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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Defining Custom Display Logic for Your Own Objects"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Overview"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In Python, objects can declare their textual representation using the `__repr__` method.  IPython expands on this idea and allows objects to declare other, richer representations including:\n",
      "\n",
      "* HTML\n",
      "* JSON\n",
      "* PNG\n",
      "* JPEG\n",
      "* SVG\n",
      "* LaTeX\n",
      "\n",
      "This Notebook shows how you can add custom display logic to your own classes, so that they can be displayed using these rich representations. There are two ways of accomplishing this:\n",
      "\n",
      "1. Implementing special display methods such as `_repr_html_`.\n",
      "2. Registering a display function for a particular type.\n",
      "\n",
      "In this Notebook we show how both approaches work."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Parts of this notebook need the inline matplotlib backend:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing special display methods"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The main idea of the first approach is that you have to implement special display methods, one for each representation you want to use. The names of the special methods are self explanatory:\n",
      "\n",
      "* `_repr_html_`\n",
      "* `_repr_json_`\n",
      "* `_repr_jpeg_`\n",
      "* `_repr_png_`\n",
      "* `_repr_svg_`\n",
      "* `_repr_latex_`\n",
      "\n",
      "As an illustration, we build a class that holds data generated by sampling a Gaussian distribution with given mean and variance. Each frontend can then decide which representation it will display be default. Further, we show how to display a particular representation."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The next cell defines the Gaussian class:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.pylabtools import print_figure\n",
      "from IPython.display import Image, SVG, Math\n",
      "\n",
      "class Gaussian(object):\n",
      "    \"\"\"A simple object holding data sampled from a Gaussian distribution.\n",
      "    \"\"\"\n",
      "    def __init__(self, mean=0, std=1, size=1000):\n",
      "        self.data = np.random.normal(mean, std, size)\n",
      "        self.mean = mean\n",
      "        self.std = std\n",
      "        self.size = size\n",
      "        # For caching plots that may be expensive to compute\n",
      "        self._png_data = None\n",
      "        self._svg_data = None\n",
      "        \n",
      "    def _figure_data(self, format):\n",
      "        fig, ax = plt.subplots()\n",
      "        ax.plot(self.data, 'o')\n",
      "        ax.set_title(self._repr_latex_())\n",
      "        data = print_figure(fig, format)\n",
      "        # We MUST close the figure, otherwise IPython's display machinery\n",
      "        # will pick it up and send it as output, resulting in a double display\n",
      "        plt.close(fig)\n",
      "        return data\n",
      "    \n",
      "    # Here we define the special repr methods that provide the IPython display protocol\n",
      "    # Note that for the two figures, we cache the figure data once computed.\n",
      "    \n",
      "    def _repr_png_(self):\n",
      "        if self._png_data is None:\n",
      "            self._png_data = self._figure_data('png')\n",
      "        return self._png_data\n",
      "\n",
      "\n",
      "    def _repr_svg_(self):\n",
      "        if self._svg_data is None:\n",
      "            self._svg_data = self._figure_data('svg').decode('utf-8')#.encode('utf-8')\n",
      "        return self._svg_data\n",
      "    \n",
      "    def _repr_latex_(self):\n",
      "        return r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,\n",
      "                                                                 self.std, self.size)\n",
      "    \n",
      "    # We expose as properties some of the above reprs, so that the user can see them\n",
      "    # directly (since otherwise the client dictates which one it shows by default)\n",
      "    @property\n",
      "    def png(self):\n",
      "        return Image(self._repr_png_(), embed=True)\n",
      "    \n",
      "    @property\n",
      "    def svg(self):\n",
      "        return SVG(self._repr_svg_())\n",
      "        \n",
      "    @property\n",
      "    def latex(self):\n",
      "        return Math(self._repr_latex_())\n",
      "    \n",
      "    # An example of using a property to display rich information, in this case\n",
      "    # the histogram of the distribution.  We've hardcoded the format to be png\n",
      "    # in this case, but in production code it would be trivial to make it an option\n",
      "    @property\n",
      "    def hist(self):\n",
      "        fig, ax = plt.subplots()\n",
      "        ax.hist(self.data, bins=100)\n",
      "        ax.set_title(self._repr_latex_())\n",
      "        data = print_figure(fig, 'png')\n",
      "        plt.close(fig)\n",
      "        return Image(data, embed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, we create an instance of the Gaussian distribution, whose default representation will be its LaTeX form:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = Gaussian()\n",
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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MzJw5M67nDUanaH/jUomKSbRgvVT6RQcvhOVAOBUvlQ1UBS/kR384+3fu3ImdO3fGdQ8V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\nw9F05h+9ALJ3fsa+sVptjrKZwNnC9ipbMpbNwgpu2uWFE9Yp4nMMs3W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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can view the data in png or svg formats:"
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x.png"
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     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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LyGCw3OHi5wW51XN1EVfZ2aVCH5h9bDfXzHd1EvutF1ReZJey46PbdKqqah0p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\nw9F05h+9ALJ3fsa+sVptjrKZwNnC9ipbMpbNwgpu2uWFE9Yp4nMMs3W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       "prompt_number": 4,
       "text": [
        "<IPython.core.display.Image at 0x1083d5510>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x.svg"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "svg": [
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        " <defs>\n",
        "  <style type=\"text/css\">\n",
        "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
        "  </style>\n",
        " </defs>\n",
        " <g id=\"figure_1\">\n",
        "  <g id=\"patch_1\">\n",
        "   <path d=\" M0 265.638 L377.925 265.638 L377.925 0 L0 0 z \" style=\"fill:#ffffff;\"/>\n",
        "  </g>\n",
        "  <g id=\"axes_1\">\n",
        "   <g id=\"patch_2\">\n",
        "    <path d=\" M24.0813 244.76 L358.881 244.76 L358.881 21.56 L24.0813 21.56 z \" style=\"fill:#ffffff;\"/>\n",
        "   </g>\n",
        "   <g id=\"line2d_1\">\n",
        "    <defs>\n",
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        "    </defs>\n",
        "    <g transform=\"translate(128.60125 16.56)scale(0.12 -0.12)\">\n",
        "     <use transform=\"translate(0.0 0.125)\" xlink:href=\"#Cmsy10-4e\"/>\n",
        "     <use transform=\"translate(81.982421875 0.125)\" xlink:href=\"#Cmr10-28\"/>\n",
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        "     <use transform=\"translate(847.751953125 0.125)\" xlink:href=\"#Cmr10-31\"/>\n",
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        "     <use transform=\"translate(997.751953125 0.125)\" xlink:href=\"#Cmr10-30\"/>\n",
        "    </g>\n",
        "   </g>\n",
        "  </g>\n",
        " </g>\n",
        " <defs>\n",
        "  <clipPath id=\"p169ef6c7ca\">\n",
        "   <rect height=\"223.2\" width=\"334.8\" x=\"24.08125\" y=\"21.56\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
        "</svg>"
       ],
       "text": [
        "<IPython.core.display.SVG at 0x1083d5c90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since IPython only displays by default as an ``Out[]`` cell the result of the last computation, we can use the\n",
      "``display()`` function to show  more than one representation in a single cell:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import display"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "display(x.png)\n",
      "display(x.svg)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LyGCw3OHi5wW51XN1EVfZ2aVCH5h9bDfXzHd1EvutF1ReZJey46PbdKqqah0p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\nw9F05h+9ALJ3fsa+sVptjrKZwNnC9ipbMpbNwgpu2uWFE9Yp4nMMs3W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        " <defs>\n",
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       ],
       "text": [
        "<IPython.core.display.SVG at 0x108861f10>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's create a new Gaussian with different parameters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2 = Gaussian(0.5, 0.2, 2000)\n",
      "x2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\mathcal{N}(\\mu=0.5, \\sigma=0.2),\\ N=2000$"
       ],
       "metadata": {},
       "output_type": "pyout",
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RlNQDCxb8rt0nwR050oBz59RMNPl4bX//ycaPWthhvz3brud6QkCbgcVi8XrN\nf/7nf+LGG2/Ezp07UVlZiTvuuANff/01evToobquoKDA/ffYsWMxduxY1e+0QzaDLtS+p0X2NMnV\nJ35VA2AazTzlPdkAomC11mLJkjtRUDDPY13buwAsWCCnns6YUQSXy4aLF1naau/SopFmMnXqGKxd\nuxcOh1ZqfwILFtzrsT5ayCdFJqKi5qK5+RVo0//6knbCUwQ1fd9t0C8yc7BgwYO656pPzioC8I70\nue09rU0LX0+A8+coUKN+HD06WXXK3a23DsDnn5+UalOy9y5cmIn9+3PgcCQC+BF0LgH6sdUflGpr\nB7AdUVFHcf31PfDcc/N1deR9xyioZwBMRnR0GP7t39Jw+nQMyso8axn6/md9Li6yGQDKAbwNJqC1\ntdlhtc6By8UFNtkaYJzGgSIubgkWLLjD47w12qCBbpLvxPlgXC5/QOfDTuVf8BHQZpCUlITjx7nJ\n5vjx40hOTlZd87//+79YsoQO9NTUVAwePBg//PADbrrpJtV14mYgQ319FQCn8kkthcbH/4CVK+e2\ne5LzTi4BMB90AWGYp/wDbr89z+NGEIzjIWkbrMGyZfvhcrFFjElJ3qXFCRMysGdPOf7f/xuPpqYI\nWCyRIMSGUaPGYdSoYcrZEFMARGLw4Bg899xkrwsdbfNIxMb2Q7duLtTXnxWu5Bx0q/Uo0tP1Kran\n3D0M3uM8xL4+DeA4nM5wTJ36GgYP3uw+4wKAsOAlgG/s+udq0Z6UHr70YyBHgbIcPaKGOXp0MjZu\nPCHcY8eOHW+rFsLKyiXYs6dccx1/L0VPUC2gQPhOHFuiNE439uZmoG9feWoT2nfqo1MBoLV1LhYs\nuAMAMGvWejgc2wAkAZgMwAbgGHr27IM//OEt/PDDWc1TWZ9v1nx/EqKmDmTA5QJ6987GsGHX6bRq\ndh5KRUWEsDDr0zj4krpFv0HbYbMVoaVFJu1nYMiQDejXz7uJsL3aKJ0PY5V/DMHTDALyPrS0tJCU\nlBRy+PBhcunSJakD+YknniAFBQWEEEIcDgdJSkoitbW1qmt8KQZ1zMg5w717P9Du6GJCZEwYPbfa\nvzQJ7TsekkFPkxOjEb0zJgJlDanron9nQsLDytGbvsVH+OJI9T3VdSkBvNfPm0Nb5sgzYoINHfqo\nzvntO1HA+BpPzDMZa8V7FC7954lmKT+fgqV8maN8ljuB4+Mne5hf3ueYmk2kHdMyZ65sjBm3mWwc\n07kgUkha5qAHAAAgAElEQVSNHNG+U9kZ45A7cP1PK+8P2UF2T4BLuAoBaQZWqxWrV69GVlYWWltb\nkZOTgyFDhmDt2rUAgNmzZ2Px4sWYOXMmRowYgba2Nixfvhy9evXSPWvs2AK3JOp0tsLhqENiYqI7\nKpeeiKQ1GdgBvIna2ndQWkq/8TW6mF0DAFOmvIQLFwCqCdjBNI4ePb7BypWLPO7WnpxL4q7vS9pd\n6uwVQd8bHv7/cN11CXA4spGYmKDYONVSED217GpoJR9vRwhqk4DV1jKtRJQSqRbgcAxETMxu9Ojx\nMi5c+B9dnbXv0fpRWP+uWLEDhYXUoevJ8a5Po53mtX785CytaYJKcydOJCIrK9dLmmo7gA347jvg\n22/Vzm+bzfuJc97Gnd5+TzWsvXt3Y9asepUZQ/9OO4wIFPrxoy8bRSYocSEB3CSUB+BrzXVU6j93\nbrN0fi1cmAm7fR2aJbwKcY4VFpbg0CHWjmxcMT+Y3uQbFlaFtrbtoGanbEREAFFRTmWOqiGzxefl\nbVC0wwhwzSULwEu6awHgwgXvkdXMBJyVlSuMCa61xscfw803/8xnooB83cjCjBlFGDZsh1RTkPkl\ntxnzXdqPoG0rAQCARGJQ75hquhlLUOWZsuYrTW/kyBzdO4FnSErKJK+0SCNKXVTUHNV36shjfp2o\n1fToca+BxGcc36DWbnyXngiRUdjyJX/L8sloE2d5l7C80fN8S8jnXYJXS8dsrDxKLJbfCRJiPomM\nvI/k5xdJymYksXqXvhl810i1bevtnf6XTV8mT9x9z+UR68qTqIkRwktUSSXVcyRf8796Tlutv5G+\nc+TIHJ/pupx6zjQX1m7yed6eBJjBylemf45/2QiCuYSHTG4ivcTAUVmZhZiYFzSOSkrj8iSV+Jq3\nJzY2GVTr4DlTgGScPHlOkGjkTkW5c6lE5UAC7GhqcgF4GDRdMv3Oan1bpdXExU1CePhstLays4NL\nAFSiZ89IFBfbvTCiZPQ7Cpn0VFxsx/LlpWhqYpqAHUCFcIXoT2HttwZAKZpljW7wHn05OUQ7uTfH\ne3l5BYDekl/tOHiQCNKa6Fikdm+rdQJcrj9AtG07ncDzzz+KUaPsEg1kM9R2dY6EhDjExflCIdbb\nmEWtZOXKLEWbE53csuloR3NzgzL2LdATKGifWCxAY+M5xMc/hnPnVkvLpi6T7OzhDKSkvIXkZCp5\n7t9/XHqokUgJbWyMANcyeJtUVz/pHrPqOeLS/E/fy+Z0jx4zpO90OsMRG3sK8fFTQEgkUlKM/V6E\nMMfuAACfgo/hx0E1BHGej0NsrJzoIEOw2F567bB9hAemzQcTIbQZWDX/M1A1r6HhQzB1ljEcCIlB\nWZn+SfX1VW7mRWzsKalzUwR3VIrf52oWdHnnyDYcSqkTy78ewHUQB6LF8iVcri2q59fV/Q9SUu7D\n6dMT0NDQH2zjOHQImDXrSaxbp2e38AGRqbyHLRJ0M4mIOILTp2N1m0lhYQmampiTlanSItc8E8CT\nAGKVa9YA2A86YNt/yL2//HnmjK2tnQ/gBd17gSI4neIkUjsW6+urUFbWHbKEZk7nX9z9yf6NHVug\nbM4y01EJTp5sxqBBnseUuLlUVZ3GoUMWNDW9g/JyHiOycmUWhg0b4hYEKGTv3IaLF4tB2/9Tdx0p\n7gPQC8A7IARoagIuXXoAqakzkJw8WFo2ZmKgJkF9eycn98PWrUvdpkcZ2MJXWFgCh+M1UPOqum1F\n8516jjDzXRIofftBMDOZzVaB+Phuks3ArrQhZxidP08FM5kTdvDgaGVdOAl6YiJzdFdDP8+BqKjt\nhs/SUmlrahwe2UK+OoV5mzC6vIzwYMfu3QdVJ/AB2rMNQsSBHCwAEFRS35xl8rN0S0lk5J0kIuKR\ndqlbejPBEmKxyFVuI4eVaOZQRyEaOdlkaiJNodujx93Sd6enz9O9W63+M4fgeEKdrcZtoE6NIYvm\nvJ/Q/DSsHWTO7Vxitf7Wa/qGQHIXqeu3iKjNhLkEmCV97rBhi4T7J0vaW96f6sRo4ph4QnWfr455\nTyYj75GwWqev1rQjb9OYmPFeo9Y9OfeNzVhq0ww3dXhvW3GOpKRMIlbrw0RG2OAkBf6d3MRqZDpi\nKVieIPysChaFr6+PzfaopM78LAFjU2IOsVgmkujoKWTkyLkkP7+IjByZozMPe0u7weeFb6m59RHO\n8DoGfUXwnhQA6GZg5DPwPND0Xn7/wvlZIi3emf6nV1APnHyDOmgXYLHO8mRs8fHTvbzL8+QxTo2h\nLV8pAe7WlG2G9JmeUnSoy+c788I4MZ22zZYQQG5jZn4WumDlEF9TIugnfS4BMqX3yjZnLTwxlWSL\nR0LCTJKePk+SkZPVQ2xDWZ+UKkn3vNugjXw16g2RHzDVo8fdqhQNxguZvm3FPuXCjvEc85xLiM0H\n47Q06vIVEWCKpk/zCUDXDf184OPLYqGLvXoRZsw25iOZRICZBuOT+rGMNgQ+PnzzH+mztMLrGPQV\nIWMmGjNmB+rrT8FieQeXLrnczJnq6mqpOqs9Czk9fR6amtaA2gX18GaOYKwHnjrB//QKopng00/L\ncfHiUMkbM2GzzVHONWDBdAyXDErp1H0jYxicOJGI8nL93fogNZbqQmsO2ABuHmL1el5aora2OoOy\nUuh9BTxCeeXKeT7w+EVfiBiJyuz/s6E1jQHH0Nx8CcXFdsUEOB3Ay9BGlcsC7/QMqGqUlcVChsOH\n5QwxEXIbs2j2UJs+n3vudwCgxGiI48AFQOvbkkwMlICQdfAlal0bJFlcbEdWVq5yngEzHXLTTEvL\nXPd13HTH+sPYbKiPVP5WuUq+/MTGJrujyz2Zq+RBX3ScT5iQgfXrIZzdzSaEaCayw+EowtixBfj6\n6+PgpkQeO0EIUFYmppmwg5orR4Iy2+wAvgI16RYI13D/VG0tMGtWDhITN7tjdljQIE/joY6dsloP\nwKUaOnRs19d7nm8BIWjbSgDwVAxfuOpbtpQqDBdtkjnfdmcGuYc/l/TsOUNi/vFN66BMpXuJVh0G\ncsiUKU+TkSNziMUyRfPbJMn1j5KUlEk+tafc/LCExMdPJ5mZS0h+fpHKjHDVVQ8qaYKZpDNRIpk8\noJM0KeNKznRikqA+5S7953v2S63EVErCwkRtQDwiVa+i5+cXCZoJM6FNIFFRD/iUypubmWRSWrbX\nvpCbICdKnzdyZI5GW9BKqtqxPYnozWTZhGsS8naXxTKoy+k5fkDN7GOaw0QSHj6eDBu2SGc21Jve\nRLaP8XySa5W0DaOiphmy79j7tWNczZQqVc6yENs230O5RM1BHA85BJimuc/7GFa/W7++6TURo/if\nn6BmYOR48SXnD89hwyKJtdIj3Z0XLfJ8epFeiqNSxOjRlPEydmyB9D6t1iHW5fDhFlCmRTbULIbp\nOHt2O/r2TaBdqkJ/yfUPIS7uHe2F0nZTO+y0OXr00asRETmIjo6H08k0nhnQa0aJ4A7w0wDqACTi\n3DnonNP6BIAMnFNfXl4hZUjpHc36xHQnTqQKmg9LLpgAWXTprl15yql521FVFY5DhwaiqenPaG6m\nEp+3MUHjQ2KglXyBxRg0KFp6j7ZPpk5NwgcfzHJHwxJSILnLrvzeW6iHmsceH+9CVdWjcDqnKnV+\nFyxtisVCEBPjQt++0Th0CDCKWq+vr5JGR8fGnkNlJdNOjU9/q6o6jcrKJsg0h4iIuXjhhUm6sbB7\nN4uLYJL3LPiiUei1yvtAHcKvobkZaG6Wp6QYPTpZV8e4uCV4+ukkdx4wHlMjkieYBiJbFgeAxim8\nBzo/GBoApAnttgQ0vkGElrxQIpSZpdqYjPBwIC4OmDp1DEaNGidoNdrIcICNCRnzym8EbVsJAAB0\nTqP2RM7y81VFzrPcCdu+w7fVTjW5E1QdK8AlUVGikNs8x4zJNzgb1liq817exW5nVnx8NrFatVKo\nTOrRajzamI5HCT/sxLstWu/UNo4f8SdSW649TBf+5nx3ZhP29dna9qX+F2Yj5rbmyMj7ffAX8Xrq\nSQUyydOo72kU8NChj5KYmDsNz9tQkyq8SZzqdoqOztY8T64F85To3qV6ruVo61ZEgN8KY2syiYiY\nrDvwRq2pG6WWLyW9e09WOct9ISvwZ2sP9ZH5HVlbsnksts104lmDk/Wptl6e42+6d9f2DV8PgrmE\nh4xmIEZdss//9//O95h8i4FTQ8V8Jlo7L5VKd+2q0kWgMhhpIQA0NlLOH9fGCnzyyWSBuw9QiWK7\npMaUO9/WZgG3NTJNoEJyvZ7LbBTFuHz52wINrwBqyKi72vww2aC00pdA2zUXwEOgdbfAmy1aLd2z\nNjbmUe/ZU47Vq0vR1HQJzc31sFofgcv1qvs6LW311lsH4JNP5gjnSGfAZitCU5M+T86hQ3PcGog3\neqt2nNXUnFVSO28DlQZpP4aFleOZZ+TJzYziKeLjZwjf6P1RnI4sp5eeOzcP587RNOZGMRDMVg5A\n0YTO6KLWafJAsZ3ovLh4Uev/yNaVMTV1MWy2RNTWej43mp/zzbQ1RkW2KH+fAPAYaHsmIiysBvff\nfzVqayNU0elqTb0EcvplBhIS3kJtbbT7XGxP7cPAny2OCZaBYAMsllmgvhf2bqbl2kF9d48AeBVA\nNPRnO7sAzATwhvK9tk/Fz1p/oRiJPAT19dVwuVqk9Qk0k60OQdtWAgAA6c4XHT1FanONiprmtvfS\nYwvvJNR+yuzGWhqeKJ3mEGAysVjuJykp07xSIvlhOqLNeSIBppDw8PGScmulABmlrZRQW6/M1m1E\nj+UaivERkDKpRCvhaaUeI6YNlbjUrJZSwm3SesnV8wEfWmmISqXduv1KOWJUK13lkqioaTppUS35\nUkndZnuATJnytOY4Q3U0rDd6q4ymbLHcryqPloEiGy9Gx3LqmS/0mfHx0zV2eC3dUmaH9v8AHHU+\nIe28MGY2iXZ4+biiz6PnhjNbvrbPmf9Mf5/+MJfFGi0737Deeiq2b+wm+mzvjCY+/sW+YWNiAgkP\nn6mqCx3PRYTOqxkE+BWJiWFjfAmh2tDDRG3NMNIUPFNig7mEB+9JAUC9GYgT+U6NWmt0VrHIAy8i\nQBZRJzVjDfowUVPClpC4uKk+qPuPSu+lXHztQNIOLjYhtGk09IsfMIFERj6i+k5cEPULlswck695\nv5aOWErUi81kImtbi2WmAdXQKJmeuIh44oprr2ffy80SWiqvkZlj5MgchYKoL09ExAMeEuw9I0kG\n5zntg+cT9YwXF28n7vFEg6J5ji10oqnxacKFCdYG95ApU57WlUnmKObpRGR0ylxisUwxPKPY2AxV\nRNTzw2hRlplMPccSZWXlCgKZflGMjtYSMHyjMevp5PJrPW+A6o2DChxa6ukSYrGMEeY2LSMlQmjH\nnZGJSS6QBHMzCBkzkczpCwAVFYzSpY8grauLAFWbc0FNGixKtifo6WEsAVeVcr8F1Dn7R+EZS5CX\ntwEAdCYC7lCrA9BDdy9NyatFJiIjH4HT+apSnr3K9yKlrQCydMFAruDE1acQ1p/kJZobRFVWhCzV\nxnC3Q/azz1rhcmnV3FZ0716rSg1NHdIWUEdbDqhD2Qpq0hLNP3Y4HImIjv5GdXjI6NFjsHEje4ZY\nBxtoP8lomtSpKlJ5KcVPbw6qqJiLIUOckI2Tlpar4XCI/aant6rPXhAphr5FWuflbVbGi3gPNcFE\nRR0DEIOpU5MMDzKaMCEDiYmb4XCIZV/vbgcaPcv+PgJgDMT8/gDw3nvcJKan6NrxySdFSE1NhMXC\nKKlWyMYhIeq01TKH+K5d3AwVExOO48cb0db2d9CxzcwgsnMMqtHUpG09+Slsu3ZVgZASJfL2DuHU\nP/WBO4WFdlxU5Q+k5bZa78IvfvF/dKcb0nTuDSCkGwYPjsYf/jDMsF8AMTW6aK7hZIgjRxqwdOkd\nQgT7BmgJDYRMhtP5F1UZ29p2gCffNIpEdrmvFyOnk5PztI0YOIK2rQQAAIQ6lGRqvCfH2gzhN9Fp\nLDvwOp8YUQSjo8d7MBGw58nuLdUd9J2QMJPExU0lnPYnC2SZqNnxWfnkJgbmODZKihcfny1QOLVS\nkWc6rBFdVgyoYhJUePhviVoL0/aLZ2cYfwaTJB8gwJ1E7pA0chgaOy+plCdTu+XtapzgTlsnKpHF\nx2cbSsvq9xpTXT2ZJfWH0ucQKmGKmqSomRr3q1zTYX8/rHmW8ZjzJdUyfRd7jpG2kU3S0+dJCBba\nIEnvDlVtkFxKipz2rE1AR814epq3L2QVdQp94zIaU5Fl7SzTuH2JROaaSzCX8BDSDB6DeBYwBzs5\nSJakjIkYLqgDpWJ0z6AOzCjlM9/VAReamohKggK2gZBrhftjQANc1PcBmeje/Qz+7d+4VHH6dBTK\nyl4H1RpeFZ4xC5Ry9goIWQPqPNNKuFqpnr5v//7jyMrK1Rwuw0CPgCSEoKSEfubvq1bKrZZUw8O/\nxv/+bwRuuOFxNDae0jjLgPDwWbjrrnQAIk10utKGJVCnApYdjsLbqbLSgoULV8JiuQ6VlSwYSsxz\n9AcAlQDmasq5DVT70CITFsufQYj+l9jYZAwYcEihVkJ4z0Do+24ADh2yGCS4kydRu/lmeSpw+fGc\nF+Br4jEGtcPUCqotbQYNpGT3vKbUx7MzXO0sF/uFOfKpo1RPHqAQ8w95O/iHvkvUBljKaCbBH8DT\nT48RDohag9WrJ6Op6RKczlbExHQDwAgB8jGUl7cB+/atkwYpNjbGAHBA1Gzj4o5h6dJHVddlZ7+A\nhoYeUB+So86jpNWCWHDYoUON4E51YxLFwoWZ2L79B8n4FE/hY+PQIVgRmGaq1abU5zNr08AHEyG0\nGchON6KwWo8iOvoYGhvVi1ZcXAsuXJiN1tYRoLnYRyi/6Bs0Lu5l1NVdBO2M9yAuaG1t2cLbZCaC\nTABLQdV2cYFaj/79be7TqQAIsQhibvkM5bls4SkHcAeAPwH4u3CdWG79Gb4JCTlISHhSxbwyzkrZ\nH1xVtYNvRlPQ2kpw4cIyhaufq7yXT6TW1unYtYsyZ9RnT88HZ5GwQV0DnnDsOGQmnMOHJ4EQ9jkT\nwAoA/1CutSrl4nxrugj+AfrIaNqWUVEvSkwNlENPs2gytbsUdOFbA61JBbgXTU1i2/MEdwkJPXHo\nkMhW0puHxEWDRq/mKO9NAt2AxCSAfBOqqPgBWVm5OHGiRndmhzo+xAUeYcuEGzZHMgEUStqGL+L1\n9aeFb8UTyVi52CanP+9brKsvCQbpJqadcxsAnEJ0dA9cc01vHDhwFH36TFYYY73R1sZYWstQU0Pb\nyWabDIslAo2NcjOgLC6FJ8ujx3QyDB4cpTt5rqEhFjRhpBY0IdywYbOVyPA/g22WJSUO0DGfC/WG\nLH/GihXhiIpqlIzPTISH/xatrdeo6tW9+zQMGzYfhw/XKjEDapNt797fY926eQamP0C7KQWEoOkY\nAQBguYm0J1kxzzz/bLM9oIpynDLlaRIW9jChuUdkTlnOX87PLyKAjKMtqmZyEwGQIVFFF+sicLl6\n7olrzMwWMmcaNfsY5V3R5m2R5Zrh94rPN4qONI6BIESb0I4QanYSWSjMkf47YmzC0arID0nUZNF5\nOo0YsSgiI+9XzHBap/XjGueyUUQpK/MMyXf5JD5+stczFowd+UWEx2N4Y5F5NoUMHfoosVgmCM9l\n84CZjmTmjsfd45xGlMsiimX9U0piYsaT+PjJJD5+uioy25fYDD3DixEuiFD+WZr3y/rkUcLNhp7f\nyWCUt0iMyeF1mC55tsgQ0pqBjExt3iOMw8PVkeEJCY8LZz/o6+VLpgV5XyCgtVdECGkGovrKpNSv\n0Nr6nnBNBpqaMpCUxM+KLSwsQVsbS6OrdYQCKSnA3r1UwpwwIQP/9V+fapxNADU9zAIh06Hm+HMT\ngdVaBpdLndcfsOHQoXoUFKxxq8BcuhsDtcQlmgBYzhnRnMUlyLCwNiQmJuLcOVGq/AYAwf79kYiL\nO4DHHhujO5dZnYZZdDoCXAkUHbXaaziYhEmlPnGYZIP2FZfs+Nmydsj551qeNXPEsecyiZc962fK\nb3rHdkSEC3V1b4KPExoNfeFCGJqbI4Xn7RDey94jSpy5mu+yAJTg3Lnr8NvfFuHpp8eoND4RetMJ\nk4rPgWqndlCzxcsAxBPhSkBNh2LeINrHlZURmDGjCOvXz3e/t6BgDZ5//hE4nRGgcR55Sp26K88V\n50orEhPpUWDLl5fC6fyr8HsNqNlKLKsYnfsyGhuT0NBAHZznztHI7D17yr2mbAagim2g0b11QnRv\nCajW/g/lau04FNt/m1JP4xgGBuYI/vZbz2YudQR0tKb+zFzLNERWNvH8AwY+FiMjv0Z4uKg5amMF\nMtDaqj6fefToq7Fy5VloNUUgUxMfYuzIDvb5BVqE0GaQCG7HbAD1B0RKrzxxgp9/xxtoGGjSsrXK\nZ3owDKA+GCYysk2yGWQgMrIAYWFvo6lJXMQ5G4ROSICaL85CtAcvWzYHAN0QxIlRUVGLkyfvQmRk\nT4SFnQMwGw0Na8HTG2QJ//MFqbZ2CGpr7aCDlw3avgD+jNZWmlpDfKcWdAEXU3Mws4OWlcIW9RxQ\nO2gDgG6wWGoxevR4AHRz++STIkHtzQBdiERz2nHhN5mpT0zKB1AmzCOgpiwGdtiKFZRhwUxEahZF\nZOQMXLzIJtQPoH6id5Q+FX0uoumCxeyLk5b9ZoGWxdbUBCxfPkd18I0Io5QZwErQgCSWpkGbNFF7\nZoc+oZmYHqOgYB5GjbLjnntWKYwvFgAobqK8fE7nbMyYUSScUyH+Pk/4DmCbSEzMHjQ22jRMF23w\nojaZnv5QGTF1DBdGWN1+J1zJNmg2DmWHWsnNxeICP2vWejgcDaBtrGUszcbo0SOQns5SgAxUfskG\nNRHfA5raohXAjZKysfbVCkq0PXv0yMb69Q+6z6v47rsLVEbXLPQJCT2xc2eBEIQXAa35C1iC+vpT\nujaUQW36Cz5CaDNoALXJs3NZcwEclF5ZXe1w/82dbidBpQruqAXowTDiBBs0KAbnzmnzzDwMl8uG\n1tYHQTvrQWjzoPDoxO/ApRza+S5XApYt+wgA8PnnJxXnE8GaNQsAUEnyxIlofP/9MVCb+CXQDSUM\n9JzXFQCegnqgiAeGMNu3t3fy3ET0bFpx4teA+iieAD+Zii0aTlBpnEpkhABr1z7pXgyffrocy5eL\ni3kM1HZoNtlYdOZcd/sDQGrqVkydOlxF3+vVqxf+8Y8yXLzI/EBsoLNo8nLIbNmENCuRuFnKNaL9\nVsxq6gCwCXSzcCh1FqmBov1X3NioMNLU1A1TpryETZv0eYv0k5ItAk5QAYb1m5bIwDZkpn3qabCy\nzKI9eqwRctAYR7RTe/cQqDUxVrZWhIXlKFo0XdRSUxcjNvYqlJXJTj0rUUV4a2nODLLsAFwYYXUT\nDeisj+KgzuOj1T6NKb30jGOAEkL02mPfvmexceMJVFZGQn8yXDlo1tFI0I1AbCtRQIBQRnVOqoSE\nnpozkftC5is7dGiOshGwEwW1hwDZAVhw4ECjYVYEhoKCNfj22zOS8gQRgdqZPvroI3LttdeStLQ0\n8sILL0iv+fjjj8mNN95Ihg4dSsaMGaP7HQChtmit7f5RnW0VeEYVAcptbZ7swzxrKQ/uYb6AHBIe\nnkPUdD0ZrZHZg2cI1xhlImR2QjH4Shv8VUSA35CwsN8Sq/V+iR1StLNr36mNZNTbnuWUUW1uFdbm\nvtmFmQ195MgcEhl5n6a9RH8PtR1HRDxEUlImk5Ej50rPf2B00+jo8YRScWUZKtWBd7xeNJJcX+4i\nge4r2vC140u09+dL6sD68AldmXlwmHYciBksZWOE2c6NAgRpv/bsOUPVVvyMbnaf/lAYTs8UfRXa\ntswhwO0kLOw37kNZqM3dU64nvS1ezAhqFDkcESH2jba8pYRG8ot0cFkZeIS22Ad0vBgH+PHALyO6\nr0jPlfl1fq1kAFjiLgc/TKlUFY1NKd1GNGhWFja+pgvlGK/8z/tdzKygnSM8qltbnhDxGbS2tuKx\nxx7DP//5TyQlJWHUqFGYOHEihgzhgRN1dXWYP38+tm3bhuTkZJw5c8bgaVrpxAVqGlEzXYBkOByV\nqqPg+HmygDcVfOXKLKxbN0OxbwLl5RcU+6aofmvzoDCK4lXQq7cMm1XZE2nwVQO45NoANRPnBIB/\noK0NaGsT381wWriWBQmVQG3SYEwgdr8LlZU0Q+fSpdlC1kMKHvDD2toJ4BiAFMgg2mhFFba42I6c\nnGU4dUrMxb5OaA8qSba0rMGRI3vR1sZMMyzw6X8QEdGA6upYOBxMC2Q+h+2g2tIEhIWFoWfPXhg0\niJ93y4PDqqGXvAGgHIQwdkkpOMOsH3iAD2+TiIgDsFja4HS6QE2V6synIu0Q0LJX8kC1183KZ0BN\n1eRSa3T0fly61AaX6x/C7yJbyg7GVjt/fhBKSlzYvftlDB68GU5nOCIjD8Lp/BbUzMGu54yTxER2\nhoVI7RT9cNtAz3XYhra2Zbh4kWZttdkmQ21O1Gp7aqiznrJ+46isXIY337wPLleb8O08sOyq4eEE\ncXEWZGYOw8cfr4fDEQbORmNaHTsG8wAWLtT7xqiZzjgokOZPKgHVdhlERl8BGL2YsswehOinnDIl\nHQ89NAF5eRtQUbFJ5y9RZ0VlvkrRN8ThctlAg163gWpBzPohMv3ofNZm0gXYEZcJoMGjDETzf3AQ\n0Gawe/dupKWlYdCgQQCA7OxsvP/++6rN4O2338Z9992H5GRamT59+sgLYt0Ll2uE8A0701dMqLUB\nQLUqMRw7T3b9+vnK4sdUPLkKnpc3C337JrjV2sTERGUTYbEIAHfuAHxRYRvGIFB7d5LwZG0ErZbG\nB1CTEIO2bOzdos3xILg5507QCZOgufcwRF8Dva8IFRVtmDCBOiGZXdPhqENY2EVcupSDtjZGj00G\n3RFREKgAACAASURBVHR8P+Sb2WtPnboJ3BZvF64QKaenlahU3ibsLGD1QqK1gdNr29oorfbcOX44\nyJEjZ4V79IkD6WIstr94ALvWpFAFq/Uc2tpaAfwITjtU236rqmrcteP+AlbWAnBhYTr0h+hkIC7u\nL4iKSsXFiywOhj0/TrhWG7W6BnV11SgrW+P+rG5ngG6IDaira4PTeUwoF0A3VUZvltnlKZqa5sNm\nextNTWxBFDc3ddvabEU4eLAVDQ1MqJEtH3YcPkxAyBOa++fBZvsaf/vbQ+6NNT19HhyO60HH/3YA\nB0BNeq8pZQM2blyi892Eh0cJB7+cAjAFQCQslhqsXPkfKCwsQXk58z2JZWBzlPmTmM9sO7iw+STO\nnt3uFn6Ki+06py4nENhBTb5LIBdMAKu1CUBvpQzzQM+s/iO4P8nYVEgIi38qADcxan0OwTMZBbQZ\nnDhxAgMHcgkiOTkZX3zxheqagwcPoqWlBb/61a9w4cIFLFq0CNOmTdM9y+V6CuoD3Wnnh4f/JyIi\nxuHSpWQQIs9Zv2oVZxfR3XwumptF5yRfoMrKzoJOOorIyCPKX6Kdug/U9kO2qIsDSJTqtFKILDVE\no/C3zAFZDOBNULaJHcAhUJ65yGD6CMD/EepUD30KDzuOHXsJN9zwOAYMiMGttw7Axo1tqK0dAbpg\nPQi68MwFHaTZULc7hewUMIBJxkyCZguGRam/lq0jxmSIg94O6txnYAOdLcCyFBcJSqoG9k6Zvfgr\nUCKB2P6iH0EcW3aEha1GU9PN4BNVPuHEzKf6My+qhPLmQsbyaW1tgMOxETzrpbq/aBkjoNYcRT8R\nQMdmmvA796+1tgIXLtgRHj4bra1rwTaqyMh74HQCese1iAykpLyF5GTKBNq/v5uE734aFotLsXsX\nCPfKhIgSEDIcMlt+Sora/xIbyzRU0Tkun9+iVkrIJfB2FM9ToEFmnPTAyspYZ0zbZtoTG59qSdtI\nI2bg2mkJeNobNqemgGs2FcjMHIS//71a8TuK1g9mYfAWx8F8TGzN0Z9pEiwEtBlYLBav17S0tGDf\nvn3417/+hcbGRtx6660YPXo0rr76as2VOwC0gS54n8Nq7YPhw/viuecWo7CwBCUlTL0DjAJ5Ll2y\nom/fBEycOACrV5cqEr84+WaBLuw86tTp3AdgEoDr3c8LD/8CYWGn0dIyFdQRmqpcL6qDPcAdpVop\nhDXrAHDJrz94WmjZJIoAj1hmm4s2ve4w8E2oRCmXdpHdBuA9lJcD5eXAzp33wOl8EuqBxKTvDbBY\nNoCQGaCDeQosFhdSUrpj6tRbUFhYghUrdqjShsvTU78GqsWI7xC1K/aZlXE9aF8zMHWdSdMFmrbR\n5s8pB6Urss+sHDNAJ7rIGGKaEzU/hYXdhYEDE9DQUI/a2mvAxwLbFPUTrqnpz8jLm6UQAWoEZpQd\n1KTFGClylk9Y2O+E8sgm9EDQjV2sr6hVMs1zGLiwojVpqemMx49/g6NHWQDeOagd12okJ/dzC1NZ\nWblKJLtYj1wQwt4lc7jyjZOm4v6ZcD+rjxUOR52K2affWL0HuBUWlijjuRDA/6e6zun8C1atysOC\nBXcgMdGFw4dzFJMh22hYGnZW3hfAA0mrQXOQ/Yh9+5pVOZ7EXEa9ejWjpkZGjWYBfHwcNzUBu3cv\nwYABUKLiT4NqBuxe0VktatR1+PLLMFgs50FJD4zGnQhgp/Iv+AhoM0hKSsLx48fdn48fP+42BzEM\nHDgQffr0gc1mg81mQ0ZGBr7++mvJZlCg+vSLXxRg5076Hd+JZZKbHceOncKxY3yB/+STIsTEXFTY\nE4lQq4mi9LUNwH+A2mH5xOrb90nMnp2GDz7YgK++ugRCxEHfAC6RMAlwv1B+pmozvwBTv8+Dc8V/\nAF08Z4BNFItFDGFvAN2gtBG4bCGcBLoZadMSaFVOO5zOWFC1n0lBPEYCOA2rtRkxMa+AkEikpPTC\nXXcNxQcf7MOLL36jspWys57lp8Gx1UM0hWmjUtl9JUpZMsET3v0INZ1QtkhoNYenwTdXhrNKeV4W\nygYwM4DVehLvvfcUAGDq1Negbjt27SvQTkzAiq++ihIWRDsiI8eDkGS0tIiMFLm5jZoK2Du0tmXW\nHuJ5vtqNlAkHJ0HH02sABkvelIFhw3bgqaduw29/W4HWVhZ9vQ90kRJPAaT1Cws7ie+/T3CzWXic\nDDc9qsem2Ke0zWy2yUhNTURERAN+/LEBzc2ZoH1zDzxRZ2kCuPVwOLRjRC3s1ddz9iAVRoxt9FVV\npzFr1ntwON4Fm58REYcFSjk3KwHNoNoVExooLf3CBWqW7N69CMePAy0taaAmwA2oq+uu3J8DfXLF\ncmhTXVRWLsPIkbOQkJCjMKCqlXtdSj9sAGUYpoFr+WuVss4T+uoMaP+PVf4xPCttB38Q5v0SY9x0\n0004ePAgjhw5AqfTiXfeeQcTJ05UXXP33Xfj008/RWtrKxobG/HFF1/g+uuv9/JkevDL2LEFSk4e\nUb0rgvYIOS5RM7v0fNTUjEBb2wyozRFauz1zsukP1tm1q1o5kvJxqHOt1EItpS4F8O+IjHxU+DwP\nlMa5TPPdNtA0FNeAmnveBnNo8VxILBYgA5SPP0dVtoSELxEfPwB0I8iEWtrT7u0loIO+SnmmmBPo\nYQAj0dKyA+fObUJd3XqcPNmMtWt/RFlZgmojAJi6vh0LF2YiIaEadEFgGABq4krVfPe20G41yjut\nQjl7KvUXbfW54CkuGJgDjmmHQ5T2uUd5dgGAPHTr1qyUq69QPtb+Tlx77QAAwKxZ76GuLhr6xTsD\nNLZjG2jb9lHaarAiYbIylsDpjEVLy1+g3vTY/xypqYvx2GNjkJrKvtfalhuU9mAHCkF5ZguobwrK\n75mgzv4M0L439vMUFpYIsQYnQcfan5V7k0D7hdavre0fOHr0VZSU/BGLFm0DAEydmgSbTTs2Wd/s\nAF1Q5yM+fgaysrbjb3+bjxdemIT6+v64cOFxUGn7PPRzlY8jgG4I69bNwMiRpxAfPwXduu1SysXK\nRwMev/22DgUFVNujwogYL6PGsWOnhHQttO9bWjaire0MuBC3SSljD6gz/jKsgcMRgUOHeqOl5Wqh\nzRLAKdM9oZ6fWr8h3N8fOdKAurpToJv4DNA1hEn700H9DsvAAy8ZWsHH/VpQ+rl6PQgmAtIMrFYr\nVq9ejaysLLS2tiInJwdDhgzB2rV0h509ezauu+46jBs3DsOHD0dYWBgeeeQRL5uBHcCbKiexOieP\nViKQScaio4xJiXZwu70dLKLXKIdMVVUN+vRJhFa61J+gBgAZuPrqt5CczB1N33/fB0ePinWizm+g\nDMCHShlFKYJJU93BBxkzReQB+BGpqZGIjY1GWdlqcM1GvFYmUUeCagHzwXMCiW3FwX0BBZI68pO0\n1q2DojpTCcvluoALF5itnEl5TIrdDn5mshXAbgDpUCe8k2t8QCZiYmLR2NiItjYxKlWe1jcp6T4c\nPboPra1WcC2MOQbHITl5O/LyNsPhYCah76CNZbBaT8PlYgwnVhYZQ405AI1NUdddl+COIh01ijoi\nKyp+QFVVjiKosMDIEUI9mOboAo0JYZpmAbj2xMgVcj8P1aSZAKWd4ieV+jKGD4fouBTzMunNeHYA\nf0JsbB8QRWXgOaxKQDU0ls5aPa9YxC2D6KidOvVlXLpEQMcNJ0Y4ncOwdCndQG69dYByhrc2lboL\nCQknceFCd6Hc/N1NTWHQjnfqwBfbiM3Ts6D9uw507BwEFQoKlOvY2M0F1/wPgvt0xPfTU+q4RYJF\nxzMt/21QM6O4mbBynAAPomX3qlNzb9uGoCHgoLM777wTd955p+q72bNnqz7//ve/x+9//3svTxKP\nfBRD2a1wOBKRklKBrKw87N7t0BwCLbNLi9VqBbfNPQlgGqjKHQXuOGSTnKvGFRWnMWiQqN5D+Y05\nr9QDXLS7AtT2SjcDtbOPLyKypj8PTiMV6W4AMBdpaduFiSRuUgRW611ISopFdfUjcDqnKeVjDBkW\nyS0mz5O9n32ndejSOjJ2kUizPHGiBj/8wDZZcUGrEj4zKawB1DfyHaiELJpjtEn7AGAgGhoSlWeJ\n0NuqExIextmz3dHaehW05gmABy1NnvyK8s4Z4NGotJ0tlq+RlNRf6TexfUQTF4sIZzu9Wljo3fs8\n1q9/SuXwZP6s+vpqOJ0D0daWBk5p/AZUSBBNL4wqLLKrnoQ+GGsDLJa70b17NK69Nh533TUUhYUl\n2L//R/Aod61fz6qUvw4yiAs1h2j+YNrl33H0KHD0KLB79yTU1TWCCleM/QJwjU4ecSsGrO3du1vJ\nKDoEego10NZGo8ITExvhcm1Q2oRplgxPwmJhrCqtcFEgXMfGHfPTiMIIo3Ey09xBcIFRG6Es9lEB\n9OwlUTgVCSZioOyfld/Z+9h6AaV+WmTguuv+x21Ct1j+KLnGPwS8GQQP7OxQlpZCPYhOnpyLwsI7\nQA+5EPnzmZLUw+IGYQMdWK9AnQPncXBqmDbXDh18VVUPKBqJuLgwJ9GD4Ivln9Cr1zWq2qgPhBHZ\nN0y91UrxjJmgXQg4mpt3aGz2/Jrbb6eOs6lTX4bTyaQ4u1K3Hkr5xYVBZmZg32klQcBqnYNevXq6\nM27SaFcmwYkLiMgMAaiEA1AHuuivyYO6j7WpG0SqZa5wH2vzU+jR4x6kp98opA6PgtrkR1kkVutJ\n2GypKCwsQWPjefBDXURzAg3paWhgBxbJHKUR4EwfkTpJ62yzzcZjj2W4He/19VVKLAV7D2PLMIly\nG4AblOdTBz7duFugj/04Dx6DkY2ICOCGG3rjuef+XZLR0q60NbNJXxDKythPWp8dBW3LWuEbRtdl\nf2tZTmtQV9cP1EnN+pK1HYvGZpIuTXfy/fdnUVCwRokSZgJYBDgV2AqeOkSU7l04dIg5b8X+o3A4\nXkJMzHio04yw+cTMqeLasgbUFDcN3LFfIJThNlCBSpwXD4DPI3GMyKjLzJ+qJZiI4wnK53WgBJci\n6PtGLZhFRMjMUYEjIJ9BcFEAOlGOQmbCaG5+BatWUf7vypVZyMrKw9Chs9G7dxHi46tgtd6FyMiv\nERaWA7XtNgZq9ko/4Xu2AMdK3+l0/hWJifWw2V4UfmPmD9GG/Xe8++5hpKfPc/s5AGDlyizExx8H\n33M3gzvxtPZldo3WD8ARFdWq2OyfVH1PzQN3oLCwBHV110PkuFMzkkMpv2jj1Nu34+K+U3wfJ6F1\nhLlcD+K9986jpOSP+PbbvkLu+SxwrrX4rCNKORtAN0OxbTMADAVfKHKVMjLYQbUFvuFTk8B64ZoE\nhIf3wFNP3YatW5fC6WyF2mabAeqf6QOX6x8oL38ZJSWZIMQF2r5yOSghIU6x74vtkwEgCxbLF+BM\nnwxwf0gBgDx3GoSSkj+itLQAZWUJqnTjaomStV2FUi9uy7bZWjXvZ+N0KajZYDNaWjajb99eKi2N\nC0gZoOM7A9Qm3QOUdns3qOlhCGT9HxU1B716OYW0B+zdzHu8GXqW00egY0WkETMWHUsHsRpUGNgM\nYD2amv6B55/fIaRG/yOoyea0Uq7PQPvSDvU8SwD3S8n776qrBiIhwQGqcYn3zlfKJKYeOQG6EWwH\nXwqZD6hCab9e4ONvL6jWIJvD7G/moyqAzdYsPFMcL9TvEh6+R/ld7K9YpW4NwnvFevwR1dWxKC7W\nxpwEjhDSDNgO3htqpy+HqMKePl2NysoINDerJXoWHNOvnxUNDdkIC2tATQ0BTTAnqs1sNwaouigG\nkdHnACX49tujcDrFQDk2kbWsnatRVsa/Y8Fwo0YNREkJU0MbwG2FRaCL6F2IjIxCjx5hChVWjHcw\nyqd/Hmp7eD3eeqsYO3YcAl1kRcwDDeZhf9NIUGomOwib7W5ERsajtfU0LJYUOJ0PQJ+vnWoYlGfO\n2kBsCzEil5Zp8OAoLF16DyZOLERbm5YN5AJdKEQpzQ6eMC8C3J7LcAzAzTA6svSHH06CRxszyGi3\nsaCboiy/D6VZLlhwB1at4sc6JiYmICKiAYcP90Fd3RHQwEO9Ge3ixQOorTWKpRCpnS7QzW49qBmP\nHwQDfI177rkGu3eLRzxqzWQU4nw4eVK0N9NcRFSKvRoiFz88fDJaW0UpdhZ4gsKTePfdnnA6bwOw\nBXTziARdEFlup17Ce94Dna8Ad4yLLLoCUE1YpPBSOJ3MFMPaqxlUg1kNqs3/DPp5xiRsGZOHIjm5\nH1588Q7cc88KIcswaxMCOregeXYGeCI/5gNighMT/LqBB4wxUE3Nar0L112XioiIBlgs9BAamn9r\nEN57b46iQasZWKmpizF1arpyFOwy0DnJ6tUfnESidSrro+KDhRDaDMRGvkv4m0+68vIKQb1kUoc2\nqpKmub7uujyMHp2I5cv3Qx2gtAFUNXwVnB7aDLU0zhcpp3My1CwZpkKKEKUNWlZ2OtPSpdMV+hxT\n/9hk4YnnXK4/ISamOxobGX+d+jEYZS8pqYfbEZmVlaukQ+BldThWYtOmMNBJJKPnicyLecLz30ZT\n05+VFBViwE+JcD1rC1EiFM1xrC3UZq3Y2AIAgNXqgtMpsx1PhnpCloNKZ+ycaTY52ft7Q72wU7ND\nWdk5TJq0ES5XKvS+BBm5YBZo+98Bow1XFmiUlZWLsrJMUNOE3owG3I+GBjFQaBt4gjats/9BUGf+\nCPA25+/7/vtZiI0F4uMp5be19QIuuBP18n7du3c30tPnoba2BseOtYDbmxOVf6egXUhaWyG0UxZE\n811TUy6o83o/KMkB4FGzZ8EpwSx2YQ1oP9pBNTsWyMjeGQPu4BXBzKXimOoGOj/OgqcOWaO5j427\nnqA+H73f6PTpKCU2JkaJUtaanJkZUCwTMxeLz9uO8PAT6N59JXr1isKJEy1wubSJDmmfXXfd4/jm\nm5chgjrEX0VTUzdQE3UjgAm46qoBUmJBc3M49u2rxYULT4L2YZNSHlkSQSPfTmAIoc1AxFPKcXDT\noOUpL18+GU1N4olb8ipUVZ3G8uUHFGmW2ZyZ1L0TdFE4AzqpbwC3B14DNe/dBvUiI6atYGCSr3rB\nq6iYiz17ypGYaMHp0y1oaxsAtaOU3tPW9nccPWoHTYE8HmFhMYiOduHJJ3+NgoJ5bkfbihU7lFO1\noLqfvn+kUq/vwCVCtkFVgUodfBOx2URJX9uOYn1FJ5jo8GWLmuw0Mk5xpAFC/wV1jno7qOniR+Ez\ns0Uz3wGjWnZX3j9DuJY55KcDKFLSL+dCb7OV0W7TlXYKA5UURfu7PjUzA+W3lyhl0gaO2QFci0uX\ntKlQJkCfJpsxrKKgX5Bo2371FRGorJRNFx2t9V3Z0dDQgrIyRo9+EjSIaiS4f+qwpCZx0OcuYu8/\nDioYiayhS6ALdwto0Bvzl61SrukOSitmgpVIwe0GeQ6pEqij+JnJwwq6+LFFv1Fzn3b+AGIqbuBa\nlJWlgY4lZqLRaoeMfiz6z5h2yzY3G4AmXHVVJCor3wUApKfPQlmZQ3gO1wqPHDkILRYuLEJdXRrU\nm/EShIdXYsGCacjL24Bp09aAkG4YPDgaS5dmY8UKoLSUjb+XwPtID1mqmEARQpuBuNAch9MZBXk0\nKGMbsAEm51s7HHVoamJ2TFESKgXwV1CJJx184qwHtQdqqZVN4JsIGyjHQTcTtsC5IPdzTBFywucq\nz7hKuELUKNYrv72EtjYa+FJY+BgApgmxZ+dK7v+dpl4QnqsOkGM56Z1OltiMQUzLzBfVsLADaGsD\n9NLwGgAvIiysCW1tMwG8oXxvR2TkC/jss+64eJEo7SnSgcUysbIyO7zoYAeo+Y6ZSKKFa5mEKmos\n+mCohISHATBKMjPVnQA9b5uZiS5gwIAB6NMnHp7AD/kxChxj7S06BvuAjjkxTTbAzRKiFsfTeIjB\nbUAJHI6BiInZjR49XlYovOI7c8F9GIVQ97uYbI7Nr9OgtFsxd5F4vbjIiCbApeDmn+2gSQ4ZK4kt\nzmIA4mbl+Tao2VIQ2lFM//IzoT2YwNVPc99JqOcPl84jIrLhcKSBx9Fo+4LVUXTYixkEtBo7Ja3w\niOlI0DnA8oVxS0BDA9C9eybCw2NhtUajV69mHDp0Edr1AFiGI0d+jalTX0Vd3c9AhZkSlJVZMWlS\nIZKTGS2Wzb9t0Off0h8uFCyE0GbApJX3wBfpAuU3cSf+CpSX64Q+5wwFz1zIFhbWuEXgi04DuArG\nbHMvQW3bBahqzyRtNlByoc6m6gCXRESIOeEzQaWpa4Xfre7rqBTFnI20vufOteDZZ/8B6qRj3zN1\n/BVwu2kT+MSOBLe3681Xzc0/AyEODBgQr9kMWHuKC9ZWREc7FROF6FRmE6dY2SioSatfPyuqq1vg\ndI6E0ylKNaJkKJbJCbrBRoEuRCVQt7e4YTBNIVbzHFHrA7RnxwIsWV8NKir+JCTOA1i0J6NIsihr\nmXagPuRHpMVawX0D4jgDqOaRIVwnwgm+SIoHrIucd053bmi4GRbLt8L9ot+GLaLihsmYRCxfDntW\nNfSnvYl9skLyjgxwTZN9vg90U9D6aZjTswY0+K8WwEKo2VLM5sVo3SydyavK7yz1QhzoHGVC2EWo\n54+IblAznbR9IdZRLSBZLPtByOn/n713D4+yOveGf5NMhoQcSIjAJEREggcEqWEXhX7XDta+JCLW\nA0XAilBNBAURtZe6K/CSirQo36vluPWr7haLVWrbS93GQ+jmhamtCNUojcaKhAghJ4wJISHJHLK+\nP9Zzzzo8a5JJMsCgc18XFzDzzPOsZx3u4+++bwi3FF/bzs4RVvc5qqPkB3djyfcpBPAlOjpGgRBK\nLS0HwNfeHlfq7k5AS8sFEMoMn1OvV0YvPhUcvxz/TEmJR1ubH0lJWdi4UXblRoaiCE20FoIh0yZs\nhIoouAZ8yB+Da/Ei0Yczi/uRkXErNmy4FgkJXojmFACf3CwILV7WRAC+6ehZSyGyQWVNm4g0G44a\n4BvLlIwmM4B88A0iIxBk3DK1X6MxUAbsJdrnz4EfqlUQgeFp4IePNGu6rwmR8TgqKxMwdWq2lBUL\niPkU6BjgWowaNcK6zuR/F+/W0bEDbW1+eL0XQ6wlaTWELiFXBFlCAJ83yqY+AC5kzpPuT0KKMo4r\nocYqdNTPGrjdRzBq1FCsX78LGzeWYdmy6aioeBaXXWayygTJ2bFEJSVbkZp6HW688f+go6MePIva\nB+4aoT3ZLf0iX3pv8kObEGI54K6vz7Tv5JwGci3xbFzG4g3XEfplBQTq5zjEXrkcnMGTy+95qFnh\nd0Nl+pdBZD7r50OmEeCCQLfM88EZc5L1rGvALUpCSxUhPr5ZegZlVFeAz5cDwHvgsYsaCG39TvCz\nb0dBJSUtxujRyRBWgDyWpXA4irV3FKiejIwvMG/epRB5F+p5aWrageXL37GqIBRAKGC0f14Gt1ZI\nQOwBV5qaofItWHOQBDMIRaAXCwtXYdq0kmB2d3X1i9i2bQmcztFoatphIeNExnikKIosA0AwRDLp\nKQeApP0L4Jr9SHAhUAIdi3/llauwf3+FBY9zQGSiUtXCByAwvXIWp+zq8UAgdj6DiqOn8QGq5Pda\ncY5fS59/qP1O9tfSYaQsyi7rGsJXr4TqM5RbNpJ5fD1EEHQ/RCezbdZ9T8C06To7/xN7967Chg2F\nweBVRUUlmprs85mTsxPLlk2X+kUAobYNr91OJjchp2C9wzRwpnA+RA6BA2pNdyfUpCWAM81rIKyw\nVHD4MWmXqkUgfMcC0kkaf3Z2imQNmd9BDsyVlGzFmjW70d2dBzGHW8HnlPoKkP9btari43+BQCAd\nQmE5AeAO6w8lBF4DjiaS/dcyBl1PviLXh4xVp+9HgidIPQjO2J6FsOCo0q0e7KdA/D7p+U+AEGcO\nRyscDuqOpnd3I01Zds/Rvv8KXAEABIJtLrhWnYNAYBy48ibHdj4BdzfJGvdTEBo8KWny+YlHUlIl\nHn54GgCgvLwUdspHcvITcDi+koLwIon01KmTeOWVTyEsHLOSwOsLvYr6erJyaS7bIQQluTsBAafW\nY4nzYAahAAAvXZGWFo9Bg/xYtqwgBHRYjAv4heE+/aMoEwbEEH3gG+FVqMlIcqE5wIQG6eiow89/\n/k/rt4+AM0ZK5roNfGEI0wsI85XMWkD1lX4Oe5p5AUQms1igwYNvR07OPBw9mgqf73aIolTUX7gD\n3GyOAz8Ew5Ge/gmGDm1HVdXXUFszkvawVPucyAOuCf4Y/GBcAM4g6b2eAA9gvgs7ebBv30GsXx+P\nQYMYrr56OFpba9DeTo3PiUlUY+fOJLz77iGMGAEkJMj+d3kcXCC2tzdBzd4ERPo9uZk8AP4P+DqW\nSNcAvGw3tPs3wp6ARwxZTfpyux9AVtYFiiAARJkFkQhIwt9OcmBu8+Y96O4mWCS95xdQ++aSlQjI\nfRK4+2ys9F03RI0bOSFQ9m+LeEdc3Hp0d/8b7LEG/pyMjCPIyGjD8eOVCAS6ceoUlTnxQNTPod+S\ndauvm+wuIcHC1zIpieHhh6/H5MkTsGpVMSoqTsLnkwUeCQJizsUQ7WZXQk1UOwYRMP4NuEUkrynB\nyuUxAyI2IytpDdYzXEhNPYGXXuIW/MKFW8D3O4FAyDVTiZ/+dCZef/1DlJfT+CmL+sdW+YsEiKQw\n3brg5PXGgwt0BwRqCuA8i5TXoxBxmjGG9wE47+F9KATReUtAc/PLSq8WAIZqwaeHokgYrACfqFng\nkna09bmMX5aDW+RvXIX4+M8xcWIqamtr4fEMgqj14QTfeKvA/bqyACC/O/nm5qKjg4KIsikow+nk\nRSVTlzayHy0tdyEQeAo+38vW5wvB/aCjIGffulybcPHFIy3I6P1W8/OteOyxN8EYMRo5YClXHSV6\nAVxL1g8V0SBwBqzj9TkTEJvOY9V6IaZQbL1bOoCr0N1diPb2MlRVOREfvxe5uQuRmJiIqqq7cUyf\nNwAAIABJREFU0dExEbzW0q/5iP2EiEq27iNbXbJWSgJcz6YmPyi5lZ6BPZbhAY+h/Dd09MfgwX6k\npV0OOwnhl5bWgEmTluKrrxpx5AhBjDk5nbyROqG3WlocsCPFSrRx079lbfsdMOaD2hODfPQkCMog\nvLSqMMnI+Bfuu2+G1TtXhl+K52RnL0ZnZw5OnqR5KZG+JyQczXkT7PE1XchUQPTTADo6PHj88V8g\nKWkXOjt98PtfA503ipO5XL+zEH87wc+MXDtpneHd6V3IA0Akxz1kliRr4R5wBU8og52dd2H//gps\n334MTU3jwNFOn0KGqcfHF2Hy5AnYvbsRnOEXgwuqP0O1vmn+zOid+voWqyMiIJj3XHAF7FNwa4jc\nnTJaSWexC8DrpTWDu75+AlEGQ83FkHs5HD1ahdNNUSQMKOBF0DZibBSQckNo7kT8YFxwwTzU1aWh\noeEkREq7LpE/Un5DG9vp/Bd+8INLcOxYFioqZkFNaCGMvgmyOBKmuivt7XJgrwxcY5cXOR9ebz5G\njlyl1DIqKVmCP/3pc1RUyOV/aWO6YBdIbTBbLEXgOGyfNQa9no0+L2VSu05iyNT8Rw1yBQLA0aNz\nMH58MoYNO44jR0rBm/IA4oA4wVFA8pzxrmeCCXZI95fHRqVFzoOwePwQboFG8EM0FEK7WwrSZg8f\nPgBhXRDpwg/IzV2BzEyGI0fmQU668vuT8cwzr+HJJw9Ygf+51jPJXVMMrpk+JI07GyJvRdb250lz\nQHBLpzRuyichEkL9yitXAYAV1OyCiThzoiJmMujBA6AagiF5wBUDPb6mH/0KqNV/tyEQ+De0tclu\nO9VCu+iixYamOLTGQyCQVPTufuv9v4ZqiXxhzYUO+ZSLN8puUk4+36/x1FOzLITVSutem5VrAoHn\nsWnTKgwaJAfzc6xvqVOg7OazJ3y63Xfi5EkTrj/N+u1TEEKeLKUNEC5geV6Og1sVVNhRLoNhp87O\neJSWelBdXQO7UmQWXP2lKBIGO8EXiYpHyYyCsvA80GvYu90PAHBZ7oufQJivQhPnC8SgtyMEXkR2\nNsPbb6/BpEnUy/RliIQWB0QQuhAiQNcNvqi3QbYMgEJ0d1PTFT84k9E1c060yFSoa9AgvxX0BkQd\nmm5wSykBdoEklyyQmftR8AN4IziDKNF+p+cpHJX+XQYetBttfaYLDjnTeqX2W9JuZLeDcHsMHlyA\nU6fkTm4k8Ki+vB+5udRU5300NxPjofyBfHBmfJH1mz3Q60kxxhEZGRn3ormZmILZB5yRQXkLas2k\nhoanwQVRMfgafw0Bj6TcBtk1chJcgyU3CWm/VCiOtHBA7YpGyDC5Om0ZgEPYu7cRf/nLWAQC/xfc\n1Wm3YFJS0qwYjiwUSWm6ElwLfgFcC3VDZ+SqFQmo2jpZxKTEmF1q9qY4sgVF61Ym3SMbfF+Pseah\nCXYmKlvtAD8LX8JecI/TqVPk1pHPvEqdnfG4+urh+Otf70ZHhxvCrdMKdW/QGpIiEg+Xax+6usag\nvZ1iIPJeL7Dej5B8sudhOPi+3gBgNjgQRO9LLf/WPMfUc7q7exRUpchh3ecPxt/1h6JIGPBNFRf3\nQ8vfKjM/U1VMbk4/99w9VqMSgGucpM2SiUlaHbV8lJnpbWhvJ22D3BHDoS7q1+DBJRljXwwVokcL\n+xxEUTAKcpt7ox49+k/ceGMFAoFLg5+5XP+Cw/E0GJPhj0ugavd8bA7H9WBMng/aIKSJjITojPUM\nxDtdb/1Nm/p86d90iE0mO6AyVieE1kqfl1j/V/MynM4muN1uVFX9WvueUCZ8PLW1W/CnP32OuDgZ\npisLvBYIuCnlm+iIjHvBtUOT8JOpy/D7MnAtVK4yexc405KZIyBcIxdBFJ+jvwEuNLZBRe24IIRF\nGThypwCqv92DEyfWQ5QuTgCPT4l96/ffhrY26pktwylJaZIF6G2wZ9cCDsd+JCQsshL2aD6I5HUn\noSUzaJHte/XVJRg0yI+pU7Mt6O0O7Te3QihTWyACtS7wfU3KVAOAHUhOPg6HwwdgtuSeWgI1gC3i\nVIGADCSQGyQJam2twbPPHkVHhwO8vtBD1liosgDdT3Z18fPi9a6E10sxI9nttRh2iC79rgxqNv/X\nEIH+LNjPG6C6Rjnl5j4KwGXFuOZCnGEqrKkL9IFR1AiDadNKrHoel+GVV6gKKW1ouRevak7PnJkP\nn+9pugtEhiRpGCPAFyQXYjIJAVSGlBRu/qWlEWqFTC96zlbwgy8zaBc4k9fRAgSZrAc3fQnZox7E\n9PT5qK5uQXf3FKgtOL8Cx9zLREgF0qBPAYhHQgJDd/ed8Pv/C0KDfhz8gMH6+1WoWk4FMjLi0NAg\nb2rZVAVErXyv9UcmGQNfCR6zkINuMsqKIIGA3w/U1i7Q7iUHlHnwrKNjh4X28UiVaOWYDllmhGQx\nbd8yeL2ytqQfGI91TQccjiqpgxfAmXYreBcxWpcR4DEQHSacDzUPhnINdGttJxITO5Cd7cWxY93o\n6hoKYZFdCJV50F6i4CQQqoKt2/0iTp3aIsUUPBDavcxY/FBrRzUCOArGkuH1dkNg/xulcevJcHI8\nibvhGhouRH29cNscOrQCw4enWZn08m92AvgYqamfweuNR1cX3Zsat8jCeBZOncoEY/9l/b8EAplG\nFvpICDcbH6PYK7pLlNcpq6w8gc7Of4N6RuMg8kXkeJBOcqwLEG4vQmwBPZdBcYLvV1JKt0BVQmQ3\nOFmkbQACYCwJPh/VgpLzbwiVuBa6MjQQihphsHt3SdBtkp3dhNraH8LlGoKkJD8KCi7Gvn1y2Wq+\nyMeOZaGwcCW6u9shFmOr9YcBaEBSUi06OvJgX3hOjY282TnPMKUFl6FytRCBPtIgTkFo4LIvU0Yh\nPQ/VwuCHLjm5FRdemIXy8pOQN61gyCshaz4c9ueDCrFbC6+XNrWuAcvuCYAfxi+RmtqKl156EOvX\n70JDwzUQmzofArVBjPkw+IZrBxfE4yHKAJNbYhp4WQcGEWPRA6aCRF9cIjkwS3WmiPLh94t+vomJ\nASxbthSzZz9pNRYnV6DJZ6pvaR36yOdPtBWUqQVcaZDvQa4Nk4XnBxf8clVcu1V0882X4bPPmlBV\n1QCRyX0+7BYYMQmq90P+dDvl5AyHw5GEigpyeZCVJ5AyfG/I44J1XQBcyMlrVIT4+H8hECBLphmi\nqQsRAzAVgEPKkgYADw4dcsDppPiKHJjmz/3e93jTnLIyUjYaoTZu8QBIkAQBIOI1o8DX8VfgOUZv\nSNeoe6W1tQEOx1J0dfmtMusUv5HfdQgEMERWhEyuGh3kQJZDlvY5AKzC4MGHkZTkk2DY8hoTOvA5\n7beyG1y4LauqAJfrJuu6JQD2QuwPee4iQ3G9X3JmiOqxl5U9jiNHXoHf/9/IyroA27Ytwe9//4RS\ntpoXWNuBiopZKCsDOjpSofrTLgKwFBMmXIFXXvkpkpIqYW6ZyZudUztHnlxFSSnF4IzxcYisZUoA\n6oAQLjJETNYi5FIAbnCf4fm4+OJM+HwuiJ63dF/S8IhZ8KQX7r83BX9J8FDiGz1vATiDolK5gNvt\nxEsvPYiZM/MloUfZqpDe5VfWO3wPHNKbA6Ell0BU+3wGoh9rHbgbpUiaO5NrpgCJifdYz1kJnr9B\n2pKpAmU+Jky4FLt3l+Dtt9dg5sx8OJ3dEElc78DednAlHI5y232AQmRmzkNGxlaoAtgLbj3S/0lb\n1C2ci8ERIyuk8ZcgPv4fiItrAGcMS6XvySr6Lfz+h/DKKydQXg5wDZGSkgrAfeErYBcKoyGS2iiw\nKt4xMXEBGhubrBiTvK9JcJFFtQb2Vq9rrfnWNcrnkZjYgcJCYNq0LOTlpVlBV/m3hJ3X3Ug8ucrv\n/yl4dVk7dXbGW2fsHfCY3CDtChmjT/ftsu5H650ADh4Qa0CW34QJl+Khh67BsGFupKYOs8rRkPWg\nz8FT0j1lpq4ntHngcn2IhIRF2pgI+SgTn+9///cLsW3bUimhswD8jMhl01u138p5CnqMLlMaE1kJ\nOrIwMhQ1lkGopAqCVtGfwsKV+OQT2aQmHLVuSntQXf05br99KwKBJjgcvwVjWcr3pH2/++6HaGxs\nQmJiAJmZc5GVlYW6upMSlIwOHAUsl4JrN3ojClmLkM0/8V51dQ+ivb0aQmOjDUDuDLnsA6Bmfurm\np0wm90QVLrssFY899pNg8gpvQk7NueUEpnXgbp9nwA+ZHkSksZHP9zi4pkjVLT0A5sLlakN3d5xV\nMVKmfGRnb0BNzWYrS3kIuMtBzkmg+3DUxd/+VovLL78f2dkpuO++AowefTEqKmRUzCFwq+gaJCSM\nhc83H4zJvmrCzFfi3nunYffuxiCc1u7+ALhVQJorWTjk670fPBhYD7KqAgFeE4eX6CaLQG4tyi0+\nv5+005chMm8BbhE1gDOLYoiOdAkQAWPa08VwOADGnkNnJ1BeTu1gX7XalerrQ0TuFZmJ64zYGo3r\nPFu3vjKK/yr7TV5cOQegDCIZUKXExEBwD27atBP79jm1joUyvBTgc/U8xNkG+PxSoyYVxXf06GdY\nvtwn8ZAS628P1Ha3oUqHyJ+tQnLyAXR3Z6Gj400ICPMp8LUlC1oN7LvdD2DKlIuwcWMZEhO/CvKS\nhAQHamvb0NDwN3Ar/0GoZ7WnGB15GorB1xcIFYccKEWNMAiVVKGXahXX0SbcCs4YVF+hw7EJbW15\n2mdPWj5i1c/f3u5TehEEArNw4oSsFZErRZfc/wl7RVM50GuuRZ6cfCM4E7sLoo+CnHkqkwnTrv+b\nxii7VoBly4ptdXZmzsxHVtbLlr+X/Mjx1h+5vZ8T9taI8oGVs1zJpZUKn28wGLsDepwkN/dRMOaE\n10sbOQucETohEn6I8fK//f7bUFFRhooKJ3bvXof4eEJVqe+UmTkXTU3zIRg8daPjMYmODj+eeGKv\n1CFKd2XoPvuF4IedNDi61gRvHAoBmdwFtd6/bPERA6Z70kGHdD1h8/U9wMeoumaA+vrnkZdXDJ/v\nJJqaKA5xvvbbYRB1tA5anyXDRBdeqDIZHhSmsuqN0rvJ2c9UXsSUJc1JLqwm9zxWOxb6tfvSWskg\niOchuqfJVIgvv/wIgYD8Oe3TMoh2ty7YS4foUNJ8OJ0vYsSIIaiqopgWWXol0u8A1U0bQGfnl3j2\nWYfS0Cg9fQXWrZuFmTPzkZu7AFVV8hi5J8PhOAincxF8Pr3kh8wTR0CUtbbXY4sEDVgYvP3227j/\n/vsRCARQXFyMRx55xHjd/v37MXXqVPzhD3/ArFmzbN+r7RyJPKioqMTVV5egtbUGgAvV1ZTZSD5n\nqtZJ0pNn+jJ2OXR8P2NAUtLd6OiQa9/oDH4rWlqcsEPZUqRnEvPrhh3yKdoxHjjQrmk/nFyuJLS3\nLwHXNKshNI06CPgqUShhY4eV5ua+jQ0blvTa9IIX3QJUxroQArERyh/fCBGk01ERgFpxE5CLxm3Y\nsASzZ/8CPDdCBM2BJ6Em/FDcRBYML8DrvQACmaIyGl6UUF5HOTjNx9fZCXR2bgW31nSGqQcJOczZ\n6fwAfj99txXcGpKJ3AafAvg7yJ/OSbf4iAGTpq4zfIAz7lBli81HNS0tBwUFHXjppd9BTXoixkwx\nDdIwV0AU/ROFEV2ujfB6c1BYuBL33VcAANi+/ZjVmGUVuEuLXCSFAP4BPs/JsAtXgLKkr7xyVLB2\nv0zCSuDlUFpb61FX96pVplu2uGsh4h8U3JeJr3EgMFn7XFauSDEbClXgyDkOKlqruZkEtawAyO5D\ne0XllpYl0Ftxyt6NwYOHSt+IGA5jz8LnIx5QDGGxUu6IHEvS80UiRwMSBoFAAPfeey/+8pe/YOTI\nkZg8eTJuuOEGjBs3znbdI488gmuvvRaM6cyOk1oqAOAogd+jqWkH9uwxaR7NsPsZKfhSEmLE+Rgz\n5kXU1h6VmLTO4D8AN7Up4YUWtwDcB+uD6ndWoZu5uY9iw4YFQZeWMLMFjR6dgqFD38GhQ8sBrAaH\nQl4EO0afj9nt/i0GD56H5mbA6+1AXNwsXHDBKFtnJdOhk4kC9Lxhuk4MAl47EpzxD4bKWLogmsjL\nqAiavxplrmlOJkwoAQB0djqhCt4KcPQUJefEQSBtKJ5gys5UhczGjdx6EKRbj4DQ8BZCP7D28t18\n3JdfXozPPqtERwcpHXqIjbT7JRD7gtaPmD0xH2LApKnLDJ+CvudDMAlV6CUlVVoVU1VKTAygrKwa\nAruul4egPbUKCQkfw+nsRHz8v9Dd7UN8/I8wdGgiGhtT0dHxR1RUABUVHBmUltaMQ4fkWlgl4Bbc\nBnAmlQ5eZ2kb7HECPocTJ5bg7bdL7IO2SG8iVFrqwaZNO7F3bxJOnKDzlwaxJh7wMt0y6UJXHgPg\ndK63XJayAkSwZnKJ2q1N0X9Z7iBXD86Qx0LlO9Cupf9znrJv30GUlnpQV1en/cYUbPcgMfEadHVd\nCMYoJkZJoDKKiEgVSAOhAQmDffv2YezYsRg9ejQAYN68eXjttddswmDTpk2YPXs29u/fb7gLp40b\nyzB//kjs3SsXTqMXNaXOHwSf/FGGa2STVmb0frhcAasVJX1HaB367U8gpkVvLxkHdSH4BkpN/REm\nTbociYkBTJmSE2xc0dXVAZdLxnJzYbFmDYdZ8uJvI6Bqy3bNasqU72L79mNobhbP/uqrImRlDUJq\n6jBbUSsTlZZ6UFy8zfIvD4GOaY6Pr0MgQJDNcgD/FzwYTYH5g+BMbxu4ZpIO7vOXBTUdSHXOW1vr\nrZK7cmVXD7hb5T5wAUNxi3cgoJx6/oJ6X7d7CADg+PF6OBxfSzBRkw9W3h8vwC7kVObrdj+ANWsW\nYP/+CqxZ8zS6uy+AMNPpOjr8w8FdXoDZF031dE7B4TgJp7MRPh8FnAutefgjOAOS16UYQDXi4pLQ\n3c2kvcTnISHhAP7+dyfa2kjwyOi1BojYBQDUwecbCZ9PjaXEx8dLgVZOalIeEQEPSMOm9SFhqJOw\n6gcN8uO++3rfn5SA6XSS1DsBLsCJTG4dUubsuRC5uW9j/vwZePbZItTXU04IoMbldI8En1uudD2N\n7u7xUGNMS2AWPnLsS7WYm5uB5ctXICXFiaamUBBUQV1d6WBsIUQzJFJeZJcf8aTI0YCEwbFjx3D+\n+cLkzsnJwfvvv2+75rXXXsOuXbuwf/9+OBzmTMKysseDfYNnzszH1VeXBMsHmFPnqZGL7munw01F\n4oZA9Ckow4EDHbjggoNIT7/dajAhu4wAfuCpnIXs0wXMTKkG3TxLDo2NddiwoVppXAEch8NxPUaN\nylLa3QHAhAm7sGfPYcP7qZpVYeFKLbjuQX29G/X14jO9Fr+e3fzFFwet5h+yi+Y6xMXFIykpDu3t\nLnAoaTWEtkG15YkhywGtMgjoH40jG2qXNU7V1ffC59OzsV8G9wcTumMlOIqmEFzgVEKNYXjAhYbQ\n6j/7bDaKi19FfT3FCYhJyGUMiOQ5ppwSEnIvQ42fBJCVdTKoufIyIXXWe8mHkYKRfogSG4BgygQg\nEFDCESMexOLFY7F3L++xXFn5S3R3XwVhuUwE1z67wF1OV6G7ey26ugDAg/j4axEXNwo+33z4fAw+\nXyHUHgQAt5Cp5AIxJsqYFUyqowOoqroFJvL59PpBBIjwgQu/RghtW8b3bwWHfmZZVj2/gvYnAGVf\nkktq+fJ3FK+A6GimC8glcLvvRHY2t4j37fsbOjpk6DV3aaWmtmLDBl7E7tlnvwC3CAkYILvoZLea\nKBXCocf3Q4WfeqDmcsgBZDn2ZYdWHzq0FpmZ5Oah/fORdIWAEjM2CmpM1GXNfQs4X5P5khpHGggN\nSBiEYuwy3X///Vi3bh0cDgcYYyHdREAJDh1KwPLlK5Gc/JgWQ5D/LZtjchs+ysiUF+4JCObFD0Eg\nwPG7TudM8MXUU9gJP68nf9E4dJfVO2hvf87a9HI9JbVMQmPj3diyZbqiHfF3TIYZ38xdAKWlHvzt\nb4e0b+yZt7JvkmC6sgBxOG60/QbIQ3f3WrS3rwRnikvB3QBEOtO81Hpn6rM7HLzuPFEt7MLVg+bm\ndJw8+U8AP4VwvbVDTRyTk3Oeh0j2A/h8UhVbQYHAcClYJ0olOxwnwVgi+KGkA6vvJz1xTHUVpKWJ\nvJdjx+rBBZmcdQ7wLFTS7t+HKLFBikIt1DaQZaivT8PmzXuwbdtSzJyZj4yMhWhpIeWDmjvJrVrV\nuFcgUIZA4HGocRXqQfBr2N0msnVlD4AL19dWcFcYL/rX1VWH3Fxy2xKDDwCYDO4OZBA+bZq3H4Fb\nDdScStChQ2tx330/Ql3dMMUSsbuk6H5Uu+cY5MRJh+MAFi8W7WBnzfoI6n5j4OUuDgDggkcO6Aqr\nSX4WINrg0h7zgCtG8ljkjP0PrOvkemUl1me6EsnJ7U5Herp8LouhAifWgmeMV0MU29wD3pnv1+Dn\njyoktCMUcqu/NCBhMHLkSBw9KjDlR48eRU5OjnLNBx98gHnzeKDjq6++wltvvYWEhATccMMN2t1K\nAAA5OcDVV1+N9vY4KYYg++/JHJM3yk7wYO4LEBjcfIhFseN3/f5MqKYdEZm8rxneuMAyHSkbWb8v\nab92Zs3zGVYpwoDDPLehvp7w5qqbYsqUi1BcvA3t7d1QqWfklQmmy5heI0kvLZEFPmdPSNdUQfhU\nSdDWQPXhy2AAYuiACIonAPhPq6LpO+DMchW4lnMVBMPXXTu0DqQVqq4Ms4+Woz4Yk0tDkCZPJSHI\nctCzbVU6evSfuOWWeiuAWm/9/n7YO3bdBuE2+yc4/JDGWiKNTSgQTU1+zJ79HMaNexl+f7s1Hirg\nRkwx1NGUhaccV8mDGlDULeYaiIxy2bLtBF9DJ+TSzz5fAFde6QdjP0JVlcO6fwK4ckCCWdfaveBM\ni95bJg8OH2ZgLByXFMABG/bANGPA3r28kB/vsU1VfuUCgLxt7PLlK5CUJFs4sl+eyrXzz3lPcLoX\nKTyUYS+Phc7BRVAFngcqj7JTTs5wLFs2PRg0/8c/2tHerveibgW37KiJ0ziIBjr0vDyI/dS7Qh4u\nDUgYfPe738XBgwdRXV2N7Oxs7NixAy+99JJyTVVVVfDfd9xxB374wx8aBIEg0oZlrG5KCrVTXAW+\nqe+EOoH5EOUY5kp3o41gwu+OgmraCeaZmHgAjzxyI7ZvX6Ew1dzct+H3n4cvv6RP9OQbav4tB6WP\ngzO+LOzbVy/1VOUuneeeA1ategGff/4RurpuxKBByRgxohtDhgzFxo0eNDePhR05pDca4c/6xz+q\nUFi4ErW1piQuplyrBnv9EIxCLswnQ3bJX/sWVGtqGOyMVXZN6LGQncjIOAKfz4e2tj0ApoMzlB+D\nH0B57KJMuV0LkpUCQoXopZsJ/0/P5vcaMuQoxoxxSpmqdyvaqtt9J2pqHPB6fww7XPU55TrgVYN1\nQiTDG4UlSeim8nLA5brO+swLFcrrh+gJAO1z+luOq9DzySLQYxcu8PWwI8B43Gwy1L4Ng7FjxwEk\nJyeBM6THITD/lLFO61MMvj7kljMJ2DIwNtHwOWCuzFoAh+MZmBwJpPRwmDlZ62UQAuoNAAk4dMiF\nuDhzQuO4cS9g+HDOlBMTA1bVYnm9BkF4FV6AWh/tzzCzTooxyooHJ6rltH79rmAPkX37KqHOJ8D5\nRw64UvUu+Jx6oeYb2ZXNSNCAhIHT6cTmzZtRWFiIQCCAoqIijBs3Ds8+y1OlFy9e3Kf75eY+iilT\ncmwujlOn5kr1ZlbCXkJBZm4yMzsFe1lcQAgBqmMuN7vvQHa2HyUlSzB5sicoxQmts3FjmSQMqqR7\nUqr5NnCh4IPQ2vh8UCAJgCIQdETF8uXvWHkPJdanxIivA9fOvoJa7VKUWCgr43V8VPJAFDwbBXsA\nLBu8ic8KcOge+Ump+iVBdgdBJEYRyUGt4+DIEupaVaJdK2IhDz1UhJtv3gqfjxjKTvB1OQ6OUvlN\n8De5uW+DscGoqtKDb8OhokKI6FDrQpM/f8yYYgwb5kZXlxPnnefH7NnZQeBCa2sNvviiBV7vRNgZ\nLXdDxccD6enA978/Gp991oSurlvBmAs+n8/yNcvzejeEy9F+iL3e/4DLtRlebyvUBkZyTwDRdAb4\nEE7nnfD7vwtzD2J6pkC48do9bog9L9flr4fA7quCorsbaGubC8EmCG0m5yPkgzPLsRClM+yw58TE\nI4aSJHwMPl+rpqnDWnMnqqrsv6AGRNzNSvN0HniF10PgmjO9gwcOxyIwZgdxyOeusHClVT5+BbgS\nSQtJyoQcJJez1InkGCMJkFvhdPoxalQ8Tp3KVpou/fWvc9HRQZVmqT1tmfVvv/U8astHlVaJBpwR\nYKQB33XGjBmYMWOG8lkoIfCb3/zG+DkAFBauCjJb3cXR0SFnDtNmPw+q/5oqXcrQvf+wvqfuRISk\n+AJCCOjN7oFTpx4MavA6AmL//gorEefHEA3N10JooRXgLiZiuKF9+yZS31/WtD8A9xneBB4wJD8q\nBUDl+Vpq5VOQZiKjPuje8oGthcjVeAG8Vy31hQA4Cog0Yh05kg21ousSCIFhdsG0ttZg48YyuFxd\n8PkA3V+fl1cc1Noov8TrTYfLddCyDslH64cZFULBTkBnSunp81FXNxzl5cLEJ+ACwAOZJ0/mwF4I\nzwO+b3YgEACamjx4+eVNYOwSCKRahXY9BYQpS9t03PJx0UUv4l//6oDfPwKqJfZnqN3RODF2HVyu\nj+D1TgcXCLIV6oDsY09KqsRNN41GWRm1NZWVKLJ6Zluf2YUV18xpbkljfQMCDw+IDoR6ue1VAL6A\n2x1AVtZ5KC/XhYQHwO/Q1kYd2lYhMfFLK2ueKzRqYpqawJaZ6QMv2zEYfM9R+0o1XsFYN5zOG5GS\nko4xY1Lw2GNzbeePu2xftUAWO2HP0paD5HKWuo4MknmSE36/HzU1FfB6VTgzLzBI6Ky/pMACAAAg\nAElEQVR/g1jjreAxS4IjP2f9rbfojTydHhHTD2KMYf36Xfj4Y1NdG8LnynGCF8AXXTZv5WAMTTbA\nF/cz2JNv1oIzb/UA1Nc/ZWTYpaUeKRFnCzgjlKGXNL6p1i969u2bSM3Epk23BbyS5U3W/xNhD4DK\nxPMpcnJWWY1HKK9iOFR/cQOApYiPb0IgAOme5BddCh5DkHvLyglLeoCvEdxqIRSQXUN0u+9EXV26\nxYw9tu9lrU0EwkkzBuLiPsL557sxdGgqKiqqLWGiP4sOmZ5lHUAg0Ib6+u3KbJGAZoxZjIdiDTI8\nVA++vgDGLobMeLzeIqkPNjHWYnAfsMlC5SSKzs0CX1+yxKgGlupnDwQmWUFkgPe+pj4R5CoFaO93\ndABff70K27YttRirXNqd5p3cO6b9Og0c+roCfL/4INprUjIauRgTIGIXieAKWj6+8506LFs2XVpL\nvh5xcR+gu5vgr3zvdXYCw4aJmIBc1oF3Brw2uDdefbUafI9ugqgkLDNlilk9B78faGkBTpwQqCY7\nnQAP2D4AYZWRxVQG4J+Ij5+JceMuQkKCAydOHEJzM48f+f0nrR7LL0DPi/F6TclhxNCHQ4W6TgDw\nPwDeA4+BENiB7s0rFzscd2pF/QZOUSMMyspo8nT8LiBcP81Qm8LPhj3zcSccjg8RH++0kk2IwdkP\nCm+ZSYxQJRPDVrX2XeAChu6/FQIOR+8QGiUUiuyZ2A5wn2o7RL0g2Z1gfoa98QjAXWkyEuoFADUI\n2CaAzw93Xww2fud03ojU1CQ0N8tWyTsQlpnM5FfB4fgCeXlDwViiZC7bcypk6C2fbxlpwV0XHJn1\nY6xa9bJVAI7uxd198fEAYz6rLwYg4iUMXq/u5uLU2RmPpiby2euF8J6B2vzFA66F60i055GQMBPf\n//4q7N1bgxMnAFEj3wPR/UqgTUjT5Ylz9A4HpN/ozwBUhncKora9HAcSQn/fvoMApmPDhkLcd98G\nHD5cBMbkLOwp4HG4bMOzlmDMmP9BY+NHaGsLQEA4SaFwweFotywIJzgzqwXBroEK7N17CoxRHtFO\nyU+fGyxZLuePVFb+C8uXdysWQXr6CixbNl3ZG9xjQIJ/OHiyogxDDt1Kku5BENfjx79Gff3zEICJ\nCnANvRii1wSvR9XRIUpMCMTZcSv2pPdpfwTCayFTgVQNQV7PdwD8KXiV210EgHqP51uf3YnBg9vR\n3HyrscJBfymu90vONOmVA4GkpBZwc1mvlaPXWMkHsAbp6cPx6qsPSZUDAbPcYzAvlJlhq1p7FUS5\naNKQL9DeoUD6fiWAEiQlzcWUKaGrDorqqbQxFoCbrF3WO7SBa0EPas8SxBnMdMM9Zd/wNnCN9TUA\nDxvu8TZychLBNWqd8pGaOhgTJ14qfUaaJjFS0gB3ISnpc/zv//3v+OCDLVIpDHEvYA2ysxOD1mFh\n4UqUlnqs+Q6FzNqJNWvmSWss0ESBwA50dwekOXwc/JA/jq4ur3QnsS4ffLAPn39OzDTfGj8vD+J0\n/hBxcc3Sb95BqA52VOztqqsIVSe7Gy6F6MnN98L8+TmYOTNfWiNZS8xH6NLZgGCgcjVdeYz8vZub\nX8by5e9g//4KOByXWglNcpvMY+DJlpS4JSg391Fs3LgcJ0+WYtq0Kdq9rwEwAoytAN+PNbbvgK04\nceK3KCt7HNu3H8OyZdODlWizs1NgWqOaGr8tr+bQIQduv/354N44duw4hMdgHjjzTrM++3/BLVeZ\nya607r8SlZWfBSsk79lTgrKyx1FZSYFmijMtAYd0noScyAaQQNmJkpKtuOWW36Os7HF88slt6Og4\nDrUHyFbwWBwVphOUlPQiHn54IvLy6uFwHLA+te/1+vrnkZXVisLCVZg2rQR5ecUA0lFVtQPNzSpY\nZ6AUNZaBIC79MjJuxcSJl1hZvdPwy1/ugtd7qXYtCQNVs3C5vrKZmHV1dVKNcTnvwOyqIL+kTEJr\n3wouRBLAD5BcU0e8A3dPfQ5+wHm8pKMD2L59BSZP9hjjBvQZz06mey4FN1vpAI+DwP/zekjAUgwZ\n0o4pU863laWgf99++/OWJkEWht1SkjX09et3oaqqxjY/wKMYPTpZs2Kc2r12QjR3n4b33qvF1VeX\noKKiEnbyoKrKYVWj5UT4cxVFIaizM16pb7Nv30HJSvGAC097/RjgQUsjI6QQf6+2NnINya6mfCQl\nLcYrrzyEVateQHm5bJ0uMI5rqJX4Lsqr0B61wyQ7OgRM0r5GRPaGLS7Xh2BsEXy+bHAoIllPlNVs\nTnp66qmbcPKknKuhX0suQjn7PQcbN5Zh/fpd1to1Qu3fIT/nKQituOdcGJoj0R1NUHe3HBSns1qI\n5uYylJU58de/bgE/fz+V5qYU/Kz9P+BuFsCeF8SppuZmdHerYxPBbQqS0x7YBRPV1DTiySc/t8ZO\nfv5LwfcH0R7wGIacy8Ddf11dfvzpT0nIznZj3rxMvPoqteS0U1paTrCsR2HhSiXeFUmKQmEAAPm4\n8sqdwQkoLfWAMQ/s7od54BjpcZAPy1dfHZfcTtzEvPfeaRJU1H4weyusBcgH/AuoAVdyQ5iYyVx0\ndKiBc/1Q6NnCU6dmIxAgBIocmP5vqAku6hinTFmllCCWaebMfEyeXGa5i/Rll4VpV9Ac5yUkFkCv\nzuhyHcSaNcusd6E5lQWDCAiPHl2M7duPaTWnqDMVJ47xVhnCoUNrkZdX3GNNHnove8Z6Gbjmbjpc\nPJ5SX79FKndCcyL2Ar3rmDGCUc+f/yu0tNC6tEOHDwKLwVhbcFwAhw0fODAbgYC5UqjsjlTXSIwX\n4NVo3e4hVsMW8tlvgR2PD9irofLg8smTciJlvuFa+pwjvpYtu0ZD9m0F8FfpWqf2u10hvgv9vrm5\nf7ZcRTLJe0nOpeDj4PvhFqhMtgHADKjBXzl7WBAvLaJTARISFsHnkxMt6awBusJ55EiDlZdAiWEU\nP5LzDZK0dxkB6qHd3b02WAsqN3cFHn54IjZv3iMprIJkL0Wo6s6RoKgUBgQxLSxcia4uJyoqKuHz\nXQTTYU1K6kJHh3wQyhAIqF2ADh1ai717V2HDhkJs2iT7c4nEAeitsBYA3HjjF1rAVbcIRCG1rKws\nw2YXh8KeLbwVZWUfQFTWpM20BNwf+xSEL/vHoA0aF/cxpkwRriETCWEmBzJVzUmGv/Lr38GhQwtB\nyWFJSZ/j4Ye/rwjLTZtWoabmuA2vn5v7KE6c8Fple8Vh8vv9wcquAuNtH6/XG4+sLL/l47b72WWy\nWykpEG4ElXJyhuO887Ik4eGBmk2bL10rNPcLL3wZ5eVU8yoBpp7azc3CpUBzxEtmyLEXMRcVFZVK\n7om9YKOoRrtxY5lkPdEY18POlEmayGu7EjyeA+1ac9/gxMSAAdlXC9E3GLDHq3qqGsAFkt6jIjs7\nxbD2BRIazuwq5M2iiKj8xhJw66ANAkxi8oSb9kU+Bg16AmlpJyzUFVlJNRDF6cQYOjvnQ5St0YvW\nfQkuUAaBx2JkC8yMMNy7Vw7yC8VJ7uh4330F1j6XBVPkKGqEQWGhwPNPmZIjaZMe8DaMutYNJCbe\njdzci7TNFFojkRvkiEJ1osbQhx9+1WthrZkz85GevkWT4HaLgFcvpYqa9vGQtFcPHGkZVE6DNrT6\n3k7n7+H3T4QMOezu7tn9RGMHuLZaUXESPl9ol8KmTcLK2LRpJ2pqGlFf34KsrCy8916tAr2VLRxR\nkrgGJ06cxOHD8bCX8ChDW9sptLY24qGH5oWYI4+lBf8JJtihnptx/Hi9hFVvBNfAfgU1H6MMCQnV\naGzUC+bJLpbQB5HHOyhJcRB0wcFJ1bRFOQQd7caf09Sk5p7opZ3larTr1+sui3xw98jH2ue0H+W1\npdwaHdrZCN0NmJ4+H42NaaiqOgWV9HvolnqBZPXJpaLlHhXPKtVR588faRR+8+dPxN695P7T3cP8\nWXy9M6HmzaSAewt+Bd6BL8PwW7nhD9GjuOCCHDzxxG0WQ6YaWVngrmD1jPh8o613fA6iigG5i9LB\nXUYEC54IXviR5tBOutuzpqYx2LZTnq8rr/QjLm4zursvNt5nIBQ1wkDvsCQEAVWx1K2CGiQkfIVj\nx/QaQr0jeKZOzcbu3XPg9V4EqpcPJODkyVeVwlr791fgvfdqlaJaM2fm4957p2HtWtnVkY+4uE24\n8MKFyMm5MCjQCGWgYv5VzZabfXIW7bjgPTntBPAVnM4f4tJLczFyZCqmTCGT0u5a6SmHgWjYMDcu\nvjgeX35ZjlOnkiXUjSCyXOhey5e/g6amZ9HUJDam/L3s6jp69J+oqcm05hcwZeAyxjNwly83MwTh\nOhICu7NzFBirV96vpGQrnnzyADo6COVSDO63pe5kLwCYCe4yeh4+n9wl7EFLY5cPOofIxsX5bQeR\nxzDo2XoZbE56gxhh1tPv7G4Lfd1M+S2AbP3ISkwChgz5GidPFqG7e2Hwc5erHHFxqVbPaECFKMou\nkD9Chd/+EydODEF5+VbYkX2mezQoVt6UKRPx+uvFqK5ug9fbgc7OjxAIlELUUloJcrUcOlSIvXt3\nBi12XfgBfH1//vOdsBPPIq6uJtg05R9RLMgNFZ8vEvccjmNg7DaoVt21yMnZGXzuvHnrrOZYBTC3\n8ixAYuJL6OxMgejP/Al4v3BAxOPuAIf/kiXTM3+yd3QEaL0PHUrA4cPvobt7qnT/nxvv1y9iUUDy\nMN54Yw9LTp7HeLrLCgbsYcCdDHjU+owxYA+Lj18U/Lf+ndO5WPo/Y7m5P2NvvLEneP/c3EcZcI/0\n2xXK9XSfpCT9Po8G77N69RaWmTmXDRmykGVmzmWrV29R3oE/Q77XHDZhwnJWWLgyeA/GGMvLK5LG\nvzrEWBgrLFypzNm0aauN102btloZR0HBCjZt2mpWULCCrV69RRsXY0lJc4zvnpk5J/i7vLx7ehyT\n+r57GDBHep89DLhdW88V0rvuCc5JYeFKNm3aapaXV8SSk281rC1jiYl3K2tpH/8KaRwrrefcaBx/\nXl4Ry8hYYPhOvocY65gxs6T33MKARcrv4uPvUvYBY4wVFOjr2fu6haI33tjD3G79LDDmdj/Abr31\nYdt+VefGPpcJCXO1dyxiwI+k64sYcLdyj57Olnnv0/susj0feJSNH7/I9o7ynuV7bwsD9HdbZJ3B\nOdK70ZovYsAsaR3134d+D3p+fPwN0l4wn8m8vCI2Zsws5nDcyTg/WS390c+CPMZHjc82n2/9+rna\nOCLHwqPGMgBEzX1RmI38hXIfUB6NDwSokJw9ADxlysRgeQFd0xBumRLY6+XLVGas804aXEnJEpSU\nmOq4mwrF5aOjA6ir24LMzHQrMEtatdzGj9LrVRM2KWkxli27TXlGa6teaoETaRimyqU8BV7Vtjs6\nUqVEKYCbuh8o5YcTE83IGXNhPNmHSpok+aWPw9S/tqbmK60d4jtob3fA5Cvu7PzP4BpwrPk4qJoy\nJS3KCXRVxvGnpeVg8mS/oQERWWvqWGtr78Ejj4yU3Bdqh6xAYD727lW1WHsMQNcM+dgPHDgadEf1\nZNm1tzdBd0XV1z+FN964CR0dalVXNROd3zMpaS5yc7OQkNCGAwdaoJYFXwnue5ezk7eCl0GJQ1xc\nIjIzvRg5MnRDJfvep/c1tUl14MsvRW6Eac/yvSfXqOJzPWzY19i+/RiampbCXqeM3oXYmwzXtUbl\n9yMu7n8hLi4ZgwYlIy0tHfv3V0ju6YXWlSb3GndR33DDJGzffgyMFYKvialEhVw4EzBZ+ibAirAC\n9TNg7l8dCYoqYcD9q1lQfZ7yEKmT2f3aL8MLAAOy2S6XGzAdUFMmdM/Zw/ZnyPd7x1jfXcXd6xh9\nXk7g4Yen2Xzkhw/Xw14M6wEsW3YzAHPlUsE4VSbH2FxMmsSLtn366TEw9ob2zqNgotbWGhQWrsT7\n78vJTtwFIN6H0upXQDAEmdaivl5kaIpxh0q40guV1cDO0GQyVablxJmZPWDLEUx+6G6Nzs5bsXfv\nTrz99hoLvWSPGXR2qn59EacRrhOfT25Sw9eiudmDsrIyeDy8mumaNfOMNatOniQEi0C2ANloazMH\nqOPijmLSJJl5Lw26IQIBL1R3F91Pdut9AKr1090NNDQADseDWLx4ON57rxbr1+/Cxo1lQSFm3/u0\nB0xtUoGurkXB+JNpz4q9Jwv3MtTWeuH307V/hp0K4HD8CiIZTp4bnr/T3c1RPX6/B+XlZfjoo3fA\nGCmZzPrb5BoLYNw4P957r1ZTgqhiAKx3/gpqbpTYLz/4QWjkHyArEQnaN2ZUWiQoqoQBr7aZDjX9\nmio3yhvUjBKR4wI6XJM2q5C4crkBvW8s1S3v+RmhyJ5FHBpz3doqR6KF9iCsHIHRpzo9n3/+Jdrb\nr4DaKKMSgwf7gwzEXLlUPuiCfL4dGDZsFRob68DYUJiYjV5ITC0rITNg2bophOjy1YxQWk1KSmrw\n36qPPTTSBaB5JoZG9fi7wLN8F0IUMCREh3jvhIQ5aGw8D+vX7wJjnyE1dRbi4tLgdHagoGA0/vjH\nA/D5GExWjHg2UWh0EFFr6wg0N5Nw2wqubSZClHZQq5nKQeXSUo+Vd0L5Jj5tXHPBGMVnVIbb3u5B\nZeUW5OYmWEle8jzr5TFo7eRcATkfhVN9/U148snf2/oS2OcFEKCH9fD7TXvv/wtaembYZIG090SZ\nar+/RLqGktfkPVuACy90oK6OsnyJaAyE6pHjWHRPyiOi/hS0l7mASEr6HDfcMA27d8vWOSlyC8H5\n1kfgZfV/BnuwehYOHkzA0KHzwNggXHhhsk34A0BaWgOczgarkgLB2OvA9/N/GeZqYBQ1wqC01IND\nh6gENKCWeZD7gFJ10NCuFJO5SZuVF6QqsiyQbqjlAVbB4ThgaQfhJ6OZ8gS4VKegVQ1Mm7WmphFN\nTX6IvsO8uYjD8RWuvXY8brttuvQe8iGfJ42LNpAHR46sDwqNzz/Xs7WB3soCV1e3gc+/3ZWTnd2I\niy4SrrfGRrmshCxM6VAQkkJo93FxPzQGq9vaRHlqlZnoCVfqGtx3XwF27twExraCt+okV8FWAL8F\nPzArYQIfOBwUJPVAZ6779q2A0+mAz6fDGYUVIzQ3HR3kwaxZ6+BybYTTmYwLL+SanGjeQtr2VIhe\nA/amM3LZBB68p/63o6EzVJGEqCOI+J7RA+EAzbNeOprWjs5gKPYQ2oUaCho7f/4MPPHEXimgLYgs\nPbsgAShQDBTjo4++BmNkBcjX6sUSeaXW22//AQDgiSdeQWfnXeD1m+id6G9ZQBFscw9EHhEljtaD\n+AQljnJAgRgnp53IyPDhyisn4cMPq3H8uH3vxcUBVVUCqlpe7sGsWRtx8cV/RnZ2CqZOzbbcVQSK\noKKL1DWPu8wSEg5LtbkiQBGLPgyAAFiBNlOwmLHBg69n8fHXaQEpCnDNZcAClpx8UzAIYw/aiYAn\nD8I9oASTXK7ZweDuhAnLtaAbD0JmZMyzBXkYMwVPV7DExNvZiBEzmMt1l/V5EdOD3MAcFhd3vfX/\nhxlQrIzV6VzMxoy5XfpMfic96EnzRoFAOagmBzgLWVxcYci5SU9fYAXC7N+PGTNXCeyp80RjmMWA\nGczhmMGAaw33MQURf6YEEfsSfGeMsZSUHzF7gHiFNq6egubm9xUgBvXPhAnLlbHyAKa+Dnqg9jZt\nbCukf8sBdntQWexlOSivXysHvOW9Ib+bCBRnZs5hq1dvYS7XDMN63MGSkv4XS0y8m4UOnprGIILg\nMhhAXjN1P6t7z7z2IrjK52G19j50begAL78fzfNKJgKw9Bv9nnMM76ffn89lcvINBpCJCESbwRn6\nnPa2P2kdze8YSRYeNZYBNxFl9xCvBjhoUC1cLjdOnRoEXjclU/oVxRC4OXzLLVuQm/tn1NSYqzd1\ndsYb2uDlw+vNx8iR3IfH65qL72hMV15phmyqPm4y9T3o7NwCgGqoy0Fium4HurtLrM+qocMN/f5n\ncOTIHOkTeal0v+EW8KQYMudLYNeG/4lA4HzwngZmbbux8WWUl5vKP3hQW5uBqirhLrD3TKgAT2oi\ny6MEdjI19OaQPpnS0hqQkcF7BPCSw0tDBlUvuigd5eX6eutJWAA1tZky5Xwpyc0DtZmOIJeLab0J\nOI0cKVxaM2fmW32s6ROzW4Vj0k1jI1flRTBRYmIAnZ10PQUiTdqznKQlJ5y1Sf9WcxuefbYIGRlA\nQ0Ml5PVwu4HnnuMWichHoYxa6w2cByzXhX28gBkaW1rqwalTCQjV0Y8STNPSGrQYh5xjoWe5A7zY\n5EFjscnq6jbLNVcCNeYg5+/IrrJ88PiD/nKmmMNaa394gkF5ORhcWLjS6legwlp5ccsJ0v1Mtbf0\n2mXmkiyRpqgRBsJElINyHvh8JejqGgW10mYxuMkkp8kfCJrD5sqnHlRUVMLvTzI+n0xVs5lrdg8B\nso9bx9LLWYmhuhTRO5vHxJhsxuvuE7mMdCfUDWWay7kQdeYBYgBO5wfYsOGh4OGdNWsjvHKtLWvM\ncrwA4EgVFYVEyXKm8RIVICnp9yFzLoR7T7iWamuLsGrVy3jkkReDSW+UvTpzZj7WrFmA669/UnuO\n6dkMcXG8B3dCAr1g6ODy6NEpGDq0931grs8EqD2FG+FwzAJjl4Hnkoy1riHmY2oGczeWLftxEHkm\nXDf2a+UkLZEJfp70brobyoP6ep53Qa6QxMQqZGd7MWTIUKsblx9r1izA/v0V+OUvd0t9JAJISQES\nEx+UlCqRoDdpUjEAF9LShgdjXGlpw1FRUWnlxaiooMGDj2D79sHaPK/AY49dY+gXrr97PpKSXsSl\nl2ZK1WsBcsm2tjLr/yYhshPJyRVwOPzo6loEn48UN8obkGOIcj0tnXnno6NDKJNEQrmtgOrCWqmN\nx8SC9ZioOTch4hQxG2MABMDoHuBYYB1XK7skZNNO/z5U7kHvOH4d856Xd0/QZNfdFMKMX63dX36O\n/G+TqWsyJxlLSblOcmnJOOUVDFjE4uKuZ4mJNzGz20g1PR0O8zOGDFmovM/q1Vtspm9iosm838MS\nEuYwgeW/pdcx5Ob+jK1evcXoQlDnUr/HHgY8oHzndj8Q/O2IET+0rbfAldvH4Xbfac3rauP3iYmL\ng6Z+qLHKe0XsW3IB2HHtwB3Sv2VXkikvYiXLyyvS7i+Pk1+bmHg7mzRpiW1cb7yxx8qfoGfp69dT\nXo1wJyUlzQnp2snLK2KFhSvZ+PGLpP0iv7c+r7rrhf/JyDCdb3tejcixKGLAPAYsYC7XjWz16i0G\nV61pbkNj+/XzzveGnGch/978HrKLrKBghfRepj1tWn/5j+5O3cP4+dL38f0skiw8cncaANELyYsi\nfLG3Giff6ZSTQkwLtIdlZMxj06atZqmpN2oT23vSB41HHERxQPQEM75JdZ9uqINh2hyzmD1msIjd\neuvD1r2JScxiwELluvj4Oczs997DUlNnBRlZaurNhueuYE7nLTYhpzNBc9KZ7ve83nDNFgbMsBLz\n5tgSsnSyJ9LRM8x+/UmTlgTHm54+n8nMdPDg69mkSUtCMpu8vCJpj9HBv44BN7C4uB+xvLx7jHvC\nRDRf48cvYi7XLYa5MK15EXM6b2DJyTdIsSWxH1ev3hKM0eTlFbFJk5aw8eMXsczMuSHjJzIJwWry\nN5vOC/nVdSXCfP6I+Ynn6EqZ/kyzEmZO+rMn4dljfapCQGugrnf4AtS0nvZ7yTEH9Q+th10omXlT\ncvJ1LCNjn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        " </g>\n",
        " <defs>\n",
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        "   <rect height=\"223.2\" width=\"334.8\" x=\"33.421875\" y=\"21.56\"/>\n",
        "  </clipPath>\n",
        " </defs>\n",
        "</svg>\n"
       ],
       "text": [
        "<__main__.Gaussian at 0x108861e10>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can easily compare them by displaying their histograms"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "display(x.hist)\n",
      "display(x2.hist)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ORK5CYII=\n",
       "text": [
        "<IPython.core.display.Image at 0x1083d5f90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5ZC9GwPHzx6XJ3GQyQa1WAwDUarXdX+SNGzdQUFCApKQkV4bRhrUBTnfu3LG7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\n/D/hAXsTS4KaZAAAAABJRU5ErkJggg==\n",
       "text": [
        "<IPython.core.display.Image at 0x104eac510>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Adding IPython display support to existing objects"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When you are directly writing your own classes, you can adapt them for display in IPython by following the above example.  But in practice, we often need to work with existing code we can't modify.  We now illustrate how to add these kinds of extended display capabilities to existing objects. We will use the NumPy polynomials and change their default representation to be a formatted LaTeX expression."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, consider how a numpy polynomial object renders by default:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = np.polynomial.Polynomial([1,2,3], [-10, 10])\n",
      "p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "Polynomial([ 1.,  2.,  3.], [-10.,  10.], [-1.,  1.])"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we define a function that pretty-prints a polynomial as a LaTeX string:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def poly2latex(p):\n",
      "    terms = ['%.2g' % p.coef[0]]\n",
      "    if len(p) > 1:\n",
      "        term = 'x'\n",
      "        c = p.coef[1]\n",
      "        if c!=1:\n",
      "            term = ('%.2g ' % c) + term\n",
      "        terms.append(term)\n",
      "    if len(p) > 2:\n",
      "        for i in range(2, len(p)):\n",
      "            term = 'x^%d' % i\n",
      "            c = p.coef[i]\n",
      "            if c!=1:\n",
      "                term = ('%.2g ' % c) + term\n",
      "            terms.append(term)\n",
      "    px = '$P(x)=%s$' % '+'.join(terms)\n",
      "    dom = r', domain: $[%.2g,\\ %.2g]$' % tuple(p.domain)\n",
      "    return px+dom"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This produces, on our polynomial ``p``, the following:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "poly2latex(p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "'$P(x)=1+2 x+3 x^2$, domain: $[-10,\\\\ 10]$'"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Latex\n",
      "Latex(poly2latex(p))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$P(x)=1+2 x+3 x^2$, domain: $[-10,\\ 10]$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<IPython.core.display.Latex at 0x1083cbe10>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But we can configure IPython to do this automatically for us as follows.  We hook into the\n",
      "IPython display system and instruct it to use ``poly2latex`` for the latex mimetype, when\n",
      "encountering objects of the ``Polynomial`` type defined in the\n",
      "``numpy.polynomial.polynomial`` module:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ip = get_ipython()\n",
      "latex_formatter = ip.display_formatter.formatters['text/latex']\n",
      "latex_formatter.for_type_by_name('numpy.polynomial.polynomial',\n",
      "                                 'Polynomial', poly2latex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For more examples on how to use the above system, and how to bundle similar print functions\n",
      "into a convenient IPython extension, see sympy's [`printing` extension](https://github.com/sympy/sympy/blob/master/sympy/interactive/printing.py).\n",
      "\n",
      "Once our special printer has been loaded, all polynomials will be represented by their \n",
      "mathematical form instead:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$P(x)=1+2 x+3 x^2$, domain: $[-10,\\ 10]$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "Polynomial([ 1.,  2.,  3.], [-10.,  10.], [-1.,  1.])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p2 = np.polynomial.Polynomial([-20, 71, -15, 1])\n",
      "p2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$P(x)=-20+71 x+-15 x^2+x^3$, domain: $[-1,\\ 1]$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "Polynomial([-20.,  71., -15.,   1.], [-1.,  1.], [-1.,  1.])"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More complex display with `_ipython_display_`"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rich reprs can only display one object or mime-type at a time.\n",
      "Sometimes this is not enough,\n",
      "because you need to get javascript on the page, or you want LaTeX and a PNG.\n",
      "This can be done with multiple calls to display easily enough,\n",
      "but then users need to know more than they should.\n",
      "\n",
      "In **IPython 2.0**, we added a special `_ipython_display_` method,\n",
      "that allows your objects to take control of displaying.\n",
      "If this method is defined, IPython will call it, and make no effort to display the object itself.\n",
      "It's a way for you to say \"Back off, IPython, I got this.\""
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import json\n",
      "import uuid\n",
      "from IPython.display import display_javascript, display_html, display\n",
      "\n",
      "class FlotPlot(object):\n",
      "    def __init__(self, x, y):\n",
      "        self.x = x\n",
      "        self.y = y\n",
      "        self.uuid = str(uuid.uuid4())\n",
      "    \n",
      "    def _ipython_display_(self):\n",
      "        json_data = json.dumps(zip(self.x, self.y))\n",
      "        display_html('<div id=\"{}\" style=\"height: 300px; width:80%;\"></div>'.format(self.uuid),\n",
      "            raw=True\n",
      "        )\n",
      "        display_javascript(\"\"\"\n",
      "        require([\"//cdnjs.cloudflare.com/ajax/libs/flot/0.8.2/jquery.flot.min.js\"], function() {\n",
      "          var line = JSON.parse(\"%s\");\n",
      "          console.log(line);\n",
      "          $.plot(\"#%s\", [line]);\n",
      "        });\n",
      "        \"\"\" % (json_data, self.uuid), raw=True)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "x = np.linspace(0,10)\n",
      "y = np.sin(x)\n",
      "FlotPlot(x, np.sin(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div id=\"47ba8d73-8a8b-4a34-b96b-378e969797f2\" style=\"height: 300px; width:80%;\"></div>"
       ],
       "metadata": {},
       "output_type": "display_data"
      },
      {
       "javascript": [
        "\n",
        "        require([\"//cdnjs.cloudflare.com/ajax/libs/flot/0.8.2/jquery.flot.min.js\"], function() {\n",
        "          var line = JSON.parse(\"[[0.0, 0.0], [0.20408163265306123, 0.20266793654820095], [0.40816326530612246, 0.39692414892492234], [0.61224489795918369, 0.57470604121617908], [0.81632653061224492, 0.72863478346935029], [1.0204081632653061, 0.85232156971961837], [1.2244897959183674, 0.94063278511248671], [1.4285714285714286, 0.98990307637212394], [1.6326530612244898, 0.99808748213471832], [1.8367346938775511, 0.96484630898376322], [2.0408163265306123, 0.89155923041100371], [2.2448979591836737, 0.7812680235262639], [2.4489795918367347, 0.63855032022660208], [2.6530612244897958, 0.46932961277720098], [2.8571428571428572, 0.28062939951435684], [3.0612244897959187, 0.080281674842813497], [3.2653061224489797, -0.12339813736217871], [3.4693877551020407, -0.32195631507261868], [3.6734693877551021, -0.50715170948451438], [3.8775510204081636, -0.67129779355193209], [4.0816326530612246, -0.80758169096833643], [4.2857142857142856, -0.91034694431078278], [4.4897959183673475, -0.97532828606704558], [4.6938775510204085, -0.99982866838408957], [4.8979591836734695, -0.98283120392563061], [5.1020408163265305, -0.92504137173820289], [5.3061224489795915, -0.82885773637304272], [5.5102040816326534, -0.69827239556539955], [5.7142857142857144, -0.53870528838615628], [5.9183673469387754, -0.35677924089893803], [6.1224489795918373, -0.16004508604325057], [6.3265306122448983, 0.043331733368683463], [6.5306122448979593, 0.24491007101197931], [6.7346938775510203, 0.43632342647181932], [6.9387755102040813, 0.6096271964908323], [7.1428571428571432, 0.75762841539272019], [7.3469387755102042, 0.87418429881973347], [7.5510204081632653, 0.95445719973875187], [7.7551020408163271, 0.99511539477766364], [7.9591836734693882, 0.99447136726361685], [8.1632653061224492, 0.95255184753146038], [8.3673469387755102, 0.87109670348232071], [8.5714285714285712, 0.75348672743963763], [8.7755102040816322, 0.60460331650615429], [8.979591836734695, 0.43062587038273736], [9.183673469387756, 0.23877531564403087], [9.387755102040817, 0.037014401485062368], [9.591836734693878, -0.16628279384875641], [9.795918367346939, -0.36267842882654883], [10.0, -0.54402111088936989]]\");\n",
        "          console.log(line);\n",
        "          $.plot(\"#47ba8d73-8a8b-4a34-b96b-378e969797f2\", [line]);\n",
        "        });\n",
        "        "
       ],
       "metadata": {},
       "output_type": "display_data"
      }
     ],
     "prompt_number": 18
    }
   ],
   "metadata": {}
  }
 ]
}