{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Moderne Methoden der Datenanalyse SS2024\n", "# Practical Exercise 6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 6.1: Hypothesis Testing\n", "\n", "\"Is this a new discovery or just a statistical fluctuation?\" Statistics offers some methods to give a quantitative answer. But these methods should not be used blindly. In particular, one should know exactly what the obtained numbers mean and what they don't mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6.1.1 (obligatory to solve either 6.1.1 or 6.1.2)\n", "\n", "The following table shows the number of winners in a horse race for different track numbers:\n", "\n", "| track ||| 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 |\n", "|------------|||------||------||------||------||------||------||------||------|\n", "| # winners ||| 29 || 19 || 18 || 25 || 17 || 10 || 15 || 11 |\n", "\n", "Use a $\\chi ^2$ test to check the hypothesis that the track number has *no* influence on the chance to win. Define a significance level, e.g., $\\alpha = 5 \\, \\%$ or $\\alpha = 1 \\, \\%$, *before* you do the test." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# pick your poison\n", "#from ROOT import TMath\n", "from scipy.stats import chi2\n", "\n", "def exercise6_1_1(confidenceLevel):\n", " \n", " # numbers given in the exercise\n", " nTracks = 8\n", " nWin = [29, 19, 18, 25, 17, 10, 15, 11]\n", "\n", " expected = np.average(nWin)\n", "\n", " return" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "144" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum([29, 19, 18, 25, 17, 10, 15, 11])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6.1.2 (obligatory to solve either 6.1.1 or 6.1.2)\n", "\n", "In a counting experiment, 5 events are observed while $\\mu _\\mathrm{B} = 1.8$ background events are expected. Is this a significant ($= 3 \\sigma$) excess? Calculate the probability of observing 5 or more events when the expectation value is 1.8 using Poisson statistics." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# pick your poison\n", "#from ROOT import gRandom, TMath, Math\n", "from scipy.stats import poisson, norm" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.036406661001083473" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "False" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def exercise6_1_2():\n", " \n", " # numbers given in the exercise\n", " nBackground = 1.8\n", " nObserved = 5\n", " \n", " return 1-poisson.cdf(nObserved-1,nBackground)\n", "\n", "display(exercise6_1_2())\n", "exercise6_1_2() < 0.0027" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 6.2: Parameter Estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6.2.1 (voluntary)\n", "\n", "Consider the following set of values approximately following a Gaussian distribution (see also excercise_6_2_1.csv):\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
xi yi σi xi yi σi xi yi σi xi yi σi
0.46 0.19 0.05 0.690.270.060.71 0.28 0.05 1.040.620.01
1.11 0.68 0.05 1.140.700.071.17 0.74 0.08 1.200.810.09
1.31 0.93 0.10 2.032.490.032.14 2.73 0.04 2.523.570.01
3.24 3.90 0.07 3.463.550.033.81 2.87 0.03 4.062.240.01
4.93 0.65 0.10 5.110.390.075.26 0.33 0.05 5.380.260.08
\n", "\n", "\n", "$$ y(x) = a _\\mathrm{1} \\cdot \\exp \\{-\\frac{1}{2} (\\frac{ x-a _\\mathrm{2} }{ a _\\mathrm{3} } )^2 \\} $$\n", "\n", "\n", "with $\\sigma _i$ being the uncertainty on $y _i$.\n", "\n", " - Determine the values of the three parameters $a _\\mathrm{1}$, $a _\\mathrm{2}$, and $a _\\mathrm{3}$ as well as their uncertainties.\n", " \n", " - Afterwards, use the transformation $z = \\ln (y)$ to obtain the linear function $z(x) = b _\\mathrm{1} + b _\\mathrm{2} x + b _\\mathrm{3} x^2$. Determine the new parameters $b _\\mathrm{1}$, $b _\\mathrm{2}$, and $b _\\mathrm{3}$ and uncertainties in two ways and compare the results: first, by fitting this new function; second, by a calculation using the results for $a _\\mathrm{j}$ and the transformation $z = \\ln (y)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### ROOT approach" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from ROOT import TF1, TGraphErrors, TCanvas\n", "import numpy as np\n", "\n", "def exercise6_2_1(verbose = 0):\n", " # read exercise_6_2_1.csv or type are values explicitly\n", " \n", " # fit a Gaussian function\n", " \n", " #print(\" -------- Fit Parameters ---------- \")\n", " #print(\" a1 = {0:.3f} +/- {1:.3f} \".format(a1, err_a1))\n", " #print(\" a2 = {0:.3f} +/- {1:.3f} \".format(a2, err_a2))\n", " #print(\" a3 = {0:.3f} +/- {1:.3f} \".format(a3, err_a3))\n", " #print(\" chi2 = {0:.3f} \".format(chi))\n", " \n", "\n", " # now with log\n", " \n", " # calculation\n", " \n", " \n", " #print(\" -------- Fit Parameters ---------- \")\n", " #print(\" b1 = {0:.3f} +/- {1:.3f} \".format(b1, err_b1))\n", " #print(\" b2 = {0:.3f} +/- {1:.3f} \".format(b2, err_b2))\n", " #print(\" b3 = {0:.3f} +/- {1:.3f} \".format(b3, err_b3))\n", " #print(\" chi2 = {0:.3f} \".format(chi2))\n", " \n", " #print(\"\\n -------- Estimated Parameters ---------- \")\n", " #print(\" b1 = {0:.3f} +/- {1:.3f} \".format(b1est, err_b1est))\n", " #print(\" b2 = {0:.3f} +/- {1:.3f} \".format(b2est, err_b2est))\n", " #print(\" b3 = {0:.3f} +/- {1:.3f} \".format(b3est, err_b3est))\n", "\n", " \n", " # draw graphs\n", "\n", " return" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Python approach" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.optimize" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def exercise_6_2_1():\n", " # read exercise_6_2_1.csv or type are values explicitly\n", "\n", " # fit a Gaussian function\n", "\n", " #print(\"Fit Result:\")\n", " #print(\"a1 = {0:.3f} +- {3:.3f}\\na2 = {1:.3f} +- {4:.3f}\\na3 = {2:.3f} +- {5:.3f}\".\n", " # format(a1, a2, a3, a1err, a2err, a3err))\n", " \n", " \n", " # now with log\n", " \n", " # calculation\n", " \n", "\n", " #print(\"Fit Result:\")\n", " #print(\"b1 = {0:.3f} +- {3:.3f}\\nb2 = {1:.3f} +- {4:.3f}\\nb3 = {2:.3f} +- {5:.3f}\".\n", " # format(*bopt, np.sqrt(bcov[0, 0]), np.sqrt(bcov[1, 1]), np.sqrt(bcov[2, 2])))\n", " #print(\"Transformed Result:\")\n", " #print(\"b1 = {0:.3f} +- {3:.3f}\\nb2 = {1:.3f} +- {4:.3f}\\nb3 = {2:.3f} +- {5:.3f}\".\n", " # format(b1, b2, b3, b1err, b2err, b3err))\n", " \n", " # plot\n", " \n", " return" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6.2.2 (obligatory)\n", "\n", "This exercise aims at constructing the error band around a function, $f(x)$, fitted to data points $(x,y)$ - i.e., the errors on the fitted parameters are transformed into errors on the value of the function at each value of $x$. (If you do not want to use `ROOT` to optimize the curve fit in this exercise, you can instead use the fitting algorithm provided by scipy, e.g., scipy.optimize.curve_fit - see Python approach)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us attack the problem in steps:\n", "\n", " - First, define a function for our problem: a straight line as $f(x) = a + bx$ with parameters a and b.\n", " \n", " - Next, consider `npoints=11` data points in the interval `[xof, xof+npoints-1]` with `xof=10` and y(x) = x. To simulate measurement errors, shift the data points in y-direction by a random shift, drawn from a Gaussian distribution with $\\sigma = 0.5$ and $\\mu = 0.0$.\n", "\n", " - Now fit the straight line defined above to your data points.\n", " \n", " Draw the data points and the fit result. Print the correlation coefficient of the errors on the parameters $a$ and $b$.\n", " \n", " Try to give an intuitive argument why the two parameters $a$ (axis intercept) and $b$ (slope) are strongly correlated.\n", " \n", " - Next, construct the error band around the fit function: write a function `make_band(f, cov, withCorr=0)`, which takes the function $f$ and the covariance matrix, as input arguments and calculates for each value of x the error on $y$, $\\Delta _y (x)$. As a first approach, use the simple formula for error propagation, which, in this case, results in $\\Delta _y (x) ^2 = \\Delta _a ^2 + (x \\cdot \\Delta _b )^2$ if correlations are neglected.\n", " \n", " Draw the curves $y(x) \\pm \\Delta_y (x)$, i.e., the \"error band\" on top of your data and fit result. Does this look correct?\n", " \n", " - Derive the appropriate formula for error propagation taking into account the correlation of the errors. Re-calculate $\\Delta _y (x)$ and plot the corresponding error band. Compare with the above result obtained without correlations.\n", " \n", "To get a better idea of what happens here and what the effect of the correlations is, you might want to repeat the whole exercise setting `xof=-5.`, meaning now that the mean of the $x$-values of the data points is approximately at $0$. Alternatively, you may choose the parametrisation of the function as `y(x) = a' + b(x-(xof+(npoints-1)/2))`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Python approach" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.optimize\n", "from copy import deepcopy" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# First: Define a function (e.g. a straight line)\n", "def linear(x, *p):\n", " return x*p[0]+p[1]" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "def make_band_p(pcov, x_range, use_correlation=False):\n", " # As first approach, use the simple formula for error propagation\n", " pcov2 = deepcopy(pcov)\n", " if not use_correlation:\n", " pcov2[0,1] = pcov2[1,0] = 0\n", "\n", " grad = np.stack([x_range, np.ones(x_range.shape)])\n", "\n", " res = np.sum(np.dot(pcov2,grad)* grad, axis=0)\n", " return res\n", " # Derive the appropriate formula taking into account the correlation of the errors\n", " " ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([1.00642896, 0.06331675]), array([[ 0.00382117, -0.0524028 ],\n", " [-0.0524028 , 0.75138922]]))\n", "\n", "(50,) (2, 50)\n", "(50,)\n", "\n", "(50,) (2, 50)\n", "(50,)\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def exercise_6_2_2(xof=10):\n", " # Next: `npoints` data points in the interval [xof, xof+npoints-1] with y(x) = x.\n", " # Shift the data points in y-direction\n", " npoints = 11\n", " x = np.random.uniform(low=xof, high=xof+npoints-1, size=npoints)\n", " y = x + np.random.normal(0,0.5,size=npoints)\n", "\n", " # Now fit the straight line defined above to your data points\n", " fit_res = scipy.optimize.curve_fit(linear, x, y, p0=(1,1))\n", "\n", " print(fit_res)\n", "\n", " # Define above the function `make_band` and draw the \"error band\" on top of your data and fit result\n", " # w/o correlation\n", " xx = np.linspace(xof, xof+npoints-1)\n", " plt.errorbar(x,y,yerr=0.5,fmt=\".\")\n", " plt.plot(xx, linear(xx, *fit_res[0]))\n", " plt.fill_between(xx, \n", " linear(xx, *fit_res[0])-make_band_p(fit_res[1], xx, use_correlation=False),\n", " linear(xx, *fit_res[0])+make_band_p(fit_res[1], xx, use_correlation=False), \n", " alpha=0.4, color=\"blue\")\n", " plt.show()\n", "\n", " # w/ correlation\n", " xx = np.linspace(xof, xof+npoints-1)\n", " plt.errorbar(x,y,yerr=0.5,fmt=\".\")\n", " plt.plot(xx, linear(xx, *fit_res[0]))\n", " plt.fill_between(xx, \n", " linear(xx, *fit_res[0])-make_band_p(fit_res[1], xx, use_correlation=True),\n", " linear(xx, *fit_res[0])+make_band_p(fit_res[1], xx, use_correlation=True), \n", " alpha=0.4, color=\"blue\")\n", " plt.show()\n", "\n", "exercise_6_2_2(xof=10)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([ 0.96363562, -0.15369415]), array([[0.00122651, 0.00038062],\n", " [0.00038062, 0.01186361]]))\n", "\n", "(50,) (2, 50)\n", "(50,)\n", "\n", "(50,) (2, 50)\n", "(50,)\n" ] }, { "data": { "image/png": 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", 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x2za7juYVFpH8E3jmP0zUtneIAHa7r2RB5Ayu7NWEHm0gKkoTUuXMVEREROS8zrQfjMswqFM1DnaswDv7fqLyD2DZJstyf8e+BmPo3SOKWrXO/HjnnWMi5YbmiIiIyHnVSIplQu8mRcemARN7NaTqB4/C6/2JzD/AIU99/uF/n8hu4/j1Xb8sIcWeYyLlioqIiIgUS/8WKUUfr7olgX4fDyDyi5cLj3OH8d6lH9L17lZ06QLR0ad/7dnmmBzMzC+T7BK89NKMiIgUWzQefhcxi9pzF2Fgc8yXwjx7Gpd27sgdHSA29sxfd745JtpErvxSERERkWIxDn3Fe1GPc5lZ+BLLR3m383XNSXTumUTDhuf+2nPOMZFyTS/NiIjIufl9+D94huhXbuQycx8ZdiIvu//D8etf5I6h5y8hcJY5Jv2anvbWXymfVEREROTsjn6Pd0ZXXGuewrR9LPG3It39V66+tQe9ekGFCsV/qP+dY7JidAcGtzrLW2qkXAloEZk0aRKtWrUiISGBatWq0adPH7Zv3x7IS4qISGmwLKz1L2G92I7II5vI9Sfxn4Lp/NY7iuMkclnji3v46kkxpZNTQl5Ai8iaNWsYOXIkGzZsYPny5Xi9Xrp27Upubm4gLysiIhfj5B68L/fGXDYG0ypgS/4N/Dt+PY0HD0RLtEtpC+hk1aVLl552/Oqrr1KtWjU2bdpE+/btA3lpEREpKdvG/vx1rMVjifRl47biWOD5E3aLe7i1q0FUnM/phBKGyvRdM5mZmQBUrlz5jJ93u9243e6i46ysrDLJJSJS7mUfxjf3ASJ+XIoL+L6gNSsSXqRNv/o0awamqSXaJTDKrIhYlsWoUaNo27YtTZs2PeM5kyZNYsKECWUVSUREALbOxf/eaCLcx/HaUSwpeIy8q+5ncDcXZ/l/o0ipKbMiMnLkSLZs2cKHH3541nPGjh3L6NGji46zsrJITU0ti3giIuVP3nF8C/5AxLezcAG7PVeyNHYGLQY24ZprCkdBRAKtTIrIfffdx8KFC1m7di0pKSlnPS86Opron68LLCIipe/7Ffjm3kdE3kH8tovlBaM51uRh+naLolo1p8NJeRLQImLbNvfffz9z585l9erV1K1bN5CXExGR83Hn4F/6OK7PXyECOOhtyKKoGTTt24IuLSFC621LGQvot9zIkSN58803mT9/PgkJCRw6dAiApKQkYs+2IYGIiATG7o/xzRpORPZuAD7I/y17G42jZ484atQ4/5drPxgJhIAWkZdeegmAjh07nnb/K6+8wpAhQwJ5aRER+Ym3AGvlUxgbXiACm6O+VBa4XqRhr/bcmgaRkU4HlPIs4C/NiIiIgw58ju/d4USc2AbAx/m/YnvdSdx4UyLnmLInUmb0aqCISDjye7HWPoex9q9E2D4y/dVYwPNc2q07t7eFqCinA4oUUhERESmhPI+PK8YtA+CbJ9OJiwqyH6UZ2/HNGkbE4c8B2FRwM19c+jc696pCnTrOxdIcEzmTIPvXIyIiF8yysDe8hL1iAhGWm1yrIgusZ6nUsT+3dzSI0T5zEoRUREREwsGJ3fhnj8C170MMYEtBF9ZXm0qn3jVp0MDpcCJnpyIiIhLKbBs2/xtryaO4fDkUWBVY7H+KqLZ3cXtng7g4pwOKnJuKiIhIqMo+hH/eA7h+WIYJfO9uw+qKL3L9zfVo3NjpcCLFoyIiIhKKtszGv+AhXO4TeO0olnmfwJ82kls6u0hIcDqcSPGpiIiIhJK844UF5Ns5pzaqu4oVCTNIG3g5TZqAYTgdUKRkVERERELFd+/jn3sfrvzD+G0XKz2/J+vqPzAgPZKkJKfDiVwYFRERkWDnzsZa+hjm56/hAg56G7E0djpX921Bl2Zgmk4HFLlwKiIiIsFs10f45/wWV9ZuLNtgrWcEh5s8wc09Yqlc2elwIhdPRUREJBh5C7BX/gk2TMOFzVFfLZZEvcjl/a+n/TUaBZHwoSIiIhJs9m/GP3s4ruPbAfi44NfsvGwi6T0TqFbN4WwipUxFREQkWPi92Gsnw9pncNl+Mv2XsDhiKnX7pDO4JUToJ7aEIX1bi4hchEOZBdRLjr/4BzqyDf/sYbgOfwHAJndfvqnzHF16V6ZGjYt/eJFgpVcZRURKaPamfUUfd3luDTM37rnwB7P88PFUrOntcR3+glyrIu/a/yK/56vccrdKiIQ/jYiIiJTAwcx8xr+3tejYsuHROVto3yiZGkmxJXuwE7vwzxmBa+9HmMBW9418WmMqXfrWIDW1dHOLBCsVERGREth5NBfLPv0+v22z62he8YuIbcPm17CWPHZqo7p4lvJnErvcyW3tDKKjSz+3SLBSERERKYG6VStgGpxWRlyGQZ2qxdzmNusg1vz7MX9YXrhRnact66pMo1O/utStG5DIIkFNc0REREqgRlIsE3o3KTo2DZjYr2nxRkO+noU1rTXmD8vx2tEs8v2ZH65fyK0jVEKk/NKIiIhICfVvkcIT8wvniawY3eH875rJO461cDTmN3Mxgd3e5qxKmkG7vo1p2DDweUWCmYqIiMhFqJ4Uc+4TvluGf979uPIKN6pb5XsYd9pDDOocSYUKZZNRJJipiIiIBEJBFvayRzE+/0/hRnW+y1geP51WN1/D5Zc7HU4keKiIiIiUtp3rCt+Wm70HyzZY5x3J8asfp096LImJTocTCS4qIiIipcWbj73iSYxPXsQFHPXVYlncdJoNaEv7pmAYTgcUCT4qIiIS1PI8Pq4YtwyAb55MJy4qSH9s7d90aqO67wBY77mTfU3+TM+eCVSs6Gw0kWAWpP+iRURChN8LH/wVe+1kXLafk/7qLI2aSqMBXenfHEwtkiByTioiIiIXqJGxl6iXu0LGVxjAZk9/ttWfTNebK1O1qtPpREKDioiISElZfn7jWsBDEe8SkeEjx6rEMtezpNzcn8EtweVyOqBI6FAREREpieM/Ejn7tzwauQGArz1d+fzSqXTtX53q1R3OJhKCVERERIrDtuGzl7GWPUGkL5ccO4YnfXeQ3nUSt7WLJEI/TUUuiP7piIicT9aBUxvVrcAEvvO25W5rEPvsZP54naESInIRNJ9bRORsbBu+ehfrhdaYP6zAY8ew2JrEjx3msc9OdjqdSFhQjxcROZPcY9gLf4fx7XxMYJf3GtZUmk6HAZdRpw7s6trT6YQiYUFFRETk57YvwZr/AGbeEfx2BB/4H8bf7iEGd4og5jx73IlIyaiIiIj8pCALe+lYjC9exwQO+hqzInEGbfo1p0EDp8OJhCcVERERgJ1rseaMwMzeW7hRnf8+slo8Tv/0GOLinA4nEr5URESkfPPkwcoJ8Ml0TOCovzbvV5jONX2uo0Njp8OJhD8VEREJGYcyC6iXHF96D7hvE9acYZjHvwdgg3cIB5o+Ra+bEkhIKL3LiMjZ6e27IhLUZm/aV/Rxl+fWMHPjnot/UJ8HVj2F/a8bMY9/T6ZVnXciZ1Hhlr/T9xaVEJGypBEREQlaBzPzGf/e1qJjy4ZH52yhfaNkaiTFXtiDHv6mcBTkcOFGdZ97+/Ndw8mk96lMxYqlEltESkBFRESC1s6juVj26ff5bZtdR/NKXkQsP3w8FXvVnzEtD7lWJd6PfI7avfsxsDmYGh8WcYSKiIgErbpVK2AanFZGXIZBnaolfBvLsR+w5o7A3LcBA9jqTeeLWs+T3r86VauWamQRKSH9H0BEglaNpFgm9G5SdGwaMLFf0+KPhtg2bPw/rJfaYe7bQIEdz3vGC+T0mskt96qEiAQDjYiISFDr3yKFJ+YXzhNZMbpD8d81k7kfe/59GD+uwgR2+NrxYdUX6X5rbS65JHB5RaRkVEREJGRUTyrG+uq2DV+/i7Xo95juTDx2DKuM8cSnD+dXbUztlCsSZPRPUkTCR+5R7AWjMLYtwAR2+65hTeUZdB7ciEsvdTqciJyJioiIhIdti7HeewAzLwO/HcFq+xGMjqO5pX0EUVFOhxORs1EREZHQVpB5aqO6NzCBA77L+aDidNoOaE6dOk6HE5HzURERkdD145rCt+Vm78OyDT607ic37TH63xhDTDGmk4iI81RERCT0ePJgxR/h0xmnNqqrw/L46bTq34YGDZwOJyIloSIiIqFl32dYs4dhntgBwAbf3Ry+6k/07hFPhQoOZxORElMREZGQEImPyNVPYa//O6ZtcdKqwfLYF2gyqAutr3A6nYhcqDJZWXXatGnUqVOHmJgY0tLS+PTTT8visiISJhobe5gf9QSRH/8Nw7b43DeQ5Q3Xkz6yC1eohIiEtIAXkZkzZzJ69GjGjx/P5s2bueqqq0hPT+fIkSOBvrSIhDrLT8THU3gv6jGuMHeTY1VmbuRruAb9HwN+VYnERKcDisjFMmzbts9/2oVLS0ujVatWvPDCCwBYlkVqair3338/Y8aMOefXZmVlkZSURGZmJon6iSNSvhz7AWvOcMz9hSOoy/3XcCDldXoPupRKlRzOJiLnVJLf3wGdI+LxeNi0aRNjx44tus80Tbp06cL69et/cb7b7cbtdhcdZ2VlBTKeiAQjy4LP/oX1/jhMXx75djxP+G5nlr89W+68hHi9LVckrAS0iBw9ehS/388lP9th6pJLLmHbtm2/OH/SpElMmDAhkJFEJJhl7sOeNxJj52pM4Hvf9ay/5EUeuaUWk5OdDicigVAmk1WLa+zYsWRmZhbd9u7d63QkESkLtg1fvo017TqMnavx2jEsNf5CRvf3uO23tUhWCREJWwEdEalatSoul4vDhw+fdv/hw4epXr36L86Pjo4mOjo6kJFEJNjkZGAvHIWxbeGpjepasKbKDG68pSE1ajgdTkQCLaAjIlFRUbRo0YKVK1cW3WdZFitXrqRNmzaBvLSIhIJvF2BNa42xbSF+O4KV9uPsuuF9br1PJUSkvAj4gmajR4/mzjvvpGXLllx77bVMmTKF3Nxc7rrrrkBfWkSCVf5J7KVjML58q3CjOv8VfJA0g/aDm5Ga6nQ4ESlLAS8igwcPJiMjg3HjxnHo0CGaN2/O0qVLfzGBVUTKiR8+wJo3EjN7P5Zt8qH9APltHmVA52j0yqxI+RPwdUQuhtYREQkjnjxYMR4+/QcAGf66rEyYzrUDWlOvnsPZRKRUBc06IiISuvI8Pq4YtwyAb55MJy7qIn5c7N2INWcY5okfANjgv4eM5k/Su3s8cXGlkVZEQpWKiIgEjs8Nq5/G/mjKqY3qarI89gWa9etM68ucDiciwUBFREQC49CWwlGQI1swgM2+wey8/C90612JhASnw4lIsFAREZHS5ffBx3/H/mASpuUlx6rC8pgpNBzQm35NwDCcDigiwURFRERKz7EfsOcOx9j3KQawxdeTLXWn0K1/NSpWdDqciAQjFRERuXi/2KgukRURf+HSXrcy6GoDM6g2kxCRYKIiIiIX52cb1X3n68An1afR/ZZUqlZ1OpyIBDsVERG5MD9tVLf4EUxPJh47lpXmk1TqeS+3XWvicjkdUERCgYqIiJRcTgb2glEY2ws3qtvla8naKjPoemsDzrCfpYjIWamIiEjJfLsA671RmPlH8dmRrGYskZ0f5NZ2EURGOh1OREKNioiIFE/+Sewlj2B89fapjeqa8EHFGXQYfCUpKU6HE5FQpSIiIudl7vwAa+GD/7NR3YMUXDeWATdoozoRuTgqIiJyVrEUMDbiLWLeWg5Ahr8eKxKmkzYgTRvViUipUBERkTMy933Ka5FP4yOCg3Zldln9OXb1BPp0r0BsrNPpRCRcqIiIyOl8bvhgIvPWfsmj3nFYmBjAqHZX8uBNFZxOJyJhRusdish/Hfoaa0YnDn74bx713oN16keEDTz/0RYOZuY7m09Ewo6KiIgUblS3djL2PzphZmzlG/9lRSWk6BTbZtfRPIcCiki40kszIuXd0R1Yc4ZhHvgMA/jadxM7Uv+KuesLLPu/p7kMgzpV4xyLKSLhSUVEpLyyLNj4T+zl4zF9+eTbSSyP+CspvQYz9GqDuE+8PDF/KwCmARP7NaVGkmapikjpUhERKY9O7sWeNwJj11oM4DtfRz6pMY3ug1OKNqrr3yKlqIisGN2BesnxzuUVkbClIiJSntg2fPEm1pIxmJ4s3HYcK80nqdzznnNuVFc9KaZsc4pIuaEiIlJe5BzBfu9BjO8WYwI7fdeytsp00m+tr43qRMQxKiIi5cE387EW/A4z/xg+O4oPeJToGx/gtutc2qhORBylIiISzvJPYC9+GOPrdzCB/f4rWVVxBp0GN9FGdSISFFRERMLVjhVY8+7HzDmAZZustX+Ht+0YBnWK0kZ1IhI0VEREwo07B5Y/AZ+9jAkc9jdgVcJ00ga00kZ1IhJ0VEREwsmeDVhzhmOe3AnAx75hHG/xR25OjyNOa5GJSBBSEREJB94CWD0R+6PnMbE57k9heYVpNO/bkesuczqciMjZqYiIhLqDX2LNHoZ59FsMYKPvdvZcPokevZNISHA6nIjIuamIiIQqvw8+/Bv26qcxbR9ZVjLvRz/PZf170K8pGIbTAUVEzk9FRCQUHf3+1EZ1mzCAr3y92Fp3Ct37V6ViRafDiYgUn4qISCixLPj0H4Ub1fkLyLOSWB75DCk3DWLwNQam6XRAEZGSURERCRUn92DNHYG5ex0GsM17A5/WeIEet1xatFFdaYqLimDX0z1L/4FFRP6HiohIsLNt+OINrMVjML3ZuO04Vph/OrVRnUGE/hWLSAjTjzCRYJZ9uHCjuu+XYAI/+tJYV+Ulut5Snxo1nA4nInLxVEREgtXWeYUb1RUcx2dHscp+jOgu93NbW21UJyLhQ0VEJNjkn8Be9AeMLe9iAvt8hRvVdRzUhFq1nA4nIlK6VEREgsn3K7Dm3YeZexDLNlljPYTnuocZdEMUMTFOhxMRKX0qIiLBwJ2D/f7jGJteObVRXUNWJEyndf+W1K/vdDgRkcBRERFx2u6Pseb8FjNzFwAf+n7LiWvG0bebNqoTkfCnIiLiFG8BfPAU9scvnNqoLpX3417kqsHtaXe50+FERMqGioiIEw58gTVneNFGdZ94f8XeKybRo1ciiYlOhxMRKTsqIiJlye+Fdc9hr/nrqY3qqrEs6nka9e1O/2baqE5Eyh8VEZGykrEda/YwzEOfYwBfeG/mm7p/o1u/KlSu7HQ4ERFnqIiIBJplwSfTsVZMKNqobpnrWVJuHsAtLbVRnYiUbyoiIoF0YnfhRnV7PsQEvvV25rOaL5A+sCbVqjkdTkTEeSoiIoFg2/D5f7CWjMX05uC2K/C+8RSVu9/Fra21UZ2IyE/041CktGUfwpr/AOaOZZjAD942rKvyIjcOrsellzodTkQkuKiIiJSmLXOwFozGdJ/AZ0ex3HqCqE4jua29i6gop8OJiAQfFRGR0pB3HGvR7zG3zsYE9niv4oOKM2g/4HLq1nU6nIhI8FIREblY3y8/tVHdIfy2i9X+3+Np8wcGdY4kNtbpcCIiwU1FRORCubOxlz2Gsfk1TOCQrxHL46eT1q8FjRo5HU5EJDSoiIhciF0f4Z/zW1xZuwFY6x1RuFFdeizx8Q5nExEJIQFbSmnXrl3cc8891K1bl9jYWOrXr8/48ePxeDyBuqRI4HkLsJc+hv1qT1xZuznmr8WbkQupdMskevdTCRERKamAjYhs27YNy7KYMWMGDRo0YMuWLQwdOpTc3FwmT54cqMuKBM7+zfhnD8d1fDsAGzx3sOfyifTolUjFis5GExEJVYZt23ZZXeyZZ57hpZde4scffyzW+VlZWSQlJZGZmUmitiQVp/i9sHYy9tpnMGw/mf5LWBo1lYY902neHC3RLiLyMyX5/V2mc0QyMzOpfI7dvdxuN263u+g4KyurLGKJnN2RbfhnD8N1+AsMYLO7L9/We46ufSqTnOx0OBGR0Fdm/5fbsWMHU6dOZdiwYWc9Z9KkSSQlJRXdUlNTyyqeyOksCz5+AWt6e1yHvyDXqsgs/oW796sMvkslRESktJS4iIwZMwbDMM5527Zt22lfs3//frp168bAgQMZOnToWR977NixZGZmFt327t1b8j+RyMU6sQvrlZvg/ccwLTdbPV14N3kD1/1mAG3aoH1iRERKUYnniGRkZHDs2LFznlOvXj2iTq1nfeDAATp27Ejr1q159dVXMUvwgrrmiEiZsm3Y/BrWkscwfTkUWBVYxp9J6jSE69oaWqJdRKSYAjpHJDk5meRijkvv37+fTp060aJFC1555ZUSlRCRMpV1sHCjuh/exwS+91zHuiov0nlAXWrXdjqciEj4Ctgg8/79++nYsSO1a9dm8uTJZGRkFH2uevXqgbqsSMl9PQtr4UOY7pN47WiW+5/AvH4Et3VyERPjdDgRkfAWsCKyfPlyduzYwY4dO0hJSTntc2X4jmGRs8s7jrVwNOY3czGB3d6rWJU4g3b9LqdhQ6fDiYiUD2W6jkhJaY6IBMx3y/DPux9X3mH8totVvt+T3+oP3NAlUqujiohcpKBdR0TEcQVZWEsfxfziP7iAg75GvF9hOi17t+CKK8AwnA4oIlK+qIhI+bFzHf45I3Bl78GyDdZ5R3C02RPc3C1WS7SLiDhERUTCnzcfe8WTGJ+8iAs46qvF0piXuOLmdlzfXEu0i4g4SUVEwtv+zfhnDcN14jsAPnb/mt2NJ9KtZwJVqzqcTUREVEQkTPm92GuegXWTcdl+TvovYUnEVOrenM6gVuByOR1QRERARUTC0ZFvC0dBjnwJwGcF/fimzrPceHNlatRwOJuIiJxGRUTCh+WH9dOwVj6Fy3KTY1ViMc9ySff+3HodREY6HVBERH5ORUTCw/Gd+Gf/Ftf+9ZjAFveNfFp9Kl361qBWLafDiYjI2aiISGizbdj0CtbSx3H5cimw4lls/ZkKHe7kto6GlmgXEQlyKiISurIO4J97P66dKzCB79xtWVPpRTr1q0ODBk6HExGR4lARkdBj2/D1LPwLH8LlycRrR7PUOw679Qhu7WxqiXYRkRCiIiKhJfcY/vd+h2v7fFzALk9zViTMoM2gxlqiXUQkBKmISOjYvgT/vAdw5R/Bb0ewwvMHsq9+iAFdI7VEu4hIiFIRkeBXkIV/8VhcX72OCzjgvYylsTNofvPV3NhcS7SLiIQyFREJbjvX4ps9koicwo3qPigYyeEmT9C7R4yWaBcRCQMqIhKcvPlYyydgfvoSEUCGrzaLIl+icd+2DNYS7SIiYUNFRILPvk34Zg0j4uT3AHyYP4QfGzxF+k0JWqJdRCTMqIhI8PB5sNY8g/Hhs0TYfk76qrPAnEqtHl25pQ1ERTkdUERESpuKiASHw98UjoJkfAXAxvz+fJU6mS69KlO7tsPZREQkYFRExFmWH+vjF2DVU0RYHnL8lVhgP0flG/pxewe0RLuISJhTERHnHP8R76wRRB5YD8BXBelsqPY8nXpVp2FDh7OJiEiZUBEpx/I8Pq4YtwyAb55MJy6qjL4dbBv7s5exlj5BpL9wo7oF3klEt7mD2zobWqJdRKQcURGRspV1AO/s+4jcvRIXsK2gHR8kvcj1g2rTpImWaBcRKW9URKRs2Db2V+9iLfw9kd5MPHYMi93j8V4znFu7mlqiXUSknFIRkcDLPYZv/u+I+K5wo7of3dfwfoXpXHvzZTRvriXaRUTKMxURCaztS/DNfYCIgiP47AiW5T/Ciaaj6d89guRkp8OJiIjTVEQkMAqy8C0aS8TXrxMB7Pc0ZmHUDJr1bU56K4jQd56IiKAiIoGwc23h23Jz92LZBivz72d/o8fo1SOGmjWdDiciIsFERURKjycP37IJRGyaTiRwxFuH98yXqN/9Om5rqyXaRUTkl1REQpxja4H83L7P8L4zjMisHQCsyb2b7bX/RNeb4qlTx5lIIiIS/FRE5OL4PPg/+CvmR88SicUJXw3mWS9Qo3MX7ugAsbFOBxQRkWCmIiIX7vBWPO8MI+rY1wB8kjeQzdWfofNNlWjUyOFsIiISElREpOQsP/51z2OsnkiU7SHbX5l53udIuK4vd3RBS7SLiEixqYhIyRz7Ac87vyXq8CcAfJ7XnY8q/532PS7hyiu1RLuIiJSMiogAcCizgHrJ5xjKsG38n/wfLB9HlD+PfCuBeQVPY1x9O7d3M6hUqeyyiohI+NDi2uXY7E37ij7u8twaZm7cc+YTM/fjfrkfrqW/x+XP45v86/m/yI9pOOhXDBqsEiIiIhdOIyLl1MHMfMa/t7Xo2LLh0TlbaN8omRpJp97qYttYX76DtfAPRPsy8VgxvJc/gdwmv2FwD5Nq1RwKLyIiYUNFpJzaeTQXyz79Pr9ts+toXmERyT2Ke84oon9YgAn8UNCCxTEzuKZPQ9LStES7iIiUDv06KafqVq2AaXBaGXEZBnWqxmF9uwj/vAeJdmfgsyNYnDuGI41+R98eEaSkOJdZRETCj+aIlFM1kmKZ0LtJ0bFpwMRe9amydDTmzNuIdGew13MFM/yrqND9D9xxp0qIiIiUPo2IlGP9W6TwxPzCeSIrB0Zz6fJ+ROXvw7JNluU8wM46j9K9ZzT16jkcVEREwpaKSDkXg5sxEW9R9733ATjsrctsazq1OrVmyA0QF+dwQBERCWsqImHkvGuB/IyxbyOLo8ZSzzwEwKqce9laYwJdesRz+eWBSikiIvJfmiMS4oq9Fsj/8nnwLJlAzL97UM88xEG7Mi/mzeJ462e5c6hKiIiIlB0VkRB2trVADmbmn/2LDm2h4IVORH3yHAYWc/ztSHc/zTWDOtG/PyQmlkFwERGRU/TSTAg771ogp33Ch2fN34lYN4kY20uWvwpv5z/LxIgoAJo10z4xIiJS9jQiEsJ+Wgvkf/20Fshpjv1AwfTuRK19EtP2sim3J/+M2MBlfXuVXVgREZEzUBEJYWdcC6Rf0/+OhlgW3o/+iX9aO2IyPiXPSuTfWS/xZeM3uH1YNVq1cii4iIjIKXppJsT971ogK0Z3+O+7ZjL3kf/2SGIPrgZga14HlsZMo+XNqVx3HURGQp7HodAiIiKnqIiEkepJMWDbeDfNhCUPE+vPxG3FMjdnAicaDGVAT5PatZ1OKSIi8l8qIg7L8/i4YtwyAL55Mp24qIv4K8nNIG/e74nbvRCAHQUtmW/OoGl6A/p0gJiY0kgsIiJSelREwkS6uZGIFx8gynsUnx3Jgqwx7K09il49ImjUyOl0IiIiZ6YiEuoKMnk28iX6u9aBF/a4mzDbmkG9jldyd2eIL/5CqyIiImWuTIqI2+0mLS2NL7/8ks8//5zmzZuXxWXDnv+7VZizR9LfdQC/bbA0+wG2V3+MG7tH07Tp+dcFiYuKYNfTPcsmrIiIyBmUydt3H374YWrWrFkWlyofPLnkzfo9rjf7EuM+wE7rEgZ6xnO85TjuGhrNlVdqcTIREQkNAR8RWbJkCe+//z6zZ89myZIlgb5c2PPv+gTvO8OJy/sRgJU593BfRFvyieHf/SBeE1JFRCSEBLSIHD58mKFDhzJv3jziirGfvNvtxu12Fx1nZWUFMl5o8bnJWzyJmM1/JwaL475LeSt/GlFNryd/e+G7bkwtTyciIiEmYL+6bNtmyJAhDB8+nJYtWxbrayZNmkRSUlLRLTU1NVDxQop14Gvy/n4DcZv/honF+rxb+EfExzTv14nBg51OJyIicuFKXETGjBmDYRjnvG3bto2pU6eSnZ3N2LFji/3YY8eOJTMzs+i2d+/eksYLL34fecsmY/+jE3HZW8jyV+UfWa/zVf0Z/OreirRtCxF635OIiISwEv8ae+ihhxgyZMg5z6lXrx6rVq1i/fr1REdHn/a5li1bcvvtt/Paa6/94uuio6N/cX55ZWXsIP/N4VQ4sRGAzfk3sSxyCq16JHP99aCnSUREwkGJi0hycjLJycnnPe/555/nqaeeKjo+cOAA6enpzJw5k7S0tJJetvywLPLW/pOoNeOpYOeTbyXyTs5fya57C4N6GNSv73RAERGR0hOwgf1atWqddhx/amWt+vXrk5KSEqjLhraT+8h5937iM9YC8K27I3PtaVzZKYWBneFM8321FoiIiIQyzTAICjYDXGuJmD6MKCsbjx3LnJw/sb/GPfTpYXLFFU7nExERCYwyKyJ16tTBtu2yulzoyDnCXyL+QaqRwTF/JPm+a5npnk6D1vW5tyskJTkdUEREJHA0IuKg/M3zmTNvJuN8Q7EwMWyb9rFXMmpAba66SuuCiIhI+NOvOifknyDr1aGcnD+KcZ5bsU79NdiGwTr3VqrXy1cJERGRckEjImWsYOtK7Hn3keg9wNdWk6IS8hPLttl1NI8aSbEOJRQRESk7KiJlxZ1D5uxxJH33LwCO+OuzIuc5jOhj/O/MGZdhUKfq+ZfDFxERCQcqImXAvWMD/lnDSSrYCcDq/GGsjfoj7XvHUStiFxMWbQXANGBiv6YaDRERkXJDRSSQfG4y5/2ZxC3PY2Bzwkrh9expuBp25I7uULcu5HlSiorIitEdqJcc73BoERGRsqMiEiCePV/heXsYSXnfAPCJ+zYW209zbZckOnU68+Jk1ZNiyjiliIiIs1RESpvfR+aivxG/+Wni8ZFtJfNWzt/JTe3Jrd2hcWOnA4qIiAQPFZFS5Dn4PQVvDiMpexMAX3l7Mds9havaVeWWLpCY6HBAERGRIKMiUhosi5PL/0H8hvEk2gXk20m8k/MMh5IH0XegwVVXgWE4HVJERCT4qIhcJN/RPeS8MYKKJ9YB8J2/E2/mTqNRy0u5Nx2qVHE4oIiISBBTEblQtk3mmjeIXTOGinY2HjuOeXl/Ylv8PXQfbNCyJbhcTocUEREJbioiF8B38jBZbzxI5YwlAOyy0vh31kukNKvPb3pA9eoOBxQREQkRKiIllLl+HtHLf0dl6zg+O4olBY/xWfT93NDXxXXXQWSk0wlFRERCh4pIMflzTnDyzT9Q5cC7ABy0r+SVzBlUuqwJd/eA2rUdDigiIhKCVESKIWvzCiIW3UcV/0Es22SlZzRreIR23aLo2BFitA6ZiIjIBVEROQerIIdjbz1O8u5XADhqN+DVrBlE1G7Jr3tAo0YOBxQREQlxKiJnkbVlPeb84SR7dwHwoXc4i9zjubZ9HF26QEKCs/lERETCgYrIz9jeAjLe+TPJ30/FwOYkqfwncxp51TvQ90Yfg95ZBJ/AN0+mExd18U9fXFQEu57uWQrJRUREQo+KyP/I/u4LrNnDqeb+FoDP/L9ids5Eml2bRHo6xMQD7zibUUREJJyoiAC238eR2c9R9Zu/4MJHDtV4M/vvHKnUg769oGVLME3I8zidVEREJLyU+yKSs+s7PDOHcUn+ZgC22jfzRubfaNS8Cvd20+JkIiIigVR+i4hlcei96VT9YgLxFJBPErPynuX7mAF062fQpo0WJxMREQm08llETuwm/+2RVD9cuFHdDjrz6okXSLm8Jvf2gFq1HM4nIiJSTpTPIrJrHbGH1+G2K7DA/Sc2m3fToYdBhw5anExERKQslc8i0vx2jmzfxcuf30ZszXoM6a7FyURERJxQPouIYRDR9XHa1IAWLSA+3ulAIiIi5VP5LCJA5crQoYPTKURERMo30+kAIiIiUn6piIiIiIhjVERERETEMSoiF+hQZoHTEUREREKeikgJzN60r+jjLs+tYebGPQ6mERERCX0qIsV0MDOf8e9tLTq2bHh0zhYOZuY7mEpERCS0qYgU086juVj26ff5bZtdR/OcCSQiIhIGVESKqW7VCpjG6fe5DIM6VeOcCSQiIhIGVESKqUZSLBN6Nyk6Ng2Y2K8pNZJiHUwlIiIS2lRESqB/i5Sij1eM7sDgVtqmV0RE5GKoiFyg6knapldERORiqYiIiIiIY1RERERExDEqIiIiIuIYFRERERFxjIqIiIiIOEZFRERERByjIiIiIiKOURERERERx6iIiIiIiGNURERERMQxKiIiIiLimAinA4SSuKgIdj3d0+kYIiIiYUMjIiIiIuIYFRERERFxTECLyKJFi0hLSyM2NpZKlSrRp0+fQF5OREREQkzA5ojMnj2boUOHMnHiRG644QZ8Ph9btmwJ1OVEREQkBAWkiPh8Ph588EGeeeYZ7rnnnqL7r7jiikBcTkREREJUQF6a2bx5M/v378c0Ta6++mpq1KhB9+7dzzsi4na7ycrKOu0mIiIi4SsgReTHH38E4I9//COPP/44CxcupFKlSnTs2JHjx4+f9esmTZpEUlJS0S01NTUQ8URERCRIlKiIjBkzBsMwznnbtm0blmUB8Nhjj9G/f39atGjBK6+8gmEYvPvuu2d9/LFjx5KZmVl027t378X96URERCSolWiOyEMPPcSQIUPOeU69evU4ePAgcPqckOjoaOrVq8eePXvO+rXR0dFER0eXJJKIiIiEsBIVkeTkZJKTk897XosWLYiOjmb79u20a9cOAK/Xy65du6hdu/aFJRUREZGwE5B3zSQmJjJ8+HDGjx9PamoqtWvX5plnngFg4MCBgbikiIiIhKCArSPyzDPPEBERwR133EF+fj5paWmsWrWKSpUqBeqSIiIiEmIM27Ztp0OcTVZWFklJSWRmZpKYmOh0HBERESmGkvz+1l4zIiIi4hgVEREREXFMwOaIlIafXjXSCqsiIiKh46ff28WZ/RHURSQ7OxtAK6yKiIiEoOzsbJKSks55TlBPVrUsiwMHDpCQkIBhGE7HcVxWVhapqans3btXk3cDSM9z2dDzXDb0PJcdPdf/Zds22dnZ1KxZE9M89yyQoB4RMU2TlJQUp2MEncTExHL/TV4W9DyXDT3PZUPPc9nRc13ofCMhP9FkVREREXGMioiIiIg4RkUkhERHRzN+/HhtDBhgep7Lhp7nsqHnuezoub4wQT1ZVURERMKbRkRERETEMSoiIiIi4hgVEREREXGMioiIiIg4RkUkxLndbpo3b45hGHzxxRdOxwkru3bt4p577qFu3brExsZSv359xo8fj8fjcTpaWJg2bRp16tQhJiaGtLQ0Pv30U6cjhZVJkybRqlUrEhISqFatGn369GH79u1Oxwp7Tz/9NIZhMGrUKKejhAwVkRD38MMPU7NmTadjhKVt27ZhWRYzZsxg69at/O1vf2P69Ok8+uijTkcLeTNnzmT06NGMHz+ezZs3c9VVV5Gens6RI0ecjhY21qxZw8iRI9mwYQPLly/H6/XStWtXcnNznY4WtjZu3MiMGTNo1qyZ01FCiy0ha/HixXbjxo3trVu32oD9+eefOx0p7P31r3+169at63SMkHfttdfaI0eOLDr2+/12zZo17UmTJjmYKrwdOXLEBuw1a9Y4HSUsZWdn2w0bNrSXL19ud+jQwX7wwQedjhQyNCISog4fPszQoUP5z3/+Q1xcnNNxyo3MzEwqV67sdIyQ5vF42LRpE126dCm6zzRNunTpwvr16x1MFt4yMzMB9P0bICNHjqRnz56nfV9L8QT1pndyZrZtM2TIEIYPH07Lli3ZtWuX05HKhR07djB16lQmT57sdJSQdvToUfx+P5dccslp919yySVs27bNoVThzbIsRo0aRdu2bWnatKnTccLO22+/zebNm9m4caPTUUKSRkSCyJgxYzAM45y3bdu2MXXqVLKzsxk7dqzTkUNScZ/n/7V//366devGwIEDGTp0qEPJRS7MyJEj2bJlC2+//bbTUcLO3r17efDBB3njjTeIiYlxOk5I0hLvQSQjI4Njx46d85x69eoxaNAgFixYgGEYRff7/X5cLhe33347r732WqCjhrTiPs9RUVEAHDhwgI4dO9K6dWteffVVTFP9/WJ4PB7i4uKYNWsWffr0Kbr/zjvv5OTJk8yfP9+5cGHovvvuY/78+axdu5a6des6HSfszJs3j759++JyuYru8/v9GIaBaZq43e7TPie/pCISgvbs2UNWVlbR8YEDB0hPT2fWrFmkpaWRkpLiYLrwsn//fjp16kSLFi14/fXX9QOllKSlpXHttdcydepUoPClg1q1anHfffcxZswYh9OFB9u2uf/++5k7dy6rV6+mYcOGTkcKS9nZ2ezevfu0++666y4aN27MI488opfCikFzREJQrVq1TjuOj48HoH79+iohpWj//v107NiR2rVrM3nyZDIyMoo+V716dQeThb7Ro0dz55130rJlS6699lqmTJlCbm4ud911l9PRwsbIkSN58803mT9/PgkJCRw6dAiApKQkYmNjHU4XPhISEn5RNipUqECVKlVUQopJRUTkLJYvX86OHTvYsWPHLwqeBhIvzuDBg8nIyGDcuHEcOnSI5s2bs3Tp0l9MYJUL99JLLwHQsWPH0+5/5ZVXGDJkSNkHEjkLvTQjIiIijtGsOxEREXGMioiIiIg4RkVEREREHKMiIiIiIo5RERERERHHqIiIiIiIY1RERERExDEqIiIiIuIYFRERERFxjIqIiIiIOEZFRERERByjIiIiIiKO+X9cTn6pdwe4NwAAAABJRU5ErkJggg==", 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