aes_exercise_01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basics:\n",
    "- Arithmetic operations\n",
    "- Types\n",
    "- Errors\n",
    "- Variables definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2+2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5454545454545454"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(30-4*6)/11"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python 3 deals with types automatically.\n",
    "\n",
    "When you divide two integers they are casted to float.\n",
    "Obviously, you cannot divide by zero: Python will throw an error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[4], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;241;43m1\u001b[39;49m\u001b[38;5;241;43m/\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m   \u001b[38;5;66;03m#call Chuck Norris\u001b[39;00m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "1/0   #call Chuck Norris"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before calling a variable, you need to define it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'n' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-ab0680a89434>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'n' is not defined"
     ]
    }
   ],
   "source": [
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.5+0.5j)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=1.5+0.5j\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Functions are called passing an argument after the parentheses. The print() function prints its argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5\n",
      "0.5\n"
     ]
    }
   ],
   "source": [
    "print(a.real)\n",
    "print(a.imag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello world\n",
      "'Hello world'\n",
      "'Hello world\"\n"
     ]
    }
   ],
   "source": [
    "print('Hello world')\n",
    "print(\"'Hello world'\")\n",
    "print(''''Hello world\"''')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strings are treated as vectors. You can index them to retrieve parts of them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P\n"
     ]
    }
   ],
   "source": [
    "s = 'PIKACHU'\n",
    "print(s[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KA\n",
      "PIKA\n",
      "CHU\n"
     ]
    }
   ],
   "source": [
    "print(s[2:4]) #(min, max]\n",
    "print(s[:4])\n",
    "print(s[4:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U\n"
     ]
    }
   ],
   "source": [
    "print(s[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'34'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"3\"+\"4\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    PIKA, PIKA, PIKA, PIKACHUUUUUUUUUUU\n"
     ]
    }
   ],
   "source": [
    "s2 = \"    \" + (s[:4]+\", \")*3 + s + 'U'*10 \n",
    "print(s2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PIKA, PIKA, PIKA, PIKACHUUUUUUUUUUU\n",
      "39\n"
     ]
    }
   ],
   "source": [
    "print(s2.strip())\n",
    "print(len(s2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['flour', 100]\n"
     ]
    }
   ],
   "source": [
    "pancakeIngredients = ['flour', 100, 'egg', 1, 'milk', 0.3, 'oil']\n",
    "print(pancakeIngredients[:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['flour', 100, 'egg', 1, 'milk', 0.3, 'oil', 'syrup']\n"
     ]
    }
   ],
   "source": [
    "pancakeIngredients.append('syrup')\n",
    "print(pancakeIngredients) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['flour', 100, 'egg', 1, 'milk', 0.3, 'oil', 'syrup', ['bacon', 'bacon', 'bacon']]\n"
     ]
    }
   ],
   "source": [
    "pancakeIngredients.append(['bacon']*3)\n",
    "print(pancakeIngredients)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['bacon', 'bacon', 'bacon']\n"
     ]
    }
   ],
   "source": [
    "print(pancakeIngredients[8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3\n"
     ]
    }
   ],
   "source": [
    "#dictionaries\n",
    "pancake_ingredients = {'flour': 100, 'egg': 1, 'milk': 0.3, 'oil': 0.5}\n",
    "pancake_ingredients['syrup'] = 0.2\n",
    "print(pancake_ingredients['milk'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "'milk'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[26], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mdel\u001b[39;00m pancake_ingredients[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmilk\u001b[39m\u001b[38;5;124m'\u001b[39m]\n\u001b[0;32m----> 2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[43mpancake_ingredients\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmilk\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m)\n",
      "\u001b[0;31mKeyError\u001b[0m: 'milk'"
     ]
    }
   ],
   "source": [
    "del pancake_ingredients['milk']\n",
    "print(pancake_ingredients['milk'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Control:\n",
    "- if/else and elif (else if)\n",
    "- for/while loops\n",
    "- try/except"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Positive\n"
     ]
    }
   ],
   "source": [
    "x = 42\n",
    "if x < 0:\n",
    "    print('Negative')\n",
    "elif x == 0:\n",
    "    print('Zero')\n",
    "else:\n",
    "    print('Positive')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "one 3\n",
      "two 3\n",
      "three 5\n"
     ]
    }
   ],
   "source": [
    "wordlist = ['one', 'two', 'three']\n",
    "for w in wordlist:\n",
    "    print(w, len(w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 one\n",
      "1 two\n",
      "2 three\n",
      "3 four\n",
      "4 five\n"
     ]
    }
   ],
   "source": [
    "a = ['one', 'two', 'three', 'four', 'five']\n",
    "for i in range(len(a)):\n",
    "    print(i, a[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please define the variable first!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(my_unamed_variable)\n",
    "except NameError:\n",
    "    print(\"Please define the variable first!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fibonacci(n):\n",
    "    \"This function prints out all the numbers smaller than n belonging to the Fibonacci sequence\"\n",
    "    prev, cur = 0, 1\n",
    "    while prev < n:\n",
    "        print(prev)\n",
    "        prev, cur = cur, prev+cur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n",
      "89\n"
     ]
    }
   ],
   "source": [
    "fibonacci(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n",
      "89\n",
      "144\n",
      "233\n",
      "377\n",
      "610\n",
      "987\n"
     ]
    }
   ],
   "source": [
    "fibonacci(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Object Oriented Programming"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Classes\n",
    "class dessert(object):\n",
    "    \"\"\"Here goes the documentation.\n",
    "    It can become quite long\n",
    "    \"\"\"\n",
    "    def __init__(self, name, ingredients): # instance attributes\n",
    "        self.name = name\n",
    "        self.ingredients = ingredients\n",
    "    def add_more_ingredients(self, newIngredient): # a method\n",
    "        self.ingredients.append(newIngredient)\n",
    "    def cook(self): # pretend we are cooking\n",
    "        print(\"Cooking using \" + str(self.ingredients))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pancake\n",
      "Cooking using ['flour', 100, 'egg', 1, 'milk', 0.3, 'oil']\n"
     ]
    }
   ],
   "source": [
    "# instantiate a class with parameters\n",
    "dessert = dessert(\"pancake\",['flour', 100, 'egg', 1, 'milk', 0.3, 'oil'])\n",
    "print(dessert.name) # pancake\n",
    "dessert.cook() # calls cook method of instance dessert"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Science\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function RandomState.randn>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.randn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "matplotlib.rcParams['font.size']=15 # this allows to enlarge the fonts in the images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of data points sampled are: 1000\n",
      "mean +/- std = 0.49 +/- 0.29\n"
     ]
    }
   ],
   "source": [
    "no_p = 1000\n",
    "random_vector = np.random.random_sample(size=no_p)\n",
    "print(\"The number of data points sampled are:\", len(random_vector))\n",
    "mean = np.mean(random_vector)\n",
    "std = np.std(random_vector)\n",
    "print(\"mean +/- std = {:.2f} +/- {:.2f}\".format(mean, std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(0,1,20)\n",
    "plt.hist(random_vector, bins = bins, rwidth=0.8)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Frequencies\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(random_vector, bins = bins, rwidth=0.8, density=True)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Central limit theorem\n",
    "\n",
    "We will show numerically that given sequences of i.i.d. random variables, their mean values are distributed like normal distribtuion. Precisely, we will consider the case where the random variable comes from rolling a dice with 6 faces. The possible outcomes are $X_i =  1,2,3,4,5$ and 6. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dice = np.array([1,2,3,4,5,6])\n",
    "mu = np.mean(dice)\n",
    "var = np.mean((dice - mu)**2)\n",
    "sigma = np.sqrt(var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability to observe each outcome is 1/6. To check this we do sample_size = 50000 rolls to create."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 1/6\n",
    "sample_size = 50000\n",
    "random_vector = np.random.choice(dice, size=sample_size)\n",
    "bins = np.unique(random_vector)\n",
    "bins = list(bins) + [max(random_vector)+1]\n",
    "plt.hist(random_vector, bins = bins, \\\n",
    "         align='left', rwidth=0.8, density = True)\n",
    "plt.hlines(y = p, xmin = 0.45, xmax = 6.55, lw=4)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To verify the central limit theorem, we need to compare the sum coming from the rolls with the gaussian distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normal_function(x, x0, sigma):\n",
    "    \"\"\"\n",
    "    This functions computes the probability to observe x \n",
    "    assuming that it follow a normal distribution with mean x0 and variance sigma**2.  \n",
    "    This function needs numpy to be imported, i.e. \n",
    "    import numpy as np\n",
    "    \"\"\"\n",
    "    return np.exp(-(x-x0)**2/(2*sigma**2)) / np.sqrt((2*np.pi*sigma**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_convergence(T_n, sigma, n):\n",
    "    \"\"\"\n",
    "    This function compares T_n with a\n",
    "    with a normal distribution N(0,sigma^2)\n",
    "    \"\"\"\n",
    "    bins = np.unique(T_n)\n",
    "    bins = list(bins) + [max(T_n)+1]\n",
    "    x = np.linspace(num=100, start=min(T_n), stop=max(T_n))\n",
    "    gauss = normal_function(x = x, x0 = 0, sigma = sigma)\n",
    "    #\n",
    "    plt.hist(T_n, bins = bins, label = str(n)+\" rolls\", \\\n",
    "                align='left', rwidth=0.8, density = True)\n",
    "    plt.plot(x, gauss, label=\"gaussian\")\n",
    "    plt.title(\"After summing \"+str(n)+\" times\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"Density\")\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iSZg6dSpxcXGEhITQtm1bcubMmexXvXr13Hdupaa1Kjg42P346tWryW73r3/9y33s7du33/GYqRnVOjViYmLuuD4wMBBI+EEJULNmTQB+//33JAurffv2MXfuXA+lzF46d+4MuEbw//HHHxOtNwyDjz/++J6Pn5Ji7O8Tijdt2jRVx0/p699ML7zwAgC7d+/mm2++ueO2N27cSDCy+r2+ZyRz029TJAnxxVH79u3x8/O76/ZdunQBXHOgpbRlIHfu3O5WqIkTJya73xtvvEH16tWJjo6mefPmjB49mkuXLrnXX716laVLl/Lss8/SpEmTFJ07tT799FMee+wxpk6d6u5nBq4PjpkzZ/L5558D0KZNmwT7xRekcXFxPPnkk+6WvLi4OH7++WceeuihZO/akjtr0qQJDz/8MOAqvCdNmuT+ID958iTdu3dn3bp19zyR9yeffEKPHj1YunRpgqLHbrcTHh7OE088wZQpUwB4+umnqVKlSqqOX6FCBfd7a/z48V7ZWtW0aVN69eoFQL9+/Xj99dcTtM7FxMQQFhbGoEGDKFmyJOfPn3eve+WVV3jyySeZM2dOguXXr19n3Lhx7p/dP98zkrmpqBL5h7CwMPbu3Qv8VSzdTfx2586dY/HixSk+10svvQTA119/Tc6cOSlRogSlSpXiqaeecm+TM2dOli1bRsOGDYmMjOTVV18lNDSUPHnyuOfAa926NVOnTr3jHGRp4XQ6WbZsGc8++yzFixcnKCiIfPnyERgYSNeuXYmMjKRy5cqMGDEiwX4hISGMHDkSi8VCWFgYlSpVIjg4mJw5c9KhQwdKlCjBBx98kC6Zs4MpU6ZQqVIlbt68Sa9evciVKxd58uShePHizJgxg9GjR7vv/gsICEjVse12Oz/88AOtW7cmT5485MqVi/z58xMYGEjDhg2ZN28e4JoP8176EwYFBbnHfhs0aBA5c+akZMmSlCpVin//+9+pPl56GTduHH369MEwDEaOHEnZsmXJlSsXefPmJSgoiEaNGvH5559z6dKlBDcNxMXFMWvWLDp37kzBggXdv5tcuXLx8ssvExsbywMPPMD//d//mfjsxNNUVIn8Q/wHREhICI888kiK9qlevTqVK1dOsH9KvPXWW4waNYq6devi6+vLyZMnOXbsGGfPnk2wXZEiRVi/fj3Tp0+nXbt2FC5cmJs3bxIbG0upUqVo27YtI0eOTDC5sCe98MILfPvtt3Tr1o1q1aoRFBREVFQUefLkoUmTJowcOZJt27Yl6Fgf7/nnn2fx4sW0aNGC4OBg7HY7FSpU4JNPPmHNmjVqqUqDQoUK8fvvv/POO+9QsWJFrFYrPj4+tG7dmt9++41//etf7hsB4gejTKnevXvz9ddf06lTJypVqoSfnx9Xr14lR44cVK9enRdeeIF169bx008/pbpgizdmzBiGDh1K9erVATh+/DjHjh1L1871qeXn58d3333Hxo0b6dmzJ2XLlsXhcHD9+nUKFChAs2bNePfdd4mIiEjQcf+dd97hq6++omPHjlSqVAkfHx/3Pg8//DATJkxg9erVev1nMRbDG9tcRUQkzf744w8qVKgAuAqW5EYFFxHPUEuViEgWFd+RvEqVKiqoRDKAiioRkUxq//799OnTh7Vr13Lt2rUEy3v16sXEiRMBGDx4sFkRRbIVXf4TEcmkduzYQa1atdzfh4SEEBcXl2C6lNdee41Ro0aZEU8k21FRJSKSSV27do1vv/2WFStWcODAAc6fP4/dbqdAgQI0atSIF154gZYtW5odUyTbUFElIiIi4gHqUyUiIiLiAT5mB8hOnE4np0+fJleuXKbOLC8iIiIpZxgG165do0iRInecWkhFVQY6ffq0bmsWERHJpE6cOEGxYsWSXa+iKgPFz+J+4sSJBJOJioiIiPeKioqiePHi7s/x5KioykDxl/yCg4NVVImIiGQyd+u6o47qIiIiIh6gokpERETEA1RUiYiIiHiAiioRERERD1BRJSIiIuIBKqpEREREPEBFlYiIiIgHaJwqERHJMHFxcTgcDrNjSDZms9nw9fVNl2OrqBIRkXQXFRXFxYsXiYmJMTuKCP7+/uTPn9/jA3GrqBIRkXQVFRXFqVOnyJkzJ/nz58fX11eTyospDMMgLi6OyMhITp06BeDRwkpFlYiIpKuLFy+SM2dOihUrpmJKTBcYGEiuXLk4efIkFy9e9GhRpY7qIiKSbuLi4oiJiSEkJEQFlXgNi8VCSEgIMTExxMXFeey4KqpERCTdxHdKT6+OwSL3Kv416ckbJ3T5T0QkJQwDLh2GiwfA+bf/hC0WyFcO8lcEq/5OTY5aqcTbpMdrUkWViEhyTu+Ag8vg5BY4tQVuXUl+W/9gKFILitWDcg9BiYaugktEsg0VVSIif+eww/6FEDYOToQlXGfzhwKVwSfgb9vHwoX9EBMFR9a4vtZ9AYWqQ4OXoVon8A1ARLI+FVUiIgCOOAj/H4R9A1EnXcusvlCpNZR8AIrVgYLVwccviX3tcGEfnPwdjofB3gVwdhf83Bd+fRfq/wvufw38gjL2OYlXGjFiBOvXr2fXrl2cP3+e6OhoChUqRNOmTfnPf/5D9erVTc23evVqmjdvznPPPcekSZPcyydNmkSvXr147733GDp0qGn5vJmKKhGRU9tgwatwbrfr+6D8ULc31HsechW6+/42H1fLVKHqrv1afQLbJsPm8a4CbfVw2PkTtB0FZZqm73PJhEoNXmx2hBQ5+kkbjxzn448/5saNG9SoUcNdQO3Zs4epU6fy008/MXfuXB5//HGPnEsylooqEcm+Ym/Cqo8gbCwYTgjMCw+9BzWeStslu6C88MDr0OhV2PczLH8HrhyBKe2g1jPwyDAIzO2xpyGZy88//0ydOnUICEj4Ghs7diz9+vWjT58+nDx5Eh8ffURnNrpVRUSypzMR8M39sGm0q6Cq1hle+R3q9PRcHyibj6tPVd8wqPu8a9n2qTCmARxd75lzSKbTuHHjRAUVQN++fSlbtiznzp1j7969JiSTtFJRJSLZz4GlMKGVq/UouCg8PRM6fw858qfP+QKC4fER0Gupa/iF62dhSgfY/kP6nE8yrfixk/z8kui7l4TVq1djsVjo2bMnZ8+epU+fPhQrVgwfHx9Gjhzp3m7Tpk20b9+e0NBQ/P39KVWqFH379uX06dNpzhwbG8vYsWOpV68e+fLlIygoiFKlSvH444/z008/pfn4mYnaFkUk+zAMV0f0X94CDCjdFJ6cDIF5Mub8Je+Hl9bDvJdg73xXR/bLh6H52xrjSpg6dSoHDhygfPnylC9fPlX7XrhwgXr16mG323nggQeIjo4mKMh1Y8S0adPo2bMnDoeDxo0bU7x4cbZt28Y333zD3LlzWb16NZUqVbrn3N27d2f27NnkypWLJk2aEBwczKlTp1i/fj3Xr1/nqaeeuudjZzYqqkQke3DYYdmb8Pt41/e1n4U2I8CWwSN9+wZC54mwqiys+9L1dekwdBznWifZxueff86ePXu4ceMG+/btY8+ePRQpUoTp06djs9lSdawlS5bQsWNHfvzxxwSXFk+cOMELL7wAuPpytWvXDgCn08kbb7zByJEjeeaZZ/j999/v6TkcOXKE2bNnU7JkSbZu3Uq+fPnc66Kjo9m+ffs9HTezUlElIlmf0wFz+8CeeYAFHv4A7n/VvME5rVZo+S7kLQsL+7tarW5dhqdnaUyrbOSXX35h5cqV7u9LlizJlClTqFOnTqqP5e/vz9dff52or9b48eO5desW3bp1cxdUAFarlU8++YSZM2eyZcsWNmzYQOPGjVN93gsXLgBQq1atBAUVQEBAAI0aNUr1MTMztTeLSNbmdMKC11wFldUXnpwCjV/zjtHOa3WHZ+aBXy44shZmPecaL0uyhRUrVmAYBleuXGHt2rWUL1+epk2b8tFHH6X6WLVr16Zo0aKJlq9btw5wXaL7J39/f7p06ZJgu9SqVKkSOXLkYPHixXz++ece6aOVmamoEpGsyzBg2WDYMQ0sNugyEaq0u/t+Gal0E3j6J9co7QeXwdwXEs4tKFle7ty5adKkCUuWLKFOnTq88847qb4cV6JEiSSXxxc5pUqVSnJ9/PJTp06l6nzxgoOD+e677/D392fQoEEULVqUihUr8tJLL7Fhw4Z7OmZmpqJKRLKu3z6Ezf8DLNDhG6jc1uxESSv1AHT9wdWStmeuq2XN6TQ7lWQwX19funbtimEYLFy4MFX7JjVEQ0p4YlLhbt268eeff/Ldd9/RpUsXrl69yv/+9z8eeOAB3njjjTQfPzNRUSUiWdP6ka5O4OAazqBmV1Pj3FX5h1zDOlisrpa15f9ndiIxQf78rmE94vsqpVWRIkUAOHbsWJLrjx49CpDkpcPUCA0NpU+fPsycOZOzZ8+ydOlSgoODGTFiBHv27EnTsTMTFVUikvUcWAorhroeP/yha+qYzKBKe1eLGrhGed862dw8kuHWrFkDQNmyZT1yvCZNmgAwffr0ROtiY2OZNWtWgu08wWKx0KpVK9q0cU3ro6JKRCSzunDQ1S8JA+q/4OqUnpnUfApavO16vOTfcGKzuXnEozZs2MCyZctw/uPyblxcHF9//TVTp04lMDCQrl0907L6/PPPExgYyE8//cTixX/Nseh0Onnrrbc4deoUderUuac7/wC2b9/O3LlziY2NTbD88uXLhIeHA1C8ePF7fwKZjIZUEJGsIzoSfnoaYqKgZGN49GOzE92bJv+GMzth30KY8Qy8sBqCC5udSjzgjz/+oFevXuTPn586deqQL18+Ll68yK5duzhz5gwBAQFMmjTJY4VIiRIl+N///kfPnj1p27ZtgsE/Dxw4QMGCBZk2bdo9H//YsWN06tSJkJAQ6tatS6FChbh69Spr167l2rVrtG3bNlsNq6CWKhHJGpxOVwvVpT9cU890mZzxA3t6iuV2x/rQyq4pbWY+A/YYs1OJBzRt2pS33nqLihUrEhERwaxZs9iwYQN58+bl1VdfZdeuXTz55JMePeczzzzDunXrePzxx9m3bx+zZ8/m1q1bvPzyy2zdujVNo6k3bNiQYcOGUadOHQ4cOMCsWbPYsmULNWrUYMKECcyZM8eDz8T7WQzDMMwOkV1ERUUREhJCZGQkwcHBZscRyVp++wjWfgY2f+i9DIrWNjtR2l06DN81d7XA1XoG2n3tHeNrpUJ0dDRHjhyhdOnS93yHmkh6SM1rM6Wf32qpEpHM7/AqV0EF0HZU1iioAPKVhc4TXHcEbp8Ku2aZnUhE7kBFlYhkbjcvw/y+rsd1esF93czN42nlHoKmb7oeL/43XD1hbh4RSZaKKhHJvAwDFg+Ea6dd8+g9mvrpPTKFJv+GYvUgJhLmv6yBQUW8lIoqEcm8Ima65vSz2OCJ78Avh9mJ0ofNBzr+D3xzwNF1sGm02YlEJAkqqkQkc7p63DWOE0CzwVCsjrl50lu+stBquOvxbx/C2d3m5hGRRDROlYhkPk4HzHvZNR5VsXrwwMAEq0sNXpzMjml39JM26Xbsu6r9rGvS5QNLYO6/4F+rwFd31Il4C7VUiUjm8/t4OLbedTnsiW9dl8eyA4sF2n4FOULh/F5Y86nZiUTkb1RUiUjmEnkKVn7oevzw+5C3jLl5MlrOUHh8pOvxxq/g/D5T44jIX7LJn3cikmUsexNir7ku+9V93uw0gAmXGys/DpUeh/2LYOEA6LUUrPobWcRseheKSOaxf4lrPjyrj2uQz+xcSDz2KfjlhBNhsH2K2WlEBBVVIpJZxFyHJf9xPW70ChSsam4es4UUgxZvux7/+i5cP29uHhFRUSUimcTq4RB1EnKX+GuE8eyu/gtQ+D7X3IC/vGV2GpFsT0WViHi/Mzsh7BvX4zYjwC/I3DzewmqDtiNdcwPumgWHVpqdSCRbU1ElIt7NMGDJIDAcULUjlH/Y7ETepUgtaPCS6/HSN8ERZ24ekb85evQoFouFZs2amR0lQ6ioEhHvtne+qzO2bxA8kkXn9kurZkNcY1dd+gN+/97sNCLZlooqEfFecdGuTtgAjftDSFFz83irgGBo/n+ux6uHw83L5uYRua1o0aLs27ePKVOyxx2qKqpExHuFjXXN8RdcFO5/zew03q32s1CgKkRf1Ujr4jV8fX2pVKkSJUqUMDtKhlBRJSLe6do5WPel63HL99Q5/W6sNnj09uXRzd/BhYPm5pE7mjt3Lg0bNiQoKIj8+fPTpUsXDh06xNChQ7FYLEyaNMm97Y4dOxg0aBB16tQhNDQUf39/ypQpQ9++fTl9+nSiY69evRqLxULPnj2TPHfPnj2xWCysXr06wfJjx47x8ssvU6FCBYKCgsibNy9Vq1blxRdf5MCBAwm23b17Nz169KBMmTIEBAQQGhrKfffdx4ABAzhz5ox7u+T6VEVHR/P999/Tvn17ypQpQ2BgILlz5+bBBx/kp59+umvutWvX0qJFC3LlykVwcDBt2rRh7969yf/AM4iKKhHxTquGQex1KFIbqncxO03mULY5VHjM1al/+dtmp5FkjBo1ik6dOvH777/ToEEDHn74YbZu3Ur9+vU5cuRIou0/+eQT/vvf/wLwwAMP0Lp1awzD4JtvvqFu3bpJFlapdeLECWrXrs24ceMAaN26NU2bNsXf35/vvvuOTZs2ubfdunUr9erV44cffiBXrly0b9+ehg0bEhcXx6hRoxIVYEk5evQoffr0YcuWLZQqVYr27dtz3333ERYWRrdu3Rg6dGiy+y5cuJAWLVpw8+ZNWrduTeHChVmyZAkPPvggZ8+eTfPPIi00TY2IeJ8zEbBtqutxq0+y98jpqfXIMDj0K/zxi2uIhXItzU4kf/Pnn38yaNAg/Pz8WLZsGc2bNwfAbrfzwgsvMHHixET7vPjii4waNYqCBQu6lzmdToYNG8Z7773H22+/zYQJE9KUa/z48Vy+fJlXXnmFr7/+OsG648ePExf3112lX331FdHR0XzxxRe88cYbCbbdv38/ISEhdz1faGgov/76Ky1btsRisbiXHzlyhBYtWvDhhx/Ss2dPSpUqlWjfkSNHMmfOHDp06ACAw+Gga9euzJkzh7Fjx/LBBx+k4pl7lv6nEhHvs/xtwICqT0CJBmanyVzyl4N6/3I9Xv42OB3m5rkTw4DYG5nryzDS9JQnTJhAbGwszzzzjLugAvDx8WHEiBHkzJkz0T7NmzdPUFABWK1W3n33XYoWLcqCBQvSlAngwoULADz00EOJ1pUoUYKyZcumaNtKlSpRuHDhu54vX758PPTQQwkKKoDSpUvzf//3fzidThYuXJjkvt26dXMXVAA2m40hQ4YAsHbt2rueOz2ppUpEvMufq+HIGrD5wUNDzU6TOTUdBDt/hPN7YddsqNnV7ERJi7sJHxcxO0XqvHUa/HLc8+4bNmwAoEuXxJe0c+fOzSOPPMLcuXMTrbt06RILFixg9+7dXL16FYfDVSzHxcVx6dIlLl++TN68ee85V506dQB46623sNlsPPTQQwQEBCS77dKlS+nXrx/Dhg3jgQcewMfn3sqJ9evXs3r1ak6dOkV0dDSGYbj7ZP3xxx9J7vPII48kWlahQgWABP25zKCiSkS8h2HAyttN93V7Q56S5ubJrILyuoagWPkBrP7YNWiqj5/ZqYS/PvSLFy+e5Pqk7pKbPn06L7zwAtevX0/2uNeuXUtTUdWzZ0+WL1/OzJkzadu2LQEBAdSrV49WrVrRu3dvChUq5N72P//5j7sYat68OTlz5qRRo0a0adOGnj17pujyX2RkJE888QS//fbbHZ9TUooVK5ZoWa5cuQCIiYm567nTk4oqEfEeB5bAqa2ugT6bvHH37SV5DV6CsHFw5Shsnwr1njc7UWK+Qa6Wn8zEN2PvQj127Jj7Lr6RI0fSpk0bihYtSmBgIAD3338/mzZtwkjFZUmn05lomc1mY8aMGQwePJiff/6Z3377jfDwcNatW8cnn3zCsmXLuP/++wEIDg7mt99+Y8OGDSxcuJDVq1fz22+/8euvvzJ8+HDWrVtH+fLl75jhzTff5LfffqNp06a8//77VKtWjdy5c2Oz2Vi+fDmPPvposs/J6sV9LL03GXDr1i3effddKlSoQEBAAEWKFKF3796cOnUqxce4evUqP/74I926daN06dL4+fmRK1cuGjRowKhRoxJ0vvsnh8PBf//7X6pXr05gYCChoaE8+eST7Nu3zxNPT0T+zumA34a5Hjd8GXIWMDdPZueXAx78j+vxms8g7pa5eZJisbhyZqavf/QBSq34/kYnTpxIcv0/ly9ZsoTY2Fhee+01+vfvT7ly5dwFFbg6vv+Tn5+rVTK5lq3kzg1Qq1Ythg4dytq1a7lw4QKvv/46165dY8CAAQm2s1gsPPDAA3z66aeEh4dz+vRpunXrxrlz5/i///u/ZI8fb968edhsNhYsWEDTpk3Jly8fNpst2eeUWXhtURUdHe2+A+D69eu0b9+e4sWLM3HiRGrVqpXiH/oXX3xB9+7dmTFjBnny5OGJJ56gfv367Ny5kwEDBrhvy/wnp9NJly5dGDhwICdPnqRNmzZUrVqV2bNnU7duXTZv3uzppyySve2e4+oDFBCigT49pc5zEFICrp91jV0lpmvcuDEAc+bMSbQuMjKS5cuXJ1h25coVIOlLXmvXruXcuXOJlscXbgcPJh6r7PLly2zbti1FWYODgxk+fDgWi4Xdu3ffcdsCBQq4h0G427bgel7BwcEEBwcnWjdz5swU5fNGXltUDRs2jLCwMBo1asTBgweZMWMG4eHhfPnll1y4cIHevXun6Dg5cuRg0KBBHD16lG3btvHTTz+xcuVKdu3aRYkSJVi/fj3Dhg1LtN+ECROYN28e5cuXZ//+/cyePZvVq1cza9Ysbt68Sffu3bHb7Z5+2iLZkz0WVt0euLLxAAjMbWaarMPHH5oNdj1ePwKiI83NI/Tq1Qs/Pz+mTJmS4E41h8PBG2+8kagfUXwH7GnTpnHjxg338lOnTvHSSy8leY7SpUtTokQJdu3axc8//+xefuPGDV544QWioqIS7TN16tQki6GlS5diGEaCPmDjxo1LcjytJUuWAMn3F/vn87py5QozZsxIsPy///0vq1atuuv+3sori6rY2FhGjx4NwJgxYxLcYjpw4EBq1KjBmjVr2Lp1612PNWTIED799NNEnf/Kly/PJ598Arg6Af7TiBEjAPjss88S3MraqVMn2rVrx6FDhxK8WEUkDbZPdfX9yVEAGrxodpqspeZTkL8i3LoCm8aYnSbbK1u2LJ999hkxMTE0b96cFi1a0K1bNypUqMCcOXPo0aMH8NclvHbt2lG1alW2bNlCuXLl6Ny5M48//jgVKlQgT5487n5O//Tee+8Brs+sFi1a0K5dO8qWLUtERATt27dPtP2cOXOoXr065cqVo2PHjjz99NM0atSIJ554AqvVmqDxYdy4cZQpU4aqVavSuXNnnnrqKe677z5ef/11AgICePfdd+/6c4gfAuGpp57iwQcf5Omnn6Zq1ar8+9//5vXXX0/dD9WLeGVRtWHDBiIjIylbtiy1atVKtL5z584AyY5hkVI1a9YESDQa7ZEjR9i3bx+BgYG0adMm3c4vIrgmTV77uevxg/9J0+3qkgSrDVrc7uOyaQzcuGRuHqF///7uriRhYWH88ssv3HfffYSHh7uHMciXLx/gKq7WrVvHyy+/TEBAAIsWLWLfvn28+uqr/Prrr/j6+iZ5jt69ezNx4kQqV67Mhg0b2Lx5M23btmXTpk3kzp070fYDBw6kX79+5MqVi3Xr1jFv3jzOnz9P165dCQ8PTzAExIcffkjv3r2xWCysXLmShQsXcuvWLfr06cOOHTvclzjvpHv37ixevJiGDRuyY8cOli5dSpEiRfjtt99o167dPfxUvYNX3v23c+dOAGrXrp3k+vjlERERaTpPfL+sv98q+vfzV6tWLckXrKfOLyLAtilw7QyEFHf1ARLPq9wOCteEMzshbAy0vHtLgqSvTp060alTpwTLHA4HGzduxGKxuP/oB8iTJw9jx45N8jj/nL/v73r27Jnk/H+TJk1KMLcgwIMPPsiDDz6Youxt27albdu2Kdq2VKlSyd7F17p1a1q3bp3kuqT2SSr33fbJaF5ZVB0/fhxIumPe35cfO3YsTecZNWoUQKKm0Iw6v0h2UWrw4iSX+xHHav/hFLHA/118mB/eXpHqYx/9JHFrsvyDxQIPDoIZ3SH8W7j/VQjMY3aqbOvw4cPky5cvQYtRTEwMb731Fnv37uWhhx5K9Me+ZA5eWVTF3wYaFJT0eCA5crguDyQ3MFhKjBs3jhUrVpA7d24GDx6cLuePiYlJMBBZUp0DRbKzzra1FLFc5oyRl1mOpmbHydoqtoaC1eDcbtf4Vc2HmJ0o25o1axbvvfcederUoXjx4kRFRbFz507OnDlD/vz53X2KJfPxyqIqva1bt47+/ftjsViYMGECRYqkzzQJw4cP5/3330+XY4tkdj7YednmmrPsf/bHiSXpviGSWHItf3fT2tqCsX67iVz9FY1/Kcd1Ev/hqJa/9NeyZUt27txJWFgYERER2O12ihYtyssvv8yQIUNSdPeceCevLKri7/ZLavwowH1bafyw9Kmxe/du2rdvT2xsLF999RUdO3ZMt/MPGTKEgQMHur+PiorSm0Xkto629RS3XuCCEcJ0Rwuz42QLS531+cNZlPLWUzxrW85YRwezI2VL9erVS/Kuc8n8vPLuv/jhD06ePJnk+vjlJUumbl6wI0eO8Mgjj3DlyhWGDh3Kq6++mq7n9/f3dw9ultwgZyLZkQ0H/WyuIUn+Z3+cGDQvXUYwsPK1vQMAfXyWEES0uYFEshivLKri73pIbtTX+OU1atRI8THPnDnDww8/zJkzZ+jfv797DI87nX/37t1JTmNzL+cXkb+0tW6ilPUcl4xc/OBoaXacbGWRsxF/OguR13KdHrZfzY4jkqV4ZVHVuHFjQkJCOHz4MDt27Ei0fvbs2QApvqXzypUrPProoxw+fJhevXrx3//+947bly5dmsqVK3Pr1i0WL07cdyG15xeRv1hx8qrPPADG29twiwCTE2UvTqyMdbjueP6Xz2ICiLnLHiKSUl5ZVPn5+fHKK68A0K9fvwRD848YMYKIiAiaNm1KnTp13MtHjx5NpUqV3KO0xrt58yZt2rRh165dPPnkk3z33XdYUjAhZnxfqEGDBnH+/Hn38rlz57JgwQLKlSuX5Ki0InJnraybKWs9w1UjB1McD5sdJ1ua72jMCWcooZYonrJlzJQg3jCGkMjfpcdr0is7qgO8/fbbrFixgo0bN1K+fHmaNGnCsWPHCA8PJzQ0lAkTJiTY/uLFixw4cIAzZ84kWP5///d/bNq0CZvNho+PD88//3yS5/vngGK9e/dmyZIlzJs3j0qVKtGyZUsuXrzImjVrCAwMZNq0afj4eO2PT8RLGbzk45qJYJLjUW4QaHKe7MmOD+McbfnIOoE+PkuY5ngIezp9HFitrr/dHQ5Huhxf5F7FvybjX6Oe4LVVQUBAAKtWrWL48OH8+OOPzJ8/n7x589KzZ08+/PDDZAfm/Kf4Gb4dDgc//vhjstv9s6iyWq3MmjWLUaNGMWHCBBYtWkSOHDno1KkT77//PlWqVLnn5yaSXTWy7qWG9Qi3DD8m2x8xO062NtvxIAN8ZlPMcpE21jB+dj6QLufx9fXFZrNx69atBPO4ipjt1q1b2Gy2ZKf6uRdeefkvXmBgIB988AGHDh0iJiaGM2fOMHHixCQLqqFDh2IYRqLiaNKkSRiGcdevpNhsNgYOHMju3bu5desWFy9eZNasWSqoRO5R/LhUMxzNuILuhjVTDH5MsrcC4CWfRUD6XJ6zWCwEBQURGRmp1irxGg6Hg8jISIKCglLUJSilvLalSkSyliqWozxo24XdsDLekfR8X5Kxpjoeoq/Pz1S2HqepNYI1zpp33+keFChQgKNHj3Ls2DHy5s2Lv7+/Rz/IRFLKMAxiYmK4fPkyTqeTAgUKePT4KqpEJEO86LMIgMXOhpw0PPsfmdybKHIy3dGCPj5Lecm2MN2KKj8/P4oVK8bFixcT9XsVMUOOHDkoVKgQfn6eHSNPRZWIpLtilvO0sYYB8K39cZPTyN99b2/Nc7blNLLtpab9ULqdJygoiBIlSmC327Hb7el2HpG78fHxSbcbzVRUiUi662Nbgo/FyVpHdfYYpcyOI39zhnwscN5PJ9u6262J/dP1fOn5gSZiNq/uqC4iWcCNS3S1rQZgnEMD5nqj/91uPWxl/R0uHTY5jUjmpaJKRNLX798RaIlll7MUG51VzU4jSThoFGeloxZWiwEbvzY7jkimpaJKRNJPXDRs/g6I70ulO768lbuv287pcOOSuWFEMikVVSKSfnbNgpsXOW3kZamzvtlp5A7CjUrsdpYCezRsnXDX7UUkMRVVIpI+DAPCvgFgsv3RdJsGRTzFwvf2x1wPN48He6y5cUQyIRVVIpI+/lwN5/eAbxDTHc3NTiMpsMjZCHIWgutnYc9cs+OIZDoqqkQkfYSNdf17X3ei0JxvmUEcPlC/j+ubTWNcrY0ikmIqqkTE8y4chD+WAxZo+LLZaSQ16vQGnwA4GwHHNpidRiRTUVElIp4X7upLRYVWkK+suVkkdXLkg5pPuR5vGmtuFpFMRkWViHjWzcuwY7rrcaO+5maRe9Pw9u/twBINBiqSCiqqRMSztk4E+y0oWB1KNTE7jdyL0IpQ7iHAgPD/mZ1GJNNQUSUinuOIc92OD65WKosG+8y04lurdvwA0VHmZhHJJFRUiYjn7F8M105DUH6o1snsNJIWZVtA/goQe901yrqI3JWKKhHxnM3fuv6t0xN8/E2NImlksUD9F1yPN38LTqe5eUQyARVVIuIZZ3e7bsG32KBub7PTiCfUfAr8csGlQ/Dnb2anEfF6KqpExDPiW6kqt4WQouZmEc/wzwW1urse354YW0SSp6JKRNLu5mWImOl63OBFc7OIZ9X7l+vfg7/A5SPmZhHxciqqRCTttk+7PYxCNSjRyOw04kn5y0HZloABv483O42IV1NRJSJp43TA77cvDdV/QcMoZEXxrY/bp0LsDXOziHgxFVUikjZ/LIerxyEgN1TvYnYaSQ/lHoY8pSE68q/LvCKSiIoqEUmb+BG3az8LfkHmZpH0YbVC/dt9qzZ/C4Zhbh4RL6WiSkTu3cU/4M9VgAXqPW92GklP93UH3yA4v9c1dIaIJKKiSkTu3ZYJrn8rPAp5SpkaRdJZYO6/Lu/+/r2pUUS8lYoqEbk3sTdd88IB1OtjbhbJGPGtkfsWwvXz5mYR8UIqqkTk3uyZ6+q4nLvk7VvuJcsrXBOK1QNnHGybYnYaEa+jokpE7k38mEV1e7k6Mkv2UPd2a9XWSa7hNETETf8TikjqndoKp7eDzQ9qPWN2GslIVTtCYB6IPOEaTkNE3FRUiUjq/X67g3qVDpAjv6lRJIP5BkCtHq7H6rAukoCKKhFJnVtXYPcc12N1UM+e6vRy/XtoheYDFPkbFVUikjo7pv81z1/x+manETPkKwtlWwAGbJ1odhoRr6GiSkRSzjBgy+1LPnV7a56/7Cy+w/r2aWCPMTeLiJdQUSUiKXdkDVw6BH65oMaTZqcRM1VoBcFF4eYl2Puz2WlEvIKKKhFJuS23L/XUeBL8c5mbRcxl84Haz7keb9ElQBFQUSUiKXX9POxf5Hpct5e5WcQ71H4GLDY4vhHO7zc7jYjpVFSJSMrs+AGcdihaFwpVNzuNeIPgIq7LgOAaDFQkm/MxO4CIZAJO518fmmqlynZKDV6c7Lpm1qpM8ltMZNhk6q9pQAx+qTr20U/apDWeiNdQUSWSDd3pQzIpD1h3Mc3vKFFGEPVnBBE9I/n99SGZvax11uCkkZ9ilou0sYYx1/mg2ZFETKPLfyJyV0/bVgIw1/EA0fibnEa8iRMr0+0tAHja5zeT04iYS0WViNxRKFd52LoVgOmOFianEW8009GUOMNGXetBKlhOmB1HxDQqqkTkjrrYVuNrcbDVWZ4DRgmz44gXukAeVjhrA9DNptYqyb5UVIlIsiw46WZbBcCP9pYmpxFv9qPD9froZFtHABphXbInFVUikqwm1l0Ut14g0ghikbOh2XHEi613VuOYswDBlps8bgszO46IKVRUiUiy4i/lzHU0SfWt8pK9GFj56XafO10ClOxKRZWIJCk/kTxk3Qb8dWlH5E5m3e6wXsf6B+UtJ82OI5LhVFSJSJI629a4O6j/YRQzO45kAhcJUYd1ydZUVIlIIhacPHW7g/pPjuYmp5HMJP4S4BO2dfgTa3IakYylokpEEmlo3Ucp6zmijEAWOdRBXVJunbM6J4385LbcoJV1s9lxRDKUiioRSST+0s0Cx/3cIsDkNJKZOLEy094MgG4+q8wNI5LBVFSJSAJ5iOJR6++ARlCXezPT0RSHYaGhdR+lLWfMjiOSYVRUiUgCT9jW42+xs8tZij1GabPjSCZ0lnysdt4HQFebWqsk+1BRJSJ/Y/ytg7paqeTexd/g0Nm2Fl/sJqcRyRgqqkTErY7lIOWtp7hp+POz436z40gm9puzFueM3OS3RPHQ7Qm5RbI6FVUi4hbfsXihoxHXCTI5jWRmDmzMdDQDNGaVZB8qqkQEgFzcpI3VNWfbjNsfhiJpEf86esC6m2KWC+aGEckAKqpEBIB2to0EWmI54CzGNqO82XEkCzhpFGCdoxpWi0EX2xqz44ikO68uqm7dusW7775LhQoVCAgIoEiRIvTu3ZtTp06l6jhr1qzh/fffp02bNoSGhmKxWChVqtQd9+nZsycWiyXZr3HjxqXhmYl4n6duX6KZ4WgOWMwNI1nGjNsd1rvYVmPFaW4YkXTmY3aA5ERHR9OiRQvCwsIoXLgw7du35+jRo0ycOJFFixYRFhZGmTJlUnSs/v37s3PnznvK8eijj1KoUKFEyytWrHhPxxPxRlUtR6huPUqM4cM8R2Oz40gWstxZlytGTopYLvOgNcI91IJIVuS1RdWwYcMICwujUaNGLF++nJw5cwIwYsQI3njjDXr37s3q1atTdKxHHnmELl26UK9ePYoVK0bVqlVTnGPw4ME0a9bsHp6BSObR1bYauP0BSLCpWSRricWXuY4mPO+zlK62VSqqJEvzyqIqNjaW0aNHAzBmzBh3QQUwcOBAJk+ezJo1a9i6dSt16tS56/E+++wz9+OzZ896PrBIJhZADB1sGwBNnizpY4ajGc/7LOUh6zbyE8lFQsyOJJIuvLJP1YYNG4iMjKRs2bLUqlUr0frOnTsDsHDhwoyOJpLlPGbdTLDlJiecoWx0prwVVySlDhrF2eYsh6/FwRO2tWbHEUk3XtlSFd//qXbt2kmuj18eERGR7lnmzp3LnDlzcDgclC5dmrZt21KpUqV0P69IRnnq9thUMxzNMLzz7yzJAn5yNKe29RBdbav51vE4uhlCsiKvLKqOHz8OQLFixZJcH7/82LFj6Z7l66+/TvD9m2++ycsvv8yoUaPw8fHKH59IipW2nKGBdT8Ow8Jsx4Nmx5EsbLGjIe/5TKGs9Qz1LAf43dAfp5L1eOWfpdevXwcgKCjpEZ1z5MgBwLVr19ItQ61atRg3bhwHDx7k5s2b/Pnnn4wZM4bcuXMzduxY/vOf/9z1GDExMURFRSX4EvEm8R3UVzvv4yz5TM0iWdsNAlnoaAT81ToqktV4ZVHlDfr378+LL75I+fLlCQwMpHTp0vTt25d169bh5+fH6NGjOXHixB2PMXz4cEJCQtxfxYsXz6D0Infng51Otwdk1AjqkhHix6xqbQ0nmBsmpxHxPK8squLv9rt582aS62/ccL0Zc+XKlWGZ4lWtWpV27dpht9tZuXLlHbcdMmQIkZGR7q+7FWEiGamldTuhliguGCH85kx8Q4iIp203ynHAWYxASyztbBvNjiPicV5ZVJUoUQKAkydPJrk+fnnJkiUzLNPflS/vmsLjzJkzd9zO39+f4ODgBF8i3uJJ22oA5jgexO6d3Ssly7G4W6viX38iWYlXFlU1a9YEYNu2bUmuj19eo0aNDMv0d1euXAH+6tslktkU5DLNrDsAXfqTjDXP0ZhYw0YN6xGqWI6aHUfEo7yyqGrcuDEhISEcPnyYHTt2JFo/e/ZsANq2bZvByVydzxcvXgwkP+SDiLfrbFuLzWIQ7qzEEaOw2XEkG7lCMMuddQG1VknWk6aiavLkyURHR3sqi5ufnx+vvPIKAP369XP3oQLXNDURERE0bdo0wWjqo0ePplKlSgwZMiTN59+/fz9Tp04lJiYmwfILFy7w1FNPceLECWrWrEnjxpojTTIhp9P9YTbD3szMJJJNxV8C7GhbD3G3TE4j4jlp6kjRq1cvXn/9dbp3706fPn3cl+084e2332bFihVs3LiR8uXL06RJE44dO0Z4eDihoaFMmDAhwfYXL17kwIEDSfZzGj9+POPHjwcgLi4OcPWHatiwoXubsWPHuluezp49y7PPPkv//v2pW7cuoaGhnD59mq1bt3Lt2jWKFSvGzJkzsVg0eJ1kQkfXUdJ6nigjkCXOBmankWxovbMaJ438FLNchH2LoEYXsyOJeESaWqr69OmD3W5nzJgx1K5dm4YNG/L9998naFm6VwEBAaxatYp33nmHoKAg5s+fz7Fjx+jZsyfbtm2jTJkyKT7WyZMnCQ8PJzw83N0fKzY21r0sPDw8wRhSFSpUYMCAAVSsWJFdu3Yxa9YstmzZQvny5XnvvfeIiIigQoUKaX6OIqbYPhWAhY77icbf5DCSHRlYmWVv6vpm22Rzw4h4kMUwDCMtB7hx4wbTp09n/PjxbN68GYvFQs6cOenWrRt9+vShbt26nsqa6UVFRRESEkJkZKTuBBRz3LoCX1QERwxtY4axy0j5HycpdfSTNomWlRq82OPn0fky9/mKcJH1/v2xWgx4bTvk9fxrUcRTUvr5neaO6jly5KBPnz6EhYURERFBv3798PHx4dtvv6VBgwbukck1mriIF4iYBY4Y9jlLsMsobXYaycZOk591zuqub7ZPMzeMiId49O6/atWq8dVXX3H69GmmTZvGgw8+yM6dO+nXrx9FihTh+eefZ+vWrZ48pYikxvYpgGtyW01oK2ZzD+ex40dw2E3NIuIJ6TKkQlxcHNeuXXPPzWcYBnFxcUycOJH69evTuXNnrl69mh6nFpHknN4BZ3eBzZ/5Dt25KuZb4awDQfng2hk4tMLsOCJp5tGiKiwsjOeff57ChQvTt29fIiIieOKJJ1i+fDlRUVH88MMPVK9enXnz5vHaa6958tQicjfbXK1UVH6cSHKam0UEiMUXajzl+ub2DRQimVma56a4cuUKU6dO5bvvvmPv3r0YhkHx4sV588036dOnD4UKFXJv261bN7p06UKtWrVYsmRJWk8tIikVexN2uQbNpfazsEWT2YqXqP0MhI2Bg8vg2jnIVdDsRCL3LE0tVT169KBo0aK8/vrr7Nu3j8cee4wFCxZw5MgR3n777QQFVTwfHx/q1avnnupFRDLAvgUQEwm5S0KpB81OI/KXApWhWD1w2mHndLPTiKRJmlqqfvzxRwoVKkTv3r154YUX3BMh303Hjh1NmwxZJFvadvvSSq1nwOqVs1NJdlb7WTj5u+sSYOP+oIGVJZNKU1E1a9Ys2rdvj49P6g7Ttm1bU+btE8mWLh2GY+vBYoX7njY7jUhiVTvC0sFw6RAc3wQl7zc7kcg9SdOfrDdu3GDz5s133S4sLIwpU6ak5VQicq/iOwCXbQkhRc3NIpIU/1xQraPr8TZ1WJfMK01FVc+ePd1z6t3J999/T69evdJyKhG5Fw67awwgcF1iEfFWtZ9z/btnHkRHmptF5B5lSOcKp9OpyYdFzPDHcrh+DoLyQ4VWZqcRSV6xepC/Ithvwe45ZqcRuScZUlT9+eefmutOxAzxY1Pd1w18/MzNInInFstfranb1F1EMqdUd1T/4IMPEny/Y8eORMvi2e12Dhw4wNq1a3n44YfvLaGI3JtrZ10tVQC1dOlPMoGaT8GKoXB6O5zdDYWqmZ1IJFVSXVQNHToUi8WCYRhYLBZ27NjBjh077rhPgQIF+Pjjj+81o4jcix0/guGA4g0htILZaUTuLkd+qNQa9v7saq1q/ZnZiURSJdVF1cSJEwHXfH69e/fmgQce4Pnnn09yWz8/P4oUKULDhg3x9/dPW1IRSTnD+OsSSu1nzM0ikhq1nnUVVREz4OEPwDfA7EQiKZbqouq5555zP548eTKPPfZYgmUi4gWOrocrR8AvF1TpYHYakZQr2xyCi0HUSdi/CKp3NjuRSIqlafDPVatWeSqHiHhSfCtV9U7gr8mTJROx2qBWD1jzCWybrKJKMhXNVyGS1dy64rp8AhqbSjKnWt0BCxxZC5f/NDuNSIqlqqWqRYsWWCwWJk+eTLFixWjRokWK97VYLKxcuTLVAUUklSJmgSMGClaDIrXNTiOSerlLQNkWcHglbJ8GLd81O5FIiqSqqFq9ejUWi4WbN2+6v08pDf4pkgEMw3XJBFytVHrfSWZV+9nbRdUP0OwtsKWpt4pIhkjVq/TIkSMAFC1aNMH3IuIlTm+Hc7vB5g/Vu5idRuTeVWwNQfng+lk49CtUfMzsRCJ3laqiqmTJknf8XkRMFt9BvUo7CMprbhaRtPDxg5rdYNNo1+taRZVkAuqoLpJVxN6AXbNdj9VBXbKC+NfxwV8g6oy5WURSIE1F1blz51i7di3nzp1LsPzw4cM89dRTVKtWjdatWxMWFpamkCKSAnvmQ+w1yFMaSj5gdhqRtAut6JoRwHDAzh/NTiNyV2kqqj755BOaN29OZGSke1lUVBQPPPAAs2bNYu/evSxbtoyWLVvyxx9/pDmsiNzB30dQt6oRWrKIv0+y7HSam0XkLtL0P+/q1aupUqUKFSr8Na/YpEmTOHfuHN26dePAgQOMGDGCW7du8eWXX6Y5rIgk4/x+OBEGFhvUfNrsNCKeU7WDa2aAK0fh6Dqz04jcUZqKqlOnTlGmTJkEyxYvXoyPjw8jR46kfPnyDBgwgJo1a7JmzZo0BRWRO4hvparwKAQXNjeLiCf55fhrVPX44UJEvFSaiqpr164RFBTk/t7hcLBp0ybq1KlD/vz53csrVarEyZMn03IqEUmOPQZ2Tnc9rq15OCULqnP7db1vIdy4ZG4WkTtIU1FVpEgR9u/f7/5+/fr1XL9+nWbNmiXYzm634+fnl5ZTiUhy9i2EW5chVxEo95DZaUQ8r0gtKFQDHLEQ8ZPZaUSSlaaiqlGjRkRERDBy5Eh27drF22+/jcVioW3btgm227dvn3vAUBHxsPhLIrV6aNRpybriW6u2TnbNHCDihdJUVA0ZMgR/f3/eeOMN7rvvPjZs2ECzZs24//773dscPXqUvXv30qBBgzSHFZF/uPyna9JZLK67/kSyqupdwDcILh6AE+FmpxFJUpqKqqpVq7J+/Xp69OhBq1atePvtt5k/f36CbX755Rdq1qxJhw4d0nIqEUnKtqmuf8u2cE1CK5JVBYRA1Y6ux/E3Zoh4mTRfK6hduzaTJyd/R8aLL77Iiy++mNbTiMg/OeJgxw+ux3XUQV2ygdrPuV7zu+dCq+GuQkvEi2iEQJHM6uAvcP0c5AiFCpoXTbKB4vUhtBLYb8GuWWanEUnEY71ajx8/zpkzZ4iJiUl2mwcffNBTpxOR+A7q9z3tmnxWJKuzWFytVb8McXVYr9fH7EQiCaS5qJowYQIffvghx48fv+u2DocjracTyZJKDV6cqu2LcJF1/r9is0Dz30pwZGXy+x/9pE1a44l4j5pPwYr34GwEnNoGRWubnUjELU1F1cSJE+nTx/WXQrVq1ahQoQK5cuXySDARSV5Xn9XYLAYbHVU4YmgEdclGgvJClfauy39bJ6moEq+SpqJqxIgR+Pj4MHv2bNq1a+epTCJyBzYcPGlbDcB0RwtTs4iYok5PV1G1azY8+hH464958Q5pKqr++OMPHnzwQRVUIhmomXUHhS2XuWTk4hdnPbPjiHjc3S+HG6z0K0zZuDO89cF7/OhomeJj63K4pKc03f2XN2/eBHP8iUj6e9r2GwCzHQ8Si6/JaUTMYOHH26203WwrTc4i8pc0FVXt27dnw4YNxMXFeSqPiNxBES7SzLoDgJ906U+ysbmOJsQYPlS3HqWa5U+z44gAaSyqPv74Y3LkyEGvXr24cuWKpzKJSDLUQV3E5QrBLHXWB+BptVaJl0hTn6o33niDKlWqMH36dBYvXkydOnUoVqwYVmviWs1isfD999+n5XQi2Zo6qIskNN3ekg62jbS3beQjew9uEGh2JMnm0lRUTZo0yf04MjKS3377LdltVVSJpI06qIskFG5U4rCzMGWtZ2hv25iqDusi6SFNRdWqVas8lUNE7kId1EX+ydVh/R3rD3SzrVRRJaZLU1HVtGlTT+UQkTtQB3WRpM1xPMggnxlUtx6luuVPdhllzI4k2ZgmVBbJBLr6rFIHdZEkXCUXS5wNAHVYF/N5pKi6dOkSo0aNonv37jz66KN89tln7nV79uxhwYIF3Lx50xOnEsl2fLDzlM11qX2a4yGT04h4nx/srst+7W0byYU+a8Q8aZ5QedasWfTp04fr169jGAYWi4WiRYu61586dYqOHTsyefJkevTokdbTiWQ7D1m3UdBylQtGCL8665odR8TrbDEqcsBZjIrWk3S0rWOK41GzI0k2laaWqk2bNvH000/j4+PDl19+yebNmzEMI8E2LVu2JCQkhLlz56YpqEh21d22AoAZjmbEpf3vIJEsyMIPtzupd7etBIw7by6STtL0P/THH3+M1Wrl119/pXbtpGcKt9ls1K5dm927d6flVCLZUinLGZrYduM0LEy3q4O6SHLmOZow2OcnKlpPUs9ygN+NSmZHkmwoTS1VGzdupFGjRskWVPEKFSrEmTNn0nIqkWwpfhiFVc77OEWoyWlEvNc1gvjZcT8A3X1WmJxGsqs0FVU3b94kNPTu/9FrChuR1PMnli62NQDuSxsikrz498lj1s3kJcrkNJIdpamoKlq0KHv27LnjNoZhsHv3bkqXLp2WU4lkO62t4eSxXOekkZ/VzvvMjiPi9XYbZdjpLIO/xe7+g0QkI6WpqGrVqhUHDhzgp59+Snab8ePHc+LECdq0aZOWU4lkO919XGPuTLe3wKkh5URSJH7YkadtK7HgNDmNZDdp+p968ODBhISE8Oyzz/Lmm28SFhYGwI0bN9i+fTvvvvsur776KqGhobz++useCSySHVSyHKeu9SBxho2ZDs1cIJJSixwNiTKCKGk9zwNW3SAlGStNRVWxYsVYvHgx+fPn5/PPP6dx48ZYLBZmz55N3bp1GTZsGLlz52bBggUUKFDAU5lFsrwetl8BWO6swwXymJxGJPO4RQBzHE0AeOb2+0gko6R50JtGjRpx4MABvv/+e3799VeOHj2K0+mkWLFiPPzww7z44ouEhIR4IqtItpCLm3S0rQdgmuNhk9OIZD7THA/Ry+cXWlq3UYSLnCa/2ZEkm/BIR41cuXIxYMAAFi9ezJ49e9i3bx+//vorgwYNSlNBdevWLd59910qVKhAQEAARYoUoXfv3pw6dSpVx1mzZg3vv/8+bdq0ITQ0FIvFQqlSpe66n8Ph4L///S/Vq1cnMDCQ0NBQnnzySfbt23ePz0jk7p6wrSOHJYaDzqJsclYxO45IpnPYKMoGR1VsFkPDK0iG8trhmaOjo2nRogVhYWEULlyY9u3bc/ToUSZOnMiiRYsICwujTJmUzUbev39/du7cmarzO51OunTpwrx588idOzdt2rTh4sWLzJ49m8WLF7Nq1Srq169/L09N5A4M9yWLqY6HAYu5cUQyqSmOh2ls20NX22pG2TsRi6/ZkSQbSFNRtXHjRlatWsW+ffu4cuUKFouFvHnzUqVKFZo3b06DBg3u+djDhg0jLCyMRo0asXz5cnLmzAnAiBEjeOONN+jduzerV69O0bEeeeQRunTpQr169ShWrBhVq1a96z4TJkxg3rx5lC9fnnXr1lGwYEEA5syZQ+fOnenevTv79u3Dx8dr61LJhBpZ91LOeprrRgDzHA+YHUck01rhrMMZIy+FLZd5zBrOz069nyT93VNFEBERQe/evdm+fTtAovn+LBbXX9f169fn+++/p0qV1F3CiI2NZfTo0QCMGTPGXVABDBw4kMmTJ7NmzRq2bt1KnTp17nq8zz77zP347NmzKcowYsQI977xBRVAp06daNeuHQsWLODnn3+mU6dOKTqeSEo8a1sOwDzHA1wnyOQ0IpmXAxs/2lvwhu9snvX5lZ9jVVRJ+kt1n6rff/+dxo0bs23bNoKCgujUqRPDhg1j3LhxfPPNN3z44Yd07NiRoKAgwsPDadSokbv4SqkNGzYQGRlJ2bJlqVWrVqL1nTt3BmDhwoWpjZ8iR44cYd++fQQGBiY5vlZ6n1+yp0Jc4mHrVgCmOB4xOY1I5veTowWxho061j+oajlqdhzJBlLVUuVwOOjevTs3btzg+eef58svvyQ4ODjJbaOiohg4cCATJkzg6aefZu/eve4WrLuJ7/+U3JyC8csjIiJSEz/F4s9frVo1fH0TX4dP7/NL9vS0z0p8LE7CnJX5wyhmdhyRTO8CuVnmrE872yaesS1nsP0FsyNJFpeqlqqff/6ZQ4cO0bVrV7777rtkCyqA4OBgxo8fT5cuXTh48GCqWnWOHz8OuMbBSkr88mPHjqUifcqZfX7Jfnyx0822CoApdg2jIOIp8e+n9raNBHPd5DSS1aWqqFq4cCFWq5WPP/44xfsMHz4cgPnz56d4n+vXXS/8oKCk+5TkyJEDgGvXrqX4mKnhqfPHxMQQFRWV4EskKY9ZNxNqieSskYflzrpmxxHJMrYYFdnnLEGgJVbzAUq6S1VRtXXrVipWrJiqyZHLlClDpUqV2Lp1a6rDZXbDhw8nJCTE/VW8eHGzI4mXesbH1UF9ur0Fdu8d6UQkE7Iw5fYgus/YVoBT8wFK+klVUXXmzBkqVKiQ6pNUqFCB06dPp3j7+Lv9bt68meT6GzduAK5BR9ODp84/ZMgQIiMj3V8nTpzwbFDJGk5vp97tef5+dLQwO41IljPf0ZhII4hS1nNwSFPXSPpJVVEVGRl5TyOkBwcHp+rSV4kSJQA4efJkkuvjl5csWTLVWTLy/P7+/gQHByf4Ekkk/FsAFjsbaJ4/kXRwiwBmOJq7vgkfZ24YydJSVVTZ7Xas1tTPbGO1WrHb7SnevmbNmgBs27YtyfXxy2vUqJHqLKk5/+7du4mLi8vw80s2cv0C7J4NwCR7K5PDiGRdUxwP4zQscPg3uHDQ7DiSRXlk7j9Pa9y4MSEhIRw+fJgdO3YkWj97tutDqG3btuly/tKlS1O5cmVu3brF4sWLM/z8ko1smwSOWHY4y7LDKGd2GpEs66RRgBXO28P0bP7W3DCSZaW6qJo8eTI2my1VX1OmTEnVOfz8/HjllVcA6Nevn7sPE7hGOo+IiKBp06YJRlMfPXo0lSpVYsiQIal9SkkaOHAgAIMGDeL8+fPu5XPnzmXBggWUK1eO9u3be+Rckk054uD37wGYaH/U5DAiWd9Ex+3W4B0/QnSkuWEkS0r1bUb/nJImpVI68Ge8t99+mxUrVrBx40bKly9PkyZNOHbsGOHh4YSGhjJhwoQE21+8eJEDBw5w5syZRMcaP34848ePB3Bfzjtz5gwNGzZ0bzN27NgEg4327t2bJUuWMG/ePCpVqkTLli25ePEia9asITAwkGnTpmneP0mbfQvg2hnIWZAlFxvefXsRSZNNzioQWhku7IPtP0CjvmZHkiwmVS1VTqfznr8cDkeqggUEBLBq1SreeecdgoKCmD9/PseOHaNnz55s27aNMmXKpPhYJ0+eJDw8nPDwcHd/qNjYWPey8PDwRB3prVYrs2bN4ssvv6RIkSIsWrSIXbt20alTJ7Zs2ZKmyaJFAAj/n+vfur2J0zAKIhnAAg1edD3c/D9wpu5zSeRuvLJPVbzAwEA++OADDh06RExMDGfOnGHixIlJjnQ+dOhQDMNg0qRJya6701ezZs0S7Wez2Rg4cCC7d+/m1q1bXLx4kVmzZqV6gmiRRE5tgxPhYPWFOr3MTiOSfdR4EgJC4MpR+EPDK4hneXVRJZJlxXeUrdoRchU0N4tIduKXA2o/63qs4RXEw1RUiWS0a+dg9xzX4/hLESKScer9CyxW+HMVnN9ndhrJQlRUiWS038eDIxaK1YdimudPJMPlKQmV2rgeh401N4tkKSqqRDJS3C3Y4hpGQXceiZioYT/XvztnwI2L5maRLENFlUhGipgJNy9BSAmopMFjRUxToiEUqQWOGNgy4e7bi6SAiiqRjGIYf11qaPAi2DSMgohpLBZo5Bpkms3fgT3G3DySJaioEskoh1fChf3glxNqP2N2GhGp0h6Ci8KN87BrttlpJAtQUSWSUTbdbqWq9YxrnBwRMZfNF+r/y/U4bKyrNVkkDVRUiWSE8/tcLVUWq4ZREPEmdXqCbxCc2w1H1pidRjI5FVUiGSG+L1WlNpC3tLlZROQvgXngvu6ux5s0vIKkjYoqkfR246Lrtm34q2OsiHiPhi8DFvjjF7hw0Ow0kompqBJJb5u/dd22XaQ2FNdE3CJeJ19ZqNja9XjTaHOzSKamokokPcXecN2uDdD4Nddt3CLife5/1fXvzp9cU0mJ3AMVVSLpafsPcOsy5CkFlduZnUZEklOioWvqKEcMbP6f2Wkkk1JRJZJeHPa/LiU0egWsNnPziEjyLBZXazK45ueMuW5uHsmUVFSJpJd9P8PVYxCU76+7i0TEe1VsDXnLQnQkbJtidhrJhDRPhkh6MAzYMMr1uP6L4Bdkbh4RSVapwYvdj7vZmjHc9zAnl31Js5+LYk/jx+TRT9qkNZ5kImqpEkkPR9bCmZ3gEwj1+pidRkRSaK6jCReMYIpZLtLGGmZ2HMlkVFSJpIf4Vqraz0COfOZmEZEUi8GPSfZWALzosxjQ1DWSciqqRDzt7O6/pqRp1M/sNCKSStMcD3HD8KeK9RhNrLvMjiOZiPpUiSTh730sUmuU72ja22CRvT6vfLoH2JNgvfpYiHi3SHIyw9Gc3j7LeNm2gHXOGmZHkkxCLVUiHlTScpbHrZsAGGvXuFQimdV39jbEGTbut+2ltkVT10jKqKgS8aAXbQuxWQx+c9zHXqOU2XFE5B6dIR9zHU0AeNlngclpJLNQUSXiIYW4RGfbWgDG2NubnEZE0mqcoy0Ow8LDtm1Ushw3O45kAiqqRDzkXz5L8LM4CHdWYqtR0ew4IpJGR4zCLHG6JkHv6/OzyWkkM1BRJeIBeYmim+03QK1UIlnJ2Nvv5zbWMEpZzpicRrydiioRD+jps4wgSwwRztKs1Z1CIlnGPqMkKx21sFkMXrQtMjuOeDkVVSJplIub9LQtB+JbqSzmBhIRj4pvfe5kW0thLpmcRryZiiqRNOphW0Gw5SaHnEVY7qxrdhwR8bBtRgU2OargZ3Hwgo9aqyR5KqpE0iCIaPr4uAYKHWtvh6G3lEiWNMbhaq3qZvuNUK6aG0a8lj4BRNLgGduv5LNc46izID87G5sdR0TSyXpnNbY6yxNgieNFn4VmxxEvpaJK5B4FEu2+FDDa0QEHNpMTiUj6sTDK/gQA3W0r1VolSVJRJXKP/t5KNc/xgNlxRCSdrXXWYJuzHIGWWPWtkiSpqBK5B65WKldfKrVSiWQXFkbaOwGuG1TyE2lyHvE2KqpE7kEP2wryW6I45iygViqRbGStswbb1VolyVBRJZJK6kslkp391Vr1jO1XtVZJAiqqRFKpu20loWqlEsm21qi1SpKhokokFYKIdt9OPdrRATs+JicSkYyXsLVKdwJKPBVVIqnQ07aMUEuU7vgTyebW/O1OwL4+P5sdR7yEiiqRFArmOi/dbuofYe+sViqRbM3C5/auAHS3raAoF0zOI95ARZVICr3os4hgy032OYuz0NnI7DgiYrJNzqqsd1TFz+Kgv89cs+OIF1BRJZIC+Ymkl+0XAL60P6k5/kQEgC9ut1Z1sq2lrOWUyWnEbPpkEEmBfj7zCbLEsN1ZjhXO2mbHEREvscMox3JHHWwWg9d9ZpsdR0ymokrkLopygadtKwH4zN4VsJgbSES8ypf2LjgNC4/bwqlqOWJ2HDGRiiqRu3jNZx7+FjvrHVXZ5KxqdhwR8TIHjBL87LwfgH/7zDQ5jZhJRZXIHZS1nKKzbQ3wV98JEZF/GmnvRJxho7ltJ/Ut+8yOIyZRUSVyB4N9fsJmMVjuqMMOo5zZcUTESx0zCjHD0QyAIb7TAcPUPGIOFVUiyahv2cfDtq3YDSuf2p8yO46IeLlR9k7cMPypZT1EG2u42XHEBCqqRJJgwclbvj8A8JOjOYeNoiYnEhFvd4Hc/M/eFoBBPj/hR5zJiSSjqagSSUIbazj3Wf/kuhHASHtns+OISCYx3tGa80ZuSlrP08O2wuw4ksFUVIn8kz2GQT4/AfA/++NcJMTkQCKSWdwkgBG3/xB71Wce3LpqbiDJUCqqRP7p9/GUsF7gnJGb8Y7WZqcRkUxmlqMpB51FyWO5Duu+NDuOZCAVVSJ/d+sKrPkMcA3od4sAkwOJSGbjwMZw+9Oub8L/B1ePmxtIMoyKKpG/W/sFRF/lgLMYsx1NzU4jIpnUKud9bHRUAUcMrBhqdhzJICqqROJdOAjh4wD4yN4dp94eInLPLAyz9wAssHsOHNtkdiDJAPrUEAEwDPhlCDjtUOEx1jprmp1IRDK5vUYpqPOc65ulg8DpMDWPpD8VVSIAB3+BQyvA6guPfmR2GhHJKlq8A/4hcDYCtk81O42kMxVVIvYYVysVQKO+kK+suXlEJOvIkR+aDXY9XvmBhljI4lRUiYR9A5f/hJwF4cH/mJ1GRLKa+v+C/BXh5iVY86nZaSQdeXVRdevWLd59910qVKhAQEAARYoUoXfv3pw6dSrVx7py5Qr9+/enZMmS+Pv7U7JkSQYMGMDVq1eT3L5nz55YLJZkv8aNG5fGZyde4dpZWPu56/FDQ8E/l6lxRCQLsvlCq49djzd/CxcOmJtH0o2P2QGSEx0dTYsWLQgLC6Nw4cK0b9+eo0ePMnHiRBYtWkRYWBhlypRJ0bEuXrxIo0aNOHToEGXKlKFDhw7s2bOHUaNGsXTpUjZt2kTevHmT3PfRRx+lUKFCiZZXrFgxTc9PvMSKoRB7HYrWgRqaNFlE0km5h6DCY3BwKSx9E56ZBxaL2anEw7y2qBo2bBhhYWE0atSI5cuXkzNnTgBGjBjBG2+8Qe/evVm9enWKjjVgwAAOHTrEE088wYwZM/DxcT3t1157ja+//pqBAwcyadKkJPcdPHgwzZo188AzEq9zdD3snA5Y4LHPwOrVDbciktk9+hEc/g3+XAV75kK1TmYnEg/zyk+R2NhYRo8eDcCYMWPcBRXAwIEDqVGjBmvWrGHr1q13PdaZM2eYPn06fn5+jB071l1QAXz++eeEhoYybdo0zp8/7/knIt7LHguLBroe1+kJxeqaGkdEsoF8ZaHJ7f93lr0F0ZHm5hGP88qiasOGDURGRlK2bFlq1aqVaH3nzq7JKhcuXHjXYy1btgyn00mTJk0oWLBggnX+/v60bdsWh8PBkiVLPBNeModNX8PFAxCUHx56z+w0IpJdNB4AecvC9bPwm4ZvyWq8sqjauXMnALVr105yffzyiIiIdD/W3LlzefXVV+nbty+ff/45+/fvv+s5xctdOeqe349HP4bAPKbGEZFsxDcA2tyeZPn37+D0dnPziEd5ZZ+q48ddk08WK1YsyfXxy48dO5bux/r6668TfP/mm2/y8ssvM2rUqASXEpMSExNDTEyM+/uoqKi75pV0Zhiw5D9gj4ZSTaDGk2YnEpHspmxzqNYZds+GRa9Dn5VgtZmdSjzAK1uqrl+/DkBQUFCS63PkyAHAtWvX0u1YtWrVYty4cRw8eJCbN2/y559/MmbMGHLnzs3YsWP5z3/uPp7R8OHDCQkJcX8VL178rvtIOtu3EP5Y7ho5vc0I3X0jIuZ49GPXSOunt8OWCWanEQ/xyqLKG/Tv358XX3yR8uXLExgYSOnSpenbty/r1q3Dz8+P0aNHc+LEiTseY8iQIURGRrq/7ra9pLPoSNetzAAPDIDQCqbGEZFsLFdBaPmO6/HKDyDqtLl5xCO8sqiKv9vv5s2bSa6/ceMGALly3X2gRk8eC6Bq1aq0a9cOu93OypUr77itv78/wcHBCb7ERL++C9dOQ94y0OQNs9OISHZXtzcUrQsxUa7LgIZhdiJJI6/sU1WiRAkATp48meT6+OUlS5bM0GPFK1++POAarkEyRqnBi9O0//3W3fzoNwmAJ890Z/M7v7nXHf2kTZqOLSJyT6w2aD8axjWBg8tg12yo0cXsVJIGXtlSVbNmTQC2bduW5Pr45TVq1MjQY8W7cuUK8Fd/LPFuQUTzic93AEyxP8xmo7LJiUREbitQGZre7pawdBBcv2BuHkkTryyqGjduTEhICIcPH2bHjh2J1s+ePRuAtm3b3vVYrVq1wmq1sm7dukQDfMbExLBw4UJsNhutW7dOUbaYmBgWL3a1miQ3TIN4l//4zKCE9QInjfx8atdUNCLiZR4YAIWqw63LsFSTumdmXllU+fn58corrwDQr18/d78ncE1TExERQdOmTalTp457+ejRo6lUqRJDhgxJcKzChQvTrVs3YmNj6du3L3a73b1u0KBBXLhwgR49elCgQAH38v379zN16tQEwyEAXLhwgaeeeooTJ05Qs2ZNGjdu7NHnLZ5Xx3KA52zLARgS14cbBJqcSETkH2y+0H4MWGywZ57rLmXJlLyyTxXA22+/zYoVK9i4cSPly5enSZMmHDt2jPDwcEJDQ5kwIeEtqBcvXuTAgQNJ9nMaOXIkYWFhzJkzh0qVKlG3bl327NnD7t27KV++PCNGjEiw/dmzZ3n22Wfp378/devWJTQ0lNOnT7N161auXbtGsWLFmDlzJhbdju/V/InlM99vsVoMZtqbss6Z8ku8IiLpJbk+ov/2eZxXfH7mwk/9eCjmJpHkTHK7O1EfUXN5ZUsVQEBAAKtWreKdd94hKCiI+fPnc+zYMXr27Mm2bdsoU6ZMio+VP39+Nm/ezKuvvkpsbCzz5s0jMjKS1157jc2bN5M3b94E21eoUIEBAwZQsWJFdu3axaxZs9iyZQvly5fnvffeIyIiggoVdDu+txvsM52y1jOcM3IzzN7d7DgiInf0tb0jfziLEmqJ5CPfCYDuBsxsvLalCiAwMJAPPviADz744K7bDh06lKFDhya7Pm/evHz11Vd89dVXdz1WkSJF+O9//5uaqOJlHrDuopfPLwC8GfcCUffwF5+ISEaKwY+BcS8z1+89HreFscJRm/nOB8yOJangtS1VIvcqhOt84TsOgKn2h1jtvM/cQCIiKbTLKMNX9o4AfOA7kaLobsDMREWVZDEGH/lOoJDlCoedhflIl/1EJJMZ62jPNmc5gi23+NJvHFacZkeSFFJRJVlKB+sGHreFEWfYeD2uL9H4mx1JRCRVHNgYENePG4Y/Da376GNL2+DHknFUVEmWUZQLfOA7EYCv7B2JMMqanEhE5N4cNwrygf1ZAP7tM5PKlmMmJ5KUUFElWYIPdr7yG02w5RbbnOUY62hvdiQRkTSZ4WjGr446+FkcjPb9iiCizY4kd6GiSrKEf/vMpI71D6KMIPrH9cOBzexIIiJpZGFQ3L84Y+SlrPUMwzTMgtdTUSWZXnPrdl7yWQTAf+Je4IRR0OREIiKecYVgXot9Bbth5QnberrY1pgdSe5ARZVkaoW5xAjfbwCYaH+UX5z1TU4kIuJZvxuVGGHvAsAHPpOoYDlhciJJjooqybR8sPO139fksVwnwlma4fanzY4kIpIuvnG0ZY2jBoGWWMb6jlL/Ki+lokoyrX/7zKSu9SBRRiD94l4jFl+zI4mIpAsDKwPjXuaskYdy1tN85Ps96l/lfVRUSabU1rrR3Y9qUNyL6kclIlneJULc/as62jbQ27bM7EjyDyqqJNOpbDnGZ77fAvCNvS3L1I9KRLKJzUZlPr49U8RbPj/QyLrH5ETydyqqJFPJQxTf+o4g0BLLGkcNPrd3NTuSiEiGmuBoxRzHA/hYnIzxHUUxi+YH9BYqqiTTsOFgtO/XFLde4KizIK/GvYJTL2ERyXYsvBXXhwhnafJarvOt7wgCiDE7lKCiSjKRt3x+pLFtDzcMf16IG0gUOc2OJCJiihj8eDF2IBeNYKpY47tEqOO62VRUSabQw/Yrz/ssBeCNuJc5aBQ3OZGIiLnOkI++sf2JM2y0s23idZ/ZZkfK9lRUifc7uJz3fSYB8GVcZ3VMFxG5bbNRmbftvQHo7zMPtv9gcqLsTUWVeLczO2FWT2wWg5n2pnzt6Gh2IhERrzLD0ZzR9tuTyC98Df5cbWqe7ExFlXivyJPww5MQd4N1jmq8ZX8esJidSkTE63xp78LPjvvBaYcZz8C5vWZHypZUVIl3unXVVVBdPwuhlekbNwA7PmanEhHxSgZW/hP3IpS4H2Ki4McnIeq02bGyHRVV4n1ib7j+Qzi/B3IWhO6zuEaQ2alERLxaLL7w1A+QrxxEnoCpHeHGJbNjZSsqqsS72GNgRg84EQ4BIdBjLuTWnX4iIikSlBeemQe5isCF/fBDJ4iOMjtVtqGiSryHww5z+sDh38A3B3SfA4WqmZ1KRCRzyV0Cnp0PQfng9HaY3g3ibpmdKltQUSXewel03bWybwHY/FxN2MXrmZ1KRCRzCq3oaun3D4Zj62Hmc+CIMztVlqeiSszndMKSN2DHD2CxQecJULa52alERDK3IvfB0zPAJwD++AVm9wJ7rNmpsjQVVWIupxMW9YctEwALdBgLlduanUpEJGsoeT90/cF1BWDfQpjVU4VVOlJRJeZxOmDBK7BtClis0PF/UPMps1OJiGQt5R+Cp6aDzR8OLIaZz7huChKPU1El5nA6YP7Lf13ye+I7qNnV7FQiIllT+Yfg6Z9clwIPLoOfukNctNmpshwVVZLx7DEwuzdEzLjdh+p7qN7Z7FQiIllb2Rbw9EzwCYRDv7rGA9RwCx6lIarlnpQavPie9svFTf7nO4L7bXuJNWy8Gvsqv0z1A/463tFP2ngopYiIJFCmKfSY7Zqx4sgamNQGesyBnAXMTpYlqKiSDBPKVSb5fUpV6zGuGwG8GPc6G5zVzY4lIpKlJfVHcHXLECb6fUb+sxEc+6wxz8YN5phRKNXH1h/BCenyn2SIUpYzzPF7j6rWY1wwguka+44KKhERk+wyytA59j2OO0MpaT3PbL+hVLP8aXasTE9FlaS7BpZ9zPV7jxLWCxx1FqRT7PvsMUqbHUtEJFs7ahR2/X/sLEmoJYoZfh/yiPV3s2NlaiqqJF11s61kmt/H5LVcZ6ezDJ1jh3LcKGh2LBERAS6Qm66x77DOUY0clhi+9fsvfW3zAcPsaJmSiipJFzYcvOczmeG+3+NrcbDQ0ZCuse9wkRCzo4mIyN9cJ4hecYOYZH8EgEG+MxnlOwZ/NEhoaqmoEo/LQxSTfD+ll88vAHwR14VX414lGn+Tk4mISFLs+DDU3pO34p4nzrDR3raRmX4fUISLZkfLVFRUiUfVsRxgif9bNLHt5qbhz4uxrzPa0RGwmB1NRETu4kdHS56JG8IVIyc1rX+y2P8tmlu3mx0r01BRJR5hwckLtoXM8PuQwpbLHHYWpmPs+/zirGd2NBERSYUwZxXaxg5jp7MMeSzXmej3OW/6TMeGw+xoXk9FlaRZHqL41ncEb/lOx8fi5GfH/bSLHcYBo4TZ0URE5B6cNArQJfY9dz+rl30WMt1vGIW5ZHIy76aiStKkuXU7v/gP5mHbNmIMX96Ke57+cf24QaDZ0UREJA1i8WWovSd9Y1/jmhFIfesBfvF/kw7W9ejuwKRpRHW5Jzm4xds+0+jmswqAg86ivB7Xjz1GKXODiYiIRy1xNmRPbClG+o6llvUQI/3G8ohjC/8X19vsaF5HRZWk3pF1LPUbTAnrBZyGhe8dj/GF/Uli8DM7mYiIpINjRiE6x77HS7aFDPCZQ2vbZupZD8C+XFD5cbPjeQ1d/pOUu3EJ5r0Mkx+nhPUCJ438PB33f3xk76GCSkQki3NgY4yjAx1iP+CgsyihlkiY0R2mPw2RJ82O5xVUVMndGQZsnwaj68DOHwELU+0P0SrmE8KcVcxOJyIiGWiPUZq2sR8xxt4OrD5wYDGMrg+bxoDDbnY8U6mokjs7tQ0mPgY/94NbV6BgNeizgnfsvblOkNnpRETEBDH48bn9KXhxHRRvCHE34Je34NtmcGSt2fFMo6JKkhZ5Cua+CN81h+ObwDcIHv4QXlgNxeqanU5ERLxBwSrQaym0HQUBIXBuF0xu67okeOmw2ekynDqqS0LRka4m3A1fgf2Wa1mNp6DluxBS1NxsIiLifaxWqNMTKj0Oqz+BLRNclwT/+AXq/QuavAE5Q81OmSFUVIlLzDUIHwcbv3YVVgAlGsGjH0HROuZmExER75cjP7T5Aur1gV/fgT+WQ/g3sG0y1H8BGveHoLxmp0xXKqqyu5hr8Pv3sGEU3LrsWpa/IrT4P6jcDiyas09ERFKhQCXoPgsOrYTfPoTT22HDSPh9PDR8GRr2zbLFlYqq7CrqjKtlastEiLndMpWvHDQdDNWeAKvN3HwiIpK5lWsJZVvAwWWw6iM4uwvWfg4bR0OtHtCoH+QtbXZKj1JRld2c3+d6QUfMAGeca1m+8tBkIFR/Emx6SYiIiIdYLFDxMSj/KOxfBOu+gDM74ffvYMv3risijV/LMt1M9Ama3SzsDyfCXY9LNIL7X4MKrVwdDUVERNKD1QpV2kHltq4hFzZ+BYdWwN75cGYHvLo9S3wOqajKbu5/DSJ+gvv7Q/F6ZqcREZHsxGKBMk1dX+f2uG6OKt4gSxRUoKIq+6n8uOZpEhER8xWsCh3HmZ3Co1RUZRGlBi9Ot2Mf/aRNuh1bREQkq8ga7W0iIiIiJlNRJSIiIuIBKqpEREREPMCri6pbt27x7rvvUqFCBQICAihSpAi9e/fm1KlTqT7WlStX6N+/PyVLlsTf35+SJUsyYMAArl69muw+DoeD//73v1SvXp3AwEBCQ0N58skn2bdvXxqelYiIiGRFXltURUdH06JFCz788EOuX79O+/btKV68OBMnTqRWrVr8+eefKT7WxYsXqV+/Pl999RU+Pj506NCBXLlyMWrUKBo0aMDly5cT7eN0OunSpQsDBw7k5MmTtGnThqpVqzJ79mzq1q3L5s2bPfl0RUREJJPz2rv/hg0bRlhYGI0aNWL58uXkzJkTgBEjRvDGG2/Qu3dvVq9enaJjDRgwgEOHDvHEE08wY8YMfHxcT/u1117j66+/ZuDAgUyaNCnBPhMmTGDevHmUL1+edevWUbBgQQDmzJlD586d6d69O/v27XMfS0REJLtJzzvP74XZd6t7ZUtVbGwso0ePBmDMmDHuggpg4MCB1KhRgzVr1rB169a7HuvMmTNMnz4dPz8/xo4dm6AI+vzzzwkNDWXatGmcP38+wX4jRowA4LPPPnMXVACdOnWiXbt2HDp0iJ9//jlNz1NERESyDq8sqjZs2EBkZCRly5alVq1aidZ37twZgIULF971WMuWLcPpdNKkSZMExRGAv78/bdu2xeFwsGTJEvfyI0eOsG/fPgIDA2nTJnHVm5rzi4iISPbglUXVzp07Aahdu3aS6+OXR0REpMux4vepVq0avr6+aTq/iIiIZA9eWVQdP34cgGLFiiW5Pn75sWPH0uVYnjy/iIiIZA9e2cv6+vXrAAQFBSW5PkeOHABcu3YtXY7lqfPHxMQQExPj/j4yMhKAqKiou+ZOLWfMTY8fM15SeXU+nU/n0/l0Pp3P26TH5+vfj2sYxh2388qiKqsYPnw477//fqLlxYsXNyHNvQsZqfPpfDqfzqfz6XzeL72f/7Vr1wgJCUl2vVcWVfF3+928mXR1fePGDQBy5cqVLsfy1PmHDBnCwIED3d87nU4uX75Mvnz5sFgsd83ujaKioihevDgnTpwgODjY7DjZkn4H3kG/B/Ppd2C+7PI7MAyDa9euUaRIkTtu55VFVYkSJQA4efJkkuvjl5csWTJdjuWp8/v7++Pv759gWe7cue+aOTMIDg7O0m+gzEC/A++g34P59DswX3b4HdyphSqeV3ZUr1mzJgDbtm1Lcn388ho1aqTLseL32b17N3FxcWk6v4iIiGQPXllUNW7cmJCQEA4fPsyOHTsSrZ89ezYAbdu2veuxWrVqhdVqZd26dYkG+IyJiWHhwoXYbDZat27tXl66dGkqV67MrVu3WLw48WixqTm/iIiIZA9eWVT5+fnxyiuvANCvXz93HyZwjXQeERFB06ZNqVOnjnv56NGjqVSpEkOGDElwrMKFC9OtWzdiY2Pp27cvdrvdvW7QoEFcuHCBHj16UKBAgQT7xfeFGjRoUIJibO7cuSxYsIBy5crRvn17zz3pTMLf35/33nsv0WVNyTj6HXgH/R7Mp9+B+fQ7SMhi3O3+QJNER0fTrFkzwsPDKVy4ME2aNOHYsWOEh4cTGhpKWFgYZcqUcW8/dOhQ3n//fZ577rlE8/hdvHiRhg0bcvjwYcqWLUvdunXZs2cPu3fvpnz58oSFhZE3b94E+zidTjp37sy8efPIkycPLVu25OLFi6xZs4aAgABWrVpFgwYNMuJHISIiIpmAV7ZUAe7C5Z133iEoKIj58+dz7NgxevbsybZt2xIUVHeTP39+Nm/ezKuvvkpsbCzz5s0jMjKS1157jc2bNycqqACsViuzZs3iyy+/pEiRIixatIhdu3bRqVMntmzZooJKREREEvDalioRERGRzMRrW6pEREREMhMVVeJxH374IRaLBYvFwrRp08yOk+Xt37+fTz/9lObNm5M/f358fX0pVKgQTzzxBOvWrTM7XpZy69Yt3n33XSpUqEBAQABFihShd+/enDp1yuxoWd7NmzeZP38+zz//PBUrViQgIIAcOXJQs2ZNPvjgA/f0YpKxLl26RIECBbBYLJQrV87sOKbT5T/xqAMHDlCzZk1iY2MxDIOpU6fSo0cPs2NlacWKFePUqVPkzJmThg0bkjdvXvbu3cvu3buxWCyMGDGCAQMGmB0z04uOjqZ58+aEhYW5b545evQomzdvTvLmGfGs8ePH869//QuAypUrU61aNaKioti4cSPXrl2jUqVKrFmzJtGd3JK+evbsyZQpUzAMg7Jly3Lo0CGzI5lKLVXiMYZh8MILL5A7d27atWtndpxso1KlSkyZMoULFy7w66+/MmPGDHbt2sW4ceMwDIN///vf7N271+yYmd6wYcMICwujUaNGHDx4kBkzZhAeHs6XX37JhQsX6N27t9kRszRfX19eeOEF9u7dy969e5k5cybLli3jwIED1KpVi/379+uPhwy2cuVKJk+e7C52BTBEPOTbb781AGPatGnGc889ZwDG1KlTzY6VrT3yyCMGYAwdOtTsKJlaTEyMERISYgDGtm3bEq2vUaOGARhbtmwxIZ1s3LjRAAx/f38jJibG7DjZws2bN42yZcsaVapUMQ4ePGgARtmyZc2OZTq1VIlHnD17lkGDBtGyZUu6d+9udhy5LX7KpdOnT5ucJHPbsGEDkZGRlC1bllq1aiVa37lzZwAWLlyY0dGEv17nMTExXLp0yeQ02cP777/Pn3/+ybhx4/D19TU7jtdQUSUe8dprr3Hr1i2++eYbs6PI3/z5558AFCpUyOQkmdvOnTsBqF27dpLr45dHRERkWCb5S/zr3NfXN8lxB8WzIiIi+PLLL+nVqxdNmjQxO45XUVElabZo0SJmzZrFW2+9Rfny5c2OI7cdPnyYRYsWAaiPWxodP34ccN0UkJT45ceOHcuwTPKXUaNGAa65XjVdSvpyOp306dOH3Llz89lnn5kdx+v4mB1AMrfr16/Tt29fKlSowJtvvml2HLnNbrfTs2dPYmJi6Nq1a4J5MiX14m/XDwoKSnJ9jhw5ALh27VqGZRKXJUuW8P333+Pr68uHH35odpws7+uvv+b3339n4sSJ5MuXz+w4XkdFVTbXsWNH9u3bl6p9pkyZQv369QF46623OHHiBCtXrtRfiPcorb+DpLz22musX7+eMmXKMHbs2LRGFPFK+/fvp0ePHhiGweeff+7uWyXp4/jx47z99ts0bdqUnj17mh3HK6moyuaOHDnCgQMHUrXPzZs3Adi8eTNjxozhmWeeoUWLFukRL1tIy+8gKR999BHffPMNBQsW5JdfflEfEw/ImTMnkPzP/caNGwDkypUrwzJld6dOnaJVq1ZcuXKFgQMH0r9/f7MjZXn9+vUjNjaWcePGmR3Fa6moyuZ27Nhxz/suWbIEp9PJrl27aNasWYJ1+/fvB1wf8OPHj6dVq1YMHjw4DUmzrrT8Dv5p3LhxvP3224SEhLBs2TKNcOwhJUqUAODkyZNJro9fXrJkyQzLlJ1dvnyZRx55hGPHjtGrVy+++OILsyNlC4sWLSJ37ty89NJLCZZHR0cDrkI3/rPgp59+ypY3yKiokjS7U1Gwf/9+9u/fT6lSpTIsT3b1008/0a9fP4KCgli8eDH33Xef2ZGyjPjLStu2bUtyffzyGjVqZFim7Or69es89thj7N27lyeeeILvvvsOi8Vidqxs4+rVq6xZsybJddHR0e518YVWdqNpaiRd9OzZk8mTJ2uamgyyZMkSOnTogMViYeHChTzyyCNmR8pSYmNjKVCgAJGRkWzfvj1RwVqzZk0iIiLYsmWLbgpIRzExMbRu3ZrffvuNRx99lAULFuDn52d2rGzv6NGjlC5dWtPUoCEVRDK9DRs20LlzZwzDYMaMGSqo0oGfnx+vvPIK4OpXEt+HCmDEiBFERETQtGlTFVTpyOFw0K1bN3777TeaNGnC3LlzVVCJ19HlP5FM7vHHH+fWrVuULl2a+fPnM3/+/ETbPPDAA/Tp0yfjw2Uhb7/9NitWrGDjxo2UL1+eJk2acOzYMcLDwwkNDWXChAlmR8zSRo8ezbx58wDInz8/ffv2TXK7L774gvz582dkNBE3FVUimdzVq1cB112ER44cSXY7FVVpExAQwKpVqxg+fDg//vgj8+fPJ2/evPTs2ZMPP/ww2YFBxTOuXLnifhxfXCVl6NChKqrENOpTJSIiIuIB6lMlIiIi4gEqqkREREQ8QEWViIiIiAeoqBIRERHxABVVIiIiIh6gokpERETEA1RUiYiIiHiAiioRERERD1BRJSIiIuIBKqpEREREPEBFlYiIiIgHqKgSERER8QAVVSIi96Br165YLBYGDRqUaN3BgwfJmTMnOXPm5I8//jAhnYiYwWIYhmF2CBGRzObKlSvUqFGD06dPs2LFCpo3bw5AXFwc999/P1u2bOG7776jT58+JicVkYyilioRkXuQJ08epkyZAsCzzz7LlStXABg6dChbtmyhQ4cOKqhEshm1VImIpMGgQYP4/PPPefLJJ3nllVdo1qwZBQsWJCIigvz585sdT0QykIoqEZE0iI2NpUGDBuzYsYPg4GCuXbvG0qVLefTRR82OJiIZTJf/RETSwM/Pj8mTJwMQFRXFSy+9pIJKJJtSUSUikkYzZsxwP96xYwcOh8PENCJiFhVVIiJpsH79ej799FMKFSrEQw89xKZNm/joo4/MjiUiJlCfKhGRexQVFUXNmjU5evQoS5cupVatWlSvXp0rV66wfv16GjRoYHZEEclAaqkSEblHr7zyCkePHuWVV16hVatWFCxYkPHjx2O32+nRowc3btwwO6KIZCAVVSIi92DWrFlMnTqVKlWq8Nlnn7mXt2vXjn/9618cOnSI/v37m5hQRDKaLv+JiKTSqVOnqF69Ojdu3CA8PJz77rsvwfobN25Qq1Yt/vjjD+bOnUvHjh3NCSoiGUpFlYiIiIgH6PKfiIiIiAeoqBIRERHxABVVIiIiIh6gokpERETEA1RUiYiIiHiAiioRERERD1BRJSIiIuIBKqpEREREPEBFlYiIiIgHqKgSERER8QAVVSIiIiIeoKJKRERExANUVImIiIh4wP8DvAzDA8jfr9kAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_vector = np.random.choice(dice, size=sample_size)\n",
    "checks= [2,3,10]\n",
    "for n in range(1,max(checks)+1):\n",
    "    if n in checks:\n",
    "        S_n = (random_vector / n )\n",
    "        T_n = (S_n - mu) * np.sqrt(n)\n",
    "        plot_convergence(T_n, sigma, n)\n",
    "    random_vector += np.random.choice(dice, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}