{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    " # Unit 6, Lecture 2\n",
    "\n",
    "*Numerical Methods and Statistics*\n",
    "\n",
    "----\n",
    "\n",
    "#### Prof. Andrew White, Feb 22 2020"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lecture Goals\n",
    "\n",
    "0. Understand the `break` statement\n",
    "1. Understand the `while` loop and know when it is more appropiate than the `for` loop\n",
    "2. Understand the definition of a prediction interval and its connection to loops\n",
    "3. Be familiar with the `scipy.stats` module\n",
    "4. Know and have intuition about the normal probability distribution\n",
    "5. Be able to compute cumulative and prediction intervals with the normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Break Statements\n",
    "====\n",
    "Sometimes you may want to stop a `for` loop early. This may be done with a `break` statement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fox 0\n",
      "cat 1\n",
      "dog 2\n",
      "crow 3\n"
     ]
    }
   ],
   "source": [
    "#Iterate through my favorite pets\n",
    "best_pets = ['fox', 'cat', 'dog', 'crow']\n",
    "index = 0 #Keep track of the index\n",
    "for pet in best_pets:\n",
    "    print(pet, index)\n",
    "    index += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The dog has index 2\n",
      "dog\n"
     ]
    }
   ],
   "source": [
    "#Now stop and report the dog index\n",
    "best_pets = ['fox', 'cat', 'dog', 'crow']\n",
    "index = 0\n",
    "for pet in best_pets:\n",
    "    if pet == 'dog':\n",
    "        print('The dog has index {}'.format(index))\n",
    "        break\n",
    "    index += 1\n",
    "    \n",
    "print(best_pets[index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Here's an example where we want to know when summing integers reaches 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 was the integer that pushed us over 50\n"
     ]
    }
   ],
   "source": [
    "#Sum integers and stop when the sum is 50\n",
    "ints = range(100)\n",
    "isum = 0\n",
    "for i in ints:\n",
    "    isum += i\n",
    "    if(isum > 50):\n",
    "        break\n",
    "\n",
    "print('{} was the integer that pushed us over 50'.format(i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "While loops\n",
    "====\n",
    "Python loops are called `for-each` loops in most other programming languages. That's because they require a list or array to do a `for` loop. You may not always have an array handy, or you many not know how big the array will need to be. For example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99 was the integer that pushed us to 4950\n"
     ]
    }
   ],
   "source": [
    "#Sum integers and stop when the sum is 10000\n",
    "ints = range(100)\n",
    "isum = 0\n",
    "for i in ints:\n",
    "    isum += i\n",
    "    if(isum > 10000):\n",
    "        break\n",
    "\n",
    "print('{} was the integer that pushed us to {}'.format(i, isum))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We needed to know before starting the loop how many integers to loop over!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can get around this using a `while` loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "142 was the integer that pushed us to 10011\n"
     ]
    }
   ],
   "source": [
    "i = 0\n",
    "isum = 0\n",
    "while isum < 10000:\n",
    "    isum += i\n",
    "    i += 1\n",
    "print('{} was the integer that pushed us to {}'.format(i, isum))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Computing Prediction Intervals\n",
    "====\n",
    "\n",
    "Now that we know how to `break` or use a `while` loop, we can return to the problem of computing prediction intervals. Consider our geometric distribution from yesterday:\n",
    "\n",
    "$$P(n) = (1 - p)^{n - 1}p$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Assuming $p=0.1$. Find the smallest $x$ such that:\n",
    "$$ P(n < x) \\geq 0.9$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "First, let's just sum to $1$ to make sure our code is correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999704873345701\n"
     ]
    }
   ],
   "source": [
    "Q = range(1, 100)\n",
    "p = 0.1\n",
    "psum = 0\n",
    "for n in Q:\n",
    "    psum += (1 - p) ** (n - 1) * p\n",
    "print(psum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now we'll stop early, when we've reached the $0.9$ probability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ \\min_x \\sum_i^x P(i) \\geq 0.9$$\n",
    "$$ \\min_x \\sum_i^x (1 - p)^{i - 1}p \\geq 0.9$$\n",
    "\n",
    "I write min, because otherwise you could trivially just pick $x= \\infty$ which is not what we want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number which pushed our sum over 0.9 is 22. The sum is 0.9015229097816391\n"
     ]
    }
   ],
   "source": [
    "Q = range(1, 100)\n",
    "p = 0.1\n",
    "psum = 0\n",
    "for n in Q:\n",
    "    psum += (1 - p) ** (n - 1) * p\n",
    "    if(psum >= 0.9):\n",
    "        break\n",
    "print('The number which pushed our sum over 0.9 is {}. The sum is {}'.format(n, psum))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "*With a prediction level of 90%, success will occur within 22 trials/attempts*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "*The 90% prediction interval is [1,22]*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Scipy Stats\n",
    "----\n",
    "\n",
    "There is a library, that we will gradually begin to use, that has all distributions and utilities for prediction intervals. Use it sparingly until you understand the concepts well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08192000000000002"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#geometric probability of 5 with p=0.2\n",
    "p = 0.2\n",
    "n = 5\n",
    "(1 - p )**(n - 1) * p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.081920000000000021"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats as ss\n",
    "\n",
    "ss.geom.pmf(5, p=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "You can plot, since this is a `numpy` supporting library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5+3NN24J9quoC8DKwPcmlwM8Dn36rJ0hyJMlMkpmzZ8+2rV2StExtQj8LtFXLPp8G7qyq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0c40a351d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = np.arange(1,15)\n",
    "pn = ss.geom.pmf(n, p=0.1)\n",
    "plt.plot(n, pn, 'bo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Scipy stats has all the cumulative distributions as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.90152290978163885"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#amount of probability between n=1 (inc) and n=22\n",
    "ss.geom.cdf(22, p=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, there is a function to ask about prediction intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#what should the rv for the cdf be a certain number?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.geom.ppf(0.9, p=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For now, I will have you use scipy stats to check your work. You may not use it on homework unless specified or you're working with the normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "One note about scipy stats is that you need to visit the documentation website to get complete function help. The docstrings often don't provide enough info."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Working with the Normal Distribution\n",
    "====\n",
    "\n",
    "Recall the equation:\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "There is not much to do with this equation however, since we must integrate it to compute probabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Computing Probability of Interval\n",
    "===\n",
    "\n",
    "Recall that for continuous probability disributions:\n",
    "\n",
    "$$P(a < x < b) = \\int_a^b p(x) \\, dx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For a normal distribution, let's try $\\mu = 2$, $\\sigma = 0.5$. What is the probability of a sample falling between $2$ and $3$?\n",
    "\n",
    "$$P(2 < x < 3) = \\int_2^3 \\frac{1}{\\sqrt{2\\pi0.5^2}} e^{-\\frac{(x - 2)^2}{2\\times0.5^2}}  \\, dx$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can use the `ss.norm.cdf`, where CDF is the cumulative distribution function. This is the definition of the CDF:\n",
    "\n",
    "$$ CDF(x) = \\int_{-\\infty}^x p(x')\\,dx'$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Using some math, you can show that:\n",
    "\n",
    "$$P(a < x < b) = CDF(b) - CDF(a)$$\n",
    "\n",
    "so for our example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.477249868052\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats as ss\n",
    "prob = ss.norm.cdf(3, scale=0.5, loc=2) - ss.norm.cdf(2, scale=0.5, loc=2)\n",
    "print(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Standard Normal Distribution\n",
    "====\n",
    "\n",
    "In the olden days, someone made a table for all these integrals and it is called a $Z$ table. We won't use Z tables, but the concept is important and I'm making you learn it. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Since different normal distributions have different means and such, they invented the idea of Standard Normal Distributions:\n",
    "\n",
    "$$\n",
    "Z = \\frac{x - \\mu}{\\sigma}\n",
    "$$\n",
    "\n",
    "and then you use this $Z$ as being a sample in the $\\cal{N}(0,1)$ distribution. These are called $Z$ scores. The input, $x$, should always be the bounds of some interval. $Z$ scores are not used to compute probability densities, only for intervals to compute probabilities. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's see how this looks. Let's say we have a random variable distributed according to $\\cal{N}(-2, 3)$. That is a shorthand for $\\mu=-2$, $\\sigma = 3$. Let's say we want to know $P( x > 0)$. We can rewrite that as:\n",
    "\n",
    "$$P(x > 0) = 1 - P(x < 0) = 1 - \\int_{-\\infty}^0 \\cal{N}(-2, 3) \\, dx$$\n",
    "\n",
    "Now it's in a form where we can use the CDF:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25249253754692291"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - ss.norm.cdf(0, scale=3, loc=-2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now we can do the same problem using $Z$-scores. Let's compute the $Z$-score:\n",
    "\n",
    "$$Z = \\frac{x - \\mu}{\\sigma} = \\frac{0 - -2}{3} = \\frac{2}{3}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25249253754692291"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = 2 / 3.\n",
    "1 - ss.norm.cdf(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Notice that by default, `scipy` assumes a standard normal distribution!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Normal Distribution Examples\n",
    "----\n",
    "\n",
    "The amount of snowfall today has an expected value of 5 inches and a standard deviation of 1.5 inches. What's the probability of getting between 3 and 5 inches?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's do this with $Z$ scores. \n",
    "\n",
    "$$Z_{hi} = \\frac{5 - 5}{1.5}$$\n",
    "\n",
    "$$Z_{lo} = \\frac{3 - 5}{1.5}$$\n",
    "\n",
    "$$P(3 < x < 5) = \\int_{Z_{lo}}^{Z_{hi}} \\cal{N}(0,1)\\,dx$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.408788780274\n"
     ]
    }
   ],
   "source": [
    "Zhi = (5 - 5)/1.5\n",
    "Zlo = (3 - 5)/1.5\n",
    "\n",
    "prob = ss.norm.cdf(Zhi) - ss.norm.cdf(Zlo)\n",
    "\n",
    "print(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Checking the assumption of a normal distribution\n",
    "---\n",
    "\n",
    "Remember that the normal distribution presumes a sample space of $(-\\infty, \\infty)$. We can't have snow return to the sky, so how bad is our assumption that snowfall is normal?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can estimate how bad it is, by seeing what the probability of having negative snowfall is.\n",
    "\n",
    "$$P(x < 0) = \\int_{-\\infty}^{0} \\cal{N}(5,1.5)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00042906033319683719"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.norm.cdf(0, loc=5, scale=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00042906033319683719"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = (0 - 5)/1.5\n",
    "ss.norm.cdf(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Looks great! There is about as much a chance of negative snowfall in our equation as reality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Visualizing the Normal Distribution\n",
    "-----\n",
    "\n",
    "Let's  try to understand the different terms. The prefactor is just for normalization. We'll write it as $Q$. The exponent is a distance measuring function, we'll call it $d(x)$:\n",
    "\n",
    "\n",
    "$$ \\cal{N}(\\mu, \\sigma) = Qe^{-d(x)}$$\n",
    "\n",
    "$$d(x) = \\frac{(\\mu - x)^2}{2\\sigma^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UpoKHFluIiIhIw8Xi4ooaKnjVai+2+JfbMCIiIhLTYnVxRY3YSuPSJScutnjXcRgRERGJ\nZd8urvBjrhrlOs53qOBVM34tthAREZHIfLu44kpM63aO03yXCt4JTN7VWmwhIiIipxXLiytqqOCd\nwLTvCH0uA7TYQkREROpm11TfyhWDiytqqOCdJPwMOS22EBERkZPY8mPYDauA2FxcUSM2U7l04pMt\n3nvbcRgRERGJJfaD1TG9uKKGCt5JjM+PGXotUL3YoqLCcSIRERGJBdZa7HtLADADBsfk4ooaKnh1\nMEOvAZ8Pyo5iP1zjOo6IiIjEgs8/hS/+CYAZMdZxmNNTwauDadsB+l8JgF21xHEaERERiQXhTnDW\nOdDrErdh6qGCdwq+4dWLLT7/FFv8mdswIiIi4pQ9GghtbgyY4ddhjHGc6PRU8E6ld1/o1BXQLJ6I\niEiys+tWQOVxaNECM3ik6zj1UsE7BePzYapn8ewHq7FlRxwnEhERERdCiytCO2uYK4ZhMls5TlQ/\nFbzTMENGQUoqHK/Arl/lOo6IiIi4sONj2L8HiP3FFTVSIjlp3rx5FBQUEAgESElJoWfPntx+++10\n7979O+cWFhYybdo00tPTsdYCkJOTw+OPPx7V4M3BtGqNuSIPu34l9r0l2FHjYv6au4iIiESXV701\nCjnnYbqf7zRLpCIqeMOGDeOmm24iIyOD48ePM2/ePH7/+9/zxBNP1Hm+z+cjPz8/qkFdMcPHYtev\nhC//BZ/8HS6I7VUzIiIiEj32m69gy/sA4Vu34kFEl2i7du1KRkYGAJ7nYYyhQ4cOTRosZuReAOf0\nAAhvbigiIiLJwRYshWAQMlpiBg5zHSdiEc3gARQUFPDMM89w7NgxzjnnHB599NFTnut5Hvfddx9V\nVVXk5uZy2223kZOTE3GoQCBAIBCo9Zrf74/4+6MtOHIcwblPYDetx3fkMKZN7O5c3RRqPnuXY5DM\n9Pm7pzFwT2PgXjKOgfWCBNe8C4DvqtGkZLZ0lqXmc9+7d2/4taysLLKysuo839iaG+UiVFpaypw5\nczh48CC//e1v6/zz0tJSunXrRnl5OYsWLWL58uXMmDGDtm3bRvQzFixYwMKFC8PHU6dOZfTo0Q2J\nGVXesTL23jkWe+wobX7477SedLezLCIiItI8jm14j5LHHwKgy6y/kXpuD6d5li9fztNPPx0+njhx\nIpMmTarz3AYXPIDDhw9z7733MmPGDLp161bv+Q888ADjx49n5MjI9o05eQavqKiIfv36EQwGGxo1\naqqe+xPeysXQoROp//UMxpc8/wvG7/eTnZ1NSUmJ0zFIVvr83dMYuKcxcC8Zx6Dyv/8Du/0jTO8+\npP7id06z+P1+tm7dyoUXXhh+7XQzeBFfoj1RVVUVAOnp6RGdb4yhIT3y5MBFRUUEg0G3f6GGjYGV\ni+HQAYJbN2L6XuEuiyPOxyDJ6fN3T2PgnsbAvWQZA3twH/bvm0IHw66Lmd+5a9euEZ1X7yILay1v\nv/02hw8fBuDQoUM8++yz9O7dm+zs7O+cv337dvbt24e1lvLychYsWEBpaSn9+/dv4K8QW0y37nDe\nRQB4K99yG0ZERESalF21BKyF1m0xA650HafBIprB27x5My+//DIVFRVkZWUxYMAAfvzjHwOhxRez\nZ88Ob4tSXFzMrFmzCAQCpKWlkZuby2OPPUb79u2b7rdoJmbk9djPCuHvm7AHvsR0Ost1JBEREYky\nW1ERWj0LmGFjMCmpjhM1XL0FzxjDr371q1P+eV5eHnl5eeHjcePGMW7cuOikizHm0sHYNu2g9Gvs\ne0swP7jHdSQRERGJMrtxNZQdAZ8PMyx+9r47kR5V1gAmJRUzdAwQ2hfHVlQ4TiQiIiLRZK3F1tyK\nNeBKTLv43PdXBa+BzLAx4PNB2VHsB++5jiMiIiLR9M9/wBc7AfCNjN8rkip4DWTadYDqmy3tqrca\ntDpYREREYptdVT171/Vc6BW/jydVwTsD4Ub/xT9DTV9ERETinj38DfbDAgDMiOsxxjhOdOZU8M5E\nr0tCzR6wKxc7DiMiIiLRYNe8C1VVkJ6BGTzCdZxGUcE7A8YYzMjrAbAfrcUe/sZxIhEREWkMGwxi\nV78NgBk8CpOe6ThR46jgnSFz5QhIz4CqqlDjFxERkfj18Ub4qgQgPIkTz1TwzpBJz8QMHgWAXf02\nNkYeYSIiIiIN59XcctW7L+asc9yGiQIVvEYIN/yvSkLNX0REROKO3bcbirYC4EuA2TtQwWsUc9Y5\ncGE/4ITmLyIiInHFrloS+qJdNvQb5DZMlKjgNZJvRHXTL9qK/fJfTrOIiIhIw9jyMuy65QCY4ddh\n/H7HiaJDBa+x+g2E9tkA2BWaxRMREYkndv1KOFYGKSmYode4jhM1KniNZPx+zIjQxsd2/Qps2VHH\niURERCQS1vOwK94EwFwxFNO6neNE0aOCFwVm6DWQ2gIqyrHrlrmOIyIiIpEo2gr79gBgRt/gOEx0\nqeBFgWnVOrQvHqHLtNbTlikiIiKxzlv+RuiLnr0xOee5DRNlKnhRYkZVP5/24D7YtsltGBERETkt\ne2AvbP8IADPqe47TRJ8KXpSYbj1Cz6gFvBVvOE4jIiIip2NXvgXWQtv2mEuHuI4TdSp4UeQbXf2/\nAAq3aMsUERGRGGXLy7BrQ/fMm+HXYVJSHCeKPhW8aOo3CNp3BLRlioiISKyqtTXKsDGu4zQJFbwo\nCm2ZEtr4OLRlyhHHiUREROREoa1RQpMwibY1yolU8KKs1pYpa5e7jiMiIiInKtoK+3YDibm4ooYK\nXpTV2jJlpbZMERERiSW1tkbpfr7TLE1JBa8JaMsUERGR2JPoW6OcSAWvCdTaMmX5647TiIiICJyw\nNUqbxNwa5UQqeE0kvGVK0Vbsni/chhEREUly9lgZtmApkLhbo5xIBa+p9B8EHToBYDWLJyIi4pRd\nuwzKj0FKKmb4da7jNDkVvCZifP7w9X27YRU2cNhxIhERkeRkvSB2xZsAmEHDMa3bOk7U9FTwmpDJ\nuwbSMqDyOHb1267jiIiIJKetG0MLHwFz9Y2OwzQPFbwmZDJbYvKuBkI3dtqqSseJREREko+3rPpW\nqQv7Ybp1d5qluajgNTEzahwYA6VfYT8scB1HREQkqdgvdsIn2wHwjU6O2TtQwWtyplNX6HsFAHbp\n61hrHScSERFJHrZm9q5TV+hzmdswzUgFrxn4rrkp9MUXO+GzIrdhREREkoQt/Rr7wRoAzNU3YHzJ\nU3uS5zd1qdcl0K0HAN6y1xyHERERSQ521VsQrILMlpjBo1zHaVYqeM3AGIO5pvq6/+b3sdUreURE\nRKRp2Mrj2FVLADBDr8WkZzhO1Lwi2sZ53rx5FBQUEAgESElJoWfPntx+++107969zvO3bNnCc889\nx/79++nSpQtTpkyhb9++0cwdd8wVw7AL/wqBUuyKxZhbfuQ6koiISMKyG1bBkcPg82FGJvZzZ+sS\n0QzesGHDmD59Ovn5+cyaNYtu3brx+9//vs5zDxw4wIwZM5gwYQL5+fmMHz+e6dOnU1JSEtXg8cak\npmJGXA+ALXgXe6zMcSIREZHEZK3FLn8DAHPpEEyHjo4TNb+ICl7Xrl3JyAhNbXqehzGGDh061Hnu\nqlWryM3NJS8vD7/fT15eHrm5uaxatSpqoeOVGTEWUlKg/Bh23XLXcURERBLTjo9hTzGQPBsbnyzi\ne/AKCgq46667+OEPf8jWrVv5+c9/Xud5xcXF5Obm1nqtR48eFBcXNy5pAjCt22IGDQdCy7atF3Sc\nSEREJPF4S6sXNPbohenZ220YRyK6Bw8gLy+PvLw8SktLmTNnDtOnT+e3v/3td84rLy8nMzOz1muZ\nmZns3r074lCBQIBAIFDrNb/fH/H3xzIz5vtUrV0OJfvxbd2I7/KrXEeqV81nnyhjEG/0+bunMXBP\nY+BevIyB3fMFwW0fAuAfMyHm80aq5vfYu3dv+LWsrCyysrLqPD/iglejTZs23HPPPdx7773s3r2b\nbt261frz9PR0yspq319WVlYWvsQbiSVLlrBw4cLw8dSpU8nOzm5o1NjUuTMHL72S8k0b8K14k87j\nvu86UcQSZgzilD5/9zQG7mkM3Iv1Mfhq3p+pBPydzuKs6ydg/A2uOjHtwQcfDH89ceJEJk2aVOd5\nZ/RbV1VVAaEyd7KcnBwKCwtrvbZr1y769OkT8fuPHTuWvLy88HFRURElJSUEg4lxSdMbMQ42beD4\njo/5cu1KfOdd5DrSafn9frKzsxNqDOKJPn/3NAbuaQzci4cxsKVfU7licehg1Pc4UHLIbaAoqpnB\nmzlzZvi1U83eQQQFz1rLO++8w5AhQ2jdujWHDh1izpw59O7du84WP3z4cN544w3WrVvHwIEDWb9+\nPbt27eL++++P+Jc4ecqxqKiIYDAYs3+hGsr27gtn58CeYqrefgX/Ty9wHSkiiTQG8Uifv3saA/c0\nBu7F8hh4y9+AqirIaIm9anTM5myMrl27RnReRDN4mzdv5uWXX6aiooKsrCwGDBjAj3/8YyC0+GL2\n7Nnk5+cD0LlzZx5++GHmzp3LrFmz6NSpE4888kjMT+k2p9DGx+Oxf/0jbN6APfAlptNZrmOJiIjE\nLVtREXpyBWCGXYtJz6znOxJbvQXPGMOvfvWrU/55zeKLE/Xr148ZM2Y0Pl0CMwOHYV+dC6VfY5e9\njrl9qutIIiIiccuuXw5HAuD3Y0bd4DqOc3pUmSMmNRUzKrSztl27DHs0UM93iIiISF2s52GXvg6A\nuWIopr2uGqrgOWSGXwct0uB4Bfa9t13HERERiU8ffwAHQtuHmGvGOw4TG1TwHDItszBXXQ2AXfEm\ntrLScSIREZH44727KPRF776Yc3NPf3KSUMFzzFx9IxgTuhfvg9Wu44iIiMQVu+sT+DS0PZvvWs3e\n1VDBc8x0OgsGDAbALl2EtdZxIhERkfhha2bvzjoHLr7UbZgYooIXA8L/i2NPMRRucRtGREQkTtiS\n/diP1gFgrrkJ41OtqaFPIgaYnr2h+mHI3juvOE4jIiISH+yy18F6kNUGc+UI13FiigpejPBdOyH0\nRdFW7Bc73YYRERGJcfbIYeyadwEwo76HSW3hOFFsUcGLFf0HQuezAbDvvOo4jIiISGyzq5bA8QpI\nS8eMvN51nJijghcjjM+Pqb4Xz35YgD24z3EiERGR2GSPV2BXvAmAGXotpmVWPd+RfFTwYogZPBJa\ntwXPC91XICIiIt9h162AQCn4fJirb3IdJyap4MUQk9oCMzr0/Dxb8C42cNhxIhERkdhivSD23dCt\nTGbgMEyHjo4TxSYVvBhjho+FtAw4fhy7crHrOCIiIrFl03qovo3JjJngOEzsUsGLMaZlK8zwMQDY\nlW9iKyocJxIREYkN1lq8t6u3E7vkUky3Hm4DxTAVvBhkRt8Ifj8cCWDXLXMdR0REJDb8YxsUfwaA\nb8z3HYeJbSp4Mci0z8YMHA6EHsFig0HHiURERNwLPwwg5zy4oI/bMDFOBS9Ghe8rKNmP3bTObRgR\nERHH7O5dsH0TAL7rvo8xxnGi2KaCF6PM2TnQ53IA7NuvYK11nEhERMSd8EMAOnaBSwe7DRMHVPBi\nmO+66vsLvtgJRVvdhhEREXHEHjqI/WA1AObaCRif33Gi2KeCF8vOvxhyLwDAe/tlx2FERETcsO++\nCp4HWW0wQ0a5jhMXVPBimDEG39ibQwdFW7G7PnUbSEREpJnZQCm24F0AzOgbMC3SHCeKDyp4sa7v\nQDjrHAC8JX9zHEZERKR52WVvwPHjkJ6BGXm96zhxQwUvxhmfDzN2Yuhg8wbs3i/cBhIREWkm9lhZ\n+KlOZsT1mMxWjhPFDxW8OGCuGAodOgFgdS+eiIgkCbtqCRw7CimpmKtvdB0nrqjgxQGTkoKp3rHb\nvv8etmS/40QiIiJNyx6vwC57DQCTdw2mTTvHieKLCl6cMFeNhqw24Hmh1UQiIiIJzK5bDoe/AZ/v\n283/JWIqeHHCtEjDXHMTALZgGfbw144TiYiINA0bDGLfDj2WzAwchsnu7DhR/FHBiyNm+FjIyITK\n46FVRSIiIgnIblwNhw4AYK6b6DhNfFLBiyMmsyVm5DgA7Kq3sGVHHScSERGJLut52CXVCwr7D8Kc\nfa7bQHGOfd11AAAgAElEQVRKBS/OmNE3QGoLOFaGXfWW6zgiIiLR9fFGqN4SzDdWs3dnSgUvzpjW\nbTF51wBgl72OrahwnEhERCQ6rLV4b1Vv6n9BH0z14zql4VTw4pAZMwH8fgiUYguWuo4jIiISHf/Y\nBrs+AcB3vWbvGkMFLw6ZDp0wg0YAYN95BVtZ6TaQiIhIFHhvzg99kXMeXNjfbZg4p4IXp8zYiWB8\n8HUJdv0K13FEREQaxX5WGJrBA3zfuwVjjONE8U0FL06ZLmdjrsgDwC5ZiK2qcpxIRETkzHmLF4S+\n6NYD+g10GyYBpNR3wgsvvMCmTZsoKSkhIyODAQMGcMcdd9CqVd0P/C0sLGTatGmkp6djrQUgJyeH\nxx9/PLrJBXP9D7AfrIaS/dgPVmOGjHIdSUREpMHsrk9h+yYAfON+oNm7KKi34Pn9fu6//37OPfdc\njh49yhNPPMGf/vQnfvGLX5zye3w+H/n5+VENKt9lzs6BSwfDpvXYt/6GvXI4xud3HUtERKRBvLeq\nZ+/OOgcuHeI2TIKo9xLtrbfeSvfu3fH5fGRlZTF27FgKCwubI5tEwDduUuiL/XuwH61zG0ZERKSB\n7O5dsOV9IHRlyvh091g01DuDd7Jt27aRk5Nz2nM8z+O+++6jqqqK3Nxcbrvttnq/50SBQIBAIFDr\nNb9fM1N16tGLyr5XYD/eCIsX4Bs4LOr/OGo+e42BG/r83dMYuKcxcK+pxqBqcfW+d53OIuXKERiN\ncZ1qPve9e/eGX8vKyiIrK6vO842tuVEuAhs2bGDWrFlMmzaN7t2713lOaWkppaWldOvWjfLychYt\nWsTy5cuZMWMGbdu2jejnLFiwgIULF4aPp06dyujRoyONmXQqdmzjwEN3A9Dh0d+TOXiE20AiIiIR\nqPxiF/vumwTW0u6Bx2h17U2uI8W05cuX8/TTT4ePJ06cyKRJk+o8N+KCt379ep555hkeeughLrro\nogYFeuCBBxg/fjwjR46M6PyTZ/CKioro168fwWCwQT83mVT+/tfYwi2YnJ6k/Mcfo3qDqt/vJzs7\nm5KSEo2BA/r83dMYuKcxcK8pxqBq9u/x1q+EDh1J/c/ZmJTUqLxvIvL7/WzdupULL7ww/NrpZvAi\nukS7cuVKnn/+eX75y1/Sq1evBocyxtCAicLvBC4qKiIYDOof9WmYcZOwhVuwxTsJbt2I6XNZ1H+G\nxsAtff7uaQzc0xi4F60xsAe+xNvwHgDmupvxjA80tvXq2rVrROfVe7PWW2+9xfPPP8+vf/3riMrd\n9u3b2bdvH9ZaysvLWbBgAaWlpfTvrx2pm5LpdQmcH5pZ9RbPb1ChFhERaW52yUKwHrRpj7nqatdx\nEk69M3j5+fn4/X6mTZsGhB4EbIwJb4NSUFDA7Nmzw8fFxcXMmjWLQCBAWloaubm5PPbYY7Rv374J\nfw2B0M7f3h/+N+zcAUVb4SKVahERiT320IHwU5jMdRMwqS0cJ0o89Ra8+fPnn/bP8/LyyMvLCx+P\nGzeOcePGNT6ZNNyF/aFHL9j1Cd4b8/Bd2E+bRYqISMyxb/0tdDk2qw1m6BjXcRKSNptJIMYYfDfe\nFjr4rBB2fOw2kIiIyEnsoQPYtcsAMNd9H5OW7jhRYlLBSzQXXxqaxQO811/SvXgiIhJTas3eDR/r\nOk7CUsFLMJrFExGRWKXZu+ajgpeINIsnIiIxSLN3zUcFLwFpFk9ERGKNZu+alwpeotIsnoiIxBDN\n3jUvFbwEpVk8ERGJFZq9a34qeIlMs3giIhIDNHvX/FTwEphm8URExDXN3rmhgpfoas3ivahZPBER\naVaavXNDBS/B1Z7FK4KiLW4DiYhI0rAH92n2zhEVvGRw8aXQszcA3qIXNIsnIiLNwr45PzR717ot\nZvj1ruMkFRW8JGCMwXfTHaGDXZ/Axx+6DSQiIgnP7tuDXb8SAHP9DzBpaY4TJRcVvGTRuy9c0AcA\n77XnsZ7nOJCIiCQy+8ZLYD1ol40ZNsZ1nKSjgpckas3i/WsXbF7vNpCIiCQsu6cYu3ENAOZ7kzCp\nLRwnSj4qeEnEnH8RXDwAAO+1F7Fe0HEiERFJRN7rL4K1kN0ZM+Rq13GSkgpekvHdNDn0xZf/wn6w\nxm0YERFJOLb4M9gUukpkbrgVk5LiOFFyUsFLMqbH+dB/EBC6P8IGNYsnIiLR4732YuiLLmdjBo1w\nmiWZqeAlId9Nt4e+OPAldv0Kt2FERCRh2J07YFtopwZzw20Yv99xouSlgpeETLcemMvzALBvzMNW\nVjpOJCIiicB77YXQF2fnhP97RtxQwUtS5sbbwPjgq4PYgqWu44iISJyz/9gGRVsB8N10B8aniuGS\nPv0kZc46BzNoOAB28QLs8QrHiUREJF5Za/EWPR86yDkvfK+3uKOCl8TMDbeC3w+lX2FXLnYdR0RE\n4tW2D0PPO6d69s4Yx4FEBS+JmU5nYYZeC4B9ayG27IjjRCIiEm+s5+G9+lzooNfFcMmlbgMJoIKX\n9My4W6BFCyg7gn1nkes4IiISZ+zGNbD7cwB8E6Zo9i5GqOAlOdO2PWb0DQDYZa9hS792nEhEROKF\nrarE1qyc7TcQc96FbgNJmAqeYMbcDJkt4XgFdvEC13FERCRO2IKlcHAfGINv/GTXceQEKniCadkK\nc93NANjV72AP7nOcSEREYp2tKMe+OR8AM2g4plt3t4GkFhU8AcCMugHatINgFfb1F13HERGRGGeX\nvwGlX4M/BXPj7a7jyElU8AQAk5aG+d4tANj338NW3zArIiJyMnv0CPadVwAww67FdOziOJGcTAVP\nwkzeNdCxC5y4YaWIiMhJ7NsvQ9lRaJEW2o1BYo4KnoSZlFTMTXeEDrZ+gK3etFJERKSG/foQdsUb\nAJirb8K0aec4kdRFBU9qMVcMheobZb1X8rHWug0kIiIxJfjGS3D8OGS2wowZ7zqOnIIKntRifD58\nE+4MHXxaCB9vdBtIRERiRuXuz/FWvwOAuX4iJrOV40RyKin1nfDCCy+wadMmSkpKyMjIYMCAAdxx\nxx20anXqQd2yZQvPPfcc+/fvp0uXLkyZMoW+fftGNbg0oT6XQ69L4JPteC/nY/sNdJ1IRERiQOlf\nnwTPg/bZmFHfcx1HTqPeGTy/38/999/PnDlzmD59Ol999RV/+tOfTnn+gQMHmDFjBhMmTCA/P5/x\n48czffp0SkpKohpcmo4xBt/Eu0IHX/4Lb+0yp3lERMQ979NCjq1fCYC5aTImtYXjRHI69Ra8W2+9\nle7du+Pz+cjKymLs2LEUFhae8vxVq1aRm5tLXl4efr+fvLw8cnNzWbVqVTRzSxMzPXqF7scDgq8+\nj1d+zHEiERFxxVpLcMFfADDdemCuHO44kdSn3ku0J9u2bRs5OTmn/PPi4mJyc3NrvdajRw+Ki4sj\n/hmBQIBAIFDrNb/f37Cg0mi+m39I5ab1UPoVRxa9iP/qm1xHSko1f/f1b8AdjYF7GgO3vI/WUbVz\nBwCpt/4INHvX7Gr+7u/duzf8WlZWFllZWXWe36CCt2HDBpYtW8a0adNOeU55eTmZmZm1XsvMzGT3\n7t0R/5wlS5awcOHC8PHUqVPJzs5uSFSJhs6d+XrcRI68Po/DC+dy1nUT8GscnNG/Afc0Bu5pDJqf\nrapi36LnAEjrP5COI8ZgjHGcKnk9+OCD4a8nTpzIpEmT6jwv4oK3fv16nnnmGX75y1/SvXv3U56X\nnp5OWVlZrdfKysrIyMiI9EcxduxY8vLywsdFRUWUlJQQDAYjfg+JDjvqRlj6OvbYUfbPeQL/7VNd\nR0o6fr+f7Oxs/RtwSGPgnsbAneDKxQT3fAFA27v/B4cOHdIYOFAzgzdz5szwa6eavYMIC97KlSt5\n/vnn+eUvf0mvXr1Oe25OTs537tHbtWsXffr0ieRHAd+dciwqKiIYDOovlAstW+EfO5HgK3MJrlyM\nHXk9plNX16mSkv4NuKcxcE9j0LxseRneohcA8F05ghbn9Sa4f7/GwKGuXSP77+B6F1m89dZbPP/8\n8/z617+ut9wBDB8+nJ07d7Ju3TqqqqpYs2YNu3btYsSIEREFktjju+Ym/B06QjCIfeU513FERKSZ\n2HcXQaAUUlLwf3+K6zjSAPXO4OXn5+P3+8P33VlrMcaQn58PQEFBAbNnzw4fd+7cmYcffpi5c+cy\na9YsOnXqxCOPPKL7JuKYSUun9eSf8PUfH8d+tBb7z39gci9wHUtERJqQLf06VPAAM3IcJruz40TS\nEPUWvPnz55/2z/Py8mrdLwfQr18/ZsyY0bhkElNajv4e3yyci91TjPe3Ofh+8Z+6yVZEJIHZ11+E\ninLIaIm5/geu40gD6VFlEhHj9+P/wd2hg88KYfN6t4FERKTJ2D3F2DVLATDjfoBp1dpxImkoFTyJ\nmOlzOVzUHwBv4V+xlZWOE4mISFPw/vYsWA+yO+uRZHFKBU8iZozB94N7wPjg4D7sysWuI4mISJTZ\n7R/B3zcDoQ3v9Uiy+KSCJw1iunXH5F0NgH1zPjZw2HEiERGJFhsM4i14NnTQszdcdpXbQHLGVPCk\nwcxNd0BaBhw7in1znus4IiISJXbNu/DlvwDw3fJvWkwXx1TwpMFMm3aYsTcDYFe9hf0y8sfQiYhI\nbLJlR0MrZwEzaDimR/1730rsUsGTM2KuuQnaZ4Pn4b38V9dxRESkkeyShaFNjVNbYCZoU+N4p4In\nZ8S0SMN8/4ehg60fYIu2ug0kIiJnzB7ch132GgDmmvGYDh0dJ5LGUsGTM2auGArVU/jegmexnp5N\nKCISj+yrz0FVFbRuixn7fddxJApU8OSMGZ8P36R7Qge7d2HXLncbSEREGszu3IHduAYAM34yJj3T\ncSKJBhU8aRRz3kWY6mX09tXnsGVHHScSEZFIWc/Dmzc7dHB2Duaq0W4DSdSo4EmjmYl3QWoLCJRi\nF5/+2cUiIhI77PoV8PmnAPhuvRfj8ztOJNGigieNZrI7Y8ZMAMAufwO7T9umiIjEOnusDPvK3NDB\npUMwvfu6DSRRpYInUWGuuxnaZcOJu6CLiEjMsovnw+FvICUV38S7XMeRKFPBk6gwaemYm6u3Tdn2\nIXbbh24DiYjIKdl9e7DL3gDAjJmA6djFcSKJNhU8iRozcBicdxEA3vy/YKsqHScSEZG6eH97FoJV\n0LYDZuxE13GkCajgSdQYY/Ddei8YA/v3YFcsdh1JREROYrd/BB9vBEKL5ExauuNE0hRU8CSqTE5P\nTN41ANg352EPf+04kYiI1LBVlXjznwkdnHdh6MqLJCQVPIk6M34yZLSEY2XYV593HUdERKrZFYth\n3x6ovuJijHEdSZqICp5EnWndFnPDrQDYtcuwxZ85TiQiIvbwN9g35wFgrroak3Oe40TSlFTwpEmY\nkddDl25gLd4LT2E9z3UkEZGkZl/Oh2NlkJGJmTDZdRxpYip40iRMSiq+2+4NHez6BLt2mdtAIiJJ\nzH5WhF0Xel64ufF2TOt2jhNJU1PBkyZjLhoAlw0BwL4yF3s04DiRiEjyscEg3otPhQ7OzsGMHOc2\nkDQLFTxpUr5JP4IWaXDkMHaRFlyIiDQ3+94S+NcuAHy3/wTj1/Nmk4EKnjQp074j5nvVCy7ee1sL\nLkREmpE9/A120QsAmCtHYnpd7DiRNBcVPGly5pobocvZWnAhItLMQgsrjoYWVuh5s0lFBU+aXGjB\nxY9DB1pwISLSLL6zsKKNFlYkExU8aRbmogGYy64CwL6SrwUXIiJNSAsrRAVPmo2ZdE/1gouAFlyI\niDQhLawQFTxpNt9ZcPH5p44TiYgkHnv4ay2sEBU8aV6hBRfVT7h47k/YYNB1JBGRhGLnP6uFFaKC\nJ83LpKTim/zT0MEXO7ErF7sNJCKSQGzhZuwH7wFgJkzRwookpoInzc5c0AczeBQAdtEL2K8POU4k\nIhL/bOVxvBeqF1b06IUZPsZtIHFKBU+cMD+4G1pmQcUxvHmzXccREYl79q2/wYEvwfjwTf4pxqeF\nFcksJZKT1q1bxzvvvMPnn3/O8ePHeemll055bmFhIdOmTSM9PR1rLQA5OTk8/vjj0UksCcFktcHc\n/EPs3Cdg0zrsxxsxfa9wHUtEJC7ZL3djl7wMgBl9A+bcno4TiWsRFbxWrVoxZswYKioq+POf/1zv\n+T6fj/z8/EaHk8Rmrroau24FfFaI9+LT+C7og0lLdx1LRCSuWGvxnv8TBKugXTbmpttdR5IYENEl\n2r59+zJkyBA6d+7c1HkkiRifD9/k+8Dvh0MHsG/Mcx1JRCTu2PUr4JPtAPhu+zEmPcNxIokFEc3g\nNZTnedx3331UVVWRm5vLbbfdRk5OTlP8KIlz5uxzMddOwC5ZiF32GvbKEZhu3V3HEhGJC/bIYezf\n5oQO+g3EDLjSbSCJGVEveGeffTbTp0+nW7dulJeXs2jRIn7zm98wY8YM2rZtG9F7BAIBAoHaj7Ly\naxduZ2o++6YaA9+Nt1G5cQ2U7Mc+/yf8v5qO8Wn9T42m/vylfhoD9zQGdat6OR+OHIa0dFIn/7RJ\nn1ihMXCr5nPfu3dv+LWsrCyysrLqPD/qBa9Nmza0adMGgMzMTG6//Xbef/99Nm/ezMiRIyN6jyVL\nlrBw4cLw8dSpU8nOzo52VGmgphyDY/f/mpL//T+wO3fQatNaWo2b2GQ/K17p34B7GgP3NAbfKt/6\nIQcLlgLQZvJPaH1Rn2b5uRoDtx588MHw1xMnTmTSpEl1ntckl2hPZowJr6iNxNixY8nLywsfFxUV\nUVJSQlBPPXDC7/eTnZ3dtGNwTk98A4fhfbCar5/9I0dyL8S013+IQDN9/nJaGgP3NAa12eMVVM78\nDQDm3J6UXTmKY/v3N+nP1Bi4VTODN3PmzPBrp5q9gwgLnud5BINBKisrAcL/PzU19Tvnbt++nezs\nbDp37kxFRQWvv/46paWl9O/fP+Jf4uQpx6KiIoLBoP5COdbkY3DLv8HfN8PRAJVzn8D3s0cxxjTd\nz4sz+jfgnsbAPY1BiLfoBTiwF3w+zJSf4QE00+eiMXCra9euEZ0XUcFbvXo1s2bNCh9PnjwZgCef\nfJIdO3Ywe/bs8LYoxcXFzJo1i0AgQFpaGrm5uTz22GO0b9++ob+DJBnTui1m0o+wc2bCxxuxHxZg\nrhjqOpaISEyxxTux774KgLlmPCZHe97Jd0VU8EaMGMGIESPq/LO8vLxal1PHjRvHuHHjohJOko8Z\nPBL7/ntQuBn70p+xF/bDtGrtOpaISEywwSDe3P8PPA86dsHceJvrSBKjtFRRYooxBt+d90GLNAiU\nYhc86zqSiEjMsEsXwRf/BMA35WeYFmmOE0msUsGTmGOyO2MmhG4DsOtXYP++2XEiERH37P692NdD\njwo1Q6/F9O7rOJHEMhU8iUlm1PegRy8AvOeexFaUO04kIuKOtRbvuSeh8ji0aYeZeJfrSBLjVPAk\nJhmfH9+Un337GLNFL7iOJCLijC1YCv/YBoDv9qmYzFaOE0msU8GTmGW6dceMDW14bJe/jt25w3Ei\nEZHmZ78qwf6t+n7kSwdjLh3iNpDEBRU8iWnm+klw1jlgLd6cP2KPV7iOJCLSbMKXZo+VQWYrfLdN\ndR1J4oQKnsQ0k5qK7+4Hwfhg/x7say+6jiQi0mzsuuWw/SMAzG33YtpqT1mJjAqexDzT43zMdROA\n0BYBulQrIsnAflWCnf9M6KDfQMygEU7zSHxRwZO4YG64XZdqRSRpfOfS7OT79OhGaRAVPIkLulQr\nIslEl2alsVTwJG7oUq2IJANdmpVoUMGTuKJLtSKSyHRpVqJFBU/iyncv1WoDZBFJHLo0K9Gigidx\np/al2tewn2x3nEhEpPFsyX7svNmhA12alUZSwZO4ZG64Hc7OCV2qfXYm9liZ60giImfMeh7enD9C\n+TFolYXvzn/XpVlpFBU8iUsmNRXfj/4n+FNCz6qdP9t1JBGRM2aXvQbVVyN8d/47pk07x4kk3qng\nSdwy5/TAjL8DALt2OXbLBseJREQazu7+HPvqcwCYwSP1rFmJChU8iWvm2vFw/kUAeHOfxB7+2nEi\nEZHI2cpKvL/8AaqqoH1HzK0/dh1JEoQKnsQ14/OHVtWmZUCgNFTyrHUdS0QkIvaNF2H3LjAG3z0P\nYjJbuo4kCUIFT+Ke6dgFc8uPQgdbP8AWLHUbSEQkAvazQuzbrwJgrr4Rc0Efx4kkkajgSUIweddA\nv4EA2Pl/wR7c5ziRiMip2fIyvGdngvWg67mYCXe6jiQJRgVPEoIxBt+Un0FWG6g4hveX/8YGg65j\niYjUyc57Bg7uA38Kvh/9HJPawnUkSTAqeJIwTOu2oZIHsHMHdvF8t4FEROrgbSzArl0GgLnxNsy5\nPR0nkkSkgicJxfQfhBkxFgD75gLsp4WOE4mIfMseOoB97snQwQV9MNd9320gSVgqeJJwzMR74Kxz\nwHp4z8zAlh1xHUlEBBsM4j3z33DsKLTMwnfPzzE+v+tYkqBU8CThmLQ0fD9+GFJS4auD2Of+pK1T\nRMQ5+9bf4LPQVQXflJ9h2mc7TiSJTAVPEpLp1gMz8W4A7IcF2HXLHScSkWRmPyvEvjEPADPsOsyl\ngx0nkkSngicJy4waB30uB8C+9Gfsvj2OE4lIMrJlR0KXZq0HZ52DmfQj15EkCajgScIyxuC7+wFo\n0w4qykP341VVuo4lIknEWot9fhYcOgApKfjufRiTluY6liQBFTxJaCarTehRZgDFn4Uf6C0i0hzs\n2mXYjWsAMDffhTmnh+NEkixU8CThmYsHYK4dD4B9dxF26weOE4lIMrB7irEvPR06uOQyzOgb3AaS\npKKCJ0nBTLgTevQCwHt2JvbQQceJRCSR2fJjeE/9Fxw/Dm074LvnQYwxrmNJElHBk6RgUlLxTf0F\nZLaEsiN4f/6/2Koq17FEJAFZa7EvPAX7doPPh+/Hj2Cy2riOJUlGBU+ShunQ6dv78f75D92PJyJN\nwq5bjt2wEgAzfjLm/IscJ5JkpIInScX0H4S55iYA7Luv6n48EYkqu6cY++JToYNLLsWM0aPIxI2U\nSE5at24d77zzDp9//jnHjx/npZdeOu35W7Zs4bnnnmP//v106dKFKVOm0Ldv36gEFmks8/0p2M+K\nYNcneM/OxPcff8R06Og6lojEue/ed/dzjE/zKOJGRH/zWrVqxZgxY7jrrrvqPffAgQPMmDGDCRMm\nkJ+fz/jx45k+fTolJSWNzSoSFbofT0SiTffdSayJqOD17duXIUOG0Llz53rPXbVqFbm5ueTl5eH3\n+8nLyyM3N5dVq1Y1NqtI1HznfryX/+o0j4jEN7vmXd13JzEloku0DVFcXExubm6t13r06EFxcXHE\n7xEIBAgEArVe8/v9UcknDVfz2SfcGFw2hKoxE/DeeRW77HXo2Rv/oOGuU31Hwn7+cURj4F4sj4G3\n65Pwfnemz+WkXP+DhLw0G8tjkAxqPve9e/eGX8vKyiIrK6vO86Ne8MrLy8nMzKz1WmZmJrt37474\nPZYsWcLChQvDx1OnTiU7OztqGeXMJOIY2H//JQf3FlOxbRPeX/9fOva7jNScnq5j1SkRP/94ozFw\nL9bGIFj6Dfuf+h1UVeHvfDadf/1f+BP80mysjUGyefDBB8NfT5w4kUmTJtV5XtQLXnp6OmVlZbVe\nKysrIyMjI+L3GDt2LHl5eeHjoqIiSkpKCAaDUcspkfP7/WRnZyfsGNh7/idMewD7zSH2Tfs5qY/N\nxGS2dB0rLNE//3igMXAvFsfAekGq/vs/sAf3Q2oLzE9+SUlZOZSVu47WJGJxDJJJzQzezJkzw6+d\navYOmqDg5eTkUFhYWOu1Xbt20adPn4jf4+Qpx6KiIoLBoP5COZawY9CqNb6pv8D7/a9h/14qn5mB\n76e/irlLLAn7+ccRjYF7sTQG3itzsYVbADCT78N26x4z2ZpSLI1BMuratWtE50X032Ce51FZWUll\nZSVAra9PNnz4cHbu3Mm6deuoqqpizZo17Nq1ixEjRkSWXMQBc96FmFt+FDrY8j72nVfcBhKRmGY3\nb8AuCd1KZEaMxTdklONEIrVFNIO3evVqZs2aFT6ePHkyAE8++SQ7duxg9uzZ5OfnA9C5c2cefvhh\n5s6dy6xZs+jUqROPPPKIrtlLzDMjrg+tqN2wCvvq89ic8zAX9XcdS0RijN23B29O9WWyHr0wk/7N\nbSCROkRU8EaMGHHKGbi8vLxa98sB9OvXjxkzZjQ6nEhzMsbA5H/H7v4cdn+ON3s6vkf/gOnQyXU0\nEYkRtrwMb9Z/wrEyyGqD7yf/C5Oa6jqWyHfE1k1GIo6ZtDR8P/1fkNESjgTwnvgttiIxb5gWkYax\nnof3l5mw9wsw1ZsZt9fVKYlNKngiJzGduuK792EwBnbvwpszE2ut61gi4ph9Yx5s2QCAmXQ3prce\nwSmxSwVPpA6mz2WYm+8KHXy0Drt4vtM8IuKW/bAA++Y8AMxVozGjb3ScSOT0VPBETsFcOx5z5QgA\n7GsvYjetdxtIRJywX/wTb84fQwc9e2PuuC90z65IDFPBEzkFYwxmys+gRy8AvGf/EFqAISJJwx7+\nBu/J38LxCmiXHdojU4sqJA6o4Imchkltge++X0Gb9lBRjvfE/8EGDruOJSLNwFZV4j31O/jqIKS2\nwPfv/w+mTTvXsUQiooInUg/TtkOo5KWkwqEDeE//F7aq7o2+RSQxWGuxL/0ZPg09mcn88H5MznmO\nU4lETgVPJAIm94LQ5VqAf2zDPj9LK2tFEphd+hp29TsAmLE34xs03HEikYZRwROJkG/wSMx1NwNg\n1y7Dvv2y40Qi0hTs5g3YhXNCB/0HYcZPdhtI5Ayo4Ik0gJlwJ1w2BAD7yly8jQWOE4lINNnPP8V7\n5vdgLeSch+/fHsL4/K5jiTSYCp5IAxifD989Pw+vrLXP/gG7c4fjVCISDfbQQbwn/g8cPw7ts/H9\n7GUJTsAAABqtSURBVNeYtHTXsUTOiAqeSAOZFmn8/+3deXgV1cHH8e+ZmwQSEsISEoxASGjBKpAg\nyFsiLoig2FrQF3ABUbGUakFpXWgQXLAVFRWqFFqoC9W4VV+hVhERhYpxZVEhoIIxrAECCDE3hCRz\n3j9GLiAgEUIm3Pv7PA+PuefO9fnlDjf5cWbmjDPidmiaDJUVuH/9M3Zrkd+xROQY2LIg7qPjYecO\nqB+LM3IcplFTv2OJHDUVPJGjYBo2xrnxDu+etSU7cR8Zjw1+63csETkKtqoKd/oDsKEQHAdn+G2Y\nFul+xxI5Jip4IkfJpLbC+e1oCASgaD3utPu0fIrICcZbDuXvsHwJAOaK32Dad/Y5lcixU8ETOQbm\n1CzMoOu9B6s+xT7xF6zr+htKRKrNvvo8duHrAJjz++Kce5G/gURqiAqeyDFyzuqN+cVAAOyH/8X+\n63GtkSdyAnDfeQM7+xnvQedszIBrfM0jUpNU8ERqgOk7CNO9FwD2zX9j33jZ50Qi8kPssg+wT031\nHrTrgHPdH7QcioQVFTyRGmCMwQy+ATK7AmBffBL3vbd9TiUih2JXr8SdPhGsCy1a49wwBhMd43cs\nkRqlgidSQ0wggDPsVmhzCgB25iPY707cFpG6wW5ah/voPVCxB5om49x0Jyaugd+xRGqcCp5IDTL1\n6uGMGAsntYSqKty/3Yct+NLvWCIC2O3FuJPvhOC3EJ+AM+ourXUnYUsFT6SGmfiGODfdBY2aQvlu\n3Efuwm5c63cskYhmS3Z55W57McTE4IwYh2newu9YIseNCp7IcWCaNsMZdRfExcO3JbiT7tDdLkR8\nYoOlXrnbtA4CAZzhozHfnUohEq5U8ESOE3NyGs5Nd0K9WPhmO+7D47A7tvkdSySi2PLd3i3I1q4B\nYzBDf4/peIbfsUSOOxU8kePIZLTDGTkWomOgeLNX8kp2+h1LJCLYigrcqffC6pUAmKt+h9P1bJ9T\nidQOFTyR48y063DgLc0m3aH71oocZ7ay0lsKJX8ZAOay63DO6u1zKpHao4InUgtMxzMw190MxoF1\nBbiPjMfuLvM7lkhYsq6LffIvsOx9AEzfK3HO7+tzKpHapYInUkucM7pjhvzOe7BmFe6UP2HLy/0N\nJRJmrOtin56K/WAhAKb3JZhfXOZzKpHap4InUouc7r0wlw/zHnz+Ge6j41XyRGpIqNy98wYA5uwL\nMf2vwRjjczKR2qeCJ1LLnJ4XYwYM9R6o5InUiIPK3Vm9MYN+q3InEUsFT8QHTu9+KnkiNeSQ5W7w\nDRhHv+Ikculvv4hPVPJEjp3Kncih6RMg4iOVPJGjp3Incnj6FIj47KCS98hd2LKgv6FE6jhbVYV9\n8hGVO5HD0CdBpA5wevfDDLzOe/DFCtyHxmK/3eVvKJE6ylZU4E6fiH3vLUDlTuRQoqqzkeu65Obm\nsnDhQioqKsjMzGTYsGEkJCQctG1+fj5333039evXx1oLQFpaGvfcc0/NJhcJM06vvrj16mGfngaF\nq3EnjsH5/Xho2szvaCJ1hi3fjfvXP8GKpQCY8/tiBg7V1bIi31Otgjdr1iwWL17MhAkTiI+PZ+rU\nqUyZMoWcnJxDbu84DjNnzqzRoCKRwDn7Qtx6sdjHJ8HGtbgP/BF7672QkuJ3NBHfuaXfUvnwHfDl\nCgDMxVdgLr5c5U7kEKo1nz1//nz69etHs2bNiI2NZfDgwSxbtozi4uLjnU8k4jj/cw7O9TkQFQ1b\ni6iYcBsV6772O5aIr2zJTrbk/Ba7t9wNGIrzqytU7kQO44gzeMFgkOLiYtLT00NjKSkpxMbGUlhY\nSFJS0kGvcV2XG264gcrKSjIyMrjiiitIS0urdqiSkhJKSkoOGAsEAtV+vdSsve+99kEt6pyNO+ou\nKh+9B3YUs2X0MKL/MJ5Aywy/k0UkfQb8ZbcXU/nwOOzGtWAMgSEjCJxzod+xIo4+B/7a+75v3Lgx\nNJaQkHDI0+WgGgWvrMy7IXpcXNwB4w0aNAg9t7+TTz6ZiRMn0qJFC3bv3s2sWbMYP348Dz30EI0a\nNarWNzFnzhxefPHF0OPhw4cfskhK7dI+qGUpF1De/CS23nkT7s4d7LlvNE1z7ie2cze/k0UsfQZq\n356vV1N8323Y4s0QCND05vHEnXOB37Eimj4H/ho1alTo6/79+zNw4MBDbnfEghcbGwt4M3n7Ky0t\nDT23v8TERBITEwGvFF555ZV88MEHLF26lB49elQrfJ8+fejevXvo8cqVKykuLqaqqqpar5eaFQgE\nSEpK0j7wQ5MUYv54P5WT76Rq21aK7x5F4JobCZx5vt/JIoo+A/5wP/+MykfugbJSiKlH0pj7KU0/\nhZLNm/2OFpH0OfDX3hm8yZMnh8YON3sH1Sh4cXFxJCUlUVBQEDrMWlRURFlZWbUPuxpjQlfUVsf3\npxxXrlxJVVWV/kL5TPvAH4GT00h+8Ak2jbkeNq2j6rFJuNu2Yi4aoPOPapk+A7XH/WgR9vGHobIS\nEhKJGnUXsWd0Z9fmzdoHPtPnwF+pqanV2q5aF1n07NmT2bNns2XLFoLBILm5uWRlZR1ymnb58uUU\nFRVhrWX37t288MIL7Ny5k6ysrB/3HYhISFRyc6JzJsJPTwXAznoamzsN6+qHrIQfd95s7PQHvHKX\nfBLOHx/ASW/rdyyRE0q1lknp168fwWCQnJwcKisryczMZOTIkQAsWrSIGTNmhJZFKSwsZNq0aZSU\nlFCvXj0yMjIYN24cTZo0OX7fhUgEMPEJOL8fj/vYw7A4D7vwdezOHTi/vhlTr77f8USOmXWrsP96\nEvvmbG8gvS3OyHGYhER/g4mcgIz9McdOfTJ//nzat2+vKWGfBAIBUlJS2KxDI774/vtv3Srs849h\n3/qPt0GrNji/ux3TRCc+Hy/6DBx/dncQ9x8PwycfegMduuAMvy30jxftA/9pH/grEAiwfPlyevbs\nWa3tdV8XkROMcQKYy4dhBlwLxsDaNbj33oIt+MLvaCJHxRZvxr1vdKjcmbMv9P7RoplpkaOmgidy\nAjLG4PS+BOd3t0O9WNi5HXfiGNwP/+t3NJEfxa7Ox733FthQCMbBXP4bzODrMVprTeSYqOCJnMBM\nZlecP94PTZOhYg92xoO4s3Oxrut3NJEjcvPm4z40Fkp2QmwDnBvvwOn5S10dLlIDVPBETnCmRWuc\nMQ/CT34GgP3P87h/fwC7++CFyEXqAltVhfviE9gn/uJdKdusOU7OREz70/2OJhI2VPBEwoBp2Ajn\nD3/CdDvPG1iS552Xt2m9v8FEvsfu+gZ38p3YuS97A+064Ix5EHNSC3+DiYQZFTyRMGGiozHX3oQZ\nMBQcBzatw/3zzdjF7/odTQQAu2YV7j2/h1WfAmB6XIQz6m5MfEOfk4mEn2qtgyciJwZjDKZ3P2za\nT3CnPwC7vsH92/2Y3v0wl16tE9fFF9Za7ILXsM8/BlWVEBODuWoEzs/P9TuaSNjSDJ5IGDLt2uOM\nm7TvvLw3ZuE+PBa7c4fPySTS2PLd2McnYZ/5u1fukk/CyXlQ5U7kOFPBEwlTplFTnJv/jDn/V97A\nFytw7xmFzV/qbzCJGHb91965oO8v8Aay/gfn9ocxLVr7GUskIugQrUgYM1FRmMt+jZvRDjvzUdi5\nA3fSnZgLLsH0G4yJivY7ooSh0CHZFx6HygpvfbtLBmMuuBTjaF5BpDao4IlEAOeMs7AtM3BnPAhr\n12Dnvoxd9RnOsFswKal+x5MwYkt24c58ZN8tx5ok4Vx3M6btaf4GE4kw+qeUSIQwzU/G+eMDmN79\nvIHC1bj3jMLNm88JcEtqOQHYlZ/gjr9xX7nrnI1zxyMqdyI+0AyeSAQx0dGYAUOxP8vCfWIy7PrG\nW2x2+RK4YjgmQctVyI9nK/ZgZ+di35gF1kJMPe9+yd176a4UIj7RDJ5IBDLtT8e58xFo3xkA+9E7\nuHf+DrvkPZ+TyYnGrlmFO36Ut3CxtdAyHWfsJJyzeqvcifhIM3giEco0bIRz4x3YBXOwLz0JJTtx\np03AnHEWRrN5cgR2Tzn2389g35gN1vUupLjwEszFV2KidfGOiN9U8EQimDEG0+MibPvTcWc+Cp9/\nhv3oHeyqT3EG34A5vZvfEaUOsmtW4T75Fyja4A2c1BLn2psw6W39DSYiISp4IoJp1hznD/dgF87B\nvjQzNJtH52ycy4ZhGjf1O6LUAbYs6J1r99ar35u1uwITHeN3PBHZjwqeiABgHAfT4xfY9p1Ds3ks\nzsNdvhTT90rMeb/Urc4ilLUW+/Ei71ZjO7d7g5q1E6nTVPBE5ACh2bxF87D/908oLcG+8Bg2bz7O\noOsx393+TCKDLdqA++zfIX+ZNxAVjenTH9PnfzVrJ1KHqeCJyEGM42DOvgDb6efYl2Zi330T1n+N\ne/9ob+mLS4dgEhL9jinHkS0vx77+Evb1F6Gy0hs8rRPOlcMxyVocW6SuU8ETkcMyCYmYa27Ennk+\nbu402FDozewtfhdz0QBMz4s1ixNmrOti31+AnfU07Cj2Bhs1xbn813B6tpY+ETlBqOCJyBGZn56K\nM3YS9q1XsK88B2VBb2bv7de82bwzztI9RsOAXfkJ7r8eh3UF3kAg4J17+asrMPXj/A0nIj+KCp6I\nVIuJisL0vgT78x7YV57F/ncubN+K/cdD2HmzcQYOxbRt73dMOQp20zrcfz0Bn328b/D0bjiXXq17\nFYucoFTwRORHMQ0bYQZdjz3vl7gvzfTuO1q4GnfiGGh/Os4vL8e0OcXvmFINtmgD9tUXsB8s9JY9\nAWj9U5wBQ3X/WJETnAqeiBwVc1JLAiPGeof1XnwC1n4Fy5fgLl+iolfHHbLYNU32Drd36a7D7SJh\nQAVPRI6J+Vkmzu0Pw9L3cF95DjYU7it6p3XCufgKFb064pDFrnES5qL+mDN76RZjImFEBU9Ejplx\nHOh8Jk6nbgcWvRVLcVcshZ+einN+X8jqinG0WHJtstbCl/m482bDJx+Atd4TKnYiYU0FT0RqzGGL\n3pf5uF/mQ7PmmJ6/wpzZE1M/1u+4Yc1WVmIXv4udNxsKV+97QsVOJCKo4IlIjTug6K1YijtvFqz8\nBLYWYZ+bjv13LqZ7b8xZvTHNT/Y7blix32zH5s3Hvv0afLNt3xOtMjC9+nrn2EWp2ImEOxU8ETlu\njONAh84EOnTGri/Azvs39sOFECzFvvEy9o2Xoe1p3mxS5zMx9er5HfmEZKuq4LOPcRfN85Y6cb87\nv84Y6HgGTq++0La9FikWiSAqeCJSK0yLdMy1N2EvHYJd8Bp20Tz4Zjt8sQL7xQrsc9MxXc/GZPeE\n9LYqI9Vgi9Zj897C5r0FO7fveyK2Aebn52DOu1gzpCIRSgVPRGqVSWyM6TsI+8vLvattF70Bn37k\n3R1j4evYha97S3Z0PhPTpTu0/onK3n5s0Xrsx+9iP17knd+4v7btMWf1wnTK1myoSIRTwRMRX5hA\nADLPIJB5BnbnDm8m6t03YfMG2LZl3yHcpsmYLmdisn7uzewFIusqXGstbPgau+zDQ5e6xMaY7PO8\nw9y664SIfEcFT0R8ZxIbY/r8L/bCS2HdV9iPF2E/fhe2Fnllb+7L2LkvQ1wDOCUTc1onzGmnY5o2\n8zv6cWFLdmHzl8KKpdj8ZQcefgVo2Ahzejamy5nw01O19IyIHKRaBc91XXJzc1m4cCEVFRVkZmYy\nbNgwEhISDrn9smXLeOqpp9i8eTPNmzdnyJAhdOzYsUaDi0j4McZAqzaYVm2wlwzZV/YW58GWTRAs\nhSV52CV5WIDmLbz737Y5xVtMOfmkE/Jwrt1eDF+twq75HPvlCli7Zt96dXslNsZ06qZSJyLVUq2C\nN2vWLBYvXsyECROIj49n6tSpTJkyhZycnIO23bJlCw899BDDhw+nW7duvPfee0ycOJFJkyaRlJRU\n49+AiISn/csel16N3bIRu2IpdsVSWPUplO+GovXYovXw39e9whffEDLaYTLaYVqmw0ktvUO8deTW\nW9ZabzZu4zrs+q/hq8+xX30OO4oP3jgqCn5yami2khatT8jyKiL+qFbBmz9/PgMGDKBZM+9wyODB\ng7nxxhspLi4+qLQtWLCAjIwMunfvDkD37t2ZN28eCxYsoH///jUcX0QihUlOxSSnQo9fYCsrYM0q\nbP4y7JpVUPAF7CmHb3fBpx9hP/2I0PxXTD04qSUmtaVX+Jo0wzRpBo2bQqMmNb4mnHWrYOc3Xmnb\nUYzdttUrohvXwqZ13izkoQSivLXqMtphfpYF7dprMWgROWpHLHjBYJDi4mLS09NDYykpKcTGxlJY\nWHhQwSssLCQjI+OAsfT0dAoLv3disIjIUTJR0dCuA6ZdB+C7deA2fI1d87l3qLPgS++QrnW94le4\nGrvf3RxC5c8YaNgIEptAbJy3vEhsLNT3viYmxtvOcdgVH0/Vt9/iui5UVkBZ0Lvyd3cw9DW7dnhL\nv+xdh+6HNE2GtJ9g2rTDZJwCaW0w0TE1+0aJSMQ6YsErKysDIC4u7oDxBg0ahJ7b3+7duw/aNi4u\njvXr11c7VElJCSUlJQeMBSLsyrm6ZO97r33gD73/1RAIQHpb7w8XA2Ar9mCLNmA3FGI3rsNuLISi\nDdjtW2H3dz+7rIWdO7w/37GH+N9XATuPJld0DDRJwqSkYlLTMKktMSenYZq3wMTGHfn1EqLPgf+0\nD/y1933fuHFjaCwhIeGw10McseDFxnqHCILB4AHjpaWloef2V79+/YO2DQaDh9z2cObMmcOLL74Y\nejx8+HA++eSTar9eRCQkPgnaJkHbTn4n8ZTugTVf+Z1CRE5Qo0aNCn3dv39/Bg4ceMjtjljw4uLi\nSEpKoqCggLS0NACKioooKysLPd5fWloa+fn5B4wVFBTQoUOHaofv06dP6By+LVu2cO+99zJ58mRS\nU7XGkx82btzIqFGjtA98ovfff9oH/tM+8J/2gb/2vv9jxowhOTkZ4LCzdwDVurSsZ8+ezJ49my1b\nthAMBsnNzSUrK+uQV8Wec845rFmzhry8PCorK3nnnXcoKCjg3HPPrfY3kZCQQGpqKqmpqaFvQkRE\nRCTSJScnhzrSDxW8al1F269fP4LBIDk5OVRWVpKZmcnIkSMBWLRoETNmzGDmzJmAdwHGLbfcwj//\n+U+mTZtGcnIyt956q5ZIEREREaklxtrvr6ZZt5SUlDBnzhz69Onzg01Vjh/tA3/p/fef9oH/tA/8\np33grx/7/tf5giciIiIiP07dWN5dRERERGqMCp6IiIhImFHBExEREQkzKngiIiIiYUYFT0RERCTM\nqOCJiIiIhBkVPBEREZEwo4InIiIiEmZU8ERERETCTLXuResX13XJzc1l4cKFVFRUkJmZybBhw3SL\nlFqSl5fH3Llz+frrr9mzZw/PPvus35EiSm5uLkuWLKG4uJjY2Fg6derEoEGDiI+P9ztaRHnuuedY\ntGgRJSUlREVF0aZNG6688kpat27td7SIYq1l3LhxfPnll0ybNo0mTZr4HSkiTJ06lXfeeYeYmBis\ntRhjGDRoEL179/Y7WsT59NNPef7551m3bh0xMTF069aN66677rDb1+mCN2vWLBYvXsyECROIj49n\n6tSpTJkyhZycHL+jRYT4+HguuOACysvLmT59ut9xIk4gEGDkyJG0atWK0tJSpkyZwtSpU7ntttv8\njhZRzj77bPr27UtsbCx79uzhueee48EHH2TKlCl+R4so//nPf6hfv77fMSLSueeey/Dhw/2OEdFW\nrFjBpEmTuP766+ncuTPWWtavX/+Dr6nTh2jnz59Pv379aNasGbGxsQwePJhly5ZRXFzsd7SI0LFj\nR7Kzs0lJSfE7SkS6/PLLad26NY7jkJCQQJ8+fcjPz/c7VsRJTU0lNjYW8I4qGGNo2rSpz6kiy8aN\nG5k3bx5XXXWV31FEfPHss8/Sq1cvunbtSiAQICoq6ohHEersDF4wGKS4uJj09PTQWEpKCrGxsRQW\nFpKUlORjOpHa99lnn5GWluZ3jIi0aNEi/vGPf1BWVkbLli0ZO3as35EihrWWv/3tbwwZMoS4uDi/\n40SkDz74gA8//JCEhAS6dOlC//79NZtai8rLy1m9ejXt2rVj9OjRFBcX06pVK6666ioyMjIO+7o6\nO4NXVlYGcNAHukGDBqHnRCLF+++/z5tvvsm1117rd5SI1L17d5588kmmT59OixYtmDhxot+RIsar\nr75K48aN6dKli99RIlKfPn2YPHkyjz32GLfccgv5+fk6ZaeWlZaWYq0lLy+PESNGMH36dDp27MiE\nCRMIBoOHfV2dLXh7D4l8P3xpaWnoOZFI8N577zFjxgxGjx6tE/t9lpiYyNChQ1m9evURz3+RY1dU\nVMSrr77K0KFDAW82T2pXeno6DRs2BKBFixZcc801vP/++1RWVvqcLHLsnS3t0aMHLVu2JBAIcMkl\nl1BZWckXX3xx2NfV2UO0cXFxJCUlUVBQEDosVVRURFlZmQ5TScR4++23efrppxk9ejRt27b1O45A\n6BebDlEdf6tWrWLXrl3cfPPNWGtDBe/WW2/lsssu05WcEhHi4uJo1qzZQePGmB98XZ0teAA9e/Zk\n9uzZnHrqqcTHx5Obm0tWVpbOv6slrutSVVVFRUUFQOi/0dHRfsaKGK+99hovvfQSt99++w+eZyHH\nj7WWuXPnkp2dTcOGDdm2bRtPPPEEp5xyin4O1YLs7Gw6duwYerxt2zbGjh3L2LFjSU1N9TFZ5MjL\nyyMrK4u4uDg2bdrEU089RZcuXYiKqtP1Iez07t2bOXPmkJ2dTWpqKq+88grR0dG0a9fusK8xtg7P\nebuuyzPPPMPbb79NZWUlmZmZ/OY3v9E6YLVkwYIFTJs27aDxv/71r/rlVgsuu+wyAoFAqFDvXYNq\n5syZPieLHNZa7rvvPr766ivKy8tJSEigU6dODBw4MHTYSmrP1q1bGTFihNbBq0V33303a9eupaKi\ngsTERLp27cqAAQM0g+2DF154gTfffJOKigrS09O5+uqrf/CIZp0ueCIiIiLy49XZiyxERERE5Oio\n4ImIiIiEGRU8ERERkTCjgiciIiISZlTwRERERMKMCp6IiIhImFHBExEREQkzKngiIiIiYeb/Aer4\nmHqAIY38AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff2fcc482b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = 1.\n",
    "mu = 3\n",
    "x = np.linspace(0,6, 100)\n",
    "dist = (mu - x)**2 / (2 * sigma**2)\n",
    "\n",
    "plt.plot(x, dist)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V2MWvYSZ+x3UkEWlmFyyANTU1AGRlZZ2xPzs7O/q1xjz33HOEQiFWrVrFU089xdVXX023\nbt2AyK9/e/bsCcDatWv55S9/ySOPPEJBQUFMoauqqqiqqjpjXyCg+4S60vDeawzcSdQxCK9cAp//\nGYC0qX+Dl57uNtAlStT3P6pTF0IjJ+IvKcGWvoI3fHzCXYeZ8GOQBDQGbjW873v37o3uy8nJaXS+\nBsRQABsmZlRXV5+x/+TJkxectJGWlsawYcNYuXIlK1asiBbAPn36RI8ZMmQImzdvZvny5TEXwNLS\nUubNmxfdnjFjxjnPRErL0Ri4l0hjYGtP8cWfIsu+BG8tIrcw8a89S6T3/+vC3/979r27FP/EcVq9\n/TpX/uBHriNdkkQeg2ShMXDr4Ycfjj6ePHky9957b6PHXbAAZmVlkZuby86dO+natSsA+/bto6am\nJrp9Ib7vk5mZGdOxsRg/fjyFhYXR7YqKCiorKwmHdWNzFwKBALm5uRoDhxJxDMKLXydcuR+MR2jC\nFPbv3+860iVLxPe/MWbcXTDvt5wofY1Tw27H5F7lOlLMkmUMEpnGwK2GM4CzZs2K7jvX2T+IcRZw\nUVERJSUl3HDDDbRu3Zq5c+fSt2/fRlv+mjVruPrqq7nmmmsIh8OUl5ezdetW7r//fgA+++wzTp06\nRbdu3TDGsG7dOpYvX84//MM/xPwiv35Ks6KignA4rL9wjmkM3EuUMbCnvsT/0x8AMENG4ud1iMwC\nTnCJ8v6fix1xO7z1GlQdI1QyF++v/t51pIuW6GOQDDQGbnXs2DGm42IqgMXFxVRXVzNz5kxCoRAF\nBQU89NBDAKxYsYLZs2fz/PPPA3DkyBFefPFFjh49SkZGBl26dOHHP/4xnTt3BuD48ePMmTOHgwcP\nkpaWRn5+Pg8++CD9+/e/lNcpIgnIvv0mVB2DQJomHMQR0yoTc/s92D8+i139Nnbc3ZgOnS78jSKS\ncIxNgvVYysrK6NOnj37icCQQCJCfn8/+/fs1Bo4k0hjY6pP4M6dD9QnMiNvxvvu3riNdtkR6/y/E\n1tXi/99/C0cqMQOH4U3/Z9eRYpJMY5CoNAZuBQIBNm/eTFFRUUzHa8l3EWlRdklJ5JZv6RmYCfe4\njiNfY9IzMBMjF43b95Zj62dpi0hyUQEUkRZjTxzHLi4BwIy8HXNFe8eJpDFmyGjI6wDW4r/+ous4\nItIMVABFpMXYha/ClzXQKogZd7frOHIOJi0Nc8fUyMb6d7F//sRtIBFpciqAItIi7LEj2KV/AsCM\nvgOT09ZxIjkfM2gYXB2ZvOeXzHWcRkSamgqgiLQIu+BlqK2FrGzM2GLXceQCjBfAm3RfZGPzB9hP\nPnIbSESalAqgiDQ7e+ggdtlCAMzYb2OyWjtOJDHpNxg6R+4D78//HUmwaISI1FMBFJFmZ0tfhlAI\nctpiiu5wHUdiZDwPr3haZGPbFvj4Q7eBRKTJqACKSLOyRw9hVy4BwNz2bUzm+e8hLnHmxpuh63UA\n+AtedhxGRJqKCqCINCu7aH7k7F92Dmb4ONdx5CIZY/Dq1wWkYiP2061uA4lIk1ABFJFmY6uOY8vr\nr/0rugOTmeU4kVySmwZCp66AzgKKJAsVQBFpNnbJ61B7CjKDmFETXceRS2Q8D3N7/V1bNr2H3b3D\nbSARuWwqgCLSLGz1ia/W/Rt5OyZbM38Tmbn5VriqI1C/pI+IJDQVQBFpFnbpAqiphowMzOhJruPI\nZTJeAHP7ZADsB6uwX3zuOJGIXA4VQBFpcvbUl9gl9ff8HXobps0VjhNJUzCDRkC7PLA2srSPiCQs\nFUARaXK2fCGcqIJAGmbst13HkSZi0tKi93C2a8qxB/c5TiQil0oFUESalK2rjSz9ApghozDtch0n\nkqZkCkdD2yvB97ELX3UdR0QukQqgiDQpu7IMjh0Gz8OMn+w6jjQxk56BGRO5l7NdtQR75JDjRCJy\nKVQARaTJ2FAIu/AVAMzAYZi8Do4TSXMww8dBdg6EQthFr7mOIyKXQAVQRJqMfW85HDoAoLN/Scxk\nBjGjI/d0tssWYk8cd5xIRC6WCqCINAlrLfat+mvC+t6C6djFbSBpVmbkRGgVhNpa7DsLXMcRkYuk\nAigiTWPLetizCwDvNs38TXYmuzVm6BgA7NtvYmtPOU4kIhdDBVBEmoTfcC3YtT0x1/VyG0ZahBl9\nJ3geVB3DvrvUdRwRuQgqgCJy2ezuT6FiIwDebXc5TiMtxbS/CnPzUADsohKs7ztOJCKxUgEUkcvW\nsO4fV3WEggFuw0iLMrdFloRh/x7YtNZtGBGJmQqgiFwWe+hgZPYvYMYWY7yA40TSkkyXa6FXAQD+\nW1oSRiRRqACKyGWxZa+D70NOW8zgka7jiAPe2PqzgNsrsJ9udRtGRGKiAigil8xWn8AuWwSAGTkB\nk9HKcSJxond/6NQVOG0ykIjENRVAEblktvwtOFUDGRmYEbe7jiOOGGMwDWcB17+L3b/XbSARuSAV\nQBG5JDZUhy17AwAzZDQmp43jROKSGTgMrmgH1mKXlLiOIyIXoAIoIpfErlkGxw6DMZgxd7qOI46Z\ntHRMUf3t4VaWYauOOU4kIuejAigiF81ai2241qvfYMxVHd0Gkrhgho2DzCDU1WKX6vZwIvFMBVBE\nLt6W9bB3N6DbvslXTFY2ZthtANilb2Lrah0nEpFzUQEUkYvml70eeXBtT8w3vuk2jMQVM+qOyO3h\nThzHril3HUdEzkEFUEQuiv3ic9j8AQCmSNf+yZlM+zzodwsAtuwNrLWOE4lIY1QAReSi2LcjM39p\nl4vpP9htGIlL3uj6Hww+/zN8/KHTLCLSOBVAEYmZPXkCu+ptAMyICZiAbvsmjbi2F3S9DgC/fqkg\nEYkvKoAiEjO7YhHUnoos/DxsrOs4EqeMMZjRkSVh2LgWe+ALt4FE5CwqgCISExsOY99+EwAzeBQm\nO8dxIoln5uZCaHtlZGHopW+6jiMiX6MCKCKx2fAuHD4IEF3wV+RcTFo6ZsR4AOyKxdiaaseJROR0\nKoAiEhN/Sf3SL737Ya7u7DaMJAQzbBykpcOXNdhVZa7jiMhp0mI5yPd95s6dS3l5OXV1dRQUFDB9\n+nRycs7+FdDWrVt57rnnOHjwIL7v0759e8aOHcttt90WPWbfvn3Mnj2bbdu20bp1ayZMmMDEiROb\n7lWJSJOyf/4EtlcA4GnpF4mRaXMFZtCwyK3hyt7AjpyA8XTeQSQexPRJnD9/PuvWreOxxx7jmWee\nwVrLk08+2eixHTt25JFHHmHOnDn89re/5fvf/z4vvPACFRWR/zx83+cXv/gFnTt3Zs6cOfzwhz+k\npKSE1atXN92rEpEmZRtmcnboBL37uQ0jCSW6VuTBffDh+27DiEhUTAWwrKyM4uJi8vLyCAaDTJs2\njQ0bNlBZWXnWsW3atCE3NxeI3C/UGENaWhpt2rQB4KOPPqKyspKpU6eSnp5O9+7dGT16NIsXL27C\nlyUiTcUePYx9bwUQucuDzuDIxTCdu8M3bwS0JIxIPLngr4Crq6uprKyke/fu0X35+fkEg0F27doV\nLXtf99d//decOnWKQCDAgw8+SKdOnQDYvXs3HTt2pFWrVtFju3fvzqJFi2IOXVVVRVVV1Rn7AlqP\nzJmG915j4E5zjkFo2UIIhyArm7TC0Vr7rxH6DJyfGTuJ0McfQsVGzBef4V3Trcn/DI2BexoDtxre\n971790b35eTkNHq5HsRQAGtqagDIyso6Y392dnb0a4157rnnCIVCrFq1iqeeeoqrr76abt26UVNT\n0+hzVVfHPkOstLSUefPmRbdnzJhxziIqLUdj4F5Tj4GtPcXeZW8BkDPuLq7o2q1Jnz/Z6DPQODvm\nDr546TnC+/fQauVi2v39vzbbn6UxcE9j4NbDDz8cfTx58mTuvffeRo+7YAEMBoMAZxW0kydPRr92\nLmlpaQwbNoyVK1eyYsUKunXrRjAYbPS5vl4Kz2f8+PEUFhZGtysqKqisrCQcDsf8HNJ0AoEAubm5\nGgOHmmsMwqvexj92BIzHl7eMZP/+/U323MlEn4EYjBwPf3iWk0tLqZ3wHUzrpl1HUmPgnsbArYYz\ngLNmzYruO9fZP4ihAGZlZZGbm8vOnTvp2rUrEJnFW1NTE92+EN/3yczMBKBr167s3buX2tpaMjIy\nANixY0fMzwVnn9KsqKggHA7rL5xjGgP3mnoMwg3XbBUMxL8yFzS+56XPwLnZwaPg1d9B7SlCy9/C\nG/vtZvlzNAbuaQzc6tixY0zHxXQ1d1FRESUlJRw4cIDq6mrmzp1L3759Gz3Nu2bNGnbv3o3v+9TV\n1bFkyRK2bt3KoEGDAOjVqxd5eXm8+OKL1NbWsnPnTsrKyhgzZsxFvDwRaW525zbYuQ0Ab+TtjtNI\nojNZrTG3jADAvlOK9VUQRFyKaR3A4uJiqqurmTlzJqFQiIKCAh566CEAVqxYwezZs3n++ecBOHLk\nCC+++CJHjx4lIyODLl268OMf/5jOnSMLx3qex49+9CN+/etf88ADD5Cdnc2kSZMYPHhwM71EEbkU\n0dt3degEvQrchpGkYEbejl32VmRJmM0fwE0DXEcSSVkxFUDP85g2bRrTpk0762uFhYVnXI83btw4\nxo0bd97ny8/P59FHH73IqCLSUmzVMex7ywEwIydgjHGcSJKBuaY79OgN27bgL32TgAqgiDNa0EtE\nzmJXLIZQCFoFMYNHuY4jScSMmBB5sPkD7IG95z9YRJqNCqCInMGGw9h3SgEwQ0ZigrHP0Be5ENPv\nFmjbDgC7tNRxGpHUpQIoImfa9B4cPgiAGaHJH9K0TFoaZnjkMiG7cgn21JeOE4mkJhVAETmD3zD5\no+dNmI5d3IaRpGSG3QaBNKg5iV3zjus4IilJBVBEouwXn0HFRgC8kRMcp5FkZdpeiekfWfnBLl2A\ntdZxIpHUowIoIlF26YLIg3a5UDDQbRhJamZU/Q8Yn/8ZPvnIaRaRVKQCKCIA2Jpq7Kq3ATDDx2N0\nQ3dpTtf2gs7dgdPWnBSRFqMCKCIA2HeXwqkaSEvDDB3rOo4kOWMMpv4yA7t+NfboIceJRFKLCqCI\nYK2N/vrX3DwUk9PWcSJJBWbgcMhqDeEwtvwt13FEUooKoIjAts3wxWdA5HZdIi3BtGqFKRwNgF2+\nCBsKOU4kkjpUAEUkuvAzXa6F7j3chpGUYobV3zr02GHYuNZtGJEUogIokuLssSPY9asBMCPG676/\n0qJMfke4oS8AfrnuDCLSUlQARVKcXbEYwmEIZmMGDnMdR1KQN3x85EHFRuy+PW7DiKQIFUCRFGb9\nMHbZQgDM4JGYVpmOE0lKKhgIV7QHwJYvdBxGJDWoAIqksk3vw+FKgOj9WUVamgkEoksP2VVLsKdO\nOU4kkvxUAEVSWPSaqx59dN9fccoMHQueB9Unse8vdx1HJOmpAIqkKHtwH2xZD4AZoaVfxC1zZXvo\newtw2qx0EWk2KoAiKcqWLwRroc0VmH6DXMcRwRtRPxnkz59gd213mkUk2akAiqQgW1eHXbkEAFM4\nFpOW7jiRCNDzJsjvBOgsoEhzUwEUSUF23Uo4cRyMhxl2m+s4IkD9/YHrJyPZteXY6hOOE4kkLxVA\nkRRkGyZ/3HQzpn2e2zAipzFDRkF6BtTWYlcvdR1HJGmpAIqkGPv5TtheAZy2AK9InDDZOZgBQ4HI\nr4GttY4TiSQnFUCRFBO9tio3H3r3cxtGpBGmYTLIvs/h4w/dhhFJUiqAIinEflmNfbccADNsHMbT\nPwESh7pdD12vA3RnEJHmon/9RVKIXbsMTtVAIA1TONp1HJFGnTEZZP272ONHHCcSST4qgCIpwlob\nPZti+g/G5LR1nEjk3MyAoZAZhHAIu7LMdRyRpKMCKJIq/rwddu8AwGjyh8Q5kxnE3DISALvsLazv\nO04kklxUAEVShF1Wfy1Vh2ugR2+3YURiYIbXr1FZuR8+2uA2jEiSUQEUSQG2+mTk+j8i/6kaYxwn\nErkwc013uLYnAP4yTQYRaUoqgCIpwK55B2pPQVo6ZvAo13FEYha9U83Gtdijh9yGEUkiKoAiSe6M\nyR8DCjHZOY4TicTO3FwIWdng+9gVi13HEUkaKoAiye7TrbBnFxBZ+08kkZiMVtGz1nbZImw47DiR\nSHJQARTEW0UfAAAgAElEQVRJctGFdDt1jV5PJZJIGtYE5EglbF7nNoxIklABFEli9mQV9v0VQOQ/\nUU3+kERkru4cnbnu684gIk1CBVAkidlVb0OoDjJaYQaNcB1H5JJFL1/YvA576IDbMCJJQAVQJElZ\na6Nr/5mBwzBZ2Y4TiVw6038ItG4D1mKXL3IdRyThqQCKJKttm2HfHuC0a6hEEpRJT8fcWgSAXbEY\nGwo5TiSS2FQARZJUdPJHl2sx3a53mkWkKUTXBDx2BDaudRtGJMGpAIokIVt1DPvBauC022mJJDhz\nVUfoVQCAv+wtx2lEEpsKoEgSsqvKIByCVkHMwGGu44g0Ga/hLOBH67EH97kNI5LA0mI5yPd95s6d\nS3l5OXV1dRQUFDB9+nRycs6+o8D69et544032LVrF9ZaOnfuzNSpU+nZ86v1x6ZMmUJGRgae52Gt\nxRjDM888QzAYbLpXJpKirO9j68+OmEHDMZlZjhOJNKG+gyCnLVQdwy5fhLnrfteJRBJSTAVw/vz5\nrFu3jscee4zWrVvz1FNP8eSTTzJz5syzjj158iTjx4+nd+/eZGZmsmTJEn7+858za9Ys2rVrFz3u\n0UcfpUePHk33SkQk4uMP4cAXwGnXTIkkCZOWjrl1NHbhK9iVS7B33odJi+m/MhE5TUy/Ai4rK6O4\nuJi8vDyCwSDTpk1jw4YNVFZWnnVsYWEhAwYMICsrC8/zGDt2LJmZmWzfvv2M46y1TfMKROQMDWf/\n6Hodpuu1bsOINAMzdGzkwfGjsHGN2zAiCeqCPzZVV1dTWVlJ9+7do/vy8/MJBoPs2rWL3Nzc837/\n7t27qaqqokuXLmfsf+KJJwiFQnTo0IFJkyYxcODAmENXVVVRVVV1xr5AIBDz90vTanjvNQbuNLz3\n3skq7Pp3I/tG3q4xaSH6DLSwq6+hrnc/7Jb12OWLSBs4TGMQBzQGbjW873v37o3uy8nJafRyPYih\nANbU1ACQlXXmdUTZ2dnRr53LsWPHePzxx7nzzjvp0KFDdP+jjz4avSZw7dq1/PKXv+SRRx6hoKDg\nQnEAKC0tZd68edHtGTNmXLCISvPTGLjXat0KvgyHMMFsOkycjBfU9X8tSZ+BllM96Tsc2rIeu2U9\n7f060vLzAY1BPNAYuPXwww9HH0+ePJl777230eMuWAAbJmZUV1efsf/kyZPnnbRx+PBhfvazn9G3\nb1+mTp16xtf69OkTfTxkyBA2b97M8uXLYy6A48ePp7CwMLpdUVFBZWUl4XA4pu+XphUIBMjNzdUY\nOBQIBGjfrh3HF7wCRCZ/HDxeBcerLvCd0hT0GWh5tltPaHMFHD/K/lf+m1bf+b7GwDF9DtxqOAM4\na9as6L5znf2DGApgVlYWubm57Ny5k65duwKwb98+ampqottfd+DAAX76058yaNAgpk2bdlEvIBZf\nP6VZUVFBOBzWXzjHNAZundr4HrZ+8gdDx2osHNBnoAUZE5kMUjoPf8ViQt+O/F+jMXBPY+BWx44d\nYzoupkkgRUVFlJSUcODAAaqrq5k7dy59+/Zt9DTvnj17+MlPfkJhYWGj5e+zzz5j+/bthEIhwuEw\na9euZfny5QwZMiSmwCLSuBOlr0YedLse0+UbbsOItAAzdCwYE1kSpv7aVxGJTUxz54uLi6murmbm\nzJmEQiEKCgp46KGHAFixYgWzZ8/m+eefB6CkpITDhw+zYMEC3nzzTQCMMUyfPp3CwkKOHz/OnDlz\nOHjwIGlpaeTn5/Pggw/Sv3//ZnqJIsnPHjtCzbvvAFr6RVKHyesAN/SFLesJv1MKEye7jiSSMIxN\ngvVYysrK6NOnj045OxIIBMjPz2f//v0aA1cWvkL4lechM4j3n89jWmW6TpRS9Blwx36wCv/p/w+A\nDrNf43AgQ2PgiD4HbgUCATZv3kxRUVFMx+tWcCIJzvo+4fq1/7zBI1X+JLXcNBDaXgnAyYWvOQ4j\nkjhUAEUSXcVGqL8nqjd8vOMwIi3LpKVhbh0DwMklb2Dr6hwnEkkMKoAiCc6vP/uX0aM3niZ/SAoy\nQ8eAMfjHjuBrMohITFQARRKYPXYkeius7PF3OU4j4obJzcf0jkwk9MtLHacRSQwqgCIJzK5YDOEw\nBLPIGjbWdRwRZwIjIpc/2IqN2P17L3C0iKgAiiQo6/vY5YsA8AaPwss89515RJKdKRhIoH0eALb+\nsggROTcVQJFE9dEGOHQAAG+EJn9IajOBANljJgFgV5VpMojIBagAiiQof9nCyINvfBPvmm5Os4jE\ng+zbJkXuDHLiOHb9atdxROKaCqBIArJHD8HGtQCYYeMcpxGJD2lXXY258VuAfg0sciEqgCIJyK4s\nA9+HYDbm5kLXcUTiRqBhLcyPP8Tu+9xtGJE4pgIokmCsH45O/jCDR2JatXKcSCR+mJsGwBXtAZ0F\nFDkfFUCRRLPlq8kfZthtjsOIxBcTCGAKI3cGsavfxtbVOk4kEp9UAEUSTMOdP7i2J6ZTV7dhROJQ\n5M4gHpyown6gySAijVEBFEkg9ugh2KTJHyLnY9rlQXQyyELHaUTikwqgSAKxKxZHJn9kZWNuvtV1\nHJG45TX8gLRtC/aLz9yGEYlDKoAiCeLMyR+jMBma/CFyTn36w5W5gCaDiDRGBVAkUWxZD4crAU3+\nELmQMyaDrHobW3vKcSKR+KICKJIg/PL6a5muuwHTsYvbMCIJwBTWTwapPoFdt8p1HJG4ogIokgDs\n4YOw6X0AzHCd/ROJhWmXCzfdDGgyiMjXqQCKJAC7fDFYH7JzMN/S5A+RWHkNdwbZXoHds8ttGJE4\nogIoEudsOIxdUT/5Y8goTHqG40QiCaR3X2h/FQC2XGcBRRqoAIrEu03vwdHDgCZ/iFws4wUwQ8cC\nYN99B3vqS8eJROKDCqBInPMbrl365o2YDte4DSOSgEzhGAgEoOYk9r3lruOIxAUVQJE4Zg/uiyz/\nApiGa5lE5KKYtldC30GA1gQUaaACKBLH7PJFYC3ktMX0G+Q6jkjCit4ZZOc27O5P3YYRiQMqgCJx\nyobqIrd+A8ytozFp6Y4TiSSwnjdBXgcAbLnOAoqoAIrEqw1roOoYoMkfIpfLeB5meOQsoF1Tjv2y\n2nEiEbdUAEXilN9wrdIN/TD1Zy5E5NKZIUWQlganarBrlrmOI+KUCqBIHLL790LFRgC8+rMWInJ5\nTE5bTP8hQOTOINZax4lE3FEBFIlD0ZmKbdvBTQPchhFJIqZhMsjuHfDnT9yGEXFIBVAkzti6Wuyq\nJQCYoWMwaWmOE4kkkR69oX49Td0ZRFKZCqBInLHrVsGJKjAGUzjWdRyRpGKMwQyPTKqy7y3DVp9w\nnEjEDRVAkThjy0sjD268GdM+z20YkSRkBo+C9AyorcWuXuo6jogTKoAiccR+/mfYXgGAN0J3/hBp\nDiY7BzNgKBD5NbAmg0gqUgEUiSPRs3/tr4Le/dyGEUlipuEHrC8+g22b3YYRcUAFUCRO2C+rsavf\nAcAMH4fxAm4DiSSzbtdDl2sBsO+UOg4j0vJUAEXihF2zDE7VQCANc+to13FEkpoxJnoW0K5fjT12\nxHEikZalAigSB6y10bMQ5ltDMG2ucJxIJPmZgcMgmAXhcPS+2yKpQgVQJB7s+Bg+3wkQvV+piDQv\n0yoTc8tIILL4uvXDjhOJtBwVQJE4EL0GqWMXuL632zAiKcQMr58McvggfPiB2zAiLSimWwz4vs/c\nuXMpLy+nrq6OgoICpk+fTk5OzlnHrl+/njfeeINdu3ZhraVz585MnTqVnj17Ro/Zt28fs2fPZtu2\nbbRu3ZoJEyYwceLEpntVIgnEnjiOfX8FUD/5wxjHiURSh+nUJXJ3kG1b8MtLCRTo1ouSGmI6Azh/\n/nzWrVvHY489xjPPPIO1lieffLLRY0+ePMn48eP51a9+xbPPPsutt97Kz3/+cw4fPgxEyuQvfvEL\nOnfuzJw5c/jhD39ISUkJq1evbrpXJZJA7KoyCNVBRqvor6NEpOVEzwJuXoc9uM9tGJEWElMBLCsr\no7i4mLy8PILBINOmTWPDhg1UVlaedWxhYSEDBgwgKysLz/MYO3YsmZmZbN++HYCPPvqIyspKpk6d\nSnp6Ot27d2f06NEsXqwLcCX1WN+P3o/UDBqOycp2nEgk9Zj+gyGnLViLXf6W6zgiLeKCvwKurq6m\nsrKS7t27R/fl5+cTDAbZtWsXubm55/3+3bt3U1VVRZcuXaLbHTt2pFWrVtFjunfvzqJFi2IOXVVV\nRVVV1Rn7AgGtmeZKw3uvMbh4/tZN+Ae+ACAwaiLeJb6HGgO39P67d1ljEAgQGnYb/psvYVcswSv+\nC0x6ehMnTH76HLjV8L7v3bs3ui8nJ6fRy/UghgJYU1MDQFZW1hn7s7Ozo187l2PHjvH4449z5513\n0qFDh+jzNfZc1dXVF4oSVVpayrx586LbM2bMuGARleanMbh4lbPLCAEZ3+xD/sAhl/18GgO39P67\nd6ljELp7Gl8seBmqjpGzfTPZIzQb/1Lpc+DWww8/HH08efJk7r333kaPu2ABDAaDAGcVtJMnT0a/\n1pjDhw/zs5/9jL59+zJ16tQznq+x5/p6KTyf8ePHU1hYGN2uqKigsrKScFhT+F0IBALk5uZqDC6S\nPVJJ3ZpyAMKFY9i/f/8lP5fGwC29/+5d/hgEMDfejN30HkdKfs+JXroV48XS58CthjOAs2bNiu47\n19k/iKEAZmVlkZuby86dO+natSsQmcVbU1MT3f66AwcO8NOf/pRBgwYxbdq0M77WtWtX9u7dS21t\nLRkZGQDs2LHjnM/VmK+f0qyoqCAcDusvnGMag4vjL10Avg/ZOdj+Q5rkvdMYuKX3373LGQMzfBx2\n03vYbVsI7foUc023pg2XIvQ5cKtjx44xHRfTJJCioiJKSko4cOAA1dXVzJ07l759+zZ6mnfPnj38\n5Cc/obCw8KzyB9CrVy/y8vJ48cUXqa2tZefOnZSVlTFmzJiYAoskAxuqwy6LXGxubh2NyWh1ge8Q\nkWbXpz/k5gNgly5wHEakecW0DmBxcTHV1dXMnDmTUChEQUEBDz30EAArVqxg9uzZPP/88wCUlJRw\n+PBhFixYwJtvvglE7rk4ffp0CgsL8TyPH/3oR/z617/mgQceIDs7m0mTJjF48OBmeoki8cd+sBqO\nH4XT7kcqIm4ZL4AZMR4777fYNe9g7/5LzcyXpGWstdZ1iMtVVlZGnz59dMrZkUAgQH5+Pvv379cY\nxCj8i3+B7R/BjTcT+Pv/57KfT2Pglt5/95pqDOyJ4/g//B7U1WK+Mx2v6I4mTJnc9DlwKxAIsHnz\nZoqKimI6XreCE2lh9rOdkfIHeCNvd5xGRE5nWrfBDBgKRH4NbH3fcSKR5qECKNLC7NLIpRHkdYDe\n/d2GEZGzmIYfzPbvga0b3YYRaSYqgCItyFafwNYv/WKGj8d4+giKxBvT7Xro3gOon60vkoT0v49I\nC7KryqD2FKRnYApHu44jIudgRtSfBdz4HvbQQbdhRJqBCqBIC7G+j11aCoAZOAyTfe4FOkXELTOg\nEFq3Aetjy0tdxxFpciqAIi2lYiMciNyj0Yyc4DiMiJyPSc/AFEbWp7UrFmPr6hwnEmlaKoAiLcRv\nmPzxjW9iul7rNoyIXJAZPg6Mgapj2HUrXMcRaVIqgCItwB46AJveB06bYSgicc3k5sNNAwDdGUSS\njwqgSAuw5aVgfchpi/lWoes4IhIjr2EyyI6Psbs+dZpFpCmpAIo0M1tXi12+GABTOAaTnu44kYjE\n7Ia+cNXVANilf3IcRqTpqACKNDO7djmcOA7GwwzXfX9FEonxvOhlG3bNMmzVcceJRJqGCqBIM7LW\nYt9+I7LR7xZM+zy3gUTkopkho6FVJoTqsMvfch1HpEmoAIo0p+0VsHsHAF7RRMdhRORSmKxszJBR\nANh3SrGhkONEIpdPBVCkGdmy+rN/13SH63u7DSMil8yMrP8B7kglbHjXbRiRJqACKNJM7OGD2PWr\nATBFEzHGOE4kIpfKXH0N9O4HgF+mySCS+FQARZqJfacUfB9a52AGDnMdR0Quk1d0R+TB9o+wu7Uk\njCQ2FUCRZmBrT0UvFjdDb8NktHKcSEQuW+/+Xy0J87bOAkpiUwEUaQZ27TI4UQWehxmhpV9EkoHx\nPMyoyLWAkSVhjjlOJHLpVABFmpi1Flt/jZDpNxjTTku/iCQLM6QIWgUjS8Is05IwkrhUAEWa2idb\n4POdAJiGa4ZEJCmYYBbm1iJAS8JIYlMBFGli0RmCnbvDdb3chhGRJmdGTog8OHoIu15LwkhiUgEU\naUL20MHoGmGm6A4t/SKShEyHTtCnP8BXd/oRSTAqgCJNyJYvqF/6pY2WfhFJYt6ohiVhKrC7tCSM\nJB4VQJEmYk99iV22CAAzdCwmPcNxIhFpNr37wVUdAbBlrzsOI3LxVABFmohd/TacrIJA4KtrhEQk\nKRnPw4yOnAW0a5djjx52nEjk4qgAijQB6/vYJZFrgcyAoZgr2ztOJCLNzQwpgqzWEA5hly5wHUfk\noqgAijSFD9fB/j0AmNGTHIcRkZZgWmViht0GgC0vxZ465TiRSOxUAEWagL94fuRBjz6Yrte6DSMi\nLcaMnACBAJysilwGIpIgVABFLpPdvQM+/hAAb8ydjtOISEsy7XIx3yoEIpNBrO87TiQSGxVAkctk\nl5REHlx1Ndw0wG0YEWlxpuEHv317YPM6t2FEYqQCKHIZ7NHD2LXLATCj78R4AceJRKSlmW7XQ4/e\nAPhLtCSMJAYVQJHLYJcugHAIsrIxg0e5jiMijngNk78qNmI/2+k2jEgMVABFLpE9dQq7rBQAM2wc\nJjPoOJGIOFMwAPI6AGB1FlASgAqgyCWy7y6FE1r4WUTAeAFMUeRaQLu2HHvsiONEIuenAihyCSIL\nP0d+yjffKsS0y3WcSERcM7cWQTAbQiHsO1oYWuKbCqDIpdjyAez7HDhtBqCIpDSTGcQMGwuAfacU\nW6uFoSV+qQCKXAJ/Uf3Cz9ffgOl2vdMsIhI/zKiJ4Hlw4jh29VLXcUTOSQVQ5CLZXdth6yYAvDHF\njtOISDwx7fIwNw8FwC6aj/XDjhOJNE4FUOQi2bdeizzo0AkKBroNIyJxx9z27ciDA3thwxq3YUTO\nQQVQ5CLYg/uw768EwIz9NsbTR0hEzmS6fANu6AeAv/BVrLWOE4mcLS2Wg3zfZ+7cuZSXl1NXV0dB\nQQHTp08nJyfnrGMPHz7Ms88+y65du6isrOShhx6isLDwjGOmTJlCRkYGnudhrcUYwzPPPEMwqHXU\nJL7ZxfPB+tD2SswtI13HEZE45Y27C/+j9bBzG3yyBXr0cR1J5AwxFcD58+ezbt06HnvsMVq3bs1T\nTz3Fk08+ycyZM8861vM8+vbtS3FxMbNmzTrncz766KP06NHj0pOLtDBbdQy7cgkApuhOTHq640Qi\nErd63gRdroXdn+IvfJWACqDEmZh+f1VWVkZxcTF5eXkEg0GmTZvGhg0bqKysPOvYK664grFjx9Kj\nRw+MMed8Tp0Sl0Rjl74JtbWQGcQMv811HBGJY8YYzLi7Ihsfvo/ds8ttIJGvueAZwOrqaiorK+ne\nvXt0X35+PsFgkF27dpGbe2kL4D7xxBOEQiE6dOjApEmTGDgw9ovpq6qqqKqqOmNfIBC4pBxy+Rre\n+2QeA3vqS8JLIwu7eiPGk5bT1m2gr0mFMYhnev/di8cx8AYMpe7VF6ByPyyeT+CBf3QdqVnF4xik\nkob3fe/evdF9OTk5jV6uBzEUwJqaGgCysrLO2J+dnR392sV69NFH6dmzJwBr167ll7/8JY888ggF\nBQUxfX9paSnz5s2Lbs+YMeOSi6g0nWQeg6o3/sjRE8chLY38qQ+QlpvvOlKjknkMEoHef/fibQyq\n7vlLjj79H/jvvkP7v/nHuP23oynF2xikmocffjj6ePLkydx7772NHnfBAtgwMaO6uvqM/SdPnrzk\nSRt9+nx1LcSQIUPYvHkzy5cvj7kAjh8//oyJJRUVFVRWVhIOa70lFwKBALm5uUk7BjYcpm7eCwB4\ng0ZwKAzs3+821Nck+xjEO73/7sXrGNibBkHrNnDiOPtffJa0Kd93HanZxOsYpIqGM4Cnz78419k/\niKEAZmVlkZuby86dO+natSsA+/bto6amJrrd0r5+SrOiooJwOKy/cI4l6xj4a5dFfoUDMKY4rl9j\nso5BotD7717cjUFaOmbkBOwbv8d/ZyGh2+/BZLV2napZxd0YpJiOHTvGdFxMk0CKioooKSnhwIED\nVFdXM3fuXPr27XvO07x1dXXU1tYCEAqFqKurw/d9AD777DO2b99OKBQiHA6zdu1ali9fzpAhQ2IK\nLNKSrLXYt16NbNx4M6ZTF7eBRCThmJETICMDTtVgyxe6jiMCxLgMTHFxMdXV1cycOZNQKERBQQEP\nPfQQACtWrGD27Nk8//zz0eOnTZsWffz000/z9NNPc8899zB58mSOHz/OnDlzOHjwIGlpaeTn5/Pg\ngw/Sv3//Jn5pIk2gYiPs3gFE1vUSEblYJqcN5tYx2KVvYpe8jh19JyY9w3UsSXExFUDP85g2bdoZ\nxa5BYWHhWQs9//GPfzznc/Xu3ZvHH3/8ImOKuOGX1k826t4Dru/tNoyIJCwzZhK2vBSOH8WuLMOM\nGO86kqQ43cdK5Bzsp1th6yYAvNsnn3ddSxGR8zF5HTADhgJgF76CDYUcJ5JUpwIocg7+my9FHnTq\nCjfFvk6liEhjzPh7Ig8OHcCuXeY2jKQ8FUCRRtjdO+DD9wEw4ydjPH1UROTymE5doN8tANjSl7G+\nZsqKO/pfTaQRdsHLkQdXdcQMKDz/wSIiMfIm1C/Ku28PfLDabRhJaSqAIl9jv/gc+8EqAMz4uzGe\nbmskIk3DdL0O+kRWvfDffBlrreNEkqpUAEW+xpa+DNZCu1zMLSNcxxGRJOPdXn8W8POd0UtNRFqa\nCqDIaezBfdg15QCY2+7CpKU7TiQiycZcfwP0iCwr5b/5ks4CihMqgCKnsW+9Cr4Pba7AFI5xHUdE\nklT0WsAdH0eXmxJpSSqAIvXs0UPYlUsAMGOLMRmtHCcSkaTVqy90ux4Av2HSmUgLUgEUqWffmg+h\nEGS1xgwf5zqOiCQxYwzehPp1Abduiiw8L9KCVABFAFt1HLsscpN2U3QHJjPLcSIRSXo3DYwsNI/O\nAkrLUwEUAezi16D2FLQKYoomuo4jIinAeB5m/OTIxqb3sLs+dRtIUooKoKQ8W3UM+/abAJhREzDZ\nOY4TiUiqMAMKoUMnAPw3fu84jaQSFUBJefatV+HUl5AZxIwtdh1HRFKI8QKYid+JbGxci935idtA\nkjJUACWl2eNHsEsXAPXX/rVu4ziRiKQaM6AQru4M6CygtBwVQElpduGrkWv/glmYMTr7JyItz3gB\nzB1TIxsfvq8ZwdIiVAAlZdmjh7HvlAJgRt+JyW7tOJGIpCrzrSFfzQjWWUBpASqAkrLswlegrhay\nsjGj73QdR0RSmPE8vDvqrwXcsh67vcJtIEl6KoCSkuzRQ9jy+nX/xkzCZOnsn4g41m8wXNMNAP/1\nF91mkaSnAigpyS6YB6G6yF0/inT2T0Tci5wFrL8WsGIjdtsWt4EkqakASsqxhyuxy98C6u/5G9Rd\nP0QkTvS7Bbp8A9BZQGleKoCScmzpy5F7/rbO0V0/RCSuGGO+Ogv48YfYjz90G0iSlgqgpBR76CB2\n+WIAzNi7dM9fEYk/BQOh63UA+CVzsdY6DiTJSAVQUop9/UUIhyCnLWbk7a7jiIicxRiDd2f9WcBP\nPoLNH7gNJElJBVBSht2zG7t6KQBmwr2YzKDjRCIi53DjzXBdLwD8V1/A+r7jQJJsVAAlZfjzfwfW\nh/ZXYYaNcx1HROScjDF4d/9lZOPzndj3lrsNJElHBVBSgt1eARvWAGCKv4tJT3ecSETk/Mx1N0Su\nBwRsyVxsqM5xIkkmKoCS9Ky1+K8+H9no1BUzcJjbQCIiMfKKp4ExcHAfdvki13EkiagASvLbvC5y\nITXg3XU/xgs4DiQiEhtzTTfMLSMAsG/8AftljdtAkjRUACWpWd/Hf/WFyMb1N0QurBYRSSDmzvsg\nLQ2qjmGXlLiOI0lCBVCSml27DD7/MwDeXX+JMcZtIBGRi2Ry8zHDxwNg33oNW3XccSJJBiqAkrRs\nqA5bMjeyUTAQU7+kgohIojET7oXMIHxZg13wsus4kgRUACVp2WVvQeV+MAbv2/e7jiMicslMTlvM\n2G8DYN95E3vooONEkuhUACUp2S+rsX/6IwDmlpGYTl0cJxIRuTxmzJ2Q0xZCoa9+uyFyiVQAJSnZ\nBfOg6hikpWEm3ec6jojIZTOZWZgJUwCw7y7F7vrUcSJJZCqAknRs5X7s4shMOTN6Eqb9VY4TiYg0\nDTN8HHToBNbiv/Qs1lrXkSRBqQBK0rGvvgChOshpi7n9HtdxRESajElLw5v8vcjGti2wfrXbQJKw\nVAAlqdjtFdF7Zpri72KCWY4TiYg0sZtuhl4FAPjzfov9/9u78/gqqvv/468zNwncLKCSEAyBEKBs\nBQKCVDBVLC7FpURFcAlYpYi2UqkKSIWv9ddWpGhFRbDghhhcCgpFRdRUEERcqFEhKCIxLGELa0xC\ntjm/P0aiCEJQkkly38/Hw4fMmbk37zsngU/OzJxTpiXi5PipAJR6w7ou7guPexvNkzCp5/kbSESk\nGhhjcAYNA+N4S8T992W/I0kdFFaVg1zXJSMjg6VLl1JWVkZKSgrDhw8nJibmsGN3797NY489Rm5u\nLvn5+YwcOZLU1NRDjtm2bRszZ85k3bp1REdHc9FFF3HxxRefmE8kIcu+/zbkrAPAGTRMS76JSL1l\nElthfnke9u3F2Feex/b5FSamsd+xpA6p0gjg/PnzWbVqFRMnTuTRRx/FWsvUqVOP/IaOQ7du3bjl\nlnQO7gUAACAASURBVFto0qTJYftd12XSpEm0aNGCJ554gjFjxrBgwQLefVf3MciPZ0tKvHv/ALqe\njunUzd9AIiLVzAy42pscurgI+585fseROqZKBWBmZiZpaWnExcURDAZJT08nKyuL/Pz8w4496aST\nOP/882nXrt0Rl93Kzs4mPz+fq666ivDwcJKTkzn33HN54403fvqnkZBl33gJ9uRDIIBzxXV+xxER\nqXam0cmYCwcBYJcuxm7Z6HMiqUuOWQAWFRWRn59PcnJyZVt8fDzBYJDc3Nzj/oIbN24kISGBBg0a\nVLYlJyf/qPcSAbB7d2EXzQPA9L0Q0yzR50QiIjXDnHsJNGkK1rsHWtPCSFUd8x7A4uJiACIjD32a\nMioqqnLf8SguLj7iexUVFVX5PQoKCigoKDikLRDQ/V5+OXju/eqD8vnPQGkJREUTNuAaTAh+L/jd\nB6FO599/IdsHgSDuoOspn34vZH+Ek/0RTtfT/YkSqn1QSxw873l5eZVtMTExR3xeA6pQAAaDQYDD\nCrTCwsLKfccjGAwe8b2+XxQezaJFi5g7d27l9ogRI4iNjT3uLHJi+dEHJZ99yo53MgE4Kf1GYtq0\nrfEMtYl+Dvyl8++/UOwDe9Hl7Hj7NUrXZMELT9C07/mY8Ajf8oRiH9Qmo0aNqvzzwIEDGTRo0BGP\nO2YBGBkZSWxsLDk5OSQlJQHeU7zFxcWV28cjKSmJvLw8SktLiYjwvkE3bNhwXO/Vv3//Q54sXrt2\nLfn5+VRUVBx3HvnpAoEAsbGxNd4H1q2g/MG/AWCaJ1HY45cUbd9eY1+/NvGrD8Sj8++/UO8Dd+D1\nkD2K8ryNbJ01ncAlV9Z4hlDvA78dHAGcMmVKZdsPjf5BFaeB6devHwsWLKBTp05ER0eTkZFBt27d\nfrDKLysrq7wPoby8nLKyMgKBAI7j0LFjR+Li4pgzZw5XX301W7ZsITMzk+uvv77KH/L7Q5pr166l\noqJC33A+q+k+cP/7MnajtxamuWoErjEQ4t8D+jnwl86//0K2DxJbYfr2x771ChWvPI/tdRYmNt6X\nKCHbB7VEQkJClY6r0lPAaWlp9OjRg3HjxnHTTTdhjGHkyJEALF++nGuvvfaQ49PT0xkyZAj5+flM\nnz6d9PR0XnzxRe8LOg5jx45l06ZNDBs2jEmTJjFgwAB69+59PJ9PQpzdvwc7PwMA84uzMe07+5xI\nRMRfJu0aiGkMpaW4zz/mdxyp5ao0Aug4Dunp6aSnpx+2LzU19bCJnp9//vmjvl98fDwTJkw4jpgi\nh7Jzn4LiQghGYq6o+uixiEh9ZSKjMQOvwz45BbLew37yAcanB0Kk9tNScFLn2HVrsO++BYAZcA2m\n8ck+JxIRqR1M73PgZ50AcJ+dgS0t8TmR1FYqAKVOseXluHMe9TYSkzF9L/Q3kIhILWKMwbn6RnAc\nyN+OfW2e35GkllIBKHWKfesV2OJNGu5cc2NIzvknInI0JrEV5leXAGAXzcPu2OpzIqmNVABKnWH3\n7qpc79Kc2Q/TtqPPiUREaifzm6ug8SlQXuZdCtYKIfI9KgClzrAvPAEHiiEyGnP5b/2OIyJSa5lg\nJGbQNw/IrV4FH73rbyCpdVQASp1gP/4A+8EyAMylQzAxjX1OJCJSu5nTfwkdUwBw58zAFn3tcyKp\nTVQASq1ni4twn5nmbbTtiDnrAn8DiYjUAcYYnPSbIDwC9u32ps8S+YYKQKn17LynYO8uCAvHuXYk\nxtG3rYhIVZimCZgB1wBgl72OXfuxz4mkttC/pFKr2c9XY5e+BoC55EpMs0SfE4mI1C3m3N9AUlsA\n3NmPYEsO+JxIagMVgFJr2dIS3Kcf9jZaJGPOv9TfQCIidZAJBHB+OxICAdi5Dbsgw+9IUguoAJRa\ny/7nWdixFRwH59o/YsKqtHKhiIh8j0lMxvQfCIB9cyF2w+c+JxK/qQCUWsnmrse+Ph8Ac8GlmKQ2\nPicSEanbzIWD4NQWYF3cWQ9jy8v8jiQ+UgEotY4tL8d96mGwLsQ3x1x8pd+RRETqPBPuPUiHMZC3\nEfvqXL8jiY9UAEqtY1+bB5tzAHCG3oyJaOBzIhGR+sG06YD51cUA2Ff/jd38lb+BxDcqAKVWsblf\nYl9+DgDTtz+m3c99TiQiUr+YtHRo0hQqynEf/ye2TJeCQ5EKQKk1bGkJ7uP/hIoKiGum5d5ERKqB\naRjEuW6Udyl481fYBc/4HUl8oAJQag07bxZs3QTGwRl2K6Zh0O9IIiL1kmnfGXN+GgD29fnYz1f7\nnEhqmgpAqRXsmo+w/30ZAHPRFZg2HXxOJCJSv5kB6ZDYCqzFfeIBbFGh35GkBqkAFN/Zr/fjPvmg\nt5HUFnPRYH8DiYiEABMejjPsVggLg907sc/O8DuS1CAVgOIray32memwbzdEROD87lZN+CwiUkNM\nYivMpUMBsCvfwn643OdEUlNUAIqv7Mol2FXvAGAGXq+1fkVEapg59zfQvgsA7jPTsXt3+ZxIaoIK\nQPGN3bUD++y/vI3Op2H69vc3kIhICDKO4z0VHIyCwgLcJx/Cuq7fsaSaqQAUX9jyctyZ90FxEUTH\neGv9GuN3LBGRkGSaxGGuHuFtZH+EfWOBv4Gk2qkAFF/Yl56GLz8DwBk6EnPSKT4nEhEJbeYXZ2N+\ncTYA9sVZ2PXZPieS6qQCUGqczVqJfX0+AObcAZjuZ/icSEREjDGY9N9Ds0RwXdx/TcYW7PM7llQT\nFYBSo+zObd9O+dK6Pebyof4GEhGRSqZhEOfGsRARAXt3eUvF6X7AekkFoNQYW1aGO2MyFBVCVAzO\nDWMwYeF+xxIRke8wzZMwV9/kbaz5CLtorr+BpFqoAJQaY+c+CV99AYBz/ShMkzifE4mIyJE4Z/bD\n9OkHgF0wB/v5pz4nkhNNBaDUCLvqnW+Xevv15Ziup/ucSEREjsZcfSM0TwLr4s68D7t/j9+R5ARS\nASjVzm7Pw33qIW+jbSdMWrq/gURE5JhMgwY4I8ZCg4awbw/uzPuxFRV+x5ITRAWgVCtbVIj7yN/h\nQDFEN8K5YTQmEPA7loiIVIE5NREz5A/exmefYOc+5WseOXFUAEq1sW4F7mP3w9ZN4Dhe8XdyE79j\niYjIcXB+cTbmVxcDYN9cgPvOmz4nkhNBBaBUG/vibPj0QwDMlTdgOqb4nEhERH4MM2gYfPN3uH1m\nGnb9Wp8TyU+lAlCqhbvyLeziFwEwZ/1a6/yKiNRhJhDAGTEG4ppBeTnutHuwu3b6HUt+AhWAcsLZ\nnHXYWVO9jXadMVcN1zq/IiJ1nImKwbl5PDQMQsE+3Gl/x5aU+B1LfiQVgHJC2T27cB+5B8rLoElT\nnBvv0GTPIiL1hEloiTP8djAGNm7APvUg1lq/Y8mPoAJQThhbWoI77R7YtxsaNMS5eTwmppHfsURE\n5AQyXU/HXOYt42k/XI595XmfE8mPoQJQTghbUU75v/7x7Uofw27FJLbyN5SIiFQLc8FlmDP6At5K\nIe6K//obSI6bCkD5yay17Jk2CfvRSgDM5ddiup/hcyoREakuxhjM0JuhbUcA7NMP434z64PUDSoA\n5SdzFz5L4WsvAWD6XYK54DKfE4mISHUz4RHeQyGntoCKCsqnTaRk3Rq/Y0kVhVXlINd1ycjIYOnS\npZSVlZGSksLw4cOJiYk54vFZWVnMnj2b7du306xZM4YOHUrXrl0r9w8ePJiIiAgcx8FaizGGRx99\nlGAweGI+ldQY9+3F2PkZADin/xIGDdMTvyIiIcJExeCM+gvuxDGwdxf5fxlF4I5JENvM72hyDFUa\nAZw/fz6rVq1i4sSJPProo1hrmTp16hGP3bFjB/fffz+XXnops2bNIi0tjcmTJ5Ofn3/IcRMmTGDW\nrFk8/fTTzJo1S8VfHWSz3sM+Mx2ABl16EPjdbRhHg8oiIqHEnBKHM+puiIzC3beHsvsnYPft8TuW\nHEOV/rXOzMwkLS2NuLg4gsEg6enpZGVlHVbUASxZsoTWrVuTmppKIBAgNTWV1q1bs2TJkkOO02Pj\ndZtdvxZ3xmSwLiYxmdgJ92PCNd2LiEgoMs1bEvbH/4PwCMjfjvvQ3dgDRX7HkqM4ZgFYVFREfn4+\nycnJlW3x8fEEg0Fyc3MPOz43N5fWrVsf0pacnHzYsf/85z8ZNmwYd955J++///6PzS8+sJtycKf+\nDcpKoUlTwv50N05UtN+xRETER067zjQZ83cwDmzcgDtVE0XXZse8B7C4uBiAyMjIQ9qjoqIq933X\ngQMHDjs2MjKSzZs3V25PmDCBDh06APD+++/z0EMPMXr0aFJSqrZWbEFBAQUFBYe0BQKBKr1Wfhp3\n81dU/HMCFBZAdCPCb/0rYbFNAfWBnw6ee/WBP3T+/ac+8F8gECCyzznsH/oHymY9DJ9/ip32dwJ/\n/D9MRAO/49V7B7/38/LyKttiYmJ+8HmNYxaAB+/NKyo6dCi3sLDwiPftNWzY8LBji4qKDjm2c+fO\nlX/u06cPq1evZtmyZVUuABctWsTcuXMrt0eMGEFsbGyVXis/XtnGDey4fzx8vR8nuhFx90wjok2H\nyv3qA/+pD/yl8+8/9YH/mg26lv1hAfY9PgWbnUVg5n3Ejp+sIrCGjBo1qvLPAwcOZNCgQUc87pgF\nYGRkJLGxseTk5JCUlATAtm3bKC4urtz+rqSkJLKzsw9py8nJoUuXLsf1AY6mf//+pKamVm6vXbuW\n/Px8KioqTtjXkEPZrZsom3QH7N8LwSicW/8fe6JPhu3bCQQCxMbGqg98pD7wl86//9QH/jukD848\nj8C+vVTMfYoDq1aw5a5bCPvDeN0rXo0OjgBOmTKlsu2HRv+gitPA9OvXjwULFtCpUyeio6PJyMig\nW7duR/xN6+yzz2bhwoWsWLGCXr168e6775KTk8PIkSMB2LRpEyUlJbRq1QpjDKtWrWLZsmX86U9/\nqvKH/P6Q5tq1a6moqNAPfTWx2zbj3nfnN8VfJM6f7sa2aH3Y+VYf+E994C+df/+pD/xX2QcXXIYp\nL8fOfwb7yYeUTbsH58axWh++miUkJFTpuCoVgGlpaRQVFTFu3DjKy8tJSUmpLOiWL1/OzJkzmTVr\nFuA9IHL77bfz9NNPM336dJo2bcro0aMri8X9+/fzxBNPsHPnTsLCwoiPj+f3v/89p5122o/5nFLN\n7I483PvHw7490DCIc8tfMMnt/I4lIiJ1gHPRINyKCuzCZ+Hj93H/NRlnxBhMWJXKD6lGxtaD+Vgy\nMzPp3Lmzfus7wWzeRtwH7oK9u6BBQ5xRf8G07XTYcYFAgPj4eLZv364+8In6wF86//5TH/jvh/rA\nWotdkIF95QWvIaUXzg2jdU/gCRYIBFi9ejX9+vWr0vGatVeOyG74HPcf474t/v541xGLPxERkaMx\nxmAGXIPpP9Br+Ph93AfvxhYV+hssxKkAlMPYNR/hHpzqJSoG59a/Ytr93O9YIiJSRxljMJcOwVw2\n1GtYtxr3vj9j92vFEL+oAJRDuB8sx334r1ByAE5qgjNmIqZ1e79jiYhIHWeMwek/EDPkD95k0Zty\ncCfdgd25ze9oIUkFoFRyl7yKnTkZKsohvjnOHZMwCS39jiUiIvWIc9YFOCPGQFgY7NjqFYFbDl9Z\nTKqXCkDBWov7nznYjEfBWkhqizP2XkyTpn5HExGResj06IPzx7ugQRD27cb9xx3YdWv8jhVSVACG\nOFtagp15H3bhc15Dh644t/8NE9PY32AiIlKvmY4pOLf9DaJjoKgQ958TcJe/4XeskKECMITZvbtw\n/zEO+8EyAEyvs3H++H+YhpHHeKWIiMhPZ5J/hjN2EjQ9FSrKsbMexn3hcayrqXyqmwrAEGW/+gL3\n77dB7noA7+ms392KCY/wOZmIiIQS0ywR58/3QYeuANg3FuA+/DdNE1PNVACGIPeDZd/M8bfbm+Pv\n93/GufAKjDF+RxMRkRBkomK8lab6Xug1rF6Fe+8Y7I6t/garx1QAhhBbUYH70mzsjMlQVgqnxOGM\nnYTpfobf0UREJMSZsDCca27EXH0jOA5s3YR7z+3Y1f/zO1q9pAIwRNg9u3DvvxP76r+9hjYdcO68\nD9Mi2d9gIiIi3+GccyHOqLshMhoKC3Af/Avui09jtcTfCaUCMATY1atw/98t8EU2AOacC3Fu+zum\n0ck+JxMRETmc6ZiCc+f90LINAHbRXNz77sTuzvc5Wf2hArAes+XluPNm4T54N3y9H4KRODeOxbn6\nRkx4uN/xREREfpBpeirOHf/AnHOR17A+G/evt2A/XeVvsHpCBWA9ZXft8C75vjbPa0hqizP+AUyP\nM/0NJiIiUkUmPBzn6hE4N46FYCR8XYD70N24c5/Clpf5Ha9OC/M7gJxY1lrsssXYfz8JB4oBMP0u\nwVz+W436iYhInWR6nInTsg3uv/4Bueuxi1/Erl6Fc90oTFIbv+PVSRoBrEfsrp24U+7Czp7mFX/R\nMTg3jcO5criKPxERqdNMXDNv5opzB4AxsCUXd+LtuAvmaDTwR9AIYD3gjfq9jv33E5WjfpzWx3uc\nvtFJ/oYTERE5QUx4OGbwMGz3M3CfehB2bsO+/Bw26z2c627BtGztd8Q6QwVgHWd3bsPNmA5rPvIa\nomMwV43AnP5LTewsIiL1kmn3c5y7HsK+NBubuRA25+Decxum/0Dvv4gGfkes9VQA1lG2tAT72jzs\nonlwcOi7+xk46TdpehcREan3TIOGmCuHY0/rjfvUQ9+MBj6PfW8pzuDfYVJ6+R2xVlMBWMdYa+Hj\n93Cfewx27fAaG52EGTQM0+ssjfqJiEhIMe06e6OB85/B/vdl2LkNd+rfoEtPnCt/h2ma4HfEWkkF\nYB1it+fhPjcDDi6L4ziYX12CueRKTGSUv+FERER8Yho0xAz+HfbMfrjPzoB1a+DTD3HXZmHOvwxz\n4RWYBros/F0qAOsAu38P9uUXsG8vhopyr7F9F5yrRmCat/Q3nIiISC1hEpNxbr8H+/7b2LlPwt7d\n2FdfwK7I9AZLzjwXEwj4HbNWUAFYi9miQuzil7CZ/4GSA17jSU0wg67H9EzV5V4REZHvMcZgfnE2\nNuV0757AN/8De3dhZz+CXfwSJu0aTI8zMU5oz4SnArAWsiUl2Lde9h7wKPraawxGYS64FHPubzAN\nGvobUEREpJYzDSMxA6/D/vIC7IIM7AfLYEcedsZkbMt5OGlDoPNpITuYogKwFrHFRdi3X8O+8R/Y\nt9trDI/wVvL49WWYqBh/A4qIiNQxJj4Bc8No7K8vw33pGVi9CjZuwH3obmjTAefXl0PX00NuRFAF\nYC1g9+/BvrkQu2QRFBd6jYEAJvU8zMWDMSc18TegiIhIHWdatiFwy13YdWtwX3oa1q+FLz/DfeTv\ncGoLb6Cl19mYsNAojULjU9ZSdkce9vX52Hcyv53LLywcc2Y/zAWXYeKa+RtQRESknjHtfo4z5l5Y\n8xHua/Pg809h6ybskw9iF2RgzhvgDcA0jPQ7arVSAVjDbEUFfPoB7pJF367eAd49fudciOl3sSZy\nFhERqUbGGOh8GoHOp2Fz1nmF4EcrYXc+9vnHsQvmYM44B9O3P6Z5kt9xq4UKwBpi9+7GLn8d+/br\nsCf/2x2NT/F+2zjrAkywfv+2ISIiUtuY5HYEbhqH3bbZm3lj5VtwoBi75FXsklehbSevEDytDyY8\n3O+4J4wKwGpky8q80b6VS+CTD6Ci4tud7bvg9O0P3c4ImfsNREREaivTLBFz7UjspUOw72Rily7y\nVtxan41dn42NecxbceuMvpDUts4/PazK4wSzrut9s6xcgl31DhQVfrszGIXp8yvM2f0xpyb6F1JE\nRESOyDQ6CdP/cuwFad59gksWwacfQsE+bOZCbOZCaJaIOaOvVxDW0fv1VQCeANatgC8/x2atxH74\nDuze+e1OY6BDV8wv+nqTN2spGhERkVrPOAHo0pNAl57YXTu8UcH3lsCOrbBts7f28PxnoG1H7/Jw\nt1/UqWJQBeCPZMtKYe3H2Kz3sFnvQcG+Qw9ITP72t4OTNY2LiIhIXWWaNMX85irsJVdCzjrvKt8H\ny+Dr/bB+LXb9WuwLj0NiK0z3MzDdzoAWybX6MrEKwCqy1sL2PGz2R9jsLPjsUygpPvSgZolex/c6\nC5PYypecIiIiUj2MMdC6PaZ1e+ygYbDmI+yq5diPP/BW7tr8FXbzV9iFz8EpcZifd8f8vLt3JbCW\nLeagAvAo7L498MUabHaWV/Tt2nH4QcntMN17e0O/uq9PREQkJJiwMEg5HZNyOra83KsXst7DZnnT\nybB7J3bZ69hlr4NxoFVbTKdumI4pXu0Q4e8tYSoAv1E5wrc+23uI44ts7zr/90VGe53XqRuma0+t\n0iEiIhLiTFgYdEzBdEzBXjkcNn6J/XQVdm0WfPmZNwtIzjpszjrsKy9AIAyS2mB+1gnTtpN3H2F0\noxrNHLIFoN27C75aj81dj/1qPeSuP/w+PvA6qU17TKfumE7dvA5zAjUfWERERGo9Y4w3TUxSW7h4\nMPZAEXy++puriR/Bti1QUQ4bPsdu+By7+CXvhfHNMa3aeiOFST/z7iFsGKy2nPW+ALTlZd7TOls2\nwpavsJtzYeMG2Lf7yC9oGIQ2HTBtO2F+9nNo9TM9uSsiIiI/imkYCSm9MCm9gG9uL1u/FvvFGuz6\ntV5NYl3YvgW7fQu8txQL3mXjZs0xLVpDYpK3IknzJO/ewhPwcEm9KQDt1wXYvI3Y7XmwPc87kXkb\nYUfeoRMwf5fjQEJLr0pv1RbTur33BI9G+ERERKQamMYnQ48+mB59ALwRwg2fY3O+wOZ+c0Vyd75X\nFG7dhN26Cd7HKwrBG6hqnoRpluiNGsYnQHxz7KnNjytHvSkAy/545dEPaNDQK/aaJ3lTtLRq6w2v\n+nwTpoiIiIQu0zASOnXHdOpe2Wb374XcL7G5X2A3fwVbNnqDW9aFA8Xw5WfYLz/zjv3mNa4x8Kd7\nq/x1q1QAuq5LRkYGS5cupaysjJSUFIYPH05MzJEfac7KymL27Nls376dZs2aMXToULp27Vq5f9u2\nbcycOZN169YRHR3NRRddxMUXX1zl0EcVjPKGTL+piE1iEjRvBU2aYhznxHwNERERkWpiGp0EXXpg\nuvSobLNlpd6I4JaNsCX3myueW2DnVigvB2uP8o6Hq1IBOH/+fFatWsXEiROJjo5m2rRpTJ06lXHj\nxh127I4dO7j//vsZMWIEvXv35t1332Xy5Mk88MADxMbG4roukyZNIiUlhTvuuIPNmzdzzz330KRJ\nE3r37n1c4Q/5IOMm48Y1g+hGtXriRREREZHjZcIjoGUbTMs2h7RbtwJ27cTZeYSZS46iSkNimZmZ\npKWlERcXRzAYJD09naysLPLz8w87dsmSJbRu3ZrU1FQCgQCpqam0bt2aJUuWAJCdnU1+fj5XXXUV\n4eHhJCcnc+655/LGG28cV/DDPsjPOmFiGqv4ExERkZBhnAAmrhlOl57H9bpjFoBFRUXk5+eTnJxc\n2RYfH08wGCQ3N/ew43Nzc2nduvUhbcnJyZXHbty4kYSEBBp858na7+4XERERkep1zEvAxcXecmeR\nkZGHtEdFRVXu+64DBw4cdmxkZCSbN2+ufL8jvVdRUVGVQxcUFFBQUHBIWyCgJ3f9cvDcqw/8oz7w\nl86//9QH/lMf+Ovgec/Ly6tsi4mJ+cHnNY5ZAAaD3iSE3y/QCgsLK/d9V8OGDQ87tqioqPLYYDB4\nxPf6flF4NIsWLWLu3LmV2yNGjODjjz+u8utFRERE6qNRo0ZV/nngwIEMGjToiMcdswCMjIwkNjaW\nnJwckpKSAO8p3uLi4srt70pKSiI7O/uQtpycHLp06VK5Py8vj9LSUiIiIgDYsGHDEd/rh/Tv35/U\n1FTAe+jknnvuYcqUKSQkJFT5PeTEycvLY9SoUeoDH6kP/KXz7z/1gf/UB/46eP7//Oc/07RpU4Af\nHP2DKj4E0q9fPxYsWMCOHTsoKioiIyODbt26ERsbe9ixZ599Nl9++SUrVqygvLycZcuWkZOTQ9++\nfQHo2LEjcXFxzJkzh9LSUnJycsjMzOS8886r8oeMiYkhISGBhISEyg8pIiIiEuqaNm1aWSMdrQCs\n0jQwaWlpFBUVMW7cOMrLy0lJSWHkyJEALF++nJkzZzJr1izAe0Dk9ttv5+mnn2b69Ok0bdqU0aNH\nVxaLjuMwduxYZsyYwbBhw4iKimLAgAE/aQoYEREREak6Y+1xzhxYyxQUFLBo0SL69+9/1EpXqo/6\nwH/qA3/p/PtPfeA/9YG/jvf81/kCUERERESOj9ZGExEREQkxKgBFREREQowKQBEREZEQowJQRERE\nJMSoABQREREJMSoARUREREKMCkARERGREKMCUERERCTEqAAUERERCTFVWgu4tnJdl4yMDJYuXUpZ\nWRkpKSkMHz5cS9DUkBUrVrB48WK++uorSktLefbZZ/2OFFIyMjL43//+R35+PsFgkO7du3PNNdcQ\nHR3td7SQ8txzz7F8+XIKCgoICwujTZs2XH311bRq1crvaCHHWsuECRP44osvmD59OqeccorfkULC\ntGnTWLZsGREREVhrMcZwzTXXcP755/sdLaR88sknPP/882zatImIiAh69+7NsGHDfvD4Ol0Azp8/\nn1WrVjFx4kSio6OZNm0aU6dOZdy4cX5HCwnR0dFccMEFlJSUMGPGDL/jhJxAIMDIkSNp2bIlhYWF\nTJ06lWnTpjFmzBi/o4WUs846iwEDBhAMBiktLeW5557jvvvuY+rUqX5HCzkvv/wyDRs29DtGSOrb\nty8jRozwO0bIWrNmDQ888AA33XQTPXr0wFrL5s2bj/qaOn0JODMzk7S0NOLi4ggGg6Snp5OVlUV+\nfr7f0UJC165d6dOnD/Hx8X5HCUlXXnklrVq1wnEcYmJi6N+/P9nZ2X7HCjkJCQkEg0HAuyphrYPH\nGwAAA6FJREFUjKFJkyY+pwo9eXl5vPHGGwwZMsTvKCI17tlnn+W8886jV69eBAIBwsLCjnkVos6O\nABYVFZGfn09ycnJlW3x8PMFgkNzcXGJjY31MJ1LzPv30U5KSkvyOEZKWL1/OY489RnFxMS1atGD8\n+PF+Rwop1loeffRRhg4dSmRkpN9xQtJ7773H+++/T0xMDD179mTgwIEaja0hJSUlrF+/nvbt2zN2\n7Fjy8/Np2bIlQ4YMoXXr1j/4ujo7AlhcXAxw2A97VFRU5T6RULFy5UrefPNNrrvuOr+jhKTU1FSe\neuopZsyYQWJiIpMnT/Y7Ukh55ZVXOPnkk+nZs6ffUUJS//79mTJlCo8//ji333472dnZui2oBhUW\nFmKtZcWKFdx8883MmDGDrl27MnHiRIqKin7wdXW2ADx4yeX7H66wsLByn0goePfdd5k5cyZjx47V\ngwc+a9y4Mddffz3r168/5v03cmJs27aNV155heuvvx7wRgOlZiUnJ9OoUSMAEhMT+e1vf8vKlSsp\nLy/3OVloODjSes4559CiRQsCgQCXXnop5eXlrFu37gdfV2cvAUdGRhIbG0tOTk7lZa9t27ZRXFys\ny2ASMt566y2eeeYZxo4dS7t27fyOI1D5j54uf9WMzz77jP3793Pbbbdhra0sAEePHs3gwYP1JKrU\ne5GRkcTFxR3Wbow56uvqbAEI0K9fPxYsWECnTp2Ijo4mIyODbt266f6/GuK6LhUVFZSVlQFU/j88\nPNzPWCHj1VdfZd68edx5551Hvc9Dqo+1lsWLF9OnTx8aNWrErl27ePLJJ+nQoYP+Hqohffr0oWvX\nrpXbu3btYvz48YwfP56EhAQfk4WOFStW0K1bNyIjI9m6dSuzZ8+mZ8+ehIXV6RKjTjn//PNZtGgR\nffr0ISEhgYULFxIeHk779u1/8DXG1uHxctd1mTNnDm+99Rbl5eWkpKRwww03aB60GrJkyRKmT59+\nWPsjjzyif/xqwODBgwkEApUF98H5t2bNmuVzstBhreXee+9lw4YNlJSUEBMTQ/fu3Rk0aFDlJTGp\nWTt37uTmm2/WPIA16O6772bjxo2UlZXRuHFjevXqxRVXXKFR8Br2wgsv8Oabb1JWVkZycjLXXnvt\nUa+I1ukCUERERESOX519CEREREREfhwVgCIiIiIhRgWgiIiISIhRASgiIiISYlQAioiIiIQYFYAi\nIiIiIUYFoIiIiEiIUQEoIiIiEmL+P8hv6xmMqGdlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff2fcbc7828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import *\n",
    "\n",
    "Q = 1 / np.sqrt(2 * sigma**2 * pi)\n",
    "norm = Q * np.exp(-dist)\n",
    "\n",
    "plt.plot(x, norm)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vz4Wf6vQmx/Lycjwej76hbKZrYK+hcP5NZyemcq/vdvG4sPt6w+UamOKxvhut\nLXhqqrBGFdhb0CAKl2swlOka2Cs3Nzeo44L6s2/WrFm88sorHD58GJfLxfLly5kyZUqPzbTXXHMN\nzc3NvPbaa3i9Xvbv38+GDRu44oor+vYViMjQc7AC3J2AJlic06h8SPD1oGi5FBHpSVABb86cOVx6\n6aUsXLiQf/qnf8KyLBYsWADAhg0b+NrXvhY4Nisri4ULF7J27VruuOMO/vVf/5X58+cr4IlIrwJh\nJX0YDM+2t5gwZjmcUNIVgPdpJq2InCmohY4dDgdlZWWUlZWd8dyMGTPOGFs3YcIEHn/88dBUKCJD\nhz+slFzg27VBzsoquQBT/pFa8ESkR9E/MldEIobpWuDY0gLHvQqco+pKTNuZKxqIyNCmgCciYcE0\nN0J9LaCAFxT/GEXjBf/agSIiXRTwRCQ8+HdlsBxQNNreWiKAlZoOWb418IwCnoicRgFPRMKC2b/H\nd2NUPlbCmWtsypks/3Ip/nMnItJFAU9EwoK/FSoQWqR3xWMAteCJyJkU8ETEdsYYqOxqheoKLdK7\nQBg+chjT3GRrLSISXhTwRMR+xxqg6TigFrw+KRwN/uVkKtWKJyInKeCJiP38XYzOGMgvsbeWCGIl\nJkFOHqBuWhHpTgFPRGwXmGCRV4QVG2tvMRHG3+JpNNFCRE6hgCcittMEi/OgmbQi0gMFPBGxlSZY\nnB/Lf84aj2KOHbG1FhEJHwp4ImKv+kPgagHUgtcvBSXg6PpVrokWItJFAU9EbGUqukJJbBzkFtpb\nTASy4uIhtwgAU6FuWhHxUcATEXv5u2cLS7GcTntriVBWSddEC7XgiUgXBTwRsZUmWISAfxze/j2+\nMY0iMuQp4ImIbYzXA1X7fHc0waLfrKKucNzSDA119hYjImFBAU9E7HOoGtrbgFNCivRdXhHE+NYP\n1Hp4IgIKeCJio8DuC4lJkJNrbzERzIqJ8c2mhZO7gojIkKaAJyL28YeRwtFYDv06Oh/+9fC0ZZmI\ngAKeiNjIdM2gtTT+7vz5J6lU7sV4vfbWIiK2U8ATEVsYdycc8E2w0Aza8xcYw9jeCnXV9hYjIrZT\nwBMRe1RXgtvtu62Ad/5G5UF8AnDK4tEiMmQp4ImILQKzPVNSIXOEvcVEAcvhhKLRvjuVmkkrMtQp\n4ImIPfyTAYrHYlmWvbVECatIEy1ExEcBT0Rs4W/B0/i7EPKfywMVGH/3t4gMSQp4IjLoTHs71FQC\nJ1ud5Pxh/hnuAAAgAElEQVQFwnJnB9RU2VqLiNhLAU9EBt+BfeBfykMteKGTPRKSUgB104oMdQp4\nIjLo/OvfkZGJlTHc3mKiiGVZJ/f01UQLkSFNAU9EBl9ggoW6Z0NNEy1EBBTwRMQG/vChCRahFzin\n1ZWYzg5baxER+yjgicigMq0uqKsBNMFiQPgDnscDByrsrUVEbKOAJyKDq2ofGOO7rS7a0BuWCanp\nAJjKvTYXIyJ2UcATkUFlKrvGhmWOwEpJs7eYKOSbaNHVilepcXgiQ5UCnogMLn+rkrpnB4zVtWWZ\nWvBEhi4FPBEZVCd3sFDAGyiBsY01VZiOdnuLERFbKOCJyKAxrhY47J9gMdrmaqKYP+B5vZpoITJE\nKeCJyOA5sO/k7UIFvAGTMRzShwFgqtRNKzIUKeCJyKDxd8+SlaMJFgPIsqyTAXq/drQQGYoU8ERk\n8Pi3z1L37IAL7GihLctEhiQFPBEZNP6woQWOB15gEkvNAUy7JlqIDDUxwRzk9XpZvnw569ato7Oz\nk8mTJ3PXXXeRmpp6xrGffvopDz74IAkJCZiuxUyLiop4+OGHQ1u5iEQU3wSLQ4AC3qDwt5IaLxys\ngNHj7a1HRAZVUAFv1apVbN26lUWLFpGSksJTTz3F4sWLWbhwYY/HOxwOli1bFtJCRSTCnTrYX120\nA87KyIT04dB4FFO5B0sBT2RICaqLdu3atcyZM4fs7GwSExMpKytj27ZtNDQ0DHR9IhIlAmPBskdi\nJZ/Z+i8DoEgTLUSGql5b8FwuFw0NDZSUlAQey8nJITExkcrKSrKyss54jdfr5dvf/jZut5vS0lJu\nu+02ioqKgi6qubmZ5ubmbo85nc6gXy+h5T/3ugb2iJbzb6r2YQBH0ZiI+1oi9hqUjMPz8Wao2ht5\ntZ8mYq9BFNE1sJf/vNfU1AQeS01N7XG4HAQR8FpbWwFISkrq9nhycnLguVPl5eXxi1/8gvz8fNra\n2li1ahUPPfQQv/rVr8jIyAjqi1i9ejUrV64M3L/77rt7DJIyuHQN7BXp5//QgX14gdRJU0jLybG7\nnH6JtGvQOmUqDa8sxxw6QHZ6Go6ERLtLOm+Rdg2ika6Bve65557A7Xnz5jF//vwej+s14CUm+n4h\nuFyubo+3tLQEnjtVeno66enpgC8U3n777WzatIkPP/yQa6+9NqjiZ8+ezYwZMwL3y8vLaWhowOPx\nBPV6CS2n00lWVpaugU2i4fyblmbchw4C0JI1ita6Opsr6ptIvQYmvesfYq+Xuq0bcYyZYG9B5yFS\nr0E00TWwl78F78knnww8drbWOwgi4CUlJZGVlUVFRUWgm7W2tpbW1tagu10tywrMqA3G6U2O5eXl\neDwefUPZTNfAXpF8/k3F7sBtb34JJkK/joi7Bqnpvl0tjh/Fs+8zTMkFdld03iLuGkQhXQN75ebm\nBnVcUJMsZs2axSuvvMLhw4dxuVwsX76cKVOm9NhMu337dmprazHG0NbWxooVK2hsbGTKlCl9+wpE\nJGp0n2CRYm8xQ41/SRoteCwypAS1TMqcOXNwuVwsXLgQt9vN5MmTWbBgAQAbNmxgyZIlgWVRKisr\n+d3vfkdzczPx8fGUlpZy//33M3z48IH7KkQkvFX6lkjR+neDzyoag/nofUyl9qQVGUqCCngOh4Oy\nsjLKysrOeG7GjBndxsvdfPPN3HzzzaGrUEQintEWZbaxikZjAA4dxLS3YcUn2F2SiAwCbVUmIgPK\ntJyA+lpALXi28J9z44UD++ytRUQGjQKeiAysU8d+qQVv0FnpwyAjEwCjBY9FhgwFPBEZUIGxXyNG\nYSVpgoUt/MFa4/BEhgwFPBEZWF0teOqetY9V7Dv3RjNpRYYMBTwRGVCaYGG/QLiuPYhpO3MHIhGJ\nPgp4IjJgTEszNPh2rVALno384doYOFBhby0iMigU8ERk4JzaJVioFjy7WGnDYJhvYXpTubuXo0Uk\nGijgiciAOTnBIhcrKdneYoY6TbQQGVIU8ERkwPiX5bA0/s52/i5yLZUiMjQo4InIwAlMsND4O7sF\nxkDWVWPaXPYWIyIDTgFPRAaEOdEERw4DJ5fpEBudOtGiSjtaiEQ7BTwRGRinjvXSBAvbWWkZMDwb\nOGVspIhELQU8ERkQZn/XbM2ReViJSfYWIz7+llSNwxOJegp4IjIg/AscW4Xqng0XVldLqna0EIl+\nCngiMjD8IULj78KGVTzWd6OuGuNqsbUWERlYCngiEnKm6TgcbQC0g0VYOXW5mgOaaCESzRTwRCT0\n/IP4LQsKS+2tRQKslDTIHAFoPTyRaKeAJyIhF9gOa2Q+VkKivcVId/4uc43DE4lqCngiEnInd7BQ\n92y4sYp84/ACs5xFJCop4IlI6Pm7aDXBIuwEFp2ur8W0nLC1FhEZOAp4IhJS5vhROH4EUAteWDp1\n0ekqLXgsEq0U8EQktAITLBxQoAkW4cZKToHskYAmWohEMwU8EQmpwASL3AKs+Hh7i5Ee+dfDC1wr\nEYk6CngiElL+fU7VPRvG/NdGe9KKRC0FPBEJGWOMdrCIAJZ/weOGOsyJJnuLEZEBoYAnIqFz/Cg0\nHgPUghfWTp1ooVY8kaikgCcioeMf0+VwQH6xraXI2VlJyZCTB2g9PJFopYAnIiHjH39HbhFWnCZY\nhDN/C6vRUikiUUkBT0RCJrCDhcbfhT//ODwtlSISlRTwRCQkuk2w0Pi7sBcI4UfrMU3Hba1FREJP\nAU9EQuNoAzQ3AppgEREKS8GyfLc10UIk6ijgiUho+FvvnDGaYBEBrISkkxMtKtVNKxJtFPBEJCQC\nISGvCCs21t5iJCj+bloFPJHoo4AnIiGhCRYRyN+VrokWIlFHAU9EzpsmWESmQBg/fgTTtUC1iEQH\nBTwROX9HDkNLM6AJFhGloBSsrn8G1E0rElUU8ETk/PnDQUwM5BXaW4sEzYpPgFH5wMkudhGJDgp4\nInLeAuEgvwQrRhMsIklgRwu14IlEFQU8ETlv/nBgFY3u5UgJO/5xePt3+8ZSikhUUMATkfNivN6T\nszCLx9pbjPRZYMxk03E4dsTeYkQkZIIKeF6vl+eee45vfOMbfO1rX+PXv/41zc3Nvb7utdde4+//\n/u956aWXzrtQEQlTh2ugtQUAq2SczcVInxWWgtPpu73/M3trEZGQCSrgrVq1iq1bt7Jo0SKefvpp\njDEsXrz4nK9paGjgL3/5C4WFGnAtEs1MxW7fjVMG7EvksGLjIL8EOOVaikjECyrgrV27ljlz5pCd\nnU1iYiJlZWVs27aNhoaGs77md7/7HbfddhspKSkhK1ZEwtD+rlBQNBrL4bS3FumXwI4W+xXwRKJF\nTG8HuFwuGhoaKCkpCTyWk5NDYmIilZWVZGVlnfGaNWvWkJCQwPTp03nttdf6XFRzc/MZXcBOp/7h\nsIv/3Osa2CPcz7+3KxQ4Si8I2xr7wuM1HGt1U3eigxMdHgAcDgepzQ6am07g9XpJiHGQkxJHVnIs\nMQ7L5opDoHQ8nnV/g8o9OCwLyxF+w7PD/edgKNA1sJf/vNfU1AQeS01NJTU1tcfjew14ra2tACQl\nJXV7PDk5OfDcqRoaGnj55Zd57LHHgq/6NKtXr2blypWB+3fffXePQVIGl66BvcLx/JvOTg4eqABg\n2JTLSMrJsbmi4Blj2Hekha1Vx9l1uJmaxjZqm3z/ub3BzSZ1WJCdEk9uegKj0hIZnZXMpYXDuCAn\nhZgwDEln0zH1CuqWAq0uMt3txBYU213SWYXjz8FQo2tgr3vuuSdwe968ecyfP7/H43oNeImJiYCv\nJe9ULS0tgedO9cwzzzB37lwyMjL6VPCpZs+ezYwZMwL3y8vLaWhowOPx9Ps9pf+cTidZWVm6BjYJ\n5/Pv3b8bOjsAaBqeQ3Ndnc0VnZ0xhsrj7XxS28IndS6217XQ1H7u83lq65xlgX8VEX8A9Bqoa26n\nrrmdD2kMHJsY42DCiCQm5SRx0chkxmYm4gzjlj4Tn+QbQ9neRv3md3HGnfm73W7h/HMwVOga2Mvf\ngvfkk08GHjtb6x0EEfCSkpLIysqioqKCoqIiAGpra2ltbQ3cP9XHH3/Mvn37eOGFFwBfMNy7dy8f\nffQRDz74YFBfxOlNjuXl5Xg8Hn1D2UzXwF7heP69e3f5bqSk4cnIxAqz+gDqTnTwZkUTb+5rpPZE\n5xnPp8Y5GJ+dyMjUOHKSYxmRHMuIlFiyk2NJiTvZJZWTk0NdXR0ej4c2t5fDLZ0cPtHJ4ZZO6ls6\nqT3Rya76Vo60uml1e9lac4KtNScAyEhwMrM4jetK0ykZljCoX3/QisbAZ9vx7tsFV1xjdzVnFY4/\nB0ONroG9cnNzgzqu14AHMGvWLF555RUmTJhASkoKy5cvZ8qUKT020/7ud7/rdv/Xv/41F154IV/+\n8peDKkhEIoh/WY2ScVhW+LRQtXR4eKeqmTf3NfJpffehJGnxTiaOSGJSTiKTRiRRmBGPo4+1J8Q4\nKEyPpzA9vtvjxhhqT3Sy47CL7XW+/+pdbo63efjTzmP8aecxijPiubY0jZnF6QxPDOpX8KCwisdi\nPtuuiRYiUSKo3y5z5szB5XKxcOFC3G43kydPZsGCBQBs2LCBJUuWsGzZMgCGDx/e7bWxsbEkJiaS\nlpYW4tJFxG7+Lcr8szDtdvhEJy99eoS1+xrp8JwcR5cW72tBu6YkjTHDEwYsjFqWxajUOEalxvGF\n0b5hKtVNHazb38ib+5o43NLJ/uPtLP2gnmUf1jO9IJVbJmWGRaueVTIWA3BgH8bdqS3nRCJcUAHP\n4XBQVlZGWVnZGc/NmDGj23i50/3Lv/xL/6sTkbBl2lxQUwXYv8BxTVMH//XpEd7c14g/18U4LC7L\nS+G60jQuyU2xbbZrXloct38um1svyqL8cCtvVDTyTmUzrW4v71Q1805VM5flpTB/Uibjsmwc++bf\nhcTthoP7tSuJSIQLn/4BEYkslftOzjqwKQxUHW/nP3ccYUNlE/6Jr+nxTv7uwuHcMCaD1PjwWc7B\nYVlMzEliYk4S35yaw9v7m1i54wi1JzrZXH2CzdUnmDIyifmTspiYk9T7G4Za5ghITYfmRkzFbiwF\nPJGIpoAnIv0SGKuVOQIrNX1QP7upzc1zH9WzZk8j/o7YzMQYvjrBF+ziY8J7iZL4GAfXj8ngutJ0\nNlQ28Z87jnCgsYNttS621VYxNTeZb0zNYVRq3KDVZFmWL6h/suXk4tUiErEU8ESkfyp8EywGs3vW\n4zW8tuc4f/yonhMdXgBGJMcyb2Im15WmEesM72B3OqfD4uqSdK4qTmPTgROs2N7AvmPtbKlpYdtf\nKpg7YTjzJmYOWmC1isdiPtmCqdCetCKRTgFPRPol0II3SF155fUuntlcR8WxdsA3k/W2z2Vy87jh\nxDrDZwZvfzgsi+mFqVxRkMLb+5tY+mE9x1rdrNjuG1f49UtzuKIgZcBnKlsl43wtorUHMW0urAQb\nuopFJCQU8ESkz0xzIxw5DPhmXw6kE+0efv9BHW/sawo8dk1xGv/j4mwyk6Jrpqdl+Vr0LstP4T8+\nOcKfdx6l3uXm5+urmTIyiW9PG0lOygB22/rDujFQuRcuuGjgPktEBlRk9WeISHjwt95ZDigcPWAf\n81FtC9/9a0Ug3BVnxPPY9YV878rcqAt3p0qKdXLnJSP4zc0lfG6krxVtW62Lf/7rft7Y14gxwW2l\n1ldWahpk+bab03p4IpFNLXgi0meBMVq5BVgJoV/ao8Pj5d+31fPnnccAiHNa/OOUbG4eNyyst/wK\ntYL0eB66roB3q5p5enMdTe0efvPeId4/eIJvTxtJ2gDMEraKx2Ia6jQOTyTCKeCJSJ8N5ALHFcfa\n+PU7NVQ1+va4HT08nu99PpeC03aNGCosy+LKojQmjkjitxsPsaWmhfcONLOzoZXvXjGSS3JTQvuB\nJWNhywbousYiEpnURSsifWKMCcygpTh0M2iNMbz86RF+8Lf9VDV24LBg3sRMHr+heMiGu1NlJMbw\n02vy+dZlOcQ5LY61unnwzYP82+ZaOjzekH2O5b+mRw5jmo6F7H1FZHAp4IlI3zTUwQnfmLhQTbBw\ndXp4fH01f/iwHrfXt/TJo18o5B+nZEf8DNlQsiyL2eOG8eRNJYzN9G1v9tfPjnPvmioaXJ2h+ZCi\n0b6xlQAVasUTiVQKeCLSJ/7uWWJiIa/ovN+vuqmDH/6tkvcOnABgZnEav7m5mAkjtETH2eSlxfHz\nG4qYNzETgN1H2vj+6v3sOOw67/e24hMgtwDQRAuRSKaAJyJ9s7+re7aw9Lw3pN988AQ/+Nt+Djb5\numS/cekIvv/5USTFhs8WY+EqxuGbeHLvzDwSYxw0tnm4//Uq/rrr2HnPsvVvU2b2a6KFSKRSwBOR\nPvG36pzPXqVeY3jxkwYeWXcQV6eXtHgnD80q4Mvjhw/4Yr7RZlpBKr+8sYi8tDg8Bv5tSx3/Z+Mh\n2t3nMS7PvzvJ/t0DtiSLiAwsBTwRCZrxenwL4IJvtmU/tLu9PL6+mhc+bgBg9PAEfj27mItykkNV\n5pCTnx7PL28s4vJ834zaN/Y1ce+aKo61uvv1foGxlSeafWMuRSTiKOCJSPAOHYT2NqB/LXhNbW7u\nX1vFxq7xdteWpLHo+kKyk6N30eLBkhTrZOHMPG77XBYAe4628aNXKznY1N73N8stgljfjhkahycS\nmRTwRCRogcVvE5NhRG6fXnuouYMfv1bJrgZfQPzaxdn88/RRxMfo11CoOCyLWy/K4icz84hzWhxu\n6eQnr1ZS3sfJF1ZMDBSW+u5owWORiKTfrCISvIqu1pziMViO4H997D7Syo9fq6SmuZMYB/zvK3OZ\nOyFT4+0GyPSCVB6aVUBqnIPmDi8/e+MA7x1o7tN7BCZaVKgFTyQSKeCJSNDMvp0AWCUXBP2aLdUn\nuG9NFY1tHpJjHfzLtQXMLE4bqBKly4XZSfz8hiJGJMfS4TE8/nY1f93Vh4WL/RMtKvdg3CFaY09E\nBo0CnogExbS5oLoKAKs0uID3+t7jPLruIO0eQ2ZiDI9dX8jnRmoyxWDJT4/niS8WUTosHoNvhu2y\nDw8HNTM2cI07O+DA/gGtU0RCTwFPRIJTsRtM19IbQQS8v+46xm831uI1UJQezxM3FlE8LGGAi5TT\nDUuM4dHrC7l4lC9Yv/TpUZ7ZXIe3t5CXlQNpGQCYfbsGukwRCTEFPBEJSuAf+RG5WKnn7mJ9+dMj\n/NsW3/Ia47MSeeyGQrKSNFPWLkmxTn56TX6ga3z17uP83021eLxnD3mWZUHpeN+drq55EYkcCngi\nEhSzt2v83ehzt96t+KSBP3xYD8BFOUk8cF0BKXHamcJuMQ6Le6aP4guj0wF4fW8jv3nv0LlDXte1\n9l97EYkcCngi0itjDFR0teD5W3V6OOa5bfUs71rA+OJRydx/TT6Jsfo1Ey6cDovvTBvJ7LG+rtd1\n+5v45Ts1dHp6DnmW/1ofOYxp7MMEDRGxnX7zikjv6mp8uxoA1ugzA54xhmc/OMzKHUcAuCwvhfuu\nztMad2HIYVncfVkOfzd+GADvVjXz+PpqOjw9bG1WNAacXa2vasUTiSj67SsivQqMv4tPgNzC7s8Z\nw5Kth/nTTl8Lz+cLU/nxVXnEOvXrJVxZlsWdl4zglomZAGyuPsGiddV0nhbyrPh4yC8BNNFCJNLo\nN7CI9M4/yL54LJbz5Hg6YwzLPqwPrK92TXEaP7gyl1inFjAOd5ZlUTYlm3/o2trsg0Mt/GJDDe7T\nxuT5l0sxmmghElEU8ESkV2avr/Xm9O7ZFz5p4OXyowDMLE7ju9NH4XQo3EWS+RdlcXtXyNt08AS/\nfqem+8QL/zWv3INxu22oUET6QwFPRM7Jt8BxJXDKoHtg5Y4j/McnvjF30wtSuEfhLmLNn5TJvK7u\n2neqmvk/Gw8F1skLLHjc0QEHK+wqUUT6SAFPRM6thwWO/7TzKM9t8y2FcmluMv/7yjyFuwhmWRZl\nk7P48gW+iRdvVTTx9Pt1vtnTWTmQ6ltaxd+SKyLhTwFPRM7p5ALHo7BS0/jb7mP8futhAD43Momf\nzMzTmLsoYFkWX790BF8c41tC5dU9x/l/Xdc50E2riRYiEUMBT0TOyR/wrNLxvFXRyNPv+3aomJCd\nyH1X5xOn2bJRw7IsvnV5DteV+na8+MuuY/zxo4ZA17wmWohEDv1mFpGzMsYEWm225k3hN+8dwgBj\nMxO4/9p8ErTOXdRxWBb/a9ooZhSlAr6xln9O7mrBa6jDNGnBY5FIoN/OInJ2hw/BiSZ2pRXyxLFR\neA0UpMfxL9cWkBSr7ceildNh8b3P53LJqGQAnj3gZN3IS3xPahyeSERQwBORszJ7d1KVlMOjn/uf\ndHghKymGB64rIDVe4S7axTgsfjwzj3GZCQAsvuAWPhg+TvvSikQIBTwROav6fRU8NPnrnIhJIjXe\nyYPXFZCVFGt3WTJIEmIc3H9tAflpcXgsJ7+Y+D/YdaDB7rJEJAgKeCLSo6Y2Nw92TuBofAbxeLj/\nmnzy0+PtLksGWVq8kweuKyDT6aHdGcejw66l6qjL7rJEpBcKeCJyhja3l4feqKI6bhhOr4efFLVx\nQVai3WWJTbKTY3ng8nRSOltojk3mwTeqqG/ptLssETkHBTwR6cbjNfxifTW7j3UAsGDnf3Dx5DE2\nVyV2KyjJ4769/0m8p4OGdnj4zYO0dHjsLktEzkIBT0QCjDEs2VLHlpoWAO7c82dmUofVtZOBDF2W\nZXFBTgo/2PFHHMZLZWM7j6+vxn3qvrUiEjYU8EQk4OXyo6zefRyAm9t28+WD67vtPytDmzV6PJce\n3ck3a14H4KNaF/93U61vvUQRCSsxwRzk9XpZvnw569ato7Ozk8mTJ3PXXXeRmpp6xrE7d+5k6dKl\n1NfX4/V6yczM5IYbbuCLX/xiyIsXkdDZUNnEsg99+8tOy0/hjlUrfE+MvsDGqiScWKXjMcANu1+n\n/uo5/NceF2/sayQnJZZbL8qyuzwROUVQLXirVq1i69atLFq0iKeffhpjDIsXL+7x2NzcXH74wx/y\n7LPP8oc//IFvfOMb/Pu//zvl5eUhLVxEQqf8sIsn3z0E+Hap+P44C+eJRgCsUgU86VI8Bhy+fzb+\nIa6Gq7p2u3jh4wbe2NdoZ2UicpqgAt7atWuZM2cO2dnZJCYmUlZWxrZt22hoOHM9pLS0NLKyfH/J\nGWOwLIuYmBjS0tJCW7mIhERNUwePvl1Np9eQkxLLT6/JJ27/Z74n4xMgr9jW+iR8WPEJkF/su71v\nF9+dPooJ2b7Z1Ys3HuLj2hYbqxORU/XaRetyuWhoaKCkpCTwWE5ODomJiVRWVgbC3OnuvPNO2tvb\ncTqdfPvb3yYvLy/oopqbm2lubu72mNOplfPt4j/3ugb2GMjz39jm5qG3DtLc7iElzsmDs4rITI7H\nvbccA1gl44iJiwv550Ya/QycZMZMwFu1D/aUkxgXy0+vLeSHf6uguqmDRW9X84vZJRRlJIT8c3UN\n7KdrYC//ea+pqQk8lpqa2uNwOQgi4LW2tgKQlJTU7fHk5OTAcz1ZunQpbrebd999l6eeeopRo0ZR\nXFzc6xcAsHr1alauXBm4f/fdd581SMrg0TWwV6jPf4fby09XfMih5g5inRa//v8mc3F+BgCH9u3C\nC6ReMo30nJyQfm4k088AuC6/kiNv/AWzfzfZGenkxCew+O+H8z+Xb+GYq5NH11Wz9B+mMjx5YP4w\n0DWwn66Bve65557A7Xnz5jF//vwej+s14CUm+prfXa7uK5e3tLQEnjubmJgYZs6cyTvvvMOGDRuC\nDnizZ89mxowZgfvl5eU0NDTg8WjNJTs4nU6ysrJ0DWwyEOffGMOT79awrdo3buqfp+eSG9tOXV0d\npuk47gMVALhyi2mrqwvJZ0Yy/QycZEbk+264O6nbtAHHBRcRC9x3dT4LX91PTWMb3/vPD3j0hiJi\nnaFbqEHXwH66Bvbyt+A9+eSTgcfO1noHQQS8pKQksrKyqKiooKioCIDa2lpaW1sD93vj9XpJSAi+\nyf70Jsfy8nI8Ho++oWyma2CvUJ7/lTuOsHavbzmU+ZMyuaooNfDeZtcnvoOcTrzFYzG65gH6GQBS\n02HEKDh8CM/OjzFjJgAwdng8350+il+9U8On9S5+824190wfhWVZIf14XQP76RrYKzc3N6jjgvrz\natasWbzyyiscPnwYl8vF8uXLmTJlSo/NtJs2baKqqgqv10tnZyevv/46O3fuZNq0aX37CkRkQLxX\n1cxz23zLoVxZmMptn+v+c2x2f+q7UTjaN6he5DTWWF+oC3yvdJlZnMatF2UC8FZFEyt3HBn02kTE\nJ6h18ObMmYPL5WLhwoW43W4mT57MggULANiwYQNLlixh2bJlABw7doznn3+e48ePExcXR2FhIffe\ney8FBQUD91WISFD2HGnj1+/6BuiOzUzgn6ePwnFaC4v5bAcA1riJg16fRIixk+CdtbB3J8btxoo5\n+U/JrRdlcbCpgw2Vzfzxowby0uL4fKFWURAZbEEFPIfDQVlZGWVlZWc8N2PGjG7j5W688UZuvPHG\n0FUoIiFxxNXJo+sO0uExZCbFcO/V+cTHdG/EN60u6Bp/Z42dZEeZEgGscRMxAO1tcGAflIw7+Zxl\n8d0rRlF3opPdR9r413cPkZ0cy9jMc4/ZFpHQ0lZlIkNAu9vLo+uqOdrqJiHG4qdX5zM8sYe/7/aW\ng/GCZcGYCwe/UIkMWTmQMRwAs3vHGU/Hxzi47+p8spJi6PAYHl1XzRFX52BXKTKkKeCJRDljDL95\n7xB7j7ZhAd//fC6lw3seW+fvniWvCCs5ZfCKlIhiWRbWWF8XfuB75jTDEmP46TX5JMRYHGt189i6\natrd3sEsU2RIU8ATiXL/ueMI71T5Fg7/xynZTCs4+7R6f2uM/x9vkbPyj9Hc/SnG23NwKxmWwPev\nzPAjru8AACAASURBVMUC9hxtY/GmWowxg1ejyBCmgCcSxTYdaGb5R74tBa8uTmPuhOFnPdZ0tMP+\n3b47CnjSi8AfAa4TcOjAWY+blp/KP0z2zdR+e38T//Xp0cEoT2TIU8ATiVL7j3WfMfudaSPPvSZZ\nxW5wu4GTy2CInNWoAkj2tQafrZvWb97ETGYU+Y7947Z63j/YfM7jReT8KeCJRKGmNjePrqumzW0Y\nlhjDwpl5Z8yYPV1gsPyIXKyMs7f0iQBYDgf4/xDoYaJFt2O7ZtaOHh6PAX71ziGqjrcPfJEiQ5gC\nnkiUcXsNj6+v5nBLJ7EOi3tn5pGZFNvr606Ov1PrnQTn5ILHO3odWxcf42DhzHwyEpy0ub08uu4g\nTe3aDUFkoCjgiUSZ/7elju2HWwH4X1eMZFxW7+uPGY8H9u703dECxxKkwFqJx49CfW2vx2cnx7Jw\nZj4xDovaE508sb4at1eTLkQGggKeSBT52+5jrN7t22N27oThXFOSHtwLq/b5Fq1FM2ilDwpLoWs7\nu9O3LTub8dmJfGfaSAA+qXOx9IPDA1aeyFCmgCcSJT497OLfNtcBcGluMmWTs4N+rdm93XcjI9O3\niO0QZ4zB4zG4O0/+19nhDdz2eIyW+wAspxNGj/fd8X8PBeG60nS+Mn4YAH/ZdYzX9x4fiPJEhrSg\ntioTkfBW39LJz9dX4zGQmxrH96/Mxek4x4zZ05y6/+w5Z9pGGGMMHe2GVpeXtlZDW6uXjnZDR4eh\ns91LR4fv+c6u0Ob1gMdj8Lh7erczl/dwOMHptHB2/T8m1iIu3iIuzvf/2DgHcfEW8QkWiUkOEhId\nJCRYWH24NuHOGjsR8+m2XmfSnu6Oi0dQebydj2pd/O79OgrS47kgiOEEIhIcBTyRCNfu9rLo7Woa\n2zwkxji49+o8UuKcQb/eeL2wp9x3JwInWLjdBtcJLyeaPbSc8NLS7KXlhIc2ly/QnWUN3pDwesDr\nMfg24QquRc+yCAS+pBQHKalOklMcJKc6SE5xEhsXWeHPGtu1L219Leb4EayMzKBe53RY/GBGHj/4\n237qTnTy87er+dXs4p630BORPtNPkkgEM8bw1Kbak9uQXTmKgvT4vr3JoQPQ4luXLDBoPgx5vYaW\nE16ajntO/tfoC3LBsCxISLSIi3cQG3daS1ushTPGwnFKa5wzBhyWBRY4HA6GDx/O0aNH8Xp9odHr\nMYHWPo/H4PGAu9PQcWrLYNf/29q8eLsmjBpDV2uih2NHPED3PVrj4i3SMpykpTtJy3CQluEkJc2J\n0xmmwa9kLMTEgNuN2f0p1mVXBf3StHgn987M48evVXK01c3P3z7Io18oJNap0UMi50sBTySC/Wnn\nMd7a3wTA7Z/L4vL8s29DdjaBrrWUVBiVH8ry+s0YQ0uzl2NHPBw/6ubYEQ/NjZ5ztsY5HJB0SktY\nUrKDhMSTXaPxCVa/u5+dTic5OUlYzmY8nv+fvfuOr+uqEj3+2+f2pt57cZNiW467424nDkkoAUIJ\nBB4PXsijZICBAIEhQwhJqCGUGTITYMhjAhPIMASwU91b4ipXWbZl9d4sXen2e/b740iyndixbMu6\nKvv7+eSTK+n6aN9ydNfZe6+1rry0h5RGsOcfmFX0+4z/zp9xHFwWDgUlHa0ROlrPrRMLAW6PRkKy\nmYQkE4nJJjzxJrQxsNQrrDYomAanj8PJY3AFAR5AQaKdLyzJ5Pvbm6jsCPDU3lY+f7mi3IqiXJYK\n8BRlnCpv7ue3B40MxCW5Hj4wc3hLY28xWKR2SqlRvDYGolFJd2eEzrYo3Z0RznZGCYcvPjOnmTBm\nt+JNeBJMeOKMoM7h0Mbs3jYhBmYMbRCf+NblcyklwYCkz6vT12sEs4MzlJGwMevn7dXx9oaorzb+\njckE8UkmEpPNJKeaSUoxx2x5V0wtRZ4+fq5Y9hW6KS+OD84M8sejnbxW1UNRop07pieO8CgVZXJR\nAZ6ijEMt3hA/2tGILiE/wcYXlmRe1YyHlPK8AsejVx4lGhkI6NojdLQZAd3FZudMZkhINBkzV4km\n4hKM/WpjNZC7WkII7A6B3aGRknbuz7KUxqxf79koPd2RgRnNKOGQsSTc1R6lqz1K1YkgCIhPMJGc\nZiYlbXQDPjHtBuSLz0NjLbLfi3Bd+Uzy3bNTqDkbZE9DH7/e30pBgo0b0p3XYbSKMjmoAE9RxplA\nROexbY14Qzpuq8Y3VmTjsFzlzFtHq1Gklusb4ElpzE61t0Roaw7T2R4Z2pN2PpdbIynVTGKyMTPl\njtPGxDJkrAghcLoETpdGRrbRjURKYy/i2U5jtrOrw5jtQ0JPd5Se7ihnKoMIAYnJJlIzLaRlmIlP\nNF2/Zc/iEhAayIGEnbKFV3wITQi+dFMmD7xUS0NviO9vN5IuUl2X78KiKMpbqQBPUcYRKSU/291M\n7dkgmoAHlmWT4bFe/fEqjxg3bA6jaO0IikYk7a1GQNfWHMZ/kWQIt0cjOc1s/Jdqxu5Qm+svRwiB\n22PC7TGRU2C89qGQTld7lM42Y1a052wUKaGrI0pXR5TKI0byRmqGmbRMC+mZZizWkXuuhcMJuYVQ\nV4U8cQRxFQEegNNi4sGV2TzwUi09wSiPb2vk8VvyLttHWVGUt1IBnqKMI38+3sXOOiPj9eNzUpmT\n6bq2Ax4vN/4/7QajaO01CgV1WpsitDSGaW8J8+Z8BItVkJZhJjXDQmqGCuhGitWqkZF9bpYvHNLp\naIvQ1hyhrSVMwGdk8zbWhmmsDSMEJKeZyci2kJFtweG89tdBlMxG1lUhK8qv6Tg5cTa+vDSL725p\noKorwC/3tPCFJZnXPD5FmWxUgKco48T+Ri+/K28HYEV+HHeWJF3T8aSuI08cBkCUll31cYIBnab6\nMM0NYbraI7y5wUNisom085cJJ/GS62ixWDUyc6xk5liN5fFenbaWMG3Nxgyf1BnK1D16wE98oonM\nHAtZeRZc7qsL9EXJHOTL/2Psw+vpRsRffZLE/Gw3H5mdwrOHO9hc3Utxkp07bxh+ZxZFUVSApyjj\nQn23jx9sb0AChYk2Pr94BMpINNSAtwcAUXLjFf3TYFCnpSFMU12YjvbIBTV+NQ1S0o3ZofQsi5ql\nizEhBJ54o6xK8XQIhyRtLWFaGoyl80jk3N69E0cCxCeayMqzkJVrxem6gtduaimYLRAJI08cRixa\neU3jvmtmMlXdAV6v7+M3B9ooSnZyi+qipyjDpgI8RRnjfOEoX99whP6Qjsdm4sEV2SOyJ0lWHDJu\nxCdCVu5l7x+JSFoawjTUhuhovXCmzmSGjCwLGTkW0jIsmC1qlm6sslgF2XlWsvOsRKOSzjZjSb25\nIUwoKIeCvYpDARKTTWTnW8nKs2Czvf17TlhtMKUEThw2lv6vMcDThOALSzJp7K2lvifE97bWM7Mg\nUzVQV5RhUgGeooxhUkqe3NnMmY7+gaSKLNLdV59UccGxB/ZKiZKyS84GSmkEAA01YZoaQhf0aNVM\nkJ5pLOulZVowm1VQN96YTMJYPs+0MHOu8Vo31hmze+GwpLszSnenn2PlftIzLeQUWEjPtKBdoquG\nKClDnjiMrDiElPKaZ5mdFhPfWJHDV16qoTcY5St/OcJjN+eirh8U5fJUgKcoY9ifjnWyq87oVPG/\n56VTlnGNSRUDZDh0rsBxyZy3/Ly/L0p9dYiGmtAF2a9CQGqGmex8KxlZaqZuItE0MZD8YkGfZ2RA\nN9aGaG4Mo0ehpTFMS2N4YAbQQm6hlYSkCz9CROkc5P/8Dro7oLURMq69M0pWnJUvL83ikS0NnGzr\n4+e7m/jSEtXpQlEuRwV4ijJG7Wvs4/eHOgB4R0k6d5Yko79dr64rUXUCQiHAmHUBo5tES2OYuqoQ\nHW2RC+4el2Ait8BCdr4Vm10tkk10mkmQnmXsoYyEJc0NIeprwnS2RQiHJDWnQ9ScDhGfaCKvyEp2\nvhWLRRildpxu8PUhj5cjRiDAA5iX7eZjN6bx/w62sbW6h+JEG++5xiQjRZnoVICnKGNQY2+IJ3Y2\nIYHiJDvfvHUGPV0dI3b8of13mbn0mRKoO+inviZEOHRuts5mF+TkW8kpsBKXcO0lVJTxyWwR5Bba\nyC204evXaawNUV8dor9Pp6c7ypH9fo6X+8nKs5JXZCWuZDZi/y7jPbbmnSM2jg/MTKGxX7LxZDu/\nPdhGfoLt2ssEKcoEpgI8RRljfOEoj21toD+sE2cz8c1VudgtJnpG8HdEjx+iNW0+daUfpvNF7wU/\nS8s0k1dkJT3LMqm7SChv5XRpTC21M6XERmdbhLozIZobjHqH9dVG4BeX+jHysqxknSpHi0ZHpL4i\nGNnAD91Wwum2XmrPBvnRDqPTxUjtSVWUiUYFeIoyhuhS8uSuZhp6Q2gCvro8i7QR/AAL+HVqT/RR\nl/NZAvZzS1x2hyCvyEpuoe3KSmMok5IQgpR0CynpFkJBnYbaMHVVQby9Or0RF0dLP8mJcD+521oo\nmJ+B2zMyQZ7TauafVufxpfVVeEM6j21t5Pu35mNXnS4U5S1UgKcoY8ifjnbyRkMfAJ+cm8as9JFZ\ngurujFB9MkhTQxipAwPBXWqqoGC6k/RMsypArFwVq02jaJqNwqlWujqi1JwO0lwbIGJxUd0G1Ru8\npGaYKZxmIy3DfM3JEZmec0kXNWeD/Pz1Zr6yNEslXSjKm6gAT1HGiD0NXn5/2Nhnt7owjndOv/pO\nAAC6biRNnKkM0t15rmeYWYbIqd9MnlZD/Ie+dk2/Q1EGCSFITjV6CvtO/Rd1DVCXv46g2UN7S4T2\nlghuj0bhNBs5BdZrKqszN8vNx8pSeaa8nR21XooTu3jfDckj+GgUZfxTAZ6ijAH1PUGe2NkMwJQk\nO59ZePVlIMIhSd2ZINWngheUOHHHaRROtZH523/C3FqHeNeHR2TsivJm9pLpTN3+A4rrX6LtK/9B\ndY2kuyNKn1fnyH4/J44EyC+2UjDFdtV9cN9bmkRVd4AdtV7+X3k7BYk25ma5R/iRKMr4pQI8RYmx\nvpCRVOGP6MTbTXz9KjtV+H061SeD1FYFiZxX5SQ1w0zRNBupGWbobENvrQOMmmWKcj2IGbORQqBF\ngmT5TpC9dj5nOyOcORmkqT5MOCQ5XRGkqjJITp6V4hk2PPFXtk9PCMH9izNp7A1R3R3kRzub+PE7\nCsj0qKQLRQFU1xdFiaWoLnliZxNN3jBmDb6+PJtUl+WKjuHtiVL+ho+N63upqjSCO80EeUVWVr3D\nw+KVbtIyLQghzpVHsTmgYNp1eESKAsITB7lFAMjjxnsuIdnM3CUu1r4zjiklNixWgdShvibElpe8\n7NneR2d7BHl+D7zLsJs1HlyRjcdmoj+k8+jWBnzh6OX/oaJMAmoGT1Fi6PeHO9jf1A/AvfPTKU1z\nDvvfdrZHqDoRoLXp3HSdxSoonGosfV20IPFxoz0Z02cizOr0V64fUVKGrKsaaok3yOHUKJntYGqp\nnfrqEFWVQfz9Oq1NEVqb+khMNlE8w0ZGtmVY2xTS3Va+uiyLf95UT31PiCd3NfP1FdloKulCmeTU\nDJ6ixMiO2l6eP9YJwK1TEnjH1MsnVUgpaWsOs3OTl12b+oaCO4dLY+ZcBze/K47pMx0XDe6kriNP\nGLMpanlWud6G3mONtcie7rf83GwWFE61seZ2D3OXOIeKaXd3Rtm308fWl7w01ITQ9cvP6M3OcPHJ\nuWkAvNHQxx+PdI7cA1GUcUpdwitKDFR3B/jZbiOpoiTVwb3z09/2/lJKmuqDVB7109N9bgkqLkFj\nSomdzJxhFCVuqIY+o6jxYHsyRbluppSA2QKRMLLiEGLxqoveTdME2XlWsnItdLRGOH0iSEdrBG+v\nzsE3fFQe1ZhSYiO/2PG2v+6d0xM50x1k05ke/nCkg4JEG4tzPdfhgSnK+KACPEUZZb2BCI9tbSQY\nlSQ7zHxteTYW08WDM6lL6uuDbH3pDN1dwaHvJyabmFpqJy1z+HXF5ODybEISZOZe8+NQlLcjrDaY\nWgoVh4ytAZcI8IbuLwSpGRZSMyx0d0Y4ddzYfuDr1zm8z8/JYwFuXGghJV3CRd7yQgg+szCd+p4g\npzoD/GRXMz+81Upegu36PEBFGePUEq2ijKKILvn+jiba+sNYNMGDK7NJdLz1OkvXJfU1ITa/5GX/\nrr6h4C4l3cyS1S6WrnWTnjW8PUqDBhMsREmZKgqrjApRYizTyopDV5Q8kZhsZuFyNytv9ZCVZwEB\nAb9k99ZWXvlrN1WVASKRtx7PajKSLhLtJgIRI+nCG1RJF8rkpAI8RRlFv9rXytFWHwCfW5TB1OQL\nl510XVJfHWLLi17K3/DR79UByC9ys3JdHEtWuUlJu7LADkCGQ3DquPFFidp/p4wOUTqwFeBsJ7Q0\nXvG/j0swMW+Ji9W3ecgrsqFpEAxIjpcH2Pj3XqpOvDXQS3Za+PqKHMyaoKUvzA92NBIdxj4+RZlo\nhrVEq+s6zz77LFu3biUcDlNWVsa9996Lx/PW/Q0HDx7kb3/7G7W1tUgpyc3N5e6772bGjBkjPnhF\nGU9ePNnNi6fOAvDekiRWF8UP/UzXJY21YU4eD+Dr04e+n55tpmSWi+kl2bS2thKNXuVsROVRCIcA\ntf9OGUW5ReD2QJ8XeXQ/IjPnqg7j9piYu9jN0lW57NpaT92ZIKGg5PihAKdPBCmeYaNgim2oO8aM\nVAefWZjOz19v4XCLj98caLvsPldFmWiGNYP3l7/8hf379/P444/z1FNPIaXkF7/4xUXv29/fz223\n3cbPf/5zfvWrX7F06VIee+wxurq6RnTgijKeHG318fS+VgDmZbn42JxUwNhj11Br1AEr3+MbCu4y\nciysWOdm4TI3CUnXvlVWHt5j3MgrRiQkXfPxFGU4hKYhZs4DQB7ac83Hi4u3cuMiN2vuiCO/2IrQ\nIBSUVBwKsGl9L2dOBolGjdm6m4sTePcMIzP975XdvHL67DX/fkUZT4YV4G3cuJE777yT1NRUHA4H\n99xzD+Xl5XR0dLzlvsuWLWPBggU4nU40TWPdunXY7XZOnz494oNXlPGgtS/E97c3EpWQHWc0StcE\nNNWH2PKyl4Ovn1uKzcixsPJWDwuWuohPHJkcKCkl8tBeAETZghE5pqIMlyhbaNw4dQzZ3zcix3S6\nNGbPd7Lm9nOBXjAgOXbQz6b1vdScMgK9T9yYxpxMFwD/treF422+Efn9ijIeXDbA8/l8dHR0UFhY\nOPS99PR0HA4HtbW1l/0FdXV1eL1e8vLyrm2kijIO+cM6j21tpDcYxWXR+MaKbLztOtte8bJ/l4++\nXiOwS88ys2KdmwVLXUP1wEZMQw10tQMgyhaN7LEV5XJumAsmM+g68uj+ET30uUDPQ16hFTGQjHHk\ngJ/NG3pprAnx5SWZZHksRHT43vZG2vvDIzoGRRmrLjtF4Pf7AXA6L6yw73K5hn52KT09Pfz4xz/m\n3e9+NxkZGcMelNfrxev1XvA9k2mEP/SUYRt87tVrcGV0Kfnp643UnA2iCfiHWdnU7A3T3Xmu80Ra\npoWSWQ4SUy7dnuxan//okX3GjcRkTIVTVQbtVVDnwDVwewhPn4k8Xo44sg/TTWuu6jBv9xp44kzM\nXWJl2swolUd81NeG8Pskh/b6cXk0Pjcji0cP1tMTiPLY1kZ+8I5C7BaVY3il1HkQW4PPe1NT09D3\nPB7PRfMhYBgBnsNhZPn5fBdObff39w/97GK6urp49NFHmTNnDnffffflR36eF198keeff37o6/vu\nu4+UlJQrOoYy8tRrcGWe2nGG3XVeUrHwvuQ02g+fmznIzHGy4KY0MrOH35rsap//1mMHiAKuxStJ\nuoILLeWt1DlwdbzLb+bs8XLk0f2kJSdfU5u8t3sN0tOheAp0dwXZt7udMyd76ffqVB8M8sm4LP7a\n3c6Z7gD/ur+Dx989U7Uzu0rqPIitL37xi0O377rrLj74wQ9e9H6XPcucTicpKSlUV1eTn58PQEtL\nC36/f+jrN2tra+ORRx5h0aJF3HPPPVc8+Ntuu41ly5YNfV1RUUFHR8fVZxAq18RkMpGSkqJegyuw\n5cxZ/nt3KzdrCRRodqJnjectIclEaZmT1AwLQnhpbfVe5kjX9vzLs12ETx4DIDh9Nq2trVf+YBR1\nDlwjWVxq/L+/j5Ydm9CuIpP7Sl+D2fMt5BXFU3HYR2tTmEBvhHWmRFpliL0nz/KTV45yz5y0Kx7H\nZKbOg9ganMF78sknh753qdk7GGaZlLVr1/LCCy9QWlqK2+3m2WefZc6cOReN4hsbG/nud7/LqlWr\n+NCHPnSl4x8a8PmDrqioIBqNqjdUjKnXYHiO1vvYt7uP95mSh2YIPHEa02fZhxqo67p+maO81dU8\n/3r5G8YNqw192kykev2uiToHrlJiCmTnQ2Mt0YOvI6fNvOpDXclr4IkXLFzuoqs9QsURP13tUdKF\nlXeak6k/GuRV0cmamQlXPZbJSp0HsZWVlTWs+w0rwLvzzjvx+Xw8+OCDRCIRysrKuP/++wHYsWMH\nTz/9NM888wwAL7zwAl1dXWzYsIH169cDRguZe++994JZOUWZaIIBncOHfTRWh5kijO0LdqdgxiwH\nOXkWxOV6xV4HQ6UpSucgLNZR//2KMkiULUQ21iIP7UF+8FOjuhc0KdXMTavdtLdGqDjkp/esTq5m\no/8YbOnoZcF8Fy632lemTCzDCvA0TeOee+656HLrsmXLLgjcPvvZz/LZz3525EaoKGNcJCw5czLI\n6RMBohEwIfCjUzzDxo0znWiX6DN7vclQECqM/rNDpSoUJUbE7AXIDX+C9hZoaRj1fshCCNIyLKSm\nm6k6E2Tv/n7c0oS3VWfzBi/5xVam3WDHZlfJF8rEMDKFthRlEtJ1SV1ViMpjAUJBo7hqSOockf3c\nvjSBeXmu2A6w4jCEQiAEYvb82I5FUQqngScevD3I8j2IUQ7wBgkhmFJsx5IIT7/axkzpwoWJmtMh\n6mtCFE+3UTzdjtmiEjCU8U1dqijKFZJSGkWKX/Ry5ICfUFAiheSI3s9z0XZunONiYd6lN76O2jgP\nDey/K5yGiEuM7WCUSU9oGmK2UWh7qLNKDOUn2XnvsiSe19vZE/USFZJoBE4eC7JxfS/Vp4LoUdXD\nVhm/VICnKFegoy3Cjtf62L/LR/9AWzFTEjwX7uAN3cvKKXFD7ZFiSeo68rBR/27wQ1VRYm1oq0BV\nJdLbE9vBAPOy3Xx8bhqHZT+/D7fhS4iiDbQ/O3rAz+aXvDTVhZBSBXrK+KMCPEUZBm9PlD3b+9i9\nuY+zXUb2WGqGmcx5Zn7V3kIfUWamO/n0/IyxUUi4rgp6jP7Pav+dMmaUzgGzBaSOHCzAHWPvmp7I\nrVMSCCL5fUc7Wokkp8AoPO7r09m/28eO1/robItc5kiKMraoAE9R3kbAr3Nor48tL3tpbTL+wMcn\nmli8ykX2HAtPHGwa6jH74PJsLDFKqHizoezZ5DSjPIWijAHCZoeBGniD/ZFjTQjBpxekMyfDKDr+\n74dbkbmSFes8pGYY29TPdkXZtbmPPdv78Pao8iDK+KACPEW5iEhYcuKIn43re6k7EwIJDpfG3MVO\nlt/ixhIveGRLA/0hnTibiW+tysFtGztlFgYDPFG2cGzMKCrKgKEZ5WMHkeGx0RfWrAm+ujybvHgr\nuoQfbG+imzCLV7pZvMpFfKJxbrc2RdjyspdDe30E/Fdey1JRRpMK8BTlPLouqTllbLI+dTyIHgWL\nVVA6x87q2zxk51sJRSWPbW2ktS+MRRN8Y2U2mZ6xU2NOdrVDfTUAokztv1PGlqE9oUE/VB6J7WDO\n47Ka+NaqXBLsJvwRne9uaaDLHyE13cLyW9zcuNiJwylAQt2ZEJvW91J51E8krPbnKWOTCvAUBSMz\ntqUxzJaXzmXGahoUz7Cx5g4PxdPtmEwCXUp+uruZyg4/AF9YkklJ6vD7yY6GoaUvuwOuoWOAolwP\nIjEZ8oqBsZFNe740t4VvrszBahK0+yI8uqWBQERHCEFOvpXVt8dROseOxSqIRo2M200beqmtCqLr\nKtBTxhYV4CmTXndnhF2b+9i7o59+r7Hskp1vMf6YlzmwWs+dJs8e6mBnndE/9p6yFJYXxMVkzG9n\n8ENT3DAXYbbEeDSK8laDy7Ty0J4xl6E6LcXBPy7NQgCnuwI8sbOJ6EDwZjIJiqfbBy76bGgaBAOS\nw/v8bH3ZS2tTeMw9HmXyUgGeMmn5+qLs393Pjtf66Go3Nk4np5lZfoubuYtdOF0Xnh4vnerm+WOd\nAKwtiueuG5JHfcyXI/0+OHHY+EJlzypj1NA+vK4OqD8T28FcxJJcD5+YmwrAGw19/PpA2wWBm9Wq\nUTrHYWzbyDMuovp6dfZs72f3ln7OdqmMWyX2VCcLZdIJhXROHQ9ScyqIPrBP2h2nUVrmIC3TfNGk\nhDcavPzb3lYAZmc4+czCMVIO5U3kwdchEgGTWXWvUMauvCIjw7uzDblnO2JgyXYsec+MJFq8YV48\ndZb1ld2kOM28r/TCizqn28TcJS6KpkU4fshPZ3uUzrYI21/tIzvfwoxZjrdcKCrKaFHvPGXS0KOS\nM5UBNq33cqbSCO5sdsGseQ5W3uohPcty0aCtssPPj3Y0oUsoTLTx4IqxUw7lzeSercaNmXMRrth3\n01CUixFCIBYuB0Du3YbUx15GqhCCe+ensyjHDcAzB9vZWn3x4swJyWaWrHazYJkLl8f4WG2sDbN5\nQy8Vh/2EQ2rZVhl9KsBTJrzB1mKbX/JyrDxAOCTRTDDtBhtrbo+jYIoNTbt4wNbYG+KRLQ2EopJU\np5lvrcrBaRk75VDOJ3vPQsUhAMTCFTEejaK8PbFwpXGjqwOqTsR2MJdg0gRfXprF9BQ7AD97vZlD\nLf0Xva8QgoxsC6ve4WHWPAdWm0DX4XSFkYhRfUolYiijSwV4yoTW1RFh50ajtZhvoLVYbqGVUG6d\nuAAAIABJREFUNbfHMX2m420bip/1R3h4cz3eYBSXVeOhNbkkO8du0oLcvxN0Haw21b1CGfNETgFk\n5QHnzTyPQTazxj+tzCHLYyGiw/e2NVLTHbjk/TVNUDDFxpo74phSYkMznWt9tuUlL80NqvWZMjpU\ngKdMSP19Ufbt7Gfnxj66O8+1Flt5q4c5C504nG//1veHdb6zpWGo1t03V+aQF28bjaFfNblnGwBi\nzmKjY4CijHGDM81y305kZOwmJsTZzfzz6lzi7SZ8YZ2HNzfQ3v/2RZotFkHJbAdrbo8ban3W79XZ\nt9PHrs19dHeO3cerTAwqwFMmlFBQ59hBP5tf9NLcYPwB9sRrLFrhYvFKN3EJl19ejeiSH+5opKor\ngAC+tDSTG9LGVq27N5OdbXC6AlDLs8r4MfRe7euFE4diO5jLyPBYeWhVLnazoOu82f3LcTg1blzk\nYvktblLSjLzGrvYoO17rY//ufnz9qvWZcn2oAE+ZEKJRSdWJgQSKk0HkQAJF2QIHK9d5SMsc3tLq\nYCHj/U3GPptPzUtjad7Yq3X3ZnLPduOG0w03zIntYBRlmERqBhROA0C+sS3Go7m8Kcl2vrY8G01A\nfU+IR7bUE4gML0EkIcnM4lUuFi534Y4zPnqb6sJs3uDleLmfUGjsJZoo45sK8JRxTUpJY12IzS96\nOX4oQDgsMZlh2g121twRR16RDXGJBIqLHetX+1rZVtMLwPtLk3jXjKTrOfwRM7Q8O3+pKm6sjCtD\ny7QHX0eGgjEezeXNzXJz/+JMACo7AnxvWyPh6PD21AkhSM+ysPJWD7PnO7DZjUSMqsrgQHZ/AH2Y\nx1KUy1EBnjJudbZH2PFaHwd2+/D36yAgr2gwgcKO2XxlpUyeO9rJ+pNnAVg3JZ6PzUm9HsMecbKp\nDhoGes+q5VllnBHzl4HQjN60R/bFejjDsqYonk/NSwPgYHM/P93dhH4FiROaJsgvNrL4p5YaiRjh\nkORYeYDNL3lpqleJGMq1U4WOlXGnrzfK8cN+WhvPbVJOyzRTWubAE391JUzWV3bzh8MdgFHF/v8u\nGJuFjC9mcPaOhGSYWhrbwSjKFRIJSTBjFlQcQn9jK6Z5S2M9pGF594wkegNR/nSsk+21Xjy2Vj49\nP/2K/m6YLYIZsxzkF9uoPBqgvjqEr09n/y4fickmSsscJKWqj2nl6qh3jjJuBAM6lUcD1J0JMXhx\nG5dgonSOndT0q1+W3FbTy9P7znWp+PLSTEzDXNaNNSnlueXZBcsQ2tis0acob0csWI6sOARH9iN9\n/QinK9ZDGpaPlqXQG4zy8umzbDh5ljibibtnX/nMv8OpMWehk6JpNo4f8tPeEqG7M8rOTX1kZFso\nKbPj9qhzW7kyaolWGfMiEcnJYwE2ru+ltsoI7uxOwZxFTlasc19TcHegqY8ndzUhganJ9oEuFePo\ntKg5De0tgFqeVcYvMfcmMJshEjba7Y0TQgjuW5DO0jyja8x/Henk75VdV328uAQTi1e6WbzSRVyC\n8XeopTHMlhe9HNnvIxhQiRjK8KkZPGXM0nVJfXWIk8cCBPzGlJ3ZAlNL7BROs2G6xnZhR1r7eXxb\nI1EJOXFWHhrDXSouZahAbFoW5E+J7WAU5SoJlxtmzoPyN4z39NK1sR7SsJk0wZduyqQ/FKW8xcfT\n+9qwmzVuLk646mOmZlhYkWamoTbMiSN+An5JzekQDTUhikvsFE2zXfEeY2XyGUdTFcpkIaWkpTHM\n1pe9HN5n/HETGhROtQ5Uh7dfc3B3ot3PdwdakKW5zHx7TS5x9vF1vSP1KHLvDsCYvRsvewYV5WKG\nZqArDiN7u2M7mCtkMWl8fUUO01McAPzi9ZahbPyrJTQx1HVnxiy7McEZgcojATZv6KXujGp9prw9\nFeApY0p3Z4Rdm/vYu6Ofvl5jOSIr18Lq2zzMnOvEZrv2t+zpzgAPb64nEJEkOcw8sjaPVNc4LC1y\n8hj0GMtBanlWGe/E7IVgs4PUkft2xno4V8xh0XhodQ7FSTYk8JNdTeyu817zcU1mwdRSo+xT4VQr\nQkDALzm018/Wl720NoVVxq1yUSrAU8aEPm+Ufbv62fFaH13tRmX35FQTy252M+8mFy73yCyd1nQH\n+PamOnxhnXi7iUfW5pLhsY7IsUfbUPZsXhEiMye2g1GUayRsNsScRcB57+1xxm018e01eeTH29Al\n/GhnI/sa+0bk2Da7xsy5Tlbf5iEr17gg7evV2bO9X7U+Uy5KBXhKTAX8Okf2+9jyopfm+oHWYnEa\nC5e7WLLaTWLyyC2bNvQGeWhTPd6Qjseq8Z01ueSM8f6ylyKDwaFZDjV7p0wUQ+/lqhPIlsbYDuYq\nxdlMfGdtLtlxViI6fG9bI4da+kfs+C6PiXk3uVh2s5vkVOPCd7D12b6d/fT1qtZnikEFeEpMhMOS\nyqN+Nm3opeb0QGasw2gttuJWD+lZlhHdU9biDfHQa/X0BKI4LRrfXpNHQaJ9xI4/2uSereDvB5MJ\nsXh1rIejKCPjhrmQYHSPkVtfivFgrl6Cw2ysDrgthHXJo1saON7mG9HfkZhsZslqNwuXu/DEGx/l\nzQ1htrzk5fA+HwG/yrid7FSAp4yqaFRy5mSQTet7OXksSDRiZMaWzLaz+najtZg2wjXomr0hvvla\nHZ3+CHaz4KHVOUxJHr/BHZz78BNzFiPiE2M8GkUZGcJkQixfB4DctXFctC67lGSnhe+szSXFaSYY\nlTy8eeSDvKHWZ+s8zFnoxO4USAm1VSE2ru+l4rCfsOpxO2mpAE8ZFVKX1NcYPWOPHfQTCko0DYqn\n21g7kBl7PdL+m3pDfPPVOjp8EWwmwT+tyqEk1Tniv2c0yepTUHsaALHqthiPRlFGllh+K2ga+PqG\nssTHq3S3lUfW5pHkMBOI6Dy8uZ5jrSMb5MGFGbelZXYsVoEehdMVQTau91J1IkA0ohIxJhsV4CnX\n1VDJk1e8lL9xrmdsboGV1bfHUTrHgXUEMmMvprH3zTN3ucxKHx8V8t+O3LrBuJGRA9NnxXYwijLC\nRGIylC0EQG59McajuXZZcVYevTmPZIeZQETy8OZ6jrSO3J6885lMguIZdtbe4WHKjHM9bo8fCrBp\nQy+1Vaq0ymSiAjzluulsi7Bzo1HyxNtjLBNkZFtYdauHOYucOF3X7+3X0BPkm6/V0eWPYDdrPLQ6\nl5np43vmDkD29yH3bgdArHyHqn2nTEja4Mx09UlkbVVMxzISsuKsPHpL3tBy7Xc2N4xo4sWbWawa\nJWUO1t4RR37xudIqh/f52fKSl6b6kCqtMgmoAE8ZcWe7Iry+tW8gdX+g5EmamWVr3SxY5sITf327\nRdQPBHfd/ggOs8a3V+dwQ9r4D+4A5O6NEAqB1Yq4aU2sh6Mo18eMMkjLBCbGLB5ApseYyUt1mglF\nJd/d0kB58/UL8gDsDo3Z852sus1DVp5RWqXfq7N/l4/tr/bR2qxq6E1kKsBTRoy3J8renf1sf7WP\n9hajJlN8oolFK10sWeUiMeX6d4qoO2sEd2cDUSO4W5NLyUQJ7qREbhlIrliwAuF0x3hEinJ9CE1D\nrHwHAPKNLUjfyNSSi7UMjzGTl+ayDAV5B5qu/2Nze0zMW+IyendnGH+He7qj7NnWz65NfXS2qxp6\nE5EK8JRr1t8X5eAb/Wx52UtLg1HLzu3RmHeTk+W3uEnLGNmSJ5dyssPPN16tHSqF8vDaXGakOq77\n7x0tsuIQtBq1wcTq22M8GkW5vsRNa8FihVAIuXtzrIczYtLdxkxe+mAJla0N7Ky7trZmwxWfaGbx\nSjc3rXaTlDJQQ68jyq5Nfby+tY+zXSrQm0hUgKdcNV+/zqG9PjZv8NJQEwYJDpfGnIVOVr3DQ1au\nddT2iB1u6edbGweKGA8UGh3sCzlRRDcPJFcUTEXkT4ntYBTlOhPuOMT8ZYBRFmgiLSWmuS08enMe\nWR6jGPKPdjTxWtXZUfv9yWlmblrjZtEKF3EJRqDX3hJh+6vGnunes6pY8kQwvrqrK2NCwK9z6niA\nujMh9IESSza7YFqpnbwiK5ppdDf+v9Hg5YfbmwjrRm/Zh9fmkjdOO1RcSrSzHXlwN6BKoyiTh1h1\nG3L3JmiuR1YegYyMWA9pxKS6LDy+Lo9vb6qnujvIz19voT+k856SpFH5/UII0jItpGaYaW4IU3kk\nQJ9Xp6UxTEtjmKxcC9Nm2vHEXd8908r1owI8ZdiCAZ3KY35qTgfRBy7wrDbBlBIbBcU2TNehjt3l\nbKnu4ae7m9ElZLiNwqLp7vHZW/bt9L38F9B1cLoQ85fHejiKMjoKp0FeEdSdQd+8AVbeEusRjagE\nu5nv3pzHd7c0UNHu5zcH2ugLRfnI7JRRW/0QQpCVayUz20JjXZjKYwF8fTpN9WGaGsJk51mYfoMd\nl0cFeuONWqJVLisY0Hl9WyuvvNDNmUojuLNYBTNm2Vl7RxzF0+0xCe7WV3bzk11GcJcfb+PxdfkT\nMriT0Sj9L/0PYOxLEraJNTupKJcihECsNGas9QO7iHZ1xHhEI89tNfHwmlxuzDRqdP7xaCdP729D\nH+UlaaEJcgqsrL7NQ9kCBw6nAAmNtWE2v+jl4Bv99HnV0u14ombwlEsKBnSqKoPUnAoSHTivzRYo\nmmanaJoNizU2NdiklPzhSAfPHekEYGqynX9enYvHNjGvMOWhPUQ72wCGMgsVZbIQi1Yin/8P8Pvo\nf+UFWP3OWA9pxNnMGt9cmcMTu5rYVedlfWU33kCUf1iSgcU0uvMwmibIK7KRk2+lrjrEqeMBAn5J\nQ02Yxtqz1JVI8ooFjolRnGBCG1aAp+s6zz77LFu3biUcDlNWVsa9996Lx+N5y327urr41a9+RW1t\nLR0dHdx///0sW7ZsxAeuXD8XC+ysVo3CaTYKplqwWmM38RvRJf/yRgubzvQAMDvdyYMrs3FaJmZw\nBxB97a8AiJIyREZOjEejKKNL2OyIxauRm9fT9+Kf0ZbfCmLiLT5ZTIKvLM3iXy0tvFbVw7baXroD\nEb6+Ihu3dfT/vmkmQcEUG7mFVurOhDhdYQR6J4/3cKoCsvMtTC2141ZLt2PWsM6Sv/zlL+zfv5/H\nH3+cp556Ciklv/jFLy5+QE1jzpw5fOELXyA5OXlEB6tcXwG/ztGDfl77ey9VJ4zgzmyB6TMdfORT\nUymZ7YxpcOcLR3lkS8NQcLeiII6HVudM6OBOnj6OPHEYANPN74rxaBQlNsSaO0AIoh2t6Ds3xno4\n141JE3x+UQYfnmV8dh5p9fHgK7W094djNyaToHCqjTV3xDF7vguny4yU0FBjLN0eeL0fb69auh2L\nhvVpvXHjRu68805SU1NxOBzcc889lJeX09Hx1v0QCQkJrFu3jmnTpqk2SuOE36dzZL+PjX/vpfqk\nscfObIGppTbWvjOOktlObPbYBlGdvjDfeLVuqPL7+0uT+NJNmaO+fDHa9L8/B4ClcBpizuIYj0ZR\nYkNk5KAtMJKLouv/iIxM3HptQgjunp3K5xdloAmo6wnx1ZdrqekOxHRcJpOgaJqduz85hdnznNgd\n5/bobXnRy/5dqrzKWHPZJVqfz0dHRweFhYVD30tPT8fhcFBbW0tKSsp1HaBy/fT3RTldEaS+JoQc\nKHdisQqKptkonGrFEsPZuvPV9QT5zqZ62n0RNAH3zk/n9mmJsR7WdSfPVMKxgwDE3f0pvOqCSZnE\ntHd9GH3PNuhoRb6xBbH05lgP6bq6ZUoCSQ4zP9jRSJc/wtdfqePBldmUZbhiOi6zWaNouoOcQgv1\n1cbSrd8njazb+jAZ2RamlthISFZb/GPtsq+A3+8HwOm8cEely+Ua+tlI83q9eL3eC75nMk3cZbjR\n1nM2wqljfhrqQjCQqGWUO3FQONWOxXJhIDH43MfiNShv6uPxbfX0h3RsJsEDy3NYnBc36uOIhfD6\nPwIgsvNxLFmNr6srxiOavGJ5DigGU14RlqVr8e/ciNzwJ7SlNyMm+OuxMC+e791q5dsb6zgbiPDw\npno+tziLdVNjc4F7/nlgtULxdDOFUx3UVwc5ecxPf9+5OnqpGRam3eAgJc2sVvNGyODz39TUNPQ9\nj8dz0XwIGEaA53AY3QB8Pt8F3+/v7x/62Uh78cUXef7554e+vu+++9RM4QhoafJRvreD2jPneh86\nXWbK5iVTMjsRi+XtZ+xG8zWQUvKng408samOqJTEOyz85H2zmZUVP2pjiKXQqQpaD+8FIOme+xCa\nps6BMUC9BrEV+vCn8O/cCG3NeE4cxLXmjlgP6bpLT4ffZqXzhf8+RG2Xj5/tbqIjZOL+VcWYtdis\nsrz5PMjMhPmLJacrezi4p4OzXSHaW8K0t4RJy3Rw44IU8ovcKtAbIV/84heHbt9111188IMfvOj9\nLhvgOZ1OUlJSqK6uJj8/H4CWlhb8fv/Q1yPttttuuyDztqKigo6ODqJRtb5/paSUtDWHOXncT2fb\nuX0rLrfG1FIHuYU2TKYIXV3tlzyGyWQiJSVl1F6DiC75tz3NvHiyG4C8eBsPrckjzRSgtTW2+1BG\nS/iZfzFuZObQP6MMJ6hzIIZG+xxQ3spkMpFSNA1t7k3oB3bR9Z//jrfkRoQ2sWfxwPig/v4teXxv\nWz3lzf38fn89lc3dfHVFDq5RzLC93HkQnwQrb3XT3BDi5DE/Z7uitDX7efmv9cTFm5hS6iAn34qm\nqUDvagzO4D355JND37vU7B0Ms0zK2rVreeGFFygtLcXtdvPss88yZ86cS17NhsPhob6BkUiEcDiM\nyWRCG+bVxpunHCsqKohGo+oP6xXQdUljXZiqEwG8PfrQ9z3xGlNL7GTmWgZOMp3hPq2j8Rr0BqN8\nf3sjR1uNGeMF2S7+cWkWTotp0rz+su4M8uDrAIjbP4g+sIyuzoHYU69B7Gnv+hD6gV3Q2kjk9a1o\ni1bGekijwmGGh1bl8OsDbayv7GZ/Ux9f3nCGb67MIStudAu8X+48SM8yk5bppqM1wqmKIJ1tEXp7\nohzY3cfxQ4LiaTbyimyYLSrQuxpZWVnDut+wArw777wTn8/Hgw8+SCQSoaysjPvvvx+AHTt28PTT\nT/PMM88M3f+ee+4Zuv3LX/6SX/7yl3zgAx/grrvuupLHoFyFSFhSdyZI1ckgAd+5SuhJKSamlNhJ\nyxy7+yHqzgZ5dGsDLX1GSYD3lSZxT1kqpkl2tacP7L0jLQuxQLUlU5TzaflTYPYCOLwXuf6PyAXL\nETFaqhxtJk3w6fnp5Mfb+Le9LTT0hnjg5RoeWJbNnMzYJl+8mRCC1AwLqRkWujoiVJ0I0tIYJuCT\nHCsPcPJ4kIIpVgqn2rDZJ8frN9qGFeBpmsY999xzQeA2aNmyZW8pZPzcc8+NzOiUYfP7dGpOBamt\nChEOnwvsMrItFM+wkZQytjOadtb18rPdLQQiOmZN8LlFGawpmhz77c4nG2vhwC4AxB0fmPCbyBXl\namjv/DD64b3QXG+cL/MnVzH9W6cmkBVn4fvbGvGGdB7eXM/H56RyZ0nSmLyAT0oxk7TMjLc3ypkT\nQRpqQ4RDklPHg1SdCJJTYKVomg1PvPp7N5LG9qe+clk93RGqKoM01YUZbF2oaZCTb6Vohg1P3Ng+\nYSK65JmDbfz1hLHfLsFu4sEVOcxIvT4JPGOdHJy9S81ALJwcS0+KcqVE4VSYOQ+O7kf/+3Noc2+a\nNLN4g2alu/jROwp4dGsDdT0hfnuwnRMdfv5hceao7su7Ep44E2ULnUyfZaf6ZJCaqiCRMNSdCVF3\nJkRappmi6TaVeTtCVIA3DkkpaW2KcOZk8ILECYtVUDDFSsEUG3bH2P9j1+kL88MdTVS0G+V2SlMd\nfGVZFslOS4xHFhuyuR65bwcA4ra7EGZ1eirKpWjv/BD60f3QWAvlb8DcJbEe0qjL8Fj5wa0F/Osb\nLWyr7eX1+j5qz9bw9eXZFCTaYz28S7I7NErKHEwptVN3Jkj1ySB+n6StOUJbc4S4eI2i6Tay8qyY\nTCrQu1rqE2QcCYck9dVBqk+H8PWdS5xwuY2TIafAitk8Pk6Gwy39/GhnEz0BY6Pue2Yk8vEb0zBP\nsv1259P/53cgJSSnIZasjvVwFGVME8UzoHQOHC9H/8t/os1eMCkvihwWjX9cmsmMVAe/OdBKszfM\nAy/X8pmFY3+bi8UiKJ5up3CqjZaGMFWVQc52Rent0Snf4+f4oQD5xeNn0mKsmXxnwzjU541SfdLo\nOBE9r0NPcqqJoul20rPGz3R2VJf8+Xgnvz/cgS7BYda4f0kGSydJ8eJLkUf3w2Dm7Ls+jDBPzllM\nRbkS2ns+in68HJrrkZv+jlh3Z6yHFBNCCO6YnsiUZDvf395Ipy/CT3c3U9Hu4//MS8dmHtvBkaYJ\nsvKsZOZa6O6IUnXSSMgIBY19eqcrgmTlWiicZiNRdcgYNvVMjVFSl7Q2R6g5HaS95VxUN7i/rmCq\njfjEsbnP4lI6fGF+sqt5qARKfryNr63IJnuUU/zHGhkOo//h340vimcglqyJ7YAUZZwQRdMRy25B\n7ngV+bc/IBcuRyQkx3pYMTM9xcFPbivgxzubONTi45XTPRxv8/OVZVkUjuEl20FCCJJSzSSlmvH1\nR6k5HaJuIHGwsS5MY12YhCQTBVNsZOVZ1PLtZagAb4wJBnTqqkPUnjb2JAyyOwQFU2zkFVux2cb2\n1djF7Krr5V/eaKEvZCwtry2K59ML0rGP8SvL0SBf+R9oawahoX3kvkm3WVxRroV438eRB3aDrw/5\np98i7v1yrIcUU/F2M/+8Opc/He3kuaMdNPSG+MpLtXx8TirvmpGINk5We5wuE6VlDqbdYKehJkT1\nqSB9vTpnu6KU7/FxrFyQV2SloNiK0z2+JjtGiwrwxgApJd2dUWpPB2mqD6Of215HcqpxtZKRYxmX\n1b8DEZ1f7Wvl1aoeAFwWjc8uymBZ/uRekh0kO1qRGwZ6zq66DZFXHOMRKcr4IjzxiPd+DPnsL5F7\ntiJXrENMnxXrYcWUSRN8eHYKZRlOntjVRFt/hN8caONgcz9fWJJJomP8fPSbzcbkRn6xlY7WCDWn\nQ7Q0hQmHJFUnjDIraZlmCqbYSMswI8bh5+T1Mn5e5QkoFNJprAlTeyZ4QbcJkxlyC6zkF9uISxi/\nVyanOwP8eGcTTd4QYGTJ/uPSLFJdan/ZIP25X0MoBJ54xJ0fjfVwFGVcEivWIXe8CrWn0Z99Cu2h\nn07KhIs3K0lz8uTthTy1p5Vttb1GgLe+mvsXZ7Igxx3r4V2R8wsn+306tVVG3ddQ8Fz2rd0pyC+y\nkVtoxeFUKyHqDBhlQ7N1VQOzded1e/HEaeRPMbJhLeO4hUs4qvNfRzr58/FOdAmagLtnp/D+0uRJ\n15Xi7cgj+6B8ILHi/Z9AOMfXH1xFGSuEZkL7yH3ojz8wkHDxN8S698Z6WGOCy2riH5dmMjfLxb/t\nbaUnGOW7WxtYXRjH/5mXjts2/iYRHE6NGbMcTCu109wQpqYqSFd7lIBPUnk0QOWxAOmZZvKLJ/es\nngrwRkkwoNNQE6KuOkRf77nZOs0EWbkW8ottJCabxk027KWc6vTzs93N1PUYs3aZHgtfuimL6SmT\ns3Dxpchw6E2JFaosiqJcC1E0HbF8HXL7K8i//hdywQpE4uRNuDifEILVRfGUpDr4ya5mTnT42Vzd\nS3lzP59ZlMGinEs3rB/LNJMgO99Kdr4Vb0+U2jMhGmqMLhmtTRFamyLYHYLcQiu5hVZck2yvngrw\nriNdN6aO66qDtDVFhjpNwMBsXbGN7AILVuv4n0oORXX+cLiDv1R0oUsQwLtnJPLRstQxn6IfC/Ll\nP0N7y0Bixf9ViRWKMgLEez+O3L9rIOHiN4hPPxDrIY0pGR4rj92Sx98ru/nPQ+10B6I8trWRFQVx\n3Ds/nbhxOJs3yBNvYuaNDkpm22muN7Y+dbVHCfiNUiunjgdJTjWRW2QjM8cybmrGXgsV4F0HvWej\n1NeEaKwNEQyci+rMZsjKs5JXZCUhafzP1g2qaPPxizeMxtcA2XFW7l+cQUmqM8YjG5tkewtyw/MA\niNW3I/KKYjwiRZkYhCfOyKr9z39F7t2OXL4OUVIW62GNKSZN8J6SJBZku/n5680cb/ezraaXQy39\n3Dc/nZvyPOP6s8lkEuQUWMkpsOLtjVJfbczqBQOSzvYone0+jh6ArBzjPkmpE+ez+M1UgDdCAn6d\nxjrjjdR7Vr/gZ0mpJvIKbWTmTqyrhp5AhGcOtrPxjJEhqwm4sySJD89KUbN2lyAjEfRfPwHhgcSK\n93wk1kNSlAlFLL8Fuf0VI+Hitz9De+hJhGt8LkFeT1lxVh69JY/1ld38rrydnkCUH+xo4sZMF5+e\nn07WBKhP6okzSq3MmGW/YDUtEoa6amPLlMOlkZNvIafAitszfmcwL0YFeNcgEpa0NIZpqA3R3hqB\n85ZgHc5zVxET7U2jS8krp8/yu/L2obp2BQk2PrsoQ+21uwz5wrNQdQIA7WOfU4kVijLChGZC+8T9\n6I9+Bbra0f/jp2if++aEnaW5FpoQvGtGEvOz3fxyTwuHWnwcbO7n/vXVvP+GJN5fmjwhLtY1TZCR\nbSEj23JuMqY6RG+Pjr9fH1rCTUw2kZ1vJSvXgs0+/h+3CvCuUDQqaW+J0Fhr1OI5PwvWbIas3Ik9\n7Xu6M8BTe1s41RkAwG7W+GhZCndMS1QZspchj+xHvvTfAIi170LcuDjGI1KUiUnkFCLuvhf5u3+F\nQ3uQr/0Vcct7Yj2sMSvTY+XhNbnsqPXy6wNtdPsjPHekk63Vvdw7P5352RPnQtTu0Ciebqd4up2e\n7igNNSEa64wl3O7OKN2dfo4d9JOSbiY7z0pGjmXcVrVQAd4w6LqkozVCc32Y5oYw4fC5qTohIC3T\neCOkZ0+sJdjzdfQF+fnuJl493Y0+8PCX5Xv45Nw0kp2qrt3lyK4O9N88YXyRPwVx1yerA8ZQAAAd\nPUlEQVRiOh5FmejE8lvhxBFjL95//xZZPANRND3WwxqzhBAsL4hjXraLPxzu4O+V3bT0hXlkSwML\nsl184sY08pMm1r7q+EQT8YkOSsrstLcOTNw0holGoL0lQntLBG0/pGdayMqzkJY5vj7jVYB3Cbou\n6WyL0DQY1IXkBT9PSjWRnWdM5VrHYeuw4QpEdP56rJM/HzuBP2xMV2Z5rNy3IJ05ma4Yj258kNEo\n+tM/gj4vOJxo930VYVZBsaJcT0II+NjnkLVV0NaE/u8/RPvWkwjXxJmNuh6cFhOfmpfO2qJ4frmn\nlRMdfvY29rO/qZrbpiXyhZsTYz3EEadpgvRMC+mZFiIRSWtTmMbaEG0tEfQoNDcYcYDJBOlZFjJz\nx0ewpwK880SjxkxdS0OY5sa3BnUJSSayci1k5U38KtlRXbKluof/PNRBlz8CgMuq8cGZydwxLRGL\naWI//pEk//p7OH0cAO1//QMiNSPGI1KUyUEMXFDpjz8AnW1G0sVnH5yQ22dGWkGincfX5bGtppff\nlbfT4YuwvrKbLdW7ueuGZO6YljAh9ue9mdksyM6zkp1nJRTUaW4I01QfpqMtQjQKTfXG14PBXkaO\nEeyNxWXcSR/gRcKSthYjOm9rChOJXPjz+MSBoC7XMikaGksp2dfYz7OH26nuDgJgEvCBuTm8u9iF\nawy+iccyefQAcsOfABCr70DMuynGI1KUyUXkFSE+9Cnks09B+evIjX9D3PzuWA9rXNCEYFVhPEty\nPfytspvnj3XSH4ryzME2NlR28eHZKawujJ+w+6+tNqNebX6xjWDACPaa68N0tF8Y7GkapKSbycyx\nkJ41dhI0JmWA5/fptDaFaW0K09EaQb+wqgkJSSYyc4xp2MlS+VpKycHmfn5/uGMogQJgSa6bT8zL\nYO7UPFpbW4lGo29zFOV8srMd/Tc/Mb7IK0Z84JOxHZCiTFJi5W1QeRS5bwfy+d8iC6chimfEeljj\nhs2scdcNydw6NYm/nOrjz4caafdF+PnrLTx/rJMPzUxhRUHchA30AGx2jYIpNgqmnBfsNYTpbDNi\niMF+uAg/SSkmMrKMYM8dF7sYYlIEeFJKerqjA61LwvR0XxikCAHJqWYycow06om+/Ho+KSWHWnz8\n/nAHlR3+oe/fkObgo2Wp3JDmxGSaHEHuSJK93ehPfAu8PWB3oN33AMKi9t0pSiwIIeDjn0fWnob2\nFvSffQftgccQOQWxHtq4kuAw87VbprM2z8HvylvZVeel2Rvmyd3N/OlYJx+elcLSPM+EDvTgwmAv\nFNRpbYrQ0himrcWorNHVHqWrPcrxQwFcHo30gWAvKcWENorPzYQN8MIhnfbWyEBUHb6gowSAyQxp\nGZaBJ948oRMlLkZKyf6mfv77WCfH288FdjNSHHykLIXZ6U61T+UqyX4v+hMPQVsTmMxo930NkZYV\n62EpyqQmHE60z/8T+g8fhD4v+k8eQvvq9xDp6ty8UrkJNr62PJvq/9/evYdHVZ+LHv+uuWVmMjO5\nXwiBEO6XkkBFKpQqSr3Q465oEd1eq32U46n28TnVUivdZ/vsc0q7rcU+D4Jba1ureDu6K7sCRxEB\nQcALiqgBuYVAArlMrpOZydzW7/yxwhAgQCKQFTLv53nWs2bWXHizVsi883t/l+YOXt7h58Pqdmra\nojzxwWFe+9LBDeNz+F6JD7t14H+GONIsybVu43FFQ22Mupo4dUdiRCOKYEBn/9cR9n8dwWaHvAI7\n+YNs5A+y43Sd37xjwCR4R1vpGmqNhK65MXHc2q9gTD58NJPOybdhTYFfvhPFEoqNVW38vaKRg63R\n5PHROU5uKc9jUqEkdmdDdYTQ//gY1FQZ68ze+xDat75tdlhCCEArGorlwcfQf/8otLWg/+HXRpKX\nk2d2aBek0iwnv7qsmH1NRqL3cU07h1qj/HHLEV78vIHrxmZz5cgM3PbUqALZbBqDih0MKnagdEVz\nU8LoDlYTI9CmE48dG5ELYXyZVvIH2cgrtJOdY8VyjnOSCzrBCwWNhK6hLo6/Ln7SqFdNg+xcK/mD\njFEu3gxLyiYvoViCd/a28F87m2kMHxtJMiHfxQ3jc7ioKD1lz825oqIR9CX/Byp3A6D9+Gdo35ZB\nFUL0J1rJSCwP/Av6H/+XsdLFH36NZcEiNN/Am/6jr4zIdrJwZjF7GsO88VUjWw+10xiK8+dP63n1\nCz/XjMrk2rHZZLsu6JSjVzSLRnaujexcG+PKXITaE0ZFsTZGQ50x/UpbS4K2lgR7d0aw2oyuYnkF\nRsLn8Z19vnJBne1Ih46/3kjmGuvjBNv1k57jdGnkF9rJL7KRm2/H7kjtpOVga4TVu5tZt7+NcNw4\nXxpwyRAP14/PkaXFzhEVj6M//Tv4+gsAtFvmY5l+hclRCSG6o42egOV/PIq+5N+MOfL+8C9GnzxZ\ns/asjMpx8ctLi6lpi7JiZxPv7W8lGNN5o6KJFbuamD7Exw9GZzI2z5VyDQpuj5Vho6wMG5VGIqFo\nbDjWhSwY0EnEuwzUoAOnSyMn30Zu5/ZNZvHQlDqxkNn/rF27lrqqYgKtJ4/gtNowTkCBnbxCGx5v\n6rbSHRXXFR9WB1i1u4Uv60LJ43aLxhXDM7huXDaDe7GQtNVqpaCgQEbRnoKKx1F/Xoz6eCMA2g13\nYJk995y9v5x/88k1MN/5uAbq0y3o//E70HUoHY3lwX+V9aFPo7fXoDkc562vm1m9p5lg9FiDTGlW\nGrNHZXFZqQ/nAJxLr7dCQR1/XSxZkTyxGglGF7O8QgcOzwFmzZrVo/e9YBK8vTsGAaBZICvH2pnV\n2sk6D3XrC9WRQJT39rfy7r7W5OTEAHluG9eMyuL7IzPIdPa+0VY+3E5NBdqMD4ijLXez52K54Y5z\n+m/I+TefXAPzna9roG9Zhzo6nVHhYCw/XYhWOPicvf9A8k2vQTims76yldV7WqhqiSSPu+0WLi/1\nMWtEJsOz0lK+cQaOjSfw18Xx18dp8sdJdJmfd2TZkR4neBdMiXb0BBfZuRaycm39fnmQvhSKJdhU\nFWDd/tbjRsMCTBqUzg9GZzKlyDPgh62bQdVUoS/53+CvA0Cb/SO06283OSohRG9Ypl2OridQLzwF\ntTXov3nIWE5wwmSzQxswXHYLs0dncc2oTHY2hFm1u5kthwKEYjord7ewcncLJRlpXDHCx2XDMshK\nob56J9I0jcxsG5nZNkaOM5ZNbWlK0Fgfp7Ghd19sLpizOL7cLd+cO8USih21QTYcaGPLoQDRxLFG\n2AynlZnDfFwzKouiXpRhRe+o7VvR/7QYImGw2dHuvB/LJZebHZYQ4huwfPf7qLxC9GW/hfY29D8+\nhjbvLrRZP5RWpXNI0zTG57sZn++mORxnzb4W1u5rpbY9RlVrhL982sDznzXw7UHpzCzNYMpgDy57\napdwLV0Ga4y1Wvnyy56/9oJJ8FJdXDeSug8OBth6KEB7l/4MNovGxYM9zBqeweSidGzSWnfeKKVQ\nq/4vasVyUAoyso21LYePMTs0IcRZ0EZ/C8ujTxit8jVVqFefg+oquPU+maT8PMhy2Zj3rVxunJDD\nzoYwa/e38kFVgHBc55PDQT45HMRh1Zgy2MN3h3qZMtgj/fV6SRK8fiwS19lRG2JrdYAPDwUIRI8f\nNTwqx8nlpRl8b5gPX1pqzDNkJhVoRS1/GrXtA+NAyUgsP30ULSvH3MCEEOeElluA5Zf/jv7cYmPd\n2g/eRdVWY7nrQZkQ+Tzp2qp375QCthwyuhztqAsRTSg2Hwyw+WAgmexNG+Ll24PS8chn3hlJgtfP\n+EMxPqlp5+Pq9uQveFejcpx8d6iX6UO9FHikBNsXlFKoze+hXv8ztAcA0KZehnbn/WiONJOjE0Kc\nS5rTheW+X6L+6yXUytdg3y70f30A7dqb0K6+Hs0mrXnnS5rNwszSDGaWZtDaEWfroXY+ONjGFyck\nexYNxue5mDLYw8WDPQz2OaSU3g1J8EwWietUNITZURvksyNBKpsjxz2uYSR10yWpM4WqrUZ/cVly\nlCxpLrQbbke7/L/JHxQhBijNYkGbcxtq2Ej0F5+G1ibUmy+iPtyA5fafoo0ab3aIA16G08bVozK5\nelTmccneV/Uh4jp8WR/my/owf/2sgUFeO5MHpVNWmM7EfLe07nWSBK+PxXXFvqYOPq8NsqM2xM6G\nMHH9+FY6p83C5EHpXDw4nYuKPGSm8Igis6hYDPX/3kCteg3inWPUJ12C5Z/vRcvONTc4IUSf0CZd\ngmX0RNTfX0BtWA1HDqH/+y/RLr0a7YY70dJlzry+0DXZC8USbD8S5OOadj6pCdIWSXAkEONIoIVV\nu1uwaMbKGuWF6ZQVuhmb6yItRfvuSeZwngWjCb72h9nZEKaiIcxuf/iksitASWYaZYVuphR5mJDv\nwm5NzV9Is6loBPXBWtTb/wmN9cbBzBwst8xHm3yJucEJIfqc5k5Hu/W/oy6Zif7CU8YAjPffRm3b\njHbFtWizrpUVMPqQ225l+lAf04f6SOiKvU0dfFLTzue1IfY0htEV7GnsYE9jB69/1YhVg+HZTsbn\nuRiX52ZcnitlGk1S46fsI7GEoqolwp7GMHubOtjb2EFVS4TuZpLOT7dRVphufMsocKfML1x/pUJB\n1IbVqDUrINBqHNQ0oxQ75zY0l9vcAIUQptJGjMWycDFqzQrUWy9DMID6x8uod/5utOhdOUcGXPUx\nq0VjTK6LMbkubi03GlS+rA+xozbE57VBDrVGSXRJ+FbsagZgkNfOqBwXo3KcjMx2MjzbOSBH6EpW\n8Q2FYgmqmiMcaDG2fU0dVDZHTiq3HlWSkca4fBfj8owtP90ufbj6AdXkR61fhVq/CsKdy7pZLMYg\nimt+hDZ4qLkBCiH6Dc1mQ5v9I9QlM1Fr3kS9/zZEOoykb91KtGlXoH3/h2hF8nfDDOkOK98p9vKd\nYqNFtSUcZ6c/zM76EBUNYfY3dZBQdJZ0Y7x/oA0AiwZDMtIYke2kNCuNYZnG5vsGKz/1Jxd29H0g\nFEtQ0xalujVKdVuUg60RDjRHqA/GTvkab5qVUdlORuY4GZPrYmyuSzp99iMq0Iba9gHq4/dhT4Ux\nnx2A3YE240pjpFxOvrlBCiH6LS0rB23eT1A/uBH13krUe28ZLXob30FtfAeKS9GmXoo29Xvyt8RE\nmS4b04Z4mTbESPgicZ3djWF2NRhVtj2NHTSG4ugKqloixy2jBsZcfSWdyd5gn4MhPgeDM9IumGnJ\nJMHDWCevtj1KbSBm7NtjHA5EqWmN0thlTdfuZDmtlGQ5Kc1MM5p7c5zSOtcPqUAb6qttqI82QsVn\n0HVVFHc62swfoM36JzRfpnlBCiEuKJrHh/bDf0ZdNcdI7tasgGY/VFeiqitR//k8jBxnJHvlU9Gy\n88wOOaWl2SxMLEhnYkF68lhzOM7exg72NIXZ3xShqqWD+mA8+VhzOM72I8Hj3seXZqXY56DI56DQ\nY6fQ46DQa+y9/Sj5G/AJXkJXtEUSNIbiNIRi+IMxGoIxGkJxGoIx6oMxWjvOvASa224xMvgMB8My\nnUZWn5VG5gXehDtQqWA77PkStesL1NdfQPWB45/gcKCVTUX7zqUw4SKZqV4I8Y1pThfaldehZl0L\neypQH25AbdsMoXbYuxO1dyfqpf+AvEK0sWUwZiLamIlomdlmh57yslw2Li72cHHxsRHRwWiCqs7u\nVweaIxxqjVDTFqU1YuQKbZEEFZ0DJ0+U7rCQn24n7+jmtiVvZ7tsZLlsfbbaVI+yE13XWb58ORs2\nbCAWi1FeXs4999yD19v9yKHt27fzwgsvUFdXR2FhIXfccQdlZWXnLGhdKUJRnZZInNaOBC0dxr61\nI05LR4LmcJymcJymUJzmDqP5tSdsFo0Cj93IyL2dzbE+B8UZaWQ5rdIq10+pYDtUH0BVH4CaA6iq\nvXCo8ljp9SirFcZPNsomk76D5pSBE0KIc0ezWJPJm7plPnz1Geqj91HbP4RoBBpqUQ21sPEdY/Bd\n4WC0YaOgeBja4GEwpBR8mfJZY7J0hzW5ukZXbZEENa0RqtuMLltHAkbFrzYQJdI5O0YwqlMZjZw0\np+1RGuBzWsl22ZJbptNGhtN60t7jsGI9i2SwRwnem2++ybZt21i0aBEej4elS5eyZMkSHnnkkZOe\nW19fzxNPPMH8+fOZNm0aW7Zs4fHHH2fx4sXk5n7z+cMeXr2ftkiCQCRBezTR46StK5tFIy/dRp7b\nTm66PXm7wGNnkNdBtst2VidTnD8q2A7+OmisQ/nrwF+HaqiDw1XQ5O/+RZoFSkYY35THToSR49Gc\nrr4NXAiRkjSbHcqnopVPRcViULkb9XVnRWHfLojHoLYGVVsDcGy2BW+GkfDlFUJOPuQWoOUWQG4B\neDMk+TORL82KL9/NuBMSP6UULR0JagNRjrR3VgpDMRqCRqWwIRhLJoAKOhukEqdMArtKd1jwOqx4\n06xkOG3MLeh5vD1K8NauXcuNN95IXp7Rf+C2227jZz/7GX6//6Skbf369QwfPpwZM2YAMGPGDNas\nWcP69euZO3duzyM7wc5umkKPcli1LpmvlWyX0RSa7bYdlyX7nFYs8p/DNErXIRYzvsl2hIxRq+Eg\nhIOoUNC4394Gba2othYItEBbC7S1QuTU1z8pK9f4w1g8DG3EOBg1Hs2dfubXCSHEeaTZ7TB6Atro\nCfBPN6NiUdi3C7WnAlVdaXQhqT9iPDnQCjs/R+38PPn6ZPJnd4Av09i8GUafYV8meHxGX2KXG1zp\n4E4HlxucbnCkGV1SLP2nb9hAo2kaWZ3l13HdjKlRShGI6jSFYkZ1sUuVsSncWYHsrEiGYsevOR+M\n6gSjOrXtxsDOc5rghUIh/H4/paWlyWMFBQW4XC6qqqpOSvCqqqoYPnz4ccdKS0upqqrqeVTdmJfe\niEdL4LUc23xagkxrHKfWpTkvDgQ6t27o3R8+P3rbynhiSfFMb6ROuHH09eqEY6rr48p4qOttFOgK\nlN7ltgJdB6WjlKLJ6SQebEclEsYABd3Yq849ibiRvMVjxsoP8dix+9EIRDsgGu3lCemGzQY5BZCb\nj5ZTAIOK0YaUwuASNI/v7N9fCCHOM83ugLFlRn+8TqojbEyiXH0ADh80KhWN9UblItJhPCkWNY51\nTsJ+4ifDaT9y7I7OZC8N7HawdW7J2zZjb7EYyaDVBlaLsbdYQNNQVhvNHg/xcBilaaBpRqXk6N6i\nAZpRh+To411uwwn7o7e7HO96rPuzd4rDvWy86eO2Hk/n1u0EOlbAbWwRpdGmW2nVrQSObsrYtysb\nkNHjf/OMCV44bLScuN3HN0mmp6cnH+uqo6PjpOe63W6qq6t7HFQgECAQOD5Du3nl7075/G9QrRW9\noIDgGZ91Fmy25LdOLd1r9EHp/GZq7LOMaQlyCyAjC80y8CakPB2r1XrcXvQ9uQbmG/DXIN0DoycY\nWxdKKQi0oRrroLEBFWhBtRrVDRVogdYWVHtbZzUkZHyh7k4samzBU7R+dP03T3O8vXc/leglB5Db\nuXVn99jfcfjw4eR9r9d7yvEQZ0zwXC6jz1IoFDrueDAYTD7WldPpPOm5oVCo2+eeyurVq3n99deT\n9+fPn8/u/3nqBE+kgIgONUeMTQghUpEzw9jySsyORJjowQcfTN6eO3cu8+bN6/Z5Z0zw3G43ubm5\nVFZWUlJi/FLV1tYSDoeT97sqKSmhoqLiuGOVlZVMnDixx8HPnj072Yevvr6e3/zmNzz55JMUFRX1\n+D3EuXP48GEefPBBuQYmkfNvPrkG5pNrYD65BuY6ev5/9atfkZ9vdPY7VesdQI9qXbNmzWLFihXU\n19cTCoVYvnw5kyZN6nZU7GWXXca+ffvYvHkz8XicjRs3UllZycyZM3v8Q3i9XoqKiigqKkr+EEII\nIYQQqS4/Pz+ZI50uwevRKNo5c+YQCoV45JFHiMfjlJeX88ADDwCwadMmnn32WZ5//nnAGIDx0EMP\n8be//Y1ly5aRn5/Pww8/fFZTpAghhBBCiJ7TlDrl0M1+IRAIsHr1ambPnn3aTFWcP3INzCXn33xy\nDcwn18B8cg3M1dvz3+8TPCGEEEII0TupNd+EEEIIIUQKkARPCCGEEGKAkQRPCCGEEGKAkQRPCCGE\nEGKAkQRPCCGEEGKAkQRPCCGEEGKAkQRPCCGEEGKAkQRPCCGEEGKAkQRPCCGEEGKA6dFatGbRdZ3l\ny5ezYcMGYrEY5eXl3HPPPbJESh/ZvHkzb7/9NgcOHCAajfLyyy+bHVJKWb58OZ9++il+vx+Xy8Xk\nyZO59dZb8Xg8ZoeWUl555RU2bdpEIBDAZrMxYsQIbrnlFoYNG2Z2aClFKcWvf/1r9uzZw7Jly8jO\nzjY7pJSwdOlSNm7ciMPhQCmFpmnceuutXHXVVWaHlnJ27NjBq6++yqFDh3A4HEybNo2f/OQnp3x+\nv07w3nzzTbZt28aiRYvweDwsXbqUJUuW8Mgjj5gdWkrweDxcffXVRCIRnnnmGbPDSTlWq5UHHniA\noUOHEgwGWbJkCUuXLuUXv/iF2aGllEsvvZTrrrsOl8tFNBrllVde4fe//z1LliwxO7SU8tZbb+F0\nOs0OIyXNnDmT+fPnmx1GSvvqq69YvHgx9913HxdddBFKKaqrq0/7mn5dol27di1z5swhLy8Pl8vF\nbbfdxvbt2/H7/WaHlhLKysqYPn06BQUFZoeSkm6++WaGDRuGxWLB6/Uye/ZsKioqzA4r5RQVFeFy\nuQCjqqBpGjk5OSZHlVoOHz7MmjVruP32280ORQhTvPzyy1x55ZVMnToVq9WKzWY7YxWh37bghUIh\n/H4/paWlyWMFBQW4XC6qqqrIzc01MToh+t4XX3xBSUmJ2WGkpE2bNvGnP/2JcDjMkCFDWLhwodkh\npQylFE8//TR33HEHbrfb7HBS0ocffshHH32E1+tlypQpzJ07V1pT+1AkEmHv3r2MGTOGBQsW4Pf7\nGTp0KLfffjvDhw8/5ev6bQteOBwGOOk/dHp6evIxIVLF1q1beffdd7nrrrvMDiUlzZgxg7/+9a88\n88wzFBcX8/jjj5sdUspYuXIlWVlZTJkyxexQUtLs2bN58sknee6553jooYeoqKiQLjt9LBgMopRi\n8+bN3H///TzzzDOUlZWxaNEiQqHQKV/XbxO8oyWRE4MPBoPJx4RIBVu2bOHZZ59lwYIF0rHfZBkZ\nGdx9993s3bv3jP1fxNmrra1l5cqV3H333YDRmif6VmlpKT6fD4Di4mJ+/OMfs3XrVuLxuMmRpY6j\nraWXX345Q4YMwWq1cv311xOPx9m9e/cpX9dvS7Rut5vc3FwqKyuTZana2lrC4bCUqUTKWLduHS++\n+CILFixg9OjRZocjIPnBJiWq82/Xrl20tbXx85//HKVUMsF7+OGHuemmm2Qkp0gJbrebvLy8k45r\nmnba1/XbBA9g1qxZrFixgvHjx+PxeFi+fDmTJk2S/nd9RNd1EokEsVgMILm32+1mhpUyVq1axRtv\nvMGjjz562n4W4vxRSvH2228zffp0fD4fjY2N/OUvf2Hs2LHyd6gPTJ8+nbKysuT9xsZGFi5cyMKF\nCykqKjIxstSxefNmJk2ahNvt5siRI7zwwgtMmTIFm61fpw8DzlVXXcXq1auZPn06RUVF/OMf/8Bu\ntzNmzJhTvkZT/bjNW9d1XnrpJdatW0c8Hqe8vJx7771X5gHrI+vXr2fZsmUnHX/qqafkw60P3HTT\nTVit1mRCfXQOqueff97kyFKHUorf/va37N+/n0gkgtfrZfLkycybNy9ZthJ9p6Ghgfvvv1/mwetD\njz32GAcPHiQWi5GRkcHUqVO58cYbpQXbBK+99hrvvvsusViM0tJS7rzzztNWNPt1gieEEEIIIXqv\n3w6yEEIIIYQQ34wkeEIIIYQQA4wkeEIIIYQQA4wkeEIIIYQQA4wkeEIIIYQQA4wkeEIIIYQQA4wk\neEIIIYQQA4wkeEIIIYQQA8z/BwTnGl8a7TifAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff2fcb59c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, ss.norm.pdf(x, loc=3, scale=0.5), label=r'$\\sigma=0.5$')\n",
    "plt.plot(x, ss.norm.pdf(x, loc=3, scale=1.0), label=r'$\\sigma=1.0$')\n",
    "plt.plot(x, ss.norm.pdf(x, loc=3, scale=1.5), label=r'$\\sigma=1.5$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Prediction Intervals\n",
    "===\n",
    "\n",
    "What if instead of knowing how probable an interval is, we want to find an interval that matches a given probability? This is called a prediction interval, and is something we learned for discrete distributions last time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Prediction Interval Example\n",
    "----\n",
    "\n",
    "What's the highest amount of snowfall with 99% probability?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.4895218110612607"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.norm.ppf(0.99, scale=1.5, loc=5)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "So a single sample will fall between $-\\infty$ and $8.5$ with 99% probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   "source": [
    "To flip your interval, you have to rely on normalization. Let's say we want the lowest amount of snowall with 99% probability. We can flip that and say instead we want the highest snowfall with 1% probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5104781889387389"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.norm.ppf(0.01, scale=1.5, loc=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   },
   "source": [
    "So the snow will be between $-\\infty$ and 1.5 inches with 1% probability, and from normalization be between 1.5 and $\\infty$ with 99% probability. "
   ]
  }
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