{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Driven Modeling\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "### PhD seminar series at Chair for Computer Aided Architectural Design (CAAD), ETH Zurich\n",
    "\n",
    "\n",
    "[Vahid Moosavi](https://vahidmoosavi.com/)\n",
    "<hr style=\"height:1px;border:none;color:stillblue;background-color:black;\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a></a>\n",
    "\n",
    "# Fourth Session \n",
    "<hr style=\"height:1px;border:none;color:stillblue;background-color:steelblue;\" />\n",
    "<span style=\"color:steelblue;font-size: 1em;\"> 11 October 2016</span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Topics to be discussed \n",
    "\n",
    "* Density Learning\n",
    "* Meta-Parameters in Machine Learning\n",
    "* Regression Problem\n",
    "* Least Squares Method\n",
    "    * Linear Regression\n",
    "    * Polynomial Regression\n",
    "    * Local Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
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       "     \"</code>\\n\"+\n",
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       "    console.info(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
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       "    console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
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       "      };\n",
       "      s.onerror = function() {\n",
       "        console.warn(\"failed to load library \" + url);\n",
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       "      console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
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       "  }\n",
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       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    \n",
       "    function(Bokeh) {\n",
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       "    \n",
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       "      \n",
       "      document.getElementById(\"a86213c6-4da0-4d06-bf5c-39c6c318661b\").textContent = \"BokehJS is loading...\";\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.6.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.6.min.css\");\n",
       "      console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.6.min.css\");\n",
       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.6.min.css\");\n",
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       "\n",
       "  function run_inline_js() {\n",
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       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
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       "\n",
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       "\n",
       "  if (window._bokeh_is_loading === 0) {\n",
       "    console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
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       "    load_libs(js_urls, function() {\n",
       "      console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
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       "}(this));"
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     "metadata": {},
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    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "pd.__version__\n",
    "import sys\n",
    "from scipy import stats\n",
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "pd.__version__\n",
    "import sys\n",
    "from scipy import stats\n",
    "%matplotlib inline\n",
    "from bokeh.models import CustomJS, ColumnDataSource, Slider,TextInput\n",
    "from bokeh.models import TapTool, CustomJS, ColumnDataSource\n",
    "from bokeh.layouts import column\n",
    "from bokeh.layouts import gridplot\n",
    "from bokeh.models import ColumnDataSource\n",
    "from bokeh.layouts import gridplot\n",
    "from bokeh.plotting import figure\n",
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import Figure, output_file, show\n",
    "from bokeh.layouts import widgetbox\n",
    "from bokeh.models.widgets import Slider\n",
    "from bokeh.io import push_notebook\n",
    "from bokeh.io import show\n",
    "from bokeh.models import (\n",
    "    ColumnDataSource,\n",
    "    HoverTool,\n",
    "    LinearColorMapper,\n",
    "    BasicTicker,\n",
    "    PrintfTickFormatter,\n",
    "    ColorBar,\n",
    ")\n",
    "output_notebook()\n",
    "from bokeh.layouts import column\n",
    "from bokeh.models import CustomJS, ColumnDataSource, Slider\n",
    "from bokeh.plotting import Figure, output_file, show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Density Learning \n",
    "## Or \"Non-parametric Density Models\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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GRsT83GsBMLbGOCcCJwJMmDBh8IM0oHsfVOAmVbPhzzXQCpI2BH4NnBIRTxT7RUQAUW28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\nBGpmZlbC/wf14xUm2tSwjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116e8a350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2,1,1)\n",
    "X1 = np.random.normal(loc=0,scale=1,size=1000)\n",
    "plt.hist(X1,bins=100);\n",
    "plt.title('A well shaped distribution: A Gaussian Distribution?')\n",
    "plt.subplot(2,1,2)\n",
    "X1 = np.concatenate((np.random.normal(loc=0,scale=1,size=1000) , np.random.normal(loc=10,scale=2,size=1000),np.random.normal(loc=20,scale=1,size=200)))\n",
    "plt.title('Not a well shaped distribution: A mixture of three Gaussian Distributions?!')\n",
    "plt.hist(X1,bins=100);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now the question is that can we learn these (not well shaped) distributions?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Histograms\n",
    "## The first and the most data driven density model is the histogram of the data itself!\n",
    "* We just need to select bandwiths (or the number of bins) to descretize the observed data into groups\n",
    "* Then, we count the number of observations within each group\n",
    "* And then, we have it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   4.    6.    7.    9.   32.   39.   49.   61.   83.   97.   89.  106.\n",
      "   93.   87.   82.   58.   38.   25.   18.    7.    4.    2.    4.    1.\n",
      "    1.    1.    0.    0.    2.    2.    2.    3.    1.   10.   10.    9.\n",
      "   13.   11.   11.   22.   30.   29.   28.   30.   33.   45.   43.   52.\n",
      "   44.   59.   39.   48.   36.   45.   47.   47.   40.   41.   35.   31.\n",
      "   14.   20.   12.   12.   11.    4.    5.    4.    6.    3.    2.    3.\n",
      "    0.    0.    2.    0.    1.    1.    1.    1.    3.    2.    7.    5.\n",
      "   13.   15.   13.   14.   16.   24.   23.   22.   12.   10.    6.    8.\n",
      "    1.    0.    1.    2.]\n",
      "[ -2.83414392e+00  -2.57783274e+00  -2.32152155e+00  -2.06521037e+00\n",
      "  -1.80889919e+00  -1.55258801e+00  -1.29627683e+00  -1.03996565e+00\n",
      "  -7.83654466e-01  -5.27343285e-01  -2.71032104e-01  -1.47209224e-02\n",
      "   2.41590259e-01   4.97901440e-01   7.54212621e-01   1.01052380e+00\n",
      "   1.26683498e+00   1.52314617e+00   1.77945735e+00   2.03576853e+00\n",
      "   2.29207971e+00   2.54839089e+00   2.80470207e+00   3.06101325e+00\n",
      "   3.31732443e+00   3.57363562e+00   3.82994680e+00   4.08625798e+00\n",
      "   4.34256916e+00   4.59888034e+00   4.85519152e+00   5.11150270e+00\n",
      "   5.36781388e+00   5.62412507e+00   5.88043625e+00   6.13674743e+00\n",
      "   6.39305861e+00   6.64936979e+00   6.90568097e+00   7.16199215e+00\n",
      "   7.41830333e+00   7.67461452e+00   7.93092570e+00   8.18723688e+00\n",
      "   8.44354806e+00   8.69985924e+00   8.95617042e+00   9.21248160e+00\n",
      "   9.46879278e+00   9.72510397e+00   9.98141515e+00   1.02377263e+01\n",
      "   1.04940375e+01   1.07503487e+01   1.10066599e+01   1.12629711e+01\n",
      "   1.15192822e+01   1.17755934e+01   1.20319046e+01   1.22882158e+01\n",
      "   1.25445270e+01   1.28008381e+01   1.30571493e+01   1.33134605e+01\n",
      "   1.35697717e+01   1.38260829e+01   1.40823940e+01   1.43387052e+01\n",
      "   1.45950164e+01   1.48513276e+01   1.51076388e+01   1.53639500e+01\n",
      "   1.56202611e+01   1.58765723e+01   1.61328835e+01   1.63891947e+01\n",
      "   1.66455059e+01   1.69018170e+01   1.71581282e+01   1.74144394e+01\n",
      "   1.76707506e+01   1.79270618e+01   1.81833729e+01   1.84396841e+01\n",
      "   1.86959953e+01   1.89523065e+01   1.92086177e+01   1.94649289e+01\n",
      "   1.97212400e+01   1.99775512e+01   2.02338624e+01   2.04901736e+01\n",
      "   2.07464848e+01   2.10027959e+01   2.12591071e+01   2.15154183e+01\n",
      "   2.17717295e+01   2.20280407e+01   2.22843518e+01   2.25406630e+01\n",
      "   2.27969742e+01]\n",
      "2200.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1123a69d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# X1 = np.random.randint(-1,2,size=400)\n",
    "X1 = np.concatenate((np.random.normal(loc=0,scale=1,size=1000) , np.random.normal(loc=10,scale=2,size=1000),np.random.normal(loc=20,scale=1,size=200)))\n",
    "# X1 = np.random.normal(loc=0,scale=1,size=200)\n",
    "\n",
    "X1 = np.asarray(X1)\n",
    "a = plt.hist(X1,bins=100);\n",
    "# a[0] has the counts\n",
    "print a[0]\n",
    "# a[1] has the bins\n",
    "print a[1]\n",
    "print np.sum(a[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ASZ6dolybNDdbwNHeUYIa/ui9GygvzOGn+7rxhco058ZnODc+g9Wi+MCl1Wkd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\njlG6Ye940fgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11741c590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a[1][:-1],a[0],'.-');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# But this looks noisy!\n",
    "\n",
    "# <a></a>\n",
    "\n",
    "## Now if we want to do some smoothing (denoising), we are in the field of Kernel Density Estimation\n",
    "\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/15255412d35488194b7e24e4518765e0af9992b5\"width =700, height=700/>\n",
    "<a></a>\n",
    "\n",
    "## where K(•) is the kernel — a non-negative function that integrates to one and has mean zero — and h > 0 is a smoothing parameter called the bandwidth.\n",
    "\n",
    "* **what happens here is that we draw a small distribution around each of the observed points and then, sum it over the whole range**\n",
    "* ** These Kernels can be any of the parametric distributions we discusses before.**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178f4750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A basic example with few data points\n",
    "\n",
    "X1 = [-2,-1,0,2,5,6,-2,0]\n",
    "X1 = np.asarray(X1)\n",
    "a = plt.hist(X1,bins=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def GaussianKernel(u):\n",
    "    # here we assume a \"standard normal distribution\" with mean zero and variance 1\n",
    "    return np.exp(-1*np.power(u, 2)/2)/(np.sqrt(2*np.pi))\n",
    "\n",
    "\n",
    "def Kde_Gaussian(h=3):\n",
    "    mn = np.min(X1)-3\n",
    "    mx = np.max(X1)+3\n",
    "    \n",
    "    # h is the Bandwidth\n",
    "    \n",
    "    \n",
    "    # range of the the data\n",
    "    xrng =  np.linspace(mn,mx,num=500)\n",
    "    \n",
    "    counts = np.zeros((1,500))\n",
    "    \n",
    "    \n",
    "    # this is just to histogram of the data\n",
    "#     a = plt.hist(X1,bins=len(X1),normed=True);\n",
    "#     plt.close()\n",
    "#     for i,d in enumerate(a[0]):\n",
    "#         plt.plot([a[1][i],a[1][i]],[0,d],'-or',markersize=10);\n",
    "\n",
    "    # Now we go through all the data points one by one. \n",
    "    # Assume that the observed point is the center of Gaussian Distribution with standard deviation equal to the bandwidth\n",
    "    for xi in X1:\n",
    "        local_counts = [GaussianKernel((x-xi)/h) for x in xrng]\n",
    "        # (x-xi)/h is to transform the data to \"standard normal distribution\"!\n",
    "        \n",
    "        counts = counts + np.asarray(local_counts)/(h*len(X1))\n",
    "        \n",
    "        # this to normalize the counts. Look at the formula above\n",
    "        plt.plot(xrng,np.asarray(local_counts)/(h*len(X1)),'r');\n",
    "    \n",
    "    plt.plot(xrng,counts.T,linewidth=4);\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RhRNRRyJqR0TPE1G1N9/ghDhK/UE3GdDOIXh3RDvUM7CiKSwivLLqaLVZOoq9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\nOKSq1/BD/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178f4e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Kde_Gaussian(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# #ipywidgets\n",
    "# from ipywidgets import interact, HTML, FloatSlider\n",
    "# interact(Kde_Gaussian,h=(.1,5,.1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  \n",
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       "  \n",
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       "      window._bokeh_onload_callbacks = [];\n",
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       "    }\n",
       "  \n",
       "  \n",
       "    \n",
       "    if (typeof (window._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "      window._bokeh_timeout = Date.now() + 0;\n",
       "      window._bokeh_failed_load = false;\n",
       "    }\n",
       "  \n",
       "    var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "       \"<div style='background-color: #fdd'>\\n\"+\n",
       "       \"<p>\\n\"+\n",
       "       \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "       \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "       \"</p>\\n\"+\n",
       "       \"<ul>\\n\"+\n",
       "       \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "       \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "       \"</ul>\\n\"+\n",
       "       \"<code>\\n\"+\n",
       "       \"from bokeh.resources import INLINE\\n\"+\n",
       "       \"output_notebook(resources=INLINE)\\n\"+\n",
       "       \"</code>\\n\"+\n",
       "       \"</div>\"}};\n",
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       "        el.textContent = \"BokehJS \" + Bokeh.version + \" successfully loaded.\";\n",
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       "        setTimeout(display_loaded, 100)\n",
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       "  \n",
       "    function run_callbacks() {\n",
       "      try {\n",
       "        window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "      }\n",
       "      finally {\n",
       "        delete window._bokeh_onload_callbacks\n",
       "      }\n",
       "      console.info(\"Bokeh: all callbacks have finished\");\n",
       "    }\n",
       "  \n",
       "    function load_libs(js_urls, callback) {\n",
       "      window._bokeh_onload_callbacks.push(callback);\n",
       "      if (window._bokeh_is_loading > 0) {\n",
       "        console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "        return null;\n",
       "      }\n",
       "      if (js_urls == null || js_urls.length === 0) {\n",
       "        run_callbacks();\n",
       "        return null;\n",
       "      }\n",
       "      console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "      window._bokeh_is_loading = js_urls.length;\n",
       "      for (var i = 0; i < js_urls.length; i++) {\n",
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       "        s.src = url;\n",
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       "        s.onreadystatechange = s.onload = function() {\n",
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       "          if (window._bokeh_is_loading === 0) {\n",
       "            console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "            run_callbacks()\n",
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       "        };\n",
       "        s.onerror = function() {\n",
       "          console.warn(\"failed to load library \" + url);\n",
       "        };\n",
       "        console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "        document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "      }\n",
       "    };var element = document.getElementById(\"9f88506a-ed48-4deb-8df1-24c74f5ec87e\");\n",
       "    if (element == null) {\n",
       "      console.log(\"Bokeh: ERROR: autoload.js configured with elementid '9f88506a-ed48-4deb-8df1-24c74f5ec87e' but no matching script tag was found. \")\n",
       "      return false;\n",
       "    }\n",
       "  \n",
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       "    var inline_js = [\n",
       "      function(Bokeh) {\n",
       "        (function() {\n",
       "          var fn = function() {\n",
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this.repeat(count);\\n    if (count < 1) return '';\\n    var result = '', pattern = this.valueOf();\\n    while (count > 1) {\\n        if (count & 1) result += pattern;\\n        count >>= 1, pattern += pattern;\\n    }\\n    return result + pattern;\\n};\\nvar cb;\\ncb = function (source, window) {\\n    var counts, data, dlen, h, i, j, local_counts, observations, u, xrng;\\n    source = (source === undefined) ? source: source;\\n    window = (window === undefined) ? null: window;\\n    data = source.data;\\n    h = cb_obj.value;\\n    dlen = data[\\\"dlen\\\"];\\n    xrng = data[\\\"xrng\\\"];\\n    counts = data[\\\"counts\\\"];\\n    for (i = 0; i < counts.length; i += 1) {\\n        counts[i] = 0;\\n    }\\n    observations = data[\\\"observations\\\"];\\n    for (i = 0; i < dlen[0]; i += 1) {\\n        local_counts = data[\\\"local_counts\\\" + _pyfunc_str(i)];\\n        for (j = 0; j < xrng.length; j += 1) {\\n            u = (xrng[j] - observations[i]) / h;\\n            local_counts[j] = ((window.Math.exp((_pyfunc_mult((-1), window.Math.pow(u, 2))) / 2)) / (window.Math.sqrt(_pyfunc_mult(2, window.Math.PI)))) / _pyfunc_mult(h, dlen[0]);\\n            counts[j] = _pyfunc_add(counts[j], local_counts[j]);\\n        }\\n    }\\n    source.change.emit();\\n    return null;\\n};\\ncb(source, 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   "source": [
    "mn = np.min(X1)-3\n",
    "mx = np.max(X1)+3\n",
    "# range of the the data\n",
    "xrng =  np.linspace(mn,mx,num=500).T[:,np.newaxis]\n",
    "counts = np.zeros((1,500)).T\n",
    "# local_counts = np.zeros((1,500)).T\n",
    "\n",
    "#unfortunately, source in bokeh needs columns with the same size. So we fake it\n",
    "observations =  np.zeros((1,500)).T\n",
    "observations[:len(X1),0] = X1.T\n",
    "dlen = np.asarray([len(X1) for i in range(len(xrng))])[:,np.newaxis]\n",
    "\n",
    "df = pd.DataFrame(data=np.concatenate((xrng,counts,observations,dlen),axis=1),columns=['xrng','counts','observations','dlen'])\n",
    "\n",
    "for i in range(len(X1)):\n",
    "    df['local_counts'+str(i)] = np.zeros((1,500)).T\n",
    "h= 1\n",
    "for i in range(dlen[0]):\n",
    "    local_counts = df['local_counts'+str(i)].values[:]\n",
    "    for j in range(len(xrng)):\n",
    "        u = (xrng[j]-observations[i])/h    \n",
    "        local_counts[j] = np.exp(-1*np.power(u, 2)/2)/(np.sqrt(2*np.pi))/(h*dlen[0])\n",
    "        counts[j] = counts[j] + local_counts[j]\n",
    "\n",
    "    df['local_counts'+str(i)] = local_counts\n",
    "df['counts'] = counts\n",
    "\n",
    "\n",
    "    \n",
    "source = ColumnDataSource(data=df)\n",
    "\n",
    "p = figure(plot_width=600, plot_height=400,title=\"Kernel Density Estimation\")\n",
    "p.circle(X1, np.zeros(len(X1)), size=10, line_color=\"navy\", fill_color=\"red\", fill_alpha=0.99,legend=\"observations\")\n",
    "\n",
    "for i in range(len(X1)):\n",
    "    p.line('xrng', 'local_counts'+str(i),alpha=0.6, line_width=1 ,source=source, line_color=\"red\",legend=\"kernels\")\n",
    "\n",
    "p.line('xrng','counts',line_width=4,source=source, line_color=\"navy\",legend=\"KDE\");\n",
    "\n",
    "\n",
    "def callback1(source=source, window=None):\n",
    "    data = source.data\n",
    "    h = cb_obj.value\n",
    "    \n",
    "    dlen = data['dlen']\n",
    "    xrng = data['xrng']\n",
    "    counts = data['counts']\n",
    "    for i in range(len(counts)):\n",
    "        counts[i] = 0\n",
    "#     \n",
    "    observations =data['observations']\n",
    "    for i in range(dlen[0]):\n",
    "        local_counts = data['local_counts'+str(i)]\n",
    "#         window.console.log(local_counts)\n",
    "        for j in range(len(xrng)):\n",
    "            u = (xrng[j]-observations[i])/h\n",
    "            \n",
    "            \n",
    "            local_counts[j] = window.Math.exp(-1*window.Math.pow(u, 2)/2)/(window.Math.sqrt(2*window.Math.PI))/(h*dlen[0])\n",
    "            counts[j] = counts[j] + local_counts[j]\n",
    "    source.change.emit()\n",
    "    \n",
    "    \n",
    "slider1 = Slider(start=.0001, end=8, value=1, step=.05, title=\"bandwidth\",\n",
    "                callback=CustomJS.from_py_func(callback1))\n",
    "\n",
    "\n",
    "slider1.callback.update()\n",
    "\n",
    "layout = column(slider1, p)\n",
    "\n",
    "show(layout)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## So, now what is the optimum bandwidth in the above density learning problem? \n",
    "* minimizing some error functions in relation to the bandwidth\n",
    "* Rules of thumb methods\n",
    "* cross validation ---> testing the learned density with new data sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# A note on the issue of meta-parameters in Data Driven Modeling \n",
    "\n",
    "\n",
    "\n",
    "### Bandwidth value is usually called a \" Meta-Parameter\" or \"Hyper-Parameter\". It is important to know that in all of data driven modeling techniques, we will always have these types of parameters, where we need to find their best values in a \"Meta- optimization\" problem. \n",
    "### Usually, we take any of the following approaches separately, or together:\n",
    "* **Exhaustive search**\n",
    "* **Random grid search**\n",
    "* **Cross Validation**\n",
    "\n",
    "# <a></a>\n",
    "\n",
    "\n",
    "# <a></a>\n",
    "\n",
    "# <a></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Density Learning in Practice\n",
    "\n",
    "# However, usually there are optimum libraries for these kinds of tasks!\n",
    "* **Scipy**\n",
    "* **Scikit learn**\n",
    "* **PyQt-Fit**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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gYHiT4tVX6Uvt7qbg5McfL+zFilK+olA7gpRa91sU3b8B7rrm9uweeaSzsku1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\nsGBBcaO+1iTklKK4Og4p2b/fmVURBs8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117d84350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A two dimensional example\n",
    "fig = plt.figure()\n",
    "d0 = 1.6*np.random.randn(1000,2)\n",
    "d0[:,0]= d0[:,0] - 3\n",
    "plt.plot(d0[:,0],d0[:,1],'.b')\n",
    "\n",
    "d1 = .6*np.random.randn(1000,2)+7.6\n",
    "plt.plot(d1[:,0],d1[:,1],'.b')\n",
    "\n",
    "d2 = .8*np.random.randn(1000,2)\n",
    "d2[:,0]= d2[:,0] + 5\n",
    "d2[:,1]= d2[:,1] + 1\n",
    "plt.plot(d2[:,0],d2[:,1],'.b')\n",
    "\n",
    "d3 = .8*np.random.randn(1000,2)\n",
    "d3[:,0]= d3[:,0] - 5\n",
    "d3[:,1]= d3[:,1] + 4\n",
    "plt.plot(d3[:,0],d3[:,1],'.b')\n",
    "\n",
    "\n",
    "d4 = 1.8*np.random.randn(1000,2)\n",
    "d4[:,0]= d4[:,0] - 15\n",
    "d4[:,1]= d4[:,1] + 14\n",
    "plt.plot(d4[:,0],d4[:,1],'.b')\n",
    "\n",
    "\n",
    "d5 = 2.8*np.random.randn(1000,2)\n",
    "d5[:,0]= d5[:,0] + 25\n",
    "d5[:,1]= d5[:,1] + 14\n",
    "plt.plot(d5[:,0],d5[:,1],'.b')\n",
    "\n",
    "fig.set_size_inches(5,5)\n",
    "Data = np.concatenate((d0,d1,d2,d3,d4,d5))\n",
    "\n",
    "\n",
    "\n",
    "# from scipy import stats\n",
    "# def measure(n):\n",
    "#     \"Measurement model, return two coupled measurements.\"\n",
    "#     m1 = np.random.normal(size=n)\n",
    "#     m2 = np.random.normal(scale=0.5, size=n)\n",
    "#     return m1+m2, m1-m2\n",
    "\n",
    "# m1, m2 = measure(2000)\n",
    "m1,m2 = Data[:,0],Data[:,1]\n",
    "\n",
    "xmin = Data[:,0].min()\n",
    "xmax = Data[:,0].max()\n",
    "ymin = Data[:,1].min()\n",
    "ymax = Data[:,1].max()\n",
    "Xg, Yg = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AVmBNZabsL6JmFDu5+zRzbDJgbnFEP5wh+g9YpxKjtEbpImGiZhQTyYj0nfcq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\nkLOIdr1S3bkAYjUD0BvIEf2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ALVJSxWpCBaNIodaPHllUbHgYEtVvXVlt3Jo5uUy1haak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\nsVgscYQN+haLxRJH/B9pmuyeoM+tzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117a13410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "val_grids = Xg\n",
    "# values = np.vstack([m1, m2])\n",
    "# values = Data.T\n",
    "kernel = stats.gaussian_kde(Data[:,0])\n",
    "Z = kernel(val_grids.ravel())\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "a = ax.hist(Data[:,0],bins=300,normed=True);\n",
    "\n",
    "\n",
    "ax.plot(val_grids.ravel(),Z,linewidth=5);\n",
    "ax.plot(a[1][:-1],a[0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SB2Lf2zNK/Ey65rwTQXZs6eSKa8ux2gyMyTSNyJBt2aVlWKRjS60dDp9w8cwL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\ntkYUSzOKq5fEaBUirzcNKZ0iTpmoedWQktCI5M9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seH6gO8KOJ3vZ+0ofkgT3/FE9t71v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\njCeONHHg9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myIrjA81UQ8EaTZm9vwuPUQjphbH/QWQFXhtrsX6duV5OlHm3nssSYmJ328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\na4oSIoVCoVCsKf8fToDUpqVCjiIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117668990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]\n",
    "positions = np.vstack([X.ravel(), Y.ravel()])\n",
    "# values = np.vstack([m1, m2])\n",
    "values = Data.T\n",
    "kernel = stats.gaussian_kde(values)\n",
    "Z = np.reshape(kernel(positions).T, X.shape)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,)\n",
    "plt.contour(np.rot90(Z))\n",
    "# ax.plot(m1, m2, 'k.', markersize=2)\n",
    "# ax.set_xlim([xmin, xmax])\n",
    "# ax.set_ylim([ymin, ymax])\n",
    "fig.set_size_inches(7,7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:red;font-size: 3em;line-height: 100%;\"> The importance of the learned densities </span>\n",
    "\n",
    "* **Resampling**: to generate data without observations\n",
    "* **Clustering and pattern recognition** and its relation to **\"Manifold Learning\"**\n",
    "    * Here we know the likelihood of the high dimensional patterns in comparison to each other\n",
    "    * Here, in a way we are learning the **joint probability distributions**\n",
    "    * In Machine Learning terms, this is an **unsupervised learning** problem\n",
    "* **Prediction**: Using it for predictions/ transfer function by conditioning the outcomes to a set of dimensions\n",
    "    * In this case, we are interested to know the likelihood of certain variables (**dependent variables**) conditioned on certain variables (** independent variables\")\n",
    "    * In this sense, we can derive \"supervised learning\" from \"unsupervised learning\"\n",
    "    \n",
    "\n",
    "## A similar Approach\n",
    "* **Gaussian Mixture Model**: To learn the distribution of the data as a weighted sum of several globally defined Gaussian Distributions:\n",
    "##  $$g(X) = \\sum_{i = 1}^k p_i. g(X,\\theta_i)$$\n",
    "### $ g(X,\\theta_i)$ is a parametric known distribution (e.g. Gaussian) and $p_i$ is the share of each  of them. \n",
    "\n",
    "### Further readings:\n",
    "* ** on Kernel Methods: http://www.stat.rice.edu/~scottdw/ss.nh.pdf**\n",
    "* **On mixture Models: https://en.wikipedia.org/wiki/Mixture_model**\n",
    "\n",
    "\n",
    "\n",
    "# <a></a>\n",
    "## An alternative approach from ML (Hopefully the next session):\n",
    "## Manifold Learning\n",
    "* **Self Organizing Maps**\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "\n",
    "# Prediction, using the learned densities\n",
    "\n",
    "### An example of prediction with the learned density in the previous example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PF0CnE9sxGsMZPbGxWpRKcbWHTqvEYNRgNGhkTFys2I7fH0CrUQbbCTFJiXpiYzQolSKj\n0SoxGjTSAxIgIXgulVKB2+9Dq1FijNEQExO6NxMT9cTEalEqFfh8PjQaJQaDWvLxiO3oiAmey+sV\nBwxGg1qmucQEPTExWpQqBR6vH3VQB7Fh54rq+2uib4ceQSFqLsaowWDQYDCoGB4Rze3x8Tp8/oDE\nGGPE6zEY1CCInysuXodSpUARvH8NBjXGYDsiI4j69volxhg819dJ39H4akK5f//+v/U1fGE8/sQP\n9/cPTae720x7h5g7dbl89PaN8U5Y7v30mSG6e6zSig2320dvr1WWn289O0RPr1VaseF2++jpsfL7\nd0L5+XPnh+nptXChTWQ8Hh/d3RZpZQHAhbYR+vqsnL8grurweP1095hl/oCLF0fp7bdy7pyYp/V6\n/XR2mXkzjLnUbqKvb4zWs2FMp0nmRejoNNPfb5VyuT5fgI5OM2+EeQE6uyz0949x6oy4OsTnD3Cp\nfVTGdPdY6R+0cfKU6Ofw+wNcvDgi8xT09loZGLRx4kSIudA2wu/eOi9N1ff1j9E/MMbxE/0Sc+78\nMG+9fQF/EBoYsDEwaJNWmQQC4nf/9h/apOn8wUE7g4M2jhwNMWfODPLOHy9JU/VDQ3YGBmwcPtIr\nMUV/eIl2fyw7iu/khbRG3k0o44rf/zv/qq2VmBMn+vnw4w5pin1k1MHgkI0Dh3qkz3r0eB+ffdaN\nPegzMJmcDAza+OxAiDl8tJfDR3qlZcJms4vBQRuffhbyqRw63MOxE/1YglPPFouLgcExmU/l4OEe\nTp4alFZjWK1uBgZtfPxJiDlwsJuzZ4cZGRG9CGNjbgYGx/jo485QO4e6OXd+WFqNYbN56B8c48OP\nQsyBQ920XRyV/Ap2u4f+/jE++DDkiTl0uIdL7aP09Y+JjMPLwIBN5ok5fKSX9vZRevtExuHw0j9g\n4733Q8yx4/10dJrp7hF9D06nl76BMZlv5viJfrq6zXR2iSuyXC4ffX1y5uSpgai+vwb6/v0f2/D7\nQRAEBofsDAyJ+hYEgUAATreK+vb5AgiCwNCwnYFBUd+CIBAATp0e5P3323F7/AiCwMiIg4FBG4cO\nh5jjJwf46ONOXC6fyIw6GBy0ceDg10fffd2/7d2/f/9/EI0vFZdNugrEfwLhoVJOHO2qIhnVxI+o\njHjfZEzka8rJ2lFFXo9yIvPnXE/kuZQKIlLJqFTKCEaYhJnYTuQ/gsjvRzzXn2ZUKmFCbntiOwJC\nxEebeD0CSsWf/j5UKiWKL/h9AkolqkAoH68O+PALk5wr8hon/F6KSV/7ImbCsUIx8Z6KaEehEFCq\n5MyE61MKk7Qj/90FYZLPNdm5JvyGyi9kIq9vvPaH/HomYf6ce3zC7z5Ru1F9hzOXp74VEb+zWjXx\nOPL3UU/yu3/R96pSfrGevi76jsaXi8vm27z5prm0bK+Rpq9TUgzs2lnLFetmSMymb1Vw9/aF0pRy\nUpKelh01XLVxpsRcf205LTtqpHxzYqKenTtquPaaMon5xtWz2LmjRpqeTYjX0bKjhhuuC+WkN24o\npWVHrZRvjovTcvf2hbL87vq1JezeWSsteY2L1bJzew23bq6UmDWrprPr7lppyWtMjIaWHTVsuXW+\nxCxfWsjunbVSTtpoULNzew3bbl8gdYRLFhewe2ct6elivtlgUNOyo4bt26olprEhjz0ttUzLEJeh\n6vUis3P7QtnS2T0tdWRmioxOp6JlRy27W2olpqY6iz276sjJFvPWWq2SXXfXsndXndTpLqjKZM/O\nOiknrdUq2d1Sx749IWZeZQZ7dtVSkC/mpNVqJbvuruGePfUSM6cinb276ygKLkNVqxXM3H8Xy8eO\nc3vXqywfPsC/nPt3NDu2UVIsLh9VqRTs2VXHvl11Umc0c+ZU9rbUUTpD9KWolCKzt6VO6kBnlExh\n7646ZgWXjyqVCvbtrmdPS63kAymensLelnoqytOCjMC+PfXs3lmHWi12WIWFSexpqWNu2LLufbvr\n2X13rbTkNT8vkb276mRLtve01NGyo0byk+TmJLCnpZbqBaHl2Htaamm5uwZtMJWQnRXPnpZaamtC\ny7F33V1Ly46FUoovc1oce1pqaajPlZi771rIzu016INLXjPSY9nTUsfixnyJueuOBdy9vUaalk9P\ni2FPSx1Ll4R8KXdsqeLu7QuldFnqVCO7d9aycnnIl7Lllnns3FEjpcumTjGy6+5a1qwulpiovv8e\n9S16TrRa1Z+v7zCmcm4Gu3fWUpAnMmq1gpYdtTJmzux09uyqlel7907xXOMDgvJZqextqaN4epi+\nW0Ttjg8IZpZ+PfUdjS8fl8032do6RMn0FMmxbjI56Oy0cL5tRGLOnh2ivCxNcqybzU46u8zSlDNA\n67lhOjvNWINLGC1mJ52dJtnSv3PnR+jssmCxjE89uujoNNN6LsRcaBuhq9uE2Tw+9eiis8ssFRwT\nmVE6O82YTCJjHXPR0WniTATT1WVmNMjYbG7a2020hi0zvNRuorPLzOhoMEVh99DeYeJM66A0xXyp\nY5SubgsjIyJjt3u41G7i9JkQ094uMsMjYhrD4QgyYe10dJjo6jIzHEyHOJ1e2i6Ocup0GNNpprvb\nwtCQyLhcPtoujnL+woiUiurqMtPdbWZwyCYxFy6M0NVtDjHdFrq6LQwMiukQj8fHhbYRBgdtEtPT\nY6Gr08LAwDjjp+94GzN9fkpsncywd2JV6tEcb6XPIxpHvV4/584P43b7pLRXX6+V7m4zfX1iWsXr\n83P23BAKQZBWqPT1WenqttDbJ6ZVfD4/reeG0OtU0gqVvn4rXd1menrHmQCtZ4dISNDh8YizSwP9\nY3T3WKSCeX5/gDOtQ6SlxkjF1QYGbXT1WOgKLl31+8V2nE6vlGIbHLLR1W2hs0tMzwQCcKZ1CH8A\nXMHiakNDNnp6LHR2miXm9JlB1GqFtIpleMROZ7eFSx2jYe0MEhurwRFcxTI8Yqez00x7h/xcKSlG\naUXIyIiDzi4zly6ZpHvzdOsgGRlx2IIrW0ZNDjo7zVwMY86cHSIvN1HGdHSZuXgxtCQ3qu+/Q32P\n2EEQV/y0XRrlQtuImK4SoKvHQnePmaERW5DxBb8zi6Tdbknf4vV4PH5R30MhfXf3WujqstAfpu/z\nF0awWFzSCrSeXiud3Wb6B4LaDerb5fZJ/r3ePlHf/QNjIIDXLzKCIIh9gAD9A2N09VjoG7CCAD6/\nn7Pnh9Dp1Hi8QWZw7O9K39H48nHZeHIc7jIGBm2Sh8Dvh5FRu6zOR1e3haFhGz29IhMIiJ33wTAf\nRk+vlaFhu+QhGGfCc7m9fVaGh+10dVskZmhInu/t7x9jeETsiMeZyJzwwKCN4REHHZ2hGgyDQ3ZZ\n3ZGhITsjo3ba282y9316IJTLHR62MzrqlD04+vqtfBrWzsiIg5FRh+zB0dc3xqefhdoxmZyMjDpp\nawsxPb0WWf7ZbHZhMjllD47uHgufhLVjsboYNTk4dz6M6TbLGKvVjcns5GzYg6Oz08SnB7qlznRs\nzI3Z5JT8CiB25gcO9UidoM3mwWR2yh4c5Qde46wihUcKNvF68nzeS5jFdZ8+yf9NaJSYC20jHDse\nqg/icHgxm52cOhNq5/yFEU6dHpA6HafTi8nslKreApw9N8TZs8PSgMHl8mEyuyTfA4hehAttI9Jg\nwOX2YTI7ZbVsWluHuNRukpanut0+TCaHjDnTOkRHp0mqtOrx+DGZnRw/3i9jurosmIO5f4/Xz6jJ\nybEw5uy5YXp6rVKlVa/Xj8nk5NixEHP+wgg9vVbJH+DzBTCZHJI/CqDt4ih9fVbJ/+PzBRg1OTly\nNKS5S5dM9A+MSdWWfb4Ao6MOyUMF0N5hYmDQJlVb9vsDjJocMu12dpmj+v470rfJLDKCICAIAl3d\nluC5xOOQvkNMR5eZz8L1bXNjMjlkfUB7xygHJ+jbIesDLraPcvhIrzTIsTs8mM1OWX2ZCxdHOH5C\nrm+TxcnpM0PS9ZxvG+bU6UHcbtG343QG+4DTgxJz9twQZ88N43R6EQQBl8uHOVK7fyN9Rz05X01c\nNukqlVJBUpJe9lpSkkGWt1YqBZISDTImeVImop1Egyy3rVAIUuXV8HbC86mCwAQmKUkvy9WKjPxc\nCQm6CfnlyHYSE3XS9KnEJE/87JqI2g0pEUxiol5aIfF5TEKCXlohETrXxOsJX0kw2TXHx+tkK3xE\nZuK5YmMimMhzJeil5a2fxwRi48hwhzrpDNcIbq2cSYjXkRCvk70W2U58vHYiM8nnSkiQM5HfYVzc\nF7cTG6ed0E4kI6660f9pxqghMVHeTlIEo9erJjmXvF2dTiVbLQOQFPH9aLXKCUxkOxrNJEzE96NW\nKyaeK+Kao/r++9J35O+TMKm+I9qJ/2J9J8RPou9IzcVN1NykTKTmIn73ydqJvMcm03fkb/q31nc0\nvlxcFoMcQYDdLbXs21Uv1UHIy01kb0sdW26ZJ5lMd+6oYe+uOqkOQk52PHta6ti2dYHE7LhzIXt3\n15MVzElnZYnMXXcskIxh226vYk9LLdlZouckc1oce3bVcfddC1EqRRPa7bfNZ3dLLbk5Yt46Iz2W\nfbvqadlZg0olGgJvu3kee1rqyAvmpNPSYrhnj5gDHmc23ziXPS11FBaIvpSpU43cs2cR9+xZhFot\nMjdcX8HunXUUBWuhTJli5J499dx3T4i57tpy9rTUS6XPU5IN3Lt3EQ/c14BGo0QQ4JqrZrFnVyhv\nnZyk57599Tz8QJPEbFxfyp6WUN46MVHP/fsa2P9gE1qtyKxbU8LeXXVSyfKEBB0P3NvA/m8vRqdV\nIQhi9dx9u+uleinx8VoeuLeBRx9uRqcTmRXLiti7u455czMQBNHT8MC9DTzyUDN6vcgsWVzA3l11\nVM3PRBDEei7V//s+Fvi6+Mdz/8EdXa/wr+f+jcTvPkRNdRaCIHYUDz3QxMMPNmE0qKVKuXt31VNX\nm4MgiL6Hhx9s4qEHG4kxahAEsQT/3l11NC7KRRBE38P+by/m2/c3EhMjMguqMtnTUkdzk1i6X69X\n8chDzXz7/kZiY7UIglg/Zd/uepYuKRAZnYr9327iwfsaiYsTmco5GezbXc/K5UUIgjjoeOShZu6/\np0HqUCvK09i7q461q4sRBHHQ8fBDTdx/T4O0BLm8LJV9u+rYsG6GyGiU7P/2Yu7bt0jq0GeWTmXP\nrrrgXj7iwOShB5q4d2+99BCaUZLC3pY6rr2mDIVCQK1W8MA9jdy7d5HkOSmensKeljqu/2a5xNy7\nt5579tRLnpOiwiR2t9Rx4w0VKBQCKpWCe/bUs293vbRFQkF+Ent21nLLTXMlJqrvvzN9t9RK9ZAS\nEnTcf08DDz/YFNL3iuns3VXHnDB933/PIh55aHGYvgvZu6uOynB937OI/d9eHKbvfPa21FE1f5qo\n7xgN376/kYcfbMKgV0sVrPfuqpXr+/5GHnogpO/6uhxR3zUhfT/0QKOo3XB9t9TRUB+m7weaePDe\nP0/fceP6nv//n76j8eXj8khXPf7D/X4qUKkVvBlcemkyOcnNTuCFn53AbHERCAQYGLCh06l4PVgu\n3mx2kZ2VwE9/dgKT2UkgEKCv30qMUSOVr7dYXGROi+PnvzzJqMlJICAuoYyN00nl0S1WFxnpcfzi\npVOMjDpEpm+MpAQDLwdLclvH3KSlxfCrl08zNGwnEICePivJyQZ+9evTgJiemTolhld+08rgoC3Y\njpXUqTH84iVxozmbzUNykoHfvNZK/4DI9PZZSU+L5ee/OAmI+fikRD2vvXGevr4xkem1kpERy0+D\nm9HZHR7i47T87q0L9ASn7nt7rWRNi+PFn58gEBCneONitbz9hzZp6r63z0p2djwv/PQ4gYCYwjEa\n1bzz7iVpWr6vz0pOdiLP//SYxOh1Kj74qENa3tvXP0ZubgLPPX8MfyCAy+VDo1by0add0vLevr4x\nCvKSeOb5o/j9AVxuHyqVMriMckRqpyA/iWeeO4LPF8Dt9pHbdYqcI+/wcVwxAQSsSgPGi2f54VCu\nyHh8+P3isuTTwSW3/f1jFBUm8dSzR/B6A3g8fnzeAK1nhzkRTD0NDI5RVJgcZPx4PH7cbtFvNJ4O\nGhgYY3rA7sYzAAAgAElEQVRRCk8+cxiPx4/X68fp8NLeYZJSPf0DNoqKknj6mSO4g4zD7qG7xypt\nyjg4aKOoSDyX2+0TqwtbXcElrmJ6YXDIxvTg9bhcPny+gFjufsQhLV8dGrZTVJjM088exen0immn\nUQcWq0taVj48bKeoMImnnzuKwyEywyMOHE4P7weXjA8P2ykoTOaZZ49gt3vw+wMMDdtxu328G1zq\nPTJip6BA/L1sthDj8wekZdwjIw4K8pN47oVjjI2J1X8HBm0ICkHaRmF01EFuXgLPv3gcqzXIDNii\n+v4b6vuP77XT2WUhgOhdyclJ4IUwfet0Kj6U6dtKXm4iz75wjMC4vjVKPv4kpO/evjEK8hJ59vlj\nYfpWcOBQj5QuE/WdzDPPH5X0LQhw9Fg/reeGJKawQLx/x/UdCAREfQdTWP39NvEef/YIXl9Q30E/\nzXhqeWBgjOmFKTz1XJi+PX4p9RXSdzJPPXdEasPp9NDRYebI8T4CwMBgUHN/ZX1H01VfTVweg5wn\nfrhfoZor1hUYCO1VYnd4ZHna0VEHNptbyuuLjFvGmExOkekLY+xyxmxxYbd7pN2YQTQMhjMWqwu7\nwyN1MOPM6TDPx9iYG4fDKxnUxNdc0oMXQmXOxzshgDGrnLHbPTidHqnOCIidt4xxeHA4PZKHAMSH\nQDjjcHpxOn2SuRRg1OzgdJgHxeny4nJ65cyo3KficvlwOr1Shwfiwy2ccbt9uJw+LraH/AFDw3bZ\n9bg9Ppwur2xPmMHBMc6cHZLy+h6PX2TCvAjzzrzDOWUK/ydrPQfiijkUW8iNJ1/kv6Y0S0xfv5UL\nbSOSqdjrE9u5EO5X6LHQ3mGSzII+XwCXy8uFMLNrV7eZ7h6LVK7e7xeZcE9DZ6eZvv4xycQrMj7O\nhTNdogl73HzrDwRwOb0yX1Nnl5mREYdkrA0EDYjhnobubgsjow4pry8+hDwypqfXisnkxGRyhjHy\ndvr6xzCZnJJvB8Dp8MrMtwMDNiwWJ8MjIcbh8HA2zD8xOGjDanVJJvTxdsI9VEPDdsbG3JJvR2zH\nKzPfjow4ovr+G+r7dKvIjPtSXJH6Hp1E3y45MzRkl9oBcSGB0+mVeY0GB220Rurb6ZExAwM2zp4f\nknw7Xq9fWtwwHn19Y7RdHJX07fOJzIWLEfruNMv17fTI+oCuLjPdvdYIffskPxJAR6eFvgFR34Ig\nSH1ApHa/an1HBzlfTVwW6SoQpyjDS2QDFOYnyfLWBoNamjoej4K8JGnJHojThvn5STImPy9RltvW\naVXS7rrhzHg1TRCnFiOZ3NwkqTQ7iF6E8WlqiclJlO0wq1JNZHJyE2VVXFVKBYUFyTImNydBlttW\nKoVJmfA8sUIhyEqIA+RmJ8py0CIjbycnO15Wdl0QkKbWQ0yClI4Yj8mYjPQ42WvTJ5wrgcxp8XIm\noh0yMphl70AREDu4srGL2OJTZEh2VryUjvi8c2VlJUxgIq85a7J2iuTnysyKm9hOxLmmZUzCRJwr\nPT2W7Gw5U1iYLPOcTJ1ilJWTF5kUGZOSbJiESZb5UpIS9YzvRP15TEK8jtwcuZ6KCpJl3pX4OK2U\n0hmPgoIkmXclNlY7QbsF+Uky70pU339jfafI9R15rpzsBNm2CjDxHhf1HSt7LVK72dkJZE6T9wGR\n7Uymua+KKYzQblZWPNmZX9BO5t9W39H4cnFZzOR87/v/uv9ffnA/11xdxvsftONweCiensLjjy4l\nxqjl2Ik+dFoVu3fWct03ZvP+B+3YHR6KCpN57JGlJCboOHqsD41WScuOGq6/tpwPPurAZvdQkJ/I\nd7+zjORkA0eO9qLRKNl+ZzWbvjWHDz/uYMzmJj83kSceW0rq1FgOHelBo1aybesCNm+aw0efdGId\nc5Obk8ATjy5l2rQ4Dh7uRa1WsPW2Km6+qZJPPunEYnWRnRXPE48vJSc7gYMHe1CpFGy5ZT633TyP\nTz/twmxxkZkZx/e+s5T8vCQ+O9iNUqlg802VbLltHp8d6MZsdjItI47vPr6U6UXJfPpZF0qlgptu\nmMPWLVUcPNzNqMlJRnos331sKTNKpvDJZ50olQquv242d96+gMNHehkZdZCWFsP3Hl/GrNJUPv6k\nE4VS4Nqry9i+rZqjx/oYHrGTOjWG7z62lIryND76uBOFQuCaK2dx910LOX6in+EhO1OnGvnuY8uY\nW5HBhx91ohAENl5Rys7tNZw6PcjgkI0pKUa++51lzJs3jQ8/7EAQBNavm8GunbWcbh1kYHCMlGQD\nj39nKdULMvngQzGNsmZVMXta6jh3foi+/jGSk/Rs/debyH76/7C28x1qTSfZ1Pc2if/2L7TFZtHb\nZyUpUc93v7OMutpc3vvgEoFAgGVLCrhnzyLaO0x091hITNDxxHeW0rAol3ffbycQCLC4MZ/79jVI\nSz8T4nU8/p2lNDXk8e57l/AHAjTU53L/vQ309Vnp6DQRH6/liUeX0txUwLvvX8Lv91NXm8OD9zUy\nOGTjUvsocXFaHn9kCUubC3n3/Uv4vH4WVmfx0AOLGTE5uHRxlJhYLY/tX8LypYX8MchUzc/k4Qeb\nsFhdtLWNEhOj4dGHm1m1Yjp/fO8SXo+f+ZXT2P/txdjsHs5fGMFo1LD/oSZWryrh3fcu4fb4mFOR\nzqMPNeNyi/8ajQYNDz3YxLrVM3j3vYu43T5ml6Xx6MPN0hS/waDmwfsauWJ9Ke++fwmXy0fZrFS+\ns38JAuIydb1ezf33LOLKDTN57/1LOF1eZs6YymOPLkGtUnLq1AB6nZp799Zz9ZUzee/9dpxOLzNK\npvD4I0vQ6VScONmPTqdm3+66qL7/mvr+VNTutdcE9X28j5FhO6mpQX3PTuejT0Tm6o2zuPuualHf\nw3amTjHyxKNLqaxI58OPO1AIAldsKGXnXQs5dWZA1PcUI088spT5ldP48KMOBIXA+jUzaNlRy5mz\nQ5K+n3h0CQuqsoL6Flizajp7dtZx/sKwpO8nHl1KTXU2733YAQRE796uOi5eGg3p+9Gl1NXm8N4H\n7ZK+9+2up6MzpO/HH11CQ12uxCxuzOO+vYvo7hHLQCTE63jskSU0Lsrjvffb8fsDLKrL5f57Gujr\nt9LRaSY+qF1J374AdTXZPHjvuL5NxMdpeSxc376vRt/nzrwUncn5CuKyGOQ89ti/7O8fms6Yzc07\nf7yI1+tncNCGRqPkyacPMzbmxu32cfL0AE6Hl7f/0IbX62doyI5Go+DJp49gsbpE5uQALrePt96+\ngNfrZ3jYgVIp8NSzR7FYgsypAXw+P2+8eV5kRhwIgsCzzx/FZHbi9vg4dWqAQABee+McXq+fkVEH\nAvDsC8cYHXXg8fg5eXoQQYDfvHYWb3Cpb8Af4PkXjzESZE6dHkCpVPDKb1qlpb5er48Xf36C4WE7\nHo+f06cHUKuVvPzKGbxeP2azE7fbz89+fpLBIZE5dWYArVbFSy+fFhmLC6fLyy9eOsXAoA2Px8+Z\nM4MY9Gp+8dJJvF4/FosLm83Dr359mr7+MZE5O4jRoOZnvxAZq1Vkfv1qKz29VjweP61nhzAaNfz0\nZyeCjBuLxcVrb5yjq9uCxyvWoImN1fH8i8fEfPSYm9FRB2++dZ6OTrPInB0mLk7Lcy8ck3a8Hhmx\n8/t32rjUbpLqYcTH6XjmuaN4veKO1xkfvUXS2WP8+7TVXNSnc0GfTuZ7v+XxgQJxd227h94+Kx9+\n3MH582LK6kLbKImJOp58WvTS2O0eenosfHqgm9azQ3i9ftoujpCYEMY4PHR1mjl8tJfTZwbxev1c\nahfb+clTh3G7/TgcXtrbTZw42c+JkwNBxkRCoo6fPHkYt9uHwyHWImltHeTY8X68Xj8dHWbi47X8\n+MlDuNzitP75CyNcaBvh8JFeaYuAhHgdP/rJISlFePb8EO3tZg4e6sHr9dPVbSE+TmScTi9Op5fW\ns0N0Bz+b1+unp8dKbKyWH/3koMi4vJw5M0Rfv5WPP+3C6/XT22clJkbDj35yCIdDrOVx+swgQ0N2\nPvyoE6/XT1/fGAajmh8/dRi73YPL5ePU6UFGTQ7e/6ADr9dP/8AYBr2aHz95CJvdg8vt49TpAcxm\nF+++fwmv1y95a3781GFsNo+kuai+/0r6fuUM/QM2vF4/ra2idn/2y5N4fQGsY25sNg+v/OYMvb1i\nH9B6bgijQcNPfxHU95gbizWo756QvuPitLzw8xN4feIO8qNmB2/9/gKd3RaxDtX5YeLjNDz/s+N4\nfQFsdg/Dow7eefcilzrNeH1+zreNEB+n49kXj4mMw8PAkJ33P2yn7dIoXl+AtksjJMTreOaFo3h9\nAewOD73Be/d820iQGSUxQS/6bXwB7E4vPb1WDhzs4ez5Yby+ABfbR0lI0Il+G69fSiMeOSLXd0KC\nniefDun7UoeJEycHOHkqTN8JOn7y9BE8Hh8Op5hyP9M6xPET/XiD23LEx+v48U/++/qOpqu+mrgs\nBjmPP/HD/fqYKnw+v1RYCgAhwMWLoVyu3e7BHwjQH5az9xOQ5XsdTq9kPhyPAMg8H06nl0AgIO3Z\nA2KONdw7Ml5bpScsr+/zy5nxXHB4Xt/nk1/PuNGuOyxn7/X5ZYzH40cRrFURes0ny4d7veJmlF1h\neX23ezJGoLMrVLMjMq/u8wVQKAVZ7Y/xomIyRiFn7A637Jr9/mA7HSFmzOaSFZLzBwIoFYK0XxGI\nBdXaO8xSzj4QYAIzv/NTOhQJvJjWyHnDNC7q07jpwsv8OG2pxJjMTnp7rVIxwEAAFAoF7RE+g8EB\nG25PaIsIhVIh+6zDI3ZGRhw4w4pzKRQK2ecYGrJjNjtxOEKMUqmQe42GbIwFHyihcwnydobt2O0e\nrMFaG+NM+Pc6MuLA4fBInhwAhYCMGTU5pZo/oWuWt2M2O3G5vIyaQoxSIW9nfFAwEubJUSgEmVas\nY25xwDEc8uQIEdczNubG5/MzGObbIYKx2T1Rff+V9B2uHZ8vgKAQpOKRIPp9vlDfdjcX2yP0rZIz\nNptb1k4gEEChVMgYq9VJe6dc35H9jcXipLMrVFRwsj7AZHLS0zcmFQMU9S1nRkcdDAzZpCJ+MM6E\n68nO8LBDVnxPqRAmeI0slkh9y5nBIRtjNrm+lRH3+F+q7+gg56uJy8aTkzrVyNw5GbLXquZlEheW\nt05JMVAZyVROk9U4SE7SM69SzsybkyGr45GYqGd+5TQ5M3caKWE1H+LjtJMwGTLvSlyclgXzM2XM\n3DnpMu9KTIyGqghmTkWGVL4dxOWQkzHhuW29XsWCqiwZUzE7XZYn1ulULFwwkQn3Zmi1SqoXZE9g\nwn0FGo1yYjvl6VLZdRD9CjXV2ROY8eWtIPoVahbKmdllacyaOTXEKBXULMyRMYrSGdRbT2HwiQ/o\nZcMHsUzLl+W2Z5elUlaWGnqPQqB2YZaMKZ8lZwQBahZmy3wpZbPSJjC1C7NlvpRZs1Kl5bbjUVOd\nJfOlzCz9HCbMlzKjZAqzyyOYBdmymipFhcnMLk+PaCdb5l3Jz0ukYracWbggS+ZLyc1JkJb/jkdV\nVZaspkpWZvwEZsH8TFlNlWkZcRPbmZ8p86WkpcVMqt3wXdGj+v4r6jvMM6XVKFkY0c6c2enS1iog\n6rt6Mn0XReh7QaR20yktidB3BFNels6s0pC+lUoFNRHnKi9Lo3xWahgjsLA6QrsRjEIhUFOdLWPK\nZqVSPjNCu9VZEfpOlbUz3geE67ts1lTKZkVqN1u2x9TM0qmURzALq7O/En1H48vFZTHIUSoF7txa\nzU2b5lKQn4ROp2Jm6RS+9c3Z3LK5EqNRTWyMhm23V7HpWxUUFojMjJIUvnXdHLbcOo8Yo4aYGA1b\nt1Sx6foKphclo9OpmF6UwqYb5rD1tvnExIjM7bfM41vXV1BSnIJOp6KoMJlN36pg65YgY9Rw283z\nuOH62cwomYJOp6IgP4lNN8xh29YFxMZoMBrV3HzTXK7/5mxmlk4VDZF5idx041zuvGMBsbFajAY1\nmzfN5VvfnE3ZrFR0OhW5OQncclMl27dVExerxWBQs+lbFVz3zXJml6eh06nIyY7nlpvmsuPOauLi\nROaG6yq47hvlzKlIR6dTkZ0Vzy2bK7n7LnGvH4NBzXXfKOfaa8qYNzcDnU5F5rQ4ttwyj5btNSTE\n6zDo1Xzj6jKuvbqMBfMz0elUTMuIZcst87j7LnE/IINezVUbZ3LtNWUsrBYfihnpsWy5dT47ty8k\nMchsXF/KNVfNoq42G51ORXpaDFtvm8/d22tITNSh16vZsK6Ea64qY1F9DjqditTUGLZuqeLuuxaS\nlKRHr1exZnUx11w1i6bGPHQ6FVOnGqn73l1M1Qd47cgD/OrofnZ0/ZqMR/fR3FSAXqdiyhQj2+5Y\nwI5t1aSkGNDrVKxYVsTVV5axbGkhep2KlBQDd95RzV3bqpkSZJY2F3LNlbNYuWI6er2K5GQD2++s\n5s6tC5g6xYhOp6KpMZ+rr5zF6pXFIpOkZ/udC9i2tYrU1Bh0OhWNi/K45qoy1q4RmaQkPTu3L+SO\nLVWkBZn6uhy+cXU5V6wvxaBXk5ioY+f2hdx+6zzS00SmZmEW11w9i6s2zsSgV5OQoGNncN+jjPRY\ndDoV1QsyuebqMq65apbE3L19IbduriRzWhw6nYr5ldO49ppyvnHNLAwGNfHxISYrU2Tmzsngum+U\nc/03Z4tMnJYdd1Vz802VZGfFo9OpmDM7neuunc0N14lMXKyW7duqufnGueRkJ6DTqSgvS+X662Zz\n4w1zMIYxmzfNJS83EZ1ORdmsqXzrutncfONcjAZRu1F9f4X6njdN1HemqO+d2xeSEC9q7htXz+Ib\nV5exYL7IZGTEctstldy9fSEJCSJz1RUzufZqUd96vchsuWUed2+vJjFRj8Eg6vvqjTOpXRjUd2oM\nt99SyY5t1UF9q1i3uoSrN85kUV2Yvm+dz45t1UF9q1mzajpXb5xFU8O4vmPYdlsVd22tJjnZgF6v\nZsWy6Vx9xSxR33o1U6YYuWNLFXdtXUBKihG9Xs3ypUVcdcVMljYXoterSUkxcuftVdy5tUrS95Km\nAq66YhYrlol9QHKygbtuX8C226uYOtWIXh/U98YwfSfr2b6tmm23zyd1akjfV185i3Xj+k7Uc/ed\nC7ljy/yQvmtz+MbVZWzcUIrBoCYpUf8X6zsaX01cFumqxx77l/1t7TkMDNj4+JPOYM7ejs3m4cmn\nD+N0+nC7fXx2sJvBITsfftwp5extNjdPPnMYh8MrMge6GRkNeQiGR+xYrU6eevoIdofoDzhwsAez\nySmaO71+RkYcWMxOngrWEHF7fBw41IPZ4uSdd0VmdNSByeTk6WePYLN58Hj8HDzUg3XMze/faZNy\n9iPDDp597ihjY248Hj+HDvdgs7l56/ciYzI7GRyy89wLx7BaXXg8fo4c6cNu9/DmWxeCOXux3sLz\nLx7DYgkyx3pxOr288bvzUs6+v3+MF352HLNZZI4e78Pt8vHboM/AYnXR02PlxZ+dYNTkxOP1c+x4\nHx63j1eDPgOr1U1Xt5mfv3SSkREHHq+fEyf78Xj9vPJqq5Sz7+w081KwhojH6w/6HgK8/Oszkifn\nUruJV15tZWBQ9AecOj2I1+fnV0Gfgc3m5uLFEV574xx9fWN4vX7OtA7h8/v55UunJE9O6uu/RNXT\nxc7CrbybWMbB2ALKf/0jvmOagdcr+m1azw7xhz9epLPLInl7fD6/5DWy2z2cPjPI+x9cor3DHPTt\njODz+3nxp8fF2hcODydO9vPRx51cvCQuV714aRSfz8/zEuPl2PE+DhwUa3+M5+x9Pr/kNXI4vBw+\n0suRY72cPTcseXK8Ph/PPHcUj9eP0+nl4OEeTpwc4EzrUDBnL177M88dDS619XLgQDdngrU/xj05\nHq+fp589ImPOXRgW/QFePz29VlweH08/e1Ra+vvpZ920XRrl6LE+yZPjdnl58pkjQcbHZ59109Fp\n5lDQQ9DXP4bL5eXJZ0Svkcvt49MDXXR1WSSPUP+ADafTy5NPHcY1znzWRW+vVfIIDQzYsDs8/OTp\nw7hconY//awrqu+vQt9uH6+9cQ6fL4DV6qan18JPfy7WCPJ6/Rw70Y/b7ZN8RFarm+5ui6Rvr9fP\niVP9eH1+sQ8I+m06usz86pUzDI/Y8fr8nDwziM/n59dBr9FYMFX16m9bGRi04/X6Od06iM8f4Fev\ntkqenLZLo7z25nn6Bmx4fQFaz4m6/OUrZyTm3IVh3vpDGz19Y3h9Ac4F98T7+cung54cL63nhnjn\nvfag/yfA+TaR+dmvTknM6dYh3v+gXdJ320VRuz8N9gEOh4cTpwf4+NMuLrab8PoCknbHvUYOp5dj\nJ/on1/eLwT7A6eXI0T6OHO0L6btTPOezwT7A6fJy8HAvx/8CfUfTVV9NXDYbdNrsHlk+HMT9S8b3\nLoHgpnWTMOP5dQhtSBcebRdHZZ4Lp8vLhYsjE5jwnOx4kbjwuHQptL8JhDakkzHto4zZQjnZcVNs\neLRfGpVqKYCYw2+b0I4Jc5gvw+cLcP7C8ATGFOa58PsDsvouIO4VNRJWKyUQYALT3mGW1UEJBODc\nueEIxiTzQcDkTH8kc34iE349gKyOBAA9PZwwZNOpF6e9+zWJGDt/KkM6wupjSOeK+H46O00IYVPX\nk11zZ6dZ2qn78665q9OC1er+k0x3j0Xm/ZnsXL29VhSC/HrOnx+W/Asg7nukjSjTf/78kIwZGrbL\nvFAAF84PSx4HEP0K4f4kQLbBKoi+pkvt8nvz3IVhaU8hEH074R4HgAsXRiQvFCANcGVMWA0jiOr7\nr6bvdtNEfbf9GfqOuH87Ok3SJprjcS7iXCJjkzMT2jFP0PcEXXZZpI1aP6+dzq5J9DSBMSMQkDMT\n+gAz+ogtLSK/584uC5bYyOuRf/ZJ9R1xPb19VuTq/vP0HY0vF5dFugrEegvLlhTKXlu9Yrosb11Y\nkMTyZUUyZsWy6WSF1UHIy01kxQSmSJa3zslOYOXy6TJm+bIi8sNqdGRmxk1gli0tktWpyEiPZfXK\nCGZJocy7kpYaM4FZ0lwg865MnWJk9cpiWb55aXOBVJodRL/CmlVyZsnifCrCcsBJiXrWri6W5aSX\nNBXKvBAJCTrWRDCLm/JlnoH4OC3r15bI8tZNjfkyf01srJa1a4plvpSmhnzqakP+mhijhvVrSmR5\n66bGfBbV50rHRoOadWtKZHlrTUMdq0yHSHcNIwT8bO55A8usuTJfSuOiPJoa8qRjnU7F+jUlMl9K\nY4Oc0WqVrFs7Q+ZLiWxHo1Gyft0MmS+lYVGujFGrFaxfWyKrqbKoTs6oVArWrimR+VLqarJpagxj\nlArWrSmR+VKqqzJZ3JgvHSuVAuvWlMh8KfMqp7G4KcQoFAJr1pTIfClzKtJZ0lwgHQsCrFlTLKup\nUl6WypLFcmbtqmKZL2Vm6dQJ7axeWUzq1BBTUjyFpWEMwOoVxTJfSlTffx19NzcVSFurgKjvtasi\n9N2YR9W8kP8oPk7LutUR+l6UL/POxMZoWLeyWOZLaVqUT12Yf85o1LB2VbFM3431uSyqCWMMatat\nLJbpu6Euh8a6XOlYr1exdlWxTN8N9XJGp1OxdnWxrGZSQ30ujWF9iVajZP3qEpm+G+rzZIxGo2Td\n6hIMYX9sGupzaVwUYtRqBevXFMv0XV+XQ+Miub7XrSmW6bv2v6HvaHz5uCwGOYIAV6wvpXlxPulp\noqkvLzeBRYvyWLVyOgqFeMOsXzuDxY35ZAT3tsnOiqepIU8SvlIpsH5tCU2N+UzLEDvPzGlxNDXk\ns25NCQqFgEIhsHZ1MY2LciVTX0ZGHIub8lm/dgZKpYBCAWtWFtOwKJecYHGn9PRYmpvyuWJdKSql\nAoVC7OwX1eWSFzT2pqYaaV5cwBXrZ6BSKRAEWLm8iEV1ueTnix3s1KlGli0pZOOGmRKzfFkh9XW5\nkvk3JcXAsqWFXHlFKWq1yCxtLqC+NlcqVJeSbGDFsiI2XjFTYpqbC6irzZE64aREPStXFHHVlaVo\n1OK+NU0N+dTX5koGwsQEHauWF3HlFTOl/W8aFuVRW5PDzKCBMCFex5pV07lyQ6m0/82i2mzqa3Mp\nC5r64uK0rF1VzJUbStEFmdqabOrqcqQ9sOJitaxdXcIV60uljqh6QRb1tTmSuTUmRsOcW9ZgUAu8\ndOwRPj6wk3VDH5N68zWSKdVoVLN+bYlsMFI1bxp1tbmSKdVgULNh3QzWr5uB0SgylXMzqKvJpmqe\nOKAz6NVs2FDKujUzpM5qzux0ahdmU10lMjqdio0bZrJuTYm0OWFFeTo1NdnSoE9kZrBmVbHUoZWX\npbKoLpf64F5aOq2SKzfOZNWK6cTHi8zMmVOpq81lUV2OtOfUlRtnsnrldGlQUzpDZBoW5UnMVRtL\nWbGsUBrUlBSnUF+bw+JG0ZytUSu5auNMViwrkva3Kp6eQn1NLksWi/vxqNUKrto4k2VLi6S9q4oK\nk6mvy2VZs8ioVAqu3FDKsiWFTJkiMgX5SdTX57A8uGePSqVg44YZLGkulAY++XmJLKrPkfb1UakU\nUX3/d/W9MahLhcCS5gLqaiL0vbyIKzfORC3pO4+62hxKS6eAIJqwVwb1rdUpERRBfS/MZmbJuL61\nrFoxnSs2lKLVqRAUAvW1udTW5Ij6FiAuXsfqlcVsDGpXUAjULcymviaH8lliO7ExGtauKGbDuhJx\n7yoFVC/IpLYmmzmz00EQ96Zbt7qEDWtLMBjUCApYMH8adQuzqKxIR1CIfcD61cWsX1uMwSgy8ysz\nqKvOZt7ckL7Xry5m/ZoZGGM0IAhUzp1GTXVQ34KAwaBhw7oZrFsd1LcgGrVrqrNZUDUtpN11M0KD\nkSBTW5NNTU02ggJ0ehUb15eyZuX0kL5npVJfm0t9TXZI3xtKWb2ymPh4HQgwa1ZQu/W5CArQ6pRc\nueQ3VMIAACAASURBVHGWTN/R+PIhBAKBL6b+xmEw5gRmzb6Puroc3gnukQOwauV0Xnv9rDTdp1QK\nNC7K4+0/tEnMyuVFvP67cxKjUAg0N+Xz5tsXJGb50kLefPuCNFWvUAgsbS7gjTfPS8zS5gJ+/06b\nNFU/vsHka2+ck5jFTXm8+267bKp+9crp0j46IP7r/+DDDtlU/ZrVxbz6m1bpuL4uh48/6ZRN1a9b\nU8Kvg/vogDhA+OxAtywls35tCS+/EmKqF2Rx+EiPbDp/w/oZ/Orl09LxvMppnDjZL5U1B7hiQykv\n/eqUdDx3TjpnWodkU/WRTHlZKm0XRxkLWx555RWl0p49IP7r7+oyy6bhI5mS4hQGB22yrQQimTt9\nB8i+eJT7Cjaj8XuYbu/mH7ufZXnJtyUmNycBl9snK91/1caZ/PyXJ6XjzMw4BORLbq/aWMrPfxk6\nV1paDHqdWpZKiWRSUgwkJOg4HzaFHckkJupJnRrDmbCy95GfKy5OS3ZWAidO9kuvbbyilF+GMUaD\nmsLCZI4e65Nei/wt9HoVpSVTORjcRwcm/u46rYry8jQ+/awrxKybIe3DBOLM1pyKDD7+pFN6LfIe\n02iUVM2bxvsfdkivrVtTzK9fDd3P46voxvfAgon3vEqpiOr7v6HvI0d7cYUxkb/hvLkZnDg1INP3\nxg2lvPRKiJkzO43Ws8PYHWH6XjeDl8LaKZs1lYsdFpm+N64r4Ze/Dl1PackUunsscn2vn8Evwu67\n4qJkhkYdspTVxrUl/DLscxXkJWK1uhkYCqW+rlw3g1+EXU9OVjxut4/esPT3xrUl/OJXISZzWhwC\n0Bm2ND+ynbTUGPQ6lWx5/JXrSvhFmJ5SkoP6DkvPbdxQyi/DmMQEHVNTjLKtQSKZuFgt2dnxnDg5\nEGLWl/LLl+X6LshP4uixPg5/eufBQCAwj2h8qbhskn9en1+2zw6INQ7Cx2g+X4BRk5wZjmD8/sCE\nnPDIqF3mRZiMGR6xy7wIgQAT2xlx/H/svXdwHOeZ//npicg5JxKRGQSYAJAAM0HJsrJEShSjbQWK\nOYoSJSrb8tXu/vZ3V3t3VXe3lmRLjuu4Xlu2IrNIEQATGJFzmMHk3NP3Rw96pgewtWtrq36q4vsP\na1AfPv1OT3/f6enn+z6PagGU/5+asYQMgNHvI3KMjXlUC+B47Oj/E+05iT7W2JhbdYMDYDJFz8et\nWgABzKaJ84m8wZlszlarR+nb8pfmY7G4VTUi5DhRc7a4VYvkZIxgtzFgSCUoaPBojfQb0zB61V4A\ni9Uz4fxMnLNX9fh/sjlbrR580efQ7FG9ttm8Sp+bvxTHbvOqUmUyo56Pw+HDYp14TUUOp8uv8mHI\njDqO262ukTNZHI83MKmeIofXK2KZoCf1a59PVNXagYnX2Lhx968d646+/wZ9W9yqGxyQG61Gzyda\n39HX3ZjFo7rBmWzOVqt3gr7NUTqwWCfqe8L5sXqw2aP0HXWerTavyrMkM64JzER9T9TuBF1OOJYH\nn0/tyYmej80+cZ2IPj82uw+jXvtXGYfTN1GXUe9rMn3fGX/f+Fqkq0D2K2x8fC7aUC7ZoNey+Ylq\nKiNqmNTWFPJEBKPXa9j8RJWqjsfCBfls2jBXyTfrdBqeeLxKecwJctpi04YqJZes1Qps3FBFzaKw\nL6WqModNT8xVcslajcATj89V+VLmzM5my8YqJZes1QhsWF9JQ304Jz1zRiabN1YrjEYj8MRjlSr/\nxvRpGWzZVK3kmwUBNjw2V+WXKC9LZ+umaiXNIwjw+PpK1q4J+xxKS1L51pZ5Sr55nPnGXWHPwNQp\nKWzdPE/lOXls3Rzu++Z05XVRYbK8/TeiFsr6R+fw4P0zldf5+Uls2zxPSeGMMw8/OEt5nZebyLYt\n81Q56fWPVvLow7OV19nZCWzbMk/Voydtw4M8MHaOOksr+Z5Rjnb+BPeau1Wek/WPzmH9I+E4Gelx\nbNsyj/SIWijrHpnN+kfmhOOmxfKtLfPIzIhTx3k0zKSmxPCtLdVkRXhO5DjhYyUnx7Bt8zxVvZRH\nHp7F+kfDTFKikW1b5pOfF/alPPzgTB6LOFZCgoGtm6pVnpMH75/BY+vCTHy8gW2bq5W0CsC990xT\nzTkuVs+2TdWq3lB331XO4+srlcU7NlbHls3zKI2oh7RmdSkbHgszMTE6tm6qUvUjWrm8hA2PVSoe\nD6NRy5bN1UyfFvacLGuYqmIMBi2bNlQp6U64o++/Sd/r1PouKU5l22a1vh9bP2eivjdVq/X9yBzu\n/cY05XVRQTJbN85T0rgA6x6ezQMRa0B+XiJbN85V6XvdQ7N5+L4ZyuvcnAS2PVFFUkSfrnUPzeKR\niHUiOzOerRuqVOmZdQ/M5NGIdSIzI44tG6pIjVgD1j04k0cfDMfJSI9j28Zqlafs0Qdnse6hcJy0\n1Fi2baxS6XtdFJOaEsPWjdVkRfjOHn1wFusi1qTkJCPbNlWr9f3gTNZFrCVJiUa2bZ6npFZBfrIT\nud7I+p5HYUHYd/bAfWp93xl///ja3OSUl2dQUJBMXOiLNTHJQH5+ksosWFGeTkF+svLlm5hgJD8/\nWcWUlaZRkJ9MYoIsvIQEAwX5SaqmfqXFqRQUJClN9BLiDRQWJKsKZpWUpFKQl6wIOC7ERDZuK56a\nSn5+ksLExukpLEymoixsTJwyJZWC/GSlGV9srE5mIgpvFRWmkJeXqCwEsbF6igpTVF82RYXJFOQn\nKcx4LY1IE2RhQQq5uYnKDUOMUUdRUQrTpoWZgoIk8vMSSU2VGaNRy9QpqUybFm4CmZefSF5uorKg\nGAxaiqemUlEebjaXl5tIfl6SclNhMGgpLk5jWkUGmtBVl5uTQF5eolKETa/XUFKcGmIEhcnPS1Ix\n2TOL0WkkXux8n7db/4GZzi7iZpYrC5NOp6GsJI3ysnCc7Kx48vOSyQp5R+SGh2mUlaUpX4hZmfHk\n5yUpjQg1GoHysnS54WToCzEzM5683CRyI5iK8nRKS9KUL8SM9Djy85IUY61GIzf1LCkOM+npsRRM\nwkydmqp8IaanxVKQn6QslIIQZsa/ENNSY8jLS1I8KIIg+2umTkkhJsSkhpjIm6XpFRly/ZvQ06WU\n5BjychNVzQqnV2RQWJii7C5LTjaSn5ekaiBYUZFOYUGy0twyOSmG/LwkldG3oiKDwoJk5cs3KclI\nYUGyirmj7/+cvlNTY0EYZ5KZFsEUFiSH9C0fy2jUMaUwhWnT0hE0gCDrOy83SblhMBq0TJ2SwrSK\nDASNBgSBvAL5mktLjwdBwBCjU/St0QogQF5eInl5SbJfSwBDjJaS4lQqKjKimEQys+MRtEKISWNa\nWThObm4ieTmJShx5DUijvDRNYXKyE8jLTZQ9XSGmtDhNbhar04Ag6zsvN5GsbJnRhZqnlpWmodOH\nmOx48nMTyclJAAG0eo2s75JUWZcCZIbi5OQmgiCg0WooV7SrBUEgIzMhag2AirIMSkpS0Ru1IEBG\nprwG5OWE9T2tXNbluL7TUmPJz0tUmhbL+k6X60nFfm2SLP/Lj6+NJ2f67OeoWVjA5xEegmUNU/ks\nIs8PcmXXMxEegqX1Uzh+skvFLKkr4tSZsIegfnGRylMAUL9kCidPhf9fXW0hZ872qJilDVNVPoPa\nRYWcPadmli8t5tPjYZ/BwgV5nP+iX8WsWF7MJ5+GmfnVuVxoHlAxq1aUqLwIVXNzuXhpQPWoftXK\nUj76OOxFmDM7m6utw6pH9WtWlar8CjNnZHH9xoiKaVxdxp8+DPsVpk/LkHtARTyqj2bKStPo6rao\nHsPf1VjGH/8UZqZOSWFg0K5Kod3VKHsqxkdRYbJS/nx8rG0s54MI5lnnSdKGu3mjeIMc1z3I/9v2\nL6ye/brCZGXG4/OLqke/d60t548RHov0tFgEjaDaPhs9n+QkI7FxegYjWgBEMwnxBlJSYlRl+aPf\ne2ysXOgsctv22jVlKl+IwaClsCBZtS05mtHp5BvByG310Z+FViswrSKD1mth/0/0567RCMyamcXl\nK2H/z+pVpXwYwQiCXFk20v8TfR0KgrxTqyniel25vISPPw0zAAvn53P+Qp/yevmyYpX/Brij7y/R\n9+pVpSpmzuwsrraOfIm+M7kRVT4gmplekcGtjjFVum7NyhL+/HH4WGUlqXT321T6XruylA8i1pup\nRckMDDpUKbS7VpfyQUScwvwkTGa3Kj3WuLKEP0UwuTkJOBw+Vepr7apSPoiYc1ZGHD5/UJX+Wbuy\nlD9G6CAtNRaNRlC1HImec3KSkdhYvar8xdqVpfwxQnPx8XpSkmPoi2jfsXZViUqXsbE6sjITVOUU\nGleV8sGfvkTfq8v44MPJ9d109tk7npyvYHytbhfFYDDq9cQbtOi/RQr3v8IEo3Lvwf8EIwbFCcyE\nOU8aJ2o+k72v6PkEJaLvTyfMORhULW6TxQ4Gg0Tf6E425+CXMMGghKT+EwEx+ljSxPlEn0MxOOF8\nRL8vpCABIZz/FgUNgvTlx5rsPGuizuFk19iE+UxgghOvqQnnebI4/4nzE3UsSfpyJhiUJlxnk10/\nE/4W9X8kaZLPJzgZ89fnM+kcJ9XlHX0r/2cSfU/2eX2ZnuQ4f50JBIOTrCUT5xx9rGh/khicuE5E\nrwGiGPzSayE4SZzJrsP/zHuPHpNdGxPe6yRxJh5r4toyYV2YdP2buHZEDkmaqN074+8bX5t01fpH\n57Bze63yyDs5ycieHbU0RuSkH3loFruerVFyyUlJRnbvrOPuiJz0/fdOZ9eztcqW4MQEA7t31nHv\nPeGc9De/MY3dO+rCj7MTDOzaUcuD94fzzXc1lrN7Z53iJ4mL07Pr2Toejcjvrl5Vyp4ddcpj6LhY\nPbuereXx9eGc64rlxezZVaf4SWJidOzcXsumJ+YqzNL6qezdtZi0EGM06ti5vYatm6sVZnFdEXt3\n1ynpIaNRy87ttTz5rfAPgZpFBezdWaekdQwGLTufreXp7yxUmAXz89m7e7Gy3Vev17Jzu1z6fHxU\nV+Wyf/dickOPYvV6DbuerWXH9hqFmTsnh/17liipFp1Ow64dtezaUaektGbPymL/niVKLRStVmDX\njjp27wozM6Znsn/vYopCnhOtVqDs8JPcY2tmw8DHLLFc4X+7/f+h2bZV8ZxoNAK7d9ayZ2c4TnlZ\nOvv3LFa28mo0Art31LF7Z52S0iopTmX/nsVKmkAQYM/OOnbtqFVSWlOnpLBv92Kmh1J8MrOYXdvD\nTFFhMvv3LFFqoQgC7N5Rx65nw0xBfhL79yxWttjLjHwOx1NjebmJ7Nu9RNWHasczNezYXqukvXKy\nE9i/ewnzIzwn259exI5nauTH68iP8vfvWcLCiFooTz+5kB3P1CiPzjMy4tizq07V++jb2+az89la\nJTWWnh7Hvt2LqV8c9qVs2VjFzu01ilckLTWWPTsXsyyirsgTj89lxzO1SkpLbj1Ry6qIWj5fub7j\n/wv6jv+a6HvXYpW+dzxTy3e2zVeYmoUF7InS945nangqYg1YMC+PvTvCjF6vYedTNWz/Tpiprsxh\n745aJR2j12nY+dQidkSsE5Wzstj3bK2SjtHpNOx8chE7n1ykaG7WjEz2bq9RfGdarcCOJxex66kw\nM70ig73baykK+VK0GoEd31moilNRmsbeZ2qZGkqTajRC6FgLFaasJI29z9ZQErEG7HpqETufWqTo\nu3hKCvu211Ie8p0JAux6ehE7nlqo+LymFiWzd0ct0yvCa8DuZ2rY8dQiRbuFBUns21mnlNkQBNi1\nvZYdT9eo9b2rTqVvuT1EWN+5uYns3b2YqrnhWkfPPl3DzmdqVHWD7oy/b3xtnuSYx1zYHT58fnmn\ngNcXwO7wqXZ/mM1u7Haf4rr3egPY7V6sEY80LRZPqJy6CAL4AkFsNi8Wq5fxcpQWmyd0LJnx+0Xs\nDi9jVo/CWO3yDoBxJiDKbRJUjFWO4/UH5DiiiN3hk3ejqBgvPl9AiWN3eDGPRR5LZsY75Qb8Ija7\nV7WbwGbzYLf7FMbvF7HavKpHtTabB4fDh9sjPyoOBERsVq9qB4Td7sHh8Co7MgIBOY6a8eJw+CPi\nyI+NI3cT2B3y+fG4IxiLh7GI3TDyI2kv7hAjilKIcSuM0+nDbvfhdoUZ54gVgkFWjrUgjEnoggF8\no2ZcLvnxdjAoMTbmwecX1XEcPiUNFgxKWCxuBEFQfqU5XT7sDr+yi0SS5B0sMTF65deVy+XD4fQr\nW2nlXTgughG/wFxuP3a7VxXHZHah12sUxu32Y7P7cIQqu8qMm/h4g7I7x+32y+fREb5+TWY3aWnh\nHTxuj3wsmy2CMbmx2jwEAmLEsdQ7VkwmFza7V2E8ngAOhw+b3aNi7DYvgVCKwuPxY7N5sNrU87HZ\nvfgjNOdwqDVnNrtC17halyrtfsX6Ho/j84nYbB7VDjB5l58XX0grPn9A1vdYBBPaBRSpp78Ux+P1\nh+PYfSpdWiyhOCGt+P0idrtXtQPNanVPqu+xiDVA1pMPrzccx2rzqHZK2eyyvj2+AGhAlIIT1wm7\nF4fTh8cvgiAQCMprWSRjd4wzoThIMhOxbjlc8rXpCa1bYlBuNTFm9cg1hgW5QrXD4VfmE0TCavPI\njBBiPH7sTi9uX8SxbF7sTl+Y8fpxuHy4vX4ljsXmwe8XVXEcDnnOglZAEsBi9yAgyE+FBLlDvd3p\nlVNlgtyd3mLzEOPVIYYYlyeA0+HD6ZaPJYHynkRJAg14fAHsTh8Otx8EuaayyeJGF6Fvl1vuNu50\n+ZQ45jE3CQkGRCkImtA1bvepdGk2u0hLi52wQ+/O+NvH16J31Zvf/edXbI6ZDAzY6B+Qc6eBgMTw\niJPPz4Vz+B2dYwwOOhRvhChKDA07VHU+urotDI046em1IQgCoigxPOLgzOc9CIKAIAj09FgZGnbQ\n3WOVmaDE0JCDM2fDTG+fjeERJ13dVuWLcnDQzukIpn/Azsiok45OS4iBwUE7p850K8zgkIORERft\nHWMIgoAkQX+/mhkadjIy4lTKsUsS9PZZVT6D4REnI6NOpVaLwkT4DkZHXYyYXEo7AUmSS7GfiGBM\nJjemURc3boY9H13dFk5E+B7MY25GTS5VTYjOrjFOnu5WbirGLB5MJhfXroeZ9g4zp86EGYtVZiK9\nI7fbTZw5263ceFhtXkwmF1dbw8zMM7/jtpDG8+Xf5reZizmeUsn60//KvyQsVZgbN0e5cKFP8RDY\nHT5MZpfKg3LtxggXLw4oHiGn04/J7OLS5TBztXWYq1eHlJL/Tpcfk8nFxcthn8qVq0Ncvz6CM3QD\n5XL5MZndtFwMM5evDHHrtknxGbjdAUxmF80t6jhtHWPYQlvoPZ4AJpNL5Xe5cnWIzs4xxWvk9YqM\nmtXM1dZhenqsyheX1ycyanJxoSnsFWm9NkJvr03xI/l8IiaTk/MXwsz1G6PKdQ5yGwOTyaXynNy8\nZaK/36aU8/f7g4yMODn3Rdh/c7vNTP+ATfE1BQJBhkdcnDsfZtrbx746fQ876OkJM8PDDpWPp7vH\nytCwk+4eazjOkIPTEZ4cRd8hD1UwKDEw6OB0hNdH1reLjs5xRi7dfypCl4ODDkZGnUqLCEmS/18k\nMzTsZHTUpdZ3v1W1BgyPOBkddSq1WmTGxslT4Tijoy5GzS5utZmVtaS7V71OmMxuRs1ubt4yM/4Y\npKvbwomI92Ue82Aac3PjlknZgt3VbeF06LMQBEHW7pib6zfHGYGOrjFOf96DNM7YvJgtbq5FMO2d\nY5y90EcwKDM2u/wDqvXGqPJeb3eYOd/cjyhKCIIga3fMzdXrIwpz87aJC6G+a4Ig4HD6MI95uHIt\nzNy4PUrLJblXlyAIOF1+zGMuLreGmdbro1y9PoLHE0AQBEW7F68MKczVa8NcD9UREgQBlzuA2eSi\n5dKQfA4FgSutw9y6ZVJ+/LjdAUbNblouDSpxrrQO0R7StyAIf1nfoXYdA72/v9O76isYX5tnYhqN\noOyYGB+R2xdBvt4SEtV/S0ychIn6f9Gv5f+nPlZ8gmFCrYRoJjHRqCqXPlns+HjDBGbisfSqkuqT\nMQkJRlXLhEnjxBtUJdUB1XZOmTGqyqVPfizDhBov0Z9FfJxBVVJ90vnEGYiN0f9VJiHeoCqpPhkj\nxcaSGggbBVMDdvy6qPMcp1dtcQdIiroW4iZhoq+pSZmoOLGxf2OcqHMYY9QpaZbwsdSM0aj70uvX\naNR+6Xz0eo1qizBAQqK6yqpOp5nkWOr56LQTmcQkNaPVChP+X/Rn8ZXq+0s+r8n+lhA/mb4nxvnv\n03f0fIyqlgmTxUmI03+pvhPiDRP1Pcn1M0G7k1y/xqg40Z9pXJx+wq6gCednsjUg+lixetUWd4Ck\nyfQUxSTGT4wz4RqPnzjn6DjRc46dLE70e4/VT7zuouLI+v7r7904yRpwZ/x942txkzPuVzi4v17Z\nSpyfl8jB/Q1s2VilMDueqeHgvnqlDkJubiIH99bz7a3zFeaZJxdxcO8Spc5JdlY8B/bW89S3wznp\nJ7fN58DeJfJWQ+SdOof21rM9Ipe8bfM8DuxZQl5oC3BGehwH9taza3uNwmx6ooqD++qV7b3pabEc\n3LdE5RV5fP0cDu5dQmGoxHxqaiyH9tWzb/diZbFc9/AsDu6vV7bupqTEcHh/PYcO1CvMQw/M5PD+\neopD22mTk40cPtDAkUMNCnPfN6dz6EC9UgslKdHIkYMNPH94qbLofuOuCg4faFC2yiYkGHju4FKO\nPr9MYRrXlHHkUIOyPT0h3sDzh5fy0tEVyqK7akUJhw/WM3OGXAslPk7PC88t46WjK5R88/JlxRw+\n0MDsWTITGyszx14MM/VLpvDcwaXMDfXoiY3RseAfD7PU18ZL7e/xxMBH/O83/y8Sjx1RenDFGHW8\n+MJyjh1doSzwixYWcPhAg+JLMRq1vPj8cl58frlyAzd/Xh6HDzZQG/KlGAxajr2wgqNHlimek+qq\nXJ472MCSkC9Fr9fw8tEVHD2yVNlqXTknh+cOLmVpwxSFeemF5bxwZJmyeM+amcVzBxuUXjY6nYZj\nR1dw5NBSZUGdMT2TwwfqWbO6VGFeemE5Rw4tVRbCiop0jhxcyl2NsndFqxU4+twynjvYoHxxlpWm\ncfjAUr4ZqoWi1Qq8cHgZhw80KJ6TkuJUDu+v54FQnRONRuC5gw0cPtCgeE6mTk3h0P56pdaRRiNw\nYN8SDu6rV7YkFxUmc3BfvVLrQ6MR2LdnMYf21ystJAoLkji4r54nHq8E/g5954zre57CPPPkIg7u\nrw/rOzuBA/vqeTrCc/LktxZwcG+9St8H9zeo9P2tLfM4uLc+rO+MOA7uq2fXs7UKs3ljFYf21ZOf\nH9b3oX317N0Vqe9KDu2rV+n78P4G9u9dEtb3I7M5uL9hor73hZmH7p/JoX31iu8sOcnIof0NPHcg\nUt/TOLR3CaUh31liopHD++o5cqBB0e7djeUc2rtE8aUkJBh4bm89Rw+GmcZVpRzes4RpoTUgPl6v\nMOM/rFYuncqhnXXMDHnT4uL0HNlbz4sHGtCH1oBlS6ZwcEcds0LeldgYHc/tWcKL++sVfS9ZVMjB\nHYupDK0BMTE6juxdwgt7l2AIecpqFuRz4NlaqkNrgNGo5YW99Rzd16Doe2F1Hgd21rEgVDPJaNDy\n/N56XtjXoNzAzZuby6Hdi6kJrQEGg5ajBxp4fl+9ou+qOdkc2lWn9OnS6zW8dKiBI/vqFU9Z5aws\nDu9ZQkPEGvDi4aU8f6hB+YE2a0YWh/fXs2JpWN8vHlnOc/sblJuq6dMyOLSvXunrptNpePF5Wbt3\nbnS+uvG18ORIEnz0STsJCQbFY9LXb6epqV/ZPipJ8PGn7aSlxzFicoEAg0N2mlr6+exkp5KD/eR4\nB7m5iQyHHq8PDTu50NSn2gb66YlOiopSlMfrwyNOvmjq45PPOpRUy2cnOigrTaM/1DZg1OTii6Ze\nPvykXWFOnOxk1oxM+gfkR+cms5tzX/Tx0cdtCnPqdDfz5ubRG2otMDbm5twXvXz0SbuSsjl1todF\niwrpG7CBIKd5zp7v4bMTnUq++ey5XhqWDMgtCgQ5zXP2XA+nz4RTP+fO99LSMkBX6PG6ze7l9Nlu\nLjT1K7nk8xf6aG7pV9oYOBw+Tp3u4krrsMI0NfXT1NxPe6iTs8Pp48SpLnmbeSiX3NwyQEvLIG3t\nctrL6fJz/GQnPb1WJYXUcnGAlosDSorN7fbz6fEORkadCnP58iBNLf3cuCmnvdyeANd+fYIin4gY\nI1DoHeFGbAHFv/kT1/UPA3I1308+7cDnCyj+jdbWYZovDtLaKpdU93pFPvm0HY1GUDpUX7sup6/G\n2yr4fCIff9pObIxO8ShdvzFCy8UBJe3l9wf56JN2UlJiFG/RzVujNLX0c+lSBPNxOzk5CYon6Hab\nST5HoZRWIBDkw4/bmFKUgtMpM23tZlouDtIUSjMFAkE+/KiNiooMpdN1R8cYTc19fBFiRFHiTx+1\nMTTiVDqjd3ZZaGrp5/wXvRHMbdl3EkqNdXdbaW7pV7ZIB4MSf/6oDbfbr2zT7emx0nxxQEkPBYMS\nH37chiRJilelt89GU0s/J093hZmP2tHrtEr6rLfPRlNzv5Jq+S/pOy2WkVCKbWDQTlNzv7LNXJLg\nk8/ayc1JCOt7yMGFC/18ErFd/dPjHUyZEqXvC70qfX96vIOysvSwvkddnL/Qx0efhLV7/GQns2Zm\n0d+v1veHKn13Ma86St/ne/kwos3E6TPd1PwlfYeYM5/3UL+4iO4eWbvj+j5zrocgslfk3IV+mi8N\n0tklH8tu93L68x6aLg4iBgFB4IuWAZnptYIGHC4fp851c/X6iOI5abo0QPOlATp6LCDI2j31eTdt\nXRYCIT9Jy9UhWq4M0d5tAY3siTn5eTe9A3b8ADoNl26McPHKMLe7LCAIuL0ix890M2py4Q9IAFZM\n6AAAIABJREFUIAhcvjFKy9UhbnVZQafBEwhy/PMe2Z8lSaDTcO22mUutw9zsHAOdBq8o8enZbnxe\nEZ8/CIJA6y0TF68O0XpbTsN5/UE+Pd2NRiPgFeU4NzrMXLwyROvNUdCALyDy6alOYmJ0im/oZruZ\nlqtDXL0+IvsoA0E+PtFFcpJRSVnfbDPTcnmAy9eGQQN+McjHxzvIzozH5QmAIHC7Y4zmi4O0XJFT\nWgFR4qPPOphSkKSktds7xmi5PEhTc6S+25lWka7qZH9n/H3ja+PJCVLFmMWjLF4gG+2utob7gIyM\nurDavAwNO5UcsM3u5WrrsJIXNZlc2GweBiLqnljtHlU/EXPITBnZ98hiVTNjFtkM3B9RO8FiUTMW\nq2wGjqyfYrG6uXwlzIyXMI9kxsbcKu+IbPT1Kh4hQRAwm11cvhJ+Xw6HD7vTS3d3mDGZ3VyKqHHi\ncPpwOHx0RtRyGBl1qjwoslnQR2dEPZfhESeXIjwoLrdszh33IgAMDztU9VTcngAOp4/29nDPp8FB\nu+pYHk8Ap9OnqhsxMGDjytVh5UvC6xUnMPOvfMhNbSb/MOVRTqbM5vPk6Wy6+D7/T/pKhenttXL9\n5qhy0+Xzi7icPm5F9Jfq6bFyu82s3Aj5/UEcTp/iWQLo7LTQ2W2JMGIHcTp9Ks9Se8cYPb025SYn\nEAjidPmUGzOQ/ST9A3bFjCyKEk6nT+Vr6ugcY2jIqRgRRVHCEcV0dlkYHnEqNyfBYIiJ8D5191gZ\nHXUpvp1x5tr1sK+pt9eGyeRSStgHJQmHw6fyR/X12zCZXYrpXJJkb1PrtfD1OzBglz1aoRsPSQKH\nXR1ncMiBZcyteHtAvqYjtTs87PxP6tujqmlitak1N2qSmUh92+zeCfq22jwqfVutHi5H6dtmV+vb\nalFrd9zkrNKu1aPSrqLv3jBjHlMztpBJfTJ9j49IfY8Pk9nN5Yi1zRnSd2StltFRF5dahxXviMvl\nx+ny0RmxToyMurh0NRzH7Q7gdPlVzPCIk8vXwozHIzPtXZawv3DYweXro0CI8Yo4XT7aQzc5CAID\nQ3auXh8NmZMFvD4Rl0cdp3/QzvVbo4pvx+cXcbj9tHWGmd4BOzdumeQt6oKA3y9r7nbHmHKsnj4b\nbZ1y7S5BEPAHgjhdXm61m5U4nT0WuntteL2ybycQCOJy+rl526QwHd0Wevusyk2OrG8109llkfXt\nks3IoijhdPm5ccukzKeja4yhIbvy40MUJZwOH9f+gr7veHK+mvG1SFeB/Bhz/LHw+CgsSFb5UoxG\nrZIaGh8F+cmqvLXBoJ0QpyAvWbVlT6/XKNuaw3GSVLltrXZyxqhiBAoK1Ex+bpLyaHSciaxEC5CX\nm6TKSWs0E5n8vCRVLlkQmCROoiq/LAgoj80VJi9R1VYBJmci2ypMxuTmJqlKqgNKl+dIJjMjXs1E\nVM8dZ7KyElR/KyxUM1JGJuXufsbvhMpdfbjj1UxOTqKSjvhLcXJyEiYwRZMx2Ymqv02Ik52gdM8O\nx1G/98zMeGVLbjiOmklPj/vSOKmpscq23fExJYpJSY5RKin/pTiJicYJTGFhisqXkhBvUNI1YSZJ\nxcTH6VWl6wEKi5JVvpTYWB15UbosLExW+VL+Vn0XFkyi7zz1ey3IT5qg78L8KKYgWaVvnVZDQbTm\nCpJU3pXJ9F2QlziJvqPWgLzECfqecKy/Vd+TMNE+nej3npuTMKHr9UQmUdniHmbU7ys3O1y9fHwU\nTcJkRa0BhVHXT05WgqqtAkBR1OeekxlPTlZ0HPWcc7LiyYmKE/2+cjITyJ7AqI+VnRlPTtSaFP2+\nMjPjVW0egAmfe3pa3CRrSbS+YyasAXfG3ze+Fk9y3nrrf77yT//4Ao+vr+T4yU5cTj/l5em89UYj\ncfF6Ll0axGDQcnDfEjY+Ppfjp7pwOv2UlaTxvdfXkJwcQ8ulAQx6LXt21bH5ibmcON2N0+GjuDiV\n772xhoz0OJpbBtDptex6tpatm+Zx6nQ3DruPqVNTeOv1RrKzE2hq7ken0/Ds04v49pb5nD7bjd3m\npagohbfeWEN+XhJfNPWj02p4+smFfGfbAs583oPN6qWgMJm3Xl9DUVEKX1zoQ6vV8J1t83nq2wv5\n/HwvVouH/Pwk3nqzkdLiVD4/34dWK7Bt8zyeeVJmxiwe8nITeevNRsrL0/n8XC8ajcDmJ6rY8XQN\nXzT1MTbmJic7ge+90cismVmcDe34euKxuezaWUtTcz8ms5vsrAS+92YjlbOzQ7vC5D5Ve3ctprml\nn1GTi8zMeL7/RiPVVbmcPt0NAjzy0Gz271nCxUuDjIw6yciI5/tvNjJ/fr6Spnjw/hkc3NfA5atD\nDA87SU+P4/vfXUvNwnxOnOoGJO69ZzqHDzTQem2YwSEHaamxfO+NRhbXFnLiZBeSJPGNuyp4/vBS\nrt8YZWDQTmpqLM/881ZKfvh/sGrgc6rtt3mm7z9I/T//iVvxBfT120lJjuGtNxtZWi9XrBWDEqtW\nlPLSC8tp7zDT22cjOSmG773RyPKlxTIjSixfVsyxoyvo6rbQ02MlKcnI915fw6oVJXx6vBNRDNKw\nZCovv7iCvj473d0WEhONvPn6atasKuOz4x0EAkEW1xXxyksrGRxy0Nk5RmKCkTdfW83axnI+O96B\nPxCkZlEhrx5bxajJRXuHmYR4A999bQ13r63g0+Md+P1BFszP57Vjq7BYPLS1m4iPN/DGq6u55xsV\nfPpZBz6/yLzqPF57eTUOp5dbt03ExRl47dgq7v3mND493onPJ1JVmcvrr67C6w1w46aJuDgdr7y4\nkvvvm8GnxzvwekXmzM7mzVdXEwgEuXZ9lNhYHS8dXcHDD8zks+OdeLwBZs3M5ruvrQFJ3p1ljNFx\n9MgyHnloFp8d78TtDjBzRibffW0NOq2GK63DGI1ajhxaxvpH53D8RCdut59pFRl89/U1xBh0XLoy\nhMGg5fCBBlnfJzpxuvxUTKbvvUvYuKGKEyc7cTj9lJWm8dYbjaQkG2m5KOt77+46Nm+s4sSpLhwO\nHyXFqbz1ZiPp6fE0N4f0vaOOrZvncfJ0F3a7j+KpKbz1pqzvC0396PQann1mEd/ZuoBTZ7qx2bxM\nKUrh+282yvq+0Kfo+8lvLeTM2R6sVi+Fhcl8/81GioqSOR/S95PfWsDT31nE2XM9WCweCvKT+P6b\njZSUhPStEdi2dR7bn1z0X9R3It97Yw0zp2dx9pys3Q3rKtm1vYYLzQOYx9xkZSXw1qtrmD07mzMh\nZv3Ds9m9vYaWS4OYTG4yM+P57rFVVFXmcOZcLwjw8H0z2bu9hktXhxgddZGREcd3X1zJ/Lm5yg6r\n+++exr7ttVy9PsLwqJP0tDi+e3QlC6vyOHW+FyS4Z005B7bXcu3WKEMjTlJTYnnj+WXULizg5Oc9\nIMFdK0s5tKOOm21mBoedpKbE8Ppzy1i8oICT53oJShKrG4p5budibnea6R90kJwcwxtHllFfU8iJ\nz3sIBiVW1k/l+T1L6Oi20DdgJznRyBtHlrN0cREnzvYgBiWW1RVxdF893X02evpsJCUaef2Flayo\nn8rxM12IosSSmkJePNBA/4Cdrl4riQlG3ji6glXLSzh+Su5AX7eokGPPLWNw2EFXt4WEBANvHF1B\n46pSPjvRSSAQpGZBAa88v5xRk4uOrjES4g28cWwld60p49OTnfj9QeZX5/PqiyuwWD20tZuJjzfw\n+suruefuCj473smtG7+68yTnKxhfi5ucN978H69Y7TPk/OinHQQlCZPZTXKykR+9fxG7w0cgEOR2\nmxlRDCr5bpPZTXJSDD/88UVsNi/+ECMIAn/6qI1gyEuQmGDk/Z9ewmr3EhCD3G4zodUK/PHPt2XG\n6iEuTs9Pfn4Zi9VDQJS43W5Gr9fwHx/cIijJdRtiY/X89N+uMGbxEAjKTEyMjt/94QZBSa7/YDRq\n+fmvrmIacyMGJW53mImL1fOb318nKEnY7F70eg2/+HUro2aXzLTJX4K/+s01gkGZ0Wo0/Oo31xge\nccpzbjeRlGjk337ViihK2O0+BAF+87vrDA075TjtZlKTY/j5L68qKQyA3/37dQYG7IiiRFu7mfS0\nWH7y8ytyusThQxQl/vDBTXr7bAqTkR7Hj396SUm7+Hwif/7wNj09VkRRor19jMzMeN778cUQ48ft\nDvDJZx10dlkQRYmOzjGyMuP50fsy43L5cbn8nDjVRXuozHxH5xhZWQn86P2L8qNkl5/8S6fJbj3P\nzzIbGDGk0GtMJ/OL47w1UkIgEJS7cFs8nL/Qx42bo4iiRFeXhZycBN7+YbPMeAKYQ9u8W6+PIIoS\n3d0WcrITePvdZvyBIB5PgNFRF1euDnM15Enq7rGSm5PI2+824fPLzPCwkxs3Rrl0eQhRlOjttZGb\nk8AP3mnG5xPxeAMMDtppazfTfHFAZvrkOD94pwmvV8TrFenrs9HZbeFCs8z09Y3HCTM9PRb6+m2c\n/6IPUZTo77eTk5PAv77ThMcj4vOJdHbJ26g/P9eLKEoMDNrJzk7gB2834fbIPqWOzjHMZjenz/Qg\nihKDQw6yMuVjud1+mekYw2L1cvJUl7JdOyMjnh+824zL5cfvF2nrMOOw+zh+UvaPDI/IN7Rvv9uE\n0+nH7w/S1m7G7fHzyWcdiKLEyKiLtNRY3v5RMw6HT2bazPhC/qZgUGLU5CI5OYYfvdeCzS4zt9rM\nBETZKxTWt5Efvq/WN8AHf7qtdBtPTDDw3vsXZe0Ggty6bUKrEfjDB7eUmkpxcXre/+klWbuBILdv\nm9HpNPz+DzdDNZVkff/kZ5cxj7kVJiZGx2///TrBoITV6sFo1PKzf7uCySQzt9pMxMXp+fVvZe1a\nbV70ei2/+GUrI6Oydm/dNpGYaPxyfScZ+eVvrxGUJOxOHxpB4De/v87QkANRlLjdPkZKSiw///U1\nxCA4nH4kCf79TzcZDK0B7Z1jpKfF8rNftxKU5JRKUJT448dt9A3YZaZrjIz0OH46zrj9+PxBPjzR\nSc+AHTEI7d0WMjPi+MlvryFKcn0ZtzfAZ2e66eqzIUoSXb1WsjLi+MlvWwlK4PYGcLsDnDrfS2ef\njSCEmHh+/OtWxKCkpLk/b+6nrctCMCjR1WcjOzOe9395lUBQwuMNYLV5uXB5iNtdYwSB7n4b2Rnx\nvPfLq4iShMcvMmbzcPHqMNfbTAQliZ5+GzlZ8bz7iysEguDxBxkdc3Hl2gitN02IQejpt5OTlcC7\nP7uEPxDE6xMZHnFys83ElRsjBIG+QZl558eX8IWYwSEnbe1jXLw6RFCS6BuwkZOVwNs/asHrC+m7\n30ZXt1XxSPUN2MnNSeDtHzXj9Yn4/CI9vVb6+2ycv9B3J131FY2vxU3Om9/951cMsQvx+UVVXl8U\nJWVRA5QFc2g4nI/3B0Ta2sK+EKfTh18MqvL6/kBQ5flwufwEAkFVXt/vF2mL8Je43X5EMagYEwF8\nvoCa8QQIBNSM1yeqjuXxBBCDEn394Zy916uO4/WJBAOSKvfv9vhVcXw+ETEoqXL/brea8ftlpqc3\nnNd3On2qc+j3BwlKKDVEABxOr4oJBIJIQUnNOKIYUW4p0RXhIbDZPYrJGOTPTwqi8hBYLG7a2scU\nT854u4hIj9CijtN0aNJ4J6+R1oQpXI8vZOvNX/Kv2WsUxmR20dNjVUrPByUJKSipfESjo076B+xy\nQUfk7FdQQjFdAwyPOBgZcSrmZEmSS6+P1z0BGBp0YDK7lJz9eJxIZmDQjtXqUUzFAFJQHWdwyIHd\n7lX17JEkSXUtDI84cTi8iicH5PYDkXFGTS6cTp+qr48UVMcxm904XT5VAbxgUFJdL2Njbtxuv6pQ\nnBhUa8Vi8eDxBlRFJ8WAOo7VJhe6G4noETZ+szw+5MJ70foOTqJvkaFo7UYyTnkNiNR3IKCOE9Z3\nWJd+v6hm3H4CoqTWdxTj9gQQA0FVTyOfV814PAFEMUhfhHY9Xr+K8XpFJOnL9R2UUDOT6DsoQU8E\no3hiIs6XFMU4nD7aIq6fwF9iIuLIrV6gO4Kx2T20daoZKYqx2Dx0dFvV+pYkuiLWrTGbh85eq2K6\nlts8yDdE48NkcdPbb1M2Q8i6RDZUh8ao2U3/oF3ZxKAwEevWyKiL4VGnUitLkmStdES818ERB+Yx\nD25PhL6jmWEHFqtHMRWPz7s9Yi0ZGnZij+rJJQXV2h0ZdYaKe97x5HxV42vjyUlLjWXWzCzV3ypn\nZ6vy1snJMROYObNyVDVDkhKNzJmVrWJmz8xS1StITDAwewKTrXQSBrkeRnScWTOzVN6VuFg9lbPV\nzMzpmarcdkyMTin9rTAzslS5baNRR2VljoqZNSNLlbc2GLTMnaNmZk7PVHlO9HoN1XPVzIzpmSrf\nhU6nUZUZl+NkqXL9Oq1G1WpgPM7UqWGvilYrMK8qT81My6SsNNzpWaMRmFetjjNtWqaq+/JkjFRa\nQo3jJoagvKDUW65gzypQx6nIUHVXB5Qt5uOjYjKmKlflOZk8jpqpqEhn2rTMCceK9KWUl01kqqty\nVUxpSRrTo5iqubkq78qUohSmT4+KU52n8q4U5CcxI4qZOzdX5V3JzU1k1gy1VuZW5qh8KTnZCUpr\nCmU+lTkqX0pmZvwkcbJVdZUy0uOYNVN9jVfOyVG25IKs7/FSAkqcOWp9pyTHMHuSNSByu21SknGC\nnmbNylbVmElMNDI7ipk9W63vhHjDBO1O0HecfoIuZ87MmqDvaF3Ompktd90eZ4w6Kueor/FJ9V05\nUbuRPhC9XkNVpXrOM6ZlkBexBuh0GuZGva/pFZkqH4pWK0xkyjOYGuEf0WoEqqOZsgxKIzrLazQC\nVVFMRUk6ZVNT1cysaCaNioiO8IIA1VHXRkVJGhURawkwybFSJ2VU2i1JY1ppuoqpnhPFlKZPYOZV\nqrVbVpKm6ggPcnuMSKakOHUCU1Wp1ndRYfKENeDO+PvG1+JJzlvf/5+v/OM/vMDDD8zi1Jku3B4/\n06Zl8PLRFcTH6bl8dYgYo459u+TeMqfPduNyB6goT+eVF1eQlGTk0pVBYmJ07N5Ry7qH54QYP6Ul\nabzywkrSUmO5eHkIo1HHs08v4vFH53D2816cLj8lxWm88sJysjLjabk4iMGo45lvL2TDukrOnu/F\n4fQxdUoqrxxdSV5uEk0t/ej1Wp769gKeWD+Xcxf6sDt8TClK4dUXV1KQn8SFZpn51pZ5bNlQxfmm\nPmx2H4UFybz24kqmFKXyRXM/ep2GbZuq2bapmi+a+rFavRQUJPHasVWUlKRx/kIfOp2GzU9U8e2t\n82lqGcBq9ZCXl8irx1ZRUZbOuS960WoFNqyfy1PfXkBzywBjFg+5OYm8fmwVM2dkcfaczDy2rpJn\nnlzIpUuDmMyyt+f1V1Yxe1Y2Zz7vQasVePSh2Tz7TA2Xr8p5/azsBF57ZTVz5+Rw+mw3GkHgoQdn\n8uwzNVy7PszIqIvMjHhef3kVVVW5nD4jMw/cN50d22u5cXOE4REnGelxvP7yKhYsyOfk6W4EAe65\nW+4zdLvdxNCQg/S0OLb/02ayf/h/81jnH1hr+oJ7TedI/Zd/oiOxkIFBO2mpsbz+8ipqawpC/h+5\nm/feXYvp7pF3QaSmxPLay6tYUlfEyVNdSJLcxX3/niX099vo7bORkhzDq8dW0VA/lRMnZI/QsoZi\nDu6rZzhUETs5OYZXX1rJsoZijp+SUzYNS6ZwaH8DI6MuurotJCUZeeXFlaxYXszxk10ERYnFdUU8\nd2gp5jE3nZ1jJCUaOfbiSlatKFE8QosWFfDCc8uw23y0t5tJTDBy7MUVNK4u48RJOfe/cEE+R48s\nl39pt5tISDDy0vPLWbumjBMnu/D7g8yrzuWl55fj84rcvD1KQryBo88v5+67KjhxohOfP0hVZQ7H\nXlxBICBy4+Yo8aHaR/fcPY0TJ7vw+UQq52Rz7OgKJOD69VFi43QcOdjAfd+cwYlTnXi9AWbPyuLY\n0RXo9Bpar40QG6Pj8IEGHrhvBidPd+HxiMyckcnLL64kxqjjSuswMTE6DuxbwsMPzOLkaVnf06dl\n8PKLK4mLN3D5yhAxMTr27l7Mow/P5tQZWbvl5em8cmwlyUkxXLo0iNGoY8/OOtY/GmJcPspK03jt\nmKzvlkuDoZ5PNWxYX8mZsz04nT5KitN49dhKsrLiaW4ZwGDQ8szTC9nw+Fw+P9eLw+GleGoqrx5b\nRV5uWLtPf2chGzdUce5cD3aH7Nt57eWVFBQkcaFJZr69bT5bN1Vz7nwvNrvs23njlVVMmZrK+S96\n0eu1bN0yj29tmcf5C31YbbJv57VjqygpVev7W1vm0dTSj8XqJT83kVdeWklFWQbnLvSi1WrYsL6S\nJ7fOp+XyEBaLh5ycBF47uoLp0zI5d0H2961/aBZPbZnP5dZhzGMecrISeOXIMtm794XsI3r4vpk8\ns3U+V2+MyN6ezHheObSUOTOzOHuhD41G4IFvVPD05vlcv21i1OwiMz2OY/sbqJ6TrTD3NZbzzOZ5\n3OocY8TkIj0tlmP76plfmcOZC30IgsDdK0t5dst82nssDI/ILQ2O7WtgwdxczlzoBUFg7fISdmxd\nQFeflcER2bdzbH89NdV5nA51tl+9tJid2xbQO2hnYNhBSnIMx/bVU7eggFNfyFWYVy6Zyu7vLGRg\nyEHfgI3kZCPH9tVTXyP7fyQJltYVse/pGoZNLnpC3r2XDjXQUFfEqZD/Z0ltEfufrWXU7KKr10pS\nopGXDi1lef1UTp7tJihK1NUUcHjPEsYsHjq7LSQlGnn5+WWsXFrMidNy+nfRgnyOHGjAbvfS3iF7\n9146spw1q0s5cbKLG9d+eedJzlcwvhY3OW+++T9e6e4vwWR2c/J0N4GAXDreHwjy9g9lf4DXJ9LU\n0s+Y1cOJ090ExCCjJhden8i7710M5ZVFmi4OYLN7+OxEF4GAXKbe4w3w7o8v4XDJueeWS4M4HD4+\nPtFJQJQwjblxewK8+5NL2J0y03x5EJfbz0efdRAQJcwWDy63nx/+5BI2h09mLg3i9Yr8+ZN2AqLs\n/3E4fLz3s8vY7DJz8fIQPr/IBx/JjMXqxWrz8v7PL2OxefEFgly8MoTfJ/KHP98iIMo9YqxWDz/5\nhez/8QeCXLo6hCgG+f0HYcZsdvOzn1/BbHbj9we5dGUISZL43e9vEAj17BoZdfKLX17FZHbjDwS5\n0joEEvz6d9dlxu5leNjBL3/dKp9zf5Croa2kv/r1NfyBIHa7l8FBu+z/GXLg9wdpvTaCRivwi1+2\n4vcHsTt89Pbb+P0fbjAwEGa0WoGf/9tVefu2w0dPr5UP/nyLvj4bfn+QGzdH0Ok0/PTnV5Qt3tkf\n/pa4rtscK9lMU1I5l+KnMu0P7/G6aZq8ldQpP8Y/fqKTztAW0pu3TBgMGt77yaXQdlM/t9tMnD7T\nTVv7GH6/nNLQ6zX86P2L+P2y/+fGzVHOne/l1m0Tfr/8aFmv1/Luj1oUpvX6CE0tA9y4MYrfH6Sj\n04JOLyiM2x3gauswly8P0XptBH8gSFe3Ba1O4J0fNuMLMZcvD3Ht+ghXrg7jDwTp6bGi1Qq8/UPZ\n2+P2BLh4aZBbt0xcvDwoM702BI3AOz+UfTseT4DmiwN0dIzRfHGAQCidIiDw9rvNCtPU3E93t5UL\nzf3hlKoEP3gngmnpV/w/4+lbSZL4wTtNeDwBvF6RpuZ+BgbtfH6ul0BAThPJTDNut8xcaO5neMTJ\n6bM9BAJB2SMmBvnBu00K09TUj8nsUvQ9POIk4BcV/498rAHGxtwcPylrd3TUhc8n8s4Pm3E6ZR9R\nU3M/VpuHT4/LN4GjIX2/88NmHCHvWHPLAA6nj48/aZfXALMLt8fPOz9qkeuzhBiXK8CHH7cRCAQx\nm9243H7efa8Fm82rMF5vgD99KDNjY24cDj/vvX8Ra4i5eGkAn0/kj3+6rfRvs9o8sgfQ6pV1eXkQ\nv1/kDx/cUvrAWawexd+n0vcfZUbR969bMY+FGYDffXBT7qXn8DFqcvFvv7uOaUzW99Vrcv2X34XW\nCbvTx/Cok1//4RajY278osS1m6MIGvjNn24TCErYXX4GR5z87s+3GB514ReDXLst+xZ/9cebBEQJ\nh8tP/6CDPx7vYHDUSSAocb3dhE6n4Vcf3CQQlHB6AvQNOvjwVCf9wzJzq9OMVqfhl3+QGZcnQHef\njU/PdNM75AgxY+h1Gn7xHzcUpqPHyqnzvXT32wkEJdq6LOh1Wn72++sEghJub4C2bgtnm3rp6LUR\nCEq091jQaTX8+NetBETZ/3Or3cz5iwO0dVsIBCU6e63o9RreC/l/3F6R67dMtFwe4ka7Gb8o0dlj\nRa8V+NEvLuMPBHF7A7TeGOFK6zDXbpoIiEG6e21otQLv/uSiwlxqHab12ghXQ2tAT68NrQbeea8l\nrO/Lg9xqM3Hp6hADPXfSVV/F+Frc5Hz3u//8SmJKHRqtoMrZGwxaVd0In09Eb9AofXRAfoQb6R3x\n+0X0eo0qZ6/X6+iOyAn7/UH0Oi0DEYxOp6EnggkEghgMWlXOXqsVVIwoShgNOvoiGM2kjFaV19do\nBFU+XBQlYgxaVT6eqPx8MChhNOomMJH+G0mSMMboVH8LBiV6++wRjPyIPfKcBcSgKq4kydVLVUxg\nIhMTo1N/Pn5R5RkCiI3Rqzw5Xk+A/n67krOfjKkZbKZfSOT3mbX0GzMYNqSyues/eDsn7MlxufyM\njLgUT85kcRwOn9LIc3zExKoZubGlT/HkgLwlOpKxWr24XD7FkyMzeqXvEcheI683oPLkxMboVJ4l\nq9UTagbri4ijU/mRxptqRnpyYmO0SgG48fcVDEoqT05sjE5VH8npkk2pY2Nhv01MjPp9uVx+kFB5\ncoxG9Zzd7gCCgMqTYzSo43g8AbRaDSMR2pWZcByvV0Sj0XypvnU6jcqTo9drJ1xjer2fI32YAAAg\nAElEQVRWKfQnM9FrQEjfEZ4cnVYz4XqeTN/RujAYdSo/nVYj0B2hL1GUMBi1Kk+ORphE39HaRe5N\nNT7+kr57+6O1q1fFlk2waiY2Vh91/CB9EedLiRNx/IAo0jfw1xmfP0B/xGcD8nXXEzFHrzfAwLBT\npe8Yo04Vx+MNMDTqVDw543G6IxiX28+o2a14ciZjHC6/fJPoj1gDjFq1j8gh1xby+iLWAKP6+8Bq\n9+J0+RRPzvixuiKuBYvNg8cjqjw5MVGM1eZVfvCp4kRoxW73Kj8u79zkfDXjv82TIwhCoSAInwiC\n0CoIwlVBEPaE/p4mCMKfBUG4Ffo39ctiAUwpSmZp/VTV31YsLVbVXSnIT6Jh8ZQJTHZEjYP83MQJ\ncZbVT1HVJsjJTmB5g5pZumQK+RH1HLIy41keFWfp4ikURXhXMtLjJsRpqCtiakRtmPS0WFYuK1Yx\n9XVFlBSHT0tKcgyrVpSomcVTKI/IEydPwiypK1JaL4DcH2fNytIoZorKdxEfb2DN6rIJTOWccL47\nPk5P4+oyVd66rraI6qqwryA2Vkfj6jJVTrqupkhpqwDyIrC2MYqpLaJmUdhfYzRqaVxTpspbaxYu\noNHaQrrPCpLEuqHPsJXPUvlSahcVUldbqLzW6zWsbSxX+VJqa9SMTqdh7ZoyVU2V2kWFSpsHkL/o\nGteUq3wpNYsKqKstUjFrV5epfCk1C9WMRiPQuKZMVVNlwbw81XwEAVavLlPVVKmqzGFx3RQVs2Z1\nmcqXMntWNovrwscCWL2qVOVLmTE9kyUTmBJVzaSK8nTql6j1tGZlqaqmSllp2gRm9coSlS+lpDh1\nArNiRYnKdzalKIVlUVpZsayEzAhfSkFB0sQ1YFmxypeSn5c0Ic6yhmJVTaCcnASWR2lu6dKpqrpX\nWZnxrIhm6qeq6g1lZMRNYBrqp6i8aelpsaxaodZc/ZIpSusFkNs4/M36jvB4JCYYWL1cPZ/FNYXM\niPCUxcfrWR0157pFhcyJWAPi4vSsXjpVpe/aeQUq70xsjI7VDVNV2q2dl8/8CP9RjFHH6iXFKqam\nOo+FleF1wmDQsqp+CtoIZlFVLosiPH8GvYZVS6ao1oBFc3OpifD86XUaVtVPVek7mtHpNKxqKFba\nTozPZ1GEV0+rEViztFhV72xRdR618/NVzOplJao1YGF1HrURa5tGI7BmRYlK3/OrcqldGF7bBEHW\nU2Svvrlzclhcq9blnfH3jf9O43EAOCBJ0kygFtghCMJM4AjwkSRJ5cBHodd/dQiCwKYNVTx4/0yK\nipLR6gQqKtK55xvTWP/obAxGLTGxOjY+MZcH7p3JlKIUtDoNZaVp3Hv3dB57dDYGow6jUcfj6+dy\n3z3TKZ6ailanobg4lfvumc7j6+ZgjNFijNHy+KOz+ebdFZSWpKLVCUydksL990xn4/pKYmJ0GI1a\n1j88i2/eVUFZWRpancCUomQeuHc6Gx+TGYNRy7qHZ3HPXeVMK09HqxMoLEzigW9OZ9PjlcTEyszD\nD8zkG43lTJ+WgVYnUJCfxEP3zWDzhrnExuowGLQ8fP8M7lpTzswZWWh1GvJyk3jo/pls2VhFXJwe\nvUHL/fdO56415cyelYVWK5CTncDD989k2+Zq4uP16A0a7rt3Bnc1llM1NwetTiA7O4FHHprJ1k3V\nxIWa/X3zG9O4a00Z86pz0eoEsrLiWffIbLZtmU9CggG9XsPdd1fQ2FjG/Oo8tFqBzMw4Hls3h61b\n5pEQagq6trGctWvKWTA/D51OQ0Z6HI+vn8PWzdUkJsjMmtWlNK4uo2ZhATqdhrS0WB5/bA5bNlaT\nmCgzq1aUcldjOXU1hTKTGkvNwcdJihH494vH+LTpEE8MfULevidZsrgInU5DSkoMGx+fy6YnqkhO\njkGn07C0oZi1a8pYWj9FZpJj2PREFRs3VJGSIjP1i4u4q7GcZUuL0ek0JCUZ2byxio0b5pIaYhbX\nFbF2TRkrlpXITKKRLZuq2fB4JWlpseh0GmoXFbC2sZzVK2UmMdHAlk3VPL6+kvT0WLRagUUL8lm7\nppy1q8uURphbN8/jsXWVZKTHodUKLJiXx11ryrlrrXxzFh9vYOuWeax/dDaZmTIzrzqXtY3lfOPu\ncUbP1i3VrHtkNtlZ8Wi1AlWVOdy9toJ775kmN+aM07NtczWPPDybnOwEtFqBytnZ3PX/s/fewXFd\nV77ut8/pgJxzBoiciAyQAINIihJzFEmREimSYpTEAAYFW5Yse+bed1+4c+vdmnk1r+rVzHhmbI/s\nsT22Zcu2bFmiJMuSmDMBgghEaqCBRgON7gYa5/1xGqfPacCya2zfKldpV6lU3fVx7ZPW6o2zfnut\n1YVs2lCC2SwRFmpm/94atm8pIzU1ElkWlJcm8fhjhWzZpDKhoSb2PV3N9i1lpKepTGlxImvWFLJt\nSykWs0RIiIm9T1WxdXMpGelRyLKgqCiB9WuK2L6tXGWsMnv3VLFlUwlZ/iKBhQXxrF9bxM7t5Vgs\nMiFWmad2L2TzphLVv2Wh+vf6YnbuqMBikbFaZXY/WcmmDSWqf8uCvNxYNm0oZvfOSqxWP7Orkg3r\nisjLi0OWVf/evLGUp55ciNUqY7HI7NxRwfp1ReTnxyPLqn9v2VTK03sWEjLLbK9g/doiCgvitaJ/\nKlOlxgCzxPat5axbU0hJsd+/M6LYuqWUvU9VERpqwmyW2La5lDWPFVBWmohsEqSlRbJtSyn79iwk\nLNSM2SyxaX2R37+TkU0SKSmRbNtcxjNPVRE269/rinhsZT4LK5KRZUFyUjjbNpWw78mFagwwS6xb\nXcijy/OoqkhFliUSE8LZvrGEfTsrNWbNigWsXpZHTUUKJpMgMT6MJzYUs3dHhRoDLBKPPZLHqqW5\n1C5MwWRW/fuJjSU8vb2cyEgrJrPMyiU5rFySTX1VKiaz6rs71pewe0uZxjyyOJtHW3JpqEnHZJaI\njQ1l5waViYq2YrLILF2czaNLcllUl4HJrPr3zo2lPLmlTPVvs0RLYyaPtuTQUq8y0dEhPLm5lF2b\nS1X/Nkssrstg9dJcli7KUpkoK7u3lrN7c6nm34vq0lm1JJdli7P9/m3h6W3lPLmljLhYlWmoTWP1\n8jxW+ONEZKSVp3dWsmtrOfHxagyor01j9SMLWL0iD7NZ9e99Ty5k57YyEhLCMJkk6mrSWL0qn8dX\nF2Ayy4RHWHjm6Wp2bivT+rN9Mf74IRT9e8M/50RC/AD4n/7/liuK0ieESAXeVRSl6PP+bXhEtlJZ\n+yWWL8vl579s177fuK6IH/nrWID61/rKRxbw018EmA2PF/LWz+9przVNJonVKxbw1s/uacy6xwp4\n+1ftGiPLgsdX5fPjtwPMY6sW8M67HVqbAFkSrH2sgB/+5K7GrF6xgF+936G9HpUkwcY1hXz/x3c0\nZuWyXC581KW9HhUCNq8r5ns/uq0xy1ty+OiTbm1boxCwZV0x3/3BLY1Z2pzFJxd7DSmS7ZuK+c73\nbmqfmxdlqdqCycAr1Ce2lvHmv9/QPjfVZ3D12oDWbgBg5/Zyvv2d69rnhrp0bt8ZYswZSJHs3FbO\nt968pn2uqU7lfseI1koAYNfOCr717QCzsDKFnh6H1iYA1Aal39Qx5WVJ2GwThpRjMPOcuETB3Y95\nJXcfYTMeciYH+Nrgd1lT8IrG5C+Iw+v1GdILu3dV8q/fuqp9zsmJQRLCsIUzeK6MjCjCQs3c1bV6\n2L2rgn/9VoBJSYkgNibU0DYh2M5sRVR9Of8nd1TwzX8LMHGxoWRnx3Dpcl/gGu6o4Fs6JjrKSkFB\nPJ9+1qt9t/OJCr6tuxeRkVbKShL5jb9wG6hNIP9Nd0/Dw8xUVaXywYdd2ndPbC/nTR0TGmqirjad\n9/39owC2by3ju9+7oaUbQkJMLGrMNPSG2ra5lH//wc0AYzXR3JzFO7+8rzFbNpfwg/+4rfmuxSKz\nbGkOP9f57qaNxfzwR3fm+rfOdzeuK+LHP71r9O9H83lL55fr1xby07fbtNSlSZZY81gBP3wr4Jdr\nHivg5++0B/xbFqxfW8QPfhjwy9WP5vOrd+8b/XtDMd/X+eWqlXm8f6HT6LubS/mejnlkWS4f/qYb\njz8FKgRs21LGd38Q8N2lLdl88tlDo39vLeM73w/YaW7K5PL1AaN/bynlO7q5GuvSuXHHZkijPLG5\nlDf/I3Be9VWp3O2wM6ZLozyxsYTv6GJSVVkSnb1jjOrSpE+sL+Y7umtYUZTIQ9sEdl2adMe6It7U\n3YuS/HiGRyYZ1KU3t68p4js/CdgpzIll3D1Fny51uf2xQt7UzZWXGY13eoYeXSruiTVFvKmzk+2v\nkqzfVv7EmkLe1J1XekokoRaZe7qt3jvWF/Nt3TVMSQwnOtLK7bZADNixoYRvfz9wvxLjw0hOCOW6\nrp3Jjk2lfFsXa+NiQsjKiOaSrv3Nzi1lfEvnc9FRVgryYvn0Yi+ffXDsM0VRAp1lvxj/qfG/pEGn\nECIHqAY+BpIVRZmN4v1A8u/4N4eBwwAWi/qDpa9/A9DfP27I205NzdCv+3EEtX6BPm+riiOdn8v4\nfIoh7w9qo7/ZAAjgm1EMuh6AgUGnIf87M6PQ229kBm3jhvyvomDQ/miMJ4iZY2fCEAABevuCmMEJ\nQwAEDDqEWTv6BQ5A7zyMfoEzH2OzTRgWOAB9vUF2Bse1Ro6BY57L2O2fzwi7nQ5rMi5TKC5CURCE\nuox6BpttwqC1Ue0YmSGbC6F7TQ4Y+hnNMqG6dBFAb6/xOg8NuQzPhmrHyNjtLsPr9vnOa2R00pCa\nmo9xjHkMuhWVMZ6X0zkfY7Qz4Zqa84z39RrtTE5OG3pJzdrR/13kdk/P8cu+/iDGM81A0PPb1+c0\n+K7X62NgYOJzmeD6N6D6zhz/Dno2+/rHDdqsad/MHJ/r73ca/dunzPG5WVH97JiZUeY8LwMDE3N8\ntz/YzuC4tsCZZeb45eA8/h0cA4bm8++5jH6BA/PEmyGXYYEDzLnOQ/ZJwwIHoD/oGbPZJ+YwfUHM\nkN1lWATNZ2doZJIJz9TvZfT3QmXG5zBGj5vHjt1lSCvD3OujzmWMJf1Bz7x9ZBJZGF8Y9AX9zow4\n3Ib0FcyNo/P59xfjjxt/9jo5QogI4LvAKUVRDFFUUV8jzfsqSVGUv1cUpU5RlDqTOYKaqlS2bCzR\n8sSyJHhiWxmF+YGcdGVFMls3BBhJEmzfXEqxTpdSXprE9s1lBmbbxlJKdXVFSooS2LapVMslCwHb\nNpVQoavVUJgfz/YgZuuGUqp02pX8vDh2bCk15Ju3rC+hVqddyc2OYcfmUsMP4Jb1xTTocsDZmdHs\n3FZmyDdvXl/MYp1WJDM9il3byw16ks0bS2hZHMjvpqdFsWt7haEWyqYNxSxbmqN9Tk2J5MknKgw5\n6U3riw16gOSkcDW9pwsOs6mw2ZGYGM6eJysNTr1xQwlrHgswCfFh7N5Vafhh37i+hHVrC7XPcbGh\n7Nm10FAvJWLj42wc+YTy8Q6ipic43f09JhYvM/Tx2bC+mA3rirXP0VFW9uxaaNCcbFhXxIZ1gZeI\nkZEWnty1kGid5mTDeiMTHm5hz5OVxOo0J6qdwFzhYWZ276w09PJa+7iRCQ01sXtXpaFeyuOPFbBx\nfYAJCTGxZ1eloV7Ko6sWsGl9ifbZalHTL/p6SCuW57FpQ4CxWGR276w01ENatiSHLZtKtc9ms8ST\nOysNvZiaF2UZGJNJ4smdFWTrNGVNDRkGRpYldjxRQa6uFkp9XTpbt5QZmJ3bK1igq4VSU53Gts2l\nAf+WBTu3VxhqJi2sTGHbllKD7+7YVmaoK1Jelsz2beXGGLC1zFA/q7QkkR3bygy+u31buUF3VlSY\nwBPBzNYyQ32o/Pw4dm6vMPju1i2l1NUENB55ubHs2F6OrNOLbd1USqNOm5GdFcPO7RVG/95QYvTv\njCh2bQvy73XFtOg0XOlpkezcWobFrPPdNUUs1WmvUpMj2LmpzBADNjxWwAqdZiopIYwdG0sMMWDd\nqnwe1WmdEuJC2bG+mBCdLmXdinxW65j4mBB2rC0mVBcD1i7P4/GlAU1QbHQIO9YWEaarmbRmeR5r\nlgbiTXSklR1ri4jQxYA1y/JYo9MfRUVY2LGumEidNm3N8lzWLA/YiQg3s2NdMdE6bdraRxawTqeZ\nCg8zs3NjKbG6GLB2xQLW6XSKYaFmdm4uNejOHl+5gHWrA3ErNMTErq3lBt3ZYysWsOHxABMSYuLJ\n7RVG/34kj41rAzHgi/HHjz/rIkcIYUZd4PyLoij/7v96wJ+mwv//wd/17/Vj0aJMKsqSNdFjQkIY\npcVJ1NSka11emxoyKS9NIjZGffgS4kIpK0mivi4N1KbkNNanU1aSSHxiGEISJCSGUVaaRENtgGmo\nSae0OJEEPxOfEEZ5STKN9ekIWSAkQX2tyiQlhSMkQWxcKOWlSSxqzNSYupo0SooSSUqOCDBlySxq\nzEQyqUxtdRqlxYkkp0QiJEFMbAiV5SksashQ3zIIVWxaXJhAaprKRMeEsLAihUWNGUiyyixcmExp\nSRKpaVEgCSKjQzQRm5DV61NRnkxJcaImwowIN1O9MJWW5izNTkVFklog0P+qNyzMTHV1GosXZWoB\nv6w0idLSJLW5nFDFjHU16SxqytQCfklxIsVFSZpQMyTERH1tOoubsjSmqDCBkqJErSlmiNVEfV0G\nixqzMJlUprAggeLiRHL8P5pWi8yCVXVYTfA/7v4dP7n8ZZoct4hesZi8XPVH02KRaWpUBcOzPwoL\nFsRTXJSoMWazpAqGdUxebhxlJYnk+398zSaJRY2ZNNZnaD8KuTmxFBclUuBfXJtMgkVNmTTUZ2h/\nEWZnx1JckkBhgbq4lmU/U5euLfqyM2MoLUnSfqBlWdDclE1tTbpWJC8zQy0MVur/gZYkQfOibGpq\n0rQfhYyMaEqKE7WCfJIQNC/OpLoqVVsYpqVGUVKcoBW4VJksFlamaAvDtNQoSkqStAJ4QqAxkZEq\nk5ISQWlxEgsrA8ziRVlUlCdri8eUlAjKSpKo8S/khVDF5JXlydriMSkpjNKSJENxxkWNGZSXJ2vF\n9hITwiktSaK2JrDYb2rIoKIsWVtgJsSHUVqaTH29kSkvTSLOv8CM9/tcg45pqMugtCRJW4TG+Rn9\nwqOuNp3SkiRNGxEbozKLdYuKupp0SksStR+p2JgQKsqSWdSUpS2yaqrTKC1JItnfTDI6KoTKihSa\nGjM1pmphCsVFCZqAOjLSqvq3zncrK1MpLU4kNSUSBERGqcziRr9fCqgoTaKkMFFtmCogIsJCdWUK\nzY0BO2XFSRQXxKubKASER5iprkhhUX2G6pcCyooSKSmIJzMjCiEJwsPN1Fam0FSbgWyWQRKUFCZS\ntCBebVYrCULCzdRWptJYk4bZIiEkQWF+PIV5sWT77YSEmqitSKGxOg2zRUZIgoK8WIry4sjNjkGY\nBCFhJuoXplBfmYLZqjL5OTEU5caRlxOrMY3VqTRUpWINlREmwYK8WApzY8nLiUFIAotVpqEylcaq\nVKx+O3nZMRQviFc3dUgCs1WmsSaNuuo0LCEmkAQ52bEU58eTvyAO4Wea6tKpr0ojJMyEkFQNV3F+\nPIX5cSDAZBY01adTV5VGSIgZhCAzM4aSwgSKCuNBgGxWY0BtVZq26MtMj6K4MJ7S4gTNvxc3ZVJT\nnUaYbrH2xfjjxp9NkyOEEMA/AnZFUU7pvv/fgWFFUf6rEOIlIE5RlPOfZys8IlsprX6ZRQ2ZfPhx\nt/b9yuV5vPPeA92c0NyUxYWPAjqDR5bm8O4HnXpzLGvJ5j2dFmFpczbvBTHLl+Tw6w8D37U0ZXLh\nN90G5pGWHH51ITD/4voMPvq0x/CqfuXSXN55L6BXaKpL5+PPHn4uU1+dyqcX+wyv6lc/ksfPfhXQ\nNNQuTFX7IOmYx1Yu4O13ApqG6spkrlwdMLzOf3yVUdNQWZ7Mzds2w6v6NY/m89ZPA0xZaSL32ux4\ndWm2tY8X8tZPA7n24qIEOu6PGLZar19byI/eCjD5C+Lo7XOqW5M1pogf6XPtubHYhlw4demxYOY5\n90ck9d7jtby9ABS4evjbjv+XR8u+qjFpqZF4vT7D1uYN64r4oU4flZwUjhDC8Go+eK74uFBCQ82G\nrbvBdqKjrMTEhBq2ggbbiQi3kJwcYSjDv35NIT/S6RVCQ01kZcZw5+7Q77Rjtcrk5cYZ9D/r1hTy\nY50ds1miuCjRoP9Z+1ghb70dYEyyRHl5MpevBPQ/ax4r4Cc6HZosCxZWpnLxUkD/89jqAt7WPT+S\nfzH/208fat+tXpXPz37RZmAa6jP4jc53H125gJ/rntXZxdCHOt9duSLPoOMRQt119L7OVx9Znsuv\n3g34DsCypTn8WhcXli/N4V3dZ1B1MXod0dKWbN67YIwBKx/J4x2dzzUvVo9P77urVi7gF7rzWNyU\nxUcfG5nVj+YbzrWhPp1PP+s1+Pdjq/P5mY6prUnj8rUg3300n7d/afTva7dsQf6dz9u/CjAVpUnc\narMb/XvVAn6qO6/SwnjaO0fx6tI/a1Yu4G1dTCrMi6Wzz5hqX7Msj5++H2DyMqPpt7sMW60fX5rL\n27oYmZMexdDIJOO6GPD40hze1t3TjOQInK4pHLoY8HhLDj/V2UlJCMc75TOkvh5vzuYnuvucGBcK\nCgb9z+MtOfxEd9/jokOwWmTD1ve1y3J5S3edoyIsREdYDdvTH1+Wx1u6Zzw8zExSXJihhcaalXn8\n5OcBJjTERHpyJHd12p61j+bzY12stVpk8nJjuXVniM/eP/KFJudPMP6cmpxm4GngmhDisv+7V4D/\nCvybEOIg0Ans+EOMKQoG5wFwuafmMO5gJihnDczJdbvnY4JsB88933eT7mmC14zB80+6p+Ywwcc8\n6fYZAuB8c7k904YFDsxzXm6fIQCqzFQQMz1HTzLnvCan5+Sk57MTrIGZezzTeD2fb2dycsqgV5iP\nwevBKQdeFY/Loci+P+R45jLBmpz/DKM2z/z8Y/Z4pw0LQFCbGhpOy+ub+/wG6Sm83rlzBTNT/sah\nBmbSqLmY9s3gDnrGXUH3y+dT5hzzZNBcM/6migZmch5mnvusH6rvBjGuucwcv3TN45eu4LnmYX7P\n8fwuJth3587lncvMsTP9+/17cnqu7wYz8/m3+z/h3x4fU8FM0H33eHxzNDCTnrnPeLDPzXl+PPMx\nxs8er8/wB9W8x+OdnueY59oJFkME23F7f39c93h9eLxzY5l+eP1NOH8fM+d6BD2b3qm5zBfjjxt/\ntnSVoigXFEURiqJUKopS5f/vLUVRhhVFWakoSoGiKKsURbH/fmuw7vFCDh+o0/LE4eFmjh2sp1n3\n+vjxVfkc2l+j1S8ICzVz9EAdS3X55lXLczm0r0ZLLYSGmDi0r4ZHdLnk5S05HN5bo71WDLGaOLy3\nxlBfoqUpk8N7a7QaBxaLzKG9NTy+MpDfXVyfwZF9tVrawGKWefapGtbptCsNNWkceaZGq3NiNksc\nerqaTWsDOpDaqlSO7K/V+muZTBIHn65m28aA7qKqMoVjB+uI8uebTbLK7NwW0EJUlifz3OEGLeVn\nkiWe3V/Lnp2VGlNWksTxww1aSkCWBYcO1LH3qWqNKSlO5PmjjdrrfkkSPLu/lgP7ajSmsCCB5441\naq/7JUlw+Nk6Dh6o1Zj8BXG8cLyJJP+rfEkIDh2s59DBwB8vubmxPH+8SatjJARkPLeXjaOfst72\nGyqd9/nr9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OefX0Tr8SZND5qXE8uZ5xZpulJJEpw/0czZE4sNtYW+GH/c+Mu4kgIuXe0n\nKyuGsXEPSDA86qKtY4Trtwa1/PflawPk58Xj8DMjjknaOuxcvzsE/gf9yi0bpaVJjE54wSQxOuGl\n7YGda3eHVJ0OcP3uENVdo4xNepEsEk7PFG1dI1xvG0Lyr85vttu53zXKqMuDZJEY907T1jnC1bs2\njbl13879bgcjEyoz4Z3i3gM7V+4EmDsPRujoGsXudCNMgnHPFHc7/Iz/L9A7nXbau0YYdnoQFpkJ\nr4+7HSNcujmA4nfyOx0jtHeOYht1g0liwuPjdvswl64PgCwQwL0HdtoejGCzuxAmgcs7za17Q1y8\n2s+MUEDAvQ47bfdH6BucACGYdE9z8/YQN24OMIMCErQ/GKHtvp2+fjW1MOme5vqNAdru27VUVFu7\nnfZ2u1rRU6i7GK7fGKS7e1RLRbW3D3O/w651aPZ4fFy91o9taEJj7nfYab9v1zqne70+uj68QdG0\nj1TPMKmeYQbM0YiPLtE1owYU75SPK1f68Hh92s6SB50jtN+30+VPY0xPz3D5ch9CEtquka6uEe4/\nsGtdv6enZ7h4uY/QUJO2I6Sr20F7+wgdHXYDExMToqXGunsctN8fpr0jkMa4eKmP1JQIbWfUw4cO\n2tvttLcP65hecrJjtPTZw14H7fdHuNembimfmVGZiYlAx/PePiftHSPca7NrzGcXe5mentF2XQ30\nj9PWNsyde0MGRpIkLQ03MOikrd2ubV9XFPjsYi9hYRYtDTdoU9Mus9vXFeDixV5iY0JxOlXGNjTO\nvfvD3Lw1qDGfXeolJTlC65xuG5rgXvsw128GUpAXL/WSlRmNw78leHjYRVv7EFev6ZjLfeQviNMq\naw/bXdy7N8y164Ey+Zcv91FakqR1Vx8ZcdHWNsRVXSn9K1f7qa5KxT6ipvNGRie5e2+Iy1d1acpr\n/dxryMDu337scLi5e2+YS5cDacrrNwZoax/W0oKOMQ+37w4Z0p03b9lou2/HNqSmBcfGPNy+YzOk\nTWeZwWEXCIFzYorb94a5eK0fRQAC7rQN0/5gBNuwC4Sayrxzb4hLOuZeh532zhEG7RMgqbtPb7cN\nc+nGADOoTHvnCO1dowyOqDHAPa3GiVsddmb8saSjd4z73aMMjkwiTAKPz8fNdjsP+sZQ/Dq9B31j\ndPQ46B91IywyXuD2gxEeDk2g+HVlDwbH6exzMuCYRLJITKNw64Gd4TEPM2YJoUDX8AQP+p30OSYR\nFpkp4GbXCOOuKXyyhJCh2+6io2+M3lGVmQZuPBjBO+VjxiIhKRIPHZM86HPy0M/4BFx/MIKkKPgk\nkCwSvSMuOvvG6B6cAFliGrjaNkyIRWZaCIRF5qHdRcfDMboGnAiTwAdcvTdEdJgFr6KASaJ3aIKO\nHofaLkKo6cUrtwZJigtTd3QJ6B0Y537nKO3+lKhvRuHStQGy0yNxT02DBH2DTvV+dIyAUDvGX7rW\nz/i4d97dvF+M/9z4y9Dk/Je/ed1LNcMjLgZsLi2XPDrq5sqNQO60f2CcEcck/YMTWg54ZHSSKzdt\nGjNgm2DE4aZPx4w63FzR5WAHh12MjLnp9TOgLpiu3ArYGRqZZHTMzcP+cY0ZHp002BkencQx5qZH\nYwT20Uku6xi7w82Iw013r1NjhkZcXNad1+iYB4fDQ9fDMe0729AEl64NaJ8dYx5GHW46ux2B87C5\nuHi1T/s85vTgcLjp6Aow/YPjfHY5wDidXpV5MKrlkvv6x/nsYiBv7BxXmfb7gX4vff1jfKbTqUxM\nTDE25qHNn48XQvDwoYPPLvZpQl+XS2Xu6epGdPc4uHS5nxk/NDk5zZjDyCy89DZ3pQT+Km8Pv4iv\n4YPoMp767J/4+9hHNObBg1Gu3xzQFjkej0/9gdHVoLnfMcLtO0Pa4sTj9ak/VHcCTFv7MG3tdm3h\n4fX6cDo93LodYO61DdHxYERbVExNzTA25uGWro9NW9swnd2j2oJhanoGx5ibmzrmXtswPQ/HtBYa\n09MKY2NuTfs0y/T2jeFwqIzPp+BwuLl+I7AYaL9vp7/fqWl7fD4Fx5ib69cDdTc7HowwMDiO3a/t\nmbVzVVdbp7NrlIHBcYb9P/QzMwqjDrdh4dHV7cBmm8A2NMvA6MgkV3RMz8MxbEMuTf+jKH6f0y08\nenudDA25tBYRigIjo0amr9/JsH1Sa12gKKpm6/KVANM/MI59ZFJrYzHLXLocYAYHJ7DbJzWNEKDq\nMHQLD9uQi5ERt6E+0tCwy8AMDbsYHXVrC3BQF2cXdYzdPsnoqNvQQ21o2MVFXX2ikVE3o2NeOv0a\nQIRgcGicS1cDmo9RhxvHmMfg3wNDE1zS6ULGnB7GJrw86A7EiQHbOJeuDxp81znh5UFPgOmzjXP5\ndiC2jbumcLq8dOiY/qFxrty1Aepnl3sap2uajt4A0zs4ztW2IY2Z9EzjdE1xXxe3Hg6Oc/W+XdPt\nuL0+lfHHPyEEPYPj3OiwMzOjMh6vD6fLS7vOTtfAOLc7R/D5dTueqRmcE17aegLXp7N/jHtdo0xN\nq7od79QMDqeHe36NpBCCjh4H97sdeLw+ZnWcTqeHO36NpBCC9q5ROrodTPp1O6rverjTPqwxbZ0j\ndHWPMeHX7Uz7/fvW3UDcausY4WHvGM5xVbcz7VMYG/No+kchBG337TzsHcMx5vlCk/MnGn8x6Sqz\nv9OtfiQmhhny1rPdrg1MQnjQLiChpZg0Jj7UkNuWpblMQmyYIbctSYKEuCA7sWEGzYkQzDmehNhQ\nQ+5WCOadKzhXG9yVNiEudI4eICnYTnzonNeeiQnhhs/xcWHaNvjZkZwYzIQaWiYAhlLkAHFxYdr2\nVo3RbecEiI8PN7RMALRX/QEmjJjYz2eU6GiyPIEf/iyPDXeIca64uFDig+5PUvBccWGG1gvznde8\nTNB5xcXOnSv4GsbEhMxlguxERVmJj/98JjLSOue5C74+EeGWuXYSjXbCwsxzns3g6xMSYprLBNmx\nWmUSgp6p4Otjschznt+kxHCDLsVsluZlgv379zL+ztr6kZgYHrS7Ssy5z0kJ4QZNmSTNZRIT5vr3\nXCbcoKkQYu51TYgPm6MJCraTEBc2178T58aJOf4dP59//54YEBNiaJkAkBj0jMVFhxAZZgliQucw\nURHGGJAYM5eJiQxmjP4eG2kl5vfYiY20EhtlZBLmMCHEBs8VG8REhcyxExyPY6KsxAXFraSg5zAm\nMkTbcv+7mKhIC/FB8ycF3YvICMucePPF+OPGX8QiRwjB2ROLOXeimYy0KCQhyM+Lo/W5RRx+pkbd\nTm2ROX2skdbji8hMj0IIQW52DKePNnF8fw1msyoeO3GontNHGtVS4wKyM6I5daiR4/68rNkkcWxf\nLacO1pOTGY0QavntU8/W8/wzdVj8zKHdCzl5oI7crBiEgIzUSE49W8/JA/WawPbgroWc3F/HgpxY\nhIC0lAhOPavmyGeZfdsrOHmwnsK8OIRQe8ucOdzA2SONWC2qmHfvtnJOHqynOD8eISAlKZwzxxp5\n6fnFWK0qs2drGaePNFJalIAQ6o/sueeaePmUqvGQZcHOLWWcPt5ERWmSurhKCOPFk8185fxSQv3M\n9k2ltD6/mIUVyepCLj6Ml88u4bVXHiEs1IwsC7ZsLOHsqWZqqlM15ksvLuP1V1cQFqYyG9cXc+bU\nYupq05EkQVxcKK+cX8YbX1lBeLjKrFtTyJnTLTTWZyBJgtiYEL788nLeeG0lEREWtRv86nzOtqra\nFUkSxMSEsPhvv0wt/fzP2/+T1s7v8jd3/x/i/9tXWdKcjSQJoqOtvPblR3j91RVERlqRJMGK5bmc\na21h2dIcJEkQFaUyr315BVFRKrNsSQ7nWlXtiiwLIiOtvP7qI3zlS48QHR2itlVYnMW51hZWr1qA\nLAsiIix89SsrefVLy4mNUZlFjZmcbW1hzWMFyLIgPNzCV19bwZdfXk5cbCiSJKivS+fs6RY2rCvy\nM2beeG0lX3ppGXFxKlNbk8aZ081s2VSCLAvCwsy88ZUVvPziMhLi1QV+dVUqZ0+3sG1rGbIsCA01\n89qXH+GV88tI9C8AKiuSOXO6mZ1PlPsZE699+RFePLdUXSQIQXlZEmdOtbDnyUpkWRASYuLVl5fz\n8vmlpCRHIAlBaUkiZ083s++pKkwmiRCriZdfXMaLZ5eQmhKJJATFRQmcPd3Cwf2qX1qtMi/5dU1p\naSpTWBDPmVMtHD5Yp/nu+VZV05WR4ffv/DjOnm7h6OF6zH6m9VQz51qXkJUZjSQEebmxnD3dwvPH\nGjX/PnViEedaW8jOUjvM52THcPZ0Cyeea9KYF443cba1hdycWCQhyMqK5lxrC6dOLsZikTGbJY4f\nbeDs6WYW5MUhCUFmRjTnzy7l3OkWlTFJHDnUwJnTzRTkxyMJQXp6FOfPLOF86xLVd00SB5+p5czJ\nZooKE5CEIC01khfPLuHFM0tU3zVJPPNUFa3PL6K4UPXdlOQIXjzdwiutLYRYTZhkiad2VtB6fBGl\nxYmqfyeFc/7E4jn+fepwA+V+JjE+jHPHmvjSiWbNv7etK+LkgToqihORJEF8bCjnjjbxyrEmjdm4\nKp8Te2uoKklSmZgQzh5s4OVDjYSFmJAlwdqluTy/q4rqkkQkAbFRVs7sreGl/XWEhZqQJMHqRVk8\nt6OS2pIkJCGIjrRwZk81L+2tITzUrPplfQbPba+kvlSdKzrCwpndVZx/qlpjltWkcXxrOU3lakyK\nCrdwdncV5/dUExGmMksWpvL89nKaK1OQJEFkmJlzT1Vzbm8NkeEWtWXCwlSe37mQpf6YFBFm5qUD\ndZw/UE90hMo0VaZwYk81K5qyNOaVI028dKSRGH+caFiYysn9taxemoskCcLDzHz5xGJefmGxFgPq\nFqZw+kgj6x7NV/07zMxrZ5fw0slmLQbUVKbSeryJTWvVGBAWauK1F5fycmsL8fFfLHT+VOMvIl31\nV3/9N697RRVCEmr7A6G+4k1LieRbP7iF0zXFDNDT58RkkvjFhU6QBKNOL6lJEXz7R7dwTkyhAA/7\nnVhDTPz8g06ELDHm8pKUEMZ3f3aPMdcUiqS+Ug0LM/O2n3G6pkiIC+X777QzqmMiwiz89IMHCJOE\n0z1NXIyV/3j3vqr3kSUe2saJjrTy1oUHCLPMhMdHTKSVH717H7vTgyIJegYniIsO4YfvdaiM10dk\nuIUfv3ufoTE/MzBOfEwo3/9lO8Kvt4kIt/CTX7YzaJ9EEdAzME5CXCj//pO7CEl9nRwaauZnv+6g\nf8iFIgQ9/U5SE8L5tx/cBP8r59AQE2//8j69A+MoQE/vGGkpkXz7ezdQUPU2FovML9/toLvXiYKg\np9dJRloU33zzmsbIsuDd9zro7HKgKNDT4yAzI5p/+dZVf8XbaYSACx920dExojIPHWRnxvDP37zM\nzIyC2z3NzAx8/Nse2trtfmaM7Kxo/vlfruDzM1ntl8m8coF3YqvwSGbspkiibl/h/7Dl4PMpagVi\n7zRXrw5w+44NRYGHvU5ysmP5x3++pDGTk9PcvDXIjZuDKIrazTs3N5Z/+MYlpqdn8Hp9TExMcefu\nENeuD6jdonud5OTE8I/fuMzUlMqMOT3cv2/n8tV+ret0bk4M//CNS0xNzTA15cMx6qare5SLl9R0\n3cDAOLk56lxer1pN1j4ySW+vk08/6zUw//hPl7SKs0PDLmxDE3z8SY/G5OTE8g9+Znp6BpttAvvI\nJB/9phtFUbf85+TE8o/fuKRVwO3vH8c57uGDD7tQUJns7Bj+6RuXmZxUmb5+J5OTU7x3oRMFNYWT\nlRnDN/7lMhOuKbWbd58Tj9fHu+91oKCmYjIyo/jnf7nC+IQXn0/h4cMxfD6FX/7qPgowbJ8kPT2S\nf/7mVcbHvdrWayHg5++0o6CmedLSIvnXb15lzOlRmZ4xTCaJt3/e5k9Fu0lNieBfv30Nh8Pj31Y9\nhsUi85O372mp6OSkCL795nVGR90aEx5m5kdv3UEBHA4PCYnhvPmd69hHJpmZUejqdhARYeWHP76N\ngqqliYsN5Tvfv8HwsMp0d48SHRPCD350G4RaOiAm2sr3f3gL25BLtdPjID4ujO/98BYItXRAVKSV\n//jxHQZtE9pW8ISEML77g1uAykRGWHjrF20M2CY0v0xKDOe7P7oFQjAxOUVoqJm33+2gb3BC9cs+\nJ6kpEbz5o9sB/7aa+MWHnfQNqRq7h/3jpCVH8p2f3UURgkmvD4tZ5tefPaTXpjK9tnHSkyP4zjtt\nKJKEe3oGWRZ8eK2fniEXyBK9wy7SkyL47i/bUCSBZ3oGIeCT2za6bAEmIzmC77zXgSILvDMKMwgu\n3x+mc2gCYZLoH50kIyGc717oQJFUxjejcO3BKA/8zMCom8ykcL77wQMUWWIKmPLNcLNzhPZ+J0IW\n9DsmyUyM4M1f32dGwJSi4Jnycafbwd3eMZD9dpIj+NY7bcwIwZQCLs80bV2j3OocAUnQb3eRlRLJ\nN396l2kFpmYUf+pulOttwyAJBuwustOi+Jf/uMX0jMo4xj10Pxzjym0bSKrkITsjin/+9+tM+RSm\nZxRGHG56+5x8dnUABcHAkIucjCj+6VtXVP+enmHI7sI27OKTi730PvjhF+mqP8H4i1jk/PV/+ZvX\nzeENuNxTWu4fVA3FvY6ALsTh9DDp9TE4FGhV7/ZM0/YgwIyNe/FM+RjQM95p7ul6jjgnvLi9PvqD\n7eh6E024pvB4p+mzBRiX28i4JqfxeH1GZnKKe7rjmXRP45mapncwiNGd16RnGq/Xx0Ndf5XxCS93\n2wPFot2eabyeaXr6AjqD8XEvd3SMx+PD456iW6czGHO6tdob4C9P7p2mqyfAOBxGLYvX68PrmTb0\nahp1THJbp1OZXQDoGbt9ktu6nkuzC4kHums/PDzB3XvDmm5HZWbo6Axcj/p773FPTuDvM9ZxKSqf\nq5F57Lv1Jv9f0iqNGRycoKNjhGmfqsnx+RSmpnzc113X/n4n3d0OTVQ8M6Pg9RqZ3r4x+vrGtVLr\nM4rC1NSMoQfVw4djDA6Oa2LgGUXBG8z0jjE87NKEvooCU16fVmNl1s7IyCROv25HUWBqysc9HdPX\n52R0dFIT8QJMeacNdvoHxhkbczOq6+vj9U5r4mRQFzVOp0cT6KqMz6B9Ghpy4XR6Nd0OqOX09Yx6\nTl5DjzCP22foz2MfmcTlmsKm8wOPx6fVhQFVXzfhmtJ0O6DW7tEzDoebEGzNCwAAIABJREFUyckp\nBnR+MBnEjI15cLun6e8f19mZ4o5OG+F0enBPTtPXH/CVSdeUwQ/Gx724PdOatgfU9gx6OxMTU6pf\n6rQ9Ey4j43JN4fZOG5mJKU0Ertqdxjs1Y9D/OCc83NVp3tzuabzTPnp0dpwTXgOj/lD6DDFgbMJD\nm86/vFM+vL4ZunXXxzHmoa1bz8ww5VPo1l1nh9ND28OArmhqeoZp34yBGRnz0KY7vmmfwpRvhu7B\nAGMfc3O/36kV6vTNKExN++jW3ffhMTedAxOaLk9lZujSxUibw03XwJjW2mbGb6dTdzyDI5P02Ma1\n9g8ziurfnbrr0z/son9wAo8/BiiKeo06dPGv1685m20JoSiqr9zvClyP3oEJ1RcmA/7t9fhofxC4\nrr39qgZufMKrszNt1DYOjDMy6mbM6flikfMnGn8R6SpQc5X5uXGG7woWxBty2+FhZvJ15fYBCvJi\ntS17oJaCz882MvnZsYTqmFCraQ6zICvWkNu2WmQWZMcamPzMGENu22KW59rJjCFS12HWYpYozDae\nV15mDNG6XLJJlijINc6Vlx2jtWcAVWdQuCDITnasIU8sS4Ki/AQjkxNryEFLkqC4IJiJMeg+JElQ\nUmhkcnPi1M7G/iGE2v7BYCc31tAyQQh1S7aByYsjO8t4zYIZJTOTqokOZEUNTDXOe4zHJRuY3JxY\nZjuX/y47ubl/APMH2MnJidG20/8uJisreg5T4k8rzI6MjChDKwiAkhIjk5oaqXVS19vR61KSk8JZ\nkGdkiosTDbqUhISweRm9LiUuNpQFQc9UcVGiQZcSExMyD5Ng0KVER1m1UgKzo6gowaA7i4y0UpAf\nxBQmGHQpEeEWrfu7xhQkaFvuQY0BwUxhQby25R7UVg/6dhoABYXxWvsVULdNFwYzC+IN2jSrVdY6\nzWtMfpxBm2axyIay/QD5C2IN2jSTSaIoaK78vHitFAao/l0UdF4LsmO1Uhig+nfhAiOTlxlDgk7j\nIUmCoqD7npsZbdDzSUJQEBTbctKjSNVpTIRA2/atMWlRpOu0RUJAUaaRyU6JJCNI11WQYWSykiLI\nCNIxFWZEz2EykyKNTNBcWckRZCUbmaKgY85KiSQ71cgUB517Vkok2WlRRiboGmamRpIddIzFC+IN\nvpueGmloBQFQ4k9Rzo7U5Ajygub/Yvxx4y/iTc7/9t/+x+v/1//5Ck9sKuGD33bjdvsoKkjgqy8u\nIyLCwvXbNkJCTJw60sCOjaV89FkPk+5pCvJiee3MEmKiQ7h+24bVIvPCwTp2rC/h48t9uCanyMuO\n4dWTLSTEhXLtjg2rWeboU1Xs2lDCJ9f6mZicIjczmq+8sIik+HCu3rFhMcsc3lnJk+tL+PTGABOT\nU2RnRPHq8cWkJkdw9bYNs1niwPYK9qwr4dObg4y7vGSmRvHqsSYy06K4fGsQs1nmma3lPL2plIu3\nBnGOe8lIieS15xaRkxHNxZuDmEwSe7eU88y2Mi7dHGTM6SE9JZLXTiwmPyeWz671qzn7beU8+2QV\nl28OMDrmIS0lkq+eaaG4IIFPLvciyxJPbinj8NM1XLkxwIjDTWpyBG+8vJyykkQ+/uwhsiTYubWM\n4wfruHp9APvoJClJ4XztyytYWJ7Mbz7pQZYET2wp5bkjDdy4ZWNo2EVyUgRff20l1QtT+ejjbiQh\n2LqljBPPLeLWbRtDQy4SE8P5+hurqK9N58PfqBWfN28s4dQLi7lzd4jBwQniE8L466+uorE+kwsf\ndSEErF9bTOvJZu61DzMwME58fBhH//s+Mr7xd2zp+gXLRq6ya/A9Yv/2v9MRlUlfn5O4uFC+/tVV\nLGnO4n1/Vd3Vq/I527qEru5RevucxMaE8vXXV7F0SQ7v+9MxKx5ZwItnlvCwd4yeh2PERIfw9a+u\nYvmyXN7/4AHKjNrh+qVzyxgYHKer20F0VAhvvL6SlY8s4L0PHjDjU1jSks3L55cxNDxBZ9coUVFW\nvvbaKlatXMB773cy41NY1JTFl19ezsjIJB0PRoiKtPLGaytZvTKf9y6oFZ8bGjJ49ZVHcPrTYRER\nVl5/dQWPP1bA+xc6mZqeob4una986REmXV7a2u1EhFt47dUVrH28iPcvPGBqaoaa6jRef3WF9hYm\nPNzCq68sZ8O6Yt6/8ADv1AxVC1P46qsrmfbNcOfuEOFhFr788nI2rS/h/QudeL0+KiuSeeMrKwG1\nQnFYmJlXzi9l6+ZS3v+gE4/HR1lpEm+8thKzWebmLRuhoSZePLeUbVvKuPBBJ26Pj5LiRL722kpC\nQszcuDFISKiJ82fUmjgXPuxk0j1NcWECX3t9FeERFq5dHyAkxETrqWZ27Sjng4+6mJycpiA/nq9/\ndRUxMSFcvdqP1Spz6sRinty1kA8/6sLl8pKfF8fXXl9FfHwYV672qTHg+Sae3l3FR7/pZmJiirzc\nWP7qjUdJTorg0uU+LBaZ40cb2fd0FR/9tofxcS+5OTF8/Y1VpKVGcvFyH2azzNHDDezfW83Hn/Tg\nHPeQnRXN1197lOysaD692IvZJPPsgToO7Kvhk88eMub0kJkRzddfW0VuTiyfXnyIySRzYG81z+6r\n4dPLfTjG3GSkR/G1V1dQkBfHJ5d6MckST++q5PC+Wi5d7WPUoabq33hpOUV6/95WxpGna7h6y+/f\nSeF89ewSSgsT+ORKH5Ik8cS6Yg7vruL63SFGHG6SE8J47cRiygsT+PT6AJIk2PJoAYefqOBWhx27\nw01SXCivHm6koiCBT24OIAnB+qW5HNlWwd3uUYYdbhJiQ/nSgXqqChL45LYNIWDt4mwObyqjvXeM\nIYeb+OgQXn66hpqCRD65o+74erQugyMbSnkw6MQ26iY+yspLu6upLUjkk7tDCAErqtM4sr6UnqFx\nBkfcxERaeGlXFQ0lSfz2jrpjcFlVGsc2ltE77GLA7vr/2XvPIDmuK8/3l6Z8VVd3V3vvu9Heox3Q\ncA3vDQlHECAJGtGAohnNyMxoY2d3IvbDxuybeLERG/FGGo3MGJmhKIkiRUoUjUiCBAkS3gNt0N6W\n9+9DFrIyC9wlQ6vVBid0I/AhK359701zTl7k+d9zSLcb+fNDbfQ05HLy/BRxYGVrAU/saWJizsft\nGS/pdiNfPdpJX2sB755RdnQOtOZz4mAb0wt+xiY9pNmNfO14N4NdRfzu9DixWJy+tgKeOdbF7KKf\nkfElHHYjX3+8l9W9Jbx9apRoNM7ytgK+8lgP84sBbo0qzF9+eYB1g2W89d4IkWiM7rYCvvr0AB5P\nkBu3FrDbjPzlV1ayYW0lb/5umEtnf/SnLzl/gPaFWOT89X/+229OLtax5Anz5slRIrE403N+REng\nuz8+hy8QIRSJcfayknr7jZOjRGNxZhcCCKLA91+8iCcYIRyLc/bKLMFwlN+eGiMKzCW26/7TSxfx\nBBTm/LVZQpEYr384RlQQmPeGiMbi/MsrV/AEo0TicO66sn3xNx/eJiYKLPrCRGJxfvjaVZYCESLA\nhRtzRGNxXjs1SlQQWPSHCUej/OjX1xRGgAs354nH4/zqvRGigsCSP0wgHOHHryr6nzv9iHH45Vs3\niQJLvhCBYJQf/fIyc+4QkThcuDaHKMLPX7+RYML4/GF+/ItLzC4EiMTiXLg6gyyJvPDKFSKxOEve\nMG5PkJ/87CLTsz7C0RgXrsxgkiV+/POLRKJxZbu4O8gLP7/E5LRXYS7PYDJK/PDfLqjM3EKAn710\nifEJD+FojIuXZ7CaZf75h2eVbZmeEDMzPn75yhVGx9xEIjEuXVFelD/4508IR2J4PCGmprz86tdX\nGR5eJByOcfnKDDabke//U4Lxhsh782XSr57jvxbv5qKtmEuWIkp/82/8x6kqwpEYXm+YsbEl3nx7\nmGvX5wiHY1y9NovDbuQfv6doaby+MMMji7x7coQrV2eVENS1ORwOI//wXUVL4/OFuXFzgVMfjnHx\n0gzhSIzrN+ZxOIyqlsbnD3Pt+jynP5ng/IVpwpEYN24u4HAY+dY/KIzfrywuzp+f4sy5ScKRGLeG\nF7DZDHzrOx+qzKVLM1y5OsvHn0wQjsQYGVnEZjPw99/+kGCiQvmFC9PcuDHPh6fHiURijI4uYbMY\n+P++/SHBoMKcOzfFyOgiH5xS8uWM3V7CbDbwrX/4kEAgojK3by9x8v0xpWzJuBuzWebv/+FD/H6l\nYvqZc5NMTHp49+RIQqPjwWSU+Na3P1SrxZ89N8n0jJe33xkmEokxOenBaJT5+384hc8XVnIfnZ1k\nft7Pm2/fIhKJMTXlRZZFvv2dD5WwbzDKmTOTLCwG+O2bNxVm2oskCnz7Ox/h8YZUxuMJ8ZvXbxCJ\nxJiZ8SEKAt/+x9O4PSFCoSifnJnEHwjz2q+vK8ysDwH4znc/YsmtMGfOTBIIRPjVa9eIRGLMzvmJ\nReN853unWVoKKv2cVe7By69cJRKJMTfnJxKJ8b0ffMzCQoBQKMrZs5NEY3FeevkKkUiM+fkA4XCU\n7//zJ8zPBwiFo+rW/p8nmIWFAMFAhH/68XnmFgKEIzHOXphGFEV+9vIVItE4i4mQ27++cIHZOT/h\ncIxzF6eRZJEXX7mqMO4QXl+IH790iZl5v2qXBqPET1+9mrDvEG5vkBdeu8b0fIBwNM7F63OYzDIv\nvn6daDyOxx/G7Q3xi7duMTnvJxKLc+nWPGazzE/fuKEwgQgL7iCvvD/KxHyASByujC5itRr46Tu3\niAoCvnCUuaUgr58ZZ2IxQFQQuDbhxmqWefHdYWKCgD8cY3YpwNvnJhmfDxCLw807zHsjxAWBQCTG\n1EKA9y9Pc3te0RvemvJgM8n89L1h4gIEozEm5v28f3mG0VkfMUFgeMaLzSTzb7+7RQyBYDTO7Tkf\npy7PcGPKQxSlH7tZ4l9ev0Y0DoGIEkr7+PIMV28vJRgvdrPMP/3yEuFYnEA4ys1xN2cuz3Dp1gKR\nOAxPeLCbZb77wgXC0RiBUJTrI4tcuDzDuatzRGJxRsbd2Cwy//ijs4QiCnMlkc/qk4vTRKJxRsfd\nWC0y3/7Bx4TCCnPhyizXr8/z0ZmJP4Wr/kDtC7HI+c9/87fftGf2gSgqybASTZIEhjUx4EAggiAq\n9VlURhR1Mdhgoo7JlKYfQYDhFEaURCY1DAK6+HM4EkOSRCa0DOhi3eFIDFEUmNDMJx7X9xOJxpAE\nQRH9JVosFtfNJxKNIwFjmth2NBpleMytOY4jiYqwUDv+sCaHRzQWRxIEXVw/HIrqcnjEYnFkSdTp\ndkKhiJLDI4XR9h0IRtREe8p5JhjN3/n8IbXu0J1rIUuiTrfj8YYYGV1SNTnxuJLh9Jbm77rHPmBE\ndPKj3BXctOQxbM7m6I2f8q28IZVZXAoyOelRNTmgFMi7dUurIwowO+NTNTmfxszN+1lcCKianDuM\nTkc058PjDqqanE9lZn34fGFVk6Mwoo6Zm/MTCERUTc6nMQsLAYLBiE6TI8t6ZjHxotZqcmRZ5KZG\nH7DkDhIOR9VcOgojKPmREk0RBcd0mhwpZSyPN0QsFtdpciRRz/h8YWKxuE5PJ0qCnvGHVZH0nSZI\n6Jg7eUq0mhxB1Pej3CdBrbelDKbvJxiMIoqCTpMD6O57KBRFFEWdJgf0/YTCUSRZ5LbGnuJxfT/h\ncAxJFnWanGgszq2RpH1FIjFkg6izy2gkxrDGBqPROLJB0ultIpEYIyn9Gox6JhSOMaq5FrFYHKNJ\n0v0WDEUZ1fqfuPL8av1NIBRRRMea8zQYJcY0ukV/MMJtzbNyx3bHNH/nC4SZmPOrmpw4YJAFxjTP\njzcYYWrBT0xTYVeWRB3j9oeZXvSrmhwAWRQYnU4yS94QM4sBwhofIAkoyQATbd4TZGEpqGpyFEZg\nWPNszC0FFB1XMKrrZ/h28v7MLSq6szuaHABZELiluYdzC4qm7I4m586ctb51YTFAwB/5kybnD9i+\nMJqc/Fw7XW35ut+WtxeSrslxkJNlpbNZz3S35JGhiX9nZVjoasrTMV1Nebo8CJlOM50Neo1HZ30u\nWZr4d7rDRGci9fed1r4shxwNk2Yz0p3ST3tdNnma+LfDaqCrMYVZlkOhJiZttxhY3qI/r7b6XIo1\nsWSbxUBPW4G+n8ZcyjRxYqtZpr+rSM8051Op0YqYTbKaZlxlWvKp0egBTCaJgb4SPdOaT71Gg2M0\nSqwcKNUxHW2FalkFUHKjrFyRyhTQ0py8P7IsMriiXBe3FpubWLV0FntEcWhbZt5jsaRap0tpb82n\ntTV5zSRJ2SL+v2LubCPXalfaW/Np0zCCAIMrynTalbaWfNpaC+5mNNqVlmY9A7ByRZlOl9LYkEt7\nyj1c0V+q06XU1WbfzQyU6XRn1VUuteyEyvSV6nQpFeUZdHUU6piBvlK1FARAWWk6nR36fvp7S7Br\nNGUlxU46U/rp6y3GodGlFBWm0d1ZlMKU4NTYbn6+g+6ulH6Wl5Cu0aXk5tjuYnq6i3W6lOxsGz3d\nRSlMkS7fT5bLyvJPYbS5ajIyLPQu1zPdnUVqeQaAdKeZ3uXFKUyhWp4BlFIufalMRxFFhUmNh91u\npK9bz3S0FVCisV2bzUBvKtOST5lG42a1yPSlXOf2xly19AKA2STR25riS5ZlU6XRipiMEn3Neh/Z\nUpOt07MYZJHeFN/WXOlimZaRRHrq9D6yqdzFMo3mRJYEuutydPbdUJpBvYaRRIHu2mzEVKYkyYii\nwPK6HD1TlkmjRuMmCtDbkKvzAU0VmTRp9GKCAP0tebq8ac1VWTTXZOuYgY4inQ9oqsmmJUWDONBV\npKun1VCTRVuKrx9YXqzTldZWuWhv0V/7P7X/vfaFWORIosDDRzvYv6ue8rJ0TGaZZTVZ3LO9nvv2\nNWG1GrDbjTx4oIV7ty+joiwDk1mmpsrF3i3LOLKnEZvNgM1m4Oi+Ju7ZVEtlWQYmk0xVWQZ7N9Rw\n/+4GbDYjNpuBI7sa2DtUTXV5JiazTGVpOnuHqjm6sx673YjNbuTQ9mXsXF1JTUUmZotMeYmTfeuS\njNVm4MCWOnatrqKuyoXZIlNa7GTvUA3HdjVgdyjM/s217FpTRX1NFmaLTEmRk3s21PDgniYcDhNW\nq4F7NtWyY20VTcuyMZlligvTOLh1GccPtJCWZsJiNbBvax2719fQ2pCD2SxTVODg0I4GHjncpjAW\nA7u31LFzUy3tLXmYzDKF+Q7u29fIo8c6SUszY7bI7N6+jF1b6uhsL8BkksjPs3P/gRa+9FAnTqcJ\ni1lm19Y6dm9bxvKuQkxmmfw8O8cOt/HYw904nSbMZpntW2rZub2e/r4SzGaZvDw7Dx5t50uPdpOe\nbsZsltm2uZZdO+pZsaIMs1kmJ8fGg8c6efyRbjIyLJjNMps31rBzxzIGV5RhMknkZNvo++ZxXGb4\n5emv8fPTX+fRsV9Q+JfPsHqwHLNJJivLyiPHu3js4S5cmRbMJpl1ayvZtaOedWsqMJtkXC4rDz/U\nxaPHu8hyWTGbZNaurmDXjnrWD1VhNslkZlp49OFuHn6wk+wsJTnbqsFydu2oZ+PGaoXJsPDoI90c\nf7CTnGwbJpPEyoEydm5fxtbNtZjNMunpZr70SDcPPdBBbo5NXSTu3lHPti1J5vFHu3ngaDt5uXZM\nJonenmJ272xg57ZlmM0yTqeJJx7r5oH7O8jPc2AySXR3FbF7Zz27d9djNsukpZl4/LHlHD3STkGB\nwnR2FLB7VwP37GnEomGO3NdGYYJpb81n9+4G7t3XhMUs43CYFF3K4TaKi9IwmSRamvPYt6eRA/ub\nsVgMOOxGHntkOUcOtVJa4sRkkmhqzOWevU0cPtiC1aLY5aMPd3HoYAtlpemYTBIN9Tncu7eJI4db\nFcZm5JHjXRza30x5WQYmk8SyumzuvaeJo0faFPu2GTn+YCcH97dQWZGJySRRW+PiwL1NPHC0HavV\ngM1q4KFjHRzc30x1ZSYmo0R1lYsD9zTz4LF2bFYDVquBB462c+DeZmprXJhMElWVmRy4t4XjD3Zi\nsxmxWg0cO9LGvfuaqKtVxM8V5RkcOtDCw8c7Ffu2Grj/vlbu3dtEfV02JpNEWWk6B+9t5tHjXYp9\nWw3cd7iFfbsbaazPwWSSKC1xcmh/M48+qPRjMcsc3NfEnh31NDcqTElRGkf2N/PoAx04HEYsFpl7\ndzWwd2sdrY25mEwSRQUODu9t4pEj7Qn7ltm7bRk7N9TQ3pSHySRTkOfg8J4mHjnYSppDGWvXhhq2\nr62mvTEXk0kmL8fOoW31HN/TiNOh2O62VRVsXVlBZ4LJzbZxaHMdD+6sJ92pjLV5oIxNPaV01+di\nNsnkuCwcGqrh6MZa0h1GLCaJ9d1FbOwuprchB7NJIifDwoE1ldy/vppMpxmrWWZdRxEbOorob8jF\nYpbJybBwcHUlh9dUkZlmwmKSWdVSwPqOIvob87CYZLKcZg6uruS+tdW40swK05zPhs5iVrTkYzFJ\nuJwmDq+r4sj6GrLSFWZlSz6blpeypr1QsV2nmaObarl/cy1ZGUpy1YG2Ajb3lzOU8FsZ6WaO7azn\n/h3LyHYpTH9bAVsGy9k4WK7YrtPMQ/uaOLq3kRyX4if62gvYPlTN5jWKL0lPM/HwoTbuv6eZ3ISf\n6OkoYMemWrZtUnyAM83MYw90cvRQG/l59s9+Mf6pfa72hQhX/fXf/O03b87UMDXn49QnikBsdsGP\n2xfiBz+9QCgSIxyNcerMBDMLAd4/q9RqmVtS0pz/80uXCEViRGJxPjw/xZw7xMlEPZd5T0hhXr1K\nKBYnAnx0aZp5X4iTF6aICQILvjALniA//O0NgrE4UUGpebLkC/PepWliosCSP8K8O8CP3rhBIBon\nKgh8cm0Wty/MOxemiIkC7sAd5jqBiMKcuT6H2xfm7XOTChOMML3g50e/voYvHCUKnLk+h9cb4o2P\nbhMTlH4mZ7388JWreEMKc/bqDF5viN+cHCUGePxhJma8/OsvLuHxR4jG4eyVGfzeEK++dZNYPI7H\nF+b2hId/ffECS94Q0RicuzSN3x/m5V9fIxpTmOGxRX78wgUWloJEonHOXZwmEIjw0qtXk8zIAj95\n4Txz8wEikRjnL04TDEb52S8vE43F8frCXL85zwsvXmR21kckEuPCpRmCwQgv/vwS0Wgcny/Mtetz\n/Pyly0xNeRXdzmWFeeHFi0SjSj95L/0QYXKCR2ue5FVXB++nVdP+wv/gPy42EIkqWprzF6b59es3\nGLvtJhJV9DahUIQf/eQ8kWgMvz/MufNTvPHWLUZGF4lEFb1NKBThX390LsFE+OTMBO+8N8LNW0rN\nrZs3FwiGIvzLD88qTCDC6Y/Hef+DUa7fmCcajXNreIFQKMo//csZIpEYgUCEDz8a56PT41y9Nkc0\nquRhCQYj/OCfk8wHp8Y4e26KS5dn1LwwwVCU7/3TJ0QiMYLBKCffH+PCpWkuXJxWctDcXiIYjPDd\n73+sMu+9P8qVK7OcOz9FNBrn9ribQCDMP37/Y8J3mPdGuH5jnjNnJ4lG44xPeAgEIopmKbG1/92T\no9y6tcDpTyaIRuNMTnrw+8J853unCYejhEJR3js5wvDoIh9+NE40GmdqyovXG+I73zutpBoIRXnv\n5Chj40r+n2g0zvS0F48nxHe+e5pgKEoorPQzMenh5AdjRKPxxPb1oMIEFebkB2NMTXt5970RotE4\ns7NK2ZQ7TDgc4/0PRpmZ8fG7dxVmbs7PwmKA73zvYwKBiMKcGmNuzs9bbw8rzLyfuQU/3/3ex/j9\nYcLhGB98OMbCQoA33rpFNBpnfiHA7KyP7/7gEzWP0AcfjrPkDvD6G4pQfGFRYb73L2fw+ZU8Qh+e\nnsDtDvKbN24kSmcEmZr28v1/PYPXG1ZqqJ2ZwOcP8+s3bxKNxVlyh5iY9PDP/3Yejy9MJBrnk/NT\n+AJhXnvrFtFYHLdXYX740iWlzlMszplL0wSCUV59Z5hoXPEBtyfd/OTVK7h9YaJxRW8YjER59b1R\nonHwBiKMTrp58c2bLPpCRONxLtycJxSN8eqpMWKALxhldMrDLz8YYdEfJibAlbFFwrE4r52+TQzw\nh2IMT3l47ePbLCTyll0bV2zvN2cmQFBy6QxPe3jr/BQLvjCIArcSOr/Xz00iiAKhaJybUx7euTjN\nnDcEgsDIjJdwJMavE/2EonGuT3p49+I0M+5gglHCzr86fZt4grk6vsR7F6eZXAwoucRmfQSDEX5+\ncoQYEIzEuDC8yPsXpxLaHhiZ9hIMRXnhDUX/GIzEOHt9jo/OTXJrwkMsDiNTHkKhKD/+1RWiiXw8\nH1+e5vTZKa6PLBKNxRmd8BAMRvjXn18kGosTDEX58OwEZy9Oc+WGouccm/AQCkX4wY/PE4kqzPsf\njXPx4hQXr8xy+8afwlV/iPbFKNCJEo8f1cRAAYbHltTaRACBYJSRlDj7yLhbzZMAShz9LmbCo2PC\nkRijmng0wKgmlwIoyahGp/XM2IyXQCjJRGNxXY4IgNFpL/7g/5oZm/bi1RRoi8XiDE+672I8mvhv\nLK7XFQGMTrhxa+K/8Ti6GDHA6LhSJ0XL3NRoZADGxj3MabQbADdSmDv1iXSMJreNwiwylXKuN26m\nMKOLaq2kJKMfi8lJLliKmDZlMA0syDast+Z0yNjtJbUm1Z12PWWssbElBO33bdDlyAGlppI5JS3+\njVRm3I3XF/5fMuMTbp0+6NOYqWkvsiylMPrzmpn1YUlJwZ/KzM/7dTlXQLnOcY3GYXEpqKu5dGc+\nWsbtvpu5fnNeLcIKim5ndFQ/1p0F4Z3m9YUZGVlMYeZ118Pvj+j0W3f60dl3IMJIynN3a3hBLbAK\nit7m1qcw2mchNX8TwPCtBZ3uKhyO3cWMjCyoNcwAotGYTucEMDy6iE9jl9FojFsjqf0s6rRZ0Wic\nmynnPjq+pNNuxGJxpSCktp9xt06/FY/Drdsp/Ux4WExlUvzE7Rky1ZSFAAAgAElEQVQv8+6g7rfh\nibuZWY+eSfVbt2d9zPtDekaj2QGYmPPhCertYCzF3qcW/HiD+gKVo7P6fiYX/HfZ92jKWJPziqBc\n24ZTfPbkvA9Dig+4lXLuk3M+vLI+6HEz5TpPzvgI+fRzTr1f03M+RP107vKjs/N+LIYvRIDlC9O+\nMFdzWXUWG1ZXqseCAFvXVlGsyV9QXZ7BxpXlur/btLKcEg1TUexkY4pWZENfKWUapjTfwcYeveZk\nfXcRlRqmOMfO+pQY+bqOYqo1cfSCLBsblxfr4s1rO4p0uSPyMq13MUOdRdRrcqHkZlrY3Feqizev\n6y6mWZN/IzvDwtbBCkRNR+v6SmnT6IayMixsW1elizcPraygSxOjz0w3s2NTrU6XMrSqgl6Nlicj\n3cyuLXU6zcnQmkpW9Cevq9NpZvf2Zbp8KUNrq1iluT9pDhO7d9brdClDa6tYs7pCPbbbjezd1aDT\npZiGVrNt/gNK/ZPIsSiPjv2MpbYeXb6UobWVDK1NPi9Wq4E9uxp0upR1KYzZLLNnV70uX8pdjElm\nz+4GXb6UdWv0jMkksXtnvU6XsmZVhY4xGET27GrQ6VJWrSxnaF2SkWWRXTvrdbqUgf5S1q+rSjKS\nyO6dDTpdSs/yYtYPJRlJEti9s54sTZ6Trs5CNm6o1jE7d9TrdCntbQVsXJ9kRFFg145lOl1KS3Oe\njhEE2LGtTqdLaWzIZfPGGj2zdRlFRUl7ql+WfRezc1udLmdSbU0WWzbXom3bt9RRpsmNVVWVybYt\ndTpm6+ZaXU6givKMu5kttbq8OGWl6Wzboh9r86Za6mqTNldc5GTHtmU62920oUaXI6kw38H2LXU6\nZvOGapo1epb8PDvbN9XotCIbVlfSqtFv5GTZ2L4+hRksp13DZGV+in0PlNKpYTKdZrYNluvse01X\niU47mO4wsaW/DFnDrGovpKc+yaRZDWzqLtYxgy35Og2O3SKzoaMIg0a70t+QR49Gu2I1yaxrK9DV\n8+uty6GnNtmPxSixrrUAk0HP9GrGMhslhtoLMRuSfqJvWS79mvMyGUQ2dRVj0fiSgcZ8Vmh0nCaD\nyLa+UmwaP7GytYBBjdbJaBDZNlipy4m2orOQ1Zp3hkEW2TlUTZrGT6zoKmbtQJl6LMsiOzbWku5M\n+oD+7iLWrUr6vz+1//32hVjkCAhsXFtBX2ehUuxOVOpJdbfms7q/FEESEWWR9YMV9LQVkJtrQ5AE\nigoddLfks7a/FNEoIRkl1q0oo7spn/wCB4JBpKDAQVdzHmt7S5BMEpJJYm1fKV31uRQVpiEZJQry\nHSxvzGOopwSDWcZgllndVURnXQ4lhWnIRon8XDvLG3IZWl6C2SJjNMus6SqiozaHsmInhoS+pacx\nl/U9JZgsMgaTxKrOQjrqFEYyKpqTnqY8NvSXYLTIyCaJlV1FdNTnUlqagWAQycyy0tdWyIYVZchm\nGdEoMdBdREdjHuXlGQiySIbLwoquIjatKsdgkhBlgb6uQrpa8hWHLwk4MywM9pSweV2VyvT3FNPV\nVkBVpQtEgTSnmdUDZWxeX6UsWATo6Sqiu6NQFSOnOUysHSxny8ZaDEYJBIHuriK6OovUxIJ2u5F1\nqyvYvLFGFeN1dRTS3VmkJg20WQ0Mratky8YaVYzX2V5IV2chDYnFmtVqoGn/WiwGgR+c/Rt+98HT\nrJ/7kOz9W1VRs8Uis2Gomo0batSFT0tzHl0dhbQkROdms8zG9TVsXF+tFjlsacqjq7OI1oTI22SS\n2bShmvXrqtXFUWNDDl2dhbQnRMQmk8SmjdUMratSRbv1y3Lo7iqiMyH+NRpENm+sZmhtJTabwiyr\nU/rpSjhPg0Fk88Ya1q6uUBdQdTVZLO8qpichXDUYRLZurmXdmko14Vx1tYvuriJ6E2JxWRbZurmG\n1YPlpCUWUFWVLrq7iunvVZywLIls21zLqpXlOBMOtrwsk+VdRQwk/gNwp7bY4MpyNSldeVkGy7uK\nGVxRpmFqWbmijMxEwrnS0gyWdxezelBx1KIosGVTNQP9pWrR0JJiJ8uXF7FmsAJBUJhNG2oY6C9V\nF1lFhU6Wdxezdk2CEQQ2baimr7dETUxZWOCgp6eEobVVKrNxqJre5cXkJTQN+Xl2+npKWD9UeafA\nNxuGqujtKVYXYnm5dvp6S9i4vhpREBAEZeHau7xEFQjn5Njo7ytVGFFh1q6uYHlXUkScnWVloK+U\nTRpm1WA53Z1FlCREsi6XwmzeUI0kCwgirFpRRndHoSo0zkg3s6KvlE3rqpEkEQSBFb0ldLcVqMnk\n0p0mVvaWsHFVBZIsIgjQ11lEV1M+FYkEpE6HiZVdxWwcLMdgFBEkgZ72Ajrq86gsSQdRsd2VnYWs\n7y/DYJIQJJGu5jza63KoKs1AkATS0owMthcy1FmEySgjSiIddTm0VmVRV5qBJCt1qVY257GuvRCr\nxYDBINFZk0NLeSZ1ZRnIBpE0h5GVTXmsasnHapGRDSKt1Zk0lWawrCQd2SDisBvpb8hlsCkPm1Vh\nmiszaUyIkWWDiN1mYEXjHcaAbBBpKs+guSyThvIMJFnEajUoYzXnY7cakGSRxnIXLZUuWqpcSLKA\n1Sqztr2A1W2Fap2s+nIXrdVZtNZmI0gCZovMuuXFrO4qVuxbFKircNG+LJu2+lwQBYxGmfV9Zazp\nK1FsV4S6KhftjXl0tOSDIGAwSqxfVcHq/lIcdiMIUFOZSXdrPss7CkEAg1Fk87oq1mps90/tf78J\n8Xj8s6n/y83uLI+3rPwm/b0lvP3BqPr70IoyXn13RD0WBYGVfcW8eWpM/W3N8mJePz2uHgsCrOwq\n5s2Pk78NthXw1rkJ9VO9IMCqjiLePDOhMv0NuZy8Mq3b1jjYnM+bZ5PM8rpsTl2Z0TErG/N4Q8N0\nVmfxweUZNWU5wGBTHr/RzKej2sWpizO67ZGrm/P41fvJc++oyeKjRL4F9Xp0FPLy726px+212Xx8\nflIXitvQW8ovfnNdPW6py+b8pWndp9/NgxW8+MoV9bi5PptLF2d0n/O3rq/mxZcuq8cNdVlcvzav\nC9vs2Fyj1PVJtLqaLEZHF3G7k5+0d25fxr/99IJ6XF3lYmrKw4ImPLZr+zJ+omG+FD5J8fA5/qLi\nKBIxar2j/O3It1m/7K9UprjISTgc1W0l3rWjnp+8cF49Lsh3IIqCLrSza8cyfvJCcqycbBtWq0G3\ndTiVycywkJFh0ZVxSGWcaSby8hxc0pTHSD13u81IaWk6585PaZg6/u2nyWtoschUV7r45Oyk+tuO\nbXW88GKSMZtkli3L5iPNc799ay0//dkl9dhoVETCpz68nWS21PHTnyf7MRhE2lsLeE/z3G3dXMPP\nfpG877Is0t1ZyO80drhlUw0/1zwbsiTSs7yIt343rP62aUM1L72cfMYkSaC/r5Q33ryp/rZhqJqX\nf5VkRFFgcGUZv3n9hvrb+nVVvPLqVfVYEJSvZq9pnvF1a5RjrX2vW1PJr167pjKrV5Xz2zdu6kJx\nG4aqePlXyb5XrSzjzd8N65iN66v45StJZsVAKe+cHNGF6zZvrOEXGqZveTEnPxrTMVs2VPMLzVg9\nnYWcOjelC9dt2VDNS79OzrmzOY8zV2Z09r1lXRW/+G3y+rQsy+by6KIuTcKW1ZW8pPETjZWZXJ/S\nh9o3D5TyssbX1hY7GV8I6ELtm5YX8+rp5PNTke9g3hvWhZrWtRbwG43/K8m24Q6EcWvSLaxuzOW3\nF5LPfEGGBV8wyoIv6ScG63P57fnkM5/rNBMKxXQhtMH6XF77JPnMZ6eZicdiTGp8yarGPF45lTwv\nl8OEjKALdQ21F/KLd5PXJ91uxC5J3NSE+Tb3lPCz15PPWJrNSLbDqCsPtHllOS9q7qnNYqA4x8YF\nTcmTrWur+Okvk7ZiMctUFDk5e2GKk7966FQ8Hu/kj9RaBFvcTfSzwUS7QfDleDy+8f/glP4g7Quj\nyYnG4rhTYsKLKXHkWDzOkkcfE17y6rUS8Tg6nYrChHRahHgc3L4Uxh/SLV5AydWgbR5/+DMZtz+s\nW+CAkrhPxySEhKlzTGUiKfHm1HN3+0I6BwhKfhQd4w3dFdtOva5ud0i3wAF0eVpAKU7oSznXxRRm\nyR3El3Kui4uBFCaAN+VcF5b0jODzMmVIA0EgisS00YkhpGfcniDh1PNa8qcwIVLC8XfNx+0JEk3R\n0iwu6s/L4w3pQneALkcNKLoUd8p1TWV8/vBd92chZaxAIPIpjL6fQDDyKWPpj0Oh6N1MyvUJh2Of\nOZ9IJHbX85J6DSPR2F3PwmLKPY1G4yyl/JZ6v2Kx+F3XPrWfePzu3xaXgnfZ96fNJ5Zic3f14w7e\nzaTMZ2kxoFu8wN3X7E7B0dQ5po4VSbXdlPkseYJ32fdiig/weMO6Bc6nMW5fWLfAgbv9psd/N+P2\n3c34U5kUn+D1h/GnzMcT0PsWXzCKLxT5DCZCMKw/99SxfMEIsRTb9aT4dW8ggl4Fd7fv9wYiIKbc\ni5R3kS8Qxp3iTFLvqT8Quevdk/qMBYKRu95zf6zmJspfU/rZYKId4nLWZ1P/99sXIlwFMNhbwsGd\nDWpuApNR4r7djbRqNCd97QUc3FKnxomNBpGDW+po18SAuxty2T9UrfZjkEX2r6umozbJtNdkcc+q\nSjWWLEsC+1ZW0KmpU9Ncnsne/jI1liyJArv7yujW5FOoL0lnz0AZRg2zq6+U3mXJOdcVp3PPigpM\niViyJArsXVHBSk0un5oiJwfWVWNOhHBEUeCeNVWs1cSJa4qdHN5cq4ZeRAH2ra9hoyYGXFWSzv27\nG1XNiSjAgW3L2Lo2qd+oKEnn2L3Nai4UQYADuxrYvTWpYSgvSeeBw21qyEQQ4ODeJu7Z3aAypcVO\nHjraoauvdXh/C/v3NanHxUVOjj/QqdOcHD7QysH9LepxYUEaxx/sVMMhANn372Pn/EkG5z+m3D/O\nX934HsHN28jWaE7uO9jK4UOt6nFujp3jD3Yp4U51rBYOHUyOlZ1t4+EHu3Sak8MHWzl0MNmPK9PK\n8Yc6KNDU6Tp0oIXDmn4yMy08/GCXLhfKgXubdUx6upmHH+zQ1fLaf08Thw8kGafTxPFjHbqaV/v2\nNHL4YKuq8XA4TBx/oFNX82r3znoOHWhRGbvNyPEHOnU1nXZsq+O+Q62qxsNmM/Dg0Q5qNTqvLZtq\nOKJhrIkt2lrNycb11TrGYpZ54Gi7Lh/S0NpKjh5pU3UgZrPMA/d30KrJxbJ6sJz7D7epi0WTSeKB\n+zt0+X5WDJRy9L5WlTEaJY4daaNboxfr6y3h6JF2VQtmNEgcPdKuhvxAyYlz7EgbxoTNGQwiR+9r\n1+V+6uwo5OiRdlUvJssiRw+3qaE6gLbWfI7d36bqxSRJ4L5DraweTOrOmptyeeC+VtUuJUngyIEW\nne6ioS6bY4da1ZCoKAocvqeZjRptWl21i6P3Nqv180RB4OCuRjZpmOqyDI7u0dv3/q11bNHo4CqK\nnNy3tQ67RWEEAfYNVbNN4ydK8xwcGqrGcYcB9qysZKtGc1KYZeOewXKVAdjZW8YmTc6kvAwLu/tK\ndcyWrmI2tCaZ7DQzO7pLSNMwG1oLdIzLYWJHVzHpmvxMG9sK2dSWZDLtRnb3lJKp0cBs7ihia1fy\nvmfYjexbUUFWWtLf7OgtZVd/mY45tLaKPI2/2bOygn1rkj4yw2HiyNZlFGj0a3vWVXOvRi+W7jBx\nbG+jLpfZ3s217N9erx6nOUwcu7dFl+toz5Y6Du5p1Gm4/phNFD//vy9K+2JMVYCCAgdZmVZMVgNI\nAlabkaxMK3m5dkSDiJjQ12RmWLA6zAgGCZvDjCvdQl6eA9EoIRol8vMduDIs2NNNSCYJu9OMK8NC\nUZ4Do0XGaJEpzHPgSjOTkW7GZJZJd1rISrdQnOfAbJaVPDQ5dlxOC5kZFswWAxkZ5gRjx2I1YLYa\nKMpV+snMtGK2GEhPV5iSPIfKFObacTlNZCbGcqaZcDnNFOc7MFlkTGaZgly7Mp9MKwaLjD3NRFaG\nhaJ8B7JZRjbL5OTYyXSacTjNCEYJk91IdqaVwvzkuWdl28hIN+NwmhAMAiabgewsq/IylkSQBLKy\nrGRkmHGkmRAkAWMif01RoRNBVpjMbBuuDAuONFMiliyRk2OjsDANQVTuV6bLgivTgt1hVmPSubl2\nCouciJKgMpmZFnWxJMsiebl2CgvSVCPPSDfjyrCqMWpJEsgozUUW4nx5+Mf83aX/l0r/bUwlBaQl\nnJckCeTl2cnPc6jGmJ6u3GfnHUYUyM93UJCfpgo1nWlmMjIs6qJLFJWQVn6uXX1BO50mXJlWdfEm\nispCLC/XoTJpDhOZmWbS0xVHKQhKQrzcXLv6glYYmyoYvsPk5NjVF7TDbiIry6Zb4BUVppGbY8OQ\n2IXlsBtxuayq3gWgqMhJTrYNQ+IlbrcbcWVayHIl+yksTCM726aOZbMacWVadQvFwsI0srKs6ove\najWQmWklOyvp3AsLHGS5bKqGymozkJVlIzs72U9BgQNXpr4fl8tKTm6yn4J8B1mJXESgFNLNyrKS\nm5NccBbkOXC5bJgTjMUsk+Wy6Ral+XmKn7ijxTJbZLJcVl3ekdxcBy6XVV1UmE0y2Vk28vOTi9K8\nXDtZLqu6qDCbJFwuK/l5yZdWbo6NLJdN1WKZTBJZWTZdodpslw1XplXdEWc0SrgyLRRqXn7ZWVZc\nmRZsNkWrYTRLZLmsSj8iICpMZoY1yZgksl1WCvIcympGFHC5rGSkmbDbjartZrusFOanJd5MAq5M\nKxlpZuxpZgRZxGgxkOOyUZhrRzSKCAYBV6aZzDQT6U4zkkHCYjOQm2mlMNuOwSgiG0SyM8xkOMxk\nOM0YDBJWq4GcDAsFWTaVcTlNZFhNuNLNGE0JJt1CvsuKyaxoErMyzDhtRjLTzRgSTG6GlbxMJU+W\nwSThSjeTbjOS6VQYi0XpJzfDgtEkIRskMpyJfpwmDAYRs1kiL9NCbqbyTMkGkUynmQy7EVeGMmeT\nSSLfZSU38WxKskC600S6w0S6w4wgCkiySL7LRm6WFaNJQpAF0pwmMtJMZGSYESQBURYoyLWTk2XD\nYJJAEnCkmcl0msl0WRKMSGG+g5wsa0K3mLDdDIsuWW1BnoOcLNtdX4b/GE3g3+ci54uhyUkvjzev\n+g90tRdy6lwyLjvQWcg7mngvQHdbAacuTqvHPU15nLwyo2N6mvM5pfmtszabj2/qt+EuX5bDR9eS\nv7VUZHIuZStoZ3UWH2m27zYUO7mQsnW3rTxTx9QVOjmf0k97WSbvX53RMWdTtjt3VGbyjiZuXVfk\n5Mw1/Zx7arN4U6PDqCtJ58KVGd2n+hVNebx+MqmfqC3L4MIlPbOqs5Bfv52MSVeVZXDt2pwuhLa2\nr4RXNbH/yrJ0btzQb/kdWlXOK68l49alxU7Gx/Vbu4dWV+o0FcVFTqanPboSCanaiMe9b5I2Pcrf\nlB0AoMQ/ybeu/h1rm/5aZbKzbYRTShuk9pOZYUEUBV1Jgg3rq3hZo59IS1MSIE5qUsGn9mO1GshI\ntzCmSXGQyphNMrm5Nl15ivVDVbyiYQwGkaIip25r+fp1lbzyalKHIUkCFeWZXNHE9YfW6vUloihQ\nU+3i4qXkM7VubQWvau6FUgE+R6f/Wbtar2UB5UvEJ2eSNrdmVTm/1mhiAFpb8jj9cdIOVw+W85vf\n6pmO9gKd/mdwRRm/1ehvQNnx9f4HST3dioEy3nxLzyzvLuK9k0lNxUB/CW+9PaxjenuKeUejEerr\nLeF37+iZ/r4S3tZohHq6i3lXYxegZJt+U2MH3V1FvK/R+wGsHCjjDc0cOzsKOKWxQVB2zb3+VrKf\ntpY8Tms0VaBcs99qdDLNDTmcuTyrY9asKOP1d5NzbqjN4kLKtv81A6X8VqOhqi3P4Oq4W8es7i3h\nDY0GsLIwjeF5ny4Ut7qjiLc1GpjSHBvTS0EiGmZlcz7vXkr62vwMC4uBMGFNKK5/WQ7va7RqOWlm\nPKEIQY2f6K508YHG/2bajfhDUV3oq7M8kw80ftRpNRAMRPFowuhd5Zm8eyU5nzSLgWgkxqImrNZd\n5eJtzTNvM8sQjTGrCS311eXwm4+Sz6rFKGEzSEzMJf3EYFMev34v+byYDBIum1FXsmd1ZyGvaZ4f\ngyySn27RbS1f01vCrzT2JIkCZYVpXL0+90fX5FSJ5vh/MX3+cNWewOU/6vx+3/aF0eQAylLzs5DU\n73yf529+v9l89tifd6zfYwJ/yM+ZAgJxko4p9Tz+T345/X3OI46AkLI2j3+efn7Pi/ZZ9/Vz9fo5\nh/6sKQqfs6PP8yx+1tift4vfZ6xP6/zz3cJU6vezud/ncflcf/N7jnb3af3hrE4A4inH/4eG+kK2\nz7Spz/Xe+ZxjfRb3f/lepGoU/z20L8xHpwM76nnsYKsab85wmvnSoTbW9yVXnnuGqjm+q1GNNzvt\nRh7Z1cjG5clY8vb+Mh7cVKvGiR1WAw9srGVDRzKuv769kCNrqlTGZpa5b3UlGzQx4MHGPA6urFAZ\nq0li/0A5GzT1ifrrcji4ooK0xJwtRoXZqhmrpzabQ4MVarzZYpQ4tKqC3Zrz6qnN5oH1NWQmwjpm\no8T9QzUc0mhpepbl8Mi2BrIToRazUeL49nqObUvGgJc35vH4/lZyE6ENk1Hi0XtbeHh/s2pb3c15\nPHmsg/yEdsVokPjS/R08/kCnaqBdLfk8/ehy9ZO70SDxxEPdnHh0ucq0t+Tx7BN9FCdyoRgMIie+\n1MOXn+hVmdbmPL78VB9liS2vsixy4olenjnRr2o8mhpzefbpflVzIssitV99jE3ujzl2+2XWzJ3m\nv179H8gPP6xqTiRJ4Jmn+njm6T61n7raLJ57ul/NhSKKAl8+0ceXT/SpYaaaahfPPT2gbmkXRYFn\nn+7n6af61M/HlRWZPPflARobclTmmaf7efqpXpUpL8/guS8P0JzQVQkCPHOijxNPJPspLUnnuaf7\n1bpYCtPPicd71RBScZGTZ788oNaPEgQ48WQvTz3Rq4Z+CgvTePbpfpYndCmCAE8+3sNTj/eooZ/8\nPAfPnOinT1OT7PHHlvPU471qWCc3184zJ/p19cYeOd6lY3KybTzzdL9Oc3L8gQ6eerxHDdlkZVl5\n5kQf69Yk8/0cu7+dpx7vVW3XlWnhmRN9bFyffH7vO9TCU0/0qtvnMzMUZsumZO6c/fc08dTjPcoW\nXJQQ5NNP9rJjW1Ivtm9PAyee6FXDm06niRNP9rJnV9IOdu1Yxokn+9SQo8Nh4ukne7l3X6PKbN9a\npzAJe7LbjTz1RC8H721Wmc0ba/jyU71qyNFmM/Lkl3o4otFeDa2t5MTjy3ElQo5Wq4GnHl3OscNJ\nndealWWceGS5Wl/LYpZ54sEuHtT0s2J5MU8+0ElOgjGbZL50XzsPaebT217Ak4fb9fa9v5WHdjeq\n9t3VkMtje5vITczHKIsc397AQ5uXqUxbVRYPb64jL3FeBlnk2Ppa7l+XzIfUUJLO/WuqVEaWBA6v\nquTgigq1n5qCNPb3lZOXngwR7+stZV9PqeoDynPs7FteQn4itCuJAnu6StjbVaIypVk29nWXUpgY\nSxRgb1cJ9/Qmc4eVZFnZ319GSSKUKgpwb18ZB1ckc4eVZNm4b1Ul5YnwpijAkdVVHB2qVkPWJdk2\njm+uozahkxEFeHjLMh7eXq9qPUty7Ty+t4mGRO4lQYBH9zbx6D3NqtazOM/Bk4faaU5oPQUBnjjc\nxpfua1d1nIV5Dk482EVHc9JPPPlAJ0882KXLHfZHa8K/z3DVF+NLjiAwOuVlZtFPiBiiUcQfjTKz\n4GfKHURMFCccX/Az6w4QkkA0ywQEmFkKMusLYUgsRqa9Iea9IeIymMwycQnmvUEWAmE1br4YjLDo\nDyOZRaySkmNhKRBmKRLFlnCe3miMpWAEg1XGbhCRJBF3MIInGsPuNEEc/MRxB8PIFhm7rDBLQaWf\nO0yAOEuBCJJFxiYKSJLAUjDCQjCMzWEkThxfXPnkKhhFrHYjoiiw6A8z4wlhsRkhHscTjjLvDRIC\nDGYZJIFZT4ixBT9i4iU16wsxs+jHF40hmmQiIkwtBBib9SIYRQRg1hNgZs6POxABWSRMnMk5HyO3\nl5T/DQowPe9jZtan7OYSBEKRGBPTXkbGkszMnJ+pGa+6eyAcjnF7ws3Y2KL66Xx6xsvMrI/5BWUX\nTSQS4/btJWZmfcoONAHmEmPNzyeZ+Ru3icdidC1domvpEmEk/DeHmQsowr9oNM5oIuPxnU/wc3M+\npme8zCX6icXijI4tIYmCutNlbt6vMInP0rFYnJGRRSwWgxqGm5/3qfNWmdFF0p1mlVmY9zM97WU2\nkaU1HofhkUVCoWiSWVTGmp7WMInsp3cy+C4uKv3omJEFTCZZDfktLgaYnvEylcjkeqcfZ5qZYGK7\n79JSgJkZL5OabK+3bi2Sk21TM/i6lwJMT3t1W+5vDS9QXOQkmAgJuD1Bpqa8uurdt4YXqaz0Eggo\nIQG3WylbMKHJ0D08vMDUtAd/gvF4QkxNeRif8GgYJRu2PxFa8HiDTE55dFXAR0cXmZr2qrv4vN4Q\nU1NeXYXv0bElZmZ8+BI7ZLzeENPTXl2agLHbbqamPXgTjM8XYnLay8iolllietqL3x8GQdkZMzXt\n0WWAvj2+xNSMF68/BKJSqXtq2sPwmFv9L/vElJfpGR/eQBhECIYiTM0otnJnNTA57WN61ofHFwZB\nIBCOKfO57VaZqVkvM3M+ZeePAKFIlKlZH6OTHgRZgaYX/EzP+/GEFNsNxeNMzfsZm/OBUUIAZrxB\nZhf9eEMRBFkgIsSZWvQzMe9HMkgQhwVfiHl3kGAkqizKBZh1B5lyBzGaZOKAJxxlwRsmIsQxmWUE\nEeZ9IWb9YYwWA8Tj+GMxlgJhIoLiawUBFvwh3MEoRrPChDAfxK0AACAASURBVOJx3MEIYZURWAxE\nCISjmK1G4vE4ERHcwTAhDbMQiBCORDGaZYhDOOFHg/G4ysz7w8RjcWSTRDwOgZjiR32h5HlNuwPI\ngqKZEeLgi8SY9wRxB8LIibxgkwt+rEaZqCAgyErpnZnFAHO+EMgicWBsxkcoGCUSi4EAS94gMws+\nZhf9IChf0kYmPMRjccKxOIgCS74QM/N+pud8Sea2G6NBIpSya+6P0e5ocv69tS9E7ar//F/+2zdD\n5k5m3UEmZ30IgkAsFmfOHeDjq7MIgoAgCIxNeZn1hZiY8ytMXFnAnLk5rzLjcz4WAyEmFwIIokA8\nDgveEBcSKf4FUWBqMYAnFGFqKah+CVjwhrg04UEUBURRWUC4gxGm3QkmYcCXJtwqM+8NseQPKwux\nBDPvDXFhfEllFnxhFrxhJhYCCUZg1h3kzPA8wh3GG2LeE2Rs1p9IMiYwvRDgwzvnnmBm5wPcmvIk\nShUITM75OHl+Uj33BU+I+Xk/18eWEp/9BW5Pe3jv9HiScYeYm/Nz9daCyoyNu3nn/VGVWVwKMjvv\n58r1ee5kWBsZW+KdkyOAwiy5g8zN+bmk0RXcHJ7n5Puj6iLH7Vbmo9WOXL85x8n3x4jHldCE2xNi\nbs7HhYtJpuHkL7giuvhG5TF+nrWcNzKaOPDOt/jvzkGVuXJ1lo8/HlcXDF5fmPkFP+fOJ2P2l6/M\ncvbspLoY8PnCzM/7OXsuGbO/cGmai5emVY2QPxBhfj7AGY2m4vyFaa5cnVVzBAUCEeYW/Doty/kL\n01y/Ma+m4Q8Go8zN383cGl5Qt+cHQwrz8SdJvcuFi9OMjCyqWqNQgtFqYi5emmHs9pK6oAuHY8zO\n+Tl9OslcvqIws3MJJhJjbt7Hhx8ltRpXr84xPu5Wy3VEIko/Wuba9TnGJ91MJTRLSr0oHx9o9Dc3\nbs4zMeFhcjLJzM75+OBUkrk1vMCkZuETjcaZmfXqmOERZZFzO7GoicXizMz6dDqe0dElpqY9jI7d\nYZTF9Mn3k8zYbWUhdKfURDwOU9MeHTM+7mZ2zsetkUUEQfETU1Me3tMwE5OeT2dO3VbtYmray9xC\ngJvDij3FgfFJDydP3VbtaXrWx/xikBvDi+riaHLKy8mPk3Y5Ox9g3h3kRmIsgPFpD++fm1KZ+aUg\nC95Qin17+eDKTNJ2PSEWfWFuTLiTzIyX0zfmVGbJF8YTjHBzyqvxm17OjSrzEwQBTyCCLxRheNan\n+E1BYHzez6UJZYEniAK+UBRvOMLovD/JLPq5mli0C6KAPxzDG4wwmvDHgiAwsejn+qyXOMqX0kAk\nhicQYUTTz+1FP1cn3MTiSj/BSAy3P8wtzXxG531cHXcTjsYRBIVZ9AS5mjh3QRC4OeXhytgSwXBM\nYcIx5t1BLo4uqszV20tcHVnAH4ommaUA568n3yuXRxa4cWsBrz+SZBb9nLucfD9duj7HrZFFJR2I\nIBAKx5if8/HJ+WmVuXhtluFRpdTO2LUX/qi1q/7uP/71Nzeb0u88up/57/vB2S9Eba0vzLpNEgUc\nmi2EAE6bPiukKChJmbQtzWLQxUFFAdIsesZhMehCoQJgN+s/ctnN+n4AbCY9YzPKd8U0ban9mD6F\nMek/TdrMsi41+53xdccWWZdSHZTQm7alWQ26dOlw9/Vx2EzqVto7zenQX1eH3Yg55VzT0+5mrBZD\nCmPWHTvTzHczzrsZbckEQLfFHACrjZxw8n/dOaEFQiaLDklzmHRlFZSxPptxpsznU/tJmY/DbvzM\nsey2u5mMlLGsVoO60+x/xlgsn8Kk68cym+TPHMtkktTdaP+zORsM4l1jpZ67LIt3PS+p11CWxLvu\nc+pYkiSoO9/+Z4woCmqGZnWsNLPevkXhU8bSM4LAXf2kp5l1JRM+7TycTrOuHMKdvrUt7VOYTxsr\ndfeM81PsKdV2U69zmt2kZg9XGXuqfRvuZlJ9gMWgprBQf0vxJTazQU1hcafZU2zZbpZ1ZRUA7KaU\nfkx3M9YU32IxylhSmFQfaTXIWI2pjL4fq/FuJnXONpN81985rPrrYzPL2FL+LvUaWs0G7Cl/57Tr\n75fVIuOwpfSTat9mWQ3H/rHbnS85/97CVV+IqQrAE0faOXFfO9mJWHJRnoMnD7ZyaFMtgqDkjXh4\nTxNf2tlITiJ2W5Bl5bGdjRxccyftOxxZX8MD62vISTjr3AwLx4ZquGegTF2h7usv4+BABTmJBzDL\nYeLAQDm7u0pIfJBha3sh+7pLyEk4p0ybkX3dJezsKFaZDU357O0sJjfRT7rVqMab7/jTocY89veU\nUZCYc7rNyIG+Mg6tKFdSzAPrWwq4b7CSokS82Wkzcv+aKh7aUIskKsymziIe3lJHeWKLa7rdyKPb\n6zmxt0ldDG3pLeWJe5qpSsSbnXYjJw608mcPdKmx5M0ry3n6aCe1iXhzmt3Ic8e7+dqJPlUrsml1\nBc8+1kNDoo5PmsPIV57s5RvPr1QXTOvXVPL8iT6aE/lSHHYjf/HsAH/11dVqvHnd6gqe//IArS1K\nTNpuM/LVr6zkm19frepJVg+W85VnV6j5UmxWA93/7c/pC9/kP139Fg/c/iX/z+X/jvM/fFXNl2K1\nGvjGV1fxl19brepJ+vtKeP6ZATVfisUi842vreIbX12FJeHAerqL+LNnV6j5Usxmmb/8+hq+/her\nVM1JV0chzz87wODKMkAp/fBX31jD1/9iUC3Z0N6Wz1eeG2DNqvIEI/FXX1/N1/9iUF3AtTTn8WfP\nrVDrUBmNEt/8+hr+4s9W4nAoTFNjLs8/u4JNGxUthMEg8ldfW81XvzKoak7ql+Xw/LMDap0lg0Hk\nG19bxZ8/v1J1oHW1WTz/7Ap2bl8GKAuTr/35IH/+3Aq1ZENNtYvnvjzA3t0NCILCfPUrg3zl+RWq\n5qSqMpPnnxng3n1NCIKyMPnKcyv4s2dXqFvYK8ozeP6ZAQ4n8vRIksBzzwzw/LMD6vb0stJ0nntm\ngPvva1PsUhR4+qk+nn92hZrHqKTYyfPPDPDgsXaVOfFEL88/M6BuGS8q/P/Ze+8oOa4zP/upqs5p\nunt6cs4Bg8EMciYywEwEkmCmslbSUom7q5VXXu6KlmzZ5/vs9a7Dd2xJFCUqi6Iyl6IkRjAhkUiD\nASbnme7pnKvq+6MaPVUN2ZJ9fLiHe3zPwSEL5+l7q6rrvn1Rv999Xw9/9pntfPiDG4pvRj/+0U08\n+unt1BT8YnW1bh799Hb+5CObisxHP7yRRz+9nbpCHqOaahd/9pkdfOJPNhXLMXzoA+v57Ke2FT1l\nVZUuHv30dh75+JYi876H1vLoJ7fRVJhPlRVOHv3kNj79iS1IksY8cLyfz35iCy0F31mg3MGjf7qV\nz358c5E5fnQVn/mTTcVyDH6fjUc/tpnPfnRTkTl2cxef+sAG2gqMr8zGZz64kc++f0Nxft+2t41H\n7huko1D6ocxl4dMPrOXReweLzI1bGvnYkb5ijT2Pw8wjx/r51NG+Yl6wPYO1fOhQNx2F++Oym/jI\njd185GBXkdnaXckDO9toL8Qbh9XEgze08dDOVsyFsda1+rlzYwNthTQAdrPE8U1N3Lepscj015dx\ndG0d7QXGZha5a309d69vwFIYa1WNh8OD9XQWvnerSeSuDfXcs3klB1lvXRl3bmikt1Bf0GoSuX9r\nMw/tbC3WvFpVX8b9O1oZaNZim9Us8sF9nXzkUFdxAdfX6OWDBzvZVPDSWMwij9yxik8e6cNRiCWr\nW/18/HAf2wvlXyxmkT+7b4BHH1pbXET1tZfzyfsH2VPILWQ2i3zuQxt59EMbcRXixKqOcj7zgQ0c\nLORMMptFPv/INv7iT7ficf/TLHT+OS5y3hNy1Ze/8h8es1dvx+4w87vTMyBpr0tb68v42RuTxAoa\ndDiZw+O28PKlBSSzSEpWaapy8dvz86RkBZNFIpbO43VbeXMshMUqkQfqyh28PrZMFk3PTeRkvC4r\nZ2aiWGwmFEmk2mPjzFyUnAg2h5mUouB1WDi3ENd+SE0SAbeFd+Zi5ASw2c2kZYUyHSOaJfxOC+/M\nRslwjVHxOsycmYtitZsQzBJ+h4VTE2GSiorFZiaRV/A7zbw2EizkYRDxOy28cWWJSCaH2SoRy+Sp\ndNt4/vwcJouEIgqUu2289M4cC9EMUuH+1PkdPHNiHFUUyKrgd1t56fQ0M8EkgiQSimZoqnbx9K+v\noIqQU1S8HhuvvjnFxKwm6QUjaZrry/jeTy+iqCrZvILHbeX1t6YYnQwXPTltzT6+/cNzKKpKLq/g\ndFp46/QsV0c1mWsplKazzc9T338HWVHJ5mUcdgunz8wVt0gvLiXp7Ajw1HfOIssquZxC6+Iwzad+\nw1lnMxYlT1K0Yp+d5O+DzeRlhVxOwWSSGLq8xIWLmjy1tJSgp7uCbz51lnxeIZ9XEEWBqyMhzhXS\nEiwFkxrz7bPkchqDqkkp1ySjYChJT3cl33rqLNmcjCwryLLK9EysWEYhGErR013Jk0+dJZuVkWWV\nfF5hbj5R3EYdCiXp6dHOJ5PRmEwmT2g5VZRNQqEUPT0VfOups6QzeRRFJZXKEYmmee11bZvw8nKK\n3u5Kvvnts6TTGpNMaNmnr22bXg6n6O6q4NvfeZtkKoeiqMTiWbI5mZcKW5uXw2l6ugM89d13SCRy\nxezCiqIWt3qHI2m6uwJ8+7tvE0/ktMzBkTSCKPLbQor7cCRNV2eA73z/HWIxLZN4OJLCbJb49W80\nJhJN09lRzne/f45oTMtGvLycxmY3FbfUR6IZOtr9fO8H54sZi0OhJC6XpVgOIhrL0Nbi54dPn2c5\nnC4yHo+NXxTKSsRiWVpavDz94wuEllOoKgSDSfx+Oz/9uVbmIh7P0tzk5cc/vUgwqMl3wWCSigoH\nzxRKYSQSWRobyvjpz4aKfqylpQTV1W6e/qlWmiORzFFf6+EX/3iFhYIks7SUpLbWzdOFshvJVI6a\nahfP/m6E+cVEca7U15fx9C+HUIF0VqaqwslvTowze40Jp2mo9fDj56+iCpDJK1T4Hbx4aprZYAJB\nFAhF0zTWevjxi6OoAmRlFV+ZjRMX5pkJaTJOMJahpc7DT9+YBFEgr2qLoTOjy8xFUkgmkUgqR1OV\nm+fenkWQBBRBwGU3c3k+zkI8g9ksEc/INFQ4eXF4CdEkgiRit0iMhVMspbSYlJIV6n0OXptYRjKL\nCCYRm1liKpLWvDsWjan12HlrMozJJCJKIlaTxEwkzWIii9kkkpYVqj1WXh9bRpQ0KcwkScxEUszF\nM5jMEsm8Qq3XxssjIQRJQJBEJElgejnF5HISk0kkkZWp99n59YU51MK/egVBYCaUYGQhjmQSiWVk\nmitc/PzNSeSCwVBVYTaU5OJkGFESiKZytNd4+MELV8kpCgogKzC/lODs1SCIEElk6Wz08t1/vEwm\nrzHZvCbTnirI4eFolq5WH9955gLpbB5FVUlnZCKRDG+cmWV6+N2Xq25x/PFy1ZPJ94Zc9Z5Z5Fgq\ntpHIyiyGU0VNOpnJc2V2RV9djmVIyypL0XSRSeVkxhdXtOVoMkdWVQnGM0UmnZOZKvQrCALxTJ6s\norKczK0weYXZWLrIJLMyOVllOZUz9DMbXWFSOYVMTjYwqays6c8FJp1XSOdkgoms4bpGdeeczikk\n0zkWoivnHE/nGJ6J6hiZeDLHbGjl/kTiGS7o/EiprEw8kWVqIV5klqNpLl5Z0ePTWZlkIsvETKzI\nhMJpzl9c0f7TGY0Zn4wWmaXlJOcurDCZQj9jRW8PLC4mCnlZtFmSycqkUllGx8LFz80vxLlwcaHo\n28nlZFLJHFdHVnLHrLvwG4alCv6u8Qivl/XwpqeLh975Nv+tYm+RmZmNMnwlWDT65vMKqXSOq7rc\nQlNTEUbHlosm3nxeIZXKcUXHTEyGmZyKFA26sqwtNPR5asbHw8zMxjST6v+IKXhOrpWsUBSVVDLH\n5eGgYazFxWSx3MK1Rc2Qjpmcimim74JvR1FVksmswfs0NR0lFEoV63+pKqSSWS7p6mbNzMYIhVJF\nQ7eqap4kvT9qbj5OOJwq+nZUVfux1zPzCwkikTRLSys5RJKJHBd1uaoWFhNEopmigRq0fvTMtWta\n0OUjiseNTDCUIhbLGMzR8USmuJAFzTwei2eY05ma4/GsgQmH08TjWWZ1puZY1NhPJJImkcwZjM/R\nmJGJxjIkklmmS5jzOv/YtXInUzpzdCSa4eLwilcjkcyRyuSZml2Zc+FYhotXV+ZlMpUjlVOYmtMx\n0TRDEytzJ5XOk84rmhlZN78v6+NEViYjK0wvJVf6iWcYLcSEa36SnKIwu5zSMVkmlldiZE5WyKsq\n87pYG05kmYlmir6dnKySVxQW49ni58LJLHOxDNe8e7Lye5hUjtloBhWKTCavMB/LrMT6ZI6ZSErz\n5AgCsqqSKYm/wXiWmWCSvKIWmVRGZqrg6xQEgflIiplggmxeYxRVJZnKMTa/cj9mQklmluKkC74d\nRdHm3NXplfs6tRBnfiFBMp1fYVI5rkyseHum5mMsLsSJJXLFsVLJHMMjK9/z1GyMYDBBNJZ91xc5\nf//Fxx+7zeUrvvH8Q3+eiL83FjnvmZdOdpuJOl1mU4CGKrfBl2KzSNTqMr8C1PkdBsZsEqku8TBU\nldmLr09B2w5ZWeIPqHBZDIwkCgRKtNPyUkaAQIkuG3Bai69hQZPQrmPcVmxmI1NVot1Wltlw6HRq\nQYBav/G6avwOQ0p1QYDGSuM9rKtwGXR8QYDGWo+RqXJd5+loqvcajutrPFSU3Ht9OQK4lq3X9QeY\nMqp1WWUBWlqMjFpdTU9yCkHVFjC9iXGSHr/xnGs91JVcR2vJWHV1v4cpGev39VN6PrW1bkOW29/H\n1FS7/2A/lRXOooSywhivK1DuMJSL0M653HDs89mvY1qafQZfirfMRkN9mZFp8Rl8KR6P9Tqmtdlv\nYFwuC/X1pWN5Db4Up8NMQ4Oxn+YmX1EiBU1ibPx9jM6XYrOZaGz0ljDeoowKmjTYVMI0NXqL8ido\n0uB1TJPX4Dszm8XrmQZvUf4ETdK7lv7gWmuoLzP4ziRJoLmhhKnzFLfTgxZLmkruc0ON2+BBFEWB\nprrSeek2eOwEARpL5k5dhdPgH/l9MaDG57jOY1JX7jQcV3nteEt8OtUlMaHCY7uOqSqJowGXFW+J\nv6WiJP75HBZ8JUxlSaz1Ocz4SzwwpWOVOy2Ul3yuNPZXeGxUlHyuPmC89kqvjSqfMbaV3udKn4Oa\nks81lcSEgNdOTcm9by555st9di2L9T9FE/6vXPVP1v7Nv/u7x/7dlz/H0X3tvPbOHKlMnvYGL1/4\n4EacdjMXx5exmCX+5I5V3LG9mVNXgqQyMi01bh49upoyp5XL01EsZpEHdrdx47o6zk1GSOfyNASc\nfHR/J2UuCyMLcUwmkSPrGti3qorL83HSOZkar40HtzTjd1oYCyUxiSKHeqvY2RFgNJgklZepdFu5\na7CegNPK2HISkyiwt6uSne0BxkIJUjmFCpeVY4N1VLqtjAaTSKLInq5K9nZWMBpKkMzKVLis3LO+\ngZoyO1cW4kiiwIG+am5aXcvl+RjxdJ4Kj40P3tBGY8DFhakwoihwy9p6jm1t5uJUhGgyS6XXxqdu\nW0V7nYczV4Na3axtLTx8qItzoyGW4xmqfA7+xUNr6Wnx81bhTc3RvW18+Nhq3rm8RCiSprLcwV9/\nYitreip5/cwMoiBw+FAnf/rwes4NLRIMJakIOPnin+9k7Zqawi4suP2mLj790U2cv7TI4lKSQLmD\nL/3LvWxYV8urr00iALfd1MVn/3Qrl4aWWFhIUF5u5189to/NGxt45dUJVODmQ538+Wd3cHl4ibn5\nOH6fnY/9+4dpevIfODT9EhujQ7x/9h/x/ed/z1VXPTOzMXxeG1/64gF2bG/m5VfGUVSVfXvb+Pxf\n3MDo2DLTM1G8ZTa+9Ph+du1o5cWXterTu29o4V/85S4mp8JMTkUpK7Py5S/uZ/euFl58eRxFUdm5\nvYkvfH43M7MxJibDeDxWvvS3+9m7p40XXx5DllW2b23kC5/fzcJCgrHxMG63lcf/Zh8HD7Tzwktj\nyHmFzZvreeyv9hAKpRgdW8btsvD43+zn0MEOXnxplHxOYeOGOh77wh6i0TRXR0O4XBb+9q/3cvON\nXbz40hi5nMK6tbX8zV/vJZHIcuVqEKfTwt98YQ+33tzNCy+NkcvKDAzU8MXH9pLO5Lk8vITTYeav\n/2o3t9/WwwsvjpHNyvT3V/HFx/aRlxUuDS3icJj5q7+8gSN39PLCS2NkMzJ9fZU8/rf7ENB2edns\nZj7/Fzdw7EgvL708TjqdY1VvJY//zX7MJpHzFxew2Ux87s93cufRPl56ZYx0Kk93V4AvfXE/NpuJ\nc+fnsVpN/NlndnDPXat56ZVxkqkcXZ0BvvzFAzhdFt5+Zw6r1cRnP7WN+47389Kr4ySTWdrby/ny\nF/fj9do5e3YWi8XEpx/Zyv33DvDKqxMkElnaWv3868cP4Pc7OHN2FotF4pGPbebhBwd55cQE8XiG\nlmYfX378AFVVLk6fnsVsEfnYRzfx/ocGOfH6FLFYhqZGL1/+4j7q6zycPD2DySTy0Q9t5P0Pr+O1\nNyeJxjI0Nnj50t/so6mxTGMkkQ8+tJYPPbyON05NE4mmqa/z8KUv7KW1ycdbZ2aQJIGH7hngww8M\n8tbZWSKxDLXVbh7/3C7aW3y89fYskihw3+FVfPieAU5fnCcczVBd4eRvP7WNzhYfb52fRxQF7jrU\nxYePrubtK0GWYxmq/A6+8KFN9Lb4OTm0iCDC4Z2tfODmHi5MLLMcz1JRZudz96yht9HHmRHt7dKh\ndQ08sKedq7NRwoksfreVR27uoae+jHOTYQRBq/h91+YmJoIJwskcXoeZD+xsp6vazaW5GAKwucXP\nbWtqmYmmiaRyuG0m7l3fSHuli+GFOAgwWO/llr4a5mMa47KZuXOwjo5KF8OLcVA1384tfTUsxjOE\nkzlcNom719bTU+Xh0ryWzXlNfRmHB+pYjGUIJbI4bRL3b2yiv97LuULaioFGH/duaWYxmmYxlsZl\nM/Ghve2say3nzGgIRVVZ2+rng/s7WYykmQ2lcNvNfOr2VWztreKNoUVkRWFDZwWP3NHHUjTN1EIc\nl8PC5+4bZPf6Ok68PUteVtnQW8WfP7iO5Wia8dkoLoeFL3x4E/u3NfHKW1Pk8grrV1fz+T/ZQjSe\nZXQyjNNh5l9+ahuHdrfz0uuTXDrz/Xf1Tck/fPHxx253//Fy1dei7403Oe+JRc6XvvJ3jyUcG8io\nKi+fm0cRBELxLA6biadfGydV0DxH5mKoosBbV4OIkkgsncduMfHc+TmyqgqSwGQwgWiWeGcmimTW\nNGGrSeS1iTB5UUAyS8zFM5glieFgEovVRB4wiQJvz0ZRRQGLWWIpmcMkiYxFUtisJlRBQBIEzi3E\nQBKxWkwsp3OIosBoOK0xooAoCLwzFwNRwGqRWE7nEFC5vJTEapFQBECANyeWyaHVhVpIZBFUODUd\nwWSRyAEKKi9eWiCRVxBNIjORFJIAL15aQJA0HVtWFJ47NUMklQdRZGIxgdUk8os3p1BFgWROJpdX\n+OWr4yxEMsjAyEwMp0Xix78dQUar/pvJyfzytyPMLiXJq3BlIoLHYeYHvxhCVrXKwsl0nmefv8rU\nbJy8rHJ1NIzXbeU7PzqPrKhaFe54hud/O8L4ZIR8XuHKSAhfmZ1vffdt8rJCIqH5TV54cYzRsWXy\neYWrIyHK/Q6++e2z5GXtFXDNyd9RefEUX6vZx7StgjFbJdUnfs2X5lvJ5xWSyRxLwSSvvzHF5WFN\nshodWyZQ7uCJb54hl1NIpnIszCd46/QMl4aWyOcVxsbDlJc7eOLJ0+RyCqlUntm5GGffnufCxYUi\nUxFw8PUnTpPNyaRSeaZmoly4uMg75+bJ5xXGJ8IEKpx87YlTZLMy6XSeyckIl4eDnH17jrysMDEZ\nIVDu5KtPnCST0Zix8WVGRkKcOjNLXlaYnIpSHnDw1a+fKjIjoyEmJyO8dXKGvKwwPROlvNzOV79+\nmnQ6TyaT58pIkJnZGG+8OUVeVpiZjeH32fjq108VGJnhK0EWFhOceH2SvKwwOxfH57Xx1SdOkUpp\nzOXhIKFQkldenSAvK8zNx/GW2fjaE6dJJHNksxoTjqR56ZVxZFllfiGBx2Plq0+cIpHQmKHLQeLx\nDC+8OEZeVlhYTOByWvj6k6eJx7NkszKXLi+SSuf5ze9GkWWVxaUkDqeZbzx5WvMPZWWGhhbJZGWe\n/82Itg09mMRuN/ONb54hGsuQy8lcHFpEzqv846+vFLaqp7BaJb711FkikQy5nLaIU1X41T8Oa1ve\nl1NYLBJPfecdwtE0ubzCpSFt2/UvfqUxy+E0JpPIt39wjuVIWlsMDi9hkgR+/svLyLJKOJxGEgW+\n+6PzBEMpcnmFoeEgFpvEz54dRlZUrTK1oPLDn11iKZQin1e4fCWIzWHmp89dQVZUovEsiqLyk+eG\nWVpOkZdVhkeXcbrM/OS3I8iqSiyZQ5YVfv7yOIvLafKKypWJMG6PlZ+8Ml6cu9m8wnNnZ1iMZVAQ\nGJmL43VbePb0NIgC6bxMNq/w6qUFgvEsqiAwEUxQ5rTw24vzCKJAVlbI5BVOT4YJpXIgalvBy5wW\nXh1bRjSJ5IBUXubSQpxwOo8oiSwmsnhsZt6aDCNJIgqapH81lCSSySNJIqFUFqdV4uR0BLHAJHMy\nI8EE4UweURJYTmVxmCXenIoU+hFIZGWuLiUJpXKFfnI4LRIvjwQRRAFZhWgmz+X5GHPxLELhfJwW\niecvzoMoIKOl9BiajjIRSmlb/qMZ3DYTP3lzEgXNk7gQ0WTB4VktD9hsKInXaeF7L46QVzXv00wo\nxfDYMufHwshoeXN8Lgvf+vkQ2bxmW5iYizIyHubs/NhmggAAIABJREFU5SVkVWV6IY6/zMqTP3iH\nTE4hk5UZnYwwOR3h1DvzTF3+8bsrVz3++GN3/C8scr4a+b+LnP9j7ctf+bvHPE27UARY0tUiQoCp\ngl8ANC+LZBYJxjIGZl5Xzj6dU5DMIsu6eiaqCMHUynFWVjBJIpH0Sl0UFQjrjvOKiihoiaGuNUVV\nWS5h1MJku9ZkRSWkG1tWVC1Aplf+LicrzOlqqciKZtwNFvwcANmcwpTOB5FXVHJZmXnd/cnkZMZm\n4wYmn5WZ1n0unckzqkuClpdV1LzClM7TkEznGR1bqbclKyqqrDKpq9WUSOQY0dVckhUVVJUJXfK0\nWDxr8NYoioqAysTkChONphkdDRc9OdeS+elrPm0ce40x0cdTNXsZcjZwxVHL+648zdeq9xeZ0HKK\nmekoeVmTtFRN4GdsfOU6gqEk8/Nxsjm5yAiCwJjuWrWkfknSuu8QQWBUV1tsYUHzrujrbQklzPxC\nnFgsQyKR0/WD4b4uLCZIJLLFXDqFoQy1rJaCWqK7qO75QIUR3VihUIpUKmeo2wXGfpbDaVKpHMth\nPaMavsNIJK3l89HNMRUMTDSqLS709b9U1cjECguQxSU9YxwrHs+SyylFwy6AoioGJpHIaQspnSdH\nUYz9JJMao/ftyIrKiO65S6U0g7Y+qWFeVgzfVzqdR1VUgydHziuMjK8wmUweVcXAZHMyo+Mrz2om\nK4OAwbeTK/yY6T8jiALTujmXzSmM6RIY5vIKSCLTCytMOiszobvOvKwimESml1buYSYnG2KkrKiY\nzCKzyylDP3O6Z0UpMAu6uJnK5FnUxS1FBZNZZEkXk1LZPCHdHFBVTYrTx7tUVvMoFhm0Z1z/d6mc\nTCiVLZaiuPZffT/JrOZj1JXSQlFUFnVzJ5bOE4wZ620psmK41kgyRyiaMSTfk2VjbA3FMoQiadK5\nlVpaiqIwMb9yn5eiaSLhNEld/EdRGdd9h0vhNPFYRkv6qGPGdM9CMJwiEc8SjWff9UXOPzz++GN3\neP74Rc5/D783FjnvGWWtvMxGb4k/oa/Vb8hD43Va6CrRtrvrPIY8CC6bibbKEv9EudOQT8Fhlmgs\n0WAbvHYcutwNVpNIXYkmXeO2GRiLJFBXovfWeGw4LUamviT3SL3Xjkd3XWZJoLVE720OOPHrdHSz\nJNJdZ7z29hpPcas8aCncV7ca72F3k4+6ipW+zSaRwUJZg2utt62cJp2fxCSJxVTk19qqrgBtzSve\nA0kS2DBYY2R6KotlFa4xG9fVGZneKnq6VsYXRaFYsqDYOrvYGruETdZ+6HcvnyVabSwst6q3kt7e\nyuKxIMCmDfUGX0pvzx9mSvsBjdH7Ukr7Adi4vt7gS+nuqri+n/X1Bl9KZ0c5q1aV9LOuzuBLaW3x\n0beqysBsWF9n8KU0NXpZ3VfCrKszpIqvr/cUy05ca+vW1hm8K7U17uv6Wbe2zuBLqa5yXdfP2rW1\nxQrfoHmN1pQyA7UGX0og4GBNf8lYA7WGnEl+n501Jc/d4EBNcTs9aHl8BgdKmP4aQz6bMo+1mLbg\nWhvor8HnW2Hcbkux5Ma11t9fVSzPAFoZh7UlzJq+6mJ5BtD8SIP9Rmb1qioqdfPZbjMxWHJ/+roC\nVOvmpdUiMVjy/PS1l1OjYyxmkYHOgIHpafIafIpmk8jqEm9aZ10Ztf4VRhIFekq9WNVuanV+FlEQ\n6CiJo41+JzW6eCcK0Boo8Uh67VTrvi8BaC6JtTUem6Gf/xFTWxJ/WwNOQ76zeq+dBt11CUB3tcfA\nNAWcNFcYfTJ9DV5DDGirdtNe4qdb01ZuiAHttR66Go33dW13hSEGtDWU0dNm9M+tW11tmN/NDWX0\nlnyH72b75+jJeU+UdZAkgY/cuZota2o4fSXI7FKC5loPx/d24PXaeOo3VxEFeN+NXWzpqeTcZJi5\nUIq6gIPbNzVR4Xfwo9cnEAQ4tqmJje0BLi/EWYimqSqzcbCvhppyB89emEcFDvZUMVBfxkQkxVIs\nQ7nLwvbWcmp8dl64qu2c2NrsZ1Wlm9lEhmA8i9duZlOjl5oyG6+Mh1BV2FDvpafCyWwyy1I8Q5nd\nzMYGL7UeGy+OBlFU2NDgpa/SxVQ0w3wsTZndzNaWcurKbPzy4jyyAtta/Wxq8HFlKcH0chKvw8KB\nniraA06+87omJezprebgqmrOT4UZWYjjd1o4sqmJ1Q1e/ssvh8jLCjeur+fI9hZODQcZmgzjd1t5\nYH8H23oq+cpTZ8jmZG7d3sJdBzp549w8568E8ZfZeP/hVUxsbODxfzhBNidzy542jt/aw5tnZjh7\nYQFfmY0P3zvAzFyMf/mVF0lnZG7Z3849R1fz5qkZTp6dxeux8bEPrGdxKcHnH3ueVDrPTQc6uOeu\nft46PcMbb01T5rHyiY9sIhxJ8xf/4llSqTwH9rVzz939nDozw4nXp/B4rOz4N5+kYseT/OLMXxG0\nlFGTCeL4xlfZf6GCV14dx+Wy8MlPbCGfl/nMn/+KRCLLrhtauOfufs6dn+eFl8ZwOi186k+3IIgC\nn/7sL4gnsuzc3sQ9d/dz8dICv/ndKE6HmU8/shWLReLq1SCxWJatWxq55+5+Lg8v8dzzV3HYzXzm\nka243BaGrwSJRjJs2lTPvcf7GR0L8ctnh7HbTHz2U1vx+x1curREOJJiw/p67r1nDRNTEX72iyFs\nNs1zUlnl4vz5BZbDKdYO1nLfvQPMzsf58U8uYrOaePTT22ioL+Ptc/OEQknW9Ndw/70DLAWT/Ojp\nC5gtklbrq83H6bOzBINJVvdVcf+9A0Qiab73w3OYzRrT3VnBqdMzLC4l6O2p5MH7B0kmc3z7e29j\nNkl85lPb6O+r4uSpGRYW4/R0VfDQ/QPksjLf/PYZTCaRTz+ylcG1Nbz51hRz83E6OwI8dP8AggBf\n/8ZpTJKWA2fThnpef3OK2bkY7W3lPPzQIFarif/2tZNIosAjH9/Czu3NvP7GFNMzUdpa/Tz84Fpc\nTiv/9b+/iSgI/OnHN7NnVysnXptkajpCc5OP9z24lnK/nX/4L28gCPDxj27i4P4OXj0xycRkmKZG\nL+97aC3VVS7+439+DVT4k49s5Jabunj1tUnGxpdpqC/j/Q+vpbGhjP/wDydQVfjIBzZw+PZeXjkx\nwejYMnW1Hj748Hra28r5f//jCRRF5YMPr+XOI328cmKCq6PL1NS4+cDDa+ntqeTf/d2ryLLKww8M\ncN+dq3n1zUmuXA1RXeniAw8MsmZ1Ff/2708g5xXuv3M19x5ZxYmT01weCVEZcPCB4wNsHKzjK//1\nNfJ5hbtv7eGeW3t4/Z05hkZCBHx23n+sny1jIf7t106Sz8sc3tfBXfs6eGtokYtjy/jLbLzvll5G\n5mL8Pz94m2xe4ZbNjdyxtZm3x5e5NBnB67Jw76425sIp/tMvL5HNK+ztr+HQQB1DszEuz0RwO7RY\nspzI8vVXRsnlFTa3l7Orq5KxUJIri3FcVhM39dWQyMl879QUWVlhsK6Mzc3lTEXSjCwlcJgl9nZW\nkJYVnjk3Szav0lvtZkOjj9l4mpFgErtZZHd7gKys8sz5WbJ5ha5KjZmLpxleTGAv9JOXVX5wZop0\nXqGnys2WlnJmImkuzMWwm0VuXFUFqsrXToyTysmsqvGws6uSiVCSsxPL2MwSR9Y3IAGzkRTJTJ7V\njT4ODNQxvhjnxNAidouJ+3e1YTdLTCwmiKVyDLb5uX1LMxPzCX57ZhqbxcSHb+mhzGFmeFrLaDzY\nEeDY3g6m5uL844lxrBYTnzi+hkCZjYsjIcKxNGu6K7n75h7mFhL87NdXsFokPvn+9dRVuTinq+7+\nrjXhvbV4+WPbe0Ku+tJX/u6xeWmQ5Uyek1eDRU9OVpb56RuT5BQVWYXzE8ukFIVzUxEQBWLpPBlZ\n5bdDi8gCqKLAlYU4OQSuBBOIJpFUXiErK5ya1T4jSSJTkRSqIDAV03JC5Aq66+XlJKJJwmyWWEzm\nUARYSOWxWEwookBOUbkSSWMyS1gsJkKZPHlFZSGdx2o1gSiSlVWGQlo/FotEMJ0jnZOZLOSfUARN\nJz89HUUVBEwmkfl4hmRG5vJSApNJIq9CIiPzwvAiWRUEk8hEOEkqneOt8eWCJ0clnMzyy7emSeZk\nVEHg6lyMVDrHC+/MoQraK9+laJqnXxolkswhA5cml8mlZZ49MY6sqsRTOeaDCX783DChqPbq9+JI\nEDmr8LPnr5KXVeLJHDMLcZ751TCLoRR5WeHi8BJKTuHHPx8in1eIJ7JMTEf5+a8uM7+Y0JjLS6Co\n/OiZC0VmfDzMr54dZmY2VvBPLCEg8IOnz5PPKyQSWaqefRrrxBh/3v4BTpT1csbdyqqfPcEXQ93k\ncpq3Z/jKEr97YYyJiTC5nKJt5xbgO997R/PkJHMMXV7i5Ve0H7FcTtG2jgvw7e+uMBcuLvL665Nc\nHVkmly/IJwJ869tvF709584vcPLUDJeHg+TyiiZ3CfDkt84WvT1vvzPP2bfniv6f8Ykwqqry5FNn\nisyZs7NcuLDAhYuL5PMKk5MRVFXliW8WPELpPCdPz3D5crDo/5majqIoKt/45pmi/+fkqRmuXg1x\n9m2NmZ6JISsqX3/y9Apzcoax8WVOn5kln1eYnY0hywpff/K05v/J5Hnz5DSTUxFOnprRmLk4+ZzM\n17+hMZmMzFsnp5mZifHGW9Pk8wrz83FyOYWvPXGKTEbz9rx5cpr5+TivvTFFPq+wsJAgk8nztW8U\nPEJZjVlcSvDqiUmNWdTqYX39ydOaRygrc/LkDMFQkpdfnSCfV1haSpJK5fn6N06TTGn+n5OnZliO\npHnxpTGNKch7T3zzdNEj9NapGaKxDL97YbRYqiIez/LNp84SLzAnT88Si2f47e80JrScIhLL8M3v\nvK35iHIyp87Okkzlef6FMfIF304kmuFbP3iHWCJLLq9w5p050pk8vy70E46kWQ6n+M4zl4jGs+Ty\nKmcvLJDNyTz3onbOkWiGUDjF9391mUg8S05WeXtokbys8tyr4+RllWgiy2I4xTMvjBJJZskrKudH\nQiiiwK9PTRc9OQvhJL86Oa3Nb0VlaDKMYBJ58cICKpp8tBhN8dLQArFMHlWAkYU4oknktZEgqiiQ\nkRWW4hlOTUeI52QQBaYLZWjOzGi5s3KKSiiZ5cJ8nGReQRAF5uNZRAHOz2ulbmQ0WepqKEkqryBK\nAsFUTjOyLyWKfpvlVI6R5STJvIIoiSync6CqnF+IF709wWSW4cU4saysldlJ5VBUlVPTkeJY8/EM\nl+biWgoPUWApkSWvKLx8VbuunAqT4STnJ8PMxzKogsB8NI0sKzx7ZgYVzbowMh/nndEQk8EkKjCz\nnEKWVZ5+dQxZ1XIWXZqM8PblJa7ORJFVlamlBKqs8P1fD5NXtO3t71wJcvFKkKHxZWRF8+SossK3\nnrlATlZJZ2XOXFhg+EqI80NL77pc9Z8ef/yxo74/Xq76/4LvDbnqPfEmBzRz65hOQwcYnYsbtNRk\nIQeCvk0HE+TkFSaTV5iLGr0K87EMOXlFt80pKkvJrIEJpXNaYbVCk1WjjwZgOZ036r8qhPVeDrTi\nn7kSJpQy9hNM5kjrrktRYSGRMTAL8QyJrGxgJkPGa59ZThFNGXX00ZJ7OLkQJ6TzdygqDE+GDczY\nTIxFvS9DhaGRkJGZjDCr8weoKgxdWTIy48uGooyAIXcLwOj4MkuLxuu4OLRgOBampjjjauWqQ5O6\nJm0VfG7qR6BTrMbGw2QzsuFzly4Z/3U0VsghZBirlBlfxl5SUqO0n/HxMOGwcRtsaT8Tk5FiHp1i\nPwUD7LV2bcHyP2Pm5uLXpfsfGlo0fG5hMWHwqfw+ZimYvI65NLRULFYKWqJBfV4h0L6vvG4+hSNp\nrpY8C0OFhdy1Fo1mrmMuXw4W64qB5skZvlLCDAeLdcUA4omsIYeRxiwZ/FLJZI4ruvxEoNUx0/ul\n0uk8w8NG5srVldpjoPlthkv6uXolWMxzBFrdsOGS87kyGjJ4qnI5zVisbyPjYaI632A+rzBc8l1c\nnQgT1jGyrDI8bmTGpiMs6xhFUbmi88ABTMzHCcWM83t03jgHp5eSLGeN/sOJJeMcnA2nSOmOVWC2\nxPO1GMuQMT6+zMeMcSuYyGKMiFrRZH1bTufIlBSoXChlUlpuIcNY0dKxcmSyRmZ6OWU4XohmULLG\nODG+aLw/c+EUUsm8HJk13ueZYIJIyWuQ4YmIYe7OLiXIl8SAodFlAzO/lESSS27iu9X+mb7Jec9c\nUnOth+0luvWOvmoCOu22rtzB+jajnrmu1U+5zrtS4bbSV6Kv9lZ7DLkbvDYz7SV5Ilp9djw6b4/T\nLNFYml/BbcWt8z3YTSINJfVm6t0WynT92E0iLSV6c4vXTkCXA8Jhlugp0b+7Kl3U6TRyp0VifUm+\nlDWNXlqrVj7nspnY2Vdt0KQ3dVfS27SiJbvtZvZtNPpStq6pYY3Op+NymDm4s8WgSW9dX8/6NSve\nA4fdzKF97YYaXNs3N7JZ569x2M3cdLDDoFtv39LEti2NxWObzcRNhzqRdN4V09Yt3Bg+RWV2GVSV\n+2efJ9qzxuBL2b61iR3bV1Y9FovETTd2Gnwp20oYs1nk5hs7Db6U7Vub2L5thTGZNEbvS9m2tZEd\n25tXGEnkpkOdBl/Klk0NBkaSBG66scvgS9m8sd7AiKLATYc6Db6U9Wtr2bmjxcDceKjLUKtqYE0N\nO3es9CMIcOhgp6E+0uq+qmJpimvt0MEOQ22q3p4Kdt3QYmQOdBTLPIBWMmLXzlKmnYDOi9HRXn5d\nPwf2tVOp85O0tfrZu6fVwOzf10519YpfornJy57dJczeNmprVp7xxoYy9u5uMzB7d7cZcvnU13nY\nt/d6pqlxxYdSU+1m/x4js3tXiyGvU1Wlk/0l57xrRzNtuvxHFQHHdf3csLWJDp03zu+zs7/k/uzc\n1FAsrQJarbh9W42+s20DtXTrzsfjtLB3nXHubllVTbcu34/LbmZHb5UhBqxtD9Cli4kOi8Tm9nJD\nP/0NXtp13hWrSWSg3muow9dV5aZV5/+xSAKrqt2GsVoDTpp0z49JFOiscBr6afI6aPI6DEx3wMg0\n++y06mK0JGhj6eNNW8BJly4vjSQKrG30YtL76Wo89On8R5IosKWzslguAqC/ycc63e+KJArc0F9j\nqOU12B5gs84rJ4oC+zY1FEtBAKzrqWSLzsMlCgIHdjTj0sWAwVVVbN/YwD9FEwCT9Mf/ea+098Qi\nRxDh8J429gzWUV/pRDKJtNV52Nlfw6ENDVitEnabiVs2NbG1u5L6Cidmi0RTlZvNnZXsWlWNzWrC\nbjOxe1U1gw1eGvx2bBaJhnI7A/VlbG72F4u1bWr20xVwUeezY7eaqPXa6apw01/l1hiLRH+1m+Yy\nO7VuKw6zRJXLQpvPQW+5E6dZxGEW6Sl30uCxUe2yYDeJVDjMtHgd9FU4cVkkjQk4afHZqffasFsk\nKl1WuipcbGj04bKZcFhNDNR56aly0xxwYLNIVHqsDNSVsaszgNNmwmaR2NwaYLDRR3utB7NFosJr\nZ2tnBTeuq8duM2GxSOzsq2ZzVyU9zVqStQqfnX2DtRzZ2YrDZsZkEtm9to4dA3Ws6gggSiLlfjs3\n7WjhzkNd2O1mJJPI7i2N7NzUQF93BYIo4PPZuW1/B3ff3oPDbkaSBHZvb2L3tmYG1lQjiFqCusO3\ndHPP0T4cdjOiKHDD9iZ27Whh3WAdgijg9do4eriX43etxuWyIEoCN+xoZs+uVjauq0UQNNPouo8d\nwWUV+MnZv+aVk5/h2OLLVH/0gaJp2OOxctexPu461ofLZUEQYOuWRvbsamXLpgYEQTOWXmM8biuC\noC1E9uxqZduWRkRRS3R3912rOXZkFR6PtWBMrmPXDS3s2N6MKILTaeaeu/s5dmQVZWUas35dLXt2\ntbJzRwuiqCW6O373ao7c0YvXqxWLXDtQw+5dLey6QVssOuxm7jnez5E7evD77AgCDKypZveuVvbt\nbkUUBex2E/cc7+eO23oo92tMf18Ve3a1sn9fG5IkYLOZuO94P3fc2kMg4EAQNKPr3t2tHCwsKK1W\nifvu6ee2W7qpqNCYVb2V7Nndyk2HVph7j/dz681dVFY6EQTo6a5g3542brm5S2MsEvfctZpbb+mm\nusqFIEBnR4C9e9q47eZuJEnAYpE4fvdqbrmxi9oaN4KgLXr27Wvj9tu6MZk05u47+7jpYCd1dRrT\n1urnwN42Dt/Wi8kkYDaL3HVnHzce7KS+3oMgaAkOD+7v4OjhVZhMImazyJ1HV3HoQDtNDWUIgmbC\nPnSgg2NHVmE2iZhNIkcPr+LA/naaCwkSGxvKuPFggTGLmEwih+/oYf/edlpbNKauzs1Nh7q4s8gI\n3H5LD/t2tdJWYGpr3Nx8oJO7DvdiMWtlBW491MnenS10tPsRRK1O1s0HOrj79l6sVgmTSeSWA+3s\n3tpEV4GpqnBw09427rq5C6tFQpIEbryhlRs2NtDdXo4gCVQEHNx0QytH93dgtZqQTCL7tzSyfU0N\n3c0+REkg4LNxcFMDh7c147CZtPk9UMum7kq6G8qQJAG/x8reAc2DY7dqzKbOCgab/XTWliFJIj6X\nhe1dlezqqsBhNWGWRAYbvfTWeGitcGGSBDx2M+ubfGxq9OG0Slgkkd5qDx0VLlornJhNIh6bmcG6\nMtbWebV+TCKdlS7a/E5a/A7MJhG3zUR/tZuBWm3DiNkk0h5w0up30FruxCQJuKwS/dVlrKv34rJp\nTEeli84KJ52VK8yGBi+bmstx2bRixl1VLvpqPPTVadfutJrY3hHghu4q3HYzkiTSW1fGYJOPtW3l\nSJKI02bm4EAt+wfr8Di1uNXX7GNzdxWbeyq1fmwmbtvSyM1bmvB6rIiSwJr2crb317BtsA5RErDb\nTBzZ285tu9rxeWwIosDqrgp2rm9g15ZGpAJz981d3Hqgg3Kf/Q//MP4f/6H952k8FlT1n+jV2P9C\n81R1qNsf/PfsXF/HqxdXpIu9g7W8ORIqbjGURIGda2o4pXutu7k9wKWlRJERBdjUWs6Q7pVkb7Wb\nuWSuyAhoReEmda9aG9xWQpk8+rvV4rExp5O1Ku1mgmkjU+UwM697DR6wmZhPZg1Mhd3MhG6sSruZ\nsXDKsD2yzmHmgm77aIPHxvmZqEEe6yp38NroyuvzzgoXZ68GDZLepmYfz52eKR6vavRy9tIiKd0r\n2wNravnJS6PF4zXt5VwaWiShe+V/67Zmnn72cvF4dVeAkavGV/VHDnbwg59cXBmru4LJiYhha/Ox\n23r4/tMXisc9XQEWF+KGLcnH7ujl+z88Xzz+mPwWLVdO8pdt78Om5GhLTvOvZ7/Loa6/KjItzT5y\nOZkp3RbOu4/18d0fnCseNzaUIYrGbeV3HevjezqmtsaNw2E2yCSlTGWFE5/PzpBOeitlyv12qqvd\nhbIWWrvz6CrDdXnLbDQ1eYt1sn4f43JZ6Gwv51ShThbAsSO9/OBHK/fQ6TDT21vJm29NF//u6OFe\nfqi7z3a7iTWrq3ntjakV5o5efvjjFcZmNbFubS2vFGpgARy+vZenn1lhrFaJTRsbeLFQ3wrg9tt6\neEb3vVssEls3N/K7F1eeqdtu6eanP79UfFVvNovs3N7M878dKTK33NTFz385VGRMksju3S089+ur\nReamGzv51bPDRSlOkgT27Wnj2UINLNDePj33/JWiFCdJAgf3d/CLX608vwf2tfObF0aRC1KcKArc\neLCTn/9yqMjs29PKC6+MF6U4QYCbb+zmZ7p+du9s5pU3JotSnCDAbTd381PdXNmxuZE33p4lq5Pr\nbr+pk5/qznnrujpODS0V0xsA3H6ok5/p7uHGvirOT0VI6+bu7bvb+MWbk8XjwfZyxoIJA3PrliZ+\nc27lGeup9zAfz5HSjbV/TQ2v6iTGloCDuKwamO1t5ZzWpZGo9djIKgopXbwZrCvjgi7WVjgsZFXV\nwPQEnAzppHafzURWVknoxur0OQz9eG0msnnFkJ6jO+Dk9PSKjOS1m8lkZcPW8/5qN69cXZEPfQ4z\nSk4xSG9bWvz8+u2V+eVzWpBk1SBj7V1dzc9eW5kXXqcFt8XEZZ1cePOGen6se549Tgt1ZTbO6eTL\n229o5Ue6Z8zlMNNa4+bMhQVOPPPQSVVV1/MutT6HTf1+Z/MfzfeeHXpXz+9/t71nPDk5WTHmv0Gr\np6JfLMiKSiRp1DwjqZyBUVRIlOi0yaxsYFQwTEKAjKxQuhxMy3+YyZboqxlZvb6fkrHSskKJBGzw\n32jHRv8PQDSdLznOGRY4AKGYUduOxDOGBQ7AUsSoW4eiGcMCB2CxxP+zHEkTL9HNF0p0/dByyuBF\n+H1MMJQsyd2CoeYRgBCNMGUNkBPN5EQzU7ZKbGmjjr68nLpOj18o6Sekq83zP2NSJfe19HyWwymU\nkn8slPYTiWQwW6T/KRONZQiWeMpKmXg8y1KolDEeJ5K5P9hPKpUv1qT6HzHpTN6w2NQY433OZGSW\nloyfW1wwMtmsfF0/i0sJgxchl1MMeXR+H5OXFUONLNC+C73XSJbV68ZaCiYMXiNZVq+7Vo3R+eAU\nlcWSa10MJg1eI1WFxaCxn2AwafAaqap2HQZmOWlY4GjXWnLO4ZRhgQOwuHz9vEyXzt0Sv+Fy/Hom\nFDfOwUjCuMABCJd4R+LpPMaejfm/QItJcglTGreSOfk6T04yb2TShc0gpZ/Tt1ROIVPyuXjJ+aSy\n8nXXHi3xUcYzeeSscaxwSRyLpXIIJXE0WOL/iaVyyKXfRUkciyezGB1c18fReDJHMFx6p9+tJhgs\nCP9c2nvmpdPazgC3bmos6rImUeCmDQ206upZ9dSXsaunqqgliwLc0FlBg+7VX7Pfwdp6b1EnFoA1\ntR4qdb6dSqeFTp/doCW3ldnx6/TVMotEo9sljUOBAAAgAElEQVRqzMvgsuLV5+QxS9S5jEydy2Lo\nx2WWaPHYDV9Ei8dGra6eS5nVxOoqNzrrCv01ZXTocm2UOy3saAsY9OZt7QEG9R6CMhs3rasz6M0H\n1tazQ+d1qvE7uHN3G1bdD/KtO5rZv3nFJ1NT4eTeW3uw667jjgOd3KjzQlRVOLnvWJ+hjs/hm7u5\n9cbO4nFlhZMHjvfj0t37I7f1cvjW7uJxoNzBg/cN4Nb5UsqO3srty2+yNjpMIBvmzya+T3LXPoPn\n5PAdvRw9vKp47PPZePD+AYPn5PDtvRw93LvSb5nG6D0nR+7o5cgdK4zHbeWB+wco13kPtH5WxnK7\nLTx43wAVOs/Jbbd2GxinU2OqdM/vrTd3cUTHOOxmHrxvwOA5ufnGTo4d6Sse2+0mHrxvwFCr6uD+\ndo4dWenHZjPxwL0DhtpQ+/a0cefRFcZqkbj/3jWGWky7b2jhrmMrY1ksEg/cu8ZQ32vH9ibuPNpX\nnHNms8h9966hvX3FT7J1SyN337nCmEwi9x1fQ5cuH8imjfUcv2t1MciaTCL33t1Pb8+KF2z92lqO\n37nCSJLAvXf3G/IGDayp4fhdq4s+L0kSOH5XvyG/Tv/qKu45vsKIosboc96s6qnk3uP9Bubuo6vZ\noMvr1N0Z4N5jq4t5TgQBjh1Zxeb1K0xHm5/jR/uKZnFB0N5ebl2/4k1ra/Jy/HZN4ioyN3axXddP\nc52Huw91FhnQ3trs0J1zfaWLoztbsOqYWzY3sa135f5U++zcvL7BEAP29teyqX3luwi4reztqcKq\nY7a2BxjQ1asrs5vZ0uQ31OEbrPfSq/cAWiQGajxYdIGrt9JFlz5HkEmkr8JtYDrLnXTq/DY2k8jq\nKjdW3VjdFU56dX4bm0lkbZ0Xu+6c+6rdDOpyh9nNItvbAoY8ZRub/GxtX/EyOiwSB/pq8Oji1o7u\nSvbqch05rCZu39SIX+eD2ztQy02bGg3MXXvaqdTFkoObG7l114qHy241cfzmbkOuo4M7mjl8aCVG\nvqtNoFDB/Y/7815p74lFjiBAX1uA5mo3Xo8Nk1kk4LPTVOWis8GL2SJhtkj0NvmoL3fgL7NhsZoI\n+OzUlTvoqHJjt0nYbRId1W6qPTYqymzYbSYqymxUuW00+x047SacdhPNfgc+m5lyhxmnWSTgMOGz\nm6lzacZit0Wizm3FYzFRbjfjNEv4bWbKrGZqnBY8FgmPRaLWpf1/wG7CZRYpt5nwWs1UO624LBIu\ni0SNy0KZzUTAro3lt5kot1uo9VhxWCTsFolatxW/w0LAbcNmNeF1Wqh0WWmtcGKzSFgtEo1+O1Vl\nWrE5i1mkzGGh3uegq86D2SJiMou0VLmoDzip9NsxmUXcTjOt1W76Wv2YzAKSSaCt3kNjtZvKcjtC\nwQfS2eilvyuAIAogQEudh+a6MqoqnCBoP6JdrX4G+ioRTQWmyUtLo1crtikIWG1mersqWLOqqvgj\n1dzopaXZS03BXGqxiKzqqaB/dSnjKxa3NJtF6jf1YhFVvnz1q3z/nX/F2tgVPBsHisUtzSaR/r4q\n1ugSbTXUa/1cKzhpMoms6a+mv0/PeGht9heLSV5jVvdVFX+k6urctDb7isUbJUlgoL+Gvt5KLBaN\nqa3x0Nrip7nAiKLAwJpqVvVUFk3NtTUuWlr8RSOrxtTQ21NRZKqrXbQ0+4qFPEVRYHCghp6uQNH4\nXFWpMa2FRJmCAGsHa+juqsBeCNSVFU5aW320ta0wAwM1dHYEcBRMjxUVTlpbfHQUAr7mCaqhs6O8\nuAgNBBy0tpYbFieDa7R+rpmjy/0O2lvL6e5cWZwM9FfT0VZeZPx+O62tPnp7VvpZs7qa9jZ/cTHr\n89lpa/WzqmclAV5/fzVtbf5i8j+fz05bm5/VugSK/auraG8rLy54vWU22lv9hqSGfauqaGspLy54\nyzxW2q5jKmlt8eMvd4AAnjIrHe1++nVMb08lba3+YhJBt8tCZ2s5/asL/9ASNPm1tcmHr/Bj53Ja\n6Ggtp39VZZHpbC+npdGL36+N5XRaaG/xs6ansviD0tHqo7mujIDPrjF2M+2NZaxuDyAWmPbGMpqr\n3VR67YiioDF1HlY1+5Ak7V/pLdUe6gMOKn12JJOA026itdpFd50HSyFONFW6qPHaqfRqsdZpN9EU\ncNJW4cRq1nxNdV47FW4rlR4LFpOIyyppyfe8tiJT5bHid5gJ/P/svXeUJNd15vl7YdJXlvdVXa69\n967aoGEIRxKECJIACcKbbgAE0GigARpRDekczVCzknZWGtkZiVYSOZyhViRFEoYAYRqGaO9NdVV1\neZtlMitNuP0jsiIjolokds8QOuDOO6f+yKgv73th3s0X937vu9EgqiIRCSrUxEPUFgUJqTIBRaKq\nKEhpWKUiYtsJB2RqYkHqikKEAjamMmYX7KyMBQioEuGgbIsBxsME8hyqiliAskiAyiK7r5Aq01gS\nobE0TFCRUCRBZSxAZSxAbUnYxgRkWiujtFTGCAYlZEVQVRyipiREQ0UEWREEAhIL6+IsqI8TDsnI\niqC2PExDRZR5VTEkSaAqEsuaSlk8r4RwUEaSBHXlEZqqYzTVFSFkgaxIrJhfzuKWMnt+C6ipjNBU\nH6d5XrHNh1EEq5ZWsait3PMC+UE1AQhJvO+/D0v7UHByimsXWFvv+b9oX13LcZf0+ubFVZwe8m6J\n3ry0inOucPmK+mL6fduvVzeW0OsKNzaXhpn2pX5ai0OMudIUFSGFjDdiSWVYZdoVRi1SbX0ad4sp\nElMuTESRmPSFNSOyxKgrjFqkyvT6QsrFiky3KxRdEVY5l6+lMtvqogFOuHLkDcVhTnSNeUL+S6ti\nvOUSmmqtinHs3Kgn3bJ5fjkvu/gcCxuKOXfW1umYbbvW1PGii4cxv6mErs5xTxj+uvZmfvpygT/R\nMq+Yvp5JMq7resM1bfzkhQIXoWleMaP58gaz7cbr5vOvP73gfN4z8yYVA5f4/ZY77XOY6eevO/+K\n65b9voOpqY6RyxmMu0L8N9+4kB//pMCNqKiIIAnhSV3cdMNCD1ejpCREJKx6pPv9dmKxAKUlYXpc\n+Xi/nUhEpboq5ikdcOP1C/jJzwrnFQoqNDYWe7Yu+zGqKtHWWsbZcwX+zw3Xz+enPytcQ0WWWLSo\nwsP/uf66+R6eiiwLli2t4viJIefYR66bzwsujCQJVq2o4cixAj/humvbPJwYIWDdmjreO1zgeV17\nTRsvvezFbFjfwLu/LPB/rtnV6uHfAGze1Mjb7xT4JLt2tvDKLzo9mPYt8zwcoat2NPPqa10ezPb2\nJl5/s9v5vGNbE6+90e3B7NzezC9cz++2rfN48+0eD2bXVS286sJs2dTIW+/4Ma284up/04Z63js2\n4Jlz1+xs4edvFDDrVtdy9OyID9PMKwcL57V6WRWnuiY88/Ka9mZeea9wDZfPL+f88LQntX3tpnm8\n7uLbLGwspi+R8dpZW8e7lwrPWHNllPGcYZdimT3XhZUcHyj4ktp4kLSJB7O2sYQLrnRdWVhBQ3jS\n6IurYnS5+C7xoOLUhJptTcUhD/8xqkpohkXOhWmMBeh02YkoEmnN8KT6m+IhD9cyosqkMxpJl79d\nUB7lqGueRlSZnKZ7yvysrC3iLRe/LqzKyIbpKZmzsaWcV1zzIhSQiSkSPS5fsmN5NS+6npegKlMd\nCXDJ1f81Gxp4wcWzUhWJpsoY5zvHOfiDuz5QzsuKWNj6wYq2Xw/MtwVvn/rfnJz/1U3z5Wl132dg\nDk/F8JNbAP/X/NokwBxOzNyewM+uuYIZ/CydK60p/XwO/2ewdXk8n825/B//uRqWOac/3bcI0wxr\nTn+aL/+c0805tjVfjlzTTQ/vAZjDKdB008NpuCImZ6D7juV8i0JJ08iIQvoqIweQTJ+dfPHRX2VH\n18w5byQ5H49H10w09dfY0U00/VeP+YoY7QoY/7n7PhuG5eF8AOSy3s+GeQU7uSvYyf3q8zJNa07/\nfu0hy5o7Rv81tKy5x/x9wdxn6kqYuX3NnZnZ3K/H+G1fEeN/NrUrjOcKdvxz7kp2/Bj/PdV0c868\nzOlz55Pf5/ifMf0Kdub6UWuOD/T7Ud205vQ11yeBKX61/zVMC8sXBJjr/+b6Ur90jI2Z6xP9dv3f\nm+sjrTnH/D7SsCwsv//zXUPDsNCF7x5qc3+v/P7P/0wZhjXnHn6Q7cOUhnq/7UORrgK4cUMDt29v\ndXLJ0aDCp9ubPZyT9oWV3LCsxskThxSJ6xZXsdiVu11WXcSGhmLU/I+bKgnW1MZpcHFgGmJB2krC\nDgdGFtASD1PuCiGWBmVqwgEHIwE1kQDFrnxvTJWoCgccHpEAqiMByl28nbgq01gURMkTFiSgOR6m\nqajAHakIqaysjDl5a1nAquo4q2td2h/FIa5eUOnU4JIlwdULq7hmSSG8Pr8qxm2bm4jnUxSKJPjk\n5nnctq2g0bGksZj7blpCWT7cr8iCu29YxF0fW+JglraWseeO1VTm6/jIsuCBT6/kvttXFezML+ex\ne9fZKa38eB6+ay0P37vOwSxeUM4Tuzc76SpJEux+YAN7HtzoYBbML+fxR7c46SpJEjTtvY+PTR7i\nk0Ovs2HqHF+7+HdYn7vT4ZwIIXhk9yYeeXijwwNpaS7liS9scdJMQsAjuzfmMTZo3rxinvjCVic9\nJAQ8smcTex4qYBobbMx8V+pntq/ZFFtdXRFPfGEzCxcU0jF7HtrInoc2OhyP2poYTzy2lSUu/aHd\nD23g4Qc3OJiqqihPPrbVwzl56P717H5wg1PzqqoyyhNf2OzhnDxw73p2P7jRScOVl0d4/LEtnlpM\n9961ht0PbXC0hcpKwzz+6GbWr6tzMJ//7Cp2P7SRQL4eW2lpiMcf3cymjQU+yR2fWcmehzY6+kPF\nxSEee2QzW11aR5/65HL2PLTJScPFi4I89shmdrg0gX7nE0vZ89BGJw1XVBTgsUc2seuqwrP58Y8u\n5pGHNzppuFg0wKN7NnKdS/PmphsW8tieTU4aLhpVeXTPRm74yAIHc/1183l0zyaiURsTiag8snsj\nH72pwIW4+qpWHnloo5NiC4UUdj+wgVtuLvDFdm5r5rGHNjoptlBQYff967j1owVM+6ZGHrlvPfE8\nfyMYkHn4rnXc5sJsWlPH7s+toTiPCagyD3xmFZ++YZGDWbesmoduW0FJHqMqEvd9YimfdmnwrGwr\n574bF1GSH48iC+68ZgG/49LXWdxQzKfbWyjOXx9ZEnxi4zxucHFOmiui3Lyi1qmfJwn4yJIadri0\nYmrjIba3lFGUv6cC2NJcxnoXB6YiorK+Lk5ULWDW1BSx3KW3UxJUWFkZIzrLRwKWV0RZ7uKpxAMy\nq6pixFy+dWVVjDU1Bf9XHFTY1FBKictHb2goYVtzmcOJLA2r7FpQQYWLA7hrQSXXLy1oh5VHA3x8\ndb2nTtfHVtfzOy4+aGU8yOd2ttLs4tPdvrOFO69d4PiAqpIQ99+8hAUuHtzdNy7mnluWOlo+laVh\ndn9mFUtdnKB7Prmc+29f5dEO+8CaEEiq9L7/PiztQxHJEUKgY6+oFVXGEiCrEoZlISmCYCg/iRT7\nwQgHFWTDJKTIWNhOI5Z3jMGAghCCoqhKzrDsBZGAkCw5Qn4hWULCnjiaaaFKAklAUUB23l5iqows\nLIoDBvkCwSiSRVjRMCw79BmRFWShEA9o6KZAlixkKUBEldAsCQuIKgJJCIqCMpphoUgCWRIEFYmi\ngAJYRFR7jNGggqKbKMLOr8uqRCSkYGE7T9OCUEDCtCxnIpmSQA0qYNkVig3TRMgSsiIhSxKGBXr+\nugIgCXTDxBQCIUtYsh1+zummfX0tMLDIGSYGBaKapptkXbsbcrrhidyYlkUuZ9hvvvn5q+kmOU1H\n12YrhdsYt4LtbGRn9u3GNC30dA4si4+PvoVkWcSMNGY647w5WZZFNquTyxXemDXNQNMK0RTLgkzW\nQBI2Huyoja6brvFANqMjKGA0zUDL6a6+bHXcTEZx3obtiIw3mjJb4mAWo2kmWs7wvOVnMjqaZnjs\nZHM6mqZ77OQ0A9MyPefljpRkMrbSq/UrxpPJ2n2b+bdW3TDz5+bFaDnDeUPWNTPfl3fMuZyBOYvJ\nXz/3eLJZHU0vnJdhmui6QTareezY527bmY1YZTM+O5qJmX+LNkyTXM70PC+zz9jsTinDMPPPlOaz\nY9iRAGE/m5pmkMkYLjs6Wq7Ql2la9v3QTGZXzjndJKcbdrRWAkvkMVmvnZxu2hEFITAR5HTfmDUD\nzchjJIEp7EhBVjec11DNMPPzMv+2LdtRWHs8NkY3TTTDwpJweDq6aebnt+1vLCkfTZEkJElC5D8b\nCNu3AsgCw7SQZQlVlpCkwvMfzNtRFHsXqixLqIqFEPlq4UI4i2JZkfL+V0LDsl8UhEBIFoG8r1Zk\new6pskA1hcNTQmBjLHuxZpHHKFIeIxBCEFRlLMtCVSQsC0cvSWD3ZQmBqspYWCh5jKyAooj8mC0s\nq/A/SRJ2FEngLDQMy0I3BZIkgQWWsMtYmMKyMcKOdOUME4T9LOhY6EY+up2/Pzndvs9WHmNYluMn\nHUw+Am35dn1+EE0Ifit3V30oODkldQutHQ/9ORuWVXPexTlZ21ZOp2+787r5FXS7eBgLq2JM+MJ/\nS2rjHg5MbTSAP1rdEAuSdH0vHpDnbDcuUkyyZsFZBSQJ3fJuPwxIAQ9GFQppw7uVWCBIukKbQUkw\n7NvCqQrh0eQpUmUu+bavlioS5118pKpYgJM9Xvnx1niIQy79i/qyMGd80vQrG4p53aXV0lQVo+Pi\nqCfEvnVpNa+9W8g3z6stoqtj3BP23rGhgVdeL3Ah6mtjDPRNedJau9qbePnVQk66tjrG2FjK80N6\n9Y4WD3/j0clXCY2P8H803WZ/JzvGd879MVev/EMHU1YaJqcZJF26Pdde3cpLPy/YKY4HEZJgwrVl\n088ViUZUwhHVs3XZbycUVCgpCTHoksv321FViaqqGH0u3Z6rd7XycxdGlgUN9cV0Xy7o9lx9VSs/\nf7WAmRXBc5dkuBJ3ZcH8cg+350rclcWLKjzcnp07WvjFa147S5dWcdrF7dmxrZnXXPwSsNWTT5ws\ncHv8nBiAVStrPPo/27bO4w0XBwVswvThIwWew9bNjRz08WTWr6vjvUMF/s/mjY28/a4Xs3F9Pe+6\nOGWzxUHdbfOmRs+xDevq+KXLLsDWrfM8HJy1q2s5fHzIg2nf0shBl9bQ6pXVHDvpLUOybWsTb7r6\nWrGkklO+Ug/b25t481BhzEvnl3O+3zt3t29s5OAJF9+mqYQO31b4nevredfFJ2mpiTGc8vqS9mXV\nHHU9Y3WlYZKWN/m+vqXMw22siAXQwYNZWlNEt4unUhRUMIXwYFrLIgy4+HVhRWAJbzqqLhpg0MWJ\nCckSmml6Uk3VkQB9Lp5iUBZkcqaH21MTUemcSHswMxndw9tpjAc57SptE5AlclmDadeic2FFxOMj\nVVkg6RbjLl+yqrGEg6cLz4IiC0JCMOj67dm8oIJfuDTJJElQHVbpcfmJbStr+IXrGRcCGipidPVO\ncvD7d36gnJeV8Yj1o02Lfj0w35peOvqh4OR8aGJOAgip3sWBexvkLMZf18e9xXG2Kb7VqnyFVbN/\nQSuYi/F/7X1hrrBQ9vd/pcW0/zQUaW5vqu+LqiTNsRX0XcOQInuk0AFCAW+ALxyUnfRI4ZgXEwrK\nzhvcbIv4aj6FggpBv+2wOueze/s6QDjixViBAHGjsOiIGWkMxddXSPGUXrhSX1fCRCLvx07A8zkY\nlH+tnWBecduDCXs/BwK/3s77waiq5CkpYWO8Y1YUiZDv/vjHo8jSnDH774UsiznX1T8eW63Zd599\nGCGu8CxcARPx9xWdG4z2f89/La40Rn/fMLevcFidM3/njDmkznkbnmPnShj/dQ4pc+elf84F5mLC\nvvkVUufOb78PCCrSHIzfb6r5CLPnmB8jroC5gk/y+7s5/lia6xMV33WXr9CX4pPhlSVpju055yWL\nOecR9NUsUGVpzm/NlX6L5vhW370IKNIc3xYJ+uauIhMKejEfWBP/ewv5v2v7/DXzuXNnq8MnqYgH\nuWNbC1ctLmwfvXFlLTcsriY2m/sPKVyzsNLDXVlXF2dVVRGh/IMdViSWV8SY59I8mBcL0hALeng7\nddEAJQGZ2XeZuCpRHAgVODkCSoIhYkqBSxNVAhSrEWfCSkBxIExJPg0FEFNkqsIBpy9ZQG006BlP\nVVhlSVmUaH6iqZJgeUWUDXWFfO/8sghXtVVSmr8+IUXimoWV3LKq3nHMaxpL+MzmJmrz+eZwQOaO\n9mbuv26BsxjauriKh29eTFM+3xwJKuy5ZRl7P7vacSrb19TxxOfX0JrPN4dDCk/evZ79ezYVMBsb\neWr3JhbluSvhkMIzj23hi3vbnTBw+6ZG9j/RzpJFdq4/FFLYv7edL+/f6fBJtmxsZP9T21ie3yYc\nDCqs+aOnuSpznv1d3+VTQ6/xZ+f/kshzT7Mqr/cTDMp8+bmdfPm5nQ5XZP3aOp59ZrvDSwkEZL70\n3E6+/GwBs3pVLc8+vZ31eS0UVZX4yhev4kv7dzp8khXLq9m/bxub87wUVbExz+3f4Sw+li+rYv++\n7Q4vRcljnn1mh7NoWLyogmef3sGOfO0sRZb4ynNX8ezT250fzoULytm/bxu78nWNZFnwpWd3sn/f\ndqfm1fy2Mvbv2+7UYpIkwRef2cEzT21z+CStLaU8+/R2h5ciSYJnn97OM09tc/gkzU0l7N+3nZvz\nOkaSJNi3t51n9m5ztmzPayxm/75t3JLXMRIC9j6+lX1PtlNcbGMa6uM8vXeboz8kBDz+6GaefrKd\n0vyW7bq6Ip7eu43bP7XCwTy6ZzP7nmx3NIpqa4p4Zu82PnfHSucZf/jBDTz15DZHo6i6Ksq+J7dx\n951rHMyD961j35PtVOZrZ1VWRnl67zbuv6fABbv3rjXse6LdqZ1VUR7hqSfaeej+wkvp5z+7ir1f\n2Ep1ns9XVhZm3+Nb2e3C3HHbcvY9toXa/FwpLQnx1KNb2HPfemfO3fbxJezdvZH6Gls/piQeZO/D\nG3ns3nUO5pbrF/DEvetpyHPT4rEAj9+zjkfvWO1gbtzewhduX0VDfjyxiMqjn1rJI59Y7szda9bV\n8/DNS2jI69BEQwoP3riEe6+Z72C2LKrks+3N1OWvc0iVuaO9hdvWNTiYlfXFfHR5DdWzHCFZ4ubl\ntVy3sNLBtJVH2dFc5tTYUyXB9pYyttQXOy9fDUVB1lYXUZpfnMkC1lQXsaoi5mCqwiorymOOvpgs\nYEVFjJUVMefHqSKssqIy5uiLSQJWVxWxvqbIGU9VRGVjXZzqPN9GFrClvpirWsod/1tbFOTqtkqa\n8v5PFoIbFlVxy8paZzHUWBrmE6vrWZTn+8iS4PZNTdzp4oO2VMW466pWVuVlG2RJ8OBHFrHno0uc\nxU9bbZxHblnK5rxGkSwJnvzUSh6/YzXhvC9payjm8TtXsz2vmSRLgn33rmfvfRvmvHB8ME0gJOl9\n/31Y2oeGk3OsK0FNVYyMaREIKSQ1g67RFN2TGUJ5h9+RSNM4ncEUEA7JGFgMJTOMZXWi+R+O0axB\nMqcTkAWqLCOA6ZyOZlnE8w+fZllopklMFVj5+IxmGFjWNBFZw47ZyJhWiKA8ioWEwMQwQZImiCh2\nWFUSKoZVQVAacTCmKTCtHGFZy5+bjGaWEpI18vIJaIZd8TwesHPkFpDUbP5IVJXsMWd1xnI6sbDN\nyUkaJqMzWXKW5fyQDiZzdIymnDeMweks3WMpJjI51ICEjkXHcJKjXQmQBBLQMTTNxf4phibSyLIg\nqxuc6Bzn1LlRW81UEpy9PMnZzgS9w0mQIJ3TOXJmmAsXRm3OkoAzHWOcuTBKd/+Ug3nv2AC9lyed\ndNWZ86OcOjNMZ74MRyaj8857vYyOpBwuz9nzI5w+M8KlfPg4m9W5+MK7tGoGUTPL0lQ33aEqGl56\nnYuU5TEGB9/uKXCAgPMXxzh1etgpz5DLGRx8qwdJEg7mwsVRTp2yzwNs3sybb10mHFIcnkVHxxin\nzw471dM13caUloScrfEdl8Y5dWbYqVau6yZvvNlNbU2Ro57c2ZXg5KkhTp/JYwyTNw520zSvxKlW\n3t09wakzw5zMp4sMw+KNN7sZGUk5FbMv90xw6vQQJ/PpItO0eP3Nbiansk6qrqd3khMnhziWT3WY\npsVrb3SRyehOGY7evklOnhpyUkqzdsCuIg7Q1z/FqVNDTkrJsuD1N7sJBGQmJ23MwMA0J88Mcyi/\npdyy4I03uykqCjpK1oOD05w6Pcy7+e3QlgVvHuymojzsbPkfGp7mxKkhT0rp4FuXqauNO2rOwyMp\nTp0a8qSr3nqnh5aWUkdBeGQkxYmTQxx0SfC/9U4vixdXOkrEo2MznDg56MG888teViyvdhSex8fT\nHDs5yEFX+urdQ32sW1PHUD6tk5jIcPzUEAff7XFSu4eODrBlYyMDeamLiaksx04PcfBQn73LSMDR\n08Oc7hhjYDQFAqZSOY6fHeGtE4NY2JyP4xdGOdOVYCAxA5IgmdE50THGka5xLNn2Cad7JjnXO8nQ\nxAxCwExW51R3gkujSYQkkIFLw0m6RlOMzWSRFYFmmVwYnGJoRnMwfVMZ+qeyTGV1m+sCXE6kSWoG\nsiwhA+NpjZEZjbRpOtGJwVSOnGU5n5OGxURWJ2saBPOhmLGM7dtmFxUzuslkTkczDEL5l5+JjE7O\nhcnkyzekNdN5GRxLa+RME1m2x5wyTBIZnZRuOouRoRkNTTfyGMF0Tmc4mWE8rTm2uxNpe3eVsFNO\nY6kcfRNpBpIZpPy5nx2aJoDNXZRkweBUms7hJF0jSRA2t+ZI5zjFQYWsbiAE9I0lOd87yYX+SZt/\ng8W754apLw7bCvMCeoeTnO1McLZz3Ks+EUgAACAASURBVMG8fXyAkbEUMz6F+Q+iiVm+129Zkw8c\nOPDvPYZf2772J39+oGjRteQETMxoeW6MIGuYDCSziDwJbTKtIWRBMmc4JDfdhCnddDBp3URVBFnT\nco6ZgG7hfNYti4BsbxufPWZhYJImbxYTEyEyWOgIMUu882IsbIKoG2NYFppluDAmmqFiYDnHdAum\ntULfhgXTOYO0UTiPjG7Snyqcu2ZaJFI5EmndOTad1Tg/OO35TmIqy8BkxjmWSGY5fmnc+TyTM0hM\nZrg8nHKOjU5mOHJ6mNkBzmR0piYzdPdNOZihsRRHjg0WrnNGZ3o6y6XuCefYwFCSY8cGnR8AG5Oj\n41KBX9LfP8XxE0MO0TGTt+OuHbX62Iuckyv5o9bb+UXZKg4WL+XOw9/mb8uvdjCXL09w5tyIs1jK\nZg2SySznzxe4EN3dE1y4OOYscjTNJJnMcs6FuXQpQWf3hLOA0XST5HTOw2W52DHO5Z5JZvILD103\nSSZznHHpEXVcGqe3f8pZeBiGZWPOejGDg0mn9IVhWExP5zhzpoC51JlgcDjpLCoMw2JqOusslgC6\nuicYGUk5iwrTzGNc3JrLlycZGUk5iwrThOnprLOgAntxNDo64ywqLAsmp7Ie/Z2+vinGxmecRYVl\nwfRUhhOnCpj+gWnGx2YcPSLbToYTLu7K4GCS8UTGWTBYFkxOejFDw/Y5ublPE5MZj9bP8EiKxESa\ngcF/GzM6NsPkZMajfZSYSHswY+NpJqez9PVPe+y4+TaJiQyTySy9LkwiMcNx17lPTGaYTuXocfU1\nlshw8sJowW9NZ0mmdXoHk86x8ck0JzsTzpybTmmkcga9Iynn2NhUltO9k853UhmdrGHQN5Yu2Elm\n6BydKczLnIFmwdBUwXdMzOTonS58zuomJjCW97VCCCYzGmOZwmfNtLCEYDLva4UQJDWDyVzBRxmW\nhYlF0uV/UzmDqZzhEIcNy94ePuPx0QaTWd3BmBbkDJNpzWVHMxhLa/ZLaB6T0Q0SGZf/y+kMTWcw\n877dtOwyDkOucx2bsRc1ev73wLTsEg0944VrODiVoXckRTY/RsOEqZTGpYGCb+0dTdEzlGQmaxQw\nyRznewr+r3tomsGBJMm0lsdYJJNZzrr8b1f/FIMDSaaSOXpO/8+BAwcO/A0fUPur//iHB+5sqXLG\n8uv+/uRc/wc6vv+v7UMTcwooEmUxL6+gNBLwcE4USVDky3HGgrKHuyIJm4fibsEr8Ftmt3Q737vC\npZJ8gTD7HcfPr/FiZDE33yr7Qn+KmDuekG+FHVbm5raLfLncopDikWYHKIv6rmEsSMT3veoSbwXc\niuIgRT4OQ21FxIspjVDiKqsAUFtV5PlcVRF1Uhazra4m5sVUxago9/bvLmsAYJWV0ZYZdESHWtMD\nZCJxD6ayKkqlSz7etuPDVEadtMb/K0xd0RUw3r5qfWMuL4tcYTxeTFlp2FMKAqDe11dJcchJsxQw\n3jEXFQXnYnx9xaIBT0kJgDqfnUhEpapqrh33YxcOK05Kx7FTG/dgQkGF6ho/psjDSwkGZaqr514f\n91baQECmxjfm2hovRlEkW2Xbh1Fc80CRr4xRXdtiZVk40gazrboq5qQ2wU7p1VXPxQR9GP+Yq6ui\nHn6NEHik/QGqyqNOWmO21ZR7n8PKkhARH0+nqtg7d8qLgo6sROGY1weURFTCPj5JsY9HVBSQPSUT\nAM+WboCoIjs0gNkW8X0nrMqe8gzAHLtBWZrjt8I+nx2SpTl+PKr6eE2KRMR3XnEf9ykWVCjyXcMy\nH38tHlIo8R2r9Pm6kmjAU+YBoKYs7MMEKff5v9pK77NRHAtQWea9zx9YE7+dise/sUWOEOLvhBDD\nQoiTrmMHhBB9Qoij+b+b3tcgBdz3kYXcsbWZmuIQsiRorIjwqY3zuH5JDaosCMgSH1tRy9ULKinP\nL34qYwF2tJSztqYIRRIokmBdTZzFpRFiqr34iaky80sj1EWDSMLuqz4aoCwUQJXsZJEqWZSGghSp\nUewElkVMiRBRypHFbC5ZJiRXEJIqnAVKUCojLFf6MOXElELeOqJEKQ6EsSsCWCgCSoJBavPnILDV\nlpvjYXuHFxCWJeaXhFlbbZ+XJGBRaYQtjaXUFNnnEQ8q7Gwu55YVtY6seXtrOZ9Y10BbVQxZEpRF\nA9yxqYnd1y8iEpRRZcENa+u59/pFLGsuRZEFFcUhHvn4Up69ay3RsIKqSHx8RwuPfGY1a5ZU2ZjS\nME/fs56vPN5OLKramOsW8Pj969m4utaWXS8L8+yjW/i9Z3dSVBRAVSU+esNCnnxkM1s2NaAoEuXl\nYb789HYOfHkX8aIgqipx0/ULeOrxdrZtnYeiSJSVhdn2l19mlRjhb0//KV+69A/8yfm/pvKP/4Cd\nO5pRFYnS0jC/9+VdHPjq1ZSUhFAViWuvaWPfk+1cfVUrqiJRUhLiq1/Zxe995WpK85hdO1vYt7ed\n665tQ1UlSopDHPjdXfzul3ZRVmpLwe/Y1sS+J9u58foFqKpEcTzI8797NV/90i7Ky8IoikT71nns\ne7Kdm29aiKpKxIuCPP/Vq/ndL11FRUUERZHYvKmBp55s5xMfX4KqShQVBXj+967hS8/tpLIyiqJI\nbFxfz97H2/nkrUttTCzA81+9mi/t30lVlY1Zt7aOvU9s5dO3LbelEqIBDnxlF8/t30F1dQxFkViz\nupannmznc7evJKDKRKMqX/3KLp57eju1NTZm1YoannqinbvuXE0gIBONqPzul67iuWd2UFdrLxJW\nLK9m7xPt3HPXWgIBmUhE5ct5jlB9fRxFkVi2pIq9T27lgfvWEwjIhMMqX3x2B/v3baexwcYsXlTB\nU09s4+EHNuQxCvv3bWf/U9tomleMokgsXFjOvie38cjDtr5OOKTw9JPtPLNvG81NJSiKxPy2Mvbt\nbefxR7cQDNoE8b1PbOWZvdtobSlFUSTaWkt5em87T3xhi00iDyo88ZjNEWprLUNRJFqaS3h67zae\neqKdUEghGJR5dPcmnnq8nQXzy1EUiaZ5xTz9+Faefnwr4ZBCMCCz+/51PPnoZhbNL0eRJRob4ux7\nbAvPPL6VcFghEJB54K41PPnwRpYssDENtUU8vWcTz+zeRDikEFAl7r5tBY/dtZYlbWUosqC2KsqT\n96xj393riOQxn71pEY/ctoKlLfa8rC6L8IVPr+LJT64gErTn5Sd3tHDf9YtY0lhilzEoDvHQjUt4\n8LqFhAMyiiy4fnUdn9rUxILqImRJUBoNcMeWFm5f10hItf3E1tZyrl9cTXNZ2JbOCCrctLSGaxdU\nEpQlZGHrjW1qKKEuZvubiCqxpaGEDbVFBPI+qbk4xPKKGFVhFQl7YbKyIsrKipgtywHUR4MsKo1Q\nEVIRQEASLCmPsqws6mBqIgGWlEWojth2grJgZWWUdVVFBOWCndVVMRry/i8oCzbVFbOjqYyQYm/A\naC4Js725nEWVMWQhCKuyzclZXks0ICMLwcKqGB9dUcu6plJkSRAJyHx24zw+v72FeFhFlgTLG0u4\nY1sL25dWo8iCaEhh9w2LePRjSymNBVFkwZq2ch64aQk3bGxElSViYZVnPrOKpz63hvKSEIosWLu4\nkj2fWsnHd7WhKhKxiMpzD2zi6Qc3/LssdISwZUne79+Hpf3G0lXPP/98Avg74NYDBw78Rf7YVcBr\nlmXddeDAgb86cODAhV9lY7Z97U///EBk8bWoQYVjvRNIsh32LI6qvNc3iZ7XNxhL5YiGFLqnMqiK\njGZBNCDTO5NDSLbGwoxuEFEVpjQjr5EjCAhB1jJRZYmgbOvvBOQchjWFKmWRRBaBhckQipRCkTLA\nDLIwkMQAqpRGFjMIISFEP6o0jSqlkcQ0oCBL/ahSGkWaAWQ0K4HssmNZQXQmUaQskpS1t5Tr9sRU\nZYFpWegmTOTsMUt5J9I5mUG37EjQjG5imRYXxmdQZAkTe8H23uUJO30nCcZncgQEvJ4PlWcNE0kS\n/OLEIGPJHAjBQCJNLCDzw3cu29XYcwYCwcvv9DAwNoNpQc/QNBWxAN9/4TymCTMZHdOyeOXgZXoG\nk5jA5f5pqssi/OM/n8I0LWbSOrph8vrBy3T3TmJacLlvkrqqGN/57ycxLYt0RieT03nr7ct0dCYw\nTYvLPZPU1cT49j8ewzAs0mmdhjPvUHfibf6lYhOTSpShQCmlx97hPw23oBsmmYxOMpXjyJEBzp4b\ndew01BfzjW8fQddtzNRUhhMnbV6MaVr09k7R0BDnG986gqbZWiYTkxnOnBnm5KlhG9NnY77+TRuT\nzRqMjae5cHGUYyeGME2LPhcmlzPJ5gxGRmfo7Epw5OgApmnRPzBNY30xf//Nww53aGg4SU/PJIcO\n9xcwDXH+/huHyWZtzMDgNINDSd79ZR+maTEwME1jQzFf/8ZhMnkNnf6BKUZGZ3j7nR5M02JwMEld\nnT2edMbWmunpnWJiMs2bb9mYoeEktXVFfONbR5iZ0dA0k8uXJ0kms7z+ZjemaTE8nKK2NsY3v3WU\nVB7TfXmSmbTGL17rsit3j6aoqY7xzW8fJZXKoesmXd0JcjmDV17txDTtKuGVVVG+9Z2jJJN5TJd9\nv1/6+SVM02JsLE1lRZhv/cMxpqdtTGdXAix44aUOTNNiPJGmvCzMd/7xGJNTWceOLEv89IULmKZF\nIpGhpCTEP373OBMTGXTDthMMKvzrT89jmhYTExmKi4J89/snSCQyGIbFpc4EobDCj39iYyYns8Ri\nAb7/z6cZS6RtTFeCWCzIv/zkPKZlMTWVJRpR+ed/PcdYwq5M33l5guJ4iP/7hQtYwHQqRzik8sOX\nLjAybvNBunonKS4J8y8vd9gplZRGICDz04OXGc5juvunKSsL88M3u7GAVEZHkQU/Pz7AyGQGy7I5\nHhWlEV440g9CkNFMFEnwTscYY8ksFjAwkaayJMxrF0YQQpAzTJvPMzzNRNpOEY0kc5THghzun0RI\ndvreAnqnskxrti+ZzOqUhFXOJdJO2snCYiyjM5P3KzO6QUyV6UnmnA0JlgUTOZ2MYWt5ZQyTiCLR\nP5PHCNvfJfIYKY8JKhK901kn+mdYMJrRSGp2X2ndJCxLzngs7JTaQDJDIqsjJMF0ziCqSM55Wdh8\nn+7EDIP5FNZERiMeVHjl/AhWvp9k1qBraJrOPGdqNJmlIhrkR+/1Ylq2ztBESqN7cJqzfZMgBKNT\nGaqLQ/zTK5fQDAvNsBidytDTP82xi2OY2NvN68ojfOeHZ8hqBjnNZGg0xeBwikOnhug59QGnq772\nhwfuml/zvtNV/+lU74ciXfUbIx5blvWaEKL5f5W9wUSakz0TnmOn+6dIuvQNEmmNrgmvbk7vVJac\na9E5o5uMZ7y6EdOa4dl6bliQNby1o3QrjSQK37PQMS2vjoVpTSCJjOuIhsW4DzPpKQdhYZAzvWPO\nmVk0sxAeNYFJnyx+Imt46mZppsVln2ZQz2SGIVdNmIxucrzXew1P9U3S6dLDSOcM3jrj1fk4dGGU\nDlfNpXTW4NX3ej26Ob88Mcjl7kkXRuflN7s8mHcO9zHo4i9kswYv5n/4Ztu77/Ux6hpPNmfw4suX\nPNo6xi8P8WLpav6p1ubglGjT3HTi99FXF/Qw3nm311OCQNdNXnzpokdW/d13e3FrH+mGyQsvdXjk\n2N95t4ewa6u1YVi8+FKHR8fn3Xd7nd1FYHNgXny5wyMK996hPk/ay8Zc9NTxOnS4nwEXd8Oy4KWX\nO0i7SIjHjg8yPl7YPg/w4ksXHSIywMlTwx59IICf/7zDc+zsuRFymu7DXHJIxoBHZ2e2vfzKJSZc\n2igdl8Y9aR6An7/SScKlF9LVNcEbeRLzbHv11U7GxguYyz2Tc+pLvfKLLo8+UW/f1Bz9nVdf62Jo\nuKAV0z8wzWuuelMAr73RxaCLozM4lOTV1716QK+/2e3h34yMpuboAb1xsJsel87R2HjaU9sK4OA7\nPXS7ahMlJjK8etA75oPv9dLp0q+amMp6NKcA3j42QKeLezSVyvHaUa+Oz3tnR+h13YtkRuets965\ne+TSGAmX70jnDA53JzyYMwNTuD1HzjA5M+ytCdg5PuPRsdBNy1OTCmAgmbML9OabYeHR9gIYTWue\nEjmmxRxNsERWJ2e4fSQMz+Q8+jtjGY20ay5bQG9+ITfbhmZyzGQ0D+bi+IxHo+fyZNozvywLTvRP\nespaXBiexsp4Mb/sGPWUdjjdO0HQZde04LWTQ2RdPvr4pXH6XKkxy4JX3usl7foNO3lxjNER7/z+\nwNpvKfH43yPm9JgQ4ng+nVX6b4GEEA8JId4TQryXTU0SCyk0+nLS9aVhVNdNCakSlT7OSVlY8XBX\nFEkQm6MVI3k4MAJQfFwaSQTxXi6BEBEfJop33Sgh8OZcJSKAu3+BInlzuYpQ5ujb+HPbUVUi6Dp3\nCZztnLOtIhrw5JslAfPKvbn/hrII5a6SFrIkWNjg5Wa01cWpdV17SRIsayv3YuaV0ODiOUhCsHxR\npQcz31WZG2wuwoqlVV5MWxlt+a2Zs5iVK6o9GJqbWZfsQMmLLG6aPMt0RZ0HMr+tnPnzvWNc6Sp9\nADB//hUwK3yYtnKnhMO/Zaetrcyp3l2wU+3hpbgrfM+2FStqPLyU5qaSK2CqPZiGhrinXMTsmN28\nlNraojmY5cuqPVpH1VVRFvkxy6s83JXKyiiLFvntVHkWNeVlYU9V8lk7QRefpLQ0zGLfs7B0WZWH\nl1JSHPKUuABYuqTSo3ETjwfn2Fm2tMqjeROLBViyxItZsrjKqaQOtsDj0sVVPkwFRS6uSjiszBnP\nkkWVTnVzsCUPlvr6WjS/gpLiAu8iGJBZ6rs+C1vLKHVhAqrEEt98WtRUSpkLoyoSS5q97rK1Lk65\nazyKLFhY7527TVUxynzzu9nHDWsoDTvSE2D7iYZiL3ekKhYk7uYRAZU+nl5JSJnjW4t9fJeiwFxM\n3KcnE1VlpxTEv2Unpspzvlfu030qDiiU+rhFNTGvry2PqFT5uJ5NvlRRTTxEve9YW02R5zejvizi\nyG7MtiXzSjx+vKEySquP97asrQzJ5Sjqq2IsaP43fxZ/4+23kZPzQW8h/0vgD7AX1X8A/DFw35WA\nlmX9DfA3AJXzFlt37ZrP2rZyLo2mGJ3OUlcS5qYVdVT3JvjFxTGEgI8srmJJdZzhVI7JjE5pWGVd\nbTG9qSxnx+23vaVlMepiAWYM0w5xKhL10QAzukEiZ6/6SwMKUSWGqc+gmwayJBGV45gYZI1hwCIg\nVaBQhkECkywCFZl6IIRpdWErtNchqAMSWGQQBJBEPSExTc60t+GqUjkycXRzBt3SkYVEVIkjSxaJ\nrP32ElcVYopKUjOZ0Q0CkkRDLEhYljk5lsS0bCXj1uIQA9NZRmdyRAIy6+uKqY0E+NHpIQzTYsO8\nEna2VXBxKEnXaJLisMotaxpYXV/M3754Ac0wuWZlLZ9pb+FkZ4KzPROUxILcc90CelbU8B++dYSc\nZnDz1iY+/7GlnDg/yvHzI5TEQzxyx2r6B6c58J8Pks3p3HRVK/d8eiUnzwxz+MQgxfEQTzywkZHR\nFL/7h6+QzujceE0b935uNafODPPLw/0Ux4PsfWQzkxMZnvvqi8ykNa6/dj733rWW02dHePudHuJF\nQXb8x/2U7/jv/MvRrzIYKGXhTB/hb/4dHzlTaW9XjgXZv28bmmayb/9PSKZy7NrZwr13raWjY4xX\nX+siFg3wzL5tyJLEE/t+TDKZY8e2Zu67ey3d3QlefuUS0WiA557eTiAo8/hT/8r0dJb2LfO49661\n9PRM8sJLF4lEVJ57ZjuxWJAv7P0RU1NZNm9s5L671zEwMM1PfnaBcFjluWd2UFYW5lJngomJDOvX\n13H/PesYHZ3hR/96llBQ4YvP7qSmOsrFjjESiQxr19Ry/z3rmUhk+OcfniEYVPjSsztprC/m3PlR\nxsfTrFpVwwP3rSeZyvE/fnCKQEDhi/t30NZaxpmzI4yNzbBieTUP3r+ebM7ge98/QUCVeW7/ThYv\ntCuVj47OsHRpJQ/etx7TgH/47jFUVea5p7ezYkU1J08OMTycYvHiCh66fwOyLPHt7xxDUSSefXo7\na9bUcfzEIINDKRYtLOfB+9YTCip8/VtHkGXB/qe2sXFDA0ePDzI4MM38tjIevn898ViQ//b1Q44m\nz7b2Jo4c7aevf5q21lJ2P7iR8vIof/tff4mQBE89vpVdV7Vy+Gg/vb1TtDSXsPvBDdRWF/EXf/MO\nAsHjj23h+uvmc+hwP5d7JmmaV8yehzfQNK+YP/uLtwF4dPcmPnrzIg4d6aere4LGhjh7HtrE/LYK\n/s8/fwssi4cf3MCtH1/K4SMDXOoap6Euzp4HN7J0aRV/8mdvY1oWD9y9lk/dupRDRwbo6BqnrqaI\nPQ+sZ/XqGv7kv7yNYZrcc/sqbv+d5Rw+McSFznFqqqLsuXsdG9fW88d//Q66YfK5W5dx563LOXp2\nmPOdCarKIzx8xyq2Xhzjj79xCN2w+NT1C7jrxkUc7xjn/OUEFcVhHrplKef7pvjP//MkmmHy8S1N\nfHp7C2d7J7nQP0VpLMBdV8+nd3yG//pyfn6vqOXm1fV0jqXoHEkSD6ncsraB8RmN7x3uRTdNNjSV\nsq21goHpLD0TaaIBmavnV5DUTH7eMYpuWiyqiLKyOs54RmcolSOoSKyriZMzTA4NT6NbFo2xIPNL\nIiRzBuMZDVWWWFQaRjfh1HgSw4TqiEpTPERKM0hkNVRJoi0ewrDg1HgK3bSoDAdojodJ5gxG89u/\nF5VGMEzsvkyLmmiAhWURJrIa/ckciiRYUx3FMuHlrnFyhkljPMSaumLGUjkujqcIyBI7W8sRFnz3\nSB8ZzWR+RZQd8ysZmspwrHeSoCJx66o6ArLEf3npPKmswZL6ODevaWA4kebguRFCqsTdu9ooCir0\njKSYntFY0VzKp3e0MppI8+KhPoIBmcdvXUZFPERn/xQTySwr51dw501LmJjI8OPXLhFUFZ66Zx11\nFTHOd3mjbR9IEx8ukb/3236jW8iff/75EuCzs5ycAwcOpA4cOGAdOHDAev755y8Bz8z+71e1r/3p\nnx+wmq9ClwVnBqexhGAqqyMEHBmcwgAsAX1TadSAzEBKQ5Ilcqa9LXsgvxVSEnYuOazKpA3To8aZ\nM1NIQkcWOpqpoUpJLMaRpSySyCCEiSQuo0hpFCmLEFNIZJFFH7LI2pwcy0DQiUQaiSyCBEJYSPQj\nkUMija2GMIws0sgih2AK3VIxmUAWGkLksLBIajpCaEhCR7NyZA2VpG7m89Z2HrhjKo1p2VGT6ZxB\nMmfQMZGG/BbPrG7wVuc4M7ph5+OnsmSyOm93jmNi57GnsxovHO5jIq1hWBaXhpNoOYMXDvVhmBap\njM5EKscPX+9kdDKDblqc65lAMiz+5dVL6IZFckZjNJHmRy92MDSaQtNNzl0aR5Hgf/zonL3tOpVj\ncDjJT1+6QP9g0sZcHCOgSHzvB6cdTP/ANC+8fJGe3ik0zeTc+VFCQZl/+t4Je4t3KkfVqz8mfukc\nf9h8O8eL2jgVa2L+C9/jD0YWoGkmqVSOrq4Er7/ZxaXOBJpmcuHiGOGwwrf+4ZiNmdG41Jngrbd7\nuNgxjqaZXOwYJxSS+eZ3bMzMjMaFi+O8d6if8+dH0TTT5mqEFL757SMO5tz5MY4eG+DsWRvT2WVj\nvp7n9qTTGmfOjnDy1BCnTg+j6TaXJRCQ+fq3jpDLGaTTOqdO2fo7x08Moekml3tszN9/0+bkpNM6\nJ04O0XFpnKPHBtF0k97eKRRV4uvfOEI2a5DJ2JiurgkOH+lH0036+qeQZcnh9mQyOseOD9DXN8Uv\nD/Wh6Sb9A9PIsuDvvnGYTMbGHD02QP/ANO/8shdNNxkYTCIJwd9/47DNn8rqHDk2wPBwirfe6UHX\nTQaHZjFHmElrZLMGR48NMDo2w5sHL6PpZj69ZPH337T5PzZmkEQizetvdKPrJsMjKUzT5BvfOkIq\nVcBMTmX5xWtd6LrJyOgMhmHxjW8dIZnMkc0ZHDk2QDKV45VXO9F1k9GxGTTNdDC5nMHR44Ok0zov\nv3IJXTcZG0+TzRp8+x+OMjWdJZczOHZ8kKym8+LPO9B1k/FEmmxW51vfPcHUVB5zchDdMPlZHpOY\nyDCT1vmnH5xiYipLTjM5fnoYw4Kfvmr3NTGZJZXK8f2fnGNiOoumm5w8PwqS4GdvdKGbFpPJHMlU\njh+8eonEdA7NMDndMY5QJV54rxfdtJhKa0ymcvz0UB+JZA7dsDjXO0EgKPPKyUEMyyKV1ZmcyfHm\nhTGmMjqmBZ0jKQIBmXc6EwUfkNE4PjhFMmf7if7JDEFV5mRe2ydnWCSzOl2TGZv7h729PKjKdE5m\nIM/JmdFMhjMaGbtQF1M5g4As6E/l8lwbyBimnY4ybaLrjG4iCRjKb6s2gYxhc3uyhuVgBNA3awdI\n6yZD6Rxp3UQISGkGYHFxMmPXI8OW3bg8mXW2rE/mDCzT4sjAFBZ2ym18JsfFkRTDyRwmMDqTQ1gW\nv7gwimHZ5z4wmeFc/xS9iTQmMDyVRcbiR4d6MSyLrG7SPZLkdFeCi/1T6KZF//gMsoDvvXopX2PM\n4FzvJOc6xjndmUA3LPpGUqiS4Ds/PktOt8jkDE53jNPRmeDEuZEPnJPz13/0Hw7cs7jufXNyvna0\n+//fnJwrNSFErWVZs8VpbgVO/iq8u02nNS6PeXOVvZNpT+42rZmMzvjyuxkdw5Xp0S2LGV+5+6xh\noMruHLCFYXnzzaaVQhZuDoMBeDk5MAVovwYzDbjtmJiWl0ujW1lM363JGN76Wynd9Jy7PUG95z6a\n0phy5XsNy6LLdw17xmcYdfF2DNPirK/eVUf/FP0uboRhWpy4OOrBXOhKcNlVV8wwLY6d9vIDzneM\nMejinJimxVFXLR6AcxdHGXNx+RLnrwAAIABJREFULCwLDh8d8GDEpUu8G1/I4WJbnbdEm+YLJ34E\nrozVuQtjnmKTMNfO+QujnlAxwJFjg3Mwfln+I8cGPFyjCxdHPSmKK2EudowxNeV9po4eH/DwkTq7\nEp4ip7MYNx/pcs8k/npzx44NoLv4Ab19U560E8DxE4MePtLgYJLTPu7V8RODHj7S8EjKo+MDcPzk\noIePNDo6w5mzfjtDngKUY+PpuX2dHPLwkRKJNKdOe/s6cWrI0R4CW3PGb+fEqSGSrtpI09NZTp7y\nYk6eHvLwkZLJHCdPe2tQnTo9xKSLj5Sa0TyaQQCnzgw7+kSAvej09XXm/IijTwSQyeqc9F2fMxfH\nGHNxB3M5g1MXvPPpbFeCUZcdTTc53enl913sm2LExYvRDYuzvd652zmUZMp13w3T4pKv3lXvRBo3\nA9G0oM/H7xtO5sD1TFnAiI9vM5HRkHzPXSLjfZ5tHqF3zk3l/L7NQDO8z7ifk5jMGXN84pivr8ms\nwYxvPg1Oe7mWo6mcI9A527rGZzzcnoGpDPjGeH5g2oPpHZtB9Y35dHfCw//pGU6RVL0+4MTFUVuM\ncNbOUBLd58c/sJbfQv7b1n6TW8j/EXgLWCSE6BVC3A/8kRDihBDiOLAL2Pt+7VUVh1jq0zBZVF1E\n1KXVUBxSqPdpFVRHAwRcIbigLBH311hSFCRRuBSSECiSN28tizjgzt2qgDfXjigH3NoIgbkYSgH3\nD6KCLLyaHaqIePR0BGKOBkQ8IDllHsDW1mnwaTfUx4MejlJQlljmu4ZLauPMc+XoQ6rMZh/vYXVb\nOQsbC1yaUEBmx9p6D2bdshqWu7gHwYDMVVvmeXgpG9bUsXp5tQeza0eLF7O2nnVrCquVQEDmml1t\nHl6KtHYNV08ep0RLgmVx69CbTLYu8fBSNq6vZ/36whgVWeKaXa0ezIZ19WxwYWRZcM2uVs8CYeN6\nL0aSBNde3erhpdh2GjyYa3a1ejRV1q2p82CEgKt3tXm4K6tX1bJxQwEDdoFOd62q5cuqr4hxc1eW\nLK5k08ZGL2Znq1MKAuySEVs2eTFX7Wh1SkGAzY/a7MPs2tHilHkAaGkunYPZsaPZs+hrmlfilLhw\nMNtaKC0tzJWGhvgVMM2Uu7RG6mqL5mC2tzdR4SJ011TH2N7uxWzb0kS1S++nqjLKtq1NHkz71iZq\nXZyy8vLIHMzWzfM8ekNlpWG2b/X2tXl9Aw0u3kVJcYhtvuuzZW0981zcmXgsQPs673zasKKaZped\nWERl64paD2bdwgqaXTyQSFBh40Lv3F3VXObhMgZViVUuXhzAwuoi6twcIVmw0Kff0lQapsrlS2Qh\naIx7F/bV0QBlPg5glY+3UxpUKQ64fdtcLk1JQPFwcGwZDZ+2T0ihzPU9AdRFAp7lU0VEpcY1ZgG0\nlIa9PJniME2lEQ9meW3cUxerrSLGwprCvRAC1reVe/igi+qLWdFc5rHTvqzGU/NqWXMpa32+dce6\nBkKu67G0tYz1Pl7gB9kkWbzvvw9L+40tcizLusOyrFrLslTLshosy/pvlmV93rKsFZZlrbQs6+Ou\nqM6vHqSAWzY2sn1hBbV5TZN5FRE2t5azaV4ZQUUipEhsbS5jUUWU0rCKIgnKIwEWlEVoiYdRJYEq\nCVqLw5SGFCJ5Mb2IIlEaUilSFeR8uqpIVQlIJShCQsJAEQJFlCBTjcBEYCJTiRB1YITAMMEIAPVA\nox3AMSyw6kDUgRm2X4+MAIJ6ZGryeju2HVUqRRGq/VlIBKRiipQgUr6vqBKgOGCPWRK2eGFZUKW5\nOGQXzhN21fTWkgjV0UBeFFFmSWWM9pZywoqtgbOmvpj1zaW0VkZRJEFZVGXngkpu3TiPSFAmoEjs\nXFrNVStrWdFchqpIVBaH+Pjmedx9w0JiEZWAKnH9pnl8ZEsTa5dU2ZiyMJ+5fiH33raComiAgCpz\nw84WbtzVxsY1daiqRGVFhM/9zjLu/9wa4kU25vqr27j5ugVs3tCAqtpaOp//zEruv3stxfEggYDM\ndVe38dEbF9K+dR6qamvpbP7S3ZSEBD8+/GVeOPwc9w78jLpn/x/23js4jis9+/2dDpNnMIOcMwgQ\nIAgQYCaYKYqUREpU5ipQOa8kUuQGa3etz76h/CXb5VC+Lrucdr1eh/VmrzdHb7DSKpIUMwASGRhg\n8kx33z960NM9Q3+rcn1Xe+nyqUIVu/n06fz2mfM87/M+zdaRVlTV9NJ58MgQjzwwRCTiQVUldu1s\n58CNPezY1oaqml46Dz0wzINHhkwPHFVi+7Y2DtzYYw1QwmEPDz0wzAP3raGiwsRs3dLCjfu7uW5P\np4kp8/DQg8McuX+QygofqiqxeVMzN93QzfV7TUxZyM0jDw9z5L41VFWamE0bmjhwQzc37FuByyUT\nCrl59KFh7rtngOoqP6oqsWFdAzfd0M2BG7txuWSCQTePPTzMvYcHqKk2MeuG67npxh5uPrDSxARc\nPPrIWj5092rqagOoqsTQmjpuuqmbQzf34nbJBAIuHn14HYfvWk1dnWmCN7C6loMHerjtUB7jd/Ho\nQ2s5fFc/DQ0hVFVidX8NBw+s5I5b+3C7Tb+dRx4a5q47+mlsNDF9vdXccmAld93Rj9tteuk8/MAw\nd962iuamMlRVYmVPFYduWcnhuwqYh44MceftfbS0hFFVie7uSm69uY97PjSAx6Pg9So8cGSIO27t\no601gqpKdHVWcNuhPu6/Z7CAuW8Ntx3qo6PNxHS0l3P7bX3cf98avB6zSOr99w5y26E+OjvKUVWJ\n9rYItx/q48h9g3i9pt/OfYcHOHRwJSu6KlBVidbmMLcf6uOBe/MYt8zhO1Zxy4099OQxzY1l3HFL\nLw8eHsDnVXG7Ze68uZeDe1ewsqsCVZForA9y+4Eejtzej89r+u3cur+bG3d0sLLDxNRXB7j9+m7u\nu6kHv1fBrcrcvKODfZuaLZ+c2nIfh7a2cXhXJz63gkuR2L+ukZ2r61jZVIYqC6rK3NywrpGDw414\nXWYM2NpTzYb2CrpqAiiyIOJX2dFdzc6uKrxqPk40RVhVF6Il7EWWBEG3wnBjmDV1IauY54oKH+1h\nL3UBF7Jk+uR0V/joinitmNQQcFHvd1PhMRMpXJKgJeimOeBGlcy4XuVVqfaqlLsVJExMQ8BFc8CN\nK99PlVelxqdS5VWt+NccdNMe8liePDU+lcaQh/qAG1mY5qk9ER99VYG8capZgXxFZYCOCjP+eVWJ\n4foyNrdGCLhkFAk6q/wMNJQx0FCGIglTj9RdzXV9tYQ8Cook6K0PsbGzkg1dVaZPjlvh5rVN3LK5\nhfKgG1WRWNNRyc7BenatqcelSAS9Cod3dXDH7k4q89+w4Z4q9m5sZt+WVlyq6ZNz/8Fe7rqxh+oi\nQ9QPogkhkFTpff9dK00UT33//7FVtvQYt734Z2wbqOf18cJ07Ob2Ci4upaxpQ1kI1reVc9E27dwZ\n8ZLSC0nbAugIe4nbpnBDKkiSc6o8qGgYFKaQJRFB5RJYCZACtErQCvVukOpBu+zEKK2g29JDpTpQ\nFm0YyOodaBTSdQURlrIusKeaG5UsZArb+BSJC9Ek9hnSoCJx0kZH1QdcvHFpgYyNyuiK+Pj+6cK5\n9tQEeP30NAlbuvO2riq++JNC2utgezlvnppmMV6YRr15QzN/9/XT1vLQymreOz3DvG36/K79K/js\nP75T6KevmtGLC0zbjvHwoT4+87dvWsv9fdVMTyw5bPnvuXM1n/7sL6zlp6XX6X73X/hk23349TTN\nqSl+feoL7Ov8uIVZ0VVBJqtx4UIhZf6+ewb4q88U+uloL0dIcOZMgQa490MDfPqvC5iW5jBer8pJ\nW4mG++4Z5K8+87q13FAfIhLxOGiS4n5qawLU1gR4/Y0CHXbP4QE+Yzuvykofrc1hXn61kCp87+EB\nx7lHIl5WdFY4ajp96O7V/PXfvGEtl4Xc9PXV8C8/KTybh+/q57OfK1znYNDN4OpaR0r23Xf287m/\ne9Oi2QJ+F2uH6/neDy5YmLvuWMXf/v1bFsbnU9m0oYlvf/echbnjtj7+4R/fsag4j0dh65YWvvnt\nsxbm9lt7+fwX3i1g3Ao7trfx9W8UrLMO3bKSL335pEXXuVwy1+3u4Kv/VHjubjm4kq989ZRF16mq\nxPV7u/jKV09ZmIM39fC1r5+26DpFkbjphm6++JWTFubG/Sv45rcL1gCyLHHwQA9f+PK7Fmb/3i6+\n84MLpC2M4OYDPfzjlwv97N3Vzg9/PmrZB0iS4NCBlXz+a4Xj2TXSws/fnLBoEiHgtpt6+Pw3z1iY\nbesaee3MLAkb5tZ9K/iiLa1906oaTl5eclAyt+9o559tqeaDbRHGF9MkbHTLjesa+eHZQrzprgkQ\nzeoks/YYUMkvrhTo56YyLxlh2lAstzX1Ic7ZKNhKj1meJm0LSp1lXlNLk29mPT4npt7vYsJG0fgV\nCS2v31lutV6VMVs/fkUimdMc0oOGgJszNhowqMokMvkSEfnWEfLw6uXCN6TMo5DKl3qwzquujO/Z\nYmTEpyKyOhdnCzTf9q4qvvJyIa6XB9z4JclBF+4fauDvv194L8qDbmoCbn5hoyZv29bG52zPRjjo\npq3az8tvTvLjv73nFcMwChVh/z9uQzUh44d3rX/f+MDvffsDPb5/b7smCnQCZHI6c0UccDSVdfCi\nmmEQK+JOkzkd+/zksuAMx3ZayZSWQaZoRQqE7kBgFPkZGAngl2FSRRgwKNb/ZDHpsELL6c5tMppO\nEQVccu6xdM4xwAGYjTs56bl4xjHAAZiYdx7z1ELKMcABGLd52QBMzsYdAxyAsStOr42JqTgzRR4v\ndt8RMD1MZos0A6NFOgMxM8N7njqiriBRgqQkF564EzM5GbM+RlY/o6WY4voZxfuanIzhKaoIPFrk\n1zQ5FXNoUK7Wz/RMnOKfE2NFmNnZBO6itNhLRZj5+SRXJpzXtXhf0cW0w2/HxDiv89JSuqSfsbGo\nQ0e0LAQv7seOSSSyJZixsUWH1iiVypUcTwkmnWP8svMYx8cXHXqkTEYrwYyNRx16pGxW53JxP5cX\nHXqkXE5nbLwUY9caaZpeejxXFh3PlKYZDm8dgCsTSw5/JF03GLvi7OfKVMyhAzEMGJtwvk8TM3Fr\ngLOMuVz0XkzNJ0s1J/NOLc3MknOAAzAdc8aA+UQW5xpYKPKuWczkHD45YBYNtrdEzhT4lqyztVRR\nPDLXOd+MjG6UxOhk0XZpzSjpK5Etjf3F66JF1yue0YgXaXJm487Yv5jMoaed12OySLO0EE+TMJzn\nfqVI/zgfSyOK7sVYURxdWEozIX6FVNA1REO933bNzDl11ARZX8R5DjWGKbdxvjUBN+0R5zRfc9Dt\n8JjxqxKhkporbmRR6EcWKopwamkkUQPYtTN+kJxcO3Iz2K1/RMBc58A0AGW2FV5k4eRpFRFGEQUu\nWRIyQVcpbx228dZuWaIj7HV8szvK/bTYrkfQrbCxrcLhG7SurYLVzYVjjvhdXD/UaFXpBdg5UMdm\nm5amPOTm0M4OB9+8d1MLO2zag0iZh1tv6HHoUvbtbGfP9nYH5s5DvQ5dyv49nVy/p8taLgu5uev2\nVQ7NiXf/dRyY/1e64mN4tDTPjH6R2LotDr+U/ftWcMO+FdZyIODirjv6HX4p+67vcmD8PtXE2HQp\n+/d1sf/6AsbrVbjr9n6HX8r+on48HoU7b+936FL27ul0YtwKd97R79Cl7Nnd4cC4XDJ33raKSpum\nYueONm7c320tq6rEnbf3O2pebR1p4cb9hX4UReLO2/ocupRlSm25ybLE7betctTc2rC+kQM39dgw\ngjtu66PRpidZO1TPwSLM7bf20dRYeMYHB+o4eGCltSxJgtsO9dHaUtCGrO6v4ZaDpZj2tsKz2ddb\nzc22foSAW2/ppbOzEBd6uqu45WCvA3PLwZUOL58VXRUcurnX8T2+5eBKh+dNR3s5txxY6cDcfNNK\nVtl8ndpawtx6YKVDL3bTvm5W9xXelebGMm69oceJ2dPJoK2fhtogt1zX6dCB7NvaxpDNp6e20seB\nkVYH5rq1TQzZfJWqwh6uH2pwYLb11tJv0+BE/C5GOqscMWBtS4RuW/2xgFthTX2ZA7OyKkCrraad\nR5HoDPsc+pbmoIc62/vlkgSN+bIPy63G66LKJuRXhKDWpzowlR6VSq89HpulHezf3yqfSp3f7ein\nJehx1BxsCLhptdXyUiRBX1XAodHsrPDTV1N45lVZsLE14qjlNdBYxrr2wnV2yRI7+2oJ2LRyG7qq\n2LaqoKVxKRI3bmyizHY9tq6qZbdNT6cqEod2dDj8kLYONbBvWyu/kib+Y/rkXDODnLUdFXRUBSjz\nqkhCUBFw0Vrpp6Pcj5RPD++qDFDjdxNwS3kuWabK76LSqyILgSwEVV4VnyLhlnRkoeOWTK8ct6Qi\nkUMiZ/5b+JGEhCRy+f4DYFSArpl/RjlI5aCpoOVAk8xlUQ2aZv5RCVIEdBfoOdAlEOXmtsv96GVI\nIoCEjMCcUVKkAG7ZhUBDoOGWVLyybNZpEWaSg1+VrXovAoi4FSp8LoL5gqRuWaLW76K7MkDeLZ2W\niJfWcj9VIRdCgM8l010TZG1HhRVkuutD9DSFaciLkX1uhTUdlYysrreCZ397OX0dFTTnRcw+j8KG\n1XVs39hkinYFrO6pYnVPJe3N5sfO61HYvK6RHSMtKHlX1FUrq+jvrbHM/7weha2bW9ixrdUS//b1\nVtO/qobOvFmaxyPTc2ALHsXgT975n3zv5eNsn3+Dipt2WeZ2brfMtq2tbN/WZg2yVnZXMbC61jK3\nc7lktm9tZce2VqugYveKSgb6a+lbWW1hdmxrY/vWVmsgtqKrktWra+nrNT9kiiKxY3s727a2WgOx\nrs4KBlfXsmpVAbNrZztbt7RYmPb2CKv7axhYvYwR7NrezpbNzdZgra01wuBALYMDZvCUZcHuHe1s\n3tSEPx8821ojDK6uZWjQFKWaoucONm1stgZrLc1hBgbqWJsXty4Lozeub7IM8JqbQgyurmXtsCn6\nloRg9842NqxrtAZ0jQ1lDK4uiKMlIdi5o511ww2E847P9XVBBgfrLDGyELB7Zztrh+uJRMxgXlcX\nYHCgjk0bmy3Mju1tDA81UJE3XautMTHL4l8hYMe2NoaH6i2hcXW1n6HBerZtabXixPZtLQytqbcK\nlFZX+RlaU8/2rQUR8daRFtYM1lmYqko/w2vq2T7Sag1qtm5pZmiwzipiWlHuZXiwju0jLRZmy8Ym\nBvprqM0XFi2PeFi7pp4dmwuC+41rG1jdW01dvp9wyM3w6jq2byxg1q2upX9FNXX5gUZZwM3aVbVs\nG26wMMM91axqr6A+f+5Bn8pQdyWbV9WaIlABAx0VdDeWUZsfOPvcCqtbI6xtrzAHWcJ8vzuqA1Tn\n76lHkeipDdFbWyi82hzxUl/mocJvCnndikRbuY+WsAc5H0tqA2ZcXTbkkwXU+t3WYMSMSSplbsWq\nEygLqFzW3+QxQZdMUJXxKwVM2C0TcRUKK/tVmZDLxIC5XblbocqjWvsKuRTCHoWy/HsqYep0GgKF\nwVHEo1AVcFHjd+cNXwVtYS9dlX5cslkUuTbgoTHipbncixCmwWJvXYj+xjBuVUIIaCz30lkbpDNf\niFaRBWs7KhjuqMCd16o0VfrpaQzTmx/Iy5Jgc18NG3pr8OZ/nLbUBunrKKe/q8LCbBuuZ8NgPX6/\n80ftB9OEOVv3fv+ukXZNaHKqWlYat3ziz9i8qpbTtum9oeYwE0XTqsMtESZt65qDHpwThNAaUknr\nhbU+BRTh1EAHVB1smhxhhJHs+hsALQK58cKyXAu5Ii212gy6HVMDsnOKW5Pa0LGZPxlhlnLObAJd\nr2XJNqvqlgTnoykHBeIWcM6WdlrlUXlz3JnG2Oh38/MLBQ1Ka7mP109OOaaHh5rCfPu1Aq+/oiHE\n26dmyNim/HevquWfbJb23a1hzp+dd1iU79vSwldtOoPOtghjlxYcacE37enkSzaNRUdbhOmJJUc6\n74H9K/jSVwq89VOpn1A3dopPdj4AhkFPYpTfPf+n7O19qXCeDSGzZpRtiv/mAz180aafqK0NIIRw\nUCkHD/TwJRumstKH16M6KKHifsJhD+Gwx6H/KcYEg25qavwO/c/Bm7od5+XzqTQ3lXHyVOG5O3BT\nD1+2aUc8boWOjnLetqU333Rjt0OD4nLJ9PRU8YZN/3PjDSv46tcK11lVzYKbr75WeF5v3L/CoXdR\nZInBwTpefqXw/N6wbwVfs2mxZFmwdriBn/28oBHat7fLoa2RZcGG9U0OjdD1ezv5528Ung1JEmze\n2MyPbCUQ9u7p4BvfKuh4hDAzrr5ve+727GrnW98558Ds2NbGd79fKNuwa2cb3/mus4zD7l0dfOd7\nhe22b2vlBz90liHZs6fDoTXaurmZH/3MWc5k754OvmnDbN7YxM9fu+yg4vbu7uCbNl3ThqF6Xnt3\nypE6fP2uDr5pO/fhvmrevLjgoOuu397Gt18t3IuBrgrOzsTJ2THrmvixLWW9pyHERCLreL939Nfy\nio1ybSn3EtOcFNGGtnJOzxTeneqAG00WDkxvdYBRG/UVcpmDFzv71BR0M22Lx+asulkPy+rbqzJj\no4w8skRW18na9lXhUZi0xQ2PLJHSNIeNRpVX5YJNI+RVJBLpHHGbLUKT38U7tm+IT5VJprIOeq67\n0s/PbGZ8PpcMGY1JW9/DTWG+91bh/fK5Zdy64JIt3mxdWc3XbeU6vC6Zap+L92yxZO/aBr72vcKz\n6XbJtFb7effsHD/67Ic+WE1OXZnxoyOb3zfe/1tf/09Nzv/OZhg46oAApHOl/G62RG9jlPDEepE6\nwjD0Em0GRs6xziBHSTOK1hlX8zcoWle8zVX6NkqGZcvHXDggTTdKNB7F3hIZXaPocpAquoapbK6E\n/y7m+RNpzTHAAYglizCpXIkGJl7k92CawxX5XRTx3/Gr+FYUY0QqxbySn14XgnklgJor6ieRLfHJ\nKe4nkciW+OQU13xKJLIUX+hiTDKZtWaDltvSVTDJoutRjEmnc44BIECsyNcjnbkKpqifTEYjUaRf\nK8aYpon/635ymk68pB/n8WiaUdpPvBRTvF1sydmvrhsl+yq+PoZReg/fDya2VPpeljx3sQzFv/fi\nxf3EsyWY4msWj2ccAxwofQ/iiYxjgAMQTxb1k8o5BjjmuuL3KecY4AAki/xkEhmt5P0ujgHpnE6u\n6LyK3/eMpoNw/nrPFmliNMMZo4CS88wZRkmoLdVIGvm+/u1+NMMoWVd8PDndKPkeZLTSbYq3SxWf\ne07HKNIWJYtiSzqrYxR9jorjaDqnO34EAsQTzuVMViORvMq35gNq/xEdj6+ZOaf1HRXs6qm2KBOX\nLLG1vYImG5/ZUe5jZXmBJ5aFWe7A7ssQcSuEVdV60QTgV7wotjpUivAhRAOFyyOQaAZhq6EkKkDt\nplCHSgJXDyg2DxO5uggjQF0Bwu6DEEGm0bEvRarFZfPpUYSbMtXpAVHuMdMql1tQlVlZ6bdcnAXQ\nVxWk3+bvUBNws7un2uKbhYDdPbXssnHJzZV+7traTjDPiQsBt4+0ceu2NgvTXh/iwZtXEs57EgkB\n99y4krtt2oz2pjIePTxAedhjYY7c3s+9d6y2MK3NYR5/cK3lhSIEPHDPIEfuGSwcT1MZTzyy3qIW\nhIC6xz7EzfM/57qZl+mJX+I3zv4l2UO3WdQCwINHhnjwyJC1XF8f5MnH1zu8UB6834mprQ3w1GPr\nabBpTh46MsQD968pXMNqP088vp7mpjJHPw/cP2SNpasq/Tz56HpabJqTB+5b48BUVPh46vH1Ds3J\n/fcMOjDlES9PPr7eoTm59/AADx5ZY2k8wmEPTzy63qE5OXxnPw/eP2RhykJunnhsnaMW0x23reLB\nIwVMMOji8UfWsaqvoBU5dHMvDx0ZsryFAgEXTzy2jgFb7a4DN/bw0JEhi170+108/sh6iz4Dc/bn\nkQfXWkVwfT6Vxx5Za1FjANdf18nDDw5b/kNer8JjD69jw/rC+7R7ZzuPPDhsUZAej8JjD69li807\nZ+f2Nh59aK1FL7rdMg8/NMy2ra0WZutIC48+OGzVznK5ZB5+cJid2wvP+KYNTTxyZNjyKFJViYcf\nGOK6nQVN2frhBh45MoQ3j1EUiYfuXcNeG2ZodS0P3zNoGUoqisQDdw2wb0cBs7qnigdv7ce/jJEF\n9x3s4wbbMfd2lHP//h78+X3JkuDwni722byXuhpC3DnSZmEkAbdsaGZnr00jVOFj/+o6y19MALtX\n1rDRpnesCbrZ3FqON38vBLCuMUyfzTsn7FFYVRlw1M/rjvhotXnn+FXJsrmw9h/0UG/TqXhks0SN\nHVPvN1PPl5tbFjQHzXTx5dYYcNMS8jr66Yr48Np0gp1hL72VNh8hRWJNfdBRz2+wLsQGmyYx6FbY\n2VVFhe0Yt3dVsqe38MyXeVUODjdSa9Mo3bCmgUObWqwYHfa7uGdXJ802rdPtW9u4+7ou6/0OB1w8\neHAl7Tb92p17V3Dvwd6S2oUfSBOYD837/btG2rUxkyPA71FwKzKKLNANA0URuFUJn0u2Bj4+l4wq\nSyiSOa2qSAKXLKHmvRSAvD+DQORnS0weWGAYBiI/oyIwEEIGQ8M0vZFBkkATea0N5rKsmj0s/+oQ\nChgy1pDekAHFrDlh6GY/KGDY+VYlv16ikHUl48zAyltpU5hUMLU5hQdNFibHLAtz7kgAqiTwKJL1\ny1KVTH5dyYMkzKKmQZuplleVTU+NfLCQhcDnVgjZXnqfW8HnUa0PkiwJAj6VUMCFsZwS7FLwelXr\ngyRJgkDA5RDsej0yXq+Kx10YdAUDbrK27BSvV8HvU62PlhACTziIhMFj419DNjRcRg6lLIQ3p1i3\nJhR0k81qiPzt8XoUfB4hiXd6AAAgAElEQVQXHm9hX6GQO29RXsD4/ar10VrGeDwKkgS6Dm63gt+r\nOgz6QmUeQiE3khBohoHHI+Pzq/hsYumyMg/BoBtJEmiagdsl4/OqDkF1WZmHYMBVwLhlfH6Xw3G5\nrMxDwO8uHI9Lxu9T8PlsxS7DXgJ+sx9dN3C5ZPw+l6XjAdOkzu93Ict5jGr63jgxbgJ+F7IsoWka\nLpd5v+yYsjK31U8uZxab9PtUArZCiGVlbnw+FVmRyOZ0VFXC73cRsH3IQiE3fp+KIktkszpq/niC\nASfG53OhKBKZjIaqmP0EQ4XjCQZd+HwqiiKTTmuoqun5E7IV3wwGzGuhqhKptDmA8ftcDpPDQMBF\nIJDHpEBRZPxel6OIZyDgwu9TUV0yyVTOPB6vSpnNkDTgdxXelaT5rvi85ruy3Pw+8x4vYyRJ4Pcp\nDtGq36Pi8yioqgypHJIk8HkUQraivD6XgicfA8Hsx+tWHAJZjyoXYgBmHPGoMj61EG9cioQr7yMG\nWLoczfZdU4RAlpYxy/HFBCzPwghAQSBTmM9WhEBIoFsYw+zDMNDzszzFsU2CvKbStv+ij6yc38aO\nUSUJYZtekSWBS5Lsxs24FQnd1pf1zbB15FVlVArxV5UFHlXGY+so4FHxq7JF17kUCa/LjKXLLehT\n8ee9fjTDHFz7vIr5fud3VxY03wPpVzKIEP8hs6uuDU1O60rj0Cf+nHUrq7lgS0FeVR8iWjTVuLqx\nzGHv3RBwl9BVTQFBxqbJ8co6quzU0viVHELYbNT1ECIz7sCgR0CzlQGQKkFzWrijNjgxciUUWXvn\npBYMW/kHwwgRyzndRHN6LXHbLKYq4MKikwKQDbhk443Dbpm3itKda7wqv7BxwnUhD2+dnnYwMn21\nIX5k45tbqgOcfG/GQX1tXlHF935W4Jtb64OcPzvnmGLfsa6R79j0E031QS6PRR2lA3aNtPItm6ah\nvi7AzGTcQWvt2dHu8Fh5avH7BGev8FttdwPQmJrmL079Nrv6/08LU1nhI5PVWLRdo717OvnGtwo6\nkHDYgyQEc7a02+v2dPBNmw4kEDA/QFM2rr1YK+L1KoTDXoe2p7gft1umuirg0PZct7vDcV6KItHU\nWMZ5mx5gz+52vvXtwvWRZUFba4QzZwvP5u6d7Q7tiBCmQPrU6YK2Z9eONr5j4/7BdEa2l23YtaPd\noVMBs+q43f9nx/Y2vvd9Zz8Dq2v5hU3/s31bK9+3aVAA1gzW8ZqtrMa2kVZ+8CMnZu1wPS+/UtCC\njWxucWh0ANava+TnNo+gLZua+bFN6wNmVphdI7RpQxM/sT2rAJs3N/OTnxbWrV/byM9fHnNgRra0\n8OOfFvpeN9TAvxaVBtm6pZkf2foZGqjj9aKSEdu2tPJDmzZjoK+at87MFmFa+JFN+9TXVcHJorT/\nbZua+Je3Cn33NIe5sOBMZd6xpp6XbX231QSYSeUc7/emldW8ZUtrry/zkCiiv4eaw5y3vRflPhVd\nlhyYFZV+rtgoxuXK4XZMU8DNnO1ddksCA+dPuEqP6sC4JJGnrAqYiEth2kbXqZIgrekOqiviVhiz\n0aIuSRBPa6SL/Hbes2mNXLIgmcoRs+2/LezjtbEFG0bCyOSYs9GXq+pC/MSmfVJlCZfuTOFf11HB\n92yeRYosqPSoXJosaIK29dfyXduzKUmCpnIv50ajH7gmZ7ghbPz4qe3vG+/9xJf+U5Pzv7vJRaPb\nYj0FkB9v/7JWjLnaNsVM3lUwRRx1yfJVtyvFCESJvuaX9XLVNUWrJJyzP1B6DWWpMJPxb2JkcybJ\nDrpaP3J+BmK5KXIppvgXilKk0lfys3Vpx7qiaybLqEZhkKoYOfSiay/LAlkvWlfUjyJLJamQJccj\nSyXblSzLkqNcxNX6kSSBrBRf16scc0k/Tq2PEKJ0u+LjkaQSjKI4+5EkUXJdi49PiNJrX3xPzeyS\n4n2VPuOlmNLnt/SYSzHva1/Fx/zvPJ5fdn3ebz9Xu+/F71zJu3I1jFR8n80Zav1/hRG//P1ezr60\nY4pjq7hKP1eNkCX9ODGSZM7E24NSSTQuDlpXAYl/a7ui5ZL9X+W8rnaMzm3AKNruateweF3xPZWE\nuGps/WX9fGBN/Gftql9pu2Gwnv29tZaeJOhWuK67mh6bP8hgbYg+my7FLQu6Iz4qbdO11V6VsNuN\nlH9FJARBVwDV5m+jighCtBVoJUMBqQvkAo+O1AzufhDLU9MucK82dTlWR63mOrE8K6OCaxWItgJG\n1CGJFgrmfzKq1IRHLug5XJKfiNttzSQKzEyCFtu0eIVHYXWVH1+eQlIkwZraIFtt/g6dFX5u7Kul\nPD8N7pIlDq6u587NrVbAGGiN8MCeLuryaahuVeLB61bw5C19hZTXniqeuXuAplqTb3a7ZJ4+PMiz\nDwxbAWNtfy3PP7Ke1jzf7HLJPPfoel54apMVaIYH6njhmU105HUpLlXm2FMbOXF0xAo0awbqOH50\nC115PxBVleh76cPsjb3F46NfZt/Mv/Lbp/4I13NP05NPD1cUiRMvbOUjL4xYH85VfdWcODpieaEo\nssSJF0b4yLER62PWu7KKEy+M0J9P/ZZliY8e38rxo1ssam7FigpOHN3K4EBdHiPymBEL09VZwfGj\nI1YNLkkSfPT4Nl54fsSi7zraI5x4YcSqiyVJghPHRjj23BZLxNzaGubEsS1WOvYy5uhzmy26rKW5\njBPHRhjZUkjHPvrcZo4+u8mi3RobQpw4NsL2vP+GEPD8hzdx9NnNePNUWH1dkONHR9i1o83CfPip\njTz/4c1Wzava2gDHj46wd0+nhXny8fU8/+wmi8KqqfbzwvNbHH4/jz+yjuef3UwwT9FUVfk59vwI\nB24s+PQ8/OAQRz+82aKMKit8HHt+C4duLvjiHLlvkOef3WRRnuXlXo4+t4U7buuzMPccHuDos5sJ\n57VgkYiXo89t5vBdBS3YXXes4uizmynPP+NlZR6OPruZew8PWJhbb+nl+Wc2WXqxspCb55/exAM2\nvdjNN3bz/NMbLR+jYMDFs09s5KEPFTA37Onk+UfXU53HBHwqzz60lofvKuzruq2tfPi+YQvj96o8\n/aE1PHxolYXZsbaRp25dRU3+mL1umcdv7uPIdYXrvGllNUd2d1Kd1ym6VYl7d3Zwx8aCVmSgOcyt\nw41U5u+FKgtuHmxg38oaC9NZ6WdnZyXhPI2tSIJtbRWsry+zMHUBN4M1QYL5eCwJGKgK0BspxONy\nj0Jn2Gf5lAmgo8xLm01LE1RlWkMeB6Y16HFgAqpMe8iD36YRai/zsiLis44n5JLpjfitFHIBrKoI\nMFwbsjDlHoUNjWGrBpcQsKU5wq7OKituVQdc7OuppiVvZSAJONBfx63DBe+w+rCXOze20J2vLSYJ\nuHdbOw/s6bKowqZKP4/s72Egb30hBDxxYCVP3LoKV/48mmsCPHPXAOvyvkqSgA8fHuTpe9eUJDJ8\nMC1PV73fv2ukXTMzOaNzCTrjaTI5DUlAKqcxl8gwb8tcmE5kiGc0S1Gf1gzimZzpepxviZxOTtfQ\n85ocHcjpGoZt7kAnhWG4AM3U06Ah9CQYSxR+P8RAj4GxPIWZBX0J9IUCRl8CPQ5CA7Gss4mb21ot\njmGk81OzeS2IkSKng26Yy1ndQMJMl1z+gZPWdKK2zIlYRiOW0Ymlc2gGZDVYSOe4spiyNDmz8Qyz\n8SzRfAZISteYWExxfjJmZSpcnk0wMZdgNr9dMq0xOhXj9KUF9PwszdhkjMtTMauScjqjcX5skTPn\n5qxfleMTS4xfWWJqJoahG6RTOc5emGd8LGrx8eNXFhkbj1pUUCar8d65OWamYtYxj1+OMjoWZTKf\n9pnN6lx54yy9OY3u+Bjd8TGWZC+u199lQmsFTEfbU6dnyGY1tPxU9ZUrS4yNRS1KKafpnDw1gywJ\nyw33ypUlRscWuZyfytc0nXdPTeP1qhbFNjkZY2w8yni+vIimGbx7cppIxGvDLDE6bp4bmJlD77w7\nRV1t0HLVnZyKMzoatVyPdd3sJ5EsZKlNT8UZHV1kND91vtyPpulWBe/p6ThjY1EuXjQxhgHvvDuF\nqkpWltrMbJxLY1EuXJy3Yabx+10k86mzs3MJRkejXLwUdWDKy31WdtD8XJJLo1GLTjMMePfdaepq\ng1Ym0vxCktHRKOdsFbPfOTlFa0vYymhaWEhyaXSBs+cKmHdPzrCiq5KlfDbZQtTcl52WO3lqhv5V\ntSzlKYloNMXo6ALvvVegZ06dmmZ0tJ6lPE25GE1x6dKCg7o7/d4so6NRFvIO3UtLKS5dijowZ87M\ncmnMhomluXgpykk75twco2OLLOTdb2PxDJdGFzh5poA5d3GB0cuLzOcx8WSWi2NRTtrKKpwfjTI2\nsWQ5hseTWS5dWeS0jba8eGWR8Zk48/nrk0xrXJyM8d5YFCP/Xo5Oxrgyn2RuKW29u2MzCS7Mxq33\n6fJcguloioVYBl0zyytciaaYTRbc42fjaRaSWZbSWXTDIKMZzMTTJLRCRtNCMkMsoxHPaui6Gdmi\naY2cTQOTyGgkchrJnG7FhaWMRs4wrOVE1vx/E5OPZdlljLmcXMZk7ZgcWb2QhRXPaMRzGvGMZmEW\n0lkyuUJq/GIqx1IqRzSVtWaTpuMZNK2Qrj6fzDKXzDKzZMY/HRibT6JSyDibXUoxHU0xMZ+0MOcm\nY5S5FStTa3YpxZW5BFfypSAMw6waH49lyeTjxMxCkvGpGGMTixi6mVN78vwc2VSO1K8iw0pwTQ1e\n3m+TX3rppV/1MfzS9t9+5w9eqhzajyZLLKZzCGHSO2lNd3C5S+kcqkt22H3r4EiPzOgGXiWHjoEQ\ny1OcGYQoBBSDHKq0iCCFNTFqpBD6FIWNUqDFwYjn1wFGErSZAsZIgcgCCdu6NEiLtn4y5FAwLLmw\nQDM0Upqwlg10Ejk3ttJVZnCyccRZ3WA2kWHBdj0W0zlO2az7k1mN6cUUV2y6ndmlFK/aaqnE0zmm\n55NcsPHGE3MJfm7TAiwls8zNJjlnK5NweXqJf7XVXIolsszPJzhzrnBdR8ejvPzaZWs6OxbPsrCQ\n5LTNO+bi6AKvvFLwGYknTMyp04WPQv/L/8RpuZLf6Lyff65cxw8jq7jn53/OH4V3WJhz5+Z4461J\na+CRTOZYWEzx7knbR+rsLO+cnLZs+FOpHNGFFO+8W9CpnDo9w3vvzVoDhnRaY2Ehxds2zMlT05w9\nN2+ldqczGtFoirdsXjanTs1w4eKClXKcyWjMLyQdepdTp2e4NLpg6YiyWZ35aJI333JixsYXieY/\niNmczvxCijdt9+e9M7NcvrLEfF4fkMsZzM8neePNAubM2TmuXFlibs7EaJrB/EKS139R0NacOz/P\nxOQSM3l7ek0zmJt3Yi5cXGBqKm75EWmauS+7/ubSpSiTU3GmpkyMrpv92DGjY1Gmp+NM5J87XTcH\nXnYfn/HxRaZn4ly5YmIMw8S8YsNcvmIe73K5BcMwy2W8Yns2JyZizM4lrbINhmGW3XjF5g01ORVn\nbiFplX8wDHOw+LLtmKdnEsxFk46SGVMzcV616ZNm5hLML6W5NL5kwyR4zfZszC2kiCYyXLJpuqbn\nErxmey8XltIsprNcmiroSabmk7x1qaAdWUxkSWY1xm26xanFFGdserJ4WiNtGEzYrAlm4xnGbcup\nnI5mGMzZvGOiqZxD65jVDXQBi7agFMvmWLSlp+cM87rZ60slspqjHIQZnw0HJpnTWcpo1qBLx0xh\nj9kw8ZzOvK2sj57fzhH/MhoTS2lL26MZEEtnmbLFzdlEhktzCWuQk9MNFhNZLtm0NZejKS5OLlmW\nJTndYCGW5qwttl6aiXPBVkcsqxnML6V492Lh/py9vMil8UWW8nEiqxksRFO8bRukv3dpgfHxKNGl\nDKNvf/7KSy+99Md8QO2Pf/u3Xnpkc3uemvzlf//HP7/7gR7fv7ddM3SVLAn8bucUnr9oSk8SptOv\nvalS6SlKRfoNidKpQVFUO8qkpYpJX3fRsucqGE/RsqsUU7Svqx1PMU+rSqU3z1OkIfApckkWQtDj\nnLwLeFRHeQaAiN95XmV+Fz63c7uKsBMTDroJ+JwGhhVFJTYiYa9FWViYcl8Jxp6BBVBZ4XcsG8Eg\n9ZnCwKguPUfa7cSEIx5HWYWr9RMOXwVTWXQ8Ea9FffxbmHDYW9JPRYUTEwq5r9KP83iCAReRsPOa\nFR9zwO+ynIOXW1XRvnw+9Zfuy+NRLLrm3zpmt1t2lJ242r5crlJMRdH1UVXJon3+rX0pilk93nHM\nFT6HzkKRpZLnpaLc59BQyLIowZQXYSRJXHVfdn2EEKXPZnm5twRTWYwJe0u0PBVF97Q84rWyFwvb\nOe9XOOS2aA0LU/SMhQMuy2HXvs7eyryl73fI64w3AZeMqyhu+otqqHkVyVEOAUrjjTufyWpvxdu4\n8tmvjnVSccwWpZiSuC5KYrunaF9uSZR8D3yqM7Z6FDND194CRbHO75IdGWoAYZ8zRvndimW7sdzK\nA0UYj0pZ0f0pDznvqd+rEA4WfTM+qLY8k/MfjK66JgY5QsAd65u4sa+OcP5Bqgq4uK67hrV5nlgS\nsLEpQn+l3+J3/apET7mPepufTIPfRdjtRRbLKdISQVcAl1TwEHFJVQjaAG9+1sGDEJ0g92DN7Mgr\nTL2NlPddET5wD5h/mK6euFbmNTjLGC8o/RiiG8NMVMcQbShSM4LlQKjikhvxKwVNjkcOUOFxWz4R\nsoAan4uuSKFWVYPfxZqaIJH8y+hRJDY0lLG3u9oUHwJrGso40F9PU/6jFHQr3D7UyCO7ulBlU1i4\no7eWh/auYEWDqaUp87t48qaVHD88iEuVkATs39DEh+8eZFVnBQIIB10cu3+YX3tqI26XjBCwb1sb\nxx5dz5pVJtdfFnLzsWc28akT2/C4FYSA63e2c/yZzQwP1pnp2kE3v3ZshJde3IXXqyIE7NnZzvHn\nt7BhXaOZYh50s+n3f40N2ij//dT/w5OjX+J3T/0hkf/rk2zeZFrlBwIufv3Fnbz0yV34/WY/27e2\ncuLYCFu3mLb8fr/Kr39iJ5/6xE4CAbPMxZbNzXzkha3s2NZmYnwqL31iJ596cSfBPGbjhiZOHBth\nz652szSGV+WlT+7iUy/uIBR0I4SZAfSRF7ayd08nQpjZVy99ahef+Ph2ykImZniono+8MML+fSsQ\nwhx0vPSp3bz40e2Ewx6EgMGBWk4cM7UrQpjp6y99ahcvfmy7NbBY3V/L8WMj3HLQrKHkdsv8+id2\n8vGPbLM+5H29ph7pjtv6kCSByyXzyV/bwcdObLX0JCt7qjhxdIS77+w3MarMix/bwcdObKMqP0Dq\nXlHJ8WNbufdDA0iSQFUlPn5iGx89vpXqfF2srs4Kjj8/wpH71liYjx7fykeOb6U272PU0VHOiaMj\nPPzgMHJeAH386BY+cmyrVTurrS3C8aMjPPbIOgvz/HObOHFshIZ6E9PSHOb4sRGeeny9Jdr+8FMb\nOXFshKZGUy/R3GRqlp55coOFefqJDZw4OmJ5HTU2hDh+dITnnt6Eopgi8scfWccLz22x6mvV1wU5\n8fwIx57JYyTBI0eGOPbMJtrymNqaAMef3cyxJzeiKhKSJHjg7gGOPr6BjlYTU13p44UnNnDs0fUW\n5vDNvTx73zCd+RpTlREvRx9Yy7H7hkyMgNv3dPL0rf105TVu5SE3z97ez4dvXoWqmCLlmzY089B1\nK+jIe0GF/S4e3ruCB3d0WO/3tpXV3La2iZZljZBb4Y61TdzSX4ci5eNEYxm7uqqoy39svYrEns4q\ntjZHrLTyjoiP4dqQVWPKJQmGaoKsrgxY3786v4sVEZ/lU6YIWBH2siLstTQwFR6FtpDbwsjC1O10\n2jDlboX2kIeIu1BCYkXYS2+F39pXpUelt9xveYcpQjBYHWRTQ5k18KoPuNjUGLZqcKmSYGdbBfu7\na3DnvxmtER/7e2tYlS9Z45Ilbh9s4EMbW63BUHdtkLs3t7Khs9JKr39kdxeP7++xBkO9zWEevaGH\nnfnY5lZljt3Rz9G7Biw7jlXt5Txz12r25cuJuF0yH394HccfXUe46IfeB9OE6b/xfv+ukXZN0FX/\n9Xf+4KW6dTcS8Ku8lZ/STWQ0qgJuTs7GSOe1KrGMRsjr4nJ+OjKrGwRUibmM6eprYDpe+lWJeM7A\nQEIzzHkTzZhHx1ynGzqKlMNgDpAwMBC4EIyCyJk3WKRBV8C4bGZVSQbgAWPMpKgkGUiD5AVxxcIY\nwoMhzQJ5nY7IoBkBMsYiOhK66XDDUlaQM2R0QyFngK4rzKRyaIbJMUvAhcUUifzUciJn1r16Zzqe\n59F1XJLgtbEo88ksmmFWG/YpEt8/OW1qcjIaXpfMj9+eZHIhhaHD9GKKyoCbL/3kArpBHqPww1fH\nGZuMY+gwMZugodzHP/zzabOfdA6PS+HHL49zKU8BTEzHaa4L8tkvvINuYHmW/PRnY5y7MI+hw5XJ\nGG1NYT7zd2+i6ybNI8sSr7wybmkxJiZjtLeG+fRnf4GmGWQyGq2jb9Hy2g/4SdlKDASLip/A+VP8\nzkyrhdF1ePudKStFenIyRmdnOX/5mdfJ5QyyWZ1cTuf06VmLMpqcjNHZUc5ffvp1cjmdbFYnk9E4\nc3aWN/J00ORUjBWdlfzFp18jm9XJ5nRSyRwXLy1YNM7kVIyuLrOfTH4/8USWy5eXLEpkeipOV2cF\nf/lXr5PJaORyOrGlNJNTMf71ZTOVeHomzorOCv7i06+TTpv6ouhiitm5pJUiPT1j9vNXn36dVN4l\nd34+yeJi2kqRnp1N0NFhnnsyaWLmZhMkkjl+9OOLNkwFf/WZ10kks2i6wfRMgmxGs8oozM0l6Ggv\n59N//Qvi8Sy6bjA9E0fXDKuMwtxckvb2CJ/57C+I5bVfU9NxBMJKc5+fT9LaGuazf/MGSzETMzkV\nR1ElK+1+YSFFS3MZf/O5N1nMa0wmJmK4PYpVDiIaTdHcVMbf/N2bRKNpDMN8Xvx+la993SwrEV1M\n09AQ5O8//w7zCykTM7FEqMzNV/JlLhaX0tTXBvmHL7zD3FwSwzCriUfCXr70NbNcxlIsQ011gC98\n5SSzNkxFhY8v5jGxeIbqSj9f+cZ7TM8mzMrhEzGqq/18IV8uI57IUhHx8k/fPcvUTAJDN7gyFaO2\nJsAXvm2eVyKVIxx08+2fjzI5l8TAfOfqqv188YfnMXRIpnIEvSo/fHeKqTy1MrmQpLE6wNfzpR9S\nWQ2/W+HVC3NMRVMYhsHMUoqGCj/fPzWFYRhkchoeVeK92TizcdP1eSGRoSbo4dXxBQzDpFUUWeJK\nPMNCynR9jmVyRHwuTs+Z55nTDSQBs+ksixnTaT2R1Qm5ZC4tpdANw3Q7FqZ2ZylrYlI5Hb8qMx7P\nmKnleWrJjklqOj5F5uJiCs0waSfDgLl0loV0fl85Db8qc3I+gWZgaXqm4hlmEsvHrFHmVnjlchQt\nX+k8ZxhcjqYYyz8bi6kclX4X3z09bf6/bsbSsdk4ZyZjGAbMxzPUlXn46qvj5HRTp5TMaIxPx3j7\n4jyGYTC7mKK5ys/fff882ZyOphvEkzkmpuO8dmoaDJhZSNFRH+KzXztJJqujaQbRWIa52ST/+ubE\nB09X/c5vvfToto73XaDzN7/69jVBV10Tg5z/9jt/8FLjhpuQXDJLNs7VELBk42lTOR2PRyZlS2M2\nDdoKfeUMA6/iLJMgRBZJLIuKTQ2MKsWBtIXByCIxb9PS5EDPgJGw5S7mwFh0YiQdSNowOkgpG0Yj\nZ6jo5Kx96QaktOVpTVN/lMzJpG25olnNcNRy0QxYTGaJ2q5PKqtxzsbHZ3WDxViGSZt3zFIyyykb\nr5/J6SzG0ozZtovGM7xj440zWZ1UPGMNaADmoynesdVcymR1UoksF2y6nZm5BO/atCzZrE46nePC\nJRtmJsHJU9OWbieb00mlNM6fL2h71p78PmeUSv6w+WZeKevmtVAnR976HH9atdvCTEwucfbcnCUq\nzmnmvs7aNEJXLi9x8dKCJQbWNIN0WnMIYsfGo4xfXrKEvrpukE7nHILY0dEoE5MxS8RrYjTes2PG\nokzPxC2Brm6YYuxizNxc0hLfGoZZ6uE9m+/J+Pgic/lBjIVJZR26pitXlohGUyzk65iZmBynbfdw\nYjJGNJqydDtgapLsmKnpOIv5QdVySyaznLbpo6ZnEizFMszMFHQgqWTOIeKdmU0Qi2UcdcSSRZi5\nuSSxWMbS7YBZBsSOmV9IkYhnLN3OMsZe62shmiKeyDIxYcMknJjoYppkMscVm6YiHs84MEtLGVLp\nLJdtOpl4IsNJ27nHYhlS6RzjRZhTtnsaT2RJZTXGbcezFM9w2vY8J5I5MrrBuK2mUiyZ5bRN65NM\n5zG267yUzHLedk3TWQ1dwIStft1SKsu4zUsnk9NBEkzbylHE0ppDb5PTDYQkWLCtS2TNQcdy0wyT\n9ovZPK9Smk4859RDCsxBioXJOTHLEc2OyWiGQ7djYBoM2rdLaTrRdMH/Z/kH7KKt3EIipzMby1gD\nJwNTlzhr8/aJpnJMLqYtcbKBea0vRwvXcCaeZnIuaWlyDMPE2OtUTUaTTM7ESeT1fYZhDkTP2Z6N\ny7MJZmbixPJxwjDMd+6sLf5emY4zN5tgMfYr0OT87m+99MjOrvdNV/3ml9+6JgY518yck0eVqS7i\nOCt8Lgc1qEqCoFrKJdvZQ0lQwhsrUt652GoCKOZF/eDQykggAk6ICOJMWJOAYBHGV9SPsFFVZpPF\nsr9moRVz0h7FyX8LsKi85Rb2qg4OWgB1Rbx+bdhLmY3OEwJaa5zn1Vjpp8K2nRA4rMgBmutD1Ni0\nGEJAZ1u5A9PSGHaUVQDo6qhwYprLaKgPOdat6HJijPo6VsUvIuUzOVYvnSMernJgmpvCjtILZj+V\nTkzz+8BcrZ8VTuLMACMAACAASURBVExTU9lV+nEec2NDqATTVbSv+rogzc3FmAqHLqWm2k9Lc7gI\nU+nAVFb6SjGdFQ5dSnnES2trKcauOQmHPbS2REowdm+YspDbonSWW2cRJhh009bq7Kezo8JKuQdT\na3Q1jMuml/D5VNranJiO9grLDRtMarC93fnctbeXOxyqPW7FUU4DoL0t4nCfdrtk2oue37aWiJVO\nD6bWqKMI09ocIWBzKlYUiY6ia9jWVObQpsmyoL3JeQ2b60IOV2RJErQVvRdN1QGHK7IkcJQRAKiP\n+BwaHCGgoUhDVR10OUodCCiJteVelUCRdiVSpFMJuhRLKmBfZ29+VXaUXgDwFy17FakEEyjS0vgU\nCV+R91NZ0b4CqkyoWEvoK46RCuVF6+qKdDKVATfVQef1aC7SlFWHPNQV6bPaimJdTcRLY9H96Wgq\nc7y7VREvzfVF34wPrL2/GZzlv2ulXRMp5JIkuGtDMwMtEcaiKRYSGaqCbnZ3VfL2dIxXxqMIAZua\nInRU+JlP50jkNAKqTHfYx2w6x3g+7bTR7ybsUsik0uQMHUVIBBU3Wb2StD4HGLilCiQCaMTNjCnh\nQRItGHjAeA8wQHQi5DowomaquOQDZSUYFZB7x8TIXRhSC+iLZvq58ILoBqIYxlnAQIgmVFFDzkij\nG0mEcOGWagi5dBYzCQwM/IqHoOpiKaOT1nUUIajzuXBJgrdn4xhAS9BDR9jLlcUUc6ksXkVmfX2Y\nOq+Lr707iaYbrG0Ks72jknNTMS7OJQh5FA4NNTLUUMYff/M0WU1nV38dd29p49SlBd4djRIJuHjs\nhpVcWtPA//2Xr5LJadywqYVHbl3F6XNzvHF6mnDIzbP3DHF5comXfvfHpDMaN2xv47F7Bjl9ZpZX\n35ygLOTm+JMbmJ6J8+JvfIdkOscNe7p44qG1nD4zy8uvXSYUdPOR57YQjab4yCe+QTKZ5frdnTz5\n6HrOnpvjpz8bJRR0s+23XqRq2xf421/8JuOeSoYX38P7F3/K3neq+OG/XCQYcPPiR7eR0wyOnvga\n8XiGndvbefKx9YyORfn+D84T8Lt48WPbkSR47oV/IhZLs22klScfX8/lK4t853vn8PtdfOLXtuN2\nKTx77KssLaXZvLGZJx9bz9RkjG98+ww+n4tP/tp2gkEPzzz/FRYXU2xY38STj29gdi7JP/3ze3i9\nCp96cSflES9PPfdlogsp1q1t4OknNrC4mOKrXzuN26Pw65/YSU11gKee/TLz80nWrKnjqcc3kEhk\n+eKXTuL2mHqbxoYyzp2fY34uyeBAHU8/sYFMRuPzX3gHl0vmUy/uoL2tgjNnZ5mdTbBqVQ1PP7kR\nA/jbv38LlyrzyRd30rOiktOnZ5mZidPbW83TT25AViQ++7k3UFWJT3x8B/2rajh1epqpqTg9PVU8\n8+RGvB6VT//168iKxMc/up3hNfW8e3KaickY3SsqeeapDYSCbv78r15FliQ+dmIrGzY08va7U0xc\nWaKzs4IPP7WBygovf/JnryBJguNHR9g20srb70wxfnmRjvZynn16I7W1Af74T15GkuDos5vZtaOD\nN9+eZGxskbbWCM8+vZGW5jB/+Ec/AwHPPbOJfXs7efPNCS6NRmlpDvPc0xvp6qjg9/7wpwA8/cQG\nDtzUw5tvTXLh0gJNjWU898wmenur+Z3f+wkY8Pijazl0sJc3357k3IV5GupDPPvURgZX1/E/f/8n\n6IbBI0eGuPNQH2+8PcnZC/PU1QZ4/okNrB+u53/84U/RdYMjdw9w+NY+3jw5zZnz89RU+fnwQ+vY\n8vYE//2PfkZO07nn0Cruu20Vb783w3sX56kq9/HMvWt468ws/+MvXyWn6dxxXRf3H+zl5KUFTl9a\noKLMw1O3ruK9y1F+9/Nvk9N0btrYzIe2d3D2yhJnriwSDrg4sruTy/MJ/uQ7Z8hqOjv7arlpTSOX\n5pJcmIkT9CjctraJuUSOv399HE3XGWqKsLW9gql4mvFoCq8qs7OzknhG47vn59AMg65yH6urgyyk\nNaYTGVyyxFBNgIxm8MrUEpph0BBw0xXxEctqzKeyKJLpW5bTDd6ei6MZpm9Za5mXRD4zSpYEHWVe\ncrrO27MJdMOgwqvSVuYlltWYTWVRhKA77EMzzH3lDIMar4uVFX4WMzmuxNMoksSa6iCGbvCdC3Nk\nNJ3GkId1DWHmExnOzydRJcGONlNX+LnXxknndNorfOzqrmYmnubN8SguWeLWgXrcsszvf+sUiYzG\nyroQN69tZnYxzU9PT+NWZR7a1UXQrfBf/vpVlpJZ+lvLuXd3F9GlNN967TJuVeb521ZRGfBw4vd/\nTDSWYXVnBQ8d7CURy/DVH57H7ZL56ENrqa/0c97mjP6BNQHI18y8x/tu1wRd9V9/+/df8qzcg1Bl\n3plYMtP8UjlcqsRbUzHL3nsylsHjVrgcz6AZZkqhLAlmkjmyeZvwWFbDo8jEcwa6IZEzBEIYZI0F\ndAQ6MjkjiyIl0YwldGSzpooAIUZBGKa+RsQAHSFNgyznaSlAjJn1FeQ8RsgY0hxIiqnJAdu+FDQj\nRc7wkNLS6IaKZpjW6QsZxdLkpDVI5gwmklmyuultoesG787FiedMj4e5VJZ0RuPtySWyOZ1ERiOr\nafzL2VkWklmyms74QhItp/ODk1NkczqxVI5URuMbr4wxvZgmm9M5PxlDxuCrPx01dSKJLPFUjq/+\nv+y9eZQc13Xm+YstM3KvrC1r33cUClsBVSisBRD7xgUkQRIkRYo7QZASqdVujY7t6TNjT093e7pn\npk/bsrXZalmWLNraKYoSKYkiQYIrABIEsS9E7ZlVucU2f0QiMiILEuk+arrpM+8cHSGSX973XkS8\nWy/f/e53nz3JpYk0mm5y/OwMAUnk2z8+bmPmNFJzOX749AkuXEqhawbHT04RDsj8tyePOpipmSw/\nfuoEZ88nbT7MiQkiIR9/+8030DST2dk84xNpfvbMSU6fmUbXTY6fmCAW8fO1v33N5rbMadT++inK\n336N/7dhJ+8GazkRqKPh5//En4y129W1C+GKX/76DO+csENWJ96dpKxM5ctftbk06bTG+QtJXnjx\nPG+/PY6um7x7cpJ4mcqXv/qKgzl3doaXX7nI0WNj6LrJqdNTlJWp/PVXD5PPm2QyGqdPT/P6G+/x\n5pHLBcw0ZXGVv/7yYfJ5g0xG592Tkxw9Ns5rr7+HrpucPjNDLObnr758mFzeIJu1Q2DvnJjk8KsX\n0XWTs+eSxGIqX/rrl8nlbMxbx+1U9JcP25hz55NEIypf+vLLZLM62azOsbfGOX9+hhcPnUfXTS5c\nSBEJ+/nSl1+yMTmdY8fGuHgpxW9eOIeum1y8mCIcVvjSX79MJqOTyxkcOXaZsctz/KrwLly6NEsw\npPClL79k6/nkDI4cvczkVIbnfnUGXTd5771ZAqrCX335ZebShXfy6GVmZnL84tlT6LrJ5ctz+FWZ\nv/rKYebmNPJ5gyNHLjM7m+eZX5xE103GxubwKRJf/tphZmfz5PMGbx65TCaj8/TP3kXXTcbH0yiy\nyFe+9grJVM7GvHmZXN7gqZ+eQNdNJibSSJLIV7/+KslkzrGj6yY/fsrGTE5mEASBr//tq8zM5Mhr\n9ngs4Ic/eQddN+2wnmXxN3/3BtMzWTTN5MjRMQRJ4PsFzPR0Ft20+OZ3jzI1XcC8NYakSHz/pyfQ\nDZOZZA7dsPjW999icjqLppscOz6O4pf4XmFeMyl7DN/9+UnGpzJomslbpybxqwrf//UZdMMildbI\n5XV++NJ5xmdsO++cnyEUVPjJ4QvohsVsxl7fz709xkTK7vfU5TnCQR/PHbc5J+m8QUYzePVCksm5\nPJphcWE6Q1iVeen8DLppkdEMsprBqZkMM1mb3ziezhPyyRybTKObFjnDJGuYXMpopDQDw7J1uvyS\nyLvJLLply3fkDIuJbJ5ZzeYSpvIGiihwJpVDt+yq4TndZKxgRy9gZEHgVIGTo5kWWd3kwlyO6QLf\nciavIwsCR8fTGKYdzp/TDM5OZxhP2xyzqYyGLMALZ6bQDJOcbjKd0TgxNseFmSy6YTE2m8cnCfz0\n6HvkdYusZnI5leP4hRlOjc2hGxaXZrIEFJHvPn+GnGaSyRmcn0jz1pkpjp2bQTcszk+kCfll/vbp\nE+Q0k2ze4NSlFCfOTPPGiUkbMzZHNCDztSeP2D4gp/POmWlOnZ3hlaNjH3646s//9Iv3buz6wAU6\n//g7r30kwlUfiU3On/2H//zF1pW7CQQVki7OiSKLpF2xXM20CAcUj06OIgqeOimmZR+Zunk6Ijqi\nmHahLBQhC+Td30QSUp5rAaOgpVP8HqQ9GEsoEJCdJjhChFe+o1t+TFeZAtMSyRre49G0bnq4Rrpp\nOwJ3z5mc7omj64bFWRefwrQgm9G47NLJyWkGp1xxY9O0MPIm5131XbI5g5Mubo1pWqAbnHN9L5PR\nOeXShDBNCwGBM+eLvIK5uTynXFwEy7I5U2dctmdnc5w5M+1wcizLll4/4+LtrDjzG86KZXyzdpQT\nwXpOBmr42Inv8lc1mxzM9EyWSxdT6EYxji5KoiOaBzYBdmxsjrwr/i9Komce4xNppqYyZF3vnSSJ\nnDpVxIyN29yVTMaLcdegusLHmZsrPjNREjx2xifSpNMaKRdfQpIETrowk5MZslnNU5NLFPFgpqez\n5HK6I2R3pS83ZmbGxky5+BuS6MUkkzk0zXS0dOy+vJjUbN7ecEwU33tR8I5ndtYWXBtz8UmEEsxc\nWsMwTU+NMASLkyeLmHRGw7Is3nNxciwsj51MVncIyEUMHk7XFX7VRRdPxjJNTrqeey5nIIiCh5Nj\nmpaHP5bPGwiCwIVLXsxp169wTTMRJJELrr50w/Tw2TTdRFIkzrvGrBkmZ133QjcsJJ/EBdd9vrIh\nudIM08Lnl3jP9Uw1w2TMpQtjWhZ+VWbcVeNJMyym827/Y4frpl21ojTTIuPyPxa2QrmbO6ObFll3\njQns33puDRzNNMkZXowo4BFs1UyLtGZQ2tx28qZFKu+tyWWZeDg5OcPexLiHpBumh5MzlzeYmtM8\nNbAMw+SSa30lsxrTyZzDyQEwdYtzLh85PZtnOpUj4youjGlx2vVMJ1M55lI5h5MDIJhw+nzxfZlK\n5kjPaaTmPnxOzn/9j/Ym54Pq5PzRtz8am5yPzNlUPOSjtUTrozkecFL/wN68VJbwUuJ+GdkV9FRE\ngUDJkZxPUhBct0JARCzh24hCFK+ejQx4Y+32td+DESgrwZTakVCEEu0RUXFSNe3xMI9rFPPLnli2\nJAjUl+gr1EVVyl3aNYok0FsS1++siVDniiUrssiSEp7Mgta4hw+gyCIrBmo9mIU9VXS6eA6KLLJy\nWb0HM9CXoK+7yJ2RZZGRoQYPZtHCGvoXVBfnJYmsXtnkwbCgj9XJI4R028FvGn+JZEO7J7a9aGGC\ngYEa51oUBVaNNHl4KQMLazwYQbALPpZiFi5MzMO4uSsL+712wMa4eSn9CxLzMcNNHk2V3p4qFl0F\n4+aldHZUOCUlrrSR4SYPL6W9rXweZuVQI6qLn9DSXMaSxV7M8FCjh7vS2BBjaSlmRQNBtyRDXXSe\nnaEVjR5eSm1thKWFEhcOZnkjERfPIVEdYtlS7/uyYrDBo5lUVRVySmU4dgYbPZpAFeUBBpd5McuX\n1ns0geLxgFNO40obXFbv0e6JxVQGS8YzuLSealcZmWjEz/KSvpYO1JJwYcIhHytK7s+S/gS1Lm5G\nMKAwuND73Bf3VFNfXbQTUGUGe6s9mIVt5dS7xuxXJBa3edduT33MKdECdiHJUh/QXhUm4XoWsijQ\nXqLPVB9TPXwWUYC6Ep5KZVBx0ryhwO0JeHVh4n7Fw50RgArV67NjfplYiZ3KEkyZXyZe8llN2Odh\nMlYGFKeEw5XW4pLdAKiL+mko0SjqTkQ89ayay0O0VXt5MgPNcY92WXtthJ4Gr69f1lXpqV/VWR9l\nQQmHa8XCGo8eUntjjIEeL7/wQ2vCByMc//86Of8DmigI7FnWwNr2SqrCPmRRoC6qMtxSztLaKLJg\nL8zl9TG6ygKEC2TjiCLRFgtQe6VWCbZ2Q8wnIQlgWRaSAFFFRpXimJaCaSmoUhxZqMQkYn9GGIlq\nLKsdw1QxTD+m1QY0YVCOYfkwKMOiBZNODEvFsPwYdGBRj2EWMGYMQWhEpBHD8mNaPgTq8EsxBMKY\nlgIEUaUYEUXGNO1fZ0FJojqooIp2cTtJgNqgj+54yFbksex6LwsSEaqDCgK2RtDSuhgbu6rwSQKS\nAIMNcdZ2VdNeFUYWBMqDPrYO1HHrmlZCBUGwzQO17BhqYqCtHJ8sUl2msm99O/fv6SMaVAgoIrtX\ntXDdhg6WL6xB9UnUVAb52HV9PHT7UsoifgJ+md3XdHD99m5GltWj+iQSlSHuuW0xj9y3nHiZSkCV\n2b21ixuvXcDaVU2oqkyiOsT9dw9y8IEhyuMBAqrMzm1d7L2+n9F1raiqTHVViDX/60NUqxbfP/wH\nfOfw/8LBs9+l7otPsHFDOwFVpqoqyMMPDnHgwSEqK4IEVJktmzq48fp+Nm20MZWVQQ48MMTDDw5R\nVWVjNm3s4MYb+tm2pZOAKlNREeSRh4d4+IEhqqtCqKrM6Po2bryhnx3bum1MeYCDDw/z4P1DJKrD\nqKrM+nWt3HhDP7t2dhMI2KJ7Bx8e5oF7l1OTsDFrVjVz495+rtvTRyCgEI+rPPrISu6/Z5DaGhsz\nMtzIjXv7ueE6G1NWpvLYwZXcc/cgdbURVFVmeKiBm25cyI039BMMKJTFbDv33LWM+vooqiqzfFk9\n+24aYN9NCwkGFWIxfwEzSEODjVm6pJZ9Nw1w2y0DBIMK0aifg4+s5O67ltHUGENVZZYsruGWmxex\n/9ZFDuaRh4a5646lNDeXoaoyAwsT3HrLAHfcvphgUCES8XPgwSHuumMprS02pn9Bglv3DXDXHUts\nTNjHQw8MceftS2hri6OqMn29Vey/ZRF337WMUEghHPbx4H3LuWP/YjrabSJxT3cl+29dxL13DxIK\n+QiHfdx/3wru3L+Ers4KVFWmq6uC229bzP33LicctjH3fXyQ225ZRE9XJaoq09lRzu23LuaBewcJ\nh32EQgr3fGwpt+0boLe7EtUv094WZ/8ti3jwnkEiYR+hoMJd+xdz696FLOipQvVLtDaXcecti3jg\nY8sIh3wEVZnbb1rIvmsX0N9did8n0VQf5Y69C3nw9iVEQj6CAZlbr+3jpu09LOyyMY21EW6/bgH3\n7V1IJKQQUGVu2tzJ9evbWNhejl8Rqa8MctuWLu7a2k04IKP6JHaPNLN9eSN9TWX22o2p3LC6lX0r\nWwj5ZfyyyDULa1nfm6AzEUYWBeJBhS0La9jWlyCg2MkMy5vjDDbaejKyIBD1yaxqrmCovgyfaP8c\n7K4I0VMRoiaoIAIBSWCgKkxfeRCloMvVGPbTEgtQGZARsLV0OssCtJepjnZXIuijIaJSXtjUKKLt\ny9pjAefHaVXAR2NUdWoQygUtnd54EKWg7VMb9NFeFqSusNHxiQL9lSGW1kbxS/aYm6Mq/Yko3ZW2\nvk5AFlnVUs5oZxVhn4QsQnd1iOHWCpY2lqGIAiGfxPb+GnYvqacsoKCIAgMNZWzor2FNXwKfLBIJ\nKOxb1cq+de1URP34ZJFlHZXsWNHE1uUNqD6RWFDhnm093LG9m0RcRVVElvdWce36NnaPthPwy8Qi\nPh7Yt5iP3dBPbYmg5ofWPmCoal5V0/+J20ciXPWn//4/fdFqHyUrwPHLs3YMNquhGyavXkqSNyw0\nw+TMdAbJJ3NxNm9rFxTivhfTmqN5MJXT8csiKc104rsmFlkjh2HJmJZM1jCQxDSamcNExrQELAwM\n67J9jYJhpRHIYzCLiYIJmGgYXLZ5PMiYzNkaEla6sFkSMC2djDmHackYloJu5cibftIGGJYP3ZLQ\nTYtLaYO8aaGZMKubzOZ1LqbzBU6OHf9+7XKKjGaiGRZj6Twz6TxH3ptFM2xOTjKr8dNjl5nN6uR1\nk1MTc6Rm8/z67TGHkzORzPHkr04zM6fZsf9zM6QzGj85dB5NN0mlNS5OzPEPT73DVIGLcPTkJLmM\nxg9+ftLh25y7NMt3f/AWE1MZNN3kyPEJtLzJP/7oCm8nz+mzMzz5g7cYG0+j6yZHC/Wl/uGf3nL4\nNidOTvGDHx3n0uVZTw2q73z3qKM3k/jht5EvnOPRzgf4eXyAlyOdDPzjX/LHU73ous2leevtcZ5+\n5iTnCvyfd05MYhgmf/f3bzqYI8cu8+xzpzl9Zsbh7RiGyX/7uzfQdZtv88ab7/Hr589y8tQUum7a\n/2+YfOObrxcwOq++fokXD513UtZPnZ7GMEz+5hs2jyiT1Tn86kVeefUSbx+fQNdNzpydwTBMvvY3\nr6Lrdi2qlw5f4I03L3PsrXGHk6PrBl/9ehFz6NB53nprjDePjjmcHE0z+erXbR5RNqfz4qHzHD8x\nwetv2PyfCxdT5DSDrxS0fXI5gxdePM+7p6Z49bVLNifn0iy5nG5r++QNcjmDF188x+nT0xx+5aLD\nycnmdL7ytcMO5oVD5zh3PslLL1+wOTmX58hkdb7ylVfI5Q3yeYMXXjzHxYspXihwhC6PzZFOa3z5\nq4fJ5WzMiy+e4733Zh2O0Nh4mrk5G5PNFuwcOsf4eNrhCF1JTbcxum3n0HkmJ9M898szBU6OnZL/\nla+/Siaro2kmh146z/RMll88d9rh5Mwks3zl66+STtvr4KXDF0imcvz8udPohsnUVJbp6Qxf+8br\nzBUwL796kdm5PD979hR6QaJ/YirD3/z9G8zO5tE0k8OvXWIuo/P0s3ZfMzM5xqfSfPN7x0jN5dF0\nk1ePXiarmTz9/BkMw5Z5GJvM8O2nT5Ca09B1kzeOT5AzLJ5+6Ty6YZGc03hvKsM//uYMybSGppsc\nPT2FCTz75iV0w2Q2qzE2k+ZnRy6TymjohsU7F5MgCvzmxAS6YZHO2aVeDp2fIVXg25ydTCNKIq9d\nTBU4OSaTGY23xmeZzRk2LyWVQ5JEjl/h5Oh2SvfZ2Rxzmq0LM5nVQYDTyRyGZRVCTAaX5vJ2DUEL\nZgrlG87OFjGzmsGFuTxzuu2jk3kD07Rsbo9pY6ZzOmdTeVJ5A8Ms1M0yTI6NzznaNhNpjXcn5pjK\n2P5/MqOR101eOjuNYVrkdZMLySxHL6a4PGunkY/N5slpBs8cG0M3LHKayanxOV4/PcW5iTS6YXFx\nOkNeM/j+oXMFjMGx8zO89s44Jy/NohsWFybSaJrJt35u86yyeYPX3p3gyPFxjp+2+YYXLs+haQbf\n+P5btsRF3uCVo5c59vYER09McvbIh8zJ+b/+9Iv3ben+wNlVf/TNVz4S4aqPRHYV2JovY6mc57Ox\ndN7DrdFMy8PZAZjVTE/c1rSYFxPWTHMeqdw0Ne+1lUMUPBFgLA8fBywy4GEAWZh4x2zitQt2gVDv\ntYlpeQfkjkcDzGk6+ZIYuTvWDDCZzpPOe/UmLkylPZiL0xlm0l5uz6lLsx7MubE5Jlz8DsuCd0vY\n/2cvJLk84bV94tSk5/rMuRkPVwLsIoceO+dmmJyY82JOeDHCxYu8EWzinGof31/2lRE6+w1vX2dn\nHP2bK+24qygi2Po2pamQbk2aK5hASQj0nRLMubNJUinvvS+1c+FCyqmj5WCOezEXL6acCu3Fvrxz\nvzxmk3Y9mBPjDocJbG6Pm8MEcOKdCQ9mairj4ScBnDgx6dQMA5vXdPqMF/POiQkM13uXTObmYU6c\nmHS4UGBzck6V9PXuyaKGEdicnFLMiZOTnnuWyeiccvGcwK5R5n7O2azOuye9mJMnp8i5/EIu79Vd\nuoLJuvhs+bzh4VQBnDw9TdrFp9A0k3dLMKfPTHt4V7pu8m7JvE6fnSHl4skYhsW7Z72YMxeTJN0Y\n0+LkxaQHc+7yLEnX2jUtODPmXV8XJjMkXfOygPMlPuByKoeXkWh/5m4T6TylLBl3bSvA1ugqUcIt\n9cepq3BtUnkvZk4zPL4NIKnNx2RL1pObQ3TFbibn/czNRQKYzmhOQdwr7eKM16+PpXKIJX25+VIA\nl2eyqCWyHycveZ/Xe1MZzLR3PKVZVGNTGaT5t+hDagLIH5ktwQduH4lwFUBjRZBFJTojC2tjxFwO\nvyLooynm1YCoD/s8mgtBWXQkxK+0sCwjC25+i4hP8sakZSGK4OLbCPgQBW98VaKiRPPGhyx4eTuy\nEEESinFiAZmg7I1tB2UZ1bXrkgVhXmw7EfRT4frjG5BFequ8ceOuqjAtLr5N2C+zskRTZXl7BX0u\nTZVoQGHTsjrPaeTqgVqWufgA0ZCP7WtbPTHptUONDC8t8hMiYR+7NnV6uCvrVzezerjIrwmHfOzZ\n3u3hpaxf08La1S3OdSiosGdnj0dTxbd+DTumXqIuN45gmdx94UckBwY9vJTRda2Mrm91rlVV5tqd\nvR5eyvp1rYyua3Ou/X6JPbt7PbyU0XVtjK4r2vH5bIybl7J+XSsbXH0pisieXT0eXsra1S1scNmR\nZZE9u3o9vJTVq5o9Y5Ylkd27ej28lOGhRjaOFscsSQK7d/Z4amcNLqtngwsjigK7dvZ4eClLFtdy\nzcZ251oQYOfObqfMA8DAwgSbSjC7dnRT5eKc9C+onmdn1/Zup4QD2FyjzdcUMQA7t3U7JRzALhmx\nZVOHB7NjaxcN9UX+SEd7OVs2d3ow27Z2efSHWlvibC3BbNnc4dENam6KXQXTSXtbca021EfZtqXL\ni9nYTmd7cc3X10bYXmLnmvXtdHcUeTE11WF2XOOd1zVrW+lxYaoqgmxb1+pZl6NDjfS5+qooU9ky\n3OTBrF1cywKXtlA87GPDIu/aXdlTTU998f5EAjIjXVUeO0ua43S6OUI+icUNXv2W3uowza73xy+L\ndFeGPH/WevNotgAAIABJREFUW2IB6lzaPooo0BL1cmDqwz4SLp6gLAg0hP0eTCLoI+FaO5IAjRHV\nM6/akJ96l5aPJNilJtxcxsaoSms86MIILKiJevTFOitD9CaK76EsCqxoKfdwPQcaylji4tLIosC6\nBQkCrr8jy9oqWOnykbIosGWwgbDLRw/1VrN6cdFHSqLAttWtTpkHgOX9NawfauRfpAn8qyzr8JEZ\n6arOSvprY0T8EqZpayf0JiJ0VoQwTBPTNOmtClEf8eMT7KwCvwh1YT8VfhnNMNEMk0pVIaxI9nGl\nYR+rhhUJnxhAM2Q0U8IvqshiGMOMoJl+dCOMIkWwqCFvBNBMFYsEohBHM+NopopmliGKFVjUkzeC\n5M0AplWPKMTQjDh5M0DejCGJ5QhWpY0xAghU4hN9GIaPvCGhGQqq5CesiOR0g5xuokoC5aqMLNjV\neC3LojrooznsR9MM8ppBIqDQHA8S88nkNRMZ6K6MMNhYhmWYGLpJb1WYBQ1l1EVVdM0gIAksb6vg\nmkW1iIBpmCxtr2Cwq4r2RARTN4n4JTYsqmXH6hbbOZgWw/0JhhfV0dNajmVaRIM+Nq9qYc+mTrsY\noAUrl9SxcrCB/u5KsCyiYYVtG9rZs60Lf8E5DA/WMzLUyECBaBwJ+9i5tYtrd/U4G43h5Q2sWtno\nEGnDIR+L79pBwC/w7df+mOcPPcau8edJ3LmXJQVMKKiwa2cPe3b1Eiw4meWD9YyMNLGssBELBhX2\n7Oplz65uR+Bt2ZI6Vq1sYsVym3AaCCjs2dPL7p29hEI2ZvGiGlatbGJohU2YVlWZa/f0smtHD+GC\ng1+0sIaRkSZWDhcwfonr9vSyY3s30cKmZqA/wepVzaxaaTs0v1/i+mv72L6li2hhU9PXV8XqkWZW\nF+pt+XwS11/Xx7Ytnc6mpq+nilUjLaxbY9e/8SkSe69bwNbNHU4hz+7uSlavambDevsPqaKI7L2+\njy2bOpz6Vl1dlawZaWHDaJuDueG6BWy6ptPZ+HR2VLB6pIXNm2zpd0URuW5PH5s2djgbn/b2clav\nbmbL5g4EUUBWRK6/to9rNnSQSNiYtrY4a1a3sG1LF2KhLtW1u3vZMNperF3VUsbata1s21bE7Nnd\ny+i6VuoKxNmmphjr17ayY3s3oiQgySK7d/Wwfl0r9YXNUUNDjNH1beze0Y0kCYgi7Nzezfq1LTQW\nBC3raiOMrmtl144eB7NjaxdrVzU7G6jamjCj69rYvd22IwiwbVMHq1c20VLYQCWqQmxc18oeF2bz\nhjZWDTXQWsBUVQTZuMZeK1d+JGwcaWblknpaG2JYlkVFTGXDymZ2rW0t1JOyWL+sgeH+BG21ETAt\ne0OzrJHtKxqw/x5brFqQYFlnJU1VYUzTIqLKrO6rYXRBDaIAlmmxpKWc/sYyGuNBLNMi5JNY3lrO\niuY4IjamJxGhsypMIuTDKJSHWZCIsKA6ApaFYZg0RVUaYwEqVBnDMJGAtrIALVEV0zTRDZNKVSYR\ntjmQhmEhWLZOWX3YZ2NMk5hfoiqgEPHZYXosqAv5qA/5MK0rGJnqgEJMkdANC0xoCPloivqxTLts\nStwvUxv2UaFK9gmhadJWptJZEQLTQtNNqoIKLfEAdTHVHg+woCbKovoYkmBnVdXFVLoTYTqrw1im\niSLAUGs5KzsrUGUByzRpqwqxsKmMhU1lWKaFLAqM9tewfqCWoCJhmRadtVEGu6oZ7KwE08InCmxd\n3sTGFY12IU/Loru5jKGFNQwP1IJlk8J3rW9l85oWYpF/idpV/Kvk5AiWZb0/6l+4VTb3WNd+7kuM\nLKzlTdeR7YrWck7OFFMoBQGWt1RwxpUi3VEeZKYk1NMVDzDlSvWrDCiU3oW4XydnFI+LVVHGIOXB\nBCQFzSoeD8tCiLyZ8WBkIUbOLI7HJ6jM6t6TJEnwM5MvjjEoC5xL5TxjCsoip13zqlQVjl1MesJ1\n9SEfh13Hn63xIIdPTqC5QIsSYX72+iXnurc+xuG3LpNzHceO9iX43q9OO9cL28o5enSMjOvYe8dI\nM08+9Y5z3d9ZwYl3Jph1HdXv2dTBd/7pmHPd113J2TMzzLjSM6/f2cPff/eoc93dWcHY5VkmXeUG\nrt/dy99/54hz/ZD+Ik3vvsrn2u/CZ+p0Zs7zf5z7Glt6/o2DaWkuI5c3uOhKAd57/QK+9e03neuG\nhigCAmdd92zv9X1869vFvmpqwgRUxRO6KMVUVgYpK1M9oaVSTDweIFEd5thbxbIWN1zX55lXNOqn\nqbGMN958rzj36/r4tgsTCip0dFTw6mvFZ3jdtX185x+KmEBApq+n2qmTBXDtnl7+wXWfVb/MwEAN\nL7x4rojZ3cs/PFnE+HwSS5fU8fxvzjqf7dndy5OuZ6ooIisGG/jlr884n+3a0c0/fu8t51qWRUaG\nm/jFc6ecz3Zs7+Z73y9iJElkzaomnvlFEbN9axc/+NHbTphNkgTWr211amCBfUrz45+842BEUWDj\naBs/+ekJB7P5mg6eevqEE4oTRYFNG9v50U+K7+81G9r52c/fdUJxggBbt3Txw58cdzCja1v4xa/P\nesJ1O7Z28X0XZt2qZn75ghezc1sX33uqOJ7VKxp48fVLaC6/tHNrJ99/5qRzPbykltfenSDvWpc7\nNrTzQ9d9Huyt5silpF2q4YqdVS089UrxuQ+02AKq7vTnrYMN/PJ4sYRFRyLMpGZ4MGu7qzy+pKFM\nJVvg3jj9N8V5yxVargr5yFuWhw7QVxXmpCv8U+aX0fCmkbfFApxy+baoTyJnmJ608paIyjsunxDx\nSWTyBnOu8Fd7TOVNV2mMqF8uyGoUfVJvVZhDrvBqVJXRNMMTnhusj/HzY5eLmICCpJucmywG9dZ0\nVfHDl84XMUGFoChywiUNsHlpPf/4bPGZRoIKtRGVoyeLfmLnSAvffar4/gRVmZaaKK+/NcavvrX/\nJcuyBvmQ2mBXtfXCn+/9wHhp2//zO8cnCMJW4D9iS/z/hWVZ/1vJf/cDXwGWARPAzZZlnSr8t88B\nHwcM4KBlWT9yfU8CDgHnLcva+X7j/MgE4AzTYraUb1NybRUKvrlbruQabO5OqW2xZGdqlmz+TObb\nMUui1JalXwXj/Z6Bibesg92/Z3wG8zZdeaN0XgYlYWsP/wZgLq97Njhg17dyt1Qm79ngAEyXxK1n\nZvOeDQ7AZEncemY2z1xJvNm9UQGb4+HWgAE8dZGuYJIlfIDJEowwm+KiL44piGQlHxd9cfw5b4x8\neiY7j5MzOenlIszM5CihwMwbz8xMlnzOKMF4555M5hBKDJXaSSVznlCZjfGOZ3Y2z/SM93ulc59L\na05NqiLGayeT8WrkXM1ONqd76lZdzU4+bzA97cVMlPCuNM1kqhRTYkfXTSZLeCClfRkFcm+pHfcy\nNAxr3js1VSiWeaWZpjVvrlNTaQ/X6GqYyam0Z2NiWcy7P1PTWQ8GYKJkXlPTmXmYyZJ5TSWzng0O\nwNRMCVckmfNscOzvlWBm854NDsD0nHd9zWS0eT6w1AfM5XRPXTyY71szeQOvZcjo3nWR1e0KfKWf\nuVvOMOZhSseXN+zkit9lJ2+Y8zAZvfQ7xrwxlvrIjGbM8xOpkrmnczpCie2ZEl83l9XncZamU97n\nPpfRmCnxE5NJLyad1Zkp8X8favs9haEKG5H/DGwCzgEvCoLwpGVZR1ywjwNTlmV1CIKwD/jfgZsF\nQegD9gELgDrgKUEQuizLEZN7FDiKrcfy/lP6vczoQ2iLmuOs76pyTslkUWBNeyX1Li5Ca3mQ/uqw\nE98VBeipCDrpiWBrMtQGi3oKtgaDlwOjSgLheTyZAIro0pIQfKiilyPkl2IoYjFuLQl+gpJXbyco\nBVCl4ngUUSTuV0r0HWTPmEOySFss4Dkh7CwP0eaKN5cHFIab455481BLOUtddXNqYio7ljbgL/Bb\nBGDLkgZGXZo3DZUhbt7QQcDV/3Xr2ti+psW5bkyE2b+nz1PHZ+/WLva4OAz1NRHu3Dfg4aXctGcB\nN+zuda7raiLctX+xE8IBuPmGfm68fkFxzIkwd9251MM5Kd93LddOvcDI9Js0ZMf4w1PfILN5O3EX\nZ+DmGxdy840Li/e0Ishddy71aKHcvLffgykvD/Dxjy2lypW+efONC9l3UxETL1O5+84lJFyck5v2\n9rPPZScWU7n7zqXU1hQxN96wwGMnGvFz953LqHfVqbnhuj6PnUjYx113LHXCKgDX7enllpsHnOtQ\nyMddd9op3Ffarh09nr6CQYW7bl/iqde0bWsnt9w84GzyAgGZO+9YSoeLB7L5mg5u3bfIwaiqzMdu\nX0y3q+bWxtE2btu3yPmR4PdLfGz/EnpdWh/r1raw/5YixueTuOO2xSzoK3IYVo80s//WRU4Ix6dI\n3Ll/MYtc+jErhxrZf8sih+elKCJ33LbYo9OzYrCe229d5PC8ZFlk/y2LPdo5y5bUsd+FkSSB/bcs\ndkKQAIsGath/64DDBRNFgVtvHmDExZdYuKCaO/YtcnRORFHg1r0LWT1cxPR1V3H7TQsdrSNRFLjl\nugWsc2k/dbWVc9uePieMKwpw044e1i8v2mlvjHHL1m4HIwhw/Wg7oy6OR3MizI1rWlGvYIBdK5pY\n01fUeaorD7BtcT2qi+O2YUENQy7OSVXYz/qOSg8vZbi1gkUufZ0yVWFZXQyfi3PXn4jQ7dLXCfsk\n+ipD+Fw+qas8RHtZcZ0GZJGueNCDaYupdJQV16AqifRWBPG7+uqIB+lx9RWQRRbVRAm45rWgOsLi\nuuLaCSoSIy3lhF3cveWNcUZc2kIhn8Q1vQniLt+2truaaxYW37GwKrN7RROVLq7c5iX17FrZXMQE\nZPZt6KTGxYncMdLCdRvaXRiF/Tt6qHf5kp3r27hxezf/Mk34fXJyVgDvWJb1rmVZeeAbwJ4SzB7g\ny4V/fwvYKNi/FvcA37AsK2dZ1kngnYI9BEFoAHYAf/FBZ/WR2ORYFtSWBSgP+hANCy2vI5kW8aBC\npMBByWsmcb9CUJbQNJ1MTkfPGwQVGUWAbN4gmzfwCTYhLqvpZDSdrKbjk0Q75TKvM5vX0Q0LQZBJ\na34yukJG8yMKCoYZI2tEyBoRdCsGgkpGryCjR8lo5UAA3YyT0WNk9Si6WY4gKGT1KFk9SEaPIAgq\neUMilRdJ5QVyhowoCMzmNbv/nF6ohW7/okgVZMtVUSSXM5jL6mSyOn5RJCQJzGU00lkNBcsusmda\n9tw1nagqUx1UyGc18jmdqCxSEfETlO24tQgkYipNlSEMzUDXTCrDPqrjQWKqjKmbKIJAfWWI9oYo\ngmWBaVJTEaS2KkhZUMHSTXwiNNZEaCvwDizToqYqRG0iQkWBF+JTJJobY3S2VzibtZqaELU1YRtj\nmigitDaV0dlm15OxTIvqqiB1NREqCxsPRRap7mtFFi3+4NTf8qWj/47eudMEe9qprrIxsmwXTuxo\nL3f+sCaqQ9TVRp0NjCgKtLfZmCt/NKsqbUx1gYQpigId7RW0tsadP4iVlUHqaqMkCkJtoijQ2VFB\nW2vc+YNYWVHAJK7YsQtttrbE8RUKDVZUBKivi1JTKOIninZx0JaWuPMHsbw8QF1dxNkICYLNi2lu\nijmYeJlKXW3Es1nq6iynqbEM1e/C1EVpaIiBYFcl6e6qpLkphhpQQICysgB1tREaG8scTFdXBY0N\nMTu7TIBYmUp9XZTGpliBpGgX42yojxIIejFNTWUOprOjgvr6KMFQARPzU18XtQuEOnbKbUzEBwJE\nSzGC3Vd9XZRwxA8CRKJ+6uqi9uatgGlvL6euLkq4YCcc9VNfH8Vd/LO1NU5DfZRItGinvj5Ke1u5\nY6etLU59bZRIgdwaCio01EXpcBX/bGkqo6424pDHgwGZ+hJMU0OUupoIsYKdgCpTXxPxFO1srI9S\nWx1yMKpfpj4Rob0himVYWKZFXVWYmoog0aCCZVr4ZIn6qpBdBNK0MbXxINWxABFVxjQtFEmkriJo\nF5MsYKqjfiojfkKKjFng0lRHVWoifkzDwNRNylSZsoAPf8EvYkF50EdcVdB0E003CSoSEZ+MZEFe\nM9B1g6hPIuaX0TUDXTfxCwIhRUKwLPK6gaYbhBSRsCyR1wzymolk2aF40bJ5M7puEJIlQpJIPu/G\nSIjYdvKFuoRRn4SmGWiagQyEfSIyFGwbRAuCgVrh74MiCEQKP2jzhe+VBxUqgz6MvIGWN/CLIvGQ\nj7Aio2smhmZSE1WpiQWwDAtdMwkpMlVRP/GggqGbmIZJY0WQhkpbt8wwTKIBhUR5gESZilXgGrXX\nRWlKRFBEAcu0iIV8JCqD1FSEipjGGI01Ec/m8UNr/3zicaUgCIdc/7vPZa0eOOu6Plf4jKthLDsM\nMgNUvM93/wPwabhKaOW3TeujwMmpaOqxtj/+X1neW83b7xU5Fkta4pwtCX8sbirjrOuovqMyRLLk\n+LizImBrOBRaVUBBK7kNiaDPk7YdksV5x5FBySLrSv/2iyLZEpBflDylJ3yiwERJ6Mcv4vksLEuc\nLjnqjEoiJ11hgaqgzJFz3hTF+rCfV10S4Y1xldePT3pCX/01EX51tBhvbkuEefXYmEf6fKSrip8d\nKnI1OhtjHH97zHMMv35xHU89e8q5bm8q4+TJKc8x/KbVzfzYxZ9oboxx4VzSk7K5ZX2bh/fQ1BBj\nrKCj4mA2dXj4Ew/NPkv8vTP8SeutALRkLvEXJ/4T1/T/iYOprgqR1wxPaGfrlk5++KNiXxXlAQRR\nYNxVbmDr5k5++OMiJhb1EwgqXHKl1ZdiwiEfZWUq51wlLLZu7uCHPy6OWVVlEomwJ227dF4+n0Rj\nQ4wTrrT6Uowsi7S1xnnblX6++ZoOfuziR0mSQHdXJUeOFvk/m65p56mni89CFAX6eqp440jxXbhm\nQ5sHIwgw0F/Dqy4O18bRNp7+xUkPZvFALYdfveh8NrqulZ/9vIgB+/TEzRFav6aFZ1zvD9inMC8c\nKvIc1q5q5he/PO3BDK9o4PkXiu/mmpFmnv2VFzMy1MivXDyiVcNNPFdiZ82aZp77VZHfMjzU6OEe\nXa3/oRUN/ObQBQ9m/doWfu7CLF9SxyHXvQD7fjzj6mvJQA2vutYgwIa1rTzzQrH/gZ4qjpya9ITi\nRlc18wvXPexrK+f42KwHs2FFI788UuR0ddZHuZTKeTDrBmo55OKFNFUGmcrrHh8w1FHJG65yFYmI\nn4xhYbgMLW6IcdzFyYmrCoYgeDBdVSFOzXj5NnkLTxmF1pjKGVeIJqRIZDVbJ8wZY9TPu67wYVAR\nyeYMTxirJRbg6OWUCyORyenMuvxNV2WIw650/YAioed0plz+ZlF9lOffLnKWVEVCMkwuu+Yx1F7B\nM68Vn7NfEQlKEudcqeVr+xM87XpXFVmkNuLnpMtPjC6r5ykXV02WRJqqQrxzaopffeeOD5eT052w\nXvgvt31gvDT673/r+ARB2AtstSzrnsL17cCQZVkHXJg3CphzhesTwBDwReB5y7K+Vvj8L4EfAFlg\nu2VZDwmCsB544l8VJwfm82Sutj8r/exqm7j/Ufu6q5n9IF3NG/NVvlWKMa+yjzVL7Zjz+zdLQIUf\nEL8TYxgWVkl/pTwi07LmPZ9SjGVeDWPOu543xnkTs9BdKf+GICKU3h/Lel87pgWCUYox52HMUsxV\n5lA61xK6AJZlzbdzlfG935itDzAvy2IeL+SD2Skd8/znc7U1OM9O6eSv0n+pHbjKmK+CmfduXmUh\nzOPTlb4/V+nLuhqmdMz6BxjP1eY1bx3MH/O8+2xaV1nzV1m774uZv8BLx2ia8z1O6Qgty5rnl+Yt\nS+b7rnnjsywsy3tKUdr3/J6u5tff329aWPPmMe/9xZo3j/nr4Cp+64Osg6vYmfdOfYB1+aE1QQBZ\nen/cB2vnAXcufEPhs6thzgmCIAMxbALyb/vubmC3IAjbARWICoLwNcuy9v+ugXwkwlUAmxbVsmdp\ngxMnDvkldi6qo7+2GCcebCxjpLncOerzSyJDDXGaoy7eTkylMx50JMNlQaCtkAp5pVWoMlUBxbk5\nInY2U9ittyOJlPm93J4yn4+w6yUJSiJxv+TYEbA5QRUuvktUkWiK+J3xiAK0xgK0uTgoiaDC0poI\n6hUOgQCD9WUMNbmO4MuDbFuQsENW2Jylbf217FxSPCHsq49y29o24oVUZ0USuGVtG/s3FrU+FrWV\n88C1fVQV4uaKLHLPnj7u2VvkeCzqruLAnUupKaQNy7LI/bct4aE7lzmYhb1VPHrfCuoK4RhZFnno\n48s5cN8Kh+OxoLeKxw6sdLRQJEngkQeGOfjQsIPp7aniEwdXOjonkiTQ8el72ZF8hVsv/pTV02/w\nZ+/8BeLdd9Fa4JxIksDBh1fy6IGVjp3Ojgo+eXDEDklgn2QcfHiYRx9Z6YS02trifOKxVXR12jF6\nQYBHD6zkkYeHnZBWS3MZjz+6ip7uSgfz2CMjHHyoiGlqivH4oyP09VZ57Tw07IS9GuqjfPLREQb6\nEw7m4IGVHHhoyMHU1UX4xMERTx2qhx8c5sBDw05orCYR5hOPjjip8QAP3r+CAw8OoRRCY9XVIT7x\nyAgrXPWa7vv4ch5+cMgJe1VVBnn0wDArXXySj39sGQ8/MIS/8E5VVAR59OGVrHLxSe64bTEP3bfC\nSfkvjwc4+NBK1rs4XLftG+Dh+1cQKGDiZSqPPDjs0Q26+YZ+Dtw/5OgPxWIqjz60ks0ujZkbru3j\n4fuHnHT+aMTPwYdWsn1L8f3ds7OHAw8MO+n84bCPAw8OsWtHkeewc3s3Bx8cJhIpYEI+Dtw/xHUu\nvtjWTR0cfHDY0SgKBhUefmAFN17b52A2jbbxyP0rHEwgIPPwPcvZ5+KUja5u4ZF7lhMvrOeAKvPg\nxwa57boiZvWKRg7csYzyAsbvk7j/1sXctqs4nuFFtTxw40IqYlfCvyL3XLuA/ZuLPLhlXVV8fFsP\nFYXwmSKL3LGxi72ris9iQVMZ+1a1EC9w5WRR4IahZnYuKr4b7dVhdvbXUlaQX5AEgS19NYx2FnlW\nDTGV9e0Vjk6ZKMDq1nKGXPWbqkI+ltfHiLg4QoN1ZSytKYZWy1WFpTVRD2ZRdYQlLkxclVleF3Xq\nWQnAYG2MocZiX+UBhVXN5U59LQFY1VLBho5Kx0dXhnxs7U1QU3heArC1N8Eul7ZQdcTP3hWNdoiv\ngLlhRRP7Vhd1wWrKAty5oYOOgtyBANy+sYO7t3Y7mNryIPfv7qWvECYVgHt3L+De6/udelY1lUEe\numUxA91Fjtu9Nw/wwP4lHu2wD7X9/jg5LwKdgiC0CoLgwyYSP1mCeRK4s/DvvcDTln0q8SSwTxAE\nvyAIrUAn8IJlWZ+zLKvBsqyWgr2n32+DAx+RkxzLsphM5pjN6mQyOoZlMWdYzGY1JlI5MlnNVvyd\nzTGX10hmNCwLcoKdYTQ5myNVUAOelEUyMdVW6xQAC9KawVRWZ6aQaihaEPfJjGfyCIKAaVpUqjJT\nWZ2UZiAAOVlElQQm0haCaO/aI7LJdM5wVD2zMvgli8vpPKIgYJgWMUViKqsxVQhP6YZJ1Ccxls6D\nYO/s5yIqE7N5J1NCNCyagn4mZrIY2D9hZrMaY6kcyTl7jGNSltmsbleXNkzAIjmXZ2wqQzadB0Fg\nYipDMpNneiZrc5SwmE7ZMvN6QXV0aiZDci5POpnFzOloOZhJ5hifSGNqJgh2xlFqNk86nccyLXTN\nYCaZZXwijVX4hZxK5kgmc6Rnc3Ys2zSYmsowMZ52fhGnZnKkkjlHRfZK9syEK2NmdjZHKplnrnAv\nDMNi9vIUmCajU68iTllIpkHu8gRz6VzRzmSavGZ47aRyzBXegysZNoIoOL+c5ubypFJ5ZgshUMuy\ns4DUgOL88p+byzMzk/FgxifSGIbpxaSyHszYeBpZFh2V33Q6TzKZczLJLAvGx+cIBRUXRmMmlSPl\nCl2Oj89RHg84mExWI5XMkZrNccWbj4+nmanJ2acDAuRyOslUjpmk185MModhmSBCNq+TStnjvrIr\nH59Mk5zNo2OBJJIzTFKzOTv7o7B7HJ/M2OUJrCJmdi5vZ+gVHPXEVNbGQAFjly6Yns07mMmZLEmX\nnbxhMpPKMp0q2plM2s8wr1sgCGQ1g2QyZ2cmFcYzOW1n5+U1EwSBvGYyk8wxNVOc19SMXcYhV8ia\ny+V1kqmsJ3NrajpLMpV1qs/n8zrJZI4JF2ZyKkMymXPUlPN5ezzuzLqpGbusRDaTB9Mkn7P7GptI\nO6dHU9MZkrMFjGGi5S2SKbuvK5jpZJbUnEY6rWEZFnnLJDmbY3wyU1yXySyzc3aWo6GbWLpJci7P\nZDKHXsBMp3LMpnVm5/JoeR0NSKbzTKZyharqMDObI53Xmc1oaLqBZkEqqzGT0chrNiaV0choBqms\nTl6319lsTreViAu+JClATjNIpjWyuomFRSpr/zuT1RAQSJoWmRLMbFYn58LMmBZZzWQmnSej2Zhk\n1i7RkM7ZmGnLIqvpzGQ0spoOlp1Fpht2qRMEezzpnMHMXJ5c3sZMpzVE0yKX0xEEmE3DXEYnOZdD\n1+yK9lOzOVRJJJu1Mam5HKmMxnQqh1bwMePTWcyQiV6ojD43Z1cbTyWzWIX7MzGVRhWxMRakZ3Ok\nZm0/cMVvTkxmKAv6PGrgH1oThN9bdpVlWbogCAeAH2GnE3/Jsqw3BUH4I+CQZVlPAn8JfFUQhHeA\nSeyNCwXcN4EjgA487Mqs+me3jwQnp7yh29r86H9hSXcVJ1w6CAPNZZwuSbdb1BznnCsNt70y5NHE\nAehMhBnPFDkwNSEfmZIj9tqQjxlXLLfMJ5EtOUaM+WSPTHlIFpkreTmDksi0S7Y8JIuMlaRwBmWR\n91wlGWKKxKmS9NVyReKEK/5dGfJx7LyXk9Mc8fOaK95cXxbgSEnZhN6aCM+7+ADNVSGOlZRNGOqo\n4LluCWvGAAAgAElEQVSXirH/5toI75bYWTVQyy+eL/IMmuqjnD457TlqXTfUyDOueHN9bYQL55Oe\nUMHommYPf6MmEWJ8LO2R8y/leDw8/TN8UxP8n803AJDITfGNt/6M0YF/62Di8QD5nO5Ja98w2sbT\nLo5QNGorrbp1e0oxwaBdINH9h2vD+jaefqaI8fslYlGVy654fKkdWRaprgpxwaXbM7q+lZ+5tFEk\nSaCuLsrZs0VeVencBQGam8o8JRBG17d69GXArkTu5vasXdPCL0o4MN09lR5uz9U4MD091Rxz8RPW\njDTxrItfArbq8ZvHivyfUk4MwMCCal578/LvxCzqT/DqG0U+yfDyBp536fgALFlYw8uvFLkQQ4P1\n/OaQ9xR8cGkdh14uvr/Ll9byYglm+WC957NSzhDM5/8sWVTL4dff82BGhhv5tWuMi/oTvHbk8u/E\n9PdW8WZJuY41K5v41cvF8fR2VPBWieT/6hWN/NrFj+pqLuNESXmBNcvq+Y1Li6m1NsLlEt7iyIIE\nh10lV+rLA0yX+K3lnZUccXFyqsI+MoY3IDTQEOMdl0+KqTJaSYi8szLk4RKGFRHN8oa6WuMBTrv4\nLsECJ8fN22mKqZxwyQ4EZJFM3lvapjUe5JiLk6PKIpmsQcblozsrQ7zi8pF+WcTM6Z7SFwvrorzg\n0hFSJBFRt5h0SWssbSvnOdezkCWBsCjynstvj/RW86xLS0cUBRJhH+dcpW1WL67j588X14EgQENF\nkNPnk/z6u3d+uJyc3lrrxb+++wPjxeF/+6GO77+3fWTCVYIAwRKdkUBJeQYBnJDOleYvLUoF+Ep2\nq+606ytNLvlMugrGLSH+WzEl3cuFqrm/q3+fJM7D+EvmFZDFeaKTpfcj4JPmjSmkKvOulRLbkaC3\nhEQ4qDipqw4m5MWEAlfBREowQcVTMgHwpI8DhMN+R6X4t2GsQIByvejMyvUUmlzSV0ghVDLGaOl4\nQr7/LkykZDzB4AfBzB9PKUb1y56U+6th/H7ZCcX8VoxPmocpnZeiiO/blyyL8/squZYk4Sp9ee1I\nojC/r5LviKIw77MPhvH2JQjzvxeN+OfpIUXn3UPfPEyp7UjYN09Pq/QdD4d989bcvL5C/nmY0jGH\ng4qnJAow7x6GAooT+nAwJWsn5JdRSpxQSC31E/Mxpb5ElSWUkr6u5mtLMaV+y69IKCX+11/CA1Ek\nYZ5PLLWjSCK+kjGXjscni/P9puLtyy+LTsr9lRb0eX2U6pMI+L2YcIkfVX3SPN8aDs7HlPq20mfq\n90mESvzvh9d+rynk/9O0j8xIb13Xxs0rm4kWXpLKsI+9y5tYV4gTC8DWBTVc01VNqPDSRv0yox1V\nLHHxdpbVRVmSiDi6OAFJZKAq7OHAtEZV2mIBR7tBEQVaowHqXC9kIqDQGPY5i1EWoDHsp871glap\nMs0R1bEjC9Aa9fJt6kN++ivDBAuL0ScKDFSFWe7Sd+iuCLK2tYKywiJSZZHRjip2Lqh1NkPLm+Lc\nsKyRRIF/FPRJ3LSimTtH253N0Nq+BPds6aK5kCIdVmXu39HLo3sXFiXml9XzyM2LaC9os4QDCo/d\ntoRP37PccbobVzbxyXuX01Xgt4SCCk88MMQfPLbKiSVvWN3MEw+vpK8Qbw4FFT77idV84TPrnE3V\n+jUtfOqxVfQX9FKCAYXPPr6GL3x+1OGcrBlp5tOPr2HRgK2XElBlBv/dp1ibP8EX3v0a+y8+xZ+/\n/X8T+cJnHV6Kqsr84efW84U/GHXqWQ2taODTj69heYGX4vdL/OFn1/NvPr/e4ZwMLqvjU4+vYbig\nheLzSXzh8+v5w8+td/gkSxbV8pknVrN6pMmD+YPPriMQsDGLBmr4zONrWFvgpSiKyBc+P8rnP7vO\n4Zz0L6jmM4+vYcP6tiLmD0f53KfXOpyT3p4qPv3Eaqd+lCyLfOHz6/nsp9Y6G4vurko+/ck1Ti0m\nSRL4/GfW8ZnH1ziblo6Ocj71yTXsKuhvSJLA5z+9jk9/YrXDJ2lrjfPEo6vYs7MHsDcUn/7Eaj71\n6IijUdTaXMYTj67ihj29DuaJgyM88cgI8TIb09QY4/EDK7m5wEsRRYHHHhri8UdGnBISDfVRPvnw\nSm4raAIJAjxy/woePzDilJCor43wyQMrueOWAQfz4McHefyREUcGoLYmzOMHV/LxO5Y4mPvvtjFX\nUvwT1SE+cWCEe+8edDYx9961jE8eXOXU16quCvH4wVU8eG+RL3bX7Ut4/OAIdQXeRVVlkMcfXcXD\n9y13MLffMsAnH17ppO9XlAd4/MBKHrm/aGff9Qv4xIPDNBZ4Z/EylU8+NMxj965wirHesLOHRz++\nnKaCDk1Z1M9j96zgsTuXOZuq3RvbOXjrYpoL44mGfDxyy2IO3jTgYLYON/Hgnj5aCvMKBxQe3N3H\nfS6uyNr+BHeMdtBYuIdBv8Sdox3sH2lxfrQNtpZzw9IGR4NMlUVuWNrAnoVF7kpfTYTN3dXUFN4x\nnySwtSfBNR1FLbO2cttvVRf8piIKrG0pZ11ruYNpjKmMNJY5GFkUWN0UZ60L0xD1s7q5nLpCX7Io\nMNpawabOKmfMTbEAGzuraCpwCWVRYGt3gt0La50frC3lQXYP1NFV8H+yKHDTskZuHW5xNkzt1WFu\nGWlhYYEDKEsCd61v574tXY6+WFddlHu3drOiu8rBHNyzgEdvXOhshnqaynhk7wBrCjpGsiTyxO1L\n+eQdywgWfElXS5zH7ljKhgLHTZYEPnPfEE/cPzRvg/ShtH9+CvlHon0kODmmZfHsa5cIqQrvjdvH\no+fm8hw9N80rJyfIFPgah06ME1FlLkxkEIBkKs+JsVneuPD/cffe0ZFc953vp6o6BzQa6EbOGRjM\nYDCYGQCT83A4MyTFOMyULclKFCVakoNWMn383j4fe5/XZ/1212/fHq9NK1umqCySoihSzGFyHuSc\nutHo3F3p/dHNRlWPfKy35zzuoe85+KNwvrh1q6rvry/q97nf3xprec3FuSheu4X51SQCsArMlDoY\nXUsTyefWFUXDLonMxjPvYztUOa1MxTNE8ymsRFZFEgRmYumCxm+TmI5nCmmueEZGBKYNmnKHhdHV\nNKF8yiqVyXn3TK0kQcixGZMuGxfmooTyDMWltEypRWIyv11UB64tRHl3LEQ0rzk7HqKxxM7E3Bqa\nDgng3ESYd64skYjnzvXu1WU21ZUyOr2GqulkUgpvX1nizOVFsvn03XuXljjXu8zEdARd1YjFVF4/\nO8elK8vI+f3xp88vcObiYq5qtaIRW8vw6pvTjIyGCmzPmXPznLmwwI2RMLqmE49nefnVSWZm1grb\nzM+eX+D0uflCxe5kSublX0+wvJwopKvOXVjgzJk5rl5dRtd0kkmZy8+8Qn1WJeuQqM2EuOKsp+UH\nz3HZkktfpdMKv3xpDFlWC9zFpUtLnDk7z+V8KiGTUXnxpVEkSSgwFZevLHPm7HyhrEI2q/KLX47i\ndFoLjs9Xry9z5tw85y+aNX6/k1T+Hl67tsLpM7Ocy28llmWNF14cobraW9gaf2MkxOkz85zOW/DL\nssYLvxilsbG0UMV6dCzMmTNznM6nURRF4/lfjNLVFSCeyDFc45OrnDk7x7v5VIeq6jz/4giLy3Fi\niQyIuarXZ87O8fbZechbITz/0hiRWCbn3GoRmZqPceb8PG+dmQOLiAa88PI46azKWiKDYBGYWYhx\n+tw8b52dQ7TngtyLr06gCQKRpIxgk5hbSXL2wiJvnJ5DsEnowIuvTWGxWViNZxFsEgvhFGcuLPDq\ne7MI+X9Ifvn6FB6PnVAsk9Os5jXvrmt+9cY0ZWVOQrE0ol1kKZLkvXPzvPLmFIIl90X2q9cnqa72\nsBROIlgElsI5za9em0TPf5H96vUpGupLWVhOgCCwtJLkndOz/PKVCXQEEODl16Zoay1nbjEOgsBy\nKMU7p+d48VfjBc7rldcm6ekKFlKQoXCKt96d5cWX1zWvvTVN38YqZvOa1Uiat96b4RevTRZ27Lzx\nzgzb+2uYzaeHItEMb52Z5bVz84X079vnFhjevMz0fAxd01mLZXj7wgLvjayg5ufTu5eXOL85zORi\nHE3LMXnvXF3m2txajkEBzo6GuDK9xtRSAlXTiSoap0dDzERShSrsl6ci3FiIMb2S08gZuDATYTmZ\nJfH+PFiIMlFfynQ4harppIHLCzFiWYVYfh6MLCeYqUwxF0mh5DU3lhMkZZVYPv6NKyozATfT4WQh\nPXV9OU5a1gqaCVllJphiMpQoOLhfXYqRlrVCFfYxOcFUOMn4cqLgoHxxbg1F0Qv9jC3HGVuOMTIX\nJSOrZIDT42EETS84sY/ORrk2F+XyZKRwP964uoxDEgqa69MRLk2EuTgaRpU1VBleObdAuctaiLUj\nUxHOjaxw9soSWt6n56W3pqkLugvze3wqwtkrS5y5uIiu6ciazouvT9Je7yMWK/aX/oDah6gm1W/b\npKeeeup/9Rj+1fbnf/U3T3k7DpLRdVYN+eWMqjNryOWupWRUYM2QX5VVjRUDA5PIquiiQMLA28i6\nzpohb5tRc8UYjDbhsqYTNWiymo6im+urZFXdxPHImk5a1Ux+OxlFZ9nAiWS1HGgXNViJJ2WVKUNu\nN6NoRFMyKwbL9lha4YahjldKVonGMywYfGHWEhkuTaznn1NZlUgszfTSeh49FE1z8fo6l5HKKCSi\naSYNNVhWVlMmziCVVojHMkxMrTMDy6Fk4YsfcmUDErEsY5PrNZ8Wl2I3axJZxsbXNQuLMS5cXCx8\nSWSyKvFEllEDNzRw8Rdck4L8VeM9vFbay1u+Lh4+9y3+e/mBgmZmZo2r11cKAF9WVkkms9wwsBDT\n02uMjIYLtu6yrJFIZrlh4FQmJyNMTK0HPEXRSCayXDPcs/GJVaZnoqTynzNF1UgkZZNmYnKVufmY\nCaBOJrNcM/Au4xOrLC4miMXWAepEUubqtRVDPxGWVpKFUhKaphNPZE2a6ek1QuEkkbV1TSIpc+X6\nCoIgIAgCM3NRQpEUq5E0giCg65BImDVzCzHCkRThVYMmKXPlxrpmYSnOah62fV8TS2RN/SwuJ4hE\n06yE/mXN8kqSyFoOyH2/REYsnuXytXXNSjhJdC3N4nIirxGIxbJcurJc0ITCK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CsUTSer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\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LLT9/a3JdI4ns6K7gl++uz4Mj2+t5/rWJwit/iySwd3MNL7w+ua7Z0cDzL08UUnGSJHBo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TH3tJfy9KkOOlO8C5tN5tknenjuiR7NMXe2FPPUqU5Wp/LdWK0yP7mwhmfPdWsLuNaVhTx1soO1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izE65Xp6izhgfvn8+jDCwkEXOTluTnw5BIe/sICmpuK8HplOtrDPPTAAr746EKCARfBoIsn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\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ag5ZFeC6n0NoW5ic/PcVUJR00lcjR2hrmB48cB8xp1+bGID//9WlrWeNUIk9bW4TvV5hC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\nLHIkSdIg/QXW1isomjHvZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1092fa3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,7))\n",
    "X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]\n",
    "cm = plt.cm.get_cmap('RdYlBu_r')\n",
    "positions = np.vstack([X.ravel(), Y.ravel()])\n",
    "# values = np.vstack([m1, m2])\n",
    "values = Data.T\n",
    "kernel = stats.gaussian_kde(values)\n",
    "Z = np.reshape(kernel(positions).T, X.shape)\n",
    "zmn = np.min(Z)\n",
    "zmx = np.max(Z)\n",
    "rng = zmx-zmn\n",
    "Z = Z.ravel()\n",
    "X = X.ravel()\n",
    "Y = Y.ravel()\n",
    "# for i in range(len(X)):\n",
    "var = (Z-zmn)/float(rng)\n",
    "# sc = plt.scatter(X, Y, s=10, marker=u'o', facecolor=plt.cm.RdYlBu_r(var), vmin=zmn, vmax=zmx, edgecolor='None')\n",
    "sc = plt.scatter(X,Y,c = Z,s=20,vmin=zmn,marker='o',edgecolor='None', vmax=zmx, cmap=cm ,alpha=1);\n",
    "\n",
    "plt.colorbar(sc,ticks=np.round(np.linspace(zmn,zmx,5),decimals=3),shrink=0.6);\n",
    "\n",
    "sc = plt.scatter(X[3000:3100],Y[3000:3100],c = Z[3000:3100],s=20,vmin=zmn,marker='o',edgecolor='red', vmax=zmx, cmap=cm ,alpha=1);\n",
    "plt.xlim(xmin,xmax);\n",
    "plt.ylim(ymin,ymax);\n",
    "plt.xlabel('X');\n",
    "plt.ylabel('Y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ma3A3JkFiuSHxn4HvAHe4qzKB/43h2MuBqSJSJiKZOI3ni7uUWQxc6y5fAbyh\nququX+D26ioDpgLL3PaTR4CNqvqTGGJIK69v3EtTW4T5Vq3lKRFh+uh8uyIxJkFiuSK5DLgEt8uv\nO91ufl87uW0eNwMv4zSKP6Oq60XkbhG5xC32CFAoIpXAbbhjeqnqeuAZYANOT7GbVDUCnAZ8Cfi8\niKx2HxfGfLYp7nernZF+504q9DuUAW/6qHw27TmE87vFGBOPWOZsb1NVFREFEJHcWA+uqi8CL3ZZ\nd2fUcgvwhR72vQe4p8u6JcCAHAa3obmdtypq+dIpE22k3ySYNjqfQ61hag4cZvzwHL/DMSatxXJF\n8oyIPAgME5G/AV4DfultWIPPS+t30Rbp4JITrForGY6xBndjEiaW+0j+A+cej98A04E7VfV+rwMb\nbH67aidlRbnMGm9TwCbD1FFOItm4K5ae7MaY3sRStYWqvgq8CiAiARH5oqo+6Wlkg8juhhY+qK7n\nlrOn4vQnMF4bmp1BWVEuH9U0+B2KMWmvtxsSh7rjXf1cRM4Tx81AFXBl8kIc+BavqUEV5tvYWkl1\n/LgCPtphicSYePVWtfUETlXWR8DXgDdxGsYvVdWuQ52YOPx21U5OGF9AWVHM/RhMAswaX8DOhhZq\nG22oFGPi0VvV1iRVPR5ARH4J7AJK3J5WJkE+2dPIhl0HufOiATf2ZMo7fpzTHrWupoGzjhnpczTG\npK/erkjaOxfcezh2WBJJvN+t3klA4KITxvgdyqAzc1wBIrDWqreMiUtvVyQnRA3OKMAQ97UA6vd4\nWwOBqvK7NTWcNqWIkfnZfocz6ORlhZhcnMdHNQf8DsWYtNZjIlFVG+zJYx9u28/2fYe59expfocy\naM0aV8CSyjq/wzAmrcU0aKPxxm8+rGFIRpDzbQIr3xw/voC9ja3sOWi1tsb0lyUSn7S0R/j9mp3M\nO240eVkx3c5jPNB5A6i1kxjTf5ZIfPLqhj00toT5q9nj/Q5lUJsxpoCAwEc7rJ3EmP6yROKT33y4\ng7EF2Zwy2Ub69dOQzCDTRuWz1u5wN6bfLJH4YO/BFt7eVMtls8fZSL8poPMOdxtS3pj+sUTig+dX\n1dChcLlVa6WEWeMLqG9qY2eDNbgb0x+WSJJMVfnNhzs4qWQYk4vz/A7HAMePHwZYO4kx/WWJJMnW\n1Rxk055DXPEZuxpJFceMzicjKKzabonEmP6wRJJki1ZsIzMU4KLjbQKrVJGdEWTW+GEsq97ndyjG\npCVLJEmI4aSvAAATQElEQVTU1Brmt6t2ctGsMRTkZPgdjoly8qQRrN3RQFNr2O9QjEk7lkiSaPGa\nnRxqDfPFuSV+h2K6mFtWSKRDWbF1v9+hGJN2LJEk0VNLtzF9VD6zS4b7HYrp4jMThxMKCB9U1fsd\nijFpxxJJkny0o4GPahq4Zm6JTaebgnKzQswaX8BSSyTGHDVLJEny1LKtDMkIctlsm043VZ08qdDa\nSYzpB0skSdDY0s7vVu/k4hPGMDTbGtlT1dxJhYQ7lJXWTmLMUfE0kYjIPBGpEJFKEbm9m+1ZIrLI\n3b5UREqjtt3hrq8QkfOj1j8qIntFZJ2XsSfSb1fvpLktwjVzJ/odiulF+cThBAPC0mqr3jLmaHiW\nSEQkCDwAXADMAK4Wka4Tk18P7FfVKcB9wL3uvjOABcBMYB7wC/d4AP/jrksLHR3KY0uqmTW+gBPc\nIctNaupsJ/mgyu4nMeZoeHlFMgeoVNUqVW0DFgLzu5SZDzzuLj8LnC1OS/R8YKGqtqpqNVDpHg9V\nfRtIm7/01z/eS1VdE1/77CRrZE8DJ08qZM32AzS3WTuJMbHyMpGMA7ZHvd7hruu2jKqGgQagMMZ9\n08LD71QxbtgQLrRZENPCydZOYsxRG7CN7SJyg4isEJEVtbW1vsSwZvsBllXv47rTSgkFB+w/9YDy\nGbed5P3N1k5iTKy8/HarASZEvR7vruu2jIiEgAKgPsZ9e6WqD6lquaqWFxcXH2XoifHwO1XkZ4W4\n6i8m9F3YpIS8rBCfmTic1zfu9TsUY9KGl4lkOTBVRMpEJBOn8XxxlzKLgWvd5SuAN9SZXWgxsMDt\n1VUGTAWWeRhrwm3f18yLH+3imrkl5FuX37Qyb+ZoKvY0Ul3X5HcoxqQFzxKJ2+ZxM/AysBF4RlXX\ni8jdInKJW+wRoFBEKoHbgNvdfdcDzwAbgJeAm1Q1AiAiTwPvA9NFZIeIXO/VOcTjkSXVBET4ymml\nfodijtJ5M0cB8PL63T5HYkx6kMEwvWh5ebmuWLEiae+388BhzvzRW1x20jjuvWJW0t7XJM7FP1tC\nKCg8f+NpfodijC9EZKWqlsdS1lqAPfCzNyoB+NY5U32OxPTX+TNHsWrbAXbb9LvG9MkSSYJtrW/i\n1yu2c/WcCYwbNsTvcEw/zXO7a7+6waq3jOmLJZIE++lrnxAKCjedNcXvUEwcpozMZ1JxLi9ZO4kx\nfbJEkkCf7Gnk+dU1XHtKKSOHZvsdjonTvJmj+aBqHwea2/wOxZiUZokkge59qYLczBBfP2Oy36GY\nBDh/5mgiHWr3lBjTB0skCfLahj28tnEPN501hRG5mX6HYxJg1vgCxhZks3jNTr9DMSalWSJJgMNt\nEe76/Xqmjszj+tPL/A7HJIiI8IXyCfxxUy1b7OZEY3pkiSQBfv7mJ+zYf5h/ufQ4MkP2TzqQfHFu\nCaGA8Kv3t/odijEpy7714lS59xAPvV3F5bPHcfKkQr/DMQk2cmg2Fx4/hl+v2G5T8BrTA0skcQhH\nOrjjubUMyQhyxwXH+h2O8ci1p06ksTXM86uOatxQYwYNSyRxuP+NSpZv2c9dl8ykOD/L73CMR2aX\nDOe4cUP51ftbGAxDChlztCyR9NN7m+v42Ruf8Fezx3P57PF+h2M8JCJce0opm/YcsnlKjOmGJZJ+\nqD/Uyq0LV1NWlMvd82f6HY5JgotPGMvwnAwefqfK71CMSTmWSI5Se6SDWxet5sDhdn529UnkZoX8\nDskkQXZGkBs+N5k3K2r54yZ/Ztw0JlVZIjkKHR3Kd55dyzuf1PGv849j5tgCv0MySfTV00spK8rl\n+4vX0xbu8DscY1KGJZKj8MOXPua5VTV8+7xpXGnT5w46WaEgd140g6q6Jh57t9rvcIxJGZZIYvTg\nHzfz0NtVXHvKRBvZdxA765iRnH3MSO5//RP2HLS5SowBSyR96uhQfvCHjfzgDx9z0awx3HnxTETE\n77CMj7530QzaI8rdL2yw7sDGYImkV63hCLcsWs2Df6zii3NL+M+rTiQYsCQy2JUW5XLLOVP5v7W7\n+O8/Wi8uY6zLUQ8aW9r52uMrWFq9j+/MO4ZvnDHJrkTMETeeOZmK3Y3c+9LHTCzM4cLjx/gdkjG+\nsUTSg+yMIPnZIX664ETmnzjO73BMihER/v2KWezY38zfLVrNuGFDOGHCML/DMsYXVrXVg4xggIe/\nXG5JxPQoOyPIw18uZ+TQLL786DK7v8QMWpZIemFVWaYvhXlZPHn9yYwpyOYrjy3j/tc/oaPDGuDN\n4GKJxJg4lRTm8PyNpzH/hLH85NVNXPvYMjbuOuh3WMYkjaeJRETmiUiFiFSKyO3dbM8SkUXu9qUi\nUhq17Q53fYWInB/rMY3xw5DMIPdddSL/Mn8mq7cd4IKfvsM3nljJupoG6yJsBjzx6n9yEQkCm4Bz\ngR3AcuBqVd0QVeZGYJaqfkNEFgCXqepVIjIDeBqYA4wFXgOmubv1eszulJeX64oVKxJ6fsb0pKG5\nnUfereaxJdU0toaZWJjDOceO4qzpI5k5dijDczN9jU9VaWnv4FBrmOa2ME2tEee5LcLhtjCH2yM0\nt0Voae+gpT1Ca3uEtojSHumgPdJBuEOJRJRwh6KqqHtMcKqDRSAoQjDgPDKCAUIBISMUICMYICsU\nIDMYICsjQHYoSFZGgKxQkOyMAEMyggzJDDIkI0i2u5yTGSQ7FCRgXe+TSkRWqmp5LGW97LU1B6hU\n1So3qIXAfCD6S38+cJe7/Czwc3EaJuYDC1W1FagWkUr3eMRwTGN8VZCTwW3nTuP608r4/dqdvL5x\nD098sJVHljjDqozMz2LaqHxGDc2mOD+LorxM8rJC7pdmiFBACASEoAiK0qHQoUo4ooQjHbR3KO3h\nDlrDHbSFI7SEnS/8w+0RWtqcJNCZDJpaw85zW5im1j8ljaNtxsl0v/wzgkIoGDiSKEQg4CYPVZx4\nO5zEEu5QIh3Oc2cSao/0/4drdkaAnMzQkWST4yacHPffLdtdHpLpJqEMJzlldz6HnPVZoQCZISd5\nZYacc8oIOutCAef8MoJCKBA48lmY3nmZSMYB26Ne7wDm9lRGVcMi0gAUuus/6LJvZ/epvo5pTEoo\nyMngr0+eyF+fPJGm1jArtu6nYvdBPt7dyOa9h6iqPUTtoda4vlyjZYYCR75YO79oczJDFOVlUpKZ\nQ25WkNysELmZIXKzQuRlOdtzs0LkZnV+MYf+9GV85GohkLCOJ6pKW6QzCTrPre3u1U/YSYSH3dfN\n7tXR4T9Ljk5iPByVLOsOtdHc1vxn+7S0J25Qzc4rrM7kHgwIAeHIaxHnSiwgILjP7r+Xs81Z3/lP\nKEeOK/zZv6p0u9glltg+h85Sw3MyeeYbp8R4pv03YO8jEZEbgBsASkpKfI7GDHa5WSHOmFbMGdOK\n/2y9qnLwcJimqC/IcEcHHapEOjjypSQCGYEAoaCQERQyg86XfGcVUVYomBajLogIWaEgWaGgp+/T\n0aG0Rl+ptUecpOUmrrZIB63tHbS5V0ptYWc57FbhHbmaiiiRDve1Kh0dzufSoep+Rp1Ve857Kuos\nu1dn7n9Hqv46fzKo/mmZqO3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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f91950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# For example, here we fix x to a specific value and would like to know what are the possible y values\n",
    "x = -5\n",
    "X, Y = np.mgrid[x:x+1:1j, ymin:ymax:100j]\n",
    "positions = np.vstack([X.ravel(), Y.ravel()])\n",
    "# values = np.vstack([m1, m2])\n",
    "Z = np.reshape(kernel(positions).T, X.shape)\n",
    "\n",
    "plt.plot(Y.T,Z.T);\n",
    "plt.ylabel('Relative likelihood');\n",
    "plt.xlabel('Expected y, given x:{}'.format(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "<span style=\"color:red;font-size: 2em;line-height: 100%;\"> From joint probability models to targeted Models </span>\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "# Regression problem\n",
    "### In comparison to density learning we have the problem of targeted learning\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zIYRvm1mrYx+R9IgkHTp0KMnH9q/FRWl6WlpdlYaGpP37/fnMjHTypO+cPDyc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117c293d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 50\n",
    "x1= np.random.normal(loc=0,scale=1,size=N)[:,np.newaxis]\n",
    "x2= np.random.normal(loc=0,scale=5,size=N)[:,np.newaxis]\n",
    "\n",
    "y = 3*x1 + np.random.normal(loc=.0, scale=.7, size=N)[:,np.newaxis]\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax1= plt.subplot(111)\n",
    "plt.plot(x1,y,'or',markersize=10,alpha=.4 );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How  to approache this problem?\n",
    "\n",
    "<span style=\"color:red;font-size: 2em;line-height: 100%;\"> Least Squares Method. </span>\n",
    "*  **Legendre 1805**\n",
    "* **Gauss 1809**\n",
    "\n",
    "### Imagine we want to estimate the observed pattern with a parametric function such as follows\n",
    "## $$f(x,\\beta) = \\sum_{j = 0}^m \\beta_j x^j\\ $$\n",
    "\n",
    "### First order linear regression:\n",
    "## $$f(x,\\beta) = \\beta_0 + \\beta_1 x  $$\n",
    "\n",
    "## Squared Residuals\n",
    "##  $$S = \\sum_{i = 1}^n (y_i - f(x_i,\\beta))^2 = \\sum_{i = 1}^n r^2$$\n",
    "\n",
    "### Least Squeares method is to minimize the above error term by finding the optimum value of $\\beta$\n",
    "\n",
    "### While, in linear regression, it is easy to find the optimum parameters, for nonlinear cases we need iterative methods.\n",
    "* Linear: https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)#Motivational_example\n",
    "* Nonlinear: https://en.wikipedia.org/wiki/Non-linear_least_squares\n",
    "\n",
    "<span style=\"color:red;font-size: 2.5em;line-height: 100%;\"> Underlying ideas behing least squares method is the essense of many (all of) machine learning methods. </span>\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intuitive interpretations to the least squares method\n",
    "\n",
    "* **solving the equations of forces of several of (selfish) bodies to the line**\n",
    "* **finding the line with the minimum energy and maximum stability** \n",
    "* **Looking at it as a democratic voting system with a apriori given structure**\n",
    "\n",
    "## And once again it's all about the inversion from knowing to learning\n",
    "### The first historical example, from Wikipedia:\n",
    "An early demonstration of the strength of Gauss' Method came when it was used **to predict the future location of the newly discovered asteroid Ceres**. On 1 January 1801, the Italian astronomer Giuseppe Piazzi discovered Ceres and was able to track its path for 40 days before it was lost in the glare of the sun. Based on these data, astronomers desired to determine the location of Ceres after it emerged from behind the sun ** without solving Kepler's complicated nonlinear equations of planetary motion**. The only predictions that successfully allowed Hungarian astronomer Franz Xaver von Zach to relocate Ceres were those performed by the 24-year-old Gauss using least-squares analysis.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linear_regressor(a,b):\n",
    "    # y_ = ax+b\n",
    "    mn = np.min(x1)\n",
    "    mx = np.max(x1)\n",
    "    xrng =  np.linspace(mn,mx,num=500)\n",
    "    y_ = [a*x + b for x in xrng]\n",
    "    \n",
    "    \n",
    "    fig = plt.figure(figsize=(7,7))\n",
    "    ax1= plt.subplot(111)\n",
    "    plt.plot(x1,y,'or',markersize=10,alpha=.4 );\n",
    "    plt.xlabel('x1');\n",
    "    plt.ylabel('y');\n",
    "    plt.plot(xrng,y_,'-b',linewidth=1)\n",
    "#     plt.xlim(mn-1,mx+1)\n",
    "#     plt.ylim(np.min(y)+1,np.max(y)-1)\n",
    "    \n",
    "    yy = [a*x + b for x in x1]\n",
    "    \n",
    "    [plt.plot([x1[i],x1[i]],[yy[i],y[i]],'-r',linewidth=1) for i in range(len(x1))];\n",
    "    print 'average squared error is {}'.format(np.mean((yy-y)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average squared error is 1.72286658308\n"
     ]
    },
    {
     "data": {
      "image/png": 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jAnvsEXk9HBTh99N1IDtamS1wyZXiTKumBi67DA47DBZMmcNe89+EXWP877C4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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117d95ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_regressor(2,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "# from ipywidgets import interact, HTML, FloatSlider\n",
    "# interact(linear_regressor,a=(-3,6,.2),b=(-2,5,.2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <div class=\"bk-plotdiv\" id=\"cf6fadef-11e9-4142-ac16-892dfd708d10\"></div>\n",
       "    </div>\n",
       "<script type=\"text/javascript\">\n",
       "  \n",
       "  (function(global) {\n",
       "    function now() {\n",
       "      return new Date();\n",
       "    }\n",
       "  \n",
       "    var force = false;\n",
       "  \n",
       "    if (typeof (window._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n",
       "      window._bokeh_onload_callbacks = [];\n",
       "      window._bokeh_is_loading = undefined;\n",
       "    }\n",
       "  \n",
       "  \n",
       "    \n",
       "    if (typeof (window._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "      window._bokeh_timeout = Date.now() + 0;\n",
       "      window._bokeh_failed_load = false;\n",
       "    }\n",
       "  \n",
       "    var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "       \"<div style='background-color: #fdd'>\\n\"+\n",
       "       \"<p>\\n\"+\n",
       "       \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "       \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "       \"</p>\\n\"+\n",
       "       \"<ul>\\n\"+\n",
       "       \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "       \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "       \"</ul>\\n\"+\n",
       "       \"<code>\\n\"+\n",
       "       \"from bokeh.resources import INLINE\\n\"+\n",
       "       \"output_notebook(resources=INLINE)\\n\"+\n",
       "       \"</code>\\n\"+\n",
       "       \"</div>\"}};\n",
       "  \n",
       "    function display_loaded() {\n",
       "      if (window.Bokeh !== undefined) {\n",
       "        var el = document.getElementById(\"cf6fadef-11e9-4142-ac16-892dfd708d10\");\n",
       "        el.textContent = \"BokehJS \" + Bokeh.version + \" successfully loaded.\";\n",
       "      } else if (Date.now() < window._bokeh_timeout) {\n",
       "        setTimeout(display_loaded, 100)\n",
       "      }\n",
       "    }\n",
       "  \n",
       "    function run_callbacks() {\n",
       "      try {\n",
       "        window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n",
       "      }\n",
       "      finally {\n",
       "        delete window._bokeh_onload_callbacks\n",
       "      }\n",
       "      console.info(\"Bokeh: all callbacks have finished\");\n",
       "    }\n",
       "  \n",
       "    function load_libs(js_urls, callback) {\n",
       "      window._bokeh_onload_callbacks.push(callback);\n",
       "      if (window._bokeh_is_loading > 0) {\n",
       "        console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "        return null;\n",
       "      }\n",
       "      if (js_urls == null || js_urls.length === 0) {\n",
       "        run_callbacks();\n",
       "        return null;\n",
       "      }\n",
       "      console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "      window._bokeh_is_loading = js_urls.length;\n",
       "      for (var i = 0; i < js_urls.length; i++) {\n",
       "        var url = js_urls[i];\n",
       "        var s = document.createElement('script');\n",
       "        s.src = url;\n",
       "        s.async = false;\n",
       "        s.onreadystatechange = s.onload = function() {\n",
       "          window._bokeh_is_loading--;\n",
       "          if (window._bokeh_is_loading === 0) {\n",
       "            console.log(\"Bokeh: all BokehJS libraries loaded\");\n",
       "            run_callbacks()\n",
       "          }\n",
       "        };\n",
       "        s.onerror = function() {\n",
       "          console.warn(\"failed to load library \" + url);\n",
       "        };\n",
       "        console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "        document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "      }\n",
       "    };var element = document.getElementById(\"cf6fadef-11e9-4142-ac16-892dfd708d10\");\n",
       "    if (element == null) {\n",
       "      console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'cf6fadef-11e9-4142-ac16-892dfd708d10' but no matching script tag was found. \")\n",
       "      return false;\n",
       "    }\n",
       "  \n",
       "    var js_urls = [];\n",
       "  \n",
       "    var inline_js = [\n",
       "      function(Bokeh) {\n",
       "        (function() {\n",
       "          var fn = function() {\n",
       "            var docs_json = 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this.repeat(count);\\n    if (count < 1) return '';\\n    var result = '', pattern = this.valueOf();\\n    while (count > 1) {\\n        if (count & 1) result += pattern;\\n        count >>= 1, pattern += pattern;\\n    }\\n    return result + pattern;\\n};\\nvar cb;\\ncb = function (source, p, window) {\\n    var a, b, data, f, i, s, stub1_, x1, y, yy;\\n    source = (source === undefined) ? source: source;\\n    p = (p === undefined) ? p: p;\\n    window = (window === undefined) ? null: window;\\n    data = source.data;\\n    f = cb_obj.value;\\n    stub1_ = [data[\\\"x1\\\"], data[\\\"y\\\"]];\\n    x1 = stub1_[0];y = stub1_[1];\\n    yy = data[\\\"yy\\\"];\\n    a = data[\\\"a\\\"];\\n    b = data[\\\"b\\\"];\\n    s = 0;\\n    for (i = 0; i < x1.length; i += 1) {\\n        yy[i] = _pyfunc_add(_pyfunc_mult(a[0], x1[i]), b[0]);\\n        a[i] = f;\\n        s = _pyfunc_add(s, window.Math.pow(yy[i] - y[i], 2));\\n    }\\n    p.title.text = \\\"average squared error is: \\\" + (_pyfunc_str((s / x1.length)));\\n    source.change.emit();\\n    return null;\\n};\\ncb(source, p, window);\\n\"},\"id\":\"9303d7b4-b69c-4171-a9cd-2cc88c8929b3\",\"type\":\"CustomJS\"},{\"attributes\":{\"below\":[{\"id\":\"08ae7084-d461-4e8c-a050-b24d40d4ff14\",\"type\":\"LinearAxis\"}],\"left\":[{\"id\":\"40f0c19b-31e2-4d0d-9d6f-34e0c56affb1\",\"type\":\"LinearAxis\"}],\"plot_height\":400,\"renderers\":[{\"id\":\"08ae7084-d461-4e8c-a050-b24d40d4ff14\",\"type\":\"LinearAxis\"},{\"id\":\"0805658e-934f-4780-a079-8e36177aa9f5\",\"type\":\"Grid\"},{\"id\":\"40f0c19b-31e2-4d0d-9d6f-34e0c56affb1\",\"type\":\"LinearAxis\"},{\"id\":\"4b3402cb-f5c5-416a-bd42-3d494b9bf6db\",\"type\":\"Grid\"},{\"id\":\"4a6bd25c-3c47-4611-bdc5-0b8a9686f370\",\"type\":\"BoxAnnotation\"},{\"id\":\"a702158e-96ca-45eb-81b5-ae1bbc83328b\",\"type\":\"Legend\"},{\"id\":\"18af9ff1-d1d3-494b-bcea-dd7d76c28a31\",\"type\":\"GlyphRenderer\"},{\"id\":\"02e88261-9486-483b-862a-98656167448b\",\"type\":\"GlyphRenderer\"},{\"id\":\"fd478188-529f-467d-ab1d-8976ae8e59f4\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"d5ddb2e5-34bc-4f03-b17e-85077a287e7e\",\"type\":\"Title\"},\"tool_events\":{\"id\":\"47ec233a-1502-4b9b-97a2-be8869a689e6\",\"type\":\"ToolEvents\"},\"toolbar\":{\"id\":\"9c009b45-5193-4e07-aaa3-f4bb03747241\",\"type\":\"Toolbar\"},\"x_range\":{\"id\":\"070555ae-1847-4a5f-8a1e-71a39445f9d6\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"83d71168-a241-4f16-99ca-8d43eb4fb45b\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"e7086944-2a00-4a96-a249-b251daff2dce\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"fd682b85-b447-4489-95ce-bf66f2a0cf7e\",\"type\":\"LinearScale\"}},\"id\":\"bf5a5f5a-3e2a-42ed-a64f-8de5ff585f2a\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"formatter\":{\"id\":\"9a793699-05ec-4206-af78-3a1655e4a5e2\",\"type\":\"BasicTickFormatter\"},\"plot\":{\"id\":\"bf5a5f5a-3e2a-42ed-a64f-8de5ff585f2a\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"b7feab66-1ab6-441b-bf7d-2b8ebb58b8f7\",\"type\":\"BasicTicker\"}},\"id\":\"40f0c19b-31e2-4d0d-9d6f-34e0c56affb1\",\"type\":\"LinearAxis\"},{\"attributes\":{\"data_source\":{\"id\":\"cebf07c6-4b1c-4f84-a758-5e1e1459820f\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"2b9134c2-0df1-40d0-815f-5bb875e87358\",\"type\":\"Segment\"},\"hover_glyph\":null,\"muted_glyph\":null,\"nonselection_glyph\":{\"id\":\"4502c7a3-b053-4f20-b1b0-5367d51af71a\",\"type\":\"Segment\"},\"selection_glyph\":null},\"id\":\"02e88261-9486-483b-862a-98656167448b\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"dimension\":1,\"plot\":{\"id\":\"bf5a5f5a-3e2a-42ed-a64f-8de5ff585f2a\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"b7feab66-1ab6-441b-bf7d-2b8ebb58b8f7\",\"type\":\"BasicTicker\"}},\"id\":\"4b3402cb-f5c5-416a-bd42-3d494b9bf6db\",\"type\":\"Grid\"},{\"attributes\":{\"items\":[{\"id\":\"5cc619ba-020f-4565-9e85-7bb1e3776672\",\"type\":\"LegendItem\"},{\"id\":\"cf0cd3f0-0fc5-4162-9baf-0cc35bbe3dac\",\"type\":\"LegendItem\"}],\"location\":\"top_left\",\"plot\":{\"id\":\"bf5a5f5a-3e2a-42ed-a64f-8de5ff585f2a\",\"subtype\":\"Figure\",\"type\":\"Plot\"}},\"id\":\"a702158e-96ca-45eb-81b5-ae1bbc83328b\",\"type\":\"Legend\"},{\"attributes\":{\"line_alpha\":{\"value\":0.1},\"line_color\":{\"value\":\"#1f77b4\"},\"x0\":{\"field\":\"x1\"},\"x1\":{\"field\":\"x1\"},\"y0\":{\"field\":\"y\"},\"y1\":{\"field\":\"yy\"}},\"id\":\"4502c7a3-b053-4f20-b1b0-5367d51af71a\",\"type\":\"Segment\"},{\"attributes\":{\"plot\":{\"id\":\"bf5a5f5a-3e2a-42ed-a64f-8de5ff585f2a\",\"subtype\":\"Figure\",\"type\":\"Plot\"},\"ticker\":{\"id\":\"83d505d7-9ef0-4454-82d8-dc40bde4079c\",\"type\":\"BasicTicker\"}},\"id\":\"0805658e-934f-4780-a079-8e36177aa9f5\",\"type\":\"Grid\"},{\"attributes\":{\"callback\":{\"id\":\"7127c138-6119-4146-a833-dd425da3b440\",\"type\":\"CustomJS\"},\"end\":4,\"start\":-4,\"title\":\"b\",\"value\":1},\"id\":\"be9627ae-9fe9-4f83-82a0-2dfa4f50e76d\",\"type\":\"Slider\"},{\"attributes\":{},\"id\":\"83d71168-a241-4f16-99ca-8d43eb4fb45b\",\"type\":\"LinearScale\"}],\"root_ids\":[\"ba2b66e2-e191-4582-9409-befb1b174f32\"]},\"title\":\"Bokeh Application\",\"version\":\"0.12.6\"}};\n",
       "            var render_items = [{\"docid\":\"8ae05c47-51e1-445b-92b7-0114f2ecb8ef\",\"elementid\":\"cf6fadef-11e9-4142-ac16-892dfd708d10\",\"modelid\":\"ba2b66e2-e191-4582-9409-befb1b174f32\"}];\n",
       "            \n",
       "            Bokeh.embed.embed_items(docs_json, render_items);\n",
       "          };\n",
       "          if (document.readyState != \"loading\") fn();\n",
       "          else document.addEventListener(\"DOMContentLoaded\", fn);\n",
       "        })();\n",
       "      },\n",
       "      function(Bokeh) {\n",
       "      }\n",
       "    ];\n",
       "  \n",
       "    function run_inline_js() {\n",
       "      \n",
       "      if ((window.Bokeh !== undefined) || (force === true)) {\n",
       "        for (var i = 0; i < inline_js.length; i++) {\n",
       "          inline_js[i](window.Bokeh);\n",
       "        }if (force === true) {\n",
       "          display_loaded();\n",
       "        }} else if (Date.now() < window._bokeh_timeout) {\n",
       "        setTimeout(run_inline_js, 100);\n",
       "      } else if (!window._bokeh_failed_load) {\n",
       "        console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "        window._bokeh_failed_load = true;\n",
       "      } else if (force !== true) {\n",
       "        var cell = $(document.getElementById(\"cf6fadef-11e9-4142-ac16-892dfd708d10\")).parents('.cell').data().cell;\n",
       "        cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "      }\n",
       "  \n",
       "    }\n",
       "  \n",
       "    if (window._bokeh_is_loading === 0) {\n",
       "      console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "      run_inline_js();\n",
       "    } else {\n",
       "      load_libs(js_urls, function() {\n",
       "        console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "        run_inline_js();\n",
       "      });\n",
       "    }\n",
       "  }(this));\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.asarray([1 for i in range(len(x1))])[:,np.newaxis]\n",
    "b = np.asarray([1 for i in range(len(x1))])[:,np.newaxis]\n",
    "\n",
    "y = y\n",
    "# xx = np.linspace(mn,mx,num=len(x1))\n",
    "\n",
    "yy = np.asarray([a[0]*x + b[0] for x in x1])\n",
    "df = pd.DataFrame(data=np.concatenate((x1,y,yy,a,b),axis=1),columns=['x1','y','yy','a','b'])\n",
    "df = df.sort_values('x1')\n",
    "source = ColumnDataSource(data=df)\n",
    "p = figure(plot_width=600, plot_height=400,title=\"\")\n",
    "p.circle('x1', 'y', size=15,source=source, line_color=\"navy\", fill_color=\"red\", fill_alpha=0.99,legend=\"observations\")\n",
    "p.segment(x0='x1', y0='y', x1='x1', y1='yy', color='navy', alpha=0.6, line_width=1, source=source, )\n",
    "p.line('x1','yy',source=source, line_color=\"navy\",alpha=0.99, legend=\"estimated: y= ax+b\")\n",
    "p.title.text = \"average squared error is: \" +str(np.mean((yy-y)**2))\n",
    "\n",
    "p.legend.location = \"top_left\"\n",
    "\n",
    "def callback1(source=source,p=p, window=None):\n",
    "    data = source.data\n",
    "    f = cb_obj.value\n",
    "    x1, y = data['x1'], data['y']\n",
    "    yy = data['yy']\n",
    "    a = data['a']\n",
    "    b = data['b']\n",
    "    \n",
    "    s = 0\n",
    "    for i in range(len(x1)):\n",
    "        yy[i] = a[0]*x1[i] + b[0]\n",
    "        a[i] = f\n",
    "        s = s + window.Math.pow(yy[i]-y[i],2)\n",
    "    p.title.text = \"average squared error is: \" +str(s/len(x1))\n",
    "    source.change.emit()\n",
    "    \n",
    "\n",
    "slider1 = Slider(start=-4, end=4, value=1, step=.1, title=\"a\",\n",
    "                callback=CustomJS.from_py_func(callback1))\n",
    "\n",
    "\n",
    "def callback2(source=source,p=p, window=None):\n",
    "    data = source.data\n",
    "    f = cb_obj.value\n",
    "    x1, y = data['x1'], data['y']\n",
    "    yy = data['yy']\n",
    "    a = data['a']\n",
    "    b = data['b']\n",
    "    \n",
    "    s = 0\n",
    "    for i in range(len(x1)):\n",
    "        yy[i] = a[0]*x1[i] + b[0]\n",
    "        b[i] = f\n",
    "        s = s + window.Math.pow(yy[i]-y[i],2)\n",
    "    p.title.text = \"average squared error is: \" +str(s/len(x1))\n",
    "    source.change.emit()\n",
    "    \n",
    "\n",
    "slider2 = Slider(start=-4, end=4, value=1, step=.1, title=\"b\",\n",
    "                callback=CustomJS.from_py_func(callback2))\n",
    "\n",
    "layout = column(slider1,slider2, p)\n",
    "\n",
    "show(layout)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding optimum parameters by grid search\n",
    "### For the case of linear regression it is easy to find the optimum parameters analytically\n",
    "* Linear: https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)#Motivational_example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Linear regression\n",
    "A,B =np.mgrid[-6:6:200j,-5:5:200j]\n",
    "A =A.ravel()\n",
    "B =B.ravel()\n",
    "losses = []\n",
    "r2s = []\n",
    "for i in range(len(A)):\n",
    "    r2 = ([A[i]*x + B[i] for x in x1]-y)**2\n",
    "    r2s.append(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calculate_loss(r2s,loss='mean'):\n",
    "    if loss == 'mean':\n",
    "        return [np.mean(r2) for r2 in r2s]\n",
    "    if loss == 'variation':\n",
    "        return [np.std(r2) for r2 in r2s]\n",
    "    if loss == 'skewness':\n",
    "        return np.abs([stats.skew(r2) for r2 in r2s])\n",
    "    if loss == 'kurtosis':\n",
    "        return np.abs([stats.kurtosis(r2) for r2 in r2s])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'cm' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-a6e773fb3ce7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mlossmx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlosses\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0msc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mB\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlosses\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvmin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlossmn\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmarker\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'o'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0medgecolor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'None'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvmax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlossmx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcm\u001b[0m \u001b[0;34m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolorbar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mticks\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mround\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlossmn\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlossmx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdecimals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mshrink\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'a values'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'cm' is not defined"
     ]
    }
   ],
   "source": [
    "losses = calculate_loss(r2s,loss='mean')\n",
    "lossmn = np.min(losses)\n",
    "lossmx = np.max(losses)\n",
    "\n",
    "sc = plt.scatter(A,B,c = losses,s=20,vmin=lossmn,marker='o',edgecolor='None', vmax=lossmx, cmap=cm ,alpha=1);\n",
    "plt.colorbar(sc,ticks=np.round(np.linspace(lossmn,lossmx,5),decimals=3),shrink=0.6);\n",
    "plt.xlabel('a values')\n",
    "plt.xlabel('b values')\n",
    "plt.title('loss: {}'.format('Sum of Squared Errors'))\n",
    "\n",
    "ind_min = np.argmin(losses)\n",
    "amn = A[ind_min]\n",
    "bmn = B[ind_min]\n",
    "print 'a*: {} and b*: {} and the minimum loss is {}'.format(amn,bmn,losses[ind_min])\n",
    "linear_regressor(amn,bmn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# polynomial regression\n",
    "## $$f(x,\\beta) = \\sum_{j = 0}^m \\beta_j x^j\\ $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression problem from the point of view of linear algebra\n",
    "\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/5d8c7215ea8715037794889054530c5b7ea2f498\" width =700, height=700/>\n",
    "## Or\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/76fdc21f089f8b3c5979010bddd1007a34bbeca1\" width =200, height=700/>\n",
    "\n",
    "## And the solution is\n",
    "\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/3dc6b1498895d5833137e28eafc4534844145a47\" width =200, height=700/>\n",
    "\n",
    "\n",
    "\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "<span style=\"color:red;font-size: 2.5em;line-height: 100%;\"> Looking at this formula we can say that polynomial regression can be seen as a type of multiple regression, where different powers of x (from 0,..,m) are new features. </span>\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "# Now Regression in practice using Scikit-learn\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tozOzyyX9qqRpSa+KBK/jkl4VPF4v6enI244E2wh0QBEldUhJClpzc36uyy1b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\n/j+iRbaIfd0yiQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119de2a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 400\n",
    "x1= np.random.normal(loc=17,scale=5,size=N)[:,np.newaxis]\n",
    "x2= np.random.normal(loc=0,scale=5,size=N)[:,np.newaxis]\n",
    "y = 3*x1 + np.random.normal(loc=.0, scale=.4, size=N)[:,np.newaxis]\n",
    "\n",
    "# x1 = np.random.uniform(size=N)[:,np.newaxis]\n",
    "# y = np.sin(2*np.pi*x1**3)**3 + .1*np.random.randn(*x1.shape)\n",
    "\n",
    "y =-.1*x1**3 + 2*x1*x1 + 2*np.sqrt(x1)+ 10*np.random.normal(loc=30.0, scale=4.7, size=len(x1))[:,np.newaxis]\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax1= plt.subplot(111)\n",
    "plt.plot(x1,y,'.r',markersize=5,alpha=1 );"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def polynomial_regr(degree=1):\n",
    "    from sklearn.preprocessing import PolynomialFeatures\n",
    "    from sklearn import linear_model\n",
    "    \n",
    "    \n",
    "    \n",
    "    X_tr = x1[:].astype(float)\n",
    "    y_tr = y[:].astype(float)\n",
    "    \n",
    "#     X_ts = x1[150:]\n",
    "#     y_ts = y[150:]\n",
    "    \n",
    "    poly = PolynomialFeatures(degree=degree)\n",
    "    X_tr_ = poly.fit_transform(X_tr)\n",
    "#     X_ts_ = poly.fit_transform(X_ts)\n",
    "    \n",
    "    regr = linear_model.LinearRegression()\n",
    "    regr.fit(X_tr_, y_tr)\n",
    "    \n",
    "    \n",
    "    y_pred_tr = regr.predict(X_tr_)[:]\n",
    "#     y_pred_ts = regr.predict(X_ts_)[:]\n",
    "    # Predicting the training data\n",
    "    plt.plot(X_tr,y_tr,'.r',markersize=10,alpha=.4 );\n",
    "    plt.plot(X_tr,y_pred_tr,'.b',markersize=10,alpha=.4 );"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IFhbqtdat0/3eTJpwWA11ZqbGPZKT1V20cKGKTE0N3HorXHtt9FwzZsDtt+v3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119e27fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "polynomial_regr(degree=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IYYH2a/bs1H7LOTmpDKSJbDVq7iMDE4LjpA+Aew91Mdg1DF4BsWCYcDiA1ztA\nPDuHY51h/OJSvBml+n+sa2J7jJzO7OSED0SjOnIOJCp2JkfFDz2ko1fPU3dFa6saTc/TEey2bXp8\nQYH68JcuPbEEsohmmbz97WMHgzdsUEO7ebOeZ/Zs+OAHta21NbWHb2enCkhRUcq3fjIjlBS58nJY\ntUr7lZwBNDZqMDgcfu0otaJCr7V2rb6fzKTxfTXUxcUa98jNVXdRXZ2KzJEjcM89cNttqXNVV8Pn\nPqdi2tamO6nt26f3dvhwyr0UCqkwJcVt/nxta2nRtQ/JWUIopEKaFMRLL9W+v+51yO7dXNL1NPcP\n/iXwl7jBIRoHZ/Iz3sOPuZsdLGKEMPFE0b4sRogTIJZYzJcKQAdopYJPxP6ZGXTz5lgTn716Kzf4\nz+Ht3K6zkuQua2PFCMbaatS2zzQSmBAkSF82kE8v2UHN0Aj6wzA0gh8LkhMY4frrwxw4cA73GBlr\nPUNXlxrFpB+4okKN844dauy2bdP3Fi/m+K5fixerwYcTxWAsdWpuVkNy8816re5uvV55ue6FfPPN\nqQ3okyPkpiY1QmPFCEZ/QSJqzOfMSYlEYoEc4bCOrEdz8KAa3QUL1Nj392uweWRE3UQzZmh7X5/e\nc2mpCmh+vt776JFu+r0vWaL3vG6dGvJYTO8nEEjNEHxf3U29vTrqTtYVKivT63Z363dVV5faqS0S\nSfXt0CGIxZDYCPOkiT/J+3c+N/MX/LbnKr587NPsCy6k38uHUIiOnvQ6Tq8tc9ERK+bnDUU83nA5\n15Uu5bsf/g3zP3AdMmtm6ruuqztR4CGVATZ6BmnbZ2Y8JgQJ1GPhqF/TjbQNUJ7VQ0cwi7ZjQZAA\n+fRzU80e/vRPrqXlkJw71+pYefjz5qmfPD0IfPnluvgq6c5JN3579ujoe86cibkBktOjQECN2IwZ\nanT370+1l5Zqff3t29XlsmJFyuCcam0BnP4WjtFoahFVSYkKRlNTKhbg+2rEFy9WcTodpU6KwooV\nKqaVlRqv2LNHg8TDw2rs9+7Va195pYrD0aOagfXJT+oCt+Sahx07VCjmztU+9vfr5z0vtUva3Ll4\nsRhvHHia1VlP0lS2lAf9u9jiFvNs7GoO9hZz8uwjYYQQv22/gsX/dx6femkrn/rsUaqPtiEzEzO/\npFEf7QpKbtdZWZmaVdn2mRmNCUECwbHSPUKt20M0P5/S6hfxaWZt4e10x3Kpu6yL5Zd34x2KUFVV\nde4GTieEHDXYAAAgAElEQVRbz5BuRJ1TIwhqiJK7cLW362h06dKU8T2VG2A8Iz1/vp472Z50haxY\nceK5JuIDG0vgTma0IxG9VjIF1TmdiRQVnTgaT98m8nSVOr1Pb3iDikxBge6nnJWlrqfiYu1vfr4K\nRFaWisC1156YbdDaqsLZ2amuq8OHU2muvq/vAwSDSMijuhr+uOn/0TyrlsO338annriFTc1laZv4\njIcwQDb/8FwdP32hlffNWcff3vofBG+9Ce68U/uS7goSUTHdvFlnd/Pm6T2mx4cskJxxmBAkaW5G\nNtRTdVU1VZ4Hsyqg72Xm3XBAR3YlM6Cpd3qmz6NdOMmSxOMZ0fT3Dh/W/idHqxNxA4xnpK+7Ts83\nUeN9qnuayMrksfqUlaWj7JUrNR7Q0TH2moXJ9GndulQGVDJTaft2NeTJiii+r0Y1Enmt372yEv7n\nf1QESkpSexwnt6/s69NZAmj8JS8PCXhUBQ9RFXmVF7/4Sx7+72w+8cxKOodzOHkqqsYQmv05/OPB\nu/nlD2rZsvMThMvLdYHZ9u0aKyks1NnSSy/pbObYMRW7970vlYVmgeSMxIQgyeh0yWTws7BQXSPn\n0/T5VEY0/b2hIS1BkJwhTOQ+Tnb+0zHeE7mPiRrtk127pubMrn+yPr3hDZoddeCA/g0UFmr7wICO\n9EEN+I03aj82b37tmo1Zs9Tgd3So8S8uViEpK9NZS9LtdsklqThEMAj5+QTE5+7Fu7jzm2/i2//Q\nyf/5rzKaeksZQQsMjtN5fIRXhi6h5oX/4t//6HtcffVaqryDyCuvaGZWW5vGNsLh1Pe+bZv2J339\nSEGB9qmgwALJGYAJQZLR7pCiolTpAjhHkeHT4GRGNP09585sFD/e+Scz4p4s5+razmlNqdZWXSwH\n+rfwoQ+pi23nTm1btEj7IjK2Oy0Zs3jsMY0LDA2pSykcVnfSLbeo266xUa85c6bO3NJcXcH5VXzy\ni8InCv+Z54Zr+ZPvL+aljmrcuIKgWUatzOaD9f+LWZvb+cjr9/LF6m4CO7aqWy35950stzF3bmqG\n2NamsZH+/tQMITdX200ILlpMCJKM5Q754Ad1JNTefuH6Sqd6FJ8JJEfFyaypnh4dENTWqutnrBnI\neO60d79bBaOpSc8Vj+vvoaJCU1g9T+MuAK97XSquk/57qqzEu66OFfX1PH/3//Dsr3p5X9Pf0eZK\nEzvAQSrVlOOve/0ceocr+NKv5/DT3Cq+FLmflUP3EyjK1wwwUAMfi6VmiMPDKk7z5qXuY/9+bTcu\nWkwIkpzMYF7otd6ncxR/ITJW1hSogR7vb+Fkfz833AB/9VfqouvsVBfRHXeQqBb42nOOfp12bm/d\nOt4ceIGWyx/hP74X5IdbX0f9yCKGyGWsrTUhgE+AHf2X8KGmv+VK78M81P9h5h9oQsKJmEVWlrqH\nnNPnc+emstJ8X1+HQlPxzRrnKSYE6ZjBNOD0U1uTnMydduedr83tP51Z2agU12DA8ft3tvGJhf9G\nw6PbeWvfo7RSTux4qWw4URSEIbLY4i/mLQO/5M/y/4P75L/wurs1FrJ5s7qmlizRGMa112o8JLlG\noqxs4n01LjimZPP6s820bV5vZCbnc+ZMsm//9V+pFNThYWIHW/nPzpV8a/j32OquTKSdCikxcImd\n6cAjTpgRrpRX+Ec+xxvmHcIbHtQYRkWFCkJurq5NSWaonQ/3bpw2E9283oTAMMbifM6lP3AAvvEN\ndTEVFKgPv74eSkuJxeDtW77Gs12LGSZESgj8xM8TZwtCnPeEf8mPCj9FMDaomU5vfave/zveocHu\n8+nejdNiokJgriHDGIvz2U3Y3q5rE6qr1Zff1KRZTUuXEszJ4cnmD/GIfwPf6vkg66mjj/zEB1/r\nMnIEeGjoXRxqi/DrwNvICh3T4HVZmZ7zfLx/Y8o5VcF0wzDON9JjGL29qfb8fGhtJdDZzntKf8Mz\n5R9hq7eMN/EbCr1+dFYw1sheeI4bmBd/hb0ldbjyOVpYzzKFMgYTAsO40Eimqh44oFlIXV06ci8p\n0efDw1BYiMyaySWlnfxP8DaeuOyzLC1uhLE2uAFAaKGCRa88xB8/dwexsnKdbWzalCrpYVy0mGvI\nMC400lNV29q00uz+/amd2QoKdPVwoqKrF/R4/fBanp+7mVmdT9JJKePNDIbJ4v8dvIuX+q/k1+X/\nTrC0SMVl3rzUdqQWL7jomLQQiEgl8H1gFjrcWOWc+6aIzAB+CtQAjcDdzrljIiLAN4HbgH7gI865\nTZPth2FkFGOV0Y5GtXbQyIjWETpyJFXqYuFCQl1dHApdxvzhLbRSyXhi4CM833EFb3r6z/jG4h9w\nw+AmvM2bdc+Gm25SEYLzN5hunDaTzhoSkXKg3Dm3SUQKgI3Au4GPAB3Oua+LyBeAEufc50XkNuAP\nUSG4Dvimc+66k13DsoYMY4Ik00sffVTLY5SUwBVXqKH+wQ8gGiXW2cuq+D18ga/Rw3jlrtUuFHgD\nvH/us9w/56sEllydyiY6dChVljxZGn305kfGtHPOsoacc4eBw4nnPSKyC5gL3AG8OXHY94C1wOcT\n7d93qkDrRaRYRMoT5zEMYyKMl96adBuFw7pKeMECFYPm5uP7LAc7O/kD+TYfc6tYyB4OMJ8Td0Pj\n+M8eP4fvNd/IYLSXv46uotprRqJRrVN01VW68GzzZt05bts2dUvZuoMLjimNEYhIDXAt8CIwK824\nt6KuI1CRaE772MFEmwmBYUyEUy14S5bP/u1vda2BiC4QC4V05N7WBs4RjsXYG7+SP+Cb/IgP0U+i\nLPbxNQbJ/ZOD/GzgHTQdquYP877DnbmDSFGRxiSKi/VnUZE+r6iwaqUXIFOWNSQi+cDDwP92znWn\nv5cY/Z+WD0pE7hORDSKyoa2tbaq6aRgXPul7HyQf9fXaniQ9s+jAAS0TsWKFum4KCjTVND+frJDH\nqsBn2J6/gluzfk2QEfS/qk/6DMEBewcr+fbgh2hyaRvYNDZqMHlwUGccyT21t2+3jKMLiCmZEYhI\nFioCP3TO/TzRfCTp8knEEY4m2luA9BrIFYm2E3DOrQJWgcYIpqKfhnFBk3QHrVunFVGTrpexNhsa\nqwheRQWsX69rBFpatODc0aOIG2Y++/hlYCUrR37Af/MOfAKJkZvWN83JipPrjXDAr+TRjhWsnDFC\n5YZHtAvHjun5Gxt1ZvDKKyoOxcXnV3kOY1wmPSNIZAH9J7DLOfePaW89BtyTeH4P8Iu09g+Lshzo\nsviAYZyCpDvo/vt1P+WNG3XE7dz4RfGSmUVLluhPz9P9pVeu1I12srP1kZsLzhHwHD8PfIC7vZ9T\nRBcB4oBPmAFKQgMMuByOxQp47tVZ3L/rzTwycAsuFE5tF/rkk7B6tV570aLxZyvGecdUzAheD/wu\nsF1EErt48GfA14EHReRjwAHg7sR7T6AZQw1o+uhHp6APhnFxM3rf4ZERDc5mZaUCtBPdNCm5+144\nrC6dQ4f0PM4RDHn8cOQeXph1O/8U/SBrR24gy4szEs9iJJRHeWWAa99aSsmOl6lvWEBtzstUDe5W\nIRoe1vjDzJmpndomsjWqMe1MRdbQbxl/77wbxzjeAZ+a7HUNI6MYvZXqkiVqvK+/Xn3/E03ZbG7W\ntM/aWo0dtLfrrCIeV2Mei+H5Pq9v/yXXe79iVeGnWSM30VVSTbR/iLpri5kxNwf/uW72xOfz50f/\nkGv8zdyZ9Utq8tqQ+fN1h7Pk5jrn0xavxrjYymLDuBAYvUeCczoTWLHi9Eba0aguMluyRNNK29p0\ne8xAQM937JiWrcjLwyss5BOla7ntyPNsX/p7PLH/ChZV+/jd8K2mt/PKQBmBAZ+fcRP/zIf5++A/\n8p7L5iB9fdDQoPs1n29bvBpjYkJgGBcC422FeboGNikozmmwuKxMC9cNDKRmHDNm6HvDw0h/H1Wl\nI1ReupchP4v6rivZsy9IQ3eAgOfIIo7zfVqYyxe7P09gx/O8u7QZb/kydRGl7+tsnLeYEBjGhcBU\n7T2dLig9PZrds3SpZhHl5mpaaSik583L01H9yAjS3cXKD+ZRW1vI178BodAQI8NC0BP6hsPECNA4\nOIs/fPANPFUE/zbwJIH8HI1BWGzgvMeEwDAuFKZij4TRBesWL9YaQsPDKgZz5qSOXbhQs4ESBeek\nqooqEW6+GX760xAu7jPiYIgsABwenX4hPzp2K8XPDPK3i36E19qq17rQ9/2+yDEhMIyLmfFKUYwu\nWNfWpmIQCqUCu8mA76iZx7ve6VhacYRnd8xg0E+ZkABxBMcg2TzQeht4Hl+b+28EduwYWwjO513g\nMgwTAsO4WJnI3sujZxkTMM6BQ8088bb7+fOZ7+HBDfM52JlHgDgePjGCxAjQRQH/eujdvNh5GQ8c\n7mWeG3Wa83lf6AzEhMAwLlbS1x4kje3J6gBN1DhHowRDHl9/z0bedU0Tv7dqOc3dhcQJMEwQwREn\nwCABnutfwju/OsRfFzvuvEtSpzndvhlnFduhzDAuVkavPUhf3DUWE6lhBMczj8T53HBpG1997xau\nLm0hGHAEEiUpBJ8sRsiSEdpaHb/4hz00P7EtVXvodPtmnFVMCAzjYiV97QGcenHXRI1zWkE7aTrA\nXZFn+fFXGnjPilaygzECqCAEA+BlBciSYQ7v6mDdNzfS9PUf4X7+iK5dOJ2+GWcVcw0ZxsXK6a49\nGL1o7WQ1jNJSWSUSoaaykgfuha7b+nny10FcXPDFoyAwwMiIcIA5PNacx3NDwo2Ht3DnUpCpWBdh\nTAkmBIZxsXK6aw9ORzjGCDIHDjXzs6+0cc99Qda8XE6cLNxwnBEXJIdBuns9uuI5tLZeQ+2OLqqX\nLtV6R2ALz6YZEwLDuJg5nbUHZ7poLS3IHOzp4QfhDay/Zhn1vZfT2F3Kbw4t4PLAQbx4Hq4H9g/O\nYceT+6l+7scpwRkasiDxNGIxAsMwUowuXT3RQnbJIHNxMV5pCTfM2M1n7mjipmvbyQ77SDjr+OGD\n8QANm3tois/V0HJBgZWqnmZsRmAYxuRIDzLn52ubCASDLKrqYXZON+0F8xBPONxfSL9z1O8t4qk9\nNcwOd/CxOU9z/dwmvLY2mxVMEyYEhmFMjvQgc0mJGvNt26CzkyrXwYcuc6zJfgdtfdkcGQ5QlX2Q\n545dSYcrYdgF+eXR67mp4Tm+/9khgk1NttJ4GhB3AewnWltb6zZs2DDd3TAMYyzGWog2b54Ws4tE\ncBs20rxmD+sOzuPpLRF2H5vFnt5yYgToJ4eAQBCfldc08P2bf4QXtJXGU4WIbHTO1Z7qOJsRGIYx\nOU4RZJaqKqrqmlmxZi+rd+cw0JWHLwGGXDZZxMkSH/Ec6xvKePGmOq6vjtpK43OMBYsNw5g8Jwsy\nJ96rvKqE5eX7iccdQy6EjxAghvgxPD9OwB9hze4KmjrycGIrjc8lJgSGYZwTpCzCvdWr+XTlY5Tn\ndAJCnCC+BMgJxekZCrG3Kcz9a6/kkU1VuLitND5XmBAYhnFuqKzEu2E5nyj6KasXfIqbs9cxM3SM\n8uxjEMzidcUtLGQP0t3J6vpCmmreqC4m57RG0aZNqVpFSU72njFhpi1GICK3At8EAsB/OOe+Pl19\nMQzjHCAC996LiDD/mWf4pfenvJj1Bta4t7BHFpI9PMSzoZsYGvboGMhmVVMWX2lswnv4Id08p7hY\nDX0yiAxWynqKmBYhEJEA8K/AzcBBoF5EHnPOvTwd/TEM4xzheXDvvXDLLXgPPcT1+/YxV3bz9Rdm\n8irz6Q8V09EhDAw5nvxJJ1XP/5b7Bh9GwokNc5YsgZde0iAyWCnrKWK6ZgTLgAbn3D4AEfkJcAdg\nQmAYFzsiarw/9zlobqayLcr8knmsf6KYrkNCdjZUlA2R23aE9R0LebtfQlXPAV15nNw1ra1NzzNe\ntVQTgtNiumIEc4H09eQHE23HEZH7RGSDiGxoa2s7p50zDOMckMgmkqVLeO+9JVxyiTBrlm6VXDmj\nD+cE33esO3IZTcH5uJxcyM7WvZWHh0+/zLYxLudtsNg5t8o5V+ucqy0rK5vu7hiGcRapqoKbb9YQ\nQH8/RPtzcMDu9jKejr2FLx34CKuOvgu/fxDmzNG9ldP2RTj+sFLWZ8R0uYZagPTfVkWizTCMDEQE\nPv5xFYL168GP57D7UCmFgSO0xss4Gp/B6qE3smVwJf88/+cEy8rOvFqq8RqmpcSEiASBPcCNqADU\nA7/jnNs51vFWYsIwMgPnNBSwbh08/bSjdf8AO7eM0N6XTcwFEHFcM7+L53aWkhUyg38qJlpiYlpc\nQ865GPBp4ClgF/DgeCJgGEYGkFgPIJs3UUUTK97g8DzhaE8u7SOF+MEsfDzizmPjvhJuv7mfeMzW\nDEwV07aOwDn3BPDEdF3fMIzzhPSidSLQ2UnlvPksv+wjrF5dSiwm+L6uQwbAh+df8Pj7e3bw+R8s\nQjybGUyW8zZYbBhGhpDc2KaqCjo6YN8+5JGfc2/Tl7j9ylcRcYCO/gPiEA9yw3Gef8mj+RebbFXx\nFGDVRw3DmF6SG9t0dUFjI5SWgufhzSjmn/P/k42tf8nG7SFw4IuQFxohJytOyVAr0e+so2rxiK0q\nniQmBIZhTC/J9QDd3anFYc5BQQHBri6eu+VvuL31Tp4/uoBcGSJH4lxW0kN5/0Eil0egOpRaVVxe\nDuGwZRCdJiYEhmFML8n1AKtXQ2enGvWaGigshLVryTp6lCdmPcHf997J8yO1lLhuygcGWVbViiuu\nYFNTNpG8QSp370FWrdJ1BjZDOC1shzLDMKafZBXRhx6C/fuhqEhF4ZVXIB6HaBSXm0dzey7R8FxK\ny0NsyFpOPXX0DmfR1xVn+bFfce/HHN7MxAzjwAH45CczutyE7VBmGMaFw6j6Q0SjcPiwuoo2bdJD\nPKEqp42qomGaKm+kvulqjnUOcaArD4aG+O7ASmTXEe4t241Y3aHTwrKGDMM4f0jf6WzxYigo0P2P\nBwagt1d/zptH1JtJb9WVHCi6mtKFESKLZlNcBOv3z6T5WJ7VHTpNTAgMwzg/ScYOKiu1El08DrNn\nQ2EhkeWX0ucVQHYuUlqKi5RBcRHx7j7WvRCkaVsnrtbqDk0Ucw0ZhnF+kqwltHQpPPggbNsGWVkg\nQmVpP8uXw3e/m4wFC/Gy2exuK4F4Nauj2SyP5nOvE2y92akxITAM4/xFRB8dHfD61x/fgEY2buDe\nT9QhUsX69TpZ2L1bKCzL5kgsG7pTInHvvZY4dCpMCAzDOL9JLjgbtQGN1xHl3nuruPVWLVIHcOSI\nozSnDxkaQsI5rH8hh1tvFYsXnwKLERiGcX5zkg1okrHlFSvA8xwcaUX27sE1NUFTE7mtrxJtG5Ui\nbxvevwabERiGcX6TDBqP3qQ+LRBcWQnLF3bw3aeHkKJSEKFqbjcFnYeJDOdwfAPE9AJ3tuH9cUwI\nDMM4v5nABjQicO9NB5DfHGB91xXkhkcoCMeoyz9EZaiI40KQLHBnG96fgAmBYRjnP0kf0EmMtTcz\nwr1XP8SthX1E+3OI5A5Q2b0TKVuhBzgH27fD0aO6crmkxDa8T2BCYBjGxUFlJbKsjqr6eqo8D3p8\nWJZwISVdQmvWwK5d0NKi9YyuvtoWnmFCYBjGxcLJXEhNTbiX6mmes5xo6xwi0Veo3LpNS1HcdFPG\nLzwzITAM4+JhHBeSa4vySMMi6nuvxJPX4ctbqMvZyMrb5iPvuC2jA8VgQmAYRgbQPDyL+pYuqud1\n43mC7zvq9y+itvQyqjJcBGCS6whE5O9F5BUR2SYij4hIcdp7XxSRBhHZLSK3pLXfmmhrEJEvTOb6\nhmEYEyEamoM3pxzvWDuuvYPOQ/0cya1he8ccW0bA5GcEzwBfdM7FROQbwBeBz4vIlcD7gdcBc4DV\nInJZ4jP/CtwMHATqReQx59zLk+yHYRjGuETKBP+yhcTzy9i6OU5jfz5tnTn0fk9oaYGPfzy1cDkT\nmdStO+eeds7FEi/XAxWJ53cAP3HODTnn9gMNwLLEo8E5t885Nwz8JHGsYRjGWUPXpAk7DpWy7dBM\njnTn4vvCkSPwL/8C3/hGauFyJjKVMYLfA36aeD4XFYYkBzm+ooPmUe3XTWEfDMMwXkMyoSgc1oSi\n1lY1/NGobnHw4x9DaWnmFqg75YxARFaLyI4xHnekHfPnQAz44VR1TETuE5ENIrKhra1tqk5rGEaG\nIqJ73eTlJQuaOvKyBsmRfmbkDrD+BUdz86nPczFyyhmBc+6mk70vIh8BbgdudKkNkFuA9MTcikQb\nJ2kffd1VwCrQPYtP1U/DMIxTUVkJy5fDhg2OgWgvxHspzR0g++gwuSVBom2XUFWVeVOCyWYN3Qr8\nKfAu51x/2luPAe8XkbCIzAMWAC8B9cACEZknIiE0oPzYZPpgGIYxUUQ0MPyB2zrJdz2UlcTJLQhS\nNSeGf+Qoh7e3ZWRB0snGCP4FCAPPiDrW1jvnft85t1NEHgReRl1Gn3LOxQFE5NPAU0AAeMA5t3OS\nfTAMw5gwngeff89+Srdqgbqc0AiHu/KgH557Ns5vd2deQdJJCYFz7tKTvPdV4KtjtD8BPDGZ6xqG\nYUyG9AJ12w/P4IltlSwq2EYgbzF+QYj6+hnU1mbOhjYZnDlrGEbGkixQ17OT8r59FLfuJtDTDQ2v\n4q37Dd6e3a/d0OYixkpMGIaReaQVqIus2Yu/dQR/YQTP8/B9h7//MJHhAlJZ7xc3JgSGYWQmiQJ1\nlVdFqZu3i/qOK/E8h+8LdXNfPnFDm4scEwLDMDIaKYuw8tId1Ba6sTe0yQBMCAzDyGxOtqFNhmBC\nYBhGZjOBPZEvdkwIDMMwJrAn8sWMpY8ahmFkODYjMAwj83AOmpsz1hU0GhMCwzAyC+fgkUegvl7r\nTfh+5tWUGIUJgWEYmUVzs4pAdXVKCOrrNVhsMQLDMIwMIBpVAUjuTZl8Ho1Ob7+mERMCwzAyi0hE\nZwHJvSmTzyOR6e3XNGKuIcMwMgvdwPi1MYIMWkA2GhMCwzAyC1tA9hpMCAzDyDwyfAHZaCxGYBiG\nkeGYEBiGYWQ4JgSGYRgZjgmBYRhGhjMlQiAinxMRJyKRxGsRkX8SkQYR2SYiS9KOvUdE9iYe90zF\n9Q3DMIwzZ9JZQyJSCbwNaEprfjuwIPG4DrgfuE5EZgBfAmoBB2wUkcecc8cm2w/DMAzjzJiKGcH/\nBf4UNexJ7gC+75T1QLGIlAO3AM845zoSxv8Z4NYp6INhGIZxhkxKCETkDqDFObd11Ftzgea01wcT\nbeO1G4ZhGNPEKV1DIrIamD3GW38O/BnqFppyROQ+4D6AKlv0YRiGcdY4pRA4524aq11EFgPzgK2i\nS7MrgE0isgxoAdILd1Qk2lqAN49qXzvOdVcBqwBqa2vdWMcYhmEYk+eMXUPOue3OuZnOuRrnXA3q\n5lninGsFHgM+nMgeWg50OecOA08BbxOREhEpQWcTT03+NgzDMIwz5WzVGnoCuA1oAPqBjwI45zpE\n5CtAfeK4v3bOdZylPhiGYRgTYMqEIDErSD53wKfGOe4B4IGpuq5hGIYxOWxlsWEYRoZjQmAYhpHh\nmBAYhmFkOCYEhmEYGY4JgWEYRoZjQmAYhpHhmBAYhmFkOCYEhmEYGY4JgWEYRoZjQmAYhpHhmBAY\nhmFkOCYEhmEYGY4JgWEYRoZjQmAYhpHhmBAYhmFkOCYEhmEYGY4JgWEYRoZztraqNAzDME6Gc9Dc\nDNEoRCJQWQki09IVEwLDMIxzjXPwyCNQXw+eB74PdXWwcuW0iIEJgWEYxrmmuVlFoLo6JQT19VBb\nC1VV57w7k44RiMgfisgrIrJTRP4urf2LItIgIrtF5Ja09lsTbQ0i8oXJXt8wDOOCIxpVAfASJjj5\nPBqdlu5MakYgIm8B7gCuds4NicjMRPuVwPuB1wFzgNUiclniY/8K3AwcBOpF5DHn3MuT6YdhGMYF\nRSSCi/s0R3OJ9ucQyR2gMu4jkci0dGeyrqFPAl93zg0BOOeOJtrvAH6SaN8vIg3AssR7Dc65fQAi\n8pPEsSYEhmFkDK6ikkf8d1H/+CCeJ/i+o27FJaysqGQ6wsWTFYLLgBUi8lVgEPhj51w9MBdYn3bc\nwUQbQPOo9uvGOrGI3AfcB1A1DT4zwzCMs0XzQaE+sJzqd3bg9ffi5+ZT3zOD2oMyHSGCUwuBiKwG\nZo/x1p8nPj8DWA7UAQ+KyPyp6JhzbhWwCqC2ttZNxTkNwzDOBzREIHiRUqAUD/D6tP28FALn3E3j\nvScinwR+7pxzwEsi4gMRoAWoTDu0ItHGSdoNwzAygkhEE4V8P5U05PvaPh1MNmvoUeAtAIlgcAiI\nAo8B7xeRsIjMAxYALwH1wAIRmSciITSg/Ngk+2AYhnFBUVmpywYOHEg96uq0fTqYbIzgAeABEdkB\nDAP3JGYHO0XkQTQIHAM+5ZyLA4jIp4GngADwgHNu5yT7YBiGcUEhomvHamvPi4XFiNrt85va2lq3\nYcOG6e6GYRjGBYWIbHTO1Z7qOCs6ZxiGkeGYEBiGYWQ4JgSGYRgZjgmBYRhGhmNCYBiGkeGYEBiG\nYWQ4JgSGYRgZjgmBYRhGhmNCYBiGkeGYEBiGYWQ4JgSGYRgZjgmBYRhGhmNCYBiGkeGYEBiGYWQ4\nJgSGYRgZjgmBYRhGhmNCYBiGkeGYEBiGYWQ4JgSGYRgZzqSEQESuEZH1IrJFRDaIyLJEu4jIP4lI\ng4hsE5ElaZ+5R0T2Jh73TPYGDMMwjMkRnOTn/w74snPuVyJyW+L1m4G3AwsSj+uA+4HrRGQG8CWg\nFnDARhF5zDl3bJL9MAzDMM6QybqGHFCYeF4EHEo8vwP4vlPWA8UiUg7cAjzjnOtIGP9ngFsn2QfD\nMAxjEkx2RvC/gadE5B9QUbkh0T4XaE477mCibbx2wzAMY5o4pRCIyGpg9hhv/TlwI/BZ59zDInI3\n8Ix6u58AAAV3SURBVJ/ATVPRMRG5D7gPoKqqaipOaRiGYYzBKYXAOTeuYReR7wOfSbx8CPiPxPMW\noDLt0IpEWwsaQ0hvXzvOdVcBqwBqa2vdqfppGIZxMeEcNDdDNAqRCFRWgsjZudZkXUOHgDehxvyt\nwN5E+2PAp0XkJ2iwuMs5d1hEngK+JiIliePeBnxxkn0wDMO4qHAOHnkE6uvB88D3oa4OVq48O2Iw\nWSG4F/imiASBQRKuHOAJ4DagAegHPgrgnOsQka8A9Ynj/to51zHJPhiGYVxUNDdDfb2juqADr78X\nvyCf+voZ1NYKZ8NTPikhcM79Flg6RrsDPjXOZx4AHpjMdQ3DMC5mom0Ob89uvP6XQTw85+PlXkm0\nbSFVVVM/JZjsjMAwDMOYYiLDh/APHcafV4rnCb7v8PcfJjJcwNlItDQhMAzDOM+oDB2hbu4h6juu\nxPMcvi/UzX2ZylARJgSGYRgZgJRFWHnpDmoLHdH+HCK5A1R270TKVpyV65kQGIZhnG9UViLL6qiq\nr6fK86DHh2V1mkN6FjAhMAzDON8Q0VzR2tpzspDAhMAwDON8RASqqjgr+aKjsP0IDMMwMhwTAsMw\njAzHhMAwDCPDMSEwDMPIcEwIDMMwMhzRskDnNyLSBhyYhktHgOg0XPdcYfd3YWP3d2FzLu6v2jlX\ndqqDLgghmC5EZINzrna6+3G2sPu7sLH7u7A5n+7PXEOGYRgZjgmBYRhGhmNCcHJWTXcHzjJ2fxc2\ndn8XNufN/VmMwDAMI8OxGYFhGEaGY0IwDiLSKCLbRWSLiGyY7v5MFhF5QESOisiOtLYZIvKMiOxN\n/CyZzj5OhnHu769EpCXxO9wiIrdNZx/PFBGpFJFfi8jLIrJTRD6TaL8ofn8nub+L5feXLSIvicjW\nxP19OdE+T0ReFJEGEfmpiISmrY/mGhobEWkEap1zF0Ues4i8EegFvu+cW5Ro+zugwzn3dRH5AlDi\nnPv8dPbzTBnn/v4K6HXO/cN09m2yiEg5UO6c2yQiBcBG4N3AR7gIfn//f3v3D9pUFMVx/HuQDlKH\nIkiXIqKLk1QHQehQBAUnEaQgCN10UFAcXQTBUdcK4tBBLcXWP6MOBXVx8L/QSXCw1HaQol0E7c/h\n3kAsSZa2PN59vw+E3LwkcA6H5CTnhrwe+Y1RRv0C6Je0GhF9wCvgEnAFmJU0FRG3gQ+SJqqI0d8I\nGkLSC+DHusMngcm8niS9+GqpS35FkLQo6W1e/wLmSecrLKJ+PfIrgpLVfLMvXwQcBR7m45XWz42g\nOwHPIuJNRJyrOpgtMihpMa+/A4NVBrNFLkbExzw6quXopF1E7AEOAq8psH7r8oNC6hcR2yLiPbAM\nPAe+ACuS/uSHfKPC5udG0N2IpEPACeBCHj0US2lGWNqccALYBwwDi8DNasPZmIjYAcwAlyX9bL+v\nhPp1yK+Y+kn6K2kYGAIOA/srDuk/bgRdSFrI18vAI1LxSrOU57OtOe1yxfFsKklL+QW4BtyhxjXM\ns+UZ4J6k2Xy4mPp1yq+k+rVIWgHmgCPAQES0zhI5BCxUFZcbQQcR0Z83rYiIfuA48Ln3s2rpKTCe\n1+PAkwpj2XStN8nsFDWtYd5svAvMS7rVdlcR9euWX0H12xURA3m9HThG2geZA07nh1VaP/9qqIOI\n2Ev6FgDpvM73Jd2oMKQNi4gHwCjpHw+XgGvAY2Aa2E36d9cxSbXccO2S3yhprCDgK3C+baZeGxEx\nArwEPgFr+fBV0hy99vXrkd8ZyqjfAdJm8DbSh+9pSdfz+8wUsBN4B5yV9LuSGN0IzMyazaMhM7OG\ncyMwM2s4NwIzs4ZzIzAzazg3AjOzhnMjMDNrODcCM7OGcyMwM2u4f68Y70i/IUt1AAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116f78650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "interact(polynomial_regr,degree=(3,150,1));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Limits of  polynomial regression\n",
    "### 1- They can't get better after a certain threshold (e.g. polynomial degree)\n",
    "### 2- They suffer from the curse of dimensionality\n",
    "### 3- Ther training time increases exponentially by using higher polynomial degrees\n",
    "### 4- Assumes functional relations between variables\n",
    "### 5- Structural assumptions about the form of functions\n",
    "\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# <a></a>\n",
    "# <a></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Limits of Regression Models\n",
    "### They can't get better after a certain threshold (e.g. polynomial degree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dimension of training data for polynomial degree 1 is 2\n",
      "degree 1 is done in 0.000731945037842 seconds\n",
      "dimension of training data for polynomial degree 2 is 3\n",
      "degree 2 is done in 0.000519037246704 seconds\n",
      "dimension of training data for polynomial degree 3 is 4\n",
      "degree 3 is done in 0.000624895095825 seconds\n",
      "dimension of training data for polynomial degree 4 is 5\n",
      "degree 4 is done in 0.000648975372314 seconds\n",
      "dimension of training data for polynomial degree 5 is 6\n",
      "degree 5 is done in 0.000561952590942 seconds\n",
      "dimension of training data for polynomial degree 6 is 7\n",
      "degree 6 is done in 0.000478982925415 seconds\n",
      "dimension of training data for polynomial degree 7 is 8\n",
      "degree 7 is done in 0.00047779083252 seconds\n",
      "dimension of training data for polynomial degree 8 is 9\n",
      "degree 8 is done in 0.000458002090454 seconds\n",
      "dimension of training data for polynomial degree 9 is 10\n",
      "degree 9 is done in 0.000449895858765 seconds\n",
      "dimension of training data for polynomial degree 10 is 11\n",
      "degree 10 is done in 0.000422954559326 seconds\n",
      "dimension of training data for polynomial degree 11 is 12\n",
      "degree 11 is done in 0.000428915023804 seconds\n",
      "dimension of training data for polynomial degree 12 is 13\n",
      "degree 12 is done in 0.000501155853271 seconds\n",
      "dimension of training data for polynomial degree 13 is 14\n",
      "degree 13 is done in 0.000458002090454 seconds\n",
      "dimension of training data for polynomial degree 14 is 15\n",
      "degree 14 is done in 0.000411987304688 seconds\n",
      "dimension of training data for polynomial degree 15 is 16\n",
      "degree 15 is done in 0.000443935394287 seconds\n",
      "dimension of training data for polynomial degree 16 is 17\n",
      "degree 16 is done in 0.000494956970215 seconds\n",
      "dimension of training data for polynomial degree 17 is 18\n",
      "degree 17 is done in 0.000458002090454 seconds\n",
      "dimension of training data for polynomial degree 18 is 19\n",
      "degree 18 is done in 0.000478029251099 seconds\n",
      "dimension of training data for polynomial degree 19 is 20\n",
      "degree 19 is done in 0.000493049621582 seconds\n",
      "dimension of training data for polynomial degree 20 is 21\n",
      "degree 20 is done in 0.000580072402954 seconds\n",
      "dimension of training data for polynomial degree 21 is 22\n",
      "degree 21 is done in 0.000566959381104 seconds\n",
      "dimension of training data for polynomial degree 22 is 23\n",
      "degree 22 is done in 0.000507831573486 seconds\n",
      "dimension of training data for polynomial degree 23 is 24\n",
      "degree 23 is done in 0.000540971755981 seconds\n",
      "dimension of training data for polynomial degree 24 is 25\n",
      "degree 24 is done in 0.000530958175659 seconds\n",
      "dimension of training data for polynomial degree 25 is 26\n",
      "degree 25 is done in 0.000581026077271 seconds\n",
      "dimension of training data for polynomial degree 26 is 27\n",
      "degree 26 is done in 0.000582933425903 seconds\n",
      "dimension of training data for polynomial degree 27 is 28\n",
      "degree 27 is done in 0.000594139099121 seconds\n",
      "dimension of training data for polynomial degree 28 is 29\n",
      "degree 28 is done in 0.000581026077271 seconds\n",
      "dimension of training data for polynomial degree 29 is 30\n",
      "degree 29 is done in 0.000651121139526 seconds\n",
      "dimension of training data for polynomial degree 30 is 31\n",
      "degree 30 is done in 0.000666856765747 seconds\n",
      "dimension of training data for polynomial degree 31 is 32\n",
      "degree 31 is done in 0.00067400932312 seconds\n",
      "dimension of training data for polynomial degree 32 is 33\n",
      "degree 32 is done in 0.000744819641113 seconds\n",
      "dimension of training data for polynomial degree 33 is 34\n",
      "degree 33 is done in 0.000752210617065 seconds\n",
      "dimension of training data for polynomial degree 34 is 35\n",
      "degree 34 is done in 0.000808954238892 seconds\n",
      "dimension of training data for polynomial degree 35 is 36\n",
      "degree 35 is done in 0.000858068466187 seconds\n",
      "dimension of training data for polynomial degree 36 is 37\n",
      "degree 36 is done in 0.000936985015869 seconds\n",
      "dimension of training data for polynomial degree 37 is 38\n",
      "degree 37 is done in 0.000910997390747 seconds\n",
      "dimension of training data for polynomial degree 38 is 39\n",
      "degree 38 is done in 0.000905990600586 seconds\n",
      "dimension of training data for polynomial degree 39 is 40\n",
      "degree 39 is done in 0.000905990600586 seconds\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model\n",
    "y_preds = pd.DataFrame(data=np.zeros((y.shape[0],0)))\n",
    "ARE = pd.DataFrame(data=np.zeros((y.shape[0],0)))\n",
    "MAE = pd.DataFrame(data=np.zeros((1,0)))\n",
    "\n",
    "\n",
    "training_times = []\n",
    "max_degree = 40\n",
    "for degree in range(1,max_degree):   \n",
    "    poly = PolynomialFeatures(degree=degree)\n",
    "    x1_ = poly.fit_transform(x1)\n",
    "    \n",
    "    \n",
    "    t0 = time.time()\n",
    "    regr = linear_model.LinearRegression()\n",
    "    regr.fit(x1_, y)\n",
    "    \n",
    "    print 'dimension of training data for polynomial degree {} is {}'.format(degree,x1_.shape[1])\n",
    "    print 'degree {} is done in {} seconds'.format(degree,time.time()-t0)\n",
    "    \n",
    "    y_pred = regr.predict(x1_)[:]\n",
    "    \n",
    "    \n",
    "    \n",
    "    y_preds['degree-{}'.format(degree)] = y_pred\n",
    "    MAE['degree-{}'.format(degree)] = np.mean(np.abs(y_pred-y))\n",
    "    ARE['degree-{}'.format(degree)] = 100*np.abs(y_pred-y)/y\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>median</th>\n",
       "      <th>1</th>\n",
       "      <th>5</th>\n",
       "      <th>10</th>\n",
       "      <th>15</th>\n",
       "      <th>20</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>degree-1</th>\n",
       "      <td>15.56</td>\n",
       "      <td>8.25</td>\n",
       "      <td>20.00</td>\n",
       "      <td>33.25</td>\n",
       "      <td>48.25</td>\n",
       "      <td>62.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-2</th>\n",
       "      <td>9.23</td>\n",
       "      <td>9.25</td>\n",
       "      <td>30.25</td>\n",
       "      <td>53.00</td>\n",
       "      <td>69.75</td>\n",
       "      <td>81.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-3</th>\n",
       "      <td>8.64</td>\n",
       "      <td>10.25</td>\n",
       "      <td>31.75</td>\n",
       "      <td>54.50</td>\n",
       "      <td>72.75</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-4</th>\n",
       "      <td>8.48</td>\n",
       "      <td>11.00</td>\n",
       "      <td>31.25</td>\n",
       "      <td>56.00</td>\n",
       "      <td>73.00</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-5</th>\n",
       "      <td>8.65</td>\n",
       "      <td>9.50</td>\n",
       "      <td>31.75</td>\n",
       "      <td>55.75</td>\n",
       "      <td>73.00</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-6</th>\n",
       "      <td>8.69</td>\n",
       "      <td>9.75</td>\n",
       "      <td>32.50</td>\n",
       "      <td>54.75</td>\n",
       "      <td>72.75</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-7</th>\n",
       "      <td>8.74</td>\n",
       "      <td>11.25</td>\n",
       "      <td>31.00</td>\n",
       "      <td>55.75</td>\n",
       "      <td>74.00</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-8</th>\n",
       "      <td>8.66</td>\n",
       "      <td>11.00</td>\n",
       "      <td>32.00</td>\n",
       "      <td>55.75</td>\n",
       "      <td>74.25</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-9</th>\n",
       "      <td>8.45</td>\n",
       "      <td>11.00</td>\n",
       "      <td>31.25</td>\n",
       "      <td>56.00</td>\n",
       "      <td>72.75</td>\n",
       "      <td>85.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-10</th>\n",
       "      <td>8.62</td>\n",
       "      <td>10.50</td>\n",
       "      <td>31.25</td>\n",
       "      <td>55.75</td>\n",
       "      <td>73.50</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-11</th>\n",
       "      <td>8.54</td>\n",
       "      <td>10.75</td>\n",
       "      <td>31.00</td>\n",
       "      <td>55.75</td>\n",
       "      <td>72.75</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-12</th>\n",
       "      <td>8.60</td>\n",
       "      <td>10.50</td>\n",
       "      <td>31.00</td>\n",
       "      <td>55.75</td>\n",
       "      <td>73.50</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-13</th>\n",
       "      <td>8.70</td>\n",
       "      <td>11.00</td>\n",
       "      <td>32.00</td>\n",
       "      <td>55.25</td>\n",
       "      <td>74.75</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-14</th>\n",
       "      <td>8.69</td>\n",
       "      <td>10.75</td>\n",
       "      <td>31.25</td>\n",
       "      <td>55.75</td>\n",
       "      <td>74.50</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-15</th>\n",
       "      <td>8.72</td>\n",
       "      <td>10.00</td>\n",
       "      <td>31.75</td>\n",
       "      <td>55.75</td>\n",
       "      <td>73.25</td>\n",
       "      <td>83.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-16</th>\n",
       "      <td>9.00</td>\n",
       "      <td>10.75</td>\n",
       "      <td>31.25</td>\n",
       "      <td>54.25</td>\n",
       "      <td>72.25</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-17</th>\n",
       "      <td>8.88</td>\n",
       "      <td>10.75</td>\n",
       "      <td>32.00</td>\n",
       "      <td>55.25</td>\n",
       "      <td>72.50</td>\n",
       "      <td>85.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-18</th>\n",
       "      <td>9.12</td>\n",
       "      <td>10.50</td>\n",
       "      <td>32.00</td>\n",
       "      <td>55.50</td>\n",
       "      <td>72.25</td>\n",
       "      <td>85.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-19</th>\n",
       "      <td>9.06</td>\n",
       "      <td>11.00</td>\n",
       "      <td>32.25</td>\n",
       "      <td>54.75</td>\n",
       "      <td>72.25</td>\n",
       "      <td>85.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-20</th>\n",
       "      <td>9.02</td>\n",
       "      <td>12.00</td>\n",
       "      <td>31.25</td>\n",
       "      <td>54.75</td>\n",
       "      <td>73.25</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-21</th>\n",
       "      <td>8.84</td>\n",
       "      <td>12.00</td>\n",
       "      <td>31.25</td>\n",
       "      <td>53.50</td>\n",
       "      <td>73.25</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-22</th>\n",
       "      <td>8.90</td>\n",
       "      <td>12.00</td>\n",
       "      <td>31.75</td>\n",
       "      <td>53.25</td>\n",
       "      <td>73.25</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-23</th>\n",
       "      <td>8.87</td>\n",
       "      <td>11.75</td>\n",
       "      <td>32.00</td>\n",
       "      <td>54.00</td>\n",
       "      <td>73.50</td>\n",
       "      <td>84.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-24</th>\n",
       "      <td>8.85</td>\n",
       "      <td>13.00</td>\n",
       "      <td>32.00</td>\n",
       "      <td>54.50</td>\n",
       "      <td>73.00</td>\n",
       "      <td>84.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-25</th>\n",
       "      <td>8.88</td>\n",
       "      <td>10.75</td>\n",
       "      <td>32.00</td>\n",
       "      <td>54.25</td>\n",
       "      <td>73.00</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-26</th>\n",
       "      <td>8.95</td>\n",
       "      <td>11.00</td>\n",
       "      <td>32.25</td>\n",
       "      <td>55.75</td>\n",
       "      <td>73.00</td>\n",
       "      <td>85.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-27</th>\n",
       "      <td>9.00</td>\n",
       "      <td>10.00</td>\n",
       "      <td>32.00</td>\n",
       "      <td>56.25</td>\n",
       "      <td>73.00</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-28</th>\n",
       "      <td>9.04</td>\n",
       "      <td>9.75</td>\n",
       "      <td>32.75</td>\n",
       "      <td>56.00</td>\n",
       "      <td>73.00</td>\n",
       "      <td>84.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-29</th>\n",
       "      <td>8.89</td>\n",
       "      <td>10.25</td>\n",
       "      <td>31.75</td>\n",
       "      <td>55.25</td>\n",
       "      <td>72.25</td>\n",
       "      <td>83.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-30</th>\n",
       "      <td>9.00</td>\n",
       "      <td>10.75</td>\n",
       "      <td>30.00</td>\n",
       "      <td>54.50</td>\n",
       "      <td>71.25</td>\n",
       "      <td>82.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-31</th>\n",
       "      <td>9.18</td>\n",
       "      <td>11.25</td>\n",
       "      <td>29.25</td>\n",
       "      <td>54.00</td>\n",
       "      <td>71.25</td>\n",
       "      <td>82.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-32</th>\n",
       "      <td>9.49</td>\n",
       "      <td>12.25</td>\n",
       "      <td>29.50</td>\n",
       "      <td>51.25</td>\n",
       "      <td>70.25</td>\n",
       "      <td>80.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-33</th>\n",
       "      <td>9.84</td>\n",
       "      <td>12.25</td>\n",
       "      <td>29.75</td>\n",
       "      <td>51.25</td>\n",
       "      <td>69.50</td>\n",
       "      <td>79.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-34</th>\n",
       "      <td>9.78</td>\n",
       "      <td>11.00</td>\n",
       "      <td>30.25</td>\n",
       "      <td>50.50</td>\n",
       "      <td>68.50</td>\n",
       "      <td>79.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-35</th>\n",
       "      <td>10.17</td>\n",
       "      <td>10.00</td>\n",
       "      <td>30.50</td>\n",
       "      <td>49.50</td>\n",
       "      <td>66.75</td>\n",
       "      <td>77.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-36</th>\n",
       "      <td>10.39</td>\n",
       "      <td>10.75</td>\n",
       "      <td>30.25</td>\n",
       "      <td>49.25</td>\n",
       "      <td>64.75</td>\n",
       "      <td>77.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-37</th>\n",
       "      <td>10.37</td>\n",
       "      <td>9.50</td>\n",
       "      <td>31.00</td>\n",
       "      <td>49.50</td>\n",
       "      <td>63.75</td>\n",
       "      <td>75.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-38</th>\n",
       "      <td>10.87</td>\n",
       "      <td>9.25</td>\n",
       "      <td>31.25</td>\n",
       "      <td>48.75</td>\n",
       "      <td>63.75</td>\n",
       "      <td>73.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-39</th>\n",
       "      <td>10.93</td>\n",
       "      <td>8.25</td>\n",
       "      <td>28.75</td>\n",
       "      <td>48.25</td>\n",
       "      <td>63.25</td>\n",
       "      <td>73.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           median      1      5     10     15     20\n",
       "degree-1    15.56   8.25  20.00  33.25  48.25  62.75\n",
       "degree-2     9.23   9.25  30.25  53.00  69.75  81.25\n",
       "degree-3     8.64  10.25  31.75  54.50  72.75  84.75\n",
       "degree-4     8.48  11.00  31.25  56.00  73.00  85.00\n",
       "degree-5     8.65   9.50  31.75  55.75  73.00  84.75\n",
       "degree-6     8.69   9.75  32.50  54.75  72.75  84.75\n",
       "degree-7     8.74  11.25  31.00  55.75  74.00  85.00\n",
       "degree-8     8.66  11.00  32.00  55.75  74.25  84.75\n",
       "degree-9     8.45  11.00  31.25  56.00  72.75  85.25\n",
       "degree-10    8.62  10.50  31.25  55.75  73.50  85.00\n",
       "degree-11    8.54  10.75  31.00  55.75  72.75  85.00\n",
       "degree-12    8.60  10.50  31.00  55.75  73.50  85.00\n",
       "degree-13    8.70  11.00  32.00  55.25  74.75  84.75\n",
       "degree-14    8.69  10.75  31.25  55.75  74.50  84.75\n",
       "degree-15    8.72  10.00  31.75  55.75  73.25  83.75\n",
       "degree-16    9.00  10.75  31.25  54.25  72.25  84.75\n",
       "degree-17    8.88  10.75  32.00  55.25  72.50  85.25\n",
       "degree-18    9.12  10.50  32.00  55.50  72.25  85.25\n",
       "degree-19    9.06  11.00  32.25  54.75  72.25  85.25\n",
       "degree-20    9.02  12.00  31.25  54.75  73.25  85.00\n",
       "degree-21    8.84  12.00  31.25  53.50  73.25  85.00\n",
       "degree-22    8.90  12.00  31.75  53.25  73.25  85.00\n",
       "degree-23    8.87  11.75  32.00  54.00  73.50  84.25\n",
       "degree-24    8.85  13.00  32.00  54.50  73.00  84.50\n",
       "degree-25    8.88  10.75  32.00  54.25  73.00  85.00\n",
       "degree-26    8.95  11.00  32.25  55.75  73.00  85.00\n",
       "degree-27    9.00  10.00  32.00  56.25  73.00  84.75\n",
       "degree-28    9.04   9.75  32.75  56.00  73.00  84.75\n",
       "degree-29    8.89  10.25  31.75  55.25  72.25  83.75\n",
       "degree-30    9.00  10.75  30.00  54.50  71.25  82.50\n",
       "degree-31    9.18  11.25  29.25  54.00  71.25  82.25\n",
       "degree-32    9.49  12.25  29.50  51.25  70.25  80.50\n",
       "degree-33    9.84  12.25  29.75  51.25  69.50  79.25\n",
       "degree-34    9.78  11.00  30.25  50.50  68.50  79.00\n",
       "degree-35   10.17  10.00  30.50  49.50  66.75  77.75\n",
       "degree-36   10.39  10.75  30.25  49.25  64.75  77.00\n",
       "degree-37   10.37   9.50  31.00  49.50  63.75  75.50\n",
       "degree-38   10.87   9.25  31.25  48.75  63.75  73.75\n",
       "degree-39   10.93   8.25  28.75  48.25  63.25  73.75"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quality = [1,5,10,15,20]\n",
    "percentiles = pd.DataFrame(data= np.zeros((len(quality),ARE.shape[1])),index=quality,columns=ARE.columns)\n",
    "for percent in quality:\n",
    "    for m in range(ARE.shape[1]):\n",
    "        a = ARE.values[:,m]\n",
    "        n = float(a.shape[0])\n",
    "        percentiles.ix[percent,m]= 100*a[a<=percent].shape[0]/n\n",
    "#         percentiles.ix[percent,m]= 100*(a<=percent).sum()/float(a.shape[0])\n",
    "percentiles\n",
    "med_error = pd.DataFrame(data=ARE.median(axis=0).values[:][np.newaxis,:].copy(),columns=ARE.columns,index=['median'])\n",
    "med_error\n",
    "percentiles = pd.concat((med_error,percentiles))\n",
    "percentiles.ix[:] = np.around(percentiles.values[:],decimals=2)\n",
    "# percentiles.index.name = 'ARE'\n",
    "percentiles.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11791d510>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UnJlNcveirAdmyyaE6T3mAPOi132AZ+JkokJuOS1Z3HZb+Cvro49yd07Jj8WL\nw1QdF19c/XGffx6qOVq2DL/bUaOqPz7X7r03XPfhh6s+prg4jF2AMFVG+bQZ++3nfvXVYZBfrqqG\nPv44tB2A+0EHhTEqhTRyZLh227ahGkoSQw6roSYBbYEpGfumxzl5IbecJouXXw635l//yt05JT9u\nuCH8rmbNyn7se++5d+gQuoIWulvm+vVh8N9224WBapnmzg0N4eC+447uTzwRjn/zzdDmUlQU3gP3\nLl3cTz/d/bHHQrVN3ORRVuY+c6b7X/4Seog1axYS5403bjrquhDKysKAvkmTCn9t+YZcJos3osfM\nZDEtzskLueU0WSxdGm7Nddfl7pySH336uO+1V/zj581znz07b+FUq/yPkKuuCq9XrAhdd1u0CA3L\nV19d9ZiMxYvd77/f/YQT3LfccmPy6NAhtDNceGGYbG/OnI1f/itXuo8dGzprdO268TO9erlfdFE4\nVhq9uMmiWYwqrZlm9jOgqZl1B84D/hO7Qqw+atcuzJuvkdzpNm1amMjuttvif6Zr17yFk9VBB4UV\n94YPD6Oer7km1Nmfcgpce231azV07gy//GXYvv46tGlMnhymRZ88OYx0XrcuHLv55tCjRxidvmZN\nGEV92GHwhz+EpWJrOmGiCGRv4Daz1sClwOGEwXLPA8M8WhApLXLawA3wgx+E9X61RkF6/e53YSnU\njz+Gjh2Tjiae+fNhl11Co3u/fiH+/fev+3nXrYNZszYmkFmzwtQ1Rx4ZklTLlnW/hjRIcRu4s5Ys\n3H0VIVlcmovA6o2ePcPcQevXh5XSJF3Wr4eHHoKjjqo/iQJCyWb0aFi+PJQomsRZfyyGzTYLS772\n6ZOb84lUkPVb0MyKgEuArpnHu3vv/IWVAr16hb/+3n8//CUo6fLCC6HkN3Bg0pHU3I9/nHQEIjUW\n50/mh4DfE+ZoKstvOCmSuRCSkkX6jBoV6v2PPDLpSEQahThl4CXu/oy7z3P3BeVb3iNL2q67hioC\nNXKnz1dfwVNPwcknh+oXEcm7OCWLy83sXsICRGvLd7r7E3mLKg1atoTu3ZUs0mjMmNDLpz5WQYnU\nU3GSxWnALkBzNlZDOWHq8oatV6/QNVPSZdSoUDVYlH2GAhHJjTjJYi9375H3SNKoVy94/HFYuRLa\ntEk6GoGw+t3EifDnP2veLpECitNm8R8z2y3vkaRRr15hzOusWcnFsGYN3Hln+Ev67LPD68bswQdD\nkjj11KREkUv0AAAPkklEQVQjEWlU4iSLfYGpZjbHzKaZ2XQzm5bvwFIhs0dUoa1aFUbldusWZsFt\n0gTuugu++12YN6/w8aTBZ5+FKqj+/TUKWaTA4iSLI4DuhBHcPwSOjh4bvh13hFatCpssli0L00F0\n7Qrnnx+mbS4uDlM3PPMMfPBBGPn77LOFiykp7mFE8tVXw377wbe+Faqhzj476chEGp04I7gbfjfZ\nqjRtGubcnzEj/9daujRM/XDzzfDll2Edg0svhQMO2HjMD38Y5gQ6/vgwcvmyy+DyyytfwyGN7rsP\nHn00fOl36RK2b3974/MuXcJxxcUwbhz861/wySdh3157wdCh4R7065fczyDSSGkei2x69crfX/Hu\n8Oab4Ut09GhYsSKM7r300qp7+nTrBq+/DuecA8OGhc8/9FD6p7z4y1/gwgtD/HPmhCRQPvFdZdq2\nhe9/Pwy6O+KIMJGeiCRGySKbXr3g/vthyRLo1Ck35/zss9BQe++9ofG8dWs48US44IKN7STVadUK\nRo4ME9ANHhz+0n7ssfDXdxoNGxZKBSedFNocmjcPifLLL0PSyNxWr4aDDw7VTs2bJx25iESULLLJ\nbOTu37/259mwIVSv3HsvPP10mGZ6n33CEpo//SlsuWXNzmcGZ54Je+4Zpr0+4IBQQklTLyH3UFX2\npz+FAXT33bexyswsTAXfrh3s1jg724nUJzma8rIB69kzPNal3eKtt2CnnUJ1yosvhtLA9OlhTegz\nz6x5oshUVBTaMfbZJ/Sa+vzz2p8rl9zh978PieLMM0NJqL60rYjIJpQssuncOVQ/TZxYu89//TWc\ndlr48nz00bDYzQ03bExCudChA9xxR2jzuPnm3J23tsrK4De/geuvD4933ZW7qbhFJBH6H5yNGZx+\nemgTmDCh5p+/6abQLjFiBJxwArRokfsYIfTaOv74jb2pamr9enjuueobnePYsAHOOgtuvz0sTnTz\nzRppLdIAKFnEMXRomFTwzDPDYLm4PvoIrrgCfvQjOProvIX3P3/8YxinccstNf/s8OFhdcBDDgml\nn9pYvz6Uou69N8Ry3XVKFCINhJJFHK1awT33hAFhQ4fG/9z554fqp0JVDfXpA8ccAzfeGJJGXPPm\nhbaFvfaCt9+Gvn1rXor68MPQ7ffBB0Pvp2HDlChEGhAli7i+9z0YNCh8EZeUZD/+uefCJIR//GMY\njV0ol10WqqFuuy3+Z847Lywd++ST4Wdr3x4GDIBrrw3JrjqrVoXSU48eIcHcemv4mUWkYXH3BrH1\n69fP8+7LL9233tq9d2/3deuqPm71avdu3dx79HBfsyb/cVV01FHuHTq4L1+e/dinn3YH97/+deO+\nZcvcTzwx7D/mmPBzV1RW5v7II+7bbx+O++lP3RcsyN3PICIFAZR6jO9YlSxqom3b0FA9bVqoj6/K\nddeFOZxuvz1/DdrVueyy0IX2jjuqP27VqlCq6NkzPJbbYoswovzGG8O0G0VF4WcuN3VqGDj305+G\ncRIvvxyO3377vPw4IpICcTJKfdgKUrIod8IJ7ptt5j579qbvvf++e4sW4S/tJB1+uHunTu4rV1Z9\nzCWXhFLBK69UfczEie5duri3auV+553uZ53l3qRJKLnceaf7+vW5j11ECoaYJYtEvtiB84GZwAzg\nYaBlhfd/CSwBpkbbGdnOWdBksXixe7t27gcc4L5hw8b9ZWXuRx7pvsUW7osWFS6eyrz6avj13nBD\n5e/Pnu3evLn7L36R/VyffOJ+8MHhfE2bug8Z4r50aW7jFZFExE0WBa+GMrNtgPOAInfvCTQFTqrk\n0EfcvU+03VvQILPp3DkMrHv11bAwUbmnngqTDl55JWy9dXLxQVj3on//UCW2evU333MPo8jbtKm+\nOq3ct78NL7wQusROmxbGjrRrl5+4RSSVkmqzaAa0MrNmQGvg44TiqL2BA0OPoYsuCt1GV66EIUOg\nd+8wajkNhg6FxYvDl3ymRx6B8eNDd9m4s7k2axYGJ2oeJ5FGqeDJwt0XAX8FPgQ+Ab5y939Xcujx\n0cp8j5lZ+pZFMwvTWJSVhTmZhg0Lg/BGjAhfrGnwve/BgQeGLrBr14Z9y5aF2W379QsjrUVEYkii\nGqodcAywI7A10MbMKk6V+k+gq7v3Bl4AHqjiXIPMrNTMSpcsWZLPsCu3445hFbdnnw3VOb/8Zaj+\nSZOhQ8OI7PvvD6+vuCKUNu64QxP7iUhsFto3CnhBsxOAI9z99Oj1L4B93f2cKo5vCix197bVnbeo\nqMhLS0tzHm9WGzaEBPHuu/DOO2EVuDRxD/EtWhQGCe67L5xxxjfbWkSk0TKzSe5exWprGyXRZvEh\nsK+ZtTYzAw4FZmceYGZdMl7+qOL7qdK0aaj/nzkzfYkCQnXZ0KGhXWXAgNAw/ec/Jx2ViNQzBa9c\nd/c3zewxYDKwHpgC3G1mVxG6cD0DnGdmP4reX0roSptebdqELa2+//0w71NJSVhXon37pCMSkXqm\n4NVQ+ZJYNVR9MW0a/POfcPHFWltCRP4nbjVUSrrtSN717h02EZFa0J+YIiKSlZKFiIhkpWQhIiJZ\nKVmIiEhWShYiIpKVkoWIiGSlZCEiIlkpWYiISFYNZgS3mS0BFtThFB2Bz3IUTr4oxtxQjLmhGHMn\nyTh3cPdO2Q5qMMmirsysNM6Q9yQpxtxQjLmhGHOnPsSpaigREclKyUJERLJSstjo7qQDiEEx5oZi\nzA3FmDupj1NtFiIikpVKFiIiklWjTxZmdoSZzTGz983sD0nHUxkzm29m081sqpmlZoUnMxtpZp+a\n2YyMfe3N7AUzey96bJfCGK8ws0XR/ZxqZkcmHON2Zvaimc0ys5lmNiTan5p7WU2MqbmXZtbSzN4y\ns7ejGK+M9u9oZm9G/8cfMbPNUhjj38xsXsZ97JNUjFVp1NVQZtYUeBcYACwESoCT3X1WooFVYGbz\ngSJ3T1V/cTM7CFgBjHL3ntG+64Cl7j48Sr7t3P2ilMV4BbDC3f+aVFyZojXnu7j7ZDPbApgE/Jiw\nnHAq7mU1MZ5ISu6lmRnQxt1XmFlz4FVgCHAB8IS7jzazO4G33f2OlMV4NjDW3R9LIq44GnvJYm/g\nfXef6+7rgNHAMQnHVG+4+yuENdIzHQM8ED1/gPCFkpgqYkwVd//E3SdHz5cDs4FtSNG9rCbG1PBg\nRfSyebQ50B8o/xJO+j5WFWPqNfZksQ3wUcbrhaTsP0DEgX+b2SQzG5R0MFl0dvdPoueLgc5JBlON\nwWY2LaqmSrSqLJOZdQX2BN4kpfeyQoyQontpZk3NbCrwKfAC8AHwpbuvjw5J/P94xRjdvfw+/im6\njzeaWYsEQ6xUY08W9cUB7t4X+AFwblS1knoe6jjT+FfTHUA3oA/wCXB9suEEZrY58DjwW3dflvle\nWu5lJTGm6l66+wZ37wNsS6g52CXJeCpTMUYz6wlcTIh1L6A9kFjVbVUae7JYBGyX8XrbaF+quPui\n6PFT4EnCf4K0+m9Uv11ez/1pwvFswt3/G/2HLQPuIQX3M6q/fhx4yN2fiHan6l5WFmMa7yWAu38J\nvAjsB2xlZs2it1LzfzwjxiOiaj5397XA/aTkPmZq7MmiBOge9ZbYDDgJeCbhmL7BzNpEDYqYWRvg\ncGBG9Z9K1DPAwOj5QODpBGOpVPkXcORYEr6fUaPnfcBsd78h463U3MuqYkzTvTSzTma2VfS8FaHj\nymzCF/JPosOSvo+VxfhOxh8FRmhTSd3/8UbdGwog6up3E9AUGOnuf0o4pG8ws50IpQmAZsA/0hKj\nmT0MHEyYMfO/wOXAU8CjwPaEWYBPdPfEGpiriPFgQrWJA/OBszLaBgrOzA4AJgLTgbJo9yWENoFU\n3MtqYjyZlNxLM+tNaMBuSvhD+FF3vyr6PzSaUL0zBTg1+gs+TTFOADoBBkwFzs5oCE+FRp8sREQk\nu8ZeDSUiIjEoWYiISFZKFiIikpWShYiIZKVkISIiWSlZSINmZi+ZWSJrG5vZf2Ick7V7ZDSz6+9y\nE5VI7ShZiOSJu++fdAyZMkYxi9SYkoXUG2bW1czeMbOHzGy2mT1mZq2j9w41sykW1v0YWXEiNjP7\nlZndlPH6zGjCtq7Rue6J1hf4dzSyFjPrY2ZvRJO7PVk+SV5UWrnRzEqjz+5lZk9YWHfi6oxrrIge\nNzez8WY2OYov68zGZnapmb1rZq8CPTL2dzOz56JJJSea2S4Z+9+Izn91xrUPjo57BpgV7TvVwpoK\nU83sLgtT9WNmh5vZ61GcY6J5oEQCd9emrV5sQFfCSOHvRq9HAr8DWhJmD9452j+KMNEdwEtAEbA5\nYQbS5tH+/wC9onOuB/pE+x8ljPAFmAZ8L3p+FXBTxjmvjZ4PAT4GugAtCLOadojeWxE9NgO2jJ53\nBN5n44DYFZX8nP0II6VbA1tGx/8uem880D16vg8wIXo+lrAWC4S1EcqvfTCwEtgxer0r8M+M+zAC\n+EUU1yuEtRYgTGQ3NOnfubb0bCqWSn3zkbu/Fj3/O3AeYSrqee7+brT/AeBcwjQuAHhYbGYCcLSZ\nzSZ8WU6Pptue5+5To0MnAV3NrC2wlbu/nHHOMRlxlM8hNh2Y6dEUF2Y2lzA55ecZxxrw52i24DLC\nFNmdCdOOV+ZA4El3XxWd85nocXNgf2BMmEIICAkKwoR55es0/APIXIzoLXefFz0/lJCMSqJztCJM\nULgvsBvwWrR/M+D1KuKTRkjJQuqbivPT1GS+mnsJ8xm9Q5jZs1zmPEEbCF+g2ZR/pqzC58vY9P/V\nKYR5f/q5+9cWVj5sGT/s/2lCWJuhpktursx4bsAD7n5x5gFm9kPC2gon1yIuaQTUZiH1zfZmtl/0\n/GeEZSnnEEoD34n2/xx4ueIHPSwys130uYeru4i7fwV8YWYHVnfOmNoCn0aJ4hBghyzHvwL82Mxa\nRTMO/zCKaRkwz8xOgDBDqZntEX3mDeD46PlJ1Zx7PPATM/tWdI72ZrZD9Pnvlt9DC7Md71zjn1Qa\nLCULqW/mEBaAmg20A+5w9zXAaYTqmfJZUe+s4vOPAq+5+xcxrjUQ+IuZTSPMrHpVLWN+CCiKYvsF\noWRTJQ/Llz4CvA38izCVfrlTgNPN7G1gJhuXAf4tcEEU63eAr6o49yzgj4SVF6cRqvC6uPsSwprf\nD0f7XyeFCwdJcjTrrNQbUfvCWHfvWYdzjAVudPfxuYorDaJeYavd3c3sJEJjt9aTl5xRm4U0ChYW\nnHkLeLuhJYpIP+A2C63TXwK/SjgeaWBUshARkazUZiEiIlkpWYiISFZKFiIikpWShYiIZKVkISIi\nWSlZiIhIVv8PiySUIFh6cNgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1171c3910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax1 = plt.subplot(111)\n",
    "# plt.title('degree-{} ARE for ts'.format(degree))\n",
    "plt.plot(percentiles.T['median'].values[1:],'r')\n",
    "plt.xlabel('polynomial degree')\n",
    "plt.ylabel('median absolute relative error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Limits of Regression Models\n",
    "### They suffer from the curse of dimensionality \n",
    "### The training time increases exponentially by using higher polynomial degrees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An example, by real estate data\n",
    "### predicting the rental price of houses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Rent</th>\n",
       "      <th>ZIP</th>\n",
       "      <th>Type_Apartment</th>\n",
       "      <th>Type_Duplex</th>\n",
       "      <th>Type_Single house</th>\n",
       "      <th>Type_Studio</th>\n",
       "      <th>Rooms</th>\n",
       "      <th>Year built</th>\n",
       "      <th>Living space</th>\n",
       "      <th>lng</th>\n",
       "      <th>lat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>645.0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1954.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>8.041672</td>\n",
       "      <td>47.397999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1340.0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1971.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>8.057444</td>\n",
       "      <td>47.379288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1380.0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1968.0</td>\n",
       "      <td>69.0</td>\n",
       "      <td>8.057165</td>\n",
       "      <td>47.378022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1480.0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1976.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>8.057974</td>\n",
       "      <td>47.400780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1500.0</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1968.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>8.057165</td>\n",
       "      <td>47.378022</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Rent   ZIP  Type_Apartment  Type_Duplex  Type_Single house  Type_Studio  \\\n",
       "0   645.0  5000             1.0          0.0                0.0          0.0   \n",
       "1  1340.0  5000             1.0          0.0                0.0          0.0   \n",
       "2  1380.0  5000             1.0          0.0                0.0          0.0   \n",
       "3  1480.0  5000             1.0          0.0                0.0          0.0   \n",
       "4  1500.0  5000             1.0          0.0                0.0          0.0   \n",
       "\n",
       "   Rooms  Year built  Living space       lng        lat  \n",
       "0    1.0      1954.0          28.0  8.041672  47.397999  \n",
       "1    4.0      1971.0          88.0  8.057444  47.379288  \n",
       "2    3.0      1968.0          69.0  8.057165  47.378022  \n",
       "3    3.5      1976.0          81.0  8.057974  47.400780  \n",
       "4    4.0      1968.0          80.0  8.057165  47.378022  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = './Images/rentalprice.csv'\n",
    "rental = pd.read_csv(path)\n",
    "rental.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12599\n",
      "8400\n"
     ]
    }
   ],
   "source": [
    "# To separate training and testing data from each other\n",
    "\n",
    "import random\n",
    "Target = 0\n",
    "\n",
    "#Data Selection\n",
    "Mat_all = rental.ix[:,:].copy()\n",
    "\n",
    "\n",
    "a = range(Mat_all.shape[1])\n",
    "ind_col = a !=np.tile(Target,(len(a)))\n",
    "Tr_data_size = int(.6*Mat_all.shape[0])\n",
    "print Tr_data_size\n",
    "ind_row_train = random.sample(range(Mat_all.shape[0]),Tr_data_size)\n",
    "ind_row_test = range(Mat_all.shape[0])\n",
    "for i in ind_row_train:\n",
    "    ind_row_test.remove(i)\n",
    "print len(ind_row_test)\n",
    "\n",
    "\n",
    "#This is fixed always\n",
    "y_tr = Mat_all.values[ind_row_train].astype(float)\n",
    "y_tr= y_tr[:,Target].astype(float)\n",
    "\n",
    "y_ts = Mat_all.values[ind_row_test].astype(float)\n",
    "y_ts = y_ts[:,Target].astype(float)\n",
    "\n",
    "\n",
    "\n",
    "X_tr = Mat_all.values[ind_row_train].astype(float) \n",
    "X_tr = X_tr[:,ind_col].astype(float) \n",
    "            \n",
    "std = X_tr.std(axis=0)\n",
    "randomization = 1e-25*np.random.randn(X_tr.shape[0],1)\n",
    "ind_std0 = std==0\n",
    "X_tr[:,ind_std0] = X_tr[:,ind_std0] + randomization \n",
    "            \n",
    "X_ts = Mat_all.values[ind_row_test].astype(float)\n",
    "X_ts = X_ts[:,ind_col].astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dimension of training data for polynomial degree 1 is 11\n",
      "degree 1 is done in 0.00388598442078 seconds\n",
      "dimension of training data for polynomial degree 2 is 66\n",
      "degree 2 is done in 0.0329880714417 seconds\n",
      "dimension of training data for polynomial degree 3 is 286\n",
      "degree 3 is done in 0.225691080093 seconds\n",
      "dimension of training data for polynomial degree 4 is 1001\n",
      "degree 4 is done in 5.10628604889 seconds\n",
      "dimension of training data for polynomial degree 5 is 3003\n",
      "degree 5 is done in 256.789484978 seconds\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11731d910>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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t3f8N+GGm/15xbK8sc8W5vXYCkwZ4P7J/kwV/BOHuzwAHBpjlOuD7HngWqDKz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\nSEb/H9T1pxeZ2w7DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178d9c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "y_preds_tr = pd.DataFrame(data=np.zeros((y_tr.shape[0],0)))\n",
    "ARE_tr = pd.DataFrame(data=np.zeros((y_tr.shape[0],0)))\n",
    "MAE_tr = pd.DataFrame(data=np.zeros((1,0)))\n",
    "\n",
    "y_preds_ts = pd.DataFrame(data=np.zeros((y_ts.shape[0],0)))\n",
    "ARE_ts = pd.DataFrame(data=np.zeros((y_ts.shape[0],0)))\n",
    "MAE_ts = pd.DataFrame(data=np.zeros((1,0)))\n",
    "\n",
    "training_times = []\n",
    "max_degree = 6\n",
    "for degree in range(1,max_degree):   \n",
    "    poly = PolynomialFeatures(degree=degree)\n",
    "    X_tr_ = poly.fit_transform(X_tr)\n",
    "    X_ts_ = poly.fit_transform(X_ts)\n",
    "    \n",
    "    t0 = time.time()\n",
    "    regr = linear_model.LinearRegression()\n",
    "    regr.fit(X_tr_, y_tr)\n",
    "    \n",
    "    print 'dimension of training data for polynomial degree {} is {}'.format(degree,X_tr_.shape[1])\n",
    "    training_times.append(time.time()-t0)\n",
    "    print 'degree {} is done in {} seconds'.format(degree,time.time()-t0)\n",
    "    \n",
    "    y_pred_tr = regr.predict(X_tr_)[:]\n",
    "    y_pred_ts = regr.predict(X_ts_)[:]\n",
    "    \n",
    "    \n",
    "    y_preds_tr['degree-{}'.format(degree)] = y_pred_tr\n",
    "    MAE_tr['degree-{}'.format(degree)] = np.mean(np.abs(y_pred_tr-y_tr))\n",
    "    ARE_tr['degree-{}'.format(degree)] = 100*np.abs(y_pred_tr-y_tr)/y_tr\n",
    "    \n",
    "    \n",
    "    y_preds_ts['degree-{}'.format(degree)] = y_pred_ts\n",
    "    MAE_ts['degree-{}'.format(degree)] = np.mean(np.abs(y_pred_ts-y_ts))\n",
    "    ARE_ts['degree-{}'.format(degree)] = 100*np.abs(y_pred_ts-y_ts)/y_ts\n",
    "\n",
    "plt.plot(range(1,max_degree),training_times)\n",
    "plt.xlabel('polynomials degree')\n",
    "plt.ylabel('training time')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>median</th>\n",
       "      <th>1</th>\n",
       "      <th>5</th>\n",
       "      <th>10</th>\n",
       "      <th>15</th>\n",
       "      <th>20</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>degree-1</th>\n",
       "      <td>13.89</td>\n",
       "      <td>4.08</td>\n",
       "      <td>19.76</td>\n",
       "      <td>37.39</td>\n",
       "      <td>53.09</td>\n",
       "      <td>64.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-2</th>\n",
       "      <td>13.08</td>\n",
       "      <td>4.52</td>\n",
       "      <td>21.61</td>\n",
       "      <td>40.04</td>\n",
       "      <td>55.67</td>\n",
       "      <td>67.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-3</th>\n",
       "      <td>12.51</td>\n",
       "      <td>4.65</td>\n",
       "      <td>21.80</td>\n",
       "      <td>41.80</td>\n",
       "      <td>57.36</td>\n",
       "      <td>70.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-4</th>\n",
       "      <td>11.14</td>\n",
       "      <td>4.94</td>\n",
       "      <td>23.95</td>\n",
       "      <td>45.65</td>\n",
       "      <td>62.54</td>\n",
       "      <td>74.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-5</th>\n",
       "      <td>10.55</td>\n",
       "      <td>5.29</td>\n",
       "      <td>25.60</td>\n",
       "      <td>47.89</td>\n",
       "      <td>64.62</td>\n",
       "      <td>76.96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          median     1      5     10     15     20\n",
       "degree-1   13.89  4.08  19.76  37.39  53.09  64.87\n",
       "degree-2   13.08  4.52  21.61  40.04  55.67  67.09\n",
       "degree-3   12.51  4.65  21.80  41.80  57.36  70.00\n",
       "degree-4   11.14  4.94  23.95  45.65  62.54  74.66\n",
       "degree-5   10.55  5.29  25.60  47.89  64.62  76.96"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quality = [1,5,10,15,20]\n",
    "percentiles = pd.DataFrame(data= np.zeros((len(quality),ARE_tr.shape[1])),index=quality,columns=ARE_tr.columns)\n",
    "for percent in quality:\n",
    "    for m in range(ARE_tr.shape[1]):\n",
    "        a = ARE_tr.values[:,m]\n",
    "        n = float(a.shape[0])\n",
    "        percentiles.ix[percent,m]= 100*a[a<=percent].shape[0]/n\n",
    "#         percentiles.ix[percent,m]= 100*(a<=percent).sum()/float(a.shape[0])\n",
    "percentiles\n",
    "med_error = pd.DataFrame(data=ARE_tr.median(axis=0).values[:][np.newaxis,:].copy(),columns=ARE_tr.columns,index=['median'])\n",
    "med_error\n",
    "percentiles = pd.concat((med_error,percentiles))\n",
    "percentiles.ix[:] = np.around(percentiles.values[:],decimals=2)\n",
    "# percentiles.index.name = 'ARE'\n",
    "percentiles.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>median</th>\n",
       "      <th>1</th>\n",
       "      <th>5</th>\n",
       "      <th>10</th>\n",
       "      <th>15</th>\n",
       "      <th>20</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>degree-1</th>\n",
       "      <td>14.13</td>\n",
       "      <td>3.73</td>\n",
       "      <td>19.20</td>\n",
       "      <td>37.00</td>\n",
       "      <td>52.21</td>\n",
       "      <td>64.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-2</th>\n",
       "      <td>13.23</td>\n",
       "      <td>4.30</td>\n",
       "      <td>20.88</td>\n",
       "      <td>39.21</td>\n",
       "      <td>55.18</td>\n",
       "      <td>66.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-3</th>\n",
       "      <td>12.63</td>\n",
       "      <td>4.21</td>\n",
       "      <td>21.92</td>\n",
       "      <td>41.27</td>\n",
       "      <td>56.63</td>\n",
       "      <td>68.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-4</th>\n",
       "      <td>11.47</td>\n",
       "      <td>4.88</td>\n",
       "      <td>24.49</td>\n",
       "      <td>45.04</td>\n",
       "      <td>60.71</td>\n",
       "      <td>72.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>degree-5</th>\n",
       "      <td>11.05</td>\n",
       "      <td>5.39</td>\n",
       "      <td>25.15</td>\n",
       "      <td>46.42</td>\n",
       "      <td>62.62</td>\n",
       "      <td>74.13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          median     1      5     10     15     20\n",
       "degree-1   14.13  3.73  19.20  37.00  52.21  64.55\n",
       "degree-2   13.23  4.30  20.88  39.21  55.18  66.80\n",
       "degree-3   12.63  4.21  21.92  41.27  56.63  68.65\n",
       "degree-4   11.47  4.88  24.49  45.04  60.71  72.76\n",
       "degree-5   11.05  5.39  25.15  46.42  62.62  74.13"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quality = [1,5,10,15,20]\n",
    "percentiles = pd.DataFrame(data= np.zeros((len(quality),ARE_ts.shape[1])),index=quality,columns=ARE_ts.columns)\n",
    "for percent in quality:\n",
    "    for m in range(ARE_ts.shape[1]):\n",
    "        a = ARE_ts.values[:,m]\n",
    "        n = float(a.shape[0])\n",
    "        percentiles.ix[percent,m]= 100*a[a<=percent].shape[0]/n\n",
    "#         percentiles.ix[percent,m]= 100*(a<=percent).sum()/float(a.shape[0])\n",
    "percentiles\n",
    "med_error = pd.DataFrame(data=ARE_ts.median(axis=0).values[:][np.newaxis,:].copy(),columns=ARE_ts.columns,index=['median'])\n",
    "med_error\n",
    "percentiles = pd.concat((med_error,percentiles))\n",
    "percentiles.ix[:] = np.around(percentiles.values[:],decimals=2)\n",
    "# percentiles.index.name = 'ARE'\n",
    "percentiles.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Limits of Regression Models\n",
    "## Non-continuous patterns (Clustered Data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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faNTkUhSCUvTZ5ub8OV0LC3SugwfJBn74MK0MeQXW0kLXfOiQt1I9r3b4u9gt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\nLiIiihQGLiIiipT/BxyDa980gyx2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1176ef050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 500\n",
    "x1= np.random.normal(loc=17,scale=5,size=N)[:,np.newaxis]\n",
    "x2= np.random.normal(loc=0,scale=5,size=N)[:,np.newaxis]\n",
    "y = 3*x1 + np.random.normal(loc=.0, scale=.4, size=N)[:,np.newaxis]\n",
    "# y = 2*x1\n",
    "x1 = np.concatenate((np.random.normal(loc=10,scale=.9,size=N) , np.random.normal(loc=13,scale=.2,size=N),np.random.normal(loc=5,scale=.1,size=N)))[:,np.newaxis]\n",
    "\n",
    "\n",
    "y =-.1*x1**3 + 2*x1*x1 + 7*np.sin(x1) + 3*np.sqrt(x1)+ 1*np.random.normal(loc=30.0, scale=4.7, size=len(x1))[:,np.newaxis]\n",
    "\n",
    "# x_tmp = x1.copy()\n",
    "# x1 = y\n",
    "# y = x_tmp\n",
    "\n",
    "x1 = Data[:,0][:,np.newaxis]\n",
    "y = Data[:,1][:,np.newaxis]\n",
    "\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax1= plt.subplot(111)\n",
    "plt.plot(x1,y,'.r',markersize=5,alpha=1 );\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XLqU0WlDAz8jlmv59OJ2MqgmXU+cA0yb2OPgDpdQRpdTjSqniWAcppR5SSu1T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\n2BVFURyGCruiKIrDUGFXFEVxGP8P/2XzYRLBAOQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117dba890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "interact(polynomial_regr,degree=(1,50,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "# Extensions to the original regression problem:\n",
    "## Local Polynomial Regression\n",
    "## Nonlinear Regression and curve fitting\n",
    "## Basis functions\n",
    "## Generalized Linear Models\n",
    "\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# <a></a>\n",
    "# <a></a>\n",
    "\n",
    "\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "# An Example: Local Polynomial Regression\n",
    "### Using kernel smoother to give more imortance on local information.\n",
    "\n",
    "### Original Least Squares Model:\n",
    "###  $$S = \\sum_{i = 1}^n (x_i - f(x_i,\\beta))^2 = \\sum_{i = 1}^n r^2$$\n",
    "\n",
    "\n",
    "### Local Least Squares Model:\n",
    "\n",
    "### $$\\hat{f}_n(x) = argmin_{f} \\sum_i K\\left(\\frac{x-x_i}{h}\\right) \\left(y_i -  f(x-x_i)\\right)^2$$\n",
    "\n",
    "Compare it with the kernel denisty learning we had above. \n",
    "\n",
    "\n",
    "### $$\\hat{f}_n(x) = argmin_{f} \\sum_i K\\left(\\frac{x-x_i}{h}\\right) \\left(y_i - a_0 - a_1(x-x_i) - \\ldots - a_n\\frac{(x-x_i)^n}{n!}\\right)^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T3Wd4WC7dHrirr7aFJP4UYTxeWN8amVMoZIRUI64gNTXJAMnhYRGPRML2avkr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11268a290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1500\n",
    "x1= np.random.normal(loc=17,scale=5,size=N)[:,np.newaxis]\n",
    "x2= np.random.normal(loc=0,scale=5,size=N)[:,np.newaxis]\n",
    "y = 3*x1 + np.random.normal(loc=.0, scale=.4, size=N)[:,np.newaxis]\n",
    "# y = 2*x1\n",
    "x1 = np.concatenate((np.random.normal(loc=10,scale=.9,size=N) , np.random.normal(loc=13,scale=.2,size=N),np.random.normal(loc=5,scale=.1,size=N)))[:,np.newaxis]\n",
    "\n",
    "\n",
    "y =-.1*x1**3 + 2*x1*x1 + 7*np.sin(x1) + 3*np.sqrt(x1)+ 1*np.random.normal(loc=30.0, scale=4.7, size=len(x1))[:,np.newaxis]\n",
    "\n",
    "y[y<100] =y[y<100] +100\n",
    "y[x1>12] =y[x1>12] -50\n",
    "# x_tmp = x1.copy()\n",
    "# x1 = y\n",
    "# y = x_tmp\n",
    "\n",
    "# x1 = Data[:,0][:,np.newaxis]\n",
    "# y = Data[:,1][:,np.newaxis]\n",
    "\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax1= plt.subplot(111)\n",
    "plt.plot(x1,y,'.r',markersize=5,alpha=1 );"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# It is use is pretty similar to the previous one\n",
    "# Here, we use PyQt library\n",
    "\n",
    "import pyqt_fit.nonparam_regression as smooth\n",
    "from pyqt_fit import npr_methods\n",
    "import time\n",
    "poly_order=5\n",
    "\n",
    "\n",
    "\n",
    "y_preds_ = pd.DataFrame(data=np.zeros((y.shape[0],0)))\n",
    "ARE = pd.DataFrame(data=np.zeros((y.shape[0],0)))\n",
    "MAE = pd.DataFrame(data=np.zeros((1,0)))\n",
    "\n",
    "\n",
    "t0 = time.time()\n",
    "regr = smooth.NonParamRegression(x1.T, y[:,0], method=npr_methods.LocalPolynomialKernel(q=poly_order))\n",
    "name = 'Poly-nonparametric-'+str(poly_order)\n",
    "regr.fit()\n",
    "y_preds_local = regr(x1.T)[:,np.newaxis]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "print 'local polynomial with degree {} is done in {} seconds'.format(poly_order,time.time()-t0)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "y_preds_['local-degree-{}'.format(poly_order)] = y_preds_local\n",
    "MAE['local-degree-{}'.format(poly_order)] = np.mean(np.abs(y_preds_local-y))\n",
    "ARE['local-degree-{}'.format(poly_order)] = 100*np.abs(y_preds_local-y)/y\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "t0 = time.time()\n",
    "poly = PolynomialFeatures(degree=degree)\n",
    "x1_ = poly.fit_transform(x1)\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(x1_, y)\n",
    "y_preds_gloabal = regr.predict(x1_)\n",
    "print 'Global polynomial with degree {} is done in {} seconds'.format(poly_order,time.time()-t0)\n",
    "\n",
    "\n",
    "\n",
    "y_preds_['global-degree-{}'.format(poly_order)] = y_preds_gloabal\n",
    "MAE['global-degree-{}'.format(poly_order)] = np.mean(np.abs(y_preds_gloabal-y))\n",
    "ARE['global-degree-{}'.format(poly_order)] = 100*np.abs(y_preds_gloabal-y)/y\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "figure =plt.figure(figsize=(7,7))\n",
    "plt.plot(x1, y, '.', alpha=0.1, label='Data')\n",
    "plt.plot(x1, y_preds_local, '.g', alpha=1, label='Local')\n",
    "plt.plot(x1, y_preds_gloabal, '.r', alpha=1, label='Global')\n",
    "plt.legend(bbox_to_anchor = (1.3,1))\n",
    "\n",
    "MAE\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "quality = [1,5,10,15,20]\n",
    "percentiles = pd.DataFrame(data= np.zeros((len(quality),ARE.shape[1])),index=quality,columns=ARE.columns)\n",
    "for percent in quality:\n",
    "    for m in range(ARE.shape[1]):\n",
    "        a = ARE.values[:,m]\n",
    "        n = float(a.shape[0])\n",
    "        percentiles.ix[percent,m]= 100*a[a<=percent].shape[0]/n\n",
    "#         percentiles.ix[percent,m]= 100*(a<=percent).sum()/float(a.shape[0])\n",
    "percentiles\n",
    "med_error = pd.DataFrame(data=ARE.median(axis=0).values[:][np.newaxis,:].copy(),columns=ARE.columns,index=['median'])\n",
    "med_error\n",
    "percentiles = pd.concat((med_error,percentiles))\n",
    "percentiles.ix[:] = np.around(percentiles.values[:],decimals=2)\n",
    "# percentiles.index.name = 'ARE'\n",
    "percentiles.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "<hr style=\"height:4px;border:none;color:stillblue;background-color:black;\" />\n",
    "\n",
    "\n",
    "# (Possibly) in the next session\n",
    "* ** practice with scikit learn using different regression models**\n",
    "    * Cross validation\n",
    "    * performance evaluation\n",
    "* **Structure Learning and Manifold learning** \n",
    "* **Space transformations and Representation learning**"
   ]
  }
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