{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Binomial, Poisson and Gaussian distributions\n", "\n", "Python notebook for illustrating the Binomial, Poisson and Gaussian distributions and how they in certain limits converge towards each other (and in the end into the Gaussian). The notebook also illustrates simple fitting.\n", "\n", "## References:\n", "- Barlow: Chapter 3\n", "\n", "## Author(s), contact(s), and dates:\n", "- Author: Troels C. Petersen (NBI) and Christian Michelsen (NBI, first Python version)\n", "- Email: petersen@nbi.dk\n", "- Date: 16th of November 2020\n", "\n", "***" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np # Matlab like syntax for linear algebra and functions\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt # Plots and figures like you know them from Matlab\n", "from iminuit import Minuit # The actual fitting tool, better than scipy's\n", "import sys # Modules to see files and folders in directories\n", "\n", "from scipy import stats\n", "from scipy.stats import binom, poisson, norm" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sys.path.append('../../../External_Functions')\n", "from ExternalFunctions import Chi2Regression\n", "from ExternalFunctions import nice_string_output, add_text_to_ax # Useful functions to print fit results on figure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We set up the parameters for the program:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# General settings:\n", "r = np.random # Random generator\n", "r.seed(42) # Fixed order of random numbers\n", "\n", "save_plots = False\n", "verbose = True\n", "N_verbose = 10\n", "\n", "# Set plotting parameters:\n", "mpl.rcParams['font.size'] = 18 # Set the general plotting font size" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting PDFs:\n", "\n", "First, we want to have a look at the three PDFs (Binomial, Poisson, and Gaussian), and compare them given \"the same\" parameters. Of course we can't give the same input parameters, but at least we can require that they have the same mean and widths (almost - one can not force the width of the Poisson to match that of the Binomial, once the mean is matched. The Gaussian will then have to choose between these two slightly different widths!).\n", "\n", "### Problem parameters:\n", "* The Binomial PDF needs two parameters: Number of trials (n) and probability of succes (p).\n", "* The Poisson PDF needs one parameter: The expected number (lambda - but in Python we write it \"Lambda\" or \"lamp\", as \"lambda\" is reserved!).\n", "* The Gaussian PDF needs two parameters: Mean (mu) and width (sigma)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def func_binomial_pmf(x, n, p):\n", " return binom.pmf(x, n, p)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def func_poisson_pmf(x, lamb):\n", " return poisson.pmf(x, lamb)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "def func_gaussian_pdf(x, mu, sigma) :\n", " return norm.pdf(x, mu, sigma)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Range of outcome:\n", "xmin = -0.5\n", "xmax = 13.5\n", "\n", "# Function parameters:\n", "# Binomial:\n", "n = 20\n", "p = 0.2\n", "# Poisson:\n", "Lambda = n * p # We choose this, as this is the expected number of successes.\n", "# Gaussian:\n", "mu = Lambda # Same here - the central value is n*p.\n", "sigma = np.sqrt(n*p*(1-p)) # For a Binomial process, the variance is n*p*(1-p)\n", "sigma = np.sqrt(n*p) # Alternatively, one can use the Poisson width " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "xaxis = np.linspace(xmin, xmax, 1000)\n", "yaxis_binom = func_binomial_pmf(np.floor(xaxis+0.5), n, p) # np.floor: See below\n", "yaxis_poiss = func_poisson_pmf(np.floor(xaxis+0.5), Lambda) # np.floor: See below\n", "yaxis_gauss = func_gaussian_pdf(xaxis, n*p, np.sqrt(n*p*(1-p)))\n", "\n", "# Note that the np.floor function takes the integer/rounded (towards zero) value of numbers." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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4ez+cMaYk0MhNFvb9T3B+b5atu+CreH6X10qsv2ftjTGNndYrhlWxyjHGzFgvu26f/WGM7W9YO9vHg7awisaYBzy8666Tc9o8XM3zq9QNTSfwsDyFNVvTLVhPoL/E+mOT37EHSql8EpF0Y0wPrMHlY4AexphNWGMxWmA9NBotIms8ZDEdeMMYMxD4GeuJc32s8VMDROSUU9ppWC1tHYBfjDHrsGZTjMeanv4I0CyX4uZnW4VpAdZg/BXGmCRsk0uIyEA3aV/nUqWg0Gd2FJHNxpgRWDec3xhjVmPd3NXD+huaBvQs5K6Rzl4xxjjPphiD1V0rFGscy8OeViwkz2DdnN8B7LGdjyysmQtLYL0LqlBe9ltAE7Be1vtPY0x3rMkpKgJNsbqn5fYC9fyYiPVS9geBeGPMZqxuey2xJrVohuduvfkiIinGmCFYLx//2DaZxV6sBw71sFq5HitAvh8ZYy5gjaUaC4wyxqzHar0KwLq2bsMan3UU60XT9nV/MMYsxuoSvNl2HZzBOs6RnsokIvuNMbOwJtpZZYz5FqsltRHWe+YWYr3OwFk9YApw0hizEetl4EVt24rG+ltkf0hQAqtS97rt7+h+rHu9elgzO6aS7SXRHly186vUjU5bxiwDgQkiclhEjmD9UR7gocuUUqqQichqrErNLKybjG5YM9ItAe4UkdzGOHyOdUOUhvXktwawHIgTka+cE4rIbqwB+//GukHphDXG5yWsJ8wXyJ3X2ypkTwOTsW6kugIP2BZ3ltt+Hse6KS90IjINSMC6Oa2N9R6kElg3y/VFZMWV2K7NvVgV6n5YXSUbYd2MvgDcIiI/X8Ft21vH2gBPAHuwrpv2WN25RmNdC2euZBnyKN9nQFvgO6xruyPW//p+IjK6ELezBqsy8B+sLm2dsCohT+C5C+vlbO8DrP1aiVXp7wicxJp2ff5l5PsZ1pizUVgT+NTE+o7diVX5+BrbZD8iMi/b6l2xZjDdi1UZj7fl0RDrBeSeDMGqEKXY1rkdq4dAU9s+ZfcVVsvvZlv57rWlPYBV8Y91aondg/UgeYmt/J2wrtFMrAcodUXkf7mUDbj651epG5lxnQ312maMGY11w9YA65/MARGp5CGtH/APrKc6lbCeeH8GPOfchcUYUxxrWtZqIrLHFhaNNftQJRHxNJW1Ukpdc4wxzwHjgMkiUpjd0pRSSilVyK63lp9/Yj2N3YP791o4m4L1JHknVleBecBQYFG2Fi97v2rn7kUns8UppdQ1zzYBwKNYY7re8HFxlFJKKZWH623MWFUR2QtgjNmOh6lhjTE3Y1XA5ovIvU7h+7DGjPydSwPt7d1JIrD6hAMUzxanlFLXLGPMk1jdOlthjSF5y97Sr5RSSqlr13XVMmaviHnBPu3qq9nC38Ea6+Ho72zrZ/0r1iBdu9uxWsfcTemqlFLXmg5AH6xJB17DmuxDKaWUUte4661lzFuxWLNbuQxSFZFzthmBYrOlnwk8bYxZizWAfyzW1MT6Bnml1DVPROJ9XQallFJK5d911TKWDzHAURHJcBOXAkQ5v2MIayzaf4EdwG6scWZPXfFSKqWUUkoppW5Yf9WWsVDAXUUM4JxTmvMAIpKJNbnH0LwyNsYMxvaiyLCwsAa1atXKYw2llFJKKaXUjWrjxo1HRSTaXdxftTKWhvV+DXeCndLkm4jMAGYANGzYUDZs2FCQbJRSSimllFI3AGOMx1dl/VW7KR7G6ooY5CauHFYXxvNXuUxKKaWUUkop5fBXrYytx9q3Rs6BxphgrFkTtTlLKaWUUkop5VN/1crYXECAYdnCB2GNFfvoqpdIKaWUUkoppZxcV2PGjDF9gIq2j9FAoDHmGdvnAyLyAYCIbDPGvA48aoyZDywGamNN0LGKSy98Lmg5OgGdqlWrdjnZKKWUUkoppW5gRkR8XQavGWNWAnEeolc5v2vHGOOP1TI2GKgEHMVqMXtORFILozw6gYdSSimllFIqN8aYjSLS0F3cddUylp8Xm4rIRWCSbVFKKaWUUkqpa8pfdcyYUkoppZRSSl3TrquWMaWUUn8tp06d4ujRo5w/r28bUUopdf0IDAwkKiqKiIiIy8pHK2MFoBN4KKXU5Tt37hx//PEH5cuXJyQkBGOMr4uklFJK5UlESE9P59ChQwQFBREcHFzgvLSbYgGIyCIRGXy5NWGllLqRHTlyhOjoaEJDQ7UippRS6rphjCE0NJSoqCiOHDlyWXlpZUwppZRPnDt3jqJFi/q6GEoppVSBFCtWjHPnzl1WHloZU0op5ROZmZkUKaK95ZVSSl2fihQpQmZm5mXloZUxpZRSPqPdE5VSSl2vCuN/mFbGlFJKKaWUUsoHtDKmlFJKXWOMMfTv39/XxciXyy1zfHw8lSpVKrTyuLN//36MMYwdO/aKpFdXnp4T9VejlbECMMZ0MsbMOHXqlK+LopRS6hq3cuVKjDEuS3BwMFWqVGHAgAHs2rXL10W8oZ08eZKxY8eycuVKXxflsq1atYpHHnmEunXrUqxYMaKjo2nevDmffPIJIuJ2ncWLF9OsWTPCwsIoWbIk3bt3Z9++fVe55H8N69ato02bNhQrVozw8HDuuusuNm/e7NW6586d45133uGee+6hUqVKhISEUKVKFXr27Onxb0RGRgbPPfcclStXJigoiKpVqzJhwgQuXLjgNv3777/P7bffTkhICKVLl2bgwIGXPROgunw6croARGQRsKhhw4aDfF0WpZRS14eePXty9913A5Cens7WrVuZOXMmn3/+Odu2baNixYqOtOnp6fj7+/uqqAVyPZS5YsWKpKenu0wcc/LkScaNGwdYrXPXs5EjR3Lo0CESExOpW7cuZ8+eZe7cufTq1YukpCTeeecdl/Tz58+nW7du3HrrrfzrX//i1KlTvPrqqzRv3pwNGzYQExPjoz25/nz//ffEx8dTrlw5xo8fD8D06dNp0aIFa9asoW7durmuv3//fgYPHswdd9zBAw88QExMDHv37uXNN99k/vz5/Oc//6FVq1Yu6/To0YOFCxdy//3307RpU9auXcuzzz7L7t27mTNnjkvaKVOmMGLECOLi4pg6dSqHDh1i8uTJrF27lv/973+EhYUV6vFQ+SAiuhRwadCggSillCqYnTt3+roIV0VycrIA8q9//StH3NSpUwWQyZMn+6Bk15a4uDipWLHiVd/uvn37BJAxY8bkK+5atHLlSsnMzHQJu3jxorRs2VIA2bZtmyP8/PnzEhMTIzfddJOcOXPGEb5p0ybx8/OTQYMGXbVy58e1ek5iY2OlWLFicujQIUfYoUOHpFixYtK2bds81z969Khs2rQpR/iOHTskMDBQst9zfv311wLIiBEjXMJHjBghgKxevdoRduTIEQkNDZXY2FiX6+PLL78UQF544QWv91Pl5M3/MmCDeKhPaDdFpZRSykfsLQ+BgYEu4e7GX9nD1q5dS1xcHGFhYURFRTFw4EBSU1Nz5L1161YSExOJjIwkODiYOnXq8PLLL3Px4kWXdP3798cYw7Fjx+jfvz9RUVEUK1aMLl268PvvvwMwY8YMateuTXBwMLVq1WLhwoU5tueuzHPnzqVz587cdNNNBAUFERUVRZcuXdi6dWt+D5WDu7FlH3/8McYYbrvtNpfwN998E2MM//vf/4Cc441WrlxJ5cqVARg3bpyjG6m7sWtfffUVsbGxBAcHU7ZsWZ588kmvp7TO77krqLi4uBytk35+fnTr1g2A7du3O8JXrVrF4cOHGThwoMv7/m677Tbi4+OZO3eux+5uzt544w3atWtHuXLlCAwMpGzZsvTu3Zv9+/fnSJvf4/Df//6X5s2bO7rVPfroo/k6XmPHjsUYw44dOxg6dChlypQhJCSExo0bs2LFCq/zycvu3btZv3493bt3p1y5co7wcuXK0b17d5YvX+74LnkSGRmZ4/oFqFOnDrfccovLuQPrmgcYNmyYS7j984cffugI++KLL0hLS+Oxxx5zuT46depElSpVXNKqq0+7KSqllFJXQVpaGkePHgWsLn3bt2/n6aefJioqinvvvderPDZv3kzHjh0ZMGAAvXr1YuXKlcyaNQs/Pz9mzJjhSLdhwwbi4uIICAjgkUceoUyZMixatIiRI0eyZcsWPvrooxx533XXXZQvX57x48eze/dupk2bRmJiIl27dmXGjBk88MADBAcHM23aNLp168bPP//sqMh4Mn36dEqWLMngwYMpU6YMe/bsYcaMGTRv3pwffviB6tWr5+MIWhISEhgzZgx79uyhatWqACQlJeHn58fWrVs5cuQI0dHRjvDw8HAaNGjgNq/atWszZcoUhg8f7thXIMfLyBcvXswbb7zBQw89xP3338/ChQt55ZVXKFGiBE899ZRX5fb23GVkZHDmzBmv8vT396dEiRJ5pjt06BAApUuXdoStX78egKZNm+ZI36RJE5KSkvj555+5+eabc837lVdeoUmTJgwdOpSSJUuyfft2Zs6cSVJSEtu2bSMyMtIlvbfHwXn81ciRIylevDiffvopffv2zXN/s+vbty/+/v6MHDmSM2fO8Pbbb3PXXXfxzTff0KZNG0e6U6dOeVUBBQgNDSU0NBTI+1jOnj2bjRs30qFDh3yXPSsri99++83l3Nm3Wa5cOSpUqOASXqFCBWJiYhxl8qZ8n3zyCampqTmue3WVeGoy00W7KSql1JV0o3VTdLfUqVNHdu3alWMdQPr165cjzBgja9eudQm/++67pUiRIi5dzZo1ayb+/v6yZcsWR1hWVpZ0795dAFm+fLkjvF+/fgLIww8/7JLv8OHDBZAKFSrIqVOnHOFbtmwRQEaNGpVnmVNTU3Ps286dOyUwMFCGDBniEu5tN8XvvvtOAJkxY4YjrHLlytK7d28BZO7cuY79jYqKkk6dOjnSuevi5k03xdDQUNm3b58jPCsrS26++WYpU6ZMnuUVyd+5e/fddz1eL9kXb45XSkqKRERESJUqVeT8+fOO8EcffVQAt9/D119/XQBZsmRJnvm7O8fLly8XQF566SWX8Pwch6ZNm0pAQID89NNPjrCMjAyJjY31upvimDFjBJBGjRpJRkaGI/zXX3+VsLAwqVWrlkv6uLg4r4+98/ZfeeUVAWTx4sU5ymDvTvj222/nWV53pk+fLoA8++yzLuFFixaVRo0auV0nNjZWypYt6/jcsWNHASQtLS1H2ieffFIAl+Os8udyuylqy5hSSqlryrhFO9h5+LSvi+GiTkw4Yzrl3kKQl8GDB9O9e3fAmjlt586dTJo0ibvvvpvk5GSXCTw8adq0KU2aNHEJS0hIYPHixezfv59bbrmFP//8kzVr1pCYmEi9evUc6YwxPPXUU8ybN48FCxbQunVrl3yyd3dq0aIFU6ZMoW/fvoSHhzvC69WrR3h4OL/88kue5bVPCiAinDlzhvPnzxMdHU3NmjVZt25dnuu707hxY8LCwkhKSmLQoEEcOHCAffv2MX36dDZv3syKFSv429/+xrZt2zh69CgJCQkF2o6zLl26uHRdNMbQqlUrpk+f7nWLgjfnDuDOO+9k2bJlXpUrJCQk1/i0tDQSExM5e/YsixYtIiAgwCUOICgoKMd6wcHBLmlyYz/HWVlZnDlzhgsXLnDrrbcSERHh9hx7ew2vXbuWbt26UaNGDUe6wMBAhg8fTq9evfIsl7Phw4e7dAUuX7489913HzNmzGDXrl3Url0bgEmTJnHixAmv8qxSpYrj98I6ltmtWbOGxx9/nHr16uVogU1LS3O7Pfs2nbd3pcqnCodWxgrAGNMJ6FStWjVfF0UppdR1onr16i5dojp27EhcXBxNmjRh5MiRfPrpp3nm4XwDaGfvBnbs2DEAx7Tk7rqX1alTBz8/P/bu3Ztn3vbub+66IpYoUcKxvdxs2rSJZ599lpUrV3L27FmXuLy6OHoSEBDAHXfcQXJyMgArVqygSJEitGzZ0nFTD1YXRaBQKmN5HXdvKmPenDuAsmXLUrZs2YIW1eHcuXN06dKFDRs28N5779GiRQuXeHsXu4yMDLfrOqfJTVJSEuPHj2fdunWO9ezcVWy8OQ7267NWrVo50tapUyfPMmVnr2y5y2fv3r2OeE/dWbVaFVEAACAASURBVPNSWMfSmb1bY0xMDIsXL3ZUmpy36W579m06b8+5fNkr8AUtnyo8WhkrANGp7ZVS6oq53Bao60njxo2JiIhwVBzyktvU8VZPmEs/88tT3p7C89rOwYMHadmyJeHh4Tz77LPUrFmTsLAwjDEMGzbssiauSEhIYMmSJezYsYOkpCRiY2MpWrQoCQkJTJs2jYMHD5KUlERUVFSeU4p7w5vjXlh5pKen4+17TP39/R3j45zZK2LLly9n5syZ9O7dO0ca++QxKSkpOSorKSkpAC6TUbizfv162rVrR7Vq1Zg4cSKVK1cmJCQEYwx///vfycrKcltmT7Jfw8YYj2nyw9t8jh8/zvnz573Ks2jRoo5KuPOxzM7bY+nshx9+oG3btkRERJCcnOx23ZiYGLfbs2/TeR3n8mVvSEhJScEYo68x8CGtjCmllFI+lJmZ6fEJd0HYWx527NiRI+7HH38kKyvLbetEYVuwYAGpqal8+eWXOd6PdOzYMY9drLxhb+1asWIFSUlJPPDAA4A106K/vz/Lli3j22+/pV27dm5vxJ3lFX+1zZ07lwEDBniVtmLFijlmLczIyCAxMZGlS5cyY8YM7r//frfrxsbGArB27VqXFluw3pkVHh7u0kXQnY8//piLFy/yzTffuLR0nj171uvufu7YJ2Zx97LjgrwkfefOnS5ddp3zcf4udO3alVWrVnmV55gxYxyzcjofy4EDB7qk+/777zHGeN3qtmnTJtq2bUuxYsVy7b4cGxvLRx99xK+//uoyicevv/7K4cOH6dy5s0vaGTNmsHbt2hyVsXXr1lGzZk2dvMOHtDKmlFJK+ciyZcs4e/YszZs3L7Q8S5UqRbNmzVi0aBHbt293jEUSEV588UUAEhMTC217nthbQLK3QLzzzjv8/vvvXo2R86R+/fqUKFGCt956i99++81ROYuIiKB+/fpMnjyZU6dOedVF0X4Tevz48QKXpzBdzpixjIwMunTpwpIlS3jrrbdyVAycxcXFUbZsWWbOnMnw4cMdx2HLli2sXLmSAQMGuIwxc8fTOf7nP//ptlXMW6VKlaJJkyYsXLiQn3/+2VEpPH/+PFOmTMl3flOmTKFr166OcWOHDh3i448/pmbNmi6tggUdM1atWjUaNmzIvHnzeP755x2tTIcPH2bevHkkJCRQpkwZR/qjR49y9OhRypYtS0REhCN806ZNtGnThrCwMJKTk3PtytuzZ08++ugjXn31VSZNmuQIf/XVVwG47777HGH33HMPQ4cOZfr06fTq1ctx3hYtWsSePXt4/vnnvdpndWVoZUwppZS6Cn744QfH+3wyMjLYsWMH77zzDgEBAUyYMKFQtzV16lTi4uJo0aKFY2r7r776iiVLltCrV68ck3dcCe3btyc0NJQ+ffrw6KOPUqJECVavXs3ixYupWrWq1+/ocsfPz4+WLVuycOFCgoODadasmSMuISGBl156yfF7XiIjI6lWrRqffvopVatWpXTp0oSFhdGpU6cCl+9yXM6Ysfvuu4///Oc/tGnThtDQ0Bzvj6pXr56jhSggIICpU6fSo0cPWrRowaBBgzh9+jRTpkwhOjqacePG5bm9xMREpkyZwt13383gwYMJDAxk2bJlbN26laioqALtg93kyZOJj4+nefPmPPLII46p7Qty3WRmZtKiRQt69uzJmTNneOutt0hPT2fatGku6Qo6Zgys71yrVq1o0aIFjz32GACvvfYaWVlZLpUlsF75MG7cON59913Hu/kOHDhA27ZtOXHiBEOHDmXNmjWsWbPGZb3ExETHhCkdOnSgY8eOjgcPTZs2Ze3atcyaNYvevXtzxx13ONaLjo7m+eef54knnqBNmzb07NmTlJQUJk2aRK1atXJM3qOuMk/TLOqiU9srpdSVdCNPbe/n5yfR0dGSmJgo//vf/3Ksg4ep7bOHiVyaCj05OdklfPPmzXLPPfdIiRIlJDAwUGrVqiUvvfSSZGZmuqSzT23vqdzvvvtujriKFStKXFxcnuVbtWqVNG/eXIoWLSoRERFy9913y7Zt29xOY+/t1PZ206ZNE0ASEhJcwpcuXSqAlCtXLsc6nqaxX7dunTRr1kxCQ0NdpozPbdp7+7TpzlPee5Lfc1dQFStW9Ho6drtFixZJ48aNJSQkRIoXLy733nuv7N692+ttLliwQOrXry+hoaESGRkpPXr0kAMHDnh9jYh4Pg6rVq2Spk2bSlBQkERHR8vDDz8s27Zty/fU9tu3b5dHH31USpcuLUFBQRIbGytLly71eh+9tWbNGklISJCwsDApWrSotGvXTjZu3OixXM7frdxegWFfsl9r6enp8vTTT0vFihUlMDBQKleuLOPHj3d5hYGzd999V+rVq+c4ngMGDJA//vijMA/BDelyp7Y3UsCBvgoaNmwoGzZs8HUxlFLquuQ8pbRSShW2sWPHMm7cOPbt2+fyagKlCpM3/8uMMRtFpKG7OL8rUiqllFJKKaWUUrnSyphSSimllFJK+YBWxgrAGNPJGDPD2/eAKKWUUkoppVR2WhkrABFZJCKDnacjVUoppZRS146xY8ciIjpeTF3TtDKmlFJKKaWUUj6glTGllFJKKaWU8gGtjCmllFJKKaWUD2hlTCmllFJKKaV8QCtjSimllFJKKeUDWhlTSimllFJKKR/QyphSSimllFJK+YBWxpRSSimllFLKB7QyVgDGmE7GmBmnTp3ydVGUUkrdoObMmYMxhpUrV/q6KD7Xv39/jDFXLL0718rxj4+PL5SXGhdWPkqp/NHKWAGIyCIRGRwREeHroiillLrGrVy5EmOMy1K0aFEaNGjA1KlTuXjxoq+L+Jf0xRdfMHbsWF8XQxXAN9984/iubNiwwev1MjIyeO6556hcuTJBQUFUrVqVCRMmcOHCBbfp33//fW6//XZCQkIoXbo0AwcO5MiRI4W1G0p5RStjSiml1FXQs2dPPvjgA95//32effZZ0tLSGDZsGEOGDClQfn369CE9PZ2WLVsWckmvP++88w7p6ekuYV988QXjxo3zUYlUQZ09e5YhQ4ZQtGjRfK/bo0cPnn/+eRISEnj99deJj4/n2WefZdCgQTnSTpkyhX79+hEREcHUqVN58MEH+fTTT4mPj+fs2bOFsStKeaWIrwuglFJK3Qjq169P7969HZ+HDBlC7dq1mTlzJs8//zylS5fOV37+/v74+/sXdjGvSwEBAQQEBPi6GKoQPPPMM2RmZjJ48GAmT57s9XqLFy9m4cKFjBgxgkmTJgEwcOBAihcvzuTJkxk8eDDNmjUD4OjRozzzzDPExsayYsUKx/coNjaWzp07M3XqVJ566qnC3zml3NCWMaWUUsoHwsPDadq0KSLC3r17HeH79++nT58+lC5d2tHV6qmnniItLc1lfXdjls6dO8fYsWOpWbMmoaGhFC9enLp16/Lkk0+6rPv1118TFxdHVFQUISEh3HTTTXTt2pWff/7ZJd3WrVtJTEwkMjKS4OBg6tSpw8svv5yja6V9DNapU6cYMmQIpUqVIjg4mObNm7Nu3bo8j4W9K+ecOXNcwmvUqIExhi+++MIlvEyZMtx99905tm8XHx/Pe++9B+DSPTR7/gUtrydnzpzhmWeeoXHjxkRFRREUFES1atUYNWpUjvPnvM9vvPEGNWvWJDg4mLp16/L1118DsG3bNu666y7Cw8OJjIxk6NChHrvc7d27l3vuuYeIiAjCw8NJTEx0ua7sTpw4waBBg4iKiiIsLIz4+Hg2btzoNs+lS5fSo0cPqlSpQkhICMWLF6ddu3asWrWqwMcoNxs2bOC1117j1VdfpVixYvla9+OPPwZg2LBhLuH2zx9++KEj7IsvviAtLY3HHnvM5YFGp06dqFKliktapa40bRlTSimlfEBE2L17NwBRUVEAHDhwgEaNGjkqCTVq1GDlypW8+OKLrF69mhUrVlCkiOd/3Y888gizZ8+mb9++DB8+nIsXL/LLL7+QlJTkSLNq1So6d+5M3bp1GT16NMWLF+fw4cMsX76c3bt3U6NGDcC6MY6LiyMgIIBHHnmEMmXKsGjRIkaOHMmWLVv46KOPcmz/zjvvJDo6mueee45jx44xefJk7r77bvbv35/rzXXTpk0JCQlhxYoV9O/fH4CUlBR++eUX/Pz8WLFiBV26dAFgx44d/PHHHyQkJHjM7+mnnyYrK4vvvvuODz74wBFubxm53PJ6kpKSwsyZM7n33nvp1asXRYoUYdWqVbz88sts2rSJJUuW5Fjn9ddf58SJEwwcOJDg4GCmTZtGly5dmDdvHoMGDaJnz5506dKFpUuX8tprr1GqVCmeeeYZlzzOnj1Lq1ataNSoES+++CK//PILb7zxBt9//z2bNm2iTJkyAFy4cIE777yT9evX06dPH5o0acLmzZtp06YNkZGROco2Z84cjh8/Tt++fSlfvrxj/1q3bk1ycjItWrRwpE1LS8tR4fQkICCA7OPuMzMzGTRoEO3ataNbt25s377dq7zs1q9fT7ly5ahQoYJLeIUKFYiJiWH9+vUuacG67rJr0qQJn3zyCampqQXqKqlUvomILgVcGjRoIEoppQpm586dvi7CVZGcnCyAjBs3To4cOSJ//vmnbNmyRQYOHCiANGnSxJG2V69eAsjXX3/tkscTTzwhgMycOdMR9u677wogycnJjrASJUpI+/btcy3P8OHDBZA//vgj13TNmjUTf39/2bJliyMsKytLunfvLoAsX77cEd6vXz8BZMiQIS55fPbZZwLIW2+9leu2RERat24t5cqVc3x+7733xM/PT3r27Cm1a9d2hE+bNk0A2bhxY47tO3MXVpjldXf8MzIy5Pz58znSPvPMMwLIunXrHGH26yImJkZOnjzpCN+yZYsAYoyRzz//3CWf+vXrS5kyZVzC4uLiBJB//OMfLuHz588XQB588EFH2Ntvvy2APPfccy5pp0yZIoBUrFjRJTw1NTXHvvz+++8SGRmZ4zobM2aMAF4tcXFxOfKdOHGihISEyN69e13yW79+fY607hQtWlQaNWrkNi42NlbKli3r+NyxY0cBJC0tLUfaJ598UgD56aefvNquUt78LwM2iIf6hLaMKaWUurZ8Mwp+3+brUrgqUxfaT7ysLMaMGcOYMWMcn/38/OjcuTMzZswAICsriy+//JLbb7/dpQsewOjRo5k8eTILFizggQce8LiNiIgIduzYwfbt27nllls8pgH4/PPPGTRokNuWtj///JM1a9aQmJhIvXr1HOHGGJ566inmzZvHggULaN26tct6w4cPd/lsb7365ZdfPJbZOe2KFSv46aefqFmzJklJSTRo0IB7772XTz75hN9++42yZcuSnJxMiRIluO222/LMMy+XU153AgMDHb9nZmZy5swZLl68SJs2bZgwYQLr1q2jUaNGLuv079/fpZWoXr16hIeHU6xYMbp27eqS9o477mDatGluW21GjRrl8jkxMZGaNWvyxRdf8NZbbwFW9zx/f38ef/xxl7RDhgxxuTbtwsLCHL+npqaSkZGBv78/jRs35vvvv3dJ27dvX+644w6Px8ZZiRIlXD7v3buXcePG8eyzz1K5cmWv8sguLS2NoKAgt3HBwcEurXb2392lDw4Odkmj1JWmlTGllFLqKhg8eDDdu3fHGENYWBg1atSgZMmSjvgjR46QmprKzTffnGPdkiVLUrZsWbdjgJy9+uqr9OnTh7p161KlShVatWpFp06d6NSpE35+1jDxRx99lIULF/Lwww8zcuRI7rjjDu666y569uxJdHQ0APv27QNwW5Y6derg5+fntixVqlRx+Wzv+nbs2LFcyw2XKkJJSUnUrFmT5ORkevbsSatWrTDGkJSURM+ePVm1ahXx8fGO/bkcl1NeT9544w3eeustduzYQVZWlkvciRMn8iwDWJWV7N3t7OH28jlXxooXL+7oiuisdu3afPHFF5w9e5awsDD27t1L2bJlCQ8Pd0kXFBRElSpVcpRvz549PP300yxZsoSTJ0+6xGV/T1uVKlXc7os3HnzwQSpXrswTTzxRoPUBQkNDycjIcBt37tw5QkNDXdKCNRV+SEhIjrTOaZS60rQyppRS6tpymS1Q16rq1avTpk0bj/FWT5bLc88997B//34WL17MqlWrWL58ObNmzaJFixYsX76cwMBAIiMjWb9+Pd999x3Lli3j22+/Zfjw4YwZM4bFixc7JhUpCE+zO3qTX2xsLOHh4SQlJdG2bVsOHjxIQkICJUuW5NZbb2XFihXUrl2b48eP5zpe7GqV153Jkyfz+OOP065dO4YOHUpMTAyBgYGkpKTQv3//HJWz3MqQ20yZ2cvn6QXW2dOJiNdpU1NTadmyJWfPnmXYsGHUrVuXYsWK4efnx4svvugyDtGePjU11WOZnQUGBjoeRCxYsIDly5cze/ZsDhw44Ehz/PhxAA4dOkTx4sWpUqVKrhXwmJgYUlJS3MalpKRQrlw5l7T28GrVquVIa4xxpFHqStPKmFJKKXUNKFWqFMWKFWPHjh054k6cOMFvv/3mVde8kiVL0rt3b3r37o2IMGrUKF5++WUWLlxI9+7dAetGPz4+nvj4eMCaNbFBgwZMmDCBr7/+2tHC4a4sP/74I1lZWQVuBfHE39+fFi1akJyc7Kg42ru9tW7dmnnz5jla6rypjHmqdFxJH3zwAZUqVeKbb75xqTj85z//uaLbPXHiBL///nuO1rEff/yRUqVKObobVq1alaVLl3L69GmX1rGMjAz27dvn0n1wxYoVHD58mNmzZzNgwACXfLNPIALwyiuveP1et7i4OMcsoPYK2P333+82bWJiImC1HNsnunEnNjaWjz76iF9//dWlVfHXX3/l8OHDdO7c2SXtjBkzWLt2bY7K2Lp166hZs6ZO3qGuGp3aXimllLoG+Pn50alTJzZt2pTj5n3ixIlkZWU5bkzduXjxotuuZLfffjtwqaXh6NGjOdatVasWISEhjjSlSpWiWbNmLFq0yGVWOxHhxRdfBMi1LAWVkJDAsWPHmDZtGk2aNHF0FUtISODgwYPMnj2bMmXKUKdOnTzzst9M2/fpavD398cY49LKlJmZycSJV761N/s2FixYwE8//eSYhRKsltOLFy863sNl9+abb3L69GmXMHvLXPYWs6VLl7qd/r9v374sW7bMq8V5+x07dmTevHk5FvuDg5deeol58+a5VB5//PFH9uzZ47L9nj17AlZXXWf2z/fdd5/LcQgJCWH69Okur2lYtGgRe/bscUmr1JWmLWNKKaXUNeKf//wny5Yto0uXLjz88MNUq1aNb7/9lrlz59KyZUv69evncd0zZ85QtmxZOnfuzO23306pUqXYt28fb775JiVKlKBTp04ADBo0iEOHDtGuXTsqVqxIeno6c+fO5cyZM/Tt29eR39SpU4mLi6NFixaOqe2/+uorlixZQq9evXJM3lEY7C1eu3btokePHo7wli1bUqRIEXbu3Om46c5LkyZNmD59Og8//DAdOnQgICCAxo0bF3iCCG9069aN0aNH0759e7p27crp06f5+OOPr/gLqaOiopg/fz6HDx8mPj7eMbV96dKlGTt2rCPdgAEDmDFjBuPHj2ffvn00bdqUTZs2MW/ePKpWrUpmZqYj7R133EGZMmV4/PHH2b9/P+XLl2fz5s188MEH1K1bl23bXCfZKeiYsWrVquVonQIcDwESEhJo2LChS1zt2rWpWLEi+/fvd4R16NCBjh07MnnyZE6dOkXTpk1Zu3Yts2bNonfv3i6Ti0RHR/P888/zxBNP0KZNG3r27ElKSgqTJk2iVq1aOd5VptSVpJUxpZRS6hpRsWJF1q1bx3PPPceHH37IyZMnKV++PKNHj+aZZ57J9R1joaGhDBs2jBUrVrB8+XJSU1MdlbPRo0c7xsD06dOHOXPm8N5773HkyBHCw8OpU6cO//73v7n33nsd+TVs2JA1a9YwZswY3njjDc6ePUuVKlV46aWXcszGV1huvfVWoqKiOHr0qEtXxKJFi9KoUSPWrFnj9Xixnj17smnTJj799FPmzZtHVlYW77777hWtjD355JOICLNmzeIf//gHZcqUoUePHgwYMMCr1ryCCgsLIykpieHDhzNq1ChEhLvuuotJkyZRtmxZR7rAwECWLVvGk08+yRdffMHnn39ObGwsy5Yt44knnnCp3BQvXpwlS5bwf//3f7z22mtkZmbSoEEDFi9ezKxZs3JUxq4F8+bNY8KECXz44Yd88MEHlCtXjvHjx+eYaRLg8ccfJzIykilTpjB06FDCw8P529/+xsSJE7WLorqqTGEMGL7RGGM6AZ2qVas2qKDT3yql1I1u165d1K5d29fFUEoppQrMm/9lxpiNItLQXZyOGSsAEVkkIoOzvz1eKaWUUkoppbyllTGllFJKKaWU8gGtjCmllFJKKaWUD2hlTCmllFJKKaV8QCtjSimllFJKKeUDWhlTSimllFJKKR/QyphSSimllFJK+YBWxpRSSimllFLKB7QyppRSSimllFI+oJUxpZRSSimllPIBrYwppZRSSimllA9oZUwppZRSSimlfKCIrwuglFKFLe1CGkfTj3Ik/Qgnz53k9PnTl5aM05y5cIbTGadJy0zj/MXzZFzMcPy0L1mSlSNfgwHA38+fYP9ggvyDCC5i/bT/HloklIigCMIDwwkPCnf8jAiMoERwCaJDoikRXAI/o8/C1PVv//79VK5cmTFjxjB27FhfF6dAjDH069ePOXPmXJH06sYxduxYxo0bx759+6hUqdJl5zdnzhwGDBhAcnIy8fHxl52fujZpZUwpdV1JO59B57cW8dvZFAg4jilyDIqcgiJnwP80FDmN8ctwu66IgaxgyAqBi6EgQSBFICsAJNT6XYqABHCp44BkzwXI4rTfBTD2JRP8ToE5Cn4Z4JcOfmkYv0wP5fCDzHC4GO74KZkRcCGSEFOKTwZ0oHp0qcI6ZOoace7cOWbPns2///1vtm3bxsmTJwkLC6N69eokJCQwYMAAatWq5etiKqyb6ttuu40uXbr4uijXpP/7v//jX//6F2FhYaSmpnq93uHDhxk1ahTffPMNqamp3HzzzYwcOZLu3bvnSJuRkcELL7zABx98wOHDhylfvjwDBgxg5MiRBAQEFObuqGvEzz//zIcffsjSpUvZs2cP586do2rVqnTv3p1hw4YRFhbmdV6LFy9mwoQJbNmyhaCgIFq3bs3LL79M5cqVc6T96aefGDlyJKtWreL8+fPUr1+fcePGkZCQUJi755ERyX6jobzVsGFD2bBhg6+LodRfjojwR9of7Dm5hz0n97D31F4OnjnIoTOH+P3sHwiXWq38KEKIXyQhfsUJ8StBsF8JQvyKE2ysn0F+4QSaMAJMUQJMMOYqtkhlynnOZ6VyXqwlI+s06VknOJd1gnQ5QXrWpeWCnHVZNzwwnArFKlC+WHluKnYT1YpXo2rxqlSOqEygf+BV24cradeuXdSuXdvXxbgq9u7dS8eOHdm1axdxcXG0a9eOsmXLkpqayubNm/nyyy85fvw4Bw8epFy5cr4urtdEhIyMDIoUKUKRItfn891z587h7+/vcoOfW+vXjd4ytnnzZmJjYwkODkZEvK6MHT9+nIYNG/Lnn38yYsQIypcvz8cff8yqVauYPXs2AwYMcEnfpUsXFi5cyP3330/Tpk1Zu3Yts2fPvqaPfWG3jF28eJELFy4QGBiIn99fvzfFqFGjeP311+ncuTNNmjQhICCA5ORkPvvsM+rVq8f3339PSEhInvnMnz+fbt26ceuttzJo0CBOnTrFq6++ir+/Pxs2bCAmJsaRds+ePTRq1IgiRYowbNgwIiIieOedd9i+fTvffPMNbdq0yXN73vwvM8ZsFJGG7uKuz7+cSqlciQgn0i6QdR08bEm9kMrukz/y84kf2Xd6D/tP7+Xgmf2kZV6qnBQPKkH5ojdxS+TtREooG/f4MbNXO2pGViI6NPov0eUv9Xwqaw/+wpC5S0mMDSa82GkOpR5i57GdLD+wnItyEQB/40+FYhUclbPqJapTJ7IO5YuWxxjj471Q7qSnp9OhQwf27NnD/PnzSUxMzJHm3LlzTJky5bo7h8YYgoODfV2My3K9l/9qunjxIoMGDaJ9+/acPn2a/DyQnjhxIvv27ePLL7+kU6dOADzwwAM0bdqUJ554gu7du1O0aFHAatVYuHAhI0aMYNKkSQAMHDiQ4sWLM3nyZAYPHkyzZs0KfwevMf7+/vj7+/u6GFdNt27dGD16NBEREY6whx56iOrVq/PCCy8wa9YsHn300VzzuHDhAo899hgVKlTgu+++c1xT7du3p0GDBowdO5YZM2Y40o8ePZqTJ0+yceNGbrvtNgD69u3LzTffzCOPPMKPP/545f8ui4guBVwaNGggSl2LZn23VyqO/OraW0b/W6qMmyrVXvo/qTn1PqnzdrzcMucWx1JnZlOp9fo9UmPyYKn24jNSZew0qfTU3Bz5dH1jta8P8RVx9Mw5qTjyK5mzep9LeEZmhvx0/CdZvHexTN04VYauGCod5neQeu/Vcxy7Zh83k0FLBsmrG1+VpfuXSsqZFMnKyvLNjnhp586dvi7CVTFt2jQB5KmnnsrXeikpKTJixAi59dZbpXjx4hIUFCS1a9eWiRMnSmZmpkvaMWPGCCD79u3LkU/FihUlLi7OJeyrr76Sli1bSmRkpAQHB0uFChUkMTFRfvrpJ0eagwcPyoABA+Smm26SwMBAiY6OlqZNm8qcOXMcafbt2yeAjBkzxiX/119/Xdq2bSsxMTESEBAgZcqUkfvuu89t+QDp16+frFmzRlq2bCmhoaESGRkpDzzwgJw5cybP49SvXz8JCgqS9PR0R9jq1asFkBIlSsjFixcd4YsXLxZA5s6dm2P7zvvjbims8opcOiebN2+W2QpF4AAAIABJREFU1q1bS1hYmERHR8vjjz8uFy5ckPT0dHn88cclJiZGgoKCpEWLFjm+L/k954Vh8uTJEhoaKvv375e4uDgJCwvzet1y5cpJ1apVc4S///77Oc7JfffdJ4AcPHjQJe3BgwcFkCFDhuS5vfx8f959910BZMWKFfKvf/1LqlSpIoGBgVK9enWX693u4sWL8s9//lMqVaokQUFBcsstt8iHH36Y6znJbvXq1XLXXXdJ6dKlJSgoSGJiYqR9+/aydu3aHOVKTk52WXffvn3StWtXKVasmISHh0vnzp1l7969bs+7/XpdsWKFNGnSREJCQqRcuXIyceJEERE5fvy43H///RIdHS0hISHSoUMHSUlJKfCxvBK2bt0qgDz44IN5pl22bJkAMn78+BxxCQkJEh4eLufPnxcRkdTUVAkKCpKEhIQcacePHy+ArFu3Ls9tevO/DNggHuoT2jKm1F/QgWNnCQ30Z3R7340/ERFOZ/7JofSdpKTvIiV9F0fOH8A+Biu8SDSlg6tTJuguSgdXo3RQVcKKFPcq76ZVo65gyX0nIsTqJnUi7bxLeKB/IDVK1KBGiRq0r9zeEZ5xMYPdJ3az49gOdh7byc5jO5mzfQ6ZYo1VKxlckttL3c7tpW6nfqn61IqsRYCfjrW42v79738D1pP9/Ni6daujJa1q1apcuHCBb775hlGjRrF3717efvvtApVn1apVdO7cmbp16zJ69GiKFy/O4cOHWb58Obt376ZGjRpkZmbStm1bUlJSePjhh6lRowanTp1i69atfPfdd/Tr1y/Xbbzyyis0adKEoUOHUrJkSbZv387MmTNJSkpi27ZtREZGuqTfvHkzHTt2ZMCAAfTq1YuVK1cya9Ys/Pz8XJ5iu5OQkMB7773H6tWrad26NQBJSUn4+flx4sQJNm3aRIMGDRzhxhhatWrlNq/o6Gg++OAD+vTpQ4sWLRg8eLDbdJdTXrtDhw7Rtm1bevToQbdu3Vi6dCmTJk3C39+fHTt2kJ6ezqhRozh69CivvPIKXbp0YdeuXQXurnbq1CkuXLjgVdrQ0FBCQ0Ndwg4cOMCzzz7LmDFjqFixYr62/dtvv5GSksJ9992XI65JkyYArF+/nr/97W+O38uVK0eFChVc0laoUIGYmBjWr1+f5zYL8v156qmnSE9P58EHHyQoKIg333yT/v37U61aNZo3b+5IN2LECKZOnUrLli0ZPnw4f/75J4888ghVqlTx6nj89NNPtG3bljJlyvCPf/yD0qVL8/vvv7N69Wq2bNniOCbuHDt2jBYtWvDHH3/w0EMPUbt2bb777jtatWrF2bNn3a6zadMmFi1axODBg+nbty+fffYZo0aNIjg4mPfee49KlSoxduxYdu/ezbRp0+jbty/Lly8v0LHMysri+PHjXh0HgJIlS+Z5TR86dAiA0qVL55mf/dpo2rRpjrgmTZqQlJTEzz//zM0338zWrVvJyMjwmNaeX6NGjfLc7uXQylgBGGM6AZ2qVavm66Io5VaZkxuZ7T+bJr94V7kpDCLCXi7wPen8wDk2c44/sbrWhWG4jWD+RnHqEkRtgih50R/O/mEtrMnfxn4p/PJfC4oAM4PTWH9mglfpg/yDuDnqZm6OutkRlnExg19O/MKOozvYenQrm/7cxIqDKwAI9g+mXnQ9q3JWuj71S9UnuIh20brStm//f/buOzyqogvg8G92s5tKQklCCV06SO+d0FSKiCBYQJCiAgoICn6KFEFBQDoWAioIdhQQ6R0EaYqgiCBI7yUhPdmd749NYkIW0nazITnv8+RJcvfemZNkk9yzM3PmCL6+vqkWjlssFm7evJnimLe3d9KaiBYtWnDy5MkUU2SGDRtGr169CAkJYdy4cRQtWjTD8axYsQKr1cr69esJDPyvUMyYMWOSPv7zzz85duwYU6ZM4bXXXstwH4cPH0612L5z5860adOGhQsXpmrz999/5+eff066AXr++ecJCwvjk08+4f3330+aamRP8gQs+cedOnViy5YtbNq0KUUyVq1aNQICAuy25e3tzTPPPEOvXr0oW7YszzzzjN3zshJvon/++Yevv/46qXjFCy+8QJ06dZg6dSqdOnVi48aNST/7QoUKMXToUDZs2ED79u3TbNueRx99lG3btqXrXHvVMV988UXKlCnDK6+8kuG+L1y4AGB3PWTisfPnz6c4v0qVKnbbCgoKSro5v5fM/P7ExMSwb98+zGbbutxu3bpRtmxZ5s6dm5SMHTt2jNmzZxMcHMz69euTphF27dqVunXtLglKZd26dURGRvLFF19k+EZ/ypQpnDt3js8//zwpuX3xxReTiqrYc/jwYXbv3k2DBg0A2/TQUqVKMXz4cIYMGcLs2bNTnD9jxgyOHTtGxYoVgYx9L8+cOWO3SMbdpLW+zmKxMGHCBNzc3HjqqafSbC+9z7WqVatm+HnpLJKMZYLWehWwqm7dugNcHYsQ9lS+uYW6+jDEpe8fQ2ZdxsIvKoY9KpY9KoarylZYo6g2UkebqKW9qa3NlMMNI8nnXMfabzCviwmnDX/w140jQINMNeFudKeafzWq+VejBz0AuBp5lYNXDvLrlV85ePkgCw4vwPq7FbPBTK3AWjQs1pBGxRpRuWDlHLH+bsreKfx14y9Xh5FCpYKVGFV/VKauDQsLo0iRIqmOHz16lAcffDDFsalTpzJy5EiAFAvVY2NjCQ8Px2q10r59ez7//HP279+ftPYmIxLXY3z33XcMGDDAbuGNxHO2bNlCnz59UiRt6ZGYiFmtVm7fvk1cXBw1atTAz8+PX375JdX5jRo1SjUaEBwczE8//cS///5LtWrV7tpXUFAQ5cuXZ/PmzYBt/d3u3buZPn06FouFTZs28dprr3Hr1i1+++03XnrppQx9LfZkJd7kcd9ZRbBp06YcPHiQl156KcWNb7NmzQA4fvx4ppOx6dOnp0r+7+bOEZ4vvviCtWvXsnPnzkwVaomMjATA3d091WOJa/YSz0n82N65iecnP/duMvP7M2jQoKREDGw/owoVKnD8+H+vAK5YsQKtNa+88kqK9Vy1a9embdu2rF+/Ps3YEn+/VqxYQfXq1TO0bnHVqlUULVqUJ598MsXxkSNH3jUZa9SoUVIiBmA2m6lfvz4rV67k5ZdfTnFus2bNmDFjBsePH09KxjLyvSxSpAgbNmxI99dj729jcsOGDWPPnj288847SfHcS0aeaxl9XjqLJGNC5EKm+AhuGAoS2C/tfwoZEWuJZf+l/Ww/v53dF3ZzMvQkAAXcC9CgaAsaFm1Ig6INKJ6vuEP7zTMu/wkfNEJHpX+KR3oEeAXQvnR72pe23cRFxEVw8PJBdl/czZ6Le5h1cBazDs7Cz92PBkUa0LhYY5oXb06Al/3RA5Exvr6+hIWFpTpepkyZpJuWQ4cOJSVhieLj45k8eTKLFy/mxIkT6DsK8qT3xvpOQ4YMYcWKFQwaNIhRo0bRtGlTHnroIZ588smkEaNSpUrxxhtv8O6771K0aFFq1qxJ69at6d69O/Xq1Uuzj82bNzNhwgR++eUXoqOj04zb3vSuxKmM169fT7O/4OBgFi5cyO3bt9m3bx/R0dEEBwcTExPDm2++SWxsLFu3bsVqtTqkXHVW4wXsjh4UKFDA7mOJx9Pbtj2Jo4MZdePGDYYNG0a/fv0yXTQjccpjTEzqbUcSnx/Jp0V6eXnZPTfx/DunUNqTmd+fu/1cT58+nfT5yZO2/3v2tqGoUqVKupKxnj178vnnn/POO+8wY8YMGjZsSPv27enZs2eaU0BPnTpF/fr1U03tCwwMJH9++7Nh7H1dGXmuZeR76eHhka4KhOkxZswY5s6dy8CBA3n99dfTdU1GnmsZfV46iyRjQuRC5vhwogzp34/jXq5HXWf7ue1sP7edny/8TGR8JB5GD+oUqUPX8l1pWLQh5QuUzxEjKvc9r4IAGKMyd5OdXt4mb5oVb0az4rZX269FXWP3BVtitufCHtaftt1MVC1UlRYlWtCyeEsqFayUbZX+MjsClVNVq1aN7du3c+rUqRQ3Pt7e3kk3LfZGG1555RXmzJlDjx49eOONNwgMDMRkMnHw4EFGjRqF1frfFg/3+tnEx6fc765QoULs27ePHTt2sGHDBrZv387w4cMZO3YsP/30U9L6iYkTJ/Lcc8+xevVqduzYQUhICFOnTuW1115jypQpd+1v3759tGvXjnLlyjF58mTKlCmDp6cnSil69uyZIu5E96oYd+eNnz3BwcF89NFHbN++nd27d1OsWDEqVapETEwMkZGR7Nmzh82bN2M0GmnRokWa7aUlq/Gm1cbdHkvedkZ+5mBLqmJj0zcrwcfHJ2mq5fjx44mIiGDAgAGcOHEi6ZyoqCi01pw4cQJ3d/dU67uSSywlbm/KV+Kx5FPFihUrdtfpYefPn0/X9g8Z+f1JlJ7ve+LH9r7/6f3Zu7u7s2HDBvbu3cu6devYvn07b731FuPGjWPZsmV2K65mRVafaxn5XlosFq5evZru2AICAuzGMG7cOCZOnEjfvn358MMP091e8ufaneXm73yuZfR56SySjAmRC3lYwonOQjJ2MvQkG09vZNvZbRy+dhiNJtArkI5lO9KiRAvqF6kva42cwdOWjLnFOjcZu5O/pz+dHuhEpwc6obXm+K3jbDu7ja3ntvLBbx8w/7f5FPEuQoviLWhZoiUNijTAZJRCIOnVrVs3tm/fTkhICJMmTUr3dUuWLKF58+Z8+eWXKY4nvyFOVLCg7blz48aNFOsvoqOjuXjxIneucTYajbRs2ZKWLVsCtjVQderUYeLEiaxevTrpvLJly/LSSy/x0ksvER0dTfv27XnvvfcYMWLEXacuLlu2DIvFwpo1a1IknxEREZkezUtLcHAwSik2bdrE7t27k0a/qlevTkBAAJs2bWLLli3Url07Rdns+1lGf+Zdu3bN1Jqx06dPExERkWKaW3Lly5enatWqHDly5K7tFS1alKCgIPbs2ZPqscRjyddb1atXj6VLl3L27NkUSd7Zs2e5cOECnTt3TvNryMjvT0Y88MADgG2a8Z0jTkePHs1QW/Xr109aM3b27Flq1arFm2++ec9krHTp0pw4cQKr1ZpidOzKlSvcunUrQ/2nV0a+l2fPns3ymrHx48czfvx4evfuTUhISIZeCEwcud+9e3eqEbo9e/bg6+tLhQoVAHjwwQdxd3dn9+7dqdqx97x0FknGhMiFPKwRRJszVnHw5K2TrDu9jvX/rufELdsf2GqFqjGo5iBaFG+RrSMjeZabmRiDF+aYUJbs/teFgZjxoC0PFWhLs3w3+SdiP/+E72X53z/w1bGvcDd4U8GnERXzNaWUVw2MKv3/SpRStK9ahIB89teD5Eb9+/dn/vz5TJ06lbp169q90bL3irrRaEx1PCIighkzZqQ6N/HmYuPGjdSuXTvp+IwZM1KNAFy7dg1//5R/HypVqoSnp2dSFbTQ0FC8vLxSbITs4eFB5cqV2b59Ozdv3rxrMpb4Kvedsb/zzjt2RyMcwd/fn2rVqvHjjz9y6tSppCqISilatmzJN998w19//ZXuYiQ+Pj4ZqgjnChn5mUPm14yNGjXKbiGTsWPHcvLkSZYsWZIiwY2MjOTMmTP4+fmlKJDx5JNPMm3aNFatWpW0vshisTBnzhzy58/PI488kuLcpUuXMnPmzKR9xgBmzpwJYLcq450y8vuTEZ07d2b06NG8//77PPTQQ0nP94MHD6aoQHgv9n4HixcvTkBAQJrPu06dOjFt2jS++OKLFN+HadOmZfArSb+MfC+zumZswoQJjBs3jl69evHJJ5/cs9LixYsXCQ0NpWTJkknTCVu0aEHRokUJCQlh+PDhSSO8hw4dYuvWrfTt2zfp75qPjw+dOnVi+fLlHDp0iBo1agAQHh5OSEgI5cuXd3olRZBkTIhcydMaSZgp7WpeJ2+dZN2/61h/2paAKRS1Amsxuv5o2pRsQ2HvtMvICseKc89PvrgwRqz4w9WhJFMM6AKqA0bv48TlO8zvcTs4HLYRHe9FXHgV4sOqY4l4AEh7g9LLYdGMaJf2QuzcwtPTk9WrV9OxY0e6du1Ky5YtadeuHUWKFCEsLIy//vqLr776CqPRmGIUoFu3bnz00Uf06NGDNm3acPnyZRYtWpSqLDxAmzZtqFSpEm+99RbXr1+nTJky7Ny5kz179qS66RswYADnzp2jXbt2lCpViqioKL766itu375N7969AVvhjoEDB/L4449TsWJFfHx8OHDgACEhITRo0OCeC+kfe+wxZsyYwSOPPMLAgQMxm81s2LCB33//PVUsjhQcHMysWbOSPk5+/Jtvvkl1/F4aNmzIxo0bmTJlCiVLlkyaYpmTZORnDplfM2av7DfA3LlzOX36NN26dUtxfO/evbRq1Ypnn32WTz/9NOn46NGj+eabb3jqqad45ZVXCAoK4osvvmDfvn2EhISQL1++pHM7dOhAx44def/99wkNDaVRo0bs3r2bhQsX8swzz9C0adM0487I709GVKpUicGDBzN37lyCg4N5/PHHuXLlCnPnzqVGjRr8+uuvabYxceJE1q9fT8eOHSlTpgxaa1atWpWuFwxGjRrFsmXL6Nu3L3v37qVSpUrs3LmTXbt24e/v75QXTTPyvczKmrF58+YxduxYSpYsSZs2bVi2bFmKxwsXLkzbtm2TPn/99df57LPP2LJlS9Iov8lkYtasWfTo0YNmzZoxYMAAwsLCmDFjBgEBAYwfPz5Fm++++y6bNm2iXbt2DB8+HF9fXxYsWMD58+dZvXp1trwILcmYELmQl44gzs1+MnY96jprTq1h5T8rOXrjaIoErG2ptgR6ZaxqmnAsn/wBdCrqQYuujlkA7Xi2fc5iLbHsv7yHrec3sOvCdiLz78fX7Edw8Xa0L9WRigWq2P0n1mrqVm5Hp17PktuVLVuWAwcOsGjRIr799lumT59OaGgo3t7elCtXjv79+9OvX78USc77779Pvnz5+Prrr1mxYgUlSpRg4MCB1KtXL9XNjtFoZMWKFbz88svMmTMHs9lMu3bt2LZtW4r9kQB69erFp59+ymeffcbVq1fx9fWlSpUqfPvttzz++OMA1KhRg65du7J161aWLl2KxWKhZMmS/O9//2PEiBH3/FqbNGnCd999x9tvv82YMWPw9PSkTZs2bNu2jebNmzvoO5pa69atmTVrFmXLlk1RBCGx3L3JZErXTTzA/PnzGTx4MJMmTeL27dsAOS4Zy8jPPCcoVKgQu3btYvTo0cybN4/w8HCqVKnCl19+SY8ePVKd/8033zBx4kQ+//xzlixZQlBQEBMmTGD06NHp6i8jvz8ZNWvWLIoUKcLHH3/Mq6++Svny5Zk3bx7Hjx9PVzLWpUsXLl68yNdff83ly5fx9PSkfPnyLFiwgH79+t3zWn9/f3bu3MmIESNYtGhR0r55W7ZsoV69eikqHzqKM7+XySXuEXbmzBm7exm2aNEiRTJ2N927d8fT05OJEycycuRI3N3dad26NVOmTEm1BqxcuXJJz8vJkycTGxtL7dq1Wbt2rUO/tntR6V1sKFKrW7eu3r9/v6vDECKV2LGF2FekB01enA9AdHw0W89uZdXJVew6vwuLtlClUBU6le1Eu9LtJAHLSRZ3gdhw6J++6S45QYwlhl3nd7Hm1Bo2n9lMrDWWMn5l6PxAZzqW7UgR7/+modSbtJE2lQN5t2t1jh49mmqBtRBCiIy7fv06/v7+PP/88xkqeCGyLj3/y5RSB7TWdhegyciYELmMjovCrOKJN+fj96u/s/z4ctb9u47wuHACvQJ5tuqzdCrbiXIFZNPyHMmrINw64+ooMsTd6E5wyWCCSwYTFhvGhn83sPKflcw6OIvZB2dTv0h9OpfrTNtSbfEwGYiOc866ISGEyAuioqJSjYAlVjhNz8iRyFkkGRMil7lx6wLr8/nwmdvPnP/pJzzdPGlbqi2dHuhEvcL1MBrSXtMjXMizIERcgwu/uTqSTPEFHvd5gMdrDOds5GV+vLiLlRd38cbON5i8ZxI++SpwM+YxoKarQxVCiPvSww8/TKlSpahbt27SxuY//vgjjRs3pkuXLq4OT2SQJGNC5AJaaw5dPcS3f3/L2lNriPEvSHHlxpgGY3ikzCP4mNMu5iFyCN+iEBMKH2d9LyRXKwG8CLwA7Pdw55t8Pmz0juCi/o1eP33PsOLDsGqr7FEnhBAZ0KlTJxYvXswPP/xAVFQUxYsXZ8SIEYwdO/aee4qJnEmSMSHuY1HxUaz6ZxVfHvuS4zeP4+XmRVv/hjzz61dcqzaSFhWfcHWIIqMavACFq4HV4upIHEYB9RLeLn3zHDML1OQP31vcirnF3zf+xs/Dj4IeBXE35p1y90IIkVkjRoxIs5COuH9IMibyptgICLvo6igy7ULkFb48vZbvzm4gLC6cSr5lGPvgizxcrBmRJw4QEPs5Ozxzx8ameY7ZGyq0d3UUTuOuPQkO9+PdLl9y6I9D+Jh9uBl9kxtRN/Ax+1DIoxDeJm/Z004IIUSeIMmYyJuWdIWze1wdRYZo4ICHO8t887HJyxMFBEdG8UzobWqdOoM6tA0A78QLvJ23n48QmRVn8MBkjUIphbvRneL5ihNnjbMlZNE3OB12Gnc3dwp6FCS/e36ZwiiEECJXk2RM5E3hl6BEQ6jX39WRpCleW1l78w8WX9nN0ahL+Bk96VOoFj0D6lHUnHr06+S1cCZsvMBzhSq4IFoh7i3W4IHJEp3imMlgItArEH9Pf8JiwrgefZ2L4Re5EnmFAu4FKOhREJPR5KKIhRBCCOeRZEzkTZY48C8H1bu7OpK7ioqP4vvj37P4z8WcDz9PWb+yjK05lg5lO+DpdvdNHc8fv8pW614Gu8uvt8h54o2emOP+S8a01klTEg3KQH6P/Pi5+xEZH8mNqBtci7rG9ejr5HfPTyHPQrKuTAghRI7hiP2a5W5N5Em3IyJZffAKkw6uc3UoqRkiwHcX+O0CYwREl4ZbfTl5sjLjfzUwnu33vDzOatvDycssFZVEzmMxemDSEQCYTCaioqLw8vJKcY5SCm+TN94mb2ItsVyLusatmFvcjL6Jr7sv/p7+93xBQgghhMgOUVFRmExZm7khyZjIk5QlBpPZne7VS7g6lCRR1hsci1rFyZhNWIihqKk2lTwexb9gJSiWsbb8PE1ULJzPOYEKkQUWoyce+joAgYGBnD9/nqCgIDw9Pe0W7TAbzRTzKUaAVwA3om5wI/oGYTFheJu88ff0l2IfQgghsp3WmqioKM6fP0/hwoWz1JYkYyJPciOegr4+vNWpiqtD4XLEZRYeWcj6v7/Dqq08UvZh+lbrS/kC5V0dmhAOZ3Hzwl3HoLXG19cXgAsXLhAXF5eu663aSmRcJFfirvCP/gez0Uw+cz6ZviiEECJbmUwmChcunPS/LLMkGRN5khvxaINrCwJcirjEwsML+e74d2itebTcowyoPoAgnyCXxiWEM2k3DzxVDHEWjdlN4evrm6l/ZDGWGL4//j0LDi/gSuQVagXW4sUaL9KwaEMZKRNCCHHfkGRM5D1WC25YsbooGZMkTORl2uSFJzFEx1swu2W+bL270Z2elXrStXxXlh9fzoLDCxi4YSC1A2vzYs0XaVCkgSRlQgghcjxJxkTeY0mYDpXNpbKvR10n5HAIXx37Cq01Xcp3of+D/SUJE3lKYjIWGmfB1yPrv4Nmo5melXryWPnHWH58OSGHQxiwfgC1A2vzcu2XqVO4jgOiFkIIIZxDkjGR91hiAdAGc7Z0Fx4bzuI/F/PZH58RbYmmS7kuPF/9eYr5ZLAqhxC5gckLdxVPTEws5PNwWLPuRneerPTkfyNlvy+gz9o+NC/enKG1h1KhgOy7J4QQIueRZAxQSg0GngWqA3u01i1dG5FwqoSRMW10bjIWa4nl62Nf8/HvH3Mz5iZtS7VlSK0hlPUr69R+hcjJlNlWxj42KhzI2qJnexKTsi7lurD06FIWHV5Et5Xd6Fi2I4NrDZaRaCGEEDmKJGM2F4HJQD2gkYtjEc6WMDLmrGmKFquFH0/+yLzf5nEx4iINijRgWJ1hVPOv5pT+hLifGJKSsQin9uPp5kn/B/vTvUJ3Fh5eyLK/lrH237X0qNiDgdUHUsCjgFP7F0IIIdJDkjFAa70cQClV0tWxCOezxEVjBHDCyNgvF39h6r6pHLt5jCqFqjC+8XgaFZP8XohEBndvAOKiw7OlPz93P16p+wpPVX6KDw99yLK/lvH9ie/p/2B/elXpJSXxhRBCuFSOSMaUUq8DtYE6QBngtNa69F3ONQBDgeeB0sBV4GvgLa21c19qFblCfFxMQjLmuJGxf0P/ZfqB6Ww9u5Vi3sV4r/l7tC/dHoPKfLU4IXIjo7ttZOzkhavE+d3Mxp7d6RQ0lDr5u/DNyY+YdXAWn//xFT0eeIF6Aa0cVnkxMJ87JQp6OaQtIYQQuV+OSMaAd4AbwEEgfxrnzgBeBr4HpgOVEz6vpZRqo7W2Jp6olHIH7nXHHaW1tmQlcHH/scTZpikqt6y/Ih4aE8qHhz7ky7++xN3NnaG1h8qr7ULcg5e3bZ3YZ9v+5Net6dvo2fE6YvSqhKXwaub/OY74yE+IudwRa3SJLLfs7mbg0Nh2eJiMDohTCCFEbpdTkrEHtNYnAZRSRwAfeycppaoCLwHLtdaPJzt+CpgN9ASWJbtkIfD0PfptBWzNUuTivmOJi7F9kIVpinHWOL4+9jXzf5tPeFw4j5V7jCG1huDv6e+gKIXInYoFFARgQruihAZWcWEkVbDqDvx8bRMrzy/httc8GhRqRZeg3uQ3F8pUi5uOXmHJ/ktEx1kkGRNCCJEuOSIZS0zE0uFJQAEz7zi+AFsBjmdIloxprZ9JOCZEEku8LRlTbpmbprjv0j4m7ZnEP6EY1V4MAAAgAElEQVT/0KBoA16t+yoVC1Z0ZIhC5F7utpGxB7cNdHEgNs2BIUoRkt+XxXozv1/dRP9bYfQJDSOjL9c0BV50z09s7BHwyp6tM4QQQtzfckQylgH1ACuwN/lBrXW0Uuq3hMczTCnlhu174QYYlFIegFVrHZvFeEUOlDhNkQxOJbwSeYVp+6ex5tQagnyCmNVqFq1KOG6tiRB5QuFq0HkORIe6OpIkPsAwoFtcGNOv7mGO4V9WFi7F6wGNaeKd/qmL5w5tovjlLVyIvg3kc1a4QgghcpH7LRkrBlzTWsfYeew80FgpZc5EEvUmMDbZ51HANqBlpqIUOVriNMX0jozFWeNYdnQZ83+bT7w1nhdqvEC/av3wcHPchrVC5BkGA9Tu7eoo7CqObVHyrvO7eHfvu7xwYQ1tS7Xl1bqvUtSnaJrXX70US/HLW7DERDs9ViGEELnD/VbqzQuwl4gBRCc7J0O01uO01uqOt5b2zlVKDVRK7VdK7b969WpGuxI5gDXelqsb3NKeRrTv0j6eWPUE0/ZPo07hOnz/6PcMrjlYEjEhcrEmQU1Y3nk5L9d6mR3ndvDoikcJORxCnCWNgiMJfxfiY6OyIUohhBC5wf2WjEUCd5tb5pHsHKfRWn+sta6rta4bEBDgzK6Ek1jjbHm74R7VFK9FXWP0jtE8t+45IuMimd1qNvNaz6Okr2xFJ0ReYDaaGVB9ACu6rKBxscbMOjiLriu7svfi3rtek/g3RZIxIYQQ6XW/JWMXAP+EkvV3CsI2hVHWeYl7ssbdfWRMa833x7/n0R8eZf2/63m++vP80OUHWpWUtWFC5EXFfIoxs9VMPmjzARZtod/6fozZNYbQmNRr3gxm22uC1ri7TeAQQgghUrrfkrF92GKun/xgQsGNmsB+VwQl7i9WS2IyljKnPxN2hgHrB/DWz29RLn85vu38LUNqDcHTzdMVYQohcpCmQU1Z3nk5/ar1Y9U/q+j8Q2fWnFqD1jrpHEPCNEVLrKwZE0IIkT73WzL2FaCxFb5KbgC2tWJLsz0icd+5c81YnDWOkMMhdF3ZlT+u/8GYhmP45KFPKOtX1pVhCiFyGA83D4bVGcZXHb+iqHdRXtv+GkM2D+Fi+EUADCbbCzyJU6GFEEKItOSIaopKqV5AqYRPAwCzUurNhM9Pa62XAGitDyul5gFDlFLLgZ+AysDL2KofLiMbKKU6AZ3KlSuXHd0JB9MJU4iMZneOXDvCuJ/HcezmMdqUbMPrDV4n0CvQxREKIXKyigUrsvSRpSw9upS5v83l0RWPMrT2UGqZbOuILZKMCSGESKcckYwB/YAWdxx7O+H9NmBJsuPDgH+BgUAH4BowB3hLa211bpg2WutVwKq6desOyI7+hGNpSxxRSvHV+c/ZeHAVhTwKMbPlTFqXau3q0IQQ9wmjwUjvqr1pXao1b+95m8l7J1PBqzRTTCYZGRNCCJFuKvl8d5ExdevW1fv3yzK1+81P3w5n/q01nDaZ6F6hO8PrDCefWTZoFUJkjtaan079xDu7JxIVd5vHfJrxv65zMRqMrg5NCCFEDqCUOqC1rmvvsfttzZgQmRZjieH9A+/zesRG4lC8XmM6bzV6SxIxIUSWKKXoULYD82tNpXlkFF9H7KT32t6cCj3l6tCEEELkcJKMiTzhj2t/0GNVDz458gltDCX55twlagTUT/tCIYRIpwDvIsy4co2B7i34N/Rfuq/qzpI/l2DNnhn0Qggh7kOSjGWCUqqTUurj0NDU+8yInCXOEsecX+fw9E9PczvuNh+2+ZAXjRVx10ZMbjKFSAjhOCYPTxTQUAXxw6M/0LBoQ97b9x591/blbNhZV4cnhBAiB5JkLBO01qu01gP9/PxcHYq4h2M3jvHk6if5+PeP6Vi2I98/+j1NgppAfByxuOFmkE2chRCO42ZO2JMwPoYArwDmBM/h7SZv8/fNv3l81eN88dcXyDptIYQQyUkyJnIdq7by6ZFP6bm6J9ejrzMneA4Tm07E1+xrO8ESSxxGTEZ5+gshHMfkbkvGVLxt+wylFF3KdeH7R7+ndmBt3vnlHQZtGsS1qGuuDFMIIUQOklNK24ucJjYCDn8LCTcV94vLceG8cXEDv0Seo7VPWcYVDSb/hb/hwt9J5/iF/UUcbrgZZWRMCOE4JpMJi1ZoS8q/m0W8i/BBmw/48tiXTN8/ncdXPs7bTd6mefHmLopUCCFETiHJmLDv2BpY9bKro8iQjV6ejPMvSKxSjLt+k66nzqAOb011XgCwX1egpExTFEI4kMloJAYTypL6RSylFE9WepJ6hesxascoBm8aTM+KPRlRdwQebh4uiFYIIUROIMmYsC8+YdPSgdvAr4RrY0lDZHwkU36by/J/f6JKgQpMqT+G0vnuHvPSX04zdv1Z9hlkmqIQwnEMBpWQjMXe9ZxyBcrxRYcvmHVwFov/XMzeS3uZ0nwKlQpWysZIhRBC5BSSjGWCUqoT0KlcuXKuDsV5rBbbe29/8C7k2lju4ci1I4zeMZozYWfoV60fg2sOxmQ03fOaCLdbxHNRpikKIRwuDhMGOyNjyZmNZl6t9ypNgprw5s43eWr1UwytPZReVXphUPIikRBC5CXyVz8T8kQ1RZ2QjKmcWf7dqq0sPLyQXj/1Ijo+moXtFzKszrA0EzGAOIutmpkU8BBCOFqsuvfIWHKNizXmu87f0SyoGdP2T+OFDS9IcQ8hhMhj5G5U2Jc4MmbIecnYjegbDNo0iJkHZ9KqZCu+6/wd9YrUS/f18QnJmJS2F0I4WnpGxpIr4FGAma1mMrbRWA5eOUj3Vd3Ze3GvEyMUQgiRk0gyJuzTVtt7Q86ayXrg8oGkm5U3G7zJ9BbT8XPP2AilxWr72oySjAkhHCxWmTFY0zcylkgpRbcK3VjWYRn5zPkYsGEAHxz6AEvii2JCCCFyLUnGhH2JNwE5ZP2CVVsJORxCv3X98DB6sPSRpfSo1AOlMp5QxVk1JqPK1LVCCHEvccqM0Zq5LUEqFKjAlx2+pEOZDsz/bT7Pb3hepi0KIUQulzPutEXOo3PONMUb0TcYtHEQsw7Oom2ptnzV8SsqF6qc6fbiLVbcpJKiEMIJ4pUJYwZHxpLzMnkxqekkJjSewKGrh+i2sht7Lu5xYIRCCCFyErkjFfZZc0YBjwOXD9B9ZXf2XdrHmIZjeK/5e/iYfbLUZpxFSyVFIYRTxCtzlpIxsE1bfKz8Y3zR4Qv83P0YuH4g836bJ9MWhRAiF8pZC4JEzuHikTGtNYuOLGL2r7Mpka8E89rMc9g+PPFWqxTvEEI4hcVgonDcCfj+hSy3VQ74QgcyyRTOh4c+5NcjX/CeZ0UKGtKuGuscCuoPgKDaLupfCCFyH0nGMiFv7DNmK3JxOTwODDpbu46IC2fqwQnsvLCFFkFteKXWG3i7+XA5LNoh7d+OjsdNytoLIZzgsHttSltO43N6l0Pa8wImAXXNMMkrlCfC9jIjHB50xSDZrbPg7iPJmBBCOJAkY5mgtV4FrKpbt+4AV8fiLKev3aYU0GDyViD7RpEM5it4FF+CwXydmCsd+PFoU37c+IvD+ylVyMvhbQohxMZ8j7HOuwtfv9DIoe0+BlS6fpThW4fzrNsV/tfgf3Sr0M2hfaRpWgVI5x5qQggh0keSMWFXRHQMVq14tX0lCniZs6XPv8J2sfrSB7gpd7oUm0SpytWd1leVYr5Oa1sIkXeZ3QyERsU5pe3KhSrzZYcvGb1jNON3j+fwtcP8r8H/cDe6O6W/VIxmsDjnaxNCiLxKkjFhn9WCBQOP1ixG8QLOHUWKt8Yz+9fZfH/hE6oHVGd6i+kU8S7i1D6FEMIZTEYD529FMXPj307rowJDichXlOXHv2X7v4cILjiSfG6BTusvUZ8YcIuMJGsllIQQQiQnyZiwT1uwYnD6xsg3om/w2rbX+OXSLzxR4QlG1R+F2Zg9I3FCCOFolYrkY+PRy8zceNzJPdXF6OPF1WJf8eX5EUSffxJLZHmn9viwWWO5cosqTu1FCCHyFknGhH3aNjJmcOLGyH9c/4NhW4ZxI+oGbzd5my7lujitLyGEyA4j21dkRLsK2dTbI5wO687wrcM5afqEl2u9TN+qfZ22of2x8W+gsli2XwghREpSUk7YZ3VuMrb21Fr6rOmDQrH4kcWSiAkhcg2lVLa9lfYrzdJHltKuVDtmHpzJG7veINYa65S+4pUbBqusGRNCCEeSkTFhl9IWrCiHT1O0aitzf53LgsMLqB1Ym/dbvk8hz0IO7UMIIfISL5MX7zV/j/IFyjPn1zmcDjvNzFYzCfRy7DqyeEy4SzImhBAOJSNjmaCU6qSU+jg0NNTVoThP0siY45qMjItk+JbhLDi8gK7luxLSLkQSMSGEcAClFAOrD2RWq1mcuHWCJ398kiPXjji0D4tyw6glGRNCCEeSZCwTtNartNYD/fz8XB2K8ySuGXNQNnbu9jmeWfMMW89tZXT90YxrNA6T0eSQtoUQQtgElwzm80c+x2Q08eyaZ1l9crXD2o5XJgzWeIe1J4QQQpIxcTdWq62aogPWjO27tI+nVj/FpYhLfNDmA56u/LTTFpgLIUReV6FABZZ1WMaDAQ8yesdoZh6YiVVbs9yujIwJIYTjSTIm7NMW4jFmuYDHN39/w8D1A/Fz92PZI8toXKyxgwIUQghxNwU9CrKg7QK6V+jOwiMLGbp5KBFxEVlq02IwSTImhBAOJsmYsEtpC1ZtwJDJZ4jFauG9fe8xYfcEGhRrwLIOyyjtV9qhMQohhLg7k9HEmIZjeKPBG+w4v4Pea3pzKeJSptuzKBNGLdMUhRDCkSQZE/ZZrVgyOU0xMi6S4VuHs+TPJTxd+WnmBc8jnzmfE4IUQghxL0opelbqyfzW8zkffp6nVz/Nn9f/zFRbVuWGm5Z9xoQQwpEkGRN2qUxu+nwt6hrPrXuObee2Mbr+aEbXH43RYHRSlEIIIdKjcVBjljy8BKPBSJ+1fdh6dmuG27AYzDIyJoQQDibJmLBP2wp4ZKSa4vGbx3lq9VOcDD3JrFazeLry004MUAghREaUL1CepY8spaxfWYZuGcrSo0szdL3VYMJNkjEhhHAoScaEXbZNn9P/9Pj5/M/0XtObeGs8nz70KS1LtHRecEIIITIlwCuARe0X0bJ4Sybvncy7v7yLxWpJ17W2ZEwKeAghhCNJMibs0xasKn1Pj2///pZBmwZR1Kcoyzoso0qhKk4OTgghRGZ5mbx4v+X7PFvlWZb9tYyhW4YSGReZ5nVWZcINGRkTQghHkmRM2JW4ZuxerNrKjAMzGL97PA2LNWTxQ4sp4l0kmyIUQgiRWUaDkZH1RjKm4Rh2nt9Jn7V9uBp59Z7XWA0m3LCANet7lgkhhLCRZCwTlFKdlFIfh4aGujoUp1EJa8buJs4Sx/92/o9FRxbxRIUnmBs8Fx+zTzZGKIQQIqueqPgEc1vP5XTYaZ756RlOhZ6667naaLJ9YJWpikII4SiSjGWC1nqV1nqgn5+fq0NxmnslYxFxEQzeNJjVJ1fzcq2XebPhm7gZ3LI5QiGEEI7QNKgpix5aRLQlmt5renPo6iG752mD2faBRcrbCyGEo0gyJuxSd1kzdi3qGn3X9mXvpb1MaDyBAdUHoDKxF5kQQoico2qhqnz+8Of4mn3pv64/285uS3WONiSMjMVLMiaEEI4iyZiwy141xdNhp+n1Uy9OhZ5idvBsHiv/mIuiE0II4WglfEuw+OHFPJD/AYZuGcry48tTPJ40TVFGxoQQwmEkGRP2aSua/zZrPnLtCL3X9CY8LpyF7RfSvHhzFwYnhBDCGQp5FmJR+0U0LNaQsT+P5cNDH6K1BmSaohBCOIMkY8IuQ7JpijvP7+S5dc/h6ebJkoeXUD2guoujE0II4SxeJi/mBM+h8wOdmffbPN7e87ZtL7KkkTEp4CGEEI4iVReEXbZpim6s/GclY3eNpVyBcsxvPZ8ArwBXhyaEEMLJTAYTE5tMJNArkJDDIVyPuk4jQxnbgzIyJoQQDiPJmLBLaSsbfWP4eucbNCjSgJmtZkrpeiGEyEOUUgytPRR/T38m753MSVWcTkrhLcmYEEI4jExTFKlorVnqE8PXBSNoXbI189vMl0RMCCHyqKcrP827zd7ljD5P/6KB3Iq+6eqQhBAi15BkTKRg1Vam7JvC0nxWGoR7Mq3FNMxGs6vDEkII4UIdy3akh/vjHDeZePbAu1yOuOzqkIQQIleQZEwkibfGM2bXGJYeXcpj4fDUjYKymbMQQggAKnlU4YPLV7kcc4Nn1z7L2bCzrg5JCCHue5KMCQBiLDGM2DqClf+sZFDNQbx4S4Mypn2hEEKIPEG5makXHcO8CgOJiIug99reHLtxzNVhCSHEfU2SMUFkXCSDNw1m89nNjK4/mhdrvIiRlPuMCSGEyOMSpqxXMgfy6UOfYlAG+q7ry29XfnNxYEIIcf+SOWiZoJTqBHQqV66cq0PJstCYUAZtHMQf1/9gUtNJdH6gM2CrpqiV5OpCCCFsDG7uAHiueZkHTJ4sNsBAPxMDf3qGmaHxNI7TLo7QAcq1hi7zXR2FECIPkWQsE7TWq4BVdevWHeDqWLLiRvQNBqwfwKnQU0xvOZ3WJVsnPWbQFqwGGRkTQghhE5mvDPPiO9O3mi9eZiNBwGfWGJ4PP8SQ/JHM8K5GC7O/q8PMvNO74NR2V0chhMhjJBnLo65GXmXA+gGcDz/P3NZzaVyscYrHFTIyJoQQ4j9GoxtT43vyaOtWeBXwAsAfWBQTyvMbnmfYzaNMrTeVNqXauDbQzFr5Mvy91tVRCCHyGLnbzoMuRVyi77q+XIi4wPw281MlYgAGScaEEEIk42ZUAMRbUk5H9HP3Y0G7BVQtVJWR20ay5tQaV4SXdUYTWOJcHYUQIo+Ru+085nz4efqs7cP1qOt83PZj6hWpZ/c8g7ZIAQ8hhBBJ3Iy2W4Z4qzXVY/nM+fio7UfUDKzJ6B2jWXFiRXaHl3UGE1jjXR2FECKPkWQsDzkTdoa+a/sSFhvGgnYLqBlY867nyjRFIYQQyZkMtpGxOIv9Qh3eJm8+aPMB9YvUZ8yuMXz797fZGV7WyciYEMIF5G47jzgZepK+a/sSFR/FwnYLqeZf7Z7nG7QVLfuMCSGESGBMSMYs1rtXTfR082Ru67k0CWrC+N3j+eKvL7IrvKwzmsAS6+oohBB5jCRjecDxm8d5bu1zxOt4FrVfROVCldO8RtaMCSGESM6UME0xzpJ6mmJy7kZ3ZrWaRasSrXjnl3f47I/PsiO8rDOYQFtA54IS/UKI+0aG77aVUhuUUj2UUmZnBCQc69iNYzy37jkMysAnD31C+QLl03WdjIwJIYRILqmAxz1GxhKZjWamt5xOu1LtmLZ/GiGHQ5wdXtYZEwpMy1RFIUQ2ykxp+zpAMHBTKfU5sFBrfdixYQlHOHbjGP3W98PD6MGi9oso6Vsy3dcasICMjAkhhEiQOE3xzmqKd2MymJjSfAqmXSZmHZwFQP8H+zstviwzJrzGbI0D5PVmIUT2yMzddhHgaeBX4CXgN6XUL0qpAUopH4dGJzLt75t/0399fzyMHnzS/pMMJWJgm6ZolZExIYQQCUz3qKZ4N24GNyY1mcQjZR5h1sFZLDqyyFnhZZ3BZHsv68aEENkow8mY1jpWa/2l1rotUBaYCBQGPgIuKqUWKqWaODhOkQHHbx6n/7r+mI1mFrVfRAnfEhlrQGuMWGVkTAghRBK3DI6MJTIajExqOomHSz/MjAMz+PTIp06IzgGMicmYlLcXQmSfLN1ta61Pa63HAmWAh4AtQB9gu1LqT6XUUKWUd9bDFOl14uYJ+q/vj5vBLcNTE5No26uesmZMCCFEIjdD+gp42L/WjXeavUP70u2ZfmB6zizqYUhYuWGVNWNCiOzjqKGPmkBnoBmggH8AKzADOKGUauygfsQ9/HPrH/qt74dRGVnYfiGlfEtlriGrBZBkTAghxH8SC3jcq7T9Pa83uDG52eSkoh6L/1jsyPCyLnHNmBTwEEJko8wU8ABAKZUf29qxfkANIA74AfhYa7054ZxgYAEwD6iV5WjFXZ0MPUm/df0wKAMh7UMo41cm841pScaEEEKkZHazvX778pe/Yvz6tyy01ApjkYtM3T+VyWuOYQ1t6pgAs6ij+pNpBiQZE0JkqwwnYwkJVj/gMcAD+Bt4DfhUa309+bla681KqcnYkjHhJKdCT9FvXT8AFrZbSFm/sllrMGFkDIOsGRNCCGFTppA3ox+uxM2IrBe4sOrX2RU2k7MBK6lfphAVPR92QIRZYzl8EKKQaYpCiGyVmZGxjUAMsBzbKNi2NM4/AezKRD8iHc6EnaHfun5YtZVF7RdRNn8WEzGQkTEhhBCpGAyKF1o84LD24qwf8uq2V9l05hMeqlqMnpV6OqztzFh8yQ/OICNjQohslZmhjxFAkNb66XQkYmitt2itW2WiH5GGC+EX6Le+H/HWeBa2W8gD+R30TzJxZEySMSGEEE5iMpiY2nwqLUu0ZNIvk/jhxA8ujUcnVlOUkTEhRDbKTDKWDyh2tweVUlWVUm9lPiSRHlcjrzJg/QAi4iL4qO1HlCtQznGNSzVFIYQQ2cBkNDGtxTQaFW3E2J/HsvbUWtcFk1hNUUbGhBDZKDPJ2Fig+j0er5ZwjnCSm9E3GbB+AFejrvJBmw+oXKiyYzuQkTEhhBDZxN3ozqzgWdQMqMnrO15n69mtrgkkaZ8xScaEENknM8mYSuNxDyBX75iolOqklPo4NDQ02/sOiw3j+Q3Pcy78HPNaz6NGQA3Hd6KlgIcQQojs4+nmybzW86hcqDKvbH2Fny/8nP1BGGSaohAi+6Xrblsp5auUKqmUStxBuFDi53e81cRW7v6s0yLOAbTWq7TWA/38/LK138i4SAZtHMTxW8eZ0XIG9YrUc05HMjImhBAim/mYffigzQeU8SvD0M1DOXD5QPYGkLTPWK5+PVkIkcOkd+hjOHAq4U0DM5N9nvztANAG+NDhkeZx0fHRvLT5JY5cO8LU5lNpVryZ8zpLrKZokGRMCCFE9vFz9+Pjth9T1KcogzcN5vDVw9nXuTFxzVjWS/cLIUR6pbe0/daE9wp4C/ge+P2OczQQDuzRWrtgfoELXDwEEws7vZs44BV/P/Z5mJl0I4w2S552bocJBTySFjMLIYQQ2aSQZyEWtF3As2uf5YWNL7Co/SIqFqzo/I4TpilqS1ya6zGEEMJR0nW3nVDCfhuAUqoU8KHW+hdnBnZf8A6ABv2d2kW8tjLq5j52RF9gjF9NOgWVcWp/iT7cdZ5bvg2zpS8hhBAiucLehQlpF0KftX0YuGEgnz70KWX8nPv/TxklGRNCZL8MD31orfs6I5D7km8xaDvBac1btZWxu8aw4eIFXq37Kk9U7e20vu40b+c6upmzd02cEEIIkah4vuIsaLcgKSFb8vASingXcVp/icmYJT42U9XNhBAiM9L8e3NH4Q7uUrgj1Ztzw879tNZM3TeVlf+sZFCNQfTOxkQMwKo1RiWvDQohhHCdMn5l+LDNh4THhjNww0BuRt90Wl8qoYCHNV7WjAkhsk96Xvz5FziplDIn+9xe8Y4730QWhBwO4fOjn/N05ad5ocYL2d6/RWsMBknGhBBCuFblQpWZEzyHC+EXGLRxEBFxEU7pJ3FkzCr7jAkhslF6pilOwFacI/6Oz4WTfPP3N8z+dTYdynbgtXqvoVwwQmXVYJCRMSGEEDlA3SJ1mdp8KsO3DmfolqHMbz0fc2IpegdRbglrxmRkTAiRjdJMxrTW4+71uXCsDac3MHHPRJoGNeXtJm9jUK6ZuW61amRgTAghRE7RqmQrJjSZwBs732D0jtFMbT4VowO3YEkaGYuXkTEhRPaRNao5yJ6Lexi1fRTV/avzfsv3MSWU2XUFi9YYJRsTQgiRg3R+oDOv1XuNDac38Paet9HacRN1lNEdAG2VZEwIkX1kI6kc4o9rfzB081BK+ZZibuu5eLp5uiwWrTVapikKIYTIgXpV6cXN6JssOLyA/O75GVZnmEPaNcg0RSGEC6SZjCmlrGR8jZjWWkuil04nQ0/y4sYXKeBRgI/afoSfu2tLylsTftqSjAkhhMiJXqr1ErdibrHwyELyu+enT7U+WW7TaDRi0Qot0xSFENkoPQnTYqRgh9NcirjE8xueRynFR20/ItAr0NUhYUnIxowyiVUIIUQOpJTijQZvEBYbxvQD0/Fz9+Ox8o9lqU03oyIeN7RUUxRCZKP0FPDokw1x5Em3om/x/IbnCY8NZ1H7RZTyLeXqkADbHmOAlLYXQgiRYxkNRt5t+i63Y28zfvd4CnkWonnx5lloTxEryZgQIpvJ2IeLRMdHM2TzEM7dPsfs4NlULlTZ1SElSUrGZJqiEEKIHMxkNDGj5QwqFqzIyG0jOXLtSKbbcjMo4jGiLbJmTAiRfSQZcwGL1cKo7aP4/ervTG4+mXpF6rk6pBSSpilKMiaEECKH8zJ5Ma/1PAp6FGTwpsGcCTuTqXaMBgPxGEFGxoQQ2SjNZEwpdUop9Y9SypTw+cl0vP3j/NDvT1prJu+dzOazmxlVfxRtS7V1dUipJBXwkGmKQggh7gP+nv582OZDrNrKCxtf4HrU9Qy3YTRAHEaZpiiEyFbpKeBxGlsBj8QiHmeQgh6ZtujIIr489iV9qvbh6cpPuzocu6zWxGmKLg5ECCGESKfSfqWZ23ou/df1Z8imISxsvxAvk1e6rzcaDMRpNwpe2gsrhjgxUhcxmqH5SPAt5upIhBDJpKeAR8t7fS7S78eTPzLz4EweLv0ww+sMd3U4d2XRidUUJRsTQghx/6gRUIOpLaYydMtQRm4byezg2bgZ0rfTjptBsdP6IN0tf8CJTU6ONJtpC4RfhqLVoU4fV0cjhEhG9gLLJnsu7lSJUPQAACAASURBVGHMrjHUL1KfiU0nYlA5d7meFPAQQghxv2pZoiVvNnyTCbsn8PaetxnXaBwqHf/PjAbFG/H9KPN4Axo/4J8NkWaj8CswrbyshxMiB8p0MqaUcgdaAmUTDp0Etmmtox0QV65y7MYxhm0ZRmnf0sxoNQOz0ezqkO7JarW9l2RMCCHE/ah7he5cjrjMR79/RGGvwgyqOSjNa9wSZoMkFrHKVRJHB63xro1DCJFKppIxpVRv4H2gAJB4x66BW0qpEVrrTx0T3v3vYvhFBm0chLfJmw/afICv2dfVIaXpv2mKLg5ECCGEyKTBNQdzOfIyHxz6gECvQLpV6HbP8xOn5sdLMiaEyEYZTsaUUj2AT7EV8pgG/IktIasCvAAsVEpFaa2/cmCc96XQmFBe3PgikfGRfPbwZxTxLuLqkNIlsYBHeqZ1CCGEEDmRUoq3Gr3FtahrTNwzkUCvwHtuCu1msL0CabHkwmTMaLK9l2mKQuQ4mRkZ+x/wF9BQax2W7PgKpdR84BfgDeC+SMYSplvOBVoDgcBFYJ7WemZa18ZZrFwMjbL7WKwlltd/fokzt88wqdEs8hlK3PXcnOZymG2mqewzJoQQ4n5mMpiY3mI6fdf1ZeS2kSx+eDGVClaye27uHhlLSMZkZEyIHCczyVhFYMwdiRgAWutQpdQnwLisBpaN3IBLQDts696qA+uUUhfTGt3769JtGr272c4jGo9iX2Py+5Wo8z158Y8wwN55OZuHyejqEIQQQogs8TJ5MTd4Lk/99BSDNw5maYeldmeqGHP1mrGE/+eSjAmR42QmGbvEf+vE7LEClzMXTvbTWkcAY5Id+k0ptRpoQhqje0H5PXmn64Opjm+/uowd136lRUAvmlbu6dB4s4u7yUDryoGuDkMIIYTIsgCvAOYGz+XZtc/y0uaX+Oyhz1LtQZaUjOlcmIwpZVs3JtMUhchxMpOMfQr0UUrN11qHJ39AKeULPAd8kpEGlVKvA7WBOkAZ4LTWuvRdzjUAQ4HngdLAVeBr4K2ExCpLlFJuQFPgvbTOLehtpmf9kimO/XjyR3YcXUrnBzozscmrsu5KCCGEyAEqFqzI9BbTGbxpMK9uf5XZrWZjNPw3A+S/aopWV4XoXAY3sEoyJkROk2a9PKVU8+RvwHYgEjislHpVKdVJKdVRKfUacAgIB3ZkMI53gGDgH+BmGufOwFbJ8U/gJeAb4GVgVUKiljx2d6WUzz3e7M3Dmw2EAosz+DVw8PJB3tr1FnUL1033viZCCCGEyB5Ngprwvwb/Y/u57by3L+VrrklrxnJjAQ+wrRuzWlwdhRDiDukZGduKrWx9colZxpRkjyUeKwVsADKy4OgBrfVJAKXUEcDH3klKqarYErDlWuvHkx0/hS2J6gksS3bJQuDpe/TbCtvXl9jOdGyjYsFa69gMxM+ZsDMM3TKUIJ8gZraaiSmxcpEQQgghcownKj7BmbAzfPbnZ5T0LcnTlW23CW7GXLxmDMAo0xSFyInSk4z1dXYQiYlYOjyJLem7s9LhAmAy8AzJkjGt9TMJx9KklJqJraJisNb6WjrjAWwl7AdvGgzAvNbz8HP3y8jlQgghhMhGr9R9hXPh53hv33sE+QTRskTL3F1NEWSaohA5VJrJmNb6s+wIJJ3qYSsQsjf5Qa11tFLqt4THM0wpNRvbNMlWWuurGbk2zhLH8K3DOR9+npB2IZT0LZn2RUIIIYRwGYMy8G6zd3lu7XO8tv01Pn3oU4p4lANy8ciYwSTVFIXIgdJcM5bDFAOuaa1j7Dx2HvBXSpkz0qBSqhS2qY/lgFNKqfCEtzV3OX+gUmq/Umr/1atXGbd7HPsu7WNCkwnULlw7o1+PEEIIIVzA082TOa3nkN89P0M2DeFatK0QdK4dGTO6gUWSMSFymsxUUwRAKVUYqAsUwE5Sp7XOcAGMdPAC7CViANHJzkn3ei+t9WnuXar/zvM/Bj4GKFW1lF75z0oG1RhEx7Id09uEEEIIIXIAf09/5rWeR+81vRm1cygYnsnl1RQlGRMip8lwMpZQsXAe0J97j6w5IxmLBO62+ZVHsnOyxZXIKzxV9ileqPFCdnUphBBCCAcqX6A801tMZ9CmQXgU+4p4S+r9Q3MFg0nWjAmRA2VmmuJIbHt8fQE8i21UaTQwGDgO7AfaOirAO1zANhXR3c5jQdimMGaoCmJWeLt5M77xeClhL4QQQtzHGgc1ZkSdkZjy/cnum5+7OhznMMg0RSFyoswkY88C67TWvYHEdVUHtNYfYtu02T/hvTPswxZz/eQHlVIeQE1siWC2KelbErMxQ0vUhBBCCJEDPVXpKWJvNuC328v58eSPrg7H8YwyTVGInCgzyVhZ/kvCEidWmwC01hHAJ9imMDrDV9j2NRt2x/EB2NaKLXVSvykkbHT98e2w29nRnRBCCCGczGg0EHe5M0XMVRm7ayy/X/3d1SE5lkxTFCJHykwyFgUk/jaHY0uOkq/jugSUyEiDSqleSqk3lVJvAv9v786jpCqv9Y8/+1R3M0ojIKKgKIOIiILMGhUTMcQrmmsiaiJeR3JVHJiiAqLihAhIHKJCHIiJiTFXc/WXGK8TGFHD5MAgEjSggqigMiPQvX9/VDW2bdNDdXedOqe+n7VqNX3OqTqbVauhnn7fd7/7SCos+d7MhpRc5+6LlFyvdrqZPWlmF6U2ap4qaba+veFznXH3Z9x9aGEh+4kBABAXeUG+ji0cqZYNW+rKl6/U2i1rwy6p9gRs+gxko3TC2CpJ7SXJ3XdKWiFpYKnzJ0r6tJqveaGkm1KPlpKalvr+wjLXXqXkurUuSgazsyTdLekUd49pCyQAAFDXEoEpT411zw/u0bZd23TFS1do686M9QWrW4l8qbgo7CoAlJFOGHtJ0n+W+v5RSWeb2ctmNkvSGZL+VJ0XdPf+7m57ePQvc22Ru09x907uXs/dW7v7CHffnMbfBQAAQJKUF5h2FbnaN22vScdN0rIvlmncnHEqjsPveoM8pikCWSidMDZZ0qWlOhreJukeSUcqOVo1XdL1tVMeAABAZgSBqdiTmz4f1+Y4jew5Us+vel73v31/yJXVAvYZA7JStfcZc/dPJH1S6vsiSVekHgAAAJGUF5h2ldr0+dzDztWKr1bovrfvU7um7TTwoIEVPDvLJfJpbQ9koXRGxnJeSTfFDRs2hF0KAACoJYnAVFTsu783M13X9zp1b9ld1716nZasXxJidTXENEUgK6UdxsxssJn9wcz+mXr8wcwG12Zx2YpuigAAxE/JmrHSChIFurP/nWpWv5mufOlKrdu2LqTqaohpikBWqvY0RTNrKOl/JX1fkkn6KvW1l6TBZvYLSaem9hwDAACIhETCtGXHLn2+6esyZxrrhj536PLZF+iKF0doyrH3KS+o9keoUBV6QgW0tgeyTjr/ktwq6QeS7pI00d3XSpKZtZJ0jZJrx27RdzdmBgAAyFr18xL626K1+tui8vcXy2vyn1pU9Ef1f2i4vv70tAxXVzN35H2qQXt9rfphFwLgW9IJY2dKesLdvxW2UqHsKjNrnbqGMAYAACLjjjOO1KLVFa0HP1wvf7ZD8/SkTjust7oWDshYbTWxcdtO7XwxIWeaIpB10gljTSS9XMH5lySdnF45AAAA4eh2QFN1O6BphdecXXydLnlhjV749Nc656jeOmKfIzJUXfo+3/S1nn0xT0YYA7JOOg083pHUsYLzHSUtSq+caKCbIgAAuSkvyNMdx92hlg1bavjLwyPR0CMRmIoUKHDCGJBt0glj4yRdbGaDyp4ws9MkXSRpTE0Ly2Z0UwQAIHc1rd9UvzrhV9q4Y6NGzBqhnVneGCNhpp1iZAzIRpVOUzSzh8o5/G9JfzGz9yS9K8klHSapk5KjYj9XcroiAABA7HRq1kk3HXOTRr8yWrfPu13j+o4Lu6Q9SiRMu5RgZAzIQlVZM3ZeBecOTT1KO0JSV0kXplkTAABA1ht48EAt/WKpHl78sDo366yfHPKTsEsqV8JMuxQo8KKwSwFQRqVhzN3T3hgaAAAgzq7sfqXe++I93fLPW9Rh7w46cp8jwy7pO4JA2uV5MrlUXCQFibBLApBC0AIAAEhTIkho0nGTtG/DfTX85eH6fOvnYZf0HcmRsVQAy/L1bUCuSTuMWdJRZvbT1OMoM7PaLA4AACDbFdYr1K++/ytt3rlZo2aP0s7i7Ao8iSA5TVGSRBMPIKukFcbMbKCk9yXNk/R46jFP0goz+2HtlZedaG0PAABKO2TvQ3R9v+u18LOFmrZgWtjlfIuZqchSK1OyLCgCua7aYczMjpH0tKS9Jd0laWjq8avUsafN7OjaLDLb0NoeAACU9R/t/kNnH3q2frv0t3pu5XNhl/MtxVYyTZGRMSCbVKWbYlnjJa2V1MfdPyl9wszukPTP1DUDa14eAABAdIzuOVpL1y/V+Dnj1bFpR7Vr2i7skiRJxbtHxghjQDZJZ5piH0nTywYxSUodmyGpb00LAwAAiJr8RL4mHz9Z9fPqa/is4dq6c2vYJUmSisQ0RSAbpRPGCiRtquD8xtQ1AAAAOadVo1aadNwkrdy4UuNfGy93D7skFZe0s2dkDMgq6UxTfFfSWWZ2r/u3t3I3szxJZ6auAQAAyEl99uujK7pfoWkLp+nIfY7UkMOGhFpPseVJLmnZX6W99gu1ljrR4hBpvyPCrgKotnTC2H2Spkt60cwmSVqaOt5F0mglpzEOrZ3yAAAAoumCwy/QO5+/o6nzp6pL8y46at+jQqvlS9s7Gcb+b1xoNdSpJm2kEUvCrgKoNktn6NzMbpc0ag+n73D3a2pUVUT07NnT58+fH3YZAAAgS23asUln/b+ztG3XNv1p0J/UokGLUOrofcsL+s92rmsHHBTK/evU7EnSiuelq1eGXQlQLjNb4O49yzuXzsiY3P1qM3tQ0mmSDpZkSu479rS7L0+7UgAAgBjZq2AvTe0/Vef87RyNnj1aM06aobwgrY9fNZIITOvz9pFadMz4vetcoxZScVHYVQBpqVYDDzOrZ2bHmVlHd1/u7ne4+6Xufom7T86VIMamzwAAoKo6Neuk8f3Ga/6n8/Wrhb8KpYZEYCouDr+RSJ0IElIRXSIRTdXtplgk6UVJP6qDWiKDTZ8BAEB1DGo/SGd2OlOPLHlEL334UsbvnwhMRVnQ1bFOBHl0iURkVSuMpbonrlVyWiIAAACq6Je9fqnDmh+mcXPGafXm1Rm9d8JMRbEdGcsnjCGy0tln7AlJg80snecCAADkpIJEgSYfP1nurtGzR2tnBqfWBUGcw1ieJJeKi8OuBKi2dALVbyQ1lPR8au3UoWZ2YNlHLdcJAAAQeQfsdYAmHDNBi9Yt0tQFUzN237xYhzE2tEZ0pdPOZ3GpP/ev4LpEGq8NAAAQawPaDtDPO/9cv3v3d+qxbw+d2PbEOr9nYKbiOK8Zk6TinZIKQi0FqK50wtgEJbcNBAAAQBpG9hiptz97W+PnjFenZp10wF4H1On9EoFpV2xHxkrCGCNjiJ5qhTEz20fSs5LWufv7dVMSAABAvOUn8nXH8Xdo8P8brFGzR+nRHz2qgkTdjeok4jxNMZGf/MpeY4igKq0ZM7PAzO6X9Imk1yQtN7NXU+EMAAAA1dRmrza66ZibtHT9Uk2eP7lO75UI4jxNkTVjiK6qNvAYJmmokm3tn5S0SNLRkh6oo7oAAABi7wcH/kBDDhuiPyz7g55b+Vyd3Sfere2ZpojoqmoYO1fSu5I6u/sZ7t5N0oOSBplZ0zqrDgAAIOaGHzVcXVt01fWvXa8PN35YJ/eI9TTFkjCWwa0CgNpS1TDWSdIj7r6p1LG7leyYeEitV5XlUi39p2/YsCHsUgAAQMTlJ/I1+fjJSlhCo2aP0tdFX9f6PXIijDEyhgiqahhrJGlNmWNrSp3LKe7+jLsPLSwsDLsUAAAQA/s33l+3fO8WvfvFu5o8r/bXjwWBqSimWeybMEYDD0RPdTZ9LvsjXPK91VItAAAAOav/Af015LAh+uN7f9SLH75Yq6+dMKmouLhWXzNrMDKGCKtOa/uTzaxVqe8bKhnIzjCzbmWudXe/s8bVAQAA5JCrjrpK89fO1/g549WleRe1atSq8idVQSIIVBTTLEYYQ5RVJ4z9LPUo6xflHHNJhDEAAIBqKEgUJPcfe2awrn7laj34wweVF1RrW9hyJQKpmDVjQNap6k/3CXVaBQAAACRJbZu01bi+4zTm1TGa/s50Xdrt0hq/ZiIwFcV2nzHCGKKrSmHM3WfXdSEAAABIGtR+kF5f87oeeOcB9WrVS71a9arR6yWnKcY1jLHpM6KrOg08AAAAkCFj+45Vm8ZtdM0/rtFX27+q0WslG3jENIwl8pNfCWOIIMIYAABAFmqU30iTjp+kL7Z/oeteu05eg2mGAfuMAVmJMAYAAJClujTvouFHDdesj2bpD8v+kPbrJCwXwhj7jCF6CGMAAABZbMhhQ3Rcm+M0Zf4UvffFe2m9Rl4izg08UmvGinaGWweQBsIYAABAFjMz3XTMTSqsV6hRs0dp686t1X6NwIzW9kAWIowBAABkuWb1m2nisRO1auMqTZw7sdrPj3drexp4ILoIY2kws0FmNn3Dhg1hlwIAAHJE7/1666KuF+mpFU/puZXPVeu5icBUVBTXMMaaMUQXYSwN7v6Muw8tLCwMuxQAAJBDLul2ibq26KobX79Ra7esrfLzEhbnkTH2GUN0EcYAAAAiIj/I18RjJ2pX8S6NeXWMiqo4GpTIidb2NPBA9BDGAAAAIuTAJgfq2t7Xat7aeZq5dGaVnsM+Y0B2IowBAABEzI87/FgD2g7Q3W/eraXrl1Z6fV6cG3gkShp4sGYM0UMYAwAAiBgz0/X9rlez+s109StXa9uubRVeH5jJXfI4BjLWjCHCCGMAAAARVFivULd87xat3LhSU+ZPqfDaRGCSFM+pikxTRIQRxgAAACKq7359dV6X8/T4e49r1kez9nhdSRjbRRgDsgphDAAAIMIu7365Dm12qMbPGa9129aVe01JGCuO5TTFVBgrIowheghjAAAAEVaQKNDEYydq666tGjdnXLnrwhLGNEUgGxHGAAAAIq590/Ya2XOk5qyeo8eWPfad80Gc14yZSZYgjCGSCGMAAAAxcFans3Rs62M1df5UrfhyxbfO5cU5jEnJ0THCGCKIMAYAABADZqYJx0xQ44LGuvofV2tH0Y7d53aPjMVxzZhEGENkEcYAAABiokWDFrrx6Bu1/Mvluu/t+3YfL1kzVlwcVmV1jDCGiCKMAQAAxEj/A/rr9I6n66HFD+mtz96S9M00xV1xTWMBa8YQTYQxAACAmBndc7T2a7Sfxrw6Rlt3bt09TTGuWUyJfMIYIokwBgAAEDONCxrr5mNu1sebPtaU+VOUSH3iY80YkF3ywi4AAAAAta9nq576ry7/pUeWPKL6B3eVlK+Pvti6e/1YnLSxhILiorDLAKqNMAYAABBTw7oP06urX9VfPp4mJS7VuQ/NDbukOjGn4U61LtoZdhlAtRHG0mBmgyQN6tChQ9ilAAAA7FG9RD3d+r1b9bO//UzH9H5Fp7e5JuySat2Tb36sHR8HTFNEJBHG0uDuz0h6pmfPnheHXQsAAEBFOjfvrEuPvFR3vXmXft71ZJ3c7uSwS6pV73z8lXZ+nJDWvCn9dWTY5dSNek2k/tdIefXCrgS1jDAGAAAQc+cffr5mfTxLN//zZvXYt4f2bbRv2CXVmiAwLfRDdciOBdKSp8Iup/YV7ZS+3igd+h9Sm55hV4NaRhgDAACIubwgT7d+71ad8cwZGv/aeN1/4v2ymDTySJhpgl+os375RNil1I33X5Ie/c9kKEPs0NoeAAAgB7Rt0lYje4zUa2te0+PvPR52ObUmEZiKimPasl9Ktu2XWBMXU4QxAACAHDG402Ads/8xmjJ/ilZtXBV2ObUiCEzFcd0/TZIskfzqtO6PI8IYAABAjjAz3Xj0jSpIFGjMP8ZoVwxGWxLGyBiiizAGAACQQ/ZttK/G9hmrd9a9o5lLZoZdTo0FJhW75HEdHdsdxhgZiyPCGAAAQI750cE/0okHnqh737pX73/1ftjl1EgQJBuRxDWLKUhNU2RkLJYIYwAAADnGzDS271g1ym+kca+Oi/R0xUSqK2RRXNMY0xRjjTAGAACQg1o0aKGxfcZq8frFemTJI2GXk7aSkbHYrhsjjMUaYQwAACBH/fCgH2pA2wH69Vu/1oovV4RdTloSqTAW246KrBmLNcIYAABAjjIzje0zVo3zG2vcnGhOV9w9TTG2I2Mla8YIY3FEGAMAAMhhzRs015i+Y7Rk/ZJITlcsmaZYXBxyIXWFBh6xRhgDAADIcQMPGrh7uuK/vvxX2OVUSyqL0cADkUQYAwAAwO7pitfNuS5S0xVzZ81YdN4TVB1hDAAAAGreoLnG9h2rJeuX6OHFD4ddTpUFVjJNMe5hjDVjcUQYAwAAgKRkd8WT2p6kX78dnemKJSNj8Z2myJqxOCOMAQAAYLexfceqSUETjZszTjuLd4ZdTqXi302RaYpxRhgDAADAbs3qN9O4vuO0dP3SSExXjH83xVQYc6YpxhFhDAAAAN8yoO0ADTxooO57+z4t/3J52OVUKJH6NBvfaYqsGYszwhgAAAC+Y0yfMWpS0ETj54zP6u6KQdynKVrq43oWvwdIH2EMAAAA37F3/b11bZ9rtWT9Ev1u6e/CLmePSsKYx3VkzEyyBGEspghjAAAAKNcP2/5QJxxwgu556x59uPHDsMspV+y7KUrJqYqEsVgijEkys1+b2UdmttHMVpvZNDMrCLsuAACAMJmZxvUdp4KgQNe/dr2KPfu6ZMR+mqKUCmOsGYsjwljSPZIOdfcmkrpJOlLS1eGWBAAAEL6WDVtqZM+Rmv/pfP3Pv/4n7HK+IxH3booSI2MxRhiT5O5L3X1L6UOSOoRVDwAAQDY5vePp6t2qt6bOn6q1W9aGXc63xL6bopTc+JmRsVjKijBmZtea2RNm9oGZuZmtrODawMyGm9kyM9ueml44xcwa1bCGa8xsk6TPJB0h6e6avB4AAEBcmJlu6HeDdhXv0s1v3JxVzTJyZ5oiI2NxlBVhTNKtkr4v6X1JX1Zy7Z2SpkpaKulySU9IukLSM2b2rb+PmdUzs8YVPBIl17r7RHffS9JhkqZLyq5f+wAAAITogCYHaFj3YZr98Wz9feXfwy5nt93TFLMoINa6gG6KcZUtYay9uzd39wGS1uzpIjPromQAe9LdT3f3Ge4+QtIISSdIOqvMUx6UtKmCx7Fl7+Hu70p6S9IjNf1LAQAAxMk5nc9R1xZddds/b9OX2yv7/XlmlIyMFcd+ZIxpinGUFWHM3T+o4qVnSzJJ08ocnyFpq6RzyrzuOe5uFTxm7eE+CUkdq/FXAAAAiL1EkNCNR9+oTTs36fZ5t4ddjqRS0xQZGUMEZUUYq4ZekoolzS190N23Kzma1au6L5iarni+mTW1pK6SrpP0XG0UDAAAECcd9+6oi7terL9+8Fe98vErYZdDN0VEWtTC2P6S1rn71+WcWy2pRRr7g7mkn0n6QMmpi/8r6a+SrqpJoQAAAHF1cdeL1aFpB014fYI279gcai250U0xT3KmKcZR1MJYQ0nlBTFJ2l7qmipz9y3uPsDdm7l7Y3dv5+6j3X1redeb2VAzm29m8z///PPq3AoAACAW8hP5mnD0BH2+7XNNW1h29UhmsWYMURa1MLZVUr09nKtf6po64+7T3b2nu/fcZ5996vJWAAAAWavrPl11Tudz9Ph7j2v+2vmh1VEyTTHere1ZMxZXUQtja5ScilheIGut5BTGHRmuCQAAICdd1u0ytWncRje8foO+LtrT5KW6lRsNPFgzFldRC2PzlKy5d+mDZlZfUjdJ4f1aBgAAIMc0zG+o8f3Ga9XGVZr+zvRQaigJY9m0EXWtM0bG4ipqYexxJRtulG2ucbGSa8V+n/GKAAAAcli//ftpULtBemjxQ1rx5YqM3/+baYoZv3XmsGYstrIijJnZEDMbZ2bjJO0jqbDkezMbUnKduy+SdK+k083sSTO7yMymSJoqabakxzJU7yAzm75hw4ZM3A4AACCrjeo1So3zG+vG129UsWc2FeVGN0VGxuIqK8KYpAsl3ZR6tJTUtNT3F5a59ipJoyR1UTKYnSXpbkmnuGfmp9/dn3H3oYWFhZm4HQAAQFZrVr+ZRvUcpbc+f0t/Xv7njN6bboqIsqwIY+7e391tD4/+Za4tcvcp7t7J3eu5e2t3H+Hu4W5yAQAAkMNObX+q+rTqo2kLpunzrZnb/ic3uinSwCOusiKMAQAAINrMTNf1u05fF32tiXMnZuy+dFNElBHGAAAAUCvaNmmrXxz5C/3fqv/T7I9mZ+SeJSNj8Z6mmGCaYkwRxgAAAFBrzu9yvjo07aCb/3mztu7cWuf3271mLMZZjJGx+CKMpYFuigAAAOXLT+Tr+n7Xa+2Wtbr7zbvr/H4B3RQRYYSxNNBNEQAAYM+6teymMzudqceWPaYl65bU6b0SOdNNkTAWR4QxAAAA1Lorj7pSzes31w2v36BddRgkcqabYob3b0NmEMYAAABQ6/Yq2EvX9rlWy75Ypt+/+/s6u09Q0sCDaYqIIMIYAAAA6sSJB56o/m3669637tXqzavr5B4l0xRjPzJGGIslwhgAAADqhJlpbN+xMplueuMmeR2MXu2ephjrkTHCWFwRxtJAN0UAAICqadWolS7vfrnmrJ6j51Y9V+uvnxoYy4EGHuwzFkeEsTTQTREAAKDqzj70bHVu1lmT5k7S5h2ba/W1EzmxzxhrxuKKMAYAAIA6lQgSGt9vvNZtW6d737q3ll87B9aMGWEsrvLCLgAAAADxd3iLwzW402A9tuwxndr+VHVu3rlWXtfMZBb3bop5K4AJtwAAF59JREFUUtEO6Xc/DbuSutH1DOnIM8OuIhSEMQAAAGTEFUddoedXPa+b37hZj578qAKrnUlaCbN4j4y16y/9e7a0dX3YldS+dculXdsJYwAAAEBdalLQRKN6jtKYV8foz8v/rMGdBtfK6waBxbub4sHHShe9EHYVdeORU3J6Q2vWjAEAACBjTml3inq36q1pC6dp/bbaGelJmMW7m2KcWZDT6+EIY2mgtT0AAEB6SvYe27Zrm6YumForr5kITEW5O7gSbTnetp8wlgZa2wMAAKSvXWE7nd/lfD39/tOat3ZejV8v9g084izHN7QmjAEAACDjLj7iYrVu3Fo3v3GzdhbtrNFrJQIjjEVVkJCckTEAAAAgYxrkNdCYPmP0wYYPNHPpzBq9Vuy7KcZZkGCaIgAAAJBpx7U5Tj848Ad64O0HtHrz6rRfJ2BkLLpyfENrwhgAAABCc03va2RmmvjPiWm/BiNjEUYDDwAAACAcrRq10qVHXqpZH8/SSx++lNZr0E0xwmjgAQAAAITn54f9XB2adtDEuRO1defWaj8/COimGFlBgk2fAQAAgLDkB/ka32+8Ptnyie5/5/5qPz8w1oxFVsCaMVQTmz4DAADUru4tu+vHHX6sR5c8qg82fFCt57JmLMKMboqoJjZ9BgAAqH1XHXWVGuQ30G3/vE1ejZEuuilGWI6vGcsLuwAAAABAkpo3aK5h3Ybptrm36flVz+ukg06q0vMSZvpq604tW7uxjisMR+N6eWqzd8Owy6gbOb7PGGEMAAAAWWNwp8F68l9P6o75d+h7rb+nhvmVh5CG9RJ67f31GjjtHxmoMBwvjjxe7fdpHHYZtS/Ik5wwBgAAAIQuL8jT2L5jde6z52rGohm68qgrK33OtDO7aemaeI6KLVmzUfe8vEJfbd0Zdil1I8cbeBDGAAAAkFW6t+yuU9ufqkeWPKLT2p+mgwoPqvD6ts0bqW3zRpkpLsMa1cuTXo5x634aeAAAAADZZXiP4aqfqK+JcydWq5lH3CQCkyQVx7VbZI438CCMAQAAIOu0aNBCl3W7THPWzNFLH74UdjmhsWQWU1FcA2mQkORScW5u/EwYAwAAQFY669Cz1KFpB90+73Zt27Ut7HJCkUilsbhmsWQYU8428SCMAQAAICvlBXka22esPtnyiX6z6DdhlxOKIDVNMbabWgepFhY5OlWRMJYGMxtkZtM3bNgQdikAAACx1rNVT5188Ml6ePHD+nDjh2GXk3FBamQs1g08pJxt4kEYS4O7P+PuQwsLC8MuBQAAIPZG9hyp/CBft8+7PexSMi41MBbfMMbIGAAAAJC9WjZsqUu7XapXPn5Fsz6aFXY5GfVNN8WQC6kru9eMxfUvWDHCGAAAALLezzr/TO0L22vi3Inavmt72OVkTMk0xXh3UxQjYwAAAEC2yg/yNabPGK3evFoPL3447HIyJtjdTTGuYYxpigAAAEDW671fbw08aKAeXPygVm9eHXY5GZHY3U0x5ELqCg08AAAAgGgY2XOkTKYp86eEXUpG0MAj3ghjAAAAiIxWjVrpwq4X6vlVz2vuJ3PDLqfOlewzFt8wRgMPAAAAIDLO63KeWjdurYnzJmpXzEdUYr/PGA08AAAAgOion1dfI3uO1L++/Jf+vPzPYZdTpxKWK2vGCGMAAABAJJx44Inq3aq37nnrHm34ekPY5dQZK1kzVhzXkbGSNWM08AAAAAAiwcx0de+rtWnHJt3z5j1hl1NnErFfM0YDDwAAACByDtn7EA0+ZLD+tPxPWv7l8rDLqRM5s+kzDTwAAACAaBnWfZj2KthLt8+9PZYbIwepT+txnaVIAw9Um5kNMrPpGzbEd34yAABAFBTWK9SwbsM0d+1cvfDhC2GXU+t2d1OMaxqjgQeqy92fcfehhYWFYZcCAACQ8356yE/Vce+Omjxvsrbv2h52ObUqEfvW9jTwAAAAACIrL8jTNb2u0ZotazRzycywy6lVJZs+F8V1ZIwGHgAAAEC09d6vtwa0HaAHFz+otVvWhl1OrUllMcV1YIwGHgAAAEAMjOw5UsVerKkLpoZdSq0paW0f+26KjIwBAAAA0dW6cWud1+U8PfvvZ7Xw04Vhl1MrgrivGdvdwIM1YwAAAECkXXD4Bdq34b6aOHeiimLwAT/23RRZMwYAAADEQ8P8hhrZc6Te/eJd/WXFX8Iup8ZK1ozFNYsRxgAAAIAYGXjQQHVv2V13v3m3tuzcEnY5NZKIfTdFGngAAAAAsWFm+mWvX2r99vX6zaLfhF1OjVhqmqLHdc0YDTwAAACAeDm8xeE6pd0p+u2S32r15tVhl1MjicDi202RBh4AAABA/Fx51JUKLNCdC+4Mu5QaCYw1Y3FFGAMAAEAstWrUSucffr6eW/mc3vzszbDLSVtgFuNuikxTBAAAAGLpvC7nqWWDlpo0d5KKI9okIjCL7z5jJSNjEX1vaoowBgAAgNhqmN9QV/a4UovXL9ZfP/hr2OWkJRGYiuKaVRgZAwAAAOLrlHanqEvzLpq2cJq27twadjnVllwzFtORMRp4AAAAAPEVWKDRvUbrs62faeaSmWGXU21BkAPTFBkZAwAAAOKpx749NKDtAD285GF9uuXTsMuploRZ/Dd9ztGRsbywCwAAAAAyYUSPEZr10Szd9eZduuV7t4RdTpWZWXxb25dMU9y5Rdq+Idxa6kKioMLThLE0mNkgSYM6dOgQdikAAACoojZ7tdGQw4boocUP6WeH/kxdWnQJu6QqSQSKcWv7IBlYXr0z+YibIL/C04SxNLj7M5Ke6dmz58Vh1wIAAICqu7jrxfrLir9o0rxJemTgIzKzsEuqVKxb20vSmb+T1q8Iu4ra9+VKae70Ci8hjAEAACBnNC5orGHdh2nC6xP0/KrnddJBJ4VdUqUCMxXFOYwd8kNJPwy7itr30dxKwxgNPAAAAJBTTu9wujru3VFTF0zV10Vfh11OpYJAinMWi62S9XAVIIwBAAAgpySChEb3HK3Vm1frd0t/F3Y5lYp1N8U4CwhjAAAAwHf027+fjm9zvH6z6Df6YvsXYZdTodivGYsrwhgAAABQvhE9Rmjbrm26/+37wy6lQrHe9DnOmKYIAAAAlK9d03b6Scef6In3ntDKDSvDLmePApOKi8OuAtUWVN4rkTAGAACAnHVJt0tUkCjQtIXTwi5lj2LfTTGumKYIAAAA7FmLBi10weEX6MUPX9TCTxeGXU65EoHJCWPRQxgDAAAAKnZul3PVskFLTZk/JStDT0A3xWhizRgAAABQsQZ5DTSs+zC9s+4dPbfqubDL+Y5kA4+wq0C1MTIGAAAAVO7U9qeq494dNW3BNO0o2hF2Od8SmOimGEU08AAAAAAqlwgSGtVjlFZvXq0/Lvtj2OV8S4J9xqKJaYoAAABA1Rzd+mgdvf/ReuCdB7Th6w1hl7Mba8YiKqg8ahHGAAAAgJQRPUZo045NmvHOjLBL2S0I2GcskpimCAAAAFRdp2addFqH0/TYssf08aaPwy5HUnJkjGmKEcQ0RQAAAKB6hnUbpoQldNfCu8IuRVJynzE2fY4gRsYAAACA6tm30b46t8u5enbls1r0+aKwy5EZre0jidb2AAAAQPVdcPgFala/mSbPnxz6RtAJk4pJY9FjNPAAAAAAqq1RfiNd1u0yLfxsoV7+6OVQa2HNWESZVbpujDAGAAAAlOP0jqfr4MKDdeeCO7WzeGdodQQBre0jq5KpioQxAAAAoBx5QZ5G9BihlRtX6n+W/09odSTMxMBYRFXSxIMwBgAAAOzB8W2OV69WvXTf2/dp847NodQQBKKbYlQxTbFqzKyBma0ws6/CrgUAAADZwcw0oscIfbH9C81cOjOUGlgzFmFBxXGLMPaNCZKyY2c/AAAAZI3DWxyuk9qepJlLZmrdtnUZv39gRjfFqGKaYuXM7ChJJ0u6LexaAAAAkH2uOOoK7SjaoQfefiDj904E7DMWWdk+TdHMrjWzJ8zsAzNzM1tZwbWBmQ03s2Vmtt3MPjKzKWbWqAb3z5M0Q9Jlkr5O93UAAAAQX22btNVPD/mp/rz8z/pw44cZvbeZ6KYYVREYGbtV0vclvS/py0quvVPSVElLJV0u6QlJV0h6xuzbu6qZWT0za1zBoySmjpT0jrvPqsW/EwAAAGLmv4/8b+Un8nX3m3dn9L7JboqEsUiKQGv79u7e3N0HSFqzp4vMrIuSAexJdz/d3We4+whJIySdIOmsMk95UNKmCh7Hmll7JUfERtXy3wkAAAAx06JBCw05bIj+vvLvWrJ+ScbuG5jRTTGqLMsbeLj7B1W89GxJJmlameMzJG2VdE6Z1z3H3a2CxyxJx0raR9ISM1sr6UlJTcxsrZkdXZO/FwAAAOLn/C7nq2m9ppq2oOxH0roTsGYsuiIwTbGqekkqljS39EF33y7prdT56npc0sGSuqUeFyk5atZN0vyaFAsAAID4aVzQWL844hd645M39Nqa1zJyz8BEN8WoisA0xaraX9I6dy+vycZqSS3MrKA6L+ju29x9bclD0hfJw77W3XfUQs0AAACImcGdBqt149aatmCair24zu+XCJimGFmVjIxVfDa7NNSeux1uL3VN2iEqNXWxaUXXmNlQSUNT3242s/fSvV8aWkjK/OYWqC28f9HFexdtvH/RxXsXbTnx/j2hJzJ2L7s+Y7eScuT9y5C2ezoRpTC2VVLLPZyrX+qaOuXu0yVNr+v7lMfM5rt7zzDujZrj/Ysu3rto4/2LLt67aOP9izbev8yI0jTFNUpORaxXzrnWSk5hZGohAAAAgEiIUhibp2S9vUsfNLP6ouEGAAAAgIiJUhh7XJJLuqrM8YuVXCv2+4xXlHmhTI9EreH9iy7eu2jj/Ysu3rto4/2LNt6/DLCwd/M2syH6ZlHb5ZIKJE1Jfb/K3R8tde3dkoZJekrS3yR1lnSFpDmSvu+egXY2AAAAAFALsiGMzZJ0/B5Oz3b3/qWuTSg5MjZU0kFKdnh5XNJ4d99cp4UCAAAAQC0KPYwBAAAAQC6K0pqxnGNmgZkNN7NlZrbdzD4ysylm1ijs2lAxMzvEzCaY2Rtm9rmZbTKzt8xsLO9f9JhZQzP7t5m5md0Tdj2onJk1M7PJZrYi9e/n52b2spkdG3ZtqJiZNTazMWa2KPVv5zoze83MzjMzC7s+JJnZtWb2hJl9kPq3cWUl1/cxsxdS7+lGM/u7mXXLULkoparvnZnVN7OLzex/zWylmW1LPecPZtY5w2XHVpT2GctFdyq5Ju4pJdfRlayR625mJ7JGLqtdIOkySU8r2Vxmp6QTJN0sabCZ9XX3bSHWh+qZoOTml4gAM2sraZakxpIelLRcUqGkI5TcCgVZyswCSc9KOlrSTEl3K9mk62xJDyv5/+DVoRWI0m6V9IWkhZKaVnShmfVV8mdytaTxqcPDJP3DzI5290V1WCe+q6rv3UFKNvF4Vcl/S9dIaifpEkmnm9lAd3+5bkuNP6YpZikz6yJpkaSn3P0npY5fLukuST9398fCqg8VM7Oekv7l7hvKHL9Z0lhJl7s7IywRYGZHSZor6ZdK/lLkXncfFm5VqIiZ/UPJDxG93f2TkMtBNZhZP0mvSZrm7sNLHS+QtExSM3ev8IM/MsPM2rn7B6k/L5bU2N0P2sO1cyUdKqmzu69OHWst6V1Jb7j7SZmpGlLV3zszay7pAHd/q8zxwyS9KWkRm0LXHNMUs9fZkkzStDLHZ0jaKumcjFeEKnP3+WWDWMrjqa+HZ7IepCfVNGiGpL9LejLkclAFZnacpO9JmuTun5hZvpk1DLsuVFmT1Nc1pQ+6+w4lm3ZtyXhFKFfJh/nKmFkHSb0kPVESxFLPXy3pCUknmlmruqkS5anqe+fu68sGsdTxpZIWi88ytYIwlr16SSpW8jfyu7n7dklvpc4jetqkvn4aahWoquFK/jaXkbDoODn19UMze0bSNklbzGy5mfFLrOw3V9JXkn5pZmeY2YFm1snMbpPUQ9INoVaHdJR8Xnm9nHNvKPmL5x6ZKwc1lZpOvJ/4LFMrCGPZa39J69z963LOrZbUIjVtAxGRGmUZL2mXJKaYZjkzO1jSjZImuPvKkMtB1XVKfZ0hqZmk/5J0oaQdkh41s/PDKgyVc/cvJZ2q5HqWP0lapeT0xMsk/cTdZ4RYHtKzf+rr6nLOlRxjLWe0XKJkGJsZdiFxQAOP7NVQUnlBTJK2l7pmR2bKQS2YJqmvpDHu/l7YxaBS90n6t6SpYReCatkr9XWTpBNS09tkZk9J+kDSrWY2kwZIWW2zklOgnlZy/VgzJcPYY2Z2mrs/H2ZxqLaSacLlfabZXuYaZDkzO1rJ9dPvKNkIBDXEyFj22iqp3h7O1S91DSLAzG5ScqrbdHe/Lex6ULHUdLaTJP23u+8Mux5US0mX0j+UBDFp94jL05Ja6ZvRM2QZM+uqZAB73t1Hu/tT7v6gkusA10qakZplgOgo+axS3mcaPs9EiJn1kPRXJdd0npxaOoMaIoxlrzVKTkUs7x+v1kpOYWRULALM7AZJ45Rsy/zf4VaDyqR+5qZK+puktWbWIbUAvW3qksLUMTq6ZaePU1/XlnOupLPi3hmqBdU3XMkP6E+UPujuW5X8ENhWyU6ZiI6SZizlTUUsOVbeFEZkkVRn4eclbVBy1gHvWS0hjGWveUq+P71LHzSz+pK6SZofRlGoHjO7XtL1kn4r6SJnL4koaCBpH0n/IelfpR6zUufPSX1/URjFoVIlTY/alHOu5NhnGaoF1Vfy4by80a+8Ml8RDfNSX/uVc66vJJe0IHPloLrMrLuSQaxk+veqkEuKFcJY9npcyX+gripz/GIl51b/PuMVoVrMbLySnb8elXQ+a1QiY4ukM8p5XJo6//fU90+HUh0q8xclPzCcY2aNSw6a2X6Sfqzk/n8rwioOlVqa+npe6YOpkejTJH0p6f0M14QaSP28zZd0hpmVNPNQ6s9nSHrJ3csbyUYWSAWxF5T8v/EEd/93yCXFDps+ZzEzu1vJdUZPKTllqrOkKyTNkfR9PtxnLzO7TNI9kj6UdJ2S2xSU9imL0KPFzA5SsqEHmz5nOTMbKukBSUskPSSpQN90/zrF3f8vxPJQATNrK2mhklNJf6/k/3fNlPxF5EGSLnP3X4dWIHYzsyH6Zvr25Ur+nE1Jfb/K3R8tde3Rkl5Wchrx3aWes6+kY9z97YwUDUlVf+9SP48LlPwZvFHl/yLkKXdn/78aIIxlsdQi5askDVXyP6F1So6YjXf3zSGWhkqY2SNKttTek9nu3j8z1aA2EMaixcxOl/RLSV2V/GXI65JudPc5oRaGSplZeyW3AfmBkh/Wtym5v+Y0d2fz9SxhZrMkHb+H09/5P87M+km6WVIfJWf+vCbpWndfWIdlohxVfe/MrL+SIboiB7P9S80QxgAAAAAgBKwZAwAAAIAQEMYAAAAAIASEMQAAAAAIAWEMAAAAAEJAGAMAAACAEBDGAAAAACAEhDEAAAAACAFhDAAAAABCQBgDAAAAgBAQxgAAAAAgBIQxAAAAAAgBYQwAgDSZWZ6ZzTGzzWZ2aJlzQ83MzWxCWPUBALKbuXvYNQAAEFlm1lbSW5JWSerr7tvNrIukeZIWSOrv7kVh1ggAyE6MjAEAUAPuvkrShZKOlDTZzBpI+qOk7ZJ+ThADAOwJI2MAANQCM/u1pEskvSbpaEk/cfcnw60KAJDNCGMAANQCM6svabGk9pJmuPvQkEsCAGQ5pikCAFA7jpB0YOrPh5tZXpjFAACyH2EMAIAaMrMmSq4TWydprKR+km4MtSgAQNbjt3YAANTcA5LaShrg7i+ZWTdJ15jZC+7+csi1AQCyFGvGAACoATO7UNJvJN3q7mNTx5oq2e4+X9IR7r4+xBIBAFmKMAYAQJpSGz0vUDJ4He/uu0qd6yfpFUnPuvupIZUIAMhihDEAAAAACAENPAAAAAAgBIQxAAAAAAgBYQwAAAAAQkAYAwAAAIAQEMYAAAAAIASEMQAAAAAIAWEMAAAAAEJAGAMAAACAEBDGAAAAACAEhDEAAAAACMH/BxOyCQ4XZH5UAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig0, ax0 = plt.subplots(figsize=(14, 8))\n", "ax0.plot(xaxis, yaxis_binom, '-', label=f'Binomial with n={n:2d} and p={p:.3f}')\n", "ax0.plot(xaxis, yaxis_poiss, '-', label=f'Poisson with lambda={Lambda:.2f}')\n", "ax0.plot(xaxis, yaxis_gauss, '-', label=f'Gaussian with mu={mu:.2f} and sigma={sigma:.2f}')\n", "ax0.set(xlim=(xmin, xmax),\n", " title='Probability for Binomial and Gaussian', \n", " xlabel='x', \n", " ylabel='Probability')\n", "ax0.set_yscale('log')\n", "ax0.set_ylim(1e-4, 1.0)\n", "ax0.legend(loc='upper right');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Looping over processes:\n", "In the following we simulate a Binomial/Poisson process with given parameters, i.e. number of trials and probability of success. For the Poisson, these can not be specified, but the resulting expected number is naturally lambda = n * p.\n", "\n", "After having simulated the process, we fit the result with the three distributions in question, and test to what extend they match." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " With N_trials = 20 and p_success = 0.2000, the average number of successes is lambda = 4.00\n" ] } ], "source": [ "# Simulation parameters:\n", "N_experiments = 1000 # Number of simulations/experiments to perform\n", "\n", "N_trials = n # Number of trials in each experiment (taken from above!)\n", "p_success = p # Chance of succes in each trial (taken from above!)\n", "Lambda = N_trials * p_success # This is the mean and the one parameter by which the Poisson is defined!\n", "\n", "print(f\" With N_trials = {N_trials:d} and p_success = {p_success:.4f}, the average number of successes is lambda = {Lambda:.2f}\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n_success: 6\n", "n_success: 6\n", "n_success: 6\n", "n_success: 6\n", "n_success: 4\n", "n_success: 4\n", "n_success: 3\n", "n_success: 3\n", "n_success: 6\n", "n_success: 2\n" ] } ], "source": [ "all_n_success = np.zeros(N_experiments)\n", "\n", "# Run the experiments, and fill the histogram from above:\n", "for iexp in range(N_experiments): \n", " \n", " # Simulating process defined:\n", " n_success = 0\n", " for i in range(N_trials): \n", " x = r.uniform()\n", " if (x < p_success): \n", " n_success += 1\n", "\n", " # Record result:\n", " if (verbose and iexp < N_verbose): \n", " print(f\"n_success: {n_success:4d}\")\n", " \n", " # Save Result\n", " all_n_success[iexp] = n_success" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot result:\n", "\n", "Define a histogram with the \"data\" (note and think about the binning!). Also, ask yourself what uncertainty to assign to each bin." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "counts, bin_edges = np.histogram(all_n_success, bins=N_trials+1, range=(-0.5, N_trials+0.5))\n", "bin_centers = (bin_edges[1:] + bin_edges[:-1])/2\n", "s_counts = np.sqrt(counts) # NOTE: We (naturally) assume that the bin count is Poisson distributed." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# We remove any bins, which don't have any counts in them:\n", "x = bin_centers[counts>0]\n", "y = counts[counts>0]\n", "sy = s_counts[counts>0]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(14, 8))\n", "ax.errorbar(x, y, yerr=sy, xerr=0.5, label='Distribution of nSuccesses', fmt='.k', ecolor='k', elinewidth=1, capsize=1, capthick=1)\n", "ax.set(xlim=(xmin, xmax), ylim=(0, 1.2*np.max(y)), xlabel='Number of successes', ylabel='Frequency');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting with a Binomial:\n", "\n", "First define the (fitting) function:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def func_binomial(x, N, n, p):\n", " return N * binom.pmf(x, n, p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then fit it with a $\\chi^2$-fit:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "chi2_bin = Chi2Regression(func_binomial, x, y, sy)\n", "minuit_bin = Minuit(chi2_bin, pedantic=False, N=N_experiments, n=N_trials, p=p_success) # \n", "minuit_bin.migrad(); # Perform the actual fit\n", "Ndof_bin = len(x) - 3 # 3 parameters in fit\n", "Prob_bin = stats.chi2.sf(minuit_bin.fval, Ndof_bin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And plot it on the figure:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xaxis = np.linspace(-0.5, N_trials+0.5, 1000) # This way we include all possibilties!\n", "yaxis = func_binomial(np.floor(xaxis+0.5), *minuit_bin.args)\n", "ax.plot(xaxis, yaxis, '-', label=f'Binomial fit: p(Chi2={minuit_bin.fval:.1f},Ndof={Ndof_bin:d}) = {Prob_bin:.3f}')\n", "ax.legend()\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting with a Poisson:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def func_poisson(x, N, mu) :\n", " return N * poisson.pmf(x, mu)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "chi2_poisson = Chi2Regression(func_poisson, x, y, sy)\n", "minuit_poisson = Minuit(chi2_poisson, pedantic=False, N=N_experiments, mu=Lambda) # \n", "minuit_poisson.migrad(); # Perform the actual fit\n", "Ndof_poi = len(x) - 2 # 2 parameters in fit\n", "Prob_poi = stats.chi2.sf(minuit_poisson.fval, Ndof_poi)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "yaxis = func_poisson(np.floor(xaxis+0.5), *minuit_poisson.args)\n", "ax.plot(xaxis, yaxis, '-', label=f'Poisson fit: p(Chi2={minuit_poisson.fval:.1f},Ndof={Ndof_poi:d}) = {Prob_poi:.3f}')\n", "ax.legend()\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting with a Gaussian:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def func_gaussian(x, N, mu, sigma) :\n", " return N * norm.pdf(x, mu, sigma)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "chi2_gaussian = Chi2Regression(func_gaussian, x, y, sy)\n", "minuit_gaussian = Minuit(chi2_gaussian, pedantic=False, N=N_experiments, mu=Lambda, sigma=np.sqrt(Lambda)) # \n", "minuit_gaussian.migrad(); # Perform the actual fit\n", "Ndof_gau = len(x) - 3 # 3 parameters in fit\n", "Prob_gau = stats.chi2.sf(minuit_gaussian.fval, Ndof_gau)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "yaxis = func_gaussian(xaxis, *minuit_gaussian.args)\n", "ax.plot(xaxis, yaxis, '-', label=f'Gaussian fit: p(Chi2={minuit_gaussian.fval:.1f},Ndof={Ndof_gau:d}) = {Prob_gau:.3f}')\n", "\n", "ax.legend()\n", "fig.tight_layout()\n", "\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And save the figure:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "if save_plots: \n", " fig.savefig(\"BinomialPoissonGaussian.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculation of Binomial $\\chi^2$-value:\n", "\n", "In this part of the exercise, you are asked to calculate the ChiSquare value yourself, in order to ensure that you understand exactly what is going on!\n", "\n", "Above, we have (using Minuit) *fitted* the distribution, but as we know the initial values, I would like you to calculate the $\\chi^2$-value between the data and the binomial they were generated from, i.e. with NO free parameters.\n", "\n", "I suggest you use Pearson's $\\chi^2$, and require `N_obs` and/or `N_exp` > e.g. 0.1. Remember that your choice should ensure, that there is no division by zero (which is a cardinal sin in programming)!" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "N_bins = len(x) # Just to know how many bins to loop over\n", "chi2_bino = 0.0 # This you'll add to\n", "N_dof = 0 " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "for N_obs, x_i in zip(y, x):\n", " N_exp = func_binomial(x_i, *minuit_bin.args)\n", " if (N_obs > 0) :\n", " chi2_bino += 0.0 # Write the expression yourself!\n", "\n", "# Also calculate Ndof and Prob:\n", "Ndof_bino = 1 # Think about the number of degrees of freedom when there are no free parameters!\n", "Prob_bino = stats.chi2.sf(chi2_bino, Ndof_bino)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Just a test printout, change to match your own results! \n", "\n", "Binomial: chi2 = 9999.00 N_dof = 9999 Prob = 9999.0000\n" ] } ], "source": [ "print(f\"Just a test printout, change to match your own results! \\n\")\n", "print(f\"Binomial: chi2 = {9999:.2f} N_dof = {9999:d} Prob = {9999:6.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "\n", "# Questions:\n", "\n", "Important: Make sure you understand what process yields a Binomial, a Poisson and a Gaussian distribution. Without this knowledge, this exercise and a large fraction of the course will be lost on you!\n", "\n", "1. Plot a Binomial ($N=20$, $p=0.2$), Poisson ($\\lambda = 4$), and Gaussian ($\\mu=4$, $\\sigma=\\sqrt{4}$), i.e. same means and widths. Which distribution has the longest tail towards high values? And which one has the longest tail the other way? Does this pattern depend on the parameters (given same means and widths)? Play around with the settings (remember also to change the scale (use log) of the plot accordingly), and gain your own experience. And most importantly perhaps, in what limits do they start looking like each other?\n", "\n", "Example solution 1:\n", "The Poisson has the longest tail towards high values, while the Gaussian has the longest tail towards low values, and it is the only distribution with a tail going below 0. This is quite general, but as N becomes large and p small, the Binomial converges towards the Poisson. The two converges towards the Gaussian, when $\\lambda = Np$ becomes large.\n", "\n", "---\n", "\n", "2. Producing binomially distributed numbers (using `N_experiments=1000`, `N_trials=10` and `p_success=0.2`), do $\\chi^2$ fits of the resulting distribution with a Binomial, a Poisson, and a Gaussian distribution. Do you get acceptable fit probabilities with all of these? If not, investigate in what cases you do.\n", "\n", "Example solution 2:\n", "The fits try to adjust to the distribution given, but like above (cell 27), the Gaussian only barely manages, while the Poisson (which also only has one single parameter) does not manage. With increasing statistics (i.e. 10000 \"experiments\" and thus entries in the histogram) the Gaussian will also fail to match the data with reasonable p-value. However, increasing $Np$ improves the Gaussian match.\n", "\n", "---\n", "\n", "3. Calculate \"by hand\" (i.e. using a loop) the $\\chi^2$ between the data and the original Binomial distribution (which the data is generated from). Since you are not fitting anything, what is the number of degrees of freedom? Does it give a reasonable $\\chi^2$-probability?\n", "\n", "Example solution 3:\n", "This is mostly an exercise in writing the code behind the ChiSquare calculation, ensuring you know how it is calculated. It also forces you to think about what uncertainty/number you divide the \"observed - expected\" difference with, and how to ensure that this is not 0.\n", "In this case, the number of degrees of freedom is the number of bins fitted, as there are zero parameters in the fit! And it should of course give a reasonable $\\chi^2$-probability (p-value) by construction, when matching to a Binomial.\n", "\n", "---\n", "\n", "4. In all of the above $\\chi^2$ fits, we have _assumed_ that the uncertainty on the count in each bin is Gaussianly distributed! Ask yourself to what extend this requirement is fulfilled? Does changing the parameters (`N_experiments`, `N_trials` and `p_success`) \"help\" fulfilling this requirement, and if so, which and how?\n", "\n", "Example solution 4: The Gaussianly assumed distribution of the bin count uncertainty depends on the number of entries in the bin, as the Poisson converges towards the Gaussian with increasing entries. So increasing `N_experiments` helps, while increasing `N_trials` and `p_success` (essentially $\\lambda$) makes the distribution wider, and thus yields fewer events in each bin (assuming equidistant binnning), which in turn means that the Gaussian assumpion worsens.\n", "\n", "---\n", "\n", "\n", "### Advanced questions:\n", "\n", "5. Using `N_experiments=1000`, `N_trials=1000` and `p_success=1/60`, is the skewness consistent with zero (as the Gaussian should have)?\n", "\n", "Example solution 5:\n", "You can either find a formula for the uncertainty on the skew, or calculate the skew many times for the above situation, and see from the standard deviation of the distribution, what the uncertainty approximately is." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example Solution code:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0001, 1.0)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xmin = 0\n", "xmax = 14\n", "x = np.arange(xmin, xmax+1, 1,)\n", "n1 = 2000\n", "p1 = 0.001\n", "lambda1 = n1 * p1\n", "sigma1 = np.sqrt(n1* p1*(1-p1)) # For a Binomial process, the variance is n*p*(1-p)\n", "sigma1 = np.sqrt(n1*p1) # Alternatively, one can use the Poisson width \n", "\n", "binom_1 = func_binomial_pmf(x, n1, p1)\n", "pois_1 = func_poisson_pmf(x, lambda1)\n", "gaus_1 = func_gaussian_pdf(x, lambda1, sigma1) \n", "bi_label = \"binominal p, n = \"+f'{p1, n1}'\n", "pois_label = r\"poisson $\\lambda$ = \"+f'{lambda1}'\n", "gaus_label = r\"gauss $\\mu, \\; \\sigma$ = \"+f'{lambda1, sigma1}'\n", "plt.rcParams[\"figure.figsize\"] = (14, 8)\n", "plt.step(x, binom_1, where='mid', label=bi_label)\n", "plt.step(x, pois_1, where='mid', label=pois_label)\n", "plt.plot(x, gaus_1, label=gaus_label)\n", "plt.legend()\n", "plt.yscale('log')\n", "plt.xlim(xmin, xmax)\n", "ax0.set_ylim(1e-4, 1.0)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(750.0, 1250.0)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n1 = 200000\n", "p1 = 0.005\n", "\n", "lambda1 = n1 * p1\n", "sigma1 = np.sqrt(n1* p1*(1-p1)) # For a Binomial process, the variance is n*p*(1-p)\n", "sigma1 = np.sqrt(n1*p1) # Alternatively, one can use the Poisson width \n", "xmin = lambda1*0.75\n", "xmax = lambda1*1.25\n", "x = np.arange(xmin, xmax+1, 1,)\n", "\n", "\n", "binom_1 = func_binomial_pmf(x, n1, p1)\n", "pois_1 = func_poisson_pmf(x, lambda1)\n", "gaus_1 = func_gaussian_pdf(x, lambda1, sigma1) \n", "bi_label = \"binominal p, n = \"+f'{p1, n1}'\n", "pois_label = r\"poisson $\\lambda$ = \"+f'{lambda1}'\n", "gaus_label = r\"gauss $\\mu, \\; \\sigma$ = \"+f'{lambda1, round(sigma1,3)}'\n", "plt.rcParams[\"figure.figsize\"] = (14, 8)\n", "plt.step(x, binom_1, where='mid', label=bi_label)\n", "plt.step(x, pois_1, where='mid', label=pois_label)\n", "plt.plot(x, gaus_1, label=gaus_label)\n", "plt.legend()\n", "#plt.yscale('log')\n", "plt.xlim(xmin, xmax)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "N_experiments = 1000 # Number of simulations/experiments to perform\n", "N_trials = 20 # Number of trials in each experiment (taken from above!)\n", "p_success = 0.2 # Chance of succes in each trial (taken from above!)\n", "Lambda = N_trials * p_success \n", "sigma1 = np.sqrt(N_trials* p1*(1-p1)) # For a Binomial process, the variance is n*p*(1-p)\n", "sigma1 = np.sqrt(n1*p1) # Alternatively, one can use the Poisson width \n", "\n", "\n", "all_n_success = [sum(np.random.uniform(0, 1, N_trials) < p_success) for i in range(N_experiments)]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.optimize import curve_fit\n", "count, bins, ignored = plt.hist(all_n_success, max(all_n_success), alpha=0.2)\n", "mid_bins = 0.5*(bins[1:]+bins[:-1])\n", "\n", "Ndof_binom1 = len(count) - 3\n", "Ndof_pois1 = len(count) - 2\n", "Ndof_gaus1 = len(count) - 3\n", "\n", "sigma_counts = np.sqrt(count) #sigma assumed from Poisson \n", "\n", "binom_1, binom_1_err = curve_fit(func_binomial, mid_bins-0.5, count, p0=[N_experiments, N_trials,p_success])\n", "y_binom = func_binomial(mid_bins-0.5, *binom_1)\n", "chi_binom = np.sum((count - y_binom)**2 / y_binom)\n", "chi_binom_p = stats.chi2.sf(chi_binom, Ndof_binom1)\n", "chi_binom_l = r\"$\\chi^2$, p-value = \" + f'{round(chi_binom,2), round(chi_binom_p,3)}'\n", "\n", "pois_1, pois_1_err = curve_fit(func_poisson, mid_bins-0.5, count, p0=[N_experiments, Lambda])\n", "y_pois = func_poisson(mid_bins-0.5, *pois_1)\n", "chi_pois = np.sum((count - y_pois)**2 / y_pois)\n", "chi_pois_p = stats.chi2.sf(chi_pois, Ndof_pois1)\n", "chi_pois_l = r\"$\\chi^2$, p-value = \" + f'{round(chi_pois,2), round(chi_pois_p,3)}'\n", "\n", "gaus_1, gaus_1_err = curve_fit(func_gaussian, mid_bins-0.5, count, p0=[N_experiments, Lambda, sigma1])\n", "y_gaus = func_gaussian(mid_bins-0.5, *gaus_1)\n", "chi_gaus = np.sum((count - y_gaus)**2 / y_gaus)\n", "chi_gaus_p = stats.chi2.sf(chi_gaus, Ndof_gaus1)\n", "chi_gaus_l = r\"$\\chi^2$, p-value = \" + f'{round(chi_gaus,2), round(chi_gaus_p,3)}'\n", "\n", "plt.errorbar(mid_bins, count, yerr=sigma_counts, xerr=0.5, label='Distribution of n-Successes', fmt='.k', ecolor='k', elinewidth=1, capsize=1, capthick=1)\n", "\n", "plt.step(mid_bins, y_binom, where='mid', label=chi_binom_l)\n", "plt.step(mid_bins, y_pois, where='mid', label=chi_pois_l)\n", "plt.step(mid_bins, y_gaus, where='mid', label=chi_gaus_l)\n", "plt.xlim(0, np.max(bins)+2)\n", "plt.legend(loc=1)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.2639110909746492 0.07734381561955864 3.4121809075567717\n" ] } ], "source": [ "N_experiments = 1000 \n", "N_trials = 1000 \n", "p_success = 1./60\n", "\n", "all_n_success = [sum(np.random.uniform(0, 1, N_trials) < p_success) for i in range(N_experiments)]\n", "\n", "skew = stats.skew(all_n_success)\n", "sigma_skew = np.sqrt(6 * N_experiments * (N_experiments-1) / (N_experiments-2) / (N_experiments+1) / (N_experiments+3))\n", "print(skew, sigma_skew, skew/sigma_skew)" ] } ], "metadata": { "executable": "/usr/bin/env python", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" }, "main_language": "python" }, "nbformat": 4, "nbformat_minor": 2 }