{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Analysis of adaptation time with generalized linear models\n", "## [Yoav Ram](https://www.yoavram.com)\n", "\n", "This notebook will demonstrate how to analyse adaptation time of a population using generalized linear models (GLM), and specificaly exponential regression. This assumes that adaptation time is a geomteric or exponential random variable since it is roughly the waiting time for an event to occur with some independent event of it occuring every generation; this neglects much of the dynamics, of course, but the idea is to get a general way to analyse adaptation time without having a clear dynamic model of the process.\n", "\n", "#### Outline\n", "\n", "1. The exponential distribution and how to fit data to it\n", "1. Exponential regression, and in general, GLM\n", "1. Simulating adaptation\n", "1. Analysing results of simulations using exponential regression\n", "\n", "This notebook is under the [CC-BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/) license.\n", "\n", "The latest version of the notebook can be found on [github](https://github.com/yoavram/ipython-notebooks/blob/master/exponential%20regression%20of%20adaptation%20time.ipynb).\n", "\n", "Thanks to [Uri Obolski](https://www.eeid.ox.ac.uk/content/dr-uri-obolski) for help with understanding GLMs." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python 3.5.2 | packaged by conda-forge | (default, Jul 26 2016, 01:37:38) \n", "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.54)]\n", "NumPy: 1.11.2\n", "Matplotlib: 1.5.3\n", "statsmodels: 0.8.0rc1\n", "Pandas: 0.19.1\n", "Seaborn: 0.7.1\n" ] } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "from scipy import stats, optimize\n", "import statsmodels.api as sm\n", "import pandas as pd\n", "import seaborn as sns\n", "sns.set(\n", " style='white',\n", " palette='Set1',\n", " context='paper',\n", " font_scale=1.3,\n", ")\n", "red, blue, green = sns.color_palette('Set1', 3)\n", "from ipy_progressbar import ProgressBarIPyNb as ProgressBar # pip install git+https://github.com/yoavram/ipy-progressbar.git\n", "import sys\n", "\n", "print(\"Python\", sys.version)\n", "print(\"NumPy:\", np.__version__)\n", "print(\"Matplotlib:\", mpl.__version__)\n", "print(\"statsmodels:\", sm.version.version)\n", "print(\"Pandas:\", pd.__version__)\n", "print(\"Seaborn:\", sns.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exponential distribution\n", "\n", "The pdf (probabilit density function) and cdf (cummulative distribution function) of an exponential distribution with rate λ is:\n", "$$\n", "f_{\\lambda}(x) = \\lambda e^{-\\lambda x} \\\\\n", "F_{\\lambda}(x) = 1=e^{-\\lambda x}\n", "$$\n", "\n", "We create two exponential random variables, with rates 1/2 and 1/4:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "([2.0, 4.0], array([ 2., 4.]))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "λs = np.array([1/2, 1/4])\n", "expons = [stats.expon(scale=1/λ) for λ in λs]\n", "[exp.mean() for exp in expons], 1/λs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we plot their pdf and cdf:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jCMNuG4LeIOuVCCEESDjp8T49Usnqj4+j02pYdsdwEsL91S6p22quaubz1Xs8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 16, 1000)\n", "for exp in expons:\n", " plt.plot(x, exp.pdf(x), label='pdf')\n", " plt.plot(x, exp.cdf(x), label='cdf')\n", " plt.axvline(x=exp.mean(), color='k', ls='--', label='mean')\n", "plt.legend(loc='center right')\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting an exponential distribution\n", "\n", "Now we draw some random numbers from the same distributions:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DAHMQnMAoyWQw3JibwrbtAGAO5pzAKIlkMNyem7Jw+ljbv8dENQDwFsEJjJLIUrtYc1Oe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\n6kjJNmgVv79fD868RhvfOdQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for exp in expons:\n", " y = exp.rvs(100)\n", " plt.plot(y, 'o')\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can try to estimate the rate of the distribution from a random samples. This can done using maximum likelihood. For a given set of samples $x$, the likelihood function of λ is:\n", "$$\n", "L(\\lambda | x) = \\Pi_i{\\lambda e^{-\\lambda x_i}} = \\lambda^n e^{-\\lambda n \\bar{x}}\n", "$$\n", "which gives $\\hat{\\lambda} = \\frac{1}{\\bar{x}}$ (although this is a biased estimator $E[\\hat{\\lambda}]=\\frac{n}{n-1}\\lambda$, see below)." ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": true }, "outputs": [], "source": [ "nsamples = np.logspace(2, 5, 50, dtype=int)\n", "estimates = [\n", " 1/exp.rvs(n).mean()\n", " for n in nsamples\n", "]\n", "estimates = np.array(estimates)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IiMjeiQ5Sa9euNQSp8vJyrF27FpmZmRYvjIiIiMjeiQ5S994J5J1BIiIiclWu93A8IiIi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\nERERERv9DSEcBsb0ZE9yAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "λ = 1/exp.mean()\n", "plt.plot(nsamples, (estimates/λ - 1), 'o')\n", "plt.axhline(0, color='k')\n", "plt.plot(nsamples, nsamples/(nsamples - 1) - 1, '--') # excepted bias\n", "plt.xscale('log')\n", "plt.xlabel('# samples')\n", "plt.ylabel('λ relative estimation error (λ={})'.format(1/exp.mean()))\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To show the importance of the number of samples, we draw n=10, 100 or samples from an exponential distribution multiple times and show the distribution of $\\hat{\\lambda}$." ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rrbfi/fff5xeHAU4bGdnqi2AiIiIiBybpRER+ZPfu3a1+VigUeP755/H888/LFBERERER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CzSiYiIiIiIiBSCRToRERERERGRQrBIJyIiIiIiIlIIFulERERERERECsEinYiIiIiI\niEghWKQTERERERERKcQ/+CLx/xGmo4gAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 3, figsize=(12, 4))\n", "reps = 10000\n", "for i, n in enumerate([10, 100, 1000]):\n", " estimates = [\n", " 1/exp.rvs(n).mean()\n", " for _ in range(reps)\n", " ]\n", " sns.distplot(estimates, kde=False, fit=stats.norm, ax=ax[i])\n", " ax[i].axvline(x=λ, color='k', ls='-')\n", " ax[i].axvline(x=λ * n/(n-1) , color='k', ls='--')\n", " ax[i].set(\n", " title=n,\n", " xlabel=('λ estimate'),\n", " ylabel=('Density')\n", " )\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red bars show the histogram; the black curve is a fitted normal distribution; the solid vertical line is the real value, $\\lambda$; the dashed line is the expected estimator, $\\frac{n}{n-1}\\lambda$. You can see the differencet scales on the x-axis, and that as the distribution becomes narrower it is less biased towards positive values - and the estimator converges to the real value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Bias of $\\hat{\\lambda}$\n", "\n", "Note that the sum of iid exponentials is Gamma distributed: $y=\\sum_{i=1}^{n}{x_i} \\sim Gamma(n, \\frac{1}{\\lambda})$ (with $(k,\\theta)$ parameterization).\n", "\n", "What is the expected estimation?\n", "\n", "\\begin{multline}\n", "E[\\hat{\\lambda}] = \\\\\n", "E[\\frac{n}{\\sum_{i=1}^{n}{x_i}}] = \\\\ \n", "n E[\\frac{1}{y}] =\\\\\n", "n \\int_{0}^{\\infty}{\\frac{1}{y} \\frac{\\lambda^n y^{n-1}}{\\Gamma(n)} e^{-\\lambda y} dy} = \\\\\n", "n \\frac{\\lambda^n}{\\Gamma(n)} \\int_0^{\\infty}{y^{n-2} e^{-\\lambda y} dy} = \\\\\n", "n \\frac{\\lambda^n}{\\Gamma(n)} \\frac{1}{\\lambda} \\lambda^{2-n} \\Gamma(n-1) = \\\\\n", "\\frac{\\lambda^{2-n} \\lambda^n n \\Gamma(n-1)}{\\lambda \\Gamma(n)} = \\\\\n", "\\frac{n-1}{n} \\lambda\n", "\\end{multline}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exponential regression\n", "\n", "Now we have some measurements $x$ and $y$ where $x_i$ is independent variable in $R$ and $y_i>0$ is exponentially distributed with $\\lambda_i = g(x_i)$. We are interested in $g(x)$. \n", "\n", "Since we know nothing about $g(x)$ we will attempt to approximate it using a linear model: \n", "$$\n", "g(x) \\approx a x + b\n", "$$\n", "\n", "For an indepth description of this approach, see [In All Likelihood](https://www.goodreads.com/book/show/2019845.In_All_Likelihood) by [Yudi Pawitan](http://fafner.meb.ki.se/personal/yudpaw/), Ch. 6 and specifically section 6.5 (pg. 163)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WPSuNYUT3EYuLk88j/+77kX/wr6D+1m8h+Zrfwf7feClOF9B0kNUvEGbTY7Qz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\n0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EMsszsNQGi25sF+PbnX9P23T1obtXm/c9rC3LnE2FyW6WigdTYyU4GR64cwnBBeEKGl\nEUoBfaG/VpTxyzO6tvIC46npJwFFtkuu6HslgcfEIpqAQRTBdCO09BhvHrfQrsmoqyKGc8KaXkRM\nSY31OfT5l2WtZraPZ0NjpXRWk0UokoCwoCPbD2K4fgTDWfoRklVUMLW9JHPZa6gJTq9qMMPOvbx7\nzDZovCyoxVaYo7t37+Kb3/wmvvnNb+JnP/sZ/vmf/xn/8A//gG9/+9v49V//dXz961/Hb/zGb0CS\ndhM8qKq6EgTR/1fV271LL2uz22QTvunp/rbkT8h3F7MLq5KAk7a64vjYBZ1HXPdJ2Lb3qGzTu+2y\n6bqTPxUvLvv8LpwOvW+skwvDGFPbwwHTxFCEh1hnRQFcVY6Z3OeQlZSgtnid3bCz2U5RIC3NhhNA\n4gFZEis3GGzKy0Vek3Dc0ZPreNjTVzbQbcRTSUmcw0fX89TGKQqAKqW3CnYtZO87e9hxPCLUnBe8\n0UPTaVfPbeMvW39ffn0P//5sCtsL0NCkRM5kv66maAcoq7cXxP9/e2cfJEld3/93z/Q87szu7O0u\nt3twJ3Aia0B+AY4cyBUVxRAxXJSziioSU5joeVZK+EORU1AIR0i8wsMyiBGhKolPMdGUUXwoUxCq\nUgVGchAICoIicAe3t3e7d7O389jdM/37Y/bb++2e7pnunn6ans+ritKbnen+dn+fPt/PI2qSoglG\nDH4M9hr/bG6ZCcZKe00cE7ujLK2u+8rxChIJAQsna6grLaSTSRw7JaEpn8RFZ091FYY+c3oMAEzX\nDqea/aOGjPJAR1Bsyk0AAk6fyuvK21QbMlbqCibHUnh1qVNCZqXe1Ma3pHRqqbFXaxQQmUBl5hzP\n4OeX8R0b/a6CcrUYyCFbkiQsLCzgjTfewNGjR5FOp5FMJnHHHXfgnnvuwYEDB3DxxRcP3MjZ2VnU\n63XUajXk8x0V5bFjxyAIAjZu3Djw9Xvhtz+Qk03YK6HG6/InPGzg9jqJ90otEJSzXT8GfUf8xtbL\ngXPQ5+XHZb9Fo5hNYXGl0dfnY9D2sPfGL3KZVBJqTUCTy7RstwSLXfoKhxbmrvFcSisVY+aIyjY3\nfsNmAoDSbmGx3ERd7izqGTGJcr2ODWMZLMDfAAN+jG0oZL1bo1T95rR0SsL0uHdeVIoAACAASURB\nVHWqDeN7NwpA04U0NrT1mn8+RYLZO7Fad/mIpmKuU1tPTAqa8PDqUlWXdoCPBEuLyS5zES/M9Br/\n7G9mfj1iQgAE8yhLs+surzbxwpEVvHa8hpYKQAVa7TZmilmsNhT8ZuGUltQTYP5njb7rjl3Nvoru\nAusAoKoCcqkExnNpjOfSOFWX8PpyHSdrEtJiAierMupyC6VcWqcVNAozvBZVabdweKmCOjdGJsdS\nePtbZjBuyJHBJ91l7TMmLQ7SYuNYOGq323jiiSfwox/9CI888giq1Sq2b9+OW2+9FX/4h3+IXC6H\nWq2G3bt3Y+/evXjkkUcGbuT8/Dyy2SwOHjyIK664AgBw8OBBTE1NYfPmzQNf3w5++QM52YS9EGr8\nKH/CU8h2qiqb5URhRSzlVjtyDujGKDsv3lEvB84qBnMutBKU+eRwPKlkJ/yZr1Zu5fMxCEaHXKPT\nKVtGnZRgsYOxJpVZNnLeFMWoNluoNRWkxKRl0kc2Jowb9vmbJ/DsaydwqqagkBM7+XzkFlYbCk5U\nmxCTiUADDAZdoyoNWVcMVVJUtNb8xZRWt7mQzQWzZ+Lf/2kTWbxxst71HUavd2J8JtM8YuiE4TPn\ne15zxSLBBABv3ljASU4jwgszbPxbrUm8ZsNYz2xiLIVcKmkaZWk2r369eAora7mqgI7QBnTKyQCC\n5g9k9q4HnaNMkDUrGiugI6C01E6KjXJVRqvdRlpMYMNaotGG1EYZUmdeS+vtZPNcTEK3xry8eArF\nXEpXR/BkVcYTLx3Hu//f6dq9jQEURtMxe5dBulo4Fo4uv/xylMtlbN26Fbt378Z73/veLu1NPp/H\nZZdd5riemRWZTAbvf//7cdddd2H//v1oNps4cOAAbrjhBk+uHxZOBBWvhJogCv7NlnJ4bblqegrn\n7xEFB3QzIUNutQAVXUk+139j7x31cuBkjqBuFzwrQTmVFLrMlmOZJCSl3bWwW/l8WNFLmLVyyJ0u\nZrT8OGIygc1TeeTTSc9ylxj7b+FkHUuVhuaAC6w5Vk9mLTMgq2uRRSqErqSPZpsbG7eVhoymAp2p\nhm3GktJGU2mZBhhE6VDAw68N7D3wtRnNsk4bk8AazelsDFgJ7U6EcjtJB8cySVQBnYA3W+pEtBVz\naWRToi5ajf1m02S387NRu6tpDrnrs5Iehaxoy/2i0pChtMyr1jfkNhIJIJkULN/1oOslE0R57V61\n2cLJasf/abXZEXYakoyxTBKZVLZLu92Q2pgtZVGuro+JuVIO5VoTq/V1Z2pJUSAmElruJt6kfrIq\n42i5jsmxtGnG/tlSDm+ZG9eeO4y54lg4+qM/+iO8733vw/nnn9/ze3/6p3+KP//zP3fdMGP4/S23\n3AJJkrBnzx6k02ns2rULu3fvdn39KOBEUPFKqAkiAm88l7I8hXt1D68wEzKUlorjq40ukwjDTvt7\nOXDyjqBuFrxem4TcUnH2afrwdQCaD4Ndnw8eO+ZcK4fcpUoTW6YLrhyE7WDWf5Ks4oTCLcbCWo2o\nHuUh5kq5rrIdvU6qlUYnZxPTrPCwsOxWS9WZDu1swE7xUtAyG9e8ycTMn8aYBJYv1qtpSXsI7U40\nAXbWQN70yRcPZ2lEmMaPfZ+9N7OoMK+c6I1tzKVFFDKilhWbkRQEJNAxzfZ612bYHQdMs68vXtzU\nFdQGgKYCVCUFM8WsafFyqB0BkU/vAADPvHZSW/OXVyUcO9V5RpbdnWlXlbaKxZU6yjVJe+9RyG3E\n4yrPkR0mJycdN4bn0Ucf1f07nU5j37592Ldv30DXDRPjAHYiqHgl1AQRgcfuAaDr9BOlKL9eCeug\nCqZRR3bb38uBE1g/cbkRFI2bhNGExE7zTOjiCwMz+vl88PQz5/ZzyK1LiisH4X6YRUYqbRWnTWTR\nVFoo5VOas25dUkz7k1HM6Z2crTc3fXb3pdWmLlQcWM+/s2Uqh/lNE442YLv4EVRhtjYwYReC2nMu\nZFJJnLEhb1oMFjAX2p2uA3bWwF4CTCaVNEREdv7XqVbeqRO92TOcOVPAyWqn8DBjLCNiqpjWCSl8\n0s1+43H9Or19VvmyIIKgQlZUFHKizreHL+Br5p/EUkTwztXLq03dupLP6H/TlNZL3wDAoeVOPipm\n2o9CbiOeSGXIjiu9BrBdQcVLoSaICDyv7uGnCaLXSXTOJKLCSft7OXAC64uLm2di17aKCDxrJm/6\n/X7XM8POxtHPIXfL1Bi2rDnMml3fbf8a78tr6TJiEtlUUttkcmkRskkRTUA/f/ptbsayFtlUEoVM\nCpWmjFJ+3el4ciyFbWdPaxuU175+fgVVmM1bXY6lNczmAtOKGA9E/N95od0pZloPvj12BRizdllR\nlxQslOuYK6FnmL+dMcyXzUmJCVx45ga8ulRBpdHRqk7kU9h6Wqfafa3Z0uUryqcT+NWRFV2EoJO6\nlMD6mOHn5/KqBKhyl5acL+Br9E9iplJj/xvXkQ2FDAoZURMATzVksOzvhWwSY5kUFlfqWFipY6aY\njURuIx4SjgKg10LmRIjwSuAIq8Cpk3v4mW5gvY3WQkFKTODcueJaW5y338yBc6UmQWmrKGSTpouL\n02vzJgwNQcWxU01s4HaGQQTrXhmPAb3pzgjbKDcUundLL/rXeF+zqBmet8wV+uaM6YWZgNPp2462\naLqYQTKRMC2t4aWvn59BFYOkovDTZG9VDLWUSyOX6RSOdYtZu4wHj1N1pWt82h3Dxu/xZXPOmR3H\niUoTKlTMz01oh4inX1lGKZ9CSsxo867abOHFhVNIiwlNc2m3LuXRch0LJ+u6edxJqAkcXjbXqq4X\n8BW6fKxYMtB+ZYjO31zCLw6XUWnqBaPzzyhprjMNqY1T9XXTXVNpdfllhVFGioQjn+m3kDmJ3PJa\nqAnCIdrtPfxMN8C3zY7Q4PYdMWG2zDQWQmch3jg+eFHkmWIWLwgrus94Hw/jBulUsO6X8Zjhtjab\nm/41jnvjfXktnTGseiyTxIZCdqCQdzMBhz+Fb5zIYq6U811wCCKows28HVS7bSe5J3vfLMy8KdVx\nztwEXl2q4vhqw9XhyazdxizTQPf4tDuGjd9j5VgUzWG/o+E8vtpEbc3PR4WAcZPot5cXK5gZ7whM\ndupSslJOR042OsWOoZ/HvIbIqPErjaW0/eZERQKQ7miD1lIq2ClDlM+IeMd5GyHJbby6VEEuLWJD\nYV3DyuaroHZ8PU9UmpBabaRFAUurTVSaMuYmcqH4qZJw5DN2FzIni1EUorz8xO90Azx+mhiZMMtO\ngWxRA7wR9Ho5vRs3SLclYKwyHgP6Dc/Je3Tav71O6Mb7sqgZPqza2A6386dfWQsrwYjd0yuzeNBl\njZpyC798vawzZ1lp+dzMp34aGLPxUq7KEJMCVECX5drtnOLbzcpXGHPsAOvjk/1/M/gx3GusHyk3\ndGsC+225dso0eIC1iwkydupSsmcyfpefx+saonXY+2c11NgzHFquQUwKgCpomlk+Mzxg7pheaciQ\nTSL0mFa9mO8kmGSCkS51QE0KxU+VhCOfCXohM+KX6SxoXyDe6dipCcI4SfVO8f6aGFnSNbNTIL/Q\nOs2OzpwarXw8rMaV3URxdh2s1+9n/z3acSjvldsG0AuXVoux1/05qIDjlSAeRFAFoym38Njz5qU6\nXkG3IOJmPvXrX7PxwpuTea2H28MT3+7fLlY0Z35jOg/mg5QxiSbjWS/Qan44Ngo6PEpLxWq9CTEh\n6A49TFPEhJJ+dSmBdQHO+F1emOI1RMY+Y0EEvJmxKbewUpewaTIHqILO/HX8VKfkyYZC1uD8bj5m\nU2ICbz19HKV8GrWmghNVSat9B3Q0S6V8hnyO4kiQCxmPXz47QfsCmTkd59NJFLKizjHRuAh32/nb\nmkaBLXh8u/3SxvXSHMpKG784vKLzjXGSHf34qbruefhrDDKuBnGwtvMe7TiU80KgnRO68b5u+7Pf\npj6IgOOlIB5UWaNfvl7WCUbAuuYhJSYtNy2779+OFtEo6BvTYxh9y9yaFZmW5FRDRrnW+W9deyR0\njdXjq40uMzNjPXGouRDFQtsbcgspTuPDCvRWGzKSLE/XWhvSotBlLub9Getr12IHl0pD0d3T6Fgt\nK21MF9fHjLHP+L7hf6e0VUiKilePV5EWE7r8RQ25hZcWKrj0nKzuOk253bNOXKWhYKqYxVQxa5rA\nlfVpkDnCSDgKgDCKkfrlsxO0L1DX5rmWZZt3TGTwxRaNZSLYdepyS1Mne91uM3ppBhfKdcyMZ5DC\n+nf6RZrwlPIZlGtNzIzr0+s7GVfmIc/OHayd0MuhXGm38OTLy9ozGes4GfHKUdOu0O+FgDOoIG7M\nJuzlZmHMFF+uKabfY5qHQd+/HbcDPskkoDcnmZXscKuN72VKhip0+7KpgqmvjzH60Xg4lpU2jq10\nBJqMmNQJYQvlBhpyS1ffjE/WOp5LmSbTzKYSyBkOVMb3YDzkvPX08a46Z3z/s74xaurERCdJZaut\nAtCXBAI6hXQrDRmpZMJ0TpnViZNb3QlIeQRB9TxHWD9IOAqAIKLDePzy2QnaF+iXr5e7BCPmA8Ac\nE9m9WYbX15armClmdac6fnIbbfN+h4laaQ7rkmKaO8asTVbvnTl2skRs5ZqEtqriZFUyLe7I00sY\nCELbaeVQrigqTlY7z55Li1q+FbNNCPDOLG0l9P/y9bJpMeQw/P78LRhtnile74miR1asIxXtYtft\nwJjckeVeMvoEuR2fvUzJK1UZEICJfEp3v9JYCi8vVgG1gpnxrGU5HOPheKFcB6BiIpfWBIuG1HFY\nVtWOdojVNzMmazUKHCzb95kzBe3wwB+wzOZxLi1iuqjPUWTW/wI6yVONmrpMKglBEJBIdj5vtVRN\nkmDCY1Nudx1QWdtqzQreNN09l2Wlras/yRjLJHUaJzMfJz8g4ShA3CyobgQqv6JZgoiSYWRSSbxp\nuoCa1OpyOK5LSmcxW1M9L640ILfaSCcT2FDIICPKug3VOLnNqkb7udGZaQ7FpNC1sPM4y47ewjOv\nndCZP6yKOzL6aQC91naajWOjQzkA/GZxdc3nQl47QYpddZz49rgV1PrV0uNNfjWp1dMJOSj81Npa\nZYov1yXTPF1AR1gYVFC2K4gbD5hnzeQHSstgxJiywpgLqFMjrjNfZaWNw8tVvHGyDrnVhqwoqDQV\nnDNbxFkzE13jg2/70XIdTVmBCgHJhIDligRBkLBhLIOm0kYhk9StC93JWvURZFaJTdkBy+48Nut/\nFYKlM/TmqSyWV2VIrTaSyY4mjz+8mpnDzeZUau23TBt2/FQTEBq6mo8zxSxeXaqamuF5HyevIeEo\nQvALtpVK0s7i7JcTuBfXdSLsZVIJUxWrpKhYrkgojaWgyC1NJSu12jhRaWJ6zezDtES98t90agvJ\nvmrzzDSHwHpJD/Pf2M+O/r+vntBVvQbMizsy7GoAvdB2Wmk7ZoqdxYz1r6y08eujq53FER3hsaG0\nMDeR007xRodTNxuh3Vp6C+U6VuqSTlALwgxrhZ9a236Z4ktjKZSr0G1Kk2MpnHdGqe917YwdpiU2\ni4Yzwh8wB0nLwOiXsoLlAuJZKNc1wQgAchkRYiKBhXIdpbz1+ChkU1iqlLWkjSyTelNuAQLwpumx\nNSds8/WdrQPriVfNNc+MExUJYxmxr/nVLNM801aV8pmOrxMnIHfezxjGMg00ZQUbJ3K6w+tYplNf\n0IjR3ymX7lgAIKjYMlXQCaQQgHPniihkU1qGf6NgBJj7OHkFCUcRwK6zrd3F2S+zyCDXdWMSsLpf\nq92GIKjIiElUm3qfCKnVhigmtMksK22M59Nd+W/YKYSZto6vSr5rBoyaQy+yozckuUswYrDijkYT\nmxMN4KDmIyttB9DQPRNfpywtCpqpgWn/jHWc3I5hO7X0TtVkHFoLKwb0gloV6DJ5BhEN6qfW1k6m\n+PHpdROPWZJL/fWcl7RQ0YnMkhQV+bRqex56NT57payYLq6b7+uSgpWapAlGbKwCncPY0mrTUlBl\nRWeNsOfMpZPIp5OmhkwmcPB+N3VJMXUKZ2sbr1ViB5JOXxtTZbR1vzMGSFz65imcOTOGlxYqOrNX\nr8zpvA8Rayt/3ZSY0H3Gt9XMh8z4ex7m4+T14ZaEowhgXEjqkoKTVVnnPMywe0r0ywnc7XXdmgTM\n7lfMidg0mYfSUiEm9FqhtChATAiatoFpiYz5b4yVue22x0u8yI6eTSVwaLlueY/VhoxZ6IWjoNJL\n9NN2MNPI0moTDbm1FjXYKccBdDbOalNBIdPE5ql8Xz8qt+0x1tJ7/URNE4zMBDU+ud4g/j9mglU/\nTZsVg/SZ15nincx1YzmWXBpQEUw9LacpK145XsFKTdZC1/l8PAxZaeNERbKIoG1blhMCADGRwHln\nlCzHlfFzNm6N/nj8oY+16YWlKl4QVnQ5ythYZf1vpZlZKNdx0VlTuPQcc02dVR07/vDDuzawAypf\n0Ha1Lne5T/A5AMWkeY1K3sfJa8saCUchY7Zg85lPzWzKdgaCX07gbq7bb5M8Wq5bagSsTFJQ0Yki\nAZBKJjo+R2uLVUpMaPkzztiQ78p/Y8dWH0RODSfv0uq7R8vWghEAFC3CrINIL9FP26GqAuY3TeDQ\nUkVbGM+aKej8OYBOnTRmfrASPNzkV+JhGpK6pOg0WPzmx+Yjn1yPx65w3UuzYlfTxjNon9kdD16F\n5vcLNDD7rtl9Bl3XnKSsqDRkzBSzSCUTaK6V0cgYzF9Kq43FUw1tgzeW22BrlzGkHuhoaN4yV7Cc\n51bvil2LrWcs0IM/9PH3MkuYWch2ataZCWwsOtgqZQZgrb3jxzNzbeD9ktKioGXF5iPe2Hd4of2c\njeOd55DW+4y/lh/5Akk4ChmzBZv3kTFLEsYPhH6LhF9RNU6ua7UpMTXuqZqkJUm0On0b71caS2uR\naFOFtJY8jJ0k9DmM9NdhJ7he7Q0yEsnJuzR+d7aUw+RYqisXDdDxC7HStrjVADr1GbPz9w2FDI6v\nStrnYjLR8SdrqRCTAs46bQxySzUVPJyYcOxoSE5UOlXls+mkLhmd1raEuQM3w45w3SsyzlhElP+7\n107IPF5pmp2Y/3p916rgqxvzvNWYtZOywjSKKwGMpUVd8kMAqDRlzOZyEBMJHOLSVCyUO2H4WqFx\nQCeEpUUB08VMVz1Efp5bvSsm0M0UMxjLiKg2Zd3aZjdh5mwph9eWq13CRymXxkqtc6AcJLFmU26v\nmQzXx3cuLXaS4K65SDDMsmJPFTN466YJLK02uzRMfuULJOEoZMwmKK96NSY4YwMhiGSMXmG1CLET\nTUpcP53bPX2zxRxgBRSzujxHvSZL2FnLvebtb5nBEy8dN41Ws8KpBtBLnzH2W7NcMGwxz4hJZER0\n1bYyCh5ONDh223N8VUIuLVqe7u0U47USdntpS8o1RZf4zpgMj2na/PBz8krT7GRuuSn46qS/+41Z\nO+PBmFsH6OQXk1ttKK11J3VBUDFdzK7lKtKPG+aLBHSnJMil7Qmh/d7rhkIahWwKmVRCd9CwmzBz\nPJfSRY9C6JRoYU7qaVFATVJc167rmMdEXX/UJQXT4+muLNtWWbHZO/LjcGAGCUchYzVBS2MpLK3q\nTwv8QDAOsiDyPrjF7Bn5+kXGDcbO6XuQxTwos1JQjOfSePf/Ox1Hy3WsNmQUs9YaIyN2tVZe+oz1\nygXD+yGY1bbiBQ+nZplKQ8ZELoVaU9GdYPn2aGMD3af78VxK85HqV4zXil7akrTYSa4nJqwzh7M2\n+qXZHPTaTuaW2Xf5gq8A1rQWzY4WaSKLpYpk2xxuZ8z2Gp9sfBnrF6bEBDZNdgIEJKUTNQZ0hGor\nx2FZ6YS2Oyk07ua9Gr9nN2Em+x0A5NLQab7Y7wb1yTSu2byWq1dWbKvf+50vkISjCMBPUD6KavOG\nPJS2CrnV0uzWwPqmEHTeh0EwLkKSoppufgy7pi23i3kYWcv9ZraU63K+tkuvBWcQ3xC7Cxr7Ximf\nhgDVUivDCx52TTjdGgShp5bR6nQvrW1wdovxmr+P3sVr82kVry3VujdYQcWxU83IzWsz3AYaMMFC\nTAKKouKVYxUcO9XEcqUJqMDcZBZtVcWmyTw2b8h3hby7EZx7jc/lShOHliumfi4psRM9xg4hlYaM\n46tSl6aGwTQ2bgqNm70rRr+kk04SZrLfsQAJ/nnN3h17bjeH00IWOi2XWcqWQepDegEJRxGAn6C/\nOLyiq9TMhtvx1YYmHLFNIei8D4NgXITkVhtvnLR2JvbbtBX0KSSq2DGXeRFGbndBmy3lUK5JtjQP\ndk04VgnuTtVlbJrMm/yuf14qO8V4zeinAZgpZvHaclX3OdugggwWGAS3gQYLa8EFx091NuflioTl\nShPKmmN+uSojm07iyMlOZXhjJK8bwZlhNj6PGhyAAX1Fe/5+rF+Z9p6H19g4WdeM78/pQcNpwkz2\nOz5Awsps3CtaU261ba2pUdfgk3AUMVJiQldri6E/7YST98EL+EXI7iYYVHtGETumh6B9tOyekO0s\nroNovfixwRLRMZwU43XyfJWG0pU5nN+ggg4WGAQ7c4vf6OdKOSyuNLTK77WmoglGAJBIAoAKSemY\n2+pFxdIpd9AxW2nIUCGYht03pDYEqKYaR2BduAP0mhe765rxwGKMerO7ZvHfc5Iw0xggYcQqWrNc\nlfHY8aOmtR6t/JSirMEn4ShC2D3thJX3wWuiPDFGAbuCQ9AnPCeah35jyKvkiU6K8To92ZsV4DQz\nM/Rqx7BhpbFU10IElbaKFhcuKCYFpJNJjGdF1OU2Wi1Vi7xyKzgbMSu6WhpL4Y1lGYq6HlGVTSW1\n1A88rF9PG890JUx0sq4ZXSzMot7cBN04Eap6vTvAPFqTtbWQTemCKHr5KUVZg0/CUYRwctoJI++D\n10R5YowCdgQHoNM3p41nfAsjt8LOYt5vDHml9bKz2TqN6LPKGRNlU4NXWGksU2IC2XQCTVlAUmBl\nNgSMrz13Jp3EeD6N6WIGWzcWsKGQcS04M6xKyhxerkFpqUgmE1DkFpR2G2dM5jGeT6OY66V5yVom\nTOwHf2DpFfXmddCNsa39tJtGeEuGMf2MHXNwFDX4JBxFCCcLYxh5H/wiihNjFOglGMhKG68tVbqi\nus5cMx1FTZC1GkNeChv9NluvCsPGXaPaS2OZSibxpqkx1IqttTpjArA2Blm28mw6gc1TeWwxqezO\nY/fwZdZvCycbWFptoJTPaNcCgHJdwtxkzrexzw4s/aLevHKb6CXQ99Nu8vCO6MZ0Aey5hm2NJ+Eo\nYjiN9ACCy/tAdIiLpquX4FCuNXW+A8B6puaopYroh1fCRq/N1svCsHHXqPbTWM6VclipyxATCWRS\nSbxxsg5BULFhLINsOoGtpxUd9V2vw5dZvzHBpJBJQRCgTwaqCjhtXF8yxMggOejYgcUq6k1pq66T\nMprRT6C3q93kM2D3izIdFkg4ihhelJQg/KFf3athfP9mgoMAVatBZ2RYIqZ4vJgnxt8aNww/CsPG\nVaPab6Ms5lKYm8yj0pBxzmwRcqut5RPqZUZzg1m/McFETCawcTyrFcTlk3HyGMfGIBpEq6g3pdVG\npbmeA2yQpIx8u90K9MZ1I5cWMTmWMl03vLJkBL3PkXAUUZwsjHFdRKNGl19Cn4KOwyC0mgkOTbmN\nV5eqlr8ZRhU54G6e2NUCxC3rup84SWjo9TjrDo/v7hc+cSJzV+B9aNhvTEuLQIWktLtyMAHOioYD\n+qi3SlPWCjJ7lZRxEIHebN04/4wJX8zBYVWDIOGIIGxgdsqyKuj44sIppMVE4JN5EPQbUXedNp64\nbfS9hFi7WoCgHKmHQeC2Q9B+Vb02WGO/8YkTjSYivi9Nw9lrClbqza4cTOvtsF80nEW9rTass8YP\nosn1QqA3CrB+WDK88uVzCglHIROXxS7uGE9ZvQo6vrxY0SXyBIKZzF7hx0YfxXHe70Tq1Ozg54Yf\n1Ok5qH4K2iWg1wZr1m9bN3b6TG6t+/7wfWk1NtKioCUFHdT3hkW9HVqqrDmnO6/l1wu/BHovNX5e\n+vI5hYSjkBimwrFRJcgN17ioWRV0ZEKTMZwVGC5/nUE2er5fUsnuhHFRGef9TqROzQ5+bvhOT89O\n2xDWehSES0C/DbZXvTOr98hHlfHRwkzrZDb/+wkcVveyk5TRLVGJjOz3nq3w08RPwlFAeOm0FyXC\n0AiEsZAbT1lWBR2Z0GQWztppe++K7VHRrrjZ6M365fipOkr5tM4HIwrj3M6J1K3ZwesN38np2e3c\niMt6ZIaT5LpmkVlWfWlVd22ulENaFMAfn3oJHP36zE+TbdhBPf2ePUxfPhKOfMYvp72wCVPzFdZC\nbqegY1oULMNZAfPJHGUtopON3vgMdUnByaqMutzq8sEIe5zb2TCnipnQEzKymmNWZhpAL3C7mRte\nmi6iJOAzvN5gKw0Zzx0u48SqhGRS0DJns7prb9004UjgsNNnxgK9kqKilBc90/CEFdRjJ5VAWHOQ\nhCOf8ctpL2zCElC8WMjdLuB2CjpOFzMYz6V0vgoMvt5X3LSIZv3CtGhWPhhhjnO7G2ZYZgdeYK5L\nCg4v13QV4c3a6nZu2M2UfqIiwSqcPuoCvhcbbFPuBFs8//oKDp+oodVWUZcUTORTmClmISYTujxI\ndgQOu32WSXXe5S9fL0NW2kiLCagQNJ+psN+xG+w+e1hzkIQjHwnCaS8MwnSSG8QG7dUCzi96ZgUd\nre6zaTKHXx1ZsdQiGv0XwtauOMGsX3jTo5kPRpjj3O6GGZbZwZhDJptKoiG1tIrwZm11Ozf6ZUr/\nzdFTOFJu6Iqpbj2tiHPnxrV5E3UB34sN9pXjFby8WEGl2clBlEwIKGRTaLVVQAA2T+VN8yD1wkmf\nvXK8k7F+nMslFKV37BS7zx7WHCThyEesOn8Qp70oEKaT3CAqcr8WcOMJG0QPlgAAIABJREFU0Woy\nGwUjoKNFXK40ICYFU/+FYdAiAubvXdvU5VaXD1YUxrmTDTNIs4PZ4WOulFurpdjSDlXGtg7iI9Ur\nU3pdanfV+Hr52CrSYkIb514elti8kVttpJIJTzbDQTfYSkPG0mon75CYMAo/QkdA0u5lX+i322dh\nHkj9wul4Ddr0R8KRj/TqfKdOe1EiTCc5tyryMBYXfjL30iIeOVHHxFhK810A1v0Xzt9c8rRNfmHV\nL3OlHMq1pk5DGpVxHrYzqhVmh4+UmMCW6THUJQUbJ7KYK3XX9xrEfGSVKT0jJnGy2p33ihVBZe+u\n3/PY2dSYxrVclbUcYuyQUBpLe2I+crvBNuW2ZibOpJJIJRO6GmOtlgpZaWO66Ezot9tnYR5I/WKQ\n8RrEnCXhyEd6dX5pLBXJhdkOYTrJAe5U5GEvLr3ur6KzuHbNRgfq+Shg1i+lsRQuPHMScqsdyXEe\nxfnX63CRS4umghHDrfnIKlP6s4fKlr+RlfU+dfs8PKzdfHJVdkhIiclA/BmtxkImldCZiacKaSxX\nJE1ASiYFTORTroR+O30W1wzsTsdrkL5tJBz5TL/OH9bSH2Hmx3Bz4g96cbFTpgDoOC1PFdJIiQk0\n5BaUlgoxKWAil8ZcaXjMakDvfumEJIfcQI64OhAPqg0zZkrnBQIjKXHd5DWoBkButTXnc2M1euaf\nyb7vtRBrZywUsilMFzNaSQ8xmcDGiSyacgvJpIDzTp/ARWdNubq/nT4L+0Bqht0x1lvodDZeg/Rt\nI+GoB16cKqOquh+UKDyXE8EyqMXFSZkCYD30X0x0HG4BgLe1DuOJcBgE/rg7EHvRB7xAsFKXNME9\nIyaRTScwXVyPWhtUA7BSk7FSb2LMIl0B88/047BgdyycNVOApLTx8mJFE+AmxlKac/qg9OuzqCRs\ntHuw6PU9oybZy8g+ryDhyAQ/TpXDsGG4YZieK4jFxWmZguliBierEioNpZP0bO3zhtxCudaMhSAd\nNYbBudXN4cOPg8qmyRx+ffQUylVZMyEVsklcMjetmzdyq42ZYhalvD0nauM8YBG8TbkJoFtbxRz6\n/dDw2h0LmVQSF2yZxNmnFXqmNXDbjn59F4UDKWBfmDRNY1OV8djxo5gZX88NZ3dvDdo1goQjE6J+\nqiTc4ffi4qZMAQCUqxKUdrsrWq2UT0dio44bYfufOYEdPioNGcurTdMx66eJ8MjJOjZNjmFyLIPV\nmgxVAMZzKRQyIjKpZM97W2E2T/jIRkEAVE57ypKq+mE+cjMWmKbDm/s77zuzA6mbNc3tb+wIk1bf\nY/5khWxKC9Kwu7cG7RpBwpGBYThVEoPhl7bLTZmC5dUmUmISW6YKXXmO+N8Q3jFMzq12Nk+/DnP8\nWsjqhvHXrzRkvH6i5vjeVvOEpStg5mc+Ws0v81HYY2HQvnMjXA0iTNtd48y+x/uTGdPYLK02cWip\n0lMTF7TfFQlHBobpVDnqhK1eNuJmoeU/62xAzq45rITtqxY151Yr+m2efh7m+q2FJyqSq3tbjWmW\nruD0yZwWKu9VniMrwhwLXvTdK8crWFptdiWP7SVcDSKQ2V3jzL7HF+tmZlJZaWvaJFlp4/iqZOmX\nBATrd0XCkYGwTxJEf6IaaeRmoR2mjdoLotJ3UXFu7YWdzdPPw1z/ta67RI6de/cb87OlXPePPMBK\nIA+vRIzzvjOmWnjhyIpp8tgqzCP7BhXI7K5XZt9jkY987Uk+bQMTmPr5JQXld0XCkYFR26yGkSj7\nhLlZaIdho/aKqPSd1SJbachrzvHhayPtbJ5GAYYVJU2LAnJp0dFhzvgu+q2FGwoZHF+VLK/X695B\njvn+ld+923D9Si9i9gy/PXYKDandqem2BssLtWWqYCpceSFM2+074/dyaRGTYymU1sqf8GY2M4Gp\nl19SEIFAJByZMEqb1bDR6+Rjx27tN+5yMEUjCsVv/DABDfrO2CLblFtd5V3C1kba2TyZAMNnlWZM\njqVw/hnu/FYEqJgt5XDaeKaruDL/XsLKx+QEuwL5IBuuW8dqu+/PeO26pKDaaGGlLuG0cb2mjeWF\n6mfGN8OOMG2378y+d/4ZE9qzMDMb03ax57LySwra55eEIxNGZbMaRsxOPr3s1mFtbG4W2mFKi+AG\nL01ATjejfnM5KhotHrub51kzBTx2/KhOMGLRjnbazz87P5deW65iy1QnP9eZ02MA0PX+opCPqRdB\nBdi4HT923p/ZM0iKikwqCbUmoKm0dKWHmnILNYtn9tIyYrfvjN9je+uJiqRpOPnnYhjrMQLB+vyS\ncNSDuG9Ww4jZycbMbh32xkZ046U/nx1H5abchiCoPTUfQLQjVO1snnKrjZnxTkkRY7Rjv/Ybn91Y\nuoNlpgYapnMpSgdJszYEEWAzyPix8/7MnoH570wV0lpWKKXVxnJFggDgzBkBLy6smh4YomAZYWbb\nmqT09UviCdLnl4QjYqgwnnys7NZA+BsbocerU2uvzahclfH0K8tQ17aMQ0tVQFAxN5FDau10bRSc\noxyh6mTzNIt2ZH+3aj//7GalO5hpo99cCvMg2VuL6H+AjRfjp9f7M2ujlhcKwOapPADglWNVlMZS\nmMinUFwbCGaHxCgJtP38kniC9vml0Cti6GClOACY2q15+i1cRLDwfccQoGI813GGtkOvPl0o17FS\n61yHbfbMSZWHbfaANxotlqTR7jM4pZBNYapo7ks3SPv5v/EmDQZv2ojqXOqlRWQCuRlebbZ+C2BW\nzzBXymFybN1pWVwrfjs3kUNdUrBSkzu+SdxYN17XakwFBRPUzp0r4szpMZw7V8Q7fmcWpTG9cBSG\nzy9pjoihgz/5mNmt9d8l+T9K8H23Wu84EasQsFBuYKHcsOUrZtWnTBhKiZ0iLPxmz0xE/Djhk3K6\n1Wh5nZrAzWl+kPbzvzUWmTVqYqM4l+yYtPw2IwUR4Wz2DKWxFC48cxJyq+MnBgBiItHlmJ9NJbGp\nlI20Bt3KLylMzRYJR8TQYmW3ZlDqhehSyKbw+omaZv5i2PEVs9qMJEXVbejGzd4Y/cJv9m43UK8c\nuQcVsgYRANhvAWglPIya2KjOJXsmrZTvm63fAlgvU1gmlcRcCThVV3BoqdplGm3ILSyU65ibzHvS\nlqAI2+eXhCNi6ImCg2EQhH2S8pJBnaBNT9J5Efm0PuM42+wBvYnIuNm7LfTqlSP3oELWIH4k/G83\nlbKaNo/B5lIUx58Tk5afm21QfjxWz1DIpiBA7RKMgI4GUIVA/pcOIeGIGHqi5GDoB1HJKu0lgzqx\nWvW5MVcRq9cFQdU0Sr0EZycbqFeO3F4KWYMIAEwTOzeZ173XVDIR2fEXtaS9YWo7Zks5vLZcNc2Y\nDVDpK6eQcETEhrDVsH4RxRw8bgVR9ju51Vuw4E/8ve5l7HOjRiklJvDW08cxU8xq1/Vqw/TKETeK\n0XL8ezUKnED4449nVDTH/RjPpSwLWAPR9BmLMiQcEUSEiVoOHrdaLLPfHT9VRymf1kLs+esVsilX\n9wpSi+iV1sKukBWGZjRq48+MqGuOg2oXH9VmTOngtRaNP+T4XRw4LEg4IogIEzWtglstltnvSvkM\nyrWmaYHJQe4FBKdF9EJr0U/ISiUToZU2idr460XUNMdhmMP91qKxZ+LL1TDTXWksHQlTq1eQcESE\nTlRPfIww2zeo6cbLtrvVIlj9LiUmMDOew+mTua7T5zBoLADvtBa9NrUwzapBJFGMEl7OlzD6zW8t\nGnsmYyb1hZU6UmIyMqZWLyDhiAiNfiersIWmKDhCOzXdOCmb4RS3WoR+v0slE5gqZjy5V1gMqrWw\n2tTCFhKj5vDsF37kqwq737yeH+yZzDKp86VmonJwGRQSjojQsDpZvbhwCmkxEXp0TFQcoe2oyo2L\nu52yGU5xq0Vw87tR01gwjJtaFITEUXB49nquR6HfvIY9k1kmdWA9j9gwPpsZJBwRodDrZPXyYgUz\n45muOmlBCiVhn/x4zLQKnTYqkFudJHf84s6f7BZW6tgytb6JDdJ2t1oEN78bFY1FP6IgJEbd4XlQ\n/JjrUeg3r2FtNiZXZbA8YsP4bGbE4ymIocPqZMU2dlnp/rtVjSA/sHPyC5qOVkHE6ydqeHFhFa8u\nVfHiwiqefmUZ5aqkfc+sbAbPIG03q41mR4vg5ndu7xUngqgN5qQtYdfi8gM/5nqU+s0r2DOx5Ko8\nLDP9sD6bGaQ5IkLB6nTBNnY+mzFPUCrbqJ78zNT/5ZqClXpT0xA5KZvhFLdaBDe/i7vGwi6jYNZy\nipdjwq+5Hsd+Y8/Ekqvy0WrD/mxGSDgiQsHKbJIWha6ClzxBCSWDmHX82syt1P9pUdAVVnVSNsMt\nbh0+3fwuaiHaQUNC4jp+BEn0m+sAsLzadPze49hv/DOdM1ukPEcE4QdmJ6vpYgbjuRTkVrfTX9Aq\nW6cnP7+j26zU+0wY4jVEpbEUXl9WkErCVtkMIvqMupAI+BckYTbXU0kBktLGiwur2mdu5nMc+y2O\nz2SEhCMiNKxOVr2EjCi0zwq/o9t6ac3mSjmkxc5iztTdhVwSpVwacquFczaOd4XLE8Qw4WeQhNlc\nf/1ELRLRqkQ4kHBEhI7xFBI1dbSdU1IQ0W291P+lsRTmN03g6VeWUcqnkBL10X7HVxskHBFDTRDh\n8WyuRylalQgHilaLGJWGjOXVZmBRWVFmmKJjgopu6xXBVWnIUCFgPJ/u8tkKMtKPsIbmt3uCDJKI\nYrQqESykOYoIUcjGTLgnqIW7VyblhXJdc8o2Iy7J2YYRmt+DE2Tuq6hGqxLBQT0cEXr5q8SRuJ2g\ng85rwrRqrCjpiwurWFxp4PByDYeWK5CV7g2EFvRwqDRk/O+rJ7G02tR9Huf57RS760EQua+0Ejww\nzwTtZ2BI3NbFYYY0RxFglOzbcT5Be53XxI7PFX8/LYRfanVlxo5TcrZhgY31pdUmDi/XAEDLCcOX\ndInT/HaK0/XAT39EY1tkRUW51kApn9b6y6/AkDivi8MKCUcRII51eKyISr0yP/Bq4ba7UJoJ1Vpy\nNqmlmdgohD8cWB8aM5YbBdc4zW+nuF0P/Agl7wrlFxOYGc9BgIo3TY/5GhgS5LropWBpLGkUhQAa\nr4ilcCRJEvbu3Ytjx45BlmV85CMfwbve9a6wm2XJqNi3R0VDNujCbXehNBOqU2ICW6bHUJcUbJzI\nYq6Ui8U7HQaMGwXrQ2PGcj5hJxCf+e2UKK0HvdqiQuja8L0WMIJ4D15qp/hryWvpQ/hC13HQesVS\nOPrXf/1XnH766fjCF76AcrmMP/7jP460cDQqRTZHSUPmFicLZa9NNZcWSTAKCLNNR261ABVIicmu\njOXAekmXYZjffqXUiNJ6YLctfpi/gnoPXmqn+GuxvGrAeqHrOFgDYikc7dq1C4LQOa21222IYvQf\nM451eIyMioZsEJwslKMiVEcds01Haak4vtrQzGd8LSqgo+GL+vz22w8mSuuB3bb4Yf4K4j14qZ3i\nr8UKhTN4rahbrVdU8ttFcjf68Ic/jG9+85vavxVFwb59+7B9+3ZceumluOeee6Cq5pEEAJDP55HL\n5bC6uoqbbroJN910UxDNHgjmr3LuXBFnTo/h3Lki5jdNDLVa0kgcK1V7jdOFkirXB4NVFJHVppNL\ni4AqoC4pANbNnZun8jjrtDH87psmIz+//Y6gjdJ6YKctdgQMv+49KF7mbeK/y/vTMWSlbfrd/tdt\naZG3ry5V8eLCKn51ZAVN2fyd+02kVCrtdht33nknHn/8cbzjHe/QPj9w4AAef/xxPPjgg6hWq/jk\nJz+JYrGIj370owCA++67D08++SQEQcADDzyAXC6Hw4cP48Ybb8QHP/hBvO997wvrkRwT95o1o6Ah\nGwSn2qCoZROPG/20J70W/7lSruuz6WJmKHwxgvKDidJ60K8tfpq//H4PXmqn+O8a/ekAfaFrJ9eN\nWrBOZISjw4cPY+/evVhcXMT4+Lj2uSRJ+Pa3v40vfOELuOCCCwAAN998Mz7/+c9rwtGNN96ou9bR\no0fxkY98BHfddRe2bdsW3EMQfaHNvD9uFsq4C9Vh0W/B7rX4p8QEzp0rAhi+KJ6g/GCitB70a4uf\n5i+/34OXJnj+WkZ/umw6oSt07cZUZySsYJ3ICEfPPPMMtm7diq985Ss6Tc/zzz+PRqOhE3K2bduG\n5eVlHDp0CFu2bOm61n333YdqtYq/+7u/g6qqEAQBDz30ENLpdCDPQvSHNnNrorRhjDJ2F2w7m86w\njfWg/YGitB5YtSUIHz8/34OX2in+WsyfjkWrublulJzzGZERjnbu3ImdO3d2fX7s2DFks1kUCusv\nemZmBqqq4ujRo6bC0d133+1rWwkiCKK0YYwidhfsKJmGvIKc/c0Z5r728tBlvNb5mztmL7fXjZJz\nPiMywpEV9XodmYy+mjjTAEmSFEaTCIIYAewu2HHV9DkRBOL27FbEoa+9PHQZr+X2ulEUxiMvHGWz\n2S4hiP07m6VjNUEQ/uB0wY6bps+OIDCqZS/i1tdRIGpaucgLR7Ozs6jX66jVasjn8wA6pjZBELBx\n48aQW0cQRJyJ2oIdBr0EgahFGBHDS9S0cpEXjubn55HNZnHw4EFcccUVAICDBw9iamoKmzdvDrl1\nBEHEmagt2FEiihFGxPATFa1cJJNA8mQyGbz//e/HXXfdhaeffho/+9nPcODAAdxwww1hN40giBGh\nkE1hqpihzZ7Dy8SCw4JVMlAifkRSc8RKfzBuueUWSJKEPXv2IJ1OY9euXdi9e3dIrRtO6ORLEISX\nRDHCyC9G1bdqlBHUXnU4Rogrr7wSAPDoo4+G3BJvoUlNBAUJ4KPHr46sWDqsx8nnaFSek1gnkpoj\nwjvIYZLwGxLAR5dRcFgn36rRhISjGEOTmggCEsBHl1FwWI9i9mbCf0g4ijE0qZ0T50XeD0gAH368\nGPNRiTDyg1HyrSLWIeEoxtCktg+ZhtxBAvjwQmPeHk6SgdLhKj7Q7hhj2KQ2Y5TrI5nRyzREWEMC\n+PBCY94+Z80UutZS3reqKbfwqyMreHFhFa8uVfHiwip+dWQFTdlcq0pEH9IcxZxRcJgcFDINuSeK\nNZGI/tCYd0Y/3yryu4sfJBzFnFFwmByUYTQNRak/SQAfPsIe81Eav04w860iQTOekHA0IsTZYXJQ\nhsk0FEU/ERLAh4+wxnwUx++ghC1oEv4QnVWfIEJimHyzouwnQiU2hoewxnyUx69bhulwRdiHeo0g\n0N/hMgrYUd8Tw0dY9bqCHvNxHb/DdLgi7ENmNYLAcJiGSH3vnGj3ZzAmJqt3EPSYj/P4jbrfXZTn\nQVQh4YggOKLsm0Xqe/sMg2+L3xFOdt9BUGM+zuM3q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1000\n", "a, b = 5, 1\n", "x = np.random.random(n)\n", "x.sort()\n", "y = stats.expon.rvs(scale=1/(a * x + b))\n", "plt.plot(x, 1/(a * x + b), lw=2, label='model')\n", "plt.plot(x, y, 'o', alpha=0.25, label='data')\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.yscale('log')\n", "plt.legend()\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now try to estimate $a, b$ from the data.\n", "\n", "The likelihood function for $a,b$ given $x,y$ is:\n", "$$\n", "L(a, b | x, y) = \\Pi_i {(a x_i + b) \\cdot e^{-y_i (a x_i + b)}}\n", "$$\n", "\n", "The log-likelihood is nicer as it has a sum rather then a product:\n", "$$\n", "logL(a, b | x, y) = \\sum_i{[log{(a x_i + b)} -y_i (a x_i + b)]}\n", "$$\n", "\n", "We define the corresponding Python, but it will be the funciton of the negative log-likelihood, so that we can minimize it (rather than maximize it)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def nloglik(params, x, y):\n", " a, b = params\n", " return -np.sum(\n", " [\n", " np.log(a * xi + b) - yi * (a * xi + b)\n", " for xi, yi in zip(x, y)\n", " ]\n", " )" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.00 ~ 5.0701\n", "1.00 ~ 1.0151\n" ] } ], "source": [ "res = optimize.minimize(nloglik, (2, 2), args=(x, y))\n", "ahat, bhat = res.x\n", "print('{:.2f} ~ {:.4f}'.format(a, ahat))\n", "print('{:.2f} ~ {:.4f}'.format(b, bhat))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fortunately, we don't have to do this manually; rather, we can use the [statsmodels](http://statsmodels.sourceforge.net/) package. The package has tools for [GLM fitting](http://statsmodels.sourceforge.net/devel/examples/notebooks/generated/glm.html). We need to specify a distribution (family) and possibly a link function (here the inverse function which links the average of $y$ to the distribution parameter $\\lambda$). The appropriate distribution is gamma, which is a generaliztion of the exponential distribution, adding a dispersal/variance parameter (see below)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/yoavram/miniconda3/envs/simarba/lib/python3.5/site-packages/statsmodels/genmod/generalized_linear_model.py:244: DomainWarning: The inverse_power link function does not respect the domain of the Gamma family.\n", " DomainWarning)\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Generalized Linear Model Regression Results
Dep. Variable: y No. Observations: 1000
Model: GLM Df Residuals: 998
Model Family: Gamma Df Model: 1
Link Function: inverse_power Scale: 1.17200700985
Method: IRLS Log-Likelihood: 168.83
Date: Mon, 12 Dec 2016 Deviance: 1220.7
Time: 09:19:06 Pearson chi2: 1.17e+03
No. Iterations: 6
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err z P>|z| [0.025 0.975]
x1 5.0701 0.364 13.917 0.000 4.356 5.784
const 1.0151 0.122 8.347 0.000 0.777 1.253
" ], "text/plain": [ "\n", "\"\"\"\n", " Generalized Linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: y No. Observations: 1000\n", "Model: GLM Df Residuals: 998\n", "Model Family: Gamma Df Model: 1\n", "Link Function: inverse_power Scale: 1.17200700985\n", "Method: IRLS Log-Likelihood: 168.83\n", "Date: Mon, 12 Dec 2016 Deviance: 1220.7\n", "Time: 09:19:06 Pearson chi2: 1.17e+03\n", "No. Iterations: 6 \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "x1 5.0701 0.364 13.917 0.000 4.356 5.784\n", "const 1.0151 0.122 8.347 0.000 0.777 1.253\n", "==============================================================================\n", "\"\"\"" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = sm.add_constant(x, prepend=False) # add intercept - b\n", "glm = sm.GLM(y, x1, family=sm.families.Gamma())\n", "results = glm.fit()\n", "results.summary() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coefs for `x1` and `const` are $a$ and $b$.\n", "\n", "Some advantages for using _statsmodels_:\n", "- Faster (~100-fold in this example)\n", "- Doesn't require initial guess for the parameters\n", "- More general, as it estimates gamma instead of exponential\n", "- Gives more statistical information like P-values (the `P>|z|` column) and confidence intervals on the coefs (last column).\n", "\n", "Next we plot the results." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GrZsB1fUM0najUK9IGJ5Iotk8TJoOfq/EYCRQkuJvpZKR9XlcFWtaQeE6L4Xn\noFHPykJmnmIZqZSljAE5kbwjjSDuyVLEfbJwjjtx9Oyzz/KWt7wFgPXr1zM7O0sqlSIUqq9thmno\nAALeQrCtuWTi97o4OpMhllboi/hJ5fSSwb2IIbGqozTWqJI4MNPKPXL57LLeG7xZt77dezCbKQRI\n94Z9HJhMkVE0jkynUDUDt+344imVuFQwOAGvu2az3kqzZ6tIXNcTLFuya5RqIsE0oPbeeeYxA0SD\n7rKlQRMnIxv2e/C5C94mWZbwWTxmZhxUO2ePNLNcdSIsIy21J65emvWOHO8ehBPhnmyEE9GL1mra\nXhxdf/31XHjhhbz//e8HQNM0/vZv/5ZHH30USZJ497vfzS233FJsgpdIJIhEIsXvB4NBkslk3eII\nnAN3rUtrhZihWTyyXOYBMr0OhiGVGKRmXO/13uDNuvVN78F0MsuekSRj8SyGAQenUsgzaTr9HpJZ\nnVROZVVHqVdLyxckhOntqdWs1zTIlWbYvREf3WFfWYxPK7EaUCdR63a5GIgGGIllq27DNLKmeJVd\nMoqWJ5nS8LolukO+YoPh4zF75HhOJW52xr0UMSDNeEdOFA/C8XxPNorworWGthVH+Xyez3/+8zz1\n1FNceOGFxdfvuusunnrqKe677z5SqRSf+MQniEQi/Mmf/AkA4XCYVGq+hlAqlSoRS/VgDdwtZJX5\nypZZNN1A0+e9I9bCgqpWHpwc8sl4ZKlm0LBJIzf4Qt3647M5tHweVTOYTuZQ5pYOR8kAoOsGOU0v\n8Yq4XRJIpenzVsFhvm6fPTvNsD2yhKLli41hrd9rxIDXGpisBtJJ1G5dWxCc1cSRdRvm7/C4XZy9\nvpsDk0mSWQ2PLC04hqydOZ5TiRc6417MwPFmvCMnigfheL4nG2Ule9HaycPZluLo8OHDfPKTn2Rs\nbIyOjo7i64qi8OCDD/LVr36Vbdu2AXDLLbdw5513FsXROeecw49//GMuvfRShoeHCYVCBINBx/3U\nwiO7SqomWwl43aia800YS+eKsTgmqZyOR5bKHuBKA2ijN3izbn1ThCk2YVRAAgwyqo6uGyV3S2fI\nQ8Ajl4jGSs16rTjNsI9MpxdkwCvNjvsi/rl9mkUZyw2oKWrr8W5ZP+MUQ3bKQEddMWTtSiOG6XhM\nJW73GXej3pF2/z2t5ni8J5thJXrR2tHD2Zbi6Pnnn2fTpk1885vf5Iorrii+/vLLL5PNZjn33HOL\nr5177rk2i6y4AAAgAElEQVRMTU1x6NAh1q1bx9vf/naefvpp/uiP/gjDMPjc5z7X9HHUuolOHQyX\ntQGRMIhWEFSqbrBxVUGo1RqEGr3Bm3XrmyJMz+dtwqhAh9+DS3Ihy/NeMKdsNROrKKmGOcNuhQG3\nP1SqlueVyRSvSPFiYLj5oNVjQOv5TDMxZItBK2ZazRimZu+3dpoZ2mn3GXej3pF2/z2tRqS3F1iJ\nXrR29HC2pTi6/PLLufzyy8teHx8fx+/3Ew7PD1J9fX0YhsHo6Cjr1q0D4DOf+UxT+zVmZ/nP7/0t\nG877n2xec3bNm6w77Kc77C95GHNqvmJrEJiv1lzLKDV7gzeetVQYxGWXC4/sKsnGA/B5ZVZ1Bjhn\nQ/fcK6V1jjoC3uLvlySD8dlcye+vNcgu1IA7iStrLJEZGG590JwMaDKrksxqxf9rGdnFmp3Va9hb\nOdNyMkyTiRyxtMLWNdGqx1Hv/daOM0M7K2HG3Yh3ZCX8nlZifXaciu+eSKwkL1q7ejjbUhxVIpPJ\n4POV3vReb8FLoyiV+4jVix6PcX/+56jP/YL+n7j5vc7t/N55HwB6qt5kpQOEWnUfjRikpbjBTRGW\nUTR6wl6mkkpRIHndEp0BL4PRAN1hb01BVqsdidPAv1ADbhdX9ppD1sBw64NmHnNO1cuO2zzH1Qb+\nVs/OGhUPrZpp2Q2TtXVOTtWZTioMdPoX3AqlHWeGdlbCjLsR78hK+D2tYCUI76VmJXnR2tXDuaLE\nkd/vLxNB5v9+/8LPXs7rQvUWBuOxkMbD2q94+Oe/YmMiwHkDv8frt/8hq8I9NWfSrTJIqp6nL+In\nGiztzVaNZh4GU2xNzOZwy4WGtLIssaYrSEfQW9dxV1P/sZTKb4anygLUTQGykPNlF0/2mkP2fmv2\nB20hg3YrxWsjx9HKmZbdMI3EMiSzalEk63mDeFpdUCuUdp0ZOrFSZtz1eOySWZXOgId0TnN89o4X\nVoLwXi7aubK8Sbt6OFeUOBoYGCCTyZBOp4tB1uPj40iSRH9//4K3r3Q4B9Duj2TYn3qMh574L/6f\nPa/He8kOPGedVSwfYGehBrbeas/1fsdpQLO2v/DILtZ0B1nV4WPPSBItny+pVF3PcVdT/yOxDNGg\npyS43Wq8FnK+7OLKWm/Jqd+a9UFb6KC90EKK5nfM/dV7HK2caVnPh+l1s3oPzVizhbRCadeZoRMr\nacZdiXJbICFhMBAN0BHwrLjfU42VJLwFzrSrh3NFiaMtW7bg9/t57rnnioUen3vuOXp6eli7du2C\nt+91+xgIDTKaGnF8f92BDNPf+h7J+/6VjlXdBC69BP+ll+LdfjaSa36QWaiBbWYmVM93klmVREZl\nJJZB0YyyGk7RkJez13c59mKrRSV1bw64Hnd5DIDVeC3kfFnFlVlvCcko1qUysT9o1kHbXqfKfL+e\nQbuR2ZmTiFV1HQzKGu+axzUSyzAYZcFLkU7n12qYFM0gp+oly6rW8g3NtkJp15lhNZZrxt0KUeZk\nCwwkZjMqQ13NZe62KytJeAsq044e2xUljnw+H+9+97u5/fbb+fKXv0wul+Ouu+7immuuacn2Q54w\n33z7veyZ2cNPDj/Jz4/8lLgSL76/er+Xo9FBAALZLGvv/xbee+9DHhzEf+klBC67lOyZp9DpjwLN\nGdhqM6HJRI5Dk0nHxq/VZk/TyWwxq86s9h1L5wj7PLhlV7Hlh8ctMzyRZE134wY07PcgUViCsTbg\nVTTD0YNjYjVezQ5IdjG6oS9YlkXo9KDF0goHJxLMZrXSytYemcFoYFEGbaeBS9MNJhLZkpYr1tgf\ngNmM1vRSZC2vommYMopW7C9nFrO00mwrlKWeGbaj16fWMbUqbiaZVZlM5BwbYR+PnhT7M2qf5LSj\n8BaU044e27YXR/alq1tvvRVFUbjxxhvxer1ceeWV3HDDDS3d3+buzWzu3syHz7yOF8af5wd7fsyu\nmV+z/Ya/wXfuXnJPP0PmxRc5zGo2TR1EHxkh9U/3c/D7/5vPfnYLm1Ih3tC7nQve8F7W9GysuPzm\nhNNMyDpQqlqeiYRSYjgrzZ5MQ/G7Q3EiAU/Ri5NTdZJZHUXLFytfZ5U8sxmFQ5MF42pfVqtmoE3D\nrmgGsbRa6o0Kugl6KxuoVhovq7iyZxFaH7TZjMIv9kwwk1J55WicrKoT8Lrmfqd7XjwuUYXjgNcN\nhlTScsXq1TNfa3YpspZX0WqYVM3g4FSyRCzCwlqhLFXsSzsG5tqPKaNouGWJU/o7SjKqWhE3k1N1\nXjoS4/BUuviavRH08eZJMYV3LKWWVbzvCnnYuqb2uWunAflEp51ipCTDMCp3zTyBuPjiiwF4/PHH\nS15PZlV2jyTQ8gpu13zMjJFMknv2WdY8+Z+4f/rfoKo89j/6+P+uGCr5fn9K5lz/Zs7bfgVnrH8j\nsqu6kTb3Z8X09gCs7QmWCBdzULN+x55xhASdQQ8hr5uppEIqpzGTKgSy93X4igOhrueRZRcDnf6S\n+CBzP5WwZ3uZoiwadLN9Q49jFls92610fhZqyH70wlFmUio5VWc0liGe0dDzeQJeF1uGosUBZeva\n6mnsjR7bVCJXsczDbKYQ5xOcu7aHp9JlA5vJ5sFISTHKWk2J7fdTpW1BYYB94uVRZlLzWZfWZddG\nrpeTWFnM2JdW3metwjwmuyfQ73Vx2pzIVfV8Q9eo2r4mE7kScWTuy/RK1rutlUQz96w1xMBJsJti\nWginE5e29xwtN6ZXxiqMAKRwGP+FFxJ+72V06RmyP/6/PJ/4DqCVfG4spPMoL/PoCy/T/1OJO7OX\nEPz9/4l74wbH/dmXIKyp6fblKaub3PodqxGWZQm3q7B0llNzgFRo/TGHWfnaFFEy5Rle1dzxTt4Q\nsxCiMfd+K9aTa3kF6jVio7FM0YhqeQNZdtEd9qJoOnoewn53MS6j3ll2vR4LJ6+LddBc2xMko+jM\nZhWiQQ+rLDFT1uWCRpYiG43J8HlkLjx9gF1HYiVLpM14eezbgMWLfWnHwFzrMdm9Glklz2QiB1Cz\naKr9Gjnd6/amyvGMgqYbuOcC6jOKRm9kYU2d2xVVz9PXESDs95QtJ9qvvfVZtTYUNychpreums06\nUcsDnGgIcVSDaoHGimag6nlc0Sj6jncw9l/fBU1z/DzASa9Okfjff0vi9r9F3rAB/4Vvw/+2t+G9\n4HxcgfmB0Ppgmqnp1sa3VkzDaX5nMpErEVPRgJ/ReKFXmGFISFJhADQLPprZSKaIqhQfVEko1DP4\nAg2XJLBTadlh98gsXrerbiOWyM7PLq0i0TvnnbE6UutdQqp3ScQp9sYcNN0yvDaWYHI2R94wkCQ4\nWdPpDfuYTCglA2vQKxP2u+sy0s0EQ/s8Mts39DQ9a86pOruOxEq8IfYBqNVipR0Dc81jstfeMlG1\nPKmcTjRY/djNa1RNhJv7UrU8mp4nllLnA+tlF2u7A8dV+r4V87db+1va3zevvXn+rNfEjLk0vWup\nXOH+tXqUzNdFeYBSjmfPmhBHNbAPaNaZvt/r4uhMhlhaYagrwKfPvptdUy+xJ/4bds/+loQ6U7Kt\nbS/OFv/Wh4dJDQ+T+udvgc+H77w3Ir3tzby0vYftZ76zuFw2nVSKwYUZRSOTVkpmRqbhNONGDk0m\ny2ZPZhwQQHfISyqn0xP2ksyp+NxyUUTFMoqjALPup97XzXPl1IC3USNdzSuwbyxJX4evzKNWyYhF\nLA+wVSSaWJcs622H0YjHwip85w10npcOJRhP5NDzhWPRtEI7l86Al57wfGyK3+vCQGqoEWqzwdB2\nr1S9hnB4IkksXTpJsA9ArRYr7ZgRZ+7TXnvLxPTQemRXXdeomgg3kyhGYhm0vEF/p5+cqqPlDdwu\niaDPWUwfD+1f6r321mfVfk2ySr4Y85dRNFQt79hX83gMam+GdozvazVCHNWBdUCzp79D4YH5xZ4J\n+joCnNyxjZM7tvFO4xpGMgcYTj3P/uQLHE4c4q1//12k//4Z2R//GOW5X4M+d2PlcuR+8lNemvgt\n3+jbiHTw/2VTKsTZXWfy+rMvJ+xfy/BEkqwyP4ib/c3sD2l32MdEorRQ5mA0UDzuoM9NT8RfjP1w\nSVLRm+PUABZqtyupZNgrNeBtdPZVLeDcDFK3zxgrGbGBaICukKe4tGatCh72y3SHfQ3WpGp82coU\nviOxDABP753k6EyaPPPeLJcscXgyRSqsFbxEcyLWes/Va6QXs+6W3RCaA5C13lRO09F0g5wmkYlo\ni5JFZL0P7RlLy1UrxVp93o7VQ+vzuGpeo1oiHArxXFYPlc8j42NeUFdaXrLvz2lwa+fBsN4JgPVZ\ntd6fJqYdKdw7le/P4y2ovRlOhMKbQhzVgTmgjcYyzKYVPO5ST0VG0ZhJFQyP+bokSQwFNzAU3MCH\nt12NLqXp8HXC5jOIfPRPyM/Okvv5U2SffJLcE0+iHzvGrjM6ADBcEq9F0rym/ZLvPftL/IpEb26Q\nVf6tnDp4CciF7CYnnAyFx+1iXW8ICYOTesMVZ33NDqJO36vWgLfR2VelgdSc/dljpEwqGbELTu0r\nZqu5ZRf9nX4CXhdnndRFb8Tf0EDajMfCnH37PS72jc1ycCJJWimcO5cL/G4Zl0tCll24JImQV2aw\nK1i23FmvkV7KulvWJQ63S+LYTKakobEsuXjdSY0FutfLUFegeF1NukIeTjm1r+X7qhdr9Xnrcrcp\ncq2Dd7VrVI8IH4gGODiVKptEmftyWl6yUm1wa/fBsB7bZX0Wzdgsq5g07Ug06C5bUrNyopcHaMf4\nvsVAiKMG8MguR1erOUg7eTDAbDZbakBcHR0ELnkngUveiWEYxHbt5uVXPguUZzNlvQZHvMfIHT3K\n1rt/RuDkTXRs3ULmzDNJ9G4lEiytR1NvMKHdEDc7iDp9L6fmeeVYvGwZ0HpO6p19VZoZet1S1RpK\nlYyYS5J4/cZeYmmFvGEQ8XsYiDovJzZ7bOBUdLJ09n1oMsWR6TS6Jc4pn4esphPxe/DJruI+nH5j\no0a61XW3nAyh/ZjsC0oehxl7I8dS7b48NpNxDMw9NpOhw+nBXALMZ6Pe6vOVrlE9ItznKWSlmctC\n5mCfVvJ484bj8pIdp2vq9HnTO5dRtLYYDK0T2ERWdXym7c+q1aNu2hHzmjiJQTi+etJBc8uk7Rjf\ntxgIcdQAlQyU6aKt5MGoZtjMAXPG30ln1yZmkq+gGc7Na9cN64QTM2Rf/B2jL7+C598eIqLG6T/n\nTHxvugDveW8ksa6XnkBPjVlo7RRr+81db6NLs5nrnpHZkpRiSTLoDvkI+txNLas4GazeiI+OgAdV\nL4/pqFUM0VpuYF1PqKFjsVPvwGevd5NVdbpCPo5MZ3C5JPJzBRgxCpWp3bKLzqCHSKD8fC+VkW7U\nEJoD0GQiVxb7EvbLnDLQgaobDfZ/q72kYx3A7YG57TCb7Q77Oe8Uf9XBuxr1ivCQr3A+3K7y0gFH\nptMlwduVsF9T6+ftJQkK+3Jx9vquZV1es98jsxmNWFopmxBa7YjVo24vL9GOFZtbyUKWSdsxvm8x\nEOKoASoZqIDXTVdofnZvjXmolT5r3qBe2ccfb7oFNa9wMPkqh9IvMZx8iaPJI8XPru3YysjaJNlU\nrviafzJH4Ef/hffRRxnt93Hb32yhPylzmnsNW096A2ee+XZ6/EOO+4RSY3dwKsW6nrCtwGTjD9Hw\nRCEI2z+XYm/G9IzFs6zqCNRdnM1KJa9WI33ohieSZcXixuJwaCrFGzb1Nlx7x7pvj9uFpuRRdb2s\nwB+Uz75Nb2NXyEdfxI9PVkkqGnnDKMYddQTcXHT6ACG/u2osymIGyNaTrWlnQ1+YWHo+7s3nkem0\nZVs2MrusZ0mn3Wez9Q7e1ahnwDY/84qlNpq5tGYP3q6E/Zpb/7cLIwAtn1/25bV6l/3q9Y63Y8Xm\nVrKQZdJ27YXWaoQ4apBKBuqUU/s4MJFi31iyxCh1BAoDeKVMEfsN5nF5i0HdmwcjZPIxHtv7DLtn\ndhF+5x+ivV3CMzGJOjyMvG8vUm6aw1qhUvdrJxc8IGNhnTEO8uTYQRj7Ht1pF6cxwBmrz+GCs65y\nTCWH+YwNoPiQNPoQWX/TYDTAbw9kigOoohnFWKRmjandq1WvETPbKhwYT6IZBj63jKbni8Itq+ic\nMtjZUJCp/dyY4ngikS0TR/bB2xoQuqEvxGQix0xaJato5A1Y3RXgwq0DbF0TdazjlFP1sqKHjQbI\n1usNrCdb07pfn0dm65oomm44trEofKa+2WW9S0DtPpttRcxOPfe6zyOzpjtYtYUI0NDgZvUG2oWR\nuRy1HN45a/PsRmNg6l1ibqeKza2iFTFDx7tnDYQ4qhvrg1ipZo/XnaGvw1dilFTdqGgA65nt9kX6\neM/pl7DryAXFujGuvj46V/czeOmFaNp1ZPYfIDv8IvuNHwG5su1MB/M8xTF+e+QQ6z52L/Fz34Ln\ntC2oJ59KpmsIyTc/kJtxU6lcoXp0o7EG1t+k5fNEQ14CPrlYkK7fUutmNJZpuu6RlXr6Vr10JMZr\nowkm5grved0Smm5grmSZS21AXQPWQmNxrAGhfq+b80/tIKPoTCcVOgIyv7elv+T7diO9kMG2UW9g\nPdmaTjWdeiM+x3MkYczdJ7WNcL0eoXaezbY6gLWewp+Vav6Y7zc6uNm9gVBee22pvHP2+zeeVoln\nco7V5JfyuFYKrfCyHu+eNRDiqCbmg2hdjrGWpren2joZpUoGsNpsNqNopHJq8aY7qTdMWtGLwsvt\ncs17fboGcK9fz/DhX0PmSMVtnrwvhS+RQH3xRdQXXyThCzEb6sbVvwr32nW416zhyKkGa9eeScTb\nVVIw0R5rkFN10jmdczZ0l3hJrL/JXDryuWV8c3eax+0qbms8nsHvkfG4XfRGfA2nBdc7yA9PJNF0\no9hUFSCWUpnNqnSHvHjdMrIslQjDWgNWs7E41mM1A0KRjLn7xs3anmDFFHnTCAELGmwbFVa1sjUr\n7dc+AKtanlg6RzToLbZRqeXtasQj1K6z2aVe8qsveLuxwa0Zb+BiDZz2a+x1S2V1tKod1/FII+e6\nlV7WpfCsLZcAE+KoBvYZM1DWxX7LUGdTBtBpwDSFgzlgmk1m+yL+EuFl7bcGBdFxw6lfYFY/ymx+\nmOdGXmD/7Kuk9fkqxacGNtHRpxDIZcl4/Xj0gvjJj42jjI2T/9VTPHpjnHxCoiPt4WSjj57I6Zy0\n7jwUdYBEVier6HOiSQIJUrvVYo8on0cu+U32WiKmC37/WIJjMxk6Q55iX7eJRBZFy7NtXVfD18aK\nfZC3itawz81kIsdsRiWd00jPxfh0+N0MdAZKAuprtWxoxsDYB2+P28VpqzuK7SOcHn4nAajqOhg4\nzpKdjt3KQrwYlbI1K+3XPgAfnEw2XPeqEY9QK2ezrTTI5r1gzSKzCovFrPlkx37OGhncqnkDS+sJ\nLV5NpErtivwemayilzRvth+XdRtLOdgu5v6aOdft4GWt55wsd20tIY6qYD6ITuX/s0qe6WSOeNpF\nNOgl7K9+KisZQPuAaQojq7u68F62pMid9Xis6exR91q6WMO6k96CYRhM5o5xMLmbQ8lXWf0H76L/\nE2cSGT7I3qeeJ/7qHuIHx0lPTONTcxid0+Tdhe3MBlV+wzHIH4MD/xeX5iKU6aZ35n/gDp6ENxKm\nI+AmnqbYI8oc4MzfBFiWjgretoyicWym8Butnd+zSp594wk2rgrX9XDWO8hbRev6vjCvjSXQ9Dxm\n5xAXEgGPm2ROIeC1Bm7WbtnQqIFpZvB2EoCabjCRyDrOkq3H7sRCvBjNzjgLv1GtWDumlihr1CO0\nkNms/XpnFA23LDkG2deLR3YxMZspqb9kZm8uVr+zxfKi1bPdxayJVOn+Nb2w1nIq9uNa6kbI1WyH\nqudbIpiaPdfL5WVtRPAsd20tIY6qYD6I9lLzZiBvOqcR9LmRMBjsCuCRpbrTyk2sA+Z0Uimb+Zik\ncjob+oKMz+aIp8u7T5tYS99LkkSffzV9/tWc23vR3HY0whvXc9bG9SSzKqdmVI6OzqDtfY2nx/4P\nsMvxOPPuPInIJKGfDZPPj+OV8uwJh+juCmMM9SCduYlEV4BIwFvymzoDHo5Mp3DLLjxumel4QRh1\nh8oHGlNw1mMs6h3krQO2ls9zUm+Y0XiGjKIjuyWiwUJMVNjnKZ77els2NGtg6h28rQLQXvUZQ3K8\nV2rN/BbiUl/IjHNhoqyyqGz1rNy8nvZl5JFYpsRD2ug2o0EfGSVfkr05k1LwyC6eeW1iQeLLicWK\nCam13cUuEFjp/jTT8ld3BSrGMTaSpdsKnGxHLKXyxMRoiQe12f0u5FxXuo7JrEoyqy2aV61ewdMO\nhSaFOKqC+SDal4dM42Y2bfXMNT71yFLZ4FGvGje9HJUKGkKhceyWoU6iQS8ShuO6fyOl7wuDtIfB\nriDJDat4Zfch/Af3k9Uzjt/1Jtx4czJm0LcyHSN97DCJZybY829pulKH+fkf9DOxJsKG7s1E+l9P\nT+dmIoGCx0jVdbpDXsI+D7phVLj56isSWO8gbx3QFa0QFL6mO0hO0zGMAAGvG7MGo6rl6Y3UbtmQ\nUTTiaZVo0LuoQYk5Ne9YV8bvkemN+HC7Ss9BvcJsIS71ZgVhK+IcrKJyMVzu1uttP+dZJV/mIXX6\nvpN4S+Xma+rsHZ2d8zIbJLOFgdnnlhckvqqxWDEhlba72PFVte7fSrWj7M9ypSzdXUdiVbsI1Esl\n22HuN+yfL/3SrDekFefaWptuodmvtWhE8LRDaQ4hjqpgPogwvzyUU3VUPY/XLRX7XZk3uaobbFxV\nqCEynVQAg+6wr+6bq94BZCAaIJZWHG+0Zkvfh/0ePvS6D3L1tj/m8OwhXpl+hd1Tr/Ly1CuMpUcA\n6PZtwH3qqRjxOPl4HCObQzLyeHWNnNuLMh3jNxEPI6EMv8qNw6GfgQFdaS99+T6C3vX0d56Dwrri\nOewO+XDPVYL2e2S6w/VVMm5kkDcHdGuPq86gp5jdYnplTlvdUWJc7Q+oXahIGMU0dvvsuRViyedx\nOdaVyao6k4kcbz9zoHicjexrIS71Zj0SrY5zWAyXu3m9nZbRoXD9nWat1YSa9R7KKBqGASGfm7F4\nFlXPo+sGuOsTX9CejV+tLEVJhWbuX/t1sF/fdE4rtnhJK3pJtexmxIHT4G7dr72bQjPekFaea6fn\naTKRI5ZW2LqmNe1+GhE87VCaQ4ijGpgPormmncppxUHdvqQFkMioxDPzCtkMqK72kFkNXqMDvpOB\nWEjpe1mSWd+5gfWdG3jnhktIZlV+c/goB2f3MhmXmKAXba5ukazkWKPG8Y0ew33kIPnYq4wO2OS8\nBDMhhRmOAkfZ/MTznPRaP9k1G0j29KH2dTN40gDBVb1s6g+XzLhrDQL1NOs0t2EO6G6Xq6SSNRQC\nOoNeA4/sKjFQ9gfQLlRMj+F8UP4iBBBKzh3dzdcb9QyY58QsBFjrHFe6Ds14JFoV57BYLnfzetuX\n0U3MgH37rLWaULMWXDS3a06wgKL3GSqLr2RWJZEpZMtaJz7t0vjVylIE+zYj0J2yaK1Mp5QSD7KZ\ntdqI2LYej9Pgbd2vUzeFRr0hrTrX9ufJPgnUdKOpbGI7jQiedggaF+KoBtYH8ZSBCLG0wqHJlOOS\nFhQGUGvKvVkgzblJZ/lg6pGlstglpwGkmoFoZbBd2O9hVaiLkPscMmGNV6U4kwkF3cgT7g7Q2TGI\n/6wzGIwG0INXYPzqb6pur2PCTc/4YYKxKRK+EJpLxh0bodfI0LO6m19vP4nHN7pY1X0aQ0Nn0RUY\nJOL3OD6Y1apmV3IRn72+i11HYsTner65Xa6K6eXWB7RaELw5oB2ZTrfUm5FT8wx2BhiJZxybiTZi\nTJe7C7tdlDXjWZ0/NudZuRmT5XReGil4aXoYc5perM/VGZxfBrEa8VpCDeYLLprL82ZJCdP7bGIX\nX9ZrYGanmtferBW23JWpnViqYN9GM+0qZdFKkoFhaeRtFS71iO1Kz4rdjpv7rdQPspp4qHT/tuJc\n258n+yTQFO0LXXJsVPAsd2kOIY7qxHwQeyK+ihVZVX0u5d9hIEtRuMGBYjHJAxOpMi/GbEbFLUus\n7w3XVSDRyUC0OhjTmn3WE/YT8nnKeqWFfDID3ev5s7P/nJcnX+Xlyd2MZ46Qp/Q8dYc2EvS9Sld8\njKzbiyp7WDd9hNWz43AQfto9zlNbApD8Hez5Lm5NojcTZNC1ii29m1izdjtnbTq/qhejIH7UEgGb\nyunsHpnF63ZhIOFxu1A0g8l0moFoafE466y/M+AhndNKZn1OHsPppPMyp7m9ZrwZPk8hiN3eTNRp\nkK5Fo8tQlT7fqIG0DxzWWkcet1yXZ9WO9Xc7xWQFvTJhv5tm2t9s6AujaHliKYVkrnDOXS5wuyRU\nTSca8tqW1GovFdizN3OqXvQ+m1gHTPP3WfsAxjMKmm6Q0woDrJmpuFTBqXZqVeluhf1p9RJipSza\nkNfNVLJQ4NJJuNSahFR6VuwxqGabqahDOYxK3pBa96/TuQZIZjVUPV/XebM+T45LytJ86ZiFLjk2\nIniWu9CkEEdNUOkCT8yqJcII5msiDXYGeelwHCgo83haIZ5R6A75CAfc9IZ9TCYUR1dmszS75GK/\nCa036VDUX9W9//b1v8/b1/8+rx6LE89kGMse4XBiP/ti+8jocQavvYHV3SH0yUn0/fvRhg/Q/+pv\ncL30WxJTsxxbXWo4NLfBaCTFKMP8NjNM11OP8f6/CBJZO8im9f2ETt+C+7TT8JxyMorLza4jsWIl\ncaBkpr1vLElfx3wBw6yiE8uoGBIlafGqlueVyRSTidzcZyV8bugJe4tisJwKy19zNBNAaJ1p2YuL\nLsRtbqXSMo7981YRYjWQ1Wo0QfnAYW4jo+olA3wjHhDzvNjbwUDhehtIju1vrNXdwTm2x+eR8bpd\nbIKotaUAACAASURBVBoI89KhGIpkILtkRmKFOlzveeM62+cbK7hoPj8HJ9Nlvc9g/rqa10DV8gyP\np5iYna98PxHP4ZYkusKFe3mxglOd7EEjYrPZYPCcqpdNcOodjKsNpNbuBlY7llE0ppKK46QHant0\nKmWUWmNQzWPauqa8JVM1b0i9k5qw34NHbs7ba09aseL3uoil1LJYqWa9ls0InsVKKqiFEEdNUEmt\nmwGVdrJKngOTBU+EGfSn5Q0UzWA6lcMtu3jpSIxosLSNx1K5zes1eCXZbTVu7oKABLdrI6uDGxmS\nzyenaoS8bjKqTqCvD7mvj663XMBJQx8FQD5wjOnf7ASmKh5rz7hBOpkmvucQ8RdeZuu99xTekGUO\nvO4Cpjedxi9fN0XIt4qujk1EO0/GMHpZ1REoDOyWwMtUTmMmpRBPqXQFvUTm1MdILEM8oyC7oDs8\nV2TO6yGRdS6zEPLJdId9TCSUsvdMmg0gXAy3uYlpzKeTSk1viNU7o2p53K6CgHxFihdFjv2esYss\n66zUzBCyL03W641StDxHptKMxLNAYcliqCtY0tLEbH/jVN19eDxFyCez1lYryjzmVFZnsCtYsrTm\nc8u8Nppg+4ae4uerLRXY26RYn5/1fSH2jCRLPMfW62peg5FYBj1f+FvPG8xmVDQ9j37E4KS+EH6P\nzIa+6o1kG6WaPVjs2jM5VeeJl0dLakKZomWYyvuo1YDa6b0z1kSL9YaCXtkxkaWeEhWVMkoHo4Wl\n756Ir2Rwr1ccNDqpWci1cUpa8XtdRANeRueeMWh8ybESyyV4GkGIowVgvcBTc14G011rJafqyHNp\n1+Z7Zud1RTOYzSokszoBr16cAZs34VK4zZt5qGrd3FYBmcioaJrOsViWqaRSnKVtWhUpGeQD/b2c\nNvBmjqWHGc0cJKXFy7crr2G034ORyTAZ6gbg1Mn9qC4PyZFxMrMxht/qAl4D9RcwCbLmoiMTImD0\n0ekZZFPn+YS7Tpq/Bnqew1MZTl/jZTatcmgyhTIXMJvKWdrFBH1IGBW9ZqY3w778tZAAwla4lu3C\nzG7MvW6JtKJZXPWln7e72j3u0iw6U+TY7xm7yCoGJM8JjkRGJeB1VxRplRieSKLqBqs6A2Qt4sUt\nSyXLo2b7G/NYrY2GAZ58eYLXb9JLBF1OzZf8XmvrGyj08WpFm5TusJ/zTvFX8da6isfh88h4ZBcz\nqWwxGUInT04r3Jvjszm6WzjSVFtStd77Vk8J0BI7tetIrEQYQWlHgkr7qGbDzL+d3tsy1EmhN5/b\nsUBkR8BTo15Q5YzSkViGrWubs5/QWHbXQpMUrHbGmrQST6vF5zXskxteclzJCHHUJJXaSZhZbdaH\nRXa5WNsTQNEMcpqOrhvIsoRHdqHqeZS5pTgzrde+7r2YN2ArM3+cDH3Y7+HIdBq3W2Zdb6jEoHrd\nrhLPVCTg5bL1f1g8nqQaZ39smAPxYRL5EWbUo/Sedzkdbz0NI5FEHxtDnzzG+KG9RPe8BFNpUt0q\nUFpMT3fnmYkkmCHBMfYjff8Qa8YMvL3d6KvWoUe7yK2KkmQ1RwigWEo1ACV9m07qDeHzuByXGxQt\nX/RKAY4CsFkWMtOyezes96e1q/r8YFH6eXu8FVAWsGku+VnvGbvIkoDxeLYoPMHgwGSSsM+DW3aV\niTQnrPerPbDW7o2K+D2MxbPFY7UKIwDdKE+f93lcFbPVoCAMW9kmpdJ1Dfs9uC2ZbGG/zNjcXMEt\nS3hlGVmai2ds4QSqmj2IpQuZumZfx3haQcsbuF0SnUEvQ1H/go4hmVWJpTXH98xrWynYvtIxm9e3\nUmHd+Xu1dDJnLrmNxLKMxLLVl6dqZJRaj7ORCU4j2V2tqgsU9ns4e31XsZ/oeDzDxGxuzh66ODSV\nLGnwu1gp9e1QskKIoyo0uuYe8smkoEwEBL0yilZYWrPGDsgucEng9brIaoWikk7r3otZ06Gehwpq\nd72vVibf+ro1dsZu1M2K2umchoFE2NPJKZ1bibpOLnPvSpEI7kiEjjduw+29jM6uAL0TCfbt/w9I\n/7Dqb5KTIWLuPD1HRwgfGyPtC6JlkxzJJohF+zh4gUR89TQdYz10egbpDK2js2MjXaEN+DwRxwHN\n9GbUEoDLhendmEzkHGNdoPR6WL0h1iybwc4AaVtcnT0t2TTEdpEVSyvFyCyvWyKZLaS0K1qedb2h\nqpmd1m1DQZBNzOaIpdSi4PHKLsI+GcVvEA26GYgGODBZ8BzMZhUSGRWXDF5ZLopfe/p82O8hGnQX\nhYgVU0guVpsUO6f0d1gSPKS5GmAFb4bPI7NhVag4SLVqAlXNHnjdhebMI4kMR2cyJUIzli7EUw12\nNb/El1PzZYLXiqrlHc+9tT6V3WuraAYSRlkzcOt37Q2ij0yny65h5Yzj2hmlrYgFslPeV7B1dYFM\nofib4Sn6O/0gUSxzYJ0oVvKIL0TYLHc/NStCHDlQLSCw3nYSpggwv/fEy6MYxry3CEDPF2aEZ6yO\nMhLLMBgNNNwOYqFUe2hUrTALrlVbpdo5MQN2KzXddDYeUknPoyPTaY7NZLFj9bB5ZBehkI/+oW2c\nO5NmLHuYscwRlHxptW+fEsQ3eBKZ2QRxXaMzM8sZo3vQXDKhbIpwLs0u2ctsWGOWJEc4CPlnIAY/\nmobeX7t4Q3qA90cuwn3yJtybNpEJRuoWgPXSypmTNY0+6JUrdlUHa9uVUm+INSbDmy/1JFXrzm4X\nZT1hL8mcOrdMNLd8Ykh0WTJ4qp0zc9um96sn7GUqWUhkGEtlUXSdkwciBL0uXj0WZzDq57cHpplM\nKMVltoBXL3rznGoXnbEmyvhs1jHuxSwKO5XIOV6bVkw2THoiPk4b6mQykSORVotxT+bxLEbz2mrb\nCXjdSKhFYaRoOnq+MMnzuiWOxbIL8mD5PK6KoQlQKNxaaduHppKO4qQgtuovituoJ92aUTqdzBU9\nl91hX/H9VsQC1Yo5bHVdoGS2IPI7gl4CXndZRXEJo+wYWiFslrufmhUhjmxUCwjclYtVnRWqet4x\nUHssnsXnkfF78kVjrur5uZmul6BX5h3bBjk2k1nymg7VHqpYutDnrFrNplrGJORTKxouj1uuaDwM\nJGYzKkNdQTb0hUnntJLZvN3r4fO45s7VGawPbykcf0phJDmO7JtmRh1hInuMTNaF/+KLMRSdSMBF\nODNLcnKCdRMHWT28i92jSTLRGZwMquGCiVCe+G9fJPbgf86fp/61xE87G3loEHloCGlogNd6Y/St\n2kxPcPWi1iNqdFuFWbRcEptjxT5YmF4ya0yGOYDZGySbx+qU6XhoMllyH43FM0CmOOAbtpWJSucs\n7PcgYczH7sku+jv9HJlK0RFw09fhpy/iL9YBOjCRZKAziMslYRggz3mO4hmVdSGvY1kEn0fmwtMH\nyiZIHllC0fIl2ZD2a7OQyUalmmVQECZZLV9S66jSOV+IsK41yHYE3OSNKSZmM6RzOoYEIa9MwCOT\nzGp1x41V27dTaEJXyMMZa6KO35tIZMEoX2IdiRdaskB5zJH5e5zEbaWJnPm+3dPkkSX2jSeKNi6V\n00nmVDatilTcd/FzDcQCLbQorp1q27SKfLP1jdUjXijn0dpGsU5jiTXDdKlLVghxZKNaQGBnwDff\n+NMB63KC1RsST6uMxbP4vS7WdAcLqez5PLLLVbzROgJeOgLeZVlrdXqoVF0nkdUYjWeLMVJmyw2z\nZlPY76k5Uz463ZzhMl8392NmCNnrF0GpkbMaErUrQHTGC6wBtgGwfyzB0ZkMeCEY8iF3hvCuXUOo\n//dYt66L2SNTxJ/9EFD5d/WPl3qxPNOTqLt3o+7eDcBsp8R//JkPZgEDetIyQ/kwg75VDHatY/XQ\nFs489S0EvaGybbdy5uSUxl5YzlLLYmLM7vOVsBtpswlyvYbYns3XEfCUNFC2L81VExkD0QAHp1LF\nwSin6ng9rmIrGjMGKqNozKRUBqJz3stcfn4pyOKtchokfR6Z7Rt6Sp7Heop81ppsOMUimfW3Kgni\nespomOehFcK62iB7aCrFdCrHTFpB00GSIJ83kCTzmahe0qKufZPE43YV79lo0M0Za6KOv8EcUJ0E\nFYbEqg4fIZ+nLtGQU3UOTiY5PJUuvmadyEGV+9Jm48z/WxkLVOtz9Qqpeu4Tp99p9Ygv1OPmhPVc\nOWUAul0uzl7ftWTLa0IcWTAMqgYEhn15VE2quH5tvWGsN5+5jp5V8sRQSmrq2L+3HCmOTg/Vbw9M\nc2wmXRKcGk8XCtFtXBWxLL9UHsTMtNBqhqtavACUL3fU62IO+wsPrKrli5kXGUVDyxv0d/qRJINV\nHcGSmiTJrMpQV4DLB2/iaPIIs9oocW2UVH6clB4rbv+Uqz9G59tA27cPbd9+XK+9RkDJkvEWDjTW\nYzGUEkyFdKaI8yJxSO2FvY/z+Q/dzGBokNzGU9DXrSdw0hrcJ53EbGgVcm8PhuRCkua300xwfKU0\ndsMAv1cm4vcW3ze9QLtHElUHVDOupp4WJHYjbS+IZy6fSJIxd59pxSXsar+zI+ApKYyZmcvoMjGF\nVvHeNQpxgNGQhyNTGXQjX/RW1fLOWu+leo2/k7iQMByL/wFl9bfMbdpFV60yGq0S1tUG2fF4hnhS\nRULCPOVmiQG/x4W3gkeyFft2wrQfTt6NQlNpqe5tDk8UvHrWZb1aMTbJrFoWa2hOfGczKqs6qouj\nxYgnrTWG1FP7q55lOuv5bIUItJ4LpwxALZ9f0uU1IY4sGBhVAwILWRke0g4DufXBsRtS60Bgz6hZ\nqj4x9WAdCI7ahBEUBptjM2kGo4HijVztIXLLEh65YCwrGS6oHC9gLruZNDszmpjNgZQlNHfO7bPB\n+e/lmUionNV/Fpu7tpYcqyznCEWSHE0e4fRV2wn7Sh/QaDzBay/sIXHwKKn0z4GXK55nl24Qnsiy\nO6eQSe6D3+0DQJNkkEDz+vjFZQGOrlXo1iJ0uXvoDg39/+y9aawkWXYe9sUekZH7y3xbvXq1dFdP\nd09N9ywccjgey0OBxFA0vYm2ObJkgT9kybAJAzQo2IZtwKYWi7AIyrBAkbJhGJZA07BoeKEgQKY4\npEGORgQ5w1l6erqnq6trefWW3DMjY1/84+aNvBEZERmZL6tHIOoAje5+ud2IuPfcc8/5zvdh0H8F\nr957E0e1G5CEcqewvDZ2UeDx0RMJU9uFKvGoaVJ8P/LBp+UyE3nvO25pidJxp6bguxdTSAK/KLOR\n8sm9V7qF10bnHABoMiC5fpyFolgcy/VhuwEcP4iDpbom4/UTOVdouMz9LHp9KZq5Ok8dL4zb+lmj\n7fppIVIgPyBmN784SxqEKzQSeSWJsoFHepM1bA8TM4CuSvBND0HE3JOIg6ZIcP3i+1TWsjb4rHGn\ng4s0WWrZgyfrs9OHuTyMDZCcFyLPo2euZjsqipCQEWEzYh+27y86NKW5v/IyiMctbUWeiUO0mHvl\nyvVZRtc12zRCja7r/szB476BdlV57vfuRXDEGAeukKvIC8K4Sybdrt2tqTFIM8uRsguOOsIPUydm\nExsazgp4nJrrR/BTtPR5i6hb0xMbQpbjejo0C8tuWQtgk5MRe6L0ghA39yq5ZVG2sy491iBQcKR1\ncK91L/OzWqOGj/2JT8Gw38DjBx5ajy4xcrLJLLuWiMs3fhBWfwS4y9KSJcl4v3MbddtATx9jVvEw\nwxCPMASi7+K3nv4O8BTgogife6TiL4zuQ7x5E8KtU4inpxBOT8FXSDaH5ckBVtvYHd/HN5+MMTZd\n7Nc1jE1vRbdrW5K5vPc9G1krLe9v3mqvZA2fjSzU89KzC0s3P1AMVKeqxFIHANmIejM7EQxrsohO\nTSgdGNH7WfZ1dhPfq1FaCeY5M9dLDyBZQqRA/ombDUA9P8R3L2YYzu1YksRwvJgiASCb9Osn9Vxc\nY5lSheOFABehqcvgeQ6W5yMMAZ4HNElES5Nw3bJa9u8GMaif3jeqHrArIPI2GBugXLYDIBxo47kX\nv0eV+bhp4Hl1YmV3WxcfmtLcX1mH0XRgBBCM6Nh0V8rGwGbP4U63irGZJNNVZT6xrj0/3Ep2aFN7\nERwxxnFYAQTSyaNIHCamFxMYHjZURODAcSSbwp4MsqJodsGd7lUKI991J7vr4JLKfZYEKyx4PL4O\ngcdJO4mVKcro9GZ2ruMCsBYvsKldjC2cj6yV8pwmi9CABYnjqhGhyOINsExquKpK+OJHfwJf/OhP\nwPItPDPOcDY7w7P5M5wb5J+9owOo/91fgBqFCAZDhBcXCM4vMDgfIZw48PsXMBvD3N+IOA7Ke08w\n/z9/f+U1vtOBcHoK984N/Pr3OeC5DlRxH75wgIp6DIXbgybJMOwAAhfE3FuKKCRKCOnrLVtWKl9+\nWra8pwPRbYCqFAP19tkUthcQ4lWBw0v7pJOQva4yh5L0XC6zCedlzGjHph8EeJbSXuS4CKKQ3TlI\nrjN7TrK/Q1m0KeN+FHExRcL+YrPywxBffrdXmn8pbyx1TYImCRB4DlVfRBBFEDiiVdioSGhXlZ3j\nJt85nyYAzwDxK64f4o3T1k5Y5Ol9TgfqeRgbamWyHVRGxHSmaFYkSOKyhPo8OrGKM7zFh6Ys7q90\npjJvfReR5JYxOm9ud6rwgyjxHNgDD0uQ/DzLbC+Co5SlAYEPr+Y4bCg4aGgxzw6LHaIPraouVbuL\nouhOTcFpJ3uyrCtbXAdwucln21WZZM8AHDRUOAu5E0r2RgGuacvK6BQ5LsMmde4ivEBZo9f3bGTj\ncvGcsspnR00NE8vLHE86SwYkgcyb4gM0UcNLzZfxUvPlxN8f9w08uCRzTOt0IHQ68F95FdzAxI0g\nRBh5sAY/W/jd3V62VE3Y7yPs9/H06m28/0OvALgE8BZ5cXHJ8lyC7NbwZu9zCOQTuN065G4bnKYl\nyr7s9Q4NB1eL0ldNk1Y2c9qifj62EmXjtNGA63kAVWVRwPnYwtnAAziSLRkYLlRJQFNT0K3Ja9Px\nRetk3Sa80tTgJyVWHvdN9A07kdFRRDEXCF/EI8NiRlgW7bntI+IiyIIQB76NCvmO0dxL+ClqZfFs\nVVVCp6bE5VEAkOLXBNw7rK+A1rc93bPlwnRgBBAf/OBqhrv7JHt0XRZ5SeDRm1qZXcppseG05WU7\n2I7CoeHGrfFp25buI8/WYYrofKPVEGp53F+sFa1bSeRzSXKLLGvNGbYXi1OzwVyawmLX9461F8FR\nytgT6XCh1Exp1Fmz3RBDY3laSGMGtomi15UtrgO43OSzVVXCSwdVPLg0YsergOgFvXRQ3Wgipk/4\nXhDG5bq0GjQbGJHPbq46z2LGqKYdC7yuafmgVioBklWTV2VSAizr6IsIRPszB48G85iS/3a3GpdX\nRIHHfqOGL+Avo2ddwI4GMKM+fH6IWdDDxCHA8Fd/7hfRmVYRPHoM/8kT+I8eI3j8CJNnV7AHIzw9\nyM+6uYoHVxlC+Qe/h5mwB9ueIQx8cIoCvtXCsCrhqFPD79818aTFIVCOMeUOMHObkNGEKok4blVw\ns12BtHCmtEXdcn08GZi5uC76THdJWkfN8UKM5x4EgQf7q7YXYGy60JXm2rm7bp28etzAxdjCzPZQ\nU6W4NJd1ombnz9Bw4IcR8QtchP26tmwG8MONfAW7QdEAyA8iVFUBlksY+OkNoCzalLgzC9tEv7NM\nMHqnW4XrhxAFHhPLjefw64s2++sCwtMb5eXEwuP+PO5EZI36YPpMr9PM8rBnoFlRYLlhAms0Nl18\n4na78LOKJOD+SXMl25G03QtTZ1kepggg2Mv9uhKTi86dZfORLHLQFRFzhzSt5I2pzLrd9Dlkrblm\nRYm7O6lvzBMGfl4KEi+Coxyjbep0kmcBtS1mcqUxA5tG0evKEVREM+/1ouh5mzbLjxzVIYs8+jMn\nDlponX8bk4TVVmhdEYAowuOBmVjEmwZhhu0l8AjqgjOGpoxtj3QntXQJ909WU8Ws0ezA20waly7K\nMo5+nWjneO4lmJ1Hc2Bkunj1qBH/1tQM0BJP0aotFeBv7lVI1rEr4WJ+jqPqMRRRA77/+1d/13Xx\n7NGvA/N/hDwTPA6yzeEg6EGMQjiijMhxEFxcQOk/Rqf/Pv7Rnz/GH36qBbA8mhEgGSq0qwpuOzfw\np7TPYqC3cXh6AL7VXGL23GQpi94HdiMrgxVZHlKitVkf8qyz57mdOiVnBa/r1snQsBP0BVPLx9h0\ncadbXTlRp/XoWF8RRVziELCpr6AblOeHsbwDNZHn4hO3KHAxizYl7szDNpUNRhVJwBunLdzdryae\nC4AE/xNrm5zuVzbKiIvLhfsZmfgigseyRp97XgabHOSKD0Q0q5Y3n5+XMHXa0pgi1mwvwLvnBj5z\nr4PXjht4MjDBgTQiGXaA0dyDLHLozxwYtp8paPw8yCazvksSeXTrGm60NHRrxRQ6z0tB4kVwVGDs\nTc8CamuKiLkbZLIE08+XjaLXlRkou2/R5/N+Z5sSxi4ET1nLBeku2sgTxkUwXT+XhTg59gDfejpO\ncJOIAuFDipnIgwhqhUezIq8NbhRJwEm7kikgS8dc5OjXiXammZ29IIRhB7icWGjpMhRRSMikAIhb\n3fszImbaEE4Q+Hxi9SZ+V5Zxevx9+NxUguH3YYUDnM8vMHWXLJo1qYP2v/0T2J9cge9dYn41hD0Y\nQH/2BPcv3wUA9PYyJhQHeKoNT7XRe2ah93/8EUSEGIYBIIrgO3uodA9h7p9g3GzhG7fewZ5+gIO9\nU7zxyuswXAG6pIPjuMIyleMR/h+avQSWzQ8fOapnblaSwEOV+ZUSDP2sJPCFweu6dfLuubESXNCA\nmdIaUEt3elJfQS2dwdnEV9AN6u3+HBGQaJyQJQ7gAF0RE35Jk0W09NWSGrDdpkZxWNQGs+wyL7Uy\np/t0uZCsP9IY4vphjI2jpkrCQlJl/fcWd7cmn3saA7dJVq0IurDLoCLP0piitPlhCMP24kOuYft4\n1J8TUmKRiwH94KJcQeNdYLyoDQ0HU9PNZeyXBB6HTQ2m6z/3e5e2F8FRgaWjZBY4rMo82lUFQRhm\n8pds+tDWRb81VcLUyuZgWvf5MqnQPAeyaYp0kxM5aTH2cXOPbCyeHwIcMJ57eHhFyk6sdEt6QzRs\nD996MsHMTt6XuR0giEJ06wr8BQcJPd3SLJwk8IXOMu0g069n3ZN1op1BuMxsUGZniudqaDK+/6U9\nfP3RGKbjQxA4CBwXdx2dDecYGC4eXs1x77AKSRRy9esA4KZ+Dzd10ln3kSOiB2f7Nh6OnuLZ7AJA\nhBvqG/HnqiBz9nZbhTjoI3j6FJOzXwBgIs/aQw8dcwRDXThF30d4cQlcXKKDr2PQkvHV/4AHwm8C\nPZB/ACge0HZEtKMK/rz3KZzuvQp//wCVG0eoHxyCEwR859kkERgBS5yJLPKZAa4i8YU6V+ukHNIB\nDmsUsyFhdS3R72N9RRCGmDuEWHMJVPZXQKX0c5s6+G5NxdscCXZpoM1xUby5aRKPwxSL9r1Xus+N\nhT/tY9LZlzKne8cL4fnByvMThQhBuBTmBspll8viLHdV4l13oNw2qNjkgFpVpVwMGxWNplJVrx43\noCuE2Zxyf9H3FQka7+LgzEIMLgowovTe7zIgK2svgqM1xj4UmnZldb/un6xigbZ5aFnpSpYP47Cp\nYWy6W0XPRalQSeB2AqLc5kROT9eeHy40fIDvXkxh2GRToafrdDmLXVg0YzQ2nRjo6odR/N17CxAu\n/Z3zsYWp6cbAyOs6y7JEaLLIYThbDW5jPJcixJkJQeDgBxEmtot2lWAtLic2vCBEEC07yuh9od1Q\neUaDOVVU8Vr3ZbzWXQLEMx3cjRsQjo/x/V/9l/BgeIa+dQUzHMKPkmWBzpufw+HNOp5eThD2+gh6\nPYS9HiKL1OFc3QOwin1yJOBc8nGOKeZ/5e+gdkmyDgYAQxRh3zjF+y99HMP9mzg/maO3N4YutlFR\nOtArRxDlO9hvvIS2vkr+2dSXIE4288d2R2ZZVoDDbvAsZ1fePb7TrSayXYbtg+Mi6IoIz192ZYKL\nEjxn2zp4lgjzzj75Djre144bmWW658XCT30M265OjS1nA/mbvSLxK4ERADQ0BQbv4bSjx6oCZUr8\nZXGWuy4VFXE0rSNOZd/LLbI363wzW3qWRQGdqoIPrpIyNaIA+H4U+8up5S/kYCS8ftIoRcKbd52G\n7ZXK8rOWpuGgHIDprlIWD7rLSkYZexEcrbEyD2VXD43FpWTxYaRJ9IDyzjUv8nb91azDNi2S25zI\nKY5LEonkwwc9A0+GDHW/yMc6YCz5Fw3m2NJFVZFgOB6aFQUiT76XglGp0XsqicsNe1tnmadblkeE\npski9moR5gNr5TVV5jGee5DqxDE1NBkT04UbEKxFQ5PjtDdtuacdYXMnQLOyPQtvXmaQ4zj89Kf+\nQ3zn2QRvn01huT5M38C5cQkjGMLnR2jf/SS8H3oFLT9cUllEEczxFPZVH/7snwL4x4Vja46S5eI5\nJ6E3dTD64Aze5RRXdQOPbjP3zAZ++wHwPz4Aqjbw+qSKnx59HMIR0bW7cXCEx3IdUPSVAMSw8zOv\nQHaAAyxOtE0Nnh8UktwpkgBZ5NGtK/D8EIdNFeO5B9tb4q9eu1GPg9nr+Ar6TNMZTrb1PO/ZXmdT\nK7I73Sq+1LtI4gflZTl7XdkJwKoMB0iW9bBRwcduNgszvqxtirN8XpmJTbqE0+993J/HzPVZBK1s\n6ZliLDkuwnGrAoHnEYQh2lUFFUWMufnYUuvcCWA6PrDg98vKlBf5jjLXVqaSwFZkqG/LC36vA7rf\n1F4ERyVt3UPZxUOjgdhXHw4y+TDSJHqbOLWsIA/YDYhynSMCkBlssDiIx/05jFT3RAQOT4ZziLwQ\nk389HpgxqR8LkhcFHs2Kgk5NgcDzUGWCHaJOhdbhs/Bh2zjLPLHcIiK0+ycNzOxVUeOmJmNsgS+v\nkgAAIABJREFUufG4jppavJG7PsFfJfAASGJWJIF/bngG2p304NLA1VSCGh2jLt+Iu9XmTgBJ4FJZ\nAw5q5wC1g4/jjekUVjhC3+5hZCe5m3ROxdEv/C0Ez57BenaO9/sm5sMpzNEUA7mJmVqFVZvmjs1Q\nAfO9ZzB++fcSf28C6DX3YR+doN6s4+/+2ByqqKAuNACxg5raRb12hEbrBHX9ALrYAM/xmQEOe5Lu\nTa3MZ8shguOFMGwrPg2zz2Zq+gAX4UZL24h4ssiuk+3IC+xpNnzb+eIFIbp1DVVVWrl3LO6OteRm\nH6KpSzgbePCjKC7zcCAYKtcPnwujOfD8MhObdAmnW/BpkJlubKD+6unQjIN4lq/o2cjEcUuDIomY\nuz4qipgpWAwQn5XulKS2bh4VXVsxnjD5bNJA+NM9HaedVd3JD9teBEf/nJlhe6X4MLYNxNjP7gJE\nSd+37vW8xXLvlS7eu5jB9oI448MGAmdDG01dgiIKMaMwm35Ng+RFnkO9IqFTkxNinq4f5baCZl1r\nkbPclggtT+3dCwJo8nJcfhhir6rAcn3wPIe9qgw7w6Esx8o/t5Mv7U7ar6tQFwF1mucon+TuPl5u\n3oeukHvphR6G1gB9q4+e1YMbuKjc/gIA4OzZBJIToAkS3HjnIzx60ofJ/wqAq9zxSXMBc0mD7i1K\neYKIJ80bROduPMfAmONBSwXgApgBeEo0hSeLfwB84f+r4ZPjDryWjPODY/QbxxD22pDabTi1Bvqq\nBFHk0ND0xLP1/BBjk4DkP+jPMTE9TCxnMce4lfLSB705Ad3viNF322fOfoZt+X40mMcaYttwE1E/\nkJWFoGUb6tdYHbKJyaMii+jPbFyMbQgCD98LYHs+JJ6HIPAYGA4eD+YwXb/U2LYtje8yM0H9xNBw\n4kwvi31kD2Rp8lo2K56WnAIIbxIlnkzzFbl+hLkT4OUDkrGvq2KhMkAR99u6a8uydYFwXiWBzpsy\nIPsPw14ER/+c2a7I8crYpkDEIqwAkC8eS0/kecHGrU4VpksyQ6pMBEGBJUkZ7TYj30kyKtRhpNm1\n/TCCFwS43aljr7Zk6/WCEGej1ZIWddJZBJBAdkbwOkRoWWrvhu3jax8MCRv7nHDHiAIH0w3AAThp\na5jbfnyaZrNf7OmuzMl325OxJPDYzwksgfIkdwf6IQ70w5UxpR3tcbeBgBfxtPeD8IUenGgMKxrD\nCsZwwmXp1fvMj+OPPvZx3LaHuDt6irPLKfzRDMJwiHA4xFxc1TNLm/7wEgdf/QrMwMdIq2PePILH\nC+hVO3BEGU9fc/DNz08h+DyajoB2qKLB1yGIbdTULjRtH3fbn0WgqHHgjoh77sKZ22Q70vc6rSFG\ngefbjJN2SmX5AIKF4uNgjKXakAUej/sGGroEkefghxEUScDlxI45oeicL1vyz8usWa6fIEHcllS3\njPVnNn7/QQ+Gvfz+qko4kSoKoYpxfRvvnhsYzp2EPmAzFV2u8lMtcZWUl4i1YMG5VK/IkEUBnu+C\nCjunrYj7Lc+KfGA6EGatqJJA//68sURl7UVw9BzsOqnZ50GOl2dlU/PrnMgm7LJZwYYiLan6NVlc\nSrcsFr2uCHHGhwXweX4IrSLitKNjapGTlCYLkAQBH/Tn6M3sWH8JQALQzp6YVZnH2ciKOWt2cSot\nU4aVhCVm4P0rAw97BoIwRKMioanJEHgepufjnfMp2rqC8dyDIvm4324mnkH6e7PAoDOLlLzyMlrr\nbP28257kLsvRSiKPuwc1HLX+NdRUES1djvFm33hyhaHThxmMURX2EOzv40y+B3HvT0IAB3bbNEbf\nBB79t4Vjq1oC5IAEBbJP5jANjADA1shrgRhiIIYYwAPJQp0BEaBe8fihX/gngChi1tqHrMmQqzqU\nqgZer4GrVXHZfob5REW1foiQu4eT9iFqch0cd32enk2yHey9zmr5ZpsgNmEedrwAT4fmiu4kxcs0\nKyIicLGiAFsGmjs+3ICQzYoC6USbmMvXOUSJjG/ZsbGZNbreKYbnnfMZelMr5oRiv3tXAewfPRph\nOHcRBgAvALIgwLAJ9cgnbu3hUd/Ao74ZZ38mlou2rsB2gTHcRFY83d3YriqQF+BqmnFnTRAIpcPj\n/hzduoKx6SVKa/SaqZ/fdM8q8gc0EM6zokoC688+TPB1lr0IjjJs24dSJJBY9iSy686JdVZmkpZh\n7t6WXRZIXjNbf56aPqqKgHtHSUdFs0Wsw3C8IGZsBojjn5geTMfHJ+/srVwrGxhRx7vOMbLzYhfP\n6GHPiDED3oLlOIwiTEwPPEf4XRoVCQ1Nxl5NiTuSRIGL2/OLjA1q6aaUFpd96+l4Iaq5XqG96Jqv\nQ3JX9Jomi3jpoBY78P7MQRBIaIhHaIhH8ftsN8TFxCbaX8zpeK96in/99C9haA/wbNqDHU1ghWNY\nwQRWOEGEEOHP/R1UTxuojPoILi7Qf9gHd2VCns4QzqZwu99BEaWBYi7G7/vQ+hcY6i1Uz8/BeaRs\nrfgu3vozY4w1DrCB/3VRJRSCCHVHQDOQ8cPGKT6vvQFhfx/8fhfC/j6E/X1w2m4wSvFYmXud5mIC\nkFpT5bPUdJ6lwbVUQPpOt4q3no4zy0A8DwAcHD8AIOCoqUCRSNepKHA4yGBaLzM2NrP2rScTdOtL\nDKfl+hjNPVhekMDzANiJ8vvj/hyP+nPMbaLPCQCi4KOuSjBs4IM+KS9Rf6lIAiKTi8kubZcC+pHZ\n3ahIAjo1JSYATXBdiYQ+Yjz34s8eNXnyXBbkrN2aSmgmNHVFSLbMoanIH9BAOM/WVRKed0avrL0I\njhiLgK0mCn3A711OV4QlWYHEslYWS7CLyHpdar4sc/d12GWzrpkopytwfS0h6gsQB/7ajTpO2pW4\nZEYtTZt/ucCVfPSkGV/rxaKdnwW8s9eUPpVmLVZJ4CAJXGJsm2B8LsYWHl4amFguEAFeGKGukfsV\nRgDPcZAlHkEIgAM0ScjFDOQZHTObIaAb1lGjEt8n0w0K+aSoFc1LLwjh+SH8MFwZ53WoJpIZzDBz\nQ6fGRavlh6rUwBvtfwGXEwt7gZ0gEYyiEFN3gokJnIcSXn39NUivv4bbIxOXD/qw3RCOF8Ce/g+A\nny8ErIpNiHfvIpwbkKczNK0pWuYYmmdDCnyogQtLX6U0CAQOo0qIEWwM//GXMPnS/756TfU6hP19\nnL+8h7/7+QCtSENTrKOpNNHUO2jVD9Dau4F29xQ3m7ch8sVzhL3XadZ/WrpaV2pOG+sjsvzASbsC\nRRJw2NTwaDCPM0VBAGgyOUCO5l7MY+T5YUIEOovVuyigTrOq0+9gOaroPGLxPKzvuK7y+3fOJ3D9\nCHVNwtTy4Ach/CDC1CYdtYTYMjmXKV9VTHYZobC7kW2WYLmujluVuMmDHvzoc5laLp4OLFSVAO2q\ngq+8NyjsiCuyIn+QdaCmr6+rJGwqk/W8MkwvgiPG/AwyvaKHwm6aluvjD98fAgsiNqoDlBZILDL2\nIRcFLM8jss5LzW/K3L0tu2xekFZ0rdR5u342hoLaxPQSz1AS+Mx6eN6YsxarF0TQFQF39ytrFyZ7\nTZLAxwK5Z2MLl1MLnh8iXNxmuilEERCSgzSCIFrZINbdV3bDYp2w4wWYOySrRgOFPD6ptGU9I3o9\n9Ld6Uwfg7NjZXpdqgv2sIvGZMj7UahUJFVnILPBpspAIjPwgXJR2FAAuHvbmwIK1m+c46LKIiWkh\nCCP8QP2nEHIGAn4KQZrDxRQ9a4CzyRWscAxx7y64n/xXUVOIO+3yEfbhQJxOEI7HcEY9ONqvFV5/\nY5pNMxBNp/CnU1zJlzir3sUZPABTAE+JrIsFoi0M4G/+jTPU9TaEThd8twO+04HQJf8tdLp4v2bD\n0AVU907gcxXIkh6XblSZR6eqJDKM6VJzvj9a9RGsH6Bzta5JOGpomC5KTYQ2isNo7sLxQgRhBD8I\ncTm1EUWIeaJod2q6FJS2PFb1TpUEI2z2iZ1HdP6zvoNVfi+bXaVm2B64ReZE4Dm0dBmeHyKIIggc\nh6pK+IXSc5kSwzY1CYos4rUb9cLuvCwpF1lcCBA7XmYmdzz3IAocRJ4r1RFXdL1FB+vrEF6WpWDI\n2hs+dWd9paKsvQiOGMvAtQHInyjsg5laHtzFZp3WAUoLJLJWhAfJI/e7jgBtWWOBzEW2CXN3mQg/\nHaSV2ZAt10dvZqOpyZm0+dKia40+w007WfIWa3/moCILuen3rMVLcQ4cgJHhYjInp0rLCyDwhMdI\n4DlIEgd+4ct1ZTVrtO4a2A1LFrk4GDAdH7YfgIsitKsq2lUlEXiVcYrsM2IzrWzWABxKlf6W17Me\nXFxVpbiUkH7OqrwsYWc55dudFsbzq/hzLOZFFnjUNFKG+FLvAt26RrhjnCWFgih0AHRgWT4+c6uN\nqenhn0176JkOwijCA2eGg4aK41YFR20drxwdxQR+hjnG6dNvwA6nsMIpZu4qPcHN/+g/QXOoILy6\nQnB1Ff87uCT/PakX30c+iGANXUSXT6C/827me379p07xB9+XzGCrDgfNV6CHKtr2CV52Pg21UUW3\n20AQNGA0mnjHDxOdn/Se0qCp7HqqqhLGpgtZIgLQthdgNHfhLzi8JqaLx0MPdzpVVBQRN9oqAbYz\n3alFGyxbpqZmuyHORiYUSUhs/ix2URKTkhs0g8ZmkspmVwGy9tpVBVVFjOlJSOaKWF2V4oxWutsW\nIEF+p6aUoi2g66VdTWI7FYlfCY4s14/Fgv0wQrSmI67swTYbR7odNcImDUl52ald2YvgqKSlJ8rK\npsmQl1GlbCVRJ0+eEorwIACHt/tzvM1NEmyheVIR1DYFUWZfZ/6Gnq7764pQirl7F5muvA0ZII4O\nEYenIxMin3TUbGcXfYab4LqyFmvZ9Hv6mlmcAyIOksgvlcYXwZHjB6hrEloVGVHEQZE43E5tBpRX\nB8h/1mldwInp4mpqww9CuH4IjgfcwIYgAJrciMfn+hGGhnstfqtNy3+srQMXs6WEtOYavf95Tvml\ngyoeXBoJsK8s8DhuazHXlu0FEHjyGdcn94oedjguIrxFlovvPJtiavkQOA5RSOaJLPAQBQ5NXUa7\nqkJXJLz1dAwRFfzk7Z+NN9ebewrMYIaxM8LQHmFkD3HY/jRsvgZF4tHMuPfhN/8e8N7/lntfNFfA\n5ctvIJyMoRkz3ByfxSBzarPa6nOxlQi2YmMEG+KTCZr/9zegBi7mAGif33n3JvakCFq9gr//o5eo\nhAoq0FATqrhVqaOh72GMFjipjZPO62hVlwFYWkSYYhOrqoCLsQUnCCDzAvwAcedab2bjtqLjZrsa\ns527fjFPFMWjZR2OooiD461u/kdNDWPTWayPZacYLUWxmaSy2VVgufbu32ziW0/GCf62qiLihz92\niLHprWC06O+XYf92vGCFEoT1QWkf5/khHl7N0Zs6sbgsx0WLztilkHFa72+drQt+NqVGKBtoFx1a\nd2UvgqOSln5o6U2zXhEToLi0DlCau4FunEPDwcBw4vbSdBswy4S8iVTEJsZO8LSUCEC4e8amkyDA\nW7IOe2hoEkzHz+yEYq+VtW0zXXmL4qip4YNeAJsJStO8RuwzLJv2zVqseel39nqyxknLW5O5B3AE\nYxCEEQaGA50CLmUBL+3ruLmno6FJ0BQxxjV5foiLsYmKIq49ybLO0XJ9OH4UN5SRdD5HBG29EFPL\njZmc6etl+GTohpPVuk1f3zWbLcu7dDmxIIsCbu5VSgVzHzmqQxZ5fPtsgpnlQZEEdBsKjhpaInMw\nNhw4foCGTr7TD6KYXPRyYuH9yxkMx4/xJIQ4CZiYPg6bHPbrJCvwsGes0BvMnQBPBg5ePe6iW+nG\nB4fzYQAajmQ908/e+jy6jWOMbRJQTZwxxs4Il8YQM3eCensP7V/6OSCKEFkW5uYMx9EMYX9AZF36\nfRiHvwcgn9tMtCWoQZLuwhZl2AHgTIbwJ08x0lWM4ICU9i7xVWAZRQH49P/SwElPw6HgQ65VoFVE\nPG3VUd9rYNzs4nElxHfkIXyuAZ+rQlKa8H0NdaUBVeRhuKT8ZPvLbBEt0bE4pLStw6O1dXnl4NTU\nJXzidgteEGJouAnl93Qn3ybZVbr2AOD7X+5gaDgwnQAVhczVw2YFLX1xYATibKsocLh3QChIiszx\nAnzp26tkskcNDQ+x9EHpBpQgTIrLRhEHw3HRrCxxWdS2IRLdBWh6E/zh87YXwRFjGR2RALInSnrT\n1GQRN1oazkYWvCAkrZTIFkg0bC9mEx4YDkZzkv6UBR66KkIUuBU8CEAW5XWkItKWnuC0PJUW/5NE\nHt26hhstLabvT5e2sGBaTbPsbkrjv37M2dcviTzuHdUxszxEUbSyWaefYdm0b3qxZqXfs64na5wU\nY+CHJIxUFAHHLQ17VRmm6+OwqaGmSrjd1XHU1BL3cGZ5+Gfv9WF5ISzPxcBwMx0ia9Q5Xo5thFGE\nVlUGEDGbOocgAt6/NFBZ4GXK8sk4XoBHfSPWaqKfZefOLmkn2N9l553vkhZy6pSLnPbcIetOEnho\nipgQ6HT9KC49asqC1RpkTbarRJJGEjk4XgDHJ882jSdp1SR06wrZdErO+7IHh5v1m7hZv5l4n2F7\nMcN9FC3mG8eBq1TgVCrwjl5OzOm93+1jPn2CiUO69NKmvfZpCCcvQ5mOEU4miCYT2IYF3gFk38BM\nXeUJS9txfwR1YuFcVHF89hRP6He7NvbmA/zBn/4Y3vnsYs7QpbP4N2+KkOw6jt/5EQQKhxu6hPqe\nikqrDr5Wh8gfIlK6mEUWNLECSUiWkfLwaFTc+XZXR1UVV9Y7zbSwyu9soJXFqr8u8GcDk3ZVQbua\nPHxdh5H7rafjRGAELBstJFFg4APJBpRufbUkXVUkcNySTgXYnEiU2q6gHWXxh8/bXgRHjIkZMgx5\nEyUrwr25p0MUeDi+j/16JVcg0fGWZRmWo8INQlhTB926Ej+ZNBB3l1IR6QlI2ac/6BmL9tmkU5AE\nPj7VpEtbAKGin1oejltLBtRdk1quWxRvnDZyxRqzrEzal12s1GnmsW3T68kaJ8U5OF6QqLIqkoCG\nLsUlVDYwomN893wKi7mXFFjteAHuiY1C9ewoAs7HJgQm6K7IYoxBcv0AFUVcuaai4JVmRVjMRBob\n8jy4ScrQSqRfp1gilmrCCwIoohSPuVtT426fuirDcgjezg0IXvDOPtFq09VVAVtJ5KGLHOoqCZTW\niRADdF1c7+DA/gbHrc639Nr6K5/76xjMHDzszWAGBubeFHN/irk/geFNoPi3IDRfQoXJdImuj3Bm\n48ZeFQ9GXwMe/WLhde3t3cBIVeDaPmxzDDUgB7+pquPB3k1M6iLyaBFCyUdoWgiePIVjz3Dh2Whc\nvgffNaG5NozBIxgA/tp//irOjhSoLlD1eNRCGTWoiPga3KiOdnAPLfEePEnBjJcgKgoauoSzkVWY\n3WDXOQ208tb5+vIPkS9KA6XT3bublp0M28PFxIbp+In1DCxxQ+nnzjagxC39i3UgCjxud6q4d1jD\n3PFBO/zWdWc/L2hHWYHeogzTruxFcMQYh81EZNMRLm0xXycs6QVLJ01JFGk5LowiBOFyA84C4u5C\nKiJrgnMAriY23CCE7YcxGzPNBpSp96YXx3Vo/LNsPd+OinZVLfyuzQnPlqe8dPo973ryxnnU1KDJ\nfGKjZh1wVlBh2B7Gi0zGssuKzJfRHAA4HDfV3Gu5uVdBuyYnKCZoZ4zpejhuVlYkQahlBa/s809j\nJmw3BIfo2rIlWVaWViJt52MLE9MFOMSbCStUTDaVAIrEoaqQTYS2RntBSDgCQJ7N517Zx1ce9DE2\nvQSvDC1VNCo0a+qtjIO1vACKbYFfd3DYhjBWkXhwHA9drEMX64nXPD9caBourVNTUNckeEGEg+pd\n/Ju3fxqGN4HpzzDzJrADA3N/CtOfYe5P0fxP/2uYQxcKgFpFQNWzEE2neHQxgTOeg6/+JoBR7phl\ni4fqOxDDAK4gIeB4aK6Nm+Oz+D1GZdEJLAO2HKIPG4ANYAwAuPGHV7j44AJTtQohCnE8ucDAmUDj\nbUx0He8dcPjNT1yiBgU1QUddrqOmNlCv7qFR34dU6eKlgzcXnY+ba46x2cs0+STbwbm5PAshkLya\n2BjSakPcMLDEDaWfO/v/WVQLrxxVcTW1lx2naygMnoeKwzZluiLKgF3Yi+Aow8pG89umRiWBhyrz\n8WbFOmJdFVCRhcwTy6ZSEXlm2KSklwYojk03dowUM8USuZWt97KLo0wNedOFUSY4zHqG162Tk+9M\npt+zrqdonBTnMHc8vHtuJHiB8gJcxwvjkywbGFGb2z7ev5pBXgSwWaesl/ZreHA1SwRIqszjzn4T\nkrC89jRPVdYGyz7/LGdL2p53T9a2Ka0EsCyD0lIm9XhpoeJOVUZNFXE+ITxlNHjkFtQcrBjma8cN\nNCsyzgZmQiC1pUv46AlhLy+HnViON83PBQAVWUBVFXPv5TaEsYXkfbqUS6fx1tMxQk/DnconY6xb\nt6big/4ScGS5PgazJU+PrCkQGjqsehOBZkL1AjTMZ/ACHnZowAkNuOE8Dj4BoHJwGx/901+Abxjg\nbQtvhq/iaHqFcDBAOBggGAwwqxYHnvWZA9E2gCiC7lmQAx++4+Lc93F89i4uXR4P/4QMElBNADwj\nqkRj0PgK/+VPvg9R3kP/4Bb4Rh1crQa+VoVe19Fta/idzgxPdQd1fQ/1eheN1hEa7SPU1SbOBxEc\nj6wb9pnSrOq25aeHPQN+ECUO1K4fJbqjl8F58TOnOC5dEVYy7UBxiaxMUL7p3rRNmS59aF3H0r+p\nvQiOdmDrgil2ogCELr9VkTGCm+mIXz1urGzAZaUiiizNy/RkYMZBmB9GsL0gDtQEBo+BaAkyBTY/\nsW6jcF+8OLcLSndVJy8P5s4fpyIJ+My94gwXNUqw6PrBSmAUhBEM28N3LwxMLAISzmJlp2DkLPb2\nhz0jxsCxm3NLl3D/pJxzZHltnhceYN33ZtFK0DKoyHPphtH47/WKhP2GirMR2byyQObtqhw/K7oW\n6pocB4XNihgTjVJbN0/YTSt971WZRwRu7dzcJotcZlzUr1CfEYGLhZ8rchTPr97MTswdxwvQmzmo\nqgLudPXEM1AkAR9v/ihs70di/cAoDDGyJjCCGSqai4pYgSIdoSEJOGpqOLnZSKwLwzUQ/sMv5l4b\nAPgvfQJi8xBwQ9iuDdGcwZ8I4IwZ7PkIlpZPPULtSj2GEAK4vEBwfo79eR+6Y0H3LNgAvvznbuIr\nn2kvBYyfJD9/+0zFF77xMoZ1wnLOaxocTcO4qaLSqMKvVvHbZxdod7qoNw9RUxuoyTXIQjb/Gs2a\n0tI8e6Cm3dGHDTUOztOW98zTAS5rRSWyPMJXSeBWmnrWHUA3qURkBe7s7512Mr9mK3sRHDEWRUSp\nfldMm0Xp1dGiY+mwQbwQ245JT6i7Zv5MM1CrkhDTyTc04vBFgcetbgXdmprIIEQMVcGmJ9ZtFe7L\ndIWUDQ53WSffNDgrGmfRa+z8GZseLDeAYbsQeB4AB4EnZTZJkNCbOQhCIj3SmzorrOzrCNu+1LtY\n2ZybFTnenNOfe54SN3n3dd3vsrQSNMChJeqGLmWKwUoiv/LZNJFpnsO/vVinec+/zDxhZTWopSVt\niubmNgeFrBN3Hs4k7TM0mZzPqbp6Q5PwnbMJ7EVWj4CbBVQVKcZy2W4Axw9IB1fEYTz3ElQKp+0u\nTtq34IdRwudkzSVd0vH3fuxXCbO5M8HMnWHqTnExG+I7F5eYulPU7nwfpNMuXJOUnjyeh3ZAuJNq\nVRHC6DeB4T/IvT+yx0O5+zJCY4ZoOkNkmpgpNewbS5Z0Qy/OjIrjOcy33oanXyb+PjIG8F0TEYBf\n/s8URE+TEbvsA7rLQQ9EfPH8FG8Kp+BbLYz1FlypBr5axX6lijCUEFVDzH0LXKTh1l4Vn32lkxuA\n5M2TwWzZvZjOGgPJKkA6855F+Or6mxEp098oMscLIQnZWX/XD1cUFHZlL4Ijxhw/wDcej7bSRMsy\n9mGm06tHTSLfMLbcFS4jauzGmZ7UmwZOWcFBU5fwdEDYkqsK+Q4WY1TEebHNiTW71LX7+nXe9+z6\ndzbN3G1qbJavooiQBA6uDwShh6pKiCS9kKhvCwIfZ/tsL8CDS2OFlT1vznhBiG6dgMDTGZPx3MNX\nHw5WaBqOWxqejax4fDR7ch2sUZmy57p5d9zS8OV3e4luHsv1cdKuQRKEQk6ZvO/Oc/iAXSrjWDRP\nFEnArU4VphtcixJhmywyG/Bl4UzyDhSeH+Lt/hz9xcZqeQRn1q4qqChkDjwZzPGoZ8ZM7Jbrw7B9\nNDQJBw017iCrqgJeWWQ1SWBKfiPPl3Ach7pSR12p46S27N67GFuQZpdwZJK5gkgOen5AMhw0SJYV\nGR89+QG8dOuIBFbOFFOXEHOO7QkG1hiKpqH53/zc8kd9H6FhoCI6qMwnCIcj2OavARjk3l/ViiAF\nq+U/acE95SpAlNEe7YqAK0YYwcP87/+/mL1FuhFNScO0cxq/rwrg0RsyfudfIX75NwfA//x1ElTV\nIhlVTkNNrOLfkz4PodkC12yCb7WgNRvQGw1wIpljisRnlnTVReaO9ftpfG2a8BVA3D2ZtqIgv0wl\nIivr35856M3sFW28XdmL4IgxP4xwMbEBbKeJxhrrWNKcGbZLFiydXN2aXJpl2fNDjE0HzYocn7Sy\nUvqr35OtPyYKHAKPZM3udKuZOkabZoOK7slqeWmzEt222bRtwKvfS6O4MBbXMrMDcBxQUSQcNlT4\nYYhxb45p6OGgoSY7V7wgJnNcF3TQuZHOmAAkqG9WpBWunmcjK856eAsGZVoG2vZQUabsuW7ePRtZ\ncaBHT8Eizy94uqRCTpms7zZsH2+fTTKDlut25ix/l8+89+zru7B1fGbpe513oGAJUGn0xs3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WmCKbxTlTGXxfgwtcmBbxfzNE9iiCV8ZX//uKUVdu9tglG1XB+juReXlVlb5z8lXsLd5t2trrnI\nXgRHKdvV6X9XxjrpwczB1z4YYmb7sa6OLHJ4+aAWK6ErkoC6Jq9MTLZrKd2BAyxPWOlFV7ZmftzS\n8N7FrJAQcBdA6HzQdr4GFIBSbcLpjSZ9rRwiPBuZOGxqqGtJbqqyoPGyciO6IsDzQ/TMJD6ipZON\nzgtCOB5J91PSu6JryRpPmWdRFER8GGslPY/pWhB5Hn4YEnxJqlTxdGjmOvRN9fyeB3g/fe80WURL\nl9BMZQNJwMCjW9cShw6W8HUTwP0n7+xhaNh499zAQUPFeO7hYmJjbLnoVBXMHX/RMbYENR801Fye\nI4CskRiw7gaJTr68oKFIkJnO6zKbPF3vrC9zvABPBnNUVRmyyK1ktQipqYIbLR/vXZJDJ8meR/jI\ncQOaJCACIAoEYkHb+OlYNg2Y2eusaxImpofLiQ0vsMHiMd0gxMBw0K6piWBgXUC2i1I+ez3s9VHf\nwnNc5nWnKSYAsobeOZ/m8uXl+SWaPS3Cy37YTTQvgiPGogiJqJl1CrsCwG1rVVXC775zBcsLE8rs\nrk8IIA+blYRjT5Mzpgnd0h04VGMqS9x2Xc187gT48rs9dOvaTggB86zIKRVpQNGxsJY1tvRGw/JL\nUR4XZSLg0WCO071qKtOQv0l5fohHfWNFgqPIga3TO7vTrRYKPO4qJZ8XRFACyCzbxVpZRxz6idst\nPOwZePtsugxeF7QUVNZiF3p+z4P2ISsrdf+ksVXAsGk5+WrqQBJ5SKKcEM4dzJwEBQj1EzPLQ2IT\nT5U0yXcty7ZZTQHUWF4hilXMEmQuswmyz5D1ZYYdgEyHCG2dfBHt8Lu1py8OTxzuHtTQ1GV893wG\ncBEqiohbHT3RSVfkEzcdI0DuKQfahRyC5wFZIOufZIOXGTsaDHhBiG5NRbMSZhKYXueAkrfGjlsa\nejM7d+05XoCvPhwkpEJYQP6DSwPdhTgzW+4swqjS7GkeXvZ7oWDwIjhizPWDRIo23YHxvYheqV2M\nLYzmHhxvVZndsGnLvJJw7OuEAlkphTQYkDV6emG7PNgOoDIpUTKe6zP8Ukunb/M2O7pRZtXMs1r8\n6UZDtKC8OBCl75MFQq5ISztlUuBEukJb+e08B0Y3EeKEV/XO8oIT9jvLtMavE1kuuq9j008IVKbt\numulDGfVSbuC/szJpKXoTR3s1xW0q+rKOHZBOHldywq68oK5dQFD2XJPXqkV8GF5YaKUxgqQcoji\nucaCp9NYL00WMwMjxwvwRx8M8d2LWdwhS7m4PnJUL8U7lUVRQI0GZ0PDwdzxUVV1qKIAgaFAQMSR\nzI21LMm2qwqOWkwmLEJpn1jGsuZZu6qQzJEfEiyZsGyoAZaZkyJSTGoXYwvnI2traZu8NUYPuum/\n07X3sGdgbCa7R2kA2q2pMGyioycKybly1NBw0q6s+CU63zQpm3D2e6Vg8CI4Yiwt8pFmxP1e6m/N\nFgFGuoZOjWzWSmJTyjqJPh1Y+MA1cO+IbMplBHbpSfdx38jMqhWlRNOMu8Dmm8y6jbJos6PYgTxw\nbnoTpxvNxPSYDF0EbTFWNyCs6SdtDZqcdEJZmxSHaKVcwl5DXjBL0u9WpmRFWXbqrPEQ8dowcerL\nex5F91UW8ykjgOszR5fJ7DheCE0W0Zs6SFF+wfYCvHtu4DP3VqOKbQkn0wHtNlmldYH+NmW8svio\ndSUN0/ETDNEAwRN98nYLlhdg7iwJbdM4JHodWYHRl759gW8+GcN2Q/ACUFVEtHUFD65mhc0B6ygK\n0ibwPHSF+KWbexVYbgDTCVBRiIyJLAoAyKYelyl1CeM5EmDwXYiOA9nzrKIIcTNMEESJzjBgma2i\nzTOs0flH1/V1pG02wf7Qe2W5Pi7GpFSdpfpguyGmloeh4aChSxAhJF47n1i4d1iPx8+ytlPdu97U\nSpCBfi8VDF4ER4xxHLeCxaHcG53aqjDsh8m0XFt8v5ih5AwsMyOs/g+d/GmhWdsLMDXdtVpDaWtX\nFfRm7srf2ZRoWpvofGyhW1dixl1gs3JbmY2yaLMjYytPVkg3Gkng8fBqBkEgZHCj+fK63SBMBKnU\nCWVtUo4XxkD4LN2mvGCW3tMsyYqy7NRZ4ykjOJp3b1jTZBEVOVo5UADXP+mVxUtRLax0Wz81Pwwz\nT89lsmpFc25o2CubV9mAn33G7KYD4Nrl53WBVd7zpHONZN+Sr9legIHh4JN39uKMZkMTMbW8zDJx\n2r72aIhvPhmTrPXC5jZpmRcFkvnLy3CsC1DzgO2igESQZ7okk3GnW8HY5BIEkAAJAO/s67h3UN+p\nL8+aZzS4JMFMZQWm0KkpieaZtLFZ4+tI25TB/oj8Ksu86QSoa2ImbhUAHDcAuGiFeoKOkWIjXz1u\n4KsPB2hWJEjishuuohAqk1sd/UPZV4vsRXCUsjQWByCkYuzC3wUILsuKgq3DpoaWLmE0X6pOU6uq\nQtytlpV2zhKaBYDezN4oOCrif6mqInozO9EGynGky6pMSSvPymyUezUld7PrLK5v0xbcZkVGuyaT\n64mSnyVK70vHlHZCyU3Kg+cHCa4qYHnSywpmgSRoPk2Otyk7NR3Pph1164KIXbW7F4kkZxl9vapK\nidQ9a7TkkweE34RwMl1mevfcWMFGlAn4aRkEHBLYFgCJMuA2VuagVrR+NZmH5a6uNcosPjRsfNCb\nJwC4HKLM5gR2TN+9mMFOrWE/iNCfOWhXFXh+mJnhKDNX2XI/PXS0dAkzKyNgXhDc0v9Ov1aRxdgX\n7urQa9geGpoE0/ET6/WlA7I+vCBKlPHuHdSxV1MKJX/YrPF1pG3WBcqSyK/sGwDp6KZBWNZe2dRl\n+OFqlyCwoIkQlv4uLVpNLQL3PQ+MgBfB0YplsYDev9lIBD277tIpG2x99pUuvvxuD36wBGVXVQH3\nT5ormxKd/Hkna2nRTbAJcDZvseuKgOOmhscMXgsAPB8QCtRXyuBSym6U6zbqTTdxloATWAakS8JN\nPv6edZ1nY9NNBEYAcWRj080MZqmxzoftJtyWnXqbjrqi+3rddveieV+W1fveQX3RKbUaeK4Dwq8j\nnMzSZ+MAHDZVSGJ5wV16nbQMcjmxwXER2roSEw0WlQHTxo5ZElZLgEUHtbzn+fFbLXzt0Sj3Pv6T\nb10mNjz62tTycNzKBtkODYeUjjJU2P0gguX4kEQ+c42Xw4UtP0efcVOXMUsFt3SsFH/I0mTQ+eUF\n0bUygsmxpec1lxlI5jcLJJtnWEtnjbeVtikKlFs6GUuWQDkRs16Oj90rmxURrxzV8a0nk0y6h6Pm\n8jD4YRFcXsf+2AdHX//61/HzP//z+NVf/dWNPkc7nrL4JDY5fZexssFWXZPxo2/eiEn3eI5DsyIX\ndrFQan7WWCBlmUm4brEDwDvns5WgEiCMu3kLvQwupWw3zrqNetNNvKomCTj3qnJcdqD3r0yWxLA9\nNCsKLDdccRbNyhJAn3Uv2ED9dK+CdnVZ2t0ma7NtR926e7dtu3uRxlizouSyerNj2aspeO24kdll\n2ptaa4HwWWOnc+5tRhw1vk9hiJHpxiK/actaT/Q6ZZFLNFQM5w4aGjlpizy3UgZM33PHC1Z4vNIY\nDXqNbz0d41anuvK88taJYXuZQQMAfPd8CjvF0l2k8bY0QmRZUUQYCy031mRJyIQrkHGWx4WxhJ8T\n04MoED6w9HWYphfjD7NIQrfNCKYta15H4FYCSTajez4ycT624vWXbp6hls4a50nbGLYHw/YLfV2e\nD7n3ShffPpsk3ss24ByluN5oiZ1ywDV1KYZYsBnXpL/+8Agut7U/1sHRr/zKr+A3fuM3oCjlSkdp\nOE/WZvM8NLw2DbYOmxoOsZ6J+E63CtPxE9IBaUXtMpNw3WJPcyixTkeVhEzgblaGYxdsxUUb9aab\neJKAU8ReTV1bSkhfy9zxMrOR6eC0KAjs1BScdpLXuk3W5joddbvm+ymjMZZm9c6bB8etpW4atU2A\n8FnWral4m1vdIJqaSkRSSwb87HVqsgiBJ68HYYTLiQvD8SELQizWOrO8zGyQJHB41J8nSn6u78P2\nQow1N26wYLNdphskgng2+5F+nnRukHEu/265PrwwzMWQsBpvaWtX5ZjIMggjDAwnDpBEnsPpXgXd\nWvakKoMLywqIZZGLs1/pkk0R/pDivlhsJLVNDr2b+HP20Pl4EYhT/0wzQrSExZbe0m32AIMBjCJ8\n9eGgFG1IkQ+hAuVZDTiSyOMjR0RrbmZ5cVB3PrZxPrYhCRwkgQOYvSDtrzeloPhe2B/r4Oj27dv4\npV/6JfzMz/xMqfdLAnnoWZsNS4xVZJtGvM8zvUiJ3wCUFh5N23UB0WUYnb9XbMXrbJvfTV+L5fro\nzcgJMOu0yt67bbJB2wZ8uwwktrGyGmMsZ1UefcGzkVUIhM/7/XX3LS+TMja90gF/+jpP2hUMDQeX\ncxt+ECIMBMgKKdXaXoDzsYWJtbrmvv10gsuphf26FpfVZ7YHy/3/2zvzIDnK++5/e6Z7rp3ZndXu\nSloJyQIFIwfMG0BEOKZcL8bBsYPMVUWVY7twYmRRLsMfNkY2+AgQHFNYphyMY4yrkvgKiZ3ygY+y\nC4eqVAnHRPBCuIwvhBZpdexKszt3d8/0+8fs0/t0T/dMd09fM/v7VFG2Zme6n+7n+j2/U8XkShj4\nhoksXjtV18tRsDY61X5YjQ1xpWzNsZWoKDN8jTcrpgtpNNUWNk1mMZVPodyQUW22sXldFuvyHcfj\nk+WG5eZtl/F+02QWz79WwtxiTS+BlE8nsW0mr/vhWPVPL/9DMSlAStqbzpwnTXW+nrN3farSxKlK\nE8kV/zkmEG2dHsNyXUa5LkNMJiAlkzi0UNWFD6W16jxdqjVRzKXw379b7CoE3K//7bSnuVQSS2r3\n8/Dj/LVTta45qbQ0jKWTOGt9rue6GVSJHr+IrXB044034rLLLsN73vMeAICqqvjsZz+LH//4xxAE\nAddddx1uvfVWCBb2bMbb3/52HDlyxNV9zQPFauO2UmUD3iTeMNSL555R9DwIB3WILo5JtgIG+8xs\nzgHCy1bsBDf3Nb/nbEoENKErkgSwykYevBDYL6LOiiDs/05rjDGcpi/gHeHd3h/oPgRZCbTFMQkC\nVrUN5nI5ve4znpOwYSKDiqyg1Upiw8Rq0ddMKoGavKrx4Z+90lT1IrSlqgKl1UZS6ERS1hUVhxZq\nmDtVA9OMpJIJzBZXO82JkMuPDZasMSUmceR0XTdxmmE13nj4NVNKJpAWk2iqnSz6p6pJnCEZtddW\nc71XxvtXTlZQb7ZxYqkBeaWfTleB0zUZF7xuXd8DmdVaOFMY6zkHnK7DTtfzTgkTGfNLdSyWZT0a\nlvk0Ms1kqaqgmDPmjzMLH68uVPQs6rxzNr/muDnkOC1Y3e/gDKBnwE8vE28/k2AYxE44arfbuPPO\nO3HgwAFcdtll+uf79+/HgQMH8PDDD6NareJjH/sYCoUCbrqpU633gQcewJNPPglBEPDQQw8hmx28\nACZgbVLq+EMYzRBeJd4w1IuDbLp+OUTzGxe/eNZlFXOLNcs8HUFpLYLCbrFgKnJzVXO78RKGEOiH\nIOEVNg755IKAdY0xhtP0BQy388rJIYiZrDo5fnI4tFCB0mrjjMmcZbkcu3awRIAQNINgNDuRRU1u\nd+XlklVNj46sN1VdcJPEBMRkAstVBZMFAYqC1azLgtblG+XUv9Cc7uHkch3ThRQWynJXKRtW442H\nf4+8SVlptXHGupyj6FW7jPdMe1iqyV1pJCqNFg6drOBPtq3rWRDZbi20MlcB9uuw1TWcjrum0tYj\nWPnIV1ntFMM9Q80BUFfyL3ULGOz6aSmhzyFz9nJzlKtdVKD5GfgIQJbp2qpgtV9WD7YWNZVWV+JL\np24MQRAr4Whubg779u3D8ePHMT4+rn8uyzIeeeQR3H///Tj//PMBALfeeis+//nP68LRzTffbHtd\nzZy8wyF2m50kduodbZ7MWqZ0d0tY6kUvm+4gDtEAUGmoK1F11inv2YS2ytMBxMF0HMUAACAASURB\nVCNqwSl2iwXbIGYKaYylxVBORP0EYfPfgxbQKw3F4J8AAIqqoVRr6AKIXY0xwH36AsDdvHJyCFoV\njDrCrqZ10nyU6jLGcylb84W5Hbl0EltncnrRV4PPTFuD2S8mJXYcm6VkoksgyKaSgKYhlUxC0TpZ\nl3UznWlz9OpfyN6DOTKJr/HGsFszsykRskVwCA+b6/0ys7faneCGqXzKUEoJ6ETBFXOSYZNlBZGZ\nf5Pde3A6Xlh9OrXd7jrsKK22bUQvfx2l1dZ9o1jf8iWh1LYGTdUsDwr8++KxSszImxf557ZzZZjI\nSnjp6JJl1KIGwSDAsjxjvNmZ96t0e6ji28P7zlmVawoD18LRJz/5SVx11VW4+OKLfW/MM888g+3b\nt+MrX/kKrr76av3zF198EY1GAzt37tQ/27lzJxYXF3H48GFs3bq153V7md560U8ylpIJV3mC7IjK\np8Ypbh2ie5VeUFptw+fmRGZmR9c4RC04pV9b1+VTgfdrP/+tXvWUehVq9aM9ZqdTSUxiZjxrSPpm\nVWPMS/oCNpfsaniZv8v7iPFO8+wQJKvG8hpWiWJZnUG2gfDz2UkyTsDaL4b50Wxel0GrBVSbqykz\nxtIJbJue0KvQi6aMy3YFpa3w4zB4qtLEck22LGmREgWU64qlky+wOn/6ZWY/Ve6YM8VkAhsmMmgq\nLT3ib9v6PA6drEFtt/X7iIkEXlqo4iVhSU+8yIRcVljWSWoKNpb5en5sLJfUNh4/eYyzJliH7+vv\nNJkw5CjiBb1UMgExIWAiJyKXsl9TzOuNVWJGu5QjdhHSz82dhmoaAvzBlQmwTMPIkm2qrTYqTQX5\ntAQxmdALQDsVZsxjj08FwOYXa3dYBeBdC0e/+93v8L73vQ+zs7PYvXs3du/ejbPPPtuXxrDrmTlx\n4gQymQzy+dWFemZmBpqm4dixYz2Fo82bN+O73/2up/aEHW4YlU9NP9wKb71SE5ijU8wTmj/pxCVq\nwSlxiMDolxbC7u9WTs2DtrfSUPD83BLUdmezs/OHMCd9s2uHEyHdS4LWptK2zGnEcrNIyU4+IbaZ\nm80XgHHcluuKbVFgp89i/hufOBBCRyObTyexYSKLY0sNiAAmct1Zl+2Kp9q9h170Ogyy975QburO\n27wQrKhtnFxudnymVjRI/N+dhnl3okY1VBfr+mdpKYn0yvUUVcNrS2WD1qZUa+qb9qGFip4FnI1B\nJ+kdgFVzk1kwnl+qA5qgR1mycWIVvr/a5gRmi1kcWqig2lCRTArYMJGBgI7Z9Q2bJ7CxmO0yMzH4\n98WvOXzeI7uUI0wQsdL6VBstQEBXdCITUFjfsPHJ7vfqUgNKqw1ZbWPr9BhmJ7Ku0iDwY88qNx8f\nXBCWq4Vr4eiRRx7B3NwcHn30UfzoRz/Cww8/jHPOOQfvete7cOWVV2L9+vW+N7Jer3eF46dSnZVI\nlrvLWfhFHDa7IHG7EToR3swnAHPeo2Kud7JD/qQTh6gFt+8oygiMfg6SrC6S3d+7nZq9wW+UrJCz\n2m4DGlaTHvbxh7BqhxMh3UuC1rRknQ2YRY+dt8X4OyvzBZ/XxSrM39wGr3m5Kg0Fm4oZg3myVFM4\nTUjCc/FUXiixitJTWm3bYsV8ziE+szsTQJi2Ztt0Xn/X7O9v2DThKsz7vDMmUG4cw+nqqpmOCVpz\np6oGwaiptFBptCCrbUxkOykFciv11+w0flawuWUlGC9VFV2gMEfJ2V1XSiZQqnVqAqrtNqrNNiZy\nGs6ZnUBxLIV8RsRiuZM13S4xJYNfc1j/99JaLdcVHF6sdJnOxlIi0lISLZuIbEXV0FTaqDRW15GO\nVjGNpbqsay5nChndT8+pMMOPPat3zAdohOVq4cnnaMuWLfjQhz6ED33oQ3jhhRfw85//HN///vex\nf/9+7Nq1C9dddx2uuOIKSJI/wkMmk+kSgti/M5lg31JYm52bTXjQ031Q5U8617bPLpyRkthUzHQt\nfPyEtkpcFwVe31GvTS9os2m/kz8rXtzr934sOuy98Ytcq6VhqS5jPRfEYOcP0Q87Ac5pjhnLfjCX\nlGCsfM5v2GZtp5jshDRXGiqkBJCSRMcBBm7zcnU+kzA7mdOf48yZXNcG6qV4asckLuD3J8qGjVNM\nAhnJuFXwc8H83vnDTkPuFGq2Et7YoemMdTnLMP5e8+9Pt0/hfw8voS6rKGQlvZzJdD5jSDvAsnrL\nqoaarOqCEYMfg73GP5tbVoKx2l4Rx8TuKEu7675ysoJEQsD86RrqagupZBInlmU0ldO48KyprsLQ\n26bHAMBy7XCr2T9myigPdATFptIEIGDzVM5Q3qbaULBUVzE5JuHQQqeEzFK9qY9vWe3UUmOv1iwg\nMoHKyjmewc8v8zs2+12F5WoxkEO2LMuYn5/HkSNHcOzYMaRSKSSTSXzmM5/Bfffdh/379+Oiiy4a\nuJEbN25EvV5HrVZDLtdRUZ44cQKCIGDDhg0DX78XQfsDudmE/RJq/C5/wsMGbq+TeK/UAmE52/Vj\n0HfEb2y9HDgHfV5+XPZbNAoZCceXGn19PgZtD3tv/CKXlpLQagKaXKZlpyVYnNJXOLQxd41nJb1U\njJUjKtvc+A2bCQBqu4XjpSbqSmdRT4tJlOp1rBtLYx7BBhjwY2xdPuPfGqUZN6eFZRnT4/apNszv\n3SwATedTWNc2av75FAlW78Ru3eUjmgrZTm09MSnowsOhhaoh7QAfCZYSk13mIl6Y6TX+2d+s/HrE\nhAAI1lGWVtddLDfx0tElvHqyhpYGQANa7TZmChmUGyp+N7+sJ/UEmP9Zo++641Szr6G7wDoAaJqA\nrJTAeDaF8WwKy3UZry3WcbomIyUmcLqqoK60UMymDFpBszDDa1HVdgtzCxXUuTEyOSbhz14/g3FT\njgw+6S5rnzlpcZgWG9fCUbvdxhNPPIEf//jHeOyxx1CtVrFr1y7cfvvtePvb345sNotarYY9e/Zg\n3759eOyxxwZu5I4dO5DJZHDw4EG85S1vAQAcPHgQU1NT2LJly8DXd0JQ/kBuNmE/hJogyp/w5DOd\nqspWOVFYEUul1Y6dA7o5ys6Pd9TLgbOKwZwL7QRlPjkcj5TshD/z1crtfD4GweyQa3Y6ZcuomxIs\nTjDXpLLKRs6bohjVZgu1pgpJTNomfWRjwrxhn7dlAs++egrLNRX5rNjJ56O0UG6oOFVtQkwmQg0w\nGHSNqjQUQzFUWdXQWvEXU1vd5kI2F6yeiX//6ycyOHK63vUdRq93Yn4myzxi6IThM+d7XnPFIsEE\nAH+0IY/TnEaEF2bY+Ldbk3jNhrme2cSYhKyUtIyytJpXvz2+jKWVXFVAR2gDOuVkAEH3B7J614PO\nUSbIWhWNFdARUFpaJ8VGqaqg1W4jJSawbiXRaENuowS5M6/l1XayeS4mYVhjfn98GYWsZKgjeLqq\n4InfnMRf/J/N+r3NARRm0zF7l2G6WrgWjt785jejVCph+/bt2LNnD6666qou7U0ul8Ob3vQm1/XM\n7Ein07juuutw9913495770Wz2cT+/ftxww03+HL9qHAjqPgl1IRR8G9jMYtXF6uWp3D+HnFwQLcS\nMpRWC9DQleRz9TfO3lEvB07mCOp1wbMTlKWk0GW2HEsnIavtroXdzufDjl7CrJ1D7nQhrefHEZMJ\nbJnKIZdK+pa7xNx/86frWKg0dAdcYMWxejJjmwFZW4ks0iB0JX202tzYuK00FDRVGEw1bDOW1Taa\nassywCBOhwIefm1g74GvzWiVddqcBNZsTmdjwE5odyOUO0k6OJZOogoYBLyNxU5EWyGbQkYSDdFq\n7DebJrudn83aXV1zyF2flfTIZ0RH7heVhgK1ZV21vqG0kUgAyaRg+64HXS+ZIMpr96rNFk5XO/5P\n5WZH2GnICsbSSaSlTJd2uyG3sbGYQam6OiZmi1mUak2U66vO1LKqQkwk9NxNvEn9dFXBsVIdk2Mp\ny4z9G4tZvH52XH/uKOaKa+HoL//yL3H11VfjvPPO6/m997znPfjrv/5rzw0zh9/fdtttkGUZe/fu\nRSqVwrXXXos9e/Z4vn4ccCOo+CXUhBGBN56VbE/hft3DL6yEDLWl4WS50WUSYThpfy8HTt4R1MuC\n12uTUFoazlpvDF8HoPswOPX54HFizrVzyF2oNLF1Ou/JQdgJVv0nKxpOqdxiLKzUiOpRHmK2mO0q\n29HrpFppdHI2Mc0KDwvLbrU0g+nQyQbsFj8FLatxzZtMrPxpzElg+WK9upa0h9DuRhPgZA3kTZ98\n8XCWRoRp/Nj32Xuzigrzy4ne3MZsSkQ+LepZsRlJQUACHdNsr3dthdNxwDT7xuLFTUNBbQBoqkBV\nVjFTyFgWL4fWERD59A4A8Myrp/U1f7Es48Ry5xlZdnemXVXbGo4v1VGqyfp7j0NuIx5PeY6cMDk5\n6boxPL/4xS8M/06lUrjrrrtw1113DXTdKDEPYDeCil9CTRgReOweALpOP3GK8uuVsA6aYBl15LT9\nvRw4gdUTlxdB0bxJmE1I7DTPhC6+MDCjn88HTz9zbj+H3LqsenIQ7odVZKTa1rB+IoOm2kIxJ+nO\nunVZtexPRiFrdHK239yM2d0Xyk1DqDiwmn9n61QWOzZNuNqAnRJEUIXV2sCEXQhaz7mQlpI4Y13O\nshgsYC20u10HnKyBvQSYtJQ0RUR2/tetVt6tE73VM2ybyeN0tVN4mDGWFjFVSBmEFD7pZr/xuHqd\n3j6rfFkQQdCgqBryWdHg28MX8LXyT2IpInjn6sVy07Cu5NLG3zTl1dI3AHB4sZOPipn245DbiCdW\nGbJHlV4D2Kmg4qdQE0YEnl/3CNIE0eskOmsRUeGm/b0cOIHVxcXLM7Fr20UEnjmTs/x+v+tZ4WTj\n6OeQu3VqDFtXHGatru+1f8335bV0aTGJjJTUN5lsSoRiUUQTMM6ffpubuaxFRkoin5ZQaSoo5lad\njifHJOw8a1rfoPz29QsqqMJq3hpyLK1gNReYVsR8IOL/zgvtbrHSevDtcSrAWLXLjrqsYr5Ux2wR\nPcP8nYxhvmyOJCZwwbZ1OLRQQaXR0apO5CRsX9+pdl9rtgz5inKpBH59dMkQIeimLiWwOmb4+blY\nlgFN6dKS8wV8zf5JzFRq7n/zOrIun0Y+LeoC4HJDAcv+ns8kMZaWcHypjvmlOmYKmVjkNuIh4SgE\nei1kboQIvwSOqAqcurlHkOkGVttoLxRIYgLnzBZW2uK+/VYOnEs1GWpbQz6TtFxc3F6bN2HoCBpO\nLDexjtsZBhGse2U8BoymOzNso1yX794t/ehf832tomZ4Xj+b75szphdWAk6nbzvaoulCGslEwrK0\nhp++fkEGVQySiiJIk71dMdRiNoVsulM41itW7TIfPJbratf4dDqGzd/jy+acvXEcpypNaNCwY3ZC\nP0Q8/coiijkJkpjW51212cLL88tIiQldc+m0LuWxUh3zp+uGedxJqAnMLVprVVcL+ApdPlYsGWi/\nMkTnbSni+bkSKk2jYHTeGUXddaYht7FcXzXdNdVWl19WFGWkSDgKmH4LmZvILb+FmjAcor3eI8h0\nA3zbnAgNXt8RE2ZLTGMhdBbiDeODF0WeKWTwkrBk+Iz38TBvkG4F634Zjxlea7N56V/zuDffl9fS\nmcOqx9JJrMtnBgp5txJw+FP4hokMZovZwAWHMIIqvMzbQbXbTpJ7svfNwsybch1nz07g0EIVJ8sN\nT4cnq3abs0wD3ePT6Rg2f4+VY1F1h/2OhvNkuYnaip+PBgHjFtFvvz9ewcx4R2ByUpeSlXI6errR\nKXYM4zzmNURmjV9xTNL3m1MVGUCqow1aSangpAxRLi3isnM3QFbaOLRQQTYlYl1+VcPK5qugdXw9\nT1WakFttpEQBC+UmKk0FsxPZSPxUSTgKGKcLmZvFKA5RXkESdLoBniBNjEyYZadAtqgB/gh6vZze\nzRuk1xIwdhmPAeOG5+Y9uu3fXid0831Z1AwfVm1uh9f506+shZ1gxO7pl1k87LJGTaWFF14rGcxZ\ndlo+L/OpnwbGaryUqgrEpAANMGS59jqn+Haz8hXmHDvA6vhk/98Kfgz3GutHSw3DmsB+W6otWwYP\nsHYxQcZJXUr2TObv8vN4VUO0Cnv/rIYae4bDizWISQHQBF0zy2eGB6wd0ysNBYpFhB7TqhdynQST\nTDAypA6oyZH4qZJwFDBhL2RmgjKdhe0LxDsduzVBmCep0Sk+WBMjS7pmdQrkF1q32dGZU6Odj4fd\nuHKaKM6pg/Xq/Zy/RycO5b1y2wBG4dJuMfa7PwcVcPwSxMMIqmA0lRYef9G6VMcr6BZEvMynfv1r\nNV54czKv9fB6eOLb/YfjFd2Z35zOg/kgpS2iyXhWC7RaH47Ngg6P2tJQrjchJgTDoYdpiphQ0q8u\nJbAqwJm/ywtTvIbI3GcsiIA3MzaVFpbqMjZNZgFNMJi/Ti53Sp6sy2dMzu/WY1YSE3jD5nEUcynU\nmipOVWW99h3Q0SwVc2nyORpFwlzIeILy2QnbF8jK6TiXSiKfEQ2OieZFuNvO39Y1CmzB49sdlDau\nl+ZQUdt4fm7J4BvjJjv6yeW64Xn4awwyrgZxsHbyHp04lPNCoJMTuvm+Xvuz36Y+iIDjpyAeVlmj\nF14rGQQjYFXzIIlJ203L6ft3okU0C/rm9Bhm3zKvZkWmJVluKCjVOv+tao+ErrF6stzoMjMzVhOH\nWgtRLLS9obQgcRofVqC32lCQZHm6VtqQEoUuczHvz1hfuRY7uFQaquGeZsdqRW1jurA6Zsx9xvcN\n/zu1rUFWNRw6WUVKTBjyFzWUFn4zX8ElZ2cM12kq7Z514ioNFVOFDKYKGcsErqxPw8wRRsJRCERR\njDQon52wfYG6Ns+VLNu8YyKDL7ZoLhPBrlNXWro62e92W9FLMzhfqmNmPA0Jq9/pF2nCU8ylUao1\nMTNuTK/vZlxZhzy7d7B2Qy+HcrXdwpO/X9SfyVzHyYxfjppOhX4/BJxBBXFzNmE/NwtzpvhSTbX8\nHtM8DPr+nbgd8EkmAaM5yapkh1dtfC9TMjSh25dNEyx9fczRj+bDsaK2cWKpI9CkxaRBCJsvNdBQ\nWob6Znyy1vGsZJlMMyMlkDUdqMzvwXzIecPm8a46Z3z/s74xa+rERCdJZautATCWBAI6hXQrDQVS\nMmE5p6zqxCmt7gSkPIKg+Z4jrB8kHIVAGNFhPEH57ITtC/TCa6UuwYj5ADDHRHZvluH11cUqZgoZ\nw6mOn9xm23zQYaJ2msO6rFrmjrFqk917Z46dLBFbqSajrWk4XZUtizvy9BIGwtB22jmUq6qG09XO\ns2dTop5vxWoTAvwzS9sJ/S+8VrIshhyF31+wBaOtM8UbPVGMKKp9pKJTnLodmJM7stxLZp8gr+Oz\nlyl5qaoAAjCRkwz3K45J+P3xKqBVMDOesS2HYz4cz5fqADRMZFO6YNGQOw7LmtbRDrH6ZuZkrWaB\ng2X73jaT1w8P/AHLah5nUyKmC8YcRVb9L6CTPNWsqUtLSQiCgESy83mrpemSBBMem0q764DK2lZr\nVvC66e65rKhtQ/1Jxlg6adA4Wfk4BQEJRyHiZUH1IlAFFc0SRpQMIy0l8brpPGpyq8vhuC6rncVs\nRfV8fKkBpdVGKpnAunwaaVExbKjmyW1VNTrIjc5Kcygmha6FncdddvQWnnn1lMH8YVfckdFPA+i3\nttNqHJsdygHgd8fLKz4XysoJUuyq48S3x6ug1q+WHm/yq8mtnk7IYRGk1tYuU3ypLlvm6QI6wsKg\ngrJTQdx8wDxzJjdQWgYz5pQV5lxAnRpxnfmqqG3MLVZx5HQdSqsNRVVRaao4e2MBZ85MdI0Pvu3H\nSnU0FRUaBCQTAhYrMgRBxrqxNJpqG/l00rAudCdrNUaQ2SU2ZQcsp/PYqv81CLbO0FumMlgsK5Bb\nbSSTHU0ef3i1ModbzSlp5bdMG3ZyuQkIDUPNx5lCBocWqpZmeN7HyW9IOIoR/IJtp5J0sjgH5QTu\nx3XdCHtpKWGpYpVVDYsVGcUxCarS0lWycquNU5UmplfMPkxL1Cv/Tae2kBKoNs9KcwislvSw/o3z\n7Oj/79ApQ9VrwLq4I8OpBtAPbaedtmOm0FnMWP8qahu/PVbuLI7oCI8NtYXZiax+ijc7nHrZCJ3W\n0psv1bFUlw2CWhhmWDuC1Nr2yxRfHJNQqsKwKU2OSTj3jGLf6zoZO0xLbBUNZ4Y/YA6SloHRL2UF\nywXEM1+q64IRAGTTIsREAvOlOoo5+/GRz0hYqJT0pI0sk3pTaQEC8LrpsRUnbOv1na0Dq4lXrTXP\njFMVGWNpsa/51SrTPNNWFXPpjq8TJyB33s8YxtINNBUVGyayhsPrWLpTX9CM2d8pm+pYACBo2DqV\nNwikEIBzZgvIZyQ9w79ZMAKsfZz8goSjGODU2dbp4hyUWWSQ63oxCdjdr9VuQxA0pMUkqk2jT4Tc\nakMUE/pkVtQ2xnOprvw37BTCTFsny3LgmgGz5tCP7OgNWekSjBisuKPZxOZGAzio+chO2wE0DM/E\n1ylLiYJuamDaP3MdJ69j2EktveWagsMrYcWAUVCrAl0mzzCiQYPU2jrJFD8+vWrisUpyabye+5IW\nGjqRWbKqIZfSHM9Dv8Znr5QV04VV831dVrFUk3XBiI1VoHMYWyg3bQVVVnTWDHvObCqJXCppachk\nAgfvd1OXVUuncLa28VoldiDp9LU5VUbb8DtzgMQlfzSFbTNj+M18xWD26pU5nfchYm3lryuJCcNn\nfFutfMjMv+dhPk5+H25JOIoB5oWkLqs4XVUMzsMMp6fEoJzAvV7Xq0nA6n6FrIhNkzmoLQ1iwqgV\nSokCxISgaxuYlsic/8Zcmdtpe/zEj+zoGSmBw4t123uUGwo2wigchZVeop+2g5lGFspNNJTWStRg\npxwH0Nk4q00V+XQTW6Zyff2ovLbHXEvvtVM1XTCyEtT45HqD+P9YCVb9NG12DNJnfmeKdzPXzeVY\nsilAQzj1tNymrHjlZAVLNUUPXefz8TAUtY1TFdkmgrZtW04IAMREAueeUbQdV+bP2bg1++Pxhz7W\nppcWqnhJWDLkKGNjlfW/nWZmvlTHhWdO4ZKzrTV1dnXs+MMP79rADqh8QdtyXelyn+BzAIpJ6xqV\nvI+T35Y1Eo4ixmrB5jOfWtmUnQyEoJzAvVy33yZ5rFS31QjYmaSgoRNFAkBKJjo+RyuLlSQm9PwZ\nZ6zLdeW/cWKrDyOnhpt3affdYyV7wQgACjZh1mGkl+in7dA0ATs2TeDwQkVfGM+cyRv8OYBOnTRm\nfrATPLzkV+JhGpK6rBo0WPzmx+Yjn1yPx6lw3Uuz4lTTxjNonzkdD36F5vcLNLD6rtV9Bl3X3KSs\nqDQUzBQykJIJNFfKaKRN5i+11cbx5Ya+wZvLbbC1yxxSD3Q0NK+fzdvOc7t3xa7F1jMW6MEf+vh7\nWSXMzGc6NeusBDYWHWyXMgOw197x45m5NvB+SSlR0LNi8xFv7Du80H72hvHOc8irfcZfK4h8gSQc\nRYzVgs37yFglCeMHQr9FIqioGjfXtduUmBp3uSbrSRLtTt/m+xXHUnok2lQ+pScPYycJYw4j43XY\nCa5Xe8OMRHLzLs3f3VjMYnJM6spFA3T8Quy0LV41gG59xpz8fV0+jZNlWf9cTCY6/mQtDWJSwJnr\nx6C0NEvBw40Jx4mG5FSlU1U+k0oaktHpbUtYO3AznAjXvSLjzEVE+b/77YTM45em2Y35r9d37Qq+\nejHP241ZJykrLKO4EsBYSjQkPwSASlPBxmwWYiKBw1yaivlSJwxfLzQOGISwlChgupDuqofIz3O7\nd8UEuplCGmNpEdWmYljbnCbM3FjM4tXFapfwUcymsFTrHCgHSazZVNorJsPV8Z1NiZ0kuCsuEgyr\nrNhThTTesGkCC+Vml4YpqHyBJBxFjNUE5VWv5gRnbCCEkYzRL+wWIXaikcTV07nT0zdbzAFWQDFj\nyHPUa7JEnbXcb/7s9TN44jcnLaPV7HCrAfTTZ4z91ioXDFvM02ISaRFdta3MgocbDY7T9pwsy8im\nRNvTvZNivHbCbi9tSammGhLfmZPhMU1bEH5Ofmma3cwtLwVf3fR3vzHrZDyYc+sAnfxiSqsNtbXq\npC4IGqYLmZVcRcZxw3yRgO6UBNmUMyG033tdl08hn5GQlhKGg4bThJnjWckQPQqhU6KFOamnRAE1\nWfVcu65jHhMN/VGXVUyPp7qybNtlxWbvKIjDgRUkHEWM3QQtjklYKBtPC/xAMA+yMPI+eMXqGfn6\nReYNxsnpe5DFPCyzUliMZ1P4i/+zGcdKdZQbCgoZe42RGadaKz99xnrlguH9EKxqW/GCh1uzTKWh\nYCIrodZUDSdYvj362ED36X48K+k+Uv2K8drRS1uSEjvJ9cSEfeZw1sagNJuDXtvN3LL6Ll/wFcCK\n1qLZ0SJNZLBQkR2bw52M2V7jk40vc/1CSUxg02QnQEBWO1FjQEeotnMcVtROaLubQuNe3qv5e04T\nZrLfAUA2BYPmi/1uUJ9M85rNa7l6ZcW2+33Q+QJJOIoB/ATlo6i2rMtBbWtQWi3dbg2sbgph530Y\nBPMiJKua5ebHcGra8rqYR5G1PGg2FrNdztdO6bXgDOIb4nRBY98r5lIQoNlqZXjBw6kJp1uDIPTU\nMtqd7uWVDc5pMV7r99G7eG0upeHVhVr3BitoOLHcjN28tsJroAETLMQkoKoaXjlRwYnlJhYrTUAD\nZiczaGsaNk3msGVdrivk3Yvg3Gt8LlaaOLxYsfRzkcRO9Bg7hFQaCk6W5S5NDYNpbLwUGrd6V4x+\nSSfdJMxkv2MBEvzzWr079txeDqf5DAxaLquULYPUh/QDEo5iAD9Bn59bMlRqZsPtZLmhC0dsUwg7\n78MgmBchpdXGkdP2zsRBm7bCPoXEFSfmMj/CyJ0uaBuLWZRqsiPNg1MTHAi7AwAAIABJREFUjl2C\nu+W6gk2TOYvf9c9L5aQYrxX9NAAzhQxeXawaPmcbVJjBAoPgNdBgfiW44ORyZ3NerMhYrDShrjjm\nl6oKMqkkjp7uVIY3R/J6EZwZVuPzmMkBGDBWtOfvx/qVae95eI2Nm3XN/P7cHjTcJsxkv+MDJOzM\nxr2iNZVW29GaGncNPglHMUMSE4ZaWwzjaSeavA9+wC9CTjfBsNqzFnFiegjbR8vpCdnJ4jqI1osf\nGywRHcNNMV43z1dpqF2Zw/kNKuxggUFwMrf4jX62mMXxpYZe+b3WVHXBCAASSQDQIKsdc1u9oNo6\n5Q46ZisNBRoEy7D7htyGAM1S4wisCneAUfPidF0zH1jMUW9O1yz+e24SZpoDJMzYRWuWqgoeP3nM\nstajnZ9SnDX4JBzFCKennajyPvhNnCfGWsCp4BD2Cc+N5qHfGPIreaKbYrxuT/ZWBTitzAy92jFs\n2GkstZUQQbWtocWFC4pJAalkEuMZEXWljVZL0yOvvArOZqyKrhbHJBxZVKBqqxFVGSmpp37gYf26\nfjzdlTDRzbpmdrGwinrzEnTjRqjq9e4A62hN1tZ8RjIEUfTyU4qzBp+Eoxjh5rQTRd4Hv4nzxFgL\nOBEcgE7frB9PBxZGboeTxbzfGPJL6+Vks3Ub0WeXMybOpga/sNNYSmICmVQCTUVAUmBlNgSMrzx3\nOpXEeC6F6UIa2zfksS6f9iw4M+xKyswt1qC2NCSTCahKC2q7jTMmcxjPpVDI9tK8ZGwTJvaDP7D0\ninrzO+jG3NZ+2k0zvCXDnH7GiTk4jhp8Eo5ihJuFMYq8D0ERx4mxFuglGChqG68uVLqiuratmI7i\nJsjajSE/hY1+m61fhWFHXaPaS2MpJZN43dQYaoXWSp0xAVgZgyxbeSaVwJapHLZaVHbncXr4suq3\n+dMNLJQbKObS+rUAoFSXMTuZDWzsswNLv6g3v9wmegn0/bSbPLwjujldAHuuYVvjSTiKGW4jPYDw\n8j4QHUZF09VLcCjVmgbfAWA1U3PcUkX0wy9ho9dm62dh2FHXqPbTWM4Ws1iqKxATCaSlJI6crkMQ\nNKwbSyOTSmD7+oKrvut1+LLqNyaY5NMSBAHGZKCagPXjxpIhZgbJQccOLHZRb2pb85yU0Yp+Ar1T\n7SafAbtflOmwQMJRzPCjpAQRDP3qXg3j+7cSHARoeg06M8MSMcXjxzwx/9a8YQRRGHZUNar9NspC\nVsLsZA6VhoKzNxagtNp6PqFeZjQvWPUbE0zEZAIbxjN6QVw+GSePeWwMokG0i3pTW21Umqs5wAZJ\nysi326tAb143sikRk2OS5brhlyUj7H2OhKOY4mZhHNVFNG50+SX0Keg4DEKrleDQVNo4tFC1/c0w\nqsgBb/PEqRZg1LKuB4mbhIZ+j7Pu8PjufuETJzJ3Bd6Hhv3GsrQINMhquysHE+CuaDhgjHqrNBW9\nILNfSRkHEeit1o3zzpgIxBwcVTUIEo4IwgFWpyy7go4vzy8jJSZCn8yDYNyIuuu08YzaRt9LiHWq\nBQjLkXoYBG4nhO1X1WuDNfcbnzjRbCLi+9IynL2mYqne7MrBtNoO50XDWdRbuWGfNX4QTa4fAr1Z\ngA3CkuGXL59bSDiKmFFZ7EYd8ymrV0HH3x+vGBJ5AuFMZr8IYqOP4zjvdyJ1a3YIcsMP6/QcVj+F\n7RLQa4O16rftGzp9prRWfX/4vrQbGylR0JOCDup7w6LeDi9UVpzT3dfy60VQAr2fGj8/ffncQsJR\nRAxT4di4EuaGa17U7Ao6MqHJHM4KDJe/ziAbPd8vUrI7YVxcxnm/E6lbs0OQG77b07PbNkS1HoXh\nEtBvg+1V78zuPfJRZXy0MNM6Wc3/fgKH3b2cJGX0SlwiI/u9ZzuCNPGTcBQSfjrtxYkoNAJRLOTm\nU5ZdQUcmNFmFs3ba3rtie1y0K142eqt+OblcRzGXMvhgxGGcOzmRejU7+L3huzk9e50bo7IeWeEm\nua5VZJZdX9rVXZstZpESBfDHp14CR78+C9JkG3VQT79nj9KXj4SjgAnKaS9qotR8RbWQOynomBIF\n23BWwHoyx1mL6GajNz9DXVZxuqqgrrS6fDCiHudONsypQjryhIys5pidmQYwCtxe5oafpos4CfgM\nvzfYSkPBc3MlnCrLSCYFPXM2q7v2hk0TrgQOJ31mLtArqxqKOdE3DU9UQT1OUglENQdJOAqYoJz2\noiYqAcWPhdzrAu6koON0IY3xrGTwVWDw9b5GTYto1S9Mi2bngxHlOHe6YUZlduAF5rqsYm6xZqgI\nb9VWr3PDaab0UxUZduH0cRfw/dhgm0on2OLF15Ywd6qGVltDXVYxkZMwU8hATCYMeZCcCBxO+ywt\ndd7lC6+VoKhtpMQENAi6z1TU79gLTp89qjlIwlGAhOG0FwVROskNYoP2awHnFz2rgo5299k0mcWv\njy7ZahHN/gtRa1fcYNUvvOnRygcjynHudMOMyuxgziGTkZJoyC29IrxVW73OjX6Z0n93bBlHSw1D\nMdXt6ws4Z3ZcnzdxF/D92GBfOVnB749XUGl2chAlEwLyGQmttgYIwJapnGUepF646bNXTnYy1o9z\nuYTi9I7d4vTZo5qDJBwFiF3nD+K0FweidJIbREUe1AJuPiHaTWazYAR0tIiLlQbEpGDpvzAMWkTA\n+r3rm7rS6vLBisM4d7Nhhml2sDp8zBazK7UUW/qhytzWQXykemVKr8vtrhpfvz9RRkpM6OPcz8MS\nmzdKqw0pmfBlMxx0g600FCyUO3mHxIRZ+BE6ApJ+L+dCv9M+i/JAGhRux2vYpj8SjgKkV+e7ddqL\nE1E6yXlVkUexuPCTuZcW8eipOibGJN13AVj1XzhvS9HXNgWFXb/MFrMo1ZoGDWlcxnnUzqh2WB0+\nJDGBrdNjqMsqNkxkMFvsru81iPnILlN6WkzidLU77xUrgsreXb/ncbKpMY1rqaroOcTYIaE4lvLF\nfOR1g20qbd1MnJaSkJIJQ42xVkuDorYxXXAn9DvtsygPpEExyHgNY86ScBQgvTq/OCbFcmF2QpRO\ncoA3FXnUi0uv+2voLK5ds9GFej4OWPVLcUzCBdsmobTasRzncZx/vQ4X2ZRoKRgxvJqP7DKlP3u4\nZPsbRV3tU6/Pw8PazSdXZYcESUyG4s9oNxbSUsJgJp7Kp7BYkXUBKZkUMJGTPAn9TvpsVDOwux2v\nYfq2kXAUMP06f1hLf0SZH8PLiT/sxcVJmQKg47Q8lU9BEhNoKC2oLQ1iUsBENoXZ4vCY1YDe/dIJ\nSY64gRyj6kA8qDbMnCmdFwjMSOKqyWtQDYDSauvO5+Zq9Mw/k33fbyHWyVjIZyRMF9J6SQ8xmcCG\niQyaSgvJpIBzN0/gwjOnPN3fSZ9FfSC1wukY6y10uhuvYfq2kXDUAz9OlXFV3Q9KHJ7LjWAZ1uLi\npkwBsBr6LyY6DrcAwNtah/FEOAwC/6g7EPvRB7xAsFSXdcE9LSaRSSUwXViNWhtUA7BUU7BUb2LM\nJl0B888M4rDgdCycOZOHrLbx++MVXYCbGJN05/RB6ddncUnY6PRg0et7Zk2yn5F9fkHCkQVBnCqH\nYcPwwjA9VxiLi9syBdOFNE5XZVQaaifp2crnDaWFUq05EoJ03BgG51Yvh48gDiqbJrP47bFllKqK\nbkLKZ5K4eHbaMG+UVhszhQyKOWdO1OZ5wCJ4m0oTQLe2ijn0B6HhdToW0lIS52+dxFnr8z3TGnht\nR7++i8OBFHAuTFqmsakqePzkMcyMr+aGc7q3hu0aQcKRBXE/VRLeCHpx8VKmAABKVRlqu90VrVbM\npWKxUY8aUfufuYEdPioNBYvlpuWYDdJEePR0HZsmxzA5lka5pkATgPGshHxaRFpK9ry3HVbzhI9s\nFARA47SnLKlqEOYjL2OBaTr8ub/7vrM6kHpZ07z+xokwafc95k+Wz0h6kIbTvTVs1wgSjkwMw6mS\nGIygtF1eyhQslpuQxCS2TuW78hzxvyH8Y5icW51snkEd5vi1kNUN469faSh47VTN9b3t5glLV8DM\nz3y0WlDmo6jHwqB950W4GkSYdrrGWX2P9yczp7FZKDdxeKHSUxMXtt8VCUcmhulUudaJWr1sxstC\ny3/W2YDcXXNYidpXLW7OrXb02zyDPMz1WwtPVWRP97Yb0yxdwebJrB4q71eeIzuiHAt+9N0rJytY\nKDe7ksf2Eq4GEcicrnFW3+OLdTMzqaK2dW2SorZxsizb+iUB4fpdkXBkIuqTBNGfuEYaeVloh2mj\n9oO49F1cnFt74WTzDPIw13+t6y6R4+Te/cb8xmK2+0c+YCeQR1cixn3fmVMtvHR0yTJ5bBXWkX2D\nCmRO1yur77HIR772JJ+2gQlM/fySwvK7IuHIxFrbrIaROPuEeVloh2Gj9ou49J3dIltpKCvO8dFr\nI51snmYBhhUlTYkCsinR1WHO/C76rYXr8mmcLMu21+t17zDHfP/K7/5tuEGlF7F6hj+cWEZDbndq\nuq3A8kJtncpbCld+CNNO+878vWxKxOSYhOJK+RPezGYlMPXySwojEIiEIwvW0mY1bPQ6+TixWweN\ntxxM8YhCCZogTECDvjO2yDaVVld5l6i1kU42TybA8FmlGZNjEs47w5vfigANG4tZrB9PdxVX5t9L\nVPmY3OBUIB9kw/XqWO30/ZmvXZdVVBstLNVlrB83atpYXqh+ZnwrnAjTTvvO6nvnnTGhPwszszFt\nF3suO7+ksH1+STiyYK1sVsOI1cmnl906qo3Ny0I7TGkRvOCnCcjtZtRvLsdFo8XjdPM8cyaPx08e\nMwhGLNrRSfv5Z+fn0quLVWyd6uTn2jY9BgBd7y8O+Zh6EVaAjdfx4+T9WT2DrGpIS0loNQFNtWUo\nPdRUWqjZPLOflhGnfWf+HttbT1VkXcPJPxfDXI8RCNfnl4SjHoz6ZjWMWJ1srOzWUW9sRDd++vM5\ncVRuKm0IgtZT8wHEO0LVyeaptNqYGe+UFDFHO/Zrv/nZzaU7WGZqoGE5l+J0kLRqQxgBNoOMHyfv\nz+oZmP/OVD6lZ4VSW20sVmQIALbNCHh5vmx5YIiDZYSZbWuy2tcviSdMn18SjoihwnzysbNbA9Fv\nbIQRv06tvTajUlXB068sQlvZMg4vVAFBw+xEFtLK6dosOMc5QtXN5mkV7cj+btd+/tmtSncw00a/\nuRTlQbK3FjH4ABs/xk+v92fVRj0vFIAtUzkAwCsnqiiOSZjISSisDASrQ2KcBNp+fkk8Yfv8UugV\nMXSwUhwALO3WPP0WLiJc+L5jCNAwnu04QzuhV5/Ol+pYqnWuwzZ75qTKwzZ7wB+NFkvS6PQZ3JLP\nSJgqWPvSDdJ+/m+8SYPBmzbiOpd6aRGZQG6FX5tt0AKY3TPMFrOYHFt1WhZXit/OTmRRl1Us1ZSO\nbxI31s3XtRtTYcEEtXNmC9g2PYZzZgu47I83ojhmFI6i8PklzRExdPAnHyu7tfG7JP/HCb7vyvWO\nE7EGAfOlBuZLDUe+YnZ9yoQhSewUYeE3e2Yi4scJn5TTq0bL79QEXk7zg7Sf/625yKxZExvHueTE\npBW0GSmMCGerZyiOSbhg2ySUVsdPDADERKLLMT8jJbGpmIm1Bt3OLylKzRYJR8TQYme3ZlDqhfiS\nz0h47VRNN38xnPiK2W1GsqoZNnTzZm+OfuE3e68bqF+O3IMKWYMIAOy3APQSHmZNbFznkjOTlhT4\nZhu0ANbLFJaWkpgtAst1FYcXql2m0YbSwnypjtnJnC9tCYuofX5JOCKGnjg4GIZB1CcpPxnUCdry\nJJ0TkUsZM46zzR4wmojMm73XQq9+OXIPKmQN4kfC/3ZTMaNr8xhsLsVx/LkxaQW52Yblx2P3DPmM\nBAFal2AEdDSAGgTyv3QJCUfE0BMnB8MgiEtWaT8Z1InVrs/NuYpYvS4Imq5R6iU4u9lA/XLk9lPI\nGkQAYJrY2cmc4b1KyURsx1/ckvZGqe3YWMzi1cWqZcZsgEpfuYWEI2JkiFoNGxRxzMHjVRBlv1Na\nvQUL/sTf617mPjdrlCQxgTdsHsdMIaNf168N0y9H3DhGy/Hv1SxwAtGPP561ojnux3hWsi1gDcTT\nZyzOkHBEEDEmbjl4vGqxrH53crmOYi6lh9jz18tnJE/3ClOL6JfWwqmQFYVmNG7jz4q4a47Dahcf\n1WZO6eC3Fo0/5ARdHDgqSDgiiBgTN62CVy2W1e+KuTRKtaZlgclB7gWEp0X0Q2vRT8iSkonISpvE\nbfz1Im6a4yjM4UFr0dgz8eVqmOmuOJaKhanVL0g4IiInric+RpTtG9R042fbvWoR7H4niQnMjGex\neTLbdfocBo0F4J/WotemFqVZNYwkinHCz/kSRb8FrUVjz2TOpD6/VIckJmNjavUDEo6IyOh3sopa\naIqDI7Rb042bshlu8apF6Pc7KZnAVCHty72iYlCthd2mFrWQGDeH56AIIl9V1P3m9/xgz2SVSZ0v\nNROXg8ugkHBERIbdyerl+WWkxETk0TFxcYR2oio3L+5Oyma4xasWwcvv1prGgmHe1OIgJK4Fh2e/\n53oc+s1v2DNZZVIHVvOIDeOzWUHCEREJvU5Wvz9ewcx4uqtOWphCSdQnPx4rrUKnjSqUVifJHb+4\n8ye7+aU6tk6tbmKDtN2rFsHL79aKxqIfcRAS4+7wPChBzPU49JvfsDabk6syWB6xYXw2K0bjKYih\nw+5kxTZ2Re3+u12NoCBwcvILm45WQcRrp2p4eb6MQwtVvDxfxtOvLKJUlfXvWZXN4Bmk7Va10Zxo\nEbz8zuu9RokwaoO5aUvUtbiCIIi5Hqd+8wv2TCy5Kg/LTD+sz2YFaY6ISLA7XbCNnc9mzBOWyjau\nJz8r9X+ppmKp3tQ1RG7KZrjFqxbBy+9GXWPhlLVg1nKLn2MiqLk+iv3GnoklV+Wj1Yb92cyQcERE\ngp3ZJCUKXQUvecISSgYx6wS1mdup/1OiYCis6qZshle8Onx6+V3cQrTDhoTEVYIIkug31wFgsdx0\n/d5Hsd/4Zzp7Y4HyHBFEEFidrKYLaYxnJSitbqe/sFW2bk9+QUe32an3mTDEa4iKYxJeW1QhJeGo\nbAYRf9a6kAgEFyRhNdelpABZbePl+bL+mZf5PIr9NorPZIaEIyIy7E5WvYSMOLTPjqCj23ppzWaL\nWaTEzmLO1N35bBLFbApKq4WzN4x3hcsTxDARZJCE1Vx/7VQtFtGqRDSQcEREjvkUEjd1tJNTUhjR\nbb3U/8UxCTs2TeDpVxZRzEmQRGO038lyg4QjYqgJIzyezfU4RasS0UDRajGj0lCwWG6GFpUVZ4Yp\nOias6LZeEVyVhgINAsZzqS6frTAj/Qh7aH57J8wgiThGqxLhQpqjmBCHbMyEd8JauHtlUp4v1XWn\nbCtGJTnbMELze3DCzH0V12hVIjyoh2NCL3+VUWTUTtBh5zVhWjVWlPTl+TKOLzUwt1jD4cUKFLV7\nA6EFPRoqDQX/79BpLJSbhs9HeX67xel6EEbuK70ED6wzQQcZGDJq6+IwQ5qjGLCW7NujfIL2O6+J\nE58r/n56CL/c6sqMPUrJ2YYFNtYXyk3MLdYAQM8Jw5d0GaX57Ra360GQ/ojmtiiqhlKtgWIupfdX\nUIEho7wuDiskHMWAUazDY0dc6pUFgV8Lt9OF0kqo1pOzyS3dxEYh/NHA+tCcsdwsuI7S/HaL1/Ug\niFDyrlB+MYGZ8SwEaHjd9FiggSFhrot+CpbmkkZxCKDxi5EUjmRZxr59+3DixAkoioIPfvCDeNvb\n3hZ1s2xZK/bttaIhG3ThdrpQWgnVkpjA1ukx1GUVGyYymC1mR+KdDgPmjYL1oTljOZ+wExid+e2W\nOK0HvdqiQeja8P0WMMJ4D35qp/hrKSvpQ/hC16Og9RpJ4ejf//3fsXnzZtx///0olUp417veFWvh\naK0U2VxLGjKvuFkoe22q2ZRIglFIWG06SqsFaIAkJrsylgOrJV2GYX4HlVIjTuuB07YEYf4K6z34\nqZ3ir8XyqgGrha5HwRowksLRtddeC0HonNba7TZEMf6POYp1eMysFQ3ZILhZKNeKUB13rDYdtaXh\nZLmhm8/4WlRAR8MX9/kdtB9MnNYDp20JwvwVxnvwUzvFX4sVCmfwWlGvWq+45LeL5W5044034lvf\n+pb+b1VVcdddd2HXrl245JJLcN9990HTrCMJACCXyyGbzaJcLuOWW27BLbfcEkazB4L5q5wzW8C2\n6TGcM1vAjk0TQ62WNDOKlar9xu1CSZXrw8Euishu08mmREATUJdVAKvmzi1TOZy5fgx/8rrJ2M/v\noCNo47QeOGmLEwEjqHsPip95m/jv8v50DEVtW363/3VbeuTtoYUqXp4v49dHl9BUrN950MRKpdJu\nt3HnnXfiwIEDuOyyy/TP9+/fjwMHDuDhhx9GtVrFxz72MRQKBdx0000AgAceeABPPvkkBEHAQw89\nhGw2i7m5Odx88814//vfj6uvvjqqR3LNqNesWQsaskFwqw2KWzbxUaOf9qTX4j9bzHZ9Nl1ID4Uv\nRlh+MHFaD/q1JUjzV9DvwU/tFP9dsz8dYCx07ea6cQvWiY1wNDc3h3379uH48eMYHx/XP5dlGY88\n8gjuv/9+nH/++QCAW2+9FZ///Od14ejmm282XOvYsWP44Ac/iLvvvhs7d+4M7yGIvtBm3h8vC+Wo\nC9VR0W/B7rX4S2IC58wWAAxfFE9YfjBxWg/6tSVI81fQ78FPEzx/LbM/XSaVMBS69mKqMxNVsE5s\nhKNnnnkG27dvx1e+8hWDpufFF19Eo9EwCDk7d+7E4uIiDh8+jK1bt3Zd64EHHkC1WsU//MM/QNM0\nCIKAr33ta0ilUqE8C9Ef2sztidOGsZZxumA72XSGbayH7Q8Up/XAri1h+PgF+R781E7x12L+dCxa\nzct14+Scz4iNcLR7927s3r276/MTJ04gk8kgn1990TMzM9A0DceOHbMUju65555A20oQYRCnDWMt\n4nTBjpNpyC/I2d+aYe5rPw9d5mudt6Vj9vJ63Tg55zNiIxzZUa/XkU4bq4kzDZAsy1E0iSCINYDT\nBXtUNX1uBIFRe3Y7RqGv/Tx0ma/l9bpxFMZjLxxlMpkuIYj9O5OhYzVBEMHgdsEeNU2fE0FgrZa9\nGLW+jgNx08rFXjjauHEj6vU6arUacrkcgI6pTRAEbNiwIeLWEQQxysRtwY6CXoJA3CKMiOElblq5\n2AtHO3bsQCaTwcGDB/GWt7wFAHDw4EFMTU1hy5YtEbeOIIhRJm4LdpyIY4QRMfzERSsXyySQPOl0\nGtdddx3uvvtuPP300/jlL3+J/fv344Ybboi6aQRBrBHyGQlThTRt9hx+JhYcFuySgRKjRyw1R6z0\nB+O2226DLMvYu3cvUqkUrr32WuzZsyei1g0ndPIlCMJP4hhhFBRr1bdqLSNovepwrCEuv/xyAMAv\nfvGLiFviLzSpibAgAXzt8eujS7YO66Pkc7RWnpNYJZaaI8I/yGGSCBoSwNcua8FhnXyr1iYkHI0w\nNKmJMCABfO2yFhzW45i9mQgeEo5GGJrU7hnlRT4ISAAffvwY83GJMAqCteRbRaxCwtEIQ5PaOWQa\n8gYJ4MMLjXlnuEkGSoer0YF2xxGGTWor1nJ9JCt6mYYIe0gAH15ozDvnzJl811rK+1Y1lRZ+fXQJ\nL8+XcWihipfny/j10SU0FWutKhF/SHM04qwFh8lBIdOQd+JYE4noD415d/TzrSK/u9GDhKMRZy04\nTA7KMJqG4tSfJIAPH1GP+TiNXzdY+VaRoDmakHC0Rhhlh8lBGSbTUBz9REgAHz6iGvNxHL+DErWg\nSQRDfFZ9goiIYfLNirOfCJXYGB6iGvNxHr9eGabDFeEc6jWCQH+HyzjgRH1PDB9R1esKe8yP6vgd\npsMV4RwyqxEEhsM0ROp798S7P8MxMdm9g7DH/CiP37j73cV5HsQVEo4IgiPOvlmkvnfOMPi2BB3h\n5PQdhDXmR3n8xvVwNQzzIK4M72gkiDUGqe+dE3ffljBMTHF7B2th/MbN7y5uY2CYIOGIIIaIYfCN\nihqz4FGXVSzVFNRlNTa+LU5MTIMQV/8eGr/hEdcxMCyQWY0ghoi4qu/jBBMsFLWN+VIdDS5LcUZK\nYlMxE/k7C9rEFFf/Hhq/4RHXMTAskHBEEENInH2jooYJFmbBCAAaSgvzpTpmJ3NRNE0n6Mzicffv\nofEbPHEfA3GH3g5BECNFPiNBgNYlGAFAJpWABiEWJoUgTUxrwb+H6A2NgcEgzRFBECPHxmIWry5W\n0ZBXTQuZVAKzE1kA8TApBG1iint4ORE8NAa8Q8IRQRAjx3hWwtapPOqyCkVtQxITyKZWl7s4mRSC\nMjGRfw9BY8A7JBwRBDFy8CaFbMr4t7VmUiD/HoLGgHvic3wiCILwEQobJwjCK6Q5IghiJCGTAkEQ\nXiHhiCCIkYZMCgRBuIWEI4IgCIIYUfzSnK41DSwJRwRBEATRg2EUDPwqOrtWi9eScEQQBEEQFgyz\nYNCr6OyOTROhX2fYoGg1giAIgrBgWKva+1V01ut1Kg0Fi+VmLDLRe4U0RwQxggyjGYAg4oQTwSCu\nc8uvorNurzPMmjYzJBwRxAgxSosTQUTJMFe196vorNvrjJIJjsxqBDFCDKsZgCDixjBXtfer6Kyb\n6/hlyosL8e1dgiBcMWqLE0FEybBXtfcrQ7zT6zjRtA0TZFYjiBFhmM0ABBFHhrmqvV8Z4p1eZ5g1\nbVaQcEQQI8KoLU4EETWjUILGrwzx/a7DNG1W2uth0LSZodWSIEaEYTcDEERcyWckTBXSNIf6MErF\nnklzRBAjxDCbAQiCGG5GQdPGIOGIIEaIUVqcCIIYTkah2DMJRwQxgozC4kQQBBEV5HNEEARBEATB\nQZojInLIBEQQBEHECRKOiMigUhcEQRBEHCGzGhEZVOqCIAiCiCNCF5LfAAAPX0lEQVQkHBGRQKUu\nCIIgiLhCwhERCaNWh4cgCIIYHUg4IiKBSl0QBEEQcYV2ICISqNQFQRAEEVdIOCIiY5Tq8BAEQRCj\nA4XyE5FBpS4IgiCIOELCERE5VOoi3pDwShDEWoOEI4IgLKEknQRBrFXI54ggCEsoSSdBEGsVEo4I\nguiCknQSBLGWIeGIIIguKEknQRBrGfI5IjxBTrqjDSXpJIi1B63rq5BwRLiCnHTXBixJp5VpjZJ0\nEsRoQet6N3T8I1xBTrprB0rSSRBrA1rXuyHNEeEYJ066pFEYHShJJ0GMPrSuW0PCEeEYJ066lMxx\n9KAknQQxutC6bg0JR4RjyEmXIPyDNHJEHKB13RoSjgjHkJMuQQwOOb8ScYLWdWvWpkhIeIacdAli\nMMj5lYgbtK53Q5qjEcdv1T056RKEd8j5lYgjtK53Q8LRiBK06p6cdAnCPeT8SsQZWtdXIbPaiEKq\ne4KIH+T8ShDDAc3EEYSKhhKMSkPBYrlJfR4TmPOrFWvZ+ZUg4gaZ1UYQUt0TFBEVX86cydv2DUEw\nyP8nWkg4GkFIdU/0Mqvu2DTR87e0KAcLOb8SvaCDTTwg4WgEobwVaxuvEVG0KIcLOb8SVgxysCH8\ng1QIIwrlrVi7ODGrWkFO/AQRLeQvGh9IczSikOp+7eLFrEr5dwgieshfND6QcDTikOp+7eHFrEqL\nMkFED/mLxoeRfNOtVgsf//jH8e53vxvve9/7cPjw4aibRBCh4tasSosyQUQPpXqIDyOpOfrpT3+K\ndDqNf/3Xf8WTTz6Je+65Bw899FDUzSKI0HBrViUnfmKtEHdXA0r1EA9GUji68sor8c53vhMAcOTI\nERSLxYhbRBDR4MasSosyMcoMSzQm+YvGg1jqym+88UZ861vf0v+tqiruuusu7Nq1C5dccgnuu+8+\naJrW8xqJRAIf/ehH8Xd/93e46qqrgm4yQcQGr1mx2aJ8zmwB26bHcM5sATs2TcRq4yAIrwxbNGY+\nIyEtJdBU2hSlFgGx0hy1223ceeedOHDgAC677DL98/379+PAgQN4+OGHUa1W8bGPfQyFQgE33XQT\nAOCBBx7Ak08+CUEQ8NBDDyGbzeq/W1hYwPXXX4+f/OQnyGTIo5QYXfw6GZMTPzFqDFs05rBouUaZ\n2AhHc3Nz2LdvH44fP47x8XH9c1mW8cgjj+D+++/H+eefDwC49dZb8fnPf14Xjm6++WbDtb7zne+g\nXC7jb/7mb5DJZJBIJJBIxFJJRhC+QcnjCMKaYYvGpLkcPbGRG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ahat, bhat = results.params\n", "\n", "plt.plot(x, 1/(a * x + b), lw=2, label='model')\n", "plt.plot(x, y, 'o', alpha=0.25, label='data')\n", "plt.plot(x, 1/(ahat * x + bhat), lw=3, ls='--', label='estimate') \n", "#plt.plot(x, results.predict(x1), lw=3, ls='--', label='estimate') # same as above line\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.yscale('log')\n", "plt.legend()\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Residuals analysis\n", "\n", "If the regression model is suitable for the data, we expect that the deviance residuals will be normally distributed - that the estimation error is normal.\n", "\n", "The left plot shows a histogram of the residuals, fitted with a normal distribution; the right plot shows a QQ plot that plots the empirical quantiles of the residuals on y-axis vs. the theoretical quantiles on the x-axis. Both plots suggest that the residuals are normally distributed, which is good." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VV1dXoqKiOHjwIK+99lpBhiyE0atYsSIhISGGDkMIUQAKZF7TO3egSxd1/wBb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(8, 4))\n", "\n", "resid = results.resid_deviance.copy()\n", "resid_std = stats.zscore(resid)\n", "sns.distplot(resid_std, bins=25, kde=False, fit=stats.norm, ax=ax[0])\n", "ax[0].set_title('Residuals')\n", "\n", "sm.graphics.qqplot(resid, line='r', ax=ax[1])\n", "ax[1].set_title('QQ plot of residuals')\n", "\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate and plot the log-likelihood for combinations of $a,b$." ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_loglik(L, xrange, yrange, xlabel=None, ylabel=None, cmap='viridis'):\n", " fig, ax = plt.subplots() \n", " im = ax.imshow(L.T, cmap=cmap, aspect=1, origin=(0,0))\n", " cntr = ax.contour(L.T, N=5, aspect=1, linewidths=0.5, linestyles='--', colors='k')\n", " ax.clabel(cntr, colors=\"#252525\", fmt=lambda x: '{:.0f}'.format(x))\n", " plt.colorbar(im, ax=ax, label='Log Likelihood', fraction=0.03, pad=0.25, format='%1.e')\n", " xstep = len(xrange) // 5\n", " xticks = list(range(0, len(xrange), xstep)) + [len(xrange)-1]\n", " xticklabels = xrange[xticks]\n", " ax.set_xticks(xticks)\n", " ax.set_xticklabels(['{:.2g}'.format(x) for x in xticklabels], rotation='vertical')\n", "\n", " ystep = len(xrange) // 5\n", " yticks = list(range(0, len(yrange), ystep)) + [len(yrange)-1]\n", " yticklabels = yrange[yticks]\n", " ax.set_yticks(yticks)\n", " ax.set_yticklabels(['{:.2g}'.format(y) for y in yticklabels])\n", "\n", " imax, jmax = (L == np.nanmax(L)).nonzero()\n", " ax.scatter(imax, jmax, marker='o', s=50, color='r')\n", " ax.set(\n", " xlabel=xlabel,\n", " ylabel=ylabel\n", " )\n", " \n", " fig.tight_layout()\n", " sns.despine()\n", " return fig, ax" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/yoavram/miniconda3/envs/simarba/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: invalid value encountered in log\n" ] }, { "data": { "image/png": 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+1sjKs7Bjhi/VJw2PQ75hYwpAVQFiLj9zkvM4dFvpFDjK+MaWR7YFkBw7qgKe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+gQP88d9W8cfvP8uc/QYKbzzXAs4FNY4Cc3azpBkcp4PyvKi3ACTZazHF+7aUl7VsjbdLCXa2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\n+oYGTEth6BrdcgIUn3sB//ngXf779J8ZdOY5DBr3M2o0hVZtoef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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "arange = np.linspace(-5, 15)\n", "brange = np.linspace(0, 10)\n", "logL = np.array([\n", " [\n", " -nloglik((a, b), x, y)\n", " for b in brange\n", " ]\n", " for a in arange\n", "])\n", "\n", "fig, ax = plot_loglik(logL, arange, brange, xlabel='a', ylabel='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red dot marks the maximum likelihood.\n", "\n", "Next, a likelihood profile for $a$:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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O0v8lHX1gYwii6pGreOjTp0+NLv7222/X6HmkWsLCwrB582YYGhpi79693Muh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, sharex=False, sharey=False, figsize=(8, 4))\n", "\n", "alow, ahigh = results.conf_int()[0,:]\n", "arange = np.linspace(0, 12)\n", "idx = (arange > alow) & (arange < ahigh)\n", "logL = np.array([\n", " -nloglik((a, bhat), x, y) \n", " for a in arange\n", "])\n", "\n", "ax[0].plot(arange, logL, 'k-')\n", "ax[0].axvline(ahat, color='k', ls='--')\n", "ax[0].fill_between(arange[idx], np.nanmin(logL), logL[idx], color='k', alpha=0.3)\n", "ax[0].set(\n", " xlabel='a',\n", " ylabel='Log likelihood (b={:.2f})'.format(bhat),\n", " ylim=(np.nanmin(logL), None),\n", ")\n", "\n", "arange = np.linspace(ahat*0.875, ahat*1.25)\n", "ax[0].axvline(arange.min(), ls='-', color='k')\n", "ax[0].axvline(arange.max(), ls='-', color='k')\n", "idx = (arange > alow) & (arange < ahigh)\n", "logL = np.array([\n", " -nloglik((a, bhat), x, y)\n", " for a in arange\n", "])\n", "\n", "ax[1].plot(arange, np.exp(logL), 'k-')\n", "ax[1].axvline(ahat, color='k', ls='--')\n", "ax[1].fill_between(arange[idx], np.nanmin(np.exp(logL)), np.exp(logL[idx]), color='k', alpha=0.3)\n", "ax[1].set(\n", " xlabel='a',\n", " ylabel='Likelihood (b={:.2f})'.format(bhat),\n", ")\n", "\n", "fig.tight_layout()\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The left panel shows a plot of the log-likelihood for the estimated $b$ and different values of $a$. The dashed line is for the estimated $a$; the shaded ares is the 95% confidence interval; the solid lines show the area presented in the right panel.\n", "\n", "The right panel shows the likelihood (no log) for different $a$ values. The dashed line is for the estimated $a$; the shaded ares is the 95% confidence interval." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example: adaptation time\n", "\n", "We simulate adaptation using a Wright-Fisher model with a single bi-allelic locus and an asexual haploid constant size population.\n", "The simulation starts with a population of size _N_, all with allele _a_ that confers fitness _1-s_.\n", "Allele _A_, confering fitness 1, appears with probability _u_ via mutation.\n", "\n", "The expected frequency of allele _A_ is:\n", "$$\n", "E[p(t+1)] = \\frac{p(t) \\cdot (1-u) + (1-p(t)) \\cdot (1-s) \\cdot u}{\\bar{\\omega}} \\\\\n", "\\bar{\\omega} = p(t) + (1-p(t)) \\cdot (1-s)\n", "$$\n", "\n", "The frequency of allele _A_ in the next generation is:\n", "$$\n", "n(t+1) \\sim Bin(N, E[p(t+1)]) \\\\\n", "p(t+1) = n(t+1) / N\n", "$$\n", "that is, $n(t)$, the number of alleles _A_, is binomialy distributed.\n", "\n", "We are looking for the first time $T$ at which $p(T)=1$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/javascript": [ "$(\"[data-key='None']\").parent().parent().remove()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", "\n", "

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v1htuIP2df2Ds1UvtWCJEZKZGCCECsLn8KwAu6X6pykmC40hVEwC9usWqnCS4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\nBPvo0bXKQ3XkD3XNSa7qR5ObfkpOTmbLli28+uqrlJaW8sA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def simulate_adaptation(s, N, u, reps=1, PRINT=False, PLOT=False, BAR=False):\n", " N = int(N)\n", " p = np.zeros(reps, dtype=float)\n", " T = np.zeros(reps, dtype=int)\n", " t = 0\n", " if PLOT:\n", " ps = [] \n", " if BAR:\n", " bar = ProgressBar(reps)\n", " bar.start()\n", " while not np.allclose(p, 1):\n", " if PRINT and t % 500 == 0:\n", " print(\"{} {:.2g}\".format(t, (p<1).mean()), end=\" | \")\n", " if BAR:\n", " finished = ((T == 0) & (p == 1)).sum()\n", " for _ in range(finished):\n", " bar.advance()\n", " T[(T == 0) & (p == 1)] = t\n", " assert ((0 <= p) & (p <= 1)).all()\n", " if PLOT: ps.append(p)\n", " # selection and mutation\n", " w = p + (1 - p) * (1 - s)\n", " p = (p + (1 - p) * (1 - s) * u) / w\n", " # random genetic drift\n", " p = np.random.binomial(N, p) / N\n", " t += 1\n", " \n", " if PLOT:\n", " ps = np.array(ps)\n", " plt.plot(range(t), ps)\n", " plt.ylim(-0.1, 1)\n", " plt.xlim(0, max(10, t))\n", " plt.xlabel(\"Time\")\n", " plt.ylabel(\"Frequency\")\n", " \n", " T[T == 0] = t\n", " if BAR:\n", " bar.finish()\n", " bar.hide()\n", " return T\n", "\n", "T = simulate_adaptation(0.1, 1e3, 1e-5, 3, BAR=True, PLOT=True)\n", "for t in T:\n", " plt.axvline(t, ls='--', color='k')\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This shows three popoulations adapting, each one finishing adaptation at a different time.\n", "\n", "We now simulate lots of adaptaions and present the:\n", "- mean adaptation time: the average of the times\n", "- the expected value of a fitted exponential distribution\n", "- the theoretical approximation to the geometric adaptation time: $T \\approx \\frac{1}{2s N u} + \\frac{\\log{N}}{s}$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/javascript": [ "$(\"[data-key='None']\").parent().parent().remove()" ] }, "metadata": {}, 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"display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"1/10 (10%) in 0.6 s, 0.63 s last iter; eta 6+-0 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"20%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"2/10 (20%) in 0.7 s, 0.02 s last iter; eta 3+-2 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"30%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"3/10 (30%) in 0.8 s, 0.10 s last iter; eta 2+-2 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"40%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"4/10 (40%) in 0.8 s, 0.08 s last iter; eta 1+-1 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"50%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"5/10 (50%) in 1.0 s, 0.13 s last iter; eta 1+-1 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"60%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"6/10 (60%) in 1.1 s, 0.16 s last iter; eta 1+-1 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"70%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"7/10 (70%) in 1.3 s, 0.18 s last iter; eta 1+-1 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"80%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"8/10 (80%) in 1.6 s, 0.29 s last iter; eta 0+-0 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .completed-part\").css(\"width\", \"90%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .running-part\").css(\"width\", \"10%\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533 > .text > .main\").text(\"9/10 (90%) in 2.5 s, 0.93 s last iter; eta 0+-0 s\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "$(\"#a8e7d06f2-087d-402d-9882-7033a2783533\").parent().parent().hide()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T = simulate_adaptation(0.01, 1e5, 1e-7, 10, BAR=True)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean T: 6664\n", "Estimated T: 5212\n", "Theoretical T: 5921\n" ] }, { "data": { "image/png": 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EzsaQRopgyzppAEMaERFJhyGNFMHWkNanTx94eHjg1KlTaLhm6ygiIiJH4t6dpAjmkGbl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\nXLhwAfn5+SgqKmp1+LQpT09PS2Azh7e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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T_mean = T.mean()\n", "T_est = stats.expon.fit(T)[1]\n", "T_theo = 1/(2*0.01*1e4*1e-6) + np.log(1e4)/0.01\n", "print(\"Mean T: {:.0f}\\nEstimated T: {:.0f}\\nTheoretical T: {:.0f}\".format(T_mean, T_est, T_theo))\n", "sns.distplot(T, kde=False, fit=stats.expon)\n", "plt.xlabel('Adaptation time')\n", "plt.ylabel('Frequency')\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mixed parameters\n", "\n", "In the above, there was a single set of parameters $(N, s, u)$.\n", "\n", "Now, let's simulate adaptations with a bunch of parameters and use *exponential regression*!\n", "\n", "We randomize 100 parameter sets, and run 5 simulations for each set; this can take some time, especially when the adaptation time is long." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The ipycache extension is already loaded. To reload it, use:\n", " %reload_ext ipycache\n" ] } ], "source": [ "# pip install git+https://github.com/rossant/ipycache --upgrade\n", "%load_ext ipycache" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[Saved variables 'dfs' to file '/Users/yoavram/Work/ipython-notebooks/mycache.pkl'.]\n", "0 1 " ] } ], "source": [ "%%cache mycache.pkl dfs\n", "dfs = []\n", "for _ in range(100):\n", " print(_, end=' ')\n", " s = np.random.uniform(0.01, 0.1)\n", " N = 10**np.random.uniform(4, 7)\n", " u = 10**np.random.uniform(-6, -9)\n", " T = simulate_adaptation(s, N, u, 10)\n", " dfs.append(pd.DataFrame(dict(s=s, N=N, u=u, T=T)))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pickle\n", "with open('_mycache.pkl','rb') as f:\n", " dfs = pickle.load(f)['dfs']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now fit exponential regression to the simulated data.\n", "\n", "The idea is that we assume that the response variable - T, the adaptation time - is exponentialy distributed with rate $\\lambda(N, s, u)$ that is a linear function of the parameters:\n", "\n", "$$\n", "T \\sim Exp(\\lambda(N, s, u)) \\\\ \n", "E[1/T] = \n", "\\lambda(N, s, u) = c_0 + c_N N + c_s s + c_u u\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the regression:" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/yoavram/miniconda3/envs/simarba/lib/python3.5/site-packages/statsmodels/genmod/generalized_linear_model.py:244: DomainWarning: The inverse_power link function does not respect the domain of the Gamma family.\n", " DomainWarning)\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Generalized Linear Model Regression Results
Dep. Variable: T No. Observations: 1600
Model: GLM Df Residuals: 1597
Model Family: Gamma Df Model: 2
Link Function: inverse_power Scale: 1.88916684088
Method: IRLS Log-Likelihood: -14884.
Date: Mon, 12 Dec 2016 Deviance: 1802.8
Time: 09:31:36 Pearson chi2: 3.02e+03
No. Iterations: 9
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err z P>|z| [0.025 0.975]
const -1.279e-05 1.24e-06 -10.290 0.000 -1.52e-05 -1.04e-05
N -1.681e-10 1.05e-11 -16.029 0.000 -1.89e-10 -1.48e-10
s -0.0001 2.94e-05 -4.629 0.000 -0.000 -7.84e-05
u -2708.0310 142.864 -18.955 0.000 -2988.039 -2428.023
" ], "text/plain": [ "\n", "\"\"\"\n", " Generalized Linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: T No. Observations: 1600\n", "Model: GLM Df Residuals: 1597\n", "Model Family: Gamma Df Model: 2\n", "Link Function: inverse_power Scale: 1.88916684088\n", "Method: IRLS Log-Likelihood: -14884.\n", "Date: Mon, 12 Dec 2016 Deviance: 1802.8\n", "Time: 09:31:36 Pearson chi2: 3.02e+03\n", "No. Iterations: 9 \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -1.279e-05 1.24e-06 -10.290 0.000 -1.52e-05 -1.04e-05\n", "N -1.681e-10 1.05e-11 -16.029 0.000 -1.89e-10 -1.48e-10\n", "s -0.0001 2.94e-05 -4.629 0.000 -0.000 -7.84e-05\n", "u -2708.0310 142.864 -18.955 0.000 -2988.039 -2428.023\n", "==============================================================================\n", "\"\"\"" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.concat(dfs, axis=0)\n", "df['N'] = -df['N']\n", "df['s'] = -df['s']\n", "df['u'] = -df['u']\n", "X = df[['N', 's', 'u']]\n", "y = df['T']\n", "\n", "X = sm.add_constant(X) # add intercept\n", "distribution = sm.families.Gamma(sm.genmod.families.links.inverse_power)\n", "glm = sm.GLM(y, X, family=distribution)\n", "results = glm.fit()\n", "results.summary() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Residuals analysis:" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cHI6OjlaOUERsSb16tpvMJrCJ7gfBwcHcu3cPb29v8zZvb29u3LhBSEhIkvL/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_residuals(resid):\n", " fig, ax = plt.subplots(1, 2, figsize=(8, 4))\n", "\n", " resid_std = stats.zscore(resid)\n", " sns.distplot(resid_std, bins=25, kde=False, fit=stats.norm, ax=ax[0])\n", " ax[0].set(\n", " title='Residuals histogram',\n", " xlabel='Residuals',\n", " ylabel='Frequency'\n", " )\n", "\n", " sm.graphics.qqplot(resid, line='r', ax=ax[1])\n", " ax[1].set_title('QQ plot of residuals')\n", "\n", " sns.despine()\n", " \n", " return fig, ax\n", "\n", "plot_residuals(results.resid_deviance.copy());" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This analysis shows that the residuals are not really normally distributed. Which residuals are to blame?" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JGovFAofDUdfvZ+pLVcLn6KOPrinAlQsYti7q3lLAbByMyWSC3W5HNBoVmVUG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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(results.fittedvalues, resid_std, 'ok', alpha=0.1)\n", "plt.xlabel('T')\n", "plt.ylabel('Absolute standard residual')\n", "plt.xscale('log')\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like the lower adaptation time co-occur with the positive residuals. Let's remove them:" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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Hmhuk/EAIIYQQogBIazrc3r3fWfDjjzBpEujoJP53mk25+Y+01AohhBBC5HPp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\nuXPnUKvVuLu7F/A7EWVNYPhVQDdK+6T/BsuSdu3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oQjd2EUP2X3zbtYPXX4dRoxSJKkSp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\nP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(results.resid_deviance.copy()[results.fittedvalues > 5e4]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like smaller adaptation times are to blame; this makes sense, as for smaller adaptation time the time for fixation is relatively large and it is not exponential distributed." ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BdsklRLdrZ3YcERGpBM4PPwQgVqNyIhIkf2EhrpUrITq62kzTVjMnYcP5wQcA\nxA66TlMsRUQikOH34/yo9EiCarDWRURCy7V8Bbjc2Hv2wFqjhtlxLgg1cxI2nB+WLoi/Vp/WiohE\nIk92Nv4jR4j+7W+J+s1vzI4jImHG+UHpyP6g60xOcuGomZOw4N21C9+uXdgaNCA6Lc3sOCIiUgmc\n75fMwKgOO9CJSGj5i4pwr1wJUVHEXn212XEuGDVzEhZOfdLiGDhQUyxFRCKQ4ff/7FN1bXIlIsFx\nf7oKw+nE3r0b1po1zY5zwaiZk7DgOjXF8jpNsRQRiUSe/2zCf/gwUZc1J7ppE7PjiEiYcb5fenzV\nddVniiWomZMw4Pv2W7xbt2KtW5eYK64wO46IiFSCwI2YRuVEJEiGy4VrxUqwWnEMqD5TLEHNnIQB\n58efAOC4+mosNpvJaUREJNQMvx9XNdy4QERCw712HUZhITGdO2GrU8fsOBeUmjmp8lyflDRzsQMH\nmJxEREQqg2dTDsWHDhHVvDnRzZubHUdEwozz49IjTarJ2XI/p2ZOqrTiH37A8++NWBITsXfvbnYc\nERGpBM5//QuA2CGDTU4iIuHG8PlwfbIUAMc11e+DfzVzUqW5li0Hw8DRtw+WmBiz44iISIgZfn/g\nSAJNsRSRYHk2bsR/9CjRbdsQ1bCh2XEuODVzUqW5Tq2XG1D9PmkREakOPNnZJbtYtmxBdLNmZscR\nkTDj/Kh0OU41nGIJauakCvMXFuJaswaio3H07WN2HBERqQTO90qmWMYN1hRLEQmOYRi4llbfKZag\nZk6qMPfq1eB2lxz+mJhodhwREQkxo7j4p4PC1cyJSJB827ZT/N132H7zG6Kq6eZJauakynItXQaA\n46qrTE4iIiKVwfP5F/iPHCG6dWuiGjcyO46IhBln6ahc7ICrsVgsJqcxh5o5qZKM4mJcy1cAauZE\nRCJV0bvvARB7/RCTk4hIOArsYlnNDgr/OTVzUiV5Nm0q2ZmodWuiUhuYHUdERELM8HpxfXhqiuUg\nk9OISLjxHfwe75YtWGvVIuaKK8yOYxo1c1IlBaZYXq1RORGRSORevQb/sWPEdOhA1MUXmx1HRMKM\na1npvWL/flhsNpPTmKdczVy/fv3YsWNHZWcRCVAzJyIS2YreeReA2PTrTU4iIuEo0MxV83vFcjVz\nBw8exOPxVHYWEQB8+/bh270ba0p9olu3NjuOiIiEmN/pxPXJJ2C16qBwEQmav6AA9/oNYLdj79XL\n7Dim0jSg6Cq7AAAgAElEQVRLqXJcK1YC4OjXv9ruTCQiEslcy5ZjFBZi79EdW716ZscRkTDjXr0G\nPJ6S46vi4syOY6pyN3NFRUUUFBSU60ukIlzLlwMlc6BFwt2uXbto06YNGzduDKo+YMAAWrRoEfhq\n2bIlS0u3YAZYtmwZAwcOpF27dowePZr9+/dX6vsQCSXnO+8AmmJ5oRiGwezZs7nqqqto3749w4cP\nZ9OmTac9580336Rv3760b9+eu+++m6NHj4a0LhJKP62X629yEvOVu5m79dZb6dixY7m+RM6Xv6AA\n94bPwWHH3rOH2XFEKsTv9zNx4kR8Pl9QdY/Hw4EDB8jKymLdunWsW7eOtWvX0qdPHwC2bdvG/fff\nz+jRo1m8eDHJyclkZmbi9/sr/T2JVJT/+HFcKz8Fu53Ya64xO0618OqrrzJ37lwmTZrEu+++S4cO\nHbjttts4dOgQACtXrmTq1Kn8z//8D2+++SZHjx7l/vvvD7y+onWRUDKKi3+axaVmjqjyPnHcuHFc\ncskllZlFBPeaNeD1Yu/ZB2tsrNlxRCpk9uzZxJ1l+sev1ffu3YthGLRt2xa73X5Gff78+fTu3Zvh\nw4cDMHXqVLp3786aNWvoVc3XDkjV5/zgQ/B6cVx7LdbkZLPjVAuLFi3itttuC3wg9OCDD7J8+XKW\nLVvGqFGjePXVVxk+fDgDBgwA4Nlnn6Vv377s3r2bpk2bVrguEkqenM34f/yR6FatdHwVQTRzffr0\noW3btpWZReSng8L7aYqlhLddu3aRlZVFVlYW1157bVD1PXv2kJKSUmYjB5CTk8PNN98c+D42NpZW\nrVqRk5OjZk6qvKIlSwCIuyHd5CTVx2OPPcbFZRz/cPLkSQzD4KuvvmL06NGBxxs0aECDBg3Iycmh\nSZMmFaqrmZNQ03Kc02kDFKkyDL+/ZOoN+gMq4c3v9zNp0iTuvfdeUlJSgq7v3r2b6Ohoxo8fT48e\nPbjppptYvXp1oJ6bm0u9X2waUadOHXJzc0P/ZkRCyHfwIJ4Nn2NJTsbRt4/ZcaqNK664gvr16we+\nX7VqFfv376d79+6cOHECp9P5q9eUitZFQs2tKZanKffInEhl827div/IEaIua05Uw4ZmxxH5VV6v\nN7DW5JcSEhJYuHAh8fHxZGRkUFRUdMZz5syZQ0JCwq/W9+zZQ35+PsOGDeOee+7ho48+Yty4cbz+\n+uukpaXhcrnOGLWLiYnRETJS5TlPnS133bVYHA6T00SOc12TatWqFfh+9+7dTJw4kUGDBtG+fXsO\nHz4M8KvXFJfLVaG6SCj5Dn6Pd9s2rLVrE53Wzuw4VUK5mrkVK1ZQt27dys4i1VxgMWvfviYnETm7\nffv2MXjw4DKPzhgwYAAbNmxg0aJFQMkucj+3e/duXnnllV+tAzz33HO4XC7i4+MBaNGiBTt37uS1\n114jLS0Nu91+xk2Sx+M56/o8EbMZhkHR4sUAxN1wg8lpIsvZrknp6ek8/fTTAHz99dfccccdNG/e\nnClTpgA/NWFlXVMcDkeF6yKh5F5Zcq9o79MHi1UTDKGczVxqampl5xDBfWqKpZo5qeKaNWvGjh07\nyqzNnDmT5cuXM3jw4NMeHzt2LOnp6dSpU4fCwsJfrU+ePBmbzRZo5E5p0qQJW7ZsASAlJYW8vLzT\n6nl5eXTq1Kmib02k0ni3bsO3Yye21FRiunQ2O05EOds16ZSNGzcybtw40tLSmDVrFjExMQDUrFkT\nh8NR5jUlJSWlQvWfT+0UCQXXipK9FWK1HCdA0yylSig+ehTPpk1YEhKI6XiF2XFEztuoUaO4/vqf\nzs5yOp0MGTKEKVOm0LVrV6Kios5aBxg6dCj9+/dnwoQJgedt3bo1sJFAWloa2dnZjBgxAig5B3Tb\ntm1kZmZeiLcocl6cpaNysTek6xP1C2zHjh1kZmbSuXNnnn/+eaKjo0+rt23bluzsbHr37g3AwYMH\nOXToEO3btz/v+uHDhwN1kVAwnE7ca9dBVBT2XleaHafKUDMnVYL7s8/AMLBfeSWWX/wlIxJOkpKS\nSEpKCnx/ak1cvXr1AutWzlXv168fc+fOpXnz5jRr1ozFixezefNmnnzySQBGjBjB8OHDmTdvHt26\ndeP5558nNTWVHj10NqNUTYbPR1HpQeFxw4aanKb6efjhh6lfvz6PPvooJ06cCDweGxtLfHw8I0eO\n5MEHH+Syyy6jWbNm/PnPf6Znz540atQI4LzqPXr0oHHjxqa8X4lM7s8/x3A6ienaFevP/h6t7tTM\nSZXw03o57W4mkaesdSxnq0+YMAGr1cozzzxDXl4el112Ga+88kpga/HWrVszbdo0pk+fzvTp07n8\n8suZNWvWOX+PiFnca9fizz1CdLu2RDdvbnacamX//v2BKZh9f7GM4dZbb+Whhx7iqquu4v777+fZ\nZ5+lsLCQ7t278/jjjweeV9G6SCj8tOO5luP8nMUoa/V9ORmGwaRJk7j77rtp0ECH9v1Sv9Kz0laU\nzu+VshnFxRxu1x7/sWOk/GcjtjK2aheRitM1Scxy9K67cS55h+QnHifhtjFmx5EqQtckKS/DMMjt\n3oPib/dT79MV+lDoZyo0ad3v9/POO+9w7NixUOWRasj71Vf4jx0j+re/VSMnIhJh/Pn5uD76GKKi\niL1+iNlxRCQM+b7ZS/G3+7E1bEhUs2Zmx6lSKrwCuQIDeyIAuD5dBYC9T29Tc4iISOg53/8Aw+XC\n0bcPtjp1zI4jImHo1JEEjr59tKTgF7SdlJjuVDPnUDMnIhJxihYuBCDuxhtNTiIi4cp16nw5HV91\nhgo1c1arlRtuuIGaNWuGKo9UM8VHj+HNySk5kuAKHUkgIhJJfPv24fni31hq1MChc6FE5Dz4Cwtx\nf/4F2O3Yu3czO06VU6HdLC0WC08//XSoskg15F5deiRBzx46kkBEJMIUvb0IgLgb0rHY7SanEZFw\n5F63Djwe7L2uxBoXZ3acKkfTLMVUrk8/A8DRR0cSiIhEEsPvp2jh2wDE/S7D5DQiEq7cp44k0L1i\nmdTMiWkMv7/ksHDA3ruXyWlERCSU3OvWU3zgAFEtLiO6TRuz44hIGDIM42cb5amZK4uaOTGNd9t2\n/Hl5RDVvTlRqqtlxREQkhIoWLAAg/qabtPuciJwX3+7dFB84gO2SS4hq0tjsOFWSmjkxjXvVKgAc\nGpUTEYko/pMncX34UcnZckNvMDuOiIQpV2CKZW99KPQrzmsDFKfTydtvv83nn3/ODz/8wFNPPcWG\nDRto2bIlHTp0CHVGiVCu0mZOUyxFRCKL8933Ss6WG3iNzpYTkfPm1hTLcwp6ZO7w4cNcf/31PPfc\ncxQUFPDVV1/hcrn497//zejRo9mwYUNl5Ax4//33GTZs2BmPZ2dnM3ToUNq1a0dGRgZff/31Ba1L\ncPwFBXg2ZmNxOLB37mx2HBERCaHCN98EIO6mm0xOIiLhyl9UhPuLLyAmRkcSnEXQzdyUKVOIjY3l\n008/5eWXX8YwDAD+9re/0bNnT2bMmBHykKesX7+eRx555Ixh1iNHjpCZmUnfvn1ZsmQJbdq0YezY\nsRQUFFyQugTPvW4d+HzEdOuKxeEwO46IiISId9t2vJu/xFq/Ho4+vc2OIyJhyrN+Q8mRBF0660iC\nswi6mVu7di133XUXNWrUOK2pslqtjBgxgp07d4Y04ClTp04lMzOTSy655IzawoULufTSS7nrrrto\n3Lgxjz76KAkJCbz77rsALFiwoFLrErxTw+aOXppiKSISSQKjchkZWKIqdJytiFRjrk9L1svZe/c2\nN0gVF3QzFx0djc/nK7NWWFhIVCVduL/44guysrK46qqrzqjl5OTQqVOn0x7r0KEDmzdvBmDz5s2V\nWpfguVavBrReTkQkkhguF0WLFgMQP1xTLEXk/J3aW0Ej/GcXdDPXs2dP/va3v3HgwIHAYxaLhfz8\nfObMmUP37t1DGvCUxYsXk5aWVmYtNzeXevXqnfZYnTp1OHz48AWpS3B8e/dS/O1+bKmpRDVpYnYc\nEREJEefHH2McP05M165ENWpkdhwRCVO+vXsp3vdtyb1is2Zmx6nSgh5GmzhxIiNHjmTgwIE0blxy\n3sOjjz7Kd999R3x8PDNnzgw6hNfr5dChQ2XWEhISqFWr1llf73K5sNvtpz0WExOD1+u9IHUJjuvU\nQeG9rtQ2syIiEaTo9ZIplvEjfm9yEhEJZ65VpfeKvXUkwbkE3czVrVuXd955h8WLF5OdnU3t2rVJ\nSEhg0KBB3HjjjSQkJAQdYt++fQwePLjM/1np6ek8/fTTZ329w+HA4/Gc9pjH48FRurFGZdclOO7S\nP6BaLyciEjl8e/fiXrcOS40axA4caHYcEQljP50vp3vFczmvBW4Oh4Obb76Zm2++OSQhmjVrxo4d\nO8779fXr1+fIkSOnPZaXl0f9+vUvSF3Kz/B4cK/fAFYr9h6VMyVXREQuvMI3Sjc+GTZMuxSLyHkz\nXC4869dDVBT2Hj3MjlPlnVczt2bNGr788kvy8/PPqFksFiZOnFjhYMFIS0tjdemGGqds2rSJ22+/\nvVLrt912W0jfR3Xgyf4PRmEhMR06YK1Rw+w4IiISAobHQ9FbCwCIvyU0H/SKSPXk/vdGDJeLmC6d\nsSYmmh2nygu6mZs+fTovvvgiCQkJJCUlnVE3o5nLyMjg5ZdfZvr06QwZMoTXXnuNoqIirrvuukqt\nDxo06IK+z0gQWC+nXSxFRCKG8+NP8P/wAzEdOxLdvLnZcUQkjLlP7WKpIwnKJehmbuHChYwaNYpJ\nkyZVRp7zUr9+fV544QWmTJnCq6++ymWXXcZLL70UWL9X2XUpP/dnJSOcWi8nIhI5iua/BkD8LSNM\nTiIi4e7UkQR2HUlQLhbDMIxgXtClSxemT59O165dKytTxOjXrx8AK1asMDlJ1VD8448cbpuGJTmZ\ni77arMNkRS4wXZOkMvi+2Utuzyux1KjBRdn/xhIba3YkCRO6Jskv+Q5+T26nzljr1iVlUzYWa9Cn\nqFU7Qf8XuvHGG3nzzTe1Lb8EzX3qoPAePdTIiYhEiML58wGIy7hRjZyIVIg7cHxVLzVy5RT0HfWE\nCRO44YYb6Nu3L82bNyf2Fxdui8XCjBkzQhZQIsdPUyyvNDmJiIiEguFyURjY+OQWk9OISLhzfboK\n0JEEwQi6mXv88cf59ttvady4MR6P54zz10TKYhgGrlMjc2rmREQigvP9DzCOH8fevTvRTZuYHUdE\nwpjh9eJeswYsFuxX6l6xvIJu5pYuXcrEiRP5wx/+UAlxJFL5duzAn3uEqCZNiGrY0Ow4IiISAgWv\nzgMgfqRG5USkYjw5ORj5+US3T8NWq5bZccJG0JNRExISaNq0aWVkkQjmKp1iqSMJREQig2fLFryb\nNmGtXw/HNQPMjiMiYc59aoqldjwPStDN3KhRo3jxxRc5duxYZeSRCHVqQatDw+YiIhGh8NSo3IgR\nWKKjTU4jIuEucCSBzpcLStDTLLdv3862bdvo0aMHqampxMfHn1a3WCwsXrw4ZAEl/BlOJ+4v/g3R\n0cR07WJ2HBERqSD/8eM4l7wDUVHE3/x7s+OISJgr/uEHvF9twZKcTEz7NLPjhJWgmzm73c7VV19d\nGVkkQrn//W9wu4np1g3rL5p/EREJP4VvLcBwuYgdNAjbRReZHUdEwlxgx/OePXV8VZCC/q/19NNP\nV0YOiWDuVaVTLLWLpYhI2DP8fgrnlU6x/MMok9OISCT4aYql1ssFq1zN3IoVK+jUqROJiYmsWLHi\nrM+1WCz07ds3JOEkMuhIAhGRyOFe+SnF+74lqsVlxHTR1HkRqRjD7//pg381c0ErVzN35513smDB\nAtq2bcudd9551udaLBa2b98eknAS/ooPHcK3YyfW2rWJbtXK7DgiIlJBBXPnApBw661YLBaT04hI\nuPNu2YL/6FGiWrbQtO3zUO6Rubp16wb+XaS8XKvXAGC/sicWa9Cbp4qISBXi3b0H96rPsCQnEzv0\nBrPjiEgEcJ06kkC7WJ6Xct1dp6amEhMTA8CSJUuIiooiNTX1jC+AuaWf2InAz44k0JkhIiJhr7D0\n7/j4m3+PNS7O5DQiEgl+mmLZ29wgYapczVxBQQEFBQXk5+fzj3/8g7179wYe+/nX+vXrWbBgQWVn\nljBh+P24fzYyJyIi4ct/8iRFCxaC1Ur8H0abHUdEIoD/+HE8//kPlrg4Yjp1NDtOWCrXNMt77rmH\n9evXB76/9dZby3yeYRh07tw5NMkk7Hm3bMF/7BhRLVtiq1/f7DgiIlIBhW+8iVFUhOPagUQ1bGh2\nHBGJAO6168Dvx96jO5bSWYASnHI1c1OmTGHDhg0YhsGkSZMYP348l1xyyWnPsVqtJCUlqZmTgMCZ\nIdrFUkQkrBk+H4WvlG58cvttJqcRkUjh+vRTAOyaYnneytXMpaSkcMMNJQudLRYLvXv3pmbNmpUa\nTMKfq3S9nF3r5UREwprrk6UUHzhAdJs2xHTqZHYcEYkAhmEEzpdz9OltapZwFvSh4aeaOpGz8efn\n48n+DxaHA7vmQIuIhLWCOS8BkHDbGB1HICIh4du+A//hXKKaNCHqFzP+pPy0V7xUCvf69eDzEdOt\nKxaHw+w4IiJynjw5OXg2bsRavx6x1w8xO46IRIhTo3J2jcpViJo5qRSBbWY1xVJEJKwFRuX+8Adt\nUCAiIeNaWbJeTlMsK0bNnFSKwHq53mrmRETCle/AAZzvf4DF4SDullvMjiMiEcJfUIBn48aS5Thd\nupgdJ6ypmZOQ8+3dS/G3+7GlphLVpInZcURE5DwVvPQyFBcTd9PvsNXSxmciEhrutWtLl+N003Kc\nCgq6mTt+/DiPPfYYffr0oXPnznTq1OmML6nefj4qp4XyUt3t2rWLNm3asHHjxtMeHzBgAC1atAh8\ntWzZkqVLlwbqy5YtY+DAgbRr147Ro0ezf//+015/rrpIRflPnKDojTfBYiFh7O1mx5EKKC4u5i9/\n+Qs9e/akffv2jB07lr179572nIpec3RNkmC4Vq4CNMUyFIJu5h577DHee+89unfvzogRIxg1atQZ\nX1K9ab2cSAm/38/EiRPx+XynPe7xeDhw4ABZWVmsW7eOdevWsXbtWvr06QPAtm3buP/++xk9ejSL\nFy8mOTmZzMxM/H5/ueoioVA4/zWMggIcA68hqlEjs+NIBcyYMYMPP/yQ5557jnfeeYekpCTGjh1b\n7muKrkkSSoZh4F65EgBH3z4mpwl/QR9NsHr1av73f/+XYcOGVUYeCXOG24173Xqw2bD36G52HBFT\nzZ49m7i4uDMe37t3L4Zh0LZtW+x2+xn1+fPn07t3b4YPHw7A1KlT6d69O2vWrKFXr17nrItUlOF2\nU/DyywAkjhtnchqpKMMwmDRpEh07lhwVdMcdd5Cens73339Pw4YNK3zN0TVJguHbuZPiQ4eIatyY\nqN/8xuw4YS/okbnY2Fjq169fGVkkAng2ZmMUFRHT4XKsyclmxxExza5du8jKyuLxxx/HMIzTanv2\n7CElJaXMRg4gJycncNMFJdfdVq1akZOTU666SEUVLVmCP/cIMZ06EtPhcrPjSAXdd9999O/fH4AT\nJ07w6quv0qhRIxo0aABU/Jqja5IE49QulvY+GpULhaCbuWHDhjFv3jyKi4srI4+EuVPr5Ry9e5sb\nRMREfr+fSZMmce+995KSknJGfffu3URHRzN+/Hh69OjBTTfdxOrVqwP13Nxc6tWrd9pr6tSpQ25u\nbrnqIhVh+P0UvPAiAAnjNSoXSV5++WU6d+7Mhx9+yOTJk7FaS24DK3rN0TVJguEKTLHsbWqOSBH0\nNEuPx8OmTZu48soradmyJY5f7EBjsViYMWNGyAJKeHF9ugrQAZAS2bxeL4cOHSqzlpCQwMKFC4mP\njycjI4OioqIznrNnzx7y8/MZNmwY99xzDx999BHjxo3j9ddfJy0tDZfLdcaoXUxMDB6PB+CcdZGK\ncC1bhm/3bqKaN8dROpojVdu5rkm1atUCSjZe6tatGwsWLCAzM5NFixbRuHHjCl9zdE2S8vKfPIln\nY7aOJAihoJu5bdu20bJlSwDcbjdutzvkoSQ8FR8+jG/7dqy1axPdurXZcUQqzb59+xg8eHCZu7UO\nGDCADRs2sGjRIoAzplgCPPfcc7hcLuLj4wFo0aIFO3fu5LXXXiMtLQ273X7GTZDH4wmsvztXXeR8\nGYZB/sxZACSMy8Ri1QlG4eBs16T09HSefvppABo2bAiUbGaXnZ3N22+/zUMPPVTha46uSVJe7jWl\nRxL06qUjCUIk6GYuKyurMnJIBAgcSdDrSt0ASERr1qwZO3bsKLM2c+ZMli9fzuDBg097fOzYsaSn\npzN58mRsNlugkTulSZMmbNmyBYCUlBTy8vJOq+fl5QWOfjlXXeR8eT7/HO+mTdguuoi4G9LNjiPl\ndLZrEsDKlStp3br1aVMhmzRpwrFjx4CKX3N0TZLycq1YAYCjX1+Tk0SO87rj9vl8vPvuuzzyyCPc\nd999PP7447z//vt4vd5Q55Mw4j51Zoh2rpJqbNSoUXz00Ue89957vPfee7z11lsATJkyhT/+8Y8A\nDB06lFmzZp32uq1bt9K0aVMA0tLSyM7ODtSKiorYtm0bl19++Vnr7du3r9T3JpEvf+Y/gNJRuZgY\nk9NIqDzxxBMsWbIk8L3f72f79u00b94cOP9rjq5JEgzD7w9sfuLo38/kNJEj6JG548ePM2bMGLZt\n20bDhg2pXbs2X331FW+88QZz5sxh3rx5JGsXw2rH8PlwrVkDlBwWLlJdJSUlkZSUFPj+1Jq5evXq\nBdat9OvXj7lz59K8eXOaNWvG4sWL2bx5M08++SQAI0aMYPjw4cybN49u3brx/PPPk5qaSvfu3c9a\n79GjxwV+txJJPFu24F71GdaaNYm7+fdmx5EQGjlyJC+++CJNmzalUaNGzJkzB6fTSUZGBnD+1xxd\nkyQY3i1b8OflEdXiMqJSU82OEzGCHpmbNm0aeXl5LFy4kOXLl/PWW2+xYsUKFixYwPHjx/nLX/5S\nGTmlivNs2oRx4gTR7dpiq1PH7DgiVcov17FMmDCBMWPG8MwzzzBkyBA2bNjAK6+8wsUXXwxA69at\nmTZtGllZWWRkZFBYWMisWbMCP+dcdZHzkf/8TADib78Nq9Y6RZQxY8Zwxx138NRTTzF06FAOHz7M\n3LlzSUhIACp+zdE1ScojMCrXV1MsQ8lilLU6/yw6d+7Mww8/THr6mXPplyxZwrPPPsv69etDFjCc\n9etXMoS8onR+cCQ78cxUCmbMJPHee0h68AGz44hIGarTNUmC4921iyN9+mGJjyfliw1Ya9QwO5JU\nA7omVS9HBg3Gm7OZOosWaifLEAp6ZM4wDGrWrFlmrWbNmmVuwy2Rzx04kkAHQIqIhJv852eCYRA/\nepQaOREJueIffsC7+UssycnEXHGF2XEiStDNXJs2bcjKyjrj0PDi4mKysrJorS3pq53iI0fwfv01\nlho1iGmfZnYcEREJgm/vXpzvvIPF4SDhjrFmxxGRCORasRIMA0evK7FEBb1lh5xF0P81H3jgAYYP\nH84111xD//79qV27Nj/++CPLly8nNzeXf/7zn5UQU6qyUweFO3pdicVmMzeMiIgEJX/mP8DvJ27k\nLVrzLCKVwrW89EiCq64yOUnkCbqZa9myJa+//jovvPAC77zzDidPniQ5OZkOHTrwt7/9jVatWlVG\nTqnC3J+WLmjVFEsRkbDi++47it5eBHY7ieMyzY4jIhHIcLtxf/YZWK3Ye/c2O07EOa9xzlatWjFz\n5sxQZ5EwZHi9uD5bDRYL9j69zY4jIiJByJ/xD/D5iB95C7aUFLPjiEgEcn/xBUZhITGdOmKrVfa+\nG3L+ytXMzZs3j+uuu47atWszb968sz7XYrEwcuTIkISTqs/zn/9gnDxJdPs0Tc8REQkjvoMHKVqw\nAGJiSJwwwew4IhKhNMWycpWrmXvqqadIS0ujdu3aPPXUU2d9rpq56kVnhoiIhKf8v88Ar5f4USOx\nNbjI7DgiEoEMw8C1bDkAjv79TE4TmcrVzO3YsaPMfxdxlZ4N4+inZk5EJFz4vvuOorfeKhmVu/tu\ns+OISITy/fe/FO/fj+2SS4hq1szsOBEp6KMJHn74Yb777rsya9988w3jx4+vcCgJD76DB/Ht2Im1\nbl2i27QxO46IiJRT/vMzStbK3fx7jcqJSKVxLV0GgOPqq7BYLCaniUzlGpnbuXMnhmEAsGTJErp1\n60ZhYeEZz1u5ciXr168PbUKpstwrVgLg6N0LizXozwVERMQEvn37KHprQckOlnfdaXYcEYlgztJm\nLvbqq01OErnK1czNnj2bDz74AIvFgsVi4aGHHirzeYZhMHDgwJAGlKrLqQWtIiJh5+T0v0NxMfG3\n/gHbRRqVE5HKUXzkCN6cHCzJycR06mh2nIhVrmZu8uTJ3HTTTRiGwejRo3n00Udp2rTpac+xWq0k\nJSXRTPNhqwW/04l73VqIjsZ+ZU+z44iISDl4d+/GuXgxFodDo3IiUqlcK1aCYeDo2wdLdLTZcSJW\nuZq5xMREOnXqBJQcU9CqVSvi4+MrNZhUbe6168Dlxt6zJ9bERLPjiIhIOeQ/+1fw+4m/bQy2unXN\njiMiEcz1ySeAZnBVtqAPDe/UqRPff/89n332GR6PJ/C4YRg4nU42b97MtGnTQhpSqh5tMysiEl48\nX2/F+f77WBITSRw/zuw4IhLB/EVFuNasgehoHH16mx0nogXdzL377rtMmjSJ4uLiwK40pzZHsVqt\ntNGuhhHPMAxcK9TMiYiEk5NTSz5oTci8A2vNmianEZFI5l71WckMrt69sCYlmR0nogW9BeHs2bPp\n0qULy5cvZ8SIEaSnp7NmzRqeeeYZ7HY7Y8aMqYycUoV4t27FfziXqGbNiPrNb8yOIyIi5+D+4gvc\nK+nW4PAAACAASURBVFdirV2bhLG3mx1HRCKc8+OSKZaxAwaYnCTyBd3M7d+/n1GjRtGwYUM6dOjA\nl19+Sd26dUlPT2fcuHG89NJLlZFTqpDAmSEalRMRqfIMw+Dk01MBSPzj3VgTEkxOJCKRzPB6cS0v\nncE1QEcSVLagmzm73U5MTAwAjRo14ttvv8XtdgPQvn179u7dG9qEUuW4PlkK6A+oiEg4cC1bjmfj\nRmypqcSPvMXsOCIS4dyff4Fx4gTRl1+OrX59s+NEvKCbuXbt2vH2229jGAaNGjXCZrOxdu1aAHbv\n3k20th6NaL6D3+P9+mustWsTc/nlZscREZGzMIqLOfn0MwAkPfgAFrvd5EQiEulcH38MQOzAa0xO\nUj0E3czdfffdrFy5krFjx2K328nIyODBBx/kD3/4A8888wx9+/atjJxSRbiWlY7K9e+HxWYzOY2I\niJxN0dtv4/vvf4lq2YLYoTeYHUdEIpzh9+MsbeYcWi93QQS9m2VaWhoffvghu3btAmDSpEnUrFmT\nL7/8kttuu43MzMyQh5SqI7Be7mqdGSIiUpX5nU7+P3t3HhdVvf9x/DUMw74oKJJe7ae4YIuillmY\nXbMiLco0b5Y3zboGbllaudwyzcy01FYzu2Uuda3U0hYrtbql2U2vWLmVUuaOIMo+zDBzfn+gUyQK\nynIYeD8fj3nEnM8Z+AzkZ87nnO/5frNnPANA+LhxOgEnIlXOsTmleJK82DbYYlqYnU6dcNbN3MaN\nG7ngggvo1q0bAFarlREjRgCQnZ3NF198Qc+ePSs3S6kR3Dk5FH6zAfz98T/x9xcRkZop71+v4T58\nGL8rrsC/h0bNiEjVs3/8MQCBvXqZnEndcdbDLAcOHEhqamqpsW3btjF27NgKJ3UmH374IX379j1l\n+913301sbCxt27b1/Hf+/Pme+KZNm+jTpw/t27enX79+bN26tcTrKxqvC+yffw5OJ/5du+ITFGR2\nOiIichquo0fJeWkOAOGPTPCsCysiUlUMw6Dg41UABPbShZ3qUq4rc/fffz+//fYbUPyHevjhhwkM\nDDxlv4MHD9K4cePKzfAPvvnmGx599FFiYmJOiaWmpjJjxgzi4+M920JOTL985MgRkpKSGDx4MM88\n8wyLFy9myJAhrF69mpCQkArH6wr7Kt3QKiLiDXJmzsLIySGw9834tW9vdjoiUgc4t27FtW8f1ubN\n8Y2NNTudOqNcV+buvPNOYmNjiT3xhzn//PM9z08+LrjgAvr06cNzzz1XJYlOnz6dpKQkmjVrdkos\nNzeXtLQ0Lr74YiIjIz0P/xOzdr377rucf/75jBgxghYtWjBx4kRCQkJYsWIFAO+8806F4nWBYbdj\n//wL8PHR/XIiIjWYc9cu8ha/Cf7+hI0fZ3Y6IlJHFHx0YojlDb00GqAalevKXKdOnejUqZPn+bBh\nw2jatGmVJVWa//73vyxatIh169bx5Zdfloilpqbi6+tbaqMHkJKSQufOnUts69SpE1u2bGHAgAFs\n2bKlQvG6oHDdeoy8PPy6XIY1MtLsdERE5DSypkwFl4uQ5CR8//IXs9MRkTrAMAwKPvwI0BDL6nbW\n98xNmzaNpk2b8vPPP7NkyRLmzZvHsmXL2LdvX1Xk57F8+XLi4uJKje3evZuQkBDGjh3LlVdeSe/e\nvXn//fc98bS0NKKiokq8pkGDBhw+fLhS4nVBwaefAhB4vYZYiojUVPb//IfCtWvxiYwkdMRws9MR\nkTrCuW07rl9/xXp+M2zt2pmdTp1y1rNZ5uXlMXr0aL766isMw8Df35/CwkIsFgu9e/dmypQp+Pqe\n3bd1Op0cOnSo1FhISAgRERFnfH1qaiqFhYXEx8dz77338s033/DII4/g5+dHr169sNvtniGXJ/n5\n+eF0OgEqHK/tDJfr9yUJrteaISIiNZFRVETW5McBCHv4IXzCwkzOSETqioIPPgAgMDFRQyyr2Vk3\nc0888QQpKSnMmDGDHj16EBQURF5eHqtXr+bJJ58kMjKSBx988Ky+5549e0g8zR+/d+/eTJs27Yyv\nf+ihhxg6dCihoaEAtG7dmn379rF48WJ69epFQEAADoejxGscDgcBAQEAFY7Xdo7vvsOdkYHtoovw\nrebhtSIiUj55i9+k6KfiBcKDbu9vdjoiUkcYhvGHZu5Gk7Ope866mVu7di1jx44lMTHRsy04OJje\nvXtTWFjI888/f9bNXKtWrdi5c+fZpuJhsVg8jdxJMTExnnvrGjVqxJEjR0rE09PTadSoUaXEazvP\nDa033mByJiIiUhr3sWNkP128QHi9SZO0QLiIVBvnjz/i+m0v1ubNsV14odnp1Dlnfc+cr68vYacZ\nutGwYUNThh6OHDmSRx55pMS2rVu3epYwiIuL43//+1+J+ObNm+nYsWOF4h06dKjU91ETGW43BScW\ngAzQApAiIjVS9sxZGMePE9CrJ/5d48t+gYhIJSlYeeKq3I03aIilCc66mbv77rt55plnPOvOnZSR\nkcFLL73E3XffXWnJlVePHj14//33Wb58Ofv27WPBggV88MEHJCcnA9CvXz927drF7NmzSU1N5fHH\nHyc/P58bbrihQvEbb6z9l5Id/9uMO+0Ivm1jscW0MDsdERH5E+f2HeQtWAj+/oQ/+kjZLxARqSSG\n203BipUABPW+2eRs6qazHmaZkpJCZmYmvXr1om3btjRs2JDjx4+zfft2nE4nbrebT0/MfGixWFi+\nfHmlJ/1nJ4d4vvrqq0yePJlmzZrx7LPPeq6sNWrUiJdffpmpU6eyYMEC2rRpw7/+9S/Pgt8Vjddm\nBR+dmGb2Bg2xFBGpaQzD4Pijj4LbTejQZHxPs0SPiEhVcGzciOvgweKT/loo3BQWwzCMs3nB+PHj\nz+oHlDV5SW3Wo0cPoPg+Q29kGAZpl12O68ABor5Yi611a7NTEpEK8PaaJKfKf/99jg0fibVJE6L+\n8wU+gYFmpyRSbqpJ3u/4uPHkLVpM2PhxWg7FJGd9Za4uN2d1jeN/m3EdOIBv69Zq5EREahh3bi5Z\nj08BIPyxiWrkRKRaGU7n7wuF33yTydnUXWfdzAEUFBTw888/43Q6OXlhzzAMCgoK2LJlC6NGjarU\nJMUcBSuLx0AH3pRYxp4iIlLdcmbOwp12BP+ruhHQq6fZ6YhIHVP41de4jx3D75JLtHSVic66mfv6\n668ZM2YMOTk5nm2GYXhmr4mMjFQzVwsYLhcFH34IFC8AKSIiNYdz505yX3sd/PwInzJFM8iJSLXL\nX7YMgMBbNPGJmc56NsvZs2fTtGlT3njjDW644QZ69uzJkiVLGD58OFarlWeeeaYq8pRq5vjuO9xp\nR7BdcAG2ljFmpyMiIicYbjfHx08Al4vQ5CTNNCwi1c6dnU3Bp5+CzUbgTRpiaaazvjKXmprKzJkz\nueyyyzhy5AivvfYacXFxxMXFUVBQwEsvvUSXLl2qIlepRp41QzTEUkSkRsl/5x0c323E2qwZofeN\nNDsdEamDCj7+GOyFBCRchzUiwux06rSzvjLn4+NDaGgoAP/3f/9HamoqRUVFAHTr1o2ff/65cjOU\nalfihlY1cyIiNYYrM5OsKVMBqPfEFCya9ERETJC/tHiIZdCtt5qciZx1M9e2bVvPFLItWrTA7XaT\nkpICwOHDhznLlQ6kBir86mvcmZnYOnbE9/zzzU5HREROyJo8BeP4cQJ69SKgx9VmpyMidVDRvn04\nNnyLpV646lANcNbDLJOSkhg6dChHjx5l5syZJCQk8MADD3DVVVexZs0aDbGsBfLfew+AoD63mJyJ\niIicZP96HQVLl2IJDaXelMlmpyMidVT+u0sBCEpMxOLvb3I2ctZX5q666iqWLFlCfHw8AE888QRX\nXnklKSkpXHXVVUyaNKmyc5Rq5M7Lw/7Jp2C1Eph4o9npiIgIYBQUcHzcOADCxo3FGh1tckYiUhcZ\nbjf5b78DQNDt/U3ORuAc15lr164d7dq1AyAoKEgLidci9k8/wygowP/q7lgbNDA7HRERAbJnzca1\n5zf8OnUieOCdZqcjInVU4fpvcO3fj2/bWGwnegExV7mauZP3yJVXjx49zikZMV/+8uUABN2iIZYi\nIjWB48cfyX1lHths1HtmBhafsx5UIyJSKfLffhuA4Ntu0/qWNUS5mrnhw4eXeH7yj/fHyU7++Afd\nsWNHZeQm1cx1+DCF//kKS3AwAdcnmJ2OSK2wa9cu+vTpw+uvv86ll17q2Z6QkMBvv/3meW6xWHju\nuee47rrryhVfvXo1s2bN4uDBg8TFxTFlyhSaNWtWTe9KqovhdHL8wYeL15S7fxS21q3NTkm83Olq\nUlk1paJx8X7u48cpWLWqeG05zatQY5Tr9N7atWs9jxdeeIGgoCDGjBnD6tWrSUlJ4YsvvmDixIlE\nRETw0ksvVXXOUkXyl78HbjeBN96AT1CQ2emIeD232824ceM8y7ec5HA42L9/P4sWLWL9+vWsX7+e\ndevW0b1793LFt2/fzpgxYxg0aBDLly8nPDycpKQk3G53tb9HqVq5c17GuXUrvm1aEzpieNkvEDmD\n09WksmpKReNSO+QvW168tty112KNjDQ7HTmhXFfmmjRp4vl66NChjBw5krvuusuzLTAwkNtvvx3D\nMJgxYwZXX61pSr2NYRi/z07UT2uGiFSGefPmEVTKiZFff/0VwzBo164d/qXMBFZWfPHixfz1r3+l\nf//im8+nT59OfHw8X3/9NVdddVXlvxExhfOnn8h+9jnw8aH+rJlY/PzMTkm83OlqUlk1paJx8X6G\nYZC3+E0Agu8cYHI28kdnPfB+7969tGjRotRY48aNSUtLq3BSUv2cP/xA0c8/Y23aFL/LLjM7HRGv\nt2vXLhYtWsTkyZNPWX8zNTWV6OjoUhu18sRTUlJKDI8KDAzkwgsv9Kz5Kd7PKCri2JgHweEgZGgy\nfnFxZqckXu5MNamsmlLRuHg/x6ZNxceJ5zfDv2tXs9ORPzinRcMXLFiAw+EosT0vL4958+bRoUOH\nSktOqk/+O+8CEHRrX91cL1JBbrebCRMmcP/99xNdyhTyu3fvxmazMXToULp27cptt93GV199Ve54\nWloaUVFRJb5ngwYNdDKtFsl9eS7OlC34tmxJ2AP3m52OeLmyalJZNaWicfF+eYtOXJUbMEDHiTXM\nWS9NMG7cOO666y6uuuoqunTpQv369Tl69CjffvstFouFN998syrylCpkFBQU3y9nsRB029/MTkek\nxnM6nRw6dKjUWEhICO+++y7BwcH069eP/Pz8U/ZJTU0lJyeHvn37MmrUKFatWkVycjJvvfUWcXFx\nZcbtdvspV+38/PxOOckm3sm5YwfZM2cVD6+cPQtLYKDZKUkNV9GaVFZNqWhcvJsrM5OCDz8Em03H\niTXQWTdz7du358MPP2ThwoWkpKSwfft26tevT//+/Rk0aBCffvopMTExVZGrVJGCj1dhZGfj3+1K\nfJs2NTsdkRpvz549JCYmljotc0JCAhs2bGDZsmUApwxnApg1axZ2u53g4GAAYmNj+emnn3jzzTeJ\ni4srM+7v73/KQZLD4Sj1XhjxLobDwbH7R4PTSciI4fh11GgXKVtFa1JZNaWicfFu+W/9GwoLCex9\ns9YgroHOadHwJk2aMH78eM/z7777jmXLltGjRw/sdju33357pSUoVS/v3/8GIEh/N5FyadWqFTt3\n7iw19uKLL7JmzRoSExNLbB8yZAi9e/dm0qRJWK1WT6N2UkxMDD/++CNAmfHo6GjS09NLxNPT0+nc\nuXOF3peYL+fZ54pnr2wbS9joB8xOR7xERWtSWTWlonHxXkZREXkLFwEQPHiwydlIac550OuRI0eY\nN28eCQkJDBo0iDVr1nD99dfz2muvVWZ+UsWcqb/g2PAtPvXrE5hwndnpiHi9gQMHsmrVKlauXMnK\nlSt5+8QCq1OnTuW+++4DoE+fPsyZM6fE67Zt20bLli3LFY+Li2PTpk2eWH5+Ptu3b9c9y17O8b/N\n5LzwIthsRDz3HJbTTIAjcjbKU5NOV1M6duxYobhqkvezr16N68ABbBdfjF+njmanI6U4qytzLpeL\nL774gqVLl7Ju3TrPttGjRzNw4MDTzrwmNVf+W28BENi3jw4cRCpBWFgYYWFhnucn70+JiooiIiIC\ngB49ejB//nxat25Nq1atWL58OVu2bGHKlCnlig8YMID+/fuzcOFCrrjiCp5//nmaNGlCV80w5rXc\neXlk3jcK3G7Cxj6M7cILzE5Jaony1KTT1ZT4+PgKxVWTvF/u628AEDz4rlKH8Yr5ytXM/fLLLyxb\ntowVK1aQkZFBXFwcEyZMoGvXrlx33XWeezjEuxgFBeQtKT5DF3zn303ORqT2+vMH4LBhw/Dx8eGp\np54iPT2dNm3a8Prrr9P0xD2rZcUvuugiZsyYwezZs5k9ezYdO3Zkzpw5+qD1YlmTJuPaswe/Sy8l\nZGiy2elILffnWlFWTaloXLyTY+s2HN98g09EBEE3JZb9AjGFxSjtTtg/iY2NpXnz5tx0003ccMMN\nNGvWDICcnBwuvfRSFi1aVGJ9ESnWo0cPANauXWtyJqXLf3cpx+5/AP/4eBq8s8TsdESkitX0mlRX\nFXzyCZn3DMESEkLU6k/xPfEZK1LbqSbVbJkjR1GwfDmhox8gbMxos9OR0yjXPXMtWrRg3759rF+/\nnk8++YQDBw5UdV5SDXJP3tA68E6TMxERqZtcBw9xbMxDANR7YooaORGpEVyHDlGwciX4+xM8aKDZ\n6cgZlGuY5ccff8zWrVt5//33eeONNzyX0K+55hosFosuo3shx9atODdvxqdRFAGa+EREpNoZLheZ\n943COH6cwJtvIvDWvmanJCICQO78N6CoiKC/9dNyBDVcuWezvOiii3jkkUf4+uuvmTNnDg0bNuTZ\nZ5/FMAxmzpzJO++8Q2ZmZlXmKpUo77XXAQi+4w4sNpvJ2YiI1D25L83BsWED1qZNqffUNJ0YFZEa\nwZ2d7VmOIOTeISZnI2U566UJrFYr3bt359lnn2X9+vVMmTIFq9XKY489Rrdu3RisNShqPFdGBvnv\nrwCbTUMsRURMULhxI9nPzASrlfovvoDPH2YbFBExU96ChRg5OQRcn4CtVSuz05EynNOi4SeFhITQ\nr18/+vXrx4EDB1ixYgUffPBBZeUmVSRv0WJwOAjs2xdrVJTZ6YiI1CmuzGMcGzYCXC7Cxo/D/5JO\nZqckIgKAu6CA3Ff/BUDoiOEmZyPlcc6Lhv9ZkyZNGDZsGKtWraqsbylVwHA4fr90/o+7Tc5GRKRu\nMQyD46NH4zp4EP+ruhEybKjZKYmIeOQveRv30aP4d+2KnxZ99wqV1syJd8h/733cR47g1/lS/Nq1\nMzsdEZE6JXfuK9hXr8EnKor6zz+HxUcfwyJSMxh2OzkvvgRA6MgRJmcj5aVPkTrEcLvJnfsKgBal\nFRGpZoXffUf2tKfAx4eIOS9qhjgRqVHy3vo37sOH8busM37xV5idjpSTmrk6xL72c4p+/hnfli0J\nuOYas9MREakzXOnpZA4dVnyf3NiH8b/8crNTEhHxMAoKyHnxRQDCHnxQs+t6ETVzdUjuyy8DEDI0\nSUN7RESqiVFURObQ4bgPp+Hfo4fukxORGidv0WLcaUfwu/xy/K/QySZvoiP6OqLwv//F8d/v8GkU\nRdAtt5idjohInZH91PTi9eTOb0bE88/qZJqI1Cju7Gxynn8BgLCHHzQ5Gzlb+kSpI3KefQ6A0ORk\nLP7+JmcjIlI3FHz4Ebkvz4UAfyLmzcOnXj2zUxIRKSH35bm4jx0j4Npr8O/c2ex05CypmasDHJtT\nKPzqa3wiIwm68+9mpyMiUic4d+zg2AOjAaj/1FP4XXShyRmJiJTkSksrXlfOYiFs3Fiz05FzoGau\nDsg+cVUuJDkJn8BAk7MREan93MeOcfSef2Dk5xN8z90E9bvV7JRERE6RPeNpjIICgm7tiy021ux0\n5ByomavlHP/bTOHatVjq1SN44J1mpyMiUusZRUVkDh+B67e9+F3ehfBHHzE7JRGRUzh+/JH8t9/B\nEhhI2NiHzU5HzpGauVoue/oMAEJHDMcnJMTkbEREar+sx5+g8D9fYW3ShIi5L2Ox2cxOSUSkBMMw\nyJr4GBgGISOGYz3vPLNTknOkZq4WK1y3nsL16/FpFEXwXYPMTkdEpNbLe+vf5L32GpagICLnv66F\nwUWkRip4/30c323E+pe/EJp0r9npSAWomaulDMMg66mnAAi97z7dKyciUsUKN2zg+IR/AlD/+Wex\nXXiByRmJiJzKnZVF1uQpAIQ/NhGLjhG9mpq5Wqpg5Qc4U7ZgPb8ZwXfcbnY6IiK1mjP1F47+Ywg4\nnYQ9/BCBPXuanZKISKmyZzyNOz0d/6uvJqDn9WanIxWkZq4WMux2sqcVX5ULnzABi5+fyRmJiNRe\nrsxjHB10F8bxLAJvvZWQ+0aanZKISKkc/9tM3oKFEOBPvalTsFgsZqckFaRmrhbKnf8Grn378OvU\niYAbepmdjohIrWXY7WT+4x+4fv0Vv8s6U3/GUzo4EpEaybDbOTZ6DBgGYaNH49usmdkpSSVQM1fL\nuNLSyDmxrlzYxEd1UCEiUkUMt5tjD4zG8d/vsDZvTsS/XsXi7292WiIipcqe/SxFu3dji2tPiCY9\nqTXUzNUyWU88iZGbS+Ctt+J/SSez0xERqbWyn5xGwcoP8ImMpMHihVgjIsxOSUSkVIUbN5E752Ww\n2ag/8xksvr5mpySVRM1cLVL43XcULF+OJTSU8H+ONzsdEZFaK/e118l9eS6WgAAi35iP7//9n9kp\niYiUyp2Tw7H7RoHbTdhDD2KLjTU7JalEauZqCaOwkONjixu4sNEPYI2KMjkjEZHaKX/FCrIemwQ+\nPtR/+SX8OnYwOyURkdM6/shEXHv34nd5F0KSk8xORyqZrrHWEjlzXqbo55+xXXwxwXcPNjsdEZFa\nyf71Oo6NegAMg3ozphN43XVmpyQiclp5b79NwdKlWMLDqf/cs1isVrNTkkqmK3O1gHPXLnKefwGs\nVuo9PV3joEVEqoAjJYXMe/7hWUtOa3iKSE3m3L6D4xP+CUD92TPxbdLE5IykKqiZ83KG08mxUfeD\nw0HIvUPwu/his1MSEal1nDt3kvH3gRh5eQTfPVhryYlIjebKPMbRIUPAXkhIchKBCQlmpyRVRM2c\nl8t58SWc3/+Ab6tWhD04xux0RERqnaLffiPjjgEYx48TeOuthE+epGVfRKTGMpxOjiUPxbXnN/wu\n70LYuLFmpyRVSM2cF3N8/33xmnJWK/Wfm40lIMDslEREapWiAwfJuO123GlHCEi4jvozn8bio49O\nEamZDMMga+JjFK5fj7VpUyLmvYLFZjM7LalC+kTyUu6cHDKHDoOiIkLvH4Vf+/ZmpyQiUqu40tLI\nuK0/rn378L/ySiLmvKR7kkWkRst9aQ55CxdhCQkhcv5rWv+yDlAz54UMw+D4uPG4ftuLX5fLCNW9\nGyIilcp19CgZ/e/A9euv+F3WmYjX/6XRDyJSo+W98y7Z054CX18iXn0FW9u2Zqck1UDNnBfKW7CA\ngvdXYKlXj4gXXtCZYhGRSuQ6epSM2/oXL/fSsSORCxfgExRkdloiIqdV8MGHHB/zIAD1Zz5DQLdu\nJmck1cUrmjnDMJg3bx7XXnstHTp0oH///mzevLnEPkuWLOHqq6+mQ4cOjBw5kszMzGqNV5fC774j\n67HJYLEQ8cLzWBufZ0oeIiK1kaeR27ETW/t2NFi8EJ+QELPTEhE5rYJPPiFzxEhwuwl/YgpBt/Y1\nOyWpRl7RzC1YsID58+czYcIEVqxYQadOnbjnnns4dOgQAJ9//jnTp09n7NixLFmyhMzMTMaM+X1m\nx6qOV5eiAwfIvDcZiooIe+hBAq7uXu05iIjUVqc0cv9+C5/wcLPTEhE5rfwVK34/NvznBEIG32V2\nSlLNvKKZW7ZsGffccw/du3enWbNmPPTQQ0RFRbF69WqguNnr378/CQkJtGnThqeffpoNGzawe/fu\naolXB3dODkcH3YU7PZ2AntcTMnJEtf1sEZHazpWWRkbffmrkRMRr5C1azLER94HLRdjERwkdNtTs\nlMQEXtHMPfbYYyQmJp6yPTs7G8Mw+OGHH7j00ks92xs3bkzjxo1JSUmp8nh1MBwOMocOKz7IaHcx\n9Z9/TlNji4hUkqIDB0jvcytFu3Zh69hRjZyI1GiG2032jKc5Pm48GAbhT04lNOles9MSk3jFzBmX\nXHJJiedffvkle/fuJT4+nqysLAoKCoiKiiqxT4MGDUhLS6vyeFUz3G6OPTCawi++xNq4MZFvzNeN\n+CIilaRozx4ybrsd1/79+F3epbjG6h45Eamh3Pn5HLt/NPaPPgJ/fyJefIHAXj3NTktMVCOaOafT\n6bn/7c9CQkKI+MMaGbt372bcuHHceOONdOjQgcOHDwPg7+9f4nV+fn44HA7sdnuVxquSYRhk/fMR\nCt5fgU9EBJH/fhNro0ZV+jNFROoK544dZNzxd9xHjuB/VTciXvsXPoGBZqclIlKqol9/JfPeZJzb\nt+PToAER/5qH/x9GjkndVCOauT179pCYmIjFYjkl1rt3b6ZNmwbA1q1buffee2ndujVTp04Ffm+y\n/txYORwOAgICqjxeVQzDIOuRR4sXfgwOJnLxQmwtW1bZzxMRqUsKN/2PowMHYWRlEdDzeiJefEHr\nyIlIjVXw4Ucce/AhjJwcbBdeSMT81/Bt0sTstKQGqBHNXKtWrdi5c+cZ99m4cSPJycnExcUxZ84c\n/Pz8AKhfvz4BAQGkp6eX2D89PZ3o6OgqjTeqoqtkhsvF8QmPkL94cXEj9+Zi/Nq3r5KfJSJS19i/\n/JLMf9yLUVBA0G1/o96M6VqvU0RqJHdODscfmUjB0qUABA24g3qTJ2HRKAI5wStm0di5cydJ6lzj\nnwAAIABJREFUSUl07tyZuXPnnjLksV27dmzatMnz/MCBAxw6dIgOHTpUWfzw4cOeeGUyHA6OjRhZ\n3MiFhBD55mL8L72k7BeKiEiZ8pcu4+igwRgFBYTcO4R6M59RIyciNVLB6jUc6d6DgqVLsYSFUf/F\n56k/Y7oaOSnBKz7Bxo8fT6NGjZg4cSJZWVme7YGBgQQHB3PnnXfy0EMP0aZNG1q1asUTTzzBlVde\nSfPmzQGqJN61a1datGhRqe/Tffw4R4ck4fjmG3wiI4l8cxF+F19cqT9DRKQuMgyD3Dkvk/1k8bD9\nsH9OIGRocqnD+0VEzFS0fz9Zk6dg//hjAPyvvJJ6M5/WsEopVY1v5vbu3esZgnn11VeXiA0ePJiH\nH36Ya6+9ljFjxvD000+Tl5dHfHw8kydP9uxX1fHKUPTLrxy9azBFqalYmzUjctFCbC1jKvVniIjU\nRYbLRdZjk8ib/wb4+lJ/5jME3drX7LREREpwZ2eTM+dlcl99FeyFWOrVI3ziowT9rZ9OPMlpWQzD\nMMxOorbq0aMHAGvXrj3jfgWffcax++7HyMnB79JLiXjtVayRkdWRoohUsV27dtGnTx9ef/31EutV\nrlu3jqeffpo9e/bQokULxo8fT+fOnT3x1atXM2vWLA4ePEhcXBxTpkyhWbNm5Y6Xprw1qTZx5+Vx\nbNgI7GvWYAkKIuJf8wi46iqz0xKpdgkJCfz222+e5xaLheeee47rrrsOqHjNUU06d+68PPLeWEDu\ny3NxHzsGPj4ED7iD0IcfxhpR3+z0pIbzinvmaiujsJCsyY+TOfgejJwcggbcQYMlb6mRE6kl3G43\n48aNo6ioqMT2nTt3MnToUHr16sWHH35I165dGTp0KBkZGQBs376dMWPGMGjQIJYvX054eDhJSUm4\n3e5yxaWY69AhMvrcin3NGnyiG9HgveVq5KROcjgc7N+/n0WLFrF+/XrWr1/PunXr6N69O1DxmqOa\ndG5cR4+SPXMWaZddTvaT03AfO0bANdcQtfpT6j01TY2clIuaOZM4t+8gPfFmcue9iiUggHrPPF18\nU6umxhapNebNm0dQUNAp21999VW6detGUlISTZs2ZcyYMTRv3pzvv/8egMWLF/PXv/6V/v37ExMT\nw/Tp00lLS+Prr78uV1zA8eOPHLnxJpxbt2K78EKiPvgAv4suNDstEVP8+uuvGIZBu3btiIyM9Dxs\nNhtQ8ZqjmlR+hmHg+N9mMkc9wOFLLyNn1mzcx47hf3V3Gn6wksgF87HFxpqdpngRNXPVzCgsJHv2\nsxzpdQPObdvwbRtLw1UfEXx7f7NTE5FKtGvXLhYtWsTkyZP582j2DRs20LNnzxLbli5d6hlylJKS\nUmJIZmBgIBdeeCEpKSnlitd1+Ss/IKN3H9yHD+N/9dU0WL4Ua+PzzE5LxDSpqalER0efMhv4SRWt\nOapJZSs6cJCcOS9z5OprSL/p5uKlBtxuAvv0IeqzT2mwaCF+HSt/lnSp/Wr8BCi1if2rr8j656MU\n/fILWK2EjBxB2AP3YzlNcRUR7+R2u5kwYQL3338/0dHRJWK5ublkZmZitVoZOXIkmzdv5vzzz+fh\nhx8mLi4OgLS0NKKiokq8rkGDBqSlpZUrXlcZbjc5M2eR8+xzAIQkJxE2YTwWq9XkzETMtXv3bmw2\nG0OHDuXHH3+kSZMmDB8+nG7dugEVrzmqSaUr+uVXCj77DPuqT3D8YYkra7NmBPe/jaA7bsfasKGJ\nGUptoGauGjh//pmsJ56k8MQNvrb27aj31DT82rUzOTMRORdOp5NDhw6VGgsJCeHdd98lODiYfv36\nkZ+fXyKel5cHwNSpUxk+fDjDhw/nvffeY/DgwXz00Uc0btwYu91+yhl0Pz8/HA4HQJnxusidk8Ox\nB0ZjX/UJ+PlRb/pTBP+tn9lpiVSLsmpSamoqOTk59O3bl1GjRrFq1SqSk5N56623iIuLq3DNUU0q\n5j5+nML//pfCr9dh//I/uH791ROzhIcTeEMvgm65Bb8ul2Hx0eA4qRxq5qqY++hRjlx9DRgGPpGR\nhD04hqABd+hMsYgX27NnD4mJiaVOFZ2QkMCGDRtYtmwZwClDLH1PLFCdmJjI7bffDhSvpfntt9/y\n7rvvMmrUKPz9/U85CHI4HJ7778qK1zXOXbvIvGcIRamp+DRsSORr/8KvU0ez0xKpNmeqSb1792bW\nrFnY7XaCg4MBiI2N5aeffuLNN98kLi6uwjWnLtYkw+Wi6JdfcG75HsfmzRRu3ETRzp3wh5pvPe88\n/Hv0ILDX9fhffjkWPz8TM5baSs1cFTPy8rAEBBB8z92EDh+GT1iY2SmJSAW1atXKs/7ln7344ous\nWbOGxMTEEtuHDBlC7969efTRR7HZbLRs2bJEvEWLFhw8eBCA6Oho0tPTS8TT09M9SxeUFa9LCj76\nmGMPjMbIy8OvUyci5s3F+qehrSK13Zlq0kknG7mTYmJi+PHHH4GK15zaXJMMw8B9+DBFqb/g3LUL\n586fKNqxA+eOHRh/GnlhCQvD79JLCegaj/+VXfGNjdX6cFLl1MxVMZ/69Wn08cdYGzQwOxURqQYD\nBw7k5ptv9jwvKCjgpptuYurUqVx++eVYrVbat2/Ptm3b6Nv394Wrd+/eTUJCAgBxcXFs2rSJAQMG\nAJCfn8/27dtJTk4+YzwpKam63qbpDKeT7GlPkfvKPACC7xpE+GMTdeZbpBR9+vThmmuuYdiwYZ5t\n27Zt85xUOteaUxtqklFUhDs9Hdfhw8WPAwcp2r8f1759FP22F9eePRgFBae+0McH3zat8WvfHr8O\nHfDr1Anf2DYaeSXVTs1cFbOEhqqRE6lDwsLCCPvDFfiT98xFRUUREREBFF+lGzlyJLGxsXTp0oUl\nS5awf/9++vTpA8CAAQPo378/Cxcu5IorruD555+nSZMmxMfHnzHetWvXan635ig6cIBjQ4fj+N//\nIMCfetOm6f44kTPo0aMH8+fPp3Xr1rRq1Yrly5ezZcsWpkyZApx7zalJNckoKsLIzcWdm4uRnYM7\nJxt3dg5GdjburCzcx4/jzsw88TiGKyMD94kHfxoOX4KPD9bzm+Eb0xJbyxh8Y9tga1P8sAQGVtv7\nEzkdi/HnGzqk0pycZnztiYlPRKTuyc/Pp1OnTixcuLDE1N0ff/wxL7zwAgcPHqR169aMHz+ejh07\nlojPnj2bjIwMOnbsyKRJk2jatGm546WpDTXJvmYtmaPuxzh+HN8WLYh4ZS62C9qanZZIjWYYBnPn\nzmXZsmWkp6fTpk0bxo0bV6k151xrkpGTw4q7BoPTWdyQORzgcGCcfBQ6oLAQo9COYS/EsNuLHwUF\nGPn5uPPzi4c7nuNkK5agIHyiorCeF431vPOwNm6Mb5MmWJs1xdq0Gb5N/6Ir/lKjqZmrQrXhwElE\nag9vrklGYSHZ02d4hlUG3tKbek9NwyckxOTMRORc9ejRA9fevbyZb6/YN7LZipuy4GAsISH4hIZi\nCQvFJywMn7AwLOHh+NSvh0/9+sWPiEisDSLxadgQnz/dSyjibTTMUkREajTn7t0cGzYC57ZtxcMq\nH3+coDtu18QCIrWAJTyc0GHDi69++fpi8fPDYrOBnx8Wfz8s/v5Y/PyxBAQUfx0QAAEB+AQFYgkM\nxBIUpCtnUqepmRMRkRrJMAzyF79J1qTJGHY7vm3bEvHSC9jatDE7NRGpJD7h4YQ9cL/ZaYh4LTVz\nIiJS47iOHOH42HHYP1sNQPA/7iF8/Ljis/IiIiICqJkTEZEapuCDDzk+fgLuY8fwadiQ+rNnEtC9\nu9lpiYiI1Dhq5kREpEZwZR4j65//pGDlBwAEJt5I+JNPYo2ob3JmIiIiNZOaORERMV3BRx9z/J+P\n4E5Px1KvHvWenErQzTeZnZaIiEiNpmZORERM4zp8mOOPPIp91ScABFxzDfVmPIW1USOTMxMREan5\n1MyJiEi1MwyD/H8vIWvKExjZ2fhERBA+ZTKBN9+sJQdERETKSc2ciIhUK+fOnRz/5yM4vv0vAIF9\n+hA++TGsEREmZyYiIuJd1MyJiEi1cOflkTNrNrn/eg2KirD+5S/Ue+pJzVQpIiJyjtTMiYhIlTIM\nA/tHH5M1aTKuQ4fAZiNk5AhCR92HT2Cg2emJiIh4LTVzIiJSZZw7dpA16XEK160DwL9rV8KnPoGt\nZYzJmYmIiHg/NXMiIlLpXBkZZD89k/y33gK3G5/oRoRPnEjgTYma4ERERKSSqJkTEZFKYxQWkjt/\nPjnPPo+RkwMB/oQOHUrIsKH4BAWZnZ6IiEitomZOREQqzHC7KXh/BdlPP4Nr714AAm/pTdj4cfg2\naWJydiIiIrWTmjkRETlnhmFQ+MWXZE97Cuf27QDYOnQgfNJj+F/SyeTsREREajc1cyIick4cm1PI\nevJJHBu+BcA3JoawcWMJ6Hm97osTERGpBmrmRETkrDi2bCF71rMUrl0LgE90NGFjRhP0t35YfPWx\nIiIiUl30qSsiIuXiSEkpbuI+/xwAS716hA4bSsjdg7FovTgREZFqp2ZORETOqNQmLjmJ4MF34RMS\nYnJ2IiIidZeaOREROYVhGBR+9RW5L71M4fr1APjUr09I0r1q4kRERGoINXMiIuJhFBVR8OGH5M6Z\ni3PbNgB8IiMJGfIPNXEiIiI1jJo5ERHBnZ9P/tvvkPvKPFz79gFgPb8ZIUlJBP+tn+6JExERqYHU\nzImI1GFFv/1G3oKF5C15GyMrCwBbu4sJHTaMgF49sVitJmcoIiIip6NmTkSkjjEMg8Kvvybv9fnY\n16wFwwDAv/tfCU1Oxi/+Cq0TJyIi4gXUzImI1CFGbi5HrupOUWoqAJaQEIL+1o/gQYOwtYwxOTsR\nERE5G2rmRETqEHdmJkX5dnxjYggefBdB/W7VpCYiIiJeSs2ciEgdYgkOJvK11/C/8koNpRQREfFy\nauZEROoQn8hIArp1MzsNERERqQQ+ZicgIiIiIiIiZ0/NnIiIiIiIiBdSMyciIiIiIuKF1MyJiIiI\niIh4ITVzIiIiIiIiXkjNnIiIiIiIiBdSMyciIiIiIuKF1MyJiIiIiIh4ITVzIiIiIiIiXkjNnIiI\niIiIiBdSMyciIiIiIuKF1MyJiIiIiIh4ITVzIiIiIiIiXkjNnIiIiIiIiBdSMyciIiIiIuKF1MyJ\niIiIiIh4Ia9o5gzDYN68eVx77bV06NCB/v37s3nz5hLxdu3a0bZtW2JjY4mNjaVt27Zs27bNs8+S\nJUu4+uqr6dChAyNHjiQzM7PEz6hoXESkNLt27eLiiy9m48aNJbavW7eOm2++mfbt23PLLbfw3Xff\nlYgnJCR46tnJmvbZZ5954qtXr6Znz560b9+eQYMGsXfv3mp5PyLincqqOWXVlIrGRaRqeEUzt2DB\nAubPn8+ECRNYsWIFnTp14p577uHQoUMA7Nu3D6fTyWeffcb69etZv34969ato23btgB8/vnnTJ8+\nnbFjx7JkyRIyMzMZM2aM5/tXNC4iUhq32824ceMoKioqsX3nzp0MHTqUXr168eGHH9K1a1eGDh1K\nRkYGAA6Hg/3797No0aISNa179+4AbN++nTFjxjBo0CCWL19OeHg4SUlJuN3uan+PIlLzlVVzyqop\nFY2LSNXximZu2bJl3HPPPXTv3p1mzZrx0EMPERUVxerVqwHYvXs3kZGRNG3alMjISM/Dx6f47S1Y\nsID+/fuTkJBAmzZtePrpp9mwYQO7d++ulLiISGnmzZtHUFDQKdtfffVVunXrRlJSEk2bNmXMmDE0\nb96c77//HoBffvnFM+LgjzXNZrMBsHjxYv7617/Sv39/YmJimD59OmlpaXz99dfV+v5ExDuUVXPK\nqikVjYtI1fGKZu6xxx4jMTHxlO3Z2dlAcTPXvHnzUl9rGAY//PADl156qWdb48aNady4MSkpKRWO\ni4iUZteuXSxatIjJkydjGEaJ2IYNG+jZs2eJbUuXLqVHjx5AcTMXHR2Nv79/qd87JSWlRE0KDAzk\nwgsvVE0SkVKVVXPKqikVjYtI1fGKZu6SSy6hUaNGnudffvkle/fuJT4+HoDU1FTsdjuDBg2ia9eu\nDBw4kB9++AGArKwsCgoKiIqKKvE9GzRoQFpaWoXjIiJ/5na7mTBhAvfffz/R0dElYrm5uWRmZmK1\nWhk5ciTx8fHccccdbNmyxbPP7t27sdlsDB06lK5du3Lbbbfx1VdfeeJpaWmqSSJSLuWpOWXVlIrG\nRaTq+JqdAIDT6fTc//ZnISEhREREeJ7v3r2bcePGceONN9KhQweguJnLzs5m9OjRhIWFsWTJEgYN\nGsTKlSs9w5L+fIbbz88Ph8OB3W6vUPxMjhw5gsvl8pz5EqmtzjvvPBYvXmx2GtWmrJr17rvvEhwc\nTL9+/cjPzy8Rz8vLA2Dq1KkMHz6c4cOH89577zF48GA++ugjGjduTGpqKjk5OfTt25dRo0axatUq\nkpOTeeutt4iLi8Nut6smiZyBatLvfH2LD/XOVHPKqikVjZ+OapLUFVVZk2pEM7dnzx4SExOxWCyn\nxHr37s20adMA2Lp1K/feey+tW7dm6tSpnn3eeustXC4XgYGBAEyZMoUtW7awbNkyBg0aBHBKQXE4\nHAQEBHiKz7nGz8Tf37/MQiYi3udMNSshIYENGzawbNkygFOGWJ48sEpMTOT2228HYPz48Xz77be8\n++67jBo1ilmzZmG32wkODgYgNjaWn376iTfffJO4uLhSa4vD4Sj1/rw/Uk0SqZ3OVJOuvPJK4Mw1\np6yaUtH46agmiVRcjWjmWrVqxc6dO8+4z8aNG0lOTiYuLo45c+bg5+fnif3x65NiYmJIS0ujfv36\nBAQEkJ6eXiKenp5OdHR0heJ/HPpZmk2bNp0xLiLe6Uw168UXX2TNmjWn3Oc7ZMgQevfuzaOPPorN\nZqNly5Yl4i1atODgwYMAWK1WTyN3UkxMDD/++CMA0dHRpdakzp07nzFv1SSR2ulMNcnlchEXF3fG\nmlNWTalo/HRUk0Qqzivumdu5cydJSUl07tyZuXPnlriUX1RUxJVXXsmKFSs829xuNzt37vQUrnbt\n2pUoGAcOHODQoUOeYZrnEj98+LAnLiJy0sCBA1m1ahUrV65k5cqVvP3220DxEKf77rsPq9VK+/bt\nS6yDCcVDyJs2bQpAnz59mDNnTon4tm3bPDUtLi6uRE3Kz89n+/btqkkicory1JzT1ZSOHTtWKK6a\nJFL1rJMmTZpkdhJlGTJkCAEBAcyaNQun00l+fj75+fkYhkFAQAC7d+9m2bJltG7dGofDwcyZM/n5\n55+ZNm0a/v7+hISEMHPmTJo0aYJhGEycOJGYmBgGDhwIcM7xk0M4RURO8vf3Jzw83PMIDAzklVde\n4c477/Q0Y5GRkcycOZPIyEhCQ0N55ZVX+Oabb5g6dSqhoaFkZGTwxhtv0KJFC6xWK/Pnz+fTTz9l\nxowZhIeHEx0dzYwZMwgJCSE4OJipU6ficrkYO3ZsqcOsRKRuO13NeeKJJwgNDS2zplQ0LiJVx2L8\n+YaOGmbv3r0kJCSUGhs8eDAPP/wwdrudZ599llWrVpGVlUVcXByPPvooMTExnn0XLVrEq6++Sl5e\nHvHx8UyePJn69etXWlxEpDT5+fl06tSJhQsXlpi6++OPP+aFF17g4MGDtG7dmvHjx3vOchuGwdy5\nc1m2bBnp6em0adOGcePGeeInXz979mwyMjLo2LEjkyZN8pxlFxH5szPVnJPxM9WUisZFpGrU+GZO\nRERERERETuUV98yJiIiIiIhISWrmREREREREvJCaORERERERES+kZk5ERERERMQLqZkTERERERHx\nQmrmREREREREvJCaORERERERES+kZk5ERERERMQLqZkTERERERHxQmrmREREREREvJCaORERERER\nES+kZk5ERERERMQLqZkTERERERHxQmrmREREREREvJCaORERERERES+kZk5ERERERMQLqZkTERER\nERHxQmrmREREREREvJCaORERERERES/ktc1cUVERjz/+OJdddhldunTh6aefxjCMc9q3onERqflW\nr15Nz549ad++PYMGDWLv3r0V2r8iccMwmDdvHtdeey0dOnSgf//+bN68udQ8XnnlFe67775Ttq9b\nt46bb76Z9u3bc8stt/Ddd9+V91chIrVATToO0nGSiIkML/XUU08Z1113nfH9998b33zzjREfH2+8\n/PLL57RvReMiUrNt27bNuPjii41///vfxu7du42RI0ca119/veFyuc5p/4rG58+fb3Tp0sX4/PPP\njd9++82YMWOGERcXZxw8eLBEHu+9955xwQUXGPfdd1+J7Tt27DAuuugiY+7cucbevXuNZ555xujY\nsaORnp5e2b86EamhatJxkI6TRMzjlc1cYWGhERcXZ3zxxReebe+9954RHx9/1vtWNC4iNd/48eON\nkSNHep7n5+cbHTp0ML788stz2r+i8RtvvNF49dVXS/zM6667zliwYIFhGIZht9uNcePGGXFxcUbP\nnj1PaeZGjx5tDBs2rMS2vn37GmvWrCnfL0REvFpNOg7ScZKIubxymOWOHTuw2+1ccsklnm2XXHIJ\nR48ePWWoU1n7VjQuIjVfSkoKl156qed5YGAgF154ISkpKee0f0Xjjz32GImJiaf83OzsbACOHj3K\nwYMHWbp0Ke3btz9lvw0bNtCzZ88S25YuXUqPHj3O/IsQkVqhJh0H6ThJxFxe2cylpaUREBBASEiI\nZ1vDhg0xDIPDhw+f1b4VjYtIzZeWlkZUVFSJbQ0aNCAtLe2c9q9o/JJLLqFRo0ae2JdffsnevXuJ\nj48HoHHjxixYsICYmJhTcsvNzSUzMxOr1crIkSOJj4/njjvuYMuWLWX+HkSkdqhJx0E6ThIxl1c2\ncwUFBfj7+5fY5ufnB4DD4TirfSsaP5O///3v/P3vfy/PWxKRCnA6nezdu7fUx9GjR7Hb7aX+Oz7d\nv+Gy9q9o/I92797NuHHjuPHGG+nQoUOZ7zUvLw+AqVOncsUVV/Daa69x8cUXM3jwYA4ePHjG16om\nidQONek4SMdJIubyNTuBcxEQEHBKgTj5PCAg4Kz2rWj8TA4dOoT76FEyh48oGbBYih/FT0ps+32z\npeR+Fgv4+BTvf3K/k9s8+/oUh318ireffFgsv2+zWoufW63FX/tYsPic+NpqLd7u61v89cn/2mzg\na8XiawNfXyx+Niw2P/CzYfHzK/7a3w+Lv7/ngc2GxfNmRKrWnj17SExMLPX/ud69e5/233FQUFCp\n38/f3/+M+1c0ftLWrVu59957ad26NVOnTi3HOwVf3+KynZiYyO233w7A+PHj+fbbb3n33XcZNWrU\naV976NAh0AxzIl6vJh0HVfQ4SUQqxiubuejoaAoKCsjPz/ccHB05cgSLxVJi6FJ59rXZbBWKl8XI\ny6Pg/RWV+fa9g8WCJSCg+BEUhCUwsPgRHIQlKBifkGAsoaH4hIQU/zcsDJ+wMCzh4fjUr4dP/fr4\nRETgU69ecSMqcgatWrVi586dp41v2bKF9PT0EtvS09Pp3LlzqftHR0efcf+KxgE2btxIcnIycXFx\nzJkzx3Mmuyz16tXDZrPRsmXLEttbtGhR5pU5ANe+/WQOH0Hw4MH4deqoky4iXqgmHQdV9DhJRCrG\nK5u52NhYAgIC2LRpE926dQNg06ZNREZG0rRp07PaNyoqqkLxsvhERRE5+fHf11sxDOCPX5/4r2F4\nNv95u+GJu3/fz7PtZPxEzH1iu8tVvN3t/v25y1X8s11ucLuLn7vdv8dOPIwiF7hdGM4icLvA6cQo\nKgJnEYbTUbzd6cQocmIUOsDhwHA4MByFGPZCKCzEsNuLHwUFcOzYufyZT/wCfYqbuoYNsDZsiLVR\nI3yio7FGR2Nt0gTfJk2wNmuKzx/G6ov8WVxcHJs2bWLAgAEA5Ofns337dpKSks5q/+Tk5EqJ79y5\nk6SkJC677DKef/55bDZbud+L1Wqlffv2bNu2jb59+3q27969m4SEhLK/gQUK3l9BwfsrsLW7mODB\ngwm6KRFLGWfQRaTmqEnHQRU9ThKRivHKZs7f35++ffsyZcoUpk+fTmFhITNnzmTQoEEAZGVlARAe\nHl7mvhWNl8USEEDANXVzhjnDMH5v7PILcOfnYxTkY+TmYuTl487NwcjJxZ2Tgzs7GyMrC3dWFu7j\nx3FnHsOdmYn76FHcGRm4MzIo2nH6Ky8+ERH4Nm+OtXlzbC1j8G3VElubNljPP19X9oQBAwbQv39/\nFi5cyBVXXMHzzz9PkyZN6Nq1KwCFhYXk5OQQERGBj4/Pafc/OUHJucQbN27siY8fP55GjRoxceJE\nT72C4lkvg4ODy3w/Q4YMYeTIkcTGxtKlSxeWLFnC/v376dOnT5mvtTZpQljfW8lbsBDnDz9y/IHR\nZE95gqABdxAycCDWxued9e9XRKpXTToOquhxkohUjMUwvPMGCofDwRNPPMGqVavw8/OjT58+jBkz\nBoA777wTi8XCwoULy9y3MuKnc3Ka8LVr11bmW69z3Hl5uNPTcaWn4z6chuvwYVyHDuE6eJCi/ftx\n7d2H++jRUl9rCQrC1rYttnYX49e+PbaOHfFt0VxDy+qgjz/+mNmzZ5ORkUHHjh2ZNGmS56zxe++9\nx4QJE1i7di2NGzcuc/+KxPfu3XvaK2iDBw/m4YcfLrFt/Pjx5Ofn89xzz53yfl544QUOHjxI69at\nGT9+PB07djzj7+CPNckoKsL+2WpyX5+PY8OG4h18fQm8+WZChyVji40tx29VRMxSk46DdJwkYh6v\nbea8gYpU9XHn5lK0Zw9Fqb9QtHs3Rbt24dz5E0WpqcVDSf/AJyICvy6X4X/55fh3uxLfmBg1d1In\nnK4mOXfsIHf+AvKXLQV7IQD+V19N6PCh+F12mf59iEiV0HGSSMWpmatCKlLmMwoKcO65nz/EAAAg\nAElEQVTcieP7H3Bu2YLjf5sp+uWXEvtYmzQhoMfVBCRch/8VV2Ap50QUIt6mrJrkysgg77XXyV2w\nEOPEMC1bx46EDksmICFBQ5ZFpFLpOEmk4tTMVSEVqZrJlZGB49v/UrhuHfb/fIVr715PzBIeTuD1\nCQT16YPfFZfr4FVqlfLWJHduLvlv/Zvcea/iOjF1uG+b1oQ98AABN/TSvwsRqRQ6ThKpODVzVUhF\nyjs4U3/Bvno19k8+xbFxo2e7tUkTgm7vT/Dt/bFGR5uYoUjlONuaZDgcFKxYSc5LcyjatQtQUyci\nlUfHSSIVp09iqfNsMS0ITU6i4fvLid74HWGPPoJv27a4Dhwg55mZHL7scjJH3odj61azUxWpVhY/\nP4L63UrU2tXUn/Mivq1aUfTTz2QmD+XINddS8MGHGH+6J1VERESqj5o5kT+wNj6P0OQkolZ/SsOP\nPiCo/21gtVKw/D3SE3qScedAHCkpZqcpUq0sVitBN99calOXfn0v7F9+iQZ5iIiIVD81cyKlsFgs\n+MXFUX/mM0Rv/C+hY0ZjqVePws+/IP3Gmzh6zz9wpv5S9jcSqUVOaepiYnBu28bRAXeS8bf+OLZs\nMTtFERGROkXNnEgZrJGRhI1+gOjvviVs/Dgs9cKxf/IpR3pcQ9bjU3Dn5pqdoki18jR1n6+h3ozp\n+EQ3wvHNN6TfkMjRe5N1okNERKSaqJkTKSef4GBCRwwn+pv1hCQnAZD7yjyO/PVqCj5bbXJ2ItXP\n4uvL/7N353FR1fsfx19nVgaQTQSFRHMLrisu5J5rXkvLNJO0NLVyyVavpWYu9TOVullaauaSSrfN\n9d60e0Ot61ppYqWo1yXDXBAQkHUWZn5/gBSJgmxnZvg8H495EPP9zpn3OY+a+Mz5Ll4jhhO8Z3fB\nFx0+PuRt3crlXr1Jnzkbe3q62hGFEEIItybFnBC3SOPri+8rMwjasR1j167kX7zIldFjSHthMvbM\nTLXjCVHtNCZT4Rcde/Ae9yRoNGSvXElS1+5kfbgGh82mdkQhhBDCLUkxJ0Q56Rs3ovYn/8Bv4Vso\nPj7kfPoZl+/+K5afflI7mhCq0Pj74zvzFYK/3oHHX/thT0sj4+UZXO73V/J27VY7nhBCCOF2pJgT\nogIURcHroaEEbf8KQ6dO5Ccmknz/A2Svi1U7mhCq0TVsSO2VKwj89BN0EeHYjp8g9eHhpD45vmgT\nciGEEEJUnBRzQlQCXWgogZ9+TK1nnwGLhfSp00h/eYYMLxM1mrFrF4L+/SV+815H8fMjb+tWku7q\nSdbyD+S/DSGEEKISSDEnRCVRtFp8XpxCwOpVKF5eZH+4htTHRmPPyVE7mhCqUXQ6vEY+SvCub/CM\nHoYjO5uMOa9y+a/3YD5wUO14QgghhEuTYk6ISma6uy91tmxCGxKC+etvSI0ejj0tTe1YQqhKW7s2\n/n9/k8BNG9CF34Ht2DFSBj1A+sszZHsPIYQQopykmBOiCugjIqizZTO6pk2x/PADKcMeJv+KFHRC\nGKOiCPr3l/i88jKKhwfZH67hcs/e5O38Wu1oQgghhMvRqR1ACHelDalH4MYNpA4fgfXnn0l9eDiB\nn/wDjb+/2tGEUJWi11Nr/HhM/fuTPuUlzHv3kvroSEyDB+M7ZxbagAC1IwohqokjJ4eczZtBUf7U\nUvh74fOKohT8s1L8eTR/fL7gZ7G+CqDRgKIpaNMU/ESjFD2vaDS//37tOW3hP2u1KFotFD4UjQZ0\nOtDqUHRa0OkK2vX6gjYhqpkUc0JUIW2AP4Eff0TKsIexHjlCysjHCPz0YzSenmpHE0J1ugYNqP3p\nx+R88ikZr75G7saNmHfvxi9mAaa7+6odTwhRDewpKaQ99bTaMSqHRlNQ1Ol0BT8NBhS9HgwGFIMe\nxWhEMXqgGI1gNBb87uGBYjKhmDzQeHqieHqieHmheHmh8fZGqeWNxrsWik8tND4+aHx9C14vRCEp\n5oSoYhp/f2p/8jEpg4dgPXSIK+MnUnvlBwUf8ELUcIqi4PVwNB49e5A+dRp5cdu5MnoMntHD8J09\nC02tWmpHFEJUIcXbG88HhhT+5ij8cZOf1x7XnrbbC17nKOkBjqJ/thf8tBf8dNgLn7PbIb/wufz8\ngmPl54O98Hd7PuTbi/+zzQq2fMjPL1iZ12b7/afVisNs/uPZVP41M5nQ+Pmh8fdHExCAJrA2mtqB\naIPqoAkKQls3GG29emjr1UPj7V1FKYSzUBwOR1X9u1bj9e7dG4AdO3aonEQ4A9v5CyTfdz/2S5fw\nGvkofvNeVzuSqGGc/TPJ4XCQ89nnZMychSMrC+1tt+G/8C2MnTupHU0IUQWc/TOpvBwOB1itBQWe\n2VxQ4FksOMyWgt/NeTjMZhx5eQWPnNzCnzk4cnKwZ2fjyM7GkZVV8M9XM7FnXsWekYEjo+BnQRFb\nOsXPF91t9dGG1UfXoAG6229H17gRuqZN0dauXcVXQlQHuTMnRDXRhYYQ+NE6ku8bRPbadegjIvAa\n+ajasYRwGoqi4DXsIYxdOpP23AtY9u8n5aFheE+cgM+Uv8ndbCGES1AUpXBopQGqYFqFw27HcfUq\n9rQ08lOvYL+Sij05hfzkZOxJSeQnJZF/8SL5Fy5iT0nBmp6B9ciR646jCQhAFx6O/i8RGFq2RN+6\nFbrGjWXun4uRYk6IaqQPD8f/3cVcGTOW9Fdmogu/A2NUlNqxhHAquttuI/CzT8heuYqMefPJem8J\n5r17CXjvXXQNG6odTwghVKVoNCh+fmj8/NDdfvtN+zpyc7GdP09+4jlsZ89iO3MG26nTWE+exH7p\nEpZ9+7Ds20f2tWPXqoWhbSSGqCiMHe/E0LZtQVEqnJYMs6xC7jp8QFRc5qLFXF0Qg6ZuXYLi/iOr\n94lq4YqfSdaEY1yZ+BS2kydRvLzwe30ung8OKf2FQgin54qfSe7EnpGB9fhxrEcTsP78M5Yff8T2\nv5O/z1GkYH6eoVMnPHr3xKNPH3S33aZiYlESKeaqkHxIiRtx2O2kjnoM886vMfbsQe21a2RYg6hy\nrvqZZM/NJWP2q+TExgLg+dBQfF+fi8ZkUjmZEKIiXPUzyZ3Zr17FcugQ5m+/w7L/Wyzx8QULwhTS\nt2yJ6d57MA26H139+iomFdfIX49CqEDRaPB/5200deti/vobsj9co3YkIZyWxmTCf8E8Aj5YjuLr\nS85nn5M88D6sp06rHU0IIdyKxscHjx498J36EnW2bKLekZ8IWLEcz4ej0dSujfXnn7k6fwFJHTuT\nPHgI2Z99jj03V+3YNZoUc0KoRBsQQMCidwC4Ovd1rKfPqJxICOdmuqc/Qf/ehr5VS2zHjpN8z73k\nbPmn2rGEEMJtaXx8MPXvj/+bb1A3/gcC13+G16OPoPj5Yfnue9Kff4FL7TuQ8dr/YTt/Xu24NZIU\nc0KoyNilM15jx+DIyyPt2ecK97gRQtyILiyMOps24jVqJI7sbNImPkX67DkFS4ALIYSoMopWi7FT\nJ/zmz6PeoYMELFuKsXs3HOkZZC17n6TOXbnyzHMyaqKaSTEnhMp8pk1F16gR1vh4stesVTuOEE5P\n8fDA7/W5+L+3GMVkIvuDFaREDyc/NVXtaEIIUSMoRiOmgQMI/PgfBP33m4KtlnRacjds4HLPXlx5\n9nm5U1dNpJgTQmUakwm/BfMBuLoghvyLF1VOJIRr8Bw0iDr/2oK2QRiW/ftJ/us9WH76Se1YQghR\no+ibNMZv3uvU/XY/3hPGoxgM5K5fT1L3u8iYv0Dm1FUxKeaEcALGzp3wHPogjqws0mfNUTuOEC5D\nHxFB0NYvMPa4i/wLF0h+YDA5W7aoHUsIIWocbZ06+M54meD9e/F85BGwWMla/C6Xe/QiN2672vHc\nlhRzQjgJn5mvoPj5kbd1K+Z9+9WOI4TL0Pj7U3vtGrwnPQV5ZtImTuLqG2/isNvVjiaEEDWONigI\n/wXzCIr7D4aOd5L/229ceWw0V559Hnt6utrx3I4Uc0I4CW1AAD6TXwAgY86rshiKELdA0WrxnTYV\n/3feBoOBzLff4cq4CdhzctSOJoQQNZI+PJzA9Z/j99bfUXx8yF2/nst9+2E+cEDtaG5FijkhnIjX\no4+ga9IE65Ej5Hz+udpxhHA5ng8OIfDzz9AEBpK3bRspDw4lPzlZ7VhCCFEjKYqC17CHCN65HWP3\nbuRfuEDKkKFkLlmKw+FQO55bkGJOCCei6PX4zpoJUDBMTCYNC3HLjO3bUWfrv9CF34H1x59IHng/\n1pMn1Y4lhBA1lrZePWp/FIvPtKlAwf66aU9NksVRKoEUc0I4GWPPHhg6dcJ+KYnsdbFqxxHCJelu\nu406mzZi7NaN/HPnSL7/Acz7ZS6qEEKoRdFoqDXpKQI//gcaf39yt/yTlKEPybYyFSTFnBBORlEU\nfF78GwCZ776HPTtb5URCuCaNjw+1136I50NDcWRkkDL8EXK/2Kp2LCGEqNGMXTpT58ut6O5ohjX+\nMMn3DcL2669qx3JZUswJ4YSMUVEYe/bAnppK9spVascRwmUpBgN+b/2dWpNfAIuFK+MnkLVmrdqx\nhBCiRtPVr0+dTRsxdOpI/tmzpAwZiu3ML2rHcklSzAnhpHz+NhmArOUfyIp8lSAuLo7+/fvTunVr\nRo0aRWJiYoX6V6Td4XCwfPly+vbtS2RkJNHR0Rw6dKjEHO+//z7PPPPMdc9v3LiRv/71r0RGRjJs\n2DAOyOpgN6QoCj4vPI/fvNcByJj+Mlff/LtMvhdCCBVpfH0JjF2HsVcv8i9eJPnBB7GePqN2LJcj\nxZwQTsrQpg3G7t2wp6WR8/EnasdxaQkJCUyePJlRo0axceNGfH19GTduHPYb7ENWWv+Ktq9Zs4bV\nq1czffp0tmzZQrt27Rg7diwXL14slmPz5s0sWrQIRVGKPb9//37mzJnDs88+yz//+U+ioqIYN24c\nly9fruxL51a8Rj5KwPvLCrYuWPg2Ga/MlL3ohBBCRYqHB7VXLMej393Yky6T+vBwbOcvqB3LpUgx\nJ4QTqzVpEgBZy97HYbWqnMZ1xcbG0qNHD6Kjo2ncuDELFiwgKSmJ3bt3l6t/Rds3bNjA2LFj6dmz\nJ2FhYUyZMoWgoCDi4uIAMJvNTJs2jTlz5tCgQYPr8u3cuZMOHTrQv39/6tevz+TJk7HZbPz4449V\ncfnciuneewiMXYfi5UX26g9Jf2EyDptN7VhCCFFjKUYjAUuXYLyrO/nnz5P68HDyr6SpHctlSDEn\nhBMzdO6EPjKS/AsXyNm0We04Lis+Pp4OHToU/W4ymWjevDnx8fHl6l/R9lmzZjFw4MDr3vfq1asA\npKamcuHCBdavX0/r1q2v6+fv789PP/1EQkICDoeDDRs24HA4aNasWZmvSU1m7NKZwE8/RvHzJefz\n9VyZ8BQOi0XtWEIIUWMpRiMBKz7A0L49ttOnufLEEzjMZrVjuQQp5oRwYoqiUGvSRACyV6yUOT7l\nlJSURFBQULHnAgMDSUpKKlf/ira3b9+e4ODgorZvvvmGxMREunTpAkBISAhr1qyhcePGJeYbOXIk\nLVq0YPDgwbRo0YKZM2eyYMGCEu/iiZIZIiOps/5zNHXqkLdtG6ljn8CRl6d2LCGEqLE0np4ErF6F\ntmFDLN9+R9qLU+XvnjKQYk4IJ+fRty/a+vWxHj2K5fvv1Y7jlKxWK4mJiSU+UlNTycvLw2g0FnuN\nwWDAcoO7MaX1r2j7H506dYqpU6cyYMAAIiMjy3S+SUlJZGZm8tprr7F+/XpGjhzJzJkzOX36dJle\nLwroIyKos3ED2nr1MO/cSerjT+CQDWyFEEI12gB/aq9dg+LnS+769WSv/lDtSE5Pp3YAIcTNKVot\nXo+N4upr/0f2qg8x3nmn2pGcztmzZxk4cOB1C4UADBo0CA8Pj+sKKYvFgqenZ4nHMxqNN+1f0fZr\njhw5wpNPPkmzZs2YO3duGc60wOzZs+natStDhw4FICIigoSEBFasWMG8efPKfBwBuka3E7jhc1KG\nDsP89TekjhlLwKqVaEwmtaMJIUSNpG/ciIAl75E64lEy5ryKvlUrjO3bqR3LacmdOSFcgFf0MBST\nidwvv5RVnkrQtGlTjh8/zrFjx657zJs3j+DgYJKTk4u9Jjk5udhQxz+qW7fuTftXtB3gwIEDjBo1\nioiICD744AMMBkOZz/fnn38mIiKi2HMtWrTgt99+K/MxxO90DRoQuOFztPXrY961myuPjZE7dEII\noSKPu+4q2B/UZiNt/ATsabIgyo1IMSeEC9D4+eH54BDIzyfno4/UjuNy2rRpw8GDB4t+z8nJISEh\n4YbDGm/Uv23btpXSfvz4ccaNG0dUVBTLli27bkhmaYKDgzl58mSx506dOkX9+vVv6Tjid7r69QsK\nurAwzHv2FAy5lDl0wok5096ZAP369SM8PLzoERERwVdffVU5JytqpFrPPoOxx13kX7xI+tTpMn/u\nBqSYE8JFeD7yCADZn36GIz9f5TSuZcSIEcTFxbF27dqiOWqhoaF07doVKNgKICUlpWgfuBv1v7ZA\nSXnaQ0JCitqnTZtGcHAwM2fOJCMjg5SUFFJSUsjOzi7z+axatYpt27Zx7tw5li9fzt69e3nssccq\n+crVLLrQUAI/+wRtaCjmb/5L6pPjZTU14ZScbe9Mi8XCb7/9xrp169i7dy979+5lz5499OzZs3ou\niHBLikaD/1t/RxMQQO4XX5Dz+Xq1IzklKeaEcBGGFs3Rt2qJ/dIlzF9/o3Ycl9KiRQtiYmJYt24d\nQ4cOJTs7myVLlhTNsdu2bRvdunXj0qVLZepfnvalS5eiKAqJiYkcP36cs2fP0qtXL7p161b0eO+9\n98p0PiNHjuT5559n8eLF3H///Wzfvp3Vq1fL1gSVQFe/PoGff1qwKMqOHVyZ9LTsQyecjrPtnXnm\nzBkcDgetWrWidu3aRQ+9Xl89F0S4LW1wMH5vxgCQMXMW+RcvqpzI+cgCKEK4EK+HHyb9p5/J/vhj\nPPr0VjuOS7nnnnu45557Smx74IEHeOCBB8rcvyLtYWFhHDt2rIypueGCJo888giPFN6tFZVL16AB\ngZ99SvKQB8nb9iVpL/wN/7ffQtHI95/COcTHxzN8+PCi3/+4l+Vdd911y/0r2n7mzBnq1q17y0PG\nhSgLU79+mIYMIXfDBtJfnkHAyhUlLnhWU8n/mYRwIaZB96N4eJAXt538y5fVjiOE29I1up3Ajz9C\n8fMjd8MGMl6eIfM1hNNwtr0zT506hV6vZ8KECXTt2pVhw4axa9eu8p+gEH/iO3sWmtq1yfvPV+R9\nsVXtOE5FijkhXIjGxwePAQMKFkLZtFntOEK4NX14OIEfrUPx9iZ77ToyY95QO5KoIVxt78zTp0+T\nmZnJkCFDWLFiBR07dmT8+PEcPny4/BdBiD/QBvjj+9qrAKTPno29jHPMawIZZimEi/EcMpjc9evJ\n3bSZWuOeVDuOEG7N0KYNtdesJmX4I2QuWowmMBDvsWPUjiXcnKvtnfnWW2+Rl5eHl5cXAOHh4Zw4\ncYKPPvqINm3alPW0hbgp030Dyfn4E8y7d5O5aDG+06aqHckpyJ05IVyMsUtnNMFBWH/+GeuflqcX\nQlQ+Y8eOBCx9DzQaMmbOImfTJrUjCTfnantnarXaokLumsaNG99w2KcQ5aEoCr6vzgatlqzlH2D7\n5Re1IzkFKeaEcDGKVovpvvsAyN0of1QKUR1M/frh98YCANKee4G8XSWvGihEdXC2vTMHDx7MkiVL\nir3n0aNHady4cQXPVIji9M2a4TX6MbBYyHi95AXCahop5oRwQZ5DBgOQs3mLLMogRDXxio7G56UX\nwWbjyhNPYj2aoHYkUUM5296ZvXv3ZvXq1Wzfvp1ff/2VhQsXcvjwYcaMkSHJovL5PP8cip8vedu+\nxHIoXu04qpNiTggXpG/RAl2TJuQnJmKVDzIhqo3305PwevQRHFlZpIwcie38ebUjiRrImfbOBJg4\ncSJjxoxh/vz53Hfffezfv59Vq1ZRv359Fa6OcHcaPz9qPfUUABmvz6vxX2orjpp+BapQ794F+4Dt\n2LFD5STCHV198+9kLnwb7/Hj8H1lhtpxhAuQz6TK4cjP58rjT5D3VRy6O5pRZ/MmND4+ascSwuXI\nZ5IoL0duLpe6dsN+KYnasWvx6NlT7UiqkTtzQrgoU+GG1Llbt9X4b6WEqE6KVov/kvfQt2mN7cT/\nuDJ+Ag6rVe1YQghRYygmEz7PPw/A1bfertF/B0kxJ4SL0kWEo23YkPxz57AeOaJ2HCFqFI3JRO3V\nq9CGhmL+7y7SZ8ys0X9MCCFEdfN8aCjakBCshw5h3rNX7TiqkWJOCBelKAqmAfcCBXfnhBDVSxsU\nRO21H6LUqkVObCzZK1aqHUkIIWoMxWDA+6kJAGS+847KadQjxZwQLsx0T38A8rZ9KXcFhFCBPjyc\ngGVLCvage/U18r7+Wu1IQghRY3hFR6MJCsKy/1vM33+vdhxVSDEnhAvTt2qFNjQU2+nT2E6fVjuO\nEDWSR48e+M6eBXY7VyY8hfXUKbUjCSFEjaB4eOA97gkAspZ/oHIadUgxJ4QLUxQFj759AMjbLquB\nCaEWrzGj8RwxHEdmJqmjRmPPyFA7khBC1Ahew4ejeHmR9+//YDt7Vu041U6KOSFcnEfh0s5SzAmh\nHkVR8Pu/1zDcGUX+2bNcmfQ0jvx8tWMJIYTb0/j44BkdDQ4HWatWqx2n2kkxJ4SLM3buhGIyYTlw\nQO4GCKEixWAg4P1laOvVw7zza67GvKF2JCGEqBG8x44GjYacjz+pcX8LSTEnhItTPDwwdusKNht5\n/92ldhwhajRtnToErPwAjEay3n2P3C+2qh1JCCHcnq5BAzz63Y0jJ4ecDRvVjlOtpJgTwg3IUEsh\nnIehdWv85s8DIO2FybIgihBCVAOvkY8CkB0bW6NW+JZiTgg34NG7FwDmr7/GYbernEYI4fXQULxG\nPoojO5srjz+JPStL7UhCCOHWjF27om3YANuJ/2E5cEDtONVGijkh3IC2Xj10EeHYr1zBevSo2nGE\nEIDv7FnoIyOxnTxJ+pQXa9Q3xUIIUd0UjQavESMAyF73kcppqo8Uc0K4CY9u3QAw79qtchIhBIBi\nNBLw/jI0/v7k/vNfZK9Zq3YkIYRwa57DHgK9ntytW7Gnpakdp1pIMSeEmzBKMSeE09GFhuC/+B1Q\nFDLmvIrlxx/VjiSEEG5LW7s2pn79wGwm55//UjtOtZBiTgg3Yeh4JxgMmA8cwJ6bq3YcIUQhj549\nqfXM02CxcGX8ROxXr6odSQgh3Jbn0AcByFm/QeUk1UOKOSHchMbTE0O7dmA2Y/nuO7XjCCH+oNbk\nFzB06kR+YiLpL74k8+eEEKKKGO/qjiYwEOuhQ1hPn1E7TpWTYk4IN+LRXYZaCuGMFK2WgHcXoQkI\nIPdfX5ATW3Mm5wshRHVS9HpMg+4HIHf9epXTVD0p5oRwI8ZrxdzuPSonEUL8mbZuXfzfeRuA9Nmz\nsZ44oXIiIYRwT55DhwKQs2Gj22/ZJMWcEG5E37IlSq1aWI8dw56ernYcIcSfePTqifeTT0CemStP\nTcKRl6d2JCGEcDv65n9Bd0cz8s+fxxp/WO04VUqKOSHciKLVYujQARwOzN/XnA0zhXAlPlNfQt+i\nBbZjx8l4fZ7acYQQwu0oioJp4EAAcv7l3qtaSjEnhJsxduoIgOXbb1VOIoQoiWI04v/euygmE9kr\nV5G382u1IwkhhNsxDbgXgLwvtrr1UEsp5oRwM8aOBcWcWYo5IZyWvkljfGfPAiBt8t/Iv3JF5URC\nCOFe9E2bogu/g/yLF7H8cEjtOFVGijkh3Iy+ZQsUT0+sPx/BnpmpdhwhxA14jhiOR58+2C9flu0K\nhBCiCpgGDAAg919fqJyk6kgxJ4SbUfR6DB3ag92O5cBBteMIIW5AURT83oxBU7s2eV/+m5zP3X8J\nbSGEqE6mgYXF3NatbvuFmRRzQrghGWophGvQ1qmD35sxAGTMnIXt/HmVEwkhhPvQN2mCrkkT7Jcu\nYT1yRO04VUKKOSHckKHjnQBYZEVLIZye6e678XxoKI7MTNInT3HrifpCCFHdPPrdDUDeV3EqJ6ka\nLlvMxcXF0b9/f1q3bs2oUaNITEysUP/S2vv160d4eHjRIyIigq+++qrSz0uIymBo2RL0eiw//YTD\nYlE7jhCiFL5zZqMNCcG8ezfZ62LVjiOEEG7Do29fAPL+455/t7tkMZeQkMDkyZMZNWoUGzduxNfX\nl3HjxmG/wbeZpfUvrd1isfDbb7+xbt069u7dy969e9mzZw89e/astnMW4lYoJhP6Fs3BbMZ69Kja\ncYQQpdD4+OD39zcBuPp/c7GV8gWlEEKIsjG0jUQTGIj16FG3HMruksVcbGwsPXr0IDo6msaNG7Ng\nwQKSkpLYvXt3ufqX1n7mzBkcDgetWrWidu3aRQ+9Xl9t5yzErTK0bQfg1svxCuFOPLp3w/ORR3Dk\n5JAmwy2FEKJSKFotHn16A5AX535DLV2ymIuPj6dDhw5Fv5tMJpo3b058fHy5+pfWfubMGerWrYvR\naKyK0xGiShjaFxZzB2VFS6j+odk3a3c4HCxfvpy+ffsSGRlJdHQ0hw79XnRbLBZiYmLo2bMn7du3\nZ8yYMZw6darY8d999126du1Ku3btePnll8nLyyvvpRFOxHfGdLShoVj27SPno3+oHUcIIdyCx92F\nQy3dcN6cSxZzSUlJBAUFFXsuMDCQpKSkcvUvrf3UqVPo9XomTJhA165dGTZsGLt27aqs0xGiShja\nyZ25a6p7aHZp7WvWrGH16tVMnz6dLVu20K5dO8aOHcvFixcBeOONN4iLi2PBggWsX7+ewMBAxowZ\nQ3Z2NlAwmuDjjz/mjTfeYPXq1cTHxzN37tyqvoyiGmhq1fp9dcv/m0v+hYsqJ0Gq2U4AACAASURB\nVBJCCNdn7NoV9HrM332HIzdX7TiVyimLOavVSmJiYomP1NRU8vLyrrtLZjAYsNxgoYfS+pfWfvr0\naTIzMxkyZAgrVqygY8eOjB8/nsOHD1fWKQtR6XShIWjq1iX/wgXyL9bsPwire2h2ae0bNmxg7Nix\n9OzZk7CwMKZMmUJQUBBxcXE4HA42bdrECy+8QFRUFA0bNmTu3LlkZmbybeFWEx9++CETJ06kU6dO\ntGrVijlz5rBp0yaysrKq4WqKqubRvTuewx7CkZVF2tRpbrs3khBCVBeNlxfGqCjIM2P+7ju141Qq\npyzmzp49y913302/fv2ue7z55pt4eHhcV7hZLBY8PDxKPJ7RaLxp/9La33rrLeLi4ujTpw/h4eE8\n//zzdO/enY8++qiyTlmIKiF35wpU99Ds0tpnzZrFwIEDr3vfq1ev4nA4WLx4MV26dCl6XqMp+KjO\nzMwkJSWF3377jfbt2xe1R0ZG4nA4+Pnnn8t+UYRT8535CpqgIMw7dpD7z3+qHUcIIVyescddAOR9\n/Y26QSqZUxZzTZs25fjx4xw7duy6x7x58wgODiY5ObnYa5KTkwkODi7xeHXr1r1p/9LatVotXl5e\nxdobN258w2GdQjgL47V5cz/8oHISdVX30OzS2tu3b1/s8+qbb74hMTGRLl26oNFo6NSpEz4+PkXt\nn3zyCVarlaioKJKSklAUpdjxdTodfn5+XLp0qUzXQzg/jZ8ffq+9CkDGzNnY09JUTiSEEK7N466C\nYs78X/eaKuWUxVxp2rRpw8E/LOqQk5NDQkICkZGRt9S/bdu2ZWofPHgwS5YsKXbMo0eP0rhx40o7\nJyGqgj6yDQCWn35SOUnVcrah2bfyfqdOnWLq1KkMGDCgxM+w77//npiYGB5//HFCQkLILRzrfyvn\nI1yTx7334HF3X+wpKWTMfV3tOEII4dJ0f4lAExSE7eRJt9qioFzF3ObNm0lT8VvCESNGEBcXx9q1\na4v+EAoNDaVr164AmM1mUlJSihYbuFH/a8OYSmoPCQkpau/duzerV69m+/bt/PrrryxcuJDDhw8z\nZswYdS6AEGWkb94cNBqsPx/BkZ+vdpwq42xDs0trv+bIkSOMHDmSZs2albiAya5duxg3bhx9+vTh\nueeeAyg6xq2cj3BNiqLgN3cuipcXOR9/gnn/frUjCSGEy1IUBY+7ugNg/ua/KqepPOUq5qZNm8a5\nc+cqO0uZtWjRgpiYGNatW8fQoUPJzs5myZIlKIoCwLZt2+jWrVvRkKPS+pfUvnTp0qL2iRMnMmbM\nGObPn899993H/v37WbVqFfXr11fnAghRRhpPT3TNmuLIzsZ2+rTacaqMsw3NLq0d4MCBA4waNYqI\niAg++OADDAZDsf7btm1j4sSJRQXpH7M5HI5ix7fZbKSnp9/wfITr0obUw+elFwFIn/YyDrn7KoQQ\n5Wa8VsztKnkBNFdUrmLOGVbWuueee4iLiyM+Pp6VK1cWK6weeOABjh07RkhISJn6l9auKAoTJkxg\n+/bt/Pjjj3z22WdFQzCFcHaG1q0BsP7o3kMtb6a6h2aX1n78+HHGjRtHVFQUy5Ytu27I5J49e3jx\nxRcZMmQI8+fPL/piCQrm3oWGhhY7/qFDh9BqtbRo0eKWr41wfl6PjULfqiW2kyfJWrpM7ThCCOGy\njJ07A2Dev98p6pnK4JJz5oQQZadv1Qpw/3lzN1MdQ7NvZej2tGnTCA4OZubMmWRkZJCSkkJKSgrZ\n2dlYLBamTp1KZGQkkyZNKmpLSUkp2hj80UcfZdGiRezatYuffvqJ2bNnM3jwYLy9vav70opqoGi1\n+M2fBxoNVxctwvbrr2pHEkIIl6QNDkbXpAn21FRsJ06oHadS6Mr7wjVr1hAYGFhqP0VRmDp1annf\nRghRQYbWBcVcTb4zd20o9cKFC1m4cCFt27a9bmj29OnT2bFjByEhIaX2L0/7taHbiYmJHD9+HIBe\nvXoVyzl69Gi6detGamoqqampdO/evVj7jBkzGDFiBI899hhpaWm89NJL2O12+vbty/Tp06v6MgoV\nGVq3xmvko2R/uIb0V2ZRe83qYndshRBClI2xcydsp05h3rcffXi42nEqTHGU4x5jeHg4gYGB183x\nKPENFIUdO3aUK5yr6927N0CNPX/hHBxmMxfuiACthpATx1F05f4OR7g4+UxybfaMDJK698CekkLA\nqhWY+vVTO5IQFSKfSUINuf/6givjJ+DR/6/UXvGB2nEqrNx/1S1ZsoRWhcO3hBDOSzEa0YeHY/35\nZ2wn/oe++V/UjiSEKAeNry++r8wg7dnnyJg5G4/u3VFMJrVjCSGESzF07gSAef+3OOx2FI1rzzpz\n7fRCiDKReXNCuAfTkMEY7owi/7ffyJTFUIQQ4pZpa9dGFxGOIz0da8IxteNUmBRzQtQAhpYFqxxa\njx5VOYkQoiIURcHvtddAoyHzvfewqbhNkBBCuKprq1pa9u1TOUnFlauYe+CBB/D396/sLEKIKqJv\n3hyQYk4Id6Bv/he8Rj4KeWYyXn1N7ThCCOFyjFFRAJgPHCylp/MrVzG3b98+li1bxrZt20hPT6/s\nTEKISqYLvwMUBWvCMRyFy+8LIVyXz98mo/H3J2/bl5j37FU7jlBBXFwc/fv3p3Xr1owaNYrExMQK\n9S/r8b744guGDBly3fMHDx5k8ODBtG7dmqFDh3LkyJHyn5wQVczQoT0AlgMHXH6/uXIVc4sWLSIk\nJITY2Fi6devGgw8+yMKFCzlw4AA2m62yMwohKkjj6YmuUSMcWVnky7AsIVyext+fWlP+BkD6rFk4\n5P+9NUpCQgKTJ09m1KhRbNy4EV9fX8aNG1e0V+at9i/r8fbt28crr7xy3bYYly9fZty4cfTq1YtN\nmzbRsmVLnnjiCbKysqrmAghRQdrgYLQNwrAnJ5Pv4nt3lquYa926NU899RT/+Mc/2L9/P+PHjycj\nI4Pp06cTFRXF+PHjiY2N5ZdffqnsvEKIctL/JQIAa0KCykmEEJXBa8RwdBHh2I6fIDv2I7XjiGoU\nGxtLjx49iI6OpnHjxixYsICkpCR2795drv5lOd6CBQsYN24cYWFh1x3/888/p0GDBkyaNIlGjRox\nc+ZMvL292bJlS9VcACEqgaF9BwAsLj7UssILoHh7e9OnTx9mz55NXFwcmzdvpnv37uzbt4+hQ4de\ntymuEEIdv8+bk2JOCHeg6HT4zZ4NQOabf8eekaFuIFFt4uPj6dChQ9HvJpOJ5s2bEx8fX67+ZTne\nd999x7p16+jbt2+Jx48qnIN0Tbt27Th8+HD5TlCIamCMKvh33tXnzVX6apZhYWEMHz6cJUuW8N13\n3xETE1PZbyGEKAf9Xwr2l5NFUIRwH8auXfC4uy/2tDQy31mkdhxRTZKSkggKCir2XGBgIElJSeXq\nX5bjbdy4kTZt2tzS8S9dulS2ExJCBUXz5g4eUDlJxZR70/Cy0Gq1tG/fvirfQghRRtc2C3eHPVWE\nEL/zfeUV8r7+hqxVq/Ea+Si6hg3VjiQqyGq1cvHixRLbvLy8yMvLw2g0FnveYDBgsVhKfE1p/W/1\neGU9vtVqLdPrhVCDrmlTFF9fbCf+hz0tDY2LrtRfpcWcEMJ5aIKD0QQEkP/bb9jT09H4+akdSQhR\nCXSNbsdr5EiyV67k6rwFBLy/VO1IooLOnj3LwIEDr1toBGDQoEF4eHhcV2hZLBY8PT1LPJ7RaLxp\n/9LaS3OjPB4eHmV6vRBqUDQaDO3aYd65E8sPh/Do01vtSOVSrmJu0qRJZe6rKAqLFy8uz9sIISqR\noijomzfHvHs31oRjGDt3UjuSEKKS1HruWXLWryf3iy8wH3wcY/t2akcSFdC0aVOOHz9+w/bDhw+T\nnJxc7Lnk5OTr5q1dU7du3Zv2L629NMHBwVy+fPm61wcHB5fp9UKoxdCubUExd/iwyxZz5ZozFxIS\nwvbt2/n+++/JyMi46UP2oRPCeejC7wDAeuKEykmEEJVJG+BPrWeeBuDqq6+5/L5J4ubatGnDwYO/\nL9qQk5NDQkICkZGRt9S/bdu25TpeScf/4Ycfij136NChMr9eCLUYIgvmgVpceLGect2Zmz59OmFh\nYbz++utMnDiRTp3kG34hXIG+sJizSTEnhNvxHv0Y2R+uwfLDD+T9+9+Y+vdXO5KoIiNGjCA6Opq1\na9fSuXNnFi1aRGhoKF27dgXAbDaTmZlJQEAAGo3mhv27dOlSpuOVZujQoaxcuZKFCxdy33338dFH\nH5GTk8OAAQOq7BoIURkMrVoBYIk/jMPhKHFos7Mr92qWjzzyCPfffz+zZ8++4SaVQgjnom8md+aE\ncFeK0YjPi1MAuPr6fByy+ITbatGiBTExMaxbt46hQ4eSnZ3NkiVLiv4Q3bZtG926dStaTbK0/qW1\nlyY4OJilS5eyc+dOhgwZwtGjR1mxYgXe3t5VcwGEqCQaf3+0t9+OIz3dZTcPVxwVGItx5coVli1b\nxvDhw2koq2ddp3fvgrG3O3bsUDmJEAXsWVlcvCMCxc+Xekd+dslvoET5yWeS+3PY7ST3vxfrkSP4\nzZ+H16OPqB1JiBuSzyThDK48/Qy5Gzfh/95iPAcNUjvOLavQPnMBAQFMnz5dCjkhXITG2xvtbbfh\nSM/A/qfJ6kII16doNPi8PA2AqwsXYs/NVTmREEI4N0Ph/omWeNecN1fpm4YLIZybrlkzQIZaCuGu\njN26YezSBXvSZbJXrFQ7jhBCOLVrxZz18I8qJykfKeaEqGH0dxQUc7YT/1M5iRCiKiiKgs/0qQBk\nLlmKXVaVFkKIG9I3/wvodFiO/OySc42lmBOihim6M/c/KeaEcFeGNm3wuOceHFevkrl0mdpxhBDC\naSkeHuj/EgF5ZpcctSTFnBA1zLXtCazHXe8DSwhRdj5TJoNGQ/bKVeTLHFkhhLghfcuCLQqsPx9R\nOcmtk2JOiBpG17QpKAq2kydlY2Eh3Ji+WTM8hwzGkZtL5rvvqR1HCCGclqFFcwCsR2pwMTd//nw+\n/PDDyjqcEKKKaEwmtGH1cWRmkn/hgtpxhBBVqNbzz4FOR/a6WGzn5b93IYQoib5FCwCsR46qnOTW\nVVoxd9999/Hmm2+Sk5NTWYcUQlQRfeG8OdupUyonEUJUJV2DBngOGwYWC5mLFqsdRwghnJIuIhw0\nGqwJCTjy89WOc0sqrZgLCwvDZrNx8eLFyjqkEKKK6Bo3BsB26rTKSYQQVa3Ws8+AwUDOJ59gO3dO\n7ThCCOF0NCYTuiZNcOTkYPvlrNpxbkmlFXO7du3CaDRSr169yjqkEKKK6Jo0AcB2Woo5IdydLjQE\nr+EPg80md+eEEOIGioZaHnWteXOVVsxt3ryZvn374unpWVmHFEJUEV3jRoDcmROipqg16SkwGsn5\n7HNsiYlqxxFCCKejv7YIioutaFlpxdyhQ4fo379/ZR1OCFGFrt2Zs8qdOSFqBG29eng9MqLg7tzi\nd9WOI4QQTsfgoougVFoxp9fr0el0lXU4IUQV0gYEoPj5Yb90CXtWltpxhBDVoNbECb/fnZO5c0II\nUYy++V+Agu0JXGnrpkpdzTI2NrayDieEqGL6a/PmzpxROYkQojpo69b9fe7cYtl3Tggh/kjj54e2\nfn3saWnYL15SO06ZVVoxN2XKFGbPnk2+iy3nKURNVTRvToZaClFj1Jo4sWBly88+k33nhBDiT/QR\n4QBYjx9XOUnZVVoxp9PpCA0NRavVVtYhhRBVqGhFS1kERYgaQxtSD69hD4HVStbSpWrHEUIIp6IP\nr8HFnBDCtcidOSFqJu+nJoJOR/Y/PiY/KUntOEII4TR04XcAYD0mxZwQwsnpGheuaCl35oSoUXT1\n6+M5ZDCYzWQt/0DtOEII4TSu3ZmzyZ05IYSz0zUIA52O/F9+wWG3qx1HCFGNvJ96ChSF7LXrsKel\nqR1HCCGcgq5RI9DrsZ46hcNqVTtOmVRqMXf16lVOnz6NxWLB6iIXQIiaStHr0YWF4cjLI//iRbXj\nCCGqkb5xI0wD7sWRk0PWqtVqxxFCCKeg6PUFawpYLNjOnlU7TplUSjG3a9cuBg8ezJ133snAgQM5\nefIkkydPZs6cOdjlG38hnJa2YUMA8n85q2qO6hAXF0f//v1p3bo1o0aNIjExsUL9K9LucDhYvnw5\nffv2JTIykujoaA4dOlTUbrFYiImJoWfPnrRv354xY8Zw6tSpovarV68yY8YMunbtyp133snTTz/N\npUuus4yycA7ekyYBkLVqNfbsbJXTCCGEcyha0dJF5s1VuJjbvn0748ePp0GDBsydO7eoeOvYsSPr\n169nqayWJYTT0t3eEMBlvn0qr4SEBCZPnsyoUaPYuHEjvr6+jBs37oZfNpXWv6Lta9asYfXq1Uyf\nPp0tW7bQrl07xo4dy8XCO6RvvPEGcXFxLFiwgPXr1xMYGMiYMWPILvyDe+rUqRw7doylS5cSGxtL\nTk4OEyZMcKlNToX6DC2aY+zVE0d6Ojn/+FjtOEII4RRcbd5chYu5d955h2HDhrFw4ULuv//+oueH\nDx/OM888w+bNmyv6FkKIKqIrvDPn7sVcbGwsPXr0IDo6msaNG7NgwQKSkpLYvXt3ufpXtH3Dhg2M\nHTuWnj17EhYWxpQpUwgKCiIuLg6Hw8GmTZt44YUXiIqKomHDhsydO5fMzEy+/fZb0tLS+Prrr5k1\naxYtW7akadOmvP766xw7dowTJ05UzwUVbqPWUxMByHp/OQ6LReU0QgihPlfbnqDCxdzZs2fp06dP\niW2tWrUiSZY9FsJp1ZRiLj4+ng4dOhT9bjKZaN68OfHx8eXqX9H2WbNmMXDgwOve9+rVqzgcDhYv\nXkyXLl2KntdoCj6qMzMz8fDwYPny5URERBS1K4pS1C7ErTDceSeGdu3Iv3iR3C3/VDuOEEKoTlfT\nirm6devy448/lth29OhRgoODK/oWQogqUlOKuaSkJIKCgoo9FxgYeMMvm0rrX9H29u3bF/ts/Oab\nb0hMTKRLly5oNBo6deqEj49PUfsnn3yC1WolKioKk8lEt27d0Ov1Re2rV6/Gx8eHli1blul6CHGN\noih4TxwPQObSpbKyrRCixtOG1EOpVYv8XxOx5+aqHadUuooeYPjw4bz11lsoikK3bt1QFIWUlBQ2\nb97MkiVLePLJJysjpxCiCmhvCwWtlvxfzuJwOIru8Lgaq9VaNN/sz7y8vMjLy8NoNBZ73mAwYLnB\nsLLS+le0/Y9OnTrF1KlTGTBgAJGRkde1f//998TExPD4448TEhJyXfvWrVtZs2YNc+bMwcPDo8Tz\nEeJmPO6+G12jRthO/I+8HTsx9S15tI0QQtQEiqKga9IEa3w8ttNnMLRornakm6pwMTd69GiuXr3K\nsmXLWLRoEQ6Hg3HjxqHT6Rg+fDhPPPFEZeQUQlQBxWBAe1towbdPSUlo69ZVO1K5nD17loEDB5ZY\njA4aNAgPD4/rCimLxYKnp2eJxzMajTftX9H2a44cOcKTTz5Js2bNmDt37nU5du3axbPPPkufPn14\n7rnnrmvfuHEjr7zyCmPHjmXo0KElnosQpVE0GrwnjCd9yotkvf++FHNCiBpP36RxQTF36qT7F3MA\nzz77LKNHj+bHH38kPT2dWrVq0apVKwICAirj8EKIKqRr2JD8XxOxnT3rssVc06ZNOX6Tse2HDx8m\nOTm52HPJyclERUWV2L9u3bo37V/RdoADBw4wfvx42rRpw5IlSzAYDMX6b9u2jRdffJEBAwYwb968\n6zJ++OGHzJ8/n/Hjx5dY6AlxKzwHP8DVmDew7P8Wy+HDGNq0UTuSEEKoRte0KQC2k6dK6am+Cs+Z\nmzZtGufOncPHx4du3boxcOBAevToQUBAAGfOnGHChAmVkVMIUUVqwry5Nm3acPDgwaLfc3JySEhI\nKHFY4836t23btlLajx8/zrhx44iKimLZsmXXDcncs2cPL774IkOGDGH+/PnX3XFcv3498+fP5/nn\nn5dCTlQKxcMD79GPAZC17H11wwghhMp0TZsAYHWBYq5cd+ZOnDhRtJ/R5s2b6dy5c9H+R3+0c+dO\n9u3bV7GEQogqVVTMufHG4SNGjCA6Opq1a9fSuXNnFi1aRGhoKF27dgXAbDaTmZlJQEAAGo3mhv2v\nrTBZnvaQkJCi9mnTphEcHMzMmTPJyMgoymkymdDr9UydOpXIyEgmTZpESkpKUbu3tzdZWVnMnTuX\nAQMGMGTIkGLtPj4+193hE6KsvEY+Subid8ndug3buXPo6tdXO5IQQqhC36TwztypkyonKV25irnl\ny5ezdevWom+LX3zxxRL7ORwO+vfvX/50Qogqpy0s5vLP/qpukCrUokULYmJiWLhwIQsXLqRt27Ys\nWbKk6DNs27ZtTJ8+nR07dhASElJq//K0L126FEVRSExMLBoS2qtXr2I5R48eTbdu3UhNTSU1NZXu\n3bsXa58xYwYGg4G8vDy2bt3K1q1bAYoWr1m2bBl33XVXlV5L4b40/v54DnuI7A/XkL1qNb6zZqod\nSQghVKENqw8GA7ZfzuKw2VB0lTIzrUoojmu32G5BZmYmx44dw+FwMGrUKGbOnEmTJk2K9dFoNPj4\n+NC0aVOXXSGvonr37g3Ajh07VE4ixI1ZT57kco9e6Fu0IOg/X6odR1Qh+UwSpbGd+YWk7neheHlR\n9+D3aGrVUjuScGPymSScWVKv3thO/I/g3bvQNbpd7Tg3VK4ys1atWkUT+deuXUvz5s3x8vKq1GBC\niOqhq18fFAXbWdfenkAIUXG6RrfjcXdf8v7zFTmffIr3E4+rHUkIIVSha9IU24n/YT110v2KuT+K\nioriwoUL/Pe//y22FLfD4SA3N5fDhw8TExNT0bcRQlQRxcMDTXAw9kuXcKSno/j7qx1JCKEi7yce\nJ+8/X5G1ajVeY0ajaLVqRxJCiGqnb9qEPApXtLz7brXj3FCFi7ktW7Ywffp08vPzi77RvzZyU6PR\n0LJly4q+hRCiiunC6mO5dAnbuXMYpJgTokYzdOyIvnlzrEePkvfVV5hk7rsQoga6tqKl7ZRzr2hZ\n4a0Jli9fTseOHdm+fTsjRoxg0KBB7N69m/nz52M0GhkzZkxl5BRCVCFt/TAA8hPPqZxECKE2RVHw\nenwsAFkrV6mcRggh1KErXNHS2bcnqHAxl5iYyMiRI7ntttto164dP/74I3Xq1GHQoEGMHz+eFStW\nVEZOIUQV0tW/DQDbOSnmhBDgef99aAIDCzYRP3JU7ThCCFHtdI0bAWA7c4ZyrBdZbSpczBmNxqJ9\njW6//XZ+/fVXzGYzAJGRkfzyyy8VfQshRBXThhXsJ5UvxZwQAlCMRrweGQFA9iq5OyeEqHk0JhOa\nunVxZGRgT0tTO84NVbiYa926NevXr8fhcHD77bej1WrZs2cPAKdOnUKv11c4pBCiaukKh1nKnTkh\nxDVeIx8FvZ6czVvIv3JF7ThCCFHtdLcXrGJpO+O8N6cqXMw9/fTT7Ny5kyeeeAKj0cjQoUOZMmUK\njz32GPPnz79uU1whhPPRFg6zlDlzQohrtMHBmO69B8xmcv7xsdpxhBCi2ukaFQy1zHfikYYVLuba\ntGnDtm3bGDlyJADTp09nzJgx6PV6xo4dy4wZMyocUghRtbT16oFWi+23c049LlwIUb28Ro8GIHvN\nWhw2m8pphBCieukaNQTA5sTFXIW3JnjhhRcYPnw43bt3B0Cr1TJp0qQKBxNCVB9Fp0MbGkp+YiL2\n5GS0QUFqRxJCOAFDu7boW7bE+vPP5G3fjumvf1U7khBCVJvfh1meUTnJjVX4ztzXX3+N1WqtjCxC\nCBXp6hcsgmKToZZCiEKKouD1WMHIm+wP16qcRgghqldRMffLWXWD3ESFi7mePXuyceNGcnJyKiOP\nEEIlRfPmziWqnEQI4UxM99+P4ueLefdurE6+ea4QQlQmXVgYKAq2X35x2mkoFS7m8vLy+PLLL2nf\nvj3du3fngQceKPYYPHhwZeQUQlQxbeGdOVkERQjxRxqTCa/oaACy18aqnEZcExcXR//+/WndujWj\nRo0iMfHmX8SV1r+sx/viiy8YMmTIdc+PGTOG8PBwIiIiin6uXr26/CcohBNQPDzQ3nYbjuxs7MnJ\nascpUYWLOV9fXwYOHMj9999Ply5dCA8PL/a44447KiOnEKKK6cIKtyf47TeVkwghnI3Xo48AkPP5\n59hlJI7qEhISmDx5MqNGjWLjxo34+voybtw47HZ7ufqX9Xj79u3jlVdeQVGU697j9OnTxMTEsGfP\nHvbu3cuePXsYPnx45Z+8ENVMd3tDwHnnzVV4AZR58+ZVRg4hhMrkzpwQ4kZ0DRti7HEX5m/+S+6W\nf+L1cLTakWq02NhYevToQXThHdMFCxbQpUsXdu/ezV133XXL/ctyvAULFhAbG0ujwqXa/ygrK4uk\npCRatmxJ7dq1q+q0hVCF7vbbMe/aje2Xsxg7dlQ7znUqfGdOCOEedIVz5my/STEnhLie16jChVDW\nrVM5iYiPj6dDhw5Fv5tMJpo3b058fHy5+pfleN999x3r1q2jb9++1x3/9OnT6HQ6wgpHeAjhTn5f\nBMU5tyeQYk4IAYAmKAj0evIvXsJxg6E6Qoiay6NXL7T16mH98ScsP/2kdpwaLSkpiaA/bSETGBhI\nUlJSufqX5XgbN26kTZs2JR7/1KlTeHt789JLL9GtWzcGDRrE5s2bb/m8hHBG1zYOl2JOCOHUFI2m\nYPNwsxl7aqracYQQTkbR6fAcUTAHKnudLIRSlaxWK4mJiSU+UlNTycvLw2g0FnuNwWDAYrGUeLzS\n+t/q8f7s9OnTmM1munTpwsqVKxk0aBAzZsxg27ZtZT1lIZyWtkEDAPLP/qpykpJVeM6cEMJ9aEND\nyE9MJP/8ebR16qgdRwjhZLyih5G58G1yN2/Bd+YraGrVUjuSWzp79iwDdH7wXgAAIABJREFUBw4s\ncaGRQYMG4eHhcV2hZbFY8PT0LPF4RqPxpv1Lay/NlClTmDBhArUK/31o1qwZ586dIzY2lnvuuadM\nxxDCWeluCy3YniAxEYfDUeJ/l2qSYk4IUUQbEgpA/vkLcIPhNEKImktbrx4efXqT95+vyN20Ga+R\nj6odyS01bdqU48eP37D98OHDJP9pmfTk5GSioqJK7F+3bt2b9i+tvTSKohQVctc0btyYb775pkyv\nF8KZKR4eaOvWJf/iRexp6WgD/NWOVEyFh1mmp6cza9YsevbsyZ133klUVNR1DyGEa9CG1AMg//x5\nlZMIIZyV14gRAGTHfuS0m+i6uzZt2nDw4MGi33NyckhISCAyMvKW+rdt27Zcx/uzp59+mhkzZhR7\n7siRIzRu3LjM5ySEM9M2KFjcJz/R+YZaVvjO3KxZs9i1axf33nsvQUFBaDQyDU8IV6ULLbgzZ5Ni\nTghxA8Yed6ENDcV69CjWn37C0Lq12pFqnBEjRhAdHc3atWvp3LkzixYtIjQ0lK5duwJgNpvJzMwk\nICAAjUZzw/5dunQp0/FK07t3b2bMmEHbtm3p0KEDO3fu5F//+hdr1qypsmsgRHXShYVh+fY7bL8m\nYnCykUsVLuZ27drFjBkzGDJkSGXkEUKoSFtYzOVfuKByEiGEs1K0Wjyjh5H597fI/uhjKeZU0KJF\nC2JiYli4cCELFy6kbdu2LFmypGguz7Zt25g+fTo7duwgJCSk1P6ltZdm0KBBmM1mPvjgA+bMmUNY\nWBhvv/120Z0/IVydNuzanblElZNcT3FUcIxE586diYmJKfO3NzVJ7969AdixY4fKSYQoG+uJE1zu\n1Qd9m9YEbf1C7TiikslnkqgstvMXSOrYCcVkom78D2i8vNSOJFyQfCYJV5GzcRNpTz+D5/CH8X8j\nRu04xVR4TOSQIUNYu3Yt+fn5lZFHCKEibUgIULgAihBC3IAuNARjjx44srPJ/UK++BFCuLeiO3O/\nOt+duQoPs7RYLBw6dIju3bsTERGBh4dHsXZFUVi8eHFF30YIUQ00tWqh+PpiT07GkZeH8qf/noUQ\n4hqvh6Mx79xJzj8+wWvYMLXjCCFEldEVLoBic8JhlhUu5hISEoiIiAAKJtyazeYKhxJCqEcbEoIt\nI4P8ixfR3X672nGEEE7Ko09vNLVrYzl4EOvJk+ibNlU7khBCVAlNYCCKyUT++fM4rFYUvV7tSEUq\nXMytW7euMnIIIZyELjQU27Fj5J+/IMWcEOKGFIMBzweHkPX+cnI++RTfV2aU/iIhhHBBiqKgbRCG\n7fgJ8s+fR9ewodqRilTKpuE2m42tW7dy8OBBsrKy8PPzo127dvTr1w+9E1WuQojSXdtrznb+PEaV\nswghnJtn9LCCYm7DRnymvuRU31YLIURl0oUVFHO2xESnKuYqZdPwhx56iJdeeon9+/dz4cIFdu3a\nxd/+9jcefPBBMjIyKiOnEKKayPYEQoiy0jdrhr5tW+zJyeTt3Kl2HCGEqDLa+s65CEqFi7mYmBiS\nk5P5/PPP2b59O59++ik7duzgs88+Iz09nTfffLMycgohqok29NqKlrJxuBCidF7RBYuf5Hz2ucpJ\nhBCi6hQtgvLrryonKa7Cxdz/t3fncVHV+//AX2eGZVgUEQSDtJQ0vC6AIi6IC+p1SbqaeS9FhLlh\nhmlyVfSqmGYKVmamltrPXCrqKmYlLaiZaymJdhX5FphiLiCoiGwDM+f3B8wogrLMMGfO8Ho+HjyK\n+ZyZeZ2Z8XDe8/mcz2ffvn2Ijo5G165dq9zerVs3zJw5s9HWDklOTsaIESPg4+ODiIgIZNUyu0xd\nt//mm29qXAA9JSUFzzzzDHx8fDBu3DicOXPGKPtBZG70yxOwZ46I6sAuZBQElQole/dBk5srdRwi\nokahbNMGAKD56y+Jk1RlcDEniiKcnZ1rbHN2dkZRUZGhT1FNWloaoqOjERERgcTERDg5OSEyMhJa\nrdag7Y8ePYqFCxdCEIQqt+fk5CAyMhLBwcHYtWsXunbtismTJ+POnTtG3zciqSkfqbhmTnPtmsRJ\niEgOFM2bQzVyBFBejuLEXVLHISJqFFaPPgoAKP/LvEYuGVzMde3aFdu2bau2aLhGo8G2bdvQpUsX\nQ5+imu3bt2PgwIEIDQ2Fl5cX4uLikJ2djUOHDjV4+7i4OERGRqJt5aKA9/rvf/+Lxx57DFFRUWjf\nvj0WLVoER0dH7N692+j7RiQ1pbs7AEBzLVviJEQkF/b//CcAoOi/OyROQkTUOMz1MhSDi7l///vf\nOHHiBIYPH464uDhs2rQJcXFxGD58OE6cOIFZs2YZI2cVqamp6Nmzp/53Ozs7dO7cGampqQ3e/pdf\nfsG2bdswdOjQGu8fEBBQ5bYePXrg1KlThu4KkdkRbG2haNkSYn4+tI3Qs05Elsc2sC+UHh4oS0uD\n+sxZqeMQERmdwskJQrNm0ObkQCwpkTqOnsHFXKdOnfDpp5/iySefxJdffolVq1Zh9+7d8Pb2xmef\nfYbu3bsbI2cV2dnZcHNzq3Kbq6srsrNr7kmoy/aJiYnw9fWt1/2vcRgaWShl69YAAM1VfsaJqHaC\nQgG7sc8AAIr+y4lQiMgyKR/Vzfh9VeIkdxlczAFA586d8f777+PYsWM4e/Ysjh49ijVr1qBz584N\neryysjJkZWXV+JOXl4eSkhLY2lZdAcvGxgZqtbrGx6vv9nW9f1lZWT32ikg+FJXFnNaCvrAw9qRJ\nhrSLoogNGzZg6NCh8PPzQ2hoKE6ePKlvV6vViI+Px6BBg+Dv748JEyYgIyOjxpyff/45vL296/ty\nEBmd/bhxAIDiL3dD5N9HIrJAVp666+bMZxKUBi0avnXrVjz11FNwcXHB1q1bH7qtIAgIDw+v1+Nf\nuHABISEh1SYiAYDRo0dDpVJVK8TUajXs7e1rfDxbW9t6bX+/Bz2fSqWq0/2J5MbSJkHRTYI0f/58\n9OzZE6tXr0ZkZCT27NkDhaL6d1q1bW9o+5YtW7B582a8+eab8PLywueff46JEyciKSkJjzzyCFau\nXIkDBw4gLi4Obm5uWLduHSZMmIBvv/0WDg4O+pzXrl3DypUrazxWEpmatVd7WHfvjrKTJ1H600Go\nhgyWOhIRkVHd7Zkzn+vmGlTMvfnmm/D19YWLiwvefPPNh27bkGKuQ4cOSE9Pf2D7qVOncP369Sq3\nXb9+vdp1bTqtW7eu1/b3c3d3R05OTrX7u1dOFEFkaZSPVA6ztJBi7t5JkICKCY8CAwNx6NAhDBgw\noN7bG9q+c+dOTJw4EYMGDQIAzJ49G3v37kVycjLCw8Oxa9cuLF26VH+MWrZsGQICAvDzzz9j8OC7\nJ8j/+c9/0KlTJ6SkpDTei0dUD/bPjkX+yZMo+u8OFnNEZHGUlTNaasxoRssGDbNMT09Ht27d9P//\nsJ9z584ZNTAA+Pr6Vjl5KSoqQlpaGvz8/IyyfU33//XXX6vcdvLkyTrfn0hu7l4zZz5jwg1h7EmT\nDG2PjY1FSEhItee9ffs2RFHEmjVrEBgYqL9d13tYUFCgv+2///0vbt++jfHjx9f5dSBqbPZPhwDW\n1ihOToY2P1/qOERERqX0rOyZM6NhlgZfMzdv3jxcunSpxrbz58/j5ZdfNvQpqgkLC0NycjK2bt2K\njIwMxMTEwNPTE/369QMAlJaWIjc3V7+OXG3b12bcuHH4448/sGrVKmRmZmLJkiUoKirCqFGjjL5v\nROZA2Vq3PIFl9MwZe9IkQ9v9/f2r9OwfOHAAWVlZCAwMhEKhQJ8+fdC8eXN9e0JCAsrKyvQ9dVev\nXsU777yD5cuXQ6lU1vl1IGpsCmdnqAYHA6WlKE76Vuo4RERGZVVZzJnTWnMNKub+7//+T9/ztmvX\nLpw6darGXrnvvvsOR48eNXZmdOnSBfHx8di2bRvGjRuHwsJCrFu3Tn/dSFJSEoKCgvSzTda2fW3c\n3d2xfv167N+/H2PHjsXZs2exadMmODo6Gn3fiMyB3K6ZM/WkSYa230v3BdOoUaNq7O0/fvw44uPj\nMWnSJHh4VKxxs3DhQoSHh+OJJ5542MtCJAn7sWMBAEU7d0qchIjIuPTXzJnRWnMNumZuw4YN2LNn\nDwRBgCAImDNnTo3biaKIESNGGBTwQUaOHImRI0fW2DZmzBiMGTOmztvfKyoqClFRUdVu7927N77+\n+uuGhSWSGbktTWDqSZMMbdc5c+YMpkyZgo4dO2LZsmXVchw8eBAzZszAkCFDMHPmTAAVwytzc3MR\nGRkJoOI4S2ROVIODITg5QX3sZ5Rfvqz/JpuISO4UrVoBNjbQXLkCUaOBYAajYxpUzC1evBj/+te/\nIIoiIiIisGjRomrfECsUCjRv3hwdOnQwSlAiMh3ByQmCSgXt9etmc7B6GFNPmmRoOwCcOHECU6dO\nha+vL9atWwcbG5sq2yclJWHOnDkYNWoUli9frr/966+/xvnz5+Hv7w8A0Gq1EEUR3bt3x5IlSzj8\nmyQn2NrCbtRTKPrkUxR/uRvNXpkmdSQiIqMQFAooPTyguXAB2uwcKD0ekTpSw4ZZNmvWDAEBAejV\nqxe2bt2Kf/zjHwgICKjy4+/vj44dO3LKbCIZEgShYq05jQba+4oSOTLWpEndu3c3Snt6ejoiIyMR\nEBCADz74oNqQzMOHD2POnDkYO3YsVqxYUeU4+tZbb2HPnj346quv8NVXX2HBggUQBAG7d+9GcHBw\nQ18iIqOyf6ZidExRYqLESYiIjMuqckbLcjMZatmgnrl7BQQE4MqVK/jpp5+qDCsSRRHFxcU4deoU\n4uPjDX0aIjIx5SOtoblwAZqrV/XDLuUqLCwMoaGh2Lp1K/r27Yv33nuv2qRJBQUFaNmyJRQKxQO3\n180w2ZB2Dw8Pffu8efPg7u6ORYsWIf+eGf/s7OxgbW2NmJgY+Pn5ISoqCrm5ufp2R0fHahOrZGZm\nAgDatGnTeC8gUT3ZBARA6eGB8vT/Q9m5c7Du1EnqSERERnH3urm/gJ7+EqcxQjG3e/duzJ8/HxqN\nRv/tse4aDoVCga5duxr6FEQkAblNgvIwukmQVq1ahVWrVqF79+7VJk2aP38+9u3bBw8Pj1q3b0j7\n+vXrIQgCsrKy9ENC7+9Je+mllxAUFIS8vDzk5eWhf//+VdoXLFiAsLCwxn65iAwmKBSwG/0P3Fm3\nHkW7voQTizkishB3lycwj545QTTw6vmnnnoKrVu3xuuvv46PP/4YhYWFmDVrFo4cOYLXX38dK1as\nwLBhw4yVV1Z0i/vu27dP4iRE9Ze/7E3cWbceTm8sheNL46WOQ0bAYxKZUlnaOeQM/TuUnp5w//ko\nBIXBqyGRheExieSoMCEBt6Jnw2F8BFose0PqOIavM5eVlYUXX3wRjz76KHr06IHTp0+jVatWGD16\nNKZOnYpNmzYZIycRmZh+RksL6JkjItOz6uQNq44dobl8Gep7riElIpIzZeUyQZqrVyVOUsHgYs7W\n1lY/C1u7du1w8eJFlJaWAgD8/Pzw559/GvoURCQBpbtu4fCaF9YmInoYQRBg94+nAQDFX+6WOA0R\nkXHoL0OxlGLOx8cHO3bsgCiKaNeuHZRKJQ4fPgygYjFca2trg0MSkekp3Csm2tDmsJgjooax1xVz\n3+yBWF4ucRoiIsPdLebMY+SSwcXc9OnTsX//fkyePBm2trYYN24cZs+ejfHjx2PFihWcKptIppSV\nsyZqLGBpAiKShlW7drD29YE2Lw+lR45IHYeIyGAKR0cIzZpVrMV7z0z+UjF4NktfX18kJSXhjz/+\nAADMnz8fzs7OOH36NCZOnIjIyEiDQxKR6Skqizltdo7ESYhIzuz/8Q/knzqN4t1fQTVggNRxiIgM\npnzkEZQXFECTnQ0riZcGMrhn7sSJE2jevLl+Cm2lUomoqChs3LgRL730En788UeDQxKR6Sns7Cq+\nebpxwyy+eSIiebILGQUIAoq//Q5i5TX1RERypnykcpI4M7huzuBi7sUXX9QvWnu/s2fPYu7cuYY+\nBRFJ5O5Qy9xatiQiqpnykUdg0ysA4u3bKPnpoNRxiIgMpr9u7soViZM0cJjlzJkzcfHiRQAVC4TP\nmTMHdnZ21ba7cuUKPCqn7yQi+VG4uQGZmRWToHjy3zIRNYxdSAjUP/+C4q+/ht3fh0odh4jIIHeX\nJ5B+EpQGFXPh4eHYsWMHAODcuXN47LHH0LJlyyrbKBQK9O7dG6NHjzY8JRFJQlk5o6Umh9fNEVHD\n2T01EvkLF6Hk+x8gFhdDqOELYCIiuTCn5QkaVMz16NEDPXr00P8+bdo0tJH44j8iMj5Fq1YAAG0O\nZ7QkooZTtmoF2z59UHrkCEoOHIDdiBFSRyIiajBzumbO4Nksly9fDgD4/fffcfLkSdy+fRsuLi4I\nCAhggUckc/qFw9kzR0QGsgsZhdIjR1D8zR4Wc0Qka7LvmbtXYWEhZs2ahYMHD0IURdja2qK0tBSC\nIGD06NFYunQprKwMfhoikoB+AhQuT0BEBlKNHAHM/w9KfkiGtrgYCg61JCKZMqdizuDZLN944w2k\npqYiPj4eJ0+exOnTp/Hrr79i+fLl2LdvH959911j5CQiCejXmsvJljgJEcmd0sUFtn37QiwqQumP\nB6SOQ0TUYELz5hDs7aHNzoFYViZpFoOLuX379mHu3LkICQmBvb09AMDBwQGjR49GdHQ0du3aZXBI\nIpIGJ0AhImOyG/UUAKB4zx6JkxARNZwgCBUzWooiNBLPK2BwMWdlZYXmzZvX2NaqVSuUSVytElHD\nKSsnQOEwSyIyBtWI4YBCgZLkvRCLi6WOQ0TUYOay1pzBxdyECRPw1ltv6ded08nNzcXatWsxYcIE\nQ5+CiCQitGgB2NpCm5sLUauVOg4RyZzS1RU2vXtDLCxEyUEuIE5E8mUuM1oaPDNJamoqbty4gZEj\nR6JTp05o1aoVbt26hbS0NJSVlUGr1eL7778HUNElmZiYaHBoIjINQRCgbNUKmr/+gvbmTShdXKSO\nREQyZ/fUSKiPHkXxnm9hN2yY1HGIiBpEUTnjt1biS1EMLuaaN2+OIUOGVLmtRYsWePzxxw19aCIy\nAwo3t4piLjuHxRwRGcxuxHDkL1iIkh9+gFhaCsHWVupIRET1pmxduXxTtrSTxBltnTkiskxKdzeU\nAdDkZMP6b52kjkNEMqd0d4dNT3+oj59A6ZGjUAUPkjoSEVG9Kd0qi7lrMi/mAKC4uBi///47ysrK\nIIoiAEAURRQXF+PUqVOYMWOGMZ6GiCTASVCIyNjsRo6E+vgJFCclsZgjIllSWsowy0OHDiE6OhoF\nBQX620RRhCAIAAAXFxcWc0Qypl9r7rq0U+8SkeVQjRyB/MWvo+S77yGuWA7ByijfLRMRmYxCt3yT\nxMMsDZ7NctWqVWjTpg0+/vhjPPXUUxgxYgQSEhLwyiuvQKlU4q233jJGTiKSiL5nLjdX4iREZCms\nPD1h7dMN2ps3oT5+Quo4spScnIwRI0bAx8cHERERyMrKMmj7h7WLoogNGzZg6NCh8PPzQ2hoKE6e\nPFnl/gkJCQgODoafnx+mT5+OGzduGG9niczQ3ZFLMi/mMjMz8fLLL6NXr14YMGAAzp8/D19fX0RF\nRSEiIgJr1641Rk4ikojCtWLSEy2LOSIyIrsRIwAAxd9+K3ES+UlLS0N0dDQiIiKQmJgIJycnREZG\nQvuAJWRq27629i1btmDz5s2YP38+du/ejR49emDixIm4Wjkl+/79+xEXF4e5c+ciISEBN27cQHR0\ntGleDCKJCLa2ULRsCfH2bWglXDfT4GJOoVCgWbNmAIDHH38cmZmZKC8vBwD0798fv//+u6FPQUQS\nUrhWfPOkzc2TOAkRWRKVrphL+pbrWNbT9u3bMXDgQISGhsLLywtxcXHIzs7GoUOHGrR9be07d+7E\nxIkTMWjQILRt2xazZ8+Gm5sbkpOTAVQUe6GhoRg2bBiefPJJrFy5EseOHUNGRoZpXhAiieiGWmol\n7J0zuJjr1KkT9u3bBwBo3749tFotUlNTAQDXrl3TT4hCRPKkrOyZ0+TymjkiMh7rJ7xg1aEDtNeu\noey336SOIyupqano2bOn/nc7Ozt07txZf/5V3+1ra4+NjUVISEi1x719+zZEUcRvv/1W5f4eHh7w\n8PB4YB4iS6GbBEXKoZYGX3EcGRmJl19+GXl5eXj77bcxbNgwvPbaaxgwYAD27t2L3r17GyMnEUlE\nUTkmXHudwyyJyLhUw4fhzh9/oPjb72Dj6yt1HNnIzs6GW+XkVDqurq7IfsAJZW3b19bu7+9fpe3A\ngQPIyspCYGAg8vPzUVxcXK88RJZCX8xJuDyBwT1zAwYMQEJCAgIDAwEAb7zxBoKCgpCamooBAwZg\n8eLFhj4FEUlI4eAAwc4O2hs3IGo0UschIgtiN2I4AKDku+8lTmJeysrKkJWVVeNPXl4eSkpKYHvf\nYus2NjZQq9U1Pl5t29fn8TIyMhATE4NRo0bBz88PJSUlAFCvPESWQj/jt4TLExhlLuBu3bqhW7du\nAAB7e3suJE5kYRSurtBcugTtzZtQurpKHYeILIR1t25QPvIIyjMyUJaRCesnvKSOZBYuXLiAkJAQ\n/TJP9xo9ejRUKlW1QkmtVsPe3r7Gx7O1tX3o9rW165w5cwZTpkxBx44dsWzZMv19ddvff3+VSlXb\nrhLJmrK1TIdZ6q6Rq6vBgwc35GmIyEzoi7ncXBZzRGQ0giBANXwYCjd/jJIffoD1Ey9LHcksdOjQ\nAenp6Q9sP3XqFK7ft/bn9evXERAQUOP2rVu3fuj2tbUDwIkTJzB16lT4+vpi3bp1sLGxAQA4OztD\npVLVeH/3yiFoRJZKttfMvfLKK1V+131zdO9kJ/d+m3Tu3LmGPA0RmQmlqwvKAGiu58LaW+o0RGRJ\nVMMqi7nvvkezaSzm6sLX1xcpKSkICwsDABQVFSEtLQ2RkZH12n7q1Kl1ak9PT0dkZCR69eqF9957\nD9bW1lUev1u3bkhJScHAgQMBAJcvX8a1a9fg5+dn9H0nMidKt4piTpsts2GW9/bMpaWlISYmBi+/\n/DKGDRsGV1dX3Lp1CwcOHMD777+PpUuXGi0sEUlDPwlKHidBISLjsu3dC4KTE9QnT0Jz/bp+IV56\nsLCwMISGhmLr1q3o27cv3nvvPXh6eqJfv34AgNLSUhQUFKBly5ZQKBQP3F4330FN7R4eHvr2efPm\nwd3dHYsWLUJ+fr4+h52dHRwcHBAeHo7Zs2fjySefRIcOHfDGG2+gX79+aN++velfHCITUpjBMMsG\nTYDi6emp/1mzZg2mT5+OSZMmoU2bNrCzs8MjjzyC5557Dq+88gri4+ONnZmITEw3tJIzWhKRsQnW\n1lAFDwJEESXJe6WOIwtdunRBfHw8tm3bhnHjxqGwsBDr1q3Tj4pKSkpCUFAQrl27Vqfta2pfv349\nBEFAVlYW0tPTceHCBQQHByMoKEj/s3btWgDA0KFDER0djZUrVyIsLAwtW7bk+R81Cbovn2Q3zPJe\nWVlZD/zmxcPDg9PSElkARWUxp8llMUdExqf6+99RvOtLlHz/Axyef07qOLIwcuRIjBw5ssa2MWPG\nYMyYMXXe/mHtbdu2rdPlMuHh4QgPD691OyJLItjYQNGyJbQ3bkBbVATFAyYhakxGWTR8y5Yt1WYx\nKiwsxIYNGzhemsgC6Io5LYs5ImoEqkEDAWtrlBw+BG1RkdRxiIjqTOGuu25Omg4sg3vmYmJiMH78\neAwYMAC9e/eGs7Mz8vLy8PPPP0MQBHzyySfGyElEEtINs9RwmCURNQJFs2aw7dsHpT8dROmhQ7Ab\nNkzqSEREdaJ0d0P5uXPQZGfDql07kz+/wT1zPj4++Oabb/D000/j8uXLOHLkCLKzsxEaGoqkpCQc\nP37cGDmJSEKKVpU9c5wAhYgaiervQwEAJd//IHESIqK60103J9W8AkZZNNzT0xPz5s3T/378+HHs\n3LkTgwcPRklJCZ57juPfieRM4SrtgYqILJ9q6FDk/2chSvbth6jVQlAY/H0zEVGj0834LdW8AkY7\nUubk5GDDhg0YNmwYIiIisHfvXgwfPhwfffSRsZ6CiCSiaOEEKJXQ5OVWWU9STpKTkzFixAj4+Pgg\nIiICWVlZBm1vSLsoitiwYQOGDh0KPz8/hIaG4uTJk/p2tVqN+Ph4DBo0CP7+/pgwYQIyMjKqPP7m\nzZsRHBwMPz8/TJ48GVeuXGnoS0NkFqw8PWH9t79Bm5uLstRTUschIqoT/bwC169L8/yG3Fmj0WDv\n3r2YOnUqgoOD8d577yErKwuzZs3C0aNHsXz5cvTt29dYWYlIIoJCAYWrC1BSCvHOHanj1FtaWhqi\no6MRERGBxMREODk5ITIyElqttkHbG9q+ZcsWbN68GfPnz8fu3bvRo0cPTJw4EVevXgUArFy5EsnJ\nyYiLi8OOHTvg6uqKCRMmoLCwEADwySef4P3338d//vMf7Ny5E1qtFq+++mpjv4xEjU41dAgAoPgH\nDrUkInlQulX2zMmpmDt//jxWrlyJAQMGICoqCrdu3cL8+fORlJQEURTh6+sLW1tbY2clIgkpXeS7\n1tz27dsxcOBAhIaGwsvLC3FxccjOzsahQ4catL2h7Tt37sTEiRMxaNAgtG3bFrNnz4abmxuSk5Mh\niiJ27dqFWbNmISAgAI8//jiWLVuGgoIC/PzzzwCADz/8EDNmzMDgwYPRvn17xMbG4saNG7gu0R8S\nImPRFXMl+/ZJnISIqG7uXooio2Ju5MiR2L9/P8LCwvDDDz8gISEBzz//PJydnY2dj4jMhG4SFI0M\nJ0FJTU1Fz5499b/b2dmhc+fOSE1NbdD2hrbHxsYiJCSk2vPevn0boihizZo1CAwM1N+uqLx2qKCg\nABkZGbh+/TqGDx+ub2/bti3279+PVpXj9onkytrHB4pWrVB+Lh3PhiAjAAAgAElEQVTlf/0ldRwi\nolrpe+bkdM1c+/btcenSJRw5cgTfffcdLl++bOxcRGRmFDLumcvOzoabm1uV21xdXZH9gDVhatve\n0HZ/f3+4V65LAwAHDhxAVlYWAgMDoVAo0KdPHzRv3lzfnpCQgLKyMgQEBODixYuwsbFBVlYWQkND\n0a9fP7z66qvIycmpz0tCZJYEhQKqwcEAgJK9eyVOQ0RUO90EKNocGfXMJSUlISEhAd7e3vj4448x\nZMgQhIWFYceOHRAEAYIgGDsnEUlM4dISAKC9cUPiJNWVlZUhKyurxp+8vDyUlJRUG/ptY2MDtVpd\n4+PVtr2h7ffKyMhATEwMRo0aBT8/v2rtx48fR3x8PCZNmgQPDw8UFhZCo9EgNjYWL7/8MtatW4eC\nggJMmjTpgdcAEsmJashgAEDJvv0SJyEiqp2iRYuKSeJypZkkrsFLE3Tp0gVdunTBvHnzcPDgQeze\nvRvvvvsuRFHE22+/jTFjxmDIkCFo2bKlMfMSkUSULi4AAG1ensRJqrtw4QJCQkJq/CJp9OjRUKlU\n1QoptVoNe3v7Gh/P1tb2odsb2q5z5swZTJkyBR07dsSyZcuq5Th48CBmzJiBIUOGYObMmQAAKysr\naDQazJ49GwMGDAAAvPPOOwgMDMQvv/yCPn361LhPRHJhGxQEWFuj9MhRaIuKoHjAv1MiInMgKBRQ\ntHKF9lo2xIICCPeMrDEFg5cmUCqVGDRoEN59910cOXIES5cuhVKpRGxsLPr374+XXnrJGDmJSGKK\nyi9mNGbYM9ehQwekp6fj3Llz1X6WL18Od3f3apODXL9+vcpQx3u1bt36odsb2g4AJ06cQEREBDp1\n6oSNGzfCxsamyvZJSUmYNm0ahg0bhrfeekt/u274ppeXl/42Z2dnODs7c3kCsggKR0fY9u4NlJai\n9PARqeMQEdVKWTkJikaCoZZGXZHT0dER48aNw/bt27F3715MmzYN165dM+ZTEJFEzHmYZW18fX2R\nkpKi/72oqAhpaWk1Dmt82Pbdu3c3Snt6ejoiIyMREBCADz74oNqQzMOHD2POnDkYO3YsVqxYUaXH\n8W9/+xtsbW1x9uxZ/W15eXm4efMm2rRpU+/Xhsgc6a+b41BLIpIB3SRx2lyZF3P38vT0xLRp0/Dt\nt9821lMQkQkpzHiYZW3CwsKQnJyMrVu36q9R8/T0RL9+/QAApaWlyM3N1V9z9qDtdTNMNqTdw8ND\n3z5v3jy4u7tj0aJFyM/PR25uLnJzc1FYWAi1Wo2YmBj4+fkhKipK35abm4uSkhLY29sjLCwMK1as\nwNGjR/HHH39g9uzZ6NixY5UZNInkTDW44rq50v37JbkGhYioPpStLKRnjogsl8JZ1zN3U+Ik9del\nSxfEx8dj27ZtGDduHAoLC7Fu3Tp9j1dSUhKCgoL0Iwlq274h7evXr4cgCMjKykJ6ejouXLiA4OBg\nBAUF6X/Wrl2LX3/9FXl5eUhJSUH//v2rtO/cuRMAEB0djTFjxmDOnDn45z//CTs7O2zYsIGTT5HF\nsGrfDsp27aC5cgXl6elSxyEieij9jJYSLE8giPzKq9EMrvxmcR8XPyULoL15E1e7dIPSwwOtT/wi\ndRxqAB6TSE5uLVqMwo8+QvP589DslWlSx6FGwGMSWYo7Gzchf/HraPbqdDSfO8ekz82eOSKqE8HJ\nCVAqZXnNHBHJj2pI5XVzP/4ocRIioofTXTOnuc5hlkRkpgSFAgpnZ4glJdAWFUkdh4gsnG2vXhDs\n7KA+fgLa/Hyp4xARPZBuNkvtddMPs2QxR0R1JucZLYlIXgRbW9j2CwQ0GpQeOix1HCKiB1K4VU6A\nYkmzWRKR5dGtNSfHGS2JSH5sBw0CwKGWRGTeFLqeOc5mSUTmTNFStzwBe+aIqPGpgu8Wc5yvjYjM\nlaKFE2BlBU1ursmPVSzmiKjOlC2dAXCYJRGZhlWbNrB64glos3NQfo5LFBCReRIUCihcXQG1GqKJ\nr/FlMUdEdaZbOFzDYZZEZCK2AwcA4FBLIjJvStfKGS1NPHqJxRwR1ZmumGPPHBGZimrQQAAs5ojI\nvOknicsz7YyWLOaIqM4UHGZJRCZm27s3BJUK6hMp0N65I3UcIqIaKVwqeuZMPUkcizkiqjP9BCgs\n5ojIRASVCjZ9egPl5Sg9elTqOERENbrbM8dhlkRkpu4uTcBijohMRzVwIACg9McDkuYgInoQpe5S\nFPbMEZG5UrpwnTkiMj39JCg//SRxEiKimkk1SRyLOSKqM13PnIbDLInIhKy8vKD09ITmYhbK//xT\n6jhERNUoXNkzR0RmTrC1heDoCPHWLYjl5VLHIaImQhAE2A7oD4C9c0RknvTzCvCaOSIyZ/oLfG/d\nkjgJETUlqgEVQy1LfzoocRIiouqkuhSFxRwR1cvdSVB43RwRmY5tv0BAoUDpkaMQy8qkjkNEVIVC\nv2g415kjIjOmcK4s5m7elDgJETUlihYtYO3rC7GwEOpff5U6DhFRFYKjI2BjA+2NmxBF0WTPy2KO\niOpF0aIFABZzRGR6qsrr5koPHpI4CRFRVYIgVIxeKiuDePu2yZ6XxRwR1YvC2RkAoL3Ja+aIyLRs\n+wcBAEpYzBGRGdKtNafJNd2lKCzmiKheFM6VPXOcAIWITMzGzw+CoyPKTp/mMYiIzI5+eYIbLOaI\nyEzd7ZnjMEsiMi3B2hq2fXoDWi1Kjx6TOg4RURW6hcNNOUkcizkiqhd9zxyLOSKSgG1/3XVzXKKA\niMzL3Rm/TbfWHIs5IqoX9swRkZRsg/oBAEoO8bo5IjIvysrlCbS5pluegMUcEdWLvpjj9SpEJAGr\nJ56AonVraC5cRPmlS1LHISLS0w2z1LBnjojMFXvmiEhKgiBAVdk7V3rosMRpiIjuUrhUDrPkBChE\nZK7urjPHnjkikob+ujkOtSQiM6Jw0Q2zZDFHRGZKcHAArK2hvXkToihKHYeImiDbfoEAgNIjRyFq\ntRKnISKqoNT1zHE2SyIyV4IgVAy1LCuDWFQkdRwiaoKUbm6werIjtHl5KD+XLnUcIiIA91wzx2GW\ntUtOTsaIESPg4+ODiIgIZGVlGWX7b775BmPHjq12+4QJE+Dt7Y1OnTrp/7t582aj7AuR3HB5AiKS\nmm2/ylktDzfN6+aMfR70sHZRFLFhwwYMHToUfn5+CA0NxcmTJ6u0d+vWTX+OpDtPOnv2rHF3msjM\nCc2aVYxeyrthstFLsizm0tLSEB0djYiICCQmJsLJyQmRkZHQPmCoRV23P3r0KBYuXAhBEKo9RmZm\nJuLj43H48GEcOXIEhw8fxvPPP98o+0dk7u5eN8dijoikoR9qefiIxElMz9jnQbW1b9myBZs3b8b8\n+fOxe/du9OjRAxMnTsTVq1cBAJcuXUJZWRl++OEHHDlyRH+e1KlTJ9O8IERmQhAEKFpWjl4qLDTJ\nc8qymNu+fTsGDhyI0NBQeHl5IS4uDtnZ2Tj0gAuh67J9XFwcIiMj0bZt22r3v3PnDrKzs9G1a1e4\nuLjof2xtbRttH4nMGWe0JCKp2fbuDSgUUP/yC8SyMqnjmJSxz4Nqa9+5cycmTpyIQYMGoW3btpg9\nezbc3NyQnJwMAMjIyICLiwvatGlT5TxJoZDlaSaRQfTnSDdMszyBLP+VpaamomfPnvrf7ezs0Llz\nZ6SmpjZ4+19++QXbtm3D0KFDq90/MzMTVlZWNRZ6RE3R3WKOM1oSkTQUzZvD2qcbxMJCqE+dkjqO\nSRn7PKi29tjYWISEhFR73Nu3bwOoKObatWtn+I4RWQCFc+UkKCb6wluWxVx2djbc3Nyq3Obq6ors\n7OwGb5+YmAhfX98a75+RkQFHR0fMnTsXQUFBGD16NL788ksD94JIvtgzR0TmwDbw7qyWTYmxz4Nq\na/f394e7u7u+7cCBA8jKykJg5eufmZmJkpISREREoF+/fnjxxRfx22+/GbaTRDJl6p45K5M8Sz2V\nlZXpx2Hfz8HBASUlJdWGONrY2ECtVtd4n/puf7/MzEyUlpYiMDAQU6ZMwdGjR7FgwQLY2Nhg5MiR\ndXoMIkvCYo6IzIFtYCDuvL+24rq5mTOkjmM0pj4Pqs/jZWRkICYmBqNGjYKfnx+AivOk27dvY9as\nWWjevDkSEhIQERGBr776Cm3atKnbThNZCFOPXjLLYu7ChQsICQmpcSKS0aNHQ6VSVTvAqNVq2Nvb\n1/h4tra29dr+frNnz8bLL7+MZs2aAQA6duyIS5cuYfv27SzmqEniwuFEZA5sevoDNjZQ//orxOJi\nCHZ2UkcyClOfB9X1POnMmTOYMmUKOnbsiGXLlulv//TTT6HRaGBX+fovXboUp06dws6dOzFz5sw6\n7jWRZVC0ZM8cOnTogPT0B68bc+rUKVy/fr3KbdevX0dAQECN27du3bpe299PEAR9Iafj5eWFAwcO\n1On+RJZGvzTBLRZzRCQdhZ0dbLr7Qf3zL1D/elI/w6Xcmfo8qC7nSSdOnMDUqVPh6+uLdevWwcbG\nRt927//reHl5PXDYJ5ElM/XoJVleM+fr64uUlBT970VFRUhLS9N39xu6/f2mT5+OBQsWVLntzJkz\n8PLyakB6IvmT4zBLU67JVFt7bWs2qdVqxMfHY9CgQfD398eECROQkZGhby8rK0NcXBz69++Pnj17\n4pVXXsGVK1cMeXmIZOvudXNNZ4kCY50Hde/evU7t6enpiIyMREBAAD744IMqQzLLy8sRFBSE3bt3\n62/TarVIT0/neRI1ScqWnAClVmFhYUhOTsbWrVv1Y7c9PT3Rr3IB0dLSUuTm5urXR6lt+9oMHjwY\nX375JRITE3Hp0iVs2bIFX3/9NaZOndpo+0hkzuRWzJl6TSZD12xauXIlkpOTERcXhx07dsDV1RUT\nJkxAYeWaNWvXrsX+/fuxevVqJCQkoLS0FFFRUY39MhKZJdvAvgCA0qPHJE5iOsY6D9JNYFJTu4eH\nh7593rx5cHd3x6JFi5Cfn4/c3Fzk5uaisLAQVlZWCAoKwurVq3Hs2DFkZmZiwYIFKCgowL/+9S9p\nXiAiCZl6AhSIMrVnzx5xyJAhoq+vrzhhwgQxKytL35aYmCh6e3uLly9frtP291qzZo04duzYarcn\nJCSIw4cPF7t16yaOGjVK3Lt3b60Zg4ODxeDg4AbsHZF5K792TfzL41Hxat9+Ukepk3nz5onTp0/X\n/15UVCT6+fmJBw4caND2hraPGjVK3LhxY5Xn/Pvf/y5u2bJF1Gq1Yo8ePcSkpCR9m1qtFn19ffXH\nnaefflr88MMP9e0nT54Uvb29xVu3bj30deAxiSyRtrRUvNz+CfGvto+Lmjt3pI5jMsY+D3pQ+8WL\nF0Vvb+8af+Li4kRRFMXi4mJx+fLlYv/+/UUfHx8xIiJCzMjIqHUfeEwiS1Sa8qv4l8ej4vV/hprk\n+czymrm6GDly5AMnHxkzZgzGjBlT5+3vFRUVVeM33P/617/4DRNRJf23TjK5Zi41NRXPP/+8/vd7\n11AaMGBAvbc3tD02NrbGGd5u374NURSxZs0adO7cWX+7buHdgoICAICzszOSk5PxzDPPoFmzZkhM\nTETbtm3RvHlzA14lInkSbGxg07MnSg8dgjolBaoa/k1bImOfBz2ovW3btjh37txDs6hUKsTExCAm\nJqYOyYksm6knQJHlMEsikpZgYwPBwQFifj5EjUbqOLUy9ZpMhqzZpFAo0KdPnyqFWUJCAsrKyvST\nEcTExCA/Px/9+vVD9+7dsXfvXqxfv77Gme+ImgLbvn0ANK2hlkRknkx9KYpse+aISFqKFi2gKSyE\nNv82lJXfQknF3NZkMnTNpnsdP34c8fHxmDRpEjw8PAAAWVlZaNmyJRYuXAgnJyesXr0aM2bMwI4d\nO6o9L1FTYNO36V03R0TmSWjeHFAqobnZhJcmICLzp2jRAprLlyHm3wIkLubMbU0mQ9ds0jl48CBm\nzJiBIUOG6NdqunPnDmJiYrBu3Tr07t0bALB69WoMGjQI3377LUaPHl3jPhFZMhufbhDs7FB2+jS0\nhYVQODhIHYmImihBoYCiRQto8/KgLS6GopHXv2QxR0QNIjg5AQC0+fkSJzG/NZkMXbMJAJKSkjBn\nzhyMGjUKy5cv199+/vx5FBcXw9vbW3+bo6MjHn/8cVy6dOmBrwGRJROsrWET0BOlPx2E+vhxqAYN\nkjoSETVhCmfnimLuxg0oPD0b97ka9dGJyGIpWphPMVcbU6/JZMiaTQBw+PBhzJkzB2PHjsWKFSuq\n9DjqrrW7d9250tJSXLp0qcZJVYiaCts+ldfN/fyLxEmIqKnTT4JiguvmWMwRUYModD1zt8y/mDPF\nmkzGWrNJrVYjJiYGfn5+iIqK0rfl5uaipKQE7u7uGDx4MGJjY5GSkqJ/fAcHB4wYMUKCV5fIPNj0\n4SQoRGQe7q41x2KOiMyUrpgTZdAz16VLF8THx2Pbtm0YN24cCgsLsW7dOn2PV1JSEoKCgnDt2rU6\nbd+Qdt1sk1lZWUhPT8eFCxcQHByMoKAg/c/atWvx66+/Ii8vDykpKejfv3+V9p07dwIA4uPj0adP\nH/z73/9GWFgYSktLsW3bNk5+Qk3avdfNERFJSdGyJQBAa4JJUARRFMVGf5YmavDgwQCAffv2SZyE\nyPgK3luD23HxaB4zF82mV1+bkcwPj0lk6XJDn0fpoUPwvMzrR+WAxySyVPnL3sSddevhtGwpHMeP\nb9TnYs8cETWIOU2AQkQEADa9e0kdgYiIwyyJyPzpJ0C5dUviJEREFWz79JY6AhERJ0AhIvOnYM8c\nEZkZmx49YDf6H1LHIKIm7m7PXONfM8dijogaRE6zWRJR0yBYWaHl2veljkFETdzdCVDYM0dEZkrh\n1AKAPGazJCIiIjIVfc8cizkiMldCi4pijsMsiYiIiO7iBChEZPYUTs0BsJgjIiIiupcp5xVgMUdE\nDSIolRCaNYNYUCB1FCIiIiKzIVhZ6c+RxPLyRn0uFnNE1GC6b56IiIiI6C5979zt2437PI366ERk\n0VjMEREREVWn0M0tcLNx1+NlMUdEDSawmCMiIiKqRlfMNfas3yzmiKjBFC1YzBERERHdT9Cvx8ue\nOSIyUxxmSURERFSdfpglizkiMlcs5oiIiIiqUzibZj1eFnNE1GAs5oiIiIiqU3CYJRGZO06AQkRE\nRFQdh1kSkdnjBChERERE1d0t5jjMkojMlO5ARURERER36YZZiuyZIyJzxWvmiIiIiKrT98xxAhQi\nMlcs5oiIiIiqE3jNHBGZO8GJwyyJiIiI7qebV4DFHBGZLYVTcwh2dlLHICIiIjIrgr09YG3NYo6I\nzJegVMJl2xapYxARERGZFUEQKq6bKytr1OdhMUdEBrHt00fqCERERERmxxRzC7CYIyIiIiIiMjJT\nLOHEYo6IiIiIiMjIWMwRERERERHJkMBhlkRERERERPLDnjkiIiIiIiIZUjizmCMiIiIiIpIdzmZJ\nREREREQkQxxmSUREREREJEMs5oiIiIiIiGTIqt3jjf4cLOaIiIiIiIiMzKpdO7j9uK9Rn4PFHBER\nERERUSOw7tixUR+fxRwREREREZEMsZgjIiIiIiKSIRZzRNQkJCcnY8SIEfDx8UFERASysrIM2t6Q\ndlEUsWHDBgwdOhR+fn4IDQ3FyZMn9e1FRUVYsGAB+vTpA39/f8yaNQvXr1+v8vgJCQkIDg6Gn58f\npk+fjhs3bjT0pSEiGTLlMU2j0eCtt95CUFAQ/Pz8MHnyZPz5558G5SEi42AxR0QWLy0tDdHR0YiI\niEBiYiKcnJwQGRkJrVbboO0Nbd+yZQs2b96M+fPnY/fu3ejRowcmTpyIq1evAgBiY2Nx9uxZbNy4\nEQkJCcjLy8PMmTP1+fbv34+4uDjMnTsXCQkJuHHjBqKjoxvzJSQiM2LqY9qaNWuQlJSEd955B19+\n+SWaN2+OyZMn1/n+RNR4WMwRkcXbvn07Bg4ciNDQUHh5eSEuLg7Z2dk4dOhQg7Y3tH3nzp2YOHEi\nBg0ahLZt22L27Nlwc3NDcnIyAMDOzg6LFi1Cly5d8MQTTyAiIgKpqakQRRFARTEYGhqKYcOG4ckn\nn8TKlStx7NgxZGRkNPZLSURmwNTHNFEUMX/+fPTs2ROPPfYYpkyZgsuXL+PKlSsNykNExsNijogs\nXmpqKnr27Kn/3c7ODp07d0ZqamqDtje0PTY2FiEhIdWe9/bt2wCAJUuWwM/PDwCQk5ODzz//HL16\n9YIgCBBFEb/99luVx/fw8ICHh8cD94eILIupj2mvvfYahgwZAgDIz8/Hli1b0K5dO3h4eDQoDxEZ\nj5XUAYiIGlt2djbc3Nyq3Obq6ors7OwGbW9ou7+/f5W2AwcOICsrC4GBgVVuX7JkCT799FO0aNEC\n27dvB1BxIlVcXFyv/SEiy2LqY5rORx99hJUrV0KlUmHDhg1QKBQNykNExsNirhHl5ORAo9Fg8ODB\nUkchalSPPPKIvtiQQllZmf56s/s5ODigpKQEtra2VW63sbGBWq2u8T61bW9o+70yMjIQExODUaNG\n6XvjdMLDw/HMM89gw4YNGD9+PL7++muUlpYCQL32R4fHJGoqpD4mGcrcjmk6w4YNQ9++ffHFF18g\nMjISO3fuRPv27eudR4fHJGoqGvOYxGKuEdna2tZ6ICMiw124cAEhISEQBKFa2+jRo6FSqar9W1Sr\n1bC3t6/x8Wr6t3vv9oa265w5cwZTpkxBx44dsWzZsmo52rVrBwBYuXIlBgwYgKSkJIwcOVL/ePc/\nvkqlqnF/HrZfRGR+zO2YpvPoo48CqBgqnpKSgh07dmDOnDl1vn9dchFR/bCYa0QpKSlSRyBqEjp0\n6ID09PQHtp86dara1P7Xr19HQEBAjdu3bt36odsb2g4AJ06cwNSpU+Hr64t169bBxsYGAFBaWoqf\nfvoJgYGBcHBwAFBxwtOmTRvcvHkTzs7OUKlUNT6+u7v7A18DgMckIrkwt2Pa/v370aVLlypDKb28\nvHDz5s063f9BeEwiMhwnQCEii+fr61vlpKGoqAhpaWnVhjXWtn337t2N0p6eno7IyEgEBATggw8+\nqDY8KTo6Gj/++KP+9zt37uDChQvo2LEjAKBbt25VHv/y5cu4du3aA/eHiCyLqY9pS5Yswa5du/Tt\nWq0W586d0x+T6puHiIxHuXjx4sVShyAiakytW7dGfHw8HB0d4eDggGXLlkGj0WDu3LkQBAGlpaW4\ndesWVCoVBEGodfuGtJeXl+vbJ0+eDJVKhXfeeQdlZWUoKipCUVERRFGEnZ0d8vLy8Nlnn8Hb2xuF\nhYVYvHgxrKysMG/ePAiCAEdHR7z99tvw9PSEKIpYtGgRvLy8EBERIfVLTUQmYIpj2r3HLI1Gg40b\nN6J9+/YAKoZ+nz9/Hm+++SZsbGxqfXwiakQiEVETsGfPHnHIkCGir6+vOGHCBDErK0vflpiYKHp7\ne4uXL1+u0/aGtF+8eFH09vau8ScuLk4URVEsLS0V4+PjxaCgINHX11ecPn26mJ2dXeXxt27dKgYF\nBYndu3cXp0+fLt64ccOorxcRmTdTHtO0Wq24ceNGMTg4WPTx8RHHjx8vZmRk1Pn+RNR4BFGsXIWW\niIiIiIiIZIPXzBEREREREckQizkiIiIiIiIZYjFHREREREQkQ1xnTkJ5eXkYO3YsNm3ahCeeeELq\nOHX21FNPwcXFBUDFAqJvvvmmxInqZtOmTUhOTkZ5eTnGjRuH0NBQqSPVyY4dO7B7924IggC1Wo2z\nZ8/ixx9/hKurq9TRHkqj0WD+/Pm4ePEiBEHAggUL0LlzZ6ljUS3UajXmzp2LnJwclJWVYcqUKRgy\nZIjUsYgaxenTpxEXF4dPP/1U6ihUg/vfnyVLluDs2bOwsrLCwoUL4e3tLXHCBysrK8OCBQvw559/\nwt7eHjExMWadV0fOf7vler4EGHaOymJOIuXl5YiNjYVKpZI6Sr3cuXMHKpUKW7dulTpKvZw4cQLH\njx9HQkIC1Go1PvzwQ6kj1dmzzz6LZ599FgDw5ptvYtSoUbI4MP30008oKipCQkIC0tPTsWTJEp4w\nycAXX3wBT09PrFq1Crdu3cLTTz/NYo4s0ocffohvvvmm2jqPZB7uf3/279+PgoICfP7557hw4QLm\nzZuHzz77TOKUD/bFF1/AysoKX3zxBXJycvDqq68iISFB6li1kvPfbrmeLxl6jsphlhKJi4vDc889\nBzc3N6mj1MuZM2dQXFyMl156CS+99BJOnz4tdaQ6OXz4MJ588klERUVh8uTJCAoKkjpSvZ07dw7/\n+9//8MILL0gdpU4ee+wxaLVaaLVaFBQUwMqK3x3JwTPPPINXXnkFQMXCwHzfyFI9/vjjWLdundQx\n6AHuf39OnDiB/v3769tu376NwsJCqeLVKjMzU3+u4ebmhuLiYty5c0fiVLWzhL/dcjtfMvQclcWc\nEUyaNAmffPKJ/vfy8nIsWbIEvXr1Qu/evbFy5UrcuwJEYmIiXFxcEBgYCKlXhqhv9mbNmmHy5MnY\nvHkzFi5ciOjoaGg0GrPPfePGDfzvf//D6tWr8cYbb2D27NmS5Abqn13ngw8+wPTp000ZtYr65nZw\ncMDVq1cxYsQITJs2DZMmTZIidpPT0M+Xjr29Pezs7FBQUIBXX30Vr776qiliE9WLoZ9zABg2bBgU\nCp4GNYbGeH8KCgrQrFkz/e/29vaNWhwZug+dOnXCjz/+CFEUkZmZiYsXL6KoqKjR8hort5R/u43x\nuQFMf75kaG5Dz1F5FDOAVqtFbGwsjhw5UuX2t99+G0eOHMHGjRuxatUq7N69u0qXaWJiIo4cOYLw\n8HCkp6dj3rx5yMnJkUX2Dh064KmnngIAtG/fHs7OzsjOzjb73C1atEC/fv1gZWWFtm3bomXLlrh6\n9arJchuSHagY3vr777+jb9++powMoOG5P/74Y/Tp0wfff2loO64AAAgmSURBVP899uzZgzfeeMOs\nv0WVu4a+T2vWrEF4eDhefPFFFBcXAwAuXbqE8PBwPPvssxg9erRJ94PoYYz5OSfja8z3x9HRscrf\nkMLCwirFnbntw9ixY+Hi4oKwsDB89tln6Ny5M1q0aGH0vMbOLcXfbmN+bkx5vmSs3Aafo5p+nXLL\nkJWVJT733HNicHCwGBAQIG7fvl0URVEsLS0VfX19xR9//FG/7a5du8TAwMAaH+eFF14Q//jjD1NE\n1jMk+6ZNm8QVK1aIoiiKV69eFYcNGyaWl5ebfe4DBw6IERERolarFfPy8sTg4GBRrVabJLeh2UVR\nFPft2ye+/vrrJsurY0jutWvXiuvXrxdFURSLi4vFoUOHijdv3jRp/qbCWMcjUaz4dz18+HDxxIkT\njR2bqF6M+TnX+euvv8RnnnmmsSI3KY31/owdO1YURVH84YcfxNmzZ4uiKIrnz58Xn332WbPeh1On\nTon79u0TRVEUL1y4IE6YMMHoeRsjt6n/dhv7c2Oq8yVj5jb0HJU9cw106tQpeHl5YdeuXXBwcNDf\nnpaWhpKSEvj7++tv8/f3R15eHrKysqo9jiAIJsl7L0Oyh4WF4fLlywgLC8O///1vxMXFQalUmn3u\nAQMGwMfHB+PGjcPkyZOxaNEiWFtbmyS3odkB4M8//0SbNm1MllfHkNzjx49Heno6nn/+eURERGDa\ntGmN+q1kU2as4xFQ8Y1hYWEh3nvvPf03h2q1utH3gag2xvyc30uKv8OWqLHeH52hQ4fC0dERoaGh\niImJweLFi40ZH4Bx9+Hxxx/HJ598gtDQUCxevBixsbFGz9sYuU39t9vYnxtTnS8ZM7eh56jyu6rR\nTISEhCAkJKTa7Tk5OVCpVHB0dNTf1qpVK4iiiGvXrqFt27ZVtpdiVkhDsqtUKrz33numjKtn6Gv+\n2muv4bXXXjNZ3nsZmn3ixIkmy3ovQ3Lb29vj3XffNWXcJstYxyMAWLZsWaNmJWooY37OdTw9PbFj\nx45GydvUmOL9WbRokXFD38eY++Dk5ISPPvqoUfPqGDO3qf92G/tzY6rzJWPnNuQclT1zRlZcXFxt\nmmMbGxsAMPtvt+WaXa65Aflml2vupobvEzUF/JybN0t4f+S6D3LNDcg3uxS5WcwZmUqlqvZm6X43\n9zXl5JpdrrkB+WaXa+6mhu8TNQX8nJs3S3h/5LoPcs0NyDe7FLlZzBlZ69atUVxcXGX62ZycHAiC\nAHd3dwmT1U6u2eWaG5Bvdrnmbmr4PlFTwM+5ebOE90eu+yDX3IB8s0uRm8WckXl7e0OlUiElJUV/\nW0pKClxcXCSZwKI+5JpdrrkB+WaXa+6mhu8TNQX8nJs3S3h/5LoPcs0NyDe7FLlZzBmZra0txo4d\ni6VLl+LkyZM4duwY3n77bUREREgdrVZyzS7X3IB8s8s1d1PD94maAn7OzZslvD9y3Qe55gbkm12K\n3JzN0gjun9Z4zpw5UKvViIyMhI2NDZ555hlMnjxZonQPJ9fscs0NyDe7XHM3NXyfqCng59y8WcL7\nI9d9kGtuQL7Zpc4tiKIoNtqjExERERERUaPgMEsiIiIiIiIZYjFHREREREQkQyzmiIiIiIiIZIjF\nHBERERERkQyxmCMiIiIiIpIhFnNEREREREQyxGKOiIiIiIhIhljMERERERERyRCLOSIiIiIiIhli\nMUeyFx4eDl9fX/z111/V2o4fPw5vb2+kp6dLkIyIiIiIqPGwmCOLUFpaitjY2BrbBEEwcRoiIiIi\nosbHYo4sQrNmzXD06FF89dVXUkchIiIiIjIJFnNkEQICAtCvXz+sWLEC+fn5UschIsLp06fxwgsv\noHv37ujVqxdmzJiBK1euSB2LiJoYb29vbN26tcpt4eHhiIqKkigRGROLObIYixcvRnFxMVasWCF1\nFCJq4u7cuYMpU6agdevWWL9+Pd544w2cO3cOs2bNkjoaERFZECupAxAZi6enJ6KiovDWW2/h6aef\nRp8+faSORERNVGZmJvLz8xEeHg4fHx8AQMuWLXHs2DGJkxERkSVhzxxZlPHjx8Pb2xuLFy+GWq2W\nOg4RNVFPPPEEnJycEBkZiaVLl+LgwYPo2rUrhzUREZFRsZgji6JUKrF06VL89ddfeP/99wEAoihK\nnIqImhoHBwd8+umn6Nu3L7788ktERkaiX79+2LRpk9TRiIjIgnCYJVmcLl264IUXXsD/+3//D61a\nteLSBEQkCS8vL7zzzjsoLy9HSkoKtm/fjrfffhsBAQHo1q2b1PGIqAnRarVVfi8qKoKTk5NEaciY\n2DNHFmnmzJlwc3PD6tWrpY5CRE3Q0aNH0bdvX9y8eRNWVlbo3bs35s+fD1EUcfXqVanjEVET4ujo\niJycHP3v+fn5yMzMlDARGRN75sgi2dnZITY2FpGRkeyZIyKT69q1KwRBQFRUFCZPngwrKyts3boV\nTk5O6NWrl9TxiKgJ6devH3bs2AFvb284OTnhgw8+gJ2dndSxyEjYM0cWoaaCbcCAARgxYgSLOSIy\nuWbNmmHTpk1QqVSYO3cupk+fDrVajc2bN6NFixZSxyOiJmTevHnw9/dHbGwsFi1ahCFDhmDYsGFS\nxyIjEUTODkFERERERCQ77JkjIiIiIiKSIRZzREREREREMsRijoiIiIiISIZYzBEREREREckQizki\nIiIiIiIZYjFHREREREQkQyzmiIiIiIiIZIjFHBERERERkQyxmCMiIiIiIpIhFnNEREREREQyxGKO\niIiIiIhIhljMERERERERydD/B+A7mqGy1SdZAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c0, cN, cs, cu = results.params.values\n", "\n", "N = np.logspace(4, 8, 100)\n", "s = np.linspace(0.01, 0.1, 100)\n", "u = np.logspace(-6, -10, 100)\n", "\n", "TN = results.predict(pd.DataFrame(dict(const=1, N=N, s=s[50], u=u[50])))\n", "Ts = results.predict(pd.DataFrame(dict(N=N[50], s=s, u=u[50], const=1)))\n", "Tu = results.predict(pd.DataFrame(dict(N=N[50], s=s[50], u=u, const=1)))\n", "\n", "TN = 1/(c0 + cN * N + cs * s[50] + cu * u[50])\n", "Ts = 1/(c0 + cN * N[50] + cs * s + cu * u[50])\n", "Tu = 1/(c0 + cN * N[50] + cs * s[50] + cu * u)\n", "\n", "fig, ax = plt.subplots(2, 3, figsize=(9, 8), sharey=False, sharex='col')\n", "ax[0,0].plot(N, TN)\n", "ax[0,1].plot(s, Ts)\n", "ax[0,2].plot(u, Tu)\n", "ax[1,0].plot(N, 1/TN)\n", "ax[1,1].plot(s, 1/Ts)\n", "ax[1,2].plot(u, 1/Tu)\n", "ax[0,0].set(ylabel='Adaptation time - T')\n", "ax[1,0].set(xscale='log', xlabel='N', ylabel='Adaptation rate ~ 1/T')\n", "ax[1,1].set(xlabel='s', ylabel='', xscale='log')\n", "ax[1,2].set(xscale='log', xlabel='u', ylabel='')\n", "\n", "fig.tight_layout()\n", "sns.despine()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This last figure shows the effect of increasing each of the paramters on the resulting **predicted** adaptaion time and rate." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda env:simarba]", "language": "python", "name": "conda-env-simarba-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }