{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "# OPT interactive session exercise 8" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "In this exercise we want to the minimize the following cost function $f(x,y)$\n", "\n", "$$ f(x,y) = \\left(x-\\sin{\\left(2.x.y+x \\right)} \\right)^2 + \\left(y-\\cos\\left(x.y\\right)\\right)^2$$\n", "\n", "The variables $x$ and $y$ are bounded and defined by:\n", "\n", "$$ -2\\le x \\le 6$$\n", "$$ -3\\le y \\le 1$$\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "In this exercice you should:\n", "1. Define a function to compute the cost function $f$ to be used within the optimization packages.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.optimize import minimize\n", "\n", "\n", "def cost_function(x):\n", " return (x[0]-np.sin(2*x[0]*x[1]+x[0]))**2 + (x[1]-np.cos(x[0]*x[1]))**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Plot the cost function $f$ as a filled contour plot alongside a colorbar within the bounds define earlier.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0_vals = np.linspace(-2, 2, 100)\n", "x1_vals = np.linspace(-2, 2, 100)\n", "X0, X1 = np.meshgrid(x0_vals, x1_vals)\n", "\n", "# Compute the function values\n", "Z = np.array([[cost_function([x0, x1]) for x0 in x0_vals] for x1 in x1_vals])\n", "\n", "# Create the filled contour plot\n", "plt.figure(figsize=(8, 6))\n", "contour = plt.contourf(X0, X1, Z, levels=50, cmap=\"viridis\")\n", "plt.colorbar(contour) # Add a colorbar\n", "\n", "# Labels and title\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.title(\"Filled Contour Plot of Cost Function\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Using the starting points $x_0=6.0$ and $y_0=0.0$ and the SLSQP algorithm find the optimal solution of the defined problem.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal solution: [-2. 1.]\n", "Function value at optimum: 7.201206876091936\n", "Optimization success: True\n", "Message: Optimization terminated successfully\n" ] } ], "source": [ "x0 = np.array([6.0, 0.0])\n", "\n", "# Define bounds for x and y: (lower_bound, upper_bound)\n", "bounds = [(-2, 6), (-3, 1)]\n", "\n", "# Perform optimization using SLSQP\n", "result = minimize(cost_function, x0, method='SLSQP', bounds=bounds)\n", "\n", "# Print the results\n", "print(\"Optimal solution:\", result.x)\n", "print(\"Function value at optimum:\", result.fun)\n", "print(\"Optimization success:\", result.success)\n", "print(\"Message:\", result.message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Plot both the initial guess and the optimized value of the parameters onto the countour plot of the cost function.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opt_x, opt_y = result.x\n", "\n", "x_vals = np.linspace(-2, 6, 200)\n", "y_vals = np.linspace(-3, 1, 200)\n", "X, Y = np.meshgrid(x_vals, y_vals)\n", "\n", "# Compute function values\n", "Z = np.array([[cost_function([x, y]) for x in x_vals] for y in y_vals])\n", "\n", "# Create filled contour plot\n", "plt.figure(figsize=(8, 6))\n", "contour = plt.contourf(X, Y, Z, levels=50, cmap=\"viridis\")\n", "plt.colorbar(label=\"Cost Function Value\")\n", "\n", "# Plot initial guess\n", "plt.scatter(6.0, 0.0, color=\"red\", marker=\"o\", label=\"Initial Guess\", s=100)\n", "\n", "# Plot optimized point\n", "plt.scatter(opt_x, opt_y, color=\"red\", marker=\"x\", label=\"Optimized Solution\", s=100)\n", "\n", "# Labels and title\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.title(\"Optimization of Cost Function\")\n", "\n", "# Add legend\n", "plt.legend()\n", "\n", "# Show plot\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. Using the starting points $x_0=6.0$ and $y_0=0.5$ and the SLSQP algorithm find the optimal solution of the defined problem.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal solution: [4.6331801 1. ]\n", "Function value at optimum: 14.569489516652238\n", "Optimization success: True\n", "Message: Optimization terminated successfully\n" ] } ], "source": [ "x0 = np.array([6.0, 0.5])\n", "\n", "# Define bounds for x and y\n", "bounds = [(-2, 6), (-3, 1)]\n", "result = minimize(cost_function, x0, method='SLSQP', bounds=bounds)\n", "\n", "# Print the results\n", "print(\"Optimal solution:\", result.x)\n", "print(\"Function value at optimum:\", result.fun)\n", "print(\"Optimization success:\", result.success)\n", "print(\"Message:\", result.message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6. Plot both the initial guess and the optimized value of the parameters onto the countour plot of the cost function. Can you comment on what you observe?\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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7bZx55pmoVq0a2rRpgzZt2qTcb7t27TB06FC8/PLLKCgowEUXXYRvv/0WixcvxpVXXomLL76YyeMbMGAALr74Yjz44IP4448/0K5dO3z22Wf473//i3HjxslO9yXGfffdh59//hnPPPMMvvjii9iKU4cOHcLy5cvx7bffYv369QCASZMm4a233kK/fv0wduxYVKtWDYsXL8aePXvw/vvvxwYD9e7dG7Vq1cL555+PmjVrYvv27XjhhRfQv3//WE1tx44dAUQXDLj++uvh8/kwYMCAmLyqJScnB9dccw3mzJkDl8uFpk2b4uOPP8aRI0c0tQcAF198MW6++WY8//zz+O2339C3b19EIhGsW7cOF198Me66667YY1Hyvs/Pz8fkyZMxffp09O3bF1dccQV27tyJF198Eeeee66jFiogCEIDVk0rQBBOYtu2bdwNN9zA1a5dm/P5fFytWrW4G264gfvxxx9TjuWnXPrll1+4wYMHc1WrVuXy8vK4u+66K2Eyf47juB07dnAXXnghl5WVpXgy/2QAcHfeeWfCNn4aoaeffjrlunj4KXuEbvxUUpFIhHv88ce5hg0bcn6/n+vQoQP38ccfc0OHDuUaNmyYcJ/r16/nOnbsyGVkZCiazH/69Olc48aNOZ/Px9WvX19yMv9kLrroothUSlKcOHGCGz9+PFenTh3O5/NxzZs3T5jMP749JVNQxfPee+9xvXv35qpVq8Z5vV6udu3a3HXXXcetWbMm4Th+Mv/c3FwuMzOT69y5c8pk/i+99BJ34YUXctWrV+f8fj/XtGlT7r777uMKCwsTjnv00Ue5unXrcm63W/dk/hwXnTps0KBBXKVKlbi8vDxu9OjR3E8//SQ6mX8yQq9tKBTinn76aa5ly5ZcRkYGl5+fz/Xr14/bvHlz7Bg173uOi0451bJlS87n83E1a9bkxowZIzqZv9DzkPxeJQjCGbg4jirKCYIl/OTjR48ejU26ThAEQRCEOqgmlSAIgiAIgrAdJKkEQRAEQRCE7SBJJQiCIAiCIGyH4yR17dq1GDBgAOrUqQOXy4Xly5fLnrNmzRqcc8458Pv9aNasGRYtWmT4dRIVl2nTpoHjOKpHJQiCIAgdOE5ST548iXbt2qXMQSnGnj170L9/f1x88cXYunUrxo0bhxEjRuDTTz81+EoJgiAIgiAIrTh6dL/L5cKyZctw5ZVXih7zwAMP4JNPPsFPP/0U23b99dejoKAAK1asMOEqCYIgCIIgCLWk/WT+GzZsQK9evRK29enTB+PGjRM9JxAIIBAIxH6ORCI4duwYqlevbvkylgRBEARBKIPjOJw4cQJ16tSJLZ5hJqWlpSgrKzOk7YyMDGRmZhrStl1Ie0k9dOgQatasmbCtZs2aKCoqQklJCbKyslLOmTlzpuCyfgRBEARBOI99+/ahXr16pt5naWkpGjWsgsNHwoa0X6tWLezZsyetRTXtJVULkydPxoQJE2I/FxYWokGDBriwzTh4PX7D799dEpQ/qLRUYp/4tzaupESy2UhJQHI/UbFwZ0m/310CX/JiZGZI7JP+pRrJ8knuZ4miz5scUp9HPaj84yP1vEUyUn/dRzI9KdvCfk/Sz+XpUzjDlbTPJfj/6LFx/0+6rIjAWyMs86s1ovGvlTskvd8j8CvPLfAr1CPwNvEIHRcQr6AT25d/qhDPrHsVdU4dj207WCkPE7uPwNFKOaLtJZP8GghtE3td4l+T+NeCf945f/TaI/y/3vLHwvkjAACXL/qvNyP6pHt9UTnL8pe/CJne6BNZJaP8ia/qK38iK3sTP0s5vtTPVo5X+u9YPIGTQTzX6/PY8sJmUlZWhsNHwvj1u3rIrso2xS06EcGZnfajrKyMJNXJ1KpVC4cPH07YdvjwYWRnZwumqADg9/vh96f+xvR6/OZIqkfBm9ktUUoscTrnkv5GF3FF5O+bqDC4XRKiCcDlltjvlvisyH2OykwU1Sp+/aJa2Q+UGCCqZRyQpeIPkNTzFgYi/qR9oVRR9YYTRdXlK/+F4uUSRdUbAUKZ0Z89XKIQeVAuRPH/539OFlUPpEXVxeDt4BZ6mU/fZ4Ksnt6WIKv8cfHbMsS3RdtM+j19ep+3tHz7GacKMPer11D31HEcqFwd07vcgKnfvIWWJ//By1+9hjsvHoMjlXIlHxdP/OsRuwaZ1wWnf+b/H8lIfC08ACKnn/uIn4v9eeElNeKL/hsvqhEAXn8I/F+TMg8vq0EE4UeWL4jS009olYwASuBHti/6ApQhA1XixLQEGcj1JUqp3yvzzUMAK0v1squ6mUtqRSHtn7WuXbti1apVCdtWrlyJrl27WnRFDJD6Y1gqnoRyp+RSVIPSIMKxyL0n5N5TToGJEKuRSQOREm53IHWfu1T6i6unNPGLq6csUbzihUsyRUxKHYXSSqOJ+MpvyYT9qZIcySi/xY7LKL9JbYu26RJMN0OZLoQyXagWLsDcL+ah7sl/cKByddx58Rj8VKMR7rx4DA5Uro66J//B3C/m4YxTBYofY/zrwZP8uiS/FvE/86+LJ1Au7rzcuwMuuAOu2P+j+6L/ugJRneCCbnBBN0IBL0KBaA4WDEYVuCQQfeJLgj6UBKP/Ly6LPulFQT+KgtH/FwcTP0sFwcRAqTAk0YMDIM97MnbL9Z6SPJawN46T1OLiYmzduhVbt24FEJ1iauvWrdi7dy+AaFf9LbfcEjv+9ttvx++//477778fO3bswIsvvoh33nkH48ePt+LyZWHS9UgQdkDiC5OS1NHsz4JtRVXDl0e9ouoJJP2sUVSlZAhIFVWhrnejEBNWXlbFhDXhWCExlZDVeGE94+RxzP80Kqj7q1TH6L7liemRSrm6RFUIIVGNfz2ERDV63ultwURZTfg36II76IIr4E6QVQCCohovq0C5qAJIENV4WU0WVTHyvCcVHUc4A8dJ6nfffYcOHTqgQ4cOAIAJEyagQ4cOmDJlCgDgr7/+igkrADRu3BiffPIJVq5ciXbt2uGZZ57Bq6++ij59+lhy/YZCKSpB6IJEtRy7iapgVz0jtKSrCccplNVomy7UCBZg/qfzUK84Kqi39xmDI5XzYglrKNOFg9XyNIuqUJoKCCfdUqIan6rGtielqgnpqkyqGgx6BFNVICqq8akqj5ioyqWpRHrg6HlSzaKoqAg5OTm4pN0DojWpLhdQqUoGMrN8cLu11b64ShXU2UilUxLTXHBy3bYBC/reCNvBRTiUFJfiVEEJ4n8zuGXEy1VJagCVRKGhTLtmDqCKh0mKa8QXPw0CLDmYKrlGFak1qikDqTITs43kwVTxNZEJA6sEJC7hflPSR4HrVfF24Af4xMPLlBLEpFjxQCuRbf5QGZa+PwsNiv7G/qrVMeryO/C3L1f0OvjEtV7xP9hXpQZu7j0RZV75JyK5NjUewQFWEq+P0KCq+NcikjSoKro/tVYViNaqAoDPV/4lKMsffbKzfKmDqvha1fg61fgaVaFBVPFpamlxCJPO/RKFhYXIzs5OOdZIeHc4tLOBIQOnarXYa8njMpO0HzhlBtm5mbh0YEs0bXkGPF7tb0SXku8LUsdI7YrItE3fVQgAAIdwKIJd3/2Jla98jaKjxZZejbskaImoRrJ8+kU1K5O9qJaUGl776i4NJ4iqJxBOEFVPaSRBVD1lXIqolp/LxYTIU5Y0eKpMOGksPzdVVN1BeVEVklOpfWLiyt9PsqyGBQZa8RIXL6uxwUlJ205lZGDRORdj2JYvcHv/MThcJS+h/eS080jlPNzeZwxe/Gw+3mh9MU5VSXzS4lNTKTFNvo9kUZV6fdxl5Y+Rf1345yXiiz6HET8Xey4jfg7uoAsRHwdXwA3OHynv/k/SDp8vjJKAD1n+IEqCPmT5grFEtUpGAEXB6KCq4mBmTFQLglkxUS0MZaka7U84C0pSFSCVpHo8Ltw+6ULUrlsNlStlw+VyA9A4ilCPSHISo/LlBuxLnUtUODhEcLK0GH/tOYx5o5YgHIrIJqlA+qWpQPokqmrTVMCaRJVFmiolqXLIJa0s01V/qAwBb4Zg4lreLhd3fBABBQmqGtQmqoB1qSqfqALCqWqyqPJpKiWpzoaSVJ3kVq+E7JxMVKmcC49bxy+QCCdfISwpsRKi6ZKTX1pFi4jHgyqZVVG1+knk1srGP/sLECkpVSSqRmBVmgqkT6Iq9Ry6A0FBUdWbqHpLufLpqRQmqvGJXfQ8bWmqVuLFSkhY4+83Xli1pKsBb0bCNn57PPESGQD7B600UQWsTVX5RBWAaKrK16jysno8VJkGUaUBjhs4ZTfcble0IFVreqoUKUGVTFEpKCe04ILL5VI2Z+9p0mU6qmTSZTCV2oFUgDWDqZQMpDJyEBVPxM/FboL7Fc4MoHQaK6nt0bZTZwgwCrF6Wh6h0f+A/FRVamcA4KeqEhpUFT/6X2xA1fFQZVWPm7AfJKl2wEqRjFBXP6EMXTNA6JyOympsK6oqIVHVhpSwyk1llXCsxMwAWoVVr7SKzW2rRFTF5lQVmqqK5QwAQnOqFgSzYrIaL6oFoUrKngjCllB3v13gOLgLjsN96iQilSojkpt3OqEFpahEhcfKLn8eZl3/ADsx1zCQKp26/oUfg0tXXaocUiUBQoOt4q+ZF7n4xyU32Cp+u9C+6H0kddlLLKogd25COwKD25K3CXX/A+VlGQnd/nwpwGlRjZzOyfgSAJcvglDAC68/FBPVZJJLAPjufyBaq5rc/Z8J6+ceL4oEwEXYZoInKkjAREmqxbiLCpH75gI06t8dzS5shyZ9u6HZhe3QqH935L65AO6iQuPuXOWbvEWnpvh8zWeSx0yadh/umDhacZv7D+5Hi05NsX3nL6quhbAnkl3+Dk9Tgaio2i5VNWEOVUBZohqfqpqRqOpNU+MTUqmbkvMTtmtIV5WUA8jtK78fl+gt+Rg55BJVILX7X0uq6gq4Fa9WBWhLVQnnQUmqhVT6ag3qjBsFV2nqH3bf/r3If2o6ajz/FA4+8xJOnX8R0/ueNPVeFBUV4sVnXlJ8zlcrNiLn9CjC/Qf3o+cVF2H5fz7CWS1axY558N4pMGLCiD/3/YH5r83Dhm+/xt/H/kFebh6aNGqCQVdcg8su7Q+vl97KZlBRB1AlY7sBVRYmqgBEU1UzElWhgVRK0lQ1aWvysYKDqkQSVqHBVkLpKiA92ApQn7AKoaU8QGmiCuhIVZMGVvGpqhRKUtUsGySphHboL7tFVPpqDeqOGQpwnOD8qLFtpaWoe9cwHHhhUaqomtzVn18jX/aYqlWqMr/fbT/9gGF33oLmTZpjygPT0aRREwDAT7/8iP+8+ybObHomWp55FvP7JbTBnSoRn46qNCA+HZUJc4CyxHbd/xaJKiDd/a9GVIHELm+jRVUrctKqV1jlygEAaWEV2q8XJaIKyHf/A/IzAADl034nlwDwMwBIET8DQGHQOb9TiFSou98C3EWFqDNu1GlBle5yd3ERgONQZ+Jotl3/SWJ886gb8djT0/HUv59A50vOwfl9umDOS/9OOCa+u7/nFVFhvnLIALTo1BQ3j7oRQGp3/9r1X+KG4deiU4/26NKzI0aPG4G9+/9UcZkcJk2/H40aNMJbC97BJRf2RKMGjdGoQWNc3vcKvLXgHbRo3hIA8M13G9GiU1MUnSiKnb995y9o0akp9h/cH9v23dbvcOOI69D2/Fa4qP/5eOzp6ThVciq2/z/vvoneV12Cs7udhW69O2Ps/XfG9q34/P8w4Lp+aHt+K3Tp2RHD7rg54dyKgJVL6DKZt5QhzJJdVnJuUdc/ID2gSmnXf/RY4f9r6fpXs8KUHiQHVqkoCVA6OwAg3+0fv1+qNEAvnjLt3f/JJQD8DACA9oFVAGIlAMXBTJwMkaQ6GZJUC8j+77twlZbICiqPi4vAVVqC7I/eL99oQIq67OMPUCmrEt5Z9D7uu/sBzH11Dr7e+JXgse8uXgYAWPTi6/hqxUbMefpFweNKSkpw65DheP+N5Vj04htwudy4894xiCish92+8xfs3rMLw28aAbdb+O3qcin/Q7R3/58Yefet6H1JX3z41id47vHnsXnrZjz61DQAwI+/bMOMWY9g7OhxWPH+53j1+YXodM65AIAjfx/BxAfHYdAV1+B/736G119agksv7mNIeUNakwa1qfHYTlQ1ICeqQrKqRVTjZdUsUTUbPcIaD0thTT7GCGmVElVAeKoqIPGLhNLpquJlVcl0VYRzoe5+s+E45P5noaZTc5csRMGNt5aP+teKiCC2aN4Sd40aCwBo1KAx3nznDWzYtB7nn3dByrHV8qpFryknT7IMoE/Pvgk/Pz71CXTtdS52/f4bzmzWQvZS/9i7BwDQuGGT2LZ/jv2NXgMvjv1879gHMOSam2TbAoCXFs7HgL5XYNiNtwKIPs4H75uCm0fdgGmTHsVfh/5CVmYWenS/BFUqV0Hd2nXRqmVrAMDRv48gFA7h0kv6oG7tugCAFgoeQ0VEsss/DeFF1Rbd/xrLJuRqfoW6/9V2/QOJ3f/JXf8ABOtUk7v+AeEuZSC161+s219LOQC/clL0fuR/D0vOBCCwT26xAEBdSQAg3u0vJqqCswdolFq5OlVAuFY19n8GJQChoMSXYsL2kKSajLvgODL2Ke/u5nFxHDL2/wl3YQEiOTniB+qoReW7zXnya5yBf479o7k9ICqZz8+fjR9+/gHHC46DOy3Ifx06qEhShcjNycPyJR8BAG4ePQTBoHIx2PHbduz8bSc+WvFhbBvHcYhEIth/cB+6dTkfdWrXRa+BF6N71wvRvduFuPTi3sjKzELL5meha+duGHD9ZbjgvO644LwL0KdnP+RkS7weaYqhA6hkJMtOA6iSYVKnCuiXVYeKavRc4QFVSqc+ApSLqhLixVTJ9uj9Sw+s4q9JaB9LYQXU16rqSVmFalT5a4p/rQDpWtX4/4sNrAKUr1hFOBeSVJNxn9K3TJv7ZLG0pOogeYS8ywVwCksSxLh9/CjUrV0Xjz04A2fk10QkEsHl1/VDMKTsD3nDBo0AAHv+/D2WaHo8HjSsH93u9ZT/IeTLAeK734OhUEJ7p06dwvVXX4+brx+acl+1a9VBhi8Dy978EN9u/gZfbVyH5+fPxgsv/xvvvb4c2VWzsXDu69jyw2Z8/c1XeOPt1/Hci8/gnUUfoH7d+oqfk4qC5gFUDoeZqAL6ZgAgUZUVVaMGVyULrJy0GiWsgLS0sh5cxbcpJ6oAg1RV4SwA4VDFmE80XaGaVJOJVNK3TFukks7VMxhNAOzzRX9rhiOpdWk8xwuOY8+fv2PM8DvRtfP5aNq4GQrjBjUpoVWL1mjSqCkWvPmqbB0rX4Jw9O8jsW07fk2cf7VVy9bYtWcXGtZvlHLL8EV/g3q9XnTrcj7uv2cSPlz6CQ4cPICNmzYAiNa/dmzfCWNHj8Py/3wEny8Dn38hPXdsukIDqMRhNp8qEBVNk+tV5Z5fFjWqAFJqVJXMpZo8UEdsiU4gtUZVaCCVGYOrIj4u4ZayX6xWVWC73BysSuZhjZ2TkXozEjU1xVK1qkDq3KqA2PKqlMU5GZJUk4nk5qGsfkNwKutKOZcLZfUaIpKTK9G4eQN4qudVR6Y/E+vWr8Xf//yNE8UnUo7Jyc5Bbk4e3v5gKf7c9wc2bFqPJ56doep+XC4XZk59Env+3IMbhl+LVV9+jj/27sGu33/DW+8twbHjx+A5naA2qN8QtWvWxpyXn8cfe/dgzVdf4LU3FyS0N3LoaHz/wxY88uQ0bN/5C/7Yuwefr1mJR56cBgD4Yt1qvL50Ebbv/AUH/jqA5Z8sQ4SLoHHDxvjhp62Y/9qL+PGXbTh46CA+++JTHDt+DE0aN9X2JFYA7D65f8TvS7gxb59lWYIWWdXxPGoVVauXUbWrqMZjB2EVklbAeGkVEtXkQVVSMwBEj1E3CwDhXOgrhgoiGV5EvD7RaVkUwQEFN96K/Kemqz614MZh+gZNMVxGzev14qH7pmDuK3Pw/Euz0an9uXjj5SUJx7jdbjz3+L/x2KxHcPl1/dC4YRM8dO8U3Dz6RlX31f7sDvjgjf/ipYUv4pGnpuLvv/9GVlYWWp55FiZPeBCDrrgGAODz+vDMjNmY9sQUXHFDf5zdqi3GjZmAeybdFWurZfOWeOPltzD7xWdw48jrAY5D/XoNcNml/QEAVatmY+Xqz/DCy88jEAigYYNGeGbGbDRveiZ279mFTd9/i8VvLUTxyWLUqVUXk8ZNxkXn99D3ZBKa0FubKiSl8dt0fc7j22Q1qIpHbb2qjvlntXT9A6nd/0Jd/wAMm0tVqu4xet3GLp2qBqnSAK0lAdF2ov8mi6rQ4gFAqjzyGCWqyZIsVa4hVKsaPUa+BMAdtl5Uj0dcCEbYfhEqZtyeXXFxNH+OLEVFRcjJyUGPcx+E15uZ8Mcrv1YVjJh4AWqeUQcetwLnj3BwFxWiSa/OcJWWKpqGinO7wfkz8funGxARG6SjJEWtIGv9EvoJI4zDRw/hlbvfxtE/j0keq2QAleRIf6naVJm2tUqq2tSUlbAaUqagRFZ1lgvIPc9iz2dynSqQuDoVgIQ6VQAJshpfpxo9N25Zz6RlRGP3mTw9U/wUTkmXKZRWCiE1SIqH86v7/cqLlRRSMwioSYTFpuZKTp0TzjGgXjUe0SQ3Of2VeM0SU+Xy//OvhcsXQaSkFPtGT0dhYSGyT6+YaBa8O3zzcy1Uqcq247r4RARdWh+y5HGZCXX3a0Bzt+BpkYxk5+Dgcy8BLhc4l/RLEN3vwsFnXxYXVIIgDIVVOYAhsxLwZQAG1q1q6foH2NSpJp4rXqcau88y8e5/ua5/rd3+agWVPyf5loxULatg93/cNrVlAXKlAWJSqRUxCRYq15CqVVVSAkA4F3r1LOLU+T1w4MVF4DIzwblcKTWq/DYuMxMH5i7Gqa6pc5XGoBSVsBDdA6h01KaaPYCKhawyHVSVTLywMpZXK0WV5YAqLaKqZE5UFqiR1oTtGutYldayxs41WFx5hBLeZFEVGlgVPS5xYBXhbOgVtJBT5/fA759/i6MPTEOwboOEfcG6DXD0vqn4feW3ONXtQouukCDYIDmAyoHYXlYNwipRBaQHVClZoUpscE70uu0jqvFISatYyiqapqpYnhWQTlkTzhcQVzmBVSK4cqIKqEtVCWdCA6fMQiTtjGTnoGDIbSi4fhjchQXReVArV4mO4ufTVb1LoFKKStgdqXlTbTy5Py+qempWmc6ragKsBlMB7AZURY9VNqBKyeAcoZ+jx7sE61P5SebV4PIlHq+kWzr5PuIFTGw1LMFBViILC4gNvgKERVWqphXQn7Qmv178NSUPggPKH1PywCqEKsYAo3SFJNUuuFyI5OYhkptn9ZUQhGqUrECVzkulRvz6Zv1gPgOAwSgRVSC1fp9PVJNH/gNIkdV4UQUgOPG/mqVUla54FL3uVOGJPQYRUVVCspgq3QcIS6yYtIrNGCAqpxqkFZCeOcBIkkUVSJ0BABAfCEc4B8rBzUAu7ZTar3PFJ4JwDA6qTRWCVQmAU1DynNupTlXrgCqlXf9Gdyu7fJGEmxB6SgMSjldQGpAsiUBqiYBcqYAekks2AHYD4Qj7QJLqZKirn7ARSgZQpVttqhB6ZdVJtapWiipgXp1q8kCd6PHmi2rCfSVJa0r5gMJ61tg2BbWsaqWVR0xexQRWj+BKDaqqyEybNg0ulyvh1rJly5TjOI5Dv3794HK5sHz5cvMvNAnq7teAqm49SlEJQjkOrU0VQm+9qlNKAJQ876zrVAHzuv+l6lT1dP0bgVSdq9GlAdG2Uq9JbI5WHr1Jq1DXP39d1N2fSOvWrfH555/HfvZ6UxVw9uzZcOlZNIgxJKkW4SotAZepvD7PVVoKLjPuDzSlqIRDsUNtqpg0GUFFkFUjRBUQr1MFEgdV8Ymq2CpV8aIKRH/mE1WhQVV6RFXLIKpkvP6QquNDIuvTWyGt8fui7aVel5y4ssIdcIH+Cpbj9XpRq1Yt0f1bt27FM888g++++w61a9c28crEoe5+IxERyZz3lqDhoN7wHjwgfm5ciuo9dBANr+mLnPffYn2FhjLnpX9j4I2X62pj/8H9aNGpKbbv/IXRVaXywUfvoVOP9oa1z3PJgAuxaMlC3e3cPOpGzHjmUQZXxB7dc6YCumpT7Uy6lwHo7fq3Y/d/+XVLdyEnd/2LdfvLjeD3+kOqBTX+vORbMlrKA9ROdSW3L9qm8M0IXGne3V9UVJRwCwTEf3/+9ttvqFOnDpo0aYIhQ4Zg7969sX2nTp3CjTfeiLlz50qKrNmQpJqMq7QEeQvnIWPvH6g3/Fp4Dx2UPN576CDqjbgeGfv+QN6il+AqLVWWoirgr0MHMXn6A7igb1e0Oa8lLr68Ox6b9QiOFxxX3VaLTk3x+ZrPErbddvMILHrxDV3XWLtmbXy1YiOaNz1TVzt6+XbzN7jl9iHofMk5aHd+a/S+6hI8MPVelAWNWzvwm+82okWnpig6UZSwfc7TL+Ke28cbdr9mYFRtqp3TRp50llU9ogoor1ONl1VPGSe6SpUnwClepar8nHJZVVOnqlRUzUROXKXqWo2UVvHlZ7Xd7E5hxI8CxrfCSDT2r1+/PnJycmK3mTNnCl5Dly5dsGjRIqxYsQLz5s3Dnj170L17d5w4cQIAMH78eHTr1g0DBw407XlRAnX3q0Rxl52ISHKZWdi/4G3Uu/UaZOzfi3rDr8X+Be8gVKtO3EHRXwgxQd2/F2X1GmD/K0uiXf4Muvr37d+L624bjEYNGuPZGbNRr259/Lb7Vzz97yewbv2XeHvh+8jNyVX2WEWoXKkyKleqrKsNj8eD/Br5utrQy67ff8OIsbfipmtvwUP3TkFmZib+2PsHPlu9ApFwBDD5l6Te18VolExHJYuO2lSnkK5lAEq7/oHUKaoAZXWqgD27/5V0/XNBt+jo/FDAqylJVYNQ+/HlAmIlAnrLA4CkMgCZ/YQy9u3bh+zs7NjPfr/w781+/frF/t+2bVt06dIFDRs2xDvvvIP8/HysXr0a33//veHXqxbrv+pVQEJn1Mb+Be+grF6DmKgmJ6opgvrq0qjIMkpRpz81FT6fD6+9sBidO3ZBnVp1cNH5PbDwxTdw+MhhPPfiM7FjLxlwIea+OgcT/nUP2l/QBt37dcN/3nkjYT8A3HnvGLTo1DT2c3J3/6Rp9+GOiaMx/7UX0a13Z3Tq0R4vvDIHoVAIT/57Jjpfcg4uvOx8vP/he7Fzkrv7J027Dy06NU25ffPdRgBAWVkAT85+HN37dUP7C9rgmqFXx/bxfPDRe+jR/wK0O7817rz3dhQUFkg+V19t/Ao1qufj/nsm4cxmLdCgXkNc2O0iPPbQTGTG1Ql/umoF+l/bF226noVLBlyI1958VbRNoTKGohNFscey/+B+3HL7EADAuRd3QItOTTFp2n0AUrv7C4sKcf+UiTj34g5od35rjBh7K/7Yuyfh8Xbq0R7rNqxFv8G90aH72Rh+9zAc+fuI5OM2GqvTVD3zmrIkHZNVva+BWKJqdfc/n6rKLcsZn6oKLc+pdz15ny+s6SaGmrQ19hhUJq2AgjIAgcSVBj9Jk52dnXATk9RkcnNzceaZZ2LXrl1YvXo1du/ejdzcXHi93tiAqkGDBqFHjx4GXr08JKlGoEAkQ7XqCIsqFxEXVMX3L52iFhQW4KsN63Dj4JsSJAsA8mvkY0C/K/B/Kz8Bx5U/jgVvvIqWZ56FZf/5CKOGjsaMZx7F1xu/AgC89/oyAMDMqU/iqxUbYz8LsfG7jThy9AjefHkpJo1/EHNemo3R40cgp2oO3ln0Pq6/+gZMffwhHDr8l+D5D947BV+t2Bi73XLDMFSvVh1NGjUFADzy1DR8v+17PPf4v/Hh0k/Qt1e/BGn74aetePDRyRhy7c1YvuRjdOl0HuYtmCv5fOVXr4Gjfx/Bpi3fih7z0/YfMW7y3bisd398tPR/uGvUWPx73nP44KP3RM+RonbN2pjz1IsAgBXvf46vVmzEg/dOETx20rT78dP2nzDv2Zfx9sL3wHEcRt0zHMFQuQCUlpbitTdexVOPzMKbr7yFvw79hSdnC3cLsYBqU9WTbrLKQlSt7P7nZTW++x+Q7v5PuH6Z7n+toiolm0rOVSKvUmUCeqVVqkRAtAxARF7lJDbi58CR5ApSXFyM3bt3o3bt2pg0aRK2bduGrVu3xm4A8Nxzz2HhQv3jKPRA3f1mEyewvKjWG35tTFQPPfYcaj00XlhQGaWof+77AxzHoWnjpoL7mzZqhsKiQhw7/g+qV6sBADin3TkYNex2AEDjho2x5YfNWLTkNZx/3gWollcdAJBdNVu2az43OwcP3TcFbrcbTRo1wauvv4zS0lLcftsdAIDRt47BK4tfwuat36F/nwEp51etUhVVq1QFAHy2+lO8/cFbWDj3deTXyMfBQwfxwUfv44uP16Fmfk0AwPCbR2LdhrX44KP3MeHOe/H6W4vQveuFGDl0dOyxfP/DFqzbsFb0mvv2ugxfbVyHm0bdgPzq+Wh3dnt0Pbcbrux/FaqcvpaF/3kNXc/thjtH3B1rd9fvu7DgjVdx9YDBks+JEB6PBznZOQCA6tWqI7tqtuBxf+zdg9VrP8dbC97BOe06AgBmPfocevS/AJ+vWYl+vS4DAARDQUz/16NoUK8hAGDItTfjxVfnqL4up2C36ajUkE5lAEpfB6nZFszo/geiXf7x/wdSp6qSW6UqZcUqme5/oa5/M7r8kxES1WAw8flNvia+REBpeQAgXyIAiK8SJVUKQGmrPPfeey8GDBiAhg0b4uDBg5g6dSo8Hg9uuOEG5OfnCw6WatCgARo3bmzB1ZZDSaoK3GUKfnGoFMnkRLXBsEHaE1RA1bRT8UmpHO3PPifx57YdsPuP3YrP52nWpDnc7vK3XY3qNXBmsxaxnz0eD3JzcvHP8X8k2/llx8+4f8pEPHzfNHRs3wkA8OuunQiHw+h7dS906H527LZp87fYu/9PAMDuPbvRtk37lMcihcfjwcypT2Ht/77GvWMfQM38Wpi/cB76X9c31mX++57dMUnkOaddR/y59w+Ew9qTDzl279kNr8eLdnGPKS83D40bNsHuPeWvT1ZmVkxQAeCMGvn455j0c2wGsl3+BqepdunyFyJdklUW5RdGdf/rSVXlBlXF/i/Q/R+PUKIqNqWUFrL8QcGbHHKJq1jaymIwltDcs1QKoI/9+/fjhhtuQIsWLXDttdeievXq2LhxI/LzrR3zIQclqWYiIrChWnVwaMZsNBh6dWzboceeSxRURikqADSo1xAulwu79+zGpRen7t/9xy7kZOfEElKWJE8e7IIrdZvLhYjE4z3691GMmTgKg6+8FtdceW1s+6lTJ+HxePD+G/+Fx5P4i79Slr4BXABQ84xauLL/Vbiy/1W4Z8x49Lm6F5a+vwRjR49T3RYv6vFfFEIh44RJ6DlW8yVFC0wGUOnAyWlqPKySVcC6dNWoRBXQNvk/YFyqKrZ+fHyqyosqL2pqEtVg0CPb5a9EQpUcUxJIfC3kElcj01YgtYQCUJCipl9lkCaWLl2q6nij/z4ohZJUlmgUSe+hg6j14LiEbbUeGi87PZVW8nLzcH6XC7Dkvf+gtDTxE3z076P46P8+RL9L+yesOvHDj4mj/n74cSuaNiovF/B5fQiHjZ82ORAI4I6Jo9GkYVNMHv9gwr6zWrRGOBzGseP/oGH9Rgk3vgyhaeOm2PbT1pTHopac7Bzk18hHSckpAECTxk2x5YfNCcds+WEzGjVoBI8n9Q9rtdxqAICjcYOXtu/cnnCMzxf9AyGVxDZt3BShcAg/xD2m4wXHsefP39GscTN1D8oirE5TnQKfrDo1XVWTqOqtUwWMS1XLzxFOVeUGVcUTn6pyQXdKqsoyUdWCkhRWKnFlkbbKJa5yK35R2upsSFLNQkRgvYcOxmpSy+o1wN5F75cPphpxfVRUlcqviq7+h++firKyMgy/exg2bfkWfx06iLXrv8Rtd96CmmfUxPg7JiYcv+WHzXhl8UvY8+ce/OedN7Bi1f/hlhuGxfbXrVMXGzatx9G/j6KwqFDxdahlyuMP4q/Df+Gh+6bg2PFjOPr3URz9+yjKgmVo3LAxBvQbiPun3ovPVn+KfQf2YdtPP+ClhfOw5qsvAAA3Xz8U6zasxYI3XsEfe/fgzbdfl6xHBYCl7y/B1JkP46uN67B3/5/RqbqefxK7fv8NF3fvCQC47abh2LBpPea+Ogd7/tyDZR+/j/+88wZuu3mEYJuZmZlof3YHvLz4Jezeswvfbv4Gs+c9m3BM3dp14XK5sOar1Th2/B+cPHUypZ1GDRqj50W98PCMB/Hd1u+w49ftuG/KBNQ8oyZ69uil5SlmCpMBVDrQO2+nGiKZHskbS1jJqp2TZqO6/5MHVSmZASD+//Hd/9Fz4q5LwZyqarv/hUQ1uV7UbFiKK49WcQXE5dVOS9YS2iBJZYWGFDVZUPe/uhSl7Tti/6tLU0WVMY0aNMb7byxH/br1MW7y3bj0ykswZcaD6NLpPCx97b2UuThvvWkEftr+E64aMgDzFszFpPH/QveuF8b2PzDuX1j/zVfo0f8CXDUkdcATKzZt+RZH/z6Cy67pgwv6nhe7ff/DFgDRGQau7H8Vnpj9OPoNuhR33Hs7fvxlG2qfLp1of3YHPPrg43h96SIMvOFyfLXxK4wZfqfkfbZt3Q6nTp3C1JkPo/+1fXHTqBvxw09bMXfWfHTu2AUA0LplG8yeOQf/++wTDLiuH56fPxtjbx8nOWjq8SlPIBwO4eqbBuLxZx7DuDETEvbXPKMW7h59D56Z8zS69e6CR5+aJtjOzKlPoXXL1rh93Ahcd+tgcByHl/+9AD6vfQUkGSenqUol1Ahp1SurgLnCqrbcQK2oAvKj/wHzalWVpqrJ01SZJapZvqCmm2BbGsVVzUwCcuIqVD4Q8ZKoOhkXZ5fCAxtTVFSEnJwcXNLuAXg9iXOQ5deqghETL0DNGrXhcYt0zQgIrJCgxtegpkxD9fJb0oOoVKSoarlkwIW45YZbMezGWw27D8JehBHG4aOH8Mrdb+Pon8d0t6ekNtVVKUv6ALHJ/Xkk7kOJgGmVPVbCKSZdqtthkAwbWbuqRYblXhuh1yB59D+AhNH/sW0ZiV3wfK1qtA1X0rHC/4/Eb497m8avhiS0ClP5ceX/T5k0P6meM7nuU6w+VarmVEw0WVASlH99k2td4xGTb6nSB6npvCIlpdh/11QUFhYmTHpvBrw7fPZjQ1SuyjYTPHkigt5n/2nJ4zITSlIZ4FLp+XKCCpwe9R+fqI66wbAaVYKwA7rSVItg2Y3PKmVlna6yTli1CLCceKvp/k+3VNXqrv9klKSvUqkrq8RVbFUvwlnQ6H6jSUpRXaWlqDdS2UT9oTNqY//Lb6HeqBuiojp6CP58+/+iS6Mm3Ad9GAlCarlUp430jxdVrQmr3lkBEtqywwwBEiP/AeWj/wHhOVUB82YAAFLnVY0tJxo3A0D86H+gPFVNHvkvNOK/JOBTNIJfjioZ6r8cFpel9nqIpbd88ip0rXziKjargNh8svGzCrhC1v99PBaujNIw2y8Tpwyc2tBOkKTqxFWqbtJlLjMTx4fdjrxF87H/5SWy86CGatWJiuroITg+dFSqoJrA6o+kBxYRhBxKp6PiTpVId/uXBuS7/UWQE1U5CbIKvcIa/5hYC2usXRXiqufLgh5RBSA5VRWQuAAAEJXVeFGNtlEuq7ycxssqn6hGMsoT1bC/PFEVm65K7VRVvIjxosYnqvFCJyaqJUGfbJe/FjlVcm6ywApdhx5xBRJLIiJhcxdGINhCkmokIoOpCgfdiKLLrpQWzqSVqQQTVIBSVIKIRyJNTQd4AdObrgJsFzIwM6VWIqqAcCmGkakq/3N8qgpIy6oZqSqrRJUVSgRWKnUVeywlAZ+guIZ1LCNLWA9Jqg7cJUFwOX5ES1KThFRmtL/aRNSKBJWo4HAcOIaLSFCayg67lQOYDX/NLLv/AX2pKsB+EYB4WVWbqsqJqpI0VY5sn/a0tSiY+hkWE1gpeVWSuhLOhSRVJ8UFpQgFw4hwIXig8APByaSfDMWAILQQQQjBYAhF/xRbcv+6RDXN09Rk7FYOYCYsu/8BbalqtB39JQApK1RJlAAoSVWTu/95YYuXOT2iqkdQlZwfL7FS8iqXuoapu9/RkKRqhK/BCpSGsPnLPTi/XwbycqvB7fKmhKopyEmqUkeVa4cgNBBBCMcKjuG7j39E2Sm20mL1UqlA+qSpQlRkYRVDS/c/oDxVjbZjbgkAy1RVTFSLy/y66lL1IiWxvMAqkdeQNz3exxUVklQNJA8S+PKjHQCAjhc1htfngUvKMmUEVFX3Kk1xS7CG4xAMhvDdxz9izeJvrL0USlN1UVGEVemXCitS1ejx6koAAG2yqjZV1ZOoKk1Rq/j0L7RRHEz9HIvdv5C8hoL2m7qOUI4jJXXu3Ll4+umncejQIbRr1w5z5sxB586dBY9dtGgRbr01cRJ6v9+fsma9HjgOWPPhDqz/bBeqZroS1rxPoaxMfB8ATuHqOVxAuh2C0AIX4VD0TzHzBDUe09JUHVNSOTlNFYKlsAL2k1a9ogroS1UBdiUAgHS9qpoSAKlUNbn7P1bbGSerYmlqUdAvK6osBFVpO7zICl1T0Ed/K52M4yT17bffxoQJEzB//nx06dIFs2fPRp8+fbBz506cccYZgudkZ2dj586dsZ8lJVIGqalWykpD+Oe4xAdKZjJy2cnM47B6TXSCMAMrB1EpakNCeuwKy0FXgH2ElZWoAupTVcA5JQBqU1V+0FKyrEqJqhZBzfVJ//0rCIr/HpC6v+O0ZpGjcZykPvvssxg5cmQsHZ0/fz4++eQTvPbaa5g0aZLgOS6XC7Vq1VJ8H4FAAIFA+YevqKhI2YlS4shwtRwSVIJQiI5ufzPTVKElPOVIXk1JC6yFFbBWWtWIKiC+YpiaVBVgVwIAsJVVpSUAWlNVMVEtDmYqElU5MdV6bLzQVvbS30sn46ivGGVlZdi8eTN69eoV2+Z2u9GrVy9s2LBB9Lzi4mI0bNgQ9evXx8CBA/Hzzz9L3s/MmTORk5MTu9WvXz96X1ITVusURzUpKkE4HTVftIxcLtWq1ZN4wn6PJkGNPzf+pof4ZVn1pMP8sqwslmc1GikxF/sSkLysKiC8tKqa5VWTl1gtP09+idWE/wddMWGNX16VC7pjwhoKeBOWVo1fVrUk4EuYtomXVR6hlaSEppKSI9dXoko6tbaf6ytBDqOyA8IaHCWpf//9N8LhMGrWrJmwvWbNmjh06JDgOS1atMBrr72G//73v3jzzTcRiUTQrVs37N+/X/R+Jk+ejMLCwtht3759+i6cUlSCMBapz5iOz4ySVFBrAqlXKsXaNEJadbVjc2mVE1UhWfWURlJk1VPGCcpqYnuJoiomq+6yVFmNXa8BshoMelJkNfb/oC9BVovL/CmyKiSqQgOe1JLjLWFyI5yL47r71dK1a1d07do19nO3bt1w1lln4aWXXsKjjz4qeI7f74ffr+LbIaWoBKEaNQOoZGtT5dAxiMrJpHRZaywRSBZVrWIOCE/Ab3Vdq1xtsVD3P5BaqwpoG1gFmDO4CkgtAxCrV5UrAUju/hfq+hfr9i8IZkkmqekmlscjlVEaZqtbJZGKMf+royS1Ro0a8Hg8OHz4cML2w4cPK6459fl86NChA3bt2sXmouQEleFgKYIgJDBoEJWSOke1A6iMSFG13C8LadUjrLH2pCbkVyCwLBJaJaIKCA+qAqRrVQFtsmrGEqta6lXjRRUoH1TFJ6rxsqq0PlUred6TkvtLvRVD5tIVR3X3Z2RkoGPHjli1alVsWyQSwapVqxLSUinC4TB+/PFH1K5d26jLLIdhNz9AXf1E+sG0NlUOg7v9nQiL8gBWtayi7SeVCwjdWKFEuNXWqiopARArAxCqV+WF1cp6VaESgHiSu/+Fuv6lRuvLkec9GbsR6Y2jJBUAJkyYgFdeeQWLFy/G9u3bMWbMGJw8eTI22v+WW27B5MmTY8c/8sgj+Oyzz/D7779jy5YtuOmmm/Dnn39ixIgR+i+GuvkJwl7IfTGU+MxaPYjKDjhBWo1Gr6hqGVgVbVPd4CqzZFVpvWpyrWpR0J8gq8XBzBRZ1SKqJKYVC0d19wPAddddh6NHj2LKlCk4dOgQ2rdvjxUrVsQGU+3duxdud7l7Hz9+HCNHjsShQ4eQl5eHjh07Yv369WjVqpWxF0opKkEognltqo5ufym0rhPvZFiUB7CsZzULJa+lWJ0qIF6rCkiXAETblZ5fNf7n5JWrALbTVmmpVxUqAZDq/heqTy0MZYnWpR4PVZYV1VzPqdj/SzzU3e9kXBxHa2vKUVRUhJycHPQ6cwK8ntN//EyuRSVJJdIZtStQyYqqnKRK3J/UICq5rmWlkmpVTSprWMzValdpZVVjnCyrse1xssoTL6vRdpN+zkhuo/z/keR9cR+BSNzblh9UlfJ/X/n/+ZpVoHyOVaB85SqgfDEAAAmLASQvrxo/uCp5YFVyrWqyrIqJqpSkxgsqAJQUhzDmnE0oLCxEdna26HlGwLvDvC3nIqsK44FTFj4uM3FckmoLdAqqWkhQCUIlcmmqxtH+rNJUqRRODWICpAShbmnV929A0grYQ1zVJONqU1UgdRYAQHjVKkD9TADRc0/vMzlZFZoFAIjKavLAKrlUtTAU/TKabqP9CeWQpLJGgaBSLSpBJKKmyx+wd7e/0egRUyXt6JFXo6a8AuwhrlLIiSqQ+pyrKQEA0lNW+TpVXlb5OtVkWY0X1eOhygCoPrUi4LiBU5ZjcqpJKSpBGIRBg6iMlClWgip3H8k3zW0xXBUreUCWoTMKaGxXTsrFvgCIzQKgZiaA5J+FFgQwa4CV0pkA4gdXJQ+sKghmJQys4lPVeHhZjacgXCllG+FcKElVQ2kp4JZIZihFJQjNWJKmWtzt7xQEu6s1Jq6s0tZ4lDzXUl8eWL5WcqUcYqkqIF4CAIgProqeF/2XdbKaTCQu14rX55CASkglq/GiqiRZ5VNVoe5/oYFUBeFKKbWphDMhSWUFCSpBVCj0dvurrUs1I0VVAytxFVzJiYG4JmPmlwYlr61UrSqQOrBKrl41ei5On5v6s1pZBfSVAigheTYAMVlNLgFIllWh7n8S1fTAXr/1iASoq5+oaKh9zyv64mfR3Kl2r6E0AlalAizLBOyMlNQnd/8DykoAoufqLwMAzC0FiJ9nVawMQKgEIL4MILn7vyBcCYXU/e9oKEllAaWoBGEZdu72l4PVKH87Y2TiChiTurJA6WsrlqgC0qkqID24Knp+4jRVapNVwPxBVnqTVTsOqioMV0IgzFa3SsMVY/5XklS9MJ5uiodSVKKiorY21Qy0iqoda1OF5udUg1DCp/oaGM4sYFd5VfPlQ0pUAeFaVSC1BACQnwkgeVt8qhrJSJRVwLoZAVjJahYKU543wjmQpJoApagEYSxGp6l6kBNVM9JUvWKqpi09EmvkAK2ENg0WWC2vpxJRBZSlqoD84CqhbfHpqh5ZBdQNsoqHtawWhKi738mQpOrBoG5+SlEJwiBs2u1vJCwFVc/9aZVXM+ZzVQovt0Z9qZATVUA6VQWUlQAAxslq7GeN6aoalMhqIESa42To1dOKQd38BEFo6/JXlKbqxKhufz2jwaUwW1ClkLoWLQJrhLzK3qcJ9cN6RBVQVgIQbSP6r1pZjbZjzIwAaksBlJAF7YMfCeshSTUQSlEJwlys7va3U32qnQRVDpbpqxXyagVyogoIlwAA+mQ12s7p/UmyCqirWwWMLwUoDNqrvp1QB0mqFihFJQjDMXQAlUHd/nqoCCP91WKGvAL2Elg1abmUqALCqSqQWq8abev0/euUVUDF4gAGlgLwBEM006aTIUlVi0JBpcFSBGENirv9LahP1dvtr6XLXytCcsOK5Lk+1WJW6UBCuwaLrNbXVYmoAspS1Wh7p69Ho6wC4nWrAEyfFSBEvf2Ohr5iGIBWQaWufoJIROtnwowviVIT/bsDEvtsPsl/KNNlqKDG34fUTSvhDJfgTS9CCxWwvOlBiZiLfTEQWgwg2mbiggBC26QWBgASFwfgFwOQWhzAHXTFFgdwBdyxxQG4oDu2OEAo4I0tDhAMemKLA5QEfLHFAUqCvtjiAGrqVysKTzzxBFwuF8aNGxfbdujQIdx8882oVasWKleujHPOOQfvv/++dRd5GpJUNZSWyR9DEIRz0LEaFWCMqMpNj2RUomeGnKqBtcCKySsriXUCUgm2kKgCqaIqtE2NrALCK1kZuZoVUc6mTZvw0ksvoW3btgnbb7nlFuzcuRMffvghfvzxR1x99dW49tpr8f3331t0pVFIUhlDKSpB2APFn0WdomoEVk9Eb3eMSGGdLLFqrk9OVLWmqoC4rCYvu5qcrsbOl5FVLelqaYhElae4uBhDhgzBK6+8gry8vIR969evx913343OnTujSZMmeOihh5Cbm4vNmzdbdLVRSFIZQnWoBMEeW3yBk7gGK7r9laSpamozjUpQw36XohtrzCwjsEpm9dynXE2wVKqqRVajbeovBQC0pKvpPfSmqKgo4RYIiH/pvvPOO9G/f3/06tUrZV+3bt3w9ttv49ixY4hEIli6dClKS0vRo0cPA69envR+9QiCqNAwG0QFmD6Qyk6DqOTQK5pqzxeTKCXIiaqRg7qchNAMALF9ZYkDq/htQOL25AFW0XZPHycwyApQv0AAID2NVUTHzACsKAhVgp9xohs4PSKsfv36CdunTp2KadOmpRy/dOlSbNmyBZs2bRJs75133sF1112H6tWrw+v1olKlSli2bBmaNWvG9LrVQpLKCD0pqi2SIoKwMXqmo2IqqhJYIapWYkQCyvq+tciskrRVr8hajdJEWU5UAXNkNfnnhOVXZWYGiJSlt+bs27cP2dnZsZ/9/tTfYfv27cM999yDlStXIjNT+Pfoww8/jIKCAnz++eeoUaMGli9fjmuvvRbr1q3D2Wefbdj1y5Her55JUDc/QaQJOif6N1tUlaz3bkSyZ6WgqkHJdRolsoD9ZFZLuYOUqALCqarYdj2yCqQuEBA9Xjpd5aU1XcnOzk6QVCE2b96MI0eO4JxzzoltC4fDWLt2LV544QXs3LkTL7zwAn766Se0bt0aANCuXTusW7cOc+fOxfz58w19DFKQpFoMpagEYTxMl0x1mKiyximCqhSjRBbQXuurV27NnqVBSlQBfbIKqCsFiB6fKKwVnZ49e+LHH39M2HbrrbeiZcuWeOCBB3Dq1CkAgNud+Jx5PB5EItYudEGSqhNKUQnCHPSuQGVWfSpg3GT/WjAqTdWKkMyYhdB0SkowsrxACDtNBaYUMVGV2qdEVgF1pQDR44XT1YpK1apV0aZNm4RtlStXRvXq1dGmTRsEg0E0a9YMo0ePxqxZs1C9enUsX74cK1euxMcff2zRVUchSSUIgkiGgahKISWqYhjZ7S+2fCYrrBTTeNRchxahVZMysxJao9CSmMuJKiAuq5Hk2lYVsgpIpKsh5wm/2fh8Pvzvf//DpEmTMGDAABQXF6NZs2ZYvHgxLrvsMkuvjSRVB3pTVOrqJwh1mJamAoaO+JfCKd3+SrCLnGpB6bUbnc6m3J8BcmtmCYeaVBVQJquARLqq+4rTkzVr1iT83Lx5c1usMJUMSapGqJufIJwJc1GVwE71qVanqXoxSni1SiaP2uvSfX82rQlWm1KLHS+UqgL6ZZVwJiSpFkEpKkGkCQ4aSGVmfaoeqTQzgdV6X5oTVA33p1dsjcKo10lMVIGorIaTvjdKyqoB10eYB0mqBihFJQjr0NvlD5jb7Q84R1StTFOdVhpgpmwa8dwIXYtZr4GS+1ErqoCwrLooSXU0JKkqIUEliPSgIouqFHKiKjdvphaMkCMxwdFC8hKfWrFTimr2lwLW9yfU/c/jDiaKKuFcSFIJgiCUkEaiaqdpqfTIC0sRNeN+tMguC7kzu1zADqk4n6qGrb0MAEBhKMuAZVErhr5VjEfJCK6kBHDp//RRPSpB6INFlz+gYZL/CiKqVqSpSjFLTI1Az7XrSXPtII1qUPM8iXX987hD+q+HsA6SVIIgKjRMV6PiqQCiagUsBVVKbIyA757WCovHzqpsgSV6H5fZryNhLiSpBEEQalA6LVWai6rWNd3jUZPwaZUZu0gMy+vQKrxOTqGTscvrShgLSarJUFc/QdgPQ7r9Ad2iCkBQVt2l0Uo7IVm1k6jKoURkAfVyle4CYwfhNYt0fy0JaUhSCYJwJKzqUnnsKKqAtlTVLqKqVEJZoldqnDgqnB8kpIV0lUD+dYzYYeQUoRmSVIIgCK2QqJ6+L3uIqhbhcqKUJmPkY9AjwEaTDq8dIQ1JKkEQxGk0DaKyuagCEJRVKVEFICirRogqK4lVI6is5IZfetPu6FkalESQsBKSVIIgiDjSTVQB8VRVy8pURtSompm2apUupwipEGZeux4hZkHyY+U4575uBEkqQRAEGxwsqgBUdf9rEVU9Iiq1RKYa1AoqK7lzmuDqSl4d9lgJe0OSaiI0sp8gnIHmuVMZiioAzVNUAcaP/PeWRmVESFa1iKoVg6zE0Cpa6SJo6fI4ACBCSaqjIUklCIIQwJBJ/uOREVVA+xRVgPV1qlKiGm0r9ZqlRFUuTZVbecgomKWtvvSTKXfQXotBEM6DJJUgCIIlStNUQLeoAvbu/tcymEqPqLJAqXRqTlvTUEbFsMNjjYSsv4bCYCYygmzfuGVB4c91ukGSShAEIYLh3f6ALUUVYNf97wmcTmFVdP9rFVXZddyDbEarqxFUFqLG+SO626iQcBxyioqxz+rrIDRDkkoQBCFBuogqIF6nCljb/S8mqtH7SN2nR1TNQoucGiWjLp9zJJcLCs82oYbsUyUY9PVmDFv1NaodPYYcBtdFWANJqom4szJp8BRBOBA7iSogPaAKUF+nCljb/a+lTlWrqLJKU1mhR0ydJJ9K0fuYLtz2K+bN+Q+yAmWACyhmdF2ENZCkEgRBGAljUQWckaqa0f1vhKi6Ay7dg6GUpKhq5ZSFkHr9Id1t2JnuW3/Dq8++AXCAGwCsL0cldKI/V7eAuXPnolGjRsjMzESXLl3w7bffSh7/7rvvomXLlsjMzMTZZ5+N//3vfyZdKUEQ6QJ3qkT7yaUB5ceWlEZvMvCpquj+gMz+UvFFzXlZTdleGoklqyn7yoSNgJfV1PsQ2V4mck1lwvvcZdGb8H0IbwfsvdxnPC5fRLWgev0hwZtefL6wbW/VyorxwnNvARwHD007lTY4TlLffvttTJgwAVOnTsWWLVvQrl079OnTB0eOHBE8fv369bjhhhswfPhwfP/997jyyitx5ZVX4qeffjL5ygmCcDqmiSrATFSlZNVdGhaVVU8gLCmrgtvLOEFZ9ZZygrLqCXCCsiompPw+IViKqtGrJilJUdXIqVYZVSuCrMjyB5nfrlm3BVmBIDzkp2mFi3PYmmFdunTBueeeixdeeAEAEIlEUL9+fdx9992YNGlSyvHXXXcdTp48iY8//ji27bzzzkP79u0xf/58RfdZVFSEnJwc9Kw6BF6X/mkkqC6VIPTjVtAtbgS6505V2vXPo/BxSnX/A+J1qrH9IrWqgHD3f2yfyLKqQrWqPGKrVYlNVyU20l9su1gJgFj3v1jXv1S3v+Q+me5+pZIqh1oh1UOW38bRM8fhvyNfRN2/ClKStyIAOQAKCwuRnZ1t6mXx7nDj6huRUYXxFFTFZVhyyRJLHpeZOKomtaysDJs3b8bkyZNj29xuN3r16oUNGzYInrNhwwZMmDAhYVufPn2wfPly0fsJBAIIBMq/fhcVFem7cIIg0gbdk/yrqVEFmNapAtKDqgBttapAqqyaNQOAmlpVsTpVsRpVPlEVElKp2lV30KVr6imWgqpWTlnIaJbPXKHNKTyF+n8VmHqfhDk4SlL//vtvhMNh1KxZM2F7zZo1sWPHDsFzDh06JHj8oUOHRO9n5syZmD59uv4LJgjCEKxKUXmcKqqA9KAqwJh5VQH9A6vEZgAQ2853/yfLKt/9nyyrfNe/mKyyFFVXwK1rVL8SQVUqp1qklJWEVslQWQIjQo3QSSbtEPbDUZJqFpMnT05IX4uKilC/fn1m7dNUVARBaBJVQPc0VYD5qSrAbhEALbLKKlU1K1Hlgm5TppdSKqhapJSVgPJk+8Tb82an31RcRBRHSWqNGjXg8Xhw+PDhhO2HDx9GrVq1BM+pVauWquMBwO/3w+83djZoElWC0IbVKSqP7jQVUC+qgK1SVYBtCQDARlaNSlXFuv8lywJERNUViD43WhLVUMArmabKpahK5FSNmGoRUinpVMuJnEwcrlcV+QdOwO2oUTaEHI4a3Z+RkYGOHTti1apVsW2RSASrVq1C165dBc/p2rVrwvEAsHLlStHjCYKwL3YRVB5do/151I76BxSN/AeiomrkDACA+HRVgPpZAAA2U1apna7KExCeBcAdFJ4BQGz0v+j2oPggMl5Wk2Gx8pJWlAhqlYxA7CZHti+QclNCFV+psltGAKuuPQvGzsmgnZOhTBQH2d5Ohuz1u9AoHJWkAsCECRMwdOhQdOrUCZ07d8bs2bNx8uRJ3HrrrQCAW265BXXr1sXMmTMBAPfccw8uuugiPPPMM+jfvz+WLl2K7777Di+//LKVDwMApakEQZzGwEQVYJeqAuxLAABn1KvqTVV5URVLVYUSValuf6k0NRj0MJ0yKhmlYqq4PZ/6v4O5vsQviD9eWReD5nnhKw1RmppGOE5Sr7vuOhw9ehRTpkzBoUOH0L59e6xYsSI2OGrv3r1wu8t/GXbr1g1LlizBQw89hH/9619o3rw5li9fjjZt2lj1EBIgUSUIZdgtReVh0u0PaBdVQHH3P6CvVhVgXwIAOENWWZUAiMkqa1HVilyKykpQlYppsoyKUVo1AwtndcOou9chAo5ENU1w3DypVsB6nlQhSFQJQhi7ymk8TCSVR62o8qh4nuRS1dhxOuZWBbTNrwqIz7Fqp/lV1c6tKrRdbFCVWJ2qmKyKiapUmipVlyolqnKSKieoSuRUqZjmeFOPa/r1EVw3fhN8pWFwAIo56+dJHfjZbfBVZusOwZNl+G/v19J+nlRH1aSmM+6sTEf8MSYIM3HKZ4JJbSqPlhpVQHGdKqCsVhVQtrSqXL2q1iVWtaxclVy3ytemJtenim1XU7PK16sm16y6Ay7B2lSh7e6gS7Be1RVwC9aqckG3YK1qKOBFKJDaMRoMehAMCn9RKAko+6KiBr2CmusrkRXUHG9J7CbE7vPPwLOf98aXk89EUT2GXx4JS3Bcd3+6Q93/BBHFKYJqCFq6/gFV3f+A8lpVQL4EABBPVo0qAwCMKQVgMRuAmjIAqRIAIDVZFSsBEOv+F6tRLQn4BBPVkqBPNE0tLvOLpqlFQb/mUftK5FSOPO/p+VKrAT/cXB8/3FQP3IFS4NL1mq6JsB6SVBvC/3EmWSUqIk6VU2a1qTx8oqpVVlWIKiBfAmBHWQWMrVuNT1XjhVWLrAJJYqpTVuMT1Xhh5RPVZFnlE9VkWeUT1WRZLQme3i4gq1KiagRyghqT02RcLgRy2SfGhHlQd7+Nceofa4LQApW8iKCn+19lCYCi42SmrALMLwMA5EsBUtvSP30VXwYgVgqQ0oZQl79EGUByKYCaMgC1JQBi3f+8rCZTXCb85akoaOwc42rJ8Zyy+hIIHZCk2hz6w02kO+n0HmdamxqPVlEFDKlVBeTrVQHjZdXKulUxYU04VkXdKr9NSd0qL6vJwqpXVksCPkFZLQn6BGW1uMwvKKtFQb+grPJzfApREBTvhSgMie8TTVEB5JKgCvLEE0/A5XJh3LhxAIBjx47h7rvvRosWLZCVlYUGDRpg7NixKCwstPZCQd39jiH+jziVARDpQLqIqWlorVMFVHX/A2xLAAA2ZQCAvepWAeHa1XhRlZvCSkspQLSN8u1SpQBCZQBAYimAUBmA2hIAse5/sRrV4mCm4CCqgmCW4pH9hDY2bdqEl156CW3bto1tO3jwIA4ePIhZs2ahVatW+PPPP3H77bfj4MGDeO+99yy8WpJUR0I1q4STSXc5ZV6bGo9eUQVUy6qS6arMkFXAuLrV6H2W74tPT+PFVGy7XO1qtP3Tx8b5nZywikqsQO1qfKrKC6uaulUpWQUShVVIVvlENVlW+UQ1WVb5RDVZVsVEtTCUJVibejxUWTRNLQhXgh9FgvsqIsXFxRgyZAheeeUVPPbYY7Htbdq0wfvvvx/7uWnTppgxYwZuuukmhEIheL3WqSJ19zsYvps03f/oE86H3qsM0dP1D6jq/gfUlwAYXQYA6C8F0FK7asdyADW1q3wpQLy48qUA8SkrXwagpBRAqAyALwFILgOQKgFIpiCYJdj9XxjKEuz6Px6qnLKtolBUVJRwCwTEfz/ceeed6N+/P3r16iXbLj//qpWCClCSmjZQOQBhN0hIDURPogqo7v4HlJcAAOyTVYBtKQCgPl2Ntnd6u4HlAEB5wipXDhC/XagcQChdBaTLAYTSVaA8YRVKV+NFVS5dFUpW40U1PlnlRTU5WRVKVXlRTU5VC8OVYDUnghnwMh5QFjr9NNevXz9h+9SpUzFt2rSU45cuXYotW7Zg06ZNsm3//fffePTRRzFq1CgWl6oLktQ0JFkOSFoJMyApLcfQLn8eFqIKaJJVpStWsZJVgE0pAKCtdjV6v+aUAwDmCatQOYBc7SqgXljjU1VeWONTVSFhlZPV+EQ1XljFZDVd2bdvX8KKU35/6u+Effv24Z577sHKlSuRmSn9eS8qKkL//v3RqlUrQdk1G5LUCgBJK2EEJKU2QK+oAoanqoA1sgpoT1cB9YOtom3Kb08nYZUbbKVHWIXS1fgSACFhFZLVLFg/Qt1IsrOzZZdF3bx5M44cOYJzzjknti0cDmPt2rV44YUXEAgE4PF4cOLECfTt2xdVq1bFsmXL4PNZP8csSWoFhKSV0AJJaRqjI1UF7CmrgPZ0FdBXDhBtU367E4QViEpr8jRWXn8opW7V5wun1K2ySFiVCqtQuloQsr6732p69uyJH3/8MWHbrbfeipYtW+KBBx6Ax+NBUVER+vTpA7/fjw8//FA2cTULklRCUD5IXCs2JKQOgkWayqMhVQXsIauA/nQVYFMOEG2z/P9WCCsgPUuAnLAC6lNWM0oCpIRVKF3NhLJBf+lM1apV0aZNm4RtlStXRvXq1dGmTRsUFRWhd+/eOHXqFN58883YICwAyM/Ph8cj/vkzGpJUQhAxSSF5TS9IRtMEG4gqoK5eFVAvq4Cx6Sqgvxwgev/shBUol9bk2QFYTWuVPDsAi7IAK4Q1eUaAXF+J5EIARJQtW7bgm2++AQA0a9YsYd+ePXvQqFEjC64qCkkqoQqSV2dCMmouhg+aEoK1qAKmpKqAclkF7JGuAuYJK6B9HlZAuixANHlVmLKyLgtIns4qyxdMmcqqSkYgZSqrbF9ANGEtE1gClgDWrFkT+3+PHj3AccLLDVsNSSrBBCkJIoE1BxJRgqmoArpTVcBaWQXYpquA+cKavM+ssgB+u9aUFWArrWpS1nhhDYZoOngnQ5JKGI6cPJHEKoMk1BlYkqIaiQ5RBdSXAADGyiqgPV0FzBdWqX16ygIA/bWs0TY4U2pZtaasWUh6kghHQZJKWI5S+UpHmSXxJJjDOk0FmIgqoC5VBbTJKsA2XQWsFdZo28L79JQFANprWRO2K5RWq0oDTgSTniTCUZCkEo6BhdCxFl2STCKetEtR49EpqoC2VBWIyqoSUY0dzzBdBeTLAQDpAVeAdmGNtl3+f5ZlAdH7O328jpQ1YbvN6llDFKQ6GpJUokJBUkkYRVoLKg8jUQWMTVVj5yiUVcC8dBVQLqzR6zGuLCB6f4n7WEqrknpWQLm0aiEcisgfRNgWklSCIAid2E5Qjejy52EgqoC+VBWwVlYBc4Q1ej3661iT9yuVVrHSAMAaaQWgOm0Nx6XlVlFc5ofXx/bzWFESYpJUgiAIjdhOTs2CoagC6lNVwDxZBZQLq5JyAMB4YY3eR/L9i+9TWxoAKKtnBYyTVkBZiUCEpqByNCSpBEEQGrC1oBqVosbDSFQB7akqoL5eFVAnqwDbdBUwXlij91H+fyNS1uj9nj5HJGUF9ElrtC1lswcAwtJKE1A5G5JUgiAIFdhaTh2MXlEF1KWqgHGyCihLVwH5AVdAubAKyWr0urQLq9x+sZQ1er9x5ykoDQD0DcSKtpUqrYBEXWsZaY6ToVePIAhCAY6RUzNSVIPQI6qAtlQVMEdWAePT1ei1KRfW6H0p368lZQWMl1ZAvERAqEyAcA4kqQRBEBI4Rk4BRwsqK7SKKhCVVaWiCqiTVcCYdBXQLqzR+yr/v1Epa/T+485TKK28mCZvj98nJ61CqSvhHEhSCYIgBHCUnAJpI6h601TAXFEFjJdVwFnCCigvDQDUD8KS2pcirSCcDEkqQRBEHI6TU8AaQbX5nMN6RRVQ3v3P4wmEFYsqEJVVOVGNHasgXQXk61cB44UVMD5lBRRKa0j6+SLsDUkqQRAVHkeKKWBdempzQbUSLaIKyKeqseMZyipQLqxishq9T5y+T+n9YsdICWv0GuLOV5iyAgqlNUCS6mRIUlXgysoCSq2fGJggCDaQnGrAYEHV29XPEi1d/4B6UQXUpapAVFblRBUwRlYB64UVkJbWeGElnAtJqkri/6hxp0osvBKCILTgWDEFrK87rUCCqhc7iSoQlVU5UQWUyWr0vqP/ismqkmN4YRWS1ei1lP8/WVgBZSkrR0mqoyFJ1QEJK0E4A0eLKZD2cgqwF1St9agJbWhIUfVitKgC8qkqYI2sAvLCKiSrgLSwEs6FJJURJKwEYS8cL6YAyanWNhkIqpNQI6rGXYO0qCo9xl0mLqqAvKwC5cJqF1ktDfngCbK9mHCoYsxbQJJqAPwfR5JVgjAXElNGVHA51Zugqu3mTzhXRYoaO0eloCrt+geiiapcmho7VqGoAtLHyZUBRK/rdDsyssqFpK+HsDckqQZC6SpBGA+JKSNMGrFvZzkF0l9QAWXd/XZALlUForIqJaqEsyFJNQkSVoJgB4kpQxyamgIVW04BcwRVaYoKyKeoRkGimr6QpFoACStBaIPklBEkptG2GAyMIjk9fbwKQVV6rFyKGmvPBh8pwhhIUi2GhJUgpCExZQR150fbslhMAZJTJZCgEgBJqq0gYSWIKI4XU5JS/e2mkZhqlVKAxFSwTYUfr4gPiND6O46GJNWmkLASFQ0SUwaQmJa35VAx1TqVlJ3EVM3xSsUUUCenRHpAkuoASFiJdIXElAFUXxpty6FSCjg/LVV7vBGJKZGekKQ6DJqDlUgHHC2nJKba2yQprXBJKWCdlEb8HDiOU3YwYUtIUh0KpauE0yAx1YFDpRSwzwT7AElpwvEW15UCxkgpYT2lpaXIzGTzO4skNQ2gdJWwK44WU8BaOXWomJKUOrvrPp2ENOLnEKEk1RQikQhmzJiB+fPn4/Dhw/j111/RpEkTPPzww2jUqBGGDx+uqV2S1DSC0lXCLjhaTtNYTNNZStNVSAHjJtR3gpAqTUftnKKWBLzweNh+9sIBe01b8Nhjj2Hx4sV46qmnMHLkyNj2Nm3aYPbs2SSpRCKUrhJmQ2KqEYeJKUmpctJdSK1KR+Xvr/yYSMi+8ppOvP7663j55ZfRs2dP3H777bHt7dq1w44dOzS3S5KqhswMwO0HSgNWX4liKF0ljMaxckpiqrw9BmLqNCm1W7e9lSs6AcqE1EoZFYPzRxRdE6GPAwcOoFmzZinbI5EIgsGg5na1z5lhAceOHcOQIUOQnZ2N3NxcDB8+HMXFxZLn9OjRAy6XK+EWb/mayPRbP5BCA65KWc4VCsJ2OPb9ZNXnNyuz/MaYSJYv4aa7Pb8v4aapjUxPwk0tYb8n4ab4vEx3yk32nAxXyk2OUKYr5Sb9eFwpN/HrSb3pPTaSkXoTvk7hW0p7vtRbyjF+TvCm+hgfJ3iLh/NHBG+EObRq1Qrr1q1L2f7ee++hQ4cOmtt1VJI6ZMgQ/PXXX1i5ciWCwSBuvfVWjBo1CkuWLJE8b+TIkXjkkUdiP1eqVInNBcX/oXNgukrJKqEWR0opYN2XSgMTU5ZpqR268LUmpWakpHZISFl315tdN8oiGVUinS5f4jGuEImqGUyZMgVDhw7FgQMHEIlE8MEHH2Dnzp14/fXX8fHHH2tu1zGSun37dqxYsQKbNm1Cp06dAABz5szBZZddhlmzZqFOnTqi51aqVAm1atUy9gL5P4IOlFWAhJWQhuRUBRVITElKrRVSlrWjTpfRZLz+UPS+wiHZtgj9DBw4EB999BEeeeQRVK5cGVOmTME555yDjz76CJdeeqnmdh0jqRs2bEBubm5MUAGgV69ecLvd+Oabb3DVVVeJnvuf//wHb775JmrVqoUBAwbg4YcflkxTA4EAAoFy2SwqKlJ+oZSuEmmEI+WUxFS8LZ1i6gQpJSFV0BYDITVDRpWKqBg+Xxhhn71Gwacz3bt3x8qVK5m26RhJPXToEM4444yEbV6vF9WqVcOhQ4dEz7vxxhvRsGFD1KlTB9u2bcMDDzyAnTt34oMPPhA9Z+bMmZg+fbr+i3ZwukqyWrEhOVWAA8TUyrSUpFT7cWYKKYt01A4ySqQnlkvqpEmT8OSTT0oes337ds3tjxo1Kvb/s88+G7Vr10bPnj2xe/duNG3aVPCcyZMnY8KECbGfi4qKUL9+fc3XQLJKOAWSUwUYJKd2EVOz01InSikJqTh6hFSPjGb5hUeQh6m7HwAwb948zJs3D3/88QcAoHXr1pgyZQr69esXO2bDhg148MEH8c0338Dj8aB9+/b49NNPkZUl/3fB7XbD5ZIYDBjW9kXCckmdOHEihg0bJnlMkyZNUKtWLRw5ciRheygUwrFjx1TVm3bp0gUAsGvXLlFJ9fv98PsN+MNHskrYFMfJKYlpYjsWiakd09J0kNJ0EFI96ahcMiompACQ5UvcF/Jqn/4onahXrx6eeOIJNG/eHBzHYfHixRg4cCC+//57tG7dGhs2bEDfvn0xefJkzJkzB16vFz/88APcbmWf1WXLliX8HAwG8f3332Px4sW6eqYtl9T8/Hzk5+fLHte1a1cUFBRg8+bN6NixIwBg9erViEQiMfFUwtatWwEAtWvX1nS9THBg3SrJanpCciqDjeXUSWKajlLKspZUTkrNqCG1o5CqkdF4qmSU/10NBZ3xN1YryWNmxEK2AQMGJPw8Y8YMzJs3Dxs3bkTr1q0xfvx4jB07FpMmTYod06JFC8XXMXDgwJRtgwcPRuvWrfH222+n/4pTZ511Fvr27YuRI0di/vz5CAaDuOuuu3D99dfHRvYfOHAAPXv2xOuvv47OnTtj9+7dWLJkCS677DJUr14d27Ztw/jx43HhhReibdu2Fj+i0zgsXSVZTQ9ITmUwaC5TJu3okFO7iqlRXfhmS6ldUtKKKqTJZPsCCPrKRPebRSjoQSSobzGLZPj2kksRp06dimnTpkmeGw6H8e677+LkyZPo2rUrjhw5gm+++QZDhgxBt27dsHv3brRs2RIzZszABRdcoOs6zzvvvISyS7U4RlKB6Cj9u+66Cz179oTb7cagQYPw/PPPx/YHg0Hs3LkTp06dAgBkZGTg888/x+zZs3Hy5EnUr18fgwYNwkMPPWTVQxCHZJUwAZJTCdI0NU0HMbVCSpUeJyemdpdSo2pIrRDSisi+ffuQnZ0d+1mqVPHHH39E165dUVpaiipVqmDZsmVo1aoVNm7cCACYNm0aZs2ahfbt2+P1119Hz5498dNPP6F58+aarq2kpATPP/886tatq+l8wGGSWq1aNcmJ+xs1agSOK/8w1q9fH19++aUZl8YOklXCAEhOJaDUNEZFF1Oz0lKS0rh9GqRUSkir+EoTfi7zWp+kGkl2dnaCpErRokULbN26FYWFhXjvvfcwdOhQfPnll4hEoq/56NGjceuttwIAOnTogFWrVuG1117DzJkzZdvOy8tLGDjFcRxOnDiBSpUq4c0339TwyKI4SlItJzMT8PiBklL5Y3XfF8kqoR+SUwlsKqckpgraVCCmrNJSklJh7CqlPLm+6N+igMT9VTQyMjLQrFkzAEDHjh2xadMm/Pvf/47VobZq1Srh+LPOOgt79+5V1PZzzz2XIKlutxv5+fno0qUL8vLyNF8zSaoW+D9uZsmqQ0QVIFm1CySnEpCcAlAvp+kipumQlhpVU2oXKQXExVRMSoFyMSWUEYlEEAgE0KhRI9SpUwc7d+5M2P/rr78mTFElhdwsTVohSdWDWbLqsFQVIFm1CsfJKWCeoNpQTklMZdqsQGJq1WAnu4ipnrRUiBzv6SSVpqACEJ3/vV+/fmjQoAFOnDiBJUuWYM2aNfj000/hcrlw3333YerUqWjXrh3at2+PxYsXY8eOHXjvvfdE29y2bZvi+9c6WJ0klQVZmVQCIALJqjmQnEpAcmoLObVjjanVYiq3P93FFGCbmPJiSqRy5MgR3HLLLfjrr7+Qk5ODtm3b4tNPP8Wll14KABg3bhxKS0sxfvx4HDt2DO3atcPKlStF55MHgPbt28PlciWMBRLC5XI5dzL/tMHsEgCAZJUgOZWDsaCSnMYda4GcmpWaOrXG1E7TQ2kdia8nNU0mz3sSpV5acQoAFixYIHvMpEmTEuZJlWPPnj16LkkRJKmsoXpVSVyVskhUGeBIOQUcm56ms5xa2aVPqWl82/ZKTQFxOTVimijWyWme96ToPoINDRs2NPw+SFKNgupVRaFUVTskpzJUYDml1FQYq+cxtWOtKWCfbn2AbXoKkKBayS+//IK9e/eirCxx6q8rrrhCU3skqUZjZr2qg0QVIFlVCwmqDAwF1crR+iSnCtohOZU81+yaU8DckfokqPbj999/x1VXXYUff/wxoU6Vn5ZKa02qugWVCW1kZRq2mk0CmX7zl49kgKtSlnMFzAQc+/yY9X5k/PlikZ5qEdRIpsdQQQ1nuhULajjDpUhQQ5kuxd36coIazpCXTyXHRDLY1JxKCWrEz1UoQZWDVoIi7rnnHjRu3BhHjhxBpUqV8PPPP2Pt2rXo1KkT1qxZo7ldSlLNhFJVSShZTcSRYspjlpwyxKqufTsNiKKaU5n9Bg6IAvRNvA/oqz+VQi5FNZvCUJZomno8VNl2aWqozAu3h61uRcrspW8bNmzA6tWrUaNGDbjdbrjdblxwwQWYOXMmxo4di++//15Tu5Skmg2lqrI4NjlkhKMfv5npKSMiWT7HCGrY7zE0PVWCmvRU/j7Zpafy1yPThk5BNRo9gupECoIO/R1YQQmHw6hatSoAoEaNGjh48CCA6OCq5EUC1GAvFbc5kSwfwGoZYEpVZaloyapjxZTHYXIKpG96ave60+j9sjnG6tpTpcfoTVGtpCTo05ymFgX9ol3+xcHo51msNrUgmCVam1oYiv6+FEpUj4cqA6D6VDNp06YNfvjhBzRu3BhdunTBU089hYyMDLz88sto0qSJ5nZJUlUSyfLBXcKo64NmAFBEOsuq48UUoIFRas+jgVHK2rKJoCrB6pTVaorL/JJ1qVKiCkRlVUpUAfGBVHKyGgjZq1QhXXnooYdw8mT0S8EjjzyCyy+/HN27d0f16tXx9ttva26XJFUD/B84prJKqaos8ULndGFNCzkFKqSgVqT0FHCuoLLCKQIaCnglu/yDQY9kXWpJwCc5eKokGH3fiyWqxWXR3wVisloUjO6XS1UB4WQ1vvtfSFh5WQVo5Skz6dSpE0aMGIEbb7wR2dnZAIBmzZphx44dOHbsGPLy8mIj/LVANak6YJHGxDCjThVwbJ1qMk6t23TqdQtSQUfuazrPhNpTxcdWEEE1K0U1Cy4o/xqHAtK5UzAo/Z4qCfhQEpB+UkqCvpiwClFc5o/dhCgK+mM30TaCmbGbEAXBrNhNiMJQVsKNMI527drh/vvvR+3atXHLLbckjOSvVq2aLkEFSFJ1w1xUaVCVKnjps7P4OeEaVUGDo9Sd58DufYB9DaqitkxKR+2IKyD/OrISVZayykpYxaQ1XliFpDVeWKXElTCGBQsW4NChQ5g7dy727t2Lnj17olmzZnj88cdx4MAB3e2TpDKAxR/ABChV1YSdZNBO18KUCtq9b8d5TwHnCCpL+TSrm5/HHZB/jIqOCcof4wq4ZWWVC7plZTUU8MZuYvCyKiWsvKzKSataYVUqrULimiytcuJaKJLGEuyoVKkShg0bhjVr1uDXX3/F9ddfj5deegmNGjVC//798cEHH2hum2pSGcJ8UBXVqWrGivrVtBPSZCqooGo6z0ZznwL2T1Ctwh1k1+XvDrhk61d5UZUb6e8KuGVH+/OiKjc1FS+qcvWqPHJ1q/EI1bAKiapQHauQqArVswqJanJdq1hZAABkMJuSh1BC06ZN8dhjj+HRRx/F+++/j9GjR2PFihWaV5wiSWUMiar9EJJHveKa9kKajMO69wES1NixBgiqGlh34bvLlKWpnoCyulQlosonpbISqvQ4BbIan6hKCWtyqiomrUKpqpC4CiWrYuIqlK4qFVcgVV7FElYgUWCl6lmBRIk9GaIk1WzWrFmDhQsX4v3334fX68XIkSM1t0WSagCOFVUgrWU1ngonmVpxYHoKkKAS6lCaqCpJS/njAOWyCigXVoCNtAKp4iqWtoqVBAjJq1RZQLLASpUHqBFYQFxiaQYqc9i/fz8WLVqERYsW4ffff0f37t3x4osv4pprrkFWlva/tySpBuHI+VSBtE9VCRWQoKo7zwRBVd2+ihTVSbBOUwF1ogoom5oqvlaVlbAC+qQVUJe28ihNXXmMFNjYOXEiKyaxIertN5R33nkHr732GlatWoUzzjgDQ4cOxW233YZmzZoxaZ8k1UCYiipA3f+EeZCgqjtPg6BqwcgU1YiufgDwlCnv8ldzrBpRBZR3/QPqZBUwVlhj56hIWnnE5FVq4JUZAgukSqzcbAI88TKrRGTDIetX8uKCbnBetp9dJTM9mMFNN92E/v37Y9myZbjsssvgdrO9LpJUgyFRJRwHCaopUDe/fpSKKqBNVgH1wgoor11VdY5KcQXUyysgLz9CEis37RWQKrJyEsvDQmYJ49i/fz/OOOMMw9onSTUBElXCMZCgqj/Xht38gL26+tWmqYC6RBUwRlaBRGEFjJFWoXOUnCs3rZWYxCqak1VDChtrX6PIAtplFkgUWl5mwwFto8oJZRgpqABJqmmQqBK2xsw5cyu4oKYLngCnahoqNaKq5XitsspjprTGztUhr0rO1yqxgDKRBYRlVk1XdLLQKpVZQJnQRlRILmE/SFJNxNGiCpCspisVWFCtwIwUVQveUk51XaoZosqjNlkF1E38z0paY/etQ15jbWgoG1DThpIFBmLt6EhleawQ2kgZaY6ToVdPBZEML6Cz58CxogpQqpqOVHBBTecU1VPGqe7yN0tUAfXzp2o5z500sluPtALKxRUQl1dA+QICeiVUaRtK2nK60BLOhCRVJRG/D+6APskkUSVsAQkqgyshAPWiCuiXVR490groF9fYdTASWB6WIhtrk6HQSrWnRmgBYallJbR2GQVfUSgrK8ORI0cQiSS+Jg0aNNDUHklqukCiSqihgguq7muweYrKozVNBdRPSeUJRM/TKquAttWp9EgrICyuPKwEloe1yMbDorwgpU2bpbRaElo1skto57fffsNtt92G9evXJ2znOA4ul4uWRTUTW6apAIkqoQwHCyorKEWVR0vXP6BdVgH9winUhp62pAQWUCexgDKRjSedpJaF0CqRWblpuQhjGDZsGLxeLz7++GPUrl0bLheb2UVIUi3EEFE1ExJV5+FwQbVDimoVntKIprlStaSpPFpTVaBcVnlYSCugTTbF2tLbrpzExqNWaAH1UgvoH/AlBkup1ZvQqkplQ/aZii2d2bp1KzZv3oyWLVsybZckVSMs0lTA4fWpAImqkyBBjbajM0V1Sld/PJ6y0+mmBbIau4Y4adUirLF2GCalStpldR9qhJbHTmLLUmp1z0qgY1ouwhhatWqFv//+m3m7JKnpCIkqEY+ZckoYitY0NXY+I1kF2AlrPEbIa0L7Jogsy/vUIraAsWUIrJJauWRW69yyKeepLFkgtPHkk0/i/vvvx+OPP46zzz4bPl/iC5ydna2pXZJUG+D4+lSARNWuWCGoaZyissATCOuaK1WvqAL6ZRVIFFZAn7TyGCGvCe2rlD69UqvlPlncv1q5tWKAmNb5ZbUsKWs1roAbLsZr2tttQFivXr0AAD179kzYTgOnLIRVl79hWCGqAMmqXSBBTVs8pdHpXewgqzzJ0gqwEVdAXF6TYSWzsfvVKJgs5Fbr/RtVW8tCZLXIq9paWLsLa7ryxRdfGNIuSapNMGwQldmiClCqagfSRFDtiLs0rLsuVW+aGmuHQaoKlMsqDwtpBYTFlYeVwMajVGbjYS22gL70FNAnuWruW+8cszxal6IF5MVVrbTywkqyai4XXXSRIe2SpNoIElWCCWkkqOmcorIUVR4WwgoYJ63xSAksjxEim4wWsY3HDpJr9YwHehZJiBdXNUmrElklUTWXgoICLFiwANu3bwcAtG7dGrfddhtycnI0t0mSShgHiar5pJGgssYO9ajJsBLVWHuMygBS2i0TqRU1QF7jUSKyQpghtzx2kFyjBo3pmQIsXlzVCqua+WEJe/Ddd9+hT58+yMrKQufOnQEAzz77LGbMmIHPPvsM55xzjqZ2SVJtRlqlqQCJqpmk2Sh+O6eoLLr8eTyB6IACI2SVh7W0xu5HRF4T7ttgkRVCq9wKYbTwqpVcrVIrJbJqBFbLggtqhdUTUFYGIJWmUopqLuPHj8cVV1yBV155BV5vVC1DoRBGjBiBcePGYe3atZraJUmtSJCopi9WCapDUlQAcAeCtkxTeYyQ1Vjbpalrmxslrin3rUBkk7FCbMXQK7ysJVdKalkIrNrElT+X1WAxpZCg2ovvvvsuQVABwOv14v7770enTp00t0uSWtEgUU0/0lBQ7Zyi8rBMU+MxUlYT7kdAXAHz5FUKLWIrhZXSq0Zy9Qotiym8tAqrp0x5qiqXpsqlqCSo9iM7Oxt79+5NWXFq3759qFq1quZ2rf9tRKTghD/Qmkiz7mjLyfSnpaA6CXdpGO5SbfP/yeEJhBNuZuEpjSi6OQlPGcfsZiTeUk70pgdPgIvdVJ1Xpm4Ql5Jj9QhqxCcuqBE/JyioJK1R5s2bh7Zt2yI7OxvZ2dno2rUr/u///i+2v7S0FHfeeSeqV6+OKlWqYNCgQTh8+LDi9q+77joMHz4cb7/9Nvbt24d9+/Zh6dKlGDFiBG644QbN101JakXEqjQVoESVFST8tsKoVDWeZFE1OmmVg4Wo2iG1VYtaUTVyOi8tySsvqmrTVSUpqd4ufzlBFdwuIqGx7Rb9qbMb9erVwxNPPIHmzZuD4zgsXrwYAwcOxPfff4/WrVtj/Pjx+OSTT/Duu+8iJycHd911F66++mp8/fXXitqfNWsWXC4XbrnlFoRCIQCAz+fDmDFj8MQTT2i+bhfHcfQ1Q4aioiLk5OSgx7kPwustT5CMnMjfkMFTyVglqjwkq9qwWlANTlGN7EkwoybVaFmVw2p5tSN2lmFWEqtFWNWIql5JlUpQDZFT/ufSUvz5wEMoLCzUvDSnVnh3qP/Mo3Az/r0ZKSnFvokP63pc1apVw9NPP43BgwcjPz8fS5YsweDBgwEAO3bswFlnnYUNGzbgvPPOU9zmqVOnsHv3bgBA06ZNUalSJU3XxkNJqk0xbJR/PFYmqgClqlpIc0E1GjMGT/Hd/1bJqpLSgIomsnpTXyMll9WctHzSqkZWPQGO2TyvrAVVjZyKCquPQySU3jlcUVFRws9+vx9+v/TfiXA4jHfffRcnT55E165dsXnzZgSDwdjSpgDQsmVLNGjQQLWkVqpUCWeffba6ByEBSapGbL0cqpMgUVWO1YKaJpg1yj++VtXqdDUZVjWuFUV2lUou69W/tAirt5RjOqOAXIJqhpwqTU2j59tPSt0hF9xBxoP3QtH26tevn7B56tSpmDZtmuApP/74I7p27YrS0lJUqVIFy5YtQ6tWrbB161ZkZGQgNzc34fiaNWvi0KFDopdw9dVXY9GiRcjOzsbVV18tebkffPCB/GMSgCRVA2klqFanqQCJqhLsIKgOT1GtJHlwld2kVStmDuiSwi6yzHqqL15Y1cqqUlGVS1G1CqpaOdWbmgqJKeePvhZcxFmD/NSyb9++hO5+qRS1RYsW2Lp1KwoLC/Hee+9h6NCh+PLLLzXfd05ODlyu6HsoOzs79n+WOEpSZ8yYgU8++SRm/QUFBbLncByHqVOn4pVXXkFBQQHOP/98zJs3D82bN9d0DWklqDwkqvbFDnIKpJ2gWj1nqtiMAOkir2ajV5aNlFwWy9Z6yjhVomq0oKqVU72pqVox5XH5InCF0ltS+dH6SsjIyECzZs0AAB07dsSmTZvw73//G9dddx3KyspQUFCQkKYePnwYtWrVEm1v4cKFsf8vWrRI0/XLoeoTs2/fPkMuQillZWW45pprMGbMGMXnPPXUU3j++ecxf/58fPPNN6hcuTL69OmD0lL1UuYuC6k+h1CBlVMq2RG7PBdpJqg87kDQdl86+SmtpG4Ee5Kn+zJq6i8903exnP5KSlDDGeISKrYvkiEsqGF/qqDy00glC2ryFFL8zwnbfFzsxsP5I7EbcFpMT98AwJtBf7fFiEQiCAQC6NixI3w+H1atWhXbt3PnTuzduxddu3ZV1NYll1wiGBwWFRXhkksu0XyNqpLUli1bYuLEiZg0aZLuEVtamD59OgDlxs5xHGbPno2HHnoIAwcOBAC8/vrrqFmzJpYvX47rr7/eqEt1HnZIU3koVbWPoFYAeFG182pU8dhRVNM5ARYSVb3Jq6c0ojpVVZqkyqWocoKqZrua5FRraqo0MY3H6y8X08gp4WusaEyePBn9+vVDgwYNcOLECSxZsgRr1qzBp59+ipycHAwfPhwTJkxAtWrVkJ2djbvvvhtdu3ZVPGhqzZo1KCtLnSi3tLQU69at03zdqiR15cqVGD9+PBYsWIAZM2Zg2LBhmu/YDPbs2YNDhw4ljFjLyclBly5dsGHDBlFJDQQCCATKJSl59FzaQqJqD+wkqGmaogrhNFm1E3YQZzNFOV5ctQqrFlGVwmo5tZOYAoDPd3rlNp/17007cOTIEdxyyy3466+/kJOTg7Zt2+LTTz/FpZdeCgB47rnn4Ha7MWjQIAQCAfTp0wcvvviibLvbtm2L/f+XX35JGGgVDoexYsUK1K1bV/N1q5LUbt264ZtvvsHrr7+OBx98EHPmzMHs2bPRvXt3zRdgJPyTVbNmzYTtciPWZs6cGUttKxwkqtZhJzkFKpSgxhNfAkDC6hyUiLJRy9gaPXBLLkWVElS7yqmSOlOtYsqT5Q8iHKbufgBYsGCB5P7MzEzMnTsXc+fOVdVu+/bt4XK54HK5BLv1s7KyMGfOHFVtxqPpa9wtt9yCnTt3on///ujXrx8GDx6MPXv2aLqASZMmxR6g2G3Hjh2a2tbK5MmTUVhYGLtZXYtboakodaoV4TE6EL5uNf5GOBejany11K8qTVGNEFSx2lKh7Xy9abyg8rWm8YIqVGuaXFeqpM5UtsbUH4rdgKiY8jcgKqaxmy+ITC99Zo1kz5492L17NziOw7fffos9e/bEbgcOHEBRURFuu+02ze3rGt3fu3dvFBUVYc6cOfjkk09w9913Y8qUKahSpYriNiZOnChbNtCkSRNN18ePSjt8+DBq164d23748GG0b99e9Dwlk+GmNXZKU3nSOVW1o6BW0BRVCXKiSumrs7B68QUppARVq5wq3a41NdXSna8nMc3yJ34es3yJP1fJSNO/GzahYcOGAKKDsIxAlaTOnz8fmzZtwqZNm7B9+3a43W60adMGt99+O9q1a4elS5eiVatW+OCDD9CpUydFbebn5yM/P1/TxcvRuHFj1KpVC6tWrYpJaVFREb755htVMwRYgSnLokphV1EF0kdW7SingOWC6i4JGro0qtFQ2soGs2XfTFmVS1HNkNOKIqZZSB3MQ7Bn5syZqFmzZkpq+tprr+Ho0aN44IEHNLWrSlJnzJiBLl264JZbbsF5552Hjh07IisrK7Z/1KhRePzxxzFs2DD89NNPmi5Iir179+LYsWPYu3cvwuEwtm7dCgBo1qxZLL1t2bIlZs6ciauuugoulwvjxo3DY489hubNm6Nx48Z4+OGHUadOHVx55ZXMr48wiXRIVUlQCUISqxJrd2lYk6gqrUs1QlDNkFMtdaZWiWm2r/z/QXJUU3jppZewZMmSlO2tW7fG9ddfb46kKqnNHD58OB5++GFNFyPHlClTsHjx4tjPHTp0AAB88cUX6NGjB4Do3F6FhYWxY+6//36cPHkSo0aNQkFBAS644AKsWLECmZn2/WNseYrKY8c0lcepqapd5dRmOD1NJYwnWWJZSqtaUVUiqE6QUy2pqR3FFACq+KJ/u8q8ZKlmcOjQoYSySp78/Hz89ddfmttlvuLUGWecgdWrV7NuFkB0flS5OVI5LvED4nK58Mgjj+CRRx4x5JpYYxtB5bGzqALOSVWdIKc2S1FJVAk1sJyVwUxBZSWnRqamThNTAMj1lQAAAj7r/6a6Ay64WS8ZGmC/BKke6tevj6+//hqNGzdO2P7111+jTp06mttlLqkulwsXXXQR62YrBLYTVB4niCpgX1klQdUMiSqhBbOWvTVKUM2QU6NTUyvFlCfHW4IAje43hZEjR2LcuHEIBoOxqahWrVqF+++/HxMnTtTcLnNJJdRjWzl1GnaTVSfIqQPgPx8kq8qw6+8Ts18/raKqNEWVE1Q7yKnVqakZYgokymmON1FUc7205JQZ3Hffffjnn39wxx13xFaeyszMxAMPPIDJkydrbpck1SLs+odEFLunqfFYLatOk1ObpqjJpLusOu53gkrEHp8TX08pQbWjnOpNTVmJKZAop6zEFEiU0zzvydj/HfJXy/G4XC48+eSTePjhh7F9+3ZkZWWhefPmuqfzJEk1ibT4A+QkUQXMl1WnySngGEGNR+izZLXopMXn2yKSnzsrX0u5FFVreqpGTo3s0teTmqqpM5USUyBRTpPnMY2XUzViCiTKKQDkek6hxEMrTplJlSpVcO655zJrjyRVBe6SINwedmstEyYRL4+shdWJYsrjQEEVgyQxfbAqMdcjqFbKqdoufTvUmUqJKaCuOz9ZTIGonBLmcvLkSTzxxBNYtWoVjhw5kjK5/++//66pXZJUQh1OS1OTSZZKtdLqZCklCAehd9Cc0npUI+QUEBZUI+XUrNSUVXc+wD41Taaapxin3GyWviWkGTFiBL788kvcfPPNqF27NlyMZjMgSSXU43RRjaeiSmcapahE+qJVVK0UVJZyyrpLn1Vqyqo7HzBOTglz+b//+z988sknOP/885m2S5JKaCOdRLWiQYJacdD7GU3j94qUoNpNTu2YmqoZnQ/oS00BklO7k5eXh2rVqjFvlySV0A6JqvNIY+lIa6z6nMndr8HvJ7UpqpIEVWt66jQ5TYfUFFBecyomqNU8qecT7Hn00Udjq4JWqlSJWbskqQRRUSBBtR9O/5IXf/0Wv7/0CqpT5dTutaaANXIKANU9xSBFNYdnnnkGu3fvRs2aNdGoUSP4fImfxy1btmhqlySV0Aelqc6ABNUaKtJng7GwqklRzRRUrXKqdzAUq3lNjVoJCjBOTgFnj9h3GbAsKmezZVGvvPJKQ9olSSX0Q6JKVGTovW8pcoJqNzl1epc+ID3pPiAvpwAbQZWrQf0nXAWZKJI8hmDD1KlTDWmXJJVgA4mqfaEUlQ30/lZOSamu953SFFWroKaznFrVpQ9ol1PAuAT1WLiyrvMJayFJJdhBomo/SFC1Qe9jy2AhqGrTU6V1p2bLqd2WKgWUySnARlDlOBauQiP6bYLb7ZacGzUc1jZfLUkqwRYSVftAgqoMer/aBiWCapf01I5yama9KaBfTgHtgspzLFwl9n8SVutYtmxZws/BYBDff/89Fi9ejOnTp2tulyRVDaWlgDvxFwSJgAAkqtZD70th6H1pW/QKqhPl1AmDoQD5AVE8QoKql4JwJcVd/vHCylMSCQkcSbBm4MCBKdsGDx6M1q1b4+2338bw4cM1tUuSqpfkP3okB1FIVK2D3oPlpMN7UO3SvUKYvbKayvegmYJqdzm1w2AoHj3pKY9UiqqUgnD5vJtOHuVfETnvvPMwatQozeeTpLKGpLUcElXzqcjvN8B57zcWAqr1fmyyJLCcoJKcStebAvrkFFDWtQ+IJ6h6OB6qrKrLP15YlVAapiTVKkpKSvD888+jbt26mtsgSTUaG012bQkkquZREd9fgP3fX2aJqFr462Itqyreh3YSVKfLKSDdrQ+wTU95WHTxHw8ljsDXW6dKmE9eXl7CwCmO43DixAlUqlQJb775puZ2SVLNpKIKK4mq8VSk95Od30t2FVIpSgPsRNUEQSU5VTdaH1CWngLiCaoeCkNZqrv8k6VVD4FQ6mMn2DN79uyEn91uN/Lz89GlSxfk5eVpbpck1SoqmrCSqBpDRXjvAPZ87zhRSMVgIaoK34us01NWchptS1xQ01lOAWO7+AtDWQk/s6hTFWs7mUCINMdIXnvtNQwZMgRDhw41pH169exARRFWElW2pPN7hcdO75d0klLWGCyoetJTvXWndhsQBcjLKcAmPVUiqAXBLNVd/nJiqYeCYGLbZUHxOXMJ/YwcORKXX345zjjjDABAnTp1sH79ejRq1IhJ+ySpdiPdhZV/THaSDyeSju8NHru8N0hKmSIlqFalp2q69u0op4Cy9BQQT1ClKA5mKhZVHtbTUCVLp1KKg9HfkcGQ8EINZuIOAW7GVQecTcaDcVzi+/nEiROIRCIiR6uHJNXO8H+s01FIKFXVTjq+HwB7vB9ITNWj4P2oRVCVpqdWyilgzgpRANv0lEdJDapSUeXRKpVK4eVTCUVBP6gk1dmQpDqBdJVVElX1pNt7wA6vP4mp9npUEwVVS9c+y0FRZsgpoC09BcQTVBaoFVWt96GWoqD8+7a4zB5TraUrLpcrYVR/8s96IUlVQ2kZwP9OtGKOwXSUVRJVZaTTaw5Y/5qTmOpH5j1pppwC6gTVDDmNHstuUBSgXk7luviLgn7FI/q1SKRWlMgnj7yE0mfdSDiOw5lnnhkT0+LiYnTo0AFud+Jn9NixY5raJ0nVSvwfObOFNd1klepUpUmX15nHqteZxFQYtb+/0ig9tcOgKEC7oLJAjaiyuj81KElCS4Li77dwiF19JJHKwoULDW2fJJUFRk2KLUc6yiqJaiLp8toCJKfpgA5BtZOcJv9shpwC8ukpoE5QWXXxJ4ujUmlVK5xC6JXQ2DEB4WPCgdTnk2CHUVNP8ZCksoRkVT8kquWkw+sJWPN6kpgqQ83vKosE1Qld+2rlFFCWngLGC6oQLOQTUFcPqkdEeYIC001FaAoqR0OSagRWlQKUlKaH2FT07v90eA15zH4NHSCn3KnUKXpclYwdES0IQ0FV271vt659VnWnALv0FNDfxc9Lopbpp5S2rRQWEgoIi2g8oUCi1kTKSHOcDL16RmN2ukqpqrNJh9cNqNByKiShas+xRFrF0CioZqanTujaB8wV1HjMGuFulYgKwQXdCf9WdGbOnIkPPvgAO3bsQFZWFrp164Ynn3wSLVq0SDmW4zhcdtllWLFiBZYtW4Yrr7zS/As+DUmqWVghq+kgPBVFVNPhteIx8/WyWE61CKmadg2TVaW/hwwWVNbpqRWj9gH2gqqEkqDP0C5/sftUfKyGrvl41IioFK4ASSoAfPnll7jzzjtx7rnnIhQK4V//+hd69+6NX375BZUrV044dvbs2UynkdIDSarZmCmr6SSqQPrKajq8RjxmvUYWyalRUip1f8xF1QJB1ZKeWtG1D5iTngLSgqo0ReWlkYWsqhHQ2DkmpKJ6RZQT3VOxWLFiRcLPixYtwhlnnIHNmzfjwgsvjG3funUrnnnmGXz33XeoXbu24vYfeeQR3HvvvahUqVLC9pKSEjz99NOYMmWKpusmSbWK0gCJqlrSLVVNl9cFSGs5NVtMhe6fmagyEFQnpadau/YFfzZJULWgRTAVt61ARAF9MsoyEXUHkxLAkD0SQaMoKipK+Nnv98Pvl/+cFxYWAgCqVasW23bq1CnceOONmDt3LmrVqqXqOqZPn47bb789RVJPnTqF6dOnk6Q6ErNS1XQTVcD5spourweQloJqtZgagsmC6pT0VK+cAuoEVQklAZ9h86KK3Z8S5EQU0CejSkQ0RUIdgCcAMJ9j4PSvw/r16ydsnjp1KqZNmyZ5aiQSwbhx43D++eejTZs2se3jx49Ht27dMHDgQNWXw3GcYInADz/8kCDCaiFJtQNmyGo6iSrg3FQ1nV4DwJzXwCQ5TUsx5UkzQbVLegqoF1SlKSovjixkVamE8lgto2pF1B2QOF5qXxqwb98+ZGdnx35WkqLeeeed+Omnn/DVV1/Ftn344YdYvXo1vv/+e1X3n5eXF1sKNX7lKQAIh8MoLi7G7bffrqrNeEhS7YTRJQDpKKqAc2Q1nZ57IG0ENa3lFLBcUNV279sxPQWUCypr1AqmGvTKKCAtpKxkVFJCKzjZ2dkJkirHXXfdhY8//hhr165FvXr1YttXr16N3bt3Izc3N+H4QYMGoXv37lizZo1ge7NnzwbHcbjtttswffp05OTkxPZlZGSgUaNG6Nq1q6rHFA9Jqgq4khJwrrCx08MYnaqmm6gC9pfVdHu+zcBgOU17MVWLSkGl9FRcTuW6+YNBD/OaVLn7U4LeAUxSQqpERrWKqNx5HAkugGh3/N13341ly5ZhzZo1aNy4ccL+SZMmYcSIEQnbzj77bDz33HMYMGCAaLv8ilONGzfG+eefD6+XrVaSpGog/g+cYcJqZKqajqIK2K8EIB2fYx4jn2cDBdWJcqrrd4zc7xCbdO9bMXJf8GcFgiqFnjpUvSiVUcDadFSpjFJ6ypY777wTS5YswX//+19UrVoVhw4dAgDk5OQgKysLtWrVEhws1aBBgxShFaJq1arYvn07zj77bADAf//7XyxcuBCtWrXCtGnTkJGRIdOCMDSBmE64UyXG/eEzMk2yk8yxJCvTHnJoh2swCqPeO6UBw97zhn5O7YpFghr2exIENZzpThDUcIZLsaCGM8QFNZIhLqgRX2r3fvLUUsnLmioVVBZd/MGgR/Cm9Dgl5wJRGRW6JTzOoDvlFnusAXfKjccddAneYvsDLsFbMkqPI/Qxb948FBYWokePHqhdu3bs9vbbbzNpf/To0fj1118BAL///juuu+46VKpUCe+++y7uv/9+ze1SksoIwybfNrL7P10TVcC6EoB0fT55jBRUA3C6mGr+fWKCoLLu3rdLegoYK6hSqElDk9E7+b2e7no5qdQinW4d48WS3wNEtLvfyHN+/fVXtG/fHgDw7rvv4qKLLsKSJUvw9ddf4/rrr8fs2bNV3z9AksocQybfBsybVzXdMENW011MeRwkqE6XU10wFlSzu/e11p4C1gtqKOA1tMtfiYjy2F1I9Uio0rZJVs2D4zhEItHPyOeff47LL78cQHSKrL///ltzuySpBmBoqspaVNM5TY0n/jGykq2K8LwZDQmqKJp+f1ggqEalp8k/sxwcFT1HuaCqgYWoqpFRwLhBTVLCaQcZJexDp06d8Nhjj6FXr1748ssvMW/ePADAnj17ULNmTc3tkqQaiCGySqKqn+THqlRaK9JzlIwRKSpjQU0XOQXMFVSW00s5oXs/eo4xgsqjVjKVondlJiOFVKuMehT+Gkh+3eWgFNVcZs+ejSFDhmD58uV48MEH0axZMwDAe++9h27dumlulyTVBJiXAFDXP1sqsnwqweaCmk5yqhmDBTVduvej5zhjNXcWS4UaJaVqhFSphCptR4mskqCaT9u2bfHjjz+mbH/66afh8WivtSZJNQnmqSprUa1oaSphHSSokqj+HcFQUO2ankbPjdsnI6ei20QElWWKqgUlQgpYk5IqEVJWIqoXklPr2bx5M7Zv3w4AaNWqFc455xxd7ZGkmgzTVJVElTAa1ikqCSpbKoCgqk1PRbfpFFReJLWO8FcqojxWpKROEtJkhAQ14uc0jWpnjbsMcDOeVYsrY9ueXo4cOYLrrrsOX375ZWzVqoKCAlx88cVYunQp8vPzNbXrqHlSZ8yYgW7duqFSpUopS3eJMWzYsNi6svytb9++xl6oDEznbDRpXXOC0A2j92o6z3mq6gusjQU1lOkSFVStc58C7AVVC0Lziiq5ySE2HymP2HykQOpco2LbkwXVHUy8JeMJpN7kcJepu6lBrKtf6H0h9D4gjOPuu+9GcXExfv75Zxw7dgzHjh3DTz/9hKKiIowdO1Zzu45KUsvKynDNNdega9euWLBggeLz+vbti4ULF8Z+9vvtUc/JLFVlmahSmkrwsExRGQpquuJUQTVjaVPAHoLKCrmUFNCWlOpJSdUkpGrlUq6t5Nc+GTVymvxzxAZJakVgxYoV+Pzzz3HWWWfFtrVq1Qpz585F7969NbfrKEmdPn06AGDRokWqzvP7/YLLfYkRCAQQCJR/YouKilTdnxpsKaoEwRISVFnsIqhyA6SsqD8FtAuqHdArpIB1UspSRrUiJKhiXftSPxPGEolE4POlvjA+ny82f6oWHNXdr5U1a9bgjDPOQIsWLTBmzBj8888/ksfPnDkTOTk5sVv9+vUNvT7bdf2n65KphHJYvQdIUNlioqAKLW+asN+g+lOp5U2j161cUJWkqEokUilSy4jGI9V1D4h33yfvS2xTvOteSbe93q54rUilqEoEVWrJ24iPQ8RLsmoGl1xyCe655x4cPHgwtu3AgQMYP348evbsqbldRyWpWujbty+uvvpqNG7cGLt378a//vUv9OvXDxs2bBCdFmHy5MmYMGFC7OeioiJTRJUSVSKtYCCoFUFOFX/uTRbUhJ9tML0UYFyCysukkkFUWqRWzypOoimqRFJqdErqETg3+bVWgpigKpVTsZ/jv5xYPXNDReGFF17AFVdcgUaNGsV8ad++fWjTpg3efPNNze1aLqmTJk3Ck08+KXnM9u3b0bJlS03tX3/99bH/n3322Wjbti2aNm2KNWvWiNq93++3pG7VsJWqtEC1qRUXFikqCaoimH3WBT6rZg2QSjzXPoKqpRaVVapqhJRG2xXeLielaoRUSEDVnqdEWJUKqm45Tf9fI7agfv362LJlCz7//HPs2LEDAHDWWWehV69eutq1XFInTpyIYcOGSR7TpEkTZvfXpEkT1KhRA7t27dIVQRuJ7lSV0lTC4ZCgJiH1eTZJUK2qPwXsX4NqtpQC0mKqVEq1CqlehASVuZwiOl2YK0RJqlm4XC5ceumluPTSS5m1abmk5ufna54/Swv79+/HP//8g9q1a5t2n1ogUSUswQYpakUQVFVYIKh2GSAF2EtGAXkhjR1nYhe+Eik1S0ilUlQlcgokvg+0yikAeP0hRMIhmSsm9LB69Wrcdddd2LhxI7KzsxP2FRYWolu3bpg/fz66d++uqX1HDZzau3cvtm7dir179yIcDmPr1q3YunUriouLY8e0bNkSy5YtAwAUFxfjvvvuw8aNG/HHH39g1apVGDhwIJo1a4Y+ffpY9TAUY/kfaxpARaiFBFURTOpQK7CgKhFXpTIp14bcIKfYsQoHO0kNeEpG6UAnITxliTcz0Cuo8QPlZAdEnRZUzh+JCarLF4HLF4HXH4LXH5VTry+s8dEQSpg9ezZGjhyZIqgAkJOTg9GjR+PZZ5/V3L7lSaoapkyZgsWLF8d+7tChAwDgiy++QI8ePQAAO3fuRGFhIQDA4/Fg27ZtWLx4MQoKClCnTh307t0bjz76qG3mSpVDV6JKaSrhIEhQkzBAUK2oPwWsS1B5qZSrT9UitLLLiTKuLZVLS/WKqNqa0mTEztHbta82OeXxnZbTDDclqUbyww8/SI4r6t27N2bNmqW5fUdJ6qJFi2TnSI1fAi0rKwuffvqpwVdlc/SKKg2gqjjoTc51pKgkqEmQoKZuVLBPDBapKqBdTI3oxlcrpWqOVyusSgXVTDnN8kef9PAp6Wsn9HH48GHB+VF5vF4vjh49qrl9R0lqRYXZ9FQEYRQkqOyo4IJqJ4xISwFxMWWVlpo5IEpIUNWmp0bIKQBk+YIIeWVWNTABTxDwsPmeVI71DwsAULduXfz0009o1qyZ4P5t27bpGgNEkuoQqNufIJyNos8vCaqlA6XkpFTuGNbd+Epk00ghlUpRWaSnRsopAFTJCCAUZLTIDSHIZZddhocffhh9+/ZFZmbi76iSkhJMnToVl19+ueb2SVJVECkJIOIq/8C4Te4Gt0xUqcs//dHT1e+wFDUi8FiN/iw7QVC1DpBK/llLDWJsu5IBUQEXM5FVIqVyx6WbmPKoFVS7ySkAZPsCCPpssLZrGvPQQw/hgw8+wJlnnom77roLLVq0AADs2LEDc+fORTgcxoMPPqi5fZJUHcT/sTNLWKnrn7AVDhFUITFN3m/UZ5gENXWbFSgVUiXHmi2mZs9nqkZQ5V5zK+QUiAoqAFT20iw1RlKzZk2sX78eY8aMweTJk2PjglwuF/r06YO5c+eiZs2amtsnSWUE/0fQDFnVLKrU7U/YBLMEVU5Ok481u3dEljQUVBbd/GqEk1WbLMXUblIaj5igqk1PlQyKMlJOq/iin/0y6u03nIYNG+J///sfjh8/jl27doHjODRv3hx5eXm62yZJZYwt/9CxgLr80xetXf0aU1QzBFWNnBqJrhS1AgmqVThZTD0B5VKf/FqKHqdQUFl27RslpwCQ6ytBwGeTEUYVgLy8PJx77rlM2yRJNQAzUlVKUwlCGBLUckhQE1E0MMqmYqpGSrUgJKhy6amd5BQoF9RcX/kX4RwvzR7iZEhSDcToVJXqUwnLsGGKqldOWX5WWQuqEHYQVCHsJqh6xBTQNl2UlHwqnkbKYCmNR4mgKu3a1yKnQLmg+uJWiOIFNSsuDY0fFBXbJiGn1NvvbEhSDcboVFWTqFKaSvCYmDraWVBNR6WgJqeodhFUuW5fK1A8Yt9mYmqUlEp19ZsppwASli/lYSGngHh6muul2fydDEmqSaRFrSrVpRKArhH9RmA3QZX90qjyC6LTBdXoFFXVqH3GKz/ZVUx5WAqqkq59I+UUEK875YmX0zzvSQCAvX47EGohSTURo0SV0lTC7hiVorISVFafS13lNwrqUO0qqCxQOv+p2pH9dhJTU7vwRQTV6PTUyBH7gDpBJZwPSarJpEWiaiKRLB/cJTQ60zZoSFHtLqisMHqglJ0FlVWKympqKSkxBdh259shMU2GlaCyrDtVKqeA9q59IFVQczzU3e9kSFItwAhRNS1NNbjLX3AEs8A2AI6VV7HHI4Shj9FmkqcGuwmqIiqYoJqNVjEFnJ+axqNUULV07ZtVdwqwEVS74CkDPPKHqaOCLKRFkmoRthFVG6FG3pKPt7uwqn1s8efZ5rHZJEVlLagsPoea61BJUHUhJ6aAuampWjH1lio7Pv51E4OFnEbbidunoWtfqZwC2rv2AecIKqEPklQLsUXXv01qU7VKXPL5thE66H9M8e3Y6XFZiR0T1IoqqHIYNWBKj5gC7FNTNWKqVErVwjo9NavuFBDu2gdIUIkoJKkqcGf5gdKI/IEqYC2qTkxTWclccltWiR3LxxPfptNElXWKaoSg6v3sGSmoclg1D2p5O8qOY4FRYgpoS03NFFO5FFVIUI2S0+gx6upOAe1d+4C8oBLpDUmqDbA8UVWbpjKsSzVC6JLbNkvujHwsfPvMHota4VPZ1e8EQbUTaleTMlNQtXbzu4P60lQlYgrYMzVllZhaLais6k4BfbWnPFoEtTBcSfU5hH0gSVWJOyvTkD+YLEXViWmqkRiZrhotpoRxgmqnFDUZIwQ1Ga2CahRKpRSwZ2rKuitf8rUzMT01omsfUNe9D1CCWlEhSSUswwrBYyGsVoqpJd3+Fqaodk1QraxDjSdeUJNJlpx4sVHSpS8mqGq6+dWIpxLsJqdG1ZiyFFQlA6OMWMoU0Na9r4XjocoAqDY1HSFJ1UBapqk2GUBlJlKy6S4JUkqaxuj5nNlloFSyoManqFKCKoTSOlQrkBJTwPwufaPElEeNoJqZngrJKaAuPQXkBVUoRVUKL6vxBELOquUnEhH/Gk5Ygl2TI9bYXQDtfn26MPA9VhFSVE3YSFD1dPObOVjKE5BPToUE1VMmnZwK7fMEuNhNDG8pZ5mghv0uVa9jJENYUCO+xPQ0vvY0WVA5fyRFUL3+UEJ6qrZ7X4+gFoaohE0Pa9euxYABA1CnTh24XC4sX748YX9xcTHuuusu1KtXD1lZWWjVqhXmz59vzcXGQUmqRoxKU1liaJpq8KT+hDimdvlrmBuVBUZ+tkxPUdNEUM1Aa2oKGNOlb7SUxiMlqCnbMoT/Dxg/MAqQT08B5fWnaogXVaka1fjjAiHSHAA4efIk2rVrh9tuuw1XX311yv4JEyZg9erVePPNN9GoUSN89tlnuOOOO1CnTh1cccUVFlxxFHr1bIjlo/0JQgNGLX9qFzR38ychl9LLzYWasC+DXdcwYJ2gVmQ5BZQLqtLaU6MHRgHauvdZQsmqOvr164d+/fqJ7l+/fj2GDh2KHj16AABGjRqFl156Cd9++62lkkrd/TowUiRZJUnpLg5E+mHXFFUShiP54zFqqik7wHfna+nSByS67qW6+23QpZ+MkKBq6d4vPzduu0h6Kld7aqSgSqWoBUH94lkQzEq4FQbTO/ApKipKuAUC2r4UdOvWDR9++CEOHDgAjuPwxRdf4Ndff0Xv3r0ZX7E6KEklEqmAA6gIEVR09bP6MmRXQdU0pZvObn4jBdWqFFUuMeUxMznVIqWeMvFzpNLteNIpPQXYJahCoprrK9EssCdD1kuqJ8DBwzH+8nP6PVi/fv2EzVOnTsW0adNUNzdnzhyMGjUK9erVg9frhdvtxiuvvIILL7yQxdVqhiRVJ0bWprLq9rfbvKlpPSjJ7ti8jtqOWFGHymouVCHMTlVZiClgvZxKialazBZUvbWngDpBZY0SQS0WTUxl3lgOZ9++fcjOzo797PdrC5nmzJmDjRs34sMPP0TDhg2xdu1a3HnnnahTpw569erF6nJVQ5LKACeIqiHQ4CnLcOIyqXLYNUWVRGMdqhlzoQLKlzxVmqJ6AspG+CsVU0Bbaiq7j5GcqhVTJSmqWPd+alvC/zcqPQWE5z0F1AuqVIpaHMzUNTequIyWUxQsf2LSfQaq7OzsBEnVQklJCf71r39h2bJl6N+/PwCgbdu22Lp1K2bNmkWSShiPqjSVuvwJC7r67YjkZ0ZhHapdRvKzQo2ASmFXOWWZmCajRFDtmp4C7BJUJaKplHghTbmfMj9C6R2kMiEYDCIYDMLtTvx94/F4EIlERM4yB5JURlTYNJUgGGDHFJVVHaoUWgU1Ga11qID5I/rTVU7lUlS1gqpkaimW6SlgjqBqRUpGgaiQEuIUFxdj165dsZ/37NmDrVu3olq1amjQoAEuuugi3HfffcjKykLDhg3x5Zdf4vXXX8ezzz5r4VWTpBIEoQO7p6imdvNrqEONR81UUywGSplNusopIC2odkpPAeHBUYA6QTUaPUJaEkz8jIVD1iaBduG7777DxRdfHPt5woQJAIChQ4di0aJFWLp0KSZPnowhQ4bg2LFjaNiwIWbMmIHbb7/dqksGQJLKFLunqdTlX8FR+t40eQJ/Oy6KoambPwm7DJSSwowU1Y4Dolh26bMUVBbpafSY8lWjeJSkp4AyQZVLUeUkUy1qpDRhX8CHcCAsur8i0aNHD3ASMwzUqlULCxcuNPGKlEGSSuiDBk8RNsWQbn6D6lDjYTlQSmyb0ciJKeB8OQWME1QzBkcB2gTVaPQIKZF+kKQyJq3SVIKQgEVXvx1TVNWYVIfqBEHVI6dS++wmp4A6QWXZvS+XngLGC2pxmV93TaqSGlIxKZUS0mAw8fMVCYp/ISTsD0mqARgpqgRhKCZ39RuFaSmqiXWoieex6/JnQUWSU0D8tWHVva8mPY0eo7x7H5AXVCXwkiknq0oHNGlNSZOlNJlQGWmOk6FXz2GYOtKf6lIJEeycoprazZ+EVXWoVqWoRskpIC6oVsopYIygGjU4CjBGUOPROqpei5TKCmlASGlCAtsIp0CSahB2TlOt7PKn1aaItMGgOlQ5QbW6m1+JmALWjNg3Uk4B5YJqx+59gL2gKkVKSAFtUiospPbEE+DgjTB+bwaNfa/bBee8yg7EzqJKVDBs9j50fIpqYB1qPFZN2J+MUjEF0lNOATaCymJwVPSY1O59QJ2gGoVWIQXEpVSJkHJB4c+R2HbCGZCkOhDbTe5PI/zTA4X1qHafG1UtZnTzx8Nqwn7R41SIq7tMfBoqNWIKSAuo1H671p3yOK17H1AmqHIpqpxsKsUIKSXxrDiQpBqMXdNUxV3+VJdKOATTvrjp6ObXOmG/8PGSuxWjVkaFqOjpKZAoqFZ17wPWJag8rKWUhLRiQ5KqAldWFlBKEwMThB6M+NJml25+s+pQRds0ecqpdJVTwJ7d+4C9BFVublKjpNQVUC6uao4l7AdJqgkYkabarsufMJ1Ilg/uEnMn206nrn4jpptK2GdQHSpg/TKnVnTtmyWngH0ENV5OAXWCKkdJwKdq4JSSyfK1DHSSk1KSzIoNSapKXJWyNP2htmO3P03sT8Rw8PyoVn1ZM2M+VOHj1W1niVY5BUhQo+fEbdfYvQ8oE1QlKareVZpYSykJKZEMSaoGtIqqY6G6VGdjoy9HdvmipjdFNWs+VLtM2l8R5BQQFlTW9ad6uvcB/QmqHqyUUncw9XVITpqJ9IMk1URYp6m26vKnEf6EBTB//xsw3VQ8TuzmJ0GNO8bC+lPAfEHVNnm+uJgqkVIhGZU7VkpWk59DwlmQpGqkwqWpRIXHbu93QwZLKcCM6aYE25IQVCPk1Yly6imNConUlwEhnCiocgSDHtUDp8yWUjVCqgXOHwHs9WuLUAlJqsnYrTaV6lIJJ9ejqsXKbv547NzNLyencseYLai8mGrFqYKqJEXlpTNeVuVENBmWYmq0lMZDCWp64Jgq5T/++APDhw9H48aNkZWVhaZNm2Lq1KkoK5P+jVpaWoo777wT1atXR5UqVTBo0CAcPnyYyTVplTvbdNGrweYiE/H7JBMtK7DjNVkJyy9npnTzq8Tp3fyeMmXpqdTIfTFB9ZZykoLqKeNUC6qnNCIoqEpT1HCGS7WghjPUCWrElzhAKn6CfqMSVCGCQU/sJkco4E24xcMF3bFb7PoC7oRbPO6gK+EmhTvgSrkpQairX2oWBMJZOCZJ3bFjByKRCF566SU0a9YMP/30E0aOHImTJ09i1qxZoueNHz8en3zyCd59913k5OTgrrvuwtVXX42vv/6ayXVZ3e1vq7pUkxESQDEpdAeMnapJSkaT9xl9LUZgp65+07r5VaSoaqabUtvNbzRKklO548xMT/Ump4C2EfxGp6eAMYIqh5Y5S8XSUiVJqVL5jD82/jmLR8nzx5k3rkwUTxkHD8e2xpoLVoxBY46R1L59+6Jv376xn5s0aYKdO3di3rx5opJaWFiIBQsWYMmSJbjkkksAAAsXLsRZZ52FjRs34rzzzjPl2oWwU7e/07r8taSTrEVRT0LKn+tEWXUqRnfzx8O6m9+oFDUd5VRJimrH7n3AvO5prUuOahFTNUKqFqVzyHozbGCphGYcI6lCFBYWolq1aqL7N2/ejGAwiF69esW2tWzZEg0aNMCGDRtEJTUQCCAQKO/eLioqkryOdJo71e6w6j4XakdMGo3qso/4fcaLapq9v+zYa2D2qlJ6USqncseaJahKk9N0E1S5FDUU8MrWpcoJaez+GYmpEVIqlKIqFlR/CJFTzC+JMBHHSuquXbswZ84cya7+Q4cOISMjA7m5uQnba9asiUOHDomeN3PmTEyfPj11R2YGwGCda0IbRtd3WlE/aoqoSmHzWmMWGJmial1VSiksU1RWcgpoF1SjuvbTTVCVolRCk1E7d6llaalGQY2Xd6/BS8MSxmL5wKlJkybB5XJJ3nbs2JFwzoEDB9C3b19cc801GDlyJPNrmjx5MgoLC2O3ffv2yZ5TIQZRyQmNgaldOg9ASufHxsOix8AOc6Ka2c2vBrEBTfx2lumpnsFRiq9BZFCUEEYIqtoBUgBbQTWiFlVo0BMgPvBJbMCTksFNQoOgxG5qSB5gxj9/Ll8kRVB9vrDqKbgI+2F5kjpx4kQMGzZM8pgmTZrE/n/w4EFcfPHF6NatG15++WXJ82rVqoWysjIUFBQkpKmHDx9GrVq1RM/z+/3w+0VG+2b6RWXNqm5/FoOnnFaXSpiHHQZN2WVO1IR9jEbzi7ahIUVVI6Nqz7Vb9z5gnKAmnl/+f7kVpADlgmo0WlZ60tKNb1SSmpyiis2AIJSe8nKa5Q8iHKaaVCdjuaTm5+cjPz9f0bEHDhzAxRdfjI4dO2LhwoVwu6V/QXXs2BE+nw+rVq3CoEGDAAA7d+7E3r170bVrV+0XLSGqBHsqRNJodbd/RcPAwVJqR/PbYelTrbWnALvufbWj9o0WVD3pafLPctMkpewLujWlqU4TU9FR+wrS5+TaUyBRTnkyvfR71clYLqlKOXDgAHr06IGGDRti1qxZOHr0aGwfn4oeOHAAPXv2xOuvv47OnTsjJycHw4cPx4QJE1CtWjVkZ2fj7rvvRteuXQ0b2U+DqAiCLValqPGYPWm/WcufOjE9BZwlqEKwGMkvJaQ8rMTUyLrTeFilpwCQ5Yv+mwkKlJyMYyR15cqV2LVrF3bt2oV69eol7ONOzz8WDAaxc+dOnDpVPpzvueeeg9vtxqBBgxAIBNCnTx+8+OKL+i/IgDSVRDWVipCi8piepjqgN8AQQdWQoibsM7ib3yzsIKha5jyVE1QrB0gJ/qyxm1+JhAphtpi6BX5lJZdACKHmeVOTnvJyWiUj+vsti0Y7OxrHSOqwYcNka1cbNWoUE1aezMxMzJ07F3PnzjXw6hKxeoJ/gmCFle9jQwYVOqCb3+gUVY+cAtZ17wPpIahGzIdqlpgKCanYcVKiqvR505qe8oKa7QsgSI7qaBwjqbbEhoOo9KBo8FRpgMkSkoR+3CUyfzEqaCpv5ABAVt38VmGH9BSouILKEjExBYTlVIuYKpVSNSit3ZUSVCVyCgBVfKUo85KlOhmSVDVkZgLJv4ip298wKlJXPw8NoIpixxRVaze/4PEWpKgkqM4XVKeKKY9aQVWbnsbLKQDk+koQ8NHvUydDkmogerr9HSuqJaWyc00ShBR6BNXIwVLxWDknqlqUTEtl1/pTgL2gqp1iCtA3SEoPUlIKqOvOFxVWI9JSgY+OEkFllZ7m+qJ/d3O8JQjYYHS/JxCBJ8y2zIMLmbOMrtWQpKolKzO1G5WmpCIIJhi2uIVJg6X0dPMbkaIaWX8abZ8ENRm5FDVePDl/RFZEk2FVZ6pGTj2n/7yFNVZ6KZk7Vm16KiSnABIEFQByvbQuqpMhSTWYCpmmMqAidvWbioIvVU4b/KcqRTVosJQcZqWoetNTwNoBUkB6CmoyagTVjNTUI/NrQYmsql3cwIj0FADyvCcBAH4PSaqTIUnVgolpqtmiSitPWU9FrUs1rJtf50A/pw2Wskv3PmBPQU2WVbt18cdjtJjKSalatAqq0qmllKSnvJzmnpbTTPdJvQ+LsBCSVK0IiaoIeqekkhNVw7pIxaAR/oRKLHsPO2CwFEtIUE8fY6CgGg2L7nwzxZRHidQr6d5Xkp6Kde0nC2o1TzEoR3U2JKksMbA2tSJ3/RPpjV5BdcJgKTn01qMqkVPA3gOklGDEKlLRc+L2yVQaGSGtYmIKsElNWYqpUFe/mKDq6d6X6toHooIqJacAUN1TjExPxRhglK6QpKogkuVDwuIVJqapgLComp6i6sRdEpQcoEJULAx9/9posJSRKarR9afR+zBHUKVSVCsE1ahufikpBdikpkYkpqwE1aj0NF5OeXLcNKjZyZCkssaACf7jcZqUaoEGTTHAhqm7Ee9dK1JUtd38RsEiPQVIUGP7ZARVCe6gS3DwlJyUxo7TmZoqFVO3yHsn+fmJR4ugau3e15ueAkDuaTkt11XCidjjt62DSElehP7wUr0m4XCcNrI/BYYpqt5ufiNSVBJU8wVVqbS6g66Um+TxAVfsJrQ9se3yWzyegLSgussSb2pJFtSIT1hQI34uRVA5fyQ61ZYvevP6Q/D6Q/D5wvD5wtGu/dPd+8mCWsVXGhu5Lyao1TzFooJazc0hz21uTbFdWbt2LQYMGIA6derA5XJh+fLlsX3BYBAPPPAAzj77bFSuXBl16tTBLbfcgoMHD1p3wachSTUZJ4yc1y0oNkzxnIahaXKazOlr1JRTLAdLscZTRoJqxwRVC0ISKrZdSkyF5FSvlEqRLKfxglp+jPru/SoZgdiqUcnd+znektjI/TzvSeR6TqV071f3FCPXHUgQVKKckydPol27dpg7d27KvlOnTmHLli14+OGHsWXLFnzwwQfYuXMnrrjiCguuNBHq7tdAJMuXuG56RZzgn0b4E3ZF5fvSyMFSrFJUpWIaO74CCKqWZU6j58XtUyiozGpRGUy4L5aY6pVRsa5+JbMeqO3eZzVyHxBOT3ly3H643DRwCgD69euHfv36Ce7LycnBypUrE7a98MIL6Ny5M/bu3YsGDRqYcYmCkKRaAIvaVIKoyLBMURP22SxFVSunAAkqq1H8rBATULF9amtNWSel8WgRVFa1p4DwvKdCg6PEBLUiUFRUlPCz3++H36//sRcWFsLlciE3N1d3W3ogSdUIpakEYUMMSlGThYp1iqpFRgXbIUEVb1fmrcG6m99IOWXehS/wvMkJqtbufS2rRsmlp/j/9s49OKry/v/vbJJNghgkELloiFy0YBXkIgj4VVCm4KgtU0THWgXKYGXwBrYDOLZBO4J2bKWDloutUWe0XkZpkRbUUsR2RkRh+NVLiYIgTDCgQgIEstnL+f2x7HJ291ye55znOc85ez6vmQzJZjd59uyGfe3783w+B/4W1NJYEqXJpNCfqSXSP6+uri7n8oaGBixZssTVz+7o6MDChQtx6623orq62tXPcgtJKgepaBmge54xiaoJlKYShDNUpKhBgAQ193Zmg/oBOftQraTU6vsy5FT/psduBq9V2gxYC6pZeZ9ltJSo9BTwt6DK5sCBAzki6TZFjcfjuPnmm6FpGlauXOl2ea4hSeWE+5SVlKYSASOwb54CmqK6xU5OgeIQ1MLrG38O8AkqC5FYiaHI2omp1XVY5dROTO1S+NJOc1FlFVS35X2R6SlgXN4PK9XV1cLSzoygfvXVV/jXv/6lPEUFSFJdQ2kqQXiHFykqT7OUarwUVLd40cUP8Asq82gpBiG1u76o1FTU9hA9ovefymyOAowFNWwpqkgygvrFF19g8+bN6NGjh+olASBJdUQY0lTt5Ckl47JokD/hCIEpqh67ZimVKarXguomRQ26oPIgS06diilLisq6/9RJed/NYH6AXVAJa06cOIHdu3dnv967dy927tyJmpoa9OnTBzfddBN27NiB9evXI5lMoqWlBQBQU1ODaNTleZtdQJIqAEpT/Yfd/sJIh7tN7LJ/PuDgzRALAXuzpMdvKapVKVo2JKjyS/w8yCzpy0hN3Qiq0/K+0/QUIEEVwUcffYSJEydmv16wYAEAYMaMGViyZAnWrVsHALjssstybrd582ZMmDDBq2UWQJLqkDCkqbb4bFYqT+OL7CYZ/c8XIaxchO1kCi5SVNEjp7xIUUlQC7E6nadMZMmpKDE1OmZ2gspb3nfaHAUgO5g/g1tBbUsVHuTjKZqTCgATJkyAppkfP6vvqYQklYNUZSmQMPkepalK8XNndqqy1HtRLTJkpah6gpCikqAWfs3TnZ5zucNSv+VoKZ/IKSBXUHnL+6zpKUAJKpELSaoLKE31B34W1AwkqpLwUYoqGxLUwq+dCqoTgiKnZrAKqt/K+244kirBiZS/mh0JPkhSObGSDUpTdZzqKEi0ZBAEQc1AouqMoKSoMkv9IgTVK/wiqCKwnX3qQk5ZxNTqOpYnLmDYr+t2/6nT8j4gV1CPkJQWFSSpLqE0VR1BElTCGZaCGpIUVZSgepGi+klQ7VLUjIDqS9ysY6ZkyqnbVFWGoKoo7+dzJFViWvI3EtPWVPrOttOe1EBDkuoASlMJp1CaKpEiTFHDKqiFt7f4vQ4EVQ/P/FNZcsorpmbHQ6Sgyi7vA/wJakZUrdLSjJwCwHfJrjgp+HSkhLeQpAqA0lTvCXKK6mdRDcybpBCkqGEWVNZRU17hFzm1wuw4idp/KrK8D+QKKg9WqWmG75Jds58fTZ3l6PeIJNKRRKRM7P/5kYQ/X0NEQ5LKQbKiFJnnGaWpBCEXr/eiOjn9afpniE9RVQiqU1QKqtsU1Q4jOQUKBZVHTkWX840uEyWooobzA9aC6nQfqpWcHjn9eZtVDE/4HpJUQRRjmqrqrFN2BDlFVYrPn2/MSEpR/QKLoEr5vQ5SVL8JqihY5RQoFFRZcmqG2V5dp4LKWt4H2PafAmIFlUVMAaA12SX9b4IkNciQpHKSrChFaSz9x0tpKuEUP5f8/UBQUlTRsAqqH8r8vFsjvBBUtymq3+WUtZmMV1BZy/sA3/5TQEyJP19MAXs5PZrIlPkFn7WP8BSSVIEUY5pqi8/OOkUUOT5LUUWW+lUJqhPsBNVO8q0ENR8v9qC6kVPAWERFJ6e8gmrXIOXl/lPAXFBbUxWGaaqRmALsctqWSL/RjSVIc4IMPXoOoDRVHUEo1xLuCGOKqlJQeVNUXkG1/XkW8mV4fUHvic3EFJAvp0aPN890A1ZB9XL/KcAvqBnMhDSDXkwBNjltjaf/7YzTa0aQIUkVTCjTVEHoU68wQCV/Too0RRUpqLJxIqhOZ6ECcvahqpJTp3uNZQqqqPFSgHNBtcJMTjNiCpjLKQCciFcinvDPxA6CH5JUh1CaSvgSxueWX/Fbiho0ZKWoLPtPZQsqC5G48b5UKzHN4HTfqeWIKcFNcCIEVdb8U0CMoLKkpoC9nALAsXgFErQlNdCQpHKQrIiAZdQZpakEIRhFKarsUn8QyvwyBLXw9rlfGwkqa4rKIqR6nKanIuXU7NiYNZOJFFQR+0+BQkHlxa2cZsQUSMspAJzorEBC0lQFwhtIUl3gOE3lgNLUM9B+1OImSCmqiFJ/EBqlZAkq77B+GeOmZJT2RSanogRVxP5TQI6g5ospIE5OAeBUvBzJBJ0WNciQpHKSrIwwJRCWaapRyZ/S1FBC+1IZKMIUNQj7UL0QVBUYySngrrTvRk6N3vDYCardiCkRDVL5cgqIEVQjMQXcl/WBXDkFgFOxciRj9P9rkCFJdQmlqRac6ihIvAg+zN7sOH0u+ZUgpahuEb1P0UmKavdG2ytB9TpFFV3al3HiBaeC6nWDFGAvqGZCqkeWnGZIUHd/oCFJdYC0NJUgiFx8mKK6KfXzSI2qMr8oQS28jfXXMuehii7ti5JT1m0Q+YLqtIPfzf5TQNwe1CN58ipDTuOn5TThwamB7Yh0JhBJig0WIsmE0J/nV0hSBcCaptpiUfIPbJpKEDa4OfWukxS14HsepaiiBdXxOizeYPOeRcoKEZ38blNU0aV9oXtOJQqq6AYpIFdQncIjp0DhvlMuOY1l9CYcMleskKQ6xEma6mYcVdihpimXFMt+Z4vtI6wpqp2IydiLKkNQRaeorIIqupNfBqxyCrCV9nn3ENumygoFlbdBCigUVN4UVY2cAlo8Ai1Oc1KDDEkqB8loCcpM/q+iNJVwSpibpyxTVJtSv4oU1UmpX8a+RZHwpKcyGqVEpqhmcgrIS0+N3lSUdWimoipDUGV18APuElQWOQXMO/bdyGmGkhhJapAhSXUBa5qqh9JUgnAIY4pqhdcpKq+gep2iei2osvah8sgp4D49FbUdwwtBNWqQAuQJar6YAmrl1N9vEQk7SFIloU/HRA7392Wa2hHjbnAhCDcpqhX6Ur8f9qKy4pWgOtl3KkNQReBWTo0uEyGnLCmqaEF12sEP8AvqkWTXnJK/kZgC4uQUOCOovMlpJOGvv3OCD5JUTpLRkpwXCX2aqi/5W0FpKkFwYjF2qlhSVL8io5MfcJeiWskpID49FZGcspxVikVQZYyYAvgTVDMxBfjlFLBPT7nlNJ4+3jTKP9iQpEpEVpoadCKn4sz7CYniJIgpKs9+VL+X+VlhPU68e3VZBLU0lrsv1U5MAfHpqRM5NRJ4s5RZtKA66eAHxO1BZZVTgL2071ROieKAJNUBUtJUDnxZ8peIm85+K1GRActjT3DicHi/HpGjleyQJaheYyaoXpb5WcQ0gx/TUyBYguoUvZwCYjr247oh/BlBJTkNH4Fpe9u3bx9mz56N/v37o6qqCgMHDkRDQwM6O01OBXKaCRMmoKSkJOfjrrvu8mjVuYJlWZakMzMJJVlR6rmgqvy9QUJkimo2doo3RRVV6pdZ4vc6RTVChKCKHtof6TTu3LcT1NKYZvh4lXVojgWV9fiwCmr2I2/ElCxB5U1RW5NdCtJTo2H8rfEqnIhX4kS8EsfiFTgWr8CJzvTHqXh5+iNWbpieJmJlOaOkSmKRHEGNxEtIUIuYwCSpu3btQiqVwurVqzFo0CB88sknmDNnDtrb2/HEE09Y3nbOnDl45JFHsl936dLF4tps5KepOd8TlaYGrYHKJ/hBElmfAxnCPIaKBz+nqE4ENUgpql8FNR+n6anbx4J1ny6PoKYvEz8DFXCXoJolp4DYfadmyamZlEZihZfTntRgExhJnTJlCqZMmZL9esCAAWhqasLKlSttJbVLly7o3bu31PXRqVL9gR8ENQOvqIYB7rNLCRjebwdLimq351K2oHqZospMmkVhJKcAW3pqhAxBNerkFyWobmagAsaCapei5osp4M2+U5ayvpGc+onIqTgipWLfLIs+zapfCUy534i2tjbU1NTYXu/FF19Ez549cckll2Dx4sU4edL6jzEWi+HYsWM5H0ZYNRXoZcnV2ZIsyp9uTidZjPhJUAkHSBjen5+iyhg7VSxd/AC7oKpMUc3SUyeC6qa0b0XQBNWK/JI+UFjWN0pPWUr78Xgp4vHSbFkfOHOWKLuyfiRWkv0wI3MsieASmCQ1n927d2PFihW2KepPfvIT1NfXo2/fvvjvf/+LhQsXoqmpCW+88YbpbZYtW4aHH36Ye0003J/Ix9M01efPG1kpqhvcJoROBdWPKarTTn4v5qECYtNTkWJqtQ2CVVBZT3PqZkg/YC2oRklpPkbJKSBm3ilraZ81NSVBLQ6UJ6mLFi0qaGzK/9i1a1fObZqbmzFlyhRMnz4dc+bMsfz5d955JyZPnoxLL70Ut912G1544QWsXbsWe/bsMb3N4sWL0dbWlv04cOAAAOOSn5M0lfsFltJUW/ycovp5bb7Bp2OnrCj2BBVwf8rTDG5TVNHpqR2lnVr2wwoWQdXDKqhaRcpTQbVDn5wChU1RAFtp3yg9NWuKMktOWSBBLR6UJ6kPPPAAZs6caXmdAQMGZD8/ePAgJk6ciHHjxmHNmjXcv2/MmDEA0knswIEDDa9TUVGBigpnL5pC0lSCCDs+H97vRlD9lqKKFFTRKarT9BQofIzsjjvvsWYV1MznPIIKiDvNqVvcpqe8+06dJqcZ9IKaKteQSpCwBhnlklpbW4va2lqm6zY3N2PixIkYOXIkGhsbEYnwB8E7d+4EAPTp04f7tkD6PyanpSLm4f6cJf+wd/pTUul/gji8X08xpaYsOBF4M0F1mqJ6Vd4X8UbA74LqJEXllVOAv2tfpJwChYJKBB/l5X5WmpubMWHCBPTr1w9PPPEEvvnmG7S0tKClpSXnOoMHD8a2bdsAAHv27MFvfvMbbN++Hfv27cO6detwxx134KqrrsLQoUOFrS3/BVCf4AgTKBcv5EHGVdOZjwizSLvdkuLnsVO8+G3klMxGKacYzT0FxJf3Wcr5LCmzDEEtq0goE1SnpX2Wxqj80j7grqyvx0xQM8eVCCbKk1RW3nnnHezevRu7d+/G+eefn/M9TUs/IePxOJqamrLd+9FoFP/85z+xfPlytLe3o66uDtOmTcNDDz3kai1u0lQ9+jTVbQOVjDRVyH7XUx10ogKCD5+MnRIN7/8Zskv9ohqlrOBNUVnTU6PLWMv7bo+r2XNHpKACcCSobtCLKeB9ad9KTCOxEst9pkaCmj2mCZLUIBMYSZ05c6bt3tULLrggK6wAUFdXhy1btkheWRrW4f6uhrZbDPcPK0FKKGluqgEBHTsVdJzuQzX+We7XYyangPj0lBWeExr4RVCdpKg8cgo4H8jPK6f5l5uJqqWglqegJQx/fChpbm7GwoULsWHDBpw8eRKDBg1CY2MjRo0apXpppgRGUoOGigaqsO9NDTp+OOuU6OdQMY6dcoKfUlRWQTW+rfXXThCZngLGx1rE8WQReD8Jqh35cgqIHchvNFKKZd+pmbRaCapReT+7rzdKlgoAR48exfjx4zFx4kRs2LABtbW1+OKLL9C9e3fVS7OEJNUhRiV/J2kqnYGKCC0BaJgqNngE1U2ZH7Av9fOkp0aXySzv2z1vrGah+klQjUTUCD+kpzxD+e32n+qPaSRO1SsAePzxx1FXV4fGxsbsZf3791e4Ijb82V1QJDhp3rAtb9q8sIdpbmqQSv1hhBqm0vitWYoFEeOmzCTUrDEqg1F534mgsjRGGWFX5g+KoLKQf7Yoo72nPGeMsmuMMmqK4m2UMivvZ+bKGh3TYib/7JixmPGWwHXr1mHUqFGYPn06zj33XAwfPhzPPPOMx6vlx3//owcIN2VD5uH+1HRUVJBYn8bozZaDhineFNVv56D3EhX7UDNCqv+wgmX/KaugiqIYBVUvp0Dh6UwBd+mpUXnfqZzmSKnN/lMAOce0qiKOqgoflPs7OtJVUZEfHennQ11dHbp165b9WLZsmeESvvzyS6xcuRIXXngh3nrrLcydOxf33nsvnn/+eS+PBDdU7hdMfslfvzdVWOOMTQMV7U0lVEMpqnNk7EcVuQ9VBqrL+xnyj5MbQc3gty5+IzkF3O89ZS3tO05NGQVVfzwBoLKsuE+Uc+DAAVRXV2e/NjsRUSqVwqhRo7B06VIAwPDhw/HJJ59g1apVmDFjhidrdQJJqktEjaPS44czUIVp2wAhFkfPHcFjp/ySovqh1C96H6poaRUlqG7lXrSgpio0qYLKm6Lq5RSQs/dUlJwCfIJqdTwrUdwTcaqrq3Mk1Yw+ffrg4osvzrlsyJAheP3112UtTQgkqRLwpIEq5Gkqlc3lIf25I+jEFFZjp4g0bgTVC/wiqKyoEtR8eATVTE4Bb9JT14P5TTr4zcr7AFBVHs8eyyrY7DEJCePHj0dTU1POZZ9//jnq6+sVrYgNklQPUDGOivAvns9L9XC2rogE3kmp346gpKgiZYtnsoHVOCW7y5ziJ0FlSVFVCqqTMj+LnAL+Sk8Ba0G1238K5ApqdXkM0RRNyAGA+fPnY9y4cVi6dCluvvlmbNu2DWvWrMGaNWtUL80SklQB8I6j0iNzHFWxp6lEAFHUMBU2rI6B032oogRV1PxTUULPI6gZVAoqS4oaxPQU4BfU/P2nGUHVH8fO4q72M3P55Zdj7dq1WLx4MR555BH0798fy5cvx2233aZ6aZaQpHqEigYqwJmo0n5UwgmqUlQq9efCK6hu56Hy4FV6ml+5Yn2O2Alqzuc+TFBVp6eWpzY9nb+kDP7E3TZI6Y+l/jieU34KsXKqSGa44YYbcMMNN6heBhckqYIo1gYqIpx4lsJTw5RnuNmHKkJcvRBUo21VVoKqf76YNUqduW7631SUT1AziBLUtkRVTpqaL6YZZKenLKX9SN7Ll1tBtZP9fEEF3M2RJdRDkioRPzRQAcVX9qemKf/BlKJSw5R0/LoPVZWgWmF2rFg6+QFzQc3AkvoBzhJUMzEF/JGe5supGSyCyrP/VD8JISOnVWUn2RZD+BKSVA9x0kDlNX4q9bOmZ04wkhuzx4bnusy/3+vmKYmIes6EuWFKBDL2oYpAhKCKlFPAeh/qmevk/qvfh6oX1AxmYsUiqKKwSk8B94Jql55ayWl+iiq6QcpIULuXtYPapoINSapAZDRQFZT8HTRQAcWXpvLCkrjxpHL51/X1mw+GtN0I6c8ZapjKQeQQej0qy/wyBZXlb47lb5q3kz9fUFMVGpOgZjASVLed/H5PT90KKkt5HygUVADoVkpJapAhSfUYVQ1UgL10+ClFFYVX5eDM7/G1rEqA+TkjqNSvh0r9aUQIqhcD+o0ulymoZtjtQ7UbNQU4E9T85C9D0AXVrrTvhaDm7z/tXtaOc07LaXijmeKAJFUwfm+gClOiGkSJ0SfqfsDq+eLqTU1eiqov9Qe5YcprRKTHZoLqVFz9IqhGf/9uBTVV7lxQjXAjqHo5Bcybo4C0oLptjuKVU8C5oLppkNILKgB0j7TbL1Q2HZ2A6JejVDhOUkCS6gGeNFBxYCQexZiiqiAI+455cf18CVHDlJf7Ue0EVcVZpWQKqut94DaNUrIFlfVsUiz4PT0FxAgqy/5TIC2omfK+XlBrSk+Aiv3BhiRVAVJEhnPfoV48ilFQVUpMsYuq6OdLsTRMeYkoQRWZovpJUO3+/jPHx0za7QQ1Q0augDPNPQC/oLKmqHbpKSC2OcqJnBphJ6hOG6QAa0Elgg9JqgTcNFDpsWygEkAQ5ZRl/JQfUrZiFVUhUMOUK2QLqhNYGqQAdYJqVuY/8/3cf4HCWahArmCxpH+AmE5+MzkFzMv7QFpQvSzvZzA6ZvrPvRTUmlIflPsJx5CkKsKsgYp5T6LDmamEfyimMVSmUMMUMyxvZL0Qcl55dSKorDNQRbzRc7IP1enZpFgElTdF5RFUEeV9t+mpodTnjeriOcUpYD1iCqAEtZghSZWEjAYqwh4/CUwxpqmicVvq91PDlOy/dxZB9TpF9Zug5v/9O22UApyd7hTgE1Qr8uUU8H9530pQZY2YshLUHqUnQDlqsPHPK3oIsHqR0Zcz9WXOnPJn/gu6RdmUIJRjlKK6LPX76U2IVySjJZ4JKqu8lnaKEdTSTq1AUEs7UkIE1fR6nLNQWQXVbli/maDmy2hrvMowPXUqqFo8Ai0eQUkswiyokXjwBRUAvkt25bsThO+gJFUhfmigKib8KDCUpnpL0Bum9CV/ntK+iPvNI6isl9sJasH1Bf6tGKWoTob1A8anOwWsBVWPXYJqlJpm8Ht5H+AXVLcjpng4kjyL+/4Q/oEkVSKiGqj0yGigIggVsMxGDWPDlKj7JaPM71dBZS3zGyFqWH8+bk95qpdTQJygWqWnTlAlqLQPNRz4L3oKGfr/XFlK/gUYlU8lNKsQBBecpX4WWMcKhQ2v9qGaCarhdWPmb8RVCapZipr+Xvpf0bNQAWfzUPPTU5WCWmrh2m4EtaoinhXUrtGYY0ElihtKUiVDDVTe4MdSP2GOjIapMCJKzO0E1kpQeeagyi7xm8Haye9HQQXMx0sBhftPAevxUizlfSsxzeBWUAHjU8XyCiqlqMUNSaoCqOQfLkK3LzWEDVMq3oiaCaroFNXPgsqSovJ08gNihvU7QVZ5HzAWVLP0NF9QkwZ/zqyCyjMDFXCWoB5JdjUV1SPJrjiVShh+jwgGJKkeYJemssxM5T5NahE2ULEM8ifCSVhL/fmIFFS78n4xCKqTTn4zQc2HJ0U1Sk8Bb8v7RumpV4JqNKSfhyM+7+LXTp2CViJ2Jramcey/CTD+jieKGCpXEmGFSv3uES3lBcIpUFANby+4ssDSKCVq1BRgLKhOy/zFLqjl5UnHgipiH2pbsouj2xH+gJJUH8KSplLJ/wx+LwUD5iX/ojvrVAhL/V4jq8zP2hjFK6hGc1DdYvacsGqUAqw7+QG2UVNGOCnz25X3AfeC6kROAWtB5TnNKc9ZpACxgtqalVMq9wcZklSP4Cn5OyLgJX/LCQYEYUGYSv08gioD2YKqf8Nmtr3Hqsx/5rZqOvkBthTVqaCK3H/K0hyVwU5QeYb0A3yCCqSFk0VUWw1S09YEJalBhiRVIW4bqHwDjbwiGKFSv3eIOvVpBpmCml9NYN1/zrsPVbSg8mImp4B35X07Oc1PUb0QVD1mw/rNRNVITI8m9AP8qeIYZKiO5iN4Z6YynSaVBJLwCgWlfkpR5cxEzcdLQbXCrszvZSc/wFfmJ0E1F1TWRqmMkLYmu2Q/9BxNnJUjqG2JKrQlzM/mRfgfSlI9hGamiof2KzISoK0fZoQ5RVVZ5rfbq6pKUDPPB5mNUiIENV9OAfmC6qS87wdBZTnlqX1yihwxbTM4/kRwIElVTNGU/AlbinpeKkNib1bqZz0Nqp+R+QaUV1BFpqhuT3dq9ny3klOW5wDLPlSArVHKrpPfCCtBPRGvRNfyDkM5BeQIqpv0FPBGUI3gHTWVj5WctsYzn4djVFOxQpLqMaJnphZ0+Qe8gYooIhhL/WZQqZ+foAuqGTlboTj2oaa/l/7XbB8qYN3J72QfKmt6CoRHUO1mobKkqBnY5DT9OMQTVG0LMiSpPoDS1EL06ZpIRJeM6XHzhrCW+lV38+vJ34ea8z1BgmqUorrZhyqjUcrJuCk3gsp6ilOZgmp0mlNAnKCykC+mgLWcEsUBSWoRwDQzldJUKaJDbzAgpdRPKaq/yvw8Z5MSmaDmw7sPFbBulMo/KxLgjaBm5BQwFlS3I6b8LKhmHE2cVZCmGokpwC6nx+IVSFBzf6AhSVWAktOkhhjZKRyJqgEuS/1hh1fCVQkq889kEFS7FNXJPlS7RinA/LSdImARVJEd/KyzT1UKqlWKaialGczkFLA/cxcRTEhSfQKJjjU8ZUAVhPbx82DEWdhK/VaCKrvML2PUlGhB5dmHCrhrlHKTonrdwc8znF8Pj6DmHy+RgmpF/hgps/TUWE7VVxBTp2JIlYhtmk1p4YiISVIVoWQclYySv8/nsHopOKEVVRv0pX6ajWqNE0EVlaLKGDUl+pS/IvahAvyNUjyCqhclwH+CmiPwHgqqE9zJKVEMkKT6FCld/iFDRQJnJ6pFPYYqg0Wpn5ewpah+wm2jFKugOinz51yXYR+qV2eUkiWobvefZnAqqBl4BNUNouT0VLwcyUSR/39b5JCk+ghPkjhqoPI9+jciQhH92CtI0f2corqtjvgpRXXbKOUmQeUt8wP2+1AB9jNK5cOaovp1xFQGI0HVI3IPKsCfohqdGYpFToFCQdXv+yWCDUmqQnhe1PRpqhlMXf4hQWUCx/tmg+WxDQx5KaroUn+xElZBZT15g1WZ32xgP8sZpYxwUuYPqqCajeUC5AhqRkQze1PNTllq17Gf/Z7BsSaKC5JUQehfSKzKZFw/06Q0TF3+hHIC0DAl429SBirTYd59qDm3lbAH1ShFzT8+rAP701/LG9gPWCd6sgSVt0GKRVAz2AlqBrclfhY5BdhK+1ZyeipWjmSxBAAhhSRVAPlJR7KixPGLIpX83UP7GIsTHpkT+TcpE7v7JDNFdXtGqcLb8slAforKOm4q/f30v/n7UN0M7M/HLkUtJkFlOZMUkD5Wdqc6ddIs5XSclJGgZo45URyQpLrE9EWE8UXR6cxUX+Dzzn6VUKe/ulK/irMxZeDZwqNSUI0QcUYpVtyW+QHjfaiAs4H9AF+KSoJ6ZjFu9qGKklMS0+IlUBvAfvjDH6Jfv36orKxEnz59cPvtt+PgwYOWt+no6MC8efPQo0cPdO3aFdOmTcOhQ4c8WrEzWJJA/Qt9jgDkn9nHrNM64IIZ1r2LrhHxuJv9DB909VsJqkp5zUd1A5ifGqUA6zI/zzxUloH9RpCg2guqEU47+VvjVQX7TllL+/knQ7AT1CrdmxMCePrpp3HBBRegsrISY8aMwbZt21QvyZJAvdJPnDgRr776KpqamvD6669jz549uOmmmyxvM3/+fLz55pt47bXXsGXLFhw8eBA//vGPhazH7kWP9UVR9QtWMRGEUj+vYNMZmoL1N2K3Vpb74nWZX4/sfai8Zf705bn/ms1DTX+duw/VaL4nYL0P1aiUfSxeEWpBFTFqKl9OgcL0NHOMT3RW5Izw4pVTopBXXnkFCxYsQENDA3bs2IFhw4Zh8uTJOHz4sOqlmRKocv/8+fOzn9fX12PRokWYOnUq4vE4yssLn7BtbW3485//jJdeegnXXHMNAKCxsRFDhgzB1q1bccUVV0hfs4i9cL4u+ROmFGXJnzFFLUj0M5dLLPWzvClUvTfVjaCKwM0+VC+G9WfIT1EB5/tQAXNBNeNYvCIrY/limiHMgspLvpgCzpqieMW0qiKO5EmumxQ1v//97zFnzhzMmjULALBq1Sr8/e9/x7PPPotFixYpXp0xgZJUPUeOHMGLL76IcePGGQoqAGzfvh3xeByTJk3KXjZ48GD069cP77//vqmkxmIxxGJn/hjb2toAAMl47jvHZAnjiwmLqMRzr6Plf60bSKwlTr8wlOHMPM1SINJ5uqwRRe4oqmgJ0GHwrjcKoMMmVrGCdVtasvA4pZK5N04lknlf56UtpXlfx42lhvkx8Yj8xzF7ed6AaS3v/kfyv04m8r42eJFNMb6ApCQ85nmPsf7xTUXLgNP3R/+46h9T/eOZjJYAeXcvGWGQO5F/jy5JRnLlLytbDIfe7H4ko2y3t8SgzJ/zTIvnlvn1z7r852xpLAneQmqyohRIxHVfR7KPdeZxT1aUAJ26f0/f7+TppaW00zIWA1JJQNNOl/k7gFTitHydAkoSKZRFE0idBJKn5St5+u8oUXZGvhImvnok+1nh31VapNKXdyTKAcRwKlYGIIlEvBRAHInOMgCJHEHVAEQSJUghLaYpACWxkuxjEEkg+3lpDOB9C6C/fur0F1rm2GT+LdOABKCl0iKvJZBznKoqEkieBCrL4kh0njlGZ5d3In76+XNWWQc6Df67OQyzvcZnnnjticrsZcfjmXcc6R9mdFwBnD62+ffQmsz9SJ5M/wxNU/jmFHFA8K9PnP7DOXbsWM7lFRUVqKgofGPV2dmJ7du3Y/HixdnLIpEIJk2ahPfff1/s4gQSOElduHAhnnrqKZw8eRJXXHEF1q9fb3rdlpYWRKNRnHPOOTmX9+rVCy0tLaa3W7ZsGR5++OGCy//f679xvG6CIAiCINTw3XffoVu3bp7+zmg0it69e+PfLX+T8vO7du2Kurq6nMsaGhqwZMmSgut+++23SCaT6NWrV87lvXr1wq5du6SsTwTKJXXRokV4/PHHLa/zv//9D4MHDwYA/PKXv8Ts2bPx1Vdf4eGHH8Ydd9yB9evXo0RggrZ48WIsWLAg+3Vrayvq6+uxf/9+z5/kKjl27Bjq6upw4MABVFdXq16OZ9D9pvsdBuh+0/0OA21tbejXrx9qamo8/92VlZXYu3cvOjvdlkCM0TStwH2MUtQgo1xSH3jgAcycOdPyOgMGDMh+3rNnT/Ts2RMXXXQRhgwZgrq6OmzduhVjx44tuF3v3r3R2dmJ1tbWnDT10KFD6N27t+nvM4vLu3XrFqo/7gzV1dV0v0ME3e9wQfc7XIT1fkciavrEKysrUVkpbvKJU3r27InS0tKC6UZ2PqQa5ZJaW1uL2tpaR7dNpdJ7pPT7R/WMHDkS5eXl2LRpE6ZNmwYAaGpqwv79+w2lliAIgiAIotiIRqMYOXIkNm3ahKlTpwJIO9SmTZtw9913q12cBcollZUPPvgAH374Ia688kp0794de/bswa9+9SsMHDgwK5zNzc249tpr8cILL2D06NHo1q0bZs+ejQULFqCmpgbV1dW45557MHbsWE86+wmCIAiCIPzAggULMGPGDIwaNQqjR4/G8uXL0d7enu329yOBkdQuXbrgjTfeQENDA9rb29GnTx9MmTIFDz30ULY0H4/H0dTUhJMnz8ycePLJJxGJRDBt2jTEYjFMnjwZf/zjH7l+d0VFBRoaGopur4cddL/pfocBut90v8MA3e9w3W8jbrnlFnzzzTf49a9/jZaWFlx22WXYuHFjQTOVnyjRVM5lIAiCIAiCIAgDAnXGKYIgCIIgCCIckKQSBEEQBEEQvoMklSAIgiAIgvAdJKkEQRAEQRCE7yBJ5WDfvn2YPXs2+vfvj6qqKgwcOBANDQ3SzibhJx599FGMGzcOXbp0KTjNbDHx9NNP44ILLkBlZSXGjBmDbdu2qV6SdN577z3ceOON6Nu3L0pKSvDXv/5V9ZI8YdmyZbj88stx9tln49xzz8XUqVPR1NSkelnSWblyJYYOHZod6j527Fhs2LBB9bI85bHHHkNJSQnuv/9+1UuRzpIlS1BSUpLzkTmDYzHT3NyMn/70p+jRoweqqqpw6aWX4qOPPlK9LIITklQOdu3ahVQqhdWrV+PTTz/Fk08+iVWrVuHBBx9UvTTpdHZ2Yvr06Zg7d67qpUjjlVdewYIFC9DQ0IAdO3Zg2LBhmDx5Mg4fPqx6aVJpb2/HsGHD8PTTT6teiqds2bIF8+bNw9atW/HOO+8gHo/jBz/4Adrb21UvTSrnn38+HnvsMWzfvh0fffQRrrnmGvzoRz/Cp59+qnppnvDhhx9i9erVGDp0qOqleMb3v/99fP3119mP//znP6qXJJWjR49i/PjxKC8vx4YNG/DZZ5/hd7/7Hbp37656aQQvGuGK3/72t1r//v1VL8MzGhsbtW7duqlehhRGjx6tzZs3L/t1MpnU+vbtqy1btkzhqrwFgLZ27VrVy1DC4cOHNQDali1bVC/Fc7p376796U9/Ur0M6Rw/fly78MILtXfeeUe7+uqrtfvuu0/1kqTT0NCgDRs2TPUyPGXhwoXalVdeqXoZhAAoSXVJW1sbampqVC+DcElnZye2b9+OSZMmZS+LRCKYNGkS3n//fYUrI7yira0NAEL195xMJvHyyy+jvb09FKeKnjdvHq6//vqcv/Mw8MUXX6Bv374YMGAAbrvtNuzfv1/1kqSybt06jBo1CtOnT8e5556L4cOH45lnnlG9LMIBJKku2L17N1asWIGf//znqpdCuOTbb79FMpksOPNGr1690NLSomhVhFekUincf//9GD9+PC655BLVy5HOxx9/jK5du6KiogJ33XUX1q5di4svvlj1sqTy8ssvY8eOHVi2bJnqpXjKmDFj8Nxzz2Hjxo1YuXIl9u7di//7v//D8ePHVS9NGl9++SVWrlyJCy+8EG+99Rbmzp2Le++9F88//7zqpRGckKQCWLRoUcHG8vyPXbt25dymubkZU6ZMwfTp0zFnzhxFK3eHk/tNEMXIvHnz8Mknn+Dll19WvRRP+N73voedO3figw8+wNy5czFjxgx89tlnqpcljQMHDuC+++7Diy++iMrKStXL8ZTrrrsO06dPx9ChQzF58mT84x//QGtrK1599VXVS5NGKpXCiBEjsHTpUgwfPhx33nkn5syZg1WrVqleGsFJmeoF+IEHHngAM2fOtLzOgAEDsp8fPHgQEydOxLhx47BmzRrJq5MH7/0uZnr27InS0lIcOnQo5/JDhw6hd+/eilZFeMHdd9+N9evX47333sP555+vejmeEI1GMWjQIADAyJEj8eGHH+IPf/gDVq9erXhlcti+fTsOHz6MESNGZC9LJpN477338NRTTyEWi6G0tFThCr3jnHPOwUUXXYTdu3erXoo0+vTpU1AZGDJkCF5//XVFKyKcQpIKoLa2FrW1tUzXbW5uxsSJEzFy5Eg0NjYiEgluGM1zv4udaDSKkSNHYtOmTZg6dSqA9LvxTZs24e6771a7OEIKmqbhnnvuwdq1a/Huu++if//+qpekjFQqhVgspnoZ0rj22mvx8ccf51w2a9YsDB48GAsXLgyNoALAiRMnsGfPHtx+++2qlyKN8ePHF4yT+/zzz1FfX69oRYRTSFI5aG5uxoQJE1BfX48nnngC33zzTfZ7xZ627d+/H0eOHMH+/fuRTCaxc+dOAMCgQYPQtWtXtYsTxIIFCzBjxgyMGjUKo0ePxvLly9He3o5Zs2apXppUTpw4kZOq7N27Fzt37kRNTQ369euncGVymTdvHl566SX87W9/w9lnn53de9ytWzdUVVUpXp08Fi9ejOuuuw79+vXD8ePH8dJLL+Hdd9/FW2+9pXpp0jj77LML9hqfddZZ6NGjR9HvQf7FL36BG2+8EfX19Th48CAaGhpQWlqKW2+9VfXSpDF//nyMGzcOS5cuxc0334xt27ZhzZo1ga58hhbV4wWCRGNjowbA8KPYmTFjhuH93rx5s+qlCWXFihVav379tGg0qo0ePVrbunWr6iVJZ/PmzYaP7YwZM1QvTSpmf8uNjY2qlyaVn/3sZ1p9fb0WjUa12tpa7dprr9Xefvtt1cvynLCMoLrlllu0Pn36aNFoVDvvvPO0W265Rdu9e7fqZUnnzTff1C655BKtoqJCGzx4sLZmzRrVSyIcUKJpmualFBMEQRAEQRCEHcHdUEkQBEEQBEEULSSpBEEQBEEQhO8gSSUIgiAIgiB8B0kqQRAEQRAE4TtIUgmCIAiCIAjfQZJKEARBEARB+A6SVIIgCIIgCMJ3kKQSBEEQBEEQvoMklSAIgiAIgvAdJKkEQRAEQRCE7yBJJQiCIAiCIHwHSSpBEKHkL3/5C6qqqvD1119nL5s1axaGDh2KtrY2hSsjCIIgAKBE0zRN9SIIgiC8RtM0XHbZZbjqqquwYsUKNDQ04Nlnn8XWrVtx3nnnqV4eQRBE6ClTvQCCIAgVlJSU4NFHH8VNN92E3r17Y8WKFfj3v/9NgkoQBOETKEklCCLUjBgxAp9++inefvttXH311aqXQxAEQZyG9qQSBBFaNm7ciF27diGZTKJXr16ql0MQBEHooCSVIIhQsmPHDkyYMAGrV6/Gc889h+rqarz22muql0UQBEGchvakEgQROvbt24frr78eDz74IG699VYMGDAAY8eOxY4dOzBixAjVyyMIgiBASSpBECHjyJEjGDduHCZMmIBVq1ZlL7/++uuRTCaxceNGhasjCIIgMpCkEgRBEARBEL6DGqcIgiAIgiAI30GSShAEQRAEQfgOklSCIAiCIAjCd5CkEgRBEARBEL6DJJUgCIIgCILwHSSpBEEQBEEQhO8gSSUIgiAIgiB8B0kqQRAEQRAE4TtIUgmCIAiCIAjfQZJKEARBEARB+A6SVIIgCIIgCMJ3/H9VmLgmue3CLgAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opt_x, opt_y = result.x\n", "\n", "x_vals = np.linspace(-2, 6, 200)\n", "y_vals = np.linspace(-3, 1, 200)\n", "X, Y = np.meshgrid(x_vals, y_vals)\n", "\n", "# Compute function values\n", "Z = np.array([[cost_function([x, y]) for x in x_vals] for y in y_vals])\n", "\n", "# Create filled contour plot\n", "plt.figure(figsize=(8, 6))\n", "contour = plt.contourf(X, Y, Z, levels=50, cmap=\"viridis\")\n", "plt.colorbar(label=\"Cost Function Value\")\n", "\n", "# Plot initial guess\n", "plt.scatter(6.0, 0.0, color=\"red\", marker=\"o\", label=\"Initial Guess\", s=100)\n", "\n", "# Plot optimized point\n", "plt.scatter(opt_x, opt_y, color=\"red\", marker=\"x\", label=\"Optimized Solution\", s=100)\n", "\n", "# Labels and title\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$\")\n", "plt.title(\"Optimization of Cost Function\")\n", "\n", "# Add legend\n", "plt.legend(loc = 'upper left')\n", "\n", "# Show plot\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "7. Repeat the optimization problem using the basin hopping algorithm. You can use the two starting points defined in questions 3 and 4. In the basin hopping algorithm you can use 10 iterations.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Starting point [6. 0.]:\n", "Optimal solution: [3.87837894e-06 1.00000000e+00]\n", "Function value at optimum: 6.016729265496596e-11\n", "Optimization success: True\n", "Message: ['requested number of basinhopping iterations completed successfully']\n", "\n", "Starting point [6. 0.5]:\n", "Optimal solution: [1.13033312e-06 9.99996098e-01]\n", "Function value at optimum: 2.0333313504890065e-11\n", "Optimization success: True\n", "Message: ['requested number of basinhopping iterations completed successfully']\n" ] } ], "source": [ "# Custom function to enforce bounds in Basin-Hopping\n", "import scipy.optimize as opt\n", "class BoundsEnforcer:\n", " def __init__(self, bounds):\n", " self.min_bounds, self.max_bounds = np.array(bounds).T\n", "\n", " def __call__(self, **kwargs):\n", " x = kwargs[\"x_new\"]\n", " return np.all(x >= self.min_bounds) and np.all(x <= self.max_bounds)\n", "\n", "# Perform Basin-Hopping optimization\n", "def run_basin_hopping(x0):\n", " minimizer_kwargs = {\"method\": \"SLSQP\", \"bounds\": bounds}\n", " result = opt.basinhopping(\n", " cost_function, x0, niter=10, minimizer_kwargs=minimizer_kwargs, accept_test=BoundsEnforcer(bounds)\n", " )\n", " return result\n", "\n", "# Run for both starting points\n", "starting_points = [np.array([6.0, 0.0]), np.array([6.0, 0.5])]\n", "results = [run_basin_hopping(x0) for x0 in starting_points]\n", "\n", "# Print results\n", "for i, res in enumerate(results):\n", " print(f\"\\nStarting point {starting_points[i]}:\")\n", " print(\"Optimal solution:\", res.x)\n", " print(\"Function value at optimum:\", res.fun)\n", " print(\"Optimization success:\", res.success)\n", " print(\"Message:\", res.message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "8. Repeat question 7 using 20 iterations instead of 10.\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Starting point [6. 0.]:\n", "Optimal solution: [0.83471727 0.79022813]\n", "Function value at optimum: 1.4932291335337022e-10\n", "Optimization success: True\n", "Message: ['requested number of basinhopping iterations completed successfully']\n", "\n", "Starting point [6. 0.5]:\n", "Optimal solution: [-2.42149144e-09 9.99996341e-01]\n", "Function value at optimum: 1.3387622825015583e-11\n", "Optimization success: True\n", "Message: ['requested number of basinhopping iterations completed successfully']\n" ] } ], "source": [ "class BoundsEnforcer:\n", " def __init__(self, bounds):\n", " self.min_bounds, self.max_bounds = np.array(bounds).T\n", "\n", " def __call__(self, **kwargs):\n", " x = kwargs[\"x_new\"]\n", " return np.all(x >= self.min_bounds) and np.all(x <= self.max_bounds)\n", "\n", "# Perform Basin-Hopping optimization\n", "def run_basin_hopping(x0):\n", " minimizer_kwargs = {\"method\": \"SLSQP\", \"bounds\": bounds}\n", " result = opt.basinhopping(\n", " cost_function, x0, niter=20, minimizer_kwargs=minimizer_kwargs, accept_test=BoundsEnforcer(bounds)\n", " )\n", " return result\n", "\n", "# Run for both starting points\n", "starting_points = [np.array([6.0, 0.0]), np.array([6.0, 0.5])]\n", "results = [run_basin_hopping(x0) for x0 in starting_points]\n", "\n", "# Print results\n", "for i, res in enumerate(results):\n", " print(f\"\\nStarting point {starting_points[i]}:\")\n", " print(\"Optimal solution:\", res.x)\n", " print(\"Function value at optimum:\", res.fun)\n", " print(\"Optimization success:\", res.success)\n", " print(\"Message:\", res.message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "9. Apply the differential evolution algorithms to find the global minima of the cost function.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal solution: [-1.27453603e-13 1.00000000e+00]\n", "Function value at optimum: 6.559615085183955e-26\n", "Optimization success: False\n", "Message: Maximum number of iterations has been exceeded.\n" ] } ], "source": [ "result = opt.differential_evolution(cost_function, bounds, strategy='best1bin', maxiter=100, popsize=20)\n", "\n", "# Print results\n", "print(\"Optimal solution:\", result.x)\n", "print(\"Function value at optimum:\", result.fun)\n", "print(\"Optimization success:\", result.success)\n", "print(\"Message:\", result.message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "10. Discuss the numerical cost (number of iterations and function evaluations) associated with the different algorithms used in 5, 8 and 9. Can you comment on what you observe?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1️⃣ SLSQP (Sequential Least Squares Programming) – Question 5\n", "Gradient-based optimizer: Uses local derivative information to find the minimum efficiently.\n", "Numerical Cost:\n", "Few iterations (typically 10-50).\n", "Function evaluations are low since it relies on gradient information.\n", "Performance: Fast convergence for smooth problems.\n", "Struggles with non-convexity: Might get stuck in local minima.\n", "Observations:\n", "It converges quickly (low cost).\n", "Highly sensitive to the initial starting point.\n", "\n", "2️⃣ Basin-Hopping – Question 8\n", "Global optimization approach: Introduces random jumps to escape local minima.\n", "Numerical Cost:\n", "Each iteration involves a local optimization (SLSQP).\n", "If we set niter=10, the function is evaluated 10× more than SLSQP.\n", "Total function evaluations = 10×(SLSQP evaluations)\n", "10×(SLSQP evaluations).\n", "Performance: Better for non-convex problems.\n", "Higher computational cost due to random perturbations.\n", "Observations:\n", "It finds a better solution than SLSQP but at a higher function evaluation cost.\n", "Works well when the problem has multiple local minima.\n", "\n", "3️⃣ Differential Evolution – Question 9\n", "Global population-based search: Uses mutation and crossover to explore the entire search space.\n", "Numerical Cost:\n", "Uses many function evaluations per generation.\n", "If we set popsize=20 and maxiter=100:\n", "Total function evaluations = 20×100=2000\n", "20×100=2000.\n", "Performance: Best at finding the global minimum.\n", "Most expensive computationally.\n", "Observations:\n", "High function evaluation cost, but it is more reliable in finding the true global minimum.\n", "Unlike SLSQP and Basin-Hopping, it does not need an initial guess.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "| Algorithm | Global/Local | Iterations | Function Evaluations | Pros | Cons |\n", "| --- | --- | --- | --- | --- | --- |\n", "| SLSQP | Local | 10 - 50 | Low (10-50) | Fast convergence | Stuck in local minima |\n", "| Basin-Hopping | Global | 10 (each w/SLSQP) | 10x more than SLSQP | Escapes local minima | Higher cost |\n", "| Differential Evolution | Global | 100 | Very high (2000) | Best global optimizer | Expensive |\n", "\n" ] } ], "metadata": { "kernel_info": { "name": "python3" }, "kernelspec": { "argv": [ "/Library/Frameworks/Python.framework/Versions/3.9/bin/python3.9", "-m", "ipykernel_launcher", "-f", "{connection_file}" ], "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" }, "nteract": { "version": "0.28.0" } }, "nbformat": 4, "nbformat_minor": 0 }