Lk5CS8vLzwta99zWG5sTTm5+chl8vR39+PmZkZcjuHw0FkZCTi4+NJsXknqKur\nQ3V1NeM2OpKDx+N9QRqPECxnGu3hoOWpbwOowoYs9BsASgFYni0cAFnYkKoeFRwYaQSAhYUFVFdX\nM/Lb2Gw20tLScOrUKbuL6sDAAO7du4eVlRWwWCzk5+ejuLh40wu2yWRCa2sramtrodPpwGKxkJWV\nhZKSEofJMkwmE3p7e9HU1ETICZfLRVpaGvLy8uzKb4Hf2eXLZDJG5drHxwfJyclISkra9Het//6j\nR4/Q1NQEYKMie+nSpT3lnen1egwNDaGvrw9DQ0N2JY98Ph95eXnIycnZ9m/o9Xp0dnaipaXFLnlw\ndXVFQUEBMjIyXuqma3l5GYODgxgYGLCRmtBmSlqtFgqFgjxnJycnElmgUqkIEbImWq6uroRESiQS\n+Pn5kQ2M2WxGR0cHqquryYY6OTkZeXl54HK5hFxOTk6io6PDhlTSF5mdkjtLCAQCG2Lp5OQEPp8P\nnU6HlZUVzM3NYWlpaVezn05OTvDz87ORu1rOTprNZjx+/BiNjY0ANgo2oaGhZDNkL7PPx8eH4dTq\n6+vL2AhqNBoy30x3Ty0jdg5avrQfPH/+HDdv3sTi4iJ4PB7Ky8uRkpKyq8egKAqLi4uMqIvZ2Vmb\nc4XFYsHPz484mQYFBcHX19duR2Z5eRk9PT02GZBCoRAGgwEmkwmenp5444034O/vD6PRiCdPnhDl\nCF3coItoLi4uKCwsRGZm5pGcn6JhNBoxOTlJDLhoQy4abDYbPB6PdNxFIhGKioqO/PN6FbCysoK6\nujp0dnYy1ikul0u8DY6qbH1iYgK3bt2CSqUCj8fDuXPnkJqauquiLkVRePHiBSGQSqWSyFst4eHh\nwehGWl6H7MFgMOD27duQy+VgsVg4e/YssrOz9/Q8Xya0Wi1+/vOfY3Z2Fr6+vvjqV7+6L7k3XVCm\niaKlLwKfz0d0dDTi4+MRFRW159njhoYGMj9KS/9pk6cvSOPRAYvFwk9+8hM4OTlBKBTafE9LSwMO\nkDTewcYc4x0Al7AhDe3+7e9R+B1pTHDUATkAL500UhSF4eFhtLS0YGRkhNzu5+eHtbU1UlGz7grS\n7oV0ZplYLMaFCxcQEBCwo7+r0WhQXV2N9vZ2UBTl8HlH+rkpFAo0NTURZ0Bgozqfn5+PkJAQrKys\noKenBzKZjNH9ok1jkpOTiWnIbjEwMIA7d+5Aq9XC3d0d165dQ3Dw9j5LOp0Og4OD6Ovrw/DwMGPT\naTkjKhKJiLnAdoupSqVCa2sr2tvbyUbL0sjF3d0dhYWFSEtLO/BNl1arxfDwMAYHBzE4OMiQXjo7\nO8Pb2xtqtZpB5CUSCTIyMhAbG4uFhQWMj4+TC7j1jKRAICAdyPHxcfI4EokEp0+fRlBQELmvyWRC\nXV0d6uvrQVEUAgICcPHiRQwODpKNOJfLRW5uLtLS0qDX6xldzM06nBqNZk8XJ4FAABcXF4hEIrDZ\nbLx48YLMC3G5XJhMpk0fl8PhwMvLCx4eHpifn8fy8jJYLBaOHz+OgoICck7TUlrLyA97kiw+n4+g\noCAGkXR2dibd4ZaWFiIhYrFYiI2NRU5ODkJDQ4+UdNUanZ2duHfvHoxGI3x9ffH6669vKw+jKIoY\n1Vh2Ee3Jhr28vEjMhVgsRmBg4J4KMptlQAK/MwObnJwk/5eQkIBTp07B3d0dw8PDqK6uJpV7V1dX\nFBUVIT09/UiQLLPZTBw2FQoFlEolY91jsVgICgqCp6cnmW8BNtaHgoICZGdnH9nO4quCxcVFNDY2\noru7m1w3oqKiEBwcDIVCwVCsREZGkhGWo9BxtJ4zFIvFuHLlyq6zIa0xNjaG27dvY2VlBRwOB1FR\nUTAYDHYNduj103K+3LoQT1EUHj9+jIaGBgCAVCpFWVnZkXgNLaHRaPCzn/2MuHt/5Stf2VVR3Gw2\nY2JighBFy3gyJycnxMbGIj4+HhEREQ5bn548eYLPPvsMwO8itr7IaTxa2E4u/Nt9xKHIU3nYML7p\ntLpdio0Zw6OCl0YadTodMbig5aJcLhepqamQSqXw8/OD0WhEa2sr6urqSFcwPT0dPj4+pFPI4/Fw\n/PhxSKXSPS1sc3NzL3Xe0fLvNDU1QSaTbZrNJxAIkJCQgOTk5E3zCneL5eVlfPjhh5iamgKbzcbJ\nkyeRm5tr89zW19cxMDBA3MAsN+xeXl7QarWkM7abbuDU1BSamprQ19dHPoyWJhteXl4oLCxESkrK\nrsj6y5JYmUwmKJVK9Pf3Y3BwkEEUORwOXFxcsLq6So5fKBQiJSUFGRkZ8Pf3B0VRDBI5Pj7OuCDR\n8Pb2RmxsLEJDQxESEgInJycsLi7i9u3bZG6noKAApaWl5HVRqVR4+PAhkTW5u7vj9OnTiI+P3/Jc\nXVtbI9I6ew6zwMaFUiAQkFnD9fX1HYXcW4PNZpNiwFbdSicnJ3h7ezOyCr29vUl30mg0YnZ2lkEk\n7b2OXl5eDBJpMpnQ1taGnp4ehvNiTk4OkpOTD4yg7OT81Ov1uHfvHsna3CqTbX19nTGDOD09bbc7\n6+rqSsghTRT3ojDYCpYZkD09PTbH4ezsjLKyMptOKUVRGBwcRHV1Nelaurm5EfJ4kLNn9OeUlpuO\njY3ZdPX9/PwQHh6OiIgIsNlsNDY2EsdsJycnYvTzeZPbft7kqbOzs2hoaGBcQxITE1FYWMgoEs/O\nzqK1tRUymYwQfk9PT2RnZ5NZ68OASqVCRUUFcdPMz8/H8ePH93W+m0wmVFdXE+VGUFAQrly5QpRI\nZrMZ8/PzDEmrPWUPbbBDE0kvLy+wWCx0d3fj7t27MJlMiIqKwtWrVw/MtGqn5+fq6iref/99LC0t\nISgoCG+99daWxWuTyYSxsTFCFC0lvnRWdHx8PMLCwl4aSW5ubsaDBw/I33z77be/II1HCEeZNFqj\nAIArgPsOOhZHweGk0Z6Vvru7O7Kzs5GRkWF3YddoNKipqSG5SjQiIyNRXl6+b5MBejNTVVXFmHcs\nKytz2EA47VTY1dWFkZERxonJ4/GQlJSEkydPvhTnMpPJhM8++4zk9sXFxeG1114DRVHEDWx0dJSx\nyZdIJHBxccHExASRlnl4eKCwsBCpqalbbr7NZjP6+/vR3NzMGB637FL6+PigqKgISUlJe1qgD2Lj\nQ1EU5ubmiJGOZbQJwIwaADbmTTMyMpCYmAg+n2/TzeZwOHByctp0s7+2tgaz2QxXV1dcuXJl0wia\n8fFxVFZWko13eHg4zpw5Q7rwKysrGB8fJ1/WJJHNZiMoKAihoaGEtNq72BqNRmKAc//+fayuroLH\n4yE+Pp7EnVh3OXcbaWIPQqEQIpEIbm5u8PT0hK+vL/z9/cHn87G0tITZ2VnSYbOWXnK5XAQFBcHP\nzw8ajQajo6OM0PDMzExkZ2c7fA7GGtudn5auiVwuF+fPn6elL9Dr9ZiZmSHdw82MaoRCoQ1BdEQY\n+k6h0+lQU1ODlpYWuxfaoKAgMn9t+XrT605NTQ3p2Lm7u+PYsWNITU19aeRRpVIRualCobD5HHp6\nehJ3U9rhdHJyEtXV1aSoKBQKiRT/8xqT8XkhjRMTE6ivr8fQ0BCAjXUrNTUVBQUFW3bo1tfX0dnZ\niba2NlL04/F4SE5OhlQqhb+//4EcPwD09vbik08+gVarhYuLCy5fvrzjOcPNsLCwgIqKCszMzIDF\nYqGoqAjHjh3b9nNjabAzOTmJ6enpLQ12+Hw+qqursb6+Dl9fX3z5y18+EMn/bs5PlUqFn/3sZ1he\nXoZEIsGbb77JKGQbDAZi2Dc4OMgoDHl4eCA+Ph7x8fEIDg4+MDVKa2srKisrAeCLTuMRw1EmjZ0A\nfgDgA2zEXnwfG4RxDMD/cNQBOQAOIY10OHtLSwu5AABAaGgocnJyEBsbuyVxMJlMaGhoQF1dHWNT\n6uHhgVOnTm3badkpHD3vSAc4y2QyyOVyQpJZLBZCQ0Ph6uoKpVJJOihCoRBZWVmQSqUvZVMrl8tx\n584d6PV6G2kh7QYWExNDDH3oTZW3tzeKioqQnJy85fuk1WrJvKKlhJHFYhFy5e/vj6KiIiQkJBxp\nyaA9rKysEAnr6Ogo44Jrudjw+Xz4+flhbm4Oer0eLBYLmZmZKCkpgUgkwvr6OiYnJzE+Po6xsTGG\nIyANd3d3xlykr68v4/Uym82MGANgg4gbjUYbJ0cul4uQkBCSkRgUFLRjKZ1MJsPHH38Mo9GIwMBA\nXL9+fdMiDUVR0Ol0WF1dRU1NDTFLEYvFCA0NJU5ka2trWF1dhUaj2VM3k8Vigc/nM7qjtEzXXnyK\nk5MTKIoirxOLxUJiYiJycnJ2JNd2NLq7u/Hpp5/CYDDA29sbpaWljE7i/Py8XaOawMBABkGkuwIH\nDdr58eHDh6Ran56ejri4OHz88cd2swktMyDpwiBFUejr60NNTQ0pbHh6eqK4uHjbtWYnWFtbw9jY\nGCGK1sRbJBIRghgREcE4r6enp1FTU0OuVwKBALm5ucjNzX1lYkKOIui9Qn19PZGbcrlcZGZmIj8/\nf1dFEdpxubW1lZB+YONczM7OfqlmOXq9HpWVlcTYLyYmBhcvXtxXUZiiKLS3t+PBgwcwGo3w8PDA\n5cuX9+yQvlODHVr5sZXh2WHixYsXeP/996FWqxEREYHLly9DoVBALpdjeHiYUdj19fUlRNHf3//Q\n9iBtbW24d+/eK08aKYrCr3/9a/z7v/87OWf7+vpI1/2DDz7Ae++9h/r6egQFBeGdd97BH//xH9uo\nN2QyGf71X/8VP//5zyESiVBWVgYWi0Xiv1paWvCDH/wAf/Znf7av4z3KpPFPALyHDdObLgD/B4Bf\nAPgDAD9x1AE5AFRjYyOioqJsNq07gV6vR3d3N1pbW8mmgMPhIDk5GTk5OTuaP1Qqlfjkk0/IoDdt\nYV5bW0tuCw0NxenTpyEWi3f59OxjbW0NNTU1e5p3pKVb9OyP5SIsFouRnJzMqLzTXbmmpibiVEi/\nRnl5eQ5xdlWr1SQaQ6lUMj4UPj4+yM3NRUREBHp6etDc3ExkqDTBi4+P3/Li+uLFC7S0tKCzs5OQ\nACcnJxiNRrJgi8ViHDt2DDExMZ87smgPer0eIyMjxI11s6xH2iQoLy/PpjMxPDyMjz76CKurq2Tg\nXq/X2420EAqFxJ3V3d2dEM+xsTFGlAiwsckKCwsjnUSxWLzr7o11dzotLQ3nzp3blmyura3hww8/\nxNjYGNhsNs6cOYOsrKxN33NaCkt3LFUqFebn57G0tASVSoXV1VVotdo9kcudwMnJCVFRUYiLi4Ob\nmxsxCRIIBA4/T/V6PW7fvo3+/n4AG1V9nU5nU+1nsVjw9/dndBE3M6o5aExPT6OyspKsVcHBwTh7\n9ixZe9fX13H79m1Ctry9vbG8vEyeI5vNRlRUFJKSkhAbGws+nw+z2Yze3l7U1tZicXGR/F5xcTES\nExN3vLHX6XRQKpWEJFo7nAoEAoSFhRGiaO+aNjs7i5qaGgwMDADY6FDl5OQgPz//0OSN/zuA7j7X\n19eTuVeBQACpVIqcnJx951rOz8+jra0N3d3dZC1xc3NDVlYWMjMzHarwmZmZwa1bt7C4uAgul4vT\np09vuQbuBGtra/j4448xODgIYCNO7OzZsw7tdls6XdNf9lyCnZ2dERkZSWSt/v7+hz7zODk5iV/+\n8pd2rxNisZhEYxyWQZLZbLaJcOjr68PFixdfWdJoMpnw1ltvobKyErdu3cLx48fJ//3oRz/C22+/\njYqKCnA4HFy4cAHvvPMO/vmf/3nTx1tbW4OrqytKSkrw+PFjxv9VVFRgYmLilSaNfwngATYI4jSA\n8t/e/j8BfMtRB+QAULT9rJubG6KiohAVFYWIiIgtF6sXL16gtbUVnZ2dZPPr6uqK7OzsHS/QWq0W\nDx8+RHv7RnSkt7c3ysvLiWSP7rTU1NQQkpOamooTJ044rEv3/PlzPHjwgOTCeXt7o6ysDNHR0Tb3\nXVxcJM6ntMQV2Ji5Sk5ORnJy8rZD7xMTE3jy5AnZVAIbg/55eXkIDw/f1UVHpVIRomgpEWWz2SRa\ngn5ePj4+UKvV5L0KCgpCUVHRlgSPoihMTEygubkZ/f395IPm7u4OjUZDyGJISAiOHTvm8By9oySx\nMpvN6OzsRG1trQ2Bo8HhcBAfH4/c3Fz4+vri4cOHRG4dGhqKS5cukU4HLYtVKpUYHx+HQqGwyTq0\nBJ/PR0BAANRqNemmBAYG4syZM3uqQq+uruLDDz/E+Pj4jogfjenpady4cQMqlQouLi54/fXXHZYT\nSlEUIZS0EcnCwgKWl5c3Jez7AYvFIrEl9HcnJye7USa0C62lZLu6uhoZGRlEXjo2Nobp6Wm7FyRL\no5qgoCAEBAQcOVOVtbU1PHr0CJ2dG2P4Li4uOHnyJFJSUmzOC4qiUF9fT2zmw8LCEBcXh8HBQSgU\nCvIa8Hg8xMTEICkpiRiWyGQy1NbWkvPYx8cHJSUldpUJtMMpLTedmppiKFE4HA4kEgkhiWKxeNPN\n7dzcHGpqaiCXy8mxZWdno6Cg4EiGne8VU1NTuHXrFjIyMsDhcEgnyd6/d3rbZv/PZrO3XTNMJhNk\nMhkaGxtJYVkkEiE3NxfZ2dkOlwBrtVpSyKav0xwOB0lJSZBKpfsqPFMUhaamJjx69Ahmsxl+fn64\nevXqvgu/w8PDuHPnDtbW1iAQCFBeXo6kpKR9PeZOodPpMDk5CaVSia6uLrsZvzwej8yUSyQSuwY7\nu8FOr+0qlQr9/f3o7+/H+Pg4Y211dnYmBW9HZTnSahVr8mf9b+vvW/kDvMqdxn/6p3/Cd7/7XXz4\n4Ye4cuWKzf+/8847KCwshLu7O44fP46///u/x9/+7d9u+ZhsNtsuadTr9fjv//5vvPXWW/s6ZkvS\naDQaMTc3h+fPn2N2dhazs7P4xje+ARwSacwD8BfYkKP+NQBPAN8EkI+NKI6jAur27dsYHh5mdMzY\nbDZCQkIIiaRnBMbGxtDS0kKqtMAGacjJyUFcXNyOK+VyuRyVlZVQq9Vgs9koKCjAsWPH7M7RabVa\n1NXVoaWlBWazGTweDwUFBcjPz3fIxsvevGNUVBROnz4NoVCI3t5eyGQyxrybSCQizqdisXjXZGlx\ncRHNzc3o6uoiM1sBAQHIy8tDYmLipq/jixcv0NfXB7lczpA8cjgcYhsdExMDoVCI1dVV3L17l1Qu\n6b9x6tSpLQmqyWRCX18fmpubyXNmsVjw8fHB8vIyIYthYWE4duwYwsLCHEYW19fXMT8/j/n5edTX\n1+PSpUuH7oy5srKCx48fEzMTZ2dnZGdng81mY3Bw0K70lF6YaCfR/Px8RjTFzMwMmUdUKpU2Bh32\nqmF0jIJIJMLMzAwhUikpKTh58uSOCymTk5O4ceMG1Go1XFxccP36dYSEhGz7e5bGCcHBwbh+/fpL\nnxukodPpSM6kZebk0tLSltEkPB4PJpPJIXOYwAZ5pwlkR0eHXSUFm80mmaB0J/Eod7BoY6Gamhro\ndDqw2Wzk5ubi2LFj227oR0ZGUFFRAY1GA3d3d7z++utwd3dHX18fenp6GMUsOgMyOTkZISEh6Onp\nQV1dHZFa+/n54dixY/Dw8NjS4VQsFhO5aUhIyLbGR/Pz86itrSVSai6Xi6ysLBQUFGybNft5wuzs\nLKqrqwlxDw8PP5C/a0kgLYklPbKg1WrJ54/D4cDNzQ1ubm7gcrlbktT9kls2m43Z2VkMDAwwskj9\n/f2RmpqKmJgY8Hg8u49Jh7JbQq1W486dO0QGm52djVOnTu1rD2IwGPDw4UOSPx0aGorLly+/9ED7\nrWA5j+fu7k4cta3h6+vLiPvYjZR+K9K4uLhIjGwsr610MVwsFqO5uRl6vR4pKSm4dOkS4+9SFAW9\nXr8p4bMMcrdHBvcDepTCUoH1qpLGlZUVBAcHIyAggLHHtMTY2Bh6e3shEon2TRodBRaLhYqKCszO\nztodEznonMatIASwvzPy5YCiKAoURWF2dhZDQ0MYGRnBxMQE48WkpVz0h2qvlbuVlRVUVlaSTltw\ncDAuXLiwo0rd0tISHj58SCrFrq6uOHHihN1K+F5gPe9oDT6fj4SEBCQlJSE8PNwhcg2NRoOnT5+i\ntbWVkHY3Nzfk5OQgIyMDQqEQi4uLhChaBtFyuVzExMQgPj4e0dHRZIOnUqnw5MkTdHR0kA0Xn8+H\nXq8Hh8PBmTNnkJmZadddtb29nZGJJxQK4eXlhbm5OfJYkZGROHbs2L46TBqNhpBDyy97BjJubm5I\nTExESkrKgc4o6PV6PHnyBI2NjTAajeBwOMjJyUFRURGjyrq2tobBwUF0d3czLOFpeHt7IyoqCk5O\nTkQSZF2VdHNzY8hNvby8sL6+TiI+lEolpqenNyU/HA4HUqkUpaWlW25i2tvbUVlZCZPJhJCQELz+\n+uvbEj+TyYSqqiqyscnMzMSZM2eOTIyCSqWySyjtnUvbgc/nw8XFBUKhEDwej0iONos0oe9Hd59j\nY2Nx+fLlz42ByujoKO7fv0/GACIjI3HmzJldSbxUKhU+/PBDTE5O2nStN8uAFIlESExMRHx8PBQK\nBVpbWzfdsNEOp+Hh4QgNDd1xh2NxcRG1tbWQyWQANj4jmZmZKCwsPLBix0Fgfn4eNTU1JJqKx+Mh\nJSUFAoEAZrOZFE3o+XbLn2kH5K1u2+r/X8XNMA1LEkkTEWBj00mvEbshs9Y/a7VaDA4OQqPRgMVi\nITIyEhERETaPs99usPUx7AQjIyO4efMmdDodiTqzlLVuZbBDS1rFYvGOCDVFUXj+/DkhirRxFvA7\nJQGd4Ws0GqHVavH8+XPIZDKYzWa4ubnB1dWVQf72c14KBAJGdh/9b+uf6e9qtRrj4+MYGhpiGNLx\neDxER0fj+vXrr+Tn5KOPPsLly5fxjW98A//5n/+55X1ramr2RRonJibwq1/9Ct/5znf2fdwsFosm\nhmCxWPD29kZAQAACAgLg7+9PqwwPhTQGAPhnAEZszDFG//b7uwBsfeUPD3aNcLRaLXp6etDW1sb4\nENMQi8WIjY1FVFQUAgMDt93IUxSFp0+f4uHDh9Dr9eDz+Thx4gSys7N3TQLGxsZQVVVFCJRYLEZZ\nWdm+SIzRaMTQ0BBkMhkGBgYYm3M2m42UlBSUlZW9NIMEo9GIZ8+eoampiTEbSjtY0uDz+YQoRkVF\nMYaJl5aW0NjYiK6uLnL8cXFxKCwshL+/P+7fv0+kwElJSSgvL4dAIMDi4iJaWlrQ1dVFqmOenp5w\nc3PD5OQkuTjExsaiqKiIkTm4HTQaDebm5mzIoT0jDWBjoaUjGoRCIQYGBhimLz4+PkhOTkZSUhKx\nHnc0aBOQx48fEzKQkJCAkydPbuosp1KpcOfOHYZd/1aSSk9PTwZJ3Ik7sMFgwNTUFCGR9sgnnTUX\nHx+P0NBQBAQEgMPhwGg04t69e0R6mJ2djbKysh258d28eRNKpRIcDgfnzp1DRkbGtsd6FKDT6Rgk\n0pJY7qbz6OXlxTArEgqFRI5UVVWFubm5LYsxRxHLy8uoqqoiBThPT0+UlZXteR7ZurCQkpKC8+fP\nM9an+fl59PT04NmzZzZGTvbg4eGB0tJSJCcn7+qYXrx4gbq6OnR3d4OiKLDZbKSnp6OoqOhQOziO\nxtLSEiHFtHNzdnY2CgsL9z0fuFNQFEVIpFqtRltbG2NkxdfXFxkZGQgNDd2SjO6HuNL/3sl9jEYj\nMdOyvsbT5NBsNr+Sm3waOyWeZrMZi4uLMJlM4HA4RDFBd5F1Oh2ZVV9dXbVRfLBYLLi6usLDwwNe\nXl7w8vKCs7Mz2Gw2dDod5ubmMDMzg6WlJbvXsf28Bzwezy7Bs0cGrYnhdsSaHtuhSa7lWiYUChEb\nG4u4uDhERkaCx+Pt6rl873vf2/Nz3g3+7u/+bt+P8S//8i/49re/jb/+67/GP/zDP2x5392SRk9P\nT0ilUgAbe5D29nb85V/+5ba/uxOwWCw8ffoUAQEB8PPzsylsHOZM42MAawCeA/jD396WhQ3J6nVH\nHZADwCCNFEVBqVSipaWFMcfm5+cHX19fYulsueCKRCJERkYiKioKkZGRNvMhc3NzuHv3LpGIxMbG\n4ty5c/uyjt/Lxt4aZrMZ4+PjkMlk6OvrY3QX6Q392NgY6R75+PiQfEdHg55x6+3tRXd3t81cgYeH\nB6RSKbKzs206PPPz82hoaCCbB2CDFNJk0RIymQx3796FwWAgcQeW3THahluhUJD3OCEhAUVFRVua\nGq2trRFCSM+izc3NbTqnx+fzCTm0/HJ3dycbxJqaGhQXF2NychIymQy9vb2MxwsKCiKmQ46Sme2l\nIGEZ3E5vPHZykQgMDERKSgri4uL2FClDu4oplUoy12r9d3k8HgICArC8vAy1Wg0ul4vy8nKkpqZu\n+/iWMlZXV1dcv379UJxIHQ26OzkzMwOZTAaFQmFXWbAZaIldV1cXQkNDSfh7UFAQYzbyKJJHg8GA\nxsZG0j3n8XgoKipCXl6eQzrHluuLn58frl+/DicnJyI3VSgUjHlwa3h6esLHxwdTU1Pksx4UFISS\nkpJtZ6aXl5dRX19PimYsFgtpaWlE8vqqQKVSoa6uDp2dnYQUZ2RkoKioiFxTD3IeXKVSoampCe3t\n7YQ4hIaGoqioCBEREUfyc0BRFMbGxtDW1sbY5wQGBkIqlSIxMRELCwu4ffs25ufnwWKxUFhYiIyM\njH2RX41Gg+7ubmIGFRgYSOI5tiLBjiLYRwU7kU/T8VVbkb+VlRU0NzfDbDYjPT0dpaWlcHZ2drih\nmGX+48DAAEPFIhKJGPmP1n/7VSWN3//+9/FXf/VX+Pa3v4133313y/vut9NYVVWFpqYmhxz3UTbC\n+Qk2OovfxkbHEQBCAPQCOLigre1BUVas4sMAACAASURBVBQFo9EImUyG1tZWzM7OAth48xITEyGV\nShmbRZ1OB4VCgaGhIQwPD9sQnKCgIERFRSEsLAyjo6NobGyE2WyGi4sLzp07h7i4OIddSPR6PRob\nG/HkyRMiIczNzUVRUZFdiRgtw6WdTy1NTQICAkgXi774bjXvuN98R4qiMDMzQ8xsLDdTtJMm7RZI\nn+RhYWHIy8tDdHQ0nj9/jvr6eiJLYrFYJONqM3mZyWRCU1MTamtryQWexWIhJiYGFEVhaGiIzOIl\nJSWhqKiIPE+Kohjk0PJrN+TQz88Pbm5u254D1hsf2thHJpOhv7+fIRcKDw9HcnIy4uLi9tQNXlpa\nwmeffUZk025ubjhx4oTdLodGo4FSqcTIyAh6enrsziMGBASQ+AuJRAKBQID29na0traSDYMlaJvw\n2NjYHXXu7cFoNKK2thbNzc1bzvmJxWISz0FndVqjo6MD9+7dg8lkgkQiweuvv/5KzX9Zgj7vW1pa\nGLb9np6ecHZ2xtraGlQqlc2FZquND4vFYpjq0HOQ1sY7lv9+mc6pFEVBLpejqqqKROUkJSXh1KlT\nDs99nJqawo0bN7CysmL3Ai0QCBAaGkokpxqNBr29vejr62N0593c3BiuuiEhISgpKbGZx15ZWUF9\nfT06OjoIWUxJScGxY8demhrhMKBWq9HQ0ID29naYTCay3hcXF9uQ4oMgjYuLi2hsbER3dzcpMMbE\nxKCwsHBHM9JHBSqVCm1tbejo6CDnn+UstJeXF65evbpv53a5XI67d+9ifX0dzs7OeO211xAbG+uI\np7Bj7KYrS/9br9ejqamJrI1JSUmIiYnZlqwaDAaoVCqoVCqo1Wqo1WpynigUCsTGxpLrpFgsJsU2\nmhDudFZ0YGAAN27cgNlsRmlpKY4dO+aQ14rOf+zv78fAwIBN/iNNFIODg+12J00mEzo6OiCVSl/J\nzvUHH3yAN998E7//+7+PX/7yl1ved7+kEQB++MMf4s///M/3fdxHmTR+HxsOqjRp5AL4MYAcAAdj\ni7UzUA8fPkRHRwfZ+ItEImRmZiIrK2vb2Q+KorCwsEBmIcfHx+1WtMLCwlBeXr6tu+heoVKp8Pjx\nYzx79ow8h9LSUqSnp4PNZmNpaYkQRUvduYeHB3E+3YoEmkwmtLS0oK6ujuQ7Zmdno6SkZFcmFxRF\nYWpqiswoWkobnJ2dERcXh4SEBEbFSqVSobm5GR0dHWQDRc8oAhsVubS0NBQWFm5aUadnJ9va2kiV\njMvl2pALWoqbkZEBg8FgQw43k1wKBAK7ncOdkMO9wGAwYHBwEDKZDENDQwyjhdjYWCQlJSE6Onrb\n7olWq0VtbS1aW1s3NVlSq9VQKpUYGxuDUqm0K9f29PQklcaQkJAtias952FLuLi4EIlLWFjYrjtA\nq6urePjwITHuATbksm5ubpibm7NZMC3ll8HBwWhpaSEy5p3KWF8VzM3NoaWlBc+ePSOfDW9vb2Rn\nZyMsLAwqlQpTU1OYmpqCUCiEh4cHmXdcW1sj/96LoYJAINiUUFr+m/5OS5928pzu379PnJT9/f1x\n9uxZhIaG7voY7cFkMmFycpLEYFg7nAIbBDAjIwORkZGbOpyaTCaMjo6ip6cHcrmckb1Gy+WAjS5W\nSUkJvL29GSQKAJKTk1FcXPzSrjOHAY1Gg8bGRrS2tpJz8jCf5+zsLBoaGtDX10cKjImJiSgoKNhR\nxNZRhcFgQEdHB6qrqxnrcmxsLHJzc/dsyKbX63H//n0yGhAVFYWLFy9+ropwFEWhsbERjx49ArAR\nz1ReXr6r64LZbMbCwgJmZmbg6+u75+KoPfT09KCiogIUReHUqVPIz8/f0+PodDoMDg6iv78fQ0ND\nNvmPNFEMCAjY0kiwu7sbdXV1UKlUr6wRzuzsLCQSCQIDAzE2Nrble7kdadRoNBAIBEQavZl7qnW2\n415wlEljAoD/C0AEgAFsuKY6AbgGoM5RB+QAkMiNwMBA5OTkIDExcc9SJZVKhbt372JkZMTu/wcG\nBhJH1s0qNPvB1NQUHjx4QFz76IF1S6Lo7OyMxMREJCcnIzg4eFcL19raGqqrq9HR0UHyHUtKSpCV\nlbXpAkpr4GmiaNmZdXFxIUQxNDR009eD7oY8ePCA0ZHk8XjIyspCYWGhXdv4+fl5NDc3MzbBfn5+\niIuLw+zsLMP1is1mw8vLi+Tm2YM1OaRly66urocmQ1pfXydujfRMIX2s8fHxSE5ORlhYGOO1NZlM\nJM6FJsJpaWk4fvw4TCYTcTYdHx+3kdNZLjre3t64du3anjZLJpMJQ0NDePr06aafFz6fj8jISMTG\nxiI6OnpH0QB6vR53795FT08P4/bg4GCcPHkSJpOJzEVOTk4yLoyWzzExMRF5eXkICAg49Iyug4Y9\nUyiBQID09HRIpdJtJfAmk4kQSEtCaUksrX/e7caCy+XaEEtrUjkwMECUCEKhEMePH0dmZua+3k+z\n2YzZ2VmGw6nlOUQ7nIaFhUGn05EOoEQiwbVr13ZkQkMXhXp6ejA0NLSttC4xMRHFxcX7Vn8cJWi1\nWjQ1NRGnSACIj49HSUmJQ7J9dwulUomGhgaSz8lms4my5VUg6QqFArdv34ZarQafz4e/vz+jAOLn\n54fs7GykpKTsePM6NTWFiooKLC0tgcPh4NSpU5BKpUdSsrsTyOVyVFRUwGg0IjQ0FNevXz8ycTVd\nXV346KOPAADnzp1Ddnb2jn5vbW0NAwMD6O/vx+joKGOtEYvFhChuZw5mNptt4oR8fX3xrW9965Uk\njQDwJ3/yJ/jxj3+M999/H1/96ldt/n99fR29vb1YW1tDaWnppqTx7bffxve//33iqLyZe+qNGzcQ\nFxeHlJSUPR/zUSaNAMAGIAUQCmABQDOA/wHg/3bUATkA1M2bNyGVShESErLnxYyiKPT19aGyshJr\na2vgcDgoLCxEQkICRkdHMTIygrGxMUZnSygUIiIigpBIRzja6XQ6yOVyNDc3M9z6WCwWoqOjkZ2d\njfDw8H13TqzzHa3nHc1mM5k1k8vlDA28q6srEhISEB8fj5CQkC03cBRFYWRkBHV1dYQI83g8hIeH\nY3l5mXS9uFwu0tLSkJubCy8vL4yOjqK5uRnDw8PkscRiMdzc3DA9PW03i8kSQqHQrqzUxcXlwC54\ne5FYraysELdGS6dZFxcXJCUlISkpiXTi6EKCWCxGVFQUlpeXMT4+TuR7NHg8HiQSCXx8fDA8PIzF\nxUUy41JcXOyQLpxKpUJnZyc6Ozs3fW9YLBYkEgliY2MRGxtrV3q3tLSEGzdu4Pnz5+Dz+bh48SIM\nBgM+++wzYj6Unp6OEydOQCQSwWQyYXZ2Ft3d3ejo6LC7Oefz+SSfi+5GHrWMwZcFs9mM/v5+tLS0\nQKlUkttjY2NhNBrxpS99ySGzgHQ+mD1yuRnR3EqCbA8sFstuB9NeF5P+4nA4oCgKi4uLjLlE66KS\nr68vicGwdjhVKpX48MMPoVarIRKJcO3aNYT9Not3J9BqtZDL5Vu6E1+4cMFhndPDhk6nQ0tLC5qa\nmsjrHB0djZKSkh1LJB0lT6WvPw0NDeS15/F4yMzMRF5ensOlzYcBk8mE6upqNDY2AtiQQV+5cgUe\nHh5Qq9Vob29He3s7uYYLhUKkpaUhOzt7U/mz2WxGQ0MDampqQFEU/P39ceXKlUMh+47G9PQ0fvOb\n30CtVsPT0xNf/vKXd12seVny6adPn+LTTz8FALz22mtIT0+3e7+VlRX09/dDLpfb5D+GhoYiLi5u\nx14DZrMZvb29qK2tJaMn3t7eKC4uJvFprypp1Gq1OH/+PJqbm/Hee+/hzTffJPvZzs5OvPvuu/jR\nj36Ezs5OXLhwAd/5znfwj//4j4zHuHXrFn7605/i008/hUajgYuLC3Jzc/HkyRPG/YaHh3Hp0iXI\nZLJ97UGPImk8DuA8NuI1fgJg1OL/vgXg/wGw/x6r42DXPXU3UKlUuHfvHulaSSQSlJeX2ywkBoOB\nWBMPDw/bdHD8/f0JgQwJCdnxZtxkMmF4eJg4n1rO6nl7e2N5eZmYlGRlZaG4uNgh1TGKojAwMICq\nqipSWRKLxfDw8MD4+DjDIdTd3R0JCQlISEhAUFDQjtxmBwYGUFdXR8iPk5MTcnJyIJVK4eTkRIb5\nnzx5wiCH1rJTDoezaaVeIBDA39+fxGrQuYypqak4f/78oZKD/V5YFhYWIJPJIJPJ7OZM8Xg8cDgc\nmw0wPXNFf/n7+6OzsxNVVVUwGo3w8PDA5cuXHRZqbwmz2Yzh4WF0dHRgcHCQLG5cLtfG4t7X1xcx\nMTGIjY1FcHAwhoeHUVFRAa1WC29vb7zxxhvkM6jT6VBXV0dMAwQCAemQd3V1obKyEmazGaGhoThx\n4gTm5+dJN9L6tWOz2QgMDCQkUiKRHJlq88vE9PQ0Wltb0dPTQ+Zr6Q4w/f1luStbg/r/2Xvv4LbS\n83r4oBCVIFhAEuy9AyxiL2LTipJW0q7Kaku86934j3iSTDyT2LEzcWbijJM4tuc3nzNxxrNOsb0e\nb6xdiVTZXdUVwSKKTRAL2KtILcEKgg0E0e73B3zf4BIgCRZRlKIzgxFFgiDKve99z/Oc5xyKgtls\ndupiarVadHd3kw0uj8eDQCDA2tratsx+aHA4HJdukgKBAAEBAQgNDUVUVBRkMhlEItGGHZjl5WVc\nvnyZyJiOHDmCgoICty7+q6urePDgAZqamkjHTSAQOJ23Xl5eKCoq2nUn9VnBbDajpaUF9+/fJ6Mi\nUVFRKCsr2/aM4G7XTnoGtr6+nlx/BAIBcnJykJub+8Kc7zqdDpcvX8bExARYLBaKi4tRXFzsdPzQ\n2cXNzc2MzMe4uDjk5OQwTJr0ej0qKytJkTcvLw9Hjhw5EBFFe4XFxUX8/ve/h1arBZ/Px4ULFxAT\nE+P27z/NmdvGxkbcunULAHDu3DkolUoA9hlcmii6yn9MTExEQkKC27Jh+hxRqVQkssjHxwclJSVQ\nKpXkGNqtE+xBh8ViwYcffoiPPvoI09PTiIqKgpeXF9LS0vDd734XjY2N+Md//EfU1tZCIpGQyDJa\nTdLb24sf/ehHOHXqFH7+85/jww8/BJvNxtGjR+Hn5wer1QqtVoumpiYcP34cVVVVu3q+B400Hgfw\nBQA9AE8Ai7DPL+oA/ALA12F3T/3/9uoJ7QF2TBptNhtaWlpw7949mEwm8Pl8HD16FIcOHXJrM6DT\n6TA4OIihoSGMjIwwJE48Ho/RhVxvlU67vNLOp46zduHh4VAqlUhOToZIJMLy8jKqq6uJ25xAIEBJ\nSQmys7N33SWiJYZ1dXWEcNGQSqVQKBRITk52W79PV63q6urIQiQWi5Gfn4+srCzw+XxQFIXFxUUy\nZzgxMYHh4eENzWgcwWazERkZiaysLISFhUEsFpPnRVEU2traiBOov78/Lly48FxLvmw2G4aHh3Hn\nzh2Xs4iAnTxGRkYiJiYGERERCAgIIAv+8vIyrl27RiRZaWlpOHHixL7k8C0uLqKtrQ1qtZp0P+mM\nsNXVVUZhwMPDg5w/cXFxOHfunEsCMzs7i1u3bpEiA5/PJ2QiLy8PR48eddow0TOd9G1qaspp0ZXJ\nZAwS6e3t/dxKsLbC8vIy1Go1enp6iGkYYD+3oqKiSCd4P7sw6+dYJRIJjh49CoVCQT4HWjLrqotJ\nZ13q9Xqsrq7u2GmRy+VuOJMpFAqJsQRgP07Pnj274Uy40WhEY2MjGhsbyTEaGxuL0tJShISEQK/X\no62tDa2trYwCHYfDQVJSEjFwO+jHocVigVqtRl1dHSH7YWFhKCsr29Jhcq9htVrR2dmJ+vp60jVZ\nf/15EUC7r9+4cQMmkwlSqRTnzp1zqxC4vngE/O/cM5fLxZ07d7C2tgZPT0+cOXNmW2TqeYLJZMKV\nK1fQ09MDFouFV199FVlZWc/6aQEA6urqcO/ePbBYLCQnJxNXdxpcLhdxcXFITExEfHz8top9tDli\ndXU1UbNJpVIUFxcjLS1tV+6pL/H0sdnn0dXVBYVCAewjaayG3fTmJuzdxP8HwAogD0AMgLdgj+I4\nSNgRaZyamsL169dJxSY5ORnHjx/fscTUYrFgbGyMdCEdZxABe1clNjYWfn5+mJ2dRXd3N0PGFxAQ\nQJxPN5IUTE1N4fbt28QFzNfXFxUVFdvOJrNYLBgaGiI5PY4VfMdNuDvzjjSsVis6OjpQX19POrAS\niQSHDh2CXC6HTqdjGNKszzVyhEAggMlkYphRcLlc5OXloaCgYEvjnqmpKXz66aeYm5uDh4cHTp06\ntSsN+X7CarViYmICjx8/xujoKEZHR502wEKhEHw+3ylbKioqCgqFAklJSRAKhejv78fVq1dhMBgg\nEAhw6tQppKSk7PdLIsRXrVYzMkRFIhGkUilmZmacOsuxsbGk+7W+ckoXBz7//HPy3gQFBeHChQtu\nxdWsra1hfHycZEU+efLESSopkUgYJNKRiL9I0Ov1xF1vvcwpJCSEyJy2mofZKWiDrpqaGphMJnA4\nHOTn5+Pw4cObzl2ZTCaMjY0R8xpH8gvYi3YREREIDQ1FQEAAyabcTC67srKyI7IpFAohkUgIyeTz\n+dDpdIzjKjQ0FEVFRYiLi3N5HI2NjeHOnTuMLhBgPw5TU1OhVCoREBBwoAjkesMMwH4elpWVITY2\ndl+fq9lsxqNHj9DQ0ECei1QqRWFhIdLT018oObrRaMTnn39OZr5TUlJw6tSpbasEVlZWoFar0dra\n6jRSEB0djfPnz78wHdmNQFEU7t27h/r6egBATk4Ojh079szWetposKenB2q1mqFG4PP5JOM6JiZm\n26YqFEVhcHAQKpWKNAjoztmhQ4c23OO9JI0HCxt9Hp2dnaiqqqJjPfaNNP4WwHsO/xcBmIBdonoW\nwOM/PMZBOoK2RRrNZjNqamrw4MED2Gw2SCQSnDx5cs+to/V6PelCDg0NuTTrEAgESElJQXZ2tlMe\n4UagDWVu375NKqlRUVGoqKjY1MzEbDZjcHCQ5PQ4kraAgAAkJSUhOTkZ/v7+xK2QNmWRyWQ4duwY\nYmNjnR6XrjLX19eT+A8ej0fC4Tcih+slp2FhYcjPzwdFUairqyObQMcTRCAQICsrCzk5OVuS+7W1\nNXz++efo7OwEABw6dAjHjx/f182DOxIWOvCeNq3ZyNjFy8sLWVlZpKjAYrFgNpsxMDAAjUaD/v5+\n8n6y2Wx4eXkRZ9uoqCicOXPmQMzvLC8vk+6jo2yUzWaTiBbHWU7AvuGmu18ymQxjY2P49NNPsbKy\nAoFAAIvFQuJqCgsLUVRUtK3PmZaPPH78mJDJ9S67fD6fEfMREhLy3Mu11h+fBoMB/f396Ovrw+Dg\nIINI+/n5EQLpjjzdHQwODuLmzZtkHYuPj8exY8dczlnRDqf0TOKTJ08YRSUOh4OwsDASgxESErLt\njR9FUTCZTG6Z/ywvL2NxcXFHmymBQLDhXCabzSZzSuvh7+9P5pqfZRSHzWaDRqNBTU0NKRD6+/uj\nrKxsz+Ko3JX/GY1GtLa2orGxkXRrZTIZioqKoFAoXjjX5PHxcVRWVkKv18PDwwOvvvoq0tLSdvWe\nj4yM4NKlS05Kn+joaOTk5GxY6HiR0N7ejmvXrsFmsyE2NhZvvPHGpl3pvZSn0nnbdBHfMUaNHtXh\ncDh4++23Xe7BtgJFURgZGUF1dTUpSonFYhw+fBiZmZmbXscMBgPEYvFL0niA4Io0dnR04MqVK6Ao\nCn8wBt030vhLAH+y7nsfAfgmAHoX9fU/fO+gwG3SODw8jM8++4xsVrOzs3HkyJGnIlmhs7s6OzvJ\nbADg+gP38/MjMlZ3IwqsVitaW1uhUqlINSojIwPl5eWkM2MymTAwMIDu7m4n+2W5XE7MbFx1EVzN\nO8bGxiIvL49ssvv6+jA1NeVkT+8IsVgMf39/+Pn5kcxGuqrp4eGB9PR05OTkQKvVMiStnp6eKCgo\nQEZGBoaHh/HgwQOy4HE4HCiVSuTn5286mE9RFNRqNW7cuAGr1YrAwEBcuHBh35zyXF1YTCYTxsfH\nCUn86quvnLobjjOdMpkMJ06cIAHKG4E223j48CFj3oHD4SAlJQWpqamIioo6MBf/rq4uXLlyxWWH\nj5Zl0zEIju+PSCRizEu98cYbsFgsuHv3LikQeHl5oaKiAsnJyTvaTNExPDSJdGUuxOFwEBwcTEhk\nWFjYtqJrDgI22/jQGV99fX3o6+tjkOjdRqrMz8/j1q1b6OvrA2Bf/44dO0ZMuID/zaOlO4mbOZxG\nR0cjLCxs37tJZrMZn332GYlJcozV8PLyglwuB4fDcSKeewGxWExev6+vL8MIiM/nP5Uun6sZKF9f\nX5SWliIlJWVP15atNuUrKytoampCc3MzUcYEBwejqKhoT3OUDwpsNhvq6upQU1MDiqIQFBSE8+fP\n7+paZrVaoVKpSJctJCQEhw8fRn9/P8Ot3NvbG9nZ2cjIyHju1rjtYGxsDBcvXoTBYIC/vz/eeeed\nDZUruyWNFosFw8PDpIi/Pt81KSmJZCjeuHEDDx8+hIeHB959991teRE8fvwY1dXVpAglEolQWFiI\n7OzsLdfLwcFBXL16Fd/5zndeksYDhPUcor29HVeuXAEAlJaW0sflvpHGRQAP//A19Yf7RwOg/fS5\nsM84HqTEYUqlUoHNZoPFYpGb4/8tFgt6enoI6fDy8kJGRgb8/PwY99vsMdz5mcViwcjICPr7+xlS\nLw6Hg7i4OKSkpCA6Ohqrq6tkMzQ8PMyQh3K5XERGRhISudVFYXV1FTU1NWhpaYHNZgOPx0NsbCxZ\nlBw35cHBwYQoblapttls0Ov1mJmZwdTUFHp7ezE5ObnpwiEQCBAUFOTkWGq1WtHc3IyHDx+ShdHL\nyws5OTlIS0vD4OAgY/7Ey8sLhYWFyMjIcFrUxsfH0dDQQGaKADuRzc/PdwrMdsTk5CQ+/fRT6HQ6\n8Hg8nD59mtZ9P3Wsrq5ibGwMjx8/xtjYGCYmJpzex8DAQAQFBUGn0xGHS7FYjPLycqSnp7u1GbPZ\nbLh//z5UKhVsNhs8PT0hFArJ5o5+TDqqZa+6RduFzWbDvXv3iNOfQqFAeXk5IbyO5lKxsbFITU0F\nm80m0QuOBFIoFCI+Ph7x8fGIjY3F5OQkbty4QbrUEREROHHihNtd/M2wsLBAZiLHx8cZzsY0AgIC\nGJLW9XPMzytoJ+Xe3l709vYyCDSPxyOzNXFxcZsW4EwmE+rr69HQ0ACr1Qoej4fi4mLk5eWRLFp6\nXRwdHXXq9tIOp1FRUYiMjNw3056NYLFYSOGOXsM9PDxw8uRJpKamujy/bDbbtl1mtyuZZbPZW7rM\nrv96KwfsgYEBVFdXk3NLKpWipKQEaWlp+1qIWlhYQENDA9RqNbm2RUZGoqioCNHR0S8cWQTsr7my\nspJcGwoKClBeXr6rLurs7CwqKyuh1WpdOmmvrq7i0aNHaGlpIYoVLpcLpVKJ3NzcPVlTDyLm5+fx\n8ccfY3Z2FiKRCG+//fa2TZw2wtraGlF7DQwMMFRYfn5+hCiu94+gKApXr15Fe3s7+Hw+vv71r2/p\nQjw+Pg6VSkVGmQQCAQoKCpCTk7Nlk8RsNuP27dtobW0FgBc2p/F5BYvFwuzsLAwGAzQaDZqbmwHY\n9zsymQynT58G9pE0PoY9g3GjqxQPQDGA0L16QnsAktP4IoImpVwul2TArCergH1BcpWV5uHhAbFY\nDLFYDA8PDyfya7FYYDKZyI12KXRnkeByuQgODkZwcLDTY6+srDiZjkilUkRFRUEul2NiYgIDAwNk\nYygSiRidi83I+dLSEumeOg7yp6WlITY2loSGO/6eyWTC3bt3iUNueno6jhw5Ah6P5/JvbQSLxQKj\n0YjV1VVy2+j/i4uLTuY1LBYLQUFBxNlULpcTeRUtQ8nPz0dRUZHbHXC9Xo+qqiqyqcjNzcUrr7wC\nLpeLubk5aDQadHZ2EmIO2F3SFAoFlErlvhkFGQwGXL58GcPDw2CxWKioqEBubi7DyOjx48dQq9UM\ngigSicgxxeFwEB0djbm5OQbB5HA4iIqKQnx8PEwmE+7fv4/V1VWwWCxkZWWhrKxsT6vkq6urePLk\nCelGuuoYS6VSBon09/d/7je1FEWRQlJvby+DPNMufrSUmJaQUxSFrq4u3Llzh6gMUlNTkZubi5mZ\nGSI5XT9XRa8X0dHRiIyM3JNIo72AxWLBo0ePUFdXR6RkMpkMq6urWFlZgVAoxLlz53YkJVsPWjI7\nNTWFhoYGhiMxj8dzkv87dju3A6FQ6EQmhUIhjEYjhoeHidpELBajqKhoT0zYtoO5uTnU19ejo6OD\nvL74+HgUFRXt2ab+IKK7uxvXr1+H0WiEp6cnzp49u6XqZDPQ6ptbt27BbDZv6aRNu2E3Nzczsngj\nIiKQk5ODhISEF04CbDQacenSJQwNDYHD4eC1117bsScCLfnv6enB0NAQ4xohl8sJUZTJZJteG2w2\nGyorK9HV1QWBQIAPPvjAJXGfmJhAdXU1wyguLy8PeXl5bhXZvvrqK1RVVWFubg5sNhtlZWU4fPjw\nS9J4gMBisbAZ59lveeqrsLun7vY++wnqyy+/BEVRxFqdoiisrq5idHSUVMU9PT0RGhpK3DvX39/x\na3d+tra2RgiC4wnF4XDg4eEBDw8Pxu9s9Zgv8eJhZGQE0dHR8PT0RGBgICIjI5GYmAhfX19i5lJd\nXU0cBxUKBY4cOeJWthJg3wB0dnbiiy++2NLtjpb7dXZ2QqPRMOYm5HI5mZV6Wt0xrVaLixcvYmFh\nASKRCBcuXNg0685gMKCjowONjY2MzlZISAjy8/ORkJBATFz6+/sZEnD6NXE4HCLVFQqFKC8vx6FD\nh55KZ8RisWBiYoLh0ro+IkIgEDBIZFBQ0DOdi9yLuZz5+XkSLD02NsZYy0JDQxESEoLx8XFivODt\n7Q25XI6ZmRlGEQOwFwfoTmJUTRb26QAAIABJREFUVBR8fHwOFMl2ZfwSGBiI0tJSJCQkwGg0oqqq\nijgVl5SUuIw/2A3m5+dRW1uL9vZ2UBRFsk8pisL4+DhD3RIREYGwsDB4e3vDaDRuaP6zvqPrDuhi\npLu5mZtJZi0WC/R6Pebn58m/zc3NSE9Ph8lkglarZRjLhYaGIjk5GQEBAeRau/5GFx6fV5hMJty8\neROPHj0CYCfIr732GsRi8Y4fc2VlBdevXyey8NTUVJw4ccLtjv3s7CxaWlrQ1tZGihUSiQRZWVnI\nzMzc1XM7aLDZbLh58yZaWloAAIcPH0ZZWRk5pjZbO5eWlkg0xujoKGNNDAsLQ1JSEhITE90ybXOE\n1WrFp59+ir6+PojFYnzwwQdktGhychIqlYp8tjweD7m5ucjPz3erWErLn2tra2Gz2eDv74+zZ8+S\nrufLPerBAYvFwk9+8hMy6kDHh9GFv5ycHGCfcxqfNzBmGm02GxobG6FSqWA2myEQCFBRUYH09PRd\nX0RmZmbQ0dEBjUZDJBuAvcqsVCqhVCq3vRD84QWQ5+5IJC0WC7RaLYn0WO8Q6IigoCBER0fD19cX\nBoMBg4ODePLkyZbSJqFQCC8vL3h5eUEikZCbyWRyktnKZDJER0dDKpVienoa/f39jE4h3bUE7BXv\nwMBAsnmfmprC5OQkmUuic9JokrITEm+z2WC1WmGxWAiBd6yys9lssNlsJ/K+XxgZGXFpOc/hcEiX\nF7B3/fLz85GUlMSIENkMq6ur+Pzzz9HV1QUASExMxOnTp91yu6MH7zs7O9HT08NwaIuIiCAxK3vl\nnNfe3o7PPvsMFosFISEhePPNN7c05aEoCg8ePMCdO3cA2DcnjjEdIpEIaWlpyMzMhJ+fH1ZWVoiJ\ny9DQ0IY5n4GBgThx4sRTD1KnKArT09OEQD5+/JhB1AF7pz4kJARhYWHE6XM/JZd7nTVGV9V7e3ud\nPgNXoB1O6W7iQXMHpWGz2dDR0YGamhqy7vv7+6O0tBRJSUlOUrK6ujpUV1cDAGJiYnDu3Lk9d6HU\n6XSora1FR0cHKIoCm82GUqmEr68vBgcHGUUUPp+PpKQkKJVKREZGOpFYm81GnGXHxsbQ2tpKrjUc\nDgcymYwYm9FEc7vdTDabDT6fTxQpgJ0sms1ml/mbG62d28FGhHKnNx6P50RMn0YBSqvV4vLly5ib\nmwOHw0FFRQWys7N3dW7Q82nLy8vg8/k4efIkyf/bLtbW1tDe3o7m5mZS+KFn53NychASErLj53nQ\n0NzcjJs3b4KiKCQnJ+PMmTPw8PBwWjvn5+fR09PDGIMC7Bv8qKgoJCUlMdQXO4XFYsHvf/97DA0N\nQSKR4PTp02hra0N3dzcA+zUlJycHhYWFbq85Op0OVVVV5Hnn5ubiyJEjZDzoJWk8WHDsNFZUVCA/\nP9/p53hJGjcFIY1arRbXr18n7osKhQLHjh1zO+zUFRYWFoi8z1GKJZFIoFAokJqaisDAwKe22Vla\nWkJPTw+6u7tdOuptB7R5RFpaGpk/XC+B1Ol0qK+vR3t7O9kYJCYm4vDhw046+rm5OVy/fp3xvHg8\nHgoLC5GbmwsAaGlpwYMHD0hVRC6Xo7i4mJgVUBQFo9HoJPFcL/t09fOtNqWbgcfjkYBxwE7cIiIi\nIBaLIRAIyI3P55N/6U0DALcIrtlshl6vJ1LKqakpzMzMbLrh4vF48PX1JTc/Pz/yNU0oR0ZGcOXK\nFSwuLoLH4+H48eM7LopYLBYMDg5Co9Ggr6+PvKdsNhuxsbFQKpWIj4/ftr03YK+M3rp1i1RrDx06\nhBMnTmzZXTOZTLh+/TqxlD98+DBKS0uxtraGzs5OPHz4kCH7jYiIQGZmJpKSksDlcmE2mzE8PIy+\nvj709/czMvBohIaG4vTp05saKe0lKIoic5G0pNVx3hSwn5+BgYGERIaHhx8YSaY7sFqtZO54cHBw\nw40GnWGbkZGBmJiYAytvc+US6ufnR4xfNjvfhoaGUFlZCYPBAKlUigsXLjyVzfTs7Cxqa2uJCRSH\nw0FmZiZSU1MxOjoKjUbDKDbSc80KhYKRATk1NQWVSkXmxXk8HvLz813K2mjJrGO3cnFxkeRkLi0t\nYWVlBUajEWazeUdyWRpsNhvBwcGQy+Vgs9kwm81b3kwm045zOrcLWlm0nlDu5MblctHT04OmpibS\n7Tl37tymruhbwWKx4M6dO4y5pzNnzritZtkMFEVheHgYzc3NZOwDsKtBcnJykJyc/Nw7TAN2wn3p\n0iWsra0hODgYb7/9Njw9PTEzM0McTx3PMS6Xi5iYGCQlJSE+Pn7PzYPMZjN+/etfM3K1ORwOsrKy\nUFRU5PZ+d71UWSKR4MyZM07y55ek8WCBJo1cLhfJyclISEhAbGws2aO9JI1bg1pbW4NKpUJjYyMo\nioJUKsXJkycZbnzbwerqKrq7u9HZ2ckgRAKBAElJSUhNTUVERMRTI4oLCwvo6elBV1eXU9WKDkHf\n6iTm8XiQy+WIi4tDeHg4mpubSVfK09OTmKzQr2FmZgZ1dXXQaDRE9pSSkoLDhw87bay/+uorPHjw\nAN3d3eR5OLpa0sRnZmaGXLzFYjH8/PzA5XKdyOBOwWazIRQKyU0gEJCvabmgY3xDcHAwcnNzycWM\noig0Nzfj9u3bsNlsCA4OxhtvvLGjbvFmWF1dhUqlQmtrK2w2Gzw8PJCWlkYCvnU6HXQ6Hebm5jZ9\nP/h8PrhcLiFBPj4+OHLkCCIjI8nc326wtraG3t5edHZ2Ynh4mHy2Hh4eSExMhFKpRHR0tFub/KWl\nJVy6dAljY2PgcDg4ceIEMjMzt/y9+fl5XLx4EVNTU+DxeDhz5gySkpIY96GzrNRqNTQaDSH+QqEQ\nqampyMzMJHOa9H1pCeX6/FQfHx9kZ2cjKSlpTzZS24HBYCARH7RJ0voNto+PD0PS6ufnd2C6cbTk\nmZ5JHBkZcdqs+/v7Iy4uDiKRCHq9HgMDAwy5MZ/PJ0Y6sbGxByJ8nZ7BrKmpIceLr68vSkpKoFAo\n3O4uLSws4NKlS3jy5AnYbDaOHz+OrKysp/L5zczMoKamhqzxXC4XWVlZKCwsxOrqKjQaDTQaDWMO\n2NvbG9HR0VhcXCQzUFwuF7m5uSgoKGB0Kmw2GxYXFzE/P8+QkdK3rVxhBQIBpFIpKcrxeDxCKKxW\nq1OGJpvNRmZmJnJzc3fUpbXZbKSTuZ5QukM83b3tB9hs9pZdT5p0On7faDSivb0dS0tLYLFYSE9P\nR3p6usvfpdUvO8X8/DxaWlrw6NEjcg0Ti8XIzMxEVlbWc1X8coWZmRl8/PHH0Ov1kEgk4PF4DHk9\nj8cjGYqOG/i9xnqFAWBfQ99//30EBQW5/TjrpcopKSk4efKkS4L7kjQeLLBYLPz0pz9lFMNpr4fE\nxER6n/WSNG4C6mc/+xn0ej1YLBZyc3NRVla27ZPWbDajv78fnZ2dGBgYIJs3LpeL+Ph4KJVKxMbG\nPpXKmdVqxcjICDo6OjA6OuokY3MFb29vhkupRCLB0tISHj9+jMHBQTInB9gPsrCwMPj7+2N8fJx0\naeRyObKysjA0NISenh5y38TERCgUCvB4PELwDAYDJiYm8OTJE8YGgSZfu6ns8vl8l8TP8WtX36MN\nbzbDwsICmpqa8PDhQyKdlclkyMvLQ1paGrhcLr766it8+umnWFhYgEAgwOuvv47ExMQdvx4aX375\nJcRiMWpqamA0GsFisZCRkYGysrINq4Grq6ukM0n/q9PpMDs7u2HmJWB/Dx27ko5dyp1supaXl0nh\nxLFwIRQKiQNrWFiYy/d/fHwcn3zyCZaXlyGRSPDmm28iNHRr76yhoSFcunQJRqMRfn5+eOutt7Y0\n6XHsPjpWe8PCwpCZmYnk5GSGC69Op0NbWxsePnzotNENDAwkJi7rHez2A3Rmp6NL6/rPXCQSkYgP\n2khpp5267cpTKYqCTqdjkERX83A8Ho8QlvXHHk00e3t7SWQPDdrMKDExEQkJCbtSiOwEdKRETU0N\nWSO9vb1RXFy8Y5dQq9WK27dvk05PamoqTp48+dQ2lVNTU6ipqSHruYeHB7Kzs1FYWAihUAitVovO\nzk50dnY6deCDg4ORlZUFHo/nRAwXFhY27RhyOBx4e3vDx8eH/EvfvL29ty273mvp9NMAPULiTufT\n1ffpcQ69Xk+iq1gsFjln6Pvtx4adLkhvJcvlcrmbklfAvv739PQQ8yR6T5Gbm4vw8PADU/TaLlZW\nVnDx4kWMj49jZGSEdHmSkpIQHR39VLuqer0etbW1aGtrY8jRtVotpqen4e/vj/fff9+tudK+vj5c\nu3YNBoOBSJUVCgX5XFZXV8k40dTUFM6cOfOSNB4g0CR+bm6OXEcdxxH22wjneQT1gx/8AIGBgTh9\n+vS2JEA2mw0jIyNktoveoNE6dKVSiaSkpD2rflssFuh0OkxPT2NmZgZPnjzB5OTkplVab29vBAQE\nQCaTISAgAP7+/pDJZBtuOmhZ5NjYGAYGBjA6Ourk4Ok457dXWF+Ncvy/r68vUlJS4O/v70QEBQLB\nvli2G41GqNVqNDU1EZdGsViM7OxsMi9y9epVUnnLy8vDK6+84nJDTlEUMUKiCbWrr6urq8mgelRU\nFI4dO7Ztq3K6G3rnzh1YrVZIJBJkZGQAAINYupoLoiEQCJykrvTX7khn5ufniUTbUVIplUqJA2tg\nYCAoikJraytu3rwJm82GiIgIvPHGG1tu/imKwv379/Hll18CsJs+nD17dtsbzYmJCTx8+BAajYac\ny3w+n3Qf17/3PT09uHHjhssijUQiQXx8/I6zCPcCNpsNU1NTDHMdx2IQYCcFoaGhCAsLI2TSXULi\nzsZ8aWmJxGC4cjjl8/lEgsjhcFBYWIiioiK3MxPn5+eJE6ujkQtglxAnJiYiMTHxqWarUhSF/v5+\nqFQqUnjw8vJCcXEx0tPT90Q+29nZievXr8NsNiMgIABvvvnmU31NWq0WNTU1ZD2jyWN4eDgePnxI\nzHq2A09PTwYRdCSGEolkT8nA80Aad4v10tHo6GicOXOG0ZWjC7Ludj6Xl5fR2dlJZm99fX0RGBhI\nHmMjArsbCfF2QJNTuui727lSV7enSUotFgs6OjrQ19eHt95666nvXRYXF1FXVwe1Wk2KCmlpaSgu\nLoaPjw8MBgN+85vfYHp6GnK5HF//+tc3vKabTCbcunULarUagF2qXF5ejpWVFUIQJycnnTKJX0Zu\nHCy46vwuLy8TP4Gvfe1rwEvSuCmo+vp65OXluXVxp+VqnZ2d6OrqYlRbg4ODoVQqoVAodlXltlgs\nmJubw8zMDKanpzE7O4vp6WnodLpNTz6JRILg4GDExcVBLpdDLBbDarW6nOdznPNb//O96PrRXcbl\n5WVyQREKhYiJiUF8fDwkEgmsVishE/TfjIuLw+HDhxEUFISmpibU1tbCZDKBzWYjOzsbJSUlzzQg\n2Gq1oru7Gw0NDWSDSHeT4+LiSBGBoih4enoiPDwcVquVQQZXV1fdvsj6+fmhoqICcXFx276YLS0t\n4erVq8TqPCMjA8eOHXMqYlAUBYPBwOhMOhLKzTqUQqHQiVDS/3c1yzQ1NUUcWB0JhL+/PzgcDnlP\nc3NzcfTo0S3PSZPJhKtXr5JB/pKSEpSUlOzqwm8ymaDRaKBWq4l7KmCftcnMzERKSgohVlarFa2t\nrbh37x55n9ZHGfB4PMTExCAhIYFILZ8FKIrC/Pw8g0SudyBlsViQy+UMSet21jLadZomievlvCKR\niMihHaWmSUlJOHr06K6k3bSZEW2k47iOyWQyQiCDg4P3ZGNIURQGBwehUqnIfJBEIsHhw4eRkZGx\n54WC6elpfPLJJ5ibmwOPx8Prr7+O5OTkPXt8iqKwsrLCkI1OTExgfHzcLYdUx+gbGgEBAUhKSkJG\nRsYLkzt6EDA9PY3Lly9jenoabDYb5eXlKCgo2NVx3dPTg+vXr2N1dRUikQinT592WzGzHWLqqpO6\nUcfVMc5rv4jH+m7oXpof0benTRaXl5dRX1+P1tZWsg4qlUqUlJQ4FZuWl5fx61//GnNzcwgJCcF7\n773ntEcYGRlBVVUVkSpLpVKsrq66LDZzOBxIJBKIxWLweDy8//77L0njAcJWcuGXM41bg3LngJ6d\nnSWbXce5Dl9fX+J8ut3Kr8ViwezsLGZmZhi3rcghDRaLBYlEAi8vLzKDQJOSzTpHW4HD4Th18ywW\nC6anp0mngsViQSgUuuxyCgQCxmxdZGQk8vLyEBcXBzabDb1ej/r6erS1tZEFbSOznOXlZVRXV5Pq\nllAoRGlpKbKysvZ04XV0ANyqA0jnqRkMhh1XWHk8HrE4Xi+hpb/n6emJyMjIHXUqHDcAQqEQp0+f\ndprtcwf0RnK93JX+erO5HJFIRAikj48PIZZ+fn7g8XgYGxsj55Tj8err64u8vDwkJydvKpeZm5vD\nxYsXMTMzAz6fj7NnzyIhIWHbr3EzTE5OQq1Wo6OjgzxHHo8HpVKJzMxMMgeysrKCe/fukeNUIBAg\nIiKCSMdo0BEHtIzV19d3T5/vdkHnodI3rVbrtPb4+voSAhkREcGIsqBVCXQ30XEGGGA6nEZFRYHL\n5eL27dukUyWTyXD8+HGXMS+7gclkwtDQEIlUcVyPJBIJEhISSBd4u+cXbeChUqmI9FosFuPw4cPI\nzMx8ql3ltbU1XLt2jRRJ8vPzceTIEbdfAy1ndCSGjv931xyMxWIhMjKS5LT6+PgQB+z+/n5oNBpG\nDi6bzUZMTAwUCgUSExOfmrz2RQetxrh9+zYsFgt8fX1x/vz5LcPaN8P6eI6YmBi8/vrrB26O0GQy\noaOjAy0tLQz1U3h4OOLi4uDr6/vczJn6+PggKCiIcduLYuLKygru37+PlpYWci4nJyejtLR001GN\nxcVF/OpXv4Jer0dgYCAyMjJI02JqamrTwvFWeNE7jRRF4Xe/+x1++ctfwmKxwNvbG93d3ST3uqqq\nCq+//joA4OrVq/jlL39JlBVarRYVFRX4q7/6K1Jkb2howE9/+lNcvXoVXl5e+P73v49vfOMbe6Ys\neUkad48NSePS0hLphDluhjw9PYmszp3ZpbW1NUxMTGBiYgLT09PEJc6VKyONvRgediXldGfej5aG\nURSF3t5e1NbWkg6QUChEXl4ecnJyIBAIsLa2hqGhIdy/f5/hxkXD398fSUlJiIuLA5/PR0NDAyNg\nmTbL2Up2OTk5iZs3bxJjIX9/fxw7dsxps0m7qbpD/By/t1OSzeFwwOfzYbPZGBtT2qmUJtkpKSnE\nmUwgELi1sdyJxGo/NwAURWF5edmJUNK3zS7AYrEYvr6+8PDwwNjYGCwWi9N8K4vFQkxMDJRKJRIS\nEhjVz/7+flRWVmJtbQ0ymQxvv/32U5Xrmc1mdHV1Qa1WM/T/QUFByMzMhEKhAJ/Px8TEBG7cuEHI\nREhICIqKirC4uIi+vj6Mjo4yCg0ymYwQSEc3ymcFk8mEJ0+eEBL55MkTp89RLBYjPDwcarUaYrGY\n8Xo4HA5CQ0NJDEZwcDA4HA7W1tZQW1uLxsZG2Gw28Pl8lJaW7kvIu9VqxdjYGJGxOna4+Xw+4uPj\niYPcVqMEIyMjUKlUZEMgEolQWFiI7OxstyW1uwVFUWhqasKdO3dgs9kQHh6ON954AxKJBDabDUtL\nSxuSws2uOYB9faflogaDAVqtlmw+aaOOjo4OjIyMALBfYwoKCpCTk+P03hmNRvT29kKj0TCMsbhc\nLhISEqBQKJ7anP+LKE81GAy4du0akQynp6fjxIkTuyLgX331FSorK6HT6cDhcHD06FHk5OQ883Vo\nM9BqL9qcj15//P39kZ2djbS0tB2/J1vNme6FEZLJZHIZCSOVShkkMjg42O3sytXVVTQ0NKCpqYms\n13FxccjOziYmg477HTpvdXFxEcvLyzAYDLuaf6X3NLSyzfFxXmTSaLVa8d577+HGjRu4fPkyysvL\nyc9+9rOf4Tvf+Q4qKyvx2muv4dvf/jZ++9vf4u7du0hNTQVgnzV95513MDs7izt37hAzva6uLiiV\nSly4cAEXL17c0+f8kjTuHgzSaDQa0dPTg87OTnJhBOwVc1pe5ufnR2bSHAnKysoKFhYWyEm4tra2\nq1gHGiwWC3w+H15eXvD29oZIJNrS5IXP5++4E2ez2dDV1YW6ujoygyYWi1FQUECMDgD7QvXw4UO0\ntLSQjRi9AdjqdSclJaG8vJzM7K0HPVvpSO4MBgNGR0fR1dXFcFjz9PQkWYurq6s7WqDozun6bt9G\n36O/dpyBWF5eRnNzM1pbW4mcy7HrGhYWhjfeeGPLjEEa2934PHnyBJWVlZifn3/mGwCKorC0tLQh\nodzs+KCDvB1JOIfDQXx8PFJTU6HValFbWwvAfhy9/vrr++qaOT09DbVajfb2dvIcPTw8oFAoSPdR\no9Hgzp07pGiQnp6OI0eOgMvlYnBwEH19fRgYGGAUK8RiMSEw0dHR+0ZCNoPVasXk5CSjG0mrC+iN\nT3BwMCIjIxEdHY3w8HDG86YoCp2dnS7fi/02qqGfD22k09vby+hY0A5yNIl3fH5jY2Oorq7G6Ogo\nADu5osnSfnfNjEYj5ufnMTAwgIaGBqytrYHD4UAkEm2ZgbiR4Qz9NZvNRnNzMxoaGsgaFhMTg7Ky\nMsa8/+joKFQqFSniiUQiFBQUIDs72+X7sbKygq6uLmg0GpcZkAqFAlFRUXumHnnRSKOjPJDP5+PU\nqVNQKBQ7fjybzYb6+nrU1NTAZrMhICAA58+f37cIob3C8vIyHj58iNbWVrK+8Pl8pKenIycn55kr\nOVzBarXi6tWriI6OhlarhVarZWRQO0IikSAoKIiodTw9PcFisQj5o80Lp6enyXnP4XBIbNdegB6/\nCQkJYex9uFwuJiYmMDQ0hMHBQcY1nW4oUBT1QpPGf/7nf8bf/d3f4dKlSzh37pzTz//6r/8aRUVF\nWF1dxR/90R/ht7/9LT0zSLC4uIjw8HBUVFTgk08+AWBfX6Ojo/HBBx/gv//7v/f0Ob8kjbsHpVar\nSVV9bm6O8YbyeDywWKxdD3uzWCxwuVwIBAKIRCIiK7VarZifn8f09DRjkywSiYgLaURExL6YvVit\nVnR0dKC+vp5IcL28vFBYWIiMjAyyGZybm0NTUxPa2trIQieTyZCbm4u0tDSwWCw0NzejpqZmU1mD\nRCKBVCqFUCgEh8Nx6v7tdLbS0U11PflzRfxowr1X5MpkMqGtrQ2NjY3EAY6GQCDA+fPnERsbuyd/\nC7BvAOrq6lBTUwOKohAYGIhz584d2A3A2toaLl++TCSKISEhEIvFmJ+fh06nc/tzDw4ORkFBAWQy\nGela7ifMZjN6enqgVqsZ0TqBgYE4dOgQEhISSM4o3V0rKSlBTk4OOBwOowPW19fHMBCgs7ri4+MR\nHx//TAiWK9Cua0+ePAGfz0dkZOSGM8ZarRY3btwgJCEkJAQnTpw4UOHdOp2OvP9095BGWFgYgoKC\noNVqyWsQCATIz89Hbm7uUytUWK1WLCwsbNgt3CpmiDacceVCKpFIXF5LLBYLWltbUV9fT7qRERER\nKCsrQ0REhMu/Q1EU6bzS749YLEZhYSGysrI2PB/1ej0hkOszIJOTk6FUKg9E1/0gwGq1orq6Gvfv\n3wdgPybPnTu3q3gfvV6Pqqoqcrzn5eWRgtbzCqvVip6eHjQ3NzOKErGxscjJyUFsbOyBOZ7oXFLH\nYrjBYIBOp8P8/DyWlpawurq6K0koYCePbDYbNpttw2uqSCSCn58f5HI5QkJC4O3tjbt37xKljFQq\nxZ/8yZ8Q6azBYEBfXx96enowPDzMeFyJRAKTyeSk2npRSePi4iJCQ0Mhl8sZOaOOoJscf/M3f4Ox\nsTHMzs66XBe/+c1v4j/+4z/Q2dmJlJSUl6TxgIP6g8XslnA16L/+5/QF28/PD4GBgQgODkZQUBBZ\nkG02G8bGxtDd3Y2enh6Gm6FEIkFycjKSkpIQFha2L0QRsG8Y1Go1GhoayMbVx8cHRUVFSEtLA4fD\nAUVRGB0dxf3794mxCmCXhISFhUEsFhPSNz8/j7m5uV3NVQL2jfNmXT8Wi4XBwUEMDw8DsFf/S0pK\nkJ2dvW/v3Waw2Wzo6+vDgwcPGBcywG5Kc+rUqV0/T51Oh6qqKrLI5+fno7y8/MBuABznEHk8Hs6e\nPcswW6AoigR9O3Ypp6amnFzZ1kMikbicn/Tx8XnqhHJ2dhZqtRptbW2kQ8PlcqFQKBATE4OOjo5N\n5/goisL09DT6+vrQ19fnJPUODQ0lHTCZTHZgNkCusH6+UywW45VXXiEFpYOKlZUV8v6vN9KhY4dK\nS0sRGRm5q9dBzwlvNFu4uLi46UXdw8ODQQS9vb0xNjZGYjISExPx+uuvu+UebLVa8ejRI9TW1hIX\n4JCQEJSXlyMqKsqt10nPeFZXVxPjKE9PTxQVFW0547mRVwDtrKxQKBAYGHigj5unBZ1Oh8uXL2Ni\nYgIsFgvFxcUoLi7e1TWjo6MDX3zxBdbW1uDp6YkzZ87s+Tzxs4ZWq0VzczPDYM/X1xfZ2dlIT0/f\ntqv2XoDePzU2Nm5IMDaDYyapq7WBzuK0Wq0uVTwsFgv+/v6Qy+UIDAyEXC6HXC5nzFE6+iDw+Xzy\nWElJSYiKikJvby9GRkYYf9/Pz49EKdHw9vaGl5cXKUq8qKTx6tWrOHv2LL7xjW/gP//zPze8n1ar\nRUhICEpKSlBdXe3yPr/5zW/wx3/8x/jJT36C73znO0+dNK6srGw4Q/uSNG4N6gc/+AGRf9IW8EtL\nSxtGWbDZbPj5+TFyDgMCAuDr6+tyPsdms2F0dBTd3d3o7e1lzJVIpVIkJycjOTkZISEh+3JxpCgK\nJpMJi4uLePjwIUNmJxKJyFC20WiEwWCAXq+HwWDY1YlPV7wA+6YnODgYQqEQy8vLLmdtAgICEBsb\ni7i4OISFhW069+TuvONPrNGDAAAgAElEQVSzxPj4OBoaGtDb20u+JxAIcPLkSaSkpLj83DeTWFEU\nhba2Nty8eRMmkwkSiQRnz551mpM4SOjr60NVVRWZQ3zrrbc2lCc7ore3F1VVVTCZTPDz80NqaipR\nBrhbmPDy8nKKC6EJ5V4SbIvFgt7eXqjVaoa8nS6uDA8PEzv7hIQEHDt2zKVj6OLiIvr7+9Hf3+9U\n0fX19SUEcj+LS+ux/vi02WxoaWmBSqWC0WgEm81GTk4OSkpKnslGbSeYnJyESqUic2MsFgtsNpvx\n/nt5eREjnYiICJdrk9lsduoQOn692bwvi8WCl5eXy24hbTjjar1wPL98fX3x5ptvbjgrbrPZ0NHR\ngZqaGnI8yuVylJWV7cipGfhfN9nq6mriAeCumyxFUdBqtdBoNNBoNIwYG39/f0Ig3ZUbPs/yVIqi\nCLkzmUyQSqU4d+4cwsPDd/yYRqMRX3zxBTo7OwHYCwunT59+Zk7O+wGDwQC1Ws0Yn/Hw8EBaWhpy\ncnK2zPDdC1itVnR1deHBgwekq87hcKDT6ZCWlkYK4pv9KxAIsLKygrq6Ojx69Mhtsx4OhwMfHx8E\nBwcjJiYGoaGhDBMzGmtra7h58yba2toA/K8cvbOzE83NzU5RaPSc+uTkJOmGcrlcpKSkIDU1FRqN\nBo8ePQKbzcbrr7+OtLQ0t/eO//AP/+DW/XaLv//7v9/1Y/z0pz/F9773PXz/+9/HD3/4ww3v19TU\nhPz8fLzzzjv43e9+5/I+t27dwokTJ/Dnf/7n+Ld/+7enThr/6Z/+Cenp6cjLy3NaU1+Sxq2xYaeR\nzWZDJpMxyKG/v/+G5NARVqsVw8PD6OnpQW9vL8Oy3MfHhxDF3YaA07N8m7l+0uTP8Xs7ldpyuVyI\nxWKIxWKysJnNZkxOTpLNB4fDQUpKCrKzsyGTyciM2uDgIG7fvk3mJCMiIlBRUYHg4GDMz89jcHAQ\ng4ODGBkZYSyMPB4P0dHRiImJQVxcnEvrdtq05/bt2+R5xMfH4+jRo24Rk/2CTqfD7du3yaYUsFfm\nSktLoVAoGMfVRhsfg8GAzz77jHQWUlJScPLkyWcaRbIZKIqCSqXa9hzi+t9LSUnBa6+9RmamKIrC\nkydPSKfC8Ryjj0+LxbJlsLhUKnUilL6+vrsmlDqdjnQf6aIIh8OBv78/ZmdnYbFYwOFwUFBQgKKi\nog1n42gn0L6+PvT39zNep1AoJBLWmJiYfZ3tdDw+R0ZGcPPmTTIjGB0djePHj+/LxmwvMD09DZVK\n5TLUns/n4/Hjx2QO0pHQ8Hg8BAQEEDc82oRmfR7meggEgg0zC6VS6Y7NgXQ6HT755BNMTU2By+Xi\n1KlTSEtLIz+nKApdXV1QqVQkbkUmk6GsrAxJSUl7FkXS39+P6upq4hy8ndxKiqKIs3J3dzfjeA8O\nDiYEcjNzr+eVNBqNRnz++efQaDQA7GveqVOndlV0efz4MaqqqrCwsAAPDw8cP34cGRkZ/2e6t7Ti\np7m5mcwkA/bs45ycHMTHx+954Y32e2hubibrBZ3rnJWVhZaWFpfHJ620oXMPtVotY458PaRSKeRy\nOby9vcHlcrG2tob5+XlotVqXv8Pn8xlmOxRFobq6Gnq9HhwOBzExMVhaWnJywQbsxUoWi8WIaQoJ\nCUFGRgZSUlLA5XJRWVmJnp4ecLlcvPnmm6QA9SKSxn/5l3/B3/7t3+J73/sefvSjH214v+bmZuTl\n5eHtt9/Gxx9/7PI+N27cwMmTJ/Fnf/Zn+PnPf/7USaMj50lMTER+fj7CwsLAYrFekkY3QP3whz8k\n5FAmkyEgIICQw+0sJhaLBUNDQ4QoOnZB/Pz8CFF0Jbeh3TfdjXyg/79bi2gPDw+yWRYKhSRLT6vV\nko02Le04dOgQY8M+NDSE2tpaIr3k8/nIyclBXl7ehhVMm82Ghw8fQqVSkUUtLS0NR44cIZsAi8WC\nsbExQiIdA+EBe+WZJpDh4eGMjb3FYkFjYyPq6upIvmNOTg6Ki4sPFKmamZnB//zP/zBmHiUSCXJz\nc5GZmbnhJmFoaAhXrlzB8vIyeDweXn31VaSmph7YDYDRaERlZSUGBgbAYrFQXl6OwsLCLZ/v+t87\ncuTIpjlkVquVZGT29vaSCiiLxSJxD35+flhcXGTEhuj1+k3l5o6E0pFU+vj4uL2xt1qt6Ovrg1qt\nZki7+Xw+WSMkEgkqKio27DrTsNlsGB8fJzJKR1kQh8NBVFQUEhISEB8f77bh0m6wsLCA27dvkwgI\nb29vHDt2DAkJCQf2mHTEzMwMampq0NXVBcBeFMvKykJhYSG4XK5Th5A+braSkLJYrA1Jobe391Nd\ni8xmM7744gvSOcjMzMSxY8cwNDSE6upqQux9fHxIseppdKvpQp5KpSJ/09vbG8XFxUhNTXXr/KGL\nrxqNhnFeA/YoJ4VCgaSkpBeiYzY+Po7Kykro9Xp4eHjgxIkTSE9P3/F5ZLVaoVKpcP/+fVAUheDg\nYJw7d+6pukwfdExPT6O5uRkdHR1k7ySVSpGdnY2MjIxdH0c6nQ6NjY0Mvwd/f3/k5+dDqVQy9ipW\nqxWzs7OYnJwkt6mpqQ0zUblcLsLCwhAfH09kphutI7QR3cTEBDHb0Wq1WxazHP9WbGwsfHx8MDY2\nxsgrFolESEtLQ3p6OvFNWFtbw8WLFzEyMgKBQIB33nmHdMb3IgngIOLjjz/Gu+++i6997Wv47W9/\nu+H9pqenIZfLUV5ejrt377q8z0cffYQPPvhg3+SpU1NTePDgAUPCHRISgvz8fNpg6yVp3ASU1Wrd\n8UXTbDZjcHAQPT096OvrY1zUfHx8EBoaisDAQHC53A3jHmgX1p2AzWZvafjCYrEwNDSE/v5+oneP\njIxEcXExIiMjAQDDw8NobGzE4OAgeezY2Fjk5+czZlvoKnJtbS2Zu1ofw+EOjEYjamtr0dTUBJvN\nBg8PDxQWFqKgoMBp/mxhYYEQyOHhYcZ77OHhgaioKEIiaanf8vIy7t27R6InhEIhysrKkJmZeSDm\nHQE7AVCpVKirq2N8n8fjISMjA3l5ecTwwGKx4O7du2hqagJgz6Y6e/bsrgwRnjampqZw8eJFzM/P\nQygU4vz5825Jhqenp3Hx4kXodDoIhUK88cYbiI6Odvvvms1m9PX1kaw4R1c52uo/Li6OWITr9XqX\nLq9bEUpvb2+XhNLb23vDDfH8/DwePXqER48eubyAh4WF4dVXX4VcLt/yddKmNHQW4fq52eDgYMTH\nxyMxMREBAQF7SuLMZjMaGhpQX19P4lKKiopcnr8HEXNzc1CpVKSjw2KxIJfLIZFIsLS0BL1ev2Wg\nPe3cTLsZOkZ5ACB5nImJifvu4khRFB49eoTPP/+crK+Om+Ti4mIyr74fz6W7uxsqlQqzs7MA7NfG\nkpISKJVKt9djs9mMgYEBaDQa9Pf3vzAZkOuNzIKCgnD+/Pldkbu5uTlUVlaSeciioiKUlJTsy+f9\nPMBoNOLRo0doaWkhhVt6Bj03N9et9ZcG3RlvbGxkjJ/ExMQgLy8PMTExYLFYRDEyMDAArVbLcDx1\nhIeHB4n+AOxF+7Kysi0Liu5gcXERzc3NaG5u3rThQJ+Trp5fcXExysrKyP9XVlbw8ccfY2JiAp6e\nnnj33XcZsvgXlTROTk4iPDwcQUFBGB0d3fSzOXToEIaHhzE3N+fyHPzWt76Fn//852hra0NqauqW\npNFsNsNqte5IgeD4ebhy/P9DF/IladwEG+Y0ro98oL+mKzjT09NbVpy3g51EPtDurq6wsLCA+/fv\nQ61WkwtsbGwsDh8+jPDwcFgsFnR0dKCpqYlUgrlcLtLS0pCbm8uQllEUhZ6eHtTW1hLJkVgsRn5+\nPrKys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1FqVKlU6O3tZSk1SqVSxMbGIjAwEEaj0SkR9NQKxz4byJR/Mv/39/eH2WxmCS64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\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OHz+ufrm5uZGeno5OpyMqKkrKd4hx6+/vZ/v27TQ0NBAQEMDGjRvx8/Ob6WaJWW4uvgLJ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\nO7fY9U6cOGH9+vUr05gV5HsaK9/zXgEAAAAEW0F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       "text": [
        "<matplotlib.figure.Figure at 0x10b945950>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Let's try an example together\n",
      "\n",
      "We will revisit the Motor Trend Car Road Tests data set used in [Lab 3](http://nbviewer.ipython.org/github/cs109/2014/blob/master/labs/Lab3_Notes.ipynb) and build a linear regression model to predict miles per gallon (`mpg`). "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Motor Trend Car Road Tests Data\n",
      "\n",
      "We previously looked at the [mtcars](https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/mtcars.html) data set in [Lab 3](http://nbviewer.ipython.org/github/cs109/2014/blob/master/labs/Lab3_Notes.ipynb). The data was extracted from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973\u201374 models). This data set is also found in the base installation of the [R programming language](http://cran.r-project.org).  \n",
      "\n",
      "Column name | Description \n",
      "--- | --- \n",
      "mpg | Miles/(US) gallon\n",
      "cyl | Number of cylinders\n",
      "disp | Displacement (cu.in.)\n",
      "hp | Gross horsepower\n",
      "drat | Rear axle ratio\n",
      "wt | Weight (lb/1000)\n",
      "qsec | 1/4 mile time\n",
      "vs | V/S\n",
      "am | Transmission (0 = automatic, 1 = manual)\n",
      "gear | Number of forward gears\n",
      "carb | Number of carburetors\n",
      "\n",
      "First, read in the `mtcars` data set using the `sm.datasets.get_rdataset` function to import the dataset from R. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your turn\n",
      "mtcars = sm.datasets.get_rdataset(\"mtcars\")\n",
      "mtcars = mtcars.data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Histogram"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mtcars['mpg'].hist()\n",
      "plt.title('Distribution of MPG')\n",
      "plt.xlabel('Miles Per Gallon')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "<matplotlib.text.Text at 0x10b7152d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OOjgF2Lm2PQT8ivTH2rnX/9rVD5x7EexNevFtWgu8H1/7ImhXO5jG3Mv5wN4c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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b9ba450>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Scatter plots\n",
      "\n",
      "Relationship between `cyl` and `mpg`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(mtcars.cyl, mtcars.mpg, 'o')\n",
      "plt.xlim(3, 9)\n",
      "plt.xlabel('Cylinders')\n",
      "plt.ylabel('MPG')\n",
      "plt.title('Relationship between cylinders and MPG')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "<matplotlib.text.Text at 0x10b751e90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vzZikUbPw0kV89ZpV9LTkaOnJM/ekWRbvSxo1FvBLkiQlZAG/JElSHTAZkyRJ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\nJEmSJEmSJEmSJNWo/w+51eH3J1C2IwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109c488d0>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Relationship between `horsepower` and `mpg`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(mtcars.hp, mtcars.mpg, 'o')\n",
      "plt.xlabel('Horsepower')\n",
      "plt.ylabel('MPG')\n",
      "plt.title('Relationship between horsepower and MPG')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "<matplotlib.text.Text at 0x10b78c590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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t2T5aMk0sPfm0suSPLWtbVCRH7Uc8p3cKSxcsnPD+JUlqBBNKcKsBJxPUkc7u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\nGx0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b425d50>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Build a linear regression to predict mpg using `statsmodels`\n",
      "\n",
      "Now let's build a linear regression model for the `mtcars` DataFrame, and estimate predicted `mpg` given a new car has 6 cylinders and 180 horsepower.  \n",
      "\n",
      "$$ MPG = \\beta_0 + \\beta_1 * cylinders + \\beta_2 * horsepower + \\epsilon $$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your turn\n",
      "y = mtcars.mpg\n",
      "X = mtcars[['cyl', 'hp']]\n",
      "X = sm.add_constant(X)\n",
      "\n",
      "model = sm.OLS(y,X)\n",
      "results = model.fit()\n",
      "print results.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                    mpg   R-squared:                       0.741\n",
        "Model:                            OLS   Adj. R-squared:                  0.723\n",
        "Method:                 Least Squares   F-statistic:                     41.42\n",
        "Date:                Fri, 17 Oct 2014   Prob (F-statistic):           3.16e-09\n",
        "Time:                        11:08:10   Log-Likelihood:                -80.781\n",
        "No. Observations:                  32   AIC:                             167.6\n",
        "Df Residuals:                      29   BIC:                             172.0\n",
        "Df Model:                           2                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "const         36.9083      2.191     16.847      0.000        32.428    41.389\n",
        "cyl           -2.2647      0.576     -3.933      0.000        -3.443    -1.087\n",
        "hp            -0.0191      0.015     -1.275      0.213        -0.050     0.012\n",
        "==============================================================================\n",
        "Omnibus:                        1.178   Durbin-Watson:                   1.667\n",
        "Prob(Omnibus):                  0.555   Jarque-Bera (JB):                1.092\n",
        "Skew:                           0.411   Prob(JB):                        0.579\n",
        "Kurtosis:                       2.623   Cond. No.                         645.\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "newX = np.array([1, 6, 180])\n",
      "results.predict(newX)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "19.878263535641754"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What if a new car had 4 cylinders and 120 horsepower? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your turn\n",
      "newX = np.array([1, 4, 120])\n",
      "results.predict(newX)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "25.554952517097814"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now estimate the least squares estimates for $\\beta_0$, $\\beta_1$ and $\\beta_2$ using matrix multiplication and the formula: \n",
      "\n",
      "$$ \\hat{\\beta} = (X^{\\top}X)^{-1} X^{\\top}Y $$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your turn\n",
      "beta = np.linalg.inv(np.dot(X.T, X)).dot(X.T).dot(y)\n",
      "beta"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "array([  3.69083305e+01,  -2.26469360e+00,  -1.91216965e-02])"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Many different types of regression\n",
      "\n",
      "You do not always have a continuous $y$ variable that you are measuring.  Sometimes it may be binary (e.g. 0 or 1). Sometimes it may be count data.  What do you do?\n",
      "\n",
      "Use other types of regression besides just simple linear regression.  \n",
      "\n",
      "[Nice summary of several types of regression](http://www.datasciencecentral.com/profiles/blogs/10-types-of-regressions-which-one-to-use). "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}