{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C system headers (glibc/Xcode/Windows SDK) must be installed.\n", "In file included from input_line_4:36:\n", "/home/turra/micromamba/envs/mamba-python3.11/bin/../lib/gcc/x86_64-conda-linux-gnu/12.4.0/include/c++/cassert:44:10: fatal error: 'assert.h' file not found\n", "#include \n", " ^~~~~~~~~~\n", "input_line_35:1:10: fatal error: 'dlfcn.h' file not found\n", "#include \"dlfcn.h\"\n", " ^~~~~~~~~\n" ] } ], "source": [ "from matplotlib import pyplot as plt\n", "import numpy as np\n", "from scipy import stats\n", "import pandas as pd\n", "from IPython.display import HTML, IFrame, Image, SVG, Latex\n", "import ROOT\n", "from ROOT import RooFit, RooStats\n", "%matplotlib inline\n", "from ipywidgets import interact, interactive, fixed\n", "\n", "ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.NumIntegration)\n", "ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.Fitting)\n", "ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.Minimization)\n", "ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.InputArguments)\n", "ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.Eval)\n", "ROOT.RooMsgService.instance().getStream(1).removeTopic(ROOT.RooFit.DataHandling)\n", "ROOT.RooMsgService.instance().setGlobalKillBelow(ROOT.RooFit.ERROR)\n", "ROOT.RooMsgService.instance().setSilentMode(True)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from matplotlib import rcParams\n", "rcParams.update({'font.size': 18})\n", "HTML('')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "#from notebook.services.config import ConfigManager\n", "#cm = ConfigManager()\n", "#cm.update('livereveal', {\n", "# 'theme': 'sans',\n", "# 'transition': 'zoom',\n", "#})" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def iter_collection(rooAbsCollection):\n", " iterator = rooAbsCollection.createIterator()\n", " object = iterator.Next()\n", " while object:\n", " yield object\n", " object = iterator.Next()\n", "\n", "# new version, for newest ROOT\n", "def iter_collection(rooAbsCollection):\n", " for object in rooAbsCollection:\n", " yield object" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def RooDataSet2pandas(data):\n", " nevents = data.numEntries()\n", " columns = [x.GetName() for x in iter_collection(data.get(0))]\n", " return pd.DataFrame([[x.getVal() for x in iter_collection(data.get(ievent))] for ievent in xrange(nevents)], columns=columns)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def p2z(p_value, onetail=True):\n", " \"\"\" pvalue to significance \"\"\"\n", " if not onetail:\n", " p_value /= 2\n", " return stats.norm.isf(p_value) # inverse of the survival function\n", "\n", "def z2p(z, onetail=True):\n", " \"\"\" significance to pvalue \"\"\"\n", " if onetail:\n", " return stats.norm.sf(z)\n", " else:\n", " return stats.norm.sf(z) * 2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Lecture 2\n", "\n", "

ruggero.turra@mi.infn.it

\n", "
\n", "\n", "## Content of the lecture\n", "\n", " * Hypothesis testing\n", " * Type or errors\n", " * Likelihood ratio\n", " * Neyman–Pearson lemma\n", " * Exclusions\n", " * Profiled likelihood ratio" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Simple and composite hypothesis\n", "\n", "* A simple hypothesis is one in which all parameters of the distribution are specified" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Error type\n", "\n", " * Type I error: false positive (excessive credulity). Rate = $\\alpha = P(\\text{reject } H_0|H_0 \\text{ is true})$\n", " * Type II error: false negative (excessive skepticism). Rate = $\\beta = P(\\text{don't reject } H_0|H_0 \\text{ is false})$\n", " \n", " * Power of the test: $1-\\beta$\n", " * Remember that \"positive\" / \"negative\" refers to $H_1$, the alternative hypothesis, e.g. positive means reject $H_0$\n", " * If $H_0$ is background only Type I is false discovery, Type II is missed discovery" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/jpeg": 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"text/plain": [ "" ] }, "execution_count": 7, "metadata": { "image/jpeg": { "width": "70%" } }, "output_type": "execute_result" } ], "source": [ "Image(\"img/type-i-and-type-ii-errors.jpg\", width=\"70%\") # from https://effectsizefaq.files.wordpress.com/2010/05/type-i-and-type-ii-errors.jpg" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Question:\n", "what is $H_0$ and $H_1$ in this sketch?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "fig, ax = plt.subplots(figsize=(10, 7))\n", "x = np.linspace(-5, 5, 200)\n", "y0 = stats.norm.pdf(x, 0, 1)\n", "y1 = stats.norm.pdf(x, 1, 1)\n", "mask = x >= 2\n", "ax.plot(x, y0, x, y1, '-')\n", "ax.fill_between(x[mask], y0[mask], alpha=0.5)\n", "ax.fill_between(x[~mask], y1[~mask], alpha=0.5)\n", "ax.vlines(2, 0, 0.5, linestyle='--', lw=2)\n", "#ax.set_xticklabels([])\n", "#ax.set_yticklabels([])\n", "ax.set_xlabel(\"$q$\")\n", "ax.annotate(\"$f(q|H_1)$\", xy=(x[100], y1[100]), xytext=(0.2, 0.7), textcoords=\"figure fraction\", size=20,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='C1')\n", "ax.annotate(\"$f(q|H_0)$\", xy=(x[90], y0[90]), xytext=(0.3, 0.8), textcoords=\"figure fraction\", size=20,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='C0')\n", "ax.annotate(r\"$\\beta$\", xy=(x[100], 0.1), xytext=(0.1, 0.5), textcoords=\"figure fraction\", size=20,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='red')\n", "ax.annotate(r\"$\\alpha$\", xy=(x[142], 0.01), xytext=(0.8, 0.25), textcoords=\"figure fraction\", size=20,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\"), color='blue')\n", "ax.text(2, 0.4, r'$q_\\alpha$', rotation='vertical', ha='right', size=20)\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that to evaluate $\\beta = P(\\text{don't reject } H_0|H_0 \\text{ is false})$ we have used an alternative hypothesis $H_1$, but remember that if $H_0$ is false doesn't mean that $H_1$ is true.\n", "\n", "The region $q > q_\\alpha$ is the rejection region where we reject $H_0$. The complementary is the acceptance region." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Hypothesis testing in practice\n", "\n", " * Define the null hypothesis you want to try to reject\n", " * Define the observables (number of events in the signal region, ...)\n", " * Fix the rate of type I error $\\alpha$ of the test statistics (5%, $5\\sigma$, ...)\n", " * Define the test statistic (trying to maximize the power $1-\\beta$)\n", " * Find the rejection region ($q_{obs}>q_\\alpha$), which is the region where $H_0$ is rejected (p-value $<\\alpha$) (Reject $\\Leftrightarrow q_{obs} > q_\\alpha$)\n", " * Do the experiment\n", " * If the outcome is outside the acceptance region reject the null-hypothesis\n", " \n", "In complex example one don't compute the acceptance region, but just compute the observed p-value" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Exercize: Lady tasting tea (Fisher \"The Design of Experiments\" - 1935)\n", "\n", "A lady claimed to be able to tell whether the tea or the milk was added first to a cup. Fisher proposed to give her eight cups, four of each variety, in random order. What is the critical region at 5%? If we ask for a $5\\sigma$ evidence, what's the minimum amount of cups we have to prepare? (Hint: look at the [Hypergeometric distribution](https://en.wikipedia.org/wiki/Hypergeometric_distribution), answer should be 26)\n", "\n", "Are we interested in the rare case when the lady never guess? What is \"more extreme\" in this case?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Example: Lady tasting tea 2.0\n", "\n", "Suppose that the lady doesn't know how many cups of a kind are present. The acceptance region and the power (using p=90% as alternative hypothesis) can be computed easily from the binomial distribution.\n", "\n", "To compute the rejection region we have to find the minimum $q_\\alpha$ such that:\n", "\n", "$$\\sum_{n\\geq q_{\\alpha}} B(n|p=50\\%, N=8) \\leq \\alpha$$\n", "\n", "with $\\alpha=5\\%$. The solution can be found iteratively or inverting the formula (see the code). The lady has to guess correctly at least 7 cups. To compute the power simply using the definition\n", "\n", "$$\\text{power} = 1 - \\beta = 1 - P(\\text{don't reject $H_0$} | \\text{$H_0$ is false}) = 1 - \\sum_{n<7} B(n|p=90\\%, N=8) = 81\\%$$\n", "\n", "Since $H_1$ is not a simple hypothesis (it doesn't tell us automatically how much is $p$) we have to assume one particular $H_1$ ($p=90\\%$) to compute the power." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "N = np.arange(1, 70)\n", "alpha = np.sort(np.concatenate((np.logspace(-8, -3, 20), np.arange(0.001, 0.2, 0.002))))\n", "\n", "kalpha = stats.binom.isf(alpha.reshape(len(alpha), 1), N, 0.5)\n", "results_must_guess = kalpha.T + 1 \n", "power = stats.binom.sf(kalpha, N, 0.9).T\n", "min_N = np.ceil(np.log(alpha) / np.log(0.5))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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w4cN26/Lz86XNmzfb/l/emM9ms9l2zT/44AO7cfQOHDgg1apVSwoLC5Oys7Ntz+/atUsCIEVFRUlHjx61PX/16lWpdevWtvOt6FjJb775pm18wdzcXNvzhw8ftt3fDRs2tNvn9ddflwBIX3zxhcOYju7Lyl7rgoICSaPRSI0aNZJycnLstjeZTHYxrNe5Q4cOdvesJEmSwWCQfvvtt3KvQ8k4zl6v/Px8KSYmRgIgLViwwG7dnDlzbPdFYWFhhY5X3v37zTffSACkdu3a2b2eRUVF0rhx42zjLzqKuWXLFrvnreNIvvDCC3ZzB5w+fVpq2rSppFar7e7na9euSdHR0RIAae7cuaXGeNy2bZt048YN2/+9NUa39R69+WfR6tlnn5UASPPmzat0XkREROQ5Jcfofu6558rd/v3337dt/8knn0iSJEmHDh2yPffwww+XG+P69eu27Tt37lxq/VdffWVbv3z5ctvz/fr1kwBIjz76qCRJxWNtW7cr+X7ttttuc1hLS5IkrV271m5M7cost9xyS6l4JcfoNhgM5Z47EREV49AlpChqtRqLFy9GzZo1bc8lJycjOjoaf//9N55++mm73pVxcXEYOXIkAJQ5LIQjH374oV2PwMaNG9tm+t6xY0elYs2bNw/16tWz/b9Xr164/fbbcfHiRQwcOBBDhgyxrYuIiMC4ceMAwDY8gBxGjhxpd5zw8HDbcbKysvDJJ5/YeiMAxb2ISw5RUJ6LFy9iyZIlCAkJwbJly1CrVi279fHx8Wjfvr3t//PmzQMAvPHGG7jllltsz0dERODjjz+GIAj45JNPUFRUVOpYAwcOxPDhw53mEh0djZkzZ0KtVts9/8EHH8BgMGDWrFm488477dYlJyfj/vvvx759+3DgwAHb8++88w4A4P3330fr1q3t9gkLC8Ndd93lNI+brV27FkePHsXDDz+MZ555xq4Xert27TBt2jTo9Xq7bwx88sknAIp7+pbs/VyrVi289957FT621cKFCwEUj2McERFhe75169aYNGlSpeM5U9lrnZeXB6PRiDZt2iAqKspu+4CAALsYly9fBgB06dLF7p4FgJCQEHTu3FmWc/j222+RnZ2N7t27Y8KECXbrJk+ejPbt2+P8+fP44YcfKhXX2f1rvde+/vpru989gYGB+OCDDxAbG4tPP/3U9pVYZw4dOoT169ejS5cuePfdd+3mDmjSpAn+85//wGKx4NNPP7U9v3jxYly5cgWDBg3Cs88+W+qbJHfeeSciIyMrdZ7luXnYk5KLs68vW4dvcTYmubW3u6NhXoiIiEiZKjLXSMlvtFn/zluHE7l5vTMlv4VWcl8rR+N0m81m7Nq1y259vXr1bO9frNtdvXrVNkyjo/G5XR1yECgesq8sjr4BS0REjrGhmxSlUaNGdo2iAKBSqdCwYUMAwN13311qn6ZNmwIoboitqMDAwFLjqgFAs2bNKh0rKCgIPXr0KPV8kyZNAMiXc3kcHceaQ1JSEmrUqGG3LjIyErVq1apwDlu2bIHFYsE999xj16jviMlkwp49eyAIQqlhOgDgtttuQ+vWraHT6WxDFZR07733lhm/T58+Dgvmn3/+GQBw3333OdzP+rW/ffv2AQAuXLiA48ePo1atWnYfErjKevz777+/QscHYJv4xtHEOn379i3VKFyWc+fO4fz586hXr57DyX6GDh1a4Vjlqey1rlOnDurVq4effvoJ7733Hi5cuOA0dvPmzREWFoYvvvgCixcvdjievRysH2hZPyy7masffDm6fy9fvozDhw+jRYsWSEhIKLU+ODgYSUlJuHHjBk6dOlVm/JLX3tHQR47us19++QVA8XBCnjJkyBCMGjXK4dK1a9cy93U2pJMkSe5IlYiIiNzIYDCUu41er7c9tjZYh4eHO1xfkRgl97WKjY211WHWBux9+/bZGtZLvj+0PrZut3XrVlsd4uh9ZMlG9pSUFEiSVOGFc48QEcmHDd2kKNZx0m5m/QTf0XrrOkeTSDpTt27dUr2BgX8KlMrEio2NhUpV+kdJ7pzLU9ZxyrqujnpUO5KZmQngn0b6suTk5KCoqAgxMTGleuRaWXu0OmrwbNCgQZnxna23FomxsbEOe5FOnToVQHGPjMqeU0VYjz98+HCHx09KSrI7PlB8/oIgoH79+g5jlnctSrJeSzlilaey1xoAli5dipo1a+KFF15AfHw8mjRpgscff7zUBDwRERFYvHgxRFHEuHHjEB0djRYtWuBf//oX9uzZI9s5WK+Xs7Gey7pHy+LoOlvHlzx+/LjTXs7WiRhLXjNHrNf+xRdfdBindu3apeLIfa9XxOzZs7FkyRKHy5NPPulwH+vvYGdvZq1vlD05bjgRERFVzd9//12pbeLi4gAUv2ezKq8jAACcPHmyVIybWXtjp6en4+zZs7aG7AYNGtg6CZXcbu/evTAYDHYTUzpq6C75fsva85uIiDyPk1GSopQ3MaNcEzfKOWu1p3IubziDso7jyfOt7LaOtnHWOF7eeovFAkEQkJycXOb+N09GKdf1sVgsAIABAwaUOVlO8+bNZTmeM3LPyu7o3nPlWt911134+++/kZqaig0bNmDbtm1YunQpli5dimHDhuGbb76xbfvwww+jT58++O9//4tNmzZh27ZtWLBgARYsWIDnn38es2bNku385P4ZdnR/Wu+NunXrom/fvmXuf/OwQM5ide/e3e4N2c2sDd4lyX1vyK1Bgwa4fv06zp8/X2ooIQA4f/68bTsiIiLyDTt37kRRUVGZE1KWbEju0KEDgOJvBDZs2BBnz57FoUOHcOXKFURHRzuNYf3WGwB07NjR4TY9e/a0DR24ZcsW2wSTNw9HYv1/UVERdu3aZcuvcePGtm8bl9S2bVtEREQgLy8PP//8M/Lz8/nBPBGRF7Chm0hBrMWfo8LI2iPTW6y9hCvSI6NWrVoICgrCpUuXUFBQ4HBcOWsP15I9NaqqXr16OH36NObNm2c3PrUzlTmnih4fACZMmFDu8CtWdevWRUZGBjIzM0sN2wMUD0dSUdZr6WwfZ8+XvO9uZrFYcOnSpVLPV/ZaW0VEROCRRx6xDWmzZ88eDB06FN9++y0ef/xxDBgwwLZtdHQ0nnzySTz55JOQJAkbN27E8OHD8d577+Hxxx9Hy5YtK3xcR6w9fdLT0x2ul/Metd4bsbGxWLJkiSyxHnroITzzzDMV2qd+/fr466+/8Pfff7v9g5aqaNOmDQ4fPowDBw7gnnvuKbXeOua7o0ZwIiIiUqZr165h6dKlGDt2rMP1mzZtwp9//gkA6Ny5M2JjY23rhgwZgjlz5sBsNuP999/H22+/7TBGfn4+Pv74YwDFH+w/8MADDrcr2Rt748aNpcbntqpbty4SEhJw4sQJfPPNNzh+/LjD7awCAgLw8MMPY+HChcjNzcXbb7+NGTNmONyWiIjch0OXECmItUGt5NfurG4e3sHTevbsCbVajXXr1iErK6vMbQMDA9GpUydIkoSvv/661PqjR4/i8OHDCA8PR5s2bWTLsU+fPgCAH3/8sULbx8XFoUWLFsjJycH3339f7vbWBmGz2SzL8YF/xlNetWpVqXU///wzrl27VuFYDRs2RFxcHM6fP4/ff/+91PrvvvvO4X5l3Xe//vqrwwlyXDlXRzp16oTHHnsMAPDHH3843U4QBPTv3x8DBw4EULGvhJb3elkntl2xYoXD9dbnS06A66p69eohISEBR44ccdqwXlGuXHvrPosWLarQ9uVdO3exvr6O7tWDBw/izJkzaNmyJRo3buzRvIiIiKhqpk6dajd/iNXp06cxevRo2/+nTJlit37SpEm2TjOzZs1yWLMXFBRg5MiRtvcoQ4YMwa233uowj5iYGLRo0QJAcb1hHRbNUQO29bmlS5fannM0bInVK6+8YusAMnPmTMycObPMb+VevnwZb775Jo4cOeJ0GyIiqhw2dBMpiHVSyxkzZtiGJwCAL7/8EitXrvRWWgCKG4WTk5NRUFCAxx9/vFQD7IULF2y9LYHiohQAXn/9dZw5c8b2vE6nw9NPPw1JkjB+/Pgyv8JYWVOmTEFISAgmT56MtWvXllp/7do1fPzxxygoKLA999JLLwEAnn32WVtPEiu9Xo9ff/3V9v/atWsjMDAQp0+ftnt9rB566CE0b94cS5YswcyZM0s1EBcVFeH777+3a9C1Tg44Z84cW08Ra64vvPBCZU7fLt6UKVPsZps/evQoPvzwQ4f7WO+7L7/80m4ynDNnzthex5tV9lqfO3cOS5YsKTUZkdFotBsbEShu0Pz+++9LXb/r16/bGvArMnRFea/XsGHDEBMTgx07dpRqAJ43bx727duHevXqOe0RVFmvvvoqLBYLhgwZ4rCh/vTp0/j888/LjdOpUyf07t0bW7ZsweTJk0v1xBdFEZs2bbJNdAoATz75JGrXro21a9fio48+KjWp444dO5Cbm2v7v7W3+4kTJyp1jlX1wAMPoHHjxjh8+DDmzp1re16v12PixIkAgOeee86jOREREVHV3HPPPSgoKEDXrl0xduxYLFu2DCtWrMCzzz6Ltm3b2hqoH3zwwVITxDdq1MhWE5jNZgwZMgT3338/Fi9ejG+++QZvvfUWEhMTsWbNGgDFY2XPnz+/zHysDdjWD/SbNGnisLa8eTug7Ibu+vXr4+uvv0ZgYCAkScJLL72EhIQEvPTSS1i2bBm+++47fP7553j55ZfRs2dPxMXF4bXXXkNeXl6Z+RIRUSVIRAqQnp4uAZB69OjhcH2PHj0kAFJ6enqpdV988YUEQHr99dcrtA8AqWHDhg6PI2esUaNGSQCkLVu2lFq3ZcsWCYA0atQou+cvXbokRUdHSwCkZs2aSQ899JDUpk0bSa1WS5MnT3a4jyvHsWrYsKFUmV8DeXl5UufOnSUAUnh4uHTPPfdIw4YNkzp27CgFBASUum7jxo2TAEghISHSwIEDpaFDh9rOr1OnTpJer6/wuUiS89enpNWrV0shISESACkhIUG6//77pfvuu09q27atFBQUJAGQrl+/brfP008/LQGQ1Gq11L17d+nhhx+WevToIUVERJS6JwcPHiwBkFq1aiU99thj0pgxY6TPP//ctv748eNSgwYNJABS3bp1pX79+klDhw6VOnXqJNWoUUMCIP3www92MZ999lkJgKTRaKSBAwdKDz30kBQVFSW1bdtW6tSpk9N73xGDwSAlJSVJAKTo6Ghp6NCh0oABAySNRmM7z1tvvbXUfsnJyRIAKTIyUho8eLB01113SaGhodLQoUOd3ieVudYHDx6UAEihoaHSnXfeKT3yyCPSfffdZ7sfOnbsKBmNRkmSJOmHH36w5dK7d29p5MiR0sCBA6WIiAgJgPTAAw9U6FpIUvmv1y+//GI7h/bt20sPP/yw1K5dOwmAFBYWJm3fvr3Cxyrv/pUkSXrhhRds91pSUpI0dOhQqV+/flLz5s0lAFKbNm0qFPPSpUtS69atJQBSVFSUdNddd0nDhw+XunXrZrumc+fOtdvn119/lcLDwyUAUtOmTaVhw4ZJgwYNkho3blzqHlu9erUEQIqIiJAeeughacyYMdKYMWMqdB2s90tZ96z1Z9nR76Zdu3bZXpM77rhDGjZsmFS3bl0JgHT//fdLFoulQnkQERGR91jfh1hr92XLlkkajcb23M3LPffcIxUUFDiNt2DBAik4ONjp/gCkxMTECtXM3377rd1+zmqc7Oxsu+2aNm1aoXPftWuXrb4qb9FqtdKRI0dKxbC+/2STDRFR5bBHN5GCxMTEYPv27Rg0aBAuXryI9evXIzIyEj///HOFx3x2p/DwcGzZsgVz585FQkICtm3bhtTUVNy4cQOjR4/G0KFD7bZfuHAhli1bhnbt2mHbtm1Yu3Yt6tSpg7fffhu//vorQkNDZc/xwQcfxOHDhzF+/HiYTCasX78eW7duhdFoxMiRI5GamorIyEi7fT788EP88MMP6N27N44ePYrVq1cjPT0dvXv3xosvvmi37aefforHHnsMOTk5+Oqrr/DZZ59h27ZttvXNmzfHoUOHkJKSgjp16mDnzp346aefcOXKFdx555344osvbMNIWM2ZMwcLFizALbfcgp9//hm7du3CsGHDsGXLFmg0mkqdf0hICDZv3ozJkycjKCgI//3vf3HmzBm88847tnNxNNnh4sWL8dJLLyEiIgIbN27E2bNn8e9//9vh0DOuXOumTZti9uzZ6NmzJ86dO4fvv/8eu3btQqNGjTBv3jxs3brV1ru/U6dOeOutt9C+fXucOHECq1atwv79+9G6dWssXboU3377bYWvR3mvV+/evbFv3z48/PDDOH/+PL777jtcunQJjz76KNLS0mQZtqSkmTNnYvPmzbj33ntx/vx5/Pjjjzh48CBCQ0Px/PPPO+3RffMkkjExMdizZw/mzJmDW2+9Ffv27cOPP/6I8+fPo127dpg/fz4effRRu3169eqFQ4cOYdy4cTCbzfjxxx+xZ88e1KlTBzNmzLAbD/PBBx/E3LlzUa9ePaxduxafffYZPvvsM1mvhTNdunTBvn37MGTIEPz999/473//i5o1a2L27Nn47rvvoFKxdCEiIvI1jz32GPbt24cnn3wSTZo0QXBwMKKionDXXXdhxYoV+Omnn8qckH7ChAk4efIkXnzxRbRt2xY1atRAUFAQ6tati3vuuQdffPEFDh06hEaNGpWbS8+ePe1qK2e9tOvUqWM3sXpZvblL6tKlC06ePInly5dj2LBhaNy4MbRaLQICAhAVFYWkpCSMHTsW33zzDS5duoTbbrutQnGJiKh8giTd9P1lIiKqlr755huMGDECEyZMwIIFC7ydDlXA8OHD8e2332Lv3r3o0KGDt9MhIiIiqpCtW7fahv54/fXXkZKS4t2EiIiowgwGA7Zt24a0tDQcOHAAaWlpOHfuHAD5fqdnZ2dj1qxZSE1Nxblz5xASEoJWrVph1KhRGDNmTKnOXhUVUOXMiIhIUQ4dOoTWrVvb9Xz9448/bGN+P/LII95KjSrBYrHg0KFDEAQBTZo08XY6RERERERE5Af27t2Le+65x23x09LS0K9fP+Tk5AAAtFotdDoddu7ciZ07d2LVqlVYs2ZNpb/hDnAySiKiamfEiBGoV68e+vXrhxEjRqBTp05o164dzp07hwkTJsg+HAfJb/z48WjTpg1OnjyJfv36ORxuhoiIiIiIiMgdatasid69e+P555/H119/bTfUZVXk5uZi0KBByMnJQfPmzbFv3z7odDro9Xp89NFHCAwMxKZNmzB58mSX4rNHNxFRNTNp0iSsXLkShw4dwvXr1xEaGoouXbpgzJgxGDVqlLfTowqwjkM+bNgwfPjhh17OhoiIiIiIiPxF9+7dce3aNbvnXnrpJVliz549G5cuXUJISAjWrVuHxo0bAwCCgoIwceJE5OXl4d///jcWLVqEZ599Fs2aNatUfDZ0ExFVMxMnTsTEiRO9nQZVwfXr172dAhEREREREfkhtVrtttjLli0DUPxNdGsjd0mTJk3CO++8g/z8fKxYsQLTp0+vVHwOXUJEREREREREREREbnPixAnbpJYDBgxwuI1Wq7UNt7pp06ZKH4M9uomIiIiIiIhINj179oQkSd5Og4iIFOTo0aO2x4mJiU63S0xMxPr163Hs2LFKH4MN3VUkiiIuXLiA8PBwCILg7XSIiIiIyiVJEnQ6HeLi4qBS/fMFv8LCQhQVFXksj6CgIAQHB3vseOS7WHMTERGRr1FKzS1JUqn6SaPRQKPReCwHALhw4YLtcXx8vNPtrOvy8vKQn58PrVZb4WOwobuKLly4gPr163s7DSIiIqJKy8zMRL169QAUF9yNG2px6bLFY8ePjY1Feno6G7upXKy5iYiIyFd5u+bWarXIz8+3e+71119HSkqKx3IAAJ1OZ3scGhrqdLuS63Q6HRu6PSk8PBwAcPZAI0RofXPI8wLJc58iVVaBZPZ2Ck7pRNHbKXiMQXLfRARVlS8GeTsFp/Qy51YgefbT1srQicrNzSBzbvmidxrkDBb33esFbvo5MpjlufYForzlipzXstAS6PK+BWbXzstYyf2MltLbWwxGHHx0ga2OAYCioiJcumzB2bRGiAh3f02TpxPRsH0GioqK2NBN5bLeq/v3RUProzV3hMr13xfuphGUm5sK7MFPRES+KS9fRMPbMxRRc2dmZiIiIsL2vKd7c3sKG7qryNr1P0KrQkS4chsDyxIoKffNQoCCc4P/tHNDpeDXQRKVmxtEeX8nCAr+wMHsoCFNKSSZG0nNMserKLEKDarlxhbdE9tslieuReb8TGb5GrotVXhdTC5eH0slG7otZfx8OhoCQhsuQBvu/oYlkY1XVAnWe1WrVSHcA28K3SFCpdy8NYJyc1NBubkRERFVhBJq7oiICLuGbm8o2eBvMBic5mMwGBzuUxGsGoiIiIiIiIiIiIjIbeLi4myPs7KynG5nXRcREVGpYUsA9ugmIiIiohIskgiL5JnjEBERERH5I3+suRMTE22Pjx49ihYtWjjc7ujRowCAli1bVvoY7NFNRERERERERERERG6TkJCABg0aAAA2bNjgcBu9Xo8dO3YAAPr27VvpY7BHt0wKpCJFj3VdFoOCJ3yUm5InkNQrePxlnaInfFTuBAoGBU8emWdR9sRvck4gqfPS5JFyMyjs51BfxYkmC9w0LjgA6GUYg7sqk0xaGVwcg7uyk03a9pNprHwREkS4v3uJJ45B1Y8K7KnjDkbJJFssuSe2FGWeGIdjfhMRkRL4a82dnJyMt956CytXrsS0adPQqFEju/Xz589Hfn4+1Go1Ro4cWen4/CtPRERERDaiB/8REREREfkjpdfc169fx9WrV22L+L+OowaDwe75/Px8u/1SUlIgCAIEQUBGRkapuFOnTkVsbCwMBgMGDhyItLQ0AEBRUREWLFiAadOmAQDGjRuHZs2aVTpvNnQTEREREREREREREQCgXbt2iI6Oti2ZmZkAgPfee8/u+aeffrpScSMjI5GamopatWrh2LFjSEpKsk06+a9//QtFRUXo27cv5s6d61LeHLqEiIiIiGwskgSL5P6vOHriGERERERESuTPNXf79u3x559/YubMmUhNTUVmZibCwsKQmJiIUaNGYfTo0VCpXOubzYZuIiIiIiIiIiIiIgIAh8OOVERKSgpSUlLK3S4mJgZz5szBnDlzXDqOM2zoJiIiIiIbf50Yh4iIiIjIU1hzuwfH6CYiIiIiIiIiIiIin8Ye3T7KIJm9nYJTOtG1GV19jV5SezuFMunEIG+n4JRe1Hg7BacMknJzy7MEezsFpwwyv6Y6UcHnalHuPeIqvbny51QgBrohE8f0Znl+nxVa5MvZYK5aLKPZtRLMaKn8fo6OZbFYnG4vQoKFvUtIoa6KKhSKnumrE6uW9x6Vs37XCsqt80yS898vrggU5K25Rcj3XkXFfmNEROQi1tzuwYZuIiIiIrLh1yiJiIiIiNyLNbd78CNoIiIiIiIiIiIiIvJp7NFNRERERDYWSYJFcn/PD08cg4iIiIhIiVhzuwd7dBMRERERERERERGRT2OPbiIiIiKyEf+3eOI4RERERET+iDW3e7ChWyYFkhkBkuc6yOtE/7hV9ZK8s6zLSScqd7Z7uelFjbdTcMogKTe3PEuwt1NwyiDza6oTFXyuFnnP1eCln3292X33eoEY6LbYzujN8l3HQot8+RvMVY9lNFetvDJaKr9/ZY9pMiv37ytRWYIgwlO/hVUK/vKrQTLJGi9U8PzfgepAlLn5QMn3HBERkS9gQzcRERER2VggweKB2dk9cQwiIiIiIiVize0ebOgmIiIiIhuLVLx44jhERERERP6INbd78LtRREREREREREREROTT2KObiIiIiGw4MQ4RERERkXux5nYP9ugmIiIiIiIiIiIiIp/GHt0y0Ymiz35MopfU3k7BY3RikLdTcEovarydglMGSbm5yS3PEixbLIOCX1OdKN95uoPBIt+1Myj4574yCsRAb6dgR292z3UttLjvPA3mqsU2mqteNhktrsdw5fgms7O/8Wan+4gQYIFQ6WNVluiBY1D1oxKKF0+4Jspb3EerlFtzGyXnvxMqK0SQ9/e4RZL3dVAL7OtFRETex5rbPfhXnoiIiIiIiIiIiIh8Gnt0ExEREZGNKBUvnjgOEREREZE/Ys3tHmzoJiIiIiIbi4e+RumJYxARERERKRFrbvfg0CVERERERERERERE5NPYo5uIiIiIbNi7hIiIiIjIvVhzuwcbumVikNRQSewgDwA6McjbKXiEXtR4O4UyGSTl5pdnCfZ2Ck4ZFPy66kQFXzeLcq+b3PTm6neuerN7fm8XWgLdEhcADGZ5YxvN8pRERovrcVzNwWRWV2r7IrMaFjNrFvJNKkhQwzcHm7wmmmWLFaVS7tu4Askka7wQQd7f9xZJlC1WoKDc14GIiMgf8S8zEREREdmIkgBRcn/PD08cg4iIiIhIiVhzuwe78xARERERERERERGRT2OPbiIiIiKy4XiBRERERETuxZrbPdjQTUREREQ2Fqhg8cCX/ixuPwIRERERkTKx5nYPDl1CRERERERERERERD6NPbp9lE4M8nYKHqEXNd5OwSmDpNzc5JZnCfZ2Ck4ZFHyP6EQFXzeLcq8bABhk/B2nNyv7XCtKb1bW7/1CS6Bb4hrM8sY1mqte6hgtMsSoYh4ms7rS+xS5sA8ASB6aGEfys4lxSB5ZZi3CXLy3K6tJoM4jx3GFTjLLGi9ScM/v9OrOJPPrECjw7TkRkb9gze0e7NFNRERERERERERERD6NHxkTERERkQ0nxiEiIiIici/W3O7BHt1ERERERERERERE5NPYo5uIiIiIbCySChbJAzPAS24/BBERERGRIrHmdg82dBMRERGRjQgBoge+9CfCz6puIiIiIqL/Yc3tHmzolkm+GARJ9M2RYPSixtspeIxBUu655lmCvZ2CxxgUfM/pROW+DgaLfNfNIAbJFssd9Gbl3iMFYqC3U5BdocU952Qwu+9aGc3ylDBGS9XjVDUXk1nt8r5FLuxrMasgmn2zZiEKFCwIFDzzhi3THCJrvEYBhbLGk1O+ZJYtVqRK3t/9ZlhkjacRlPt3XIQoWywVRyklIiI/xIZuIiIiIrLhxDhERERERO7Fmts9+DEvEREREREREREREfk09ugmIiIiIhvPTYzjX+MFEhERERFZseZ2D/boJiIiIiIiIiIiIiKfxh7dRERERGRTPAO8+8fy88QxiIiIiIiUiDW3e7ChWyZ6MQgQ1d5OQxEMksbbKXhEniXY2ymUySAq93XQicq9dgaLcq+bQQzydgpO6c3KvW4FYqCs8fRm77wOhRZ5z6Mkg9l9sZ0xmt1Xghgt8sWWI0+TuWr1QZEL+1vMrn9pT4QKFg986U+Ef32NkuQRIIgI9NH3a1kW+f5+1FcXyRZLbjrRJGu8cJW8f6OMknz5aQTP//0kIqLqgTW3e/jk0CV5eXmYOXMmunTpgujoaGg0GtSrVw+9evVCSkoKbty44XC/7OxsTJkyBQkJCQgJCUFUVBS6d++OTz/9FJKfjVlDRERERFQW1txERERE5Et8rkf3li1b8PDDDyM7OxsAEBAQAK1Wi6ysLGRlZWHr1q24//770bZtW7v90tLS0K9fP+Tk5AAAtFotdDoddu7ciZ07d2LVqlVYs2YNNBrl9kokIiIicjdOjEMAa24iIiIid2LN7R4+1aN7165dGDhwILKzs9GnTx/s3LkTRqMR169fh8FgwP79+/HKK68gMjLSbr/c3FwMGjQIOTk5aN68Ofbt2wedTge9Xo+PPvoIgYGB2LRpEyZPnuylMyMiIiIiUgbW3ERERETki3ymR7fBYEBycjIKCgowZMgQfPvtt1Cp/mmnDwkJQfv27dG+fftS+86ePRuXLl1CSEgI1q1bh8aNGwMAgoKCMHHiROTl5eHf//43Fi1ahGeffRbNmjXz2HkRERERKYkIFUSOF+i3WHMTERERuR9rbvfwmR7dy5cvx5kzZxASEoJPPvnEruAuz7JlywAAI0aMsBXcJU2aNAlarRYWiwUrVqyQLWciIiIikteSJUsgCEK5yy+//OI0BseQdo41NxERERH5Kp9p6LYWzvfddx9q165d4f1OnDiBc+fOAQAGDBjgcButVovu3bsDADZt2lTFTImIiIh8l0USPLZUhUqlQkxMjNPF2RjQaWlpaNWqFebMmYOTJ08iICDANob02LFj0b9/fxiNxirl5stYcxMRERG5n6/U3L7GJ4YuMRqN2L9/PwCgR48eOHPmDN5++21s3LgRV65cQc2aNXHHHXdgwoQJpQrro0eP2h4nJiY6PUZiYiLWr1+PY8eOueckZGaQ/GMCnzxLsLdTcMog+sdrAAA6UcGvg0W5r4NBDPJ2Ck7pzcq9bgBQIAbKFktvVu7r4MuMZs+VEEaLvMeSM3eTWV3lGEUuxrCYK99fQfzfPmIZ+1qggsUDfSEsVfwaZf369ZGRkVGpfW4eQ3r58uVISkpCUVERFi9ejMmTJ9vGkP7444+rlJ8v8oWa+0RRLEKMnvn901aT6ZHjuCLbUvXfPSXFBYiyxpOTSsF9s0ySRdZ4gYJ8r6sIeV9TJb8ORES+yFdqbl/jE3+tMjIyUFRUBAA4f/48Wrdujc8//xxXrlxBaGgosrOzsWbNGtxzzz146qmn7Pa9cOGC7XF8fLzTY1jX5eXlIT8/3w1nQURERETedPMY0klJSQD+GUN6+vTpAIBFixbh5MmT3kzVK1hzExEREZEv84mG7uvXr9sez5gxA4GBgfj666+Rn5+P69ev49y5cxgxYgQA4JNPPsEHH3xg216n09keh4aGOj1GyXUl97mZ0WhEXl6e3UJERERUXYiSymOLp3EM6bKx5iYiIiLyjOpcc3uTT5ytKIp2jz/55BOMGDECgYHFX22vX78+VqxYgXbt2gEA3nrrLZjNZrfkMmPGDERGRtqW+vXru+U4RERERCQfjiFdPtbcREREROTLfKKhOzw83Pa4fv36GD58eKltVCoVpkyZAgC4evUq0tLSSu1rMBicHqPkupL73Ozll19Gbm6ubcnMVO7YfURERESVZR0v0BNLVVy5cgXt27eHVqtFSEgImjRpgkcffRRbt251uH1lxpAG4DPztsiJNTcRERGRZ/hKze1rfOJsS47z17x5c6fbtWjRwvb47NmzAIC4uDjbc1lZWU73ta6LiIiAVqt1up1Go0FERITdQkRERESuuXl4CqPRWKH9DAYDDhw4gKCgIIiiiPT0dKxYsQK9evXC6NGjS/U05hjS5WPNTURERES+zDNTlldRVFQU4uPjkZWVBUEQnG4nSf/MJGrdrmSPnaNHj9oV5iVZe/m0bNnSpRwLJA0ESd7Zzz0lzxLs7RQ8xiBqvJ2CUzrRj14Hi3JfB4MY5O0UnNKblXvdCsRAWePpzcp9HQot8p5rRRnM7juu0ez5csBoke+Y7sjfZK763/SiKsawmF3rjyC6uJ9tfwAWyXm9JRfrIBk3D0nx+uuvIyUlxel+cXFxeP311/Hggw8iISEBGo0GFosFv//+O15//XX88ssv+OKLLxAWFoYPP/zQtp+rY0iX1Rhb3fhCza2BGcGCVP6GMvirKFbWeC01F2WNJ6dLFvl+5uNkfktkkEyyxgsVvPN3vCJMkkW2WIGCvC+ECLH8jSpI5Rv97YiI3MrTNbe/8Jm/MH379gUAHD9+3K64Lun48eO2x9YJhhISEtCgQQMAwIYNGxzup9frsWPHDrvjEBEREfkjESqPLQCQmZlpN0TFyy+/XGZ+ffv2RUpKClq3bg2NpvgDQLVajS5dumDjxo247777AAAff/wxTp065d6LVQ2x5iYiIiJyP0/X3P7CZ872iSeeAFD8Zuibb74ptV4URcyZMwdA8dcub7/9dtu65ORkAMDKlSuRkZFRat/58+cjPz8farUaI0eOdEP2REREROTIzcNTWBuvXaFSqTB79mwAxbXh2rVrbevkHkO6umLNTURERES+ymcaurt3746HHnoIAPDUU0/hm2++gclU/DW2zMxMjBw5EgcPHgQAvP3221Cp/jm1qVOnIjY2FgaDAQMHDrRNmlNUVIQFCxZg2rRpAIBx48ahWbNmnjwtIiIiIkWxSCqPLe5wyy23oHbt2gCAM2fO2J6Xewzp6oo1NxEREZH7+XrNrVQ+MUa31ZIlS3D58mVs374dI0aMgEajQWhoKK5fv27b5rXXXsOoUaPs9ouMjERqair69euHY8eOISkpCeHh4SgsLLQV7n379sXcuXM9ej5ERERE5BmeGkO6OmDNTURERES+yKea9cPCwrBlyxYsXrwYd955J8LCwpCfn4/4+HiMGDECu3btwvTp0x3u2759e/z555+YPHkybr31VphMJoSFhaFbt25YvHgx1q9fX6WvyhIRERFVByIEjy3ucPr0aVy9ehXAP+NHAxxDujJYcxMRERG5l6/X3EolSM5mmaEKycvLQ2RkJBYeaI8QrU91kHcbg+gfb150YrC3UyiTwaLc18EgBnk7BY/Qm5X7GhSIgbLG05uV+5oWWuQ9V2+5Xhji7RTsGC3u+ZtnNLvvb6nJrJYtVpEMsSxm1/sbiC7uK/4vb7GgEJkTUpCbm4uIiAgA/9Q089I6eaSmKcg345n2e+xyKI8kSRAE58W6JEkYMmQIfvjhB6hUKhw7dgwJCQm29dOmTcNbb72F0NBQ/Pnnn2jUqJHd/rNmzcKLL74ItVqNY8eOcXgNBbHen8sP3obQcPl+ln1Vq6Bsb6fgMTFq5b7eIYJyawy14FN92qpE5Vv994jIj+TpLKjZ7IzP1dy+jH8RiIiIiMhGyeMFnj17Fh07dsTChQtx5swZWPtriKKIPXv2YMCAAfjhhx8AAOPHj7dr5AY4hjQRERERKYOSa25fxi7IRERERGRjgQoWD/SFcPUY+/btw759+wAAGo0G4eHh0Ol0MBqNtm2eeOIJzJs3r9S+HEOaiIiIiJRA6TW3r2JDNxERERH5hJiYGHz44YfYvXs3Dh06hCtXruD69esIDg5G48aN0aVLF4wePRpdu3Z1GsM6hvTMmTORmpqKzMxMhIWFITExEaNGjcLo0aOhUvnXGwIiIiIiouqADd1EREREZCNKAkTJ/ZPWuHKMkJAQPP3003j66aerdOyYmBjMmTMHc+bMqVIcIiIiIiJXKLnm9mXsrkJEREREREREREREPo09un2UQdR4OwWP0InB3k7BKYPFP14DADCIQd5OwSm9WbmvQ4EY6O0UnNKblfuaAkChRbnXzmBWbm6uMlrcUw4Yze4rM0xmtVviFskU12KuWl8C0cX9RRnyFz00XqDI/hbkgjRDY2hUnvk9fGf4Xx45jitOm6NkjXdr4DVZ4/mLAskka7wQQb572yKJssUCgECBTQdERHJize0e/nW2RERERERERERERFTt8GNZIiIiIrIRJRVEyQO9SzxwDCIiIiIiJWLN7R5s6CYiIiIiGwsEWOD+SWs8cQwiIiIiIiVize0e/tWsT0RERERERERERETVDnt0ExEREZENv0ZJRERERORerLndgw3dMjGIGkiib15OnRjs7RQ8xmDReDsFpwxikLdT8Bi9WbmvQ4Eo32z3ctOblXuPFFqUe90MZnlzM5q987veaFHW3xh3XQeTWS1rvCIZ41nM8hSJYhXjiC6ek2QWHD4m8iXBKhM0Hnq/tlffVNZ4XcNOyhpPThmmSNli3Rp4Q7ZYAHBDNMsaL0ql3JrFKMl3rhpB3r/TJhlzC5Q5NyIiIiv/atYnIiIiojJZ8M+Yge5diIiIiIj8ky/U3DqdDikpKbjtttug1WoRGRmJDh064D//+Q+KioqqdP7fffcdBg8ejLi4OAQFBSEsLAwJCQkYO3YsDh065HJcfpRKRERERERERERERACAs2fPomfPnsjIyAAAhIaGwmg0Yv/+/di/fz9WrFiBzZs3o2bNmpWKazQaMXToUKxdu9b2nFarRVFREU6ePImTJ0/i888/x+zZszF58uRK580e3URERERkYx0v0BMLEREREZE/UnLNbbFYMHjwYGRkZKBu3br4+eefodfrYTAYsHLlSoSHh+PgwYMYOXJkpWO/8847tkbuf/3rXzh//jx0Oh0KCgqwf/9+dOvWDaIoYsqUKdi/f3+l4/MdBhERERHZWCSVxxYiIiIiIn+k5Jp7yZIl+OOPPwAAq1evRp8+fQAAKpUKw4cPx8KFCwEA69evx+bNmysVe9myZQCAHj16YP78+YiPj7fFbt++PVJTU6HVaiFJElavXl3p3PkOg4iIiIiIiIiIiIiwdOlSAECvXr3QuXPnUutHjBiBxo0bA/in4bqiLl68CABISkpyuD4yMhLNmjUDAOTn51cqNsAxumWTLwbDLPJyAoDBovF2Ch5hEIO8nUKZ9Gb/eB0KxEBvp+CU3qzce6TQotzrBgAGs3z5Gc383Vwed10jk1ntlrgAUCRzbItZns/+RRniiFU4N8ksVPn4EgSIqHqcihyHqLKCVCZofLSrzv6CxrLF6hL6t2yx5HbWHC5rvCaBOlnj5Uom2WJFqZRb65llnvJXI8hXm4kQZYsFACr23yMiH6TUmttgMGDXrl0AgAEDBjjcRhAE9O/fHwsWLMCmTZsqFb9JkyY4fvw40tLSHK7Pzc3FyZMnAThvDC8L/yIQERERERERERER+bnjx49DFIs/kExMTHS6nXXdpUuXcO3atQrHf+qppwAAW7duxcSJE5GVlQUAkCQJBw4cwKBBg5Cfn49OnTq5NAY4G7qJiIiIyEbJ4wUSEREREVUHSq25L1y4YHtsHT/bkZLrSu5TnokTJ+KFF16ASqXCxx9/jHr16iE8PBzBwcFo3749/v77b7z00kv49ddfERBQ+W8e8x0GERERERERERERUTWVl5dntxiNRofb6XT/DBkWGhrqNF7JdSX3KY9KpcKMGTPw+eefQ6vVAigei7uoqAgAUFhYiNzcXOj1+grHtIvv0l5EREREVC2JkuCxhYiIiIjIH3m65q5fvz4iIyNty4wZM7xy3levXkXv3r3x+OOPo3Pnzti5cydu3LiBixcv4vvvv0d0dDQWLFiAO+64wzasSWVwhi4iIiIisrFABYsH+kJ44hhERERERErk6Zo7MzMTERERtuc1Go3D7cPD/5lU2mAwOI1bcl3JfcozatQobN26FT169MDGjRshCMUN8ZGRkXjggQfQtWtXtGrVCmfOnMFLL72E5cuXVzg2wIZun2WwOL4hqxuDqNyZzPVm/3gNAKBAlG+Wdbnpzcq9Rwotyr1uBrNycwMAo1m5f56MFu/k5s5rYjKr3RbbmSI3HtNilrdgFGWKJ8pwzpLZtV7QgklV5v+JfMXOq7cgoMAzNdg9MUc9chxXHCpsIGu8DiFnZI0nJzWU++2PXNEka7xIlbLrMyIi8l0RERF2Dd3OxMXF2R5nZWWhdevWDrcr2du65D5lOX78ONatWwcAmDJliq2Ru6Q6deogOTkZc+bMwffff49ly5Y53M4ZvsshIiIiIhsOXUJERERE5F5KrblbtGgBlaq4ufjoUecf+lvXxcbGIioqqkKxjx07ZnvctGlTp9vdeuutAIp7jV++fLlCsa3Y0E1ERERERERERETk50JDQ9G1a1cAwIYNGxxuI0kSNm7cCADo27dvhWNbG9AB4OzZs063y87Otj22TlhZ4WNUamsiIiIiqtZEqDy2EBERERH5IyXX3KNGjQIAbNmyBb///nup9atWrcKZM8XDniUnJ1c47u233257vGDBAofb6PV6LFu2DADQunVrhIWFVTg+wIZuIiIiIiIiIiIiIkJxQ/dtt90GSZIwZMgQbN68GQAgiiJWrVqFsWPHAgAGDBiA3r172+2bkpICQRAgCAIyMjLs1jVs2BCDBw8GAKxduxaPPfYYTp8+DUmSYDKZ8Ntvv6Fnz562RvQpU6ZUOnflzvZFRERERB5nkQRYPDB+tieOQURERESkREquuQMCArBmzRr06tULGRkZ6NOnD0JDQyGKIgoLCwEA7dq1w4oVKyod+/PPP0f//v2RlpaGL7/8El9++SVCQ0NRVFQEs9ls227q1KmV6i1uy73SexARERFRteWpiSI5GSURERER+Sul19yNGjXCkSNHMHv2bHz//fdIT09HYGAgWrVqhYcffhiTJk1CUFBQpePWrl0be/bswdKlS7Fq1SocOnQI165dQ0BAABo0aIAuXbpg/Pjx6Natm0t5s6FbJgZLEERLoLfTcIlBrPyN6av0Zo23U3CqQPTN+8cVerNy77lCBf8cG8zKzc1oVu6fE6NFublVhsms9nYKdoo8mI/FLO9Ia6LM8YpjVv16SOaqFbqCiSPSUfUXEmBGYIBn7vWtOQmyxutf+6is8eT0R2F92WLdHuJ8cilXZFnkrRvrq4tkjScnnWiSLVakSt73PSbJIlusQEHeGkKEKFssFUd3JSKyCQ8Px/Tp0zF9+vQK75OSkoKUlJQytwkICMCYMWMwZsyYKmboILbsEYmIiIjIZ0mSCqLk/jf6kgeOQURERESkRKy53cO/zpaIiIiIiIiIiIiIqh326CYiIiIiGwsEWOCBiXE8cAwiIiIiIiVize0e7NFNRERERERERERERD6NPbqJiIiIyEaUXJ+dvbLHISIiIiLyR6y53YMN3TIpEIMgioHeTkMR9GZ5Z/iWU4EfvUZ6s7wz1CtVoUW5r6nBrNzcjGZl//o3WpSbn9KvnSuKzGq3xLWYPfPFMdGNxxFlujaSuepFrGBy8TwdHbuMfEQPTYzjiWNQ9ROsNiFQ7Ztfwd16PUG2WP1rHZUtltyCYPF2CmXKtsj3Ny8uQJQtltzypSJZ42kF+d5bmCR575FAQb7XVIS8r6mKX6InIidYc7uHf50tEREREREREREREVU71a9bGhERERG5TIQA0QOT1njiGERERERESsSa2z3Yo5uIiIiIiIiIiIiIfBp7dBMRERGRjUUSYPHAxDieOAYRERERkRKx5nYP9ugmIiIiIiIiIiIiIp/GHt0yMZg1MJsDvZ2GIhSI/nEd9Gb5Zh5XukKLcl9Tgx/93BnNyv2VbbQoODeZr5vJrJY1XkUVeem4zljM7vmsXHRT3OLY8l9DyVz1HhKCSYZzliEPK84AT0qmUZkQpPavnkmOBAoWb6fg1J9FcbLGa6s5L2s8OV2R+WWIUfC9rVLwGK8WSZQtVqCg3JqWiKoX1tzu4TNnu2TJEgiCUO7yyy+/OI2RnZ2NKVOmICEhASEhIYiKikL37t3x6aefQpIkD54NERERkTKJECBKHlgU3Gjiz1hzExEREbkfa2738LmPK1UqFaKjo52u12g0Dp9PS0tDv379kJOTAwDQarXQ6XTYuXMndu7ciVWrVmHNmjVO9yciIiIi8hesuYmIiIjI1/hMj26r+vXr49KlS06X7t27l9onNzcXgwYNQk5ODpo3b459+/ZBp9NBr9fjo48+QmBgIDZt2oTJkyd74YyIiIiIlENCcc8Pdy+Sn/Uu8TWsuYmIiIjchzW3e/hcQ7crZs+ejUuXLiEkJATr1q1DUlISACAoKAgTJ07E9OnTAQCLFi3CyZMnvZkqEREREZFPYs1NRERERN7kFw3dy5YtAwCMGDECjRs3LrV+0qRJ0Gq1sFgsWLFihafTIyIiIlIMj4wV+L+FqhfW3EREREQVw5rbPXxujO7KOnHiBM6dOwcAGDBggMNttFotunfvjvXr12PTpk223iZKViAGejsFj9Cbg7ydgscUWvzjNQUAg1m552o0K/fXotGi4NwUfN1MZrW3U1A8i9k9n3uLbopbHNs9r6tklrcQFEwyXIMq5KSyOFkhuhySyCFP1dx7zjeCOjS4SrlWVJ/GJzxyHFfszLtV1nh9Iv+UNZ6c/iqqI2u82zTZssaT0zVRvslao1Xy/p0skEyyxQoRlPtegIiIfJvP9ei+cuUK2rdvD61Wi5CQEDRp0gSPPvootm7d6nD7o0eP2h4nJiY6jWtdd+zYMVnzJSIiIvIloqTy2ELKxZqbiIiIyH1Yc7uHz52twWDAgQMHEBQUBFEUkZ6ejhUrVqBXr14YPXo0zGaz3fYXLlywPY6Pj3ca17ouLy8P+fn5TrczGo3Iy8uzW4iIiIiqC36NkgDW3ERERETuxJrbPXymoTsuLg6vv/46Dh8+jMLCQly7dg0GgwG7du1Cnz59AABffPFFqVncdTqd7XFoaKjT+CXXldznZjNmzEBkZKRtqV+/vqunRERERESkKKy5iYiIiMhX+UxDd9++fZGSkoLWrVtDo9EAANRqNbp06YKNGzfivvvuAwB8/PHHOHXqlNvyePnll5Gbm2tbMjMz3XYsIiIiIk8TIXhsIeVhzU1ERETkfqy53cNnGrrLolKpMHv2bACAKIpYu3atbV14eLjtscFgcBqj5LqS+9xMo9EgIiLCbiEiIiIiqu5YcxMRERGRkgV4OwG53HLLLahduzauXr2KM2fO2J6Pi4uzPc7KynJaJGdlZQEAIiIioNVqK338AjEAFtE3Z4/Wm4O8nYLHFFp88zVyhcHsH+dqNCv315jRouDcFHzdAMBkVns7BaeKvJSbxey+z6ZFN8Z2fkzPXEfJLH8PBsEk4/WqYn4qi2v7CSbnx/XUWH7+Nl5gdeHtmjswQIQ6wMUbv5K2Zd4ia7wBjY7LGk9Ov+U3ky3WXRF/yhbLHU6ZomSL1TwwR7ZYcrsmmsvfqBJqq+R7b2GU5M1NI8hX15pkzi1QxtyIqHphze0e1aJHd1lKzvpecjb4m1nXtWzZ0u05ERERERFVJ6y5iYiIiMjbqk1D9+nTp3H16lUAQOPGjW3PJyQkoEGDBgCADRs2ONxXr9djx44dAIrHJSQiIiLyV5wBnsrCmpuIiIio6lhzu4dPNHRLklTu+ueffx5A8diBgwYNslufnJwMAFi5ciUyMjJK7T9//nzk5+dDrVZj5MiR8iRNRERE5INYdPsv1txEREREnsGa2z18oqH77Nmz6NixIxYuXIgzZ87YinBRFLFnzx4MGDAAP/zwAwBg/PjxSEhIsNt/6tSpiI2NhcFgwMCBA5GWlgYAKCoqwoIFCzBt2jQAwLhx49CsmXzj0xERERER+QrW3ERERETky9w2M8KVK1ewc+dOqNVq3HnnnahRo0aV4u3btw/79u0DUDwLe3h4OHQ6HYxGo22bJ554AvPmzSu1b2RkJFJTU9GvXz8cO3YMSUlJCA8PR2FhIUwmE4Dir0/OnTu3SjkSERER+TpOjOM75K63AdbcRERERJ7Amts9XG7o3r9/Pz7++GO0atUKU6ZMsVu3cuVKjBkzBoWFhQCAsLAwLF26FA888IBLx4qJicGHH36I3bt349ChQ7hy5QquX7+O4OBgNG7cGF26dMHo0aPRtWtXpzHat2+PP//8EzNnzkRqaioyMzMRFhaGxMREjBo1CqNHj4ZK5XoHd4MlCCZzkMv7VyeFFvlm5FYyg9k/zhMAjGblzhZutCg3N7kp+XUwmdXeTsGpIgXnVhmiWVlfwhI9eF0ls/uLM8Ek8/WVIWeVpWr7CybnOZQ9QAUphSfrbcA3am5NoBnqQN/8vf5r1q2yxRpQ75hsseS2Sydvb/2e4cdljSen06YassZrHnRD1nhyUgvKbSgxo4p/MEvQCPK+xxMhyhpP5Rtfyici8hqXW02++uorLF26FLNnz7Z7/sKFCxgzZgwKCgpsz+Xn5+ORRx7B0aNH0bRp00ofKyQkBE8//TSefvppV9MFUFy8z5kzB3PmzKlSHCIiIqLqSgIgwv0NGmxsL58n622ANTcRERGRp7Dmdg+XPw7cvn07AODee++1e37RokUoKChA69atcerUKWRmZqJHjx4oKipy+BVHIiIiIqKqePfddyEIgm0pS3Z2NqZMmYKEhASEhIQgKioK3bt3x6efflruZIyexnqbiIiIiKjiXO7RffHiRQiCgIYNG9o9/9NPP0EQBLz11lu23iQffPAB2rZti19//bVq2RIRERGRW/naeIEnTpzA9OnTK7RtWloa+vXrh5ycHACAVquFTqfDzp07sXPnTqxatQpr1qyBRqORJbeqYr1NREREVD35Ws3tK1zu0Z2Tk4MaNWogIOCftvKCggIcOnQIGo0Gffv2tT3funVrBAUFISMjo0rJEhEREZF7WYtuTyxVzlUUbeNUd+7cucxtc3NzMWjQIOTk5KB58+bYt28fdDod9Ho9PvroIwQGBmLTpk2YPHlylfOSC+ttIiIiourJl2puX+JyQ3dAQADy8vLsntu3bx8sFguSkpIQFGQ/MaNWq4XZbHb1cEREREREdj788EPs2rULI0eOtGv0dWT27Nm4dOkSQkJCsG7dOiQlJQEAgoKCMHHiRFuv8EWLFuHkyZNuz70iWG8TEREREVWcy0OXNGrUCMePH8e+ffvQoUMHAMCaNWsgCEKpmdgtFgtyc3MRFxdXtWzJptAi72zQSmUw+8d5AoDR7PKPo88xWpR7rv7yOpjMam+nUKYiGfOzmDk7fXlEL9wPktl9PQsEk5tecxlzVlmqHkMwuZaPYBYglHEuvvI1yvT0dLzyyiuoVasW5s6di/nz55e5/bJlywAAI0aMQOPGjUutnzRpEt555x3k5+djxYoVFR4OxZ1Yb5eWd7ImVMHBHjlWdKsrHjmOKzZfTJA13uB6f8gaT057Da5NrurMnWF/yRpPThmmMNliNQ00yBYLAHJFk2yxIlXKfY9nlOQ7TwDQCPKeqwhRtlgq1/s9EpEMfKXm9jUu/2a7++67IUkSJk6ciN9//x0//vgjFi1aBAAYPHiw3bZ//PEHLBYL6tWrV7VsiYiIiIgAjB07Fnq9HnPmzEF0dHSZ2544cQLnzp0DAAwYMMDhNlqtFt27dwcAbNq0Sd5kXcR6m4iIiIio4lzuujh16lQsXboUaWlp6NKlCwBAkiTcddddtv9bWSfMKW/sRCIiIiLyLl/oXbJ48WJs3rwZffr0QXJycrnbHz161PY4MTHR6XaJiYlYv349jh075nJucmK9TURERFQ9+ULN7Ytc7tEdHx+PLVu2oFevXggODkZsbCzGjh2L1atX220nSRK++OILSJKEXr16VTlhIiIiIqo+8vLy7Baj0Vjm9llZWXj++ecREhKChQsXVugYFy5csD2Oj493up11XV5eHvLz8ysU251YbxMRERERVVyVBqNt06YNfvnllzK3EUURmzdvBlD2GwsiIiIi8j5JEiB5oOeH9Rj169e3e/71119HSkqK0/3Gjx+P3NxczJw5E02aNKnQsXQ6ne1xaGio0+1KrtPpdNBqtRWK706st4mIiIiqH0/X3P7C7bOuqdVqNGzY0N2HISIiIiIZiBAgwgNfo/zfMTIzMxEREWF7XqPRON3nyy+/xE8//YS2bdviueeec3uOvoL1NhEREZFv8XTN7S9kbei2WCy4du0aACAqKgpqtVrO8ERERERUzURERNg1dDtz+fJlPPvss1Cr1Vi8eDECAipexoaHh9seGwwGp8czGAwO91ES1ttERERERI5VuaFbr9fjk08+wcqVK3HkyBGYzebiwAEBaN26NUaMGIHx48cr4quf7lRoCYTFEujtNFxiMPtm3q4wmt3+JQbFMFr841yV/JqazMptfChScG4AYDG7PIWE24leyk1U2Gsmmd3TM0Awefj6ynweKos8cQRT1fISqnBeSp0Y58UXX0ROTg6eeuopNG/evNQY2kVFRbbH1nVBQUEICgpCXFycbV1WVpbThu6srCwAxY3vSqpdWW//QwyQgEDJI8fKPllb1ngNW16UNZ6cfr7UXLZYg+L+kC2WO/xe0FS2WN1DT8oWS26ZZuffjnFFw4Cy50+oDJ1oki0WAESq5D1XIiJPUGrN7euq1EJ06NAhPPDAAzh37hwkyb7gNJlMSEtLw4EDB/DRRx/h+++/R7t27aqULBERERH5p/T0dADAggULsGDBgjK3tfbG/r//+z+8//77SExMtK07evQoWrRo4XC/o0ePAgBatmwpR8qyYL1NRERERFQxLjd0X7hwAX369MG1a9cQFBSEhx56CHfddZdtApysrCxs2bIF3333Hc6ePYu7774bR44csetRQ0RERETKUh0nxklISECDBg1w7tw5bNiwAUOHDi21jV6vx44dOwAAffv29VhuZWG9TURERFQ9VceaWwlc/n7wm2++iWvXrqFhw4Y4dOgQvvzyS4wePRr9+vVDv379MHr0aCxfvhyHDh1Cw4YNcf36dbz55pty5k5EREREfmLr1q2QJMnp8vrrr9u2tT73/vvv255LTk4GAKxcuRIZGRml4s+fPx/5+flQq9UYOXKku0+nQlhvExERERFVnMsN3evWrYMgCFi8eDGaN3c+pltCQgIWL14MSZLw008/uXo4IiIiIvIA63iBnlg8aerUqYiNjYXBYMDAgQORlpYGoHhs7wULFmDatGkAgHHjxqFZs2Yezc0Z1ttERERE1VN1rbm9zeWhS7KzsxESEoI+ffqUu22fPn0QGhqKK1euuHo4IiIiIvKA6vo1ysjISKSmpqJfv344duwYkpKSEB4ejsLCQphMxROj9e3bF3PnzvVoXmVhvU1ERERUPVXXmtvbXG7ojo6ORl5eXoW3V6lUiIqKcvVwildgDoDJHOjtNBTBaK7SHKc+w2jxj/MElP2amsxqb6fgMUUKPleL2eUvCLmdqODclEIyu6f4EUweuvZuyh8AVBZ54wmmqucqVPF8VSZAMlU5DZ/Uvn17/Pnnn5g5cyZSU1ORmZmJsLAwJCYmYtSoURg9ejRUKuX8zmC9XZoUIEEKkMrfUIEyTsbKFqtFq0zZYslt8xXn3z5wxeCYI7LGk1NaYSNZ43UKOS1rPDmpBeU2lORLRbLF0gpBssUCAJMkbyERKMj3fkCEKFssAFC5PmAAEZFsXP5N1Lt3b+Tn59u+9lmW/fv3Iz8/H71793b1cERERETkAZKHvkIpd++SlJQU29jcZYmJicGcOXNw8uRJFBQU4Pr169ixYweefPJJRTVyA6y3iYiIiKorX625lc7lav7VV19FWFgYxo4di5ycHKfbXbt2DePGjUNERAReeeUVVw9HRERERORXWG8TEREREVWcy+MRBAUF4dNPP8X48ePRokULPPXUU+jVqxfi4+MhCALOnz+PLVu24JNPPoHJZMLixYsRFBSEc+fOlYrVoEGDKp0EEREREclDAlBOp2jZjkNlY71NREREVD2x5nYPlxu6GzdubPf/t956C2+99ZbT7UeMGOHweUEQYDabXU2DiIiIiKhaYr1NRERERFRxLjd0lzf+oafjEBEREVHViRAgwP1j+YkeOIavY71NREREVD2x5nYPlxu609PT5czD5xnNAbCYXb6c5ITR4j/X1OhH94/JLN9s4XIrUnBucrKYlTXh2s1EBecneukekczuK1AEk4KutxvPU2VxT1zBJG/OQhWvgcpUteNLHpq0xt8mxnEF6+3SpCARUpDo7TS87tipeFnj3d78rKzx5PTz1ZayxhscfVjWeHI6VCjfEEMdQjJkiwUAlyzy/c6OU3C5bZCq+Ef0JlohSNZ4Fkm+33+Bgv+8/yRSItbc7uHyb7aGDRvKmQcREREREZXAepuIiIiIqOL4ER4RERER2YiSAMEDPT9EP+tdQkRERERkxZrbPRT0XWUiIiIiIiIiIiIiospzuUf3smXLXNovOTnZ1UMSERERkZtJUvHiieNQ2VhvExEREVVPrLndw+WG7scffxyCULnu74IgsPAmIiIiIqoA1ttERERERBXnckN3gwYNyiy8c3NzcePGDQBAWFgYateu7eqhyAGjhcOru8Jo9p/rZjIreDpzGRUp+DwtZuWODiUqODe5iTLfI5LZO2OcCSaFvWZeug5WKot74gom95yXINP1UpmquP//rptUxvXjDPDKwXq7tIhjgVBrAj1yrLx2RR45jhIcPN1AtlhdE/6WLZY7bL7eQrZYA2sdkS2W3P4wxssar70mU7ZYV2X+Gx6jVu77ASUzSWZZ4wUK/vNem0gOrLndw+XfRBkZGeVuc+rUKbz11ltYtWoVZs6ciWHDhrl6OCIiIiLyABbdysF6m4iIiKh6Ys3tHm79yO3WW2/F0qVLERgYiOTkZDRr1gxt27Z15yGJiIiIiPwG620iIiIiomIe+R50SkoKioqKMGPGDE8cjoiIiIhcJEqCxxaSD+ttIiIiIt/Bmts9PNLQXa9ePdSoUQPbtm3zxOGIiIiIiPwK620iIiIi8ncemS2gsLAQeXl5CAz0zMQxREREROQaSSpePHEckg/rbSIiIiLfwZrbPTzS0P3FF19AFEXEx8s787OSGC0BsFh8c5Zho9k38/Y2k9l/ZvcuUvC5Wswe+WKKIogKPldRwfeIZPavr2q5xAvXSGXxzHEEk3vOTZD5mqlMMsXx0HUl5fGHehsAxABA8FDpqv0jSNZ4hnYFssZTqt2nG8sa765mJ2WNJ6dfb7SQNd49NQ/LGk9OgYJyW0quiWbZYtVWyfthoVGSLzcACFXJ+3uJiKi6cblMPHfuXJnrCwsLkZmZidWrV+Pzzz+HIAh44IEHXD0cEREREXlAce8ST8wA7/ZD+DzW20RERETVE2tu93C5obtx44p/Ui9JElq1aoVXX33V1cMRERERkQdIkuChopvftigP620iIiKi6ok1t3u4/D14SZIqtDRp0gSvvvoq9uzZg8jISDlzJyIiIiKqtlhvExERERFVnMs9utPT08sOHBCAmjVrIjQ01NVDEBEREZGHSf9bPHEcKhvrbSIiIqLqiTW3e7jc0N2wYUM58yAiIiIiohJYbxMRERGRt+h0OvznP//B6tWrkZ6eDrVajWbNmmHEiBGYNGkSgoKqNkHupUuXMH/+fKxbtw7p6ekoKChAnTp10KJFC/Ts2RNTpkxBYGDlJgn20Jzl1V+RJQAWMy8nAJjMam+n4JOK/Oi6Wcwuj5rkdqKCc5OTqPD7TTIrdxwxweSle0Rh10Rl8dyxBJP7z11ww/VVmWSOV8VrXjIfyex8O44XSEomBgJC5d7vKEbw0RDZYpna6WWLpXTb0m+RNV7/psdljSenLbktZYs1oOZh2WIBwF+mWrLFahmYI1ssuV0T5f3jHa2uWiPQzYySfPlpZP5lKkKULZbK9VF2iXyG0mvus2fPomfPnsjIyAAAhIaGwmg0Yv/+/di/fz9WrFiBzZs3o2bNmi7F/+abbzBu3Djk5eUBAIKCghASEoJz587h3Llz2LhxIyZMmIAaNWpUKq7Lvz2Kiopw5MgR/PXXX+Vu+9dff+HIkSMwmWR+xwfg3XffhSAItqUs2dnZmDJlChISEhASEoKoqCh0794dn376KSR/m4aUiIiIiBSN9TYREREReZrFYsHgwYORkZGBunXr4ueff4Zer4fBYMDKlSsRHh6OgwcPYuTIkS7FX7VqFR555BHk5eVh+PDhOHjwIIxGI27cuAGdTocdO3Zg8uTJle7NDVShofubb75Bu3bt8P7775e77dtvv4127drhu+++c/VwDp04cQLTp0+v0LZpaWlo1aoV5syZg5MnTyIgIAA6nQ47d+7E2LFj0b9/fxiNRlnzIyIiIvI5kgcXKhPrbSIiIqJqSsE195IlS/DHH38AAFavXo0+ffoAAFQqFYYPH46FCxcCANavX4/NmzdXKvbFixcxfvx4iKKIyZMnY+XKlWjbtq1tvVarRbdu3TBnzhyEhYVVOneXG7pXr14NAHjsscfK3XbMmDGQJEnWwlsURYwZMwaFhYXo3Llzmdvm5uZi0KBByMnJQfPmzbFv3z7odDro9Xp89NFHCAwMxKZNmzB58mTZ8iMiIiLySf/7GqW7F3DoknKx3iYiIiKqphRccy9duhQA0KtXL4c14IgRI9C4cWMAwLJlyyoVe968ebh+/Trq1auHd999t9K5lcflhu6jR48CANq0aVPutu3btwcA26cBcvjwww+xa9cujBw5En379i1z29mzZ+PSpUsICQnBunXrkJSUBKB4/JeJEyfaeqksWrQIJ0+elC1HIiIiIiJXsd4mIiIiIk8yGAzYtWsXAGDAgAEOtxEEAf379wcAbNq0qVLxrQ3jjz76aJUns3TE5YbuCxcuIDIyElqtttxtw8PDUaNGDVy8eNHVw9lJT0/HK6+8glq1amHu3Lnlbm+9iCU/cShp0qRJ0Gq1sFgsWLFihSw5EhEREfkiSfLcQmVjvU1ERERUPSm15j5+/DhEsXhy2cTERKfbWdddunQJ165dq1Ds9PR0XLhwAQDQo0cPHDx4EMOHD0dsbCw0Gg3q16+PESNGYPfu3ZVLuoQAV3cMCgpCQUFBhbaVJAkFBQUuDSLuyNixY6HX6/Hxxx8jOjq6zG1PnDiBc+fOAXD+SYRWq0X37t2xfv16bNq0qcLjEJZkMqshmtWV3o/KVuRH19Ri9p+ZpUU/OVd/+p0gmZU7BIFg8o/7rSpUFvfEFUzeuS8EN92PKvnn+JPt2rsjN/I+1tuliYGAIM8p+jT10cqPWVkWVbtcWeMpWViAf4wTHywo9w/DGXOErPGaB+pkjSenXFHe16GmSiNbLJMkbwEYKMj33keEKFusylK53h+UqFqwNkQDQHx8vNPtSq67cOECoqKiyo1d8lt9e/fuxVtvvQWTyYTg4GCEhITg/Pnz+Oabb/Dtt9/i7bffxssvv1zp/F3+CW7cuDGKiooq1Mr+22+/wWg0omHDhq4ezmbx4sXYvHkz+vTpg+Tk5HK3t37lE6jYJxHHjh2rco5EREREvsoTYwXaxgykMrHeJiIiIqqePF1z5+Xl2S3OJgjX6f758DA0NNRp/iXXldynLNevX7c9nj59OmJiYrBhwwbo9XrcuHEDx48fR+/evSFJEv7973/jxx9/rFDcklxu6L777rshSRJeeuklmM1mp9uZzWa8/PLLEASh3LH9ypOVlYXnn38eISEhthk+y1PZTyLy8vKQn59fpTyJiIiIiKqK9TYRERERyaF+/fqIjIy0LTNmzPB4DtYhUayPV61ahX79+kGlKm6ebt68Of773/8iLi4OAJCSklLpY7jc0P3MM88gODgYO3fuRJ8+fXDw4MFS2xw4cAC9e/fGzp07odFo8H//93+uHg4AMH78eOTm5iIlJQVNmjSp0D5yfxJhNBpLfQpCREREVG1YZ2f3xEJl8td6G2DNTURERNWch2vuzMxM5Obm2hZnw4KEh4fbHhsMBqfpl1xXcp+ylNyuW7du6NSpU6ltwsLC8K9//QsAcPjwYWRnZ1cotpXLY3TXq1cPCxcuxOOPP44dO3YgKSkJsbGxaNiwIQRBQHp6OrKzsyFJEgRBwKJFi9CgQQNXD4cvv/wSP/30E9q2bYvnnnvO5ThVNWPGDJfHFCQiIiJSOk9NFMnJKMvnr/U2wJqbiIiIqjdP19wRERGIiCh/jgRrb2qg+Jt+rVu3drhdVlaWw33KUvKbfy1atHC6Xcl1Z8+eRUxMTIXiA1Xo0Q0Ajz32GNauXYuGDRtCkiRcvHgRe/bswe7du3Hp0iVIkoQmTZrgp59+wqOPPurycS5fvoxnn30WarUaixcvRkBAxdvn5f4k4uWXX7b7BCQzM7PCuRARERERVYY/1tsAa24iIiIib2jRooVtKJGS87DczLouNja2QhNRAkDLli2hVhdPXCsIzr/dKZX4BKCs7RxxuUe31T333INTp05hy5Yt+O2333Dp0iUAQN26ddGlSxf06tXLdoFc9eKLLyInJwdPPfUUmjdvXmpMv6KiIttj67qgoCAEBQWV+iTC2acX1k8iIiIioNVqneai0Wig0cg30zERERGRokj/WzxxHKoQf6u3AdbcREREVM0ptOYODQ1F165dsWPHDmzYsAHPP/986ZCShI0bNwJApeaHCQ4Oxp133oktW7aUOTn58ePHARQ3cjdq1KhS+Ve5oRsA1Go1+vTpgz59+sgRrpT09HQAwIIFC7BgwYIyt7X2Dvm///s/vP/++3Yzvx89etRp13jrJxEtW7aUI2W3KzKrvZ2CT7KYq/Ym0JeIfnKuoh/9LEhm5Y5nK5gUfL8p+LpVhsrivtiCSTnXSPDA66UyuTm+zK9VVfMVHMxh6Og5UjbW28Wij5gREOiZGzg7SZa3Sj7B8kekbLFCbr8mWyx32JDp/KvSlfVgw8OyxZLbzvwEWeP1CXfeq8/bMszBssVqElAoWywiIl81atQo7NixA1u2bMHvv/+OO+64w279qlWrcObMGQBAcnJypWI/8cQT2LJlC3bu3Indu3ejc+fOdusNBoOtFr3jjjsQHR1dqfgKbpmQR0JCgm2swg0bNjjcRq/XY8eOHQAq90kEERERUXUjSYLHFqoeWG8TERERVY6Sa+5Ro0bhtttugyRJGDJkCDZv3gwAEEURq1atwtixYwEAAwYMQO/eve32TUlJgSAIEAQBGRkZpWKPHDkSHTt2BAAMHz4cGzduhCiKAIC//voL9957Ly5cuACVSoW333670rn7REP31q1bIUmS0+X111+3bWt97v3337c9Z/10YeXKlQ4v8vz585Gfnw+1Wo2RI0e6+3SIiIiIiBSF9TYRERERAUBAQADWrFmDRo0aISsrC3369EFYWBjCwsIwbNgw5OXloV27dlixYkWlY6tUKvz3v/9Fy5YtkZmZif79+0Or1aJGjRpo0aIFNm/ejMDAQHzyySe46667Kh+/0nv4oKlTpyI2NhYGgwEDBw5EWloagOKxBhcsWIBp06YBAMaNG4dmzZp5M1UiIiIi75M8sFC1wnqbiIiIqJIUXHM3atQIR44cwWuvvYbExEQIgoDAwEC0b98es2fPxp49e1CzZk2XYsfGxuLAgQOYPXs2OnTogKCgIBQUFKBRo0YYPXo0Dhw4YOs1Xll+MfBcZGQkUlNT0a9fPxw7dgxJSUkIDw9HYWEhTKbigS/79u2LuXPnejlTIiIiIu/y1LAiHLqkemG9TURERFRxvlBzh4eHY/r06Zg+fXqF90lJSUFKSkq522k0GkyZMgVTpkxxOT9H/KJHNwC0b98ef/75JyZPnoxbb70VJpMJYWFh6NatGxYvXoz169dzZnciIiIiIhex3iYiIiIibxIkSeKXR6sgLy8PkZGRaLr8ZahD5Zvt2ZMsZr/5vENWoh9dN9Gs9nYKHiOZ/aOHoWBS+P2r4NdBZfHOcQWTsq6J4OXXSGXy0HHc9HrLmb9grvw+FmMhTrz/b+Tm5iIiIgLAPzVN/U9ehyrE/TWNWFCIzAnT7XIgcsZ6f94x+E0EBPpmzZ3dwX/qKTnVanfZ2yl4zEMNDng7BY/oEXbC2yl4TKMADxUsLogQlPvBY6DgF4MPkB/I01lQs9kZ1twepPCWDiIiIiIiIiIiIiKislWooXvevHn47LPP3J0LEREREXmd4MGFrFhvExEREfkT1tzuUKGG7meffRavvfaa3XNNmjRBp06d3JIUEREREZE/Yb1NRERERFQ1FR74SBRFu/9nZGSgsLBQ9oSIiIiIyIuk/y2eOA7ZYb1NRERE5CdYc7tFhRq6w8PDce3aNVgsFqjVnESFiIiIqNpi0e0VrLeJiIiI/AhrbreoUEN3q1at8Pvvv+P555/Hk08+Ca1WCwCwWCzIzMyEJFX8qjVo0MC1TBVONKsAM+f2lJvoR9dUNPvPm1rJ7B9jRAkm/7l/oeDXVGXxdgbKJ3jh9VOZPH5It94L7jgfwVz1GConMSQZYpO8WG9XjCVIgBCo3L85Zal9WCx/Iy+53EG51/TKn9Gyxqvf5oKs8eSUeuE22WINq5cmWyy57StoLGu8riF/yxpPThdkfj9bL0C+Fqt8qUi2WACgFYJki2XyYqESKFR44AMiUqAK/QSPHTsWe/bswQcffIAPPvjA9vzVq1fRqFGjCh9MEASYzXxnRURERKRYklC8eOI4ZMN6m4iIiMiPsOZ2iwp9vPjEE0/gvffeQ0xMDCRJsvUosT6u6HLzuINERERERMR6m4iIiIioqir8nYwpU6ZgypQpuHr1KvR6PRo3bozo6Gjs3bvXnfkRERERkQdJUvHiieOQPdbbRERERP6BNbd7VHrwodq1a6N27doAALVajYYNG8qeFBERERGRv2K9TURERERUeS6Psr9lyxYEBck32QARERERKQBngFcM1ttERERE1RRrbrdwuaG7R48ecubh80SzCpB5RmWSn2hWezsFj5HM/jHhgGDyo587Bb+mKou3M/AcweSd10FQ2OuvMnnwWB68v9x5XoLM8wOq3DXfICfGUQzW26VJagFiAO8dudU+KF+syx2V/Y767LG6ssVq3uacbLHktja7tazxhsamyRpPTmmF8n3rpVNIumyx3EFdsWnWvKJAkq+I0qo0ssUiUizW3G7hckN3SdnZ2fjuu++wf/9+XL58GYIgIDo6Gh06dMCQIUMQExMjx2GIiIiIiPwS620iIiIiorJVqaHbYrFg2rRpmDNnDkym4k/vrDPEC4KAZcuW4bnnnsOUKVPwxhtvQK32n960RERERL5IkIoXTxyHysd6m4iIiKj6Yc3tHlVq6E5OTsbKlSshSRI0Gg2SkpJQr149AMD58+exf/9+GI1GvPvuuzh37hyWL18uS9JERERERP6A9TYRERERUcW4PMDTjz/+iK+//hqSJOG5557DxYsXsWPHDnz99df4+uuvsWPHDly6dAlTp06FJEn46quvsGbNGjlzJyIiIiK5SR5cqEyst4mIiIiqKdbcbuFyQ/dnn30GQRDwyiuvYPbs2ahRo0apbSIjIzFr1iy88sorkCQJixcvrkquREREROTnDhw4gOnTp+Pee+9F8+bNUatWLQQGBqJWrVro2rUr3n77bVy7dq3MGNnZ2ZgyZQoSEhIQEhKCqKgodO/eHZ9++qltWBAlYL1NRERERFRxguRiNR8bG4ucnBxcvXoVkZGRZW6bm5uLWrVqoXbt2rh06ZJLiSpVXl4eIiMj0XDxNKhCg72djktEM8dydIVk9p+ZawWTcmf3lp2fvK4qi7czKJtgUu7rIHjpHlHJN5G9x3jrPvPEtRLM7outkil2WXEsxkL8+cm/kZubi4iICAD/1DT1574JVYj7axqxoBCZk6fZ5VARTz/9NObPn2/7f3BwMAIDA6HT6WzP1a5dG2vWrEHnzp1L7Z+WloZ+/fohJycHAKDValFYWAizufiC9e3bF2vWrIFGo3H11GTDevsf1vuzd4spCFB7/7VxRU6HWt5OwSdd6Sh6OwWP6dD6tLdT8IiH6uz3dgoec3twlrdTcCpGVaWRbN0qVBXktWOrXO8PSlRKns6Cms3O+GTN7atc/gm+fv06IiMjyy26Adi2u379uquHIyIiIiJPUPjXKDt27Ij33nsPu3fvxvXr11FQUIC8vDzodDosWbIE0dHRuHr1Ku6//37k5uba7Zubm4tBgwYhJycHzZs3x759+6DT6aDX6/HRRx8hMDAQmzZtwuTJk11LTmast4mIiIiqKYXX3L7K5YbumjVrIjc3F3l5eeVum5ubi9zcXNSsWdPVwxERERERITk5GVOnTkWnTp3shvLQarUYNWoUvvzySwDA5cuXkZqaarfv7NmzcenSJYSEhGDdunVISkoCAAQFBWHixImYPn06AGDRokU4efKkZ06oDKy3iYiIiIgqzuWG7g4dOkAURcydO7fcbefOnQtRFG1vJoiIiIhIoXy8d0mnTp1sj8+fP2+3btmyZQCAESNGoHHjxqX2nTRpErRaLSwWC1asWOGeBCuB9TYRERFRNeXjNbdSudzQ/cQTT0CSJLz55puYNm0a8vPzS22j0+nw6quv4s0334QgCHjyySerlCwRERERUVl27Nhhe9y0aVPb4xMnTuDcuXMAgAEDBjjcV6vVonv37gCATZs2uTHLimG9TURERERUcS7PPvDggw9i2LBh+Pbbb/HOO+9gzpw56NChA+Lj4yEIAjIzM7F//34UFhZCkiQMHz4c999/v4ypExEREZHsPNXzQ8ZjGI1GXLx4EampqXjttdcAALfccgsGDx5s2+bo0aO2x4mJiU5jJSYmYv369Th27Jh8CbqI9TYRERFRNeWDNbcvqNI0u8uXL0e9evUwb948FBQUYPv27RAEAQAgScVXMiAgAP/3f/+Hd955p+rZKphoUQNmtbfTUATJLHg7BZ8kmPxodmc/uUdUFm9n4DmCSbmvqeAn91tVKOleVZk8ezzB7N74KjfElyOmoKDXvCqCg4NhNBpLPd+1a1d89dVX0Gg0tucuXLhgexwfH+80pnVdXl4e8vPzodVqZcy48lhv30StLl58UK0DN2SLdfkO/xmLPeqgvK93zh0e/kNTCXv/Kj2kkqt6Jp6QLZbc1l1rLWu8B2unyRpPTseK6sgar01Qtmyxrony/ixEq4Nki2WUvPdzqhEC3RJX5fqACkRUCVVq6A4MDMTs2bPx3HPPYfXq1di/fz8uX74MAKhTpw6SkpIwZMgQxMXFyZIsEREREbmZJBQvnjgOUGqiRY1GY9dAXZbY2FgUFhYiPz8fer0eANCrVy/MmjULDRo0sNtWp9PZHoeGhjqNWXKdTqfzekM3620iIiKiasjDNbe/qFJDt1VcXBwmTZokRygiIiIi8iJBKl48cRwAqF+/vt3zr7/+OlJSUioUIyMjw/b48uXLWL58Od5++2107NgRr776Kt544w2ZsvU+1ttERERE1Yena25/IUtDNxERERGRKzIzMxEREWH7f0V7c9+sTp06mDJlCrp3747OnTvjzTffRMeOHTFo0CAAQHh4uG1bg8Fgd8ySDAaD7XHJfYiIiIiISNk4SBARERER/UPy4AIgIiLCbnG1oduqY8eO6NatGwBg0aJFtudLDu2RlZXldH/ruoiICK8PW0JERERE1ZSHa25/wYZuIiIiIqpWrBNK/v3337bnEhMTbY+PHj3qdF/rupYtW7opOyIiIiIicgcOXSITySxAMvvXAO+eIJj4WYzL/OR+VFm8nYHnCCblvqaCn9xvAKDy0iTwSrvXvXUdHBHMnjmOyo3HkTO2p66Hkp05cwaA/dAjCQkJaNCgAc6dO4cNGzZg6NChpfbT6/XYsWMHAKBv376eSZYqRVILkNT+8zfHmej9N2SNl925hqzxlKzmgUDZYt24wyhbLLltO3GrrPHuaeX8A0Jv23gjsfyNKui+mgdki+UOQYJyf//livIVhzVVVft2lxKJECu9j4p9U4kqjT81REREROQTLBYLJKns719u3rwZe/fuBQD07NnTbl1ycjIAYOXKlXYTWVrNnz8f+fn5UKvVGDlypCw5ExERERGRZ7Chm4iIiIhsBPwzC7xbFxdyy8zMRLt27bBw4UKcOXPGrtE7MzMT7777Lu677z5IkoSoqChMnjzZbv+pU6ciNjYWBoMBAwcORFpaGgCgqKgICxYswLRp0wAA48aNQ7NmzVy9hEREREREZVJyze3LOHQJEREREf1DEooXTxzHBYcPH8aECRMAAEFBQYiIiEBBQQH0er1tm8aNG2P16tWIjY212zcyMhKpqano168fjh07hqSkJISHh6OwsBAmU/FXrvv27Yu5c+e6eFJERERERBWg8JrbV7Ghm4iIiIh8QlxcHL799lts3boVv//+Oy5evIirV69CrVajQYMGaNOmDe677z488sgjCAkJcRijffv2+PPPPzFz5kykpqYiMzMTYWFhSExMxKhRozB69GioVPzSIxERERGRr3G5ofuuu+6CIAhYtGgRmjZtKmdOREREROQt0v8WTxynkoKCgjB06FCHE0lWRkxMDObMmYM5c+ZUKY67sd4mIiIiqqYUXHP7Mpcbunfu3InAwEAW3UREREREbsB6m4iIiIio4lxu6I6JiUF+fr6cufg0waSCEMCvuSqe2b/GJpKLyuLtDDxHMPnHPSIo/GdBZfJ2Bv7FG9dbMHv+mFYqDxzbHceQ65qpTIBU1mvO3iWKwXq7NClABSlA7e00qp06+3WyxbrUOVy2WEoXcUAjazx9J4Os8eS08VQL2WI90PyIbLHk9nPebbLGGxx5UNZ4p0xa2WIlBCr370uuaPTasWuqgt0SN1DgyMF0E9bcbuFyy+ydd96JvLw8nDp1Ss58iIiIiIgIrLeJiIiIiCrD5YbuqVOnIiAgAFOmTIEk+dnHA0RERETVlCB5bqGysd4mIiIiqp5Yc7uHyw3d7dq1w9dff42tW7eia9eu+OGHH5Cdnc0inIiIiMiXSR5cqEyst4mIiIiqKdbcbuHyIEFq9T9j4/3+++946KGHyt1HEASYzV4clJOIiIiIyEew3iYiIiIiqjiXG7rZk4SIiIioGuLEOIrBepuIiIiommLN7RYuN3Rv2bJFzjzKdeDAAaxduxZpaWk4efIkrly5gry8PERERKB58+a455578NRTTyEqKsppjOzsbMyaNQupqak4d+4cQkJC0KpVK4waNQpjxoyBIAgePKMqMvtQrtWUyuLtDDxHMPF+c4XgRz+nKpO3M3CuuvysKu0aCx7sMKryYudUdx7bHddQafcJVY2n621A+TW36uQ5qIQgl/evDEtiE48cp7qJ2auXNd7FrmGyxlOywMBqUrSUI/V0K1njjWiWJms8OW3JbyFrvAHhR2SLddaskS0WANwSyCKkLCap8oVfoOBykx2R33L5p6ZHjx5y5lGuzz//HPPnz7f9Pzg4GCEhIbh27Rp+++03/Pbbb3j//fexZs0adO7cudT+aWlp6NevH3JycgAAWq0WOp0OO3fuxM6dO7Fq1SqsWbMGGo28v+yJiIiIfImnJq3xt4lxXOHpehtgzU1ERETkCay53cPlySg9rWPHjnjvvfewe/duXL9+HQUFBcjLy4NOp8OSJUsQHR2Nq1ev4v7770dubq7dvrm5uRg0aBBycnLQvHlz7Nu3DzqdDnq9Hh999BECAwOxadMmTJ482UtnR0RERETkfay5iYiIiMhXydbQLUkSrl69inPnzskV0k5ycjKmTp2KTp06oUaNGrbntVotRo0ahS+//BIAcPnyZaSmptrtO3v2bFy6dAkhISFYt24dkpKSAABBQUGYOHEipk+fDgBYtGgRTp486Zb8iYiIiHyCJHhuoUpxd70NsOYmIiIi8gjW3G5R5YbuAwcO4MEHH0RkZCRiYmLQpIn9WHbXr1/H+PHjMWHCBBQVFVX1cE516tTJ9vj8+fN265YtWwYAGDFiBBo3blxq30mTJkGr1cJisWDFihVuy5GIiIhI8SQPLlQhSqm3AdbcRERERLJgze0WVWroXr58OTp37owff/wR+fn5kCSp1OzwNWvWRHp6OhYvXoyff/65SsmWZceOHbbHTZs2tT0+ceKErdfLgAEDHO6r1WrRvXt3AMCmTZvcliMRERERUWUoqd4GWHMTERERkXK5PBnl8ePHMXbsWJhMJjzzzDNITk5G//79bRPPlJScnIxffvkF//3vfzFw4MAqJVyS0WjExYsXkZqaitdeew0AcMstt2Dw4MG2bY4ePWp7nJiY6DRWYmIi1q9fj2PHjrmWjFkoXnyQyj8m91Y8weSb948rBB/9WfE2lR9NZK7k30veeh2Eyk/U7nUqBeTsqRzc+frIec+pzMUNpJLZedcOToyjHEqotwGF1dwqFSB4Zpoh9bEMWeOZ2jQpfyMqJWZvgazxLnYLkTWenFQHwmWLFdjpmmyxlO6HjNayxXqs6V7ZYrnDDkMz2WLdHebi72Enzsv4Hq+hyy1VVaf20N+YihAhVmg7le9Mv0clsOZ2D5d/fcyZMwdFRUWYOHEi3n//fQCAWq12uO1dd90FANi9e7erh7MTHBwMo9FY6vmuXbviq6++spvF/cKFC7bH8fHxTmNa1+Xl5SE/Px9arVaWXImIiIiIXOHNehtgzU1EREREvsXlhu5ff/0VgiDgxRdfLHfbuLg4hIaGyjZxTmxsLAoLC5Gfnw+9Xg8A6NWrF2bNmoUGDRrYbavT6WyPQ0NDncYsuU6n0zktuo1Go13Bn5eX59I5EBERESmSp8by87PeJa7wZr0NsOYmIiIichvW3G7h8vcbLly4gLCwMNSrV69C24eEhKCgQJ6vnWVkZODSpUvIz89HdnY2Zs+ejUOHDqFjx462r1O6y4wZMxAZGWlb6tev79bjEREREZF/8ma9DbDmJiIiIiLf4nJDt0ajQVFRUanJcBwpKCjAjRs3EBkZ6erhnKpTpw6mTJmCDRs2QBAEvPnmm0hNTbWtDw//Z5wzg8HgNE7JdSX3udnLL7+M3Nxc25KZmVnFMyAiIiJSEOmfMQPdufhb7xJXKKXeBlhzExEREcmKNbdbuNzQ3ahRI5hMJpw6darcbdetWweLxYKWLVu6erhydezYEd26dQMALFq0yPZ8XFyc7XFWVpbT/a3rIiIiyhwrUKPRICIiwm4hIiIiqjYkDy5UJqXV2wBrbiIiIiJZsOZ2C5fH6O7fvz+OHDmCDz74APPnz3e6XU5ODl544QUIgiD7DPA3s05u8/fff9ueKznr+9GjR9GiRQuH+1pninf1zYFKBFQWl3atdgSTfLMtk+sEGWe9VjKVydsZ+Cal/77i6+pZKrO3M/iHt3IRPHRcd93bKrOfVbB+Qon1NuDdmhsqVfHigwKPZsgWq6hNE9li+ZvY3aUnWHVVVg9N+Rt5ieVAlKzxat5xWdZ4SvXdudtljZfcaI+s8eQUKIjeTsGpC158r1IPRW6JG6oKcktcABBR+ddS5Xq/VyJFc/nOnjx5MrRaLT755BNMnz7dbgIaoPjrk1999RWSkpKQnp6OWrVqYcKECVVOuCxnzpwBYP81yISEBNtkORs2bHC4n16vx44dOwAAffv2dWuORERERIrG3iWKocR6G2DNTURERFRlrLndwuWG7piYGHz11VcIDAzEG2+8gejoaOTk5AAAWrVqhaioKDz22GM4e/YsNBoNvv76a5e/cmixWModm3Dz5s3Yu3cvAKBnz55265KTkwEAK1euREZGRql958+fj/z8fKjVaowcOdKlHImIiIiI5OTJehtgzU1EREREvq1K31UYNGgQtm/fjvbt26OoqAhmsxmSJOH48eMwGo2QJAnt2rXD9u3b0bt3b5ePk5mZiXbt2mHhwoU4c+aMXQGemZmJd999F/fddx8kSUJUVBQmT55st//UqVMRGxsLg8GAgQMHIi0tDQBQVFSEBQsWYNq0aQCAcePGoVmzZi7nSUREROTrPDEpjm1yHCqXp+ptgDU3ERERkaew5nYPl8foturYsSP27t2LI0eOYOfOnbhw4QIsFgtiY2PRtWtXJCUlyZEnDh8+bPsqZlBQECIiIlBQUAC9Xm/bpnHjxli9ejViY2Pt9o2MjERqair69euHY8eOISkpCeHh4SgsLITJVDxYZt++fTF37lxZciUiIiIikoun6m2ANTcRERER+a4qN3RbtW7dGq1bt5YrnJ24uDh8++232Lp1K37//XdcvHgRV69ehVqtRoMGDdCmTRvcd999eOSRRxASEuIwRvv27fHnn39i5syZSE1NRWZmJsLCwpCYmIhRo0Zh9OjRUPnoxDZEREREVP25s94GWHMTERERkW8TpPIG4qMy5eXlITIyEo3eehuq4GBvp1PtCGbB2ykQAJXJ2xl4jsqLM3z7MiXfI4LZ2xnIQ6Ww81BSPt54jd19z6vM8pZnN79elqJCHFj5CnJzc21jOltrmqYvvwO1B2oaS2EhTs/4t10ORM5Y788+UU8gQBXk7XSqnYKkJt5OgQBk3Rno7RQ8ot4d572dgs96vP5ub6fgVJeQDG+nIIs4tXJ+DjWCcnIBAFXVRj/2S3k6C2o2O8Oa24Nk6dFdVFSEn3/+Gfv378fly5cBAHXq1EFSUhLuvvtuBAWxGCUiIiIichXrbSIiIiKislW5ofujjz7C9OnTce3aNYfro6Ki8Nprr2HSpElVPRQRERERuZmnJq3xt4lxqoL1NhEREVH1wprbParU0P3kk0/iiy++sM3IXq9ePcTHxwMAsrKycP78eeTk5ODZZ5/FwYMH8fnnn1c9YyIiIiIiP8F6m4iIiIioYlweYOerr77C559/DkmS8Oijj+LkyZM4d+4cdu/ejd27d+PcuXM4deoUkpOTIUkSli5diq+++krO3ImIiIjIHSQPLFQu1ttERERE1Rhrbtm53NC9YMECCIKASZMmYdmyZbjllltKbdO0aVMsWbIEkyZNgiRJ+Pjjj6uULBERERGRv2C9TURERERUcS4PXXLkyBEIgoDXXnut3G1fe+01fPTRR/jjjz9cPZziCWYBglnwdhrkQSqTtzPwXSqLtzPwDH+6RwSztzPwHJWXztVbx3UXb94znv7ZVJnd15XCLfeFp3p/+GEPk8pive2ASiheSFYhB9K9nYJT+juaeDsFj6m7W75f6lk91bLFktu5Q/GyxmvZQbn3r9xCVUZvp+DUIWNd2WJ10FyQLVZlqVzvDyo7k1T1N84aIVCGTMgtWHO7hcsN3YIgoEaNGqhVq1a529aqVQs1atSAxeInrVtEREREPooT4ygH620iIiKi6ok1t3u4/FFVs2bNkJubi/z8/HK3zc/PR15eHhISElw9HBERERGRX2G9TURERERUcS43dI8ePRoWiwUffvhhudt+9NFHsFgsGDNmjKuHq/ae6doJCx+8F0Nua4maIcHeToeIiIj8lScmxfHTyXEqi/W2vOrUi8LsNVMw+tX70TypMQSBQ6AQERGRl/hAza3T6ZCSkoLbbrsNWq0WkZGR6NChA/7zn/+gqKjI9cAOTJgwAYIgQBAENGrUyOU4Lg9dMmHCBGzbtg3Tpk1DUVERpkyZAq1Wa7eNXq/Hf/7zH7z55psYMWIExo0b53Ki1V2vW5ogMaYO7rqlCSQAaecvYOPJU/j55Glk5eV5Oz0iIiIi8jDW2/Kqf2ssWt1xC5onNcHQSf2Qm6PDztSD2L3+MA7vPAGzicO+EBEREQHA2bNn0bNnT2RkZAAAQkNDYTQasX//fuzfvx8rVqzA5s2bUbNmzSofa+vWrVi0aFGV4wAVbOgePXq0w+dDQkIQHh6ON954A++99x6SkpIQHx8PQRBw/vx57N+/HwUFBYiMjERwcDDGjBmDzz77TJbEqyNrrxIBQPv4umhfLw6v9u6JE1euYsOJU9h08m+cuHLVu0kSERFRtcbxAr2D9bbnqNXFX2qNrBWOfo90xcBRd6JAb8TeTUewa90hpP16DIb8Qi9nSURERNWZkmtui8WCwYMHIyMjA3Xr1sWyZcvQp08fiKKIVatWYezYsTh48CBGjhyJdevWVSk/g8GAJ598EgEBAWjTpg32799fpXgVauhesmQJBEGAJNlfnZLPGQwGbN++3eH+N27csMVg4V0xKtU/o8o0q10LTWtF4f+6dcaF3DysP3EKm4+fxoHzFyBKfJdYXajYicglKpO3M/AcweztDDxH5UfnqgRKv7e8/XOuMnvmb6277nu1qXT+kofOiSqO9XbFmK/mAEKgS/tackt/SzIgUA0ACAnToOug29HjgQ4wm8w4uPkofvvlT+zZ+AduXNVVKWeqmrB9GbLG03VpLGs8paq7S5Q1XlZP5Q71c/RQI9lidepwQrZY7vD9lfayxXos5jfZYsntmKn8SZjdJUi45pa4NVUat8Qtj1GqeCGtcfHvK1U/S5YswR9//AEAWL16NTp37gyguK1y+PDhEEURjzzyCNavX4/Nmzejd+/eLh/rlVdewenTp/HKK6/YOnFURYUaupOTkzmGnRcJgoCA/13/uMgIjGrfDmM6tseNgkL8/Ncp/HziNH5LP4ciC1tKiYiIqIo8NX4229rtsN72Pmujd0BgAG6/uzWS+rXBM7OAvw5mYFfqQfy24QguZlzxcpZERERULSi45l66dCkAoFevXrZG7pJGjBiBV155Benp6Vi2bJnLDd179uzBvHnz0KxZM7z66quYMGGCS3FKqnCPblKOgP993bJGSDAeaN0SQ9vdhkKTGVv/PoOfT5zG1lPp0BmNXs6SiIiIfJKCi+7qjPW2sliHN4EAJLRrhIS2DfHk6w8i89Ql7Eg9iN0bDuPvI5neTZKIiIh8l0JrboPBgF27dgEABgwY4HAbQRDQv39/LFiwAJs2bXIpLaPRiNGjR0OSJCxcuBDBwcEuxbmZy5NRkjIEqIt7ngQHBqBPs1vQv0UzWEQRv589j01/ncLmk6eRrdN7OUsiIiIiIt+kUgkonkWneELL4ZP64pHJA5CTnYudaw/it/WHcPT30xAt8g4VQURERORpx48fhygW1zSJiYlOt7Ouu3TpEq5du4aoqKhKHeeNN97A8ePH8eSTT6Jnz54u53szNnRXI9ae3mqVCnc0rIdOjeojZUBvHL2YjQ3HT+GXE3/jTM51L2dJRERESqbkiXGIlEAdUNzRpFZMJAaO6o77nuwJfV4Bdm84gt/WH8KBbcdhLPCjSUSIiIio0jxdc+fl2c9VotFooNGUHjv+woULtsfx8fFO45Zcd+HChUo1dB88eBCzZs1CTEwMZs2aVeH9KoIN3dWUusRkli1j66BFTPT/t3fn0VFV6d7Hf6cqEyEJk0iYg8ocZhAUQRAEcZ5BUbBB7as0jqCt3Qq0Xm0V9bbX4dXWq3Kbliut3dIo85gwgyCEABlISAiEIYGMZKx6/wgVgiSQVE5Nqe9nrVqrqHPOPk8VO1VPPbXP3ppxw3U6lH1aS/claMWBZO05kslVwwAAAICTHPN6N45opBF3DdTo+werpLhUO9bEa+NPv2jLyjjlneLqSgAA4Fnt27c/79+zZs3S7NmzL9gvL+/cItyhoaE1tld1W9VjLqWsrExTpkxRWVmZPvjgAzVr1qzWx9ZGvQrddrtdX375pRYsWKDdu3fr1KlTKisrq3F/wzAuuh2uYTEM6eziRh2bN9XUawbqt0Ov1smCQi3bl6gVB5K07dBhldq43BIAAL/npfMF+ivybd/hKHoHBQfq6tHRuuamPrKV27R3a7Jif9ylTUt/0YkMrq4EAABye86dnp6uiIiIyoerG83tDn/+85+1a9cu3Xrrrbr//vtNb9/pQnd+fr5uvvlmbdiwQXY731SMUslircfxbnwJA86O9r6scajG9+uliQP7qKC4RKsPJGvl/mTFJKWqsJTLLX2dhf9Cpxh+Uhuw+MnzlBrOc/XFvukN70OWMvfnKK7uc9ZS8i5/Qb7tuxzTm1isFvW8+kr1HHylnnj9Ph2Mz6hYzHLZHh06cNTDUfqn8C1pprV1elhH09rydpEbzWvr6EjvHWC1aXdnU9sb0z/O1PbM9K+sAaa2N+Gyzaa25ymBZwcJmi3fXuKSdiUpwjCnYFlqdy6JDTSYLMIXREREnFforkl4eHjl/cLCwhr3q7qt6jEXEx8fr9dee01hYWH6+OOPa3VMXTndG2fPnq3Y2FhZrVY9+OCDGjt2rFq1aqWAADq4L3HM6904OEjjenbRbb27q7S8XBuS07Rif6JWHzioU4VnPBwlAABwG0Z0ew3y7YbBYj03pWBUtzbq2KW1Jr9wq46lZynmx13atHS39u1I5ccMAAD8iZfm3G3atKm8n5GRod69e1e7X0ZGRrXHXMy0adNUUlKiOXPmqFmzZsrPzz9vu+OqRLvdXrktODhYgYGBtY7f6Sx54cKFMgxDf/nLX/Tkk0862wy8SIC1YuRJoNWqYVd11PWdo2S/Tdp1+KiWxydqxf4kZZzOvUQrAADAl7EYpfcg3254LBZDslSMFmzVvoXufHSE7v2PUcrNzteGJb9o49Ld+mVDokpLfPAyHgAAUGvemnN3795dFotFNptNcXFxGjduXLX7xcVVXLESGRlZ64UoU1JSJEkvvfSSXnrppRr3S0tLqxwl/v777+uZZ56pdfxOF7qPHz+ugIAAPfroo842AS/mWMzSkNS3XWv1bdtavx97vZKOZ2lpfIJW7k/W/mMnPBskAABAA0a+3fAFnJ3iJKJ5mG68f4jGTRyqosISbVkZp01Ld2vbmngV5hV5OEoAAOAvQkNDNXToUMXExGjp0qWaOXPmBfvY7XYtW7ZMkjRmzBh3h3hRThe6W7durVOnTikoKMjMeOCFKhazrLh/1eUt9MRlg/W7EdcoMydPS/clatX+JP2cdkTlXG4JAIDv89LLKP0R+bZ/cSxmGRIapKE399H1t/dXeVm5ftmYqNgfd2nzijidOs7VlQAANAhenHNPnjxZMTExWrNmjbZs2aLBgweft33hwoU6ePCgJGnSpEm1bjc1NfWi2x955BF9/fXX6tix4yX3rYnl0rtUb+zYscrNzdX+/fudbQI+yjHaO7JJuB4a1Ff/+8j92jjzP/Sft9+okV2uUHBAPVblBAAAgCTybX/mGOltDbCqz9Aumv7meM3f/pr+69/P694nRqlNp5YejhAAADRUkydPVq9evWS323XPPfdo1apVkiSbzaaFCxfqsccekySNGzdOo0aNOu/Y2bNnyzAMGYbhdLG6Ppwe0f3SSy/pu+++01NPPaUff/yxThODN0SW8oqb03x0VJNjMcsmjUJ0R+/uuqdftIpLyxSTkKoV8YladyBFuUXFHo4S9WUwTaRTLH70uvnTc22Ifw+WUk9HcI6lzLMfiO7uy9ZS1z3fi/2/Xmybt84X6I/ItyFJ1iqLWXbp00Gde7fX1D/cocMHjyv2x13auGyPEnenezBC/9V0g7mve/aIDqa2561axZo7MOrYKC9KZH5l+d4eprZ3b9+fTW3PTD/l9DWtrfuabjWtrbo6WOqaq6iuCnRdP823l9T5mCaWENPOb5OtTvtbnB9z26B4c84dEBCgRYsWaeTIkUpNTdXo0aMVGhoqm82moqKKKdX69eun+fPnmxxt/Tld6O7QoYN+/PFH3X///RowYICef/55DRw4sHKy8Isdh4bJsZhlcGCARnS7QqN7XqVym03bUzO0fG+iVu9L1rHc/Eu0AgAAAIl8GxcyLIaMs3MKtrvict33xChNmD5G2cdzFfvjLm1avkd7tiSrvKxuRQcAAICqoqKitHv3bs2dO1fff/+9UlJSFBgYqJ49e+qBBx7Q9OnTvXJ6PacL3ZLUtWtX3Xbbbfrwww81ZcqUS+5vGIbKyhrgUDhcwDHS22qxaGBUWw3q1E6v3HaD9h05rpX7knSq4Ixp58ouOKMNSYdUUFz3XzEBAMCvePF8gf6IfBsXYz07xUnzyyN080NDdftvhqswv0ibl8dp/85U2Wzm/KHZ7Xbt25GqlH1HTGkPAAC/5wM5d3h4uObMmaM5c+bU+pjZs2dr9uzZTp3vq6++0ldffeXUsQ5OF7pPnjypESNGaN++fZIqkp9Lqc0+aHgcc3pLUtfWLdUl8rLKkShmsFgMlZaXa8vBdK3Ym6Q1+5N1Mr/QtPYBAPArPpB0+wvybdSFYzHL0LAQDb+9n0bc2d+0tg0ZMiyGThw5pZgff9GmZbsVvz3FtEI6AAB+h5zbJZwudM+ZM0fx8fEKDQ3V888/r7Fjx6pVq1YKCKjXIHE0cBbDkAzzitwOgVarrrmyg4Ze1VGz7hilPYcztWJvolbGJyktO8f08wEAALga+TacFeCixeFbtmmm2x8ZprsfG6G8nEJtXLJbG5ft1s7YBJUWcyUBAADwLKez5H//+98yDEP/8z//o/vvv9/MmACnOEaOG5J6tYtUdNtWmnHTcKWcyNbSuASt2pes+CPHPRskAABezjh7c8d5cHHk2/BGjpHj4U1CNeqeQRo7YYiKi0q0bc0+bVyyW9vWxCs/x7xpCgEAaIjIuV3D6UL38ePHFRQUpHvuucfMeHyWpUyy1GMRXXestOpPqo4c79SyuR4bfrWeGDlEx3PztXxPolbHJ2tHSobKbCzU4wkWBvw4xZ9eN8OPnmtt1eczxhUsZd7zweXJvw1rqfteB2/rA3A98m14O0fROzgkSNeMjtZ14/qovNymPVuSFbvkF21esVdZx7i6sraaxxw2ra0To9qZ1pa3uywm0LS2skcVmdaWK3wf38e0tib12mJaW2ZbktfbY+e+K+Jnl7R7uKzu5cZOAa4rURba6r7GWajFnIUHbapbHcYiy6V3As5yutDdpk0bHT9+XFaray6LA8zkWBzz8ogwTRjSWw8N7af8omKtik/Wqr1J2phwSGdKqawBAMB8gd6DfBu+xHq26G21WtRr8JXqPeQq/e61e5W4J12xS3Zr0/I9Sk/m6koAACSRc7uI0z+L3H777SooKND27dvNjAdwuYCzXxbDQoJ1S5+u+uDh27Vh1hP6cNLtunNADzUNDfFwhAAAoCZZWVn68ssv9dBDD6lHjx5q3LixgoOD1a5dO91555365z//eck2jh07pueff15du3ZVo0aN1Lx5cw0bNkyff/65Vy3mSL4NX2W1WmSxVIxEvKpnO016fpw+W/l7fbH2Zf3mhVvUrW9HGS5YtwcAAPg3p0d0//GPf9TChQv1H//xH1q5cqWaNm1qYliAeziK3sEBARrWtZNGdL9Cdrv086EMrYhL0qq9STp6Os/DUQIA4D6G3T1Tqjl7jsjISJWVnbsKKyQkRIGBgcrIyFBGRoZ++OEHjRs3Tv/4xz8UGhp6wfE7duzQ2LFjlZWVJUkKCwtTXl6eYmNjFRsbq4ULF2rRokUKDg52LkATkW+jITAshqxnZwht0/Ey3f3YCN3/xCidzsrXhiW/aOPyPdq9OVllpeUejhQAAPfx9pzbVzld6I6Li9Mbb7yhp59+Wj169NBjjz2mq6++WuHh4Rc9bvjw4c6eEnApx/QmhiH169hG/Tu21Uu3jVDC0RNatidRq/YmKfFYloejBADAxbz8MsqysjJdffXVeuSRRzR27FhdccUVkqTU1FS9/vrr+uKLL7RkyRL99re/1f/+7/+ed2xOTo5uvfVWZWVlqVu3bvrf//1fDRw4UCUlJfrrX/+qZ599VsuXL9ezzz6rjz/+uL7PsN7It9EQBQRUDDRp2iJMY8cP0S0PDdWZgmJtWbVXG5bt0Y51+3WmoNjDUQIA4GJennP7KqcL3SNGjKi83CwnJ0evv/76JY8xDOO8ETiAt7Jazs3q0znyMl3ZqoWmj7lWR07latmeBK3am6xf0o7K5kWXNwMA4A9Wr16tkSNHXvB4VFSUPv/8cwUEBOjTTz/V3/72N73xxhtq37595T5z585VZmamGjVqpJ9++kmdOnWSJAUFBWnatGnKzc3Vyy+/rM8++0zPPPOMunTp4rbnVR3ybTR0jsUsGzUO1nU399GI2/urtLRMu2ITtWHZbm1euVc5WfkejhIAAPgKpwvdkuo8h6E3zXloNqNMMuqzTlDDfWl8nmEYsp79ktmmWYQeHtpfvxk+UKcLzmjlniStjkvSlqR0lZRxuaUnWPgu7xTDj143S6mnIzCHpcz3Pii89e/TWuqZ19IdfdFSWrtV7C+5nxd3t+qK3FVNnTpVn376qSRp+/bt5xW6582bJ0maMGFCZZG7qunTp+uNN95Qfn6+5s+frzlz5pgYuXPIt+EvHCO9AwMD1H9YFw28vpuefkPatytNsUt3a9PKvcpMz/ZwlL6j5bpMU9vLvLG1qe15qyYxjUxtr3C0906D+U3CAFPbe6z7BlPb85QQw3u+1x+tZSjtAgJdG8hZxfa6JbPBhjlx2VS7/NbB4vxyhO5H2mY6pwvdNlvdOhrQUDimOGnauJHuHNRD9w7ppTMlpVq/L0Wr9iQpZn+K8otKPBwlAAD+KSTk3KLS5eXnviEeOHBAaWlpkqRx48ZVe2xYWJiGDRumJUuWaPny5R4vdJNvw19ZA86NIOrWt7269W2vx1++TWlJxxSzpKLonRx/xIMRAgAAb1SvEd2Av3MsZtkoKFCjoq/S2D5dVFZu09akdK2MS9KauGSdzCvwcJQAANSery+Ms3bt2sr7vXr1qrwfFxdXeT86OrrG46Ojo7VkyRLFx8e7JD4AdWOpMqVgh6taacITN2ji9Bt1MjNHsUt3a+OKvdq7I1W2cn4YAgD4Dl/Pub0VhW7AJI6R3gFWiwZ3bq8hXTro1XtGKS4tU8t3J2p1XJIOnTzt2SABAGjATp8+rTfffFOSNGzYMHXt2rVy25Ej50Z/tm3btsY2HNtyc3OVn5+vsLAwF0ULwBmO0d6XRTbRrQ9dqzsfGab83DPauDxOG1fs1c4NCSop9tK5swAAgEtR6AZcoOpilj3at1L3dpfruVuH6dCJU1r2S4JW703W3vRjHowQAIAauHkF+Nzc3PMeDg4OVnBwcJ2bs9lsevjhh3X06FEFBwfrv//7v8/bnpd3bp7U0NDQGtupui0vL49CN+DFHPN6h0U00g139teYeweppLhU29Yd0Mblcdq6dp/yc854OEoAAKrh5pzbXzhd6P7Tn/7k1HGvvvqqs6cEfJLFMKSzi1l2bNlMU0YO0uOjB+tkXoFW7E7U6rhkbU8+rDLm4QQAeAF3X0ZZdbFISZo1a5Zmz55d5/aefvppLV68WJL08ccfq0+fPvUN0ePIt4HacxS9g4IDNeSG7ho6Jlq2cpv2bEvRhmV7tGnlXp3MzPFwlAAAVGDqEtdwutA9e/ZsGWeLd7Vht9tlGEaDTbwtZZLFeun9AMcUJ5eFN9Z9Q3rpgaF9VVBUojVxyVq9O0kb96fqTAmXW3qKwUvvFEvdFuD2aZayhpcpWLy831tLveM1d3c/t5S67gdQi5e8ppKUnp6uiIiIyn87M5p7xowZ+vDDDyVJ77//vqZMmXLBPuHh4ZX3CwsLzztnVYWFhdUe4wnk24BzHNObWKwW9RrUSb2u7qQnZ92ppJ0p2rAuQRtXxist+biHo/QtkWvMe70ybrrctLa8XXCMuZ8jxqhsU9sz0/8mX21aW9O7rDWtrbqKOXOlS9q9ITTJJe1K0rHyElPaaW0NufROdVBqL7/0TtUINgJNjQP+xelC9/Dhwy+aeOfk5Gjfvn0qLi5Ws2bN1Lt3b2dPJUnKysrSokWLtGrVKv388886dOiQysrK1LJlSw0cOFCTJ0/WXXfdddE2jh07prfffluLFy9WWlqaGjVqpJ49e2ry5MmaOnVqnb5IAGZwLGbZOCRIN/XrqlsHdldJWbk2Hziklb8kav3eFJ0q4HJLAIAbufkyyoiIiBqLzrXxwgsv6N1335UkvfPOO3rmmWeq3a9NmzaV9zMyMmo8Z0ZGRmVcnp62xN35tkTOjYbHYj03peAVfaLUqXdHTX5mrDIPZytm2R5tXBmvA7+ky273nh8AAQB+gKlLXMLpQnfVFe1rkp+fr3feeUf/+Z//qdtuu03PPfecs6dTZGSkysrODTkLCQlRYGCgMjIylJGRoR9++EHjxo3TP/7xj2rnXdyxY4fGjh2rrKwsSVJYWJjy8vIUGxur2NhYLVy4UIsWLXJqFBFgBsdI76AAq4Z2j9KwHp1kt0u/pB7Ril8StWZPso5k516iFQAA/MfMmTM1d+5cSdLbb7+tGTNm1LhvdHR05f24uDh179692v3i4uIkST169DAxUue4O9+WyLnRsFkshqSKH1oi2zXXXZOv031Tr1dOdoFil8dp06p47d6SrNJS50YhAgAAz7JcehfnhYWFac6cOXrhhRf0wgsv1CpZr0lZWZmuvvpqffzxx0pOTtaZM2eUn5+vlJQUTZ06VZK0ZMkS/fa3v73g2JycHN16663KyspSt27dtG3bNuXl5amgoEAffvihAgMDtXz5cj377LNOxweYyWqxyDAMWSyG+kS10Yw7rteSV6fquxcf1m/HDlGXNpd5OkQAQAPlmC/QHbf6mDFjxnlF7pkzZ150/65du6pDhw6SpKVLl1a7T0FBgWJiYiRJY8aMqV+AbmJmvi2Rc8O/OOb1btK8scbeO1Cv//U3+nbLq/r9uxM0fFwvhTbmBxkAgGv4Ss7ta1xa6HZ4/vnnZbfb9c477zjdxurVq7VlyxY98cQTuuKKKyofj4qK0ueff16ZbP/tb39Tenr6ecfOnTtXmZmZatSokX766ScNHDhQkhQUFKRp06Zpzpw5kqTPPvtMCQkJTscIuILFYpwdfSJdGdlCvx07WAtfeFjLZj2qGXcOV/8r2lYseAkAgJ+YMWNG5XQlc+fOvWSR22HSpEmSpAULFig1NfWC7R999JHy8/NltVo1ceJE0+J1BzPybYmcG/7LUfQOaRSk68ZE66X3HtT/bXpFr/31Nxp33yA1u8yzUxkBAIBLc0uhu0WLFmratKm2bt3qdBsjR4686HbHCBNJ2r59+3nb5s2bJ0maMGGCOnXqdMGx06dPV1hYmMrLyzV//nynYwRczTAMWS0Vf7aRzcL1wLC++vKp+7XuP/9DsyfcqOt7XqHgQFZFBQDUg92NNye8+OKLlUXu9957T88//3ytj50xY4YiIyNVWFioW265RTt27JAklZSU6JNPPtErr7wiSXr88cfVpUsX5wL0EDPybYmcG5DOLWYZEGhVv2uu0vTZd2n+upf1/oIndM+UYWrdoYWHIwQA+Dwvz7l9ldNzdNdFXl6eTp8+7dK5+EJCzq0OW15+bk61AwcOKC0tTZI0bty4ao8NCwvTsGHDtGTJEi1fvrxytEldWMokSz3qi/52KQHM4VjMMiI0RLcN6q67hkSrqLRMsfEpWr0zSTF7U5R3ptjDUfovS6mnI/BdljLeFH/NUnbpfdzJWuq9/0fe8rdnKbW58Vx1+/+4aGRevDBOWlqa3n77bUmSxWLRW2+9pbfeeqvG/WfMmHHevN1NmjTR4sWLNXbsWMXHx2vgwIEKDw9XUVGRSksrOs6YMWP0/vvv1z04D3NHvi15PucG3M1aZTHLLr3aqUt0Oz0682al789Q7PoEbVgVr6T4Ix6M0Pe0WXnS1PbSb/ajaR1jmpvWVNPRmaa1ZbYvD13rsXNP67TWJe1uLupQ52OGNUpzQSQ1O2krqvW+l1sauSyOUnvdvvgEGm4pbZrPi3NuX+aW3vDuu+/KbrdXO7LDLFXnI+zVq1flfceCQtL5ixD9WnR0tJYsWaL4+HiXxAe4mqPoHRIYoBHRV2p0n84qt9m0I/GwVu5K1NrdyTqeU+DhKAEAcJ7NZjvv/rFjxy66f35+/gWPDRgwQHv37tVbb72lxYsXKz09XY0bN1Z0dLQmT56sKVOmyGJxy0WPpnJHvi2Rc8O/VX1vaN+tre6/KlIPPD5SWSdyFbs8ThtX71Pcz6kqL3PfD50AAOAcpwvd69evv+j2oqIipaen67vvvtOyZctkGIYeeOABZ093UadPn9abb74pSRo2bJi6du1aue3IkXO/rrdt27bGNhzbcnNzlZ+fr7Cw6udgKy4uVnHxuRGyubm59YodcIWAsyNPrBaLBnRup4Fd2uvl8aMUn3ZMK3clas0vyUo5lu3hKAEA3shdi9Y4c46oqCjZ7fUPrlWrVnrvvff03nvv1bstV/KmfFsi5wZ+zTHFSYuWEbpl/GDdMfFaFeQXadPqfdq4Kl47NiWq+IyXXGYEAPAq3pxz+zKnC90jRoyQUYsF8BxfRkaOHFnrhYLqwmaz6eGHH9bRo0cVHBys//7v/z5ve15eXuX90NDQGtupui0vL6/GpPvNN9/kMkv4FGuVkSfd2l+uru1a6qnbr1P6idNasTNRa3YnKe5QpkyoGwAAABN5S74tkXMDl+JYzLJxWIhG3Nxbo2/vp5KSMu3YkKiNq/Zq89r9yss54+EoAQBo2Oo1dcnFRtRYrVY1a9ZMffr00QMPPKBHHnnEJZeBPv3001q8eLEk6eOPP1afPn1MP0dVL730kp577rnKf+fm5qp9+/YuPSdgFothSGe/MLdv2VSTRg3QlDGDlJ1XWDHSe3eytiWkq6ycyy0BwG8xX6BX8YZ8WyLnBurCUfQOCgrQ1cO6aMiIbrLb7dq785BiV+zVptX7dPzoac8GCQDwLHJul3C60F11jkRPmTFjhj788ENJ0vvvv68pU6ZcsE94eHjl/cLCQkVERFTbVmFhYbXH/FpwcLDLF/kB3MUxxUnz8FDdfW207h/WR4XFJVq356DW/JKs2PgUFRZzuSUAAJ7gDfm2RM4N1IdjehPDMNSzb0f17NdRT/z+VqUkZCpmRZw2ropXauLF1xsAAAC146NLk0ovvPCC3n33XUnSO++8o2eeeaba/dq0aVN5PyMjo8akOyMjQ5IUERFR4yWUF2OUS0bdFoY9n5/9wgLv41jMMjQ4SDf266xxA7uptLxcW/anafWOJK3ffVDZeYWXaAWuZCnjjcIZlvq8N3sRa2nD+v+3eOlvaJZSzxUWLW74P3ac42LvJ4bdLsMN81m54xyoP2/LuQFfZrGeu+IiqnMrdbiipSZNG61jh05o/T82afOe49q3O102G++PddF+2SnT2jp0ezPT2vJ22TGRprbXYdQhU9vzlHCL90wxtKu4Zb3bGBR80oRILnTKVuT0sc0sISZGIpXa6/aFL9DwjlIoObdreMf/bh3NnDlTc+fOlSS9/fbbmjFjRo37Vl31PS4uTt27d692P8dK8T169DAxUsA3OYregVarruneUUN7RMkuac/Bo1r1c6LW7krW4ZM5ng0SAOAaXEaJs8i5AdcxDKNytHerji1111M3677AAOWeLtSG1fHatGa/dm45qNKSBvKLPQDgfOTcLuFzhe4ZM2ZUjip5++23L7ngTteuXdWhQwelpaVp6dKluu+++y7Yp6CgQDExMZKkMWPGmB804MMci1kaknp1aq1enVrrufuuV8rRbK3YkaC1u5K1P/24Z4MEAACmIucG3CsgsOKreUTTUN14ez+Nu3ugiotKtTUmQRtWx2tbbKIK8pwfQQkAgD+od6E7OTlZ3377rXbv3q3s7GyVltZ8LbJhGFq1apXT56qacM+dO1fPP/98rY6bNGmSXn/9dS1YsECvvPKKoqKiztv+0UcfKT8/X1arVRMnTnQ6PqChs1iMyvudWjfX1HFX6/Fbh+j46Xyt3JGotbuStDMpQ+VcbgkAPsuwV9zccR7UjjvzbYmcG/A0x2KWwSGBumZkNw27safKy8q1e3uqYlfFa9Pa/co+kefhKAEA9UHO7Rr1KnTPmTNHr7/+umw220VXhHcwDOOS+9TkxRdfrEy433vvPT377LO1PnbGjBn6/PPPlZmZqVtuuUXz5s3TgAEDVFJSoi+++EKvvPKKJOnxxx9Xly5dnI4R8DfWs/MMXt40TPeP6KMHR/VTXmGx1v6SpNU7k7QlPk1FpVxuCQCAs9yZb0vk3IC3cRS9rQFW9R7USX2vvkLT/3CbEvZmKGbFXm1as0+HD2V5OEoAALyD04Xu+fPna86cOZIqFp8ZO3as2rRpo4AA82dDSUtL09tvvy1Jslgseuutt/TWW2/VuP+MGTPOm0OwSZMmWrx4scaOHav4+HgNHDhQ4eHhKioqqhwRM2bMGL3//vumxw74i4CzRe/w0GCNu7qbbrump0pKy7QhLlWrdyUpZvdB5RYWezhKAMAlMV+g13Bnvi2RcwPezlplMcvO3dvoqm6tNfWZMcpIy1LMir3auGafEvceqdWPYgAADyPndgmns+SPPvpIknT77bfr22+/VVBQkGlB/ZrNZjvv/rFjxy66f35+/gWPDRgwQHv37tVbb72lxYsXKz09XY0bN1Z0dLQmT56sKVOmyGKxVNMagLpyLGYZFBigYb2v0Mh+V6ncZtPOxAyt2pmktbuSdOzUhX+nAADgHHfm2xI5N+BLDIshQxVXcLTt0EL3TR6qCVOH61RWvmJX7tXGNfu1e3uKystsl2gJAICGw7A7+XNvRESECgoKlJ6erjZt2pgdl8/Izc1VkyZN1PuRN2QNCnG6nb+9/KB6dGxlYmSA96n4Am3IYjF0IO24Vu9I1Jqfk3TwCJdbupuFGWWcZi1teD+JW2qe7tdrWUq954u7xQN9or7nLCsrUuya2crJyVFERISkczlN/wf+s145TW2VlxTp52/+cF4MOB/59jmO/jlCdyjACHSqjYFj++rNJX8wOTLA+5SVlikgMECFBcXavP6ANqzZr+2bk1R0xgc/8H1cyp18vjmjz8gET4dguifarPZ0CHXWJ6jA0yFUamJxfW76axbV/4f53LxyNetykJzbjZwe0W0YhiIiIvw+6QZQe1VHcHVu31JXtbtMT9w1VEdO5mjltgSt3ZmkPQePiqstAcCDuIzSa5BvA3BGQGDF1/zQxsEafmNP3TCut0pLy/Xz5mTFrtmnLTEJyjld6OEoAcDPkXO7hNOF7m7dumnXrl0qLi5WcHCwmTEB8AMWw5DOLpjV5rImenDMAE0aN0in885o9Y5Erd2ZpG3701VaVu7hSAEA8AzybQD15VjMMjDQqoHXXqWrr+ssu13atztdMav3aeO6/Tp25LRngwQAwCROj8N/9NFHVVpaqoULF5oZDwA/5VjMsml4I90+rKc+ePZurf7gSb3x21t046Auahzi2nlJAQAVDLv7brg48m0AZrJaLTKMimkEu/dup8efuVHzfnhany54Qg89dr2u6MxUmgDgLuTcruH0iO7HHntMP/74o5566il16NBBw4cPNzMuAH7MsZhlo+BA3TCgs8Zc3VVl5TZt25em1TsStX5XsrJyudwSANCwkW8DcJWqUwp2vKKl2kcN18OPj9DxzBzFrIrXxnX7Ff9Lumw2P6uQAAB8mtOF7j/96U/q06ePYmJiNHLkSA0dOlSDBw9WeHj4RY979dVXnT0lAD/kGOkdYLXo6u4dNLhnR700abTiUzK1anvFFCfpx097NkgAaEiYL9BrkG8DcAfDMGS1VkwpeHlkE90x/mrdM/Ea5eWe0YY1+7Vx3X7t3HpQJcWsZg4ApiHndgnDbndu2TeLpeKyJ0lyNOH498WUlzes+XYdq6X2fah+q6X+7ysT1T2KS8WA2qoYXWKXxWLRoaPZWrUtQet2JGtf6jFPh+aXrKV+9unpAZZST0dwPkupzdMh1JnFi/qpO2Op7v+qrKxI62P/VO0K8APud98K8Du+9Z8V4J1Bvn2Oo3+O0B0KMAKdamPg2L56c8kfTI4MaNjKSssUEBig4uJSbd2UrA3r9mvLxiTl5xV5OjS/dPCeUE+H0OCNuv4XT4dQaWrL9Z4Ooc66B3pXDhJqcd8UqJZqZofOzStXsy4HybndyOkR3cOHD69Vog0ArmCxGJIq3oM6tm6uSbdcrSm3D9HJ0wVavS1Ba3ckaWdChsrLfa8YBwCe5m9z+Xkr8m0AnhYQWFEyCA4O1LXDumjYiG4qL7dp9840xa7dpw3rE5R1Ms/DUQKAbyLnNp/The61a9eaGAYA1I9jipPLmjbW3Tf01v039lP+mWKt/zlZ8SnH5OTFKxew2Wz6JfGIktJPmtIeAHgdu73i5o7z4KLItwF4E+vZfNtqtahP/w7q07+jps8Yp8QDR7VxfYLycs+Ydq6srHzt2HpQZwpLTGsTALwKObdLOF3oBgBv5VjMMqxRsMYM6aqbrulmXuOGIYthKDMrV6u2Vowc35N0VDY/+/AAAACA/6q6mOVVXSJ1xVWtZOYFKBaLRWVl5fp5W4pi1x3QppgEnT5VYN4JAAANEoVuAA2ao+httsgWERo/pr8mjhuo3PwirdmRqLU7krQtPk0lpd41LxkA1IVhd89llFyqCQANQ9XFLM0UEGDVgKuv0KAhV+rZF2/Wvr0ZillTMV3K0YxTpp8PANyJnNs1KHQDgJMc06VEhIXolqE9dMf1vVRUUqaNvxzUmu1J2rA7RfmFxR6OEgAAAPBNjulSJKlbj7bq1qONfjv9RqWlntT61fu0Yf0BJSVkejBCAIA3odBtEkuZZLlwgdXa87NfWICGJiCgYuR4SFCAhve/SjcM6qLycpt2xKdr7bZExe5I1olT+R6O0ndYSj0dgfexlDashVUtpb7zwectsbqtD9jlnrzEO15WAICPqLoYfYeoy/TApGv10JRhOnkyT+vX7teG2ATt3pMmW3nD/YCJ+neRaW0dvDfYtLYakqaBhZ4OodJ3pwfWu42Hm28yIZLaO1SPi5uvCDD/auxie92+WDYy3Ph3Qc7tEhS6AcBkAVUW6hnQs70G9uygF6aM1r6DmVqzJVHrdyTp0JFsD0cJAAAA+C7r2aLYZZeF6/Y7++vuewcpP79IG2ITtCE2Qdu3HVRxcZmHowQAuBOFbgBwIWuVSz26dmqlLlGX68kHhik985TWbEnQuu1J2ncw098WQgbgxQxbxc0d5wEAwAyOqyvDwkI0anRPjb2pt0pKyrRt60HFxhzQ5k1Jys094+EoAeAccm7XoNANAG5iMQw5lqNvH9lMD946SJPuGKzsnAKt2ZqodduStHNfusrK/eyTCIB34TJKAIAPcxS9g4ICNOSaq3Tt0M6y2+zasyddMesPaENsgo4fz/VwlAD8Hjm3S1DoBgAPcUxx0rxJY90xspfuubGvCs+UKObnZK3blqjNv6TqTDGTVQMAAADOcCxmaVgN9erdXr16d9Dvnhqj5KRjWreuYl7v1JQTHo4SAGAWCt0A4AUcI09CGwVp1JAuGju0u0rLyrV1zyGt25ao2J+TdYrLLQG4gWGvuLnjPAAAuIulypSCna64XFGdWmrK1OuVmZmjdWv3aUNsgvbFZ8hm4wMKgOuRc7sGhW6TWMrsstaj9xhM0AvgrABrRdE7MMCqIb2jdG3fTrJL2ptwVGs2Jyhma5KOHM/xbJA+xFLKVDCXYin17c8gb47fU/3vUue1lPF3AQDwXxaLIaliSsHIyCa6555BGj9hiHJzz2h97AHFbkjUz7sOqbS03LOBulDUInMX6jw43jC1PU/5v+2DXNLu40PWu6TdS1mU29e0tu5v8rNpbVXnSD2m8GxnDTYlhmJ77a+oDjYCTTknzEWhGwC8WOXllpJ6dm6tnp0j9dTkEUpJP6k1mxO1fmuiElO53BKAiex2uWWFXH7kBwB4iYDAioEmERGNdNOYXrr15r4qKirVpi3Jit2QoC1bk1VQWOLhKAE0KOTcLkGhGwB8RNWRJ1HtWmjy3c015b5rdDwrT2s3J2jd1iTt2Z+hci63BAAAAJzimFIwJCRQw4Z21sjru6mszKZdvxzS+tgEbdiUqOzsAg9HCQCoDoVuAPBBhmHIaq0oel/eIlx3j+2r+28ZoLyCIq3fmqT1W5O0dfchlZSYe0kigIaP+QIBAKjgKHoHBFjUr29HDegfpeeeHqv9B45q3fr9it2YqMMZpzwcJQBfRM7tGhS6AaABcCTh4Y1DNHZYd90yMlrFJWXavDNF67YmauOOg8orKPZwlAB8gv3szR3nAQDARzimFJSkrl0i1aVzK/32sZFKP5xdWfQ+kJDpwQgB+BRybpeg0A0ADYyj6B0cFKChA6/U9YM7q9xm0674w1q3JVHrtybpRHa+h6MEAAAAfJNhGDKMiqsr27drrgfGD9FDD16rrOx8rY+pWMzylz3pKq/H4noAgLqj0G0SS6lkufRuNfOzX1gAuEfA2ZEnVotF/Xq0U78e7fXc1FFKOHhMazceUMzmJKUezvJwlL7FUsobttRwXgdLqfd9AfV0TFxGCQBA3ThGe7doHqbbbu6ju+4YoILcQsVuT1HM5kRt+zlVRcWlHo7StaL+ZV5baRMa3vSLn+8aWudjZg5c7oJInLeioKtTx90Wtt/kSC500lZU52MutzSq1zlL7Zfup6X2mvN6cm7XoNANAH7CYjn3c1znTpfryo4t9fhDw3Uk87TWbDygmC1Jik844m+LMgMAAACmCQisKLM0jgjVqOHdNPaGniotLdfWnSmK2ZiojduSlZN7xsNRAkDDRKEbAPxQ1cUs20Q21fg7Bmni3YN1OqdQazclKGZzon6OS1NZmfeNdgXgYna73PKLF7+qAQAaOMeUgoGBVg0ZcIWuHXSl7HYpbl+G1m1MUOzmRGUez/VwlAA8gpzbJSh0AwAqpzhp2iRUt47upTtv6qszRSXauC1Z6zYnavOOgzpT1LAvtwQAAABcxTG9iWFI0d3bKLp7W01/7AYdTD2htRsqphQ8mHrCw1ECgG+j0A0AOI9j5EmjkCBdf00XjRrWXWVl5dq++5DWb0pU7NYkncop9HCUAFyF+QIBAHCtqlMKdup4mTq2b6EpE6/TsRO5Wht7QLGbExW3/4hsNj4sgYaKnNs1KHQDAGrkKHoHBFg1qE+UBvfrpJlPjlF8wlGt3ZigmC2Jysg87dkgAZjLLvcsku1nSTcAANWpOqVgq5YRuue2/hp/1yDl5p2pGGSyOVE7dh1SSWm5hyMFYCpybpeg0G0SS6lNFtVjLls/63gAfI/jcktJ6t65tbp3jtS034zQocNZWhtzQDGbEpWYfMxzATZwllL/+KCwlPrWvPDeEq9RUrcvv0Y5X5YBAPBGjoEmEeGNdNPIHrp1TG8VnynRlh9/1pqMLG3ccVD5hcUejtK12vwz0GPnznrQe65c/WDvSJe1/WrvH13W9q/FnOlQr+NvDD1sUiTny7XX/e+omaVRnfY/+xsW3IhCNwCgziwWQ1LFp3bHdi008f4hmvzAtTqZna91sRVF791x6SrnckvA53AZJQAA3iEgsKJkE9woSEPvHKThAVaVl9u0c2+61mxOUOz2ZJ3MzvdwlACcQc7tGhS6AQD15ljM8rLmYbrj5r665/YByi8oVuzmRMVsTNC2nakqLi7zcJQAAACAb7KeHelttVrUL7q9+kd30MzHb9T+5Eyt2ZSg9VuTlHYk28NRAoBnUegGAJjKcbllWONgjb6+u24aFa2SkjJt+zlF6zYmaNPWZOXmFXk4SgA1stkrbu44DwAAqDNrlcUsu1zRSp07Xa4nHhquw5mntGZjgtZvS9S+pEzZ+agFvBc5t0tQ6AYAuIyj6B0UFKAhg67UtYOvks1u1569h7V+Q4JiNyfp2IlcD0cJAAAA+CaLYUhGxZSC7SKb6YE7Bunhuwcr+3SB1m5OVMy2RP28N11lZd6xrggAuBKFbgCAWzgWs7Qahnr3bKfePdvrqf8YraSDx7VuQ8W83imHTno4SgCsAA8AgO9yTCnYvGlj3T66l+6+qa8Kz5QodnuS1m9N0uadKTpTVOrhKAGQc7sGhW6TWErtstSj9/jb5PAA/JulyuWWV0S1VKeOl2nqw8OUeSxHazcc0Ib1CYrff0Q2P7vMylMspQ1rhI8vPB+jpNyz57/Ia2TITQvjuP4UAAD4NcfVlaGNgnTDkK4aM6yHSkvKtHPlbq3IOKnYnck6lXvGw1F6l6bfh7mk3dKJWS5p11nvJo6u1/GvdfvBpEgubVtxM6ePvTY4x8RIpHxbcR2PCKxxiy/k3Hl5eXr33Xf13XffKSUlRVarVV26dNGECRM0ffp0BQUF1bnNjIwM/fDDD1qzZo127typjIwMSVJkZKSGDBmixx57TDfccIPTMVPoBgB4lMViyPHxG9mqie69fYAm3H21cnPPaH1sgmI3JOjnXYdUWurZwiAAAADgqwICK4regUEBGjCmjwZZLbLrRu1NOqrVWxO0bnuyjpwwtygIwHcdOnRII0aMUGpqqiQpNDRUxcXF2r59u7Zv36758+dr1apVatas9j9EpKenq2PHjrJXWUAgNDRUdrtdqampSk1N1YIFCzRlyhR99tlnslqtdY7bculdAABwH8fIk4iIRrppTLT+/J/3adF3T+vVP9yhG0Z0V+PQuv9qDKAO7Hb33QAAgNtZA6wyDEMWw1DPK1tr+gPX6/v3p+qbtybr0buvUZeOLT0dItDweXHOXV5erttuu02pqalq3bq1VqxYoYKCAhUWFmrBggUKDw/Xzp07NXHixDq3a7fbNWrUKH399dfKyMhQQUGB8vPztXfvXt1xxx2SpP/5n//R7Nmz6xy3xIhuAIAXcxS9Q0ICNWxoZ428vpvKymza9cshrY9N0MZNScrKzvdwlAAAAIBvqri6skJUm+Z65I7BevTua3Q8O0+rtyZq/Y4k/XIgQ+VMKQj4ja+++kp79uyRJH333Xe65pprJFVMQTp+/HjZbDY9+OCDWrJkiVatWqVRo0bVqt1mzZppx44d6t+//3mPWywW9ejRQ//85z918803a+nSpfqv//ov/eEPf1BISEidYmdENwDAJziK3gEBFvXr21HPPjVG/1gwTZ/89yRNuH+w2rV1fu42AOcYdvfdAACA9zAMo3Ixy8ubh+ve0X308R/u19JPntAfHx+jYf2vVHAg4yUBM3hzzv31119LkkaOHFlZ5K5qwoQJ6tSpkyRp3rx5tW63SZMmFxS5qzIMQ1OmTJEk5efna9++fXUJWxIjugEAPshqPfc7bdcukerSuZV+++gIHT6crXUxBxSzIUEHEjI9GCEAAADg2xwDTcIbh+ima7vr1uHRKi4p0+bdqVqzLVEbd6Uot6DIw1ECMFNhYaE2bNggSRo3bly1+xiGoZtuukmffPKJli9fbur5q47gLi+v+zpdFLoBAD7NMAwZRsUll+3aNdeE+wdr4gPXKDu7QOti9it2Y6J+2Z2u8nKbhyMFfIT97M0d5wEAAD7BUfQODgrQ0H5X6PqBV6ncZtOuAxlac3aKk+NMKQjUnpfm3Pv27ZPNVvHdOTo6usb9HNsyMzOVnZ2t5s2bOx1iVWvXrpUkBQUFqUuXLnU+3mcK3YWFhVq3bp127Nihn3/+WTt27FBaWpokadasWbWapPzYsWN6++23tXjxYqWlpalRo0bq2bOnJk+erKlTp1YWSpxhKbPLUp8eypc9ADCFY7R38+aNddstfXXXHQNUWFisDRsStSE2Qdu2HlRRUamHo/R9ltKG+cOBUVL3UQPuZpS6NkbDbpfhhoUi3XEO1J2359wAAM9zTG9itVjUr0tb9evaVjMm36D9ace1ekeC1u5M1sEjWR6O0rsY37Wo8zFNJh52QSTmeDd1jNPHvnbFv8wL5BLiSwOdOq5PkDn5dq695u+d3ppzHzlypPJ+27Zta9yv6rYjR46YUuhOSUnR//t//0+SNH78eEVERNS5DZ8pdG/dulU333yz08fv2LFDY8eOVVZWxZttWFiY8vLyFBsbq9jYWC1cuFCLFi1ScHCwWSEDADzMMfIkNDRYI0d21403Rqu0tEzbt6coNiZBmzYmKifnjIejBADvQc4NAKgLS5UpBbu0b6nO7S7Tk3ddp4wTOVq1I0FrdyZpz8Gj4vdtwLNyc3PP+3dwcHC1+VheXl7l/dDQ0Brbq7qt6jHOOnPmjO677z4VFhaqRYsWevPNN51qx6cWo2zWrJlGjRqlmTNn6ptvvlFkZGStjsvJydGtt96qrKwsdevWTdu2bVNeXp4KCgr04YcfKjAwUMuXL9ezzz7r4mcAAPAUR9E7MDBAV199pWbMvFn/+P5p/eWDh3TPvYMUGdnEwxECXsLmxhu8Ejk3AMAZFsOQ1VJRZmrbsokevHGA/uelB7Ti/Sf08sOjdU3PKAWezckBv+fmnLt9+/Zq0qRJ5c3ZQrIrlJWV6cEHH9SOHTsUGBiov//97xcdTX4xPjOie9iwYcrOzj7vsd///ve1Onbu3LnKzMxUo0aN9NNPP1WuDBoUFKRp06YpNzdXL7/8sj777DM988wzTs0BAwDwHY7pTQxD6tGzrXr0bKcnp41WSsoJrVu7Xxs2JOhg8nEPRwkA7kfODQAwi2OKk6ZhjXT7dT119/W9daa4VOt/SdbanUnauCdVBUUlHo4S8A/p6ennTQVS09V14eHhlfcLCwtrbK/qtqrH1FV5ebkeeugh/etf/1JAQID+/ve/a8wY56fG8ZkR3Var87/6zZs3T5I0YcKEyoS7qunTpyssLEzl5eWaP3++0+cBAPgei8Uii6VivtioqMv08KSh+uvnU/XN/03TE0+OUq/e7Su3A79msdvUOzdFI7L2qHduiix23x+m7Jgv0B03eB9ybgCAKwSc/XxpFByoUQO66M3f3qpVf3lCHzxzt+4a3kstImqeIgFQuV0Rm87osh/yFbHpjFTu+3mku3PuiIiI8241FbrbtGlTeT8jI6PG+Ktuq3pMXTiK3P/3f/8nq9Wqv/3tb7r33nudasvBZ0Z0O+vAgQOVC+iMGzeu2n3CwsI0bNgwLVmyRMuXL9ecOXPcGSIAwEsYhiGrtaKoffnlEbrzrgG6976rlZdXpNiYA9oQm6AdO1JVUlLm4UjhDYZmx+vJtCVqWXpuvrsTgRH6uMM4bWjew4ORAe5Hzg0AqC3HSO8Aq1WDu3fQNT076qWHR2tvSqZW70jUmp1JOnz8tGeDhNdovrRAneZkKfjouQUii1tblTKrhbJvauzByBqm7t27y2KxyGazKS4ursa8Li4uTpIUGRnp1EKU5eXlmjhx4nlF7vHjx9crdskPCt2OF16SoqOja9wvOjpaS5YsUXx8vFPnsZTa6jWKi1FNAOB9HPN6h4eH6MYx0Rp3cx8VF5dq66Zkxa7br62bk5WfV+ThKH2TUWLOSuaeMjQ7Xq8m/98Fj7cozdWryf+n18rv04am3T0QWfWMX/04Y5Rf5Mca+9mbqzlxjsLCQq1bt047duzQzz//rB07dlQWV2fNmqXZs2dfso1jx47p7bff1uLFi5WWlqZGjRqpZ8+emjx5sqZOnSrD4AoOZ7gr5wYANCyVUwpK6hnVSj07ttLT9w1X6rFsrdiZqNW7k7Qv3T+nFMz6vn292+j64AETIjHXX47UflqKq9ce1HMvr7jg8aDMcnV94rjS/l9z5Y5rZGZ4kqSDTo5ruiog8Lx/X3QaDS/NuUNDQzV06FDFxMRo6dKlmjlz5oVN2u1atmyZJDk1zUh1Re4JEybUuZ3qNPhC95EjRyrvX2wic8e23Nxc5efnKywszOWxAQB8h6PoHRwcqGuv66xhI7qpvNym3bvSFLN2vzbGJCjrZP1Xm4b3s9htejJtiaSKL2XnbVPFei//kbFMm5p0lc3wmVnizrHbK27uOE8dbd26VTfffLPTp9yxY4fGjh2rrKwsSRUjjPPy8hQbG6vY2FgtXLhQixYtqvFSTtSMnBsAUF8Wy7m8KapVc/3mxkF67KbBOpGTrxU7E7VmT7J2JmWozOb7U8Xh0oxymyb/18aK+7/eZpfshtR6do5yx4RIVh8cqODFOffkyZMVExOjNWvWaMuWLRo8ePB52xcuXKiDBw9KkiZNmlSntsvLy/Xggw/q22+/VUBAgGkjuR188NtX3eTlnSs6hIbWPOdT1W1Vj/m14uJi5ebmnncDAPgX69mit9VqUe++HfS7Z8dqwb+e0kdfTNGDk4ZqwKBOatGC4k1DFZ13SC1Lcy9IuB0ski4vzVV0fpo7w/IbzZo106hRozRz5kx98803ioyMrNVxOTk5uvXWW5WVlaVu3bpp27ZtysvLU0FBgT788EMFBgZq+fLlevbZZ138DBomcm4AgNkcU5y0bBKm+4f11l+n36u1f/4PvfbQWN0yqLu6tm2poADn15aAd+v+S6YuO15QY85t2KWgo+VqvJUFTc02efJk9erVS3a7Xffcc49WrVolSbLZbFq4cKEee+wxSRXT1Y0aNeq8Y2fPni3DMGQYhlJTU8/bVl5erocffriyyP33v//d1CK35Acjus325ptvMp8gAKCS43JLSercOVJXXtWq8rGC/CKlHDyhg0nHlHLwhFIOHtehlJNMd+Ljmpfm126/strt520Me8XNHeepq2HDhik7O/u8x37/+9/X6ti5c+cqMzNTjRo10k8//VS5WGJQUJCmTZum3Nxcvfzyy/rss8/0zDPPqEuXLnUPEKYh5wYAVOVYzDKsUbDGDeyq2wZXrIdSbrPpSFau9h8+rqSjWUo8clJJR07q8Mkc2Zgi1qc1PVlYq/0CjvvmlIjenHMHBARo0aJFGjlypFJTUzV69GiFhobKZrOpqKjiu2y/fv3qvLj4hg0b9M0331TEZRiaPn26pk+fXuP+f/nLX+pcCG/whe7w8PDK+4WFhYqIiKh2v8LCc39AVY/5tZdeeknPPfdc5b9zc3PVvn39500CAPg+w2LIWmXMQeOwEEX3bq+u3dsoIMBSOffvqex8JSce08Hk40o9eEIpB08oLfUki1z6iOzA2o3Wzw5gVL/ZrFbnR23NmzdPkjRhwoTKIndV06dP1xtvvKH8/HzNnz+fImsdkXMDANwloEo+YLVY1L5lU7VpEaGRva+qHAVeUlau1GPZOnD4hJKOnqwogB/N0vHTvjkQwR+dvqzmK8SqKrucUf2uEBUVpd27d2vu3Ln6/vvvlZKSosDAQPXs2VMPPPCApk+frqCgoDq1aasy7VBpaamOHTt20f3PnDlT57gbfKG7TZs2lfczMjJqTLozMjIkSRERERedKzA4OJh5GwEAdRIYeH7y1ax5mAYMaqy+/aMUcHabzWbX8WM5SkrIVEryCaWmHFdK8gllZGTLVs5oFG8SF95RJwIj1KI0t9o54GySTgZGKC6sg7tDM4cXzxforAMHDlQuWlnTyvFhYWEaNmyYlixZouXLl1PoriNybgCAJ1kt52dlQQFWdWnbUldEtpBhnNteUFSipKMndeDwCSU7RoAfPancwmJPhI2L2NcnUicvb6zmxwuqzbnthlQaaVXB1XUrtnoNH8i5w8PDNWfOnDrlxbNnz65xgfgRI0bI7uLn3OAL3VVXfY+Li1P37t2r3c+xUnyPHj2cOo+l1CaLvR4LIlDDAAC/YlgMBVjOFcAtFkORrZuq5eURGjK0c+Xil6Wl5Tqcnq3k/UeVevC4UpNPKCXpmE4cY77amhilrr180S7pk7Zj9UrqQtl0/oInNlUslvP/2o51eiFKg5H9pnPkedL5ueGvRUdHa8mSJYqPj3dHWA2Ku3JuAADqIsB6fj7WOCRIfTq1Uc+2l8sSYJXFUnHF5ekTOUredUh7gkuVlHlSiZlZOngsS2dKfTsv2/vPri5pd+SE7S5p99f+NbO/ps6MkV3nL0jpKKHNe+5a/ZLt3BVfz16+ur7hXeBo+fnfQ/LKWTjV3Rp8obtr167q0KGD0tLStHTpUt13330X7FNQUKCYmBhJ0pgxY9wdIgAAlay/SsYDA63qdEVLte9wdjTK2e1FZ0qUevCEkg9knlcAz82p++VdqLsNTbvrtaj79ETGMrUsPfejw8nACP2/tmO1oWn1RT5fYNgqbu44j6QLFhl0xUjeI0eOVN5v27Ztjfs5tuXm5io/P/+iI45xPnJuAIAvCQg6vxzWtGUT9R/dS71tNgWenRrFZrcr83Se9mUcV2LmSSUdy1LC0ZNKO3laZTYKmO7wyw3t9cU7w3TPOzvU7Pi56c9OtwrVdzMG6JcbfHdaM3fn3P6iwRe6JWnSpEl6/fXXtWDBAr3yyiuKioo6b/tHH32k/Px8Wa1WTZw40TNBAgBwEQEB5xfAQxoFqVvPtrqqS6QsVkvlaJTc04U6mHRMBxOPKTX5uHbvTNOR9OzqmkQ9bWjaXZuadFV0fpqal+UrOyBMcWEdnB7J7TXcfBnlr+ddnjVrVo2XOzorLy+v8n5oaM3zPVbdlpeXR6G7jsi5AQC+zDCMyiK3JFkMQ22aRSiySZiGd+9Uua2s3Ka0k6cUf+S4kjKzdODoCW1JSldJmW8uiujtfrmhvXZf31ZX7jyhJifPKOeyRkru11J2Kzl3rc/jR3yq0H3q1CmVV7kMwDGJeWFhoU6ePFn5eEhIyHlfTGbMmKHPP/9cmZmZuuWWWzRv3jwNGDBAJSUl+uKLL/TKK69Ikh5//HF16dLFTc8GAID6C/jV/N8RTUPVZ0CUevbpULkA5v69GVr6w06tW7lXBfnMP2gmm2HR7vAoT4fh09LT08+bz5l5mT2PnBsAgHMsFst5U9UFWC26olULdbismYw+FfN/5xcVa/HP+/WvHXsVl37xBfZQd3arRUkDW3k6DPgAnyp09+vXT4cOHbrg8XfeeUfvvPNO5b8nT56sr776qvLfTZo00eLFizV27FjFx8dr4MCBCg8PV1FRkUpLSyVVXD75/vvvu/w5AADgaoZhnLcAZpfurdW1RxtNmzlOG9bs0/LFv+jnrQdls/nXr/uoJbvcs3bI2XNERETUuHChWcLDwyvvFxYW1ni+wsJzl8RWPcbfkHMDAHBpVef/DgsJ1r2De2nCtX106OQpfb91r/79c7yO5xZ4MEJ4NTfn3P7Cx8f5196AAQO0d+9ePfvss+rcubNKS0vVuHFjXXfddfrrX/+qJUuWMIIIANAgWSyWyuL3dTd01xsfTNSCn57T1N+NUodOl3k6PMDl2rRpU3k/IyOjxv0c2yIiIpi2xEnk3AAAf+UofHdo0VRP3XStVr78mP762N0a17erggOslzgagBl8akR3ampqvY5v1aqV3nvvPb333nvmBFSFUVouw1aP+Zj8bM4cAIBnBJxNsps2b6x7H7xG4ycNVeK+I1r2r51au2yP8ljM8jxGSZmnQ6gTo7R28RrlNe9n2O0y3JCXuOMcDtHR0ZX34+Li1L179YuFxsXFSZJ69Ojhlri8lTfn3AAAeDvDMGQ1KtbPubpTO13TuaMKS0q0OO6A/rkrXjvTj1yiBe+34t8DTWvr4XtXmdZWXXyTM8DpY6c2/blW+5Wf7QfVaYg5tzfwmxHdAADgfNazC1xe2TVS0168WQtWztQrc8dr8PAulduAhqBr167q0KGDJGnp0qXV7lNQUKCYmBhJFdNrAAAA1Jf17CCT0KAg3d2np76ZMl4rn5qiJ4YPVpsm/jtNGuAqPjWiGwAAmM9iqShqB1isuub6rrpuVA/lni7UisW7tG5ZnPJzi2rVTn7eGeWcKrz0jvBuDXQF+EmTJun111/XggUL9MorrygqKuq87R999JHy8/NltVo1ceJEt8YGAAAaPsfUJu2aNdHvrh+ip0deq22ph/Xdrr365fBR2WuRG9klHT6Vo3I/G6XbIDXQnNvTKHQDAIBKjlEnEU1DdeeEwbrnoWtrfWxZWbn++t5y/eubza4KD+5gl2Rz03mccOrUKZWXn5suzmarCLawsFAnT56sfDwkJOS8ebZnzJihzz//XJmZmbrllls0b948DRgwQCUlJfriiy/0yiuvSJIef/xxdenSxbngAAAAasF6dqBJ/w5tNCiqXZ2O3XvkmJ76drEycnJdERrcxctzbl/FdckAAKBa1joumhMQYNUTL4zTq+9OUGgYi83BNfr166eWLVtW3tLT0yVJ77zzznmP/+53vzvvuCZNmmjx4sVq0aKF4uPjNXDgwMpFJ5988kmVlJRozJgxev/99z3xtAAAgB9yFLzromurlvrhiYc1sssVLogI8G0UugEAgKmGXN9V/+/bJ3VVt9aeDgVOcCyM446buw0YMEB79+7Vs88+q86dO6u0tFSNGzfWddddp7/+9a9asmSJgoP5kQYAAHivAKtFoUGB+uSBOzTzxmEKcKJYDs9ryDm3JzF1iUmMUpsMW/mld6yJf/U7AEADZrVadNnlEfrLvMf08RuL9dO3Wz0dkkcZpWWeDqFBSU1NrdfxrVq10nvvvaf33nvPnIAAAADczGIYkqTfDOmv/lFt9btF/1Zmfr6Ho3LO/yy5wZR2Xrr9n6a0UxuLC66s1X5nCsskHXNtMDgPP/sAAADTWa0WBQRa9dSsO/T7d8arUWiQp0NCbdl1bnEcl948/UQBAAB8m8ViUa/IVlryyCQN/9VC2/By5NwuQaEbAAC41LCx0frou9+pU5dWMgyjXjcAAAAA5wRYLAoLCtKX996t54ZeqwCLRYbk9A3wZUxdAgAAXMpqtahVm2b65J9P1butf3+zWR+9/m8TokKNHKM/3HEeAAAA1Jvl7DzdTw4ZrGnXDKlXW6eLijT+mwVKyso2IzTUhJzbJRjRDQAAXM4aYE7KcdsDQ3T18K6mtIUa2Nx4AwAAgGnMuAIyLChIb990U+U84HARcm6XoNANAAB8hs1m0zOv3aXQsGBPhwIAAAA0OAEWi3pHttIj/ft5OhSgzpi6xCRGSZkMq9X54/3sUgIAAJxhsVjUpFljPfbcWH3wyveeDsf9SkvNacdWczuG3e6WvITcBwAAwDsZhqGZw4dpRWaSUnNPezqcWnl9zR2mtPPfN84zpR1JKrSW17iNnNs1GNENAAB8itVq0bjxg9X32qs8HQoAAADQIFkMQ++MuIkFKuFTKHQDAACfU15u03Nv3qeQ0CBPh9LwOBbGcccNAAAAXinAYtGg1u30UM++ng6lYSLndgmmLgEAAD7HarWo+eUR+mrN71VSZM50HlnHc/XCxE9VWlJmSnsAAACAr3v12pF6ou/VprX37rYN+i5hr2ntAVVR6AYAAD7Jaq2Yr9ssLVs3Vf+hnbVlzT7T2vRJ7hr54WejSwAAAHxRoMWqNmERprRlt9v1aO8BFLolcm4XYeoSAAAASWVl5brupl6eDsPzuIwSAAAALmAYhrq3uFztw5t4OhTPI+d2CUZ0m8QoLZNhszrfgJ91PAAAvE1AgFVDx0Trg98vUGlJzSuk+7ySUsnG9CwAAABwv3K7Tbf0uFKf7dvs6VCq9fSWCaa0839DP1N+gM2UtlB7jOgGAAA4q1HjYPW9tounw/AsmxtvAAAA8CuGDN3aoYenw/A8cm6XoNANAABwVllpua67uY+nwwAAAAAaJIthKLp5pNqEmjPvN1AVU5cAAACcFRBo1fW39dVlkebNG5iwO11fz/3JtPZczbDbZbhhSjV3nAMAAADex2a36fPr79fJMwWmtFdmL9dbu9boQM4JU9pzB3Ju16DQDQAAUEVwSJD6D+tqWnu9r7lKf/uvpSov87PrBgEAAIBqWAyLujW9XGpqTnvldpt2ZR3xqUI3XINCNwAAgAsFBFjVNqql0pKOeTqU2nHX6ux+NroEAAAALmKXOjdp6eko6oac2yWYoxsAAMDFOnSJ9HQIAAAAQINktVjUo2krT4cBL8CIbrOUlUq2evxu4Ge/sAAA4C/KSssVdeXlii0p9XQotWOzS4Yb8hIbuQ8AAADM0SGsqS5rWqwye7mnQ5Ek/TbuIZUXFkuaW/0O5NwuQaEbAADAhQyLoY5dW3s6jNrjMkoAAAD4GKvFoo6NWyg5/7inQ6kdcm6XoNANAADgQlarRb2v7awn//M+U9u126Wlf9+olPgMU9sFAAAAfNFT3cbq6JlTpraZeSZXXx1cb2qbcB0K3QAAAC4WGh6imyZea2qbgYEBspXb9Oms70xtV3LT6BL51+gSAAAAuE65zaYhl11lapuBFqsk6bu0rcorKzK1bXJu16DQDQAA4GIBAVbT2ywvt6lJizDT2wUAAAB8jdVikfkZd4VmwY1dUOiGK1DoBgAA8EFWq0XNL48wv2HmCwQAAAAqNQ8KU1pBlrmNknO7BIVus5SUSRaL88f7WccDAAD117xluFRSWvcDbU4cAwAAAPihbs3syrFn1/m40sAS7XZBPKgZhW4AAAAf1eSycPMbtdnllrn8bPzIDwAAAO9mt9vVJJCc21dQ6AYAAPBREc3DdPcTo2WrYwJ7prhQK+d+Wf1Gu63i5mruOAcAAABQDzbZdHe7MQqyBNb52DN5hfq3vqh+Izm3S1DoBgAA8FG2cpumzLq7zoNBCgrz9ezcR1wSEwAAANBg2KUWQc00KeruOh9akJevaS4ICTWj0A0AAOCjLNZ6rA9SExbGAQAAACRJVovV6WPLbGU1byTndgkXfDsCAAAAAAAAAMB9GNFtlpJSyWI4f7yf/cICAAC8FAvjAAAAAPVmv8iAbnJu12BENwAAAAAAAADApzGiGwAAAOcwXyAAAADgWuTcLkGhGwAAAOfY5aak2/WnAAAAALwSObdLMHUJAAAAAAAAAMCnMaIbAAAA53AZJQAAAOBa5NwuQaHbJPaSYtmNenQeP1sFFQAAAAAAAADM4ndTl+Tl5Wn27Nnq1auXwsLC1KRJEw0aNEjvvvuuSkpKPB0eAACAZ9ls7ruhwSLnBgAAuAhybpfwqxHdhw4d0ogRI5SamipJCg0NVXFxsbZv367t27dr/vz5WrVqlZo1a+bZQAEAAAAfRc4NAAAAT/CbEd3l5eW67bbblJqaqtatW2vFihUqKChQYWGhFixYoPDwcO3cuVMTJ070dKgAAACe45gv0B03NDjk3AAAALVAzu0SflPo/uqrr7Rnzx5J0nfffafRo0dLkiwWi8aPH69PP/1UkrRkyRKtWrXKY3ECAAB4FEk36oGcGwAAoBbIuV3CbwrdX3/9tSRp5MiRuuaaay7YPmHCBHXq1EmSNG/ePLfGBgAAADQE5NwAAADwFL+Yo7uwsFAbNmyQJI0bN67afQzD0E033aRPPvlEy5cvr/M5vs/4RBEREfWKEwAAwONsdkluGPlh86/RJf7AHTn3DznzyLkBAIBPCAy6SNmVnNsl/GJE9759+2Q7u8podHR0jfs5tmVmZio7O9stsQEAAAANATk3AAAAPMkvRnQfOXKk8n7btm1r3K/qtiNHjqh58+YX7FNcXKzi4uLKf+fm5poUJQAAgOfZ7TbZ7Ta3nAcNCzk3AABA7ZBzu4ZfjOjOy8urvB8aGlrjflW3VT2mqjfffFNNmjSpvLVv3968QAEAAAAfRc4NAAAAT/KLQreZXnrpJeXk5FTe0tPTPR0SAACAeez2irn8XH3zsxXgUTfk3AAAoEEj53YJv5i6JDw8vPJ+YWFhjftV3Vb1mKqCg4MVHBxsXnAAAADexO6mhXH8LOn2B+TcAAAAtUTO7RJ+MaK7TZs2lfczMjJq3K/qtqrHAAAAALg4cm4AAAB4kl8Uurt37y6LpeKpxsXF1bifY1tkZGS1i+IAAAA0eDab+25oUMi5AQAAaomc2yX8otAdGhqqoUOHSpKWLl1a7T52u13Lli2TJI0ZM8ZtsQEAAAANATk3AAAAPMkvCt2SNHnyZEnSmjVrtGXLlgu2L1y4UAcPHpQkTZo0ya2xAQAAeA273X03NDjk3AAAALVAzu0SflXo7tWrl+x2u+655x6tWrVKkmSz2bRw4UI99thjkqRx48Zp1KhRngwVAAAA8Enk3AAAAPCUAE8H4C4BAQFatGiRRo4cqdTUVI0ePVqhoaGy2WwqKiqSJPXr10/z58/3cKQAAACeY7fZZDdcP5ef3e5f8wX6C3JuAACASyPndg2/GdEtSVFRUdq9e7deffVVRUdHyzAMBQYGasCAAZo7d642b96sZs2aeTpMAAAAz+EyStQTOTcAAMAlkHO7hN+M6HYIDw/XnDlzNGfOHE+HAgAAADRI5NwAAABwN78rdAMAAOAibHbJcMPIDz8bXQIAAABUIud2Cb+augQAAAAAAAAA0PBQ6AYAAMA5drtkt7nh5vzokry8PM2ePVu9evVSWFiYmjRpokGDBundd99VSUmJiS8GAAAA4AJ+nnMfO3ZMzz//vLp27apGjRqpefPmGjZsmD7//HPZ6xEzU5cAAADAZxw6dEgjRoxQamqqJCk0NFTFxcXavn27tm/frvnz52vVqlUsdggAAAA4yZU5944dOzR27FhlZWVJksLCwpSXl6fY2FjFxsZq4cKFWrRokYKDg+vcNiO6AQAAUMlus7vtVlfl5eW67bbblJqaqtatW2vFihUqKChQYWGhFixYoPDwcO3cuVMTJ050wSsDAAAAmMNfc+6cnBzdeuutysrKUrdu3bRt2zbl5eWpoKBAH374oQIDA7V8+XI9++yzdW5botANAACAqtxyCeXZWx199dVX2rNnjyTpu+++0+jRoyVJFotF48eP16effipJWrJkiVatWmXeawIAAACYyU9z7rlz5yozM1ONGjXSTz/9pIEDB0qSgoKCNG3aNM2ZM0eS9NlnnykhIaHOsVPoBgAAgE/4+uuvJUkjR47UNddcc8H2CRMmqFOnTpKkefPmuTU2AAAAoCFwZc7t2L9qG1VNnz5dYWFhKi8v1/z58+saOoVuAAAAnOOtl1EWFhZqw4YNkqRx48ZVu49hGLrpppskScuXL6/fCwEAAAC4iD/m3AcOHFBaWtpF2w4LC9OwYcPq3LYDhW4AAAB4vX379slmq7j0Mjo6usb9HNsyMzOVnZ3tltgAAACAhsCVOXdcXNwFx1+s7fj4+Fq1W1VAnY8AAABAw2W3Sar7XH7Onaf2jhw5Unm/bdu2Ne5XdduRI0fUvHnzuscGAAAAuJIf5tx1bTs3N1f5+fkKCwu7ZNsOFLrryW6vuAQgNzfXw5EAAADUjiNvceQxVZWpVKr74ux1VqbS82JxCA4OVnBw8AX75+XlVd4PDQ2tsd2q26oeA99Gzg0AAHwNObc5bVPodiPHf1L79u09HAkAAEDd5OXlqUmTJpIqVjqPjIxUbOZPbjt/WFjYBTnUrFmzNHv2bLfFAN9Azg0AAHwVObf7UOiupzZt2ig9PV3h4eEyDMPT4TR4ubm5at++vdLT0xUREeHpcODj6E8wG30KZnNVn7Lb7crLy1ObNm0qHwsJCVFKSopKSkpMO09t4vh1/lTdyBJJCg8Pr7xfWFhYY5tVt1U9Br6NnNt9+CyD2ehTMBt9CmZyZX8i57542zW93vXJ5yl015PFYlG7du08HYbfiYiI4AMNpqE/wWz0KZjNFX3KMaqkqpCQEIWEhJh6HrNU/YKQkZGh3r17V7tfRkZGtcfAt5Fzux+fZTAbfQpmo0/BTK7qT+TcNbdd0+vtaDsiIqJO05ZIkqVOewMAAAAe0L17d1ksFalr1RXbf82xLTIykoUoAQAAgDpwZc4dHR19wfEXa7tHjx61arcqCt0AAADweqGhoRo6dKgkaenSpdXuY7fbtWzZMknSmDFj3BYbAAAA0BC4Mufu2rWrOnTocNG2CwoKFBMTU+e2HSh0w6cEBwdr1qxZNc4lBNQF/Qlmo0/BbPSp802ePFmStGbNGm3ZsuWC7QsXLtTBgwclSZMmTXJrbEBDwfsOzEafgtnoUzAT/elCrsy5HfsvWLBAqampF2z/6KOPlJ+fL6vVqokTJ9Yxcsmw2+32Oh8FAAAAuFlZWZn69++vPXv2qG3btvr66681atQo2Ww2fffdd3r00UeVm5urcePG6aef3LeSPQAAANBQ1Cfnnj17tubMmSNJSklJUVRU1Hnbc3Jy1K1bN2VmZqpHjx6aN2+eBgwYoJKSEn3xxRd65plnVFJSoieeeEIff/xxnWNnRDf82iOPPCLDMGq8PfbYY54OET4kNTW1xr70yCOPeDo8+KC0tDQ99NBD6tatW+VCHNHR0frTn/6kvLw8T4cHH5Sfn6/Zs2fr1ltvVWRkpM+9PwUEBGjRokWKiopSRkaGRo8ercaNG6tx48a6//77lZubq379+mn+/PmeDhXAWeTbMBs5N8xEvg2z+Xq+Lbk2527SpIkWL16sFi1aKD4+XgMHDqz823vyySdVUlKiMWPG6P3333cudqeOAhqI3/72txo9evQFj3/11VdatWqVbrnlFg9EBV936623avz48ec9duWVV3ooGviyY8eO6fDhw7rrrrvUvn17Wa1Wbd++Xa+//roWLVqkTZs2KTAw0NNhwoecPHlSc+bMUevWrTVw4ED9+OOPng6pzqKiorR7927NnTtX33//vVJSUhQYGKiePXvqgQce0PTp0xUUFOTpMAGcRb4NVyHnhhnIt2G2hpBvS67NuQcMGKC9e/fqrbfe0uLFi5Wenq7GjRsrOjpakydP1pQpUyoXxKwrpi4BfsVms6ljx44qKirSkSNH+FBDraWmpqpTp0568cUX9ec//9nT4aABe+edd/TCCy/oxx9/1M033+zpcOBDiouLdfLkSbVt21ZFRUVq1KiRJk+erK+++srToQHwI+TbqA9ybrgD+TacRb7tWUxdAvzKypUrdfjwYT300EMk3XBaUVGRzpw54+kw0EA55jk7deqUZwOBzwkODlbbtm09HQYAP0e+DbOQc8NVyLfhLPJtz6LQDfzKl19+KUn6zW9+4+FI4Ks++ugjhYaGKjQ0VFdeeaXef/99cfEM6qOoqEgnT55Uenq6/v3vf+ull15SSEiIhg8f7unQAACoM/JtmIGcG2Yi3wYaBgrdME1hYaGWLFmi119/XXfffbc6duxYuSjI7Nmza9VGXl6eZs+erV69eiksLExNmjTRoEGD9O6776qkpMS1T0AVq7/+61//Uv/+/dW7d2+Xnw8188X+ZLFYNGrUKL355pv64Ycf9Omnn6p58+Z67rnnNG3aNNPPh7rxxT7l8Pnnn6tly5bq0KGDbr/9dgUFBemHH35Q+/btXXZOXJov9ykAvqkhvO+Qb3sXX+xT5Nzeyxf7kwP5tnfy5T4Fz2AxSphm69at9Zq76tChQxoxYoRSU1MlSaGhoSouLtb27du1fft2zZ8/X6tWrVKzZs0uOLakpES7d++u1XkaNWqknj17VrttwYIFKioqYnSJF/DF/tShQwetXLnyvO1Tp07VDTfcoE8++UTTpk2rse/B9XyxTznceeed6tatm3JycrRx40atXr1aubm5Tj8XmMOX+xQA39QQ3nfIt72LL/Ypcm7v5Yv9yYF82zv5cp+Ch9gBk6xZs8berFkz+6hRo+wzZ860f/PNN/bIyEi7JPusWbMuemxZWZm9V69edkn21q1b21esWGG32+328vJy+4IFC+zh4eF2SfZx48ZVe3xKSopdUq1uPXv2rDGOIUOG2IOCguxZWVlOvw4wR0PoTw4//vijXZL9v/7rv+r8OsA8DalPffvtt3ZJlXHAM3y9T505c8YuyT558uT6vAwA3MjX33fsdvJtb9MQ+pQDObfnNaT+RL7tHXy9T5Fvux8jumGaYcOGKTs7+7zHfv/739fq2K+++kp79uyRJH333Xe65pprJFVcljZ+/HjZbDY9+OCDWrJkiVatWqVRo0add3xkZKTWrFlTq3M1bty42scPHDigzZs3695771Xz5s1r1RZcx9f7U1WOhUyysrJq1SZcoyH1qbvvvlshISH68ssvNXr06Fq1C/M1pD4FwDf4+vsO+bb38fU+VRU5t+c1pP5Evu0dGlKfgntQ6IZprFar08d+/fXXkqSRI0dWvvlUNWHCBP3hD39QSkq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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(15, 6))\n", "p = ax[1].pcolormesh(alpha, N, power, vmin=0, vmax=1, cmap='viridis')\n", "div = make_axes_locatable(ax[1])\n", "cax = div.append_axes(\"right\", size=\"5%\", pad=0.05)\n", "cbar = plt.colorbar(p, cax=cax)\n", "ax[0].set_xscale('log')\n", "ax[1].set_xscale('log')\n", "p = ax[0].pcolormesh(alpha, N, results_must_guess, vmin=0, cmap='viridis')\n", "div = make_axes_locatable(ax[0])\n", "cax = div.append_axes(\"right\", size=\"5%\", pad=0.05)\n", "cbar = plt.colorbar(p, cax=cax)\n", "\n", "ax[0].fill_between(alpha, min_N, color='white')\n", "ax[1].fill_between(alpha, min_N, color='white')\n", "\n", "ax[1].set_title('power')\n", "ax[0].set_title('minimum corrected guess to reject H0', fontsize=15)\n", "ax[1].set_xlabel('alpha')\n", "ax[1].set_ylabel('number of cups')\n", "ax[0].set_xlabel('alpha')\n", "ax[0].set_ylabel('number of cups')\n", "\n", "ax[0].plot(5E-2, 10, 'ro')\n", "ax[1].plot(5E-2, 10, 'ro')\n", "\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Neyman–Pearson lemma\n", "Having two simple hypotheses (no additional parameters) $H_0: \\theta = \\theta_0$ and $H_1: \\theta = \\theta_1$, define the likelihood-ratio test:\n", "$$\n", "\\Lambda(\\vec x) = \\frac{L(\\theta_0|\\vec x)}{L(\\theta_1|\\vec x)}\n", "$$\n", "\n", "which rejects $H_0$ in favour of $H_1$ when $\\Lambda < q_\\alpha$ (rejection region) with $\\alpha=P(\\Lambda(\\vec x)\\leq q_\\alpha|H_0)$. The likelihood-ratio test ***is the most powerful test with size $\\alpha$***." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Example\n", "Suppose you have a rock that seems to be opal (density 2.2 g/cm3), but may be also quartz (2.6 g/cm3). You have two instruments to measure the density, the first with resolution 0.2 g/cm3, the second with resolution 0.5 g/cm3. Opal is much expensive, we want to check if it is opal. $H_0:$quartz. What is the rejection region at 5%? Assume gaussian errors." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "ws = ROOT.RooWorkspace()\n", "true_density = ws.factory(\"true_density[2, 3]\")\n", "ws.factory(\"Gaussian::pdf1(density1[0,50], true_density, resolution1[0.5])\")\n", "ws.factory(\"Gaussian::pdf2(density2[0,50], true_density, resolution2[0.2])\")\n", "pdf = ws.factory(\"PROD::pdf(pdf1, pdf2)\")\n", "\n", "pdf_opal = ws.factory(\"EDIT:pdf_opal(pdf, true_density=density_opal[2.2])\")\n", "pdf_quartz = ws.factory(\"EDIT:pdf_quartz(pdf, true_density=density_quartz[2.6])\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1) RooRealVar:: density1 = 2.69947\n", " 2) RooRealVar:: density2 = 2.11305\n" ] } ], "source": [ "# do the experiment, use H1 to generate (opal)\n", "data = pdf_opal.generate(ROOT.RooArgSet(ws.var('density1'),\n", " ws.var('density2')), 1) # generate with 1 entry\n", "data.get(0).Print(\"V\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "opal_model = RooStats.ModelConfig(\"opal (H1)\", ws) \n", "opal_model.SetPdf(pdf_opal)\n", "opal_model.SetParametersOfInterest('density_opal') # not useful\n", "opal_model.SetObservables('density1,density2') # no space\n", "opal_model.SetSnapshot(ROOT.RooArgSet(ws.var('density_opal')))\n", "\n", "quartz_model = opal_model.Clone(\"quartz (H0)\")\n", "quartz_model.SetParametersOfInterest('density_quartz') # not useful\n", "quartz_model.SetPdf(pdf_quartz)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# define the test-statistic: -log L(H0)/L(H1)\n", "\n", "test = RooStats.SimpleLikelihoodRatioTestStat(pdf_quartz, pdf_opal) # null, alt\n", "test.EnableDetailedOutput(True)\n", "\n", "hypoCalc = RooStats.FrequentistCalculator(data, opal_model, quartz_model) # alt, null\n", "hypoCalc.SetToys(20000, 1000) # generate much more toys for bkg-only\n", "\n", "toy_sampler = hypoCalc.GetTestStatSampler()\n", "toy_sampler.SetTestStatistic(test) # our test statistics\n", "toy_sampler.SetNEventsPerToy(1)\n", "\n", "htr = hypoCalc.GetHypoTest()\n", "htr.SetPValueIsRightTail(True) # the \"extreme\" cases are on the right tail\n", "htr.SetBackgroundAsAlt(False)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot = RooStats.HypoTestPlot(htr, 100, -15, 15)\n", "canvas = ROOT.TCanvas()\n", "plot.Draw()\n", "canvas.Draw()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed qvalue: 2.3903879176554472\n", "observed p-value: 0.015\n", "k_alpha = 1.1855245352433041\n", "power = 0.694\n" ] } ], "source": [ "print(\"observed qvalue: \", test.Evaluate(data, ROOT.RooArgSet(ws.var('density_quartz'))))\n", "print(\"observed p-value: \", htr.NullPValue())\n", "alpha = 0.05\n", "kalpha = htr.GetNullDistribution().InverseCDF(1 - alpha)\n", "beta = htr.GetAltDistribution().CDF(kalpha)\n", "print(f\"k_alpha = {kalpha}\")\n", "print(f\"power = {1 - beta}\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Exercize\n", "Show that the in this case the likelihood ratio is equivalent to the weighted mean of the two measurements" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def eval_test_stat():\n", " d = ROOT.RooDataSet(\"d\", \"d\", ROOT.RooArgSet(ws.var('density1'), ws.var('density2')))\n", " d.add(ROOT.RooArgSet(ws.var('density1'), ws.var('density2')))\n", " return test.Evaluate(d, ROOT.RooArgSet(ws.var('true_density')))\n", "\n", "fig_opal, ax = plt.subplots(figsize=(12, 7))\n", "\n", "x = np.linspace(1.3, 3.5, 100)\n", "y = np.linspace(1.5, 3.5, 100)\n", "\n", "qvalues = np.zeros((len(x), len(y)))\n", "pdf_opal_values = np.zeros((len(x), len(y)))\n", "pdf_quartz_values = np.zeros((len(x), len(y)))\n", "for ix, xx in enumerate(x):\n", " for iy, yy in enumerate(y): \n", " ws.var('density1').setVal(xx)\n", " ws.var('density2').setVal(yy)\n", " qvalues[iy, ix] = eval_test_stat()\n", " pdf_opal_values[iy, ix] = pdf_opal.getVal()\n", " pdf_quartz_values[iy, ix] = pdf_quartz.getVal()\n", " \n", "c = plt.pcolormesh(x, y, qvalues, cmap='viridis')\n", "cs = ax.contour(x, y, qvalues, [kalpha], linestyles='dashed')\n", "ax.clabel(cs, fontsize=14, fmt=r\"$k_\\alpha$ = %1.3f\", inline_spacing=30, use_clabeltext=True)\n", "ax.contour(x, y, pdf_opal_values, cmap='Blues', alpha=0.6)\n", "ax.contour(x, y, pdf_quartz_values, cmap='Oranges', alpha=0.6)\n", "ax.plot(ws.var('density_opal').getVal(), ws.var('density_opal').getVal(), 'o', label='opal (H1)')\n", "ax.plot(ws.var('density_quartz').getVal(), ws.var('density_quartz').getVal(), 'o', label='quartz (H0)')\n", "ax.text(1.5, 1.6, \"reject\", size=20)\n", "ax.text(1.8, 3.2, \"accept\", size=20)\n", "datalist = [x.getVal() for x in iter_collection(data.get(0))]\n", "ax.plot(datalist[0], datalist[1], 'v', label='observed', color='red')\n", "\n", "ax.set_xlabel('density1')\n", "ax.set_ylabel('density2')\n", "ax.legend()\n", "ax.set_aspect('equal')\n", "plt.colorbar(c)\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can easily show the acceptance / rejection region in the space of the observables" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig_opal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercize\n", "Compute the acceptance region using the simple mean as test-statistics: show that it is less powerful. What kind of shape is the acceptance region in this case?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Plot the power as a function of the size of the test for the likelihood ratio" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alphas = np.linspace(0, 1, 100)\n", "powers = []\n", "\n", "for alpha in alphas:\n", " kalpha = htr.GetNullDistribution().InverseCDF(1 - alpha)\n", " beta = htr.GetAltDistribution().CDF(kalpha)\n", " powers.append(1 - beta)\n", " \n", "plt.plot(alphas, powers) \n", "plt.xlabel(r'$\\alpha$')\n", "plt.ylabel(r'power')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Exercize\n", "Compute $\\text{power}(\\alpha)$ for the simple mean and compare with the weighted mean.\n", "### Exercize\n", "Explain why the previous plot remembers the ROC curve (bkg-rejection vs signal-efficiency)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Exclusion and frequentist intervals\n", "\n", "By now we have done statistical test to discover something (a signal), defining the null hypothesis to be the background only case. Suppose we have counted $n_{obs}$ events in a Poissonian process with mean $\\lambda$. What are the values $[\\lambda_{up}, \\infty]$ that we can exclude? This is something called hypothesis inversion. As usual we define the null hypothesis: $H_0: \\lambda = N$ with $N > n_{obs}$. The likelihood:\n", "\n", "$$L = \\text{Pois}(n|N)$$\n", "\n", "than the p-value of our observation $n_{obs}$:\n", "\n", "$$\\text{p-value} = \\sum_{n\\geq n_{obs}} \\text{Pois}(n|N)$$\n", "\n", "if p-value $<\\alpha$ we consider $N$ to be inside the exluded region $[\\lambda_{up}, \\infty]$. The general approach is to scan for many value of $N$ until we found the one with p-value $=\\alpha$, which is $n_{up}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Example: RooFit asymmetric error bars\n", "\n", "Let's do a two-side test and compute the excluded intervals $[-\\infty, \\lambda_{down}]$ and $[\\lambda_{up}, \\infty]$ with $\\alpha=1 - 0.6827$. This means that every single interval should be tested with $\\alpha=(1-0.6827)/2.=0.15865$. We can solve it analytically or with a scan. Suppose $n_{obs} = 4$." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "NOBS = 4\n", "ALPHA = z2p(1) # 0.158...\n", "\n", "def compute_pvalue(nobs, ntrue, left):\n", " if left:\n", " return stats.poisson(ntrue).cdf(nobs)\n", " else:\n", " return stats.poisson(ntrue).sf(nobs) + stats.poisson(ntrue).pmf(nobs)\n", "\n", "fig, axs = plt.subplots(1, 3, figsize=(13, 4))\n", "x = np.linspace(NOBS, NOBS + 3 * NOBS, 20)\n", "\n", "axs[1].plot(x, compute_pvalue(NOBS, x, left=True), 'r')\n", "axs[1].hlines(ALPHA, np.min(x), np.max(x), linestyles='--')\n", "\n", "x = np.linspace(max(NOBS - NOBS * 3, 0), NOBS, 100)\n", "axs[0].plot(x, compute_pvalue(NOBS, x, left=False), 'b')\n", "axs[0].hlines(ALPHA, np.min(x), np.max(x), linestyles='--')\n", "\n", "from scipy.optimize import brenth\n", "lambda_up = brenth(lambda x: compute_pvalue(NOBS, x, True) - ALPHA, NOBS, NOBS * 3)\n", "lambda_down = brenth(lambda x: compute_pvalue(NOBS, x, False) - ALPHA, 1E-5, NOBS)\n", "\n", "axs[1].plot(lambda_up, compute_pvalue(NOBS, lambda_up, True), 'ro')\n", "axs[0].plot(lambda_down, compute_pvalue(NOBS, lambda_down, False), 'bo')\n", "axs[1].set_xlabel('$\\lambda$'); axs[0].set_xlabel('$\\lambda$')\n", "axs[1].set_ylabel('$P(n\\leq n_{obs})$')\n", "axs[0].set_ylabel('$P(n\\geq n_{obs})$')\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "x = np.arange(0, NOBS * 3)\n", "axs[2].step(x, stats.poisson(lambda_up).pmf(x), 'r', label='Pois[$\\lambda=\\lambda_{up}$]')\n", "axs[2].step(x, stats.poisson(lambda_down).pmf(x), 'b', label='Pois[$\\lambda=\\lambda_{down}$]')\n", "axs[2].vlines(NOBS, 0, 0.3, linestyles='--')\n", "axs[2].legend(fontsize=12, loc=0)\n", "axs[2].set_xlabel('n')\n", "fig.tight_layout()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.0856608137771175 7.1627531722609445\n" ] }, { "data": { "text/latex": [ "$\\lambda = 4.00^{+3.16}_{-1.91}$" ], "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(lambda_down, lambda_up)\n", "Latex(\"$\\lambda = %.2f^{+%.2f}_{-%.2f}$\" % (NOBS, lambda_up - NOBS, NOBS - lambda_down))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question:\n", "why we assumed that the central value for $\\lambda$ is $n_{obs}=4$?" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "(2.085660813777117, 7.162753172260944)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def get_confiderence_poisson(n):\n", " ym = np.array([0], dtype=np.float64)\n", " yp = np.array([0], dtype=np.float64)\n", " ROOT.RooHistError.instance().getPoissonInterval(n, ym, yp, 1)\n", " return ym[0], yp[0]\n", "\n", "get_confiderence_poisson(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the function used by RooFit to draw error bands" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(7, 5))\n", "trues = np.linspace(1E-5, NOBS * 4, 100)\n", "obss = np.arange(0, NOBS * 3, dtype=np.int32)\n", "v = np.zeros((len(trues), len(obss)))\n", "limits = []\n", "for ix, obs in enumerate(obss):\n", " limits.append(get_confiderence_poisson(int(obs)))\n", " for iy, true in enumerate(trues):\n", " v[iy, ix] = stats.poisson(true).pmf(obs)\n", "ax.pcolormesh(obss, trues, v, vmax=np.percentile(v, 99))\n", "ax.plot(obss, np.array(limits).T[0], 'k', drawstyle='steps-post')\n", "ax.plot(obss, np.array(limits).T[1], 'k', drawstyle='steps-post')\n", "ax.set_xlim(0, np.max(obss))\n", "ax.set_xlabel('obs')\n", "ax.set_ylabel('$\\lambda$'); plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Question: explain why this is a frequentist procedure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian approach\n", "\n", "$$P(\\lambda|n_{obs}) = P(n_{obs}|\\lambda)P(\\lambda)$$\n", "\n", "We assume the prior $P(\\lambda)$ to be flat (and zero for negative values), equivalent to a constant we can ignore. Everybody agree?\n", "\n", "$$P(\\lambda|n_{obs}) = P(n_{obs}|\\lambda)$$\n", "\n", "note that $n_{obs}$ is fixed, so this is a real function $f(\\lambda)$. Let find a region [low, high] such that\n", "\n", "$$\\int_{low}^{high} P(\\lambda|n_{obs}) = 68\\%$$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.8403088555932197 7.162753172255066\n" ] }, { "data": { "text/latex": [ "$\\lambda = 4.00_{-1.16}^{+3.16}$" ], "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def f(true):\n", " return stats.poisson(true).pmf(NOBS)\n", "\n", "import scipy\n", "from scipy.optimize import brenth, brentq\n", "def f_low(x):\n", " return scipy.integrate.quad(f, 0, x)[0] - z2p(1)\n", "\n", "def f_hi(x):\n", " return scipy.integrate.quad(f, x, NOBS * 10)[0] - z2p(1)\n", "\n", "lo_bayes, hi_bayes = brentq(f_low, 1E-5, NOBS), brentq(f_hi, NOBS, NOBS * 5)\n", "print(lo_bayes, hi_bayes)\n", "Latex(\"$\\lambda = %.2f_{-%.2f}^{+%.2f}$\" % (NOBS, NOBS - lo_bayes, hi_bayes - NOBS))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.289882379081169 6.402859007849325\n" ] } ], "source": [ "def invert(f, y, a, b):\n", " return brentq(lambda x: f(x) - y, a, b)\n", "\n", "lo_bayes_el = brenth(\n", " lambda x: scipy.integrate.quad(f, x, invert(f, f(x), x * (1 + 1E-5), NOBS * 20))[0] - (1 - z2p(1) * 2),\n", " 1E-2, NOBS - 1E-2)\n", "hi_bayes_el = invert(f, f(lo_bayes_el), NOBS, NOBS * 5)\n", "print(lo_bayes_el, hi_bayes_el)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.289882286599089 6.402858915367273\n" ] } ], "source": [ "def width_interval(x):\n", " return brenth(lambda y: scipy.integrate.quad(f, x, y)[0] - (1 - z2p(1) * 2), x, NOBS * 20) - x\n", "\n", "sol = scipy.optimize.minimize_scalar(width_interval, (1E-1, 3), bounds=(0, NOBS), method='bounded')\n", "lo_bayes_min, hi_bayes_min = sol.x, sol.x + width_interval(sol.x)\n", "print(lo_bayes_min, hi_bayes_min)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "x = np.linspace(0, NOBS * 3, 100)\n", "\n", "fig, axs = plt.subplots(1, 3, figsize=(14, 4))\n", "\n", "axs[0].plot(x, f(x))\n", "axs[0].fill_between(np.linspace(0, lo_bayes, 50), f(np.linspace(0, lo_bayes, 50)))\n", "axs[0].fill_between(np.linspace(hi_bayes, NOBS * 3, 50), f(np.linspace(hi_bayes, NOBS * 3, 50)))\n", "axs[0].set_title('equal probability (central)', fontsize=15)\n", "axs[0].text(7, 0.16, '$\\lambda = %.2f_{-%.2f}^{+%.2f}$' % (NOBS, NOBS - lo_bayes, hi_bayes - NOBS), size=15)\n", "axs[0].text(4, 0.04, '68%', size=15)\n", "axs[0].set_xlabel('$\\lambda$')\n", "axs[1].plot(x, f(x))\n", "axs[1].fill_between(np.linspace(0, lo_bayes_el, 50), f(np.linspace(0, lo_bayes_el, 50)))\n", "axs[1].fill_between(np.linspace(hi_bayes_el, NOBS * 3, 50), f(np.linspace(hi_bayes_el, NOBS * 3, 50)))\n", "axs[1].set_title('equal likelihood', fontsize=15)\n", "axs[1].text(7, 0.16, '$\\lambda = %.2f_{-%.2f}^{+%.2f}$' % (NOBS, NOBS - lo_bayes_el, hi_bayes_el - NOBS), size=15)\n", "axs[1].text(3.5, 0.04, '68%', size=15)\n", "axs[1].set_xlabel('$\\lambda$')\n", "axs[2].plot(x, f(x))\n", "axs[2].fill_between(np.linspace(0, lo_bayes_min, 50), f(np.linspace(0, lo_bayes_min, 50)))\n", "axs[2].fill_between(np.linspace(hi_bayes_min, NOBS * 3, 50), f(np.linspace(hi_bayes_min, NOBS * 3, 50)))\n", "axs[2].set_title('minimum interval', fontsize=15)\n", "axs[2].text(7, 0.16, '$\\lambda = %.2f_{-%.2f}^{+%.2f}$' % (NOBS, NOBS - lo_bayes_min, hi_bayes_min - NOBS), size=15)\n", "axs[2].text(3.5, 0.04, '68%', size=15)\n", "axs[2].set_xlabel('$\\lambda$')\n", "for ax in axs: ax.set_yticklabels([])\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "slideshow": { "slide_type": "slide" } }, "source": [ "## Profile likelihood ratio\n", "\n", "Suppose you have composite hypothesis as \n", "\n", "$$H_0: \\theta\\in\\Theta_0 \\quad H_1: \\theta\\in\\Theta_0^C \\quad \\Theta_0\\subset\\Theta$$\n", "\n", "where $\\Theta_0 = \\{s=0, \\ldots\\}$, $\\Theta_0^C = \\{s\\neq 0, \\ldots\\}$. $x$ are the data.\n", "\n", "$$\\lambda(x) = \\frac{\\sup_{\\theta\\in\\Theta_0}{L(\\theta|x)}}{\\sup_{\\theta\\in\\Theta}{L(\\theta|x)}}$$\n", "\n", "For example it can be $H_0: s=0$, $H_1: s\\neq 0$\n", "\n", "$$\\lambda(x) = \\frac{\\sup_{\\theta}L(s=0, \\theta|x)}{\\sup_{\\theta,s} L(s, \\theta|x)}=\\frac{L(s=0, \\hat{\\hat\\theta}(0)|x)}{L(\\hat{s}, \\hat\\theta|x)}$$\n", "\n", "\n", "where $\\hat{\\hat\\theta}(0)$ is the value of $\\theta$ which optimize the likelihood for $s=0$ (conditioned likelihood), while $\\hat{s}$ and $\\hat{\\theta}$ are the values that optimize the likelihood without any constrains (unconditioned likelihood).\n", "\n", "\n", "It varies between 0 and 1, low values mean that the observed result is less likely to occur under the null hypothesis as compared to the alternative. (numerator $\\leq$ denominator)\n", "\n", "The profile likelihood ratio is nearly an optimal test-statistics" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "As shown it is important to have an analytically expression $f_q$ of the distribution of the test-statistics $q$ to compute the p-value: $\\text{p-value} = \\int_{q^\\text{obs}}^{\\infty} f_q(q) dq$. Otherwise toys must be run.\n", "\n", "## Wilks's theorem\n", "\n", "The quantity $t=-2\\log(\\lambda)$ is aymptotically (large sample) distributed as a $\\chi^2$ distribution with $n=\\text{dim}(\\Theta)-\\text{dim}(\\Theta_0)$ degrees of freedom when $H_0$ is true." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let resurrect the simple Poisson model $\\text{Poisson}(n|s + b)$. This time, instead of using the number of observed events as test-statistics, let use the profile likelihood ratio." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed = 229.0\n" ] } ], "source": [ "S, B = 30, 200 # expected values\n", "\n", "ws_poisson = ROOT.RooWorkspace('ws_poisson')\n", "b = ws_poisson.factory(\"b[%f]\" % B)\n", "n_exp = ws_poisson.factory(\"sum::n_exp(s[%f, -500, 500], b)\" % S)\n", "pdf = ws_poisson.factory(\"Poisson::pdf(n_obs[0, 1000], n_exp)\")\n", "aset = ROOT.RooArgSet(ws_poisson.var('n_obs'))\n", "data = pdf.generate(aset, 1) # generate with 1 entry\n", "print(\"observed = \", data.get(0).first().getVal())" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# create a MC linked to the ws\n", "sbModel = RooStats.ModelConfig(\"sbmodel\", ws_poisson) \n", "sbModel.SetPdf(pdf)\n", "sbModel.SetObservables('n_obs') # it understands variable-names\n", "sbModel.SetParametersOfInterest('s')\n", "# save the value of s for (s+b)-hypothesis\n", "sbModel.SetSnapshot(ROOT.RooArgSet(ws_poisson.var('s')))\n", "getattr(ws_poisson, 'import')(sbModel) # import is a keyword in python\n", "\n", "bModel = sbModel.Clone(\"bmodel\") # create a bkg-only model\n", "ws_poisson.var('s').setVal(0) # with no signal\n", "bModel.SetSnapshot(ROOT.RooArgSet(ws_poisson.var('s')))\n", "getattr(ws_poisson, 'import')(bModel);" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "profll = RooStats.ProfileLikelihoodTestStat(bModel.GetPdf())\n", "# this modify a bit our test statistics\n", "profll.SetOneSidedDiscovery(1)\n", "\n", "hypoCalc = RooStats.FrequentistCalculator(data, sbModel, bModel)\n", "hypoCalc.SetToys(100000, 5000) # generate much more toys for bkg-only\n", "\n", "toy_sampler = hypoCalc.GetTestStatSampler()\n", "toy_sampler.SetTestStatistic(profll)\n", "toy_sampler.SetNEventsPerToy(1)\n", "\n", "htr = hypoCalc.GetHypoTest()\n", "htr.SetPValueIsRightTail(True) # the \"extreme\" cases are on the right tail\n", "htr.SetBackgroundAsAlt(False)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pvalue = 0.02451 significance = 1.9684176737724473\n" ] }, { "data": { "image/png": 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", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot = RooStats.HypoTestPlot(htr, 50, 0, 10)\n", "canvas = ROOT.TCanvas()\n", "plot.Draw()\n", "canvas.SetLogy(); canvas.Draw()\n", "print(\"pvalue = \", htr.NullPValue(), \" significance = \", htr.Significance())" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "The distribution under the $H_0$ has a peak at 0, which does not follow the $\\chi^2$ distribution. Explain why (see test statistics for one-side-discovery and SetOneSideDiscovery(True) option)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We can also use the AsymtoticCalculator, which instead of using the empirical distribution of the likelihood ratio from toys, it uses the asymptotic distribution ($\\chi^2_1$ distribution for the simple likelihood ratio)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pvalue = 0.022544284300433422 significance = 2.003827251118166\n", "AsymptoticCalculator::EvaluateNLL ........ using / Migrad with strategy 1 and tolerance 1\n", "Minuit2Minimizer: Minimize with max-calls 500 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 3.63616348402820222\n", "Edm = 4.8258587877775207e-08\n", "Nfcn = 18\n", "s\t = 28.9953\t +/- 15.1301\t(limited)\n", "AsymptoticCalculator::EvaluateNLL - value = 3.63616\tfit time : Real time 0:00:00, CP time 0.000\n", "MakeAsimov: Setting poi s to a constant value = 30\n", "Generated Asimov data for observables RooArgSet:: = (n_obs)\n", "AsymptoticCalculator::EvaluateNLL - value = 3.63834 for poi fixed at = 30\n", "\n", "AsymptoticCalculator::EvaluateNLL - value = 5.64383 for poi fixed at = 0\n", "AsymptoticCalculator::EvaluateNLL - value = 5.78359 for poi fixed at = 0\n" ] } ], "source": [ "hypoCalc = RooStats.AsymptoticCalculator(data, sbModel, bModel)\n", "hypoCalc.SetOneSidedDiscovery(True)\n", "htr_asym = hypoCalc.GetHypoTest()\n", "print(\"pvalue =\", htr_asym.NullPValue(), \" significance =\", htr_asym.Significance())" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## On/off problem\n", "\n", "Let's introduce a classical problem in high-energy / astro / ... physics. Suppose you have a source that can contain signal and background events. You have an other source that contains only background events and the background in the two source is correlated.\n", "\n", "This is the case when you have a control region, with only background, and a signal region with signal plus background. Usually the correlation of the background between the two region comes from a simulation. In astrophysics this can be the case when with telescope one wants to see if there is source in a particular region of the sky, using as control region the average of regions where there are no known source.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In term of random variables:\n", "\n", "$$ N_{SR} = S + B \\qquad N_{CR} = \\alpha B$$\n", "\n", "with $S$ and $B$ distributed as Poisson distribution. What we observe are the number of events in the signal region $n_{SR}$ and in the control region $n_{CR}$. $\\alpha$ is assumed to be a known constant. We can write the likelihood as:\n", "\n", "$$L(s, b|n_{SR}, n_{CR}) = \\text{Pois}(n_{SR}|s + b) \\text{Pois}(n_{CR}|\\alpha b)$$\n", "\n", "remember that $\\alpha$ is a known constant. The test statistics is based on the profiled likelihood ratio:\n", "\n", "$$-2\\log\\lambda = -2\\log\\frac{\\sup_{b \\in [0, \\infty], s\\in\\{0\\}}{L(s, b)}}{\\sup_{b\\in [0, \\infty], s\\in [0, \\infty]}{L(s, b)}} = -2\\log\\frac{L(0, \\hat{\\hat{b}}(s=0))}{L(\\hat{s}, \\hat{b})}$$\n" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "RooWorkspace(ws_onoff) ws_onoff contents\n", "\n", "variables\n", "---------\n", "(alpha,b,n_cr,n_sr,s)\n", "\n", "p.d.f.s\n", "-------\n", "RooPoisson::N_CR[ x=n_cr mean=alpha_x_b ] = 0\n", "RooPoisson::N_SR[ x=n_sr mean=s_plus_b ] = 0\n", "RooProdPdf::model[ N_SR * N_CR ] = 0\n", "\n", "functions\n", "--------\n", "RooProduct::alpha_x_b[ alpha * b ] = 500\n", "RooAddition::s_plus_b[ s + b ] = 50\n", "\n", "parameter snapshots\n", "-------------------\n", "sbModel__snapshot = (s=15)\n", "bModel__snapshot = (s=0)\n", "\n", "named sets\n", "----------\n", "bModel__snapshot:(s)\n", "sbModel_Observables:(n_sr,n_cr)\n", "sbModel_POI:(s)\n", "sbModel__snapshot:(s)\n", "\n", "generic objects\n", "---------------\n", "RooStats::ModelConfig::sbModel\n", "\n" ] } ], "source": [ "ws_onoff = ROOT.RooWorkspace('ws_onoff')\n", "model_sr = ws_onoff.factory(\"Poisson:N_SR(n_sr[0, 5000], sum:s_plus_b(s[15, 0, 100], b[50, 0, 100] ))\")\n", "model_cr = ws_onoff.factory(\"Poisson:N_CR(n_cr[0, 5000], prod:alpha_x_b(alpha[10, 0, 10], b))\")\n", "model = ws_onoff.factory(\"PROD:model(N_SR, N_CR)\")\n", "ws_onoff.var(\"alpha\").setConstant(True)\n", "\n", "sbModel = RooStats.ModelConfig('sbModel', ws_onoff)\n", "sbModel.SetObservables('n_sr,n_cr')\n", "sbModel.SetParametersOfInterest('s')\n", "sbModel.SetPdf('model')\n", "sbModel.SetSnapshot(ROOT.RooArgSet(ws_onoff.var('s')))\n", "getattr(ws_onoff, 'import')(sbModel)\n", "\n", "bModel = sbModel.Clone(\"bModel\")\n", "ws_onoff.var('s').setVal(0)\n", "bModel.SetSnapshot(bModel.GetParametersOfInterest())\n", "\n", "ws_onoff.Print()\n", "ws_onoff.writeToFile('onoff.root')" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "model\n", "\n", "\n", "\n", "model\n", "\n", "RooProdPdf\n", "model\n", "0.000000\n", "\n", "\n", "\n", "N_SR\n", "\n", "RooPoisson\n", "N_SR\n", "0.000000\n", "\n", "\n", "\n", "model->N_SR\n", "\n", "\n", "\n", "\n", "\n", "N_CR\n", "\n", "RooPoisson\n", "N_CR\n", "0.000000\n", "\n", "\n", "\n", "model->N_CR\n", "\n", "\n", "\n", "\n", "\n", "n_sr\n", "\n", "RooRealVar\n", "n_sr\n", "2500.000000\n", "\n", "\n", "\n", "N_SR->n_sr\n", "\n", "\n", "\n", "\n", "\n", "s_plus_b\n", "\n", "RooAddition\n", "s_plus_b\n", "50.000000\n", "\n", "\n", "\n", "N_SR->s_plus_b\n", "\n", "\n", "\n", "\n", "\n", "s\n", "\n", "RooRealVar\n", "s\n", "0.000000\n", "\n", "\n", "\n", "s_plus_b->s\n", "\n", "\n", "\n", "\n", "\n", "b\n", "\n", "RooRealVar\n", "b\n", "50.000000\n", "\n", "\n", "\n", "s_plus_b->b\n", "\n", "\n", "\n", "\n", "\n", "n_cr\n", "\n", "RooRealVar\n", "n_cr\n", "2500.000000\n", "\n", "\n", "\n", "N_CR->n_cr\n", "\n", "\n", "\n", "\n", "\n", "alpha_x_b\n", "\n", "RooProduct\n", "alpha_x_b\n", "500.000000\n", "\n", "\n", "\n", "N_CR->alpha_x_b\n", "\n", "\n", "\n", "\n", "\n", "alpha_x_b->b\n", "\n", "\n", "\n", "\n", "\n", "alpha\n", "\n", "RooRealVar\n", "alpha\n", "10.000000\n", "\n", "\n", "\n", "alpha_x_b->alpha\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.graphVizTree(\"on_off_graph.dot\")\n", "!dot -Tsvg on_off_graph.dot > on_off_graph.svg; rm on_off_graph.dot\n", "SVG(\"on_off_graph.svg\")" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed N_SR = 57, N_CR = 447\n", "\n", "best fit s b\n", "SR 12.3 44.7\n", "CR 447.0\n" ] } ], "source": [ "sbModel.LoadSnapshot()\n", "data = model.generate(bModel.GetObservables(), 1)\n", "print(\"observed N_SR = %.f, N_CR = %.f\" % tuple([x.getVal() for x in iter_collection(data.get(0))]))\n", "model.fitTo(data)\n", "print(\"\\nbest fit s b\")\n", "print(\"SR {:>8.1f} {:>8.1f}\".format(ws_onoff.var('s').getVal(), ws_onoff.var('b').getVal()))\n", "print(\"CR {:>8.1f}\".format(ws_onoff.function('alpha_x_b').getVal()))" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "profll = RooStats.ProfileLikelihoodTestStat(bModel.GetPdf())\n", "# this modify a bit our test statistics\n", "profll.SetOneSidedDiscovery(True)\n", "\n", "hypoCalc = RooStats.FrequentistCalculator(data, sbModel, bModel)\n", "hypoCalc.SetToys(10000, 500)\n", "\n", "toy_sampler = hypoCalc.GetTestStatSampler()\n", "toy_sampler.SetTestStatistic(profll)\n", "toy_sampler.SetNEventsPerToy(1)\n", "\n", "htr = hypoCalc.GetHypoTest()\n", "htr.SetPValueIsRightTail(True) # the \"extreme\" cases are on the right tail\n", "htr.SetBackgroundAsAlt(False)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pvalue = 0.0443 significance = 1.702829395744341\n" ] }, { "data": { "image/png": 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", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot = RooStats.HypoTestPlot(htr, 50, 0, 20)\n", "canvas = ROOT.TCanvas()\n", "plot.Draw()\n", "canvas.SetLogy()\n", "canvas.Draw()\n", "print(\"pvalue = \", htr.NullPValue(), \" significance = \", htr.Significance())" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pvalue = 0.046960674305756095 significance = 1.6750656653467675\n", "expected p-value = 0.15202103457917066 significance = 1.027803925955747\n", "AsymptoticCalculator::EvaluateNLL ........ using / Migrad with strategy 1 and tolerance 1\n", "Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 6.91233052650801483\n", "Edm = 1.27558666860002018e-07\n", "Nfcn = 25\n", "b\t = 44.6991\t +/- 2.11354\t(limited)\n", "s\t = 12.3028\t +/- 7.76596\t(limited)\n", "AsymptoticCalculator::EvaluateNLL - value = 6.91233\tfit time : Real time 0:00:00, CP time 0.000\n", "MakeAsimov: Setting poi s to a constant value = 15\n", "MakeAsimov: doing a conditional fit for finding best nuisance values \n", "Minuit2Minimizer: Minimize with max-calls 500 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 6.97007284951206429\n", "Edm = 5.23661835873340247e-08\n", "Nfcn = 13\n", "b\t = 44.5114\t +/- 2.03345\t(limited)\n", "fit time Real time 0:00:00, CP time 0.000\n", "Generated Asimov data for observables RooArgSet:: = (n_sr,n_cr)\n", "AsymptoticCalculator::EvaluateNLL ........ using / Migrad with strategy 1 and tolerance 1\n", "Minuit2Minimizer: Minimize with max-calls 500 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 6.93171467586148538\n", "Edm = 1.03434489300778293e-15\n", "Nfcn = 17\n", "b\t = 44.5114\t +/- 2.03447\t(limited)\n", "AsymptoticCalculator::EvaluateNLL - value = 6.93171 for poi fixed at = 15\tfit time : Real time 0:00:00, CP time 0.000\n", "\n", "AsymptoticCalculator::EvaluateNLL ........ using / Migrad with strategy 1 and tolerance 1\n", "Minuit2Minimizer: Minimize with max-calls 500 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 8.31525301811981876\n", "Edm = 6.67260538981602789e-05\n", "Nfcn = 13\n", "b\t = 45.7946\t +/- 2.03932\t(limited)\n", "AsymptoticCalculator::EvaluateNLL - value = 8.31525 for poi fixed at = 0\tfit time : Real time 0:00:00, CP time 0.000\n", "AsymptoticCalculator::EvaluateNLL ........ using / Migrad with strategy 1 and tolerance 1\n", "Minuit2Minimizer: Minimize with max-calls 500 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 8.98770905692225597\n", "Edm = 1.86449348747825478e-09\n", "Nfcn = 13\n", "b\t = 45.875\t +/- 2.04159\t(limited)\n", "AsymptoticCalculator::EvaluateNLL - value = 8.98771 for poi fixed at = 0\tfit time : Real time 0:00:00, CP time 0.000\n" ] } ], "source": [ "hypoCalc = RooStats.AsymptoticCalculator(data, sbModel, bModel)\n", "hypoCalc.SetOneSidedDiscovery(True)\n", "htr = hypoCalc.GetHypoTest()\n", "print(\"pvalue =\", htr.NullPValue(), \" significance =\", htr.Significance())\n", "\n", "pvalue_exp = RooStats.AsymptoticCalculator.GetExpectedPValues(htr.NullPValue(), htr.AlternatePValue(), 1, False, True)\n", "significance_exp = ROOT.Math.normal_quantile_c(pvalue_exp, 1)\n", "print(\"expected p-value = \", pvalue_exp, \" significance =\", significance_exp)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create profiled log-likelihood\n", "prof = model.createNLL(data).createProfile(ROOT.RooArgSet(ws_onoff.var('s')))\n", "# multiply by 2\n", "minus2LL = ROOT.RooFormulaVar(\"minus2LL\", \"2 * @0\", ROOT.RooArgList(prof))\n", "frame = ws_onoff.var('s').frame(0, 30)\n", "minus2LL.plotOn(frame)\n", "frame.SetYTitle(\"-2 log#Lambda(s)\")\n", "canvas = ROOT.TCanvas()\n", "frame.Draw()\n", "canvas.Draw()" ] } ], "metadata": { "celltoolbar": "Slideshow", "hide_input": false, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.8" }, "latex_envs": { "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 0 } }, "nbformat": 4, "nbformat_minor": 4 }