{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fourier Basis Function\n", "\n", "Example created by Wilson Rocha Lacerda Junior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example shows how changing or adding a new basis function could improve the model" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from sysidentpy.model_structure_selection import FROLS\n", "from sysidentpy.basis_function import Polynomial, Fourier\n", "from sysidentpy.utils.plotting import plot_results\n", "from sysidentpy.metrics import root_relative_squared_error\n", "\n", "np.seterr(all=\"ignore\")\n", "np.random.seed(1)\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the system" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simulated system\n", "def system_equation(y, u):\n", " yk = (0.2 - 0.75*np.cos(-y[0]**2))*np.cos(y[0]) - \\\n", " (0.15+0.45*np.cos(-y[0]**2))*np.cos(y[1]) + np.cos(u[0]) + \\\n", " 0.2*u[1]+0.7*u[0]*u[1]\n", " return yk\n", "\n", "repetition = 5\n", "random_samples = 200\n", "total_time = repetition*random_samples\n", "n = np.arange(0, total_time)\n", "\n", "# Generating input\n", "x = np.random.normal(size=(random_samples,)).repeat(repetition)\n", "\n", "\n", "_, ax = plt.subplots(figsize=(12, 6))\n", "ax.step(n, x)\n", "ax.set_xlabel(\"$n$\", fontsize=18)\n", "ax.set_ylabel(\"$x[n]$\", fontsize=18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulate the system" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = np.empty_like(x)\n", "# Initial Conditions\n", "y0 = [0, 0]\n", "\n", "# Simulate it\n", "y[0:2] = y0\n", "for i in range(2, len(y)):\n", " y[i] = system_equation([y[i-1], y[i-2]], [x[i-1], x[i-2]])+np.random.normal(scale=0.1)\n", " \n", "# Plot\n", "_, ax = plt.subplots(figsize=(12, 6))\n", "ax.plot(n, y)\n", "ax.set_xlabel(\"$n$\", fontsize=18)\n", "ax.set_ylabel(\"$y[n]$\", fontsize=18)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding noise to the system" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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03ICBQVNDdpkrm4DIoDJMQGRgYGBgYGBQGZ4IiAxDZNAikOsQGYbIoApMQGRgYGBgYGBQGUYyZ9BqMAGRQQaYgMjAwMDAwMCgMoxkzqDVIAdEXqlx52HQEjABkYHBRMOy5wHPrf45AwMDA4FgQmkYomZG0fXw0CurGn0adceC1YMouhmLksu224bZNKgCExAZGEwkrHgRuOj9wP2/bPSZGBgYtBIEQ2Qmlk2NM+94GZ+59Ek8v6Sv0adSN/SPlPHB3z6A79/wfLYNZYbIBPIGVWACIgODiYT+5eznW8809jwMDAxaC4Yhagm8sZrlyqwZbB+J2EjZBwA8/OrqbBvKAZEJ5A2qwAREBgYTCYTXJDODg4GBQRaYHIyWgBV08e3Tx9v8ovys11Q2DJFBepiAyMBgIoGIR94MDgYGBhlgJHMtAYsvevl+g09kDOD5GdueJxmBmHZrUAUmIDIwmFAwDJGBgUENELbbZjGlqSECIq+N+njBdmW+JMU8qH3uh8HYwAREBgYGBgYGBpXhGdvtVoDNZ3XtJJkTxFDmIM+XAqI2uh8GY4OWCIgKhcLsQqHwZqFQ2KHR59IqGBgYwKWXXopPfOIT2H333bHrrrviyCOPxLXXXgu/hbn0NWvWYGhoqG77O+6447DffvuN+7YDAwNYu3ZtTduOCiQYLcf/2AYGBq0LI5lrCQQMUesO8xGI3KHMkjnfhU/JGJyRQTui6QOiQqGQA3ARgOFqnzVgeOONN3DEEUfgd7/7HQqFAr71rW/h61//Ojo6OvCTn/wE3/ve91py9ejBBx/Ehz70ocYEEnXE/Pnzccghh+DVV18d/4MHpgptNFoaGBiMPYxkriVgWe0nmfNrkMz1Lu/H359YgDJsZN7YYELCafQJpMBvAfwJwKmNPpFWQLFYxFe/+lX09fXhhhtuwA47hKTa5z73OfzsZz/D1VdfjXe96134zGc+08AzzY7nn38eGzZsaPRpjBqvvPIKVq5c2ZiDG1MFAwODWuAZhqgVIBiiVlz0TIIghrK4zN3z0gpsTHy4sNEBF2bMM6iGpmaICoXCCQBW9fb2/rPR59IquPrqq7FgwQKceuqpSjAk8P3vfx9Tp07F3//+9wacnUHjYRgiAwODGuAa2+1WgM27+MwW1U0Mn0dEWa6pp8OBAxeuYYgMUqLZGaLPAaCFQuEAALsCuKJQKHykt7d3eWNPq3kxb948dHd349BDD419v7OzE9dddx0222wz5fV///vfuOCCC/Dcc88BAHbeeWecfPLJePe73x18Zr/99sM+++wD3/dx2223Yfr06fjHP/6BI488MvH1OXPm4Morr1SOtd9++ymv77fffth7772x66674k9/+hPWrFmDHXbYAaeccgr22msvAMAPfvAD3HzzzQCA/fffH3vuuWew/WuvvYZzzjkHTzzxBMrlMt7xjnfga1/7Gt7//vcrx33sscdw3nnn4eWXX8bMmTPxrW99K/V9TbvtnXfeiauuugovvfQSisUiZs+ejQ996EM45ZRTkM/ncf755+OCCy4AAHzmM5/BnDlzcN999wEA/vWvf+GSSy7BCy+8gIGBAcyYMQMf/OAH8Z3vfAdTpkxJfa4VYeoQGRgY1ILAVMH0Hc2MdswhogFDlH6bSR0OHPgoBdNc024NKqOpA6Le3t59xe+FQuEBAF82wVAyKKV46aWXsNtuuyGXyyV+buutt1b+vvfee3HSSSdhyy23xFe+8hUAwPXXX48TTjgB5513Hvbff//gs/PmzcM222yDH/3oR1i9ejVmzJhR8fW0eOyxx3DrrbfiuOOOw6xZs3DNNdfgC1/4Ai699FLsueeeOOqoozAwMIC7774bp556Kt72trcBAHp7e3H00Udj5syZ+NKXvoRcLofbb78dJ554Is4++2x8+MMfDvb/xS9+EVtvvTVOOeUUrF27Fj/60Y9ACMG0adOqnluaba+//nqcdtpp2G+//fCd73wH5XIZd999Ny655BJ0d3fjpJNOwoEHHohVq1bh2muvxZe//GXsvPPOAIBHHnkEX/ziF7Hbbrvh61//OgghePTRR3HttdeiXC7jzDPPzHQ/k8HlFKAwqaYGBgapIQqzmsWUpobIIfKzGhA0MWphuyblbQAeXD7N9X2/uSVRBg1HUwdEY47/XAM8e1Wjz0LF3GOBXT9d06br1q2D67qYNWtW6m1c18XPf/5zbLzxxrjxxhvR09MDAPjUpz6Fww47DD/72c+w7777BgHWyMgIfv/732PLLbdU9pP0elq89dZbuPDCC3HAAQcAAD760Y/i4IMPxtlnn41rr70Wc+fORaFQwN13340DDjgAm2++OQDgF7/4BWbMmIGbb74Z3d3dAIBjjz0Wxx9/PH75y1/igAMOQD6fx29/+1vMmjUL1157bXCN++yzD44//viqAVHabS+99FLMnTsXf/jDH0D4Kt3RRx+N/fffH//85z9x0kknYYcddsCuu+6Ka6+9Fvvssw/e8573AAAuv/xybLrpprjsssuQz+eDbY866ij885//rFtAtKK/iI0BrOkvYmZd9mhgYDAhEEjm2mei3Y6wRWHWNgpca7mWrryNMny41AYI4Po+8mNwbgbtg5YJmHt7e/+nt7f35UafRzPDstjX6Xle6m3++9//Yvny5TjmmGOCyT4ATJkyBcceeyxWrFiB+fPnB69vueWWsUFP0utpse222wbBEADMmDEDH/3oR/Hcc89hzZo1sdusW7cOTz75JD7wgQ9gZGQEa9euxdq1a7FhwwYceOCBWL16NV544QWsWbMGL774Ig499FDlGvfaay8UCoWK55Vl21tvvRUXX3xxEAyJ7adMmVLVKvyiiy7CjTfeGARD4vp6enrqajO+tI+ZNa4fNvkABgYGGWDqELUE+DSgzVzmatvOhhe4zJXK6edFBhMTE5sh2vXTNbMxzYipU6cil8tlsqVesmQJAGCbbbaJvLftttsCYOzN3LlzAQAbbbRR7H6SXk+L7bffPvLaVlttBUopli5dGrv/N998EwBw5ZVXRvKUBJYtWxawW3EB27bbbovnn38+8byWLl2aettcLoennnoKt99+O9544w0sXrw4CObmzJmTeAwAsG0bb775Js4991y89tprWLx4MVasWFFxm5oQmCm0z2BpYGAwDhC222000W5HkIAhavCJ1BG1MEQUgAMvMFUou22UVGUwJpjYAVGbgRCCuXPnYv78+XBdF44T//Wec845ePPNN3HqqadWtOYU78n5SLZtx3426fU4xDFYcTlP4nNJ+xbvH3PMMQq7JGP77bcPAotiMbrCWa1IrRhc0mx79tln4+KLL8aOO+6IXXfdFR/96Ecxd+5cnHHGGVi2bFnF4/z973/HT3/6U2yzzTbYY489cNBBB2GXXXbBlVdeidtuu63ittnAvlMLZnAwMDDIANeYKrQCAslcG0VENQVElMKBhzKf5pY8t96nZdBmMAFRm+HAAw/Ek08+iTvuuAMf+chHIu+PjIzghhtugOd5mDZtWsBcvPHGG5HPLliwAACwySab1HQulmWhVFKlWa7rYt26dRHGZfHixZHtFy1aBNu2g3whHeLcbdvGPvvso7z32muvYcmSJejq6sKcOXNACMHChQsj+xAMWRLSbrt06VJcfPHF+OhHP4pf//rXyudWr15d8RjFYhFnnXUW3vOe9+DSSy9VAtlzzz234raZwYM40j5jpYGBwXjASOZaAtxTAeU2spljwxbFbPSl3oZSwCZ+IJkru0YyZ1AZLZNDZJAORx11FObMmYP/9//+H1555RXlPc/zcPrpp2P16tX44he/iFwuh3e+852Bq9vAwEDw2YGBAVx99dWYNWsWdtppp5rOZebMmViwYAFGRkaC1+67775YtuWFF17Af/7zn+Dv1atX49Zbb8Vee+2FqVOnAghzpARzNXv2bOy00064+eabFXlZuVzGD3/4Q3z961+H67qYMWMG3v3ud+PWW29VgpNnn30WL774YsVrSLvt+vXrAUSlfw8++CAWLlwI1w1Xp8R1CIZpZGQEw8PD2HrrrZVg6KWXXsKTTz4JAMr2o4KQzJmIyMDAIAuEqYLpOpoaHXQEh1n/gttmDNHn7TvwZOfXgNWvpdqGUiGZ4wyRkcwZVIFhiNoMHR0duOCCC/C5z30ORx55JA4//HDsvPPO6Ovrw5133omXXnoJH/rQh/DZz34WAJOq/fjHP8Ypp5yCI444AkceeSQA4IYbbsDKlStx3nnnBRP4rDjssMNwxhln4Atf+AI+8pGPYNGiRbjuuuti82ny+Ty++MUv4vjjj0dnZyeuvvpq+L6P733ve8FnhJX3X/7yF+y7777Yf//9cdppp+H444/HEUccgU9/+tOYNm0a5s2bh+eeew7f/va3MX36dACsIO0xxxyDT37ykzjmmGMwPDyMyy+/PHi/EtJsu/3222OzzTbDn/70JxSLRWyyySZ4/vnncfPNN6OjowODg4OR67jmmmuwevVqHH744dhll11w0003oaenB9tssw1effVVXH/99cG9HxwcDALDUYEHk8TkARgYGGSBZ1zmWgGHLPk95uZvw/XrdgOwXaNPpy6gFPiU/QD7ozRQ6aMBfEphw8Mw7QRgGCKD6jABURtixx13xC233ILLL78cDz30EO644w5QSlEoFPCrX/0Kn/jEJxQntIMPPhiXXnop/vCHP+DCCy+E4zjYZZdd8Mtf/hJ77LFHzedx9NFHo6+vDzfccAPOOOMM7LDDDrjgggtw6aWXRpzTdt11Vxx66KH4wx/+gP7+fuyxxx749re/jR122CH4zKGHHoq77roLN910E5588knsv//+mDt3Lq655hqcf/75uOyyy+C6LrbZZhucddZZ+PjHPx5su9NOO+HKK6/E2WefjQsuuABTpkzBSSedhPnz5+OZZ56peB1pts3n87j44otx1lln4YorrgClFFtuuSV++MMfwnVd/PKXv8T8+fOx0047Ye+998YhhxyC+++/H48//jgOOuggnHvuuTjzzDNx4403olQqYc6cOTjxxBOx3Xbb4eSTT8bjjz+Ogw8+uObvIgSXzNVhTwYGBhMEvgdQPqE0iylNjWklVqrRShk4tAJ8SrEdeYv94XSk2oaZKhjJnEF6kEpJ9c2OQqGwNYAF9957b2KeiYEGtwQQC7CbJxbeb7/9MGfOnESnOIP64Zn7b8JuD34Wb+a2wRY/+k+jT8fAwKAVUBoCfrUp+/3o64G3H9TY8zFIxBu/OxDbbngSN7zjXBx51AmNPp264NnF6zD30q3ZH199HJj9jqrb3Dl/Oba+7gAspTOxv/0sni98He/69Blje6IGrYDE9WCTQzTR8ItZwAW1sz4GrQ2xAEKM7MXAwCAtPNkcx/QdzQzK53teFQfVVoLvS+xO6kV85jK38bSejNsZTFSYgGgiYt2CRp+BQaPAZS9GMmdgYJAackBkJpZNDfHteG1kqkBqkP/5lBVmnS0CIhPIG1SBCYgMDCYSgsmMGRwMDAxSwjWW260CSnkdoph6f60Kqrisphu7mMucD1i58AUDgwponkQSgwmL++67r9GnMHFgJHMGBgZZYSRzLYOAIWqjAID62ctOUFDYxAPl+dKtnC9vMD4wDJGBwUQCNS5zBgYGGWEkcy0DkUPkt1FhVnjl8PeU7Y9SIAcPVDBEJpA3qAITEBkYTCgIhqiNBksDA4OxhSSZe2NVfwNPxKAaQoaoffp46meX/4k6RMQ2kjmDdDABkYHBRIIvGCIzOBgYGKSExBCtHihV+KBBo+ELhqiNTBWozBBlGLsc+AFDZCRzCeh7k5VjMTABkYHBRIIIhIgZHCrjj+8FHj670WdhYNAckAKiKZ12A0/EoBpCl7l2YojK1T+kb8Nd5mA54QsGKsrDwO93Am49qdFn0hQwAZGBwQQCbSMZxZhixXzg3p83+iwMDJoDkmQuZ5sMxGaGmPf7bRQQQTZVSBnY+JTCgQ9iO/ApgckhikF5mP185Z+NPY8mgQmIDAwmEHxqJHMGBgYZ4RlJTatAmCrQNrLdhleDyxwFHLiAZbPRzjBEUYh7QkwoAJiAyMBgQoGaHCIDA4OskOsQma6jqRF8PTR7ENGskG230zJflPqwCQWsHA8STcONQChGTEAEwAREBgYTCiYgSgGzkmhgoEJJam8jKVYbQhRmRVsxRGH7c9P2zzyIIpbDAiLTr0cRBERGBguYgMjAYEKBmjpE1eFlT+A1MGhreDJDZCaWTYE/7ANc/MHIy0IyB9o+/RiRGKK0ZhGEW3UT2+HLf6bdRkB50GwYIgCA0+gTMDAwGD+EDJFZ5U2EyZcwMFCweNU6bMl/N9PKJsHKF2NfDr6fNmKI5DpErpeyBQrJoGGIkiECTRMQATAMUeuhONDoMzBoYRiXuRQwAZGBgYLHepdJf5mJZTMj6OHbKocoZLs8LyVDxI0YiO2AicRNu43ABEQKzF1oJax8GThzDvD8dY0+E4MWBQ3kBmZwSISRzBkYKKCukcy1CkQOEfHbhyEiNZgqBAGhnTMuc0kI2ogR0QMmIGotLHkSAEDfuL/BJ2LQqhAMkWUGh2QYhsjAQIEtrdCbrqO5EXw9fvswRHUxVTCLgFEYhkiBuQsthBUrVwAAXlpnvrYJjxUvAhd9ABhZn2kz3xeDghkcElFDVXQDg3aGJT8TJiJqaghTBdJGkjlIbJefNodImCqYHKJkiPtqXOYAmICopbB+3SoAwOv9uQafiUHD8eD/A5b9B3jtnmzbCYbIBETJMJI5AwMFNpVZU9N3NDP8ICBqH8mczHa5aV3maOgy54OAmPzZKAxDpMDchRZCrrQBADDiTG7wmRg0HN0z2c/BNZk2C00VzKQmEUIyR+zGnoeBQZNAlcyZvqOZIb4dq61yiML2lzaHSLCazHabmHYbB8MQKTABUQvBKTF5VNnubvCZGDQck3hANLQ602ZhHSIzOCRCBESWqUpgYAAYhqiVIOb9BO0TEKGW4M4PXeZMi01AwLyZgAgwAVFLwSn1AwAs03YNujdiPwdXZdqMpnXomcgQkjnbSFMNDADAaad8lDaHkIa1E0Ok5nVmNFWwc4DJIYqHKcyqwNyFFkKuzBgiu9aimqZDaB+IDmwwG0Mk2oBhiCrASOYMDBQoDJEZR5oaoui21U5BrBTcpW1+IofIsrjtthnzojA5RArMXWgh5Mosh8iqVe9pkgrbB+K7HKoxh8hMapIRSOZMQGRgAACOX4YL8zy0AiwRCLSRZE51zMvoMmcb2+1E8IAorXFfu8MERC2EPA+IbFJjYNNOFHqrYvHjwKre0e9HfJcZGSIhmbNqZRknAniFc5NDZGDAYKOMEriE1CymNDUCyVwbucwRyfkzbesLjBi47TYx7TaC4SJb/Fu6vljlkxMDZsRvFVCKrtJaAIBNanywDUPUeFx6MPt5erb6QRGIwW6kL9tmpg1UhzFVMDBQ4PguysgBGDFuXU2MkbIHyhfL2iogkq/FT9f+guu3bVAYd8Q4lMtldAEYcc29AQxD1DpY/2bwq5HMGQQMUdZOPvi86QATIQIi2wREBgYAY5S9IKfO9B3Nih1+fGew6t9OAVFNxbK5GiIozGrabQQ+Z96oCQUAmICodbDk38GvtZsqmICobUBrqx8gJHNGPlABXii1MDAwYBbOPp8umK6j8ajEdgg5dFvlECmmCukaYFBiglgwLnMx6HsTXU9fBACgpg4RABMQNTVue+4tDJV4PsOy/wSvWzVL5tqng5zwCOyzMwZEpjBrdUiSuVX9RawbLFX+vIFBm8OiPnzOEBmHysbDqyAbEwumNvXaRiYmmyrQ1O1PMESWYYjicPUn0bH0cf6HCYgAExA1LZ5etBYnX/Mszrj9v+yFkQ3wCFuxNjlEBjUHtyLh1gwOyZBst9/9y3sw94y7G3s+BgYNBqF+yBCZvqPhcCsFRNx0ySZ+xcCplUD8Wlzm+HyHWMZ2Ow4jG4JfqbHdBmACoqbFukEm21mxgbt/SCt0NX9pbbJa1A7Y+gfzMFgcRZ2IGh0DDUOUAkYyZ2CggMAHFTlEZhxpOMpe8uKmkMw58CoGTq0EWTKXdugiXDJICGeITLtVIZWVoIYhAmACoqYFLfbj5vxPsJW7gL/gwecMUe2SOcMQNRNWbBipfWPBEGVkioSEwuQQVYBI4DWmCgYGALhkDsZUoVngVigcE0jm4MFvk36eKKYKaRkiPtZZPIfItFsV8oKfYYgAmICoaTF9xeOYa72Gj6+7lL3ghwyRXeuDbeoQNRVy9igev8BlLmOQ65uguCqM7baBgQIL4fjTLnkprYxyhX48ZIj89mGIapGI822Yy5xZBIzAzgW/GoaIwYz4TQpS6gcAFK1J7AVphc6qte0ahqipYNf8RUJiiLJ+pzzR1KyWJUNI5syqmYEBfJ/ygIg9D7UKFAzqg4POeRA7bTYVv0t4X2GI2iYgkkwV0gY2Qg1BCCiIyX3TYRiiCJo+ICoUCjaAPwMoAPAAfLa3t/f1xp7V2IOUBwAAJbubvSBL5mp9sE1A1FSouZ4UEDI9Wb9Tk0NUHZwhMivhBgaARykbcwRDZPqOhuKVFQN4ZcUAftcZ/77TZgzRpY8swJS31mFnu/pnFQjbbcuGsd2OgZRDZAgihlYICw8HgN7e3vcC+AmQuDDSVrB5QFS2OUPke0FhPOEikxkmIGoqjGpiIRiijBI4Mck3LnMVwBmi1f3DMIGjwUSHFzBEJoeoFWC1GUN07r2vwpZrKqUObMI6RMZlLgaKJLwVQoGxR9Pfhd7e3n8AOJH/uRWAFY07m/GDCIhKjiSZE3Ugal3pMHWImgqjGqtqzSEKAiITHCeCM0Sz1r+AhZ3HgJh7ZTCB4fkUthwQmZX2psWvnD+jYC0B0D4MUc62kKulyKwoQm5ZoIQYqacOK8whylrgvV3R9JI5AOjt7XULhcJfAXwcwJGNPp/xgF0eBAC4dhd7gXrwRuvyYxiipsKoJFk15hBR+fO+D1hNvyYy/vDUQqzdKDboRAwMGg+XM0SBZM5MLJsWRzv3B7/bxGuLOkQ5mygMUfpxU7jM2dw0wMx/FEgMkalDxNAyd6G3t/d4AG8H8OdCoTCp0ecz1hABUVCE1feDwqw1BzZmJGsqjOrrEIXqsrJ+ssTOBMjx8NT6UJMwCnt0A4MWh5DMUZ5zYAxZWgMO2iMgcmwS5EUBGZaDxfgmJvutfyvqC9uYKuho+rtQKBSOKxQKp/I/h8DC/LbXfuVcJplzxFNM/YAhIrVOZP1adLgGY4XRBUQ1mCoMrsHmxdekE2j7x6g2aAxRDxlu0IkYGDQeru/DlgqzmpGjNWDDh9cG43zOtuAgXKRKG5AH8yRC4MMy0mcdEkNkBHMMrSCZuwnAZYVC4SEAOQCn9Pb2tv2SrRMwRGLi68Hn8WvNUiuqsQMkq22LQT0xqqJ5tUjm/vw/eNfwYukETEAUB+qXlQFium0kcwYTF55PYREaymoMs9wSaBeGKGdZgZU4kMV2W2aIiHEN1SEHRCYiAtACAVFvb+8ggE82+jzGGzmPBUSOCIh8FhB5tPaKy54fZiGxzsIERI3EqLrnWkwV+harfxuGKBbUVQOiGTkTEBlMXLgeZZIlLtk208pmQPVvwYbfFgGRYxPNVCEtQ8S34S5zRuqpQQqILLPIAaAFJHMTFY7LAyKE0igfnPqtsfGOlMrhH+YBaDjqwhABma23w+1MQBQH6pWVv2fYpYRPGhi0P4TLHOUTKDOxbDzSfAc5uG0SEFnoIiMo0WySzYARIhYzVTAMkQo5IDIWfABMQNS0sCmblAW6Vy6Zo0DNwUzRBERNhdHlEMn5YKYuVT2hB0RTHcMQGUxcuD4FkXOIzMSy4UhTR65dAqIOi2J78hZep5uxF1IOW8HciUvmDLepwQ5tt2vOS28zmICoSREsbkgFOD1YoLBQ64M9UpLcs8wD0HDUxXYbqP279AzzEQc9IJpmt33KooFBIgRDJCrb11wHz6BuSBMQdZFSW9Qh2pSuQg8ZwUt0q0zbhaYKNl9IrvuptTYUUwVzcwATEDUxuIe+lDzPJHOk5gmwkcw1F0ZXmFU2yKhR+uYa5iMOekA0hZiAyGDiQg+IDBqPNIW1O1AanSy7SbCN9wYA4CV/S/5KyrkLNQxRRcimWmY+CMAERM0L3pGRIHmeSeb8UWhhi65hiJoJdDQddF0YonL1z0xEaPelixrbbYOJC1aHiEqFWc3EstFIs6LfhRJcr/W/q838ZQCA1+gcABmmP1JARIkJiCKQnIOMZI7BBERNimDQkRgiJpkjNTfekmGImgq1eiGwjesREBmGKA7U1wOioQadiYFB4+H6bCkuZIjMxLLRSJVDRDzQNpBFC4e5IkTOS1rbbZF3QAAQIwvTIUWWpkYTgwmImhaaZM73JMlcjQxRWQ6ITOfQaDScITKSuXhoDFGnbxgig4kLIZkjRjLXNEgjmQMAv9z6fZdtMSqDZiwfSmSGCDBzHh3SvMHkBTKYgKhZQfUcIg8e5faRNUbzpXIdJtEGdQGBXz+XuVrts41kLh7a/TQMkcFEhutTzhDxJGwzeWo40jBEAIBy6+c/2twSOgyIshdmpSaHKIKB4XBB1DBEDCYgalaIQUfoquogmSuWTQ5RQyFNJOzRBkTy91frjoxkLh6aZK6DmvtkMHERmioIVyozsWw00jJEtNT6izk24QwRFT/TbRdI5ISpggnkFbz0Vl/wu8khYjABUdNCl8z58KiQzNW2x1LZ5BA1FFpANCoHoHrkELmtry8fE2jMmVk9M5jIcD2frdJbxlShWZCaIXLbgCHis9TgitO2P81UweQQqejpCKf/5t4wmICoSSGapyKZA4EPC7VL5gxD1FBI99yBN7ouSMkhSieZ83UNtmGIYkF8t/qHDAwmCDy++EKkuiUGjUV6yVwb5BDxYSsYv1IGRESx3TbQ4cguc2bRD4AJiJoXkRwiH67IIaoxmCkb2+0Go7EMEdUf9zZwIBoTaJI5k3BqMJHh8XGDGJe5pkHaCSxxWz8gsohqqpC69Ym5k8ghMv24Cmkh1YxxDCYgalqwBrr54IvAoscA34NHyahyiKhSzNMEROMO6Z7b8EYnPanBZY7qK2VGMhcLwxAZGISgAUPEAyIzeWo40jJE7RAQ1WqqEMkhMoG8CtllzjBEAExA1Lzgg85GpaXAZYeAUg+DZcpp49oebKXRm4Bo/CFNJJx6usyl/C59aLa5RjIXi2hAZAZSg4kLz+PPg5HMNQ1SB0Rt4DInEAREtRRmNQxRFMZ2OwITEDUt1Aa6YaiEko9R1SFSnclMQDTukO65BR9+vVzmUtpu+zpDZCRzsSC6ZK5B52Fg0AzwPdbXWLax3W4WxLnMUUpRpmzR6w7sA6A9GCI9Z5qmlQuKMdLi7rxmYUsFvz9l5AxDxGECoiaFPgmjvgufjs52W51Emwdg3KGbKjQ6h8hI5mJhGcmcgUGAgCGyje12M2Am1uOhjlMir/sUWI9JuNl7L87F0QAA0gYuc6AUPk8XyLqdp4x5pt0qoBTz6bZ4qud/TLDIYQKiJoXeQAn1kc/lgFG4zBHDEDUYkqkCGS1DJAdE6XYUZYiMZC4C349ZLTODhcHEhe+xvsYyhVmbAofajwd5NTJ8ygro9tNuvHOrTQEAVhswRJEkgbQuc/DDIIrUXq6kXUGox+YExDJ1iDhMQNSs0B56Ah90lFpYy+QQNRaKqYIPOpoeuiaGSFthMwxRFJpcDjA1GgwmNgRDZFl2lU8ajAdmkP7Y133KevhtZ03GDz4yFwBgea0fEIFS0Fp6YeoHVt10opsq+B4wtFZ9jfoACAuIJvK9kWACoiaFTg4TygIin9RJMmcCovGHUpjVG91CK/UAOx/+ngI+CSc0HiUmhygOXjQgMjCYyPCFy5zDGCJTmLWxmI74gIhStug5pTuHjq4eAABx20EFQNXFvJTNj1A/kImzHKIJPOe57wzg19uoQRH14cMGhRWbkzYRYQKipoXOEFH4ZJTJgSYgaiyUHKLRusz5gJWL7LfiJpLLXAk5I5mLA2eISlRaDTcTQIMJDFGHKJDMmdXkhmIG2RD7OqV8IZVYsG0bRZqD3Q4MEddSZK5DBKowRJmc1CgF1rye5SSbG/+9hf0cXhe8RCgFJYwhMgERgwmIWgQW9cDMNmuXzJkcogZDYYhGWZiVemGScw2SuRJyRjIXBy4PKiEXvGTkBG2IVb3tNeEZQwjJnO0YyVwzYEYCQ8QkcxQgFhyLoAgHVhuoACLDZNocIqrlEGXpx5/6C3D+bsCSf6ffptXAGTRqcogCmICoSRExVeA5RL4xVWhhaJK50ezK90KGqAbb7TIcI5mLA3eYK8PUXGlrXLgnm/AYVIXLGSLbFoy0WSBoJKZXyCGy4IMQAosQeLBTy6mbGQQih0gqzLrqFeBfF1bdzpckc5nw1rPs56qXM55t64BQL2CIzKIfgwmImhRxLnM+sUdnuy3t88g/PoL+EZMvMa7QbLdHzxCJHKLsttslExBF8do9wGt3A+D3x8DAAB53mbMdwZrWYfJEKXDP6UDf4tHva4Jho8SAiDuycYbIg5V6saypQSnUrGoK/GV/4J8/DBj9OBDqSYFQRsmc08F+tkUOVhIoKGwumTMBEWACoqaFvp7BNJ4WYkwo0+9TmjiXXQ+vrBio9fQMaoHUIVvwR1+HKGOhRF8OiKjT5p19DbjqCODWkwEAJWokcwYGABsrAIAKU5Z6MEQrXgQeOQe47jOj39cEwyTE5wVRwRCBwBIBURswRCKH6MeH7cj+ogCKG4L3kjfzlTEv07zJbtOASHp2mVGXYIiMYggwAVETQ314LeqDWqy7q0cOkVkRaABkhoiM0lSBetlNFSTJXBE5wxBVgGGIDAwYfL4KT+w65hARvuTXbhPOMQaNFBsNIRgi8H7ehwXSFkWmWfL/5M4YU48KY5+Q2gFgE/8sc56AIWqDwrYytLQJCstI5iSYgKhJEZtDxC0Sa43m5e3MA9AAKHWIvNEVZvX97LbbUHOIqHGZS4RsqmBctQwmMoSpQl0ZIrE40w6SrnEEpdBYjxDMVMEPgk0XdnvkClOAzVhirrtC+2FpBpJkrqaAqM3GSGmuIAw4QIhZIOcwAVGTQpfM2byjoySjFlaGwhC1QUfZcgi/N2e0krlaXOaIbLvtGJe5CpAZopii8AYG7Y1/fBV49R4Aoe02CQqz1iMgEsGVCYiyIokhohpDRNuGIZLc4qDVwao49vmaqUINAVG7LRpK7UE1VTDzQcAERC0Fyk0Vas4hkrYzKwINgBaQjo4hcmuoQ6TabtN2W/2qI1TJnHlWDCYY/vM34G9HAABckbjO6xDV5WkQwZVhiDKBQu3Hlfd4DpEIiDzSJjlElF03iZutVpLMUSqxSiTbwpbTyX622xgpPW8sh8iYKsgwAdFYoRjvBJMWcfQuJTZLmayRBrekztEyy97jDyozRB5GNbXwJZe5tLbbuqlCq+YQ3XQicOcPx/QQsqmCgcFEhif6Fx4Q1axQkGEkczWB0mQDaZ8CNqEgXCbmw26T+0t5Qfrw7/DXSjlEch0ibbtqEGNru+QQiWdWaQ9CMmfBagdpZR1gAqKxwIr/AmduDsy/aRQ7iXl4CeE5RKOXzBHQIK/VYJyg5BCNkiGiHmBnY4gittutKpl7/lrg8co1KEYLY6rQpnjxH8zhzCA1hGROsDq0LpI53he1A4MxjmAG1PH33/f5OCAkc6Q9AiICYbvNJyzy5VdhiBTJXJZAXjCYrTpGJoFqDBEIiGVMFQRMQDQWWLeQ/Xzumpp3ERersBwQkj1RcvHjwIs3K43+CPvhms/NoDZQLSCqeaFVDHwZAyLZZa6EXHvoo689dpQLD/GQTRXMYFED7vox8Ju3Nfosorj+eOCP+zT6LFoKPq9DBCJyFuux17gVa4NqYHlCCQGRGAcEQ0RsJWek1UGCFdyUOURUzj3KaKogBud2YYgE5BwimSEyYxwAExCNDRxGt/YtX1jzLuIeXkIs+CTjgw0Alx4MXH+C0nkcaT+EjjXtW4W5GeFLlJA9msKsYpXHylY53odmqtCqkjkZL90G3PDZuu+2bHKIRofHzgMGVzb6LAzqAN8XpgradOGFG4Dn/l7bTkWfZRiiTKBIlsxRPr4QyVShLe4vZZxkYKGdRTJHajRVEPtt44DIoh5nEy2WQlEPKWyLwwREY4EyK5xGNiyBV6MuKj6HyGKSuRobrq4TJbQJVo+G1jKJ4QSAJ62GOqMJiMR+AoYobQ5ROJSWaQtL5sYBRSOZM2hHFPsBr5xpE08vzCocqW78PHDzl9QPP3IO8M8fpZhcGYaoViRL5rzgEwBniNoiN0TLIZLbVkXbbRqOeVnTA8Qx2mHREAjrfmk5RJRYgFjoaIu2MjqYgGgMMDjADBWmkqHaJ70xiAxImaFuR0XiYCPxlwOAP+7Nfh9YCaxf2tjzGUP4Xnj/82QUwSgPgAZcoalO6zKnS+ZavLMfwxWtMpVstw1DZNAuOHNz4G//m2mTkCFKUYfontOBf10AvFhFxmoYoppQ6dYHdtRWmEPUFrbblAdEcUnPFcY+C57qMmcYoojLnJDMAQA1ixMmIBoLrO3rC34XVb6zIvbhJRarPl1jJK9v5zXDgsDa18Pff/s24JwdG3cuYwyZIepCcdQM0d29a9nfNeUQOa1vKTqGg/0wOsI/TDxk0E544/5MHw9yiAJThWT0+puzX/oWp9x5MwxCrYWkib2Y0BLJVKHWuUJzgSb/WdV2W8jsMpoqBAFRi4+ROrTCrBRWUBPMN8+iCYjGArQ0FP5eYyNLCojoKKzhXlqyRn3BzyadMBgdPE8OiEq1Exy8U3NptloekRwiv8UZonoGRNqXMYCu+u3bwKCVoD0LNDBVsOBTUlF9JMYtWk2WZxiimhAUX41BkKPK5wjUsptDFj9KBIFNXCGiiu3HD+dLWXOv2zUgUkwVGENELHaP5PnJRIUJiMYAtBwGRPVsZNSyue12bUFWF1T6l7qt31m2EjwpOO4gpdpttznrWETWwqyqZI60umQuYy5ERWhB5RDtDH43kjmDCQUtIAqYbWKzJ6GiTIltO1Ks1reYHKJaIOwFYt8LXObajSEKDRUASRoIZCrMWpupQrsFRFItykAyJxgi8yyagGgsIAVEtTayJJc5iqj0LS0maQGR3w764haCzBYyhqjGiTa3yx5BXuw43fGlQaVEHdaOapR0NgXq2X41tnRQlsyZgKg9MNFdlFJfv/o5WTKX7HHGwApOAxsGh9Odi2GIMiOZIWLjQJBrQ2xYbcAQifYYb7ud3KYJ/MBUQS3smuaQ7ZpDpDJE1ApziExAZAKiMQEphYNBXXWZxAZGUZi1m2gMUTNNhieAftX11Byimudnbm0BkS/JLQNb6VZmieoZEGlsk2tc5toPE33AT/u86JK5JNvtGDiE3eP+oSoBkWGIakKlOkSCIQpyiCynTRgizWw8A0PkB0ZUhiECoNwvtrxuBe3Fa4qk8sbCBERjAXdscogor0OULTkw/Gw3tIe7mRgieaWwnlKoJoIcHHeTolKoNRN4EDNMOYuRcj9EajZB4dFWLs5aV4ZI3dc2M3uC341kbhRopoWOic5G1Niv+opkrvL408HdMwdHqvQrwT7Ms5UFFNVtt4VMjBCL1ZppccjmCIDWYirZbiMszEoJyRYcis+28oJhHGSGiFIQYgULHcZUAc29DFooFHIALgWwNYAOAL/o7e29taEnlQJEkszVOumN7fQsG8w+MsM+pRWOLi0gai6GSOrYSoNA17SGncpYQV6BOcJ+GMW79wX2XJR9RwFDlC2HSB5KSuLRb+VaRPUMnLV9yavhtduYVMGSp4G/Hg584zmgZ9ZYHaWxoB6aZt1torMRqU10YiRzFrPdrpZDlOOSuXIpZQ6RQSZQWqEwKw8yRZI8LBsE7dHmme12+Ff4RiWGyJcCqaySuTYN2GXbbfjMot3YbgdokpEqEccCWNPb2/t+AIcAuKDB55MKxJUlc7XmEMW8lrEw62DRxa4//kfwdxdRBynarAyRFFC2E/QVmI5yX2074qtWxYySORlFwxBp+1Ini1YKedCo8fDZQHkQePPxsT9Wo9BMg2zcavlEyCvyysCdpwIrXkz3ef2eiH6LVLfddsCeSbfaQstEuO9jAMYQJcAXuTa877KcSDH21gQPa0RElNZ2WxQeDbatQTLXLu1UXIc0ZlrwAYQMkddMfXWD0NQMEYDrAdwg/d1EM/hkWFIiXq0BkRUrmbMZ9ZvywV47WEIXwoFJZ4iaSjKnMETtGhDVqcPRc4hS7zdsN0Hh0VaWJ45hDpGaLzE2g2J5eAMLS/M91T7aumgmyU5ce/E9wG72YXCUeOw84PE/ABvSFr0O2zulVCrMalVNTneoCxDAK1frV9pkojnOqJRDFEobQ4aoHSRzoBSURUTiBem9apI5zn7UWpi1LQJKCdL9skBBLTs0VTC2283NEPX29g709vb2FwqFyWCB0WmNPqc0sOuQQxQLixdmTSmZyzsWukglyVwTPQByx1YaaNx5jCHqtgLDWZ2sOUTyalcomTMMUdy+CAlrNo1FDtFI2cOLC/kENT+p7vtvGjTThCKuL26HCWM1zL+Z/eyaEb5WqS+S+omyR2GL8YZLtiutmucMQzTmqGaqIArownJqLtHRXKBcMhcTiqcszFqt3Ub361Xdf0tCk8wREpoqULkOyNKngd+8DRhaO95n2FA0dUAEAIVCYQsA9wO4sre39+pGn08a2F7IENUzICIihyjlg20RogRB3URniJqIHZDvU5tL5lyro8onq4BPNrLmEMkDaZm0gWSujuwW1ZJn0zhqjQaeTzFJPJvtPDlsJhlGXPDTTCz5WGFwJftZGgxfk3+PQA6IfNhESOYcUXY1fjPfg82dW7yqNe7auM2PJSoWZlVtt4llw4ZXe3mHJgGR/geQ3mUOviSZy7iwJfbbTP1XPaBI5igvzMru0dTbPwc89Rf25sO/Y/3GwkcacZYNQ1MHRIVCYWMAdwH4fm9v76WNPp+0sD0ph6iWFQb+wD/qvVN9mUvm0g4mFFQJiCIMUTNNBhSGqNJg3brwuakCtUYp0eFBjMghSm/cEbYbYnO5XUtL5uo3WLnSBM6lFuxxkMxNIryfaKbnsN5ophXWuPbSbhMeHZ4LDK5iv8v9aspFp7LnhxPJKosEnsQK0Wr9SotP0huFSoVZxT0VK/7EcmDDh1tzBfAmAWVXLQI91WWuSkAkM0SZjikkc23SPwh2TWaIqM+CId5eOpb9G5j3bfamYBnbeWyKQVMHRAB+CGA6gB8XCoUH+L+uRp9UNThSQFSTLI13bE/6O+Aa94PBy4GpQtoJGlWNFDqhyRiaqbHrLnNtCBEcW6O872+uXg8AGKY8IKphUkcczlK1tGSufsGcWwrvgwcb9hjHQxRAjyiU3C6DbhyaKeCYaAzR0FrgzDnh5E6WIlfqY2VpreuHkjliVbTdLkvPkF91oaXFJ+kNQqU4MjTtCXOIbPgouU20KFETuGQuNoco+dosGuYQodYcombqv+oB3VSBWIo8PHyTL9q22/VXQVNnk/b29n4DwDcafR5ZYXslFKmDDuJmS6Sf9x1g7evAMcxHgmqPMLG4qUJKGR6Fygp1EBcutdCHHswkG5prMiCfS5tK5oTtNpGrh583FzhhHjBls9T7Oe+uF/GbXGiq4Pt+qpUNuQ4RcTqAElpbMlfH9ivnPLiwYEl69bGw3aaUYhIMQzSuiLvPzXR+9cZbzwKSwY/Sr6aUzJW8MCAiNq9DlDCxdMvSgpvnwvMpbCvh6TEMUU2oVIdIL8wqGKJyyxfc5FctpIDy/Keqy1xYh6g2l7k2Cwg0UwVYNk/F0EAMQ2RQJxDqocxjTZqFrn7qz8Dr9wWDBSfAg7eZHjZ9HSJKozK5InL4aPEM9kczRf/UA2zOWrQpQySYHMX5Z+0bwJJ/Z9pPB9jqaxAQpWYhw7Zo5fi9bmXJXB3PXZ7MubCVidxYmCpQIMi3aKrnsN5opglFrGSujQf8runq32klc1KwUpQYIrGSTCnFBfe9GtlMZllteOgfqfB8tnMgOsZIrkMkTBV4QGSzHKK2YYiCgEhqVyld5mquQ0T99grefTUgIpLttoKAIWrj/jEGJiAaAxD4cMEGD7+mCYEIiIhSoZkQm0vm0u6FRmsPgQTn1lSN3feAXCf7vU0DIj8pOF77Rqb95LmTUzFgiDIGRJ+6GnauHSRzdcwh0gMiOYe3bkeR9invtJ0Doma6trhJeDOdX90hNbL8ZE0yV8nJM9xuuORhMnjw1DkVFMCSdUP47V2vRLZyy2Ff4sBD31ClBYs2mmSOI1hh1iRTC9VUweIMUanFGSLCc4iCv31pTpPBZS6tGRUAuHLR+nboI6i2+EYpLEJZ8BwbEPE5YjMtaI0DTEA0BmAMEV9Nq+VhGtnAttUlc7aoQ1Q7Q0RB4DVjQER9QCT63/NT4PSpjT2fMUBi4JI5IGITDZFDJNpLNRBQ9ObeAexwqMQQVaso38SoY/v13HDy9pS/A5wxZoiUXS57DhhYWf9jNAOaaUCdaAyR3MambKYuNFViVxWGyMM0MgDXmQTYOTZ+JCzsuNIz5MDDW+uHYz8XOTeD1KgkmfOFqQKfzBLbgQMfZa8dbnbI8FgKQ1TZVMEX0i8CZGl0/1kk2U03Ux9WK8Q18P4udCS0YBHDEAmYgGgMQKgPN5DM1bA6M7CCbQsoDBGEZC7lSodPQ5e5Is0Fr7via6/S2F9d0Z/MatQbvtf2MgoxkRiesq36Ro0MkZDMdT72G+DVe6pvKK2YWYKNa2mGqP6SuR+Uv4BTyl+FnPowJpI5+dwf+BVw/h51P0ZToJlWV+MmNu0w2UkEb7dHXw/kutIHRBJGyj6mkUF4HdN49hBBjhZxQe7c4DNL+4bx9KJ18GTJHPGxaE2lXNB2mKSPP2iM7baw1RaLr0FdVsuG1SamCkB4XUSat4xUKACs5BBlMaMCMFJqM4bIV3OiAldVq5pkrg2uPQNMQDQGsODDpUJvXXtABE0yB0u4zGVgiEgJHiUo8po1FJAYouTG/vLyDTjwnIdw4f2vZT//WvDIOcDQGvW1dtLuIrQ5X/LeX+Bx/x3hG2sXZNpPnpThUiuUPgLAm49nOxlL1CFqXYaoVBqp/qGU8Lmpwn/87TGCDtVlbgxA9cKVxfVje8BGoZme4bgFoHYe8MW9JwRwOlSDhYqLCeF3dsxfnsBUDMDvnBZMSHcvPoXD7CeCz3zwtw/giD8+Bk9aXMnDw8I16ZzsDNKDxkzqg3SXwHabjQuWk0OOeK1vqkC5KUJMDtHqDcksJFFc5viOUsK2ZCe7NugjRN8XMET8mogNy67kMmcYIoNRQpbM+bV0RpJ8RpHMESezW0oXihhCp1yBJhVD9FYf62ieWrQu9bFGhef/Hn2tlRP+Y+DxVRor141n/e3DNzYsAcoV5CUa8nBRQg6Kt1x+UqZz8S1Rh6h1A6IfXJvNjKISRA0V8dzaCkNUf7R6scTUaKbJxISrQyTaGAnlyAJehYmO1jankQHQzunhHrX3BQMh5+F1ORSLDUNUf1Cw3A/lNcEQRQuzAkCx3NqTWhKEgVzdUCkgGtnA5Pbzb4QFKYeIZDNVcOR73A5BQRAQ8WeVGzFZlgUrzmVOvObWb9GxFWAConqDUlYMrZYcIofLmALJnGaqwBkiK+VkilKgG0WMIB/sR2aISIVzE51ql9fP6lmMAVZsqPKwuemDhFaA0O3atsbuAMC6Ran3k0cZJTjwlICop+p2RBogfJszRC0smesg9QuYPS69EPfUVkZP/rxtWAaU6mUJP0EmhM0UcMSaKrTBZCcJAUMExhDJqLgQogVEGAS6pvMsDgKC+O+0WGR9iWfl0W1TLFidkiFa+EiFczGoBhEuBGoUnhNiOWyVX7FDb0mIzCkREIXXs7pfm0P08XH0od8yiZzIjyHZ6hDZ8mdrSXtoNmg5RJ5wpiUWLK1Q/OI1Q9hQ5NdcNgGRwWjAO6UghyjLSrCY1Eo5RDJYVeH0DzYFRScpYZjmlcAqjcuc+PRFSz8B/HqbVMfLivf86t7KH2izh1Gs4Dm2jUjloLWvp94PC4hy8OU1r1QMEQ2F2DYPvluYIRL24/WAKCQpnlubxKwn/m4H4MqP1+V4E4Uh8ioxEeONuOCsmRisukMERFZY0kCgkmQuwhD1g3RPD3NTEmTgA0NsscB3upC3fKwdTBl0XX5ohc8ZyIjrN478wyPYMFKO1CGy+US33OIMkch9Dbpkqe2u6dcWTaXcFyaZC13msknm5OO3QR8RuMuxn4GpgmWB2GpAtO9v7sd1T3IZ/0O/BhY8PG6n2WiYgKje4A2vFDBEGToj8aAPM5lalCGqXBhPh3CZG0Y4GFKQcCJNk8/NbQZnmjZjiDw+mNm2DZfqAVF6Y4UO4qIEB4qYS5fExICZcYRVzAG09Ap5PQOiQDLHc//kAZGAhpPErLlaSZggAVGQvNsMiJvYtHD7r4ogcCGAk0Eyp+4E0zAIa9IM/pe8XxWDw6y/9p0uOPAwXK4wkZwg7b/eiAuInl+6Hne/uCI0cBKSOT7R9Vu+jbNxS4jeiiOhqmHNgLZoKhUUteDz2o1s3qMrDSuByG28mVjuWuFrDBHvl4kVn0PkyCzwXw8b89NrFpiAqN4QLh4QnVEGulUkWgcBkQpCCCixYKU1VQDQhRKG0RHsi3LZQ5naFSVzFQezcQK994wxk+s1AkI+adt2aGwBsGAmQ0CUR1lxDQSQstMOJXO2xetRtfBgmQ8CotFn+VBXMETRgIjpTOvLpE0YhqiZJhOxpgptIIeJw+AaYA03xCEkE0Mkt80pGEKOeHCCgCi57MPgEJucUqcTNjwc7t4NLH066Sja+bTp91BnxJk0EVCsGSyGpgrCdpuzJX4zLUrUAOFuKOAOh2UmSkkuc74bKcyahSGS520XPxQtQtxyqGCqQOxc5ONOgiy23WEConrDFwFRDYWtPL7ykcAQWYRruFPnEFF0kSKGaYeSQwTwXIkKk+FmCIjI/BuAed9q9GnUDaFkzlLzfybNBob7Uu8nZIgkpA1sAktWXo+qhQMikUNE4+RtGSEkc55waNJ3Wa5X7hBDTe6TLQJ5Qu0102RsItUhOm8ucOvJ/A8Sk0OULiDaiLDJp80lcxQEdkxAtLDzaBz04nfZ9k43HOriV86fgT/vF3uMvqEJ4rJYZ4iv5rUt/hdru8PyDWsGSwFzZ1kqQ9RUstWa4DOOiNtD28Org3ciZU2Cib+n2G5nzSGSawZe8Wh6OXvTIsgh8vkPyVRBk8wBekA0FrZCzQkTENUbvOF5WesQeW4oRUgKiCyr4gpd5FQgJHNqDhHAAjZSIViz+t/Cws6j0537WCKjJXUzIzBVsGx4cjG0/KRMDMSUnI8ScjjsXZuGL6YKvEPJnGNxt8FmWsHPCCGZq4errM8Zoq5OlluluszROpopcLQxQVSU6p40k2Tu/15YGn2xHfID4iAFGJc8uhBUl9SmZoi4MUK+J5AsJU0scz5b0KNOFyaXVoRvvBbNFe0f0fq7NlICjCWEgcJw12y8MvtDAFiPvnagFNQMFDlEwj3Mb/GAiEndwg45XwqdbyPFziUmxNJst7MERPK8LW4BoOWgMUSeGDRjcogAwCHSNXdNG+OTax6YgKje4A+ob2UNiKQBQpLMqbbbFiixUsfrLIeohKGIZI4xRKTC6mhXX5PQxG00UIqAyLItzTK7O5O9ZQdcTOruwid2myPtvPqgJ7cbux0YIh4Q6cF+LaB8xby7swtAjKlCHEP04G+Af3yttuO1cUQ0UAzbVPejZwX9WaNx7ZMLoy9efmgmdrYVcfdLKzHoa3kCFSbJMns5mfA8Tm7aQgE42gSxE6pTJc11qTu86hORhZec/nw18jsYWts6JR6CYNUKc4VAsXawBEpFYVYth6jFAyKAqQBEQN7jhv1JMkPkai5z2QqzypK52T3RgKGlIN8jYargibZiwY5liKQ20zltLM+uqWAConqDDyY+yZhD5IWDCg0mEFGGiD3YaVcsmGRuRDNVAKozRMNejDd9HZE6h2JodfXPtAiCHCLLhi9L3nLdmeyvHbhwkeMSSo40TA8Nc4gs0voBUb6OpgqU3//uLjaZs3SGKC4guv8XwH+uqu14bZxDNCgFRB1vPgLc+cMGnk0IfSIf4K1nx/dExhmUEqzUHbBTMkSTwdt9rjuQzHVAZXdm2wPqDvSACIj0T5E87uEGLnz9ehvg+hMad/wMSM4hKgXfGxWyX1sYO7VIsJcIyT4ewDQa5hBFTKsk84DRSObkcikb91Q3LGpqyPdIMET8p2XZsGJziAxDZFAPCIaIB0RJjjwRcEMFNz8FRGKLFJc5UlmyoCNwmaN5iN4kzCGqPBke1lcU64zU88HyUNs4EvmBy5wFX5bM6VXkq8CBC584cCxpHykCIiJJ5uxAMte6AZHIISJZ7IOS4JVQpA6mdrPBz5ErleuSOXf0BgvtnEMkM0QAmsYt0iYJ9zxjUeNWAwXwjxe0haWUOURTCG/3+e5gJLK1522WFhCRXHd0p9X6mUaxiOJaX769McfPCOqL4IBAnr6tHSwFzmhhDhGb6AY1Z1oWYtziDBEZCXJwIwvOIvjzPeYyJ9x+M6oI5P55emeLT5PlhW8+TwiYNSuJIZK26Zo+lmfXVGjxb7oJwRsfzSiZGxlhk4aFI2GBTf0hJhbhkrl0E0BfkczpOUQWrAq22yNj3IdmmsIW+8fqNMYVVEpkVFzmnM5sFaEpkxDYFsGrPpfNpQxsxIpZO0nmHPijD5q9EspwMKWLPbcW0brGsrTEPtI3umMBbRPkx2FgRG9TzZGUO70zYZFHNxwYa6z477h+/xRENWFxuioGRH4cQ5TvYS6nMd/ldGnFHgBIPoYh0tUI+rjYKGl0y/V/UkCUKJnj5gOCIWp1yRyl0lIew4DDXQ+TJHN0dKYKMkOUqXRKVrx2D9B759jtH9AYIq0OEYk3VbDlgKhz6pieXjPBBET1hp5DlDJp98/3vwQAWEWnBa/pOURskmZlcJnz0M0lc+EWPIeIVpbMjXV160ySoTYJiETSq23ZMQxResmcYHpsi+AjpTPYiynamTwg2ISwWkhtYKoAAHj1rlHti3hFlOBgSidbVZVXwQmgMkR1yHdoa8lcSZtA6MFlgzC9K+E8xpOte+MB4I97A8/8ddwOSQEUIclicl2pC7NOJqFkTuxLR4+vOsSRWMmc2iYi7b9RkrkWK0wd3rYwPLg+/zPQYj/CMkSsnZPAVKF1+3hAXCkBkXTMg7kqAVGM7XamgEjqE+hY3r+rjgCuOWrs9g8oYzwNGKLQdttyogFRTg6IrBbPocqA5hip2gliYmqxASgtQ9Q/yFagVyGMxqO220xqlbYOEcpsks0kc+E+AcYQVapDNOYBUZYPt0lARANJgwVPLsyalSECIAKigGnKuIrVXnWIAFz9ydGtuntllOGgOx9liFgOkST7qgND1DIB0dN/Bf57S6ZNRspa/9QkAdG0JIZoPBcFRG2gt/4zbofce/uZ2H27TcIX7FxqydzRNneIy08KJqY6pkPtn0k+TjKn32Ot/Zf0JKdxQosFRPKkXpAfO1sLsa/1PIplXmyTv2E5fA7SKoYRiaARZnJQMES6ykXKIbKoZKoQWDKkPKI0b2v5wrbSs1fi8zpfsIkWgR2bQyRdcxvLu3U0x0jVTvBVyVzaxrTFFDZYr6WTg9dEEVUBsUKSdqWD8En2iGS7LecQVWSI3LHtRCkFXus4Nt2HSwPVP9MCkCuJl6lWmDUDQyS+RRYQ8Uc4ZWFWOYeoWi2qZofIIQowilpBxCuijBy68+x7GZ61E9sl4YsJsmSuDgF6q8RDuO3rwHWfybRJ0dXaYpMERF1Owk0fz4CI1FCfbpTYeEo3dpgzM3zBylV57sMxaxavQyRMFeIwg6jPg9U5JWaX6vVGcuga1Q+JYIGMbc5svRDcNy2HKAcPawfZeE+4VM4ShVlbWAUAyLmvYQMsWUzmmiyZ85lkDqFkLtMyrHTPWv3+yc9W4DjoCcmcHV+HiPigm80FujcyAZHBKCAaD2eI0rrMbdTJHtYRyGyOJpmzSCb7SCHX8yWmSXWZSx6EvDEOiHxKVa/7SihuqP6ZFkAYEFlw5fUqpzOzZI4SVksoS0AkDxC2xYOyVg6IdJe5kdrbieWVUSY5dPGAqLTxrsD3F2H+tA9CN1VIrI6eCa0SEWVHlCFqjhwikjSwj+czYAlGd/wmGZM7c7A6JNbGdiozRH5M2+R5VrE5RBJDNNwxE7l8TE6WLpnTL79R/ZDod61WCYjEb0R5rmx4WNvPAyKRJ+qIgKh1+3gALIdIb3Z8kaVSYG3BB9WZ/tSHlBiiJqqlVgtk23Xxe5DKYVmwnTiGyAPtmAJMmmUCIoPaIQIJUQMgbQ6RxTXdRSkg2nu7mcg5YUdtEQsUWQIi9rlP7LZ50EkG51lFMufVZdKXHSUaMzAV24Mh8oOOhaDk155DJPbBbLcJ00mnGfQoDQZRZrttjW3C6Bijk2jnPlJ7tXvil+DCQWeOtT/bsgK7UQKASuzTy2+N3hErdtLZJiiWm5MhspIG9vEsztoAhmhyVx7etG3CF6xcZdvtuBcJ4aYKUcgLE127fSrIOfDkWWykn2F7Wk6nszonjZJ1Cclci+RJiDFdH88d4mHNQJG/Jwqz8jlIi5sqiIU8+Zp98RwlFWYFC4hqrUMkBwGtPEYCwIr14fzJ10wVYNlB4CxA4LOAiDjs/pmAyKBWBJXZeWXwtBMfi3fMRRpG6915B9vPDiV0xGLF2FLnEPHOs8Oxg5o1MkNkVRiUvTpYC6c4tQjKiBmY2kQyF1w00Qqzihyi1Doq9jnHZt+lb9kZJliy7bbd0oNlt6Wd+yiYRMsvwSU5dPGAyAkSeNnPoYFw3yNFLXitSVLRvoPMiNukDBESvqfxnPCICdo4TjK6Oxz4G70tfCFDDlEa2MTHYPfmwHE3Awf8DOKZkdUOev8kVuC/UjqF2Z43QJbk+zS8Dy0TEIWSOaowRD76hrSAyBEBUYtLvgDojJgwS4hK5jxpCzX3KFMOkRIQtfb9GypKZVwChih0mdMZIocHRPe9ug5lHy2k7x49TEBUZwS5N0EOUVqGiDXaPd+2WfiiKpsNCrOmRtB5hqxLmENkVZbMjfFEmSas1vhx19cmpgrh92ExQwOOB97YAICmXiUVmWQ2n7RT4qSa1MkDQjvkEOW1ApGjkczZfhkuyaMrz9pfzlalFuvWh+xTUQ+IaljdbmuGqEld5pIlc+MYnFoJK9tjeUhC4HT2SC9U7i8qBURxkrkcXLbP7fZjcjxuQCKrHSI5RPye+yD8fMaXIRoouvjYj87HrU+9wl5oFclcMG6qkwMHHlasZyw2sTSGqNX6+P4VQP9y6QUe2MQxRNRX26vUF9uyZI5Y2Sb2sqlCiweUSn/MlSgiMCIkWodo5027YcODBxvDZWoYIoPa4fKHhzgZGSIeEHV0hlpvAmazHfxNLFAQ2ClXl4OOgsTnEFViiMZ6gEq6L6ITv9w9CPd9+EH2YtsFRFLuD4BHFvDrS+k0R8Ckb7Zg/Uha+2w1h6jVGaK8nkNUrF0yZ/lluMTB+7afheP33grbzuLFOnn9isH+cN+lkhaI1eBUlbQg0A6I5lg1CUOUNDFsCEM0njI9grwU4DOGKLnNVhqz4gIiGz6o7FTFDUjmY/vwtQTJHAVh5zPOk/bB5a/j1o4fY/snTmMvtAhDJEP+JvbaKjSyCBgiIdtvNYbj7LcDZxfCv2lkbTgIdCz4cOX2KrWjDpSwsmOr4O9MqQbUhxcEXa07RgJAsRT2x8JoSzzjJKYw66d33ww5eHBhwyfEBEQGtcMNcoj4AJGRIersDqum64OPRUi44pFitSMMiKL78mjlgKhS0dZ6IGlCKK5vAd0U/flZTHrYLgERQsmcHBAFNUJS5hFRyr7PkCGyU5sqiGZgEwKP2q23eiihmw6rL4yKISrBI3nMmtyBn310p4AhonwYHRoaDOScxVIJ85dKwVcN97BlbLdrQKmsM0TNERAl5hA1wlRhHCcZhBDkbAv/W/wJHtvlTNanVmQ12bn9vHxc5J24VpuDByIHFNyA5Nn8XNw8+2t8l1r/RMOAaM2wj3X9tTtE1gLCg7YdrUXshVYJiPxwkVN+rvbYcnIgpbeE3Je3tVbu4xnEbEGSzPFgxQKF68UHRIv82Xhm2sH8r/S220XXhwUKn4iAsrUDghKfkw7RDlguGzOD3HZiB/bsAh02hQ0PLljOugmIDGqGyCESAVHEBSUBIofIkquma0+wZZHwsU6132gCplKHqEJAZI/xCmZSJyOocAqg7FEg39NGOUShqYInSebCgCgDQwQEAZFPUrrFUdV220WrF2bVVrmz5BD5PnDFR1mlcAA2LcOzom47wrbC98oo8e+pXC7h8TfWhB+qF0P0yDmZ99OMKOkOlc0imUti1seVrclik18vWMjZBE/RHfDaJh+uLpnjk+5+RAusxk0qHbiM5RHgwUZH12S8WuZ23wmFWSmAFQMenl20Kv3l1AGe3am+0CoBEUKVgRwQddnhkicRzIbVHjlEQhEhr6uEDBFFWZ5LSO3sebpt4PYrmP408CmFRSj8oJZkaweUZc4QDaITlicYIp5DZFmRtp8nLnLEgwsHi9YOY8GqdlmQro7mGKnaCB4PiCxuqpA2uhbBiSw9IFqnZ1lWmEiZhiEKOgpLScAEWB2iSgzRmAdESQyRFCiUPR/o6GkblznZVEEuzCqMNDYMpLtOkUPkyAxRiu9Lt932WrwwawRZGKLyIPDGA8C1rMaOTcvBAKiA8CUI30eZsPdLpRLWDkpBUC0OWXGypHtOr8FtsPlQbtocIvUZucI/hP0yrs9AlgWtBFAK/OtCYLgv9SFzDvsOSq5f3VSB980+jX5vSZI5hSHiE/KOnulYNSjqwiQzRC4s5MfZZITqdYdaJYcoGPdVEVmHRQOGSNQrDHKHfZcF4OsWjd+J1hXcZU6argpTBQs+yrKJi7TQsJBuEk6fMtQh8ilfBOMMEVpYVg6EC1QDtBOOJxgiwSba0GtwdRAKBx5casEHwZtr2mT+lQLNMVK1EQRDZOXE6kLajl5oOuXGqRdmtYKOIM2AGgQdCQyRheQH3a7wXj2QdF9yOT0gmtI+kjk5IJIevU1nTgMAPLtgRbrdAACpgSFC2JoszhC1cg5RBJlc5jTbWlqGZ+UjnxLPC6EeXB4Qvbq8D4++In1XNVW7b2PJXJMyRPoC0Iiwvh9PSYzot0fDEL1xP/DPHwJ3/iDVx4llBTlEJc+vbrvN+6mP7bY5sOXewF5fC9+LNVXwwkLkAHDA6cC+38OqLQ7E6iF+ndr1yiUIXNjochosy2mZwqyh6kNWflhUqmwnnjdLOLG5wANnAee+C1i3cPxOtk4glEbaXSiZS84hWkQ3lqY+6SVzlLLgMpDMtbhkTEiYh9CJnM/cbEVeGbFIZDGg2+3jkjkbfoYyL+2A5hip2gjCnc3KKJkLOjq5cRI1ILKJFXaCafYbWCvqKYmACwd2hUFZ1tsPoDvxczUjIXG3u4ObUYCw1cx8T9sUZiWS3EF2mZs2mVmrd66eD6x4McV+mPQtCIhSSt8IEDCFNmkPhkiRvtRUh4jLD5MYIrD7TaiHMmFt0y2X8fJba8MP1DOHqMUHXwAo6zlEzWKqoLEQZUgr6OMFEZSN5nsWC0QpF4oISJATV3YpZ4gqSObkjI3P3Ql86FcV928TT5XddM8A9vsRNp3Wg5LPv3v9HkuSORe2UjxyPBBZkGsZyZyA+kwR3w3at2WJgEiSzC3gBkWKe1trIWC+oOYQlb14ydy//bfDk3Ku0kvm2H590SZ8j1m0NwrrFgHP/q3mzcvc5GZASGDdEalIvBPJ8XzP3R9DN4oow4EPgtwEihIm0KWOD1wREHGXudSrj5IlcwCt1gCxIJkqpGCIgo8QaYWF/VxHe9Dj9yVuKxii56YfiGHEVB6vBQsfAf6PrWrSJImEtFJ3ySML4Nq1FC2NwUUfAJ7+6+j3MwpQqXOWGaKOTtZRvee5HwF/3KfqfqI5RE5qlznx/TtBDlFrB0TKyvQoTBUcWoYfwxDJEifBENnwkJcZ1FoYonYOiCIMUXMERDpD5IqaZ7U8A31vAg/9NpV0WYEYD0YjSRZyNzs+gI+AWLAtAotw1r2KzXXYT8W8F/P5CEPEsdm0rjBXcukzgR03248kmaM2bG8E5aG+dNczGlx2KPDsVdEFiRYJiELFnLbI6bMUePaWsJqWigA3oP5VvUCkcUtAzIssEm+qsNfI+VhIN8VwOWQiUzMdPCCiQX/vq3lK443LDgFu+WrNxYsFQ1S2eEBUHg5MFYRFu45JpMgKt4MgbyN7P9eiMAFRnSFyiJwcZzpSDnyENzjLriSZs0PJXKqHW1QjtoJPi8BoBaZjsteX+JCJHCKP5FIeKwWu+CjwxB+B4kCytavEkC1bP4LX1xTrYwG+7D/AbV8f/X5GgXCFWjVV6OrKxsDpDBFNGdjIOURWkEPU2gm3tjQp9LMwRGJiwJ+7XGJAxD7DJHPsfQc+q70iUEsdosQ3Wn/giTBETTIJI9RXFiLKVJowZsU1nwbuOwPoy5iXUQ/JnHjWExhNHUJVkHcsFhBVySGS3TCj78TlEHmxAcXGUzrhijyku34E3PYNaUdhQGQ5OexmvYbcr7eK7KOu8H1g0SPALV+L5LAOtcq6kFwwVPp+CHWDCT/RGSK/tQMiICqZY6OZxXKIFIaIPVcrMB0AMFwSbmrpJXM+pSDwA8WAQzw16BpvDHB5do1jQ9ll96Bk83lGeThYmCEV5MwuHPjUwm7+fOBn04GHz67p+K0EExDVGR5vfMItbvbqJ1KZAgSVg/WBRa5GbVnwRcCQYlU68JqPuPgDy+kMtqKUQKHbvKo7JQ6segVEkzdlP/sWJUsJ+aqW6NwHy2h5FkOAJuQQ7bz1xtn2A7ZCVksOkWhPtsWkKq1+b4lUQ2FkYF36DbX258AFtWMCIj6QEurzxQH22dEGRO3NEGltqknaGIHP5KUc7mgkcyN9fKcZh9B6SOYyMkQiIMrZVphDVKnNUnncqI4cvNjgbGZPh3K/seTf0iFCyVxPl+b4NlaQ3Ep9bcX/ldXD+qebErKpgkK8SgyRFeQQ8bHUdxvkblgfCJc5vTlSYvOASGaIyrxUArve4WBxJr2pAgUU2+2ILK9RqJFVdrlkriwFRKHLXHLunAtmqsAPDrxyV03HbyWYgKjOEFpoh5sqbLf0FuCGz6XYMmZVTpOaEGKhaPM6RSn040HQESNZWUHZCgr6l8Vua1MXPkQAVqeAaNqW7Oe6hckBkfaAlqnd8i4vAkSSRcoB0Tu3mJ1tP/ynw1cCPWJnnmBZhDCnOzEZHFoLvHxHpn00BaSJmDuUJYco5ExBKTpQBo2Z1MmmCl6wYugjR6Q2WQODmSgZbYOAyI0ERM0xCbOoC192sQwCohruuXhusibj+/UIiPhiWGrJHGeIbIkh2rAEmH9T/CnKtW6iO4u8YsMD7ChDNGNSXsmVVH2TQ4ZooykSQz6W0iTBIFtO5P77LTIVkk0VFPWI78UwRKIOkRfe+1bsX6gwEpLaD08nsEDharbbgTscQoaIZLXdlnKIbD3oGm+IILjG705ImMuOCIiGJMlc8qIHM1WQ3h8cX2v8RqA1eoEWgsghsnPSavObT1TfMKgcnCyZsy2CEYsl4KdLIA9Xk8TELpDMiYBow1uxW9rweE0gAqteMp4gIKogM5nGZBNr6FQA3AmqSVaYR48wQJUDIuQnxX88AYTXExJ9mZ9BMhfmEFlwYYOIArzXHgv8/dPA4OpM59JwSM+LXcrgRhgMMlRacY/myok6RIT6oLBALQeH7DhLySGibg11iBKTdNtAMqfnEDVNQOTDJzJDNIocomCbjN+XWOUdV8kcu+acbYWmCgBww2fjT1HYN8cERHFX68ADJdGAKO9Y6OiQxkHp3ouJ/TcPfDumTpICopocG1NCsHq5SRGGVgncmgnFAUDqX8RCIiVEuZ/MVEEwRDG228FnW7d/URlLdv1RhshlC4QcIoeIEiu10oUGOUSCIfKbgyGqsc8QjL3n9PAXZMlccu6cS21Vqthqc4MaYAKiOsPnkyvHkQaCVG5AvIFKOUSRVSBCUHL45DlFQBRKtMJ6RqKBL6czAAClvqWx29rUg0ccgNTRdrGLHRN9i5InhO87Bfjfv2Ke/x4AQH+Zgo42h6hZ8jIUyZw0AHdNz7ojJuXisjk/bS6QdB9sCywoE9sJO9aUxWGbBtv+DwDg1dwO6PQH03/X8uf4JCxWMofQZQ6WDWLl8PZZnfjdJ3YM3h8ayX7Pkl3mmqStjgJCsx5gPAufVkBdJXNim6yTlCB3bTxNFbhkziFsYleuIg8LmmBcQBRvux3HEAHAFEUOJ2/LDjJ9UgdyeWkhYkwDIj5m5ifB154zv1kDojPnAJccEPwZsEB6Tgx1scvmU9h7Wg6RYqrQJIsT2cAW8tQAnQDEjnGZ85SxdaTsBZ8noMn9rnw0nkNEFYZoDAKirGxojQyRy/vj/CTWPhhDJBVmTdqO224HKK5XgvN2hAmI6oxQMidNrtIMfkHsIn8lmm6WEAzbgiGq7qgl0+uSQAgAsBaTUaY27nri+dhtbbjwic07oXpN0vh+NixNNpuwc8A7PwZx4cNuHWrlNI1MIGTsXLnoYcfkGvYl2WenzCEioJI7D1FziMgoJoeNxPYHAD9chvlT9oUNHygNptsuaBM0nIQ5MZI5fr8IfGb1ajFHv13nhKvaGwZSHlPdc5Xzal1EJXPj3Kb6lwPXHR/J3bSopwzwgWSuluAkkL5l3NavA0OUUTInGIMgh2jN6xU/H9avS3c6EdttCT3dUrAj18OTSkI4OWnbGp20UkEKiPSFB9oktbJisey54NeA2NbmBsQv44vv25r9LlhzK4YhGsuAc4wQ5BCpLwasj+4y58EKipYPiSLR/HalWW8KbbdFzqg3NpK5rP3iKCVzU6ZMAwAMDPSHDFGFgIg4HejIa8/1UHuzRE3cC7QmhKlCLp/gWJWAoIq6RPdSxS4bILBQFLRnCoaIyAxR9F0MI49Va/tit2WSOScT1VwV4nx8L7ln0jT5Lmz4ugQnK5plVSzBVCGrLbHM2JU8H29tKLFijf++rMp24f+OzVzmiLg3VouuIOYnAfluWF189St1zarwHlLBiiVI5gBu2UwsNsnwykpe24bB7AnZiQxpWwZE49ym7jsD+O8/gBfVHBlmjBH2Ly4dxSKAmLjXuso7mu+5kmTutXuAV+9WX5NyiEquD6x5jb0+Ld7VLUi4jo2IEhiiBPmewhDFSOYIISCyu+NYTtiH+9jP/KRIDqtNWoWZFYYX4f8AyyEK68Xw14M6On5LB0TCZS4qmSNMzqblELmwsek01u4ClzlYsAjF/b0rUx1NziEaM8lc6n5ndDlEoj+eOpUpUVat65MWJJKZ0detrRAJEdo8j8gERHWGzxt5Lldb7R45h4hIUjf2HkFJBEQpJn6htagF0UnKAVYROUzJxU9WHOpxGUEG//6qJxRaziZS1/z67zzl/bjg6Lm8aN8oO/FmmWQqpgq1SzQYZxd+j56Y2N1+SrUTgGgHjCGyAJFDFMgrmuRepUWOMTV2N+vsvbS1TCTbbbfM2hdJdJljOUQsIHLYQCa1yf7BoZpPP3perTIxiwelNMijDFCTJM0H/nNNbcFUUtcCT5PMSRPGzOfHrykrQ1RPyVwcK3PVEcDfjlRekl3m7vrvCjw6h5v8TN0i/hTF/Cs2hyjJdju+P5syKUEyJy0OKdt6dag5l4SAIeqJFGYlLfLchTWiLHUhzXfVeyr9JFRmiMaQgRsjBOUiNFMFQik+6/wTPcufDF/3XbjUwqZTWc2dkbKaD/f5v4ZOh0lgDJGv1CEaE9ttuV9848EUn6+tzxCL9BvN2AgAsLZvPSg/diWG6PX8O+DrfUCb5xGZgKjO8L3aGKJgxUoeHPTiayAoBpK5FKYKAS0qmyqEKCGHHid+MmDDg285mdxZqkOMtBUCIr5iscMmU7DL5tOYrMsb5Qpzk0zyQ5c5zVQBQBnJyY3xO2M/vntwAV7qCgsIBhXb0hiiRknm+t4EFlcwHVn0mGLXG0GeBUT5SdMAAIMb1qY7rtQmykXG8JCYRYygbhN89mzauUhANDCUPSBKziFqjrZaK4quH7Zz8VqphknYs1cC//gy8MSfRnE26nNhUTWHyHYc9v2OZw5RIJkbDUPE72dKmZdujnDMC7sCW70PSZFjkKeSsl9x4MU6NALA1Eld0o6l85WtvWXp33hI5nJdkTpElHpwmyFxvgpoAkOEwdXAjZ9nv4vvO5DMSTlErcgQMYu5SA6RXWa52Ts++cPwZd9DmVqYM421u1LkO02bQ0SDHCILfsx+6gC537niI4zdrXhiNTJEfIFq5gyWw923YX34/FWw3b7o8/tKdS85TEBkkAUihyg7QxS13SaAuipiEcByMIyOdKYKUgJmkHMirQgUaQ49TvxkwAZniOppqiDZRybaDksP6OwpHTzPZbSmCs0iA0uQzIHXEsq6HwBf++D26OpM19bk79HmDFHgMicPnuOJyw8FLj0oeSJ02SHAX/YP/45UmGeTqc7JjCEaWJ82IAr345bZqnQcQyS7zEHKIZLPd2C4FiOK9rTd3jBcZrlcEvr6NwBXHQksfDT9joRWvSaJRsJEn/pKrkg+56R2aEw8RmaGqMbcIxmi7aXcB+V9y9pBaTJMSGJbC+rXpXaZ8xPzmWZOkQOi6J4IISrTNR4uc9SPSFYtUAwUU7aDP+8P3PfL+p5bWsQYJQEAFknPVlCHKMZUodkDopgcUJZDlBygy0wm9cooUwuzJ2tjomDLUgVEgG67PSbBsv78JTj+hp+vsQ4Rl8zluthi+sjgQJDDbWkB0fNHPwt8/VngG89h+9k9CB5a0X7EM9SmaImAqFAovKdQKDzQ6PNIA48HRPkO7YGsMtEUq6pyxE51lzlYIIRgA7ozu8yJbsCxLDz2g/0AMIaoi8Sfl0093iGkr/BcHWEOkS5ZCCAFBh2ODcfJIe8PA6dPrZoMnHzYJplkSt+HHhBlkdDJ9tkA0Km3teQTCLazLQKP2qzd+b4UEI2zpEIUBl4Wb+4RAb+Hyya9A7DzwDQm+5k0hQVEw/3rUu4nNFVwS1wy50QDIsrbvyVkQRYP0KWJxfBwDTlEiRKdJpLu1CAj2jBSZmyahOmrnwFeuxu467R6nVk66HXcoFa878w5vIbXKIKTrH1LPeoQuUV1X1UgTBVWD0hyNCu5dplfIfdU3L+XZxyAYasH62k3HLiR3E+BzWbIhjHSxDUoMzGeAREfM/1ypG1b8LF+OGXft/TfwEO/rvPJxSDu+62YF6xBFDmX6xA1s0vY6leBX20WeVl/btmL4d8y6+u5ZZSpjandOXz34AL+8bX3ip3IPyqCapI5h4xRHSJ9IaZanyDag+cCj54HlNMtxJV5YVZR3mNkeDCxHXXkc8CMbYHpW7NTEoGQwxc2WlBymQVNHxAVCoXvAfgLgHEqZz06+LzROjpDNLIeWPJ04iQjDF6kHCLt8RUrdgPoTpdDFAQdUjIrATbjdHIROdh+vGZbuMwJr/80dpXVT0hiiJKSyjVNqzLZf/5aVkA083GbIyBitr/sO9QDIC9lTREG1XWnM5dObkcQrqbZFglth6kXtrvx7vDm7MZ+Ln4MGFjF/lUEazevTnsf8ONVQOdUAMCkyUwOMDLYl/LAoi3SoE6DE2cdLFz5kJxDNFQDQ9QSkrkazmX9sBsxYcn7PGDc/N31OKtRgCoSkFyO28qOqiZQjTlEozmmy+9nXCAXY5Qgxo2iy449uYOVU0hkiAL2Ju5dPgblN8Iz0z8EAs4QxTg0AsBm03ukTaVxSHLclAOiWmp6pYawG/e9iELBgo8Nw03msBnTF4dPFtEcaSW0KkO0Yn7CG9x2WykiSpR3BUaKRbiwMbOnA1/74PbYdYtp/J30DJFPKSxCAcviplKacUO9EAmIqpybeF6fvQK4+8fAo79PdZhhIVm2c/BhYWhkhBXrBWDZ6jwkn1MXBYP+UiwWjveC6Tij6QMiAK8D+ESjTyItKM93sfUB4rlrgL/sBzxzRex2wYNqycELURNbCYFFCNbT7lTJ44pkLtgP+3nXN/dFGTlYCQ3cgc8qPvN6B4l1JDNBYogSH35txUIOiB78f8D5u9Vw2CZZdafhSpdeCNAj2XLO5PuUS2D5IltI98GyJJbKd0OGaLwDos5p7Oeql4Hfbs/+pYE2W5s6hcsBhlPm80gMkcddDC0niaWjsChn0YKAKLxPxWINkrl2DIgWPIS333IYOpDQhjLX26oRCfeWSebCdtPhOGxhYjTBSZp75LnARfuyHIF6mCpUYoi6psVsoD4rPZ0JAZHvA3edBqd/CX8hZnoQDCMsqd+CzyaPCQUeN5kmB0RxpgpqDlG5NJZ10MT448ZK5tYNNVmwEDM2B+5g0POLJQQBkTBVaJGAKOE5jGeIwl/l99YNDMODjXdvPUP7vMi6olXlbz6l4QIYsZGDh5HSKJ7XxAPpAXjKgEjIClPUtxwpe0EdIhALPnEwUiwG91o3Vch3qPPWoL8UDqyjLYHS5Gj6gKi3t/dGIGmEbT6IHCJLD4hWv8p+rno5fsM4hoioVpOEEBACDPl5PLdgWdVzkSfAoakC+/n2jSejq6sbTgJD5MDjeS2EMRt1YYjkyUC6CWEksBxOKYmS0SxW0tQP7r9gitztDwYAXLktl2A4XbGbytCHwXymx4MzRISohSkDi9ZxftSEq1TaFbggGVvF5B428RIGCWn3A4Qa60hb40cioLCJzyxKrRzPIQqfm5FidmcscfSVW3wII12bxJ5Xw5H1ubn165i8dj62JAnWtg3O5dMnVh05hxcnHsUgn+Ye9S9jtWRu/Xp9TBWETbzoK4WdNIA4owV1ZR1M/hMXEC1/DnjsfMz+51fYdpVyiIgFCoIc+L1LyCHK5+XX5VV9dmyLWIpld7FSkeO3nk1Vfy8R4tnyykFgsXT7TwNgeSKKpLAZELs4xa6BVoiH5MAzDPhJhX02CRKeJUrF2Ws1GsVm0uvrBoZh2Q623qgbcSAARtzKzx4FC5BBLBC/jC87t8FZlMIFLiv06622uFITYy/ldBIL1LJBPRdDnDWyNKfKjpwWEEUYIhMQGWSAoCKjCdrVvOR9+DSuGrPMEFkgYJ2c7uQUey4BQxTabsvwrDxsGt9BijpEsNgx6zJPk+sQpZwQRALLmo6bcKzTpwIPjoMWPDwRaUJG8N6Rc+EdeRkAoG/KDriUHo40OSR6DlEwKUlxfAE7whDxjnGsBsx1i0LJigyx2p06dyZe+zypu5vvLiNDRCkWr2aTrBmTo4MolSVzQQ6Rq0g3qVcKCwCmhGBIV235Ybzxrm9Gz2tgFfDH9wLrFmbab12RdgD2ymyiKuSYSYxllgF9TAJDVTLXkbOZ9fxoBvk0QR7f/4YSxfVPLeSvjeI5E7kDvgfMvwn4f1sBS5/h5xO9xxYPkv5wDGPXB4plFhDpEzLhqsUleXHfgLqwRlgNImnb6MGl1xWXOek1KW82kW31PeDi/wGuPir+/TQI5IpucAJrN/sAym/7MN5pLcLm8/9Y+77HAjFsjmp4UYUhAuATi9VQE+10LG3NR4uE55BJvaFdbviHS8PfS6UScrlcJJgXpBABlWoTxYNSVoeISovTirV3vZBVMlfDwu66oRIsIjkYWw4ceOgb5O1AWyyJBESBY6HDFuuNZM4gC0QOUWSAoFUCIsrCF6JJ5JTCrIQEUicbaQbi0NVMnogHb9t5zPRXAW8+FdnUgcs7BCaLqAtDJAWFiob7w78Fpm8TvKecR0yie/bDxtxzcT33j59bENFsf5diFhxuG92Zs1D0SfpOT2onuYSgNrKJZqoQMkSypGIMOjxKgXPfBVz3meh7+mp3mn0B0CcDxM6hDBteWsmN1J6feoMxGtvPnhr5GBuHKVtlE5I5r8xc0JwueFYOebhYuSHjREOyYHe7ZkbP64Xrmab+8dHYTo8Sab+T608AztoiaENOkoNe2ra96hXgzQpW7FWR0EYkhhZgDJFLU5gq/PdWtngSx06kuSb+mTVDHlZs4IsCo3nOgmfGYwWZAWA5NyWJ+c7ENX94503x7QPfjpEy74cSHBsF4nJUgrtHLBACJpcDQOLy79gb0u/S/kRJCE0yVxLP79Ba4OYvh7IgMXl88/H442SB74b5tcSCw6Wye75xwej3XU9UkrfpdYjUN4PffLF4GiTkN/GEVn8Og0VTxtkoNRml310//N2GBxoj3yyJQBIUI+VqARFA4CvHe5POSnkRGRBhiJJUM9UW05PRNyQzRDaInYMNDyvWs37I0sxQkhiiN/tKoHauudtPHWACojpDMERRCUGagIhomk7dJYkEDFHipEPZZTjp0s4CAOBbHZhB1wOXHBDZ1g5yiMaAIaJe1FRhj8+yn5PUjsfOjRFD1AAZnc7sACwwAYBOx0aZWkHBtMpQ751N0+nCCRCu4vM6RADUHKKxWAES9/rVu6LviSTq1J19sstSGTn4KZ135Hv46nLmPhXHRopPWfCZA6TIIRpcDUyahXLnTMwmfViVVW4j1WHpn/MB3Oi9n7/uqz/TuEnVA/+5Gvjdjipzm/Y7efl29pN/lx1WEkOU8pm78N1SWxnF9ce5zBGZIXLg0RSLEMJRbO0b0fcyMEQ+scPJyagCogo5RDEdtSyZm9zJJosuJdHvVx+zKhVm1RmKJFMYhSGKSuZ0l7mAIXrsPJZ3++Sf2d9BIdxRSA1lhkh6/hLNCcYTvh/Nz4htI+L6VTm9AoUhsllpBXH/WimHiD9bhGtdknoCV5pLWNSLLWEhu8QNVwmIWGFWqgTzfSN1zu2kFHj0XOWlkXKVPqEGyXHfUCk0ubFs2HYOeeJj+XqmpNBtt3OO9izwZ3bYpSzQNJK5xqO3t3dhb2/vXo0+j1QIGKKEASKhQycQCb9SHSICZRARyjcXVsTaNuFgfD+St4psVxlTd0XAgcsLs7JVwLoyRL4PpTAe9YF9vg78ZG0kKThXF4YopiNpwINNKQ1yh3R0cscrAlo1+iQUykq3kzqIoUpA5NZLMje8juVIJCEYhGOuPVjtTtm+EhgiACiTfPqASDJVGC7y84sZSMW0z1YCIo/Vx5m0EcpTtsQWZCUG09YwCY4aBna2beF+b9fgHfXnOAVEt5wEbFiqPhdpB2CRcDuwAgDQ4yR8l2Ph1JQBROszO3JOykWICt9BKoaIuxg6uaDfpqNZeKjkMhczvsgT555ONi6V/ZjPan/HXXXYOjWGIlEyJ03OlR3Fu8yVRUDkcFPZwBmuDv11INl2VTl5phpwGVEeCevLDK4B1i+J/9xNXwDO2Eh9Lc5lLhzIkxdL5DGecIZI7KuZA6IIQxQGRJWuV35+HeGOq0Go5AgohqpJ5kB5QBQeb7Cak+j//aB6YVUZCx4Env+78tLagSrHqJEhsqQcImLnMK2TBFbcuqmCLjUUDJEPi80XDENkkAVEPNR6BeBUkrk4a0lpVY3YsAjhDFH1gViuQxQ7vNkd8oeV7UKGiF2HX4/JTDCaajlEok5CTNVkZ8wYonEMiC4/DPj1dry4Z3ynPrnTgUdFgFKlZpXWWVt+WoYozGGyCatDxI4n1RGppcP76+HMRSsJYvIXVxVbrHbXgSFyrXwYYFXdjZRPJQaMmPNj94sNkMSyAVtliLypW2FLsrKqDCP5MggciwSBsrAAz1RvpC4I2dvwpZRB6iQu+eP5CVNy/H7mJmmHqIGVTXv9Cx9lUjsg8bwJjeYQebACU43qiNlvmnbrh0Y7oq2Nyl5aZoj0a41jiKR7GDBEaQKiigyRNnVIMFVQTtuP7k9nZ8olfm1BQMRzAuvC6AtTBUkyZ5FYKV/dcP3xwO/ewX7/7fbAOe+M/9z8G6OvxQUvgtmqkEKk2pvzHKKAIWriCW1FkwGND5Ou0fHCPr8aQ5Qmh8j3pTIL27BxbWSkilnP05cDr2YIiGL6jarFX2vKIVIlc7BszOgkAWtE4sZkGSQMiNaXgL7BYdaGqj0nlxwE/C6hrTcxTEBUb/guS1aPDCbVAyI/QoOrvR4hQjKXModIWoUTyXEys0AdKSCSAgRKgRw8lkPEt6ury5zvqQxRheDEycUwRG6N+RoyxjM5cOHDwNBqEFAlh0jGlK5cKGFLNXGsEBA9dQmwPKmmQxxD5I1OMrf8hcrvi0E4biU2Yw5RIAONNQnpAEnbNqTj2ZUSwyOmCmpARKdtjU3IOux3y3uAv/1v/LFW9QIrXtQOH0ribCvMFSwPrgMeOz9sA+sWAn1vprum0UBaPZdOMt22k2Yqf/bYfB/H34a+bQ4N36i3TNX3w4H58g8zqZ2CaB8s22535tkzJ2zXE1EpKEtzTbz9+7CDiYhF3cTALe3+4nMjYxgiaRVYBESxDJF+LRWDUV0yV51lKUsTvsA+2lIli64IiHLc4MSVDCRGC0kyRyXJnGr2UOc2+sqdfL80+wp/rO22xKxVq0MExhCxBUh+XVnHzvFExGSAM0SUghI1QJefnJzklMsWcuMYIvF9o3oOEShfdLQAbnpULJYqByxy0JkGIuCX4HpJ5yXmjtn7i76hEvKWkMyxOnpdjmDdAMuqHAL4/J57IHDhYMGKPuCMmcBNX6x84DefADYksKFNDBMQ1Rta4nz4evh+PHjCr8wQcZtt6QUATDKXLocozpFG2qEsmZNWjnxKpeREHkjVc4VOzyHKJVtN5/MxAVFW69W4jqQhOUR+omRualdOdX2ruB/1eiy+kuha/F7N+xbwp/fGbCdtk5RDNBpJRdKqkVeBIfKyucwF7SZmsubZHSCpXZTC4zkVGCJVMufwgKjMJHPdG8GasTUAIF9eH58j9dLtwIV7An/cJ+HoBGUvlFKSV+4E7joNWPMae/vl24Hf75TymkYDERDJDFHKCVy3GhBNsUUhQCdIWGf7G+UzN7IeuO0bQHGA/X3hnrGV7ZPakgVfYYg68w5c2HCrBUTBbmMmJmmuiT9THmxM65LvR41sRIXirn5cQCRNkGf2sEWwEQ/Rc8/CEFmqc2nUVTUKhYmTJ/bScd2yCIjGUjJXlhhY1eVuzJQDtQS/sZK50IwiMYdIU5W45TKKZd6vy/17cQB47d7s5zUWWPgo8NBv1NeC9h2TQSTXE6MSQyQWcjWUhIkHaNUcIspziAixAubThlvZrtv3si0myuocDreKHXgt/efitUOY3sUX+vj12NQNZHRVGSLRXxILtpPDmn5eA2n+DZnPpRVgAqJ6w/cSWQAAyfM+yuhtRUIQ4zLn+hQetUMrxQoQmvmklRVllULqKCl4HSLLDrYNJqJDa4FX/ln12LFQZIPs3DZM3g7Y/YTETXL5aMeBYsaAKC74aURyoK9OyGRM6ZQDoowdn5hwkWqyFRqMK46l1SEKJHNjYEEsBoq4Fc2Mkjk5kIi8Z3fCShsQyQxRYEsaZYgoSOAyZwmGaLiPBXKTZsGeNif5GIufAK49JuH4YkIG7L7VdMyewhYFghyoRhXAk9te2nbYOUX5cwbhzmD5HuSIzASPMiB6+GwmTXmardpizathPk0cdFMFqtYhmtzJKreXqyUz65AnqqkYIvF8WsjJ/Xat90Myp9ExOBJd0JD7/znTWDsbLMcwFtrfcX2VqG1HQbQVluoMkSfLBOXFOuk6vHKSZK4eAVEMQ0SgSszGSlJWy2JAzOJUsBhWib2Tx3tiwSY+Xl66lu9Tur7bvg5c9Yl4s5DxxuUfjtYYpGEQA6glSeRgsBNFFEXxUS2/VkDEQKkkc4HtdlgjKwcveTtK2fc7yj7bq9bGa+gvXls5gFmTREDExi8mFBYMUeXnlgaSORu5fAeGquVStThMQFRv0ISAqFqFcurH2G5rq3DEQrHswYOVKodIyNz0wnwBEiRzPs8hYg8QfyDE+V/zKeDqT7LV2syQVqH5ub329hMr6s/zcZK5rMdudA4RR2icEcWULicMiKoMnnoOEeGyEpfkK65EEmFfCvBcNNlUoQ4uc0kddpJkjtLMpgrhCmnMm04HcrSULp9HahMzOsNVsChCyVxgqjC4mr3VNR0dXZOTj1GxiLCQcFiwLYJDdmZMhy8mjWna54ZlwNoF1T+XBUoOUUoGQ/vep4KvInZMVvupuHa9fmkFeacGwQzFrK6mgyqZm9zVARcWyuWMfYEcdMdd0xsPKHWqRPv3YMPWzWQEFjwE3P7NdMcXxxS5lxKGijHPr/SZSR0OZkzKY7DkxwREXtJm4WvBhNyCYgCUgiGinizL5hMyojJEXlnrD4KaS/Xor8MconBpRU3WL2UNjtOiluA3rg5RRlOFMmXyeovGuMyteZ39lAv7NhOkexYZN2WGiLhY188WRojI/dEwY1IHf7+6yxxjiHyFIXLgJY8rQaCdoe3E9BtVc4gyMsqu52PhmkHM6uEBkahDRL0gr8iyq4UAfP5HLNi2k2re2cpIsIYJUSgUfjLKY1zR29u7cJT7aBkQ6sOPm1hVtQ3lpgrSpJEA6sSXEBRdn+cQ+fB8Gtg2xyKQpdmaXSr/NSczROHDLDoEn9hh5zK4GiguAVa+XOU6KkBiiFQ5XzLyHXVgiJooIErMIcrKECkOT6xYaInkManCdRGJIVLqEHl1KsyadOxAMqdduxddMa4GRUOvw+lAJ+lH/4iLzlyVFWvpeFtOywNrkJBDhIAhIrYNEAco8wl/5xTkunpSnXfk8JJ9LgA4NjcvESvkaVaUf7cD+3l6LYsTCaglh0hrr5Mpfz7zk2BTaX9xksrf78SOk3QNXhm49ljgf04N5VMVJLbsvBNMFTTJ3JSuHNbDSi+ZE5CZDv1ZLQ4AV3wU2OI9wOe5hJIHUD40Zl/+jv96OPt56O+q5O5AXVyLmCrE5RCp+9t8ehcGhn1AdwNM4TIXvpmdISLS9VJZsiYdN1gQEJ8VDNFo7LY5+kfKmMwOEhY4tW1loaZYKqHWcLsiamKIov0plZjlxG9Imn8MlZncN8gjkftcEcQ2q9GCbqqgPxeHnYP1D/0JUzf0YnBwAJjeEzI7Gj6086bACtaXV1sw86mUQ8THhBzxkgMp0QdkmVPEfLZqLmPGNrR47RDKHsXMbpUhsuBJOUTVGKIw95xaueSAaMm/WS3JSRvFv98iqBoQATgdsSLOVKAAHgGwsIZtWxPUg4+YRiY6okQHJJ5DpDz0Uclc0fXhgtWzKHs+7IoNWkpcjTFVsBSGSAuICGMTBDU95R+fAVY+j6AZ1CT3CBki1QEvGXqhMABhsb7Uh40ZTOslSXJLrNOskpwIIOJyJWNypxMGS2lc5mR84V7g4g+wLy6lhbBNCIrg99YrYlQucwJVJXNaW5UTfFO5dXkgT17E9xUXEHWiA+VUDJHnh0/pVjM6kwMi/gTYhMKyHBYQCXRMDpO/gx2XUzluBfNi/pWLXJtMDNFYoBbbbe1cJ3n9bDKR61bbU0qbaAUr5gOv38fsiqdtyV7Ld1feJti3lmtH4xiiFKYK+tDnVWi3op9f9XLkNZc4sOVzinvOvTJQpdRAseyySXvaOkSICYjW+4Ctmypof8cWZqXx76Vq8/J9lhbEpON6ItclMAGIMkRrBoroytvozqeZvoR4bvFavM8Gl8wJS2fVnKBUHEUOZSVkKTwt2mhsPme4IJS8mBi+PnVSJ6wNPrpsCnhICIiawWiBIJJPINUhYj/VuRH2+ByWLl2Hqc/+HKXhAf6qWnxZIO84wb6q226LOkTMHMsnDhy4yZK5Whz84vL/qs1JMi4KvNXHnp0gb1HkECHMIQoCovd8JawnJ0NymaMWSQ6IrvgYsPdXgQ/+MNM5NhvSSua+CWCbjP92R21BVEuD+F48QxQERNUYIs1UQZfMuR6XXngoVknCi19ND393bOl1mSEKXFZIMNG3+pcG7wKoacK2flha/QsKT1Zugh2dUTeW7C5zY5hD9ItZbAU7BQhNlsw5tgVHVHvP6DKHzXbFnfmDuI65cqcc2G7bBEXKJzHuSDgIj4lkjn/vevCeNSB69io4D/yS/xGTQ8QDomrPBaA6+mw+NRd/fvw4Ql5AbFsNmjqmRAOilHJOqg3ygiGinjYhHG/UYqqgPUtd3gYg38PalPxepWuqZuNKKVDibIFu5524jc54qOt6ecdmSedZbbcXPpp4jDA3TGpLgcucFVrgRrbl55XCNn7DcHLeXVx9Ot3aes60LgwUfcmxMe58ELvoICaneh0iklSHSN42ztJdk8zRJIZIake7/+IeHPz7h6oeL3ruHH4ZwXeplXsolccoIEr7PMsBregL5LYkKysSJXPh9z1tUhc2nZxj1tvyPoEw8G6G2kQdMdJjyVQhslgsBC951he4RcbaE0oT5hRsg7ydRjJHQ9ttANRyqkjmYhiil+cBz1xR4SAxAVG1hZn+5ZnGBZf3qUpZCcvhpgqay9whZwHfjEqXxXzBJxao5SCPmHOkFCj1A6XB1OfWrEi7xLK6t7d3UZYdFwqFgRrOp/VBfdCKDFGy7bYeEEUKsxKgWPZ5DpGPoWqaU2kVLnbVBPJkRbXdDlZI+HalTd+NrjfujP18WjzUuwKH21AZoioxc2ecy1xdbLfruALfOy/Vx3TJjo5cPg+4SNnpqffNsiwQtzJDJLcChSEqj4T3aFSSuaSAiJ+TPlApk78Y5lRf7ZaDjViGqAMdKGODW/3++VJAtO1MLsFKkMypq2nSs90xOcpWDK8LbKgXrx3ClspB/WCBQZEMgQXEgDQhHE1A9MINTLI1bYvs2/oxk9YKGCi6WLlyPbaVXusorwd6ZvP9pWScSv1A59SYN8T3TMPJcVV5lmzeor6uyGm4Lt6v1ub1tvbwb4H8ZHbO+vfkx7R13l+5sEGSAiI7x8aIFJPToPK8cmzC/49hiLTzn9adZ3WIysPAon8BW+3Nz0e9FqtCQES0/NZ0DFG0bRE9INIXBBJc5t5cW6UuTAws+d7wPokFFuF3VSzVITh4/E/AOw4HpkqGK6kZIh/BOnWcO6diu109IILF1CSWWNmX5Z4iF68ZJHP5SVEpfMAQAUmOu3YHD4hGQoYoPvmNvdbhWChVXUhmioDA8dfKMVOFLJK5vx/Nfu72mcrbyMet9j3c/CVg2fPAlE0rf04cQuTpwUfQXiwblmSqUM1lTvSXFBaolUMHiXnuxLXUQdbaaKRhiPYGUIutWB/f9qkatm1ZEFobQySoXnU1L1rPKMwh8pS6DgCYrOSGzweDiGpRHJXM5eSASBqIfb5CQokVDqb6ZKaGTjSY2lA/WBGulkPU2Rmj6E5bfFOgBXKIACAv5IEZbbcBwLJttgJbJSASDJVlAUXwYNOtU0Akt5H+FcCix9j3PLCcn4DW+So5RDHfUcUV7JjJmtOJDpKOIZLrauWkSt5REOQIH5gtR5345Xui9SSkZHqLaN9TTAAomr/jiBwubYU8K3wPuPHzwKUH17h9thyiqx5fhJXr1ZVBi7pAB8+tUiRzFfaXZKUf9D80ez6JbhIQkdMQENtRguPK++M/y8PAprvEHiPWUZF/pzpDpEhkbOlZrIIwIIo+6/EBkdquO3lBWjLSB1z2odDUIgNDFHHws6oHRBaVF92kgOg9XwLefghKyIW2+UFAVD9TBaI4HorAVZPMlarlcVRZJBhaC9z5/Wih6kwBkTjHqNSYJtx/BVp+aQdKyNMYVtGWFAINhp+PycX0ZclcOIdhL3JmvYMtSLkjnCECEhYdeUBkk6oBkS/yy/h9p3YVhki01aSxk1JWG1Be0IsNiFIE4y/fnmqhCghJdwIaBtVWDjb1Qia5ikJHkcwRGx0yQ+R77CCNVjXUEVUDot7e3id6e3vXZN1xb2+vx7fNmPDR2mCyqDh7YdHYExqzsItU6hBFP1Z0vSCHKPJg33kq84fnxeDkwSvuqHkiNWBFMicYImmw0B/W0eQQ0bAwa5KETMCJ09Nnpfjj5DiNqENEwxXqI3bbHPu+fZbyfmeeD1BVBk/dZQ5gk3UCv3JARNnWAOBYVsgQucXwmKOSzEnHvmhf4LJDgAfOBK7jq2R6npU8EMcGrdp3JH0mLpAmTic6kM5ljsptQpx3Qg6RgBWRzE2OTkwqOctJ16szpDlRr2e0OUSCPd2wtPLnkiBP8FM8I1O7cvFFosUEJ61kLo3UsJQyIFLs/UNYeg4fseA4KRgi0QYk2+ZAbqRfUyBzkgOieJc5T95WtKv+5cDjf6w46QkmM0owxidxsXWI1DbalbPVemhDq+OvJTYg4kfTJFvEri42kQOi4HwtAnTPAI7+O9bZG4EERWcFoyEYomjb8fx0E8Pw3MPPE17MmhBLCTjK1SRzSd+LXth4aLU67ih29hXar/ydBlJj6d5KUsPExUSFIXKww9DTmEl5v6QERLwNP/3X+rtVZsSSwZhriav7FYCPY52MIfJ431CdISKhRXcC/OC7ChkiB24yQxQnmZOx5ClWG/C2U6LbKLup7yKtJxYdqBe2CcuBRUOGKLZYunxOgiEijCFSVEXXfAr4v++Fc4Z6FzVuAGqy3S4UCnahUNiuUCjEVcWb0CDUq00yF8cQKQVVuWSOM0QO8VHWH2zRwa1+DTh9KqauYyt/RKLX5QAkJ1sGy5I5X0y6Q4aI6JOGGibOdjCv8KQVwipNMG6SWhfJ3PjLBOQV6rM/uQuu+NyeyvtOwBClMVXQJHO2zSZDFSd34XYWAaZP4d9/vRgi+bwFKyQnalaSzMUNepEOVvpMzKBn5dPnEPl+zMS/Sh6EZTvqZ+JWNaWAKDJfK0tyA81lMcgf80e52iZW2KsMdInIyBBtNCkfXyS6IyYgqrS/ROdI6XvOzBDpOUTaZImw7zR10Wl54iPkRuVh4Km/hJPcOHmoF0rm5ODRk3OXxGr99ScAd/4AWPZc4mkEE/uYNhy79KUHRHmrcmmI4DgVjq2XhEgREMXlEBHpPHySC/vliGQu+h2tHsg2DqgBkSyZC6+jOkOU0PZ+Ng244XNq/9m3UNpO/q4qTHzl/ce4c8YXW9cht3G91IF0HmK+8Mb9wOWHJZ/TOGB1KWbhUzJVoIQobolBv8klc16R9Q2h1D8eHY5VfXwQ3wFnVYjNJXMl/vpTlwBLng4/X40hEm14cFV0Gxmpxt70iwCBtT31w3Zg8xwi4epTzdFS5BCBLQYqOURrFwB9i8M+L5DOZVuoaCZks2kBUCgU3gvgBgCz+d/9AJ4F8Iz07+Xe3t7WvSujQaJkTkTR8bdFFA1UAwRtFY4QlkNE2WeKes0E0cG9fBsAYOtFvJqwpBOVm7+7++dwzyO34gD72YipQpBUmMgQZV/NCPozqQ5RcqfOEadNz8oQNYlkzqKVc4gC2VSac9M6Msuy2XdWbVsR4BKCfQpzgOeBUnEI+XoEREueAiZvota3UgL8jKYK+rVUk8zlOtFJyihWcRECQlmEcpw4PbV0ny3LBij/TH5yvLOg5NgUSVqXAiLdZTHnaHkDNTNEMQxFFmQMiCiQwBDxYJtfjwsbTk0MEQ1/iqTdSuc1tBYY4oKGmJV4RTJHLFh2Tp2oxyGQ7ckMEW/jD/4/YKSPXe8uR4UTerktBQyRhbzMEMlSPSE5W/8mP1byOYnVXep7klFAckBEtHbalbOxTr4PCYxafBsS+9fk3CnamyKZg7ogAACelYPla5LRGJc5gSXrhrHxlBjTnaTjKzlEZX58Szn3slttbKkwrZl/I7D/T8O/y9KCj68HRAlOgkpAFDVVkEI6JI6dGkOUuH9ZfVFTXcEU8MpsISM2PzBEZ/cUQM86D9p0+L+OPC974BdlhiimLfLXOm2Wh10JwQKJaJt2Dg7xsEEwRPO+xX6KUgGibWbos0tuOdoCUo+9KSVz/GMWfEkyxxgiAgqfktg8QQUBQ0RA7Rw6iHSO7gjr73SZd6McUuuAWkbNcwH0APgVgJ8CuBPA5gBOAXAlgPkAxujpan5Y1IuXzFXVWfJVkAqDDAEClzkAUXckMUiLjoRGOxR5QjClZxIudvnKkMSY+NxUgULKIdIZlRoafWBqR/3Q9rTaAxnLEDUwh+iB/wecPrWmFXyChBpVHI4I/mqgni27ekCkT5b22G4TAMDqvv76SOZu/Dxb3ZYh3/usLnMRyZw6HdBh8/o05VL19qGwAsGKYLStKRkntg043IAhyRpZXljQJRCunJCqB0R8NdIbrWSOX3uKujCxkIOIFAGR79N4hoi7P4n2NISO+HYtFnGScoiCmjtIxxD9ehu24h3zuchkiViMWfVdScJYAXLytOhrR/r4Tz7kBUWIpZbDv1MKAluqQ6QERDrDUoGtFBN7Zfugr68umevUJXMJJhS6XTd7LV6yVbUfB0KnMyBkiKRVf2rlYekMkUDM87B8fbZxwJG/+iDYIMqzUs7CEIlnJU5+CyTnSGZmiOJc5oDE1X0lh0gbb5T+WFpsjHN5qweuPwE4a8uqH3OtmFzhoL0wZYPMJop5TI5L5ihfLBHzlgi40c1sewNKKQugihwiwRBVd5lLaDuiz5H6mDdXRzNJaJo+nyJVvwyEklLW74U5RBZ3mfOrLUYDUHKILEfNIXJHWBsNnll+XlkVPE2EzAwRgB0BnNXb2/tz+cVCoTAVwG5gdtu71eHcWhIsh6iCZC7poaFRyZwsdQNCyZzLH/hI5x0ERFwOIMkCwkAo3F9P3oEb1J9RE14D6pl3qERnZWrQu9qEAhTMbchXJ4SJqItkLqYjq3XC+eBZ/BxGwklfSlSqQwQATk4wRNklc7btMMlcxYBI3ayzi52/PxqXOX0iuex59W/5WpIYIhFkRPZdwVQhQTIHAK7INakAP26CEhOsqnXAbGAWL4YqWAgdXpkFzP/zQ/jQFMXlqERQTDpzok6G6B9qtcKNy2HJgpduAS45APh2b6rA3KcJDJEmmSvSXHy7znWxc06SzMnbiGCvRlOFSA4RCGwnBwIfI2UfXflqxXzFBNgLA7nIe6ItSfvi7ZxQn8lXODz5WdP3V0HyKHKIPM8NB3DR14NiRW5zbFxeEu5KK8zKcoik+5DIEEWPHbykS+Yq9eNb7AW8+bgSEIXsqSSZs3PRgCjIzYm2nYFitr7KIQjXIWi8y1z1HCKt37DyYaFm/TyTanBlDYiUthAydEQ3bQlQSTKX8OykDYiKA2xhQrhIVkNcbZsY0DjWw/eAh3+HrehSrCEFlZDkfwiGiPLFEiLXcZIxhTn+bYo1WF0lhygITMTcp1pAFEjmEr7X4HzCa+y04643pWQu5WKsH+QQSVJhzhDZ8FMFROHivgUQLSAqj7C2rOf9yWOX5KzaCqjlTJcDWKW/2Nvbu763t/f+3t7e3/b29h49+lNrTbAcogoMUcKEk/XVOkMEpbMmILjwmN3Q1cEGz0iFdVt1KSOKk0iUIbIsgnxeBFEqQxQm7iflEI2CIYIfK5mIRVxAVBfJXI05GnQ0qyDJdYgAwHHS5RABiJHMWcwZsMK9IdwuQyCXy6FEbdDySDjxyHpv9XahMxOVGCLR5pwO9XNxk6ArPw6UQk1FnI28k2eBlVesbsnr66u6xI4fSPXV1k3eVXnHYtL+wK+i90ZiiEK3KGG7zVcjxT3RpTuUsn8LHo4GofK1iOPXGhA9+Wf2c/kLqQIPj9L4Yn0iv4pPEorIqXlbAiIYFkyLjuAcqPpaGnvwGIZIl8zZtgMbPvrTTK5lSYijrWjrCwoxpgoA1VzmElbrgYoMn2BpPHkCxu+HRSlenPQe3L7tj6XPa5K5vB2fQ6R9P3H5nYmFWSv145//Jy7GEYpkjsT1/1YONtUTtClrQ+uiSf8DxWx9uB3DEOmSuciYqkMprMs/K9dfkSe1csHTJBZJR3k4XFQK+mKt7QOJajl89v/UCWikP46RCgNA55Tkc5Jx0b7Ab9+W7rNZEPcMr38TuPdn4d8xbayDL+oJOXKc4RCAICDaGGtSSOa0HCLLQYflVSjMWoUhCnYcXmNc3iJJO6dKuSCkBESBZM6GBcEQVR8jgrksAWBrOUSuFhAFxZRl5UdrGS3UMmpeB+B/6nwebQNmV12BIUq0ZuSDtcwIab0eIcBuW07H/757awAxemetrgCRZGlJa0mdHWKbcF9yDpEYFJet1VZwa5BWiYVKQv1IHZZExOUQ1cNUYbS1F7xS8kQsAdEVahU5HhBVo87jvk0xsXPLlbZVt8s7ForIg7rD0RXutNDli/r3KXeI+kAlvgM7p628xmiRX78PeP0BaVfRQc/unsZ+SZpcy6elTAy8RImSchRiA9O3qbxjOU9Iv5dxpgr8zxwPiCxxT/Tq8b7H6gv99TDg2Su19+RBKqaYYxYE50xStW/fVyf5AcSK8xwmFuin3fGV2MX3mCSZi3tOKU1n5x1XmFVdZobj8IBopFK759sM9wHzvs3avK1LfEQQn2y7TainrOorAY3ez1XoF4Vkjt1P1d0slAVKC2nVXOaSJHOxQY7E7Ov5dRXgE5udN59shil0kmTOzsOhLsvvkyeMd34fuOM7wZ95rn0bLFbpqzwXePh3wXPnyF+9uF8Wgeoyl0EyJ9pgUUp+SZTMJTBHgPqc3fYN4KL3M7fBGJm9nHsY+/1stY/6d6U8TPmc0jJEa1+v/P5/rgZeSscK6efVD01x8cINyp9qX8z+srhKg7hyQBTz7PTMBiwHs+ia6qYK/BmmhI8Jdg55y4+6zAnGv2ruTJQhElb/l7ofCj+VSjKXgSESsTP1wjZu59A9shJfdm5LFRAFzzghvA6RvAhTViVzAUMkLwS0Vj5RLQHRhQDeWSgUjqn3ybQDSNUcoqQOV+TsqC5zimSH/7T4xDky+bU1K9hACysVNdP60I4OvkIr5z7Q0K1FdLo5oh1rVAyRtP24SObGwFTBLaoDWQVXKAECL5bZEMjltNywl+cBF+4VXbmV/hewHQc2oSiVk+8Nk8yF2+Vtbr1dlq4la6AYCYh0FkiTzHku8M8fAQMrg/eGfVvL6fHUn8G+pHOLaTdOz0YAAGtkXdXTVmrP+G7iirzC6Fk2W3199xeBD50Vv+NyKNeL5BAppgrsZ1iHiK9GihVyfbHDKwHrFrLfxc/gPW3VTt5xVqSxyXZLwE1fAta8Ds+ncEjM5zqnsZ+fuBh37vN3rKM98fV+RL+YVOU8GGy1VXJFllFl5ZaD6PkFnCGyiI+BigERx4O/Zo5yQDSHTHeaiguIQGErkjk5h0gLiFLYbiv3k+/XYjoDVTVVLYco8K3Q7mMFyRzVJXNV5Dce0Q1j+PnK52bnkYOLEddTz6X3/5R92XybwVKV7+yF6xjD8MCZ/FhRUwUmBQq/q+2X3MAkr9Vy2oDwOy9J+SBKQJQQtOtjj/y5N59gP0fWh59Tghj2g33HKaZvkeAr5vwBoCMlQ1QN//gKcO0x7B5KNdmqgcDHCmu2Ot6v/K/0CbW9hYYHDkpwQHjfaiUVP7dsYPJmmOWvqmq7LRgiItXuyZOYwqzCSTW1ZC6Ez/u1XrpF+LG0i8xUnd8lIWCINFOF4P0MOUQAibLYgMYQ8euX21yL1SaqJSBaBGAzAFcUCoVbCoXC0YVCYds6n1fLQklgkxGs/MZIkp67FjsOPskyQyz1oY9dCef5BhF6P6iNwRqmJeVGxOUQAVLhU9l2W5gqSHICpYgrUFNDVwYk3es/caM4yVzGgCi2DtEoAyKvpHZIF+1bdUXdTgqWOUTNpcA98JaTgFUvKVbOlNLAhlTZN2cYSiPVEo2lgMjhAZFch8grAQsfDaVT1aAHRJEkXumeWDbwxgPAvy4Abv9m8B2sGKRYtl5iTwKGSGtjyrMTbTe5ySxx1k4TECmTDL9CErsWEAHAob8F9vpK/MfliX3EVCHGZpy3B7EQYguXrQhDVEY4cyUx74ljFtVzHQ2SBtzFjwHP/x24/ZSgiHMEwlUqPwkjs94FDxb8uGeumqueJDdTzksedB/9farzJ6Da8xcyRAOV2AbxrMl5TjpDFMkhigZEFvWVe6W6zFVwA9Ng837U973wtgT3j6oFtRGVvjHJXHWGKG56ECt1AyJ5SjoC1YRYfRcJ31Y0IBoueeqzr/UDYqJXnSHibYTn+xGpLxJudsQiSp/19pW8Bv2Gt9R9vfUfbrUc7uOZBSvZL6WkHKKEoD0SEEmfC1xdy+ECipx7lSRZTIK+eJgUmGXMh02F5S9Ix63CNnOXXeW65P6SqG1ODsBH0AHLFS5zCQwRAEzZDBu5q6oWZoWQdlohQ9RBYnKI+kVAJFzmMkjm+LP/2fe/PXjNSjsnSRof9Y8pttv8nkhBTZaAiIBEjV8A1k4rSeZajCGqxVThHAC7ANgVwOH8Hy0UCuvBLLefBvB0b2/vdfU6yVaCRX3QuMmIaCRxqwg3n4gpAAbJxlHbbUT/tHnDdPUE0GDQUXOIWD8SzSECgK4OblsqTTB8SkHgK/rqvB4Q1SA5U2I9KtmeVtwojiFqYA5RcA7F6IoqTQiGOWxUDojyeXatQWKvYPw09o5BD4j4thUc1thgIR3PtlCkOTieZqrwHJc97PnFxH0F0AfcSkm88rWXh4J26sIGldnOJIZIfnbiikZ2M4bIKVYPiKLJ0dUDCFJFhuY7XbAUyZz2jCgMUcje8l8AALaYMLpF9Ruu9LzJ90V8H7XmEAkQJE/KxQQw3wOfJrjMdU0Lf+U5KwGjsegxlmhvWRJzXiUg0gNYeRJ5/y/jt9UmYWxiIL1ALOQcB2XQKpI5Don9W1ckmK4eTD3fmIBo1/Iz6KHh5Nn3XVaEdeVLySYNFa6J+hKTIhbBhCxQzj3VgpXuvK2uoicYF8Sm1AUBgZpzV60f97WxKdxQKgnh8ICo7Kmfi/SzHt5DXsbRr54L+P+X/OyKPK+YouhCnmRp9yo8hnb/7zmdPVufvjp4adHq9cw9Skjm7A6NrU3IpUgTEPluGIB7LjC4Bpi0kSq1TcMCVyqortzjbPJvJJkXKMeS9195bCRBSQppn7IJTSS/Ovy9SDpguYIhqhAQ9cxGz8rnUaxUGBcAFQySCJQtBzniYUTPPRpczTeoIpkLzicaEAW1B4HA6KMyaPL4qCHwrZLvvfSsVFKrhCcl5RDFzcV8WTIn5hByQNTmDFFvb++3e3t7D+jt7Z0JYGsAHwdwBoCHALwNwHcBXFPPk2wlMJe5uA42xoFDg6+7zEmBDPuNT5q4ZM6L0OHqg0mE/bbCEKmY1MUDImnyxlLvVRvwSOL0aCVzYnKU0gdfQSNttwW8YnS/VR5+B26qHKKicA8UMhrRwTxzBejSp0Fivk3BGpaLVQKiGIaIKAxRkV3HyProRDtO1iTnxQAxSbyaZE6875WDHLgyHM3kIGEFzK8cEKFrBruuYl/0PQ1KQrswVYiDfJgEt5y3tv44AIBaOc1xqkIOkc728HYuEs89Xfoo56zp1+7HTMJqzSGSEWd0AUgB0SR4foLLnFR3pDtvw4PFJvBvPAhcdgjw6DnszWoBUZwNsx4QJZ6/fl66ZI4gl3NgxTFEL9zAClyzD7IfknvhDf9ZDo9K34Ov9e8xpgpyMATwHKI7fwA889foZGPdwvjnTQ/ktWeFgI0/StynqwIcG7587oG1uT4pjll0EL9YRHu/cj/uB5I5dTInT3ItJ4884QxRkrQLgE1d/DF/DnYcfKKyLCtYUBLPEkWJquYlVJPMJaI0yPv88B6VS2UWbM3nuS5OR7JkLi1DJO4j9UIr9/Ig8JttgWI/Qs2cfv8TkFYyl3U8TPP5uNIGyR9mqge5b5MCSn3Ek1tqiXTA9ti4xxZyE+5L5xR0+YMpCrPythkwRHnkEWOqIAJWX1pMlP+O7FfKIRLPqyS9JWmDh4wMEYGnBHcCXpYcolSSOcEQldT3WwijWkbs7e1d3Nvbe0tvb+/pvb29H+vt7d0KwEwAB9Xn9FoPFrzKk5FKA3lEImdpq3Dsp52UQ6QPjmLFgVhqw5bQ1SkYIlkyJ2y3w1XAqGQuO0Nky5K54NyqdOr5ScD7vqm+VheXuVGaKrilmICo8sPPJHPJ15vPs86xJL5X0XmJlbJbT4Z9yf6xq4MiKV9hiKrkHoUBkcQQuUV+HVQ1J7joA8CvNBtp8XnlIJVyiKzwmnwPq9ezCV9JD4hke2NlX+F3FnsX85NQRA75cl/cu+quUpoqKF0kif/Mm+//DbYfuYJN+mTLb40Nlu3A9cKsYlImXLYC6VywrwqSOa8UHmu0ttsyaMKEpshzJvKTOENUIYcIYUDk+25YrX35fHbfq9m9x0nqdMlc4vmrz2cgAxYglmSqoO3vxs8DF+yunUvY1oc9Em9drVn2AkjMeVSCcp0huvYY4KojoxvpdXC0opBihVw29tELs1oWCfMj5HPWJYYxCwAhQ6SOTdX6cSqer8j3Jo1vTh75gCFKlsw5tBwaecT17S/dxnJYBrikzQ1zuMpCFOMLhQISxmstOBQLRVK/MTQ8DDx2LvDC9ewFO68FRLKpQlz+EofcPgKGyIsWSy0OKIsiaWo/RcbKJMlcVjewNHm8Sf1HDIKSFNLzSRXJnH69MkPUCccb4XJyJKswOqaiyxtAUbSvh88GBiKGycF5U8mIwInLIRLfj84Q6XOL4LuX2V2+aC25VRJarl4PjVJpAaNKQCQoIkohmyoEu8rEECVJ5qSAaIKaKlREb2/v2t7e3nvrvd9WAOV6+liXOYEKDcSHqv3WV+HEb46QzOnyO624JtFlOewPZZN8R17Zhu2G8nyfkLHK64nTteQQxWxfVTJHCHDA6cGfJTiNq0Mkr3zEMkSV98kYouS2kef0eUQy5w5HPqt3ZoIh8uSAKDL5UGUOwmXOkvOhRLE1IKy1QynLZYqDZIUNoDJDJE8yfBcr+1hA5OQ6QqtTILKKHF5P5RwiEIINmIxOPSB64YZIThTVJ1xpJHMJn5nc1QEXDjwrp5oqaO2hKNi71+/D7o9+WbsK9ptwEIs4CVYKAG74HHAGkwuOujCrfD5VGSImmYt1mZMYoq6cw4IH3wOczvA8vRQriXFV4FMzRDEucxpyTo7lEFWSzMVMPF2q1/LRbbel+59wrkr7iHPTXPxY3EbS714kmBHW+uowEj1/24kLiHTJXIUJE6lmo6DCF/2emAiK/AbJC9vKdYQ5RBUkZg4vLAkgXi3w3N/ZT5GU/8r/AbecBELDgKjIcy2JZaeTzAmJtPT6UHFEdZiLMEQJLnOVciPFPffdWGMHGqz618oQaQtBm7yL1VbLyvikef4ySPKYskab7yh5lOq1ym2zbHXC8Ud47rMf/30CQOcU5P1hlnu9+HHg3p8DN58Y/RyfVxHJiCCoQySzPMPr1ev0yoyx1GvUxTCwQjJHJNbFpm5UlheB5DJXRfon4iGLeuE9kRb+kr2HpaPJ9zKWIZIkc7qxDNB+AVGhUNinUChslHXHhULB5ttOru3UWg9e/0qWa1NpMlKlI5HzFKKFWTXJnG4RGlCWrLO3IAdEIodIhZPr4PuS6Gnx4FrqKqBrSauYaRv6i/9gq3Ublqk5RCKYy+iGNUzzoFlNFYJBLEbiAlTXT1MKrF+qJlXHMURVVmyqMkRBQKRJ5sr6oB9d23GE0Yb82dj7FG6ZswmKNAfiS8FdwBAh7NhjaoAE0AMifTAqa4yVJJFatYFNrDs7O9WAKEmTrbBN8fdxgzUFXXpAdOPnmW2vFNAqK3G0QkCUQjI3pYvfezhKQKS7BpXE93rlxwOJh84QJaJSv7H06fD3QDKX7bmKhZ63IyAFRJ6fxBCpkjkfhLGAQV5HyoAokSFKMyHTGVJtsiTVIUoyVQhWWTW4sFTJibYYFZdDpMOLc92rBl3ypJk52PD5arosvY62LTsFQxQHpQ5RBobID5hhdqwgh056wGynQ8ohSg6IcnDDIDzu3sosi8CzV4KAYgis/ZWG+8Pjx7rC6izOCJ+Ahu1hZKQU1LcBwCabSQFRVlMF340yRKA1M0Q3ePti9bYfizJEls2C9zQLnIIZBtItSioBYQrJnM46akjKry5bncj5w9zgpUJuE++TtqFL4ItaT6/fF712Mf5YEkMk2qU0bowM8FxVuUzEr7cBfveO+P0JuCXYpT52FZJkzoGHvuEMUuAq8w1PGJcodYjCgCh2ISsCYfpDQOIWbWRTBXE+LWyqkIYhehjAwTXsexrf9t01bNt68MqwL9wdu1hvVGaIKqz0Ulggtj7IRBminD5xDnaQ8IAodYg0qVWOPZCeNFkMCigSS5FN+ER6INKaKjzPvTWWPKmuSIhK4ZnWGYEhdMIvjbBJ2dOXVw9mgATJnBv/exye+Stwzo7MIU2ghhwiu0oOUUee3d+IZE5jiLTUMgBhYU+vJHVG2nekrwgJ2+1NNzwPLHyYH2skvA4REL31n8RzVlZIgZiASMqDWPIkcNUn2O++i9UbuDOQnVdd3xJd5iTJXMKgN2BNQZebYJm76NHwEPoEJYXLHEn4zJQuLmHVJHM6Q1QqRZ+ZIOG9WkDkl5XJUGK7r5epAqAeQwmI+Hee64RP2cAakankuoJfhWQOviexnqV0K4lxOUYpJXMjmqQ4znYblgWb+OhPCIj+u2wD4lbiy1QLiCqZKiTkPPpZFmXEx3R7+oBB89T2oVgUR/cjXCmDbeWfYrM445LEgKhyeysRzgzKk2pI7R+ALTNEFeRcOeKFk7m4exvkKeqTS4p+MgUA4PA8Q+YyV8EVVsAtRRii4ZER9R5QWoEhkvu3FJI5rxwNiHw37MH1fJsPngYc94+Y62D7vsg9DMWOjWICIoddf9aAKM2ipLwYVlUyF2WIZETyi+RUI7sTeb8In1YxVeDW4nd2/AD41/nh6wmMTtDfWznMKr+F04fOBB1aHXxspJ8HRNUCFL249N+OwHYvX8R3HQZEOXjoG0rhVJc2h8j3MZe8ys6LRAOiNAyRmkMUZ6rgSn0Qu8631krtNmUR2WZBGpc5AmCjQqGwZcZ9z0AqTrdNQH0Q0WHUHBDFhAcxOUSWLSbOFRxk1J0krpoEAZEUXIUOWGpdJM/KIVgMThv5T2JWyEzPLeuo+UphxpXsIdoBv1yEffdPWE2QKZsDbzug8kbVbLd9N16yArBaQP/8Eft9yb/D191idL++Cyx4iNlxvuuTkV058FCuMHHo4DlEZbcyQ8SYP3U/DmcNfTlx3yuxXI0HzgT+9/JI7hEhBB26FLI8EmWIdOMEGdUkcwmgvou1/Sx4sJwcd8LhbyatWCsTifj7OGJ1Y7rPcwc8F7jrR0DPxsDACiaT2O6DfNeqfC+VCUHCtfXkHRDC3PJkhkh/RuKKPpKgEniV50DPIUoaaMRERVzPa/cyh6wv3pfcxuNASGh8AkB5dsV3Tn34vo8c8UCdbvXapesRLnPKZF5niJL6xVjJHE3FEPUPF9Ep/S2MYpRz5AVDkyRzqwfiJ34uLNW2Vi8mrDgqJgREUj2UDcMjmJJ4JSGoHx6VUC2HSLJylwONuKalBkQuc/6768fqh2I2tOSAKIOpwhpnNgBg4esvYetNdgrOlUjPsZPLo4O4GCq6USZMQo7ffQDxTAWJD4gIpei3pwIe0F1exy8xwVQhErSMAP4k5byKpSI8txSKoP2yFhDJdYgqMURyfTV+LqUB9izLrJPI7QS720rA+oHvRq9B2vcw8swERJdcWg5guenGc4UhSsFkyAt5qXKIkucpevuSZ0osIBqRSgAkS+YErA1Lw9c18xIqCtsHDBGbJn+QPgH/P38Pjlwa7GO/VAsmdcncgofC85D6ZAceVlULiNgJqj8TsO3yO3Fzx0+BVwFssjN7UTpeKoZIPEsE8QyR74bPGfWwYPUgzp/3PH6Xl95vIaRdRvw9gAUZ/z2NqEKrfSFHzwnSGgDRjlYG0VflElZM+INaLOkJk/EPiDw46gFIR95BmdoKQ0RlhkgaLBbNeG+YA5A6IJrFfg6uVluDYIgyrmSPIA/qFsOEWVnGlgTRIcnXLg9ClVab/350OAF0tWAjjiH66+HATfF21Tlahl8xIBJmGfx8hGbXHVZWkCeRYqRZ5LhkzpfdybwSK5T38u3AivkRlzkAeAdZpO7IjQmIKq0Gaiu+ad3NBoaLKHE2y3JyquyKt+OFq7TvVrHwTtixZYefW/gw8MSfWDAEANLqHtUnXEkMUQprYcsi6OlwUKaOMrha2up1qVxChAlILZmTJ00k/vnz/ahk7taTgeXPh/cgC6pJ5nwfvuhzHDn0UNGZYwwRkRkNt5hRMqclaKcIiMoxDJGy5MQnw7EucxyR2iNi39SOl8zFMURyoChBZoieX7gy4SqSt2H3U1otDvo51VU07lHJ6TlEvXcARZWRqMjeR1bsKwdEK51NAQB/veNBAAAVhVmlsSmXZ21opDiiTTLVZ0aWzFG+WPOXh9/Ahfe/xmrMJDBEBD5G7MlwqYVuT5ejaYgzPqCqZOrlpevwm3nPS9tI5iZiGwEl/0YPiGJyZYSlM3fODLZLcppMvA52D0ZoB1xKEMllshz2L2JtTiWXRQ55rE3FEKUPiCBY5ip5a7G/Ww4seFJB+cqSuQBTNufnqT2f4lylwqzBW1JelzvUx0+9SkAULJxGp8Mi/QEAHOJhfTXJ3MBy4JkrUh23oyQ5MAbmCOFzny4gEv2YFb+gptUhWjtYQp6E7fvcu1/Cyg0ZXYEbiDQM0c9GeYw3Rrl9a0DRpteWQ+RDs0slRGOJA4oIAFDSA6KEB0RNwNQCIseCCz0gipdFDOZmAN95BThry3ACs34JcM47gc/fA2wRo44UE6XBVSDSAyjqQKTSQUsYQgfg9UvnlUUyF7OiC6QP7uQBzo2TzFVxmYOP+OkJQ5BD5PL9yAxRlc4vn+OmCkoOUTloK9T3WECk3e9ZpE/dEfXC6xSWtpX04jUyRP1DI5g9yQEtWbDsnFrc0/fxyKurcd51z+C6jvjtk9oNIXziDUS/D+l6IjbfieetDrxJmNKZY5a+0iTALqv3xi27EXkGSR0QacFUXFuTv7ssK3NJcq1qpgrUC2WBFQIix+KObNQP9ymbd1Q6X7GApKy2p5PMlbWK9HGFWWHZsDSXOd8PhXVJSc6uHhCJfiguhyhJMidNjPNIJ0GWc5oIJIaIqgGRHLzHmSrkpfonbJU3ev/jXOaC64zImyr344P2VAzQTmxBVim7kTfLc8fTweHhiqvfObhBke+RkRF0AfjFPGb6ssMmk7F/AkMEAJbtoA89mMIDImJZ8ZP12BwiVTLnEC90X93zRGbmkMZU4W9HAF99HHjgLOB/TlXZFvFdiX6iazowyINl39XGshRjpwiIkINLtWv1XSZt1XOfACZHv/0U4LP/B2y1D3stK0OUQTIHKp7NhGuqNE+wHFjU44LY6pK5ALPeDmxYojqDAuFYG0jWw/HPK48EjCDVXebisH5plCES+6IEluTcloOL9cMZ3G/l465bBNz2deATfwZ6GBs7kJ8Zvh9TByyLZI6QBMkcVfOCXc9HF8L7dff8pbh1+eO499v/k+qSGo2qAVFvb+9oA6KJAUJALYdN9MXkau6xuLN3Az40dKv6Wd9PYJHUAAiWVnFG/MobZkleAX3tHjXHRd6rZQf70dPxOxwbZdjw3PBBpIHtpOp658GRbJP5sQX9++9L4gMisZI0sCI+JyEjQzRMO7j7DBEnW32j0eYQCehyND0YSFq157DhVizMKiRzrh4QucMx+1b3IyY4EYaIHy+U2qjf/9ecn+JCV3vExXWJQblSbZsIQ5Tu+/TcMracmQdZnYNj2/B1hujxP2Bva2HyDpICIpkh0r/34bXAql7gwj0xY8sPq8dL5TKXfG09HQ5KRVtZOc2V1XuzaPUGbN+3RPvmsjBErK0/+voa9Hqv4nP6Z3wpIIorAJ2EpPZfzXbb98LjiJyh7Q8EjrxE2Q3h0rSKDFFSgKOZBgSvpWCIXFfdJ6FR220hmesflgOi0D/uw/P2BDbbObLvErVUl7nAYSnGLCZJMictcnSTdKUEfH4fPErYIoJ8f+Q+NUZqLaMjLw39ifczuqGYREWKFFdZ2LItC2/SWdiCrGRBHfXhU6KwULkcD4iGhiouAMls8tr1GyDZGrAAVjyn2jVZ8OHYFvpoD7Ynb/HTTgiIZCWH5wYBp9w2cvCQJy48WLCdTtaG09QhAoC7TmNj9volwHu/Eb4u2qdQQHRNV84pJIgqycuiGEEeHkU0ICLCVEG7B0IevvrVMCCSx7tUDJEUaFRzmRPqhcR+UL9WyTTEcmDDYzlEpEJA1KkFRDMLzFShrErmAidEMSaIUgEA3OIQhBrMLvUrn4/FOTuyItQAAAr8eT/lbVm6moNbPYdIxqpXgPN2Az5yHvDouWz+t+AhYGdm1+/JjrYBaxp+b9kYIoA4CZJrMS+iHgaKLmZLi6wOfLy+ahDrh8qY2p1Bst0gZM68LRQK5xQKhTRy54kHUadENL6PXoirpn8t+rmEB4gSdYAgWuXmML+N15yRc4iuOgJYMT/+tKTVPL1bEQyRrxTT8vh2qqmCBzukj0VnHyRJJ3SQ4vX1SyCzOYIhyuwyhw5YfqlCxxmDarbbaQ0i5Gv896XA+btpx4npYKRjO/Aqmip0cQv0smD+LJkh0tqMdtuEy5yvs1gkZIjYduqGz+d3xdKO7dWdCQZAD4jiVoh0U4WUDJENF7O6bcBy4Dg2bKIyNu97/Wx8M3djhT3EtxvLtgO7+WhAtI7l1ACYulyyNK5kqqBIM5KvrSNnwaXqPhwtIFrRN4jFby1L3H1FSBO0J95Yi/PufjnmM2444CXWwohBXPuX2Rz2QvirtDIq7GPBJ7PId0elKQCoZfGcF+FElNJlLu79tJI5zcXNgq8tMJHgOx0uhvvzpOvOu1r75ih6pLLLnIwY23wACkvZRdL1QcKNsQw2CVRNFUL2QF7IipO+degMUcx5x7VNS2aIEurCxMG2CN6ks7EDeRMD3PKa6sfgC0BDwzH9Xdw5AFi5bj3mPR8+U67vhws3MZbThBCsJ+H0hVgk/tl49DxgJX/GgmfKgyvVjrLhYaupTHJehsPapDKuJBvcINfN91lWF9rEuCYm4V3TwvekHKLULnM7fgwAc8BcNVCO5mYFpgoJ44siM0+QAybBTc8QkaqSOZL8p+XA4sEqey8pIJqm/j3r7eynzhAFhVl5O5Kk1l4p/K46PN43VJPMvfk439hVHEFtQmFJY0oeLvp0hqhSv726F1j7OrDkKeDVu9hr8jUqrqzRZ8JKxRCFOa5JpkJB+/WZ9Hhjsi54SxTtfmFpFYlqk6AWK6KvAnitUCh8qVAoZJvNtjn+f3vvHSfLUd57/6q6e2bzyTpH0lEOIwnlgIQyAgkkGYGIJoMBm2CTwSaay8XGcMEBm4uvebENNsk2YGMDxsaALMDkHDQSKCGUjnTyhgnd/f5RVd1V1dVhZmdnZnef7+dzzu7OTHfXdFd6clJ8TtOe+b6djQhZP171sm0hYjA1feqXxEJUbRFl2kSTiSEKOLrwEXfbwqXo4P1pXIBlIWqDG4U1AWjVwHM2KOr1g/eZJtqkMF6vAlENnr54V8li4ooh6sdCpE/wu3I2pJnX0ucblFiIPGk+X1ICUaGFyF4gxHlNC5HuMqctpho1jyO0z2ULRFql9wztA0BtVmtHtYxFPiJsmZYCkeeZMUSZdLMO8jwruJe6zNl9Y2EPsO+X4hLTWpHZikkVWE5hVkAoFjpWjSnbQuQhQvug6TIXV7YQmePLd2n34jB1ZbE3YEV93Ol+F+fHEKlxEIWI1Vj0J9PjHDBlIdJTs6o2+hMVxqBlXa6gxOg6XOZ05ZCKIQKA+aV24o4WZ1JtZzvbgl2YVZEEGCsBKcydG2NtgzlR2UIkvlMHYhPoCrgHN+dtp4Uo0PpynsvcAGOIPM7wyfASHMF3Ifz2B4WLFJjpzifXkqWlhcJ5XXev/dj//Bwv+ch3k787oWYhyMQQCa+HA3xWey3HQvTLrwMfkPXl1eY/DhPvCUDM56dsn0AbAXYvxab7kD9hWUCt51ublq93rGQksu1qDqxrc2vY1SxEJfE2iif8f8Brb8O1px+K79ypFBnKvVMTiDIxRI5zGVazKi5zuoVoAFnmjAO0/s09eAgRhyUCUcZl7qS0nT/+BPA314rkIrbLnGYhUgJRBz5m4nnM2wlAinC4znqay1ydOSxEVc6tuytHHZHU6ZO/hYf//O3p6+qeaIKscjstRLnMgYHZxaMV6jlLC9GhSGOXrjxJVOz54a/2ll9rDOhHIDodwLcBvA/A9xqNxuUDbdEqRglEegFHn/OMm1reZjxbXcacIJJFTl7HlbXKScHEWfc9tOEjCjsih/67TkBS0Uu6uig6MZe1iXg6Oaq6Iongs8sMxlQDcH6XMbiZskL1mIhwIZbXU9dX2onbbgR++U33QYNymSvTiuXFdUg8hIUCkRJe5g7I+6c+WyGGKHlO+qQbphYixJEzqULgCQuhQZ7LXKLdbwN/eYkwz7cOmlpMxistlh5CbKxzgHsIfM803+sZgHLJsRBxH2k8h3XPFncLX2sAoTeVvl6UVMGIISqwEPmeiCHSCCzrgocIkQrEVWfvJamC3MjEEEV+M0ShJqx0s+/l4ey3keXiqmeITLMKzS5J16MkzXbOIss8MyuabiEKpnqMeapmIQq75jkzabeRWogOLLVx7Os/iziOHfWBst8pBEcYp+fatX9RXVT8VPe7IEOjnnVvokoM0Z47MPlBUQGjy3xwRKnb3c8+nRYktcs1OIbKREYgctXzyXeZA/OyCSoK8DjDv0fn4ZbocPi3/DviOMpmVZUbrsXF4vlO12wzy3WrGxYnVQAYFrzUgskZy990KsuepgAINQvR/7t4AVsmRLHw3aoZ6nkHU8D3/j49V8ZCNJm+bliI5B1RSilfC6LUs8yximunFwBTm3HVKdvTrIi6myX33DFELvTPVLEQGa6iFVzm8jL+yU+Yf2n92wvgIUS7WxKX7Pm46+zXpn9vPFL8/MmnxNi54yvAt/6/dG+i+tHm4wAA++NJhNKatMQmUWdd3Hb//mXtHzw//b4ButnSDFUEIv3687uAdzeAH34Mk11NsehwmauCnnWbeWUWohAHl7rYznbj/ngjAOD4bZM4Y+eG4sLXY0TPAlFTcA2AxwCYBPBfjUbjnxqNxlEDb90qI1adThMiAs+hSczdjFsaM0sLl1qIxPm7lS1Exl/Ge3Wfoxt7SapJQPNtZ74xuXTUhk+fQJUVQy0+7zoe+Itz0gtoAXezkZalJrFC9SYQLUEJYLK9arH64K8BH7jSfZAzqUI/LnMl2VJci7j2mrCCFHxfuSm/bO+ngLu+o2nTXS5z1nlcm4D2fOJPH3c74sq2hdA3N3YAECcWIiupgmrP3jtE5rJ/e6UQnnQzPfeym6tzfwM49YnGS1vYAfj77gC4j8C2EO2/G2XkZnzzuKjMDWQXk/ZB4EEhbLLIygCVW5hV12AXxH/5HG1LsPQtVymPhYgX91qnVwJRyTjQYogmaj6O2eLINqG7zCV9mqXv5ZFn2cyrk5Ns+iM884fPFr8r7WGei4ey3Cm3lrBlCkRVxyBQPYYozApEdmFW9bcSyOfboVkfSF3PPjfMpAq37VLxBHaRwvw5Q3eZq6OCxv3Gd4PvFxbOmImCsktLWj/+zCvF12KeEaPqdJmrlbvMFQtELuVdPh4XQtq3ogYm7/22sAjYp5FrSau15HZzVh9j+n0z292J4lS5YfQpBsjnv+hrlgIuX3eRZPlM579Q9o2IecD3P4JZLKIDH7sXZZvU5tDWptv9NQlyz7EQyTn4Mz/bm74XdQCVXQ+2y2IxUzU/3YfYAhFzuMy5CB0WooXdwA3/R4xrOw6pVwtRSWFW64j0N1lceUkJEwWxngfO+x1c2voTfPvC96VWupv+LXU5W9idWgHVM3rS3+A7V3wYe+OZJKth7In5984H9lXyiADgdJ31rHUntJNVVDm3/hnNmmWeOMdzoIRU+ZBTmBUwLURLHRzKduNXsUjocMi0j4//1sPw6qsaPV13VPRjIQIANJvNzwB4CIDfBfBIAD9rNBp/0Gg0pgfVuNWGKshqWIg8q14FkHbgOBaBlep4OLLKuVwflEDUrdi5GXNYnwT1gKOjXOZUO9TExs2K551IS0Npp5fttrMB9oChFdkQpr6laQxRb11wAZZFqqhGjqJKHaIq9CIQqY2htrDzTJYrC/29+fvTdnequMxJ07auAWod0NxHWs4sczWfo6umAbmIJ5ue1n7xXPXvHUXpOeNIWIj0mBHmZSddfzK7QQCAn/+nqALue2aWuQoCUa6FyPPBEAtNseu5PtAUn7PjV6okVShwq6sHHK3IiiEKTd90DxGwtMd4LfXRru4yF0bAGYfOZD+jJ1VIsp1VEIiqxBC5Ckvqm+iSGkfCldF6Juq6tSn3hjwP+zw52JaevDpEQCoQ7dl/EPyOrxnHOQWi2APXAqL3L1qCaAULkS541eIKmtulvcmvQa0GzmLsOehI6c24qUF3WYgMgSh09gHu6JPJqWxtfpnLnHz/W1EDfucANh38ubQQacdJa0grk3bbaruWxcrOzheGegyRtqbVppPNneH6k5dUAdBclpVAFCGSFqJbd1wDtA/Cv/0GhCzAT++Tc6TaHNprhd2/E8VF1+ojykIk1tK7DlqZJZP6TfnuZS6mamlipXT/occQFQgs3Raw+1bzmah78rnXAl96G3Dju4C3brKO6yWGSK6Nedkq7b6oG+65Dx8R2t2O+7MaM3Ufd8bbcdvmS4DAsVVd3J1aiGRcLiY3oXXYBWgjQKxc0gPRV+/atbdQeDdwWIi4ZXWJ7X5T5dz6XJjEQ1l9Y1GuO9t6E0xSfV0Fl7koRGd+DyZZOxGItk55mAg8I73+ONO3QAQAzWaz22w23wXgBAAfgRCObm40Gs8cRONWG3GSVEEzg/ICC9EPPgr8w7O04y1dXt4iIzVgVQUi09/YthB42IfppHK3+ITyxfWMGkZtZUngfjo5JtmVWsCtN2Qvrm3QZ2LNhajftNvKZU4JcGVCClAhhqjiZszOKmdjnFPdH2shqOAyB8C0CjksRFkFrRTG9Y1+64CxOchzmUssRInbk8bi7mz6WHXxOBL3RHeZc1mIvCD/e3MPnHtmTEwVl7k8rwgu3O+WuhH2HEif14Jn+o+zyPpOFVzmcoNKoVzmzO/oh5aFCBF4Xq2XHtJud6MYm6Ycn4+6ZkxJXpruhd0iu5LrPYUtEP3yG8BNn5VtUdZZbYFX96bAQiSyomkLfGIhmqyuZVXXqKDpzApEEaBrobWkCkogn/riGzD9j08yT+Ro26NO22lsZg4uWoJoBQtRrN33Smm3deuitF4w131gpiLLNVQm9CxzUdd9Pwvm5qyFtngeVxuiH8bHAgA2H7hJHGNYiMSGSwhEXcBz59yfQXpPbQtRN4o1q3g6xiN/QvQbxo0aTIUuc4lApFzmIkTys/dtOU9s3hceQBs+bt9ruXDbgrCt+Zfv7zk4j5/eea/2hlJGibmrBU1w1WOIeG9r52RNs2gaFiK/3GXu318HvOcss5aZWtfV9/zJp7LH9VCHSBTmZsAzP4XwnOeWfBuYimJPJBhRKfKL7st0XfT7hXYI+I4N/sKedG+irccTNQ9tBGBd00L0ywf2LctlzvdMJVtsf6ZXl7nEZdNay5VAdM5zsfvCN5afU6JGudAd5SgEtSxzsfQqUS5zWyarJVkaF5YlEGlsAvBlAF8BcCiAv200Gl9vNBqOPMxrF+UyZ1qIWDapglpgH/yFdQYrO5DtC65+l5uPODSz3uTBkFqIsmm3OXbFG1BbSjOppK4cZnvuXwhFnnw9K42aobttYNfP0hPrr/vZjbZK812UythF4jKnUl52FvM3YUlbXBYifWNWcUJTGdXytFjaZm9+cTHzGoDCLHPGpnwxnZhdFqKMxU9t7GyBSCVVkAuyfaeEhUj2DZX5CMBiLBeLhQctC1Go3e9YXMOwEDliiLxavhsD9wEw+Ex3mSsXiPIWPe6JjfdiO8Q+TSC6p2NqAzMWolzrj6GKzG1P3edoWTFE3Ep84CGCZwtEvKJApPXhbhRjwhUQqwtE6u/kd+3+fuzpwN9dD6gig1UEoo8/HfjYU8XvLoEocZlzz0dJsovIJRBN9+4y14eFCBkLEc9YiHDXtxzXywpEXuAbfWZhSdP4A5p1N2vB2X/lH8uv0YMQCKSbGgCRnCs8lyBlBdy76hBNVnCZcw2xNO22JcxUtBDdHu9AyAJMtx9ADOmxlnxIFqZuLYln7LsFommmCURWdj6RVEG5lGv1Y3g9sZCrjJyi2Tx//bAzqMZh0qcifxI47CwAwOTERJpQpbMo5mY7VsOeE5UmP+zge7/QMk+qfi1d5pbimvleMr54LwYiTNU8RwyRdBV2JVVIYMI9Gkh/AqmAp9YsV+HnIpe5KAK++Aci5hiqX3Fgy3HwrniToxl2DFEK93z4LEoL1RdY8qfr4r28QsxY3J20VVeATQYi1prJtTDiom/uOzBfXZnjGGPcFjL6cZnT+5a65xmBaK/4yRg6h56DqhhDvNRCFKGzJPY9ByH2SHVeMeHEmNBP2u0djUbjukaj8bZGo/EfjUZjN4CfAfgggIsB/BjA3wDYCuB/Go3GO9ZLNjplIdIHknCZy7EQOTbL9rB3ZgtK/N5DLORUUjfOwtPzZrLM+RwPxBtQb2nZr6IoOU7fqN22u4Vr33OjWLhsTWjYBnbflp5DbXDCFsI5vVKEIE0I0aOFSAlEajPXXcqtBJ/giiEyCj1WnNCUhajmMLUDxiZt1z53Ss7ipArpJqVzcHdxDFFOljketUXWN8YNCxELW8LJwjqs5nHsWxIbgoNhev1dsRRyFh40J2m9lozamOoCokt779UKLEQ+wJiZVOGAY3HNHuh81eOirsxSJ0SgbRbnYQqxXLcQRVFB2m3t1wK3uprP0Y6KtWEeIvjt/TnvlowD6/nXPVeWucgSOPQ6KOL4Ox6cR/TAzeK1pGaRy2UuzB8XauzrgnLiMpeTZY5z4bLk0mb69epaVkB+zyoWIvOc2aKNLBFyVf/bv29v9kQOd6LArxmDKVAxcMm8qAQieY+ksuGHGx+J8MgL5UeqzTt3PriA133yR+jMpwKRWmuC2CXImAJRucuc20LEHGMsTbttuuWV9V/PE++H8LB7UoQbx9b6lgggUVsUrc3ZgM0gne9r6OBodg8u4z8AYCZVUJvX/wzPQaQKU4MZFiIwVmDVVLFIaVIZpSzknCexk9s3b8A5xxwim75g1n9R2AKRrH3jI8QE0+MZu8Y1W9AFog4mF+9J2t2LhWi65ruTKrC8pAqay/dW6WZ130+17yPb7GmKMxstxXRGILrza8B/vxP4F1GWJEm7DRQqnhL0wsOyPk5bpc4vuC81j8PnTGSHc9E+CE+6OhsWosBDCwFYKAUiaSEKO44C7T2QccO2Bekq5zYEIi2ph442XzKXZSyvfckvvFIdoo7Mwjc9LT0yepnXx4B+LER3A/gUgNcDOBvA1wD8PoCrAGxsNpunN5vN5wM4CcCbALwSwNtzzrWmSGOItOrDnGXTGstO8v4bbrGOt8ZyXhpKeX6fhVhoVRCIGE8EIfts9cDDA/EGTHT2ps3T0m7rfuTd2MNdexbF9cMO8MtvmS5zusVLTvid9hK+/YAv6jQAolo20hpKvVqIEpe5ltxYdhZT4SiPsjpE++823VHyUBNPzRG/YZ1z6bZvAF/5k+y1iwQiz8e/XfppAEDrwINmHEJZUgWl6Y47gOeLdK2WhUik2bTcujQL5l2aR+Dt8Q7xy51fz1qIdOtgHFnxI3GOy5w58d+7/TLxC/cBxg2BKF7cjVJyFj3PFwG2i50w9fcGMB+bGrNsDJH7ueibPl4gENV9jqW4WCAKWIRax+yrVbPMRWEIXdio8SoWoqxAdNn/+TIeXNDGrPaewWdfA9z0mezr7QVN2aHdQyXM56Xd5r5wxdUXeKUl19NuVyi0HNsJH3KIHDFE0Gu7aRaip5wr0rBPaZvTO6NtAIDFttWfAfhBgEjb+HosQqwrAxJlhtwsKCUK4/DkeLHbl8cXb7oPH/3mnWJOUN9N3m+XQGRvll0b56mJ8hgi1+5AWYjiPmOIAOAOT2T3yssyF6ArhNkcC9Ec02rBoIO3+n+LD9begcv590RSBdnHuNy8zqOOOOwmcSqmyxxHnhDvshApgYgxnjxT7tVw9HYRP/Pln9wpsrHa2GNM9v2AdXHolCNhiWRJF4i+9QGc/d3Xa+9WXzsna17qnWC7zLkKsybt6QCzci3Yf5f2ulUaooy8cS2VjCzW4lsdc6E7A69Aua62WnKdKrAQMcYwXffzBSIAtdYedeLktcnAQzv24ck5UwlE3W5reZt++7vaLnNVlCa6wlIVmXW5v0t41WeGdO5gQG5ShTixEHUTgeg5D3+IfK1HK/iI6Ucg+isAzwVwUrPZ3NpsNn+t2Wy+rdls/lez2Uy2VDK+6O0A3gXg2QNq71gTqYFoJ1VQE6Tq/LKTcJeFyF7IdA21+l0KRBwx5tvlg9F0vXNYiGAVUtQclXWBJUnPzH3g+x8GPvBIoekBxMS5WxeIxMDYve8gWnGAlixaqbRnaVHZ3ixEbeawELUsgej+n6UZ0oBkAQgBvOoffoA4jg3/ffzTc4E/O8Ns+8H78wezXhtCR1tUTvrCs4EvvCV7jrKNw7YTcW+8SViIVBtb+7MxRPaBss/5URsxD4D6HOLWfty+Wy4SaqK1DvzF/fPJM1nUFt874u1YPOoK4Jt/ZQXHapsnZZHQJ8o4ysSSdVmAb95huoptPuzYtN22O0SZxQ/5LnOe54EhxmI7RKSlfT1YaCHq5lqIzEKeRS5zHpai4um0xmPUO7bwXk0gCrsdseGWx9RZjpBvJC0w3efU8Umsk7o/LmvLwoNp5iWd+fvd8TFJPE2eQCRTqxsWIiUQ1XoSiH78q73VYoissSdcpvQXWHLfX/pwkVp3UgvYV/Pd7gPZxAi1IDCsvT5CtLra90uUGaaFKOI+PF/VBqumWe7KMgi6ZUSVeAicLnNeaX+arFmuWI6sfa7sdLkucyV4mm/ct/eJ9SabZU60qYauEBZzLESz2n2oo5OM0av5t2QyFbm+yn7diUXMq6pDxXXlB6+SVCFNu62EWM45UJeKMb+Gw7cIjfhEvJQtYwA4LESiT/kIMeelz7DdMT/XhjYv3X5j8muv9z/jMvcPzxJjPK8wq/ps2MGDB5eyr9suczbbTgKmD0n/jiN89kf34INfu12eRsW2Std5mRLdeM9ojq0ATH9VAlGnvSQ/Wtz3Z+o+DroUyVLROSm9ZfQ008JlLoBnWYiidmt5m35LycbsflLJQqQJUUrJVCgQ5cfCZj6rFCBILXE2nSUphEUhwpa4vqf2SFW9b8aEngWiZrP5wmaz+aFms3lzxUN+AGB7r9dZjSgLke4XasQQqSDROEQUxZkYg+wMVxxD5CNEZ9etwFssgSbTrrQkamxdwucMD9oCkRpgVoE/QyBSKPemxb0i5eMhp4i/5YS/tLSAFoJkMlb3Iokh6jGpQpvLjW1Sh2jBtBBFIfB/LwA+rAVGy0mlG8b4xHfvwje+/S2wn33aPLGWwQn/8hJRjymvQKhtjk6u7YrFMCeEqEB7BQjT/L54GmxpTzrRzj9QwUIk/g4gM6bVZrB4cB9+fI+MtUomTfO45n0HkmeyGKca2S48PHDIw8Qz1YXLKMI/fFO4RkYqzoRbAtHnX2dc49M/uh8/Ue2Q1OryHvKChAt94HkyqUInRKRp2w7CshAZxX3zkypkLbZu6j5P09K74AFqPIIXtRBpgzCNISoeB51uB7fcJ/p5DIbA5ZutW++AjIVoUbrXJkk0lEBSNYYOAPZr8Q7d6haixLqmCzIdzUIUdhBFcSZVtosHD7pcSLPYLmlJHSJdEy3bpSxuUw6BqO5lv1NQqyfzPSDm4oV2mLUQqe8oN1sx48m9qOoy1wmz14+4Eh7KLUQuDMu8LUgnp3EJROo9D6ioLABSgejYrdNoReL3vMKsAULsW1hEl7sFojmmCUSsg5qsyRWwLkLNQqTowEesuczpbWUMFQSitDB1mMSX8NRTwKvh0M1CIJpk7YoCkXKZizDNO0nyhAOLqfDRiv2su33ScNtlsZgJXxeIYuCn/yJ+zyvMqnYMYRuf+6FmGfICsY9JXObyrA3McqWO8OIPfxe//+mfCMVMUuBdJjDQ3Vmdlvh8C5GyuLbbSulXfF+m6x4WXIpk6dpfb++Wp0nbMTPhow0fvlSkqaQKUbe9vE2/NW7sulqVzm3MqcoNuUAg6sVlLvWZA+clAlGseWUoi/g6cJnrlc8DeNoQrjNyoiTLnFaHiPPEZW4hTieBThSZcRMAMoPerkOUWIhUIHCI4J5vl7aLF1iIGGPYxzeZr8lOzTSXEkATiPRJUE1sylQ7LdxM0J5HJ4zQbS9JdzkpEKmAV1U0sWeByBronSWRvlmx53bx857vp68pv295qc/9syiY94PoWPdF7v6e+Pn9j2Tf40GqGbQIXVn/bE12ycah5nPsxQz40r50Mll4EPfumbc+6XaZq6Mt3Gmky5xaUA/Oy+Ot+/2Wx5yS9E/dQhSC4y+/Jje/ugtbHOLj3xAC0a79i4jjyFzAHJuLH967kE0soiZl6TJnczDOSVyhvm6ByxxXLnNd3WXOshDFVvKBPEHVqANWYCEKuKnNtfEn4LMYLA7TAGwg/e5lAlGng/v2y3GJCLW8pAq6QGHEEIXYI6ugq3HcWprHgwdbuHt3icupzgEtJbrhSqmum28hEm3SFnwlLHg1IOrg+vd+BSe/6XOlTWi1O9UEIqsvOmOIksLFYuPhazVuuvJ5Bizbp2tBLWMhmm9plpbIsqLJDUIML6lObwtErs3v3oW2TJxj3lcV1M1d99tSZDnR70Oey5xzrtLqENkpzAtQLnNHbJ5KBHJmt12uKzV0sGvfAn6+x/2MlYUoZhw1dDArBaRJ1hXCo3VfWwhEQg/5/HULAuc9JFUAkuQ0TCqdxEkCeHI+m0AbXXB8ITzLPJct6LdToW6KtTEvlVG+Ni+1EeDQje54VQZNmVIBzlma0Uy3wJcVZg075j6F+8KVMbEQuTfJB1od7O1o/Ue7x/fd/C3gex+Sr8sU17FWksJpGczuWxSebxaqL7MQTdX8JKnCL6dPTd+YE26zE8pCpCnJPM4Ar4YgNl3mwmW7zFnPMGyLPYwsID6QpApzhwNnPSP50+vJZU78jMHSNOSSuCatQElh1ihNG672SCQQmTSbzT3NZvNj/RzbaDR4o9H4y0aj8T+NRuPLjUbj+EG3b5Ao7T83kiqkabcPdFUxNjFxG8UokU14wBgzFt3kXeUehQjtEjcddZ6iqfOAbwlEqlMzbky6TguRbX6tp4PkwYNtBHEHG2ZnE+2UEhq7FWoGuOhyy6/8thuAG96R/n2/zHS36ej0NbkxUq4VE7II4ju7T8leYNfNqZVLT02s8Gq5LnNLrkK5lk9wYZY5CIFoXzwN3tqbaofaB/Fnn/ue+UH7gSpNN+uK2Ib6LJhWF2rX3gPyMPPA51x0DDbPCmtNksEP4lkn8VqGhShMUmRzSG2s/gwdrjf3tqeyApGyljItpkM/Jt6cec0gZwPme0IgWuqERtpd20JkEFVNu11kIfLQlRaimGsBzEnDaqixCJ1u1wi6rpp2u9vtYKkjFheOGLWeLUQd7F0Q90Ndf+++A7j6z27Eqz9erlRJ0GtE6X1bJU45+TrnYUnKVn3jrccQAfjRr/Y6rOZZlto5aaLta0YR4l99D/iXlyCOQnFuvb9pabcRRdgC0yKs5jvP4VJYqwWGhchDJCxESghLkiqoGCIxxmLuJRvT//qZnm4Z6LLsRvCfv/crdMIIW2AKrVGBllf0qZJ5NSMQuVzmXOfW8j73kFRBpd3eMl1LxgZHbA5jGTNUY11wRDjYdSsplEAUTW5GHZ3k7wneRTeKMlr1qYk6orCbxqkYayrLtxBxy2UOwIe/disAKeDpWnC5yZxECyE8PL/zGtwQnp6eK8dlDhB1lRakS6++J+jAw9Y597zFCmoL5qEEcSOLZyIQWRvvJM6oY841PBBroLonOe5X9+xdxD0HtePiCFM18Tx3fPRK4LtCILrrwQP49b/6n3ILUY5HBJC6coXSZa4sKcOMFkP04ol34FPhReINmS3Vk0W7M65lfj0RDmM5Z0Wddn78VRUsRRwP28J9/89k3xlEUoWX/xh47HvTawS9JFVIBVluCapMCj2eipOMQzC1JtRIIFoJHgdgotlsPgzA7wF492ibU8x+6ZeqZycJPJ64yLRjOcFGIdrdrIXInuBy3YSTGKKoNG5BnIdpwlb2jC3f3OCrXPuMuV3mYu7QcCtUCubOAhbaXdRYFxMTE8kiGCcpUftzmYvKKoArgWjjUelr1qSiBCLdRUycPATee56oXA2IeAkblbDAQauVrTNw5y67EGfx9615HHvjGdQW70vjDwBsjqzz5GSZq6MjhI/6LFj7QLLBPOHm9+deU7kG6AG8XXjJIm1sMOIIPkvdHJitdZdCyLvCpyYv3RCdnhUE/dR91CUM3B1vyW2vaHOOQGQkVUjvn20hMui2ctw0ql0TkC5z0qIQRkArtrRw/gR8JsZ8V7sXdubIPMJuF4ttGb+AGDWH1cLIACgOQqwWtKiLvYmFSFxr34H9uP9AK82QVoFf/ELzlNatPVObgTfcC5z9LOdxyeZCF6L0LHMQ7p7VBKJqFiKGCPjIU4Dv/T2iA/fBVZg4LTIc4jsTLzLeUvOcYU2UBDXTQhSgK9xw7PpsauMoi0DGjCf3wp7/XS5ikzUPnSjGMf4DxuuRl9+fGeflhndDIMpxmXNsLFOlnOWWV2YhkqfaPF1LFITMTqsgN3GTaMFDhHbs3mwrlzneOoArve/iKC7m6brDQhTGDBeduAPCYSyWcbr6+OPAznNzGm27zAE/uFM8B2EhkgJR2EqsGlsnwmSdNCzBcp36++4jEE9uST0qANTjFg7KpC96PbaIBagFedkve3OZAwBfJZPYp7nAJUkVrDlAS5xiJHDxfCHcq7GbE+cVg5k1lOIIx2zNWrsWl1r4+q27xVgt7EPlLnNJmvWSuXS67mG+JUqW3HzfgURBFMlNfBJfaq0JXEvyEcvvHYdtMx65V2yXucjaz1RwmYu6+RaiCCwjIObFArlIdICMZZMxyPs1IVPfd7odeLFKPKWUBWs8hmjIXAzg3wGg2Wx+HUDOzDUe7DogOsNkPe04vlaYNXGpibrohBE8a1Njp2SOYbvMmTFENXTQqVKHiKf+3i6tUte3XMC6qabFyDInJ45Qdw2yJ4O6TLfYWcRCO0QNHUxMTiX3QG0ykixzvQpEOX7lCQ80xU/Z7vn7bwdu+CP5ZoyNUwEmWBvt2Mv6ettaZ1kjIXN99R0t2o5sVK/+qFXXpCSGqOZz/Ht0nsh080AzESBDPXYDcGzsxOemsYi2NwnUZ8HbBzVrjtRsueICVFBq7KWbenhpinMgtaDEqYUo0WYaApHoO4uRh8+ED8UnwkuwiIlspsVEIIqcC9hP46Mzr1mtdr7qex48FmOxHRnC8qnHZFO/G23Oqy2lW4gKFtqaz5MNUBzHWfc5r4Y4CuEhMi1EBYoKo4ndDloyBshjUU4MkdzYKv/xqIMDS+KYXz64PxGI1PUPHBRWQx/VF/Q777g1+b21pLnebD5GLMJ59aGSFMa6v7vcFMq+4CHCmTvdY0un1XHXzbHZzvYkAmG8dCDJMoanfQw4/kpZH0u5zGXvZ8Rk8VPHteq1mjGWK1uImJ9sUGzhL2P9BrB3oYNuGOEobs5FkeOzCRWSKujvR/0kVdCz9clXqjA3mSajYLC6i9zETaItBCK4N27KIsS2nmi8XkcXX/jZfbh7bypshOCYrNdEUWSZVEHfIDLOgMbVwCtvwtK2043zJQKRJvirOY9xnirGwk7y2Ym4lViKO/ocIPv9jdHpWJjeaayb9biFCZmm2NOUE5FXg58bAM96cpkDkGbX2/fL9MW8pAqqz4cdQ/myvx0j8qfSsZvjMseAjEDk8kxU3zfNAKneKOjf9jmUhajinmK6Llzmbn9wAa1uhK0z4lrKTVtZhO1CpF6gC0TisyIj4uBiiLg9DitYn26/T1OWts0scxlPBfSWVMFwGLet0nboQBShDlVbTlqovvKnvdWYGzHjLhDNAYYfQ9hoNKo/zSFz5pHC9WxmMh04vscTdyG1wfzmrbuwe75duhGxF6TkL08E9L42+Ac89JsvK20X0wUrx2QxMWHFV4RKs25q09REr2u4M4XEJpRAtCAFoi6mJqe0wrDKQlReM8BF4UaA+8AB6YYiN+b3//WvJ2+zOMbhGydxdWMjllDLThb2ZOSwEN07H+I797oHeKvtcK1h5jMurEMEYVH8YnQWFidFqtPWxFYAwCFsr/VJq+2Jy1yIJT4tBKLOQWOBFUc5tL7y2A1TNfh1MZF2Y25aVYJU46P6rdocGPdR3sMOPLyk83K8qvMi+RnbZU7VHAmdfeCO+JDMa2aj8y1EALDY7hia3Qsbh+Wfq7PorloOU4AsthClwiRDnN3MeTV0ux1wy0JUlGpWpxuGaCmrKiJnXIsQiEIgEM9tqdXC/iXxrD77/buwR7rMqesfOKAEouoL+hY/tbrtlYVv31t7LnDcFYXHJYlmHO4df/fte2U7urj+zENL2xCFYSWt7Gn8dnA5hm/55T1y08WA4x8JPOOfTPcphyZzZkrcR1dsYL1WNxKk+EzGECmNrl6fDUgFbi1dtW0hWgw2Zq6ze76NThgnVhBFVLRhZKy8nIHW9na7nRND5HpJ7mo5t+Sh4nlcJspD4HEEgRQ0EZlJFeQ9mmAtcETGhvqueCv+IxB9bI4toOtNCcFWo8a62HWghRtuSuuYReBJKn4g6zKX/D53KHyV6EXhiCFSY4VzrlmI2sCs6Ld+J01SY9QjipQyguNgaG5hWGcRM7PCs0KPYWNeDZ5duFO9x4CqQmjSdhUDoluImOdOqhCmApGufDnQYTgY11J315zNte8x08IXR+iEETZNmfNiImDqdYiA5N4milRHOIH9vVILUbHScabuY77dxU33CjfU7RvEmvdAWzxvZSFilrDn1dL1MPbTjIjdTlaZUB1TSuy2l6y3ywWifQe1+OLEZU65Wmb7iB9UFzaNOD/brdzylPEQoa6SvCiXuQN3Az/6p8rXGzXjLhDtB6Dfdd5sNsfWKdFTi5A2IAMv9fWdl3EMf/IfP8NLP/o9TFgZgmy3Isa4sYFNkypwxJMlMRb6eUo0SUdsMv2UlR8o4xx6KXE10XdZOlGEtkCUxBAtYL7dRYAuJicnk3ugNhEqoDhTmKyEjMuc5JuzV4oNoRKI5MQw00o1qwwxaj6HH7fQQi27Sbc3WY7JqBt7+Nwt7rTQW3+UdUsLbKG3ZONb94XmdVdL3JcHmXjOWYHIQjvvApsGginwcCm72XVtcuSi5ns+mNyUhPCwqFuI1AQbR4mFKClm2dLcPGTf6VgWksy9VhvEyO0ytz/OKX6b4L6PvtQWtjodI4Xp7FSBy1wc5mokzT1fscvcg3G6qWnZAhH3wGNhIdK1qlVjiFqLC2CyT3PECFyuZSqGSFqI3vTJ7yVa2d0HFrBv0bQQffMWEQ+ksnR1XfVTLOLFVD+lFr87ZV2ZIpRWUk90oTZVd+1XFscIx27JyeCowRDhvj0HSz+n84ef/B9HUgXATqqgs3FGtMXlUli3Yoh8hCKLn4pXTFzmWoYlKmZeck07Q9yD08djzyX/y3xtvo1OGOFIZlmICgQixryeXOa6HbcLossimpyWeeilMGskJaLAYwj8tGyEcRRjiIMpTKIN3xKI3te9Dl/Y/jwAwkIUBtPAhp3AlhOSz6j7qQuaIUTdJ85i8TpjZlIFPTHGhKXxVu9pMUSmQCQ/rwQiOe78oIY/fvIZRtzk126+J2nPwa51XzsL8Cey8x338wUioLfCrAAQKOHloFb4OuoYSRV+cvc+kalPzp2t1hI8bR0MY46FuI64LVzi82Ivo9gSCOMI7TDCpSduMz6nvGRESnRdIBL3NlUs5bvM+YGyEKlkUMX3Zabu4+BSF7/aI+bTTVNiT/HJH4oxpoQS7pnPydcEIkgLUQ3dSpkxc/EngR2nA48WcdCGAvWBW4Bbv1R6ilCrt5fUPUsEoqxZrh8LUcyQFX5rpkDEWZyEIxjF6/UMvmPOuAtEXwVwDQA0Go0LAPxotM0pQ7m0aQsl54mWXplkfYS45f6DRs0Lcbit9c9xmQOA6eIYC/O0untDdrI4ytqEqGrMdmHW514iFp+Wn7q13PCzu4xjlTvZ/bv34JQv/ybqrAu/NpEsfSGz/OeXG0Mk+ekeeR4V9C03j3NxGozMEKHuc/hRC0uxQyCqYNrtwM8N0J/ee1PmNXvTUxYIW/NFmw52xX26uyvu5zZbIMqLhQBwEFOAPwEeh6nGJu84pO5M3OOJoNIFx7xeu0e6/Ny3bx5TvphkVbDtvftTwWN+YV4eby7kob3ZNmKIsm06gEl0/YLNcc5t9OQitvvAortwaB45RSCruszVA46fx6kVKhNDxD1smw7gIcLkhO6KmG+5VYQxwwl3fBRP9/9LHIIYgaxDNM+0hUcJRHIx3L3/YNKf5pda2DOvLEQyZmxBCBVqk2cUgcxhJk4FEdW3Yla+wCoLUeQoIqg2vj5CHDJT4VyI8a1bHfF9BWzAvChMnJljZT/95G86LiSLnzos+fVaPakFBAjXn/lWmGTPXJLW4pvv2Y2DXY6ujCONlYsSstZjxjjaJz3WeO3Bgy10wxg78ABaUzuS1+MyC1Gpy5ym6Ao7bpc511zB9DpE1WOIolgJRKmFKJNUAQALpjCJFjgzXeY68LFlVgocLELXl/1ec9tRgr3uih6CJ7Ezvkqqoa+purLQrt0iBQG9npnnFIg64pybjwUAHLV1Do854zDDcr6wKNajCByL9twQh6hPZeNSmV9LEyHY73GGXi1EymXufj2rZHteCOhxhO/esRvXvucr+Ouv3Jb0h3/5zu3YfTBVAHbgY39Yw30PPohT3vx5mQExSxjFpiU8jtHuRqjZQoayEMVuC1FHua1m5KGshSix5JZYR+cmA3SjGA8cFPuvyZo4PtkPKIWwNa8FhoVI/H4avxUz33lf4fUK4Rx44Y3AqU8AYO0X/uJc4HOvLT2Fa35SLmuuHsJy9lAu9LTbmTXUkW13irWE0lt3QVeZf1cB4y4QfQrAUqPR+BqAPwHwihG3p5jE/cWsQ6QWPmUhUpPqBLMXIdtFLn/CY9Nbe2lY6rLmWLiO3GJqp7jUiDHOjQQRpx8lrvnLpbSzM0uIaAdikPztl36C7fcI7YZfm0gmO2UhChJTeW+Teqy5zOka7f2Qm2fl2yw1JYlPK5SFyBMCkctlrkJcQgd+EgBbhXrGQlQSQ+SZ8WYPdMW9noNtlcrZ2AHYF08mG/wpZpngHajNKuNeclwIz0w6ISfYF/ztN5Igc1VY+N4DqWB/869EylI7IDpzr3WXOUcfOBBP4btX/yt21Y9wtjlPC6j663/8+O5UsAcMTeZ+1/PLWyQMJXiBQOR7uC1O3b0ywjbzcMi0hxqPDctCYgEuOLftfscRwZcC0X5vY/qGiiGSwmvYbqEeyHEXdnH3PjEmlHCqtHnqXBmrloMNLHXPUIt3XCEhhSfvf6Sn6pYWIvX9AnSxdaa8DRzZDJ1lbGRCkMu4rKpnsSurzEiSKjhSnE9M2HWIIiy0u5hfknVKpIXoR3fcjzZ8/OKBxfT6sg32RoZxDs+6l7vn2+hEETbiADqTqXY9yhXgAbCM7cX5GUXY7fTu58+sDXmJAKa7zNWUQMTi7DgOpjDFRFIFfX6PvBo2TqfrTqhceJVQUp9LitTqsVkReGI1Fq6+pjuhK6mDotVp40+/cDN+9UBqFVXrFmc83RAqYXKLEIjg+eJ7asHrSlgLwbEQZsdLfTIrEHnBRL6FyBZIKxDIBA03350m6AjbC8nc+L3bxeu3PjCPeVkPyWehMdZCcOzpBGhJZcrP79OEKwvbQtQJIwS+2U+UYjSTnEfe28VIzdv539X3bQtRcV+cnRDnvGffEmbqfiIoqjXKj1UMkbmG1eq6C7kYfy/wP1t4rQw8wD9ccaPjS4j1Z8pWkleg5hSICvYoPaTdNpyL7OMcyaWmsCSUNfo89uDPK19v1Iy1QNRsNiNZCPbCZrP5sGazmV21xhGtM8zU/aTDqloDahKwLUSZTWPBpMemqluI8tPVCY7aPGVotP0lOWFaWeaO3DqHa087FP9zd7rg2Iv6x7+/G1HMcAJPLUf1hXs1gUymsk2CU3ub1HVz7y5sTH4/EOuLGTMytCXHIkbN4/DCFpYQZFNBV7IQecUpnC1qrPc6REC6Od3XEfer1Jqobc72hpOJhmY6M8EWBFkyplmIzKQKyoWv3emC6cX0ANy9LxU61Sa5q7nM/fp5R+CqU60YnpIsc3swg3DjMfj21usz74lr5/Qbea4HDixhfkETIrV+43x+FSxERRuQus8NwUXdh8+yS0Uq6k1Hi+8ah4ZFJRlfBf1Cd1EFlIVIjMF5PWV+HCKOQnz7bvnMo3YSo+EhxC/uF8KMmmcmuWjj5ccJVz/DRdJByALMIRWIPCkohKyCEOO0EInno+aeOo8x5RePjzBmYEjdNquyEdKyZd/nIm1ygVVxIqgZFiJVmHW+JYVM2b6NNRFP9vVbH5TX113mbIHIy8T+PDjfRjeMsREH0NUEIt1C9O7OE/GJ8JL0PIybsTku9KQKHXdxySLXI8Y8ayqpZiHyPZafOQ0AgklMyCxzulJh3tuAuan0O4e+JRDFsdNlrgsvCbr3pACmu2lzni8Qff+O3fjTL9yCH9+RupilLnOaFlytG9JCpPxUt22YyhwXguNeh8c1r2dd5rygnsb9WIi4YOdbuSiXubq2Jv3szvuSMXDrffvwLO/zqIfzuPluUWqhZmV+5H4ND7Q9THMxx3z/Tq0kg0YMZlmIIrQKLEQckeUyJ+5HEgNbGEMknm+UFHsvE4jE5+/Zt4TpuofAUzFfXLZJrm+WMBrUtXWjIMtjIX4dtWlHllo5nnWFk4vuBb9t/L0Y19zFmQsKs/ZS6oTpv9nzYS1rIZpmLeHOyxjwqLeLEiYkEK1THJub847enAgNykKkFssJtN3HJ387XlM4OmNBw1A0ex6zddrIinXUT94nm2O5F3gBrjxlO3bHmpuC5fbxqwNdLKKGs9ktyWsBi5L4qAjKfUEtwBVn9TOfDjAvTR0K4E4t8F7XbkcbjxIWIodQVPcYPGkhsrWorXYqPORpWLvwS4uG6mS0N2Vpt5VAJDeJnZijFQeYYqZgkzmL1udu2c/w+n8V6ZEzFqKCLHMxUpe5Z110HD7zyquSz9y8IGsOIAK3tPO/2pe2TX1fPeXsyx55Ak4/Qot5C6ZSASQnhujueCsCjxkWyrLvIb8MAOlW03ZbiOZ7sRBVjJNQlph7401oszq21MUY/x+cDjzl78T5pSY5dvrd55/bC6ykJ4gQSCvdQpDe16VWG3HUSepH1dFNbpOPELc9IBZbFbh9yIRUzHhiA7djiyZcOViqb0GNZTfOlSxEfjaGKG4vIIpZEm82E8SJm9KHulfiv+qPzJynA19aiHrz29/MDsjf8hUJALDn8MvT9hUIRPWaZxx7LLsb0fwD6HSUskBuIsM2OrGv+eKnGeBsZRJnPC2eKdktY4g2xPvRnUy9AnSB6AFswG1R6k4nLPtlLnPp+3v352j5C85hl2QodZmTJiKPMdSDAgE6mMQk2uCIEkEGAA56mw0LUaSEF5Xm/fCzkvtpW4i4XSbCSLtdYCFqd3Dohgm0W2nNIGVN5TxVHiVzx6Fnip/S2njoxvR8ap3cvmHKaSFyafSDWkEMEWM9e1coC5G+Jt1x7y58/DsivonddgPeGnwQFzTfkdzLAF1D+TBVD/BAy8dkLObWVsc9Dl/feZ5R2DSKhIWonmMh4nZKfLm/SS0mDmWxOoevUmBXS7s9Jy1E9+5bwnTdh79RKOt2x8I9PZAWIl6Qdjs/K2kJXg2Tdcex8twbUCwQ+Zf/rvH3EpvIzCOd2EsUgJnix0BPlkW9MCt4WkIGQJpAS2MSS+na/rAXiwQ2++/OL348ZpBANFCyMUTbZuuYSFzmZFpHuaGctASibNHOAkGmlw7Gijd1R2yewuSkY5PIuPCVVnAfh8zVsRdZv23FwQ5D15tMsiK9qvNCeFe9NXHVUy4riRavbOFWPO7/Ar+/22j9nVEqEOkWia8+OAN0ljC/xyx8CAB1H8JCFGdd5l7+kTRF9n7PvTmcQDsRbKtQt59xyWTtS42lEvC68NCCjymUCDZan7t7qYaFSBw/g0Xzc47n7yUCUbrIH7d9A44+JJ3w7mHiXh/HfpUJMj/YTvuiiivRkyoYWsGTHwO8/EdpEoOcGKI2AgRegaY793VxrRO3TZvuitrmthcLkTl0iixE4v5f2vpTfPrRX0MgNwx7leWSe0lGRsNlLknEkn/uySmzvRwxgvZeAMBXDn1O8vr+hUUgDBNLTw0dzUIkgpovb2zDcVukO6W0EE3IWDDfoaU2vuPGdNOtP98qMUTKFezWe/agLbNVhu15hOCJJnnSRyIQnXbuJbj4jJMy51ECkW1BKGMDUxYie2NlniMOtHtQEHxc97kh2NZYiGf++PmIZAreIG4D++9Bt70EFtS17GxeMudlLUQ8o5VeaIcIW/OYRAvRlGYh0vprKw7MJCbWpt+JNl8sLbo3YUVWpjgTw1JmIZLn5CIhRS5JUoUw2cADwEKwCVMTqdIilK7ZOOka4C37gG0nJRtZzxKIDPcdxgw/IEPhUjMFohqP8byLjzHiMJOYF88DZg4BHv5G4Gn/IN484nzxU7qFHr45XSfVpnXz7JTbNdUlELE4IyAn7UaxBc+Fcg3T+90UWrh5l1gjDuwTVkyvtS9p76QXGZlKpwKO+biOuprf5rNKx5e0X4rvxieiXk/76EK7g3Y3SqwxSZuUNcYWiI58GADgQS48YbIKSu1vlbCkq7LDVbMQ3b1vETN1H+ySV+OV7Rfi36ILAMhyJrGX6f9MG3OsoDByIX4dMxOO588YQhak81QeluIu8iaSeFJFB35usoteeXCDSEV/88x58txaf1Q1JzWm0DKtU9NbhSKw3VsSnFFBAtEgccQQAemgt4uvTbBidyYx4eU8oioVjPV2FaTdBgA/yGotGPdM8zP3ccjsBPbG+QLRvlaMDhfnWojr+Jz3cLCpTZmkCkrT1quWK9QEwdtjfYOW3vP7sBnoLmLv7mzg9YTP4IVLWEIt4zJ3565UU/ogcwtEM1jExFR161zWQlQ85NQipyx2ETi6LHD4Fudrug/E6aKbOc7x/FVhO2EhkpO+NaH+8KCY/N5Tey+e4pmZb3TBUrkIGgKRz5Fku9l8rJgkEwuRuw4RIOIN8ha33L2AXBzPPGLWdCXQvo/TwpcTpB5X3PQprWMbAWamp+FLbeXeSBOIEguRHkOkj0vz/Ad2XgZsPjaT/pUjgt/aAwTT2LfpFFzW+mMAwP6FFlgsLLSALHQqb5TayM1NBNg2Ke7pY1qfwTO8/8QElwuqpSG38bVELm0tAUNUQSBSQuD+hcVEYPPDJdG/5dg9wnswcd0668jNotaPRch8cBYjQIiwrCaZxiblMmfPp5YWONLvQcGmQtSzMd/f0r4Lse569scngYVtTExMJgJRUpg65o4YIs9Zd6ZzQGxUwyndQpT24RZqZhIT23rj/ALpfch4KqiPFMWwojcLkZq1OUuzzDmpTWGStcAR4+EnpzF5rdpGI8FAJqmEV4PvcJmLwM31mHFwY33WLUSmUDJbZzjt8A3GPOLrMUSMAZe9Bth6vHhzg1nrTLcwqHXgtJ2b0HIlLwmyyggetQ2PCAPLe6MKtcRCpLnMxUcl66CyYkVgidJrQ80sFlv3GRbiuhBY0U0toRrqfJP19HvuX2ghilMPCEVuDNHDXgK88Cv4kXey/L75LnNqHN6354B8r3iN3TApFYAxMF3zAb+GT0aXJu32WIwIPCuC6emqi2L4ivDrmKq5n2nk1UotRLZA5E3OZlzmOvBw2+7eY5Fc7N10Kk5a+hv8bO5iAFaypLpDIGItQ3CEmrPmH8h8dhwhgWigZC1EQGoRWpAWImXSz1iI7EFf5Cc8U1KnJdMupv3uwKHxYIyZFiIvwPa5uiEQ2Yv6nXvbCOVivYgapmqaOxaASG7u1AJR6tphoVwvANNlrqMF8T8gTd+Le6xipgDqHsDDJbRQy1jkdDecu2N3jNYMW8QRh26v3N5MlrmKacbVotkFR8jrzsBuA63vHEAqENnaI2eWOV+lBE5d5uzN3l1xuhk7nd9mvKcLDUkKZ23irPlcE+CVD5cSiLq5AlHNZ0aWQ/N7FL++c+OEWeel3xiiipu+LTPp8XMTATyprd4dyo0OSwWiSI+5MeQt8zvtP/mpwEu/l5lPOGL4S3uAqc2YrvnJQr7/4EEwxInLXI2lLnN1aQWanfCN5CGP925EXQlEtWKBCJMbk1/bTJsvKmgjj9suxmQNnWQeBMTmSQnP72q/LY3H4J7zvBEPwBDBY2FSLb4KO5gsXmjPN9Z4NCxEjuvff9yTcLAmxoLtKriXbQSzFFU1dMGDevqYeRrAHVjuxsK9K9uvY7mZiKa1lMW6hQiB4fIsztGDQJRJ7qNOVHAOuw5RmYVIztucsUx/NggmccJGYJp3sElzkfNqZoKBjNupX09dnXSBiFkWIjBznBl1kMS88DfdR+Hr0cmYrXE85PANTguR5+XMP0/9OPCsfxG/69lm5XH1WpAtCA64x153KWNRSZtdIZOgfQk/dZm7KT4S17T+EH/cfSJOO0KsdY89VfSvCAwTnmhvjZkxRDWexhpOYknW9jJJkhNoLo97F8QGPWMhUi6ItkDEGLDjNO21or4o+4JKHV8xhggAZibSfqQrSLvgmeleF8iZX8us5Z24wtru1TFdz0lVzmtJ8pdcrPlhw9wGbLb0e234+NMvigLarufTC4wBS1psqSkQabFQ8hlMogWmK9dVrPuCO9Zs3CCBaJCoEZSzQVBJFZR1JBsMZ7tBFTyeh78ee3ixz7/ertKsQ5r2MTmMexlNzEzdxx7kC0RdeKKSNcTE2VWVlpmyEJmpbJdjIXr2tZcZ11XsjsVAbe+9O3O8EoiWUMukgtaz6dzecgQ+QliIHnHuqfid9m8737exY6yqBjSqLG0hPMzNZLWHGQ2wtvgeiCdNt4zDz0mPc1wrDTKOcy1ERRnIzj92KxYvezOAtE8/7pyjk/cDrglE6vsnLnNRplVfDs8Qx3kcLG9DUJJUYcdskIwz+/voG/KEPJc5449qfVVfcPdEmoDpiCEq0rInGmbrWXBE4K09wOQmTNU8hHIh/tS3xCKoijwGYlkHAMzV5M/JANDqZtwUHYm6SlNc5hevuUjoCSSiCkK+SpkcoItu7KVuc+CmpVbVSGHcmQ0p4oGswxQWFye1OIXfIX/LHzcAzPoZjusfct1bMPP6X8hjzfeb0aGZYqsnb2bYMDOdsRBF4BnrcTuC00WKLcmEDNO6y5xuIQrwe9eenn6e8fJkNZUsRAWHMwajyHPFtNvlAtEUpvf/QmSy1M454XMznsZeY72ajG+MjE2gy2XOVMLpApEQsH2E6MQeJnyRFElPQmBYiFw0Hg0ce7k8dXrdIzeI9i6G2Rpt6ntn6LZQy9P7sN7rECUWItbB8Ts2Idh5Jrrwcax0jb742I0AhIJr2hP9OICZZc5jAJNjZAot54ZbjedAixXbOy8EIttCpBACUbZfJErLjKtr1kIUVFSyzukCkSacxCK1Q/Id7PvradY6znjGWuMUdG38Wr5AVGAh+tsNLwae94XM66w2ncn024FvZvgbIKrvhrUNwJbj03sg56MptMADy2UOABbIQrQOcbvMKdK026JqdiZA2Wkhypn0gkn81+xj3e852yVjePKWuSd/EDj/hcZLMeOmlpD7YIwZGd3sLGohPMRyQCzEdexd6BjXDRMLkdIE9ygQafuNcxvHJr/rLnMHZArucL9WgE611+Ng3SUsxUEmhki3puTVZAlYiEc9ZAei47MB3y5sobeqVi+pzeL5qNezFo1M+nRmfn+jDs6mY7AveWbZ+x3JBYXFsWYhslyJCqaKx5y5E5MPfxV+GRydaFPPOy61onHOUp8Z9f2VRdLOMnfl/8YLOy8HABlDlLsjcL8u271tJjBTM2ub10yNIKAgqYJx0cJ3N8oq7NP19N7tUQVmDZc5TSAyNpWWO4lyLbLmE44IfFFYiBhLszmpvrZ548bkb5UAY07KDraFaDdmRb/ngVMA2OVplmhNIOK1tE+2q2hG5f2fQAch0ox80xM1c4Oo6ogx7lQsxVzFEIUVn5lFXtptdf4ylzntNVtD3I68jCV3u3cAXlBHMgC4UnRkXeY6IZxB9LOhcOWNp9MxpbuMLcU1M6aB91aHKE8gKhJyGLeyzFUWiJCfKAUwyTsU0wAAYaBJREFU3dZ2NdM2Bl6pQASITXGxyxzLV0LIc9TQRQSOCS7arGLtAKswaxna96wfEAL5lQ85DIducijb9O+tvlu3hSD3MumabgS6F1DTkipwv4ZOV9ynOVW0Ws4Lx22bwVxN1o1C16jrhDgCr4sxMsXcAtEzLjgGTzv/SJx+ZOplsa9UIIrcfSh5rchlzoyNKuv7EwFPYnX1uRpIU4W71jvDQuR5mXo+SiBq1zbhq0f8lvviwRSmc1zmYl7DxpwsczdNnQ0cIeJ4cMrj0jgdr5bUTUraEXvVhLMeULc7BEcn9vCL5/1EuIqqeUgqFCdZy3QtTCxEDw60PSsFCUQrQc5kqZIqvCN4P57hZaV9V+Bg0eDOr2Jtn4Zp80rO5LlhJ/Dw1xsvcdvfWk7Ui7XUMpVZ1OGByU2FnrZZbUQiq9hh7oY3B91lTjfZ6puqpVhMVI2b3585vu5DCESOOkRv/bUTneezmQg8vPfp51Vqr60FdtWBcqE2jLVa4HRnzGzOtfv49696Al726FRjDO6nE7zjfqeJHmIgsFzmnvVp/MuZ788WVjWuLfrIjg2TqEuLWGDHf8SmpTARvGyXucPOSkz0ged2IQLKLUTbZ3wjGFjfQD3iIYfbRxW4zFXXgr/hGuHvfshcqr1PUlnrGzhjg5ZzLSBNh+5wmWOLu4HJzVjqhMmzVcKoshDV0U1qRc1KC9HsRGCklw/QFYKaV8sIGB1vGv+8+XnpC5pAtGVjmnCjkquIfN6TrIUQHFNTQlDk3DOTbtzyH+Knw0IUxgxgnsiyhzD3mf3wpJebAsPc0cnvmfFn9y/DZc4hOOuvyWf6k/ho/GL6rIx7EQBgfhfg1ZONY5GFaGoicAoLSSreyc3pi5aFiGvuSYx55daDKhaigrmZlWQutUmTKpRYiPSA7Mt+L21jwI2SCxmByFeZFTvGMwhhCtbCepajhFBCFesiBIfatx63uZbJjsqrrL2OZzA3OYEnPvSY7Gd1gUiNs24LuVnotTW9qlNUXQpEdXTAvQBbZ8U9m56UY0XOC41DNyRWBx9dq+ZXDE/WCJpEK9vfARy2eQZ/eP1pSWwqkLrM1TxXn4mzMUTJO2rdst/JCkRBRYGIMZbUIrKtNep6LgsL1/oRZyydn+YOR/zsf0uEkJ9c9KfYO3OC++K1GUzVfPxZ9/F4Sful5rW9GuaYIyc7hLCU8OQPAq//FfCGe2XfNnsAD+qYnSq2nn/x1D/Cd676p8LPuOhA7CWShBNqbyLH7bZ61/Q0UBYiiiFah+QkVVDMa8Hcv+n9m+N4O+AXKFp08qpYO06sCVsFi5jtgsIt1ws5AXzptVdi94t+DCC74Q/BwaQGSfc9TZMqSC1c4krWv8ucXin5+B0bk9+VdacWZv1x6x4D6y6hhSCjBTpxq6b1tgSibmBp9SqkGgZg+J8DyO0bNmpCrtdq1VJ8slTgOWzrZmycM/17ixZNtUlj0C1E8vsfexn27zg/W7PJce1A649BYE/IsdnOpDBrlCsU1AqSKuR2G/ldtk0HZq0azweufTdw3BXuDEGV3K+K++qTzj0Ct//RtZip+7jtvLfgB9Gx6THa9zLiHwwLqeUypxZcq69de9p24ZM9tRmtTpgsxFNcjKkN8tnrQc8zgXSZm/CFEHrmM7DAp8X4jbri/lgCwHfO+t/o1DW3XN1CFPRoIZL3fBJCIEqeAfdweE3Tiv7w4/JWsEx7QnCAcTzG+zpO5neawbsa3fomMC25gZ49j9njz55zS1zmjGfhpYlPuF+TNVuskdbaD3i19MnK603UApx5mOkmdcL2OeemUFn+eC2dB2yXOa716UxKbBd6UVmW3dSK85TFEFXfPugxRJlnoKOKnF71B8DOc/DhU9+Ph7fejYnASjiRYyGqoYtjt5gxapksc3lJFbRzhOCoSQtRPW4ndYKUF0Gl2FfX9+ReOq51dEF8YqP42V1yChz9ogri1tABPB/vftIZeOtjH4LtG+W1laKE8eR3H11TsRRH8CfEunsuv9nZviRphnbf9y/kW4hERcDYeU9TZV1WWZzAzURNyIvv0lCxQzMyxvmqU4T1Vbn/utY7vSYU5166hu08F+yYS5J5mHM/icvNUJ9Fzef4k+4T8RmZ1U4RFSWJsdcs7gkh2mHF3rllA048tDic4oonvgjnXHhl4WeAbDLjbuwhBIen1i11fTkX19r7zJIwtRlxn8hCtA5Rgzdns7xzR+p+MukIZLUtRKzk8fhF9RyME1XU5tkuKDkWoi0zdWyelQuElYK5Cx+e3FTs2LIZf3j9aQDSiS3mHmLwvl3moijGw5b+HN+4/kbD7/r1v5ZaRBZz3N0AYIKHYHHoTLutuxLpSRqAdHPwoIxPqirY9BtDpFwAt83Wna5Bmc3KzHbgghcDLxGpw6emdNcfL98XG8ARW8QEdvrhc84YoieevROvetTJ+Y1l2XMHNWuzmokhynGZ034PfAYvN8tczn2UY6/uIWshOu/5wDM/ZdaTUOSlUe0hk5bO7lOfg8e232ZeX2K6zOnnty1Eso9ZfW02ALC0D5jagmtPPyxZvI/bLOaDDTMz6MQeLvN+ADa/CwBw8a6P4mr+DaEZDcWGaKI+gZMPmcDOOSkM2ZXZ/SBJJy5e0IRsbUPejir0ac3HPISXHs88/HDqAnwyvNj8PPMy7Ym5j6l6Ouc5nyPkZjVKx52vC+eZfZV5b1mtxGVO38wm1h4G5tdRQwe+K/mJX0tc6dS4DXwfG2rmZ4UbmnkvGaIkfbynfQ+mtaOFIKnFIs5TQVipMA8Vxnf2atmv6jIn+yvmRIa5vVvOxm3xoeCMWS5z1jlkX3ie/1kcvvfbyctxjMz8YswdDpe5QLrM8X2/BG79snBJkmuNmlPy5iUD1/dknnM+N5IqKMVD2EY7p84PEzcSQIEbvH2JQAkOEcADbJut41kPOzqtFyQLJQuBSBYYjk0XRMRxIhD9r+CDTutiEjukff99i8pClL0n01xa9Vx9KsdlzvjTiiEqLUoM4CGHSiu69El83zPOwc1vu1ok4UCOy5wmEDHO0zVDCgCJQOT7SZmBDJoS16Ywa2aee7BRFkXedy8wranLIPF0lzdc9AaWuBymLvCa0vbil6e/MyZiHxf3DKQ9Kw0JRAOl2EL0zqddmPxu16cRx9l+stnXdGYnq2i1RbsquRlzjv0nPE77M7UQRbHl6pBTXLAbc0DGFxx96DY87fwjAeg1lhgi7ieLfOHi6KAbxbgHW8DmdjoXMwC4/mR3QgQASYFT4TJndX/NleiIbRvMOCLGcHXr7Xh06x3i74rtfqL33+YLFTfVqm2Xn7A5xzXI4frz6LcnKWCnp7WJl/vJoum6+ozcZG6frTtjiCZrHi48viCroWadUuQKRKoFysJwxRvzBaJCC1Gxyxx+9q9JZjUAhrVBdy9KyLUQ5VtwirALEOr3U6/bw3K+O5CmQ89szBd2A4iByc1o7JjFj996DQDgiuPFIr95dhLMr+FsblYIf0fwfhFQHHUAHoD7dVxw1By8uOt0mfODINlEATA3bdoC2KmyjMhzT7K2tBCl/aw2OYNXdl5sfp7xjIWoHtQwraXy5RkrpDrWGpuGRj7/uQCoYCHSXNO05+IF9UwRy/TNeqL3SRQZ2qZTO2GmD0z7aZymLhDp7W7FNfNe9Jh2O/8jxVbhXoL6E5c5xnJdygGkrjUygYRKUdyNYvgeE+sLkGshepH/r+bLCE2XOdhzSnYNmfRCoWRY2gt86LHAgbuTvp9kmasy/7vuMefu+laBQyCqzeCk7e7aYAy9J1Wo62PZsFLL79KRNeviOEl/78s+3WZyvMYRFjcenxyaFDy+7s/Tr6Kuo42VPfOirwcOl7nDvT3wmNtlzqVsy/ydCESizXGF+JkLjxexLQ8cFO3yOEPN58nc3HVZiLTnZliI5JzRlZZyzwvysxDW8vcmYUEhaDteKW2I9hzVPsEL3FbIZaBud0emLuG2QKRnlttxmnnw1e8Ezn3uQNuzUpBANEhKav3MzG5MfrdTbuecsHADnQRDlp6GQ038ZTEsey54nXGc2rBlJgg1CVmJIV7yyJOwdaM012qTvJq8GWOIedB/ljm5siYbzuv+HHjBl4zNy+WPfgK63H1vzmmKmi0ulzldq/yU84/D73qvxq2yAjyDqNmwCxvlF+pz6FS0LKmF30dU0Z3LZHraTB+cWMOKFp04ys0yV7iJcSxatdwYIs2K+pZ9ot5EjpXE5yxTLTz5WEkMEf7zzajHWrCp7v/tsgZVKbTXwwZkwo6Gdm1AYFn6bAuRss7Y92BRpjBVGyeexgaov32HsNDhdRyzdVpkmfNkEoWwk1iMbAGkFviWQKT1KU1Ib0fVY4gA6Y6i7jfzROY7G1eWOcvykScQZeLOjHtvvWePR02Dy5wCkWbpkxskjjgRiJzp8b0gyTJn9P+uSyAy+9imCRFr1IVvZKDTBeklBMaGqVJK5ioCUZGBqKrXgeSwjeL5z036hiCZ4aKXiXt8qMg0OS1dmqIoTt10gOw5cjaMfty1FHmWoKd/Sdm/H3biTjzilLQGEoBkLQuSGKIqFiLH9wy77tg0XSAKpoBr3gU897NwhtxAPf9eBSLtunrfTixE0nVVK6LpxR14CNHhaVZQf2oTXtR+GQBgC9uPfWwOOPtZyTG1xGUu/f679i/K97L37VSZAbKXNOLG/G/HEFXwOnnyuUfg+Rcfg9+4yIznUp4skUOo8gyXOU1hI/tNR7cQ5cWYybjnT//2RbjxtQ833grqBWUP8mJc9T6mxoBXAy+q9dUDtstcCOkyZ1vu1Pyu3D11Tv414LCzBtKelYYEooGiohxzIja0TUGmPgyQLprqb16sBdowXVUg0qeP4slCN7Uy5qWbC3sSz9moPvPC41O3E02jHGvCYsSDxGWuVy2Xcr1Qpm6c/Szg8LONiWHDtp3A6+5yHn/UvSJo+4F4Q9ZlTtfYegG+ys7G9e23inbaJ+qx3elx1YZcEtQZdZ2TYdl9m560Nd0V3F/iKA1qthfzIkFO13pLgprVN+2kCq7rW78zltYhymRSyo0hKr+/Xi8xRAUCSxEZ1xDt/uWn3baalBNDhKX94qfavGtZqZK/HX1my4ZZUS8pbIvPeDXxu7QYZVzmghrqgXbtDUekv+suc1XMz9o9D8HT+815kgb3r077aPp5h4UI3DeeB8t7Zvb9cli28z7LDZc5l0Ck9U+VnRExeFBHjQmHktg+zq+n9nGXhUg9P0f/2jgp3ItDHqRaWWjulJA1yzzdcuWVT0+VXObyP8OY19Mc+OZfewje89SzcM5Rm4u9AhqPBt78YCLsT0oLURjFCDhP18icpAo2HiJz7mJWsXF90B11IfCINyN47J+awgOQcZmrlGXOnjMf8fvAthPdlkc9qQJjwENfAGw5Lr8Au5Y+vKrLXK6FSLWzLV3mlHvT5CYEURseoqTYOhCj5nPsgdjYb8W+zPUTC5GWiVXFGmUEIq+GhzBZ167IZa6XtNsVlI4TgYc3/top2LHBXKeUhcjlMmdaiDgwIRPLyDVTrdm+V+4yd/rOjThisykAzU27rYFAjlcDYPYxNSevoIWoCyuGKHGZk+NPZZVbpZBANEiSQZojEJUUMLSnNTHR5D+ijdOOApN5Z04sNMWfNAYe54mvdFCzBljepMP9dHLXN4HJ9+CIeSBM5OhdIEotRLZbTKpxBkriq07/dXw2Ot8hEGkJELwa/vIZ5+CKk4SFqJIFoQJxxUK0iUUudmfTKrP0cd2Ezb3UZbJQIMmvQ1ToIqje0607gW0hUhryMoHIfJ9LFamRsVC8U9yWAjyXZSG38nifLnMZC5G5KUt+LbIQ5cQQYWmf+KmCV9Vx3SV5YM48o4TdqCMtRFIgCrW/NWq1AHVd07jxqPR32b+iWHNjKsK2EHm6hUhc4+DscennmcO1yHYpy3lmGauicT/sjZXZdj1RAyvzw+ephYj7ddTQhccc21OvDmbPd1qh3kQ4dAlEE56wELFa6rcPGNk5WzCfHeOs3BW5inBfqEPpzbY/WfNw3RmHAXA8nwLUdw7jGJ7HknUj6zLn7gs+s1zmiixEjAGXvEpkxsq4UloWokouc9YduuDF7rYDlkCkte+4hwNHPgw4/dftk/doHwLqNd2a4LIQSZe5xb3i5+xh8KOWFIiUhUgIRKrW3xa2PyM8qOQNOOI84IVfla0Vz+3CvzvO+CwOORmnQAhELhfNVCi3wwmyApGK1+212LsBz/GIAeAHlkB07vPEH91FeYx0mfN9o2aRQS1f6CnaY3h5Ao7hMpdaiKon3OqNDjzEYJpApCxEsv+qrHKrFBKIBkqJhajHgVqWVKEstWJ6ojTLXJk2KWMWlpMzc2lrXegCkdEG5VZlZ9nq7Z4kFqKMpkm2T98kPfFvgGd+Cjj/ReZnDz8bAHPEEGkWIsZw7tGb8SfPvhS49LVgz3ZkBeyDqm4BqYXIXW+ldDn0/DQdMveRLigFx8VRbh2iYgsRN38C2TbbLnPG8QVCQdIOhoWTnqB9rMRlLkM6Jp3atlyBKKedJRTGEBmB+fr5zWM81U57rCmBqD6XtkvfYHPPFO4Vfl1k9YsjGTPkay5zQdZlzg+sTVTWPaMDD1HOdGd+mfT+htASJnAvsRBN6PU5uOew0LBKAlHmORna8AJB9S37DM2u02VOv0ziMhdh28YZbKjFqHswkrMAEBrbpGmybZynz0hdx9F3N9RTC5Fn1IRLPyvup5nsofftcpZC16MeLUTmeasLRMoqFsexIRDCtsDmPCsfobnGFCVVMBppnT+TVKHCd7e/p1JSudz78vpofRb4jX8Hrnmn2TyGpO2VLUS6ckMfW2ocqXlFZQSbOwxe3EHAumgrC1Eco+Zx7ImFMmYjm8/W89PnV/ldRDFlR4KI2UOxUcUhOZ5FviJPXzMsl7l+3dmRWohcSh4jy5znAac9EXj8+4ELRfrsxGXOC5wFlkUjC9ziClzjgzwXTSPrpVJmBunasUxiS7nfjX3TZc5+LmQhIhLKLEQuJjclv9opWx0u5Qa9pN2utCEGrIGk+SlXjSkxFub0WklQP+NJLSLRmv4sRBnTu2qfvtic+njguCuAq/8Inz82rWmBGZli0+7+SsOuwxhwxRuAQ07qqZ0Gz/yUdr6qFqKsy5xdCLKMJEjTqEPkstBognw/FiJXalR7M1soELld5gDTNWXf1e/VD8ppS047Nd9mp4UoZzEyLZjV+2pu/wQApt/b/PMnwqB970PpGlc3E2ckGl7uuwWiYDLdrCuXuVs+D9z8ObfLXC0w3Wx0kvS0XjImC9GElzDW3OG0GKIJXauq1/nQXzOE7rwscwUWIrv/Zaxy+vlLLPr6PCYtRMzl4uSnFiLDvVQ9x8Ra5rIQMdRYFyGvwTfc9XIs5JAa8tJ5pvyZFc3NjDH3XFKFHgQitfEKy2KILOFYrTceQpgWWV5tw2yvb3JsKVf3ShaiWk5GMZfwprfJde6JDbjjaf+dfpzxntdOI/OY/ruKRZy/X/xckIkt5oRFbxpL6LA0hmjTdIC9SJMD2AKRUaNJE4im4FhfvSCJfXQ9F1Zl36LSbqOHlOi55xJtLyvMytXm7PQnA1ObAaRrtu97/QlEBRYiVzIK0RCHhWhmW76LXY/Yuv2OdJlLb7FsV0u6cZNARGSwe9ElrwaOudT92ev+Ap8/7CXyj6xZuNA1St/8/eYN8rUcDXyRy5SGUXyMa1rAkgDjwtf069qxAT0uql25+fJtDZ1qX05w7dlHaQN1VrjBZVzmOtqE7bDyXXT8Frzx2oL003nok2DlOkTyOYad5DvFPd63iXpaU6goy5zhMnfURcAZTwO2npjzmYLjyxb1vBZYAtFJO9LFVheIPO0757pa2td95FuAl/0AmNmWvOR0p8zb/BrySg8Cka3RM9LXV3OZSywUeWNK33Bxz4whsq0UgNg06lYJfaw4XeZqmAis+3n9XwEnX5d8hy68xGpbiC4QgafjVbcQBdZGKvO9bYHIfV+yAlFBDJE1Hg0LUUHWJ3He1EKUVIyPsrGhRh2iRDGhWfEKBKINE8JCFLHAqFCQKWhtJFXgFeShCgLRALPM6VQqairZJouHHrdtxpjziwRCAIill4JvZZkDy0/UYmDfQLnhu4j/GEDF73DOc4Ar3ph93dWvCpRCycu2ZatHC5E5P2ttULEwKuW5Yk4UsJ7CUuoyhxjXnXE4XnPNqUltvtjeRrLseAt4jBksZtvk1dKMu661MSfLnOkypyxESiDq3zqqlI4ulzm9z7mef+oyV8tPqtCnhcjPFYi067RkMoytjRVwmZOKCXBEMU+VM+r5kEBEZMizED3iTcCz/9V9jBcknYplMhRpFhoX+mBI6nq4HqluISrG17UUXNMC5tVUAMyBnLNI6hWn9Y19r+bt119zMhgDZqwK00mGuBw3mm2zmhuftBBliq919Qk7u2H48PMvwPMvOban9mbaVOH7vvCy4zCnEmZEWuXnHOtbLtqmM1k0nccpC1EEzG4Hrn9f1u2xioVI/fRq2esUWYisLHP//JKL8IM3XyVOpWvFDYGopC0KfxLYdLT5EdlfK8W+5LWzBN8WiAw3UT2moWAjpMZXXp+xLUShJhDZKZ0BcS8SC1GQcbNyZZkL7GxFZzwFeMrfJW3rglezEHE/+R71Wi29B4wnMUSTNeteuCxE+rjMCTjnnIt6XIc8JPmu3TwLqdWv9XS5zgK+enO0LHPwaiLeL0cQzcRMcj2GqMhlzkMdXUS8ZvZ/Y1zAmGN4JStIFS+GAgvRALTwVTjjiI348PPPx2sffZLlMmj1S61oMIBk4+kjshQQHJVq32Xi9sSGbwcTCQe8KuuWFwCXvsbxumOzWiF5i73J7lkgNcpU6ALRRvFTrxXDeKJEqrHQSLvtcYbfvPQ4xJPCMpJRLDrmtLm6h2nmshDVUIulhcjVp1jml+zfmTpEvXlSGBRYiPQ+4RKqVdpt3yuyEBXEfVdx27bRx8HeO8TPrSfCH5jLnCBNquCbFiL1xrnPA466OI2TW6WQQDRQNNejqnA/Mc+7sswVbqANgchMKmCeSHdvKHGZ07TnhuuFM+OSvJZvZxRLy3klL6mkDuBmlq0eF9anPvRI3Pb2a7MbzmlZJ+fhr3cfqC8GUiDK3Isb353+3sszLEO7P3GFhfT3rj4Jr3203MxpqbCjyVT7UmkpVPdZjyEqSmpQ9J0LY4jUxl1t9tK+cvaRG8UvarIPHJkRrc3AROBhw5Q4h1p4Yph++7mbgZIsYgCSzcA8qmRpLNfcVkLr5/lZ5nLanvddbQuR7jLnEha4J9L+AlmLUGc+s1ET2ZLyfNfF61341SxEjCXj4JxjtqbX1i1EhstcTgyRboFxWWMAkWVq24nASdfKaxS4jNqFWQ0LUYnLnJdmmcstnAgYFqLUu5SnLroFFqK5OhMWIks4NNoJmEqpkuykVSlOu13R9cxBL0kVAOCi47ei5nPDZTAjVFiaaZZYiLqWxYJV2zCrNm47WawtF/6O9fYy5oK8vuKytBtv631TtxBVxLAQafdPxSLqTG4yrBkdJvufNq9EUpDKKBa5eb8B4PxjNmE6x2WuOONs3rjNF4iWJawnrsCOc+gWIsc1Upe5IN9CUyuyEKk5MXtsrs5Jv9fq2Ww9YWAxRDYdWZg1jSGS92HucOC5nxEK1VXMyqSiWK/0E0PkBYULS3G1cIcrSG7QekWBKJMNS21yC9zjggmgtS99XbqkYcPO5CXDQqS7dwwg+BeAmGjesi//ff2+FE1KCYMUiLTMVVU3EereRt1kooymtgH7blcnKj+HWtA0lzmnDkSPIcptTxULkeleeesfXpM289LXiM+d9az84x3XSQvA2YrdnPuYcSVyuceJ15xawCKWs8k06kXoFlJdICq2XhgE0+b7i3tSDW/eRj7sZGOIFEv7sxs17uVnS5JzT6dqDBEgzt9ZENrLxCriYeemSTAGMwWuy0LE/aRgJACjbpjxsaRUgLJCsXSDY2+GrY2NmVShLIaoRCDivmhjnI6+JCWwKkAKFAtENVGHKLKq2Gc2j8Yc45VvCisIsRm3PP36nPUfQtSjQKTQFSLcFpYtCxEzLESmRZZVEWbUc5rdDrzk68B9P7Xe72HuuOjlwOTG9G+97XOHA/t/lV4zjrJ9VB1mTIDpylmWcTQ9RBco9ZpEvlCuaPWHMLnZUOR1E4Eo7Tc16ZK9ddZSLLGsQHT1qdtx4RmbgU9YbfJqqBW6zLm/G3NZiGSWuV4TNRnIczkFIsNClG1X4jIX+PDz5s0ilzI1hmszoiiwRq7SSZ/rt58K3PdjYMMR8IL78q/TB+rbfiU6Db9iW/F8O+32CmW1GzZr41usZrjmMme9xcCK5ReXb3zORJ1kmSuZO3WXEZFlztzkmg2Un7VNvQ+5XizyjavT62vtW06Wub5ZjnZ/uXi9ucwBAE5+DPCzTwNXvAm4SWS4i6b0lJYVFsGtJwK7fyEEIsaAOG99qSDI91KHyFPWHe1itWngEW/OOT7fCqPcRGIw83xVY4hcwoGKyQKAl34f2HeX+1z2dZYjEBkxRFUtRPJzrsWwnhOwbZ3fQKXYBmRWOe1zrf1Ziwz30yKLmWtITWpc0WUOMN16E+ulh2O3zeCbr3+kiBdhXG4KefZ7bD0BOHh/+neOQMSUu4qe2a+ihUjvYz25zLncXTYfBzzQBJb2gbNIdDh1/QVdIMp3mZutM9RYB5FnVrjnhhsYMwUiXsF6U6VOSVn86hCSKugYcaOZLJi2gCieHWexucYwhip1apLzJ4lp7GN6+O5X/i/zb33z+DvfTYX8nHiZ5Iq2+3Cva2eehQgQAqUhEG0y3LsWuLQiXZ4mJ1IxdhN2TCbPzuccMTZ5LWTwasXJEBLPEmuO0T8qn01tgC5z7dilANbHXH4Mke8FWQ8WQCRXsty3DZRixPa4QYH+Qm/H4/9KWDM5N0MfloN14Y+EjwAAvMD2OCqLt1wlkMvcINkmA+5nejAbekHSqTMuc2WZfIxBqfmmuz6a/CyeyI3AVaa7zDnOm+cyx5ioTuw4hoGZMUSFrRkgvQpER5zf2+fPez5u9o53v+dPpBqnqotYfQZ46keBjUcAHVEwL57epn2gwp1TmfEWHiwOvK3iMtdrDFEvFAgdXFMWVEqqkCdUOF6LwIHNxwDHXFLUuIL3ykmyzWntiA13J+u7G8Kh+pzjueRlsLKuZRB2UiGCWy5zrQOOmB0Px2zNuU5iIfKrpd0GUrde7hkWIiANnk+zzzksRDtOsyxEeS5zpmAOpNbATL+xE1lof5en3RbvCwuR9tlLXwtc9+fAWc8Qfy/tzabd1ikozDpTA2roILYtRNxD9/F/jVe1X4gjN08Zz5JzXt5rtxwHXPMu4PIcF+O8tibvcfS7feB5/bP0OG38l2mkrWKsya+MVQu6t+cyewO8LPdZra8EE2ltmhKlpsfMeUPNHctOqgBkY7Bq04aQ3eJ14YHx0Bdo58iJcXR5rsSRKXApjDhG1/dWAhGzXrXnTU9Lu718S34bvSe+UGm3/SAwUnQnHHdF8bXV/XYIM1HeJKuPpWAyiftyXn8l6HfNH1PIQjRILn2N2FwddWH1Y7ifaEZsgShmJak1rew5xk+bihlpeKbWRYEGwIhRKUHXfhlJFYYlEvWgyShyvSu8RM4i6dfRYnVMxYv9LaTzoi6EIRBVuW1KQL//Z+kBuS6VyK+K7jguZjxNMZwGRogfvW54ChYa5asfg4FXsdZkXKJKLEQryA2vuRzT9dQSkrZJj9Mz3WCMhAiFFqLZ7GvJ+XOEV8NCZLnMhW2Hi1qB65UWfNyzhYj7+Zp3LxDJIRjPjtUdpwHNz6V/5whEabry9P7lu8zlb3TLqr1zI6mCZiGqTQFnPwu4+fPi75ntmsucdT8f95fAbf8N3PVN53M7ZP9PcBBdw81YfEcO//Qn4BHsQrz2qE2WUsGr5pr70BcA3/1Q+vcrfoqf33UPjv/HR7jbaly/xHuhgF6yzOVRtWhu9nde6AqYfk4lDFLj1970L2PdyutXRcpHILV8AtJlUQkLFTFq1pQkpahNp8U2odXFM86XI8i75vM4SmMcdex08RbJtsbeG9nfmnvww8Gl3W65BKKibJUQ8ZRASVKFItT86LAQ5ccQuUsKeEWF6XvATqqQYY25zJGFaJB4PnD0xT0eEzgHF6CEhSKBSDtObZYf8fvF1+thHjctRK7MOJ75swDDZc6IoVj+4lgJNaKLsrws7wKoBzlaEn8izdLTj0AkN8jR7GHa1So8yBMfJUz0F74UUVFSjaRN1S1ETJ+0bU1hzxaiApc5I5BV+1je9y9KuZycVPS/TLpYZ9v63/gctWUaW2eU5SPPZc767roQUGSVKxSIrLF6yuOAEx8t+lFeljn1mg7TFCI2LE12EVZNQKKEBqZbiKxnkGRG5OYie8QFoj8bFiJHRjdoGyLt+1RNqmAKROl7362fZ9YTQyoQMURuTfeJjwKe8QngYb+dbOiSy7/0+8ArfgKc+dS0YzvmhsNveDXqrJvEayTXlsdcc9qh2D5nv1fRCgKYz3x2B5gWYF+krCpV1hVQlqxiIOcwxptlWamUdlsJRCtgISoTiHLObSiENHf6/pIqVLAQaQlwIqdAlHVNzfytC0StA9lz6GuF43unxekd3jPGNf2BJFVghRaiMoGIJ+fw+xEQ1L1wpN/OjyFyeRQAtQG5zJVO7Szzy6qGBKJRw/OTKgh5qKLLnC9N2mc/O+9C6qDKTWO6n3hRHaIKE1BamJVZm74hDaS8eKcBcsSWaXUx8w3PR5uJCaqvzEwPfz1wyavROen69LUqG/XJjaIGzxHnJW0qjCEqtBDZmnzHQuZwVapGfhyN2vjZFqLcDV/GZS4/qUKlxMODsmDq7i7GZs767oY2Wx7jWpV6cZk76VrxvMIO0JXWJ7+eFVxdSQzy+qt8Lvsxne/OYaMX/eUOyxlguszpz+55nxdCoG4VCtvAdX+RbZpnnZsxLe18mYVI72Ppe83g5IzLS24MkX6N4x8JeL42zcn7ufmYNOlMSezIkXMeDtlkZgIr2tRzzqsrmnTB1LIIFvV8oSzrVyAagBKsX5e5IqunTlkM0aBc5ozXS1zmrPThy3KZs8e6nWnOshBddOIhjvamSUvM6zgEh399GXDrl7Pn0NrhtNzlJKrKCkQBaky5zC0/hqgVl1mIsvf8spOkwpL78O3C3FVIXObkT21+jqskVdDun7PW3jLIVX7oAu8agASiUeNpLnOZTl+SPrUorsdCJVPoZQkz0267rpXjhuI+mfjBmGkmH5bLXCIQrZCFiLF0I+aY2NvMYSmoytRm4BFvstxEeh26BYtnP1nmjGKz1kI+QJc5PcmHZ/SVnO9fKYaozyxzy8El6ADmwio3penfBTFEdvryN9xrXuvadwNHXwK8cZeopu7VpMucDGz2auam6Op3Ol3mylwT74k3V7cQJQIRz9e86xnXXIK1biG67HeBs58pignrzbazzMVx/rMucPfRU+tmaq0gdalL6hDlnRPAPiYsepHLQm27nNrX6RwEsxQ5rrS/yel6SXhgbfz18xZZmfQNea8MxGXONa4f9tv6RZy/i1wEVSzDlstcZo1bQZe5PAWpXiNLiy+uLhDp7vB22vLN5t/BlCHkb5h29Nu8GKI817Lbbsiew3CZy1+bsu9Yr9RnMId5cfmBWIgKPGK0dulsnZMKUe71F8OTWIhk/9D2KpVc5rT7HgxaICpzmVtxB/ThQALRqOFB4k6WEYcYL+5mTjc2d89N9Cw9CCCsLIZITRCVNvnp5J1bh2UlGYKFCMdcJn5uODzzlhKI+q3dAQDLcQWIE4HUpYWrMKnZx+kbO1vDPcgYIrsApeP3wnYWxBBVa9uA+mdeTIN9LX2zVBRDZPuZ68+De8B5zwee829pgK5flwKRKgaq3YMr3gic/1sOlzlPe7bWGJfuanfHW6qX7FIfnD00f1OoKxVcc04kNZFP+fs0VvOZnwJekaZFTiwQ2jXCxJ0l3yKUXDf5lSebzdN3bso0JU26YAlEjvnwfRPPw5s6z8GeHZdmv1OZlrV1IONGU2RlYZxb7lUFqHvsOQSigo02417fMsFyNqzJ9V3958r/DTz+/fIDunuYuUHvKYYob41bCQtR3lhTh2nXjFkftaaKLETHXm7+XZux5pQil/l8pULpfdLGTegolJ3GSdk1Gq0P1ucwxxble8tZY1UMkSuNfrHLXGox8xD0I/TbSapOvCp5q1Laba3fDCrLXK5lSqHqP1KWOaIvJjaIGiIKL9AGsDXoUSIw9GQaLoghycFIu11Uh6jC4mAIfYZWaNgxRGKyufG1D8cXXunYnCyHS18jYgO2NjJvdbiKn+h/yJlJBXo7tpIWsReXudogLUT5LnNG1i/bh95FDzFEOzZUqUc1IIFIX6CKNkROjZ9LIHII9snmzSUEBkIY0l3mlPuZ0kS6LER5iTIOCIvUvbGlWS5CpTffeqIm7Fl9LnGZ89xuUXqWPIVfT2ufQesnmoUtKtG+pwdrFiLGk3Od5hCIzKQKxRaiNp/C34VXgXsFMXx5m484ymSeKtr0ibTbFfutVyAQFViIOGdafEdv8AEEYDvXDc5T1y/dtdLIMsfdc0L2AtbPYcYQue+7pydV0D43kBii4x5h/l2bMpUuvaz/xt8l/dDIBOnCLRBlzqvHQC1DiaW8MNwWohJBzwtEuzgXtdZ6Rc2F9VmRjv2x703e2rkpZ63KaVMtGMy+arImzjNVyxmz1/+l8EbYcdpArjdqSCAaNr93J/Db30r/5kG+zytnKHxEPWhCUstQrzFE8hquRczWohWfTbQDpivMwAqzll7edJk7YvMUjj+kIDC99wuI57H5GOfi0WXLF4gKi3hWaZ99juStkg0ZkN1E6K6HdobDAVqIXK5KxrWKzpXXFpUueVg1sABzc6GPpYzLnEPjV8VCBKS1ifKsYraFSAkXSSID6zg9hsh+/vtEMcm74y04eksVwRLAvjvFz22N9Jq2QKQEizhyC47KZc6ej/TkG4mVKb23uXWIbAyXOU0gdIxbVQ2eIyoViJI6hoXjz7oXV7xJu5jlMlcwj1QqzJqcSMVbZWuHlRYM73PqZgPJMpez4VSCo16jysrGWqkwrJ0wYJhZ5vJc5qw6RKzXuOAiC5FfA170NeCws8XfgSUQudb4PIEozyX4pF/LnqPEQpS42tsCkX3/J9IYqH4L/4rLiev1k2VOxEaKz3j99HE9a+uW4wyl129eeqz7mJyajqp+3HvjJ/feDo0nnL0Tr3lUAy97xAnuD0xtFt4IQ8sWvLKsjVx5qw3dFO35aWeKbQsRR2HSgX4sRL10XL24mFNDVN1lTlmIIsAMpBx2YVY79mIlcNwPZSHiUbv/0+qblR53I4lA7DqsUtpt60DDZc5yneh1QSqwEE1ITZdn9ZP8OkR2TIorqYJahMvv4cBcOo3CmTlJFVTabUWO5RiA2+2vNgss7XMXLFVJFfQYIrsgpMstKE9DvukoAMDzr78aR510ZvZ6RWw5Hrj9q+L3jEAkv78rDTiQav4LXDRcG6LcOkQZ0vdFamkmbr+rphr30yP8MoGIGT+tE4mf9r2YS7NK2hbBIisL50zLKllCYiGShUyNcVYUQ9T/2Oi3DpFx/bzvrwTHqAtc//+A7Q+xYoh4bzFEuRaiZcwLuRbi4vXUs1L0V84kaJ8fcK/n2x8CTG8Vv9dmLPfdgnjlzL3JERzOfLr4KQuNA7AEoqIYohILkZ4dcRkCkQpSaLuSKpRkmcPJj9GKT/fRP9T+zz73IadYz14jJ6lC4DMcvfQRTAYeXtJ7SxJ8j+MlDz9+GWdYXZBANAoMU3SgLeCuTCoFA6uXhaWPAcqgbYiKYoiqWD30wOGR1CGSuDTrOpM9uADl4XguHS6uy7uOWgwVMV1UehSIks87npVy8Tv2suondMUQ9VuHyC6ypzE3KTY4ST2f5GNVXebykyosy+2lV3QNf5GFyJlIoKKF6FF/AHzqt9IU/Mb1bZc5zUJUpOlNrH7WfX3k/wJOexLO23lu9lp5XPxK4Ef/KPqOugd5FqKo6352iYWoSCCyvoeeVKHUZc56HgVae8/X024XxxCxRCByXVNZAq17YSjOLJc5L/97MMZ7sBApgUi6/w3BhXkQSRVyhSpfE4jO+HXx++Ke5G1WNfYm4wY8yBiinO9fYiHyrDpEioFkmVMoC3JtyhwLRQrRqkkVXCVGtHZ0HQKRUvzZ72QUgrqFaBl7Ci7nl1ILkeueH/FQ8Q/or38kFiLt3K+8qbjEQo4VL5DzQ+UacQQAEohGg+E+E6QDzd74sBI7QN7EevwjMe9twHTzE443BxlD1HtShQjMqtkxJIGouyR+FglEG48UMUD9cNI16e9OgahutqMPmOHO0p/LnPN+bz8FePUt7o10Hs6kCv3GEBX4ZudlGarsMpcfQ1St7w3KQpT2u/y02yzn3lWMIXrI48Q/F64scypBgRYMbMAKBKJgAuhFGAKAR/6++KeuD+THEIVt9/NRbS5IjOHacEeMi9uYt1HZcKT4memL+S5zKsscs9vjsNyroeu2EOVYaHW31EyWueKkCpW94RN3SekyZ3z/YgtRv0LBICxEPC9GQ30fPYbIqvtVSSCzi04PMstc2dyV5zKnx0KBIXZZVAqvW+LxAaQKk9q0+XpPMUQ5AhH3s99dGzeRSyBK1rwSl7lBWYiKBKIyC5Hx2T7GxnFXiIQzF708fW3u0OJj9HlB+941mfa7GxV4fRAZSCAaBdyeJHL8ZMGKN215LnPP+ATmf/rflkCkYniqY6TddsYQaRupiY3Z4m4aSVKFGMmiFcVseK6nHSmIFBVm9Sd6d/cCRP0nHVcMkXKZW4aFyNys9HZsUhg378AZR52JIlYs7XaOJtbqKLkxFD3EEFWzbA5KINJqSvAchQBj7jFd1UJUhPrO7QX5d10r0pqj2OA++rf6laDugS0EnPp44M6vCeWEC2UhKmqP47kWWohe/HVgZrvjfW3+dQlEvpZUIcd1Jflsbvpg7fMZC5GuODMFQK9gnuLcgyscw/1hlZFPusx5JVpwdVg/Wc4kXj8piS1yLWCqX+XGEFV0mbMFItuishLWZXU7K8xtjPOklEZfFqI8tz1lIQpsgcjR3xIPEev6eQou20J0+eutTJBZ4jwLkf2CtvdYVpY5Ob84kyqUxRAZJ+qjDdNbgVfd1NsxhoVIiyGSFqJBG4g+8aILsetAa7AnHSOG6DNCOGFMKz5pvcXLXOYKtIQ5Gq3Kk2dyjoINke7z/Nrbiq0rWs0EJhffGA7T90qhBJGijeSgUkc6hMdFfyOAHD/pivTsM24eLf4f1O0utBAtJ4Yo6xxReozxehWBqHoM0cAwLEQ5m07Gc/qgnBme/glRWwjoPX28ctlrz8vjq7rM5WnIl0leUoXzng+8/u58gSgqd5lzJeIojCE65OS0DkveZs5xnKeEiAouc9WSKlhbQn2usp53kTDCuFc9vb/tMlcxcYt4q98YohVMqqD6co5AxBirtmFOBG9tjXvzbq0BKzF3qE6S51LHrE/2aiHSPp8Xg5UIRHJ+P/yc/PPZ88acLDfBc8YQ1wSiR78DuPx3jXGzdTarrEwNRD0kVViGsMpj0W+chVnLsszlfXYlySkIHRS41C6Hc47ahEefuqP8g6sUshCNAXmFWUv9nQsGHbcHRD8xRJwDTLbJtVHTgyrLFhmmCX1yMYsxRAtRV2o1igSigk1WT+gL2pyoRv+lbU/HT+85gCOOeCLO6vO0vJcJ2aKfLIOF2HVvgLSPLcdCZGXTysQnqb/yvkalGCIp6A/VQqQlVSjKMuWMm1HaaqQblp4FIrnxaB9I/1bP0P6pt0cxcAtRTgwRY1l3HZ24PKmCq8/ESR2iXmKINIVUgYWIIbbcgB2f5UUxRDkWIv0ZW3EExYVZWfU4CttlzkgLXiAQoX8L0SDSbvNcgUiOf10g0l3NOK8mkNkWIv3c9uuDosRlLmO97NXrw5hnc1xOQ2k1Vn3v5OuAX30HOHBP9rO2Zfl5/wnc/d2Ca/rIJI7Q2nHSoVkPk7SPORJO6dTTY5eVZS5SFiKXQFRNWSDeH5JA5FqHkSbgOPeoTcNpxxqBBKJxQBcWjNdLXOYKNim5C38Pi5gpEBXFEJUP/jTLHE8sRFHflSz6oCMtREVZ5nop2FmEmgwvejlw+esAALE3gT8Ln4C3s/6H3Iql3e4Hf4ViiOzNUm578yxEFQQiQDzrSovWgO6XpwtEeryJZSEqFMqZtmHp02WudVD+XQOuepsQ2Bsy/m3DTuBJfwv843PStiUCyIBHap6FqIwoJ+22xrZZOw24VocIJZslW+lQmFRBWYgqCESsYPwlApH1uv6MtRgJcT538wGhDIuq+syp8SH7pOGKVxpDVO0SNkXuflXJjQNKBCI9hkhzNauadlvFXuRaa1Zg5VJuyBWs34zrDvZ9uMzlubfbhZsveLGYc855TvazdlKFDYdni5JnLERWTGLJuEn2RhllsfU5zUJUODjKkIK0M4aosAH2+6OwEJlt+s9XXIpDNxaECBAZyGVuDOBy0s1UYy5zSyjxI9eJE21S9cnCqMPh2oAwz/xZiKbNMixEQzIRyTTB2H5q/mcGZiGSw6o+kwhgSkO8nKwvxt6534OXc79f/qPE4mW6zFla9OVkmcu85Y4hyk+7XcFlDpACUfm9GFj31BeuvDiNyc3A1JbssXo61sjS4FYlsRAdlBZdD5jcBDz8deY88pDrzeOiCjE7/ZAXQ1RKgcU6OXc2tiGJISpb8WwtfEe5GGYFUMNCxMsEogrXLLQQ2QJRkcscr+4y59kuc9WOE/JQvxai5W87WN7zV7FgF7/cfRzj1b6jnZI+e6byc/SKKnZd4Zr68628puvjPE8gOv+F4qe6j34NuOw1Yq7InC/H1VbHcNPTXOZY1kLkFojkz0wcpfWdtfGxLJdMKRA5LUTG5cfFZS5fMXbC9lnM1Mnm0Qt0t8YAFRuS3SqXucwVCETMFoj6aBfj6ZG9ZJlxnkt+xxiay9DQIoiAhzwe2Hg0cPjZ+Z8ZmECUdbNRe4CoqPhp6Wn7txApl6FeBOIMG49MF21nUoUBuMxVfW85abcB6b4xRAuR7v9vFYpMuP4vxd8//Wfr4Dj9rLIQ2a6FZaiNR+tgb8KUcj0aeAxRjstc5eOLXOYcMURK6dTLRoZxYGYHcPBeZ1FJVY2eM8tCVJB22zn+q8QQWS5zru7fiT0ELARnXvV4wySGSCVVsN2ycmCoOH6yeIOIb8gb18FkNsmNBuOsMGV5guqXZSmyB4lSMuVe03RnjHvV1lSxEJ3/m+JfFZJnUNGtX48hSpJV6F4Z2fMoHxLbQpT57rV0PVpWbUOpAHLGEBkNGxeBqMd1gCiEBKIxgOVoQUQdoP4sRJlq4H2oujnn2sJQEEPUZ9rtuL9m9QdjwM6CAFEAuOx3B3Ux+SO9L76cpAdXF6DXxbBgQ9YLymIQuLLbWO4QldtWtHi4v2fuxrYXC1Glezj4DmoWldTOrwL7bZJnxpYRQ6SyzB3szTVUjf9BuZMm7clJu12VKjFEjWuAUx4LXPlWxDeJiu12nKbjYO1XBvzml4RgUp/JfNKT97TGkclklmmuPK1z/CVlF2wLkTbGJkwLkUtR1oWHAKGIk4mqCkSy3fJ+GgWQCyZnkWWu2iVsvEFM+v1aLKtaiKISC9GKCETTJde0+mavU7l+3lq2P/dMXpY54zO6hUgvQq/mlRKXOdUfrbGR6f9aVrzBWIhK+lepQDSkjY1PLnGDhASicSDPZa5My1foMmcP2N5d5sSY9oDNx4rq8pkPWObv8pMhBgOXm7mhusyV8cKvADtOG8y5HLVblIvLoASiXu9b4jK5jCx34gRKINItRJYvec8WoqL3cgSi3BgiWyDKizUIqi1aK9A9WV7abcULvgjs+1X697aTgNtvFAJTKC02vcYQKe3z4p7ehJttJ4s4goe+oLfrlZG4zPU5HooC81V/rE0BT/6QuIzsFwwlApidWW7usPzPcs1lztisurLMpRby7DWtTaKiIKmCi66Mj+KIq2vJ1X2UPw2ByNH5H9X6IzTYXfh957vV4MvKlqlO0ueml3GjwGkurqQKxnmW+R1e8KWMG2S5y5zJxikxjqequkWVZE3smbz6ibmf1yxELkWL02VOjRtbWWyhWYiWtadIYohK5kiyEK1JSCAaA/I2d6zfOkQoMhv3IhDJ67/0ezkXUdrF3mKIlIbclR53ZAzSJcgRiO17gxWIeifPLbNHVLCxq/7BIJIqZN7LGRt5myr7XHmuVV41gWglnDpZWZatw88x090+6g+AU64TAnu/MURqY7/7NmByY/XjOAce/fberlWFqi5zT/24272nUpa5lEgKC6UWIjvJRRGqnx99sfV6vkDkttAq85HlMqe7RQZ2oogs/4LL8Az8O5hfA8KKljfLZY6VJFVoxkeiGR+JtzDWd6KNkVqIULHdpS5zy/wOLtftJKlCtfW0JteUelUXxEFv0vMyRRZ9PmmDHAclAlEy/5al3dbGx3IKsw7OQmS9P2iXY0WvijGikFUhEDUajesBPKnZbD5t1G0ZGFe9TWxOoI1te9BzVrwh6yGpQj8WolLsLDMFqO8YgSVFKgfaluUy0MUi+722zojvPDMxqCHXn8ucq/hdT6jFb+gxRPb3XW4MUVDpmffsp18BM+12hfP7deCYS8Xv/brMqbo+7QPAzLbejl0JqiZVaDza/bpL0OW+2NC4BCL5mlc2Aqw4jUI4B178DZGdL/cc5ktOhYgSfneeZ76uC84V+uH/wXPwzqUn4L9rU2CthdLPi2uYabfN75x/TYb+lQWDsRD1N4/GsK1geR8ssRCtBCrdfBUBg7G06mbVOWrgAlGOq2censtCVGwtT609JS5zeqr+ZVmICgqzmi0oeVu71y//UbbQ7aAgC9FAGXuBqNFo/BmARwH4/oibMlgu/J3k1zwTLwMv3pAVaB2YtWCsxMYuU8StgOO2zQD3AWcduTnZEI6VQDSAVLAJiQtMuvn5jYuOwexEgCefe8Rgr1H58yo4dVAucwMszJr0A1fb8mKI8ixEg027vRI9lFWM03DSb9rtyU2iVkdrX+8JGVaCftNuK5xJXoJcgShO0sv1oBKosoE85CTHcdn+r+qCOA1Exz0ceNXNwOz20sv9UefX8UTvv+FwYEbEOA5gWtQIqppA1irMWrU/irTb/Y0Ob6QCUcW024lAtEKafRdKyaQyG5aixRZWYdB7gOVYiOJqFqLUZc562e7fZbFIVZEWom7cQ3r+svfzikwPgnEJOVgjDFH90TdfA/CiUTdiOGTNwoVZkQom9txMPoMcQLd8Qfy0U/U6mAhEW6frflKHZVTOY076mUSf8xngsf+34FzpN/Q9jqc+9MjBbAbQu5+02hAu22NPufWshMucS9uVk3a79FzJ33kxRD4qbSRWwkJk3J9+BaI+hBq1MPsDTpDQD71upmxcz0VtrhzzYhJD1EvMUr/PvqAOUW5SkwrCEAD8ZXgdHtl+l/O9JE4JcXUrDOeivereVcxkyViJ90IBg3GZ609QqSwQKTdNK5nFiqLiYNoVrHvLyDg6MJJ5rOKY8gIk812PMUTZvVHBdQYgEIW91CsbdBuIkTE2FqJGo/E8AK+wXn5us9n8eKPRuHwETRoaeUIPYyXbpR5iiNI6RAPk2ncDN38OOPJh5Z9NJjYG7q0Rl7mjL87GD+j0u9lbCdQ6tNzzKAuRy9VhuQKRy3LRawxRxmUu57lWTSywApsNY7Pa6/mjPi1EgBCI7vvR4DPG9YN65nbczHIosDqpOkSslzHZ76bGGUMk27GCWqDpmod9ix1Ecf6a4oQH7pisQoEIfZtPB1Ljt89xGYNXe64Xv0LUBTvjqX1dpy8SC1EVd0fWf0KSQWFbe8pwJVUoy84IdYmSGCJXu/rhqrdh8ZO/jb0oycJX1v9IIFqVjI1A1Gw2PwDgA6Nux0jIiSFiZbUGClYWO7CQOX5bNmc9XfyrhNo0M7BgDF3mBjmBOVzmBk7P7VUa6mVeN7EQacKLnW2oZ4FI3i+X5SInhqhy2u08vFoqXBQ1rdrZesNoY68Ckcwy149QoyxE4+Ayl5dZrYwXfgX45Tfd76l7Emafa+IyZ9f6KaLfOcFx3LZZIcBOBMubZ+o+R6vrvmcffsEF+MwP78amqQD75rvVT7rh8GwcVAkM6N9lboRuPjFQ7bn69er1eAaFEojaVV3mFD3ez0Gk3Ab6cJnzsnFHJUlMWI7QVWydXEb/OuMpeMNNDWSrjmUaVvI+CUSrkbERiNYz6eC2027z/lNIWgOyF+HjO9EJOIff0t91S2Gay9waFYhynudg6S+GKFp2DFGB73dZZqaStrk36r3GEFX8fsddnqawLmQFLESDcHfp10IElBcg/q0bgYP39X7+XmCWEF2VHaflp8d/yt8BX/1TYHZH5q3EZa4ni1S/c2+2/7/p107GaYdvwMXHb+3tXOc9H9h0dPLnF199OW5/wL1hPmbrNH77ihNEE3rxhn/hV3t2wWSs/5IJg3Ib7oe4LHPrKFGJATqL5Z9lDH2tL0/5MHDo6b0f56IvxVeBIsQpEKkYoiG5zAH446ecuazjB9EGYjSQQDQG5CdV6HFhMw42F+XUZa58MXha+w2YxSK+3d+Vc9qTWoi4P4YxRANNqmAJCCtAz2t6El+wTBKXuSKBqF+XOZfbjjuGqJJL0FEX5b936Wsqtq3ax3phWZXUFWVCjYskhqhk8zuoDVMRqo9USMhSmZ3nAk/5e+db35i8BOcvfQUHNzqSIOQxQAvRVM3H087vI7j62ncbfx6+cRKHbyy/Z6xqKmbAqOFSFbE29Tc4Rll7LhpngUiNhaouczM7gDOfATz0+dWvcXKp7aM6vWaZA9yW4bmdwP67eoshKup74yCMjGsfIwpZFQJRs9n8MoAvj7gZK0Ze2u1ljalMcHlRJi+TFmrlhcn6hXFwuZmLximnx2pzmesZ0aZw2S5zqjCotqlerkCk+qTL6pGnLCgaHE/+EHDomcCmo3psh/NKAziHdcblxBBd+27gq+/pb3JILERjEEM0dxjwyLdUSsgyCL4xfTmOv+dk/M3cMdUP6ncCHkiQzPJYaaGDszEWLAph47FhdqHSr5/x6+WfVXWgHvfelW1TEf0kRlHJKvSyDRsOFwJRdyn7+TyXuZWKISLWNatCIFrzyMHNbJe55WizciaFFUm/XYlUIGPjaCEaaHrVlXeZ6yloGkj6w7LdFJ31I6z4jCHEEBVyymN7u34hKyAQLWfBPu/54l8/jJNAxJgIXB8SnDF04femo+jbQjTEVM058BWe54U8NIK15IIXA9/7cN+HB4E/vhvmucOAt+yr+OExEEbt2NEqXPQysT6c85z0tQ07gV9+Azhwb+bjzGVRAglExMpAPWcMSDdI2Yml/xiiMZgwdTSXOXcRwBEzUAuREhAGd8rsNXq7dyqGIo6W6canYjD0eB9muU706n4YOdzwyhhWHMIgx9F5zweC6dG5DE1uFLWI1mF1c3XPc9Neuw/q82LLnEtqs8s7HsOa/kfQjx/9duB1d/Z8mJr/Tjhkdm1smMdhfU8E/x7GlF8HLnmlqVC76m3AyY8BTrome4nctNsFz3Ac7o1CqzdJjD9kIRoD8gPEk//6OKk9YYzLJMGSje9YJVUYpJtLvxm0erlEz5+XG8LlCkRbTwR2/SwnhqjPLHNhS/x0pt3OSUk/JF1Ov3ESTq59N3Dtu8H33TO4c/bK495rBOmvF5T83JsXa78uc8u0EL3yp85MeT01YRgWohEmR+gVxjwxH7MxdplbbSy3lphi7rDc2L+0oPgQFBmDprK1jxgXSCAaA9Lh64gh6nds52aZK59Yvviqy3DL/Qf7vHBug+QPllRFj8ZJIFptWeZ6nfSTbD3LXLye/Wngnh+aAqQtAPYqEHWlQOR0mcuLIertEn2zIkkVRuhSdfJjRnftEaIeY28WosElVeiJYRYD7ZP+y7KOCL149JoQiMbg7icC0Uq6hrs1Gaus960sr7q5YiIOogwSiMYBFUPkyixZNnk/6g+B7admX7c3XT3sII/dNoNjtw2oVkHm+mNqIVoRl7lxSrutsswts00zhwAnPNJ57sT1rWcLUVv8LLIQ2Vnmxqnv9MhKa++JLDxRCPRwUN8uc2s/hogzLFsr8at4Cw4fTHPK4R4QAmOdVKEXxmEOUUqxFc2mmiMQuayTv/4R4AcfXbG2jC2z20fdgjUDCURjgErDa29WWRUT0cNe4n49d9IfcVIFLYZozSZVGILLXK8cunEK2AOcdujy4xNy6TeGSAlELgtRXh2iYWXyWoGNx7KSKhB90V8M0YgsRANgpffL4n72/z0bS3+LGAw3D65Jxaj5nXGMhXVl2YzBd0gUXyvvCeGIrs5+9qRrxT+C6JPRz9xELkIJN5gYovERPlgSULlmLURj6DK3cUpYX3bM9VaAsSeS6uM93svGNcBZzwCufmfBh+zvO5y+syKxSuOg3V1nKIVyNJQYotEvqyseQ4RlrE0QpR3a6KOWVr/olublzPWbjxtMe5bLOMwhQ3GZg/Ma4/D1ibUHWYjGgdziY8vY9uUmVRi1aBQDjKETe+MlEA20MGtfEdw9XqI/l7kVdeNTabd73XD4deCxefU03O0dWkD3SlyGVvOhk3b/FbQQMS4D98dBIFrZ86+6MkSJkLrMhv/WDUDrwECatDzG4Obb2UVX4hK5GXjH4PsTa47Rz9wEupPbAAA3BycbrzO2jLpBeYVZR1Us1Lp+Bz7ieIwmtUFuYo693Py5EvTcL4YgEPdrIapCJoZoWFPXikhEK3BOogie63pTQJ+1vsYhhmilU7szxkaXPr4fjKQKy2h3fVZkRRs143Dvh2EhgnvfspoyHBKrB7IQjQHtuaNxZeud2Lz9FFynvc7A+o83GAMtpYm5Ie/CG7mtymCQ9+uIhwJv3j1Yq5NFz8vBMBI9qHMP8l7mtXdoBqIVuNA4bGbWGUogWtE6RMwD0F3RcT9OrC6BSMUQraI2jzu8jzpEPV8jL+02PUdi8IzbrnldwhjDLfFOhPCs15cTQ2QdF+e8PiwsC1Eb/ni5zA36vqz4pqhfl7kVTPSwkhYi6/uuape5cer364TfuPgYAMBDj9lc/aBe+zHXA/fXA6voe665ZzMGcwgfhsuczMCLyH5jxa5JrF/IQjQGbJeB7uce7Vis1+i4FxaiNfrlhkHP2us8X+wBEvUZQ1SIu73DSl29Il6da2ZTtno456hNuP2Pes1A1Y+FSPu5xllVe1KmxRCtBcbh5icxRCu3pjR2iJpcx2+bNi+9Vp4jMVaQQDQGHLVlGl981WU4cvOU8bqY8wY08HOytYyKTuyPV2HWVUbvrpRDtBCthHWM2X9Sljlihen1OXEtTmVdsIr68ZpzmRuD7zEEl7m5CVGKYdOUmZGQYoiIlYAEojEhrxDq4Ab+qCcQM4aoQxai4TKUGKKVdJmzWNUbm9Xc9nVEXzFE64dVtSlVz3JVzxsa4/A9kjWlRMn25L8DpnpwVdXZea74ecpjzUvTHEqsACQQjSGfCC/BE7wb5aAf1OZyxJYhR5Y5H+EIG7TK6XmzJn8OJYZogIvVhiOB854PnPs84+WhFTddiY3HOGxmiMGTxFSsk3ltGf34Iy84HzP1IW4/EmvGGhl7YzGHVPQ6OOW64veL2HoC8JZ9uZcmiEGyXmz7q4pXdV6Eo5c+MliXOcnorDKuLHM0q/VL78k2hpF2ewViiDgHrn03sP0U4+VhZbhamZwKNO2uSR7x++LnxIbRtmNILEdLf+FxW3H6zo2Da0wZbK0lVRgDRljKY2QWoqf9I/Cot4/m2sSKQ7PDGMMweEUQG5WlyPoiHYxJDNEZTxt1C4ZDVfeG5ZCk3R6C69DQNKRUh4ioyNnPFNpsvz7qlgyFsTBSVCWpQ7SaGj3mDCNRT+61R/QcT7wKeNiLR3NtYsUhgWiMYQMtBz4mC0E8ZjFE17/PbZIfe/rMMrdq026bDK0GCrnMEUQOq2j7sNZc5saJlVxT8qDHSKwAq2hGW38w7f+1RiceszpEq4yeBYJhuDcMVSAaztS1MrIL9Xti9bO6kioMQSG03hhGop68S9PWlVgBqFeNOYPThI9Hum0zhojom543I0PYvKxIHSI3ZCEiiNGyqjJ9JZv3dZLwYhjMHQZsPBK4+p1Dv/TQ5n9iXUFZ5sYY4TEnBn4UL08nMvLFy7JQtOGDNOX90/PzHGba7ZWoQ2QxvJ6zEgIR6aGIleeH0TH4z/AcvGqlLrCapu8kAyBZiAaGXwde/qPRXJsEImIFoJV5jBHC0GAG/rhZYz4UXoX3dR8z6masWvp3mVvBDcGFvy1+bjl+5a4hWVXuOja0mBND4Lr2H+DPw8ev2PlXlduSUkJEJBCtBchCRKwEZCEad1bzxs/ATPv839EZAID3jKg1646VyAj09E8A++9K/37I9eLfEBiWxZMWXoLIYRXJQ0nmS7IQrQlG7vFCrElIIBpzBqeFG6/CrMSwWQEL0QmPHNy5emR4FqLVtOsjiOGxqjalFEO0tlhFXY9YPdBqP/YMZuSPfvEa9fXXFr27zI0uI9BKMKwscwSxmnnkydtX7Nx8NVlPVQxRRALRWoAs98RKQBaiMScxrCzzPDHNH2uLXgWCYcQQDZUhdWiSu4hVyq1/eM3Aw9Xe9aQz8KWb7hd/rKZN6dQW8dMLRtsOYiCMXsFLrEVIIBp35Mb3j7pPxRtG3JTBsDYsFCOn183IzCHi59TmwbdlFAxpM0YLL7Fa4SvgVvrEc3biiefsBLDKrLTXvQc46kLgiPNH3RJiEKwmYZxYNZBANO4whqOXPgIAq1sgohiigdLzcnDBS4DpQ4DTn7ISzRkBtCASxEhZTZvSyU3ABS8adSuIQbFmkk0R4wQJRGPOalpzijGzzBHLo2cfas8HznzqyjRmFAytMOsq0oITxBChOA5iVJDlnlgJaLUfc9bMwB9UMBQhWSP9Yuyh+0wQLmhkEKOChHFiJSCBiCCIVciwYogEEWUlIQgTclsiRsSaURQTYwUJRGPOoBUhZKBZG6x7Ddmwvr/c9NG4IQgT2pQSI2O9r3/EikAC0Zgz6HE/ummEYogGyrqPbRluT45p80cQBjFtSokRse4VgsSKQEkViOFAWeYGyrpfECjtNkEQ/fKbNwC16VG3gugTmpeJlYAEojFn7Qx8shARg2RIAtF6FzwJIpdVPDYOO3PULSCWw3p3kCBWBBKIxpxl7cd+57uZytwjE0doYzlQ1v1Gfcjfn1zmCMKGxgQxKqjvEYOH5Oy1zJbjgI1HjroVJtJl7sTtMyNuyCpnvQtEQ1oQKU6CINzUfG/UTSDWKeteIUisCGQhGnMGPexHn1RB8O8vu5Sc55YDLQhDghk/CIIQBB7pU4nRsHZCCYhxggSiMWft7XuFGMSphsWyWPd3b1hJFZJ6wuv+jhMEQYwHa29jRIwBpOIZQx569OYVO/fIY4goy9xAWPcuA0PLMkdT5Lrj5McAG44YdSvGn/U+BxEjY92vf8SKMNYWokajsQHA3wOYA1AD8Mpms/k/o23VyvOh5z0UB1td+ddaGfhr5XuMC7RRHwq08K4/nvL3o27BKoHGBjEaSCAiVoJx31W9EsB/NZvNywA8B8B7R9uc4TAReNg6UwewlgqzKshCNAjW7Xpw3BUjuSy5zBEEQYwHJBARK8FYW4gA/AmAlvzdB7A0wrasCUbmsXbqE4Av/yFw2pNG1IC1xbpdEJ7yYWD+/qFdbr3eZoIohQYHMSIoqQKxEoyNQNRoNJ4H4BXWy89tNpvfajQaOyBc514+9IaNmEEN+5FPH1uPB96yb9StWEOM/ImOhtoUUDt6eNeTmz6yaxKEzTqdg4iRwygpE7ECjI1A1Gw2PwDgA/brjUbjNAAfA/DqZrN5w9AbNmIGZQmgDd3agurjDAeliSSXOYKwoDmIGBGMjXu0B7EaGRuByEWj0TgFwD8CeEqz2fzBqNuzFqA1bG1Aj3E4kCBEEHkw6ydBEMTqZawFIgBvBzAB4M8ajQYA7Gs2m48dbZOGy+CWGqnpJlPRmoBcBoYDKRAIogQaJMTQoT5HDJ6xFojWm/DjYlBrDSOnuTUFBZUOh9Rlle43QRiQIDR8GtcCzc+MuhWjh/oesQKMtUBE0MaXyIEWhCFBMUQE4YbGxNB56kdG3QKCWLNQZBpBrEpoMzIMlNxJ9lWCsCClDEEQawgSiMacQa05pOFeW6zbOkRDJqYpkiBKoLmIGDK0/hErAK32BLEKIYFoSNBtJogcaHAQo4L6HjF4KIZonUBJFdYWtBwMB3WfycJKrBte9DWgdaD8c6SUIUYF9T1iBSCBaMyhcU84oY4xHOg+E+uN7Q+p+EE5NmiMEASxBiCXuTFnUK5RsabrJtYAVIdoKDAqPkkQJdDYIIYN9Tli8JBAtE6g9N1rC3qeQ4KptNsEQRiQZYgYFdT3iBWABKIxZ1DDPqYtHUH0AS28BOGGxgYxKqjvEYOHBKIxZ/CKEJpI1gKM0dAdBpTNjyByoLFBEMQagnZV6w6yFK0FaKM+HNLCrHS/CcKExgQxImj9I1YAEojGnEHFilDMyRqDHueQoBtNEIXQ5pQYOtTniMFDAtGYQ2sN4YLR0B0OSVIFGogEYUCLEzEqqO8RKwDtqtYJlFRhbUEucwRBEARBEIOBBKIxh7a9hBMSiIYCCZ4EkUMyNmiMEMOG+hwxeEggGncGNO5P3D4LADjhkNnBnJAg1hHkMkcQOZDSgBg21OeIFYAEonXClukaAGDrTG3ELSEGAa0Hw4JuNEG4obFBjArqe8TgIYFozBl8djiKJVoLUB2i4cA4LbwE4YS0MgRBrCFoVzXm0JpDEKNDKSTIZY4gbGhMECOCNkbECkAC0bqDJpK1AAX7D4kk7TZBEG5oLiKGDfU5YvCQQDTm0LAnXJDFYjjQfSaIHEgpQ4wK6nvECkAC0ZgzeEsA6brXAr5HQ3e40AJMECY0JgiCWDvQrmq9QBqVNcXgk20QTmjcEIQbNTZojBBDh/ocMXhIIBpzBjbsY7IMrSloEzIUaNgQRA40OIhRQesfsQKQQDTmDH7c00SyNqDnOAzUno9iiQgiDxobxJAhgYhYAUggWneQVo8gKkMLL0EQBEGsefxRN4AoZmCxIrSxW1vQ8xwSK1SH6OU/Guz5CIIgCILoGxKIxh3a9xLE2mPjkaNuAUEsE/I2IAhi7UAuc+sFCoBdW5CFaDjQfSYIN8EUMLkZuPZdo24JQRDEsiEL0ZhD+zGCGB2kRyCIHLgH/O5to24FQRDEQCAL0ZgzMHmIJKs1Bj3PYRLT+CEIgiCINQsJRASxGqEN+lCI5W2mtNsEQRAEsXYhgWjMYYPa+JLvzxqDNugEQRAEQRCDgASiMYe2vQQxSmgEEgRBEMRahwSiMWdgnlHkYrW2oOc5FGKyrBIEQRDEmocEIoJYlZBANEwohoggCIIg1i4kEI05jDZiBEEQBEEQBLFikEA05pBnFOGEOsZQ2LlxAgCwZaY+4pYQBEEQBLFSkEBEEKsSEoiGgbrLPvdG2g6CIAiCIFYOEojWC8dcJn6ecNVo20EMBrIQEQRBEARBDAR/1A0gihnYvvfws4G37BvQyQhivUBZ5giCIAhirTPWAlGj0ZgG8BEAmwHMA3hms9ncNdpWjQYyCBAm1CGGCt1ugiAIglizjLvL3AsAfKfZbF4C4GMA3jji9gwdlWWOyqEQBiQhEwRBEARBDISxthA1m80/bTQaKpr5SAD3jbI9o4D2vQQxQhJNBA1EgiAIglirjI1A1Gg0ngfgFdbLz202m99qNBpfBHAagCuH37LxgAQjwoQ6xHCQAhENQIIgCIJYs4yNQNRsNj8A4AM5713RaDROAvAZAMcNtWEjhrZhhBPaoBMEQRAEQQyEsY4hajQar2s0Gs+Uf84DCEfZnlHAaONLOKF+MRQoeI8gCIIg1jxjYyHK4a8BfFC603kAnjvi9owM2v4SxCihEUgQBEEQa5WxFoiazeZ9AB496naMErUNO3zT5EjbQYwZZDkkCIIgCIIYCGMtEBEA5wzve/rZOOvITaNuCjFWkEA0FDYeBZz4aODS14y6JQRBEARBrBAkEK0Crj7t0FE3gRg3yEI0HDwfeNrHR90KgiAIgiBWkLFOqkAQBEEQBEEQBLGSkEBEEARBEARBEMS6hQQigliNkMscQRAEQRDEQCCBiCAIgiAIgiCIdQsJRASxKiELEUEQBEEQxCAggYggViPkMkcQBEEQBDEQSCAiiFUJCUQEQRAEQRCDgAQiglhVkCBEEARBEAQxSEggIohVRSx+kMscQRAEQRDEQCCBiCBWJSQQEQRBEARBDAISiAhiVUGCEEEQBEEQxCAhgYggViPkMkcQBEEQBDEQSCAiiFUJCUQEQRAEQRCDgAQigliNkIWIIAiCIAhiIJBARBCrCRKECIIgCIIgBgoJRASxKiHBiCAIgiAIYhCQQEQQqxGyFBEEQRAEQQwEf9QNIAiiH0ggIgiCINYRL/wKsO+uUbeCWKOQQEQQqwoShAiCIIh1yI7TxD+CWAHIZY4gViPkMkcQBEEQBDEQSCAiCIIgCIIgCGLdQgIRQawmyDJEEARBEAQxUEggIojVxAmPEj8ZDV2CIAiCIIhBQEkVCGI18cS/Bg7eC3Bv1C0hCIIgCIJYE5CamSBWE8EEsOnoUbeCIAiCIAhizUACEUEQBEEQBEEQ6xYSiAiCIAiCIAiCWLeQQEQQBEEQBEEQxLqFBCKCIAiCIAiCINYtJBARBEEQBEEQBLFuIYGIIAiCIAiCIIh1CwlEBEEQBEEQBEGsW0ggIgiCIAiCIAhi3UICEUEQBEEQBEEQ6xYSiAiCIAiCIAiCWLeQQEQQBEEQBEEQxLqFBCKCIAiCIAiCINYtJBARBEEQBEEQBLFu8UfdgCo0Go2TAHwDwPZms7k06vYQBEEQBEEQBLE2GHsLUaPRmAPwbgCtUbeFIAiCIAiCIIi1xVgLRI1GgwH4KwCvB7Aw4uYQBEEQBEEQBLHGGBuXuUaj8TwAr7BevgPAx5rN5g8ajYbrMA8A7r333hVuHUEQBEEQBEEQq5VHPOIRRwO4q9lsdu33WBzHw29RRRqNxs8B3CX/vADAN5vN5qXa+xcDuHEUbSMIgiAIgiAIYlVxTLPZvN1+cWwsRC6azebx6vdGo3E7gKusj3wLwCUA7gEQDq9lBEEQBEEQBEGsMu5yvTjWAlEZzWazBeAro24HQRAEQRAEQRCrk7F2mSMIgiAIgiAIglhJxjrLHEEQBEEQBEEQxEqyql3mxoVGo8EB/F8AZ0DUS3p+s9n8+WhbRYwTjUYjAPDXAI4GUAfwNgA/BfC3AGIAPwbwkmazGTUajRcA+C0AXQBvazab/zaKNhPjQ6PROATAdwBcCdEv/hbUb4gCGo3G6wBcB6AGsT7dAOo3RAFynfogxDoVAngBaL4hCmg0GucDeEez2by80Wgcj4p9pdFoTAL4ewCHADgA4NnNZnPXSL6EhCxEg+FxACaazebDAPweRCFZgtB5BoAHm83mJQCuBvAXAP4YwBvlawzAYxuNxg4ALwVwEYBHAXh7o9Goj6jNxBggNyn/D8CifIn6DVFIo9G4HMCFEP3hMgBHgPoNUc41APxms3khgLcC+ANQvyFyaDQarwXw/wGYkC/10ldeBOBH8rMfAvDGYbffhgSiwXAxgH8HgGaz+XUA5462OcQY8o8A3qT93QVwDoTWFgA+B+CRAB4K4KvNZrPVbDb3Afg5gNOH2VBi7HgXgL8EcLf8m/oNUcajAPwIwKcA/CuAfwP1G6KcmwH40utlDkAH1G+IfH4B4PHa3730lWTfrH12pJBANBjmAOzT/g4bjQa5IxIJzWbzYLPZPNBoNGYB/BOENoQ1m02V1eQAgA3I9iX1OrEOaTQazwGwq9lsfl57mfoNUcZWCMXckwC8EMCHAXDqN0QJByHc5W4C8H4A7wHNN0QOzWbzExBCs6KXvqK/Phb9hwSiwbAfwKz2N3dVwSXWN41G4wgAXwLwd81m8yMAIu3tWQB7ke1L6nViffIbAK5sNBpfBnAmhGvBIdr71G8IFw8C+Hyz2Ww3m80mgCWYGw7qN4SLV0D0mxMhYqI/CBGDpqB+QxTRy55Gf30s+g8JRIPhqxC+t2g0GhdAuCoQREKj0dgO4D8A/G6z2fxr+fL3pK8/IOKKbgTwTQCXNBqNiUajsQHAyRDBicQ6pNlsXtpsNi9rNpuXA/g+gGcB+Bz1G6KErwB4dKPRYI1G4zAA0wD+i/oNUcIepFr73QAC0DpFVKeXvpLsm7XPjhRy6xoMn4LQ4n4NIpDsuSNuDzF+vB7AJgBvajQaKpboZQDe02g0agB+BuCfms1m2Gg03gMxOXAAb2g2m0sjaTExrrwKwPup3xB5yCxOl0JsRjiAlwC4DdRviGL+BMBfNxqNGyEsQ68H8G1QvyGqUXltajQa7wPwwUaj8RUAbQBPG1mrJVSYlSAIgiAIgiCIdQu5zBEEQRAEQRAEsW4hgYggCIIgCIIgiHULCUQEQRAEQRAEQaxbSCAiCIIgCIIgCGLdQgIRQRAEQRAEQRDrFhKICIIgCIIgCIJYt5BARBAEQRAEQRDEuoUEIoIgCIIgCIIg1i0kEBEEQRAEQRAEsW7xR90AgiAIghgEjUbj3QBeCeAoAC8G8BQAOwD8FMDLms3mV0bYPIIgCGJMIQsRQRAEsVY4E8A+AJ8DcByAdwF4B4AGgE80Go1gdE0jCIIgxhWyEBEEQRBrhTMBbADw0maz+SH1YqPR8AG8AcDRAG4ZScsIgiCIsYUsRARBEMSqp9FoHAVgM4DP6MKQpCV/Lg63VQRBEMRqgAQigiAIYi1wlvz5Mcd7pwI4AOBXw2sOQRAEsVoggYggCIJYCyiB6OuO984B8L1msxkPsT0EQRDEKoEEIoIgCGItcCZEQoVf6C82Go2NAI4F8N3hN4kgCIJYDZBARBAEQawFzgLwXYcV6GwADCQQEQRBEDmQQEQQBEGsahqNxhYARwD4juPts+VPEogIgiAIJyQQEQRBEKsdFT/kEnrOAbAA4KbhNYcgCIJYTbA4phhTgiAIgiAIgiDWJ2QhIgiCIAiCIAhi3UICEUEQBEEQBEEQ6xYSiAiCIAiCIAiCWLeQQEQQBEEQBEEQxLqFBCKCIAiCIAiCINYtJBARBEEQBEEQBLFuIYGIIAiCIAiCIIh1CwlEBEEQBEEQBEGsW0ggIgiCIAiCIAhi3fL/AxB4jbRZUrglAAAAAElFTkSuQmCC", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Noise free data\n", "ynoise_free = y.copy()\n", "\n", "# Generate noise\n", "v = np.random.normal(scale=0.5, size=y.shape)\n", "\n", "# Data corrupted with noise\n", "ynoisy = ynoise_free + v\n", "\n", "# Plot\n", "_, ax = plt.subplots(figsize=(14, 8))\n", "ax.plot(n, ynoise_free, label='Noise-free data')\n", "ax.plot(n, ynoisy, label='Corrupted data')\n", "ax.set_xlabel(\"$n$\", fontsize=18)\n", "ax.set_ylabel(\"$y[n]$\", fontsize=18)\n", "ax.legend(fontsize=18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generating training and test data" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "n_train = 700\n", "\n", "# Identification data\n", "y_train = ynoisy[:n_train].reshape(-1, 1)\n", "x_train = x[:n_train].reshape(-1, 1)\n", "\n", "# Validation data\n", "y_test = ynoise_free[n_train:].reshape(-1, 1)\n", "x_test = x[n_train:].reshape(-1, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynomial Basis Function\n", "\n", "As you can see bellow, using only the polynomial basis function with the following parameters results in a divergent model" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\wilso\\Desktop\\projects\\GitHub\\sysidentpy\\sysidentpy\\model_structure_selection\\forward_regression_orthogonal_least_squares.py:481: UserWarning: n_info_values is greater than the maximum number of all regressors space considering the chosen y_lag, u_lag, and non_degree. We set as 15 \n", " self.info_values = self.information_criterion(reg_matrix, y)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "nan\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "basis_function = Polynomial(degree=2)\n", "sysidentpy = FROLS(\n", " order_selection=True,\n", " n_info_values=70,\n", " xlag=2,\n", " ylag=2,\n", " basis_function=basis_function,\n", " model_type='NARMAX'\n", ")\n", "sysidentpy.fit(X=x_train, y=y_train)\n", "\n", "yhat = sysidentpy.predict(X=x_test, y=y_test)\n", "frols_loss = root_relative_squared_error(y_test[sysidentpy.max_lag:], yhat[sysidentpy.max_lag:])\n", "print(frols_loss)\n", "\n", "plot_results(y=y_test[sysidentpy.max_lag:], yhat=yhat[sysidentpy.max_lag:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ensembling a Fourier Basis Function\n", "\n", "In this case, adding the Fourier Basis Function solves the problem and returns a model capable to predict the defined system" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.36333394055181595\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "basis_function = Fourier(degree=2, n=2, p=2*np.pi, ensemble=True)\n", "sysidentpy = FROLS(\n", " order_selection=True,\n", " n_info_values=70,\n", " xlag=2,\n", " ylag=2, # the lags for all models will be 13\n", " basis_function=basis_function,\n", " model_type='NARMAX'\n", ")\n", "sysidentpy.fit(X=x_train, y=y_train)\n", "\n", "yhat = sysidentpy.predict(X=x_test, y=y_test)\n", "frols_loss = root_relative_squared_error(y_test[sysidentpy.max_lag:], yhat[sysidentpy.max_lag:])\n", "print(frols_loss)\n", "\n", "plot_results(y=y_test[sysidentpy.max_lag:], yhat=yhat[sysidentpy.max_lag:])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "interpreter": { "hash": "d637594906b92e2064a8978fcd7d47bb213aa9d5bb48152798bc86e8ea48bb1d" }, "kernelspec": { "display_name": "Python 3.8.11 64-bit ('neural_prophet': conda)", "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": "3.8.11" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }