{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Approximating Runge's function\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demapp04.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-22\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "\n", "Uniform-node and Chebyshev-node polynomial approximation of Runge's function and compute condition numbers of associated interpolation matrices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from numpy.linalg import norm, cond\n", "from compecon import BasisChebyshev\n", "import warnings\n", "\n", "warnings.simplefilter('ignore')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Runge function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "runge = lambda x: 1 / (1 + 25 * x ** 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set points of approximation interval" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a, b = -1, 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Construct plotting grid" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "nplot = 1001\n", "x = np.linspace(a, b, nplot)\n", "y = runge(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot Runge's Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialize data matrices" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "n = np.arange(3, 33, 2)\n", "nn = n.size\n", "errunif, errcheb = (np.zeros([nn, nplot]) for k in range(2))\n", "nrmunif, nrmcheb, conunif, concheb = (np.zeros(nn) for k in range(4))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute approximation errors on refined grid and interpolation matrix condition numbers" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "for i in range(nn):\n", " # Uniform-node monomial-basis approximant\n", " xnodes = np.linspace(a, b, n[i])\n", " c = np.polyfit(xnodes, runge(xnodes), n[i])\n", " yfit = np.polyval(c, x)\n", " phi = xnodes.reshape(-1, 1) ** np.arange(n[i])\n", "\n", " errunif[i] = yfit - y\n", " nrmunif[i] = np.log10(norm(yfit - y, np.inf))\n", " conunif[i] = np.log10(cond(phi, 2))\n", "\n", " # Chebychev-node Chebychev-basis approximant\n", " yapprox = BasisChebyshev(n[i], a, b, f=runge)\n", " yfit = yapprox(x) # [0] no longer needed? # index zero is to eliminate one dimension\n", " phi = yapprox.Phi()\n", " errcheb[i] = yfit - y\n", " nrmcheb[i] = np.log10(norm(yfit - y, np.inf))\n", " concheb[i] = np.log10(cond(phi, 2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot Chebychev- and uniform node polynomial approximation errors" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1, ax = plt.subplots()\n", "ax.plot(x, y)\n", "ax.text(-0.8, 0.8, r'$y = \\frac{1}{1+25x^2}$', fontsize=18)\n", "ax.set(xticks=[], title=\"Runge's Function\", xlabel='', ylabel='y');" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 1.0, \"Runge's Function $11^{th}$-Degree\\nPolynomial Approximation Error.\"),\n", " Text(0.5, 0, 'x'),\n", " Text(0, 0.5, 'Error')]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2, ax = plt.subplots()\n", "ax.hlines(0, a, b, 'gray', '--')\n", "ax.plot(x, errcheb[4], label='Chebychev Nodes')\n", "ax.plot(x, errunif[4], label='Uniform Nodes')\n", "ax.legend(loc='upper center')\n", "ax.set(title=\"Runge's Function $11^{th}$-Degree\\nPolynomial Approximation Error.\", xlabel='x', ylabel='Error')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot approximation error per degree of approximation" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 1.0, \"Log10 Polynomial Approximation Error for Runge's Function\"),\n", " Text(0.5, 0, ''),\n", " Text(0, 0.5, 'Log10 Error'),\n", " []]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig3, ax = plt.subplots()\n", "ax.plot(n, nrmcheb, label='Chebychev Nodes')\n", "ax.plot(n, nrmunif, label='Uniform Nodes')\n", "ax.legend(loc='upper left')\n", "ax.set(title=\"Log10 Polynomial Approximation Error for Runge's Function\",xlabel='', ylabel='Log10 Error', xticks=[])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 1.0, 'Log10 Interpolation Matrix Condition Number'),\n", " Text(0.5, 0, 'Degree of Approximating Polynomial'),\n", " Text(0, 0.5, 'Log10 Condition Number')]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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e3h4zZ86ERCLJ9FrPnj0DABQrVizL+SV7m9fV//3f/1m8jpKn9Evu3gAkfbsUGRmJzp07o3HjxmLc1dUVn3/+ebbzzUzy63DmzJlwdXUV425ubvj+++8BACtWrEh13LvvvmuRX/HixcVvTl59PFmV3IXtyZMn+OGHH7J9fFa9+l62s7MTvwWoXLkyBgwYIO5XuXJlVKpUCSaTKc1uIFOmTBH7owNJ35q0atUKL168wN69ewEkdRG6dOkSAgICMHbsWIvXdefOndGiRQvcu3cPhw8fTnX+vn37iv/P6P1ABR+ffSpUjEYjLly4AJVKhSZNmqTa7urqijp16kCv1+Py5csQBAEnT56ERqNB/fr1U+2f/IfpbST/Ek6vwBD+674ivOWMIt7e3qliyYOwXi8G05I8z/GrBfSr56lWrRoiIiJw9+5di21Vq1ZN95weHh5pdqtp3rw5AIj9k8+cOQMAaN26dZrnSe5akLxfWho3bowFCxaI5wYAg8GAq1evilPpvcmsHtl9Tb3Kx8cnzf2BrD0nr2vbti0Ayy4mERERYteS9F5jAwcOxNKlSy0Kj5iYGJw6dUp83rNzbzJ6zl9XoUIFjB8/Hnq9HsOGDYPBYMDHH3+M0qVLZ+l4O7ukSbgy66qRljd9XZUoUSLVgFAnJycoFArxQ/Srx6U1eDUwMBCOjo7Zzjk9jx8/xuPHj1GhQoU0u/PUqFEDFSpUwJMnTyz6RwPWfx1KpVJ8/fXXUCgU2LBhQ4bvy7fx+u+05A/v1apVS/VaT57l5fVuW0qlUhyj8KqmTZsCSCq2gYx//wEpz3FaYyo8PDwyfiBUaHDKQCpUoqOjkZiYCHd3d/GP9euS/9i/ePEC0dHR0Ol0qFChQpotFFktDDKS3G84vUE+yX1d1Wr1W13HyckpVUwmkwHIWkH/9OlTAMiwTymQNCjp1UI6resmS2+WhuTZXpJbMZOnXHR3d09z/+TnIaOpGYGkbxU2btyI/fv34+7duwgPD4fZbM5Si2p6svuaelVaRVd2npPX1a9fH0WKFMHu3bvx8ccfQyKRiLOWtGvXLsNjw8PDsXbtWpw+fRr3798XZ59IvjfZySej5zwtgwcPxtatW3Hz5k1xYaisKl68OOLi4rI96A9489dVeo/Pzs7OYpBc8nGvfphJJpFI4O7ujhs3bmQ777Rk9liApMdz//59vHjxAmXKlBHj1n4dAkmty6NHj8bcuXPxySef4K+//nqj86RHoVCk+nYw+bXq7Oycav/03uPu7u5pbkt+zpJ/ByX//lu4cGGGaye8PkBWpVKxDzeJWHRToZL8BySjIiu5e4RCoRBbz9L7w/O2rc9AUqvZ9evXU/0hTJb8x/RtpwZ7m8ISSBqkJZFIMl1N7vV5gzP6OjW9IjX5OUjentnz9upzlp7w8HD06dMHYWFhcHZ2hre3N9q3b4+aNWuiatWqmQ6UTE92X1Ovetvn5HVyuRxBQUHYvHkzLl++DG9vb/z7778oWbIkateune5xx48fx6hRo6DX61GmTBnUrVsXVatWRa1atRAZGZnt1V6z+xV6WFiYuNDO1atXcfPmzSy3DtasWRP379/HpUuXMh20fODAATx8+BBNmzZF+fLl3/h1Za3nLb3X/5vIS6/DZCNGjMDOnTsREhKCefPmperCkxUmkynNuLXuXXL3vdcl38/k6yTfu9q1a2fY2OLl5WXxM7uT0KtYdFOh4uzsDLlcjqdPn8JoNKb5izv5q1cXFxcULVoUSqVSbBF9/RdocuvH26hSpQoOHjyIO3fuwNfX12JbTEwMXrx4AXd3d4v+o7ZQokQJPHr0CB9//DFcXFyscs70loxO7j+c/BV+iRIlACQ9N2kVj8nPWUb9eufMmYOwsDD06dMHn3zyicVzf//+/TfKH8j+ayqntWnTBps3b8bOnTtRpkwZnD59Gv369cuw+9Knn34KvV6PH374IdWHjz/++CNH8xUEAZ988gn0ej3atm2Lf//9Fx9//DF+//13sbU1I82bN8f27duxZ88ejBgxIsN9f/75Z5w/fx7x8fEYPXq0VV5XGUluLX38+HGa509uRbWGVx9Let728WSXnZ0dvv76a/Ts2RMrVqxIs4sbkFT0p1dcx8bG5mSK6X47ljy+I/l3UHJ3m5YtW2Lo0KE5mhMVXPwIRoWKXC6Hj48P9Hp9mnNfv3jxAmfPnoVGo0HNmjVhZ2eH2rVrQ6/Xp7kc+P79+986p+QBTK9PNZYcM5vNFoOcbCW5aEjrvhkMBnTt2hX9+/dHREREls959erVNLsFJN+L5H6SyQMAd+/eneZ5kvswBwQEpHutixcvAgCGDx+eqjBOnif6TVZazO5rKqc1bNgQjo6O2LNnD3bv3p1p15LIyEiEhoaiTJkyabb2p3VvrNkyum7dOpw+fRoBAQGYM2cOGjdujMuXL2P58uVZOr5Vq1YoXbo0Ll68iL///jvd/fbs2YPz589DoVCga9euAKzzuspIcsv7nj17Um27fv16pt2hssPd3R3u7u548OCBxdz7ya5du4bQ0FCUK1cuze4uOcXLywuDBg2CyWTCV199leY+Go0GBoMh1aJFjx49suo9SktERARu3ryZKp78mqhTpw6AlNdKWgMlAWD27Nno2rUrtm3blkOZUkHAopsKneSFPL788kuLFs64uDj873//Q2JiIrp27Sr2F0yeleCrr76yaJm6fv06Fi9e/Nb5BAYGomLFiti7d69F0RAaGorZs2dDIpFg4MCBb32d7FAqlTAYDBb9U5NbS2fNmmUxo4HRaMSXX36Jq1evwmQyZasVLTExEdOnT7cY3LR06VJcvHgRgYGB4oCw9u3bo3jx4ti1axc2bNhgcY5169Zh3759KFGiRIb9zZNbrF7/oHTs2DFxtcK0BlkByHQFw+y+pnKSQqFA8+bNcf/+fSxfvhzu7u6pvkF5lbOzM1QqFZ4+fWpRrJnNZqxYsUIcZPrqvcnqfclMWFgYfvzxR8jlcsyYMQMSiQSff/45lEol5s+fn2pQblpUKhWmT58OiUSCjz76COvWrUu1+MiePXswZcoUAMC4cePEotMar6uMtGjRAqVLl8a///6LrVu3ivGXL1/i008/zfJ50no/piX5d9VHH31kMX7g2bNnYhehN+ni8bYmTJiAChUqpNuyn9yVaM2aNWJMp9Phiy++yJX8pk+fbtGivn79ehw5cgQVKlQQB1TWr18fVatWxfHjx7Fo0SKLD6GHDx/G8uXLcf36dYuZnYhex+4lVGDs2LEj3VYIIGkBiCZNmqBt27bo168f1q5di44dOyIwMBBqtRqnT59GdHQ0AgIC8L///U88rmXLlujcuTO2bNmCtm3bom7dukhISMDJkydRqlQpREdHQy6Xv3HeMpkMX3/9NYYMGYLJkydj/fr1KFKkCE6cOAGtVovJkydnukCItZUvXx43b97Ee++9h8qVK2PWrFnw9fXFpEmT8OOPP+K9996Dl5cXSpQogStXruDJkydwdXXFd999l63rFClSBMeOHUPr1q3h4+MjttKVLFkSX375pbifRqPBTz/9hFGjRuHzzz/H+vXrUbFiRdy9exc3b96Ek5MTfvrppwy74CQvUDJjxgxs27YNJUqUwP3793Hjxg24urpCIpEgJiYGCQkJYp/X8uXL4+7duxg5ciSqVq2KmTNnpnnu7L6mclqbNm3w119/4f79+xg8eHCGLdMymQx9+/bFsmXL0KNHDwQGBkKlUuHq1at48uQJqlSpgtu3b1sUcS4uLnBycsKTJ0/Qr18/1KhRAx9//HG28/z000+h1WoxevRo8TVetmxZjBo1CnPnzsXHH3+M9evXZ9ovNigoCLNmzcK0adMwY8YMLFiwADVq1IC9vT1u3LiB+/fvQyKRYNiwYRbTfFrjdZURlUqF7777DiNGjMCUKVPw22+/wdXVFadOnYJcLoe7u3uWpqlM6/2YlkGDBuHs2bPYu3cvWrVqJc60cfLkSWi1WrRt2xaDBg16o8fyNlQqFb788st0FxMbPHgwzp8/jzlz5mD//v1wdXXF2bNnYWdnh/r16+P48eM5llupUqXw+PFjtGrVCnXq1MGTJ09w+fJlODo64scffxS7OEkkEvz4448YNGgQ5s6di40bN6J69ep48eKFuJDXZ599hgoVKuRYrpT/saWbCgyDwYAXL16k++/VVqJPP/0Us2fPhre3N86fP4+jR4+idOnSmD59OlatWpVqppBvvvkGH3/8MUqVKoUjR47gxo0b6Nevn1hkvm1/a39/f/z2229o3rw5bt26hZMnT6Jq1aqYPXt2pv1Uc8KXX36JatWq4ebNmzhy5AhevnwJIGlg1LJly9CgQQPcv38fhw4dgkqlwoABA7B58+Z0ZyNJT4kSJbB27VqUK1cOBw8eRFRUFHr37o3g4OBUf7zq1q2LTZs2oXPnzoiMjMTevXsRHx+P3r17Y/PmzeLXwOlp1qwZfv75Z/j5+eHOnTs4duwYgKRC5a+//kLDhg1hNBotuoh89NFHqF27Nh49eoSTJ09muDx7dl9TOalx48awt7cHgExnLQGS5jv+6KOPUL58eZw9exYXLlyAm5sbpk2bhi1btqB48eK4cOGC2BVIKpXiu+++Q4UKFXDhwoU36mYVHByMY8eOoXz58hg9erTFtmHDhqFixYo4f/68RetnRjp27IitW7eib9++cHFxwdmzZ7Fv3z7o9Xp06NABv/32Gz788MNUx73t6yozderUwe+//442bdrg/v37OHLkCHx9fbFu3bosz/KS3vvxdTKZDPPnz8f//d//oVKlSjhx4gTOnDmD6tWr47vvvsPcuXNtNrAvMDAQvXr1SnNbmzZtsHDhQvj6+uLGjRs4c+YMGjZsiI0bN6aamtHaihQpgvXr18PHxwdHjhzBgwcP0KZNG2zcuDHVoEhPT09s2bJFnHf74MGDePz4MZo2bYrVq1dbzMdNlBaJYI3pF4gKsNu3b8Pe3h4lS5ZM1WK4e/dujBs3DsOGDUvzDzqlLSwsDC1atEDVqlUz7IdLRERUULClmygTCxYsQLNmzSz6ZAJJ8zMnz9caFBRki9SIiIgon2CfbqJM9O/fH3v27MHUqVOxevVqlC1bFnFxcTh37hy0Wi2GDBmS7vLaRERERACLbqJM+fv7Y+PGjVi5ciVOnz6N27dvQ6PRwNvbG7179xaX3iYiIiJKD/t0ExERERHlMPbpJiIiIiLKYQW+e4nZbIbJxMZ8IiIiIspZcrks3W0Fvug2mQRER2ttnQYRERERFXCuro7pbmP3EiIiIiKiHJaniu7p06ejf//+Ge4TEhICLy8vzJ8/P5eyIiIiIiJ6O3mm6A4ODkZwcHCG+xiNRkybNg2JiYm5lBURERER0duzeZ9uk8mExYsXY8GCBZnu+8svv+DWrVu5kBURERERkfXYtKXbYDCgS5cumD9/Pjp16gQ3N7d0971x4wYWL16MMWPG5GKGRERERERvz+ZFd1xcHGbPno3vvvsOdnZpN7wndytp0KAB3n333VzOkoiIiIjo7di0e4mDgwN27dqVbrGdbOnSpXjw4AEWLVoEo9GYS9kREREREVmHTVu6pVJppgX3rVu3sHDhQkydOhUlS5bMpcyIiIiIiKwnz8xekhaTyYRp06bB398fPXv2tHU6RERERERvxOazl2Rk2bJlCAkJwfr16xEZGQkAiImJAQDodDpERkbC2dkZUmme/uxARERERIVcni66Dx8+jMTERPTo0SPVtmXLlmHZsmXYu3cvypQpY4PsiIiIiIiyJk8X3VOnThVbtpO9ePECH374ITp16oTOnTvD1dXVRtkRERERUV4h0UdBfXEZ7CJvIL7+NJicK9k6JQt5uuj28vJKFQsLCwMAlC1bFg0aNMjtlIiIiIgoD5Fon0Nz4ReoL6+GxKgFABiLVoW23hQbZ2YpTxfdRERERERpkcY9hvr8z1BfXQeJySDGE0v4Qu/V34aZpY1FdyGl1cZj69bN2LNnJ8LCHsJkMqFixUro0KEzOnbsbDE4tXv3jihZshQWLFhilWtb+3x57Xrp+frr/8M///xtEZNKpVCp1ChfvgK6du2Bdu06ZPu8eeXxvak3zT8rx6V1z+VyOYoVK46GDRtj6NBRcHJyeqO8M7Ns2S9YsWIpgoP/QqlS7jlyDSKiwkga8xCac4uguv4HJOYEMZ5YKhDxARORWLYJIJHYMMO05amie9++fZnuU6ZMGdy4cSMXsim4Hj68j6lTJ+HJk8do3bod2rfviISEBBw5chCzZn2DixfP49NPZ0CSB1+wBcGECZNQpIgzAEAQBMTHx2Hnzn/w9df/h+joaPTu3c+2CeayCRMmQ61W5fA1Uu65wWDA/ft3sXXrJly/fg2LFy+DTCaz+jWbNg1CmTJl4exc1OrnJiIqjGTRd6E5Ox/KG5sgEUxiPKFMY2jrTESiez0bZpe5PFV0U84zGAz46KPJePnyJX79dQ2qVKkqbuvdux9+/PE7bN4cjOrVa6JHj/dsmGnB1bhxs1Qtnx06dEK/fj2xcuVSdOvWEwqFwkbZ5b4mTZrl+DXSuudly5bHjz/OxIkTx9CwYWOrX7NKlaoW7y8iInozsoiQpGL79jZIBLMYN1RoCa3/eBhL+tswu6zjBNeFzObNwXj48AHGj/8gzYJg3LiJcHR0wtatf9ogu8JLqVShYcPGiI+Px717d22dTqFQu3YAAOD+fd5vIqK8yO7ZJTj9MwwuG1pCdWurWHAbKrdHVM9/EfPOynxTcANs6S509u7dBbVag1at2qa5XalUYcmSlShZslSqbbt2/YvVq5fj0aNQuLmVwnvv9UHnzt0t9rly5RJ+/fVnXL16BQDg5VULw4ePRo0aqWei+fvvLVi1agUiIp6jcuWqGDZsFOrWrQ8A+PnnBVi7diXWrPkDFSumTPljNpvRpUt7eHv74ssvZwIArl69ghUrluDKlcuQSqWoWdMLo0aNR+XKVaye/w8/fItt27Zgy5Z/UbRoSrcBvV6PDh1aIiioFT7++PM0721mJJKkz8Amk1GMXbx4HsuXL8W1a5cBANWr18SQISPg61s7zXNk9b51794RdevWh7e3L9asWYnHj8NQooQbevTojW7dLFd/zUoO3bt3RIMGjVC1qifWrVuNZ8/CUalSZUyaNAVubiUxZ84POHHiGOzt7dGuXQcMHz5aHDfwet9sQRCwdeuf2L79L9y/fx8mkxElS5ZC+/Yd0bfvQKt1e3r27CkAwN29tEV8//49+PPPP3Dr1g0YDAa4upZA8+YtMGzYaPEbiISEBCxePB9HjhzCixfPULSoCxo2bILhw0eLfcTT6tO9ZctGbN68EWFhoVAqVfDx8cPw4aNRqVJlqzwmIqKCwO7pWWjOzIXyQUq3Y0EihaHKu9D6j4epmKcNs3tzbOkuRARBwM2bN+DpWQ12dul/3ipbthzkcrlFLCTkGubMmYXmzVtg3LgPoFDI8cMPM3Ho0AFxn9OnT2DcuBGIj4/D8OGjMHDgEISHP8W4cSNw8eJ5i/PduHEds2fPQosWrTBixBjExcViypT3cfr0SQBA69ZJHwr27dttcdyFC+cQEfECLVu2AZBUEI4bNxz3799Dnz79MXDgENy7dxfjx4/EkyePrZ5/q1btYDKZcPDgXou8jh49BL1ej9at22X0FKTLbDbj/PmzUCgUqFAhqVg+cuQgxo8fifDwpxg4cCgGDhyK8PCnmDhxNI4cOZjmebJ63wDgxIljmDPnBzRv3gLjx0+CSqXG7Nnf4/jxI+I+2cnhyJFD+PXXn9GxYycMHjwcDx7cx/TpU/H++2MglUowbtz7qFSpMtasWYGdO3ekey+WLl2MH36YiQoVKmH8+A8wYsQYKBRK/PzzAvz77/bs3dj/xMbGIDo6GtHR0Xjx4jlOnz6JOXN+gIdHNTRq1FTcb9u2Lfj004/g4OCA0aPHY+zY9+HmVhLr16/B2rUrxf1mz/4e27ZtRsuWrTF58lQ0axaEv/7ahM8/n5ZuDrt2/YMffpiJqlU9MXHi//Dee31x+fJFTJgwEnFxcW/0uIiICgxBgPzRMRTZ0gtF/+wkFtyC1A66ar0Q1ecAYlsvyLcFN8CW7kIlOjoaJpMJxYoVz/axBoMBCxf+Ck/PagCAhg0bo0ePd3Hw4D40adIMZrMZs2Z9i+rVa2LBgiXiwLRu3Xph8OA+mDNnFlasWC+eT6fTYdasOahfvxEAoH37jnjvva5YvHg+6tSpi0qVqqBy5SrYv38Phg4dKR63Z89OODg4oH79hgCABQvmwMmpCJYtWyMOlKtfvxH69euBzZuDMWbMRKvm7+3tg5IlS2H//r0WreR79+5GsWLFxS4LGYmNjYFarQGQ1Kr95MkT/PHHety+fRO9evWBRqOB0WjETz99j+LFXbFs2WrY2zsAADp16oYBA3rhxx+/Q716DVN9eMrqfQOAZ8/CsWLFerGbUZMmzdC5czvs2vUv6tdvlO0cnj9/hpUrfxO/YYiNfYn169egRYtW+OKLbwHgv4G7QTh16kSaM7UYjUb8+efvaNGiNT755P/EeMeOndGxY2scOLD3jWZ4GTIk9eBUpVKJefN+sfiAuWHDWnh5eePbb38UW9S7dOmOnj074eDBfRgyZASApAL6nXfexciRY8Vj1WoNTp48Dq1WC41Gk+p6u3b9g4oVK2H69C/EWNWqHli4cB7u3r0Nb2/fbD8uIqJ8TxAgf3gA9mfnQf7kdEpYqoC+xnvQ+o2G2amsDRO0HhbdGbj6JAa/nngIbYIp851ziUYhw7B65VCzVPanOZPJkr7YMJvNmeyZWtmy5cSCFQBKliwFZ+eiiIyMAADcvHkDjx8/QufO3REbG2txbMOGjfH77+vx7Fk4SpRwAwBUrFhJLLgBwMmpCFq3boeNGzcgIuIFihUrjpYt2+KXXxbg7t3bqFSpCoxGIw4d2o8mTZpDoVAgKioSISHX0KtXX7HgBoBy5crj119Xw82tZI7k36pVW6xfvxpRUZEoWtQF8fFxOHHiGLp06W4x1WJ60ioAFQoFunfvhVGjxv+XTwiePQvH6NHjxWIXABwdHdG1a0/88ssChIRcg5eXd6pzZXbfXr1Pr/brL1asOFxcXF65J9nLoXTpMhZdesqWLQ8AaNKkuRhTq9UoWtQFEREv0rw3dnZ2+OuvXRZdbICkD4wajT10Ol2ax2Xms8++RNGiLgAAozERT58+xZ9//oFx44bj++9no06dpBHvq1ZtgE6ns+jCEh0dBUdHR2i1Kdd2dXXDvn27Ua1aDTRu3AyOjo4YPnw0hg8fnW4Orq5uOH36JJYvX4J27TqgVCl31K/fyOJ9QERUaAhmKO7thubsPMifXUwJ26mgq9kPOt+RMDuk7uqan7HozsBv5x7hyN1IW6eRir1Chq/eyX7R7ejoBLlcjqio7D+m5ILlVUqlEomJiQCAR4+SVgpdtGguFi2am+Y5Xi26y5evkGp76dJlAABPnjxBsWLF0apVWyxZshD79+9FpUpVcPr0SURHR4v90Z8+fQJBEFCmTOpPwB4e1Sx+tmb+rVq1xZo1K3Dw4D507twdhw8fREKCIctdS14tAGUyGRwcHFC+fEUolUpxn+SuMeXKlU91fIUKFQAkPf60iu7M7luytKayk8sVMJlMb5TD6/c4+duC1+NSqTTDD35yuRzHjx/B4cMH8fDhA4SFhSI2NgbAm31gBIBatXxSzV4SFNQSvXp1wZw5P2Dduo0Akor+kJBr2LNnJx4+vI+wsDDx/fLqOIf//e8jfPbZNHzzzReQyb6Cl5c3mjRphnfe6QQHBwekZfDgYbh69RKWL1+C5cuXoEKFSmjUqAk6duwsvvaJiAo8swnKOzugOTsPdhHXU8Jye+hrDYTWZwQETfa/kc8PWHRnoHft0ohPMOW5lu7e/m/2B1oikaBmzVq4cSMERqMx3X7dS5YswqNHYZgwYZLYFSWzwWtmc9I9GjZsFGrWrJXmPuXKVXg1m1Tbhf9GJSe3yJcsWRK1avlg377dGDp0JPbt2w0Xl2JiFw6TKWn/rLQuWzP/SpUqo3Llqti3bw86d+6Offt2o1y58hYt6RlJqwB8nSAIGeSatO31fvfJMrtvyTK7J9nNwRpzXQuCgBkzPsWePTvh7e2LWrW80alTV/j61saECaPe+vyvKlLEGbVrB+DQof2IiYmBk5OTOBDVw8MTNWt6o02b9vDy8sHs2d8jPPypeGxAQCD+/PNvHD16CMeOHcGpUycwf/5s/P77eixbttZikG2yEiXcsHLlbzh37gyOHDmIEyeOY+3alfj993X46acF8PPLPyPwiYiyzWyE8uYWaM7Oh130nZSwsgh03kOg8x4CQVWw1zVg0Z2BmqWcMLtL6lk38rOmTYNw4cI57Nu3O82WWYNBj7//3gqz2WTRZSMzyUWkRqNBnTp1LbZdv34VMTExFi25T58+SXWO0NBQAJazSbRq1RY//jgTDx/ex7Fjh9GqVTuxuCtZMqn7SFhYaKpzLVo0D46OTujff1CO5N+6dVvxw8np0ycxcODQLF0nq0qWTMrnwYP7aPzaFNIPHz4AAPFbg7RkdN9yK4c3cfHieezZsxODBg3DsGEpRbbRaERMzMtUM428reQPelKpFE+fPsHatSvRpk17fPrpDIv9IiIixP8nJCTg1q2bKFGiBFq2bIOWLdvAbDZjw4Z1WLRoLvbu3Ynu3VPPcX/nzm0ASQV7QEAgAODSpQuYMGEUNm7cwKKbiAomkwGqkI3QnFsIWcxDMWxWuUDrOwJ6rwEQlDmzMnBew9lLCpl33+3y3/Rsc3D37m2LbSaTCT/8MBORkRHo02dghjOcvK5atRooVqw4goN/h1arFePx8XGvfA2fUvTduHEdN2+GiD9HRkZg164d8PHxsyj2g4Jaws7ODsuW/YKXL19azL5RvLgrqlTxwJ49OxEfnzL7w+PHj7Bx4wZERaUUStbOP7nQmjv3RyQmJqY7BeObqlatOooVK47NmzdaPLb4+Dhs3hyMYsWKw9OzerrHZ3TfciuHN/Hy5UsAQIUKFS3i27ZtgV6vF7u+WENkZATOnj2DqlU94ODggJiY5GtXstjv+PEjCAt7KF47JiYGo0YNxpo1K8R9pFIpqlev8d//0/5w8+mnU/Hll59ZPAYPj2qQy+XpHkNElG8ZdVBdWg6XtY3geGCqWHCbNCUQ1/AzRAw4AZ3/uEJTcANs6S50lEolvvlmFiZNGodhwwaideu2qFatBmJiXmL//j24desmmjdviffe65ut89rZ2eGDDz7EZ59Nw5Ah/dCxYycoFEps27YZT58+wWeffWlRxDs5OWHSpPHo1asvZDIZNm8OhtFoxPjxkyzOW6SIMwID62Hv3t0oVao0vLwsu35MmDDpv8cyAB07doZEIsWff/4OBwdH9O07MMfyd3MrCR8fPxw7dhg1a9ayep/cV/MZOnQAOnbsBADYtm0rIiJe4Msvv8uwW01m9y03cngTtWp5w97eHvPn/4Tw8KdwcHDEuXNnsG/fbigUSosPRNlx+PAB8cOcIAh49iwcf/21GXq9DiNGJM1AUqFCJbi5lcSaNSuQkGBAiRJuuHbtKv75Z9t/144HABQvXhytW7fF5s0bodfr4eXljZcvX2LTpj/g4lIMQUGt0syhT5/+mDnzK0ycOBrNm7cEIODff3cgISEBXbp0T/MYIqJ8JyEe6qtroDn/C6S652LY5OAObe0x0Fd/D7BT2TBB22HRXQh5eFTDihXr8ccfv+H48aPYu3c3BMGMypWrYtq0z9C+fcc3WoCkWbMW+OmnBVi9ejlWrlwGqVSCSpUqY+bMn1Its123bgNUq1YDv/22Bi9fvkSNGjUxY8a3qFYtdctpq1ZtcezYEbRs2TrVttq1AzBv3s/iQiRKpRI+Pn4YM2ZitqdGzE7+QNL0dxcunEOrVtlvRc5OPitX/ooVK5bCzs4ONWp4Ydq0T+Hj45fp8Rndt9zKIbtcXIph1qy5WLx4PlauXAaFQo6yZcvj//7vG1y7dgUbN25AZGQEXFyKZeu88+b9JP5fJpPB0dEJ1avXwLRpn8Hfvw6ApBlkZs2aiwULZiM4eAMAAe7uZTBx4v9gNBoxd+4PCAm5jmrVqmPKlE/g7l4Ge/bsxJ49u6BWq+DvH4gRI8bA2dk5zRw6dOgMmcwOGzf+jiVLFsJsNsPTszp++GFulqaaJCLKyySGGKgvr4T64lJI9VFi3ORUHlr/cdB7dgNkigzOUPBJhIxGSxUAiYkmREe/WesY5Q179+7C559/jLVrg1N1O6D08b4REVFOk+ijoL74K9SXVkCaECPGjUWrQOs/HoaqnQBp4WnjdXV1THdb4bkLlC8lLQm+CTVqeLFwzAbeNyIiykkS7XNoLvwC9eXVkBhTGjeNxaojPmAiEiq1AzhexQKLbsqTjEYj/u//PkF4+FNcv34VX3/9va1Tyhd434iIKCdJ4x5Dff5nqK+ug8RkEOOJJXygDXgfCRVaAm/QRbUwYNFNeZKdnR3CwkLx5MkjDB48HE2bBtk6pXyB942IiHKCNOYhNOcWQXX9D0jMCWI8sVQg4gMmIrFsExbbmWCfbiIiIiJKkyz6LjRnF0B5409IhJQpTxPKNIY2YAISS9e3YXZ5D/t0ExEREVGWySKuJxXbt7dB8t9CYgBgKN8C2oAJMJbkgl7ZxaKbiIiIiAAAds8uQXNmLpT3dlrEDZXaQRswEUbXgrVSd25i0U1ERERUyNk9OZNUbD/cL8YEiRSGKu9C6z8epmKeNsyuYGDRTURERFQYCQLkj45Bc2YuFI+OpYSldtB7dIPOfyxMzpVsmGDBwqKbiIiIqDARBCge7ofmzDzIn55JCUsV0Nd4D1q/0TA7lbVhggUTi24iIiKiwkAwQ3FvV1Kx/fxSSthOBV3N/tD5jYTZvqQNEyzYWHQTERERFWRmE5R3/obmzDzYRd5ICcvtoa81CFqf4RA0xW2YYOHAopuIiIioIDIlQnlzMzTnFsAu+q4YNiuLQOc9FDrvwRBURW2YYOHCoruQ+frr/8M///wNqVSKrVt3omjRtN9sAwf2xp07t9CuXQd88sn/5W6SeVj37h1RsmQpLFiwxOrHJT83r5LL5ShWrDgaNmyMoUNHwcnJ6Y3yzsyyZb9gxYqlCA7+C6VKuefINYiIKJeYDFBdD4bm3ELIYkPFsFnlAq3vCOhrDYSgSH8RF8oZLLoLKbPZjGPHDuOdd95Nte3x40e4c+eWDbLK+yZMmAy1WpXD15iEIkWcAQAGgwH379/F1q2bcP36NSxevAwymczq12zaNAhlypSFszNbPIiI8q1EHdTX1kF9/mfI4p+KYZPGDbrao6Gr0QeQa2yYYOHGoruQKlWqNI4cOZhm0X3o0H44OxdFdHSUDTLL25o0aZbj12jcuFmq1uayZcvjxx9n4sSJY2jYsLHVr1mlSlVUqVLV6uclIqKcJ0mIg+rKamguLIFU90KMmxxKQ+s/FvpqPQG7nG0wosxJbZ3Aq6ZPn47+/funih8+fBh9+vSBj48P/Pz8MGjQIFy4cCH3EyxAGjdugtOnT8Jg0KfadujQATRq1MQGWVF6atcOAADcv383kz2JiKiwkOijoTk9Gy6r68Lh+DdiwW0sUgExQT8ist8R6L0GsODOI/JMS3dwcDCCg4MRGBhoET916hSGDx+OqlWr4oMPPoDRaMT69evRr18/rF+/Ht7e3jbKOH9r3LgZ/vjjN5w+fcqiwI6KisSVK5fQv/8g/P331lTHXbx4HsuXL8W1a5cBANWr18SQISPg61tb3Kd7946oW7c+vL19sWbNSjx+HIYSJdzQo0dvdOvWM0+cr0GDRqha1RPr1q3Gs2fhqFSpMiZNmgI3t5KYM+cHnDhxDPb29mjXrgOGDx8NqVQqHvtq32xBELB165/Yvv0v3L9/HyaTESVLlkL79h3Rt+9ASCSS7D85aXj2LOlrQnf30hbx/fv34M8//8CtWzdgMBjg6loCzZu3wLBho6FQKAAACQkJWLx4Po4cOYQXL56haFEXNGzYBMOHjxb7iKfVp3vLlo3YvHkjwsJCoVSq4OPjh+HDR6NSpcpWeUxERPRmJLoIqC/+CvXllZAmxIpxo4sntP7jYajSAZDmmRKP/mPzZ8RkMmHx4sVYsGBBmtu/+eYblCpVCn/88QfUajUAoHPnzmjfvj1mz56NFStW5Ga6BYa3ty+cnZ1x5MhBi6L78OGDUKnU8PcPTHXMkSMH8fHHH8LdvQwGDhwKANi2bQsmThyNr7/+Ho0aNRX3PXHiGPbt24Pu3XvBxaUYtm7dhNmzv4e7uzvq129k8/MdOXIIBw/uR8+evWE2C1i9ejmmT58Ke3t7VKpUGePGvY+DB/dhzZoVKFeuPNq165DmfVy6dDFWr16Odu06oGPHLtBq4/Hvvzvw888LUKxY8XSPy0hsbAzU6qQ+d0ZjIu7du4s5c36Ah0c1i8ewbdsWfPfdV2jUqAlGjx6PxEQjDh7ch/Xr10ClUmPIkBEAgNmzv8fu3f+iR4/eKF26NO7evYM///wDYWEPMXv2wjRz2LXrH/zww0y0bfsOunXrhejoKPzxx2+YMGEkNmzYAgcHh2w/LiIiejvS+HCoz/8C9dU1kBh1YjyxuBe0AROQUKktIMlTnRjoFTYtug0GA3r06IEbN26gc+fOOH78uMX2ly9fIiQkBIMHDxYLbgAoXrw46tSpg6NHj+Z2ygWGTCZDgwaNcfToYZjNZrEl99Ch/ahfv6HYSprMaDTip5++R/Hirli2bDXs7ZOKrk6dumHAgF748cfvUK9eQ9jZJb2knj0Lx4oV68V+wk2aNEPnzu2wa9e/qF+/kc3P9/z5M6xc+RsqV64CAIiNfYn169egRYtW+OKLbwEArVu3Q/v2QTh16kSaxbPRaMSff/6OFi1aW8zw0rFjZ3Ts2BoHDux9o6J7yJB+qWJKpRLz5v0CuVwuxjZsWAsvL298++2PYot6ly7d0bNnJxw8uE8sunft+gfvvPMuRo4cKx6rVmtw8uRxaLVaaDSpB9Xs2vUPKlashOnTvxBjVat6YOHCebh79za8vX2z/biIiOjNSGMfQXN+EVTXNkBiMojxRLfa0AZMREL5IMBK36xSzrF50R0XF4fZs2ejffv2CAoKstju4OCAf//916LgThYVFZUjszi8yi78PDRn5kKSEJej18kOQeEAbcBEGN383vpcjRs3xY4d23D16mXUquWD+Pg4nD17GtOnz0i1782bIXj2LByjR48XC1oAcHR0RNeuPfHLLwsQEnINXl5J3X3KlStvMTCvWLHicHFxQWRkRJ44X+nSZcSCG0gaqAgATZo0F2NqtRpFi7ogIiJlUMqr7Ozs8Ndfu2AyGS3i0dHR0GjsodPp0jwuM5999iWKFnUBkNTS/fTpU/z55x8YN244vv9+NurUqQcAWLVqA3Q6nUUXlujoKDg6OkKrTbm2q6sb9u3bjWrVaqBx42ZwdHTE8OGjMXz46HRzcHV1w+nTJ7F8+RK0a9cBpUolfaOQ/K0CERHlPGn0PWjOLYTqxkZIzCl/axJK14fWfyISyzRksZ2P2LTodnBwwK5du8TWx9fJZDJUqFAhVTwkJATnzp1Do0Y5WwCoL/4K5f09OXqNNyHIHRDbOu3uONkRGFgPKpUKR44cQq1aPjh+/CgkEinq12+Yat8nTx4DSCp+X5f8HD19+kQsatOaek4uV8BkMuWJ8yUXtcmSP8C9HpdKpTCbzanOmZKDHMePH8Hhwwfx8OEDhIWFIjY2BgAyPC4jtWr5pJq9JCioJXr16oI5c37AunUbASQV/SEh17Bnz048fHgfYWFhiIqKBACULFlKPPZ///sIn302Dd988wVksq/g5eWNJk2a4Z13OqXbTWTw4GG4evUSli9fguXLl6BChUpo1KgJOnbsjNKly7zR4yIioqyRRd6E5uwCKG9tgURI+VuSUK4Z4v0nwOieugso5X02LbqlUqnYrSGr4uPjMXXqVADAiBEjciItkc5nGCSJ8XmupVvnM8wq51IqVahTpy6OHDmI0aPH49ChA6hTJzDN7gaCIKR7HrM5adurXR8yG0Bo6/NZ41sSQRAwY8an2LNnJ7y9fVGrljc6deoKX9/amDBh1Fuf/1VFijijdu0AHDq0HzExMXBycsLPPy/A2rUr4eHhiZo1vdGmTXt4eflg9uzvER6eMj9rQEAg/vzzbxw9egjHjh3BqVMnMH/+bPz++3osW7Y2zQWSSpRww8qVv+HcuTM4cuQgTpw4jrVrV+L339fhp58WwM/P36qPj4iIANnzq7A/Ow+KOzsgQcrfNUPFNtAGTICxhI8Ns6O3ZfOBlNmh0+kwevRohISEYOTIkalmOrE2o5sfYt5ZmaPXsLXGjZvhm2++wN27t3HixDFMnDg5zf1KlkxqeX3w4D4avzZN9MOHDwAkFWpZldfPlxUXL57Hnj07MWjQMAwbllJkG41GxMS8TDXTyNsS/mvtkEqlePr0CdauXYk2bdrj008tuwNFRESI/09ISMCtWzdRokQJtGzZBi1btoHZbMaGDeuwaNFc7N27E927v5fqWnfu3AaQVLAHBCS9zy5duoAJE0Zh48YNLLqJiKzI7uk5aM7Os/h2XYAEhiodofUfB1PxGjbMjqwl3wxxjYmJwZAhQ3Dy5El069YNH3zwga1TKhAaNmwMmUyGBQvmwmDQpzs/d7Vq1VGsWHFs3rwR8fEpLf/x8XHYvDkYxYoVh6dn9SxfN6+fLytevnwJAKhQoaJFfNu2LdDr9WLXF2uIjIzA2bNnULWqBxwcHBATk3ztShb7HT9+BGFhD8Vrx8TEYNSowVizJmWWH6lUiurVa/z3/7Rb/D/9dCq+/PIzi8fg4VENcrk83WOIiCh75I9PoMhffVD0z3fFgluQyKD37I6oPvsR22YRC+4CJF+0dEdERGDo0KG4fv06evXqhS+++MJq8x8XdkWKOKNWLR+cOnUctWsHiMuPv87Ozg4ffPAhPvtsGoYOHYCOHTsBALZt24qIiBf48svvstVVKK+fLytq1fKGvb095s//CeHhT+Hg4Ihz585g377dUCiU0Gq1b3Tew4cPiM+DIAh49iwcf/21GXq9DiNGJM1AUqFCJbi5lcSaNSuQkGBAiRJuuHbtKv75Z9t/144HkDTTT+vWbbF580bo9Xp4eXnj5cuX2LTpD7i4FENQUKs0c+jTpz9mzvwKEyeORvPmLQEI+PffHUhISECXLt3f6HEREREAQYA89BA0Z+ZB8eRkSlgqh75aT2hrj4G5SOrxSZT/5fmiOy4uTiy4Bw0ahGnTptk6pQKnSZNmuHDhHJo2bZ7hfs2atcBPPy3AypW/YsWKpbCzs0ONGl6YNu1T+PhkfzaVvH6+zLi4FMOsWXOxePF8rFy5DAqFHGXLlsf//d83uHbtCjZu3IDIyAi4uBTL1nnnzftJ/L9MJoOjoxOqV6+BadM+g79/HQCAQqHArFlzsWDBbAQHbwAgwN29DCZO/B+MRiPmzv0BISHXUa1adUyZ8gnc3ctgz56d2LNnF9RqFfz9AzFixBg4OzunmUOHDp0hk9lh48bfsWTJQpjNZnh6VscPP8wVV8ckIqJsEAQo7u+G5sxcyJ9dTAnLlNDV6AOd32iYHd0zOAHldxIhoxFouSwoKAilS5fGmjVrxNiUKVOwdetWDBgwAJ988km2z5mYaEJ09Ju1OBIRERG9FbMJirv/wP7MXNhFXBfDgp0GuloDoPUZAcG+hA0TJGtydXVMd1uebum+c+cOtm7dCkdHR1SvXh1bt6ZelrxTp042yIyIiIgoA2YjlLe2QHN2AeyibqeEFU7QeQ+GzmcYBFXq2aOo4MrTRfepU6cAALGxsel2K2HRTURERHmGyQBVyEZozi2CLOaBGDarikLnMwK6WgMhKJ1smCDZSp7qXpIT2L2EiIiIcpxRB9W136A5vxiyuCdi2KQpAZ3fKOhq9AUU9jZMkHJDvu1eQkRERJSXSRLioLqyBpoLSyDVPRfjJgd3aGuPgb56L8BObcMMKa9g0U1ERESUTRLDS6gvrYD64q+QGqLFuMmpPLT+46H37ArIFLZLkPIcFt1EREREWSTRRUB98VeoL6+ENCFWjBuLVoXWfzwMVd8FpCyvKLUsvyoWLFiABg0aoHbt2jmZDxEREVGeI40Ph/r8L1BfXQOJUSfGE4vXhDZgAhIqtQMk+Wahb7KBLBfdv/76KzQaDYtuIiIiKjSksY+gOb8IqmsbIDEZxHiimx+0Ae8joXwQwFWyKQuyXHQXK1YMsbGxme9IRERElM9Jo+9Bc24hVDc2QmI2ivGE0vWh9Z+IxDINWWxTtmS56J46dSo+/vhjhIeHo1GjRnBxcYFMJku1X506dayaIBEREVFukUXehObsfChvbYVEMIvxhHLNEO8/AUb3QBtmR/lZlufprlatWspBaXyyEwQBEokE169fT7XNljhPNxEREWXG7vkVaM7Og+LOP5AgpTQyVGwDbcAEGEv42DA7yi+sMk/3t99+a5VkiIiIiPIKu6dnoTkzD8oHe8WYAAkMVd+F1n8cTMWq2zA7Kki4IiUREREVLoIA+ePj0JyZB0XYkZSwRAaDZ1doa4+DqWhlGyZI+ZVVV6Tct28fDhw4gMePH2PSpEnQaDQ4duwYunXrBqVS+VaJEhEREeUYQYA89CDsz8yD/MmplLBUAX31ntDWHgOzUzkbJkgFWZZbuhMTEzFhwgTs378fMpkMZrMZy5cvR1RUFCZNmgQvLy8sW7YMRYoUyemcs4Ut3URERIWcYIbi3m5ozs6D/NnFlLCdCroafaHzGwWzQykbJkgFRUYt3VmexX3x4sU4ePAgvvzyS+zduxfJtXrr1q3xySefICQkBAsXLnz7bImIiIiswWyC8tZfKPp7axT5Z6hYcJvl9tDWHoOI/scR3/gLFtyUK7LcveSvv/5Ct27d0KNHD0RFRaWcwM4O/fv3x71797B37158/PHHOZIoERERUZaYEqG8tQWas/NhF31XDJuVRaDzHgKd9xAIqqI2TJAKoywX3U+fPoWXl1e62z09PbFx40arJEVERESUbSYDVNeDoTm3ELLYUDFsVrlA6zsC+loDISjS//qfKCdlueh2c3PD3bt3091+6dIluLq6WiUpIiIioixL1EF9bR3U53+GLP6pGDZp3KCrPRq6Gn0AucaGCRJlo+ju0KEDVq1ahaZNm6J69aQ5K5MXyVm3bh02b96MwYMH50yWRERERK+RJMRCdWU1NBeWQKqLEOMmxzLQ1h4LfbUegJ3KhhkSpcjy7CUJCQkYMWIETp48CRcXF0RGRqJ8+fKIjo5GdHQ0atWqhVWrVkGjyVufJDl7CRERUcEi0UdBfWkF1JeWQWp4KcaNRSpA6z8eBo+ugExuwwypsMpo9pJsLY5jNpuxZcsW7Nq1C6GhoTCZTChdujSCgoLQo0cPKBQKqyRsTSy6iYiICgaJ9gU0F5dAdXk1pIlxYtzo4gltwAQYKncApDIbZkiFndWK7vyIRTcREVH+Jo17AvX5n6G+tg4So16MJ7p6QxswAQkVWwOSLM+CTJRjrLoi5YEDB3DgwAE8evQIMpkM5cqVQ8uWLREYGPhWSRIRERG9ShrzEJpzi6C6/gck5gQxnliqDuL9JyCxXDPgv/FlRHldllu64+LiMHbsWJw6dQqCIKBIkSIwm82IjY2FRCJB+/bt8f3330Mmy1tf67Clm4iIKH+RRd2B5twCKG9sgkQwifGEMo2hDZiARPd6LLYpT7JKS/ecOXNw6tQpjB07FgMGDICTkxMAIDIyEsuWLcOyZctQoUIFjB8//u0zJiIiokJH9uIaNGcXQHl7GyRIaRM0VGgJrf94GEv62zA7oreT5Zbuhg0bokWLFpgxY0aa26dOnYqTJ0/iwIED1szvrbGlm4iIKG+zCz8PzZn5UN7fJcYESJBQuX1Sse2a/uJ8RHmJVVq64+Pj4enpme52f39/7Ny5M3uZERERUaElf3wSmjPzoAg9KMYEiRSGqp2h9R8Hk4uHDbMjsq4sF90NGzbEP//8g969e0MqTT1C+ODBgwgICLBqckRERFTACALkYYehOTMXiscnU8JSOfTVekBbewzMRSrYLj+iHJJu95LTp09b/BweHo5PP/0UNWrUwKBBg1CxYkVIJBKEhYVh48aNOHPmDH766SfUr18/VxLPKnYvISIiygMEAYr7u6E5MxfyZxdTwjIldDX6QOc3GmZHdxsmSPT23mie7mrVqonLvCdL3jWj+PXr198qWWtj0U1ERGRDZhOUd3ZAc3Ye7CJSagTBTgNdrYHQ+o6AoHG1YYJE1vNGfbq//fbbHEmGiIiICgFTIpS3tkJzdj7sou+IYbPCCTrvIdD5DIWgKmrDBIlyV55akXL69Ol48OAB1qxZYxEPDQ3Fd999h1OnTgEAmjVrho8++gguLi6ZnpMt3URERLnIZIDqejA05xZCFhsqhs0qF2h9R0DvNQCC0smGCRLlHKutSBkXF4fLly/j2bNnSK9W79y5c7aSSxYcHIzg4OBUK1tGRUVh4MCBSEhIwLBhw2AymbBs2TLcuHEDwcHBUCgUb3Q9IiIisqJEHdTX1kF9/mfI4p+KYZPGDTq/UdDV7AvINTZMkMi2slx0nzhxAhMnTkRMTEy6BbdEIsl20W0ymbB48WIsWLAgze0rV67E06dPsW3bNlSuXBkA4OPjg8GDB2PLli3o2bNntq5HRERE1iNJiIXqympoLiyBVBchxk2OZaCtPQb6aj0BO5UNMyTKG7JcdM+cORNyuRwzZsxAmTJlrLLcu8FgQI8ePXDjxg107twZx48fT7XP9u3bERgYKBbcANCgQQNUrFgR27dvZ9FNRERkAxJ9FNSXVkB9aRmkhpdi3FikIrT+42Hw6ALI5DbMkChvyXLRff/+fUyePBk9evSw2sUNBgPi4uIwe/ZstG/fHkFBQRbbX758idDQULRp0ybVsTVr1sxzq18SEREVdBLtC2guLoHq8mpIE+PEuNHFE9qACTBU7gBI375hjqigyXLRXaFCBcTGxlr14g4ODti1axfs7NJOIzw8HADg5uaWapurqyvi4uIQGxsLR8f0O60TERHR25PGPYH6/M9QX1sHiVEvxhNdvaENmICEiq0BSerF84goSZaL7g8++ABTp06Fj48PGjZsaJWLS6XSNFe3TBYfHw8AUKvVqbYplUoAgFarZdFNRESUQ6QxD6E5twiq639AYk4Q44ml6iDefwISyzUDXlu/g4hSy3LRHRgYiBo1amDYsGFQqVQoWrRoqkVyJBIJ9uzZY7XkzGZzpvtkVLQTERHRm5FF3YHm3AIob2yCRDCJ8YQyjaENmIBE93ostomyIctF94wZM3Ds2DEUL14c5cqVs8pAyszY29sDSOr7/brkWPI+RERE9PZkL65Bc3Y+lLf/hgQps5UZKrSE1n88jCX9bZgdUf6V5aJ79+7deOedd/DDDz+kauHOKe7u7gCA58+fp9r27NkzODk5QaPhnJ9ERERvyy78PDRn5kN5f5cYEyBBQuX2iPefAJNrTRtmR5T/ZbnolkqlqFu3bq4V3ADg5OSEMmXK4OrVq6m2Xbt2DV5eXrmWCxERUUEkf3wCmjPzoAg9JMYEiQwGj87Q1h4Hk0tVG2ZHVHBkuUN0q1atsHPnzpzMJU2tW7fG8ePHcefOHTF27Ngx3Lt3D+3bt8/1fIiIiPI9QYD84QE4b+oK583dxYJbkMqhq9EXkX0PIbblXBbcRFYkEdJbXvI1x48fx0cffYSSJUsiKCgIxYoVS3OqvzddBh4AgoKCULp0aaxZs0aMRUZGokOHDpDJZBgyZAgMBgN+/fVXlCtXDhs2bMh0GfjERBOio7VvnBMREVGBIZihuLcLmjPzIH9+KSUsU0JXsy90fqNgdnC3YYJE+Zura/oz6mW56K5WrVqm+0gkEly/fj3rmb0mraIbAO7evYtvv/0WZ86cgUqlQtOmTTFlyhS4uLhkek4W3UREVOiZTVDe3gbN2fmwi7yREpbbQ19rILQ+wyFoXG2YIFHBYJWi+9SpU1m6WGBgYNayyiUsuomIqNAyJUJ5cxM0ZxfA7uU9MWxWFoHOewh03kMgqIraMEGigsUqRXd+xaKbiIgKHaMequu/Q3NuEWRxj8SwWV0MWt8R0HsNgKDgwnJE1pZR0Z3l2Uu2bNmSpf3epk83ERERvYWEeKivroX6wi+QaZ+JYZN9Sej8RkNXow8gT73KMxHlvGz16ZZIJEhr91enEXybPt05gS3dRERU0EkML6G+vArqi0sh1UeJcZNTOWhrj4G+Wg9AprRhhkSFg1VaulevXp0qZjKZ8OLFC2zfvh0PHjzA4sWL3yxDIiIiyjaJLhLqi79CfXkFpAmxYtxYtAq0/uNgqNoZkGb5Tz0R5SCr9ekePnw4ihcvjm+//dYap7MatnQTEVFBI40Ph/r8L1BfXQOJUSfGjcVqID5gAhIqtQOkMhtmSFQ4WaWlOzOtWrXCjz/+aK3TERER0WukMWHQnF8M1fUNkJgMYjzRzQ/agIlIKN8CyMWVo4ko66xWdN+7dw9Go9FapyMiIqL/yKLvQn12IVQ3/4TEnPK3NqF0fWj9JyKxTEMW20R53FvPXpKQkIDr16/jjz/+QIsWLayVFxERUaEni7gOzdkFUN7eBolgFuOGcs2hDZgAY6k6NsyOiLLDKrOXAEDNmjUxf/58uLvnreVj2aebiIjyG7vwC9CcnQ/lvZ0WcUOlttD6T4CxhLeNMiOijOToipRSqRSurq4oX778m2WXw1h0ExFRfiF/fBKas/OgeHhQjAkSKQxV3oXWfxxMxarZMDsiygxXpGTRTUREeZUgQB52GJozc6F4fDIlLLWD3rM7tLXHwuxc0YYJElFWvdHsJY8fP36ji+W17iVERER5kiBAcX83NGfmQf7sQkpYpoS+xnvQ+o2B2bG07fIjIqtKt+gOCgqyWGkyKyQSCa5du/bWSRERERVYZhOUd3ZAc3Ye7CJSVnEW7DTQefWHzncEzPZuNkyQiHJCukX32LFjs1R0X758GQcPJvU9K1WqlPUyIyIiKkhMiVDe2gLN2QWwi74jhs0KJ+i8B0PnPRSC2sWGCRJRTnrjPt1xcXH46aefsGHDBkilUgwePBhjx46FSqWydo5vhX26iYjIpox6qEKCoTm3CLLYUDFsVhWFzmcEdLUGQlA62TBBIrIWq69IuX37dnz77bd48eIFAgIC8H//93+oUqXKGydIRERU4CRqob66Furzv0CmDRfDJo0bdH6joKvZF5BrbJggEeWmbBXdDx48wBdffIHjx4/D2dkZ33zzDbp27ZpTuREREeU7EkMM1JdXQn3xV0j1kWLc5FgG2tpjoa/WA7DLW98KE1HOy1LRnZCQgCVLlmDp0qVISEhAt27d8OGHH6JIkSI5nR8REVG+INFFQn3xV6gvr4Q0IUaMG50rQes/HoaqnQGZ3HYJEpFNZVp0Hzt2DF988QUePHgADw8PfPHFF/Dz88uN3IiIiPI8afxTqM8vgfrqGkiMOjFuLFYdWv8JMFRuD0hlNsyQiPKCdIvuFy9e4Ntvv8WOHTugVqsxdepUDBw4EFKpNDfzIyIiypOkMaHQnF8M1bUNkJgTxHiimx+0/hOQUKElkM2pd4mo4Ep39pI6deogLi4OAFCvXj2ULFky85NJJPjmm2+sm+Fb4uwlRERkTbKoO9CcWwjlzU2QmI1iPKF0fWj9JyCxTCMW20SF1BstA1+tWrVsX0gikeD69euZ75iLWHQTEZE1yF5cg+bsfChv/w0JUv50Gso1hzZgAoyl6tgwOyLKC96o6C4oWHQTEdHbsHt6LqnYvr/bIm6o1A5a//EwlvC2UWZElNdYfZ5uIiKiAk0QIH98Apoz86AIO5wSlkhhqNoJ2trjYCrmacMEiSi/YdFNRESUTBCgeLgfmrPzIX9yOiUslUNfrTu0fmNgdq5owwSJKL9i0U1ERCSYobj7b1Kx/fxySlimhK5mX+h8R8Hs6G7DBIkov2PRTUREhZfZCOWtv6A5uwB2UTdTwnJ76GsNhNZnOASNqw0TJKKCgkU3EREVPqYEqG5shObsQshiHohhs7IIdN5DofMeDEFV1IYJElFBw6KbiIgKD6MOqmu/QXN+MWRxT8SwWV0cWt8R0HsNgKBwsGGCRFRQZavoNpvNOHnyJJ4/fw6z2ZzmPp07d7ZGXqlcuXIFP/74I86fPw+pVIrAwEBMmTIFlSpVypHrERFRwSFJiIPqympoLiyBVPdCjJscSkHrNxr6Gr0BO7UNMySigi7L83SHhIRg5MiRePbsGdI7JKcWx7l79y66desGtVqNQYMGAQBWrFgBQRCwdetWuLm5pXss5+kmIiq8JPooqC8th/rSckgNL8W4yak8tP5joffsDsgUNsyQiAoSq8zTPXPmTMTExGDSpEmoXr06FIrc+yW1atUqaLVarFu3DjVq1ACQtDR9jx49sHLlSkydOjXXciEiorxPon0OzYUlUF1ZDWlivBg3FvWANmA8DFU6AlL2sCSi3JPl3zgXLlzA8OHDMXz48JzMJ01hYWEoWrSoWHADgLe3N5ydnXHz5s0MjiQiosJEGvsY6vOLob62HhKTQYwnunpDGzAeCRXbABKpDTMkosIqy0W3RqOBs7NzDqaSvvLly+PYsWOIjIyEi4sLACA6OhqxsbEoUaKETXIiIqK8Q/ryPjTnFkIVshESc6IYTywViHj/8Ugs1wyQSGyXIBEVeln+uN+mTRts27Yt3f7cOWnYsGEoWbIkJk2ahJCQENy4cQOTJ0+GXC5H//79cz0fIiLKG2QRN+C4ezxc1jWB+tpvYsGdULYJortsRHTXTUgs35wFNxHZXJYHUh47dgzTp0+Hq6srWrVqBRcXF0ilqWv2nJq9ZMOGDfjyyy9hNBoBADKZDPPmzUPLli0zPI4DKYmICh67Z5egOTsPyrv/WsQNFVpDGzAeRjc/G2VGRIVZRgMps1x0V6tWLdN9cmr2kjlz5mDx4sUIDAxEz549YTKZsGHDBly5cgXz5s1DUFBQusey6CYiKjjkj09Cc3YeFA8PijEBEhiqdITWfxxMxWtkcDQRUc6yStF96tSpLF0sMDAwa1llUUxMDBo2bAgPDw/88ccfkMlkAIDExER0794dL168wP79+9OdTYVFNxFRPicIkIcehObMfCienEwJS+2g9+gGnf9YmJy5ZgMR2Z5Vpgy0djGdVffv30dCQgI6dOggFtwAIJfL0bFjR8yaNQt3797NUks8ERHlI4IZinu7oDk7H/JnF1PCMiX0Nd6D1nc0zE5lbJggEVHWZWuS0ri4OPzyyy/Ys2cPHj9+DLlcjlKlSqF58+YYMWIEHBysv3Rucgu2yWRKtS15Vcz0VsckIqJ8yGyE8vY2aM4ugF3kDTEs2GmgqzUAWp8REOw5cxUR5S9Z7l4SFRWFPn364N69e6hYsSIqV64Ms9mMe/fu4d69eyhfvjyCg4Ph5ORk1QRNJhOaNWsGJycnbNq0CUqlEgBgMBjQpUsXREZG4vDhw5DL5Wkez+4lRET5hCkBqhsboTm7ELKYB2LYrCwCXa3B0PkMhaAqasMEiYgyZpXuJXPnzkVoaCjmzJmDtm3bWmzbs2cPPvjgA8yfPx+ffPLJm2eaBplMhs8++wwTJkxA9+7d0b17d5jNZvz555+4e/cuvv/++3QLbiIiygcSdVBfWw/1hZ8hi3sihs3q4tD6DofeawAERfp/yIiI8oMst3Q3btwYbdu2Tbeo/vrrr7Fnzx7s37/fqgkmO378OBYtWoTLly8DAGrUqIFRo0ahSZMmGR7Hlm4iorxJkhAL1eVV0FxcCqkuQoybHEpB6zca+uq9AbnahhkSEWWPVVq6o6OjUalS+qPDK1asiIiIiHS3v6369eujfv36OXZ+IiLKHRJ9FNQXl0F9eQWkhpdi3FikAnS1x0Lv2Q2QpT0jFRFRfpXlort06dI4ceIEevfuneb2EydOoFSpUlZLjIiIChZpfDjUF5ZAfWUNJMaUbyCNLp7Q+o+HoUoHQJqt8f1ERPlGlpeB7969O3bu3ImZM2ciMjJSjEdGRuLbb7/F7t270aVLlxxJkoiI8i9pTBgcDn4ClzUNoLnwi1hwJ5bwwct2yxD13m4YPDqz4CaiAi3LfbrNZjPef/997Nq1CxKJRJylJCYmBoIgoEWLFpg3b57FXNp5Aft0ExHZhizqDjTnFkJ5cxMkZqMYT3CvC63/BCSWbQJIJDbMkIjIuqyyImWyQ4cOYd++fXj06BEEQUDp0qURFBSEpk2bvnWiOYFFNxFR7pK9uAbN2flQ3v4bEqT8iUko1wzx/hNgdLfNYmtERDnNqkV3fsOim4god9g9PZdUbN/fbRE3VGoHrf94GEt42ygzIqLc8Uazl2zZsgUBAQEoU6aM+HNWdO7cOVvJERFRPiYIkD86Bs3Z+VCEHUkJS2QwVO0Erf84mFw8bJggEVHekG5Ld7Vq1TBr1ix07NhR/FkikSCjhnGJRILr16/nTKZviC3dREQ5QBCgeLAPmrPzIH96NiUslUNfrSe0tcfAXKS8DRMkIsp9b9TSvXr1alSuXNniZyIiKuTMJiju/gPN2fmQv7gqhgU7FXQ1+kLnNxJmB3cbJkhElDelW3QHBloOdClTpgxcXFygUqnS3D8mJgY3btywbnZERJQ3mBKhvLUFmnMLYRd1WwybFY7Qew2E1mcYBE1xGyZIRJS3ZXme7hYtWmDPnj3pbt+1axdGjBhhlaSIiCiPMOqhurIGLuuawGnvB2LBbVYVRXzdDxE54ATi63/EgpuIKBPptnQ/evQImzdvFn8WBAG7du3C/fv3U+0rCAL27dsHpVKZI0kSEVEuS9RCfXUt1Od/gUwbLoZNGjfo/EZCV6MvoLC3YYJERPlLugMpBUFAz549cfny5aQdMxlEKZVK8cEHH2D48OE5k+kb4kBKIqKskxheQn15JdQXf4VUHyXGTY5loa09BvpqPQC7tLsZEhEVdm88T3dcXBxevnwJQRDQsmVLfPzxx2jRokWq/WQyGZydndPt721LLLqJiDIn0b6A5uJSqC6vgjQxTowbi1aBtvY4GKp2AmRyG2ZIRJT3WWVxnFOnTqFy5cooVqyY1RLLDSy6iYjSJ419DPWFn6G+th4So16MJxavCa3/eCRUagdIZTbMkIgo/3ijKQMfP35sMVtJmTJlYDAY8Pjx4wwv5u7OqaKIiPI6afQ9aM4thOrGn5CYE8V4YsmApGK7fBAgkdgwQyKigiXdlu7q1avj+++/T7U4Tma4OA4RUd4li7gOzdkFUN7eBolgFuMJZZtA6z8Oie71WWwTEb2hN2rpHjt2LDw9PS1+zkrRTUREeY9d+HlozsyH8v4ui7ihYhto/cfB6OZno8yIiAqHLPfpzq/Y0k1EhZYgQP7oGDRnF0ARdjglLJHCUOVdaP3HwlSsug0TJCIqWN6opZuIiPIpQYDiwT5ozs6D/OnZlLBUDn217tD6jYHZuaINEyQiKnzSLbqz2of7dXmtTzcRUaFhNkF5Zwc0Z+fDLuKaGBbsVNDV6Aud30iYHTjYnYjIFtItujt37pyq6N6zZw8MBgMaNWqESpUqwWw2IzQ0FAcPHoSDgwN69OiR4wkTEdFrTIlQ3twEzbmFsIu+K4bNCkfovQZC6zOMy7QTEdlYukX3zJkzLX5es2YN9u/fj61bt6JiRcuvJcPCwtCnTx8OtCQiyk1GHVTXf4fm3GLI4h6JYbOqKHQ+w6GrNRCCsogNEyQiomRZHkjZtGlT9O7dG6NGjUpz+5IlS7Bq1SocPXrUqgm+LQ6kJKKCRpIQB9WV1dBcWAqp7rkYN9m7Qec7CrqafQG5xoYZEhEVTlYZSBkbGwuFQpHudrPZjISEhOxlRkREWSbRR0F9aTnUl5ZDangpxk1O5aGtPRr6aj0AmdKGGRIRUXqyXHT7+vpizZo1eOedd+Dm5max7fbt21i5ciUCAwOtniARUWEnjQ+H+sISqK+sgcSY8s2dsagHtP7jYKj6LiDlZFRERHlZlruXXLlyBf3794dUKkXTpk1RtmxZJCQk4N69ezhy5AgcHR2xYcMGlC9fPqdzzhZ2LyGi/EoaEwrN+Z+hur4BEpNBjCe6ekMbMB4JFdsAEqkNMyQioldl1L0kW4vj3L59G/PmzcORI0eg1SYVsg4ODmjVqhUmTpyIkiVLvn22Vsaim4jyG1nUbWjOLYTy5mZIzEYxnuBeF1r/CUgs24RLtRMR5UFWK7qTCYKAqKgoSCQSFC1a9K2Sy2ksuokov7B7fgWas/OhuLMDEqT8ak4o1wzx/hNgdGcXPiKivMzqK1JKJBK4uLi8cUJvIjIyEj/99BP27dsHvV6PmjVrYvLkyfD19c3VPIiIrM3uyWlozsyD8uF+MSZAgoTK7aD1Hw+jay0bZkdERNaQ5ZbuhIQEzJs3D9u2bUNERARMJlPqk0kkuHbtWhpHv524uDj06NEDz549w6BBg+Dk5IR169YhPDwcwcHB8PDwSPdYtnQTUZ4kCJCHHYbmzDwoHp9ICUtkMHh0gbb2WJhcqtowQSIiyi6rtHR///33WLt2LSpXroyAgIAMpw+0tqVLl+LevXtYs2YN6tSpAwBo3749WrZsiV9//RXff/99ruVCRPRWBDMU93ZBc3Y+5M8upoSlCuir94K29miYncrZMEEiIsoJWS66//nnH7Ru3Rrz5s3LyXxSEQQBmzdvRrNmzcSCGwBcXV0xZcoUyOXyXM2HiOiNmI1Q3voraan2yBtiWLDTQOfVHzrf4TDb573B6EREZB1ZLrrj4+PRuHHjnMwlTWFhYQgPD8ewYcMAJBXhWq0W9vb26Nu3b67nQ0SULSYDVCEboTm3CLKYB2LYrCwCXa1B0PkMg6DK2wPSiYjo7WV5glcvLy9cuXIlJ3NJ04MHSX+kihUrhu+++w4BAQGoXbs2WrVqhX379uV6PkREWZKohfrCUrisaQDHA1PFgtusLo64+tMQOeAEtHU/ZMFNRFRIZLmle+rUqRg2bBg8PDzQrl27XJu9JCYmBgAwd+5c2NnZ4ZNPPoFUKsWyZcswduxYLFu2DA0aNMiVXIiIMiPRR0N9ZRXUF3+FVB8lxk0O7tD6jYK+em9ArrZhhkREZAtZnr2kXbt2iIyMFIvgNE+WA7OXbNmyBVOnTkXRokWxc+dOFClSBEBSMd6qVSuUKVMGf/75Z7rHc/YSIsoNEu1zaC4uheryakgT48S40bkStLXHwuDRBZDl3gB0IiLKfVaZvcTHxwcSG6yAptFoAACtW7cWC24AcHJyQlBQEDZv3oz4+HjY29vnem5ERNKYMGguLIbq2mtLtRevCa3/eCRUagdIZTbMkIiI8oIsF90zZ87MyTzS5ebmBgBpdmdxcXGxGFhJRJRbkpZqXwTlzU0WS7UnlgxIKrbLB3GpdiIiEmV7Rco7d+5g7969ePz4MeRyOdzd3dG0aVNUqlQpJ/JD1apVoVAocPv27VTbwsLCoFQqc311TCIqvOyeX4bm7II0lmpvCq3/eCSWqstim4iIUslW0f3DDz9g+fLlMJvNFvFZs2Zh0KBBmDJlilWTA5K6lwQFBWHv3r24desWqlZNWqEtNDQU+/btQ8uWLSGT8atbIspZdo9Pwf7sPCgeHrCIGyr9t1R7CW/bJEZERPlClgdSBgcH49NPP0WzZs0wevRoVK5cGWazGXfv3sXSpUuxb98+fPPNN+jSpYvVkwwLC0OPHj0AAAMGDIBcLsfq1auh0+mwadMmlC1bNt1jOZCSiN6YIED+8EBSy/aTkylhcan2MTC5eNgwQSIiyksyGkiZ5aK7U6dOcHZ2xqpVq9LcPnDgQMTFxWU4k8jbCA0NxaxZs3Ds2DEIgoCAgABMmTIFlStXzvA4Ft1ElG2CGYq7/0BzdgHkzy+nhGVK6Ku/B63fKJid0v+wT0REhZNVZi+5d+8epk6dmu721q1b44cffsheZtlQtmzZXF+CnogKGVMilLe2JC3VHpUyjsQst4feqz+0PiMg2JewYYJERJRfZbnotre3x/Pnz9Pd/uzZMyiVSqskRUSUq4w6qK7/Ds25xZDFPRLDZqUzdD5Doas1iCtHEhHRW8ly0d2oUSOsXbsWbdu2RbVq1Sy2Xb9+HWvXrkWzZs2snR8RUY6RJMRCdWUNNBeWQqpLaVQwadyg8xsJXY2+gILTkRIR0dvLcp/ux48fo1u3boiJiUGjRo1QsWJFAMDdu3dx9OhRODo6Ijg4OMNBjbbAPt1E9DqJLhLqS8ugvrwSUsNLMW5yKget3xjoq3UH7FQ2zJCIiPIjqwykBJJmEfnxxx9x8OBBaLVJhaxarUaTJk3wv//9L88V3ACLbiJKIY17AvWFJVBfXQuJUSfGjUU9oPUfB0PVdwFptpcvICIiAmDFojuZ2WxGVFQUBEGAi4sLpFLpWyWYk1h0E5H05X1ozi2GKiQYEnOCGE8s4ZO0emTF1oAk7/4eIyKi/OGtZy8JDw8Xl2MHAKlUimLFiuH8+fN48eJFqj7eRER5gSwiBJqzC6C8/RckQsqiXgmlGyStHlmmEVePJCKiXJFh0R0TE4NPPvkEBw4cwPHjx+Hg4GCxfeHChTh69CiaNWuGr7/+msuxE1GeYBd+PqnYvrfTIm6o0DJp9ciS/jbKjIiICqt0i+64uDj07dsXt2/fRsOGDaHValMV3e+99x7s7Oywf/9+DBw4EH/88QfUanWOJ01ElIogQP7oGDRn50MRdiQlLJHCUKUjtLXHwlS8hg0TJCKiwizdPt2zZ8/G0qVL8eOPP6Jdu3YZniR5ifhx48Zh3LhxOZLom2KfbqICTjBDcX8PNGfnQx5+PiUslUNfrTt0fqNhcq5kwwSJiKiweKOBlG3btkWtWrUwa9asLF1k1KhRCA0Nxfbt298syxzCopuogDIbobz9NzTnFsAuIkQMC3Yq6Gr0hc53JMyO7jZMkIiICps3Gkj56NEjDBo0KMsXadCgQY4uA09EBAAwGaAK2QjNuUWQxTwQw2aFE3S1BkHnMxSCupgNEyQiIkot3aK7SJEi4lzcWWVvz5XbiCiHJMRDfXUt1BeXQBYfLobN6mLQ+gyH3msABKWTDRMkIiJKX7pFd9WqVXHs2DEMGTIkSyc6evRonlwch4jyN4k+CupLy6G+tAJSQ7QYNzm4Q+c7EroafQA5B3ATEVHelu5qEN27d8fRo0exbdu2TE+yY8cOHDp0CO+++65VkyOiwksa/xT2R79EsVV1YX96tlhwG50rIyboJ0T2OwKdz1AW3ERElC9kuCLlqFGjcPjwYXTp0gU9e/ZEzZo1IZPJAAAmkwlXr17Fxo0bsWnTJtSoUQNr1qyBUqnMteSzggMpifKXdFePdK0Frf84JFRsC0hlNsyQiIgobW+8DHx8fDxmzJiBrVu3QiKRwM7ODs7OzjCbzXj58iVMJhMEQUD79u3x+eefo0iRIjnyAN4Gi26i/EH24ho05xZCeXub5eqR7vWSVo8s24SrRxIRUZ72xkV3smvXruHvv//GtWvX8OLFC0ilUri6usLPzw8tW7bM08vAs+gmytvsnpyB5twCKO/vsYgbKrSEtvY4GEsF2CgzIiKi7Hnrojs/Y9FNlAcJAuShB6E5uwCKxydSwlw9koiI8rE3mqebiMjqzCYo7v4DzbmFkD+/LIYFqQL6aj2grT0a5iIVbJcfERFRDmHRTUQ5z5QA5c3N0JxbBLvoO2JYsNNA59UfOt/hMNuXtGGCREREOYtFNxHlnEQdVNd/g+b8z5DFPRbDZqUzdN5DoPMeDEFV1IYJEhER5Q4W3URkdRLDS6gvr4L60jJIdRFi3GTv9t+CNn0BBVewJSKiwoNFNxFZjUT7HJqLS6G6vBrSxDgxbnIqD23tMdBX6w7I8tZc/kRERLkhS0V3QkIC7t69i8ePH0On00EikcDe3h5ubm7w8PCAVJruwpZEVAhIY0KhufAzVNc2QGIyiHFjserQ+o+DofI7gJSf8YmIqPDK8K9gaGgo5s2bhz179kCv1wMAkmcYlPy3SIVSqUTbtm0xZswYlCtXLofTJaK8RBZ5M2lBm5tbIBFMYjyxZAC0/uORUD6IC9oQEREhg3m6r127hgEDBkAmk6Ft27aoWbMmXF1doVKpAAB6vR7Pnj3D1atXsXPnTgDA6tWr4enpmXvZZwHn6SayPrvwC9CcnQ/lvZ0W8YRyTZNWjyxVl8U2EREVOm+0OM7AgQPx/PlzrF27Fi4uLhleIDIyEv369UOpUqWwbNmyt8vWylh0E1mJIED+6FjSgjZhh1PCkMBQ+R3o/MfC6FrLhgkSERHZ1hstjnPp0iX873//y7TgBgAXFxf07dsXs2fPfrMMiSjvEsxQ3NsNzbkFkIefTwlL7aD37Aad3xiYila2YYJERER5X7pFd5EiRfDkyZMsn+jZs2eQy+VWSYqI8gCzEcpbW5MWtIm8IYYFOxV0NfpA5zsSZsfSNkyQiIgo/0h32pHWrVtj1apV2LhxI4xGY7onMJvN2LhxI1asWIG2bdvmSJKvCgkJgZeXF+bPn5/j1yIqlIx6qK6shsu6JnDaM1EsuM0KJ8T7T0DEgJOIbzyDBTcREVE2pNvS/f777+PBgweYPn06vv76a3h4eMDNzQ0qlQoSiQR6vR7Pnz/HjRs3EB8fj7p162Ly5Mk5mqzRaMS0adOQmJiYo9chKowkCbFQXVkD9cVfIdM+E+NmtSu0vsOh9+oPQZF+XzUiIiJKX7pFt0ajwS+//IKjR49i+/btuHr1Kk6dOoX4+HgIggB7e3uUKlUKbdq0QZs2bdC0adMcT/aXX37BrVu3cvw6RIWJRPsC6kvLob6yClLDSzFuciwLrd8o6Kv3BOzUNsyQiIgo/8t0tYqGDRuiYcOGuZFLhm7cuIHFixdjzJgxmDt3rq3TIcr3kha0+QWqa79ZLmhT1ANa/zEwVOkEyDhOg4iIyBryxRJxyd1KGjRogHfffZdFN9FbkEXcgOb8otQL2rj5QVt7HBIqtgIkXGWWiIjImvJF0b106VI8ePAAixYtynBQJxGlz+7pWWjOLoTy/i6LeELZptD6j0Wie30uaENERJRD8nzRfevWLSxcuBCfffYZSpYsibCwMFunRJR/CALkDw9Ac24hFI9PpIS5oA0REVGuSrforlatGiTZbPWSSCS4du3aWyeVzGQyYdq0afD390fPnj2tdl6iAs9sgvLOdqjPLYT8xVUxLEjl0FfrDp3faJicK9kwQSIiosIl3aL7+++/xxdffAGtVosGDRqgRIkSuZkXAGDZsmUICQnB+vXrERkZCQCIiYkBAOh0OkRGRsLZ2RlSKfufEgEATAaoQjZCfX4x7F7eF8OCnQY6r/7Q+QyD2aGU7fIjIiIqpCSCIAjpbbx+/Tr69++PChUqYMOGDbCzy93eKP3798epU6cy3Gfv3r0oU6ZMutsTE02IjtZaOzWiPEWSEAfV1bVQX1gKmTZcjJtVRaHzHgpdrYEQVEVtmCEREVHB5+qa/noWGRbdALBnzx6MGzcO77//PkaNGmX15DJy5coVsWU72YsXL/Dhhx+iU6dO6Ny5M/z9/aFUKtM9B4tuKsgkugioLy5LPce2gzt0viOhq9EbkGtsmCEREVHhkVHRnWnTdcuWLdGzZ08cPXoUw4YNy9XWbi8vr1Sx5IGUZcuWRYMGDXItF6K8RBoTBs2Fn6G6vgESo16MG4tWhbb2GBiqduYc20RERHlIliroGTNm5HQeRJQFSXNsL4by1hZIzCnTZyaW8IXWfxwSKrbmHNtERER5UJ6fMpCI/ptj+9wiKO/ttIgnlG0Cbe2xSCzdgHNsExER5WGZ9unO79inm/ItQYA89GDSHNuPjqeEIUFC5fbQ1h4LYwlvGyZIREREr3qrPt3JsjJvt0KhQLFixeDt7Y2xY8eiatWqWc+SiJKYTVDe2fHfHNtXxLAglUPv2Q262mM4xzYREVE+k+WW7gULFmDNmjWIjY1Fw4YNUalSJSiVSty/fx+HDx8GkDToMjY2FidPngQAbNiwAZ6enjmXfRawpZvyDZMBqht/Qn1uMexe3hPDgp0Gupr9oPMdzjm2iYiI8jCrtHQn27RpE6pVq2YRCw0NxXvvvYcqVapg5MiRePHiBfr27Yv58+djwYIF2c+YqBDJeI7tIdDVGsQ5tomIiPK5LBfdf/zxB/r375+q4AaSpu/r168f1q9fj5EjR6J48eLo0aMHli1bZtVkiQoSiS4C6kvLob688rU5tkv9N8d2H86xTUREVEBkueiOi4uDRpN+AaBUKhEdHS3+XKRIEej1+nT3JyqspLGPoD7/M9TXf3ttju0q0PqNgcGjMyBT2C5BIiIisrosF91eXl747bff0LVrVzg7O1tsi42NxYYNG1C9enUxduLECZQrV85qiRLld7LIm0lzbN/c/Noc2z7/zbHdhnNsExERFVBZLronT56MgQMHok2bNujUqRPKly8PhUKBe/fuYfv27YiMjMRXX30FABg2bBiOHj2K6dOn51jiRPmF3dNz0JxbmHqO7TKNofUfxzm2iYiICoFszdN95coVzJo1C6dPn4bZbBbjfn5+mDp1Knx9ffHixQv07NkT7777Lt5///2cyDlbOHsJ2YQ4x/YiKB4dSwlDgoTK7f6bY9vHhgkSERGRtWU0e8kbLY4TExOD0NBQGI1GlC1bFi4uLm+VYE5i0U25ymyE8vY2aM4thl3ENTEszrHtNxqmopVtmCARERHlFKtOGRgdHY1jx47h0aNHkMvlCA8PR4MGDeDg4PBWSRLla4k6qK5vgObCEshiQ8Vw0hzbff+bY9vdhgkSERGRLWWr6F6/fj1mzZoFvV6PVxvIlUolpkyZgr59+1o9QaK8TKKPgvryKqgvLYdUHynGzepiSXNsew3gHNtERESU9aJ7z549mDFjBmrUqIFhw4ahUqVKEAQBd+/exYoVK/DVV1/B3d0dzZs3z8l8ifIEaewjqC8sgfrab5AYU7ovmZzKQes7EvrqPQE7tQ0zJCIiorwky326e/XqhcTERGzYsAEKheUcwomJiejVqxfUajXWrVuXI4m+KfbpJmuSRYQkTft3a6vltH/Fa0JXewwMld8BpNnutUVEREQFgFX6dIeEhGDSpEmpCm4AkMvl6NSpE+bOnftmGRLlcXaPT0FzfhGU9/dYxBNKN4S29hgklm3Caf+IiIgoXVkuuhUKBXQ6Xbrb4+PjIZPJrJIUUZ4gmKG4vweac4sgf3omJQwJEiq3h9ZvNIxuvrbLj4iIiPKNLBfdderUwbp169C1a1eUKFHCYlt4eDjWr18Pf39/qydIlOtMCVDe3ALN+Z9hF3VTDAtSBfTVekDnNxIm50o2TJCIiIjymyz36b558yZ69eoFqVSKzp07o0KFCgCAu3fv4q+//oLJZMJvv/1msRR8XsA+3ZRVkoQ4qK6th/riUsjinohxs8IReq8B0HoPhWBfIoMzEBERUWFmtcVxLl26hK+++gqXLl2yiHt5eWH69Onw9fV94yRzCotuyoxE+wLqS8uhvrIKUsNLMW7SuEHnMwx6r34QFOm/iYiIiIiAHFiRMiIiAo8ePYIgCChdujSKFy/+VgnmJBbdlB7pywfQXPgFquu/Q2IyiHGjc2Xo/EZB79kVkCltmCERERHlJ1YvutNy8uRJ3LhxAwMGDLDG6ayGRTe9zu75FajPLYLyzt+QCGYxnujmB23tMUio2AaQSG2YIREREeVHVl0GPj07duzAH3/8keeKbiIAgCBAHnYUmvOLoAg9ZLHJUK45dLXHING9Hqf9IyIiohzBVTyoYDOboLj7T9K0f89TxiIIEhkMVd+F1m80TMVr2DBBIiIiKgxYdFPBZNRDFbIR6gs/w+7lfTEs2Kmgq94bOt8RMDuVtV1+REREVKiw6KYCRWJ4CdWVNdBcXAap7rkYNyudofMeDF2twRDULjbMkIiIiAojFt1UIEjjnkB98Veorq6DNDFOjJscSkPnOxy6Gn0AucaGGRIREVFhlm7R/fjx42ydKD4+/q2TIcouWdRtqM8vhurGJkjMiWLc6OIJbe0xMFR5F5DJbZghERERUQZFd1BQECTZmMlBEIRs7U/0NuyenoXm3CIo7u2CBCmzXiaUqgtd7TFIKB/EmUiIiIgoz0i36O7cuTOLaMpbBDMUD/ZDfX4RFI9PWmwyVGwDbe0xMJb0t1FyREREROmz2uI4Oe3w4cNYvHgxrl69CqlUCh8fH7z//vuZLj3PxXEKAJMBqhubob7wC+yibolhQSqH3rMrdL6jYHKpasMEiYiIiHJpRcqcdOrUKQwYMABVq1ZFt27dYDQasX79ejx79gzr16+Ht7d3usey6M6/JPpoqK+sgeryCsi0z8S4We4Afc2+0PkMg9mhlA0zJCIiIkqR74vuzp074+XLl9ixYwfUajUA4MWLF2jfvj1q1qyJFStWpHssi+78RxoTCvXFpVBf2wCJMeW5M9mXhM57KPQ1+0JQOtkwQyIiIqLUcmUZ+Jzy8uVLhISEYPDgwWLBDQDFixdHnTp1cPToURtmR9Zk9+wi1Od/gfLO35AIZjFuLFYNWt9RMFR9F5ApbJghERER0ZvJ80W3g4MD/v33X4uCO1lUVBRkMpkNsiKrSR4ceeFnKB4dt9iUUKYxtH4jkVi2KWciISIionwtzxfdMpkMFSpUSBUPCQnBuXPn0KhRo9xPit6eODhyCeyibophQSKDoeq70PqOgsm1pg0TJCIiIrKePF90pyU+Ph5Tp04FAIwYMcLG2VB2SPTRUF1dC/Wl5a8NjrSHvkZf6HyGwuxY2oYZEhEREVlfviu6dTodRo8ejZCQEIwcORKBgYG2TomyIGlw5K9QX/vttcGRbtB5D4O+Zh8IyiI2zJCIiIgo5+SrojsmJgYjR47EuXPn0K1bN3zwwQe2TokyYffsEtTnf+bgSCIiIirU8k3RHRERgaFDh+L69evo1asXvvjiC66YmVdxcCQRERGRhXxRdMfFxYkF96BBgzBt2jRbp0Rp4eBIIiIiojTli6J7xowZuH79OgYMGMCCOw/i4EgiIiKijOX5ovvOnTvYunUrHB0dUb16dWzdujXVPp06dbJBZsTBkURERERZk+eL7lOnTgEAYmNj023lZtGdu+yeXYL6wi9Q3v4bEsEkxjk4koiIiChtEkEQBFsnkZMSE02IjtZmviNlTBwc+QsUj45ZbOLgSCIiIiLA1dUx3W15vqWbbMxkgPLmFmjO/5Lm4Eid70gYXb1smCARERFR3seim9LEwZFERERE1sOimyxwcCQRERGR9bHoJgAcHElERESUk1h0F2ZmExT3d0N9aRlXjiQiIiLKQSy6CyGJ4SVU1zZAfXklZLGhYpyDI4mIiIhyBovuQkQWdRvqSyugCgm26K9tVjhBX/09Do4kIiIiyiEsugs6wQzFwwNJXUgeHrTYZHSuDJ33EOg9uwMKexslSERERFTwseguqBLioboRDPWlFbCLvmOxyVCuOXTeQ5BYrikgkdooQSIiIqLCg0V3ASN9+QDqyyuhur4B0oRYMS7YaaCv3gO6WkNgKlrZhhkSERERFT4sugsCQYD80TGoLy2H4t4uSCCIm0xO5aCrNQj66r04vzYRERGRjbDozs+MOqhubob60nLYRYRYbEoo3QA676FIqNASkMpslCARERERASy68yVp3GOoL6+G6to6SPVRYlyQKaH37ApdrcEwFa9hwwyJiIiI6FUsuvMLQYDd07NQX1oG5Z0dFqtGmuxLJnUhqdEHgtrFhkkSERERUVpYdOd1JgOUt7dBfWkF5M8uWmxKLBkAnfcQGCq1A2RyGyVIRERERJlh0Z1HSbTPob6yBuorayDVPRfjglQOQ5WO0HkPgdHN13YJEhEREVGWsejOY+yeXYL60nIob/0FiTlBjJvVxaHz6g99zX4w27vZMEMiIiIiyi4W3XmB2QjF3X+hubQM8ienLTYlutaCznsoDFU7AjKljRIkIiIiorfBotuGJPooqK6ug/rKKsjinohxQSKDoVK7pC4kpeoAEokNsyQiIiKit8Wi2wZkESFQX1oO1c1NkBj1YtysLAJ9zb7QeQ2E2bG0DTMkIiIiImti0Z1bzCYoHuyF+uIyKB4dtdhkdPGEznsI9B5dAbnaRgkSERERUU5h0Z3DJIYYqEL+gPrSCshiHohxARIkVGgJnfdQJJZpyC4kRERERAUYi+4cIou+mzQLSUgwpInxYtwsd4C+xnvQ1RoEc5EKtkuQiIiIiHINi+4coLi3G07/DIVEMIsxY5GK0HkPhqFaTwgKBxtmR0RERES5jUV3DpBF3RIL7oSyTaHzHoKE8s0BidTGmRERERGRLbDozgE63xEwOVeCybkyTC5VbZ0OEREREdmYRBAEwdZJ5KTERBOio7W2ToOIiIiICjhXV8d0t7G/AxERERFRDmPRTURERESUw/JN0R0aGopx48YhMDAQgYGBmDJlCiIjI22dFhERERFRpvLFQMqoqCgMHDgQCQkJGDZsGEwmE5YtW4YbN24gODgYCoXC1ikSEREREaUrXxTdK1euxNOnT7Ft2zZUrlwZAODj44PBgwdjy5Yt6Nmzp40zTO3qkxj8euIhtAkmW6dCREREVGhoFDIMq1cONUs52ToVC/mi6N6+fTsCAwPFghsAGjRogIoVK2L79u15suj+7dwjHLnL7i9EREREuc1eIcNX77DozpaXL18iNDQUbdq0SbWtZs2aOHDgQO4nlQW9a5dGfIKJLd1EREREuUijkKG3fxlbp5FKni+6w8PDAQBubm6ptrm6uiIuLg6xsbFwdEx/XkRbqFnKCbO7eNk6DSIiIiLKA/L87CXx8fEAALVanWqbUqkEAGi1XPyGiIiIiPKuPF90m83mTPeRSvP8wyAiIiKiQizPV6v29vYAAIPBkGpbcix5HyIiIiKivCjPF93u7u4AgOfPn6fa9uzZMzg5OUGj0eR2WkREREREWZbni24nJyeUKVMGV69eTbXt2rVr8PLiYEUiIiIiytvyfNENAK1bt8bx48dx584dMXbs2DHcu3cP7du3t2FmRERERESZkwiCINg6icxERkaiQ4cOkMlkGDJkCAwGA3799VeUK1cOGzZsyHAZ+MREE6KjObsJEREREeUsV9f0p7DOF0U3ANy9exfffvstzpw5A5VKhaZNm2LKlClwcXHJ8DgW3URERESUGwpE0f2mWHQTERERUW7IqOjOF326iYiIiIjyMxbdREREREQ5jEU3EREREVEOK/B9uomIiIiIbI0t3UREREREOYxFNxERERFRDmPRTURERESUw1h0ExERERHlMBbdREREREQ5jEU3EREREVEOs7N1AmRb3bt3x+XLl1PF27Rpg3nz5tkgI0rP9OnT8eDBA6xZs8YiHhoaiu+++w6nTp0CADRr1gwfffQRXFxcbJEm/Se954vvubzl8OHDWLx4Ma5evQqpVAofHx+8//778PX1FffheyzvyMrzxfdY3nL8+HHMmzcPISEhcHBwQNu2bfH+++/D3t5e3KewvMdYdBdigiDgzp07aNmyJVq3bm2xrXTp0jbKitISHByM4OBgBAYGWsSjoqIwcOBAJCQkYNiwYTCZTFi2bBlu3LiB4OBgKBQKG2VcuKX3fPE9l7ecOnUKw4cPR9WqVfHBBx/AaDRi/fr16NevH9avXw9vb2++x/KQrDxffI/lLSdOnMCQIUNQs2ZN/O9//8OTJ0+wevVqXLlyBevWrYNUKi1c7zGBCq2HDx8KHh4ewp9//mnrVCgdRqNRmD9/vuDp6Sl4eHgI/fr1s9j+008/CdWrVxdu374txo4ePSp4eHgIv//+e26nW+hl9nzxPZe3dOrUSWjWrJmg1WrF2PPnz4U6deoIgwYNEgSB77G8JCvPF99jeUuXLl2E5s2bCzqdToytXbtW8PDwEA4cOCAIQuF6j7FPdyF2+/ZtAEDlypVtnAmlxWAwoEuXLpg/fz46deoENze3VPts374dgYGBFs9hgwYNULFiRWzfvj030y30svJ88T2Xd7x8+RIhISFo27Yt1Gq1GC9evDjq1KmD8+fPA+B7LK/I6vPF91jeYTAYULRoUfTs2RMqlUqMJ38DeOPGDQCF6z3G7iWF2K1btwCk/HLSarXQaDS2TIleYTAYEBcXh9mzZ6N9+/YICgqy2P7y5UuEhoaiTZs2qY6tWbMmDhw4kEuZEpD58wXwPZeXODg44N9//7Uo4JJFRUVBJpPxPZaHZOX5Avgey0uUSiWWLVuWKn79+nUAgLu7e6F7j7GluxC7desW7O3t8e2338LPzw9+fn5o2bJlgftkmV85ODhg165daN++fZrbw8PDASDNFlVXV1fExcUhNjY2R3OkFJk9XwDfc3mJTCZDhQoVUr1/QkJCcO7cOfj5+fE9lodk5fkC+B7Lyx49eoRNmzbh66+/hoeHB1q1alXo3mNs6S7Ebt++jfj4eMTGxuL7779HTEwMVq9ejUmTJiExMRGdO3e2dYqFmlQqhVSa/ufi+Ph4AEiz5UepVAJIauVxdHTMmQTJQmbPF8D3XF4XHx+PqVOnAgBGjBjB91ge9/rzBfA9lldFR0eL3/6p1WpMnz4dSqWy0L3HWHQXYj179oTZbEbfvn3F2DvvvIMOHTpg1qxZ6Nixo/iVHeU9ZrM5030yKwIpd/E9l3fpdDqMHj0aISEhGDlyJP6/vbuPpjLb4wD+RclNNNO9KMVkVh1uTnJWCEklpFKmJEfhhjukbqGZ8tLMmJpmebma7lXdirnpjhF3VURDL2NS9/Y23aaRkRAqL8lrI+8OnvtH6zzjOAeHiWPy+6xlLWef/Tz7t/fzbPZ5nv3sY2Jigh9++GHA7aiPyYak4wVQHxut5OTkcPDgQXR0dCA+Ph4eHh744osvoKamNuC2b1Ife3NqQgbNxcVF5A8TACgpKcHBwQG1tbXsAylkdBKucdre3i72njCt5zqoRPaoz41OL1++hKenJ77//ns4OjoiICAAAPWx0aqv4wVQHxutJk+ejJUrV+K9995DQkICNDU1ER4ePub6GA26iRjhYvQtLS0yjoT0R1NTEwBQU1Mj9l51dTVUVVXpAaLfCOpzslNXVwd3d3fcu3cPzs7O+PzzzyEnJweA+tho1N/x6g/1sdFDSUkJS5YsQWVlJdTV1QGMnT5Gg+4xqqqqCqtWrcLhw4fF3nv8+DEAYMaMGSMdFhkEVVVVzJgxAw8ePBB7Ly8vD1wuVwZRkb5Qnxt9mpqa4OXlhYcPH2Lz5s3Yt2+fyACO+tjoMtDxoj42uhQXF8PKygoJCQli7zU3N0NOTg6Kiopjqo/RoHuM0tDQQGNjI06fPo2mpiY2vbKyEsnJyViwYIFUc62IbNna2uLWrVsoLi5m027evInHjx/3u4oGGXnU50afffv24eHDh3B3d0dwcLDEPNTHRo+Bjhf1sdHlnXfeQWNjI5KSktDR0cGmV1RU4PLlyzA2NsakSZPGVB+TYxiGkXUQRDYyMzOxbds2zJ49G05OTmhubkZCQgIEAgESExPpywVGGSsrK0yfPh3x8fFsWn19Pezt7aGgoABPT0+0t7fjyy+/hLa2NpKSkt6sr8/9jZF0vKjPjR7FxcVYuXIlVFRUEBISIvHhOgcHB+pjo4S0x4v62OiSmpqK3bt3w9DQEGvWrMGLFy/Y43Hq1ClwOJwx1cdo0D3GZWZm4vjx48jPz4eSkhJMTEywc+dO+sM0CkkaxAFASUkJwsLCcPfuXSgpKWHx4sXYvXs3O4eRyEZfx4v63OiQmJiITz/9tN88wm/Moz4me4M5XtTHRpeMjAx8+eWXKCwsxMSJE2FqaoqAgADo6OiwecZKH6NBNyGEEEIIIcOM5nQTQgghhBAyzGjQTQghhBBCyDCjQTchhBBCCCHDjAbdhBBCCCGEDDMadBNCCCGEEDLMaNBNCCGEEELIMKNBNyGEEEIIIcOMBt2EvIGCgoKgq6sr8sPlcrF48WLs2rULjx49knWIo8bJkydhYWEBAwMDREVF9Zu3rKwMurq60NfXR01NzQhFOPyE58tIa2pqQn19Pfv60KFD0NXVRXl5+YjFUF5eLtZXhP3F0tISwcHBeP78+aD3m5ycDF1dXXz//ffDEPXwG2r8v/V6EzKcxsk6AELI8AkODsbbb78NAGhtbcXTp0+RnJyMS5cuITY2FgsWLJBxhLJVUFCAsLAwGBoaws/PD3p6ev3mP3/+PCZOnIiWlhakpaXBy8trhCIdXs7OzjAzMxvRMnNzc+Hr64uoqCj2PLSxsYG2trZMvoXOyMgIGzZsYF93dnaiqKgICQkJuHXrFtLS0qCqqjriccmKsbExIiMj6VscCXmNaNBNyBvM2toaM2bMEElzd3eHo6Mj/P39kZmZCWVlZRlFJ3uFhYUAAB8fH1hZWQ2Y/5tvvsGCBQtQUVGBlJSUN2bQzePxwOPxRrTMwsJCVFdXi6Tp6ekN+MFnuGhpacHBwUFi+t69e5GUlARvb28ZRCYbWlpa0NLSknUYhLxRaHoJIWPMtGnTEBgYiPr6epw9e1bW4ciUQCAAAKk+eOTl5aG4uBhGRkawtLTEo0eP8NNPPw13iETGVq5cCQC4d++ejCMhhPzW0aCbkDHIzs4OioqK+O9//yuS/uOPP8LDw4O98unp6YmcnByx7a9duwYnJycYGhpi2bJl+Prrr7Fnzx6Rq8Vubm7w8vLCwYMHwePxYGZmhoKCAgBAUVERtm3bBiMjI8ybNw98Pl8slsHkk6SgoABbt26FkZERDAwMsGHDBmRmZorEFxwcDODV1f+B5jSfP38eAGBiYgIbGxsAr+av9ubm5obNmzfjypUrWLlyJQwMDPDee+/h0qVLQ87XVzsOVMf8/HxwuVw4OzuDYRg2/dixY9DV1UVSUhIA8TndQUFBsLe3xw8//ABnZ2cYGBhg2bJlSElJgUAgwIEDB7Bw4UKYmJjA398fL168EIn54sWLcHV1xfz588HlcmFlZYXIyEh0dHQAeDV3u2fbC8+b3nO6Dx06hLlz5+LJkyfw8fEBj8eDsbExAgMDxcqsqqrCrl27YGpqivnz52PXrl3IzMz81fOLFRQUAABdXV1sWmtrKw4cOAArKyu2flFRUWhtbZW4j8bGRhgYGMDPz0/svVOnTkFXVxdFRUXsfOj8/Hx88MEHMDY2Bo/Hw7Zt28TmuUsTQ8/97dixAzweD6ampoiIiEBXVxdSUlKwfPlyGBoags/nIz8/X2zbnm339OlTBAYGwtLSElwuFyYmJtiyZQs9I0KIlGjQTcgYNGHCBGhra4v8k71x4wbc3NzQ2NgIPz8/+Pr64tmzZ9i0aRPu3r3L5svKyoKvry8EAgECAgKwfPlyREREiAz2hO7du4f09HTs2rULa9euxaxZs1BQUABnZ2cUFRXBx8cHAQEB6OzshLe3NzIyMthtpc0nSU5ODpydnZGTkwMPDw/s3LkTAoEA27ZtQ0JCAgBgy5YtcHZ2Zn+PjIzsc3/d3d3IyMiAhoYG5s6di3nz5kFdXR3p6ensQLKn4uJi7NixA8bGxvjwww8hLy+PHTt2sAP3weaT1I7S1FFPTw8+Pj7Izs7Gv//9bwDAo0ePcPjwYSxatAh8Pr/POtfU1GDLli2YP38+AgMDMW7cOISEhMDHxwe3b9/G1q1bYW9vjwsXLoi03enTp+Hn5wcVFRV8+OGH2L17N6ZPn45//vOfiImJAfBq7nbPtg8JCem37d3d3aGsrIzAwEDY2tri3Llz+PTTT9k8TU1NcHV1xbfffgtnZ2ds374deXl52LNnT5/7ldbNmzcBAHPmzAEAdHR0wMPDA7GxsTA1NUVISAhMTEwQGxsLT09P9u5JTyoqKli8eDGuXbsmNjDPyMiArq4uZs2axab5+vqioaEBAQEB4PP5yMrKgr+/P/v+YGPw9vaGgoICgoKCoK+vjxMnTsDb2xsHDhzA+vXrsXXrVhQUFGDHjh3o7OyU2A61tbXYsGED7t69C1dXV4SGhsLe3h7Xr1/H1q1b0d3dPaT2JWRMYQghb5zAwECGw+EwZWVlfebh8/kMl8tlGIZhurq6mGXLljF8Pp/p7Oxk8zQ3NzM2NjaMg4MDm2Ztbc3Y2toyra2tbNq3337LcDgcZunSpWyaq6srw+FwmNu3b4uU6+rqylhbWzPNzc1smkAgYDZu3MiYm5sz7e3tg8oniZOTE2NoaMhUVlayaW1tbczatWsZAwMDpq6ujmEYhjl79qzEGHu7desWw+FwmH379rFpe/fuZTgcDpORkSFWPw6Hw8TFxbFpra2tjI2NDWNhYcF0dXUNKV/vGKWtY0dHB7N69WrG2NiYqampYdatW8eYmJgwVVVV7HbC86X36/j4eDbt6tWr7DHu2fZ8Pp+xsLBgX9vZ2THOzs5Md3c3myYQCBhLS0vG3t6eTZPU9tHR0SLnrfB1WFiYSN29vLyYOXPmMC0tLQzDMMzhw4cZDofD3Lhxg83T2NjILFmyZMDjW1ZWxnA4HCYgIICpq6tjf0pKSpizZ88yZmZmDI/HY9v51KlTYseNYRgmNjaW4XA4TEJCgsT6Xbp0ieFwOEx6ejq7zfPnzxk9PT3m+PHjItv85S9/Edn3J598wnA4HObx48dDimH79u1snpcvXzL6+vqMnp4eU1hYyKZ/8cUXImX0jv/48eMMh8NhioqKRMqMiopiOBwOk5ubK3E7Qsgv6Eo3IWNUZ2cn5OTkALyar1xWVgZra2s0NDSgvr4e9fX1aGtrw9KlS/Hw4UM8f/4c+fn5KC0tBZ/Ph5KSErsva2triascKCkpwdjYmH394sUL3LlzB4sXL0ZbWxtbzsuXL2FjY4Pa2lr89NNPUueTpLa2Fvfv34eDgwOmTp3Kpk+YMAFeXl5oa2tjr15KS3jlWTitpOfvKSkpYvlVVFSwceNGkXZwcXFBdXU1cnNzB52vdzsOpo7jx49HWFgYmpubwefzkZubi9DQUKirqw9Y7571nTlzJgBg0aJFUFRUZNNnzJghsnxiWloaYmJi2HMLAOrq6qCqqoqWlpYBy5RkxYoVIq//+Mc/orOzEz///DMAIDMzExwOB+bm5myeSZMmwcXFReoy0tPTYWZmxv7Y2dkhODgYU6ZMQUxMDNvOV65cwaRJk7Bp0yaR7d3d3TFp0iR89913Eve/ZMkSqKio4OLFi2zahQsXwDAMVq1aNWB9gVfHfSgxWFtbs7+rqKhgypQpmDlzJmbPns2mCx+47mspTG9vb9y8eVOkn7e1tUFe/tUwYqjHlpCxhFYvIWSM+vnnn9ml2UpLSwEAkZGRfU6zqKysZFebeOedd8Te19HRwcOHD0XS3nrrLfafMvBqnWsAiI+PR3x8fJ/ljB8/Xqp8klRUVLDx9CYcMDx79kzitpJ0dHTg8uXLUFZWhqamJju3dvr06VBWVsb169dRXV0tMojV1tYWGZgCv7RZRUUFDAwMBpWvdzsOto76+vpwc3NDXFwcLC0t2YcDB/L73/+e/V04t7lnmjCd6TFffPz48fjf//6Hb775BiUlJSgtLUVdXR2AV202FL2XEBS2mXCe9ZMnT2BhYSG23bvvvit1GRYWFuxqNHJyclBUVMS0adOgqakpkq+8vBxaWlrsOdozJi0tLfbY9KaoqAgbGxtkZGSgpaUFEydORHp6Ong8nli7CJf57Ku+g43hD3/4g8jrcePGSTyOAPqdJiIQCHDw4EE8ePAApaWlKC8vZ2Oi6SWEDIwG3YSMQU1NTSgrK8OSJUsA/PIP08/PD4aGhhK3effdd9mBXO+BIvDqKmtvwn/kQsJ/0Js2bRK5+tbTrFmz2EHDQPkk6TkA7E1Yz96Dlf5cu3YNL1++BCB65ben1NRUvP/+++xrSfsXlt2zTaTN17sdB1vH7u5u/PjjjwCA7OxsVFVVQUNDo899CI0bJ/4voucVbEkOHDiAmJgYzJkzB4aGhnBwcACPx8Nnn33W5welgQxUZmdnp9TnZF/U1NRErpT3ZaC27+/cWrNmDZKTk3H16lUYGBggJycHn3zyiVi+nh+wXkcMvc8fYOA27S03Nxdubm5QUlKCubk5HB0dMWfOHJSWlmLfvn2D2hchYxUNugkZgy5evAiGYbBs2TIAv1yBnDhxotjAIycnBw0NDVBSUmLX7ZV0ZfHJkycDlissR0FBQaycoqIilJeX43e/+53U+foro6SkROy9x48fA4DIlIyBCKeWBAUFia1bXF1djb179yIlJUVk0F1eXg6GYUQGNsL26XmXQNp8vQ22jv/617+QnZ2NnTt34siRIwgNDcWxY8f6rfdQVFRUICYmBg4ODmJ3TIRTI4aDlpYWW++enj59+trLmj59OrKzsyEQCEQGtx0dHSgvL4eRkVGf2y5YsABqamr47rvvUFNTg3HjxolNJRnuGIYqMjISioqKSE9PF7nzMBznESFvKprTTcgYU11djejoaGhoaGD16tUAAC6XCzU1NcTHx6O5uZnN29TUBH9/fwQHB0NBQQFcLhfTpk3DmTNnRFbtyM7ORl5e3oBlq6urg8vlIiUlBVVVVWy6QCBASEgIu3qCtPkkUVNTA5fLRVpamsjXd3d0dCAuLg6KiopYuHChVG3V1NSEq1evQktLC5s3b4a1tbXIz8aNG6Gvr4/i4mLcv3+f3a62thYXLlxgX7e2tiIxMREzZ84UWZpP2ny/po6lpaX4+9//DgsLC/j4+GDLli3IysoSWyHldWhoaAAgfhfi2rVrePLkicgxE17NfR3TEmxsbJCXl4fs7Gw2raOjA2fOnPnV++7NysoKTU1N7AoxQqdOnUJzczN790gSeXl5rFq1CtevX8fVq1dhamo6pG/f/DUxDJVwOlrPeBsbG9lnGnouqUgIkYyudBPyBsvMzGTnh7a3t6OkpATnzp1De3s7YmNj2Ychx48fj48//hj+/v5Yt24d1q9fjwkTJuD06dN49uwZoqKi2KkGQUFB8Pf3B5/Ph4ODA+rr6/HVV19JvL0vyUcffYQ//elPcHR0hIuLC9566y2kp6fj/v37+OCDD9h4pc3XXxnr16+Hi4sLlJWVkZaWhgcPHuCjjz6S+uu8L1++jPb2djg6OvZ5O57P5+Pjjz9GcnIy5s2bx7ZncHAwHjx4AHV1dZw9exZVVVViVwWlzTfUOjIMgz179qC7uxuhoaEAgD//+c9IS0vD/v37YW5uLja399eYNWsWNDU1cezYMbS3t2Pq1KnIyclBSkoKJkyYIPKBTjh4S0xMRG1tLfsBcCg8PT2RmpoKDw8PuLu7Y8qUKUhNTWWvfg92KkV/nJyckJKSgvDwcBQWFoLL5SI3N5c9/k5OTv1ub29vj5MnT+LmzZuIiIiQSQxDYWlpidjYWPj5+cHCwgI1NTU4c+YMewej57ElhEhGg25C3mBhYWHs78rKypg2bRqsrKzw/vvviz2Et3z5cpw4cQJHjx7FP/7xD8jLy2P27Nk4evQoli5dyuazs7PDwYMHcfToUfz1r3+FhoYGgoODce7cOdTX1w8YE4/HQ2JiIg4dOoS4uDh0dnZCR0cH4eHhWLt27aDz9VdGdHQ0Tpw4ge7ubujp6eHIkSN9zhGX5Pz585CXl++3PHt7e0RERCAjI4Ndb1pdXR0hISGIiIhATU0N9PX1ERcXJ7ICyWDyDbWOSUlJuHPnDvz9/aGtrQ3g1Xz80NBQbN68GXv37kV0dLTU7TEQRUVFxMTEIDw8HF999RUYhoG2tjZCQkLQ2dmJzz//HLm5ueByuTAzM8OKFSuQlZWF27dvw9bWdsjlTp48GV9//TXCw8MRHx8POTk52NrassdG2g+E0tbx5MmTOHLkCC5cuIC0tDRMnToVPj4+8PX1HfB5gblz52LmzJmorKwc1Ln4OmMYiu3bt6OrqwsZGRnIysqCuro6zM3N4enpiVWrVuH27dt9PvNACHlFjunviQxCCOmhq6sLDQ0NEm+Jr169GqqqqmK3vMcaNzc3VFRU4MqVK68lHxlYfX09Jk+eLPbA4IkTJ9gvbuo9H1+WVqxYAV1dXfztb3+TdSiEkBFEc7oJIVLr6uqCpaWl2IoLhYWFePToEbvEHSEjKSIiAmZmZmhra2PTurq6cPHiRUyZMmXISxUOhzt37qCkpATr1q2TdSiEkBFG00sIIVJTVFSEnZ0dzpw5Azk5OXC5XFRXVyMxMRFvv/02PDw8ZB0iGYPWrFmD1NRUuLu7Y82aNZCTk8OlS5dw//597N+/f8Al+EbCuXPnkJWVhRs3bkBPTw+LFi2SdUiEkBFGg25CyKDs378fOjo6SEtLQ0pKClRUVGBmZgZ/f3+pvuWQkNdt4cKFiImJQWxsLKKjoyEQCKCrq4tDhw79qrnir5OCggL+85//QEdHB1FRUa/14U5CyG8DzekmhBBCCCFkmMn+nhshhBBCCCFvOBp0E0IIIYQQMsxo0E0IIYQQQsgwo0E3IYQQQgghw4wG3YQQQgghhAwzGnQTQgghhBAyzP4PL1qRNZmfZSAAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig4, ax = plt.subplots()\n", "ax.plot(n, concheb, label='Chebychev Polynomial Basis')\n", "ax.plot(n, conunif, label='Mononomial Basis')\n", "ax.legend(loc='upper left')\n", "ax.set(title=\"Log10 Interpolation Matrix Condition Number\",\n", " xlabel='Degree of Approximating Polynomial',\n", " ylabel='Log10 Condition Number')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "nteract": { "version": "0.21.0" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 4 }