hw4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " # Homework #4\n",
    " \n",
    " By 👦Franklin Marsh👦\n",
    " \n",
    " MATH0154 Computational Statistics\n",
    " \n",
    " with Dr. Gabe Chandler."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " # Problem 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider drawing data from a mixture distribution of two normals, one with $\\mu=7$ and one with $\\mu=10$, both having $\\sigma^2=.5$.  The observation is drawn from the first normal with probability $\\delta$.  Thus, \n",
    "$$f(x)=\\delta f(x|7, .5^2) + (1-\\delta)f(x|10, .5^2)$$\n",
    "where the RHS functions are normal pdfs. [5pt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f <- function(x, delta = 0.7) {\n",
    "    #\n",
    "    # produces the pdf as described in problem 1.\n",
    "    #\n",
    "    # Args:\n",
    "    #    x: the value at which to evalueate the pdf\n",
    "    #    delta: the delta value in the pdf formula\n",
    "    # Returns:\n",
    "    #    y: pdf value evalueated at x\n",
    "    \n",
    "    return(delta*dnorm(x,7,0.25) + (1 - delta)*dnorm(x,10,0.25))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's display a plot of the pdf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5h197rrDjvbZp/sqxEgQIAAAQIEJi2g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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(seq(6,11,0.01),f(seq(6,11,0.01), 0.7), type= 'l')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## a)\n",
    "a.  Write a function that samples from this distribution (so it will call $\\delta$ as an argument).\\\\[5pt]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Draw <- function(n, delta) {\n",
    "    #\n",
    "    # Draws n random variates from the distribution f.\n",
    "    #\n",
    "    # Args:\n",
    "    #    n: number of random variates to draw from the distribution.\n",
    "    #    delta: delta parameter in distribution.\n",
    "    # Returns:\n",
    "    #    out: a list of n random variates drawn from f.\n",
    "    \n",
    "    out <- c()\n",
    "    \n",
    "    for (i in (1:n)) {\n",
    "        \n",
    "        if (runif(1) < delta) { #if a random uniform is less than delta\n",
    "            out[i] <- rnorm(1,7,0.25) \n",
    "        }\n",
    "    \n",
    "        else {\n",
    "            out[i] <- rnorm(1,10,0.25) \n",
    "        }\n",
    "        }\n",
    "    return(out)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## b)\n",
    "b.  Let $\\delta=.7$.  Sample $n=100$ observations from this distribution and present a histogram.\\\\[5pt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAwIgEdhzRWA2VwH4huPPIGU7K+M8duYHhEyBAgAABAgQWCiiQFtI40KDA\nazOmxyeXNzi2IUPaNZ22JE8a0lkfAgQIECBAgMAYBXYa46CNebQC9Xx/U/KEkQpsybj9mx/p\n5Bs2AQIECBAgMEzgOsO66UWAAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQ\nSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9A\ngdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIE\nCAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECA\nAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIE\nCBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKN\nAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1\nP8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQID\nBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECA\nAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIE\nCBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CA\nAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+x\nERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF\n0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECg\nfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIE\nCBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECA\nAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQE\nCBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQ\nSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9A\ngdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIE\nCAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECA\nAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIE\nCBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKN\nAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1\nP8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQID\nBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECA\nAIH2BRRI7c+xERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIE\nCBAgQIDAQAEF0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CA\nAAECBAgQIECgfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+x\nERIgQIAAAQIECBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF\n0kAo3QgQIECAAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECg\nfQEFUvtzbIQECBAgQIAAAQIECAwUUCANhNKNAAECBAgQIECAAIH2BRRI7c+xERIgQIAAAQIE\nCBAgMFBAgTQQSjcCBAgQIECAAAECBNoXUCC1P8dGSIAAAQIECBAgQIDAQAEF0kAo3QgQIECA\nAAECBAgQaF9AgdT+HBshAQIECBAgQIAAAQIDBRRIA6F0I0CAAAECBAgQIECgfQEFUvtzbIQE\nCBAgQIAAAQIECAwU2Glgv5a67ZnB7JHsmnwjuTC5NNEIECBAgAABAgQIEBi5wFiuIN0l8/za\n5KvJ+ckXk9OSs5Mqkk5PjklunGgECBAgQIAAAQIECIxUYAxXkF6QuT1yMr9fyvKEpIqkKozq\nStJeyQHJk5Mjkqcnb040AgQIECBAgAABAgQINCXwmIzme8m7k7uuMbIdc+zw5BNJ9b93orUn\nsCVDqoy1bcnAKxoBAgQIECBAgMACgdbfYveojPsLSS1PXGBQu6so+mDy4OSS5FcSjQABAgQI\nECBAgACBkQm0XiAdnPmst9RdNnBeL0i/k5P9B/bXjQABAgQIECBAgACBhgRaL5C+nLm6W7Lz\nwDmrb7iroqq+wEEjQIAAAQIECBAgQGBkAq0XSK/LfN4ueWtyyBpzW59BOiw5Lrl+8o5EI0CA\nAAECBAgQIEBgZAKtf4tdfRvdPslRycOTc5L6au/zkouT3ZP6FrtbJPsmVyTPSj6SaAQIECBA\ngAABAgQIjEyg9QKpvnzhZck7k6OT+qa62StJ38y+c5OXJK9Izko0AgQIECBAgAABAgRGKNB6\ngdRNaX2T3WMnG3XVqP7+0fWS+sOxFyUb3W6WO6yibOhnn6pfXem6UVJFnUaAAAECBAgQIECA\nwLUgMJYCqU9bb62rdG3XrNRb7E5Prux2XsPl13L7v0h2GXg/B6bfM5MqlC5PNAIECBAgQIAA\nAQIECGwzgVvmnp+aPDrZbfIo9ZmjtyT1d4/qqs2lSb0Nb+hVn3TdsHav3FOdw9CCasMeeGR3\ntCXjrYy1bcnAKxoBAgQIECBAgMACgTFcQXpGxv7S3vjPyPo9k5cnRyQXJu9O7pw8N7l18vOJ\nRoAAAQIECBAgQIDAyARa/5rvn8p81pcvnJr8VlLfUFefQfpw8nPJ7yX7JQ9NbpW8Ian9P5lo\nBAgQIECAAAECBAiMTKD1K0j1lrp661x9c10tq9UXNrw9OTup4qn73NG3s/6U5CGT/FOWGgEC\nBAgQIECAAAECIxJo/QpSFUb1x1+74qim9p+TKobelXTFUVavat/Kf09LbnP1pv8SIECAAAEC\nBAgQIDAmgdYLpAsymVUk9cf5zWw/P/lMMttumB33SOrvImkECBAgQIAAAQIECIxMoF84tDj0\nepvczZP6koab9gZYb617ZW+7Vuvb616U1Nd+/0uiESBAgAABAgQIECAwMoHWC6T6proTk/qC\nhjOSPZN5rb7Nrj6T9OvJ+5K/STQCBAgQIECAAAECBEYm0HqBVJ81um9ydHJyUm+5m9dukJ31\nN4jqqlJ9o139TSKNAAECBAgQIECAAIGRCbReINV01hcv1GeO6m8fLWp/lwM3SupKUxVVGgEC\nBAgQIECAAAECIxRo/Wu+h05pFVEaAQIECBAgQIAAAQIjFxjDFaSRT7HhEyBAgAABAgQIECAw\nVECBNFRKPwIECBAgQIAAAQIEmhfwFrvmp9gACXxfoL6MZO+kvrVxrO2TGfiZYx28cRMgQIAA\nAQJbF1Agbd1IDwKtCPxYBnKr5OBWBrTkOHZL/zclT1zydroTIECAAAECIxJQII1osg119AI7\nRuCLyW1GKrEl477uSMdu2AQIECBAgMBAAZ9BGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAA\nAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoR\nIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT2\n59gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCg\ngAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQ\nINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAA\nAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQ\nIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2\nQgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBA\nGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0\nL6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAA\nAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQ\nIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAA\nAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC\n6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7Qso\nkNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAA\ngYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQ\nIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAA\nAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoR\nIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT2\n59gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCg\ngAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQ\nINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAA\nAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQ\nIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2\nQgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBA\nGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0\nL6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAA\nAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQ\nIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAA\nAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC\n6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7Qso\nkNqfYyMkQIAAAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAA\ngYECCqSBULoRIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQ\nIECAQPsCCqT259gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAA\nAQIECBAgQGCggAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoR\nIECAAAECBAgQINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT2\n59gICRAgQIAAAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCg\ngAJpIJRuBAgQIECAAAECBAi0L6BAan+OjZAAAQIECBAgQIAAgYECCqSBULoRIECAAAECBAgQ\nINC+gAKp/Tk2QgIECBAgQIAAAQIEBgookAZC6UaAAAECBAgQIECAQPsCCqT259gICRAgQIAA\nAQIECBAYKKBAGgilGwECBAgQIECAAAEC7QsokNqfYyMkQIAAAQIECBAgQGCgwLIF0qtyv49M\ndh54/7oRIECAAAECBAgQIEBgZQSWLZAempG9IzkneXly50QjQIAAAQIECBAgQIBAEwLLFkj3\nyqh/Ozkr+a3kU8lJSe3bJ9EIECBAgAABAgQIECCwsgLLFkhfzUhfkdwtuWPy/yY3Sl6W1FWl\ndyaPTrwFLwgaAQIECBAgQIAAAQKrJbBsgdQf3anZ+L3kgOT+SX0+6dDkbcm5yUuT2yQaAQIE\nCBAgQIAAAQIEVkLgmhRI3QAPysrhyf2Sepvd95K60lRvuzsteUGiESBAgAABAgQIECBAYNML\nrLdAunFG9pvJx5P/TP4g2XuyvHWWd0iqcPr75MjkCYlGgAABAgQIECBAgACBTS2wbIF0REbz\nD0m9he6VyZ2SNyUPSm6Z/H7yhaTaF5OnXLW2ww4PnCwtCBAgQIAAAQIECBAgsGkFdlryzP40\n/asQ+ljy18n/TS5KFrUrcuDM5MRFHewnQIAAAQIECBAgQIDAZhFYtkD6s5z4Pyb12aIh7bx0\nOnBIR30IECBAgAABAgQIECBwbQss+xa7+ma6Ko7qLXP1GaOu7ZeV1yfeSteJWBIgQIAAAQIE\nCBAgsHICyxZIVQgdm7w3OaQ32ltl/XGT/X/Q22+VAAECBAgQIECAAAECKyOwbIH0kozsIUm9\n1e6fe6P8cNYfnHwo+V/JvRONAAECBAgQIECAAAECKyWwzGeQdszIHpm8Pamv+J5t78mOTydn\nJb+QfDTZjG3PnNQeya7JN5ILk0sTjQABAgQIECBAgACBkQsscwXph2P1Q8nxa5h9Occ+mRyw\nRp9r49Bd8qCvTeoP2J6f1FeQ12epzk6qSDo9OSapv++kESBAgAABAgQIECAwUoFlriBdHKP/\nTO68htXOOVafR/rIGn2296EX5AGPnDzol7I8IakiqQqjupK0V1IF3ZOT+jtPT0/enGgECBAg\nQIAAAQIECBBYU+A1OVp/2+ixc3rtln1/lXwvqc8pbYb2mJxEnc+7k7uucUL19sHDk08k1X97\nf4bqXpPH3SVLbdsJbMldV8baPpeBV8batmTgFY0AAQIECBAgsFBgmStIdSd1NeZuSV1h+f3k\nP5L6DM9+yT2T+nzPG5IqSDZDe1RO4gtJLS9b44SqKPpg8uDkzORXko8mGgECBAgQIECAAAEC\nIxJYtkCqz/D8ePLK5P5JFR519aVafZ7nucn/VxubpB2c86i31K1VHPVP9YJsnJzs399pnQAB\nAgQIECBAgACBcQgsWyCVSn1251cnPPUZngOSuupy8WTfZlrUl0bUFa/6bNR3BpxYXQGrouqY\nAX11IUCAAAECBAgQIECgMYHrXMPxXJTbn5JsxuKohva65HbJW5P+H7bN5lSrq2CHJccl10/e\nkWgECBAgQIAAAQIECIxMYD1XkB4Qo8cl+yT1td/dW+yy+v22JWtVnFzbrT4rVed5VPLw5Jyk\n3gp4XlJF3e7JXsktkn2T+gKKZyUfSTQCBAgQIECAAAECBEYmsGyB9HPx+b8DjD4woM/26FJf\nvvCy5J3J0cnhyeyVpG9m37nJS5JXJPWHbjUCBAgQIECAAAECBEYosGyB9IcxujR5cvK+pL60\nYV777ryd1+K+L+SxHzt5/LpqVJ+dul5S519vE9zoVp/L+udkl4F3vOvAfroRIECAAAECBAgQ\nILANBZYpkG6Q87hNUl9gUG9dW8VWn7mqt9Yt+szUdXOsCqhvJd9O1tvqyyGOSnYeeAcHpd/z\nBvbVjQABAgQIECBAgACBTSBQxcWFyYs3wbkscwo3Sed6W+D5SX0DX135uk8yr905O+tteb8/\n7+A23HevyeMOveK0DU+l6bvektFVxto+l4FXxtq2ZOAVjQABAgQIECCwUGCZb7Grt83VZ4vq\nrWrL3G7hg2+HA7vlMT6R1Gen6urQ2cn9kg8mRycaAQIECBAgQIAAAQIEvi+wbKHza7llfanB\nW5LDk/qszd5zUt9utxna7+Ykbp4cmdwsqa/8vkfy6aT+qO1LE40AAQIECBAgQIAAAQJXCSxb\nIB2bW+2TPDqpq0lnJl+fk9/Lvs3Q7p2TqC9iqM8DXTI5oX/Lsoq7DyXPSKqI0ggQIECAAAEC\nBAgQILDDMl/SUFyfSs4d4PaZAX22R5f98yBVCNXfN+q3+ua6n07q2J8kVej9baIRIECAAAEC\nBAgQIDBigWULpF9fMasqfB6U1Fd6z34rXX2T3UOTE5LXJeck9RXmGgECBAgQIECAAAECIxVY\n9i12fab6nNGdkkMmO+trwDdbOz4nVH/z6EXJfnNOroqin0jq7Xf/mDws0QgQIECAAAECBAgQ\nGKnAegqk+mKGejtaXW05OXlxUu2NyVHJZvqjp3+W8/mPpD5rdFbyC8ls+2x2PDj5blLnX23H\nqxf+S4AAAQIECBAgQIDAmASWLZD2Dc6JyWOS05J6C1vXqqh4XlJfglBvadsMrd5WV1e4Xpl8\nKbk8mddOys67J8fNO2gfAQIECBAgQIAAAQLjEFi2QKpCo95ad1hy+6SKpa4dkZWjkzskj+92\nboJl/XHY30pumbxjjfM5Pccektwzeesa/RwiQIAAAQIECBAgQKBRgWULpAfG4dXJh+d4XJl9\nRyb1DXGHzjm+GXbV2+i21uoPy56ytU6OEyBAgAABAgQIECDQnsAyBdLuGf6eSX1mZ1H7Tg6c\nmlQ/jQABAgQIECBAgAABAislsEyBVF+L/ZXkHmuMsIqoeotdfT5JI0CAAAECBAgQIECAwEoJ\nLFMg1cDenTwpeVqyW9JvN8zG65P6Wu339A9YJ0CAAAECBAgQIECAwCoILFsgPTODOjd5VVJ/\nQ+jeya2S+vKD+pKDRyZbkuMTjQABAgQIECBAgAABAislsGyBdGFGd9fkmKS+yvsmSf0B1iqM\nqj09qStMGgECBAgQIECAAAECBFZOYKd1nPHXc5unJr+R3CK5aXJGUleWNAIECBAgQIAAAQIE\nCKyswHoKpG6w9bXeX5ik22dJgAABAgQIECBAgACBlRVY9i12KztQJ06AAAECBAgQIECAAIGt\nCSx7Bak+e1SfO9pa+5t0qGgECBAgQIAAAQIECBBYGYFlC6SfyMhuuZXRnZ3jH9hKH4cJECBA\ngAABAgQIECCw6QSWLZDukhHMvi2vtm+W3DF5WVJXjmqpESBAgAABAgQIECBAYKUEli2QLlow\nuvOy/9+TU5NPJR9Kjk00AgQIECBAgAABAgQIrIzA7NWga3riJ+UOzkzqrXgaAQIECBAgQIAA\nAQIEVkpgowukXTP6vZN9VkrByRIgQIAAAQIECBAgQCACy77F7nq5zY5z5Op+bpwcleyWfDLR\nCBAgQIAAAQIECBAgsFICyxZI/5HRbe1b7OqPx/7FSik4WQIECBAgQIAAAQIECERg2QLpg7nN\nf86R+272XZycnLw2WfRlDjmkESBAgAABAgQIECBAYHMKLFsgPWFzDsNZESBAgAABAgQIECBA\n4JoLbPSXNFzzM3IPBAgQIECAAAECBAgQuJYElr2CdEzO8ybrONc35DZvXcft3IQAAQIECBAg\nQIAAAQLbTWDZAungnNkdk/qmumpXJhcmeyXzvt0uu69qH+9WLAkQIECAAAECBAgQILBZBZZ9\ni93jMpBLk2OTuyX1td83miwfkuVnkiqG6ipT/T2kLi/LukaAAAECBAgQIECAAIFNLbDsFaS/\nzGg+lTw6qW+u69rlWTku+XTy2eRnktckGgECBAgQIECAAAECBFZGYJkrSLtmVIcmb0z6xVF/\nsGdn46Tkfv2d1gkQIECAAAECBAgQILAKAssUSFdkQN9I9l9jYDvn2EHJeWv0cYgAAQIECBAg\nQIAAAQKbUmCZAqm+kOE9yXOTe84ZzfWzr/uWu3q7nUaAAAECBAgQIECAAIGVElj2M0gvyuju\nm9QXMXwwqS9luCS5WfKAZJ+kPqf0rkQjQIAAAQIECBAgQIDASgksWyCdnNHdI/mr5LDk8KRr\n/5WVpySv7XZYEiBAgAABAgQIECBAYJUEli2QamxfTuorvevtebdN6iu9T0/OSb6XaAQIECBA\ngAABAgQIEFhJgWU+gzQ7wPpWu/pShm8n9e119RkkjQABAgQIECBAgAABAisrsJ4C6YCM9m+T\n+oOx9Za7FyfV3pgclVThpBEgQIAAAQIECBAgQGDlBJZ9i92+GeGJyd5JfUFD/6rRjtl+XvKo\n5O5JXVnSCBAgQIAAAQIECBAgsDICy15BemVG9kNJfUHD7ZMqlrp2RFaOTu6QPL7baUmAAAEC\nBAgQIECAAIFVEVi2QHpgBvbq5MNzBnhl9h2ZXJQcOue4XQQIECBAgAABAgQIENjUAssUSLtn\nJHsmn11jRN/JsVMn/dbo5hABAgQIECBAgAABAgQ2n8AyBdLFOf2vJPV3kBa1KqLqLXanLepg\nPwECBAgQIECAAAECBDarwDIFUo3h3cmTkqcluyX9dsNsvD7ZI3lP/4B1AgQIECBAgAABAgQI\nrILAsgXSMzOoc5NXJfWHYe+d3Cp5R1J/LPaRyZbk+EQjQIAAAQIECBAgQIDASgksWyBdmNHd\nNTkmuV5yk2S/pAqjak9P6gqTRoAAAQIECBAgQIAAgZUTWPbvINUAv548NfmN5BbJTZMzkrqy\npBEgQIAAAQIECBAgQGBlBZYtkOorvr+V/M/kiuQLk2ShESBAgAABAgQIECBAYLUFlnmL3a4Z\nav0B2J9OqjjSCBAgQIAAAQIECBAg0JTAMgXS5Rn5Jcn1kx2bUjAYAgQIECBAgAABAgQIRGCZ\nAul76f/oidqxWf5kclBSf/toNnW1SSNAgAABAgQIECBAgMBKCSxTINXAXpzUFaR6m91xyeeT\ni+bkOdmnESBAgAABAgQIECBAYKUElv2ShtMyugsGjPCzA/roQoAAAQIECBAgQIAAgU0lsGyB\n9KRNdfZOhgABAgQIECBAgAABAhsosLW32B2ex3rABj6euyJAgAABAgQIECBAgMCmFdjaFaRX\n5sz3SG45M4I7ZXvv5P0z+20SIECAAAECBAgQIEBgZQW2dgVp0cCOyoH3LTpoPwECBAgQIECA\nAAECBFZRYL0F0iqO1TkTIECAAAECBAgQIEBgTQEF0po8DhIgQIAAAQIECBAgMCYBBdKYZttY\nCRAgQIAAAQIECBBYU0CBtCaPgwQIECBAgAABAgQIjElAgTSm2TZWAgQIECBAgAABAgTWFNja\n13zXjfdM/mTmXm4/2Z7d33V7T1be221YEiBAgAABAgQIECBAYBUEhhRI9XeQnr1gMIv2fzP9\nFUgL0OwmQIAAAQIECBAgQGBzCmytQHpeTvuG6zj1k9dxGzchQIAAAQIECBAgQIDAtSqwtQLp\nH67Vs/PgBAgQIECAAAECBAgQ2I4CvqRhO2J7KAIECBAgQIAAAQIENreAAmlzz4+zI0CAAAEC\nBAgQIEBgOwookLYjtociQIAAAQIECBAgQGBzCyiQNvf8ODsCBAgQIECAAAECBLajgAJpO2J7\nKAIECBAgQIAAAQIENrfA1r7FbnOfvbMjQIAAAQIECGxd4Hbpct+td2u6x4czutOaHqHBEdgg\nAQXSBkG6GwIECBAgQGDTCtQftv/Z5L827Rlu2xO7Se7+LcmvbtuHce8E2hBQILUxj0ZBgAAB\nAgQILBaojxS8LXnC4i5NH9mS0flYRdNTbHAbKeAfy0Zqui8CBAgQIECAAAECBFZaQIG00tPn\n5AkQIECAAAECBAgQ2EgBBdJGarovAgQIECBAgAABAgRWWkCBtNLT5+QJECBAgAABAgQIENhI\nAQXSL/GmtAAALMNJREFURmq6LwIECBAgQIAAAQIEVlpAgbTS0+fkCRAgQIAAAQIECBDYSAEF\n0kZqui8CBAgQIECAAAECBFZaQIG00tPn5AkQIECAAAECBAgQ2EgBBdJGarovAgQIECBAgAAB\nAgRWWkCBtNLT5+QJECBAgAABAgQIENhIAQXSRmq6LwIECBAgQIAAAQIEVlpAgbTS0+fkCRAg\nQIAAAQIECBDYSAEF0kZqui8CBAgQIECAAAECBFZaYKeVPnsnT4AAAQIECBAgsDWBO6bDjyY/\nsbWODR9/Zcb2Jw2Pz9A2UECBtIGY7ooAAQIECBAgsAkF9sg5XZL87iY8t+1xSk/Ng1SBqBEY\nJKBAGsSkEwECBAgQIEBgpQWqQHrzSo9g/Sf/4PXf1C3HKOAzSGOcdWMmQIAAAQIECBAgQGCu\ngAJpLoudBAgQIECAAAECBAiMUUCBNMZZN2YCBAgQIECAAAECBOYKKJDmsthJgAABAgQIECBA\ngMAYBRRIY5x1YyZAgAABAgQIECBAYK6AAmkui50ECBAgQIAAAQIECIxRQIE0xlk3ZgIECBAg\nQIAAAQIE5gookOay2EmAAAECBAgQIECAwBgFFEhjnHVjJkCAAAECBAgQIEBgroACaS6LnQQI\nECBAgAABAgQIjFFAgTTGWTdmAgQIECBAgAABAgTmCiiQ5rLYSYAAAQIECBAgQIDAGAUUSGOc\ndWMmQIAAAQIECBAgQGCugAJpLoudBAgQIECAAAECBAiMUUCBNMZZN2YCBAgQIECAAAECBOYK\nKJDmsthJgAABAgQIECBAgMAYBRRIY5x1YyZAgAABAgQIECBAYK6AAmkui50ECBAgQIAAAQIE\nCIxRQIE0xlk3ZgIECBAgQIAAAQIE5gookOay2EmAAAECBAgQIECAwBgFFEhjnHVjJkCAAAEC\nBAgQIEBgroACaS6LnQQIECBAgAABAgQIjFFAgTTGWTdmAgQIECBAgAABAgTmCiiQ5rLYSYAA\nAQIECBAgQIDAGAUUSGOcdWMmQIAAAQIECBAgQGCugAJpLoudBAgQIECAAAECBAiMUUCBNMZZ\nN2YCBAgQIECAAAECBOYKKJDmsthJgAABAgQIECBAgMAYBRRIY5x1YyZAgAABAgQIECBAYK6A\nAmkui50ECBAgQIAAAQIECIxRQIE0xlk3ZgIECBAgQIAAAQIE5gookOay2EmAAAECBAgQIECA\nwBgFFEhjnHVjJkCAAAECBAgQIEBgroACaS6LnQQIECBAgAABAgQIjFFAgTTGWTdmAgQIECBA\ngAABAgTmCiiQ5rLYSYAAAQIECBAgQIDAGAUUSGOcdWMmQIAAAQIECBAgQGCugAJpLoudBAgQ\nIECAAAECBAiMUUCBNMZZN2YCBAgQIECAAAECBOYKKJDmsthJgAABAgQIECBAgMAYBRRIY5x1\nYyZAgAABAgQIECBAYK6AAmkui50ECBAgQIAAAQIECIxRQIE0xlk3ZgIECBAgQIAAAQIE5goo\nkOay2EmAAAECBAgQIECAwBgFFEhjnHVjJkCAAAECBAgQIEBgroACaS6LnQQIECBAgAABAgQI\njFFAgTTGWTdmAgQIECBAgAABAgTmCiiQ5rLYSYAAAQIECBAgQIDAGAUUSGOcdWMmQIAAAQIE\nCBAgQGCuwE5z97a9c88Mb49k1+QbyYXJpYlGgAABAgQIECBAgMDIBcZyBekumefXJl9Nzk++\nmJyWnJ1UkXR6ckxy40QjQIAAAQIECBAgQGCkAmO4gvSCzO2Rk/n9UpYnJFUkVWFUV5L2Sg5I\nnpwckTw9eXOiESBAgAABAgQIECAwMoHWC6THZD6rODoueV5yYjKv7ZidhyUvSd6UnJF8NNEI\nECBAgAABAgQIEBiRQOtvsXtU5vILSS0XFUc13d9LPpg8OLkk+ZVEI0CAAAECBAgQIEBgZAKt\nF0gHZz7rLXWXDZzXC9Lv5GT/gf11I0CAAAECBAgQIECgIYHWC6QvZ67uluw8cM7qG+6qqKov\ncNAIECBAgAABAgQIEBiZQOsF0usyn7dL3pocssbcdp9Bqs8qXT95xxp9HSJAgAABAgQIECBA\noFGB1r+kob6Nbp/kqOThyTnJ2cl5ycXJ7kl9i90tkn2TK5JnJR9JNAIECBAgQIAAAQIERibQ\neoFUX77wsuSdydHJ4cnslaRvZt+5SX2D3SuSsxKNAAECBAgQIECAAIERCrReIHVTWt9k99jJ\nRl01qr9/dL2k/nDsRclGtwNzhx9Ohn72aSzzsNHO7o8AAQIECBAgQIDAhgqM8YV5vbWusi1b\nXYV6WrLLwAe5TfodNbCvbgQIECBAgAABAgQIbCOBMRZI24hy6m6vzNYyX/Rwr6lb2yBAgAAB\nAgQIECBA4FoRaP1b7K4VVA9KgAABAgQIECBAgMBqCrR+BenXMi31maNl20dzg/oDsxoBAgQI\nECBAgAABAiMSaL1A+n8yl3dex3y+MLdRIK0Dzk0IECBAgAABAgQIrLJA6wXSQzI5b0vqMz71\nVd9/lQxpnx3SSR8CBAgQIECAAAECBNoSaL1A+kqm68eTDyRVLB2ZfCrRCBAgQIAAAQIECBAg\n8AMCY/iShssy6idORv6qHxCwgwABAgQIECBAgAABAhOBMRRINdRTk+cm9YUNd0o0AgQIECBA\ngAABAgQI/IDAWAqkGvhLkoOTU2pDI0CAAAECBAgQIECAwKzAmAqk2bHbJkCAAAECBAgQIECA\nwJSAAmmKwwYBAgQIECBAgAABAmMWUCCNefaNnQABAgQIECBAgACBKQEF0hSHDQIECBAgQIAA\nAQIExiygQBrz7Bs7AQIECBAgQIAAAQJTAgqkKQ4bBAgQIECAAAECBAiMWUCBNObZN3YCBAgQ\nIECAAAECBKYEFEhTHDYIECBAgAABAgQIEBizgAJpzLNv7AQIECBAgAABAgQITAkokKY4bBAg\nQIAAAQIECBAgMGYBBdKYZ9/YCRAgQIAAAQIECBCYElAgTXHYIECAAAECBAgQIEBgzAIKpDHP\nvrETIECAAAECBAgQIDAloECa4rBBgAABAgQIECBAgMCYBRRIY559YydAgAABAgQIECBAYEpA\ngTTFYYMAAQIECBAgQIAAgTELKJDGPPvGToAAAQIECBAgQIDAlIACaYrDBgECBAgQIECAAAEC\nYxZQII159o2dAAECBAgQIECAAIEpAQXSFIcNAgQIECBAgAABAgTGLKBAGvPsGzsBAgQIECBA\ngAABAlMCCqQpDhsECBAgQIAAAQIECIxZQIE05tk3dgIECBAgQIAAAQIEpgQUSFMcNggQIECA\nAAECBAgQGLOAAmnMs2/sBAgQIECAAAECBAhMCSiQpjhsECBAgAABAgQIECAwZgEF0phn39gJ\nECBAgAABAgQIEJgSUCBNcdggQIAAAQIECBAgQGDMAgqkMc++sRMgQIAAAQIECBAgMCWgQJri\nsEGAAAECBAgQIECAwJgFFEhjnn1jJ0CAAAECBAgQIEBgSkCBNMVhgwABAgQIECBAgACBMQso\nkMY8+8ZOgAABAgQIECBAgMCUgAJpisMGAQIECBAgQIAAAQJjFlAgjXn2jZ0AAQIECBAgQIAA\ngSkBBdIUhw0CBAgQIECAAAECBMYsoEAa8+wbOwECBAgQIECAAAECUwIKpCkOGwQIECBAgAAB\nAgQIjFlAgTTm2Td2AgQIECBAgAABAgSmBBRIUxw2CBAgQIAAAQIECBAYs4ACacyzb+wECBAg\nQIAAAQIECEwJKJCmOGwQIECAAAECBAgQIDBmAQXSmGff2AkQIECAAAECBAgQmBJQIE1x2CBA\ngAABAgQIECBAYMwCCqQxz76xEyBAgAABAgQIECAwJaBAmuKwQYAAAQIECBAgQIDAmAUUSGOe\nfWMnQIAAAQIECBAgQGBKQIE0xWGDAAECBAgQIECAAIExCyiQxjz7xk6AAAECBAgQIECAwJSA\nAmmKwwYBAgQIECBAgAABAmMWUCCNefaNnQABAgQIECBAgACBKQEF0hSHDQIECBAgQIAAAQIE\nxiygQBrz7Bs7AQIECBAgQIAAAQJTAgqkKQ4bBAgQIECAAAECBAiMWUCBNObZN3YCBAgQIECA\nAAECBKYEFEhTHDYIECBAgAABAgQIEBizgAJpzLNv7AQIECBAgAABAgQITAkokKY4bBAgQIAA\nAQIECBAgMGYBBdKYZ9/YCRAgQIAAAQIECBCYElAgTXHYIECAAAECBAgQIEBgzAIKpDHPvrET\nIECAAAECBAgQIDAloECa4rBBgAABAgQIECBAgMCYBRRIY559YydAgAABAgQIECBAYEpAgTTF\nYYMAAQIECBAgQIAAgTELKJDGPPvGToAAAQIECBAgQIDAlIACaYrDBgECBAgQIECAAAECYxZQ\nII159o2dAAECBAgQIECAAIEpAQXSFIcNAgQIECBAgAABAgTGLKBAGvPsGzsBAgQIECBAgAAB\nAlMCCqQpDhsECBAgQIAAAQIECIxZQIE05tk3dgIECBAgQIAAAQIEpgQUSFMcNggQIECAAAEC\nBAgQGLOAAmnMs2/sBAgQIECAAAECBAhMCSiQpjhsECBAgAABAgQIECAwZgEF0phn39gJECBA\ngAABAgQIEJgSUCBNcdggQIAAAQIECBAgQGDMAgqkMc++sRMgQIAAAQIECBAgMCWgQJrisEGA\nAAECBAgQIECAwJgFFEhjnn1jJ0CAAAECBAgQIEBgSkCBNMVhgwABAgQIECBAgACBMQsokMY8\n+8ZOgAABAgQIECBAgMCUgAJpisMGAQIECBAgQIAAAQJjFlAgjXn2jZ0AAQIECBAgQIAAgSkB\nBdIUhw0CBAgQIECAAAECBMYsoEAa8+wbOwECBAgQIECAAAECUwIKpCkOGwQIECBAgAABAgQI\njFlAgTTm2Td2AgQIECBAgAABAgSmBBRIUxw2CBAgQIAAAQIECBAYs4ACacyzb+wECBAgQIAA\nAQIECEwJKJCmOGwQIECAAAECBAgQIDBmAQXSmGff2AkQIECAAAECBAgQmBJQIE1x2CBAgAAB\nAgQIECBAYMwCCqQxz76xEyBAgAABAgQIECAwJaBAmuKwQYAAAQIECBAgQIDAmAUUSGOefWMn\nQIAAAQIECBAgQGBKQIE0xWGDAAECBAgQIECAAIExCyiQxjz7xk6AAAECBAgQIECAwJSAAmmK\nwwYBAgQIECBAgAABAmMWUCCNefaNnQABAgQIECBAgACBKQEF0hSHDQIECBAgQIAAAQIExiyg\nQBrz7Bs7AQIECBAgQIAAAQJTAgqkKQ4bBAgQIECAAAECBAiMWUCBNObZN3YCBAgQIECAAAEC\nBKYEFEhTHDYIECBAgAABAgQIEBizgAJpzLNv7AQIECBAgAABAgQITAkokKY4bBAgQIAAAQIE\nCBAgMGYBBdKYZ9/YCRAgQIAAAQIECBCYElAgTXHYIECAAAECBAgQIEBgzAIKpDHPvrETIECA\nAAECBAgQIDAloECa4rBBgAABAgQIECBAgMCYBRRIY559YydAgAABAgQIECBAYEpAgTTFYYMA\nAQIECBAgQIAAgTELKJDGPPvGToAAAQIECBAgQIDAlMBOU1s2CBAgQIAAgRYFXphBPavFgQ0c\n067pd+rAvroRIDByAQXSyJ8Ahk+AAAECoxA4MKP8ePKKUYz2Bwd5THbt9oO77SFAgMAPCiiQ\nftDEHgIECBAg0KLA2RnU37c4sAFjeumAProQIEDgKgGfQfJEIECAAAECBAgQIECAwERAgeSp\nQIAAAQIECBAgQIAAgYmAAslTgQABAgQIECBAgAABAhMBBZKnAgECBAgQIECAAAECBCYCCiRP\nBQIECBAgQIAAAQIECEwEFEieCgQIECBAgAABAgQIEJgIKJA8FQgQIECAAAECBAgQIDARUCB5\nKhAgQIAAAQIECBAgQGAioEDyVCBAgAABAgQIECBAgMBEQIHkqUCAAAECBAgQIECAAIGJgALJ\nU4EAAQIECBAgQIAAAQITAQWSpwIBAgQIECBAgAABAgQmAjuRGJXAXTPaB4xqxNODvUM2vzy9\ny9aIBPbKWPdNfmdEY54d6vHZ8anZnbYJECDQuICf/zvs4Of/Ek9yBdISWA10/c2M4eHJFxsY\ny3qGcMfc6IbruaHbNCHwoxnFzZoYyfoGccvcrH5J8D/Wd3O3IkCAwMoK+Pnv5/9ST14F0lJc\nK995x4zgXckTVn4k6xvA59Z3M7dqSODsjOUeDY1nmaFsSef6GaARIEBgjAJ+/o9x1tc5Zp9B\nWiecmxEgQIAAAQIECBAg0J6AAqm9OTUiAgQIECBAgAABAgTWKaBAWiecmxEgQIAAAQIECBAg\n0J6AAqm9OTUiAgQIECBAgAABAgTWKaBAWiecmxEgQIAAAQIECBAg0J6AAqm9OTUiAgQIECBA\ngAABAgTWKaBAWiecmxEgQIAAAQIECBAg0J6AAqm9OTUiAgQIECBAgAABAgTWKaBAWiecmxEg\nQIAAAQIECBAg0J7ATu0Naasj2jM99kh2Tb6RXJhcmmgECBAgQIAAAQIECIxcYCxXkO6SeX5t\n8tXk/OSLyWnJ2UkVSacnxyQ3TjQCBAgQIECAAAECBEYqMIYrSC/I3B45md8vZXlCUkVSFUZ1\nJWmv5IDkyckRydOTNycaAQIECBAgQIAAAQIjE2i9QHpM5rOKo+OS5yUnJvPajtl5WPKS5E3J\nGclHE40AAQIECBAgQIAAgREJVGHQcqti59Dk9sllAwZan086M6krSE8d0H9Rl1vlwL8luyzq\nMLO/3upYn4mq/lfMHNvIzXqb4eOTyzfyTlfovq43Oddvr9A5b+SpGv/VmmOe/++GYKz//rtf\nCG7Ln7Eb+e91o++r/v9S/88f8v/CjX7szXB/fv5dPQtj/vlXAmMdf73G3JI8KdEGCHT/wxjQ\ndSW7HJyzrrfUDf0fwgXpe3Kyf3JN2hm58c8lOw+8k/qf1o2Sbf0/7nq74dsGnlOL3ertlNXO\nv3oxuv8a/9VTPtb53zvD/14y5vHXM+C8+s8IW/37r//XjHn8Ne1jff77+V+zP975r7GfVP/R\nCJTAPyefSYYWKnUF6eLkTxONAAECBAgQIECAAAECTQn8UkZTvzE9NjlkjZHVb9XqM0gfT+oq\nzn0SjQABAgQIECBAgAABAk0JVOHzjKT+zlEVSmcnH0v+Ifk/k2W9Be/cpI5/J/mtRCNAgAAB\nAgQIECBAgECzAvWlCVUQnZNUIdRPFU+fS16c3DzRCBAgQIAAAQIECBAYqUBdYRlb2z0Drr9/\nVN9oU3849qJEI0CAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBLafwI7b76E80iYR2GWTnIfTIECAAAECBAgQ2D4C\nl2+fh2njURRIbczj0FF8LB0PGdpZPwIECBAgQIAAgSYEPp5RHNrESLbDIHbaDo/hITaPwBdy\nKuclR22eU3Im21Hg+ZPHMv/bEX0TPZT530STcS2civm/FtA30UOa/000GdfCqdT8X3QtPO7K\nPqQCaWWnbl0nXpdXv5acsK5bu9GqC9TcVzP/VzuM7b/mf2wzPj1e8z/tMbYt8z+2GZ8ebzf/\n03ttLRS4zsIjDhAgQIAAAQIECBAgQGBkAgqkkU244RIgQIAAAQIECBAgsFhAgbTYxhECBAgQ\nIECAAAECBEYmoEAa2YQbLgECBAgQIECAAAECiwUUSIttHCFAgAABAgQIECBAYGQCCqSRTbjh\nEiBAgAABAgQIECCwWECBtNjGEQIECBAgQIAAAQIERiagQBrZhBsuAQIECBAgQIAAAQKLBRRI\ni20cIUCAAAECBAgQIEBgZAI7jWy8Yx/u5WMHGPn4zf+4nwDm3/yPW2Dco/fv3/yPW8DoCawh\nsFeOVbRxCpj/cc57N2rz30mMc2n+xznv3ajNfycxzqX5H+e8GzUBAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgACBVRC47iqcpHPcEIGb5l7u\nl9wquSS5NNHaFdgxQ7tlsudW8q0cvzLR2hW4XoZ2t+TeyW7J1xNzHoSRtB/KOGv+75J8Obk8\n0doWODDDe1hyyhrDrNd/90rumVyRnJ9obQgcmGFsbf77I31UNur58LX+TusEWhfYPQN8W/K9\nXupF8XMSrV2BH87Q+nO+aL3+56i1K/CADO2MpD//X8x27dfaF3hkhvjVpJv/Ko7ek9QvzLQ2\nBer/+f+R1C9CF7Xb5MBnku55UctTk5sn2moLDJn//gh/LRs1/8/q77ROYAwC/5pB1pP/Rcmd\nkick9YOw9v1CorUpsGuG9dIFeWP21/yfm9wo0doUOCDDujC5IHl2cofkd5PzkouSAxOtXYH7\nZGjfTeqK4eOSevfAEck5yQlJ/YzQ2hKodwwcl9TP90UFUr274IPJxckvJ7dO6kXyN5Mzkxsk\n2moKDJn//sjqFyj1S5N6viiQ+jLWmxeoS6z1xH/NzEhvP9n//pn9Nsch8NYM87Kk3l6htSvw\nOxla/fv/g5khvnCy//kz+222JfCJyTzfd2ZYddW4CqeXz+y3udoCj87p1y+96t98/XxfVCD9\n+qTPU7Lst+5Kwuz+fh/rm1dg6PzXCPZOul+UfjvrCqRS0UYl8L6Mtn57XJ9BmG31Fpt7zO60\n3bzAYzPC+mH4wuZHaoB/HIKa60fMUNS//dr/6pn9NtsRqKtD9bmSTy4YUr0Fq15Ma20IPCTD\nqH/TdbWw/r2fmCwqkD6eY/Wi+IZJv+2ejXr7fRXW2moJLDP/NbJ6DtTz5W+TX5msu4IUCG08\nAnUJ/djJcOuy+h2Sg5OdJvssxiVw0wy33l712cTba9qf+wdmiPU/wbfNDPV1k/31wVytTYED\nM6ya+7paPK99LDvr+P7zDtq3cgI/kTP+w2SvyZkvKpB2zvG6unTypN/s4lPZUW+5qn7a6ggM\nnf9uRH+elQdNNh6RZf0sUCBNQCzaF9g9Q6wn/Z8lden1a5Pt2lcvko9ItHEJdC+Mf25cwx7t\naOtbiY5M6krCp5O6olQvnOrtVS9JvAgKQqOt5vY7yUlzxle/KKlvMaz/F9xpznG7Vl9gUYG0\nT4ZW8/6+BUM8fnJ8vwXH7V4NgUXzP+/sH5Gd9ZxQIM3Tsa9JgR/NqOpJ/+9JXU6vF0RVKNXn\nEqpAqmM/mWjjENgzw6y3T9TbarwwHsec1ygPSuq3xfXvvcvns36bRGtb4H0ZXs357C9E6oVQ\n91y4d9sEox3dohfIt57M/d8tkKn99dzw82EB0IrsXjT/805fgTRPxb6mBQ7J6Lr/CdZ7TPut\ne+tNfc2nNg6Bp2eY9Xx44TiGa5QRqBfG30xOSOrzhjeYLD+c5aXJ7Avn7NIaEqirQ/V2qrpa\n9Pqkfjn2huSS5ANJ/Tz4sURrT2DRC+SbZag1729dMOS3TY7fasFxu1dDYNH8zzv7R2RnPSdc\nQZqnY1+TAgdkVPWkr7+BMduukx1fTur47Ac1Z/vabkPglAyj3nLjrRNtzOeQUVRhVB/a7j6X\n0N1mj6zUlcS6uqy1LXCXDK/+1EMVSfXvv4rj+yavTern/4GJ1p7AohfIO2Wo9Rbb9y0Y8vuz\nv54Xey84bvdqCCya/3lnr0Cap5J99UJZa1OgXgDVD8J5BVL/B+SN2xy+UfUEDs36HZO3J765\nqgfT8Gr9u75n8qHk/JlxXpTt9yQHJ/WLFK1dgfrQfT0Pdk/qbbZVHFWRVFcI6uriOYk2HoEr\nMtR6TTD7S5NOoPbX8+LCboclgbEKKJDanfn6Qfj55EeS688Z5r7Zd0FSfbS2BeotldXeefXC\nf0cgUFcM6uf7PgvGustk/3UXHLd79QXqN8NPnAyj3lL5jcn6jbK8T1Jf9VtXlbRxCdRb62+f\n1POg3+qXKvXZ5X9L6ueHRoDA/9/e3QfbVtZ1AC9Ab6n4Ehj40lBGYIagQKmVMhmkJWGa+VrR\nlBQ1QzUxYTO9iHOtKZvpj6xomspJtJqyW2oOWJbFZG+aNSHiS8WoJBiGVgaGkH2/nrVwue7e\n++x9/6B7z/78Zr53rfWsZ62z1uece+9+7rP2vgT2rMDFubNOl18+u8P+y3EHUK+ftdvcmwKv\nym315+CMvXl77mqJwHVp70f2nj3b/7Bs91+Ib5y129xbAq/J7fT3/RNnt/Wz2e4L4CfN2m3u\nHYG351b+a8ntPDPt/bm4bLb/R4b2Z83abR55Aqu+//O76T+k9Ofh0vkO2wT2ssC+3Nw7k/7w\n/2Ly1OSi5EPJzUkfs1B7X6B/WHZA3J8HtT0CfWHcF8K3Ji9KviZ5YfK+pH8mfEOi9q7AObm1\n/r5/T3JJcn7y60m/9y9N1N4VWPUCuTPLfV3QPxv2J+cm/Xno9oFEHfkCq77/87u7IA39M8EA\naS5je88LHJs7fHXSTzPqb4I+UvGW5MxE7X2B/mV4W+ITC/f+93rRHXaQdG3S3/tj3p318xK1\n9wWem1u8KRm/9/0vH16eHJOovSuw2wvkPl53VdL3I48/G2/M+omJOvIFdvv+T+/QAGmqYX0r\nBfqeg9OTDpgUAQLbJXBcbvespO8zUNsl0MHQKUkfse1HvSsCo0BfD/TPBQOjUcSSAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAwJYIfPaW3KfbJECAwLYLfGMAjpkgfDLr\ntyW3JDcOyywO67p3rm5/8orkXUuu9JvS/t7kuiX7j07745KHJP+YtO+y2qTvsnMsa394djw2\n+e/kb4ZlFiurf2d/4coeOzs/mMX/JM9Peg9XJooAAQIECBAgQIAAgYnAx7LeQdGi3Jn2Vyan\nJIdz7c/FXZv0Rf+iuiiNvb9LF+1M25ck1ydTgw6kviCZ1yZ958futv2SdPhEMl5H/S/b7aDs\nP3ZyzHjsouVXDOc6K8uPJ6cP2xYECBAgQIAAAQIECAwCHSB1tuLCSb476z+adAajL7T/PXlo\ncjhWX+TfkTxtycU9fdjf+1g0QOrsyzXJfybfmpycdEDVWbT3JfdNxtqk73jMusvz0rHXeCDp\nDFIHM1cnbbskWVX7svPnluRVae85Ont0fDLWb2blrcmyQeXYz5IAAQIECBAgQIDAVgl0gPSR\nJXd877T/VtIX2Fct6fP/3fzaXMA7FlzEcWkbBwedLek9LBogfe+w73uynFYHST1m2r5J3+m5\ndlu/TzrckPSRxumApf5t/8CsPZtr1++lZx+re8LsiDOy3ft7zqzdJgECBAgQIECAAIGtFlg1\nQCpMZ03+LOmL6QuSsZ6clW9O+iL+4qQzTqclY3W2oi++fyLp7Mb3Jacn0+rxi16gn5v2C5MH\nTTtn/dFD+4OH9lOz/N/kx4bt6WKc/fqdNH570utfNEBqvw6gHphM6/7ZuD3pLMtYm/Qdj1ln\n+fXp1Ov76QWdf3LYt2yGbMEhdzc9bzj28rtbPnPlXdmc3t9n7rVFgAABAgQIECBAYAsFdhsg\nlaSPnvUF/Eu6MdTrs+wjaL+QdF/zx0mrj7XdkrTtP5JxBueurE/fU/Oaoc/8vT43De39utM6\nkI0OWu47NL4sy36NDpTm9Utp6ECrdUHSfvMB0r3S1tmVfijDovr7NPbxvfbbpO+ic61qe3F2\n9vqeuaBTLbuvfTapE9O5j0a+O9m35MD9ae+5H7Nkv2YCBAgQmAgcNVm3SoAAAQLbLfCO4fYf\nNWN4WLZfkFyU9JPR+oK7My9XJv175MuTz0uOS56R3Jlcnjwgab1uZ/FZTxmWXZye9MV9q7NU\nY3Wm6rzkTUnfM9XqC/sOpjoImFdnrNp3VXWGquftQGJR3ZrGDow6Y7VJ30XnWtV2wrBz0XX0\nGlq13qR+Jp1r/+NJB4GL6k+HRgOkRTraCBAgMBM4ZrZtkwABAgS2V+Dfhlt/5Izg6Gz3Bfiv\nTtofn/W/TH43edvQ3gHNHyR/lJyfdMaoM0tvSO5Kvi4Zz9FB0J1Jj50OkM7J9v2Snmes07Ly\n/nHjEJYdzLU+vLM46NdxcNIZq860tNbpu9Nz/V9XXcf0GtY9Ywdzz046ePz9FQeNdl+2oo9d\nBAgQIDAIHEWCAAECBAgMAp0Bao0zNztbO7/2fTnT+utsPDX5taGxMzAdWD03GWdK7jPs64zJ\nW5I+CtfBVquDpbclVycnJY9IWucnfb9RH+1rdRDwkOQD3TjE+vhw3LK/88Zr6iBuk76bXs6q\nc0+vYd3zfls6fk7yK8knVhx0Y/Z14Hfaij52ESBAgMAgsOwvC0AECBAgsH0CXzzc8r8suPUb\nFrSdnLYrkuuT24blq7M8JWn1gx/G6mN2HeycnfRF/ROTPhr35qT15J3FpwZInZkaZ7MeNbT3\nRf6h1s05sAOEPoq2qMb2znZt0nfRuVa1fXDYOX69ad+xrdewbl2Ujp2F6wBpVfXRu1uS0XJV\nX/sIECCw9QIGSFv/IwCAAAECdwucOawteq/PHXf32ll5ZBZ/m7ww+efkxcnTkhOTDpLm9bqh\noe9D+urkc5M/Sf4q6YxVB0hfmjwimT5e19mk1gN3Fof0awcRHXCNg5D5SdreAd5Hk036zs+z\n2/Y6A6R/3e0kw/7HZ9kZoT5aN5532HXQon/X9/G+uw7ao4EAAQIEDhI45qAWDQQIECCwjQJ9\nLO4Hkg4QXrEGwPenT2eEviP5jWRapwwb42Nj3Xxv0pmmDpD2JbcnHRz10bBrkg6Q/iFpTQdI\nN+00ferxvWH1kBb92h2YHZ98eHKGB2e9A7NeyziA2KTv5FS7rva8rXOS+XuG2tbqoHOd+tqh\n02vX6HxS+nTWbrRc4xBdCBAgsL0C/VclRYAAAQLbLdBH5X476SzDK5P3J7vVFw0dbph1fGy2\nnzC03Wu2r7NIj0uenvxF0ke/Wm9KTkguSfpJep2RGquzI33vzqljwyEuX57j+o+C3zk7/ruG\n9p+ftG/Sd3LYrqt/nh7XJs9Jaj3WA7LStg4Qrxkbd1l2UNcaP3lwZ2vxr53tay16dHJnj18J\nECBAgAABAgQIbJnAx3K/fUyuszNj3pz1vmjurNEnkzcmnWmYVj8sofumL+i7/4eH9r/L8nnJ\nVyYvSvpel34oQ495RjKt9ml7c9lkx+mT9v2T9nH1DcP+zx8bliwvGPpdumD/UWl7Z9JZon6N\nc5OXDtsHspzWJn173NVJ7+kp3dilatW+dXtW8i3J25N+D85MptXrat+5Y/uMx+zrxi71g9nf\n8zx/l352EyBAgAABAgQIENgagQ6Q+iJ5mtuz/U9JX+A/O+kMy7yWDZCOTscrknFw1fPenPSD\nA85Ouv3LybQ68PhQ0n1nTXb0wxwWtY9dLs5Kj9ltAHLB0G/RAKnnOj65Kun7mnq+poPCE5N5\nbdJ3kwFSv84LkluT8Rq63pmseR1IQ/vMB0h1vC25Plmn+ghkH2V80Dqd9SFAgAABAgQIECBA\n4NAF7p9DH5M89NBPseuR90uPPmr3h7v2XK/DsenWAdqigdH8DOv2vS4HbvL/DHVQePJwzDqz\nQPPrWnf7hHS8Pbli3QP0I0CAAAECBAgQIEDg8Be4MJfYmZ9HH4aX+qRcU2fAOrNzuNVP5YI+\nmnRGTBEgQIAAAQIECBAgsEcEOuPy1uTKw/B++n6sTWaP7qlb6OzXR5Ifuqe+oK9DgAABAgQI\nECBAgMA9J/BV+VJ3JCfdc1/yiP5KHbi9J5l/muARfVMungABAgQIECBAgACBTwuckVWPi33a\nY9Xaqdn58FUd7CNAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgT2isD/AQ5dtdEma3ivAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Histogram of Draw(100, 0.7)”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(Draw(100,0.7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## c)\n",
    "\n",
    "c. Consider a Bayesian analysis and find the posterior distribution of $\\delta$ given that the prior distribution on $\\delta$ is uniform (a so-called non-informative prior).  Plot a function that is proportional to the posterior distribution (the best you are going to be able to do)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Bayesian inference on this data set:\n",
    "\n",
    "$f(\\theta|x) \\propto f(\\theta) \\Pi_{i=1}^{n} f(x_{i}|\\theta)$\n",
    "\n",
    "The prior is proportional to the uniform, so we can set $\\theta = 1$ for the support."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Prior <- function(x) {\n",
    "    #\n",
    "    # A function for a uniform prior, which always returns 1.\n",
    "    #\n",
    "    # Args:\n",
    "    #    x: value for which to evaluate the prior\n",
    "    #    \n",
    "    # Returns:\n",
    "    #    y: 1.0\n",
    "    \n",
    "    return(1.0)\n",
    "}\n",
    "\n",
    "BayesInf <- function(obs, f, prior, delta) {\n",
    "    #\n",
    "    # Evaluates Bayes' formula for a function with a prior and a set of observations.\n",
    "    #\n",
    "    # Args:\n",
    "    #    obs: set of observations\n",
    "    #    f: pdf which is being evaluated\n",
    "    #    prior: Bayesian prior function\n",
    "    #    delta: the delta value \n",
    "    \n",
    "    # Returns:\n",
    "    #   \n",
    "    \n",
    "    terms <- c()\n",
    "    \n",
    "    i <- 0\n",
    "    for (ob in obs) {\n",
    "        i <- i + 1\n",
    "        terms[i] <- f(ob, delta)\n",
    "    }\n",
    "    return(prior(delta)*prod(terms))\n",
    "}\n",
    "\n",
    "BayesGrid <- function(obs, f, prior, inputs) {\n",
    "    #\n",
    "    # Evaluates the posterior probability at a variety of deltas\n",
    "    #\n",
    "    # Args:\n",
    "    #    obs: set of observations to use in Bayesian analysis\n",
    "    #    f: the pdf \n",
    "    #    prior: the prior in bayesian analysis\n",
    "    #    inputs: the values of delta for which to evaluate the posterior\n",
    "    # Returns:\n",
    "    #   out: the Bayesian function evaluated for many deltas\n",
    "    \n",
    "    out <- c()\n",
    "    i <- 0 \n",
    "    \n",
    "    for (p in inputs) {\n",
    "        i <- i + 1\n",
    "        out[i] <- BayesInf(obs, f, prior, p)\n",
    "    }\n",
    "    return(out)   \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "obs <- Draw(100,0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now plot the posterior distribution of $\\delta$. We can see that there is a peak around $\\delta = 0.7$. This is the $\\delta$ that we used to generate the distribution, so this is a good sign."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iQr0BCoiUDVC6TzdBx97dFdik+tc/up4sLpEsUXXEZtJ91x8bRUuSx6klsEEEAA\nAQQQKFRgVGPrjCAVehjYOAL1Eah6gfQnHUp/Kaw/fbpe8cjQmcoDygRltnK/8rTiU/G2UD6l\n3KPQEEAAAQQQQKB4AZ9e56/l8PXDRTWfft/8oWpR/WC7CCCAQGoC62lN31QeUzxC5JnqmvOy\nHv9K2U4pok3SRt0fZrErQp9tIoAAAgiELPAJde7Bgjv4f7X9RwruA5tHIGSBSs1i50kM6tA8\nQvSlRlbWra818sWWryg+p7nIT6W0eRoCCCCAAAII9CPgEaQirz9ytxhB6ufg8DQCVRSoS4HU\nfOw8i50vtnRoCCCAAAIIIBC2QCgFkq9p9qRPz4fNRe8QQGCgAlW/BmmgPrwfAQQQQAABBIoV\nCKVAsgLXIRX7d4GtI5CLAAVSLsxsBAEEEEAAAQR6FAihQPKokb9QngKpx4PI2xAokwAFUpmO\nFn1FAAEEEECgfgK+Zrjoa5A8kdKTCgVS/f7+scc1FKBAquFBZ5cRQAABBBAoicCa6qdneA3h\numEXSBuUxI1uIoDAAAQokAaAx1sRQAABBBBAIFMBjx65hVAgeSY7CqQ3Dwd/IFBtAQqkah9f\n9g4BBBBAAIEyC7hA8rU/zwawE5xiF8BBoAsI5CFAgZSHMttAAAEEEEAAgV4EXCB55MbXABXd\nGEEq+giwfQRyEqBAygmazSCAAAIIIIBAYgHPYBfC6XXuOCNIiQ8fb0CgnAIUSOU8bvQaAQQQ\nQACBOgh4BCmkAmn9OqCzjwjUXYACqe5/A9h/BBBAAAEEwhXwtNohFUiD1Z+1wuWiZwggkIYA\nBVIaiqwDAQQQQAABBLIQiK5BymLdSdfpU+zcmMmuz4E/EaisAAVSZQ8tO4YAAggggEDpBUI6\nxe45aS5VOM2u9H+t2AEEOgtQIHX24VUEEEAAAQQQKEZgFW12HcWzx4XQlqkTTyuMIIVwNOgD\nAhkKUCBliMuqEUAAAQQQQKBnARci/j0llGuQvCNPKRRIlqAhUGEBCqQKH1x2DQEEEEAAgRIL\neIIGt1BGkNwXX4dEgWQJGgIVFqBAqvDBZdcQQAABBBAosYCvP3pBeSWgffAIEtcgBXRA6AoC\nWQhQIGWhyjoRQAABBBBAYKACHkEKafTI++MRJAokS9AQqLAABVKFDy67hgACCCCAQIkFQiyQ\nGEEq8V8ouo5AXAEKpLhSLIcAAggggAACeQqEWiBxDVKefwvYFgIFCFAgFYDOJhFAAAEEEECg\nq0CoBdKa6vngrr1nAQQQKK0ABVJpDx0dRwABBBBAoNICLpBCmuLb2L4GyY3rkPoc+BOBSgr4\nS9iSNH9qsrcyrimeZeZZxT80blN+p8xQ3lBoCCCAAAIIIIBALwIukKKCpJf3Z/EeX4Pk5gLp\n0Tfv8QcCCNRWYIz2/IfKy4oLnyieetPfKh09jm5n6rkPKLR4ApO0mO2GxVucpRBAAAEEEKi0\nwBDtnf9fHB/gXi5Qnz4YYL/oEgJFCqyqjYf6bzaxS7cRpEFa44nKV5VlyhTlcuU+5XHlOcVt\ndWWssnXj9v26/a1yjXKCcq9CQwABBBBAAAEE4ghEEyGENs23++4PhjnFLs5RZBkEKigwWPt0\nl+Ih5I8pSUc3DtF7rleWKl9WaP0LMILUvw2vIIAAAgjUT8Cn8/vTaP8uElq7QR06KbRO0R8E\nChao1AhSp0kaPLp0seJRoXOVhUqSdpUWnqDsqyxK8kaWRQABBBBAAIFaC/j6o+eVxQEq+Dqk\n9QLsF11CAIGUBDqdYueC6JspbOdWrcOhIYAAAggggAACcQR8il2Ip9e57y6QNvYdGgIIVFOg\n0whSNfeYvUIAAQQQQACB0AVCnMEuMuMapEiCWwQqKtBpBKndLjPNdzsVnkMAAQQQQACBNAU8\ngvRkmitMcV2cYpciJqtCoMwCY9R5pvnO7ggySUN2tqwZAQQQQKB8Av+tLn8j0G4fpn75a09o\nCCCwXKBSkzR0G0Fimu/lB557CCCAAAIIIJCPQMgjSD7FzjP7DlcolPL5+8BWEAhGYLB6wjTf\n+RwORpDycWYrCCCAAALlEPAMdn8XaFdHqV+egnzzQPtHtxAoQqBSI0idJmlgmu8i/nqxTQQQ\nQAABBOot4A9o11JCvQbpmcbhYarvev89Ze8RQCBjAUaQMgZm9QgggAACpREYrZ56hGbTgHs8\nX307POD+0TUE8hao1AhSt2uQ8sbNens+Z9jnNY9UPHq2QHlW8VA+DQEEEEAAAQSKF/D/026e\nLS7UxlTfoR4Z+oVACgJ1KZD2ldW3lN2Vdvv8iJ6/XPmaskihIYAAAggggEAxAi6Q/AFmyP8f\nu0DiFLti/n6wVQQyF+h0DVLmG89pAz597VplG+V2xT/U3BYrZymX+oHa55Tpyo5+QEMAAQQQ\nQACBQgRcIIV6/VEEQoEUSXCLQAUF2o2mNO+mi4sRzU/EvH+Llrs15rJZLraXVn6u8iPlRMWf\nRrkojEaU/E3dRyrLlAnKz5TblC2VOQoNAQQQQAABBPIVWF+bK0OB5N8haAggUEOBO7XPvlAy\naU4KxOqb6seflZXa9MfTc3q/Dmx6bYzuv66c2vRcHneZpCEPZbaBAAIIIFAGgZ+ok78MvKNf\nVf9uCryPdA+BPAVqNUnDwZK9TBmv/FbxCEucNjPOQjksM1HbcIHkQqi1PawnFioukK5pvDhb\nty4KxzUec4MAAggggAAC+Qr4FLsH891k4q1xil1iMt6AQHkEVunSVc8g827lesXF0imKC4iy\ntOfU0WhihqUtnd5Mjz2rXXNbWQ9GKX9pfpL7CCCAAAIIIJCbgAukabltrbcN+buQmKShNzve\nhUDwAnEmaVisvfinxp74Wp4ytavV2a2Vc5TmYmhtPY5Gw27Qfbc1lNOUdRVfQ0VDAAEEEEAA\ngfwFynIN0uqiWS1/HraIAAIhCXiWt7uV7UPqVJe+eITsdsWn2Pn7jqY0Mr/x3CW6jdrjuuPl\nZig+jzLPxjVIeWqzLQQQQACBUAX8wa3P+Dgg1A42+rWpbv07w+jA+0n3EMhLoFLXIOWFVuR2\nhmrj31HmKf5h5nho/IvKICVqnu773xQvn3ejQMpbnO0hgAACCIQo4LM4/P/0tiF2rqlPPivF\n/fRp/DQEEOgbXPC/ifFglE/Aw/brBNhtCqQADwpdQgABBBDIXWBHbdG/ZK2V+5aTb/BlveWw\n5G/jHQhUUqBSI0jdJmlodwRH6klfrzNY8Q+HFxTPBleG5pEjf+dRf82TNPh7n/x9Sa/2txDP\nI4AAAggggEAmAv4g09c++6yP0Jt/p2CihtCPEv1DoAeBOJM0eLU7K+cp/mHgH1qzlAeVOYqL\nJE+Z7YkQQhyd8Q+vixX3+0XlOmVvpV3z9VVe7sR2L/IcAggggAACCGQqsIHW/nSmW0hv5e6n\nTwmkIYBAxQTiFEhf1z7PUDyTnUdWblWuVFx0TFX+RxmqfEx5QPkHJZQ2XB25QzlK8eiQC7oJ\nyg3KaQoNAQQQQAABBMIR8AjSk+F0p2NP/KExBVJHIl5EoJoCR2q3fC7wFGWXDru4kl7bT3Ex\n4uX3UkJo/t4m9+dkxdNxuu2qRF8e+703n1n+x0666+VPWv5ULve4BikXZjaCAAIIIBC4wA/U\nvysC72PUvZ/ozkXRA24RqLlApa5B6jaC9CEd7EcU33oUqb/mosKjMgcpLykfVUJoLtT8Cc+p\nivvlNl1xMXejcoLyBYWGAAIIIIAAAsUL+BQ7f0l9GRqn2JXhKNFHBHoQ6FYg7aB1+pQ6XzAZ\np/n7hfxdSRvFWTiHZdwPF0L+ToXmtkAPPPOM+/ptxafg0RBAAAEEEECgWAGfYleWAolT7Ir9\nu8LWEchMoFuB5POAfUraoJg9GKnlXFR5AocQ2qPqxIHKkDad8YQNhyi+LukCpb+JG/QSDQEE\nEEAAAQRyEKBAygGZTSCAQGeBbgWSC4exir9EdY8Oq1pJr+2rTFWGKqGcP3yt+uIpyb+hbKi0\ntrl6YqLi0++uUg5VaAgggAACCCBQjIALpDJN0vBO9bfb71LFSLJVBBDITMCFj6/TWaj4OiOP\nttymeBa7XzVufQreE4pfX6J8WgmleeToPsV9e135sNKu7aQnfXqgl3NOVvJsTNKQpzbbQgAB\nBBAIUWA1dcr/B3f6QDakfm/X6K+LJBoCdReo1CQNcQ/mZlrQBZFHXKIiIrp18fSQMlkZpYTW\nPNX3D5VZyt926Nzmes2z9Xm/TlbybBRIeWqzLQQQQACBEAU2Vaf8f/DoEDvXpk+e4tv93bbN\nazyFQN0EalkgNR/kEXrgQmhLxaevlam1DoMPUuf9iZVHyqK2m+74C2PzbBRIeWqzLQQQQACB\nEAXGq1MuONpdNxxif/07hc9O2T/EztEnBHIWqFSB1FowxLH0F646fq9HZ4YpZWnLWjp6uh6/\nongiiqj5u5zuiR5wiwACCCCAAAK5CPj6oxeUV3PZ2sA34t8pnlc8kkRDAIEKCawSc1921nKf\nVD6grNPmPY/ouWuUryrPtnm9jk9FRWScfe+lUI2zXpZBAAEEEECgLAIukJ4qS2cb/eS7kEp2\nwOguAnEE4hRIX9eKTmms7DHdelKGecrLik+xW0vZRPmYcoRyvHKRUufm65lmKi6SaAgggAAC\nCCDQXaCMBZI/FGYEqfuxZQkESiXQrUA6Unvj4miq8hVlhtKu+RqefZXvKr9UZiu3KHVtD2vH\n91R8Pmac5pG5E+MsyDIIIIAAAghUVKCMBRJfFlvRv4zsVr0FuhVIHxKPT5/z7eIOVL6o8gbl\nIOVR5aNKnQsk7f47/uQ/YrZxMZdjMQQQQAABBKoq4AJpVsl2zgXSxiXrM91FAIEuAt2ufdlB\n7/cpdZ2Ko+ZN+LuE7lY2an4y4Pu/UN9czJXtB3LApHQNAQQQQACBngTW07vKdg2ST7Frd212\nTwC8CQEEwhDoViA9qW56hjdPhx2njdRCLqoejLNwAMt4lOdCxbPQ0BBAAAEEEECgOAFOsSvO\nni0jgECTQLcC6QItO1a5VOn0zdbRNUhTtdxQ5Qol9ObvP9peifZrWOgdpn8IIIAAAghUWKCM\nI0hcg1Thv5DsGgL9CbjwOUFZqPg6oznKbcqVyq8atz4F7wnFry9RPq2E3Dzj3iXKMsV9vlFx\nu1w5VRnsBzk3vig2Z3A2hwACCCAQlMCa6o3/T/bXipSp7aPOut9xz7Qp077RVwSSCHhiMv9b\n8Bc+16Ztpj11QTRX8c43x8XTQ8pkZZQScttAnXtOcf/vV2YrUYHkUS8/f68yRMmzUSDlqc22\nEEAAAQRCE9haHfL/wf5/ukxtK3XW/d6wTJ2mrwhkIFDLAqnZcYQeuBDaUvH3IJWp/VqddUHn\nT3zcLlOiAmll3fcIkn/Q/bOSZ6NAylObbSGAAAIIhCYwQR16XVkltI516U808rVTl+V4GYGq\nC1SqQOp2DVK7g/minnxc8ajRgnYLBPzcAerbWcpNbfroH8ynKN6nPdu8zlMIIIAAAgggkI2A\nJ2jwhElLs1l9Zmt9QWv25QXrZLYFVowAArkL9FIg5d7JlDboka+RyswO6/MPufsay3VYjJcQ\nQAABBBBAIEWBMk7QEO2+T91fN3rALQIIlF8g7QLpEyL5s/LxAGk88vWUsluHvrmI8pe2Pthh\nGV5CAAEEEEAAgXQFPIL0dLqrzG1tnsmOEaTcuNkQAtkLpF0g+ROgHRTfhtimqFPHKscpw1s6\n6POIf674uqqrW17jIQIIIIAAAghkJ1DmESS+LDa7vxesGYFKCIReILkIekzxRAy+1sgjSp6Z\n7wrF5z77+fOVvBuTNOQtzvYQQAABBEISuFKdmRxShxL05Zda9icJlmdRBKooUPtJGjodVA+P\n362EOkzuiyl3Uc5RPJW3CzpPzflBxe14xSNMNAQQQAABBBDIT4ARpPys2RICCHQR6GU6TU90\n4NPQBisvKy46Fiplab6Y0tdIfVIZrfi859nKEwoNAQQQQAABBPIXcIEU6oer3TR8DdLu3Rbi\ndQQQKI9A3GuQdtYunaf4h8A8ZZbiiQzmKC6SHlY8KlOmixQ9rbfja5E8+8xqCg0BBBBAAAEE\n8hVYSZtjBClfc7aGAAIDFPi63u9rc5xHlVuU3yv/qUxRbleeVPy6R2f+QQml+QtfL1Jai5/t\n9dwdSrRfvvVI2ImKvzA278Y1SHmLsz0EEEAAgVAE1lJH/P+wJ3kqY/uQOu3fIWgI1FmgUtcg\ndTuQR2oB/9ByIeRrd/pr/vRnPyUqOvbqb8Gcn/+Ztuf++5TAqI3SHf8g8/Pu748VF1EeDfNz\n31PybhRIeYuzPQQQQACBUAS2VUf8/69HkcrY9lan3X//gkhDoK4CtSqQPDOLT5/z9UZxmq9P\nelFx0RFCa1cgeZ/8g+y4lg4O1ePotQNbXsv6IQVS1sKsHwEEEEAgVIF3q2M+5T3uaf+h7cdW\n6pB/r/CkTzQE6ipQqQKp2w8jD3ffqiyOebTna7m7lY1iLl/EYh7d+h/lzJaNv6LHxyqe7vs9\nLa/xEAEEEEAAAQSyEfDI0bPKsmxWn/lafX22m69npiGAQAUEuhVIvrZoV2VQzH31CJKLKk/g\nEGoboY7d00/nFul59327fl7naQQQQAABBBBIV8AFUllnsLOET9tfopRpoir3m4YAAv0IdCuQ\nLtD7xiqXKnv0sw4/7WuQ9lWmKj5V7Qol1DZdHfMkDe3a2npyN8WFIQ0BBBBAAAEEshdYX5so\nc4FkIU9SRYFkCRoCFRBYpcs+XKTXPWR8qvJ+Za4yR3le8bVGHo1ZSxmtbKAsVT6n3KyE1HxK\n3Z8UF0e3KF9TPqD8TonaJrrzbcXnUF4fPcktAggggAACCGQq4BGkpzLdQvYr9ymCFEjZO7MF\nBIIS2Ey9+ZXiAskXIjZnoR4/pExWRikhtb9TZy5THlGa++z7jylRO1R3PDzu513ceUQszzZJ\nG/O2h+W5UbaFAAIIIIBAAAJXqg+nB9CPgXThGr3ZHybTEKirQKUmaeg2ghQdZBcYf9944FEj\nT5s9RPGFiQuUUNtv1DHHzX3eqSnNRZC/+8jXH7kIPEFxsUJDAAEEEEAAgewFPIJ0XfabyXQL\njCBlysvKEchXIG6B1Nwrn1rnlK25kPOpc+1On7taz/v6I48i0RBAAAEEEEAgPwEXSGW/BskF\n0sb5kbElBBDIUqDbJA1ZbjukdXv0iOIopCNCXxBAAAEE6iLga52rUCBxDVJd/sayn5UXoECq\n/CFmBxFAAAEEEAhWwBM9+doFCqRgDxEdQ6B+AhRI9Tvm7DECCCCAAAKhCPj0OjcKpD4H/kQA\ngQAEKJACOAh0AQEEEEAAgZoKuEBapvganjI393+k4kmfaAggUHIBCqSSH0C6jwACCCCAQIkF\nXCD5uxVfL/E+uOvPKZ4d951+QEMAgXILUCCV+/jRewQQQAABBMos4AKp7KfX2T8aAWOihjL/\nbaTvCDQE0i6QjtV6b1WmKd9XdlBoCCCAAAIIIIBAO4GqFEgeBfOpgowgtTvKPIdAyQTSLpD8\nHQB7Ko8rc5TLlfUVGgIIIIAAAggg0CpQlQLJxdE8hRGk1iPMYwRKKNDLF8V22s3z9OJUxcVR\nVCA91ekNvIYAAggggAACtRVwgfRQRfbep9lRIFXkYLIb9RZIu0CKCqNI9ZHoDrcIIIAAAggg\ngECLgAukm1qeK+tDT9RAgVTWo0e/EWgSSPsUu6ZVcxcBBBBAAAEEEOgo4AKpKmeaeASJa5A6\nHm5eRKAcAhRI5ThO9BIBBBBAAIEqCqyrnarCLHY+NpxiV8W/oexTLQUokGp52NlpBBBAAAEE\nChdYQz0YojxTeE/S6QAFUjqOrAWBwgW6XYM0ST0c0UMvb9F7PN03DQEEEEAAAQQQaCfg0+vc\nqjKC5GuQOMXuzUPKHwiUW6BbgfQv2r2detjFk/UeCqQe4HgLAggggAACNRHw6XVvKIwg1eSA\ns5sIlEWgW4F0sHbkMmW88lvlZ0qcNjPOQiyDAAIIIIAAArUV8AjSfGVJRQSYpKEiB5LdQKBb\ngeSZZd6tXK+4WDpFuVOhIYAAAggggAACAxFwgVSV0+vs4FPsBim+tmqBQkMAgZIKxJmkYbH2\n7Z8a+/ejku4n3UYAAQQQQACBsASqViB5BMmN70Lqc+BPBEorEKdA8s7dp3xZ8YQN2ys0BBBA\nAAEEEEBgIAJVK5A8guRGgdTnwJ8IlFYgboHkHfyusoNyjx/QEEAAAQQQQACBAQi4QKrKBA1m\neFV5WWEmO2vQECixQJICqcS7SdcRQAABBBBAIDCBqo0gmdejSIwgBfYXje4gkFSAAimpGMsj\ngAACCCCAQBoCnua7SpM02ISZ7NL4m8E6EChYgAKp4APA5hFAAAEEEKipACNINT3w7DYCoQtQ\nIIV+hOgfAggggAAC1RMYql0arjCCVL1jyx4hUHoBCqTSH0J2AAEEEEAAgdIJePTIrWoFEtcg\n9R1X/kSg1AIUSKU+fHQeAQQQQACBUgpEBVKVZrHzgeAapFL+daTTCKwoQIG0ogePEEAAAQQQ\nQCB7ARdILymLst9UrltgBClXbjaGQDYCFEjZuLJWBBBAAAEEEOhfoIoz2HlvGUHq/5jzCgKl\nEUi7QDpWe36rMk35vuIvlqUhgAACCCCAAALNAh5Bqtr1R94/jyCNUFb1AxoCCJRTIO0CaWMx\n7Kk8rsxRLlfWV2gIIIAAAggggEAk4AKpatcfed88guT2zr4b/kQAgTIKrJJyp8/T+qYqLo6i\nAumplLfB6hBAAAEEEECg3AJVPcXOI0huLpCeePMefyCAQOkE0i6QosIogngkusMtAggggAAC\nCCDQEPAI0gMV1JivfXpdWaeC+8YuIVAbgV4KpJHSWUMZrLysvKAsVGgIIIAAAggggEAcgape\ng/SGdv55hVPs4vwtYBkEAhWIew3Szuq/T5/z+cLzlFnKg4pHjFwkPayco/CJiRBoCCCAAAII\nINBRoKrXIHmnfZodBVLHw8+LCIQtEGcE6evahVMau/GYbj1LnYskF0YeSVpL2UT5mHKEcrxy\nkRJiG6ZObaB4FMzF4QLFF1T60x4aAggggAACCGQvMEib8P/DVZzFznr+vYIPjC1BQ6CiAkdq\nvzxcPEXZpcM+rqTX9lPuULz8XkpIbV915mZlieL+tcYjYJOV1ZQi2iRt1H1yAUdDAAEEEECg\nygIbaef8f96WFd3J32i/zqzovrFbCPQn4Knt/e96fH8LVOn5X2pnXDz4eqM4zZ8Ivaj8OM7C\nOS3j4uM1xaNeNymeVc8H8FXFP8D8g8z76OfuV3ZU8m4USHmLsz0EEEAAgaIE/IGr/8/1WShV\nbGdrpy6u4o6xTwh0EKhUgdTtGqQdBOFT6hZ3AGl+ab4e3K3406EQmkeyzlVcsLlP+ygbKvsr\ndzbuH63bLZR3K0OU2xR/nxMNAQQQQAABBNIX8BTf/r3Cp7lXsXENUhWPKvtUK4FuBdKT0thV\nGRRTxSNILqo8gUMI7f3qhAu2TyuLGh1aptvrlY8ohysujPxJ1jTlPYor4I8rNAQQQAABBBBI\nX2A9rbKq1x9ZiwIp/b8zrBGBXAW6FUgXqDdjlUuVPTr0bCW95ut8pipDlSuUENpEdeLPigug\n1ubT6jw9+YFNL8zWfY8sjWt6jrsIIIAAAgggkJ4ABVJ6lqwJAQQyEOg2i91F2qaHwk9VPBoz\nV5mjeNY3X2s0QllLGa14drilyueUm5UQmj/F2V3xfrpvzW0zPWidFGFlPTdK+UvzgtxHAAEE\nEEAAgdQEXCD5a0Oq2p7VjjHNd1WPLvuFQJOAi4lfKS6QPBrTHI/CPKRMVlxchNRcrLmvP1Wa\ni6G19Xia4tcOUdzWUL6l+LnjlDzbJG3M223uY57bZ1sIIIAAAgjkJXChNuT/l6vadtGO+f90\nf4hMQ6AuAr5ExX/vazGLXbuD6n/wLoS2VFxUhNw8cnS74gPmT3SmNDK/8dwluo3a47rj5WYo\nPsh5NgqkPLXZFgIIIIBAkQL/rY1/o8gOZLxtfzekf5/wh8s0BOoiUPsCqWwH2tdEfUeZp/gH\nlvOM8kVlkBI1X2f1b4qXz7tRIOUtzvYQQAABBIoS8LXBnylq4zls19+p6N81Ol27nUM32AQC\nuQrUpkDySNH5iqfF7rW5ADlG8el3IbT11YkQv92aAimEvx30AQEEEEAgDwHPkPv3eWyowG34\n8oNDC9w+m0Ygb4FKFUh/00FvkV5bU4muL9q6w7KtL/laGn869LDyA+UeJYTmkSOfatdf8yQN\nnqp8SH8L8DwCCCCAAAII9Czg3zv8QWWVp/k2jieJYqIGS9AQqKjAUdqvpxQPF/s7hU5WjlZ8\nEZa/UNXXIe2q/IPiU9QuUTzLnWeN+39K0T8g1lMfLlZ8it3LynXK3kq7tpOe9H6e1O7FDJ9j\nBClDXFaNAAIIIBCMgIsj/z+7XTA9yqYj07VaTxRFQ6AuApUaQYp70HxdzieVvyr+wdYpLoyu\nVEL44Tdc/Xis0d8FuvUX2PqLYl9XTlNaGwVSqwiPEUAAAQQQSE9gnFbl3yFcKFW5/UE7980q\n7yD7hkCLQKUKJM/yFqe9ooXOUs5WNlf8Ay7KRrr/rOJzim9TpigerQmhfUGd8Ix7pyjfVV5S\nPNr1M+XLii+k/KxCQwABBBBAAIHsBXxWhz+k9JkmVW7+vajqRWCVjx/7VnOBuAVSxOTRF1+T\n5FwRPRnw7V7qm687OlXxyJabh733U/5LOUFxYXe6QkMAAQQQQACBbAVcIPn6HP8+UeXmfRxT\n5R1k3xCoskCnSRqqsN8e3bpRiYqjaJ98ut1hiq+p+rbi66xoCCCAAAIIIJCtwLpafdUnaLCg\nC6Sir8F2P2gIINCDQNIRpHO0DX/6k7RdqDdcmvRNKSz/qNZxoOJZ6V5tWd+LenyIcqtygTJX\nWajQEEAAAQQQQCAbAf8OQYGUjS1rRQCBlASSFkg7aLvbKcMb2/d5xC8oaykrNZ5rd3N7uydz\neO5abeN9yjeUycoTSnNzUTRR8SjTVcp3FBoCCCCAAAIIZCPgAsmnvle9MYJU9SPM/iHQJLCF\n7nvK798quyhRgeWZK1yI3K/cpngI3UVTlCG6X0Tzdu9TPGOOi7kPK+2aZ6+br0Sz853cbqEM\nn5vU2PawDLfBqhFAAAEEEChawNf/etKkqrcJ2kFfZ7Vy1XeU/UOgIVCpWeySXoP0UyHcqRyu\nzFCia3te0/2pykHK9srfKp7JLkrr6W16KZfm7e6hnKF4um/3s127S0++S/E+0BBAAAEEEEAg\nG4E6nWLnM2v8QTENAQQqLDBY+7ZY+ccu+3izXv9Vl2WKejlOQbibOuciL8/GCFKe2mwLAQQQ\nQKAoAV8bfExRG89xuy4EfVbKNjluk00hUKRApUaQolPk4oB6tOhlxTPD9dcG6YXNFY8yhdha\npxV1f23gkSb/IHO7o++GPxFAAAEEEEAgZQGfgl+Ha5Ce13769wpmskv5LxCrQyAPgTgjKlE/\nfA3P1Yq/YHX36Mmm26G6H81yV5ZT1fz9R68o/vJYGgIIIIAAAghkJzBCq/a1wXWYxc4fKvsr\nRSiQhEBDoGwCSUaQvG/fUPZRPCvdDcoDykvKxsp7FH8y5OuUfq/Uufl0xI8oHqGK0/aOsxDL\nIIAAAgggUGIBn3bmVocCyfvpmezW8R0aAgiUSyBpgXS3ds/X6PxM2VfZT4maf+D9s3Je9ESN\nb10oHq/4fMw4bY04C7EMAggggAACJRaICqRnS7wPSbru/WQEKYkYyyIQiEDSAsndflI5WPHp\neVsp/oH3sDJXia7j0d1at8e19zsmEJikZc9NsDyLIoAAAgggUDYBf3g4X+lvRtmy7U+3/vJd\nSN2EeB2BQAWSXIPUugs+jcynkHmCgzmKr0GiIYAAAggggAAC7QT8gWpdTq/z/lMgtftbwHMI\nlECglwJpE+3XJcpCxafcTVbcfqGcqrhwKktznz+qzCpLh+knAggggAACJRWgQCrpgaPbCNRN\nIGmBtIGAZihHKg8q/j6DqPkL0b6iTFc8S03obTV10N/r9BfF03EOU2gIIIAAAgggkI2AC6Q6\nTPEd6fkaJCZpiDS4RaBEAkkLpDO0by4sPEHDtoqLpagdoTunKeOUY6InA7yt0ghYgLx0CQEE\nEEAAgbYCvgaJU+za0vAkAgiEJJC0QDpAnT9LuanNTryu505RPO//nm1eD+GpKo2AheBJHxBA\nAAEEEIgrwCl2caVYDgEEChVIUiD5C95GKjM79HiJXruvsVyHxQp7qQojYIXhsWEEEEAAAQQG\nIFDHAmm4vMp0bfYADi9vRaA6AkkKpBe1208pu3XYfRdRPsXO1yeF2Mo+AhaiKX1CAAEEEEAg\njoBPsavTNUiexc6N70Lqc+BPBEojkKRA8k5NUY5VjlP8qUhzW1MPfq74S0+vbn4hkPtVGAEL\nhJJuIIAAAgggkEjAkzf5/+E6XYPkSRrcmKihz4E/ESiNQNIC6bPasyeUHyn+Yti9lM2UKxR/\nWewHlf9QrlVCa1UYAQvNlP4ggAACCCAQR8Cn17nVqUDyNdlLFUaQfORpCJRIIGmB9IL2bRfl\nHMWfBvkH3oaKCyO34xWPMIXayjwCFqop/UIAAQQQQKCbQB0LpDeE4q8RoUDq9reD1xGokMDK\n2hePHnkUyUVSGZpPA3xM8Q8tf7Lja6o8EuYRMP8Q8/PnK3m3Sdqgtz0s7w2zPQQQQAABBHIQ\neL+28XIO2wltE/eqQ74sgYZA1QVW1Q76d9nxVdjRpCNIzfvsab0fUW5RfNHl1oq/LDbkVvYR\nsJBt6RsCCCCAAAL9CXgEqU6n10UOnqiBEaRIg1sESiLQS4HkL4T1KXZR86dCHn3xzHUejTlY\nCbn5h9XHlaHK5sreykbK2oqvrXLhR0MAAQQQQACB9ATq9iWxkRwFUiTBLQIlEkhaIH1I+/Yb\n5aOKR4s8Y92FyurKfys+RexXiguP0Fs0AvaQOuqZdZJahL5/9A8BBBBAAIFQBBhBCuVI0A8E\nEOgqkLQoOElrnKXsofg8Q0/O4CJpsvJeZefGYxdSZWmfV0cfUNYsS4fpJwIIIIAAAiUTqGuB\n5Km+mea7ZH9Z6S4CqyQgcDE1VvmecnfjfYc0bi9t3PqaJBcbnukuhLaDOtFt4gOfXufmL8D1\nVOBujytz3rzHHwgggAACCCAwUAEXSH8Z6EpK+H5OsSvhQaPLCCQpkHwanaf29sxvbisrBynz\nlDuUqHkZz2QRQvu5OrFjzI5MbVruZN0/pekxdxFAAAEEEECgd4G6jiBRIPX+d4Z3IlCYQJIC\nydNiuxjaV/FkBhOVkcpFyjLFzafYbar82g8CaD9WH76vuGj7neLRrdb2bj2xu3KGsqjx4s2N\nW24QQAABBBBAYOACFEgDN2QNCCAQqMAP1S9fezRN8aciLowmKG5fUxYqnvxgGyWUNk4d+bPy\nivIpxZNLNLdv64H3aa3mJ3O+z/cg5QzO5hBAAAEEchMYpC359wV/wFq3tqt22L9j+CwcGgJV\nFvDZOUi0RAAAQABJREFUY/67XonvQUp6oDwS49PWPNLi7z76pBK1a3THRchHoicCuh2svngi\nCf+A9mx70XVHuvsOCiQr0BBAAAEEEMhGwF8m71+ctspm9UGvdXRj3zcLupd0DoGBC9S6QIr4\njNA6EuMJEUL/hOQ96qMnYPCpgh9W3CiQ+hz4EwEEEEAAgSwEfPq9CyTPelu35u9c9L77VH4a\nAlUWqFSB9Dc9HqnX9D7/g29ud+vBS81PBHj/j+qTC7mrFX9f00XKSIWGAAIIIIAAAtkI+Pqj\nxcqCbFYf9Fp9Zo3Punln0L2kcwggsIJAkkkaVnhjiR/MV9+PVn6vnKmMUGgIIIAAAgggkI2A\nC6Sns1l1KdbKTHalOEx0EoHlAr2OIC1fQ3nvXaiuewrw3yjTlCUKDQEEEEAAAQTSFaBAYgQp\n3b9RrA2BjAXqOILUTDpbD45sfoL7CCCAAAIIIJCqQN0LpGeluU6qoqwMAQQyFajzCFKmsKwc\nAQQQQAABBN4UqHuBxCl2/ENAoGQCFEglO2B0FwEEEEAAgZIJUCBxil3J/srS3boLUCDV/W8A\n+48AAggggEC2Ai6Q/N2JdW2MINX1yLPfpRVIu0A6VhK3KtOU7yueUpuGAAIIIIAAAvUVYASJ\nEaT6/u1nz0spkHaBtLEU9lT8ZaxzlMuV9RUaAggggAACCNRPYGXtsr8D6Kn67fpbe8wkDW9R\ncAeBcgikPYvdedrtqYqLo6hAqvMPxXL8LaCXCCCAAAIIZCPg4sgfxtb9e5D8pfR2WKbQEEAg\ncIG0C6SoMIp2+5HoDrcIIIAAAgggUDsBn17nVvcCycXRWoqvR6IhgEDgAklPsTtL+zNZSbuw\nCpyJ7iGAAAIIIIBADwIukPxF7PN7eG9V3uJT7Nz4LqQ+B/5EIHiBJAXSYO3NMcphytLg94wO\nIoAAAggggEDRAtEMdm8U3ZECt/+8tu399+mGNAQQKIFAkgLpNe3PS8pQZaUS7BtdRAABBBBA\nAIFiBeo+g531/aHyAoUCyRo0BEogkKRA8qcfhzf26Xe6fa+yuTKiTTzaREMAAQQQQACBegtQ\nIPUdf74Lqd7/Dtj7kgkkKZC8a77+yCNIPs3Os9X9VfGnIq35kp6jIYAAAggggEC9BfxVH3We\noCE6+kz1HUlwi0AJBJJOtvCg9inOhZYzS7DvdBEBBBBAAAEEshXwCNKd2W6iFGtnBKkUh4lO\nItAnkLRAOhY4BBBAAAEEEEAgpoALJL4PsW96b65BivmXhsUQKFogaYHU3N/RejBW8bz+Hjqe\nocxTaAgggAACCCCAgAW4Bqnv74F/T9qh7y5/IoBA6AK9FEjbaqfOVvZr2Tl/z4Gf/4xS5+k8\nW1h4iAACCCCAQC0FfJ2zv/uHa5AYQarlPwB2urwCSQukUdrVWxXPXOdJGnxe8QuKnz9EOV4Z\nrkxSlik0BBBAAAEEEKingE8pW1mhQOo704ZT7Or574C9roHAZdrHxcoBbfZ1kJ47U/Ho0T5t\nXuep/gVcUNptWP+L8AoCCCCAAAKlEthevfX/bRQGfbP/vlyqo0dnEUgmsKoW97/38cneFubS\nSaf5nqDdOEe5ts3u+BQ7n17n82z3V2gIIIAAAgggUF8BX3/kL0l9vr4Eb+25Z7Hzh6BD3nqG\nOwggEKxAkgJpDe2FJ2S4t8Pe+Aehp/jepcMyvIQAAggggAAC1RfwdyA9o/hT5bo3F0hujKb1\nOfAnAkELJCmQoi+D3anDHnl4bRtlVodleAkBBBBAAAEEqi/gESSm+O47zj67xs2TVtAQQCBw\ngSQFknfFEzP4epnD/KCledjYs9itrVzX8hoPEUAAAQQQQKBeAi6QmKCh75j7Q2ZfisAIUp8H\nfyIQtEDSWexO1N68V/kv5SbFs9jNVzyL3URlY+U3yu8VGgIIIIAAAgjUV8Cn2FEgLT/+Ps2O\nEaTlHtxDIFiBpAXSo9qT7ZTzlPcp+yhRe0V3vq6cHj3BLQIIIIAAAgjUVsAjSDNqu/dv33EX\nSIwgvd2FZxAITiBpgeQdmKscrAxXxir+Aehrjh5WPAU4DQEEEEAAAQQQ4BS7Ff8O+DokRpBW\nNOERAkEK9FIgRTvysu78KXrALQIIIIAAAggg0CTAKXZNGLrLCNKKHjxCIFiBbgXSSPV8kDJP\n8RTenoDB34rdrS3UAg4NAQQQQAABBOon4EmgfDoZs9gtP/YukDyqRkMAgcAFus1i59nofIFl\nNLX3HY3Hfq5TPq/XaQgggAACCCBQTwGfSuYPVP27Aq1PwKfYcQ0SfxsQKIFAtxGka7QPDyme\nqc5tirLum/c6/3F/55d5FQEEEEAAAQQqLBCNlDCCtPwgc4rdcgvuIRC0QLcCqd1IkGey+6Li\nU+5oCCCAAAIIIIBAq4CvP/L3/vgUfVqfAJM08DcBgZIIdDvFrnk3BuvBMcphCsVRswz3EUAA\nAQQQQKBZgBnsmjX67rtA8rXcK739JZ5BAIGQBJIUSK+p4y8pQxX+cYd0FOkLAggggAACYQl4\nBInT61Y8Jj7FztdleQIsGgIIBCyQpEB6Q/txeGNffqfb9yqbKyPaxKNNNAQQQAABBBCopwBT\nfL/9uHsEyY3vQupz4E8EghVIUiB5JyYrHkHyaXZTlb8qC9rkS3qOhgACCCCAAAL1FPApdowg\nrXjsPYLkxkx2fQ78iUCwAt0maWjt+IN6IprRrvW15sczmx8EdH+Y+rKB4uFtF4cu7vyJzvMK\nDQEEEEAAAQTSEfAI0m3prKoya/GkFf69gxGkyhxSdqSqAkkLpGNLCrGv+v0tZXel3T4/oucv\nV76mLFJoCCCAAAIIINC7AKfYtbfzKBIjSO1teBaBYASSnmIXTMcTdGSSlr1W2Ua5XYm+tG6x\n7p+lXKq4fU6ZruzoBzQEEEAAAQQQ6FmAU+za0/msFUaQ2tvwLALBCMQtkHxK2sHKJ5UDlbJM\nwrCX+nqu8mNlI2UfZUNlf+XOxv2jdbuF8m5liOJTAjZWaAgggAACCCCQXGCQ3uLprJ9K/tbK\nv4MCqfKHmB2si8Dh2tGXFc9iF8XXGO2mhN6+qQ7+WWk3Lbln4PP+uOCL2hjdeV05NXoip1uP\ncrkvw3LaHptBAAEEEEAgKwF/IOn/07bMagMlXu9P1fcLS9x/uo5AfwKr6gX/ux/f3wJler7b\nCNJY7YxPQfPIynWKT0nzKWpbKRcpxgi5TVTnXCD5gLW2h/XEQqW5QJqtxx5ZGqfQEEAAAQQQ\nQCC5gK8/cmMEqc+h+U+uQWrW4D4CgQp0K5D+t/rt0Zd/Vd6jHKeMUn6m+LS0o5SQm38Q9Tcx\nw2Z6rXXExl/g5v1jogYh0BBAAAEEEOhBwAWS/x/1l8vTVhTgFLsVPXiEQJAC3QokT1jg0+u+\n39R7T1MZPfZIUsjtanVua+UcpbkY8rnRLvLcbui7eccauj1NWVe5pfEcNwgggAACCCCQTMAF\nEqNH7c0okNq78CwCpRK4Tb19rE2Ph+s5n7Z2QZvXQnpqFXXGM9e5r/6hNKWR+Y3nLtFt1B7X\nHS83Q8n71EGuQYqOArcIIIAAAmUX+Ip2gA8a2x/FQ/W0T++nIVA1Af/u7N+ja3ENkq89er3N\nEXyl8dzqbV4L6aml6oxnpztd8elz72vEo2BfUv5Ridr/6M6/K57p7rXoSW4RQAABBBBAIJHA\nelqaEaT2ZP6wdmgj7ZfgWQQQKFzAIyxVby7m/rURD/u74PMPqNZ2ROsTPEYAAQQQQACBxAKc\nYtc/WfT7xzpa5NH+F+MVBBAoUqDbNUhF9i2LbT+jlUY/nNqt36NM/s4nj5zREEAAAQQQQCC5\nAAVS/2bR7yAukGgIIBCoQJwRpBHq+2da+u+Z7dw2V1pf8/O3NeL7RTcP9Z+heMpvnx95h/JV\n5WaltW2vJ+5UTlZOUWgIIIAAAgggkEyAAql/L0989apCgdS/Ea8gELzAXeqhL7hKmpMC2TNP\nJuFJJtz/BcqDyjLFp9l5xrrWtpOe8LJ5959JGlqPBI8RQAABBMoq4Om9P1DWzufQ78e1jY/m\nsB02gUCeApWapKHbCJKn8+7lU45QZq/5gvrv7zXyaNB3Ff/Q3lXxFN9fVlZTPqvQEEAAAQQQ\nQGDgAsO0Cn84ySQN/Vv6NLt39v8yryCAQNEC3QqkC4ru4AC3v5fe7+uOTlU8o53bdGU/5b+U\nE5QnldMVGgIIIIAAAggMTMCn17lRIPU5tPvTBVIvHz63WxfPIYBABgJVn6RhI5ndqETFUUTo\n0+0OU+5Wvq0cpdAQQAABBBBAYGACFEjd/SiQuhuxBAKFClS9QHpUugcq7Wale1HPH6LMUTxS\ntrdCQwABBBBAAIHeBVwgzVP4PsH+DSmQ+rfhFQSCEKh6gXStlNdQvqFs2EZ8rp6bqPjapKuU\nQxUaAggggAACCPQmsIHexul1ne0okDr78CoChQtUvUA6U8L3K77WyLPGfFhpbTP1xEGKZ7fz\ntUpuK/Xd8CcCCCCAAAIIJBDwCBIFUmcwCqTOPryKQOECVS+QXpXwHoq/B+kxpb8hf09n/i5l\nqkJDAAEEEEAAgd4EXCB58iNa/wIUSP3b8AoCQQisEkQvsu2Ev5Tt0410Kggf1jIHK7spLqxo\nCCCAAAIIIJBMwKfYPZDsLbVb2gWST//398b098Ft7VDYYQRCEuhUMITUz7T64tPomtsgPfB3\nITWfUneHHt/TvBD3EUAAAQQQQCCWgEeQOMWuM5ULJDe+C6nPgT8RCE4g7QLpWO3hrco0xV8y\nu4MScjtdnXtF8ZfH0hBAAAEEEEBgYAKcYtfdLyqQ+C6k7lYsgUAhAmmfYrex9mJP5RfKHOVy\nxdNn1+3TJH//0q8VD5/HaWvHWYhlEEAAAQQQCFjAH7quq9Tt//ykh+QFvcHfz0iBlFSO5RHI\nSaBbgTRW/ZilLI7Zn/O03FTFxVFUINXxB6W/A+I/FZ/CF6d5IokxcRZkGQQQQAABBAIV8Clj\n/r2CSRo6H6A39PJzCgVSZydeRSBYAZ9+dm5T7zxd9v5Nj8t+9wfaAf+g8gx2RbZJ2rj7MazI\nTrBtBBBAAAEEBiCwo97r/8vWGsA66vLWu7Wjn67LzrKftRDwWVP+9z++Cnvb6Rokj354Z5s/\n4fiUHk+owo6zDwgggAACCCCQqoCvP/IZJz6LgtZZ4Bm93Pz7VeeleRUBBHIV6HSK3RL1xN8P\ndIhysXKvsqayn/JVpVO7QS86obdfqIPTlVmhd5T+IYAAAgggELiAp/h+OvA+htI9T9RAgRTK\n0aAfCCQUeJ+WX6B4yCxJTtbyoTdP77294ut/3Io8vY1T7PqOAX8igAACCJRX4Evq+m3l7X6u\nPfcX2F+W6xbZGALZClTqFLtOI0hm9IQLmyibKx49+qXyB+VCpVN7pNOLBb/m/Zms/J3i7z+6\nSdlX8WjSfcq/Kz5FgIYAAggggAAC8QV8ih0TNMTz8il2u8RblKUQQCBvgW4FkvvjEaQZjY75\n1t9zdG3jcdluPPzvffC02v6m76FK1FwsfUX5kOJJG15VaAgggAACCCAQT8D/x9Zx5tp4Oisu\nxSl2K3rwCIGgBDpN0tCuo4fqyXPavVCS5zyk7VPrPGK0rRIVfrr7jiOU05RxyjEKDQEEEEAA\nAQTiC7hAYgQpnhcFUjwnlkKgEIGkBVIhnUxxowdoXWcpPq2utb2uJ05RPGK2Z+uLPEYAAQQQ\nQACBjgIUSB15VnjRBZIvXYhzJs8Kb+QBAghkL1CnAmmEOEcqMzuweuY+X4fk5WgIIIAAAggg\nEF+AAim+la9B8qn9zGQX34wlEchNoE4F0otS9bnRu3XQdRHlU+we7LAMLyGAAAIIIIDAigL+\n/9PX9XKK3You/T3yCJIbBVKfA38iEJRAnQokw09RjlWOU4Yrzc1D3T9X1lCubn6B+wgggAAC\nCCDQUcAz2LlRIPU5dPtzvhZYqqzbbUFeRwABBLIWcBH0mOLvdPK1Rh5RmqtcoTyv+Pnzlbwb\n34OUtzjbQwABBBBIU2CCVuZrebmmJr6qi8m/j784SyIQtEClvgepbiNIL+ivlr934BxliLKe\nsqHyQcXteMUjTDQEEEAAAQQQiC/g/0t92phHRWjxBHwdEiNI8axYCoFcBdL+pMfFxT8pi5U7\nFY/G3K2E1J5TZz6ufFIZrfi0gNnKEwoNAQQQQAABBJILMEFDcjMXlFyDlNyNdyCQuUDaI0gb\nq8eeIvtxZY5yuRKdl6y7QTWfCvCIMl3x9UgrKzQEEEAAAQQQSC5AgZTcjBGk5Ga8A4FcBNIe\nQTpPvZ6quDiKCiRf51N021QdeK/ytOIJGF5W/MP8R4qfd4H0ivID5WTF033TEEAAAQQQQCCe\ngP9P5UyMeFbRUh5B2iR6wC0CCCCQp8AJ2tgbTZml+x7SvrjxnGeSuUrxD3Yv5+fzbkzSkLc4\n20MAAQQQSFPgWq3s39NcYQ3W9RXt48012E92sR4ClZqkIa1D5pGorRV/6VlI7X3qzDLlXsUT\nMHxW8Wx1MxUXQ/+qrKa4edIGT/Pt5z2qlGejQMpTm20hgAACCKQtcL9W+C9pr7Ti6/P//Q9V\nfB/ZvfoI1L5AOkLH+pym4/1+3feU2S4sPApzsBJKcz9fUoY1dehDuu+++jqp1uuOXCx5yNun\n2uXZKJDy1GZbCCCAAAJpC3iW2MPTXmnF1+ffR/z7Ew2BKgjUukCKiotFOpIeLVpD8Q9Fj9L8\nQfE/dD/eXAmh3aVO/LqlI/6mb/f/7Jbno4c36s6V0YOcbimQcoJmMwgggAACqQv4w0V/8LhH\n6muu9gr3argNrvZusnc1EahUgZR0FruTdJBnKf4h6B+GH1RcJE1WfFrazo3HLqRCaL6+yH1t\n3k9PxvBV5QGlta2pJ3ZTPBJGQwABBBBAAIHuAv4OJLcn+274M6aAZ7FzY6rvPgf+RKCUAi4y\nFimnNfX+P3W/9VMjn4f8y6Zlirz7xUb/fqDbbtOND9Iy/6+x/N/rNs/GCFKe2mwLAQQQQCBN\ngX20Mp9J4k+QafEFRmhR/w7lL7CnIVB2gUqNICU5GB4p8j/kTzXe5Ot35ime9KB5hOYRPW49\nrU1PFdI88cJ0xf1+VRmptGu+ruppxcv9Ucl7sgkKJKHTEEAAAQRKKXCUeu3rd2nJBfy7iSeU\noiFQdoFKFUjNhU23A+Pri1wQ7dtYcKJuXXBMVfzJkZtPsfN3DrlICqH5B48/2TpNuVvxKXft\n2jA96QN7hnKI4kKJhgACCCCAAALdBTbQIk90X4wl2gi4sOQUuzYwPIVAmQR+qM66eJimPKe4\nMJqguH1NWai8rmyjlKn5AtPWGe3y7D8jSHlqsy0EEEAAgTQFvq2V+cNSWnIBn+Xy+eRv4x0I\nBCdQqREkf39RknaiFvao0ZGKp8/26XbXK24ulHxq2jFKuwkQ9HSwzddW0RBAAAEEEEAguYAn\naWAEKbmb3+GJGtbt7a28CwEEshJIWiD5lLWPKscqSxSPJkXNX8I6S3HhREMAAQQQQACBegj4\nFLvb6rGrqe8lBVLqpKwQgYELJC2Qoi2+pjuefWUrZbjysHKP0lww6SENAQQQQAABBCouwAhS\n7wfYBdK43t/OOxFAIAuBJJM0RNvfSXeuVBYodyjXKY8p/kd+nNJr0aW30hBAAAEEEECgZAIU\nSL0fMEaQerfjnQhkJpC0mNlWPblJ8axvNyj3KS6UNlYOUH6k7Kl8RKEhgAACCCCAQLUFhmr3\n/DUgfElsb8eZAqk3N96FQFACf1RvPFNdNNV3c+f8nUM/UXya3eHNL3C/qwCz2HUlYgEEEEAA\ngQAFtlCf/P/+qAD7VoYuHaxOMlFUGY4UfewmUKlZ7JKcYufRJo8O/UC5sY2SJ3D4hPKUclCb\n13kKAQQQQAABBKol4NPrXCD5/35acoGn9RZ/wOzrumkIIBCIQNICyUXSnA59X6rXHlU83E5D\nAAEEEEAAgWoLuEDyaWKe2ZaWXMB2bkz13efAnwgEIZCkQPII0W3K0Up/X6rqa5F2UdqNMOlp\nGgIIIIAAAghUSIAJGgZ2MKMCab2BrYZ3I4BAmgLdCqTVtTF/MWwUf9eRC6DfKrsqgxQ3n3f4\nXsVfGvsHxdci0RBAAAEEEECg2gIbafeeqPYuZrp3r2ntLyiMIGXKzMoRSCbgU+Y6NY8E7dhm\ngUP1nLNM8aQNLqSi5n/kn1e+FT3BLQIIIIAAAghUUoARpIEfVmayG7gha0AgVYFuBdI0bW12\nD1vs5T09bIa3IIAAAggggECBAi6Q/H2ItN4FKJB6t+OdCGQi0K1A+kwmW2WlCCCAAAIIIFAF\nARdIc6uwIwXug2ey4xqkAg8Am0agVaDbNUity/MYAQQQQAABBBCIBLgGKZLo/ZYRpN7teCcC\nmQh0G0HqtNHRenGsspbyrDJDmafQEEAAAQQQQKD6Ap7AaTWFEaSBHWuPII0b2Cp4NwIIpCnQ\nS4G0rTpwtrJfS0f8HQh+3qfl+UvjaAgggAACCCBQXQGfXufGLHZ9Dr3+6REkTrHrVY/3IZCB\nQNICaZT6cKvib3yeqtypeHpKP3+IcrwyXJmkeIY7GgIIIIAAAghUU8Cn1/nDUZ9FQutdwCNI\nTPPdux/vRKBwgcvUg8XKAW164u9EOlPx6NE+bV7nqf4FXFDabVj/i/AKAggggAACQQn8b/Xm\n0aB6VM7O7K1u+3cAf6ckDYGyCvjvr/8ejy/rDjT3O+kkDRP05nOUa5tX0rjvT5F8ep0/Sdpf\noSGAAAIIIIBAdQU8gsT1RwM/vj7Fzm2dvhv+RACBogWSFEhrqLOekOHeDp1eqtdmKrt0WIaX\nEEAAAQQQQKD8AhRI6RxDn2LnxnVIfQ78iUDhAkkKpAXqrbNTh157eG0bZVaHZXgJAQQQQAAB\nBMovQIGUzjF8Uat5VaFASseTtSAwYIEkBZI35okZfL3MYX7Q0obosWexW1u5ruU1HiKAAAII\nIIBAtQQokNI7nsxkl54la0JgwAJJZ7E7UVt8r/Jfyk2KZ7Gbr3gWu4nKxspvlN8rNAQQQAAB\nBBCorgAFUnrH1qfZMYKUnidrQmBAAkkLJM9Ws51ynvI+pXm2ulf0+OvK6QoNAQQQQAABBKor\n4N8fPDU1kzSkc4wpkNJxZC0IpCKQtEDyRv3D8GDF33c0VvEnHr7m6GHFU4DTEEAAAQQQQKDa\nAhto93yaPgVSOseZAikdR9aCQCoCna5B8pfBnq9E35TdusGX9cSflCuV+5V2xdEgPX+MMlmh\nIYAAAggggEA1BHx6nRsFUp/DQP+kQBqoIO9HIEWBTgXSIm1nTeUhxQXO1krc5i889XcieVTp\nB8o9Cg0BBBBAAAEEqiHga47nKf5dgTZwAQqkgRuyBgRSE+h0it0SbeVw5SjlDOVzigudy5QH\nlMeUx5WXlC0UF1A+5c45QPH3Jp2r+Lqk5xQaAggggAACCFRDgAka0j2OFEjperI2BHIRGKqt\nfFL5q/JGlyzV6z7tbjuFFk9gkhazq0feaAgggAACCIQu8B118KrQO1mi/k1QX19XVi5Rn+kq\nAs0C/i5U/y47vvnJst7vNILUvE+v6MFZytnK5sq4pvhTpGeVJ5XblCmKh91pCCCAAAIIIFBN\nAZ9ix/VH6R1bjyD5sod1lKfSWy1rQgCBXgTiFkjRupfpjq9Jcq6InuQWAQQQQAABBGol4A9H\n/1irPc52Z10gua2vUCC9ScEfCBQn0GmShuJ6xZYRQAABBBBAIGQBRpDSPTrztbrXlPXSXS1r\nQwCBXgS6jSB9Vysd08OKL9Z7LunhfbwFAQQQQAABBMIX8AjSnPC7WaoeMlFDqQ4Xna2yQLcC\nybPR7dgFwN+HNLxpmUW6/6emx9xFAAEEEEAAgeoI+DqZwQoFUrrH1AWST7GjIYBAwQLdTrHb\nT/1bqym76f4C5ffKnspqyuqNfEC3M5WrldOVEJtnidtC8X7soXhK8rUVGgIIIIAAAgjEE/Dp\ndW4USH0Oaf3pa484xS4tTdaDQI4CviBzmtLfNJSj9ZpnvPuEElLbV525WVmieArC1vgLbScr\nLviKaEzzXYQ620QAAQQQ6EXg/XqTzx6hpSvwE63ul+mukrUhkJtApab57jaC1Kzq4fS9lF8r\nnqu/XXtUT96l7NPuxYKec/FxrbKNcrvytOK2WDlLudQP1PxFuNOVbqcUelkaAggggAACdRXw\nCBKjR+kfff9+wil26buyRgQSCyQpkJZq7QuVDTtsxSNLY5S5HZbJ8yUXdOcqP1Z8QakLN/d/\nf+XOxv2jdevT7t6tDFFuU/zDn4YAAggggAACbxegQHq7SRrP+BQ7CqQ0JFkHAjkLXKTtvaS0\n+5ZcjzCdrfj0NZ/SFkL7pjrxZ2WlNp3xF966rwc2vTZG9z06dmrTc3nc5RS7PJTZBgIIIIBA\nGgIXaCX/kcaKWMcKAn+nR8+t8AwPECiPQKVOsVsloft3tPwE5RblOuV+5UXFozOe8c63HrG5\nWQmhTVQnXCC5EGptD+sJj4i5QLqm8eJs3XpkaVzjMTcIIIAAAgggsKLAKD0M5f/5FXtW7kce\nQfLEWIOUJeXeFXqPQLkFkhZIvr5oV+V8ZX/Fp6VF7VHd+Yzyw+iJAG79SczuivdzaUt/NtNj\nz2rX3HyKoH/w/6X5Se4jgAACCCCAwFsCnGL3FkWqd3wNks948Ux2c1JdMytDAIHcBFxMbKu8\nR3lnbltNtiFPvODRo58qzcXQ2no8TfFrhyhuayjfUvzccUqebZI25u029zHP7bMtBBBAAAEE\n4gp4ttpD4y7McrEF/LUp/l3gXbHfwYIIhCNQqVPswmHNpiceOfLMdf6B86wypZH5jecu0W3U\nHtcdLzdD8UHOs1Eg5anNthBAAAEEehXwB4z+v3KHXlfA+zoK+NT/wzouwYsIhClQqQKp2yl2\nI3UMfC7sPMWnqPkHo0eOujX/A3eKbu6zTwM8WTlWeZ/i5mLpS8p3/aDR/ke35yseRXqt8Rw3\nCCCAAAIIILBcwKehu/lDRVr6Ak9qlcxkl74ra0QgVQFfc+RPiqLh3kcaj/1cp5yk10Ns/qGz\nToAdYwQpwINClxBAAAEE3ibwfj3z8tue5Ym0BG7Sir6a1spYDwI5CtRqBOkawT6k+JQ0N5+i\ntu6b9zr/4dntQmyeIYaGAAIIIIAAAr0JbKy3zentrbwrhoB/T2EEKQYUiyCQpcAqXVb++Tav\ne7a6Lyo+fa1s7W/U4WUdOu3TB0coi5RXOyzHSwgggAACCNRRwKfYcXpddkeeAik7W9aMQGwB\nFwxxm78I9hjFFw+WqTjydJkXK76Oyt/ZdJ2yt9Kuba8nvdyJ7V7kOQQQQAABBGouQIGU7V8A\nF0gbZLsJ1o4AAt0EkhRInrjgJWWo4nn6y9CGq5N3KEcpHh3yaQETlBuU0xQaAggggAACCMQX\noECKb9XLkowg9aLGexBIWSBJgfSGtn14Y/u/0+17lc0Vn5LWGo82hdC+oE74h/kpis+bHqvs\nptyrfFn5nkJDAAEEEEAAgXgCm2gxTrGLZ9XLUp7FjhGkXuR4DwIFCnh2lecUF0udcrJeD6Fd\nrU74m6lbr7Xyl8J6FMn74CIqajvpjp87KXoip1tmscsJms0ggAACCPQs4LNHFisH9bwG3thN\nYBct4N9D/MEzDYEyCdRqFrvWA/OgnohmtGt9rfnxzOYHBd7fSNu+UWm9ZmqBnvO1VH7t24on\nnmj+0lg9pCGAAAIIIIBAk4Cv6fUvQYwgNaGkfNen2Ll5FMnXTdMQQKAAgdaRlW5dOLbbAoG9\n7sLnQGWI0jornX/wHKLcqlygzFUWKjQEEEAAAQQQeLuAT69zo0Dqc8jiT5/14tl2XSCF8mFz\nFvvJOhEIWiDJNUhB70g/nbtWz/t0um8oG7ZZxkXRRMWTT1ylHKrQEEAAAQQQQODtAr6m12eR\n8EWxb7dJ65nXtaJnlfXTWiHrQQCB5AJJC6Tm5Sdocx9oyQ7Ju5DpO87U2v2ltSco/sTrw0pr\n8yc0Pp/an9ic2njR51nTEEAAAQQQQGC5gEeQHlv+kHsZCfg0O48g0RBAoCCB5oKnvy64WPig\ncotydNNCngHuty25Ro89YhNK82l1eyhnKP6h7qnK27W79OS7lKntXuQ5BBBAAAEEEHgHBVI+\nfwmYyS4fZ7aCQL8Cca5B+ne9+yuKZ1W5rGVNPjXt3MZzW+rWI0qeAe6zjedCuPGpAJ9upLUg\nHKTnbeBC6mHlYMXTgPsxDQEEEEAAAQSWC1AgLbfI8h4FUpa6rBuBFAT21Tp8PqxPU9umZX1/\n0uPmoXZPhDBb8SjNaKUM7QfqpAs/jx4V2SZp4+7HsCI7wbYRQAABBBDoIOAvXv/XDq/zUjoC\nPt3fZ+TQECiTgGe49O+y48vU6f762m0E6V/0RhdIPrXugf5W0njeoy6TlR8peyueQa7OzQWl\n/7LEaf4SWxoCCCCAAAIhCzCClM/RYQQpH2e2gkC/At0KJE+6cLdyT79rWPGF2xsPd9TtRSu+\nVKtHW2hv71OY7KFWh52dRQABBCor4LNE1lWazxyp7M4WvGMUSAUfADaPQKcCydfnbKVc2A/T\nDD0/suU1F1IeXtu25fm6PfyrdniE0sm32eSjevDD5ie4jwACCCCAQEACHj1yo0Dqc8jyTxdI\n/v2q3Xc4Zrld1o0AAg2BTr/AL9Uyy5S1+9H6WJvnR+k5j5r4S1jr3jw5RNy2KO6CLIcAAggg\ngEABAi6Q/HvBEwVsu26bdIHk5qm+Z715jz8QQCBXgU4FkkeC5ijbJ+iRrz1yK8s/6F+or9NL\n1F/b0hBAAAEEEMhbYLQ26N8J/MEpLVuBqEDyF9yX5fepbEVYOwI5C7ROe926+Sv1xKbKoa0v\ntHnsYusfG89f1ub10J5aTR1arPxFeV5hBjkh0BBAAAEEEGgj4BGkuk++1IYlk6f8u8k8xSNI\nNAQQKECgW4H0E/XJQ+q+Hdehfy6OPCnDgcotiq9PCrX5h/wlykLFE1B45j23XyinKoP9gIYA\nAggggAACbwl4BInrj97iyPyOT2X0CBINAQQKEHBh06l50oUvKi4i7lTOU25W7lKeUnZW/B1C\nhyj+ziRfe/S/lFCbP41x8ebrqjxt+VAlar526ivKhxTvE18WKwQaAggggAACEnCBdCMSuQm4\nQGIEKTduNoRAbwL/R297QXmjQ1xMbaeE3H6tznnkaJ9GJ30qYPQDf2Xd9wiS9/GflTwbXxSb\npzbbQgABBBBIKvCI3vBPSd/E8j0L/IfeeUHP7+aNCOQvsKo26d+hx+e/6fS32O0Uu2iL5+vO\n5sonlKsUj748rfgUNRcdRyi7KvcqIbcD1LmzlJvadNJfiHuKskDZs83rPIUAAggggEAdBfy7\nwsbKo3Xc+YL2mVPsCoJnswhYoNspds1Knsjgx400P1+W+yPUUX+vwMwOHV6i1+5rLNdhMV5C\nAAEEEECgNgK+FsbfjUiBlN8hp0DKz5otIfA2gbgjSG97Y8sTLrS2VlZqeT6kh74+ytdN7dah\nUy6iPBnFgx2W4SUEEEAAAQTqJDBaO+tTZ5ikIb+jToGUnzVbQuBtAr0USD6d7pymNb1f9z26\n5KJirnKwEmqboo4dqxynDG/p5Jp6/HNlDeXqltd4iAACCCCAQF0FxmjHfVr94roCFLDfLpD8\ne8lqBWybTSKAQEIBz/DmT5EWKR4tcjHhyRv8xXF/UHz9jh/7eqUQm3/Y+BMw74P76hElF3VX\nKC7y/Pz5St6NSRryFmd7CCCAAAJxBTzD661xF2a5VARGaS3+nSTU36dS2UlWUimBVbU3/js7\nvlJ7FXNnPNW3Z7LZobH8R3VrjO80Hm/WePy5xuMQb96pTvlaKn8S5r5HcYH0KWVlJe9GgZS3\nONtDAAEEEIgrcK4W/FXchVkuFYFBWos/fPZXqNAQKINApQqkJKfYedmxin9IevY6N3//kdul\nfTdvFk+e4W6XxuMQb55Tpz6u+DuQ/MnM3spGytrKjxTPZkdDAAEEEEAAgT6BMbqZ3XeXP3MS\nWKLtPKv49xMaAgjkLJCkQFpdfRui+LQ0N4+0HKTMU+5QouZlXEWG3lwIeTTsFuWJ0DtL/xBA\nAAEEEChIYIy2ywx2+eP7dxPPIEhDAIGcBZIUSL5mx8VQNNw7Ufc9bfZUxcPAbjsrmyouPEJs\n3fbXRZ/3yUUeDQEEEEAAgboL+HrjTZRZdYcoYP/napuMIBUAzyYR6FYwtAr9Qk8cqUxTfN/X\n7/jcZLevKTcpLpb+QwmlraeOXKy4uPNU39cpeyvt2vZ60sud2O5FnkMAAQQQQKBmAhtofwcr\ns2u23yHsLgVSCEeBPtRSIGmB5MLhQmUPxYWQJzW4XnGboPiTpmOUB5QQmqfy9ul/RykeHZqj\nuJ83KKf9//buA16OqnD7eGISAgkktNBLpBMwQKgBAalSpIiCCBZ8ISq+IiKC7S9FwAY2FAVf\nhKggRf8IKB0bIJ0AoYsQAoFAIIGEnlDe5yEzHyfj7t6du7OzZ2Z+5/N5sjOzszPnfM+9uXt2\nyioUBBBAAAEEEGgu4LNC3lamNl+FZ7ok4AESp9h1CZfNItANgYW0UQ+GkmWsZnydUkjleFXG\n/7Efp8R121jTdyte/kMlWTbUjJcfm1xYwPSEaL/DC9gXu0AAAQQQQKBdgQO1ItfptquV73oH\na3OP5LtJtoZA1wQ8NvB76Erc5jvrEaRYda4mfJ2OT0nz0SQX/xK/+M5UOP9sqarMUE5U4rrd\noeltlOuVI5SjFAoCCCCAAAII/LeAjyA99t+LWVKAgAemHEEqAJpdIJAW6M8AyRdrXqi8rPh2\n36coLucoHoj4XOVQii9u9EDojVSFZmv+A4rr/z3Fp+BREEAAAQQQQGBBAQ+Qpiy4iLmCBHyK\nnT+MXqqg/bEbBBCIBLIOkHyx5iTFN2p4UJmqxGWgJr6h+AhNKHeBc/12bFIf37DB3+M0Tfm1\n0uzGDXqKggACCCCAQC0F3q1WM0DqTdf7/YmLP+ylIIBAgQJZB0inqm6LKL7V9xjFg6W4fEgT\nvvHBeson44U9fvyL9j9S+bbS6DC1P53ZSfHpd5cruysUBBBAAAEEEJgvwACpdz8Js7TrV5WV\nelcF9owAAu0I+Jf1+4kVL9K0T2GLyxBNvKCcHS/o8aOPZN2nvK28qeyvNCq+OcPzitdzjlOK\nLBO0M++XmzQUqc6+EEAAAQRaCQzWkz5FfftWK/FcVwUe1tb9HoGCQOgCtb1Jwwj1jL9E9aEW\nPTRPz3lA4vVCKK+pEr6JhI98Pa745hKNyl1auIniL72lIIAAAggggMCAASsLYZDyKBg9E3hS\ne+YIUs/42XFdBbKcYudrdp5WNm2B5UGUT7Hz9UmhlJdUkcMVnyZwcYtKPaLndlU2U/63xXo8\nhQACCCCAQB0EVlMjfQTpiTo0NtA2eoDENUiBdg7Vqq6AD59nKVdo5UOUe5WJSrIsrpmJiq/5\nuUYJsfjLbfsqt/W1As8jgAACCCBQAwEPkHz2hU9Rp/RGYJp2u0Fvds1eEUCgXQEPgvyfpa+X\n8a2yfUTJn274yMxMxcvPVijZBCZoda5BymbG2ggggAAC3RX4jjYf6gee3W15OFs/TFXxh9IU\nBEIXqO01SO6YF5RxyhmKb4CwrOK7w+2luHxB8REmCgIIIIAAAgiUW8CnpnP9UW/70EeQuAap\nt33A3mso8K5+tPk5veazyjBldWUrxefH+ovMfqpwKF4IFAQQQAABBEou4FPsppS8DWWvvgdI\nvnRh0bI3hPojUCaBrAMkD4B8tGiI4oGQP1m6UXlKoSCAAAIIIIBAdQT8IahvYETpnYAHSC4c\nRZrvwL8IFCKQdYC0m2rl64183dGPlQ0VCgIIIIAAAghUS8BHLZZUOMWut/36jHY/T2GA1Nt+\nYO81E8g6QBovny8qvuXn4cqdyl2Kly2jUBBAAAEEEECg/AI+euTCEaT5Dr3613ff9Vk6K/eq\nAuwXgToKZB0gzRDST5SNlfWV7ytLKz9SfFTpEuWDik/BoyCAAAIIIIBAOQU8QJqlvFDO6leq\n1v5QmgFSpbqUxoQukHWAlGzPfZr5irKK8j7F1ydtoVyk+NOOHyprKhQEEEAAAQQQKJfAaqou\np9eF0WfcyS6MfqAWNRLoZIAUM/lTpm2UbRWfZufv8/GRJp9296ByjEJBAAEEEEAAgfIIrKGq\n/rs81a10TTmCVOnupXEhCvR3gDRKjfGXl92i/Ev5lrJU9Oj/VNdTPHD6k3K8cpBCQQABBBBA\nAIFyCPhvONcfhdFXDJDC6AdqgUBTgQ/pmcsU31HFR4peUc5RdlAGKuniL5L1er9NP8H8AgIT\nNGen4QssZQYBBBBAAIHeCDyu3R7Um12z15TA3pqfnVrGLAKhCSykCvm9rG/oVvoyOGMLTtb6\n/mbtm5WzlQuUVr+0b+j5qcokhYIAAggggAAC4QsMVRX9BfAcQQqjr3wEaUSUOWFUiVogUG2B\nrAOkn4njcsXXFrVTZmql0e2syDoIIIAAAgggEITAaqqFT8HnGqQguuOdr1ZxTXxTrHvDqBK1\nQKDaAv4PMEvxnen6GhwN0jo+tY6CAAIIIIAAAuUT8LXELyvTy1f1StbYN756TeFW35XsXhoV\nokDWI0hug8+F9bVI/pbt+PuOfP2Rt7WI4v9Yf6Ecp1AQQAABBBBAoFwC/ooOTq8Lq8+mqTo+\ngkRBAIECBDyoyVI+pZXP6uMFD+v5u/pYh6cRQAABBBBAIEwBf9Dpv+WUcAR80wyOIIXTH9Sk\n4gJZT7E7Wh6+QPATii/gfEn5mrK2coDyvHKtcrFCQQABBBBAAIHyCXiAxPVHYfWbB0gcQQqr\nT6hNhQWyDJB8bdHqypXKb5WnFH8P0paKvwvpPGUH5TPKpgoFAQQQQAABBMon4FPsOIIUVr8x\nQAqrP6hNxQWyDJAWlYWvObouYeIbNmyQmL9T0x4s7ZVYxiQCCCCAAAIIlENgqKrpIxUMkMLq\nLw+QVg2rStQGgeoKZBkg+fuOnlPWSXB4gOT/SJN3rfMv8ZjEOkwigAACCCCAQDkEfKaI3xsw\nQAqrv/ydkr60Icv7trBaQG0QKJFA1l8033zBd7HbPGrjPdGjl7kspmyt8EVm1qAggAACCCBQ\nLgGfXufri6eXq9qVr60/fPZZPMtXvqU0EIESCmyoOs9V3lK2UjzA8q1AfX/+ixXfq/9t5RMK\npX2BCVrVbsPbfwlrIoAAAgggkLvAUdripNy3ygY7FfDXqPh9gq/7piAQosBCqpR/RseHWLms\nderPEaRdtJOrlWcVD5T2VWYpvu5olHKuco5CQQABBBBAAIFyCayl6vpaYkpYAq+qOv4Q2pc1\nUBBAoMsCWb8HydX5a5S4av6kyffm980aXlAeVSgIIIAAAgggUD4BD5D+Ub5q16LGvg5pdC1a\nSiMR6LFA1iNIzar7pp7wQInBUTMhliOAAAIIIBC+AEeQwu0jD5BWDbd61AyB6gjkMUAaJg5/\n75HPj6UggAACCCCAQDkFRqjayymcYhdm/z2majFACrNvqFXFBNodII1Vu7+qHKLEd1DxdyWc\nr/hapFsV3wb8VwoDJSFQEEAAAQQQKJmAjx65PDT/gX8DE+AIUmAdQnXqLXCMmu+7UsSZqem1\nlROjZf5upH8ovrW31/mDQskmwF3ssnmxNgIIIIBA/gIHapNP579ZtpiTwB7ajm/BTkEgRIGF\nVCmPAypxF7u+gN8fNXaKHr+oHKrcpzyuzFMuVAYpLkspdyu+HslfNEdpX4ABUvtWrIkAAggg\n0B2Bb2mzf+/OptlqDgLv0Tb8BtR3DKYgEJpArQZI35e+fxnHJXrBR4/eiJb77nXJ8nHNeP39\nkguZ7lOAAVKfRKyAAAIIINBlgQu0/TO6vA8233+BxfRSv8fydd8UBEITqNQAqa9rkMZI37fu\n9h3q4uJzk59R5irT4oXR48PR4wqp5cwigAACCCCAQNgC66h6D4ZdxVrX7kW13pc5jK61Ao1H\noACBvr4HaSXVwb+Q6eIbM7j4k4xkeS2aGZlcyDQCCCCAAAIIBC3gD0zXUhggBd1NAx5T9UaH\nXUVqh0D5Bfo6guQW+pqidPEpdm+lFzKPAAIIIIAAAqUUGK1aL6wwQAq7+x5T9d4ddhWpHQLl\nF+jrCFL5W7hgC4ZrdnllCcWDQ9+a3EfDfMiaggACCCCAQF0FfHqdzwKZWleAkrR7iuq5fknq\nSjURKK1AOwOkRdW6j6Va6DvWDWuwfNXUeqHMbq2KfFfZTGnU5ke1/I/KN5VXFQoCCCCAAAJ1\nElhXjfU1xpwdEnave4C0R9hVpHYIVF/gLjXR1xllzbEB0fgOcb6hxCzlBuVpxe3xJ2U/U/y9\nTY8oXna/soFSdOEudkWLsz8EEEAAgaTAmZo5L7mA6SAFdlWt/EHuwCBrR6XqLFCpu9g1OpqS\n7NyzNeNT0rKWf2Z9QZfW31Lb/aXyU+Uriv9T8al18REl321vX8WfmG2rnKXcrKypTFMoCCCA\nAAII1EHAR5CuqkNDS97GKar/worfmz1V8rZQfQQQ6JHAd7Rff3lto09a/GW2Pmq0oxKX0Zp4\nUzkxXlDQI0eQCoJmNwgggAACDQV8loU/MKSELeDBkT/U3SrsalK7GgpU6ghSO3exK3Mf76TK\ne4DkgVC6+LS6l5XkAOkxzd+prKdQEEAAAQQQqIPAcmqkb17k08wpYQv48gAfOVot7GpSOwTK\nLVD1AdJz6p5mN2bwfy6+q12yDNLMygo3akiqMI0AAgggUGUBfyjor+/4V5UbWaG2Paq2MECq\nUIfSlPAEqj5AukbkaytnKMnBkO/C5+uNXK6b/zDAX257krKMcmO0jAcEEEAAAQSqLjBGDXxY\nmVf1hlakfQyQKtKRNAOBXgkM1o5vUXyK3bPKFVGej5ZdqMe4PKEJrzdJ8XmURRauQSpSm30h\ngAACCCQFTteM7+hKKYfAsarm9eWoKrWskQDXIJWos33KwHbKyYpPn9slij8l+5pyoBKXWzVx\ngvJeZW68kEcEEEAAAQQqLuBT7O6reBur1DxfQ716lRpEWxBAoLcCvhB1VG+r0HDvHEFqyMJC\nBBBAAIECBLiDXQHIOe5ivLblM16G5bhNNoVApwIcQepUsIevn6F9+1S7ZsVHmXwnH99Gk4IA\nAggggEDVBfx9gP67xxGk8vS0jyC5cKOG+Q78i0DuAlW/SYPBllUuUPwJ2Rzlb8pWSqPyHi30\nel9p9CTLEEAAAQQQqJiAT6/zaeXcwa48HesPe19UOM2uPH1GTUsmUPUB0qLqj9uU/RQfHZqm\nbKv4znW+Yx0FAQQQQACBOgv4g8GHFF+zSymPgO9kt0Z5qktNESiXQNUHSEepO/y9RscrKynr\nKJsq9ypfV36oUBBAAAEEEKirgAdI99S18SVu98OqOwOkEncgVQ9boOoDpC3F70PRJyo+HO1y\nh7KNcr1yhOJBFAUBBBBAAIE6CqyvRvtDQ0q5BP6t6jJAKlefUdsSCVR9gLSi+sIDofSpA7O1\n7APKZOV7ik/BoyCAAAIIIFAnAb8H8DVI/ltIKZcAA6Ry9Re1LZlA1QdIU9UfOyqN7krnGzbs\npkxTfq00u3GDnqIggAACCCBQOYE11aJFFAZI5etaD5BWUYr+YvvySVFjBPohUPUB0l9kMlL5\ntrJCA58ntWwnxaffXa7srlAQQAABBBCog8BYNfIF5Yk6NLZibfQ1SH4Pt1rF2kVzEAhCoOoD\npJ9J+X7F1xr5D8D+Srr47j07K28pvlbJZeD8B/5FAAEEEECgsgIeIHGDhnJ271Oq9suKjwJS\nEEAgZ4GqD5Bek9fmyqnK48pcpVG5Sws3Ua5s9CTLEEAAAQQQqKDABmqT//5Ryingo0hrlbPq\n1BoBBEISaGdA6NuA+7anRZYJ2tnbyvAid8q+EEAAAQRqLeDrdA+utUC5G3+hqn96uZtA7Ssk\nsJDa4vey46vQpsFVaESGNvg0umQZohkb+EiTO9XFXyxLQQABBBBAoMoCS6hxvsj/7io3suJt\n8xGkSrwZrXg/0bwSCrRzRKWEzWq7yidrzVeUjdt+BSsigAACCCBQfgGfXvemwncglbcvfQ31\n2uWtPjVHIFyBuh1BKqonfOe8byo+3NhOWa+dlVgHAQQQQACBnAQ20nYeVHwGBaWcAh4g+Q69\niyovlbMJ1BqBMAUYIHWnXzwwWknxKXztlMXbWYl1EEAAAQQQyEnAA6Q7c9oWm+mNwL+i3fpG\nDZN6UwX2ikA1BRggdadfn9Vm98+wad+k4ZcZ1mdVBBBAAAEEOhHwAOnsTjbAa3su8Lxq4Pcb\nPs2OAVLPu4MKVEmg7tcgVakvaQsCCCCAAALtCCyildZVeFPdjlbY6/g0Sa5DCruPqF0JBep+\nBOkc9dkdypQS9h1VRgABBBBAoD8C/oJYf0DKKXb90QvrNR4gebBLQQCBHAXqfATJn6C9rvgc\n3pnKcIWCAAIIIIBA1QXGqYGPKrOr3tAatM8DpHVq0E6aiEChAnUcIPl7H/zlai8rk5VTFBcf\nTTpRGeoZCgIIIIAAAhUV2ETt8tkTlPILeIDkmzTU8f1c+XuPFgQrULdfqOXVEz7nel/F/6n4\nW8TjMlAT31D8R2PheCGPCCCAAAIIVEzA3/13e8XaVNfmPKCG+z3L6LoC0G4EuiFQtwHSqUL0\nqXVbK2OU5AWqH9L8SYq/k+iTCgUBBBBAAIGqCfhvoP/OcQSpGj3rD3pfVbgOqRr9SSsCEajb\nAGkHuZ+m3NDA398ofrzic7K3aPA8ixBAAAEEECi7wIZqwCCFAVLZe3J+/d/Sg8+I8Ye+FAQQ\nyEmgTgOkETJbQvE3Tzcr8/TEfYrXoyCAAAIIIFA1gU3VIN+ciBs0VKdnfZodR5Cq05+0JACB\nOg2Q5sj7acV/HJoVD6J86oE/jaEggAACCCBQNQH/Dbytao2qeXv8wa7fu1AQQCAngToNkEx2\nhXKI8nllUSVZFtfMb5SRyjXJJ5hGAAEEEECgIgKbqx23VKQtNGO+gAdIPsXON5uiIIAAApkF\nPAh6XHlb8ekFPqL0pHKxMlPx8rOVossE7dD7Hl70jtkfAggggEBtBJZUS/23ZrPatLgeDV0j\n6tdV69FcWhmowELRz+H4QOtHtfoQWFrPn674S2L9hyKOB0iHKb54tejCAKlocfaHAAII1E9g\nFzX5NcVvZCjVEfDZQL6T3W7VaRItKaFApQZIdTvFzj9vzymfVYYpqytbKSsqSyk/VXw3OwoC\nCCCAAAJVE9hCDbpTmVu1htW8Pb6T3f3Ke2ruQPMRyE1gcG5bKt+GPBB6NEr5ak+NEUAAAQQQ\nyCbgU19uyvYS1i6JwL2q5/olqSvVRCB4gToeQQq+U6ggAggggAACOQv4An7foIEBUs6wgWzu\nHtWDI0iBdAbVKL8AA6Ty9yEtQAABBBBAoC8B3wbad2llgNSXVDmf9wDJ34VU5zODytlz1DpI\ngar/IvnmB/5uo6zlRr2APyJZ1VgfAQQQQCBUgS1VsceVaaFWkHp1JDBZr/ZF8usoPt2OggAC\nHQhUfYD0Odls2A+f4/QaBkj9gOMlCCCAAAJBCviGRP7wj1JNgelq1rPKWIUBUjX7mFYVKFD1\nAdKusrxI8YWplyhnKe2Uh9pZiXUQQAABBBAoicB7Vc8flqSuVLN/Aj6K5AHS7/r3cl6FAAJ1\nEhiqxt6s+HuPNgq04XwPUqAdQ7UQQACBCgisrDb4O//85plSXYEfqGlXVrd5tCxwAZ/i6f9n\nfFCi9KUON2nwwOjgqKf8PUcUBBBAAAEE6iSwjxo7T+HUq2r3ur/jqj+XFVRbhdYh0A+BOgyQ\nzHKf8nVlhMJtMIVAQQABBBCojcBaaulVir9QlFJdgbvUtGWV5arbRFqGAAJ1EuAUuzr1Nm1F\nAAEEihXwkaOjit0le+uBgK8rf1Xx9dcUBIoW4BS7osXZHwIIIFKAPb0AACiWSURBVIAAAgj0\nS2CUXjVG+Xu/Xs2LyiTwhirr70PauEyVpq4IhChQl1PsQrSnTggggAACCHRb4H3awYvKpG7v\niO0HIXCHajEuiJpQCQRKLMAAqcSdR9URQAABBBDoQ2A7PX+98mYf6/F0NQQ8EGaAVI2+pBU9\nFGCA1EN8do0AAggggECXBXbQ9v/S5X2w+XAEbldVVlV8aiUFAQT6KcAAqZ9wvAwBBBBAAIHA\nBVZS/XwHOwZIgXdUjtXzDTn89Sab5LhNNoVA7QQYINWuy2kwAggggEBNBHZUO2covnCfUg8B\nf9/V3QoDpHr0N63skgADpC7BslkEEEAAAQR6LLCT9n+t4m+3p9RH4FY1dbP6NJeWIpC/AAOk\n/E3ZIgIIIIAAAr0WGKgKeIB0Ta8rwv4LF2CAVDg5O6yaAAOkqvUo7UEAAQQQQGD+ncx8of5V\nYNRO4Ba1eBlldO1aToMRyEmAAVJOkGwGAQQQQACBgAR2UV18Lcr0gOpEVYoReFi7maWML2Z3\n7AWB6gkwQKpen9IiBBBAAAEEdhPBFTDUUsDXnN2sMECqZffT6DwEGCDlocg2EEAAAQQQCEdg\nKVVlc+XycKpETQoWuEn7Y4BUMDq7q44AA6Tq9CUtQQABBBBAwAK7KrOVGz1DqaWA+35DZVgt\nW0+jEehQgAFSh4C8HAEEEEAAgcAE9lB9fHrdm4HVi+oUJ+AbNbj4SCIFAQQyCjBAygjG6ggg\ngAACCAQssJDq5iNIlwZcR6rWfYGXtYu7lK27vyv2gED1BBggVa9PaRECCCCAQH0FtlfThyrc\noKG+PwNxy6/TBAOkWINHBDIIMEDKgMWqCCCAAAIIBC6wj+p3rfJi4PWket0X8ADJN2oY0v1d\nsQcEqiXAAKla/UlrEEAAAQTqKzBITd9buai+BLQ8IXC9phdRNkksYxIBBNoQYIDUBhKrIIAA\nAgggUAKBbVXHJZSLS1BXqth9AX9Z7GRlu+7vij0gUC0BBkjV6k9agwACCCBQX4H91PS/KjPr\nS0DLUwJ/0/z2qWXMIoBAHwIMkPoA4mkEEEAAAQRKIDBYdfywcn4J6koVixP4i3a1lbJwcbtk\nTwiUX4ABUvn7kBYggAACCCCwswgWVbj+iJ+FpMA/NONr0zxIoiCAQJsCDJDahGI1BBBAAAEE\nAhb4mOp2mTI74DpSteIFXtIub1LeX/yu2SMC5RVggFTevqPmCCCAAAIIWGCE4rvX/dYzFARS\nAj7Nbt/UMmYRQKCFAAOkFjg8hQACCCCAQAkEfHOGlxUfQaIgkBaYpAWjlRXTTzCPAAKNBRgg\nNXZhKQIIIIAAAmUROFgVPVeZV5YKU89CBTxwflrZtdC9sjMESizAAKnEnUfVEUAAAQRqL7Ce\nBLZQzqy9BADNBN7WE5crH2i2AssRQGBBAQZIC3owhwACCCCAQJkEPqvK+iL8e8tUaepauMCl\n2uNOyiKF75kdIlBCAQZIJew0qowAAggggIAEfFvvjyu/QAOBPgSu0fMDFQ+SKAgg0IcAA6Q+\ngHgaAQQQQACBQAU8OJqrXBho/ahWOAKvqCpXKfuEUyVqgkC4AgyQwu0baoYAAggggEAzAR8N\nOFz5pfJ6s5VYjkBCwF8ivKcyJLGMSQQQaCDAAKkBCosQQAABBBAIXGB31e/dymmB15PqhSNw\niaoyTOE0u3D6hJoEKsAAKdCOoVoIIIAAAgi0EDhaz52rTG+xDk8hkBSYo5krlf2TC5lGAIH/\nFhj834sqv2QJtXCkMlR5SXlB8RfsURBAAAEEECiDwHtVya2UT5ehstQxKAEPqs9SfCTJ1yVR\nEECgxgIbqe3+jogZir8PIJ1HtOwMZZTSizJBO3Wdhvdi5+wTAQQQQKBUAlerttyYoVRdFkxl\nF1ZN/MHwgcHUiIpURWAhNcTvZcdXpUFVb8cxUYe506YqNyp/Vs5XrlBuUXyKgp9/TjlAKbow\nQCpanP0hgAAC5RTw0aO3lPXLWX1qHYCAPxC+NoB6UIVqCTBAKlF/7qu6euDjgdC4FvX23YC2\nUW5TvP6WSpGFAVKR2uwLAQQQKK/Adar6eeWtPjUPQGBz1cGD7NUCqAtVqI4AA6QS9aXPtfXp\nc77eqJ3i65N8EePp7ayc4zoMkHLEZFMIIIBARQV8i+a5yuoVbR/NKk7gbu3qO8Xtjj3VQKBS\nA6Sq38VurH4gb1La/Y6I57XuZGVFhYIAAggggEAoAkNUkZOVnyv+4I+CQCcCv9CLD1Ha/QC5\nk33xWgRKJ1D1AdJ09cjGiv+wtFN8BMmDqgfbWZl1EEAAAQQQKEjgCO1nSeX4gvbHbqot8Fs1\nz3cy5mYN1e5nWodAQwH/4vuaoksVn3PbrPgapK0V37DhDWUrpcjCKXZFarMvBBBAoFwCq6i6\n/loKf+JPQSAvge9rQ/cqfg9EQaBTgUqdYtcpRuiv9y+9P3Xz9xx5oDRNuVm5TDkvevQpeE8p\nfn6ecrhSdGGAVLQ4+0MAAQTKI+AbDV2v8Ea2PH1WhpquoEr6EoQ9ylBZ6hi8AAOk4Lvovyvo\nO7V4QPSk4oFQMh48Paycoqys9KIwQOqFOvtEAAEEwhc4WFV8VVk7/KpSwxIK+JbfvoMvBYFO\nBRggdSrY49eP0P49EFpTGdnjusS7Z4AUS/CIAAIIIBALrKGJF5Uvxgt4RCBngVW1PR9F2ivn\n7bK5+glUaoBU9Zs0NPrxHKSFjtu+qDJcoSCAAAIIIBCSwMKqzIXKP5WfhFQx6lIpgalqjY8i\nfUfxeyMKAgjUSGAjtfVMZYaSPL0unvYtU/0fxCilF4UjSL1QZ58IIIBAuAJnq2pPKL36uxSu\nDDXLW2BpbfAF5f/mvWG2VyuBSh1BqkPPHaNGxgMhf1Jyo/Jn5XzFF776znXTFa/znHKAUnRh\ngFS0OPtDAAEEwhX4sqrm6442DbeK1KxiAj6Nc5aybMXaRXOKE2CAVJx1x3vaV1vwwMcDoXEt\ntuY7A22j+EJFr7+lUmRhgFSkNvtCAAEEwhXwh3T+uon9wq0iNauggE+vu1O5oIJto0nFCDBA\nKsY5l72cq6349LmhbW5tCa03Rzm9zfXzWo0BUl6SbAcBBBAor8AHVXV/3cQXytsEal5iAV+O\nMFfZv8RtoOq9E2CA1Dv7zHu+R684J+OrbtD6f8r4mk5XZ4DUqSCvRwABBMot8FFV329Ov1ru\nZlD7kgt8TfX39Uirl7wdVL94AQZIxZv3e49X65UPKEPa3EJ8BOnkNtfPazUGSHlJsh0EEECg\nfAK+5sin1XE77/L1XdVq7Dv8+rIEf8C8WNUaR3u6KsAAqau8+W78QG3O1xRdqmzeYtO+Bmlr\nxTds8B+prZQiCwOkIrXZFwIIIBCGwDBV4zfKq8pHwqgStUBggD8sfki5Smn3A2bYEGCAVKKf\nAQ98jlBeVjxQmqbcrFymnBc93qTHpxQ/73O/D1eKLgyQihZnfwgggEBvBTbW7u9XpiiepiAQ\nksBqqozfG12kMEgKqWfCrQsDpHD7pmnN/IvuAdGTigdCyXjw9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BBBBAAIEeCfh0\nLl/bROmtgK8Z85EzCgIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg\ngAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAII\nIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAAC\nCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAA\nAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCA\nAAIIIIAAAghUTuD/A3wXkSt1ORLLAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(seq(0,1,0.001), BayesGrid(obs, f, Prior, seq(0,1,0.001)), type = 'l')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## d)\n",
    " \n",
    "d.  One estimate that is often used as a point estimate is the posterior mean.  Use an independence chain Metropolis Hastings algorithm to sample from the posterior and return an estimate using a candidate distribution that is uniform over the support (i.e. the candidate distribution is the same as the prior, which is often a good idea without other information).  Return the estimate of the posterior mean, and create plots that asses the 'mixing' of the chain (how quickly the chain explores the space). Use a starting value far from the true $\\delta$, say $\\delta_0=.1.$\\\\[5pt]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Metropolis Hastings ratio (R) is:\n",
    "\n",
    "$$R(u,v) = \\frac{f(v)}{f(u)} \\frac{g(u|v)}{g(v|u}) $$\n",
    "\n",
    "with a uniform prior:\n",
    "\n",
    "$$R(u,v) \\Rightarrow \\frac{g(u|v)}{g(v|u)} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "MHStep <- function(x, eps, obs, f, prior) {\n",
    "    #\n",
    "    # Function which performs one iteration of the MH-algorithm\n",
    "    #\n",
    "    # Args:\n",
    "    #    x: starting value for the metropolis-hastings algorithm\n",
    "    #    eps: maximum step size to take in a MH algorithm step.\n",
    "    #    obs: the input observations\n",
    "    #    f: the pdf of the function, which takes a delta argument\n",
    "    #    prior: a function of the prior distribution\n",
    "    #\n",
    "    # Returns:\n",
    "    #    y: the next location in the MH algorithm path\n",
    "    \n",
    "    y <- x + eps*runif(1,-1,1) #the proposed step\n",
    "    \n",
    "    met_ratio <- min(1,(BayesInf(obs,f,prior,y)/BayesInf(obs,f,prior,x))) # calculate \n",
    "    \n",
    "    if (runif(1) < met_ratio) {\n",
    "        return(y)\n",
    "    }\n",
    "    \n",
    "    else {\n",
    "        return(x)  \n",
    "    }\n",
    "}\n",
    "\n",
    "MH_alg <- function(x, eps, obs, f, prior, n_iters) {\n",
    "    \n",
    "    #\n",
    "    # Function which performs n iterations of the Metropolis-hastings algorithm.\n",
    "    #\n",
    "    # Args:\n",
    "    #    x: starting value for the metropolis-hastings algorithm\n",
    "    #    eps: maximum step size to take in a MH algorithm step.\n",
    "    #    obs: the input observations\n",
    "    #    f: the pdf of the function, which takes a delta argument\n",
    "    #    prior: a function of the prior distribution\n",
    "    #\n",
    "    # Returns:\n",
    "    #    y: the next location in the MH algorithm path\n",
    "    \n",
    "    path <- c(x)\n",
    "    \n",
    "    for (i in (2:(n_iters + 1))) {\n",
    "        path[i] <- MHStep(path[i-1], eps, obs, f, prior)\n",
    "    }\n",
    "    \n",
    "    return(path)\n",
    "}\n",
    "\n",
    "IterMH_mean <- function(x, eps, obs, f, prior, iter_seq) {\n",
    "    #\n",
    "    # Function which performs n iterations of the Metropolis-hastings algorithm.\n",
    "    #\n",
    "    # Args:\n",
    "    #    x: starting value for the metropolis-hastings algorithm\n",
    "    #    eps: maximum step size to take in a MH algorithm step.\n",
    "    #    obs: the input observations\n",
    "    #    f: the pdf of the function, which takes a delta argument\n",
    "    #    prior: a function of the prior distribution\n",
    "    #    iter_seq: the sequence of numbers of iterations.\n",
    "    #\n",
    "    # Returns:\n",
    "    #    means: the posterior mean evaluated for a range of number of MH iterations\n",
    "    \n",
    "    means <- c()\n",
    "    \n",
    "    for (i in (1:length(iter_seq))) {\n",
    "        means[i] <- mean(MH_alg(x, eps, obs, f, prior, iter_seq[i]))\n",
    "    }\n",
    "    return(means)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will draw 1000 samples from the posterior distribution, starting the chain at $\\delta = 0.1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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6vHg5oVEx6vaG37vAnrZ1006xjX8Q9L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3VtwHHkgt8wA6LptrZkflesV3EMcodyoXK3Hxo3kzFA9q47tS8TrdPN2oZzvPucjP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\nEEAAgY4J/D/OIybz4uFDmQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Histogram of MH_alg(0.1, 0.05, obs, f, Prior, 1000)”"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(MH_alg(0.1, 0.05, obs, f, Prior, 1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will see how long it takes the chain to explore this space, by performing several MH algorithms with different number of iterations. We will start at 1 iteration, and then move up to 1000 iterations, to see how fast the posterior mean converges on its expected value of $\\delta = 0.7$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "iter_means <- IterMH_mean(0.1, 0.05,obs, f, Prior, seq(1,1000, by = 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0Knfo4e13uV8eej93fN67WPUbslD16W\n/P7oBT/XFuh7gTQa/bl58OSlJ/ULV79sOyT1xbFXJhoBAgQIECBAgACBWQnskh2NipjRzypg\nRo9X+jl6v/5OHb8Npv7B/+rkihXytRVeG9/u8rxfV03VPrQJBYZSII1z1C9JRSNAgAABAgQI\nECCwkkDdk768iBkVMMtfHz0ff3/rZTu9Js/HC5fR47r94wurvFfbVIFzZVJngbSGBIZYIDVE\n6zAECBAgQIAAAQILEqgrhUaFy+jneAEzem385/j72y7rd92SccUKuSivnbXC66Ntq8Cpxzcn\nWkcEFEgdmSjdJECAAAECBAj0QKDujdk+2TGpszT1c6MZ//zO2U9dmjYqeOoY4+36PBkVLeM/\na+Guc1Z4b3TmZlTg3Di+M4/7LaBA6vf8Gh0BAgQIECBAYC2ButdlFgXKNPtYrT91n8wNyXUT\n5j/Gtrs2j+tStPHipx6PCpzar0ZgIgEF0kRMNiJAgAABAgQILFSgCpnDkzsno2Jk/AzK6LVp\nftbnt0tWa3XfS515WalgqYJkvJipS9AuWWXblT6/0mu1D43AwgUUSAufAh0gQIAAAQIECKwo\nUCvvPjJ5TPLoZK+kCpOViot6rQqM0Xt1NmX8DMvo9bV+jn++tnPWJQja8AQUSMObcyMmQIAA\nAQIE2itwj3TtsUkVRUcndQbnn5IXJ+9NLko0AgTmKKBAmiOuXRMgQIAAAQIE1hGo1dKOSUZF\n0cF5/JXkPckfJh9OvpNoBAg0JKBAagjaYQgQIECAAAECSwJ3ys9HJVUUPSKpJak/mpyY/N/k\nrEQjQGBBAgqkBcE7LAECBAgQIDAYgVra+rCkLpurougBySXJKckzkn9M6p4hjQCBFggokFow\nCbpAgAABAgQI9E6gvpfnYUkVRLXAwg8kn0nqDNGvJv+e1CpxGgECLRNQILVsQnSHAAECPRC4\na8bw3OQ/J7US1mVJfRfJ8p8rvVbfW+Ib54OgdVKgfvdHZ4l+LI/rd/mfk99P6p6iCxONAIGW\nCyiQWj5BukeAAIGOCNQlRPWv5S9I6l/Lz0hek9S/kO+R7Ln0s25AHz0e/Rz/xvv6osirklEx\nVUXUqJAavTb6OXp99PPqbKsRaFJg6xzsIcmoKLp3Hp+X1FmiVyX/mtQqdBoBAh0SUCB1aLJ0\nlQABAi0U2C19elryvOSg5P8kP5Z8JJm07ZQNx4uo8cejIqp+Hrhsuzvkef2BOmo35UEVS6OC\nafnjUWE1+jm+nT9iR4p+ridQv4u1wEIVRT+R1H8H/i35u6TOEn0+0QgQ6LCAAqnDk6frBAgQ\nWKDAvXLsX05+Ibkm+Yvkdck3k2lbfTllZdrLj+qsVf1xOl5EVXG1vMDaN6/dZ+n10Xu75vl4\nq0sBxwumlYqo0Wujn6MCzCWB45L9fPxDGVbdS1RF0VHJVcn7kucntdBC/U5oBAj0RECB1JOJ\nNAwCBAg0IFBna+ryufqj8OHJx5PnJG9LbkyabnU53pVL+eqUB6///1upmFr+2t2XthsVYfV+\nLck8atWHurRvVDQt/7lS0VXbVFwSGISWtprj/5SMiqI6e/nFpM4Q/U5yaqIwDoJGoI8CCqQ+\nzqoxESBAYLYCVRw8I6kzRndO3pockZyWdLXV5XjfWsq0Y9gxH6hCaVQ0Lf85eu+AZdssvySw\njn/OstQXhNZrFyVaswJ3yeHqHwCqKPrxpP5B4IPJCUndUzRtEZ6PaAQIdFFAgdTFWdNnAgQI\nNCNwWA7zvOQpycXJicmfJ5cmQ251OV7lG1Mi1CWBuyZVUO2V1Nmpuy3lx/KzitBaCrq2q0sO\nq1CqgmlUNI2Kqa/ntZsSbXMCt8/HH5iMzhIdmsc1p+9N6nf+A8m1iUaAwMAEFEgDm3DDJUCA\nwDoC2+b9n0rqMrofST6YPDX5++TmRNu4QF2Od9VSvpafn0qWt7q0a1Q0jX7eL6/VnNRlXjU/\nVRzV2YxRwTT+89y8XsWbtrLA7nn5EUkVRY9KqlD9ZPJ/kipQP53UPGkECAxYQIE04Mk3dAIE\nCIwJ1KVzz0rqnqI6y/HG5NlJ3XehNSdwfQ71haUsP+rWeaEu26vCafzs09F5XisI7pLUH/d1\nFmS8aPrK2PO6J2po7Z4ZcC2uUEVRFf1l/I/Jbya1wILLGYOgESDwPQEF0vcsPCJAgMAQBR6U\nQdfZoiclX0v+OPnr5MpEa5fAzelOnTmqfGCFrt0pr40XTlVIVVFQr9WZkmr1RbxVMI0XTaNi\nqgqrKrC63rbLAI5JRkVRjf/spO4jenny4WQRi4rksBoBAl0QUCB1YZb0kQABArMVqMu4fjZ5\nQXJY8r7k8Us/+/AHcoYyyFZnQiq1wtryVmcFx4unevzg5L8kd0nqfpw6szIqlsZ/VjF1XtLm\noqKKw1pgoYqiRyT1O/6R5HXJe5IvJxoBAgQmElAgTcRkIwIECPRCoC7PqkvonpXU5Vp/nfxM\nUn8Ma/0WqCXF6/6ayvJWZ1zumoxfunePPK97dOr17ZObk/OTUeE0fgaq7nu6Jmmy1UIWVdzX\nGbLKEcklSS2w8Izk/Und76URIEBgagEF0tRkPkCAAIHOCfyn9Lguo/vJpO4p+p3k75JvJxqB\n74TgrKUs16hCZP+kiqfxPCXP676n3ZNqdeaqiqfxwmlUTH2rNphB2zn7eFhSBVGdKaovAP5M\nUmeI6mzovye3JBoBAgQ2JaBA2hSfDxMgQKC1ArukZz+fVGFUZwPendQflx9MNAKTCtQll3Xm\nqPKvK3xor7w2XjjdPc8fsfTanZe2rzM5o2Jp9HNUSF2Q99YqauoM1qgg+rE8vjn55+S4pO4p\nujDRCBAgMFOBbWa6NzsjQIAAgUULVDH03OSXkrqn5PVJ3YdRf4hqBGYtUJe1VT6xwo7rjE+d\nZbp7MiqiDs/jWhDkwGTrpM5efTUZL5yq6DkyqbNE907OS+os0auSKtLq91ojQIDA3AQUSHOj\ntWMCBAg0JnD7HOknkjpb9MjkU0uP35qfNyQagUUIXJuDfm4py49ff3/8YDIqnEY/H5rX9k/O\nSP42qbNEn080AgQIEBiYwLEZ761J/WubRoAAgUkF7pANfy2py5WqEHpj8sBEI0CAAAECTQps\nl4PV37JHNXnQeR3LGaR5ydovAQIE5idw3+z6V5L/klyenLSUi/NTI0CAAAECBAh0XsAZpM5P\noQEQmLtA/YPWE5O6B6P+le7DSd3L4R+6gqARIECAwEIFnEFaKL+DEyBAYFgCe2e49Y8otfDC\nnsnJya8mdY+GRoAAAQIECBDopYAzSL2cVoMisCmBB+TTb0hqxa5a4etFyR6JRoAAAQIE2ibQ\nqzNIbcMdan8USEOdeeMmsKVA/R9MfXdRLZlc3w3z/uRxSa1SpxEgQIAAgbYK9KpAcu16W3/N\n9IsAgSEJ7JfBPid5VrJDUmeOagGGLycaAQIECBAgQGBwAs4gDW7KDZjAdwWOyX++Lbkx+WJS\nK9PtkmgECBAgQKBLAr06g+SyjS796ukrAQJ9ENgpg6h/FPls8i9J/Z/Ko5J7J69Nrkk0AgQI\nECBAYEECLrFbELzDEiAwOIGDMuJfTn4pqfuL/jL5yeS8RCNAgAABAgQIEBgTcIndGIaHBHok\nsFXG8sjkH5Kbk9OTKpDqPiONAAECBAj0RaBXl9g5g9SXX0vjIECgTQK7pTO/kNQ9RXdN3pHU\n/UanJhoBAgQIECDQYgEFUosnR9cIEOicwL3S4+clT0vqXqKTlvLN/NQIECBAgAABAgQmFHCJ\n3YRQNiPQQoGt06cnJB9Ibk3qLNGTk20TjQABAgQIDEHAJXZDmGVjJECAwDoCdR/RM5MXJXdK\n3pz8cFL3GWkECBAgQIBARwVcYtfRidNtAgQWJrBzjlxf6lqFUf1v6J8mdSndpYlGgAABAgQI\ndFxAgdTxCdR9AgQaE6iFF2rRhV9Pbkr+JHldcm2iESBAgAABAgQIzFDAPUgzxLQrAjMW2CP7\nOy65PPl68vzEMt1B0AgQIECAwJJAr+5BMqvtEFAgtWMe9ILAuMDeefKK5Krk3OTZSf0fgEaA\nAAECBAhsKaBA2tLDsxkIKJBmgGgXBGYksG/2U5fP1aVzZyW/kLgcOQgaAQIECBBYRUCBtAqM\nlzcuoEDauJ1PEpiVwP7Z0WuS65LPJ09Jbp9oBAgQIECAwNoCCqS1fby7AQEF0gbQfITAjAQO\nyn7+PLkhqSW6n5hslWgECBAgQIDAZAK9KpD86+hkk24rAgT6J3DPDOlvkrqM7v7JTyeHJ+9I\n6gtfNQIECBAgQGCAAgqkAU66IRMYuMAPZfz1pa5fTOrs0WOSI5N/SDQCBAgQIEBg4AIKpIH/\nAhg+gQEJjM4OnZEx1wp1P54ck/xjohEgQIAAAQIEviugQPKLQIBA3wUelAG+J/lUsmPykORh\nyQcTjQABAgQIECCwhYACaQsOTwgQ6JHA0RlLnR36WHJj8oDk0cnHE40AAQIECBAgsKKAAmlF\nFi8SINBhgTo79KHkg8nlSS3A8FPJaYlGgAABAgQIEFhTQIG0Jo83CRDokMDo7ND70ufzkvsk\nP5t8LtEIECBAgAABAhMJKJAmYrIRAQItFajvKxqdHXpXHn8hqeW7n5acmWgECBAgQIAAgakE\nFEhTcdmYAIGWCNT/dtXZoVqRrpbs/rfk7skzk3MSjQABAgQIECCwIYFtNvQpHyJAgMBiBOp/\ns56S/Hayf/LnySOTbyQaAQIECBAgQIBATwSOzThuTXbuyXgMg8CsBbbLDkdnh67K4/+e1HcZ\naQQIECBAgMDiBer/p+tv2aMW35XN98AZpM0b2gMBAvMT2CG7fkby4mTX5DXJnyWXJRoBAgQI\nECBAYOYCCqSZk9ohAQIzENgp+3h28htJ/avUnyZVHNXZI40AAQIECBAgMDcBBdLcaO2YAIEN\nCNRZol9Jfj25JfmT5H8l1yYaAQIECBAgQGDuAgqkuRM7AAECEwjcIdu8IPmvybeT45O/SK5L\nNAIECBAgQIAAgYEJWKRhYBNuuP9fYK88enlyZfLV5DlJXVKnESBAgAABAt0R6NUiDd1h73dP\nFUj9nl+j+36BO+el/5Fck5yd/GLijHYQNAIECBAg0EEBBVIHJ63tXVYgtX2G9G9WAnfJjl6d\n1KVzX0iemmydaAQIECBAgEB3BRRI3Z271vZcgdTaqdGxGQn8YPZzYnJD8pnkp5OtEo0AAQIE\nCBDovkCvCqTbd38+jIAAgRYLHJy+/XVSl9EdnjwpOTR5e1JfKKcRIECAAAECBFoloEBq1XTo\nDIHeCNwnI3lT8qWkiqTHJg9M3p1oBAgQIECAAIHWCgy9QKp7H+6e1BLDGgECmxcYnR36XHa1\nb/Lw5EeS9ycaAQIECBAgQKD1AkMokPbJLNS9D3WZz6jtngevS+rLJ+vSn0uTM5IXJhoBAtML\njM4OnZ6P7pxUUfTQ5F8TjQABAgQIECBAoCUC9R0rFyR1r8OHlvq0bX6etvTazflZf8D97+S8\npdeqcGq6cDx26dj1h6VGoEsCo7NDt6TTf58c0aXO6ysBAgQIECAwE4FeLdIwE5EW7+SV6VsV\nR7+VbL/Uz19beu3P87O+i2XUamJfldT2dVlQk02B1KS2Y81C4Mezk/rHhfpHhrcl90s0AgQI\nECBAYJgCCqQOzfvH09dzk/EzQu/M88uTOpO0vNV25yd/tPyNOT9XIM0Z2O5nJvCo7OljyU3J\nG5N7JRoBAgQIECAwbIFeFUjjhUMfp3WbDOrTSV3+M2r1L95VBN04emHsZ233jeTgsdc8JDB0\ngfq+oickn0rqMrpame6Q5OeXHueHRoAAAQIECBDoh0DfC6S61+jhyR3HpuvDeXyPZO+x10YP\n65K7uofis6MX/CRA4HYvjsFbkk8m9Y8Hz0i+kmgECBAgQIAAAQIdE6hi54bk68nRS33fKT8/\nmtT9Ez+w9Fr9qOWJv5xcn9w3abK5xK5JbceaRqBWfLwsefY0H7ItAQIECBAgMCiBXl1iN4SZ\n+8UM8rqkLp+rM0N/lfzF0vPv5OcXk4uSWpyhtqlipemmQGpa3PEmFTg+G341qf/h0wgQIECA\nAAECKwkokFZSaflrd0r//jCpe4/q5vIqhsZzTZ6/OfmhZBFNgbQIdcdcT6AuTb0qefp6G3qf\nAAECBAgQGLSAAqnj0791+r9fUl9sWQXRHZJFNwXSomfA8VcSOCEvnpXUf2c0AgQIECBAgMBq\nAr0qkGqVt6G1WsXuwqUMbezGS2BSgVqw5LnJLyX13xmNAAECBAgQIDAIgSEWSE1MbFXRP5vU\nz0naQybZyDYEGhT43Rzr3OR/N3hMhyJAgAABAgQILFxAgbTlFNS/mD8neV1y4pZvTfWs/vX9\nt5NtJ/zUrhNuZzMCTQjsn4M8M6kivxYu0QgQIECAAAECBAYqcFzGXYs3vLTh8bsHqWFwh1tT\n4PV5t74UViNAgAABAgQITCLQq3uQJhnwkLap1e7ul9TPJpsCqUltx1pL4G5588bkkWtt5D0C\nBAgQIECAwJhArwokl9iNzWwe1vchVTQCQxV4WQb+78n7hwpg3AQIECBAgMCwBYZYIO2RKd89\n2T6p7z+6Irk20QgMXeBeAXhy8rChQxg/AQIECBAgQKDvAodlgHVfxcXJ+BfEjh6fk9dPSvZO\nFtFcYrcIdcdcLvCOvPBPy1/0nAABAgQIECCwjkCvLrFbZ6y9ePslGcWoEDovjz+WvCd5S3JK\n8onkm0ltc0nylKTppkBqWtzxlgscmhdqxbqjlr/hOQECBAgQIEBgHQEF0jpAbXr7SelMFT5V\nCB2+Rse2ynvHJJ9MavsHJ002BVKT2o61ksD/zYvvXukNrxEgQIAAAQIE1hFQIK0D1Ka335TO\n1OVzdb/RJK3uT7oq2cx3IE1ynOXbKJCWi3jepMCROVidPVrrHxGa7I9jESBAgAABAt0S6FWB\ndPtu2U/d21qy++PJDRN+8vJsd0ay34Tb24xAHwRekUG8PTm9D4MxBgIECBAgQIDAZgT6vopd\n3Vv0w8m2SX23y3qtziBVUVULNmgEhiDwoxnkjyX1e68RIECAAAECBAj0XOCpGV/dU1T3VtRl\nRKu1ugfp6KQWbLgpeUjSZHOJXZPajjUu8JE8+dvxFzwmQIAAAQIECEwp0KtL7Pp+BunkTO4+\nyfHJ45ILkwuSS5O612i3ZM/kwGTfpIqjFyanJhqBvgs8KgN8UPKLfR+o8REgQIAAAQIECGwp\ncFCevjmpAqnOKI2nviT27OSEZP9kEc0ZpEWoO+a/h+DPMRAgQIAAAQIENinQqzNIm7To5Mfr\nrFEVQgcnu7dkBAqklkzEgLrxUxlrLV5ywIDGbKgECBAgQIDAfAR6VSD1/RK7lX4F6tK6ikZg\nqAJ1z91xSS1Gcn6iESBAgAABAgQILAkMsUAy+QSGLvBzAagzqD8xdAjjJ0CAAAECBAgsF7j9\n8hc8J0Cg1wJbZ3QvTf5nUsvgawQIECBAgAABAmMCCqQxDA8JDEDgaRnjfskfD2CshkiAAAEC\nBAgQmFpAgTQ1mQ8Q6KzAtun57yV/mlzS2VHoOAECBAgQIEBgjgIKpDni2jWBlgk8M/3ZI3ll\ny/qlOwQIECBAgACB1ggokFozFTpCYK4CO2Tvv5P8j+SKuR7JzgkQIECAAAECHRZQIHV48nSd\nwBQCv5xtt09ePcVnbEqAAAECBAgQGJyAAmlwU27AAxTYOWN+cfKK5JoBjt+QCRAgQIAAAQIT\nCyiQJqayIYHOCvxqen5zcmJnR6DjBAgQIECAAIGGBHxRbEPQDkNgQQK75bgvTH43uW5BfXBY\nAgQIECBAgEBnBJxB6sxU6SiBDQm8KJ+6OvnLDX3ahwgQIECAAAECAxNwBmlgE264gxLYM6Ot\ny+v+a/KdQY3cYAkQIECAAAECGxRwBmmDcD5GoAMCv5U+Xpz8XQf6qosECBAgQIAAgVYIOIPU\nimnQCQIzF7hT9vgrSX057E0z37sdEiBAgAABAgR6KuAMUk8n1rAGL1BfCvvV5K2DlwBAgAAB\nAgQIEJhCwBmkKbBsSqAjAndJP5+VPDm5pSN91k0CBAgQIECAQCsEnEFqxTToBIGZCrwke/tC\n8q6Z7tXOCBAgQIAAAQIDEHAGaQCTbIiDEjgoo/2F5PHJrYlGgAABAgQIECAwhYAzSFNg2ZRA\nBwSOSx8/lZzSgb7qIgECBAgQIECgdQLOILVuSnSIwIYFDsknn5I8YsN78EECBAgQIECAwMAF\nnEEa+C+A4fdK4Pczmg8l/9KrURkMAQIECBAgQKBBAWeQGsR2KAJzFLh/9v3TyY/M8Rh2TYAA\nAQIECBDovYAzSL2fYgMciMDxGed7k48NZLyGSYAAAQIECBCYi4AzSHNhtVMCjQo8MEd7TPKA\nRo/qYAQIECBAgACBHgo4g9TDSTWkwQm8PCN+Z3La4EZuwAQIECBAgACBGQs4gzRjULsj0LDA\n0TneQ5O6B0kjQIAAAQIECBDYpIAzSJsE9HECCxaoe4/enHx+wf1weAIECBAgQIBALwScQerF\nNBrEQAUemXE/JLnXQMdv2AQIECBAgACBmQs4gzRzUjsk0JjA7+dIf5Oc3dgRHYgAAQIECBAg\n0HMBZ5B6PsGG11uBx2dkhyY/29sRGhgBAgQIECBAYAECziAtAN0hCWxSYKt8/mXJXyRfSzQC\nBAgQIECAAIEZCTiDNCNIuyHQoMDP5Fj3TB7d4DEdigABAgQIECAwCAFnkAYxzQbZI4GtM5bj\nktcm30g0AgQIECBAgACBGQookGaIaVcEGhD4+RzjLskfNXAshyBAgAABAgQIDE5AgTS4KTfg\nDgtsm76/JHlV8q0Oj0PXCRAgQIAAAQKtFVAgtXZqdIzA9wn8Ul65Y/In3/eOFwgQIECAAAEC\nBGYioECaCaOdEJi7wPY5wu8mJySXz/1oDkCAAAECBAgQGKiAAmmgE2/YnRN4bnq8Y1KX12kE\nCBAgQIAAAQJzElAgzQnWbgnMUGCn7Ou3kj9Mrp7hfu2KAAECBAgQIEBgmYACaRmIpwRaKPCC\n9OnW5H+1sG+6RIAAAQIECBDolYACqVfTaTA9FNgtY3pRcnxyXQ/HZ0gECBAgQIAAgVYJKJBa\nNR06Q+D7BH49r3w7ef33veMFAgQIECBAgACBmQtsM/M92iEBArMS2DM7+rWkiqQbZrVT+yFA\ngAABAgQIEFhdwBmk1W28Q2DRAr+ZDtQXwr5h0R1xfAIECBAgQIDAUAScQRrKTBtn1wT2SYef\nlzw7ualrnddfAgQIECBAgEBXBZxB6urM6XffBX47Azw/eXPfB2p8BAgQIECAAIE2CTiD1KbZ\n0BcCtwnslx915ujnk1tue8l/EiBAgAABAgQINCHgDFITyo5BYDqB38vmZybvnO5jtiZAgAAB\nAgQIENisgDNImxX0eQKzFbhrdvdLyU8l9eWwGgECBAgQIECAQIMCziA1iO1QBCYQeGm2OT35\nvxNsaxMCBAgQIECAAIEZCziDNGNQuyOwCYF75rN139EjN7EPHyVAgAABAgQIENiEgDNIm8Dz\nUQIzFnhZ9vfR5J9nvF+7I0CAAAECBAgQmFDAGaQJoWxGYM4C983+fyY5Zs7HsXsCBAgQIECA\nAIE1BJxBWgPHWwQaFDg+x3p/UmeQNAIECBAgQIAAgQUJOIO0IHiHJTAmcEQePy554NhrHhIg\nQIAAAQIECCxAwBmkBaA7JIFlAi/P83cln1r2uqcECBAgQIAAAQINCziD1DC4wxFYJvAjef7w\n5P7LXveUAAECBAgQIEBgAQLOIC0A3SEJjAnUvUdvST439pqHBAgQIECAAAECCxJwBmlB8A5L\nIAJ15qjOIN2HBgECBAgQIECAQDsEnEFqxzzoxTAF/iDD/tvkrGEO36gJECBAgAABAu0TcAap\nfXOiR8MQqFXrDk+ePIzhGiUBAgQIECBAoBsCziB1Y570sl8CW2U4v5+8Pvlqv4ZmNAQIECBA\ngACBbgs4g9Tt+dP7bgr8dLp9SPLYbnZfrwkQIECAAAEC/RVwBqm/c2tk7RSo/869LHldcmE7\nu6hXBAgQIECAAIHhCiiQhjv3Rr4YgafmsAck/30xh3dUAgQIECBAgACBtQQUSGvpeI/AbAXq\nktaXJq9OLp7tru2NAAECBAgQIEBgFgIKpFko2geByQR+MZvtlZww2ea2IkCAAAECBAgQaFpA\ngdS0uOMNVWD7DPz3klcmlw0VwbgJECBAgAABAm0XUCC1fYb0ry8Cz8pAdkr+rC8DMg4CBAgQ\nIECAQB8Fhr7M94GZ1HsmdT/IWcl1iUZg1gI7Zoe/nfxxctWsd25/BAgQIECAAAECBCYVeHY2\nPDmpP1DH233z5JPJrWO5Io9fnGydNN2OzQGrLzs3fWDHa0TgN3OU/0jqDJJGgAABAgQIEOib\nwHYZUP0te1TfBtbH8fzV0mTtPja4/fO4iqGaxCqSTkyqiLogqdfqHpGmmwKpafHmjrdrDnVJ\n8vzmDulIBAgQIECAAIFGBRRIjXJv7mArFUhvyi6rEHresl3Xv+6P3nvYsvfm/VSBNG/hxe3/\nJTn015NapEEjQIAAAQIECPRRQIHUoVldqUD6avr/iVXGUJfi1b/2v2KV9+f1sgJpXrKL3e8e\nOXydraz51QgQIECAAAECfRXoVYE0xFXsdstv5udW+e2sRRrOTH5olfe9TGAagd/IxpcmfzPN\nh2xLgAABAgQIECCwOIEhFkinhfu+q5DfMa8/IPnmKu97mcCkAntnw7rv6LjkxkQjQIAAAQIE\nCBDogMBQCqR/z1y8Kfn15GPJEclPJuPtgDz5n0mdIvzQ+BseE9iAwH/LZ2rhj5M38FkfIUCA\nAAECBAgQIDAXgZ/OXt+ZnJvUwgzjOT/PR+0xeVD/yl/vn5pslTTZ6h6VOrZlvptUn9+xfiC7\nrss1nzS/Q9gzAQIECBAgQKA1Ar26B2mb1rDOpyNvz24r1Wqp70PHMl4E1Xcf1R+0b05+Lali\nRSOwUYHfzQfri4dHv3sb3Y/PESBAgAABAgQIEFiIQK1et+1CjnzbQZ1BWiD+jA/9g9nfDcnj\nZrxfuyNAgAABAgQItFXAGaS2zswm+lVnjzQCsxCo7z36TPIPs9iZfRAgQIAAAQIECDQr0PdL\n7KbVfG4+8JzkdcmJ0354bPt9lj4/6Vmp/cc+62F3Be6Rrj8teVR3h6DnBAgQIECAAIFhCyiQ\ntpz/O+Xp/ZL6uZl2fT5c36dUpxsnaZNuN8m+bLM4geNy6FOTf1pcFxyZAAECBAgQIECAwOwE\nZlUgTdsj9yBNK9a+7evLhW9Ojm5f1/SIAAECBAgQIDBXAfcgzZV3sTu/KIevaASmFfj9fOAD\nyUem/aDtCRAgQIAAAQIE2iMwxEvs9gh/Lfm9fXJNckVybaIR2KjAD+eDT0getNEd+BwBAgQI\nECBAgACBJgUOy8Fen1ycjH9Z7OjxOXn9pGTvZBHNJXaLUJ/dMU/Jrt41u93ZEwECBAgQIECg\nUwK9usSuU/Ib7GwtuzwqhM7L448l70nektQftp9IvpnUNpckT0mabgqkpsVnd7wHZ1e3JPef\n3S7tiQABAgQIECDQKQEFUoem60npaxU+VQgdvka/t8p7xySfTGr7+qO3yaZAalJ7tsf6l+yu\nim2NAAECBAgQIDBUAQVSh2b+TelrXT5X9xtN0ur+pKuSzXwH0iTHWb6NAmm5SDee/3i6eVNy\nSDe6q5cECBAgQIAAgbkI9KpAuv1ciNqz0/pOo48nN0zYpcuz3RnJfhNub7NhC/xBhv/GpL7z\nSiNAgAABAgQIEOiBQN8LpLq3qFYY23bCuaozSFVU+YN3QrABb/aYjP2IpJb31ggQIECAAAEC\nBAh0QuCp6WXdU/Tu5Mg1elz3INUXfNaCDXXJ1EOSJptL7JrU3vyx6vfltKTpSzE333N7IECA\nAAECBAjMXqBXl9j1/XuQTs7875McnzwuuTC5ILk0qXuNdkv2TA5M9k2qOHphcmqiEVhN4D/n\njfskj19tA68TIECAAAECBAgQaLPAQencm5MqkOqM0njqS2LPTk5I9k8W0ZxBWoT6xo5Zl6V+\nPvmzjX3cpwgQIECAAAECvRPo1Rmk3s3OBAOqs0ZVCB2c7D7B9k1sokBqQnk2x6jLNquovtNs\ndmcvBAgQIECAAIHOC/SqQOr7JXYr/bbVpXUVjcC0AvXfl+OS1yQXJRoBAgQIECBAgEDPBPq+\nil3PpstwFizw9By/7mn74wX3w+EJECBAgAABAgTmJKBAmhOs3fZOoE4d/17yp8llvRudAREg\nQIAAAQIECHxXQIHkF4HAZAJ1n9iuySsn29xWBAgQIECAAAECXRRQIHVx1vS5aYEdc8DfSf5H\n4v61pvUdjwABAgQIECDQoIACqUFsh+qswK+k51sntTiDRoAAAQIECBAg0GMBBVKPJ9fQZiKw\nS/by4uQVSS3vrREgQIAAAQIECPRYQIHU48k1tJkI/Nfs5YbkpJnszU4IECBAgAABAgRaLTDE\n70Fq9YToXKsE7pDevDD5reT6VvVMZwgQIECAAAECBOYi4AzSXFjttCcCL8o4Lk/+qifjMQwC\nBAgQIECAAIF1BJxBWgfI24MV2Csj/9XkecmNg1UwcAIECBAgQIDAwAScQRrYhBvuxAJ1Wd2F\nyRsn/oQNCRAgQIAAAQIEOi/gDFLnp9AA5iCwb/b5y8kvJjfPYf92SYAAAQIECBAg0FIBZ5Ba\nOjG6tVCB+lLYs5O3LbQXDk6AAAECBAgQINC4gDNIjZM7YMsFDkz/jk1+Jrm15X3VPQIECBAg\nQIAAgRkLOIM0Y1C767zA72UEn03+vvMjMQACBAgQIECAAIGpBZxBmprMB3oscPeM7enJY3s8\nRkMjQIAAAQIECBBYQ8AZpDVwvDU4geMy4n9L3j+4kRswAQIECBAgQIDAdwWcQfKLQOA2gfvk\nx5OThwIhQIAAAQIECBAYroAzSMOdeyPfUqAWZjg1+dCWL3tGgAABAgQIECAwJAEF0pBm21jX\nEjgib/7rWht4jwABAgQIECBAoP8CCqT+z7ERri9Q/z24f3La+pvaggABAgQIECBAoM8CCqQ+\nz66xTSpwSDbcJVEgTSpmOwIECBAgQIBATwUUSD2dWMOaSuCHs/W3kgun+pSNCRAgQIAAAQIE\neiegQOrdlBrQBgSqQPrkBj7nIwQIECBAgAABAj0TUCD1bEINZ0MCVSC5vG5DdD5EgAABAgQI\nEOiXgAKpX/NpNNML1H8HLNAwvZtPECBAgAABAgR6KaBA6uW0GtQUAvfMtrsmziBNgWZTAgQI\nECBAgEBfBRRIfZ1Z45pUoC6vuyS5YNIP2I4AAQIECBAgQKC/Agqk/s6tkU0mYIGGyZxsRYAA\nAQIECBAYhIACaRDTbJBrCFigYQ0cbxEgQIAAAQIEhiagQBrajBvvuMBWeXJocvr4ix4TIECA\nAAECBAgMV0CBNNy5N/Lb3c4CDX4LCBAgQIAAAQIEthBQIG3B4cnABOryukuT8wc2bsMlQIAA\nAQIECBBYRUCBtAqMlwchUAXSpwYxUoMkQIAAAQIECBCYSECBNBGTjXoqYIGGnk6sYREgQIAA\nAQIENiqgQNqonM91XWC0QIMviO36TOo/AQIECBAgQGCGAgqkGWLaVacEDk5vd0sUSJ2aNp0l\nQIAAAQIECMxXQIE0X197b69AXV53WXJee7uoZwQIECBAgAABAk0LKJCaFne8tghYoKEtM6Ef\nBAgQIECAAIEWCSiQWjQZutKogAUaGuV2MAIECBAgQIBANwRmVSBtk+HWl27Wje8agbYL1O/p\nYYn7j9o+U/pHgAABAgQIEGhYYCMF0hPTx5PG+vm4PL40OTO5MHlUohFos8Dd07ndEwVSm2dJ\n3wgQIECAAAECHRB4Qvp4a3JdUv8KX39kXpHckrw/uXLp+d3yU5tc4NhsWq47T/4RW25C4Ofy\n2VqgQSNAgAABAgQIENi8wHbZRf0te9Tmd7X4PUx7Buml6fJXkyOTQnh8UkXSCckjk7psqZ5X\nIaURaKuABRraOjP6RYAAAQIECBBYsMA0BVJte0jy5uSMpX4/eunnO5Z+npufX0oOX3ruB4E2\nCligoY2zok8ECBAgQIAAgRYITFMg7Zr+7pD8x1K/t87PRyR1qdInl16rH7VNnWbTCLRVwAIN\nbZ0Z/SJAgAABAgQILFhgmgKp7i+qYujopT4/PD/3SN6X1D1I1eoPz7smdSZJI9BGgVqg4Q7J\n6W3snD4RIECAAAECBAh0S+BV6W7de/TB5JKkCqMfTar9XnJtcnNyr0SbXMAiDZNbbXbLn80O\nLt/sTnyeAAECBAgQIEDg/wv0apGG+v6iadqLs3GdNXpScnXy/ORDSbUqlGplu6cndR+SRqCN\nAu4/auOs6BMBAgQIECBAoOMCVSVWMTTe7pcndZ+SNr2AM0jTm230E/+cD/7RRj/scwQIECBA\ngAABAt8n0KszSNPcgzQu8Z08qUvtxlutbFdnlTQCbRY4NJ07rc0d1DcCBAgQIECAAIHFCUx7\niV319KHJf0n2SXZMlp9Jyku3+5vkDfVAI9AigYPSlz0TBVKLJkVXCBAgQIAAAQJtEpi2QPqZ\ndP6tEwzgQxNsYxMCTQvU/UdXJlZZbFre8QgQIECAAAECHRGYtkD6g4yrVqp7VvKvycXJSm20\n7PdK73mNwKIERgs0LL88dFH9cVwCBAgQIECAAIGWCUxTIO2cvh+cnJSc3LJx6A6BSQRGBdIk\n29qGAAECBAgQIEBggALTLNJwXXyuSuoMkkagiwL1RcbuP+rizOkzAQIECBAgQKAhgWkKpLps\nru4tenIyzecaGorDEFhT4K55946JAmlNJm8SIECAAAECBIYtMG2hU9/X8+3k7ckxyQFJ/dG5\nPLW6nUagTQJ1eV2dAT2nTZ3SFwIECBAgQIAAgW4L/Fu6X6uA1U3ua+W4vK9NLuCLYie32uiW\nf5gP/stGP+xzBAgQIECAAAECqwr06otip1mkoUQ+nXxjVZrvvfGl7z30iEArBOoMksvrWjEV\nOkGAAAECBAgQaK/AtAXSc9s7FD0jsKZALdDwV2tu4U0CBAgQIECAAIHBC0x7D9IkYFtnoztN\nsqFtCDQk8IM5zl6JM0gNgTsMAQIECBAgQKCrAtOeQapxPiF5YrJ7sm1Sbauk9lWLM9w9eV1y\nXKIRaINAXV53dfKVNnRGHwgQIECAAAECBNorMG2B9IsZynqXKZ2dbT7T3iHr2QAFqkA6PamF\nRTQCBAgQIECAAAECqwpMe4ndb2ZPtVTy05L9kmuS/5bcM3lKcnnygeRdiUagLQJVILm8ri2z\noR8ECBAgQIAAgZ4I1L1F30neOjaeKobePfa8boS/OXnA2Gseri9gme/1jTazxcX5cBXwGgEC\nBAgQIECAwOwFerXM9zRnkHaJZd1z9OEx0zPz+P5jz2sZ8C8njx97zUMCixQ4MAffO3EGaZGz\n4NgECBAgQIAAgY4ITFMg1RfEXpIcMja2KpAOSMZXrTs/z+89to2HBBYpcHgOXpeC1r1xGgEC\nBAgQIECAAIE1BaYpkGpHtfhCrWJ3ZD1J+9xtP777Wj3cNTk6qfuUNAJtEBgt0HBLGzqjDwQI\nECBAgAABAv0SODTDqfuQ6o/NhyRVYJ2TXJ/Uwgx1r0etFFaLOHSl1eVXdVZs2mJxluNzD9Is\nNbfc1yl5+sotX/KMAAECBAgQIEBghgK9ugdpIy4PzYfel9xj6cN1CdM3kiqMKm9MFlls5PBT\ntT/K1tXvPaf61Gw3ViDN1nN8bxflyVPHX/CYAAECBAgQIEBgpgK9KpCm/R6kkvyXpYxU6/tl\n9k9qsYYrknOTtrT7pSM7r9OZWq68Wq28N7o08Ot5fEG9qHVaoH4v90ks0NDpadR5AgQIECBA\ngEA3BHZMN++bjO5HWq8QWcSoPpODjs5sTfPzpQ131hmk+YA/IbutBRq6dEZzPhL2SoAAAQIE\nCBCYn8DgzyAdENsTkp9Otko+mtTCDHVp3ReSP0huSNrQTkwn/jTZIXl38qVkeftPeeGByauT\n65bePHXppx/dFrBAQ7fnT+8JECBAgAABAq0X2Dc9rKW+62zMF5OvJR9JqtUiDfX655MqSNrS\n7pOOfDb5dvL8pIq68eYepHGNfj1+b4ZTBbJGgAABAgQIECAwP4FenUGa9tKjOstSl9bVGaP6\nrqO6/2jUnpgHL0+qIHn66MUW/KyzWnWG6H8lr0ren4zuO8pDrccCh2ds7j/q8QQbGgECBAgQ\nIEBg1gLTFkg/ng68NqnL6pa3m/PCy5L6QtkHLX9zwc/rkr8XJQ9L7pXU9zf9XKL1V+AuGdqd\nEgVSf+fYyAgQIECAAAECMxeYpkDaLUffIzlrjV7cmPfqjE1t18ZWK/DVynb/lLw5OTlpa1/T\nNW0TAnX/UV1W+eVN7MNHCRAgQIAAAQIEBiYwTYF0VWz+I3nAGkZVRNUldmeusc2i37o8HfjZ\n5GnJY5JaQU7rn0AVSJ9O6symRoAAAQIECBAgQGAigWkKpNrhKckzk+cluyTj7Q558rfJ7kmd\noWl7+7t08P7J25MPJnX2S+uPQBVILq/rz3waCQECBAgQIECglQJVBJ2f1Gp1da9RnVG6MKkV\n7C5N6vW/TrTpBOosVtntPN3HbL2GwDfyXp0l1AgQIECAAAECBOYr0KtV7DZCtVc+VN8vVAsf\n1B/1o1SB9Pxk60S77ctJtwnEJHl2tlMgze63Zr8lz7rcUyNAgAABAgQIEJivwOALpBFvFUIH\nJQ9OfmD0Ysd/Pjf9/2zynE2O4275fF2yNyoeJ/3pDNIm4Zc+/pP5WQs0KNZn42kvBAgQIECA\nAIG1BHpVINXZjY22uvn93KVsdB9t+1wtC12r3NXPzbRz8uGHJNtOuJPHZbsXT7itzdYXqO8/\nskDD+k62IECAAAECBAgQWCawkQJp1+yjboCv75lZ7V/oP5P36kxM19rr0uF3JhfNoOP/PsU+\n6kt3tdkJWKBhdpb2RIAAAQIECBAgsIbAj+a9Kh7Wu2TsuDX24a3vF7BIw/ebbOaVWjjk6ZvZ\ngc8SIECAAAECBAhMLDDoS+xOCtM+yV8ldYaovhtppVZnkNra9kjHainy7ZNrkiuSaxOtHwL7\nZhh1T9xp/RiOURAgQIAAAQIECLRVoL73qM4c/U1bO7hGvw7Le69PLk5WOvtV9wxV8bd3sojm\nDNLs1B+bXdUCDRu5fHR2vbAnAgQIECBAgMBwBAZ7BqnOslyWfKtjc/2S9PdlS32u73D6eFLj\nqLNHdSZpz+SA5FnJE5MXJCcnWjcF6v6jOoN5Uze7r9cECBAgQIAAAQJdEnhDOltfDrttRzr9\npPSzzhidktTKZqu1rfLGMcknk9q+li5vsjmDNDvtd2dXr5nd7uyJAAECBAgQIEBgHYHBnkEq\nl/qeoPcnH0j+MqkzMrXc9/J2Xl6o9xbdnpAOnJvUzxvW6EwVRR9OHpFU35+WfCzRuidQZ5Bq\nJUKNAAECBAgQIECAwNQC096nUQsc1GcelNQZl9Xay/LGcau92eDr98ux6pK6tYqj8e5cnidn\nJPuNv+hxZwTq+6ss0NCZ6dJRAgQIECBAgED7BKYtkP4mQ6ji6AvJR5K6l2elVmdj2tC+mU7U\nGYW6JPDGCTpUBWAVVbVgg9Y9gSPS5euTL3Wv63pMgAABAgQIECDQNYG6trBWB+vSpWdPTX/r\n8rm6L+XIZLVW9yAdnXwiqZv7H5I02dyDNBvtl2Q3dcZQI0CAAAECBAgQaE6g6oT6m/uo5g45\nvyNNcwbplnSj7jf6x/l1Z+Z7Pjl7rO9tOj55XHJhckFyaXJVsluyZ3Jgsm9SxdELk1MTrXsC\ndbbw9O51W48JECBAgAABAgS6KvCedLyKh9t3bAAHpb9vTqpAqup2PLV8+dnJCcn+ySLasTlo\n9WnnRRy8R8es4veXejQeQyFAgAABAgQIdEGgV2eQpgWvAuJryXuTRyWHJHdcITvmtba2OmtU\n4zg4qe9BakNTIG1+FupMYRWZ99/8ruyBAAECBAgQIEBgCoFBF0gfC9SVyfgZmJUeHzcFqE1v\ndzsF0uZ/Cx6dXdQCDdtuflf2QIAAAQIECBAgMIVArwqkae5BKqPPJvVFses1q4itJ+T9WQvU\n/Uf1+znJaoWzPrb9ESBAgAABAgQI9ERg2gKpvih22vaIfKDuDfnitB+0PYEpBA7PtqdNsb1N\nCRAgQIAAAQIECHyfQBOLLbw8R3389x3ZCwRmK1BnkBRIszW1NwIECBAgQIDA4ASaKJAGh2rA\njQvslSPWwhsKpMbpHZAAAQIECBAg0C8BBVK/5nOoozkiA/9O8oWhAhg3AQIECBAgQIDAbAQU\nSLNxtJfFCligYbH+jk6AAAECBAgQ6I2AAqk3Uznogbj/aNDTb/AECBAgQIAAgdkJKJBmZ2lP\nixNQDWo3IwAAQABJREFUIC3O3pEJECBAgAABAr0SUCD1ajoHOZg7ZtQHJBZoGOT0GzQBAgQI\nECBAYLYCCqTZetpb8wIWaGje3BEJECBAgAABAr0VUCD1dmoHM7C6vO6MpFax0wgQIECAAAEC\nBAhsSkCBtCk+H26BgPuPWjAJukCAAAECBAgQ6IuAAqkvMznccVSBdPpwh2/kBAgQIECAAAEC\nsxTYZsqdvTbbX5f8VnLThJ/99Wz3zQm3tRmBaQT2zMYHJhZomEbNtgQIECBAgAABAjMR2D57\nuSY5cyZ7s5NxgWPz5NZk5/EXPV5X4BHZou49qt9NjQABAgQIECBAYDEC2+Ww9bfsUYs5/GyP\nOs0ldvWH6NXJTslWs+2GvRHYkEBdXve55IYNfdqHCBAgQIAAAQIECCwTmKZAqqrwp5Y+/+78\nfGRyt2S3FeJf9IOizV2gCiSX182d2QEIECBAgAABAgRWE/ho3rgkqWJprRyX97XJBVxiN7nV\n+Jbn5smzx1/wmAABAgQIECBAoHGBXl1iN+0iDXX/0eUTkJ81wTY2IbAZgT3y4bsmziBtRtFn\nCRAgQIAAAQIEthCYtkB65haf9oTA4gTq8robk7oHSSNAgAABAgQIECAwE4Fp7kFafsAd88J9\nkyOX3rAC23Ihz+cpUAXS5xMLNMxT2b4JECBAgAABAgMT2EiBdECM3pZcm5yRnJBUe2NyfGKB\nhtLQ5i1ggYZ5C9s/AQIECBAgQGCAAtMWSPvG6PTkSUndj3ReMmq19PfvJHVPyA6jF/0kMCcB\nBdKcYO2WAAECBAgQIDBkgWkLpFcHqy6tOzq5d1LF0qg9MQ9entwnefroRT8JzEHgDtnnQYkF\nGuaAa5cECBAgQIAAgSELTFsg/XiwXpt8dAW0m/Pay5Irkwet8L6XCMxKoM4e3ZR8blY7tB8C\nBAgQIECAAAECJTBNgVRfCFtLK6+1hHetKvaFpe3yQyMwF4EqkGqBhuvnsnc7JUCAAAECBAgQ\nGKzANAXSVVH6j+QBa2hVEVWX2NX9SRqBeQlUgeTyunnp2i8BAgQIECBAYMAC0xRIxXRKUt+F\n9Lxkl2S81X0hf5vsnvzT+BseE5ixgAJpxqB2R4AAAQIECBAgsDGBKoLOT25N6l6jOqN0YfKu\n5NKkXv/rRJtO4NhsXna+S2p9tyrAb0lG37+1/idsQYAAAQIECBAgME+B7bLz+lv2qHkepM37\n3iudOzGpL+gsiFGqQHp+snWiTSegQJrc66HZtO51q9UUNQIECBAgQIAAgcUL9KpA2mYDnpfk\nM89JfiU5MLlz8rXkG4lGYN4CdXndF5Pr5n0g+ydAgAABAgQIEBiewLQF0kEhqkvr6mxRLet9\n7lLy47vt9vnP+o6k2uYz333FfxCYrYD7j2braW8ECBAgQIAAAQJjAlXQTNM+kI1rgYbV2vZ5\n44PJs1bbwOsENimgQNokoI8TIECAAAECBAisLrDeGaSD89Fjxj6+ax4fnjxj7LXRwyq2Dl16\nctnoRT8JzFCglpG/W3LaDPdpVwQIECBAgAABAgQmFqg/SOveotFCDJP8vCbb17/ya5MLWKRh\nMqsfy2Y3JTtNtrmtCBAgQIAAAQIEGhDYLseoOqEXq9itdwapvhz2scm9k2qvTD6S/J96sqzV\n0svfTk5Pzl/2nqcEZiEwWqChfs80AgQIECBAgAABAjMXWK9AqgNWwVOpdkTy4eSd9UQj0LCA\n+48aBnc4AgQIECBAgMDQBNYrkPYIyLbJZUld2vQHydbJPsla7dq8WdEIzFKgCqTXzHKH9kWA\nAAECBAgQIEBgGoFaqruuJ6wzR9VqWe9J7kN66Xe39h+TCrgHaX2pWiCkLuPsxbWt6w/XFgQI\nECBAgACBzggM6h6kWtb77OTypek5JT/XO3tUm35xaXs/CMxKoFZPrALps7Paof0QIECAAAEC\nBAgQWC6w3iV2L1r2gV9Z9txTAk0J1OV1X0os0NCUuOMQIECAAAECBAYoMO0XxQ6QyJBbImCB\nhpZMhG4QIECAAAECBPosoEDq8+z2a2wKpH7Np9EQIECAAAECBFopoEBq5bTo1DKBXfL84OS0\nZa97SoAAAQIECBAgQGCmAgqkmXLa2ZwEaoGGahZouM3BfxIgQIAAAQIECMxJQIE0J1i7nalA\nXV53ZuK7tWbKamcECBAgQIAAAQLLBRRIy0U8b6OA+4/aOCv6RIAAAQIECBDooYACqYeT2sMh\nKZB6OKmGRIAAAQIECBBoo4ACqY2zok/jAjvnyT0SCzSMq3hMgAABAgQIECAwFwEF0lxY7XSG\nAoct7eszM9ynXREgQIAAAQIECBBYUUCBtCKLF1skUJfXnZVc06I+6QoBAgQIECBAgEBPBRRI\nPZ3YHg3L/Uc9mkxDIUCAAAECBAi0XUCB1PYZ0j8Fkt8BAgQIECBAgACBxgQUSI1RO9AGBHbK\nZ+6ZWKBhA3g+QoAAAQIECBAgML2AAml6M59oTqAWaKjfUQs0NGfuSAQIECBAgACBQQsokAY9\n/a0f/GiBhqtb31MdJECAAAECBAgQ6IWAAqkX09jbQbj/qLdTa2AECBAgQIAAgXYKKJDaOS96\ndZuAAslvAgECBAgQIECAQKMCCqRGuR1sCoEds+0hiQUapkCzKQECBAgQIECAwOYEFEib8/Pp\n+QlYoGF+tvZMgAABAgQIECCwioACaRUYLy9coC6vOzu5auE90QECBAgQIECAAIHBCCiQBjPV\nnRuo+486N2U6TIAAAQIECBDovoACqftz2NcRKJD6OrPGRYAAAQIECBBosYACqcWTM+CuWaBh\nwJNv6AQIECBAgACBRQookBap79irCRyaN7ZOPr3aBl4nQIAAAQIECBAgMA8BBdI8VO1zswKH\nZwdfSa7c7I58ngABAgQIECBAgMA0AgqkabRs25SA+4+aknYcAgQIECBAgACBLQQUSFtweNIS\nAQVSSyZCNwgQIECAAAECQxNQIA1txts/3h3SxXsnp7W/q3pIgAABAgQIECDQNwEF0u1ut30m\n9R5JLQqgLV7g/unCNokFGhY/F3pAgAABAgQIEBicwFAKpLtmZp+T/FSyy9Is75ufb08uSc5K\nrkpenmybaIsTqMvraoGGKxbXBUcmQIAAAQIECBAg0F+BX8vQbh3LV/N47+StS69dnp/vTb6x\n9Lxeb7odmwNWH3du+sAtPN5fpk9vaWG/dIkAAQIECBAgQGBlge3ycv0te9TKb3u1TQI/kc7c\nknw+eUHy68mlSZ0xqkn8zaS+lLRa3fvyt0m9/sikyaZA+p72Z/LwN7731CMCBAgQIECAAIGW\nCyiQWj5B4907KU+uTsbPzDwhz6sI+nqy/L6jKpa+lfxZ0mRTIN2mXfeDfSd5aJP4jkWAAAEC\nBAgQILApgV4VSH2/B+nITPX7kmvHpvwf8/j65D3JzWOv18PrkjOTg+uJ1rhALdCwbWKBhsbp\nHZAAAQIECBAgQKAE+l4g1f1FVSSNj/Pbef67yZeS5e0OeeEBSd2PpDUvUAs0nJPUvGkECBAg\nQIAAAQIEGhcYLxwaP3gDB3x/jrF/8srkzmPH+5M8fvXY83pYZy5ekdRlXv+SaM0LVIF0evOH\ndUQCBAgQIECAAAECwxCohRfqC0frnqO6rG6PZKX2xLx4UVLbVXG0VdJkcw/Sbdp1ad2Lm4R3\nLAIECBAgQIAAgU0LuAdp04TN7aCKoh9JXp6ckax26VYt4lATW2eVHp1UoaQ1K1Bn7u6TVEGr\nESBAgAABAgQIECCwQIFavW75inZNdscZpNvu/arCdM8m4R2LAAECBAgQIEBg0wK9OoO0zaY5\n+rGDWr1OW6xA3X/01eSyxXbD0QkQIECAAAECBIYsoECaz+zX2ajHJFVNT9IOn2Sjnm9TBi6v\n6/kkGx4BAgQIECBAoO0CCqQtZ+i5efqc5HXJiVu+NdWzWjmv9jFpgVT33wy91Rmk/z10BOMn\nQIAAAQIECBAg0CaB49KZug/mpQ13auj3IFUheUPy8IbdHY4AAQIECBAgQGDzAu5B2rxha/dQ\nZ33emdSS31pzAvfNoeq/WL4DqTlzRyJAgAABAgQIEFhBwCV2W6JUYaQ42tKkiWd1ed3Xkkub\nOJhjECBAgAABAgQIEFhNYIgFUn1Z7O5J3fdzTXJFcm2iLU6gCiQLNCzO35EJECBAgAABAgSW\nBG4/EInDMs7XJxcntYx0LSd9ZnJBUkXSOclJyd6J1ryAAql5c0ckQIAAAQIECBAYqMBLMu5a\neKFyXvKx5D3JW5JTkk8k30zq/UuSpyRNtyEv0rBtsK9PHtE0uuMRIECAAAECBAjMRKBXizTM\nRKTFO3lS+laFTxVCa33X0FZ5/5jkk0lt/+CkyTbkAqnmpcz3ahLcsQgQIECAAAECBGYmoECa\nGeX8d/SmHKIun5v0e4bq/qSrks18B1I+PnUbcoFUY//a1GI+QIAAAQIECBAg0BaBXhVIfb8H\n6X75rfl4Ut+xM0m7PBudkew3yca2mYmA+49mwmgnBAgQIECAAAECsxDoe4FU9xbVH+DbTohV\nZ5CqqKoFHLRmBGp+fP9RM9aOQoAAAQIECBAgsI5A3wukN2T8hyTvSI5cw6LuQTo6eV+yU/Ku\nRJu/QBWu9SWxlviev7UjECBAgAABAgQITCDQ9+9BOjkG+yTHJ49LLkxqae9Lk7rXaLdkz+TA\nZN/kpuSFyamJNn+BH8oh6v4wZ5Dmb+0IBAgQIECAAAECBP6/wEF59OakCqRaMW089SWxZycn\nJPsni2jH5qDVp50XcfAFHvOZOfb5Czy+QxMgQIAAAQIECGxeoFeLNPT9DNJous/NgycvPamz\nRrsnOyT1xbFXJtpiBCzQsBh3RyVAgAABAgQIEFhFYCgF0vjw69K6irZ4gcPThX9YfDf0gAAB\nAgQIECBAgMBtAn1fpME8t1egivP7JRZoaO8c6RkBAgQIECBAYHACCqTBTXlrBnyf9KQuc7RA\nQ2umREcIECBAgAABAgQUSH4HFiVQ9x9dkFy0qA44LgECBAgQIECAAIHlAgqk5SKeNyVggYam\npB2HAAECBAgQIEBgYgEF0sRUNpyxgAJpxqB2R4AAAQIECBAgsHkBBdLmDe1hegELNExv5hME\nCBAgQIAAAQINCCiQGkB2iO8TuHde2TGxQMP30XiBAAECBAgQIEBgkQIKpEXqD/fYdXndhcl/\nDJfAyAkQIECAAAECBNoooEBq46z0v0/uP+r/HBshAQIECBAgQKCTAgqkTk5b5zutQOr8FBoA\nAQIECBAgQKCfAgqkfs5rm0e1dTp3v8T9R22eJX0jQIAAAQIECAxUQIE00Ilf4LBrgYadktMW\n2AeHJkCAAAECBAgQILCigAJpRRYvzlGgLq/75lLmeBi7JkCAAAECBAgQIDC9gAJpejOf2JyA\n+4825+fTBAgQIECAAAECcxRQIM0R165XFFAgrcjiRQIECBAgQIAAgTYIKJDaMAvD6UMt0HD/\nxP1Hw5lzIyVAgAABAgQIdEpAgdSp6ep8Zw/JCCzQ0PlpNAACBAgQIECAQH8FFEj9nds2jqwu\nr7so+UYbO6dPBAgQIECAAAECBBRIfgeaFKgC6VNNHtCxCBAgQIAAAQIECEwjoECaRsu2mxWw\nQMNmBX2eAAECBAgQIEBgrgIKpLny2vmYQP2uHZpYoGEMxUMCBAgQIECAAIF2CSiQ2jUffe5N\nLdCwc6JA6vMsGxsBAgQIECBAoOMCCqSOT2CHul+X112cXNihPusqAQIECBAgQIDAwAQUSAOb\n8AUO1wINC8R3aAIECBAgQIAAgckEFEiTOdlq8wIWaNi8oT0QIECAAAECBAjMWUCBNGdgu/+u\nQP2eWaDBLwMBAgQIECBAgEDrBRRIrZ+iXnTwnhnFLsnpvRiNQRAgQIAAAQIECPRWQIHU26lt\n1cDq8rpvJV9vVa90hgABAgQIECBAgMAyAQXSMhBP5yLg/qO5sNopAQIECBAgQIDArAUUSLMW\ntb+VBBRIK6l4jQABAgQIECBAoHUCCqTWTUnvOrRVRmSBht5NqwERIECAAAECBPopoEDq57y2\naVT3SGd2TU5rU6f0hQABAgQIECBAgMBKAgqklVS8NkuBurzukuT8We7UvggQIECAAAECBAjM\nQ0CBNA9V+xwXcP/RuIbHBAgQIECAAAECrRZQILV6enrROQVSL6bRIAgQIECAAAECwxBQIA1j\nnhc1ylqg4bDE/UeLmgHHJUCAAAECBAgQmEpAgTQVl42nFDg42++WKJCmhLM5AQIECBAgQIDA\nYgQUSItxH8pR6/K6S5PzhjJg4yRAgAABAgQIEOi2gAKp2/PX9t67/6jtM6R/BAgQIECAAAEC\nWwgokLbg8GTGAgqkGYPaHQECBAgQIECAwHwFFEjz9R3y3i3QMOTZN3YCBAgQIECAQEcFFEgd\nnbgOdPvu6ePuiQUaOjBZukiAAAECBAgQIHCbgALJb8K8BOryusuTr83rAPZLgAABAgQIECBA\nYNYCCqRZi9rfSMD9RyMJPwkQIECAAAECBDojoEDqzFR1rqMKpM5NmQ4TIECAAAECBAgokPwO\nzEvgsOzY/Ufz0rVfAgQIECBAgACBuQgokObCOvid1gINd0gUSIP/VQBAgAABAgQIEOiWgAKp\nW/PVld4eno5ekZzblQ7rJwECBAgQIECAAIESUCD5PZiHgPuP5qFqnwQIECBAgAABAnMXUCDN\nnXiQB1AgDXLaDZoAAQIECBAg0H0BBVL357CNI6hL7Nx/1MaZ0ScCBAgQIECAAIE1BRRIa/J4\ncwMCB+UzeyQKpA3g+QgBAgQIECBAgMBiBRRIi/Xv49Hr8rorEws09HF2jYkAAQIECBAg0HMB\nBVLPJ3gBwxvdf3TrAo7tkAQIECBAgAABAgQ2JaBA2hSfD68gMCqQVnjLSwQIECBAgAABAgTa\nLaBAavf8dLF3Fmjo4qzpMwECBAgQIECAwHcFFEh+EWYpcNfsbM/EAg2zVLUvAgQIECBAgACB\nxgQUSI1RD+JAdXndVck5gxitQRIgQIAAAQIECPROQIHUuyld6ICqQDo9sUDDQqfBwQkQIECA\nAAECBDYqoEDaqJzPrSRggYaVVLxGgAABAgQIECDQGQEFUmemqhMdtUBDJ6ZJJwkQIECAAAEC\nBFYTUCCtJuP1aQV+MB+4Y2KBhmnlbE+AAAECBAgQINAaAQVSa6ai8x2py+uuTs7u/EgMgAAB\nAgQIECBAYLACCqTBTv3MB16X11mgYeasdkiAAAECBAgQINCkgAKpSe1+H8sCDf2eX6MjQIAA\nAQIECAxCQIE0iGluZJAKpEaYHYQAAQIECBAgQGCeAgqkeeoOZ98HZKh7JRZoGM6cGykBAgQI\nECBAoJcCCqReTmvjg6qzR9ckFmhonN4BCRAgQIAAAQIEZimgQJql5nD3VQVSLdBwy3AJjJwA\nAQIECBAgQKAPAkMrkNYb79aZ1D2SHfowuQ2Owf1HDWI7FAECBAgQIECAwPwE1isY5nfk5vZ8\npxzqrcllyVXJvyYPSVZq982Ltd2LV3rTa6sK1BLf7j9alccbBAgQIECAAAECXRHoe4G0Sybi\nk8nPJHV26ILkR5MPJy9PtM0L7J9d7JMokDZvaQ8ECBAgQIAAAQILFuh7gfQb8a0/4F+W3CU5\nJHlA8vnkt5NXJtrmBEYLNHx5c7vxaQIECBAgQIAAAQKLF+h7gfTgEF+cHJ9cvcRdZzqOST6S\n/FpSRZS2cYEqkD6dWKBh44Y+SYAAAQIECBAg0BKBvhdI+8W5CqGblnlfmeePTc5I/iipS/C0\njQlUgVQr2GkECBAgQIAAAQIEOi/Q9wLpvMzQw5KVVqWrBRsendR9SW9IVlu4IW9pawhYoGEN\nHG8RIECAAAECBAh0S6DvBdI/Zzp2T16R/MAKU3NhXnt4UpffvTd5TKJNLlD3ddUqgRZomNzM\nlgQIECBAgAABAgQWJlBnjr6Q3JrcnPxcslI7NC9entR2leOSJtuxOVgdd+cmDzqDYz0++7gm\n6XuhPQMquyBAgAABAgQI9FZgu4ys/pY9qg8j7Psfttdnko5MXp2cn3wnWal9Ji8ekbxvpTe9\ntqpA3X9UdhZoWJXIGwQIECBAgAABAgTaKzBJQVjLgN+34SF09QzSe+L0qoatHI4AAQIECBAg\nQKBdAr06g7RNu2zn3ptJznTUF8tqkwnUGaS3TbaprQgQIECAAAECBAi0X2BoBdJ6M/LcbPCc\n5HXJiettvMb7d8x7JyTbrrHN+Ft3G3/Skce16MWdEws0dGTCdJMAAQIECBAgQGB9AQXSlka1\nItv9kvq5mVZnqr6d1OnGSdqNk2zUsm3q7FGN8cyW9Ut3CBAgQIAAAQIECBCYkcCsCqRpu9PF\ne5COyyBPnXagtidAgAABAgQIEOidgHuQejel3xvQRXlY0dYXqDNILq9b38kWBAgQIECAAAEC\nHRIY4iV2e2R+6stjt0/qO3yuSK5NtOkEqkB6+3QfsTUBAgQIECBAgACBdgtMsux1u0cwWe8O\ny2avTy5OLku+mtS9MxckVSSdk5yU7J1o6wvsm00qziCtb2ULAgQIECBAgAABAq0SeEl6U9/s\nWzkv+VhS39/zluSU5BPJN5N6/5LkKUnTrWv3ID02QLVAw9ZNQzkeAQIECBAgQIBA6wR6dQ9S\n63Rn3KEnZX9V+FQhdPga+94q7x2T1Hcg1fYPTppsXSuQXhqcKjQ1AgQIECBAgAABAr0qkPp+\nid0T8vt6blI/T1/jd7eKog8nj0iuTp6WaKsLWKBhdRvvECBAgAABAgQIdFig7wVSfafRx5Mb\nJpyjy7PdGcl+E24/1M2qQFqr4Byqi3ETIECAAAECBAh0XKDvBVLdW1R/zG874TzVCndVVPny\n09XB6ruifiCxQMPqRt4hQIAAAQIECBDoqEDfC6Q3ZF4OSd6RHLnGHNU9SEcn70t2St6VaCsL\nHJGXr0++uPLbXiVAgAABAgQIECDQXYG+fw/SyZmafZLjk8clFya1tPelyVXJbsmeyYFJLVt9\nU/LC5NREW1mgzsh9NikrjQABAgQIECBAgACBDgoclD6/OakCqRZkGE99SezZyQnJ/ski2rE5\naPVp50UcfMpj/n22f+2Un7E5AQIECBAgQIBAfwV6tYpd388gjX4NayW7Jy89qbNGuyc7JPXF\nsVcm2uQCtVx6FUkaAQIECBAgQIAAgd4JDKVAGp+4urSuok0vUJcr3iWxQMP0dj5BgAABAgQI\nECDQAYG+L9LQgSnoVBfr/qNaoOELneq1zhIgQIAAAQIECBCYUECBNCGUzb4rUAXSGYkFGvxC\nECBAgAABAgQI9FJAgdTLaZ3boKpAcnnd3HjtmAABAgQIECBAYNECCqRFz0C3jq9A6tZ86S0B\nAgQIECBAgMCUAgqkKcEGvPneGXstg+4M0oB/CQydAAECBAgQINB3AQVS32d4duOrs0c3JBZo\nmJ2pPREgQIAAAQIECLRMQIHUsglpcXdGCzTc2OI+6hoBAgQIECBAgACBTQkokDbFN6gPu/9o\nUNNtsAQIECBAgACBYQookIY57xsZtQJpI2o+Q4AAAQIECBAg0CkBBVKnpmthnd0rRz4gOX1h\nPXBgAgQIECBAgAABAg0IKJAaQO7BIers0XeSz/dgLIZAgAABAgQIECBAYFUBBdKqNN4YE6gC\n6XNJFUkaAQIECBAgQIAAgd4KKJB6O7UzHZj7j2bKaWcECBAgQIAAAQJtFVAgtXVm2tUvBVK7\n5kNvCBAgQIAAAQIE5iSgQJoTbI92e8eM5cDktB6NyVAIECBAgAABAgQIrCigQFqRxYtjAofn\ncd17VPcgaQQIECBAgAABAgR6LaBA6vX0zmRwdXldrV5ngYaZcNoJAQIECBAgQIBAmwUUSG2e\nnXb0zf1H7ZgHvSBAgAABAgQIEGhAQIHUAHLHD6FA6vgE6j4BAgQIECBAgMDkAgqkya2GuOUe\nGfRdEws0DHH2jZkAAQIECBAgMEABBdIAJ32KIdfZoxuTz03xGZsSIECAAAECBAgQ6KyAAqmz\nU9dIx6tAqgUabmjkaA5CgAABAgQIECBAYMECCqQFT0DLD+/+o5ZPkO4RIECAAAECBAjMVkCB\nNFvPvu1NgdS3GTUeAgQIECBAgACBNQUUSGvyDPrNO2T0ByUWaBj0r4HBEyBAgAABAgSGJaBA\nGtZ8TzPaOnt0U/K5aT5kWwIECBAgQIAAAQJdFlAgdXn25tv3KpC+kFw/38PYOwECBAgQIECA\nAIH2CCiQ2jMXbeuJ+4/aNiP6Q4AAAQIECBAgMHcBBdLciTt7AAVSZ6dOxwkQIECAAAECBDYq\noEDaqFy/P7d7hndQYoGGfs+z0REgQIAAAQIECCwTUCAtA/H0uwKH5z9vTj7LgwABAgQIECBA\ngMCQBBRIQ5rtycdal9d9MbFAw+RmtiRAgAABAgQIEOiBgAKpB5M4hyG4/2gOqHZJgAABAgQI\nECDQfgEFUvvnaBE9VCAtQt0xCRAgQIAAAQIEFi6gQFr4FLSuA7ulR3dPLNDQuqnRIQIECBAg\nQIAAgXkLKJDmLdy9/dcCDbckFmjo3tzpMQECBAgQIECAwCYFFEibBOzhx0cLNFzXw7EZEgEC\nBAgQIECAAIE1BRRIa/IM8k33Hw1y2g2aAAECBAgQIECgBBRIfg+WCyiQlot4ToAAAQIECBAg\nMBgBBdJgpnqige6arQ5OLNAwEZeNCBAgQIAAAQIE+iagQOrbjG5uPBZo2JyfTxMgQIAAAQIE\nCHRcQIHU8Qmccffr8rozk2/PeL92R4AAAQIECBAgQKATAgqkTkxTY510/1Fj1A5EgAABAgQI\nECDQRgEFUhtnZXF9UiAtzt6RCRAgQIAAAQIEWiCgQGrBJLSkC7ukHxZoaMlk6AYBAgQIECBA\ngMBiBBRIi3Fv41FrgYZqn7nth/8kQIAAAQIECBAgMDwBBdLw5ny1EVeBVAs0XLvaBl4nQIAA\nAQIECBAg0HcBBVLfZ3jy8bn/aHIrWxIgQIAAAQIECPRUQIHU04ndwLAUSBtA8xECBAgQIECA\nAIF+CSiQ+jWfGx1NLdBwz+S0je7A5wgQIECAAAECBAj0QUCB1IdZ3PwYDl3ahQUaNm9pDwQI\nECBAgAABAh0WUCB1ePJm2PW6vO6s5JoZ7tOuCBAgQIAAAQIECHROQIHUuSmbS4fdfzQXVjsl\nQIAAAQIECBDomoACqWszNp/+KpDm42qvBAgQIECAAAECHRNQIHVswubQ3Z2zz0MSCzTMAdcu\nCRAgQIAAAQIEuiWgQOrWfM2jtxZomIeqfRIgQIAAAQIECHRSQIHUyWmbaafr8rovJ1fPdK92\nRoAAAQIECBAgQKCDAgqkDk7ajLtcBdLpM96n3REgQIAAAQIECBDopIACqZPTNtNOW6Bhppx2\nRoAAAQIECBAg0GUBBVKXZ2/zfd8pu7BAw+Yd7YEAAQIECBAgQKAnAgqknkzkBodRCzTU78Cn\nN/h5HyNAgAABAgQIECDQKwEFUq+mc+rB1OV1ZydXTf1JHyBAgAABAgQIECDQQwEFUg8ndYoh\nHZ5tff/RFGA2JUCAAAECBAgQ6LeAAqnf87ve6CzQsJ6Q9wkQIECAAAECBAYloEAa1HRvMdgd\n8+zeiTNIW7B4QoAAAQIECBAgMGQBBdJwZ//+GXrNvwUahvs7YOQECBAgQIAAAQLLBBRIy0AG\n9LQur/tKcuWAxmyoBAgQIECAAAECBNYUUCCtydPrN91/1OvpNTgCBAgQIECAAIGNCCiQNqLW\nj88okPoxj0ZBgAABAgQIECAwQwEF0gwxO7SrHdJXCzR0aMJ0lQABAgQIECBAoBkBBVIzzm07\nSi3QsHVigYa2zYz+ECBAgAABAgQILFRAgbRQ/oUdvC6vOye5YmE9cGACBAgQIECAAAECLRTY\npoV9mmWXjs3OdtvADj+Wz3x8A5/rykfcf9SVmdJPAgQIECBAgACBRgX6XiD9cjQP3YDocflM\n3wukkzfg4iMECBAgQIAAAQIEei3Q9wLpUZm9dyZHJX+f/FUySTtrko06uk0t0HCf5LSO9l+3\nCRAgQIAAAQIECBDYhMD2+ey/JTckh21iP/P8aF0KeGuy8zwPsrTvBy4da48GjuUQBAgQIECA\nAAEC/RfYLkOsv2XrpETn2xAWaajC6BlLM/Wazs/Y5gdQ9x+dm1y++V3ZAwECBAgQIECAwP9r\n706g7KgKNI4nJEAMEAhbQLYYA0KQsEtwDkScZCCgURhgRGTxsA8yIyCoDCMSwAFZ1JlB8Qg4\noCiIQlAYcFRgUGEIB9CwCmIAwxKWEPYlLPN96Xuhuk6913Xp192vqv73nC/16tZ9tfzq5vW7\nXfVeI1AvgSYMkHzG7lKOU/yFDZsoTS58QUOTzz7HjgACCCCAAAIIINBWoCkDJCOcqUxW7vBM\ng8sWOnY+f9TgDsChI4AAAggggAACCLQWaNIAqbVCc5b481gfVBggNeecc6QIIIAAAggggAAC\nCQIMkBKwatDUtxcurdxWg2PhEBBAAAEEEEAAAQQQ6LgAA6SOk3b1Cv35o3nKwq7eS3YOAQQQ\nQAABBBBAAIEhEqj730FKZT1MTzhU+Y5yTuqTM+0n6LFvY/NXHpYpI0KjN8s07kcb3143px/P\n56kIIIAAAggggAACCNRagAFS79M7TrP+IgdP+1Me1JP3VHw7W5mykRqdobxRpnE/2pys53LV\nsB+APBUBBBBAAAEEEEAAgSYJdGqAlGrmP6rlP65V9opT6vppjwACCCCAAAIIIIDAQAnU6g/F\ncgWpdzdZoFmHggACCCCAAAIIIIAAAg0UaOIAaazO84qKv/L6BWWR8qJCQQABBBBAAAEEEEAA\ngYYLNOXzKJvrPJ+rPKH4G9z8TW73KvMVD5IeUL6rrKZQEEAAAQQQQAABBBBAAIHaCnxFR+bP\n9zgPKTcqVyoXK1crNyuPKV7+lPJpZbALn0EabHG2hwACCCCAAAIIINApgVp9BqlTKN26nj20\nYx74eCC0RZudHK5l2yu3KG7/YWUwCwOkwdRmWwgggAACCCCAAAKdFGCA1EnNAV7XRVq/b5/z\n543KFH8+6TmlP38Dqcx28m0YIOVFmEcAAQQQQAABBBCoikCtBkh1/wyS/6bRTcqrJXvXM2o3\nV1mrZHuaIYAAAggggAACCCCAQI0E6j5A8meLtlTK/sFWX0HyoMpf4EBBAAEEEEAAAQQQQACB\nhgnUfYB0gc7nhsrPlG3anFt/Bmk75RpltDJboSCAAAIIIIAAAggggEDDBOr+d5B+pPO5unKy\n8nHlEcVf7f204s8ajVFWVtZT1lReV45Wfq9QEEAAAQQQQAABBBBAAIFaCkzQUf1Y8QDJ31KX\njf9I7P3KGco6ylAUvqRhKNTZJgIIIIAAAggggEAnBGr1JQ11v4IUT/hf9GCvMOOrRisqoxT/\n4dhnFQoCCCCAAAIIIIAAAgggMKwpA6TsqfatdQ4FAQQQQAABBBBAAAEEEOglUPcvaeh1sMwg\ngAACCCCAAAIIIIAAAu0EGCC102EZAggggAACCCCAAAIINEqAAVKjTjcHiwACCCCAAAIIIIAA\nAu0EGCC102EZAggggAACCCCAAAIINEqAAVKjTjcHiwACCCCAAAIIIIAAAu0EGCC102EZAggg\ngAACCCCAAAIINEqgiV/z3c0n2H9kayDLCK2cQfFACrNuBBBAAAEEEBgKgcVDsVG2+bbAQL+H\nfXtDg/GAAdJgKPe9jfif+vm+m9ICAQQQQAABBBBAAIGuFHitK/cqcaeGJ7an+cAJbKVVLz1w\nqx/2t1r3McoXBnAbrLp+AmN1SKcpxylP1e/wOKIBFHC/+ZkyZwC3warrJ3CwDsl/zP3i+h0a\nRzSAAtO07i2VfQZwG6y6bwEPjm7tuxktEOgegT21Kwu6Z3fYk4oIrKP9fEuZUJH9ZTe7R2C+\ndmXv7tkd9qQiApdqP/+zIvvKbnaPwFHaFd6Yd8/5qPye8HmUyp9CDgABBBBAAAEEEEAAAQQ6\nJcAAqVOSrAcBBBBAAAEEEEAAAQQqL8AAqfKnkANAAAEEEEAAAQQQQACBTgkwQOqUJOtBAAEE\nEEAAAQQQQACBygswQKr8KeQAEEAAAQQQQAABBBBAoFMCDJA6Jcl6EEAAAQQQQAABBBBAoPIC\nDJAqfwo5AAQQQAABBBBAAAEEEOiUAAOkTkmyHgQQQAABBBBAAAEEEKi8AAOkyp9CDgABBBBA\nAAEEEEAAAQQ6JcAAqVOS3b+e17SLi7t/N9nDLhNwv3Gh7/Q48G95AV5zylvR8h0B95v4uvNO\nLY8QaC9Av2nvw1IEEGghMEL141ssoxqBdgIT2y1kGQItBNZT/cgWy6hGoJXAqlqwYquF1CPQ\nQmCU6tdqsYxqBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAAB\nBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAA\nAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBA\nAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQ\nQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIHuFRjRvbvGnnVQYG2ta6ri\n6RPKYoXSTIEJOuxtlUnh8J9uw5DSb/xa4vV+SHldWahQ6inwXh3WNMWvJS8XHGJKX0hpW7Ap\nqiogsIb20T9//NrzvPKiUlRS+0LK61PR9qjrXoFR2rUtlQ8ryytPKW8orUpKX0hp22p71COA\nQA0ETtQxeED0VojfvB6rUJol4Dcps5XYD+L0WtX5jUu+pPSb9fXke5S4Tk/vUtZRKPUS8JvY\nGxWfYw+I8yWlL6S0zW+H+e4XGKNdvEzJvi54QP3lgl1P7Qspr08Fm6OqiwU+qn17UMn2m3ma\nd31RSekLKW2LtkUdAgjURGC6jsMvMv4htbni3+5fo7juCIXSDIGldJjXKz7vlygzlKnKecqb\nyp2Kf2MXS0q/Ga4n3aA8p3xGmagcpLykPKQsp1DqI/AVHYr7kZMfIKX0hZS29dFr1pHMCf3k\na5puouyv+Bcn7jufUmJJ7Qspr09xG0yrIbCudnOR8oziX+RurByj+E6HZ5XxSrak9IWUttlt\n8BgBBGomMFrHM0+Zr/i3vrEsoweu/6uSrY/LmdZPYKoOyW9K/Jv/fLlKFV62R1iQ2m8OC88/\nJDw/TjxI8nrz9XE50+oJ+BcsvhrtW+t8bvMDpJS+kNJWm6JUTGAX7a/7yDm5/Z4U6q/P1Kf0\nhdTXp8xmeFgBgS9oH91vZuX29auh/vhMfUpfSGmb2QQPEUCgjgIzdFB+oTm14OBOCcv8Q4xS\nf4H9dIjzlAMLDtW/yXU/OSEsS+03N+t5rygrhefHiW+v8e00t8QKppUWWE57f7/yW+V0xX1m\nipItKX0hpW12GzyuhsB12k1fBchemY577lulto4zmqb0hRlq777Hz7UMYI0e+rz6/M7MHZP7\njOvPztSn9IWUtplN8LDJAks1+eBrfuz+ba/LnJ5Jr39j3Va9apmpq8AFOrD3KecWHOCEUPdA\nmKb0m6X1nM2U+xTfFpEtvuXuXmVTxe0o1Rb4hnZ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/0eNsbtX8cMW/4Xe5v2cybKMwzU58ZSJb/OUMLhv2TLru33vCHk0t2LNYNyezzO0n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\nIIAAAggggAACCCCAAAIIIIAAAjmB/weR0xjrWUEeIAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(seq(1,1000, by = 100),iter_means, type = 'l')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.686915484064143"
      ],
      "text/latex": [
       "0.686915484064143"
      ],
      "text/markdown": [
       "0.686915484064143"
      ],
      "text/plain": [
       "[1] 0.6869155"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "iter_means[length(iter_means)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that after 1000 iterations, we come to $\\delta = 0.687$, only 0.013 away from 0.7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2\n",
    " \n",
    "Consider trying to estimate $\\pi$ by performing a random walk inside the unit\n",
    "square, where at each time point we select a point within a square centered at\n",
    "your current location with side length $\\epsilon$. We then look at the proportion of time\n",
    "spent in the inscribed circle, which we suspect might approximate the area of\n",
    "the circle, from which we can estimate the value of $\\pi$. Consider two approaches:\\\\[5pt]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## a)\n",
    " \n",
    "a. if you are offered to move outside the square, just ignore that value and do\n",
    "it again until you are offered a `legal' point, but you move on each iteration.\\\\[5pt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A_UnitWalk <- function(epsilon, n_iters, initial = c(0.0,0.0)) {\n",
    "    #\n",
    "    # Function to perform a random walk within the unit-square, rejecting possibilities outside the unit square\n",
    "    #\n",
    "    # Args:\n",
    "    #    epsilon: the maximum step size\n",
    "    #    n_iters: the number of times to perform the random walk\n",
    "    #    initial: a vector of the starting x and y values\n",
    "    #    \n",
    "    # Returns:\n",
    "    #    data_frame: a dataframe with the x and y walk positions, and their distance from the origin as a third column\n",
    "    \n",
    "    x <- c(initial[1])\n",
    "    y <- c(initial[2])\n",
    "    dist <- c(sqrt(x^(2) + y^(2)))\n",
    "        \n",
    "    for (i in (2:(n_iters + 1))) {\n",
    "        \n",
    "        newx <- (x[i-1] + runif(1,-epsilon,epsilon)[1]) \n",
    "        newy <- (y[i-1] + runif(1,-epsilon,epsilon)[1]) \n",
    "        \n",
    "        while (abs(newx) > 0.5 | abs(newy) > 0.5) {\n",
    "            newx <- (x[i-1] + runif(1,-epsilon,epsilon)[1]) \n",
    "            newy <- (y[i-1] + runif(1,-epsilon,epsilon)[1]) \n",
    "            }\n",
    "\n",
    "        x[i] <- newx\n",
    "        y[i] <- newy\n",
    "        dist[i] <- sqrt(newx^(2) + newy^(2))\n",
    "           \n",
    "        }   \n",
    "     \n",
    "    return(data.frame(x,y,dist))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A_walk <- A_UnitWalk(0.1, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>x</th><th scope=col>y</th><th scope=col>dist</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>-0.02437151</td><td> 0.01841545</td><td> 0.03054667</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>-0.05430019</td><td>-0.06773976</td><td> 0.08681697</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>-0.06260117</td><td>-0.03003455</td><td> 0.06943328</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>-0.152463879</td><td> 0.008530315</td><td> 0.152702327</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>-0.12891288</td><td>-0.03574339</td><td> 0.13377638</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & x & y & dist\\\\\n",
       "\\hline\n",
       "\t1 & 0 & 0 & 0\\\\\n",
       "\t2 & -0.02437151 &  0.01841545 &  0.03054667\\\\\n",
       "\t3 & -0.05430019 & -0.06773976 &  0.08681697\\\\\n",
       "\t4 & -0.06260117 & -0.03003455 &  0.06943328\\\\\n",
       "\t5 & -0.152463879 &  0.008530315 &  0.152702327\\\\\n",
       "\t6 & -0.12891288 & -0.03574339 &  0.13377638\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "            x            y       dist\n",
       "1  0.00000000  0.000000000 0.00000000\n",
       "2 -0.02437151  0.018415445 0.03054667\n",
       "3 -0.05430019 -0.067739757 0.08681697\n",
       "4 -0.06260117 -0.030034547 0.06943328\n",
       "5 -0.15246388  0.008530315 0.15270233\n",
       "6 -0.12891288 -0.035743388 0.13377638"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(A_walk) #inspect the dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now write a function to calculate Pi, given a dataframe like the dataframe above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "CalcPi <- function(square) {\n",
    "    #\n",
    "    # A function to calculate pi, given a dataframe of x, y coordinates and distances from the center for randomly drawn\n",
    "    # points in 2D.\n",
    "    #\n",
    "    # Args:\n",
    "    #    square: the input dataframe, from one of the UnitWalk functions defined previously\n",
    "    # Returns:\n",
    "    #    pi_estimate: a float of the best estimate of pi\n",
    "    #\n",
    "\n",
    "\n",
    "    #subset the dataframe\n",
    "    in_circle <- subset(square, subset = (dist < 0.5)) #find the points in the circle\n",
    "    out_circle <- subset(square, subset = (dist >= 0.5)) #find the points out of the circle\n",
    "\n",
    "    #plot the points \n",
    "    plot(out_circle$x,out_circle$y, pch = '.',\n",
    "        xlim = c(-0.5,0.5), ylim = c(-0.5,0.5))\n",
    "    points(in_circle$x,in_circle$y, \n",
    "        xlim = c(-0.5,0.5), ylim = c(-0.5,0.5),pch = '.', col = 'blue')\n",
    "\n",
    "    #estimate pi\n",
    "    pi_estimate <- (length(in_circle$x)/(length(out_circle$x) + length(in_circle$x)))*4.0\n",
    "    print(pi_estimate)\n",
    "    \n",
    "    return(pi_estimate)\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 3.318868\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "3.31886811318868"
      ],
      "text/latex": [
       "3.31886811318868"
      ],
      "text/markdown": [
       "3.31886811318868"
      ],
      "text/plain": [
       "[1] 3.318868"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VqpABWgAlSAClABKkAFqAAVaCrAF6Sm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\n5tFc0V+J36rjFeciDWHXNbd0Fn/M65iX7nv3f+++3BLBw2j532l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oP1if93WFztmqtVZWxyxGy28Xpubdyt+aG8HYUU+LYzQX8RipKcrR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JjXa8qu4Wrp7T/WpurVE19ir/J3K+Sqsv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\nPTHOC9I99+0i1vIhx8N/ER1X2gjHlm9rvUVoNL6FL9flfsn1K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c3Cw7PRio+uU77IFfWPYF/h66lnlvZX1Ls+Z/QF6ZMKxd9b2lcoVOlX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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "CalcPi(A_walk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## b)\n",
    " \n",
    "b. do the same as in (a), except once you are offered a legal point, only move to\n",
    "that point with a probability given by the Metropolis ratio.\\\\[5pt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Overlap <- function(c, eps, l) {  \n",
    "    #\n",
    "    # Function to calculate the overlapping length of a line segment centered at 0 with length l, and a line segment \n",
    "    # centered at c with length eps.\n",
    "    #\n",
    "    # Args:\n",
    "    #    c: the center of the line segment.\n",
    "    #    eps: 1/2 the length of the line segment centered around c.\n",
    "    #    l: length line segment centered around 0.\n",
    "    #\n",
    "    # Return:\n",
    "    #    overlap: length of the overlap between the two line segments    \n",
    "\n",
    "    if (abs(c) + eps <= l) { # if the line segment is entirely within the square\n",
    "        overlap <- 2*eps\n",
    "    }\n",
    "        \n",
    "    else if (abs(c) - eps > l) { # if the line segment is entirely outside the square\n",
    "        overlap <- 0\n",
    "    }\n",
    "        \n",
    "    else { # if the line segment contains the boundary of the square\n",
    "        overlap <- (l - abs(c) + eps)\n",
    "    }\n",
    "    return(overlap)\n",
    "}\n",
    "\n",
    "B_UnitWalk <- function(epsilon, n_iters, initial = c(0.0,0.0)) {\n",
    "    #\n",
    "    # Function to perform a random walk within the unit-square using a metropolis-hastings algorithm\n",
    "    #\n",
    "    # Args:\n",
    "    #    epsilon: the maximum step size\n",
    "    #    n_iters: the number of times to perform the MH-walk\n",
    "    #    initial: a vector of the starting x and y values\n",
    "    #    \n",
    "    # Returns:\n",
    "    #    data_frame: a dataframe with the x and y walk positions, and their distance from the origin as a third column\n",
    "    \n",
    "    \n",
    "    x <- c(initial[1]) #first x from initial coordinates\n",
    "    y <- c(initial[2]) #first y from initial coordinates\n",
    "    dist <- c(sqrt(x^(2) + y^(2))) #calculate the first distance\n",
    "        \n",
    "    for (i in (2:(n_iters + 1))) {\n",
    "        \n",
    "        newx <- (x[i-1] + runif(1,-epsilon,epsilon)[1]) #calculate a new x\n",
    "        newy <- (y[i-1] + runif(1,-epsilon,epsilon)[1]) #calculate a new y\n",
    "        \n",
    "        lx <- Overlap(abs(newx), epsilon, 0.5) #calculate the length of the possible values\n",
    "        ly <- Overlap(abs(newy), epsilon, 0.5) #calculate the length of the possible values\n",
    "        \n",
    "        met_ratio <- min(1, ((lx*ly)/(4*epsilon^(2.0)))) #compute the metropolis ratio, comparing the area of the intersections.\n",
    "        \n",
    "        if (runif(1) < met_ratio) { #update according to the probability. Move if runif is less than met_ratio\n",
    "            \n",
    "            x[i] <- newx\n",
    "            y[i] <- newy\n",
    "            dist[i] <- sqrt(newx^(2) + newy^(2))\n",
    "            \n",
    "        }\n",
    "        \n",
    "        else { # if runif is greater than met_ratio, do not move. \n",
    "            x[i] <- x[i-1]\n",
    "            y[i] <- y[i-1]\n",
    "            dist[i] <- sqrt(x[i-1]^(2) + y[i-1]^(2))\n",
    "        }\n",
    "    }\n",
    "    return(data.frame(x,y,dist))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 2.854915\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "2.85491450854914"
      ],
      "text/latex": [
       "2.85491450854914"
      ],
      "text/markdown": [
       "2.85491450854914"
      ],
      "text/plain": [
       "[1] 2.854915"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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qe5Umq35PPa7jxPWRsfZY1X8eK8dMQGArcicPd3jlsN1t3/it2npdH60M6IfcLr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\n6NfqaT3QL3nIRg3ggjglPqW2khStXclXto3Gqc0LmWP2OdVAOnb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5Qzuxl3HzsWjxlX4tO/StJWAZw1zZiO+S+XD1uwy9p12tIR+0W1y/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iV51fjU2mvadmn3MDql1lN07jIXhnXs9s8P6K/Y3eZb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bdC0tra2+XLdmrKO15xr4mnVLTfKc7TxHTQ1Rubz6PH6zfHgs8vgjjDRjkOfLr2u6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\nUdhmnDaYCxgI+Q7vA3HV7ZXzyrF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bxBWiwhgAMGwMBsBpabgD1CeLHkVYkua2Mi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\nBEAMGKB+PbNPp3y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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "CalcPi(B_walk) #the algorithm is not working properly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## c)\n",
    "\n",
    "c. How does the value of $\\epsilon$ affect the estimate of $\\pi$ in (a)? Give a brief explanation\n",
    "of why (b) works but (a) does not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algorithm (a) tends to overestimate Pi because the points are drawn from the center of the circle too frequently. If a point is drawn within $\\epsilon$ from the edge of the unit square, there is a chance that the choice will be rejected and that the point will have to be redrawn.  This keeps the algorithm in the center of the circle for too long, especially if $\\epsilon$ is large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algorithm (b) should work correctly because the probability of moving from point x is proportional to the ease of moving to point x. Therefore, if the algorithm lands on a (difficult to land on) location near a corner, it stays for more iterations to compensate for this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "HOWEVER, my Algorithm (b) is not working. I think this is because the overlapping area of the two squares is not calculated correctly. I wrote the \"Overlap\" function to compute the overlap between two line segments. I compute the overlap independently for the x and y coordinates and multiply the x and y overlaps together to get the area of the intersecting square. If the intersecting area was calculated correctly, the metropolis ratio would ensure that random points were being drawn from the unit square.\n"
   ]
  }
 ],
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   "language": "R",
   "name": "ir"
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   "file_extension": ".r",
   "mimetype": "text/x-r-source",
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