{ "metadata": { "name": "005-Simple-Linear-Regression" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Regression - introduction \n", "\n", "This notebook is based in part on chapter 3 of \"The elements of statistical learning\" by Hastie, Tibshirani and Friedman (get full pdf [here](http://www-stat.stanford.edu/~tibs/ElemStatLearn/)). \n", "\n", "## Why model? \n", "\n", "Models are mathematical constructs used to explain measured data. In cognitive neuroscience, models are usually used to quantitatively describe specific parts of the nervous system (e.g. neurons, voxels, etc.). Typically, we seek to understand changes in the level of a signal measured from the unit (e.g. spike rate, or BOLD response), as a function of the inputs into the system (e.g. stimulus presented, cognitive state of the participant, etc.). Accurate and precise mathematical models derived from the data are useful in the following ways: \n", "\n", "- **They allow you to explain the data you have**: summary statistics of the data, such as the mean of the responses of a voxel, or the variance of this variable, are often not that informative (especially if normalized...). A model can give you a good explanation of the data you have observed, in terms of background knowledge, or theory.\n", "\n", "- **They allow you to predict data you haven't collected**: In many cases, assuming that the parameters don't change with changes in the independent variables, models allow us to interpolate and predict what the dependent variables would have been like in other values of the independent variables. Even extrapolate to conditions that have not measured. For example, because measuring in these conditions is difficult for practical reasons. \n", "\n", "- **They allow you to specify your confidence in a specific theory**: By performing some form of statistical testing, you can specify your confidence level in the veracity of statements about responses to a particular condition, or differential responses in different conditions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Definition of a linear model:\n", "\n", "Assume that we make a measurement $\\bf{y}$. Here *bold-face* indicates that we are talking about a measurment *vector*. Say, of length $N$. This measurement is a response in our unit-of-interest to some inputs: $(\\bf{x}_1, \\bf{x}_2, ... \\bf{x}_p)$. Each one of the $\\bf{x}_i$ vectors also has $N$ elements. We will make this more concrete later on, but for now, you can think of the $\\bf{X}$ as representing different input streams. For example, different locations on the screen.\n", "\n", "A linear model assumes that the expected value of $\\bf{y}$ given a specific input $\\bf{X}$ can be expressed as a linear sum of the $\\bf{x}_i$. That is: $E(\\bf{Y}|\\bf{X})$ is linear in the inputs. \n", "\n", "Let's break that down a bit. All this means is that in the noise-less case $\\bf{y}$ is a function of the inputs, $f(x)$, such that there exist $\\beta_i$ which satisfy: \n", "\n", "$f(x) = \\beta_0 + \\beta_1 \\bf{x}_1 + \\beta_2 x_2 + ... + \\beta_p x_p$ \n", "\n", "You will notice that bivariate linear regression, which you are probably familiar with is simply a subset of this, with N=1" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def linear_function(x,a,b):\n", " \"\"\" \n", " A linear function\n", " \n", " Parameters\n", " ----------\n", " x : ndarray\n", " Input variable\n", " \n", " a : float\n", " offset parameter\n", " \n", " b : float \n", " slope parameter\n", " \"\"\"\n", " return a + b * x \n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at a simple case:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 100\n", "x = np.linspace(-pi, pi, N)\n", "\n", "a = np.random.randn() * 10\n", "b = np.random.randn() * 10\n", "y = linear_function(x, a, b)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, y, '.')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The linear relationship holds, even when the input is not a linear function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t = np.linspace(-pi, pi, N)\n", "x = np.sin(t)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x)\n", "\n", "y = linear_function(x, a, b)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(y, '.')\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, y, '.')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi-linear regression: \n", "\n", "Now, let's generalize this to $p$ inputs, where we choose $p=10$\n", "\n", "For example, let's consider an output which is a linear combination of $p$ sine waves. \n", "\n", "To account for $\\beta_0$, we make sure that the first column is all 1's:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "p = 10 # Number of inputs\n", "\n", "# Preallocate a matrix (make it a matrix of ones to account for beta_0):\n", "X = np.ones((N, p)) \n", "for ii in range(1, p):\n", " X[:, ii] = np.sin((ii+1)*t)\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1) \n", "ax.plot(t,X)\n", "ax.set_ylim([-1.1, 1.1])\n", "ax.set_xlim([-pi, pi])\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "output_type": "display_data", "png": 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YUP3uf1L6ceDAAYkI1hg4dECKYy5YsIDm5mYW5C2gOLuYhr6GlPOOhU8PEVit\nCEuCRaCzkuGQfNWXXCKtw3lxdJSL8vLQahfhdjchRHpXjNPvZCroxi7T0+hyMeweZmPnRkoNpXi9\nXqxWKxUVFUnnWCwWtBoNYmAgTgQAZjNTzYOE/WHUc6WyC0NDkJ0t/WQyGb8997c8Zn+UQpmX1l0z\ns3n7WFwrcTp3sLDwDAacAynHGSbK8Jg84HBIbqE774Q//hGESHELRbFq1SoaGxtjC1UAegpXUdP5\nFgTifVq+XFKq+31+dk9OovANJAUl1RlqCrMLGZocihEBQNWGDRi3b8e5dYzMgkxU5TOXHAioOpGN\nluFrS30+XV1dVFbWJll0+/fDihVKGhoa8Hg8UgAtt5qiIrBvb4O5c6k0VjLoGoJly/4h7qHw/n20\n55TT0bGROeesQdMTpqBrDpraUdo6ZPTm5xMeGkIhz8RgWIvD8R48+SS5Z+Xg3D9FwB5/BhlyOWcZ\njbwRsQq+/e63uXTBpawqSYgXZWVJMaGnnopvi1oDEQQr5mCxuijUxd1vFTmV9E8Msn699PfJ5Sdz\ncvnJ+EreihFBYnwgisrKyhgRuN2H0emWpB0HRXs/Cp8c7/yIph6ZuSd3T5K9XCpzkijnAJXGSgac\nA7E4gYiYzeksgrIyKeTwtt3O+tzclOvHLAKrFSLvQaVajdVopDvNgrwoEi2Cyckd5BtXx+U8AVKc\n4D1EOAj33UffuTckWQMgcXB5OVgPDicTgcUCNhvOrRPoT85D1t0laYwRTE1N0dbWxoIFCzCsNdDW\n20Z1bjV6vZ68vDzp3TBW/lVxgk8PEdhs2LCgVkNRUZhJdT/yUWlF4nHHQXOr4MPxcc4xmcjIMKJU\n5uDzdadtqsPeQZWxigvMZt51OPjJBz/hgrkX4PQ7aW1tpbq6GqUytYbQmro6QkJIM3wUZjO+nX3k\nnBqPD3R0xDw1AORp8rjjjDvI1o1w+H1v2j4Fw0F6J3qpMFYgRJjJyV0UmU4hJEK4p9xJx2rs2biM\nY4SeeATOPVeyCCYnweWakQi0Wi3z5s1jT8IkOeDUU1wEbNwY21ZQAFot/Gb3KJeYzXQ5jqRkp1i0\nFmwuaxIRnD13LkcKCrA/umlGt1AUHk8rmVNVuPalBkQ7OzupqVmWRASNjbB8eQbLli1j8+bNtNvb\nqcmtoaQE3HtbobaWAl2BlPmV6Nv6pBAKoW7t5LByEaOju8k72YS2W4auQ4ey1E5bG2ydmkKbnY3N\nZpO0Svv8rKJ9AAAgAElEQVS7cN99KL5xA8bTjYy9kuwKirqHNnVt4p0j73D7abenXvfyy+Hpp2NB\n+ulEMF5iYpXPlJT04BstIJhlY8GCeDM/O+Nn7Mq4m7c3+tizZw9r1qxJuVSya6gVjWZu+rF4+WVc\np5XickfcMJFg8eQeiQgS5TwKfZaekAgRLg8jU8jwtEilHGa2CATv2O2cPY0IJicn6ezsZHFtrWQZ\nJrynU8XF2Nvb0/cZYsoFSBaBXr9SknN3cmHMrKxiMjMtuLb8DgIB+izHpxABSO6hkaZhKY4XhUoF\nWi2uTb0YTsqR4kIJK7ebm5upqKhArVajXaSlJ6OHCqU0TgsXLqSpqSku5x8Tnx4isFo5OFLAiSeC\n39+PMBuQ2aQsmKIi6BkQnGQwYIhM4Frt4hnjBNHA0BqDgTeH+3m26Vn+65T/wuaypXULRbGmspJx\njSZ5o9nMVNNgSnygelpm35V1V6Iw9bJ9S/qH2DPeQ4GuAJVShdfbjlJpJCvLklYYFQPDUFLGxPv3\nwNe+Jm00mWB0lPb2dqqnXzyCk046ifr6+tjfg4NQfMHyJGEEaS59scHPF81m2sfak8x4gAJdAfbB\nSC5spOJstlJJz+rVBN/a+JGIQKOuTUsEXV1dLFhwclKwf/9+Ket13bp1bN26NfbSlpRAqKUNamvj\n4/SPyBzq7GRSn4XNtoDCQh+TunbkAchtChPIHaO9XVA/7qRqzhy6u7slrXLoVURmBqxdi+k8U5JL\nBGCDycR7DgffePfb3HP2PeizUgOLLF4sxQuiSQDTiGAwX81ilzbplO5DFuR6G4llvor1xXz3knMZ\nGPQzb95p6HS6lEtFiUAIgcfTilo9AxE0NBA8eXn83TMaIRTCs3MI3XJdkpxHIZPJsGgtDHuGY1bB\n4KA0b05X+svLobkrjDEjg3JVstW5Z88elixZQsbEBOTlkXiThrlzUQ6kWtdALDunJrcGIUJMTu4m\nO3vFjJOu0Xgm9m2/ga99jd4+GWVlqW0uWgTOI9NcQwCFhfi2dqE/UQ9f+pJk0UUsoAMHDlBXJyWp\nyOQyrOVWCvsLI+0t4tChQ2nng4+CTw8R2Gzs6LawerU0kWTlzYNQCNxuzGZwT8g4LzueynY0Ioia\npmsNBuonxvnO6u9SlVuFa8rFweaDMxLBssJCphtlIi+PcLc1Fh+A9ESgkCs4fqWRluYA4TQuq+ka\nSTSH2aKzpApjXx9ZmjIcx4VhVcRdkJcHY2N0dHSktQggNWA8MADFV54Gr74qBZwjWLo8TNf+DGoz\nAshkMnLVyW+jRWfB135YygpJeNlyV5yO0b47bTZEIrzeVrItC1KIIBQK0dvbS03NKoSYYmpKChg3\nNsKSJVBRUUFvb69kEZgkiyCzS3INWXQWrC7rP4YIDhygvViDf6iayko1k65dhGoqKe1zYZcNozUI\nLBPZVFdU0N3djUazgLB7At83vwgyGbqlOtyHkq2+vIwMiuR+3OpqLp5/cfrrymTxyWR8XHKe18Wz\n3dpzBNXJ/MK41UhQ7sIf9Cdtv231N5Dp68kwnp72Urm5uSgUCoaG2gmH/WRmFqTv0+gomSUJ755M\nhigrJ9zShW6JLknOExGV8+h6gnRuIYi7hmZyC61atQpGR6X3IQHzli0j1+EgmCZbY8w7FpNzj6eV\nzMx8MjJMcZmaPhYsx6Fpgauuoq+PtBbBwoUw1TecQgQiv4BgWx/Zx2dLPm6vN5b9FQ0UR9Fv6Cev\nUbqPRYsW0dTUNGOfjoVPDxFYrbx/uCAydm1otPOkQR4eJkAYkTvFqmD84et0i2dMIe1wSIGhtsGt\nhAMuzlx8LXKZHLPWTGNH44xEME+vp93tTipKNRU0oAyPo6qKaycdHVKgeDrO/dx8XM58Xmh6IWVf\ndHIDyUcZXT9g0aZ58H19ZPZ7cS/LjU/ECRbB0Yhg69atCCGYmpJCDPkLzVJBs9deix2nW+BF3WFg\nYLyTmtyalCqxFq2FcIJbKIo58lqUCiuhY0idx9NGTm0drv2upLEcHBzEZDJJpnGEyMfHpbWEVVVQ\nWlpKz0APNpeNMkMZpaWgt7YmWwRz5khugaGhmTvwt8aBA+wxhdAHiykvL8Hl2k+4sI5yrRub24ah\nYor5dhNzIhaBzOMhuzmA+zRpMZFmvgZvm5dwIK4gCCGYGHyLeXP/bcYqvYDkHnruOaivhxUrSIz8\nH9C7KbIlp0DarHKy5WaG3cNJ2zMVmZi1Y7SNh1KLx0VQVVVFc/OHaDRzZ+7T2BhZRcmuvVBOEdkF\nDhQaRZKcJyIq5zmn5TCxZYLDB8NpiSA/H3xuGadkpq5RicUH0hBB7QknUOz3s91uTzkvag3IZDKc\nzh1kZ8ffvXTat27zAO4aJWRnz0gEixaBbHSaawgIZOahK3Cj0Cqkd/fyy2NxnmigGMAX9DEqH0Xz\noeSBWLhw4axFQCCAGB9nx5E8li4lbppaLDA8zJaJCbT5QQKj8RS8Y1kEVcYqvvfe9zhRr2OHS/Lb\nW7QWWvpaZiQCo9eLTaFgIMHEdHapUOsmk16MdBYBQO3yTGwyLfc+dy/BcPLisugKQoj7KCGiKU1/\n8H19ZG5vxWeK51yTl8eU1crQ0FBK6mgUxcXFaDQaOjs7GRqShk+hIK5VRu+p0oG/RUv72Azam9ZC\nRm9fChGEh9RkCSeH3O6Uc6IQIozX24GheCEKnQJfdzx43dXVFQvSR59fY6Ok5CoUUFZWRqejk/Kc\ncpRyJWVmL9luK8yZE7ecZLJP3CoQBw5Qb5zAENRTWKgmK6scX1YtBSoHDp+DqeIJ8m2GGBHw7ruo\nRCFeufRcFRoFWaVZeNvj8aNXWl9B7zrM4bBhxokZkJ5BTY2UNLAieQHUtsxhDANjSQuphobAmJl+\nMskIjzIVMLK5e3PaS1VVVdHSsnvm+ADA2BjqkmX4/YOEQpLF51cWoC+Q0uUS5TwRUTnPyM1AM1fD\ngQ8DaYlgMhRE5Psod6bW+D8aEWRVVlIqk/HCwdQ5IdFKmZxMePdmmHQz//IBIVWIUMhFby9pXUPV\n1aDzjODTJ1sEPr8RfVGCJfylL8XiPI2NjTHXUFTOA60Bgs4g8+fPp62tjTx13mc4RjAyQthoItes\nIDMz4mPWzJXUA5uNHU4nBYUiqYSyRjMPn6+LcNif0lyHvQOH14Hda+eKsjq2TEwAkK/Np3+8n9ra\n2rTdkA0NoSwrS1pYM9GkJEM2EftbiJmJoLwcRkUWdUPLeLLxyaR9UU0pHPbjdh9Cp5NSCqXAbMKD\nn5iAYBCVyMcXHohnRplM2NvaKCsrSxvojiLqXhkYkDJfAbjoIti0iWhua6NyHEMu7OiYQXvTWdD0\nD6cQgatTSVbQy46j5Mj6/b1kZOSiUOjQLdUluYc6OztjRBC16KJuIZA+ZmSdssYmkiqOMJBZAUpl\n8kv7CRNBaP8+WguyycSB2exDr1/JpKcEbagXo8rIcEE3sj5NnAhefRV18Qp8vnjGiHaRFvdBiUCF\nEPzkg59w5wnXExKCZo9nhitHcPnlsHOnlJ6YgAPebinyn5BOOzSURqYimJxspyJ7NXfU35H2MlVV\nVXR0HJ45PhAOw/g4MlM+Gs1c3O4mADxeM1qdFAw/mkUQ7ZO2TkvzYSkNczreHx/HWBxiZCB5seLQ\n0BAej4fKysq0REBeHlohqE+TSJDYp2O6ZV0uZA1bUakr8Xo7Z7QIMjKgKGOYDmcyEbjt2agN8fmC\nRYvAYMD6yisEg8FYaf4OewfVpmp0y3U4tznRaDSUlJTgGfF8hi0CqxVfTgHRj5lJWQu1MYtg1+Qk\nVSXyJCKQy7NQqSrxeJJr3E/6J5mcmuTxxse57cTbOMVopD5CBJqwBkORAbV6hq9vDQ5imDcviQgc\nB5UoPHFzc2REEoJ0X+3MzIR8fZi141/iji13xEs1ENdKXK79aDS1KBRSkC9FK+nvB40GxTkXoVQa\nmZqK3HReHhOdnTO6haIoLi6mv78/mQj0ejjzTPjLXxBCsHVigrpFcHBgBu1NayFnyJFCBO7DXqa0\n2Rw6Sl2XxECj7jgdrv1xIpBSRyV3SdQiiAaKAdRqNVmFWRSrpY4Xu1tpExJp52vzGXGPSPGXhQul\nlJNPApOTyGw2RrLnEgx2kJs7THb2SsZtRWSOdaDXmDGW2ejrUMSJ4LXXUC3ZgNcbLz6lXRwnglfb\nXkUg+Ny8CzkrN5f3jrb4BOALX5DqMSQEeaNyLq+uSUpRHBqCIkOqphsMBpmYaCU7XE3raCu7Bnal\nXKaqqorOzh7p3UuHiQmJeDIykizyyZFcspDIaMYYQYKcaxdoae9XpLUI3rbbqZ4ji60ujuLQoUMs\nWbJEssxHR1NcMshkOLOzce/fjycUStoVtVJCIS8eTzM63dKUPsXwzjuwahVqbQ0TE93Y7VKmXTqY\nxTAHrfF+CCGY7NOSlTHteX7pSxx49FHq6urimYeRdQ05ayVXGUjuIWuHNS7nHwOfDiKw2XDrLBQU\nQCjkZWrKiko1J2YR7HQ6WVSekeIWThcn6LB3UKIvYcfADq5achW1ajWeUIg+nw9cYCo/SsbL4CAF\ny5fHUjBDnhBeWyZM+cAvWR4zWQNRVMwRjDflYlQbeaP9DUBKHe0Z76HSWBnRSOL54imuob4+6Vrn\nn49aXYnXG3nJTSa8vb3HJIKSkhIGBgaSiQBi7qEjPh9ZcjkVRQp6XTNbBJZhdxIRiJDA0+qBvFza\nZ8jOgARrjggRzGARaLWL8HgOs3+/iBEBgLpEjSEkrXo1DrdxMDCXQEBaHKXN1OLwOqR4ybEmz78V\nDh3CXlGAwl2Ly9WEXt9Jtm4ljrZsZJ4JsoN6FpRP0NYG5eXl9HR1IfLyUFesjj87QLdYChhHrYEf\nnfIjqWZVdjZ70tQdSoLFAgaDtKAsgmiKtKyqKkYEQkhEUJ6XqularVZyc6ew2RR8a/W3uLP+zpTL\nVFVV0dMzOrNraGxMGnskIne5DhL2h3EO5pDhHEyS85RbSJDzQKkWt1/GtOoRgEQEK6ozU4hgYGCA\nkugJIyOpFgEwZTYzr7c3pvhFEbUIXK59aLULUCjU8T5NtwhefRXOPx+VqpKurmGKiiLu1enw+8kK\ne9nbGXdh+Xv9TMlMKJzJ8Rkuu4zGTZtYsnhxUp+qc6sxrDEwvkVabb1o0SLamtvicv4x8OkgAquV\ncZVkEXi97ahUlchkSrBYcA0OEhSC+SXKlK9rabV1KXGCDnsHU6Epbjz+RjQZUoG4NQYDWyYm8Nv9\naPOT0+2SMDhI8fHHS1VIAW+7F3W1BllenqSFcGwiqFms4EiH4NZlt/LrHb8GoHeiF4vOgkqpwuM5\njE4XF4iUFLb9+6WyjKtWoVJVxbXKvDyCw8MfiQhSLAKQitft3MlWq5XVej35FoEt2J5ee9PkU2wP\nIsrLY9t8XT4y8zPJyjczNTqKI5B+4dzRiCDRIlAqDWRk5NHVFSbxlmQmGSq3FJiXd7RhM9TGFIAC\nXYE0meTmQpqg4N8F3d0MmlUEbVU4HPvQ67tRDFeRkZeFbN48SoblzLM4GRgApVJLtlKJ7bTTUKkq\n8Pt7EELSTrWLtLgOuvig5wO8AS8XzpVKNByfnc3uyZm/4BWDXp/0BbOY5l1dLQklUhkWpRLKjAUp\nmm5fXx+lpUqsVvjKsq/Q0NfA4ZHDScdUVs6hr8+DWj2DjCUQgU4nvXvuQ26oLEfW15Mk59ORKOe9\nCi1lci/T49FDfj/OUIjjqzLSEkHsi4fpXEOAvLSU0sHBJAsrmjpanVuNx3MYrTb+7kUtgliMJhSS\nShicfz5qdRVdXa60biEARkaYMpg51BS/Cec2J1nLypFN11grKmhUqViSkJoetQiyV2THkiqiKaQx\nOf8Y+HQQgc3GqEKyCBInEiwWxgcHWZGdTXGxLA0RpAaM91n3MTQ5xE0rboptWxshAuegE2XODP51\nIWBwEHNdHUORB+lp8Uiric1mSQvh2ERQNVfOiF7HOeFzODxymEPDh5JWWvp8PWRlxSfYFPN082bJ\neapQoFZXxv3MJhNyu33GNQRRFBcXp7cI1Go48US2trWx2mBAZx4jHAaTOtVC0toncWXBZGY8COlu\nckuVV3NzWRkIsGuGycvrbUWtllwLqjkqQq5QrNBYokUAkJFxHG63LMnN5tP4CI9FzOLWVlyFtUQ9\nUTE/s9H4yVkEDgfWDD8TXVXo9aPodHl4DgTQ1mkJL1hA4VAAs9xFWZmkmM8Rgu66OhQKDUplLn6/\nJLTqajVTQ1M8tOUhbl6RUDlWq6XT68U9zZ2RAiGkuEhk0oqtlE2wCIaGpDBCugSEvr4+ystNCAFh\nv4avr/w6dzXclXSMyRTE5ZKl++KihGkWgdt9EOduJ6qVFWC3c2SwKX3pbJLl/Mh4JmVhN8HJ5ISK\nvS4Xy3Q65syRJVXIBYkIiqIr/mcgAk1tLUabjY0JsjHmlWIXJrUJn68HlSr+7mkztShkCianIrK8\nY4dkfVVUoFZX0tcXmJkIhoeRW8wkxqYntk2gWluRtgTKAYWCuogyCfEU9wxTBvIMOQFbIDlz6GMG\njD8dRGC1MiSiFkFbnAjy8/FbrazU6ykqSv3erk6XSgRvdrzJquJV5GvjQZy1OTlsmZhguHOYYNYM\npaIdDlCrMRQWEggEcLlceFo9aOZpPhYRVFbCcLYO3x4fNxx/A/fuuDepzonP1y25vSJIMU8PHowt\nGlKrky2CLJfrr7cIAM44gwafj9V6PeGcDrS+1NRRALq6GMjLSkprdTe50S7QQm4ux01Nsd2Z/hur\nHk/8+ckiOfSu/S68Xi92uz3+MgM+3ypyc10xzdAf9ONVeHEPRLKS2toIVM6NE0E0x9po/OQsAoeD\nPrkL70ANZWUClWoOrkYXuiU6bBYLlW45Lu8ItbXQVj/MnHCYbq1kdarVVTEilyllZNRkcGTHEa5c\ncmWs+Uy5nIVaLY3Hcg+5XJJ/PlJYLSZTCRZBjAjSpCT39/dTVlZKQYE0T9204iZebnmZUU98cvL7\nOyguVtM504c1EoggM7MQIcJMNHWRvSIHiouxtexJWZwYRaKct7TIqMkP4GlJDpLvnZxkWXZ2UgXS\nKD6KRaCbOxeLz8fhkRF8kdXY0cWlMpksQgRzUvoVG6uIWwhApaqir0+eNmMIgJERMovzsVrjn0t2\nH3SjPaEIpqaS1u0AdE5OUhOpG+UP+rG6rJTnSKSknqvG0+Zh7ty5dHd3Y1abP/Zagk8NEfQHCmIW\nQSxrwWJBMTzMiuzstESQlVVOMOgkEJA0AG/AS9NwE9cdd13ScUt1Onq8Xvpa+nDLZkh9jBSbk8lk\nFBUVSVkKLX8dEQyGVTh3OPnq8q/y3OHnODh8kOrcaoQQKVqJIcvAVGgKb8Ar2fY2G9FyoSpVPEbg\n0+kwBAKUJ7hr0uFoRDB+xhl0ZWWxVKfDo2pH6ZzhRrq6GM3XJRGUu8mNdqEWTCbm+3zsSEMEoZCb\nQGAk6f6i7qGenh7KyspQJDhcPZ6lGI3x0gudjk7MmWb6e/uliT4QILsqP9kicEcsgomJeOmFvyOE\nw0EX45hkBRQXa1GpynEfcKOt09KWlUVVMBOb28bcudD2ejtzamrojqiz0vOLT6o9BT18XvH5lFXE\ny4/lHhJCUlTOOkv6Ij0fwSJwpVoEJSUlFBREUkzVRi6cdyFP7H8idozH00p5uTlWaiIFCUQgk8nQ\n6RbjHGlEt1wH5eVMtB+Y0SJIlPPmZphbLfA0TyOCiEVQXCz1MfF79IODg8d2DZWUUKPVUjI8HEtx\nTrbGu5OscZjmmn31VekbC4BKNYfBwWxKSmaQseFhZJZ8cnPj30/wtnvRzNUSG+QIJicnEXI52c3N\nMD5Op6OTMkMZSrnkndDUavC0esjMzKSiooKMqYzPrmuoy2PBYkl2DYXNZrLHxliRnY3JBG63tFAv\nCplMFilAJ1kFzx9+HrlMzmmVydUVlTIZx3m9ZAotI96R9H1IqDpaVFTE4ODgX00EvQ4l7sNuLDoL\nF869kA+6P6Amt4ZgcAy5PBOlMj4RyGQy8rX50oN/+22p2FgkvVVyDUkTSefEBHkyGcq0kas4LBYL\no6NjDAyIpNp5ADvKylh+5AgZAwOMyzsIjcxgXXR1MVFkShJGT5MHzUIN5OZS4fGw3elMyX/3ettR\nq6uQyeJ9jKaQTncLAbjd8zAY4oHnDnsHFfoK+vr6pBepuJiSUlkqESiV0tdMPopv/f8Iz/AALrUK\nfVaAgoJMVKrymEXQkplJeVCBzWWTLILdE8w58UQpc4ioRSdNqoFQgPcz3+dk38kp1zg+O5s9R7uX\nyUmpHsP69bG6UbH6+mYz0dWDiRbB9Imkv7+f0tK4RQDw1eVf5eG9D8eeo8fTSmXlnKMTQcKKX41q\nEX55M7olOigrI9B5ZEaLIFHO+/qgapEihQj2uVwcp9NJ2Xf5yYpfzCIQYkYioKSEcqWSApuN/REL\nK7q4FEhRwiBhrDo7pXd8pZRaqlCoGRmppKBglLQYlhaTRda8EvKECIwGyCrNilUhjWJwcJDCwkJk\nJ50EmzcnfRsBQDNXWnAIUsBe7pV/RonAaqXNWYDFIuKpo0C7RoPe5cIslyOTpYwvEPVVSku4H97z\nMAJBUXbR9CtQMTyMvqgKp9+Zvt539IM0SEQwMDAguYbmxonAbpfiSelkMIq8PAiEZAy3Sn7xW1fd\nSoejgzk5c9IKIiSYp6+8IlUKjTgmMzIshEIegkEn7QMDkhvnGDnnSqUSs7mWjAzB9JIyWycnOcnv\nh40bGQ524B2Y2SLwlcY1JRESeNo8aOdLFkH2xAQ6hYIOb3KBvXQ1aqIppImLyaKYmCjBYOghFJLa\n6bB3MM8yj97eXkkDNhopKSHJNRTT3j4h95B3eICgupCMjAEsFkFGuJTASAB1lZqmzEyKfGFsbhu1\nxW5abTnMOfvsBCKIE/lLLS8RrgmjOpIaSF2u0x3dIrDbpQn41FOhvh7X5BgTvglJzmWy2NfKokRg\n0phS5DxqEURL5gOcWHIiGfKM2AIzj6eVmpr5MxOB3R6zCACUjloUdd3SB4rKy1H2DcxoEUBczkdG\noHhpFu7Dcet8LBDAHghQFUntTnQPBYNBRkdHsVgskjaoVEoxr+koLiZ/agr14GCcCCJBdSGCTE0N\nkZWVnKoUk6lXX5UKPCaUvR4drcBsnuajimJEqjMU1RG9HV5UlSpkChlJg4y0BqKoqEj6VOC776ak\n2Kpr1VJGHkiE4ZZ9RmMENhuHxyzk5o4Aitjn8XZ5PLhzcmLaeDr3kEYzF6+3g/axdg6PHqZUX4pc\nljosuWNjBAsKydPkpSy/B1Isgr7DfSgNSpR6pTS7j4zErIGjVQSQyaCyCgaDWQTsAY4rPI6wCNMy\n2pISKI4iVu3z3XclAY/M4DKZLDaZtLe349Fo4nboUWAy1WEypUb8tjqdrC4ogHffZcQ/wNRoSTQr\nNhnd3YTLymJaibfTS6YlE4VOEcvYWaXXs2Pa5JUU6I9AM1+Dr8fHkdYjsYyhKEZGlJjNfnw+6YtQ\nA5MD1BbUMjY2RmBkBHJykokgUdPNzf1EAsYh+xhuRSHh8BHy8jyIwXw0CzX4CNOmUmHyBLC5bJRb\nd9CXUcmc+fNjRCBlfUmT6v277mf9uetTag4BLNRq6fb5cM0UMI4SQW4uzJvH4JY3KMouist5xJcS\nJQK5TJ4i5+ksAplMxleXf5WH9jwESIH+uXNXfCTXEAC9pcjKIy9keTmG4QlK9GlyQiOQYhc2Rkeh\ndKUqySKIWgPRbxNHPnMASKmveXl50kLKGVJHASgsROfxEO7piRHBgHOAEn0Jfv8AmZn5yOXJXwSM\nydTGjcRqd0dgsxWQlzfDepVhqc5Q1CLwtnvR1ESygqa5hoaGhigsLJTW8mzcyMDkACXZ8XFKtAgK\nCgoIOUOfQYvA70e4XNgCuWRktCRNJLucTgJms+Q3Jz0RZGWV4Pf387v9v+PsqrMxadKvE1Da7Yzr\n9TPX8phGBL0tvZJbCGIWwbHcQlFUVsoYsxjwdniZCk0hQ8azTc8e1SKwdR2SzN5p0alowLi9vZ2g\nwRBLYz0a9Pr5ZGcnT9IhIdjhdHLCCSfAe+9h99oxqU0Mp+FEurpQVFbHxsnT5JHiA0DUKXqCXp8S\nME5HBPIMOZr5GtoPtKdYBDYbmM1B/H5pprd77Zi1ZoqKinB0dcWIoK8vYZw+YYtAPj6BPWTG7W7C\nZBon2GZCt0RHk8eDwWRC5fIw5h3DePA9RsO50lqCnh6EEDESbxpuom2sjQtOuYCwL5z0uUaIB4z3\nzxQwjhIBwBlnYN/2frKc5+TA+HiMCCCZNIPBIMPDwxQWFiYRAcCVS67krY63sDq7CQTszJt3wkcm\ngmCnkbBBEqBAaREljlD6KqoRWHQWukdsqNWQs0CNv89P2C/54PdNTnJcQlnphE8hf6T4AACZmYRz\nchBtbRxwuQgLEZPzoyphk1apllPC5zsnJ2FqKhOVqjnlHCDmGjKbpf962jyoayJWyjTXRYwI6urA\n4cA+2pf0/NRVanzdPsKBMIWFhfhGfZ9Bi2B4mFCumfwCeUod9J2Tkygjq4thJiIoxevr5Yn9T3By\n+ckplTSjcI+OIjOZMM6UmjWNCPq7+pOJYHSU3l5JQI+FaOaQt8OLw+vAqDbyXtd7jLtaUrIWIBKw\natkjpY1Oy1eLBow7OjqQm80fySJQq6tRqZIJo83jIT8zk7zKStDrsTtt5GfnRjk2ZSw0lbWxcXI3\nudEsiIyFyQR2e1oimKmOvW6xjq7OrhSLQFKq5Pj90kxv99rJVedSVlbGRE8P5ORQWCgRRjBIcn71\nJ2QRZDhd2LwWxsb2YDRa8e/LQVen44DLRXFBATLHODmqHKb2vkVAKJHLtWRnZ2O1WsnIyCcc9vHE\nvt9y7XHXkqnMlFYYp7EKlh8tTmC3x5eyn3km9n1bk+U8QgQJ3s2kIOjQ0BBms5mMjIzpyio5qhwu\nmmYo6qUAACAASURBVH8RLxy4B7W6msrKKvr6+ggG02TXTSeCZiMh1TBChJgwG6iYkB21gF6BroDu\nURtmM8gz5ajmqGL1l6KB4igSXUMfJWMoCllJCaKnB6NSSafPF5OpdBlDEFEurB1SUCJhCXFfHxQX\ne/H7Z8igiriG8vMjrqF2L+raBCJIYNvBwUHJNSSXw+mnY+9vT3p+cpWczKJMfN0+CgoKcFldn0GL\nIKG8RGLqaCAc5oDLha6o6KgWgUpVitN9hPKccnSZuhmJwGq1UlFUhDLTmH6Qh4aSiGDIOpRiEYyM\npK5sT4fKSrAq1HjbvTGN5Nzac+ka3ZbeItBasPW3SCb+NCJIdA1lFRd/JItALi9FLk8Ophxyu1kc\nSWvkzDOx+xwU5KQhAp8PhMBsiruGYhlDEHMNHafT0ex24424M6Q69m1p69RkVWbRM9yTYhEMD4PF\nkpVCBKWlpbj7+8FoJDNTmntsNqnMxLB7WApufkJrCVSTXvocBUAXOTkavHtAu0RK96wsKIDxcSxq\nM8N9zZjNMkZGiFchlcnIUlXy4ZE/c9WSq4DkUhOJOOrCMocjbhGsXo19uIdcRUIAKJ1FkLCWIBof\ngJQ5CoDrl11PQ+czqNVzycrKwmKxSAH76ZhGBL72EEpZDlNTNkbzNBQ5xVEzuSxaC/0OW+wd0szX\nxOIEeycnOS6BCBJdQx9lDUEUirIy/j95bxYkyX3fd36yjjzqzLr77jkBDO4BKApYSqQoS4ZIKShZ\nsSa5YceuN/ZBD7Yj/OoIPzBi/eJ3P6zeNkKxJuWQZdEyQZCSRZlWQBJAEjM4ZjAzPZirr7rvqsyq\nysp9yKMyK7O6eygBFqjfGwbV1dmZ//x9f9/v7yroOs/F41wbDNwzpesr2HiyQrV+z8cGAHvG0NzX\nHe6zn0YaAovRNfcDfirxRILxrTHr6+u099uLc35G+5kAgkEqWDr63nDIeUUhvrZ2IiMQxTVMo83/\n9eL/4T708F9zzJWtLWbxXHiN7hIjOG4fW4licIHglDPo2rlzcDiVGO+N3Wv6Zy/8M/rDvdWHsfXQ\nyg0EGMFFer07HB8fk9jePhMjMIwK06k/yfX+cMizNhCMf/kXMeYzNkqJIBB0OqCqvvrqABA0myjR\nKE8lEly3y/Qmk2MiEZl4PDiESa/oMIfc0oCmWg3W15M+achhBFq1ajk4cPMEckxGiSm0tfYnIw3N\nZsS1KY3hOtvbVknh8IMhyWeTvDsc8uT6OgwGrE9Ejl+4QLEk0GgsgACgb6R4JpfjiYJVAOEdPue1\nUxmBAwSSROvp8+Qbnu9QVaaNDpOJe8t8vQROfgAISEMAr2y9wqZi0phaEa13W5nPloBgvDd2pdmm\nOWSgRAnXGhfXdNTzA8Ho5oj+bMa+rnMluej6/5swgqdSKS5qGm93GhimQSKesPt3VhRqjGoBILDY\nv+Qr//WZRxqq188oDYEVhI1b5CX/dFWnl2B9fZ3qQXVxzs9on34gqFbpSMHS0bf7fT6bTrvzhsDy\n08tVQ9Vhg/YEfuvyL54KBFd3dxlEMkFGMJ9bb4f9sNbX16lrdXdHMfk8dLu06saZgKBUgs406gOC\nXz7/y2RjGh/1gk6gMhKoxu0mlBBGcHS0R6FQsKShMzACTcszGvnX9nmBoP3zL5AfwVrRCL633a4F\nBLaENp/OGd8ek7hig2I2azU3zWY8m0zygQ0E3mqvZauKVTZjmwHZoFaDzc0cmhZkBLNGIwAE4MkT\nfBLSUKfDUI6RkVJsbamIwjaCKBBTY1wfDHghk4F0mnPHGtXnL7pOwQsEH7Tb/OrOM+5XrpKGnkkk\neKBp9MMkGS8QAK0ntsk/8JRBqyrjow5ra4tCBm+OwMsIHCnDm5cWBIGfL6/zl1XrOXj3F7um61aZ\nqq3jz3oz5uM5cmoHXX9Ea9xilJKsQGKFVVIV6uMFECSvJBndHHHdPpsxz/lwFtRYDf9nzBEAbG5y\nUZbZHA75cfuQvJL3NJOFAEGiTFUYYf7iL/r+/dEj2N2VMU2d2WzpbxoOLZ+RSlnu6chkPpwjbtiJ\n6JCqIRcIdnZoKZC/7/dBiSeshHGlUqFarYbPQTrBPv1AcHxMPbrG2tocXX+AolgbX97u9/m5dNpd\nCA3hjOD3rv8e82iRuGmNnc7LQSAwTZPj42Ne3d2lIaSCN7jZtA64JAGgoBAxI+hZu6QmGrWiruPm\nmaShYhE6Iz8QmPMRSjTG733wXwKfr9x4QLUgW94uwAjOcXR0YJXO2VvKTrNOJ0W3658j4wWCljQn\nb8pURvfDGUE2S0pMIQgC9Vt1xHXRWrQBls5pSxHPeIBglSwEcGgcUplVfP9mmg4QlNH1R5h2Yi8n\n59jZ2XGZCRBeOfRJMIJ2m44SIRWNsr4uExttopxX2Nd1xEiEsiiCqrJzv0P1QsVJJblA0Nf7/OXx\nfa6oi+gv+WzSHT7ntXgkwrOrEsbLQLBdJP/h/cX/V1Umta5vSrXXkVhzhpySZOu2LscTG/Kcb9/9\nCRNjEs4InB4C21mP71rlkrK87QKBnpStQGKFVZIV2hMPI3g6wfDm0JKFvHvCsUYriaL1a33S0ElV\nQwCbm+xEo+T7fd7rHLmB4apkcer+IQICg3V/kcmjR7CzI/jnfTlm5wcQBAsIDk2US8oi0CmXrQu3\nQd3NEWD5opYCub/wj1FPPGk1lcmyTDKZpCAVHitP8OkHgmqV43mFQqFLLJYnErGc8QfDIc+nUu6W\nMggHgm++/01KmafR9f2VjKDf7xONRvm5SoVDM8HxMhB4ZCGA8a0xJanE0bGHftjh3lkYQbEIjTbM\ntTmNdsPVKCV5m//vvf8QWFpT+esPqCpGoE4brHHb/b5KqZRxt5SdZo2GSKNxnbmt144Ng4e6zmW7\n9tq5T+X6ByulIWfP7IP3H1ijJbxmy0NeIND1R8hyeD/+g8YD1lln1ln83d2u1SOVzW6i6/uMZ2Mi\nQgQlrrC9vU18MHATpP/TGEG7TVsSiE3n1nvfXke+IPPucMgLjoyhqmzda1ItJ5wqYxcI/vDmH1LK\nvgCzRdNcPBdHEAWm9WAvy2dWTSJdBoKEYElDDp1TVYxWxw8EHkbglYYgXB4yZ1Xy6Su8sfeGJY0u\nf2DpbGp3NZRLiisNtcYtZunEyUCQqtA3PUBgl02+0+37EsWOOfJQQBo6KRrb2mJ9PmfeajHUO6Sl\nHKY5X3k+hf/xP6iQDJnNZMVkvgnAjtUWKypLJWg0WchCYAWOhQLUaoxGIyaTCaodDIxnYyKRKMqb\nb/m+UnnCkobAUiTSQvrvHyN4OFkjn28gSdbDNk2TG8MhVxIJHyPIZq1+K+ddudW4xdHgiK3cS2ja\no5VAcHx8zNraGqlolFKywqPlHMESEIw+HFHJVjj0ok6xSLR1NiBIp0HTBKIXEtQOa3bVwn0yyctc\nyF3gjb03fJ/P/fe/ZsQUs2tF48s2GBQoFKQzMQKryVQgnR7TsEHjw9GIS4qCaDfLtMYt8rkNKg/f\nDgKBLQ2B9eI+uvPI6ij2ml059EwyyQd2g5uuH7jPb9nu37/PTmmH8UeLBjTnXYpGs4BJrX/ffXY7\nOztI4/HpjOATAIKmbGCOdMplDfOwjHxe5vpgYAUpAJEI61KB6rQdkIZ+793f45cu/m+BiFI5r6Dd\nC/Z5rBw1sQwEWpv8zlPwV39l/YPN0E5iBFuemc/LCeP5fMJs1uYrV/53/sN7/8GVJ3wWkh9QLipI\n0rb17mktjEz6RGkoJ+eYMiJr97hEk1HEisiDWz1eWmIEsCghfZwcAZublHSdarXKudiUSDzDdFoj\nGk25O0B89sMfWvLQktN9+NABgotuU6BrnqoRVYXhWCB6canBzb7JR0dHrK2tuWzB9VF/+Ze+zXLS\nlsSsM2PWn7G2toZsyH//GMG9UYVc7tB1JIeTCUo0Sj4e9zECQfDnCX7/g9/nHz/9j1GUhU55EhAA\nPJ/bDiJtCBBsVDZ8QGAUSqS1epifDpggWO+MvpOi3qj7ytf+6XP/lG++/83Fh2s1hMMjKuk1zE43\nFAh6vTS5nHAmRuCsqNze3mDf9p5eWQjsw7h+nsqtH1KtLlUmdBZgVElWODg8WCTNHbMZwY4k0Z3N\n6MxmdsNOOBDs7++ztb2F9tHC+TlAIAgCkrRNtfeh++xUVSVrmvTtcRpeIHBLSD8BachstWjKM/RO\nm0Khx/yjEsoFxWIEDhDoOuXCLtVB1ZWGnF6CHx/8mF+78n+i6/uY5oINyeflUCB4MWWVpQbMWz6K\n/fyuXLWcCYCqEuv7gcBbansaI5hMjhDFCv/rM1/lu3vfJakmw4HAA0bjuwsgcN49M5s9kREIgkB8\nUiGmLr5buqIwv6X5zqdjGxvw0UcahmGQdd6L04CgXCY1HlOtVlmP6ExjqZWlo4AFBOXzPqdrmguV\ndnleFOBjBJEIqOIMrbLEaOyEsVcWAvvZpUqWk/BM1hMiAsolq9JwfX2duP5484Y+/UBwfMyt7hqq\n+sB1JDeGQ552Znc7QGCjpyMPmabJt97/Fl9/9us2PT0bELyU22Sod/3yTAgQbO5u+oBAS5c4l6yf\n2FXstWIRxpUkjW7DBQJJ2uW3r/w237n9HWvIHFiNLJ/7HGtKGWEwsMTRJet0RFR1eiZG4Aybc4bP\nwQogKGxRSQ2pHS11s3q0+UqqwnH3GPn80lgEu4Q0IghcSSS4MRwymaxmBLVajY0LG4zv+hmBs5FO\nkrao9vbcZycIAjlBYN92igFG8AlJQ3rjmI4cpd/ZJ5+vMfkg7zICVxrqdCiUd6kOq640lEwmiSkx\nvrzxZRJiBlFcQ9MWc5Xl87Jvl7NjTyYS3BmPMZbLBr3lo9jP78VXfUAgjv1AUFAKdLQOY31MvV5f\nJCsJAoHD5oqJIr+484u803+H2nIVwTIjuDtGvij7pKGIMwzwBIuMKggpzzDDS3GuHsaQI0FXVijA\ngwcDNuxhkMDpQJDJIGkax0dH5BkzEJIrE8U8eACaRqVy0RccNpuWbJlK4R8F75gHCABywpRBbokR\n2CWkvkQxHkbwquf52ebkCdbX1zEH5t8/aehGa41M5i6SZDnjG6MRTzsvmixbYxdsyrm+bvnt92vv\nM5wOeWXrFTsqWZ0j8ALBC+kMcTFLfeipujg68jWTjG6N2H5q2wcEA6XElnK6Pu9YsQijvEJr6G1o\n2aWSqvDS+kt87+73rA/+8Ifw+c+zGytgyFLoOqR2GzKZ4ZkYgQMEzl4CWAEEcp7i//IE7W7EN+XR\nJw0lK9RGNeRzS0BgS0OAmyewnElwxhPYQPDURqg0BFZTYK1/b/Hs5nPSpsl929FvblrPfD731Md/\nAoxg3DimKymMRg/I5+foN0SEXZEHmsaTiYSVDKzXUUvbLiOwp6Ewz875hcwvAEF5QT4nM743Dvy+\nZDRKRRS5t7wQYFkaGrfIf/aXrP0EsxlksyQmHdbXFgASjUQpKAU+uPcB5XLZt+d6uanMYnPWs/sn\nz/0TXj96nXq97uaYgHBp6JKCJG0ymRzTGjWJ5QonSkMAZr/CTF44uIMdgSsH4YMUCwXY3x8vZKH5\nPHAvAhaPM5ckeoeHpOZDWsgrE8XOu7e8v2F/H3d72spksSdPkZ3qdBNL74hHGloJBG++6fsRp3Jo\nbW2NWWf294gRjEaYkwktI0s8fs+NKH2MAEIrh771wbf46jNfJSJE3O7ijtYhpwTr2L1A8FwqhSku\n9RJ4nJ9pmIz3xuw+v+sDgm68xEZ8xeTSECsWYZCUaU/bgYaWrz7zVf7jB//R+qB9GM+hoqek0O9q\ntSak0y0rRJlO/SNYl+zMjEDJE/3cK+TiAz+2eKShslKmbtaRtpauyzN795lkkg8HTebzMbFYcLyH\naZrUajW2n9/2SUPV6gIIZHmbxtDTZNPvM4nFeGADmZVUtt4/tz4+k7HKbcPKLf+WbNI4phNNUigY\nJBLnmBxO2CsaPJFIWPmWa9dAVUmZceqjOvnCnEYDbjdvM0/MWY9YDmA54bhKGgJ4KpHg5tBTXjoe\nW7We9vswN+fWOV87Z9VYvvsuxOPoSGyq/rLUSqrCe/fe8+UHIJgjmEwWsuxXnvwKf3301yRTSdpe\nxuUBgrk+Z1qbIm/LRCIi8XiB5qiKmC+dyAhMEybtCnps4eDulg3WVvg7q5FwugCCTsdKwMXjK38H\ngJnJMDo+Jjrr00ZhML4Xzgh++EP4whcC+xu8pEOWd9H1A+ZzT3LfE8VMm1NUYUp7srTwypaGHocR\nKE8qLiMY18ePtZPg0w0E1SqzQoW1dYHJZKEx+xgBhACBLQs983UARLFCV2uRFJPujG+veYHgkqIw\ni6nc73tCou5Cm9fua8TLcbbOb/mAoBktUREeDwj6kkiHjo8RAPz2ld/m9TuvM24cW3toX36ZLTPN\nMCmGfle9PiCZPLZ0xVPkoWVG0JvNaEynnJcXEYv3MFbMqj9h7JGG8uM8nXyHSHzpmHlWRT6dSPBo\ncB9R3AgdLzAcDhEEgcIzhYA0tGAEWzSGxwsg6HSYJBK+7lZn5pCbBI1ErGd2SgT6N7FZs0FLSLO+\nbiDOtxHXRN6djHjeOZs//CE89RTRbo+MlCGablKvw3+68Z84v3WeRt1CWO/wOVidLAa4kkhw0zth\n1pGF7Hvb03uLc+5xJl1BZV3x34tKssLtw9u+/ACslobA2tr160/8OlJW8ucJPECg3dOQtiWEmHVN\nkrRFc9xELqyd+DwGA4iOrRJSxz7IT0kdhncjOwTYBYLTSkdtE1SVSa1GR2uzkSzRHH60GghCGIGX\n/EQiIpK0jq57GjQ9h3d0e0QpZ1KvL519m3aF5giUPLz8Mty86Zsm7GUEvaPe3yNpqFpFy1rNZI7G\n7KsYcmyphPT9uy0iQoSX1l8CQBCijCmTk8MHXnmBICYIZBMl3ml5duF5gGB816K8zk4Cx2rzEgXz\n7EBQKEB7EqMn9UhNRKbTFqJoRQblZJmXN17mx9/+f+DqVRBFNuZJBnI4Ra7VGqjqnNmsb33xGYDA\nYQQfDIc8nUy6Ux3BcxhffJHK9BHVe55I0sOO1I5KJxfyYi9JQ43RwxPzA+VyGXlXRj/QmU/n9r/7\npaHWuO4DAiOdtsZR2+aMnKokK/4xEx+jPGS2mrRMlUplRHS0gXJe4d3BYJEo/su/hGeegXabSrLC\nJF6l04E/+OA/8+LFF6nbOpEs77jd0wDSroT2UMM0giMEAkAQJgs598kGgskE2nOVQnQJCFIV7tXu\nBRhBGBB4E/1fe+Zr6JLuzxN4vKOTKHb/Hmmb9rhDorR+IiOo1SAd8Tvdt7MakcNp6L0oFKDTifrH\nS5yhkSeSy5GYzWgMG1xMlxmHjZdoNi197JlnAqshl6u4Jcn//LzS0PjOmNKaEGzMtAO2lYxAluHZ\nZ+FHP3L/n1NCura2RutR67HGTHy6geD4mEHSGi/hRCV1eyl62Uv/lhjBjY86fP3Zr/siUD1SQpWW\nqlvcX7MAAoCN1Bo32p4H62UEDzTkXZn19XWOjo7cB3E0K6FOH48R1JtzxuIYHtaQpC3fwpavPv1V\n9v/sP7uLMCozma4cfOiz2YxOp0Olss5kcmg3KazOEywDwbIsBJ7DKIpU8jNqf3Vv8T890lCmlqGd\nCEnIeqShHUlCMaoQXwt+DqhWq5TLZSJiBHFNRH9oNektA0Fb6ywcXLuNkM/7GIHzK5W4ghgV6erd\njz9h3OnQmBUplzsILauH4Lq3Yuitt+CllywgSFVoalXSGYMHR31evvSy60hF0X52tkWVKPF8HP0w\nOAP8sYHgzTepVmEYV4n0goxgv7Mfygi8OQIrCFtErb964VcZikPuPPR0p3u8o5MfcCwW32QwHZMo\nbJwIBPU6qPEFEIwNg4dMiRfiTI4mgc9by6iks5eO2iZks+yqKrV+jSfSJSKT/WDV0I9+ZEXl0eiJ\njACs5+fsngZ8h3d8Z8z6TsTNDbmWzUKvtxoIICAPxXNxInKEQqRAdb+6OOdnsE83ENRqtMUypdIE\nMIlGM64s5JMZPIxgfd3k+CjC1575mu+rRqZKVgyXVpaB4Hxmnbs9z4Pt9dxqHf2BjrwroygKiUSC\nlh1xPtKt8tGzWrEIx+0OyXmS0UFQo/xHV/4R6Ws3mLz8ovX5aZyWGJxHX6/XyefzKMomk8nRqYzA\nKYDa3Nxkf3+f9waD1UAAVM7JVK95vIJHGsocZGjGQn6XRxoSBIGnxR59oRz8HAtGANa4XSdh7K8a\n2qatDcjJOfca4qWSDwg8JGQhD33MjCDS7tOlQC43xDywegjeGwys4X21mnVurlyxBs/Z/Q3xdJdf\nKv9jKuWKDwh03T8bZVXl0JVkkptDT+dxWOmo40ieesraTPZBE11RA7KMc03LQKCq1sQIB290/dDH\n6JS4wu7mLn/23p8tfmiJEcgXF1LjJFIkFY8TzedPlIbqdSjKi+j7znjMBVlGORd+LwoF0LTkYwMB\n2SzbmQzNUZNn0ykMIBbzz/bhrbfcIMy3rpIgEEjShvXuwaIl3mYEo9sj1i/Hgowgk4Fu97GAACx5\nSDwWmUwmlEP6G1bZpxsIOh3aZo5SqedqzIFEMfgYQS1yDaNX5uniM76PjMw0mVjwdhiGQb1ed50R\nwBV1iyPvDV5iBNKOlRz1ykMPBwWUYcPXBHKSFYtw3GuhRlRGzaBGWU6W+fnDKH9WtBqI8tMo9Xiw\n27RarVKpVBbO5BRG0GxaH8lkMgiCwPVq9UQgKD+Vp3rbE3V4pKHY/RjzyJzhZGk2jtcrA+ejbapm\n+AvqA4ILipsw9jKCWCxNf8YCyDsdxHLZJ0148c+tkf+YGYHYHdAXcqTTQ+Z3S0x34pjYbPXtt+Ez\nn7E1wLbrTDTpIa/kfoOy5/p9jsS2VQnjYjyOGIlwPLEj5LDSUceRRCLwyisc/fc7zNJBIFhLrdGe\ntAPSkCBYrKBatZL5YT0gVy9d5e07by/+4QRpaGRmyMRj1jt0CiNYTy/6Gz4cjXgqkUDeldEeBO+F\nqoJhKJTLZ5s86lo2y0YiQXfS5dnEjAYhbPXtt+Hnfg6AtJjGMA33nC+1TNiMzn5+/b41+8Lu0h/f\nGbPxdDyUEZjdLv1+n4IHVUKBwONT5HMy+kOdtbU1cqsmJYfYpxsIej2a04yvqziQKAbf4Lk/OfhD\nYtEog4E/OTOcy6RjwYi62Wyiqipxj9T0Un6H1sjW30zTerg2I3CkIfADwXFbwpASZ05OFovQGLTI\nS3nGw5DJhwcHJM0Y/2/nzwHIaFCNBquBHCCQJFteOIERGIYVpKqqFalvbW3x/oMHPiCYGlNG05G7\nQKTy8jbVg+lifLBHGtLv65TEUvAwejd2A2tCk3tGsFoLLCCo2KG/fEFmfHfMdGpdp3cYaX8WJxXV\n3WuIl0pMJhM0u5TSQ0IWmu7H3F0sDzR68wzJZJvJjTzHGwJPJBIWW33rLcuR2NdQSVbYa+2hiQds\nx6/6gCAazWCaMwxj0Sx25oTxSdIQwKuvcvSTQ8xsCCNIVeib/QAjgEWewDC6CEKUWMzf2fsLV36B\nhwcP6ek96x3xXId2V/MBwXCeJBPH7XBeZfU6bKkLRuACwQpGAHOgjSw/JhBkMpRlCX2uc0kc8Mgs\nM/MGcKa5eH7gjlNxzvmJ0pAngjFNk/GdMVtXxXBG0OuxVqkQ8fRI+J7f9ra1dvPeQpqVdiX0hzrr\n6+ukCJmLtsI+3UDQ7VLTMuTzx6tLR8EXBf/Rh39EuWwGZqX0Z3GS0aDOuCwLATyV3WQ+aVNz5lXI\nsvVAAP2hHgoE9ToY+bNN/wQ7aB63KKQKTOaPgnXMb79N5Odf4bt330Cf6SSGOo34FH3m140XjMCO\nKk9gBN2udf6cVoTSxgZ6rcaGRzJra9aiHEd6qzyRpRrdgFu3rFLM0chdland11hLrwUPYzZrfc7O\n56hmnZvT8JbrZWlI+0hziz+8PUT9GSQjtvNrtxFyOYrFoptw9eLfJ9JLYBjI+pTeVCGbHaG/m+Cj\nssGTzq7ct9+2pAXb+VWSZX509CPObSRpN+OUy2X32q3u6Q2fPHRSCeljA8GHXaL5oBMuKkUm8Ung\n/MMCCFaNBtnZ2CE3z/H6ndct1JZlEEVMw0S7ryFfWEhDg7lEKjqzDl+/v3InQb0OW8Ucg8kAfaaf\nyghqtRrRaIdeT1x8wRkZgSoKyMiY030G0XXue3sz9vcD2wC9IzlOlIacgXPAtDFFiAtsXIoHgUAU\nmUcinKv4hy36np8gBPoJ5B0Z7aG1oEaaSn9/GMHROEs2+3B16ShYjqffZ6+1R31YZ7MiBwJBy5EE\nx/uGAcFaeg1h0uLOeOzLD5gzE/1QR9oOSkONBghlT8fQKVYsQnfSopgrMpP3g4zg7beRXvkcz5Wf\n4wf3f4DQ7WFk0oF9yn5p6GRGsExpE5UKG72eL9+y7EgqFajJOxZF7fWsex2JMJ/MmVQnrOXWgvXM\nguCL/kTjmJ/owaFh4AcC+YLM+KPxcmMmAL3pjIRgywp2nsIbVS8zguPB8ccrDXW7DKUoxsigVFxn\nPjS5mZrwRCLhjyglCWIxNiIqd5p3ePHCpl3cUvI1ZS0njFc1lYGdJzgJCLwTdn/+5zk6NIkXMwEg\nkKYSQlrwNZM55iSMvc1kXqtUKqQmKf7w5h/6PKO+rxMvxokqi8KH/lQgFZ1gRkyr32HFys16HSrl\nCKVkidqwdiojODg4QJaHi+P+GNJQSjCJz+Jo2n0i4g63vAl4RxbyvBfeXoLlqqEAI7DzA07QmMlY\nM76W23umisLFpSqnMCD35gmkHQntgcb6+jpRLXrmXoJPPRAc9DKoqtVM1pxOGRuGL4IFXJr17Q+/\nzVee/Ar5vBAIBHtTg4QQHNgVBgTFRBFj2ufmoOfLD+iHOvFSnIho3VYHCEzTOoPRtbMDQSoFs3gL\nNVvEzFeJG0tLve3D+JUnv8K3b30bul2ErBqIAPzS0MmMYLnp0iwWyS45yjAgqM5L1mH0ykL7cL69\nDwAAIABJREFUOtK6RCW9YsezLQ+ZpokxOebAyNGahuc4vDmC8d0x1arpAwJ9pjOdm0QNGwRtIHCc\nKSwxgk9iFHW7TUcWmPU1Sukd5HMyt8Zjq6P4/n1LJ3aSmKqKPNDo6l0+c/kc9TqIokgymaTjgKVX\nZ2Z1shhsRuA0lZ3GCDIZjpQLKLFZAAiMvoEpm4Fpt7BoKvM2k3mtXC5jDAy+d/d7aNXDlYligLbW\nRZUUy1meIA85VZeVZIWjwTG3bCCQdqVQRnBwcEAyqfmB4Cxz4LNZkvMpUT2Krj8kJe+GA4HHvJVD\nYdKQ++w8QKA9tPKJgrDY8+C1sSiy69E/9ZnOxJiQjHsC3SUgkHdlVxqa9+d/NxnBG2+8wVNPPcXl\ny5f5d//u3wX+/5//+Z+TzWa5evUqV69e5d/+23974veZ3S6PuhnS6VtI0gY3RyOuLFcMgZuB/6Nb\nf8RvPfVbyxI1AB19TDIyZj73H6gwIIhFYsjxJO/36qGlo445QDAcWnJL7DGAQBAgUWghm3koNDCP\nPSfLNN3D+JtP/ib/5dZ/wex2EVSV9tjvuAPS0AmMYBkIxqqKvJS8W3YkpRLUhwnmb//YlyjW7mvI\n52QKSiFwTYCbMJ5OG0SjKS6l8u5Iaq95GUEsH0MQBI7vGXgZc1tro0pJJhN7XHMIEHgZQSFhX9PH\nyQjabVoyGIMx2cgmygWFW6ORJQ05spBjuRx7H72NHJPZqMRdnF5OGHulIWlbYnI8cfsqvBaQhlZV\nDdnWkLdR9E4gUdtpdYgZMUvnX7LTpKFKpUK9Vufq2lWuffCnKxPFzjXl5JxVa39CwtgBgkKiwJ1e\nDTUWIxOLuc7PnPsLMQ4PD1FV46diBPJ0wnw0R9cPKCXP8aEXCDwVQ44559wwfK8BYFUcmebUyvF0\nOu5Lpj/UkXcsf1EKcQ3DaJQtz+ywttZ2F+W4dvUqfPihtSIW61xoDzUqlQp6Ww9/90LsEwMCwzD4\nF//iX/DGG29w48YNvvnNb3Lz5s3A577whS/wzjvv8M477/Bv/s2/OfE75+0ePSFLNHoXUdwMzw8A\nZDKYvR7vHb/LL5//ZZ9TcKw1blFIFP2NH4QDAUBayvJht7qQQ1iUjjrmAIF7/sKe9gkmqi2iEwVh\nqjDd9zz8vT0L3CoVniw+SUpMMawfIKgqHc0fTQWkoRMYwXIk00kkEE4BAkmCZEqgfatmF3rbQHDP\nAgJVVunoIRGe/RCcRsBnEgl3JLXXvEAgCALyBZn9mzMfI7AciepuKqNtraJcxQhU2b5PH2eyuN2m\nJRskIzOETh7pvMw9TeOSovgSjQDkcty6Y42E9h4RLxAsS0OReARpXXL7Kry2JUn0DIPubHY6IwBa\nQh6lexSIxOv1OuJcDJwpOB0IUqkUpmny67u/zrWbP1jZQwDQ0loUEgVr97SqrgQCJ5hWZZWbvRpP\n2e96NBElmo4yrfkZ5cHBAcWi8FMBgaRpzHozJpNjdlMeaWg+t2Y0LTEC55w7Uyy8apogCIuqPY+U\n7DAC8FW4u9YTBDY8/ix0FpqiwKVL8P77AMTSMSJShHKqzKAxCH12YfaJAcFbb73FpUuXOHfuHPF4\nnK9//et8+9vfDnzucRYuG+0uUinjOpObYfkBAFHEiEX4je1/gByTVwJBMbERAAJnHviy5ZUce4PG\nIsPKakbg5qic8ZJntFi6hTmSiExKaA89TGWJmn7lya8wbBwSzRVWAoEblajymRlBLZlktuQcwg5j\npSJQ3f4MXL/uG7XhAkHYYbRpmeNInkkmubHECAzDoNVqUfS8vMpFheN7RgAILBC3gSCEEWQy1obA\n6XQJCD4maWjSqNKSIZMYYR7nGG1bA+GUaDTw/Ixshgf3r6PPdPKFuQ8InOtflobAyhOEJYwjgsCT\nimKxgpPKR51/m6RIHdwOBQJFUFYCwSJHEAQCQRAol8u8mn+V+3s/Yp63WIn2kYZyIcgICok16/md\nMPbDybOqsspev+4CAViSyLJUdnh4SKUSs477dGodgLPMgc9mkUYaWltD14+4nDnHLUfAv3PHOjdL\ngOKcqeVgyjE3YeztOVpiBMtA0DYMKqcBAViNbT9ebCyTd2Vy8xzdavfvHhAcHBz4ytC2trbc6ZaO\nCYLAm2++yQsvvMCXv/xlbty4sfw1AHzjG9/gG9/4Bv939Yhh4n0mkxqiuL6aEQADSeC3N38FYCUQ\nlFK7i6jStlWMoKSoPBo2mXt0ce2BhrS7GLC2trZGtVqlVptb50ZVrYNwRhMSLYyBSHxeQX/kifyW\nqOlvPvmbzDsdYupqIHCikokysrJSk2CFlBcI9PmcViJBfwk0wtZ5VipQu/gKfPBBQBrKStnww2hL\nQ06y8Ql7hLLXms0muVzOl6yUL8gcH5ghQLBmz+03Q4EgElkQAPeaPkZpaFg7oCNKqNkuxkOV6rrA\nE4pi1ej+5CdWD4Ftx3GN56VtEvEEitp3CVupVFopDYGVJzgxYTwcnsoITBPa/RjpRzcC96Jer5OM\nJUOfn9MKstxV7LVKpUJ0FOXcPMN+3LpO7aH/HXGuqZjcPlEaGg6ta00mref3cNjwA8G5YOVQvV5n\nbU20gMCphAgZVx2wbJb4cISgCWiayJaiMjQMOrNZqCwEizMVsiQQ8AC5V0peYgTLMWJjOqXoOfsn\nAsFPfuL+p7QjkdNyHO8d89F//sj1lyfZJwYEYQPFlu2ll17i0aNHXL9+nX/5L/8lv/VbvxX6OecP\n+8bcYPvyLxGP54lE4uEVQ8BgMqAZn/IrBSsKWwYCZ99tKX1+EVXatgoICkqOjDmm02r5cwQ7C0Yg\niiKqqnLvXt8CAjtpfVYzpRaTrkw8XjmREby69Sqp0YxxMu6TYQzDoNlsUrKTU6K4jj45CtTxO+aN\nZj4aj9kql2ksnc5wRgDVtRfh9m0/EJw/hRG0Wm6y8bKiBIDAKws5plxQAlVDFhCUiEQkZrOWr2qo\n7rl+Rx76JBiBXj+iE1PI5xtM99LcW5tbieKbN61w2uOcb8/rvJK6giqrxJId6nXL6Z0kDcHpCeNb\nvZ5VgWOfT+ece59fvw+JhED8wnbgTNTrdbJiOJA7GLrcVew15/pfiG1xbWq9V/ojHXnbnyxujVuU\n03YQtiJZ7OQHBMF6fofD1qmMoF6vs7kpW3/WWUtHwWIEgzHpeJJ+v4AgWCB+azQKTRTD6YzAlWZX\nMIIwaaiqaeQ8Y+VXAsFLLwUYQbqbZtgbEvli5O8WEGxubvpa/pfX3wGk02kS9sP90pe+xHQ6dUc0\nBGwyQZhNSZdniOIm/dmM5nTKjhQcxfwnd/8EI50iYwfVy0AwnA4RoyLZ5PnQHIG3xdsxVVYpRSZ0\nms2VOQKwWMH9+wOrUOAxgWAWb6G1E0iJ9QUjmE4tCebll93PRU1ITmFvUqWrLaKpZrNJNpt1m+Fc\neroiT+ANHm+Pxzyxvk7TruxxPxNyGMtlqKpPWIs6QqQh7zW5tiQNnZdlHmkaU08NubdiyDH5gkyj\nG/Eli51rkqRt9OE9q0chnfZF1M6vbLUgK2fp6l1MJ0Jfnt//t2CTRo22kCafrzO5keJGYWoxgiVH\nYpom17UHvCBuo8oqk0iXaNTy30EgOFt3MVhA8LBadct5YXHOpdjiHXGf+csvW6jgedb1ep2ckgt9\nftYoHBNNayGK4XOinJWVl80cb45uMZ/MmTamiOv+qj4LCC4vpKEQRuAd4a/KKnWtcyojaDQa7O4m\nF4wgzEOHWTaLPJygigl6Pes8P5VInAoEXa0bKMF2bFkamutzpq0p4pp1L5bTh9PplLqukzIWTa4r\ngeCFF+DGDZflyzsys4MZ+USertY9k9z+iQHBZz7zGe7cucP9+/eZTCb8/u//Pl/5yld8n6lWq+5F\nv/XWW5imSX7VEoleD03Kks50kaQN7moaFxXFNyXTsdf3XkcprLlOeBkIfI7Ewwg0TWM0GpHztrDa\npsoqOXT6rZaVjDbNUNpbKpU4PJz8VIxAi7QYNlIo2a1FUvCDD6xGFu8msn4fI6HwfuumL3pzZCHH\nXGeyonLICwR3xmOuqCqyLNP1vJgrGUF8y+reTqetHoLaBGlTWs0IPNKQJG0iRiJsSpJvqUoYI5C3\nZVrjaIAROM9vUr9t3ZtIxCcNOb+y2QQxKiJGRUaz8ccmDxmtBk1UioV9opMSHwj2MpolaeHa8TWG\nSZHiJObeK2dlpZfRxGI55nMNw1gk1E/rLq5Vq6fnB5xn/tnPWuG2J2Ffr9cppIJyI1hVcOm0yWRy\nAUEI9hmABQS1Wo3CGO5F+9y9eRdxTUSI+t/R1rjFWvYpKwhbkSz2AoEYT6NPemx6gj5pVwowgkaj\nwfnzGSvm8RR1nGqiyCwqsCEq9HqWwvBkIsGtft/a3+AJwhw7CyPwAoFTXu3ci2VGcHx8jJFKEfHs\noF4JBMkknD9v+QYsaUh/oLNR2SAWiTGaBoswlu0TA4JYLMa///f/ntdee42nn36ar33ta1y5coXf\n/d3f5Xd/93cB+IM/+AOee+45XnzxRf7Vv/pXfOtb31r9hd0u43iGdNoaL3FnNOKyogQ+Zpomr995\nnVx513XCS6NuPI5kywcEXn192VRJJWWO0dptyGaZNqZE5AixtP+lKBaL1GrGYwPB3JwzNtv061mU\n0ib6vl0eFxaRdLtEc3nute9RHy0cXxgQnFQ55I1mnPtZKpXcJfbee+W1SgWqLdFqfhgM0B/pSBvW\nvPmzJIudhqRleSgMCMRNidYsTrEYZCmStMWktufKU8tA4A0A3DzBxyQPGY0WHUGlUBgjrxW47fQQ\nLD2/P779x1y48BJCp0NWtq7JqSnwMgI3x+PtJViRLAZrb8ak0WB+SumoCwQvvWQBgUeWaTQalNPl\n8KovQFUn6PrllfegXC5TrVYRmi2uPPk5/uKv/sJttnRsbs5pj9tUMk8ynTaYZ5InSkMAA0EhaY59\nQd8yI5hOpwwGA86dS1sxj0eSOYsNlAg70TidjhWxP5lIcKtatRxuKtj8+LjSkP5Id/MD1r3yA8HR\n0RHRpZziSiAAX55A3rW6i9fX10lGwnM8y/aJ9hF86Utf4tatW+zt7fGv//W/BuB3fud3+J3f+R0A\n/vk//+e8//77XLt2jTfffJNXXnll9Zf1egxjWZLJY0Rxk73x2CrNW7Jrx9dIxpOkiotZ56sZwRa6\nvkhgr8oPgCUvyPMRhp38CZOFwHFGwmMDQV/vI0cTdJpJ5NQG0VSUaX1qaYGeRCMA3S6RrMoLay/w\noLNYgLEMBC49DcuW4++IvD0ec1lRfGMaYLU0VK/bf1+97spCzn06OUewKD+8nEiwdwoQjMwoUeaI\n40WTk/f5Gc0Hi30IqspoNELXLTYVWkL6cSWMW106ZChksoi7Ms3plG1BsCj81avux/749h/zzBO/\nAO12gBEsS1vLQCBuiMw6M4xRcEZWPBLhKU1j6ImCVwFBLge8+KI1IsQD+vV6nbXc2kpHks2OGY0u\nrbwFjjREs8lnn/s13r/+fiA/0Nf7JOIJxJiCKJaZJc1TGUHTFJEMf4WZkyNwFIVms0k+n6dUitBq\ngdl9PCDoygLbokC7bbnIJxMJPhwOg++ecy/sc37WqiHtoT+fuCwNVatVaxrrKWzcNU+ewOkuXltb\nQzTDy3+X7dPbWdzr0SdDMmk5klVA8Pqd1/ny5S+7871hkY9y5GjnBsfjRWazjrtW7iQgUGWVqDFY\nPNil0lHHisUinU70sYGgNW6RFfN0OgqStG7RvUc6vPOOz5EAbiXCF8990ddJuJIRODNdln/nkjT0\nRCIRiKrDDqNbji9JsL/vAwIlpjA352izpci1UMBsNZnNesTj1ht+FkZQq0FenKE9Wnyfc02iWGHe\nPHIbqARBoFgsuozGi38fd8I41u3TmafIyXkGa1EuKQqRmzfh3Dl3beRh/5C91h5PX/4cdDo+IFhm\nBOBUDi0SxkJEsF76FQnjy7pO1+P8TmQEqZQ1D+jaNcBi0o1Gg83C5glA0Gc0OrfyHrjX32rxuRd/\nk9ZHLSIbfpfjvaZ4vMI0OT+VERzPJYQlIIhlrPr5WXNmf75OsVhEFK0/S2v0rQL/M1pbnLMVn9Nq\nWSD7hKJwNxrFWH73bHPOeb2tnSANeRjBw5MZQaPRIF4o/FSMQKyIGF2DtdIasVnsTDsJPr1A0O3S\nJUMicd+ShuwIdtm+c+c7/PrlX/c54VjMOvfOPXZusCBEiccLTO0FMqcBwXw2ROr3maTTgdJRx4rF\nIv2+ZB3idDqQkFtlzjW12xlEcc3qGLw3tBpHnn8+cC/IZvny5S/T03vMTQvhVjKCEEDyTh4dGoYV\nwUqSTxoy5gY9vYcq+2ezu0AgCPDRRz4gEAQhPGFsS0OiuI4gWMfwkqJwx6NReyePLv4NCgnDV067\nAII15u2ar63zpKayrt792JrKpP6IjqGQj5ZplLFmDF27ZkXetn3n9nd47eJrxApFlxF0ta4rDRUK\nBTqdDjN7r/LKhPEKILgwGlH3OL8TgQCse/HOOwD0ej1EUaSULoUn+4F0us1otBX6/8BiBM3jYxiN\nyFa2eXr6NPcT9/2/33NNorjGVNFDGYFnMgP7RhxjFpxH5K0cajQabrVcoQBa7eyMwJgbtEWD9eiE\nZtM6Z4lolHK/z4MXXgj9GeecV7vd0GRxLJZnPhljahokkwFG4BQ7Oq00jUYDsVQ6OyN48UV47z2Y\nzawAYUuiIBUQdOFnnxG0jCyy/BGiuBHKCBqjBu/X3ufzu58POD9vdLgclUzsnainAUFX61AYDnkk\nSScygtEoYTGCaNTqBAwZpbBsVl+DSrebJxbLI+/I6O8cWFtjlg+03cvwQuUFTNPknSPrZV6ZLA4B\ngk5nMXl0z174EbEjaseRdvUuaSlNNOJfieney+kU9vbQ7o1cIHDuVeAwZjIwHiNFFhVZy4wgrGqo\n0YBCxlwBBBXMdtMHBN6Eq7dq9uOWhpIjjaYmkptW2C/MrdES16752Nzre6/zG0/8hgtGqmR1pzrS\nUDQaJZ/P07QvOhQIVkzeBNgaDjn0lFOfCgSViptwrNfrlEql1TkeIJVqMByGvx/W11XQncolQeDy\n5DJvm2/7PuMHggrTpHaqNPRgFmUcMvbCmydoNBpuI2KhAJPG2YGgq3cZJeLkIkPqdRtwDIMn79/n\nwwsXVv6cKqs0Bp1QRiAIAsqsDOkkCEKAEYCfFTQaDZRK5eyMIJ22xlLb0xqkHYkCBcyx+TMOBN0u\nrWkGRbmFEVujPZv5qggAvrf3Pb54/otWuZw9b8gxr1NYjkomE2ti32lA0NE6ZEcj7ojiyhxBPl9k\nMkktXrYzykPWNSWYz6OMxxGLEVw/8kWU3ntBNktKtJJY//X2fwWCQBCL5TGMEfOkFJCGwmQh8EfU\nqw6iG1T3erC5iXajjXz+FCAQBEw1SUJf1Hafl2UOdJ3J3NlLHJSGnOvU98MZAZ12gBE48oq3SMDN\nXXwc0tB8TlKb0tGjyK0id/KGdT/fecd9fhNjwg/u/YDXLr7mapXONXn14mBTmb+XQNqSfPfCa5XB\ngAePAwQ7O3D3LnBWIDim319dm5/P56Hfx7QdcLFb5Puj768sRxbFNXR5cKI0NDdNHkwj6LNxYBie\nlxE41w/Wc581zw4ErXELPSmTMQfU67bP2NvjqWaTWyf0Q6mySmsUDgQAyrSEmbaC1WVGAEEgSG5s\nnJ0RgC9PIO/IJMdJjJHxMw4EvR41PUsyWeP+VHYjWK+5shD4cgSwmhGIYoXp9HRG4FSdpAYDbsZi\nvs1kXpOkNQRhiLvX5jGAICuKqKpVmyzvyOh3+ycCgSAIpMQU37nzHSAIBNZc+3VmCSNwDT4g8FRg\neTX2VQcxkQBjZmJ2u/CZz/ikIVidMDayMvJoUdUSj0TYlmW3hDQMCNptyJcFlxHM5jMGkwEZKYMo\nVhA6fUxPgvTUeUMfByPodhmKEUQB5o9U3s3qFiO4ft19fm8+epMnCk9QSpasaG48JhdNuVVDYYPn\nwhjBSUCQ7/fZkxfPIez5+SZQXLxozdqfzVyNfWVnOJBM7tPrhS8UAohEIuyoKjP7LAmHAsPSkGvH\n10KvSRQraFJ3JSMol+FwMkGNx8lImYBkdRIjmHceDwimKYXUXOP42F5Ade0aT0aji1ETIZaVs5ZK\nsAIIJD3PPClaW91CGIF3zESj0SC9teW+p95zvtI8eQJpVyI9SDPtTX+2gWDa6tElTTarsqdpXF4a\nLWHMrRG4X7r0JesfzigNeRlBrVZzo4plU2WV8bBDxDS5MZ+vlIYEoYQgeEo1HwMIMvEIuZw1T13a\nltCP58FEMfjGHRYSBW7Ub9AatwJAYP1960yVaeAavKWjtz35lrMwAkGALXWAKcnMX/o5Jt0I0sbi\nkLt6/JIZ6Sjy2H+wL9ny0HA4ZDabkV5K8LXbkF+PuMnijmYlWSNChEhEJj6MMc96qzHCJ5CqkidH\n8LfNCNpt2rJAggnGI5WfyGOeqNetxJR9nt7Ye4Nfu/Rr1uft/QzFaZyu1j1l8NwSEGyvBoJUt8s9\nRUG3GdaZpKFkEj780McIViUbFeUB/f7JCdjtbBZdkjBGBsbA4PNXP8939767+P3LjCDWtBqjlkaS\nO4zg7njMRUUJvS5vL4EDZGBX8TxG+Whr3GKWVkhOE4iiSK/Xg2vXuFws+nJYy5aJq8xi3bDqUgDk\nSRYjFWPWniHEBGKZ5VLzRaDSaDTIbW9bMrJh+M75SvPMHJJ3ZBKtBFpH+9lOFk9qXWZKcmXF0F/t\n/xVbmS22s/Z8ozMDwSJH4E04LVtGyhDp9jEyGe43Rsy1OfFSPPA5w1CZz2sLOnxWINBaZOKQz2s0\nGiBtiWh9+URGAJCTc7y0/hJv3HkjsGvZ+vs2mMijUEbgRDLL0tBpjABgJ9vFSKtMdl9CjPURYgt2\ntkpemCVMpInfkVy2E8bOtS/3cLRaUNqJuoxg+ZrEkcTM8yL+T5lA2m7Tkk2y8THRSJlYPEr+3Xd9\nz+67e99dBCkAqkpeE3x9BBA2ivrs0lCk3SZWKLjbtU4FAlW1/uMnP3HPfkbK0Nf7bgGCY7NZn3S6\nSbu9tPtjybYyGUbxuNVAtSXx2qXX+N7d7y1+v7b07k1rARlX0yxsyGRw3/WwM+XNl3jf3WIRIoPH\nA4J5WkbUFCqVCsfHx/DOO1w8f567J3Shy6gk8h1WqUeinsZIWqMllvspwH8UG40GxXLZCh76/dNl\nIbCCxOvXre14uzJyTWbYGtIZ/ywzgmaPWUpZCQSv79llo46F5AhOYwTNZtO3ONpr0UiUipmATJrO\n/RHyjhzaeNbrSUQiTfqOJv8YjCAVnZHPGxYQ0GQ6zzIvVoIf9gCBKqtcXbvKt699m2QyibSUN5Gk\ndXR5+FjS0GmMAGAz1WGiZNFzTyDNjqwyJNtWAcFUmSFq/ufmJIzDKobAelFKuzH0A6vBbvma4sM4\n09Tid3uBIJm0Ak1N88hVH4M0NG3WaCsmarKNIZWtRjJPoviwf8h+b5/Pbvp3EmTtxJ6TLF6+/lis\ngGEMfTszHCAIHSPQapEtldzejDMBQSoFP/6xywiikShJMUlf9+eUJpMDCoUordbJM8TWk0mGTnJ0\nW+IL577AT45+4u44CH33lsZMOGOCBMFmBHL4DCvvprJlaSg2fjwgMNMS8ZHI2tqaBQTXrrH7/PMc\nTyYuw1q2+FxFya12uuJYYabMfcPmvBYAgmLR9RdnAoJs1toYdOuW9f37EDfi1AenTzz+1AKB0e4y\nT8YQxbXQ0tHv3lmKuB4jRzCZVDEMg06nEzpewrHNeQoznSRxaBDbCY+MGg1QlOGiO/exgGDs6sXC\n+9cRpRGTw+AWr2UgeKr4FH/63p+GOlJRXGci9VZKQ93ZjOF8zrrozEA5XRoCWFe66IqK3o0jyQNr\nZ4JtqrQKCHRiYz89vqwo7NlAsMxmwHpRCmtWB/e0Pg0CwUBgmlhMVvXv/l0kjD/OPoJh7YC2GCef\nP2aQLFpBiqd09I29N/jVC7/qr77K5ciM55YEoFqzhqbTsO7iRaAC1vx5ISYw6wS3iNHpUC4WuXsK\nELhHPJu1aquvXfMlW8Ocrq4fUSjET711JUWhC2iPNKRtiUQ8watbr/Jn9/4scE1uxd7S4Dlvk9ZJ\njCCWi4EBs94skCwWtccDAtIx4qOoxYj39mA2I7a9zZYk+fcXe3//VEXKngAEmsg0MbMG7+0EZWQH\nCGazGb1eD1VVXVA8ExCAdcauXXMlQ1VWafRP35P+qQUCs9vDzEQRxUqAEdSGNe627/Lq1quLH1hy\nwN4KkrCopN1uk81mQ/e1OrZuKExTCs+2RMab4Z+zpGHtpwKChDCkVLLnqb/zDlLR8DVSueYZhZ2V\ns0gxieQkSSIXHMktihuM462V0pADqg67yWQy6LqOpmmhI6gdW5M7jOKqPUMlalFU21Yli6eyRmzo\njyidHEFY6ahznfm8rY0/0gMvSLQ/R08sEnqrxkx8nMnice2QTkymlO/TKMa5KMu+iiFffsAxVSU1\nnNDVuwiCST6/mDfkbypbP7s81OuxXi6vZATjsdXS4r46qmr9w/XrPkcaljCeTqsUCsHd38tWFEU6\n87k1UsGWQ37t0q/xxt4bgWuKxVTmcw0zk/YxAnvPELDIEYSdKUEQEDdF9H09wAjkyeMBgZCOEhvY\nDYkOiAsCF2XZBdaA6VliqdVAEBvGmCjaiYyg1YJ2u42qqkSj0cdjBGANoLt+nagSJZqNosZVWqPT\nA51PLRAI/R5kDMxYicZ0ypZHAvmTu3/CF899kXjUo9k7Dtim0I5DGE/HzM05Ssx6G5yoxHuQVlnF\nkNFSMhcbEVpr4RS50YBsdrpwRo8FBD1KJcmSCa5dsyqHQjZSLTOCrtblucRzTJTgzgFJWkeLNwKN\nbY6DXZ7Z5O3OPekwluIdBrEs+r6OeD7jA4KwxJ5hjJkpBpGhP5I9J8sc6jqHK4DAcQoIWGRRAAAg\nAElEQVTStoT2SAsBghm6sujTWB7T4B1F3dU8DWWPsRDpNNMbx7SiKdbVKfuFORdnM+uZnz/PbD7j\nTz/6U6ts1Gu5HLHewBqGNx2t7C5eWTn0aOlczGag65zL59kbjwPnHBbP3FU0HSqiKNQPDnyMYPn5\nTSZVSqWENb7hhFuXj0ZpTia+8dOvXXyNN/beCIzFthhPxUr2hwCBaZrctbe8rZpqK21Z58IHBNkZ\n4lxbdG2dYq1xi0gaosO5dfZv3XJB/KKirAQCc6wSUVYnZmMjgYk88o2f9t0rOybx+Z7HZQQ2EICV\nMM5Fcz/byeLooIuQ1WmYKudlmahHn//e3e8FX7R43FoYbmf9HSBY3gMajxcwjB71+vHK/IBjpZnE\nOBFnvS5wVAp/GxoNyOfNn4oRKLSoVFIuEEhPF4MvPPiBwG5KOieeoykEJ4yK4jqT+bE1DsJTAeE4\nhdueRLH7d9oJ45MOYyHepSfYjOC5ijWl0bYwGj+dViGTRljqZ4hHIuzIMnuHhycDgR0FB4Cgp6PJ\ni9+Vy+UYDAZM7SqUACMQRetsnFAN8rim1eq0IynKisjdvMHFBw+sFzQS4a/3/5pddZf19NJoc1X1\nzRtyGOvyTgVRDCaM5W05yAj61kiFS/b8prB9t8sb6VxJ5oUXqB8fu84o7PlNJlXS6TyCYDGLVZYV\nBGq67mMET5eexjANbjdvB5P94hpGKuaThhz5qjmbIQD5eNw958smbUm07raIxWIoTuWb3GcgpFmZ\nxV0yCwhmRPoTCoUCzQcP3PzORUVZmTCeDVRMaTUjiAynTBWd8WH3xByBDwh+GkZgv3tOU1l/Ghwn\nE7i207/576bFxz0Etc+BkfVFsHNzzvfvfp/XLr0W/CGPE3YcwvINFoQI8XiJavXuqYygMI0zkKOo\nNZN7+eDgL3DoPY8FBE6kJJt1KpUMjeMpHB8jPbfmX1DjmKd81Hlp1blKS2gFXmDLkQS7i50cQVi+\nxUkYn3QYc3RoYwPBZy8EGEGYIyGTDb0XlxWF+8fHASAwTT8jCEhDug4zAz26AMBIJEI+n3fvv8MI\nfHJHOv1Y48FPs0mtSUdIkZsXuKFOufjee64jCVQLOWZ7Aee6HKewzGgk6Yy9BHa55HlF4YGmURs1\nT+4hgMWayOefp95un5gjmEyqiGLl1KKrlGlSHQ7dHAFYkf9rF1/ju3e+a++bXuThRLGCkYwEGEE+\nb8lCjgS8qgBB2pI43jv2vbv5WI8eZx841xq3iKTGRPqaxQiOjs7ECCY9FSO+GgiEXh8yWfTe0Yk5\ngr8RI9jetpC5XkfelSnMCgyN0ycZfDqBwDSR9B5CtsVHs7QvP/Be9T3SUpoLuZBW8DMAAVhRSbV6\n/1QgyE0i9OUIctXgw2xIEhcLCNbW4o8FBKPpiKgQRY7JlMsyjQMdnn0W+ZwSZASGYUWzdvGyo512\n210ubFzgB/d+4Pu4xXj6lg7rbV93cgQh47wdnf2kw5g1O7QNSxqSfu6c5VDsJEyYxjyZVBEyuZVA\ncBwiDQ0GFpERRTsKXgaCTgdTzTCZVn0/F1ZCKsdkTExrGN6KIXw/rc2bbdpmkvSgSLVkUvjRj07O\nD4DlBTyD5xynoKoq4/EYzY5Cz9xU1utBOo0cibAminzYPT65Ygis6WzRKKPz55kZhtvDEabHT6cW\nEKwYZOtawjA46Pd9jACsPMHre68TFaIo8cV5E8U1ZinTxwgc8N+z8wOrrglA2pQ4vucHgtS8R8/M\nnHn/UGvcIpbsI/RGFBMJGsMhPPkkwIk5gnEnyzR6Qqlmr4eQKTCZHyNuBItL/lYYgSBYs8iuX7ek\nIT1n7UpZHvq4ZJ9OINA05kSQMkd8OEn4gOB7d7/HP7z4D8N/zuOEncRMcxQGBBXq9YNTpSFVF+hK\nJpGjKe9mgno8WE5nc1N5LCCwoqQMkrRuNZk0TLh61dLFlxmB/cI7W6gcR9JoNHj54st8/6Pv+z4u\nCBFEcc1qdV8Cgnye0FLcs+QIUvMu9WmWydEEaUuG555zKeqqiFJQS6EO+JKi0KzXA1VP3qRhKCOw\nV1ROTwACx3E5Q8I6WuexFwadZkKvR3cuo3Yr5DcUBDvZWB/W2Wvt+YsYHFuShhynIAiC7/rDpKFQ\nIOj33eToJUU5GxDY19HO5ShFIq6MdBIjOA0IZF3noN/HNExi6qKg4lcu/ApvPnoz9N2bJmahOQKn\ndHTVNTn3on5Q9/X/CIM+o3gmbBdTqLXGLUSxBYJAsVqlqShWNRVwQVG4p2nMQxIjo6aKxslAQKJI\n7EKHSDzoeh2fVK//DRgBuHkCaVsiM84gzsWVgwMd+3QCQa/HKJYhm9W5rc18EWxofsAxT32yM572\nqBPOCOr1w1MZQUYzaUXmRKQIB/EZYyMoD7XbsL2dfKxkcWvcQpUSiOKaVT7aE+HFF61k8TIj8FQM\ngXdlXpPPX/k837/7fZZNFNeZJ0X3OpzJo6RmTEyTUtzfGFcqlajVa7S1NjklvJw2OelwPFKJ5axx\nwN6kVVhibzqtEVXL4YwgkaDfaISPl7AfVWiOoNNByBWYTGqYngYor84emECqdf/WpaFYf0h3JiIK\na1xQJPjoI3jmGf7bvf/GF859wV/E4JiHEXT1rk9y8TeVPZ40BLac0a+dGQg6QMkw3OGIbhe2xyaT\nGvH46dJQZDBAi4kYm4YvP6HKKpfylxCj/shYFNeYJPRQINhbkoZWJYvrx3X/u9vroYvpMwGBaZq0\ntTaZuICQzVK+f5+GZ+F9MhpFjcU4nAQDv35dZWye4HB7PcxYkdj58M84bPfoqOdnBD8tEGxJpAYp\norPoqWMmPp1A0O3SF9IUCoLvcAwnQ946eIsvnvti+M+FdBfvN1cxgvqpQJAaz2nMJ8hbMrsh9cWm\nzXB3d7OPzQhUSUYU10gkwJybjJ56iVghxlybYww8gONJFEOQEYynY+627vq+X5LWLR3WjsadyaMP\nJ9bU0eXGuFKpxGHjEDkm///cvUmwHGd6nvtkZuVQ83gG4AAEcECwyW4eULLUarWGe7tJsFvtCGvh\nsCSHF/ZS4QjbW3vpCK8Uce9O4Qg5vPLCDt/NDfW9IctNwKbdk1q3W1ITzZk8mIEz1JRZQ1Zm5XAX\nWVmVY50CSDkC/HY8qDrM8+f//+/3vt+UOrihadaQJ+Ma6oUF/b9+fckIKkqFmTNj7q7kM9s+Rmqe\nz1yLq6qKPRym1j+a865eULEeJ4BgMEBoNJGkCo6zup3y2kwsJavPWRpSTJMpCjNpm6ujEbz0EigK\n3/v0e3xrP4etLhhBKHlEL9g4I3h6IHixWOT++HRjIBg9fsxWpRK0PCftffu+v7E0hGEglOuYO2k5\n5Zd3f5m5F5dUZXkHu2hmSkOfRqShXEawp3LaizMCDIN5cTNGMLJHaJJKWTsP9TqtTz6h58Qz264u\nal2SNjytYHvxfR4zw8B3txEv5F/KzSY8eTKLM4KnkYZgefbUPZXioLhRK+rnEwgMg6Ffo9EqcDKf\nc3FBF9+++za/cu5XqKo5/U8ygOBYH6T66yvKLr3e4EwgKE3nnGKh7CnsZ2QTjEYB69jdbT8VEAxm\nAyoFCUU5B/M5bb9Hb/crQdO4Rdrk0nKAoNfr0el0+NbVb8VK+oO/7xxuieVzhBdCOPc5aZ1OhyfD\nJ6l1iv1OU+fxtLECgggjEARhOTA+NNs+RmrsZV7ANdOEYhE/UcMRlYZEVaTQLDCYRt7fMCgQC4oC\nV0VXZ7aZ+JyloeLMwhZFhnKHq48ewWtBe/C3Dt/izatvZn9pkbETlYbCCzbKCGR5KzY8CUCqS+AF\nhVRLG60GsbxYLPJk2ku9v1gxWeQ5Jo8fBxdphNFFLxLXNRAEGUkqnQ0EoxFSscGkmQ5YfqnzpZRX\nH3QgHW3ECLIuN3lLZjAb0G5EZF3DwC1vBgQDc0B9wcap1ah+9BET215mnUF+nKDfE6gp9fx0TV3H\nne0ibOUvWLMJx8d2ShoazNL3VK69+ip89BFKCypGBW/qfYGBwKuhNRQuqSqFhQf7vcPv5ctCkAkE\n3bGeWmBZ3qHfN86MEWimzREm6gWVq8Uih4nNEW7gaAfPTS4dfaZTKfjBZvzoI5rKmIEVpHRqFxO1\nBAkgCL3cMOD0ravfSslDsryNU/KXzxFmDB2aJvsZQLC1tcWJfrJ2I8rjIQ+nTZS9BRAcHARjGRfe\nVDJgPJ8fU2i9kLkWer9PoV7nXgJYo0AAQZxAt3Tq6uLvX8QIgqLAVZwgmnmTOaXscwaCiuXgFDwe\nak2ufvghXL/OB90PkASJa62cGb8LVhJWYedJQ0FW22p4UvAzId18LsEIuuYwEwiyGIF1dERnb28J\nBMnAbBgfgA0Ksw0DSW4yrafTc7dKW1iuxZNRZPymsoNV1FNAoFQdRq67rHjP64oqiAKj0oi6FBlU\nbxj41c2AQLd0qoq2BALx8DA2EwKC9UwCge8v0pKL+d1aMQyc0RZ+LV9Lazah23Vj0pBvGOizyD4/\ny4pFuHQJ4ZMPabfbOGPniwkE3kCn7zShrsS6jv7XT/5rdtpoaIkeJq0WDKbpBVaUXQaD6ZmMQB3P\nOBFnqBdU9jO8hNDjarVaDIdDXNdd6dFrqnB0S6ckOcFmfOcdmjV3eSmEQdLVh+NAUFNrjO0xrudS\nKpW4sX+Dt+++HaOrirKDU3JSjOBwNmNfS6e1dTodepPe2o0o6EOmUg1na/H9SgX29uCjj4C0pmvb\nx8jtK5kXcLfbpdRqcZgAgtTFdREkpGDeBESAYHNGoFv6anLc52G+T8V2EYoWH1eKXP3Zz+D69SUb\nyOpHBSzB6KwYAcSHJ4WWKipLxAh0y0i1MM4DAvv0lK0XX8yN8dj2MbIcAMHawmzPg/EYhRYjLb2+\nI3vExdpFbh7eXP5MUXYxlX5KGtLLAVtdVrwv9nmyGR7ASBnR8COgZxgI9Q2BYKZTlYPWNRQKUKvR\n7nRiQJCVQmoYAfvPi12E2X3z4w5eKf9BwvWMMgJ/OEQSI/t8E1sw8u0L29iG/cUEAvPEYFIoM5Dq\nyyyC+/p9+mafX9rN6M4ZWgYjGM6CgSBRC4DAOhMI5NGEx4UJ6p6aWWgSerCSJNFoNOj3+0FESBSD\nnPccG86GlEQ72Iy3b9NsSzEgSElDkUEskihRKpRon2sjCALb5W32m/v85NFPIn/fTlB1HAGCdjvQ\nYPMYwcAcpNYpZrqOL1cxGxEgicQJklTeto9RqovOsIm16PV6NFqtXIYVmnXRokpEBlwEzrMYQTJG\n4PsRT/fzZASmiS1BXfW42/K48MMfwvXr6+MDEHhxtk2jUFkbI4D4zIzQUnGCiDRUliRkd4IjxgsF\n84DA6/fZevXVYPSh76feXRgfANZLQ5MJlEqU5lVGchoIhrMhX2p/ibcO31r+TJKqOBUfXw/+f95i\nhPGJYsZky7xmeAC6qFONdrU1DKTmZkAwnA0pF8RAlnUc2NuLM3qyi8rCfki5g3zGY6hUcO7WceX8\n3j/NJui6FGMEnj7cnA2Etjh7lYsVCvMCR8OjtR9/LoFgdqRjKUWeePXl5rh5eJM39t9Y3687o9/Q\naJ5mBJLUYTLx1jacAxBHYx6rkyUjWHdxxTZTogFe0nRLpyiYwWZ85x2a54srINhTsR9FMhYSjACg\nXCjT2F2BQ1IekuVtbM1MM4JIel7U2u02I3tETckpypnNwPNQhALTcuT7icyh8IB4no3rjigUWpne\neChrJb2uFBCct6hEe04vvODAY85mBMVigMPTaaQZ3ucJBIaBocKW7CHuShQEAbvT5Pv3v8/rV17P\n/54gQLVK21VSQNBut2MeqaJsY9snsa+ngCDRf1/1phjE322qoAyWsYqty5eDd3P3bjaIbwIEi2eo\nmlX0jGwa3dJ5bfc1bh7eXHZPFQQBsbkDQx18n9EoeGd3nXRac96lO3SHVKdxIJDbm0tDZckLnLDp\nFLa2AkZ8BiMIz1AuECzWwv6wjCOcZneLBWo1F9suUwvfXb0Ohr7eCcuySOZQ2St/QYHg1MAqKtxz\nqksP9q3Dt7hx5cb6L2YwgomTXuTRKGhLIgg50X8A10WYmjwpjlDOK5n5xblAcMbFo890NGG0koYu\n12JAYD2KHPhE+ihASShR2VpdkN+++u0YECjKDnakFXWvB42Wz0PL4lIGEMiyjFbX0IT0vwUPHIBR\nxXOYaJGsohwgmM9PkOWtYGh9xlr0ej3Ob22dKQ1Z2xZlO9I/ZpE7ryi7MY852aYh1YH0c5SG5oMe\nIxV2JKjVbbh+nR8/+DEvtV+iXVofc6JWozUvLIFgOAyYS9IjzZWG1gCB5E7pE5cWMhlBvY44GgXB\n4sX7q6tBADS8vJIxglxpaDTCr1YpG2V0NwMIZjr7zX20gsa7p++u/r7yOSiIYJqZNQSh5V26A2tA\n2YjsC8NA3dpcGlrKsot93W63Y+vfLhTwfJ9+JIB8JiMwDPxaDeehhCjIuG72+VfVKcXi+ZWEWKsh\njsZPzwhCINhTKbtlToyTtR9/LoFg3jOYF0U+mlfZ1zQ83+PW4a38jIzQMmIEpp9mBL1ej0ajkDps\nMRuNECoVCp6Cs+NQliTqhQJPIvnFzw4EA4qCiTyWYDCgeSkCBBcSQJDBCBRfodxeHYTfuPgby6ll\nsAACxVhefv0+iLU5u4qCImZviVKrRMHJ6cSq6/iNBmXbZhzNkY8AQTTgGL1I8oDgha2tM6Uhs2VS\nnsQPfAAEcUbQarXQdT2I0bCaV/23ESye9I8wZIkdQWTH6y7jA7lFjlGrVmksgEBRAhVxPM5iBDvM\n5xswgsh0N9+dcOyt3s18Hji8qYacjQbKZBIAwaJCVZZkFElhMg8yf5IxgnWMwC9VaSgNesP0LRwG\n+t+8+iZvfbqShxRlB69WCrJlMjKGQssKGDuOw2g2QutGQMMwKO1szghKohUAwekplEopIBYEIZVC\nGgJBXsUzhoGvVZHbMoq6k2J0oRUKBqoaGY+raeB5dKT1k+BStrcHjoNSManYFXqT9X/8cwkEbk/H\nKfm8Z5e5rGm8c/wODa3BC/UX1n8xgxFYpBlBt9ul2VTXA4Gu49fqVGYVJqXggCTTyp4VCAZml7rW\nQHj3PXj1VZotcQkEyp5yJhDIrkyxsTo0akHlN1/4Td6++zYAklRjXnKXOmy/D1Zlnpk6uvwdNRVx\nnrNdhkP8Sp1awUE3Iz32L10KbrJuN1aUdBYQdLtdXjx3jsPZLEahU0DQMCmOIs+8BIJ4jCCM0YSX\naawDqaV/vkDQPcKQZdpFlav37sDBAd/79Hu8uX+GkwJQq1G3WAYbQ287WxpKMIJk1lCkshhgbo84\n9lZsbRFXT/dhq9WQZ4s89pyiwI1jBIaBJ1fobMelldD0WXD23tx/MxYnUJRdvKoKw2FmDUFoWV1R\n+/0+jVoD51EkldYwKO7W8plL9JksHU2Yosxrwd4VxdT6Q1oeWjKCjOK74BfreHIZ9YKKLG+nYjyh\nieKQQiFSAyEIzMtFdt38s5lpi1YT6vQeNbPGwFz/xz+XQODpBk7ZRix0KEkSb326Jj87aokD32h6\nzKV0NkWv16PZrMS8ypTpOn6pRtWtLl/8frEYkzOiGmx05OPZjKBPs7gVBFqvX4/Rb7kj445dXNNd\nPkcSCERbRKnFC79uXLmxzM4QBAGh1sI3+ou/FyalWWagODS5KkNeuxJdx1OrNGt+/LCFfU/eeSdG\nmaMeZZYs0+v1uLi1hSwIdCP0OyllTMtTysMyvrMAi0WANMkIIDuFdOm9fY6VxcbRCSNJQVM7XL19\nG/2lS3zQ/SC7rUTSajUqs1XOd/jeY1lnPL005Pke5nzEA2cF0pmyEOCUSpQch1arFetkmXx/IRDU\n68GyZxTVB/n7UpnOubhHHZpuBanbr195nR/c/wGWYy3/PrdaWDKCetPnyLZ5YQNpKIwvxeJohkHl\n3IZAMBtSEqYoHx7BYnh8khFAOmC8iTTkSBWUPSU2DjdpntdHEOIvxqpo7Hjp2SJn2muvoXY/oD6u\nLyfC5dlzCQSCPoCaz8VSEBC9eefm2fEBSF3AWm2M6JQoiHHJo9vt0mrV1jMCw8BTKtSoLV980ktI\nMoJN20wErRy2g0N4cBADAkEQUM9HAsYZQOCbPlJZiv3sxv6NWJqe2OjgL2Syfh+GRTMzdTQ0qSTh\nTrI7rDIc4koVmlne4cKrjMcIzpaGOp1OJrBGGYE+16mKVeyjxVosg8XbzOddfD97ZGWUEXzelcX6\n0SmGpOAUd9n/q7/iVvEJv33ptzdL/atWUabWshle+N4LhQLVapXhIqUySxoqNAt4VqTqPAIEY3tM\nUS5x14qDalYuxMBxaEgSoijCtWvw5ElQ35ADBKK4alqaMsPA9YtsX9zOZATDWZAN0yq2eLnzMj9+\n+OPF37eLWxGWQFCoulzUtGW9UGhZl+7p6Snbu9vYJ/bKQTAMahdqG42dGEyPqallhNvvwdWroOvZ\nQJBg/5sEi12/hLqnLoAgWxpynBP8aOorYBZltp31s6Ez7bXXUO//FfVhnbEzXvvR5xIIxMkQryGz\nr2nMnBk/evAjvnklp61E1BIxgkJZBysdhOl2u7Tb7TMZgSuWqRdWmuDVRObQWmlIz6CPCzOsMc3S\n+SB9L8EIIBEwTqSPArgTF6EYPzQHOwcMZ0PuDe8BIDZ2g+E+LBpdldLUO2q+5jMf5ZfOO36ZVkdI\ne10HB3D7du5FkicNtdvt2Hp6XvCx6J+qW4G0sFyLxeUnijKFQp35fHX5RDM/UjMJPkdpaHx8iiEq\n9Eq77Msy33v8/c1kIYBaDSFy6SYzh8L9kyUNCYIQjx9F0kf1mU5DrWP7PsNFgV8eI+jO5zTCOFGh\nAC+/DO++m8/oWCMPjUbM3RI7+zv0er1UpkwoDQFBnGAhDwV1Lt5SGqI6z8xmy2UEWx3kjhxzELTt\n2pmzEyCUZVvB2fvyl0HXN5KGQmBdBwTzeQAE66QhyzrGceLxgGlJpjXP6E91lh0cIL3/12y5W0y9\n9fM2nksgKEwNnJbEfrHIjx78iK9sfWWz8utkMZem45v1lJfQ7XbZ2sp/WQDoOg7lWHAo2WbiWWME\nI3tKOwSCBCOARJwggxHMx3M8JV5oIwoib+y/wa07twCQmucRRsHm6PXgiTJeywg82cMc5pwiw8Bx\ninTOi+kLYQEETxssbrfbsfU0jKBGTYoQHX2m0yg3Mi+/ZJwgephTjOBzlIamJ6eMRIVhsUH55ZeD\ntOYrb2z25UhRWRIIokAWXCSnscZ6ECkq8/0YIwgBc1/TuBOOrcwBgtPZjGr0QITvbxGYdd0x4CNJ\nq6y03Opiw8CxizQuNxAEgWli+E+0KvzN/VXAWFF2mZedJSOwK3ambJkVLA6loSUo+n6g9VerZzbI\nAxjO+jSLnYCNv/ZaLiNIVheHZ31dsHhuF1EvqGulocnkIZYVn6Q2Koq0LCnz82vty1+Gjz7ifOkc\nlpBftwTPKRBoloHZDnL31/ZvSZosxyZzWegIdj01nCqQJs6tZwSGwdwt0yivgkNnSUObAMHMmeHj\nU5kWgy83m+sZQUb66Gw4w5XTMs6NKzeWXpdcOwdzF3c2xzB87sqTtTGCuTRnOsjxKkYj5pZG56KU\nPmivvgrvvUdDrsaCxXkxAt/3V0AQYQRZUoZu6TRqCyBwnKCeYTGOMFlLEF3/MGuoLJexHIt5UQ1c\nxUyh++nM7vcZCwqOqNK/dpGRPeLV7Vc3+/ICkOpqHX2mpxhBCASiqASFV058sZdxAssK4jOL8a1h\ne4Ko1JYHBMfTKSXXXTlLEUanW/oSxKMV0rnVxYaBbWqoe2rKq545QSKAVgicj69f+DofdD9YtIDe\nwS7OYDik34dpycp0UrKCxeGsZXVvsRbTadDSs1DYCAh0y6BRXEzY++pXcxnBnqrScxymiz0TnvWs\nZ1quxUQ9Uxoajx9gmmrMOR2pAg17s+lqMSuV4OJFzpWbuML6vf18AoE9xmjJ7BeL3DzcMD4QWuQS\n1i0d2aunvJlut8vOzgtnZg3NrRKtamvpAezIMlPXxVjQ7ygQbBosDvoMyaiPp8EhJD1WV72wiBHM\n58HlV6nEfse0P830AG7s3+DW4S0830NWdvHKMvrDEbU6IPq0CjnpoYCFxeg0R0c3DOypxtaVQtoz\nrNVga4vGibFRjMAwDDRNQ1XV2MWVjA+Ea9VqtoK1CNnA4oJK1hJED3N4cS2b4c0XhSPj9TrqRmYM\nGYsKpbnBTzsWN/Zv5LeVSFrYbyiHEUS90rWZQ4nU0ZARXIkAa2YxGXAyHOKLIsspLglpL8bmFpYr\nDRkG1lhD2VNSzx/KQuHaqAWV33rht3j77tuLOpcp/mjEYABG0eJKhpOyLli8BMUIM9oECAxrTMur\nBiC6vx8wtEaD0WgUazwnCUKs43C4nuukIWukouwpa6Whfv8YVfViIauh6lObPeNM7YMDdkoFRHv9\nVf9cAkHZHXHSUmn6Jh92P+TrFzfIyAgtEifQZzoaeUBw5cwYgW2qQUbH4sULgrC8vMIW1E8bLNYt\nnYosohwOgowbgj1ZKKzG6i4ZQbjJExfN+HTMzE+n+FxqXKKhNbh9fHsxElBCf2BQafqxPi5ZZnom\n+nFOXGOxybevydkH7fp1Gp883EgaCgPFQIwRZAKBpdPqtIK1SKRLJjOHokAQvRA+b3moMB1higW2\neh/w/yh3n8lJyepAmvRK12YOJdbiaRhBr9fDUtXVWoRAsJBhkvEBWCMNjUZYupzJCGLNAhf2xpU3\nuHl4E0mq4JZF/GGXwQB62jSXEWQFi7e2tlbS0FMCwcie0tKl4OwVi+A4iIssqn7ij8xyVPKAwDcM\nZsMoI8gGgm63S63mxZ5zoLhUrGcEguvX2cWEM2IjzyUQWILGoKHw7qMf8Fsv/FZuj/xMSzCCkpQN\nBLu7185kBJah0d5qx158eHmFLajDGS/VahXLsoKRg2cyAh/53UdLIID4Jl4CQbjPf3kAACAASURB\nVEZ8YDabMR/PGTnZ3nuYPaQo27hlgdEjA6XmrpWFXM9l5s3oPckuSvENg9lAZfcVJfugHRxQffdj\nxvYYx7VwnCGy3AkXJrYWYaAY4KKmcWzbWJ6XeXHpM53Obmd14CNecDJGEPVIM4Hgc8ocUmcmlqRw\nvvsR/9f4J7yxv2F8AJZrkRcs3qSobPZglqoqjsUINgACpxiZXrcbFDfVFz3tY2xuYXmMwB/ozK0i\nckfOZATJuF4ss61exxueMBj4HKnZPbCy9PglI9h7ekbgei6m69B8PAvOniAsEzuy5KEw5hKdpV1V\nqsumj7G16AWZdYVaYa00FGQsxp+zJzuUTSfz82fawQHb5gmemW7OF7XnEgh0v0alVea/3bnJjf2n\n8LggdgkPZ0MqhTQQ9Ho9trcv4fs2rputi/tDHWtapL0dB4IwTpD0YAVBWAX81gBB0HDORfnp4VIa\ngvgmXgaLDSMFBL1ej1aplU1PWRy2OzeR5SAzY/LEQKo7awPFhmVQVar0e9mVQ35fxxVKtC5I2Tnl\nBwdIt9+lolTojg8pFFoIwiL4lbiAw/gAQEEQuKCq3JvNMhnBcDakvddOeX6wOSOIDaf5HBhB0bKw\nRZm9okCj3Dq7yDFqi7XIGk6zkTQU9qFKrEWYprkfaZWemzXU7eJVKqt3IghwcEDjWF8rDWVdsF5P\nR2w3EEQhdZFmNXsMM9vu6/cRai08vUtvAHLNoZEhW37e0pBhGZQLEtrH3dXZWygIWQHjKwtGYJrB\nMhWLQTO8ilJJ5e37PR1pOwA+SarjeTM8L83ag+eXYndSV7IoTte0u1lnBwdUjt9DOiPY/FwCgUGN\nZqvDrTu3Ns/ICC2SuhnQ00Zs0R3HQdd1Wq1WyquMmncyhHqNZqkZCw6FdDHr4lpuprVA0KckOcjv\nP1oOzIYEIzivYj+x8Yd6qkdAr9ejXW7nzij95uVv8sP7P8QX6zhFh9mJgXtGVXHoUc7nc8yM/Du/\nZyBuN5AkgWo1IzM2ojP3xnfiF0liLWKDuwmANW89dUtn64Ut7Ed2UBMRA4J01lAeI9Bnn191cWVu\n4xUUfHXybHvTMJbVqesYQaY0FDLFSPYUrAq3Lmsa9y0L1/fXMgI/KZMdHNB4cBoLFkctlxH0dYSd\n4LJPMYIMaUgURF6/8jq3Dm8hNDpgDOn1fS5vZceuslo+fxZpSLf0oPPo7QgbjwBBFiM4zHD6sgLG\n/kBH3A0+JAhCJpBPp1N836fTEWPPeVyYoU3WD5/Ptf191NEhirU+/fS5BIKxVKZYqKHPdA52Ds7+\nQtQinT/1mU6jGGcEg8GARqOBJEmpzJOo+d0h4nYz5ZWEhSZZF9cyYLzm0ulPH1EtyAjXXl7pSsQ3\nsaiKFOoFnAeDFBB0u12269uxJmFRaxabvNx5mZ8df8y85GCdDpmV7LWMIPQosw4DBJtcWnQ7zbwU\nXnoJHjygodToju+uBYIoI4BFSq5ppi4u3/cxLIN2pw0CeCd6QhpKZw2Fz14uB3F22/78G89V5g6u\nrPGe8vjp2eoaaSi59lnSkLwl4xgOXk/PjBFookhHlnlkWbkFZd1uF7HRiO/P69dpHD56+hiBYVDY\nC15aKkYwy+6oeWP/Brfu3EJq7ODrOmND4MWt7Ess2QwvfP5Op4Oyp6QchLOAYDgbUpY85F88hFde\nWfxP6ktpKMkI8py+LKYijEZIF1ZSWJY8FD57s7mqx/F9n2PJRB6dIfLnmSShfKmDauafb3hOgWBa\n0BhODV6/8vr6ttNZlogRtEpxIIgGK7P6vofmD4ZI59JAcBYjOD09XQ8Ek8fUkGOyEKQ3sbqn4tzv\nZTKCrdYWqqQum4Ql7Y39N7h19228iord6zEuWWtjBOGhzdJJARgZSHvNzOcEAkB76SUarkxv8iAO\nBAnvM7r+kO91TedTZFFGluTFWvRja5H0mMPMD8dxEITliODPvaisOncRtRL/r3Inf3Z2nq3JGkpe\nRJlFZaKAsqvgPOhnxghgsZ6z2VpGUGi10ozg/btrYwRZF6wwGVO42Mx8/ixGAKuAsdjYxdcnyEWf\nFyvZl5gsybF9HnrU5XIZqSghlkXcJ4PNgcAcBp1HG5eDAB+sl4YWMZd+3z8bCKYjCi+sHJyszKEV\nEKyeczqfMikWED+DkyL/8j7F2RcQCExF5X733af3uCAOBDOdTqUe2xzRYOW6oI4wGiFdbKcCVpc0\njQezGb3E5oDNpKGBeUzNkc4Gggsq7qNsRtDpdPILW4j0HaqUmff7TEozXlDzWyCEhzbrMAAIkxGF\nS8GtkptTfnBA3fTpTR7HPcpEjCC6/pAPrNHLTdlTcBJroShbOE5/2WZCFEWazeYy8yNcz4bWYGh9\nfkBQsz00WcN55WWaxQyXe+2X01lDYSvqTaQhCBwE9/EwLg1Fxhxe0TQ+mZixjLao9Xo9lHY7zo6+\n8hXq7x8+dfqoYI6QrwTvMsloou8valeaVygrZbqyDCML+YxEhug+T8qKwRkZbgwE/eljKpKI+Mpr\nqx8u9meWE1QvFFAFgXtdJ7aWqUI3z0OwJyj7qw9lZQ5lAYFu6fi1LL11cxOuH1Cx1/cqej6BQFV5\n995bT6/BQipGsF2PM4LoZpLltNcVmjA1kC+1UjqlJopsKwp3E5sDIkCgaUEBVKRldWhD85TG1DsT\nCJQ9BfdomAsEuSPzCNpS3z6+jVerMtcHNJsg57SfhlWGRyYj8H1Ea4J8pbV8zkyZ4OCAhm4xNE/S\njGA0WhZJrGMEUQ82mnWi7ql4x3FpSBAKFAqNWJuJrIBxWLz1uUhDnkfJ8ampKl87+J2n/35YUKYF\nkoeiBLVQ0VbUoQySJQ1BuBaDfEZQLPJh16JcDlKSo2bbNqZponQ6cVCsVGg0dtHNbCDIfOe2jeC5\nKJeC50gxgplOQ83uBvDGlTf4hd1DmlhQWZ/IEN3nSVlRvaDiHW3OCPrTh9QoxM/eApzznKD9YpGP\nT5wUI4idvckET9RQL64u43XSUBRY9ZkO9cZnc1IODmhY63tdPZ9AUFSo+hOuNK88/ZcTMYLdZpoR\nnCkN+T6iNUa+2l5WRs6cVTDniqZx7zQbCE5PT1dpaRkXz3DWpzmwN5KGvNOcYHG7nV/YAhTlIl+7\n8DVGqogwMthtrd8G4UWSeRgsCx8B9VJwCecyguvXaXTHDMxu/CKRpCDdYhLQ+zxGkKTfUWkhWIs0\nKCaBPCtg/HlKQ9awz0SGmmo/m5OiqiAINIVSqgOpqqpomoaxeMZQGkrGgbLWIsoI9jWNj47nuWyg\n1WohZKyF9pXXwPeZORaSFPfkkwWPAIxGuFIZ5UJwAW3KCCCIE/xg+CnSbI5bnmUWk4UW3ecpRrCn\nBkkdGwLBYPqYuiM8HRBoGndP00AQO3uGgSuWUfdWl/Gm0pBu6Uj1xmdiBBwc0Jp+AQvKpmWFNy//\n9rN9OZE+er4VB4JkjCBTGprN8AVpefllxQke9bxMIFgehpyLZzjp0TD8YLBExLKAwO+lgSDKCNYN\nrL5x5QYn0pzCZMKlrfWpZeFFkskIEpt8LSN43Gcw66c8yqg3nvTqGoUCiiDQS0hD0fRDdU/F76fX\nIgnk0fX/2wCC43sPGCkittzjN1/4zWf7JbUazbmUAgKIM5qg14+w6P2zMmVPCdYiwo6ia7VfLHJ4\n6uSmjnY6nWwn5eCAhi9jCZ1U4WGxGOB5rFWLYeAsum0mn335TDlTt16/8jpvP7rNXCkga4O1smV0\nn6cYwZ6KP9g8WDyYHlObuplAkBcfu1Is8rDnrgcCXcfxyih7q3qnTaWh4WyI1GjGWPNT284OW3Z+\n1wD4XwwEf/7nf87LL7/MtWvX+KM/+qPMz/yLf/EvuHbtGq+99hp//dd/nfmZaUl+tvgApILFF7ca\nuTGCXGlI13GEYMgEZACBpnHSS8cIYpsp5+IxJkOa2naqWjgLCNDjBx42YwQQBIwPPR11NuHq9vrU\nsrUxAsPA8UrLTZ572Pb2aExc9OkQWd6O/1tkLZLSEASXVz9DGgovEmVPAWOUAQTx2b5Z0tDnmTV0\n+N6HGLKIt8WSKT61VavL4q3oc0J2LUGqqGxPBX2UkoZCGW1f03h46uYygna7nV1lfXBAzfGxhOy4\nR9IB8HUDxy2ing/OSKVSYT6fBwWV5GcNAXRKHRqVK5iywk7JyJ2aB2czAl/fPH10ODoKZNnLl1c/\n3IARHCecvmXcaWFedxicke0VEAR3S17WUIQRzHSqpWaAtp+hBcq5nLUO7X8ZELiuyz/7Z/+MP//z\nP+e9997jP/2n/8T7778f+8yf/dmf8cknn/Dxxx/z7/7dv+Of/tN/mvm7jDJPn5ER2iJG4PkeY3vM\nha3qU0tDvq4HL/Z88GKTgdn9YnF9HUH4HFlAYE9p19JFSFkxgmQrgejzZ3VmjNqvnPsV7gszivaU\nlzYBgpysoWCTF5ebPLfvjCBQ37qIbo3TjGCxFr7vp6QhgMsFDXMSx7yotKDuqUFL7QQoJgOqyeri\n2HCaz4ER3HvvPQy5wP5rLz37L6nVKM3coBmeO49JbVnVxVm1BIxX+yLc51UlWJtdRWGqi9Saae9y\nCQRZa3FwQNV2MP1a6nuQfu/O/T5eoYyoBVeMIMSLyvKyhkL77cvfYlrQeKG8vidEdJ8nGYGypyCM\nx8u1KBYDpzqvFfVw+JiGWAuGLIQWAYIsRrBfLKbYavLsze/28JQKgrRy7rLulnDvJ6WhulY/s3X9\nWbbX3ln777lA8N5776V+9vbbbz/zg/zlX/4lL774IpcvX0aWZf7hP/yH/Omf/mnsM9/97nf5J//k\nnwDwta99jeFwyPFx+iI2qyJb5a3UzzeyRYxgZI0oy2VaTYnxeFUNmwSCLGnIud/HFctIpUBSSQaH\nrmgahi48ExCMXJvW7ldSP89iBIKZBoIoI8jsgrgwSZSobV+j5Ez5ys76Fh3r6gjm9waxTb7O66rv\nXWHk2LmMYDqdIooipVI8w+H8vIxa9WLnM8oI8tYiGVDNYwSf17jKo0/uMJJkvvqNf/Dsv2QxkyAM\nGK+rJcgrKouuRbjPJTHYq4Ig0J4VkarplgUxaSi5FteuUXUcZk529knyvc/v9vGKcWCO7v91jADg\njSs3GItlrqjrZ+1G93kWI4iuhSCs35/DaZ9GMXGvhJlcjQaGYeA48XXb1zSMoZBiBNH7wLk/wC/H\n1yJPGtra2koFi+tqPRbbfBa7dHV/7b/nAsHv//7v80d/9Ef4vs90OuWf//N/zr/6V//qmR/k0aNH\nXLx4cfnfFy5c4NGjR2d+5uHDh6nfJXUqqZ9tbIsXGyKtKAY/CicsxVocFJq47gjPi2f3OHf6+Nrq\nxWZJQzNdfCZpaOx6tK9+LfXz5AYuNAtI7gS3EO9dvmmMAODcua9R9Ue8urV+Hmq0jiBJj517PfzS\nai1yg8VAZf8Sk7mAKCYYyEKWSXp0oW3NihRq8b4VUY9S2VEQ51O8UnxfJHPtz5SGPiMQjJ48YlQo\n8HcuP0UTxKSd0W/oLGlI2VMQ7Qn+oiNtVlC2bhbxq+mWBTFGkJTJCgWqRZWpnt3qIMUIHvShEr/8\nnooRvPDb6GKVC2p2+nZoa2MEF1REexxjiuuAwLAntJqX4j9cnNNk+nFoF1WVmS5Sqa96+STPnvuw\nD9VkIkMbxxng+ytgWTpxiyQhz4us02d0VF789V9d+++5EYSf/OQn/Mt/+S/5+te/zng85h/9o3/E\nj370o2d+kE1b8SazILK+99/+8ofwr/81AN/4xjf4xje+sfmDhEAQ8SjDzdFux70KQRCR5S3m8xNU\n9cLyV8zv92MI39AaDGar3bWrKLjGHKXmAqtAbKlUWgJrKePFeo7D2IPOQTrjJJqZIQjBusgFE9vU\nCK/xMP2vVqvR0Bp83P947VJ0tr5NXfivtApnBIsXGnMWI3AeDGKbPDdYDFT2LzB+J+MfFmuRJQtB\ncHFRnQMr5qJbOi+1AglGKAgUpCnzmUY0rHiWNDQYQE2tBU3CKmWkzxgjcMcGY0lZet/PZJGisoE5\nWNuBNMurlIoSBaY4bgmZOHMKrTRVsNrpC73b7XL+/PlcUCxXVSa97CLF5AXrPU7XuITr7/v+mYyg\nrJTRadBwD3M/A8T2eZIRFJoFfC9wlsI3shYIPIv2uQQbj5zTcP23t1eMVhZFCmOZWdkGtOUzRe8D\n92iI0IyvRZDe3GI+76Iou7Hnl6Sg+t0wIvv8GYDg7bffXqo41jj7vYWWCwSFQoFisYhpmsxmM/b3\n94M5ps9oe3t7PHjwYPnfDx484MKFC2s/8/DhQ/YS2TMAv/7aK/zrBRA8tS0WdGgOlhsxujmSmykM\nOEaBwH3UR4xs8nTOvgDjAkNtCqy81KhOmgUE44//P0SgvJ1Oi9W0QLo0zWDeBIAkTJiO1SUQhB6F\nIAhr6whCM9RfoYbBp4NPuda+lvu5ZdZQNc0I3CcDxPpmHlfp8g6Tn/mBq5Ohw2YFigEqU5V5OS7s\nJpuWFYQJ5igOBJtIQ6IgUlWqwfCPz8gICvaMqfQMIwWjFkoRxVW/oVCl7XQ6vPvuu8uPyvIOpvlh\n6ldIwoTZWEUmu7mbMlaYvjAB4j/v9XocHBzkXjrlisK0mw2WSSbonugUWvHfH66/6ZiIgnhmQH3o\ntyjZ652ZdXUEgiBQEKbMRiqhoJW7P32fke/Ruvpr8Z9HJJncgsqxzLA4JgoE0bPnnQwptNOgF0rP\nirKbio+Fz7l8f88ABFEn+f/+2X+B//P/yP1s7s3+a7/2a2iaxk9/+lO+//3v8x//43/k937v957q\nQaL2q7/6q3z88cfcvXsX27b5z//5P/O7v/u7sc/87u/+Lv/hP/wHAP7iL/6CRqPBzk46yNEbnj7z\nc1AogKYxHhynGIHjOIxGIxqRwbhZOmwS4etqPZYlMB6DpMCDjO6C66qLu++9TXmNM5ncxJI3wdJX\nV1/0IJwVLAZ4z6xS8Sf890//dO3nQnmhXq9jmiZ2pBDOPxkiRg58brAY0Eow8oDDhJd3BiOQJzJ2\nxcb2VvQ76emK7oSZHo91ZElDWY3n6lqdoex+Jurt+z5F18bcZEj9OotMKXuWNhP4PpJnYg0CQMps\n7jaW0YvpvbkE4pxLp1QWGXez91Qqa6g7ROjE/7/h3j+LDYTWd1uo1qdrPxPd50knDstCwMPqrlSF\nXCB4+JCxD529X4r/PLIWeQFj15Doaav1TCaP+D0dcSedbRXNSpxMJkvnG1bnKBYj+AzB4h/81Xo1\nJxcI/v2///f8m3/zb5BlmXPnzvHd736Xv/f3/t4zP0ihUOCP//iP+fa3v82Xv/xl/uAP/oBXXnmF\nP/mTP+FP/uRPAPi7f/fvsr+/z4svvsgf/uEf8m//7b/N/F0n05ybZlOr1TC7R8vNGC76YDCgXq8j\nRQbjZlVw+qdDhM4KLJIewGAAWs2NDbIPbR0Q9O79jKqYn+8b28Sui+jOsLorDzR6EM4KFgN83ANb\nVHjn4/+y9nPhZhQEgVarFTsM3qLzaGhhQzcrY0SqJoyYAP47CX0oEiPIYgT6QKTc8Lgf+aUx7Xsx\nmtFKyMmyHLy7UG5MDrCPdiAdilZutfcm9ungU4ruHFtdH2850yJtJpLjKrMaz6WAYDLBL6hYR0FM\nJevSdY0Cp2p6by6BuFIJigK8eA/7ouYx6WfvqeQF6/dXjQhDCxnBWfEBgKHjMHDaVJ1jutO0Fx7a\numAxoxGuXMZ+vJLB8oDAvf1TJi60SnGVIikNJRlBcMQFHvirIoq6WsewjJXMretI59NAEM0cSj57\n+JyxrKHP4Kgc3U3HWqOWe+t89atfTf3sH//jf/zMDwLwne98h+985zuxn/3hH/5h7L//+I//+Mzf\n0/PW611nWq3GbHBKoxxs1HDRUxuJbK/L7+uIB6sNkwwODQZQa7AcAhK1pTyRBQTdj6i28jN4Ypt4\nPMZXSlhPVps8ygg2CRbfO3WZFoo8uv+XeL6X2cDP8RxmzoyKUok9/7lz54K1GOqIu5eXn49mZixm\nmqzM7aIKIuPbP6P69//+6ue1Gjx8SE/TMhnBYADtpsChafLiwmOKMQLDwNcqqznOC5OkIoKg4LoG\nhUKdVqvFYDDA8zyaTTEOBGHm0GgUBIue0r7/N9+l7NoMK9nplRtbrQZ37y7f35dzCspgBXQxMww8\nrRLMJSBeQxCaqYsca1M830eMxOCW+0cUA/0xknoJUCxMue95cHwMO2f0GzJGSOfjVWvtdpuf/exn\nGzGCO6bJcN5ir+Dz3+/8d37vK9lqRLhOpmniOA7lciR5wjDwtWpsX+QBgfnhX2B7UFXjAW5UNQBE\ny8qUhgYDqNQ97lirsy5LMlpBC9J21SqMDAoX0xV80azEXCCYffZg8XQ+hdP1Ds5zWVk8VOx8/WET\nq9exB92UNJQFBJnNvXQ9tsmzgKDZZDnGLmrrGEF//JCamp8RFdvEoxF+Ob7Jk4zgLCB43POYKUWu\nSiX+5uhvMj+jz3SqanUZtE8eBsEwkC7EN3le5pBtH1MvFBl+kPh/nSENDQaw0xZi6xljBIaBX64u\nL7+oRYG8UChQrVYZDof5raif8bB9/MM/o+LaKI3sgquNLZo1ZD2DNGQYENkXWcFifSBQa/gcJdhP\njJEl9qfn2ZREE6NRgdu3U4+dumAno2Xn0dBCRrMJI/hkOmNot9hizq07t3I/F7678NljySWGgV/Z\nDAi6D35KSRLTySmRdjBZ0tDyrCfYf/hcvucjmiOkF9JAEJWG/jYZwQ/v/5At8wvYdG5UnGduxo2t\nVsMd9DYCgszmXqNRDOGTevxgANst4emkIcti4OvUyvkXSWwTLwZuRDd5LEagnR0jOOn72FqJv1M8\nvxoRmLDkoY16pb7vB+11Ewc+L3PIto+pqVWGh4kalTOCxYMBXOhIsfWMXXCLwrokI4A0kIfPH21F\nHZtS9gyZQ57vcfzJIyquQ2Xv/FN/P2aLtciKEYQXUSg5BOnNEzwv8ncvhtIsgSDj0h0M4MpWIQas\njuNgLPLll88RWYv5/IS61mRYUzPPXhT83amL5EyQzudIQxswgg9OLaZKhbLl5u5NWO3zzNTjjDOS\nCwT9D6nKOYH+SJuJLEaw1RJS7D98rnl3TkEykbbSDfai0lDy+VOM4DPECG7duUV9/AWcUDZV7c8G\nBPU6rp7OGtpEGnKnLpIb3+RJPX4wgL2OyJ3ZLJUOmysNvf8+w45Gs5jRBGZhSSAQmvVgHN/Cos+v\nFTQEhFgzvKg5vo8+AK9c5kWpnut1JWfLRr0ip+9QEKepTZ4XMLbtYxrVLfT+43h55yJGkMcI+n24\nvCUtL65wKE2UEQiNbCDIyhzKajz3WaaU/fzo5+zNrlFz53ReuPzU349ZJH00jBGErajDQrvpoqnP\nKr05kjxhGNCsx4Egcuk6TtDf71pHiQFrdCATkGJHtn1Ms9hBLwqQjPEQB3/rkYWsmAiJMarLYHGG\nXJW0D09s7EqVwtjGsAzuDe9lfi7c549PHqedCMNAaMXPSCYQzOf0Z0fU1ByvOVJdfHoaT1QJgWDu\n+wzmK5k2vBOshxYFaZJKpYX10lCrBb1+ZJ9/BkZw684tSsb6UZfPJRDMNAvnZ++f/cE8q9fx9VXT\nq/Di2kQaCjb5NLbJs6ShrZZITZJS9DuXEdy+zaAuU9eeAgjadeanc3xn1cI51rBtjTz00LLQpgp+\npcKOI/KjBz/CctIXafIiiV6k1iOLgjxLbfI8aWg+Dy6T4ZVzq5xIOJMR9PtwbVteXlxje4xW0CiE\ngfXFWliPrBTwJoH8b6Px3M3DmzTFPWrOnL2rV5/6+zFLFJRFW1FDVi1BQh4yDMR2fSmTJZu7DYeB\nc3m1pMUYQQqEE2th28e0SrsMpWw2Hn3nweU3Te2L8NnXNZwL7dMTB79WQ5zMuXHlG2fKQw9OH2Qy\nArFTj0mGmUDw8ccMzpfyZdk1bSYCaUgIBtlH1jN8f9Yji4IwTc0Wh7OloZNhZJ8/497sm30+6N9B\nM76AMQJbs7H/5sHZH8yzWg3BGG3ICOIepf3IpiCZsU2eFyMIh1tHLZcR3L6Nrvk0i4n2CxFLAUG9\nhtyRsY+Cl5x8/nVAcGiaFCcK1KtIoyFf3voyP37449Tnkhpz9DBYjywKYvrAZ0lDvu9j2yc0S9sM\n98/HL5MIEOTFCL58TlketFS17GiE2KojSAKuHq9AzpOGwudcAoH17I3nbh6+he0LVOcu565ePPsL\n6ywxnCb6nLBB5tBohNCu445dvJmXkmHCvXk1Msge0k5ENhCcZ+hO4f33Vz1ZFtZYdEr2vMUZIe0F\n1+t1ptMp/Wn/TCC433WRW3XkaYE3L391rTzU0Bo87D7MZATidgP7xMZ3AwchEwhu32awW6am5gT6\n1zSeC9dzv1jMBoKHFpI7zgSCZNZQUho6NSLv7hmB4O27b/NLl3+H8vgLyAgczWH2Qf/Z27LW60ij\nyYbB4i3m8y6+H6TSLRE+sslLcgnbtbHd4EJebo7FUJWoxRhBVPO7fRtddGmW8ptDpWIE1epqSDfp\nzbQOCO7MZhQmCoVmA18fLEcEJm0dI7Af2Uj+JNXsLUsacpwBklSiWWwzvLgVB4KFF5y1/hD8ritb\nBbwF/U4FQMO12FNT8lASyLMaz30WRmA5Fvd+8UMGgkht7tJeZFM9s0WkobxW1NHLKJXMsHAQlHMK\n1mMrFSOI7s1PE0AQW/tUjOCYenEP27Oxd7fg03h+vyQFWae6HpwR0Z2m9kWYfnyin6yNEbi+z0nf\no9yuU5iK/Mb5V7h151bmDG4I3t/R8CiTEQiNOnJLxj62U2u5tNu3GTSkfLlqsS+WM8cjlree4fuz\nH84QnWmwOAkLi1V930+tf6sF3XHk3T1jjODWnVu8tPe/U5x8ARmBoAn01B24l60bnmm1GoXxdCNG\nIIoyklTDcYKbzXpoITnxtDpBEFaTrmA5GDzpJUDkIqpUYDYLRFuA27cx6cROvwAAIABJREFUPItW\nKV1JHVpWsFi9oC410LBpVWjrAsaHpolvFJA7bXxDXw4NT9pZjEBy0p5fFhCEQ8/rah19p55iBP5o\nhG3bVDIOTL8P7bawHFKTYgThWmQCwdn9hpbv7hmA4McPf8x3Zhfo2j41C7RWPqPbyCJTyjZlBLEu\nlom1SDKCcFbxfoKtpqShjBiBqu4Ga/Xal9bKQ9bDGeI87SCEz39qnK5lBA8si8pUQ+vUkaY+W1qB\nilLhFye/yPx8XatzYpyknYhFEoGypyz3RR4QDDWPRjEnbTgM4NfrjMdj5pFYQJQRRNcz3FPzO318\ntRQgZcJEUUOSSjjOIDNGMJh+dkZw8/AmndZ1VPMLyAjQ4Lhx8dkDxvU66thcegDrYgQQv0yCTT5O\nXX7RgPFSGtK0fGlIEFaHrdfDmxlMXJdmKd+jzASCvTgQJKWhvDYTh7MZc0OitL0FoxFfv/B1fnHy\ni9Tn18YIHpoIczPl7WTFCMKh5w2twbBZjL+7Ugksi+1WK5W+FzpZxeKKYaUYQcaBD21jaegZZxLc\nPLzJt6fnMcwxsgtCaX2a3pm2eIaGWl/up7zhNACKsptiBFSrKHsK9iM7FZgN9+Y5RWHoOEwXEk8m\nI0gAQfj+9Ff2c1NI+32w7w1BVtOzMBfP35/21zKCQ9OkaWoUd2qIExfbPubN/Tdz5aGG1qA3zs8a\nUvfUZZygVApUrdixfOcdDMGmkSfLRhrPJQsq1zICa4jzoI+/prYkfH9ZQBDb588ABA/0B/TNPo6k\nollfQEbgyz6PteqzA0Gthjaxl4tcrQYXzunpMAcIVpeJ/WAUFNwkpiZFqfw6aahcLuO6LqZpruje\n7dvYX/sSU1dem02RywgeWViWhWma1NcEsaN2aJpMdZHSbofCBGTB4dcv/Dr/497/iH0uGdiLXkTz\newN8rRTvG0R2jCB6kQxlL1jwkGYLAm6pxKWMsVmhBwuczQgi7Ci0s6Shzxosvnl4kxeMMu50xEgR\nUgOFntoWLVBqbiFohue5Z9QS7GDbR6vvL0AxxggypCFRELgcCXBmBosjoBgyuobWYHgt2wkLHQDn\n/gC/kmYDEKz/wBysZQSHsxmVqUZtS0UQBOzRY27s3+DmnXwg6E/76bO7GNwUlU9TragNA05PGTpT\nWnlOWKLNRHT982Iu4Z5yH/UR6vlAEDgqR6kYTasFhh3Z59VqkDGQqPZeZ7fu3OKbl7/JqfkYzf4C\nMoKCW+CB6D4zELjVKqWZs6wiDHPKT0/nmUAQreB0H6R7i0MOEGQEi2MDOsKGVu+8w/y1F5i4a3RK\n1ktD0YZzWc+UtEPDwp2D0qkhzzTm82NuXLmR8rqSHmVUmnAfDlKthiFfGloCgTUMxgFG3p9TLHIh\nI8UulNkgzghi6xSJlySLyp6qFfVTAsFwNuTd03fRxz6eNcOQP0PX0ahVq4ijYJiMYRlnSEMZjGAB\nBNNHUybzSaxaNgasEUflrGBxjNFd2lnLCNzHfci5/DqdDoZlrN3nh6aJOlFotcCraLiDB3zz8jf5\n/r3vL+NwUWtoDXRbTzMCXQ/Yf0IyjJ2jX/wC/9VXGM1nnwkILmsaDy2L+eKiDveUdzxAaOf/rcH7\nO0oBcbUKtqBTUxbflaRVtfeGdvPwJm/uv8lw9oRSThp5aM8lECiewkPPeGYgmBQlWrYUa6nQaPiY\nphbzqJf/v8hl4j4eZG7yJBC0WnBBVenO58wSKL7cTFFG8MouY4e1lHmdNHR6ehqLDwA01PjIvNBG\njsN4MUxDqNeQTRnbPuKN/TdScYKkRxkd0OE+GSA00muRJQ3FPMpZGggsVeV8hqYcvbiuLGIuqfTD\n0AvOYASSVMf3bVw3uPDWDrB/Smno7btv87/tfI27jovv2IyU9XNhN7ZE5tDZragjjCCyL3pPelSU\nSmyfhxcXxB2VlDSUESNYAkG7DA8fJoYULxyAroffH2XuC4CtrS3GznjtPv/UNBFHMu02+NUS7uAx\n7VKbl9ov8ZOHP0l9vqE2GM/H2YwgBIK8WoJ33mH+q9eYugqNvNTtCBAkA8bheiqiyK6i8GDRD6uh\nNRiMB4juGFrrgGCHweAesiwvG85B4JwWm0NUP7JOT+Go+L7PzcObvHHlDSbTIyruegB5LoGgJJQ4\ntntB5kJWd7MzbKQJ1K04ha9W59TrlzLnH4TSkO/6eN0hQjO9icPgnu8HudrNJkiCwAVV5W5ewDgE\ngnfewb5cZ+x4aylzuE9MkxQjyIpv5AWL78xm7Nllms2gfF6eiNj2Mb+8+8scjY94PHq8/GxShpEk\niUajQe+oF4xEzFiLLGloPj9BUXZWgdmDg1hhkinL7Gbo6ykPNpSGkllDOUAgCAKyvBrgklVHUFNr\nQZOwp2wxcfPwJv9AepW7115DdOdMlc/Ygjq0hSwTvr/kuMq4NLSbSh8NYwT9k3SaZgwIIoxgXR2B\n7zs4zhBZ7gTP5IzhpZcg0hIbgt/bve+iNa1cOaTT6WB65pnSkGsUgvdereIOg78vTx6qa3Wm3jSX\nESRjR0kgsK9fxPTkfHDagBFAIA+FcYK6Wmc4HqI17VRhXdQUZZfj43uZadNqXafgPBsQ/OLkF1SU\nCuXKBepTi7qwPuPouQSCilKhSw/v8ovwwQdP/X1d8akn8KNctqhULmV+PpSG7GMbtZq9ycPA7HjM\nsggI4GpGnCBWSzAYwLvvYm/LjOf2maX3y00cCZDaj21OT09TQJAXLD6czdixy8EGrteRpmDbR0ii\nxDcvfzMmD2X1qmm32zx+/3GwyTPknLAaNkqEYh5lBiMYiyI7EY8otCgQXNI0HsxmDJItCiLS0OxB\nmgJHGV249r7vL9cybBJmFuWnBoJvGm2OW19C9uZMlWccWJ+0SFGZbukxqS0pDRUKLVzXWLWZiDCC\nQX+Q2k/JmMuneYwgEiOw7VMKhRaCIK32VOL9wSL3/aGH1rQzK2nD57cE68xgsTkQg+es1fH1oJr3\nxn5augSoFCo4BYda8v+p69BoxILF4XPGgOClLSaumA9OCSCIVhfnMayG1mA4HaLV0gWXUVOUHU5P\nM2ogALmqI86fDQjeOnyLN6++yaFpsj31aPAFBIKaWsOoGthXf+2Z5KGB6lGZxeUaVZ1SLl/I/Hx4\nkViPLNScTR7KMNGNAXEvIbQYI/j0U+h00P0+BVFCkdbPD15u4sWBl4oSUkXi6O5RWhrKiREcmiZt\nU1sBwdhbygtv7r/JW4dvLT+bNeqw0+lw/PFx7oEvFFYTlkJLAcGrrwYe5QItRsCWlr5IQ5kNQBVF\ndhSFo2RB0mIt5I6MN/Fwp/lFZaqqoqoqo9EodiE0tAaG4m980B4aD+lOu1y6r2MIO6iug5UBZM9k\nCWkoCgRJRhC0mdhezdYOgeC8ymCUDso+CyMI4wMQkRszgKDVgv6Rh1rPB4Jqq4rgCbn7fOg42L6P\nMRBotUCot/CHAfD95sXf5OdHP085N6ItIlflNJtfEyMYDgnqkG7fZn6xymSdLJvDCGazIAMpJLJX\nI5lDDa3B0B6iVGaZxWShKcoup6dHmUAglXSYRb77FLUENw9vcuPKDQ5nM6pjj7L/BZSGmloTo2pg\nnb/+TEDQl2xU21vl8AOFwghVTfZNDizsCWI/stHq2QgfHtosIPhkHRB88glcv05/8pCaUuYsSwIB\nBHNqT+6m86jzgODObEbNLAYXbL2ONLKWF+WbV4M0vbB4J48RHB8eo9aszFzx2HMubD5f1BGEElq9\nHtwcd+4AMPQ82hlNv6IeLARe15E5SFUWU6shCEIsQyS0vEllSSAYqt7GMYJbh7f45pVvItz+Be4M\nSp6DU8ppUfC0ligqa7chJAFZbQ5itQQLaUjURGaNGTUxvleTHuyd2QzHdRkOh7SiCx2RyUIQB3IZ\nHQS/t3fqB5dfzr7QGhriPP/aOTRNrhaL9PsC7TaI9Q6MDHzfoygXMzPbfNNHSk50CjXaeh2pJoEP\njuEsn3MwAO7fh0oFW5kwdtyNGUEIBOFahvizH5WGtDqGZ6Co2e0lQlOUHbrd00xpSCjqeObTMwLL\nsfjB/R/w+pXXOTRNSt05c3G9g/lcAkG73GasjbGa1zIbYJ1lum0wK8qxQy+KOrKcnUccaMzHWA8t\nlLKVCQThBZe8uK5G6Pfy+aNZQ/fuwfXrDMwjGlo+hQwtCwjUCyonD9NAkDel7FPTpDRVloxAGM2w\nrScA7Df3KcmlZfHOcDZMZXh0Oh1OHpzkrgXEM4eC9hLBZaIVNERBDJrhXb++fH99x6GRUXSTAgJN\no2cO01lDkbVIp5BmZw5VKkEbattevD/F25gRfO/we9y4cgPz/fdpToeUPRtq62W9jS0xpSy6ltVq\nFdu2mUX2VJh5AsTWwjpnUXXiF3J0PcuSRL1Q4KPTU8rlMnIUiCOXThQIlnGn8N1Fqn3DWMa6y0+u\nyrAmgeVwNuOSUMRxAk9bqDeQTW1Z0JlVT+CMHYRigg2YZpBpowYpqJlFZe+8A9evY9vHGLZ9ZmUx\nZANBaFcj0pBW0BB8AUHObi8RmqLs0u0OMhmBr+g448gzbQgEP374Y17uvEyz2ORwNkPpWszkbGAO\n7bkEgu3aNhN5gqVegJ///Km/P5wNmZXVGM3y/T6imF1ZGAaLZ49mKMX1jKDXi881uZooNIEEI3j0\nCA4O6E+OqKvrOzLCYhP3/aUuDgsgODrZWBr6xDRRxgsgkGVQFZzhk+W/h/LQ3J0z9+aU5HgQt91u\nc/r4FEUzNwIC1x0hCAUkqRR/rtdeW76/U8si67hE00ch8LpiWUO+HwD6oqgtCwjyhthHW1E3tAY9\nyQ7W9YzWJZ7vcfPwJr9T/xXuVKvsz4dUfRs5+qCfxRLSUJQRCIKQ0qmXdS6OE+gVi+Es5pZJ2Yqz\nzOTlta9p/Pzx47RHGosRBGwOIu/u/PlA1jtaZSw1mzAcC8jyNFjYDBOLIu7UzW0X8alpcs4qB7KQ\nEDyHYpWX7y8rTmCPbDwlkV+/kIVCi6YWL4Hg9m04OGAye4Tje6l9HluLjKyhqGwJq6Ky8G8LQHi4\nNkYgy9sMBqNMRuDKQ2zj6RnBzcObvHn1TSBgWELXwTrDyXwugWC3sYtZMLGnpSCF7fTpZhjrM515\npRhbVMc5xfezN68klREEidnxAFkxMxE+DKJlSRl3ZzO8yMaPMYJuF65fZzjr0ljTgjq0ZhOMk1kg\nxC8i0uqemtm5M2tcpeP73LcshLG8uhDqdbxBGgh0S6em1lLaa6fToXvapSDnA0FUdol6lOFzJYHg\nxDSpZFwOWYxgYkdaUE+noGnLKtY8RnDWEPuG1mDgTYLfkzFQKGq3j29TU2tcemDw6a//Og3rmCoW\nWufpJ5tlWgQIdEunXg/+zLCzwdbWVgIIFowgBMTF+zJbJqXJ6nKz7eB3RId47ReLvP/kSdoj1bTl\n6M5YjCAMFgtC7P1BsJb6VKIgTHKBwBIsBEtgMsmeMnhommyZxZUzVa2imMVlDOSXdn+J48kxj4xH\ny+/MhjMcyYn/oiQQRFJIk4ygP3lIVSllZgwCwYKZJrhuDISToNqSZSRBoLeQnCuzCr6jr2UEoqhg\nGAqtVjq+ZIs65vDpYwRvHb7FjSs3gIBheT2HeWm9k/lcAsG51jlmhRmzh1ZMXtjUdEtnXinFFtW2\nj3Hd9cg9Mx5ndtuEfEZQliSahQKPImmuS0agKDCd4l19AcM2aWhbqd+btFYLpkdG7BnUCyo9PQ0E\nyWZ4AA9mM7ZlGWNRRxA8fBN/eLr0ZF6/8jo/vP9DTifZPWHa7Tb9QZ+CaOZqwVFGEMYHkmsVvjvf\n93kymVDMmBecBayWPYqNqUyuRVZ18VlD7J+mqOx7n36PN/ffhNu3+fTVV/Fnj6h5FsWtzwkIwjYT\ni2cKq2HD9UwDweLvW8RKQjPrJiVjBQSDQXA/R++7fU3jk+PjtEcatkAZjbJjBBC8vwgQtFpgzCUk\nL18O0Wc6Kmqqr39oh7MZtWlx9c5rNeSZsoyBSKKUapA46o3wBC9ebJYFBDnS0GD6hHpe59HEWqyT\nhiCeHFKelBFsYy0QAIxGCvV6+iq20Jn2n44RDMwB752+x29c/A1mnsfQGsFQwi2vf4bnEgg6lQ5S\nSaJ3r5fySjYx3dLxqpXYoprmY2w7P1irKDvY5nFme13IBwJIxwmWm6nfh2IR2+thUT0zdRSC320e\nG7ELWL2g0p/0U9KQIAipFNJPZzOuFouxTSzUG8gTGddd9LYpNnll6xX+573/mflMnU6HvtHPXQuI\nA0EWI9AtHa5dg6MjjIcPGcsyhYyqyTQjUHGd6aplsJFeC+tBWhpKtpmIDrEPO5DqM32jcZVvHb7F\nt65+C955h08vXWJqH1FzLaq7aZ33mSyjFXW7vQ4IFowgAYqT8gStv8rESq4lLBjr8XGmRh3KQ7lA\n8NprMSes8v+T915NkqP3me8PQGYC6ZG+bFe76W6O7+GQc4YypFacISmapaTlamNv9B32Soo4F7zU\nF9CVLk4oNkKOK4nkkiI5pChKlOiG5PT4aVPtymelNzDpcC4AZAIJZFbVcKjQUP+Iueia7GwU8OJ9\n3ud5/iZhYVoiotFdyAjaZpuEmAh08XTjrq6T7Mt+INAis6wo4MVLL/LS3Zemf67X68TFuD+byEkd\ndSMABI0J3L8P167R1O3pa0vDeSaJRALLstA0LRQI3EysiTkh1U8haN0TgaDTkchk/Gx4Yk0wJl26\nNc/7dQog+Kf7/8Svbf4ackTmgWHwqKwh9hIn+lfvSyBQFZVIKkJ1t/rugMBoY2UzPkbQ6+2g64vz\nwKPRCkOzijgO3/xcY28hEHh8gqk0sbcHUbuqV7eSpwYC89j/wsfWYjQH4YbTvGF8x8nK8C1iVUU2\ns75T8wsXX7CBIIQR5NU8LbOFGNJ51A3vCdbeSGZG/NRwlCR47DGOf/AD+6VtBf2M+c1LnhggybTH\njiY8dwo+i1nsXqfbgbRlnjyuUh/q/HD3h/zW+d+C115jR85Ro016PCBdOpnRnSrcbpeeZ5fPz3yC\ncrnsA4KpBzIHBJqiodRma3rRxnVwHJ614l6H7RHYz8+3nubeveHxgLQwYtxsLWUE6Wg6lBEMJxN2\nTROpF529Q5kMkiYE1ua3t7/NxGkNX6/XSUpJvx82xwgCZvHxCC5dYhIRnJYXJ7A55164Hk2tVlvM\nCAyDwcGAtJBG7HSXegQAnY5FJuPvBdQb9FCkBM2GJ4HiFEDgtpUAG1Q/EOsh9aSl/Y7gfQwEYkKk\ndlTDmqOnp4m22UbI+PW2TucB/f7iFKsIJaxcE7HfCX2waTlNf9inVh8HgWDOME6lUgyHQ4ztbbAs\nGwgm8ROHdYANBIOa/xrMjEmMGPJcIzwIGsbbus7leNxvwmazKEbG16rghYsv8OO9H4eCU2aSoS22\nEbrh9wL8bSa8ZmPgmp56iuOXX0bK5wNAMBza2rj3n+iYHaLR9Cwld14a2gwzi4uMRi0sy9ZuvSfq\ns0pD//rwX3my8iTZaAreeotWM8qRBZnRgHhh8SyJM8WcNARnYAQedtSL9JAPZmsiFAjicY4XjAh1\n74XXI3DX+XgyhkcftetgHLY72BuQiY2ZNNtLGUFGzoQygh3TZFWWaTdEHyOQNHyttrfULfLxPDcO\nbwB2DUQmllkKBN4DQi4HzZYATz7JcFjFIHvyISzEMF4ErNu6jrlrko1miXT7JzKCVmtEKuX3pdpG\nm4yc9Vfon8IjeGn7JT5+0fYHtg2Di9EukiYg5X8FgSArZ7EUi47cYVi5Cjdvzpy0U0TbaCOped8L\n32xu024vbhom6gUim93AxjP9/4JIRs5w3OkE6Pc8I3BPFXXnugeDQ7RJ7MQ5rmBvCOOm/xqagyZZ\nITvNk/bGvGF8R9e5pCj+jIds1jHkZi/b85vPs9fZIx4JmlgpPUVH6ARO496Y9whCzWKwgeCNN4iV\nywEgcFt1eDXtttkmHsv4gcCz+UVLUUbtERNPwaAgSEQieYZDe/P5RYDgpbuOP7C9zXhlheHBiKoh\nkRmOSRZ+waE0bnjNYkfu8DKCUqlEtTqTSqZ1BHM7U1foIu/LWBNbdgiThtZiMfRWi0xI51fSaax2\ni+GwPmUE7jrvmB27A+/ly9Oxo+auSTYxQWi3lgJBPpEPZQR3DYOLiuK/zkwGqT/ySUPgyEPbtjxU\nr9eDiREtPytRzilTyTCZhOFIYPDo0wwGhxikT373QqqLFzGCu7qOuWeiylli/eWVxZZl0WwaJJN+\nFuo2e/QBwQlrc7uxTX/Y58nKk4D9rm9JHaLamGjhV1QaGkfHaKrGoCnB1taZWk20jBbRfGGKrpqm\nMZl0GQ7tzIqwELo5hNXWQiBwr+u41zrRIwDHsHznHTAMBvoe/bF0KkZQLMJkjm7W63Vyci5wEnav\nKYwRzEtDMU3xMYKYFONC7oL9ws9FopOgO+5izW3C3ljqEch+w7F2+zbKykoACOZTR8F+dhk5OwOC\nOTASRAF5TcbcXywPlcvl6UZ61sZz396e+QN7zz/P+bpIVVNIDyzk3C/XI/ACgXcjjURyjMc6k+ax\n74a1Bi2y0SzDqn1ICtu4REEg0esxCnuOmQzj1j6SlEEUZzUGiwxjc9dETVtI3cXSUMtoUUgVQoFg\ne1pM5gGCdBqxN/D3U8IPBLVajUKysJQRREtRxp0xY31spw1LPZrnrzMYHKBPkie/eyG1BIsY1rZh\nYO6alJQ0E4FAy3pv9Ho9otEIotjw/bxltMgnsnS7nrrXkw4p2y/x4qUXp9lPd3SditAmZhjI5V9F\nRqBkGYpDusmurfud0Sdom21ianF6U+v1OqVSEVUVQoeuA1DLIZSaJwJBQwsHgjue/GKAYjpNLRKB\nVIpRa2d5ibsnCgUQ5ySZ4+Nj8sn8iUBgWRbbus66EPeVxpPNEu1HAi/befU8B70D5mO8PyYZS2K1\n2+86fXR6envySY53d0murtpA4LlHYSfYttEmp2RnDCvkeYT7BLOiq0VA0DbaS+n3Ue+I+637fHj9\nw/Dqq2w/8wyXWgI1XSZjCCdqwacOB4yyij2cZmJNfMA6DwSCIBCLlRnX93wncbtP0WxdhG1cALFu\nF20REDT3fc8OFhvG5q5JOWPYzzCkXQjYz6+cKYdKQ3d1fcoIvB6B2DX8HVaBj53/GD/Z+wn9Qd9+\nf9OlpUAgiE5R2a4JlkV+ckxj7XHHn1POJA0tA4JNp+Nwf9dgVU6gJ5dX9NqtPbKB38+dLJfNes5H\nmcxSaehb29/iE5c+Mf3zbU1DpYFs6sQrv4KMICJGiApRGqmG/WDPCAQNvUGitDa9qW7nztAxdk5M\n9nOg1pcCQVbO0hm0AptXIRLBsiwanpYWBUGgvrUF2Szjxh7twZDColF5nkilIDHqMErOrqFWq1FQ\nC4HWCuDvQHo4GJCUJMbdiF9yUVUifSmwGEuJEveb9wPFP+aOSS6VW3ov5hmB1yPwdUVVVY4VhXw0\nOk2ndSMMCBp6g9VkcaFHAOGZQ7HYKoOBDWqFQoFWq8V4PPabxUZroWkNTpO5C79FRIzAjRtsX73K\nVq9Ly0iQGVgL2dGZw9l0ImKEeCROb9Bbygjs32+FSWPfBwQNvUGpXJo24gu7nwA0m7QXMoLDABAs\nMozNXZMNtYMZVxcO6GnoDTbyG4uloXicet0vDdHtMxgc+tZhKpbi2bVn+cc7/0i/36eUWQ4E4MhD\nD004PKQo1KlH7Bbe3VHk5HfvlEAgCQLnZJnmA42yItOPL29NbgNB3j9u1LlPhUTBP9vDnV8SEsPx\nkO/d/97UKB5ZFg9ME0nvkLE6xIq/gowAICEmaMiNGSM4ZS2BPrRP5jG1ML2pXiCYb5/sxuh+lkm0\naldTLjjtJCWVWLo97TzqhiAIXJ7zCYqDAbVy2X7ZGge0Bwb5UxSUCQKU4x00yQ8ExWIxnBHIs9N3\nWOooYPdj6VuBxWhhIYkSb9fe9v3c2DFYUXP2yW8B7T21RwAcZzIUe73AJrwICDZTpYUeASxiBKuY\nThuNaSttT7+h6TUtOQ1M/QGwgWB1lZJRZzSOMRGEpRLAmcJTwOQylWWMwP79Klj16hQI3HWubqhT\nUFzECIx6nWrIrGjSaSataigjmDI6FwgsC3PXZC3XQY8tPn029Aabxc1QRhAqDaVSCJqGRHzaZsKN\nT1z6BF979WvkcjlySs7vEcylj4KTSLBjwo0bFHNjanUB0zygO+Lkd++UZjHY8pC2Z1JUZLrK8ol1\n9rtbCRzCGnqDfDzvB4JUCvr90CllP9z9IZfylygl7cw1t16oWdfJR9q/mllDAOlomkbEYQRnyBxy\nb7CgqgFGEDZQxY3R7QwMq1iZzMLTjoJKqhh+mpw3jIudDrVsFrJZrFaVltk7FRAAlOQOXU8zsePj\nY8or5ROloTth/gA4jedGoYvx2bVn+dadb/l+bj40OVfIMYrHF96LRMLWNvv9PpY1RpJmm3UACGSZ\nUr1uv7ge6hsKBEaDjWSR/mRCZzQKNazDgECW1xgMZnMWXHloygi8zfBCFoFlWTN/oFaDToftWIzE\n6JjYZEJffo+G0oA9+jOZhF4vtM2Eqqr0+30GHkMrFlvBatanD9Zd58qmshQIhsMhZq/HTkjDPzIZ\nrHbDx+Zg7vlVKnYa8N4e5q7JSr5HL7LYeG3oDc6vnA8AmStbBqQh517ExyuY5r7v77x46UW+8+Z3\nKBaLwXYqCxiB8dCAV16hUIlSq9nt1zvD8ZmAYJlZDHaW4HhvQCkepX3C2cCWpVcZDutY1qxrbsNo\nkFfmgGDJlLJ5WejONDtwRE46uajtfQsEqqLSFJs21dvYsF3eo6MT/577gngf7GmkocFdkZguQ2Zx\nh8nYREVRlwCBxzAuHB9Tj8exslkmzToNvU0ufrpeNYVIh47lZwTlzXJgTCP4X9rtsBoCAFX1dSB1\no6E3+OjWR/nm9jd9Pzd3TM6VVMx56uMJQbA38aOjOrFYJTBC01u5Qfu8AAAgAElEQVT8cwyU9vfx\nC6KLGUEhXpil5IZJQyEppF5pCIJAoEQUJFFikEmFSkOvHb1GIprgcv4y3LgBTz/NXdMkYh2TZEAv\n8R7NInAjpN+QuyGIohgYkBKNVuzrdk7B7jr3gmLY/azVauQKBbbDBjxlMlid5nKPwGk1Yd141fYI\nsl06YjgQWJZFQ29wcfViAAiOh0MigkA+GvVLQ851xEdF3/MDuL56nUa9QUpNnQoIfIzgfGoKBO3B\n4MxAcHRkJxQkQ2pQL8oKkeqIvCLRkpf3rbL3nhKRiDrNaoPZ8/M+9+l1hPgEL22/5PcHdJ1HHCDI\nsljCdeN9CwS5eI7WpIXxwAjte7IopkDgMQVPAgLLsjAeGiiDApPU4hdeHGaJZU7BCFotiv0+tdEI\nK5Ng0otMh6OcJlSpQ3PsZwSVC5VQRuDV4++E1RCA04FUt6ewec1avcHHL36cH+z8AH1oX/vEnDBs\nDDlXUtHCTpGeyOfh+LgZOFHOF7kdGwal7e1TS0P5eJ7LbnvvdyENQRAI3OvqJSKhi+Abd77Bpx75\nlP0HBwj2axpm8ohcxMBIndxC/EzhFpV5ppR5u08HU0hXoN0NAsGmvJQRVKtVVstljkJGqrpV1gGP\nYH7y3VNPMfrRW4gJkaLcoR3aPhD6wz5RKcpqaZVut8vQk/J9W9e5kki4ihi+YXXpNLKZCwCBKIg8\nnnqckTwKXtNc+iiAfE6eMoLi1cIUCFqm9i6AYEJYMTbA5V4UIy2QHkyox4Ip3d5w9575Niih0hCE\n+gQ1rcat+i2e33x++rM7us4jikSrpZC2Tq5uft8CQSldojPuYO6Ydp70KX2Cd8MIRvURYlxEGeWY\npJacgk2VSGoBEHiLyl59lcKFC9TqdcYpCfrJU8tCAFk61Id+RrB6ZfVEaWg7rIYAQFURWm0kKcFo\nNLsBDb3BlrrF9ZXr0x7w5p6JvCazkkzQE5cvn1wOjo+DG8n86a3WalFqt+3j1VmB4BeQho6Pj0ml\n7BIUw3CG0yTEUEbwzTvf5JOXPmn/4ZVXaDzzDLmqRSd/TF4yGC5hiu8qnJNfGCOA8H5DYrsfCgSu\nWbwICMrlMluyHOiSaxu1veDzk9UAEJg/vY+8IZOlTWMSzgjcaxJFkXw+75urcEvTeMRhq4XCnOKY\nySCbakAaArgsX6Yltk4nDW0qmA902N+neK1IrWYxGBzQNDpnBoJ6XVgIBOfqIvUiJIwxtciCfHQn\nZkCwcjogCEkh/fb2t/nY+Y/5hv3c0XUuR/to2hap8eLsPjfe10DQH/cRUgLD4+G7ZwSW5fMIwsxi\n46GBck5BMTOMk4tvmaWpiInw9C4fI7hxg+Jjj1Gv1+3v68tnAoKU1eHY9APByqUVxr2xr5AK/DLM\nMo+AdtuXYmlZFk2jSU7J8YlLn+Cbd2x5yNwxkTdlyvE4nRPaNefzUKtpgY0kEU0wnAwxRya6rjMa\njUg9/rhtKswBwfzG5T6/S15GMLfIY5UYw/qQyWB2L2xpaJZ54p6oBWGWo68qKs04gdNAx+zws4Of\n8bHzH7N/cOMG2489xhOtGO34MaqgMVFPTv09UzhjtFxjNpmcAZZ7/fPVxWLHDHgE8rrM4GDAZGSF\nAsHR0RHlcplHEgluhwCB2NVDPQKfMfvUU5hvVpE3ZNLjFrXRciBwr98rbblSRkAWcq5DNpMBRgBQ\npsy+tU8qlprJjZYVLg2dkzEfGliPPU6xIlGrjQCBptEid8peQ+BmnUUoFsPXf/kIdsoWka5GKzbB\nHC2eq16v1ykUCk6bkJlHdxYg+Nb2t3jx4ou+n93Wdc5Huuj9NeRRf9qmfVG8b4Egn8wTy8QYbYxs\neeiUhvF0McqybUQZxomMwHxob34xI8l4iQIw6qtYcjgjWJdlGqMR+nhsA8Ezz1Cr1RgmJwj9yJmA\nIDHqcGTMmcWVMrG1WCCF1D0pNYZDRpZFMRoNbgipFGgaUWFWdNUddIlH4kSlKJ+8/Em+tW0bxi4Q\nFKJRmmP/SMj5sIHACADBtBme2eb4+JhSqYTw1FN26qgHCALMhQXS0BwQCJJAbMWe5eyGJCUQhBij\nkf393lqCUsnuZK4qKo3YJLAI/vHuP/L8xvMkY042z717bK+t8UgrQluok6NHpHj653eqcFLYvB1I\nl7aZiJaRuqPp5jc9fcdEovko7QcDBAHmp2lWq1UqlQqPxOPc9qTuAvbUt555IqPj2jXMwzHyqkRy\n1KJqhoPiPBB4r9+VhkJTXDMZYkY8FAi0lkaxVORu4+7smjTNnrMx52FFMhGwxowe/RCFAhwfjxhJ\nK9N1vjQ8G3AsFkOW1wP9gdyY7Azorkp0Gw0G6USgFbw3vIzAm7W3FAh8c1Qs2x+4PPMHxpbFPcOg\nLLQYtfIMY0nbaF4S71sgUGUVOSujlTXbMH7sMXvsY5jp5YmGMVuM7sM9CQhcRhA14gzjize/QUdl\nHA0HAkkQ2FIUe4LRK69Q/MhHOD4+ZpQYIfROkb7mCWXQ4bBn6+LD4ZBut4uqqqH58+5L61YUC4IQ\nPGmLom3IDfPTU4n3pb2+ep26VudB6wHGjoG8KZOPRKif0NYjl4N6fRQ4UbrX1TZsICgWi/D00/bN\nP4M0tG0YC2sZTpKHvEBQLNqJQKqi2ppup+NL0fvm9jf51GXHH3j9dbh6le3hkHM1kareQ510iVXe\noxbUbjgpbF4ZZr7NhA8IRhmsCNMUVu86lzdljt4ahGa4uNLQIyEjVa1UEqk/8jUMhBAgiMUw81eR\nIy3iZptDQw2d7eNdU/PDdVxpaBEQRHU5VBo6OjriQ1c+xA93fzi7ppDUUTeUeAdz44POM7fQyZ/u\n3Zs7iScS50gmw2cqGA8MxHMxus0mo1QiMGPZG36P4BSMYM4jeL36OvFo3E5icGLXNClGowijKpNm\nguEpJh++f4FAUYllYmh5zWYEimK3NT5hhrF3MbqSyKkYwTmZmB5jFF+8+enNLEMxHAgA+xTb7cLN\nm6Q+/GEsy6Ir9hF7kzMBQczosNe1H26j0SCft3VXZUux74UnUrEU/WGfW1qPS85x8PjYPgX7IptF\nNrLTU4n3PomCyIuXXuRb29/C3DFRNhWygkD1hAEu9iIeI8vrgf/nGsYuI+CZZ+xpV0uAYGJNaBu2\nbr4hy9QHA6ww/YiTM4fCGEFWydIcdW2vwnnZLMviG7eDRvFNTaNyLHDYjJCbdIkV36OGc244jMBr\ngnoZwXwHUqk7YZSC8djenLzPT96Uqd4eLgWCy/F4QBoaxodImoAo+pMYAsYsYGYuIWsPifRatAWV\neZVp/pq80tDEsmxz05GGAv3vMhkieiSUERwdHfHbj9vzCfrDPqPJKFQWckMeH2KqVygWoV6PoFnZ\ndwUEsryBLIe3IjEfmiS2FIxmk0k6FTol0A13oJTXI/Cu8/kkgfnr+Pqtr/PpRz7t+05XAh4M9pm0\nZcbJX2EgyCpZpKREL9WzMwHA3kx+/vOlf88HBJkMlgMEhULhREYQ0SQGiZAV7kS/rmKw+KFfUhS2\n79+HixcREgkqlQq1YQupd4o8ZjdGI6TxgP2WnVYx3UghFAjcJmFvdo65fCIQpEMZAcAnL3+Sb975\n5lQaSozHHJsmo9HirAj7UCuEAoF7qpxe/5NP2kDg7HSTyazpnBtto01aTiOJEqIg8ChgSVJogd8i\nRuBmDnk3Uq80NC0qcwDp7drbiILI1cJV+0scILil62QaGtVjlfxYQymuLLwP7yqcxeg9fS9jBEKr\nxTgTnW4mASC4OwqtKvYygnkgMGNtIpoVGN0ZNgLVlFaQa29Dq8UklQ19jxYxgv3BgEwkQjoSCWcE\n6TQRTWAwOAhUuR8dHfHRxz/KTmeHdCxt98ZaBATDIUr/Hoa0hqpCrxehO8qc7t1ze1A5/34kUkGS\nwt9144FB8WKSkZO5tAgILMefLBQKPkbgXecneQT/cOcf+J1Hfsf3va7fYpp7CB2RySlmab9vgUBV\nVIS4QFfu2tIQwAc/CD/72dK/N88ItIMDYrEYiqIE0dcJlxFIGphyOB0E6B6r6NZiGng5HudOtQrX\nrwOwsrJC1WwR7Q3JK6cEgm6XSTJNvWGnVbhsBkA5r2DcD57SVUXlVud4OSNQVWQ9EbqRgF288917\n30Xf0ZE3ZcRej3Fi8YARcPey6OmAIB6H9XXY3QXstZ5MTidQhl7Tk8Mh5gIJYFEKqSsNedMvp9KQ\nHKwudtnAtA7ilVewHEYQ61dpNldRRyaJcvB3/IXClYY8xuy8R+BNH6XVYpKRw4FgQ6a2M17KCM4p\nCsfDIZrH9xlYVayoaFezemK+DgTA1NPID34K7TaTjLoYCJQgI7jtyEKwoA1GJoPYM3wejxtHR0es\nr67z4qUXiYpR+7oWAcE77yDnhphVC1GEbFaj2k2fDggkyV6jzr0QhBKCELJZYAPB5uU0QruNoIbP\nDQfodDrTvcfLCLzPbplH0NAbvHr4Kh/d+qjve11GYJp70B6dWFUM73MgmMQmdCKd2Sn4XTCC7v7+\ndCMtlWwgmNc3XUYg9cYM5M7Cwdvtaob+qDMdmDEfVxIJbhqGrYcDlUqFA61FrHeKghY3HE3c3X+9\nQCBvyQFGAPa9utuzGYFl2UBQLs99KJslqssLGUE5WeZq8Sr9+33kTdke0pHJcLSkiC+XG9NuJxZ7\nBB6zGLD72zvft8wfcONRw6C3SAJYCAQ2I1BVFU3TME3TxwjaZns20R7bH5imjY7H8Prr1B57DICR\neUizUyBnjoiX1xbeh3cVc2YxLGcENhAkQp+fsqlQP5iEAoGbNSQJAhdcD8sJ09xjnFUCNNltQ+2u\nc8uyMKqg3PshNJtI+Wxo9t0is9g9wQL+quLpP2ifgmXZXxRoGAaappHL5fjU5U8xnAztexVSQwDA\nK68gX05PFQRV7XDcU07/7nlO45NJnvH4MPARN3Pvkc00kW4XSS0sNIsPDw9ZXbVbl3sZgfc+ucX2\nU8vK4xG8tP0SHz3/UeJRfwaAFwiEnomU+xVnBKPIiLbVnjGCp56CN99c3EuaEEbgAYJYzC5k8aaR\nT8wJw9qQ2GoMsasxTkrTkY6B765FSEQT9AbBEnCAa4kEN2V5CgQrKyvs9zvI2tmAQFQztNv2vuST\nhpYwgge9GpcUhX7fztEOVESqKtG+tJARAHx247NM9AnRYtRuipbP+0+lc5FO1+n1Sr4Wxt5rahkt\narXaDAieeWa66SxLHXXjEcOguSA/Wt6Y5c9Pf+aRhgRBmG5Gi6Sh3qDHj3Z/xH+58F/sL7hzB8pl\nbkajPDmJQ6ZB20yR1yXE/C/JLD5lK2p780uHejzypky9agWA1bKsKSMAAplDprnHJJcO5FRHRP86\nHx4NkdIRpEvrUKsh5pcwghBp6Jau84hTQbYofdQubFvzAYGb8SQIAp+8/El7MJRWW8wIbtxAeXJl\nmlCRzTY47gnvCghMM+urS3HDeGAfGi/E4yR6PSQ1v5ARHB4esrJiS4r28KQmljXy3SenQfEsUchz\nDV+//XV+5/LvBL7X9VsGgz0ivT6Rwq84IzAFk3qvzlgbM+6P7d3twoXpoIywmGcEerXqG/FYLoN3\nb3MLqARJsE/B2aKvQtWN4dBmjWFGmhub0ShNWab7xBPOv1Viv6cT10ZnAgIhkyGdtt99nzS0qWDu\nmlhjP2NJxjL0zDbrshwuC4HTilpcyAgAPpH8BLVszZZJ2m1ixeJSRpBKHdDthlfdBMxigOeem1Lv\n0zCCLU3jaEF+tLKpzA4ITnilIZj5BK40NH12DiP47r3v8qG1D5GWncrlV16B69e5pWk81Y4hXWzT\nG8fIGYQ3nflFwjWL5XCzOJ/P0+l0ZtW5Tk5w2POTN+XQ+9nr9ZAkiaRzKpg3jAeDfchnQ/VS7zo3\n7hso5xUbyNttYmX1VIzAKw1dOUEasoFg1Zc5dHR0RKVis81KqkIymuTHuz9eCgTyRy5P10U2W6Wu\nncGf88gyhpFE13cCHzEeGMjnZCKCgNrv08vkTgUEghAhEskzGBwH1rlPHnLuxXgy5pt3vhnwByZO\nz6YLcgTTbBDRusgndB6F9zEQZOUshmVwcHhgV0+6hvESn2AwHmCMDNIx58XOZhm46YtOBIDA8QcA\n+zSeK4WeBNwTbJiR5ob44AGXq1VuOaefUinOoRYnbozIn1TQ4oYjDbmnw2PP9YuKSLQQZXDgZ0RC\nJEVZGCAKwlIgELtjhsNjLGsSCgSX9EvUsnY5O/U6sdXVpUCQSOzR6YRr+F6PYHr/P/IRu6hsMDgV\nEKz3euyFNXsBYqsxRs0RY32mec/3G3J19kWM4P/e+r989spnZ1/qyRi62oogbbbRkcgZ1i8HCJrN\nWTM8y/JJQ4Hq3FYLcgUGg6PAOo+txqj3REpzBVBeNgAEDGPT3IN8MbTK0rvOp0Dw9NNgmiTKqTMx\ngncrDXmBAOwRlj/Y/UF4+qhl2UDwW09gHtiHpXR6n6ahn5kRTCbQ78v0eg8CHzEeGChbCgyHyMMh\n7fjig6EXCGA2ae5EIGi3eXn/ZSrJClvqlu8790yTXCRCdHzMcHiRfLSL+KssDckRGUmQ2K/uz/qM\ng30qWQAETd2ulJ0af9kso0bDBwTupuCGsWNTPQA6HSR1LTSNzU17CzPSpnHjBld1nZsO/S4UotTb\nMcyIQGF8yhbGDhDY6W/4pRXCM4eGUpKiaIPDQiBQVcROD0nKMBzWQ4HA3DVRzil8/dbXoV4nvrGx\nVBpSlPv0esmwrrnhHkE+b+tWP//50mIyNwrdLvuJBGbIPyBIgp1C+mDGCtx+Q67H46aQlkqzOoK2\n0YZcDqvZ4Gu3vsZnr4YAga5zri5hqMdEFJBH7+EsAjccaUiRZCJiBH2kB9pM+FJIWy3EnK0zz69z\nMSrSlmVyEX/qcwAIEglfLYFp7iEWVxYCgbvOp0Bw9SqIIrmCeCIjcJvmjSYT7jrt0WGBNORk7MxL\nQ/NAcK1wzZ5jHMYIHj4ERUE8t0o0H8U80Ein92iZ3TMDQbsN8fiERiN4CDIfmDYQdLuYqRRdcXFB\nWRAI7Mr+wDr3PnfHI/j67a/z6SufZj68spBhXKMin9xeAv6dgKDRaPDCCy9w5coVXnzxRVoLBn+c\nP3+eJ598kuvXr/PhD3/4xO/Nyln2G/v+ze+DH1xoGAc2t0yGSbPp20hPYgRSbj1UGvICwcK84Z/9\njGuyPAUC+9An0JYt8oPllX/TmGMEXmkIwn0CXUyQxf7ZMkZAu+2cuvbDgWDHZP3KOl+7/TWo10lt\nbS1lBOPxLqnUIHSoUiBraPoLKPDDHy5sQe3NrpJaLax8Ptgjx/2qCwr6vdn/i0TSCILIeGxrrC4Q\nuC9aJqZOpaHq7i1URZ0V6liWva6eeYZbmkbpyKIpHlJURvTjsYXtuN91uCXAuj69V0sbz7VaiIU1\nTDP82bUjMurYzxRPwwjE4nqoNBTKCM6dg8mEgjoOzb7zGdiKgizLvFmtUo5GSTiVr6HSkCPVLZOG\nAK4Vr9E22/Rq+0Eg+NnP7EMitlTW39kjlzPoDJunBwJnE67VIJ+fhA7XmTKCdptxOk3Dks/ACOzf\nb36dh0lD/3D7H0L9gdseo9gwLpKPdk5sOAf/TkDwJ3/yJ7zwwgvcunWL3/7t3+ZP/uRPQj8nCALf\n+973eOWVV/jJT35y4vfmE3maepPIRmTGCJ5+2i4qC8lvD7wg2SxWuz117iGEETy0K2kB6HSIFrYW\nSkOFQrCzpi9efpmrKyu84wCBqg6ptYa0FYhry5tTTSNEGjqJEbQsmcTE/jer1cWMgFYLWd7ANHcX\nAsHVJ65y48GPsQYD8ltbSxmBae6RzQ5DT4dZJUtTb9Lr9ch5ZZVMBl5++VTSEI0G8WKRt+dbI7j3\n4kIQFMOKyqJR25Cb6NmpNHS4+45fFnrwACIRRmtr3DUMkjtjmuMauaiJlnyPW1C74bACd00tbTzX\nbBIpnl/47JpWFHWu6t7NGHJjU5apOymk47HOeNxDLG2EMgLvOp8CwWgEsRjlwW6gI7w+1BlbYxLR\nWVvRUqnEz3d3p7JQaOdRmLrkJ0lDqqKyld2iun87uPm9/DJ86EOAPZegd/CQQmFMfxK8VwvD2YTt\nrDshNHXaeGAgb8nQbiNksxxZsVMDwaJ3bx4IJp02d5t3+cjmRwLf6c0Y0rTz5KX/QIzgq1/9Kn/4\nh38IwB/+4R/y5S9/eeFnF6VmhkVWyZIpZ+ipvdnml07D5ia8/Xbg82GMQOx2fUAQxgiUc7bmx2BA\nNLu1UBrK55cwAsuCn/6Uq9eucdM5dWWzOnXNoJ+IIiwZSu2LExiBvCUHNr+6JRNxgOBkRrCJae6E\nbibGjkHmQoZPqM9iZpKUK5WljGAw2COft0KBQFVU6r36tCp6GoUCvP76qYEgWy4vBoLzCsa9sMyh\nWZsJb1GZ1rKb4Q3TSbqHD/xA4GwkDwyDSjTK6L5JrV9HFfuYmfe4BbUbcymkLiNwXxEfELRaREsX\nGA6PqWnVwLNrDKKku37m5GbduCE6KaR3dJ3B4ABZXkUINMS3I5QROGmblfqbzJ8PmoZ98vbOpSiV\nSrxxcDDNGHIPUwFylU7DYEBsUvAdwsKAoJKq0DvaWQoE8qaMXt+jWASdswNBrQYrK5FAK23wM4Jo\nLsfeKHJqIFCU8HcvbErZi+c/Htof6Y6TgTUY7KNpG2SFzn8cIPC5+0s2D0EQ+PjHP86zzz7Ln/3Z\nny38vi9+8Yt88YtfpPYPNeSYTDPenJnFsNAnCGMEUU1jbW2WAz4PBMZDOwvA3YBjnhREb/g8gjBN\n8M4dSKe5urHBbU1jYllEIg3EpIieiC0dSu2LZhOyWQoFu1dKqDTkYQRjy6JqxWBkp/qdBggMw16M\n8x0Z3fYSnyl8hHrCWvoswWYE+bwYahyqikrT8MtyAKytwe3bNOrBvPcwIChWKrw9V/DkRvxCPAAE\nXkYQLCqzm+Hdo0Wsp/v6u/OTn8CHP2wbxYkE2r0+jVabDB0m6skv2rsKT3Vx22gTj9t1TS7uzQOB\nkCsQi5U57t7z3SdNg5ElEDkMAkF5rqDElYdMc49YbJ2AHuWEu86tieXb/CiVqDz8aYARhB0sisUi\nt/b3l2cMAW7HvVg35vN4woAgFUtBp0NX8Uitkwn89KczIDgnY3T3KRYjDKTgOl8YHiAoFoVACu9k\nYKeay2v2fhFTVXQpSVM/LSPYPJkRSBKGLPH59d8O/c6bTnGeae5x48Yh/1//bb74pS/xxS9+cemv\n9p4BwQsvvMATTzwR+O+rX/2q73OCIPhOBd74t3/7N1555RW+8Y1v8Kd/+qd8//vfD/2cCwTP/s9n\nKV8t04w0/amCC3yCMEagDAYLpSHLsmaMwAGC+b72bpzoETgnknQkghqJsGOaDAYHZFfS6PEzAEGt\nBqUShQIcHo4QRZGEh0srW3455L5hkFdydB1wWmYWu9JQq38fURB9hSqWZU3bS/xW+gl2InbXx2q1\nupDFmeY+hUJsISPoDrpBICgWIZejsaefihGseaS2+VAuBBmB13Bc1IH0282fsT5K2EPq3XCe3y1d\n55oYZzRs0GorZGkhFBaPZvyFIqSWYGFRmTOdTJY3OO7d992n42MoqhOMe6cAAscwHgz27IrwExjB\n4GiAlJGQkpJ9DevrVG7/66mAoFQq8eDoaHlVsRvFIpG26Xg8do+fMCDoDXqURzL/3Lox+7u3b9ug\n6tbbbCoMjAOyRQksMVCQtTB8QABra2vs78/2AnPHRF6VESJ2erWQyXA5VaQVcjAcj8f2ZEHP/bel\noXBG4D5zbajRjI75VOXXAt85dIz3q4kEprlHLvdJ/l8lxRf/1//69wOCb3/727z++uuB/z73uc9R\nqVQ4PLTzmw8ODgKLzw13Qy6VSvzu7/7uiT6Bqqgk8gnqozrmvid/fhEjMPw32FQUUuMxBU++mpcR\njFojECGSjcwYgXOinN/8TgsEAFcTCW5qGoPBIZlKCl15d0BwcDDwXTvYQGA+NKfX946mcTFdnF7T\naRjBce9e4KUdtUYg2PdidSjTTyu8Vn+NeDweav6Pxz0sa2hnRoUYh6lYCmNsUCjN5QqqKqyv0zga\nngoIttbWuKnrTELAKMwjkOVVnzQU1oH0W/UfkTc8h5Xx2D5YPPssNzWNx2sRYo/2qNXWyAtNxIW7\n1y8YIdXFC1tRO3UEsrzJcX/Xd5+qVShXwNj234tFjOCWpmGae8jyWkiPAzvca5rKQmADwcWLZN74\nAYOB5Ws8t4gR7FWrvmKyQOqoGzYF9tWChAFBy2ihmgL/t/ovs7/reffAloaGkyNiWRH0Mzw7J3Vz\nERBM/QGYZi5dSxfQh5rdDM8TtVoNVVWJeqb8edn4Ikbw0vZLDFNx1EFw676j62zKMoooYpp71Go5\n4qP/QGbx5z73Of78z/8cgD//8z/n85//fOAzmqbR7dpI3+/3eemll3jCKbxaFFkli5yVOTw+9OfP\nX79uzyaY65c/f4OPdJ2sIPg0ai8jmLIBmAKBJKWxLGt6Kpl+90lmsSMtgB8IEoU0unxGICgWKRSg\nWh352AyAlJSQUhLDqq1dvqNpXE2XfEAQisPOvGBF2aTW3wv6A/cMlAvOvajXya5d4MvvfJlKpRJq\nGNsbyTrlskBIcgWiICILMpnSnKyiqlAu02gKPiBw59365jo3GmRKJbKSxE5I+/FoKcpYHzPqzl7C\nebN4vvFcKpbiX7tvovQ8m+Y779hD2vN5bmkaF6oisas96vUyBTpECgtGVf2i4ZrFnuIt7+lwev2T\niYexblLvHwWAYGVDxLhv2NP8nJg3i8Gufn/bAYJl0pC7zn1A0G5DuYywtko5N/KxgjAgyBeLtOt1\nLjpNA09iBNTr0xRgt/163vMXskqWlt5E7pv8/d4/Mhw7+r3n3QNbGhpJx4hJCUvLc0I3dc8F2zuy\ne5gKMIKHTuqoey+yWa4mU8SiSbsZnifmZSGASCTHZDIMrKnJDksAACAASURBVHMvEHzl5ldQcqXQ\n/eItTePRZBLLshgM9qjVUsjmfyCP4I/+6I/49re/zZUrV/jud7/LH/3RHwGwv7/Ppz9t58IeHh7y\nG7/xGzz99NM899xzfOYzn+HFF19c9rWoskokFeHw8BDlnEcbV1VYWYGbN32fn1+Me50OScvy9Z4v\nOvUz47HHH4DpiyYIgiMP+X2CpWbxaGQD0wc/CNgv2zv9PoPBIfF8yp79+y6AoFazWF8PNjvzppC+\no2k8nq2czAicl1G2itT6h4GXVt/WiV+KT3/ZjQtP8Xdv/x3lcjnUJ3CBYGXFbioaFvJEJlWcqwxW\nVaxMhoYe920KvUEPJaLMxvG547rSaT6QTIYaxoIgBAxjrzTkVtT2+/1pLYE5MlkvX0KwLKZHWs+J\n8qauU9kH6UKHRqNAbtJ771tQu+EyAlmlZYYzgmq1anfFdDr0yfIGdb3mP/AcQWVVIJKP+Ib1hDGC\nx5JJ3tI0THPflobcXWhBB9IAI8hm4ZlnqMTbPq8tDAhQVeLdLjHnILYUCBxG4L57VacjgPcQpyoq\nw04LQZY5X3qE7z90pOU5RhCrxLBSNXqDGNFRPpSxhoZzWljGCOYPjlficaRIOrAnhAGBIAhMohso\nUsw3dtJ9BKPJiK/d+hrZylZgShnAW/0+H0gkpofU2iFIQyOkn0ww/l2AIJ/P853vfIdbt27x0ksv\noTpVf2tra3z9618H4OLFi9y4cYMbN27wxhtv8Md//Mcnfq+qqKDYcpO8JfsN4w9+0DaIPDG/GA+q\nVQaRCPRmvYEiEXstNxpzjKA9S8Oar1AFvzTUNObc0TfftDOZnL9/NZHgvnaMIEhE0jG6gng6IHA7\nxhWLFIvQbkfCgcCTQvqOpvG0ukLX7NLrjxkOF9Q+CQJks0i9Mb1xhJzi36D1O34gqJx7FGNkEFfj\nCxlBLGYDwUHQWwcgMoqg5OZSL1WVUSSOaI2Jx2aMLrCRuGPWBIEPJBKnNoy90hDMNtNi0b61db3O\no6XHfK2oefll+PCH6Y3H1IdD4rsjxPUGrVaW7FBHKb3HDefc8JjFTd1eU6H9hhx/wP79NmkaraA0\nVIb4xTj6tg1uo9GIZrMZkBaL0SiyINA1dm0gUBT7pZgDWnedB4BAVeGDH6RiHQYZwVyHXT2dRvFs\naKFVxdMLmzGCwWA/IAuBzVLEThcrm+VzVz/HV25+xT4wvPbatIYAQBAFhEqD5vEExcoTkgW6+BpO\nAIJ5aehKIsEkkpo+PzfCgADAEEqoc++eCwT/9vDfOJc9RzxfDgcCTeNRxx+IxdbpHfSYJNOnqnF5\n31YWg90R04yYHBwc+KuLwe5b86Mf+T4fAIKDAwxZDmzCrkzgYwSeo/R8YQvMgKCcLFPtz22Mc9T0\najxOU7uHLJ9DSAh0LE4HBJpmP9REgkIBej2ZtbXljOBtTeOxVNpuRb1bp1Rasi4cw1gnRybqT00z\ntg3il2dAIBSL/O4Hfpe21A5lBIOBfaJcXV3MCCRDQkrPFdKpKkZTYyVahzfemP44zB9wj48fcOSM\nsJg3jOdB3FtdXK1O2GnvcC57zteKmp/8BD70IW5rmp2jfdeA4hHtThrVHJD4ZQGBIw1515RXJrBn\n57YY12rTFheKsknL6IUCgXJRQb9rA0G9bqfuRrx9vp14LJlEN3dn7cND5CH3mgLSkKrCc89R6d09\nURpqqSqi53tDq4rd8HgEpnkQCgSSKLE5STPOpPivV/8rX735VazXXrP7j3lOP5Y1wcof0zwckxTP\nAAQuIzi2FjOCOWnokXicQSTDUd//jiwCAp0CaszfZcBdin//zpf5/NXPh84tBpsRPJpMMhjYQGBU\n26dqQQ3vcyCopCr06HF4eGinhHkLqT7yEfjhD32fn1+M+/v7jBKJwE11DWMfI3DfJghIQ5Y1A4JK\nqkK1P5dJM0dNzykKsdEuUfkc49iY5mByOiBwjyK4hacTisVzgY+57ahrzpziSjRKJVXh9v5RuCzk\nhmMY9ycpMlH/0piXhigU+L1rv8fOZGeJNLS2VBqiD5PEXHsIVWV03GJV1X3P7xcCAo9hLEkZLGvC\naGTTZ1dnL5Xg3n6PUrKEMTZmrahN025ieP06N3Wdq4kExj2DUWqP3jBKXpeQflkegSMNVVKV6Ubi\nZQSSJKGqKp2HDz2MYIPWwAxnBJfiGHcN52dBWciNxxIJrOEhsZgDcCGZQ+461+/rQWnoQx+i3LrF\n0d5MfA8Dgv1MBt2zOE7jEbjvXhgQAJwXcwySCo+XH7f/je9+xffuAQwGh4ijNMdHLdKRM0hD8ThE\noxi1XnjW0AOPR9CxTdp8NEoklud2239w9Lag9oZmZclE/eAci4GiWPz9q9/h89c+H5hbDHaa+G1d\n55rDCEaji+TEDqJ6slEM73cgSFZoDVu2NHRO9jOC69fh1i2f7BPGCCbp9GJGcM+D8B6XdZ4RaNps\nboUSUVAiil8TdE6UbkiCwOPROpq0zkAaUNMGpwcCz04eibRJJrcCH3MZwTuaxrVEAkEQqCQrbB+d\nFggU0hG/0a5v6yiXZmYxhQK/fu7X6UV6bO9sB77KpaeVig0EYRmmw+aQQWyuolpVmTRbrG5IpweC\nBR6Bey+8bSZsjydYXVwswsHRkF/b/DWOekczaejVV+0RqIkEtzSNK4p9qm4PHiAk4hRM6b1vOOeG\nwwgqyYp9TQSTeEqlEt2dnSkQxGKrdIZjVHkmL/gYgSMNLQOCJ+JDhshIUmJ2HXO7pbvO60f12Tvi\nSkOJBJUVgaM3ZlkCYUBwR5Yxej0MZwbCaTyCZdIQwKaVQU/GEASBz1/7PEf/9LUAEBjGfaLjDWr1\nGqp8BkYAWKUS8d4xquoHAmtiYe562tF4pORCssKbzV3f9yxiBP1JgnQk+LJkcgOsXskGuJBRivcM\ng0osRlKSMM192u2rbOVOZxTD+xwIVlIrVLUq0WgUM2/6GYEs2/MJXn4ZgPFkTNfskpVnCHlwcICg\nqgsZgXZbI/6Icwr29GaYlxfm094qydkJDk2zAempp3z/xiWpTl1YQbM0DlpaKNULhIcRAFhWHUUJ\nyhLKloL5wJwCgXuvHjZOAAJHGuqNoyTFGahOjAmDowHKph8IJFHiuWvP8drd1wJf5eahJxK2zDyf\nYWpZFr3DHoNoEAjEdovVa9mTgcDZgCvRKGPL4jhkDkV4LUEQCPKFMb1WnM888hn72bmMwGsUaxof\nMBWQoFrbIZpJ/3JaULvhvPArqZVQRgA2EGj7+1MgmFigjyEuzDyTatVOeopfnDGCsIwhN65FWjQF\nz0JZkEJalsu0K22khCPvebp+Vh4tUL3t0f/nnt/IsrhlGKyurk4306Xpo3NZQ4eHh6FAsD5J0UvY\nJ+ovPPoFkq++5ZNlAQzjAXJsi3q3TiFxNiAYqiUuZY4RRfvet1otBoMBg8MBUlZCinvuhZO2uZVZ\n5XYnyAhCgWAcIxUJtseRskc8r/6eXYM1X/WKIws57/pgsEe7fYFz2dO1l4D3ORCkYiksy6K8UaYZ\na2I8MPySzPPPTzeTltEiI2eQxJkmfXBwQDSfD5zGy2U4fDDGGlpEy45WvkQamtc2K6nZCY4bN+zJ\nW3NzddeEI3asMt1Rl51aB+uM0pBlWYxGh0hS8GVwi8re6fenQFBJVdhvn44RdIaQFGcbiX5PR9lS\n7EKZuV/4E09+ggf7wXa8btYQwOpq0DBut9uIukhrbvQgqkqk32L10Zx9z523NNQsdq5BcA3jEFbg\nmsXedeHNHHLN4lfq/4qAyLXcdT8jcIxisDOGLh4JKI8OabUspFQUVR8HWx6/V+FIQ+467w16gcN5\nuVxGPziYglHLaJGMRBj6WjHMpKHTMIJzUoP9SX52zxYUlZXEEr2LniFMnslglWc3OdqbbWjzz++O\nrrMuy2xubLDrjCcNG0Y0jbmsoUWMoDJWaMv2Ov1/ck+wWRvw1opfajHNBySyF2gYDcrpswGBmS5x\nIWUzHVEUpzVSPn8AfEBwJbvOTtf/AiwCgu5YIiUGmyh2Yjd5VHaqiSsV5iv23tI0PuBkB5nmHq3W\nBmup/ySMQBAEKqkK+XN5jvvHCBGBYc2TFPz88/CDHwALNMr9feRKJVQaOtgek7iSmFVBL5GG5k8y\n3hPcvCzkRm5ywK1x0c68QMZa0JHVF07GEDgbqdhE1+c7dNlFX0JU4P6BBwiSFar9UwBBq0V7MCQh\nzO6JsW3M/AHL8qV3fOqpT9Fv9jnszbReyxozGBwRi9kaaJhPsLu7SylRmgGm5xpko83qmmhvwA6Q\n1/W6P+tkTke4lkiEVhhH1AhCRGDUmG1KYUVlf/fO35JWB0i6w+Zc+u08v7Fl8Xa/z/qBQOyJJv1+\nCVGeEB9OTv2ynTkcMBIsa3q4mN+T19bWMA8Pp2DU0BtkYwqmaQ9NmUxm54doJcq4P2bUGS0FAnl8\nRFsss+vWZiyoJSiOinQ3nHoay5rq4gCV37zKUTM21QTn3783+30eTyZZX19nb2+PyWTGXELDYQS2\nxzPi8HA/FAhKoxhN2ZY1xVducHy+zN/c8fc2M4wHJMuXaFktVjK5MwFBP1HiXHwmebnykM8fAN+9\neDK3wfFcAskiIGgPxiSEru/gcqt+i2HiPunhVfsHJzAC09yj2aywIS/KFQ/G+xoIwN7gMqsZDg8P\nSVxJoN/0oOnzz9uZQ04xknchDodDms0mSjmYilUuw+HOZCYLgU8aCmME89LQdGP0nCi9ERvt8XM9\njTbUSBRWEbrdcCHdGx5GsL+/TzJpLjS6lPMKzbuaDwjq5uHJ0lC7TWtgEGe22/iM4k7HNkNidp7z\n5vomYl/kK+98Zfr54fCYSERFFO3PhAHBzs4OG+qGD0DsC1ewEFgvGD5Gt8wjgLNmDq0Fisr+9u2/\nZX0lxrCToz/oM8yk7FPXw4fw2GNs6zrlWAzx4RDpco1eL0ta7NrtQcRf0msUjdr3utudyo3ze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heSk7w+vNpI5GhiNo2uZxux1YrM3YomEMFX+mzqOyycHipRiB10tEr2d8UpIdchcTGQjy14M5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\nytHZniUZAWQzv55fXGSz1coN12h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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's define our $f(x)$ as a function of beta coefficients:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def linear_model(X, beta):\n", " \"\"\" \n", " The linear model\n", "\n", " Parameters\n", " ----------\n", " X : 2d array\n", " The design matrix : a matrix of regressors\n", " \n", " beta : 1d array \n", " Model coefficients\n", " \"\"\" \n", " return np.dot(X, beta)\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where `np.dot` is a matrix multiplication:\n", "\n", "$\\bf{X}\\beta = \\beta_0 + \\beta_1 \\bf{x}_1 + \\beta_2 \\bf{x}_2 + ... + \\beta_p \\bf{x}_p $\n", "\n", "## Aside on matrix multiplication : \n", "\n", "The multiplication of two matrices $\\bf{A}$ and $\\bf{B}$ is denoted $\\bf{AB}$. This is only defined if the *inner* dimension of the multiplication matches. That is, if $\\bf{A}$ is $m$ by $n$ and $\\bf{B}$ is $n$ by $k$. In that case, element $i,j$ of the multiplication is defined as following: " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\bf{AB}_{ij} = \\sum_l\\sum_k{A_{ik} B_{lj}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A special case is the matrix that has 1's on the diagonal and 0's everywhere else. This is known as the *identity matrix* and is denoted by $\\bf{I}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "A = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])\n", "print A.shape\n", "B = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])\n", "print B.shape\n", "\n", "C = np.dot(A,B)\n", "print C.shape\n", "print C[2,1]\n", "\n", "D = np.dot(B,A)\n", "print D.shape\n", "print D[2,1]\n", "\n", "I = np.eye(4)\n", "IB = np.dot(I, B)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(3, 4)\n", "(4, 3)\n", "(3, 3)\n", "288\n", "(4, 4)\n", "152\n" ] } ], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Back to our regression problem\n", "\n", "We choose a set of random $\\beta$ coefficients and generate $f(x)$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta = np.random.randn(p)\n", "f = linear_model(X, beta)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(t, f)\n", "ax.set_xlim([-pi, pi])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 7, "text": [ "(-3.141592653589793, 3.141592653589793)" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, $\\bf{y}$ is not going to be linear in any particular $\\bf{x}_i$, only in a combination of them:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(X[:, 1], y, '.')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 8, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "But that's hard to visualize, because it's happening in 10D!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Noise\n", "\n", "Unfortunately, the noise-less case is not a very realistic one. Let's assume that the output is additionaly corrupted by noise, $\\epsilon$: \n", "\n", "$\\bf{y} = f(\\bf{x}) + \\epsilon$\n", "\n", "which is distributed according to a Gaussian/normal distribution with zero mean:\n", "\n", "$\\epsilon \\sim \\mathcal{N}(0, \\sigma)$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y = f + np.random.randn(*f.shape)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(f, label='f')\n", "ax.plot(y, label='y')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "output_type": "display_data", "png": 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EArzX9B5vWMLb49/qaSWx30BBAWg0Mx8/npyEEl7dP73PfsR2hJTE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\ndkqyZWGflEx15pgFVHuPndXlBl56SZhbub1sO38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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the linear model\n", "\n", "Solving the linear model, means finding an estimate of the $\\bf{\\beta}$ coefficients that generated the data we observe\n", "\n", "In other words, we are looking for procedure to estimate the coefficients (we call the estimated coefficients $\\bf{\\hat{\\beta}}$)\n", "\n", "\n", "### Criterion for a solution\n", "\n", "A 'good' estimate of these coefficients would produce an estimate of the output, $\\bf{\\hat{y}}$, which would be close to the measured data points.\n", "\n", "Where: \n", "\n", "$\\bf{\\hat{y}} = \\bf{ X\\hat{\\beta}}$\n", "\n", "One way to define this is by saying that we want the residual sum of squares to be small, where the residuals are: \n", "\n", "$\\bf{y}-\\bf{\\hat{y}}$ \n", "\n", "and the residual sum of squares (or RSS) is: \n", "\n", "$RSS = \\sum_{i=1}^{N}(y_i - \\hat{y_i})^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding $\\beta$\n", "\n", "Since $\\bf{\\hat{y}}$ is a function of $\\bf{\\beta}$, we can think of $RSS$ as a function of $\\beta$ and we want to optimize it with respect to a choice of the elements of $\\beta$. That is, we want to find a minimum of $RSS$ with respect to $\\beta$. \n", "\n", "Mathematically speaking, we want to find a value of $\\bf{\\hat{\\beta}}$ for which the first derivative of $RSS$ with respect to $\\beta$ is 0 \n", "\n", "To find the derivative, we re-write $RSS$ in the following way: \n", "\n", "$RSS(\\beta) = (\\bf{y} - X\\beta)^T (\\bf{y} - X\\beta) $" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The derivative of this function is (we leave it as an exercise to the reader to prove this:)\n", "\n", "$\\frac{\\partial RSS}{\\partial\\beta} = -2 \\bf{X}^T (\\bf{y} - \\bf{X}\\beta)$\n", "\n", "Setting the first derivative to 0 and dividing both sides by 2, we obtain\n", "\n", "$\\bf{X}^T (y-\\bf{X}\\beta) = 0$\n", "\n", "$\\bf{X}^T y - \\bf{X}^T \\bf{X} \\beta = 0$\n", "\n", "$\\Rightarrow \\bf{X}^T y = \\bf{X}^T \\bf{X} \\beta$ \n", "\n", "If $\\bf{X}$ is 'full rank', then $\\bf{X}^T\\bf{X}$ is [positive definite](http://en.wikipedia.org/wiki/Positive-definite_matrix) and it can be inverted. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Determining the rank of the design matrix - Singular Value Decomposition\n", "\n", "The singular value decomposition of the matrix $\\bf{X}$ is defined as: \n", "\n", "$\\bf{X} = \\bf{UDV}^T$ \n", "\n", "Where $\\bf{U}$ and $\\bf{V}$ are unitary matrices (meaning that, for example $\\bf{U}^T\\bf{U} = \\bf{I}$) and $\\bf{D}$ is a diagonal matrix (meaning that off-diagonal values are equal to 0). " ] }, { "cell_type": "code", "collapsed": true, "input": [ "import scipy.linalg as la\n", "\n", "U,D,V = la.svd(X, full_matrices = False) # We call full_matrices = False, to conform with the conventions in the text\n", "\n", "# We convert D to a diagonal matrix:\n", "D = np.diag(D)\n", "fig, ax = plt.subplots(1) \n", "im = ax.matshow(D)\n", "fig.colorbar(im)\n", "\n", "fig, ax = plt.subplots(1) \n", "im = ax.matshow(np.dot(U.T, U))\n", "fig.colorbar(im)\n", "\n", "fig, ax = plt.subplots(1) \n", "im = ax.matshow(np.dot(V.T, V))\n", "fig.colorbar(im)\n", "\n", "np.allclose(np.dot(np.dot(U, D), V), X)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 11, "text": [ "True" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If all the singular values of the matrix $\\bf{X}$ (the values in the diagonal of $\\bf{D}$) are non-zero, the matrix $\\bf{X}$ is 'full rank' and can be inverted. \n", "\n", "Importantly, for the matrix to be full rank, the eigenvalues should all be non-zero.\n", "\n", "If this is the case, we can obtain the unique solution: \n", "\n", "$ \\Rightarrow \\hat{\\beta} = (\\bf{X}^T \\bf{X})^{-1}\\bf{X}^T\\bf{y}$, \n", "\n", "This is also known as the **Ordinary Least-Squares** solution to the regression problem (or **OLS**)\n", "\n", "Let's make that a function, which we can reuse: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def ols(X):\n", " \"\"\"\n", " The matrix which solves the OLS regression problem for full-rank X\n", " \"\"\"\n", " return np.dot(la.pinv(np.dot(X.T, X)), X.T)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compute $\\hat{\\beta}$, using this function: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta_hat = np.dot(ols(X), y)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We display the estimate, $\\hat{\\beta}$ against the actual parameters, $\\beta$: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(beta, beta_hat, 'o')\n", "plt.xlabel('Real parameter value')\n", "plt.ylabel('Estimate parameter value')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "output_type": "display_data", "png": 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BRESSsWgQEZFkLBpERCQZi4adaTQae0cwW3fODjC/vTF/92SXovHCCy8gJCQE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\n", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using $\\bf{\\hat{\\beta}}$, we can calculate back $\\bf{\\hat{y}}$, the estimate of the output and compare it to the actual output: \n", "\n", "$\\bf{\\hat{y}} = \\bf{X} \\bf{\\hat{\\beta}}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_hat = np.dot(X, beta_hat)\n", "fig, ax = plt.subplots(1)\n", "ax.plot(y, label='$y$')\n", "ax.plot(y_hat, label='$\\hat{y}$')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 15, "text": [ "" ] }, { "output_type": "display_data", "png": 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8usdHqhy7SiX0fq4+FUVgQCA9Q9J28a/t0EJ3JrGur7eMUlFSQHOvb4Td4YA/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\nCPQMvO+57Ne1VRB1zoIqwJXnFvKLgp1M2UznmUgMSkRmJbs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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The so called \"hat matrix\", or $ H $ is the matrix which defines the transformation from $\\bf{X}$ to the estimate $\\hat{y}$, so it's the matrix that \"puts the hat\" on $y$: \n", "\n", "$H = \\bf{X}(\\bf{X^T}\\bf{X})^{-1} \\bf{X^T}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H = np.dot(X, ols(X))\n", "H.shape\n", "y_hat = np.dot(H.T, y)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(y, y_hat, 'o')\n", "plt.xlabel('The original output') \n", "plt.ylabel('Linear estimate of the output')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 17, "text": [ "" ] }, { "output_type": "display_data", "png": 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Hr8ddd/0TXbrcgrlz42+6+7b2n2xLm96P3L8TLvhqxpy+k4BMNTU1IjQ0VJw+fVpUVVWJ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\nMm0bGaGRi9myqbq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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Other methods\n", "\n", "### The bias-variance trade-off\n", "\n", "When estimating the linear model, there are two kinds of errors that you can make: \n", "\n", "- **Bias** is a systematic tendency to make errors in estimating $\\bf{\\hat{y}}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_hat = []\n", "\n", "for ii in range(1000):\n", " y = f + np.random.randn(*f.shape)\n", " y_hat.append(np.dot(H, y))\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(f)\n", "plot(np.mean(y_hat,0))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 19, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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sMPVCj8lMkGFUfAEOBzPDfpv7dYjypbnQdmwIuFYflDVQG2n4ZWkt+KMhyEyY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\n6hST7fI65E37HfJafIe8Ft8hrwVzKAf7Y489ht/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"text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bias can occur (for example), when the assumptions of the OLS are violated. Here, we choose the noise from a different distribution: \n", "\n", "$\\epsilon \\sim U(0,1)$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_hat = []\n", "\n", "for ii in range(1000):\n", " y = f + np.random.rand(*f.shape)\n", " y_hat.append(np.dot(H, y))\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(f)\n", "plot(np.mean(y_hat,0))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 21, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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YMfFBO3gQ0uyL6R/tD6rc6JmobKpkQ94GnnhCFJpcWmxyyy0iT3n3btHAyVOf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\n+fn5nD17lry8PGJjY3u8npWVRUREBEajka1btw640KGkoqK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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- **Variance** on the other hand is a tendency to estimate different parameter values in each iteration, leading to less confidence in the value of the parameters estimated. Let's examine the variance of the OLS:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(np.std(y_hat,0))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 22, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, there is a trade-off between bias and variance. Models with a lot of flexibility tend to be unbiased in the long run, but they will also tend to fit the idiosyncratic noise in the sample too well, so they will be very different depending on the particular noise in that sample. \n", "\n", "The OLS solutions are unbiased (when fit for Gaussian noise), but they have relatively high variance. \n", "\n", "**Shrinkage methods** are methods of fitting a linear model, which reduce the variance of the estimates. We will look at one of these methods:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ridge regression \n", "\n", "This form of regression regularizes the regression by optimizing a variant of RSS: \n", "\n", "$\\hat{\\beta}^{ridge} = argmin_{\\beta} [(sum_{i=1}^{N} (y_i - \\beta_0 - \\sum_{j=1}^{p} x_{ij}\\beta_j)^2 + \\lambda \\sum_{j=1}^{p}{\\beta^2}]$\n", "\n", "Where $\\lambda \\geq 0$ is a complexity parameter that controls the amount of \"shrinkage\" of the model, by controlling the sum of squares of the parameter values and will control the bias-variance trade-off\n", "\n", "The solution to this problem is: \n", "\n", "$\\hat{\\beta}^{ridge} = (\\bf{X}^T\\bf{X} + \\lambda \\bf{I})^{-1} \\bf{X}^T y$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's write a function to do that: " ] }, { "cell_type": "code", "collapsed": true, "input": [ "def ridge_regression_matrix(X, L):\n", " \"\"\"\" \n", " Calculate the matrix for ridge regression\n", " \n", " Parameters \n", " ----------\n", " X : 2d array\n", " The design matrix\n", " \n", " L : float\n", " ridge parameter for regularization \n", " \"\"\"\n", " return np.dot(la.pinv(np.dot(X.T,X) + L * np.eye(X.shape[-1])), X.T)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "beta_ridge = np.dot(ridge_regression_matrix(X,10), y) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(1)\n", "ax.plot(beta_hat, beta_ridge, 'o')\n", "ax.plot([-2, 2],[-2, 2],'k--')\n", "ax.plot([-2, 2],[0, 0],'k--')\n", "ax.plot([0, 0],[-2, 2],'k--')\n", "ax.set_xlabel(r'$\\beta(OLS)$')\n", "ax.set_ylabel(r'$\\beta(Ridge)$')\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 25, "text": [ "" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "H_ridge = np.dot(X, ridge_regression_matrix(X,10))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "y_hat = []\n", "y_hat_ridge = []\n", "\n", "for ii in range(1000):\n", " y = f + np.random.randn(*f.shape)\n", " y_hat.append(np.dot(H, y))\n", " y_hat_ridge.append(np.dot(H_ridge, y))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(f)\n", "plot(np.mean(y_hat,0))\n", "plot(np.mean(y_hat_ridge, 0))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 28, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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2MYfP5xHfrEWWZFwqBgsL+lasZnbl1wxqTNN2WJCwnz59moiICEJCQrCysuLW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\n7owM3XMfWi3Hq9P4aaTxgz1ilA/ZHjW68f7eKiw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"text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(np.std(y_hat,0))\n", "plot(np.std(y_hat_ridge,0))\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 29, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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PKGSK8noyqQwRQRE4mXUS3UO7i/9r7zL69AHmzgU++MD0GBFz8xgjXuorSZlJ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\n6wd3d3dMnToVkydPNqkza9YsJCQAWf4nkd4iHWg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"text": [ "" ] } ], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "In this segment, we looked at the basics of linear regression. Linear models are very popular in neuroscience (and science in general), because:\n", "\n", "- They are relatively easy to understand and easy to intepret.\n", "- There are good, fast computational methods to fit linear models to data.\n", "- Linear models are relatively robust to violations of their assumptions, to low SNR, or to partial, or limited data.\n", "\n", "We have shown here an approach to solving a linear model, using the 'ordinary least squares' solution. We have examined a tool for examining and analyzing the inputs, or design matrix: the singular value decomposition. Finally, we have examined a shrinkage method to reduce the variance of the parameter estimates: 'ridge regression'. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extra stuff : more derivations from the SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using our SVD from before, we can derive the OLS solution: \n", "\n", "$X\\hat{\\beta} = \\bf{X}(\\bf{X}^T\\bf{X})^{-1} \\bf{X}^T y = \\bf{UU}^T y $" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x_beta_hat = np.dot(np.dot(U, U.T), y)\n", "plot(y)\n", "plot(x_beta_hat)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 30, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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Xg4NrGRoCFxd7z3Q6+fnj/1+xwn7zkCXSP378OH/961/5+OOPyc7OJjs7m4MHD8pxKpPR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\nbds2rF69Gi0tLRg7diy2bdsm9ymIiGThCP36evWEvuzlnUG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"text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where $\\bf{U}^T y$ are the coordinates of $y$ with respect to the orthonormal basis $\\bf{U}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_coords_in_U = np.dot(U.T, y)\n", "plot(y_coords_in_U, beta_hat, '.')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 31, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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IZ5GGHR0dbdkSvkcAZDIZqvEqOo5bVsY7RAoCO4fWaOTH1lauGKIARAsCD3zy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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "matshow(np.dot(U.T, U)) # Shows that U is an orthonormal basis set" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 33, "text": [ "" ] }, { "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way to rewrite the ridge regression, using the results of the SVD: \n", "\n", "$\\bf{X} \\hat{\\beta} ^ {ridge} = U D (D^2 + \\lambda I)^{-1} D U^T y $ " ] }, { "cell_type": "code", "collapsed": false, "input": [ "D_sq = np.dot(D, D)\n", "lamb = 10\n", "UD = np.dot(U,D)\n", "Dsq_LI_inv = la.pinv(D_sq + lamb*np.eye(D_sq.shape[0]))\n", "DUt = np.dot(D, U.T)\n", "svdRR = np.dot(np.dot(UD, Dsq_LI_inv), DUt)\n", "x_b_ridge_svd = np.dot(svdRR, y)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(f)\n", "plot(x_b_ridge_svd)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 35, "text": [ "[]" ] }, { "output_type": "display_data", "png": 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8nn37HuPuu827x6BukNoeLetCBY7DYIixj/gY2vfGxwvz/m/qaeKdgnd4N+8j\nTtd9gbs+kNZntEgltsu1qGivwG0onJh48+LWygAl1WFl1NXZyLCr0I3oaNDnjzmP1Ry2pGzhZ5o/\nc/jwo3z/+6Od3meffdaq9a36S4WHh1Nd/XVKYHV1NRERwjQ4Mgdtu5oob2HdFbkc9B3ChWKqqsAn\ntpTEYMuEHSDRJ4MzNVbs4AG//XAnYb1rCPH3HPN4SgpIStez48K1EY7ZdvQMvi7+k1YC36i4kQGf\nIt7db35qYcGlAvz18SQprC+euxo/Nz9kEmfy1cLtBW16/Zv8v7cOkft/j3P/pXq6mn35tHDiLz5r\nUbeqce6KN7sqVxmgZMTffsJe3lqOrC+EdNXYY/tMZa1yLbW6HD4/X2+TOLtVwj5//nzKysqoqKhg\ncHCQ7du3s379eqFsM5n6ATWJZsTmTCEszJDyKJSwazTgFmFZqqORxTHzKe85Z5UdH2ve5TblneMe\nl0hgZcxqzjWcskl3y+nGgepdrIwYPwxjxEXmwgblJvbVvWP2B/FY1TH8OjNNzs82lyBZHDmVwmyg\ntve3c7zuMN+R/5umo7fzr//1JnHgfn6/701B1h8PTZuG4aZ4sydLKQIU9HnYT9hz6nMZrk23ehPc\nzcmN9Um3Ip39nk36xlgl7E5OTvzlL3/hxhtvJDk5mS1btqBSCVdZZwp6PbRJykmLFN5j764Trkip\nogJGLEx1NHLz3Hm0up21ODOmd7CfRtfj/HD9jROetzrLE9/eeZypPWPZjWYIvb1Q672Tb2fdZtL5\njy6+h2HV25wz87v1ePVxRiqXCJ4RYyTKK57iS8Lk/L19fheSiuX86Hu+X3VY/ObCezje+oFN202U\nt6rprY0nPNy865SBStqlZXbbPD1alotnZzpeXtavtSVlC7I52zl2zPq1rsbqoNnatWspKSmhvLyc\nn/zkJ0LYZBbNzSAJVJMcKrywt1UIF2OvroZuN+s89kUJCejdm7moabXo+h3HT+HamYIicuKZsMuX\nQ09FMoVNjt0q+N1DZTh5tXND/AKTzs+MysTFp53X9pieyqDX6zlWdYzW3EybCXtqaBKVPcK4ff93\nfBtzpFvw8Pj6tQduD2ekdi7vF3wsyD3GorBejc9wPK5mRquifKPoHGmgpt4+8wrOVOcS7Tb5SEtT\nWB2/ml6PIvadFLgJFA5QeWrowy5sqiOAry/o2sOp6awRpEipvLqTQUkn4T5muiSXIZVI8e2dy64z\nloVj3j9z1rzXAAAgAElEQVSfjdIpa9LzEhNB0qLijHZqhb2vD5s+Yr95ZhcpzreavCkolUi5Mfxu\nPqp42+R7VLRXoNON0N8QS1iYpZZOzPUKFS2SIqtrHJp7mynsOsHDS2694vXAQEgcuJ+Xst+w7gYT\nUN6qJtzD/OlnTlInAt1mUd1mH5e9pDOXObMsT3W8HBeZC2uiN5B96T1B1rucGS/s6ooBdG6NRPla\nOfb9KiQSCA/2wkXiRmufZR7y5ZS3lhHpobQ6syDWbR7H1JZVhp5pymZ5bNak50kkkBig4kLd1Al7\nfz/cvH6QpWsb0elsc4/TnbvYmDx5fP1ynly5hRrfd+nuNk1Fj1cfJ9Ejk/Q0icUFLZMxP1rFSGCR\n1TUOO/I/APWNbFo/Os7wH4s3ktv2uaAFe0b0ej21PVqLnbMInwjqe4T3eq+mobuBgeEBMuKES/38\nj0V30h6+Q3AHZsYLe26lFm99FE5SYXtwgCEcE+gizAZqdW8pigDrn8Xny+dT2G6+sPcP93PJ6Qz3\nLF1i0vmpoSoqeqZG2IeGYMsW0KY8RvW6ubzxnvCTFNp6uuj0yOFbayaeV3k1S+IycHWV8O99pmUn\nHas6hlfrEq6/3hIrTSMhMAG9n4biUuvCEf/8Yjsx3XcRGjr62F0bvaFsHW9d2G7VPcaiobsBZzyJ\nC/e26PqYgAgGXGtsNqfWSH5jPp7dc0hKEu4benX8SqTBpezKFrb38owX9qJGNaEuNqjMwJAZ46OP\ntHoDVa+H5hE1qXLr0yLWpM6nQWp+KObT/FNIm1O4Lm3i+LqRtFg5g7p+QZ5WzGFkBB56CKp8tuEU\nd5QV8vX84PA3GRkRtsfpthPHcW+fR0iAiY1JvkQikbDA/U5eP7/DpPOPVx+n62ImixZZYqVpuDu7\n46mL4ESx5ZkxDd0NFLWd597r1o55PCwMFL338fcTwmfHqNvUeA2an+poJMInAu/wGptvoJa3ljPU\nkECC5fkPo3CWOZPudhvvXBA2HDPjhV3bribaxzbCLpeD26D1HntTEzgFq0kMNj+GeDU3LohnUNpO\nfYd5z907TmUTNZJlcuWjUinBvSeJIjtvoD7zDJS3aKmZ/QTbN2/jw0f/RJ+bhh+98y9B7/NRfjYK\nWZZF1z503Z3kDu2YdO+lra+NivYKirLTbOqxA4Q5qzhfZfnf6t2L7+GkvZk7Noz/RffQ0jVUdJRT\n3SFsO2t1qxqn7jizUx2NRPpE4jbL9sJe0lROb2284BWuW2Zv5vyAaY6Cqcx4Ya8fMK+/hDnI5SDt\ntl7Yq6rAaZYwG7zeXlLc2+fykZk5d8frslkSkWXy+QoFjFxSUdRsX2F/9/0h+tfdw0+W/oS5YXNx\nd3Hl58nv8OeipylpLhHsPudbj5AZmWXRtfeunMNQvwuHSiYOiZ2oPsHsgOtwdXLG1nV7Sj8VJa2W\n/61eO7MdT+1dpKSMf87mO5wYqVrEyerTFt9nLNRtanRN1nnsUv9qm+ey59eqCZbF42x+U8cJ+daq\nFfS4llNQUyHYmjNe2Nul5aRH2U7YdW3WC3t1Neh8NIJ1nwyXzOdQsenC3j/cT63+DHdeb1p8HSAm\nBnorVVxstJ+wt7aCNuI5wgL8+P713//q9R89pMLz1K+47c17BOkV3z3YTZMkn40LLHOjXV0lxPbe\nyZ8PTexlHa8+TsjAEpuGYYykR6ioHbDsb9Xe305BSy6b5q6ecIM3NhZ8uuexN0/Yts6aNg3d1eYX\nJxmJ8IlA51Fjc2FXtwrbQdaIt6czIa238+eDwoVjZrSw9/cbujrOi7OdsPc1Wi/s5ZV9DDk3E+Ej\njNuWFjyf3EbTP1xHtafgUgrLF5sWXwdwdYVAvYqcGvsJ++nT4JS+jf+34ldXZA+5uMDP1z5KfeMw\nx6uOW32fI9rjUD+X6+ebF1+/nPXxd3KwYeJwzLGqY4xUZNo8DAOQmaii3dmyv9XRyqO4NV/PxvWT\nJ5En+c7ndI111c9XU9aipq82nhALe/hF+ETQ52xbYdfr9dT3awSvcDeyLPhOPqkQLhxjc2F//JPH\nbbZ2ZZUOiX8FikDrY9djIZdDR5X1m6eFdVr8pVHIpDJB7FqWMI/KYdOFffupbIJ6ssyullP4qihu\nsZ+wHz7ZyrBHNemho/OEv/UtCf1nt/DaWeuzMj48fwT/DvN/H5dz76pUBrs9OF07dlhiYHiA8/Xn\nqTpxvV2EfZFChc6/mOYW859o9pVm01eUxdKlk5+7OGYe5b1nBR1AU96iJswtzuLOl2HeYXTTSE3d\nsGA2XU1DdwNOes9Ji/ss5e7rl3NpSIu2TSvIejYX9jfz3qJ7sNsma58vr8V5OAAPZ4/JT7aAsDBo\n1kRYXaRU3qIm3F24b/pVc+MY1HfT2N1o0vnZ2mwWzsoy+z6pEbG0DjTQO9Rr9rWWsL/4BCqf68ZM\nXfXygkU+m3m/6D10I9YltmdXZJPhn2XVGhkZEqRFW3jl9Nhe1vn688T7KynN92HuXKtuZRJ+7r44\nj/jwxUXzny4/K8km2SMLF5fJz108JxT9oAfadmEEqGugi56hbmKCLK/ecpG54OscSGWzaZ8HS1C3\nqXHvtzxcNBlLlzjh/NZhQjwsL2C8HJsLu3P9Yj4utU0pcm6VGr8R2zwaAXh7g2TIGyeJk1UNsap7\nhK2MVSolUDefY5rJH4n7h/upGDrDhrmmx9eNJCic8NEpBN20HI+RESjsPsbqxMxxz1mfqcS5X87R\nqqMW36dnsIfK/jxWq6xzo2UyyPS7i+2Fb3Gp59Ko49svbifRdRkpKZg86s1a/IdVHC817wmrvb+d\nyu5S1qSY1lZh9myQ1M/nXJ0w4Rh1m5ogWRxRkdblhsu9IqntFjZb53LUrWokbbYT9sBASA5KpbrC\nhG9XE7C5sPecvpPtBcKm8hgpblQT6mqjlnl8OftUDrPcrIuzN+s0pMiFE3YnJwgamsdn+ZOHY7Ir\njiBtms2qpeY/QioU4NJhn8yYkhKQRB3nRtX4wr5iBegL7mTHRcvfTyeqT+DWnsHiBdY/5d2WmURU\n60M8svuRK57o9qn38W7hu6iaf2qXMIyRSHcVeWZWCx+tPIpXx/XcsMQ0QYmJAV31fI5phdlA1bRp\n8B6yXjBjAiK41G+76lN1m5qBBtsJOxj2mBItbyV1BTYX9vih29hXfoCugS7B167oVBNjoxx2I3I5\n+Mssj7MPDUGvq5qMaGHtTPKZz6maydPO/vXFdty1d1r0hlQoYLDWPsL++YkBhoLPszB84bjnzJ4N\nI/mbebfgfYZHLIunHtJk01+cRboA7T7WrIHGbb+krrOev575KwCXei7x0M6HeP221yk4FWyXjBgj\nSYEqyjvM+1sd1mbTU5Bl8heQVPplWwuNMMKublXj3G15qqOR2MAIdJ41dAkvM4Bhg7e3Jl7w0YaX\nI2TLCZsL+7KF/kSzlI9KPxJ87cZBNaoQ2wu7x7DlHntdHciC1SiDhN3gXR67nOLeY3QOdI57zsDw\nAJ9qd3FjxGaL3jRxcdCpUVF4yfbCvifnHHLnJLxdxy8rl0ph9fx4vEYi+bzSssEPnxZnIx9cJkjb\nVaUS5qa5cPvI22w9spWCSwU8uPNBHkx/kBWxK/niC+zqsc+PUdGoM+9vtbc4m5C+LIKCzLiPfB5F\n7ecF2UBVt6kZbrK8OMlIhE8EHqG2K1IqbiwnUCJ8DrutsLmwZ2aCu9a6x+fxaJeqyYixvbA791ku\n7BVVOnTeFcT5Cyvsi9IC8W7J4oOiD8Y9Z596Hy7tydy1zrI0S3d38NepyG+wvbCfbjjG4sjJ9wFW\nrgT/OsveTz2DPRS3XWBJlHBu9FNPwRt/SuA3K54j85VMWvta+WXWL6mpAZ3OELqwF8tSVHS5mf63\nau9vR9NZyvJE0+LrRq5LmYVs2Ad1m/XDPdRtanpqrPfYI3wicA60XcqjtsN2Fe62wC7CXrVvA4e0\nhyb0Ls2lb2CYAa9ils9OEmzNsQgLAzotF/Y8TR2uI8Jn7mRmQu/J+3j13PitVN/M3U7vmbtYs8by\n+yQGJVDZqbE49GEKXV3Q5Hac9enjx9eNrFgBNfs280HRB2bbdLTqKAEDGSycO/ZYQEu44Qbw9wd/\n7Tf48ZIfs+2ObTjLnDl+HBYtEvbxejLS4kLRS4bQNprWgfFo5VH8e65n6WLzNuxmzwbX5vmcrbM+\nHFPeWk5LqcJqjz3SJxJ8bFN92tHfQf9wP/GhFibaTwE2F/aoKHCX+DE/eBm7S4Sbo3kkvwyn/jBm\n+domr9SIXA6DTZYP3CioUxMoFf6b3tMT1sTcwrm6nDFt6xvq4+PSj8n032RV2CEh1h0fiRx1qzCj\n18bi1Ck9kujjLIud3GOPjwf3/lhC3WI4pD1k1n12lexCpr6V+fMttXQ0EonBa//d7yQ8lfkTYv1j\nKS+H//ovePhh4e5jClKpBI8eFYfyTfPasyuzGSjOYvFi8+4zezZ0l82zOjOmb6iP+q56aI/F17oR\nokT4RDDgZptQjLpNjZ8+jugoO35LW4ldKk+XLIH4fmHDMYeLLhA4JEzD+4mQy6HLihF5Zc3C5rBf\nzubb3Qi8dAdv548e/LCnbA8+3fPZvM46L0OhAJ8B226gfnyyBA8nb5OGkEgkhnCMcuAuthVsM/ke\nI/oRdhfvpvnYBkE2Ti9n/Xro7oZDhwztI1avhl/8AjaY1+pdEIIlKk5rTPtb7S/LZlidZXYmRnAw\nuLfN57iVmTHqNjVh7jFERThZ/WQj95bTK62npk745v3qVjXufdY/VdgTuwh7Zib0567nSOURwQYk\nn63JJdbdPsLeVhFJdUe1RZtF1T1qwePrRm6+GZoO3M+/c98YZds7+dvp/GILt9xi3T0UCpC2qihs\nKrRuoQk4rD5Guv/kYRgjK1ZA7+m72Fm8k/7hfpOuOVd3Dhe8ifNNxFO4SAxg2NT98Y8NYr5qFXz3\nu/Ctbwl7D1OJ8TKtv097fztlraVkxi6wqOJzTvA8LjSdt6p3T0lzCSFOiYIIpquTK54yf7SNo2sK\nrEXdZtscdltgN2E/c8yX5THL2VW8S5A1y7pymRMizOzBiQgLg4ZKHzycPWjobjD7+madhpQw23js\nfn5wQ0wml9o7yWvM++r17sFu9pZ9hnJoo9VdBRUK6K1KpLxVmGHJV6PXQ0nfcdamml5AtWIFnDog\nJz00g09KPzHpml0lu4gf2sAS8+u0TOKee6C2Fu66C/7zP21zD1NID02nrHfyIeSHtIcIGVxE5iLL\nCmLmqQJxHQmgrKXMousBSltK8RlMsHrj1EiIewRV7cLnsqvb1PTXi8I+itRUaGiAtVFb2H5RmAks\njZJcblDa3mP38jI0oYr1VVLWav6buMvZdk3KAO7YKCW44T7eyDNsoupGdLyS8wrB/UvYuDbQ6vXj\n46G5LA5Nm8bqtcaioQGGwo5xyxzTPXa5HEJDIdPnXt7Kf8uka3aV7GL44m1kZVlo6CS4uEBxMTz7\nrG3WN5WN85bSLMunqWfifv3vFb6HtOR2i7/oZs8G7875nKu3PM5e0lKCc6cwHjtApG8E9b3CV5+q\nW9W0aURhH4VMZsjn9am/lePVx2nptW7UWUN3A8MjQyxOtXGT6y8JC4NQF4XZ3klPD+h81MyLtZ2w\nb9gA1Z/cx5t5b3L/h/cT8vsQXs19lcFDT7F+vfXre3uDjy6O0mbbbJ6eL2xD4tVIcnCyWdetWgWS\n4o0c1B6cNLynblXT1NNE/qcLWbbMGmsnxs3NdmubyuLr3JBWrGL7+T3jntM31Meesj00HN7IAvMy\nHb9i9mwYrJxnlbCXtpQy3Cicx64IjqRlqMbqod5XU9ZSjqwj3uoNXntit7a9mZlw/qQXN8bfOGHu\ntSmcrMiFhnSi7LRLLZdDgN58j71A3YbEaYhgTzOqP8xk1iyYF6ViufejLIlcQs6jObx9Qw6ymhtI\nEyhSlRASSUtfk8nxbHM4VlKE33CS2UO+166F7L1+rIpbxfuF70947q6SXWQG30qAv5RwYXosTVuc\nnCBZtp63zo5fELi3fC9x7nNJiQnBw8Is3ORkaLmYTk5droWWGoS9q0I4YY8NjAAfYatPB4YHaOxp\nJNovyq6pq9ZisbD/6Ec/QqVSkZaWxsaNG+no6Jjw/MxMOHYMtqRYH445VJiL/2A6MmG64E6KXA4e\nfUqz48xn1Wo8B+KR2PgdsXEjuJ18lm/P/zY99ZE88wzccotwOdRKhQw/aSSV7ZXCLHgZubVFRLmb\n560DZGVBTg5siLuHtwtGZwVdzq6SXQS1bLCptz6duD11HefbD4z7Rfxu4bsENGxm7djjTU3CwwPC\nZRmcq8uxKKmgpbeFoZEhaktDBCviivCJwG2WsEVK2nYtQc6RREeO7jg6nbFY2NesWcPFixe5cOEC\nCQkJ/Pa3v53w/Ouug7w8yApfx9m6sya3nB2Lc7W5xLrZPr5uRC4Habv5Hnt+jYYAie2r1W6/HXbu\nNBTELF9uqHZ85hnh1lcowHPANnH28o5CkoJUZl/n7m5Io3XS3ExOfQ51XWN/mpt7m8ltyOXSyZXX\njLDfuiIYWctssiuyRx0zhmHKdm9k40br7pOhDEE64mZRKnBpSynKgAQa6iWCxa4jfCKQ+tVQWyvM\nemAI4/mNxBMdLdya9sBiYV+9ejXSL/OkFi5cSE3NxLvRHh6Qlga5Z925JeEW3iu0fAxUaWcuc0Ls\nK+xDjQrKW8vN8k7KBO7DPh6RkfCzn8FPf2rIo37+eSyeRjMWMTEg67KNsDfqilgQY76wgyEcc/Az\nN25Lum3cnPZPSj9hVewqjmW7XzPCnp4O+uL1bMsZXRD4mfozErznIu0NsTpUN3s2BA6lk1OfY/a1\nJS0lhLsmEh6OYP1XInwiGPaoFrRISd2mxm2G5bADCPJ88corr3D33XePeWzr1q1f/RwXl8Xhw1ls\nuX8Lz594nu9c9x2z79Uz2EPbSBXXK2zbSuBy5HI4dswHr0gv6rrqTCqkAajuVrMwwsLdKTOxZYpd\nVBQM7YkTpDfI5YyMQLd7IctTzQ/FAKxbB889Bzt+8Qh3f3AXW1K2XPG3aelt4Vef/4ofqP5Ijhcz\n7sNpKTIZLA5Yz0elK9Hr//eKUOCOizuY1byZzNutD9WpVOD0eQY5DTlsSDKvGqu0pRTf4QTiBCzx\niPCJoN+5jpraEYTaPlS3qaE1nigby012djbZ2dmCrTehsK9evZqGhtG527/5zW+49dZbAfj1r3+N\ni4sL99xzz5hrXC7sBw7A1q3w861reHDng9R01pg9B7TgUgGuXUkkJ9qvzVpYmKFLozLAEI4xVdgv\njRQzJ+JeG1tne6KjoasqHk2b9fNGL0dd1YPe4xKzI2Itul6hMLRW8GpbwuPzH+fWd27l84c/x8vF\ni0HdIHfsuINNyZuQlN5qszTH6cqtixM51+JJTkMOc8MMI5yMYRj5J3/kqT9Yfw+VCrpfSSe3wbSU\n08spaSnBv+tOQYXdzckNN6kPmsYmQJhHVk2bht7a5TZ3CrKyssi67E36rJV5sxN+re3fv5/8/PxR\n/4yi/tprr7Fnzx7eesu0P+zixZCbC8MDrhM+Pk9ETkMuwzXpJCSYfanFyOVfCnug6Ruoer2eTvd8\nVqXOsbF1tic8HDor41C3ChuKOZxfgme/0qpZsGvXwqefwlOZT5ERlsG9H9yLbkTHE58+gY+rD79e\n8Wuys7lmwjBGsrJAUrr+iv5Mn6k/Q+WXQWtViCB94hMSoCk/w6JQTGlLKUMNwnrsAEEuEWhbhCtS\n0rZpadPGzrinPYufV/bu3cv//M//sGvXLtxMTOD18ICMDDh+HB5Of5hXcl4xe0f9VEUusqZ0s/pH\nW0t4ONTXQ7yf6RuoJY2V6Pu9maO0vkhoqnFyglDXWDRtGkGHGJ/SFDJLall83cjatbBnD0gkEv52\n89/oGuhiyStLOFF9grc2voVUIuPIkWtP2OfMAV3het658C5/Ovkn7thxB4/sfoTo9gdZvx5BMsrc\n3SHCM46W3jazalN0IzrKW8vp0CgFF3a5VwS1XcIUKen1eiraK2hVx9p0wIYtsFjYn3jiCbq7u1m9\nejUZGRk8/vjjJl23fDkcPgyZUZno9DpO1pw0675nanKJcUu3a06pm5thM9JXZ3qR0v68PDy759gt\nJdPWxMp9ccKNpt6JKxrNofBSEXE+1gl7VhZcuADt7Yahxu/f+T7RftHsvms33q7eFBcbBMiefdGn\nA1IprFAuwn0whuLmYjYmbSTn0RyqP3rI6myYy0lWSYlySeNC4wWTr6nurCbQPZCqci/BhT0uIIpL\nA8IIe1NvE85SV0L9fWbMgA0jFm+elpVZ1iNi+XJ4+mmDh/WN9G/wcs7LLIo07blQN6KjvDOf2+zQ\nI+ZqlEqQdZjusZ/U5hEqmflhGCNRUVAjNWTGzPKcJcialb2F3B039t6Mqbi7G2ok9u+HzZvB392f\n7Zu+rpM4coRrLr5uZOVyJ3JzP+HvPzL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