{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "377155b7", "metadata": {}, "source": [ "# Analysis of the simplicial contagion\n", "Here we show how to simulate a simplicial social contagion on a random hypergraph and on a real-world social network\n", "\n", "Source: \n", "\n", "[1] Iacopini I., Petri A., Barrat A., Latora V., _Simplicial models of social contagion_, Nature Communications *10*, 2485 (2019)\n", "\n", "[2] Vanhems P., et al., _Estimating Potential Infection Transmission Routes in Hospital Wards Using Wearable Proximity Sensors_, PloS one, *8*(9), e73970 (2013)\n" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ".. admonition:: Definition\n", "\n", " Simplicial contagion allows higher-order interactions to trigger infection beyond pairwise spread.\n" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ".. admonition:: You will learn\n", "\n", " Simulate simplicial contagion and compare with pairwise-only dynamics.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "- Simulate simplicial contagion on synthetic hypergraphs.\n", "- Compare dynamics with and without higher-order interactions.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import matplotlib as mpl\n", "\n", "mpl.rcParams.update({\n", " \"figure.figsize\": (6, 4),\n", " \"figure.dpi\": 120,\n", " \"savefig.dpi\": 150,\n", "})\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "d319e615", "metadata": {}, "outputs": [], "source": [ "import sys\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "sys.path.append(\"..\")\n", "from hypergraphx.core.hypergraph import Hypergraph\n", "from hypergraphx.generation import random_hypergraph\n", "from hypergraphx.readwrite import load_hypergraph\n", "from hypergraphx.dynamics.contagion import simplicial_contagion\n", "\n", "np.random.seed(123)" ] }, { "cell_type": "code", "execution_count": 2, "id": "41895503", "metadata": {}, "outputs": [], "source": [ "# We first analyze the contagion on a random hypergraph\n", "# We define the random hypergraph\n", "N = 2000\n", "E2 = N*10\n", "E3 = N*2\n", "hypergraph = random_hypergraph(N, {2 : E2, 3: E3})" ] }, { "cell_type": "code", "execution_count": 4, "id": "4ce89a4a", "metadata": {}, "outputs": [], "source": [ "# We set the contagion parameters and run the simulation with and without the simplicial term\n", "mu = 0.05\n", "beta = 0.75*mu/20\n", "beta_D = 2.5*mu/6\n", "I_0 = {}\n", "\n", "for i in range(N):\n", " I_0[i] = 1*(np.random.random()<0.8)\n", "\n", "T = 500\n", "\n", "rho_t_simplicial = simplicial_contagion(hypergraph, I_0, T, beta, beta_D, mu)\n", "rho_t_simple = simplicial_contagion(hypergraph, I_0, T, beta, 0, mu)" ] }, { "cell_type": "code", "execution_count": 5, "id": "44f86bd0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We plot the results\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(range(T),rho_t_simplicial, \n", " lw=2, c=plt.cm.Accent(4),\n", " label=\"$\\lambda_\\Delta = 2.5$\")\n", "ax.plot(range(T),rho_t_simple, \n", " lw=2, c=plt.cm.Accent(5),\n", " label=\"$\\lambda_\\Delta = 0$\")\n", "\n", "ax.set_xlim(0,500)\n", "ax.set_ylim(0,1)\n", "ax.tick_params(axis='both', which='major', labelsize=13)\n", "\n", "ax.set_xlabel(\"time, $t$\", fontsize=15)\n", "ax.set_ylabel(\"fraction of infected nodes, $\\\\rho(t)$\", fontsize=15)\n", "ax.legend(fontsize=15, frameon=False)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "cfe4c885", "metadata": {}, "outputs": [], "source": [ "# We now simulate the process on a real-world system\n", "# We consider the face-to-face interactions occurring in a high school\n", "high_school_hypergraph = load_hypergraph(file_name=\"../tests/test_data/hs/hs.json\")\n", "high_school_hypergraph = high_school_hypergraph.get_edges(up_to=3, subhypergraph=True) ### FIX SUBHYPERGRAPH\n", "\n", "average_degrees = [np.average(list(high_school_hypergraph.degree_sequence(size).values())) for size in [2,3]]\n", "avg_k = average_degrees[0]\n", "avg_k_D = average_degrees[1]" ] }, { "cell_type": "code", "execution_count": 10, "id": "6c487dda", "metadata": {}, "outputs": [], "source": [ "# We set the contagion parameters and run the simulation with and without the simplicial term\n", "mu = 0.05\n", "beta = 0.5*mu/avg_k\n", "beta_D = 2*mu/avg_k_D\n", "\n", "I_0 = {node: 1*(np.random.random()<0.5) for node in high_school_hypergraph.get_nodes()}\n", "T = 500\n", "\n", "rho_t_simplicial = simplicial_contagion(high_school_hypergraph, I_0, T, beta, beta_D, mu)\n", "rho_t_simple = simplicial_contagion(high_school_hypergraph, I_0, T, beta, 0, mu)" ] }, { "cell_type": "code", "execution_count": 11, "id": "a638e89d", "metadata": {}, "outputs": [ { "data": { "image/png": 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c7Swxtm9Ftm/n8XiTBrjLNp/HmP/uwF8nExCdlCuVQujEJOfV++C0uRJFw+y0TuXP2ESZ8zXyi8qw/4J2Do6Lg5XB57E+d2cbCNqTicjIbXhArT/3J8KEi8T8fTIBfx41LNcoVWlw8orhd5z+932H8r79giDgzZnhWPhQL2kdgb9PJfJAuhliQN2MXU/MkT6gbKwqJmI0xsTEG8m5+OL3yyZZ0U4/aOreXpvhValFfLa1Yhnvu/v5w9pSibcf6yP9bI62lljwUC9pG7llH9cTcxFxLhnZ+aX4fNtl/GflwWq7MZyPycSaHVcAAAoBeG16GBQKARMHB0qTQv48erPa07aX9c4kZOQUY/vR5lHrlp1fKtWE68Sm5BkNJPT/bvcPDqzYPrWeAXW6Yc/YLu1cYGWp/ahpygy1fp1sXlGZrNf23ycTcDMtH9FJufj3nPYsxjkj2XxdGUFuYSl+johBfpEK/9t2CaevGpYM1fcgBTB8jenLKSjF8l8uQBRFnLmegW92RCGrvK67tRJFEWv1ugtNv6sDAMC7jR1Cyw/w4lLzERWfbZL9nb1+C7/sv4HcwjIs+/k8thy4Id0X5O0oXb5dardTs4qkxE4HP2fp/V2Z3Az1P2eTUFqmPVN5V29fWCiN78dCqYCrgzUAeTXU+mfv6lLmVxcJ6QX4cNM56bp+trnye9pYhhrQBtX33RGIgeUZ+qy8EkTqdf+i5oEBdTMVn56P/ecrJjmNDK+YUHO9EVrnvfXDaazbfQ2vf3eywc+RX1SGqJvZUjbO3sYCM+/qKN2vm1jS1tUW4R3cAQCBXo5Y9vQAjAj1wftP9MXIMF+4OFgBAPZfSJZV9lE5aDkfk4mZH0Rg874YRN3Mxo3kXGg0IjQaER9uPCsdvDw+tpM0Pmd7KzwwpD0A7UqDP+4xnqWuXOv+w+5rKFNpx65Sa5Cmd2pPoxGRnFlYY3YsI6fYJO3tbho5gCgqVVc51QgAZ/W+QMb3bydlQ6rLphaWqBB1MxtRN7ORnV8RwOl6xro728DO2gJWlkp0D3QDACRnFjZ67apO5a4icvqJ65f7JJeXdlReMER/O/1MZEZuCf6pNBGxvgG1KIrSF6ijnSUevjMYoSFt4OqoDSIib2bjm51X8Pyqw1iz8wo+/711nxI+Gpkm/b46+Dnjjm4Vmc27K2Wp60ul1lQ5YPnuryvS5byiMmmCtVIh4NVHwqT7qut0k5FTLL2XWsLS6Pqv3wGdPdCj/P1dmdyOQrv0/j5369USG6Oro76VW9Lgz079z7r49ALZHUPKVBosXntSOvM3tq8fFjzYU8qmVw6KdckyhQAEeRuevQWAQXqv49uxa1JLx6XHm6Ev/7iM7/++ZnDb+P7+2HnsJjQicN0EWWR9hSUqaYLEjZQ8pGQWwsvNrs6P12hEbIqIwZd/XpayCQDQK6gN+nf2QIiPk8GYZ97VAQqFIF0P7+AuBbC66/+c0WYmUjKLjK6MVRf6H/p21koUlqhRXKo2mBQ2tq8fhvb0llo9dWnngsfGdDR4nodHBGPzvhgUl6qx9XAsHh3dAW5OFTV7eYVlBu3/AO3s9r9PJmBsP3889ckBRN7MxrCe3nhgaHus/PUiopNyMXV4EOY+0KPKuP84Eof3fzqLLu1csGb+UIPfVX0l6NUz29lYSB/ssan5Bn9j/YmkTnaWCPFxgr+HPWKS83AzLR8qtcYgO5SWVYRp7/8jlfAoFQI+f/EOBHk5IStfWx/sr/d3Cwtpg9PlK06ejb6FsfV4fTVESmZhlYz0mesZmDIsqEHPpx9Q6w4IjJWvJJUH25UPeit/wcfVM6BOySqSgriuAa54YWJ3AMDeM4l47VvtQfA3OyuCusqnklsTlVqD1dujpOuPj+kIQah4D90Z5oNlm8+jVKXB7lOJeGFi92ozn5UVlqgw84N/kZZdjP+bFoqxff1xKTaz2vK0Qd3aomuAKwK9HBCbko9LsdoFjpzttUmDohIVPt922SCj7Whnie8XDId3m8Z9j8ihH3gGeDnCylKJU0ZWlE28pU0c6P/+6yols1B6jwW0dUBnf5cat/dwscHVBO1Z3ay8EoOJinWhWwdB39nrtzBKrztMfX35Z6QUNPt52OPlB3vC3sYSAW21r4driTkoLVPDylIJlVojfWf5ezoYnJXWGagXUB+5nIrZ4zs3eGxkeiYJqEtLSxEZGYn09HRkZ2fDxcUFHh4e6NKlC6ysrEyxi1ZDFEX8fsSwXMDFwQrdAlzh7+mAuFTtaecnl+3HgC6eeHJcZ5SUqfHJ5gu4Xt4BpJ2nAxZM7QVb67r9eWOScg06bNQl4IlNycM3O68g6VYB8grLqqzsBAADunrCylKJtf8drm38L4pwsrOq9YNOv3F/YkZBrQF1ek4RvtlxBaUqDV55sKf0c8fplSp8MXcIth6KlTJHOrtOJEgdSABg9rjOVb5cXR2tMfGOQGz4NxqlZRr89E80nru/m3S//mnjzv7OiIrX/h32X0hGiK+T9IG673wy9un15P79cBz+M6ErrCr1Vf2rfBJO5M1sJN4qgL+H8VZRdaFf4jKgiyf+OaPNlN5IzjOY4BOTkofc8trg0JA2UCgEBHo5IiY5Dyq1iMSMAgS0rTh1ve98shRMA9qAcdfxBIzuU/Hlo7+9/sTEz7ddxu+H4zC2rz/uHdiuQV+2+kRRxJodVxCTnItHR3dE53YuOHy5avbm7PVbDf5yT9Q7dZ2SWYS8wjIpaLZQClCpxfLttO+D2sqy6puh1m9H1qWdi3R5RC8fKVjTl5pVhFu5xWjjVL+gojnSaESs2noJRSUqPHtfNzjaWda4/be7rkjvuSBvRwzr6W1wv4OtJQZ08cT+CynIzi9FcmZhnd9jJ6LSpdfCBxvOob2XI776syJ4d3eyRkZuRfZal1Ud1M0LsSnXoRGBNTuikJhRgJyCUqRlF1fJguYVlmHtX1exaFooAO3r+3+/X0Z6djHmTekBJzvzf6fqv37bezmirV7bOgBSEqWwWIWcglK4OFjj5JV0bN4Xg36dPfHA0Pa17kP/rN/IMN9a37e65ccB7XdCfQPq9Jxig880ADgTndHggPpYZBp+Kp93Y6EU8M5jfWBvo33tdmnnitiUfKjUIq4l5qJboCviUvOls5q6+unKPF1s0cHPGdcSchB5Mxtr/7qKY5FpKFVpg/Jpd4ZgSA+vBo23OflmRxSik3Mx8y7t53lL0eCAOj09HWvXrsX27dtx/PhxlJRUrdmztrZGv379cM899+DRRx+Fh4eHrMG2Bql6mShfd3sM7t4Wd/X2g5WlEh19nRGXql3p7lJsFi7FZmFQt7a4npSL34/ESc9xOS4bAW0d8NiYTtXuR1eD1buje5Uv/7PXbxlM3tGn0YjYvD8G//vdMButMyrcF872VvB1t8fE8jpcZXlwVle+epmZ2ia17DmdiKWbzkkTxYJ9nPDIyBAAFR/6VhYKBPs4YcHUXhgV7ov955ORV1iGHeWnE3WlKF3auWBAV+OzyKeNDMGWAzdQqtLg1wM3MH1UCFzKa/b06+AmDw3Cyt8uIq+wDOeiM6WsrDFFpWqcuX4L/SvNXNcPgtOzi2UF1PqLugzt6S0F1IcvpcDD2Qb9unjAyc7KoNwjNFh7tqC93t/sRkqeQYBsbMXOyJtZBgc/+oFf9/auUuCZkaMNIs5cv4V/zibh1UdCDb4M6+vk1Qx8u0ubnT1wIQXT7gw2yB57udkiJbMIWfmliEvNr9drEago0dFJySzEpbgs6SB0cHcvaQKTLkNdXb22rZUSRaVqpGUXo6CoDPa2NQeHOvqvMV3nGQBQKAQ8Nroj3lx32shjsm+LL9d/zyVh47/RALSfWx/M7oeE9AKk5xQjNLiNwRmc09cypNpppULAfx8KNXqGx0+vn3FaVlGd32P66wKUlKkx66N90mTktq62WPpUfzy2NAKiqJ0Tois1uaNbWym4+mX/jSrPa22pxJg+fth7JlHbb/j4TTw+tiO83Oxw6moG1peXmgV61fy53lT0D+AC2jpAqRCk93dbV1v0CHKTzkrGJOch4twVbN6n/bkPXkzBsF7etQa8+qVhAW1r//voLz/ekFINY6VtZ6/fQmJGAW7llqBnkPGylur8sLviLPOz93UzCAy7BrhI5UaX47LQLdAVR/SSACG+Vcs9dAZ19ZTq1yuvE3AtIQe/vTW6ykGnWiPizLUM+HnY1+vsszlE3szCmvKzbfvPp+DxsZ3w2JiOUMo4U9tU6l1Dff36dTz88MPw9/fHf//7X+zfvx8ODg4YNGgQ7rnnHkybNg3jx4/HoEGDYG9vj/3792PBggXw9/fHtGnTcP169Z0SyPCo/K7evpj7QA90C9R+gU4dEYy2roaBx7WEHFyNrxrc1DSDXa0R8Z9PD2L+l0exfMuFKqenq5uMkXyrEM9/dhgrtlw0CKYFQRvIfvb8ILzzeB+8/GBPPHxncJ1Po1bmo5ehrmlSy45jN/H6dycNWvQdvKitO1epNVL7tnaeDtKbMbyDO+Y+0AOvzwiXAn6dxyqdGtbn7myDCYMCAGgD4U0RMdJ9+tnDboGuUjY2p6AUWw9VHOj07eQBV0drg8xw5Tq44lIV0vTaPsmt4dPVMysVAgbqHSycvJqB19eexEPv/oOfI6Kx4Z9o6b7wDtrxB+oF0JUzoLoaYUHQdkTR3aY/Ua9rgIt02cbKAk/c3RnWlkro/4qPRaZh7udHZNXK6y92oNaI+GHPdVws713bxskakwZXZMMa0mUkI6dYyhwBQFp2kcF75o7ubaV688SMAqjUGkQna38/+pO1rCwUGNarIltaXftCY/RrLfV/r4B2fsVd4b7wcrXF/XcE6j3G+CTGluZ8dEW3jP0XUjDvi6N46N29ePbTQ9iu97cXRRFLNpyVDnSeHNe52iDIUy/4MjafoDqVa151wbSFUsC8yT3Q0c8Zc+7pAk8XG7z4QHfp7FPPIDc42FbNXykVAvp0dMe6hcOxaFqoVJKkUov4YY82INM/mIqsNFfDHPRLI9q62sLexlJ6f7s5WuPJcZ3go5cUeemLI1IwDWh/Z3VZuCslq+Kzvy5BoLvM1nnGAuqY5Dw8+PYezFl+wKCMqDZqjSj93dq62mLqcMNSsy7tKg6KI29mo7hUjZ/KP4MFAVXOqugb1K36g+SCYhV+3hdT5fYt+2Pw/GeH8eiHEc2+Rv+8XncctUbEmh1R+PVA1YPQ5qheGernnnsOq1evhlqtxogRIzBt2jQMHz4c7dtXf/omJiYG//77L3766Sf8/PPP2LJlC5566imsWrVK9uBvR/pfgpW/OLsFumLr26Nx8ko6nv/sMABt5lD/gyDYxwnRSbm4mVZQfuRb9Qsl6maWFCDtPpWIgEqrT91MK5BOF5+8ko53fzyD7PxSlKnU0C8FfXBYEJ6Z0AU2VqYtxdfPUFc3qeVmWj4+/vm8dF2XHbkQk4ncwlJk6k1MaV9NRvKFid1x8UYmriXmonuga63ZvOmjOmDroVio1CI274vBtDtD4GhnicvlfzM7Gwu089T2XT5Qvmqerrbayc4SK/4zEAqFgPyiMoxduBNqjYhDl1Ix94HuUiCfUKl0Rs4iBdqWedrn83W3g5OdFXq0dzNosZaVV4LlWy5K19t52iOk/HRjoLd+QF3xGtMPGP3c7dEzuA22H70JtUaUDhCsLZVVMsGPjeko1acfuZyK9386i4ycYsQk52HP6cRqz4okZhRgwdfHYG9jiflTeqCTXi1lYYkK+8qzw1aWCqjVokG98ug+ftIBAgCcuZZR5UCqNpXPkmhEGNTMBnk7wdvNDjfT8pF0qxDxafnSAecd3byQdKsAV+JzMKhbW3T0c5H66sam5EkHyzVRa0RE3az4cq5cxmGhVODtx/sA0B70bi3vg155omxLdbnSgcFRvUU3jkWm4d6B2gPdrLwS6f3T2d8ZM8o7exijX6JQ1wVXRFGUAloHWwtoNCIKS9QI8XHC4hnh6OCnfd88OrojHh1tOA/DQqnAqHA/bD0UCytLBZ6d0BWThwZVyZ4/NCIYP0dEo7BEjT+O3MRjYzoazD9pjA5PNSlTafDKV0eRnlOMj57qDx93e2TmlUhn9fTf4/rvb/3VQI2dybyemGMwwc6Y5FsVfxcvt9rPYHkYWdzl0MUULNt8AaP7+OLpe7vW+PgbekkD/c9JqR3qX1cQGtIGfTvVfqY9NiUPReUtNLsFulZJ1HTwdZK+sy7HZeH3w7HSmekRoT41nkXrFugKfw97xKcXwMvVFq9ND4OXmx2mvrMXao2ITRHReGh4kMHZr33lDQ5yC8tw+WZ2nX4GczF20HjgQkqD5780pXpFQt9++y2eeeYZLFiwAD4+PrU/AEBQUBCCgoLwxBNPIDExEUuXLsWaNWsYUFfDsFbS+Jdte/1AJzVfamvm6mCFh0cE490fzwAAdhyPx63cEqRkFuK+OwJhXZ4t0W/dVFisMtp+58z1WxgV7ovPt12qksHxcrXFq4+EoU8jvSk9XW2hVAhQa0SD2lWd0jI1Xv/upPSBdc+AdrC3scCmiBioNSKOR6ZDqaz4AAuo5sPJxkqJL18aguORaQjv6F5rjV5bV1uM798O2w7HoaBYhb9PJmBoLy8pG9LF3wUKhYAwvQBOR//UtIOtJXoFayfpJWZoVyTUlVPol2gA2hZQpWXaL1dfD/tqFzbQOXU1HfHpBbhnQDskZxZKfZF1S/Z+NKc/Dl5MQUmZGkcupUkZfUB7APfmzN5SNr+dhz0UgvYLRb9mMiG9QPqSDPF1Rtd2LlKbQF0w29nfucYzFAO7tsVbj/bGs58eAgCs/esq7urtZ/S03ufbLkmTRp/4eD/m3NNFCpb2nUuWXgfj+rXD1OFBOBt9CxpRhIu9Ne7o3hZKhSBNSv3nbBIeiL6FXsGGf6P88s4Mndu5VPmyMXaWRL9jSEBbB/i6awPq4lI1jutNCOzg64SXH+yJ89G30Lezh0H2pa7tCG+m5qGwRPszdqmlntDLzRauDlbIyi9FZFxWg2vGmwuVWlNjNlP/dam/sE63QLcaTxF76p3pS82qOGgVRRE7jsXD2cEKg7sbHmAnpBdIgWRosDvmT+mB2NR8hIe0qTIPwpgXJ3VH/y4e6OzvUm3G1dneCpOGtMf6PddRptIg4myyQceY5MxC5BeVwaGOpUJp2UX48+hN5BeVwUIh4M4w33rVpB65nIpj5QeP3/11Fa8+Emaw0mpgNaUYPkYmVI7t6ycdTNalH7eu5MNCKcC9DnMBjC0/vnpHFJIzC/H939cwZVgQ7Kwt8NvBWKlXdWhwGwwtzwbrvx8fGNq+Sm93UQTeWncK6xaOgFt5d53q6J9VMPaetbJUooOvMyJvZuNmWr5BE4LHK02Kr0w3AfzSjSz07ewh1WWP6eOHHcfjkVdYhl8O3JAO6tQa0WCeT2xKXrMOqHW/O0sLBSwtFCgsVtU65yQtqwi/H4lDYYmq/ODVFx39jNehN6Z6BdQxMTHw8mp4TZ6vry9WrlyJRYsWNfg5bmcajYjI8he+p4tNtTVmbo7WcLS1RF5RGS7HZhlkC4aHeuOjn8+jpEyN3w7G4tcDsQCAwhK1lD2ort2O7jkBbe1YsLejNMHOwdYC3m3sER7SBk+O61znD/SGsFAq4OVmi8SMQiRmFEAURRSWqGBrZQGFQsDnv1+WvmQD2jpg3uQeuHAjUyrDOHQpBe30su7VZagBwM7aAsND63ZwCACThwVh22FtGcfOE/Gw1zuNqzuj0MHX2aCjBgCp963OoG5tpfrqw5dSpYC6cp/s9Jxi/HYoFiu2XIRSIWDDq3dKwTGgfc2UqjSwsVIi8mYWXvz8CNQaETkFpQYf+rq2dc72Vhjfvx0AYOIdgdh5PB47jsdjQBdPPDTCsEzHylIJX3dtJiQuNR8J6QVo62prUD/dwdfJoKZXp4uR2yoL7+CO0OA2OBt9C3Gp+Yg4l4SRYYYTgGKSc/Hv2YqJnGqNdoJWJ39n9OvsadD2bGw/PwR6ORrN7jwyqgNWb4+CWiPije9P4fv/Dpc6LQDABxvOYm95ffn4/v6Y+0AP6TVurI5fVwKiO+Xt06aiTGmf3oIQIb7OcHO0ll5jlevS6+KkXg9rY79rfYIgoEs7Vxy+nIrcwjIkZhTWu0tOUYkKlhaKBpdsmVJ0Uq508Da8lzfautoiI6dY+lvFpxdIHWj0l373da+5REC/dE4/Q73hn2isKu+X/8WLgw3et4Z17NqguD71qDZWSgzvVftnzahwX6lm+lhUWpUOQtFJuVUOCKvzwYazOHK5IqP/68FYbHnzLoPXfk30D2b+OZuE+VN6VJmQaIz+xHJA27lk7gM9sPdMEspUGlxLqnvJR1tXuzp1OtLPUGfkFCO/qMxg/Gejb+HKzWz8oNf6dMM/0VjyZF8M7+UjnYVzd7LGXeG+uHgjE2lZRZh1dyd88ftlHItKx63cEqzZEYUFUyvWSzDGsETL+Hu2S4ALIm9mQxS1C0cBwNAeXtIZwpp/VlsMDzXM2j86piN2noiHKAJf/xmJgmIVnry7ExIzCgy+ixqyqFRjKylTQyEIKC5VS2dVO/o5w0Ih4FxMpvT3NBZ3iKKIhWuOG/zOdxy7ia1vj27yz7B67U1OMN0Yz3O7uZmWL73wa/riFISKSX55evVQgV6OsLexlOo09UuodRMeMnKKccVIzTWgnZGu+9w6cSUd249VBCtPjuuMdf8dbhBoNCZdgKKdoBOPMf/diSlv78E3O6/g5/LA2cpCgXcf7wNbawuEhbjDzlqbJToamWYwKay9V8Mn9VUW4uMkre54KTYLX/5RMSlEN7nQQqlAz/aGpTZhIe4G1/X74up3Gam8THhGTjEulGc11RpRak0liiK2H72Jcf+3C5Pe+BsXb2Tiu11XpQzxnlOJBvXCYSFVv4AFQcC4/u3w2fN3YPqoDkY/fHRfmCVlakx5ew8mvbnb4As6xNcZwT5OUg2xTuVyperotyj837bLVVYB1V+co5N/xRfNoYupSMsuwsmr2uyZr7tdld+5vkdHd5SCo9SsIoOlyGOSc6UADQC2H4vH86sOSXXdNdXx696H+gGc/u+98kqgbV1tpddpdGJurf1yVWoNfvqnIgCoPIHVGP3ffX3qqMtUGnz1ZyTGLNyJR97/B0Ulqtof1Mj0y1Z6BbfB3Ad64N1ZfaUlxMtUGmkiqH6GWv8AxxhXB2tYlJ/F0vWILypRSXXLAAwmegPAZb0v7LocMDZUiK8z7MsXkzpyKbXKa8TYhGBjVGpNlVZ2BcUqaYJnXejvq7BYhQMXUgwyudWVJlT+jpg6PBjO9lbS9jdT8w1WFa0sr7BMWpCqLuUegLasTrfCa3pOMc5F3zL4Djxz7ZbB+1zn/R/P4kp8NrLL230GejlCoRAwf0pPfPhUf3Tyd8HiGeHSKr67TyXUuhKu7uBLEAw/t/SN6VPxfQtoy+TktMFr5+mA+wYFAtCeVfxh9zUsWH3c4HULNGxRqcZ0IzkXk9/ag3H/txN/Hq14z3Vp51Jt2aG+w5dSq5xlv5VbIq0X0JRkhe933XUXfvjhB1ONpdW7VMtpIn3GMgO628b3r1qLejkuC8WlKoOZxJX1Cm4jBfI30/KxofyLXKkQcFdvv2of1xh89AKUz7ZeglojIulWIdbsqJgY8vzEbtLRvKWFAn07aYON7PxS6YNTqRDgJ6NLhjH6tb66cphuga4GvbT1M1t2NhZVZm3rygQA7STQW+WnICu3H0zPLja47XJcFlRqDf7vmxN498czyCkoRVZ+Kf67+rhUtw1oe5UfKi/nsLJU1Pp6qk7XSjW+GTnFBlnhEF9tMF05cKyuXKmyfp09pDripFuFmPXxPqz96ypUag2uJeRg7+lEANrWkUuf6i9NaDxzPQMHL6RIX5hj+vjXWNqgVAh4a2Zvafb7ntOJ0uQc/aBd9xRR8Tm4VD6xsaZOM7pT3sYCOEdbyyqTiAVBQEc/FwDa3tL6nQCM2XUiHimZ2tfYgC6edTqNqR/s1bWOOjmzEE8s24+1f11FmUqDm2kF1fZWNpXkW4V4+4fTNS6uon9A0EXvQMEg019eglCfDLVCIcCzvEQgtTxDvfVQrBRUAUDE2STkFpZizY4ofPrbRZzSO1PQ0PdTXSgVAnoFaT8/jB1v1XX5cv3sfs+gihKYzftiDCZy1/Yc+nYejzeYoFxTrW/vjtrPQ1srJR4sr38N8dF+TmjEmjOl+h0+6noWQBAE6XsjNiWvSvC853SidPDVPdBVmviXV1SGuf87UuPP5OZkI51lyi9SGSRBKispU0t/o/blSS5jega5Yds7Y/DlS4Px5UuD8eubo+qUna7J/Ck98PS9XaSDxWORaVUm9DWnDHVxqRqvfXeyPAOt7cmu0zXA1XBivJESOVEU8Z3e57f+95CxVr6NTVZAvXfvXvz777+mGkurp18/Xdup3UAjWVfdB0G/zp54ZWpPPDq6A0aEaj80VGptqz39co+hlSbhhfg64ZkJXaWjZt2H+YCunrXWjJmar16Aov8lpzO0p5e0gqGOsUkufh72VbKnco3u44fKZyArLx6hH1D3bO9WJfsrCBUHKRpRu7Q1UPVDICO3WOrUAWhfI78fiZPatOlkGllqWtdXunugW51qPI2ZMiwIj43piNF9/KosNOBoawmv8oBR//XqZGdZa0CjIwgC3pzZW/qiValFfPVnJGZ9tA9PLT8gvQYfGhEMTxdb6QvnelIu/ir/nQHa10NtPF1tMaZ82V+1RsSJK+m4mZZvELQ/e19Ff3Fddk6XodZllvXpAjtfI2UVIb5ORoP82eM7S6+fNTuiDOqq9anUGsPayrF1a5emH+wdvpQKTS1Z8NIyNRatOV7l7EB1S52nZRXJWsZd5+PN57HzeDze+/FMtd1sdAcESoWATnoHE8a+aPUz1HVZFEVXR51XWIacglL8uNewA1VRqRr/WXkI3+y8gg3/REs/s5+HfZ1LJhrK2DwMnbpmqPWzdsN7+WBceaKloFiF//1+GQcuJEsH8sYUFJVVmcNyLDJNmiDr6mhd4+/hlQd7YurwIKx4dpB0IKsf8NT0c+h3+PB2rVuGGoBUUqMRq66CmVNQ8T0yItQHrz4SJmW/9b9jqitjGdu3IqlU00HgtfLFZYDaD7zcnW3QK6gNegW1MVgsrKEslAo8OrojXp7SU7qt8kF1Vn6pwcq25vTpbxel+TGA4QJYXQNcKpXIVe2KdOJKupT4CPZxwoN63VQql0o1hSYpMHnmmWfQv3//pthVi6b/BVbbxBFjR9H6Qfakwe3x9L1dMaRHRfudI5fTpAlTLg5WeHJcxeklGyttvWx4B/cqfU6r677QmHyMBGSd/J3h6miNHu3d8H/TwqoEKyPDfar0K62pfrqh3J1t0Ldzxan3Tv7OVYL57oFuGNS1LRxsLfDwncFGn6fyB3R+UVmVJY3LVBppQhqgLU/YfTJRuv7SA93hpNdz1NpI4Bxax3pLY+ysLTDnni5469HemFTpACZYL2DU/+LoElB1VntN/Dzs8c3LQ7UraJY/7FpirnRKOMjbEZPLF4LQla6IYkV7JXcn6zpPQNH/Ox26lIp1f181CNp76JWNXE/MRVGJSjpYCSmvjdenex8GezsaTGKzs1Zi6nDjf3f995haI+LtH04bDXr3nU+Wulb07uhe5z64ro7W0t/8Zlp+lYOvyr74I1IqA9Pv5WtssnJadhEefGcvpi/5F4u/O2kQpNTHrdxiHCvv1qHWiDhrpJ1hUYkKN8q7yQR5Oxp0EzJ2KliXoXZ1sKo2K6jPU28S2/d/XcWt8gVZ9D9DjB04NGZ2WsfYe9bFQRu8Rifl1WlpbYOa70AXzLyropfv1kOxWPD1ccxY8m+Vzxyd68kVP7su46kRIX0e1fbZGtDWEXMf6GHwutXPwNaUadedlQHqnqEGDD9TazKoW1s42lni3cf7GhwU+HvYY2S48YVcenf0kN4fRy6nVvt703/f1PVMnamNCvc1aNlZWeU2qOZw+lpGlYXWdOxtLODv4WAQ5xjLrOuf4XtsdEe086zYvvJ8pKZQ74D6mWeewdq1a3Hx4sXaNy5XXFyMkydP1ndXrUppmVpqj9TO06HWOuXKAbWDrYXRmdD6tbMb/42WarTv6O6FEF8nBJdnBvt09JA+bB8fW1Fv6uFiU2W2e1PwNXIK/el7u2L7e2Pw1UuDjWZG7G0s8c38obhnQDvpNv0yDFPSz47PHte5SgCpVAhY9swA7PpgHPp1Nl73GtDWUSp3uJaYa9BqqjoasaLDhKeLDaYMC8Krj4RJ9/9nQpcqZxOM1U83xLQ7gw0+pPWzTX06ekj1i4OqWRynJlaWSjwzoSu+fGmIwZLlk4YEYs38oVKAFGYk0BjYrW2dA/jwDu5Spn3f+WSp64CjnSUmD2mPYJ+K99X1pFzpFDGg7VzgVSlbpnsfCoKAj+b0x96Px2PP0nHY9cE4g57TlT0+tiO6l//tEzMKjNY6H9Y7rTx9VPUt4Ix5VK82fe1fV6rtSX80Mk2qqbW0UODjOQPg7qR9/UTezKoS6B+PSpPqR3efTsT09/+pUvdfF3+fTDQICvV73ydlFGD2J/vxwFt7pIOdymfsdB1oAG1NaEmZWmqV5uNet0mYbfUOHv48WtHP+vXpYVW6VOgfsA3sWnO7N1Po3M7F4IyQLpMJaEsKEjNqP50dWSm77+dhL63cqJOVX4oN/0YjKaMAz356CP/3zXEUFGvPbF1PqAh4pwwNqnKmT1fSUR91zVDrL6RUnyXYA9o6Vpm/Ufk96+tuJx00dQt0xfb3x2LP0nHYs3QcNr0+stqsu1IhYKzeGa6/TyUY3a7ygYw52NtaYlgPw88fC73OV82hjnr3qYrE0IuTuhs0YejSzqW8LMtGOjNYOaAuLFFJ81V82thhRJiPwXdHfFrTl3zUu4HwV199ha+//hqA9ktk586deOyxxxAaGorQ0FD06tULrq6GH35paWmwt6/fTPPW5npSrtQ5oC4Tutq62EqrrgHaL3ZjQYV2Jrp2pTj9L7BpdwZDEAQse3oAjkelGfRgtlAqsPyZgfjnTCJ6BLlVOdXfFCpnqG2slAgLaVNr4GRva4lXHwnDvQMDkJpViBH16OBRH0N6eGHlswOhVAjo3bH6FkS1re40tq+fdMpqtV59uK7NW010geTQnt74cu5gZOWXYFhPb1xNzJXa2CkVArq3N02WpI2TDe4fFCgtHNCpvBYY0J4+//KlwUhIL5D1O+/R3g3f/3c4/j2bhIC2DlX6qBvrblBbP1t91pZK9OnogYMXUwzqSKcOq+jb6utuh8SMQkQn5RpkOXzd7ZFbWCadonQzcsrbzrpuH6kWSgXuHRggLUBz+FIaOrdzxZ7TiQhs64BO/i7SgZOVhaLeB0X9O3ugSzttF4Fribk4eDHVaJ91/Qlqz9/fDR39nNElwBUHLqQgv0iFhIwCg445lfsgZ+SW4Ks/I/HurL71Gt/OE4anzHU/a5lKg1e/PSF1F9KpXMtfuQNN8q1CqZ7eWMs2Y/Rb5+kmdzvZWaJLO1fc3c8f35Sv1jakhxc+nN0Pp69lILugFCPq0KlDLgulAj3au+FE+RnFDr7aydD7zmvPNny36wrCQtyNlmIB2ux+jJHs/vwp2oXCsvNL8O0ubb38lv0xOBqZJpX8WFsq8cbM3gadOIaFemNkuA9OX7sFURTh4WIrTQytDxcHa7g72yAjpxjXE3OrbetoUENdj5IPQDu5Xr/M4ZFRIVi2uWIS8qBKB+BKhVDnFUvH9vOXuoR8u/MKhvfyMZgncS0hR1qN1spCgRCfpm/dpnN3P3/sPl0RtOqv6FrXlp2NRRRFHL5UPsfHQoH7BgVAEIAV5Wsi6BJNugYMl+Oyy9vAqqTX8sUbmVJM06+zJ5QKAS4OVlK3MnNkqOsdUO/atQvHjh3D0aNHsXPnTqSmpmLdunVYt26d9CL18/NDr1690L17dxQWFuLvv/9GaGioqcd+W6lP/TSgnVQT0NZB+uLRrymsLDS4DXZlVhxND+/ljSBvbaagrauttDCCPhsrJcb1b1fl9qbiZGdl0MavbycPo+UM1dGeZqzfUrH1VV3muT5Ghfti5a8XoVKLBqt79QxqY7CAhTH6nUL0A81BXdtKAXWXABeTLrwz6+5OSEgvgEIhYGS44Rdql3auJjnFaWttUe1rz9XRGu29HKUMi4VSqHdP1UHd2hr037azscAUvdq7EB9nJGZoe3gfuVTxN/BpY4csvdrD+i5hXtnAbvorZqaguEyNn/Zeh521EiueHSRlx7sFutbrtQ9ov4geH9sJC74+BgDYFBFdJaBWqTU4Xx7IujtZS2U1XQNcpAmul+OyDAJq/dP0gqAtvdEG3zX3Ri4qUaG0PGEQn5ZfpV47JjkP2fklWPf3NekzzdZKCSd7K3Tyd8ZoI5Oi23s5Ij69AMWlaoMJg5VbtlWn8oRRQDv3QaEQ8PCIYFxLyIFSqV2+XBBqPnBuDKEhbaSAOsTHyaBcYteJBOw6kYCUrEI8Nb6LweN0vbt1+RP996SNlYW0mmZadjF+OxiLwhK1wd9j14kE9O3kgWi9v3WIjxPsbSyNLhRWXyE+TsjIKUZeURniUvONvo90JR8KwfDApy70P1MBYGhPb2w9FCeV79S00mBtgrydcGeYD/45k4TcwjK8+f0prHp+ECyUChSVqPDadyel1/kDQ9qbfP5OffTt7AE3R2upZG1cf/+KgLqeGWpda8r60mhEoy0Po5NypRWBwzu4w9baAhPvCETUzWykZRfjgaEVZ4AD22oDalEE4lLzpYW9jHWxEgQBfh72iLyZjdSsolq7sZhavX9Do0ePxuuvv47t27cDAB588EHs27cPK1euxGOPPYawsDCkpaXhzz//xAcffIBPP/0UCoUCr732mqyBajQaLF++HJ07d4aNjQ38/f0xf/58FBTULa2fn5+P999/Hz169ICjoyPc3d0xaNAgrF27ttrToU2pco/TutD/IKqpni2sUtnDY7U0jm8u9LPU9clCtiQuDtZVTsMCxktV9BM5VhYK9KnmC35AV08pWBjbx7T17872Vlj2zAB8NKe/yVfIrCv9bG1YiHud6mX1VX4tTR7SHk52FZlm/dPS+ktbd2nnIi2zDhifGFwfHs62UilBVHwOfinP/BeWqPHRpnPSdpV7mNfV4O5tpdOoxupVr8TnSGe4wkLc9erh9ZZF1jvQF0VROk3v7myDKUO1ByGlKg3+qaFc6dtdVzDqle0Yu3Anxi7cidmfHJDu0y9P+vLPSGzQKz/5Yu5gbH17ND6c3d9oFlZ/waZDlyoOkOqcoXYxElAHa9939raW+PCp/nj/iX6NPgGxOiPDfKSAbFgvb4R3cK8ylgPnUwyur/z1IkbM/xPvlS/uBVT/fTLjrg4GZ9D0Ly/ddF46e+Lrblfv91hN9EtFKk8E1dFlqN2dbeodyLk4WGNcP+0BeVhIG3i62Eq11X4e2rUU5PjvQ72krPnZ6Ft478czSMoowKvfnpAmwnX0c8bT93ap6WkanYVSIU3S83W3x4AubaXJoXUNqMtUGjyz8iBGvbIDX2+PlM6i18VfJ+Jx58vbMf/Lo1Vq/vUXl9N9HluVnxn5/IU74OFc8d6svJCdjv68C/3PSF0CQBRRp9IoU5L1jfjhhx/C09MTQ4YMwZAhQ6Tb1Wo1IiMjERkZibKyMvTv3x/BwcYn6NTVSy+9hE8//RQTJ07E/PnzERkZiU8//RRnzpzBnj17oFBU/6bTaDS4++67cfjwYTz66KN4/vnnUVhYiA0bNuDxxx9HZGQkPvzwQ1njk0s3kUGpEOrcOqdLu4pljGuaxNing7u08uAd3dsaLN3cnIX4OOFKfA6UCuG2DagB4OUpPeFsbyUt5mBnraxS2mBpoUAnP2fpSy6s/KjeGDtrC3z/3+FIzSqq0s7udtC3kwd+LZ/MUtty8ca0dbVFZ39nRMXnwMZKiYdGGH426b//dF8EHf2c0d7byWCylCkmpw3q1lZafKJU78tKv7Sicg/zuhIEAe08HZCRU4ycgtIqWWT91R5D9bpK6H+W6B/op2cXS2UyIT5OGNvPTyr/2Xk8HhOMnOkqLlVj3d/XjLZ/s7RQ4JkJXfDej2cBANsOVfSgffa+rrV+TuknEfR7o8vJUIfX0F2jqQW0dcQvi0ehVKWRFufZ9PpIXIrNwmdbL+FGSh6ik3ORU1AKZ3sr5BSU4ueIaGhEw25B1fXM9nazw7j+/vjjiPag8YWJ3XAtMRd/Hr1pkNkzddnC/XcEYt3f15BXVIadx+Mxa2wneLexg1ojlrdtVCOrvOtGfSYk6ntlak9MGBQgtSt9ZGQI+nbygK+7fYM7Huk42Vnhrcf64D8rD0KtEaWzBTq2Vkq883gf2fsxhRmjOqB/Z0/4l3e7au/liPMxmUjLrn6hFH07j8dLget3u65i37lkBHk7wd7WAvcPCqw27riemIP3fzqLUpUGhy+l4p8ziQatd/W7jd1Ry3e7sYmJJWVqqc2wr7u9wcFx5Tpq9/ZNV24sK6B+5ZVXjN6uVCrRvXt3dO/eXc7TSy5duoRVq1Zh0qRJ2LJli3R7+/bt8cILL2Djxo2YNm1atY8/duwYDh48iLlz52L58uXS7f/5z3/QuXNnfPXVV2YNqAuKy6Sapg6+TnU+vTthUACSM4vg5mhdY42lj7s9Xp8RjkuxmXji7oY3jm9qT4zrDAulNhNrLJt0u7CyVOLZ+7phSA9v/HEkDkN7esGvUg25r7sdugW6SgF1bR9CzvZWZsusNbahPb0xa2wnFJeppdPX9bV4Rjh+3ncDo/v4wrXSJM7KPcOBik43/bt44slxnVFcqsIYE2T/7+jW1qAPdmVKhSBNXmwInzZ2OF0+ET7pVqHB5Dr9iYD6kz2d7a3g52GPhPQCXE3IkU73Vl4hs7O/CwK9HBCbko+z128h+VZhlQlkZ65lSMGZr7s9AsqzRxZK7aJC4R3c8f5PZw0W4Lije1upb3FNqjsrV9cMtbO9FawsFVKvZm2/ePPVvBpTudzB2d4Kg7q1xYkr6biRklfe7eYWhvTwxtHItCoHLtaWSgR5V3/28sWJ3WFjpYS3mz2mDAtCSZkaBcUqgwnSxt4PcjjYWmLKsCB8u+sK1BoRP+y5hgVTe2HHsZsG6wwAMDgjVB8WSoVUhwtoDy5NmUjqGeSG16eH4cON56SzPID27/Pmo70NyqTMSaEQDIJeXUANAM9+egiLZ4RLjQkqU6k1WLfb8LMpJjlPmkPy55GbeHR0Rzw+tqPBWYSiEhVeX3vSIEGw9q+rGBnmC4VCQE5BKS6WL+se6OVQ6yRi/XJWXdnO5bgsKVte+Qyen97vPj49H2FNGFCbf23ZOtiwYQNEUcTcuXMNbp89ezbs7Oywfv36Gh+fm6v9I/j4GNZ8WllZwd3d3ewTJq/E50hfKPVZgcvGygIvTuqOGXd1qHWy3pg+fpg3uWeLCrK83eyw8OFQjOptvI3R7aZnkBtefSQMQ3p4w8XB2uAUbDsPB9wzMAB2NhbwcrPF6D5Nu9BOc6JQCJg9vjOev79bg2sU23s74b8P9TKa/fV2szNoj6dUCBjdx1fa9xN3d8Kz9zV83/q6BLhK7dB0+za4v51LtWci6kK/H7j+widqjYhz5RlqFwerKnWsunkcpSoNfth9DWqNaJA1D/F1hiAIBi01fz1ouIAEYHhq97n7umLZMwOw7JkB+PCp/hjWyxuOdpYGQay7sw1ee6RqS0xjQnydDLJRgDZQ96jjwbcgCAYH6r30Fj9p7vTb6p25pv076mf9OpQfOE0aElhjyYS9rSXmTe6Jh8snqdtYWeC9WX3wxsxwONtbwdHOUurdbkoPDg+Sujf8efQmMnKKpQmX+uq6SqI5jOnrj3ULR0jJrKE9vfDT/43AgDqsZmouEwcHSq/xqwk5eGbFQaRlFxnd9u+TCVIf8i7tXKoE3mqNiG93XcGTy/ZLE2AB4OvtUVXa8sUk52H/+WQUlaiwausl6cCvLh1zfNrYSaUq52MyodGIhvXTlc7mtvM0zFCnV/PzNYZ6fVJfunQJ3bp1q31DEz/PiRMnoFAo0K9fP4PbbWxsEBoaihMnTtT4+H79+sHFxQVLly5FYGAg+vfvj8LCQnz//fc4deoUvvzyywb9HKbSkPppur0pFALcnW2klRj9PB0Q4uOE7e+NhaWFosV88bdECoWAEB8nKZPTv7Mn2phg0QVjlAoBI8N8seXADdhYKfHx0/3x+NJ9UnZHbstD/RUc9Rc+iU7KlZZ2Dg2u2j1nYFdPabGhr7dH4fiVdNjonTnTlRKN7euP1dujoNaI+GnvddzRzUvKGGln8muDPAulgL6djdf8D+nuhWsJOVAIwFuP9oaLQ90WkbJQKvDmo73x1CcHpNIclVqs13ujrYut1Ou7oaU15tAruGJy4NnoW1BrRBwtXwXX3sYC3748FGUqTYMOxnQHSnf19oNKran3hNi6cLa3wqQh7bF+z3WUqTT440gcTl7JqLKdufo415Wfhz3+9+JgFBSXmbTOvLF08nfBmvlD8dYPpxCbko+8ojLsO5eMKZXOCKk1osGiUi9M7I5ewW5Izy6GWiNix7Gb+O6vq1BrRFyJz8HjS/fh/6aFYnioj7R8uLWlEs9M6CJ17nj/p7OwsFAY9O8eWYdOMQqFgNDgNjhwIQU5BaW4kZJnUD9d+TPS38MwQ/1zREw9fkPy1CvF0rNnTzz88MM4f/58g3Z25swZPPjgg+jVq1e9HpeUlAR3d3dYW1f9oPX19UVGRgZKS6tfYMDV1RW///473Nzc8OCDDyIgIABdunTB559/ji1btmD27Nk17r+kpAS5ubkG/0xJv8VPc/8AoabjodeXs115Js7GSslgugnol0aM7de4ZwOeu78rXpnaE1/OHYwgbyeDuvBQmUFedRnqs/rlHkaC9jF9/PDIyBBpIuzZ67ekrjNWFgr4l59Wbetqi1l3axep0YjAG99XLPYSm5In9RMODW5TbcDx6OgOeGVqT3wxd0i9+8Z3DXDFU+MrytgG1bNHtH6JSkMnf5qDi4O1VMpxJT4bx6PSpJVR+3X2hIVSIevMBqA92GuMYFpHv+b++7+vSaVB4/v7453H+mDxjPAGzZEwh5YQTOt0bueCN2f2lq7rl37pRN3MliZYhoW0QWh5y1pPV1t4t7HDE+M6Y/X8IdLE7FKVBh9uPIftR29KB+p3hvngwWFB0lyTPL2Fy6wtlfjvQ73q3DVG/zPq0MUUnIupWIuhcpmZg62lVMZ3PTEXf+pNLG9s9Qqo33jjDWzfvh1hYWEIDQ3Fhx9+iKNHj6KkxPiKQcXFxThy5AiWLFmCHj16oE+fPti1axfeeOONeg2ysLDQaDANaLPUum1q4uDggO7du+Pll1/Gr7/+ijVr1iAkJATTpk3D7t27a3zskiVL4OzsLP3z9zdd5wSVWoML5S8OWyul7FZcdPvQX7XOv5nU5LUWk4e2R7CPE0aE+jRaL3MdGysLTBrcXqrxnD2+M4K8HTG8lzf6VZPVrStjGWqNRsTeMxU1ssaCdkEQ8Nz93fD5C3fAwdYwMGvv7WhQRvDo6I5SIJyWXYwnPt6Pc9G3Ks3krz4wsrJUYtLg9nVeCbKy6aM64OERwQjydsTM0fVbAGfKsCAEeTvi3oHtZNWqm4PuAEAjAl/+ESndXtv8iubC39NB6pGvPwlycHcvjOrti7v7+RttuUbyhfg6S+/rs9dvVel0FqfXp3pIpQVidLq0c8V3rwyXPh+LStVYvqWi3/fd/fwhCAJefrAnfN3tYWdjAXsbC/Tv4ol1C4fXa/6L/sHu97uvSfMeBvfwMloepisFyysqM6jlbmz1OoRdvHgxnn76abz33ntYt24dFi1aBEEQYGFhAX9/f7i6usLR0RF5eXnIzMxEfHw81Go1RFGEs7MzXnzxRSxatAgeHvX7krCzs0NamvGevMXFxdI21blw4QIGDRqE5cuX4+mnn5Zuf/jhh9G9e3fMnj0b0dHRUCqNH40vWrQI8+bNk67n5uaaLKjefSoRGeVL3oaVd+MgArSrD/57NhkuDtpevNR0Ato6Yv2iEWbb94//d6dJnsvFwUpaJEjXQmr9nmtSOYuXm221k5IAbRnEoofD8Oq3FWV1lScDKhUC3pgZjsc+jEBWfikSMwrw9IqDBtvc0b3xgjyFQsALkxo2Ab6jn7PJftdNLSzEHb8eiAUAqVMMoC3XaSnu7uuPizcqSh5rKg0i01EqBPQMaoPDl1KRlV9apR+4fpcYf8/q55jZWCnxwsRuOHAhGSq1KPX+9nSxkQ6yuwa44pc3RskabwdfZ9jZWKCwWCWt9gxAao9Y2cCuntJnXFOq96waT09PrFy5EklJSfjuu+8wadIkuLm5ISYmBqdOnUJERAROnTqFGzduwN3dHZMnT8batWuRnJyMTz75pN7BNKCdTJiRkWE0E56YmAh3d3dYWVU/2W758uUoLi7GlClTDG63s7PD+PHjERcXh9jY2Gofb21tDScnJ4N/pqBrE6QzfVSISZ6Xbg/33xGIL14cjO//O7xFnVKk5kMQBClLnXyrEOdibuHr7VHl9wGvPRJW60H8nWE+GKfXK71nUNXSCE8XW3w1b4jRVTnbedo3m64Ht5OwkDZV/nbdAl3h1kj1/o1hZLivwZLYNZUGkWnpl1HoT/IDtIsv6dT23vVys6sS2I7p42fS5KCFUoGe7Q3PYLXztK+hx3pHrHx2IN6YGY5FD9WvxFiOBhdZ2dra4tFHH8Wjjz4KAEhPT0daWhpycnLg7OwMT0/PBgXPxvTt2xd///03jh8/btDvuri4GGfPnsXQoUNrfHxionb5TbW66qo5KpXK4P+m9O+ZJKlOKTSkTYuaFEONT6EQWlRdJzVPPu52uJ6UC7VGxBtrT0kT+B4d3bHOq/+9MrUXnB2sUFKmxj0DjGeF/D0c8OXcIdi8Lwb7zidDpdbA3toCj4/tZLKfhSq0cbLBgod6YeexeKg0GjjaWlZZNbG5c7a3wh3dvKQOH3JWMaT60Q+oz0bfwsTBgdJ1XYZaqRDq1IZy5ugO2H7spvTZMtbIYmVyhYYYrh6sKykxRqkQpJWMTT3nrSYmW+rMw8PDZAF0ZVOnTsX777+PFStWGATUq1evRmFhIR555BHptujoaJSVlaFz54qJKl27dsXff/+NtWvXYsGCBdLt2dnZ2LZtG1xdXRES0rTZYY1GxHd/XZGuP95CVi8kopbFV6+OWtc1JsjbEU/cXfdAV3tqt/ayCqVCwEMjgqsslkONY8LAAKML6rQkj4wKwaFLKXCwtZTaU1Lj6+TvAlsrJYpK1ThzPQOiKEIQBIiiKGWovdvY1WmlSl93e8y4qwPW/nUVo8J9EeRt+gXFKiccTbEOgKnJDqiLioqwYcMGHD58GIWFhfDy8kJYWBjGjBkDT0/T1HL16NEDzz77LD777DNMmjQJ48aNk1ZKHDZsmMGiLiNHjkRcXJxBkf3cuXOxbt06LFy4EBcuXMAdd9yBzMxMrF69GsnJyfj888+rrZ9uLAcupEgN0rsHuqJvJ9aNEZHp+bhXzTBNGBRQ7yWdiRpDj/Zu2P7+WFhZKGBjZbIcH9XCQqlAjyA3HI9KR3p2MWJT8tDe2wm3ckukxWoq93mvyZx7uuDBYUFwaqS1Lrq0c5FWBO3byaNKd4/mQNar9+bNmxg5ciRiYmIMAljdRMUpU6bggw8+gJ+f/LZTK1asQGBgIL7++mts374d7u7ueP755/H222/XuOw4AAQEBOD48eN4++23sXfvXmzcuBG2trYIDQ3FsmXLMGnSJNnjq4uMnGLcTMtHzyA3g+z0Y2M61mkhAyKi+tLPUAPaLLL+MsBE5uZk13IWHLudhAa3wfGodADA0ysO4pWpveCmt3JsfbtLVV511pQsLRT4eE5/HLqUiokNXCG3sQli5X4p9TBp0iRs3boVXbp0wYwZM9ChQwdkZmbi1KlT+OOPP5CcnIw2bdrg999/x8CBA005brPKzc2Fs7MzcnJy6jxBsahEhQfe2oOsvBL4e9hLNUqd/J3x3SvDGFATUaOIS83DQ+/+I10f1K0tlj09wIwjIqLmIDOvBI8tjUB6drF026hwX+w5rZ13Nn9KD0weGlTdw1uEhsRrDSXrnN8///wDLy8vHDt2DAsXLsQDDzyA2bNn48svv0RCQgI++ugjFBYW4t5770VCQoKpxtwiXU3MkZqa67ekYXaaiBqTl5sd9D9i7m6ECUNE1PK4OVrjh4UjcKfeioW6YBqovcMHGZIVUBcUFGDYsGFwcKj6SxcEAfPnz8eGDRuQmZmJd955R86uWryEtIIqtwV5O2JoNU3TiYhMwdpSKc3Ud7C1wODu7KRARFrO9lZ4+7E+BguJ6egv4021kxVQe3h4ICsrq8ZtJkyYgL59++LPP/+Us6sW76ZeX8dgHyeEBrfBa9PDuBIUETW6Fyd1R1hIG7w6LQw2Vk07AZuImjelQsCYPobzKiwtFPB0tTXTiFomWZMSx4wZg40bNyImJgZBQdXX2YSEhODChQvV3t8a6Jd5LHmyL4/8iKjJDOnhXe0SwkREY/v6Y/2e69J1P3d7rtxcT7Iy1B988AFsbW0xbtw4nD17ttrtLl68iODg1t2XVNfXUakQ4O3W/Nq9EBERUesU7OOETv7O0vX6tMwjLVkBddu2bbFp0ybExcWhX79+mD59OjZv3oykpCSUlpYiOjoas2fPxoULFwwWVGltRFFEQoY2Q+3rXrdG6URERERNZWzfignL9W2ZRyZY2OWuu+7CwYMH8cwzz+Cnn37Chg0bqmzz3HPPYfTo0XJ31WKl5xSjWNconS9SIiIiambG92+HP47EITOvhN2AGkBWH2p9oiji4MGD+P333xEREYELFy6gtLRUu5Pynk1eXl4IDw+X/t13332m2HWTq29fw1NX0/HcqsMAgIdGBOPFSbUv4UtERETUlERRhFoj3jZn0puyD7XJ1vkUBAFDhgzBkCFDAAAqlQoXL17E6dOnpX/nz5/H9u3bsX37dgiCALVabardN2v6ExL9PVmXRERERM2PIAiwUHIyYkOYLKCu8sQWFggNDUVoaChmzZoFANBoNIiKisKpU6dw5syZxtp1s6PfMo/dPYiIiIhuL40WUBujUCjQtWtXdO3aFTNmzGjKXZtVgl6GmisPEREREd1emjSgbg1EUcQv+2/gUqx2wRsvN1tcuJEJALCyVMDDuepqRERERETUcjGgNrFTVzPwyS/GF7Hxc7fnyohEREREt5nbYxpnM3ItMbfa+1juQURERHT7YUBtYmnZRdLl1x4Jw+DuXtL17u3dzDEkIiIiImpELPkwsdSsioA6NKQNxvX3x8GLKUjJLMK9AwPMODIiIiIiagwMqE0sXS9D7eFso+3P3cPbjCMiIiIiosbEkg8TSy0PqN0crWFlqTTzaIiIiIiosTV6hnrWrFmwtLTEo48+ikGDBjX27sxKpdbgVk4xAKCtq62ZR0NERERETaHRM9Rr167FmjVrMGTIEIwdOxbHjx9v7F2aTUZOMTSi9rKnCwNqIiIiotag0TPUb7zxBjQaDc6dO4f9+/dj4MCBUKvVjb1bs0jVq5/2dOUCLkREREStQZME1DqiKOLMmTONvUuzSc8qli4zQ01ERETUOjTppERBEBAeHt6Uu2xS+hlq1lATERERtQ7s8mFCaVn6JR8MqImIiIhaA1kBdWpqKvbv34/U1FSD26Ojo/HQQw+he/fuGDduHI4ePSprkC2F/qIubVnyQURERNQqyAqoP/jgA4wYMQI5OTnSbbm5uRg8eDA2b96My5cvY9euXRg5ciSuXbsme7DNnW7ZcUEA3J05KZGIiIioNZAVUEdERKBr167o2LGjdNvatWuRmpqKhx9+GFeuXMEnn3yCoqIiLFu2TPZgmztdQN3GyQYWSlbTEBEREbUGsqK+xMREBAUFGdy2fft2WFhYYMWKFejQoQPmzp2LXr16Yd++fbIG2tyVqTTIzCsBwAmJRERERK2JrIA6Ly8PdnZ20nW1Wo0jR46gd+/ecHd3l27v3LkzEhIS5Oyq2UvPLoLIRV2IiIiIWh1ZAbWPjw+ioqKk6wcPHkR+fj6GDx9usJ1KpYKVlZWcXTV7bJlHRERE1DrJCqgHDhyI8+fPY8WKFbhw4QJee+01CIKAe++912C7yMhI+Pr6yhpoc2fQMo8ZaiIiIqJWQ1ZAvWjRIlhbW2P+/PkIDQ3FoUOHMHz4cAwaNEjaJjY2FpcvX0b//v1lD7Y5S8vWWyWRy44TERERtRqylh7v1q0bDh48iJUrVyIjIwO9e/fGK6+8YrDNX3/9hV69euH++++Xs6tmjz2oiYiIiFonQRR1U+mornJzc+Hs7IycnBw4OTkBABZ8fQwHLqQAALa9M5plH0RERERmZCxeayxslmwiugy1UiGgjRNLPoiIiIhaC1klHzq3bt3C+vXrcfz4cWRkZGDkyJFYsGABAODSpUuIjo7GqFGjDFrs3W50i7p4ONtAqRDMPBoiIiIiaiqyA+rNmzfjySefRH5+PkRRhCAIBh09EhMTMXHiRHz//feYPn263N01SyVlamTnlwIAPFjqQURERNSqyCr5OHLkCKZNmwYLCwssW7YMx48fR+WS7JEjR8LZ2Rm//vqrrIE2Z2nsQU1ERETUasnKUL///vtQKBTYvXs3wsPDjW6jVCoRHh6OixcvytlVs2bQg5oBNREREVGrIitDffjwYQwcOLDaYFrHy8sLycnJcnbVrBm2zOOERCIiIqLWRFZAXVhYCA8Pj1q3y8rKkrObZk+/5IMZaiIiIqLWRVZA7evri0uXLtW4jSiKuHjxItq3by9nV81aapbeKomclEhERETUqsgKqMeOHYsrV65g48aN1W6zZs0axMfHY/z48XJ21axxUiIRERFR6yVrUuLChQvx008/YebMmThz5gwmTpwIACgoKMCZM2fw22+/YenSpfDw8MBLL71kkgE3R7pJiRZKAa4O1mYeDRERERE1JdlLjx85cgQPPPAAUlJSIAiGC5qIoghPT09s27YN/fv3lzXQ5qTyUpaj/7sDeYVl8Gljhy1v3mXu4RERERG1ek259LjshV0GDhyIK1eu4JtvvsHu3bsRGxsLjUYDPz8/3HXXXZgzZw6cnZ1NMdZmqahEhbzCMgCckEhERETUGplk6XFHR0fMnTsXc+fONcXTtSiGLfMYUBMRERG1NrImJVKllnnsQU1ERETU6tQrQ71u3TpZO5s5c6asxzdH7EFNRERE1LrVK6B+7LHHqkw8rAtRFCEIwm0ZUKdnswc1ERERUWtWr4B68eLFVQLq6OhorF+/HnZ2dhg9ejQCAwMBAHFxcfj7779RUFCA6dOnIzg42GSDbk5yyyckAoCzg5UZR0JERERE5lCvgPrNN980uH7t2jX069cP06dPx4oVK+Dm5mZwf1ZWFubOnYs//vgDR48elT3Y5ii3oFS67GzHgJqIiIiotZE1KXHRokVwdXXFd999VyWYBgBXV1d88803cHFxwaJFi+TsqtnSz1A72VmacSREREREZA6yAuqIiAgMGDAASqWy2m0sLCwwYMAA7Nu3T86umq28wooMtSMz1EREREStjqyAuqioCMnJybVul5KSguLi4lq3a4l0GWo7ayUsLdiFkIiIiKi1kRUB9uzZEwcOHMCePXuq3Wbv3r3Yv38/evbsKWdXzVZueYaa2WkiIiKi1kl2DbVGo8E999yDWbNm4a+//kJUVBSioqLw119/4YknnsD48eMhiiIWLlxoqjE3G6IoShlq1k8TERERtU6ylh6fMGEC/ve//2HevHlYu3Ytvv/+e4P7RVGEtbU1Vq1ahQkTJsgaaHNUXKpGmUoDAHBihpqIiIioVZIVUAPA008/jXHjxuGbb77BwYMHkZSUBADw9vbGkCFD8Pjjj0u9qW83efodPuyZoSYiIiJqjWQH1ADQrl07vPXWW6Z4qhYlr6iiwwcz1EREREStE9tSyJBXpJIus4aaiIiIqHUySYYaAI4cOYIDBw4gMTERAODr64shQ4Zg4MCBptpFs5NXwB7URERERK2d7ID66tWrmDFjBk6ePAlAOxERAARBAAD06dMH69evR4cOHeTuqtnJK+IqiUREREStnayAOjk5GcOGDUNqaip8fHwwZcoUBAYGQhAExMbGYvPmzThx4gSGDx+OkydPwtvb21TjbhYMJyUyQ01ERETUGskKqN99912kpqbipZdewpIlS2BlZRhUfvjhh1i0aBE++eQTvP/++1i1apWswTY3uYX6kxKZoSYiIiJqjWRNStyxYwc6deqEZcuWVQmmAcDS0hIfffQROnXqhD///FPOrpolgww1a6iJiIiIWiVZAXVycjLCw8Nr3EYQBISHhyM5OVnOrpol/RpqR2aoiYiIiFolWQG1k5MT4uPja90uPj4eTk5OcnbVLLGGmoiIiIhkBdQDBw7EoUOHsH379mq32bFjBw4dOoRBgwbJ2VWzlFueobZQCrC1Upp5NERERERkDrImJS5cuBA7duzAxIkTMXXqVEybNk1aZjwuLg4bNmzAxo0boVAosHDhQlOMt1nJLywFoICTnZXUJpCIiIiIWhdZAfXAgQPx3XffYc6cOfjxxx/x008/GdwviiJsbW3x1VdfYcCAAbIG2hxpSz6s4WTP+mkiIiKi1kr2wi7Tp0/H8OHDsXr1ahw8eBBJSUkAAB8fHwwZMgRPPPEE/P39ZQ+0OSosVcPCih0+iIiIiFozkyw97ufnh7feessUT9UiscMHERERUesla1IiaTFDTURERNR6mSRDXVhYiJMnTyI5ORklJSXVbjdz5kxT7K7Z4SqJRERERK2X7IB68eLFWL58OQoLC6vdRhRFCIJw+wbU7EFNRERE1GrJCqiXLl2Kd999F0qlEuPHj0fHjh3h6OhoqrG1GMxQExEREbVesgLq1atXw9bWFgcOHKh1CfLbmSNrqImIiIhaLVmTEuPj4zFs2LBWHUwDzFATERERtWayAmovLy/Y29ubaiw10mg0WL58OTp37gwbGxv4+/tj/vz5KCgoqPNzZGZm4uWXX0ZISAhsbGzg4eGBESNG4MCBA7LG5mjLgJqIiIiotZJV8vHQQw/hm2++QUFBQaMH1i+99BI+/fRTTJw4EfPnz0dkZCQ+/fRTnDlzBnv27IFCUfOxQVxcHIYPH478/Hw88cQT6NixI3JycnD+/HkkJibKGpudjUmapRARERFRCyQrEnzzzTdx+PBhTJgwAV999RVCQkJMNS4Dly5dwqpVqzBp0iRs2bJFur19+/Z44YUXsHHjRkybNq3G55g+fTpUKhXOnz8Pb29vk47PzpoBNREREVFrJSsSHDduHDQaDSIiItClSxcEBATAz8/PaLZYEATs3bu3QfvZsGEDRFHE3LlzDW6fPXs2Fi5ciPXr19cYUO/fvx8HDx7Ep59+Cm9vb5SVlaGsrAx2dnYNGk9ltgyoiYiIiFotWZFgRESEdFmtViMmJgYxMTFGtxUEocH7OXHiBBQKBfr162dwu42NDUJDQ3HixIkaH79jxw4AQLt27XDvvfdi586dUKvV6NChAxYvXozp06c3eGwAM9RERERErZmsSPDGjRumGkeNkpKS4O7uDmtr6yr3+fr64vDhwygtLYWVlfH2dVeuXAGgzWh36NAB33//PUpLS7Fs2TLMmDEDZWVlePzxx6vdf0lJicEKkLm5udJlSwsFLC24gjsRERFRayUroA4ICDDVOGpUWFhoNJgGtFlq3TbVBdR5eXkAAEdHR/z777/Sdvfffz+CgoLwf//3f3j00Uerndi4ZMkSvPXWW0bvs7VS1utnISIiIqLbS4tIrdrZ2RlkiPUVFxdL21TH1tYWAPDwww8bBN2urq6YMGECUlJSpCy2MYsWLUJOTo70Lz4+vmJs7PBBRERE1Kq1iGjQx8cHly9fRklJSZVMdWJiItzd3avNTgOAn58fAG3f7Mp0HT+ysrKqfby1tXW1GXLWTxMRERG1bi0iQ923b19oNBocP37c4Pbi4mKcPXsWffr0qfHxusmMCQkJVe7T3ebp6dmgsTGgJiIiImrdWkRAPXXqVAiCgBUrVhjcvnr1ahQWFuKRRx6RbouOjkZUVJTBdvfffz8cHR2xfv165OfnS7cnJydj69at6NixY4N7aLNlHhEREVHr1iKiwR49euDZZ5/FZ599hkmTJmHcuHHSSonDhg0z6EE9cuRIxMXFQRRF6TZXV1d8/PHHmDNnDgYMGIBZs2ahtLQUX3zxBUpLS7Fq1aoGj40ZaiIiIqLWrcVEgytWrEBgYCC+/vprbN++He7u7nj++efx9ttv17rsOAA89dRTcHd3x9KlS/H6669DoVBg4MCB+Omnn3DHHXc0eFy21uzyQURERNSaCaJ+KpfqJDc3F87Ozujz1E94cGRXvPJgL3MPiYiIiIj06OK1nJwcODk5Neq+WkQNdXPGkg8iIiKi1q1e0eC6detk7WzmzJmyHt8cMaAmIiIiat3qFQ0+9thjEASh3jsRRRGCINyWATW7fBARERG1bvWKBhcvXlwloI6Ojsb69ethZ2eH0aNHIzAwEAAQFxeHv//+GwUFBZg+fTqCg4NNNujmhCslEhEREbVu9YoG33zzTYPr165dQ79+/TB9+nSsWLECbm5uBvdnZWVh7ty5+OOPP3D06FHZg22O7KwYUBMRERG1ZrImJS5atAiurq747rvvqgTTgLb/8zfffAMXFxcsWrRIzq6aLWaoiYiIiFo3WQF1REQEBgwYAKWy+l7MFhYWGDBgAPbt2ydnV80W+1ATERERtW6yAuqioiIkJyfXul1KSgqKi4vl7KrZYpcPIiIiotZNVkDds2dPHDhwAHv27Kl2m71792L//v3o2bOnnF01WwyoiYiIiFo32TXUGo0G99xzD2bNmoW//voLUVFRiIqKwl9//YUnnngC48ePhyiKWLhwoanG3KywhpqIiIiodZMVDU6YMAH/+9//MG/ePKxduxbff/+9wf2iKMLa2hqrVq3ChAkTZA20uWIfaiIiIqLWTfbS408//TSioqLw+uuvY/jw4ejYsSM6duyIYcOG4fXXX0dkZCT+85//mGKszY4gADaWnJRIREREjevQoUMQBAGOjo645557kJGRYe4h1VlhYSG2bt2KJ554Ap06dYKNjQ3s7e3Rq1cvvP3228jPzzf3EGUTRFEUzT2IliY3NxfOzs4Y+twm7Fv1oLmHQ0RERLe5gwcP4ssvv8TOnTuRmZmJ559/Hp9++qm5h1Una9aswezZswEAXbp0Qffu3ZGbm4vDhw8jLy8PnTt3xr59++Dp6WnS/eritZycHDg5OZn0uSuTnaFuzWzYMo+IiIiawODBg7F+/XqsW7cOgDZj3VJYWlriqaeewuXLl3H58mX8/PPP2LVrF65cuYKwsDBERUVh7ty55h6mLCbJUN+6dQvr16/H8ePHkZGRgZEjR2LBggUAgEuXLiE6OhqjRo2CnZ2d7AE3B7ojnvsXbcVv799n7uEQERFRK5GXlwdnZ2dYW1sjPz+/xrVAWoIjR45g0KBBsLa2Rm5uLqysrEz23E2ZoZY9o27z5s148sknkZ+fD1EUIQgCfH19pfsTExMxceJEfP/995g+fbrc3TUrNpyQSERERE3I0dER7dq1Q1xcHK5fv45OnTqZe0iy9OrVCwBQUlKCW7duwdvb28wjahhZJR9HjhzBtGnTYGFhgWXLluH48eOonPAeOXIknJ2d8euvv8oaaHPElnlERETUlC5evIikpCQAwPnz5808GvliYmIAaMtC3NzczDyahpMVUL///vtQKBTYvXs35s6diz59+lTZRqlUIjw8HBcvXpSzq2bJ1pIBNRERETUNjUaDJ598EmVlZQCACxcumHwfw4cPhyAI9fq3du3aBu9v5cqVAICxY8fC2traRD9F05MVER4+fBgDBw5EeHh4jdt5eXnh2LFjcnbVLNnZtOy6JSIiImo5Vq5ciWPHjsHPzw8JCQm1BtTFxcXw9PSERqNBWlpaneayjR07FoGBgfUaV0hISL2219mxYwe++eYbWFpa4p133mnQczQXsgLqwsJCeHh41LpdVlaWnN00WzZWDKiJiIiawuNLI3Arr8Tcw6izNo7W+G7BcJM9340bN/D666/Dy8sLP/74I4YNG1ZrQL1jxw7k5eUBALZv344pU6bUup+mWtk6KioK06dPhyiK+Oijj6Ra6pZKVkDt6+uLS5cu1biNKIq4ePEi2rdvL2dXzZIdJyUSERE1iVt5JUjPLjb3MMxmzpw5KCgowLp166SuGDExMSgoKIC9vb3Rx2zatAn9+vWDKIrYtGlTnQLqppCYmIixY8ciKysL8+bNw4svvmjuIckmKyIcO3YsvvjiC2zcuBEPPfSQ0W3WrFmD+Ph4TJs2Tc6umiV2+SAiImoabRxbVn2tKce7du1a7N69G5MnT8akSZMAAF27dsWZM2dw8eJF9O/fv8pjCgoK8Oeff+Ktt94CACxevBj5+flwcHCocV8ffPABoqKi6jW+J598EoMHD67TtpmZmRg9ejTi4uLw+OOP4+OPP67XvporWRHhwoUL8dNPP2HmzJk4c+YMJk6cCED7Rzxz5gx+++03LF26FB4eHnjppZdMMuDmxJ4BNRERUZMwZflES5Kamor58+fDzc0Nn332mXR7r169cObMGVy4cMFoQP3nn3+isLAQkydPBgC88sor+OOPP/Dwww/XuL9du3Zh37599Rrj8OHD6xRQ5+fn4+6778bly5cxadIkrF69GoIg1GtfzZWsiNDPzw/bt2/HAw88gI8++ggff/wxBEHAL7/8gl9++QWiKMLT0xPbtm0z+XKSzQFrqImIiKgxPf/888jMzMQPP/yAtm3bSrfrao6rq6PetGkT+vTpI00w7Nu3LzZt2lRrQB0REWGScVdWUlKC++67D8ePH8eYMWOwYcOGFr8ojT7ZKdaBAwfiypUr+Oabb7B7927ExsZCo9HAz88Pd911F+bMmQNnZ2dTjLXZYQ01ERERNZZt27Zh8+bNGDduXJXF8WoKqPPy8rBz506p3AMApkyZgtdffx25ubmNvmpgZWq1Gg8//DD++ecfDBkyBL/++qtJV0RsDkyy9Hhro1vK8s+DURh/R8teoYiIiIian5ycHHTt2hX5+fm4dOkS/Pz8DO7PzMxEmzZt4O7ujvT0dIP71q9fjxkzZiAmJkZqChEbG4v27dtj3bp1mDFjRpP9HIC23d/cuXMBABMnTqw2oP/444/h7u5usv22mKXHZ82ahcGDB2PWrFk1brd27Vrs378f3377rZzdNTu2zFATERFRI1iwYAGSkpLw5ZdfVgmmAcDNzU3qR52cnGywZPemTZvQu3dvgw5rgYGBUtlHUwfU+u2Tf/vtt2q3e/PNN00aUDclWSslrl27FgcPHqx1u0OHDuH777+Xs6tmyc7i9qn9ISIioubjq6++giiKmDNnTrXbxMfHQxRFg2A6Ozsbf//9tzQZUd+UKVPw999/Izs7uzGGXK0333wToijW+q++C8o0J02SYi0tLb2tCs91HK/dAkIDzT0MIiIiIgDaDHBpaSmsra2xdetWg/usrKxQVlaG3377DY8//rh5BnibavSAWhRFnD59uk4rKrY0dgfjgCm9zT0MIiIiIgDacg8AmDdvXo3bMKA2rXoH1HfeeafB9V27dlW5TUelUiE6OhopKSlNXq/TFKwO3DT3EIiIiIgku3btMvcQWqV6B9T6/QkFQUBKSgpSUlKq3d7S0hL33HPPbbMSjj7N2VRokvOg8HY091CIiIiIyEzqHVDfuHEDgLaUIygoCJMnT8ZHH31kdFsrKyu4u7vD0tJS3iibMdWOa7B6ItzcwyAiIiIiM6l3QB0QECBdfuONNxAaGmpwW2tTtpMBNREREVFrJmtS4htvvGGqcbRYqj3REEtVEKzYk5qIiIioNZLVhzo/Px/nz59HRkZGtdtkZGTg/PnzKCgokLOr5iuvFOrD8eYeBRERERGZiayA+pNPPkFYWBiio6Or3SY6OhphYWFYuXKlnF01a6oDceYeAhERERGZiayA+o8//kBISAj69+9f7Tb9+/dHcHBwlebitxMG1EREREStl6yAOiYmBp07d651uy5dukjdQW4ngr8TAEB9OB5iqcrMoyEiIiIic5AVUBcVFcHW1rbW7WxtbZGfny9nV82SxUB/7YUiFdSnks07GCIiIiIyC1kBtb+/P06cOFHrdidOnICPj4+cXTVLFoP8pcuq/bHmGwgRERERmY2sgHrMmDGIjY3F8uXLq91m5cqVuHHjBsaOHStnV82ScnA76bJ6P+uoiYiIiFojQRRFsaEPTkhIQI8ePZCbm4u7774bTz31FIKDgwFou3t8/fXX2LlzJxwdHXHu3LnbZgGY3NxcODs7Izs7G0KXryGmFgCOVnC6tRCCUtYxChERERGZgC5ey8nJgZOTU6PuS9ZqJH5+fvj999/xwAMPYMeOHdi5c6fB/aIowt3dHZs3b75tgml9giDAYmggyjZf0vaj/vcGLEYFm3tYRERERNSEZGWodbKysrB69Wrs3bsX8fHaRU78/f0xatQoPPnkk3B1dZU90OZE/4jHZks0ip7cBgAQApzhePppCC61T9QkIiIiosbTlBlqkwTUrY3+H8jRzh4Fo76H+sBNAIDFA11ht2kKBEEw8yiJiIjodnHo0CEMHjwYDg4OGDZsGNauXQt3d3dzD6teioqKsGTJEmzcuBE3b96Em5sbxo4di3feeQe+vr4m319TBtQs+JVJsFDC7ocHILjaAABUWy5DteOamUdFREREtxNRFPHII4/AysoK27dvx9tvv23uIdVLcXEx7rzzTrzzzjvIz8/HfffdB39/f3z33XcICwtDTEyMuYcoi0kC6lu3bmHlypV45JFHMGbMGCxdulS679KlS/j9999RWFhoil01Swp/Z9h8Nl66Xrr2jBlHQ0RERLebwYMHY/369Vi3bh0Abca6JXn33Xdx9OhRDBw4EFevXsWmTZtw7NgxLFu2DOnp6Zg1a5a5hyiL7IB68+bNCAoKwrx587Bhwwbs2bMHUVFR0v2JiYmYOHEifv31V7m7atYsJ3eF0NYeAKD68yrErCIzj4iIiIhuN0OHDoUgCLh8+TLUarW5h1MnpaWl+OyzzwAAn3/+ORwcHKT75s2bh549e2Lfvn04deqUuYYom6yA+siRI5g2bRosLCywbNkyHD9+HJVLskeOHAlnZ+fbPqAWLJSwfLiH9kqpGqU/XzLvgIiIiOi24+joiHbt2qG4uBjXr18393Dq5NChQ8jJyUFwcDDCwsKq3D958mQAwB9//NHUQzMZWQH1+++/D4VCgd27d2Pu3Lno06dPlW2USiXCw8Nx8eJFObtqEaxm9JIul60/Z8aREBER0e3o4sWLSEpKAgCcP3/ezKOpm3PntDFReHi40ft1t7eUn8cYWQH14cOHMXDgwGp/QTpeXl5ITk6Ws6sWQdHLC4rungAA9eF4qK/fMvOIiIiI6Hah0Wjw5JNPoqysDABw4cIFk+9j+PDhEAShXv/Wrl1b43PevKnthObn52f0ft3tcXEtd9VpWQu7FBYWwsPDo9btsrKy5OymxRAEAVYzeqH4v7sBaGuplXMHmnlUREREdDtYuXIljh07Bj8/PyQkJNQaUBcXF8PT0xMajQZpaWmws7OrdR9jx45FYGBgvcYVEhJS4/35+fkAUO3+7e21c9Dy8vLqtd/mRFZA7evri0uXaq4VFkURFy9eRPv27eXsqsWwGFHxc6rPpphxJERERLeP/H5fQZOSb+5h1JnCywEOx+eY7Plu3LiB119/HV5eXvjxxx8xbNiwWgPqHTt2SEHq9u3bMWXKlFr3s3DhQpOMt7WRFVCPHTsWX3zxBTZu3IiHHnrI6DZr1qxBfHw8pk2bJmdXLYaimwegFAC1CPV5BtRERESmoEnJh5jYcjKYGhM/35w5c1BQUIB169Zh0KBBsLa2RkxMDAoKCqQMb2WbNm1Cv379IIoiNm3aVKeAujHounpU10K5oKAAgHbCZUslK6BeuHAhfvrpJ8ycORNnzpzBxIkTAWh/MWfOnMFvv/2GpUuXwsPDAy+99JJJBtzcCTaWUHRyh+ZyOjSX0yGWqiBYyfo1ExERtXoKLweTB6mNSeHlUPtGdbR27Vrs3r0bkydPxqRJkwAAXbt2xZkzZ3Dx4kX079+/ymMKCgrw559/4q233gIALF68GPn5+QYt64z54IMPDNof18WTTz6JwYMHV3t/u3btAAAJCQlG79fdHhAQUK/9NieyIj0/Pz9s374dDzzwAD766CN8/PHHEAQBv/zyC3755ReIoghPT09s27YNnp6ephpzs6fs2Raay+lAmQaaK7eg7NHW3EMiIiJq0UxZPtGSpKamYv78+XBzc5N6OQNAr169cObMGVy4cMFoQP3nn3+isLBQakn3yiuv4I8//sDDDz9c4/527dqFffv21WuMw4cPrzGg7tVL2wXt9OnTRu/X3d6zZ8967bc5kZ06HThwIK5cuYJvvvkGu3fvRmxsLDQaDfz8/HDXXXdhzpw5cHZ2NsVYWwxlLy+UbdS2CVSfS2FATURERA3y/PPPIzMzEz/88APatq2IJ3RBanV11Js2bUKfPn2kCYZ9+/bFpk2bag2oIyIiTDJufXfccQecnZ0RHR2Ns2fPIjQ01OD+X375BQBw7733mnzfTaVebfPuvPNOg2XF9+/fj6tXr8LR0RFz587F9u3bcenSJURGRmL37t1YsGBBqwumAUChF0Crz6eacSRERETUUm3btg2bN2/GuHHjMH36dIP7agqo8/LysHPnToOa6SlTpmDXrl3Izc1t3EEbYWVlheeeew4A8Oyzz0o10wDwySef4Pz58xg2bBh69+7d5GMzlXoF1BEREQZ1NcOHD8eHH35o8kG1dMpeFQG15hwnJhIREVH95OTk4D//+Q+cnJzw1VdfVbm/poB627ZtKC4urhJQl5SUYNu2bY036Bq89tpr6N+/Pw4fPowOHTpg6tSpGDBgAObPnw8PDw98++23ZhmXqdQroLaysjI4qgBQZalxAgRvRwju2l6LzFATERFRfS1YsABJSUlYunSp0QVR3Nzc4Ofnh4yMjCqL523atAm9e/c2aFkcGBgolX2Yg42NDf7991+8/vrrsLOzw9atWxEXF4fHHnsMp0+fRlBQkFnGZSqCWI+IuHv37khJScGWLVvQvn17BAYGYvLkyfj444/r9HjdLM+WLjc3F87OzsjJyYGTk5PRbfJHfw/13hsAAMfE+VB4tdxWMERERNQyZGdno23btnjrrbeq9JT+6KOP8OqrryItLQ0uLi7mGWATqku8Zir1mpT41FNPYe7cubjzzjul27Zs2YItW7bU+lhBEKBSqeo/whZK2dNLCqjV51IZUBMREVGj++2331BaWgpra2ts3brV4D4rKyuUlZXht99+w+OPP26eAd6m6hVQv/DCC/Dz88O2bduQkJCAf//9F56enujcuXNjja/FUvasqKNWbY2E5Zial+UkIiIikktX0jFv3rwat2FAbVr1KvmoTKFQ4LHHHmvxheT1VZdTCJrEXOR1WAmUqAEAdr89BMsJPPAgIiIiagpNWfJRr0mJlb3xxhu4//77TTSU24vC1wk2y8ZI14ue2AZNYtO3qiEiIiKixiUrQ91a1fWIRxRFFE7eBNVWbatBq6f7wPbze5pqmEREREStVrOdlFidwsJCnDx5EsnJySgpKal2u5kzZ5pidy2GIAiwXT0BeX9HA4VlKNt0ETafjIVgbZJfOxERERE1A7Iju8WLF2P58uUoLCysdhtRFCEIQqsLqAFA4WYHy/s7o+ynCxCziqHafhWWk7qae1hEREREZCKyAuqlS5fi3XffhVKpxPjx49GxY0c4OrI9XGWWM3qh7CftSkal688zoCYiIiK6jcgKqFevXg1bW1scOHAA4eHhphrTbcdiZBAEbweIyflQ7bgKTUYBFO725h4WEREREZmArC4f8fHxGDZsGIPpWghKBSyn9dReKdOg7OdL5h0QEREREZmMrIDay8sL9vbMtNaF1fSe0mXVn1fNOBIiIiIiMiVZAfVDDz2EiIgIFBQUmGo8ty1Fj7YQvBwAAKrDNyGq1GYeERERERGZgqyA+s0330SXLl0wYcIEXL9+3VRjui0JggCLIQHaK3ml0JxLNe+AiIiIiMgkZE1KHDduHDQaDSIiItClSxcEBATAz88PCkXVOF0QBOzdu1fO7lo85dAAlG3W1k+rDsRB2dvHzCMiIiIiIrlkBdQRERHSZbVajZiYGMTExBjdVhAEObu6LVgMDZAuq/bFwnruQDOOhoiIiIhMQVZAfePGDVONo1VQdPWA4GYLMbMI6oM3IWo0EIxk84mIiIio5ZAVzQUEBNTrnxwajQbLly9H586dYWNjA39/f8yfP79BEyILCwsRFBQEQRDw3HPPyRpXfQgKBZTlddRiZhE0l9ObbN9ERERE1DhaTHr0pZdewrx589C1a1esWrUKU6ZMwaeffop7770XGo2mXs+1ePFipKebJ5g1KPvYH2eWMRARERGR6cgq+Wgqly5dwqpVqzBp0iRs2bJFur19+/Z44YUXsHHjRkybNq1Oz3X69GmsWLECS5cuxfz58xtryNXSD6jV++OA//Rr8jEQERERkenUK0MdFBSE4OBgqXY6KCiozv+Cg4MbPMgNGzZAFEXMnTvX4PbZs2fDzs4O69evr9PzqNVqzJ49G2PHjsWkSZMaPB45FL28AHtLAIDqRKJZxkBEREREplOvDHVsbCwAoKyszOB6Yztx4gQUCgX69TPM5trY2CA0NBQnTpyo0/MsX74cUVFRBlnupiYoFVCGe0N94CbE2Gxo0gug8OBqk0REREQtVb0y1BqNBhqNBh07djS4Xtd/DZWUlAR3d3dYW1tXuc/X1xcZGRkoLS2t8Tlu3LiBN954A4sXL0ZgYGC99l9SUoLc3FyDf3Io+/pKl9XMUhMRERG1aC1iUmJhYaHRYBrQZql129Tk6aefRlBQEObNm1fv/S9ZsgTOzs7SP39//3o/hz5lHwbURERERLeLFhFQ29nZoaSkxOh9xcXF0jbVWb9+PXbv3o0vvvgClpaW9d7/okWLkJOTI/2Lj4+v93Pos+inH1AnyXouIiIiIjKvFtHlw8fHB5cvX0ZJSUmVTHViYiLc3d1hZWVl9LElJSWYN28exo0bBy8vL1y/fl16HADk5OTg+vXrcHd3h4uLi9HnsLa2rjZD3hBCoAuENrYQbxVBfSIRoihyJUkiIiKiFqpFZKj79u0LjUaD48ePG9xeXFyMs2fPok+fPtU+tqioCOnp6di+fTs6dOgg/Rs+fDgAbfa6Q4cOWLNmTWP+CAYEQZDqqMWMQohx2U22byIiIiIyrRaRoZ46dSref/99rFixAkOGDJFuX716NQoLC/HII49It0VHR6OsrAydO3cGANjb22Pz5s1VnjM9PR3/+c9/MHbsWDzxxBPo2bNn4/8gepR9faHapc2Wq44nwirQtUn3T0RERESm0SIC6h49euDZZ5/FZ599hkmTJmHcuHGIjIzEp59+imHDhhks6jJy5EjExcVBFEUAgKWlJSZPnlzlOXUt/4KDg43e39iqdPp4sHuTj4GIiIiI5GsRATUArFixAoGBgfj666+xfft2uLu74/nnn8fbb78NhaJFVK4YUPb1kS6rdl2H+OFdEFrgz0FERETU2gmiLpVbB3feeSfGjh2LBQsWAAD2798PLy8vqS91a5GbmwtnZ2fk5OTAycmpwc+TP3gN1EcSAAB2W6bC8v4uphoiERERUatmqnitLuqVEo2IiEBUVJR0ffjw4fjwww9NPqjWwnphRT14yfv7UY9jGyIiIiJqJuoVUFtZWaGgoMDgNgaBDWcxviMUYV4AAPWpZGmSIhERERG1HPWqoQ4JCcHevXuxb98+tG/fHgCQn5+Pmzdv1unx7dq1q/8Ib2OCIMDm/4aicMrPAICSTw7D8u4OZh4VEREREdVHvWqoP/30U8ydO1dahKQ+C5IIggCVStWwUTYzpqzJETUa5HX8FOKNbMBSAaesRRBs67+aIxERERFVaMoa6nplqF944QX4+flh27ZtSEhIwL///gtPT0+p5zPVn6BQwGJEe5TdOAOUaaA+mgCLEe3NPSwiIiIiqqN6t82bNGkSJk2aBABQKBS4++678e2335p8YK2JxZAAlH17BgCgOhDHgJqIiIioBZHVh/qNN95AWFiYqcbSalkMC5Quqw7EmW8gRERERFRvsgNqkk8R4AKhnTPEmzlQH4mHWKqCYNVi1twhIiIiatVMFrUdOXIEBw4cQGJiIgDA19cXQ4YMwcCBA021i9uaxZAAlP14HihSQX0yCRaD2BGFiIiIqCWQHVBfvXoVM2bMwMmTJwFU9KXWdf/o06cP1q9fjw4d2A6uJhZDywNqAKr9cQyoiYiIiFoIWQF1cnIyhg0bhtTUVPj4+GDKlCkIDAyEIAiIjY3F5s2bceLECQwfPhwnT56Et7e3qcZ921EODZAuq7ZFQXyuHwQHazOOiIiIiIjqQlZA/e677yI1NRUvvfQSlixZAisrK4P7P/zwQyxatAiffPIJ3n//faxatUrWYG9nig5tIPg5QUzIhfp4IvLDv4TFPZ0ASwUsJ3eDRV9fcw+RiIiIiIyo18IulbVv3x42NjaIjIysdhtRFNG1a1cUFxfjxo0bDd1Vs9JYjcLLtl9F4UObgcIywzscreB4/UUo3O1Nti8iIiKi21lTLuyikPPg5ORkhIeH17iNIAgIDw9HcnKynF21CpbjO8LhzNNQDvI3vCOvFKUrj5pnUERERERUI1kBtZOTE+Lj42vdLj4+vtGPDG4XypA2sN8/Cw7nnoHdjumApfZPVPLZcYjZRWYeHRERERFVJiugHjhwIA4dOoTt27dXu82OHTtw6NAhDBo0SM6uWhVBEKDs3haWY0JgOTNUe2NuCUo+O27WcRERERFRVbJqqI8cOYKhQ4dCEARMnToV06ZNQ2BgIAAgLi4OGzZswMaNG6HRaHDgwAEMGDDAVOM2q6asydHEZCKv8ypALQJ2lrBdPhaWT4RLbQmJiIiIqKqmjNdkBdQAsH79esyZMwdFRUVVgjxRFGFra4uvvvoK06dPlzXQ5qQp/0AAUDh7G8q+PSNdt5zeE7ZrJzKoJiIiIqpGiwqoASAhIQGrV6/GwYMHkZSUBADw8fHBkCFD8MQTT8Df37+WZ2hZmjqgFgtLUfTiToOg2v7obLbSIyIiIqpGU8ZrJll63M/PD2+99ZYpnoqMEOysYLf6PhQHu6Hk1b0AAPW+WAbURERERM2ArEmJ1LQsJ3SSLqv2x5lxJERERESkw4C6BVF08YDgbgcAUB2Mg6jWmHlERERERMSAugURBAHKIQHaKzkl0FxINe+AiIiIiIgBdUtjMTRAuqw6wLIPIiIiInNjQN3CGATUrKMmIiIiMjsG1C2MokdbwNkaAKA+EAcTdD0kIiIiIhkYULcwglIBizvaAQDE9EJoojLMPCIiIiKi1o0BdQukHFixUI76PCcmEhEREZmTSRZ2KSwsxMmTJ5GcnIySkpJqt5s5c6YpdtfqKbt4SJc1UelmHAkRERERyQ6oFy9ejOXLl6OwsLDabURRhCAIDKhNRNFVL6C+zICaiIiIyJxkBdRLly7Fu+++C6VSifHjx6Njx45wdHQ01dioGopgV8BSAZRpoGYNNREREZFZyQqoV69eDVtbWxw4cADh4eGmGhPVQrBQQtGxDTSX0qG5kgFRpYZgoTT3sIiIiIhaJVmTEuPj4zFs2DAG02Yg1VGXaaCJzjLvYIiIiIhaMVkBtZeXF+zt7U01FqoHhf7ExEjWURMRERGZi6yA+qGHHkJERAQKCgpMNR6qI/2AWs2AmoiIiMhsZAXUb775Jrp06YIJEybg+vXrphoT1YGSnT6IiIiImgVZkxLHjRsHjUaDiIgIdOnSBQEBAfDz84NCUTVOFwQBe/fulbM70qPo2AZQCIBGZKcPIiIiIjOSFVBHRERIl9VqNWJiYhATE2N0W0EQ5OyKKhGsLaAIdoXmWiY0kekQNRoIRg5kiIiIiKhxyQqob9y4YapxUAMounhAcy0TKFJBvJkDIdDV3EMiIiIianVkBdQBAQGmGgc1gLKLB1S/XwEAqC+mQcGAmoiIiKjJyV56XOfIkSM4cOAAEhMTAQC+vr4YMmQIBg4caKpdUCWKUC/psvpUEizv6WTG0RARERG1TrID6qtXr2LGjBk4efIkAEAURQAVNdN9+vTB+vXr0aFDB7m7okos+vpKl9XHE804EiIiIqLWS1ZAnZycjGHDhiE1NRU+Pj6YMmUKAgMDIQgCYmNjsXnzZpw4cQLDhw/HyZMn4e3tbapxEwAh0AWCux3EjEKoTyZBFEVO/iQiIiJqYrIC6nfffRepqal46aWXsGTJElhZWRnc/+GHH2LRokX45JNP8P7772PVqlWyBkuGBEGAso8PVLuuQ8wohBibDaE966iJiIiImpIg6mo0GqB9+/awsbFBZGRktduIooiuXbuiuLj4tukKkpubC2dnZ+Tk5MDJycmsYyl+81+UvLMPAGC7YTKsHuxu1vEQERERNQdNGa/JalycnJyM8PDwGrcRBAHh4eFITk6WsyuqhlK/jvoE66iJiIiImpqsgNrJyQnx8fG1bhcfH2/2TO7tStnXR7qsPplkxpEQERERtU6yAuqBAwfi0KFD2L59e7Xb7NixA4cOHcKgQYPk7IqqofB0gBDgDEDbOk9Ua8w8IiIiIqLWRVZAvXDhQigUCkycOBEzZszAzp07ERkZicjISOzatQuPPvooJk6cCIVCgYULF5pqzFSJsk952UdBGcs+iIiIiJqYrEmJALB+/XrMmTMHRUVFVVq2iaIIW1tbfPXVV5g+fbqsgTYnzWlSIgCULDuE4gW7tVccrGD9yh0Q2thJ9yu8HWAxoRMEhazjJyIiIqIWoynjNdkBNQAkJCRg9erVOHjwIJKStHW8Pj4+GDJkCJ544gn4+/vLHmhz0twCajG7CPn9V0NzPbPabWw+GAXrVwY34aiIiIiIzKfFBdStTXMLqAFAzCtB0fy/UPbNaaP3C262cIyZC8HRusbnKV1/DsWL9sBqTh/YvDasMYZKRERE1OgYUDdzzTGg1lGfTYb6fKp0vWzTRah2XQcA2CwZBUWPtlAfS4DVs/2g8LA3eKzmViHy2i8HCsoAAXCMfQkKP+cmHT8RERGRKTRlvCZrpURqfpSh3lCGVizxruzni/y/rgMiULz4H6BM2wVEfToZ9r9PM3hs6cqj2mAaAESgbMMFlokQERER1aJeAXVQUBAEQcCePXvQvn17BAUF1fmxgiAgOjq63gMkeZSdPWA5pRvKfr4kBdMAoNp+FepTSVD21vaxFrOLULLqmMFjS384B6uX76gy2ZSIiIiIKtQroI6NjQUAlJWVGVyn5s361aEo++UyoBEBpQCotVU+xe/th/2vDwEASj47DuSWGDxOcykdmrMpUIZ5V3lOIiIiItKqVx81jUYDjUaDjh07Glyv6z8yD2X3trD79SFYvzoUDpHPQ/B2AACotkVBfSEV6sh0lHxwoHxjAVYvVyzCU/rDOXMMmYiIiKjFYGPiVsLy3k6weftOKIPdYP3KHdLthVN/RuGDPwNFKgDQdvdYOASwUgLQ1lGLPBgiIiIiqpasgHrWrFn49ttva91u7dq1mDVrlpxdkQlZze4NwU8721Vz5RY0l9MBAIpuHrBZOhqCqy0sRgcDAMS0Amiu3jLbWImIiIiaO1kB9dq1a3Hw4MFatzt06BC+//57ObsiExLsrGD/90woe+vVRttYwG7DFAi2lgAA5cCKxXjUx7mcOREREVF1mqTko7S0FEqlsil2RXWk7OQO+0NPwmbJKChHBMLul6lQdvOU7rfo4yNdVp9MMscQiYiIiFqERu9DLYoiTp8+DQ8Pj8beFdWTYKmE9YLBsF5Qtde0Uj+gPsEMNREREVF16h1Q33nnnQbXd+3aVeU2HZVKhejoaKSkpGDGjBkNGyGZheBiC0XHNtBcvQX12RSIpSoIVlwHiIiIiKiyekdIERER0mVBEJCSkoKUlJRqt7e0tMQ999yDjz/+uEEDJPNR9vXVTkgsVUN9PhUWfXzNPSQiIiKiZqfeAfWNGzcAaEs5goKCMHnyZHz00UdGt7WysoK7uzssLS3ljZLMQtnXB2U/ngcAqE8kMaAmIiIiMqLeAXVAQIB0+Y033kBoaKjBbXT7UPatCKDVJxKBZ/qacTREREREzZOsotg33njDVOOgZkgZ6gVYKACVBuqTxicmihoNVH9cBWwtYDk6pIlHSERERGR+strm5efn4/z588jIyKh2m4yMDJw/fx4FBQVydkVmINhYQtGzLQBAczkd6qh0g/s1N7NRMOYHFE7aiMK716Ns+1VzDJOIiIjIrGQF1J988gnCwsIQHR1d7TbR0dEICwvDypUr5eyKzMTy7g7aCyJQ+PAvEIvLAACqE4nI6/UF1P/ckLYtfvNfiKJojmESERERmY2sgPqPP/5ASEgI+vfvX+02/fv3R3BwMLZu3SpnV2Qm1gsHQ9FN20Nccz4VxXN3QcwqQuFDm4HcEoNtNaeTodp13RzDJCIiIjIbWQF1TEwMOnfuXOt2Xbp0kbqDUMsi2FnB7qfJgI223L509SnkdfwUYmw2AEA5wA+2a+6Tti95bx+z1ERERNSqyAqoi4qKYGtrW+t2tra2yM/Pl7MrMiNl97awXTVOui5mFmkvuNjA7scHYPloLyi6a5ctVx9JQMmreyGWqswxVCIiIqImJyug9vf3x4kTJ2rd7sSJE/Dx8al1O2q+rGaFw373TAjtnKXb7L6eAEWgKwSFAtavDpVuL/nwIPIHroEmKdccQyUiIiJqUrIC6jFjxiA2NhbLly+vdpuVK1fixo0bGDt2rJxdUTNgcWcQHM8+A5vPxsFux3RYPtBVus9ySjfYLBmlbbMHQHM2BYXTfoGoUkN97RbKtl+FqFKba+hEREREjUYQZRS8JiQkoEePHsjNzcXdd9+Np556CsHBwQC03T2+/vpr7Ny5E46Ojjh37txtswBMbm4unJ2dkZOTAycnJ3MPp1lRn0lGwf0bICZos9PKEYFQH7gJqDSwfmsEbF4bZuYREhERUWvQlPGarIAaAA4cOIAHHngAGRkZEATB4D5RFOHu7o7Nmzdj2LDbJ5BiQF0z1aGbKBjxHaA2fGkJ3g5wjJsHQSnrxAgRERFRrZoyXpO1UiIADBkyBFeuXMHq1auxd+9exMfHA9DWV48aNQpPPvkkXF1dZQ+UWg6LO9rB+s0RKHn9H4PbxeR8qPbGcEVFIiIiuq3IzlC3RsxQ105Ua1Dyzj5ormRA0bENSt7dDwCwfKQn7NZNMvPoiIiI6HbXojLURMYISgVs3hwBABBLVCj9/DjErGKU/RYJMb8EgoO1mUdIREREZBotpphVo9Fg+fLl6Ny5M2xsbODv74/58+ejoKCg1sdevXoVixcvxoABA+Dh4QFHR0eEhobivffeq9PjSR7B2gKWD3bXXiksQ+mPF8w7ICIiIiITkl3yIYoifvzxR2zbtg3Xrl1DXl6e0ZXyBEFAdHR0g/fz4osv4tNPP8XEiRNx9913IzIyEqtWrcKQIUOwZ88eKBTVHxssXLgQn3/+OSZMmIABAwbA0tIS//77L37++Wf07NkTR48erdMCNTos+ag/1ZF4FAz+RntFAKxeHACLgf6ArSUs7mwPwdayTs+jPpcCwd0OCl/+3omIiKh6LabLR2lpKcaPH49//vmn2uWmBUGQ7tNoNA3az6VLl9CjRw9MnDgRW7ZskW5ftWoVXnjhBfz444+YNm1atY8/efIkOnToAGdnZ4PbX3vtNbz33ntYtWoVnnvuuTqPhwF1/YmiiMIHNkG1LarKfcqR7WG/c0at3T9Klh9G8ct/AxYKWL82FNYLh0CwVDbWkImIiKgFa8p4TVbJx7Jly7B3717cc889uHbtGmbMmAFBEFBSUoLIyEi8+eabsLe3xyuvvNLgYBoANmzYAFEUMXfuXIPbZ8+eDTs7O6xfv77Gx/fp06dKMA0AU6dOBQBcvHixwWOjuhEEAXabH4TNB6MAK8MgWL33Bko+OFDj41VH4lH8393lVzQoeTMCBXeuhVhQ2lhDJiIiIqoTWZMSN23aBDc3N/z000+wt7eXyi4sLS3RqVMnLF68GCNGjMCIESPQqVMnzJo1q0H7OXHiBBQKBfr162dwu42NDUJDQ+u0/LkxCQkJAIC2bdvWuF1JSQlKSkqk67m5XFK7IQSlAtavDIbF/V2g2nUNYlYxSt7ZB2hElLwVAYthgbAYXHXxHzG7CIWP/FKlr7X6cDxKPjsGm/8OaaofgYiIiKgKWRnq69evo1+/frC3t9c+WXlArVZXLDE9ZMgQ3HHHHfjf//7X4P0kJSXB3d0d1tZVO0P4+voiIyMDpaX1y1Sq1Wq88847sLCwqLFcBACWLFkCZ2dn6Z+/v3+99kWGlB3awPr5AbD5//buOzyqYv0D+Pds301CKCFAEqpU6ZDQA0ovFkKx0LGAShFQ+YmgFFGvXu8VKRZEVBAE0UtRQEApudfQRELvUkMEEklCsn3P/P5Ys7DsJmSzSTbl+3kensedM2fOexhPeDM7Z+aNB6B9/e8NfxwCxmHfQ/7L6FHf/MYOiIvpznM7VkfQ9lGAwrmJkPXfuyGyrBAOGcLGrc2JiIio6PmVUCuVSrepFNmJ9Y0bN9zqRUZG4tSpU/m+jtFo9JpMA85R6uw6vpg0aRJ2796NOXPmoEGDBrnWnTZtGtLT011/sjevIf9pp3eGsrNzVFpczoDp2Q1u8/HlqxmwLjng/BCkhmH5QKi61IL6scbOc1KMMD2zHrdq/Bu3qv0T1iUHcpzPT0RERFQY/EqoIyMjXdMmAKBuXecOeHv27HGrd/jwYQQHB+f7OgaDwW3KxZ3MZrOrTl69/vrrWLhwIcaMGYNp06bds75Wq0W5cuXc/lDBkJQKGJYPgFTRucqKfd1JGHsth/GJNbCuPAzL+wmAxTnyrHmhDRQ1ywMAtK91drVh+/YYxJ+ZEDfNMI39AcZHVkJkmF3HhSzD+uVBGB//FlmDVsM4ei0cp1KK7iaJiIioVPMroW7Xrh2OHj3qSnb79u0LwDn6+9NPP+HIkSOYMGECTpw4gbZt2+b7OhEREUhJSfGaVCclJSEsLAwajSZPbc2aNQtz587F6NGj8cknn+Q7Jio4iqhQ6D9/1PXZ/ssfsK05BtPw/8D64d+/nOlV0E5u76qjbBwO1YBGXtuzbzoD49PrIYSAfDkdxt5fw/T0eti+Ow772hOwLTsE45NrOJJNREREBcKvhHrgwIHQ6XTYunUrAOcI9aRJk3Dp0iX069cPLVq0wKJFi2AwGPDee+/l+zoxMTGQZRn79u1zKzebzUhMTER0dHSe2pk1axZmz56NkSNHYsmSJZAkKd8xUcFSP9IQ2mk5v1yoebY1FFXcv+XQze0GqZIeUpgB+mUDYFj3JFDeOQXI/p8TMD21DreafwT7L394tCcfugb7D/mfhkRERESUze+NXbxZtWoV1q1bh5s3b6J+/fqYOHEi6tWrl+/2jhw5gubNm+e4DvXy5csxbNgwAMC5c+dgs9nQsGFDtzbmzJmDmTNnYvjw4fjyyy9z3QjmXrgOdeERN00QJhsce5NgGvcjxLUswKBGyMkJXjdzyX4RMXs9atv6kzAOWOVRT4oMgf6ThyEyLDANdf4/pIyOQNCeZyFJEmybTsMydxdUfepB+3+dYP/xNCzz90DVqy500zp7tEdERETFW4nZ2GXKlCmoWLEiZsyYUZAxeTVhwgQsXLgQcXFx6Nu3L06cOIH58+ejY8eO2L59uytBrlWrFi5evOj2df6iRYswfvx41KhRA2+++aZHMl2lShX06NEjz7EwoS4ackoWbN8cgbJddahiIvN8nmniJlgX3f42Qz2sGfQf9oFUXg8hBDKjP4Wc+CcAwLBxKFSxNXHrvnkQN5wvtkrVgiGSM13nB5+cAGW9Sl6vJYSA49dLgF2G6oHaud9PUgbsuy5A3b8hJEPepigRERFR/hRlvubXOtQLFy7Eo48+eu+KBWDevHmoVasWFi9ejI0bNyIsLAwTJkzAnDlz7jnanL1O9aVLlzBy5EiP4126dPEpoaaioQgLgnZCO5/P073XAyLdDPl0KrRTO0Edd3uutSRJ0L3WGcbHvgUAmKf9DM2TTV3JNAC3ZBoA7JtOQ/liewhZBuy3NygSqSaYxm+EfZ1z90fdh32gHe/+roAQApIkQb6agczoTyGuZ8E28H4EffuYz/dFRERExZNfI9R16tRBy5Yt3aZhlAUcoS7ZhCwjs/WnkA9f8zimqF8J8ulUIEgNZNkAAKpudaB9qxuMD69wS7w9aJQI/vVpKFtFwHH8Okwv/Aj52A1op3aEbes5OLafd1UN/m0slC2rFfi9ERERkVOJmvKxbNkynD9/HiEhIQUZV7HGhLrkcxz+E5ntPnMtyQcAqv4NYVg5CI5fL0HRrAoy2yx2biijVkDZrAocB5K9N6ZSuEaupZqhUHWqCdt3x9za9jglrhGCvnu8QO+JiIiIbivKfM2vVT5mz56NGjVqoG/fvjh48GBBxURU6JTNqkL3r15uZbrpnSFpVVB1rQNFWBDUfes7D9hkVzItVTZA2bmm64/m+RiEnH0RyugIAIC4mA7bisPek2mFBKnC36uQrD0Bx1HPEfKcyKlGCLMtH3dKREREhc2vEequXbvCZDJh7969kCQJ1apVQ40aNVy7F7pdSJLwyy+/+BVsccER6tJBCOFcn/qrRKifbgXD4kfcjts2nYbx4ZVuZfqvB0LzZFOPthxnU5EVuxTiepazQCFBM6Et1H3rwTRuI+Q/bkL3bg9AKcE8ZQsA5yoj+pWDoLyvYq5x2jafgXHAKiiiyiF4/xhI5fV+3DUREVHZUGKmfPiy9JwkSXA4cv4KvCRhQl16CCEgUozO9azv+v9ZmGzIqPwuYLIDcM6vDj46DpLS+//3IssK+UIaAECqEgRFWJDrGkgzQ6qghzBacavuh87lAAEgSA3dez2hGRvtdV104ZCR2WSRc143AP2SR6EZ3bIgbp2IiKhUKzGrfJw/f/7elYiKMUmSIFUO8n5Mr4bqwdqwbzoDANC+GptjMg0AUpAGysbhXq+BCs5RZcmggWHDEBifWANxPg3IssE8biPs609Cv+RRj7W2bWuOuZJpwDlqzoSaiIioePEpoe7atSt69+6NqVOnAgAuXryIqlWron79+oUSHFGg6d7sCuPpVChbR0A9xHOqR36ooiMRkvg8zK9shXXxAQCAfes53Gr2EfTz+0I9pCkkSYKQZVjejnc7177tHITVDknj1+/CREREVIB8mvKhUCgwatQoLF261PV59OjR+PzzzwstwOKIUz6ooNh+OgPTsxsgrt66XahTARIAAcBs9zgnaNsIqLrWKbIYiYiISqJiu8qHRqNBVlaWW1kh7FxOVGaoe9dD8KHnoX6iye1Cs905b/uOZFo9rJnrv21/T0EhIiKi4sGn743r1q2LX375Bbt27ULt2s5tljMzM3Hp0qU8nV+jRg3fIyQq5RQVDTCsGARbXCNYFu2DSDPfPigB6n71oZncHraVRwBZwL7pNPB+r5wbJCIioiLl05SP+fPnY9KkSa7VCLK3Vc7ThSQJdrvn19clEad8UCBkdlkKx/+cv7zqv4qDZljzAEdERERUfBXbVT4mTpyIqKgorF+/HleuXMGOHTsQHh6Ohg0bFlZ8RPQ3dVwjV0JtGrkW1o/2QSqng6JuRej+0R1SsDbAERIREZVNfq9DfedLimUFR6gpEITNAdPItbCtPupxTD2kKfTLBuT5GyMiIqLSrti+lHi3mTNnon///gUUChHlRlIrYVg5CPqVgyBFhLgds608AtuyQwGKjIiIqGzza4S6rOIINQWakGUg0wrbD6dhGvEfZ6FBjaANQ6BoXBnmqdvgOHYduqmdoB7cOLDBEhERBUCJ2Xq8rGJCTcWJ8dn1sC09eLsgVAukW1wf1U80gf6jhyCF6gIQHRERUWCUmCkfRBR4+nl9oOxa+3bBHck0ANhWHYVx8LfOUW0iIiIqcEyoiUo4KUiDoC3DoftXL0CrBACoHm0I/acPA+Wdo9L2X/6A5Z+/BjJMIiKiUotTPvKBUz6ouJKvZUL8mQlFsyrOtd93nEdWj6+c25grJQTFPwVVu+qBDpOIiKjQccoHEeWLokowlM2rupbPUz1YG9ppsc6DDgHTuI3g79BEREQFiwk1USmnnfkAFC2rAgDkxD9h33g6wBERERGVLkyoiUo5SaWE7vUHXJ8tb8VzlJqIiKgAMaEmKgNUD9eHolkVAIBjXxLs284FOCIiIqLSgwk1URkgKRS351IDsLz3vwBGQ0REVLowoSYqI9QD74eiXkUAgGPHBcgXbgY4IiIiotKBCTVRGSEpFVCPbOH6bF15BI6zqTC99BNMz/8A0/iNsO+6ELD45ItpMM/aAduGk5zjTUREJQrXoc4HrkNNJZV8MQ236swDACjuqwDhEBAX0m5X0CoRvPtZKJtXLfRYhBCQz/4FmGxw7E2C6ZUtwC0rAEA18H7oP+oHRVhQocdBRESlU1Hma6pCbZ2IihVFzfJQPlALjp0XIJ/zMuXD4oBxyHcI3jcGUpCmUGMxv/AjrIsPeD1m//44MvcnIXjfGCgqM6kmIqLijVM+iMoYzbDm7gXldQjaMer2WtUnU2CatNnruSLDDONT65AZ+zkyYz+HcdRaiDSTzzFYlx/ymkyr+jeEVEnvvNaldJhGr4OQZZ/bJyIiKkpMqInKGPXARoDu9pdThs8egapzLRhWDgKC1AAA29KDsK464naeEAKmMT/A9lUiHAmX4Ui4DNvyQzA+s8HrnGc5+RZsW89CWO3O82+aYPvuGKxLf4dp/Mbb8TzeBJoXYmDYPAxB3z+B4N+fgxTuHJW2bz4D6/y9ft+zSDPBvuM8hN3hd1tERER34xzqfOAcairpLPP3wPJWPDQvtoPutc6ucuuyRJhGr3N+CNEg5PfnoKjjXBnEuuQATGN/8NqeblE/aJ+LcX0Wtyy41XghRNItKJpVgebZ1rDM3gmRYnQ7Tz2yBQxL+3u0Z9t6FsY+Xzs/KCRoX+0E7etdIGl8n6Vm+/44TC/8CJFihPLBWgj6aTgkldLndoiIqGQpynyNCXU+MKGm0sw44j+wrTgMAFC0qIqg/zwBx4kbMA5aDZico82GVYMBtQLGgaudJykkIFgDRZUgGFYMgv2XP2Ce9nOu11E0qOScqx2s9Xrc9Oo2WP/56+36LarC8GUclE2r5Ok+hBAwv7gZ1kX73Mq1MzpDN7trntogIqKSiwl1MceEmkozccuCzOhPnStwAIBe5UqkAUAzNhr6jx4CAJgmbvJIWKWaoYDRBnHDfTQaAFSPNoSqW21IGhVUjzaAIjw45zhkGZZ//A+WOTsB29/zqNUKaGc/CO3LHQGFBPvaE5BvGKEZ0RySXg37L3/Acew61MOawb7uJEzPbvBsWAKCfh4J1QO1ffuLISKiEoUJdTHHhJpKO8eRa8h6eAXE5Qy3clXvujB89zgkvXOutTDbYBq3EY69VyBSjB5JtCquEZRNw2HfeQGaZ1pDPaQpJEnyLZbEZBhHroV89LqrTNk+ClKw1rWFuqJBJShbVINt9VEAgFQtGCLdAhhtAADdwn4QN02wvL7dWb9+JQQfH+9zLEREVHIwoS7mmFBTWSDSzTBN2gzbskOAQQ3dez2heS46xyRUvpSGzFafQNw0u8qCE5/P8xSNXGOx2GGZtQOW9xMA2bcfWZpnW0P/ycMQDhlZnZfCsecKACDof09D1b6637EREVHxVJT5Glf5ICKvpFAdDF/EIfj0RJS7NAXa52NyHdFV1CgP/ZJHXZ+do9P+J9MAIGlV0L3TA0G7RkNxX4Xb5REhruX+AADltFDG1rgdU+PK0P27l7OuUgHNmGjXMdvyQwUSGxEREUeo84Ej1EQ5s646AsdvV6F9LRaKioYCb19kWWH5cA9gskE7pQMQrIF18W+Qz6dB+2I7SFHlYFt1FI7fr0I7uT0UEbefUXHLgoyI9wGjDVIFHUKSXoak5f5WRESlEad8FHNMqIlKLuPw72Fb6Vxj27DmMagH3B/giIiIqDBwygcRUSFRD7+9U6SV0z6IiKgAMKEmojJF1a0OpGrO5frsm89ATskKcERERFTSMaEmojJFUiqgHtLM+cEmw/btscAGREREJR4TaiIqczR3TPvgah9EROQvJtREVOYom1aBorlzST/HviQ4TqUEOCIiIirJmFATUZnkNkr9NUepiYgo/5hQE1GZpH6yKaBwblRjXXYIIssa4IiIiKikYkJNRGWSomoIVL3rAgDElQyYXtwc4IiIiKikYkJNRGWW7v1eQJAaAGD74iCsq44ELBYhBGxbz8Jx7q+AxUBERPnDhJqIyixlgzDoF/RzfTaNWgvzP/4LYXcUeSyWt+Jh7PM1Mtsshnw5vcivT0RE+ceEmojKNPWI5lAPu70utWX6L8jqtRzCbMvxHPtvScjs8BnS1bORrp6NjJr/hvWLg5AvpyMr7htkRL4P87t5T8zlVCMs//zV+SHNDMv7v/p7W0REVIQkIYQIdBAlTVHuDU9EhU9Y7bDM3AHL+wmA7PyRqBnfBvoP+7rXszlgeTselrfiAYeXH51qBWCTXR+VMRFQtokC9Cponm0NZd1KXq9vnrkdlrnxtwt0KoScexGKqiH+3xwRURlVlPkaE+p8YEJNVDrZ4y8gq/dywOIcWdZ/0R/KmEgAgEg1wjzlJzgOJLvqS7XKQwrVQj507Z5tSzVDEfL7c5DK6yFfSYe49feqIhY7Mrt+CaRb3OprnouGZnzbHNtTVAuGVF7v4x0SEZUdTKiLOSbURKWX5eN9MI/flHslpQTt9M7QvtYZkloJ24aTMI39AeJ6FtRDm0E9tBnMEzdBPuv+gqHqofqATYZ9y1mvzaoebgD7tnOA2X7vQFUKaF/tBO30zpA0qrzeHhFRmcGEuphjQk1UegkhYBy0GvZ1J70eVzQKg/7LOKiiI93Ps9ghbmRBERXq/Gx3QD52A+KmCcZBqyFumnO/sEqB4GPjYF20D9b5e/Mcr6JlVQSte9J1XSIicmJCXcwxoSYq3USmBZZ//A9y8i23cmWTcGiei4GkV/vUnm3tCRgHrXZ9lqoFQ9WzLiBlN6yAOq4R1H3qQRitzmsnZeTcoMkO2/fHAbtzvrayXRSCdo6GpFb6FFdBkK9mQD6fBmWH6pAkCeKmCY6DyVB2qQVJyffeiShwmFAXc0yoichX5nfiYf1XAlQPN4DuX72gqGjwqz3HgavIGrwa4qJziT3t/3WC7u3uBRFqnsl//IXMtp9B/GWCZkp76F7rjMy2iyGfuwlVXCMY1jwGSZLu3RARUSFgQl3MMaEmovwQQhRogmnfn4SsTp87R6olQP/Zo1CPalEkSaywOZDVeSkc+5JcZYqWVSEf/NP1WfdhH2hzebGSiKgwFWW+xjdZiIiKSEEnuqqYSOje7gbz1G2AAEzPrIdt7QkoW1SFFKqF+smmUETk/I+InGqEbdURKFtWg6pDDZ+ubX59u1syDcAtmQYA8ytbIa7eAkI0UA+8H8r6YZCTb8H2zRGItDvmlEuA6oHaUD1Y26cYSgL5Uhpsa09A1a0OlE2qBDocIiokHKHOB45QE1FxIWQZpud+hO3z3z0PltdBP78v1EOaeiTzth9PwTRmA8S1LACA5vkY6N7tASlIc89rOhKTkdn6U+cHtQLKmEg4Ei67jisfqAXHzgvuJ2mV0DzbGrYVh3N8QVM9vDn083p7LAcohADscoHOERc2R6HOORdCwLb0IExTfgIyrc5VWWZ0hubpVoBSASk8iNNhiAoZp3wUc0yoiai4sX1/HKYXfoRIMXocUw1oBP1HD0FROQgiwwzTlC2wfXHQo56ibkXov+h/z9HqrEGrYV97AgCge6c71M+0Qlb7JZDP/gXN5PbQvdUNWQ9+AcfepFzb8UaKKgfD549C1f0+AIB19VGYX94CSEDQ2iehbB3hc5t3s355EKbxG6G8vzL0nz4CZctqfrd5N9PzP8C6+ECOx5UdqiNo6wifX3AlorxjQl3MMaEmouJIZFrg2H8Vwi7DtiwRtpVHXMek8CAo21eH4/erEJdvryCi7FQDjgNXAdPfa18rJKh63gdoVVC2qgbt5PZuo9aOo9eQ2fxjZ5tVgxFy7kVIOjVEhhnyxXQomoQ7V/sw2eDYnwRYHbBtPgPrh3uAv/+1UT/WGOqnWiF7gNZxJhXm134BMm5vbqPqXgfCYofjv5dcZYo6FRB8YCykcjrPexcCtm+OwL7zAjRPtYSqXXWvf0eOg8nI7LAEsP69LbxKAd1b3aB9uaNnmxlmWBbuA+wytK90zHPya12WCNPoda7Pyq614dh1wWN3Tc3zMdAv7JenNonId0yoizkm1ERUEti+O+YctU41eR4M1kD/r15QP90K8plUmEavg2PPFY9qiroVoZvbDQjVAgCsC/fBvvE0AED3fk9oJ3fIUyz2/16E9etDUPeqC/WA+z2Oy5fSYHxmPRy/nM+1HVVcI2jGtL7rZAHrR/tdcUEhQfNSB6i63jUnWwDmFzdBPuO+4Q4A6JcPgGZIMzjOpEI+fxMi1QTz9J9dq6ioR7eEYcmjkFOyIK5nQdGostcpG47TKciM/hTIsjnb/ewRaJ5qBfv+JFg/2Q+RZnZu7PP3LzCGNY95/fsgIv8xoS7mmFATUUkh/3kLphc2wr7+9kY1ym61Yfj0EShqV3CVCYcMy/u/wjI3HjDa7tmuFGZAyB+T8jTnOq+ELMP68X6YZ2x3jVZL4UHQvhYL88wdHtuz+0MZHQFVtzqwvPs/Z0GIBupHG8L29eEcz1GPagHb6qOAyQ71oPuhW9QPirCg2/Fb7MjsuMT1cqZ6VAsYPu/v0Y518W8wPf+j8/4q6Jx/j15G3YnIP0yoizkm1ERU0og0E4TZDmiUua6BLcw2iDQzxJ+ZMI3b6HXUGgB07/WA9iXPaRIFEqvVDvGXc1RdCjNAUilhW3MMxifW5HqeVCUI6sGNYf30N8Am51wxRIPg38ZCWbcSjCP/k2sSrbi/MuTjN7wfLKeForIBUkU9NJM7wLHnsmuXS0WDSgjeP9brLxx378ap/2YQNI81yfXeiMh3TKiLOSbURFQWCLsDtm+PQT6d6lauqBHqXO9aUbQ7Ido2nnbOy/ZCqqiHekhTKMKC4DhxA7b1JwGz3bOiUoL6kYZQNq8KABC3LMiM/hTy2b+ngQRroBnTGlKQBsrG4VANbATT6HXuSXewxrlyR060SgQnPANli5xfdrRtOwdj7+UAnKubGL6My/3michnTKiLOSbURESlh+PYdZie+wFS1WDo3+vpNhUGcCbdpmc3QE6+Be2MLlA2CYf55S2wbz8P2GXXaHo23fw+0I7LfUMbYbEjo/K7QJYNUmUDQq6+XOS/oBCVdkyoizkm1ERElM266gjM4zdC3DRDPeh+6FcNztMa01kDVrnmtgclPANV26jCDpWoTOFOiURERCWE5ommUPeuC8fxG1C2i8rzhi3qvvVcCbV902km1EQlGBNqIiIiP0nl9T5v367qW8/137b1J6F6qIHrs7JuRUgV9N5OcxEOGeJapsf28kIIiKQMSJHluBsjURFhQk1ERBQAiohyULSsCvngn5CPXEdWu89uH9QooZv9IDQvdYCk9Jxbbdt2DqZn1kNcyYB29oPQzegCAHAcv+5cU/y3q1ANaATD6sGcm01UBJhQExERBYh6UGNY/l632o3VAfO0n2H97ACkCu5rVAu7DPnQNddny8wdUEZHQD5+A+YZvwAW5y6Q9v+cgPX9BGindirUeyAiJtREREQBo53cHpJaAflSuqtM/GWC7ZsjgADkP27mqR3jQytcW7vfyfz6dkCrhBSidT8gSVB2qgFlvUr+hE9Ef+MqH/nAVT6IiKgw2f93EaZJmyEfvub1uBQeBO20WNg3nYH9p7N3HAA0k9oDSgnW9xNyv4hSgnZ6Z2hf6wxJrSzA6ImKBy6bV8wxoSYiouJAvp6JzJjFEFcyINUqD8PS/lB1qQVhdyCr21dw/O/SvRtRKwCFBGWratB/2BfK1hGFH/hd7L/8AdPLWwCVAvoPekMK1sD04uacN/Ipp4X+44ehjmtUxJFSScKEuphjQk1ERMWFuGmCffdlqDrXhBR8e2qHuGWBbcMpwGjzOMdxJhXWebsBx10pgEoB9fDmkEK1HufcTaqoh2ZUSygiPf8ddJxJhW3NMah63AdVTCTk5FuwfnEQItXoGf+fmbCtOnpHwwCUCsCey/bxABCkRvCB51zTVhxHr8G2+iiE0QZJo4RqwP2ua9uWH4KyVTWout93z/ui0oMJdTHHhJqIiEo6+29JsMzZBTkpAyLVCHE5w/dGyuug/3dvKDtUv93u5jMwT/vZufW75Nxa3f7DKYibZp+bl6LKQQozuJWJNDPEhTQAgKJVNRi+Hgjb98dhmbMTsN2RhHu5tnp4c2j/rxOgynnlE0VECKQgjfs1HTLkC2mALCCV00JRJdjne6Gix4S6mGNCTUREpYmw2mF5+7+wvB3vOWpdFHQq6P7RHTDbYX5jB2CXof2/TtC+0QWSxn39BJFpQWbMYsinUwsnFr0Kuje7QvNiO0gKBew7zsP4zHpXEg8Auvd6QPtSx8K5PhUYJtTFHBNqIiIqjeTrmZDP5WFlEVnA+vF+52okOVA93AD2LWcBq3MZP/XgxtBMaAsoPDebUTYKg1TeuZGN/JcRsMm5jgI7EpOR2X6Jq20AgEKCdmpHqB5qAPuuC7DM3uk6rup5H+x7rgAZlnvfW3ZzTcIhVdTDEX/Ry0EJQTtGQdWpZp7bo6LHhLqYY0JNREQE2H48Bdu6k4DtdmIr6dVQD2kKVedacBy9BuuXiVDF1oT60YYFe+1t52BbdQSwy5CCNVCPbAFVm9vbt999bflSGiyL9kH8mZljm+KWFfYNJ70uQahsGwkpWAv7L38477N6Oej/1Rsop4UqtgYknbpA74/8x4S6mGNCTUREVDrZd56HadxGyCdTnAXlddDNfACa8W0AAWT1+AqOXe6j1op6FaH/Ig6q9tW9tEiBwoTaC1mW8eGHH+LTTz/FhQsXULlyZTz22GOYM2cOgoKCCv38OzGhJiIiKr2EEECW1flBp4Kkur1Ot3wlHZmtPoFINbmfpJAgVXZ/gTInyvbVof9XLyhqVfB6XL6UBtNLW+BIuAwI4Vx3/NVYaJ5o6h6n1Q7LO/+Fdfkh52ouGiXUgxtDN/tBSAaN17bLEibUXrz44ouYP38+4uLi0KdPH5w4cQILFixAbGwsfv75ZygUOb+xWxDn34kJNRERUdnlOJMK+4+nALsM29oTcOz1vl52rkI00DwXAynorqkiJjssH+/3Ot9b9WhDKFtWdX22rT8J2cvW9Yr6laB+sqlzCUIfKWqUh/rJJh4vg5ZETKjvcuzYMTRt2hRxcXH4/vvvXeULFizAxIkTsWLFCgwZMqTQzr8bE2oiIiICAGF3wPrBbliXHYLwsua3R/2bJiA9jy9HhmohldPee0lDlQJSVDmIq7fcX9TMJ0WzKtAvfgSK2uXz3YakVECqoPc7Fn8wob7LjBkz8NZbbyE+Ph6xsbGucrPZjEqVKqFLly7YtGlToZ1/NybURERElB8iwwzTlC2wfXEw13rqEc2hn9cHUqgO1lVHYB6/0eta3orGlWH4Mg7KVhFwnEqBadRaOPblY8S8EChjIqBf/AiUzareu3IhYEJ9l169euHnn3+G0WiEVuu+e1PHjh1x+vRp3Lhxo9DOvxsTaiIiIvKH4+QNyOfTvB5T1AyF8v5wtzKRboZ97xW3dcKlYA2U7aIgqW/P8RYOGY59SRBpvm+kA5MN5jk7IR+57vu5OVEroOpbP9fNdApLhs2IiHWjiyRfKxETZK5evYqwsDCPZBgAIiMjkZCQAKvVCo3G+wR8f8+3WCywWG5/PZOeng7AmVgTERER+SxCC0RUyfn43TmGBKBduGc9UxZw1/uRaBwKIDRfYYnYJ2D9ZD/suy97XT4wr+SzfznXNLcCWHco/w354ZZw5m5FMXZcIhJqbyPL2XQ6natOTgmxv+e/8847mD17tkd59epcHoeIiIioOEtNTUVoaP5+wcirEpFQGwwGXL/u/esHs9nsqlNY50+bNg1TpkxxfU5LS0PNmjVx6dKlQu8g8k1GRgaqV6+Oy5cvczpOMcO+Kd7YP8UX+6b4Yt8Ub+np6ahRowYqVqxY6NcqEQl1REQEjh8/DovF4jHSnJSUhLCwsBxHlwvifK1W63WEOzQ0lA9QMVWuXDn2TTHFvine2D/FF/um+GLfFG++LI2c72sU+hUKQExMDGRZxr59+9zKzWYzEhMTER0dXajnExERERHlpEQk1I8//jgkScK8efPcyj/77DMYjUYMHTrUVXbu3DmcPHky3+cTEREREfmiREz5aNq0KcaNG4eFCxdiwIAB6Nu3L06cOIH58+ejS5cubpuydOvWDRcvXnR7o9OX8/NCq9Vi5syZOb7oSIHDvim+2DfFG/un+GLfFF/sm+KtKPunRKxDDQAOhwPz5s3D4sWLceHCBYSFheHxxx/HnDlzEBwc7KpXq1Ytj4Tal/OJiIiIiHxRYhJqIiIiIqLiqETMoSYiIiIiKq6YUBMRERER+YEJNRERERGRH5hQ55Esy/jggw/QsGFD6HQ6VK9eHS+99BKysrICHVqZIkmS1z/eXiw9deoU+vfvjwoVKiAoKAixsbHYvn17AKIufd555x0MHjwYderUgSRJqFWrVq719+7di+7duyMkJATlypVD7969kZiY6LXu1atXMWLECFSuXBl6vR7R0dFYs2ZNwd9EKeVL34waNSrHZ+q7777zqG+xWPDGG2+gdu3a0Gq1uO+++zB37lzYbLZCvKPS4fTp03jjjTfQrl07VK5cGSEhIWjRogXeeustr/+O+PLzKz09HRMmTEBkZCR0Oh0aN26Mjz/+2OPlfMqZL/0za9asHJ+b999/36Nt5g/+OXXqFIYOHYpGjRohNDQUBoMBDRs2xJQpU5CcnOy1fiCenRKxbF5xMHnyZMyfPx9xcXF46aWXXMvuHTx4ED///HOR7MJDTrGxsRgzZoxbmVqtdvt87tw5dOjQASqVClOnTkVoaCg+++wz9OrVC5s3b0b37t2LMuRS57XXXkPFihXRqlUrpKWl5Vp3z549eOCBBxAZGYk5c+YAABYuXIjY2FgkJCSgadOmrrp//fUXOnXqhOvXr2PKlCmIiorCypUr8dhjj2Hp0qUYPXp0Yd5WqeBL32Rbvny5R1mbNm08yh5//HGsX78eTz31FNq3b4/du3fj9ddfx9mzZ/Hll1/6GXnptnTpUixatAiPPPIIhg4dCrVajR07dmDGjBn49ttvsWfPHuj1egC+/fyyWq3o0aMHDh48iAkTJqBRo0bYvHkzXnjhBVy7dg2zZs0K0B2XLL70T7YPPvgAYWFhbmWtW7f2aJv5g3+uXLmC5ORkxMXFISoqCiqVCkeOHMHixYuxatUqJCYmIjw8HECAnx1B93T06FEhSZIYMGCAW/n8+fMFALFixYoARVb2ABAjR468Z73BgwcLhUIhDh486Cq7deuWqFGjhqhfv76QZbnwgiwDzp075/rvxo0bi5o1a+ZYNyYmRoSEhIgrV664yq5cuSJCQkJEjx493Oq+8sorAoDYsGGDq8xut4uYmBhRsWJFcevWrYK7iVLKl74ZOXKkyOs/Axs3bhQAxJQpU9zKp0yZIgCIX3/9NV/xlhX79+8XaWlpHuXTp08XAMSCBQtcZb78/Fq0aJEAIObPn+/W7oABA4RarRYXLlwo+JsphXzpn5kzZwoA4vz58/dsl/lD4fn2228FAPHuu++6ygL57DChzoPsByo+Pt6t3GQyCYPBIPr06ROgyMqe7ITaYrHkmFxlZmYKrVYrunbt6nFszpw5AoDYu3dvYYdaZuSWtJ05c0YAEE899ZTHsaeeekpIkiSSk5NdZZGRkeK+++7zqLts2TIBQKxevbrA4i4L8ppQy7Is0tPThcPhyLHu0KFDBQBx6dIlt/JLly4JAOL5558vqLDLlMOHDwsAYuzYsUII339+dezYURgMBmEymdzqxsfHeyQb5Lu7+0cI94Q6PT1d2Gy2HM9n/lB49u7dKwCIV199VQgR+GeH3zPkwf79+6FQKDy+AtXpdGjRogX2798foMjKpu+++w4GgwEhISEIDw/HhAkTkJ6e7jp++PBhWCwWtG/f3uPcdu3aAQD7rIhk/z3n1BdCCBw4cAAAkJycjKSkJFcf3V33zvaoYIWGhiI0NBR6vR49evTA3r17Pers378fkZGRqF69ult59erVERERwb7JpytXrgAAqlSpAsC3n1+yLOP3339Hy5YtodPp3Oq2adMGkiSxX/x0d//cqVmzZggNDYVOp0OHDh2wefNmjzrMHwqO2WxGSkoKrly5gq1bt2Ls2LEAgL59+wII/LPDOdR5cPXqVYSFhXndujIyMhIJCQmwWq3QaDQBiK5sadOmDQYPHoy6desiIyMDmzZtwsKFC7Fr1y4kJCQgODgYV69eBeDsm7tllyUlJRVp3GWVL33Bfit6VatWxeTJk9G6dWsEBQXh0KFDmDdvHmJjY7Fp0ya3+YZXr17F/fff77WdyMhIV+JBeedwOPDmm29CpVJhyJAhAHx7Dm7evAmTyeS1rlarRVhYGJ8ZP3jrHwAoX748xowZgw4dOqBChQo4deoU5s2bh379+mHp0qUYNWqUqy7zh4KzZMkSTJgwwfW5Vq1a+PrrrxEbGwsg8M8OE+o8MBqNOe4Dn/2bjdFo5ANRBO4eORsxYgSaNWuG6dOn48MPP8T06dNhNBoBwGuf3dlfVPh86Qv2W9H7xz/+4fa5f//+GDJkCFq0aIHnn38eZ86ccR27189B9o3vJk2ahN27d+Ptt99GgwYNABTcM5Ndn/2Sf976J7v8bk899RSaNGmCyZMnY9CgQa6Vp5g/FJz+/fujYcOGyMzMxMGDB7FhwwakpKS4jgf62eGUjzwwGAywWCxej5nNZlcdCoxXXnkFGo0GGzduBHC7L7z1GfuraPnSF+y34qFevXp47LHHcPbsWZw+fdpVfq+fg+wb37z++utYuHAhxowZg2nTprnKC+qZya7PfsmfnPonJ5UqVcJzzz2HtLQ0JCQkuMqZPxScqKgodO/eHf3798fs2bPx1VdfYerUqXjnnXcABP7ZYUKdBxEREUhJSfH6F5+UlISwsDD+dhlAarXa1UeAs78A79MDssu8fc1DBc+XvmC/FR/Za1ffOfoTERGR41egSUlJ7BsfzJo1C3PnzsXo0aPxySefuB3z5TmoUKEC9Hq917oWiwUpKSnsl3zIrX9yk9Nzw/yhcDRr1gwtW7bERx99BCDwzw4T6jyIiYmBLMvYt2+fW7nZbEZiYiKio6MDFBkBzn64cuWK66WRpk2bQqvVYvfu3R519+zZAwDssyISExMDADn2hSRJrnVbq1WrhsjISFcf3V0XYL8VleypHne+iBUTE4OkpCRcvnzZre7ly5dx9epV9k0ezZo1C7Nnz8bIkSOxZMkSSJLkdtyXn18KhQKtWrXCwYMHPRK2ffv2QQjBfvHRvfonNzk9N8wfCo/JZMJff/0FoBg8O74uU1IWHT58ONd1JJcvXx6gyMqWlJQUr+Uvv/yyxxI3gwYNEgqFQiQmJrrKsteirFevHtehLkD3WpotOjpahISEiKSkJFdZUlKSCAkJEd26dXOrm92X3tahLl++vMjIyCjw+Euz3PomMzPTY7koIYT4/fffhUajEY0aNXIr//HHH3Ndh/q///1vgcVdWs2ePVsAEMOHD891iUJffn4tXLgwx7V0VSpVntZKJqe89I/NZvO6XvWlS5dExYoVRaVKlYTRaHSVM3/w351Lq95p+/btQqFQuC2TF8hnRxKCe5PmxYQJE7Bw4ULExcWhb9++rp2OOnbsiO3bt3OnoyIwefJk7NmzBw8++CBq1KiBzMxMbNq0CTt27EDbtm2xY8cO105WZ8+eRZs2baBWqzF58mSUK1cOn332GY4cOYKNGzeiV69eAb6bkm358uW4ePEiAGDBggWwWq146aWXAAA1a9bE8OHDXXUTEhLw4IMPIioqyvWG9oIFC3Dt2jX8+uuvaN68uatuamoqWrdujdTUVEyZMgWRkZH45ptvsHPnTixZsgRPP/10Ed5lyZTXvklMTESfPn3Qv39/1KtXz7XKx9KlS6FQKLB161Z06tTJre2HH34YP/74I55++mnXTomff/45hg0b5nW3Rbpt0aJFGD9+PGrUqIE333zT49+MKlWqoEePHgB8+/lltVrRoUMHHDp0CBMnTkSjRo2wadMmrF27FjNmzMCbb75ZpPdZUuW1f9LS0lC7dm30798fjRo1cq3ysWTJEmRmZuKbb77B4MGD3c5l/uCfuLg4JCcno2vXrqhZsybMZjMOHDiAVatWwWAwYOfOnWjRogWAAD87PqXfZZjdbhfvv/++qF+/vtBoNCIiIkJMnjyZO7cVoXXr1omePXuKiIgIodVqhcFgEM2bNxdvvfWW15G248ePi0ceeUSEhoYKvV4vOnbsKLZt2xaAyEufLl26CABe/3Tp0sWjfkJCgujatasICgoSwcHBomfPnuLAgQNe275y5YoYNmyYqFSpktBqtaJly5Zi1apVhXxHpUde+yY5OVkMGzZMNGjQQISEhAiVSiWqV68uRowYIU6cOOG1bZPJJKZPny5q1qwpNBqNqF27tpgzZ46wWq1FdHclV/YmOnl9bnz5+XXz5k0xbtw4Ua1aNde3CwsWLOA3cT7Ia/+YzWbx9NNPiyZNmojy5csLlUolqlatKgYOHJjjhmHMH/yzevVq0a9fPxEVFSW0Wq3Q6XSiQYMGYvz48eLixYse9QP17HCEmoiIiIjID/yegYiIiIjID0yoiYiIiIj8wISaiIiIiMgPTKiJiIiIiPzAhJqIiIiIyA9MqImIiIiI/MCEmoiIiIjID0yoiYiIiIj8wISaiIiIiMgPTKiJiIiIiPzAhJqIqASQJAm1atUKdBhEROQFE2oiogC7cOECJEnCAw88EOhQitSWLVsgSRLGjh0b6FCIiPyiCnQARER0bydOnIBarQ50GAVq7969AIA2bdoEOBIiIv8woSYiKgEaNmwY6BAKXHZCHRMTE+BIiIj8wykfREQBNGvWLNSuXRsAsGvXLkiS5PozatQoV72751DfOU0kKysLU6ZMQfXq1aHX69GqVSv88MMPrrpr1qxB27ZtERQUhCpVqmDixIkwmUw5xnT58mWMHz8e9913H3Q6HSpWrIiHHnoICQkJBXLP7733HiRJwqZNmwAAzZs3d91zt27dCuQaRERFiSPUREQB1KJFCwwcOBDff/89qlSpgt69e7uOderU6Z7nW61WdOvWDefPn0fnzp2RkpKC+Ph4xMXF4aeffsKRI0cwdepUdOnSBb169UJ8fDwWLFiA1NRUrFixwqO93bt3o1+/frh58yYaNGiAfv364caNG9iyZQt++uknrFixAo8//rhf9xweHo7BgwdjzZo1CA8PR58+fVzHHnzwQb/aJiIKBEkIIQIdBBFRWXbhwgXUrl0bXbp0wc6dO73WkSQJNWvWxIULF9zOAYCuXbtiw4YNCAoKAgB8+eWXGD16NOrWrYvU1FRs3boV0dHRAICrV6+iZcuWuH79Os6dO4c6deq4rpGRkYGGDRvi+vXr+OqrrzB06FDXsd9++w09e/aEzWbDH3/8gcqVK/t1z/Hx8ejSpQuGDx+OZcuW+dUWEVGgccoHEVEJplAo8PHHH7uSaQAYMWIEwsLCcPbsWYwbN86VTANARESEK1GOj493a2vp0qVITk7GpEmT3JJpAIiOjsbrr7+OzMxMfP31137HnZiYCMA5Qk9EVNIxoSYiKsFq1aqF+vXru5UpFArUrFkTANCzZ0+Pc7JHpZOTk93Kt27dCgAYMGCA12vFxsYCAPbt2+df0GBCTUSlC+dQExGVYJGRkV7Lg4ODczyefcxisbiVZ08n6dixY67XTElJ8TVMD4cOHQLgfCGRiKikY0JNRFSCKRS5f9F4r+N3kmUZADBo0CC3KSR383cJP7vdjmPHjiEqKgqVKlXyqy0iouKACTUREQEAoqKicOrUKbz66qto3bp1oV3nxIkTsFgsHJ0molKDc6iJiAJMo9EAcI7cBlKPHj0AAGvXri3U65w4cQIA0KRJk0K9DhFRUWFCTUQUYGFhYVCr1Th37hwcDkfA4hg7dizCw8Px3nvvYfHixa4pINnsdju2bNmCo0ePupXPmjXLYyOa3NhsNgCA0WgskLiJiAKNUz6IiAJMo9Ggd+/e+OGHH9C8eXO0atUKGo0GHTt2xOjRo4ssjvLly2P9+vV4+OGHMXbsWMydOxdNmjRBhQoV8Oeff+L3339HWloa1q5d6za6nJ14q9XqPF2nbdu2UKvV+Oijj3D27FmEh4dDp9Phk08+KZT7IiIqbEyoiYiKgSVLluDll1/Gtm3bsHLlSjgcDtjt9iJNqAGgXbt2OHLkCD744ANs3LgRu3btAgBUq1YNXbp0QVxcHLp37+52TvaKHSNGjMjTNerWrYvVq1dj7ty5iI+PR1ZWVqHO2SYiKmzcKZGIiPJNlmVUqlQJ0dHR2LZtW6DDISIKCM6hJiKifDt48CDS0tIwZ86cQIdCRBQwHKEmIiIiIvIDR6iJiIiIiPzAhJqIiIiIyA9MqImIiIiI/MCEmoiIiIjID0yoiYiIiIj8wISaiIiIiMgPTKiJiIiIiPzAhJqIiIiIyA9MqImIiIiI/MCEmoiIiIjID0yoiYiIiIj88P/rp1YLHTfdHAAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We plot the results\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(range(T),rho_t_simplicial, \n", " lw=2, c=plt.cm.Accent(4),\n", " label=\"$\\lambda_\\Delta = 2$\")\n", "ax.plot(range(T),rho_t_simple, \n", " lw=2, c=plt.cm.Accent(5),\n", " label=\"$\\lambda_\\Delta = 0$\")\n", "\n", "ax.set_xlim(0,300)\n", "ax.set_ylim(0,1)\n", "ax.tick_params(axis='both', which='major', labelsize=13)\n", "\n", "ax.set_xlabel(\"time, $t$\", fontsize=15)\n", "ax.set_ylabel(\"fraction of infected nodes, $\\\\rho(t)$\", fontsize=15)\n", "ax.legend(fontsize=15, frameon=False)\n", "\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "hgx-installation", "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": "3.9.17" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 5 }