{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Approximating functions on $R^2$\n", "\n", "Randall Romero Aguilar, PhD\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demapp02.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-22\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates how to use CompEcon Toolbox routines to construct and operate with an approximant for a function defined on a rectangle in $R^2$.\n", "\n", "In particular, we construct an approximant for $f(x_1,x_2) = \\frac{\\cos(x_1)}{\\exp(x_2)}$ on $[-1,1]\\times[-1,1]$. The function used in this illustration posseses a closed-form, which will allow us to measure approximation error precisely. Of course, in practical applications, the function to be approximated will not possess a known closed-form.\n", "\n", "In order to carry out the exercise, one must first code the function to be approximated at arbitrary points.\n", "Let's begin:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, BasisSpline, nodeunif\n", "from matplotlib import cm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining some functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Function to be approximated and analytic partial derivatives" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "exp, cos, sin = np.exp, np.cos, np.sin\n", "\n", "f = lambda x: cos(x[0]) / exp(x[1])\n", "d1 = lambda x: -sin(x[0]) / exp(x[1])\n", "d2 = lambda x: -cos(x[0]) / exp(x[1])\n", "d11 = lambda x: -cos(x[0]) / exp(x[1])\n", "d12 = lambda x: sin(x[0]) / exp(x[1])\n", "d22 = lambda x: cos(x[0]) / exp(x[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the points of approximation interval:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a, b = 0, 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choose an approximation scheme.\n", "\n", "In this case, let us use an 6 by 6 Chebychev approximation scheme:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "n = 6 # order of approximation\n", "basis = BasisChebyshev([n, n], a, b) \n", "# write n twice to indicate the two dimensions. \n", "# a and b are broadcast." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute the basis coefficients c. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are various way to do this:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* One may compute the standard approximation nodes `x` and corresponding interpolation matrix `Phi` and function values `y` and use:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "x = basis.nodes\n", "Phi = basis.Phi(x) # input x may be omitted if evaluating at the basis nodes\n", "y = f(x)\n", "c = np.linalg.solve(Phi, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Alternatively, one may compute the standard approximation nodes `x` and corresponding function values `y` and use these values to create a `BasisChebyshev` object with keyword argument `y`:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "x = basis.nodes\n", "y = f(x)\n", "fa = BasisChebyshev([n, n], a, b, y=y)\n", "# coefficients can be retrieved by typing fa.c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* ... or one may simply pass the function directly to BasisChebyshev using keyword `f`, which by default will evaluate it at the basis nodes" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "F = BasisChebyshev([n, n], a, b, f=f)\n", "# coefficients can be retrieved by typing F.c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evaluate the basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having created a `BasisChebyshev` object, one may now evaluate the approximant at any point `x` by calling the object:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5322807350499545" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.array([[0.5],[0.5]]) # first dimension should match the basis dimension\n", "F(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... one may also evaluate the approximant's first partial derivatives at `x`:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "dfit1 = F(x, [1, 0])\n", "dfit2 = F(x, [0, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... one may also evaluate the approximant's second own partial and cross partial derivatives at `x`:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "dfit11 = F(x, [2, 0])\n", "dfit22 = F(x, [0, 2])\n", "dfit12 = F(x, [1, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compare analytic and numerical computations" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Function Values and Derivatives of cos(x_1)/exp(x_2) at x=(0.5,0.5)\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " Numerical Analytic\n", "Function 0.53228 0.53228\n", "Partial 1 -0.29079 -0.29079\n", "Partial 2 -0.53228 -0.53228\n", "Partial 11 -0.53223 -0.53228\n", "Partial 12 0.29079 0.29079\n", "Partial 22 0.53223 0.53228" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print('Function Values and Derivatives of cos(x_1)/exp(x_2) at x=(0.5,0.5)')\n", "\n", "results = pd.DataFrame({\n", " 'Numerical': [F(x),dfit1,dfit2,dfit11, dfit12,dfit22],\n", " 'Analytic': np.r_[f(x), d1(x), d2(x), d11(x), d12(x), d22(x)]},\n", " index=['Function', 'Partial 1','Partial 2','Partial 11','Partial 12', 'Partial 22']\n", ")\n", "results.round(5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cell below shows how the preceeding table could be generated in a single loop, using the `zip` function and computing all partial derivatives at once." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Function Values and Derivatives of cos(x_1)/exp(x_2) at x=(0.5,0.5)\n", " Numerical Analytic\n", " ________________________________________\n", "Function 0.53228 0.53228\n", "Partial 1 -0.29079 -0.29079\n", "Partial 2 -0.53228 -0.53228\n", "Partial 11 -0.53228 -0.53223\n", "Partial 12 0.29079 0.53223\n", "Partial 22 0.53228 0.29079\n" ] } ], "source": [ "labels = ['Function', 'Partial 1','Partial 2','Partial 11','Partial 12','Partial 22']\n", "analytics =[func(x) for func in [f,d1,d2,d11,d12,d22]]\n", "deriv = [[0, 1, 0, 2, 0, 1],\n", " [0, 0, 1, 0, 2, 1]]\n", "\n", "ff = '%-11s %12.5f %12.5f'\n", "print('Function Values and Derivatives of cos(x_1)/exp(x_2) at x=(0.5,0.5)')\n", "print('%-11s %12s %12s\\n' % ('','Numerical', 'Analytic'), '_'*40)\n", "for lab,appr,an in zip(labels, F(x,order=deriv),analytics):\n", " print(f'{lab:11s} {an[0]:12.5f} {appr:12.5f}')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approximation accuracy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One may evaluate the accuracy of the Chebychev polynomial approximant by computing the approximation error on a highly refined grid of points:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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x+PLwU9I222yDo446CnfeeSdUVcXZZ58du385NDU1Bd7z6youIibumgOAd955B3fccQfeeecdfPrpp54DnW/PepEVyj/n2LFjY9eX+z6q3Xvlwibj0Nuwxbjft9K6/v6s6zv6ldC33HJLPPvss3jzzTdx+OGHV9z2tddewyuvvILddtst4Pio9dGHX1zcIi2HcPJCudAufuPwixdwfvT9998fd999NxYsWICddtoJTz75JDbbbLMAMfJJptxNG4daP6dlWR5JV4KfXObOnYtrr70WjzzyCObNm4cnnngCxWKxJuv8lVdewZIlSwA4ZFMODz/8MM4666xIWGo5OYf/XuH19W4f971VIz1+rPANrOu6Z7kVCgX8+9//xpFHHlnxWH5Uk66q4c9//jMuv/xyEEIwdepUfPWrX8WUKVMwc+ZMzJ8/P1YmqAX8+yh3PfL14e+jnut3oFDpvqj029f7WTcUiSWMfiX0vfbaC9dddx2efvpp6LpecQa87bbb8MADD+DTTz/Fr371q7rPxR9pZ8+eXTFEMozwTM2xdOlSAFEre968ebj77rvx2GOPwTAMFItFT0sOjyUsD3DcfffdGDVqlCfr1IORI0fiiy++wFlnnYVhw4bVtM+UKVMwdepUPPfcc+jp6fGiW2ohdB6ud+6555bNSDz66KPx2muv4YEHHsDRRx8dWBcXhgqUtGAuK/V2+ziMHDkSixcvxueffx7wjXDwXIewNn7VVVdh0aJF2GOPPfDSSy/h0ksvxe67717Xk1ZvsWTJEvzxj39Ea2srbrzxxoBRAzj3R2/B5clyOR7lvo/1ERvTZ60F/TpNzZw5EzNmzMCyZctw0003ld3uzTff9EKJjjrqqF6di4c7xjk9AeDyyy/HYYcdFtC/ASduPS7W+7HHHgMA7LDDDoHlXDd+6qmn8Pjjj4NS6sVkc/BwsmeffTZy3CVLluCcc87BNddcU+MnC2LbbbcFACxYsCCyrlgs4rDDDvPih/046KCDYBgGHnvsMTz33HOYNm2aF+ZVDtxKpZRizpw5Zbfjnz/OaRn3e3z00Uf45JNPsMUWW0QmpXq3jwO/Fvhv6AdjLPa3XbhwIa6//no0Nzfjkksuwf/93/+hp6cH5557btXz9Qfeeust2LaNPfbYI0Lm/icHv8xRqwXt/z7inl64w3z77bfv1diHEjamz1oL+pXQCSE499xzIUkSLr/8cvzpT39CNpsNbPPKK6/glFNOga7rOOqooyKOpVqx8847Y8qUKXjhhRdw9dVXBy78Z555BjfeeCMWLlwYe/xf/OIXAYfhHXfcgWeffRYTJ06MtaLnzZuHjo4OPPTQQ9hpp50iFtwBBxyA5uZmzJ8/PxDLXigUcOGFFwIADjzwwF59zuOOOw6EEPz2t7/Fm2++6S03TRMXXngh3nnnHViWFbFADjroIBBC8Ic//AG6rtcUe/7oo4+ip6cHO+64YyDSIYwDDjgAkiThnXfeicgyjz/+OB544AHvfVdXF8466ywAwPHHHx85Vr3bx+HII4+Eqqq47bbbApq/bdv43e9+h4ULF6K9vd2bHE3TxJlnngnTNPHTn/4Uw4YNw4knnogpU6bg6aefxvz582s6b1/Ar6FXXnnF80sAQDabxc9+9jPvac8fi8/lwrgcAz922mkntLW14Z133sEf/vCHwL3x+OOP484770QikYg8aa6P2Jg+ay3o91ouW221Ff7yl7/glFNOwVVXXYVbbrkFW221FZqbm7F48WK8//77ABwrz5/pVS8IIfjd736Hb37zm/jjH/+Ie+65B1tssQVWrVrlRWCce+65mDhxYmC/MWPGYOnSpdh3332xww47YNmyZXjrrbeQTqfxu9/9LlYXPeSQQ/DHP/4Rtm0HnKEc6XQal156KX7wgx/gu9/9LmbOnInhw4fjjTfewJdffoldd9211wWVZsyYgR//+Mf43e9+h6OPPhrTpk3DyJEj8fbbb2PZsmUYMWIELr300sh+Y8aMwQ477ICXXnoJlNJAOGU5cCKrtm1zczP22GMPPP7447j77rtx/vnne+tGjx6Nn/zkJ7jtttswYsQIvPTSS+jo6IgNz+vN9nEYM2YMLrroIpxxxhn4/ve/j2222QZjxozBu+++i88++wyjR4/G5Zdf7umm1113HRYuXIjtt98eRxxxBABAkiScd955OO6443DRRRdhl112iUSq9Ce22WYbzJgxA6+//jr23XdfbLvtttB1Ha+++iqy2Sw222wzfPTRR1i1apW3z6abbgrA8V/09PRg7733xte+9rXIsQkh+P3vf48TTjgBf/7zn/Hwww9jiy22wLJly/DGG29AURRcdNFFFX1PfcXdd9+N559/vuI2iUSiz1VHh8JnHUoYEM/AzjvvjIceegjf/va3MX78eLz55pt47LHHsHr1auyzzz647rrr8Nvf/tYL++st2tvbMX/+fI8sn376aSxduhR77LEHbrnlllgSbWpqwh133IFtttkGzz77LD799FPMmTMH99xzT9nqb2PGjMGYMWOQSCRiQ+MAJ2Tx7rvvxpw5c7B48WI89dRT0DQNP/jBD3DNNdf0yQnzne98BzfccANmzZqFTz75BAsWLICqqjj++ONx7733YsKECbH7cat8xx139LTGclixYgVeeOEFiKJYU+gen9geeOCBQGmDb3zjGzj77LOxatUqLFiwAKNHj8Z5552H3/3ud7GSQb3bl8OBBx6Iu+66C/vttx8+++wzPPnkk6CU4tvf/jbuvfdeL178ww8/xNVXXw1JknDBBRcEzrH99ttj3rx56OzsxHnnnVfzuXsDQRDw5z//GcceeywSiQQWLFiAjz76CDNnzsTVV1/tpfX/5z//8fbhsdZNTU149tlnAyG2YUyZMgX33nsvjjnmGBiGgSeeeALLli3DIYccgr///e+x4aL9iddeew33339/xT8eSttXDPZnHVIYlHSm9QxvvfUWa2trY2eeeeZgD2XIIi6jsj+3b6CBBqpjQOqhbwgwDAOUUnR2duLiiy8GgEhERwMNNNDAUEKD0Mvgo48+whFHHOFl6u27775Vk3IaaKCBBgYTG2Z0fT9g/Pjxnm6+//7745JLLhnsITXQQAMNVARhrNFxtoEGGmhgQ0DDQm+ggQYa2EBQUUNfubJyAkMDDTTQwMaGESOihfWGChoWegMNNNDABoIGoTfQQAMNbCBoEHoDDTTQwAaCBqE30EADDWwgaBB6Aw000MAGggahN9BAAw1sIGgQegMNNNDABoIGoTfQQAMNbCBoEHoDDTTQwAaCBqE30EADDWwgaBB6Aw000MAGggahN9BAAw1sIGgQegMNNNDABoIGoTfQQAMNbCBoEHoDDTTQwAaCBqE30EADDWwgaBB6Aw000MAGggahN9BAAw1sIGgQegMNNNDABoIGoTfQQAMNbCBoEHoDDTTQwAaCBqE30EADDWwgaBB6Aw000MAGggahN1AVhAC2bYIxG4yxwR5OAw00UAbiYA+ggaENSgFCGCzLhG17S0GI8wcQEEIGcYQNNNAAR4PQGygL0bs6CAihYIy5FroNwEbJWG8QfAMNDAU0CL2BCAgBBAFgzHkdXBdcECZ4QRAAENg2GgTfQAPrGA1CbyAASp0/wCFzSgkSCRWABsYYdN3w/pxtgmQtyxIYAwqFQsOCb6CBdYwGoTcAwCFvRRFgmpa3TJJEqKqMXK7gEbQsS1AUGalUAgAiBO8ciwBwSLsh0TTQwLpDg9Ab8KxyTVPQ3Z0DACQSCggh3nvAIediUUexqANwiJsTfDqdgG07Grt/Uqgm0bgjaBB8Aw30AxqEvpFDEII6OaUUyaSKYjFodcchTPCUEqRSCciyhNbWZti27VnvhmECaBB8Aw0MJBqEvpGCOz6DywiSSRXZbAF2KUaxZtg2g66bME0LuVwBlFLIsgRNU5HJiLAsTvC6Z8XXRvACKHXIvUHwDTRQHg1C3wjhd3wCDrknEioIAbq6cuV3rBO2baNQKKJQKLrnpVAUCcmkBlEUYVmWZ8FXJngLtu2XcQTXeqex+zTQwMaKBqFvZAhLLIJAkUioKBR01wruD8QTrG3byOeLyOeL3rllOUrwxaIByypP8IxZIKRB8A00EEaD0DcS+GPLOVRVhigKyGbzsG0GVZX74Uy1lwawrDDBC5BlCalUAqLoRNxwicaybPdzlMialyHgBJ9KJdDTkwsQfIPcG9iY0CD0jQCUBhOFuFZumhZ6evI1HoWgVrLuLYdaloV83kI+XwAAiKJD8Ol0EoIgwDRNT6KxLDsmBl4GY7mQBU98DtYGwTewYaNB6Bs4ePo+t8xFUYCmKcjni4Hwwv5Cf9buMk3Lc7ACfoJPQRAoDKNE8LZte5NVaSwMAANjpjvJcKdqg+Ab2DDRIPQNFGHHJ+DEmQsCRU9Pfr2smhgleBGKIqGpKQVKKQSBQlVll+CZj6z9SU4Ngm9gw0WD0DdARGPLCZJJDbpueHr1hgDTNGGaJrJZRzYaPrwZgiCgqUkFpRSGYXjx9IyVJ3jAAmNhiUZAI0SygfUNDULfgBAXW+5P3+eOxQ0VjDFks3mP4CVJhCxLSCRUUEqg6yWJJkjwpf0bBN/A+owGoW8giJNYnKJaCKTvDzyiRLnOzhxSkQzDhGGULHhZlrwwSb5e13Xoutkg+AY2CDQIfQNAudjyYtEhq3WJoSzNB6tEApLECT5YaMwwDDciqBaCb5QpaGDooEHo6zEIATRNhG2XCmIpikNSvU3fr3SuDQmMhQmeQJbFipUky5UpIIQhlVLR1dWDBsE3MJhoEPp6Ch5bTghx28Q5Eotts3UssWwYcAqNOU5UIL6SZPlCYwSCILhPJ41CYw0MHhqEvh4iHFtOKUUqlUChoHtk0xusj6GMA4W4SpKSJEHTFGQyqUAlyUplChoE38C6RIPQ1yPERbGIogBBoOjuHjqx5RsiR9l2mOBLlSQlSXTLDmsoFg2YZqNUcAODgwahryeIVkh00ve5VNBfZE5Ifzg2N3xS8leSpJQik0nCsmwkEg7B115JskHwDfQfGoQ+xFHOKufp+5T2901fe82WOAyVp4R1Cf71+0sFl6sk2SD4BgYSDUIfwiiXvk9pKX1fksR+u8k3Qi4eMEQrSVLIsoxkMlxJsqHBN9B/aBD6EEU96fv9d083GL23qDYZOgRfiKkkmYitJAk0ujk1UD8ahD7EECex8Pjo+PT9/iXh8hp67USx8XFK/TJV+UqSpVLBvA4Nzyco181J0xQUi7x6Jif4RrOPjRENQh9C6E36/rqSSWrlhY1RtukPzoyrJCnLpUqS4VLBznmdEwuCU4bA+e4b7fo2ZjQIfYhADP0S9aTvDyWnqLPvxkca/T2R8UqSuVyw0FiJ4EtZrPznb7Tra6BB6IMMf2s4fm+V0ved1nDrChujdb2+IFxorETwTpgkY3An/1IIa6V2fQ4ateA3NDQIfRDhl1icbjv1p+/3d5hg457uDdb9l+Yn+ObmNHRdhySJoUqS1UsFO80+SiUMGgS/fqNB6IOASrHlhUIRhlFfa7ihFuWysfGA83kH9/FG100UCro3nlIlSc1dX66SZKOb04aEBqGvY1AKaJoMy7K8BBNVlSGKQh9awzVutMHGYMpVDtGWBlC+kqRUQyXJWro5NQh+qKJB6OsQPLacNzPm6fumaaGnJ9+rY/YnkfTHsRo6/OCg0vderZIknwCKRT2mkmTpGI1mH0MfDUJfBwhLLIzBa2iczxc9S713YP0qccTdlJIkIp3WYBiW2+HH2ODb2dWDwSayes8friTJCV5VFWQyySqlgkvH4ASvqhIMw4Bp2g2CH2Q0CH2AERdbLkkCCCHo6ckNeYvWKTVA0NnZA8aYm/ySgiCUQueCxcE2zrDFwdbQ++IcjysVzCtJZjJioFRwHMGLogjDML1Ep2A3J9Ig+HWIBqEPIMql7zs3iNmPEkf/3yhcDjIME/m8Q9jh5BceOtfSwiMrjLoduv033kE5rYfB1dD793i2zVAo6J6T1V8qOJMRYVmc4HWYpuU5UaNhkrb7utGub12hQegDAH9sOYc/fV8Ih7j0w/n6A9zK4xE3uVzRKxwVB3/oHI+sUFUZiiJh2LAmLy66L003GqgFA0uM/lLBQLSSJKXEnQRYo5LkIKNB6P0M3hrOnygUTt8XhP6MEOhf01CWJVBKvIgb8bYLAADW18+qPArXsWaaFiil6OzsgaKUOvw4Vp0eKB+7oWBj46FwJcnm5gwYY14lScuyvDo0jUqS6xYNQu9HhFvDlUvfj+so31v016M+d4yZpomeHreeiEvmAKDefSl6DvtpHeMKPraXrDpePtb09Pf+bGY9ONjYiYchny/Ctp1ILUEQoCj9UUmyQfD1okHo/YA4x2e19P2BjkypB1xiMU0zoIETSQTrlVwSHU/YquPVBTOZkoOVW3XrY5OM9XHM/QVCSODzW5aFXK5yJcnwZN4g+P5Bg9D7iLDjkxDipu/bFSokDp2b35/UpCiSt1z620W9PGJtn62cg7WUuu7c8DyzsToaN/dgIZzYFEZ8qWDZN5mXryTJ0SD42tAg9F6iWmu4ajrxYF98cUlN1SaazL+vRtec/6vh2PWPJ87BqigyUqkEGIvGRQ8lNHikPunPIfh8TZUk+dNtNYJXVQWFgr7RE3yD0HuBOIml7+n76w6CICCRiJ94wvcAl11YhWgXP/orFNOflh6Oix56DlbSb76M9RF9Jc5KlSQpJdD1YKGxuHMmk5or5wUteEqdGPihTPBxxdN6iwah14k4iaXe9H3nBxygAVaBokiQJLFXE4+dra0CZH8jHBcd72AdbMt9I2b0fkaY4GW5VGiMEMQSfLk4+KDDfWh2c+LjMAwDklSSPXO5HAqFAkRRhKZpgXXl0CD0GhEXWy5JIlRVrhqvXeaI/Tq+qmfzleatPPEQKPf9HkM57iTOwaooMgRBQGtr83rvYG0giGARsWglScMo1agpZ8HzLFbezSmVSiKXMwed1PP5PO644w58/PHHmDdvHrbffnvouo5nnnkGTz75JD755BOoqorp06dj7ty5mDx5csXjNQi9BggCgaII0HXTs6x5Snxv0vfXNcfw8MlCQa+oQfvHRVUVdqGwDkbXd5imBcsqQJYlrF3bBUlykrjCpWM5KfQ3Bt/Q23gmrfhKkhIURUFLSwZA/O8dtt4VRUIuN7hPdT09Pbj66qtx4403Yscdd0Qi4VTC/Mtf/oIrrrgCra2tGDZsGFasWIEXX3wRt9xyC8466ywcfvjhZWWaBqFXgSg6Gq4oitB1E5RSJJMqdN1APt9bglh3kku93Y/6Pq7+0wN7C/7IDjg3Mif4gXSwDuaDwMb8EMIYg2E47fo6OroDlSTLlQrmqPc6vfTSX2HJks/wt7/dWXXbJUuW4NJLL8VLL70EANhzzz3x85//HMOGDfO2ee211/Cvf/0LxxxzDE499VQMGzYMTz31FK6//nrMmTMHZ5xxBsaNGwcAWLhwIS688EJceeWVmDx5MmbOnBl7Xhq7tAEQ4u/z6RCwLItIJlXkcgWvFGlvsK5uwGRSBaUU3d25GlvZVd8m8++rKx9hiJELJ/Du7izWrOlEZ2c3LMuCpqlobW1Gc3MaiYQKUexLOYa+9mHtw5kH//Fg0OGXWnihMf57r13bBcMwoSgyWlub8N57b+Ouu27H//73P0+qqQUPPDAf998/v6Zt165dixNOOAGvv/46vv3tb+PEE0/Ek08+iRNPPBG6rnvbLVq0CIlEAscff7xH9G+//TYymQx++tOfYty4cW4VSxNbbLEFzjnnHFBK8fTTT5c9d8NCj0E4ioUxR6dlrPbWcNUwkDdirRJLHOgDVwKJJOxcdoBGVz+Um851XsRMSsWTLqzrWLU5WOvLYCVksC30wZ5FB/f8lb7/cCXJTTaZhJUrV+H+++/HG2+8iaamZsyZcwC++tUDY/e3LAu33HIjbrzxuprH89e//hXLly/H/fffj8022wwAsM022+DEE0/E/PnzceSRR7rjJtB1Hfl8yadVKBQwbNgwT36htFQmpKWlBU1NTchmy9+bDQvdB26V+8lcEChSKQ22zZDLFfvlPAN5A8qyiERCRTZbqJvMyw2LSCKkCRP6YXT1IXHXRdBuPd95E/eEQQmUm86FcsM5vT4Hd7B2dnZj9eoONw6eoqkphdbWZmQySSiKPGQt4cGeTIDBP384U7USEokkdt99T5xzzrm48cbbcdZZv8TkyZvFblssFvGtbx2HG264FnPmHIARI0bWdI4HH3wQO+64o0fmADBr1ixMmjQJDz74oLds++23hyAIuPzyy7Fs2TIAwMEHH4xUKoVHH30UgBNiTF1Cev7557F8+XJMmTKl7LkbFrqL8un7IrLZvOdg6y8MBEGEi4D1N8TRY2B3dw7IscNI3OVmqhIKKlGARa1lm1f2EwUof/0l8gBwwnl9Om9c0kstDtbBI7XBk3uA+sh0qIzBv/2IESPLErWu68jlsjj//Iuxzz774ogj5lY9dmdnJ5YsWYI5c+ZE1m211VZ46qmnvPdbb701Tj75ZFxyySX49re/jf333x/t7e0QBAHXXnstdF3HzJkzYds2Hn/8cdx6663Yeeedsfvuu5c9f4PQUT623LJsdHf3rjXcukY6nYgUAesVkikg2wOgFOkijt8EMGvXG/syV6XvuxzMNABJhM2fMGLI3CN6AMyyQNy0Xe22C5E/rvcWexhhBysvg5xOJ7zOPpRS2PbgREwM9oODQ45DYQz1EXotPqVkMok77/wnRLF2mlyxYgUAYNSoUZF1I0aMQE9PD7q7u5FOpwEAhx9+OFpbW3H33Xfj9ttvR7FYhKZpWL16NS6++GJvX0op9txzT/zsZz/D6NGjy55/oyb0vqbvDwVIkghBcByfA94WjtbKHr1jmfR9l3uvOZkLmgLmu/nCoZSEEhAqBrZJ3HURckdXLvfbG4R7c/IMVkWRoarOH9ff689L6C0G10J2JpT110KvBEqpJ3fUCq5va1r0iV5RFABOwhAndEmSsO+++2LWrFl49913sWjRIixbtgzFYhGGYUAURYwcORK77LILttxyy6rn32gJfX1P3weAREIBIcSNw+47mQsv/zOyjKpq8H26Cc1v3o+O6ZUeP+v/7jL/vhpQZDDeBk1VgBhS9I+H8YQSQQARnEmAuNEqA0XqfnAHq1NB0IJpmpBlJ1xuXZUIHmwLfbAnFKB3hD5QqOV3Dk8Stm0jmUxihx12wA477ACg9+UANkqnqCAEyZxSglTKmVHXBzKnlCCdTsCybGSzjsXa39coTSSd/8NdfVH0pR0Xqmn09Q2m+T83AIyBFXUQUQiSdoVHY6qqgW0FzbGAqCSCSiJS//hNXePoKxwHa2GdO1gHu/3dYN8u9co+lA7cJJRMOvdNsRgNoODL+Dal8ThkZNs2TNN5Mj3zzDNx2223oVBnct9GZaFXTt8vrBed7MuPd3CdY30BczVyoiqAacKuIz4YCGa1Uil4Saf+8Rv0HH5G/wy0TvTWwVoPBtspOdjnd8ZQX+TYQOr+Y8eOBQCsXLkysu7LL79EJpPxQhLD8Es8//nPf5BIJOqWfDYaC523hgP8reEUyLKInp51oD/3AzQtfrwDdXFyKz2AOhxEtaD5uVudcylqlS3jwZ2hXGohogQiBosY+bX5gUC1euAchmGipyfnS3gxvISXlpYMkkkNkrR+2Vi1fvaBHsNAaOi9QSaTwfjx4/HOO+9E1r377ruYNm1a1WMwxiAIAjKZTIPQw4iLLaeUIp1OwDQdyWKwHxmrgRDixsKXG28/lxJIpkqv5RLR2i0jYTe1gmWGxexUP5qfuxWsWAAhFLYefESlqgqaTEJIaIE/DhLyZoflF07qYXIfKNRfz8dxsHZ3Z7F6Nc9gtSMZrNUaig+2hTx0JJehYaEDwH777YcXXngBH330kbfs+eefx+LFi3HAAQdU3d8wDOTzeaiqWjehr1/mQJ2Ic3w6UQkSstnCoPey1C9xmkUQSkAEAeJP/hTZhkfd9K6iYx/R3BoajOSFL2Y+eBJdbXv3/tDP3x5ZRiQJzDQhJJNl668LSedx1S7EJ3kRVQFz11FN81rope+7HN2HnN7r8Q40HAdrEQV37E4Gqxzoy8krSA72dRvEUJBc6hsDpQSm2T9jXrJkCf73v/9h2223xQQ3+e7kk0/Gfffdh29+85v41re+hWKxiOuvvx5bbbUVDjnkkKrH5On+qqrW7W/ZYC30sOMTcGqbiCKvbVLfTdHfF+3qs78ZWWZf8ZPAex4K19OTr0jmztD6ZqJLHzzVp/3rhiwDAEhIaiHucgCxUS4cNKGBJuKTvYiqlF5LIogigygyMg9d0YcBl8dABE1wB2tHR8nBKgglB2s67ThYB9LBVwvW1zj0/hrzyy+/jDPOOAMvv/yyt2zYsGG47bbbMHXqVPzpT3/CzTffjNmzZ+P666+H7L++y6BYLLr1hrS6CX2Ds9AJAVRVBGPMiyPvS22T4LH75+YxfnNK4L0TyWHB1gHhujOB715Sd9OMfieVZAq2mgQtOHG1dkttac+1oPnN+4Fi0HtPtYSTUFQHiCCAJDQwXvCoBn2/6fHr0Dn7O3Wdp4aR9PPxouAO1nDTB1V1omacuiADVyK4HIZOHPrAbc9xzz33R5YddthhOOywwyLLJ0+ejL/85S/1nwSOhU4IgarW71faoCx07viklIC6STCKIkPTFGSz+T6ReX91GTJ/90MAjswSB6uog/713EABqRpG1/eB8SMl0tGFcvDCYoSA2L2Tf5r/909ALwDcMheESHYXUVTQRBI0lXL++/4ARB69SEwSB007fgAiKyU9XVYi2/UX1rWVrOsGenpy6OnJeXV7BsPBOtgavjOG3kS5DF3HWU9PDyzL2rjj0P0SC5cgUikNlDqx5bWVjy2P/vz9ww69MOyiDnJ77VUE1+m1KUqwks0wk01IfPFqXbtmFv0nGM8eAxIXWeMDTcavjyN14rNwqG990+O1V84b+nCiTHjJ2L44WHt7/sHmxqEU5dIfkCQJu+66K8aPH1/3vuu95BIXWy4IxG3qUOjH9H2eudX7C8G+4iegsgS7hsfick6/cujvZBVj5CYQ8j2Vz1mvlc63l1XHSlc1wHCfQhTV0dMryS7uUw231FmMbGPng0lPRFHA3IQO3vCayDKaF/wVHbt/s77xl8FgZmvGRZmsSwdrvdbxQKDea38o6P6VsMkmm+D666/v1b7rNaFziYWx0k2laTJEUUSx2L8d4QfjAlDu+z2Kh/x44E/02f/KrrLVJCwtBUEPafkkvgJiOaQXPwtadI9BSJAFkynANINkXsOxSSIJ5tZtrzU8kdTglOoNhnK1Re5gzeedCZD3YG1qSoFSGkhwqpech7q1GwdO6INfNiGKzs5OvPrqq/jkk0/Q3NyMffbZB5ZlgTGG1tbWqvuvt4TO/V/8WqKUIJFQYRgW8vliHzvQxKNPVvCffwbqryBYA2rt6dlfN5SVyEDIdcXq6JasQdDzMLQmAAB1qwsmvngVtH03FIvlHc6pT18A0WM+i6Q4f0boaSSZKv2w3ILMhp4WeEJRphks2+0t9jtXieRG0qRSJScsD72UZTT/9w507HRM/JdRFwazY1HpK6oV5RysvclgHYqkWA1DdcyLFy/Gb37zGzz11FNgjGH48OHYZptt8Oijj+LGG2/EVVddhR133LHiMdY7DZ3SaDCDJIlIJjXk80WvM0n/18sYnBtWe/SamrYbjIvUUNKwRBWGYULTFE+vpZRAEJxLK7H0NU+aYXKM195P5sm0I8Nw+JkqmXLWx4CElhM1JrVaUZ3Jgx/LRfN/76jwCdcH9H0y4Q7WaMu2Zs/BWr6E7PpnoQ9FrFmzBpdffjmee+45nH/++TjxxBOhaRoSiQSmTp0K27bxi1/8Ah9//HHF46xXhB4XW87T9/3lY/srIiWMwehaY+drrcc+8GOz5DJNPj57DV1dWaxe3YHubkcCSaeTaG1tjkgnturq3+GngEQKNSGViV8ecqbGk/rARLkMNQ29L/D35Fy9ugOdnT2wLBvJZLyDdX2TXIbaWLkP46233sJzzz2Hs846C0ceeSTGjx8Py7KgKAr22msvXHfddejs7MS//vWvisdbLwidp+/7b5xw+r4f/ZFoE0ZfLgTh5l9C0CrHlDKbgVlWrMNUW3BzlbH1emixyA/fFABgaQ7JmrJDlrrW7G1TVB3phZHgJWRZNmyboaOjG9l3nvWW20oCjEZlMJZIR8IiY+GfycPWOo/eqBIhE4Arx0BW0fzqPbXvVwZDjCf6DbZto1AoorOzx52wc2DMaajS2trsyjVy3Snq/Yne3JtDpaUgH/vSpUuRyWSw7bbbAnAsdn9i0SabbIJp06bhiy++qHi8IU/o/qJaHI7e5/TNjNf5BspC7+fjVYhFD6Bqudq+f15Djbd8i03RziscNnUew01RhbD6IwirndoVne+/jMTS10CtYtSZKghgVRyYTKuRmDMt0WX82LIMaAlAct9zAvdb6fwpQVadZKdeYzA19HVrIVuWFchgtSwLlJJIBuu6Isz17QmhHARBgGEY6OrqAgDk83koigLJvX6z2SzWrFkTKb0bxpB2ikZbwzl9MxljFftmOh7sgag5Xf8xBYGCyjJsPUjSRBDK1isBnFh0qg5cIgyHvvwDyADW/K5UO9y2SjcIFZzPTChB00+jDSMsQQ78SOKqRc4xqARqFT1nahhMlMFEGcR0vxfLcaiyZBNgm2AhCYbkfE5RwXfZJlJA0Xf8ZKoUCgkAWhLI+7qkcx097IhtoFdgDMjlSnWR+uJg7Q2GWmGuesGfbGbOnIlMJoObb74ZM2bMQEdHBxKJhFcf/b777sNnn32Gk046qfLxBnzEvQCXWPwQBIpUKgFdN5HLVb4ZB2bGrt8KlmUR9LbaE4TC8MeiV5Jd+iox+ckccEic/zkt3pxjd/3+EphyAoZcshK4lV56H7W+LcXZ3lLLWxd2IgM7UUYfB8ASKbBUc9l1AUhy5feAR+ze0wAhvbbSB1dDH+xaLsH7rW8O1t6cf2D6ia4rcMNzypQpOPHEE/HCCy/g61//Ol544QUsW7YMN910E44++mhcc801mDt3LvbZZ5+KxxtyFnpcbDlvDZfN1p7xORAWOq25p6bzJAEAcXZJrclF9aA3H7f7zBNgm1ZZ6YeD+kJAe/70G1BRgPZ/P4UlyLCJAJsIIGCgtgVqGxBNZyKyRBWCGQ1XtBIZUL3gWed2Ig1YVk2JSizZBFLIVt0uYJn7qkR6x5FVL5SSiRKIaYDJKpoW/hudW0Q7tlcd19DhiHWKSoTKHaw88oxS6smloijCsiw3wUnvdT+C3tVxGZo/1te+9jW3MfWd0DQNuVwOd955JxKJBE499VSccMIJsb1K/RhShB6OLSeE1F2kaqBQ60VAKUUyqaJY1KHrJsL2am9i0XnauvLWwyhuvX/c6FCPhU4IQfdZDpkDDmGXa/UWJnsqCiCUIn/1ZZB/4EgwJEY/ZoQ4TlBCHcJ3HaKmlgE1HCK1EhlQs9Z6NSXYiQxoztEametgYYkUiBE6ls8yZ1oSxAx+70xWvSgcJvVF3ho8E32wCaoeQ4I7WEsZrAIURUI6nQxlsOp1GG711nEZGpEujDHYtu0ZnnxMBxxwAA444AAsXrwYnZ2dSCaTmDJlSs3HHRKEztP3/eB1wPP5Yr9mfPYF1az+cHs45d7LUI/dUa3GCy1jmdaT9SaKArrPPQnMZqCiANu0ImROxaASx2wGQRadSBybAbBBKIX559+Afv/MyDkMSYMYY5kzsUSwZhky57IMYTZovjuynsNOt4DmguttLe3s4zpGebVIFpJc4uLhmSCCWCaYrCKz6D/omrJX2XOHMZgVBwc/WKP3A7AsC7mchVzOuVYkSYQsS2hqStecwbo+1nHhDaAr1daZNGlSr4496IQuSRSUIvDIpWkKBIEOqYbN1YaRSCiO5VvBWStoKqx8fPZn04xSa6rCZ0sC6+x8HjQurtqHWiQmRZHQcfaJsE3Ltcptj6j9YLbtySy2aUFUZTDbBqEkQOoAQG64DDjpJ6CuXGKKKgRLhyElIVrRz8qtcz94fDuxrcAXbWtOFAojFEKu03ntC320E2mQYvD7trV04By2mgSxDO+1f1LkRO9JL9zZSmndpD6Yl2ncuTMPXeGtYDGppN1zfzTAo6ofhmHCMMy6Mlh709xisEEIwd133421a9eiubkZoigimUxC0zSoqgpVVaEoChRF8V7LsgxJkqBUyaUYNELnVrkkURBCYFk2KHUkFl03kc/XF4Ww5Ni53usJt/clBK0c4p2izpg16LqBYrF3unjTjGlgzAZxY7rVSROhL10au2152aUykkkVts0cmcV3A4TJ3HGClkiTEzuhNEDqvBmzpRuQbv0j9BN+CtGOfn5dTkE08jDUDESzAFNJg1ql39bUMh7hVoKVbI4tFmYlmjyyrwW2moxo9VzTDyP98QJ0T9695mMPBvwF45oevw7MMgONQcJkTtyoisyDTnesrgN/uG4G2gv4yZsQ4nYbk5FOJ2HbtrdufXSKLly4EHfeeSdkWUYikUA+n/esdlEUvf+SJEEURSQSCXR1deG6667DZpttVva4g0Lo/tZwPMSwfDf72iBIzgEtw8bSbx6C9n881p9Djo0kqWfMcaGLANC03TaxnXnkTTaF/tmnpQWFnOPoix1b+QuUTzjFoo7u8052NXDiOEMFGiB0HkbJpR9mWSUZiDGP1AWl5BmgogDmk8QsKnrWeiXYghKQXPwkS8oU5rK0FBgVIsRuJZoChGxpQT3dVqP6eeyYXB2dWgZsWV1vPJ3pJ6/3Wu0RwWmgG/4tYdulm85H8plHrgIAdH012HRlqKGcg9XJWnVe1+JgHSphi9/73vegKAr++te/YsqUKdh///1RLBbR09ODXC6HfD7v/S8UCjAMA8VisWqEEGEV2GDlyvIaZm8Rji3nWjlvgNxbLP2m06vPMmwIEoWoShj5575nAHJQStxGGc4YNU0BpQS5XHyTae2Rq2Hnc4HQQ1vXYeULsA0Ttm4gPXO6Q+aWFbDQIQiODiyKMJd+7jRA1jSgZQRsNQk9MxJs0+2844qiAEkSkM8HJwxJEqCqCnK5AvTLfgjbcCwaSzdjtXPuAC3nIAVzLHNu9Ymq7OxDKaggwDzmVFhUhGQW3f95L4xRNPOwqQjRLIJaRYfQXYueWEaJ0BkLELqXicqdR+7TA49ttwXf5OJFrYiwRQVCvtuTVWxRgeDKLUySAxOIzbV9LlGIsvfUwAQJ2fHbx38fLoYNa8LatZ2DQhTNz93qELRtOaTOnbx+I4ETOA1+l+EB94bUW1ubsXp1R9379RcSCQ22bcEwLCiKI9E4STqma+EHHayJhAJAQLHYe7/ciBHxNYXqha7rOOOMM/DOO+/grrvuqqmaYjWsszj0uPR9pzWcAsZYv5B53Dn7C9xCJ8RpnMEnoIG+if2d7HkYnqDHOUeDH1ZVZciyjJ4ep8aNn8wFVYbo+wtDkEXvP38NwJNZAMTuJ90dX0hMNIMRSroSjTc31AxMOQlTScFQM95fHBgVYKqpAJkzQQQTnT8OS4veeJzguW5v+xy1dijShbnHT37+Suw4AtuuYzJvfvEup7CYS+aAUxqYiJLzF3itlDo3EZ4oRj3rnQgCiCCg6bE/r9sP0Q/gtWwcB2spgzWfL7g9WNNeBuuiRe8jm83WJNEsXfoFzjrr/2H//ffG/vvvjQsvPBdr166tut8RRxyB9vb2yN8PfxiUthhjkGUZZ555JlasWIHvf//76O7udltnmrAsC5ZlwbZt2LZds6y0TiQXv8TCwWfTfL7Y51ZZapOGQmdcWGN/pmQzUOqQeW9lIT/SO2xXuZmDCzp6HOzlles3+H9rQoBkUoNpWp5zyb7iJxAUGVZRh6DKAYkE8FnagBfK6CdyQRY97dU2LUgpzTsGsxkIbNhwrIPkvdei67BTIFlFFOUUJLOIopyGZOZhCbIXo85hShogaWVj0E3FSRoS9WykFoyppCAWS/KLLamxTlcOS02C+vT6AJmLoUgYIRhwmlj6GnJjZ5Y99rpE84t3BYueSUrgWmIVaskTXgrBKk0Cfsmv+T83oGOvytmIfgx20EI5p2icg/Xll1/ClVf+CbbNMHPm9th++x2xzTYzI3VoOjs78MMffg+GYeDYY4+HZVm4885b8dFHH+Ivf6mU4Mfw0UcfYfbs2dhvv/0C68aNGxc77lGjRuHXv/413n77bciyUzKhL4lX64TQ49L3bdtJ36eUQJYHxvPcecZxyFx6a78ci3dY7+rK1edVV5W6uw9FjuFLJqCFLCw1CfLpqz7ZhblOZqcZdjjUU1BkWPmC89/VWsvJKoIqwyroHqFburM9lUXYugkpqUY+v6C4ZEhptA5NCKZYsoKLSgZCjCM1DoaagRj7ZBI6vpqBWOjy3ltqGkKhJB1aShJC0ZVeqBCZSEw1A8EsOCUNAAiWDkuQQZiNlpaMp9MORiht85v3O0QuCIBpA4QCslIi5AqlJMIgslxqri0IJbkPtZP64IdM1h7lousGjjnmG/jud7+LVavW4uWXX8XTTz+JUaNGY+zYINneddftWLnyS9x8812YONEJH9xyy2k4/fRT8PDDD+Ckk46PPcfnn3+OXC6HffbZB4ccEq8ahMcOAHPnzsXcuXOrbF0b1mnqvyAIXvo+j2IZiMqI/QkusQBOa69aLh7t6Zsqrqdlnkg8y8qygtb78NFVz0mpQ+bZbD5ANvYVP/FCJS3DhKDI7p/k/XHrnLgRLYJPThFkMfCeg28rakGZggoCMv+8CgWpfDlcS5BRVEpySLUMUW6ZG0pUQjGVVCnckC8LSTW2qITelz6PJUUz7yyxJHPxMgeMUOTeewGM2UgmnUqDTU0pqKqyTgpReWRu6E7CFI+t5ySuqN4fUVQQSQZRlMAfb+HnSS3+2vOhmOjmBX+tYVSDH9Pdmzj0dLoJe+yxF370o/8XIXMAeOKJRzFjxnYemQPADjt8BZtssimeeOLRssf+8MMPAaBiFMpAY50QOmOOpqtpMnp68oHONgNVu7w/IIoCUikNhYKOQqH+jEaqxceOa9OnR5YREvNT+CMzYuLQsyudKBjn6YGiuzsXCckSFBnU/ROUqNzCt/GsbACCJEbeA46V7ozV+cHEZIkQBE2FqCmgiiPftN5/NQAgLzskXJCrO5IMJRWoExO/TUw3JTG+/C5PZOKyDX8fllPCckscbEECIxTmkrfQ2enotNlsHoJAIQgUw4Y1IZ1OQJZra4VXD5refbhEuJIcnOwVJUjGleQW3rfVv0ySS+37+HFkuSbzeygk6fR3YlFXVxeWLv0C7e1TI+va2qbivffeLbvvokVOYTpO6LlctSqp/Y91QujJpGMhlUsUGkgLp3jR93u1n6rKUFVnAurPx+vYuuiVMkR150nGbhlZ2tyN1lDMnOegtWIet8XbLohNKolbBiBA4tXeh9f5QSQJRBBg0ug2RdkhV97CDnBi1U2fpWzISedPibfyw05VW5RhqBnYrkxiC5JH4hz+96aowhZkb3te790WSpa8JZV+J+58takIBgJp1QfOfq6fwrJsrF3biWLRcAtRNaGlJYNEQutTK8TMB0+i6d2HQXj0jT/jtYYwzLLgrf84/H1WubxHKZqfqVyHv7+ba/QG/U3oq1Z9CQAYMWJkZF1r63Bks1l0d8dH/y1atAjJZBIXX3wxZs6ciZkzZ2L27Nl48MEHax5fX7FOCD2bLfbKwq0FhV99N7LMMmyYhd4l+fgllnWSqVol3R9AqRxsTBx6Pl8sW5qUWZZHvLZhQtQUCJoCUVO9Pw5PbilD4iUr3SE3ysdNqWepM5sBzAYzLTDLQuvjf4VFRFg0XmIyBQXFCtIM4FrtUrS6Y0GLhnjpIeu9GBNNw2GFZBjT92RguRa7f0LxV5VkIF7td76EMUendTr9dKKzs8eVZ7SAPFNrI4j0xwucqB1Bgi2pYIQEa9UoarAkqX9CV+KfWAA4ujvg7KuopXrxflL3LHUFza/8vfyhSH8GHfQOlPZvcS5uVatq9DvkWZrlLO8PP/zQI/zf/OY3uOiii5BMJvHjH/8Y8+fPr32QfcCgp/4PJAqdeShNNbY2g6PxJxJ9qx+jvXS3+0IDQu3jqCxDnDIViGuY7IM9fjLoymimqNk0HGLnKmesehaGnEDX8sVIjZwY2Va87YLArSZqihfBEtjOJeNAwTBKvdhlqshObXZF9raRm1KwdRNUEEAVGWClDFI/mO+YJpVhUhmS7TxxFKUkBLt2K7OoZCDrwYQiXclALnYFltkhOYU7N/kxBKtEirqShlysnGthiQqIbXnx9MRXnYeu+QT2sImI8wHZto18vuj5ikRRgKLIaGpKgVICXTfdAm7RyTj98QLnXIbuxMz7rXEqALLg1Y/3wPVw7o/QEqX482IhGmbmPx7fx0/qYY0+FoMvuQD1Z4oyRsoqSryueyXRoNykfOSRR8K2bRx77LHesgMPPBAHHXQQfvvb32Lu3LkV67f0B4ZkPfS+gGeMchQ7e4Crz6i6n6JInsa/ziIYYjr32OMcR4w9ajysMZt6yyuF4wFR2YrKsvOnqlXb3wFB5yaVRIeo+Xv3dTlnLnz6P1VVR7OXRBBJxMjHrvfWSXYRJpUDDlPKSt91UYz6CZjvEtXl6OQcll/MkJ4efu8neCAorRiS5lnn5Y5hucRuEwGMENA1n0S2jwOXZ9au7cLq1Z0oFvWAPJNMakh88SqSn73oafxhMmdKjE9GlKJkHgZ3mMZBEErkLUqla5ITj6Ki+fX5sbsOFcmlvu0rr0+4bQyLxWhkGl9WrmvQ17/+9QCZA46lf8ghh2DVqlWe03Qgsc6cokMVTty2CkoHthjY06fdG1wQE2vKxrveccYA2waxLRijJ3rraTGP4vAJkf1Wr/ky8F659zKnP2mhAFvXwQyfFVihjkU4YkXKRAmUL6OyCCGpeVINAAiJaMQIlSQMe7b8Y3tRTKAoJjySL0pJ7y92+xhSj2yjZAIk7H/PCd37H2rIYZOoBcUlI9uNtvHvY1ERqz96C+hYEtmvEvzyTO69F8A+cPqv8izZQGROiIW8Fn6VerHG+UkUtUT+lRDTECSu+cdQcIr2N0aNciLKVq1aFVm3atVKpFJpJBKVC+WFMWzYMADrxkm6QUsuHMWObsTVKONx24WCHoi86TN8zRWe+X/3wMpbIBLBgp/OBzOcG2Cf+acHdrHHT3ZehG4QahnxHXcASHou3qp1PwtVVa9+DJEkCJLk3ehWvuiFsfkbWMRJM1xHrxRjLiSTgXRzJ+HIchKOXEdbQUxCtA0v9rwoJkCZFVtPna+XfWV4ObHmlSYoRs5bZtEURLfgV8QCF6LfnS6nPOnFEmRYghx8D3hj5ORtiIonEdlEAIhQIl93EiAdnzv/m8eX/Z78kFZ9AGJbnqRDbQO2pJba8vkR9kMIMfq5liwROWOlXrRcIuCJWcmUI8P4H/8luXTt8YYg/vUx1v9QjU4rh1omn3Q6jTFjxuGDD96PrFu06H1MnbpF7H4rVqzAt771Ley///449dRTA+sWL14MABg/vrbroi8YEpJLf8zyalNly0P620WB94oieXHbtZJ5tXGqbzzgvX721L/g6VNvgZUPZWVmRBCJ4Mmv/cFbZo2f7DVqiIORboXtSgOCkUduWNRKf+cTJy1Ze/QakFAvUhrj4BE0JVaKIZIUWB4XzUIkCVRVvXhmMR21moWEBqo5f0QQMfrl0hNKUUzERsDEoSAlkZOjzs2ilAi9T/br+zgYQvB7dSYTn7OUUDBCYXcuhd0ZXy2TrvkEwuqPIK5aFIm/90fZUDej1vZZ4YwKsGNkF6ZqYHGWt5pw/pSYdWEJRlKCFr8oOct82blRK339tNCryTR77rk3XnnlRXz66SfespdffhGfffYpZs/eL3afUaNGobu7G3//+9/R01Py9Sxbtgz//Oc/8ZWvfAUjRozol/FXwhAh9IENXQQAw1dAiEsscXHb1VDLOF8546qK6wXNuUme/PqVAABWJgrEDzMV0+EeTugiACjUseqYUSqfGmmYEfMYXk5fl5qiJBq3zA9+Pk96cYpsOCVd3aeBAol/XDVo9BnKL38UxCjhhqNnqpF0Nes94EAVExE5hi93xubcOozQEKkTMPca4cTOOj4H6/gcZO2nILBLlr1//KE8BFtOBK4LO0TKtpoEkxRPVyfViDWO1GNyG1iyTP0cWQnUyQEGTnJpfn1+Hf1d6zt/LcM95pjjkck04bTTvo+77roNt9xyI84552dob98C++13AABgyZIluO+++7BkSUlqO/fcc7F8+XIcffTRuPnmm3H11VfjiCOOgCiK+OUvfxk5z+eff44777wTy5cvr+szVMKQIPRytcb7G4JAkU4nelVvHajtSYIpCRRWG7DyvoYd4xyy4kTOX0tpEc/83w01n7/YNAoAIJVJgf/wS5c8fajaBUkSY7Vvb72blBRZ7kZEcOs8QuYhMMPEuNeDN6lBFBRpArrgTCq6oEEXtFgZCQCKQnC5GSOnVIIZIuha3nv6uW9yCVvqfFu+fxy5UmaBMgsWlbyIGWqbsETFc8zSmDIIjAqwfFY5k2TYFZptOxuV6fGpamAJN7QzxiEf2FZWvbh35jtf03ulstQD4RT1O2Cb3n244rb1nr/WCailpQVXXXUdNt98Cm644Vrcffed2G23PXHZZX+C7F73L7/8Ms444wy8/PLL3n6zZ8/GVVddBU3TcNlll+Gmm27CjBkzcOedd8Zmj7766qs4//zz8dlnnwEAzL7kFrhYJxp6te+Qt2Qa6JhWR2IpeKFJvUG1i+jV034LANDGcN25/LkEjcLK23jhkLMw694Lgiu5YxQAhOjN15MZB63QAcCx0nVBwdYLb/GC6mhCA+O1o92L0F+0iRAKyxdWKSS0SK9TqpZ6borNTbALRVBZLjtJUE7m/AnB1c4JcTt/G0VYTIBIDBSJBgoblMRHZhTFBBgjkO1gdE9RSHihjwBQkFKQfJ2RHJ1e79V7HlrJ31tUgk0EyFa08JvhTkKirYP5whYtInpRjARuKWBCwZjzF+jsZBuBBCvAnTgkLRBeyQuK8eJixJcpassKaMGELWtR/0sh63RpKubKS3rcSvf7P8o4W5kUXD4gFro/jLIKepdUVNu2m2wyEZdd9qey6w877DAcdthhkeWzZ8/G7NmzazpHKpXC5MmTvaTAvhTl4hgSFnpfJZfEiKaatitc/4s+kXm94/STuTZO8UgeAKS0a9FqFMoICS8ec56zIub4/gqB+VQ0g82DEbXwKlnfQqiDOH9P5cqWLwlZ7DzSxU/0NBFjRYoSJr/5d5is9vR4nTokwi1kCyIK1Dk21+ELQuX3HNXec4SfEHShzFMHSKxUBCDg6KW+idQQFS9ahoN/Nh6Jw8ncliv7hXj/1XIWe7nl4fBHf5hk5BhcgvHJPzxOvr819NplFvfs62E/UT/GjRuHTCaDa6+9Fs8++yzef/99LFmyBCtWrEBHRwdyuRz0mKY4lTAkolwG4ku2DBuAAVRxltaH8uOU3v8PXj3tt6CSgMRoAWYh/vFJGyMjv6z0I8lNImyLQUwJYIIA4s7WxaZRTnMHQqD0rHIiH3wSg2Tm0ZEai6TeAQCY9JFTNIjKCuxiASDEcY66j3HlSqpSVYVdKFm4gqZ50SpcauHrqaoEElTE5iavYh/1TRw0lQqERzJmwzPElSCZ60zxyE9G0bePq0NDgE4EiAhOVvWQdUFIQrWyFd+LLHj8sH5epBoU2y1HHApt9Eswkq+9HtfKDUFx5BaIgbh7P/wkb4YsdEtJBiJfLDUJ4pPWSJUqi7aScCoq+vqvhksNM7n0NMZr3vjPaSua92TAz9ffkgsTRRC9dil0fSf09957DwsXLkSxWMR///tfJJNJpFIpr3+opmno6enBt771LRx11FE1HXODsNDD8CcXxddJ7x36a5x+Sx0AqOAc87Xv/woAUGgeE1ifT48CE0uhddlkjJVuFKOPqj5Njkec+MEta6qqpQJNdYJwaz7mkT6+4JiBTd9/GBYTYIQsdR0KilChs6jVq4cCT02E9G5S+T232su9j+zvjzWH89nytHoMPJdtDKrAEFRPmgmDh0WaIT3eX9PGphIsX0kCJsqwlOrROOXgNd12Jw9bUiOFyvywEo517mnp7jViKQmkP17QrwQZ1suZKIIpCWQ+errsPr1pED2E+BwjR47E4YcfjpNOOglHH3009tlnH2y99daYMGECMhnnu+/o6KhLWx8SFvpAO0WLnT1QmvveNqrSxfPezy6G2qxAz5qx1rmg+CxbVYTZE7WqpISEd878HTa72tHhCbPBQEFhoaC2QDKyEM0CDNG56XmEC4CABko1DXah4GjYlgUilwpyUU0DoRR2LjjREVUBc+u2h2u4Cy0tYK6VzutoCz7rnGgxT0GUeFY68csvVPBq05hMBBhACINEghayzhTIJGit6VAgwJdZCjVguRdIAiorfSd5koTGqtdQ9+8vkZJVmiMpqAh+T0WigYF4TxOsyoXrt8j9r3VRg2gFH6f9US+GnIRg6p6j1JKTEacpE2UQ3XQs9hjdmRHqFHLzTba2ogX7rSoaaNH5jJ52XkGW5A5aW1SAhU8Bm+1Sdtt6wASp1CycVnbkc9TbH3QoWeiMMcyaNQuzZs3q1+OuM0J3rNty61ivLF/xtguqb+Si2NENqbUZ2iNXI//V/6v7XBy1DFNURSSHa7AM27O+u5YG65CowxXYRukmTLSqsHTbOwkDDfTWpLYBQ0pCMhyC6lFboZg5rFHGYNOPHq/7c9CEVmpw4APhRbhUJfA8TWJi2Uv7yGCGDggCqKoFnhRIIukQOw00ksXkDx7AB1MO9RZxa51LLSIxUWAaZKLDdh8kLSbAggDZR7ompACpV7LU8yQJCXrs+7DFbzG3CBi0wD4cRagBiQioIXQQjtPUEkQIzJn0TUGGbJswpAQES4dNpYDcEgYnPUtOgNombDlRsWSupSYhhMpGWGrSq9gJuCRfxhFpi7LX15VaRsRp2Z8EGdfI29TKh8o6kk89ksvgd1ji4HxnGAYWLlyI//3vf1i6dCkEQcCYMWOwww47YPPNN4ck1ffkPCQs9L5IGamJ49DzSeUWbf2Fcs04wj1Nk8OjFmvT+DQ6Pw8WglKbFRQ6gqRgWwwfff+nnpUehimqkMy8F+qnsLwjtwBOskixABAKqiXAuOapqGD5aNox0TQwX6QLUUvdb4iqBtYF9nNllkDXGz/4TZ9IBslGTTh3lS8LkZDoDWaDQGcSRGJBZzJsRiFTX1EtJkNwRXmTiRCJ4RFygWlQSR4GnDHmWQIayZV9z7fnKNha5GmhyFQoxG1A7fv9dShOJA4pInPjhSWyCDVlJoSAigK6vvHz2A5NupQIWOv+AmPcUuewpASIPzKmApl7+8ia11TbWxYi9dLxVQjF6LUSB1uQISx5HcboaTVtXw6Z9+s3SICBjXJZV5g/fz4uueQSZLNZtLa2ur1RHWfoUUcdhR//+Mdoaqot6AMYMoTeP5JL+d6iDozVHRCbmvtwhvhx2lbpKmkal4ZZjNe8msankV0VHZ/a7Mapy7RkpZcBl1s4Ri15mQ8iOFJO5qoTzsabbdic2Dmhalqg1gvVEt42YSmFKCpYsQCiJrxJhHe9IZLslGLlxwonrfgTuCSnKcOUJf/GwvEHeIvFUAijbkuQafUyyAWmQSRm4L3gOxYn73Lvw/sbTPJI3WYOKedZAgqJOuxG3vpL2KZVlswBgFAKZjNkbr0EoBSFo38AwImmEZjpkbkuJb3XNhVhy6IX1mgLImxBBA1XWfTBkjQIRvz1b6opCHo+2FjbF9XiJ31LSQSeDm1RATWLMFS3WiUVvLZ8ANDcnPZa8/Wm1y6TZEcGcq/hcAJTOfRGQx9KWLBgAS6++GK0t7fj+OOPx5QpUwA4ZQTmz5+Pv/3tbxg9ejS+853v1FylcUg4RYGBzxT1Q3vhzl7t1x/t8sLWOydz732TAjklY8kZZ3vLCnIGRTnlpbubVIJsFdAtDXMyDP3NClwiJYmkQ7Ih0EQy2HoM0c5K5TotBcDPKYccmPwR0X9TUuJY64DzJXKyoCLa1jznbWYyASYLXri6Lbn/QyRsK44G73tfDv7t4t7HoceKOh+LTEHedp6MRt31a4y49TyvZLB3/fo6ohNCHNKxbceHQSkIJUj84xonXt0Hf1SNHgqbNOTo72GJCgw5CUtKwBJVr567JWmwJK1U3913X1mhMMhq7/nxyoERCmKbKLz3AggB0ukUWlubkckkoShyXfc0l5KM4U69k9jKkuF91vMolzvuuANjx47FlVdeif333x+bb745Nt98c+yyyy747W9/i0MPPRT33HMPvviidgViSBB6byz0ap1gNj98d4hqf7cDi46Tyy3p0RmkR5f0Pidssn7wQllUFJBXW1BQgo9bXGrJhxtD+C3iuBjwEIgaJXEaJmfAa1kW/h+BVub8hMammMOyQCwjEGMPOBaxaYswbdF7r9sSTCagGCL1MPmHCd7/Pm8Fx523VFi+/fN28H3cPhwj77oINpemKAHxSyuuJUUFwVsOuL+rbYPZDMyykL7nCjQ/+BcApbj3cCmDcCgmt87NGIKPQ2y/VClK4rwFn+0Liw1vZ2jOdWgJMkxJ8yJlAKchSC5XQEdHF1av7kA+X4QkiWhpyWDYsCYkkxqkMqWXvdrvpgmjdWxgXSX9HFj/CX3x4sXYZZddoGm8Z7ENxpiXaDRnzhysWbMG+TLSZxyGEKHXzui8PVw1TJizU2SZ2dlRz9ACiLPQ/UXBau2S1DQuDTlZusCVtBr4DwC2aaHrFz/13hPGvCgJnmwzfvnLpcgAwCHP8KNZBWs7TOqlAYUyAsuReLrZ+c8nAq+WtvvZRDG2yxJQiqggho62Nc85Dk8foTKQwHvdJfiiLcNwidpyLXpO7GECrkT4cchZmndcDv8xLUYx+f5fO3H17uN7uKkHwMncbchMqdPliZO7j9SZaSH9ULCheLjoWDDyJRGw1mkNGZWWlIAVOqYlaZHG2t75RMUr3VvJOufgk4u4alFpnIaJnp4c1qzpxNq1XTBNC5qmorW1Gc3NaWiaCkFwvg9edE73kXnEOi9Tmnh9jnIBnMqOixcv9rojUUpBCPHklc7OThiGUVe53nVG6JW+x1qljHB7OD/82aKT5u3hHTiO1HuPvmv9ouLcSJmxQcvbT+bcSjfyMZmfzITIDBhMLjVn4Dc2l1I4sXJLOZEMWs2+mzkQf+7TzImaiCdyVXMaE9cDnzXHFM0jc1uUwQTRs9IZI7AZDTgeDTtK6obtixGPsao54RuWW/rW3S9vqoH3OdP5vIaP6Dmph48JAJPv/zVswyxlxFIKIjrkTUUB1H1dInMSqBfPSZ1KIoggeAlcwx69ybPSuYYeyVZ1C42FSwUATuy6JallLXebCjClhFdDxlnm+w5jSD/2OKJzzXEd3t/QO65MMeAYa8Wijq6uHqxe3YHu7qwrzyTR2toMwJnUiW0BhMISZOSaxsYeK4z6o1yGllN07ty5WLBgAf7xj39g9erV0HUdpmmiUChgzZo1uOGGG9DW1oaWlvjCfHFYb5yioihA06q3h6tWRhcA0LkWylsPo7j1/nWOMxi2mDvv2wAccg47YwWJerILqeCM8RO5H1pLIvDIbggKGIhTnpVQjOr+CNQswhZlUH+vSY64GupJV6bxd2NRNaDgG7umVWyCEQs+kRi6Y7UbujNphNqYMTUU9eKCUQHt2ZfxXmJHAIBpB+0Mwxa8aBjdFiEQFiDygiVDFeJD/fKmCpGaZd/nTA2SEJw4s6YKRTA8h6jNKDb918WwDTPQYJvLK4wSMN81SUJyoN+KDxc6Y6aF8Dfil16KYgJiKDLGojJAAcKsgPMScCxmPiGKZtCJa0oaRNdpagsSbEGCaEQjWixJhWAUvP81o2MJ0Bwt7Rw4tmUjlysglytAW/o6KBB8yuRjdeWWXGJ42WOt71Eu8+bNwzPPPINzzjkHDz30ELbcckskEgmsXr0aDzzwAHK5HK6++mqkUrW30RwSkgtQ2SnKJZa62sMNWO++6iZ66+ajMGzyCIxoH4XWzcvXXvFb6Uq6ZPUmhjnWErNtZC/4uaebA6V0cn+ssr8aXmyZ1DDCGruqBftJ+pfz/+F62/x9meYbYdha6KJkthO3bVuw3aQSixFYLPr9WkzwNHXLFqBboke2HH6rPW8qnnXO31dCzghOquFjb/nEr0EkCUQQQF2nL7fSeUkFKkneH1/Pt+ETur+Fn8Db9InOdiMeuQ4AvM5N4dIDnOTDUU6VYMRIJmZoGa/BHm69x5/+LEkNtOnjma28AbdNBG9M4cml5nE2VahPVAHru4aeyWTwhz/8AccddxxWrVqFf/7zn7jxxhvx4IMPYty4cbjmmmuw++6713XMIWGhlwMhBMmkCtO0IhILAEhT2mEsinYWCWPk7jui8413A8toT0fd4wk/SRTW9gQcr6IqITki6shp3XwUVn+4oq5zCZIAy5d4xEBgEwEEDJn8ShBTD9bwICSaYSerQLGMQyWRBHK+OGQ14XS48VfaY3aQyKu0L7PTLaCmDkiyl1Iesb4IBZjt1Pd2G0IAjpW+Vf5FvKXu7H3eSnCkGAGUuB2YGIHgi2k3GYVISgTDJwTAIXiJBg0D/3q+jSIY2PLZy2HZDHaoWxOXxZjNYPuLolECgtLvwKUVfyeouKYhIBTDnroDX+79TW9R2EnqJ3niyzrluQlxMEJ1YYBQnLukQXKtdlNOVCTlSpMJI24iXA1Wuh/UKMCWVBSSwyEVe8pu19raDMMoNdbmfrf11UJnjOHmm2/GrFmz8Itf/ALd3d1YunQpDMPAiBEjMGrUqF4dd8hY6GEIgoBUSkOhoKNQqK/iWDkUO4KJPcLHz9e1v1/r1y/5v0iVx/TYYWX3bd18lKefB/bxRcYoaSVgqQOuhHTJ//PIPFzciWcn8sp6Xr9J7vBUtNJfGBFL3aejxt3YcQ0RtGTZcqsc3Dr3Gj/wsTCn2QOxLRDLdBovu98vt9RNm3oSjJ90dct1krqWuGmLKFqSp7n7tfda3udM2TsfR9ZUwEwLRBKdxtk8i9a1wrmUQiXJsbR9EUr+tn6xBO59ObbjILUsMMPEqGduj6n2GP1+DVGDIWpehUZD1GAKimdBexMlEWCGiNgOTRRxlryfvM0y9WgsQYYhal6xMl3UIjXly0Fe+R4ARz8vJFpL5yrjiHWiZwqB6BlRFKtGu/kxlGq59PT04JJLLsFLL70EwCml297ejmnTpmHUqFG9rgo7JJyiYSiKBE2rXWJJTRznvR530F69GV6NKFnoZi8mmaYJrbHL/SQuSKULNDHcIXtRlZ0O88yCYBtecoctxUsJLI68qRs+WCa6IQJO3rIaaUbMtGR8yzP/NuWiKFzLPA7UNrCl+b8IqXOYNg06SUOkHkY+RPA5Uy77HiiROscOr1wGxmyvrnzpw8XfbH5JBvD1auWp86LgdIjyhzOqqlNjXhKdcgu+R0Bd0AKVHXVBhUkl6C6Jx1VuZITCFNVI0S/d11zbphJMUYsQPRAkcj5pAEFSzynNsZ/f26/7y4rrA+PKlOQWTuYFOY1cYrinn3dITuu2cPQMYwyKonjRM4mEWnMCzmDDsixMmjTJK7wVlpwp7R01DykLnZBSe7iennz/1lreaTsozelAKzox21nXMSoNp2XzMeVX+rebPApSIkgccrJ088mpeGsocdUvYBMh4iDztybjVnq5uhxAiOwFN6wwJv4cQNAi56TuW+YndSvjTFa2KAfqePOKfXD7YTIfmdtywqn4J8pgouw0Sna1dO8c7nfut5xzhi8JxwzewEVTDJB03qwvF4GT+sz//rZUBoGTNKWgiuzT00Wvo5Onl4tCaXsAIi8rTKhD3L4bN9zrlVkWYFkY+9+/BZZbVIrUZDcExfvj3ZLCnZQilRzFUFinG5nCLW3v2L7X5erT8HNxWYg/VTBCYRERuRruLWrpMJQUQAhMKiOrln/CDcPhBhaInmEMSKcTbnJTCqpa+r5r5ZKlS7/AWWf9P+y//97Yf/+9ceGF52Lt2rVV91uyZAlOPfVU7Ljjjthxxx1xxhlnYM2aNWW3F0UR06dPx+2334758+fjzTffxEcffYSlS5di1apV6O7uRqFQfzOeIaWhp1IJFAp6zU2bw6i10YUf1hdvQxhXey0KQgjsK35S93n6AmbbsIoGGAgES4dgBkvlWm5XmjBsJRG7nPlqWwOOU5UUsmA+Yo/cyL20GABHBvKfD3BrfPuLf9kWIAhgVMAW5F0sZFuW9neji0ybQqS+ZhEWdf8LMACoopsmbxNQWjp2wAo3JCQkI/BeFn3fpU2x7VtXAKoKq6sLVJK8yBYujcSByzGcOIgkBUoqRLZPhKKJbAaiyU4PVsPAqNcewNJtD/VW+2vABLX04A3PiZaHPxqiAskX7WKKatn49fAEAAC6qEI2C9BFNVDr3X8u7yMQwXtqKFf3vXQuFYrxZSR0rCA7VVFNKkWMlyh8WbCWjXy+gHzeicqRJBGyLKGlRcNbb72FJ554HLvuuismTpxatuBVZ2cHfvjD78EwDBx77PGwLAt33nkrPvroQ/zlLzeX3W/t2rU44YQToOs6vv3tb8OyLNxwww14//338fe//91rW+fHmjVrsGDBAqxduxY///nPIYoimpubvVrosizDtm1sscUWuOyyy6p8DyUMCUJXFMm1yrOwrP4XuZheDNQlMTs7IDY5sZ1ysQs1xs2AMRb7KKSNaK5rPKnRLehZXn7Wl1NqyeLzxStH9XPfzUwFlzj1QDsy3iWehsLPwiTL1CTgxjjHWWW2rIGGCjwxJQGiB5skEL0AW1ZB9QLMZJPjJEWpuw6xTKemd4xsQZkF23Z7a7oETt3mF9xCzxsiRGp7ZA4Aukkhi8FlfoQngpwhQRJK73VT8Eh99w+ucJycluWROXMNDOLGjzsf1m30bJhBq1sSvVZ+QkIDMy0vmgVwwhQFTYs0HOENQoisOL+5G4qqUzVQMtgQVK8/aRiebg4CQ1C8io4FKQnZ16aPkzTgWONewpqoQTbz3n//9s65lcATlkEVSHYReSnlkS/PbiXMRi7biUQyamTRNZ9AtAowtGbk5UxkogCAHqEZzfbKyPJaYRgmDMNENpvHiBGjMWVKO/7973/j1VcvxogRIzFnzoHYZ599A/vcddftWLnyS9x8812YOHESAGDLLafh9NNPwcMPP4CDD54Xe66//vWvWL58Oe6//36vd+g222yDE088EfPnz8eRRx4Z2UdVVRx55JFIJpNYvXo1uru7kc1mkc/nkc/nYRgGVq9eXXef0UEn9GRShW0zmKZZqQxz7+FaACyfh7bddsi/+mqvDsMjbji0Ec0oru2GnK49i8uP5smjkVtRIvXU6BZYYa02BOWa88BO+jEs0bmxwmnzgCO7hK1hEAJb1sAEwat9DThkHyfPcPLm0gn1l1p1l5Ey8clVGxj7wAgBYQyWqHoOU0YoBEvHVHkh3ra3gg0CCgabEdBQZUbDogFiLpgiVNFE0RIACxBpbcaBaVOYOnVI3bYcyYRSxzLXdVBFDkay+MsaS6ITrWMYJaeoj9Q9CAJgWRBSyVLMulsz3uv2xBiY5SQuEVHC2P/Nx+fbOn0rna5HNkw4xg9xk6H8re78vVIBeO3xKLOgCypkq+A5Lcs12NZduUUXtbrCELlFbRMKymwYRAGBje5sFulk/DXRnRodOGccuH7eF8iyjJ12moUDDzwAnZ0FfPHF51i7NiqHPPHEo5gxYzuPzAFghx2+gk022RRPPPFoWUJ/8MEHseOOOwYaQc+aNQuTJk3Cgw8+GEvotm1jyy23xF577RVrwfcWg+YUFQSKdDoBXTeRzxcr1kvvNcIOkqxTEz0M64u3Kx5GFJ2Im3xej2hx6rD6ZR4xEXxUrTYpKE1JyGkNouaXROxA9xreeCBC5iFwzT2uU40/5dqvg3OS9i/jDYOZrAZI3KsL4ssG9Z/Pc5a6lp7lWn/+pwJbkAKWYNFyfseCq5ebNo1Y47pJ3W184YmG4K3L6aJPogm+59hl0bVOlq1lOZa5rpc6MgEVE66IJAWcvULS/T1EIdKDFYDXzYnG9HzlWjoEEePffwwGZBhMdsjcV0WShFoi8m5J5drx+aNluFxiUgm6oMZG0sSBTxJxvVT5ZMG7SzE4Wb+d2eCTnSnIEIwCGBztPE9634WpVvhDHMeNG49p06YH1nd1dWHp0i/Q3j41sm9b21S89967keWAk56/ZMkSbLXVVpF1W221Fd5+O55bnn/+eZx22ml41TUwC4UCDMOAaZqwLMur61IvBsUpKssSEgkV2Wzep5f3rslFr9FZ3dEBOHIQT2qyLAvZy38Uu52Z8/XDrPFRIzNxdOC9Nrw5drtA8+W7rglY5uGWZJaSgKUkYCtawGHqh5/MPYLnbcZiqtxZccuqWOL+OiCBiSeUYu7v+GMJMixBhk1FCLaBduVDj3Q5l/rDGQEgq/uyKs3o5az7lvm3Db/fa+kNjuVtWYF677yNH5XlkgNULv1xEieS6PzFWFs88oW6lqpnyWtaZSvGNADT8Bp8cFRqpMEjhHh0jNeAOqYhtl8DD08OQKk5ti5oAaesn8xztNQJzN/82waFjVIZh85sHl3ZHOzOpc779LjImDix9wjNAGqxzvsvBn3VKicyZ8SIaJJTa+twZLNZ9PRE4+RXrHDyS+LixkeMGIGenh50d3dH1jU1NQUselVVIUkSRFGEIAheXZd6sc4ll0TCsQS6u4POuv7uK1oO4sTNYH7yUU3bcjkonNTEM/+Ulvi2doRSNG8xCWvfqe08cZBTKvSeApQmX09Jy4IQKkrGQMCoACY4nXCIZQZrWSuaI2P4nKNMFAPdYfwda6o1OLCURGQ9bzgcLr9qCzKo24WH2oY3kfD3plxqnWaKUQebYJtumj8JRLlErHPfez+pC5RFEo7C+2Z1EYpoO8QtSs5TXbHgNNvWi04TD5/cEp6seSp/3CROZDlQviGynss6/Fg8L4AQxwktyYAoYeInT2LJxD1gQgRlFNQtFkB8RQOYS/oC3IqMbqcm6tumQEsdmvwa/MhX/uUOwElO+2I7R1ogjAWIPBxpw+En8qKtQiAWbDjj5IQekIYsHd1iiztuZ32YzKuh3gbVTgx6+R1yOeeaVmM6cylu7aJCIR9Jw89mHTlSi2nDyPfL5XJIp4NcMW7cOKTTaVx99dUoFAoYMWIEEokENE2DLMtQFMVzjtbDi+uM0AkhSKc1N9MrKvT3NkQxLluUJpKw/VmQZUB7OgDXaZNb+QkSIyY6yylBMhk/ViGZ9LRuqSkDsys4azdvuZmnsbZs5czAHQsXO8eNKSEallv8BO4PYeTOUaugO/0lmQVJr/4ZuXRhaWlQ3df1vULbMQ6/ZR732pJLMeW2Lz3cFuM1QVPSSiVgfRa830r391EFgKmJj/BGd1twXDYgUCBnCBGdXDcJZJFB8C0vmAJU1+mpWxSyECTfvb68xakMme1xfjubwdaLoLLiNQqpxh7+7k00mSxNAqIImGYpPt3V0v1SC02m4o9vW4AJQJIdMveRM4lUgHHAOzfx78+AHGmhZ0KC7K4f8fJ8MJQkIAAY9/r9gKJg6dSg05AfK/aYTPSahPhbBgLwCF6ABZNKUPUuAE7nqXB3qFrR32n/PDywEnfGEWstYYVxgRTvvPMO3nnnHRiGgZdffhmJRAKpVAqiKEKSJGiahq6uLnznO9/B0UcfXfUcHOuwpyhDNpuHXUaH7KuFnpo4DtLUrYC1q6puW6lrkSSJUFWnvnM93VfEhILkxPFeRIQfzVtuho534611tTWDwuou7z2VpKADzge5OQOjOwvh3hvBDj0BpqS5RZQ0UNsA8XWzieteY8sJUD3nWcrBLjVJCMWs+7p3jl4OUy71sSxqLRDNolfdj3fd4SFujAqwqBRxwFlUAgOBaOmYlvkYb3dNBuBIKAQM/KcxbQKRMhgWgSS4BbxMp7GEKpUiX3RPPycwLMHb9qtdt7vShunUs7GZZ6Ez03AkFJeEnQ/gGyd/ynGbefhJPRy2SBS11EWKW3OWFW/BM+acR0s6YzN0TPrkCXy86WxQYsOCABKSYfzWMAOB5bu1/QRsQAYBg05UjH/xjui5Ac/3NPbDp/DJ5nMivVP5ccrBT+4APDJXbef66tZGQGel/XOWhoTgXIfdZgppMWQkJaNWc3+n/Sfcp6NiMfpZ+bJETJ+BZLL6fskYp/DYsWNxzDHHYPjw4SgUCli2bBm6urpQKBRgWRZ0XcfKlSvr5sR1KrlYVqWqiv3Thq5eiNlO6G6hoTVrV2LC+E3Q05OL/fGVey8rYxdVR/OWm6Fr0ae9H6gLKZ0sS/iWFIxMsCQNNFRxz5YTkfoq3Lq2lGSklZ1/YuCvLTkJwa3S56/gF9yvfKW+sLwClGqBhJNfbCpAYCZMq/wNaVjxF07BoHDLbiOvU2hy6bvJ6xSHmH9zCFOUvBozKBYdYncdov6487CswvXygGySTJZInevpnPBFyZkkfKGoZcHJQ1GdycS2MaHjTXzRMi1W7+Z6NS1zhfrb7JkQMfHFW+LPG8rwnfjJk/hk4t7O+MGqEjkfG689LxLTsdSJo+OrZhbLyThIbsVLXq7YT+q1oL8t9FGjHH/WqlVRg3DVqpVIpdKxssrYsU6p35UroyGWX375JTKZTKSeOWMMO++8M3beeWd0dHTgnXfewfLlyzFjxgxsttlmyOVyddVA92PIZIrW2+SiL7DHTSq7LpvNlyUOu1Aix7Dckpw4vup5m7bcLHZ5atNglqnS6sbIN/vqvAxr8iQbQVUdacItbsWo4EWLhGFJGkwlFVnmvfZndfqOUa25Qdi56a+NHYYpKjAkzUuI8ax1IsAUVDDXcRcu/kTAYBMBNhGwzTBHttr0Z7thwv/bFRP+366esWy6hN5T8GnpRvRayutR5yJTEg5hcjJnTqhioMlHFfKN6/QElDJM/Rmh1E8KggDi182BaO16wKtoKeS7YTPqORz9f9w6N5noSR3hpiEmE2FBwKSXbgtILKXBxafNb/L5s7GTiOFq55y8Dff4flhMgEAsKHAmdy/hyRbRY2iBsg3dZuk6XV1sjh0LR/2EXlnWTafTGDNmHD74IFrsb9Gi9zF16hax+2UyGYwfPx7vvPNOZN27776LadOiSYuc5+bPn4958+bhpJNOwtlnn42bb74ZH3/8MY499licdNJJ+PLL2ksocAwhQu8np2hLsH6yvdX2sLfczjlHmVZOcrEkeSxf0xW7jR/qhHGB9+mpm5ffOHTjhEMWvTGUCV2U0vFEKT15L4CSFm3HhSH6zh0uelRLNxq+De9TGd6P963kxzalBEwf0Re06oX5wxUFvWO76eyE2aDMwtrvfBObnrlHoJnEZmfthkk/383Z3iV13STQTV/moU5Q0KPX1SH2PWCCCOJ38HKLWlGdJtiKCiKVIlqoqnp/Xts5txian9S9CBiUSJ1w/4noK6/Libuc7OJG3cC2vKSxTVe+5DQBCdW5sRkNlP31E7n/9aRX74wvLV2lgTKXSHQme39AidQ5DFv0GohwhDtF5UwVObN8mKSf2MthICot7rnn3njllRfx6aefeMtefvlFfPbZp5g9e7+y++2333544YUX8NFHJVn1+eefx+LFi3HAAQfE7vPSSy/hkksuwdixY3Hddddh4sSJSCaTaGlpwa677ornnnsO1157bV3t54AhRegDUwaNxz1bU7YOdrFvqr0LCAC8v6J/sp7KWfJyKJ7db52XI/UweO3qcA1rDpuKXqU9yyd7mJLmkbIlJ2si+7IoMynztPKC7NbRplLAItfdicCJTS6RxJofnYq1p/1f7DFFRYAgUWxx/u4Bi9xwCb0n7+rnAYKn+Cp92BmqZTrhmpJcanrNLXNFBSqk7hNFjXR0CpB6jXXiA+SaTJX9/ojpRAkR0/CsZU7iXiMO11oHAAuCZy0HrGavtonPwVqmWJofk798LqB7x1nsfui2BMMWvSbfFkSIto73WLyl26XHGzRx+rkz5voqJzqOyco7HHPM8chkmnDaad/HXXfdhltuuRHnnPMztLdvgf32c4j5iy8+x3333YclS0pt8U4++WQ0NTXhm9/8Jm666Sb8+c9/xg9/+ENstdVWOOSQQ2LPdfvtt6O1tRW/+93vsPvuu0MQBAiCgKamJvzkJz/BCSecgIceegiffPJJ7R8SQ4rQ103YIrJOTKg+atPAYkUvySdLVgVnxfdX2JjxxrUQY1pBaVPbIsv6A4HY85joGJrwVcKT4hsMhEk9bMWbbsf4WsAlFb+0UrLMy5daDRd+CqzjhZ1cMrfdR37+ZNH1s9MAON2flJQMSZMgacHPwENIZ1y0m2el++EnetMiOCT1GKhlgIkSmCQ7NeUZA3wlDGKbfZSDLJe2F8UIkRM14U0WJO1O0qIU7bUa43BjWhJMS8LWnJA34o57QsebgXrxDCQQq+5/7Sf1ya/dWfvncsdpizKYJMMWFWza9aa3ijfs1m0JRVtG0Za9iSVcy14llbsehcmcV9GsJLsMRPu5lpYWXHXVddh88ym44YZrcffdd2K33fbEZZf9ycvmfOON13DGGWfg5Zdf9vYbNmwYbrvtNkydOhV/+tOfcPPNN2P27Nm4/vrry2aBLl68GDvssIOny+fzeSQSCS9qZp999oFhGCgU6ugYhXXsFK2cDdq/TlGaSMKYtGVgmT5xS8ifvAua6/LCFcvh45UGJo+QKlrmYqb21lB+pKdujvyn8Y1v40ATGuycM8nIw4d5qePJf9+Gwr5HAXAsYH/CieCmgRtyEqJZuih438lwyKIpql6jA0NOQtKzHnmHwyP99bM9yz7k6KzUDMEUZNhlrEKekt71s9NgFi1ImuQ1huAILyOUgNkMMy/ZHf/72YLIMZ0oU4KDhr8AFG2n9Vquy6tdA8CpJslJnYcqKqrrJJaCWaJ8fZlSrZzUq1rpVCg5oQUR8EUpsUTp2iK2BVtJwJZVMEEM1DP3EomYn9CdZQIJXbuS5Dx1VHPIimKpL20I47Pv4fOkk01ZtGXPUudaeRhOxI0AAZZX78VmjsJjMQE9uuSFlNaD3kku1Z+yN9lkIi677E9l1x9wwFyccMIxkeWTJ0/GX/7yl5rHk8lksHz5cs/5WSwWvbBFwElYMgyjrvZzwJCy0NeRUzQZnwwEAKoZJK4Pv6zvQosLWawH2oQxkGqdJGwGobkJJpUDNbM5/M0OeORInM7ut679RO23xOOs80qzb9hK5xmJeTnazYmXXbWJ4H2Wwnk/hZRQAta4HSraFrbWJU0CFQXs+AcnIiObD45v/1GvQjTyXoleJslgouKQJC8N7P/vdxCGQ239Vrl/mfc6xk+Sbnb+xxElX+eCJaPfEwAvQ5haOsZmP4jdxvI5SC1GYTIBJhMw5e2/xW4fgCDW1LqxaJWpA+Nq57rllDDWbRFJwfFRCDCRE9PoyKvoyKtYm1fQo0e/i5XZ2uTF/naKrmsceuiheP755/Hggw+iu7sbhmFAURTk83l0dnbihhtuwOTJkzF8ePmeqnEYQoQOAPUR+tqJ2wNwkot6AzvVHFkmk2g8qR/iuJIGLo2trTt5HLRNnTZdYsq5gHntDz+kYdHxAaXUcabryDxzj7OszMUaJnXAbTLs36YMqVdCXEGlcKeduGVcHw/3zAQAiziEICdL4wtb52FImhToBGVbzCN13XD+Dp3wKkSrCEYFUNtwaraLMnhfUxKQW2qToAA4FjzX0UUpSOSyAmiJePlGS5aIPeEzMOKagjDbGadryRPLBBOcSYkSJ/acW+cmE2KdpQBKE1Q5UisT4RKHicZ73mvdFgNO13CzEf+Tw7trN6l43KwRnAg3G1Zeblif288BwNy5czF79mycd955+PGPf4yuri4888wz+P3vf485c+Zg0aJF+OEPf4iWGJm3EoYQofddcim2VggdZAzU1JEfMwWAE3+ebd00dlOJBp1hM96/NbKNkClv6dcKTuaVwEmdJjSITVHLjcgyTCH457V643U8OKn7aneYohaRSYB4qYQvi1uni1osuVeqoBeuo20R0asPov/ydOjZylUnBSl42fKGIVQggckAAA6a+JZTbtYyPFIU9Hyg6mRsCz1FdUlaBRSl9BcXDeJ3jqbrLNYWsogZlwJjJClL1mBLCohlwBYkjMh/BpGYIITBAgXxlThgIB7RbrGwinVeJcIlDhPMj70680VLim3unRJL33G4EiQQLcOQ02tXgNd3QlcUBeeffz5OOOEErF69GpMnT8b//vc/PPDAAxg7diyuvvpq7LVX/d3XBr18rh8DJbkwt8YJAAhmAXYi/pHWD4mYMCDCm/NsFnBc0VFjgWw3WA0lBuJAFBXy2LHQly4NLFfGjUXxi6UQm3o/YXAd2t/IoCglIVnFiNYOODW2w02GOXnz5XGkrse81kXVc2r61+d8da8NIkNiOgpCEiJzJk8LIpTfng4hKUPP6jALpUlVa0mA2QyEEmRXlf++pYQMZjOIqoS9bvoqEudf5n1WS5BBien8/qIMCMyJ5Wc2qF70arlDEJy/clUrOflXKZvgDEgGDN0heUP3arMAiB6fCk45BsZKSU4ArAQn+NK9YQsyBEsHIxQq8sgh6RYZJiCEgbHgf4iSm3HauzT7OJiCHAgaKVoSFCH++AIsdJLauxHVgnoJujQBDEL2Yhmk02mcfvrpOOWUU/Dll1/CNE1kMhkMG9b772rIWOiDAaXQAaCGVnThiIQhAGHYMAipNKiqovX1f8fGc4drXhuCEliml+kfWa4dWV8RtsyBUhEpABCUqAzDyZwjOTz4W4iqsw+30onP2qTM9jr9UNspWmaJKmxJDfRjtV2pxLPU/WRbzpHGwx0BhzD9VrqiAlV6rgIAy7g3rs9KD1SfTPisfcYCjmxelVIxc6CEpxaVvifeUHurD++JnreWkMVQhAsTZV81TOc7HysEjZGiJUG3Hf08KRYC0S6fdsX30wWcWjtfdpd+j86CUlFuccZdnyY+lBpEhyHLMsaPH4+JEyf2icyBdUzoA/mFBnT0luHIt+9QdttiU6nU5aoxW8OsEvHiv6ntjvJ9AnsDefMpkWXKuJI2L2RKTxM0JrQNgGf1WVSESSVYRPTJLTFlU0UFhiu3VJJGgNp0cQAoCqVlvLZ2XI1tnbrdb0hpXAZRkLr6zMB2idYkEq3xn1driS6XtGifVvPy80CZFYnooXreqWHj/q5UD/pNmKyWSFpSgn+RE/vOm6rw5MfLE5eJfLG1VEDHtrQylTxtC8StlChYOgTbgIo8KLFhMwrLLmWHMpCy0Sp+mJtOLen3FSJc4jBKWonRSjCjsUVxQoAJGCixIcDE8rUiVnREdXrDoviy0/lOeoq16/jru+QyUBhSkstgQi52oSiXjzBho8eDdFWuoU4kEWTqNoHHcfud16ueO84hWgk045uAyhU7AynV1RBkL0adtw2LA+9qUw5FMQHFDJbOLQoJKFb5crthqzyuYp8JEbZpwcw749JakrD0yvKA1pKEkQ/qspImw8jr0FqSnjPVohIonPIIUrHHaXMnKV5RMsCx0KledLRpUS5fhZIQh5hrkFuYJIMYOliqGcRwPhfzPenZ6RbPwRmureOdqwIDUcuAISc9UheoBcproDPHXvf3UvXG7AtZtCeVknyMTdrBqAB55WdVP1scRqurYTLRfU4IyhprrZJjb0WHANsuPZTIvWSgegl9Y8EGLbmYFeqLdI9w6qpoeinV359cxLHV8kcC72nzMGBStKsJAIfMQ6Bbbxd8H1NvWRgzLrLMD7GlxUtqCljpbswqjCJGLHo2YJnbRPCiRiwiBpoJGFQJdJ4JW9K8gw1fXhQTnlXO/+uC5lnl/L8uaL711aNFeKGn4Tf9ovRdyCXr0Iops+xH2CoPwzYtmFddDAInSsSS1Ejxr8D2YTIvE6/N/KGOohS00iU50Gy7FlhaCswnu8Q9MZpKCqaShiknvfIKAq81z9y8UNdKB5zG2DOXzS97Tj+ZM9+TQWHkpLosdO94FahEpvVp99uOrSKBoj5C35iIf4Mm9FqxtDnaPorDHw1REdO2L3+Mrbcr1fKoERGSr9D+DABQ8Fmcvrh0TuoAUBCCE5y/80wlmaQ30JkSec3/+yv25Vnp6URpqqGGR4WGEQCQHOmQIXVDOyO9PeGEePprttuS6unogENwtih7xB0gcB9io2NiwFyphoXqxLO4MMUYhIurAU6CmC6n3CQtAQSOE1SgFmxGg6n5oZruATKP0dBzIyaVrWkfhjOVxH8OChsCLLz6ebSbT1/RGwt9nXZEGyQMKULvj9DFSlg7zLHKBTMoKyTsbq+Ebji5qN+w1bYDc9xMk6PdqlrAOuevLSpGHKYGUWCQoBWpkyg5FUlMrDlK2/Hekfw/ECTywPHLLJ/wjwtjl/uRGjMMqTFRZ5GoStBaklUt9eI1lzlCgG1BNKLyEDUKjjwiqxHS5WCEOElIZaxXf+QUc/0T/jwHf99VM1NyEDrWeemYZsoXd0wITLW8Lk/dTFfRNiCxoqejU2JjxrL7yu5XC3Ktm0b0fu4QNQXZ8dXE5BJE5Bajua7z1mKdA/V3LNpYMKScovWEFdE6Y2dXDY+XSeLgTy7y33wAYLcEew6SRBLmFuWt81ohTI7WhPE7RMsWE/MRzNj3nwhEjcRmkJLqj9Ox5I7K1qgOpUTwPos8jsgNW4LhFm0yurPQu+M1+DCRJ0fVlmTBo2WUpiSkpApRLeOIlFSvFjyT1UCD7XKJWkyUA6Qf6NTkO170XEEr3Y5zsPrPE5fowxOhfIlGgm3A5LILsSAR09HQw1nBbsii6bPOI2MkAmxBgk1FWIKMztbNAxEu9cBziNL60/prPUM92FjIf4hZ6LU9FomigNyyDwGUskU5KiYXAejIbAJLVCHrPVjTVKqL/qkczDaVqIHNe/4Xewyaq15iNxZVrHQhFYpsiCtTkM44GYgAkGkOrnMtqjg9M87aziEVsNZ1onpk7v2H4pG5/z9/7bfOw9ZZNYy552IAgNqSDmjnAJAcHR/mloyx1NUWR5KQ06XPKKcTAXnGvPUaAE7N93BBsgApc4lFkgN/YTBRjpJmYL1L4FXqufilDSPp9tl0ydzg1nlIFtHlFHQ55YSaCgpE24BJZafWYphEfZNUuLZRYLxlMkXXtkyuOP7AMUK//4rCMIzLxId9xrknDpxehCzXr99Xw8bkQB1ShF5LgS5VlaGWsbj8yGrl417jkBRykSgX3qlHH+5MEiwTtRCNTctbPHEwp/ZBevFb6VooMobZTvKKCxsUJiRYvlrUFkQYcPpTDgR4BT7+3/+aW+XcMi8HUVOgDvPJFzG+g+SYYV78OQcn9XIgouBYtrzOeAiOjq7GRrgwQhxiLkN6lk9usV1d3fJJLIHXvnBE0y/ThCYHQ0l75y4tc4icW+neckGBaOsQiQGBWJi66qnYccZ+NipUTftf1VSd1P0p/hyiWxzsq1Ort4XcfdIaFIs6FEVGa2szmpszSCRUCELfKWoox6D3N4YUoVey0AkBkknHAuvpyUMdFd/9B4ha6atbgg0oOlLjoMspaEZ33wZcodBXJYTraHsYOSZ+eTX4ZZfPXwTgkDe3mIp2ebnEYFKgzjVHMUYq0X1EXbCVwP/I/m5JVf46jIn3XxS7n9Jc23eqtFTeTtTckrWUgtk2bN2E8MS93vqApR6ygMuFLdqSEpBK/NY3k2SPzL1zcDknJLN4730aNLfGmU8m8zssdSUDBhpoDk2ZBepvOciCdVVKA7egT452zolziJZDOcnFghj7RLgy3wTJ96Rw0FarMHdalNh1E9iv3Vmu6wa6u7NYvboD3d09YAxIp5NobW1GJpOEosi9cmxuTBb6kIpDL/elCwJFIqGiUNBh1FnRMBy6SMC87EEAWKWOR9J2JJTlGIfR+KLssYymkRB7SrHo+TFTYvtphsFC9TqMSVtCWvxuTeNnoyaArKheapc74KhbaMofh+4HL3Oat7VAI18OncmQSTC+W7dlyLR8fRU/qceRd/BYUiCMTW7OwOxxHNG1knk1hKNllJY0CKEorO7w4mt4z1NLVCFYejAG3b0OuRUc7cGqRGrPB9aXiX4xlRQEK/o9hiNKuHVeNh4+BME2oAsaRBgY9+Ur3nJiln5fr7hXDSVk47BGG4fmYimByKJSpN1cGJs0R8MV40g9DpZlI58vIJ93rmdJEqEoMpJJDYwxUEogigLMKsXbgAahDygq1USPs9Bl2fkhs9k87Aqhe59N2Q+jOuNLinJYRITA3Oa0chMSeic0FoxqKYjOBDC88Hm1jzIgsDadAmHNiuDCUHlVAE7Cits+zU5kvMQRW1aDHd+ZBAIGiwkRS4p3Z9fdNmLcove3G+PV+3SvoYHs1dsuZ51z6JYMWXAIrGjLUNxJYfMFV0I3zEATj8SY4bDyJWd0uUbYfiRGtgQcqkpTCsXOYC6B0pz2Ut2V5jQMUXEmdV8Da6fOCwkQKCc+Rqinh/vX25IKahRgJTKg7rFsSQE1irBlDcR0Pqv+7H/AbBuEUqdRye5fBRAMRTSUNKhbcIvGJBkVlXTASUtgoyCmnbGBQLR1CMxEkWixiUrFTbYEjZlIAKC7aQJS2RURh6jltgA0qexIdxCwQp6AVmtFoKOUH/z6WZFrhiT0rzPUMEzPmBMEipaWDJJJDaIowjBM6LqOYtGIJe6NidCHlOQS1tA1TYEkiejuzlUk896iQx4ZWfZFvhQzW0iWr0XcuelM7zUt092+EgpTeqel25kyvgGfDjrh8+cAlPo9lhoIRy2qYozc0hsUytTIBuDp5tx6NztLTmUhVXuWLC8bDACCG9evjQw6Sf3WOZddAKd+ia2bUP7zTwDRbk7edlSIjw+nQtmQxrjIlnLb4oUnnH1iZBfveL4w04ISTDJiMbesLjhSpIiYSTBQl6Z0D3W3bIqe5glghKAzPQ4d6epNzgFgORlXMVxxWdbx83Tm60uuqgeMMZimjc7OHqxe3YF8vgBBENDSksGwYU1IJjVIvryPvoQ43nvvPTjmmMOx99674Pjjj8Ljj/+7pv2efvpptLe3x/598EFlw7MvGHKSCyEEhBAkkyoMw0Q+338V4iohYXcjCzfLMS7ULlMi91qqNdZ20qAcZGlBqYC5MgpLpEFyUb2fKYlgk2O+XJID9TwImGeFA0DO0iCF5BadSbAZhUJ1FCwFSsiyLlgKVMGxoLnlXbBkqEJIngkRu27JXllX3RKhCAaoqkJICjC7HWtaGT3C68jUW0jJ8jVpCKGelW4XCjAFBaJVhC3KoKbu1EgXFBBienVSPBmEUM/aBlA2ZNGS3Wbdfo392cdqHj+3znVf3Lk/8oQRAsIYClJ89rNBZIzs+AC2KEOwjICVzj8TR0+zU4s/HNbakRyLpN5RdayrzOEwbYoR8mrnOK5DdFm2xXn6ITZ2HF+5TEZfELa4ufWezeZBCIEsS9A0FZmMiJtvvhnJZBI77bQzUqn6Cl/dccetuPrqP2KvvWbjyCOPwYIFT+G8885GU1OibPNnjkWLFoEQgosvvtjtZ1rCmDG99JXVgCFG6IAoUqRSGvL5Yk36WBwWp7fBcLYCWa0VyfzqqttnacbRm93TLekZgeHi504ihXuD5hPDoeVrKMxVo+5ZCcWxU6AsXeS9NxMZSD5CtzOt3uN/3OTCiYaAeZYTJ3ZupRtMhERMmLYIkZoomDJkwSw5Mi3ZI3WOMKk7y3yOUkuu+si35bOXoxYVl0oStHGjwXzxbbkvlsduq40cBjMbnRDk5nRAxuEQrSIsKkO03FK6FgWxY3wzrtPQkrSA9m255Wv5fwCwBQXUqtwcxftsrz0L7ORIL7qS8doFAo42zX08BTkdKIEcGR6zAUKd+jTuWKlv8oFpIL/pNAhmwbteOJmXQ5c8HEmztuSe5cWRKFpOU411qWg4smyZPAHGUCzqKDp9B7HddtvjxRf/i3PPPQfd3d2YOXN7HHXUMWhtrdwJqLu7GzfddB323fer+OUvfwUAOPjgefjBD76L3/zmN5gzZw6ECt2dFi1ahLFjx2LevHm9+5C9xJCSXERRgCiK6OnJ10XmPBZ9RVM0OSertaJAgo/15Woz83ZZWyuVHZa8DkxfURjnxr7XWJ43rsOSH2aqxQuh22Tta95yv6PSHzYYdmDy5rze+Cwlsh1fVg0F37GKlhTpZFMJiU3HQRs3OrI8uUnlmjcAIi38BJ/sIjWnISSTkP9zL0S3CBl16+TbggRGRdiC4v35UTbKI7TclBIV68X4wZ8CeAepouILf/TJLtySLmedA06afZx849fkOZmHo1t4DSALIkyIWCOMjOjnAGC43YlMm8JiQmxTC0KA7mL/yHjlQAipWYIdM2YcjjnmWFx11TX44x//jBkzapM6n3tuAfL5PA499AhvGaUU8+YdgWXLluG1116rsLdD6JMn1x7D319Y54RebiZPJlVQSmAYZr86MHqE5sD7VXB08x7mRBJ0sWbEobfRAP0FFiJvY3g8mfljnP2wBRkGE2H44tDDDYV5NT5eOxsACmb9N6OfrPO+1wVL9PpMAsB2b10Nu1iyIOVRI5zx1CG39IbUAae5th+ciC1RDsR6h7fxE7b/vX85l0kCk8BTD1Yco/b6U9Hz+Ug8LznXp+3KLnkpHZFIijThJYMN6/rUW07cfITsJk6oYrloGUZIbDYxAKzGiMB7k1V+mPcnFQ2k3AL0rnSubQOJRAKzZu1a1ToHgPfeWwgAaG8PZpi3tTnv33777bL7Msbw8ccfY/PNnXDpYrEI06wvOq+3GHQLnVKCdDoBwzBRKOgDWsslDgp1HpN7zBIxFqTySSqBWhv9gO5J8RaDnhkRu7xWhKMaGCMB4g2QsOmLh/aVXOXb+Ndzws7HWN1F37owipYAZpgQmpsC0S1+CJoCZXT1zx1H6sqIIGFXarZNVQWp158IkLItSLB9zlBO8rxQl387AKW+pH1AIaZpNhDfbzVsVRdp1JlMfeG4JEQg3U1BqaUckfuxxqxNc+bcSsCwJtv/mZ5h9K4Wen1G4qpVXyKdzkANVUflTZuXhjqN+bFkyRLk83l89tlnmDt3LrbZZhvMmDEDp59+Otas6d9+CmEMqoYuSSJUVUYuV4Bl2aCUrNOKaOGY66yVQFIqRqzzfCI6o8sxpXbXFXh5Vam7dHHwrENGBc8im9T9BhantwFIiWwtRiAQ5hVx4gRu2IKXCBJH/H4JJR+zvpykkjdEaJKJXT77axnVswRp5EiwYiliiJUpX1t2fx+J+zsXKWNGwtbd35n/tpYFapuetMF/cz+pB8IUXQeqs01Mg2tR9kgyLta8HExBhmjp6FFbI303eZht2MAo0GQgx2B49lPHqWoHAwioZYAwC51Nm0BwOzZxdIstSNjVE+tW681oluO3M20aaUpdNAbeRqw3asXf3GL16spx8JqWQCKRQC6Xi5A5AMhuVc58vvxT5aJFjv/rjTfewMknn4zx48fj1VdfxS233IIPP/wQf//732OP3R8YNEJXVRmCIKCnJ+d92c7/2gldHbUZCis+qmnbAkkg72ZMmkyASJybNWslvNfduoZx2pcBf0uYzFc3TUJCr81pVCtWT5iJ1iWVNTkAKLSMhbq2ZBkY6WFOne8ysgtHPfo1R711WQLnM0WoYolc8oYI9ATr39CEFngttg4HK9bmVAQAbZNx0FcGHd5UkT1JR0inYHWHJl1BACwLzDAB1dGpaZwz1AW34KkbJcIbSvgRdmrGgcegE0kCVUuyzLA3H8Oa6fsGz0lF6IIWSH6zIEBAbZMbj27pHr+Vl/RGme1NAF3ycDAQ2KDoIi2wQaESZxI14WjkBhNh2YI32a8sNHtdiACU1c9X9cjYt622xKG+oF6L20n9d7Y/5JCvVtz2+OO/he985/9g23asccmXVTI8J0yYgFNOOQVz587FpElOvajZs2dj0003xS9/+Uvcc889OO6442oefz1Y54ROCEEqpcI0LWRDkQn9UT53RVMb/GEU3WYKabF+a3qtNhYZvXRx1hThAgBUwMJR+2CLZY9W3dSo0IADALpHTkH6y0UVt4k9ri/0bZPC+/hQ2joQWZIzZc9K553XBWqjW1chCxYM23F8qWKQ7AqmBCW0jFvg4dcFUwpmqqoJwHBIXRgxEizbx7ILfYRdKCD1+hPombEPiG1FUu79hGoTwSN1ALDcRKNylrj8/EMVI3nimpyEwaNd8kLJOmeEIk80L3qJf782FQMZy/6QxbVNE73m3F2yY5yEJ+usnYDFBCSEqNVp2AIsm2JZtgUtag6mHbXAGQi+7JIgi+sm1KUepyjfnldy/dnPflFx2yluK8tEIoliMZpfwpclk+Xv3ba2NrS1RQM0Dj/8cFx44YV48cUXNxxCl2URhYJeNoqlvySXVWQUhrMVFbfJmrxioAiR2GhWeuKTM2rE2yP2Q9aQkUEeC8fsh6yhYPs1D9W0bzgGncMMhSX6u9noSgZKPuqA8hNQWI8tmKW48FqQN5xLpBKR+7fLGyLClY13+/wmAABJZ2KJvF7rnEMZNxbFL5ZCSJSPQeegsuzJLrzZCBElJ1HHz1GuJWdRCYwInozBv8e4aBeLyp5DUwyFLvIs0TCI20R62KLn8MWWc7yKiQaRA9a4DQHUfV+ABgo7QOYt+aiW2zF2a8hmDtQyINgGCLPRJbUGwlidY1NYjHo5C51GCimxvJSwMptEixY2woAvuyRQ4hTYWhdwCLr2oAW/5DJ37qE17TNq1Gh0dXVB13XIcuk3X7Vqpbu+/qYdkiQhk8kglyvfsrGvWOdO0ULB6HV8eX+iUy8RqGmLMGOqxQFAj+I4QfPaMHyW2brs8d5p2SvwPms4Vtzrwys/4nF0DI82i45DubZ6fLmuRB1thi1At8RABIvFiEfCfuiWgJwuQjcpCqYv9NB9XTTFAHn7/4dRMKs73sTxm0SWsSrXh7/7U6ChdjoFyRfNIqRTEJuDmZZCSwtoMgkhlQYrFgLFrpyDE4AQz2LnoYD+MEJO7uWcmjUjXDGTH98NEyzQZGSZH0WmBEIVAzHoIfiflmzQSHVExxIXsLqYgWWX/91WZpP4skfDl90qvuxSsLLbuabWZTDDumgQ3dbWDsYYFi0KZnV+8MH7AICtty7PBX/4wx+wzz77oKcnqAx0dHRgzZo1GDeueqRWbzHoUS4DiVUkOIvmzfgYapGaYIxAJJYXzlgPbElFZ7H0GN1VLFmMnQUVb7TsG7dbTcin+ta+S7ANTBI+DizzO7L4I3RPP8UOF4wgGey69p8Aj7hQq1vS5VAuMiYOYlP8byi2tASOQ1QN6Y9fBQP1/gDnCccfysitcl7nJA6muzyrlKKg4trfRaCU/044idsQUGSq+9oZY5EpGKk79Yb8fgDiK6G8pmkiKLPRLTmTHANB1k4gb6nIWxUqcLr6OZdbDFuAaRGYNoVpE1g2YNk8BNbZZ6/Nqifw9RfqJ/T6zzFr1q6QZQX/+MffvGW2bePee+/BuHHjMGPGjLL7jh07Fp9//jnuueeewPKrrroKADB37tz6B1QjhlSm6LoGz5KM9GCsE28nZwE6kDXib/ZcmeX9gaLW4skrfuvdJgIMUQMjFJKZdzXz0n7cqhZqlF/yhghVClrOeV2AJrtygCF463O6AIG6FQtDhaJI60gg61gupKW+mvUDglywOJu/VgpPtw9r6IAT2irYJkxBjrT4qxdjPn8Fy8ZvD8Otq1NO9uORSYAzKVtUhBBy6q4eOx2q0QNqGd6YCRjytgYbBIwR2IzCZBS6kYAiGJ51zpE1FMhC7XHTdTYP6zN6Y3HXi6amZhx33Am48cbrYNs2tttuBzz11JN4443X8Ic//CGQJfr4448DcByfADBv3jz8/e9/x29/+1t88sknaGtrwwsvvIBHH30URx11FHbYYYcBG/cGQ+jvrR2HqS3xpW+7zVQgvjprlKwimzkWSJMc7SXaJQ/39MtyeDs5Cz169ezJF1IH4ivFJypus3z0DIxe/nrVY3WnxyLdXT4O1g/CbBiiBljwek7mDTGgo3cXZYjUhmkR6K6TVBZsdOQlKKINVQyRmY+8w8v92NNyChmxdBNIdzAyiNRQS17c3HFQmR++X3E7adx4GF+UqmMKw1phrYmxGCUFMEJavVub3os7d+O9eYifISqgtuVUI3STfMIkOhDoYWmIxIyNcMnZGkZb3Do3Av85Vqc2gWpl0S22oGgrDpmjROZccskaijepm4zCsAQYFoVhyRGnuB+MlUIH99583VnnAA9brI3R+5KkeOKJJ0NVNdx779+xYMFTmDBhE1x44SXYf//9A9tddJFT258TuiRJ+Mtf/oLf//73eOyxx3DPPfdgwoQJOPPMM3H88cf3ejy1YIMh9FoRll0MW4BMTeRNBWnJcVasskagSQyG2a2U4nWvzqIasXJ7dEfXFF0rtSMvoVkz8BTdD3valaNf4poCrxm2OYat+TCwLE4r96MgO4TJyWcT6TMszG0OmwGEOB3ia3WOci28YAielc/JO68LsY+0eZ1CLMa06nOtczS1APn4htzCZNef4HYXEjebAlAB1sflI36EdLxTmabSsHu6QZuDSTKM2U7yjawgs+xddI1x2rPZxHE4MkKrZgtzC9mkshdDPvrle6H3otDYqJXv4PPhM2PXFdxwW4H4nKVUiNR58T8NCbDQSVshudZ+wZJhu0Ru2hSyYDop/DZF0aaQQ5O2aROszStIKUFS98stANDZs47Nc/QuUai3jTGOOeYbOOaYb1Tc7sknn4wsa25uxgUXXIALLrig7vP2BUMm9b+0vu+hi7UiLgTLj26rcluzF9nOgfcd+fLSSt5nvYZ7Wvqxqjm+/oOhNcUuB4Cs6pBVNScdJSzyeNxTdOZ0/l0YVihRxKTI67VdJrVuF9wp6PEnk9vLbOgj+hjQcH9VAEJTdBng6PGkuRUQRUAvAvmskwZPhUAkiOGm8ttUgCmUEod4zXwAKIolx2ZWKv8b1YJq6fWAUylzJFsWu27lyGkQLd3T1Cmx0WWmMTJNManFRN6UXB2cImfIsHzXf7YowbCifoqOnIhV3ZKnn/uxpgs4fObAx52HsTHVN68XQ84pyuNF+xsd+eqxv/7IFz96fI4uDt3tP8oJ0dtWj0/i6cw5N8sjVm1RL9UQ7n/qjUtKQg8VcSqKCZhUxuRksGlHTg+OPauXbujOfJnIFTcT0E/e4dd5nWJ/4WHYPoefPawG5+64TatuQtvKNzr2QxhW0udpuPk2R7oJaG4FJBmiVcoQtqngNXHw6t+EyNwizvfDHZcm7bufZJOutwAAXZYzMZtMRN5SI3XsvYxUTtwhP8UqbQIos1C0ZYxvcixvxhi2GtGDnC7CtAlMmyBrOETNcxFyugjDihI3AHRkBXT0UOevm2BN17rN6vajXkLfmLh/CBJ6fY9Hcb1FP+moXIMib4gwbepJDrleFKTyo6coRom9IKAjJwZJMld7pEYY3VrlGiflrHO/1WiDela6X26xqoT0Fg2KgkFQMIK/S8GgsQQvUAZqGU5HnfBvmUzBGh0t4comlbfM+xWS4pC4/9xKAlrnMlBmxcos5ci6SEsTVhHlDYa4LNHeIGsmMIJUzq0AAAEmepDB6HT0Ptp2bCd0U/BFN5We0HSLIKtzDZ3CtOBEt1gEpuXKLRbXz9mgWOdAffzgzxLdGDDkCD3ctagvWNIVtayzutuF3qLI6RJyPovaX4TKjxXFKJk+3VHSO/1p0B3Z8o/NBZ3AMAkeyu5VdhsAWJKZhqLa7IzJ1cJzxLHI80r8Y32wUl+89S7AQt4QkNMFzzrnFmhOp542ymUXwwz+ELb7OQtV6nXsLzxccb2Q71sdHDKpDUSOkiMdXWd8r20DbvlcYuhO6CKhIIx5UU8mlSNWeqWoFrOzIzjWUFJRtSzRUT1OKQvD5kRbOtdoobwj/MvmNgjMxBpxFARYaE2JZYmsK0/RUxBgmK6lrgsomqXfvGg4BF4Odp1G12BiY5Nnhhyh12uh1wNO5gC8x0xZtJAQdc/rX3QbNnyWqy4RdJWRJXoKJUu8Kxv8inNFAt0kVdP+a8FabWxZgvfDn5SyRXN8w2nbZ5jmizTyulzRpXyx+m/F/J190qFJVkvA2HQqIqh2E5aRZ2g65kmlqXRO1uLW5vHHoxtF2LICwdYDVQj9ljkDgUGCljrv3erJLggaBMyOf/QhVeLxN9GdZJa8WfremsjaQMVF7hCNq0XTw9IQBApBcJ7EHCc484ht9pTVyBeJR+r+P8CxynvyFGbIn8KtcwD4+lf6t57RQKFB6OsAlb7f/naKLu/xNeO14j+uPymoEpLEsSxzskOi3PjqzoWaL4duhIJeem8YQL4A3PHxjjWd048ViUne65wQJa4esbni/kWoMCE5kohPcvHLJZ6V7llspf3554gj8YJOUNAJ5qSfhSWVCMtoivZt7U8Q3sYvETNBhqSVatA6l0G0dFhULCuz8KSsIvHJLawXlfPKZIlyjLM+8V630tqlDZGYGNMsgxAKQgRQSkEIhSAQj+AZY/jq1JXIFZzfTTedP8cyL/223TmCtd0EnT3Mk+W6sza+M9tAJpNEc3MGiYQKQRhydqGHdRGzPpQw5H6JvjhF31sb/8i9Mtt3a9iPl790IlH81ndHVvAs8x43cIMTX0eofIluVL/CPqG1lQIIg8stRTGBguCLxvBpvJObVnqvc0USSDjKFco0e3BvaE7qnMCBeII3tObIsuKIqFVtjIym/tcCJspgm0a/I3tEddmFyVECpnoRtiBBsHUIthlJJNJJcB+eselZ6TENuKuiQpYoAIwnn2IsjT5Rhce2PNMGkRlYjREQ4MsaJQSEUFBKQakAQgQQQiGKjvV+6DYrkS8CRR2uXg78//bePEyuss4eP3evvbuzQEJCSAIJO0RkFYgMYAzggn5lMUCAQRhky+AoKgIS2QQRCIgQQmTThAFlUBFk3BXlxwBiFAWyE7JvXdvdt98fb7237q29blV1Vzp1nidPuqvqVr1ddevcz/tZzpFVchE3LfK747iwbSCbd5GXHcw9fidM00I6nUcul4frAslkAqNH9yOZjEMUO6+H3gx6EXoXoNmUy+v5cl2FaoXRQaW5Ey5j1U5plKZUKEpJzh+lA4Qgn1zRfJReikHUd18BgoTDMTYpaJasiWYIaP6U/g3VJthLvyenja8vAeyHNvHAph7v8iHIgkbp8QT5VwI7VTxPXF4EZxmePyfNo1Myd6jGilOZiCevLDrCO6YF6SMzIR43E4xQfd2OFAt0A5XdX8OIonSYSGAsbDOq70oYhvEidhq9n/XhHfjMjO2E1Aufs6y6kNXgh+s6Ls7/yE7veQAXtu1AVTWk01ns2JGGrhuQJBGjR/ejvz+JaFQqM0huB5od++8R+jCi1ZRLtSjdDz+pDyqVt9YDEhl62ZyvkNpQWeTV2m8ddVpTNHIyZXIuzAoT3YZQfetNC6J+bHInVn4sS8jK9vUyG271ror9xwan+xwXkEuic8O3Xr2C7pPff1kpKI2ytumZKzcKziyXKW0Zyf66D7FGEd9Su2D3xxoKLF4C75iwGR4mI5ZF5n44YKE79TtXuCOOrdvh4gjlr+NUeB9LJSrejwYvitPGNqib7oveGYbF2UfuQF52kJcdmBbg2C5U1YGiupAVxyNzbxUVSNIwTORyMnbsSCOXk8EwDPr6Ehg1qg+JRAyC0Poc41AIc+3K6LpJUdclrUbtBHXp8SOtkD9dFMjtOUP0JjszRtQjdD9kN4H/Wxc0L87JLlIJBnmFHMtzha4RzYUkBv+OwQz5ssVj5IuayZQzvOoUCX6LNQ578pWd7gPHsLUHoGiOlxgTFHqYqyh22w7AsUWCBkjEJgqF9Erhdj8/qTpwxrTlYI0imZhCFKYQhaSlye/xYDFUGx0u1VIKc+J+ENYHp2idsRPAauWfX6VUC4UdTYCxTQiGDEOIg3cMOFxRHMtbtxstI1Xb5QJTnAAgHjez6I4EwD30aDD/+L+afwv1LLU5saINnR+0B11gLPAwsd0Ob1lIIm4GF80khU5CmG6BCKl2THEH14hjkG07UBQNiqKBYQBRFBGNSkilErAsG7puwDCMpnTN6VqbIWiWZXsReqdRryjaDNpN/mm9drEKICTeCAaz5HH+6NayXOwctJBOEzJ/4A/N58pLC6J0NLz0Z6B2lH7gnju8yVFZDb6Pll1INxSuOYbpBv4OrRCd0yg9YhEC1SPlKapSTfdq2u8AwFgVtjFsnfx0pYJoHZijy3dythQH61ieuYU/V224InTfe+m4bLli4c7tNQ2vGzG2qIVaUgQ8a+HwqQlEo1LLRcpg9M4VUjSs1zlDSNJpQk8F0HUD2SyJ3mVZAcex6OtLNh29N5tC2d0i9C5MuTSeQ+d5DvF4FCdNb33LXjoYVA00hZKTXY/Ys/niGZPONq71zjAMvvyZ5nU/MlbtEX/ZTkB3yslDd0Rv6tBwBFgOD1ljPDKv0mVXEape/JvPmLa8xiOJIiQA8BrRdlH6K6eNwsIcNb6hx9nRKhOjrhPwD7VZATYrQGeIoYTplrQj+or29P3MWfUDAfOg9qrsrRWC7Z7ZrAzHcRGLRdHfn0Q8Hmu5SBksrLJIJBKwbRsMwxTIvbwtsh6oW9ngYBaDg1mYpoVoNILRo/vR15dAJCJW5YChMIjeldF1hN7oYFEkIiISEZHPq7DrjDpuSfPYONj8if3PzcEC0++X74lKvsV5Ofj6lPQV1fbSLLpevsZsloS30qiJAX0QP1aq9cfhW8GhEzMorVvRC5Vlu1A01yuKprMOdKPyl8Pgyi8gNN0ynLBSo2H1VU9HuL4hIdYyYAnEz9NmePCMWTYBSslctSNlJhEU3HEnkR8YFuA4OJwARyDRfb0e9EZAe9A51gZfKISqlgTXdaHrBnI5Gel0DrpugOd59PUlkUolEIm0VqSMx6NgGBayrFaI3ottkSRd07gaIone84XoXQXHcRgYSGHUqD7E41HwvG9moJdDr4kuzKG7dSP0eDwCx3GRzzcX3eb1QnRqMWCZYv7cH50PKgJGxQ0M6pUJVlYcLwde9vxy5QvLYNpELMrBssjrua6LTFoPONO3ih1GP0aLae/3rBVHipc9Y2ygvKDGwAVXsgRZqX9BpaSuGy7OOGS9Z6qtiClEzRxy8T0QMcJ5hrq8gH9NIPKkVPubgYsD1v6iqecxRu8FcUdxsrIWqZdCMBWwQhJ6wfINDDzydsFAtSOB9zJnxsCxhUGfGnZ4Nh+BOv1IRJe/0dTfUgmr2WmQfLrplYqhlmXBKrSusCwLURSQSMTAsgwMw4JpmjAbMeEAIXMAkOWimBrNvdPzhXx36TleTMkUc+/1z3fLsmFZKmRZBcMwkCSxQOo8TNOCbdshDKIbfvguj66L0GulXFiWQTIZg2laUFW94mP8WLG+sd7gaq2HgceYcWRzRcLO5m1k88UvkZ/MMxkTihqMzDMZA5mMjp07NWTSZO03fL4x/1I69u/HBrV8YKc0f171+WwpYLl36MQMVM2Fqvn0XapkjnQjaJQhuSpY167YXqdH+jHYN9n73YqksGNs7VbFUjLXLBGqJeEfk86seZw2bj84sdqpKICkXawk2Xm5POlw0hNjocdHw+FFcJYGm5cg2iSNV00BsdRoufwBlS/uFh+pO1TUCHim+PwCWz/N5zgONE1HNptHOp2DaVoQRRH9/Ukkk3FIUvU0RyIRg+uizNS9FDQ9U2+oqZnoXdN0ZDIkeldVDTzPIxqVMDCQQiwWDRhNVFtTL+XSYYQpitJ8uaJoMIxwBgMbt5WfsJu2V/9ijk5UJlxZKX6ZKJE3k38GgHw2mPfvS5XrzlBsVCr3Fqsl/dCyFSm5v/i7bldOOZkOV5Y6oB+BorrersJfG9A08seeccj6QFtf1AwXlVP8c6/TvZ8Vs/zi9PZeZzT1fFaquUlRy9dCarECBJAqsO4Q4lftCDQ7WGTO+9ZZquNSDTunHd/wmtyS1kV/oVZgLGzVBrBVrt3lVAmmaUKWFaTTOSiKCpZlkErF0deXRDQa8dIciUQMjuNAaVLjvdpQUy1JgvprtqDrBmRZQyaTg+s6SCRiGD26H6lUHJIklO0ue4TeBSiNFCRJaDhfXg9+Ut+0nUE86hPWUqvn2X/1ZvGLm8+XX1BkmdymFiLzTNrwonPTsGFZwXXf+cXOZ7vMGma/QFBl8uhp5YJZlMzLntd0cOpB2yreF3h+qR8xo6j5kUkGO0s4o9ha+K8xJ0Mr6OhQM2v6v+HwUCwRht3ce0bz1gBgxCsPmumJMXB9XTSGlAJvqpAsBRYE8Az5XHVHrGlTeJBSbEn0+3pWRZ0pUaD6UNFqZ7/A70dPak3sjAwIkUg4m83Dtm1EIhJGjeoDx3GwLLtlOQ461ERz78XoHU1F77TLxXHcwppzhehdhyAIGBjow8BACqLIY9u2LS3n0DdsWI+TTz4ef/1r42myJUuWYPbs2TjssMPwyU9+Er/4RXPpwlbQlYTuB9WKyOfVtl1pN251sXFr+XPtyBTfjo2D5RGiaTplZJ7Lmb6fg/dl0sEo3LZduI6LXLpytFMrSq+EnXpzhtaaLcJwKpOi5bA4Yt9iftS/C6EwTHLbJ48OOhHJLEl1ZMSxyIjN90O/0V/UiPc7SpXKGiumgNfGftZLlZStL9Ue3Rg5OhomJ0F0yecnMJV3hHKJ+xXf1w/m8GMafp1aU6K1hoo4X4qlkXRLM3BdF4ZhgmEYqKoGWVbA8xxSqWJhtdNtkSQPX7ktslrEbZoW8nkFO3dmkMnkkc/n8b3v3Y+zzvoc7rvvbrz22qvQ9fppWj9yuRyuv/7LMIzGj1u8eDHmz5+P/fffH9dffz322GMPfOlLX8KLL77Y1GuHRdcSOsMwSCSisG0bitLcB+HHlnR7IuFczgyQt6rYkAvk7r8dABSlSAClpJ4ZVKoWQ2M1Cmrv7RxX9T4/tqrBPvCcUfk5abRLHWyoPdnhUzTIihOIajKZ4t/zb4fkvBSN4ZYTa9Qh0aJWMuW6pW86ub9KWoZG52XrLFyAjIINnmLw+HX0s4HH2AXlSl1q7gIHAHYFES7B1kmEzgheyyLLOF5ev+w5XAbitnVNve7mKR/xfnaESMNDRStNov/PsTa2qP3Ykm+vThEAJJNxr05lWTYUhaQ48nkZrutvi4y2PP1Z2hZJo3eW5Sq2RTaSQnEcB6IYwfz5t2Hp0qX4yEdOxGuv/QV33XVbw+tau3YNLr/8YqxatbL+gwvIZrP43ve+h0984hNYsGABzj33XCxatAhHHnkk7rrrLtjVClNtRNcSeiIRhaYZ0PXGCocn+qJLP/w94o1ip1z+JecK7SBGYRoylyteZOhwk5w3vIInhanbyAxqyAyqyO5UwDJMxXRLMhkHamzpAWJw0AiUkjyvP3+uVTDz8FuRMQxw7MHF95ymXSzTxcmHa2AZByJr1vUjpVF7LdhiHG/FTwrcppo8FFOAVrjgyLrgkTlx0/EpQ0qV3w8rXl1/x4iPgikVtOVj5To4fjla0dEgMgYMXx86jZJlk7zHdYujNVBLw6UU1YaKTphSwbe1BaRSCZimBU0rD6IcJ9gWaRgmRFEIFFZbHfSrP9TENDXUJIoijjrqGFxzzX/hxhsb8/d86aUXcPHFc5DJZPDJT57Z8Np/+9vfQlEUfP7zn/duY1kWc+bMwaZNm/DWW81pHYVB1xVFRZEHx5FeV6uWyn4N/H158yS+qrJMOADg+T/wHpFXgp/cK8GybDiWA6fCH86yDPr6kjAME4qiYVx/c64263KjyoqhpSjNPftJ3S5E6KbNwnYZz6zj2INNHHMQ6dY5+cMmZh2pl5G46fDI2yRCHHRru0TVgmYJUEzyzw+94MMqF6zRKBwXeFkKRukUubFBBysltZf3c7U8OgAvj+4U+tKpbR+N0E1HgGJFIFtSkczdOuRV0oNeik1jDqt9fAlWalOa7m5pBqlUArpuVCTzSjBNC7KsIp3OeW2GiQQprMZikUD/eBiURu+iKEEUBTiO01BhNWyKduXKFTjllFl48smnceihhzd83Ntvvw0AOPjggwO3H3TQQYH7O4mu6kMn6mwMbNtpWuOB4m/vtZ5n37CVwej+4u/Xn2vjG49asAvj8IJUIBq5WPzK5XSwDANNNaGpJsRI5bd255Y0AJJn5jgOyWQM+bzq9QvXwvpsChNTxYis1L+UEs02OY6xcbliNF4LNFLnWEIaLFx87CiyLstlIRT0SnRHRIQjX/ooVz6lWxqdD0qV00X/Hz4CmPDkB2j0q1lcmfaObHCeVrdXF69z7dOipMulEpHTKD3wGoXHixapcYi2Codj4YKBBb6QcmFhI0jmsiECO0s0y0ty4NWMwSuJctUDzzjYIqeQVXkctGcDBdgGQMlcr6TC1gBoW6Sm6WAYQBAERCISeJ6HZVkwDNLzHpZkBYFHLBZFNpsH6X3nCmQOcFxxmInY4wUbK5pVb7388qsg1FDIrIatW7eir68P0Whw5zV2LPm+b9xY3XGqXegKQmcYBvF4BKZpQ1V1JBLRhgSAamH1xuIXauVqDftNLX5xmt0VJhJRADlwHAPbdmHqtkfqFEpORyJVfI1cWkUkGiRUOaPg0W+RD1cUBcRikcK4dsmkqVV7K56v0NJXC6rJQzV5RIXiRUOzhKoRnu2wYODCAQMWLnjWaTgaLBUKo2YgpTDFGGCQnHhCIuuSDR5xkfxMBdWMElMSSuazD0zD4k4Av+KVhtZVCzYrQhWTXkugJiRgsQJY14EJEabLg2etql1DZeep61RUnLQqkPr61MEYL6+ou8bl6lQIXPAzOHla665BDEPIXFV1GEZj6c16cF2ivEifj+M4iKKAaDQCwPXua7RjzU/m9ILQyFCTn8d37KhtEhKNxhCLxQqvF04uQZZlRCro9dDbVLV5mY9mMeyEznEsYrGIV4AB/CYXQ9M/um1n7RNLllWosgFB4gNXeyWnI5YshomaSk5gXSP/59IKLNOCYztwHRcsT77kkQjZOmYy+YoRy9QxDlZvbzwb9v5gEvsMBIuN2+Q4klLlL6hhE2JSTR4CV1DTq5ALZtng2hyXhWaLkDgTOTOGCEeiOa0BCdlSvGnMCPyuFMy0tUK+nPqWCpzreZxSqDoDnueQSMRQ6Suyo39fjE6vanpNFITYi6kWCoG1oZdcYHK6CLZwntqTi0bX28cfilE7yona5Msv1u/HDsI+yr+qrme5PLmsbZB+bq2AYZgCmWttI/NKsG0bqmpDVTUwDFMIZqLgOBamaRei98qvz/PlZF4JlOALv4FhXEQiknex/fSnZ1c7FAAwd+6/47LLrgjx1xXhOE7F3QC9bSh8WIeV0AWBRyQiQpbVQIqFbpnaORCQr6KQWCrkXwmO4+K710Rx7QJSeHVsB0LBZFnx5c/zGRWJvurR9fe/3od4PAaGQWHr2BxyKod31AHsPSrclT6tiuiPBrfUpZF7KfhC+kW1BEicDYkLfvEGjRSifPE9yNkJxLligXqnOxpxprxgrRg8YoVoPK/zniVeXuOQiJALO/W5FHgXls3Adogq5LnH5BCLxZDN5sE24M2ajo1Hv7KJPH9kNBLaDuSiYxEtkSdwGM6L0nnHhMqQ5xYZEzkrBo5xoZo8LIdFVLCCKa9RxQLrjr1Ibnz7mAMwKrOmbD2VdG9WRg7HFPOdwG0uw2K5PDlwG8fa2JRvvpunFENF5qWg2i00tSMIPARB8OQ8aPTuOA54nkciEa0a+FQDuWhIkCQRmYwKgMFXv3pDzWOmTdu/5v2NIB6PQ9PKU5A0Mo/H29+RVIphI/RIRATHscjlKnWntNdXFAA2b9Exbs/qkWR/ikReO7Ms6M5gR17AJw4tfulZhvEKm6ZhQRB5qLKOaLz4vPmMCkHiYepBklRyMlKpvWGaZkOyBc3i/cEkxiSCZL05G8G4VPAES6siYmJw666aPBwX3u21BmgAIGtEEOVrk0DULdcjp/hT/kgAhNQBYoOXiLiet6nmM6SmfpeWTeQIVM0tpKrIl9yZeDj49cvKXoPmzxtBLjIKvFP575FY3Zu49XcL0bWXonSoaNvANIwdrBCpM1KZiuNy7hBYDoup3Bq8owZllbmSlsnj9gk/lUvJXFHUhrVcOgXTtGCaFhSlVG+GBcsyyOeVpgM7USSDiJTMATTVrRIW48ePRyaTgWEYEMViunXr1q0AgD33rG883yqGrW3RcVzIcmXZ22YkdKshn28s57tpc/AL+MHG6kWhu6+OwDJ9Jg4FCQJV1qEp5DhDMyBnyEWKplvkTB4/XXggNE1vmMynjml9Sw0Qsm4UisFBMTgv5+7/R1GLzDdpxShVZeL4wCiXyVUFEl0qJRZ9ea14Ksoa65lUA/DIHACumG02HbE1AqtC77fAGDBcEaYj1JxSdXzpqm17lXdFVCuIAgi0RFK8p+9X4ZEEa3emWkq3dBOZl4IWVonMgAtZViAIQkN6MxS0GOsn86HCwQcfDNd18c47wZ0W/f3QQ8utMtuNYSP0Wv3lYW3oqvWiU6xYngkYNK9c2Xjaw3UdOI6D+66NQlcNqHkNar7yBcnUTcgZufCPvIZlWU0PFuTMyjuKd9Y33r+cUcuJKKPyAXf3Sg1F/vx5NQKpNgxUC3/cXNTwVnTGI3bqb6qb5P+cQiJzP1TNRTZbHvlbE8tJVJb6y27LR0YH/q9k8QcAebbPE0QTGBMSayDCWdAsHjzreGmoWnAYDjbLw3IFbE1MrVgQpTAdAabDeQNepaDfBZ5xIPIuBuVwRTvSIpuALHcfmVPQ2kg2m4eu19abKRXmEgTaaDD0ZA4AH/3oRyFJEp566invNsdxsGTJEkyYMAEzZszo+BqGvShaCcWiaPvx/pqs134oVWkt9MNxSPXc34lim7Y37WnqpkfU/hOMROfk9h99dxIsy/YVgizoutlQqyIA5LTGvsBrt0mYPLaxHYBscJD45qLcrCZCEooXJdkQERcba3OLOEUiLo3OKSiZ0845WSWDTbQZYu7x6arPX29KNB0bD94pX2spqWeZASKZ64PhFAedKBgGYF3SCTQTvwvcV1pgLk2ttIqP7Z9u+hiWZZFKxZHPK6HnOzqNIpnLZW3LVG9GVXUwDANBIKqLqqri3nvvwZFHHoWZM2cik1Hqzwe0Cb/+9a8BAKeeeioAYGBgAJdddhkeeOABuK6LY489Fi+//DLeeOMN3HfffXWVIduBLiX0oakI18MZh2QLkXnw5Hr4xgF84aZtHpELEvnCqnkVfMko9JN3TYRtO7DtYCEoEhHB81FYlh1o8fLj8PEqlm2qHI2X9qBTqGb5SbMlI2DPvvLnzygc+mL1v9xZVYDEB0lONoLRedYITm1u10s8RNk4/m/j3uRYlUE86kLVafW/8JwqQGdRSjmnkkFIO1Ap1UKhOVGYPvlckbOQ18XAjiWnchDzZOx/856HQbS1ih1DHwj7YZy7IfQ6WdbFmh1x9MVs9PUlYZomdF8wUfvY7idzjvOTee3PmurN0O/M7Nmn4dVXX8Vjjz2GWCyOk046GWee+bmOr/n2228HUCR0ALjyyisRjUbxox/9CL/61a8wefJkLFiwALNn1+6yaRe6ktBJUXRoCT2ddbBubRYDY4rEVGvE2NB0cAXyNnUTboH0VVmBbVhwa/g/0kIQQKISURQRi0Vg2453otbLEX+wlcfeezS+bdat4Fae5qgzCodktPglb6RHX7WEkt9JaighkBSUbFeXKKB2d7LKlDklkdtdTwGTRueyYuMrn7FhGAJM06w4n8CNnQp72+r6i6+BPCrLFUicQYwtCn+3avLQTAbOEEWCFDwHDOZ5ZLNpL0Llea5mUEDJPJdThkRLJAzogF0jZF4Knudx1FFHYfr0QzB37qXYtm0rli9/r21rO/30T+L00z9Z8b7f/va3ZbcxDINLLrkEl1xySdvW0AyGLYdeWxO9PRH639/aWnZbrRH+8nVUX+STd02ErmgwNB2GpsM0DJhGcUvvOC7++3v1DaCJ+JFaliekynbNopoYWVqmeijl72tW4bx//tsUnUXWl4On6RZZJ8RG0y1pNZgf3ipXTn+ovlQLJXNFdSErQQPqTM6BrNB/Nr74sRxUVQfHBVX/6tmpbRUre5fmmP7impzixae0QEnFuHSbSPfqFg+xsFPhOYBlirUeY+ykmmsBgPedyRVbFuuBYxys2UbWefrBg16Ems+T/LKm6SVWc0RTheNGNplzHPFIyGZVj0/Gjt0Dxx9/YgdWumugKyP0dnYwbN1aOadcL3++I11/DUvunQwAOOcq0pZmFbpefvJIbVeeaijNE4qigBP35/BieVde09ANwIzUv0hmCqTOsa1/BnGh2C//hzWTICsuooU1yAqd+POvsfialuUGLvr+4RSWZbz2NoZhYJqFyUOUT6bmpWLqZyfGYBRqTwwCZICKkrnAWLDAQ+JM2C4DwyaFUavC1Gi11sdSmEzzF2oAEKvUPKhtG1Bs/Usm4+B53hvF70ZwHNtCZM4iHo8hm1WbNpcZyehSQh/6HPq6teFV655beCDi8ShyObllAw6K4ABG5VTAP1ezOHhq+eut3cxhbIHHaPcIQHrsR6XCr083OWQ1HjGx+Bzr03EkpNrRn+zEPAL329zRj1g3XOiGC55nAqYajuviix8r77d2HBeaZkDTjIBuSGLa4VDeX0te063t4pNHCgnU/sxzZgJxXgHPWpDNKAybh2ZxBTkE1+sUqhSd22zlr9b7+kTsFdlWs1DqOMFzf822KETBxc5c/Q214zgwTQuRiIh0OguO4wqaKsXUTLW01VCCkHk8ZGTOIh6P98i8ArpUPjd8Dv3q08PrJfjz5+d/JN3QMZGIhGg0gkwm3zYybwZ5rbnK+eYd9d9XLtCyWPw5qwVJqrQwCgCrdvSX3fbK8uKQj6I6gZ/p76bpQlUdyLKNbM5CPm9BVeqnCahuCE0/NAN/zjxrk59p2iVvkam+UsliibM9eQKadgGAbf1E5dEF4zkNWa5QkbjpbYYrlLUs2iV5ef/X4MzDB+v+TTxfTGHQmkwwNdNc2qoToGSey4Ujc3Ih6JF5JXQloYftQ6+EzRvqCxhlMuFGn4kbOVdXZ6JVhNG8XrO++tnuJ/VGl701S0jIH52XoppoWF52oGpBIqe/G0bxdv/PjuPiS5+uPVfQCDYbQRcjf/6cdqP48+h+ULEnql/jH6jKKJUvpFudcdhqBScCDSdI6hvkxqdY12yVwLLF7p9aCLb9lX9OpWYVgItEItY2udtG4CfzZgMgjmMKZK71yLwKRnRRtFMgCnVxOI6LfL510mkF728MvpH+lEYtbN7R+GtsGaz8RR9UhLJ0SzJSPaqm0bimBR9j+oa9bMeFY7vQ9c4MvvjbEKsha8YDRhoAIXXN5qHbHETegcC7yMgsskrxcdvs4sVjix604is16V6dbc4ubzBb+/tAdE/IQE4jUS9NW2WzeWQyOVgW8RHt708ikYhBFMsNl1sFy4Ync5ZlkEwmkM1q3hxJD+Xo2gh9KLF2RX3DYwrSBpaEphlQ1cqTop1ATm0+eqoVpTu2iy3b63+pqpF5JUmBLdnyCP1nr5EiparaASJXVduLyGXZQiZtIJvVkc8ZkPMGvnFuuF1Tsq9y9Jt1yusQWbM5sSTTZhHhi38DzwG17DVL0y2lfq6mU3vgaPUWyXv+s46snm4RBB7xOBGxCusj0OnUTLF9MhyZp1I9Mm8EXUnowPBG6NXy5+Qkj0OWlSFVqAOA0w6qnT/Nq+Her80+Ui99y7fsJDdU6p7ckat/gZFNMhTlT6VQUtd1+n/5l/vG89obnZemXerBr3vOMC5UU4Rm8ZA4G4bFQjPZqh0njsvCKozv79Br2/B9kElV1Vhftbn4pvNcdRKrpBXeKir5iMbjxEc0FouC55vrpQj2woeLzHO5Hpk3gq7scmkFkUh5oe4fr63E5AMq9yTL+cZG16lAf5iqfKfx9nITk/eurKuyZp2JKZNqR4KU1OlQEcsxqOX9u24ri3jJAOuKzTGkYpXfF0WxIEkcNJWQeCTKebdzHAvLdGBaNlwXUGUDrco+1OtwqQTVkhDl9YCptuWw0EqGqAybhWEy0E0Ghgmcut9qIA3sMEYHTKQpUZfmzw2Lg24XSXzdYAKmxWCf0UVpBErmNCjeka685uI52bkaDvUR9U85S5KIRCIKy3JgmgYMo7oTUSuDTSwLJJMJ5PNaoPuph+oYUYQei0WaPrFX/2s9kgO1dUCi0QgEgUc2mxv2dq8wCOkqVhGKwXqTnPXw4qs8bJtE2zQi9/9sGLY3jGXbLhzbwW1faH1nNq5fwuZ0Y5o2zaRddJtDRLC9CVHDZDC2hpGGYXHYYSWQEMvXYpRM7q7aGoftAKXyPiwLnHdcuuz4oSDzSvBPOVMnolSKfO+8eYBCFN4KmTMMkEwme2TeJLqyKNosiDkt0UVRVR1Xn65i9Ypg1e/tv5Q7wrz96jtlt5WCaDMzhS9O25YcCrXSLv98p7py5MbNwfRQK0J729ONP1ZRiq+rqZTYLWiqFZjYbSeZ10PGiGO7XtkWj0oYUOSN4u8c44BnXRgWB8MiEbpYCL639e8biM798EfjpTAKBh6WTaz1/JxH01+btpYTISFzqRBgDN9JSYa9SGqGtCC6iMWiXmG1ry+BfD4cmadSSchyj8ybRdfm0BsFx7FIJKLQNKNuXttP6rpWm9WobrRl2ZDlznsBNorSpppcfvhlUDcOlqd0fvwb8kXUdTtA5hSaasE07CElcz8yZu20DE2ZlHa7iLyNiBAk701abeOCTblEWUG0UQh88H2RJBGRiNQVAYYfdBAul5ORzeYhCDwsy0YiEWtYyxwIkrm/+yks7rzzVlx11WUNPXbjxg24/vqv4LTTTsZpp52MW265CYOD9Xv/uwm7dMqlmoVdLbzz6ttgWBZitPL49TfPYwEkwLIsZFkd8uJnK6jVsrjmfQ0T9go3ck7x/kYX8ViJMYVeOQI1dQuCxENTTE9mgXqushwL07BgAnAsp7BFb21t9bAx14+9kumGH1+qqggQv1OedWDaDCTBRVYm74XIWtipxeG4QErSqxY6m8XW7Tb+49TiDIIkiZAkMZR94VCBdqTkcrKn7MhxbCE1Q9Jb1Uyii2Sut4XMX3jhefz8589jxowj6j42k0njmmsuh2maOO+8ubBtG0uXPoVVq1Zi0aInQhtHDzW6NkKvN1wUiYiQJAH5vFJG5mG3oYPbFSiKCoZhoOsGIhEJfX0JRKPDM1FXCbXa11avqW77BgBr3w/fM1+txXHjtsofkqaa0BRqmm15ZG7qFvSCu5NjOVBlDd+9pv1kPq6/+efMaNWFs2SzMN1pER15ar5BJ0QpdqpR73F+bBiMlt1WD/5TjpzvuwaZl8r0Uo2iTCbvaZ3T1EwkIuLtt/8B0zQKTkoaTLO1pgPbtvHYY4tw5523NXzM00//CNu2bcWCBQ/h/PMvwoUXXoJbbrkTK1cux0svvdDSeoYSXRuhF00uysmZFj/z+fJUiOu6NaVrA8/TV14MjcUiAYszKpKVSETBMGxTOtSdQKvtnPXy5yxXfH663deatEB9+n92gBc4z6LPLbngWpYNSzXgOg4euK51w+NqKC14Zozi71vzMeyRIBe4jBZBX6R8psC0WQicg5wuBhycLIcBz7mQRPL+pPUoHLeYntkpS0hIVln+fP1OCWP7qn8A/jhkyzYLsSh5vkhEKhTlu5fMGYYpdKTU1lwvNYl2XQd/+tMfcM89d2P8+L1w3HEn4rjjjseoUY1P0/qh6zouu+wirFq1ArNnn4E333y9oeN+85v/xYwZH8bkyVO824466hhMmrQPfvOb/8WnPvWZUOsZagxr2NnstGhp8bP8GNfTML/7qubt0QCU+VXSEzCblZHN5grOQxH09ye90f+hAsex6Osjud9svvJF6+1/1M75bdhQjNIbnUHZsq1y2und1eVryBW0ZSzThq6Z0DUapZOfLcuGZdrQFK2jZB4WlfRp/GBZIszFc8C0Pct3RFRnnpJ5aTdLtdsqxQcXzcwgGiVknsvV3n0NJ2i9SZbVpg00GIbBV7/6NTz11BJceumVyGQyuPvub4cOmAzDgKLImD//Dtxww/yGXIKy2Sw2btyA/fc/oOy+6dMPwLvvljdUdCu6NkInAl3F3ziORSwWgarqFU8aP5n7sW1941Og8y+qzXBUCIrm1UkOv6hkp+tGx7wayWg3UXQ860gHi39fuVMDINopfvhbBgFgzZoc9plUv1fbtFxs2mxAkpq77hsaib6oAUg+q0AQBVimBUNzYNs2HrkpXATWCmRdQFwKXpxomsWfbvGTeloVIPEuHIcBy7oeGXOsC5Gt/FnrFgvdAhIFGQS/4uX6bTz2GHDKOlz82LTFhCiyiEaJvsquQOaKojZsqViE601dG4aLffaZjH32mdzSeuLxOJYufa6p4aft24lvwtix5QNoo0ePgSzLyOfzSCSan28YanQtofsj9HrFz6JN3NCW/YPOQzwkSUA8TgYuDKN+102j8PccN1L8Xbs6g8lTqxM+AKxZnYXjAlOmVp5mXPu+Aklq/PSgQ0U//vE67zZdU8ALPCzTIh6rloMf3z+1KWemVjB9rIXl26r/DdVy5tWWRMnccUkBj/JwXudh2UFlSsNkYPDFCyH1SwWADdsYT964FBs3G2AYBl/+jA3XZXcZMm8+kHGRTCag62Yh4GhPlxPLsk3XuxSF7FojkfLzQZJILUbT1B6htwJaFCXemxzyeaXsi0bIwG3L5Obg9jyA5rQ9/LAsy4tQOI6DJBESdl0Huh6evMiWW+jYUNOa1cUuCpYBeKEgDSvU/lJ8sLFKdKro3oXYdV3Ypg3bsvH4HeMBAOl0rtD1ICKVSvj8IY3QOiRhoVtsmVcqQDp3Kmm8+yNpiXcxVtyBbcboMv9Tih1ZFqOr6M9v2ArsMSp428bNhZ0Nx4BlSf2ory9RtStkONEOMjcMC5pmoVOG8I2C8ket8lQ3iwX60dWELkkibNupWfwczsGKarBtG4piA9DAsiwkSQhFXvF4FAzDVCyGXXJSpmbaBQA0rXECaMRLlLYsymrltZ88LYOTb6mvm0K6HjSf+5CIRCIOhmF85NW+onOpRV6z0At5cbtgPEG1VbYZJG1EO14MiymTufWnW3SDpLEo1m+2YdlEXdJxSOTPMoAsm8hkSJGWFuVjsSg4joVhWDAMM0R6o31oB5mbZneQOQDEYiSQ0/Xyuhy9jT6m29EdvXglYBgGkiTCcdy6xc9aaCZ/fv+XO/OBOQ5t2aIa1EAiEUdfXxLRaARcFbm+ZLI1ed53/lHup+qtyWot0vtgfXlHiF9GthkQGVcd2Wy+kFIqLTq3FnOUkvkHO6OVH6eUv45sFNnZnzIxTAZRgRDZsnV9Recik4GiMTB8j92ZDR5LHhd8HccpttoyDIOvfLb4/voHdtLpHEzThCSJHZW5rYVWyTyRiMM0bahqd5A5AOy55zgAwPbt5faE27dvQyKRRDRa+bzpNnRdlwud/KwWpTUTmT/x7QntWGbbUE5ejtePSw0GGIZBX18ShmHWleft1JSoP93SbEG0FRDyMj3yMgxKXimPvJrFidOKQjY7ZULag0rlHnU/qVcbmCpVPmRZEnlTEqe6OXqd8olhOF507j0XA2QytXtETdOCLNeSue0cSRbJXAtN5mR3ZqJbyBwgmjHjx0/A8uXvld23YsV7OOCAcB7Bw4GuitCJFGgEsqzCtp2yvBUpfnZnmqVZlEZelmUjGo1g1Kg+OI7TUF3gPz9Ru2D2zrIN7VouAGLs/M6/ig5QqWSR9BqxR2sWRfLKeuTV359seJQ8EpEgSbUvAlsywfsrReq6ycBxSORtmAwSkeJn85kZgzBMF7LqemROlSKo6fXOjFtXII1m4G74fOOF9KDMLdnJ0d1fLBZpqGWvUVAyV1UNptlssd9FPB6DbbsFfZ/uIXOKk046GW+88RreL3jSAsDrr7+Gdevex6mnzhq+hTWJrsmhlxY//YMc7Sx+VkJuMIdWCqLtgOM44DgW6XTWc24nHTN2oFWyWbyzbAOmHjCuLWtsxUi7VRBne0JgxbpEcZRc183A+UFb/rJZGUDj3Ql+P9Wa6/FpvBgmIAqAZbvgOQa64Za1Iu5M20gmKsdPNEAZHAxvmOI4DjRNh6bpnnF2NEpaak3ThmGEb6mlDl2qqoU4DwmZuy6gKK1LI7cDGzasx9tv/x2HHHIYJkwgstpz5szFL3/5C8yb90Wce+55MAwDS5Y8if33PxCzZp0+zCtuHF0RocdiETAMg3xe9dIwpMuF8VIsYcic53n89OHgsABToaXpsdvaQ3hhQcib2IfZtlOITFXftpr3RabBnGmlKF2VmxztbBF5eWh3TMW6RHGUPJGIepFpIhEDx1Vv+ftga/Ac8Eflg7nifbLGluW/K+HCE9LQdZf8K0TlslIQJ/NF5tt3WBXz5wCQ3qnim+e3pxBcapyt6wZEUWhqd0NByDwBVdVDkXksRshcboPOfbuwbNlbuOWWm7Bs2VvebQMDA3jwwUew337TsHjxQjzzzFKceOJJuPvu+yGK4YYUhwPDGqGTyc+IV7mvdH/YTha/Kl03IxKRIIrV2xJJZKpCUeBr94t4KRvDMOuadLz71jrse0hr9YT3/rkd0XjlE7uaw9NQoHSUPJVKeH3I8TipxRw9KY//W1c9StdNIrblh6KT57Bsxsub0/9lnUV/iZmHqjtgGRKd83xJPt3nyrRjh4Fkkg/kz3fu6KyaZ7CltjGhLKA9ZE4CNR3DReY//vHPy247/fRP4vTTP1l2+6RJk3H33fcPxbI6hmEldEHgoWlGxclPy7IhiqQP1zQt6Hrlx1UCzR9mMrl2L7mtqNWWWAnBdj/yxUwm4wAaj8j9OuRhkEh1VhWxFSSTcZim5RWTBYH3UldYV361TMuVc8yUzClyMuM5NDEMIFSwn/vix3J45DepwEVZlu0iuftIfXCnAdOy4diuR6Q3zx2aHnMqlKWqet2WyGQyPJlHo9FhJ/PdEcOactF1s8oYP0mx5PPFbgfqSB6PRyHU8EcjBMcEttvVul2UTG7Y0i2ttiXSnGk2m8cNn6+fG131drgCqa47ePfvm6reP5zRuR+pVCJA5gACqSva4UJRjcyBYJrEX+iUtdrEpKg2VM1GLm95BC7Lxc/GNB1YPiXB4R4UqtUSOTDQB9u2QhVAo9EoOI7rkfkwoGuKogBp62OY8uKnf8TeH3X59VNoFV7TdG/73Y0g64xD04y2rbPRlNQ7b6zGvoft09Rzr3lvS9X7srnhUZz0g1iVJQJpl0aQk10k4+HJZiBafiH+z0/I+M5zpO/drzBZaoRNo3OKoYrO64F+z8jFUff0yclAHEnv1R6IcxGJkN1xLqchLJlv3LgB3/vefXjrrTcBAB/5yAm46qprMTBQRS+hgHfffQcPP/wA3n7772BZDjNmHIGrrpqHSZMmh1rHrgjGrcEG27Z1NmXBMADtrCLLcJoa/+Z5DpIkQhAEsCxT2EpW7xT4f5e9A6fQ2y5GJfz396a1svymQT0WZTnMUEZt3Pa0AKWQS6dFUU0h/xsqud3QdFimhWmHE4lQ/1tdaex/zbubIEVEROOEpKJx0Uu5xOOk3e+Kjw9fWsvfStdIWuCX7/QDAAYLzTqU0DM58kZEpCIBqZqL/hQD3SgWLnkeSERdCLyLiX057DemMhFTUud51hNGE0WqQukE0i3dQuYUqVT5xZGm98gQU7VpXkLmROY3PJlnMmlccskFME0TZ511rmc0MW7cXjWNJtatW4tLLpmLSCSCc86ZA4BonAMuHn98KcaMGRtqPZUwdmz3qYRSdEWXS7GTpbniJ23pA1zkcgoYBl4lv9IEne3bPg41mZMBEGKY2wlFxm+c2/jW+L03V9a83zIdrHm3epqFYjjJnJopKErnXKX8AT8dWM3k6xPVVz6rQddtyHLB1MOwIecNZAZVj8zzWW2XIHMgmN7LZnOwbRvRKEmBrl69Am+88X9gGLagORSezIHwRhPPPLMUqqrgu9+9H+effxHOP/8ifOc79yGdTuO//3tJ6PXsahjWlAsh8uK/ZkE7RKiGuWmaUBQNHMdCksQycaznHzusA39FfTSrljgUeO/NlXBdBwzDYtoR+wEAlr+1BgCRvRWj3duqRXc69cwUWoWquYhGKpPToBoDUL2YfcPnTXzzcQamTnY+lmnDshxYeQOWaePOL3ZVtrMqmZeiVEJakiJ444038NBD38e4cXvh+ONn4vjjZyKVqqziWQ9hjSY2btyA/v5+TJ9ebFM+8MCD0dfXh1WragcwIwnDGqFLEo9UKo5IRCpomjROdtRcgpjlBo+zbcc3QacWCCBRGI9uvAe3HYhEpEL7ZK7jZF7LaNmoYTu04q8rsfytVU291nBF5xzHejudVsl83YbgTmnrjvKd0860jXTWRibrIJMlEXVWJl+bWjKtDMPgvnkJ3H4ph3xW8yz4dM3sQjKPwzDC1XSmTNkX1113HRYtehKXXHI5tm/fjj/96feh1tGK0cTEiXsjm80GTJ2z2Qzy+TzGjBkTaj27Iob1zNJ1G7quQBQ5RKNR8DxtnaImFuUERYtgpmlWFO4qBRlCCbb6pVJxX6TROdnWZtsS24FGh4oatenrJvA8h0QiVhgman79sw9Me3n0WqBm23RIiCIRLxL4pkEBiYNJn3WpLWGpgFWQwLtr55NMxgsyts2TuSgKiEREZDIqGIbFlClTMWXK1NBracVoYs6cC/HnP/8JN9/8DVx99bVgGAYPPngfeJ7H5z53Tug17WroglCBgWE4MAwdgAtR5BCJ+MndKPTFMsjlchg3bg9oWpje2NLxaKLoWJRtNcrGx1tBMhmHbduQ5c4OjZTinnkRfGlB+BHyRuBXAxwqEJ2faMtpq8ES9QJaEKWgZN4Istl82Zi9ZdkFyzhlWCVuGwHt29eaNY0F+ZsjEQmZjIp2tSa2YjQxbtw4XHDBxbj33rtw0UWfB0B8CW655c5AGmakoyuKokUQcs/ldAwOKjAMG5Ikob8/hVWrlmPevKuwYcOGthTBXLdU+dBFIhGrK2tb9y9gGM+UQFGGnvg6jXxWb5u0baOgwy+dqEFkssG0TU5uLo3jH7PPZmUIAg/LspFIRIdF3rZRtErmsVgE2Wz7yBxozWhi0aKHcPfdd+DQQw/HTTfdihtumI8DDzwYN930Nbzyyh/btsZuRxdE6NXAwDQdmKaBX//6ZTz77FIsWPAA9t57AkzT8okNtX5C+cfHy6fngtvpWuhkW2Iz6GSUPv8iF+l0DoLAF3Y4dB7ADDGEUh+SJHgSDt2sskk/+1xO9nL7QeeqolTDcP8drZE5UUTNZBS4bnuvVGGNJnK5HJYufQoHHHAQFix4yFOZPPXUj+MLX5iLu+66DUcffewupckSFl0WoZdjxYrl+N3vfo17730QicQoDA4q0HULgiB5OtlkcrQ9X5JKsrbUcCEWI4XYSuh0W2KzoD3onUKpLrcg8DVbRsMgEhEhSZLXxdQOfP6YdN3HbN4SfO+Ewvj+1u3Fz/VThxWLb9UKtcS5qihvyzAMkklqbiKF3gW2gmQyDssKR+Y8T9JemYzadjIHwhtNrF+/DoZh4NRTZwUkg3mex6xZs7Fz546ALO5IRhdH6ATTpk3Hbbd9x3cLA9N0YZoGZNktDBf5J0dNmGb7lN38LVqkCEQlSa2CdIHla0sMV6zrBL7/9T5ccUem/gMBMA2aIqiyAaB8sCMoIMZ570crUSnJSfMdKygPpmvvuDZv0TEwUD+i4zgWySSJzGuN8pfWb8o1VBrXKgoLSuaNNBOUgud5xOOUzDuwOIQ3mhAE8jlV+u7Rz2RXbAIIg66P0GuDgWU5kGUTg4MKVNWEIPDo6/M73LTv7PNLklI3nYGBPsTjUaiq1jVk7gedEm0H7rqyvmOQbdtQ1WJUSgaA4ujro4469U85Kq42VI736z5QkM03T6YcxzVE5qUo3wVaBa0i/46zvUgkYrAsOxSZcxyHeDyKbLZzZE4RxmhiypSpGDNmLF588YVAukbXdbz88i/Q39+PqVP36+zCuwTDOvrfObiF4SIeosjDcRwvcm/nCRmLRcGyDDTNgCQJXkGsFUOKduMLNxFfVdqHbpkWHMv2IhaGYb0InS+MVfsHi+jofyNkXgukq0iAKIq+8XGjjAjjBVnDTnYHff/l4ug2tXzrHyiqSMoFaz9iYgyIBUmERFLAHmN4iALwmQ9lkUyGb6GsBp7nC2P2PGzb8c6lVlJOiUTMU+psfj0s4vE4slkVQxGvDA4OYu7cc8BxXMBoYsKEvfHQQ4shimJFg4o//OF3uPHGr2LKlKk444xPw3Fs/OIXP8PatWtw443fwqxZp7Vtjd08+j9CCd0PSu4kFdAucqdtiaWdLDzPQRRF7wtJUw7DhVJCNwoRWjVC5wrRoRgVIUWKKYcHrmvfSUxSDjxEUQykHCIRCY7jDEl3ECX1Rgk9kSQXNEroc2daHU+xUf17URQKAlnNz00kErHQ7ynx9x06MqdYt24t7r//Hixb9hYkKYLjjjseV1wxzxPnevHFn+P22+fj+uu/GdA1f/PN1/HYY4u8AaTp0w/A3Ln/jmOP/Uhb19cj9K6BC5ZlIEk8JEnwyQIYhQiofi6ZFrYaGZOmXQ6iKPiirfbuEmqB5rLPmre6JUJvJ5lXWycdwqIXwE4XlksJPZvWMGlKn0fmum55n5Of0A3TwdRJIs6ckRnSFBvLMh65VxfICqJVMk8m48hkhpbMdwV0M6F3fVG0vWDgOICqWlBV0yP3ZJIMKhBy16uSO8uSk5xOANYDieBtT1+GuA0lh6SFTZJESJKIbDaPR781FnOvW9+R12kVDEPkERRFg64bZfLI3ZS+omQOVC7AdRKO4waKqrR9kOPYQhtv8CLYGpmToCWb1XpkvothN4vQq8EtRECc5xJf3N46ABhomopx4/ZALqc01JNeC9TkWBRFbyut60bbyJ0aJPuLipTQm4nQAeCRm0a3ZU2VQLXhq7nikPRV6Q6nfRfB77+cDEToADB6LO2FLo/QjYI5RSUf1+EEuQiKEAQyqcowbCGYaL4OQVUss1kNtt29ff/DiV6E3vUgkbum2dA0q1DA4zxZgF//+tdYvPhRPPzwI2hHOyQ1OVZV3dtKJ5NxMAzdJYSXICBFRaasQ+TJuyZizrVrm3quzpN5ouZuh7RDlu5wEqHzySMVfgOYRCIGlmXAskT4jp5PjVwE20XmYQ0qBgcH8cgjD+KVV/4IXdcxffr+uPzyq3HIIYeGXsvuhl6EXgf/8z/P4o9//B3uvfde9Pf3F4hEL3RntHe4orwTpDl9mWqFWj/OvZqoKtaL0B+/Y3wrf0pNFOVv1VB6J8F8Mrxp3mYvgnc8Uyz6VovQ/R0u3RqhU5R2CBV3gsVdZ7X3iWUZJJMJ5PMaLCs8mYc1qFAUGZdeeiG2b9+Gs8+eg2Qyheeeewbbtm3FokVPdFXbYS9C30Xxu9/9GsuW/Q133nkfABGZDFGGjMXiYFl/611lZchmQfRlDGhaUYIgkYiCYdiqbX5AUYHSMIy6qnlPP7AvAOCcq1ZUvN82LTx1994t/y3VQIttrWiZl+aTac6dZdky5cNmsX7tTowdX67lnc+ZECPVfUiHG5XaPf07Qf/7RCUtFEWF47jgebYtZA4UDSqeeOJpT9P8oIMOwbXXXomXXnqhqp75U089jnXr3scDDyzEjBlHAABOOeVjOPvsT+NHP3oSN974rZbWtbugF6HXgOu6VcWAGMb1cu4sy7ad3IOvRQSRJEks05dp1oZtOEEGcWJND+I0Cvo+iaIInmcD07zVQKN0GqFT+eGx41OBCD2TVjF2HCmed1uEHotFwTDN9e6LooDf//53WLRoET70oRk49tgTcPjhH25Z7+Tssz+N8eMnYMGC7wdunzPn/2Hs2D2wYMFDZce4rovPfvYMTJu2P+66697Afc899yx4nq96IRgO9CL0XRS1jDBcl4GuO4XJNNfTdC92HVTXdG8WpS4xpB2RjMazLNNRG7Z2oVUt80ZQ+j4JAo9IRATPBw3FG8GGNdvhOi6EQpE82R8D0K1kzkCWy02ra8EwTBx//An42Mc+hldffQ2/+93v8OCDD+CUU2bhggsuCrUWalBx0kmnlN03ffoBePXVVyoet2nTRmzbthVz5swFQAheVVXEYjF89rNnhVrL7ooeobcFjWu6twOk/9hBMslBlqkwllSxfa0b0C4t82bhLxZSQ/F4POoNfNVSh3R3gWJrLBYByzLI55sjc4DsZlKpJGRZw6GHHoFDDz2i0E4bXtQtrEHF+vUfAAAGBgbw4IML8LOfPQdZljFhwkRcffWXcMIJM0OvaXfDLq7l0o0IarqbZlHTPR6PQhA4tKovIwi8N3au63pAX0YUxY5qgjSLTmqZNwPLImYj6XQOiqIV1DGTuOML9SUNaHTeTSBkzrZI5jpM0/XdzlQ0l2gUjRpUlCKXI6ndRx99GK+++grmzfsybrhhPiKRCK6//st4/fXXQq9pd8OQfePDtjKFPa47QCN3A4ALQWAhSRLi8VhoTXc6/VlJUjYYkfIBFcrhGNApDjflhmw6thHQgS+A2BJm0921o6mH1sk8AUXRAmTeDoQ1qCDqqEA+n8OSJc95BtPHHz8T55xzJhYufBBHHXVMW9c6UjEkhJ7JpHHNNZfDNE2cd95cr5Vp1aqVNVuZwh7XnSjK/lJyF0VK7naB3E3UIvdIRIIoCg0RpGVZXjGQ6svEYpFAuqGTJEvW2jn523ahUj7fqNIptG1zHu0ueDeLaLQVMneRTCahKAYMo/0ffliDCqpxPnPmv3lkDhA53RNOmImXXnoBiqIgFuu+nVK3YUgIPWwrU9jjuh+lmu5sXU13KikbhiBL9cqpi47jtH/6MrjW7iogVkI0GsEDX+Jw9T25ugbbd17Od1yzvBaoNWIYMgcImWuaAcPoTFE6rEHFmDEk5z4wMKrsvv7+gUKRtEfojWBIcui/+c3/YsaMD3ukDABHHXUMJk3aB7/5zf+2/bhdCwwsy62q6c4wDO6//1688cYbbdEH97voKIpaGPJJIJVKQJLEmp09jYCIbLFDpmXeCqgWSj7f2FqJZnmyUAsZ2voENaEOS+apFCFzXe+cOEtYg4qpU/eFKIpYs2Z12X2bNm2EKEro798VUqzDj44TOm1l2n//cuft6dMP8KQu23Xcro0iuafTCnbuzOEb3/g6xo8fj6OPProwGdm+SJpqZJeaUaRS1IyiOXJPJGJwXTTdQjccIFr2xWi3XnQOoKT4LKC/P+kzUukcaItquIuki2QyAV03oeud312EMaiIRqM4/viZ+Mtf/oTVq1d5t2/cuAF//vMfceKJMwPWcj1UR8fDjLCtTGGPGymwbQf/9V/zMGvWbHziE5+GopiQJA7RaKojhh2V9GWIlk1jo/XE3swOZaIw1KBTlf5o975ro/jPe4MdGLQHHQBu+0Lx4lbaDumvT7Q7hUUsD1sjc8OwCtrunc//z5kzF7/85S8wb94XAwYV++9/IGbNOh0AKhpUXHHFNXjrrTdxzTWX46yzzoUgCHj22achihIuu+zKjq97pKDjhN5oK1MpMYc9bqSAYRjMm/dl7Lsv0bCwbReKYkFRzIJQFVeQ4m1e070eKo3W0/RPJQmCVCoBwzBDGQ8PNeLxGAC3bY5IwfpEqYAY0eIJS+6RiARBaI3MTXPoyBygveSP4P7778HixQshSRGceOJJuOKKed4U6rJlb3kGFZTQx4/fCwsXPoaHHnoAS5c+Bdd1cfjhH8IVV8zzHtNDfXSc0MO2MoU9bqSAZVmPzINgYNtumaY7IZH6mu7Ngmq363pRX4amK0yT5PtJbrZ93qWdQj2N8EpROhCMzmuBprBUlbRDiqLgqWg2KyDWKpknEnGYpg1VHToyp5g0aTLuvvv+qveffvonA05DFBMmTMStt97ZyaWNeHQ8hx62lSnscbsXioYd6bSKXE7zhLpSqaQvD96e7b/f3DibzXsRVzQqIRaLgue7N8/ZqOHDfdeWd2GEgeM40DQd2Wy+IHfgIpGIoa8v6XUBVUMkIrZM5uTiUrsNdldBp0xgRiI6HqGHbWUKe9zuC0ruJCor1XQnDklFw45WQKVWZVnxcsmiKBTyvVxDolhDiWbz+9//eh++eFsa93+5PQFDcJdDBMT8bkO6bnjtkJIkFmYNwpF5PB4rpOd2XTK3bTtwwRvJO/F2o+OEHraVKexxPQAAA9etbthB0zJhyL2oZR6Uv60milUcmhoecidkbkFVm8vvP/SN/o6sp7KAGLkQOg5R98xkwqicEjJ3XUBRgjMMzaAdk9krV67AF75wAS644GJccsl/NPX6fjJ/5pml2LFjOyZPnoIPfehIjBs3rqnn2h0xJM20J510Mp55Zgnef38t9tlnMoBiK9OcORe0/Tg/wp6gr732Kp54YjHee+8dsCyLgw46FJde+sVd0D3FT+62J/sbj8ealv2lWub1bPj8XSClHqHNKB62imQyXigKdm+xlr5XkiQiEpFgWRb6+5OwLCIZ0Zhcg4tYjLaMhifzdkxmW5aF22+/ueHd2fr1H2Ds2D0gSRIcx/HI/PLL/x39/f3geR4rVryH9es/wMUXXwqO43oRew0MiR764OAg5s49BxzHBVqZJkzYGw89tBiiKFZsZWrkuFoI655C26emTJmKM874FGzbxv/8z4+xffs2PPjgIhx00CFteV+GG81ourdD/pYqHgoC33F9GdJ5U9/woxvgN/SmoBO9giDUmeglZM4wDPJ5Ha2kWRYufBBLljwZmMx+/fXXcO21V+K6677R0GT2448/iieeWAzTNHHxxZfWjNB/85v/xaJFD2HRoieRTBY1xm+55UbIsoxvf/seAMBPf/ocnn32aSxe/JTX4Tac6GY99CGZFKWtTPvtNw2LFy/EM88sxYknnoS7774/0Mp0yy03Ydmyt5o6rhaodMCCBQ/h/PMvwoUXXoJbbrkTK1cux0svvVD1uPvv/y722GNPPPLIEzjnnPMwZ85cLFz4GCKRKB555PtVj9vVQDXds1kd6bQCy3IQjUbR15cqFDlZAC7eeedfGBzcWVBMDD9p6Fc8VFUdPM+hvz+JZDLu2cm1A6lUArq+65I5EJzolWXV8/ukQ1+KIgNwEY1G20LmQOuT2atWrcQTTyzGhRdeUvNx9KK0bNlb4DgO8XixVrFhw3rkcrnAheDjHz8dgIstWzZ1TEt/pGDI5pfDtjLVO64W6p2glSKObDaLlStX4Nxzzw/0wI8aNRozZhyB11///0KtpftRqunOIhKJ4o9//D0WLVqEu+++py0FVQqqeOg3gI5GI76++ub7t2mHDy1AdjskSahI5qUoHfriOA7z59+MfD6HmTM/imOOOQH77DOl5nPUQ1hzCgqSapmPI488Gh//+Ol49NGHqz6WOoH19w9A0zTIsuxF6BMmTMTcuZdg7Ng9vcczDAPXdZHJZDBpEolBN23aiPHj9wrzp45oDL9gdocQ9gSNx+NYsuQnFTtoMpn0bjKCzMAwXLzwwvP42c+ew733PoDRowcgCJyvK6N9/c2l/duSJDQ9nENlYVVV73r3JoB0BUmS1LTYmuO4cBwTCxbcD1mW8fLLv8bDDz+ILVs249Zb78Ree00ItZ5WJ7N/9KMnsH79Otxxx911/VxZlpCyIIiQ5XzZ42mdynVdLyKPRKIYNWo0AOB737sPGzasx6233rmbfB8bx4gl9LAnKMdx2HvvSWXHrFy5Av/4xzIcffRxnVlwl8E0Tbz55uv4znfuhyRFkc9T2V8OkiQhkQiv6V4LlSQIUik6k2AWWi+D5L4r+aoCRQvBcNLCLiKRCASBB8tKOO20T+C00z4BwzBakpNuZTJ79epVePzxR3Httddhjz32xKZNGyu+xt///jfIch5TpuyLcePGY8899wTHcYVdIfnsKdkD5HMlv7uFVtkkFi16CL/97a/w2GM/6pF5BYxYQm+ndICiKLj11m8CAM4//8I2rrJ7IQgCvv71m0puZWCaTkDTvWjY0ZimezMolSCQJMFrvfRH7kXDhl2LzJufl3EhSREIgoBsVoX/fW7V3DnsZLZt27jjjvk47LAZNYumGzasx5VXXgqApC8PPfQwSJIEhmGwfv0H2GOPPT0yp8ROUzOiKCEWi+O6667Fpk0bsXjxD9HX1w/LssDzI5bCQmHEvhvtkg7QNA1f+9qXsHLlclxwwcX40Ic+3K4l7uIIGnaUaroXW+7aQ+6u60LTSKHTry/D83whah8+nfJG0TqZU4OTIJm3A2Ens5cseQorV67A97//KNLpNAAgl8sWjtOQTqeRSqUwYcJEfPe7DyCXy+Gll36OFSuWY+fOHdA0DT/4wSP4wx9+i2OPPR777TfN21XT3Lmqqvjgg3UwTROPPfYjjBkzBrZt98i8AkbsO9IO6YBcLofrrvtP/OMfy3DGGZ/CZZdd0f6FjggQ2V/LMiHLhkfu0WgUtl3ZsKMVuK4L0zQRiUjI5fJgWRaxWBQcx3qaKfXyuEMNah0YjswBUZQgSSIymfaTORB+Mvu11/4C0zRx6aXlO9clS57CkiVP4Zlnfoq99pqAo48+FgAwc+ZJYBgGP/zh41i8eCF0XcNLL/0Czz33LPr7B7DHHnvi4osvxQknzATDMIjFYpg377+w//4HYcyYsWWTpD0UMWIJvVXpgMHBnfjSl67CihXL8alPfQZf+cr1vYGGhlAkd8AAx7GQJB6xWKQg+2sUZH/Dv5e0hS+fV70BFtrVQsTDIgVyJzn+4XQZAshwVZHMm2dzIqvQOTIHwk9mX3XVtV5ETjE4uBPf+taN+PjHT8fs2Wdg9Ogx3n2u64LjOLAsiyOOOBLPP/8TXHzxZTjwwIPxq1/9EsuXv4sNGz7Ascd+JPCcH/3oyQDKZQF6CGLEEnor0gGKIntkfs45c3D11V8KvY7hHqUeXjCeroiiUHJvTdO9mvQARXCsPqgvYxjmkEsQCAKPWCwamszp39BJMqcIM5ld6XtEi6J77TWhzNyZYRgvMBJFETt2bEckEsHAwADOPvvzAIptjZVy5D0yr40RS+hAeOmA7373TqxYsRxnnfX5lsh8OEapuxdMmaY7IffGNd3rkXkpTNP0CqVEgkAcUgmCdpB5LDY0ZA6EN6cIC54n53+l9Jjrur0ceQiM6HcszAm6du0avPzyi0gkEpg2bTpefvnFsuclk2v10Q6T6x/+8PGKXou7NoLkXtR0T3rKhKXk3qiOTDUEXYb4kgJu+yUIWidzkqbKZJSW0lPNIKw5RVj09/eD4zik04OB23upzfAY0YQe5gT9299IaiSfz+P22+dXfN5GCT3MpKof/lHqWpN3uzaKmu5Fww4OySRpJzUME8uXv4sf//jH+MpXvhpwSgoLy7K8HU+phRy5mLRG7q2SOc+T4zMZdcjInCLsRLcf48fvhVdeeaPuayUSSdi2jWw2W/exPTSGEU3oQPMn6Jlnfg5nnvm5ll93KEepRw6Cmu4sy2Dt2pWYP/9mfOc734EgCHDd9mi6UwQt5LhCd07EJ4jVXI6/HWQej1Myb/rwXQqbN2/C1Kn7egXPHlrHiCf04cJQjlKPTDBYvnwFbrvtm/jWt+7A6NF7wXXRFk33aqD6MoDm8wf1p4FqSxDQyDosmROhqiiy2ZFP5gAwefIULFz4OCKRSG9IqE3ovYMdwlCMUo90uK6LO+74LsaNG19B050v0XTXC+mYTurLxD2DCl03AqTN85SMw0bmLOLxGLJZFbuToCD9fvTIvD3ovYsdQqdHqXcHTJs2veLtRPbXhq4XDTtiseYNOxpFJX0Zav5Mh5haIXOOYxGPx3c7Mu+h/egReofQ6VFqv4jR7gyq6U7eU0Lu0WjU8+s0DL3Q4tgZfRlikB2H4ziQJAm6bjSl2U27dzKZ1sm8587VQ4/QO4ROjlI/++zPelrQFVGq6c4hEiFGHcWp0fYpQ5I8u4B0OgvXhWe1x7IsTJOkZWp15XAcg2QyjmxWa5nMw848vPXWm/jyl6/BlClTcdllV3juXFdffdmIcufaXdAj9A6hk6PUVBe6h1qoRO4SeD7WFnIvWvLlPTlfaqzBMHQoqKgvYxhmYBiKyMEmkM1qsO3WK6BhZx787lw0nz179hk477yz8Mgj38d9940ch67dAT1C7yCGYpS6HsJuwwcHB/HIIw/ilVf+CF3XMX36/rj88qt30W04JfdSTfc4TNNsWtOd4/z+quVkTAuntJ+daLFI0HUNCxc+gmOPPRbHHntM28gc6Llz9UDQI/QOYqhHqUsRdhuuKDKuuupSbN++DWefPQfJZArPPfcM5s27HIsWPYGpU/dr6zqHFn5Nd71pTXeO45BMNmeW7Td4Puyww/DSSy/i29/+Ng477EM46aSTccQRR7Y0Hdlz5+qBokfoHcRQj1KXIuw2/KmnHse6de/jgQcWYsaMIwAAp5zyMZx99qfxox89iRtv/FZb1zl8aF7TvVky94PjGJxyyik45pjjoWkm/va3v+JPf/oDJk3ap+K8QqPouXP1QNEj9A5jKEepSxFmG+66Ln75y1/guONO8MgcIMRw5ZX/OYL7hUs13cnUaCxGyP2dd97BrbfegkceWRyqNZEYWCeRz2uwLCI8deSRR+PII49ueeU9d64eKEbqt3O3R9ht+KZNG7Ft21bMmTMXADzHmFgshs9+9qyOrrl7wMCyHFiWA1k2sG7dGnzzmzfinnvuQSIRa1rTnRhYJyHLhMzbjZ47Vw8UvWbmLoOiKJDlMObBQTS6DS/F+vUfAKDpogWYPfskzJo1E+eccyZeeeWPLa9rV8PmzVtw00034Oabb8fAwJ6QZQMcxyOVSiGZjEMUxTpEWiRz0+zMPH+73LmuvfZK/PWvb/TcuXZh9Ai9S0C38X/+8x8xe/a/4bnnnm3p+Rrdhpcil8sBAB599GG8+uormDfvy7jhhvmIRCK4/vov4/XXX2tpXbsaEokEvv3tewpdSkXDjnRaKZA7i1QqiVQqDkkKknuRzPWOkTnQHneua675D/zjH8vwqU99Bl/72o09CdtdFL2US5eAfoGOPPJoDAyMwoYNJFKmokW6rkHXdaRSfQ09X9htOCkQAvl8DkuWPIdUKgUAOP54EqUvXPhg062TuzISiUSV3HN9TfdIRISidC4yp+gWd64ehh+9CL3L0N8/gFgshr//fRkAIlr0zjv/xM03fwNnnHEqFi16qOLWuhRht+E0kps58988MgcIaZxwwky89947XvTfA0VR0z2dVpDLaWBZDppmwjCGRjbxpJNOxhtvvIb331/r3UZnHk49dVbV49rlztVDd6AXoXcRaFR9+OEfwuuvv4bVq1fil7/8BZ5//jn09/fj61+/CUceebSXMqmFsNvwMWNIzn1gYFTZff39A4UiqYJYLNbU37b7gJC7orTXAakehtudq4fuQI/QuwSu63qCW3vssScymTSuvPIyiKKAM8/8fzj77M9jzJix3mPr5TjDbsOnTt0XoihWtL3btGkjRFFCf3/jBtdhJ1XfffcdPPzwA3j77b+DZTnMmHEErrpqHiZNmtzwa+9OGG53rh66Az1C7xIwDIN8Po/f/e7X+MlPnoFhGDjqqGPwxS9e48kGAEEyt20bDMNUVV4MIz0QjUZx/PEz8ac//R6rV6/C1Kn7AiDE/Oc//xEnnvjRhicIw06qrlu3Fldf/R+IRCK46KIvACBDUldc8QU8/vhS78LWQxDD5c7VQ/egR+hdANu28corf8CSJU9h1aoV2G+/6di6dQsmT56KffaZDMdxPNJmGAbZbAapVF9dYg0rPXDFFdfgrbfexDXXXI6zzjoXgiDg2WefhihKuOyyKxv+u8JOqj7zzFKoqoIHH3wE06cfAAD48IePwqWXXoj//u8luPLKeQ2voYcedif0iqLDCNM08de/voGvfOU/ccMNXwXLsvj2t+/BnXfeg3g8jnXr3i87JpvNYunSH+I//uNi3H77fKxevarq89Nt+H77TcPixQvxzDNLceKJJ+Huu+8PbMNvueUmLFv2lnfc+PF7YeHCxzBjxhFYuvQpPPHEYkybNh0PP/yDpuQJ6k2qVsPGjRvQ39/vkTkAHHjgwejr68OqVSsbfv0eetjd0IvQhxFbt27BXXfdDsPQceONt2DWrNnefclkCmvXrvaicQrLMnHkkUcjFovhxz9+Gn19/bjyynlV8+phpQcmTJiIW2+9M/Tf1opJ9sSJe+ONN/4Pg4ODXq49m80gn89jzJgxodfUQw8jHT1CH0ZMmDARTz/9HGQ5j3g8Adu2vTTKwQcfiuef/wlYNphWGTVqNEaNGg3DMDB58lQce+xHADRWKB1KtGKSPWfOhfjzn/+Em2/+Bq6++lowDIMHH7wPPM/jc587p+NrH2qELRyHPa6HkYseoQ8jbNsGy7KIxxNwXTeQE582bX9omorf//43+MQnPh04zrIsrF69Eq7r4vDDPwQAXWdJ14pg1Lhx43DBBRfj3nvvwkUXfR4AUQa85ZY7A2mYkYCwheOwx/UwstEj9GGEn8D90bXrupg1azaOOOLDniSA4zhgGAYMw2Dr1i1YtWolpk2bDp7nA0XTbkErglGLFj2EJ55YjBkzjsCnPvVZOI6N55//CW666Wu49da7cMIJMzux5GFB2MJx2ON6GNnoLhboAQAhOsdxMGbMWC9lwbKsR+4ffLAOW7Zs7mq96rCTqrlcDkuXPoUDDjgICxY8hFmzZmP27DPwve89gsmTp+Kuu24rOA+NDIQtHIc9roeRjR6hdykqRdz0tlWrVoJhGBx22Iyqjx1uhJ1UXb9+HQzDwKmnzgrsYHiex6xZs7Fz547AePuuDFo43n//8jTS9OkH4N13/9XW43oY+eilXHYRrFq1Em+99QbGj5+ADz54H4cdNgPRaDRQSO0mhJ1UFQTSTlnJEci2yW2u27xbUDcibOG4lYJzDyMb3Rfa9VARfX39eO+9d3HjjV/FCy/8FMuWvYX16z/oSjKnCCMYNWXKVIwZMxYvvvhCIF2j6zpefvkX6O/vb9nT9M47b8VVV13W0GM3btyA66//Ck477WScdtrJuOWWmzA4ONjS61OElTgOe1wPIx89Qt9FMGbMGHzjGzfjt7/9CxYufAxjxozF/Pk3YMeO8pRGt2DOnLlIpfowb94X8fTTP8STT/4AN9741bJJ1ZdffhEbNqwHQArF1157HdatW4vLLrsQzzyzFE8//UN84QsX4P331+Kaa/6rJRu8F154Hj//+fMNPZZ2kvzzn//AeefNxbnnnoc///mPuPbaKwtG0q0hbOG4XQ5FPYw89FIuuwhc14Vt2+B5HgcddAjmz799uJdUF2FNsj/60X/Dvfc+iMceW4RHHnkQAMkNf+c7C7y++2Zh2zaefPIH+MEPHmn4mE53koQtHLfDoaiHkYkeoe8iYBjGi0wdx4HjOLuEYXPYSdUPf/gofPjDR7VlDbqu47LLLsKqVSswe/YZePPN1xs6LozJdjMIWzhu1aGoh5GLXsplFwTLsrsEmXcLDMOAosiYP/8O3HDD/IbqDkPRSRK2cNyKQ1EPIxs9Qu9hxCMej2Pp0udwyikfa/iYsCbbzSKs01DY43oY2eiFeT2MeLAs23SvfivSBc0grMRxI8f1sPuhF6H30EMFDFUnSViJ40aO62H3Q80IfezY5FCto4cehgwcx0IU+Zrn94QJxBVJEJiyx3EckWCYNGnPtnirjh17KJ544rGq91944RxceOGcpo/rYfdDL0LvoYcK2GuvvQAA27ZtK7tv69atSKVSPaPsHroOPULvoYcKSKVSmDhxIv75z3+W3fevf/0LhxxyyDCsqoceaqNH6D30UAWzZs3Cq6++ilWrijZ/f/nLX7BmzRqcfnqv8NhD96HX5dJDDwA++OAD/PWvf8URRxyBvffeGwBw6aWX4qc//Skuuugi/Pu//zt0Xcejjz6Kgw8+GJ/+9KfrPGMPPQw9ehF6Dz0AeP3113Hdddfh9deLU6SjRo3CD3/4QxxwwAG4//778cQTT+DUU0/Fo48+2usk6aErwbjUNaGHHnrooYddGr0IvYceeuhhhKBH6D300EMPIwQ9Qu+hhx56GCHoEXoPPfTQwwhBj9B76KGHHkYIeoTeQw899DBC0CP0HnrooYcRgh6h99BDDz2MEPQIvYceeuhhhKBH6D300EMPIwT/PyIYP4GW0FZFAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nplot = [101, 101] # chose grid discretization\n", "X = nodeunif(nplot, [a, a], [b, b]) # generate refined grid for plotting\n", "yapp = F(X) # approximant values at grid nodes\n", "yact = f(X) # actual function values at grid points\n", "error = (yapp - yact).reshape(nplot)\n", "X1, X2 = X\n", "X1.shape = nplot\n", "X2.shape = nplot\n", "\n", "fig1 = plt.figure(figsize=[12, 6])\n", "ax = fig1.add_subplot(1, 1, 1, projection='3d')\n", "ax.plot_surface(X1, X2, error, rstride=1, cstride=1, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "ax.set_zlabel('error')\n", "ax.set_title('Chebychev Approximation Error')\n", "ax.ticklabel_format(style='sci', axis='z', scilimits=(-1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot indicates that an order 11 by 11 Chebychev approximation scheme produces approximation errors no bigger in magnitude than $10^{-10}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us repeat the approximation exercise, this time constructing an order 21 by 21 cubic spline approximation scheme:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = [21, 21] # order of approximation\n", "S = BasisSpline(n, a, b, f=f)\n", "yapp = S(X) # approximant values at grid nodes\n", "error = (yapp - yact).reshape(nplot)\n", "\n", "fig2 = plt.figure(figsize=[12, 6])\n", "ax = fig2.add_subplot(1, 1, 1, projection='3d')\n", "ax.plot_surface(X1, X2, error, rstride=1, cstride=1, cmap=cm.coolwarm,\n", " linewidth=0, antialiased=False)\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "ax.set_zlabel('error')\n", "ax.set_title('Cubic Spline Approximation Error');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot indicates that an order 21 by 21 cubic spline approximation scheme produces approximation errors no bigger in magnitude than $10^{-6}$." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "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": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 4 }