{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Refresher  for CS 237 and CS 132\n",
    "\n",
    "This document summarizes what you need to know about Python for CS 237 and CS 132. \n",
    "Even if you already know the language well, you should look this through,\n",
    "as I explain how to avoid nasty bugs in your coding this semester. \n",
    "\n",
    "\n",
    "NOTE: To see a video walk-through with my comments, check out my YouTube video <a href=\"https://youtu.be/ikfXoX4X_eE\">here</a>. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here are some imports which will be used in the code in the rest of the lab  \n",
    "\n",
    "# Imports used for the code in CS 237\n",
    "\n",
    "import numpy as np                # arrays and functions which operate on array\n",
    "import matplotlib.pyplot as plt   # normal plotting\n",
    "import seaborn as sns             # Fancy plotting \n",
    "import pandas as pd               # Data input and manipulation\n",
    "\n",
    "from collections import Counter\n",
    "\n",
    "import math\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Python Programming"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "here is a definition\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'Hi there, Paul'"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"here is a definition\")\n",
    "\n",
    "def sayHi(name):\n",
    "    return \"Hi there, \" + name\n",
    "\n",
    "sayHi('Paul')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optional Arguments\n",
    "\n",
    "Python allows a lot of flexibility when you define functions; in particular,\n",
    "it allows you to define functions with a variable number of arguments,\n",
    "and optional arguments with default values. This simplifies the syntax\n",
    "when you have a function which you want to use in a variety of contexts;\n",
    "many of the statistical functions operation in this way, for example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All the arguments: (2, 2, 5, 4, 7, -3)\n",
      "Number of arguments: 6\n",
      "Last argument: -3\n",
      "Sum =  17\n",
      "\n",
      "All the arguments: (4,)\n",
      "Number of arguments: 1\n",
      "Last argument: 4\n",
      "Sum =  4\n",
      "\n",
      "All the arguments: ()\n",
      "Number of arguments: 0\n",
      "Sum =  0\n"
     ]
    }
   ],
   "source": [
    "# Variable number of arguments, this looks a lot like how it is done in C\n",
    "\n",
    "# The following function collects together all its arguments into a tuple,\n",
    "# which can then be accessed as usual inside the function\n",
    "\n",
    "def my_sum(*args):\n",
    "    print('All the arguments:', args)\n",
    "    print('Number of arguments:', len(args))\n",
    "    if len(args) > 0:\n",
    "        print('Last argument:', args[-1])\n",
    "    return sum(args)\n",
    "        \n",
    "print('Sum = ', my_sum(2,2,5,4,7,-3))\n",
    "print()\n",
    "print('Sum = ', my_sum(4))\n",
    "print()\n",
    "print('Sum = ', my_sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 5 , a = 3 , m = 7 , b = 1\n",
      "2\n",
      "\n",
      "x = 5 , a = 2137 , m = 6827 , b = 0\n",
      "3858\n",
      "\n",
      "x = 15 , a = 23 , m = 6827 , b = 0\n",
      "345\n",
      "\n",
      "x = 15 , a = 7 , m = 11 , b = 0\n",
      "6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Optional Arguments with Default Values\n",
    "\n",
    "# You may give arguments with default values using\n",
    "# an initialization in the definition, as shown here:\n",
    "\n",
    "#           x is a normal parameter, you MUST supply it \n",
    "#                          m is optional, if you leave it out it will get the default\n",
    "#                                         b ditto\n",
    "def LC_Hash(x, a = 2137, m = 6827, b = 0):\n",
    "    print('x =',x, ', a =',a, ', m =',m, ', b =',b)\n",
    "    return ((a * x) % m) + b\n",
    "\n",
    "# Here we give all four values\n",
    "\n",
    "print( LC_Hash( 5, 3, 7, 1) )         # x <- 5, a <- 3, m <- 7, b <- 1\n",
    "print()\n",
    "\n",
    "# Here we give only first, rest will take optional values\n",
    "\n",
    "print( LC_Hash( 5 ) )         # x <- 5, a <- 3, m <- 7, b <- 1\n",
    "print()\n",
    "\n",
    "# Here we give first two\n",
    "\n",
    "print( LC_Hash( 15, 23 ) )        \n",
    "print()\n",
    "\n",
    "# Here we give only first three\n",
    "\n",
    "print( LC_Hash( 15, 7, 11 ) )         # x <- 5, a <- 3, m <- 7, b <- 1\n",
    "print()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x = 15 , a = 11 , m = 23 , b = 3\n",
      "7\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Is best to give values for a prefix of the arguments, in order, and not skip around\n",
    "# When in doubt, use the name of the parameter\n",
    "\n",
    "print( LC_Hash( 15, 11, m = 23, b = 3 ) )      \n",
    "print()"
   ]
  },
  {
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OLd0+vU8GOENOI1ljfRN7Uw+zYPNoizjLRKsT1sk2KbZpdqfs0xySHGOcfJ3tXPT2aboa7Hc5EHUwx+0WqdW9y6PD875XofdhH0dfaT9KvwX/voCGwPKgguCMkIRQ8iFXslYYd9ha+FDEzcjkKPdo/RjpWP7DnEdYjzLG0RzDHFuOf3e8K+F2Yk5S1In9ySYn9VLMUklpx9OvnXp8euLM54ylsyuZS+e+Zy1mf8pZyP18/ucFmnyVguDC0os9l6Yuz1+Zufqm6GVxf8mTa02ljde7yj7d4K3YX1l482U1wy2L2ynw7rV6X7LGs7agbqAB/UC+8eDDE02lzY0tTY9utJ5tO9oe1RH/OKPz4pPip5e6zjyL6LZ9LtGD6hnrvdOX3u8/YP1Cf1B/yHrYfSRiNOnlybGjr7xf646zjS9M1L85Oen0VuId7t37qbbpizOH3mvNUs4OzhXPH/vg99FzwfdT0OfQL6GLoV/J3yK/x/yIWvJbNlyhXrn7U//ns1WX1U+/+tYpN8a2518MtEOm0CjCC4lBZqDEUL3oWIwUZh57DeeLl8KvErooLlNGEW2oZKmpqJdpXtK20JXTZzEcZfRhsmFWZxFhZWRdZ5tjH+Bo4qziKuYu4Mnlzd6TwZfMHylAEtQX4hH6Kdwtclk0TMxInFcCITEvOSL1RLpB5oZsnly8vJuCiiJGsVcpR9lJhVXlpepFNc+9suoY9QmNGs0MLV9tPR1BXRo9oPddf9Zg2PCBUa6xl4mAyaRpnpmlOda8zSLR0tiKxeqDdZNNlq2vnZo90X7C4abjEScTZ0bnNy5l+0Lg8391/8MD8Qd13XBu/aRC9wCPvZ6UnmNe170P+Sj7rPs2+8X7awWAgJbA40G6wajgjpATodqhPw9VkJ3hM7s83DL8R0Re5N7Iiaj4aM7ohzFusUyxY4crjiQedYoTjls+1hafddwnQS9RNInlBEUySP5xcirleWp12ql00in509jTY2duZaSdDcg0PEd37nHWvqyF7Ngc7Vyd8ykXcPlpBdMXWS/JXla5onJVoUiqWLiE9xprKe11Qhm+nBqOJPVKt5snq25Wv7i1fkf4rsu9c/f7axnqnOsLG0Ya0Q9Fmgyb3VuOPbrU2tT2pn3zMW+n7hOfp6e6bj8b7t7oEend13e+f+KF7ODpoc8jtqP1Y7yvcsal3lC9jZpOn4v5ZPFtedV6a/53vvdtFYwiAFlwnulwGq7zAGTWwnnmAwCYCQBYEQGwUwGIk1UAYVgFoIATf88PCE48cXDOyQS4gQiQhzNNM+ACZ83RIBXOKCtBExgA78E6RAeJQFpwfhgGnYbzwQ5oCgEheBE6CE/ESTjLG0D8QvIhzZGxyDLkCAqHUkUFoYpRL9F0aFM4I2vDQBgtTDymFYvGmmDPYkdxvLhAXD0ei3fEl+F/EcwJVwkrFBYUZZQoSnfKNqIAMZX4mcqOqhHOdDJpAM0hmmlaZ9peOgO6h/TK9DUMqgxtjDaMU0wRzBjmXBZBljpWC9Y5thR2GfYpjsuc7lxiXD+5H/Pk8HrukefD8L3ivyuQIRgoZCosJkIUWRQdEnsgfkkiTtJVSkWaQXpR5rnsDblUeV8FE0VJJUalTeVPKhOqA2pdezvU2zU6NXu0xrTndJb1gD4G3udwRjhjvAmlKYMZr7m8hYVlsFW2daPNjB3RXt7B2fGo0xXndpdZV4r90gccDh5xKyH1uP/05Pey9T7h0+j7y1834ELgarBHyMAhA3JjuHxEdZRE9O3YvYf7joYc44gfTshOMjuxfDI7VTyt45TXGcaMN5nPs8ZzNvN48lUKzS4dvBJTdKVk7LpE+ZVK6arJ21fvHailqK9q3N8s1srdYfCkqJuyV7h/eTBzRPhl/+tLb86/G3jvNr/6ie5L5TfwQ3pZZWVzNe1X3drg+oON4t+hm0rb+we0/c2BDrADQSALNIE5cAVBIA5kghJQD3rBDNiAmCApyATyhhKhIugR9A6BQgghzBBkRD6iDfEFyYE0RR5BViOnUWwoG1Q6qgMNodXRh9EP0OsYTUwi5imWBuuMvYb9htPGZeHe49XwWfgFggE85+sUThT34EyYTDlIVCFeoaKgiqaapXam7qExoGmh1aBtptOl66K3pR+HM9NfjBlMokzPmA+xMLHUsFqzvmeLYSeyl3BocUxzZnKZcFNxj/Pc5T2zx49Ph5+F/6PAQ8GzQt7COiIConRiOHG0BE6SSopOmlYGJ7MqOyc3It+l8EjxkVKX8iuVb2pUe6XVrTX8NMO1yNq+Ok66hnoq+vIGyoaGRgeN40yumnaaLVqwW+pbBcBnWrbtebsc+2yHK47NTl9dFPbFuz4/wHUw3K3Xnc/D2zPH6753j8+075o/U4BcoF1QZHB+SEvoBzJzmEF4ZMT1yLFomhjz2IzDo0cF444emzruk0iT1JUcnoJJPZmOOpVyhj2jLTMhyylH97zaBbUCtYsql0Wuoooel0SWsl9/WO5ewVg5XtVxq/fO0n2Z2iP1zxqpm/RayK2l7fOdOk/vdMv0FPaND/wY/Do8Ozo1Nvf6xxvoLWGKYYZ/1mg+d0HpS9r30pXA1Z61pPW2jR+/V7fnHwGvflrABSSABrAG3uAoyAW3QDf4AOEhMcgcIkN5UAv0AcGE0EOEI0oRY0hapDEyCdmC3ECpoWJRDah1tDY6DT2CEcEcx4xjNbBFOBwuBDeIV8FfJCAI/oQhCj2KB5QqlI+IVsT3VAnUvNQtNK40y7Rn6STontMHMxAZyhh1GF8zxTBzMfewnGF1Z9NhF+Vg4FjjHOeq4z7HE8Rrtkeaj4Ufw78q8FXwi9B34Q1RKjF+cS0JN8l4qYvSdTIvZL/LsykYKyYotalQqrqq3VLHwnfVJu09Oll6TPpVhi7GtCb9ZvkWIVb2NrK2Y/YuDt1ORs4v9nm7/jyQ6AaRQt2HPJW8Cn3wvsf9CQHFQeYhILSWHBLOFdEWFRHjefhzXEl8zPHhhPUkxAlcMs1JuZSw1MF0+1PzZ1LOSma+zErJUcv9mleef6CQcPH6ZaUrD4s0i1uu6ZV2lVmVD1bYVfZVGVTX3xa+c/4e7v7RmvW61AbBB30PE5oVW+ZbC9stH6M6HzwNeybWPd1zqc9pgOHFwFDGiMno5ljla8vxuTcRkxvvEqaRMwmziLnED6iPxxY+fzb4ErN48evpbxHf9b6v/LixZLH0atl3eXklcmX+p+vP3lXd1YpfxF+hvwbWFNby1r6uG68Xra9t2G3c/I387fS7chPatN+8sTX/Yd5ystvHB0SpAwB6YnPzuyAA2HMAbGRubq4VbW5uFMPJxmsAWgJ3/kPaPmtoACh8s4W6RIfi//1fzv8B7B3fj0cqVUcAAAGdaVRYdFhNTDpjb20uYWRvYmUueG1wAAAAAAA8eDp4bXBtZXRhIHhtbG5zOng9ImFkb2JlOm5zOm1ldGEvIiB4OnhtcHRrPSJYTVAgQ29yZSA1LjQuMCI+CiAgIDxyZGY6UkRGIHhtbG5zOnJkZj0iaHR0cDovL3d3dy53My5vcmcvMTk5OS8wMi8yMi1yZGYtc3ludGF4LW5zIyI+CiAgICAgIDxyZGY6RGVzY3JpcHRpb24gcmRmOmFib3V0PSIiCiAgICAgICAgICAgIHhtbG5zOmV4aWY9Imh0dHA6Ly9ucy5hZG9iZS5jb20vZXhpZi8xLjAvIj4KICAgICAgICAgPGV4aWY6UGl4ZWxYRGltZW5zaW9uPjczNDwvZXhpZjpQaXhlbFhEaW1lbnNpb24+CiAgICAgICAgIDxleGlmOlBpeGVsWURpbWVuc2lvbj4xNjA8L2V4aWY6UGl4ZWxZRGltZW5zaW9uPgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KHtWNqQAAQABJREFUeAHtnQd4FFUXhs9uQg099N4h9N67IkqvIgqoWBBEpCgiv4qIIiCoFBUFBKQXKdKlIwjSe++9957szn++u9xlsslmN21Jwjk8y5Rb553Z7LlnvrljMdhITAgIASEgBISAEBACQkAICIFYJWCN1dqlciEgBISAEBACQkAICAEhIAQUAXG85UIQAkJACAgBISAEhIAQEAI+IODvbRuXLl0iu91OadKk8bZIjOQ7d+4c3bp1K0bqkkqEgBAQAkJACAgBISAEhIAvCVitVsqcOTNlzJiRvHa8L1y4QAULFvRlP51tFS5c2LkuK0JACAgBISAEhIAQEAJCIL4QCA4OpuPHjyvH22upCaLdYkJACAgBISAEhIAQEAJCQAh4TyBRokRKNYISXjve3lcvOYWAEBACQkAICAEhIASEgBBwJSCOtysR2RYCQkAICAEhIASEgBAQArFAQBzvWIAqVQoBISAEhIAQEAJCQAgIAVcC4ni7EpFtISAEhIAQEAJCQAgIASEQCwSeiuMdEhISC4dCdPDqVRqx6T+68eAB9V6xPFba8GWlwfxAa/+1a+ny3bu+bNZjW3G1Xx47HoczXLx7hw7x9Wv38Ytkz92+Tbt5qtBbDx/GYTrSNSEgBISAEBACCYOATx3vTZs20bRp02jKlCmxQu+T5csoKEMG+nb9OsqeKpVXbdzlKV4WHTlMHy37mwatX09frV1DIT6awWXohg0RtrX9/HkasO4fslgsXh2LrzJF1C9PxxRbfZy9fz8dv3EjtqqPtXpX8vRCRX7+icqPGUMlfx3FTvDFWGsrvIo/5u9MhTGjadO5s+Elyz4hIASEgBAQAkIgBgn41PFOnTo1FS9eXHXfiOHI3tKjR8nKDmqOVKlp8eHD9G6Zsh4x3Xn0iCqPHUNLjhyhMlmy0LJjR+nbdet84uieYCfxs1UryY8nVXdnpblPp7t1p/TJk7vL8lT2u+uXN8cUWx3utXw5R20fxFb1sVLvPR70vbtgAf3SoCGd+rAb3e/zPyqZKXOstOWu0nGNm6ikkhkzucsi+4WAEBACQkAICIEYIuD/6/DtlL9QWnquXu4YqtJ9NYUKFaLbfGt769at7jNFIgWOc5fFiwjSh39OnaLMAQHUauYMFUX+cMkSdmgaRFjbQI6Mw+Ee/uJLKl/VHDlp2H8bye9xhHnViRM0dMO/tOnsWcqcIgW9V64cdS5XnuDkf85Oc9pkyQjR3yaFCtOey5foJktc5rR+hQoFBhKcUMhElh0/Ruk537tly1L7EiUpOc/lOHXPHlp78iRl4P4O/+8/1XYpfqNRzVy51Pqx69fptTmzycbH9Q4PIN4pU0bthyzg5VmzKLGflY5wnvxp01Im7teKY8dodKNGqh+3mcn3HEmfvncP3WHH7s2Spagjt501ZUpVx6x9++iPXTtp45kz6q7AA5b97O38PnkTU3fXL1Ts6ZhU4xH8t/3CeZq8ezdtY571CxSgPzmCXT5rVnVuIjomnPcNZ07T2du3aDEPoFafOKkGKq89HuBdu3+fvlyzmvefoAt37lC+dOno9ZIl6b2y5SLojSMJso8JO3fSL1s2q/NZjN84lcTfn0a+VJ/yMfsj166pOxJrT55SBRoXKkhf1apNKRInJkSS13CbNXPnpjn7D3C7aenHei9SUPr0Ku+PGzfSyhPHVb/H7dhO+LxdugxVy5mT+q5ezcdymGa0bEWPbDZ6fd5cVWZFu/bq+vF0TOtPn+YB5D/quq2QLZs6/40KFlJ1wNkfuXkT/c3XMPpZJ3ceypYylboWVQb5TwgIASEgBISAEIg1AtaJY3dT315rKSQk/r0gB05sn2rVlePQqEBBeqNUKcrGEhM4v5/VqO4RGiLkK9k5+mXLFloHx52d2O9fqKfK7eA3dbaeNZOa8lsz/3v7Hepcvjz1/PtvgjNeNUcOgtNfjR31z2vUoEm7d9HHlauo8nBOH7Kz1HjaVMqVJjX988ab9HP9BvTFqlU0Zts2Vff5Ozz4OH+OirIsBo4QPv6myHcOvjMwtlFjdrD9KW3SpM7jyMiOOhy3VEmS0MSmzdjhPMPOdzpqxw79prPnVL5ey5bRXh4ETG3Rglayo7b+9Ck1OEEijqnzooX0AzuA53r0pJZFiijnyxunG+Xd9Qtpno4JedwZBiFNpk+nvOzMtmeneDhLkmD9atZSy4iOCfr3LefOUZ40aQg3UcAS51VbJz5e8Nr8zru07s0OanDkrQxp/M4d9N2/69lxLUdL27aldDyAggMfyEsMBupM/ENdewvatKEfX6xHs3iw8CMP3GC4HqGdRl9mtmpJwXxNLOc7KtrKs0OM+nAtNSlUiJry4K0IXw+w5kGFVVkMqnLzcfWuWpWOspOP6x0W0TFhMNBs+jRqW7wE7e7UiVoVKaoGa0f5uoS9wU48rmEMIMtmyUqf8LMQNXLlVGnynxAQAkJACAgBIRC7BPxbtytCBTji7e/vXvIQu12IWu1wbhG9DbbbaDxHCz+qUkU5trU4wrj/8mXlMHuq+SN2luHMzD14gKOMq9hBS8rO2ZsqYgrn5us6dVQUEvUgQjqAZShHr1+jytmzKz1xF3bGF7CspQFHaJsHBdH3HMVMxhFRRM0RXU1k9aMpHMWFQS5ylh1uWI9KlWkRl4Pz06hgQbXP/F8idsKhVT909QpB1qENzvmpWzfpw4oVVbQ6JUcs/1e9On3zzz+UlNv9lyOdcBZ7Vkb9R1QxOJ1nbt1S66nZiYfDCGcyU0AK5ejOe+UVXb3Hpbt+oaCnY3JXOe5W4K7FeJY81MmTR2XbdfEiD0T81B0FT8cE7geYU+40aenTatXCNIOBC6K7j2x2ysDnAIMgRKE9Gc5fb5avLGjzKiFqDBvFkhBEwNNwnZC2VOfodP/atVVaYR4Qzct7kA5cuaK2L/GAAOUGPve8uptQIlMmum96qBgO9+/bt1PjgoWoWeEgVUb/d+HOXeUU41qCPQyxEa5rbe6Oiccd1G3pEhXVh979+PYdZPA/2E4edOHhzW3nLyiHHHWD3cx9e53HpzLKf0JACAgBISAEhECsEbA2e7kQ1XzOIXGItVZioeKH7MTcDwlWsoqXixZVUTxETBE1NAU83bYMScNedtB7V61GS19rS0e7fkiP2InfyU4fooaIDtfLl99ZHjIPRFfhTCGiXIAlC5CaINpaK1duFeVGFLskO1iTdu1ih7qQioAjio7PpxyZh6MNw8ObkAMUZ+mCO0PkHIZj0oZyiA6XZlkKJC41WJoCh3sLtwupyqz9+5TDlo+j4LrdxhxNhbMJS8WO+qr2r1PhwPR05d49+pgfKP1tqyMKr9vwtAyvXyjjzTGFV/dZHhQcZt6aBQZUy1k6A5kJzNMxIQ+kQGDianDqMSCAxMdqISXteJnvYngzcwiiwjDtdGMdgycMamAY7DXkqLY2G4fbITeqntPxXdrM56R+/gJOCc92vp5c9duQyJR9fJy6HixxbVbI5jh+bK89ddLZj4iO6QIP7Fbww5oYzOnznyVFSvqdBzUv5MtHv27dQh1Kl1KDQ9QLyQoGGGUyPxncYb+YEBACQkAICAEhEDsErK80mkOvNZ3L75B3RMZip5kntdrZGYJF9+FKRHJrPHZy+taoSSc5wgcHEzpZaK492e/sOPX4e6nS0CIvoqwwOM6IaMIQDYQjiEghJBpdOdJcgh9C23LuPFXiqDcMzhN04ntZVgC5A5xxRM5thl1FFF9lrTHkIXDmIVGAwYmHwVmF8zP/0CH66+BBtQ9nAU7cVnboq3BUFE6idhT3czQVunA4U3DsymfNpupYzU4iHM+ARInVA4bP582rdMwVeZCA+hP7+6m4ZxDPnnH53l3qVqkSDXvxRUIUVssXVOMR/BdRv1AsomOKoFp1PIjcvzX/L75T8B+9MGmicsS1Ix3RMel691y6rO58QGYCydDPrMmGYQD03sIFSoKEyHO3ipXU/vucz5NlCEiu7g7MP3RQnQ/IRlr/OUvNgIOykKssOHxI8cUgBndMYG+VLq2W0NCXzuIYDEBHbx4cgCWkOYhK49qAM202XDuImON4cF2M5cg4BlawiI4pKUuTYKkSJ6G2JUpwJL0wPwMQoNqCnhuylbkHDigZC44HbHAHBNp1MSEgBISAEBACQiD2Cahf6kxZUsR+S9zC5MmTycaOLGzSpEmUgiPBzZs3V9tR+a/PyhU06Pm6NGLzJjWLCTTQ3ho0r4hqZ//hexXJTJcsudJNI1IIwwOXXZcs5ocoHQ4VHnD8vHoNmrF3r7qdjzxdKlRQTsxP7Oi1Zi0tHClMDzfo+eepzew/KfPQIcimouMoH8DODwxtIFpdfNQvahsygs+4blhRdo7N0+Kl+HaAcugXvvqamvYNeX7btlVpfsdx9Lt9yRLYpZyzzuXL0fLjx6jgyBFqHxzaN0qVplw808ulu3eUk4WHM/EwHawuO+hwwr0xd/3axw9mwiI6pojqD2Cpz46O79GY7dv4bsMFFUWGVEhH+iM6Jl0vHqTsyLOD4ANH9oMKFVXSHnYuoYPPMOQ7xRBSGzywCCfUk+GhQ5wz8IKhXjizdfPmU9sY5L3Mjng2vn5gz7FMZlKz5kqr33zGdOVof7ZyJe/PSzl//EHl6bdmDf1Uvz614HQ8CArT5fHgJAZaMAyo8NBt4HeDnVKkPitW0PNv5yVPx/RDvXrUfelS9XAn6sJ1pgccmOlnNjvemD4Q14ZuDw8Z46FQMSEgBISAEBACQiB2CViCg22GN/ruHTt2UGGOoPnaznHkN2s4t+PRDzjBkJkgKlgvf35K4ufndfcQxcbDgojUpuboeXhT9iEijcgjoszQN0fGEKXGS1EQsUV0Pjy7ztFoOOOJI9Hv8Opx3XeVI7CIqgayNIIVFk7DrCtoD1HvDMkDQj3Q6cwUzZXoHhMGO3iZy/gmTUP1xN0x6UyI3OJYzU419iGif/vxy2H0nQxdxpsl5nl/xBFr3MlwNTCGvCM13+Hw9s6Bax3uthHtxjVkPh7k9eaYEEHHQCuQB5OQIpkNd1OQBo2/+SFUcx5ZFwJCQAgIASEgBGKWwAEOfJXiSUAsLPmA/+DR4qLj7bHTkiFeEMBLgvZxlBtyHwx25vKsNAUDA+NF36WTQkAICAEhIASEgBDwREA73qHDYZ5KSboQiAUCVbLnUFKVDiyLgXY+pqPHsdBlqVIICAEhIASEgBAQApEmII53pJFJgZgmAI17Lcod09VKfUJACAgBISAEhIAQiFMEIidcjlNdl84IASEgBISAEBACQkAICIH4Q0Ac7/hzrqSnQkAICAEhIASEgBAQAvGYgM8db8zjHezFPMrxmKl0XQgIASEgBISAEBACQkAIhCHgM403nO0VPBfxJZ5b2cKvlszAb5isW7cu+cXwVHphjlB2CAEhIASEgBAQAkJACAiBOEDAZxFvONzX+aU1TZo0US/NucrzaGNqFTEhIASEgBAQAkJACAgBIfAsEPCZ452NX1/eunVrSs0vrQngF9Ik4xeSXOA3R4oJASEgBISAEBACQkAICIFngYDPHG/AtD5+++MZfo33nTt3qFixYs8CYzlGISAEhIAQEAJCQAgIASFAPnW8wfsyv6Fw1apVFBQURJkyZZJTIASEgBAQAkJACAgBISAEngkCPnW8r1y5QkuWLKHs/HbC8uXLPxOA5SCFgBAQAkJACAgBISAEhAAI+MzxvnHjBi1evJgCAwOpbNmydPr0adq5c6ecBSEgBISAEBACQkAICAEh8EwQ8Nl0gvv37yfDMAhR77lz5yq4kJqULFnymQAtBykEhIAQEAJCQAgIASHwbBPwmeNduXJlwkdMCAgBISAEhIAQEAJCQAg8iwR8JjV5FuHKMQsBISAEhIAQEAJCQAgIAU1AHG9NQpZCQAgIASEgBISAEBACQiAWCYjjHYtwpWohIASEgBAQAkJACAgBIaAJiOOtSchSCAgBISAEhIAQEAJCQAjEIgFxvGMRrlQtBISAEBACQkAICAEhIAQ0AZ873phSMDg4WLf/1JdLTy6nkTtGPfV+xOcOnDhxgg4dOhTrh/DA9jDW24hLDTyyPyKD/7mz2OJx89FNd02S3bDTneC7btMlQQgIASEgBISAEHBPwGfTCaILK1asoHPnzqn5vNOmTUv169cnPz8/973zQcqcw/No68Vt1KXUe5Fqbd3Zf+l28B16KfcLEZYbMWIEvfPOO5Q0adII8yFx3bp1hPnOtWGO8woVKuhNtbTZbDR79mzasmULpUyZkrJmzaryFCtWLFQ+1w1dd+LEialJkyY0f/58evDgAeXLl4/q1Knjmj1S2127dqVly5bR/fv3PZaLDA9Udi/kPr2/thstPrWUcqfKTRubrw7VRp2/XqLtl3c4931cujv1KdPLuR0fV+afWETfbBtMO6/soiUN51HNrNWdh+GJhzNjFFYWn/qb3l7dma49uEbZArLSD1UHU6Pc9Z01vbP6fZp2ZCaF2EOoTraaNPvFaZTEL4kzHS/IwvUYlbn5MXDDC7VatWrlrE9WhIAQEAJCQAgkNAI+jXjDUWzYsCG1bNmSbt26Rfv27XvqPIfWHER/t1gQ6X4sObGMZhycFWG5iRMn0vTp071yulHRpUuXaP369QRH9siRI3Tx4sVQ9eNOAZzmnj17EgYueBnR+++/rxz2UBnD2bhw4YKqF87NvXv3aMeOHWobbxCNro0ePdqrKiLLA5X6W/2oapbK1K7Qa2Rjh8/VTt0+TUOqDKQVjRepz/vFOrpmiXfbgUnT0SelelCKRAEU7HLMnnhE52AHbR9KXYt3ojvvXKYOQe3pvbVdnRF3RN7z8sBnx8sb6WS7g7T18naadGhaqObSpElDjRo18moAFqogb2TOnFldy7t373ZNkm0hIASEgBAQAgmGgE8db0Rv4TAmS5aMEiVKRA8fRl06sOj4UsoztjD1WNOLWsx/hQqOK06tFrxKJ2+dUidn1ek1Kh37d1/ZS1Wm1aaUIzNQ99Ufq/SbD2+qMsX+KEP9//s21Ants66vKvv2sk6U4ZfsFDS+FC0+8bfKAwfk+63DaPmplbT54lbqu6G/+qw580+oOhCZ/vbbb+ndd98NtT+ijebNm1O3bt0oW7ZsNGjQIOXEmPP//vvvtGnTJjpw4AD17t2bfvzxR2rRogVZLBZztnDXMdiB9ejRQ0Ulv/jiC7XdunVrtcSdCOTJnz8/FSlShAYMGKD26/9Wr15N6F/GjBmpTJkyKg8GCmZD3Uhv27YtnTlzxpxEUeGBChJbE9PbQW9QsXRFQtVn3kjPjqqdJUyl0pek1IlTm5OivI7+dunShUqUKKGOCevXr1/3WJ/xiOhkp0R0vG3Yz/VZ3t3dqZK5EjXL25gSm6LJumFveOi8kV0ub7SQPindk/wsflQjSzUV+b764KqqxkIW+rTMx5QvVV5KnzSQP+nJVZKCF2SlT5+eMMCKrKVKlYreeOMNGjhwYGSLSn4hIASEgBAQAvGGgE8db1A5efIkTZ06lex2O3mSR0REsVaOGlQuUxn6ZedoSuafnHqW7UbHbh6nilOq0+1Hd6hK1kr0x4tj6fTtM1R3Vn1qG9SGxtf7jSpmcUg3UidJTXMaz6CWBZrTwWuHQzXVvWwXuh98n9af3UAzG02hurnqUI/VT+QL1x7coAcsgXhke0R3H91Vn4e8brYNGzbQ8ePHlZzGvD8665BzIKKYPHlyZzWjRo0i7Tw7d0awggj8H3/8oc6BORu093Xr1qVFixbRlClTlFMPB19b+/btlZN//vx5Gjx4sIq2uw6c4KwuXbpU3c1AG2aLDR6o32qx0ivLXqeXFjahrBPyEmQaMWWFChUiDHY2btyoBjtz5szxqmqDx5P2R5YwHyPuPNoQ7nH4Wx3KM+i4P9vUT0lc4GCbbfmZVZR7UhA9sD2gNwu3MyepdQzexo0bF2a/NzsaNGigZFQ3b7rXmHtTj+QRAkJACAgBIRBXCfhU4w0IGTJkoMKFC9PevXuVnrl06dJRYpPcPxllTJ6RSqQvRpNe+l3V0bJAU8o+Oj8t5eh0y4LNqXj6omr/0hbzqWSGEmHaKRoYRLlS5aR9V5/oqpEpQ7IMlCxRMvqm6pdUK3sNCkpXmEbvHsfOxkNKylHIr6v2VXWduXOGhtQMP0J3+PBhdayIAEbXID+pWrUqQS5SvHjxUNWlSJEi1LanDQx8ELmF3MRscLyvXr1KnTt3Vo4z0jZv3qzOFdbhFI0cOVLpcAMDA2nChAmUI0cOJDntm2++IfQHkUs4rGaLSR7meme8MJEKpy3MWuPE1GdjX+r5b+9QumRz3sisQ9aD5w8wyMAABLwweOjQoUPE1fBQNlFWg/xuh83ml8b9g5Jhcz+9PW+sfJcO3zxK21ttCNOJkoHF6KOSH1Lfzf1p8uHp1KXYe6HyYDDdv39/NbC2WiM3rsedFtixY8coqn8XQnVGNoSAEBACQkAIxDECkftljIHOI1oLqULevHnVD2x0qwxMFuisIiBxCtYE+4eRXoTndDsLRbCSPpnDaQ5grS0MkUCz3Q95YN4MtQ79dUw43aj0+eefp7t37yp5x7x580K1E9mNXr160ddff019+zoGD7o8Itp4wG3o0KGENuD44K6Eto8++og++OADwsOZeAAUspNdu3bpZLXUg4CAgAAlLTEnxiQPc72Ql2AwBCnEqwVb02keDGl5hM6HKD2eJwBDb23IkCE0ZswYJf3BnYY2bdqE4uGuHoNl6Pf3WOn+bkuYT/BZz5Igd/VGZj8GDThHuOMSWXtvzQd812AhrWy8mDLyANTVMCjtWqIzdWYt/cSDU1yTCZIR2O3b4Yw8wuQOvQPPgMAwwBQTAkJACAgBIZAQCfjM8YYeeM+ePWomDUQPoSnGA1XRNWi5ITeBjrvT8g/I3+JPjfM1VNVi9gWYzbCpj9p4/B+02thvsDOt110da+w3G6LC2tKwVGXThc1qajVIXIZtG0kbzv+nkylXrlxhdM7OxAhWINeAYak/2EbbnTp1Ug7VV199pR68vHbtmoouevtwI+rRzrQ+Fr08deqUmt0EGm9EdteuXevMi3LQ70KfD6d97NixFBQUpO5aIE3XgXWYbsOx5fg/qjxQGucB50Z/dL2Y4WPd+X/VLBt3Q+7RsF0/Ucn0JSiQNchmq1evHpUtWzZSDt3Zs2epYsWKagACNpBHuR6nuQ29bk1KlH/uIyq4Muwn/duOc6vzRrTEtQnDMYe5Dt3w0PUtWLBADW7xjEFkrPv6XiqKPbPeFJZvJaX//fclXb5/WVWx6+puGn9gEt14eIMu8b6FJxfTc9lrh6n+8mVH/tSpI6+1xx0XGJ5xEBMCQkAICAEhkBAJ+MzxhtOCGTVmzJhBs2bNUg9XlipVKtpMy2cuR8O3/0QVplSjS/cu07wmMymRNRF1WdmdcowuoOpPMSI94QPnWFvdWQ3Uvl7//I/gvCM9YEQg4aHLjsu70IW7F+nF2Y3VdHaVptZQxUpPqqiLU7sir6p28PBl0QllaMqB6RTAWnNt0Acj6gdph7eG2UyqVatGcPoQPdYflPf391dO4LRp05TkI3fu3MpB2b59O73wwgsem0DdMPQLMp8sWbKobTjzMMgDENVGlP67776jxo0bK9mJOcKOKHfOnDkpT5486o4FtmG6feh7IWPBfjyMaX5AMyo8UPehG0co+W+B1Hnth7Tv+gEKGJ2eZQ5fI4kdwEvUbElrSjkmI6X/Pbuafm9Y1e9Umv4P0W7IXKCDx9SJ3hq4rFmzhtKlS6e07ZDawPkGo9i2NqxZTzE6g3q4scniVpRqTCYlc0K7EfHQ/UK/YXjY1Vt7yDKqMfvHq0FMo0UtqNCUkvT9zuF0n7XcMAxie2/8jLKwjj7XxEKUJkka+rD4+2GqhzypRg3H9yVMoocd27ZtUzlwN0xMCAgBISAEhEBCJGBhh/hJGDeCI8T0c9BmR9fgjGJGE2/mtUZbiIxjbuDw7P2V3XjKtRQ0qLrDEQsvT2zvu/7gOuvBkyu5g2tbmB8bzih00zFpOGWYNQS35jGFW0wZJAqY5hEable7ceMGIYqJiCYGBOYHPF3zutuOLR4X7l3kafeCKUeK7GGaxiCvXbt2ajYYV318mMzh7MCUjpipxZuZY8Ip/lR2QSsNqdDkyZNjvP2zd88Rnq9ImyRtmLpxhwaDsmHDhlGzZs3CpHva8dZbb6lr7Pvvv/eUVdKFgBAQAkJACMQrAnheDAFnnz9cqXWc0aW18/IuWnZyBU+5llhFqd8s2p5nLCkf3WojXT5t0rAOiK4EkhBMJ9ixY8cYfVEQnEDXBxt1m9FZYkAUntONOrWDDyc0qhZbPDInz+S2S9CWIwIfFacblWbK5L5ut40+xQS8xOjRo0cELX9sGF6s487wAh3IRDDzTmQNAxy81AkvhhITAkJACAgBIZBQCfg84h1ZkO4i3kdvHKOZh2c7q2uctyEVCYx+RN5ZYQytLF++nKpXr05JkiSJoRrDrwYSFWi+wzPIVFwfhAwvny/2+YqHL45F2ghNALIn3J2KymAFkiA8BxKVt16G7oVsCQEhIASEgBCIewR0xDveOt5xD6n0SAgIASEgBISAEBACQkAIhCWgHW+fPVwZtguyRwgIASEgBISAEBACQkAIPDsExPF+ds61HKkQEAJCQAgIASEgBITAUyTwVBxvzJ7h5WQqsY5m6cnlNHLHqFhvRxoQAkJACAgBISAEhIAQeLYJ+NzxxstVZs6cSbNnP3kw8mmegjmH59GEvRMj3YV1Z/+lxfxqek82YsQI9dIgc76QkBAaOHBguC+aMeeTdSEgBISAEBACQkAICIGEQ8DnjvfWrVsVPf2GxqeNcmjNQfR3iwWR7saSE8toxsFZEZabOHEiTZ8+Pcyc5ZhlBC85wRsgxYSAEBACQkAICAEhIASeDQI+dbzv3r1LBw8ejJEpwxYdX0p5xhamHmt6UYv5r1DBccWp1YJX6eStU+rM4W2USMd+vE6+yrTalHJkBuq++mOVjjdUIq3YH2Wo/3+hX63dZ11fVfbtZZ0Ib6YMGl/KGd3G67u/3zqMlp9aSZsvbqW+G/qrz5oz/4S6YjCwwCu7MY93eIaX6uBtkQ8eON4MGF4e2ScEhIAQEAJCQAgIASGQcAj41PFeu3YtFShQgJIlSxZtgrVy1KBymcrQLztHUzJ+VXvPst3o2M3jVHFKdbr96A5VyVqJ/nhxLJ2+fYbqzqpPbYPa0Ph6v/FLdiqotlMnSU1zGs+glgWa08Frh0P1p3vZLnQ/+D6tP7uBZjaaQnVz1aEeq5+8kOTagxv0IIRfVGJ7RHcf3VWfh7xutg0bNtDx48epfv365t3O9dq1a6u3QK5atcq5T1aEgBAQAkJACAgBISAEEi4Bn725Ei/IwAteXnjhBTp58qQiigh4QEBAlOjitdUZk2ekEumL0aSXfld1tCzQlLKPzk9LWXvdsiC/rTB9UbV/aYv5VDJDiTDtFA0MolypctK+q/tDpWVIloFfA5+Mvqn6JdXKXoOC0hWm0bvH0QPbQ/Vq+K+r9lX5z9w5Q0NqDgxVVm8cPnyYMmTIQOnTp9e7Qi3x2vWgoCA6evRoqP2yIQSEgBAQAkJACAgBIZAwCfgs4n3q1CmC/GLy5Mm0bt06JbFYtmxZtKkGJgt01hGQOAX5W/0Jr1Q3W3hOtznd3Xr6ZA6nOSCRY3BgN+yhst4PcS8TwavK3TnduhK8hv3ChQt6U5ZCQAgIASEgBISAEBACCZiAzyLe5cqVo6JFHRFoRLx3795NDRo0iDZaaLkhN6mWrYrSXvtb/Klxvoaq3hB7iFraDJta+ln8nO1Bqw1H2sCH/yGPhf9ZLU/GIthvNvMUiGlYqrLpwma6E3yXLt27RPOPLqQKWcpT5SwVVZFcuXLRmTNnzMXDrMPpzp49e5j9skMICAEhIASEgBAQAkIg4RF44mXG8rH5+fkR5BUnTpwgzGzy6NEjNbNHdJstn7kcDd/+E1WYUo0d4Ms0r8lMSmRNRF1Wdqccowuo6lOMSE/4DNs20tlc3VkN1L5e//yP4LwjPWBEIOGhy47Lu9CFuxfpxdmN6R5ruStNraHKlZ7kcKqx0a7Iq6odPHxZdEIZmnJgOgWw1lxboUKF6Pbt205Zjd6vl5cvX1YacD0Y0ftlKQSEgBAQAkJACAgBIZAwCVg4ihs6rOvmOHfs2EGFCxd2kxp7u8+dO0dZs2YNt4H3V3ajFIlS0KDqX4eb7oud1x9cZz14cqX9dm2vTp061LJlS8IMJq42YcIEGjp0KIGr1eqz8Y9rN2RbCAgBISAEhIAQEAJCIJYJHDhwgEqVKkXx1uPbeXkXLTu5ghYeX0zvLf+A/ju/OZaRhV992qRpw3W6kfurr76ikSNHKm27a+mffvqJBgwYIE63KxjZFgJCQAgIASEgBIRAAiXgM413TPNDpLtDsded1aZMnNK5HldWqlWrRsOHDye8qRJSG214e2e/fv3opZde0rtkKQSEgBAQAkJACAgBIZDACcRrqUkCPzdyeEJACAgBISAEhIAQEAIJgEC8l5okgHMghyAEhIAQEAJCQAgIASHwDBGItxrvZ+gcyaEKASEgBISAEBACQkAIJAAC4ngngJMohyAEhIAQEAJCQAgIASEQ9wmI4x33z5H0UAgIASEgBISAEBACQiABEPDa8Za5phPA2ZZDEAJCQAgIASEgBISAEPApgeDgYOf00V5PJ5g5c2afdtLcGJ4EFRMCQkAICAEhIASEgBAQAvGNAILX2o/2ejrB+HaQ0l8hIASEgBAQAkJACAgBIRCXCHgtNYlLnZa+CAEhIASEgBAQAkJACAiB+EZAHO/4dsakv0JACAgBISAEhIAQEALxkoA43vHytEmnhYAQEAJCQAgIASEgBOIbAXG849sZk/4KASEgBISAEBACQkAIxEsC4njHy9MmnRYCQkAICAEhIASEgBCIbwTE8Y5vZ0z6KwSEgBAQAkJACAgBIRAvCYjjHS9Pm3RaCAgBISAEhIAQEAJCIL4RiPOO91/XrtHgs2fDcD3/6BGtv31bfW7ZbGHSo7Pj3P1r9NaWn+lOyAN6d+soOnrnQqSqsxuGKnfm/tVIlYtqZvRz07UjdPXR7ahWEe1yiy9sp2GHF0a7Hl9WEGy30d2Qh26bBFebYXeb7inhgS3YU5YI0689ukP3bOH371bw/XDLor8RHRMKhRg2uvTwZrjlPe30dEx7b52mLdeP0iN7iKeqQqXjO4PzEZO26vIe6r9/Fh3h7y++xwb/iwm7a7fThsd/e04/DP/82Ph4Ohw5QifdpMdEP9zVcTsk/GvDXX7ZLwSEgBAQAr4j8NQc7z+vXqV+p0+H+Sy+fj3U0SPfTP642vDz5+lt/mF75eBBmnz5smtytLavB9+l30+sJAv/G318OV14eCPC+lx/0G9weZQ7cDvsgCHCijwkrr2yjxae3xomF5zeqqv+RyOPLA6T5qsds85soLEnVviqOdWOOx6eOgGHuuWGIZR4dmtKM6+9Wjc7iodun6MSy3pQyrltKcXc15Tz5qlOnQ5Hue2mYareKqv66N3OZbVVn1GyOW2cn6/2zXSm6RWcR7SdbeE74Q5mcG2mnteOll/apYuo5c9Hl1DgX2+oPrfaOFQ52OYMZ3lAiT4lm/0qVVr5KV14EPF1rct6OiadD84zuJZf8Qltvn5E745wuf/WGar3T39KMvsV+nzv1AjzmhNdv3PmNL2+88YJ+uPkajr34Jr6PuL7HBO24sYNeov/9rQ9dIi6HT8ebpXXORiwjPPtvXcv3PTY2Lnx2iHKteg9SjW3HaX/602acebf2GhG6hQCQkAICIFoEPD6lfHRaCPcoqc4EjSVHeak/BrNIsmTqzyIDq25dYteSpvWWeanvHnpAf+gu9q3uXIRPjX27ImhONaTFjIlSaM2AvyTUFK/RKS3n+RwrB1kB63//pk0/fS/dK7haMqQJJVKSJc4BZ2sP4qyJwt0LRKt7UXntxGi6A2ylA1VT6vslenPsxtD7fP1xvBSb9FDe/QivJHtszsenurZefME/Xv1IB1/6WdKwuc3aOmHNOnUWuqQu44qOvn0P5SNz92G2t/S9hvHqfrqz6hdzhqUOyCjp6rJ3+JH1dMX4WshNa1wcYxR+OS9yzSsZAcqkzavqit/isyh6sRdg492/UE/l3mH3snzfKg0bCCa2WvXRErhn5QemiLqiHK/v30M/Vn5YyqWKgeVXdGLll/cRS9mLq3qQKS66N/dqFSa3HTspZ8oR/L0Yep2t8PTMelyVouF9tcbppw+vc/TMjl/x1rnqEr3bY94oOD93YV3OIK97OJO+rJIa2qXq4bi7tpW5qRp1XcyI58L8Iopa5wuHeHz+alTtM+NY53e35/WFitGOZMkialmPdZzj6+BQcXbUdOsFWjwwbkqyt8yW2XCeRETAkJACAiBuEHgqTne3bNmpVU3b1LhZMlocO7cBEnJPb6FO/biRUXmekgIVd+9m3DzuWaqVDQqXz6viYWwo9775ElV50OusyqX75olC1VKmdKrOgKTpKBPCjVVeXvxMkfy0A40nLYv9k6jNZf3UftcNekAOxva6f6ab23/fHQp+Vms9E+t/k5nbQFHqnG7u0X2SnTi7iXadfMkO0F52Al7U+Ups/xjFYHMnDQNbXv+O5UXZeDE737he/ru4Dz6mx0NOF7/2zNF9e35TCWodoZizmNaenEH/XpsmZInfB7UknoWbKzSEM1FmXEnVtHN4HtUlB2zYaU6UM0MRWjeuc3Uadtv7CwGKWcU9ePYPy3c3FlvRCuI7pdc1lPJBHBsI9gB19Zr90SadHIt1eV+zj77n2KEdAwcPPGAROAX5jitUncqkhKO5MeqjZU1v6RCKbN6xUP3w3VZNbAwnWowyumswfldf+WA0/HuG/QywVdBhLRc2nwq3yaO4HrjeCe2+lPHvHXVHZPwHG/0JT0P0BAdRt1mpwjnqfeeSfR1sTb0Vu7nXLuttj/dPZley1mdlvC5Nhui/7Bm2SqoftfJWJzmnNvkdLx/PLxADYz+rv4FoY+uNv30esL5Onf/uroWuuR/iZpnq6iyeTqmudzOgP2z6XrwHWrCTh+kLNogaYGT/Pfj/pZPm18d8+qaX6ksuZJnUNyXXgh9PEiEbOZz/p79xtc0rtvWOapQtwINFbdRZd6lyaf+oX77ZlD3neOod6FmhD6bHezyzBcccyfPSB89/i7ofsXm8gt2yHGXDu7uX0FBlD/pE6cfgYJrwcFUjIMNkKvk5bSf+W9bEP8dhG2+c4e6chT9HAch0rHz3iZDBvW3CwEKT4Zzrq0kD7B8PRDWbctSCAgBISAE3BPw/NfcfdkYSfmHf3x68A9NjxMnqClHkcbkz6/qTcs/OpMKFqQ6qVPTsQcPItXWRI6kQ6KCiPgqjjrhR6s1S1JOeKm3hMM1sHhb1WY/jqglsSZS69B6Q4Lw3NovqWK6AnSh0RgaW64z5TNFLTvlq0cLqjlu498yaS3rZCxG5dPlV3KQ5H5JlHOL+kot/0g504hwnn9wXTkPaAwOBrYHl2in2obeF1FBOGeQSuBjjngiE6Kzw9mhHlridRU11TpgOLCjjv1N35Vor5x6RD1rrfmCcJv/+YwlqHjqnMoxHlrydS7/FvVhJ91bvXiaRAG0sFofFbU8cCu0tAbODmQK/1zZT/OqfEL1MpWiD3aMVcfjiUdn5ojBC+QQGAj9VbW3qktrk73hoRpy8x+iuDA4rFuvHyOcN21whrUsYcCBP8mfr58mWcvr5GgtUXeLDd+payjdX6+rgY+u8NCdc4TINKLefn+2ojb//UBXHj7R7eN8TWDpBBxzV8PACcc05dQ6OnXvCg8K99Jq/miD3jmEB6EBc16jHAs78l2a9TqJIEF5hdv6MH8DOl7/Z2qTs5rqI+RDnmzRhW3U7N/BVDptHjVYgxQKTrK2Omu+pG3Md1SZjnwN9FZ66x0sAfHG0McfDs+nceXfpyMvjSR8byqv7EOn+fhwrK/nqsXR+59pRqWeBOc/7bzX6dsDs51V43v5Vp7n1F2rvkVedu6P7RUM8sfz37G7LDdxff7km5w56Sbvh058fIEC6m7eENMzLO0PH6aciRPT0qJFaQD//Rp14QJ1PnYsUl1uvfF7avrvIHVnxTywi1QlklkICAEhIARihUDY0FesNOO+0qTsiGRM5HBs4SDnMt2aLRUQoLYP37/vvoJwUn5i/XdKPz9awRF1fPy4DdzEns9R9Q/4RzGq9oClFNcf3VWOOCLcyfwSh6kqMHFKwgfOmtngNGTiW94lU+em6ZV6qKSXs1elDPPfJEgmcLsdkcxRR/9WEUA4WJUDC1L9zGVUXj0QOM1SE0SrwzNE91qy7ATWc9cE2nT9sHKsET1G5P7N3LVVGgYLkKZAUvF10TaEKPvruWvRy9mrqPSPWeqw8eohFZnGQ5s/HV2s9pv/68BtIWIOK5YqJ0cVM9Cem6fMWQi3+HHcuP2NaFwRjrRjAADn0hseOnoJJxjc9ADIPDAKjwei8N12jAvzMF0VjnQjGq0Ndx2eW9NPMUD02dWgpQa7NbW+crbtDQ/Xeszbc6r0UhH8JH7+SjLSlQci2qmHwwxrlLUcvZ/vReU8jTi6iDD4gyFyjPOV0t8RHb3KgzFENcEFrIaVepPe2/arGpQhPwZY2k6wxAXX5Kqa/WgDn9u2m4ar6DSkVEMP/aWcU8hgcGcFhv1TTq9zXk+6HtclBgm4Dn5lxxqGgRx0xjA81IiHLZfX6EvPPY7GbqgzQN0NUBk8/DeAnegsLBeBZAYfDMQQTcczDe+azmP6JCnVXQSkYUD2tC09/z3DJzynt8Dj6Pc4drohR3k7Y0YayX+vYAv4+ZY77JSn4L9deIYFlorX17L8LjKGQTu+A7iDge+1/t5Epg7JKwSEgBAQArFD4Kk73uVTpKDe2bN7LQPxBsM1lqnAgc/GkSNtcLgbmrTjen9klpBoQKLw17kt6kGwT/dMpu4FGrGko5Fytr2pC06CNjhLiNxZeGAAG1DsNeW0QIbx/aH5tL72Nzqrc4motzvTchekwzmDnAH/EIGEZEUbHBikm2eogJOsLVUiLvtYOY8fcETSXc3biDjK6X5pR9quhkGOGiPigRzmPoZ36zw8HpgdA1FVczuoC7ptbXtunaKKK3tzRLQO/S+ohd7tXELGgJltplXsTjVYs60tujzKpMmrq2Jtck0awk4votrgoJ3/nnxNFWQ5DTTnE1l7rh3v9VcPED7dWFoBe33zCCqcMhtV4DspsM7srMMhxd0QRLUrpSuo9uO/qoGFqGAKllvxPtytgU4cUhjIfo7evUip/JOH0n3DwYdW3ZNBDmLmimtH2wO741o1n2NIS/Tx6HzulhgIlGY5llmP/iNLs7RuHdKrz/ZMVdfnBywzGdtwDGXiQWRkDHfTLrP0I4ilH3ByfWVwumFoUz/BcuRxgAF/uxAsgLVKn57ymIIRaqeH/zBgn1/1U/XAKuRwL2Qq6aGEJAsBISAEhICvCDxVxxs/OPhAk12LJSVmw35MyWXOg58i/YOk01EG+VAH0pCnJEfKD/KPGKQreHBzC+smMfPJOf6BzWPSW6JsZA0tIEKJzzrWBX+2dwp9N38enecffTgY2tlFvXBK8IGjq23Fpd1KblKDo4R4AApRyGZZK6rknPzAG6LSjdZ/q3S22qHSZSHrQCQajtVFlmDg9nol/pGFZtng49fOss5v57bRX2jBBx6Yo/LBUfvl2FIlY2nMkVUYWCKvNvQZxwHDj/auut/rpDBLnCHkRdv4h7Jo0xztc5zFJ0UfV612RMQDOlXMzADdMiQUGECYy0bEY0fdIU8adFmDxAczbyA6Cy07ZBh7b552ynygR8fMJENYmgO+0BgXYm6I7HrigaacTMCFP5oFZDeYaq8KO8EPbSEq0gzHUjumGPxAbz6L70ZApgPHsi73UdvlRuNYahSsWNdY/Tl9HtTK6XTrPLeDH1Dn7b+pAcsnrHvWBu01HPXLD28RJC2IDlfmfsBwV+Uv1vrD8ccxnr53lSAzweBEX4Pujqlj3hfo1f9+5Gu4giqPwSgMxx2UMrsakH6443caW7YzZUmWloYc/Evp+zc9N1Dl03kdS8d1p3nV5WtvM99xaZSlHA9EstDOGydZ171WyY++OzSPxvMzC9B2r6jZ13kXwFmplysv7ttH91n2sZC12CX474a3hr83+u8T1s1/m/R+1KX/Nvk/dqQd3yrHdw5l9DbyPp8mDQ09dw6r1IOfgcEzLwv4Lh1036+y1tuTQcdfjSVHuKam8t0KWInUuTwVk3QhIASEgBDwIQELO2zmv/0+axo/eOaptqYVKkRVTQ8/1uaHkI6Eo+3eVaoUQf8dtH27ui1r7nBRdrKXFClCl9jBbsma7uOm8niYCQ9omqUs5rLRWdcRS9zCD28KuQ/y11faazxcCXkDdMrH+QFLOH6IttbKUNTZPNLxsOLm5wY5I6A6EXpnRGm1JAHyi/HluxBm6Xhj80iVbS0/0Dnx5Bo1fRp2XGs8QTlZrTYOUQ+DYh+i7D+yLAFyBvxAw3GCQRIwh53On3haOtgFLyKIcACh4Xa1600mUI+d49UDnUi722yyOi7IDzDAwKwvnngguttk/SClN0cZcINO+U6zSer2uTseZomFa7+wjQf28BCs2SCz0RKgCit6h5kOD/IcPeuJuZzrOma6Kby0a6jdfdi5/6bYq+qc4xkBDJxg0Nb/WuY9JSnSBfCwK/S5MES957MuGkuzYQpEraM+3eBXNXsOBmLNNgxmR/UoZWUHd0HVPqp+XQ53DqDr/+/aYXX+exduRv2LvqKS4VTjAVs8mKsNfRtR6m3liEd0TLi7UH/dN86pDRFNh2Yejv3D5tMIZRuuH+C8ZjHwg1RKR2ExqOnI8hiz4QFaPDSMQUKTfwcqaYxOR7R7dFmeMo8j9Jh1yDyo1Xm8XSLaXZP/zuAB72WsqfbW2rEOezVL2MwGx/p42bJKFvIaTzPoao04CPAzz9BUhP9u3WY5SXa+Gzef/1aV3uF4qPQFdrrHsi4cmu5vz5zhwZXDAnhg/l7mzNSNHXFPhsEi7tTAUidKru4sfFiggadiki4EhIAQEAI+JPDUHG9fHCMebIITnptv1eqIky/addcGHM2UfCseDz+6s64cHYRWGs6HO4OOFRpp6HAjY3D4UBaztDjuDUSmdMzn9YYHWtUDG3c9iCoPd/XF9n48NAuHFYOJ8AxOMvLk8WL6Ql0eEWYM2rIlS+eU9ug08xIPJqZl2ZGW/ZjT8OAuHrTMlNShzTeneVrHOYADj+cbwjMMDAJYWhVeu+HlN+/DTDtXWY6Tna9bDBpjyqCtHsQPNroO+mOq/qjWgyg5plZNxQEGLUnxti6cQ9zRKZwqW5z4jnvbb8knBISAEHhWCDxVqUlsQ4Z+0pe6zYiOBzppTPeHqdlu8AOab/MczdBiavuBbxPD4cYDfbjdjxlJzHpZnQ9Ls17bvN/TOpyeqDg+nuqNSronHuY6tRTDvM+8HlUe5jp8uY4HBiMyDKgi43SjLsgzPEX6kc+sl8a22XBtRrZdXd7TOYis9lrXiyWeR9APlJr3R3cdg3JM9We+0xbdOmOiPCRzmGYwKoZzGJQqe1SKShkhIASEgBDwAYEE7Xj7gJ/XTcBxML8QxdWpxswidzkijdv/iOpF5xa61516ihk98XiKXZOmnxECX/HUfmJCQAgIASEgBHxJIEFLTXwJUtoSAkJACAgBISAEhIAQEAIREXgy3UZEuSRNCAgBISAEhIAQEAJCQAgIgWgREMc7WviksBAQAkJACAgBISAEhIAQ8I7AM+142/+cTcZ2x3Re3uGSXKEI8OwLxtGjRBcvhtod4xuY8ZJfivRM2SPHy2fCPebY4oF67z153XuYttGnZ+08hIEgO4SAEBACQkAIRJ3AM/1wpX3OPLLWqkGW0qUiRdC+aLEqY4no9fO3b5N9wSKytnG87ttTA6iTuIw2S/VqZHGdu5dfHW1fuJiMkyfIkjkLT8jtT9YmjXjah/CncNN1OevmuYKtpUqSfS3P9cvzYVvKlSNLvrw6W+SX/FIiW69PyZIjO/n96P4lO6riSPJAGePUabL/+hsZO3aStUUzsnZ480kf+QVJIa+24zeU2Jz7/L75iizFizu34+OKfcpUsi9ZSnSJX/G+eAHxa02dhxEhD2euqK3Yp04j+6QpiqelYEGy9upJFn6jrDK+7mxffEnGgYP8Bis/sjbnc/GW6VxwJpS3vvgiUdo0ke6AsXotUcYMZCkSFOmyUkAICAEhIASEQHwi8ExHvP1HDCNre3beImkGO7+0d1+EpWyD+c2Jly9FmCdUIr80w/h7OakoPK/T7Tuhkg1+o13I6x3IPn8BWbJlI2PTJnaUJpNx7nyofOFtwHG1/zGJiOcsNjiiafyznuyTpxKxQxUty5iRrB3f8aqKSPPgWi1Jk5ClRnWyBBVmh1C/UuRxc8EcAWfn22/IYMfnhyHsuHl+xblXnX2KmXBurW1fC7cHEfIIt4T3O+1Tp5PfV1+S/7zZRMmSOq4XXfzBQz4PNch/xjTyGzyQ7DNn8XV3Tqc6lnfukm3Ak7dRhk70sJUyBdl69yEyvfDKQwlJFgJCQAgIASEQLwnEy4i3fdwEsi9bTtaG9dkB3cwO5G2O3pYl65v8Yhp+C52KGnK02VKyBFkrlCf7hD/IuHad/Hp0I0utmhxB3UG2wUPVCfN79221T589W/eeZFy9ShZ+k53BkWE4fdbuHypnl/htdfb5C8ngt8vZV60my5mzqpj1pXpEmTLpKsg4zU705i1kHfWzc5+nFeu775Cd+05HjpJfzx5hstu//5EjkNnIb/iPjihoyxaOiG+YnGF3ICpu27rNGTG2tmxO9vF/OCP9xubNZB81Wh2XJUN6srR5haz1XnBWZJ82XQ0KDEhK0qYlC7+QyG/sb85048pVsn3wIUfiT5GlWlXuf3cVGdUZosJDlYVjz/1A391aigAino/ZkiuX2yyRTuDjtH0zkM/jaZ4g20rW5+uQtdN7nqvhV3vbp89UdxNCZeagtbVFC6+iwZaafAeG7yS4DDMc1XnDI1TD3m/4z+E3eXI0G4bIs33ZiieFORptbd7UkZYjh2P/fcfbN3UmpIe81p6Mg4fIUqig3u3V0lK2DBG/WdY+dx5ZX/HuDpFXFUsmISAEhIAQEAJxjEC8jHgrJ4ClEojaIsppqVeX7CtWkq3f1wqvtXFjsjZqSAY7x7ax45TDaX27A9FjaQicar/+X5IlfXrlZJvPiYrg8m1+aF39Bn9LxG+QM/6c48gCfSvkINw2PQrmiCvrYTnqarjoXg3IRljWYckdQ84gtNR79pKldm2H043esJPuP3qU91IRjibaZ891fP7913E8+n+rH1lYyuE35ldeslP+0y9O59E4dUo56dYvPiP/uX+yE/ocGTdu6JKO5ZUr7HBXI79+fclYt54MF0c5xnmgVatDgmF7732ydf6AbG+9GzYKG7qXXm9B6mypXIn8vv9ORYEhGTKOHvNcHgUfPeQPa6FDffha4bc6xml77HQTn1v73L/I2pglTC6GAVhI2/ZkqVI57HUXyG9DxZ0YXPtRMGvN6kqaFYWiUkQICAEhIASEQLwhEC8j3pQ6NVHiRGRt1pSUQ824LfwyDFu//ir6TalSqugwlv6/jFQaaIeb9vi8JErEjkM+otSpwpwoS+bMap/fRxx1Zu002lCyDOxl58LaqaNygq0v1CVL3efClMcO4/iJsI5JuDk97ITTf/gIWfLmURktmTKGLsADh0jZyZOO7BdcHobkCDYce/uUaQ6Hlp1GRHsRRVY684AAQsSdcn5T2DMAAB1eSURBVOVQgxW/r/qGahZ5rK1bqX2WihXI2LWLLHynQVuM8dAVYpkiBTvGLC+BDIX7a/u4Nxmz/iRL1w/MuaK2bvDA6sZ1sn/9LRk8sIKpY/Kkh2fNPQXyOTHpzlVhXHx+8eCrxsdq69aDLPnzk7UVR+hdDIMR63V2zBfwXZ9Dh8lSsEDoHLyNcx0Vs+TnuubNZ9AY9YT6tkalOikjBISAEBACQiBOEoiXEW8nSY4qOw3OOMz+5GE7RLQ9PXjoKBTO//qBRcg/4Ay4mBHMUU13hoiw7o+7PF7sR5TVPoQlMXwbnhInJjtHk6Ns/ApqSGbUhx+OcxpH622f9yULDyr8BvQnv6+/ciTpY2aphV//fmQpX5bZcuT9v01k+/QzdSfAWQcPcLRZ0FfOF8piiEeoOnlDPYwHJ40HDhZETDdtcc1CxomTjplX9PGEyRF2h/1/X7Bs5jRZefDl/+NQHnxkCfcaCFMSA5bjx7nNE2E+9DC0NCNM2ZjawbIrg+VKxHKpSBnf4bF168ksk/I10C9c5xcDMQw8LblykrF6TZjqLfydMa5dC7Pfqx2s81bm8myDV2UlkxAQAkJACAiBeEIgHoTh3JO0z5jhcIpSpSL7z7+QpVQpJfFQjrJ+GA+yEDhn5iganDD9Qbo5j/YZkY4y4Tls7FyqaQg56m0cY0fr3w1kbdrY0Ta6C0eNNeWRMrQDh1UtuU8wWwgZ6BsbIpD2aTPIzpF6a4OXyLh4iexjxvL+lkrLrjK5+w/HhHpQt8sxQZ8NuYylTi2yBKRQ+nhVzWPnGTNZ2P73Ofn9MJSskM6wDCek/RtksA5ZzXqBOsOYy76o8NB16voRhdb9Rxq3b7Cm2pInD7O+xhKHJWStU4sTTMZ9tb3X2SHLmTWdo85+pkT3q8b16/z8QAOCVAgzwECjbnEdTIRXnAdbfp98HF5K5PY9Pucqco4outnc8XicxzbyJ/VsAjTp0PZ7ZRh8df+IjLt3CTPDwHk2oLd+rGs31rM0CXeJypQmg59rgJbf+tqrYao2IDniZwSiYngGQ5lpEBeVeqSMEBACQkAICIG4TMDlVz0udzVs36Dvtg39Qc2GYH2uDj8U2FplCnn9TeUgYiOkvsP58PtphEP+wTKAkMYc8X0sBzC2bCX72HFKn4oHBkP4IUGYrcuH5DfwG7J99bXatg8fSdauXdS6tX1b5YyGNGyitiGvQERaG2QsdpY9RMZCWnLf2fGB6T5jXctMrK+2UTOdwNnGR6XVZmfZ9Xa/Sgn9n61vP+Vch7RpS34fsh7620Eqg33WbMKDlhaeUtHWyXFslmJF1QDC1rkL+U/43eGsQoIAB5YlJ3iQ0dqgvnK6DZas2H8Y5qiLZ03B1IT2pX+rbUuJEmSpVNGxHgUeKGhnZ9o+fISqA648NOp+g75VAw01IPiGNfhwpvlcqodrzZF85N/meChTOYleOt1oDA/p2n8dTfbfRhPxXRPIWcDcwo61O3kRysWEhbR4+cl1wNeXpUB+8uPZd2AR8dBtK309X4vW+i/qXR6Xxv797EyfVPlsHfk8w9gBdjreeKgYun98Z5ijegC0ahVHPtP/xr79ZOWHQ6Nixp49alrKqJSVMkJACAgBISAE4gsBi8EWXzpr7ieirn4fdiU1I4I5wZfrkFBwtB0zX4Qy3h/yymsODXJMz03M0UnMqgJpCB6wjDHj6LFyYsOrk+ULlJzbgowA7UbCiVX9iy0e7AiqaHRgunAlRbavB6hZb/xnsnad5SiRMuasHqTlWVzijfFsLJhy0vpG+5ifHYT/TBg8HaUFs/dw9NvVIK/Bg65+43/nOeY5T2SMI/whTVuQ9f1OZJ5NJzJVSF4hIASEgBAQAvGBgIvHGB+6zIoDvv1PV6+RfcZMsg/jiGh056OO6mFDY+7qdKMu3o+ZV+zTZ0S1ZvflWHqgJB7hOcjuS3lO4YcV3TryuP0PyQNPZxdppxstxxYPRF8hf9F6fNejZIdfvcAosk436sHxxienm7tsXLqk7kpYm7DsKaaNJUrqugvH6UZT9pn8YCvuOkXW6eaySi/OA1jctRITAkJACAgBIZCQCcTLiDfm4Tb2H3CcF3Z8rQ0a8CwXLIOIS4ZoLD8MidvysWmI+GImCncG6Qim+Xvq5iMeT/04n9EO4DkHS/ly4UbDPSEx9vJUmYik42FoMSEgBISAEBACCZhAvHS8E/D5kEMTAkJACAgBISAEhIAQSKAE4qXUJIGeCzksISAEhIAQEAJCQAgIgQRMQBzvBHxy5dCEgBAQAkJACAgBISAE4g4BcbzjzrmQngiBWCWACYz69etH69ati9V2pHIhIASEgBAQAkIgfAKi8Q6fi+wVAgmOwODBg2nEiBF0k+fl3ssPNObIkSPBHaMckBAQAkJACAiBuExAIt5x+exI34RADBFYu3YtTZ8+nXbwjEBjx46ll19+mV9mym8DFRMCQkAICAEhIAR8RkAi3j5DLQ0JgadH4NSpU5SC52pPl45fNsS2fft2KlWqFFl4fm4xISAEhIAQEAJCwDcExPH2DWdpRQgIASEgBISAEBACQuAZJyBSk2f8ApDDFwJCQAgIASEgBISAEPANAXG8fcNZWhECQkAICAEhIASEgBB4xgmI4/2MXwBy+EJACAgBISAEhIAQEAK+ISCOt284SytCQAgIASEgBISAEBACzzgBcbyf8QtADl8ICAEhIASEgBAQAkLANwTE8fYNZ2lFCAgBISAEhIAQEAJC4BknII73M34ByOELASEgBISAEBACQkAI+IaAON6+4SytCAEhIASEgBAQAkJACDzjBMTxfsYvADl8ISAEhIAQEAJCQAgIAd8QEMfbN5ylFSEgBISAEBACQkAICIFnnIA43s/4BeDt4dvtdurTpw9duHDB2yLOfNEp66wkkitXr16lXbt2qc/du3cjWVqyuyMQEhJCBw4coCtXrrjLEmr/gwcPaPfu3eo8XLx4MVQaNuLiecKx4dq5fv16mP7Glx3nz5+P98cQX1hLP4WAEBACkSEQfcf7/n0yVq4i24CBZB/zO9mHjySy2SLTB7d57YsWk8E/IDFpxs5dZJ8+I8zH2LI1JptJcHXdvn2bvv32Wzp27FiYY5s2bRqdOnUqzH69I6KyOk9MLydNmkTt2rWjkiVL0qJFi2K6+nhZ3+DBg/mrGfXv5qeffkrp0qWjmjVrUtWqVb1isGnTJnrjjTeobt269NVXX4UpExfP0/jx46latWo0bty4MP2NLzt+/PFHdQx//PFHfOlyrPTT09+mWGlUKhUCQkAIREDAP4I0r5Jsn/QhslrIUrs2GevWk8HRLesrrYkyZvCqfESZjIWLyZI4MVGWLBFli1waR0LtC9kRC7GRpXQpR9lz58hYv4H8ypWNXF3PUO7UqVPT2bNnKXPmzGGOGj/uSZMmpZw5c4ZJw46IyoZbIAZ2fvjhh4RP8+bNY6C2hFHFJ598Qm+++SZlyBD57ybO/cCBA+nw4cOUP39+r4HUqFGDtm7dSj/99BPt27cvTLm4eJ4++ugjOsd/E+KzDRo0iHC34Vk3T3+bnnU+cvxCQAj4nkC0It4GRzmNQ4fI7+v+ZG3SiPwGDSBLxQpEifzJWL2GQl5tpz7GqtWEvCFtX3dsL1uhouNItw35nkKatSTbGx3I2LTZQeDmTbJPmkIGyxrsXNY+/g/1IdOtamPzZrK99S6FNGisytqX/u2kZ/uol2rH9sWXhDIh7d9Q2/aZs8hSpzZZK1ciS5nS5PdxT7LWqkHW114l8nOgsE+Z6ig76DtCv9GvkMbN1PGgAdtnXzjqmjffcQwvv0IhLV52RuYNPjbVHvcLx2tfsBDFlHkqqzLx7W37sBFkX7zkcSnPiyFDhqjILpybpk2bqkhXv3796N69e6pwcHCwcpoKFSpEqVKlohdffJEQidS2cuVKatiwoUorWrQo5cuXj7E9kQWgXkSOGzVqRLiFrQ234keMGEEHDx6k2bNn09ChQ9UHTpo2d2WRfvnyZerYsSPlyJGDMmXKpJxC7fAsX75ctfnBBx9Q2bJlVZ9GjRqlq1WRW5TVx4T1a9euOdOjs4L+N27cWPULLMyR2n///Vf1q0KFCuq4Nbcvv/xSNQnWs2bNovr161PLli2pZ8+eKv+SJUuoffv26ljgEP3zzz9qf20esMLGjh2rthFpxTnCcYMLHFfNc//+/c7zhP2IzD569EiVxwADferevbsq//LLL9OJEydUGmQTP/zwg1r/+eef1TnCeYNsxBtDVPqdd95RWfv27UuvvfYazZw501l0zpw5qm30G+dq8uTJzrTorLi7bnGNoB1ck4jswnAslStXVvu+++47xaVHjx6E61n3CxH7yBqubd0WrnEYrvtOnTqpaxbXHwYkly5dUmk47+gXljDIs7D93HPP0TfffKPWUd9N/hsHg2OIdOzTEhd9TaFufI/v811FmP4u4RzPnz9fHS++NwsWLFDpR44cUdcYroPOnTtHShYWW9e87vNm/nsNbugbjhd3zmLzmvfmb5OCJv8JASEgBHxNwIiOBQcbwY2aGiEffWLYliw17MdPPKnt/n0jpF9/I/i19obx4IFh2GxqO6RLV8O4d88wrl83gpu3MkJef9Owb99h2IaPVOuqgitXDNvPo4zgpi0cdf/8i9q2nznjrN++ZathW7jIsJ87Z9j+mq/6gTZg9pMnjeB2r6uyxs1bKs02eqxh3L6j0m1cX0iHdwzb+AlGcP1GhsHHYVy8pNKQxzZlmhFcr77qu33NWsM27y/DfuCgI53zhXz2hUrHcdv/26Ty43hw/ChnmzLVsJ86bdhmzHRsMxtlEZR1ZGBMM/90tM31qH7phAiW7HAaRYoUMVKmTGnwj7vxyy+/GHnz5jVeffVVVYpvmRvZs2c32CE0WJ9rfPzxxwZfZwb/UKv0jBkzGhMmTDDYeTGWLl2q6jnJDLXxj5ixZ88etR/ltbHe22CnVNXNjp7BToLaPn78uM7CWMIviwwsQTDq1KljrFu3zvjvv/+MBg0aGCVKlDAePnzIl8g9g6Uiqk2Wihjs3Kk+oz4Y+vr999+rcjiO6tWrG7/99ptKM//XrFkzY8aMGeZdHtdPnz5tsMOgWHG0VvWBo7WqHPqGvoIfGIMb+jdv3jyVPnLkSHUu2KEy2CFT+XAc7DwZ7Gyo7Rs3bqjjY+dbbaMgy3HUMbBTZYwZM0btx3mrV6+eagN5wKZr164GO9TG+vXrFXd2JpFk7NixQ5V56623jC1btiiWn332mUrjQZY6L+hzr1691Dr6xk67Svf0H44d1xTKs8OtPvo6OHTokNqP4z569Kg6B8jnyhzp7Ay6bSq88+TuukWbXbp0MXDN4drfuHGjWuJcoW12zBUzfCfYwTVYR260bdvWePfdd92275qA88ADWvV9KliwoLFs2TL+8+L4+8KDKaNWrVqKOTjgui1fvryqQp8HcILxHQLVp9WrV3Ps4ZRax3nHNYBziP7h+kCdOB/4noITmP/1118G2tbcbt26pa5LHGOZMmXUdTdx4kRj586dBjv+6jp95ZVX1HcF1wHy8cBE9cPTf7F1zeP7qvvKz3oYPHhU3xtck7F5zXvzt8kTE0kXAkJACMQGAYpupXA2QwZ9pxxdOJ0hHfnHFY4s7OJF5UTad+9RTi+cXPu+/Y40/j+4TVvDvvYfxzb/gKI8e13O9JDOHxj2v5c7t80rqFO1y449nGyUtbND4jT+kQp5823lWMOJN5tyvN/tZNjmzHU43uZEXkefglu1NgyuIzyzff+jEfJJH85oD5UcMmCgEdKtR+h9n/c11GDj8V53ZZ2FrlxVx2Wb+5dzlzcr+OGHM6UNjgJ+ePHDhx9vOD7a4LTiB54j1GoXfqTx4whn4+uvvzY4gqazhlrCQdcOlznhpZdeMjgaaN4VZt217BkeRKF/cFS0wYHGPvwow+CM9O7dWycrh3bVqlVqG47s8OHDjSZNmqjjw/G8/vrrzrx6JTyHTqe5W8JBwiACzjycXQxo4ARqg7OEfu7du1fvci7h7C1evNi53a1bNwMfGBwrlIPTBeOIv9pWG/wf31FQDrxmwxFfgyPpBhxo7aRjHYMdfFhnrZwYlIdzaa577ty5qv+6biyRzncyzLu8XodjhvKuxpF5A4zN1qFDB+WMmvdFxfGO6LrdsGGDOnbNFOcL1y2cYJi+ltAXDE5+/fVXNWAx9ymidXwXcN5xzByJdmaF84t9cOT1eYDjjH1gBENZnEsYSz5C8cF3ZerUqcohRhk4n/juYTCHgTHaxOBOGwZwyIdrAYZBHrjoa0jn4+ixge+Yzof9uBa9dbxj65pHPzBIQb+1oV/6Ox7b17w3f5t0v2QpBISAEPAFgWhpvI2Dh3Dflfx6fcS/DWzXbxBHsMnYsJEs1auxzjsjWZ5/jiUZY8lSvDhZChciS1BhR179P2uHlbFGWJnyDxyr+N8IfkSWJ5uONb6tbPu8L1kbNiDrgP5qn+3dTpwZv1GPLVEilrzwx8+P2MNxpFlMNRXIT9amTcjCSyWZWbGKrG++rkuTJX16opQpnduuKyhH5vqQATM98O32UIbtG47bynp/uGV1YmA61si/7Ghf7/NyGRgY6Myp1/EwHeQh0Flr82MmeEiOf+DVLnZuiR0ZYkdS6XDZuSN2iNUtYV3G01LX5SmfTsdsFjBzvyAJgFmtTxRQ+jiwP23atIQZUmC4vQ+5AztUSnM8bNgwpyRDZYjGf23atKFcuXIR6sStfEgrdLvmatmBMG+qdWjdtcQHO/BgKTtTofKxs6i2zflCZeANlPH39+dLOJGSTfAdCJUF8hPNBw8t8oAjVFHNMyAgINw+R/Y8hao8nA3IPnAtmQ3nCTKi6Bj/8YvwuuWBJt25c4f4joN60PPPP/9UM6RAIgTDswiQ83CkWclAIHmA3EfLRbzpGyRZ7GgrudDvv/+uuGs5E55nyPL42RMs2cHjP3cZVbXQiGfLlo14kEg8kCW+o+NsDpIg9IOddNVvyHJ4oKWkJpBj4PzhvGtLkyaNuhbM11+ePHlCfW+QF+np+W+Wuaz5u6Prc7eM7WvefN25057Hl2veHUPZLwSEgBDwhsATD8eb3C55jN17yNb/GzK0phdOEWZNSJrEmdPvjfZkHDhI0Fdb33XoRJ2JWDE7y67byZOTsX0HBJysJT/s0HnfuMEhKHbaWPdoqVOLLAEpyGC9tTL7Y8ebHUpbz15E+fKS/zTWm/KPnK1vvyezrSAf2uX+WoKCiM6cdbSj27c5nDuku+2fwWku6ZZqVcn4b5NDq85pxtZtSidubd3K0T99rOGUdWTg5lgjjkFEyGvtHfXrBC+W0LZCG81SA4KelaUmhB9f/NhD4wuNMH4AOXqrphp7/vnnVa0ccVPOE5xZaE7hUGIKOG34UdezYWCp13U6fjDh5ECTi3LQemsHxV3ZwoULK6cRGlboY+GIcwSRKlWqpJwQ1A3nCx9taFc7IHBWoOmFNhZOKXTI5rxY1/3UfTan6zrDW6I+sOHIIrEcQDlvul3kd63XXAfLGZT+F3re999/X+lYdTqcaNTJ0WjlkGt9su4X2tDrugyW2Idj1cYRVoKGG84lywzUbl1OL3Ve8xLnCcejNea6fXOe8NZRpx4s4Bzjow16ZGh14eCCC+pnyQ+xFERnUfv1sSGPmSXqduWJfRYe1EZ03WLwCAbQcUMPj2PCdQ1nGQZHecCAASqN74zQ559/TtCie2voA65F6PXxUCjLs1S/MfBhiZEaWLRo0UJpqvF9YSmWcyCbNWtWYkkPsYxK9YfvmjibhfYbgwVcv3iwFPXiuQwcD/JjP3T40HVz1J7wkCTyJU6cWF0Hmp0rR7BCPzHAwPMZYIHvpM7v7ICbldi65tFccQ66QJOOaT0xywhLrpzXub4uXLsF/jF1zbv72+TapmwLASEgBHxCgP/ARdlsS/926pGDW7/q0FKzDMPVQnr3ceitTQm2oT84y0IDrmQhLBeBbESbfdduVSdkJErG8sWXhnH3rkoO+Xags3xIz48N1T6kKixhgKRF5f+wO+7vP9lmKQikHro+8xJ9hGnZijnNfuSoSlO69Md9caZDI66NpSe2n34JVT+OU0lSWPLhLKPrMJd9XId98xZH31km4ypl0c2Et4TUhB+AU7ff2cFSWl7cPoZBBws9LF9Q6oN0aEO1YRtpuFWND27/siOjkrdt2+Ysp8tjiVv72nDbGOV0OqQruIXuqSw/9Kdus+tyuAWNMjD+oXbWBy1s3759ndu49Q+JCjTWKIu2+WE3tQ4NNAwSEV2vXkIS4I2BjWYCGQCkFKiDo6oGPywXpl5osrWxQ2Tww6pKv46+QJ8L6YE2aMJ13ZDJoF7II/hhR2e90OxiPyQqWluN44VuWJdFOnjxgENVjX5iH26tQ4aAdXy0zhuZoIHX+8EMzwN4YzwbirOcLs+OrSrKjpOSw+j9WEJHjv0w/TyBOR1ta4voPHm6bnmQqfoFPS8kSahLGzT6uk1cJ/hMmTJFJ0e4BDOUHT16tMoHCRO2wR5SDpwfsNf143jYsQ8l84AkC+k8EA3TFiRCuCa0PAjXujZItlCfrhvfRUiSYPiO6/16CS24NvM1hP7p/BxJ11ncLmPzmof2HvIY9Bl9wvGBJWQw+jhi65p397fJLQhJEAJCQAjEMgEL6uc/flEzjjIZFy6ShW81sxCSLLlyKmlHqMr46X3MXuI37Aey5M8XKsnrDY5yKwmHSYKgyvKtZkhJKFkyr6vySUbMFgEpBaQfptvGXreN8pEsh9kC+GFDNaOJu3YgbWCnTN0iR0RRG+vACbe0EXnmH0RKzncaomKIcuNWOaJ3kTG0j8hXZG6N6/rxQh/IQczHo9Ois0RUFzNP4PZ9dAwRzooVKxIPHJzVYAYORGhTpEjh3OftCjjhmCEl0bISb8siH9qG/AVykJg01ItIKztVSh4Tk3W7u27xp+v48eMqAo08OC5cCzBzZB7nUctCYrJfmIUEfcA14nr94e4N7jCxnjtMk5DhQJKE7xpmnoFsRcuHkBl14hxDeoXzHBnDHS18xzWHyJSNzWse/cD3PCrXXXSvebQd1b9NKCsmBISAEIhJAtFzvCPoCV58Y0ybwVNnHCV+qknpwC01a0RQQpKiSoAf5qPWrVsTR04J+k/cvo7KD1xU25dyoQlg2kPoe6GTh74eGl+z3CB0btlKSAQg8cAUhJCIQAoDGU5UBljxjYlc8/HtjEl/hYAQeFoEnjzFE8M9wItvDNagWjJzNLJalbAPHcZwe89ydYh84q2SMESbzQ9YPctcntax82woKoKJhzKhU43KC2ueVt+l3egRwLlG9J1ncVHfw8je/Yle60+vtFzzT4+9tCwEhED8IhBrEe/4hUF6KwSEgBAQAkJACAgBISAEYpdAtGY1id2uSe1CQAgIASEgBISAEBACQiDhEBDHO+GcSzkSISAEhIAQEAJCQAgIgThMQBzvOHxypGtCQAgIASEgBISAEBACCYeAON4J51zKkQgBISAEhIAQEAJCQAjEYQLieMfhkyNdEwJCQAgIASEgBISAEEg4BMTxTjjnUo5ECAgBISAEhIAQEAJCIA4TEMc7Dp8c6ZoQEAJCQAgIASEgBIRAwiEgjnfCOZdyJEJACAgBISAEhIAQEAJxmIA43nH45EjXhIAQEAJCQAgIASEgBBIOAXG8E865lCMRAkJACAgBISAEhIAQiMMExPGOwydHuiYEhIAQEAJCQAgIASGQcAiI451wzqUciRAQAkJACAgBISAEhEAcJiCOdxw+OdI1ISAEhIAQEAJCQAgIgYRDQBzvhHMu5UiEgBAQAkJACAgBISAE4jABcbzj8MmRrgkBISAEhIAQEAJCQAgkHALieCeccylHIgSEgBAQAkJACAgBIRCHCYjjHYdPjnRNCAgBISAEhIAQEAJCIOEQEMc74ZxLORIhIASEgBAQAkJACAiBOExAHO84fHKka0JACAgBISAEhIAQEAIJh4A43gnnXMqRCAEhIASEgBAQAkJACMRhAv8HfQ+QvTtBF8YAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basically, Python matches the parameters and arguments by position, and THEN by\n",
    "name:\n",
    "<pre>\n",
    "print( LC_Hash( 15, 11,  m = 23, b = 3 ) )      \n",
    "     \n",
    "   by position: ****** |\n",
    "   by name:            | +++++++++++++\n",
    "\n",
    "\n",
    "</pre>\n",
    "\n",
    "\n",
    "If you try to do the reverse, it will complain:\n",
    "\n",
    "\n",
    "![Screen%20Shot%202020-01-31%20at%207.14.28%20PM.png](attachment:Screen%20Shot%202020-01-31%20at%207.14.28%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## List processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = [1,2,3,4]\n",
    "B = [\"hi\", \"there\", \"Paul\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4]"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Paul']\n"
     ]
    }
   ],
   "source": [
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paul\n",
      "Paul\n"
     ]
    }
   ],
   "source": [
    "# Pulling stuff out of lists\n",
    "\n",
    "print(B[2])\n",
    "\n",
    "# Using negative indices (going right to left)\n",
    "\n",
    "print(B[-1])     # last element of the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['there', 'Paul']"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['hi', 'there']"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['there', 'Paul']"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B[1:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding, replacing, and finding elements and combining lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find location of an element\n",
    "B.index(\"there\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Hagstrom']\n"
     ]
    }
   ],
   "source": [
    "# Replacing an element\n",
    "B[2] = \"Hagstrom\"\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Hagstrom', 'and', 'Wayne']\n"
     ]
    }
   ],
   "source": [
    "# Appending two lists using +\n",
    "\n",
    "C = B + ['and', 'Wayne']\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hi', 'there', 'Hagstrom', 'and', 'Wayne', 'Snyder']\n",
      "['Well', 'hi', 'there', 'Hagstrom', 'and', 'Wayne', 'Snyder']\n",
      "['Well', 'hi', 'there', 'Paul', 'Hagstrom', 'and', 'Wayne', 'Snyder']\n"
     ]
    }
   ],
   "source": [
    "# Adding a new element to end of list\n",
    "C = C + ['Snyder']                            #   could also write:    C += ['Snyder']\n",
    "print(C)\n",
    "\n",
    "# Adding a new elements in the beginning of a list\n",
    "\n",
    "C = ['Well'] + C\n",
    "print(C)\n",
    "\n",
    "# Adding a new element in the middle of the list\n",
    "C = C[:3] + ['Paul'] + C[3:]                       # 3 is the location of the new element\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WARNING\n",
    "\n",
    "When you are changing a list, remember about the global memory.  **Run \n",
    "the previous cell 4 or 5 times, and watch what happens!** (It should\n",
    "keep adding the elements over and over.)\n",
    "\n",
    "Again, you need to restart the kernel if you have some problem like this. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WARNING:   There are list processing functions for permanently changing lists, for example by deleting element and moving everything over, or appending to the end of a list.   These are notoriously hard to understand, and I STRONGLY advise you to not make changes to lists in place, but make new versions of the list. All the functions above will not disturb the original list. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Four Most Important List-Processing Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the Length of a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the location of an element in a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(   B.index('there')    )      # This shows another way of calling a function in Python, using object-oriented syntax.\n",
    "\n",
    "# Note: This will cause an error if the item is not in the list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sort a list\n",
    "\n",
    "There are two ways to sort a list, depending on whether you want to sort the original list *in place* (changing the order in your original list) or produce a *sorted copy* of a list (leaving the original list unchanged):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 7, 5, 2]\n",
      "[1, 2, 5, 7]\n",
      "\n",
      "[7, 5, 2, 1]\n",
      "\n",
      "[1, 2, 5, 7]\n",
      "[7, 5, 2, 1]\n"
     ]
    }
   ],
   "source": [
    "X = [1,7,5,2]\n",
    "\n",
    "# Producing a sorted copy of a list\n",
    "Y = sorted(X)\n",
    "print(X)\n",
    "print(Y)\n",
    "print()\n",
    "\n",
    "# make a copy sorted in descending order\n",
    "Z = sorted(X,reverse=True)\n",
    "print(Z)\n",
    "print()\n",
    "\n",
    "# Sorting a list in place\n",
    "X.sort()\n",
    "print(X)\n",
    "\n",
    "# Sort into reverse order in place\n",
    "X.sort(reverse=True)\n",
    "print(X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Copying a List"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 7, 5, 2]"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [1,7,5,2]\n",
    "Y = X.copy()\n",
    "Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Passing lists as parameters to functions\n",
    "\n",
    "Remember that parameter passing in python is by reference. Thus if you pass an array into\n",
    "a subroutine, and modify the array in the subroutine, the modifications will still be in effect after the subroutine exits\n",
    "(i.e., modifying an array creates side-effects).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4]\n",
      "[5, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "def changeList(L):\n",
    "    L[0] = 5\n",
    "    \n",
    "Lst = [1,2,3,4]\n",
    "\n",
    "print(Lst)\n",
    "changeList(Lst)\n",
    "print(Lst)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shallow vs Deep Copies of Lists\n",
    "\n",
    "This discussion is based on the one found <a href=\"https://www.afternerd.com/blog/python-copy-list/\">here</a>.\n",
    "\n",
    "The question is:\n",
    "\n",
    "> How do you make a copy of a list?\n",
    "\n",
    "The answer depends on what you mean by a *copy*!  If you mean another reference to the same list, that is called a **shallow copy** (like the fact that my oldest son is called \"John\" or \"JH\" -- two names for the same person),\n",
    "just assign the list to another name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4]\n",
      "[1, 2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "A = [1,2,3,4]\n",
    "B = A\n",
    "print(A)\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But to see that there is only one list (which now has two names), just make changes to each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 2, 3, 4]\n",
      "['a', 2, 3, 4]\n",
      "\n",
      "['a', 2, 3, 'c']\n",
      "['a', 2, 3, 'c']\n"
     ]
    }
   ],
   "source": [
    "A = [1,2,3,4]\n",
    "B = A\n",
    "\n",
    "A[0] = 'a'\n",
    "\n",
    "print(A)\n",
    "print(B)\n",
    "print()\n",
    "\n",
    "B[3] = 'c'\n",
    "\n",
    "print(A)\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A shallow copy only copies the *reference* to the list, not the list contents:\n",
    " \n",
    "         A = [1,2,3,4]        \n",
    "                             A -> [1,2,3,4]\n",
    "                             \n",
    "         B = A \n",
    "                             A -> [1,2,3,4]  <- B\n",
    "                             \n",
    "         A[0] = 'a'\n",
    "                             A -> ['a',2,3,4]  <- B \n",
    "                             \n",
    "         B[3] = 'c'\n",
    "                             A -> ['a',2,3,'c']  <- B \n",
    "                             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a **deep copy** of a list, making an entirely new list with new elements, you can use\n",
    "a slice, a list constructor, or Python3's `copy` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['a', 2, 3, 4]\n",
      "[1, 'b', 3, 4]\n",
      "[1, 2, 'c', 4]\n",
      "[1, 2, 3, 'd']\n"
     ]
    }
   ],
   "source": [
    "A = [1,2,3,4]\n",
    "\n",
    "# Copying a list by slicing\n",
    "B = A[:]\n",
    "\n",
    "# Copying a list using the list constructor\n",
    "C = list(A)\n",
    "\n",
    "# Copying a list using Python3's copy function:\n",
    "D = A.copy()\n",
    "\n",
    "# These are all different lists:\n",
    "\n",
    "A[0] = 'a'\n",
    "B[1] = 'b'\n",
    "C[2] = 'c'\n",
    "D[3] = 'd'\n",
    "\n",
    "print(A)\n",
    "print(B)\n",
    "print(C)\n",
    "print(D)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A deep copy makes an entirely new list:\n",
    " \n",
    "         A = [1,2,3,4]        \n",
    "                             A -> [1,2,3,4]\n",
    "                             \n",
    "         B = A[:] \n",
    "                             A -> [1,2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             \n",
    "         C = list(A)\n",
    "                             A -> [1,2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             C -> [1,2,3,4]\n",
    "                             \n",
    "         D = list(A)\n",
    "                             A -> [1,2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             C -> [1,2,3,4] \n",
    "                             D -> [1,2,3,4]\n",
    "                             \n",
    "         A[0] = 'a'\n",
    "                             A -> ['a',2,3,4] \n",
    "                             B -> [1,2,3,4] \n",
    "                             C -> [1,2,3,4] \n",
    "                             D -> [1,2,3,4]\n",
    "\n",
    "         B[1] = 'b'\n",
    "                             A -> ['a',2,3,4] \n",
    "                             B -> [1,'b',3,4] \n",
    "                             C -> [1,2,3,4] \n",
    "                             D -> [1,2,3,4]\n",
    "                             \n",
    "               --and so on--"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## List Comprehensions\n",
    "\n",
    "A list comprehension is a great way to create lists with a minimum of fuss and bugs. \n",
    "The basic idea is that instead of creating a list by specifying every step, say like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a list of the first 10 squares\n",
    "\n",
    "L = [0] * 10         # create a list of 10 zeros\n",
    "\n",
    "for k in range(len(L)):\n",
    "    L[k] = (k+1)**2\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "you can do it all in one line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]\n"
     ]
    }
   ],
   "source": [
    "L1 = [  (k+1)**2  for k in range(len(L))  ]\n",
    "print(L1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea is to collect together all instances of the expression at the beginning, for all values of k produces\n",
    "by the for. Some examples may clarify. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.4044216757044765, 0.0015464960773501346, 0.2995554765920614, 0.6614565365796136, 0.7507767879926917, 0.43036645074052493, 0.4162504140646396, 0.7651207176585524, 0.24706617964254396, 0.024107540359731394]\n"
     ]
    }
   ],
   "source": [
    "from random import random            # The function random() returns a random double in the range [0..1)\n",
    "\n",
    "L2 = [  random()  for k in range(10)  ]\n",
    "print(L2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use multiple for loops:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['0A', '0B', '0C', '0D', '0E', '1A', '1B', '1C', '1D', '1E', '2A', '2B', '2C', '2D', '2E', '3A', '3B', '3C', '3D', '3E', '4A', '4B', '4C', '4D', '4E']\n"
     ]
    }
   ],
   "source": [
    "D = ['0','1','2','3','4']\n",
    "L = ['A','B','C','D','E']\n",
    "     \n",
    "X = [ d + el for d in D for el in L ]\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List comprehensions can do a lot, especiallly if you use conditions in the \"loop\" part:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[63, 241, 7, 43, 99, 132, 6, -3, 71, 235, 24, 66]\n",
      "[7, 43, 6, -3, 24]\n",
      "[63, 241, 99, 132, 71, 235, 66]\n"
     ]
    }
   ],
   "source": [
    "L3 = [63,241,7,43,99,132,6,-3,71,235,24,66]  \n",
    "\n",
    "# let's pick 63 as the \"pivot\" for quicksort and partition the list into those\n",
    "# numbers less than 63 and those greater or equal:\n",
    "\n",
    "left = [ x for x in L3 if x < 63 ]\n",
    "right = [ x for x in L3 if x >= 63 ]\n",
    "\n",
    "print(L3)\n",
    "print(left)\n",
    "print(right)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-3, 6, 7, 24, 43, 63, 66, 71, 99, 132, 235, 241]"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  List comprehensions can be used to write very complicated algorithms with very few lines of code!\n",
    "\n",
    "def quicksort(L):\n",
    "    if(L == []):\n",
    "        return []\n",
    "    else:\n",
    "        pivot = L[0]\n",
    "        left  = [ x for x in L[1:] if x < pivot ]       # partition list around pivot\n",
    "        right = [ x for x in L[1:] if x >= pivot ] \n",
    "        return (  quicksort(left) + [pivot] + quicksort(right) )\n",
    "\n",
    "quicksort(L3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sets\n",
    "\n",
    "A set in mathematics is a collection of elements in which there are no duplicates and order does not matter.\n",
    "In Python, we can create sets, which are implemented by hash tables, and are much more efficient than lists, if\n",
    "a set is really what you want. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{2, 3, 4, 5}\n",
      "{3, 4}\n",
      "\n",
      "True\n",
      "True\n",
      "\n",
      "{2, 3, 4, 5, 7}\n",
      "{2, 4, 5, 7}\n",
      "\n",
      "A = {'d', 'a', 'c'}\n",
      "B = {2, 'd', 'c'}\n",
      "C = {1, 2, 3}\n",
      "\n",
      "A U B = {2, 'd', 'a', 'c'}\n",
      "B U C = {1, 2, 3, 'd', 'c'}\n",
      "A U B U C = {1, 2, 3, 'd', 'a', 'c'}\n",
      "A.union() = {'d', 'a', 'c'}\n",
      "\n",
      "A n B = {'d', 'c'}\n",
      "B n C = {2}\n",
      "A n C = set()      <- this is how empty set can be represented\n",
      "C n A n B = set()\n",
      "\n",
      "A - B = {'a'}\n",
      "B - A = {2}\n",
      "A - C = {'d', 'a', 'c'}\n"
     ]
    }
   ],
   "source": [
    "# create a set\n",
    "S= {2,3,4,5}\n",
    "print(S)\n",
    "\n",
    "# duplicates are ignored\n",
    "T = { 3, 4,3 }\n",
    "print(T)\n",
    "print()\n",
    "\n",
    "# membership test\n",
    "print( (3 in S) )\n",
    "\n",
    "# subset test\n",
    "print(  (T.issubset(S)) )\n",
    "print()\n",
    "\n",
    "# add an element to a set\n",
    "S.add(7)\n",
    "print(S)\n",
    "\n",
    "# remove an element from a set\n",
    "S.remove(3)\n",
    "print(S)\n",
    "print()\n",
    "\n",
    "# create a new set using set operations union, intersection, and set difference\n",
    "\n",
    "A = {'a', 'c', 'd'}\n",
    "B = {'c', 'd', 2 }\n",
    "C = {1, 2, 3}\n",
    "\n",
    "print('A =',A)\n",
    "print('B =',B)\n",
    "print('C =',C)\n",
    "print()\n",
    "\n",
    "print('A U B =', A.union(B))\n",
    "print('B U C =', B.union(C))\n",
    "print('A U B U C =', A.union(B, C))\n",
    "print('A.union() =', A.union())              # just make a copy\n",
    "print()\n",
    "\n",
    "# return a new set which is the intersecction of others\n",
    "print('A n B =',B.intersection(A))\n",
    "print('B n C =',B.intersection(C))\n",
    "print('A n C =',A.intersection(C),'     <- this is how empty set can be represented')\n",
    "print('C n A n B =',C.intersection(A, B))\n",
    "print()\n",
    "\n",
    "# return a new set which is the set difference with another\n",
    "print('A - B =',A.difference(B))\n",
    "print('B - A =',B.difference(A))\n",
    "print('A - C =',A.difference(C))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dictionaries\n",
    "\n",
    "A dictionary is a data structures which stores (key,value) pairs (typically implemented as a hash table).\n",
    "This is a great data structure for storing information about objects without having to muck around with lists.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': 2, 'c': 8, 'b': 1}\n",
      "{}\n"
     ]
    }
   ],
   "source": [
    "D = { 'a' : 2, 'c' : 8, 'b' : 1}      # Dictionary storing, say, how many times a letter appears in a string\n",
    "print(D)\n",
    "E = {}        # empty dictionary\n",
    "print(E)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic Dictionary Operations\n",
    "\n",
    "Most of the manipulation of dictionaries looks like array or list manipulation\n",
    "but using the keys instead of the position of the elements in the list. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the value associated with a particular key\n",
    "D['c']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 4, 'c': 8, 'b': 1, 'z': 23}"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Insert a key-value pair \n",
    "D['a'] = 4\n",
    "D['z'] = 23\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 4, 'c': 8, 'b': 1, 'z': 25}"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# update a value associated with a key by doing both\n",
    "D['z'] = D['z'] + 2\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['a', 'c', 'b', 'z'])\n",
      "['a', 'c', 'b', 'z']\n",
      "[4, 8, 1, 25]\n"
     ]
    }
   ],
   "source": [
    "### Miscellaneous functions\n",
    "\n",
    "# get all keys\n",
    "print( D.keys() )\n",
    "print( list(D.keys()) )       # to just get a list\n",
    "\n",
    "# get all values\n",
    "print( list(D.values()) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "# Default values for dictionaries\n",
    "\n",
    "# simplest: use the function get(...)\n",
    "x = D.get('q',0)         # first argument to get is the key, the second is the default\n",
    "                         # value if the key is not in the dictionary\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "# The second way is to use a different kind of dictionary, which you have to import,\n",
    "# and then define a function to return the default value\n",
    "\n",
    "from collections import defaultdict\n",
    "\n",
    "def get_default():\n",
    "    return 0\n",
    "\n",
    "A = defaultdict(get_default)\n",
    "\n",
    "A['a'] = 5\n",
    "print( A['a'] )\n",
    "print( A['b'] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counter creates a dictionary giving the frequency counts of each element in the list.\n",
      "Counter({3: 5, 4: 5, 2: 2, 5: 2, 8: 1})\n",
      "The list has 5 instances of the number 3.\n"
     ]
    }
   ],
   "source": [
    "### Calculating frequency counts using a dictionary\n",
    "\n",
    "#from collections import Counter        <- this was imported in the first code cell\n",
    "\n",
    "F = Counter([3,4,2,3,4,5,4,3,2,3,4,5,4,3,8])\n",
    "\n",
    "print(\"Counter creates a dictionary giving the frequency counts of each element in the list.\")\n",
    "print(F)\n",
    "\n",
    "n = 3\n",
    "print(\"The list has\",F[n], 'instances of the number '+ str(n) + '.')"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Floating-Point Arithmetic\n",
    "\n",
    "This section will summarize a few important points from the lecture notes in CS 132:\n",
    "\n",
    "       https://www.cs.bu.edu/fac/snyder/cs132-book/L02Numerics.html\n",
    "\n",
    "Python has both integer and floating point types. Integers, as long as they are not too large, can be stored precisely; however, real numbers (such as $\\pi$), can only be approximated by storing the number in scientific notation in binary:\n",
    "\n",
    "![Screen%20Shot%202021-05-24%20at%205.55.43%20PM.png](attachment:Screen%20Shot%202021-05-24%20at%205.55.43%20PM.png)\n",
    "\n",
    "Because only a fixed number of bits are used, most real numbers cannot be represented exactly in a computer.\n",
    "\n",
    "Another way of saying this is that, usually, a floating point number is an approximation of some particular real number.\n",
    "\n",
    "Generally when we try to store a real number in a computer, what we wind up storing is the closest floating point number that the computer can represent.\n",
    "\n",
    "Problems arise when we work with floating point numbers and confuse them with real numbers, thereby forgetting that most of the time we are not storing the real number exactly, but only a floating point number that is close to it.\n",
    "\n",
    "Let’s look at some examples. First:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ((1/8)*8)-1\n",
    "a = 1/8\n",
    "b = 8\n",
    "c = 1\n",
    "(a*b)-c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that 1/8, 8, and 1 can all be stored exactly in IEEE-754 floating point format.\n",
    "\n",
    "So, we are storing the inputs exactly (1/8, 8 and 1), computing the results exactly, yielding \n",
    "\n",
    "  $$(1/8)∗8=1$$\n",
    "\n",
    "and representing the result exactly (zero).\n",
    "\n",
    "OK, here is another example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ((1/7)*7)-1\n",
    "a = 1/7\n",
    "b = 7\n",
    "c = 1\n",
    "a * b - c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the situation is different.\n",
    "\n",
    "1/7 can not be stored exactly in floating point format.\n",
    "\n",
    "In binary, 1/7 is 0.001001⎯⎯⎯⎯⎯⎯⎯⎯⎯, an infinitely repeating pattern that clearly cannot be represented in a finite sequence of bits.\n",
    "\n",
    "Nonetheless, the computation (1/7)∗7 still yields exactly 1.0.\n",
    "\n",
    "Why? Because the rounding of 0.001001⎯⎯⎯⎯⎯⎯⎯⎯⎯ to its closest floating point representation, when multiplied by 7, yields a value whose closest floating point representation is 1.0.\n",
    "\n",
    "Now, let’s do something that seems very similar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.3877787807814457e-17"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ((1/70)*7)-0.1\n",
    "a = 1/70\n",
    "b = 7\n",
    "c = 0.1\n",
    "a * b - c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, neither 1/70 nopr 0.1 can be stored exactly.\n",
    "\n",
    "More importantly, the process of rounding 1/70 to its closest floating point representation, then multiplying by 7, yields a number whose closest floating point representation is not 0.1\n",
    "\n",
    "However, that floating point representation is very close to 0.1.\n",
    "\n",
    "Let’s look at the difference: -1.3877787807814457e-17.\n",
    "\n",
    "This is about $−1\\cdot 10^{−17}$ =  -0.0000000000000001.\n",
    "\n",
    "Compared to 0.1, this is a very small number. The relative error abs(-0.0000000000000001 / 0.1) is about $10^{−16}$.\n",
    "\n",
    "This suggests that when a floating point calculation is not exact, the error (in a relative sense) is usually very small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Punchline 1:  Do not compare floating point numbers for equality¶\n",
    "\n",
    "Two floating point computations that should yield the same result mathematically, may not do so due to rounding error.\n",
    "\n",
    "However, in general, if two numbers should be equal, the relative error of the difference in the floating point should be small.\n",
    "\n",
    "So, instead of asking whether two floating numbers are equal, we should ask whether the relative error of their difference is small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3877787807814457e-16"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 7\n",
    "b = 1/10\n",
    "c = 1/a\n",
    "r1 = a * b * c\n",
    "r2 = b * c * a\n",
    "np.abs(r1-r2)/r1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "finfo(resolution=1e-15, min=-1.7976931348623157e+308, max=1.7976931348623157e+308, dtype=float64)"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.finfo('float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "print(r1 == r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead, when comparing floating-point values, we should test whether they\n",
    "are \"close enough.\" \n",
    "This test is needed often enough that numpy has a function that implements it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.isclose(r1, r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Punchline 2:  Beware of ill-conditioned problems¶\n",
    "\n",
    "An ill-conditioned problem is one in which the outputs depend in a very sensitive manner on the inputs.\n",
    "\n",
    "That is, a small change in the inputs can yield a very large change in the outputs.\n",
    "\n",
    "The simplest example is computing 1/(𝑎−𝑏)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r1 is 0.1\n",
      "r2 is very close to r1\n",
      "r3 is 0.1001\n",
      "1/(r1 - r2) = 7.205759403792794e+16\n",
      "1/(r3 - r2) = 9999.999999998327\n"
     ]
    }
   ],
   "source": [
    "print(f'r1 is {r1}')\n",
    "print(f'r2 is very close to r1')\n",
    "r3 = r1 + 0.0001\n",
    "print(f'r3 is 0.1001')\n",
    "print(f'1/(r1 - r2) = {1/(r1 - r2)}')\n",
    "print(f'1/(r3 - r2) = {1/(r3 - r2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If a is close to b, small changes in either make a big difference in the output.\n",
    "\n",
    "Because the inputs to your problem may not be exact, if the problem is ill-conditioned, the outputs may be wrong by a large amount.\n",
    "\n",
    "Later on in CS 132 we will see that the notion of ill-conditioning applies to matrix problems too, and in particular comes up when we solve certain problems involving matrices.\n",
    "\n",
    "### Punchline 3: Relative error can be magnified during subtractions¶\n",
    "\n",
    "Two numbers, each with small relative error, can yield a value with large relative error if subtracted.\n",
    "\n",
    "Let’s say we represent a = 1.2345 as 1.2345002 – the relative error is 0.0000002.\n",
    "\n",
    "Let’s say we represent b = 1.234 as 1.2340001 – the relative error is 0.0000001.\n",
    "\n",
    "Now, subtract a - b: the result is .0005001.\n",
    "\n",
    "What is the relative error? 0.005001 - 0.005 / 0.005 = 0.0002\n",
    "\n",
    "The relative error of the result is 1000 times larger than the relative error of the inputs.\n",
    "\n",
    "Here’s an example in practice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9e-08\n",
      "8.999999989711682e-08\n",
      "1.1431464011915431e-09\n"
     ]
    }
   ],
   "source": [
    "a = 1.23456789\n",
    "b = 1.2345678\n",
    "print(0.00000009)\n",
    "print(a-b)\n",
    "print(np.abs(a-b-0.00000009)/ 0.00000009)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know the relative error in the inputs is on the order of $10^{−16}$, but the relative error of the output is on the order of $10^{−9}$ – i.e., a million times larger.\n",
    "\n",
    "A good summary that covers additional issues is at https://docs.python.org/2/tutorial/floatingpoint.html."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python in Notebooks\n",
    "\n",
    "Python (literally iPython) in Jupyter notebooks has become a \n",
    "standard in machine learning and data analysis, and so we\n",
    "will use this framework for submitting work in CS 237. The following\n",
    "introduces the major concepts that you need for CS 237. For a more\n",
    "complete introduction, read through the following tutorial\n",
    "up to Section 4.7.2:\n",
    "\n",
    "https://docs.python.org/3/tutorial/\n",
    "\n",
    "This tutorial assumes you have read or at least skimmed the\n",
    "above resource, and will concentrate on those part of Python\n",
    "that we need to know about for CS 237. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Features/Bugs of Python to Watch out for\n",
    "\n",
    "There are three things about Python that you need to know, if you\n",
    "are more familiar with a language like Java or C. \n",
    "\n",
    "(1) Python is an **interpreted** language, which means it are processed\n",
    "in a \"Read-Eval-Print\" loop: \n",
    "input expressions or definitions or assignment statements are read, evaluated,\n",
    "and the result printed out, and then it starts all over again with the next expression. \n",
    "You can see the order in which the cells were evaluated by looking at the number in square braces to the left: \n",
    "\n",
    "    In [87]:\n",
    "\n",
    "(2)  Python is a **weakly-typed** language, which means that values have types (of course) but \n",
    "variables don't have to be declared with a type and only contain values of that type.\n",
    "Any variable can represent any type of value. \n",
    "\n",
    "\n",
    "(3) Python maintains a **global memory** of all definitions (function \n",
    "definitions, and assignment statements), which is maintained until\n",
    "you terminate or restart the kernel.    This feature causes a lot of problems!\n",
    "\n",
    "Features (2) and (3) make it difficult to keep track of the variables\n",
    "in your program, and are the major source of bugs when you are\n",
    "first learning Python.  Unfortunately, Jupyter notebooks do not\n",
    "help, and in fact make these features more difficult to handle. \n",
    "We will develop strategies to minimize\n",
    "these problems. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Managing variables in a weakly-typed language (feature 2)\n",
    "\n",
    "\n",
    "Python does not force all variables to be declared with a type, as in Java and C,\n",
    "and this leads to problems. The main problem is that you create a variable\n",
    "accidentally with the same name, but different meaning. Here\n",
    "is a variable X being used in three different ways. Confusing? YES. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "hi\n",
      "['hi', 'folks']\n"
     ]
    }
   ],
   "source": [
    "X = 4\n",
    "print(X)\n",
    "\n",
    "X = 'hi'\n",
    "print(X)\n",
    "\n",
    "X = [X, 'folks']              # The second X refers to the previous definition \n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might think this is not a big deal, but if you make a habit of using only a small number of variable names\n",
    "such as X, Y, x, k, i, etc. and if these occur over the WHOLE range of your notebook, you will almost certainly have some confusion somewhere about what a variable means. \n",
    "\n",
    "Even worse, Python allows you to redefine the standard names of functions, so the following, if you uncomment the last two lines, \n",
    "creates a confusing bug:\n",
    "\n",
    "### TODO:  \n",
    "\n",
    "In the next cell, remove the hash mark from the last two lines, to \"uncomment\" them. Run the cell, and observe that it\n",
    "seems fine. \n",
    "\n",
    "Now run it once more: it will generate a weird error, because the call to the constructor <code>list</code>\n",
    "is now calling a list [2,5,4]. You've destroyed the binding between the variable list and its definition\n",
    "in the standard library. \n",
    "\n",
    "Finally, put the hash marks back in, and hit `Restart & Run All` from the `Kernel` menu. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>NOTE:  IF YOU GET A WEIRD BUG THAT MAKES NO SENSE, DO `Kernel -> Restart & Run All` BEFORE DOING ANYTHING ELSE. IT OFTEN FIXES THE PROBLEM.</b> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4]\n",
      "[2, 3, 4]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([2,3,4])\n",
    "print(A)\n",
    "B = list(A)                 # the function list is a constructor for lists\n",
    "print(B)\n",
    "\n",
    "#list = [2,5,4]              #  You are REDEFINING the variable list\n",
    "#print(list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Punchline:  Use as few global variables as possible. Do NOT reuse common names (X, i, lst) as global variables. Do NOT use the  `sum`, `list`, `sqrt` as variable names, as these are <b> function names</b> predefined in Python. \n",
    "\n",
    "Either write a function for each problem, storing everything as local variables, or give each global variable a unique name by adding the number of the problem. \n",
    "\n",
    "Example:  Suppose you have the following code which is your solution to a Problem Four in a homework:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6]\n",
      "[2, 5, 4]\n"
     ]
    }
   ],
   "source": [
    "A = [2,3,4]\n",
    "B = A + [6]                 \n",
    "print(B)\n",
    "\n",
    "X = [2,5,4]\n",
    "print(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6]\n",
      "[2, 5, 4]\n"
     ]
    }
   ],
   "source": [
    "# Here is a way of avoiding global variables by wrapping everything in a function (all variables local)\n",
    "\n",
    "def solution4():\n",
    "    A = [2,3,4]\n",
    "    B = A + [6]                 \n",
    "    print(B)\n",
    "\n",
    "    X = [2,5,4]\n",
    "    print(X) \n",
    "    \n",
    "solution4()             # be sure to call it! \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 6]\n",
      "[2, 5, 4]\n"
     ]
    }
   ],
   "source": [
    "# Or simply add the problem number to the name:\n",
    "\n",
    "A4 = [2,3,4]\n",
    "B4 = A4 + [6]                 \n",
    "print(B4)\n",
    "\n",
    "X4 = [2,5,4]\n",
    "print(X4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Caveat:</b> You do NOT need to do this for all variables, since local variables in for loops or functions\n",
    "are not a problem. Use the usual variables x,y,i, X, etc. for local variables; there is\n",
    "no problem with these. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Managing the global list of variable bindings (feature 3)\n",
    "\n",
    "Python is an interpreted language (feature 1) which uses a \"Read-Eval-Print\" loop to read\n",
    "an expression, evaluate it, and print out the value. For definitions, such as\n",
    "assignments and function definitions, there is also a change to the global master list\n",
    "which holds all variable and function definitions. \n",
    "\n",
    "If you use unique global variable names, you should not have too much trouble with this,\n",
    "but still there are strange things that happen if you don't know about this feature. \n",
    "The problem is about \"old values\" which were stored in the past, even if you don't need them. \n",
    "\n",
    "Let us look at one example to show the problem, and you can keep a watch out for this.\n",
    "\n",
    "Suppose you write the following and run it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now there is a binding in the global memory:  <code>   X = [1,2,3]   </code>\n",
    "\n",
    "But then suppose you change your mind and delete this statement. The problem is\n",
    "that the binding is NOT removed unless you **Restart** the Kernel (in the Kernel menu). \n",
    "\n",
    "Thus, four hours later, you have completely forgotten about this X, and you write this\n",
    "code, but you make a very small error, and leave out the '1' in 'X1'.  It's hard\n",
    "to see that the single character is missing, and when you run it, PYTHON \n",
    "STILL HAS THE BINDING FOR X AND YOU WON'T KNOW ABOUT THE ERROR EXCEPT FOR THE RESULT\n",
    "BEING WRONG.  You'll have to see the missing '1'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2]\n"
     ]
    }
   ],
   "source": [
    "X1 = ['a','b','c','d','e','f','g']\n",
    "\n",
    "print( X[:2] )        # expecting to see ['a','b']  but Python finds the old value of X and doesn't complain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PUNCHLINE:   If you have a nasty bug that you can't figure out, try Restart and Run All from the Kernel menu.  ALWAYS Restart and Run All before submitting to make sure everything works as it is supposed to. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting Points\n",
    "\n",
    "The <code>scatter(...)</code> function is used to plot points from a list of x values and the associated y values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This is the list of points: [(1, 2), (2, 3), (3, 6), (4, 8)]\n",
      "They must be input to the function as separate lists:\n",
      "\tX = [1, 2, 3, 4]\n",
      "\tY = [2, 3, 6, 8] \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To plot the points (1,2), (2,3), (3,6), (4,8) we would list the x values and the corresponding y values:\n",
    "X = [1,2,3,4]\n",
    "Y = [2,3,6,8]\n",
    "\n",
    "print(\"\\nThis is the list of points:\",list(zip(X,Y)))\n",
    "print(\"They must be input to the function as separate lists:\")\n",
    "print(\"\\tX =\",X)\n",
    "print(\"\\tY =\",Y,\"\\n\")\n",
    "plt.scatter(X,Y)\n",
    "plt.title('Graphing Points with scatter(X,Y)')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting Lines and Curves\n",
    "\n",
    "If you call <code>plot(...)</code> instead of <code>scatter(...)</code> you will display a curve created by connecting the points with straight lines. Essentially you can only plot straight lines between points, but if the points are close together, you will not notice, and it will look like a smooth curve. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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15l1cMqwL14/oQ+MaMjhYZdOZrCJSLWzZVcAdb83nhRmr6daqIS9cPZwh3VpEXVZCU8CLSOTemZfN71/NZOOOfH56dA+uPa4X9WrXvMHBKpsCXkQik7NtN7e+Po+35mbRr10THr3sMAZ0bBp1WUlDAS8iVc7deeXLNfzpzfns3F3Eb0/qw5ijulM7tWYPDlbZFPAiUqXW5O7i5pfn8vHXOQzu0py7zx5Az9YaHCweFPAiUiWKi51npq7g7kkLceDW0w7i0uFdSdHgYHGjgBeRuPsmZzs3TpzD9OWbObJXK+48awCdWmhwsHhTwItI3BQWFTP206U88P5i6tVK4a/nHMw5gztqmIEqooAXkbiYt3YLN0ycQ+aarYzo35Y/ndmf1o01OFhVUsCLSKXKKyjiHx8s5uGPl9K8QR3+ddEgRg5oF3VZNZICXkQqzYzlm7h+4hyW5uzgnMEdueWUfjRroMHBoqKAF5EDtmN3IX99ZxFPfrGc9k3r89QVQziqd1rUZdV4CngROSCffJ3DTS/PZe2WXVw2vCu/PakPDesqWqoDbQUR2S+5O/O5/a0FvDRzNd3TGvLi1cPJ6KrBwaoTBbyI7LNJc7P4/Wvz2Lwzn58d04NfHKvBwaojBbyIxGz91jz+8No8Js/Lpn/7Jjx5xWH0b6/BwaorBbyI7JW789LM1fz5zfnkFRZzw4i+jD6yG7U0OFi1poAXkQqt2rSTm1+Zy6eLN3BY1+b85eyD6ZHWKOqyJAYKeBEpU3Gx89QXy7nnnUUY8Ocz+nPR0C4aHCyBKOBF5HuWrN/GDRPnMnPFZn7YO407zkqnY3MNDpZoFPAi8q2ComL+/fE3/P0/S2hQN5X7zj2Esw7toMHBEpQCXkQAyFyzhd++NIcFWVs55eB23Hpaf9Ia1426LDkACniRGi6voIgH3l/MuE+X0qJhHf59yWBO6t826rKkEijgRWqwacs2cePEOSzdsIPzMjpx88n9aNqgdtRlSSWJa8CbWTPgESAdcOAKd/8inusUkb3bllfAPZMX8fSUFXRsXp9nrhzKEb1aRV2WVLJ478H/DZjs7ueYWR1AP8OLROzDRev53ctzydqaxxU/6MZvTupNgzr6Mp+M4rZVzawJcBQwCsDd84H8eK1PRCq2u7CIm1/OZOKs1fRq3YiXfnI4g7s0j7osiaN4fmx3B3KAx83sEGAmcK277yg5k5mNAcYAdO7cOY7liNRceQVFjHl6Jp98ncPPj+nJL47rSd1aGhws2cVzIIlawCDgX+5+KLADuLH0TO4+1t0z3D0jLU0XCBCpbDvzC7niiel8ujiHe84+mN+c1EfhXkPEM+BXA6vdfWr4+CWCwBeRKrJ9dyGjHpvOlKUbue/cQzj3sE5RlyRVaK8Bb2bXmlkTCzxqZrPM7MS9vc7ds4FVZtYnfOo4YP4B1isiMdqaV8Clj05l5srN/O38Qznr0I5RlyRVLJY9+CvcfStwIpAGXA78Jcbl/wJ41szmAAOBO/erShHZJ1t2FnDJI1OZu2YLD144iNMOaR91SRKBWH5k3TMIxcnA4+7+lcU4MIW7zwYy9rc4Edl3m3bkc/EjU1myfjsPXzyY4/q1ibokiUgsAT/TzN4FugE3mVljoDi+ZYnI/sjZtpuLH5nK8o07GHdZBj/srQMXarJYAv5Kgu6Vpe6+08xaEnTTiEg1sn5rHheMm8La3DweH3UYh/fUmak1XSx98A4cBPwyfNwQqBe3ikRkn2Vt2cV5Y6eQvSWPJ68YonAXILaAfwgYDlwQPt4GPBi3ikRkn6zatJNz//0FG7bt5qkrhzKkW4uoS5JqIpYumqHuPsjMvgRw983huDIiErEVG3dw4bipbMsr4JmrhnJIp2ZRlyTVSCwBX2BmqQRdNZhZGvqRVSRy3+Rs58JxU8gvLGbCmGH0b9806pKkmomli+bvwCtAazO7A/gMHc8uEqnF67Zx3r+nUFTsPDdmuMJdyrTXPXh3f9bMZhKciWrAme6+IO6ViUiZFmRt5eJHppKaYowfPZyerRtFXZJUU3sNeDPrDOwE3ij5nLuvjGdhIvJ9mWu2cPGjU6lfO5Xxo4fRrVXDqEuSaiyWPvi3CPrfjeDwyG7AIqB/HOsSkVK+XLmZSx+bRpN6tXluzDA6tdD1c6RisXTRDCj52MwGAVfHrSIR+Z4Zyzcx6vHptGxUh/Gjh9GhWf2oS5IEsM/DBbv7LOCwONQiImX44puNXPrYNFo3qcvzY4Yr3CVmsfTBX1fiYQrBmO45catIRL712eINXPXUdDo1b8Czo4fSurFOIpfYxdIH37jE/UKCPvmJ8SlHRPb4cOF6rn5mJt1bNeTZq4bSslHdqEuSBBNLH/xtVVGIiPzPu/Oy+dn4WfRp25inrxhK84Y6eVz2XbkBb2ZvEJ69WhZ3Pz0uFYnUcG/PzeKXE74kvUNTnrxiCE3r1466JElQFe3B31tlVYgIAK/NXsN1L3zFoM7NeGzUYTSup3CX/VduwLv7x1VZiEhN99LM1fz2pa8Y2q0Fj152GA3rxvITmUj5YjmKphdwF8GY8N/+hO/u3eNYl0iNMmHaSm5+ZS5H9GzF2EsyqF8nNeqSJAnEchz848C/CI6gOQZ4Cng6nkWJ1CRPfbGcm16ey9G90xh3qcJdKk8sAV/f3f8DmLuvcPdbgWPjW5ZIzfDIp0v5w2vzOOGgNjx8yWDq1Va4S+WJpZMvz8xSgMVm9nNgDdA6vmWJJL+HPlrCPZMXccqAdjxw/kBqp+7zieUiFYrlL+pXQAOCa7IOBi4GLotnUSLJzN352/uLuWfyIs4Y2J6/KdwlTio6Dv4c4E13nx4+tR24vEqqEklS7s697y7iwQ+/4ZzBHbn77INJTbGoy5IkVdFuw0XASjN7ysxGhpft2ydmttzM5prZbDObsf9liiQ+d+euSQt58MNvuGBIZ+5RuEuclRvw7n4W0BP4D0H3zCoz+5eZHbWP6zjG3Qe6e8YB1CmS0Nyd296Yz9hPlnLZ8C7ceVY6KQp3ibMKO/7cfau7P+nuI4EBwGzgH2a2qkqqE0kCxcXO717N5InPl3PVEd249fT+mCncJf5i+mXHzJoDPwLOA1oQ+2iSDrxrZjPNbEw5yx5jZjPMbEZOjkYhluRSVOzcMHEO46eu5Jqje/C7U/op3KXKVPQja2PgTOACgjHgXwduBz5093IHISvlB+6+1sxaA++Z2UJ3/6TkDO4+FhgLkJGREetyRaq9wqJifvPiV7w6ey2/Or4X1x7XS+EuVaqi4+CXAe8QnMU62d0L9nXh7r42/He9mb0CDAE+qfhVIomvoKiYXz0/m7fmZPHbk/rws2N6Rl2S1EAVBXxnd9+5vws2s4ZAirtvC++fCPxpf5cnkijyC4v5xYRZvDNvHbec0o+rjtSwTRKNikaT3O9wD7UBXgm/ktYCxrv75ANcpki1lldQxDXPzuKDheu57fT+XHZ416hLkhosbuORuvtS4JB4LV+kutmVX8SYp2fw6eIN3HnWAC4c2jnqkqSGK/coGjM7tyoLEUlkO/MLueKJ6Xy2ZAP3nHOwwl2qhYoOk7zUzCabmToQRSqwfXchox6bztRlG7n/3IGcm9Ep6pJEgIr74E81szOBt8xsPMHRNMUlpm+qgvpEqrUtuwoY9fg05qzewj8uGMQpB7eLuiSRb1XYB+/ur5rZMoJDG6/kfxfhdkB79lKj5e7M55JHp7EweysPXTSIk/q3jbokke+o6ESnusAtwDnARe7+ZpVVJVLNbdqRz0WPTOWbnO38+5LBHNu3TdQliXxPRXvwcwiGJBjk7ruqqB6Rai9n224uemQKKzbu5JFLMziqd1rUJYmUqaKAP8vd51dZJSIJYN3WPC4cN4W1uXk8fvlhHN6jVdQliZSroh9ZFe4iJazN3cWF46aQs203T105hMO6toi6JJEKxe1EJ5FksmrTTi4YN4Utuwp4+qqhDOrcPOqSRPZKAS+yF8s37ODCcVPYkV/E+KuGMaBj06hLEonJXseDN7PeZvYfM8sMHx9sZrfEvzSR6C1Zv53zxn5BXmExE0Yr3CWxxHLBj3HATUABgLvPAc6PZ1Ei1cGi7G2cP3YKRcXw3JhhHNS+SdQlieyTWAK+gbtPK/VcYTyKEaku5q/dygXjppCaAs9fPYzebRpHXZLIPosl4DeYWQ/Cs1jN7BwgK65ViURo7uotXDBuCvVqpfD8mOH0SGsUdUki+yWWH1l/RnBJvb5mtobgSk8Xx7UqkYjMWrmZyx6bRtP6tZkwehidWjSIuiSR/bbXgA/HdT++5BWa4l+WSNWbvnwTox6bRlrjuowfPYz2zepHXZLIAdlrwIdj0pwNdAVq7blosLvr8nuSND7/ZgNXPjGDds3qMWH0MNo0qRd1SSIHLJYumteALcBMYHd8yxGpep98ncPop2bQpWUDnr1qGGmN60ZdkkiliCXgO7r7iLhXIhKBDxau4ydPz6JH60Y8c+UQWjZSuEvyiOUoms/NbEDcKxGpYu/My+bqp2fSt11jJoweqnCXpFPRePCZBFdwqgVcbmZLCbpoDHB3P7hqShSpfG/NyeLa575kQMemPHnFEJrUqx11SSKVrqIumg7AwKoqRKSqvPrlGq57YTaDuzTn8cuH0KiuhmSS5FTRX/Yyd19RZZWIVIEXZ6zi+olzGNatJY+OyqBBHYW7JK+K/rpbm9l15U109/viUI9I3IyfupKbX5nLkb1aMfaSDOrXSY26JJG4qijgU4FGBH3u+83MUoEZwBp3P/VAliWyv578fDl/fH0ex/ZtzUMXDaJebYW7JL+KAj6rkk5muhZYAGgoPonEuE+WcsfbCzipfxv+ccEg6tSK5eAxkcRX0V/6Ae25A5hZR+AU4JEDXZbI/njwwyXc8fYCTjm4Hf+8UOEuNUtFf+3HVcLyHwCuJzjcskxmNsbMZpjZjJycnEpYpQi4O/e/9zV/fWcRZx3agb+dN5DaqQp3qVnK/Yt3900HsmAzOxVY7+4zK5rP3ce6e4a7Z6SlpR3IKkWAINz/+s4i/vafxfx4cEfu/fEh1FK4Sw0Uz2PEfgCcbmYnA/WAJmb2jLtrqGGJG3fnjrcW8Mhny7hoaGf+fEY6KSkH3NsokpDitlvj7je5e0d370pwib8PFO4ST8XFzq2vz+ORz5Yx6vCu3H6mwl1qNp3lIUmhuNj53auZTJi2kjFHdeemkX3ZM7S1SE1VJQHv7h8BH1XFuqTmKSp2bpg4h5dmrubnx/Tk1yf2VriLoD14SXCFRcX8+sWveG32Wq47oTe/PK5X1CWJVBsKeElYBUXF/Oq52bw1N4vrR/ThmqN7Rl2SSLWigJeEtLuwiJ+P/5L35q/jllP6cdWR3aMuSaTaUcBLwskrKOKnz8zkw0U5/OmM/lw6vGvUJYlUSwp4SSi78osY8/QMPluygbt+NIALhnSOuiSRaksBLwljx+5CrnxyOtOWbeKv5xzCOYM7Rl2SSLWmgJeEsC2vgMsfn86Xq3K5/7yBnDGwQ9QliVR7Cnip9rbsKuCyx6aRuWYL/7jgUE4e0C7qkkQSggJeqrXcnflc8ug0FmZv5aGLBnFi/7ZRlySSMBTwUm1t3L6bix6ZytINOxh7aQbH9GkddUkiCUUBL9XS+m15XDRuKqs27+Sxyw7jiF6toi5JJOEo4KXayd6Sx4XjppC9NY8nLh/CsO4toy5JJCEp4KVaWZO7iwvHTWHj9nyeumIIGV1bRF2SSMJSwEu1sWrTTi4YN4Utuwp4+sohHNq5edQliSQ0BbxUC8s27ODCcVPYVVDEhNHDSO/QNOqSRBKeAl4it2T9Ni4cN5XCYmfC6GH0a9ck6pJEkoICXiK1KHsbFz0yBTCeGzOM3m0aR12SSNLQpeYlMvPWbuH8sV+QmmI8f7XCXaSyaQ9eIjFndS6XPDqNRnVrMX70ULq0bBh1SSJJR3vwUuVmrtjMReOm0qR+LZ6/epjCXSROtAcvVWrask1c/vg0Wjepx/jRQ2nXtH7UJYkkLQW8VJnPl2zgyidn0L5ZPSaMHkbrJvWiLkkkqamLRqrEx1/ncPkT0+ncogHPjRmucBepAtqDl7j7z4J1/PSZWfRs3YhnrhpKi4Z1oi5JpLmbFoMAAA3JSURBVEaI2x68mdUzs2lm9pWZzTOz2+K1Lqm+Jmdm85NnZtKvXWMmjB6mcBepQvHcg98NHOvu282sNvCZmU1y9ylxXKdUI298tZZfPT+bQzo25YkrhtCkXu2oSxKpUeIW8O7uwPbwYe3w5vFan1QPhUXFTFu+ibfnZjF+6koyurbgsVGH0aiuegNFqlpc/9eZWSowE+gJPOjuU8uYZwwwBqBz587xLEfiJL+wmC+WbmTS3Czenb+OTTvyqVc7hTMP7cDtZ6bToI7CXSQKcf2f5+5FwEAzawa8Ymbp7p5Zap6xwFiAjIwM7eEniLyCIj5dvIFJmVm8P38dW/MKaVgnlWP7teHk9Lb8sE+agl0kYlXyP9Ddc83sI2AEkLmX2aWa2plfyIcLc5iUmcWHC9ezI7+IJvVqccJBbRmZ3pYjerWiXu3UqMsUkVDcAt7M0oCCMNzrA8cDd8drfRIfW/MK+GDBeiZlZvHRohx2FxbTsmEdTh/YgZHpbRneoyW1U3U6hUh1FM89+HbAk2E/fArwgru/Gcf1SSXZvCOf9+avY1JmFv9dspH8omLaNKnL+Yd1YkR6O4Z0a0FqikVdpojsRTyPopkDHBqv5UvlWr8tj3fmrWNyZhZTlm6iqNjp2Lw+lx3ehRHp7Ti0UzNSFOoiCUW/gtVga3N3MTkzm8mZ2UxfsQl36N6qIVcf1Z2R6e1I79AEM4W6SKJSwNcwKzbuYFJmNpMys/lqVS4Afds25trjejEyvR292zRSqIskCQV8DbBk/TYmzc3m7cxsFmRtBWBAh6ZcP6IPI/q3pXtao4grFJF4UMAnIXdnftZWJod76kvWBycUD+7SnFtO6cdJ/dvSqUWDiKsUkXhTwCcJd2f2qtxvQ33lpp2kGAzt1pJLh3fhpP5taaMhekVqFAV8Aisqdmau2MykzCzeycxm7ZY8aqUYh/dsxU+P7sGJB7WhZaO6UZcpIhFRwCeYwqJipizdFIT6vHVs2L6bOrVSOKpXGr8+sQ/H92tD0wYatVFEFPAJYXdhEZ8v2cjbc7N4b8E6cncWUL92Ksf0TWNEejuO7dtaozWKyPcoFaqpXflFfPx1DpMzs/jPgvVs211I47q1OK5fa0akt+OHvdOoX0fjvohI+RTw1cj23YV8sHA9kzOz+HBhDrsKimjWoDYjB7RlZHo7Du/Zkrq1FOoiEhsFfMS27Czg/QXrmJSZzSeLc8gvLKZVo7r8aFAHRqa3Y2j3FhrMS0T2iwI+Ahu37+bd+UGof75kA4XFTrum9bhoaGdGprdjcJfmGsxLRA6YAr6KrNuaxzvzsnl7bhbTlm2i2KFziwZceUQ3Rg5oxyEdm2qIABGpVAr4OFq1aSfvzAtOPJq5YjMAPVs34mfH9GREelsOaqfBvEQkfhTwlWxpznYmhSM0zl2zBYB+7Zpw3Qm9GZnell5tGkdcoYjUFAr4A+TufL1uO2/PzWJyZjaL1m0D4JBOzbhxZF9GprelS8uGEVcpIjWRAn4/uDuZa7YyKTMI9aUbdmAGGV2a84dTD2JEelvaN6sfdZkiUsMp4GNUXOx8uSqXSXOzmDwvm9Wbd5GaYgzr3oLLj+jGSf3b0LqxBvMSkepDAV+BomJn2rJNTM4MQn3d1t3UTjWO6NmKXx7bi+MPakOLhnWiLlNEpEwK+FIKior5/JuNTM7M4t1569i4I5+6tVL4Ye80Rg5oy7F929C0vgbzEpHqTwEP5BUU8eniDUzKzOL9+evYmldIwzqpHNO3NSPT23F0nzQaajAvEUkwNTa1duYX8tGiHCZlZvPBgnXsyC+icb1anNCvDSMHtOPIXq2oV1vjvohI4qpRAb81r4APFqxnUmYWH3+dQ15BMS0a1uG0Q9ozIr0th/doRZ1aGvdFRJJD0gf85h35vLdgHZMzs/ls8Qbyi4pp3bgu52Z0YkR6W4Z0bUEtDeYlIkkobgFvZp2Ap4C2QDEw1t3/Fq/1lZSzbTfvzAvOJv1i6UaKip0OzepzyfAujExvy6DOzUnRYF4ikuTiuQdfCPza3WeZWWNgppm95+7z47Gytbm7mBwOETB9xSbcoVurhow5qjsj09syoIMG8xKRmiVuAe/uWUBWeH+bmS0AOgCVGvA78wu5cNxUZq/KBaB3m0b84thenDygLX3aNFaoi0iNVSV98GbWFTgUmFrGtDHAGIDOnTvv87Ib1KlF15YNOOGgNoxIb0uPtEYHVqyISJIwd4/vCswaAR8Dd7j7yxXNm5GR4TNmzIhrPSIiycTMZrp7RlnT4nr4iJnVBiYCz+4t3EVEpHLFLeAt6Px+FFjg7vfFaz0iIlK2eO7B/wC4BDjWzGaHt5PjuD4RESkhnkfRfAboEBYRkYjoFE4RkSSlgBcRSVIKeBGRJKWAFxFJUnE/0WlfmFkOsGI/X94K2FCJ5UQpWdqSLO0AtaU6SpZ2wIG1pYu7p5U1oVoF/IEwsxnlnc2VaJKlLcnSDlBbqqNkaQfEry3qohERSVIKeBGRJJVMAT826gIqUbK0JVnaAWpLdZQs7YA4tSVp+uBFROS7kmkPXkRESlDAi4gkqYQKeDN7zMzWm1lmOdPNzP5uZkvMbI6ZDarqGmMVQ1uONrMtJUbi/ENV1xgLM+tkZh+a2QIzm2dm15YxT0JslxjbkijbpZ6ZTTOzr8K23FbGPHXN7Plwu0wNr7xWrcTYjlFmllNim1wVRa2xMrNUM/vSzN4sY1rlbhN3T5gbcBQwCMgsZ/rJwCSCUSyHAVOjrvkA2nI08GbUdcbQjnbAoPB+Y+Br4KBE3C4xtiVRtosBjcL7tQkulzms1DzXAA+H988Hno+67v1sxyjgn1HXug9tug4YX9bfUWVvk4Tag3f3T4BNFcxyBvCUB6YAzcysXdVUt29iaEtCcPcsd58V3t8G7Lm4ekkJsV1ibEtCCN/r7eHD2uGt9BEVZwBPhvdfAo6zanaV+hjbkTDMrCNwCvBIObNU6jZJqICPQQdgVYnHq0nQ/6Ch4eFX00lm1j/qYvamgourJ9x2qehC8STIdgm7AmYD64H33L3c7eLuhcAWoGXVVrl3MbQD4Oyw++8lM+tUxSXuiweA64HicqZX6jZJtoAv65MuUT/tZxGMMXEI8A/g1YjrqVB4cfWJwK/cfWvpyWW8pNpul720JWG2i7sXuftAoCMwxMzSS82SENslhna8AXR194OB9/nfHnC1YmanAuvdfWZFs5Xx3H5vk2QL+NVAyU/vjsDaiGo5IO6+dc9XU3d/G6htZq0iLqtMMVxcPWG2y97akkjbZQ93zwU+AkaUmvTtdjGzWkBTqnG3YXntcPeN7r47fDgOGFzFpcXqB8DpZrYceI7gcqbPlJqnUrdJsgX868Cl4VEbw4At7p4VdVH7w8za7ul7M7MhBNtqY7RVfV+MF1dPiO0SS1sSaLukmVmz8H594HhgYanZXgcuC++fA3zg4a971UUs7Sj1e87pBL+dVDvufpO7d3T3rgQ/oH7g7heXmq1St0ncrskaD2Y2geAohlZmthr4I8GPLrj7w8DbBEdsLAF2ApdHU+nexdCWc4CfmlkhsAs4v7r95wvtubj63LCfFOBmoDMk3HaJpS2Jsl3aAU+aWSrBh9AL7v6mmf0JmOHurxN8mD1tZksI9hLPj67ccsXSjl+a2elAIUE7RkVW7X6I5zbRUAUiIkkq2bpoREQkpIAXEUlSCngRkSSlgBcRSVIKeBGRJKWAl2rPzFqWGCkw28zWhPdzzWz+ASz3OjN7tMTji8zsrVLzdDWz1WaWUur52eFx8OUte5SZ/XN/axOpDAp4qfbCMxUHhqerPwzcH94fSPljesTi78BgM/tBeDLN7cAvSq17OcHYIEfuec7M+gKN3X3aAaxbJO4U8JLoUs1sXDhW+Lvh2Y6YWQ8zm2xmM83s0zCUvyMczOka4EHgHuAxd19axjom8N0TTs4Pn8PMTgvH7f7SzN43szalX2xmT5jZOSUeby9x/7dmNj0cKOu28LmGZvZWOKBZppmdtz9vjIgCXhJdL+BBd+8P5AJnh8+PBX7h7oOB3wAPlfVid/+c4NT24wlCviwvAGeGY4MAnEcwlgjAZwTjkx8aPnd9rIWb2Ylh/UMIvo0MNrOjCMZaWevuh7h7OjA51mWKlJRQQxWIlGGZu+8ZVmAm0DUcDfJw4MUSQ2nXLevF4bwZBMNEpBEM9vQd7p5tZvMIxuZeBxS4+54rcXUEng/HQ6kDLNuH2k8Mb1+GjxsRBP6nwL1mdjfBRSE+3YdlinxLAS+JbneJ+0VAfYJvprlhP/3e3AY8A6wD7gd+XM58e7pp1oX39/gHcJ+7v25mRwO3lvHawrCmPQOa1QmfN+Aud/936ReY2WCC8XvuMrN33f1PMbRF5DvURSNJJxzDfZmZ/Ri+vSbsIaXnM7MBBFfXuZugS6eLmZ1QzmInEgRuye4ZCIZzXRPev6z0i0LL+d8QtmcQDioHvANcEX6LwMw6mFlrM2sP7HT3Z4B7CS7tKLLPtAcvyeoi4F9mdgtBoD4HfLVnYrgn/S/g/9w9L3zuGuApMxvo7vklF+buuWY2BWjj7iW7YW4l6ApaA0wBupVRyzjgNTObBvwH2BEu810z6wd8EXYlbQcuBnoCfzWzYqAA+OkBvRNSY2k0SRGRJKUuGhGRJKWAFxFJUgp4EZEkpYAXEUlSCngRkSSlgBcRSVIKeBGRJPX/AYrVCLDOCSEXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To plot a curve through the points (1,2), (2,3), (3,6), (4,8) we would use: \n",
    "plt.plot([1,2,3,4], [2,3,6,8])\n",
    "plt.title('A Sequence of Straight Lines')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()\n",
    "\n",
    "X = np.linspace(1,20,100)            # returns a list of 100 equally-spaced values in the range [1..20]\n",
    "Y = [np.sin(x) for x in X]\n",
    "plt.plot(X,Y)\n",
    "plt.title('A Smooth-Looking Curve')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you leave out the $X$ values, `plot(...)` will assume that you want the x-axis labeled 0, 1, ..., (len(X)-1),\n",
    "corresponding to the labels on an array or list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BLyIx9032Lm6dNI+ZK7dxbI+W3HtePzo0V3OwWFPAi0jMFBYVM+7T5fzt/aXUrVmDP4/sz8hB7dVmoIoo4EUkJhas38Etk+aRuW4nw/u24e5z+9KqkZqDVSUFvIhUqryCIv754VIenrqcZvVr8+9RAxnRLy3ssqolBbyIVJpZK7dy86R5LM/ezchB7bnjzD40ra/mYGFRwIvIIdu9t5A/v7OEp75YSdsm9Xj6qsEc1zM17LKqPQW8iByST77O5raX57N+xx6uGNaZX53eiwZ1FC3xQHtBRA7K9tx87nlrES/NXkvX1Ab859phZHRWc7B4ooAXkQM2eX4Wv3ltAdty8/nJid244SQ1B4tHCngRidqmnXn89rUFTFmwgb5tG/PUVUfSt62ag8UrBbyI7Je789Lstfz+zYXkFRZzy/DejDm2CzXVHCyuKeBFpEJrtuZy+yvz+XTpZo7s3Iw/nt+fbqkNwy5LoqCAF5EyFRc7T3+xkvvfWYIBvz+nL6OGdFJzsASigBeR71m2KYdbJs1n9qptHN8zlT+cl077ZmoOlmgU8CLyrYKiYh6Z+g3/+GAZ9euk8JcLDue8I9qpOViCUsCLCACZ63bwq5fmsShrJ2f2T+POs/qS2qhO2GXJIVDAi1RzeQVF/O39pYz/dDnNG9TmkcsGcXrfNmGXJZVAAS9Sjc1YsZVbJ81j+ebdXJjRgdvP6EOT+rXCLksqSUwD3syaAo8C6YADV7n7F7Fcp4jsX05eAfdPWcIz01bRvlk9nr16CMf0aBl2WVLJYn0E/3dgiruPNLPagD6GFwnZR0s28euX55O1M4+rju7CL0/vSf3a+mM+GcVsr5pZY+A4YDSAu+cD+bFan4hUbG9hEbe/nMmkOWvp0aohL/34KAZ1ahZ2WRJDsfy13RXIBp4ws8OB2cCN7r675ERmNhYYC9CxY8cYliNSfeUVFDH2mdl88nU2Pz2xOzec3J06NdUcLNnFspFETWAg8G93PwLYDdxaeiJ3H+fuGe6ekZqqGwSIVLbc/EKuenImny7N5v7z+/PL03sp3KuJWAb8WmCtu08Pnr9EJPBFpIrs2lvI6MdnMm35Fv5yweFccGSHsEuSKrTfgDezG82ssUU8ZmZzzOy0/c3n7huANWbWK3jpZGDhIdYrIlHamVfA5Y9NZ/bqbfz9oiM474j2YZckVSyaI/ir3H0ncBqQClwJ/DHK5d8APGdm84ABwL0HVaWIHJAduQVc9uh05q/bwYOXDOSsw9uGXZKEIJoPWfc1oTgDeMLdv7IoG1O4+1wg42CLE5EDt3V3Ppc+Op1lm3bx8KWDOLlP67BLkpBEE/CzzexdoAtwm5k1AopjW5aIHIzsnL1c+uh0Vm7ZzfgrMji+p05cqM6iCfiriQyvLHf3XDNrQWSYRkTiyKadeVw8fhrrt+fxxOgjOaq7rkyt7qIZg3fgMOBnwfMGQN2YVSQiByxrxx4uHDeNDTvyeOqqwQp3AaIL+IeAYcDFwfMc4MGYVSQiB2TN1lwueOQLNufs5emrhzC4S/OwS5I4Ec0QzRB3H2hmXwK4+7agr4yIhGzVlt1cMn46OXkFPHvNEA7v0DTskiSORBPwBWaWQmSoBjNLRR+yioTum+xdXDJ+GvmFxUwcO5S+bZuEXZLEmWiGaP4BvAK0MrM/AJ+h89lFQrV0Yw4XPjKNomLn+bHDFO5Spv0ewbv7c2Y2m8iVqAac6+6LYl6ZiJRpUdZOLn10Oik1jAljhtG9VcOwS5I4td+AN7OOQC7wRsnX3H11LAsTke/LXLeDSx+bTr1aKUwYM5QuLRuEXZLEsWjG4N8iMv5uRE6P7AIsAfrGsC4RKeXL1du4/PEZNK5bi+fHDqVDc90/RyoWzRBNv5LPzWwgcG3MKhKR75m1ciujn5hJi4a1mTBmKO2a1gu7JEkAB9wu2N3nAEfGoBYRKcMX32zh8sdn0KpxHV4YO0zhLlGLZgz+phJPaxDp6Z4ds4pE5FufLd3MNU/PpEOz+jw3ZgitGukicoleNGPwjUo8LiQyJj8pNuWIyD4fLd7Etc/OpmvLBjx3zRBaNKwTdkmSYKIZg7+rKgoRkf95d8EGfjJhDr3aNOKZq4bQrIEuHpcDV27Am9kbBFevlsXdz45JRSLV3Nvzs/jZxC9Jb9eEp64aTJN6tcIuSRJURUfwD1RZFSICwGtz13HTi18xsGNTHh99JI3qKtzl4JUb8O4+tSoLEanuXpq9ll+99BVDujTnsSuOpEGdaD4iEylfNGfR9ADuI9IT/tuP8N29awzrEqlWJs5Yze2vzOeY7i0Zd1kG9WqnhF2SJIFozoN/Avg3kTNoTgSeBp6JZVEi1cnTX6zktpfnc0LPVMZfrnCXyhNNwNdz9w8Ac/dV7n4ncFJsyxKpHh79dDm/fW0Bpx7WmocvG0TdWgp3qTzRDPLlmVkNYKmZ/RRYB7SKbVkiye+hj5dx/5QlnNkvjb9dNIBaKQd8YblIhaL5jvo5UJ/IPVkHAZcCV8SyKJFk5u78/f2l3D9lCecMaMvfFe4SIxWdBz8SeNPdZwYv7QKurJKqRJKUu/PAu0t48KNvGDmoPX86vz8pNSzssiRJVXTYMApYbWZPm9mI4LZ9B8TMVprZfDOba2azDr5MkcTn7tw3eTEPfvQNFw/uyP0Kd4mxcgPe3c8DugMfEBmeWWNm/zaz4w5wHSe6+wB3zziEOkUSmrtz1xsLGffJcq4Y1ol7z0unhsJdYqzCgT933+nuT7n7CKAfMBf4p5mtqZLqRJJAcbHz61czefLzlVxzTBfuPLsvZgp3ib2oPtkxs2bAD4ELgeZE303SgXfNbLaZjS1n2WPNbJaZzcrOVhdiSS5Fxc4tk+YxYfpqrj+hG78+s4/CXapMRR+yNgLOBS4m0gP+deAe4CN3L7cJWSlHu/t6M2sFvGdmi939k5ITuPs4YBxARkZGtMsViXuFRcX88j9f8erc9fz8lB7ceHIPhbtUqYrOg18BvEPkKtYp7l5woAt39/XB/5vM7BVgMPBJxXOJJL6ComJ+/sJc3pqXxa9O78VPTuwedklSDVUU8B3dPfdgF2xmDYAa7p4TPD4NuPtglyeSKPILi7lh4hzeWbCRO87swzXHqm2ThKOibpIHHe6B1sArwZ+kNYEJ7j7lEJcpEtfyCoq4/rk5fLh4E3ed3ZcrjuocdklSjcWsH6m7LwcOj9XyReLNnvwixj4zi0+Xbube8/pxyZCOYZck1Vy5Z9GY2QVVWYhIIsvNL+SqJ2fy2bLN3D+yv8Jd4kJFp0lebmZTzEwDiCIV2LW3kNGPz2T6ii389YIBXJDRIeySRICKx+B/YGbnAm+Z2QQiZ9MUl3h/axXUJxLXduwpYPQTM5i3dgf/vHggZ/ZPC7skkW9VOAbv7q+a2QoipzZezf9uwu2AjuylWtuem89lj81g8YadPDRqIKf3bRN2SSLfUdGFTnWAO4CRwCh3f7PKqhKJc1t35zPq0el8k72LRy4bxEm9W4ddksj3VHQEP49IS4KB7r6niuoRiXvZOXsZ9eg0Vm3J5dHLMziuZ2rYJYmUqaKAP8/dF1ZZJSIJYOPOPC4ZP4312/N44sojOapby7BLEilXRR+yKtxFSli/fQ+XjJ9Gds5enr56MEd2bh52SSIVitmFTiLJZM3WXC4eP40dewp45pohDOzYLOySRPZLAS+yHys37+aS8dPYnV/EhGuG0q99k7BLEonKfvvBm1lPM/vAzDKD5/3N7I7YlyYSvmWbdnHhuC/IKyxm4hiFuySWaG74MR64DSgAcPd5wEWxLEokHizZkMNF46ZRVAzPjx3KYW0bh12SyAGJJuDru/uMUq8VxqIYkXixcP1OLh4/jZQa8MK1Q+nZulHYJYkcsGgCfrOZdSO4itXMRgJZMa1KJETz1+7g4vHTqFuzBi+MHUa31IZhlyRyUKL5kPUnRG6p19vM1hG509OlMa1KJCRzVm/jisdn0KReLSaOGUqH5vXDLknkoO034IO+7qeUvENT7MsSqXozV25l9OMzSG1UhwljhtK2ab2wSxI5JPsN+KAnzflAZ6DmvpsGu7tuvydJ4/NvNnP1k7NIa1qXiWOG0rpx3bBLEjlk0QzRvAbsAGYDe2NbjkjV++TrbMY8PYtOLerz3DVDSW1UJ+ySRCpFNAHf3t2Hx7wSkRB8uHgjP35mDt1aNeTZqwfToqHCXZJHNGfRfG5m/WJeiUgVe2fBBq59Zja90xoxccwQhbsknYr6wWcSuYNTTeBKM1tOZIjGAHf3/lVTokjle2teFjc+/yX92jfhqasG07hurbBLEql0FQ3RtAMGVFUhIlXl1S/XcdOLcxnUqRlPXDmYhnXUkkmSU0Xf2SvcfVWVVSJSBf4zaw03T5rH0C4teGx0BvVrK9wleVX03d3KzG4q7013/0sM6hGJmQnTV3P7K/M5tkdLxl2WQb3aKWGXJBJTFQV8CtCQyJj7QTOzFGAWsM7df3AoyxI5WE99vpLfvb6Ak3q34qFRA6lbS+Euya+igM+qpIuZbgQWAWrFJ6EY/8ly/vD2Ik7v25p/XjyQ2jWjOXlMJPFV9J1+SEfuAGbWHjgTePRQlyVyMB78aBl/eHsRZ/ZP41+XKNyleqnou/3kSlj+34CbiZxuWSYzG2tms8xsVnZ2diWsUgTcnb++9zV/fmcJ5x3Rjr9fOIBaKQp3qV7K/Y53962HsmAz+wGwyd1nVzSdu49z9wx3z0hNTT2UVYoAkXD/8ztL+PsHS/nRoPY88KPDqalwl2oolueIHQ2cbWZnAHWBxmb2rLur1bDEjLvzh7cW8ehnKxg1pCO/PyedGjUOebRRJCHF7LDG3W9z9/bu3pnILf4+VLhLLBUXO3e+voBHP1vB6KM6c8+5Cnep3nSVhySF4mLn169mMnHGasYe15XbRvRmX2trkeqqSgLe3T8GPq6KdUn1U1Ts3DJpHi/NXstPT+zOL07rqXAXQUfwkuAKi4r5xX++4rW567np1J787OQeYZckEjcU8JKwCoqK+fnzc3lrfhY3D+/F9Sd0D7skkbiigJeEtLewiJ9O+JL3Fm7kjjP7cM2xXcMuSSTuKOAl4eQVFHHds7P5aEk2d5/Tl8uHdQ67JJG4pICXhLInv4ixz8zis2Wbue+H/bh4cMewSxKJWwp4SRi79xZy9VMzmbFiK38eeTgjB7UPuySRuKaAl4SQk1fAlU/M5Ms12/nrhQM4Z0C7sEsSiXsKeIl7O/YUcMXjM8hct4N/XnwEZ/RLC7skkYSggJe4tj03n8sem8HiDTt5aNRATuvbJuySRBKGAl7i1pZdexn16HSWb97NuMszOLFXq7BLEkkoCniJS5ty8hg1fjprtuXy+BVHckyPlmGXJJJwFPASdzbsyOOS8dPYsDOPJ68czNCuLcIuSSQhKeAlrqzbvodLxk9jy658nr5qMBmdm4ddkkjCUsBL3FizNZeLx09jx54Cnrl6MEd0bBZ2SSIJTQEvcWHF5t1cMn4aewqKmDhmKOntmoRdkkjCU8BL6JZtyuGS8dMpLHYmjhlKn7TGYZckkhQU8BKqJRtyGPXoNMB4fuxQerZuFHZJIklDt5qX0CxYv4OLxn1BSg3jhWsV7iKVTUfwEop5a7dz2WMzaFinJhPGDKFTiwZhlySSdHQEL1Vu9qptjBo/ncb1avLCtUMV7iIxoiN4qVIzVmzlyidm0KpxXSaMGUJak3phlySStBTwUmU+X7aZq5+aRdumdZk4ZiitGtcNuySRpKYhGqkSU7/O5sonZ9KxeX2eHztM4S5SBXQELzH3waKNXPfsHLq3asiz1wyheYPaYZckUi3E7AjezOqa2Qwz+8rMFpjZXbFal8SvKZkb+PGzs+mT1oiJY4Yq3EWqUCyP4PcCJ7n7LjOrBXxmZpPdfVoM1ylx5I2v1vPzF+ZyePsmPHnVYBrXrRV2SSLVSswC3t0d2BU8rRX881itT+JDYVExM1Zu5e35WUyYvpqMzs15fPSRNKyj0UCRqhbTnzozSwFmA92BB919ehnTjAXGAnTs2DGW5UiM5BcW88XyLUyen8W7CzeydXc+dWvV4Nwj2nHPuenUr61wFwlDTH/y3L0IGGBmTYFXzCzd3QnIcW0AAAz3SURBVDNLTTMOGAeQkZGhI/wEkVdQxKdLNzM5M4v3F25kZ14hDWqncFKf1pyR3obje6Uq2EVCViU/ge6+3cw+BoYDmfuZXOJUbn4hHy3OZnJmFh8t3sTu/CIa163JqYe1YUR6G47p0ZK6tVLCLlNEAjELeDNLBQqCcK8HnAL8KVbrk9jYmVfAh4s2MTkzi4+XZLO3sJgWDWpz9oB2jEhvw7BuLaiVosspROJRLI/g04CngnH4GsCL7v5mDNcnlWTb7nzeW7iRyZlZ/HfZFvKLimnduA4XHdmB4elpDO7SnJQaFnaZIrIfsTyLZh5wRKyWL5VrU04e7yzYyJTMLKYt30pRsdO+WT2uOKoTw9PTOKJDU2oo1EUSij4Fq8bWb9/DlMwNTMncwMxVW3GHri0bcO1xXRmRnkZ6u8aYKdRFEpUCvppZtWU3kzM3MDlzA1+t2Q5A7zaNuPHkHoxIT6Nn64YKdZEkoYCvBpZtymHy/A28nbmBRVk7AejXrgk3D+/F8L5t6JraMOQKRSQWFPBJyN1ZmLWTKcGR+rJNkQuKB3Vqxh1n9uH0vm3o0Lx+yFWKSKwp4JOEuzN3zfZvQ3311lxqGAzp0oLLh3Xi9L5taK0WvSLVigI+gRUVO7NXbWNyZhbvZG5g/Y48atYwjurekutO6MZph7WmRcM6YZcpIiFRwCeYwqJipi3fGgn1BRvZvGsvtWvW4LgeqfzitF6c0qc1Teqra6OIKOATwt7CIj5ftoW352fx3qKNbM8toF6tFE7sncrw9DRO6t1K3RpF5HuUCnFqT34RU7/OZkpmFh8s2kTO3kIa1anJyX1aMTw9jeN7plKvtvq+iEj5FPBxZNfeQj5cvIkpmVl8tDibPQVFNK1fixH92jAiPY2juregTk2FuohERwEfsh25Bby/aCOTMzfwydJs8guLadmwDj8c2I4R6WkM6dpczbxE5KAo4EOwZdde3l0YCfXPl22msNhJa1KXUUM6MiI9jUGdmqmZl4gcMgV8Fdm4M493Fmzg7flZzFixlWKHjs3rc/UxXRjRL43D2zdRiwARqVQK+BhaszWXdxZELjyavWobAN1bNeQnJ3ZneHobDktTMy8RiR0FfCVbnr2LyUGHxvnrdgDQJ60xN53akxHpbejRulHIFYpIdaGAP0Tuztcbd/H2/CymZG5gycYcAA7v0JRbR/RmRHobOrVoEHKVIlIdKeAPgruTuW4nkzMjob58827MIKNTM377g8MYnt6Gtk3rhV2miFRzCvgoFRc7X67ZzuT5WUxZsIG12/aQUsMY2rU5Vx7ThdP7tqZVIzXzEpH4oYCvQFGxM2PFVqZkRkJ948691Eoxjunekp+d1INTDmtN8wa1wy5TRKRMCvhSCoqK+fybLUzJzOLdBRvZsjufOjVrcHzPVEb0a8NJvVvTpJ6aeYlI/FPAA3kFRXy6dDOTM7N4f+FGduYV0qB2Cif2bsWI9DRO6JVKAzXzEpEEU21TKze/kI+XZDM5cwMfLtrI7vwiGtWtyal9WjOiXxrH9mhJ3Vrq+yIiiataBfzOvAI+XLSJyZlZTP06m7yCYpo3qM1Zh7dleHobjurWkto11fdFRJJD0gf8tt35vLdoI1MyN/DZ0s3kFxXTqlEdLsjowPD0Ngzu3JyaauYlIkkoZgFvZh2Ap4E2QDEwzt3/Hqv1lZSds5d3FkSuJv1i+RaKip12Tetx2bBOjEhvw8COzaihZl4ikuRieQRfCPzC3eeYWSNgtpm95+4LY7Gy9dv3MCVoETBz1VbcoUvLBow9risj0tvQr52aeYlI9RKzgHf3LCAreJxjZouAdkClBnxufiGXjJ/O3DXbAejZuiE3nNSDM/q1oVfrRgp1Eam2qmQM3sw6A0cA08t4bywwFqBjx44HvOz6tWvSuUV9Tj2sNcPT29AtteGhFSsikiTM3WO7ArOGwFTgD+7+ckXTZmRk+KxZs2Jaj4hIMjGz2e6eUdZ7MT19xMxqAZOA5/YX7iIiUrliFvAWGfx+DFjk7n+J1XpERKRssTyCPxq4DDjJzOYG/86I4fpERKSEWJ5F8xmgU1hEREKiSzhFRJKUAl5EJEkp4EVEkpQCXkQkScX8QqcDYWbZwKqDnL0lsLkSywlTsmxLsmwHaFviUbJsBxzatnRy99Sy3oirgD8UZjarvKu5Ek2ybEuybAdoW+JRsmwHxG5bNEQjIpKkFPAiIkkqmQJ+XNgFVKJk2ZZk2Q7QtsSjZNkOiNG2JM0YvIiIfFcyHcGLiEgJCngRkSSVcAFvZsPNbImZLTOzW8t4v46ZvRC8Pz24m1TciWI7RptZdolOnNeEUef+mNnjZrbJzDLLed/M7B/Bds4zs4FVXWO0otiWE8xsR4l98tuqrjFaZtbBzD4ys0VmtsDMbixjmrjfN1FuR0LsFzOra2YzzOyrYFvuKmOays0vd0+Yf0AK8A3QFagNfAUcVmqa64GHg8cXAS+EXfdBbsdo4F9h1xrFthwHDAQyy3n/DGAykc6iQ4HpYdd8CNtyAvBm2HVGuS1pwMDgcSPg6zK+x+J+30S5HQmxX4Kvc8PgcS0itzAdWmqaSs2vRDuCHwwsc/fl7p4PPA+cU2qac4CngscvASdb/N15O5rtSAju/gmwtYJJzgGe9ohpQFMzS6ua6g5MFNuSMNw9y93nBI9zgH03vS8p7vdNlNuREIKv867gaa3gX+mzXCo1vxIt4NsBa0o8X8v3d/a307h7IbADaFEl1UUvmu0AOD/40/klM+tQNaVVumi3NVEMC/7EnmxmfcMuJhoV3PQ+ofZNBdsBCbJfzCzFzOYCm4D33L3cfVIZ+ZVoAV/Wb7LSvwGjmSZs0dT4BtDZ3fsD7/O/3+qJJhH2R7TmEOn7cTjwT+DVkOvZr+Cm95OAn7v7ztJvlzFLXO6b/WxHwuwXdy9y9wFAe2CwmaWXmqRS90miBfxaoOSRbHtgfXnTmFlNoAnx92f3frfD3be4+97g6XhgUBXVVtmi2WcJwd137vsT293fBmqZWcuQyypXFDe9T4h9s7/tSLT9AuDu24GPgeGl3qrU/Eq0gJ8J9DCzLmZWm8iHEK+XmuZ14Irg8UjgQw8+sYgj+92OUmOhZxMZe0xErwOXB2dsDAV2uHtW2EUdDDNrs2881MwGE/n52RJuVWWL8qb3cb9votmORNkvZpZqZk2Dx/WAU4DFpSar1PyK2T1ZY8HdC83sp8A7RM5EedzdF5jZ3cAsd3+dyDfDM2a2jMhvvovCq7hsUW7Hz8zsbKCQyHaMDq3gCpjZRCJnMbQ0s7XA74h8eIS7Pwy8TeRsjWVALnBlOJXuXxTbMhK4zswKgT3ARXF48LDPvpvezw/GfAFuBzpCQu2baLYjUfZLGvCUmaUQ+SX0oru/Gcv8UqsCEZEklWhDNCIiEiUFvIhIklLAi4gkKQW8iEiSUsCLiCQpBbzEPTNrUaJT4AYzWxc83m5mCw9huTeZ2WMlno8ys7dKTdPZzNaaWY1Sr88Nzrkub9mjzexfB1ubSGVQwEvcC67qHRBc4v0w8Nfg8QCg+BAW/Q9gkJkdHVyAcg9wQ6l1ryTSG+TYfa+ZWW+gkbvPOIR1i8ScAl4SXYqZjQ/6a78bXCGImXUzsylmNtvMPg1C+TuCZk7XAw8C9xO54Gx5GeuYyHcvOLkoeA0zOyvo2/2lmb1vZq1Lz2xmT5rZyBLPd5V4/Cszmxk0lbsreK2Bmb0VNM/KNLMLD+YLI6KAl0TXA3jQ3fsC24Hzg9fHATe4+yDgl8BDZc3s7p8TaQNxCpGQL8uLwLlBbxCAC4m0eAb4jEhP7yOC126OtnAzOy2ofzCRv0YGmdlxRPqTrHf3w909HZgS7TJFSkqoVgUiZVjh7vsuYZ8NdA46Dx4F/KdEK+06Zc0cTJtBpCVBKpFmT9/h7hvMbAGR3twbgQJ333fXp/bAC0HvoNrAigOo/bTg35fB84ZEAv9T4AEz+xORG1l8egDLFPmWAl4S3d4Sj4uAekT+Mt0ejNPvz13As8BG4K/Aj8qZbt8wzcbg8T7/BP7i7q+b2QnAnWXMWxjUtK95Vu3gdQPuc/dHSs9gZoOI9Im5z8zedfe7o9gWke/QEI0knaBf+Aoz+xF8e+/Rw0tPZ2b9gDOBPxEZ0ulkZqeWs9hJRAK35PAMRNq5rgseX1F6psBK/tfu+RyCBmZEms1dFfwVgZm1M7NWZtYWyHX3Z4EHiNxGUOSA6QhektUo4N9mdgeRQH2eyL1vgW+PpP8N/J+75wWvXQ88bWYDglspfsvdt5vZNKC1u5cchrmTyFDQOmAa0KWMWsYDr5nZDOADYHewzHfNrA/wRTCUtAu4FOgO/NnMioEC4LpD+kpItaVukiIiSUpDNCIiSUoBLyKSpBTwIiJJSgEvIpKkFPAiIklKAS8ikqQU8CIiSer/ARx90z82U9PZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a list against the indices\n",
    "Y = [2,3,6,8]\n",
    "\n",
    "plt.plot(Y)\n",
    "plt.title('Graphing lines with plot(Y)')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to do both, you can simply call both functions before you call show(). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([1,2,3,4], [2,3,6,8])\n",
    "plt.plot([1,2,3,4], [2,3,6,8])\n",
    "plt.title('A Curve Through Some Points, Showing the Points')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to draw a single line from $(x_1,y_1)$ to $(x_2,y_2)$ you can plot $[x_1,x_2]$ and $[y_1,y_2].$\n",
    "\n",
    "Here we have added a zero line to our sin curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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drXeVPHayl6triinMWVnvL1q0gMSZobFpnmnp57dW6L6yyEr3cvO2ch490at9wavgGbMkyWoeYACvaSjDI0YShGbl/LIpwO7qAvx5mZffeRFu3OKnY2iCNj0easW0BkK09IW4fXt83FegBSTuPHqih7mw4vWrcF9Z/NauCgbHpnnhrCOqtdiKp1v62ezPZV1h9qqOL8rN4MqNRdqNsgqGx6d5+cIQN61SvOGi8OtBhSvncbPRc1scK3trAYkzhTnp/NauSrYvUTojGm7cUkZWumf+C6GJjqnZOV5oG+TVdaWX33kZbt1WzsnuUTqH9ZiElfDr5n7CCm5ag/99fXEONaW5/EoLyIp57EQPO6vyqVpl4ykatIDEmTt2VvLld16xptLg2RlertxYpAPpK+TlC8NMzMxx3RoF5JZthgvgFzoba0U81dRHUU46e6qjT11fjBu3+Hm+bUBX6F0BfcFJXm4f5vbt8Z1XSAuIQ7i6poSm3iDD49PJNsUxPNPSj0fgmtroBg8uRa0/l5rSXO3GWgHhsOJXTQFu2OKPevDgUtywpZTJmTAHz2kXbrQ809KPUsQt+8pCC4hDuLqmGKXgRR0HiZqnW/rZs75wzRNziQivaSjjubYBpmd1IkM0HO8aYWBsmpsaVh//sLhmcwkZXo+Og6yAF88OkZeZtmTV6VihBcQh7FlfSGaaRwfSo2RkYoYj7cNrjn9YHKgpYno2rNN5o+SXpwOIwA31axeQnIw0rqop0nGQFXDw3CBXbipac+/vcmgBcQhZ6V72bSjkhbM6DhINz7cNEFasOf5hceXGYgAatRslKp5r62fnuoJXzLi5Fm7c4udMb0gXV4yCwbFpWvpCXLWpOO7XSvaMhHeISJOItIjIxxbZ/kUROWwuZ0RkOGLbXMS2hxNreXK4uqaEk12jjE7OJNsU2/NMSz/Z6V72bSiKyfn8eZlsKsmh8dxQTM7nZmbnwhxpH+HKjbG59wDX1xk9med0YdHLYjVyDtS4WEBExAt8GbgT2A7cKyLbI/dRSn1EKbVXKbUX+CfgvyI2T1jblFJvTJjhSeTqzcWElW4FR8PTzf1cvbmYjLTYfcWv3FjMofNDelT0ZTjdE2RiZo4rYiggDRV5+DLTePnC8OV3TnEOnhskw+tZVeWLlZLMHsgBoEUp1aaUmgYeBO5aZv97ge8lxDKbcsWGIjK8Hl5o0wKyHH3BSdr6x3jVGrOvFnLVpiIGxqY5q0dFL8tLF4xe2hUb1pa+G4nXI+xZX8DL7boHeDkOnhtiz/qCuFTfXUgyBaQKiCz232GuuwQR2QjUAL+IWJ0lIo0i8ryI3L3URUTkfnO/xkDA2UG4rHQve9YX8LwOpC/LkXYj0B0r95XF/k3G+bQba3leOj9EeX5mzAew7VtfxKnuoJ6fZRnGp2c53jmSkPgHJFdAFksPWMo38HbgIaVU5Ddng1JqP/AO4EsiUrvYgUqpB5RS+5VS+/3+tWeEJJura0o43jlCaGo22abYlsPtQ3g9ws51se3C1/p9FOWk03heC/hyHLowxBUbitY0eHYx9m0oZC6sONqh3VhLcfjCMLNhlRIC0gFEzjBTDXQtse/bWeC+Ukp1mX/bgKeAfbE30X5cvbmYubDi0HndCl6KI+0jbK3IIzsjtl14EeHKjUU06nu/JH3BSdoHJ7gixr0/YH4ytpfbtYAsxcFzQ4gQ0/jTciRTQA4C9SJSIyIZGCJxSTaViDQARcBzEeuKRCTTfF0KXAecTIjVSebKjUV4RAfSlyIcVhxpH2bPCmZ+XAlXbiymLTDGQGgqLud3Oi+dNx7u8XiAlfiMTLiXL2gBX4qD5wbZWpFPQfbaBs9GS9IERCk1C3wIeBQ4BfxAKXVCRD4tIpFZVfcCD6pXpr5sAxpF5AjwS+BzSqmUEJCcjDS2lOdxrFMPaFuMtv4xglOzK5o6eCVcZcZBdA9wcV6+MESG18POqviMgN63oYiXLgzrTLhFmJ0L89KFIQ5sSkzvAyAtYVdaBKXUI8AjC9Z9csH7Ty1y3LPArrgaZ2N2VhXwVFMfSqmY+5mdzmHTvREvAdlZVUCG10Pj+SFuj2OZbKfy0oUhdlblk5kWnwygfRsK+eHLnXQOT1BdlBOXaziV0z1BxqfnuDJB8Q/QI9Edye7qAvpD03SPTCbbFNtxuH0IX2YatX5fXM6fle5ld3WBdiEuwvRsmCMdI3GJf1hY59bjQS7F8krsXWP145WgBcSBWAOEjnZoN9ZCjrSPsLu6IK41gPauL+Rk96ieIXIBJ7tHmZ4NxzWA21CRR1a6RwvIIhzrHCE/K431xfGb/2MhWkAcyLbKfNI8wrFO/SOKZHJmjlPdo3ELoFvsqMpnciasp1ldgBUXimUJk4Wkez3sriqcH6youciJzhF2VhUk1K2tBcSBZKV7qS/P41jnaLJNsRUnukaZDau4xT8srPElx3Uiwys42jFMZUEW5flZcb3Ovo2FnOwaZWpWDyi0mJkLc6onyM4ElC+JRAuIQ9ldVcCxDp2NEkm8A+gWm/0+stI9HNcC/gpOdo2yY118558AY0T69FyYk136/ls094aYng0n5P5HogXEoeyqLmBofIaOIV3e2uJIe2JawF6PsK0ynxN6bpB5JqbnaA2E2B7j0f+LYaUIn+zWAmJhzVOTiAKKkWgBcSi7q7UbZSGH24fXPP92tOxcV8DJrlHCYd0DBDjdM0pYwfY4z4AHUFWYTX5Wmu6BRHC8c4TcDC+bSnITel0tIA6loSKPdK9wVAsIYMxAeGFwnF3ViWmB7ViXT3BqlguD4wm5nt2xegOJcKGICNvX5eseSATHO0fYsa4AT5xnIFyIFhCHkpnmpaEij2M6lReA0+bDJBEtYGA+WHlCt4IB4z7kZ6VRXZSYFNLtlQWc7g4yp3uAzIUVJ7tHEx5ABy0gjmZXVSHHOkd0IB1jFC4YKc6JoL7cR7pX9BzpJie7Rtm+Lj9hKaTbKvOYmJnj3IBOpW4NhJicCcetfMxyaAFxMLurCxiZmKF9UAfST3WPUpSTTnl+bObgvhyZaV7qy/J0DAqjBXy6Z5QdCQigW2w3XWU6DnIxDqp7IJoVMT8iXQ8o5FT3KNsqE9cCBiMb6GTXaMr3AM/2Gy3gRLkPAerLjBigjoMYI9Cz0j1xK9+zHFpAHEx9uQ+vRzjdHUy2KUllLqxo6g0mzH1lsWNdAQNj0/SMpnZNMisOtCOBLpSMNA91ZXm6BwKc6Bxle2V+XMv3LIUWEAeTmeZlc2kup3tS+0d0tn+MyZlwwgXE8jmn+oDCk12jZKQlvgW8vVJnYoXDihNdI0lxX4EWEMfTUJE3H0BOVU6ZD5GtFXkJva7hMiPlBxSe6BqloTyPdG9iHyfb1+UTCE4RCKbu5F7nB8cZm55L+Ah0Cy0gDmdbZT4dQxMpPUf6qe5R0jxCfXliW8A5GWlsLs1N6R6IUkYLOJHxDwvrmqdSuBfS1GM1nlJQQETkDhFpEpEWEfnYItvfIyIBETlsLu+P2HafiDSby32Jtdw+NJQbre6mFO6FnOoepdbvi9skRsuxfV1BSrsQe0YnGRqfSWj8w8ISkFR2YzX1hBAh4Y0ni6QJiIh4gS8DdwLbgXtFZPsiu35fKbXXXP7VPLYY+EvgauAA8Jcikrh5HG1EQ4UWkFPdQbZVJtZ9ZdFQ7kvpHuCJzsQO4IykICedqsLslA6kN/WOsqE4h5yM5Ewum8weyAGgRSnVppSaBh4E7ory2NcCjyulBpVSQ8DjwB1xstPWVBdl48tMS9lW8JCZBZXoALrFFrMH2NybmgI+H39K0v1P9ZImTT3B+e9gMkimgFQB7RHvO8x1C3mTiBwVkYdEZP0Kj0VE7heRRhFpDAQCsbDbVohISgfSrQdYsgTE6gGeSVEBaeoNsr7YaMQkg+2V+bQFQkxMp97cIJMzc5wbGE948kgkyRSQxZKWF47I+jGwSSm1G3gC+NYKjjVWKvWAUmq/Umq/3+9ftbF2pqEij6aeYEoOaDuZZAFZX5RDVrqHpp5QUq6fbM70BufjcMlgW2UeYQXNfakn4K2BEHNhlbI9kA5gfcT7aqArcgel1IBSysrR+ypwZbTHphJbK/IYmZihdzT10hlPdQcp9WXiz0tMCZOFeDzClvK8lOyBTM+GaQuMUZ/EB5h17TO9qSfg1ncuVXsgB4F6EakRkQzg7cDDkTuISGXE2zcCp8zXjwK3i0iRGTy/3VyXklgtwFMpGAc53TOatAC6xZbyPJpSUEDODYwxG1ZsSVIGEMDG4hwyvJ6UjEGd7gmS7hU2lSZ2DpBIkiYgSqlZ4EMYD/5TwA+UUidE5NMi8kZztw+LyAkROQJ8GHiPeewg8BkMEToIfNpcl5JYOeCplok1F1Y094WS6kIBQ8ADwSkGx6aTakeisVrAyXShpHk9bPbnpmQP8ExPkFq/L+EDOCNJTuTLRCn1CPDIgnWfjHj9ceDjSxz7deDrcTXQIRTkpFNZkJVyAnJhcJzp2XBSH2AAWyIC6ddsLkmqLYnkTG8Ij5CUIn6RbCnP49D5oaTakAyaeoJcVVOcVBv0SHSXkIqZWJbbIlmDqCwaylMzE+tMT5BNJblkpSd+AGckW8p9dA6n1lic0ckZukYm57MAk4UWEJfQUJFHa1+Imblwsk1JGM19RuC0riy5AlKen0l+VlrK9QDP9AWTLt5wMZCeSnGQM+Z3LdnuWy0gLmFbRT7Tc2HO9qfODG3NvUHWFWSRl5WeVDussTip1AOZnJnj/MB40t2HEDmYM3UysaykDd0D0cSEVCxpcqY3RJ0NHmBgZmKl0FictsBY0scgWGwoziEzzZNSAt7UE8SXmUZVYWLmoF8KLSAuoaY0F49AS19qtMLmworWQIgtSXZfWTRU5DE6OZsyY3GsgXt2EBCvR6j1+ziTIt99sEqY+BI6A+diaAFxCVnpXjYU56SMgLQPjjM1G7aFDx4uPkhTZTxIU0+QNI9Qk8QxCJFsKfelTAxEKWVUAEiy+wq0gLiKujJfygiIFUBP5ijoSCwBOZMiLsQzvSFqSnPJSLPHI6S+PI/ukUlGJ2eSbUrcCYSmGBqfob4s+d99e/z3NTGhriyPtv4QsymQiWX5u5OdgWVRnJuBPy8zZVKpm/uSWwV2IakUSG+Zbzwl/7uvBcRF1JX5mJlTXBgcT7YpcaelL0RlQRb5Sc7AiqS+zEdLwP0PsInpOS4M2iMDy8Iqp5IKbqxWm6SvgxYQV1FvfqGaU8CNdaY3aBv3lUVdmY/WvpDrM7Fa+kIoRVJrYC3EqoqcCkUVW/pC+DLTqMjPSrYpWkDcRK0pIG6Pg8yFFS19oXnBtAt1ZT5CU+7PxDozXwHAPgLu8Qh1Zb6UKOveEghR689NegYWaAFxFb7MNNYVZLleQDqHJpiaDduqBQxQ508NAW/uCxlVYEtykm3KK9hSlhqDOVv6QtTZIIAOWkBcR20KtMIuBtDt8SOyqJvvAbr7/rcGQmwqySUtiVVgF6O+PI/e0SlGJtybiTU6acz7Y4f4B0QhICLyByKSLwZfE5GXROT2RBinWTn1ZXm09o0RDrvXD99soyyUSPx5meRlpbk+kN7aF0p6Bd7FsFyarS6+/y02CqBDdD2Q31FKjWJM2uQH3gt8Lq5WaVZNfbmPiZk5Oocnkm1K3GjuDVKRb68MLDBqYrl9LM70bJjzg+O2eYBFYsUAW118/50oIFak5nXAN5RSR1h8TvIVIyJ3iEiTiLSIyMcW2f5RETkpIkdF5EkR2RixbU5EDpvLwwuPTVXm3SguboU194Vs1/uwqPP7aOlzb0HL8wNGDSy7PMAiWV+UTYbX4+rvfmtfiAyvh/VFya2BZRGNgBwSkccwBORREckD1jxSTUS8wJeBO4HtwL0isn3Bbi8D+5VSu4GHgL+L2DahlNprLm9EA0QEcl2azqiUUQPLji4UMAS8PzTFyLg7/fBWC9iO9z/N62FTaQ6tLhbwlr4Qm/32iT9FY8X7gI8BVymlxoEMDDfWWjkAtCil2pRS08CDwF2ROyilfmleE+B5oDoG13U1RbkZlPoyXOtG6RmdZHx6bt5dYTcu9gDdGUi34gub/faogbWQWr/P3TGQQMhW3/1oBERh9CkNJGwAACAASURBVBA+bL7PBWIxgqUKaI9432GuW4r3AT+LeJ8lIo0i8ryI3L3UQSJyv7lfYyAQWJvFDsHN+fDzPmAbtoAhMhPLnQ+xlr4Q6wqyyM1M6mzYS1JX5uPC4DhTs3PJNiXmTM4YFQDs9N2PRkD+GbgWuNd8H8RwPa2VxeIoi6YOici7gP3A30es3qCU2g+8A/iSiNQudqxS6gGl1H6l1H6/379Wmx2BISDuHBFtBUhry+zZAq4uyiEjzeNeAbFZC3ghtX4fc2HFhQH3lfNpC4yhlH0C6BCdgFytlPo9YBJAKTWE4cZaKx3A+oj31UDXwp1E5FbgE8AblVLzQ3yVUl3m3zbgKWBfDGxyBfVleQQnZwkE3TciujUwRl5WGn5fZrJNWRSvR9hcmutKAQmHFa19Y7aMf1i4uQdoJQc4TUBmzIC3AhARPzEIogMHgXoRqRGRDODtwCuyqURkH/B/McSjL2J9kYhkmq9LgeuAkzGwyRXUubgmlhVAt0MZh6Woc2lRxe7RSSZm5mz1AFuIFZtxYxykpS+ER7DNHCwQnYD8I/BDoExEPgs8DfzNWi+slJoFPgQ8CpwCfqCUOiEinxYRK6vq7wEf8B8L0nW3AY0icgT4JfA5pZQWEBOrhdjmwh+RnTOwLOrKfHQMTTA54y4/vJ2qwC5FToYxzasbeyCtfSE2FOeQle5NtinzXDYSppT6rogcAm7BiFvcrZQ6FYuLK6UeAR5ZsO6TEa9vXeK4Z4FdsbDBjZTnZ5Kb4aU14K50xqBZxsGu8Q+LujIfShk+6+3r8pNtTsywcwpvJJv9ua777oNVA8te9z6aUiYbgHHgxxgupjFzncamiAi1Ze5LZ7QeCnZ/gLl1MGdLIERBdjqlvliEQONHnfndd1M5n7mw4my//eJP0eTi/RQj/iEY6bs1QBOwI452adZIrd/Hi2cHk21GTHGCCwUMH7VH3BfINWpg2aOM+HLU+n2MT8/RMzrJukJ7jNheKx1D40zPhW2XAXfZHohSapdSarf5tx5jAODT8TdNsxY2l+bSOTzB+PRssk2JGa2BEGkeYUOxvcqILyQzzcuG4hzX1WRqDdjPhbIYbszEsrwJtTYbwLni8fBKqZeAq+JgiyaGWC2VNhf5glsDITaW5JBukzIOy7HZZSOih8en6Q9NO0JALDePm+6/VZ5lc6m97v9lXVgi8tGItx7gCiA1hnQ7mMgf0c6qgiRbExtaA/bzAS9FrT+XZ1r6CYcVHo+9XT7RcLEFbP/7X+rLoCA73VUC0tYfoiQ3g6Jce8WfomnK5UUsmRgxkbuWPUKTdDaW5OAR9/RAZubCnOsfs50PeClq/T6mZsOuKatvtYCdICAiQq3fXYM5W/vGbFl/LJo03r9KhCGa2JKV7mV9cY5rWmEXBseZDStHPMDAcGGB0XJfb/OYTTS0Bswy4g75LHVlPn5x2j2OktZAiNu2lyfbjEtYUkBE5McsUZsKQJdQtz+bS92TD++UDCwLK9jZFhjjpoYkGxMDWgNjbCrNwesQd1yt38cPGjsYmZihINteE4+tlOHxaQbGpm3ZeFquB/KFhFmhiQu1fh/Ptg64wg9vCaEdu/GLUZzrLj98WyDElnJ7zUG/HJsjqjHs21CUZGvWhp2/+0sKiFLqV4k0RBN7assu+uGd4npYitZAiLK8TNtNY7sUlh/eDQIyMxfmwuA4d+6qSLYpURPZA3S+gNg3gSGakej1IvKQObVsm7UkwjjN2pividXvfDdWayBkyxbYctT6fa5IYjg/YMSf7JZCuhzri3NI84grBLwtMEa6V6i2yTS2kUSThfUN4F+AWeA1wLeBf4unUZrYYLXCnD6gTSlljoJ2zgMMDDdKX3CK4KSzp7e1inI6JQMOIN3rYUNJjisEvDUQYlOJfaaxjSQai7KVUk8CopQ6r5T6FHBzfM3SxILi3AwKc5zvhx8Ym2Z0ctZxAhLpRnEydvbBL4dbpre1cwXqaARkUkQ8QLOIfEhE7gHK4myXJgaIiJmJ5ewfkdWDctoDbLNLRkS3BUL4HRR/stjszzXcb3OxmL4oOczMhbkwMG7b7340AvKHQA7GnOhXAu8C7ounUZrYYbTCnN0CtmI4dm2FLcXGEnf44dv6x9hso0mMoqXW72N6LkzHkHMHc9p9/NOSAiIibxaRLKXUQaVUSCnVoZR6r1LqTUqp5xNppGb11Jb5CASnGHWwH74tECIzzUOVwyqrusUP32rzedCXYt6F2O9cAbd633a9/8v1QN4JXBCRb4vInea0tjFFRO4QkSYRaRGRjy2yPVNEvm9uf0FENkVs+7i5vklEXhtr29zCxdkJnfsQaw2MGSXSHTiWZXOps/3wg2PTDI/POLIHYmWNWWVYnIjV+3acC0spdQ9QBzyJ4b5qF5F/EZEbYnFhU5C+DNwJbAfuFZHtC3Z7HzCklKoDvgh83jx2O8Yc6juAO4B/jofAuYHNLsjEarNxEPFy1Jblcq5/nDmHTm7U6sAMLIui3AyKczMc3wOxc/xJlIruiy0iJcCbgQ8CxUqp9Wu6sMi1wKeUUq81338cQCn1txH7PGru85yIpAE9gB/4WOS+kfstd839+/erxsbGlRv7s49Bz7GVH2cDwigOnh2ksjCbDUXOG0wYVooXzw1SVZjNegfa3xecpK1/jL3rC8lKc14bx+n2n+gaAWDHOmdWpD7eNYII7Khco/0Vu+DOz636cBE5pJTav3B9VInFIlIE/DbwNqAY+M9VW3KRKqA94n2HuW7RfZRSs8AIUBLlsZbt94tIo4g0BgLuKa4WLR6EzHQvk9NzyTZlVUzOGnZnpzvv4QWQnWHYPeHQ+z8xM4cIZKbZbwxCNGSle5mccea9VygmZ+Zs/d1frphiHnA3cC/GHCAPA38N/FJF221ZnsUc2gvPu9Q+0RxrrFTqAeABMHogKzFwnjUotx348rcbOdc/xuPvvTHZpqyYXx/v5gPfeYkf33M9pdXOa0XOjk3z9s88zid2beO/37A52easmM986yAd3gl+/t6YeK4TzhO/auVvf3aaI2+7nYIce7qBlmIwNMWb//oJ/uLW7Wy+vibZ5izKcs2KsxjxhX8B1iul7ldK/SJG4gFGryHSDVYNdC21j+nCKgAGozxWY1Lr9zk2H95KQa6xaRDxcjjdD98asOc8FNEyP7GaA++/EwZwLicgG5RS71RK/VgpFY8c0INAvYjUiEgGRlD84QX7PMzFMSdvBiwBexh4u5mlVQPUAy/GwUZXsNmf69h8+NZAiIr8LHyZl526xrbU+nMdmQk0PWsUUXRqAgM4O4nEKiFTZ+P7v1wW1ng8L2zGND4EPAqcAn6glDohIp8WEWuuka8BJSLSAnyUi8HzE8APgJPAz4HfU0o509GZAC4WVXTij8jZLWAwiyo68N5fGBxjLqwcff/XF+eQ7hVHFhRtNcc/rbPx+KekNuuUUo8AjyxY98mI15PAW5Y49rPAZ+NqoEu4WFRxjJu3JtmYFaCUoi0Q4q69i+ZHOIZav48HD7YzPD5NYY695rRejnkXioOq8C4k3ethQ3GOI3sg1vgnO0/itdxI9Lcm0hBN/CjMyaDEgX74/pBRRNHJLWCIcKM4bDCnk8eAROLUoopOGP+0XAzk3SLycxFxXuqI5hI2O9APb/mAN9v8R3Q5ah1aVLG1b8zx8ScwBPDC4DgzDkoimZqdM+NP9m48LRcDeT3wFeCnIvIXIlIqIsXWkjgTNbHAia0wq8Vu9x/R5aguyibD63FcORmjBpaz7z0Y3/2ZOUX7YFzDujHlwsA4YWX/xtOyo4OUUv8PIzvqj4FG4JC5rGI4tyaZ1Pp9DIxNMzw+nWxToqYtECIr3cO6AvsGEaMhzethY0mOowRcKWXreShWQq0DXYh2nsY2kuViIJki8hngQeCdSqlNSqkac9FuLYfhRD98ayBETanPkUUUF+K0HmAgNEXQgZN4LYYT52VxwhgQWL4HchTwAlcopX6SIHs0ceJiVV5n/YjqHB7Atagty+XCgHP88Fa8zO4PsGgoyE7Hn5fpqEwsa/xTrs3jT8sJyD1Kqf+plHLe6DPNJVQXZZPuFcf0QCZn5mgfsn8QMVo2l/qYDSvODzjDD+8UF0q01PqdNTNna2DMEfGn5YLoJxNpiCa+pHk9bCrJdUwP5Gz/GEq56AFW5qweYGsgRE6Gl4r8rGSbEhOsmTljV4kpfiilaOtzRvzJmSU2Natis4NaYW5rATstBmXVwHJD/AmM79HIxAwDY/ZPIgmEpghOzTpiEi8tICmEVVTRCX741r4xRNzhgwfIz0qnLC/TOQLukBZwtFg9QCfEQaz4kxMGcF5WQERki4g8KSLHzfe7ReTP42+aJtbU+g0//AUH5MO3BEJUF2WTZeO5EFaKU3qAE9NzdI1MuEtAHNQDdFLvO5oeyFeBjwMzAEqpoxhjQzQOw8poanFEK8xdLWAwiyo6wA/vtvgTwLqCbLLSPY4Q8LbAGNnpzog/RSMgOUqphaXSZ+NhjCa+WO4guwtIOKxo63engDjBD3+xBpY73IcAHo+wudQZY3FaAyHHxJ+iEZB+EanFnPFPRN4MdMfVKk1cyMtKpyI/y/Z+4K6RCSZnwq4ZA2LhlLkpWgMhRGBTiXsEBIyYghMEpMVBve9oBOT3gP8LbBWRTuAPgd+Nq1WauFHngB+R1UNyyo8oWi4WVbS3H741MMb6ohxXxZ/AiIN0DE3Yeo708elZOocnHNN4uqyAKKXalFK3An5gq1LqeqXUubhbpokLhoDY2w/vliKKC6kqNPzwdnchGvEnd917MARcKSPGY1esgpuuERCzJtY7gD8APiIinxSRT17uuMucs1hEHheRZvNv0SL77BWR50TkhIgcFZG3RWz7poicFZHD5rJ3LfakErX+XEJTs/SMTibblCVpDYQozEmnONc5ky9Fg8cj1Pp9tNi4B+jW+BM4o6y+1biod4uAAD8C7sIInI9FLGvhY8CTSql64Enz/ULGgXcrpXYAdwBfEpHCiO1/opTaay6H12hPylDrgEyslr4QdX4fIvYPIq6UujIfLb3BZJuxJFb8ye5lxFdDTWkuIth6XpyWvhBej7DRIfGnaCp1VSul7ojxde8CbjJffwt4CvizyB2UUmciXneJSB+GG204xrakFJGpvK+u9yfZmsVpC4S4ZWt5ss2IC/VlPn50uIuxqVlbFsqzGhZOcaGshOwML1WF2bbugTT3BdlYkkNGmjPGeEdj5bMisivG1y1XSnUDmH/LlttZRA4AGUBrxOrPmq6tL4pI5jLH3i8ijSLSGAgEYmG7o/H7MsnPSrPtj2h4fJr+0LSrUkgjsR7Mdr3/TnOhrJRav88RvW+nsNx8IMdF5ChwPfCSiDSZD+xj5vplEZEnzHMsXO5aiYEiUgn8G/BepZRVg+PjwFbgKqCYBb2XSJRSDyil9iul9vv99mxxJxIRobbMvj+iVocFEVdKXVkeAM299rz/zb0hSn0ZFLks/mRRb2YhzoXtl0QyMxfm/MC4o777y/Whq4BVB6fNzK1FEZFeEalUSnWbAtG3xH75wE+BP1dKPR9xbmscypSIfANjxkRNlNT5ffyyyZ69sVaXpvBabCzJIc0jtg2kN/cFHfUAWyn15T6mZsN0Dk2woSQn2ea8gvMDY8yGFfXlzrn/y7mwziqlzi+1rPG6DwP3ma/vwwjUvwIRyQB+CHxbKfUfC7ZVmn8FuBs4vkZ7Uoq6Mh/9oSlGxmeSbcoltAZCZHg9VBfZ68cdK9K9HjaV5tqyB6KUorkvRL3ZS3Ij8z3APvslMszHn/zOuf/L9UDKROSjS21USv3DGq77OeAHIvI+4ALwFgAR2Q98QCn1fuCtwA1AiYi8xzzuPWbG1XdFxA8IcBj4wBpsSTnmA+mBEFduvCSDOqmc6Q2y2Z+L1wFlHFZLfZmP0z32e4D1BY1pbJ3UAl4p1ne/uS/ELdvslahhNSqcFP9bTkC8gA/jIR1TlFIDwC2LrG8E3m++/g7wnSWOvznWNqUSdRGlre0mIM19IfZtsJdNsaauzMejJ3qYmp0jM80+o70vtoDdKyAF2emU52dyxoap1C2BEFWF2eRk2C87bymWs7RbKfXphFmiSRjVRUaaoN388GNTs3QMTfC2/euTbUpcqSvzETZHRG+tyE+2OfM0mw/VOhf3QADqy/JsmUTS0hdyxBwgkSwXA3GvDyHF8XqEzaW5tvsRzaeQljvHB7wa7FpWv7kvREF2On7fklnxrqC+3MhCDNsoEyscVrQGnJXCC8sLyCUuJo17sGMqb/O8gDjrR7RSav0+ROyXymsE0N1ZASCS+rI8xs1Js+xC57BRAcBp3/0lBUQpNZhIQzSJpc7vo31onIlp+1Qmbe4NkuH1sLHYnRlYFlnpXtYX5djOhdjSF3LcA2w1WJ+x2UYNKKdWAHDGeHlNzGmoyEMpe42ItjKw0rzu/1rWlflsNS/IQGiKwbHp+TRXN2O5iZptFEh3agKD+3+pmkXZYsYZmmyUTtrcF3J9/MOivsyY3nZ2Lnz5nROA20uYRFKUm0GpL9NWLsSWvhAluc6rAKAFJEXZVJJDhtdjm3RGKwNrSwo8wMCIQU3PhWkfsocfvtmhLpTVUl/ms5UL64xDKwBoAUlR0rweast8thGQVMnAsrBa+nZxo7T0hcjN8FJZkJVsUxKClYllh4nVlFKc6QmytcJ5330tIClMQ7mPMzbpxqdKBpaFJZR2EfDmviB15Xmuz8CyqC/Ps83Eah1DE4xNz7FFC4jGSdSX59E5PEFwMvk1sVIlA8vCl5lGdVG2bUqaNPeGUiL+YXGxB5j8BpTViNA9EI2jaJhvBdvjR5QqGVgWWyvybJHEMDI+Q19wypE++NViCYgdeoBWI8KJ7tvU+bVqLqGhwj5ulFTKwLJoqMijrX+MqdnkjsVpMv//DQ5sAa+WEl8mxbkZthhMe6Y3SFVhNvlZ6ck2ZcVoAUlhjMJt3qS3glMtA8uioSKfubBK+hzdp3tGAdhmo7pciaCuzDcvnsmkqSfIFofG/rSApDAej1Bfnpf0uRFSLQPLwvJ5N/WOJtWOU91BCnOMKrWpxLaKPM70BJNaE2tmLkxrIESDQ8VbC0iK01Duo6knud34VMvAsqgpzSXdK0kPpDf1jNKQQhlYFtsq8xmbnqN9aDxpNpztH2NmTtFQ4czvflIERESKReRxEWk2/y46AYSIzInIYXN5OGJ9jYi8YB7/fXP2Qs0q2FKeR39oioHQVNJsaOoZJSMtdTKwLNK9Hmr9vqS6EMNhRVNPkG2VzmwBr4Wt5mc+1Z28+2/97xvKnXn/k9UD+RjwpFKqHnjSfL8YE0qpvebyxoj1nwe+aB4/BLwvvua6l4uB9OT1Qk51B2koz0upDCyLZGdiWWMQnJhCula2lBtVka0YUDJo6gni9YijZiGMJFm/2LuAb5mvv4Uxr3lUmPOg3ww8tJrjNa9kS5IHtCmlONU9yrbK1HuAgRFI7x6ZTNr89KfMh+fWFOyB5GSkUVOSy+lk9kB6g9SU5tpqZsqVkCwBKVdKdQOYf8uW2C9LRBpF5HkRsUSiBBhWSs2a7zuAqvia617K8jIpyE5PmoD0BacYGJtOSRcKXAykn0lSIsPp7iAiODYLaK1srcybF9Fk0NQTnB+P5UTiJiAi8oSIHF9kuWsFp9mglNoPvAP4kojUsvhMiUumUYjI/aYINQYCgRV+CvcjIjSU5yVNQE52Gz/e7SkqIJYLMVmB9KbeUTYW5zhqHu5YsrUin/MD44xNzV5+5xgzPj3LhcFxR4+/iZuAKKVuVUrtXGT5EdArIpUA5t++Jc7RZf5tA54C9gH9QKGIWN/4aqBrGTseUErtV0rt9/v9Mft8bqKhIo/T3cGkFJY71Z26LhSAyoIs8rLSaEpSK/h0d9BW87Inmoup1IkXcCvuuEX3QFbMw8B95uv7gB8t3EFEikQk03xdClwHnFTGU+6XwJuXO14TPdvX5ROcmqV9MPGlxU91G6NwC7KdNwo3FohI0gLpE9NznB0YY2uKxp+Aedep1ZBJJGd6nFsDyyJZAvI54DYRaQZuM98jIvtF5F/NfbYBjSJyBEMwPqeUOmlu+zPgoyLSghET+VpCrXcZO9YZP6ITXSMJv/bJrpGUjX9YNFTkcbon8T3AM71BlHL2A2ytVBdl48tMS0og/XRPkKx0D+sdnL6eFMenUmoAuGWR9Y3A+83XzwK7lji+DTgQTxtTiS3leaR5hONdI9y5qzJh152cmeNs/xi/lcBr2pGGinyCkxfoHplkXWF2wq7bNN8CTl0Bt3qAyUjlPdk9QkN5Hl6Pcwdwpl7iveYSstK91JX5ONGV2B9RU0+QsDJcaKmM1QNItBvlVM8o2eleNji4BRwLtlXmJzwGGA4rTnSOsrOqIGHXjAdaQDQA7FhXkHABsR6Yqe7C2l6Zjwgc70zs/T/dHaShIg+Pg1vAsWBrZR5Bs6BnorgwOE5wapZdWkA0bmDHunwCwSn6EjhD28nuUXIzvKwvSu0WcG5mGptLcznWmbgYlFKK0z2jKR3/sLBceIlMpbb+17oHonEFFwPpiWsFn+oeZWtlfsq3gAF2VRVwrHM4YdfrGplkaHwm5d2HkBwX4vGuEdK94ugUXtACojHZnuBMLKUUp7uDKVvCZCG7qgvpHZ2iL5iYHuCxDkOsdlcXJuR6diY3M42NJTmcTGDj6UTnKA0VeWSkOfsR7GzrNTEjLyudTSU5CeuBdAxNEJyaZXuls7vwscLyhR9PkBvrSMcIaR7RLiwToweYuMbTsc4Rx8c/QAuIJoId6wo4nqAeiCVUugdisGOdEUg/1pEYAT/aMczWyjyy0p1ZxC/W7F1fSOfwBIFg/Kc16BiaYGRihh3rtIBoXMT2dfm0Dxpf7nhzrHMYr0dSegxCJIkMpCulONoxot1XEVj34mhH/ONQVi9T90A0rsIKpCfCF3y4fZitFXlkZ+gWsEWiAunnBsYJTs6y2wUPsFixsyofj8CR9gQISJfhPnRyEUULLSCaeawudbwD6eGw4mj7CHvX6xZwJDurChISSD+qA+iXkJORxpbyPI50xL8HeKxzlPpyd7gPtYBo5vHnZVKenxn3QHprIERwalYLyAKsB3q8A+lHO0bITPOk3Bz0l2NPdSFHOobjOiJdKcWJzhF2uiR9WguI5hXsXBf/bJSXTTfBvg1aQCJJVCD9aMcwO9blk56CUwgvx+71BQyPz8S1KnX3yCQDY9PsqnaH+1B/gzSvYN+GQlr6QgyPT8ftGi9fGCYvK43NpboFHEkiAumzc2GOd45q99Ui7DHvyeE4BtKt3qUbMrBAC4hmAVduLAbgpQtDcbvG4fZh9q4v1CPQFyHegfTWwBgTM3PsdkkLOJY0VOSRmebhaBwD6cc7R/CIe2bg1AKieQV71xfi9QiHzsdHQManZ2nqGdXxjyWIdyD9iA6gL0m618OOdfnz9ygeNJ4fYltlvmuyD7WAaF5BdoaXHevyaTwXHwE51jFCWKEFZAms+/LS+fg8xI52DOMzXWWaS9ldXcjxzlFm58IxP/fMXJiXLwxz1abimJ87WSRFQESkWEQeF5Fm82/RIvu8RkQORyyTInK3ue2bInI2YtvexH8K93LlxiKOdAwzE4cf0WHTPaAFZHF2VReQmebhxbODcTn/0Y4RY8yDdh8uyt71hUzMzNHcF4r5uY93jjAxM6cFJAZ8DHhSKVUPPGm+fwVKqV8qpfYqpfYCNwPjwGMRu/yJtV0pdTghVqcI+zcWMzkTjks67+H2YTYU51Diy4z5ud1AZpqXKzYU8eK5gZife2J6jlPdo+zR4r0kVmwoHiPSD54zGgVX1VzSXnYsyRKQu4Bvma+/Bdx9mf3fDPxMKTUeV6s0gNEDAeISB7EC6JqlOVBTzMmuUUYnY1tSpvH8IDNzims2l8T0vG5iU0ku+VlpcXEhvnh2iE0lOZTlZcX83MkiWQJSrpTqBjD/ll1m/7cD31uw7rMiclREvigiSzZnReR+EWkUkcZAILA2q1OEioIsqgqzOXQ+tm6UnpFJukcmtYBchqtrigkrOBTjONTzbQN4PeIqF0qs8XiEqzeX8FxbbHuA4bCi8fyg6+593ARERJ4QkeOLLHet8DyVwC7g0YjVHwe2AlcBxcCfLXW8UuoBpdR+pdR+v9+/ik+SmuzfVETjuaGYjsq1UoP36gGEy7JvQxHpXuGFGMdBnmsdYHd1Ab7MtJie1228qraEC4PjtA/GzuHRGggxPD7DVTVaQKJCKXWrUmrnIsuPgF5TGCyB6FvmVG8FfqiUmu/PK6W6lcEU8A3gQLw+R6qyf2MRfcGpmM4T/XRLP77MNFdUIY0n2RledlcX8uLZ2LWCx6ZmOdoxot1XUfCq2lKAmPZCXrTiH7oHEhMeBu4zX98H/GiZfe9lgfsqQnwEI35yPA42pjRXxCEO8pvmANdsLtElNKLgQE0xRztGGJ+ejcn5Gs8PMRtWXKsF5LJsKfdR6svg2Zb+mJ3z4NlBSn2ZbCrJidk57UCyfsmfA24TkWbgNvM9IrJfRP7V2klENgHrgV8tOP67InIMOAaUAn+dAJtTiq0V+fgy02iMURzk/MAY7YMT3LClNCbnczsHaoqZDStevhCbYO5zrQOke4X9m9yTARQvRIRra0t5tnUgZi7cg+eGOFBThNHmdQ9JERCl1IBS6halVL35d9Bc36iUen/EfueUUlVKqfCC429WSu0yXWLvUkrFPmk7xfF6hCs2FvFsS2y68b9pNlpz19dpAYmG/RuL8Agxi4M81zbAnupCcjJ0/CMarqstoS84RWtgbM3n6hyeoHN4wnXuK9Aj0TXLcHODn7b+Mc72r/1H9JvmAFWF2dToEdBRkZeVzo51BbwQAz98cHKG4506/rESrDjIs61rd2MdPOvO+AdoAdEsw81bywH4UkPDzQAAEEFJREFUxenlchwuz+xcmGdbB3h1fanruvDx5EBNMS+3DzM1O7em8zSeG2IurLi2VgtItKwvzqaqMDsmPfBfnQlQmJPONpcUUIxEC4hmSTaU5FBf5uMXp3vXdJ6jnSMEJ2e5vl67r1bCdXUlTM+Gea51bQ+x59oGyPB65geIai6PiHBdnTEeJBxefRxkZi7Mk6d6uWVrOV4Xlo/RAqJZlpu3lfFC2yDBNYyK/s2ZfkTgulotICvhVbWl5GZ4+fnxnjWd59nWfvZuKHTFFKqJ5FW1pYxMzHCye/UlfV5oG2R0cpbX7iiPoWX2QQuIZllu2VrObFjNB8FXw9MtAXZVFVCUmxFDy9xPVrqXm7eV89jJ3lVXh20fHOd45yg3b71csQfNQl5luvzW8t1/7GQPWekeXl3vzkHMWkA0y3LFhkIKstN58tTq4iDByRlevjCss69WyZ07Kxgcm54fiLZSHj7SBcDrd1fG0qyUoCw/iz3VBfzkaNeqjldK8diJXm6o97tm/o+FaAHRLEua18NNDX6eaupjbhW+4F+c7mM2rLhhiztbYPHmpgY/WemeVbuxfnykiys3FlFd5K4BbInirr1VnOgapbk3uOJjj3WO0DM6ye07KuJgmT3QAqK5LLdsK2dgbHpVM7U9dKiDqsJsDrgwhTER5GSkcdOWMn5+vGfFwdzm3iCne4K8Qfc+Vs0b9qzD6xH+3+HOFR/72IlevB7hFhe7D7WAaC7LjfV+vB7hyVMry8bqGBrn6ZZ+3rK/Wk9gtAbu3FVBX3CKl9tXVlbmx0e78Qi8TgvIqvHnZXJdXSk/Oty1YgF/9EQPBzYVuzr2pwVEc1kKctJ5VW0JDx3qYHo2+mDufx4yWm1vvrI6XqalBDdvLSPD6+Fnx6J3Yyml+MmRLq7ZXOKq+SeSwT371tExNMGhC9ELeFsgRHNfiNtdmn1loQVEExW/c30NvaNTPHKsO6r9w2HFfxxq57raUu1/XyN5WelcX1/Kz473RF2b6UTXKG39Y7xhz7o4W+d+bt9eQXa6lx++HL0b66FDHYjg6vgHaAHRRMmN9X7qynz869NtUT3EnmsboGNogrdetT4B1rmfu/auo3N4gkdPRNcL+fGRLtI8wh0uf4AlgtzMNG7fUc5Pj3ZH1QMfGZ/h28+d53U7K6kqzE6AhclDC4gmKjwe4X3X13C8czSqAn8/aGwnPyuN27e7uwufKF6/ex21/lz+4fEzl82GGxqb5sGD7dzUUOZq/3siuXtfFSMTMzwRRRzwG8+eJTQ1y4durkuAZclFC4gmau7ZV0VxbgZfe/rssvv1h6b4+fEe7t5XpUc/xwivR/jIbVs40xvix0eWH5fwpSfOEJyc4Y9fuyVB1rmfV9eVstmfy+d/fprJmaVrkwUnZ/j602e5dVu5K2tfLUQLiCZqstK9vOuajTxxqnfJCr1KKT7+X8dQCt597abEGuhyXrezkq0VeXzpiTPMLDEy/UxvkO+8cIF3XL2BrRXuf4AlijSvh7++ayfnB8b556dal9zv28+dZ3Rylg/f4v7eB2gB0ayQ/3bNRtI9Hv7qxycWfYh9/2A7j5/s5U/vaKCuzJcEC92LxyP80e0NnBsY579e6rhku1KKz/zkJLkZXj56W0MSLHQ3r6or5e696/jKU620BS6dgmh8epavPX2WG7f42V1dmAQLE09SBERE3iIiJ0QkLCL7l9nvDhFpEpEWEflYxPoaEXlBRJpF5Psioh29CcKfl8lfvnE7TzUF+MPvH36FP/5c/xif/slJrqsr4Xeuq0mile7l1m1l7Kku4AuPneHlBWmlj53s5TfN/fzBrVso1rGPuPCJ39pOZrqHv/jR8VckkwyOTXPf119kcGw6ZXofkLweyHHgt4FfL7WDiHiBLwN3AtuBe0Vku7n588AXlVL1wBDwvviaq4nknVdv5BOv28ZPj3bzpw8d5VjHCA++eIEPfvcl0jzCF96yRw8cjBMiwt/+9m4yvB7e8pXn+OenWmgLhPjDB1/mA985RH2Zj3dfuzHZZroWf14mf/raBp5pGeDtDzzPw0e6ONE1wt1ffoajHSP80737uHJj6lRdkFjN+buqi4s8BfyxUqpxkW3XAp9SSr3WfP9xc9PngABQoZSaXbjfcuzfv181Nl5yKc0q+d9PNPPFJ87Mv8/PSuPv37KH1+rU0bgzMjHD//zhMX561BiXk5Xu4b5XbeIDN9TqzKs4MxdWfO3pNv7t+fO0D04AUOrL5KvvvpJ9G9w554qIHFJKXeItsvMEyVVAe8T7DuBqoAQYVkrNRqyvWuokInI/cD/Ahg0b4mNpivLhW+rYVpnHzJxiZ1U+64tydM8jQRRkp/N/7t3HzQ1lnOkL8r7ra/SI8wTh9Qj331DL+6/fzDOt/bx4dpC3XbU+JQfMxk1AROQJYLGm6CeUUj+K5hSLrFPLrF8UpdQDwANg9ECiuK4mSkTE9SNt7YyI8CZdJiZpeDzCq+v9rp3rIxriJiBKqVvXeIoOIHIYczXQBfQDhSKSZvZCrPUajUajSSB2TuM9CNSbGVcZwNuBh5URtPkl8GZzv/uAaHo0Go1Go4khyUrjvUdEOoBrgZ+KyKPm+nUi8giA2bv4EPAocAr4gVLqhHmKPwM+KiItGDGRryX6M2g0Gk2qk9QsrESjs7A0Go1m5SyVhWVnF5ZGo9FobIwWEI1Go9GsCi0gGo1Go1kVWkA0Go1GsypSKoguIgHg/CoPL8UYg2I3tF0rQ9u1MrRdK8Otdm1USl0yYjKlBGQtiEjjYlkIyUbbtTK0XStD27UyUs0u7cLSaDQazarQAqLRaDSaVaEFJHoeSLYBS6DtWhnarpWh7VoZKWWXjoFoNBqNZlXoHohGo9FoVoUWEI1Go9GsCi0gC/j/7Z19jBbVFYefXwUsVaJQP4pgilijrTWsLCFUqyHRbhGr2KoVQ1NaTAylmtpGLYmNQdPEoFYTrcVKJWo1ulpLJX51aWtSjAWMsCCIygqblK8lUQGpaatw+se973Z2nNl9d3Zn3jacJ5m8d+49M3P23Dv37r0zc46kaZLektQhaX5G+eGSWmP5KknjKtDpREkvSdokaaOkH2XITJW0V1J73G4uW6943U5Jr8drZoUmlqR7or3WS5pYgU6nJuzQLmmfpOtSMpXYS9ISSbslbUjkjZK0XNLm+JsZB1XS7CizWdLsCvS6Q9KbsZ6WSjo659he67wEvRZI2p6oq+k5x/Z675agV2tCp05J7TnHlmmvzL6hsjZmZr7FDTgMeAcYDwwD1gFfSsnMA+6P6ZlAawV6jQYmxvQI4O0MvaYCzzbAZp3AMb2UTwdeIESSnAKsakCd7iJ8CFW5vYBzgYnAhkTe7cD8mJ4PLMw4bhSwJf6OjOmRJevVAgyJ6YVZetVT5yXotQC4vo567vXeHWy9UuW/AG5ugL0y+4aq2pjPQHoyGegwsy1m9m/gCWBGSmYG8HBM/w44T1KpgcDNbKeZrYnpDwjxUXLjwP+PMQN4xAIrCdEkR1d4/fOAd8ysqAeCAWFmfwXeS2Un29DDwCUZh34dWG5m75nZ+8ByYFqZeplZm4U4PAArCdE+KyXHXvVQz71bil7x/v828PhgXa9eeukbKmljPoD0ZAzw98T+Nj7ZUXfLxJttLyGoVSXEJbMzgVUZxV+RtE7SC5JOr0glA9okvSbp6ozyemxaJjPJv7EbYS+A481sJ4QOADguQ6bRdptDmDlm0Vedl8E1cWltSc5yTCPtdQ7QZWabc8orsVeqb6ikjfkA0pOsmUT6Ped6ZEpB0pHA08B1ZrYvVbyGsEwzAbgX+EMVOgFnm9lE4ALgh5LOTZU30l7DgIuBpzKKG2Wvemmk3W4CPgYeyxHpq84Hm0XAyUATsJOwXJSmYfYCrqT32Ufp9uqjb8g9LCOvXzbzAaQn24ATE/tjgR15MpKGAEdRbMrdLyQNJTSQx8zs9+lyM9tnZvtj+nlgqKRjytbLzHbE393AUsJSQpJ6bFoWFwBrzKwrXdAoe0W6ast48Xd3hkxD7BYfpH4DmGVxoTxNHXU+qJhZl5kdMLODwOKc6zXKXkOAbwGteTJl2yunb6ikjfkA0pNXgVMknRT/e50JLEvJLANqbytcBvwl70YbLOIa64PAJjO7K0fmc7VnMZImE+r23ZL1OkLSiFqa8BB2Q0psGfBdBaYAe2tT6wrI/c+wEfZKkGxDs4FnMmT+CLRIGhmXbFpiXmlImgb8FLjYzD7Mkamnzgdbr+Qzs2/mXK+ee7cMzgfeNLNtWYVl26uXvqGaNlbGmwH/zxvhraG3CW903BTzbiXcVACfJiyJdACrgfEV6PRVwtRyPdAet+nAXGBulLkG2Eh4+2QlcFYFeo2P11sXr12zV1IvAfdFe74OTKqoHj9DGBCOSuRVbi/CALYT+IjwH99VhGdmfwY2x99RUXYS8JvEsXNiO+sAvl+BXh2ENfFaG6u9bXgC8HxvdV6yXr+NbWc9oWMcndYr7n/i3i1Tr5j/UK1NJWSrtFde31BJG3NXJo7jOE4hfAnLcRzHKYQPII7jOE4hfABxHMdxCuEDiOM4jlMIH0Acx3GcQvgA4jiApM8mPKvuSnh/3SPpjQGc9yeSHkzsz5L0XEpmnKRtkj6Vym+P36jknft7kn5ZVDfHGSg+gDgOYGbvmlmTmTUB9wN3x3QTcHAAp74HaJZ0toJ79J8D16au3Un4/uKcWp6k04ARZrZ6ANd2nFLxAcRx+uYwSYtjvIU2ScMBJJ0s6cXoJG9F7PR7YMHh5jzCx5S3A0vMbEvGNR4nfD1do9sJpKSLFGLPrJX0J0nHpw+W9JCkyxL7+xPpGyS9Gp0R3hLzjpD0XHQmuUHSFUUM4xza+ADiOH1zCnCfmZ0O7AEujfkPANeaWTNwPfCrrIPN7BWCm+3zCYNIFk8Cl0TfSgBXEFySA7wMTDGzM2PejfUqLqkl6j+ZMJtqjs78pgE7zGyCmX0ZeLHeczpOjSF9izjOIc9WM6tFm3sNGBe9n54FPKX/hoM5POvgKDsJGAocS3CF0QMz2yVpIyG+TBfwkZnVfCaNBVqjT6hhwNZ+6N4St7Vx/0jCgLICuFPSQkJgrRX9OKfjAD6AOE49/CuRPgAMJ8ze98TnJH1xC/Ao0AXcDVyeI1dbxuqipxPIe4G7zGyZpKmECH1pPo461RzsDYv5Am4zs1+nD5DUTPCbdJukNjO7tY6/xXG68SUsxymAhZgLWyVdDt2x3yek5SSdAVxICBH7APB5SV/LOe3ThA49uXwFIWTA9pjOi1vdCTTH9AzCbAeCd9U5cRaEpDGSjpN0AvChmT0K3EkI1+o4/cJnII5TnFnAIkk/I3TYTxC8rgLdM4FFwI/N7J8xbx7wiKQmC6FXuzGzPZJWEqLJJZepFhCWyrYTPAeflKHLYuAZSasJ3lf/Ec/ZJumLwN/iUtt+4DvAF4A7JB0keJj9wYAs4RySuDdex3EcpxC+hOU4juMUwgcQx3EcpxA+gDiO4ziF8AHEcRzHKYQPII7jOE4hfABxHMdxCuEDiOM4jlOI/wAu+Jc8As2doQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(1,20,100)            # returns a list of 100 equally-spaced values in the range [1..20]\n",
    "Y = [np.sin(x) for x in X]\n",
    "plt.plot(X,Y)\n",
    "plt.plot([0,20],[0,0])\n",
    "plt.title('A Smooth-Looking Curve')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For further details on drawing plots, particularly on color and format, see the Appendix at the end of this document"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bar Charts\n",
    "\n",
    "If we do the exact same thing as we did with a simple plot, but use the function <code>bar(...)</code> we get a bar chart:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kSXcwb0BX1U+XshBJknS7YWYSkyRJS8yAliSpQQa0JEkNMqAlSWqQAS1JUoMMaEmSGmRAS5LUIANakqQGGdCSJDWot4BOsmuSC5J8LcmlSU7sqy1JkibNQnez2l43A4+qqk1Jdga+nOTTVXVej21KkjQRegvoqipgU/dy5+5RfbUnSdIk6fMImiQrgPXAfYGTq+r8OdZZA6wBWLVqVZ/lqGGrTzhr1CVMnA0nHTHqEiRth14vEquqX1XVgcC+wCFJHjTHOmurarqqpqempvosR5KksbEkV3FX1XXAucBjl6I9SZLGXZ9XcU8luWv3fDfgcOCbfbUnSdIk6fMc9D2Ad3XnoXcCPlRVZ/bYniRJE6PPq7i/Djy0r+1LkjTJnElMkqQGGdCSJDXIgJYkqUEGtCRJDTKgJUlqkAEtSVKDDGhJkhpkQEuS1CADWpKkBhnQkiQ1yICWJKlBBrQkSQ0yoCVJapABLUlSgwxoSZIaZEBLktQgA1qSpAYZ0JIkNciAliSpQQa0JEkNMqAlSWqQAS1JUoMMaEmSGmRAS5LUIANakqQGGdCSJDXIgJYkqUEGtCRJDTKgJUlqkAEtSVKDegvoJPdK8oUklyW5NMkL+2pLkqRJs7LHbW8G/ndVXZhkL2B9ks9U1Td6bFOSpInQ2xF0VV1dVRd2z28ELgPu2Vd7kiRNkj6PoG+TZDXwUOD8OZatAdYArFq1aoe2u/qEs3bo9gQbTjpi1CVI0rLQ+0ViSfYEPgK8qKpumL28qtZW1XRVTU9NTfVdjiRJY6HXgE6yM4Nwfm9VfbTPtiRJmiR9XsUd4FTgsqp6Q1/tSJI0ifo8gj4U+HPgUUku7h6P77E9SZImRm8XiVXVl4H0tX1JkiaZM4lJktQgA1qSpAYZ0JIkNciAliSpQQa0JEkNMqAlSWqQAS1JUoMMaEmSGmRAS5LUIANakqQGGdCSJDXIgJYkqUEGtCRJDTKgJUlqkAEtSVKDDGhJkhpkQEuS1CADWpKkBhnQkiQ1yICWJKlBBrQkSQ0yoCVJapABLUlSgwxoSZIaZEBLktQgA1qSpAYZ0JIkNciAliSpQQa0JEkNMqAlSWpQbwGd5O1Jrk1ySV9tSJI0qfo8gn4n8Ngety9J0sTqLaCr6ovAT/vaviRJk2zk56CTrEmyLsm6jRs3jrocSZKaMPKArqq1VTVdVdNTU1OjLkeSpCaMPKAlSdKvM6AlSWpQnz+zej/wFeD+Sa5M8qy+2pIkadKs7GvDVfWUvrYtSdKkc4hbkqQGGdCSJDXIgJYkqUEGtCRJDTKgJUlqkAEtSVKDDGhJkhpkQEuS1CADWpKkBhnQkiQ1yICWJKlBBrQkSQ0yoCVJapABLUlSgwxoSZIaZEBLktQgA1qSpAYZ0JIkNciAliSpQQa0JEkNMqAlSWqQAS1JUoMMaEmSGmRAS5LUIANakqQGGdCSJDXIgJYkqUEGtCRJDTKgJUlqUK8BneSxSb6V5DtJTuizLUmSJklvAZ1kBXAy8Dhgf+ApSfbvqz1JkiZJn0fQhwDfqarLq+qXwAeAo3psT5KkidFnQN8T+MGM11d270mSpEWs7HHbmeO9+rWVkjXAmu7lpiTfWmS7+wA/3s7aWjQW/crrtmr1sejTVhqbPrmvxqdP7qvx6dNW7Kth+7TffAv6DOgrgXvNeL0v8MPZK1XVWmDtsBtNsq6qpre/vLZMYr/s0/iYxH5NYp9gMvtln+bW5xD3V4H7Jbl3kl2AY4AzemxPkqSJ0dsRdFVtTvI84F+AFcDbq+rSvtqTJGmS9DnETVV9CvjUDt7s0MPhY2YS+2Wfxsck9msS+wST2S/7NIdU/dp1W5IkacSc6lOSpAY1G9CLTROa5BlJNia5uHv8xSjq3BpJ3p7k2iSXzLM8Sd7Y9fnrSQ5a6hq31hB9emSS62fsp/+71DVurST3SvKFJJcluTTJC+dYZxz31TD9Gqv9lWTXJBck+VrXpxPnWOdOST7Y7avzk6xe+kqHN2Sfxu77b4skK5JclOTMOZaN1b7aYpE+bfu+qqrmHgwuKvsucB9gF+BrwP6z1nkG8OZR17qV/XoEcBBwyTzLHw98msFvyB8GnD/qmndAnx4JnDnqOreyT/cADuqe7wX8xxx//8ZxXw3Tr7HaX92f/57d852B84GHzVrnOcBbuufHAB8cdd07oE9j9/03o/aXAO+b6+/ZuO2rIfu0zfuq1SPoiZwmtKq+CPx0gVWOAk6rgfOAuya5x9JUt22G6NPYqaqrq+rC7vmNwGX8+ix447ivhunXWOn+/Dd1L3fuHrMvrDkKeFf3/HTgsCRzTaTUhCH7NJaS7AscAbxtnlXGal/BUH3aZq0G9LDThD6pG148Pcm95lg+biZ1etSHd8N1n07ywFEXszW6IbaHMjiKmWms99UC/YIx21/d8OLFwLXAZ6pq3n1VVZuB64G9l7bKrTNEn2A8v//+AXgZcOs8y8duX7F4n2Ab91WrAT3MNKGfBFZX1UOAz3L7v7rG2VDTo46ZC4H9quoA4E3Ax0dcz9CS7Al8BHhRVd0we/EcHxmLfbVIv8Zuf1XVr6rqQAazFR6S5EGzVhm7fTVEn8bu+y/JE4Brq2r9QqvN8V6z+2rIPm3zvmo1oBedJrSqflJVN3cv3wocvES19Wmo6VHHSVXdsGW4rga/i985yT4jLmtRSXZmEGLvraqPzrHKWO6rxfo1rvsLoKquA84FHjtr0W37KslK4C6MyWmZ+fo0pt9/hwJHJtnA4LTlo5K8Z9Y647avFu3T9uyrVgN60WlCZ53vO5LB+bRxdwbw9O4K4YcB11fV1aMuansk+S9bziElOYTB37mfjLaqhXX1ngpcVlVvmGe1sdtXw/Rr3PZXkqkkd+2e7wYcDnxz1mpnAMd1z48GPl/d1TstGqZP4/j9V1Uvr6p9q2o1g+/0z1fV02atNlb7apg+bc++6nUmsW1V80wTmuTVwLqqOgN4QZIjgc0M/oX1jJEVPKQk72dwlew+Sa4EXsngAhCq6i0MZl17PPAd4Cbg+NFUOrwh+nQ08Owkm4GfA8e0/D9c51Dgz4F/784DAvwlsArGd18xXL/GbX/dA3hXkhUM/jHxoao6c9Z3xanAu5N8h8F3xTGjK3cow/Rp7L7/5jPm+2pOO2pfOZOYJEkNanWIW5KkZc2AliSpQQa0JEkNMqAlSWqQAS1JUoMMaGnEkuw940431yS5qnt+XZJvbMd2X5Lk1Bmvj01y1qx1Vie5MslOs96/uPsd9HzbfkaSN29rbZIWZ0BLI9bNNHRgN7XjW4C/754fyMLz+y7mjcDBSQ7tJr54DfD8WW1vYDD38R9seS/JA4C9quqC7Whb0nYyoKW2rUjy1gzuC3xON7MUSX47ydlJ1if5Uheqd9DdbOA5wMnA3zKY8OfyOdp4P3ecEOKY7j2S/HEG9+W9KMlnk9x99oeTvDPJ0TNeb5rx/P8k+Wp3o4ATu/f2SHJWBjfkuCTJk7flD0aadAa01Lb7ASdX1QOB64Ande+vBZ5fVQcDLwX+aa4PV9W/MZha8HAGIT2XDwFP7OY+Bngyg3mFAb7M4F7ED+3ee9mwhSd5TFf/IQxGAw5O8ggG80r/sKoOqKoHAWcPu01pOWlyqk9Jt7miqrZMy7keWN3djer3gQ/n9lvl3mmuD3frTjOYfnWKwc0I7qCqrklyKYN77/4IuKWqLukW7wt8sJtPeBfgiq2o/THd46Lu9Z4MAvtLwOuTvI7BDe6/tBXblJYNA1pq280znv8K2I3ByNd13XnqxZwIvAf4EfD3wJ/Os96WYe4fdc+3eBPwhqo6I8kjgVfN8dnNXU1bbsixS/d+gNdW1T/P/kCSgxnMZf7aJOdU1auH6Iu0rDjELY2Z7h7OVyT5UxiEYpIDZq+X5MHAEcDrGAyJ75fk0fNs9iMMAnPm8DYMbvd3Vff8uNkf6mzg9lvoHUV3sxQGN7t5ZncUT5J7Jrlbkt8Cbqqq9wCvBw5auMfS8uQRtDSejgVOSfIKBoH4AeBrWxZ2R7KnAC+uql907z0HOC3JgVX1y5kbq6rrkpwH3L2qZg5jv4rBUPpVwHnAveeo5a3AJ5JcAHwO+Fm3zXOS/C7wlW4ofhPwNOC+wN8luRW4BXj2dv1JSBPKu1lJktQgh7glSWqQAS1JUoMMaEmSGmRAS5LUIANakqQGGdCSJDXIgJYkqUEGtCRJDfr/XLH0+ypBRJUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To plot the points (1,2), (2,3), (3,6), (4,8) we would list the x values and the corresponding y values:\n",
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.bar([1,2,3,4], [2,3,6,8])\n",
    "plt.title('A Bar Chart')\n",
    "plt.xlabel(\"The X Values\")\n",
    "plt.ylabel(\"The Y Values\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "If the Y axis is probabilities (in the range 0 .. 1), we get a distribution of the probabilities among the outcomes of an experiment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the distribution of probabilities for a coin flip:\n",
    "x = [0,1]\n",
    "y = [0.5, 0.5]\n",
    "labels = ['Heads', 'Tails']\n",
    "\n",
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.xticks(x, labels)\n",
    "plt.bar(x,y)\n",
    "plt.title('Probability Distribution for Coin Flips')\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Outcomes\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a few tweaks, you can create an attractive bar chart for arbitrary probability distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fYFlVXV1VdwFnA4cMTlBV11TVZcC942dO8gTgN4EvdFijJEm91GXA7wqsGOhf2Q6bVJL7Ae8G/qKDuiRJ6r0uAz4TDKsh530FsLiqVqxroiTHJFmSZMmqVaumXKAkSX01s8NlrwTmDPTPBq4fct4nAU9J8grgQcDWSe6oqjUu1KuqU4BTABYsWDDszoMkSb3XZcBfAuyZZHfgOmAh8KJhZqyqI8a6kxwFLBgf7tLmZJfZc7nxunU2SAlgxlYkEzX+jc7Ou87hhpXLR12GNGWdBXxVrU5yLHABMAM4raqWJjkRWFJVi5LsA3wa2BF4dpK3VdVeXdUkjcqN161gt+POH3UZa7j2pINGXcJ93XO320naSLo8gqeqFgOLxw07YaD7Epqm+3Ut43Tg9A7KkySpt7yTnSRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST3UacAnOSDJVUmWJTl+gvH7Jbk0yeokhw4M3zvJ15MsTXJZkhd2WackSX3TWcAnmQGcDBwIzAcOTzJ/3GTLgaOAj44b/gvgJVW1F3AA8L4kO3RVqyRJfTOzw2XvCyyrqqsBkpwNHAJcMTZBVV3Tjrt3cMaq+sFA9/VJbgJmAT/tsF5Jknqjyyb6XYEVA/0r22FTkmRfYGvgRxOMOybJkiRLVq1atd6FSpLUN10GfCYYVlNaQLILcCbw0qq6d/z4qjqlqhZU1YJZs2atZ5mSJPVPlwG/Epgz0D8buH7YmZNsB3wOeFNVfWMj1yZJUq91GfCXAHsm2T3J1sBCYNEwM7bTfxr4cFV9osMaJUnqpc4CvqpWA8cCFwBXAh+vqqVJTkxyMECSfZKsBA4DPphkaTv7C4D9gKOSfLf927urWiVJ6psur6KnqhYDi8cNO2Gg+xKapvvx850FnNVlbZIk9Zl3spMkqYcMeEmSesiAlySphwx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphwx4SZJ6yICXJKmHOr0XvTQKu8yey43XrRh1GeqLGVuRZNRVrGHnXedww8rloy5D05wBr9658boV7Hbc+aMuYw3XnnTQqEvQ+rrnbt9P2izZRC9JUg8Z8JIk9ZABL0lSDxnwkiT1kAEvSVIPGfCSJPWQAS9JUg8Z8JIk9ZABL0lSDxnwkiT1kAEvSVIPGfCSJPWQAS9JUg8Z8JIk9ZABL0lSD3Ua8EkOSHJVkmVJjp9g/H5JLk2yOsmh48YdmeSH7d+RXdYpSVLfdBbwSWYAJwMHAvOBw5PMHzfZcuAo4KPj5n0I8Bbgd4F9gbck2bGrWiVJ6psuj+D3BZZV1dVVdRdwNnDI4ARVdU1VXQbcO27eZwIXVtUtVXUrcCFwQIe1SpLUK0MFfJJPJnlWkqnsEOwKrBjoX9kO22jzJjkmyZIkS1atWjWF0iRJ6rdhA/ufgRcBP0zyriSPHGKeTDCshlzfUPNW1SlVtaCqFsyaNWvIRUuS1H9DBXxV/UdVHQE8HrgGuDDJfyV5aZKt1jLbSmDOQP9s4Poh69qQeSVJ2uIN3eSeZCeaC+JeDnwHeD9N4F+4llkuAfZMsnuSrYGFwKIhV3cB8IwkO7YX1z2jHSZJkoYw7Dn4TwFfBR4APLuqDq6qc6rqlcCDJpqnqlYDx9IE85XAx6tqaZITkxzcLnefJCuBw4APJlnaznsL8HaanYRLgBPbYZIkaQgzh5zuQ1W1eHBAkm2q6ldVtWBtM7XzLB437ISB7ktomt8nmvc04LQh65MkSQOGbaJ/xwTDvr4xC5EkSRvPOo/gk+xM8/O0+yf5Hf736vbtaJrrJUnSNDRZE/0zaS6smw28Z2D47cAbO6pJkiRtoHUGfFWdAZyR5PlV9clNVJMkSdpAkzXRv7iqzgLmJXnd+PFV9Z4JZpMkSSM2WRP9A9t/J/wpnCRJmp4ma6L/YPvv2zZNOZIkaWOYrIn+H9Y1vqpetXHLkSRJG8NkTfTf3iRVSJKkjWqYq+glSdJmZrIm+vdV1WuSfJaJH9d6cGeVSZKk9TZZE/2Z7b9/33UhkiRp45msif7b7b8Xt498fSTNkfxVVXXXJqhPkiSth6GeJpfkWcC/AD+iuR/97kn+pKo+32VxkiRp/Qz7uNh3A39QVcsAkvwW8DnAgJckaRoa9nGxN42Fe+tq4KYO6pEkSRvBZFfRP6/tXJpkMfBxmnPwhwGXdFybJElaT5M10T97oPvHwFPb7lXAjp1UJEmSNthkV9G/dFMVIkmSNp5hr6LfFjga2AvYdmx4Vb2so7okSdIGGPYiuzOBnYFnAhcDs4HbuypKkiRtmGEDfo+qejPw8/b+9M8CHtNdWZIkaUMMG/B3t//+NMmjge2BeZ1UJEmSNtiwN7o5JcmOwJuBRcCD2m5JkjQNDRXwVfWhtvNi4OHdlSNJkjaGYa+i3wl4K/BkmhvdfBV4e1X9pLvStLnYZfZcbrxuxajLkLYcM7YiyairWMPOu87hhpXLR12GBgzbRH828BXg+W3/EcA5wB92UZQ2Lzdet4Ldjjt/1GX82rUnHTTqEqRu3XP3tPrMgZ+76WjYgH9IVb19oP8dSZ7TRUGSJGnDDXsV/ZeSLExyv/bvBTRPk1unJAckuSrJsiTHTzB+myTntOO/mWReO3yrJGckuTzJlUneMJUXJUnSlm6dAZ/k9iQ/A/4E+ChwV/t3NvDaSeadAZwMHAjMBw5PMn/cZEcDt1bVHsB7gZPa4YcB21TVY4AnAH8yFv6SJGly6wz4qnpwVW3X/nu/qprZ/t2vqrabZNn7Asuq6uqqGtspOGTcNIcAZ7Td5wL7p7lypIAHJpkJ3J9mp+JnU3xtkiRtsYY9B0+Sg4H92t4vV9VkV3jsCgxeWr0S+N21TVNVq5PcBuxEE/aHADcADwBeW1W3DFurJElbuqHOwSd5F/Bq4Ir279XtsHXONsGwGnKafYF7gIcBuwOvT3Kf398nOSbJkiRLVq1aNUk5kiRtOYa9yO6PgKdX1WlVdRpwQDtsXVYCcwb6ZwPXr22atjl+e+AW4EXAv1fV3VV1E/A1YMH4FVTVKVW1oKoWzJo1a8iXIklS/w0b8AA7DHRvP8T0lwB7Jtk9ydbAQprb3A5aBBzZdh8KXFRVBSwHnpbGA4EnAv89hVolSdqiDXsO/m+A7yT5Ek2z+n7AOn+61p5TPxa4AJgBnFZVS5OcCCypqkXAqcCZSZbRHLkvbGc/Gfg34Pvt+v6tqi6b2kuTJGnLNWnAt1e1/yfNUfQ+NIF7XFXdONm8VbUYWDxu2AkD3XfS/CRu/Hx3TDRckiQNZ9KAr6pKcl5VPYH7NrFLkqRpaNhz8N9Isk+nlUiSpI1m2HPwfwD8aZJrgJ/TNNNXVT22q8IkSdL6GzbgD+y0CkmStFGtM+CTbAv8KbAHcDlwalWt3hSFSZKk9TfZOfgzaG4wcznNUfy7O69IkiRtsMma6Oe3T3QjyanAt7ovSZIkbajJjuDvHuuwaV6SpM3HZEfwj2ufBw/NlfP3b/vHrqKf7JGxkiRpBNYZ8FU1Y1MVIkmSNp6pPGxGkiRtJgx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphwx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphwx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphzoN+CQHJLkqybIkx08wfpsk57Tjv5lk3sC4xyb5epKlSS5Psm2XtUqS1CedBXySGcDJwIHAfODwJPPHTXY0cGtV7QG8FzipnXcmcBbwp1W1F/D7wN1d1SpJUt90eQS/L7Csqq6uqruAs4FDxk1zCHBG230usH+SAM8ALquq7wFU1U+q6p4Oa5UkqVe6DPhdgRUD/SvbYRNOU1WrgduAnYDfBirJBUkuTfKXE60gyTFJliRZsmrVqo3+AiRJ2lx1GfCZYFgNOc1M4PeAI9p/n5tk//tMWHVKVS2oqgWzZs3a0HolSeqNLgN+JTBnoH82cP3apmnPu28P3NIOv7iqbq6qXwCLgcd3WKskSb3SZcBfAuyZZPckWwMLgUXjplkEHNl2HwpcVFUFXAA8NskD2uB/KnBFh7VKktQrM7tacFWtTnIsTVjPAE6rqqVJTgSWVNUi4FTgzCTLaI7cF7bz3prkPTQ7CQUsrqrPdVWrJEl901nAA1TVYprm9cFhJwx03wkctpZ5z6L5qZwkSZoi72QnSVIPGfCSJPVQp0302vh2mT2XG69bMfmEkrQpzdiK5j5l08fOu87hhpXLR13GyBjwm5kbr1vBbsedP+oy1nDtSQeNugRJo3bP3X43TTM20UuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST3UacAnOSDJVUmWJTl+gvHbJDmnHf/NJPPGjZ+b5I4kf95lnZIk9U1nAZ9kBnAycCAwHzg8yfxxkx0N3FpVewDvBU4aN/69wOe7qlGSpL7q8gh+X2BZVV1dVXcBZwOHjJvmEOCMtvtcYP8kAUjyHOBqYGmHNUqS1EtdBvyuwIqB/pXtsAmnqarVwG3ATkkeCBwHvG1dK0hyTJIlSZasWrVqoxUuSdLmrsuAzwTDashp3ga8t6ruWNcKquqUqlpQVQtmzZq1nmVKktQ/Mztc9kpgzkD/bOD6tUyzMslMYHvgFuB3gUOT/C2wA3Bvkjur6gMd1itJUm90GfCXAHsm2R24DlgIvGjcNIuAI4GvA4cCF1VVAU8ZmyDJW4E7DHdJkobXWcBX1eokxwIXADOA06pqaZITgSVVtQg4FTgzyTKaI/eFXdUjSdKWpMsjeKpqMbB43LATBrrvBA6bZBlv7aQ4SZJ6zDvZSZLUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMzR13AdLbL7LnceN2KUZchSVofM7YiyairWMPOu87hhpXLN8m6DPh1uPG6Fex23PmjLmMN15500KhLkKTNwz13b9Hf4TbRS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDnQZ8kgOSXJVkWZLjJxi/TZJz2vHfTDKvHf70JN9Ocnn779O6rFOSpL7pLOCTzABOBg4E5gOHJ5k/brKjgVurag/gvcBJ7fCbgWdX1WOAI4Ezu6pTkqQ+6vIIfl9gWVVdXVV3AWcDh4yb5hDgjLb7XGD/JKmq71TV9e3wpcC2SbbpsFZJknqly4DfFRh8FNvKdtiE01TVauA2YKdx0zwf+E5V/aqjOiVJ6p0unyY30TP6airTJNmLptn+GROuIDkGOAZg7ty561elJEk91OUR/EpgzkD/bOD6tU2TZCawPXBL2z8b+DTwkqr60UQrqKpTqmpBVS2YNWvWRi5fkqTNV5cBfwmwZ5Ldk2wNLAQWjZtmEc1FdACHAhdVVSXZAfgc8Iaq+lqHNUqS1EudBXx7Tv1Y4ALgSuDjVbU0yYlJDm4nOxXYKcky4HXA2E/pjgX2AN6c5Lvt3290VaskSX3T5Tl4qmoxsHjcsBMGuu8EDptgvncA7+iyNkmS+sw72UmS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPbIdFF8AAAdXSURBVGTAS5LUQwa8JEk91GnAJzkgyVVJliU5foLx2yQ5px3/zSTzBsa9oR1+VZJndlmnJEl901nAJ5kBnAwcCMwHDk8yf9xkRwO3VtUewHuBk9p55wMLgb2AA4B/apcnSZKG0OUR/L7Asqq6uqruAs4GDhk3zSHAGW33ucD+SdIOP7uqflVV/wMsa5cnSZKG0GXA7wqsGOhf2Q6bcJqqWg3cBuw05LySJGktUlXdLDg5DHhmVb287f9jYN+qeuXANEvbaVa2/T+iOVI/Efh6VZ3VDj8VWFxVnxy3jmOAY9reRwBXdfJiNtxDgZtHXcRmwO00HLfTcNxOk3MbDWc6b6fdqmrWRCNmdrjSlcCcgf7ZwPVrmWZlkpnA9sAtQ85LVZ0CnLIRa+5EkiVVtWDUdUx3bqfhuJ2G43aanNtoOJvrduqyif4SYM8kuyfZmuaiuUXjplkEHNl2HwpcVE2TwiJgYXuV/e7AnsC3OqxVkqRe6ewIvqpWJzkWuACYAZxWVUuTnAgsqapFwKnAmUmW0Ry5L2znXZrk48AVwGrgz6rqnq5qlSSpb7psoqeqFgOLxw07YaD7TuCwtcz7TuCdXda3CU370wjThNtpOG6n4bidJuc2Gs5muZ06u8hOkiSNjreqlSSphwz4DiWZk+RLSa5MsjTJq0dd03SVZEaS7yQ5f9S1TFdJdkhybpL/bt9TTxp1TdNRkte2n7fvJ/lYkm1HXdN0kOS0JDcl+f7AsIckuTDJD9t/dxxljdPBWrbT37Wfu8uSfDrJDqOscVgGfLdWA6+vqkcBTwT+bILb9arxauDKURcxzb0f+PeqeiTwONxe95FkV+BVwIKqejTNBb4LR1vVtHE6za2/Bx0PfLGq9gS+2PZv6U7nvtvpQuDRVfVY4AfAGzZ1UevDgO9QVd1QVZe23bfTfCF7R75xkswGngV8aNS1TFdJtgP2o/nlCVV1V1X9dLRVTVszgfu399Z4ABPcQ2NLVFVfofm10qDB24WfATxnkxY1DU20narqC+3dVgG+QXNvlmnPgN9E2ifl/Q7wzdFWMi29D/hL4N5RFzKNPRxYBfxbeyrjQ0keOOqippuqug74e2A5cANwW1V9YbRVTWu/WVU3QHNAAvzGiOvZHLwM+PyoixiGAb8JJHkQ8EngNVX1s1HXM50kOQi4qaq+PepaprmZwOOBf66q3wF+js2p99GeQz4E2B14GPDAJC8ebVXqiyR/RXPq9SOjrmUYBnzHkmxFE+4fqapPjbqeaejJwMFJrqF54uDTkpw12pKmpZXAyqoaawE6lybwtaY/BP6nqlZV1d3Ap4D/M+KaprMfJ9kFoP33phHXM20lORI4CDiiNpPflxvwHWoffXsqcGVVvWfU9UxHVfWGqppdVfNoLoa6qKo84hqnqm4EViR5RDtof5o7PWpNy4EnJnlA+/nbHy9GXJfB24UfCXxmhLVMW0kOAI4DDq6qX4y6nmEZ8N16MvDHNEel323//mjURWmz9UrgI0kuA/YG/nrE9Uw7bQvHucClwOU033Gb5V3INrYkHwO+DjwiycokRwPvAp6e5IfA09v+LdpattMHgAcDF7bf4/8y0iKH5J3sJEnqIY/gJUnqIQNekqQeMuAlSeohA16SpB4y4CVJ6iEDXtoCJJmd5DPtU8N+lOT9SbaeZJ43bqr6JG18BrzUc+0NXz4FnNc+Ney3gQcB75xkVgNe2owZ8FL/PQ24s6r+DaCq7gFeC7wsySuSfGBswiTnJ/n9JO+ieSLbd5N8pB33kvZ52N9LcmY7bLckX2yHfzHJ3Hb46Un+OcmXklyd5Kntc7avTHL6wPqekeTrSS5N8on2uQ0keVeSK9rl/v0m2k5Sr8wcdQGSOrcXsMbDfKrqZ0mWs5bvgKo6PsmxVbU3QJK9gL8CnlxVNyd5SDvpB4APV9UZSV4G/AP/+8jRHWl2Lg4GPktzZ8eXA5ck2Zvm/vpvAv6wqn6e5Djgde0Ox3OBR1ZVJdlhI20HaYtiwEv9F2CiW1aubfhEngacW1U3A1TV2POynwQ8r+0+E/jbgXk+2wb05cCPq+pygCRLgXk0z9SeD3ytOYvA1jS3CP0ZcCfwoSSfA84fskZJAwx4qf+WAs8fHJBkO2AOcBtrnqrbdi3LGHZnYHCaX7X/3jvQPdY/E7gHuLCqDr/PypJ9aR4UsxA4lmYHQ9IUeA5e6r8vAg9I8hKAJDOAdwOnA1cDeye5X5I5wL4D893dPu54bBkvSLJTu4yxJvr/oglhgCOA/5xCXd8Anpxkj3aZD0jy2+15+O2rajHwGpoH60iaIo/gpZ5rm8mfC/xTkjfT7NgvprlK/i7gf2ievPZ9mqewjTkFuCzJpVV1RJJ3AhcnuQf4DnAU8CrgtCR/AawCXjqFulYlOQr4WJJt2sFvAm4HPpNkW5qWg9eu3yuXtmw+TU6SpB6yiV6SpB4y4CVJ6iEDXpKkHjLgJUnqIQNekqQeMuAlSeohA16SpB4y4CVJ6qH/DxqtgC1UQ8bMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show the distribution of probabilities for flipping two dice\n",
    "x = [k for k in range(2,13)]\n",
    "y = [1/36,2/36,3/36,4/36,5/36,6/36,5/36,4/36,3/36,2/36,1/36]\n",
    "\n",
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.bar(x,y, width=1.0,edgecolor='black')\n",
    "plt.title('Probability Distribution for Tossing Two Dice')\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Outcomes\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Histograms\n",
    "- If you give a list of values to <code>hist(...)</code> it will create a histogram counting how many of each value occur; this list can be unordered;\n",
    "- You will get a cleaner display if you specify where the edges of the bins are, and make sure the edges of the bins are visible, as shown in this example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(num=None, figsize=(8, 6))\n",
    "plt.hist([1,2,4,2,6,2,4,5,6,4,6,3,4,3],bins=[0.5,1.5,2.5,3.5,4.5,5.6,6.5],edgecolor='black')\n",
    "plt.title('Sample Histogram')\n",
    "plt.xlabel(\"Outcomes\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Customizing Your Plots\n",
    "\n",
    "One thing you have probably noticed is that when you write \"bare-bones\" code such as we have above, certain\n",
    "defaults are used for the size and layout of the figure and the style of the drawing. One of the most noticable is that when you draw multiple lines, Matplotlib will change the color each time you call the same function (notice that this doesn't happen when calling a different function, e.g., plot followed by scatter). \n",
    "\n",
    "## Using Colors\n",
    "\n",
    "Matplotlib cycles through a sequence of 10 colors, which is fine if that is what you want. For my taste, they are pretty ugly, and in the next section we will show you how to use the colors you want. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The 10 Matplotlib color sequence, starting at 12 o'clock and going clockwise:\n"
     ]
    },
    {
     "data": {
      "image/png": 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tZHbL3zE9XluFqCHQUoj206dRvuZLoS3+kbnQBQU1cQchrRcFW4Qo4Nprr4XZbL507XA4sH37ds3Gwxjzmd3SJJUoKZI/2V6K5APgmJ5ASyGWvPEm4G7ca83UvTsib7tNwxERohwKtghRQFBQEMaNGye07d27FxVey9vVFgipxHZbJO9THK9usCVNITIwTVOIdVlZqPxBPM0gfv48MK/FJYS0JRRsEaKQ4cOHIzw8/NK12+3G1q1bNRuP/1RiuqpjSDG30yJ5jbd9CLSNTC1pS4XroL59Ef6rX2k0GkKUR8EWIQoxGo2YMGGC0JaZmQmr1arJePynEtU9K1G6IrFdzGxxrnkaMZBSiLbMTFRnZAht8fPngeno44i0XfTbTYiChgwZgujo6EvXHo8HGZIPGjUlJIpbQKidSkyWrEjMtdnh8nDV+tdEdTFQ55U+NpqBiC6qdR9IKUTOOSyvpQltIYMHI2ziRE3GQ4haKNgibQ7ngfPhrdfrMWnSJKHt8OHDKCoq0mQ84WH9NU0lRhoNSDQ11uU4OUdeXRtPJfqcidgHUHEWZ/0Z8XgeLVOItl27YJNs8hv/2GPCIe5aC6T3D9J2ULBF2gzu5qhYexrlX+ZoPRTBgAEDkJCQILRt3qz+Du5AYKQSk9vbsT0a12tJz0LUKoXIOUexZFYrdPRohI4aqcl4/OEejrX/PorMDWcp6CKyomCLtAmuCjss7x1GVUYBavZegO2nYq2HdIlOp8PkyZOFtqysLBQUFGgyHq1Tie1uJ3kNj+kJpBRi9aZNqDtyRGiLf2yBJmNpyk8b85H7kwU7v8jBD28fRl21tueakraDgi3S6nHOYf0sC468ykttZWty4LTYLnOXulJSUtC5c2ehLT1d3ZWAF2mdSmx3RfIazmwFSgqRu92wLBVXIIZPvR4hAweqPpamXMitwO6vfr50nXekFBmfZl3mDkKuHgVbpNVjjCHq1l6AobHugzvcsH6WBe4MjONgGGOYMmWK0Jabm4vc3FxNxqJlKlFaJN/u0ohx6q1EDJQUYuX338N+yiu9zxji583TZCz+1NU4sf79Y/B4LdYIMhswemZvDUdF2hIKtkibYOoUhqibewptzvM1KP9e/WCmKT179kSPHj2EtvT0dE1qQ7RMJUpntnJsdfC01foYmxWo8Upp601AdJIqXftLIU7tPlWVvr1xhwOWN94U2iJn3IKg5GTVx+IP5xzpH59AlVUM+if/LhURcSEajYq0NRRskTYjdFRHhAyME9pqdp+H7bBFoxH5ks5uFRQUIDs7u4lXK0fLVGKc0YBog/7Sda2HI7/OoUrfqpPOasUmA3p1dkn3l0JMMCc08WrllK9ZA2d+fmODwYC4Rx9VfRxNOZxegNOHSoS2QZO7oOfgeI1GRNoiCrZIm8EYQ/TMZOhjxJmTsi9OwVVaq9GoRF26dEFKiphGSk9Ph8ejbrqTMeYzu6VWKpEx5lu31VZTiRoWxwdCCtFTV4eSt98R2qLumAlT166qj8WforxK7Fwjrl5O6B6O0bdT+pDIi4It0qbogg2IvbsvoPeq37K7UfpZFrgrMOq3pPtuFRUV4dixY028WjlanpXosyLR1kZXJGpUHJ9flR8QKcSyzz6Hq7gxjcqCghD3pz+pPg5/7DYn1r9/FB53YwrbFKzHtAcGQG+gj0YiL/qNIm2OqUs4om4Ua6Oc56pR8cNpjUYk6tChAwZKVmFt3rwZbrdb1XFomUpsN0XyGh3T4+8sRLVTiO7qapQuWya0Rd9zD4yJ2p3JeBHnHJs/yUJliW+dVmQ81WkR+VGwRdqk0NGdENI/Vmir3lmI2qMlTdyhrokTJwq7ZlutVvz000+qjkHLVKLvzFZbDbYk9XgqrUQMhBSi9b8fwV1efulaFxqK2AcfUH0c/hzdcg4/Z4q1nAMndEavoerXtJH2gYIt0iYxxhB9Rx/oo8UZFOvqbLis2n+wx8bGYujQoULbli1b4HSqu4miVqnEPn52kW9zO3bbq4BKr41rmR6I7aV4t4GQQnSVlcH64YdCW8x998HgdU6oVixnq7B99SmhLa5rGEbfQXVaRDkUbJE2SxdiQOzdqWL9Vp0bpZ+dCIj6rfHjx0Ovb1yVV1lZif3796s6Bq1SiR2DjAjTN779VLk9uOBoY7t1l0hmtWJ6AIYg/6+VUSCkEEvfex+emppL1/qoKMTc+3tVx+CPo9aFte8dhcfVGNgbg/WY/uAAGIz6y9xJSMtQsEXaNFPXcET+SlK/VVCNirV52gzIS2RkJEaOFM+F27ZtG+x29YrFtUolMsZ8zkhsc8f2aFQcvy5vnXCtdgrRWVSEsk8/FdpiH3oI+rAwVcchxTnH5k+zUGkRVyZP+k1fRCWYNRoVaS8o2CJtXtjYTghOjRHaqrefQ+3xUo1G1Gjs2LEwmUyXrm02G3bv3q3qGLRKJSaHSork21rdlgbF8flV+TheevzStRYpxJJ33gH3+sJgSEhA9N13qToGf45tK0TOfvHM1P7jOiF5uPYF+6Tto2CLtHmMMcTc2Qf6SEn91qpsuMq0/YAPDQ3FddddJ7Tt3LkTNpt65zqGh/VHSIj6qUR/dVttigbF8VqnEB1nz6J89RdCW9zcudAFBzdxhzpKCqqwfaVYpxXbOQxj7wyMXexJ20fBFmkXdGYjYu7uK/zG81oXrJ9ngbu1rd+67rrrEOz1YWS327Fjxw7V+q8/K1H9VGKb39hUg5ktrVOIljffBFyuS9fGrl0RNfN2Vccg5ahzYd17x+D2qtM0BOkx/cH+MJioTouog4It0m4EdY9A5PQkoc1xtgoV689oM6AGwcHBGDt2rNC2Z88eVFWps8Eo4JtKLC1VPpXoE2y1pTSisxYo9/69YkCcsrvHa51CtJ86hcpvvxPa4v/8KJjRqNoYpDjn2PL5SZQXiTPFE+9OQXSHUI1GRdojCrZIuxI2rguCU8Tl59VbClCbZdVoRPVGjhyJMK8CYpfLhW3btqnWvzSVyLkDlpJNivbZNdiEYJ3XXmNON0ocrsvc0YqU5gDca8Y0qitgUrYIW+sUouX11wGv7TuCknsj4qabVOvfnxM7zyN7T5HQljq6I1JGddBoRKS9omCLtCtMxxA9KwX6CJPQXrbyJFwV2q2GM5lMGD9+vNC2f/9+lJWVqdK/v1RicfGPivapZwy9pSsS28rslgYrEbVMIdYeOYKqDRuFtvj588H02qXpSgursW25WDcX0ykU4+aodz4lIRdRsEXaHX2oETF3ifVbHtvF+i3tNtYcOnQooqKiGsfk8WDLli2q9a9FKrHNHtsjDbbaeArR8lqacB08cCDCpkxRrX8pp92NdcuOwuX0qtMy6TD9gQEwUp0W0QAFW6RdCuoRiYip3YU2R14lKjdqV79lMBgwceJEoe3QoUOwWCz+b5CZFqnENntsj09xvLIzW9LjedRMIdbs3oOanTuFtoTHFgjHUalt6/KTKLsg1mmNn5OCmE5Up0W0QcEWabfCJ3RFUHKU0FaVkY+6bHVSd/4MGjQIcXFxl64559i8ebMqfWuRSpRubNpmZ7aUDrbOaHMWIuccljRxVss8ahTMku1M1JS1+zyydl0Q2lKu7YDU0R01GhEhFGyRdozpGGJmp0AX7lW/xQHripNwV2pTv6XT6TB58mSh7fjx4ygsLFSl/0RJsKV0KtF3ZqsN7CLvdgLWn8W2eOXSiFqmEKszMlArOUA9fsF8zWa1rOdrsOUzMdCN7mDGeKrTIhqjYIsoas9Xq7BjxScBe8iwPsyEmDkpgNdng6fGCevyk+AebcacmpqKjh3Fb+Hp6cpvMgoAYWH9VE0l9ggJgsHrz/683YlKl1ux/lRhzQU8XqsqwzsCwZGKdadVCpF7PLCkLRXawiZNgnnIEMX79sfpcGPde0fhcjTWaemNOkx/cABMwQZNxnQl3OPB+mVv4GjGxiu/mLRqFGwRxRz4/its//wj7F6zAls//TBgA67gXlGImNJNaLPnVqBy01lNxsMYwxRJcXFOTg7OnFG+nkztVKJRx9AjRCySP9XaU4k+KURlNzOVphCnJ01XtL+LKn/8EfaT4r9r/Px5qvTtz/YV2bAW1ght42f3QWxnbc9kbIrH48bad9JwZNM6rHt3KU5sz9B6SERBFGwRRRza8CMyPn7/0vX+b9cg46P3AjbgCp/cDUG9xNmHqvSzqMvRpn6rV69e6N5dLODftGmTKn9+WqcSW/3mpj4rEZULtrRKIXKXCyWvvyG0Rdx4I4L7qnPYtlT23gs4vuO80JY8IhGpYwKzTsvtcuGHN/6J41sbZqw5x49v/Qun9u3SdmBEMRRsEUUkJPVEkFlc+XPwx2+w6YO3wT3aHo/jD9MxxMzpC12Y127XHLAuPwl3lUP98TDmU7t19uxZ5OTkKN632qnENndGoorH9PhLIcab4xXr76KKr76Cw3umVa9H3J8fVbxff8qLbMj4VAxwIxNCMPGeFE1XRDbF7XLi+6V/w8mdW4X20MgoxHbuqtGoiNIo2CKK6JicgjufeQnBYeFC+6ENP2L9sjfg8QReXY4+3ISY2ZL6rWonrCu0qd/q3r07kpPFg3I3bdoEj8LBan0qUdz5W8lUou8Zia28SL5EvTSiFilEj90Oy1tvC21Rt/8aQT16KN63lMvpxtr3jsJpb3w/0RsCt07L5XTim3+9jFN7xa0ywuPiMXvRq4jp1EWjkRGlUbBFFJPYszdmPbsEIRFieu7o5g1Y93YaPO7AC7iCk6MRPkn8dmnPKUfV5nxNxiOd3bpw4QJOnDiheL+JKm5w2qb22vK4gZJTYptC2z5olUIsX7ECrvONKTtmNCJu7lzF+/Vnx6oclBZUC21j7+yN+K7hTdyhHafDjq//8SJyD+wV2iMTEjFn0auI6hCYKU8iDwq2iKLiu/fA7OdehjlS3M/q+LbN+OGNf8DtCryz8CKmdIepR4TQVrnxDOy55aqPpWPHjujfv7/QtnnzZrgVDlTVTCX2DAnynkxEfp0DNnfgpZqvSvkZwOUVLJpjgdC4pl/fAtIU4tDEoYqnED01NSh5999CW/Tdd8HYUf1A4dT+Ihzdek5o6zU0Af3Hd1Z9LFfirKvDV68+j7yfDgjt0R07YfaiVxERr94ZlkQbFGwRxcV26YbZi15BWHSM0H5y1zZ8l/Yq3C6nRiPzj+kZYuf0hS7UKw3BgdLlJ+GuVr9+a9KkSULtSUlJCQ4fPqxon/5TiT8o0leIXofuIY17nXEAP7fW2S2LeBafksXxPhuZdld+I1PrJ5/AbW08tJ2ZzYh96CHF+5WqsNiw+f/E2riIuGBM+m3fgKvTctTasOaVRTh79JDQHtOpC2Y99wrCY5UJxklgoWCLqCKmUxfMXvQqwuPEb945+3bhm38ugcsZWAGXPjIIMbPED0pPpQPWldmq12/FxcVh8ODBQltGRgZcCs8K+qYStymXSmwrRfIqFcdrkUJ0l5ej9IP/CG0xv/8dDLGxivbrMw6nB+veOwZnXePsrs7AMP3BAQgKCaw6LbutBquXPIuCE0eF9riu3THruZd9voCStouCLaKaqA4dMWfRq4hMSBTacw/uw9d/fwFOR2AVRgenxCB8oliwas8uQ9XWAtXHMmHCBOj1jQfoVlRU4MCBA5e5o+XUTCUm+2z/EFi/C1etRDKzpVC9lhYpxNIP/gNPVWOwrYuMROx99ynapz871uTAclYM+sfM7I2E7hFN3KGNuupqrH7xaZzPFgPw+KSeuPPZJQiNitZoZEQLFGwRVUXEJ2D2olcR3bGT0J536CC+enUxnHWBNaMRMTUJJsmbeOX6PNjzKlQdR1RUFIYNGya0bd26FQ6HcmlNNVOJ0pmtVruxqc/MljLHxKidQnRZLLB+8onQFnv//dBHqBvg/JxZjCObxS87PYfEY+DEwFrFZ6uswKoXnsKFn8XFEh16JWPWM0tgjlDuRAESmCjYIqoLj43DrOde8VnmfPboYXzx8nNw1No0GpkvpmeIuasvdGav9IQHsH6eBXeNuqnPcePGwWhs3AespqYGe/bsUbRPtVKJyaHiLvKtcmNTzn1rthSY2dIihVjy7r/Bvb4I6ePiEPObexTtU6qypBbpH4vBbHhsMN8YW0QAACAASURBVCYHWJ2WraIcq154CsV54vmYHfv0xR1Pv4jgsMDc0Z4oi4Itoomw6BjMeu5lxHUVd0k/l3UMq5c8C7utpok71WeICkK0pH7LXeFA2Sp167fCw8MxatQooW3Hjh2ora1VrM/6VGLj3xHnDlgs8p/jJp3ZOl1rhyMAN7+9rMpCwOEViJrC689FlJnaKUTnuXMoW7lSaIt7+GHozGbF+pRyuzxY995ROGob6xR1eobpDwxAkNl4mTvVVV1mxYrFT6DkbJ7Q3iV1AO548nmfjZ5J+0HBFtFMaFQ07nx2CeKTegrt57OzsPrFp1FXXd3EneoL6RuDMMmS8rosK6q3n2viDmWMGTMGQUGNs0B1dXXYtUu5Iz78npVokX+D0zCDHp2DGj803RzIrW1ldVv+iuMVmHFZl7dOuFY6hWh5623AawGLsVMnRM26U9E+pXZ9+TOKz4gzqtf9uhcSewROnVZVaQlWLl4I6zlxT75uAwbh9oWLYApRLzglgYeCLaIpc0QkZj2zBB16iTulX/j5FFa+8CRslerWRl1O5PQkmLqJmyVWrM2D/WylamMICQnBmDFjhLZdu3ahWsHAVLVUos+KxFYWbKlQHJ9flY8T1sZNbZVOIdpzc1Hx1VdCW9yjj0JnMjVxh/xOH7Lg0CYxgEkaFIdrpgTO0TaVlmKsWLwQZecLhfakwcNw2+PPwRgc3MSdpL2gYItoLjgsDHc8/SI69UkV2i15uVj1/JOoKdfmMGgpptch5q6+YN7HgHg4rJ9lwWNTr35r1KhRCA1tTEc4nU5s375dsf5USyVKd5JvbUXyKhTHq51CtLz+BuCVzjX17InIGbco1p9UZWktNn0knpgQFh2EKb9PDZg6rfIL57F80eOoKLogtPccNhK3/uVpGE1BTdxJ2hMKtkhACDKHYuaTi9EldYDQXpJ/BisXP4Fqa6lGIxMZooMRc6c4C+cut8O6Khucq1O/FRQUhHHjxglt+/btQ3m5Mjvcq5VK9DkjsbUVyVukZyLKP7OlZgqx9tgxVK1dK7TFz5sHZlBnLyu324P17x+D3dZYp8V0DNMeGIDg0MCo07IWFmDF4oWoKrEI7ckjR2PG/zwBgzEwxkm0R8EWCRimEDNuX7gI3QYMEtovvqFVSt7QtBLSPw5hY8StK+pOWFG9o7CJO+Q3fPhwRHgtu3e73di6dati/amRSkw2S1YktqaZLc59Z7bi5J3ZUjuFaFm6VLgO7tcP4dOUP3vxoj1f56LotJiiv/bWnujYKzC2TSgtOOv3i2DK6PG4af5foTdQoEUaUbBFAooxOBi3Pf4ckgaLe0qVXziPlYsXoqK4SKORiSJv6AFjF3EJd8WPp+HIV2aHdSmDwYCJEycKbZmZmSgpKVGkPzVSidKNTXNr7XCpvFt/s9WUALVe6W5DCBDVrenXN4OaKUTb/v2o2bpNaIt/bAGYTp2PjLwjJchcf1Zo69Y/FkOmyvtn2lyWM6exYvETPiUO/cZNwo1//l/oVZr9I60HBVsk4BhNQbj1L0+j57CRQntFcRFWLF6I8gvnNRpZI2bQIfauvmBBjbu6w81R+nkWPLXqHK59zTXXINbrqBTOOTIyMhTpS41UYozRgDhj44eU3cNxtk79syibxWdWKxnQ6f2/tpmkKcTpSdNlff5FnHMUv5YmtIUMH4bQsWMV6U+quqwOm/4r1mmFRgXh+vtSwXTa12kV5eZg5fNPolayeGfApGmYPncBdDL/vZO2gYItEpAMRiNm/M8TSB45WmivKrFgxaLHYS1U/8gcKUNsCKLvEFNFbmsdyr5Qp35Lr9dj0qRJQtvRo0dx4cKFJu5omURJsKVEKtGnbqu1pBJLpPVa8p6JmF+pXgqxZvt21EqOgkpYsECVgnSP24P1HxxDndeGwUzHMO3+/ggJU28FZFPO55zEqhefQl21+Ht/zdQbMe2hRynQIk2iYIsELL3BiJvm/xUpo8cL7dVlVqxYtBClBWebuFM95oFxCL1O3Liy9mgpanarM/vWr18/JCaKZ02mp6cr0ldYWKriqUSfFYmtpUjepzhe3mBr3RlxVmto4lDEhcTJ2gdQP6tlkcxqhY4bB/Pw4bL35c/eb0/jfI44YzTylh7olBylSv+Xcy7rOFa/+DTsNeKGy0NvmIEp9/9JtRQraZ3ot4MENL3BgBv//L/oN06cwbFVlGPF4idgOXNao5E1irqxJ4ydxJ2hy7/LheOc8puy6nQ6TJkyRWjLzs5Gfn5+E3c0nxqpRGmR/MnWMrOl8EpEab2WUinEqvUbUHf8uNAWP3++In1JnT1eigPrzghtXfvFYNj07k3coZ7840fwxZJn4ZCc1jBixkxM/P2DAbMNBQlcFGyRgKfT6TF97gIMmCQuc6+trMDK559EUW6ORiOrx4w6xN6d6lu/9dkJeOqUr99KTk5G167iBo+bNm1SJJWpdCoxpa3MbMXJN7OlVgqRu90+KxDDp09HyID+svclVVNux8YPjwNev7LmSBOuv7ef5nVaZw7/hDUvL4LTLv4uXjtzDsbdfS8FWuSqULBFWgWdTo9pDz2Ka6aKH/Z11VVY9cJTOH/qZBN3qsMQF4Lo2yX7b5XWoWzNKcXrtxhjPrNbeXl5yM3Nlb0vpVOJ0l3kT9ns8Ki0f1mz1ZYD1V51cjojENNDtserlUKs+OZbOLx/Z3Q6xM/7s+z9SHk8HBv+cwy1VV51WgyY9of+MEdoW6d1OnM/vvzbYrgc4mkGY2b9BmNm/YYCLXLVKNgirQbT6TDl/j9h6A0zhHa7rQarX3oaBVnHNBpZPfM18Qgd1UFoqz1cgpq9yhSse0tKSkKvXr2ENiVmt/ymEot/kO35CSYDIg2NM4Q2twfn7Ortzt8s0mN6YnsBevn2WFIjhehxOFDyxhtCW+SttyJI8julhH3fn8a5bHFD3hE390DnlGjF+76cnP178PU/XoTbKf7+jbv7Xlw7c45GoyKtFQVbpFVhjGHi7x/EiBkzhXZHbS3WLHkO+ccOazSyelE394Sxg6R+69uf4ShUvn5r8uTJwnVhYSGysrKaeHXz+aQSrdtlSyUyxtBHOrsV6HVb/g6glolaKcTyVavgLPTalNdoRNwjj8jej1R+lhX7f8gT2jqnRGPYDUmK93052bu349t/LYHbJZYBTPzdgxh56x0ajYq0ZhRstXNHMgqw/4c8eFrL5pGo/0D29+3Saa/DmlcW48zhnzQaGcCMesTc0xfM5PWflqvh/ES7svVbnTt3RmqqeL5keno6PF5n28lB8VRiaCvbSV7B4nhpCnFY4jDZU4gemw0l77wrtEXPmgVTl86y9iNVU2HHhv+IdVoh4UZM/UM/6DSs0zqxYwu+W/o3eNxuoX3K/XMx7KZbNRpV83CnB+Xf5cJ2RJnNjsnVo2CrHSstrMaO1TnY800uvvrXQVSW1F75pgDBGLtUN+HN5bDjy78tRm7mPo1GBhjjzYj6tVi/5SqpRfmXOYrXb0n33bJYLDhy5IisfTDGfGa35EwlSme2Av6MRJ/iePmO6ZGmEKclyX8WovXTT+H2OnmABQcj7uE/yt6PN4+HY+OHx1Fb6bVpLQOm/qE/QiO1O7j52JZN+PGNf4J7f0FhDNP+OA+Dp93Y9I0ByHmhBsVvZaJ6+zmUrTkFd4X9yjcRxVCw1U65nR5s+OA43K76N5XzORVY8eJenNyjfH2RnK6dOQfj77lPaHM7nfj67y8hZ99ujUYFhA5JgHm4uP+V7ScLbPuVPW4oISEBgwaJZ0tmZGTA5ZJ3Vk1atyVnKtFnr62aAP+QUGhmS40UoruyEqXvfyC0xfz2NzDEK3MM0EUH1+ahIEs86mb4DUnomhqjaL+Xc3jTOqx9Jw2cNwZajOlww9zHMHCycgd+y417OKq2n0PRm5lwXrDVt9W6YF2VDd6KMhhtDQVb7VR5sQ22SvFDzFHnxsYPj2P9B8dgtwV4UbKXETNmYtLvHxTaPG4Xvn3tZWTv3q7RqICoGb1gSDQLbeXf/AxnUU0Td8hj4sSJ0HltsFhWVobMzExZ+1AylSg9IzHbVqfKjvzN4qgBKrw212U6ILa3LI9WI4VY+uGH8FQ0biKqCwtD7P33y9qH1LnsMuz9Vtwfr1NyFEbclKRov5eTue47bFj2Rv2B4g2YTle/x9/4yZe5M7C4Kx0o+e8xVHyXC7jE/2ZcJbVwV7aS46/aIAq22qnYzmGY/fRIdOsf6/OzU/uKsPzFvTiXXebnzsA09MZbMeX+uUKbx+3Gd0v/hhPbMzQZk86kR+zdfcGMjf+ZcacHpZ+egMfhvsydLRMTE4OhQ4cKbVu3boXTKV8ArWQqsXOQEWZ9459ZhcsNi0Od8yZ/MelKxOgkwBjs96W/lNIpRFdpKawffSy0xd7/B+ijlNutvbbKgQ0fHPOOaRAcZsTUP/SHTq/Nx9GB779C+n/EmjWdXo+bFzyOvmMmaDKm5qg9VoKitAOw+3nfNg+OR+KCoTBEaZeibe8o2GrHQiODcPOjgzBudh/ojeKvQrXVjq9ey8SuL3++lGoMdIOn3Yhpf5xXv0lPA+7x4Ic3/4ljWzZpMiZjYiiibhVnOlzFtSj/+mdF+x0/fjwMhsZDnauqqrBvn7x1bP5SiU5nZYufq2MMvSU7yQds3VYrTiGWLnsP3Ga7dK2PiUH0b38nax/eeEOdVk2FOLty/X39EBatTRCw9+vVyPj4faFNbzBgxv8+iT6jxmgypl/K43CjbM0plH5yAh6b+KWEBekRMycFMXP6QhdsaOIJRA0UbLVzjDEMmtQFdz4xHLFdwsQfcuDgujP44m8HUHZB2dSXXAZOnoYb5j4Gxrx+tTnH2nfScHjTWk3GFDo8EeahCUKb7UARag4oV78VERGBkSNHCm3btm1DXZ18QYu/VGJJiTypRGmRfMAe26NQcbzSKUTn+fMo+/xzoS3ujw9BHxbaxB0td3D9GZw9bhXahk7vju5+ZtfVsOuLz7Hts/8KbQajCbf+v2fQa9goTcb0Sznyq1D8eqbfvfxMSRFIXDAU5sEJfu4kaqNgiwAAYjuF4c7Hh2Pw1G4+P7OcrcLKl/bh6NZzgVs746Xf+Mm4cd5fxINhOceGZW8ic913mowp6tbeMMSHCG3lX+XAWWxr4o6WGzt2LEymxh24a2trsXu3fIsG/KcS5Tkr0ffYngAtkldoZkvpFGLJ2++AOxpnmAwdOiBqjnIbdRbmlGPPN2KdVsdekRg1Q76d9q8W5xzbl3+CnSs/FdoNpiDc9viz6DF4mOpj+qW4h6My/SyK3zkEl3QVuY4hYnoS4h8aBEO0PClt0nIUbJFL9EYdxszsjRkLBiNUktt3OT3Y8tlJ/PDOEdRWBX6RZd/R43HLgoXQ6fVCe/p/3sWB779SfTy6ID1i70kFDOrVb5nNZowePVpo27lzJ2pq5JulVCqVKD22J2D32iqRBlst39BU6RSiIy8P5WvWCG1xj8yFLkiZVF5dtbO+TstrJVxQqAFT71e/Totzjq2ffog9X64Q2o1Bwbj9iUXoPnCwquNpDldZHSzLDqNy/RlAsrrQEBeChLnXIGJSV83PlCQiCraIj659YzDnmZHoNdR3+Xfe4RJ8/sJenDlaqsHIfpnkUaMx43+fhN4g1ipkfPw+9ny1SvXxGDuEInqGePyJq8iGim/lP8Pwouuuuw5mc+OKSIfDgR07dsj2/PpUYtKla7lSidLtHwIy2HLZAavk706GNKLSKUTLG28CXht2mrp3R9Rtt8n2fG/cw7Hxo+OoLhNnJq+/tx/CY9SddeGcY/NHy7D/WzHQNIWYMfOpF9C130BVx9MctsxiFKUdhCPP9wtN6MgOSJg3BKYu4RqMjFwJBVvEr+BQI6Y/OACTf5cKY5A4O1Rb6cB3bx7C1uXZcCm4qk4OvYaNwq3/7xkYjOKBtts//wi7Vn+uelrUPCIRIYPFILZm3wXYfipWpL+goCCMHTtWaNu7dy8qK1s++wRcTCXeILTJkUrsFmxCkNc38xKnC1ZngK1ILM0BvPZkQmRXICis6ddfJSVTiHVZWaj8/nuhLW7en8GM8p3l6O2njfk4c0T8YjZ4ajckDZT/IO3L4R4PNn3wNjJ//FZoDwoNxZ1Pv4jOKalN3BkYPLUulH6eBeuKk+B28T1XF2pA7G/7Ifr2ZOhM+iaeQLRGwRZpEmMMqaM7YvbTI5DYI8Ln50cyCrDy5f2w5MuzmaVSegwehtsefxYGk5gm2bnqU+xY8YmqARdjDNG/7g1DnFi/VbYmB06LMvVbI0aMQHh447ddl8uFrVu3yvZ8JVKJBh1DzxDx7yvgzkj0qdcK/BSiZenrwnVQSgoibrihiVe3zIXcCuz+Slx1m9gjAtfe1lOR/pri8bixftkbOLRB/BIQHBaOO59Zgg695dvxXwn23AoULT2I2kMWn58F9YlG4oJhCNFokQG5ehRskSuKjDfj9r8MxYibkrx3VQAAlJ2vwepX9yNzw9mA3p24+8DBmPnEYhiDxNTFni9XYuunH6oacOmCDIi5uy9g8NqiwuGG9bMscKf822wYjUZMmCDuF3Tw4EFYrdYm7vhl1EolBlyRvM9KxJYHW0qmEGt/+gnVmzcLbfHz54sLSWRSV+PEuvePCmeuBpkNmPZAf+hVrNPyuN1Y+3Yajm7eILSHRERi1nMvI7FHrybu1B53eVCxNg+W9w7DXS753TcwRN7SE3H39oc+3OT/ASSgULBFropOr8PIW3ri9v83DBFx4oegx8Wx84scfPP6Tz61GYGkS78BmPnUCzCFiLu67/92DTZ/tEzVgMvUKQxRN4tv9M7zNSj/Tpn9t4YMGYLo6OhL1x6PBxkZGbI8W6lUYsAXyVuyxGsZZrakKcTpSdNb/MyLitOWCtch11yDsEkTZXv+RZxzbProBKqt4nvB5N+lIiI2pIm75Od2ufDDG//AiW1igBkaFY3Zz72M+G5Jqo3ll3JabCh+5xCqMvKFg7qB+trPxEeHIHxMZyqCb0Uo2CK/SIeekZj99Ej0va6Dz88Kssqw/IU9yDmgTP2RHDqnpOLOp19EUKi4n1Dmj99i4/tviQfQKix0VAeESGpXavZcgO2wb7qgpfR6vc8h1YcPH0ZxsTx/VwkJNwnXpdZtLU4lBnyRvHT3+BYGW2crz/qkEK/vfn2LnnlRza5dsEm2/Yh/7DEw6VS1DA6nFyDvcInQNmhyF/QcrOx5i97cLie+S3sVJ3dtE9rDYmIx67lXENvFd4ubQMA5R/We8yh+PRPOc9U+Pw8b2xkJjw6GsYNy+6ERZVCwRX4xU7ABU37fD9MfHIAgs7jSz25zYd17R7Hp4xNw1AVYQXODDr374M5nliA4XKxDO7xxLdb9+3V4POoU/TPGED0zGXrJqqyyL07BVVrbxF3NN2DAACQkiBscpqeny/LssLC+klSis8WpxD6hkpqtQNpF3u0CSk6JbS1cibj+jDirJVcKkXOO4tfShLbQ0dch9Fr5N+4syqvEzjU5QltC93CMvl2e8yKvhsvhwDf/XIKcfbuE9oj4BMxe9CpiOnVWbSy/hLvagdKPj6P8yxyfcgJdhAlx9w9A1M09wQz0sd0a0d8aabbewxIw55mR6JwS7fOzrJ3nseKlfbiQW+HnTu0l9uiFWc8ugTlSPAfuWMZGrH3rNXjc6gRcumADYu/uC+i96rfsbpR+lgUu8zFJOp0OkyeLh+pmZWXh3LlzLX62EqnEniFB3n8sOGd3osoVIKtfy/IAj9dZk2GJgDmmRY9UKoVYnZ6OusOHhbb4BQtkebY3u82J9e8fhcfdmPcyBesx7YEB0KsUIDgddnz19xeQe1A8mioysQNmP/cKohJ9Z+QDQd1JK4qWHkTdCd86ypD+sUicPxTByb7vs6T1oGCLtEhYdDBunT8Yo2/vDZ1eTElUWmqx5h8Hsfe70/C4A+98xfhuSZj17MsIjRLfxE5sz8D3b/wDbpc6M3OmLuGIulHcSdt5rhoVP5xu4o7mS0lJQefO4jf7TZvkOTdS7lSiSadDD+mKxECZ3ZLWa7VwVkupFCJ3u2GR1GqFXT8FIYMGtfjZQj+cY/MnWagsEf9+Jv8uFZHx6tRpOevq8OUri3HmcKbQHt2xM2Y/9woi4gPv2BrudKP8m59R8uExeKrEg+KZSYfomcmI+U0q9KHKbM1B1EPBFmkxpmMYMq0b7nh8OKI7iMXn3MOx77vT+PKfB1FhkT811lKxXbpi1nOvICxGXDqdvWsbvkt7FW6Xs4k75RU6upPP8u3qnYWoPVrSxB3NwxjDlClThLbc3FycPt3ywE6JVKK0SP5UTYAswPApjm/ZMT3SFOLwDsNlSSFW/vAD7Ke80p2MIX7evBY/V+rolnP4OVOsNRw4oTN6DVUnwHHU2vDFy88h/5g4gxfbpRtmPfcywmPV3dfrajgKq1H05k+o3lno8zNT13AkzhuK0BEdFKmrI+qTJdhijP2KMXaSMZbDGFvo5+f3MsYsjLGfGv55QI5+SWCJ7xaOO58cgYETfGsiLuRWYsVLe5G163zAna8Y06kzZi961eebb86+Xfjmn0vgcih/PBFjDNF39IE+WpzJsa7Ohssq72xOz5490aOHOJO2adOmFv+9+EslFhX/0KJn+hTJB8rMlszF8T4bmXZv+Uam3OmE5fU3hLaIW25GcB9595WynK3C9tVi/Vpc1zCMvkOdOi27rQarlzyLc1nHxDF0S8KsZ5cgLLpl6V25cQ9H1bYCFL/1E1xFkr31GBA+pRviHx7ksxcfad1aHGwxxvQA3gJwA4B+AO5ijPXz89IVnPPBDf+839J+SWAymvQYf1cKbnpkEELCxalvZ50bmz46gXXvHUNdjTozRlcrqqGmI1JS05F7cB+++vsLcNqV/5DXhRgQe3eqWL9V50bpZydkr9+S1m4VFBQgOzu7iVdfPWkq0drCDU77mAN0Y1MZt31QKoVY/sUaOPPzGxsMBsQ/+miLn+vNUevC2veOwuNqDNSNwXpMf3AADEbldzOvra7Cqheexvls8e8jIcl/TabW3BV2lPznKCq+Pw24xS83+phgxD98DSKndgdT+cxIojw5/kZHAsjhnOdyzh0AlgO4VYbnklYsaWAc5jwzCt0H+u5s/PPBYix/YS8KTpZpMLKm1a9WegXRHcWZuTOHM/Hlq8/DWaf8B72pazgifyWp3yqoRsXaPFn76dq1K/pIZjjS09PhaeHWF3KnEpMDcWbL4wEs0pmt5qcRlUgheurqUPL220Jb1MyZMHWTb8sDzjk2f5qFSkl5wKTf9EVUgrmJu+Rjq6zAqheeQlGuOKtWv9r4JYSE+556oSXbkRIULT0Ie065z8/MQxOQOG8IgroH1piJfOQItjoD8Pr6hIKGNqmZjLHDjLHVjLGuMvRLApw5woSb5g7ChLv6wGAUf9Vqyu34Oi0TO7/IgVuBXdObKzwmDrMX+e7Dk3/sML54+Tk4apU5Usdb2NhOCE4VUx/V28+h9ri8h39LZ7eKiopw7NixJl59depTieLxPS1JJfY2B8O7YuVMrQO1Wi+2qMgHXF4BRnAUENr8PaSUSCGWffY5XF57qDGTCXFz/9Ti53o7tq0QOfvFfdr6j+uE5OGJsvbjT015GVY9/yQseeJB4J36pOKOp15EcFjLz6iUi8fuhnV1NqyfnoDHJi66YcH1p0nEzEqBLtjQxBNIWyBHsOWvek9a/PEtgCTO+SAAGwF85PdBjD3EGNvPGNtvsci/sSNRH2MMAyZ0waynRiCuq+QNkAOZG85i9d/2w3q+RpsB+hEaFY1Zzy5BnGSH6XNZx7D6pWdQV+O72aCcGGOIubMP9FGS+q1V2XCVyTez06FDBwwYMEBo27x5M9wt3PZCelZiS1KJZr0OXYMbjyPhAHJrNS6S9zkTsS98zrG6SkqkEN3V1Shdtkxoi77nHhgT5QuCSgqqsH2lOKMU2zkMY+9Mlq2PplRbS7Fy8RMoyT8jtNefEPE8gszKz6pdLfvZShS9fhC2/UU+PwvqGYnEBUNhHqTeZq9EO3IEWwUAvGequgAQlldwzks55xffId8DMMzfgzjnyzjnwznnw+Pj6RewLYnuEIo7Hh+OodO7+YTnJfnVWLlkH45kFARM8bw5Mgqznl2CBMnZaedPncTqF59GbbWyh2/rzEbE3NUX8DqOg9e6YP08C1zGmZ1JkyYJq52sVisOHTrUomfKnkoMtGN7SuQ7gFqJFKL1o4/gLm9MVenMZsQ+9GCLnunNUefCuveOwe1VR2gI0mP6g/1hMClbp1VZYsGKxQthLSwQ2rsNHIzbFy6CKTgwisq5m6Ny4xlY3j0Ed6nk91XPEHlDD8Q9MBAGyRcq0nbJEWztA5DMGOvBGDMBmAPgG+8XMMY6el3OAHACpN3RG3S47te9cduCIQiTrLpzOz3Yujwb3799GLZK5Vf/XY2Q8Ajc+cxL6NBbrG0qys3BquefhK1S2Q1bg7pHIHJ6ktDmOFuFinVn/N/QDLGxsRgyZIjQlpGRAaez+QsY5E4lSneS1zzYkrE4Xu4UoqusDNb/fCi0xdx3HwzR8myIyTnHls9Oolyyim7i3SmIVvgImYriIqxcvBDlF84L7T0GD8Ov//qszyHzWnFZ62BZdhiVG88Cku9FhvgQJMwdjPAJXehcw3amxcEW59wF4FEA61AfRK3knB9jjD3PGJvR8LJ5jLFjjLFDAOYBuLel/ZLWq3NKNGY/PRK9h/vuwXPmSCmWv7DH52w1rQSHhuGOp15Epz6pQrvlzGmsXPwEasqVLfIPG9cZwZId+qu3FqA2y3en6eaaMGEC9PrGGYnKykocOHCgRc+UM5UYcEXyPmnE5gVb0hSijulanEIsff99eGoaU/L6yEjE3Hdvi57p7cTO88jeK6bEUsd0RMooZXdmL7tQiBWLFqKiWOy71/BRmPGXp2EwZ11MGAAAIABJREFUmZq4Uz2cc9QcKELR0oNwnPH9XQ+9tiMS/jwEps6BU09G1CPL+lLO+Q+c8z6c816c85ca2p7lnH/T8P+f4Jz355xfwzmfxDnPuvwTSVsXHGrEtPv74/p7U2EMFlMPtVVOfP/2YWz57CScDu2PZwkymzHzqefRpZ9Y31RacBYrFz+Baqu8hevemI4helYK9BHih0nZypNwVchTuxQZGYkRI0YIbVu3boXd3vzn+08lbmjWs1ICKY3IuWwrEeU+C9FZVIyy//tUaIt96CHoZSoWLz1XjW3LxX/3mE6hGDdb3n27pKyFBVi5aCGqSsU63uRRo3HLYwthMGq/u7rH5oT18yyUrcoGt4vvWbpQI2J/3w/Rt/WGTuE0KwlctJkH0QxjDCnXdsScp0eiY69In58f3XoOq5bsg+WssvVRV8MUHILbFy5Ct4GDhXZrYQFWLF6IyhLlFnToQy/WbzW2eWwX67fkqXEbN24cTF6zAzabDXv27Gn28/ynEpt3VqJ0Zut0rR1Oj0a1fVUXALtX+tgUBkQ072DjdXnrhOuWphBL3n0H3CtANiQkIPqeu1v0zIucdjfWvXcULq+VwwaTDtMfGACjggFESf4ZrFi0ENVl4kxu3zETcPP8x6E3aB9o1f1cjqKlB1HrZzY+OCUaiQuGIiTVdwsc0r5QsEU0FxEXgtv+ZwhGzejhU8dQdsGG1a/ux8F1Z+DR6gO2gTEoGL/+67PoMVhc31F+4XxDiuOCYn0H9YhExNTuQpsjrxKVG+Wp3woNDcW1114rtO3YsQM2W/O3upArlRhh0KODqfFD1cXrAy5NSIvj4/o0ayXi2cqzyLI2TvC3NIXoyM9H+arV4tDm/gm6YHnqmLYuP4myC+Lvwvg5KYjppFydVnFeLlYufgK2CnFfqv4TpuCGR/8HOr22s0Tc5UH5j6dR8v4RuCskdaYGHaJu7YXYe/tDH659ipNoj4KtVqh661Z4WvAhGIh0eh2G39gDt/+/oYiQHFzrcXPs+vJnfJOWiSqZj675pQwmE2b85Wn0Gi4GJpWWIqxY9ATKLviecyaX8AldEZQs7ohdlZGPumx56sZGjx6NYK8PZ7vdjp07dzb7eWFhfWE2N27Q2pJUYsAUyctUryV3CrHkzTcBr4PTjV26IOr225v9PG9Zu88ja5f4RSLl2g5IHd2xiTta7uIilNoqMTgfOHkapj88HzqdtoGWs9iG4rd/QvWWAp+NjowdQ5E4bwjCruvU5s41rK2tRW5u7pVfSHxQsNXKOPLzkf+nuciZcj1K3ntPKIZtCzr0iMTsp0YgdYzvG/m57HKseHEvTvnZs0ZNBqMRtzy2EH1GjRHaq0otWLloIUrP5TdxZ8swHUPM7BTovL8pc8C64iTclS2f6QkODsbYsWOFtt27d6OqqnlpXMYYEuKlZyU2L5UoPSPxlFZF8jKtRJQzhWg/dQoV33wrDuvPj4LJUDRuPV+DLZ+JAWZ0BzPGz1GuTqswOwurXnjKZz+7a6bdhKkPPgqm0+5ji3OO6l2FKHo9E85CyXsvA8LGd0HCI4NhVGEHfTXZbDakp6cjLS0Ny5cvb9GMd3tFwVYrU/LvfwNuN9xlZbD881/1Qde/l8Fd3XaCLlOwAZN/m4pf/XEAgkLFXZXtNhfWv38MGz88Dketq4knKE9vMOCm+X9F3zEThPbqMmv9hotn85TpN8yEmDkpwl5lnhonrMtPgsuQZh05ciTCvAqqXS4Xtm3b1uznyZVKDJi9tmQojpc7hWh5/Y36wv0Gpt69EHHzzc1+3kVOR0OdlqOxTktv1GH6gwNgUmi384KsY/hiyTOw28T3s2E33Yopf3hY00DLXeVA6UfHUf71z4DkrFJ9pAlxDwxE1I09wAxt52PVZrNh06ZNSEtLu7RoxuFwYPfu3VoPrdVpO78V7YCjoAAVX30ttLnLy2F57TX8PGUKSt59F+5qZXc3V1OvIQm465lR6NLXd4+gk3suYMVLe3HezzljatHp9bjh0f9B/wlThHZbRTlWPv8kivOUmW4P7hWFiCnicUL23ApUbjrb4mebTCaMHz9eaNu/fz/Ky5v35yxXKlE6s6XZ9g/Sma24Xz7DI2cKsfbIEVRtEP884+fPB5Ohnmn7imxYJbM342f3QaxCWxfkHzuMNUueg6NWPGtx5K13YMJvH9A0JVebZUXR0oOo87PlSsigOCTOH4rgXoF16HVL1NTUYOPGjUhLS8O2bdvgcIg1aXv27EGt5O+JXB4FW62IPjwcsQ/cD12ob1Gqu6IClrSl9TNd77wDdzNTP4EmNCoIM+YNxpg7ekNnEN9sK0vq8OU/D2LPN7lwa3Renk6nx/SH52PglOlCe21VJVY9/ySKcnMU6Td8cjcESVZwVqWfRV1Oy+u3hg4diqioxg8Oj8eDjIyMZj1LrlSidGbrZ5sdbrVPG6gpBWxeK870QUB00i9+jDSFOL379CZeeWWWtKXCdfCAAQi/vmV7dQFA9t4LOL5D3Dw0eUSi3/S+HPIOZ2LNK4vhtItB9LUz78LYu36vWaDlcbhR9lUOSv97DJ5qcaNfZtIj+s4+iLmrL3Rm7VdFyqGmpgYbNmxAWloatm/f7hNkAYDZbMa4ceOEvfnIlVGw1YroIyORsGABem/aWL/SyM/+OZ6KCliWvo6cKdfD8tZbcFc2byPJQMJ0DIOv74Y7F47wWf3EObD/hzx8+Y+DKC/Wpo6A6XSY+sAjGDz9JqG9rqYaq154CoXZ8m8rx3QMMXP6Qhfm9SbPAevyk3BXtWwHfoPBgIkTJwpthw4dQnPPK5UjlRhnMiDG2PjmXufhyK9T+aQBfysRf2Gh9pnKMz4pxCndp1zmjqbV7NmLmh07hLb4xxa0ODApL7Ih41Px3zUq0YyJ96QoEvTkZu7DV397Hi6HWHc4ZvZvMWbWPZoFWo5z1Sh+MxM1u8/7/MzULRyJ84cgdFhimyiCr66uxvr165GWloYdO3b4PUHCbDZj6tSpmD9/PsaOHStsFUOujIKtVkgfFYX4efMagq650IWH+7zGU1mJkjferA+63nizTQRdcV3CcOcTwzFochefnxWdrsSKl/bh+I5CTc5XZDodJt/3MIbddKvQbrfVYPVLz6Ag65jsferD/dRvVTthXdHy+q1BgwYhLq4xtcU5x+bNm5v1LNlSiVrXbfkUxzcjhZgnTwqRcw5LWprQZh45EqGjR//iZ3lzOd1Y+95ROL025tQbdJj+YH9F6rRy9u3G139/CW7Jh/v43/wB194+W/b+rgb3cFRtyUfx2z/BVSxJlemAiOu7If6P18AQGxjnMLZEVVUV1q1bh7S0NOzcudNvkBUaGopp06ZhwYIFGDNmDIKC6DzH5qBgqxXTR0Yift6f64OuRx+FLiLC5zWeqiqUvPUWciZPgeX114UDalsjg1GPcbP64JY/XwOzZFd1l92NzZ9kYe2yo6irbv7Zfs3FGMOE3z6AkbfeIbQ762rxxZJncfboYdn7DO4djfBJXYU2e045qja3bEWkTqfD5MmThbbjx4+jsPCXb20hVyrRp25L9WCr5cXx0nqt5qYQq7dsQW1mpjicBS2f1dq+KgelBWLd59hZyYjr4vuFrqVO7tqOb197GR63uNBl0r0PYcQt8mxb8Uu5yu0oef8IKn7MAyQbButjgxH/8DWIuL47mL51z2ZVVVVh7dq1WLp0KXbt2gWXy3ex0cUga/78+Rg9ejTNZLUQBVttgD4iAvGPPlIfdM37M3SRvruxe6qrUfL2O8iZcj2K09JafdDVrX8s5jwzEj2u8Z0VyM20YPkLe5B/Qr7zA68WYwxj7/o9rrvjLqHdZbfjy1cWIe/QQdn7jLi+O0w9xL/zyo1nYM9t2d9xamoqOnYUa3TS09Ob9ayERDHF2pxUouZF8i0sjpcrhcg9Hp9arbCJE2EeOqSJO67Oqf1FOLb1nNDWe1gC+o/r1KLn+nNiewa+X/o3eNzi0TbXP/AIht4wo4m7lGU7bEFR2kHYc30PmDcPS0TivCEI6ub7hbY1qaysxI8//oilS5di9+7dfoOssLAwTJ8+nYIsmVGw1Ybow8MRP3cuem/aiP/P3nkHNHXub/w5GQQSNoS9lyAqIihOUHFXbd12W2ur1apt76+32lbtsrXtvb11a6211g631lUXIIoLRByIIFM2JGwC2ef3B0pychJIWILm81/evOfkQCDnyXc8X/57y8HUJrpEIlRs294kuv73I+RVnTtIuTMxszDBxEV9MfLlXmCZUP+URTVSHFt/CwkHMiGXde18RYIgMHTWyxg+9zXKulwmxdHvvkDOzaSOfT0GAbu5vcBQt8kggYq/MqCob3tdE0EQtOhWVlYWHj403LXenNer3alEzSL5TFEXu8jTDE0Ni2xpphDDHcPblEKsO30aknSq8OMvX2bwedSpLm9A3O/Uc1ram2LkK4EdXpOUeuE8Tm36L0hSramFIDBu0TKEjJ2o+8BOQimWo3J/Bir/TAcppooPwowF25eDYDsrAAxO59hddAW1tbU4deoU1q9fj+vXr2sVWRYWFpgwYQKWL1+OIUOGGEVWB2MUW08hTHNz2C9aBN+YGPDffx9Ma3pLslIkQsX27ciOHoPy//7QY0UXQRAIHuGKOZ8MgoMnPdVxO6YAB9clo6K46y0xIqbNRtQr8ylrCrkcf/9nLTKTrnboazGtOLCdTTXYVNZJUbn/Qbvqt/z8/ODhQbWZiImJMbguTnsq8ZRB59B0kc9sEHddfZ64FqhTS6EyWICtj0Gn0EwhtsXIlJTLIVi/gbJmOWkiTIOCDD7XYxQyJc7+fA8ysepLCYNFYPxbfcAx61iBcef8aZzZ+iPFF4wgGJi45AP0HdW+2ZBtQfKwFmUbUtBws5z2HMfPGk7vDQC3b9ud/Z80NTU1OHnyJNavX4/ExEQoFPQvnhYWFpg4cSKWLVuGwYMHg90NBns/jRjF1lMM05wH+4Vvw/f8efA/+EC76GpoQMWOHU2Rrv/8B/LKrk+9dQTWjlxM/3cYwiZ4UgrGAaCiqB4Hvr6B27EFXV48Hz5lOkbNW0hZUyrkOPG/dci4mtChr2XayxYWI6nNA5IHVai7WNjmcxIEgehoaqorPz8fWVmGW1rQU4mXDUolOpmwYcFUfWTVK5QokXRRbZ5Qo17L1gdg6f/Nv6NSiDVHj0KqHllkMmG/dKnB51Hn8uEs2rD3YTP84ODZsSmzlNPHcW7HJsoawWBg0rL/Q+8Rozr0tVqDVJCoOfcQgm23odAcAcYkYDXJG/bz+4Bp1TOLwaurq3HixAls2LABSUlJWkWWpaUlJk2ahGXLliEiIsIosjoZo9h6BmCa82D/9lvwizkPh//7F5i2trQ9ZEMDKn7eiazoMSj77nvIKyqewJW2DyaTgcEv+GLaBwNgbkv9kFTIlUjYn4kTG29DVNO16acBE6dgzIIllDWlQoGT67/D/Utt6/DTheVYL5ho3CRrz+ZBkkevQ9EXT09P+Pn5UdZiY2MNFq7tTSUSBAH/J1W31c4xPR2RQlRKpRBs3kJZs5r2Ajje3jqOaJ3slHLcjaOKcZ9QPvqOpHf8tocbJ44gdtd2yhqDycKU91cgcGikjqM6B7mwEYJtt1EXk0+ba8hy4MJhSX9YRLqBYPS8Ivjq6mocP34cGzZswI0bN3SKrOeeew7Lli3DoEGDjCKrizCKrWcIBo8HuwUL4Hf+HBw+/BBMOzvaHrKxEZW//NIkutZ9C3kbvZWeJC7+1pj76SD4D3SkPZefVom9XyYi51bX/lwhYydi/KLlgFr9C0kqcWrzD0i9cL7DXodgEo9MFtXSP0qg8q90KERtjwJp1m6VlJTg/v37hl0bQdA8twxOJT4p+4f21mt1QAqxeu8+yEtUnk8Emw3+4sUGn+cxtcJGxP5GFZEWdqYY/WrH1mldP7If8Xt2UtaYLBam/utj+A9qn1WFIZAkCVFSKco23IS0gG76bD7UBY5L+8PEpXMc8juTqqoqHDt2DBs2bEBycjKUSrrJs5WVFSZPnoxly5Zh4MCBYLF6bg1aT8Qotp5BGFwu7N6c3yS6PvoITHv6N2xSLEblr78ia8xYlH3zDWTl9JqG7gyHy8a4N4Mxdn5vmJhSjSfF9TL8s+0u4v5Ip/gJdTZ9Ro3FxCUfgCDU/u1IEme2/og750932OuwrDmw0ajfUtRIUXWg7fVbLi4u6N27N2UtNjZW64d6S9ANTi9DJtM/6kYfSN1FUUpNsWWvf2SrI1KISpGoaS6qGtYvzgXbpW2dggq5Emd2pFLmizKYBMYv6ANOB7mhkySJKwf+RMLe3yjrLLYJXvhwFXzDBnXI6+iDQiRD5R/3UXUoE6SU+jfLMGfD7o1gWE/1BcHuWa7olZWV+Pvvv7Fx40bcvHlT6/+jtbU1pkyZgqVLlyI8PNwosp4QRrH1DMMwM4PdG/Pgd+4sHFeuAJOvRXRJJKjc/Ruyx45D6dqvISvrWaIrYJAT5qwaBGc/emdm2qVi7P86CeUPu87wtfeIUXhu+Ye0gbrndmxCyunjHfY6ZoG2MI90payJ0ytRn1Ck44jWGTVqFCXiIRQKceeOYd5h2lKJAgNSif5canq4yyJbmu7xBqQROyKFWLnndyjUUvsElwv7t9826BzqXD2SjfKH1OjOkGm+cPTumDotkiRxed8eXD34J2WdxeFg2oo18Oof1iGvow/izCqUrb+JxlR6aYRpkC0c3xsAs1700oruTGVlJY4ePYqNGzciJSVFp8iaOnUqli5dirCwMKPIesIYxZYRMMzMYPv66/A7dw6OH38MFp9P20NKJKjaswfZY8ei9Ku1kJWVPYErbRuWdmZ44YMBiHjeBwyNOozqsgYc+jYZN/7Jg7Kdruv60mvICEx5fwUYTOqHX+yu7bhx/HCHvY7VeC+YeFA7NGtO50GS3zZxyefzERISQlmLi4vT2kauC22pxHIDDE61GZt2etODtAGoUre7IAB7f70Pb28KUVFTg4qd1DSc7WuvgqUlIq0PubcFuB1DNb316mePkGh3HUcYBkmSiP/9F1w/sp+yzjY1w4yVn8OjT4iOIzsWUq5E9YkcCHemQllLtUAh2AxYT/OD3Wu9wTTvORYHFRUVzSLr1q1bWv/2bWxs8Pzzz2Pp0qUYMGCAcYZhN8Eotow0wzA1he1rr8L3/Dk4fvopWI70midSKkXV778je8xYlH7xJWSlpU/gSg2HwSAQPtELMz4Kg7Ujl/KcUkni+t85OPrDTdRWdM0ke/9BQzH1Xx+DqfFtU9tNqq0QTAZsXwwEod6+ryRR+Wc6lA1tq98aOXIkGGpRuZqaGty8aZhRa3tSie6mJjBTE8xVcgWEMv3FXpuoyASlktrGE2DrN6qlI1KIFTt/gVJtsDzD0hJ28+e3cIRuaisaEbObWmtnbstB9OtBHVKnRZIk4n79CcknjlDWTcy4mPnJF3AL6tPu19AHWZkI5ZtuaY3ksl3N4bAsFOYRzj1mrmFFRQWOHDmCTZs26RRZtra2eOGFF/Duu+8iNDTUKLK6GUaxZYQGg8OB7Ssvw/fsGTiuXgWWkxNtDymToerPP5E9dhxKPv8csjaMcXkSOHhaYvbHA9Fbiyt2SVYN9n2VhAeJXSMgfcMG4YV/rwaLTf1mnbD3N1w58EeHRGxYNqawnUl1OldUS1B54EGbzm9tbY3w8HDKWnx8PKRS/c1T25NKZBAE/Lq6SL4dY3ram0KUCwSo3LOHsmb35ptgahnN1RoKRZOflqRBrU6L0VSnZcprf50WqVTi/I7NtHQ4h8fDrFVr4RLQdi8wva+BJFF/uQhlG29BViqiPkkAFiPd4fBOCNh8rvYTdDOEQiEOHz6MTZs24fbt21r/Z+3s7DBt2jQsWbIE/fv3N4qsbopRbBnRCYPDge1LL8H37Bk4rVkNlsboFqBJdFX/tRdZ4yegZM1nkBW1vSaoq2BzmBj1ciAmLupLu8lIG+U490sazu68B0kboz+G4BUyANNWrAFLY7jr1YN/IWHvbx0iuMyC7WA+jCouxfcrUX+5bQJ5xIgRlPoPkUiExMREvY/v6FRipxfJt2NMT3tTiMLtP4FsVEVbmXZ2sH31FYPO8ZjrR3NQlktNIUe84AMnH3o9o6EolQqc2bYBd2KojR6mFpaYvfobOPnqn3ZtK4o6KYS77qH6eA4gp9YwMa054L/VD1YTvECwuv9tTyAQ4NChQ9i8eTPu3LmjU2RNnz4dS5YsQUhIiFFkdXO6/1+dkScOw8QENi++CN8zp+H02WdgudBFF2QyVO/bh6wJE1GyajWkhd1fdPn052Pu6kHw6E0vjs1MKsPerxJRnNn5MyQ9+oRgxsrPwTalpqYSjx5A/J6dHSK4rCZ6g+1GbWmv+SdXawt8a1hYWGDw4MGUtYSEBDQ26p+CbU8qscuL5GnF8fpFttqbQpQVFaFq3z7Kmv2iRWBwDY/K5N0VIuVcPmXNs48dQsd46DhCf5QKBf7Z9APuxVMtTLhW1piz+ms4eBnmtN8WGtMqUPZjMiQP6JMwzEL4cFw+AJwOEJWdTXl5OQ4ePIjNmzfj7t27Wv/37e3tMWPGDCxZsgT9+vWjpPWNdF+M75IRvWGYmMBm7hz4nT4Npy8+B9vVlb5JJkP1gQPInjABxZ9+CmlBAX1PN4JnxcHkd0MwfLY/mBrfeOsrJTj6w01cO5oNhcIwiwNDcQvqg5mffAETM+qNNPnkUcTu2g7SQIsFTQgWA3YvBYFQt8FQkKj48z6UjYbXPA0dOhQctWicWCzG1av6jyBqSiWqbsKGpBK1Fcl3Km302GpvClGwZQsgU0VXWS7OsJ4zW+/jH1NfJUbMr9Q6LZ41B9Hzgtpt3KmQy3Fyw/dIvxxPPb+NLWav+Qb2Hl7tOn9rKKUKVB3JRMVvaVCKNOYacpiwndMLdi8GgtHBY4c6mrKyMhw4cABbtmxBamqq1j18Ph8zZ87E4sWL0bdvX6PI6mEY3y0jBkOYmMBm9mz4nv4Hzl99CbabFrdpuRw1Bw8he8JEFH/8CaT5+fQ93QSCQSBktDtmrQyHnSs1+kOSQPLphzj8XTKqyxo69TpcAoIwa9VamPKo13DrzAmc/3lLuwUXy9YUNjM06reqJKg6aHj9FpfLxbBhwyhrV69eRX29fjMom1KJ1FmJ+qYS6WnEThRbcilQkU1d07MT8UzeGcrj8V7j9X5ZSU4uao4cpazxl7wLhoHDgZUKJc7uvAexmqEtwSAw7s1gmLWzC08uk+HEj+vw4Bp17JS5nT3mrPkGdq4d092oC2lhHco3pEB0nV5jaeJlCcflA8ANdejUa2gvZWVl2L9/P7Zu3Yp79+5p3cPn8zFr1iy888476NOnj1Fk9VCM75qRNkOw2bCeORO+/5yC89q1YHtoSUkoFKg5fBjZEyeheOXH1Llu3Qw7V3PMXBGGkDH0m0T5wzrsW5uIe5eKOtVqwMnXH7NWfw0zC2oB9J2Y0zizbQOUyvaZsHL72oM3hJoGbrxXAdG1Eh1H6CYiIgJctZSWTCZDQoL+8x7bmkr0MuWArdZFViaVo7qzOhIrcwBS7Xdu6QqYtl6c/rD2ITKqVBExBsFAtIf+KUTBxg2Amrg28faG1fNT9T7+MYnHc1GSRf2dDpriDRd/+pxUQ5BLpTj237XISrpGWbfkO2DuZ+tg46wl6t1BkEoStXEFKN9yG3KhRuqaQcByvCf4b/cDy9ZU+wm6AaWlpdi3bx+2bt2KtLQ0rXscHByaRVZwcLBRZPVwjO+ekXZDsNmwnjEdvqdOwvmbb8D21CG6jhxB9qTnUPzRCkjz8rr8OvWBxWZi+Ex/TF3eHzwr6jd/uVSJC39k4J9td9FYr3/3naE4ePlg9uqvwbWi3hDvxZ/HP5t+gFLLvDNDsJ7kA7YLj7JWfSIH0iL9olKP4XA4iIykzrVLSkpCTY1+tVdtTSWyGAR8NOq2Oq1Ivo3F8dpSiHZm9PFY2hCnpaHuH2qhOX/5MhAGmlLmp1Ug+Qz1y417b1uEjfc06DyayCRiHP3+S+Sm3KCsWzs6Y85n62DlQO9e7ijk1WIIdtxB7Zk8QMMXj2VvBod3QmA5yqPbzjUsKSnB3r17sW3bNp3jrhwdHTF79mwsWrTIKLKeIozvopEOg2CxYD3tBfiePAmXb9fBxMuLvkmhQM3ffyN70nMo+ve/IcnJ7fLr1Af3IFvMXRUBn1C6wWvubSH2fpGI/HudN6zb3sMLs9d8A54NtXg//XI8Tm74HgoDjEQ1IdiP6rc4Wuq3xIadNywsDJZqNgQKhQLx8fEtHKF2He1IJWoWyWd2Vt1WG+u12pNCLF+/nvKY0zsIFuMM62IUVUtwflcaxR6Ma2WCMfN6t0uIyMRiHPn2Czy8k0JZt3Fxw+zPvoGlfeel7RpulaPsx5uQ5tJNeXmDnOCwNBQm7hZajnzyFBcX46+//sL27duRnp6udY+TkxPmzJmDhQsXonfv3kaR9ZRhfDeNdDgEiwWr55+Hz8kTcPn+O5h4e9M3KZWoPXYcOZMno+j/PoQkO5u+5wljas7GhLf7YNSrgWBxqG3VDbVSHN94G5f2PYBc1jnzFe1c3TFnzTcwt6MWVT+4loDj/1sHuazt1hQsezPYTKfWHikqxKg6nGlQmpTNZmPkyJGUtZSUFFRU6CdE25pK1Kzbyuisuq02jOnJq8lrcwqxITkZoviLlDWH996jjXdqCaWSxLlf7qGxTq1OiwDGzQ8G17LtdVqShgYc+mY1Cu5RRzTZuXlgzppvYGHbNkf71lCK5ajcm47KvRkgxdT/NQaXBbtXg2Az3R8MTvezPiguLsaff/6Jn376CRkZGVr3ODs7Y+7cuVi4cCGCgoKMIuspxfiuGuk0CCYTVlOmwOfEcbh8/z1MfLS0gCuVqD1xAjmTp6Dog39BkpXV9RfaAgRBoPcwF8xLzLZPAAAgAElEQVT5ZKDWuXF34gpx4JsbEBYaloLTFxtnV8z9bB0s+VQ3/+wb13Dsv2shN8BMVBNuCB+8CGrKp/GOECIDTV1DQkJga6uKwJEkibi4OL2ObWsqMUDD2LTrIlutiy1Nby19U4gkSaL8f/+jrJmFhYE3YkTr16lG0slcFD2gWpYMnOwN1142Bp1HHbGoHofWrkJROrW+iP84Amvd9nO3hCS3BmU/3kTDLQHtOY6/ddNcw+DOEXntoaioCH/88Qd++uknPHjwQOseFxcXvPjii3j77bcRGBjYY9zsjbQNo9gy0uk0ia7J8Dl+DC7//Q9M/Hzpm0gStadOIWfKVBS+/z7EOj6gnhTWDlxM+78BCJ/kBc3PxMpiEQ6sS8Kt8/kgO2G+opWDE+Z89g2sHamF7bkpN3D0+y8hk7RdaFhP9gHbSaN+63g2pMX6i0cmk4lRo0ZR1lJTU1Gqxygn7anEU60eR7N/6IzIllIBCDOpa3qkETXrtfRNIYoSLqPxRjJlzeG95QbdhAvSK3HjVB5lzbWXDcImeul9Dk0a6+tw8KtPUZJFFZ4O3r6YtfprcC073r+KVChRcyYPgp/uQFGtUY/HImA12Qf2b/QB05Kj/QRPiMLCQvz+++/YsWMHMjMzte5xdXXFSy+9hLfeegu9evUyiqxnBKPYMtJlEEwmrJ57Dj7HjsH1fz+A4+9H30SSqPvnNHKnPo/C5e9BnNF9RBeTyUDEVB9M+9cAWNhRb/ZKOYnLB7NwbMMtiDRvDh2Apb0DZn/2DWxcqDYbD++k4Mi6zyEVt22mI8FmwvblQBAmah8F8kfzEyX6128FBwfDUWOWZmxsrF7HOjo8R3lcWXml1VSijxmH8uFVKJZBJO/gdG5VHqBQey95fIBLN8BVp60pRJIkIdCIavGGDwd34EC9L1dUI8G5X6h1WmaWJhg7vzdtALu+NNTW4MAXH6MshxpxdvbrhVmr1tK6ZjsCmaAB5Vtvoy6ugPKzAADbiQvHd0NhMdy1WxXBFxQUYM+ePfj555+RpSM67+bmhpdffhkLFixAQECAUWQ9YxjFlpEuh2AwYDlxIrz//huuP/4IToD2Dq+6M2eQ+/zzKFy6DGIdRaVPAmc/a8z9dBB6DaZ3XRWmV+GvL68jO6W8w1/XwvaRf5EbtduzIO0uDn29BpKGtvmAsflc2Eyj1m/JhY2oPpKld/0Wg8HA6NGjKWsPHjxAgR6mtjxegMGpRFMmA55m1PqjrMYOFrmaKUR7w1OIAx0H6pVCrDt7DmINCwD+e++1fo2PUCpJnN+VhsZatbQyAYyd3xs8q7ZFf0TVVdj/+UoIHlKbWFwDe2PGJ1/S/ODaC0mSqE8sQfmGFMi0pOXNh7nAYUkoLRL7JMnPz8dvv/2GnTt3IltH3ambmxteeeUVvPnmm/D39zeKrGcUo9gy8sQgGAxYThgP76NH4LphPTiB2lM0defOIfeFaShcuhRiHe3SXY2JGQtj5vXGuAXB4HCpLfkSkRynt6ci9rf7kBrY3dcaPGsbzF7zDfie1KaD4ow0HFq7CmJR22rHuKEO4IZTI1MNtwRouFGm9zkCAgLgpmFwq090q8NSiR1dt9WG4njNFOI4r9a7CEmFAoINGyhrFuPGwaxPcOvX+Ijkf/JQmE4dVRM+0QvugS1H4nRRVynEvs9XoqKQakbsHtwP01d+Dk4bRga1hEIkQ8We+6g+nAVSRjXvZViYwH5+H1hP8QXB7h63rIcPH2L37t345ZdfkJOTo3WPu7s7Xn31Vbz55pvw8/MziqxnnO7xl2vkmYZgMGA5bhy8Dx+C26aN4AQFad1Xd+48cqdNR8GSd9Gow225q/EPd8ScTwfBNYBuEnn/Sgn2rU1Caa5+vlP6wrW0wqzVX8PRh5qGLcnKwMGvPkVjveHzDgHAeqovWI7Um2j1sWzISkV6HU8QBKKjqSmz3NxcnTcjddqSStQsku9wsWVgcXxbU4g1x49Dqh4VYTDAX7ZU78sselCFpBPU6JOLvzUGTtbSBawHtcJy7P9sJaqKCynrnv1CMe2j1TDRmOHZXsQPqlD2YzLEafQOVtNgOzi+NwCmAZ1TgG8oeXl52L17N3bt2oXcXO22NR4eHnjttdcwf/58+Pr6GkWWEQBGsfXEkCgkOJFzArVSumfMswrBYMBizJgm0bVlM0x799a6rz4mBnkzZqLgncVoTH3yosvC1hRT3wvFkGm+YDCpH6y1gkYc/v4mkk7mQtmB8xXNzC0w89Ov4OxPFQBlOVk48PlKNNQaLvAYJkzYvRRIiR6QMmWT/5ZUv3oob29v+Gh0ncbExLSajmxLKtG/s8f2aBqatiK22pJCJKVSCDduoqxZTZ0Kjp+WekYtNNRKcXbnPaj/ek3N2Rj3ZnCb6rRqykux77OVqC6jThTwDg3HCx+uApvTca7spEyJ6uPZEP6SCmUd1caEYDNgM90fdq8Egcljd9hrtpXc3Fz8+uuv+PXXX3WKLE9PT7z++ut444034OPjYxRZakilQpSUHu3U6RvdHaPYekJcL7mOlZdWImpvFBaeW4j9GfshaKC3Nz+LEAQBi9Gj4XXoINy2boFpsPZ0Sn1cHPJmzkTBwkVovHu3i6+SCoNBYMB4T8z8KBzWGtEhUkki8Xgujv6QglrN8SLtwJRnjhkffwnXQKooFeTnYf/nKyGqrtJxpG7YjjxYP0+90cvLG1F9VH9LDs3oVlFRkU6Poce0JZVIj2x1YM0WSQICjeaMVjoR25JCrDp4ELKiItUCmw37d5fod4lKEud/TUNDDdX+Y8wbvcGzNrxOq6q0GPs+W4laATV17Bs+GFP/9QlYBs5lbAlZqQhlm1JQf7mY9hzbzRwOyweAN8jpiQoWkiSRk5ODXbt2Yffu3cjTMfXCy8sL8+bNwxtvvAFvb2+jyHpEY2Mh8vN/QXLyXFxKGIK0tH+hvl77aKJnAaPYekLE5McAAOSkHFeKr+DLa18i+kA0Xjn1Cnal7kJ+bfcd3NxVEAQBi1Gj4HXwANy2bYVp375a99XHxyNv1mzkv/02Gm/f7uKrpML3sMDsTwaiTyR9NlxJdg32fpWI9GslHfYNj8PlYvrKz+Ee3I+yXlGYj32frUBdpdDgc/LCHcEdQHUCb7hZDlGyfvVbrq6uCNSov4uNjYWylUHa9FRiywanmi7yeY0SSNo5rLuZmkJAppY+5VgB5o46t7clhahsbIRw61bKms2sWTDRNthdCzfPPkRBWiVlbcB4T3gG6zcWSJ2KooKmv5cK6he+gMHDMeX9FWCxOya6RCpJ1F0qQtnGFMg1B7sTgMVodzi8EwK2fcemKg2BJElkZ2dj165d+O233/BQxzxXb29vzJs3D/PmzYOXtmkZzxgkSaK+PgM5uRtxPXEKrlyNQmbWWlTXJAFo+r8sF5xt+SRPMUax9QRQKBW4UHCBtk6CxG3BbfyQ/AOeO/Icpv09DZtSNuF+xf1nOvxKEAQsRo6E1/59cP9pO0xD+mndJ7p4CXlz5iJ/wVtoSEnRuqcrYJswEfVSLzy3uB/MLKg3KZlYgZhf7+PsznsQi9ruAK+OiakZpn20Gp79QinrVSVF2P/ZStQKDe+MtH7eDyw+9YZXfTQLsnL9Oh41OxPLy8uRmpra4jH0VKIcAoHuVCKPxYQrR/X7VQLI6agZidqK41uIWLQlhVj1xx9QCFRimDA1hd2ihXpdXnFWNa4fo6aznH2tEDHV8Dot4eNIaBVVuAUOi8Jzyz4E08CZjLpQ1Eog3JWKmpM5gIL6eca04YC/sB+sxnmBYD6Z29JjkfXLL79gz549yM/X/oXXx8cHb7zxBl5//fVnXmSRpBI1NTeRmbUOV6+NxvXEScjN/VFnBEtgFFtGuhKJQoJpftPgZenV4r6s6ixsv7Mds0/MxsTDE/Ft4re4UXoDCmXnjIfp7hAEAfPISHjt3Qv3HTtg1r+/1n2ihAQ8fPEl5M9/Ew03b3bxVarw6mePuasi4NmHftPNulGOfV8loijD8FSfNtgcU7zw4Sr4DKD6MlWXlWDfZytRU26YKzyDw4Tdy0EAS6N+6w/96rccHBzQrx9VFMfFxUHRwhDtplQidXxPuaCVVKLm2J6OKpI3sDje0BSioq4Owh0/U9ZsX3kZbIfWZwuK62U4t/MexUCXw2Nh7JvBYBgoVMrzcrDvi4/RUEN1nA+OGoOJ734ABrNjRuA0pgpR9uNNSDKrac9xQx3guHwAOF4db46qDyRJIisrCzt37sSePXt02pX4+vpi/vz5eO211+Dp2b5h3j0ZpVKKiopLSM9YhYTLw3AjeRby83egsbHlbIy5eRAcHCaCJJ/R+1d3jZiEh4eTN27caH1jDyenOgcx+TGIyY/BvQr9ir1tTW0x0n0koj2iEeEcAQ6ze7kodxUkSUJ05QqEm7egsQVRxRs6BPZLloAbFtaFV6eCJEmkxhfh8qEsKDTa2kEAoWM9EDHVB0xW+7/7KOQynPjxW2QlXaOsm9vZY/aqtbBxpqc3W0KUWIqqw1QnbN5AJ9jM8NdxhIrKykps2rSJkj6cPHkywsPDdR5TX5+B64kqwUUQLIwYngg2W/uNeE1mEbYXqlJf//JyxIfezlr3eq04SXmct+45rfsAAMeWAjd/Uz0e9xUwVHuHYF5NHqYcndL8mEEwEDsrtsXIlmDDBgi3qFKIDHNz+J47C5ZNy113pJLEya138PAutXPvuSX94NXXsLE1pdmZWu1C+kVPwJgFiw2ax6gLpUSB6uPZWi1ECFMmbKb5gRvSecOrW+KxyLpw4QKK1OvmNPDz80NUVBTc3d278Oq6FwpFAyoqLkIgOAthRSzkcn06nglYWYXBgT8OfP5YmJl5tH5ID4cgiGSSJLV+wHVMfNhIm/Gx9oGPtQ/e6vcWSkWliMmPQWx+LG6U3YCS1F5/UimuxOHMwziceRhcFhcj3EYg2iMaI1xHwNykY40GuzMEQcB82DDwhg5Fw7VrEGzeTBt3AgCiK1chunIV3MGDwV+y2CBX7o66zr4j3eAaYINzu+5BWKB2cyOBlLP5KEyvwtj5vWHTTsNGJouNye+twKmN/8GDawnN6/UVTb5Jsz5dCzs3/W8a3IGOEOdUo1FtNp0oqRQcXytw+7d8k7S1tcWAAQOg/qUpPj4eISEhYOuoAXqcSmxoaLKLeJxKdHGZqXU/3Wurg9KIBhTHG5pClFdWovLX3ZQ12/lvtCq0AODW+QKa0Oo/1sNgoVX8IB2Hvl4NaSM1Ldx//GSMfmNhhxR5SwvqULk3HfIKerTRxNsKtnMCwLLuuO5GfSFJEpmZmbhw4QKKi+kF+o/x9/dHVFQUzTvuWUEmq4JAGAOB4BwqKy9BqWz9f4sg2LC1HQq+/TjY88eAY9L95lY+KYxiqxvhxHPCy0Ev4+Wgl1ElrsKFgguIzY/FleIrkCq1DxxukDfgTN4ZnMk7AzaDjQjnCER7RGOU+yi9nKufBgiCAG/IEHAHD0bD9UQIN29GQ1ISbV/DtWt4eO0auIMGwX7JEvAiBnXpddq68DDz3+G4fiwHKefzKaNIBPl12L82CcNm+iE40rVdNzsmi9Vca3M/4ULzuqiqEvu/WIlZn34Few8vvc5FEARspvlBVlgPuVonZdXhLLBdzcHmt2xuGRkZiVu3bkEubzJ3raurQ1JSEoYOHarz9RwcJiEvT2WHUC44pb/Y6gj7B5Kk2z7Ya59yABieQqz4aQeUam7/TBsb2L72equXVZpTg2tHqS7ljt6WGPyClgHvLVB4PxWH130OmcaIp7DJ0xD1yvx2Cy1SSaIurgC1MQ8f10WrYBCwHOcJi0i3Lh+3Q5IkHjx4gPj4+BZFVkBAAKKiouDqalgU+GlALC6GQHAOAsFZVNck6ZXyYzJ5sLOLAp8/DvZ2I8FiWXTBlfY8jGnEHkCDrAEJRQmIyY/BpcJLqJO1HsIlQCDUIRSjPUYj2iMabhbP1rcz0WPRlZiocw83PBz27y4BNyKiy9u1C9Mrcf7X+1rnKHr1tcOoV4PAtWxfq71SqcDZbRtxL/48Zd3UwhKzPv0KDl7636SlxfUo33ILkKs+L9jOPDgs7t+qq/fZs2dx5cqV5sdmZmZYvnw5TE21RzW0pxKvg82mG8dWy+QITFAV3rMJArmR/cDSciPXO41YXw78Ry1NyuYCK4sALWk1Q1OIstJSZI8bD1Kq+vLksOIj2M2bp/1aHiEWybBvbSLqK1V/LxwuC7M/GQhLO/079/JTb+PId19ALqH+3Q16YRaGz32t3f8H8koxKvdlQPqQ7h/I4pvBdk4vmLh17c2YJElkZGQgPj4eJSUlOvf16tULUVFRcHFx6cKre/KIRFkQCM6iXHAWdXX6Weiw2bbg248Bnz8ONjZDwXxGS1k0aSmNaBRbPQyZQobE0kTE5McgriAOwkb9Wvt72fRCtEc0RnuMRoDNszMEtSEpCYLNW9Bw7ZrOPWZhYeC/uwTcwYO79PciFslw4Y8MZN+kdwuaWbAx+rUgg9NDmpBKJc7v3II7509T1k155pjxyZdw8m299uox9ddKaH5bvAgn2lxFTUQiEdavXw+pmsAYOXIkRo4cqf2aSRLXro9HQ4MqihMU+K3O6Fa/y6kol6rGIiVEBMKPSxdyeout3IvAbpWAgnN/YGG81q0/3fkJG1M2Nj+OcIrAz+N/1roXAEpWr0H1/v3Nj1lOTvA9cxoMju6bFUmSOLX1LvLuUP/XJy7qC5/+fJ3HaZJ3Kxl//2ct5DJqlHzIzJcwZOaL7frbJ0kSDbcEqD6aBVJCj4bwIpxg9ZwPGCYdU3CvD0qlsllklZbqbhAJDAxEVFQUnJ211/o9bZAkidq6OxAIzkIgONucsm8NU44L+A7jwbcfB2vrMBBE172XPQVjzdZTBJvJxjDXYRjmOgyfDv4UdwR3mgvsC+p0D/3NqMpARlUGttzeAncLd4x2H41oz2iE8EPAIJ7eplTuwIHw/HUXGpKTIdy8GaIrV2l7GpOTkf/GfJgNGAD7JYvBGzq0S0SXKY+N8W8FI+OaHS7ufQCZ2k2qsU6Gk5vvoG+UK4bO8AOrjTcpgsHAmAVLwGSxkXL6ePO6WFSPA19+ghkffw6XAO3jkTThRThBklONRrWbvuh6KTi+1uD2033T5/F4GDp0KC5cuNC8duXKFQwaNAhcLTP2Hhuc6p1K5JqiXKqqg8sUibWKLb0xoBPxTN4ZyuOWUojShw9RfegQZc1+8TstCi0AuBNbSBNaIaPdDRJa2cmJOP7D11DIqbM6h899DRHTZut9Hm0oG+WoOpqFxtt0U2YGjw2bGf4w6911JQ1KpRLp6emIj49HWZlub7hnSWQplTJUVyc2pQiF5yCR6NedzOP5g88fBz5/HCzMg5+ZL+mdgVFs9WAYBAP9Hfqjv0N/fBD2ATKrM5sL7NMr03UeV1BXgN1pu7E7bTfszewxyn0Uoj2iMchpENjMJz8aozPghoXB45df0HAzpUl0Xb5M29N48yYK3lwAs/79m2q6hg/r9A8XgiAQOMQZzn7WOL/rHkpzqOmXu/FFKMyowtg3g8F3b1v6hSAIjJr3NhgsFpJPHGlelzY24ODa1Zi+Yg3cgvrodR6b6f6QFtVDoVb0XHUoEyYu5mC1YEQ5ePBgXL9+HY2NTXVCUqkUCQkJGDdOuzhx1KjbajI4rdaaSvTnmSKhWiW2HogkmKi/DqGjp9jKq8nDgypVIX1rRqaCjZsANesLtqcHrKdNa/FSyvJqceUwNZro4GmBIdN9WzxOnczEKzjx43dQKqhCK+rVNxE+ueXXbw1JTjUq9z2AooaeDjftZQObmQFgWnSc83xLKJVK3L9/H/Hx8Sgv1+0tFxQUhKioKDg5OXXJdT0pFIpGVFZeQrngLITCWMjl+o3wsrQMhQN/LPj8ceBy2zZf0wgdo9h6SiAIAgE2AQiwCcA7Ie+gsK4QsfmxiMmPQUp5CkhoTxcLG4U48OAADjw4AAu2RXNn43DX4eCyWy5+7olwB4TCY+fPaEhJgXDLVoguXaLtabx1CwVvvQXTkH7gL1kC3ogRnS66rPhmmPavAbjxz0PcOJVH8VCqKm3AwXU3EPG8D0LHeLSpsJggCES9Mh8sNhvXj6jSWDJxIw59swbT/r0aHn1CWj0Pw5QFu5eCmuq3HhlTkhIFKv5Kh8M7ISB02FeYmppixIgROHtWVUyemJiIwYMHw9LSkra/qSvRtzmV2NSVeF5rdKvDi+RpxfHaxZYhXYjijAzUnqSmMflLl4FowZld0iDDmR2pUKoZgJqYsTD+rT5624RkXL2Ekxu+B6nhrD/6jYUInTBFx1GtQ8qVqD33EHUXC0H7aGExYD3JG7whzl0SCVEqlUhLS8PFixdbFFm9e/dGVFQUHB11TwLo6chkNRBWxEEgOIuKiotQKlsfD0YQLNhYD34UwRoDDufp/f08SYw1W88AFY0VuFBwATH5MbhWcg0yZevO5SYMEwx1GYrRHqMx0n0kbExbb0vviTTevg3Bli0QxV/Uuce0b1/YL1kM86ioLrl5lObU4Nwv91ArpIsG1142GDMvCOY2bUuTkSSJa4f24sqBPyjrLLYJnv+/T+DVXz8vsvorxag+Ru2M4w1xhs3zugcoy2QybNiwAXV1qgaP8PBwTJ48Wev+7Jz/UaJbdnZR6B/yC21fQlUdZt5SXUs/czOcHUgXSHrXbH3vD4jUbtrvJgP29J9rxrEZlMjWqsGrMLuX9pRcweIlqI+NbX7MCQiA99EjOr2sSJLE6Z9SkZNCTc1NeLsPfAfo50uVdikOpzf/D6SGhczYt95FvzET9DqHNmTlDajclwFZUT3tObYzD7Zze4Ht2D4LE31QKpW4d+8eLl68CIFA91zZ4OBgREVFwUEPw9ieiERSBoHgPASCs6iqvgaSlLd6DINhBju7yEcdhKN0+tgZMQxjgbyRZuql9c2djRcLL6JB3vr4FQbBQJhjWFOBvftoOJs/fTUOjXfuQLh5C+rjtRdCA4Bpnz6wX7wY5qNGdrrokorluLQ/E+lX6N1THC4LI18OhF9Y228e148eQMJfVK8nJouFKR98DN+w1i0xSJJE5e/30XiP6vlk+3IQuC0U9SclJeGkWoSHwWDg3Xffha2tLW2vvl2JAqkMfS+rDIHNGASyI/uBofEe6SW2GiqB79RSJ0wT4OMSgElNAhjShdh46xby5r5IWXPbshkWGiON1LkTV4hL+6heX32jXBH5YstO9o9JjTuHM9s3NNlYPIYgMH7hMvQZNVavc2hCkiRE10tRczIHpKY5LwDzSNemcTsdYM7bEkqlEqmpqbh48SKEQt0NQn369EFkZORTKbIaGnIfdRCeQ22tfqPJWCxr8O1Hg88fB1vb4WAyn9z8yacVY4G8kWbMTcwxwXsCJnhPgFQhxbWSa4jNj0VcQRwqxZVaj1GSSiSVJiGpNAnrEteht11vRHtEI9ojGj5WPk9F0aRZv35w374NjXdTIdyyBfVxcbQ94tRUFC5eDNPevZsiXaNHd9rPbmLKQvRrQfAMtsOFP9IhaVB9W5U0yHFmRyoe3nXCiDkBMDEz/N844oVZYLJYiN+zs3lNIZfj2H+/xuT3/g3/Qdp9sB5DEARsZgZAWnwTiipVvU7VoQcwcTUHy1Z75C00NBRXrlxBVVXTmCKlUokLFy5g+vTptL36phLt2SzYsJiokjfVQzUqSRSIpfA0a0M7ulDDzNTOjya0AC0pRCfdKcTyH9dTHpuG9IP5qFE6L0GQX4fLh6iu/fbu5hg6U3fUUJ3b5/7B+Z83U9YIgoGJS95H0Ajdr9sSinopqg5lQnyf/hnBtDSBzewAmPp1bvRboVA0i6yKigqtewiCaBZZfH57Cve6FyRJoq7+XnMHoUiU2fpBADgcJ/D5Yx91EA4Cg2G85T8pjL/5ZxgTpgki3SIR6RaJVcpVuCW41VxgX1Sve3xFWkUa0irSsDFlI7wsvZq9vPrY9+nxnY1mffvAfesWNN67B+GWraiPiaHtEaeloXDJu+AEBcF+8TuwiI7ukNEm2vALc4CTjyVidt9HYTp1jmL6tVIUZ1Vj7PxgOPkYngYInzwNTBYLsbu2N68pFXIc/986TFr6fwgcGtni8QyzR/Vb226r6rfEClT8eR8Oi7TXb7FYLIwcORJHjqgK9e/cuYPhw4fTIhBauxLLT9LEFkEQ8OeZIrFG1LyW2SBpm9jSszie1oXoqb3QX3T1Ks12xOH993WKdGmjHKd3pEKp7mdmysT4t/qAxW69I/XmP8cR9+t2yhqDycSkpR+i15DhrR6vjcaMSlQdeABlPb38wKyvPWym+YHB7bzGGoVCgbt37+LixYuorNT+hZAgCPTt2xeRkZGwt386XMtJUoHq6htNAkt4DmKx7s9kdbhcX/D54+DAHwcLi75PxZfhpwFjGtEIDZIkkVGVgfMPzyMmPwZZ1VmtHwTAgevQ3NkY7hQONqPndzaK79+HcMsW1J07r3MPp1cv2C9ZDIsxYzpNdJFKErdiCnDt72zKjRgACAaB8ImeCJ/kZfAgYgC4c/40zv28mZJyIggGJix5H731iITUXSpCzUmqV4/5cFdYT9ZumqpUKrF161ZKnU1QUBDmzJlD26tvKvH/0gvwe4kq2rHa1wWLPajiTa804umPgWtqUaGRK4GRKyhbcmtyMfXo1ObHulKIJEkib+5ciG/faV7jDhkMz1276K/7aP/ZnfeQdYNa5D1uQTD8w1svWk46fhgXf6fWtDGYLEx+/yP4DxzS6vG065EpUH0qF6Kr9FQ2YcKE9VRfcMMcOu1mrlAocOfOHVy6dKlFkdWvXz9ERkbCzq7nT8xQKCSoqrr8qIMwBjKZ9p9bE0uLfs0WDTye/p2qRjoWYxrRiEEQBIFA20AE2gbi3dB3kV+b3+zldVtwW+dx5Q3l2JexD/sy9sHSxBJRbiv+e+UAACAASURBVFGI9ojGUNehMGP1zPoA06AguG3cCHF6OoRbtqLu7FnaHklGBoqWLQcnIAD2ixfDYtzYDhddBINA6FgPuAfZ4OzONFSVqKI4pJJE0sk85KdVYuz83rBqZYSOJv3GTACDxcKZbeubBRdJKvHP5h+gkMvQd1TL42fMh7tAklNNSTHVJxSB42Ol1V+JwWBg9OjR2LdvX/Pa/fv3UVRURBuRom8q0Z9HjWJltrUjUY8xPZrjeXSlEOvj4ihCCwAc3ntP50vfu1RME1rBI1z0ElrXDu/D5X17KGtMNhtTP/gYPgMMnwUqLa5H5d4MyMvpNZ0mHhawndMLLAOc6w1BoVDg9u3buHTpUnO6WROCIBASEoIRI0b0eJEll9dBKIyDQHgOFRXxUChErR5DEExYWw18JLDGwtT02XK974kYI1tGDELQIEBcQRxi8mOQWJIIuR6dL6ZMUwx1GYoxnmMQ6RYJK07P7XwRZzyAcOtW1J05Qy0+VoPj79+UXhw/vlMiXXKpAleOZONuXCHtOTaHiRFzAhA4xMngiMP9hAv4Z/MPNJuAMQsWI2TsJB1HNaFskKFsQwoUauOHCDMWHJeFgqWlc5IkSezYsYMyo87X1xevvvoqbS+tK9E2Ev37U6NDcRW1ePGOKroWZsnFyTCqUNIrsvW/PkCNmjnwO1cBx96ULfp0IZJKJXKffwGSTFVtjXl0NNw3b4I2hIV1OLguGQq56ndv52qOmR+FtWhoS5Ikrhz4E9cO/UVZZ7FN8PyHn8IrZIDOY7WeT0miPqEINWfymlPDzRCAZbQHLEZ5gGB2fDTrsci6ePEiqqurte5hMBjNIktbU0VPQSIVQvhoBmFl1VWQZOsd4gwGB7a2Ix7VYEWDzX46O8R7MsZuRCOdQq20FhcLLyI2PxYJRQlolLfu6cIiWAh3Cm8elu3I65meLpLMTAi3bkXtP6d1ii4TP1/Yv/MOLCdMAMHs+NEWD1MrEPPbfTTW0oeU+w7gY+TLgTDlGZbKzbiagFMbv4dSQR25Mmre2xgwcaqOo5qQPKyFYPsdQM0jzMTDAvyF/UBoSW9mZ2djzx5qNOb111+HtzfVSFGfVGKRWIqwq2nNjy2YDDwYQa1XaVVsSeqAb9RmiBIM4JNSgKWKmumbQqw5fgLFH36odi4C3kePwrQXPVImFctx4JsbqC5TRZFYHCZmrwyHjZNuCwWSJJHw124k/n2Qss7icDDt32vg0aefzmO1Ia+RoGp/BiTZdPNLpq0pbOf0AseT7onWXuRyeXMkqyWR1b9/f4wYMQI2Nj1TZDQ25qP8UYF7Tc1N0A3K6LBYFrC3a+ogtLOLBJP59HkfPk0YxZaRTkcsF+Nq8VXE5MfgQuEF1Ej0cyvuZ9+vucDey8qrcy+yE5BkZUG4dRtqT53SLbp8fJpE16SJHS66GmqliPs9nTbOBQB41hxEzwuCe6BhEYCspGs4/r91NMfxyFfmY+AUetegOnXxhaj5J5eyZh7pButJdCdqkiSxe/du5OXlNa+5u7tj/vz5FJGkz6xEkiThd+kuRApVZOjW0GA4cVRis1WxVZQM7FCzY7DzA5YmU7Zsv70dm26polMRzhH4eRx1FiIpkyH7ucmQ5ec3r1lOmQLX77/T+js4vysNDxKpY2XGvNEbvSJ0O5yTJIn4PT8j+eTflHW2qRmmr/wMboHBOo/VRsNdAaoOZ4FspEequWGOsJ7qAwanY6tO5HI5bt26hUuXLqGmRvvnBYPBQGhoKIYPH97jRBZJkqivT39U4H4W9fW6p3qoY2LCb+4gtLGJAIPRNQ78RtqPUWwZ6VLkSjlult1srvMqa9A9n0wdXyvfJuHlGY3etr17VBeNJDtbJbqUdA8iADDx9ob9O4tgOWkSCFbH3bhIksS9S8W4fCATci3+R/3HuGPw875gsvVPaeakJOHYf7+GQkZNbwyb8yoGT6cXsjdfi5JExe57EGdQa23s5gXDTIvoKygowM6dOylrL730EgICqBEgfVKJE248wK06VXRof4gvIm1VI45aFVu3/gKOLlI9DpwMzKWav+qTQqzatx+la9aoFphM+J46CRNPT2iSdrkYcXuoN+GgYc4Y/arueZWkUonYX7fj1hnqz8Ph8jB95edwCQjUeawmSokc1cdy0JBM/x8lzFiwmebX4tzLtiCXy5GSkoJLly6htrZW6x4Gg4EBAwZg+PDhsLamj2jqrpCkAjU1KY8sGs6hUZzf+kEAzMw8mzsILS37g+jhXd3PKkaxZeSJQZIk0irSmoVXTo1+E+adec7NEa9Qh1Cweog/jCQnF8JtW1F74qRu0eXpCbt3FsFq8uQOFV1VpSKc+yUNgvw62nN2buYYO7837FzM9T5f3p0U/P39V5BLqXPvBs94EUNnvaRTDCtEMpSvvwmFWnqTwWXBYfkAsKzodgx//vknHjxQCRhHR0csXLgQDLV6N31SicvuP8T+UpXI+8rfFQvcVEKhVbF1bg1w+UfV4+EfAGNUoklbCjFudhxsTVUiUikWI3v8BMjVBiBbz54N5y8+p/3cFUX1OLjuBkUg27rwMHNFONg66rRIpRLnft6MuzFU6wlTnjlmfvoVHH308+ICmtK+lfsyoKikNxNwfK1gM7uX1verrchkMqSkpCAhIUGnyGIymc0iy8qqZ9R2KpVSVFVdfdRBeB5SqW6jVXUszIObIlj8ceDxAnrUl0sj2jF2Ixp5YhAEgWD7YATbB2PZgGXIrclt9vK6K7yr87gSUQn+uP8H/rj/B6w51hjpPhLRHtEY4jIEHGbH3QA6Go6PN1y/+w7277yDim3bUXPiBGX4MABIHz5EyYqVEG7dCvtF78BqSseILhsnHmb8OwyJx3Nx8+xDSklIRWE9DnxzA0On+6HvSFe9Pti9+oVi+oo1OPLtF5BJVDfka4f+gkIuw4gXX9d6HiaPDduXAiH46Q7wSEcoG+So/Csd/Lf60YqrR48eTRFbZWVlSEtLQ58+quHY2rsSz8HFZVbzHn+uxoxEkYEdiZqGpnxqhEhbF6K60AKAqr/2UoQWYWIC+8Xv0F5KJlHgzI5UitBimTAw/q0+OoWWUqnA2W0bcC+e6v1mZmGJmZ9+BQcv7VYbmpAKErWx+aiLy29+f5phErAa7wXz4a5tmsGpDZlMhps3byIhIYEyqonyskwmwsLCMGzYsB4hsuRyESoq4yEQnIVQGAeFgj66iA4D1tbhTR2E9mNhZubW+iFGnhqMkS0jT4xSUWlzZ+ON0htQkIpWjzFjmWG463BEe0Qj0i0SFiYWrR7zJJE+fAjhtu2oOXaMJroew/bwgP3ChbCaOqXFwcSGUPSgCud3paG+SkJ7ziPYDqNfCwRPz6hFUXoaDq9bA2kjtQEi7LnnEfXqAp3CrTauALVn8ihrFiPdYTXBi7b34MGDSE1NbX5sZ2eHxYsXg6lW45aT8yNy8zaq9mikEs8Ka/DaXVW92GArHo4O8G9+3Gpka0MoUKkWeX07HnDp3/ywtRSiol6E7LFjoVCzK7CdNw+OKz6i/bwxv6Yh/VopZS369SAEDtE+CkupUOCfzT8g/TJ1nBTXyhqzVq2FvTs9RakNeUUjKvdlQKol+slyMIPt3ECYGBD9bAmZTIbk5GQkJCSgvl67GHkssoYPH651IHl3QiqthFAY86iDMAFKJb0xRROCMIGt7TA48MfB3j4aJiY926bCSMsY04hGuj3V4mrEF8YjJj8GV4qvQKKgiwRNWAwWIpwiMNpjNEZ7jIa9Wfd1jpbm50O4fTtqjv6tW3S5ucF+0UJYPf98h4guSYMM8X9mIFPDuwkATM3ZGP1aELz76fc7K8nMwKGvV0PSQPUA6j/+OYyet1CrxQWpJCHclQpJJrXDzH5+H5gGUIudhUIhNm/eDPXPo6lTp2LAAJV1QWupxNwGCYZcv9/8vB2bhXvDVdGxFsWWTAx87QyoD23+uBgwaeoG1CeFKNiyBcINKjHI4HLhe/4cWBoWBelXSxCz+z5lLXCwE6LnUS0mHqOQy3Fqw/d4cP0yZd3cxhazVn8NW5fWIyQkSaIhuRzVx7JBSul/f7whzrCa6A1GCzYT+iKVSpGcnIzLly/rFFksFqs5ktWdRVZjYxEEwqb6q+rqJNBDgXSYTHPY24181EEYBRarY8Srke6PUWwZ6VE0yBpwpfgKYvJjEF8Yjzqp9tSDOgQIhPBDmmc2ulu6d8GVGo60sBAV27ej+shRQK7do4zt6gq7hW/D+oUXQJi0rxOJJEk8SCzDxb8yIBXTb7LBI1wwbKY/2JzWb7JlOVk4uHYVxPXU96Pv6HEY+9a7WgWXol6KsvUpUNap1W/x2HBcHgqmJTWyduzYMdy8ebP5saWlJZYtWwbWoxSr9q7Edc2pRAVJwufiHUjUrCdSh/WBvUnT8S2KrdJUYNsw1WNrD+A9VZq7tS5EeVUVsseOg1JNXNgvXgz+sqWU16wsFuHAuiTIpaqbto0TFzNXhMPElJ5KlstkOPHjOmTfuE5Zt7DjY9bqtbBxat3MUtkgQ9WRLDTepdcSMczZsJkZoLV5wVCkUilu3LiBy5cvQyTSbszJYrEQHh6OYcOGwcKi+0WlSZKESJTZ3EFYV3ev9YMAsNl24PPHNA15thkCBqP7ljoY6TyMYstIj0WmlCGpNAmx+bGIzY+FoFHQ+kEA/G38m4VXL5te3a74VFpYhIqffkL1kSOATLuhIcvFGfZvL4T19GntFl21wkac/zUNJVn0FntrRy7Gzu8NBz08lMrzcnDwq0/RWEctcA6Oisa4RcvAYNBFmzi7GsKf71JqyEy8rcB/qy+lLqimpgYbNmyAQi3yN2HCBAwePLj5cWupxOikdNyrV9VqHQn1wxDrpshCi2Lr7kHg0Juqx35jgVdU/lWtpRDL//MfVPys6qpkWlnB9/w5MNUEhUyqwMF1N1BZrBIiTDYDs1aEw86VHv2QS6U49t+1yL1FtZ+w5Dti9uqvYeXQukedOKsaVfszKM0KjzENtIXNTH8wzdv3tyWVSpGUlIQrV660KLIGDhyIYcOGwdy8e0V6SFKJ2trbEAjOolxwFo2NeXodZ2rqDodHI3KsrEJBEB3vpWekZ2EUW0aeCpSkEneFd5sL7B/WPtTrOFdz12bhFcIPAVOLIHhSyIqKINyxA9WHDusWXc7OsH/7LVjNmAFGO0SXUkni5umHSDyRC1JJ/b9nMAgMmuqN0HGeYLRSGC0seIgDX36ChhpqejBwWBQmLvkADC1eYrXnH6L2PLUN3iLaA1ZjqbVGp0+fxjW1wc08Hg/Lli0Dh9MUKWgtlbjoXh6Olquu67sAN7zm2pQqbVFsxX0NxH+rejzkXWD8WgCtpxBlZeXIHj8epFgl8hw+/D/Yvakm3gDE7bmPtMvUOYOjXglE7+H06JRMIsbR779C/t1blHVrJ2fMWvU1LO1btmMg5UrUnM1D/UX68GKCzYDVc97gRTi360uIRCJpFlkNDfSxPgDAZrMxcOBADB06tFuJLKVShqrq600F7oLzkEj1s6cx5/V6NCJnPMzNA7vdlzgjTxZjN6KRpwIGwUAIPwQh/BC8P+B9ZFdnN1tK3K+8r/O4ovoi/Jb2G35L+w22prbNw7IjnCNgwnyyhoFsV1c4f/YZ7N9+G8IdO1Bz8BBIDdElLylB6edfQLj9J9i9tQDWM2eCwTE8TcFgEAif5AX3IFuc++UeagSqgnelksS1oznIv1eJMW/0hoUtfcTOY+zdPTHns3U48MXHqK9SzUNMvxwPpVyOScs+BFOju9JitAckuTUUd/K62HxwvC1h6qeq3xo+fDiSk5Mhe/Q7EIlEuH79OiIjIwG03pUYwNPoSNR3RqLmTES1TsTWuhArtm+jCC0Wnw+bl16iXkdiKU1o+Q90RNAwekG8VNyIo99+gYI0areurYsbZq1aC3PblousZWUiVO7NgKyEHmViu5rDdk4vsB3a7kQukUiQmJiIq1evtiiyBg0ahKFDh4LH0+2C35UoFA2oqLjUJLAqYiGXa7efoELAyir0UQfhOHC5+jUiGDGiiTGyZeSpoLi+GLH5sYjJj8HN8ptQkq0XsvLYPES6RmK052iMcB0BHvvJ3xRkpaWo+GkHqg8coImux7AcHWG3YAGsZ89qk+gCmkbEXD6QSRMAAGBixkLUSwEIGKjbwRwAqkqLceCLT1BXQU3t+oZHYPJ7K8DSKPJX1ElRtv4mlPWqn4thzobj8gFgWqhEb2xsLC5evNj8mMPh4L333oOZWdPg45ZSiSfKq7HgXl7zc5E25tjfv8l7qsXI1uYIquB68xzgPggAMP3YdGRWqWYcrh6yGrMCmsSdtKAA2RMnUervnNashs2LLzY/ri5rwP6vkyCTqNKj1o5czFpJr9OSNDTg8LrPUJyRRlm3c/PArFVrwbPW7aJOkiREV0tQfSoXkGv8/ROARaQbLMd6gmC1zTBTLBY3i6zGRu2juUxMTDBo0CAMGTKkW4gsmawaQmEMygVnUVmZAKWydfFNEGzY2AxutmjgcDrW1NXI04sxjWjkmaJSXIn4gqbOxqvFVyHVo0XbhGGCwS6DEe0RjZHuI2n+SV2NrKwMFTt+RvX+/SCl2q+f5eCgEl2muiNRLZGTIkDc7+kQi+jCLiDCEZFze4FjpjsAXlNehgNffoyacmoaxrt/GKb862OwTahiUJxVBeHOVEr9FsfPGvbz+zTXbzU2NmL9+vUQq0WLhg8fjjFjxgBoOZWYIRIjKlElmpw5bKQMbRpdo1NsKWTAWmdAqfY7+OghYGZNSyEyCSZiZ8c2/30Uf7QCNX+rRuawXV3h+8+p5ho7uUyBg98mo6JQVTjPZDEwc0UY7N2oBeJiUT0Ofb0apVlUvy++pzdmfvoVuJa6/acUdVJUHXxAc+4HAKYVBzazA2Dq2zYndrFYjOvXr+PatWstiqyIiAgMGTIEXO6Tnd8nlpRCIDgHgeAMqqsTQephKcNkcmFnGwU+fxzs7UeBxep+xftGuj9GsWXkmUUkEyGhKAEx+TG4VHgJ9bLWzQcZBAOhDqHNdV4u5q13fHUWsrJyVOz8GdX79oOUaLfDYPLtYb9gAaznzGmT6BJVSxDz/+ydd3hb9b3/X0db8pI17NiO7Xhlk70niSHsTUpbVqGUFtrS9td7e9tCbwelpe3t7b6kQMOGElYZZSQ4e4dMMr3jbUuyPLWl8/tDsoYlx0piQgLn9Tx+Yp1zvuccK7b01vuznj1G49HOuH1pBg2X3D2R3NKh36h7rBZe/eWD2FtbYrYXXDSN6//zIZTq2HvqXltP7/rGmG3plxaSXl4QfrxlyxYqKiLNO5VKJQ888ABpaWmhqsTLcTiqw/sHqhI9gQDFmw/hi3pZq1x8EekK+dBiy1IJf5sd9UPnwPeDgu1UVYjuqipqr70uZiZmzqO/Rn/99eHHG188wZFBeVNLvzyOyUvyYrY5e3t49ZGf0FFXE7M9u7iMmx78BdrUod/8ncds2F+tIpBAMGunmMi8vhSZ7vRbibhcLnbu3MnOnTtjhG80arWauXPnMm/evE9VZPX314YrCHt6Dia1RqnMxGQqD1UQLkQuP7MPLBISA0hiS0IC8Pg97G7bTUVDBRsaNmBz2ZJaN8EwITw6qFRf+qkkxXo7Ouj8x2rsL78ckx8UjdxkwvjVr5L5xVuQhUJuySIGRA5taGLHGzX4B4WgBAFmXF7I7KuLkMsTh6D6Om288vCDdLY0xWwfPXEyN/zXT1FpIvcjBkQsT3yMpy6qMlIA89cuQl0cFHUej4c//elPMdVtc+bM4corg47WqUKJi3cdo8oREabvzihjRkbK0GLr6Fuw5vbIjqKlcOdbwKlDiE3ffoDedevC+1QlJRS/9WZ42HjVR+2sfTK2dUDpzCxW3DMp5nfI0d3Fq798CEtDfcyxOWXjuOnHv0CtSxyOC3j8dP+7lv5dbXH7BLUc/XUl6KZnnfbvq9PpDDtZpxJZ8+bNY968eeHw7rlEFEV6ez8OVRCuixHep0KtzgnPIMzImIXsAhkDJnFhIImtT4O3HoDUbDCNBVMpGMtAff5U43ze8Qf8HLIeouJkBR82fEhzX3zVViIK0gooLyhnecFyppinIDvHA2N9Fgu21U9hf+mloUWX0Yjx7rvJ/NIXkZ2m22Br7mPtP47EtCcYIKswjUvvnoQ+O/E5+7vsvPrLh7A2xlaJ5o6byI0//BnqqHvx97iD/bei3BhZmirYfyvUimDXrl289957kf0yGQ888AB6vf6UocSvHq7j35aIkPvD+Hy+lGMcWmxt/h2s/2Vkx5yvw5W/PWUI0fnxYepXrow5X96f/0T6ihUAdHWE8rSiepulm7Xc8uPZqKLCsn32Tl795UPYmmIrNfPGB58zlTbxc+1p7qPzn8fxWeLDeqrCdAy3jENxiiKHRDidzrCT5R7CRdVoNMybN4+5c+eec5EVCPjo6t4THvLsdsfnGyYiJaUMsyk4gzAtbbJUQXge0e31UeNwU+VwU+Nw4RPhv0s/vUjC2SKJrXONqwceTdBUMy0XTGWhr7FgLA1+nz4aEjSElDg3iKJIpb0yXNkY3U/pVJi15nBl4+xRs1HKR2bUTjL4bDZsq1djf/ElxCHyaOQGA8a77yLzS19CdhrJyj6vn51v1HJwUKgPQKGWs3hlGRMWJm4b4Ojp5tVHfoKlPnbg+KjSsdz0o1+giSr/d1Xasa4+HHOcukyP6a5g/pbP5+Mvf/kL3d0R4TR9+nSuu+66U4YSf1Pbyh9ORnLI7ss389PSvKHF1mv3wMevRHZc9XuYfU9cCHFezjyeWPEEAA33fI3+rVvD+zSTJjHm1VcQBAG/N8Brv9sbMxBcphC4+QezMBdEwoG9nVZe+cWD2FtjhX7+pCnc8IP/RpkgJCwGRHo3N9Gz7iT4B712yyC9vJC0i/Pj5k+eCofDwc6dO9m1a9cpRdb8+fOZO3cumjPMDzwT/H4XnZ1bwxWEXm98Tloi0tOnhR0sna7oE75LiVPhF0UaXR6qHW6q+13UON1Uhf61eGIbO6fKZVQtvuiCFcSS2DrXNO+DJ5Ylf7xCGxFe0ULMWCq5YZ8Cjb2N4crGAx0HEBn+byRNmcaS/CWUF5SzMHchOuW5yV/xdXbSuXo1nS++hDhEGb48MxPDXXeR+eUvI09NXnQ1HLVR8fQxHAkaYhZNNbHs9vFoEzTEdPb18toj/017bVXM9qwxJdz80MNo0yLNU7vfr6d346D8rcvGkL4s+GFl//79vBmVgC4IAt/85jcxmUxxoUSDYTHTpz3N6+127j8acdcuMabz/JTiocXWqsXQdiiy4yv/hjGLhgwh9u/eTcMdd8acK//JJ0ldFOxAv/mflXy8MTacuviWsUxZFhmr02PpYM3DP6a7PTYEWDhlOtf9x4NxeW4Avi4XnS9XxoZfQyiMGjJvGYe6IPnRNw6Hgx07drBr1y48QxRhaLVa5s+fz5w5c86ZyPJ6e7DZNoQqCDfj9yf+vY5GEBRk6ucGE9zNl6BRn7qSVmLk6fH5qXa4qHG4g8LK4aLa4abe6Y6Z6jAcBxdMIlt97j64jiSS2DrXHHwZ3rh3ZM6VnhclwMoigiw9L5hMI/GJYnVaw8Oyd7XuwhdIPGInGrVczfzc+cHKxtEXo9ecWRXY6eCz2+lc/RT2F14gMJTo0usxfOUrZN52K/IkG0w6+zxseO44dQfjR73oMlSU3zmBgonxfZ/cjn5e+/VPaa2M7V9lKhjDyod+iS4j+JyIfhHL44fwnIzqeSQD871TUI/JwO/389hjj2G1Rq4/adIkVq5cSV9fJbt2XxHePhBKPOFScclHEXeyQKNi9/yJicVWwA+/ygVfVEj2P2uo9fVw3b+uC28aCCFmqjM5eettOKPGCulmz6bg2WcQBIGafR28/3isW1c83czl90bCV13tbbzy8I/pscTOrCyeMZtrvvcjFAka1zoOWrC/UYWYYOSSblY2+mtKkCUxcgmCvct27NjB7t27zxuR5XZ3YLF+iMWyFrt9J6KYuO1JNDKZBqNhMWbzZZhMy1Eqh67WlBgZ/KJIU8ilqgmJqQFh1eEZ/rUxGV6dVsKizAuzGlQSW+ca+0mo2wTWSrBWB/+110MSJchJo0wBY0koJywkwIxlQTdM9emWXn9W6fX0sqVpS7CysXkLTl/i8F00ckHOzOyZ4QT7USmf7Cdun91O59PPYH/+eQJDjE6RZ2Rg+MqdZN5+e1KiSxRFjm1rZcuaypiZfgNMXZ7PvBuKUShj3+w9TgevP/pzmo/HJokbRxdw80O/JDUz2D7B1+Wm48/7CDgiL9bydBVZ35mBPEXJkSNHeOWVV2LO8fWvf52cnBx27LwsLpSYmX0TxZsPhf1IAahZMoWJD74Xc476R6+Czjr487TIRq0B/quOVQdX8bcDfwtvHggh9m3aROPXvxFznsIXX0A3YwbdFidrfrUHjzPyc6QZNdzy4GzUoWpAe2szax5+kD5brHgtnT2fq7/7A+SK2E/0AZePrjdrcOyPHyYu0ynIvLEM7eTkhon39/ezfft2du/eHW4aOxitVsuCBQuYM2dOuGv/J4XDUR/Kv1pLd88BSMJBVijSMZmWB4c8G5Ygl5/75PzPA30+f1hEBXOqgv/WnqZLNRxKQaBIq6ZUF/wq0WlYZkgjS3K2zh0XtNhKhM8D9jqwVgXFly0kwqyV4IoPC5wVGfkR8RUdmkzLkdywEcLtd7OzZScVDRVsbNyI3Z1cLslk42TKC4MJ9sUZxZ/Y/fm7urA98wz2556PGY4cjSwjA8Odd2C4/faYGX5D0dXuYN3qI3ScjB8MbsxL4dK7J8XN+PO6XPzrd7+g4fChmO2ZOXms/O9HSDMEhYLzeCe2p2NFmWa8AeMdExEReeKJJ2htjSREl5WVceuttw4ZSpy74ygnXRHXZt2ssVzzyIaYmwgm7AAAIABJREFU89c/ehVUfgAvRmYcUrAA7n4vYQjx5tKbqLvpZtzHItMKUpcuJf/vq/D7Arz+u70xz41MLnDjf8wkuygY2rM1NfLKwz+mvyv2d2Xs/MVc+a3vx3Xdd9d30/nyCfz2+DwqdZkew8qxccO8E9HX18f27dvZs2fPkCJLp9OxYMECZs+e/YmJLFEU6es7RoflAyyWtfT3J5cbqVZlYzJfSpZ5BXr9HGSyC/ON+HwjEHKpBof9ahxu2jzDO4ung1GpoEynpkSnplSnoUSnpkynIV+jQjHMeLALCUlsnc+IIvRbwRYSYdaq4JetKuSGDd8JPWlUqVG5YQMJ+mODDplS+oR4pvgCPvZ37A/nebX2J1clVZRRFO7lNck46RNJCvV3d9P5zLN0Pvvs0KIrPR3DHXdguON25Omnzvnx+wPseaeOfe+fZPBLh1whY/4NJUxZNjpmwLTX4+at/3mE+oP7Yo7PyB7FF37yK9LNWQB0vVsbN8sv48oi0paMpqqqihdeeCFm31133YXR6E4QStzJ3cfsrLNFQpN/m1DA9/+4I2Z9/aNXwbY/wbr/jmyceRe1Sx5IGEJUbNhF8/f+X8w5it54Hc2ECWx9pYqDFbG5ZwtvLmXaJcHeYZaGel55+EGcPbEfrCYsXsbl9303Zp6k6A/QU9FA74bGeLNHLpBxRRGpC3JjnuNE9PX1sW3bNj766KMhRVZKSkpYZKnOcth5IkTRT1f3vrCD5XI1Db8I0OmKMJuCQ57T06cgnOOq388S/T4/1c6giBpITK/ud1HndOMcQZdKIUCRNl5QlejUZCo/Hy02JLF1oeJzB8Mc1sqQGIv6co+kGyaAPj/khIVaVQzkiKWNktyw00AURY51HgsPy67uSq7/T7YuOxxqnJk9E8UI9//xd3fT+exzQdHVG+9MAcjS0jDcfjuGO+9AnnHq/JeW6i4+XH2U3s749hP5EzIpv3MiKfqIQ+LzeHj7D7+mdt+emGPTzVms/Mmv0GePQvQHsPz9EJ6oKj5kAuZvTEGVn8ZTTz1FQ0OkRUJBQQF33XVXgqrEX/OkYxH/1xgJvX23MJtVj8eKvfpHr4J/3Q8HokTc5Y+ySivEhRAfX/4YtVdfg6e+Prw97YrLGf2HP1B30MK7j8XOMRwzxcSV9wWrqtrranj1kZ/g6o2dxTfp4ktY8fVvI4sajO61Oul8+QTexvj/I0W2DsMXx6PKOXWRQ29vb1hk+XyJ82hSUlJYuHAhs2bNGnGRFQi46ezcHmoy+iFeb3yz3ESkpU0ODXleQYru0+lnd6ESEEVa3N6wOxWdU9XqHlmXyqCUU6rThMN+A45VgUaN8jPkUp0Jktj6rCGK0G+Jd8KsldDVMMJuWFqs+BoISxpKQCl1XB6Okz0nwy0lDlkODb8AyFBnsHT0UsoLylmQuwCNYuSeZ39PD53PPUfnM88S6Ek8iFeWmkrm7bdhvPNO5Pqhk/vdTh+b/3mCyl3tcfs0KUqW3T6e4mmRuXJ+n5d3/vhbqvfEOkypRhNf+MkjZObk4bO7aP/zfsSovCe5Xk32A9NptLTw1FNPxay97bbbkMneiQslnsj+Pd89HnGarjRlsP6F2HmD9Y9eBU+UQ3PU68ztb3Djkb/GhRAv/VhG64MPRT1JMorfeQd3xijWPLIHd1S+WapBzS0PzkGToqStupJXf/UT3IPy56ZeegXld9+HEGr5Iooijo/a6Xq7BjFBXlzqwlwyLi9CUA7t8PT29rJ161b27t07pMhKTU1l4cKFzJw5c0RFls/Xi822iQ7LWmy2Tfj9w09qABl6/WyyQgJLo7lw+yudK/r9fmoThP1qHK4Rdankp3CpDJ8Tl+pMkMTW5wmvCzpro8KS1ZEcMXcyU+6TRQB9QXyCvmkspGZJblgCOhwdbGgIVjbuaduDTxy+eker0LIwdyHLC5azNH8p6arkS/tPhb+3F/vzz2N7+hkC3YldUllKCpm334bhzjtRZA49ALlqTzsbXzwRkxg+wMSFOSxcWRYeuOz3+Xjvr7/nxI4tMcel6DNZ+ZNfYRydj/OIDdtzscJIMyGYv/XCCy9QXR1xsXJycvjyrReze1CD09Spm7j2YKStQqlOTdMbsb2/6n99Jfw6HzwRF6n2ng+4ruJr4cdyQU7F9e/Tef2X8bVEwsMZN91I9i8e5o3/2Ud7XeTvSiYTuOE/ZjCqOIPmE8d4/dc/xeOMrQ6dfsU1LLvz3rBz4+/3Yn+9CteR+IkGsjQlhpXj0Iwd+vnv6ekJiyy/P3ERTmpqKosWLWLmzJkolSOT8+TxWLFYK7BY1tLZuR1RHH4GqUymwmBYjNm0ApNpOSrVpzuD9HxEDLlU0YnpA4nqzSPsUmUq5GExVRoSVqUpagoll+qMkMSWRNAN62tPkKBfFXTDkqgEShp1euIEfUMxKD7ZCqcLhW53N5ubNrO+YT3bWrYlVdmoEBTMHjU73MHerDMPu2Y4/H192J9/gc6nnsI/lOjS6ci87TYMd31lSNHV2+niw6eO0lLVFbcvw6zl0q9OIntMUCgG/H4+eOyPHN0Sm7CuTc9g5U8ewVwwhq63a+jbFjtrMePqYnqLBR5//PGY7V/4whfo7vleTCgxv+w3LKkuDT+WC6D4oBkh6te8/sfT4X8nRDao0lh11UNxIcTftC+l/ZFHwtsEpZKS999jz04n+9fFdn6ff2MJM1YU0nT0MK8/+jO87tgw66xrbmTJrXeFhZaryk7nmkoCvfFCRTPRSOaNpeGO+oPp7u5m69at7Nu3b0iRlZaWxqJFi5gxY8aIiCynsymcf9XVvRcY3kWXy1NjKggViuR7vX2WcfgD1CYI+9U43Tj8IxedkAtQqBmo9os4VKU6DUaV5FKNJJLYkjg1XmfQDYtxwkLhSU8y4YAkEWSgL4xP0DeVQYr5c+uGOX1OdrTsCFc29niScyCnmKeEE+wL0wvP6h78ff3YX3yRztWr8XfFCyYAQafDcOuXMdx1FwpDvCMRCIjsX3uS3W/VERgU0pDJBGZfXcSMywuRyQQCAT/rHv8rhzesizlOk5bOzQ8+TFZ+ER2rDuJtivr9kwtkfWMq/9rxHkePRpwvk8nEFVf4qD8ZG0r8quM/aYlyAlRb25H1R9y3+q9p4bkbIufPm8WN2RkxIcSfTv8hU+57DL8t4jpl3n47rmvv5d9/iw0LF042ctX9U2g4cpB//fZhfJ7YKsK5N9zCwltuQxAERG+A7g/q6dsaPyZKUMrIuKaYlNmjEuYtdXd3s2XLFvbv3z+kyEpPT2fRokVMnz79rESWKIr091fSERJYfX1Hh18EqFSm8IiczMx5yGQjn3x/ISCKIm0eL9X9bqpDiekDjtVIu1QZCnnEnYpqpTBGq0IlTSg5J0hiS+LMEEXobUucoN/dyIi6YZqMxAn6hmJQfH5eqL0BL3vb91JxsoL1jevpcMT3V0pEqb40nGA/wTDhjJOLA/392F96Cds/VuO3J25nIWi1ZH75SxjvvhuFMb6hacfJHtatPkpXe3xz1ZzSDC75ykTSTVrEQICK1as4uO7dmGPUKSnc/OOHMRkKaP/zvphGnvJMNbIvF7Bq9d+Jfu26+uoZdPd8L3KPgoLH9G+ypSviLCkP2JC3Rx7XX98A7/8w/Lj2ohu4rm9v5FqCnLd7v0LfX/4e87OPevUdXvu/GlxRcx1T9GpueWg27dUf8+b/PILPG+tULfjCrcy/6UsAeNv66fzncbxt8c+PcnQqhlvGoTTH98rr6uoKO1mBQGLnIz09ncWLFzN9+nQUijNzLUQxQHfP/rCD5XQ2DL8I0GoKMJuDAisjYzqCkFyT1c8CTn+AOmd02C8S+usfQZdKBhRqVZSEBZUm7FiZlAqpqOBTRhJbEiOPxwGdNfEJ+tZq8CZupnlGCHLILIx3wkxjQWf8TLthATHAEeuRcIJ9fU99UutyU3LDwmt61nTkstN/0ws4HNhf+ie21atjXJ1oBK2WzC9+EeNX70Zhim2s6XX72fZaNUc2xzs3Ko2cJV8ax7i5oxBFkY3PPMG+996KPUar48Yf/RyD14zt+WMx+7STjGxJq+TAgQPhbXq9nrnz3sXhqAlve8fwJC/ZI2FPRXUPippIflb9wnWwN5Jwv2rmDfytMyK2lmbM4tu/OhpTSJB579fZHlhMa3Uk5CrIBK7/f9Nxdp/g7f/9Nf5ByemLv/wV5lx3M2JApG97C93v14Fv0OuuAGkX55N+SQGCPNaFsNvtbN26lf379w8psjIyMli8eDHTpk07I5EVCHiw23eGKwg9HktS61JTJ4QrCFNTxn2m3+xFUaTd44tKTI+EAJtcnpH86Em6QkaJNpg/FR32G6NVoZZcqvMWSWxJnDtEEXpaBjlhoRyx7vjBxmeFRp84QT9zzGfSDavtqg0LryO2I8MvAAwaAxfnX0x5QTlzc+ailp9ezlzA6cT+z5ex/eMf+K3xI3sABI2GzFtuwXjPV1GYY/PI6g5aWP/ccVx98SGTstnZLP3SWFRaBZtfeIqP3n49Zr9SreHGH/6MlCoN/Ttie5cJl2bxj20vx4iP8nIHHu9r4cc7U+7jL45Lwo9lrQ5UhyJuXf3Yv0LD9vDjGyfNpcoRuc7fqhdgfmVzZH16OrbvP8X+DbHzDOddX0x6Zgvv/Ok3BAaF9S6+4x5mXnU9/h4Pna9W4q6MdwvlejWGW8ahLoptt2G329myZQsHDhwYUmTp9XoWL17M1KlTT1tk+Xz92Do3Y7GsxWbbgM+XuCVILAIZGTPDFYRabf5pXfNCwBVyqRJ1UO8bQZdKIDhKanAeValOjVkluVQXIpLYkjg/8PSDrSY+Qd9WDd7hh80mjSAHQ1F8gr6xDFLiw14XIm39beFeXnvb9+JPYhSUTqFj8ejFlBeUszhvMamq5IecB5xO7C+HRJdlCNGlVqO/5QsY77kHZVZWeHt/t5v1zx6j4Uh8v6VUg5pLvjKR3DI929c8z87XX47Zr1Cpuf77D6HZAt7m2Pyt/VOt7D0acbdMJg8TJkbWnxAm8Qt+Ebm/Xi/q7ZGwbL3h2+AIuna1SgXXjY60HjD0y/j74zJEVyTs6Lv7x2yuzYu5v4KJBkpndPPe336POEgQLb/7G0y/7GqcR6zYX6uKGUc0gG6aGf31pcg0EaHU2dnJli1bOHjw4ClF1pIlS5g6dSpyefLOpcfTidW6Hot1LZ2dWwkE4rvTD0YQVBgM84MVhOZLUKuSGw90PiOKIhaPLy7sV+1w0zjCLlWqXBaXR1WqU1OkVaORSy7VZwlJbEmc3wQC0NuSOEG/Jz4MdVZoDfFOmKks6IbJL8wxIF2uLjY2baSioYIdLTtw+4d/A1XKlMzNmRsclp1/MSZtcm+gAZeLrjVrsD3xJD5L4lCToFKh/8IXMH7tHpTZ2UDwze3jjc1sf60av2+QgBBgxopC5lxTxO43X2b7mthO8Qqlimu//iNUH3oR3RFR6cqEf3o3xfSUWrKkApFgFWMvqXxDeCZyIr+IuqIFQQQDPezTRGYcrjIY+VtGpEruh9vNzNgUcbm82WPYM/tHuPoi19JlqJi23MGGp/6KGN3bThC49GvfZPLiS+l+p5b+3bFOGICglpN5Qym6aRFRarPZwiJrqNflzMxMlixZwpQpU5IWWS5XCxbLWjosa+nu/ggxCWEul6dgNC7FbF6ByXgxCsWFORjYHQi5VP3uuFYKvSPsUuUPcqkGvs+SXKrPDZLYkrhwcfcFna9oJ2zADUuiXULSyBSQWRSfoG8qA92F0wvI4XWwrWUbFQ0VbG7cTK93+NCQgMD0rOnhPK/RaaOHXRNwu+la8wq2J57A15E4iV9QqdCvXBkUXaOCA7htLX2s+8dRbM3xVa7mgjQuvXsiVbveY8uLT8fskysUXLfyByh3xgqFfTnN7LMfDz8uLjlCXl6kU/w3Zc/SJUZElGpLGzKHn7nCMV5WPxzefmPhGKpkwTdfU7fIXx8HmS94rYAg4+g1/0NHTyQEKwhw0ZIedr/5D6LnFgmCjMvu+w5lxXPofPkEPmv876hqTDqGW8ahyAw2q7XZbGzevJlDhw4NKbIMBgNLlizhoosuSkpk9fdXh2cQ9vYeHvZ4AKXSgNl0SaiCcAHy0ww5f1qIoojV64txp6r73dQ4XTQ4PUk0p0ieFLlsUGJ6sIP6GK0areRSfe6RxJbEZ49AAHqaEifo97YMv/500BkTJ+jrC0F+/vap8fq97GnbEww3Nq7H6kwc/hvMuMxx4V5eYzPHnvJTecDtpuvVV7E9/gS+9vhO8hDsS6VfeTPGr30NZU4Ofm+AnW/WcODD+Bw+hVLGwpVluHv3sPHZJ2P2yeRybljynyjqI69ZLrysSd2Jxxes/tPpupg56+3w/l8Kv+AYk8KPlftsyC0ubpV/yCPK1UB8CPG+dwMsOxh5i66ffAu1piUx9zJ6bBPVu9bE/pwyGVfc///I8xbT82EDDO7oLRNIv7SQtKXB2ZFWq5XNmzfz8ccfn1JkLV26lMmTJ59SZIligJ7ej8MVhA5H7ZDHRqPR5AUT3E0r0OtnntcVhJ5AgHqnJy6Pqtrhpts3vFt3OozWKOPyqEp1GrIll0riFEhiS+Lzhbs35IQNStC3VYMvfpbfGSNTBltTxIUlS0E7dMfvT4OAGOCQ5RDrG9bzYcOHNPYmV6wwOnV0sJdXYTlTzVORDTEQOODx0P3aa1gffwJf6xCDuJVK9DfdiOnee1Hm5tJ4rJOKp4/S3x3f0HPMFBNZo+vY/MITMdsVchXXT/4u8p7IG95+ZR175RFxMXPW2+h0wV5hT/E1PhQuj6yv7EZR18dPFc9wl+IDAFbp0/lbZnAsUY5N5A9P+JGFXhY79eM4MO3bBANFQVLSj2M7GduuQiaXc/U9/0FGZTqe+vg+aQqTFsMXx6EanYbFYmHz5s0cPnx4SJFlNBpZsmTJKUVWIOClq2s3Fss6LNZ1uN3x4cpEpKSMxWxeQZZ5BampE88r8SCKIjavP6rSLzKS5qTLjX8E3650chmlWjWlKRpKtGpKU4KCqkirRie5VBJngCS2JCQg6IZ1Nw5ywkKCrC+5N6qkSTEnSNAvPS/cMFEUqeqqCifYH+88PvwiwKgxsqxgWbCycdRclAly3AIeD92vv4H18b/HjLeJQalEf8MNmL5+L/6MLDa+cJya/fH5X9p0FcUXtbP330/HhOrSlUYuL/wqgj8oEjz4WKPdgSs0Lqag8CCFhcGGox9wBc8K94TXypodqA7beV75CIvkwYrOG/JGUR2aE/idf/lZeCx4LbcqnT1zH8Ijj4QhBXE/zq7YzvcyuYLrbvoB6kPE5JQNkDJnFBlXF2Pr7mTTpk0cPjx0WM9kMoVFlixBib/f76SzcwsdlrVYrevx+ZIbSJ+RPj3UouFSdLqipNZ8kngDIvVOd9zg5BqHG/sIu1R5amVMP6oBxypHrTyvhKbEhY8ktiQkhsPVExJggxL0bTWQRMJ50shVETcsOkHfWAraoYc+f5I09TaxvmE9FQ0V7O/Yj5hELVaqMjWmslGnjG3CKXo8dP3rX9hW/R1vyxBhXYUC/Q3XY7j3Xmob5Wx5uQpvArGSU9xK/b6XY5LQC1MnMc98dfjxYXkDO5XBzu/RocTDXMSvhZ+FjxO6Pah3Wtip/iajBHtMCLGwXeR3q4PXFxE4MPVb2DPHh9f6XDvxOSOtIgA0qlSumf8Asob4+5alKMi8cSy9Zj+bNm3iyJGh23WYzWaWLFnCpEmT4kSW19sdriC02TYTCAzvzgqCgszM+aEQ4SWo1VnDrvkksHl8Mf2oBkKA9SPsUmllsvB8v2hBVaxTk3Ia1ZoSEmeDJLYkJM6UgD84OzIuQb8qOGtyJEnJSpygry+AM2hMeibYnDY2NgYrG3e27sQbGH6kiEqmYn7u/HBlY6YmEkIVPR663nwzKLqah6gsVSjIuO5aVLfczcb37DGDnQfQ6Orobn0zpr3CbNPlFKdNBcCHn1fUO+gXgsJ4xsy3SEnpxo6ebwn/iJzIF8BUUcNhTdDtig4h/tcaPzNrgq+HdYWXU1d0TfBnEEV8ru34Xbti7mlUajFLCr+A4Ih/DVWPzcR7sZ6tH22PGS00GLPZzNKlS5k4cWKMyHK724PhQcta7F27EJMYWi6TaTEal5JlXoHRuAylcmSGlg+HNyBy0hWq9ut3UeOMJKh3ekfWpcpVK8N5VNGiKletRCa5VBKfMpLYkpD4JHB1D3LCQgn6nTXgj89DOmPkajCWDErQDzljmk/uDbXP08fW5q1UNFSwpXkL/UlMBpAJMmZmzwwm2OcvJyc1BwDR66X7rbewrvo73sYh8sXkctKuuY7GyTezf5udwS9NAX8V3t5/hx0uuaDgktw70KuCjVSPy5vZqgyGRAdCiSJwL8/iECKhwBmbd/CuGBzTMxBCHNck8vBzQWFgzyhl/7TvgCALCi3nFvzuyGuRDBlTTBczNm02cW/vCgHPonT2dB/j2LFjg/eGycrKYunSpUyYMCEsshyOuvAMwp6eA0OujbmcQo/ZVI7ZvAKDYRFyuSapdWeCfVDF34BjVe90xzXEPxs0MiHUOmHQSBqtmhSF5FJJnL9IYktC4lwS8EPXyfgEfWsl9Cc3BiVpUkclTtDPyB9RN8zj97CzdSfrG9azoXEDna74BqWJmGicGB6WXZxRDD4f3W+/g3XVKrwNQ8zck8vxXXEb++UL6O2OdXT8nhq8jncg1CsqTWlkRe4dKGQqAgR4VbWTHpkzJpT4Mx6hSoiEA5fvX8+LPT+PhBBFkZ+94GdiI3iUqeye9SM8an1IaG3E794fXpumNDA/+1oyldlxt91t8nHI3MKJuqq4fQNkZ2ezdOlSxo8fjyAI9PYeDo3IWUd//9DrolGrRwVnEJpWoNfPQSYbuRxAX0CkweWJyqWKVP6NtEs1SqWMhP3CSeoa8iSXSuICRRJbEhLnC0570P0anKDfWQtJhOySRqEBQ0l8gr6pDNRn16DSH/BzwHIgnGDf3Jdc49kx6WPCvbwm6cfT++93sT22Cs/JkwmP9yl11F/8XRq8sV3b/d46vH1vAcE3/zGpk5lrvgqAGlkbG1TB3KiBUOLj3M8moTy8/rLK9TzT+nMe06fzf5l6ptQGeOjlACICB6fcT6dhYkhorcfvPhheV5I2lWnGchRCbGGAVejlUHYrtV1DV3iOGjWKpUuXUlZWQm/vvmCCu2UdLndybUp0upJwBWFa2kVnndjd5fXFdU6vdriod3rwjuB7gkYmUKRVJ+ygniq5VBKfMSSxJSFxvuP3RblhlbGzJR3J9cdKmrSceCfMNBbSR8NpDrkVRZET9hPhmY1V9uTcmSxtVrCyMe9ixu21YF/1OJ76+oTHdmTN4MTEO/ASETl+bwPevn8BQedrjulKitIuQkTkddVu7LK+cCjx31zDi8JXwmuXtWznpaofBUOISiW/ftpPSRvUF6ygtvi6oNByrMPvCVYNqmVaZpuuIC+lLOa+rEIP+zQnaRATN3WFAZG1AJPJgsW6Dqu1Aq83OVcwPW1KeMhzSkpJUmui8YsijS5PMI9qkLCyeofPATsdslWKqLBfJKdqtEaFXHKpJD4nSGJLQuJCxtGZOEG/sxYCI/imqdCG3K9BCfrGUlAnN0exoachXNl40HIwqcrGdFU6F+cu4araDLLWbMJbVx93jEut5+j4O+jKHBfeFvA24un7F+BFLii5NPcOMlQmTsosrFMdCocSDzCd3wkPhddN6T7OqiPf5LrRucw5EeA/Xg/QlVHC/mnfIYCA17GWgCeY1D5KW8Qc05VoFZGf3yL0sE9RR6N8aBGcl2dg1iw1CsXH2Do34/cPn+8mCHL0+jmhCsJL0Whyhl0D0OPzx/SjGvi+zuHGM4Kv7ypBoDhKTEW7VGmSSyUhIYktCYnPJH4v2E/GJ+hbK8GZnHuSNOl5iRP00/OGdMOsTivrG9azvmE9u9p24UtCGGoFNbe1FbPkw3bUDbGOkYhAQ345tUXXIIbylAK+Zjy9bwAeMpQmLsm9A7lMwduqj+iQ9TBj5ls4UlR8V1gVPo/e28MDR29lVUYGv3/ST1ZPCntm/QiXKh1v//sEvCeQCwqmZC5lbEbkdbND6Ga/oo5GuS3hvSuVTopLeinIt+H2HEQUhw8Ly2RqDIbFZJlXYDItR6lM3AzXL4o0uTxxeVQ1DjcdnpF1qcwqRcKRNJJLJSFxaiSxJSHxeaPfFhWKjErQ76wLJ5ePCEpdsFIy2gkbcMNUkQrAHk8PW5q2UNFQwdbmrTiHmWspiCILjgvcukuFqdURs683dTRHJnwFR0rQ+Qn4WvH0vQ6im+LUKcw2X0GLrJN3VfspKDxIfuHH3MPzuIVIpd7MunspPNrPt94ROXTRN7AaJuDtf5eAtwq9ysw88zVkhKocO4Ru9inqaEogsjSaXozGRnJz29FomyEJJ0+hSMdkXI7ZvAKjcTFyeaRHWa/PH1PpF3apnG7cg8f/nAUqQWCMVk1ZijqcmF6qDSarZyjP3xFUEhLnM5LYkpCQCOLzgL0+3gmzVoKra2SvlT46QYL+WFw6Aztad1LRUMGmpk10uYe+riCKzD0ucvO2AAVRhZx+mZLqkhtozlsKQMDXjqfvNRBdzDNfTWHqJN5V7qcrrZaZs97mIX5DnVAaXp/Z+ise+/PHuNPKqSq+Fm//OwS8tYxNn80UwxLkgoJ2oYt9ijqa5dEuoUhKih2jqRGjsZHUVHtST4VKlRWsIDSvICNjDs0ekZpQ2C8y489F+wi7VCalIiaHauD7fI0KhUxyqSQkRpJTiS3pI4yExOcJhQrMY4NfXBXZLorgsCVO0LfXn5kb1tMU/KqNHW+jUaawzFTKMmMZvuwr2adRUuFqY731AG2O2EaxoiCwc4LArvECc06I3LQtwJgOkAe8jKtag9F2hGPjb8OrykacM98sAAAgAElEQVSVthJP76t8ZF1LpmoUs4Ri3nJ00t+fQW5KM3VExFZJRy6aQC9HxlyFt+8t1KKVOaNuYZR2DG0hkdUSFlkB0tOtGE0NGI2NaLV9yf38mnE49ddg186jWcymxuGhutpFnfMYrhF0qZSCwBitKuFIGr3kUklInBdIzpaEhMSp8XnAXhefoG+tDDZ2HSFE4KihgIqMTCrkXmr98aJGEEVmVQadrqKQLvMoUzk2/jZsxosI+G14el9Fr9RxSc4drFcfRSz+kAOFJawRbgufZ8WO9Sw+kUOfbwu5Kg2zTJfTqXCxX1FHi9yOIPjR69tCAqsJlSrxiJwAAjZMtJJLC3lYlRfRoRhLkz+Tdu/IvrYalPKwiCqNavhZILlUEhLnBVIYUUJCYuQRRei3xjth1spgG4uoWYZnQp1SQYVOx3qdlo816rhrz6oSuXlrgOL2oFBrzl1MdcmN+OjH0/sKJamlFJsX8r7+A8TZ7fxB+K/w8tIWK1947w2mZUxEk5HPfnktHSoLmZnNGE2NGAzNKBSRBHcXGlrJoZU8WsgLi6s2cvEIg+7tLFAIMEYb249qIARokFwqCYnzmk9cbAmCcDnwJ0AOPCmK4qOD9quBZ4GZgA24RRTF+lOdUxJbEhIXMD53sDXF4AR9azW4T98Na5PL2aDTUpGi4yONGv9AVZwoMrM6KLpK2qBfl82RCV+hR5eOp+8V5huXUZMZwDX3TX6S8uvw+dI8fTxRcZKqtAZ85sMYjY1kZLbRLdOHxFSsqOoUTCP1zACQqZAH3alQgnpZSlBQFWrUKCWXSkLiguQTFVuCIMiBSuBSoAnYA3xJFMWjUcfcD0wRRfEbgiB8EbhBFMVbTnVeSWxJSHwGEUXo64hP0LdVBdtYJFHN1y2TsUmnpUKnZbtWg0smA1Fkeo3Iyq0Bitvk1BZdzcm8OQT632Je7pUcnPgyPx/zQ3xR3d9v6FuDoBNpFYKiqpXcmIrFs0UuwBiNelDYL+hYGVWSSyUh8Vnjk06QnwNUi6JYG7rYP4HrgOhR99cBPwt9/yrwV0EQBPF8jWGeIWN++O9P+xYkJC4gskNfCwFQ46FQaKdEaKFYaKVE1kKx0EKJ0EqaEGkVkREIcG1fP9f29eMUBLZrNVTodGws0vLjEjnTakVu3vomMz4+yuFxN3PYsp2MthmMGtNCE4Xh86QdbSbL1Yve40YVcOEXnVjIgPjx0mdMc+hr84idUULi80P9o1cNf9AFwkiIrTwgeihYEzB3qGNEUfQJgtANGIERnkMiISFxoeJGRaWYT6WYH9wQLoAUMdNFqSwkwoTIv3mClXKHk3KHEy/wkUZNhVnHn7+sJaexhpu2/RF3+g3IGmSMmtVOkzIitrw5U8l8Yx9NU//NEr2Tnzsc5LiV1Ik51Ii51ASC/9aKuZwUs/GgHHzLEhISEkkxEmIr0cfAwY5VMscgCMK9wL0ABQUFZ39nEhISnwEELGRiCWSyg0kxe9R4KBLaQg5YC8X+Vq51tPCA0Eq9JkDF1VoaO15g2tHZZPfMDX7EC9FuEphrHMfivWPw+N7moUXp9OX7We6wUd7fxPVuNwNDaPyiQKOYFRJfIREWEmM20hlJN0xCQuKzx0iIrSYgP+rxaGDwKPuBY5oEQVAAGUDcPBFRFB8HHodgztYI3JuEhMRnGDcqjosFHBdDH86i3LBst53i3laKhWY6pteR0nISjIsQRD/mgI2AV4YmT0+7uxqF+D1+8MaL1JmaeHVRGs/lp2Pw+1nmcLK838E8p4sxQjtjaKec/TH30C3qwg5YTSAoxqrFXBrEbLxSK0MJCQlGJkFeQTBBvpxgesIe4MuiKB6JOuabwEVRCfI3iqL4hVOdV0qQl5D47CGKIh0eX8zg5IEO6o0uTxLp8cmjFfvJpZkcWsgRW1D3+zB3QcERA90dm3h55d186eS7TKu6nO1t61HqrqXk5IcUNFZwpBBeWSTjWEHQsUoJBFgcClcudjhJSeZ1U5BD5pjYWZIDsyV1RpDmDEpIfKb4RBPkQzlY3wI+INj6YbUoikcEQfgF8JEoim8B/wCeEwShmqCj9cWzva6EhMT5i8sfoM7pDo+hCc75C8786/WfXf+taAQxgAlLSFQ1h8VVLs2k+vuwd+Zhs+ajs0yhpM9MpfUEmrajeJbXckw7AV3WkzQ2u7koYxIHu16nuuhmbIZJTDz+DD9/oYsjBfDqIhlHCgTeT03h/dQUlKLIPKeL8n4HFzucGAND/DyiHzprgl+V78fu02ZGia/SyGxJQxHIpdwwCYnPGlJTUwkJiTNCFEWsXh9V/W5qnC6q+93h4cmNLg8jJ6lAIzrIpYWcQaJqFG2o8ISP83rV2GyjsVnz6erKId87imneIqxdRznS10phdxrrxr/C9bp07rh4FT8P/Bed22dyY/9y9rW/Q6urE1XazSj9MsZVvkS2ZR8AR/ODTteRQiHGkZKJItPcbsr7nZQ7HOT5znLIt0wRcsMisyTDsyV1hrM7t4SExCeKNBtRQkLijHEHAtQ7PVSHwn3Rg5N7fCPoUgF5KsiVWcnyHsPsOxYWVnrsQ6agu1wp2Gz52Kz5dHdnATIK/WaW+orQekV2Wf6N1a8lU5yCuvv3+Is8tLWMBqBVyGOU+SQH3HXMNV3FBy1P4exdA2krOTLpq9jaJjO2ag0TG1389KUAx0YHna6PxwRFV0AQ2KfRsE+j4XfGTMbL0yj3yym3Wyntajn9tPmAL9gA1lYdv09riHfCTGMhs1BywyQkznMkZ0tCQiLsUtU4Iu7UQNjvpHNkXSqdXBYZQ6NVMkpsJNO5DbX9LfA0Dn8CoL8/IySwCujrMzBQDTjGb2a6rwijmEZD3zE+sn2AX1GCRrWEOft+x1+usnKN3s4B+0qeuOQurhHf4DJ7BUcOXcpKz3w8zk7Wt74IsjSUqTcjk2egcVqZeOwZ9D214esfzwuKrkNFwpC5VwWpoyk3TmG5OpspDgeyzurQXMlq8CWetXhGyBRgKA6Jr7KIE2YsldwwCYlziORsSUhIAOAJuVQ1UXlUA45V19mGwAaRp1ZGBienaCjVqilNUWOW+7Hbt2KxrMXSuB6fryup8/X0mLBZ87HZCnA602P2FfmzmOYbg1FMwxtws8v2DvV9R5CrJqPUXcr4Y0/TlNnBgRIZf2x08qqYB0Azeej1bciVTvYHalmqmcSUzCUctG/E07cGVepKXFoT+6Z/jzEn32fMyfeQiQHGN8NDLweozA2GFw8Wx4uuhr4mnupr4inArDWzLH8Z5QvuZXbWTJR9baEu+tWxsyV7W0//iQ74Qt34K+HEoH06U+IEfX0hyKWXfwmJc4X01yYh8RnEFqr4iw37uTnpcuMfQTNbK5PFjKEZ+L5IpyZFLg8f5/X2YLOtp6P5A47bNhMIOE9x1gHk9Pfl0do6CpstH49HF7tbhKJAFtN9RRjEVACsriZ2Wt6h39eNXD0VhXY5uW3bGdXxEX//koy5Ljf6QIDqwIDYykcQREymRqpaNUwRChmvn0uHq4FWZy2e3pdRpa1EJjdQP+ZKOg0TmXjsaXROCwBjW+DBNQFaClJ4Zq6L/SUkdLosTgtrKtewpnINaco0luQvobygnIUz70CnjPq5XD2RMKK1MjLc21YNfvdp/d8A4LBCgxUadsRulymDbliMExb6Xqs//etISEicEimMKCFxgeINiJx0uUOJ6ZFWCtUOF/ZPwKUamPFXolOHHasctRLZEGE0t7sDi/VDLJa12O07EEXfsNeRyTQoFdOorcug4WQGPp86/iARigPZTPeNITMksgJigCNd2zjWtQMREbl6BgrtUlL7W5i173cczffx8Jfl/Mxio7wXprkfx3XZaATRz2pupd9u4vDHlzDGb+YS7xTcficfND+F098Lgi4kuIIdUeV+N2VVr5DTtiMuJ8tRlseHyzP5p7EKnzj8/4FarmZ+7nzKC8q5ePTF6DVDCJ2AH7ob450waxX0tQ17ndMixZwgQT/khsnkw6+XkPicIoURJSQuYDpDuVTRiek1Djf1Tje+EXWpBEoGwn5Rw5OLB7lUp8LhqA+GBy1r6e45QDKDpRWKDEzG5Tgc49i9uw+LpTvhcQJQ7M9mmq+ITDElvL3Xa2eX5R1s7mAvZbl6NgrtIuQBD5OP/gN5wMs/l8qRiyLlDifVYikDOV6iIKdNzCVf34BC4aIeCxZfD2Z5OvOzrmFD60uIogNP7xpUqTcjU5jxy9UcH38bNuMkxp94CaWvP3wvuqpmrq1q5qaJE2haOZ93ctrY0rwVh8+R8Gdy+91sbNzIxsaNyAU5M7NnsrxgOeUF5YxKGRU5UBbq2ZU5BsouiT2JqzvkhA0IsMqIO+b3cNr0W4JfJ7fFbperwFCSwA0rBU3G6V9HQuJzhORsSUicB/hCLlVQVLmjcqpcdHpH1qXKUSvjwn6lOg25p3CphkIURfr6jtIRElj9/ZVJrVOrR2E2XYrRWE5Tk44tW7Zjs9kSHisgUMIoprkL0UeJLIDa3kPst1XgE4OiQq6Zh0IzH0EQmHDsWXLad7GnTOB3N8tZ4HDy93YLL/mW8SPf13BdFgwlfkv8X+azjarKebS1lZHnN3CFdzoAR7t28LE9NEZa0KBKvQmZIjt8fQ1Oxh98EoP9eOKfc+IE9N/4Gocn6KhoXM+Ghg3Y3faknqNJxkmUF5RTXlBOsb44qTUxBPzQ1RAKQ4ZE2IAz1t9x+uc7FanZiRP09QWSGybxueFUzpYktiQkziFdXt+gar/g9/VOD94R/FvUyASKtcHE9BKtmrKUoGNVolWTqji7Nz9R9NPVtReLdS0Wyzpcrqak1ul0xZjNKzCbV5Cim8jhw0fYvHkznZ1xk7sAEASBcemFXNSRQ4YYm6/lCbjYY3mPJkdE3Ck0C1Bo5wEwqm0nE48/RwD4wVflNGQJ/Nxi48a+fh723so//FeFxdYN4ivczD+x23M4/HHQNbrSM4PcQCYAm9rW0OasC92UGlXqjcgUOTH3UyxUkb/pr8gDiUOl6vHjMX3zfrTLlnLAepD1DeupaKigtT+5hPgx6WPCwmuyaTLC2Xafd3ZFuWGVUW5YDQS8Z3fuaORqMJYMStAvDX6vSR9+vYTEBYQktiQkziG+gEijyxMX9qtyuLF5h89bOh1GqZRxYb8SnZrRGtVpu1SnIhBw09m5PRgitH6I15tYIA0mLe0isgYEVkopfr+fQ4cOsXnzZuz2xA6PIAhMLpnIpCYzqV3xwrDddZJdHe/g9PeFtym0i1FoZgOg629l9t7fIg942DJR4C/XBUOIGxua0QcC3On5LzYFpobF1hxxO9/h94iiwM4dN+PzacgKZHCNZyYCAi5/Px80P40rdD1BpkKZcgMyRV7MfWWaFEzr+gDhw9eHfD7U48Zhuv9+0i69BASBY53HqGioYH3Deqq7EvTWSkCWLovl+cspLyxnZvZMlLIR7LHl90HXycRumMM6ctcBSB2VOEE/Ix9kspG9loTEOUASWxISnwDd4Vwqd0wrhTqne0RdKnXIpYpOTB9IVE87S5fqVPh8vVhtG7FY1mKzbcLv7x9+ETIy9XNCDtalaDS5APj9fg4ePMiWLVtOKbKmTpnKdHkJ8h1dceleogwO2jZwomt3zHaF9mIUmhnBq/s9zNr3W1L7W/EL8N175bQbhHAIEWCB68+0YAqLrTyxkd/yXYBwKBHgMs9U8gMmADqcDWxs+ydi6KZkChVy7XXIFfkx9yJXyJi1MI3sHc/Rt/aDIZ8ldVkZpm/eT9qKFQghYXGy5yQVDRVUNFRwyHLoFM9xhAx1BktHL6W8oJwFuQvQKDRJrTsjHJ2xbthAxWRnbbD9xEih0ARDkIMT9I1loE4duetISIwwktiSkDhD/GLQpap2uKnud1HjdFMV+tfiGVmXKkulCLtT0TlVozUq5OdoaLHHY8Vi+RCLdS2dnTsQxeETrGUyFQbDYsymFZhMy1GpIo00fT5fWGR1dSXupyWTyZg6dSoLJs9BfL8dT2Nv3DH+VJEPK5+hy90es12hK0ehnhp+PP748+S2BdscrJsm8MQVQTE6EELsF9VMcq8GhLDYkoteVnMrCvwxoURjIJXrPXMQQsn0R+zbONy1NXwtuVJFiulGPK7cuPstmGhg4SI1jucep/f9D2CI11l1WSmm++4j7bLLEKKKEDocHWxo2EBFQwV72vbgS6KSU6vQsjB3IcsLlrNk9BIy1Ocoad3vBfvJKCesKuKMORLn4Z0xabmDOuiHvtJHS26YxKeOJLYkJIahx+cPh/uic6rqnW7cgZH7G1EJAkUJwn6lOg3pn6BLdSqczkYslrV0WNbS3b2XZCoI5fJUTKblmM0rMBqWoFDEJq77fD4OHDjAli1b6O5OXF0ok8mYNm0aixcvRlXtpuvtGkRPfK96d6Gfdzb/GV8gWvgJKHSXolBPDm/Jbt/NxGPPIAAeOTzwDTmd6UJMCPFgoJjrPL8ECIstgN+JD5BLc0woEWC5ZzLFgWBCvIjIptaXaXedjDwPCiWjL7qN9vrMuPvWpCpZdtt48lK6sD62ip733htSdKlKSjDddx/pV1weI7oAut3dbG7azPqG9Wxr2YbTN3yPMoWgYPao2ZQXlLOsYBlZuqxh13wiODqjnLCodhX2uhF2w7QhJ2xQgr6xVHLDJM4ZktiSkCDoUjWFXKrBHdQ7RtilMqsUkcT0UKJ6qU5N/jl0qYZCFEX6+k+EWzT09R1Lap1KZcZsugSzeQWZmfOQyVRxx/h8Pvbv38/WrVtPKbKmT5/O4sWLSVOm0PV6Fc4j8Q6ILFVJd1kv777x5xiRIggCqvQrEGTjw9t0biuzdv8KRajx59tzBJ4rD4qW6BDia/5FfN97PxArtr4r/pbZ7AJiQ4kZ6LjJNRcZQdfEr/TzTs1juKJCqjK5gplXf50Tu3V4XPGVoxMX5bJoZRmBpvqg6Hr3XQgkHoCkKi7GdN83SL/yyjjRBeD0OdnRsoOKhgo2NW2i2534OR7MFPOUcIJ9YXphUms+UfxesNfHO2HWSnAmV62ZNOl58XlhprLg9k/5b1His4UktiQ+V/T5/DFjaAYS1WtH2KVSCgJFWnVM2K8s5FRlKM+vFnaiGKC7Z39YYDmdDUmt02oLwhWEGenTEYTEoRqfz8e+ffvYunUrPT09CY+Ry+VMnz6dRYsWodfrcVXZ6XylkkBPfKhSM8FAk6Geiucfi9kuyGTo827A2RcRDDIhwMzdj5LW3wyAWyVw/30yenXBN9KBECLAb7xf5DH/tUCs2Fopvsj1vAYQE0oEWOydwDh/JFTo0Xv51/4/hPO3AGRyOcvu+g61BzNorY4XQPpsHZfePZGswnTctXVYVz1Gzzv/Hlp0jRkTFF1XXYWgSPy75Av42Nu+N5xg3+5oT3jcYEr1peFeXhMME86+snGk6bclDkl21kESjWKTRpkSqpQclBdmLAWVbvj1EhKDkMSWxGeOQMilih+c7KbNM4Kl64BRqQiLqOgO6vkaFQrZefZGFUUg4MFu3xmuIPR4LEmtS02diNm8gizzClJSxp7yzdjr9YZFVm9vfK4VBEXWjBkzWLRoERkZGYi+AN3v19O3tTnuWEEpI+PqYk5YdrHxuSdj9snkCsZMv5WWGmPM9vH1r5NbXxF+/OpCgTVLgq6QXISNDU3oQ6LmHs/3+TAwE4gVWwvEzXyTPwEgijJ27rgpHEpMU6Vwc88c5ESEpqPIzdvr/xh774KMy7/5PRx9Rex5u47AIGEvkwnMvqaIGZcVIpMJuOvqsK1aRffb7wwtugoLMd73DTKuvnpI0RW8Z5EjtiPhBPu67rohj40mNyWX5QXLWV6wnBlZM5Cfzz2xfJ6IGxYdkrRWgiu5+ZpJk5Ef1a4iKjSZliO5YRJDIoktiQuWfp+fameo2WcoMb2630Wd041zBF0qhUDIpYrtoF6iU5N5nrlUp8Ln68fWuTlUQbgBny+xAIpFQJ8xK1xBqNXmD7vC6/Wyd+9etm3bdkqRNXPmTBYtWkR6erCnkre9n86XTuBti69sVOalYvjiOPZvf5ctLz4dey6FgpnX3s+hDbH/F6NT7ZS981B4bI43Rc099/pwaoJbFrr9rGqJiLqL3b+nXgz2yIoWW0VCC78MfDv8uLp6Aa0tJeHHi9KnML7DHLmwAL2z3Lz7yp9i87AEgcvv+y7mMbNZt/ooXe3xneNzSjO45K6JpBu1AHjq67Gu+jvdb78N/sTOjbKwANPXv0HGtdecUnQNUNtVGxZeR2xHhj0eIFOdycX5F1NeUM683Hmo5QlGJZ2PiCL0WxO7YfZ6EBML2TNClRqVGxY10shYAkrtyF1H4oJEElsS5zUBUaTF7Q27U9E5Va3ukXWpDEp5VGJ6JOxXoFGjPI9dqlPh8XRita4PVRBuIRAYvoJQEFQYDAuCAstUjkplSupaXq+Xjz76iG3bttHX15fwGIVCwcyZM1m4cGFYZImiSP/2FrreqyNuxtD/Z+88A6Mo17f/276bns0mJKRCQkLvnUCAUFRUihR7QY+oWE4//yOWY8HjKa8eCyr2rhRRsFICSaihSO8pJKGm1832eT9s2N3J7iYLBKTs9W2eeZ6Z2TrX3Pd1X7cEgjPiCRmXwJbli9i0+Avx8RRKMn/3ZzZ9a8bsookK0Srpt/LPyBqdabufrtfxcV9nlMM1hWgUFHQ3fogVe/TGlWwpJVY+sN2KFPuN2WZLY+OGwY79gQEBzDQMR6Z3SR0GK6kdoufn919FcL2hSySM/91cuqWPZ8PSoxxYf9LtPVKqZWTcnkbqYGdLHlNJiZ10LV/unXTFx6N7aA6hN9+MROGbv9bpxtOOVOOOMzuw+pCKC5AHkB6bTmZCJiPjRhKsDPbpXJcdLEZ7+tEtGnYUfNS7+QYJhMW7G7fqUiE42h8Nu0bgJ1t+XBZotFop9JD2K9Ab2jVKJWuOUnlqnKy9gqJUrcFgOOmoIKyp2Qa0/fQukwUSETGaqMgJRERkIJf7fgM1mUwOktXY6NlvSy6XM3DgQEaMGEFwsPPY1noTVUuOYDziLnyWhanQzkxD2SmEjYs+J+/bReJjKlXc/Men2PazhfISZwRNKpcwOmwnLH3POTkinDvvq8OksN/YZEjJLi5xpBAP2hK43vSyY3rAjQmiVkivCo8QxVndk4zt22bR1ORMq43qM4zUPLGWR9UljMqu1fz05n8RWqQCx85+iH4Tb6RwVznrPjuEodH9waHLoA5k3JaKKsBJnEylpVQsXEjtd8vB4rlwQxEXR8ScBwmbPBmJ0r1QwRtqDDVkH88mqySLzSc3Y2wuKGgNcqmcITFD7JWN8WPQaXwj5pc1BMHe/9GTQL+mpJ2jYcFi8nXWukKbDIqL6IvmxyWHn2z5cckgNEepPDVOPtHOUapwucwt7ZcSqCLxCo5SeYMgCDTq8x0C9/r6fT6tUyi0jgpCrXY4Uum5pYZ8JVmDBg1i+PDhIpIF0HSgkupvjmBrdCcNmr6RhE9OQaKWkfvFR2z/Xuy8rlBrmPa3Zynco2Rvtrgl0PCJUaifuR3Mzu/U4dkZPN3B2Tx5RFAi7+xd79j+3jqUx8yPO7b7zkxlS63zNT2t+oSuhhXOkwh3sd65HLVazX09p2LeIO4rGDIxiTMBpfzw2r+xWcWvc/TdDzBg0hQaa42s/eQgJQfcnfeDtCrG39edjl3E9hGm48epXPguNd9+6510dexIxJw5hE2dck6kC0Bv1rPx5EaySrLILc2l3tx2ylmChL5RfclMyGRswljig9tOOV9xMBvsRq0tHfQr88Houfjj/CCx945smZLUdbH3mvRHw644+MmWH+0OvdVGoYe0X0GTEb21/Z4KZRJIVKscflSuDuoRyqsjSuUNgmCjrm5Ps8B9FXq9b6JntTq2WX81kbDQ/kgk5y56NplMbNu2jY0bN6LXu+uOABQKhYNkBQWJvYxsJiu1PxbSmHfabZ1EJSN8SgoB/aIQBIF1n7zLzp+/F81RagK45cnnaGqI4Jd3xcSyc79Iehd9Rd133zqvJTaWvz4cwNFG53v0XHAvpu350bH9ink6r1unObZn3tebT086LSfmhhcyvOovju3Q0KGsWd0Lg8HgGEsfkU7vgkhMx1xuulKIfLA3xysP8/0rL2FtQYzSb7uHIVNmINgE9mQfZ/OyAqyWFr8RCQyYmMigmzohk4krPs0nTlDx7nvULFsmIpeukHeMQffgg4ROm4b0HEkXgNlqZtvpbfZ0Y+laKpp8a82TGp7qsJRIDW+9mOKKhyBAwxl3B/2Ko/ZomA/+dD5DFeLuoK9LBW1nkF8hWrprEH6y5cd5QRAETpvM5DcayW8Wpp+NWLV3lCpULhMZfZ7VVCVplCivIWdom81MTc1WyspXUVGxBqPRnax4QmBgqqOCMCio+3nf9IxGI9u2bWPTpk2tkqzBgwczbNgwN5IFYDpeT9XXh7FUuJtvKpNC0M5MQ65VI9hsZH34NrtX/yyaowoMZPqTL6AJjWfxS9swNTnJS4hOzeTbIjkxY4qogk/29B+4xfKGY1sukbNOiCOsKNcx9ojpcX6yDXVsz5s7mKfzneL5W3RyppVPdmxLJDLksldZu3ab6LXPve9h9O8fxqZ3XpcsREnUE/0pPbqH5f+dj8Us1s0Nn3EHQ2+5FYlEQuWJBlZ/eIDKE+6at6jEYMbP7kFYB3frAfPJk1S89x61S79B8Ea6YmKI+N0DhE2ffl6kC8Am2NhTvsfRLLuk3jebkLigOIelRJ/IPpd3ZWN7w9xkj4aJImHN6UmTZ23jeUEihbBEz9GwwEh/NOw3hp9s+dEqmqw2ippc037O1F9jO0appECiRuloQ+PqoK5TyK/up+JWYLU2UVW1nrLylVRUrMNi8U24GxrSz+GBFRCQdEHXYDQa2bp1K5s2baKpybNDuVKpdJCswMBAt0yegv0AACAASURBVP2CTaA+5zh1q4uhpQZPKiFkfALBGfFIpBJsNiur332TfetWi6apg0OYPu8FdPGdWPafHZQVu+i0ZBKm/WUA5lefoX6ls++gMjmZlS9cx9t7FzrGRnQcwTt7c6HOSabGG//NUSHOsf3JX0cxa3eBY7t/SADPWn5PQ+Nhx1hKynMsXnRKlEIdMmQIozsNofJjcZWfOi2ciHt6UHpgD9/++3ksRrEeasjUmYyYdRcSiQSL2cqW5YXsXlPq9j7KlVLSZ3She3pHj78J86lTVL73HjVLlnonXR06EPG73xE2YzpS1flHQgRBIL8m3yGwP1jlmwFuhDqCMQljyEzIZEj0EBSydmyWfSVBEKD+tGeBfm0p7RoNU4e668IiujRHw86PePtxbvCTLT8QBIEzJouLMN2ZAjxuMLXnT54QudRNmJ7SHKVSXUNRqtZgNtc6KggrK3Ox2QxtrpFI5ISHD2uuIByHSnXhLVgMBgNbt25l8+bNrZKsIUOGMHToUI8kC8BSbaBq8WFMRe6aFrlOg3ZWGsp4u57LZrXyy9v/4+D6daJ5AaFhTH/qRSITktiw+Ci714qJSPqMLqR2qOPY9Omi8djXX+Mu/QIKawsdY88N+j+mLX7EOUkio0vTR5hxpp43PzeefpsOOLaDZFJWxeVQdMzpn6UNH4HJNJeff3ZG32QyGY899hhsqqYhV6wlC72+E8EZcRw/sI9l/3oOs0H8ng64cSoZd852kKjSA1Ws+eQA+lr3CtJOfXSMubMrmmDPN0rz6dNUvvc+NUuWIJg8V6DKo6LspGvmjAsiXWdxouGEI+K1s2wnNh+E5EGKIEbGjbRXNsaOJEDhNwwFwKSHqgJ3gX5FPph9afruIyQyCE90j4TpUiEgwh8Na0f4ydY1BENzlMqTg3pDO0ep4tVKZ9ovUEWyRk2XwGs7StUaDMbTVJSvobx8FdU1eQg+NBeWSjVERGQ0VxCOQaEIaZ9rMRjIy8tj8+bNIk2SK5RKJUOHDmXo0KEEBHi/Qep3lVH9XT6Ch1Y1gYOjCZ3UGanKnlKyWiz89Ob/48jm9eJ54VpmPDWfiLh4CneV8/M7e0X7O/XRcf1DvSh9cA6NLqp1dY8eWN77J9O+d2qx5BI560b+j7BPbnYeIKILSSeeEx2z6J830GX9XtHvYkPfQIp3XufYlkhkDB2ygYULvxC1H+rXrx8333gT5Qv3YHKpkkQKkXP6oEoM4eSRg3zz0rOYmsTp2H7X3cSYex90/EYMDWbWfXGIwp3uprMBIUrG3tONxB4RbvvOwnymjMr336dm8WIEo+fqQnlkpD29OHMmUnX7VMBVGarILnVWNpptbUsLlFIlwzoOIzMhk9HxowlXu/eUvOYhCFB30t24tTK/ORrWjlCHuTvo61IhPMkfDTsP+MnWVQZBECg3WdzSfvl6I6XtHKUKlkld0n5OK4VOGhVqmT9K1Rb0+iLKmisI6+p2+bRGLg8jUpfZXEGYjkzWfuXhTU1N5OXlsWXLFq8kS6VSOSJZrZEsm8FCzXf56He5kwRpgJzwW7qg6eG0CbBazPzwv3+Tv22zaG5QhI6ZT88nPCaWusomFs/fhtFFDxWkVTFr3mBsB3ZRfNfdorXx773HJ8G7eWf3O46xER1H8I5uJCx3iWx1vZGkXbeL1h57eRI37DjCr3VOMrSoTzLqo7NEqcSuaS9y5kwaK1Y4KxUlEglz584lTB7Emdd2IrjoymRhKjo83g9pgILT+UdY+tLTGFtUcvYedx3j7n8ESXOkVxAEDm46xfrFR7EY3Ulr7zFxDJuajFzpXQdlLiuj6oMPqP56kVfSJYvUEXH//YTPmoVU034mnI3mRtafWM/a4rXknsil0YfIjFQipX9Uf0dlY8egjm2uueZhaoTKAneBfmU+mD1rLM8LEhloO7k76Ed0gUDvxP9ah59sXaEw2pqjVI1GNyuF+naMUkmwR6nEaT87sYpS+qNU5wJBEKiv39dcQbiaxsajPq1TqaId+quw0EFIpe1badnU1MSWLVvYsmULRi83YpVK5Yhkadq4ERuLaqladBhrjfuxVF3C0M5IQxbifDK2mEx8/+o/Kfx1m2huSGQUM595idCoaKxWG9/+91fOuKQipVIJU//cnw6dQii+8y6aduxw7AsYOJCEzz5lyvIp4hTi8OeYVrQTNr3uPNHIP5O0ur/o3MdensQTB0tYdNppx/BCSizjLF9TWCROJfbu/RFvvfUWlZXO6sUePXowY8YMmg5UUvnpAdGx1d20RNxtL1Q4U1TA0vlPY6gXp1h7jB7HhDmPIXURkteU6Vn94QHKjrmnY7UdAxk/uwe6OPeiBFdYysup/OBDqr/+GsELoZbpdETMnk34rbOQtkKozwcmq4m8U3lklWSxrnQdVQZ3uwtP6Kbt5qhsTA5L9v/vnAtsNqg/6Vmg76JbbBdotO6RMF0XezTsWtXmNcNPti5jCIJAhdkiik7lNxopaDJQ0mTywarSdwTKpC2E6XYH9SSNCo0/SnXesNks1NZut1cQlq/GYHR3DPeEgIAUoiLHExk5geDgXhfl5qLX69myZQt5eXleSZZarWbo0KEMGTKkTZIlWG3UrSmhPrvUXdsrlxB6XSeChndE4uJzZjYZWf6fFynes1M0PbRDNDOffomQSLv2bOM3+exaLa58Gz4thX4TEmjIzaX0wTmifYlffM7JzqFMXTHV5RLkrJu5jrBlc+DIL87J094j6Uux3uzYy5NYUFLGCwXOz+vujhE8G2diS94El5lSRqZv4ciRUyxdulR0jDlz5hATE0PND4VuvR5DJ3UmeKTdpb685BhLX3wKfa24h1+39NFc98gfkMqchMtqtbH9x2Ps+PkYLf+epXIJw6Yk02dsvOg99gRLRQWVH35E9VdfIXjR48m0WiLun034bbe1O+kCsNqs7C7f7WgddKLBtxt/Ykiio7Kxl64XUi8N0P3wAcYGe+TLNRJ2Nhpm8fy9OC9I5RDeyTMRC9C233kuY/jJ1mUAk81GUZPJRZjudFCvtbRjJ3sgTq0QCdPPEqwO/ihVu8FqNVJVvYHy8lVUVGRhNru7o3tCSEgfInX2CFZgYOeLdn16vZ7NmzeTl5eHyYt4Wq1WM2zYMIYMGYLaBx2PuVxP1aLDmI+7l7IrogPQ3toVRbSY0JgNBr799/OU7t8jGg+PiWXGM/MJ1trTjMf2VvDjAvGcxF4RTHq4NyBQNH06xgPOSrjAjFEkLFzIgl0L3FOI49+B1/rY++KdxZxckl4Ti9mPvTyJ1RW13LXX6c01NDSQ7/p3IS/vBrdUYkzMLN59911On3bacXTp0oU77rgDwWKj7J3d4vdGJiHqoT6OwoDK46UseXEejdXiSE/qsJHc8OifkLXoeXgqv4bVHx2gvtI9OhXXNZxx93YnMKxt0bulspKqjz6i6suvELzYecjCw9HOvg/t7bcj9VIEcaEQBIEj1UdYU7KGrJIsjlb7FvWN0kQxJmEMYxPGMih6EArptR09aTfYbFB33LNAv963B0afERDhWaAflgiyq8cv0U+2LjFKmoysr24Qpf1KDCas7fhWB8ikpGhUpASqSdbYBeopAWo6aVQE+KNUFwUWSz0VFevsTZ6rcrBa29ZISCQywsIGN1cQjketjrmo19jY2MjmzZvZunWrV5Kl0WgYNmwYgwcP9olkCYJA47bT1H5fiGB2j7UGpccSOjEJiUL8vTM16Vn28nOcOCS2SIiIS2DG0/MJDLOLo+urDCyavxWji8t8YJiKWU8NQhOkpO6XlZz4/e9Fx+i07BvU3bsz+bvJohTi88OfZ2rSdTA/BmfoTQJPniTpGXH147GXJ1HcZGTIFieJ0ypkHEjvRVHRG26pxH79PuXIkSN8+eWXouPMnj2bhIQELFUGzrz+q6hQQBauosPj/ZFq7DeU6lMnWPzCPBoqxaahKYOGcePv/4pMLiYSpiYLuYuOcHiLu9+aKlDOmDu7ktzPt6pUS1UVVR99TPUXX2DzRrrCwtDedx/hd9yBLOjikK6zKK0rdUS8dpfvRvBBbRqsDCYjLoPMhEyGdxzur2y8WDDWN0fCWgj0K/PB0nbltM+QKuzWFK7RsJRxENyh/c5xCeEnW5cYS09X8ehB34wA20KsSiHyozobsYpRKfxRqksAo7Gc8orV9grC6i0IQtsVV1KpCq12JFGRE9DpxqJQXPyKq8bGRjZt2sTWrVsxe/Fe0mg0DB8+nMGDB6Py0QbA2mim+pujGA5Uuu2TBivRzkxF3cX99Rn1jXzzz2c5deSQaDwyIYnpT88nICQUAJvVxnev7ORUgbPSTyKVMOWP/eiYEoZgsVB482RMhU5CFXz9dcS9+ir51fluKcTsWdmEVhXDwpHOk4Ylwu/3kPR/Tjd5sJMtqyCQkrtH1Jtz34ieaMzFHlOJCoWWDz/8kNJSZ1VYYmIi9957LxKJhKZ9FVR+Lvai0vSIQHtnN8fvtbbsNIuff5K6cnHbn879B3HTH/6O3IMZ6dHtZ8j58rCocOAsug2PIX1mF5Rq3yIElupqO+n6/HPvpCs0FO199xJ+553IPBjXtjcqmipYW7KWtSVryTudh8XWdqWuWqZmWMdhjEscR0ZcBqGq0It+ndc8bDZ7RaQoEtZMyBp8M2BuE/d8D51Gtc+xLjFaI1tXT/zuMkJKwLlVj2mkUoco3ZVQdQ5QESi7hlyYLxPo9cWUV9grCGtrd+KL8aBcHoIuYiyRkROIiBiJTHZpnrgbGhrYtGkT27Zt80qyAgICGD58OIMGDfKZZAEYjlRTteQwtnr346p7RBA+rQuyQPeUTlNDPd/Mf4YzheI0UVSnZKbPewFNsNO+Iu/7IhHRAhhycyc6poQBULviexHRQiol8jF7f8OVxSvF62KG2G+45YdF40R29foaZRIJKQFq9jY4tStHGg0MD08mKDDNJZVoo7x8FbGxt5GZmcnHH3/smF9cXExBQQEpKSloeuoIHBZD4+ZTzvdjfyWNm08RNNxebRcaFc2sf7zM4uefpPaM8wZV+Os2vvvPC0z+8zwUKvF/SJeBHYjuHErWxwc4cUSs+zq46RQnjtYwfnZ3oju1TTjk4eFE/fEPaO+7l6pPPqH6s8+xtaiWtNbWUv6/16j86GMi7r3HTrqCfW9cfq7QaXTMTJvJzLSZ1JvqyT2eS1ZJFhtObKDJi67IYDWwrnQd60rXIZPIGBg90F7ZGD+WDoFXZmTksodUavfsCk+ELuPE+wx1zQSshUC/sgB8aHjugC61fa/5MoE/snURUG+x0mX9XrfxjiqFQ5juaqPQUaVA6o9S/WYQBIGGhoOOJs+uWp3WoFRGEdkscA8PG4L0EmpJfCVZI0aMYODAgedEsgSzjdpfimjY6K7bkCilhN2UTMDADh4jq/q6WpbOf5ryY4Wi8eiUVG558nnUgc4oScn+Sr5/Y7doXkJ3LTc+2sfuMm8yUXjd9ZhPOq8j9JZpdJw/H0EQ3KoQnx/+PFO7TIW1L0Luf5wHHf4YTHjRY2QL4JEDxSw749TcvZwax72xOoqK3qSw6FXH+NlUIsBnn31GQYHTfT4mJoYHH7R7ZwkWG2Vv78Z8ooV+65G+KGOdr7++qoIlz8+j+pRYNB7fozdT//oMCg8pXptNYNfqEvJWFGJroUuQSCUMmpTEgOsSkZ6DlMBaU0PVp59S9eln2Bo8t5aRhoSgvedutHfdhSykfbzefIHBYmDLqS1klWSRXZpNjbGm7UVAL10vh8C+U2ini3yVfrQKm9XeO9JNoH/U3mvSFcpg+HvpFWu06k8j/gb486FSolRyR5QqWaMiUO6PUl0uEAQrtbU7KS9fRVn5KgwG38wCNZokopotGkJC+iC5xFVS9fX1DpJlsXhOtQQGBjpIlvIc++OZTzdS+dUhLGfc00uK+GC0s9JQ6DxXLDbWVLPkhXlUHhen0DumdWfa//0DlUu1W2ONkUXzt9LkEjULCFUya95gApotI6o+/4IzL77ocgEKUn75GUVsLEerjzJthdjINHtWtj2ytehOOOjS2HryAuh3p1ey9b9jp3m5yBlhuj9Wx/zUOBobC9mSN95lhT2VqFRGcOLECd577z3R8WbOnEn37t0BsFQ0ceaNnQgunlmyCDUdHuuH1CXd5+09i+1qf8+UGs8R0vKSelZ9sJ8aD59TdOdQxs/uToiXz8kbrLW1VH36GVWffoqtvt7jHGlwMNq770Z7z92XlHQBWGwWdpbtdOi8Tjf6lrbqHNrZYSnRPeL8+4b6cRFgqBVHwqxmmPDCb31V5w0/2fLDD8BmM1JVvbk5grUGs9ldh+QJwcE9XCoIu/wmf9b19fVs3LiR7du3eyVZQUFBjBgxggEDBpwzyRJsAg0bT1L7SxFulRwSCB4TT0hmAhIvEZOGqkqWvDCPqpPiir+47j2Z+rdnUaqdN36b1cby/+3i5FFnlEIigcl/6Edsql3/ZdPryZ8wEWuFU0gefuedRD81D8C9CjF2BO+Ma95+c5D9z/ssHsiCuIFeydaP5TXcv++YY3xkeBBL+qYAeKxKjI29DYBFixZx8KBTn6XT6XjkkUeQNhuV6veUU/WlWLOm6a1De1tX0XdIX1fL0hfmUV5yTDQ3pksa0/7+nCga6Aqzycqmpfnsy3W3U1CoZYy6NZW0IdHn/H211tVR9dlnVH3yKbY6d78vAGlQENq770J7993IwsLO6fjtAUEQOFB1gKxie8/GgtqCthcB0YHRjI23R7z6d+iPvJ397Py4tuEnW35cs7BYGqiszLFbNFRmY7V6TpOIISUsbJA9RaibgEYTe9Gv0xvq6urYuHEjO3bsaJVkpaenM2DAABSKc09lWuuMVC05gvGoe4pGFq5COysNVZJ3LVBdRTlLXniSmtOnROMJvfoy5S9PuemP8lYUsv2nY6KxwTd1YtAkZ7qn4t33KH/lFce2RKMhZdVK5JGRracQLSZ4KQZcBdb/VwLqUK9k62ijgZFbnaQoWqlg14geAG6pxPDw4fTv9xkAZWVlvPXWW6JjTpkyhb59+zq2q789SmOeOAITNiWFoKHiqtSm+jqWzn+asiIxaejQOYVb5r2AJsi7XurYngrWfnZQFCU8i5QBUWTcnobag7auLVjr652kq9Zzc3RpYCDhd91JxL33/iak6yyO1R5zNMveU7Gn7QVAmCrMUdk4rOMw1PL269Tgx7UJP9ny45qCyVRJRUUWZeWrqK7eiM3m2QLBFVKpEm14OpHNFYRK5W/bkqKuro4NGzawY8cOrFbPPmzBwcGkp6fTv3//8yJZAE37KqhedhSbhyq3gH5RhE1OFqW9WqK27AxLXniS2jKx9qJT3wHc/Kd5bpV1pQerWPH6LlHNQVzXcG56vC/SZpNOa10d+ePGi6IqEQ8+SNQf/wDQegqx7BC8NcR58OCO8Cd79Mkb2TLbBDrn7sHs8l94OL0noQp5q6lEgG+//Zbdu526s7CwMB599FHkzZ5ZgtlG2Vu7MJ9yEaDLm/VbHcURK0NjA8teepZT+WLNYGRiJ6Y/9aKjgtMT9HUm1n56kOJ97tHaoHAV4+7tTmza+VXFWhsaqP78c6o++hhra6TrzjvR3nsP8vDftt/hmcYzrCtdx5qSNWw/vR2r0LaPoUauIT02nbEJYxkVN4oQ5aVNkfpxdcBPtvy46tHUdMJRQVhTsx188N6XyYLQ6cbYKwi1o5DLL36Je1uora1lw4YN/PrrrxeVZNmMVmq+L0C//YzbPolaRvjUFAL6tO7fVH36JEuen0d9pbg3YvLAodz4+78hb3FtjbVGFs3fRlOdk/xqQpTc+pRTpwVQ9tprVL7tTBFKg4NJWbMaWaidbLSaQjywHBa79E/sPBruXg54J1sAo/IOcUTv9A/6oX8XBobafaZaSyVWV1fzxhtvYLM5v2+TJk1i0KBBjm1zuZ6yN3YhmJyfp1ynIeqxvkhVYiJr1OtZ9vI/OHlY3P6npTeZJwiCwL6cE2z8Jh9rSz80CfQbn8CQmzsjk5+fztDa0Ej1F19Q9dFHWGs8C9WlAQGE33EH2tn3/eakC6DWWEvO8RyyirPYdHITBmvbHlFyqZzB0YPJTMhkTPwYIgMiL8GV+nE1wE+2/LjqIAgCjY1HmvVXq6lv2N/2IkCp1KHTjSMqcgLh4UORSn2v0ruYqKmpYcOGDezcudMryQoJCXGQLLn8/LUmptJ6qr4+hMWDM7myUyjaWanIw1pPqVSeKGXpC/NoaOmGPmQENzz+Fzc3dJtNYMVruzhx2MVpXwI3P9GX+K7OVh6Wykryx08QOZ1H/v736B6yt+oRBIHJyydTVOt0fXekEAFy/g3r5jvPMeQhuP5fQOtk64F9RfxQ7ozavNI1nttj7NGr1lKJAD/++CPbtjl7PgYFBfH444+LdHP6XWVUfS2OWGn6RqKdleamqTIZmvjuX89TekBc0aztGMeMp+cTpG096lp1spHVH+2notQ9Za6LD2L87B5oY87fsNTW2EjVl19S9eFHWKs9d06QBASgvf02tLNnI9deHq1amixNbDqxyV7ZeDybepPnIgBXSJDQO7K3Q2CfEJJwCa7UjysVfrLlx1UBQbBRV7eLsmaLhqamYp/WqdXxjgrC0NB+SCSXT1VoTU0N69evZ+fOnaLoiCtCQ0NJT0+nX79+F0SyBJtA/bpS6rKK3QN/UgkhExIJHhXXZs+9itJilrwwz63PX9cRGVw/94+iPn9nse3HIrZ+XyQaGzgpiSE3iVsWnfnnP6n65FPHtiwigpRVKx0tZFpNIQIsnQ37vnEe8MZXYeBsoHWy9e+iU7xyzBnleyg+kn+k2LV6baUS6+vree2110SauvHjxzNixAjR+aq/OUrjNrF+K3xaFwIHR9MSZqOB5f+d79ZPMiw6hhlPv0SIrvVoi9VsI29FITvXlLjZxMkVUobfkkLPjNgLKvawNTZS/fXXVH7wIdYqz82mJRoN4bfdRsT9s5FH/LapeVeYbWa2n95ub5Zdso6yprK2FwEpYSlkJmQyLnEcaeHuRNmPaxt+suXHFQubzUR1dV5zinANJpNvf4pBQV0dFYRBQV0vuz/F6upq1q9fz65du1olWSNHjqRv374XRLIALFUGqhYdxlTsXl0mj9SgnZWGMq5t08qyY4UsffEpmurFx+mRkcmEhx5HKnUnWicOV7P8fztFTZVjU8O4+ff9HDotAPPJkxRMvA7BxTesw5NPor37Lsd2qylEgLfT4YxLROjenyDJTnpaI1vfnanmoQNO8j5WG8yXfZId23lbJ9HQ4BTRp6W9QFzs7Y7t1atXs3HjRse2RqPhiSeeELVDspmslC3YJbbVkEvp8Ghft56SABaTiRWvvETRTvH/YEhkB2Y+M5/QKHeS1hLHD1Wx5uODNNa4m0om9opg7F3dRCnc84FNr6f660VUfvAB1krPFb4StZrwW2+1k67IyystZxNs7KvY5xDYH6s75tO62KBYh5dX38i+yDx89/24tuAnW35cUbBa9VRW5jZXEK7FYmk73A8SQkP7Exk5gajICWg0l2e4v6qqivXr17N7926vJCssLIyRI0fSp0+fCyZZgiCg31lGzfICkefTWQQOiSZ0UmekyrZvFGcK81n64lMYGsXpqV6ZExn/wFwkUnctkL7OxKL5W9HXuui0ghXMmjfYrYnyqaefpmbJUse2PCaG5JW/IG1Ox7WZQrRZ7T0RXd2q/1IIgfaISmtk60BDE2O3OdN88Wol24Z1d2y3lUrU6/W89tprGI3Oc2dkZDBmzBjROc1lesre2CnqMSmP1BD1aD+kKvfPwGI288P//kXB9i2i8eCISGY8M5/w6I5ua1rC0Ggm+4vDFPzq/qCiCVYw9u5uJPXStXmctmBraqJ60SIq3/9AZNnhColKRfits9Defz+KKN96Ol5KCIJAYW2hw8vrQOWBthcBWrWWMfH2ZtlDY4ailF0YgfXjyoSfbPlx2cNsrqa8Iovy8tVUVa3HZmu7vYNEokAbPqy5gnAcKtXl9cTsiqqqKnJzc9m9ezfefnPh4eEOkiVrhzZNtiYL1d/l07S73G2fNFBB+C1d0HT3LbVz8sghlv3zWYx6cVuXvhMnMfbeOR6JlmAT+P7N3ZQeEKeYbnqsDwk9xOc1FhVReONN4KJXi5n/ImG33OLYbjOFWFkAb/R3HjRAB391Wim0RrYMVhudc/eIsqsFo3o52mW1lUoEyMnJYd06Z7NrpVLJE088QWCgOGrVuOMM1UuOiMYC+kehnZmGJ1gtFn56/T8cydsoGg8M1zLj6flExMZ7XOcKQRA4vOU0uV8fweyBdPfMiGX4LSkofCDdbcHW1ETN4sVUvP8+1nLvpCts5kwiHngARYfLj3SdxamGU6wtXUtWSRY7zuzAJrRdeBOoCGRk7EgyEzJJj00nSPnbF974cWng743ox2UJg+GUo8lzTc1WBB9KtGWyACIiRhOpG49ONwa5/OL1a2sPVFZWkpuby549e1olWaNGjaJ3797tQrIAjIU1VC06grXWnbSq08IJn56KLNi3p+/jh/bz7cv/wNQk7lE3YNJkMu56wGuK9tdVxW5Eq/91iW5EC6DijTdFREuZlETo5MmiOauKV4m2h3QcIm4+XCEmMER6Ji+eoJZJSdQoKWpyRuAK9EZ6B9sd3AMDOxMU1NUllWijrHylKJU4dOhQ8vLy0DeL+00mExs2bGDixImicwUO6ICxoAa9S6RJ/2sZquQwAge49/STyeVMeuKvSBe8wqGNOY7xxuoqFj/3d2Y89SK6hKRWX59EIqHrsBhiUkJZ89EBTheK08D7ck5w4nA14+/vQWT8hf2mpBoN2nvuIWzWLGoWL6Hy/fexlImjaoLRSPVnn1GzaBFhM2YQ8eDvUHS4/PoZxgTFcEe3O7ij2x1UG6rJLs1mbclaNp3chMmLpUyjuZFfjv3CUwhxAAAAIABJREFUL8d+QSFVMDRmKJkJmYyOH02E5vLRrflxaeEnW35cUjQ2Fjh6ENbV+2Y+qFBo0ekymysIRyCTXR4VhK2hoqKC3Nxc9u7d65VkabVaRo0aRa9evdqNZAkWG3Wri6nPPe7eP1suJWxSJwKHxvisYSvdv4dv//U8ZqO4cnHw5Omk33aP1+OczK8hb4VYEB+TEsqQm9z71BkOHaLup59EY5GPP4bEJYUqCAIrj4kbT09MFJMYysVu7edCtgBSA9UisnWk0eAgWwBRkdeLdFtlZT+LyJZKpSI9PZ1Vq5ykcOvWrQwdOpTQULFHVtiUFEzH67GUOQlszXf5KOOCUHRw129JZTKuf/SPyOQK9uescYzra2tY/PyTTH/qRaKSOruta4nQyACm/qk/238uZvtPxxBszi9J9Wk9S1/ezpDJnek3LqHNQom2IFWr0d59F2GzZlKzZCmV772H5YzYakQwmaj+4gtqFi92kq7otrVovwXC1eFM7TKVqV2mojfr2XBiA1klWeQez6XB7Nks2Wwzs/7EetafWI90i5S+kX3tlY2JmcQG/XZmyX5cevjTiH5cVAiCQH39XkcFoV7vW1sNtaojkY4KwgFIr5C2GuXl5eTm5rJv3z6vJCsiIoJRo0bRs2fPdiNZYNcDVS06LG6A3AxFTCDaW9M83si94dienSz/z4tYTOLo2LDptzFs+u1eiVZTg4lFL24TibLVgQpmPTWIoHB3S4nShx6mITvbsa3q2pVOy74RpSbbTCECfPsw7P7SuX3dv2DoQ47N1tKIAC8WnOTNEmcE5vGEKJ5MdmqifEklms1mXn/9depdegsOGDCAm266ye11m083UrZgl1i/1SGAqLl9vWroBJuN1e8vYG+WmHiqA4O4Zd4LRCd38bjOE04X1rL6w/3UVbhbgMSmhZF5T3eCte3nqm4zmahZupTKd9/DctpzX0OJQkHo9FvQ/e53KDq2rUe7HGC2mtl6eqtDYF9p8K0NWFdtV4fAvkvYb9MGzI/2hV+z5cclhc1moaZma3MF4WqMRt8axgYGdnEQrOCgHlfUn095eTk5OTns27fP65yIiAgyMjLo2bOno39ee0AQBBrzTlP7Y6Hoxn0WQaNiCZ2QhOQczCwLd25jxf97CatZ3AIm/da7GTJ1pvdrsQn8+NYeNyfzSXN7exRh63fupPi220Vjce+8TfDo0aKxN3e+ycI9Cx3bblWIAO+OgZO/Orfv+g6SnQL1tsjW4tNVPH7Q2RD6el0oH/USR+LaqkoE2L59Oz/88INjWyKR8OijjxLhwfqgcdtpqr85KhoLGNgB7fRUt7lnIdhsrP14IbtWil+PUhPALU8+T8fUrl7XtoTJYGH94qMc2nTKbZ8qQM7oO7qSMqB9NVU2k4naZcuoWPgullPu5wVAoSBs2jR0D/4OReyVEwGy2qzsqdhDVrFdYH+84Xjbi4D44HiHl1fvyN5IL3GDez/aB36y5cdFh9VqoKpqvT1FWLEWi8Wzw3RLhIT0IypyPJGREwgIcE8xXe4oKytzRLK8QafTkZGRQY8ePdqVZAFYG0xUf3MUw0F3nyNZiJLwmWmoU86tZ93RbZv54dV/YbOKW/hk3DmbgTdN87LKjl9XFbN5mTh62W98AsNvSXGbKwgCJffci37rVseYpl8/Er/8QkS026xCtE+Cf8aBySWq98dDEOLsQdgW2dpZp+f6HU7dV7JGxcah3URz2qpKBLBarbz55ptUuxh+9urVi1tcxP6ur6160WH0u8RFDNpZaQT0805yBEEg57MP2PHjd6JxhVrDtL//g7iuPbyu9YT8HWVkf3EIo4e2TV2HRjNyVipKTftGlwWTiZpvv6Ny4ULMJ096nqRQEDZlChFz5qCMu3JIF9g/oyPVR1hbYhfYH64+3PYiQKfRMSZ+DJkJmQyOHoxCdn5dIvy49PCTLT8uCszmOioq11JevorKylxstqY210gkcsLDhjZHsMahUl1+olhfcObMGXJzc9m/37tzfWRkJBkZGXTv3r3dSRZA0+Eqqpccwdbg3oBY00tH+NQUpAHn9kd9ePMGfnrjP9hauNiPuXcO/a93T4W54nRhLcv++6tIBxTdOYQpf+qPTOb++hs3baJk9v2isYRPPyFw8GDRmE8pxNrj8KoLwVCF2BtQu5C2tshWg8VKynqnR5cUKMrojcrls/OcStyMUimO2u3Zs4dly5aJxh5++GE6eBCB24wWyt7YhaXC+fuRKKVEPdYPRWSA2/yzEASBDV9/ytbvlojG5SoVU//6LAk9e3td6wkN1QayPjnI8UPurvAhOjXj7utBTLL3/oznC8Fkomb5cirfWYj5xAnPk+RyQqdMRjdnDsr4tqsvL0ccrz/uSDXuLNuJ4CaqdEewIpiRcc7KxgCF9++DH789/GTLj3aD0VhGebm9grC6ZguC4P4k3BJSqZqIiFFERk5EFzEGhaL9/7AvFc6cOUNOTg4HDnj334mKiiIjI4Nu3bpdFJIlmK3U/FRE42b3FIxEKSNscjIB/aPOOQ17cEM2P7/5CkKL8vZxD8ylz/jrW11raDSzaP5WGqqcOi1VgJxZTw32qPsRBIFjM2dh2OskN4EjRpDwwftuc31KIeavgc9dIkdxg+CBNaIpbZEtgAGb9nPC6CSv6wal0S1II5rjSyrRZrPxzjvvUOZShZeWlsZtt93mdk4A08kGyt7aBRbn/7EiOpCouX2QKLzr+gRBYPPSL9m89CvRuFyhZPJfniKpT38vK70czyawK6uULcsLsFnE9waJBAbekMTAG5KQeiDPFwrBbKZ2xQoq3n4H83Ev6TeZjNDJk9E9NAdlwuXppecLKpoqyC7NJqski7xTeZht7g9MLaGSqRgWM4yxCWMZHT+acPVv33vSDzH81g9+XBD0+iLKy1dRVr6aurqdbS8A5PJQdLqxREVOQKsdiUymaXvRZYzTp0+Tk5PDwYMHvc7p0KEDGRkZdO3a9aKQLLDflKu+PoylTO+2T5kQjHZWGvKIc3+v92WvYeU7ryGyeZdImDjncXqOGe99IfYbftYnB0VECyDznm5eBdYNWVkiogX2Hoiejt3S8sGtChGgvEWK5hwrEc8iNVAtIltH9AY3stVWVSKAVCpl7NixfP31146xw4cPc/z4ceLi4tzOq+wYRNhNydR8m+8YM59upOaHQsKnehe9SyQShs+4A5lcwYavnW2OLGYT3/37eW7+0zw69x/kdb3b8aQS+o1PIL5bOKs+OED1KaevmiDAth+PUXKgivGzuxPaStTtfCBRKAi75RZCb76Z2hXfU7FwIeaSEvEkq5XaZcuoXb6c0JtuQvfwQygTE9v1Oi4FdBod01OnMz11Og2mBtafWE9WSRbrj69Hb3H/bQMYrUayj2eTfTwbmURG/w79HTqv6MDLs4LTDyf8kS0/3CAIAg0NBygrX0l5+SoaG4+2vQhQqaKJ1I0nMnI8YWGDkUqvfK3BqVOnyMnJ4dChQ17ndOjQgdGjR5OWlnbRSJZgE2jYcILalcfA2uI3K4WQsQkEj0lAIjv3ooI9a35h9XtvisYkEinXzf0D3UeO8bLKiV1rSti4NF801icznvQZnkmCYLVSNGUKxqPONcHjxxP3xutuc31KIQKseBx+/cS5Pf4FGPG4aIovka1nj55g4XGnfurPSdH8uZP4RuZrKlEQBN5//31OuKTGOnXqxD333ON23rPzq746RNMesRGo9rauBPRp27B3+/fLyPn8Q9GYVCbnxj/8jS6DhrW5viUsJiubvi1g7zr3KJNCJWPkrC50Hea7jci5QrBYqP3+ByreeRtzcYnnSVKpk3QlJV2U67iUMFqN5J3KszfLLs2myuC552RL9Ijo4SBencPatgDx4+LAH9nyo00IgpWamh3NFYSrMBi8aCdaICCgs6OCMCS4F5KrpIrm5MmT5OTkcPiwd1FrdHQ0GRkZF5VkAVhqjVQvPoyxoNZtn0yrRjsrDVViyHkde+cv37P2o4WiMYlUyqTH/0LasJFtrj9TVMfmb8WC+KikEIZNTfayAup+/FFEtJBIiHz8MY9zW3pruRmZnoVbZMv3ijxXpAaKI3FH9O62CJ4NTle5RbckEgmZmZl8+qkz4lRUVERhYSGdO7vfECUSCeHTumA+0YCl0nne6mVHUcYGIde1HrEceNM0pHIF6z52fp42q4UfXn2ZGx77C2nD0ltd3xJypYxRs1JJ7BFB1qcHaapzepCZjVbWfnqI4r2VjL6jK+qg9n+wksjlhE2dQuhNN1L3449UvP0OpmPHxJNsNmqXL6f2++8JuXESuoceRtX5yiu0OQuVTMWouFGMihuF1WZlZ9lOh87rZKOXIgJgf+V+9lfu5/Wdr5MUkuQgXj10PfyVjZcJ/GTrGobVaqS6elNzBeEazGbfnqKCg3sR1UywAgPdq8yuZJw4cYKcnByOHDnidU5MTIyDZF1sewr93nKql+UjNLlr4wIGdCDs5s5IVef3M97+w7fkfPaBaEwqk3Pj7/9Kl8HD21xv1JtZ+f4+bC6RNqVGzsQHeiDzYjMhmEyUvyGOooXefBOqLu5RMJ9TiILgwdDUu3VCa+gSIDbMPdLoTrYAoqJuaDOVCNC5c2c6depEUZGzkjIrK4tOnTp5/O5I1XK0t3ez67ea31fBaKXyy4NEPdwXiaL1G2f/629CrlCIIpU2q5UfX/s3NouZbj5EKlsisWcEtz41mHWfH+JYi6hbwc5yThfWknlfd+K7as/52L5AIpcTOnkyITfeSN1PP1Hx1tuYisSGudhs1K34nroffiTkhhvQPfwQqmTvhP9KgEwqY2D0QAZGD+Svg/7KoapDjp6N+TX5XtcdqzvGB/s+4IN9HxAVEMXY+LFkJmYyoMMAFFdBtuFKhT+NeI3BYqmnojK7uYIwB6u1sc01EomMsNBBzRGs8ajVV4bZ4Lng+PHj5OTkcPSo95Rpx44dycjIIDU19aKTLJvRQs2KQvQ7zrjtk2jkhE9LIaDX+feCzPt2sUjjA/a2MDf98UmSBwz2ssoJQRD4ZeE+CltYFlw3pyfJrVgWVH/9Naf/8ZxzQC4n+eefPFaYHak+wi0rnKJ3rynEhjL4rwtZk2vgyZPQItroSxqx2myh2wanjYdSIqFwVG/kLdzU9foiNm8Z5zLiOZUIUFpaygcfiEntrbfeSteu3qNvDZtOUrNCHDEMHBZD+GTfHm72rVvNyoWvn5cGzxsEQWD/+pNsXHIUiwc/t77j4hk6ORlZG4TwQiFYrdT9/AsVb7+NqcCLSbJEQsj116N75GFUKVfXAyFAcV2xw1Jid/lun9aEKEMYHT+asQljGd5xOBr5la2jvRzhTyNe4zCaKqgoX0N5xSqqqjYjCJ57erlCKlWh1Y4kMnI8kbpMFIqrs/Ll+PHjZGdnk5/v/UkxNjaWjIwMunS5NC7PxuI6qhYdxlrlHlVRJYcSPjMNeej5tSyyV699xealX4rGz7V6bW/2CTei1Wt0XKtEy2YwUPHW26KxsBnTvZbyrzomjmoN7TjUSwrRQ1TrPNO64Qo5kUo55SZ7JNEkCBQbjCQHiNOLAQGdfEolAsTHx5OWliZKSa9du5bU1FSv6efAYTEYC2po2u80h23cfApV5zACPJjDtkTPMeORyuX8suBVZ3WpILDyndewWixtVpd6gkQioeeoWGJTw1j94QHKS+pF+3etKaX0UDXjZ3cnouPFa74skckIvXESIddfR/3KlZS/9Ram/BakSxCo++kn6n7+meDrJqJ7+GHUqecX7bwckRiSyH097+O+nvdRri9nXek6skqy2HpqKxYvFeJ1pjpWFKxgRcEK1DI1I2JHkJmQyai4UZ5/V360K/xk6ypFU1NpcwXhKmprd+DeKM8dcnkwuoixRDZXEMrlvrd2udJQWlpKdnY2Bd6ejIG4uDgyMjJISUm5JCRLsArUrS2hfl0JtAwcyCSETkwiKD32vHvWte7L9AwJPfv4dJzykno2tnA9j0wIZoQH41JXVH/5laghsUSlQvfQw16vtWUKcULiBC8X1EKvpTu/SsSzSA1QU+5ijnqk0eBGtsBTKvEnj2QLYMyYMSKyVVZWxv79++nVq5fH+RKJhPDpqZhO7RSR7upvjqDsGOhTxWn3kWOQyeX8+Pp/EGzOL9Sa9xdgtVja9E3zhvDoQG756wC2fl/Er6uKRX8tlccbWPLP7Qyflkyv0XEX9XcjkckIueEGgq+7jvpVq6hY8BbGlpFpQaD+51+o//kXgidORPfII6jTrh7SBRAZEMnMtJnMTJtJnamO3OO5rC1Zy4YTG2iyePY+NFgNjpSkXCJnYPRAMhMyGZswlqiA9u0Y4IcdfrJ1lUAQBBoaDzuaPDc0eLcocIVSGdkcvZpAePgQpFLlRb7S3xYlJSVkZ2dTWFjodU58fDwZGRkkJydfspZBlsomqhYdxtQiWgAgj9KgvbUryguIFrTqOP5/zxLXradPxzE1WfjlvX0iDyaFWsaEB3q0mj6yNjRQ+e67orHwO+9A0cHzH/vRmqMix3i5RM7YhLGeD95Otg9nkRqoZmONk2wd1RvxFAfqEHUDhYWvOLarq/MwmSo8phKjo6Pp1asXe13sLtatW0f37t299seUauRE3NaVsnd2O/VbBiuVXx0i6qE+PrVfShs2Eqlc7tYRYN3HC7FZzG12BPAGmVzKsKnJJPTQsuajAzRUO20/rGYb6xcdpXhfFWPv7krgeUZhfYVEKiXkuusInjCB+tVrqFiwAKMHzWX9ypXUr1xJ8Pjx6OY+grqVNO6VihBlCDd2vpEbO9+IwWJg08lNZJVkkXM8h1qje4ENgEWwsOXUFrac2sL8vPn01vV29GxMCk26tC/gKoafbF3BEAQbtbW/NhOs1TQZvJRHt4BGk+Bs8hzS76qpIGwNxcXFZGdni4TKLZGQkEBGRgadO3e+ZCRLEAT0O8qoWVGAYLK67Q8cFkPYDZ1aNbb05RxrP1rIrpU/iMbtvfSeo2NqNy8r3Y+z7vND1JWLn5bH3NmVsKjWPZeqPv4Ea42zhZM0MJCIBx7wOt/nFCJARftUIp6FryL5c0klAowePVrUoLyqqopdu3YxYMAAr9eijA8m9PpO1P7gfDgwH2+g9uciwm7yTQDeZdAwJv95Hiv+33ysFifhyvn8Q6wWS6u9LttCbGo4tz49mJyvjnB0m1hfWLK/kq9f2MrYu7vRqXfbqc8LhUQqJWTiBILHj6N+zRoq3nobowfLlvrVq6lfvZqgcZlEPvII6u7dL/q1/RZQy9WMTRjL2ISxWGwWdpzZ4ahsPKN314KexZ6KPeyp2MP/fv0fyaHJduKVmEl3bfcrql/t5QY/2brCYLOZqK7eTFn5Kioq1mAyVbS9CAgK6k5k5ASiIicQGHjxBd6XC44dO0Z2djbHWpaMuyAhIYHRo0d7rRC7WLDpzVR/m0/TXvfPUBqkIHx6KpoLrPASbDbWvP8We7J+EY2rA4O4Zd4LRCd7N8xsif3rT5K/o0w01mNULF0Gtt5yyVJdTdVHH4nGtLPvQx7uWQd4TilEuCiRLVd4sn84i3NJJUZERNC/f3927NjhGMvOzqZ3794oFN6rxIJGdMRYWIvhgFO/1bDxJKrOYWh6uDe39oTO/Qcx5a/PsPw/L2IxOzWbG77+FKvFzLDpt5/3d18VoGDC/T1I7BlB7leHMRmcDw2GBjM/vbWHHiM7MmJ6FxSq839o8BUSqZSQCRMIHjeOhrVrKX/rLYwH3CP9DWuyaFiTRVBmJrpHHkbT49z6SV5JkEvlDIkZwpCYIfx98N/ZX7nfkUZ0jSC3REFtAQV7C3hv73vEBMY4Uo39o/ojk178z/Jqgr8a8QqAxdJIZVUO5eWrqKhYh9Xa0PYiJISFDnRUEGo0V2Y/sfNFUVER2dnZFBcXe52TmJjI6NGjSUpKuuTk05BfQ/Xiw1jr3IsV1F21hE/vgizowlK6NpuVVe+8wf4ccdsaTXAI0596kagk380Py0vr+eZfO7BanNqfiLggpv9tAPI2om5n/v0fqj50mm3KwsNJXr0aWZBnTaDPVYgATdXwryTntlQB806DzP050pdqRIByk5leG509LzVSKQWjeiH18B05l6pEgNraWl5//XWsLr0nJ06cyLBhrZuO2vRmzry+E2uNM10nUcvp8EQ/5OGeXfo9oWTfbr799/NYjGK3/8FTZpB+690X/Duoq2hizccHOJXvnrIK6xDA+NndiTpPT7jzhSAINKxbR8WbCzC00mYraMwYdHPnoul59ZIuTyisLbRXNhZnsa9yX9sLgHBVOKPjR5OZkMnQjkNRyS5uqvhKgb834hUIk6mKioosystXUVW9AZut7QpCiUSJVjvcTrB0mV7/8K9WCIJAUVEROTk5rZKspKQkB8m61BAsNmpXHaMh1900VqKQEjqpM4FDoi/4pmezWvl5wSsc2pgjGg8IDWPGUy+iS0jy+Vgmg4XFL22jtsyZPlSoZMx8chBhHVpPH5rPnKFgwkQEl5t71N/+RsR993pd07IXYnpsOm+Pe9vz5JI8+NAl6hXZDeZu8TjVV7IlCALdNuyjxuIkRFuHdiNB4/mGkrf1RpFG0lOvRFesXLmSzZs3O7YDAgJ44oknUKlav2EZS+oof2cPuDT6ViYEEzmnN5Jz6FV4/OA+lr38HGaDOB08YNIUMu66/8K/ezaBX38pZtsPRdhs4vuLVCph8M2d6DchEel5FnqcLwRBoCE7m4oFb2HY551UBGVkoHt0LhovxQtXM043nmZtyVrWlqxl+5ntWAV3aUNLBMgDSI9NJzMhk5FxIwlWBl+CK7084bd+uEJgMJx0VBDW1GzDvSTNHTJZEBERGURFTiAiIgO5/Nr7oguCQGFhITk5OZS07KXmgk6dOjF69GgSf6NeauYzjVR9fRjzKXdvM0VsENpZaSja0D75AqvFwk9v/JcjWzaIxgPDtcx4ej4Rsb5HOQVBIPuLwyKiBTD6jrQ2iRZAxdtvi4iWPCqK8NtubfV8LV3jW08htrR9uLAUItgrAVMD1WytdX5OR/VGr2QrKup6EdlqLZUIkJ6ezo4dOzCZ7A9Qer2eLVu2kJGR0ep1qRJCCL0uidqfnGkfU0k9tSuPEXaD71HKuG49mT7vBZb981mMeudr3PHjd1gtFsbe+yCSC+iIIJVKGHhDEvHdtaz+cL/ou2OzCWz5rpCS/VWMu6+7196ZFwMSiYTgMWMIGj2axtxcyhe8hWHPHrd5DTk5NOTkEDhqJJFz56Lp41uV7tWA6MBobu92O7d3u50aQw05x3PIKsli08lNGK1Gj2v0Fj2rilexqniVI12ZmZDJmPgx6DTX1gN/a/BHtn5DCIJAoz7fUUFYX+9bCFeh0BKpG9ds0TAcqfTaDOEKgkBBQQE5OTmUlpZ6nde5c2dGjx5NQkLCJbw6JwRBoHHzKWp+KgJLCwItgeBRcYSMT/SpuqwtWMxmfnztX+RvE0d3giJ0zHx6PuExsed0vAMbTrLuczGh6T4ihjF3tS2qN5WUUHDDJHARZUf/4x+E3zrL6xq3FKJUTvZMLylEgF+ehC0LnNsZ/wdj/u5xqq+RLYA/HSrhi1POjgrPJnfk4QTPlZPnmkoEu89Wbm6uY1ulUvHEE08QENA6gRVsApWfHsBwSNztIeLeHues7ztdcJRv5j+NoVEsS+iVOZHxD8y9IMJ1FiaDhY1LjnJg4ym3fUqNnIzbU0kd9Ns0URYEgcYNG6h4cwFNu70bgwamp6Ob+wgB/fpdwqu7vKA360WVjfUm96rplpAgoW9UX4fOKz746pey+CNblxkslkaOHVtAecUq9Hrv4kRXqNVxjgrCsND+SCTXrjhREATy8/PJycnh+HH3JrlnkZycTEZGxm9GsgCs9Saqlx7BcLjabZ8sVEX4zFTUyWHtci6LycSKV16iaKf4ISUksgMzn5lPaNS53dQqTzSQu0hcQq/tGEj6LN98isrffFNEtBTx8YTd0rrVgFsVYkwrVYjgoRKxfTyUWorkj7YikrdXJXZziW61XpUIMHz4cLZu3YrBYD+u0Whk48aNjB/furu7RCohfEYqZa//irXWKS2oXnwYxeP9kYf5/uAVndyFGc+8xNIXn6Kpvs4xvjdrJTaLhQkPPY70AkXQSrWcMXd1I7GnjnWfH8LQaHbsMzVZWP3BAYr3VjLqtjRUmkt7O5JIJASNHElgejqNGzdRsWABTTt3us1r3LCBxg0bCBw+HN2jcwno75vx79WEAEUA4xLHMS5xHGabmW2ntznSjeVN5R7XCAjsLNvJzrKd/Hf7f0kNTyUzIZM5vedck+J6P9n6DSCTqTl5akmbvQiDAtMcBCsoqNs1U0HoDYIgcPToUXJycjhxwnuj7JSUFDIyMoj34kx+qdB0sJLqpUexudxgzkLTW0f4lBSkAe3Tq8xsNLD8v/Mp3iO+WYR1iGHGM/MJ0Z2bUaHJYGHle/uwurRlkSulTPxdTxTKtv8ojUePUve92Goi8vHHkLRSdXfOKURotwbULZHawsTUm/3DWZxrKlGtVpOens6aNc7ihby8PIYOHUpwcOtSAFmgAu1tXSl/d49DaWDTW6j66hCRD/Y6J/1WVFJnZj7zEktefAp9rdOaY39OFlaLhevn/hGpFx+wc0HnfpF06BRC1qcHKT0g/t87svUMp/JrGTe7Ox1T2ufB41wgkUgISh9B4Ijh6DdvpvzNBTT9+qvbvMZNm2jctImAYUOJnDuXgIEeAxhXPRRSBcM7Dmd4x+E8OeRJ9lbstVc2FmdRUu9dxnGk+gg24f+zd97hURVYH37v1PRe6AkhoUvvvQqKKCIQxE9du6JA3F1XQREUEVzXXcDedV2VLqCCgKH33ltooaf3Nu1+f4TI3JkJZGbuJBO87/PwQE7mFlJmzpzf75xjYXy78dV4t96DkmzVAILqV0ExAAAgAElEQVSgJjJiEFeuLrT9DMHB7a8b3Afj5xdbE7fndYiiyKlTp9i4cSNXrlyp9HEJCQn07duXBg0aVOPd2WMxmMn79SxFO6/ZfU7Qqwm5rwl+7aNkS54NpSUse+dNLh47LImH1mvA6KlvERjmvG9i0/xT5FwrlsT6jmtGWN2qbRXImCfdy6dPSCDo7rtvekxKbgrn88//8bFGdZNBpgBlhZBnJR8LKgiXZw9egoPxD6IoVvo9c2bAaQVdunRhx44dFBaWy3gmk4lNmzYxbFjl8mYF+thggu6MJf+383/EDKn55K9NJXho41seb01Eo1jGTJvFohmvUpRzIxE6sXUjFrOZuyf8HbXG/ZcK/xA9w19oy6H1l9j+0xlJZ2tBdinL3ttHh6ExdL6nMWonEka5EAQB/x498OveneIdO8j48ENK9uy1e1zx9h2kbt+BX9euRDw/Hv8ut94leruiElS0jWxL28i2vNjhRU7nnv5jltfxbPtxGwMbDayBu/QOlGSrhoiMvJMrVxciCFpCQ7tdT7AGodcrqxIqqEiyNmzYwNWr9p6PCpo2bUrfvn2pX985P5InMFwuJHv+CUwZ9msydDFBhCU2QyOjKbisuJils6dz5aS0pT28QSNGT52Jf4jzOy2Pb7vKyR3SRLF5tzo071a3SseXHD5MwVrpuInIpEkIt6iQ2Fa1bi0h2kwJD20MGnn8i/X1WvzVKorM5QlBvslCusFEtN5xZc4VKVGn09GnTx9Wrlz5R2zv3r306NGD0EpmkFkT2KcBZWfzKDt1Q6Iu2HAJfeNgfJo5598Kr9+QxOmzWfTmqxRk3ZCFTu3Ygtlk4p6kl9HcpCpZVQSVQNuBDWnQPJQ1Xx4l+8oNg74owt5VqVw8ls3gx1tVqQHDEwiCgH/37vh160bxzl1kfvghxbt32z2ueOdOLuzciV+XLkQ8/zz+Xf+8SReUf90SQhNICE3g2bbPcrnw8h/Lsven78ciWv7UydbtPzrcSwkN7UGrlv+md69dtG/3DQ3qj1MSreuIosiJEyf47LPP+PHHHytNtJo1a8bTTz/NuHHjajzREi0i+Rsukv7RAftESwVBg2OIfLqNrIlWaVEhS2ZOtUu0ImMaM2baLJcSrewrRWyaL5XmQuv40efBqnf5ZfxnjuRjnzZtCBhwkwoV1weZ2vi1hsQOucWFPCMhQvkLR3wVJ8lXEBUlXeqTnr6ykkfeoEOHDoSE3JDOLBYLGzZsqNo9qgTCxjRFFSidx5a98CTmfMedYzcjtE49EqfPIihSOqT2zJ4drHhvJibDrcfPVJXw+gGMntyJtgPspf701AIWzNzF0c2XqckGLkEQ8O/WlZjv/kuj/36LX9euDh9XvGsXFx59lNT/e5iiHTtq9J69ifoB9Xm45cN8M/Qb1o9Zz9u93qZ52O23IqmqKMlWDaFW66lT5z602uod8OfNWCwWjh8/zqeffsr8+fMrTbKaN2/OM888w4MPPki9evWq+S7tMeWWkvH54XJJxyx9otWE+xD5bFuCBjZCUMvnuSspLGDxW69x9bQ04YiOi2f062/jF3STilAlGA1mVn9xBJPByqelve7TquLk76IdOynatk0Si3ox6ZaSqSMJsX/D/je/mIfM8RXYmuRP3sQkD+VSojUVUuLN0Gg09OvXTxI7dOgQ6enpjg+wQR2gI/zBZmD15bUUmcj68SSi2fkX/eCoOiROn0VItLSKeW7/Hpa9OwNj2c2/Bs6g0arpNSaB4RPb4hckTRhNBgsbvj/Jqk8OU1IoX5LnKv5duhDz7TfE/O87/Lp3c/iY4j17uPCXx8qTrm3blKTLijCfMIY3Gf6n9h0ryZZCjWOxWDh27BiffvopCxYs4No1e68TQIsWLXjmmWcYO3YsdetWTdLyNMUHM0ibsw/DOfuJ2X6dooma2AF9I3kT6uL8PBa9MZm0s6cl8brxzRj12lv4Brg2a23zglMSWQeg99imhNev2gJsURTJmCOtavl164b/LaajgwsSIni0sgX2JvmUW1S2KqTEG5RLibeiTZs2RETc8HaJosj69eurfJ/6uBCCBklnxxnO5ZGfXPlg35sRFBFF4vTZhNaTeh9TD+3np9lvYCi1l8jdoVHLcMa+3oXGbe39becOZjJ/xi4uWK0qqkn8OnUi5uuvifn+f/j3cPxzXbJ3Lxcef4LUcQ9RuGWrknQpAEqypVCDWCwWjh49yieffMLChQtJS3O8HLVFixY8++yzJCYmek2SZSk1kb3gJNk/nkAslU5ZVvlpCP+/FoSNaopK5l1wRbk5LHxjMhkXzkvi9Zu35IFXZ+DjX7XEyJaTO69x3GYWUtMu0bToUfWvd+GGDZQcOCCJRSVNuuVxLkmI4JGBptY4syOxAlekRJVKxQAbmfX48eM37bi1JbB/Q/Q2nXwF6y9SmmI/cqQqBISFkzhtFuENpGNTLh47zJK3p1FWXFzJka7hG6DjrmfvoP//NUejk74sFecZ+HneQTYvPIXJeOuJ5tWBX8eONPrqK2J++AH/nj0dPqZk/34uPvkkqWMfpHDzFiXp+pOjJFsK1Y7FYuHIkSN8/PHHLFq0qFLJpGXLljz33HMkJiZSp07NDD50RNn5PNLm7qN4v/196xNCiE7qgG9r+ScnF2RnsmD6K2RdkrZXN2zVhpGT30B/i4GYlZFzrYgNP0irRCHRfvQd16zKZX/RYiFjzlxJLKB/f3zbtbvlsS5JiMZSyDkvjUXILCPaVbZu7YNyRUqE8jcUtm8k1q1bV4W7LEdQCYQlNkMVYGViFyF7wUnMBa7JcP4hoYyZNovIGGl345WTxxwOQ3UXQRBo2aseia92ISrGvjp7aN0lFs3aQ9Zlea/rDn4d2tPoyy+Inf8j/r17O3xMycGDXHzqKc6PHUvhpk1K0vUnRUm2FKoNi8XC4cOH+eijj1i8eDEZGY6H4bVq1Yrx48czZswYoqOjHT6mJhDN5XsNMz49hDnH5oVXLRB8TxwRj7VGHST/RP/8zHQWTp9MzlVptSOmTXvuf/l1dD6+Lp3XZDCz+vOjmMpuVAzUGhVDnmqFzqfqzcr5q1ZRdlKasEVWoaoFLkqIWadBtJrGH9wIdFUbS1FVGvnq0Fvt78s0msgymG5yhOtSoiAIDBwo7dQ6c+YM58+fr/L9qgN1hI218W8VGsmefwLR4toLvF9QMKNff5voOOlIjaunT7JoxquSYahyERLtx8h/dKTjXTHY5vrZV4pYNGsPB5Mvuvx/8gS+7drR6PPPiF24AP++fRw+pvTgIS4+/QznxyRSsGGDknT9yVCSLQWPY7FYOHToEB999BFLliwhM9PxO/3WrVszfvx4Ro8eTVSUd3VmmjJLSP/kEAXrLoLNc6Qm2o+oF9oT2Ks+ggeW6+alX2PB9MnkpkllvsbtOzHipalo9a53OG5ZlGJXKeg1JoGIBlX3fYkmE5nz3pfEgoYNw6fZrWU9lyVEO3O8vBIigFoQaGKzD/Fmk+QrsJMS036t5JFSmjRpYre3c926dU69KPvEhxI4QCr9lZ3Jo2Bd5cMmb4VvQCCjXnuLugnSr3H6uTMsenMKxfn2fkV3UatVdLuvCSP+1sFuf6LZZGHLohR+fv8ARbnOd116Et82bWj06afELlpIgE3jQwWlhw9z6dnnOD96DAXr1itJ158EJdlS8Bhms5mDBw/y4YcfsnTpUodJliAI3HHHHTz//POMGjXK65IsURQp2n2NtHn7MF603wcW0LMe0S+0R1fFYZ/OknP1MvOnv0J+htTP1qRTN+7926todLpKjrw1KXvSOLpZOiQ2vlMUrXo71+GZt2wZhlQrM7ZaTeSEF6p07KmcU85LiODAHC9/sgXOre2pwE5KzN1VJSlREAQ779aFCxc4ffp0JUc4JmhgI/Rx0spgfvIFSs/kVnLErfHxD2DUqzOo37ylJJ5x4TwL35hMUa5r3rBbUS8+hMSpXWja1b7CffF4DvNn7OLsfscV8prE9447aPjJx8QuXlzp2JPSI0e4NH485x8YRUFyspJ03eYoyZaC7JjNZg4cOMCHH37ITz/9RFaWfSeRIAi0adOG559/ngceeIDIyMgauNObYy4ykvW/4+QsSUE0SBdIqwK1RDzempDhTRC0nvk1yrp8kQVvTKYwS/pC3bRbL4a/+IpbQyZz04vtFkwHR/rS/6HmTrVnW8rKyPjwI0ksZORIdLGxVTp+Taq0qtW9bvdbS4jgcXN8BQlOru0B16VEgJiYGBISEiSx5ORkLBZLJUfYI6gEwsY2Q+Vv49+afxKzG2MUdL5+PDD5TRq2aiOJZ126wILpr1CQfeuE0hX0vhoGP9aKO59ohc5mf2JpkZFVnx5m/XfHMZTeXOKtCXxbt6LhRx/SeOkSAgY5HuhZeuwYl55/gXMjHyB/7VpEJ77XCrUHJdlSkA2z2cz+/fv58MMPWbZsGdnZ9rsfBUGgbdu2vPDCC4wcOVLS8u5NlKbkkDZ3H6VH7RNFn5bhRCd1xKep80NDq0pmRcUgR/o1bNGrH8MmvuTW+hST0czqz49gtOqiVGkEhjzV2u7F7FbkLliAyWoemqDTETH+uSod60hCvDP2FrsQK8iwmR4fUT2VrVNVMMmDfXWrqlIiYFfdunbtGseP268+uRnqID1hiTb+rQID2QtOuuV10vr4cP/LrxPTpr0knnP1MgunTyY/s2rzwVwhoXM0Y6d2oV6C/f7EY1uvsnDmbtLOye8hkwOfli1p+MEHNP5pKYGVLBsvO36cyxMmcu7+keSvXqMkXbcZSrKl4DZms5l9+/bxwQcfsHz58kqTrHbt2vHCCy9w//33Ex4eXgN3emtEo4XcX86S+eURLPnSKoCgVRE6MoHwh1ug9pdngbQj0s+fZcGbUySLgQFa9R3E0OdfdHsx8LbFp8m8aOPTGpVAZCPn5nNZiorI/ORTSSz0wQfRVnE8h8sSotlUbpC3RuaBphW4IiOCvW+rqlIiQN26dWnVqpUktm7dOsxm58Ye+DQNJbCfdEJ7WUouBRsvVnJE1dDqfRjx0lTiOnSWxHPTrrJg+ivkpjmekycHgWE+3Pdie7qNiENl44/Myyhhybt72bPyPBYvMs9b49OiBQ3en0fj5csIvNPxG4uykye5PGkS50bcT/5vvylJ122CkmwpuIzZbGbv3r28//77rFixgpwce9+GSqWiffv2TJgwgREjRnhtkgVgvFZE+of7KdxiP99I2yCAqInt8e9Sx6NTkK+dSWHRm1MotenyajNwKEOenYhK5V6idXpvOoc3Sv9/ce0jad3X+XVH2d99h9kqsVb5+RH+zNNVPt5lCTHnHFiMNz4OqAO+nqkyNvbVYT34/0qZkQLTrZMed6REgP79+0t+zrKysjh06FCVj68gaFAMuljpUN38NamUORjC6wwanY57/zaF+M7Saer5GekseOMVu65ZOVGpBDoOjeWBlzva7U8ULSI7V5xl2b/3kZ8p7/BVOfFp1owG8+bSePlyAocOxa7tEig7dYrLSS9y7r77yF+1Skm6ajlKsqXgNCaTiT179jBv3jx+/vlncnPtjbcqlYoOHTowYcIE7rvvPsLCnFuMW52IFpGCLZdJ+2A/xms2wxqF8oGRUc+1RRvp2cW4V04dZ9GMV+3mF7Ubcg+DnnoeQeXer2teRgnrv5PKUUERPgx42DmfFoA5N5esL7+SxML+8iiaKn6f3ZMQbf1anqlqAehUKuJc6EgE96TEiIgI2tnMKNuwYQMmk3O+JEEtEPZgc1R+VvKwCNk/nsBcZKz8wCqg1mi5J+kVmnaXzpcqzMpkwRuTybrkXgXtVkTFBDFmSmda9bF/o3D1dB4L3trFyZ3XvNp47tOsKQ3m/Ie4FcsJuvsux0lXymkuv/hXzt57L3m//oroZIVTwTtQki2FKmMymdi9ezfvv/8+v/zyC3l59u+OVSoVHTt2ZMKECdx7772EhnrO1yQH5nwDmd8cJe+Xs2CSPimrQ/REPt2G4CGxCGrP/qpcOn6ExTNfx1AiTfY63nM/Ax57xu1qmtlkYc0XRzBY+7TUAnc+2Rq9n/OSaNaXX2EpuNGdqQoOJuyxx6p8vMsSIjhItjy73Nbet+W6lFhWRSkRoG/fvqisEuy8vDz27t1b5eMr0ATrCR0j9bSZ8w3kLHTPvwWg1mgYNuHvtOjVTxIvyslm4ZuTybTZdCA3Wr2afuOacff4NvgESH+ODaVmfv/6GGu/PEpZsXuJpafRJyRQ/9//Ju7nFQQNG+Yw6TKcPsOVv/2ds8PvJe/nX5Skq5ahJFsKt8RkMrFr1y7mzZvHr7/+WmmS1alTJyZOnMjw4cO9PskCKDmaSdqcvZSdspc//dpFEp3UAX1j5xc6O8uFIwdZMmsaRpudc13vH0Pf/3tcFtly+9IzpKdKR1f0GBlPdKzzextNGRlkf/edJBb+5BOoA6vu+XJZQgR7c7yHOhErsO9IrJpJvlxKtB6VYCEjfXWlj7clJCSETp06SWKbNm3CYHC+o9C3eRgBfaS7DktP5lC42X25T6VWM/T5F2nVd5AkXpyXy4I3p5B27ozb17gVjdtEMHZqFxq1sq+spuxJZ/5bu7js4Pfc29DHx1P/vX8R9+svBA0fDg6q2YazZ7ny0kucvWc4eStWIDpZ7VSoGZRkS6FSjEYju3btYu7cuaxcuZL8fPtOH7VaTefOnZk0aRL33HMPISH2nULehsVgJmdpClnfHcdSLH2iEnzUhI1tRtjY5qicmKDuKucP7OWn2W9gKpO+gHcfNY6eiQ/LkmidPZDBwXVSSadx2wjaDGhQyRE3J/OTTxFLb1R31JERhD30UJWPd0tCBPvKloc6EStw1SQPEO3CrkRrevfujdZqxEdRURE7d+506hwVBA+JQWfTBJG3+hxlqe538KlUaoY8O5E2g4ZK4qUF+SyaMYVrp09VcqR8+AfrueeFtvRObIraZhxLYXYZy/6zn+0/ncFs8n7vkz4ujvrv/pO4X34h+L57HSdd585x5R8vc3bYPeQuW6YkXV6Okmwp2GE0Gtm5cyfz5s1j5cqVFBTYD/NUq9V06dKFiRMnMmzYMIKDPV8BkgPDxQLS5+2naJd9x5SucRDRkzrg1656Bque2buLZe/OwGSUVip6jX2EHqPHyZJo5WeVsO6/Up9WQJieAY+0cOn8xsuXyVm4UBKLePZZVE7sZXRLQrRYIDNFGvOwjJjgJ/VsVVVGBPelxMDAQLp27SqJbd26lZIS583fglpF2LjmCNbjPSzl/i2LDDKboFIx6MnnaT90uCReVlTEorde48op58ZXuHQPgkCb/g0YPbkT4fVtlrKLsG91Kkv+uZeca0Uevxc50Mc1pt4779Bk5a8EjxgBDjqRDampXH1lMmeGDSN36U9K0uWlKMmWwh8YjUZ27NjB3LlzWbVqVaVJVteuXZk0aRJ33313rUmyRItI/roLpH98EJNtl5JKIGhILJFPtUET6vrqG2dI2bWNFe+9jdnmibHvw0/Q9f4xslzDbLaw5oujlFlV71QqgSFPtsbHxdEVGR9+BMYbL8za+vUJHT3aqXO4JSHmXQCT1ffPNxT8PTurrYmfj/W4Ki6UGigxV6064q6UCNCzZ0/0+hsJX2lpKdu2bXPqHBVoQnwIGy1tKDDnlpG96JQsRnJBEOj/l6fpNHykJG4oKWbxzNe5dOyI29eoCuH1Ahj9SifaDWpo97mMCwUsnLmbI5sue7V53hpdbCz1Zs8qT7pGjnSYdBlTL3B1yhTO3HU3uUuWIBq926f2Z0NJthQwGAxs376duXPn8ttvv1FYWGj3GI1G80eSdddddxEU5LzXp6Yw5ZSS8dkh8tekgo0hWBPhS9T4tgT1b+iRvYaOOLFtEz//ZzYWszTRGvDYM3S6537ZrrNj2Vm7IY/dRjShTpxrCXLZ2bPkLVsmiUW88AKCEyuD3JcQbdf0NHdoJpYTP7WKRj43/o8icKYapURfX1969uwpie3YscPh72mVztcynIBe0g6+0uPZFG65UskRziEIAn0eeszuTYOxtIQls6eReviALNe5FWqtip6jErg3qR3+IdLqpMloYeMPJ1n58WFKClyfql/d6GJiqPf2TJqsWknwAyPBwXBj48WLXH31Nc7cdTc5ixYpSZeXoCRbf2IMBgPbtm1j7ty5rF69utIkq1u3brUyyQIo3p9O2px9GM7b+1L8u9YhamJ7dE4sXXaXY5vXs3Lev6QzcwSBwU+9YCe/uMP5w5kcWCtdPhxzR7jDd/pVJWPe++Uy3nV0TZoQfK9z9+yWhAjVthPRlgTbjsTiqi9AdldKBOjatSv+/jf2bxqNRjZv3uzUOawJHhqLtqGNf+u3cxgc7P90BUEQ6Jn4MD1GS718prIylr3zJucPON9V6SoNm4cxdmoXmrS3Xwl2/lAmP87YReoR+00R3oyuUSPqzZxJk99WETJ6lOOk69Ilrk19nTNDhpKzcCGiC40VCvKhJFt/QgwGA1u3bmXu3LmsWbOGoiJ7/4JGo6F79+4kJSUxdOhQAp3oNPMGLCUmsn48Ub6epEzaIq3y1xD+cEtC709ApXNvSKgzHF6/hlUf/htRlCZaQ56dZGcsdoeC7FJ+/+aYJBYQqmfQoy1drt6VHD1KwW+/SWKREyciODnN3i0JEeyTLQ+b4ytoatORmOKEb0sOKVGv19O7t3Se1Z49exzOuKsKgkZF+IPNEXysvn9mkawfjmMpkcfzIwgC3Uc9SK8HH5XETUYDy96dwZm9u2S5TlXw8dcy5OnWDHikOVq99Ge2JN/ALx8cZNP8U5gMtWucgq5BA+rOmEGT334jZMwYcLAv1XjlCtden8bpoUPJmb9ASbpqCCXZ+hNRVlbGli1bmDNnDmvXrnWYZGm1Wnr06EFSUhJDhgwhICDAwZm8m7KzeaTN3UfJwQy7z+mbhhKd1BHfVtU7yf7g2pWs+WQeWHlEBEHF3c//ldb9Bt3kSOcwmy3lc4WKbrxgCiqBO59oZTeHyBky5s6VfOzTqhWBdzre8VYZjiTEIbFDnLyR6llAbUuCv41J3gkZEdyXEgE6deokqSybzWY2btzo9Hkq0IT5EDbKxr+VU0b2Ynn8WxV0HTGafo88Kb2OycSK994mZZdr3jNXEASBFj3qkfhaZ6Ib21foD2+4xMJZe8iQqbpXnega1Kfum28Qv/o3QsYmOky6TFeucm36dE4PGUrOjz9iUZKuakVJtv4ElJWVsXnzZubMmcPvv/9OcXGx3WO0Wi09e/YkKSmJO++8s1YmWaLJQt5v58n4/BDmXBuZRyMQMjyOiMdaoQ6susdIDvatWsHvX3wkianUaoZN+gctejshoVWBXSvOcfWMdA5a13sbUzfe9ZEcxXv2ULRJKllFJk1yupvRoYTYyIn/vyhCpu2MLc92IlbQzG7WlnPJlhxSokajoV+/fpLYgQMHyMx07jzW+LaOIKBHPUms9GgWRdvk8W9V0HHYCAY8/qwkZjGb+Pk/szmxbZOs17oVwZF+jPx7BzoPi7Wz++VcLWLxO3vYv+aC2wNfawJtvXrUnT6d+DWrCR33IIKjpOvqVa698SZn7hxC9vffYymruiSu4DpKsnUbU1payqZNm5gzZw7JyckO28V1Oh29evUiKSmJwYMHS3whtQljRjHpHx+kYMPFcgezFdo6/kRPaE9Az/oe3WvoiN0/L2X9N59JYiq1huEvTqZZ916yXiv1aBb7VqdKYo1ahtHhzhiXzymKIun/mSOJ+XbqiH8v5+999XmpdNa9bneCdE54AAuuQpmV904XCEH1Kn+8jNh6ts6VlGFwYledHFIiQNu2bSWrr0RRZP369U6fx5rguxujtRmTkLvyHIZL8lZ42g+5h8FPvSBpaBAtFlbO+xfHNq2T9Vq3QqVW0WV4HCNf6khQhPR7azGJbFt6mhXzDlCYUzsTEW3dutR5/XWarF1D6EMPOWxiMV27RtqMtzgz+E6yv/ufknR5GCXZug0pLS1l48aNzJkzh3Xr1lWaZPXu3ZukpCQGDRpUa5MsURQp3HmV9Hn7MV62N/gH9KpP1Avt0EZX//9vx9IFbPqfdH+gWqvlvpdetVvg6y6FOWX8/rXUp+UXrGPgX1z3aQEUbdlCic2KmKikJKeTVlEUWZu6VhJzX0Js6vFOxAoCNWrq6m9UCUwinCtxToaRQ0pUq9UMGDBAEjt69ChXr151+lwV/OHf0tv6t05gKZV3ZlObQUMZ8uwkacIlWlj10X84vL7qi7rlok5cMImvdqF5tzp2n7t0Iof5M3Zyem96td+XXGjr1KHO1NfKk66HH3acdKWnkzZzJmcGDSb7v//FUupc1VahaijJ1m1ESUkJGzZsYM6cOaxfv55SB780er2ePn36kJSUxMCBA/FzYhilt2EuNJD13XFyfzqNaJRWGVRBOiKeaE3IPXEImur9MRdFka0Lv2frAulKG41Wx4iXphLXvrOs17OYLaz96iilhTdavAUB7nyiFX5BrkumoiiSYVPV8u/TGz+bFTJVwW0JEezX9FSTOb4CW5N8TUiJAC1btiQ6OloSc7e6pYnwJfSBBEnMnF1KztIU2WdRte43iLtf+Jt0sboosuaTeRxc63wC6i46Xw0D/9KSIU+1Ru8n7eorKzax+vMjJH97DIPMiWd1oo2Ops6rU2iydi2hjzyMoNfbPcaUkUHa27M4PXgwWd98g8WFwbkKlaMkW7cBJSUlrF+/njlz5rBhw4ZKk6y+ffuSlJTEgAEDanWSBVB6Mpu0ufsoPWbfsu3bOpzoSR3wSaj+/YyiKLL5x2/ZseRHSVyj13P/K9OJbdtB9mvu/vU8V1KkXWmd72lM/abu/f8L1qyl9Ji0WhY5aZJL57KVEHvU6+GchAg1Zo6voKmNSd6ZtT0gn5SoUqkYOHCgJHbq1CkuXLhQyRFVvL82kfh3lVZ4So6A7UkAACAASURBVA5lUrTTftuCu7To1Y97Jv0DlU036+9ffMS+VStkv15ViO8YxdipXajfzN7feGL7NRa8tYtrZ+33wtYmtNFR1JkyhSZr1xD26KMIPvZDnM0ZmaTPfofTg+8k66uvsTjw+Co4j5Js1WJKSkpYt24dc+bMYePGjZQ50Nx9fHzo168fSUlJ9O/fH19f3xq4U/kQjWZyV5wh8+ujWAqkw/oEnYrQBxIIe6gFahcnpLt1b6LIxu++YPfyxZK4zteXB6a8SaPWbWS/5sXj2exZdV4Sa9A8lI53xbp1XtFstutADBw6FN9WrZw/lwMJ8c4YJwaZVlBD5vgK7BdSOy+32EqJaem/unYvCQk0bCidmZacnOx2FSrkniZo60ol99xfzmC44toA1ZvRtFsvhr84GZVaWk1a/81n7F6xRPbrVYWAUB/um9Se7iOboFJLJer8zFKW/msfu345h6WKGwS8FW1UFNGTXyH+97WEPfaY46QrM5P0f/6zPOn68isl6XITJdmqhRQXF/+RZG3atKnSJKt///4kJSXRr1+/Wp9kARiuFpH2wQEKHXRK6RoGEj2xA/6d61S7CR7Kjb7rvv6Evb8ul8T1fv6MevUtGjR3Pkm5FUV5Zaz9+pikIcA3SMfgx1uhcnMaft6KnzGcPXsjoFIROXGCS+eSRUIEx56tasSdhdQV2EqJubm7XZISBUGwq26lpqZy1vp75gKC9vr+ROv5cyaR7B9OYCmTX0aL79yN+156FbVN19ym779mx5L5sl+vKggqgQ53xjDq5U6E1pEqAKJFZPcv5/jpvX3kZdR+mU0TEUH0y/8gPvl3wp54HMHB64Q5K4v0d9/l9KDBZH3xBRYHI4MUbo2SbNUiSkpKSE5OvmmS5evry4ABA0hKSqJv3774OHjHUtsQLSIFmy+R/sF+TGk2764ECBzYiMhn26CJqJmEUrRYWPv5BxxYLa1S+PgHMHrqTOomyC93WSwia786Rkm+lUlbgMGPt3TLpwVgMRjIfP99SSx4xAj0cXEunU8WCbEoE4qtJGOND4S43mXpCraVrdPFZZidrCTJJSUCxMbG0qRJE0lMjuqWNtKP0JHxkpgps4Scn057ZJdgXPvOjPjH62h0Upl268L/sXXh/2psf2Fko0BGT+nMHX3r233u2tl8Fry1ixPbr9aa/Yo3QxMeTvRLLxGf/DvhTz2J4MBmYs7OJv1f73F60GAyP/tcqXQ5iZJs1SJKS0vZunUrBgfD6CqSrEmTJtGnT5/bIskCMOeVkfnVEfJ+PQdm6ZOaOsyHyGfbEjw4BkFdMz/KFouZ1Z/M5fA6aSeVb2AQo19/m+i4+EqOdI+9q85z+WSOJNbp7lgaNg+r5Iiqk7toEcYrVtVDrZbI58e7dC7ZJETbyfHhCaCqvun/AOE6DeHaG5JXmUXkgpMdiQDRUXdLPnZVSgTsOhOvXLnCiRMnKnl01fFrF4V/Zxv/1oEMinenuX1uR8S2ac/IV6ah1Uuft3Ysmc/mH7+tsYRGq1PT58FmDHu+Db6B0uqbscxM8rfHWf35UUqLbo/9g5qwMKL+9rfypOvpp1E5Srpycsj67DNl56KTKMlWLSI0NJS2bdtKYr6+vgwcOJCkpKTbKskCKDmSSdrcfZSdtl9J4tchiuiJ7dHH1NyuRovZzKoP/s3RjcmSuF9wCGOmzSIq1rVK0K24fDKH3b+ck8TqNw2h87DGbp/bUlxM5sefSGKhiYlo69u/u68KnpMQq9ccX4G7JnmoREoss992UBXq169PixYtJLF169ZhcWIGWGUED49DEy19sc1ZcQbjNc/ISA1bteGBKW+is5Gydi9fzIb/flGjFaTYOyIYO7UrMXfYb544sy+d+TN2celEdg3cmWfQhIYS9dcXaZL8O+HPPoPKZjRQ2CMPow52baH9nxUl2apl9O7dG0EQ8PPzY9CgQSQlJdG7d2/0Dlp5ayuWMjPZi0+R9b/jWIqlPhHBR0PYuOaEjWmGysd++Wp1YTaZ+GXuO5zYKl2XEhAaRuL02UQ09IzEVZxvYM1XR623/uAbqJXFpwWQ/f33mK0mkgs+PkQ887TL55NFQoQaN8dXYCslnnTBJO/nF2svJWa4JiUC9O8vTV4zMjI4fPiwy+erQKVTE/5QCwSt1cuEyULW98exlHlmh2D95i0Z9epb6P2kL+77Vi4n+atPpAvcqxm/IB3Dxreh74NN0WilL51FuWUsn3uArUtOYzbWbvO8NZrQUKKSkohP/p2I8c+hCghA5e9P2COP1PSt1TqUZKuWERYWxrhx40hKSqJXr163VZIFUHYhn7R5+yjeYy9X6OOCiU7qgF+byBq4sxuYjEZ+/s8sUnZK97oFhkcyZvpswuo18Mh1RYvI798cozhP6tMa9FhL/EPc/zkw5+eT9cWXkljYww+jiXTt6y2bhAg1bo6vwNYk7+yOxArspUTX50tFRUXRpo2003X9+vWYTO4b2rVRfoSMsPFvZZSQu/y02+eujLoJzRg9dSY+AYGS+ME1v7L28w9qNOESBIHWfRswekpnIhrarDQT4cDaCyz+5x6yr95eJnJ1SAiREycSn/w7DT54H3WI6+u//qwoyVYtJCEhAZ2DScC1GdEskp98gYxPDmLOsnkBUwsE39WYiCfvQCNDUuEORkMZK/71Fmf27JTEgyKjSZw+m9A6nlsfs3d1KhePSaWKjkNiaNRSnqXa2d98gyXvxhwhVWAg4U887vL5ZJMQwd6zVUOVLdsdiSlFrq04kVNKBOjXrx8qqyGhubm57N+/3+XzWePfMRq/jtIhqsX70ily8IZILqLj4hk9dSa+gdIq6OF1a1j9yVwsFs9U1qpKWF1/Rr3ciQ5DGoFNQTnzYiEL397N4Q2XbgvzvDXq4GD8u3ev6duolSjJlkKNY8ouJeOzQ+SvTQWbN62aSF+ixrcjsG8Dt9bOyIGxrJRl/5zBuQPS9TUhdeqSOH02wVHRlRzpPldSctm1QtrWXzc+mC7D3fdpAZiyssj65ltJLPyJx916ByubhFiaV74XsQKVBsI844e7FbY7ElOKS116QZVbSgwLC6NDB+nA3I0bN2KUycQccl8TNFFSL1Xu8tMY0zxXwYmKjWPMtFn4BUt/Bo9uTGbVB//GYq7ZhEutUdH9/nhGJLUnIFT6JtBstLBp/il+/fAQxfnON1Eo3H4oyZZCjSGKIkV700ibuw9Dar7d5/271SVqQnt0NktyawJDaQlLZ0/nwuEDknhYvQYkTptNUITnpM2SQgNrvpT6tHz8tdz5RCtUMnVhZn32OaJVK7c6LIywhx92+XyiKLImVdqh6bqEaOPXCmsC6uofWgsQrdMQZLX+qchs4UqZawmNnFIiQJ8+fdBobvgYCwsL2bVrl1vnrEClUxM+TurfEo2W8v2JBs8lPRENY0icPpuAUGmX7YmtG/ll7juYTTXfEVe/WSiJr3UhvlOU3edSj2Qxf8ZOzh9yfpaawu2FW8/UgiCECYKwVhCElOt/O9wPIgiCWRCEA9f/1MwuBgWvwlJsJPvHE+QsOoVoY7ZVBWgJ/0srQkfEo9JVb3u/I8qKi1ky83UuHTsiiUc0jGHMtFkEhMkj4zlCtIj8/vVxinKlctXAv7QgIFSezlPj1avk/ChdLxThoAPJGU7lnCI1P/WPj92TEL2jExHKPTtyTJIH+aXEoKAgunTpIolt2bLF4fouV9DW8SfkXulcL1NaMbkrzshy/soIq9eAMdNnExgufUOTsnMbK/49C5MXjCCoePMz6C8t0PpIn7NKCoz8+tEhNv5wEqMHE1MF78bdt8WvAMmiKCYAydc/dkSJKIrtrv+5181rKtRySs/kkjZ3HyUO3u35NA8jelIHfGWYFyUHpYWFLJ75GldOHZfEI2PjGP362/iHeHb/4v7fL3DhqHT/Y/vBjYi9I0K2a2R+9DGi1ew2Td26hCQmunVO2SREgExbv1bNJVsgn0nezy+WwADrzQLuSYkAvXr1kvg5S0pK2L59u1vntMavUzR+7aRJT/GeNIr3p8t2DUeE1qnnUKo/u3cXy//1FkaDa945OREEgWbd6jL2tS7UbWI/FuHIpsssens3GRcKauDuFGoad5Ot+4AKo8e3wAg3z6dwGyOaLOSuOkfmF4cx59n4GDQqQkY0IfzRlqgDvcP8X1KQz6IZr3LttFTGio5LYPTUmfgFeXbOzLWzeexYJvVp1YkLousI+fxKhvPnyV26VBKLfH48Kje6XB1JiENih7h8Pm8xx1fQVCaTPNhXt9yVEv38/OjRo4cktn37dopkWrEiCAIh98fbbWvI+SkFY4ZnJ4oHR0UzZtpsQutKm1DOH9jLsn/OwFgmTwXPXYIifBnx1/Z0Gd7Yzmeac62Yxe/sYd/qVCyW28s8r3Bz3E22okVRvApw/W970bocH0EQ9giCsEMQBCUh+xNiTC8m/aMDFG68JNnlB6Ct50/0xPYEdKtXI3sNHVGcl8vCN6eQfl4qkZS3pb+Fr01butyUFhlZ/cURRKsnZL2fhjufbI1axmn5Ge9/AFZGY11MDMEj3PsVdSQh9mvYz/UT2iVbNVvZsjXJu1rZAkdS4i63pESA7t2742c1+dtgMLBlyxa3zmmNSl8+6w7Njd9V0WAh+/sTiEbPymRBEZGMmWY/XuXC4QMsnT0dQ6l37CtUqVV0HtaYkS91IChSmphazCLbfzrDijn7Kcj2jgRRwfPc8llbEITfBUE44uDPfU5cp5Eoip2AccAcQRCaOHqQIAhPX0/K9mRkuPeEo+AdiKJI4fYrpL+/H+MVm3fXAgT0bUDU+HZoo+zXQtQUhTnZLHhjMpkXzkvi9Zu3YtSrM+wGLsqNKIokf3ucwmwbn9ajLQgMk29DQOmJE+T/Kl0VEzFxAoLGvWGxskqIhiLIvWAVECDcMyuQqkpTP2nV71SRax2J4EhKFN2WEvV6Pb169ZLEdu3aRZ7VWA930dULIGS49GnceK2I3F/cW4RdFQJCwxgzbZbd4OBLx46wZObrlBV7z4yrOo2DSXy1My161rX73OVTuSx4axcpHhyhoeA93DLZEkVxkCiKrR38WQ6kCYJQF+D63w6Fe1EUr1z/+yywAWhfyeM+E0WxkyiKnSJdHKSo4D2YCwxkfXuM3OVnEG2mKquDdUQ8eQchdzVG0HhPU2xBdiYL35hM9uWLknjDVm14YPIb6Hw9nxQeTL5o173UdmBDGreV93ciY+48ycf6Zs0IuuuuSh5dNWSXEDNTkJRCQ2NBWzMLxyto4KPD13qmlclMptH1AaJyS4kAnTt3JjDwRvXVbDazadMmt89rjX+XOvi2kXoHi3Zeo/ig598o+4eEMvr1t4m0WYl15dRxFr/1GqWFhR6/h6qi89Ew4OEWDH2mNXp/6RuZsmITa744yu9fH8NQ4v4QWgXvxd1XuRXAo9f//Siw3PYBgiCECoKgv/7vCKAncMzN6yp4OSUnskmbu49SB/vCfNtEED2pAz5NvGsKcX5GOgumv0LO1cuSeEyb9tz/8utoq2HvZNq5fLb/JJUuo2KD6H6/w2Kwy5QcOEDh+vWSWGTSJASVe08JskuIXrKmxxqVIJBgU91yZW1PBZ6QErVaLX379pXE9u/fT3a2fPv7BEEgdGQCmnDp70XO0hRMmZ6X8/yCghk9dSbRcQmS+LUzKSya8SolBfbjZGqSJu2jGPtaVxo0t2+qObnzGgtm7uKqgz2wCrcH7iZbs4HBgiCkAIOvf4wgCJ0EQfji+mNaAHsEQTgIrAdmi6KoJFu3KRaDmZxlp8n65iiWQmlLtqBXEzq6KWEPNkflVzNzkiojN+0a86e/TF7aNUk8rkNnRrw0Fa3e84lWWXG5T8tivlHJ0flqGPJkK9QyV//S58yVfOzbrh0B/fq5fV5ZJUTwmjU9tth2JKYUu26S94SUCNC+fXtCQ2+8sFssFjZs2OD2ea1R+WgIG9cC1Fb+rTIzWT8ct6tmewLfgEBGT32Luk2lSXj6+TMsfHMKxXnelbwEhOq5d2I7eo6KR6WR+lPzM0v56b197FxxFrP59tmvqFCOW8/goihmiaI4UBTFhOt/Z1+P7xFF8cnr/94miuIdoii2vf73lzc/q0JtxXC5kPQP9lO046rd53QxQURP6oB/x2ivMcFXkH3lMgumv0xBprSaEN+5O/f+bQqaaliNJIoi6/57ggKbVUUDH2lBUIS8slnR9u0U79ghiUW++KLb3xfZJUTwuk7ECuSatVWBJ6REtVptt6T60KFDpKXJ6xHS1Q8g5B6pnGe8UkTuSs/7twD0fv6MmvIm9Zu3ksQzL5xnwRuTKcyRr5onB4JKoN2gRox+pTNh9aT+T1GEPSvPs/TdfeSme7a7U6F68R6zjEKtRbSIFGy8RPpHBzCl28gHKgga1IjIp9ugkdHcLRdZly6y8I1XKMyWzrJq2r039yS9jFpTPRW4wxsucfaANNm7o38D4trL69MSRZH0/8yRxPx79MC/a5dKjqg6skuIYJ9sRdRsJ2IFTf3tTfLu4AkpEaB169ZERUmbxNfbyMdy4N+tLr42s9+Ktl+l+HD1NDrpfP14YPIbNGotXcidfbn897sgy/smuEc0CGD0K51o099+cX36+XwWzNzNsa1Xbrv9in9WlGRLwS1MuWVkfnGYvFXnwCx9UlCH+xD5bFuCBsUgqL2rmgWQceE8C954haLcHEm8Re/+DJvwd9RuduVVlfTUfLYuOS2JRTYKpOdI+bvuCteto/TQIem1XkyS5dy2EmLPej3dkxBNBsi2qY54rYzoXrLlKSlRpVIxYMAASezEiRNcunTJ7XNbIwgCoQ8koLZ5Q5WzOAVTVvWMY9D6+DDi5WnEtpXuiMy5eoUFb7xCfoZnB6+6gkanpndiU4ZPaItfkLSCbiozs/67E/z22RFKC2t+Sr6CeyjJloLLFB/KIG3OPsrO2reU+3WKJnpie/SN3Hix9SBp58o9HSX50ntv1W8QQ8cnoVJXz5qgshITqz8/gsV0I1HV+qgZ8lQr1Fp5fz1Fs5kMG69W4OBB+N5xh/vndrQLMdbFXYgVZJ8B0WpuU1AD0Ht2vllVifHRo7OSXdMNJnLc6EgEz0iJAM2aNaN+/fqS2Lp162Q5tzUqHw3hDza392/9eALRVD0eJK1Oz31/f424Dp0l8bzrnsxcG0+mt9CoVThjp3ahcVv7zRBn92cwf8ZOLh7zLjlUwTmUZEvBaSylJrIXniT7hxOIpdIXGMFXQ9hDLQgb1RSVvnoqQ85y9fRJFs2YQqlNt1LbwXcx5JmJqFTVk2iJosj6706QnymtivT/v+YER8o/YiJ/5UrKUlJuBASByIkTZTm3ZyRE7zTHA2hUAnE2HYkpXiolCoLAwIEDJbGzZ89y9qz8nipdw0CC72osiRkvFZZXvqsJjU7HvX+bQkIX6ST9gswMFkx/mewrlys5smbxDdRx17N30O+hZmh00pfmojwDK+YdYMuiFEweHhyr4BmUZEvBKcpS80mbt5/iffYleX18CHWSOuAn494+ubl8snwOT5nN+pL2dw1n4BPj3R594AxHN1/hjM3XsVWf+iR0iq7kCNcRjUYy5r0viQXfOxx9QkIlRziH7BIieK05vgJbk7w7HYngOSkRIC4ujsaNpUnQunXrPOIHCuhZD5+W0uXshVuvUHK0+nxTao2WYZP+QbPuvaX3kZ3FwjdeIevShUqOrFkEQaBV7/okvtqFqBj7Ku7B5Issnr2HrMveM0dMoWooyZZClRDNInlrU8n45CBm2xUTaoHgYY2JeLw16mDXd+p5mvIJ01MxlEg9JJ2Gj6T/o09Xa5dkxsUCtixMkcTCGwTQa7RnpqPnLlmK8aLVoFaNhogXXpDl3B6REMHr1vTYIrdJHiAq6m7Jx3JJiYCdd+vSpUucOnWqkke7jiAIhI1KQB0i/fpkL0rBlFN962nUGg13T/g7LXtLOzKLcnNY8MZkMlKrr9rmLCHRfoz8R0c6Do0Bm6elrMtFLJq1h4PJFyXrvBS8GyXZUrglpqwSMj45SEHyBbu9hpooP6Keb0dg7wZ2S1e9idTDB1gya5rdstqu9yfS56HHqjXRMpSW+7TMVj4WrV7N0Kdao9HKL2FaSkvJ/OgjSSxk1APoGjaU5fwnc05KJEStSuu+hAhe24lYga1J3p0diRV4SkoEaNiwIU2bSqXYdevWYbHI76dS+WnL9ydaPSeIpSayfzyBWI0zpFRqNUPGJ9G6/2BJvCQ/j4VvTiHt7OlKjqx51GoV3UY04f6/ticgTJq4mk0WtixK4ZcPDlKU515FVaF6UJIthUoRRZGiPddIm7sfw8UCu88H9KhH9IR26OoF1MDdVZ1zB/ay7J03MRmkT0o9xjxEr7EPV2uiJYoiG74/SZ7NiIx+DzUjJNozq4ByfpyPKf2GXCno9UQ895xs519zXlrVcnuQKYDZBFk2L4TeVtmSedYWgJ9fjJ2UmJ7xm9vnrcC2upWWlsbRo0dlO781+kZBBA+NlcQMFwrIW33eI9erDJVKzZ1PT6DtYGnVsLSwgEVvvcrV0ycrOdI7qJcQytjXupDQ2d5ecOFYNvNn7LIbG6PgfSjJloJDzEVGsr8/Ts7iFESD1JCpCtAS8VgrQu5tguCBSoycnNm7k+XvzsBkNEjivcf9he4PPFjt93N861VSdkuHSrbsWZemXep45HrmwkKyPv1UEgt96CG00fL4wjwmIeamgtkqOfaPBL8w988rI3F+eskT6OUyI0Um983LtlJievoqt89ZQZ06dWjdurUktn79esxmz5iuA3rVx6e59PtWuOkyJQ7WeHkSQaVi4BPP0eGueyXxsqIiFr/1GpdPHq/W+3EWvZ+WO59oxeDHW6LzkT7nlhYaWfXJYdb/7wTGMsU8760oyZaCHaWnc0ibu4+SI1l2n/NpEUZ0Ugd8mnnXC58jTu3cyor33sZsknZM9nvkSbrcN6ra7yfrciGbFkg9MmH1/OmV6Lkuu+xvv8Wce2Nlicrfn/CnnpTt/J6TEG07Eb3LHA+gV6lo7GvTkeimSR48KyUC9O/fX1LNzc7O5sCBA7Kd3xpBJRA6uinqYOkMqZyFJzHlVq/8JQgC/R59ik7DR0rihpISlsycysVjh6v1flyhaZc6JE7tQt34YLvPHdtyhYVv7yY91bt2QiqUoyRbCn8gmizk/nqWzC+OYMmXVoIErYqQ++MJf6Ql6gDPr69xlxNbN/LLnHew2LxjH/D4s3QcNqLa7+cPn5bVvjiNTsWQp1qj1XmmOmjKySH7q68lsbDHHkMTar8I11U8IiGC15vjK0iwNcnL4NvytJQYHh5O+/btJbGNGzdiNHpmcKbaX0vYg80lrzaW4ur3b0F5wtXnocfoNjJREjeWlbJ01nRSD3sm6ZSToHBfRvy1A13vi0Nl45PNTStmyTt72bPqPBbFPO9VKMmWAgDGtCLSPzxA4Wb7GTTa+gFETWxPQNe6XrfX0BFHNyaz8v33EK2Nv4LA4KdfoP2Qe2rknjbNP0XONemus77jmhFW17+SI9wn64svsFiNuFCHhBD2l0dlO78oinYjH2SREMHrzfEVeMK3BZ6VEgH69u2L2mpwb35+Pnv27JH1GtboY4MJujNWEjOk5pO/NtXxAR5EEAR6Jj5MjzEPSeImQxnL3nmTcwf2Vvs9OYtKJdDprlgeeLmjndfTYhHZufwsy/69j/xqmt6vcGuUZOtPjiiKFG69TNr7BzBelc6eQoDAfg2Jeq4tWg8M2fQEh9et4beP5yCKNxItQVAx9Lkk2gwcWiP3dHzbVU7ukE6ubt69Ds271fXYNY1p6eT873tJLPzpp1EHyNfMcDLnJBcKbswrkk1CBAcyoncmWwkyr+2pwNNSYnBwMJ07S6esb968mbIyz0l7gX0aoG8qraoWbLhE6cmamYze/YEH6T3uL5KYyWhg+bszOLN3Z43ck7NExQQxZkpnWvauZ/e5q6fzWDBjF6d2eefU/D8bSrL1J8ZcYCDrm6Pk/nwWbNZpqEP0RD7VhuChsQia2vFjcmD1r6z5dB5YDWoUVCrumvA3WvUdeJMjPUf2lSI2zZdWaULr+tNnrGeTh8xPPka0euHUREUROk7ehgCPSYgWC2RKZ5B5o2cLHIx/kKmy5ecXQ2Cg56REgN69e6PT3bAEFBcXs2PHDlmvYY2gEggb0xSVzQ7A7IUnMdfQ+IIu942i3yNPSWJmk4kV773NqZ1ba+SenEWrV9P/oebc9ewd+PhrJZ8zlJpZ+9Ux1nx5lLJiZb9iTVI7XkUVZMd4rYi0OXspPZlj9znfdpFET+qAPs7ehOmt7P11OclffSyJqdRq7pn0D1r07Fsj92Q0mFn9xRFMBiufllbFkKdaodV7rovTcPEiuYsWS2IR459D5eNTyRHO40hCHBI7RJ6T518Co1WV1ScYAqLkObfMxNus7EktMVAqkw8pKtKzUqK/vz/dunWTxLZt20ZxcXElR7iPOkBH+NjmkkGdliITWfNPIJprxmPUcdh9DHxcOgrFYjbzy5x3OL51Y43ckyvEtYtk7OtdaNTSvnkpZXca89/aRYHtQGqFakNJtv6kaCJ8UQdJXygEvZqwxGaEj22Oytc79xo6YtfyxWz47+eSmEqtYfiLk2narVcN3RVsnn+K7CtSabb32KaEe3guWeYHH4BVB6a2YUNCRo68yRHO41kJ0WaqeWRz8FKvoL9aTQOfG9UEC3C2RJ4qjWMp0X5Nljt0794dH6skvKysjK1bPVvR0ccFEzQoRhIznMsnP7n6/VsVtBsyjMFPT5D8nIkWC6vef4+jG5Nr7L6cxT9Yzz0vtKXXmATUNopESJQfASHeu+HjdkdJtv6kCBoVYWObwfVfSF1sENGTOuDX3jsrCJWxfcmPbP7hG0lMrdUy4qXXiO/czfFB1cDJndc4vu2qJNa0SzQtenjOj9YCBAAAIABJREFUpwVQlpJC3oqfJbHICS8g6OTtIHUkIQbq7He5uYStXyvCexZQO8JTJnnHUqI8uxIr8PX1pVcv6RuSnTt3UlBgP8RYTgL7N0QfHyKJFay/SGmKfaW9umgzcAhDn0tCEG68LIqihd8+nsPhdWtucqR3IagE2g5oyOjJnQivX/7GTu+vYeCjLb16y8ftjpJs/YnRRvsTMqwxQUNiiHy6DZow+WQmTyOKIlsXfMe2hVITuEan5/5/TKNx+041dGeQc62IDT9IfVoh0X70HdfM492cGfPel3jW9AnxBA0bJus1PCohQq2YsWWNrUlejvEPFXhaSgTo0qULAVaNEyaTic2bN8t+HWsElUBYYjNUAVYeIxGyF5zEXGCo/EAP06rvQO6a8DfpQnpRZM2n8ziw+tcauy9XCK8fwKhXOtJ2UEP6P9ScgFClqlWTKMnWn5yA7vUI6t+oVr3jEUWRTd9/zY6lCyRxrd6HkZOnE9OmXQ3dGZgMZlZ/fhST1SRntabcp6Xz8aw0W3L4MAVr10pikZMmIajl9Yd5VEIEyHQgI3oxzTxU2YLqkRJ1Oh19+vSRxPbs2UNOjmerTOpAXXl13dq/VWgke/6JGl2w3KJnX+5JehmVze9N8lcfs/fX5TV0V66h0arpNSqBJh1ql2JxO6IkWwq1ClEU2fDt5+z5eakkrvP15YEpb9Kw5R01dGflbFmUQtblQkms15gEIhrIJLHdhIw5cyUf+9xxBwED5e/CtK1qySohiqKDypaXy4h2HYnyddZVh5QI0KFDB0JCbsh6FouFjRs9bw73iQ8lcEAjSazsTB4F6y5UckT10LRrT4b/dQpqjfQN0ob/fs6u5YsrOUpBoXKUZEuh1iBaLCR/+TH7Vq2QxPV+/ox69S3qN29ZQ3dWTsqeNI5uviKJxXeKopWDGThyU7RzF0U2xuaoF5Nkly1FUbTza8kqIRamQWnejY+1/hDUQL7ze4AEm47EcyVlGGWszNhLiStlO3cFGo2Gfv36SWIHDx4kI8PzC46DBjay63zOT75A6ZncSo6oHuI7deW+l6ai1krHKWz+4Ru2L/mxhu5KobaiJFsKtQKLxcyazz7g4FrpC41PQCCjp86kbkLNDr3MTS9m/f+kFZngSF/6P9Tc4z4tURTJmDNHEvPr2hW/7t1lv5bHJUS7NT1NQeXdT1PBWg3RuhsVEKMocl6mjkRwJCXull1KBGjTpg0RERF/fCyKIuvXr5f9OrYIKoGwsc1Q+dv4t+afxFxYc/4tgMbtOnL/y9PQ6KQJ9baF37N1wXeIorISR6FqePezmIIC5TNvVn80hyPrpRUV36Bgxrz+NtFx8TV0Z+WYjGZWf34EY+kNn5ZKIzDkqdboqmGERuHGjZTs3y+JRSZN8kiSZysh9qzXUz4JEWrNmh5bbKVEuSbJQ/VJiSqVigEDBkhix44d48qVK5UcIR/qID1hiTb+rQID2QtO1qh/CyDmjnaMnDwdrV76Pd6xdAGbvv9aSbgUqoSSbCl4NWaTiZXv/4tjm6XvsP2CQ0icNovImMY1dGc32Lb4NJkXbXxaoxKIbOR5n5Zosdh5tQL698fPZtGwLNdyICHKtguxgszasYDalgQPmuSheqREgBYtWlC3rnQ8ybp16zxyLVt8moYS2K+hJFaWkkvBxovVcv2b0bDlHTww5U10vr6S+J6fl7Lh28+VhEvhlijJloLXYjYZ+XXuPzm5XdqGHhAaRuL02YQ3aFTJkdXH6b3pHN4oXd7dpEMkrfvWr5brF/z2G2UnpPJl5KSJHrmWxyVEcCAj1o5ky84kXyzv+pnqkhIFQbCrbp0+fZrU1OoZOBo0KAZdrHTlU/6aVMrO5VVyRPVRv3lLRr32Fnp/6fL4fatWkPzlx9LF9woKNijJloJXYjIaWfHvWaTs2iaJB0ZEkjj9HcLq1bxpOi+jhPXfHZfEgiJ86P9wC4/7tABEk6l8rpb19e++G5/mnhmV4HEJEWrdjK0KbE3yKTJXtqpLSgSIj4+nUSPpG5nk5ORqqd4IaoGwB5uj8rOS30XI/vEE5qKa3+1XN74Zo1+biU+A9Of+4NqVrPnsAywWcyVHKvzZUZItBa/DaChj+bszOLt3lyQeHBXN2OnvEFLHs1PYq4LZaGHNF0cwWPu01OU+LX01rTrKW74cw/nzNwJqNRETXvDItapFQizOhiKr7je1HkJiKn+8F+HIs2WWOTmJipIOp/WUlCgIAgNtRoZcuHCB06dPe+R6tmiC9YQmSiua5nwDOQtr3r8FEB0Xz5hps/ANknZQHlm/htUfzcFiVhIuBXuUZEvBqzCWlrLsnTc4f3CfJB5atx6J098hKNI7hvNt++k06anSlSY9RsYTFRNUyRHyYjEYyPjgQ0ksZOT96Bt7xsN2IvtE9UuI4fGgrh07OiO0GsK0N4ZgllpELpXK20kXXU1SIkBMTAzx8dLGk+TkZCzVJJX5NgsjoK+0el16MofCzZeq5fq3IrJRLInTZuEfEiqJH9u8npXv/wuz1W5SBQVQki0FL8JQUsySWdO4cOSQJB5WrwFjps0mMDyikiOrl7MHMji0Tvqk37htBG0GVJ+0mTt/AaarN3YvClotEePHe+x6a1KlVS2PSIi11BwP5dUgT5vkfX0bOZASf5P1GtbYereuXbvG8ePHK3m0/ATfGYPOpskkb/V5ylLzq+0ebkZ4g0aMmTabgLBwSfzk9s38MucdzKaalz0VvAcl2VLwCsqKi1j89utcPnFUEo9oGMOYabMICA2roTuTkp9Vwrr/Sl9wAsL0DHikenxaAJaiIjI//VQSCx33INq6npFXq0VCBAfm+Nrh16rA0yZ5cCQlyr8rsYJ69erRsqV0UPD69esxV5NMJqhVhI1rjmAty1sg+4cTWIq9I5EJq1efxGmzCYyIlMRP797OivfexmT0jvtUqHmUZEuhxiktLGTxW69x9ZRNV11sHKNff9uuVF9TmM0W1nxxlLLiGxKBSiUw5MnW+Phrb3KkvGR/9z/MWVl/fCz4+RH+9NMeu161SIhQ69b02NLUprIlt0keqldKBOjfv7/kTURmZiaHDh26yRHyognxIWy09OfAnFdG9qJTXjNuIaROXcZOf4fg6DqS+Nl9u1n+7gyMBvmTboXah5JsKdQoxfl5LJwxhWtnUiTxOk0SGDP1bfxsTKg1yY5lZ0k7J5Uwuo1oQp246rtHc14eWV9+KYmFPfoImvDwSo5wn2qREAEyatcCalsS/KUdiadkHGxaQXVLiZGRkbRt21YS27BhA6Zq9CT5tgwnoJd0lErp8WwKt3h+2GpVCYqMIvH/27vzMKmqM3/g31NbV/W+szTdQEu3bILIDoLNIggqELcxmrgE45hoXDJ5fuIyUcwszh+/XxJJzMSoMclEB5c4aiTjApJWRARUkL2hAVl73/fuOr8/upuqWwugXeee27e/n+fhkXuo4r5SXdVvn/c95zz2JNKGGI/mOrLjM/zPf6xGR2vsvxaof2GyRdo01dbglSceRsWRUsP4kMLRuO7Rf4E3MVFTZOGOfFmJL94zHo47/KIMXLwwN8oz1Kh67nn4GwKN+Y6UFGTcfruy+5lWQmytB+qD+uCEE0i/IPb3USh0ZutAU6uS2RczS4kAUFRUBEfQkUl1dXXYvn270nuGSrliBNy5If1b/3sY7ccaojzDfEkZmbjhsSeRnmP8TPhq10689u+Pob2lWVNkZAVMtkiLxppqvLz6IVQeM26WOGzMeFz38BOIi0+I8kzzNVS34v0X9hjGEtPisPDWsRAOc/q0AKCzogLVf/qTYSxj5Uo4k9WtgDSthFhpnNlEej7g8sT+PgoNiXMj0Rn4SG3s8uN0e+x7dswuJaampmLKlCmGseLiYrS3m3duoXA5kPHt0RDewIpPdElUvbgX/hbrrPxLTEvHPzz278jMG2EYP7FvN179t5+irblJT2CkHZMtMl1DVSVeXr0K1SeNK/ryxk/ANaseh8cXrymycF1dfrz33G60NQU+0IVDYNHKcfAmmtenBQCVv30GsqXlzLUzMxPp37lZ6T1NKyH245WIvSKvSIx9v053KXF80IjaUiIAzJkzBy5XoFG9qakJW7ZsUXrPUK50L9KvC+nfqmlD9avW6d8Cuo8Su+Gn/4bsEcaZ2VMH9uHVf3kUrY2NUZ5JdsZki0xVV16GtY8/iJpTxn6LERdPxooHH4Pb643yTD0+ffMwTh0yHhUyfdlIDBmVamocHSdOoHbtWsNY5l13wRGvLjGVUobtGq+khAhEaI7vf8kWoPZA6mDZ2aFnJaotJSYlJWHGjBmGsU2bNqElKPk3g298JhJnGfuiWndXoelj6/RvAYAvKRnX//O/YvAoY3J4+lAJXv7Zw2iu13/8EJmLyRaZpvb0KaxdvQp15WWG8fzJ07D8J4/C7YmL8kw9ju6uwmfvGMuceePSccki83c1r3j6acigZeTuoUOResP1Su+5r3ofjjUEDgFWVkIE+n1zfK/QY3tivddWL7NLiQAwa9YsxMUF/v9aW1uxefNmpfeMJGXpSLhzjP2ctesOo/24dfq3AMCbmIjrHvkZhhaOMYxXHCnFK088jKbaGk2RkQ5MtsgU1SePY+3jD6KhssIwXjBtFpb9+CG43OaW5M6lsaYN7//e2KeVkOLBwtvM7dMCgLbSw6h7/X8MY5n33AOHR21Pk2klRMC2M1uqki0dpcT4+HjMnj3bMLZ582Y0mlwWEy4HMm4aDREX2r+1D/5W6/RvAUBcfAKufXg1ho0ZbxivPHYUL69+CI3VVVGeSXbDZIuUqzr+FdY+vgqNNdWG8QtnzcWV9/0fOF3WSrT8XX689/xutDYGZpKEABbdMQ6+JPObtivWPAUEHZPiyc9HyrKrld7T1BJiRwtQcyRoQAAZBWrupVj4xqbqlvybXUoEgOnTpyM+qHTd0dGBjz76SPl9Q7kyfEi71vg10lXdiprXSizVvwUAHl88rln1OPLGG7fQqD55HGtXr0J9yA+gZE9MtkipiqOHsXb1Q2iuqzWMj50zD0t/9E9wuqx39t3Wt4/gZIkx3mlXj8TQAvM3V23dswcNfzPOWGTdey+E4n83U0uIVQcBBH2DTM0DPNZZJPF15Ho98AbNfFZ3dKGyXc1si45SYlxcHObOnWsY27p1K2pra6M8Q534CVlImGE8NaHly0o0bTkV5Rn6uL1erHjwpxhx8WTDeO3pU3g5QmsF2Q+TLVKmrPQgXn7iYbSENIOOn7cIi394PxwOZ5Rn6nNsbzW2/e2IYWzY6DRccsUILfGU//KXhmvv2LFIWnS58vuGlRBzVJYQ+/9KxF5OITBK8RmJvXSUEgFg8uTJSA7abqSrqwvFxcXK7xtJ6pX5cA8xbhNT+9dStJ+03oo/tycOy3/yKPInTzOM15WXYe3qVag9bb0kkWKHyRYpcapkP1752SNobTQ2rU68fCkW3XmPJROtpro2vPf8bsMkiy/Zg8u/Nw4Ok/u0AKB5+3Y0/d34TSzrgfshHGrfthFLiMMVlRAB2/Rr9Qptkle1IhGIUEosW6fsXr3cbjeKiooMY59//jkqKyuV3zuUcPecn+gJ+jzplN3nJ7ZZq38LAFxuN5b9+CEUTJ9lGG+orMDaxx8M2w6H7IPJFilRfqQ0bAO/S5Ysw4KVP1CeLHwTfr/Ee8/vQUtD0CaUArj8e2MRn2x+n5aUEuU//7lhzDdlMhIuvVT5vU0tIQL9/gDqUGY1yQMRSol125SXEgFg4sSJSE8PHA4vpcTGjRuV3zcSd1Y80q4ZZRjrrGxBzV8OWq5/CwCcLjeuuu9BXDjLWI5tqqtF1YljUZ5F/Z31vuuRLUy8fAmKbrnjzPXUZdei6NbvGw61tZLtfzuCE/uNS7GnLB2B3NHpUZ6hVtNHm9CyzXgkSvb995vy7xc6q6W0hAiEJ1uZ/Xtmy6y9tgB9pUSn04l58+YZxnbt2oXTp08rv3ck8RdnI2Gq8SDolh0VaN5qzV4oh9OJpT/6J4ydO797QAgsufvHKJg6U29gpIz1upPJNiZfuQJdnZ3oaG3BrBu+Y9lE68T+Gmz962HDWE5hKqZeOVJLPFJKVPziF4axhDlzEB9yZIqqe4f2ayktIXZ1ANWHjGNZhZEf20+YsYt8sOzspWho2HXmurxsHXKH3aL0ngAwbtw4fPTRRygrCyQ0GzZswE033aT83pGkXJ2Ptq/q0VkWOIOw5s1D8OQlwT3YOsd/9XI4nLjiB/fD5fZgSOFojLm0SHdIpBBntkipacuvw+x/+K5lE63m+na8+/xuBFcbfElubX1aANDw3nto3b3bMJZ1332m3Nv0EmJ1KeAP6q1JGgp4U9TdzwQjfXFwBX3pnG7vQH1nl7L7RS4lqp/RcTgcmD9/vmHswIEDOHZMTynM4XEi4+YxEO6gb2udflT9eS/8ber+/ftCOBy4/M57ML5ooe5QSDEmWzRgSb/E+y/sQXNd0IG6Alh4+1gkpOrZzV52daHil08ZxpIWL4Zv/DhT7m9+CTG0Ob5/z2oBgNshMNIX0iSvsG8rYimxXH0pEQAKCwsxbNgww9j69eu19Uq5s+ORuiKkf6uiBbVvHNQSD1EvJls0YG1/5yiO7TFutDp58XDkjc3QFBFQ99ZbaD8UVFZzOJB1749MubfpJUTANsf0hArt29qvsG8L0LPBKdB9+PaCBQsMY0eOHEFpaakp948kYfIgxE8eZBhr/qwcTdus2b9FAwOTLRqQTpbU4tM3jd8QhoxKwbSr9fRpAYBsb0flml8ZxlKWL0fcBReYcv+91XsNJUSPw4N5ufPO8owYCJ3Zyuz/M1sAUGjSXlu9dJUSAWDkyJHIz883jOmc3QKA1OUXwJVt3Bi39o2D6ChrivIMIrWYbNGA09LYjnefM/ZpeRPcWLRyHBxOfW+JmldfRceJE4EBtxuZd99t2v3fPWKc1ZqVMwuJnsQoj46RSntt+9ArbEWi4iZ5naVEAGGzWydPnsS+ffuiPFq97v6t0Yb+Ldnh7z4/sd2a/Vtkb0y2aECRfon3f78XTbXGb34Lbx+LxDRvlGep529pQeVvfmMYS7vhBniG5Zhyfy0lRH8XUFliHLNpsqXyjMRegzSVEgEgJycHo0cbX7sNGzbAH3Smp9ncgxKQusw4K9xZ1ozaNw9FeQaROky2aED5/L2v8NXuKsPYpEV5GD5eX58WANT8+c/oqgjswC28XmTe9Y+m3V9LCbH2KNAZlITEZwAJel+HWMn3xRk+XI+3tqOpS+2MSmjflpmlRABhKxMrKirw5Zdfmnb/SOKnDEL8pGzDWPO2MjR9rn7jV6JgTLZowDh1qA6fvGHs0xqcn4zpy/OjPMMcXQ0NqPzds4ax9O9+B66sLNNi0FJCtGlzPAD4nA7k+QInD0gAh5pVlxJztZYSs7OzMWHCBMPYxo0b0aU4yTwbIQRSV4yCK9NnGK99vQQd5c1RnkUUe0y2aEBobezAu8/ugvQHGrXi4l1YdMd4ODX2aQFA9e9fgL8ucFi3IzERGStXmnb/SCXExSMWq7+xzc5EDGV2kzygt5QIAEVFRXAEHcdVU1ODzz//3NQYQjninEi/aTSCNz+T7X5Uv7gXsoP9W2QOJltke1JKrP/jXjTWGGcWFtw6Bknp+vq0AKCzuhrVL7xgGMtY+T04U1NNiyFSCbFoWJH6G9vsmJ5QBWHH9qid2QL0lxLT09NxySWXGMb+/ve/o6OjI8ozzOEZmojUq439Wx2nm1H7V31bVNDAwmSLbG/H+mM4srPSMDZxQS5GTjSvTBdN1TO/g785UM5wpqcj7bvqj1oJpqWECERYiWivZEvHzJbuUiIAzJ07Fy5X4CS4hoYGbN261dQYIkmYNhi+CZmGsaYtp9G8o0JTRDSQMNkiWys7XI/NrxtXH2WPSMbMb5mzd9XZdJw+jZoXXzSMZf7jnXAmmneOm5QybNd4U0qIUkbo2bJZshW6ItGEZAvQX0pMTk7GtGnTDGMffvghWlvN+f+PRgiBtGsK4Mowvi41fylBZ2WLpqhooGCyRbbV1tyBd57dBX9XoE/L43Nh8R3j4HTp/9KvfPo3kO2Bo4Jcgwcj9cYbTY1hb/VeHG88fubatBJi/UmgvSFwHZcMJA1Rf18TFcQbj+w50tqGNhO2QtBdSgSA2bNnw+MJLBBoaWnBJ598YmoMkTi8LqTfNAZwBvVvtXWh6sW9kB36tqkg+9P/HYdIASklNvxxHxqqjD9NL7hlDJJDVibp0H70KGpfe80wlnn3D+GIM/dMRm0lxEjN8RY9rPybSnQ5kRPnPnPdJYFSE/q2ukuJFwWNmF9KTEhIwKxZswxjH3/8MZqa9O/g7slJROpVxhXIHSebULuO/VukDpMtsqUvNx5H6RfGXoyL5g1D/iT9fVoAULHmV0DQknjP8OFIXbHC1Bi0lRAB2zfH9yqIN79JHgg/vqesfJ0p9w02Y8YM+HyBH2za29uxadMm0+OIJGHGEPguCunf2nwKzV+yf4vUYLJFtlN+tB6bXjtoGMvKS8Lsa0Zpisiodf9+1L/9tmEs894fQbjdUZ6hhrYSImD75vheuvq2QkuJdXXbTS8ler1ezJkzxzD26aefor6+3tQ4IhFCIO3aAjhDViPXvFqCzir2b1HsMdkiW2lr6cQ7v9sFf2dQn5bXicXfHwen2xpf7hW/fArBBzPGXXghkpcsOcsz1AgtIc7OmW1OCREIn9kaKMmWCcf2ANYoJQLA1KlTkZSUdOa6s7MTxcXFpscRicPrQsZNo8P7t17aB9nJ/i2KLWt89yGKASklPvjTPtRXGr+hzfvuGKRkxWuKyqhlxw40bthgGMu67z4Ih7lvxUglxEUjFJ+FGLi57Tc07RXaJF9i0swWYI1Sotvtxty5cw1jn332Gaqrq02PJRLPsCSkLBlpGOs43oi6vx3WFBHZFZMtso3dxSdw6DPjmWfj5+Zg1OTsKM8wX/kvfmG49k2ciMR5RabHobWE2FQJtNQErl0+ICXPnHubLHRj00PNbegMOsVAJSuUEgFg0qRJSEtLO3Pt9/uxceNG0+OIJnH2UHjHGs/kbNx0Ei27K6M8g+jrY7JFtlBxrAEfvWLs08rMTcTs663RpwUATZs3o3mzcfl71gMPQGhYhRc6q2VuCTFkViuzADB5Zs8s6W4XsjyBDT7bpcTRVnOa5K1SSnS5XCgqKjKM7dy5E+Xl1jgMWgiB9OsK4Ew1zkJWv1KCzmq9e4ORfdjzE44GFCklil86gK6gPgt3nBOL7xgPl9upMbIAKWXYrFbCrJlImDFdSyyh/VqmlRCBCM3x9jmAOpKwFYlN5iRbgDVKiQBw0UUXISvkYPUNIeV0nRzx7u7zEx1B/VutnajjdhAUI0y2qN8TQmDx98dhyKiUM2NFN1+I1EHW6NMCgMYPPkDrjp2Gsaz779cSi9YSIjBgmuN76WqSByKXElvbTpt2/14OhwPz5883jO3btw8nTpwwPZZo4vKSkXLFiDPX3jHpSP1Wgb6AyFaYbJEtJKZ5seKBSbjkiuEYO2coCqcN1h3SGdLvR8XPjbNaiQsXwDdhgpZ4tJYQgQHTHN8rtEnerO0fgMilxAoNpUQAGD16NIYOHWoYW79+vZZYokm8NAfecRlIuXIkMm4ZC2eCuduxkH0x2SLbcDgdmLniAhTdZK1v3vVvr0NbSUlgQAhk3Xuvlli0lxCBCGci2ruMeKHGmS0gUinR3LMSewkhsGDBAsNYaWkpDh+2zso/4RDI+M4YJM0ZpqWXkuyLyRbZjpU+JGVHByrWrDGMJV99FbyFhVri0V5CbKkFGoPKWA43kDYy+uNtoDBCz5ZfmrMiEbBOKREA8vPzMWLECMPY+vXrIU389zgXK31+kH0w2SJSqPYvr6Pjq68CAy4Xsu65R1s82kuIlSGzWhmjAKcr8mNtIsvjQoorsFCjxe/HibYO0+5vpVJipNmt48eP48CBA1GeQWQPTLaIFPG3taHy6acNY6nXXgtPnp49paxRQhxY/VpAd4IROrtlZt8WAAwKmd3SVUoEgNzcXBSGzOxu2LABfj93bSf7YrJFpEjNSy+hsyywiaTweJD5wx9oi2dP9R69JURgwK1E7FWYoK9JHgCyQ/q2dJYSAYStTCwrK8OePXs0RUOkHpMtIgW6GptQ9dtnDGNpN98M96BBmiLSfBZirwGabIXttWVyk7yVSokAMHjwYIwfP94wtmHDBnR1dWmKiEgtJltEClT/8Q/oqgkcSeOIj0fGnd/XFk+kEuLiEYvNDyQs2bL3SsReYXttmTyzBVirlAgARUVFhmb06upq7NixQ2NEROow2SKKsc6aGlQ//3vDWPrtt8MVdD6c2SKWEHOLzA2irRGoC1osIBzdDfIDQOgZiSXNbaavwAsvJW7TWkrMzMzEpEmTDGMbN25ER4d5iweIzMJkiyjGqp97Dv7GxjPXzpQUpN9+m76AELmEmOBOMDeIqhLjddpIwBUX+bE2kxPnRrwz8HFb19mF8vZOU2MILyVCaykRAC677DI4nYGVmvX19di+fbvGiIjUYLJFFEMdZeWo/q8/G8Yy7rwTzkSTe6OCSCnDtnywRglxYPRrAYBDCK07yfeyWikxJSUFU6dONYwVFxejrc288yOJzMBkiyiGqn77n5CtgW+iruxspN18k8aIukuIJxoDZ9BpKSECAzrZAsKb5M3eSR6wXikRAC699FK43YFjcZqbm7FlyxaNERHFHpMtohhpP3YMNS+/YhjL/OEP4PB6ozzDHJYoIQIDtjm+V9ixPRpmtny+XCQnGc/k1F1KTExMxMyZMw1jmzZtQnNzs6aIiGKPyRZRjFT+6tdAZ6APx52bi9RrrtEYkYVKiED4hqaZeo4s0sUKM1tA+OxWWfk6LXEEmzlzJrxBP5S0tbXh448/1hgRUWwx2SKKgbaDB1GU4cpIAAALGklEQVT31luGsax77obweDRF1M0yJcTONqAm5MDhAZZshW7/UNKkpy/JahucAoDP58Ps2bMNY1u2bEFDQ4OmiIhii8kWUQxUPLUGCDpuxDPqAiRfdZXGiLqFlhAvzblUTwmx6iAgg45jSckD4vQtGtAhz+tBnCOwr1RlRyeqO8xdkQhYs5QIANOnT0dCQuBrs6OjAx9++KHGiIhih8kWUR+1fLkLDe8ak5qs++6DCFrSrkOkEqLpZyH2CjsTcWDNagGAyyGQ7zOuSCzR0LcFWLOU6PF4MHfuXMPYtm3bUFtbqykiothhskXUR3Wvv2649o4fj6SFCzVFE2CZEiIAVBwwXg+w5vheYTvJW6RvywqlRACYPHkyUlJSzlz7/X7s3LlTY0REscFki6iPBj36CHL+3/+FZ/hwAEDWA/cbjiHRJXRWS1sJERjwzfG9CkOb5DXNbFm1lOhyuVBUVASg+/zEm2++GXPmzNEbFFEMuHQHQNTfCYcDyUuXImnRIjQWFyNh1izdIUU8C1FbCREAKjmzBUQ4tkdTkzzQPbtV3xCYNSorX4fc3Nu0xdNrwoQJiI+PR0FBARwOzgeQPfArmShGhMuFpPnzLTGrZakSYlcnUBlyVM8A7NkCgMKEkF3kNZURASA7ZDd5q5QSnU4nLrzwQiZaZCv8aiayIUuVEGsOA/6gw4UTBwE+fYdy65Tvi4MzKBc/2daBhs4uLbH4fMPCSonlmo/vIbIrJltENmO5EuIAP6YnmMfhwMjQFYlaZ7eMjfJMtojUYLJFZDOWKiECEbZ9GJj9Wr2s0iQPWLeUSGQ3TLaIbMZSJUQgvDl+gK5E7BXWJN+sr0mepUQiczDZIrIRy5UQAc5shSiMD2mS1zizBQDZg4yzW0y2iGKPyRaRjeypslgJ0e+PsKHpwO3ZAiJsbKo72cqKsMFp6ylN0RDZE5MtIht556jFSoh1x4DOlsC1Lw1IyNIXjwVcEO9F8OYgX7W2o6XLH/XxqkUsJVbo3+CUyE6YbBHZRKQS4uIRizVF0yNsJeJowAL7kOkU73Qg1+s5cy0BHNK4IhFgKZFINSZbRDYRqYR4We5lGiMCj+mJoiB0RaLGJnmApUQi1ZhsEdmE5UqIAFAZYWaLwnaSL9Hct8VSIpFaTLaIbOJw7WHDtfYSIsANTaMIa5LXXEYEwkuJTU0lUR5JRF8XD6Imsok1C9agtK4U7x55Fx8c+0B/CVFKrkSMwkobm/bKzlqC8rJ1yM5eguzsJfD5cnWHRGQbTLaIbCQ/JR93TbwLd028S3coQMNpoK0ucO1JBJJz9MVjIaEbmx5uaUO73w+PxsOXfb5hmDr1dW33J7IzlhGJSI1IzfEDfCVir2SXE4M97jPXnRI43NKuMSIiUonJFhGpEXpMD5vjDazWJE9E6jDZIiI1wo7pYb9WMCs2yRORGn1KtoQQ1wshdgsh/EKIKWd53BVCiP1CiINCiFV9uScR9RNciXhWYXttcWaLyLb6OrO1C8A1AIqjPUAI4QTwawBLAIwF8G0hxNg+3peIrI7J1lmFzmyVcGaLyLb6lGxJKfdKKfef42HTAByUUpZKKdsB/DeA5X25LxFZXFMV0FwZuHZ5gdTh+uKxoNDtHw42t6FLSk3REJFKZmz9kAPgWND1cQDTTbgvEekiBDD/n7tntyr2dSdbDqfuqCwlw+NCnteDdLcLhQlxKIz3ot0v4XNyxSaR3Zwz2RJCvA9gcIQ/ekRK+cZ53CPSJwd/fCOys/h0YO5PAtecsYloy4wxENwOg8j2zplsSSkX9vEexwEEb0U8DMDJSA8UQtwJ4E4AyMvL6+NticgymFBExESLaGAwY+uHrQAKhBAjhRAeADcCeDPSA6WUz0gpp0gpp2RlZZkQGhEREZFaferZEkJ8C8AaAFkA3hZCfCGlXCyEGArgWSnlUillpxDiHgDvAHACeF5KubvPkRMRfQ1HnrxSdwhENED1KdmSUr4OIOwwLSnlSQBLg67XAVjXl3sRERER9UfcQZ6IiIhIISZbRERERAox2SIiIiJSiMkWERERkUJMtoiIiIgUYrJFREREpBCTLSIiIiKFmGwRERERKcRki4iIiEghJltERERECjHZIiIiIlKIyRYRERGRQky2iIiIiBRiskVERESkEJMtIiIiIoWYbBEREREpxGSLiIiISCEmW0REREQKMdkiIiIiUojJFhEREZFCTLaIiIiIFGKyRURERKQQky0iIiIihZhsERERESnEZIuIiIhIISZbRERERAox2SIiIiJSiMkWERERkUJMtoiIiIgUYrJFREREpBCTLSIiIiKFmGwRERERKcRki4iIiEghJltERERECjHZIiIiIlKIyRYRERGRQky2iIiIiBRiskVERESkEJMtIiIiIoWYbBEREREpxGSLiIiISCEhpdQdQ0RCiAoAR3XH8Q1lAqjUHQTFDF9Pe+HraT98Te2lv76ew6WUWZH+wLLJVn8mhNgmpZyiOw6KDb6e9sLX0374mtqLHV9PlhGJiIiIFGKyRURERKQQky01ntEdAMUUX0974etpP3xN7cV2ryd7toiIiIgU4swWERERkUJMtmJACHG9EGK3EMIvhIi6gkIIcYUQYr8Q4qAQYpWZMdL5E0KkCyHeE0KU9Pw3LcrjuoQQX/T8etPsOOnszvV+E0LECSHW9vz5FiHECPOjpPN1Hq/nbUKIiqD35B064qTzI4R4XghRLoTYFeXPhRDiqZ7Xe6cQ4hKzY4wlJluxsQvANQCKoz1ACOEE8GsASwCMBfBtIcRYc8Kjr2kVgPVSygIA63uuI2mRUl7c82uZeeHRuZzn+20lgBop5SgAPwfwH+ZGSefra3x+rg16Tz5rapD0db0A4Iqz/PkSAAU9v+4E8BsTYlKGyVYMSCn3Sin3n+Nh0wAclFKWSinbAfw3gOXqo6NvYDmAP/T8/g8AVmiMhb6Z83m/Bb/OrwJYIIQQJsZI54+fnzYjpSwGUH2WhywH8EfZ7RMAqUKIIeZEF3tMtsyTA+BY0PXxnjGynkFSylMA0PPf7CiP8wohtgkhPhFCMCGzlvN5v515jJSyE0AdgAxToqOv63w/P6/tKTm9KoTINSc0UsRW3zNdugPoL4QQ7wMYHOGPHpFSvnE+f0WEMS4F1eRsr+fX+GvypJQnhRD5ADYIIb6UUh6KTYTUR+fzfuN7sv84n9fqLQAvSSnbhBB3oXvWcr7yyEgVW70/mWydJynlwj7+FccBBP+kNQzAyT7+nfQNne31FEKUCSGGSClP9Uxbl0f5O072/LdUCLERwCQATLas4Xzeb72POS6EcAFIwdnLGqTPOV9PKWVV0OXvwB68/s5W3zNZRjTPVgAFQoiRQggPgBsBcAWbNb0J4Nae398KIGzmUgiRJoSI6/l9JoDZAPaYFiGdy/m834Jf5+sAbJDceNCqzvl6hvTzLAOw18T4KPbeBHBLz6rEGQDqets7+iPObMWAEOJbANYAyALwthDiCynlYiHEUADPSimXSik7hRD3AHgHgBPA81LK3RrDpuieBPCyEGIlgK8AXA8APdt63CWlvAPAGAC/FUL40f1Dy5NSSiZbFhHt/SaEeALANinlmwCeA/AnIcRBdM9o3agvYjqb83w97xVCLAPQie7X8zZtAdM5CSFeAlAEIFMIcRzAYwDcACCl/E8A6wAsBXAQQDOA2/VEGhvcQZ6IiIhIIZYRiYiIiBRiskVERESkEJMtIiIiIoWYbBEREREpxGSLiIiISCEmW0REREQKMdkiIiIiUojJFhEREZFC/x9xh+UCF3fqFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"\\nThe 10 Matplotlib color sequence, starting at 12 o\\'clock and going clockwise:\")\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "for k in np.arange(0,2*np.pi,np.pi/20):                 # arange is like range, except it allows you to use floats\n",
    "    plt.plot([0,np.sin(k)],[0,np.cos(k)],lw=4)\n",
    "plt.title('Line Colors',fontsize=14)\n",
    "plt.xlim([-1.2,1.2])\n",
    "plt.ylim([-1.2,1.2])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an example where we simply change the colors of the plot using the appropriate parameter; see a complete list of colors here: https://matplotlib.org/2.0.2/api/colors_api.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa6303ecd50>]"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 712x712 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EXAMPLE: Plotting a square with lines of different colors\n",
    "plt.figure(num=None, figsize=(8, 8), dpi=89)\n",
    "plt.plot([0,1],[0,0],color='red') # Line connecting (0,0) to (1,0)\n",
    "plt.plot([0,0],[0,1],color='green') # Line connecting (0,0) to (0,1)\n",
    "plt.plot([0,1],[1,1],color='orange') # Line connecting (0,1) to (1,1)\n",
    "plt.plot([1,1],[0,1],color='black') # Line connecting (1,0) to (1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Changing the Style of Plots\n",
    "\n",
    "Here is an example showing how to\n",
    "\n",
    "  - change the size of the whole figure\n",
    "  - change the color of lines or points\n",
    "  - change the style of lines or points\n",
    "  \n",
    "To see a complete list of lines styles see:  https://matplotlib.org/2.0.2/api/lines_api.html\n",
    "\n",
    "To see a complete list of colors see: https://matplotlib.org/2.0.2/api/colors_api.html\n",
    "\n",
    "To see a complete list of marker (point) styles see:  https://matplotlib.org/2.0.2/api/markers_api.html#module-matplotlib.markers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EXAMPLE: Plotting a square via lines \n",
    "plt.figure(figsize=(12, 12))             # the size is (horizontal, vertical)\n",
    "plt.title(\"Line Colors and Styles\",fontsize=16)\n",
    "plt.plot([0,10],[0,0],  color='red') # Line connecting (0,0) to (1,0)\n",
    "plt.plot([0,0],[0,10],  color='green') # Line connecting (0,0) to (0,1)\n",
    "plt.plot([0,10],[10,10],color='orange') # Line connecting (0,1) to (1,1)\n",
    "plt.plot([10,10],[0,10],color='black') # Line connecting (1,0) to (1,1)\n",
    "plt.plot([1,9],[9,9], linewidth=5)    # give a linewidth in points, default is 1.0\n",
    "plt.plot([1,9],[8,8], linewidth=5,color = '#eaafff')    # for custom color give the RGB value in hex\n",
    "plt.plot([1,9],[7,7], linewidth=5,color='0.75') # for grey give the percentage of white in quotes\n",
    "plt.plot([1,9],[6,6], lw=4,linestyle='--') # Linestyles\n",
    "plt.plot([1,9],[5,5], lw=3,linestyle='-.') # Linestyles\n",
    "plt.plot([1,9],[4,4], lw=2,linestyle=':') # Linestyles\n",
    "\n",
    "plt.scatter(range(1,10),[3.5]*9,marker='.')  # various markers, if you don't specify the colors it will cycle\n",
    "plt.scatter(range(1,10),[3]*9,marker='o')    # through a bunch of colors, starting with blue, orange, green, etc.\n",
    "plt.scatter(range(1,10),[2.5]*9,marker='x')\n",
    "plt.scatter(range(1,10),[2]*9,marker='s')\n",
    "plt.scatter(range(1,10),[1.5]*9,marker='^')\n",
    "plt.scatter(range(1,10),[1]*9,marker='D')\n",
    "print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Et Cetera\n",
    "\n",
    "Then you can start getting obsessive, adding gridlines, changing the background color,  adding legends, text, and so on. \n",
    "\n",
    "Another nice feature of matplotlib is that you can insert simple Latex commands into titles and text....."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [i for i in range(11)]\n",
    "y = [i**2 for i in x]\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $x = x^2$')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.grid()\n",
    "plt.plot(x,y)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $y = x^2$')\n",
    "plt.grid(color='w')                # grid of white lines -- don't use points with this, they look funny\n",
    "plt.gca().set_facecolor('0.95')    # background of light grey\n",
    "plt.plot(x,y,color='b')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $y = x^2$')\n",
    "plt.grid(color='r',alpha=0.1)       # alpha sets the transparency, 0 = invisible and 1 = normal           \n",
    "plt.plot(x,y,color='r',lw=0.5,label='Curve')\n",
    "plt.scatter(x,y,color='r',marker='o',label='Points')\n",
    "plt.legend()\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Graph of $y = x^2$',fontsize=16)\n",
    "plt.xlabel(\"X\",fontsize=14)\n",
    "plt.ylabel(\"Y\",rotation=0,fontsize=14)\n",
    "plt.grid(color='0.95')\n",
    "plt.text(0,90,\"The title has been enlarged from default 12 points to 16 points.\")\n",
    "plt.text(0,80,\"Notice that the $y$ axis label is rotated to be upright, \\nand the x and y labels are also bigger, at 14 points.\")   # lower left corner of text string is at point (0,60)\n",
    "plt.text(0,60,\"When drawing points and lines together it looks \\nbetter if you make the lines thinner.\")\n",
    "plt.text(0,40,\"Honestly I think it is also better to just use\\nthe default marker (circles) when you draw \\nlines, these triangles are kinda fussy\\nand they don't seem to be centered on \\nthe data point.\")\n",
    "plt.plot(x,y,color='b',lw=0.5)\n",
    "plt.scatter(x,y,color='b',marker='^')\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}