{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "Bode_python_notebook.ipynb", "provenance": [], "collapsed_sections": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "7oKHWtG4q8vL", "colab_type": "text" }, "source": [ "En este tutorial aprenderemos a graficar diagramas de Bode usando python. \n", "\n", "Estudiaremos primero una transferencia sencilla de primer orden:\n", "$$H(j\\omega) = \\frac{a}{(j\\omega+a)}$$\n", "La aproximación asintótica ya la hemos trabajado en el teórico. Consiste en una recta horizontal de baja frecuencia, asociada a la ***ganancia en continua***, que se pega con una recta a -20db/dec a partir de la ***frecuencia de corte*** $\\omega=a$. \n", "\n", "Estudiaremos primero una transferencia de segundo orden:\n", "$$H(j\\omega) = \\frac{\\omega_n^2}{(j\\omega)^2+2\\zeta\\omega_n(j\\omega)+\\omega_n^2}$$\n", "En este caso, ya sabemos que la aproximación asintótica consiste en una recta horizontal de baja frecuencia, asociada a la ***ganancia en continua***, que se pega con una recta a -40db/dec a partir de la ***frecuencia de corte*** $\\omega=\\omega_n$, con la particularidad de que cerca de la frecuencia de corte, puede existir un fenómeno de ***resonancia*** asociado al valores pequeños de $\\zeta$. Por eso, al hacer la representación asintótica, igual marcamos el efecto de $zeta$ en el entorno de $\\omega=\\omega_n$. \n", "\n", "Finalmente, estudiaremos la transferencia del ejercicio 3c del práctico.\n", "\n", "$$H(j\\omega) = -\\frac{5(0.1j\\omega+1)}{j\\omega(1+0.5j\\omega)(1+j0.6\\frac{w}{50}-\\frac{w^2}{50})}$$\n", "\n", "Para definir la función de transferencia, vamos a usar la función *ZerosPolesGain* del paquete de señales del módulo *scipy* [(link)](https://docs.scipy.org/doc/scipy/reference/tutorial/signal.html). Para ello debemos calcular los ceros $c_i$ (raíces del numerador), los polos $p_k$ (raíces del denominador) y la ganancia $K$ del sistema:\n", "\n", "$$H = K\\frac{\\prod_{i=1}^{N}(j\\omega-c_i)}{\\prod_{k=1}^M(j\\omega-p_k)}$$\n", "\n", "Ejercicio: Calcular los ceros y polos de la transferencia y verificar que ésta puede factorizarse como:\n", "\n", "$$H = -50^2 \\frac{j\\omega+10}{j\\omega(j\\omega+2)\\left(j\\omega+0.3\\cdot 50-j\\sqrt{1-0.3^2}\\right)\\left(j\\omega+0.3\\cdot 50+j\\sqrt{1-0.3^2}\\right)}$$\n", "\n", "Tenemos entonces $K=-50^2$ y los conjuntos de ceros y polos son\n", "\n", "$$\\mathcal C = \\{-10\\}$$\n", "$$\\mathcal P = \\{0;\\quad -2;\\quad 0.3\\cdot 50\\pm j\\sqrt{1-0.3^2}\\}$$\n", "\n", "
\n", "¡Grafiquemos! Correr cada uno de los bloques de más abajo dándole play al botón de la izquierda." ] }, { "cell_type": "code", "metadata": { "id": "QmiT_jhn2Gtl", "colab_type": "code", "colab": {} }, "source": [ "# Importar paquetes\n", "import numpy as np # calculo numérico\n", "from scipy.signal import ZerosPolesGain, TransferFunction, bode # transferencia + bode\n", "from matplotlib import pyplot as plt # gráficas" ], "execution_count": 1, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "17aS4Nl0E5Ry", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 549 }, "outputId": "1b756df9-ca56-4c72-c351-6a00164b379d" }, "source": [ "# Parametros de la transferencia de primer orden\n", "a = 1\n", "num = a\n", "den = [1, a]\n", "\n", "ww = np.logspace(-2.0, 2.0, num=100)\n", "\n", "Ha = TransferFunction(num, den)\n", "w, mag, fase = Ha.bode(ww)\n", "\n", "# Graficas:\n", "# Módulo\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, mag)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$|H(j\\omega)|_{dB}$')\n", "plt.show()\n", "# Fase\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, fase)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$Arg(H(j\\omega))$')\n", "plt.show()" ], "execution_count": 13, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "code", "metadata": { "id": "5am-XlMMJIA4", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 549 }, "outputId": "88437ac0-23a2-4abf-ae2b-713dbed44577" }, "source": [ "# Parametros de la transferencia de segundo orden\n", "wn = 1\n", "seda = 0.85\n", "# seda = 0.01\n", "num = wn*wn\n", "den = [1, 2*seda*wn, wn*wn]\n", "\n", "ww = np.logspace(-2.0, 2.0, num=100)\n", "\n", "Ha = TransferFunction(num, den)\n", "w, mag, fase = Ha.bode(ww)\n", "\n", "# Graficas:\n", "# Módulo\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, mag)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$|H(j\\omega)|_{dB}$')\n", "plt.show()\n", "# Fase\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, fase)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$Arg(H(j\\omega))$')\n", "plt.show()" ], "execution_count": 15, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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5ZfkHnHjLNL5x84s898Y7xBiTjihJaccSKEmSalyLxjn8+OA+vPCL0fz26/1Zs34L379jJkdd9zyPzVlNaZllUJJqiyVQkiTVmsY5WZw2vAdFFxVw5Yl7s3V7Kefe+yqHXj2Z+2euYNv2sqQjSlK9ZwmUJEm1Ljszg28M7cwzPx3FTacOoVFOJuMenEPBFZO444WlbCnxvQYlqaZYAiVJUmIyMwJHDerAY+cdxB2n70unlo347b/mc9Blz3Fz0WKKt25POqIk1Tu+RYQkSUpcCIGCPdpRsEc7Xlr6Ptc/t5DLnnyDWyYv5vvDe3Dagd1p3jg76ZiSVC94JlCSJKWUYT1acfcZ+/HIOcPZt3srrpn4JsMve47Ln3yDdcVbk44nSXWeZwIlSVJK2rtLC279Xj7zV2/gxqJF3Dx5MX994S1O3a8rY0f2pF2zhklHlKQ6KSXOBIYQrgghvBFCmBNC+GcIoUWlbReHEBaFEBaEEA5PMqckSap9/Ts248ZThvDMT0dx5MD2/PXFtzjo8kn85pG5rFm/Oel4klTnpEQJBJ4BBsYY9wLeBC4GCCH0B04GBgBHADeFEDITSylJkhLTu10uV580mOcuHMXx+3TibzOWM+ryIi75539Y+cGmpONJUp2REiUwxvh0jPHj239NBzpXLI8BJsQYt8YYlwKLgGFJZJQkSamhW+sm/PGEvSi6qIAT8ztz/8wVFFxRxC8emsPydZZBSfoqIcaYdIbPCCH8C7gvxnhPCOEGYHqM8Z6KbbcBT8QYH9zB88YCYwHy8vKGTpgwoTZjV0lxcTG5ublJx5BqlXOvdOXs1551m8t4fGkJk1dupyzCAR2y+HqvbNo3SYm/dacV517pKFXnvrCwcFaMMX9H22rtxjAhhIlA+x1suiTG+EjFPpcA24G/7ezxY4zjgfEA+fn5saCgYNfD1pCioiJSMZdUk5x7pStnv3adAKzdsIU/T1nC32YsY9qazRw7uBPnju5Nz7ap98tZfeXcKx3VxbmvtRIYYzzky7aHEE4DjgYOjp+enlwFdKm0W+eKdZIkSZ/RrllDfnV0f84e1YvxUxZz9/RlPPzaKo7ZuyPnju5D73aWQUmCFHlNYAjhCGAccEyMsfLF/I8CJ4cQGoQQegB9gJeSyChJkuqGtk0bcMnX+jN13Gh+MKInT817h0OvmcyP//4qi9Z+lHQ8SUpcqrxP4A1AA+CZEAKUvw7w7BjjvBDC/cB8yi8TPSfGWJpgTkmSVEe0bdqAXx61J2NH9uQvU5dw97Rl/GvOao7eqyM/Ht2bPnlNk44oSYlIiRIYY+z9JdsuBS6txTiSJKkeaZPbgIuP3JOxI3py6/NLufPFt3jMMigpjaXE5aCSJEk1rXVuA35+RD+e//lozh7Vi2dff4fD/jTFy0QlpR1LoCRJSiutmuR8pgxOfP0dDr3GMigpfVgCJUlSWvq4DE4dV8hZIz8tg+dPeJVFa4uTjidJNcYSKEmS0lrr3Ab84sjyMjh2ZE+envcOh10zmZ9MeJUl71oGJdU/lkBJkiTKy+DFR+7J1J8X8oMRPXly3tsccvVkLrjvNZa+tzHpeJJUbSyBkiRJlbTJLX9rianjRvP94T3493/WcMjVk/nZA7NZts4yKKnuswRKkiTtQNumDfifo/sz9eeFfO+A7vxr9mpGXzWZcQ/OZsX7m5KOJ0m7zBIoSZL0Jdo1bcivv96fqeMK+c7+3Xj4tdUUXlnExf/4D6s+3Jx0PEnaaZZASZKkKmjXrCG/PWYAUy4q5JT9uvLQrJUUXDGJ/3n4P6xZbxmUVHdYAiVJknZC++YN+b8xA5l0UQEn5nfhvpdXMOryIn776DzWbtiSdDxJ+kqWQEmSpF3QqUUj/t9xg3juwgKOH9KJu6cvY8Tlk/jdY/N596OtSceTpC9kCZQkSdoNXVo15o8n7MWkCwv4+t4d+esLSxl5+ST+8MTrvL9xW9LxJOm/WAIlSZKqQdfWjbnyxL2ZeMEoDh+Qx/gpSxhx2XNc+dQCPtxkGZSUOiyBkiRJ1ahn21z+dPI+PPPTkRT0a8cNkxYx4rJJXPPMm6zfXJJ0PEmyBEqSJNWE3u2acuMpQ3jyJyMY3rsN1z67kBGXPccNzy2keOv2pONJSmMpUQJDCL8LIcwJIbwWQng6hNCxYn0IIVwXQlhUsX1I0lklSZJ2Rr/2zbjlO0N57LyDGNajFVc+/SYjL5/EnycvZvO20qTjSUpDKVECgStijHvFGAcDjwG/rlh/JNCn4mMscHNC+SRJknbLwE7NufV7+/LPHx3IwE7N+cMTbzDi8knc/vxStpRYBiXVnpQogTHGDZUeNgFixfIY4K5YbjrQIoTQodYDSpIkVZN9urbkru8P44GzD6BPu1z+77H5jLpiEndPe4tt28uSjicpDaRECQQIIVwaQlgBnMqnZwI7ASsq7bayYp0kSVKdtm/3Vvx97P7ce+Z+dGnZmF89Mo/CK4u47+XllJRaBiXVnBBj/Oq9quMLhTARaL+DTZfEGB+ptN/FQMMY429CCI8Bf4wxPl+x7Vng5zHGmTs4/ljKLxklLy9v6IQJE2riP2O3FBcXk5ubm3QMqVY590pXzr52RoyRue+V8o9FJSxdX0a7xoExvbI5oGMWGSEkHa/KnHulo1Sd+8LCwlkxxvwdbau1ElhVIYSuwOMxxoEhhD8DRTHGv1dsWwAUxBjXfNkx8vPz48yZ/9UTE1dUVERBQUHSMaRa5dwrXTn72hUxRp59fS1XP/Mm89dsoHe7XH5ySB+OGtiBjIzUL4POvdJRqs59COELS2BKXA4aQuhT6eEY4I2K5UeB71bcJXR/YP1XFUBJkqS6KoTAIf3zeOy8g7j51CFkBDj33lc56rqpPDXvbVLtj/eS6qaspANU+GMIYQ+gDFgGnF2x/nHgKGARsAk4PZl4kiRJtScjI3DkoA4cNqA9j81ZzZ8mLuSsu2exV+fm/PTQvhT0bUuoQ5eJSkotKVECY4wnfMH6CJxTy3EkSZJSQmZGYMzgTnxtUAf++eoqrn12Iaf/9WWGdmvJhYf15cBebZKOKKkO2unLQUMIe4YQDq1YblT9kSRJklRZVmYGJ+Z34bkLC7j0uIGs+mAzp/xlBt8aP52Zb72fdDxJdcyuvCbwemBACOGfwF0hhP+r5kySJEnagZysDE7drxtFFxXwm6/3Z+HaYr5xyzS+d/tLzFn5YdLxJNURu1IC58cY/wSsiTGeCLSq5kySJEn6Eg2zMzl9eA+mjCvg4iP7MWflhxxzwwuMvWsmr6/ZkHQ8SSluV0rgASGEG4DeIYRBgK9KliRJSkDjnCzOGtWLKeMKufDQvkxbso4jr53Kufe+wqK1xUnHk5SiduXGMNcCS4G2wIlAt2pNJEmSpJ3StGE25x3ch+8e0J2/TF3C7S8s5fH/rOG4fTpz/sF96Nq6cdIRJaWQXSmBa4H/BRoA7wFzqzWRJEmSdknzxtn87PA9OH14d26ZvJi7pi3jkddWcWJ+F84b3ZuOLbynn6RduBw0xvg0MCPGOAL4LpBb7akkSZK0y1rnNuCSr/VnyrhCTt2vKw/OWkHBFUX89tF5rP1oS9LxJCVsV14TCNAshDAE2Ao0qcY8kiRJqiZ5zRryv2MGMulnBRw/pBN3T1/GyMsn8YcnXueDjduSjicpIbtaAi8ADgJuAZ6svjiSJEmqbp1bNuaPJ+zFsxeM4siBHRg/ZQkjLp/E1c+8yYYtJUnHk1TLduU1gcQYS4DrqjmLJEmSalD3Nk245qTB/KigF9dMfJPrnl3InS++xdiRPTntwO40abBLvxpKqmO+8js9hNC1isf6MMboG9NIkiSluD55Tbnp1KHMXbWea555kyueWsDtzy/lhwW9+Pb+3WiYnZl0REk1qCp/7rkTiHz5+wFG4A7grmrIJEmSpFowsFNzbjttX15Z/gFXP/0mv//36/xl6hLOHd2Hk/K7kJO1q68ckpTKvrIExhgLayOIJEmSkjGka0vu+cF+TFu8jqueXsCvHp7Lnycv5vyD+3DcPp3IyrQMSvXJTn9HhxCahBC8RkCSJKmeOaBXax44+wDu/P4wWjXJ4aIH53DYNVN4dPZqyspi0vEkVZOvLIEhhIwQwikhhH+HENYCC4C3QwjzQwhXhBB613xMSZIk1YYQAqP6tuWRc4bz5+8MJTszgx///VWOum4qT817mxgtg1JdV5UzgZOAXsDFQPsYY+cYY1vK3yJiOnBZCOHbNZhRkiRJtSyEwOED2vPE+SO47lv7sG17GWfdPYsxN77A5DfftQxKdVhVSuAhMcbfxRjnxBjLPl4ZY3w/xvhQjPEE4L7qCBNCuDCEEEMIbSoehxDCdSGERSGEORVvUC9JkqRakpEROGbvjjz905Fc/o29WFe8je/d/hIn/Xk6M5asSzqepF1QlRvDlACEEK4D+lF+J9DZwL0xxtcq77M7QghdgMOA5ZVWHwn0qfjYD7i54rMkSZJqUVZmBt/M78Kxgztx38vLuf65RZw0fjoj+rThgkP7sk/XlklHlFRFO/OOoPOBfwHZQH/gnhDCLTHGG6opyzXAOOCRSuvGAHfF8usNpocQWoQQOsQY11TT15QkSdJOyMnK4DsHdOfE/C7cPW0ZN09ezHE3vcghe7ZjZMvSpONJqoKwq9dzhxAaAi/HGAftdogQxgCjY4znhxDeAvJjjO+FEB4D/hhjfL5iv2eBn8cYZ+7gGGOBsQB5eXlDJ0yYsLuxql1xcTG5ublJx5BqlXOvdOXsK11s3h55ZlkJTywtYfN2GNY+k2N759Ax17eVUHpI1Z/3hYWFs2KM+TvatjNnAgEIIZwN9AaaAht24nkTgfY72HQJ8EvKLwXdZTHG8cB4gPz8/FhQULA7h6sRRUVFpGIuqSY590pXzr7SyZHAbzaV8D/3TOLZlWXMfGEzxw/pzPkH96FLq8ZJx5NqVF38eb/TJRB4HDgUOB74Q1WfFGM8ZEfrQwiDgB7A7BACQGfglRDCMGAV0KXS7p0r1kmSJCmFNG+czQl9c/jtKQdwc9Fi7pq+jEdeW8VJ+3bh3MI+tG/eMOmIkipU+Tx9COGBEMKeMcblMcbbgK8Dl+5ugBjjf2KM7WKM3WOM3YGVwJAY49vAo8B3K+4Suj+w3tcDSpIkpa7WuQ34n6P7M+WiQk7atwv3vbyCUVdM4vePzWdd8dak40li584E3g3cF8pP180CcoGyL3/KbnscOApYBGwCTq/hrydJkqRq0L55Q35/7CDOGtmLa59dyO0vLOXel5bz/eE9OHNET5o3zk46opS2qlwCY4yPAo+GEPYG9qb8LOLj1R2o4mzgx8sROKe6v4YkSZJqR5dWjbnyxL05e1Qv/jTxTW6YtIi7pr3F2JE9OX14D5o02JVXJ0naHV95OWgI4f9VfB4ZQmgeY5wdY7wrxnhHjHFtzUeUJElSXde7XS43nDKEx388gmE9WnHl028y4vJJ3Dp1CVtKfGsJqTZV5U8v91V8/gGwdwihMfA65W8YPxuYEWNcUUP5JEmSVI/079iMW7+3L68u/4Crn3mT3//7df4ydQnnju7DSfldyMnyrSWkmvaV32UxxtkVn78bY9yb8jeK/xWwEDgAePjjs4WSJElSVezTtSV3n7EfE8buT5eWjfnVw3MZfVURD8xcwfbSmr7thJTeqnI5aKj8OMZYUumS0AtjjEOBI2osoSRJkuqt/Xu25oGzD+CO0/elZeMcLnpwDof9aQr/mr2asrKYdDypXqrK+fZJIYTzQghdK68MIeSEEEaHEO4Ebq2ZeJIkSarvQggU7NGOR88dzi3fHkpWRuC8v7/KUddN5Zn571B+r0BJ1aUqJfAIoBT4ewhhTQhhfghhKeWXg34L+FOM8aaaDClJkqT6L4TAEQPb88T5I7n25MFsKSnlzLtmctxNL/L8wvcsg1I1qcqNYboBN8cYbwohZANtgM0xxg9rNpokSZLSUWZGYMzgThw1qAMPzVrJdc8u5Nu3zWC/Hq246PA9yO/eKumIUp1WlTOBDwLrQwgzgT8DJwNDQwjtajSZJEmS0lp2ZgYnD+vKpIsK+O3X+7P43Y1845ZpnPbXl5i7an3S8aQ66yvPBMYYB4UQGmkVKnUAABiMSURBVAB7Uf7m8BuBo4EBIQRijO1rOKMkSZLSWIOsTE4b3oNv7tuFO19cxi2TF3P09c9z5MD2XHBoX/rkNU06olSnVOVyUGKMW4GXQwjFMcbzPl4fQmhZY8kkSZKkShrnZPHDgl6cun9Xbpu6lNueX8qT897m2MGd+MkhfejWuknSEaU6YWffjfMzr8aNMX5QjVkkSZKkr9SsYTY/PbQvU8cVMnZkT56Yu4bRV03m4n/MYfWHm5OOJ6W8rzwTGEK4EXil4iN8xe6SJElSrWjZJIeLj9yTM4b34MZJi7j3peU8NGsVp+7flR8V9KZt0wZJR5RSUlUuB50NDAa+CzQNIcwH5gHzgfkxxvtqMJ8kSZL0pdo1a8j/jhnImSN7cv2zi7hr2jImvLSC04Z356yRPWnROCfpiFJKqcqNYcZXfhxC6AwMovxGMUcDlkBJkiQlrnPLxlz2jb04a1RP/jRxIbdMXsw905Zx5siefP+gHuQ2qNLtMKR6ryqXg3bdwep5FR+Vt38YY9xQjdkkSZKkndazbS7XfWsfflTYi6uffpOrn3mTv76wlB8W9OK7B3SnYXZm0hGlRFXlzyF3fsH6j28SEyqW7wDuqoZMkiRJ0m7r174Z47+bz+wVH3Ll0wv4f4+/wa1Tl3Le6N6ctG9XcrJ29h6JUv1QlctBC2s6RAjht8CZwLsVq34ZY3y8YtvFwBlAKfDjGONTNZ1HkiRJ9cfeXVpw9xn7MWPJOq58egG/emQet0xewvmH9OH4fTqRlWkZVHpJpYm/JsY4uOLj4wLYHzgZGAAcAdwUQvD8vSRJknbafj1bc/9ZB3Dn94fRqkkO4x6cw2F/msK/Zq+mrCx+9QGkeiKVSuCOjAEmxBi3xhiXAouAYQlnkiRJUh0VQmBU37Y8eu5wbvn2ULIyAuf9/VW+dv3zTJz/DjFaBlX/hVQY9IrLQU8DNgAzgQtjjB+EEG4ApscY76nY7zbgiRjjgzs4xlhgLEBeXt7QCRMm1FL6qisuLiY3NzfpGFKtcu6Vrpx9paO6OPdlMTJ9TSkPL9rG2k2Rns0z+EbfHPq39uIzVU2qzn1hYeGsGGP+jrbVWgkMIUwE2u9g0yXAdOA9ym8w8zugQ4zx+ztTAivLz8+PM2fOrNb81aGoqIiCgoKkY0i1yrlXunL2lY7q8tyXlJbx0KyVXPfsQlav38IBPVvzs8P7MrRbq6SjKcWl6tyHEL6wBNbam6XEGA+pyn4hhL8Aj1U8XAV0qbS5c8U6SZIkqdpkZ2Zw8rCuHLtPJya8tJwbJi3mhJunUbhHWy48bA8GdmqedESp2qTEawJDCB0qPTwOmFux/ChwcgihQQihB9AHeKm280mSJCk9NMzO5LThPZgyroCfH9GPV5Z/yNHXP8+P/jaLRWs/SjqeVC1q7UzgV7g8hDCY8stB3wLOAogxzgsh3A/MB7YD58QYSxNLKUmSpLTQOCeLHxb04tT9u3Lr1KXcNnUJT859m2P36cRPDu5L19aNk44o7bKUKIExxu98ybZLgUtrMY4kSZIEQLOG2VxwaF9OO7A7t0xezJ0vvsWjr63mm/t24bzRvenQvFHSEaWdlhKXg0qSJEmprFWTHH551J5MGVfIt4Z15YGZKxh1RRG/e2w+7xVvTTqetFMsgZIkSVIV5TVryO+OHchzFxZwzN4d+esLSxl5+SSufGoB6zeXJB1PqhJLoCRJkrSTurRqzJUn7s3TPx1FYb923DBpESMue44bJy1i49btSceTvpQlUJIkSdpFvdvlcuMpQ3j8xyMY1qMVVzy1gJGXT+LWqUvYUuL9DJWaLIGSJEnSburfsRm3fm9f/vGjA+nXoSm///frFFxRxN9mLKOktCzpeNJnWAIlSZKkajKka0v+9oP9uffM/ejYoiGX/HMuB181mX+8spLSsph0PAmwBEqSJEnV7sBebXjohwfy19P2pWnDLC64fzZH/GkKT/xnDTFaBpUsS6AkSZJUA0IIFPZrx7/OPYibTh1CBH74t1f4+g3PM2nBWsugEmMJlCRJkmpQRkbgqEEdeOonI7nqxL1Zv7mE0//6MifeMo1pi9clHU9pyBIoSZIk1YLMjMAJQzvz7AUF/P7Ygaz4YBPf+st0vn3rDF5b8WHS8ZRGLIGSJElSLcrJyuDb+3dj8kWF/M/X9mT+mg0ce+ML/ODOmby+ZkPS8ZQGLIGSJElSAhpmZ/KDET2ZMq6QCw/ty4yl6zjy2qmce+8rLH63OOl4qscsgZIkSVKCchtkcd7BfXh+3GjOKezFc2+s5dCrJ3PRA7NZ+cGmpOOpHrIESpIkSSmgeeNsLjq8H1PGFXLagT14ZPZqCq8s4tePzGXthi1Jx1M9YgmUJEmSUkib3Ab8+uv9KfpZAd8Y2oV7Zyxn5BWT+MPjr/PBxm1Jx1M9kDIlMIRwXgjhjRDCvBDC5ZXWXxxCWBRCWBBCODzJjJIkSVJt6diiEX84fhDPXjiKIwd2YPzUJYy4fBLXPPMmH20pSTqe6rCUKIEhhEJgDLB3jHEAcGXF+v7AycAA4AjgphBCZmJBJUmSpFrWrXUTrjlpME/9ZCQH9W7Dtc8uZMTlk7hl8mI2bytNOp7qoJQogcAPgT/GGLcCxBjXVqwfA0yIMW6NMS4FFgHDEsooSZIkJaZvXlNu+c5Q/nXuQezduQV/fOINRl4xiTtffIut2y2DqrpUKYF9gREhhBkhhMkhhH0r1ncCVlTab2XFOkmSJCktDercnDu/P4z7zzqAHm2a8JtH5zH6ysnc//IKtpeWJR1PdUCIMdbOFwphItB+B5suAS4FJgE/BvYF7gN6AtcD02OM91Qc4zbgiRjjgzs4/lhgLEBeXt7QCRMm1MR/xm4pLi4mNzc36RhSrXLula6cfaUj5772xRiZt66Uh94sYemGMto3DhzbJ4dh7TPJCCHpeGkhVee+sLBwVowxf0fbaq0EfpkQwpPAZTHGSRWPFwP7Az8AiDH+oWL9U8BvY4zTvux4+fn5cebMmTUbehcUFRVRUFCQdAypVjn3SlfOvtKRc5+cGCNPz3+Hq59+kwXvfES/9k258LA9OGTPdgTLYI1K1bkPIXxhCUyVy0EfBgoBQgh9gRzgPeBR4OQQQoMQQg+gD/BSYiklSZKkFBRC4PAB7Xn8/BFce/JgtpSUcuZdMznuphd5fuF7pMKJH6WOrKQDVLgduD2EMBfYBnwvlk/qvBDC/cB8YDtwTozRV71KkiRJO5CZERgzuBNHDerAQ7NWct2zC/n2bTPYv2crLjp8D4Z2a5V0RKWAlCiBMcZtwLe/YNullL9mUJIkSVIVZGdmcPKwrhw3pBN/n7GcGyYt5oSbp1G4R1suPGwPBnZqnnREJShVLgeVJEmSVM0aZGVy2vAeTBlXwM+P6Mcryz/k6Ouf50d/m8WitR8lHU8JsQRKkiRJ9VzjnCx+WNCLqT8v5McH92Hygnc57JopXHD/ayxftynpeKpllkBJkiQpTTRrmM0Fh/Zl6s9H84MRPfn3nDWMvqqIS/75H95evyXpeKollkBJkiQpzbRqksMvj9qTKeMKOWW/rtw/cwWjrpjE7x+bz7rirUnHUw2zBEqSJElpKq9ZQ/5vzECeu7CAY/buyO0vLGXk5ZO46ukFrN9cknQ81RBLoCRJkpTmurRqzBUn7s0zF4yisF87rn9uESMue44bJy1i49btScdTNbMESpIkSQKgV9tcbjhlCI//eATDerTiiqcWMOqKSdz2/FK2lPh23fWFJVCSJEnSZ/Tv2Ixbv7cv//jRgezRvim/e2w+hVcWce+M5ZSUliUdT7vJEihJkiRph4Z0bcnffrA/9565Hx2aN+SX//wPh1w9mX++upLSsph0PO0iS6AkSZKkL3VgrzY89MMDuf20fJrkZPHT+2Zz5LVTeHLuGmK0DNY1lkBJkiRJXymEwOh+eTx23kHceMoQSssiZ9/zCsfc8AJFC9ZaBusQS6AkSZKkKsvICHxtrw489ZORXPGNvfhg0zZO++vLnPTn6cxYsi7peKoCS6AkSZKknZaVmcGJ+V147sICfjdmAG+t28hJ46fzndtmMHvFh0nH05ewBEqSJEnaZTlZGXzngO5MvqiQXx7Vj7mr1jPmxhcYe9dMFrz9UdLxtAOWQEmSJEm7rVFOJmNH9mLKuEJ+ekhfpi1exxHXTuH8Ca/y1nsbk46nSiyBkiRJkqpN04bZnH9IH6aMK+Sskb14at7bHHz1ZH7x0BxWfbg56XgiRUpgCOG+EMJrFR9vhRBeq7Tt4hDCohDCghDC4UnmlCRJklQ1LZvk8Isj+zFlXCHf2b8b/3hlFYVXFPHbR+fx7kdbk46X1rKSDgAQYzzp4+UQwlXA+orl/sDJwACgIzAxhNA3xliaSFBJkiRJO6Vd04b89pgBnDmyJ9dNXMjd05dx38srOG14d84a2ZMWjXOSjph2UuJM4MdCCAH4JvD3ilVjgAkxxq0xxqXAImBYUvkkSZIk7ZpOLRpx2Tf2YuIFozi0fx63TF7MiMsmcd2zCyneuj3peGklpNKbOoYQRgJXxxjzKx7fAEyPMd5T8fg24IkY44M7eO5YYCxAXl7e0AkTJtRe8CoqLi4mNzc36RhSrXLula6cfaUj5147Y8VHZfxj4TZeXVtK02w4qmcOB3fNIiczJB1tp6Tq3BcWFs76uFd9Xq1dDhpCmAi038GmS2KMj1Qsf4tPzwLulBjjeGA8QH5+fiwoKNiVw9SooqIiUjGXVJOce6UrZ1/pyLnXzvoO8NqKD7nq6QXct+A9itYEzh3dh5Pyu5CTlVIXLX6hujj3tVYCY4yHfNn2EEIWcDwwtNLqVUCXSo87V6yTJEmSVA8M7tKCu8/Yj+lL1nHlUwv41cNz+fPkxfzkkL4cO7gjWZl1owzWJan0L3oI8EaMcWWldY8CJ4cQGoQQegB9gJcSSSdJkiSpxuzfszUPnH0Afz19X1o0zuZnD8zm8D9N4bE5qykrS52XsNUHqVQCT+Zzl4LGGOcB9wPzgSeBc7wzqCRJklQ/hRAo3KMd/zr3IG4+dQgZIXDuva9y9PXP8+zr75BK9zOpy1LiLSIAYoynfcH6S4FLazeNJEmSpKSEEDhyUAcOG9CeR2ev4ppnFnLGnTMZ0rUFPztsDw7s3SbpiHVaKp0JlCRJkqRPZGYEjtunM89eOIr/d9wgVn+4hVNuncEpf5nOK8s/SDpenWUJlCRJkpTSsjMzOGW/rhRdVMCvju7Pgrc/4vibXuSMO15m3ur1ScercyyBkiRJkuqEhtmZnHFQD6aMK+Siw/fg5bfe52vXPc85977C4neLk45XZ1gCJUmSJNUpTRpkcU5hb6b+fDTnFvZm0htrOfTqyfzsgdmseH9T0vFSniVQkiRJUp3UvFE2Pzt8D6aMK+T04T14dPZqRl9VxK8fmcvaDVuSjpeyLIGSJEmS6rQ2uQ341dH9mXxRASfmd+HeGcsZecUk/vD463ywcVvS8VKOJVCSJElSvdCheSP+33GDePbCURw1sAPjpy5hxOWTuOaZN/loS0nS8VKGJVCSJElSvdKtdROuPmkwT/9kJCP6tOHaZxcy4vJJ3DJ5MZu3lSYdL3GWQEmSJEn1Up+8ptz87aE8dt5BDO7Sgj8+8QYjr5jEnS++xdbt6VsGLYGSJEmS6rWBnZpzx+nDeODsA+jZpgm/eXQeo6+czP0vr2B7aVnS8WqdJVCSJElSWti3eysmjN2fu88YRpvcHMY9NIdDr5nCo7NXU1YWk45XayyBkiRJktJGCIERfdry8DnDGf+doeRkZvDjv7/KUddN5Zn57xBj/S+DlkBJkiRJaSeEwGED2vPE+SO49uTBbCkp5cy7ZnLsTS/y/ML36nUZtARKkiRJSlsZGYExgzvxzAWj+OPxg3h3wxa+fdsMvvWX6cxa9n7S8WqEJVCSJElS2svOzODkYV2ZdFEBv/l6fxat3cgJN0/j9L++xNxV65OOV60sgZIkSZJUoUFWJqcP78GUcQX8/Ih+vLL8Q46+/nl+9LdZLFr7UdLxqkVKlMAQwuAQwvQQwmshhJkhhGEV60MI4boQwqIQwpwQwpCks0qSJEmq/xrnZPHDgl5MGVfIj0f3ZvKCdznsmilccP9rLF+3Kel4uyUlSiBwOfC/McbBwK8rHgMcCfSp+BgL3JxMPEmSJEnpqHmjbC44bA+mjCvkjIN68O85axh9VRGX/PM/vL1+S9LxdkmqlMAINKtYbg6srlgeA9wVy00HWoQQOiQRUJIkSVL6ap3bgEu+1p8p4wo5eVgX7nt5BaOumMTf39jKlpLSpOPtlJAKtz4NIewJPAUEyovpgTHGZSGEx4A/xhifr9jvWeDnMcaZOzjGWMrPFpKXlzd0woQJtZa/qoqLi8nNzU06hlSrnHulK2df6ci5Vzp5d1MZDy8qYeWGEn47vAkhhKQjfUZhYeGsGGP+jrZl1VaIEMJEoP0ONl0CHAz8NMb4UAjhm8BtwCE7c/wY43hgPEB+fn4sKCjYvcA1oKioiFTMJdUk517pytlXOnLulW5OBCY+N4nCwsKko+yUWiuBMcYvLHUhhLuA8ysePgDcWrG8CuhSadfOFeskSZIkKXFZGal1BrAqUuU1gauBURXLo4GFFcuPAt+tuEvo/sD6GOOaJAJKkiRJUn1Qa2cCv8KZwLUhhCxgCxWv7QMeB44CFgGbgNOTiSdJkiRJ9UNKlMCKG78M3cH6CJxT+4kkSZIkqX5KlctBJUmSJEm1wBIoSZIkSWnEEihJkiRJacQSKEmSJElpJJTfe6V+CSG8Cyz7it2aA+ureMiq7vtV+7UB3qvi16zLdubftq5mqK7j785xduW5zn3Nce5r5zh1Ze4hPWbfua+9Y+3sc537mpMKcw81m6Ouzv3OPqcq+9blue8WY2y7wy0xxrT8AMZX975ftR8wM+n/7lT7t62rGarr+LtznF15rnOf+jORyhmc+53bLx1m37mvvWPt7HOd+7oxE6mao67O/c4+p4ozXS/nPp0vB/1XDey7M8esz1Lh36GmM1TX8XfnOLvyXOe+5qTCv4Nzv/vPce53Tir8O9SVud/dY+3sc537mpMq/w41maOuzv3OPqcq+6bK/97Vql5eDpqqQggzY4z5SeeQapNzr3Tl7CsdOfdKR3Vx7tP5TGASxicdQEqAc6905ewrHTn3Skd1bu49EyhJkiRJacQzgZIkSZKURiyBkiRJkpRGLIGSJEmSlEYsgSkihHBsCOEvIYT7QgiHJZ1Hqg0hhJ4hhNtCCA8mnUWqSSGEJiGEOyt+zp+adB6ptvhzXumoLvxebwmsBiGE20MIa0MIcz+3/ogQwoIQwqIQwi++7BgxxodjjGcCZwMn1WReqTpU09wviTGeUbNJpZqxk98DxwMPVvycP6bWw0rVaGdm35/zqi92cu5T/vd6S2D1uAM4ovKKEEImcCNwJNAf+FYIoX8IYVAI4bHPfbSr9NT/qXielOruoPrmXqqL7qCK3wNAZ2BFxW6ltZhRqgl3UPXZl+qLO9j5uU/Z3+uzkg5QH8QYp4QQun9u9TBgUYxxCUAIYQIwJsb4B+Dozx8jhBCAPwJPxBhfqdnE0u6rjrmX6rKd+R4AVlJeBF/DP8CqjtvJ2Z9fu+mkmrEzcx9CeJ0U/73e/yOqOZ349K++UP4LQKcv2f884BDgGyGEs2symFSDdmruQwitQwi3APuEEC6u6XBSLfii74F/ACeEEG4G/pVEMKmG7XD2/Tmveu6Lfuan/O/1nglMETHG64Drks4h1aYY4zrKr5eX6rUY40bg9KRzSLXNn/NKR3Xh93rPBNacVUCXSo87V6yT6jPnXunO7wGlK2df6ajOzr0lsOa8DPQJIfQIIeQAJwOPJpxJqmnOvdKd3wNKV86+0lGdnXtLYDUIIfwdmAbsEUJYGUI4I8a4HTgXeAp4Hbg/xjgvyZxSdXLule78HlC6cvaVjurb3IcYY9IZJEmSJEm1xDOBkiRJkpRGLIGSJEmSlEYsgZIkSZKURiyBkiRJkpRGLIGSJEmSlEYsgZIkSZKURiyBkiRJkpRGLIGSJEmSlEYsgZIkVZMQwjEhhIc+t+6HIYTrk8okSdLnWQIlSao+lwK/+dy6xcCeCWSRJGmHLIGSJFWDEMLeQEaMcW4IoVsI4YcVm7KBmGA0SZI+wxIoSVL1GAzMqlg+FOhTsdwfmJ1IIkmSdsASKElS9cgAckMImcDxQNMQQiPgNODeJINJklSZJVCSpOrxONATeA24BRgAzATGxxhfSTKYJEmVhRh9mYIkSZIkpQvPBEqSJElSGrEESpIkSVIasQRKkiRJUhqxBEqSJElSGrEESpIkSVIasQRKkiRJUhqxBEqSJElSGrEESpIkSVIa+f8E07E7KjbYEQAAAABJRU5ErkJggg==\n", 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\n", 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" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "code", "metadata": { "id": "mJcaKjZIJAhE", "colab_type": "code", "colab": {} }, "source": [ "" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "V3ozKyAz0xXg", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 549 }, "outputId": "3bc4f02d-5202-4f3a-ecb9-966cd4c37a33" }, "source": [ "# Parametros de la transf. del ejercicio 3c\n", "seda = 0.03\n", "wn = 50\n", "\n", "polos = [0, -2,\n", " -seda*wn+1j*wn*np.sqrt(1-seda**2), -seda*wn-1j*wn*np.sqrt(1-seda**2)]\n", "ceros = [-10]\n", "G = -50**2\n", "\n", "# Definimos la transferencia\n", "H3c = ZerosPolesGain(ceros, polos, G)\n", "\n", "ww = np.logspace(-2.0, 4.0, num=1000)\n", "\n", "\n", "# Hacer bode\n", "w, mag, fase = H3c.bode(ww)\n", "\n", "# Graficas:\n", "# Módulo\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, mag)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$|H(j\\omega)|_{dB}$')\n", "plt.show()\n", "# Fase\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, fase)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$Arg(H(j\\omega))$')\n", "plt.show()\n" ], "execution_count": 16, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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\n", 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\n", "\n", "Otra forma de definir transferencias es con la función *TransferFunction* del mismo módulo [(link)](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.TransferFunction.html). A ésta hay que pasarle los coeficientes del numerador y denominador.\n", "\n", "A modo de ejemplo, mostramos el ejercicio 3a)." ] }, { "cell_type": "code", "metadata": { "id": "6yeEdf42vRe5", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 549 }, "outputId": "3b91056c-0366-40e3-900c-5d80eca5c48a" }, "source": [ "num = [2, 2]\n", "den = [0.1, 1]\n", "\n", "Ha = TransferFunction(num, den)\n", "w, mag, fase = Ha.bode()\n", "\n", "# Graficas:\n", "# Módulo\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, mag)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$|H(j\\omega)|_{dB}$')\n", "plt.show()\n", "# Fase\n", "plt.figure(figsize=(15,4))\n", "plt.semilogx(w, fase)\n", "plt.grid()\n", "plt.xlabel('$\\omega$')\n", "plt.ylabel('$Arg(H(j\\omega))$')\n", "plt.show()\n" ], "execution_count": 7, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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+Ele+fjKlxV4FlLR/BkFJkqQeKplK84O/LeNHf1vKmEF9uf2K0zhx7KB8lyWpBzAISpIk9UBrtu3hP26bz/w1O3nHiWP4yluPoV95Sb7LktRDGAQlSZJ6kBgjd85bz5d+t5BEIvDDi6bxlqmj8l2WpB7GIChJktRD7NrTwhfufpp7n9rI9AmD+e67T2D0wD75LktSD2QQlCRJ6gHmrdnBx349n021jXz6TUdyxesO9+Hwkg6aQVCSJKkbS6cjv3h4Bf/3p+cYMaCc2684jWlOCCPpEOVsXuEQwmEhhL+HEBaFEJ4JIfxHtn1wCOH+EMLS7LLNd7YQwiXZPktDCJfkqm5JkqR82VHfzGU3zeHr9z3LG46u4g9XvcYQKKlT5PKKYBL4ZIxxXgihHzA3hHA/cCnw1xjjNSGEzwKfBT7T+sAQwmDgy0A1ELPH3hNj3JHD+iVJknLmiVXbuerW+Wyra+a/3zqFi08bRwjeCiqpc+TsimCMcWOMcV52fTewGBgNvA24MdvtRuDtbRz+JuD+GOP2bPi7Hzir66uWJEnKrXQ68uOaZVw46zFKixPc8ZFXccmrxhsCJXWqvHxGMIQwHpgGPA5UxRg3Znc9D1S1cchoYG2r7XXZNkmSpF5jW10Tn/jNk/xjyRbefPxIrjn/OJ8NKKlL5DwIhhAqgTuAj8cYa1v/dSvGGEMI8RDPfzlwOUBVVRU1NTWHcrouUVdX1y3rkrqS416FyHGvjli2M8WPFzRR2xy5+JhSZo7cxdzHHsl3WR3muFeh6mljP6dBMIRQQiYE3hJjvDPbvCmEMDLGuDGEMBLY3Mah64EZrbbHADVtvUaMcRYwC6C6ujrOmDGjrW55VVNTQ3esS+pKjnsVIse92iPGyK8eW803nljEiAHl3PShkzh29IB8l3XQHPcqVD1t7Ody1tAAXAcsjjF+p9Wue4C9s4BeAvyujcP/DJwZQhiUnVX0zGybJElSj7WnOcnHb1vAl373DK+ZPIx7r3xNjw6BknqOXF4RfDXwfuDpEMKCbNvngWuA34QQPgisBt4FEEKoBq6IMV4WY9weQvgq8ET2uKtjjNtzWLskSVKnWr6ljo/cPJelm+v41JlH8NEZk0j4gHhJOZKzIBhjfBjY37vbGW30nwNc1mr7euD6rqlOkiQpd/749EY+/dunKC1OcNMHpvOaycPyXZKkApOXWUMlSZIKUTKV5ht/epafP7SSqYcN5CfvPZFRA/vkuyxJBcggKEmSlAPb6pq48tfzeXTFNt5/6ji+eO7RlBUX5bssSQXKIChJktTFFq7fxYd/NZctdU18651TueCkMfkuSVKBMwhKkiR1obvnr+czdzzF4IpSfnvFaRw/ZmC+S5Ikg6AkSVJXSKbS/O8fn+W6h1cyfcJgfvzeExlaWZbvsiQJMAhKkiR1utafB7z0VeP5wpuPpqQoZ49vlqRXZBCUJEnqRH4eUFJPYBCUJEnqJPc8uYFP3/6knweU1O0ZBCVJkg5ROh359v3Pce3fl1M9bhA/ed9JDOvn5wEldV8GQUmSpENQ15Tk47MX8MDiTVx48mFc/bZjKS3284CSujeDoCRJ0kFas20Pl930BMu31PPfb53CxaeNI4SQ77Ik6RUZBCVJkg7CP5dv5aO3zCNGuOkD03n1pKH5LkmS2s0gKEmS1AExRm5+bDVf+f0iJg6t4BeXVDNuSEW+y5KkDjEISpIktVNLKs2X73mGXz++hjOOGs73LjyBfuUl+S5LkjrMIChJktQOO/c089Fb5vHP5dv4yIzD+dSZR1KU8POAknqmDgfBEMLRwJgY4/0hhD4xxoYuqEuSJKnbWL6ljg/e8AQbdjbynXdN5fwTfUi8pJ7tYK4I/hC4N4TwUSAZQlgcY/zSKx0UQrgeOBfYHGM8Ntt2G3BktstAYGeM8YQ2jl0F7AZSQDLGWH0QdUuSJHXYQ0u38NFb5lFalODWy0/hpHGD812SJB2yg3nIzaIY4/eAjTHGdwLtfTe8ATirdUOM8d0xxhOy4e8O4M4DHD8z29cQKEmScuKmR1dx6S+fYPTAPvzuylcbAiX1GgdzRfC0EMKPgEkhhOOAdt0cH2N8MIQwvq19IfPAnXcBrz+IeiRJkjpVSyrN1b9fxK8eW80bjh7O9y6cRmWZUytI6j1CjLFjB4TwPmAlMAw4ETgxxnhuO48dD9y799bQVu2vBb6zv6t9IYSVwA4gAj+LMc46wGtcDlwOUFVVddLs2bPbU1pO1dXVUVlZme8ypJxy3KsQOe57pvqWyI8XNPLMtjTnTCjhgiNKSPiQ+HZz3KtQddexP3PmzLlt5ayD+dPWZuC/gTJgK7DwEGsDuAi49QD7T48xrg8hDAfuDyE8G2N8sK2O2ZA4C6C6ujrOmDGjE8rrXDU1NXTHuqSu5LhXIXLc9zyrttbzgRufYO3OyDcvOJ53Vh+W75J6HMe9ClVPG/sd/oxgjPEvwOMxxtcAFwOHFHtDCMXA+cBtB3jN9dnlZuAuYPqhvKYkSdK+Hl+xjbf/+BG21zdz8wdPMQRK6tUOZrIYgP4hhBOBJqDiEGt4A/BsjHFdWztDCBUhhH5714Ez6ZyrkJIkSQDcPmct77vucQZXlHL3R1/NKROH5LskSepSBxsEPwGcDvwU+FN7Dggh3Ao8ChwZQlgXQvhgdteF7HNbaAhhVAjhvuxmFfBwCOFJ4F/AH2KM7XpNSZKkA0mnI9/407N8+rdPMX3CYO76yKsZP/RQ/8YtSd3fQU1/FWNsAX7QwWMu2k/7pW20bQDOya6vAKZ2vEpJkqT9a2hO8Z+3LeBPzzzPe04Zy3+/dQolRQf7N3JJ6lleMQiGEMa281w7Y4y1h1iPJElSl9tU28hlN85h4YZdfPHNR/PB0ycQnBlUUgFpzxXBG8k8tuFA746RzAPjb+qEmiRJkrrMMxt28cEb5lDb2MLP31/NG46pyndJkpRzrxgEY4wzc1GIJElSV3tg0Saumj2fAX1K+O0Vr+KYUf3zXZIk5UWHPyOYnbmzMcaY6oJ6JEmSOl2MkesfWcX//GERx44awHWXVDO8f3m+y5KkvGnPZwQTZGb2fC9wMtAMlIUQtgB/AH4WY1zWpVVKkiQdpGQqzVd+/ww3P7aGN02p4rvvPoG+pQc1X54k9RrteRf8O/AA8DlgYYwxDRBCGAzMBL4RQrgrxnhz15UpSZLUcbWNLfz7LfN4aOlWPvy6iXzmTUeRSDgpjCS1Jwi+Ifu4iJeIMW4H7gDuCCGUdHplkiRJh2Dt9j184IYnWLm1nm+84zjefXJ7J0KXpN6vPZPFtACEEH4AHEVmhtAngV/HGBe07iNJktQdzFuzg8tvmkNzMs1NH5jOqyYNzXdJktStdOQG+UXA74ES4Bjg5hDCT2OMP+qSyiRJkg7C75/cwCdvf5IR/cuZffnJTBpeme+SJKnbaXcQjDH+tNXmfSGEHwFPAAZBSZKUdzFGrv37Mr71lyVUjxvErIurGVxRmu+yJKlbOpjHR1wBTAL6AbWdXpEkSVIHNSVTfO7Op7lz3nrefsIovnHB8ZQVF+W7LEnqtg5m7uT7gDcC5wP/27nlSJIkdcyO+mY+fPNc/rVyO//5hiO46oxJhODMoJJ0IIn2dgwh3B5CODrGuCbGeB3wFuBrXVeaJEnSga3YUsd5P36EBWt28v0LT+A/3jDZEChJ7dCRK4K/Am4LmXfXuUAlkO6SqiRJkl7BYyu28eFfzaUoEfj1h06hevzgfJckST1GRyaLuQe4J4QwFZhK5mrifV1VmCRJ0v7cPmctn7/racYNqeD6S05m7JC++S5JknqUVwyCIYSvxxg/H0J4LfBkjPFJMs8RlCRJyql0OvLNvzzHT2qWc/qkoVz73hMZ0Kck32VJUo/Tns8I3pZdXgY8GEJYGkK4J4Tw1RDCBSGEw9rzQiGE60MIm0MIC1u1fSWEsD6EsCD7dc5+jj0rhPBcCGFZCOGz7Xk9SZLUuzQ0p/joLfP4Sc1y3nPKWH75bycbAiXpIL3iFcHsFUBijBcDhBD2PlB+KnAa8LkQwp9jjJ9/hVPdQOaZgzft0/7dGOO39ndQCKEIuJbMTKXrgCdCCPfEGBe9Uu2SJKl32FTbyGU3zmHhhl188c1H88HTJzgpjCQdgvbcGhpijHHvdoyxhcytoU+26jMPOGAQjDE+GEIYfxA1TgeWxRhXZF9rNvA2wCAoSVIBeGbDLi67cQ67Glr4+furecMxVfkuSZJ6vPZMFvP3EMIdwO9ijGv2NoYQSoHTgUuAXxxCDVeGEC4G5gCfjDHu2Gf/aGBtq+11wCn7O1kI4XLgcoCqqipqamoOobSuUVdX1y3rkrqS416FyHF/6OZvTvLTJ5uoKAl8prqM4s2Lqdm8ON9l6QAc9ypUPW3stycIngV8ALg1hDAR2AH0IfP5wr8A34sxzj/I1/8J8FUgZpffzr7WQYsxzgJmAVRXV8cZM2Ycyum6RE1NDd2xLqkrOe5ViBz3By/GyHUPr+QH8xdz3OgB/OLiaob3L893WWoHx70KVU8b++0JguOAn8QYf5z9fOBQoCHGuPNQXzzGuGnvegjh58C9bXRbD7SekGZMtk2SJPVCzck0X/rdQmY/sZazpozgu+8+gT6lRfkuS5J6lfYEwd8C40IIS4CngKeBp0IIT8cYNx/Ki4cQRsYYN2Y3zwMWttHtCWByCGECmQB4IfCeQ3ldSZLUPe2ob+Yjt8zlsRXb+feZh/PJNx5JIuGkMJLU2doza+hxIYQy4HgyD5CvB84FpoQQiDGOaM8LhRBuBWYAQ0MI64AvAzNCCCeQuTV0FfDhbN9RwC9ijOfEGJMhhCuBPwNFwPUxxmc69s+UJEnd3bLNdVx24xNs2NnId989lfOmjcl3SZLUa7XniiAxxiYyj22oizF+bG97CGFQe18oxnhRG83X7afvBuCcVtv3kQmhkiSpF3po6RY+ess8SosS3Hr5KZw0bnC+S5KkXq1dQbCV+JKNl8/wKUmS1CG/enQVX/n9IiYNq+S6S6sZM6hvvkuSpF6vPc8RvBaYl/3yJn1JktQpkqk0V9+7iJseXc0ZRw3n+xdNo7Kso3+jliQdjPa82z4JnABcDPQLISwCniHzQPdFMcbburA+SZLUC+3a08KVt87joaVb+dBrJvDZs4+myElhJCln2jNZzKzW2yGEMcBxZCaPORcwCEqSpHZbvqWOy26cw7ode/jGO47j3SePzXdJklRw2nNraFvvzs9kv1rv3xljrO3E2iRJUi/zjyVbuPLXmUlhfv2hUzl5vJPCSFI+tOfW0Bv307534piQXb8BuKkTapIkSb1MjJHrHl7J1+9bzJEj+vPzi09yUhhJyqP23Bo6MxeFSJKk3qkpmeKLdy3k9rnrOGvKCL79rqlUOCmMJOWV78KSJKnLbNndxBU3z2Xu6h1cdcZkPn7GZBJOCiNJeWcQlCRJXWLh+l1cftMctu9p5tr3nMibjx+Z75IkSVkGQUmS1Ol+t2A9n7njKQb1LeW3V7yKY0cPyHdJkqRWDIKSJKnTJFNp/u/PzzHrwRVMnzCYH7/3RIZWluW7LEnSPgyCkiSpU+zc08zHbp3PQ0u3cvFp4/ivc4+hpCiR77IkSW0wCEqSpEP27PO1XH7TXJ7f1ehD4iWpBzAISpKkQ3Lf0xv51O1PUllWzOwPn8qJYwfluyRJ0iswCEqSpIOSSke+c/9zXPv35UwbO5Cfve8khvcvz3dZkqR2MAhKkqQO21HfzFWzM58HfHf1YVz99imUFRfluyxJUjvlLAiGEK4HzgU2xxiPzbZ9E3gL0AwsB/4txrizjWNXAbuBFJCMMVbnqm5JkvRST6/bxRU3z2XL7ib+9/zjuGi6nweUpJ4ml1N53QCctU/b/cCxMcbjgSXA5w5w/MwY4wmGQEmS8ue2J9bwjp/+kxgjt19xmiFQknqonF0RjDE+GEIYv0/bX1ptPgZckKt6JElS+zW2pPjKPc8w+4m1nD5pKD+4aBqDK0rzXZYk6SCFGGPuXiwTBO/de2voPvt+D9wWY7y5jX0rgR1ABH4WY5x1gNe4HLgcoKqq6qTZs2d3TvGdqK6ujsrKynyXIeWU416FqLeM+60NaX40v4lVtf/S0JUAABUYSURBVGnOnVjC+ZNLSISQ77LUTfWWcS91VHcd+zNnzpzb1l2V3WKymBDCF4AkcMt+upweY1wfQhgO3B9CeDbG+GBbHbMhcRZAdXV1nDFjRleUfEhqamrojnVJXclxr0LUG8b9g0u28LXZ80mmEsx6/zTOnDIi3yWpm+sN4146GD1t7Oc9CIYQLiUzicwZcT+XJ2OM67PLzSGEu4DpQJtBUJIkHbpUOvL9B5bww78vY/LwSn76vpOYOKz7/aVbknRw8hoEQwhnAf8PeF2Mcc9++lQAiRjj7uz6mcDVOSxTkqSCsnl3I/9x6wIeXbGNC04aw9Vvm0Lf0rz/7ViS1Ily+fiIW4EZwNAQwjrgy2RmCS0jc7snwGMxxitCCKOAX8QYzwGqgLuy+4uBX8cY/5SruiVJKiT/XLaVq2YvoK6phW9ecDzvrD4s3yVJkrpALmcNvaiN5uv203cDcE52fQUwtQtLkySp4KXSkR/+bSnf/+tSJg6t4JbLTuHIEf3yXZYkqYt4n4ckSQVuy+4m/vO2BTy8bCvnTRvN/7z9WCrK/BVBknoz3+UlSSpg/1y+lY/PXsCuhha+8Y7jeFf1YQQfDSFJvZ5BUJKkAtSSSvPd+5fwk38sZ8LQCm78wHSOHtk/32VJknLEIChJUoFZva2eq2Yv4Mm1O7nw5MP40luOcVZQSSowvutLklRA7pq/jv+6+xkSAX783hM557iR+S5JkpQHBkFJkgrA7sYW/uvuhdy9YAPTxw/muxeewOiBffJdliQpTwyCkiT1cvPW7OA/Zs9nw85GPvHGI/j3mZMoSjghjCQVMoOgJEm9VEsqzQ//toxr/76MEf3L+c2HT+WkcYPzXZYkqRswCEqS1Ast2bSbT/xmAQvX13L+tNF8+a1TGNCnJN9lSZK6CYOgJEm9SCodue7hFXzrL0voV1bMT993EmcdOyLfZUmSuhmDoCRJvcSabXv41O1P8q9V2znzmCq+fv5xDK0sy3dZkqRuyCAoSVIPF2Pk1n+t5X/+sIiiEPj2O6dy/omjCcEJYSRJbTMISpLUg63bsYfP37WQB5ds4fRJQ/m/C45nlI+FkCS9AoOgJEk9UCoduenRVXzzz88BcPXbpvC+U8aR8LEQkqR2MAhKktTDLNm0m8/c8RTz1+xkxpHD+Np5x/lweElShyRy+WIhhOtDCJtDCAtbtQ0OIdwfQliaXQ7az7GXZPssDSFckruqJUnqHpqTab73wBLe/IOHWLW1nu++eyq/vPRkQ6AkqcNyGgSBG4Cz9mn7LPDXGONk4K/Z7ZcIIQwGvgycAkwHvry/wChJUm80b80Ozv3hQ3zvgaWcfexIHvjE6zhv2hgnhJEkHZSc3hoaY3wwhDB+n+a3ATOy6zcCNcBn9unzJuD+GON2gBDC/WQC5a1dVKokSd3Crj0tfPv+5/jVY6sZ0b+c6y+t5vVHVeW7LElSD9cdPiNYFWPcmF1/Hmjr/26jgbWtttdl2yRJ6pXS6cgd89ZxzR+fZceeZi45bTyfPPMI+pWX5Ls0SVIv0B2C4AtijDGEEA/lHCGEy4HLAaqqqqipqemM0jpVXV1dt6xL6kqOexWigx33q2tT/GpRM8t2ppk0MMFVp5Uzrv8W5j62pfOLlDqZ7/cqVD1t7HeHILgphDAyxrgxhDAS2NxGn/W8ePsowBgyt5C+TIxxFjALoLq6Os6YMaOtbnlVU1NDd6xL6kqOexWijo77XQ0tfOcvmdtAB/Ut5ZsXHMU7ThzjIyHUo/h+r0LV08Z+dwiC9wCXANdkl79ro8+fga+3miDmTOBzuSlPkqSulU5H7py/nmv+uJjt9c2879RxfPKNRzKgr7eBSpK6Rk6DYAjhVjJX9oaGENaRmQn0GuA3IYQPAquBd2X7VgNXxBgvizFuDyF8FXgie6qr904cI0lST/bYim187Q+LeXr9LqaNHcgN/zadY0cPyHdZkqReLtezhl60n11ntNF3DnBZq+3rgeu7qDRJknJq+ZY6/ve+Z3lg8SZGDijn2++cynnTRnsbqCQpJ7rDraGSJBWMbXVN/OCvS7nl8TWUFSf49JuO5IOnT6C8pCjfpUmSCohBUJKkHGhsSXHDP1dx7d+WsaclxYUnH8bH33AEw/qV5bs0SVIBMghKktSFWlJpbp+zjh/9bSkbdjVyxlHD+ezZRzG5ql++S5MkFTCDoCRJXSCZSvPQuhb+69s1rN3ewAmHDeRb75zKqyYNzXdpkiQZBCVJ6kypdOT3T27g+39dysqtzRw3egBXX3osM44cRghOBCNJ6h4MgpIkdYJ0OnLfwo1874GlLNtcx1Ej+nHVtDL+812vNgBKkrodg6AkSYegOZnm7vnr+dmDy1m+pZ5Jwyu59j0ncvaxI3jwwX8YAiVJ3ZJBUJKkg7C7sYVb/7WG6x5eyabaJo4e2Z/vX3gC5x4/iiKfBShJ6uYMgpIkdcDm3Y3c8MgqfvXYanY3Jjlt4hD+74KpvHbyUK/+SZJ6DIOgJEntsGTTbn75yCrumLeOllSas48dwYdfezhTDxuY79IkSeowg6AkSfvRkkrzl2c2cdOjq3h85XZKixNccNIYPvSaiUwYWpHv8iRJOmgGQUmS9rG5tpFf/2sNt/5rDZtqmxgzqA+fPfso3lV9GIMrSvNdniRJh8wgKEkSmcc/PL5yOzc/vpo/L3yeZDryuiOG8fXzxjHjyOFOACNJ6lUMgpKkgrZm2x7umLeOO+evY+32BvqXF3Ppq8bzvlPHMd7bPyVJvZRBUJJUcOqaktz39EZ+O3cd/1q5nRDg1YcP5RNvPIKzpoykT2lRvkuUJKlLGQQlSQWhJZXmn8u38bv56/njwudpaEkxYWgFn37TkZw3bTSjBvbJd4mSJOVM3oNgCOFI4LZWTROBL8UYv9eqzwzgd8DKbNOdMcarc1akJKlHak6meWT5Vu57aiN/WbSJXQ0t9Csv5u3TRnPBSWM4cexAn/0nSSpIeQ+CMcbngBMAQghFwHrgrja6PhRjPDeXtUmSep6mZIpHlm3lD089z/2Lnqe2MUm/smLecEwV5xw3ktdMHkp5ibd+SpIKW96D4D7OAJbHGFfnuxBJUs+xZXcT/1iyhb8/u5kHl2xhd1OSfuXFvPGYKt583EhOnzyUsmLDnyRJe4UYY75reEEI4XpgXozxR/u0zwDuANYBG4BPxRif2c85LgcuB6iqqjpp9uzZXVrzwairq6OysjLfZUg55bhXZ0rHyKpdaZ7ckuKpLSlW1qYBGFgWOH5YESdVFTFlSBHFeX7kg+Nehchxr0LVXcf+zJkz58YYq/dt7zZBMIRQSibkTYkxbtpnX38gHWOsCyGcA3w/xjj5lc5ZXV0d58yZ0zUFH4KamhpmzJiR7zKknHLc61Ct3b6HR1ds49Hl23hwyRa21TcTAkw7bCAzjxzOzKOGM2VU/271mT/HvQqR416FqruO/RBCm0GwO90aejaZq4Gb9t0RY6xttX5fCOHHIYShMcatOa1QkpQzG3Y28OjybTy6YhuPrdjGuh0NAAyuKOX0SUN5/VHDee0RwxhcUZrnSiVJ6nm6UxC8CLi1rR0hhBHAphhjDCFMBxLAtlwWJ0nqOql0ZMmm3cxfs5N5a3bwxKrtrN62B4CBfUs4ZcJgLjt9AqcdPpQjqiq71VU/SZJ6om4RBEMIFcAbgQ+3arsCIMb4U+AC4CMhhCTQAFwYu8s9rZKkDttW18SCtZnQN3/NTp5cu5P65hSQueJ34thBXHzaeE6dOJijR/QnkefP+kmS1Nt0iyAYY6wHhuzT9tNW6z8CfrTvcZKk7i3GyLodDSzaWMszG2pZtKGWRRt2sWFXIwBFicAxI/vzjpPGMG3sQE4cO4ixg/t6xU+SpC7WLYKgJKnn27mnmaWb61i2uY4lm3azeGMm+NU2JgFIBJg4rJKTJwzmmJH9mTZ2EMeNHkCfUh/rIElSrhkEJUntlkyl2bCzkdXb61mxpZ5lm+tYunk3yzbXsbWu+YV+fUqKOHJEP86dOoopo/pzzMj+HDWiv6FPkqRuwiAoSXqJ2sYWNuxsYN32BlZv38PqbfWs3pZZrtvRQDL94ke0+5UXM2l4Ja8/ajiTh/dj0vBKJg2vZPTAPn6uT5KkbswgKEkFpK4pyabaRjbXNrF5dyPrdzawYWcDG3Y2smFnA+t3NLC7KfmSY/qVFTNuaF+mjBrAOceNZNyQvowdXMGEoRVU9S/z83ySJPVABkFJ6sFijNQ1Jdle38zWuma21zezra6JbfXNbKtrZktdE5tqG9myO7Pck52Zs7WBfUsYNaAPYwb15dSJQxg1sJxRA/swamAfxg+pYFDfEsOeJEm9jEFQkvIsxkhDS4rdjUlqG1qobUyyu7Els93Ywq6GFnbtaWHnnhZ27Glm597thmZ27GmhOZlu87yVZcUMrSxleP9ypozqz+uPGs7wfmUM719GVb9yhvcvY8SAPlSW+b8CSZIKjf/3l6R2iDHSlEzT1JKmMZmisSVFY0s6u0zR0JKioTmz3NP80vU9zUnqm1LUNyWpb05S15TMrDelqGvKbKfSB340anlJgoF9ShnYt4QBfUoYP7Qvg/oOZEDfEoZWlDG4opQhlaUMqShjSGUpgytKKS9xYhZJktQ2g6CkTpVOR9IxkoqRGCGV3a5vieyobyYVI+l0Zn8qHUmneXE9RpKp7DKdaUulI8l0mnQakuk0ydSL+/ZuZ9Yz283JdGY9laYlFWlJZbZbUunMVzKz3pRK05LMtqUizck0TckUTck0zalM4MssU5llMk08cFZrU2lxgr6lRVSUFlNRVkRFWTGVZcUM71f2wnplWTH9ykvo3yez7FdeTP/yEvqXZ7YH9i0x1EmSpE5lEMyhbXVNfO0Pi3l+UxP3bFrQZp+D+D2z3eLB/Ba799hXPPfBH/9Kdb1sb9x3c//H73vql223Onbvvthm//3321t/fIX9Lz8+vrgeX6wls/7iy76kX/Z8sXW/l2xn+u7dF7Nh7IX2fY+PkXR2fzr9Yr3pCOnsElptpzPnSbfq8+L23v4H8Nf7X6FD5ytOBIqLAiWJBCXFCUqLEpQUB0qKMuulxQlKihKUFAUG9i2ltDhBWXHihWVZcdEL6+UlRS8sM18Jyosz631Ki+hbWkSfkuwyu15clMj5v1mSJOmVGARzqCmZ5onV22lsSLG2cft++wW6blKGQ5nv4ZUOfaXJJA649xVOvu/ufV/rQIfvW9a+39+2ym59/tBGv73re8/14vZLO+x77IvbL+5/ybla9QshsxJIEMJL+72wHsILfcM+2xBIhL37wgvn2Ps6iZDdT2adVv2KQiCRePEcL/QNrfdn1vfuS4RAyK7v3b93X1EisHz5co6YPImibHtRIrzQryjBC23FiUBRIkFRAooSCYqz/YuLMsuSoky/kqLEC/2LixIUZfcVZ0NdcSKzdJITSZKklzMI5tCogX146P+9npqaGmbMmJHvcqScqkmtYcarJ+S7DEmSJAHesyRJkiRJBcYgKEmSJEkFxiAoSZIkSQXGIChJkiRJBcYgKEmSJEkFxiAoSZIkSQXGIChJkiRJBcYgKEmSJEkFJsQY811DlwkhbAFWH6DLAGBXO0/X3r7t6TcU2NrO1+2pOvK97ak1dOb5D+VcHT3Wcd91usO4h66to6eO+44e056+jvuMQhj3nXn+nj7u29OvEMY9dI+x77g/9GMK4XedcTHGYS9rjTEW7Bcwq7P7tqcfMCff//bu9L3tqTV05vkP5VwdPdZx3zPGRHeto6eO+44e084x7bjv5DHRnevorPP39HHfnn6FMO47c0x05xoc9x3r19PGfqHfGvr7LujbkXP2Zt3h+9DVNXTm+Q/lXB091nHfdbrL96Er6+ip476jx7Snb3f5751v3eX70FPe83v6uD/YOnqj7vB9cNwf+jEFO+579a2h3VUIYU6MsTrfdUi55LhXIXLcqxA57lWoetrYL/QrgvkyK98FSHnguFchctyrEDnuVah61Nj3iqAkSZIkFRivCEqSJElSgTEISpIkSVKBMQhKkiRJUoExCHYjIYS3hxB+HkK4LYRwZr7rkXIlhDAxhHBdCOG3+a5F6kohhIoQwo3Z9/r35rseKRd8j1ch6gm/1xsEO0kI4foQwuYQwsJ92s8KITwXQlgWQvjsgc4RY7w7xvgh4Arg3V1Zr9RZOmnsr4gxfrBrK5W6Rgd/Bs4Hfpt9r39rzouVOklHxr3v8eotOjjuu/3v9QbBznMDcFbrhhBCEXAtcDZwDHBRCOGYEMJxIYR79/ka3urQL2aPk3qCG+i8sS/1RDfQzp8BYAywNtstlcMapc52A+0f91JvcQMdH/fd9vf64nwX0FvEGB8MIYzfp3k6sCzGuAIghDAbeFuM8X+Bc/c9RwghANcAf4wxzuvaiqXO0RljX+rJOvIzAKwjEwYX4B9j1YN1cNwvym11UtfoyLgPISymm/9e7/+EutZoXvzLL2R+ARh9gP4fA94AXBBCuKIrC5O6WIfGfghhSAjhp8C0EMLnuro4KQf29zNwJ/COEMJPgN/nozCpC7U57n2PVy+3v/f7bv97vVcEu5EY4w+AH+S7DinXYozbyNxDL/VqMcZ64N/yXYeUS77HqxD1hN/rvSLYtdYDh7XaHpNtk3o7x74KnT8DKkSOexWiHjvuDYJd6wlgcghhQgihFLgQuCfPNUm54NhXofNnQIXIca9C1GPHvUGwk4QQbgUeBY4MIawLIXwwxpgErgT+DCwGfhNjfCafdUqdzbGvQufPgAqR416FqLeN+xBjzHcNkiRJkqQc8oqgJEmSJBUYg6AkSZIkFRiDoCRJkiQVGIOgJEmSJBUYg6AkSZIkFRiDoCRJkiQVGIOgJEmSJBUYg6AkSZIkFRiDoCRJnSiE8NYQwh37tH0khPDDfNUkSdK+DIKSJHWurwFf3qdtOXB0HmqRJKlNBkFJkjpJCGEqkIgxLgwhjAshfCS7qwSIeSxNkqSXMAhKktR5TgDmZtffCEzOrh8DPJmXiiRJaoNBUJKkzpMAKkMIRcD5QL8QQh/gUuDX+SxMkqTWDIKSJHWe+4CJwALgp8AUYA4wK8Y4L5+FSZLUWojRjyxIkiRJUiHxiqAkSZIkFRiDoCRJkiQVGIOgJEmSJBUYg6AkSZIkFRiDoCRJkiQVGIOgJEmSJBUYg6AkSZIkFRiDoCRJkiQVmP8PVfRq2pSnINsAAAAASUVORK5CYII=\n", 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nLWFLRj7TL++vgif1wjUnduDvZ3dnflomV81eQWFphdORROQ4U8kTERGpBRl5JVwyfSn7cop5/sqBnNQlwelIIt+7bEhbHrqwN0u2H+ayZ5eRW1zudCQROY5U8kRERI6z/TnFXDxtCRm5JcyeNJAhHWKcjiTyP87vn8hT4/vx7b5cJsxcSk5RmdORROQ4UckTERE5jtKzi7h4+hIOF5Tx4uRBDGgb7XQkkZ90Rs8WTL8shS0HCxg/YxnZhSp6IoFAJU9EROQ42XO4iIunLSW3qJyXJg+iX1IzpyOJHNOoLvFMv7w/2w4VMH7mMo6o6Ik0eCp5IiIix8GurEIunr6EwrIKXrl6ML1bRzkdSaTaRnaOZ+blKew4VMD4GUs5XFDqdCQR+RXqvOQZY9zGmDXGmPerbrczxiwzxmwzxrxmjAmq60wiIiK/xvZDBVw8fQmlFX5emTyYHq2aOh1JpMZO6BTHsxMHsDOrkPEzlpGloifSYDmxJ+8WIO2o2/8CHrHWJgPZwFUOZBIREflFtmXmc8n0pfj8llevHky3lk2cjiTyiw3vGMtzVwxg95FCxk1fyqF8FT2RhqhOS54xJhEYA8ysum2Ak4C5VQ+ZDZxTl5lERER+qW2ZBVwyfRkAc6YMpnPzSIcTifx6Q5Njee6KgaRnFzNuxlIy80ucjiQiNVTXe/IeBW4H/FW3Y4Aca+13s3CmA63qOJOIiEiNbT9UwLgZSwF49erBJMer4EngGNIhhuevHMD+nGLGTV9KZp6KnkhDYqy1dfNGxpwFnGmtvd4YMxL4A3AFsLTqUE2MMa2Bj6y1PX7k+VOAKQAJCQn958yZUye5a6KgoICIiAinY4jUKW330hhtP1TAE+td+K3ljwNDaRmhccwkMG0+4uORVSU0CzH8cWAo7vJC/c2XRqe+ftcZNWrUKmttyo/dV5cl737gMqACCAGaAG8BpwHNrbUVxpghwN+staf93GulpKTYlStX1nbkGktNTWXkyJFOxxCpU9rupbHZlVXIOU8sxO3x8uqUwXRK0B48CWzLdx5h4qzlJDYL5abufn5z2iinI4nUqfr6XccY85Mlr85+erTW/slam2itbQtcAnxurZ0AfAFcUPWwicA7dZVJRESkJnYfLmTcjMpBVl6+epAKnjQKA9tFM+uKAezNLuKBFcWaR0+kAagPx5fcAdxqjNlG5Tl6zzqcR0RE5H/sOVzEuOlLKSn3cfvAULo01yia0ngM6RDDsxMHkFFkmTBzGTlFKnoi9ZkjJc9am2qtPavq+g5r7UBrbbK19kJrrcbqFRGRemXvkSLGzVhKUbmPlyYPonVkffiNVKRuDUuO5ZZ+wWw/VMClzy4jt6jc6Ugi8hP0KSUiIvIz0rOLuGT6UgpKK3jpqkF0b6mJzqXx6hHrYdpl/dlysIDLZi0jt1hFT6Q+UskTERH5CQdyixk/Yxl5JeW8dNUgerRSwRMZ1Tmepy/tR9qBPCbOWk5+iYqeSH2jkiciIvIjMvNKmDBjGUcKy3jxqkH0TFTBE/nOyV0TeGp8P9bvy2XirOUUlFYc+0kiUmdU8kRERP7L4YJSJsxcxsG8Ep6/cgB9Wkc5HUmk3jm1e3OeHN+Xtem5THp+BUVlKnoi9YVKnoiIyFGyC8uYMHMZe7OLmHXFAFLaRjsdSaTeOr1HCx69uA8rdx3h6hdWUlLuczqSiKCSJyIi8r3c4nIum7WMHVmFzLx8AIPbxzgdSaTeG9u7JQ9e0JvF2w9zzYurKK1Q0RNxmkqeiIgIkF9SzuWzlrPlYAHTLuvP8I6xTkcSaTDO75/I/ef2ZOGWQ9zw8hrKfX6nI4k0aip5IiLS6BWWVnDlcyvYsC+Xpyb0Y1TneKcjiTQ4lwxM4v/O7s78tAxumbOGChU9Ecd4nA4gIiLipOIyH1fNXsGavTk8Oa4vo7slOB1JpMG6fEhbyir83PtBGl73Wh6+qA9ul3E6lkijo5InIiKNVkm5jykvrmT5ziM8cnEfzujZwulIIg3e5BHtKfP5eeDjzXjdLh44vxcuFT2ROqWSJyIijVJZhZ/rX17NV1uz+PeFvTm7TyunI4kEjOtHJlNW4efR+VsJ8rj4xzk9MEZFT6SuqOSJiEijU+7zc9Orq/l8Uyb3nduTC/onOh1JJODccnJHyir8TE3dTpDbxV/HdlPRE6kjKnkiItKo+PyW3732DZ9syOBvY7sxflCS05FEApIxhttO60xZhZ+Zi3YS7HHxxzO6qOiJ1AGVPBERaTT8fsttc9fy/roD3HlmF64Y1s7pSCIBzRjDXWO6UubzM+3LHQR5XPz+1M5OxxIJeCp5IiLSKPj9ljvf+pY3V+/j96M7MeWEDk5HEmkUjDH8bWx3yir8PPH5NoLcLm46uaPTsUQCWo1LnjEmHCix1vpqIY+IiMhxZ63lnvc2MGfFXm4clawvmCJ1zOUy3HduT8oq/Dz02RaCPC6uOVE/tIjUlmOWPGOMC7gEmAAMAEqBYGNMFvABMM1au61WU4qIiPxC1lru+zCN2Ut2c/WIdvz+1E5ORxJplFwuwwMX9KLM5+f+jzYR5HFxpQ6ZFqkV1dmT9wUwH/gTsN5a6wcwxkQDo4B/GWPesta+VHsxRUREas5aywOfbGbGVzuZOKQNd57ZVYM+iDjI43bxyMV9KPf5uee9jQR5XEwY1MbpWCIBpzol7xRrbfl/r7TWHgHmAfOMMd7jnkxERORXenT+Vp5O3c74QUn87TfdVfBE6gGv28UT4/px7UuruOut9XjdLi5Kae10LJGA4jrWA/674Bljwo0x7p97jIiIiNOe/Hwrjy3YykUpidx7tiZiFqlPgjwupk7ox4iOsdwxbx1vrk53OpJIQDlmyTPGuIwx440xHxhjMoFNwAFjzEZjzIPGmOTajykiIlJ9zyzczr8/3cJ5fVtx/3m9cLlU8ETqmxCvmxmXpzCkfQx/eGMt73yzz+lIIgHjmCWPynPyOlB5Tl5za21ra208MBxYSuU5eZfWYkYREZFqe3bRTv750SbG9m7Jgxf2xq2CJ1JvhXjdzJyYQkrbaG59fS0frDvgdCSRgKBz8kREJGC8sGQXf39/I2f0aM4jF6ngiTQEYUEenrtiABNnLeeWOWvwuA2ndW/udCyRBq3G5+T90seIiIjUpleW7eEv72xgdLcEHh/XF4+7OgeriEh9EB7s4flJA+mZ2JQbX1nNgrQMpyOJNGjV/gQ0xjxujPnUGPOJMeYBY0yf2gwmIiJSXa+v2Mudb33LSV3ieXJ8X7wqeCINTkSwh9mTBtKtRROue2k1qZsznY4k0mDV5FNwI/Ag8BiQCbxkjLmxVlKJiIhU0+sr93LHm+s4oVMcUyf0I9jjPvaTRKReahLi5YVJg+jUPIIpL67iq62HnI4k0iBVu+RZa5+x1n5mrf3QWvtvIAW4pvaiiYiI/Ly5q9K5Y946hifHMv2y/oR4VfBEGrqmYV5enDSIDnERTJ69kq+3ZTkdSaTBqfHxLMaYa40x/6Zyj17e8Y8kIiJybHNXpXPb3LUMT45lxuUpKngiAaRZeBAvTx5Eu9hwJj2/QkVPpIZ+yUkLHwJpQCJwf3WfZIwJMcYsN8asNcZsMMbcU7W+nTFmmTFmmzHmNWNM0C/IJCIijcg8FTyRgBcdHsQrVw/+vugt2qqiJ1JdNRl45Q1jTFdr7R5r7bPAWOAfNXivUuAka21voA9wujFmMPAv4BFrbTKQDVxVg9cUEZFG5s3V6fxh7lqGdVDBEwl0Rxe9q2ar6IlUV0325L0AvGaM+dYY8zzwOuCv7pNtpYKqm96qiwVOAuZWrZ8NnFODTCIi0oi8tSad37+xliHtY1TwRBoJFT2RmjPW2p9/gDH3WWvvNMacAKwF2lC5J84FfGitrfb4tsYYN7AKSAaeonK0zqVVe/EwxrQGPrLW9viR504BpgAkJCT0nzNnTnXfts4UFBQQERHhdAyROqXtXurK4v0VzFhXSpdoF7/tH0Kw27mJzrXdS2Pl5LafX2Z5YEUJBwv93NIvhB6x+pFH6kZ9/Zs/atSoVdbalB+7z1ON579WtZwM9ALCqTwnby1wgjFmmbV2b3WCWGt9QB9jTBTwFtClOs+reu50YDpASkqKHTlyZHWfWmdSU1Opj7lEapO2e6kL81alM/PbtQxuH8OsKwYQGuTslztt99JYOb3tDxtWxoSZy3jimwJmTkxhRMc4x7JI4+H0dv9LHPNwTWvt2qrl5dbaPkA34M/AVmAI8LYx5r6avKm1Ngf4our5UcaY78pmIrCvJq8lIiKB7bUVe/jD3LUM6RDDs1ekOF7wRMQ50VWjbravml7hyy2aR0/kxxyz5BljfnA8jLW23Fq71lr7grX299ba/sDp1XiduKo9eBhjQoHRVO4R/AK4oOphE4F3avhvEBGRAPXS0t3cMe9bRnSM49mJAwgLqs4BKCISyKLDg3jlu6L3wkq+2FTtM4dEGo3qDLzyhTHmJmNM0tErjTFBxpiTjDGzgZnVeJ0WVa+1DlgBfGatfR+4A7jVGLMNiAGerdk/QUREAtFzX+/k7rfXc3KXeE10LiI/0Kyq6HVOiGTKiyv5ZMNBpyOJ1CvV+Un0dGAS8Koxph2QA4QAbuBT4FFr7ZpjvYi1dh3Q90fW7wAG1iS0iIgEthlf7uAfH6ZxWvcEnhjXjyDPL5nWVUQCWbPwIF6aPIgrnlvO9S+v5tGL+zC2d0unY4nUC8csedbaEmAqMNUY4wVigeKq8+pERESOq6e+2MaDn2xmTM8WPHpJH7xuFTwR+XFNQ728eNUgJj23glvmrKHc5+e8folOxxJxXHXOyev83Xl5VefjHVDBExGR481ay6Pzt/DgJ5s5u09LHlPBE5FqiAj28PykAQzpEMPv31jLnOV7nI4k4rjqfHrOBXKNMSuNMbOMMb8zxpxsjImv7XAiItI4WGv596ebeXT+Vs7vl8jDF/XBo4InItUUFuTh2YkDOLFTHH9881teWLLL6UgijqrO4Zo9jTHBVM6R9yFQCJwFdDfGYK1tXssZRUQkgPn9lnve28DsJbsZN7A1/zinJy6XcxOdi0jDFOJ1M+2y/tz4yhr+8s4Gyir8TB7R3ulYIo6o1ljU1tpSYIUxpsBae9N3640xzWotmYiIBLwKn5875n3LvNXpXD2iHXee2ZX/mrlHRKTagj1upk7ox2/nfMO9H6RRVObjppOS9XdFGp2aTjhkf3DD2uzjmEVERBqR0goft7z6DR9vOMitozvpi5iIHBdet4vHLulDiNfNw59tIbe4nLvH6AckaVyOWfKMMU8Bq6su+n+HiIj8akVlFVzz4iq+2prFX87qxqTh7ZyOJCIBxON28eAFvYgM8fDsop3kFZdz/3k9da6vNBrV2ZO3FugDXA5EGmM2AhuAjcBGa+1rtZhPREQCTF5JOZOeW8HqPdk8cH4vLhrQ2ulIIhKAXC7DX8d2IyrMy6Pzt5JfUsFj4/oQ7HE7HU2k1lVn4JXpR982xiQCPakciOUsQCVPRESq5XBBKROfW87mg/k8Ma4fY3q1cDqSiAQwYwy/PaUTTUK8/N/7G5k8eyXPXNqf8OCanrEk0rBU53BNY639/lw8a206kA589FOPERER+W8Hcou5dOYy0rOLmX55CqM6ayYeEakbk4a3o0mol9vnruXSZ5fx3BUDiAoLcjqWSK2pzoHJXxhjbjLGJB290hgTZIw5yRgzG5hYO/FERCQQbMvM5/ypi8nIK+WFSQNV8ESkzl3QP5GnL+3Phn15XDxtKZl5JU5HEqk11Sl5pwM+4FVjzAFjzEZjzE5gKzAOeNRa+3wtZhQRkQZs1e4jnP/0Esr9lteuGcyg9jFORxKRRuq07s157soB7M0u4sJpS9h9uNDpSCK14pglz1pbYq2daq0dBiQBJwN9rbVtrLVXW2vX1HpKERFpkOZvzGDCzGVEhwfx5nVD6d6yqdORRKSRG5Ycy8uTB5FXXM55UxezLj3H6Ugix121x5E1xmylcpCVKcCJxpg2tZZKREQavNdW7OGal1bROSGSudcOoXV0mNORREQA6JvUjLnXDSU0yM0l05fyxeZMpyOJHFc1mSxkGnAQOAycAWwwxnxrjPk/Y4y3VtKJiDitKMQAACAASURBVEiDY63lyc+3cse8bxmWHMsrVw8mJiLY6VgiIj/QIS6CN68fSrvYcCbPXskbK/c6HUnkuKlJybvUWnu9tfZJa+21wHDgCyAPeLhW0omISIPi81v++u4G/v3pFs7t24qZl6doqHIRqbfiI0N47ZohDO0Qw21z1/HEgq1owHgJBDUpebnGmF7f3bDWfgOcaK39NzDsuCcTEZEGpaTcx02vruaFJbuZckJ7HrqwN0GemnzMiIjUvYhgD89OHMC5fVvx0GdbuPvt9fj8KnrSsNXk59VrgJeNMd8A3wCdgaKq+zTRiIhII3a4oJSrX1jJ6j053D2mK5NHtHc6kohItQV5XDx8UW+aNw3h6dTtZOaX8vglfQkNcjsdTeQXqdZPrMYYF3AeMBD4GIgHtgFnGWPCgTm1llBEROq1bZn5nDP1azbsz+PpCf1U8ESkQTLGcMfpXbjnN92Zn5bB+JlLOZRf6nQskV+kWiXPWusHzrLW+qy1b1hr/2ytfdRae9haW2itvbeWc4qISD20eFsW501dTHGZjzlTBnNGzxZORxIR+VUmDm3L0xP6kXYgj3Oe+prNB/OdjiRSYzU5WWKdMeavxhhTa2lERKTBeH3lXi6ftZyEJiG8df0w+iY1czqSiMhxcXqPFrw2ZQhlPj/nP72YVE2xIA1MTUpeNHAJcMAY844x5u/GmAtrKZeIiNRTfr/lwU82cfvcdQxuH8Pc64ZqDjwRCTi9W0fxzg3DSIoOY9LzK5i9eJfTkUSqrdolz1p7kbW2K9AGuIfKc/IG1VYwERGpf0rKfdw8Zw1PfbGdSwa05rkrB9A0VFOlikhgahkVyhvXDuGkLvH89d0N/OWd9VT4/E7HEjmmGk9eZK0tBVYDq40xUcc/koiI1EeZeSVc89Iq1uzJ4Y9ndOGaE9qjI/hFJNCFB3uYdlkK//wojRlf7WT34SKeGN+XJiH6gUvqr2qVvKoRNLsDPY5a9gDCARU9EZEAt2ZPNte+tIr8kgqeubQfp/fQACsi0ni4XYa7xnSjfVwEf357PRc8vZhnJw7QoepSbx3zcE1jzC5gC/APoC+wHegJ9LXWquCJiAS4N1bu5eJpSwnyuHjz+qEqeCLSaI0bmMTsSQM5mFvC2CcXsWhrltORRH5Udc7Jew84Asyw1t5krZ0KlFprNcyQiEgAq/D5uee9Ddw2dx0pbZvx7g3D6dK8idOxREQcNSw5lndvHE58ZDCXz1rG9C+3Y611OpbIDxyz5FlrbwLOAs40xqwwxpwB1HhLNsa0NsZ8YYzZaIzZYIy5pWp9tDHmM2PM1qqlxuAWEXFYdmEZl89aznNf72LSsHa8MGkgzcKDnI4lIlIvtI0N583rh3Fa9+bc9+Embnp1DUVlFU7HEvledSdD322tvQK4ArgaaG6MGVXD96oAfm+t7QYMBm4wxnQD/ggssNZ2BBZU3RYREYekHcjjN08tYuXubP59YW/+MrYbHndNZtwREQl8EcEepk7ox+2nd+aDbw9w3tTF7Dlc5HQsEaBm8+Rhrd1grT0PGAXcZYxZWIPnHrDWrq66ng+kAa2As4HZVQ+bDZxTk0wiInL8vLd2P+dNXUxZhZ/XrxnCBf0TnY4kIlJvGWO4fmQyz10xgP05xYx9chFfbjnkdCwRzK85htgYc7K1dsEveF5b4EsqR+jc890ALqZyLO7sHxvQxRgzBZgCkJCQ0H/OnDm/OHdtKSgoICIiwukYInVK231gKPdb5mwqY8GeCpKjXNzYJ5ioEO29+yna7qWx0rb/0zKL/Dy+uoR9BZYLOnk5s51X08wEiPq63Y8aNWqVtTblx+77VSXvlzDGRAALgX9Ya980xuQcXeqMMdnW2p89Ly8lJcWuXLmytqPWWGpqKiNHjnQ6hkid0nbf8O09UsQNr6xmXXouV49ox+2nd8GrwzN/lrZ7aay07f+8orIKbpu7jg/WHeCUrgn8+8JeRIXpfOaGrr5u98aYnyx5dfopbozxAvOAl621b1atzjDGtKi6vwWgUTtFROrI/I0ZjHn8K3ZmFTLtsv7cNaabCp6IyC8UFuThyXF9+ctZ3Vi4JZMxjy9i9Z5sp2NJI1Rnn+RVh2I+C6RZax8+6q53gYlV1ycC79RVJhGRxqrC5+f+j9KY/MJKWkeH8f5Nwzmte3OnY4mINHjGGCYNb8fca4diDFz0zBJmfrVD0yxInarLn2uHAZcBJxljvqm6nAn8ExhtjNkKnFJ1W0REaklGXgnjZyxj2sIdjB+UxLzrhtImJtzpWCIiAaV36yg+uHkEJ3eN594P0rj6hZXkFJU5HUsaCU9dvZG1dhHwU2efnlxXOUREGrMvNmdy2xtrKSrz8ejFfTinbyunI4mIBKymoV6eubQ/zy/exX0fpjHm8UU8Pq4v/dtoWmipXTrxQkSkESgp9/G3dzdw5XMriI0I5p0bhqngiYjUAWMMVw6rPHzT5YKLpy1h2sLt+P06fFNqj0qeiEiA23Qwj7Of/JrnF+/iquHtePuGYXRMiHQ6lohIo9K7dRTv3zSC0d0SuP+jTVz67DL25xQ7HUsClEqeiEiA8vstsxbt5DdPfs2RojJmTxrIn8/qRojX7XQ0EZFGqWmol6kT+vGv83vyzd4cTn/0S975Zp/TsSQA1dk5eSIiUncy80r4w9x1fLnlEKd0TeBf5/ckJiLY6VgiIo2eMYaLByQxuH0Mv3vtG26Z8w0L0jL5+9k9aBrmdTqeBAiVPBGRAPPZxgzumLeOorIK7j2nBxMGJVE5i42IiNQXbWLCef2aITydup1HF2xlxa4jPHRhb4YmxzodTQKADtcUEQkQOUVl/O61b7j6hZU0bxLC+zcN59LBbVTwRETqKY/bxU0nd+TN64YS6nUzfuYy7n1/IyXlPqejSQOnPXkiIgHgkw0Hueut9eQUlXHLyR25YVQyQR79jici0hD0bh3F+zcP574P05i5aCepWw7xwAW96JekqRbkl9E3ABGRBuxIYRk3v7qGa15cRXxkMO/cOIzfje6kgici0sCEBXm495yePH/lAIpKKzj/6cX833sbKSqrcDqaNEDakyci0kB9vP4Ad7+9ntzicm4d3YnrRnbA61a5ExFpyEZ2jueT353Avz7exKyvdzI/LYN/ntdT5+pJjejbgIhIA5NVUMqNr6zm2pdW07xpCO/eOJybT+6ogiciEiAiQ7zce05PXpsyGJeB8TOX8cd568gtLnc6mjQQ2pMnItJA+P2WOSv28q+PN1FUVsFtp3VmygntVe5ERALUoPYxfPzbE3hk/hZmfLmDLzZncu85PRndLcHpaFLPqeSJiDQAG/fncffb37J6Tw6D2kXzj3N7kBwf6XQsERGpZSFeN386oytjerbg9rnruPqFlZzevTl/HtuNVlGhTseTekolT0SkHissreCRz7bw3OJdRIV6efii3pzbt5WmRRARaWR6JUbx7o3DmfHVDp74fCsLHzrETScnM3l4ew22Jf9DJU9EpB6y1vLJhgzueW8DB3JLGD8oidtP60xUWJDT0URExCFBHhc3jErm7D4t+fv7G3ng483MXZXO38/uwTANzCJHUe0XEalndmYVctXslVz70iqiwoJ48/qh3HduTxU8EREBILFZGNMuS+G5Kwfg81smzFzGDa+s5mBuidPRpJ7QnjwRkXoit7icJxZsZfaSXQS5Xdw9pitXDG2LRwOriIjIjxjVOZ4hv41h2sIdTE3dRuqmTG4+uSNXDGtLsMftdDxxkEqeiIjDKnx+Xl2xl0c+20J2URkXp7Tm1lM7ER8Z4nQ0ERGp50K8bm45pSPn9m3FPe9t4P6PNvHysj388YwunNGjuc7hbqRU8kREHPTllkPc+8FGtmQUMLh9NH8+qxvdWzZ1OpaIiDQwSTFhPHvFAL7ccoh/fJDG9S+vJqVNM+4a05W+Sc2cjid1TCVPRMQB2zILuO/DND7flEmbmDCmXdafU7sl6BdXERH5VU7oFMew5FheX7mXhz7dwrlTFzO2d0tuP60zraPDnI4ndUQlT0SkDu3PKeax+VuZuzqdMK+bO8/swsShOndCRESOH7fLMG5gEmN7t2Tawu3M+GoHn2w4yJXD2nL9yGSahnqdjii1TCVPRKQOHC4o5akvtvPS0t0AXD6kDTeMSiY2ItjhZCIiEqgigj38/tTOjB+UxIOfbGbawh3MWb6XKSe054qhbQkPVhUIVPpfVkSkFuWXlDPjq508+9UOist9XNA/kZtP7khiMx0yIyIidaNF01AevqgPk4a14+HPtvDgJ5uZtWgn143swKWD2xDi1dEkgUYlT0SkFpSU+3hhyS6mpm4np6icM3s259bRnUmOj3A6moiINFI9WjVl1hUDWLU7m4c/28y9H6Qx46sd3HhSRy5OaU2QR1P2BAqVPBGR46iwtIKXl+1m+pc7ySoo5YROcdx2amd6JmrETBERqR/6t2nGy5MHs3h7Fg9/uoU/v72eaQu3c/PJlVMxeDU/a4OnkicichzkFpfzwuJdPPv1TnKKyhnRMZYbR/VlUPsYp6OJiIj8qKEdYhlybQwLtxzioU+3cPvcdTy+YCvXnNCeC1Na6zDOBkwlT0TkVzhSWMasRTuZvXgX+aUVnNI1nhtGJWtOIhERaRCMMYzsHM+JneKYn5bJ1NRt/PmdDTy2YBuTR7RjwqAkIkM0GmdDo5InIvILHMgtZtainby0dA8lFT7O7NGC60d10ETmIiLSIBljGN0tgVO6xrN0xxGmpm7jnx9tYuoX25g4tC1XDmtHdHiQ0zGlmuqs5BljZgFnAZnW2h5V66KB14C2wC7gImttdl1lEhGpqW/Tc5m5aAcfrDuA31rO7tOKG0Z1IDk+0uloIiIiv5oxhiEdYhjSIYZ16TlM/WI7T36xjZlf7eTiAa2ZNKwdSTEaIbq+q8s9ec8DTwIvHLXuj8ACa+0/jTF/rLp9Rx1mEhE5Jp/fsiAtg5mLdrJ85xEigj1cMbQtE4e2pXW0PuhERCQw9UqM4pnL+rMtM5+nU3fw0tLdzF6yi1O6JjBpWDsGt4/GGON0TPkRdVbyrLVfGmPa/tfqs4GRVddnA6mo5IlIPVFUVsHcVenMWrSTXYeLaBUVyt1junLRgNY00fkJIiLSSCTHR/LQRb25/fTOvLhkN68s38NnGzPo2qIJk4a1ZWzvlhqkpZ5x+py8BGvtgarrB4EEJ8OIiABsy8zn5WV7mLcqnbySCnq3juLJ0zpzevfmeDSstIiINFIJTUL4w2mdufGkZN75Zh+zFu3itrnr+OdHm5gwuA2XDkoivkmI0zEFMNbaunuzyj157x91Tl6OtTbqqPuzrbU/OiSdMWYKMAUgISGh/5w5c2o/cA0VFBQQEaGJjqVxCZTtvsJvWZ3h4/O95Ww64sdtICXBzSltvCRHuXQ4ivxAoGz3IjWlbV+OZq0l7YifT3eVs/aQD5eBPvFuRrX20C3GjStAPjvr63Y/atSoVdbalB+7z+mStxkYaa09YIxpAaRaazsf63VSUlLsypUrazXrL5GamsrIkSOdjiFSpxr6dp+eXcSry/fw2op0sgpKaRUVyvhBSVyU0pq4yGCn40k91dC3e5FfStu+/JRdWYW8unwPb6xK50hhGa2jQ7lkQBIXpiQSH9mw9+7V1+3eGPOTJc/pwzXfBSYC/6xavuNsHBFpDErKfcxPy2DuqnQWbjkEwEmd47l0cBtO6BSH2xUYvzyKiIjUlbax4fzpzK7cemonPt2QwSvL9vDgJ5t55LMtnNI1gfGDkhieHItLn7F1oi6nUHiVykFWYo0x6cBfqSx3rxtjrgJ2AxfVVR4RaVystaxNz2Xuqr28+81+8koqaNE0hBtGJnPJwNYkNtMomSIiIr9WsMfN2N4tGdu7JTsOFTBnxV7mrkrn4w0Hadk0hHP6tuK8fq009VAtq8vRNcf9xF0n11UGEWl8MvNKeGvNPuauSmdrZgHBHhen92jOBf0TGdohVnvtREREakn7uAjuPLMrvz+1E59tzGDeqnSmfbmDqanb6Z3YlPP6JTK2d0tNsl4LnD5cU0TkuMstKueTDQd5b91+vt6Whd9C/zbNuP+8nozp1ULTH4iIiNShYI+bs3q15KxeLcnML+Hdb/bz1pp9/PXdDfz9/Y2M7BzPef1acVKXeE3FcJyo5IlIQCgsrWB+Wgbvrd3Pwi2HKPdZ2saEcf3IZM7r14r2cfVvVCwREZHGJj4yhMkj2jN5RHs2HczjrdX7eGvNPuanZRAe5ObkrgmM6dWCEzvFqfD9Cip5ItJgFZVVsHDzId5fd4AFmzIoKffTsmkIVw5rx9heLenRqommPhAREamnujRvwp/ObMLtp3dhyfbDfPDtAT5ef4B31+4nItjD6G4JjOnZghGdYgn2qPDVhEqeiDQoRwrLmJ+WwacbDvLV1ixKK/zERgRxcUprxvZuSb+kZhq5S0REpAFxuwzDO8YyvGMs/3d298rCt+4AH284yFtr9hEZ7OHkrvGM7tacEzvHERGsCnMs+i8kIvXe3iNFfLqxstit2HUEv+X7+exO7dacAW2b4XG7nI4pIiIiv5LX7eKETnGc0CmOe8/twdfbsnh/3QHmp2Xw9jf7CXK7GNIhhtHdEhjdLYGEJg17Dr7aopInIvVOuc/P6t3ZfLH5EKmbM9l0MB+AzgmR3DgqmVO7N6d7Sx2KKSIiEsi8bhcjO8czsnM8FT4/K3dnM39jBp+lZXD32+u5++319EpsyuiuCYzqEq/vBkdRyROReiEzr4TULZWl7qutWeSXVOBxGVLaNuPOM7twarfmtI0NdzqmiIiIOMDjdjG4fQyD28dw15iubM0s4LONGXy6MYOHPtvCQ59tIS4ymBM6xnFi5zhGJMfSrBFPzaCSJyKOKCn3sWLXEb7edpivth5iw/48ABKaBHNmjxaM6hLHsORYIjXdgYiIiBzFGEOnhEg6JURyw6hkMvNL+HJLFgu3HGLBpgzmrU7HGOidGMWJVYd+9k5s2qhO7VDJE5E6UeHz8+2+XL7elsXX2w6zanc2ZT4/Xrehb+tm3HZaZ0Z1jqdri0gdaiEiIiLVFh8ZwgX9E7mgfyI+v2Vdeg4Ltxziyy2HeOLzrTy2YCsRwR4GtYtmSIcYhnSIoWvzJgE9UJtKnojUinKfnw3781ix8wjLdh5h2Y7D5JdWANCtRRMmDm3DsORYBraLJixIf4pERETk13O7DH2TmtE3qRm/PaUTOUVlfL3tMEt2ZLF4+2EWbMoEICrMy5D2MQztUHkIaIe4iIAqffpmJSLHRUm5jzV7cli+8wgrdh1h9Z5sisp8ALSNCeOs3i0ZlhzDkPYxxEQEO5xWREREGoOosCDG9GrBmF4tADiYW1JZ+LYdZvH2w3y0/mDV47yktGlGSttoBrRtRo9WTRv03HwqeSJSY9Za9ueWsHp3Nu+llfLYxq9Zvy+Xcp/FmMpRMC/sn8iAdtEMbBtNvIY3FhERkXqgedMQzu2byLl9E7HWsvdIMct2HmblrmxW7D7C/LTKPX3BHhe9W0cxoG0zoot9jHQ2do2p5InIMRWWVrB+Xy5r9uawZk82a/bkkJlfCoDXBX2SDJOGtWNgu2hS2kTTNEyDpYiIiEj9ZowhKSaMpJgwLkxpDUBWQSkrd2WzctcRVuzOZtrCHZzZruFVpoaXWERqVVFZBRv25/Ftei7r9+Wybl8u2w8VYG3l/W1iwhjaIYZ+bZrRt3UzMras5pSThjobWkREROQ4iI0I5vQezTm9R3Og8nvRFwu/cjhVzankiTRihwtKSTuQT9qBPNIO5PFtVaHzVxW6+MhgerZqypieLeiV2JQ+raP+53y6w9sC5yRlERERkaOFBXkI9za87zoqeSKNQGmFj51ZhWw+mM/GA3nfF7tDVYdcwn8K3Zk9W9CzVVN6JjYlQefSiYiIiDQ4KnkiAeS7Mrclo4BtGflsyShgS2Y+uw8X4avaPRfkdpEcH8EJHePo2iKSri2a0KV5pEa8FBEREQkQKnkiDYy1lkMFpew4VFh1KWBnViE7sgrZc+Q/Zc5loG1MOB0TIjizRws6JkTQuXkkHeIi8LpdDv8rRERERKS2qOSJ1EPfFbk9h4vYdbiIPYcL2XW4iN2HK8tcfknF948N9rhoFxtO1xaRjOlZWeY6JUTSPi68Qc/vIiIiIiK/jEqeiEMKSitIzy4i/Ugx6dlF7M2uXO45Uszuw4XfTyQOlXvlWjULpU10OOf0aUX7uHDax0XQPjacVlGhuFwN74RgEREREakdKnkitcDvt2QVlLIvp5j9OSUcyC1mX04xB3JK2JdTWeayi8p/8JxQr5vEZqG0jg5jcPto2saEkxQTRtuYyiIX5NEhliIiIiJybCp5IjVUUu4jI6+EjLxSDuaVkJFbwsG8yktm1fJgbgnlPvuD54UHuWkRFUrLqFB6JTYlsVkYraNDSWwWRmKzUGLCgzBGe+RERERE5NdRyRMBKnx+jhSVcbigjKyCUrIKSsnMK+VQfimZ+d8tS8jML/3B+XDfCfW6ad40hIQmwfRPavZ9mWvZNKRqGUqTUI9KnIiIiIjUOpU8CUhlFX5yiso4XFhGdmHVsqrEZVetP1xQyuGC/9xn7f++TqjXTXyTYOIiguncPJLhybHERQaT0CSkqtRVXpqEqMCJiIiISP2gkif1lrWWwjIfucXl5BaVVy6Ly8kr/s/17KIycorLySkqI6eovOpSRuFRg5b8t6ahXqLDg4iNCKJDXASD2gcREx5MbEQQsRHBxEQEExMRRHxkMBHBKm8iIiIi0rCo5EmtqPD5KSzzUVBaQUFJBQWl5eSXVBx1u4L8kspLXkk5+SXl5BVXkF9atSwpJ6+k4vs5336My0BUWBBRYV6iQr00bxJC5+aRRIVWrosOD/rBpVlYEM3CvHg0R5yIiIiIBDCVvEau3OenuNxHcZmPorLKZXF5BcVlforKKigur1xfVOajqLSCwjIfRWUVVesqKCz1UVhaWdqKyv5zvbTCX633jwj20CTEQ2SIlyahHuIjQ0iO+8/tpqFemoR4aRpaeWlStWwa5iUiyKOpA0RERERE/otKXj1graXM56eswk9pxQ+Xldd9368rrfBVLsuPul7hp6TcV3WpvP79uh/c56sqdP9ZV/Eze8p+TJDbRViwmzCvm7BgD2FBbsKDPCQ2CyMi2E14sIeIYA/h312C3ESGeIkI8Xxf6L67Hq6SJiIiIiJy3NWLkmeMOR14DHADM621/3Q4Uo3d894GNm4vYc7eVZT7/JT5/JT7/JT7bOXtCv/3Re772xWV95f5qrfX6+cYAyEeNyFeFyFeNyFeN8EeF8FeNyEeF9HhQYRWrQ/xugn1ugkNchHicRMaVHkJC/puveeo65Ul7rv7vTrUUURERESkXnO85Blj3MBTwGggHVhhjHnXWrvR2WQ18216Lul5fnJsIV6Pwet24XW7CPW6aRLiweN2EeRxEVy19P7XMtjjIsjtIth79NJNkKfy/pCqwhZc9dgfXPe48bqNBggRERERERHnSx4wENhmrd0BYIyZA5wNNKiSN/e6oaSmpjJy5AlORxERERERkUasPpS8VsDeo26nA4P++0HGmCnw/+3dS4glZxkG4PdLNCAqLrzMIhNiAoM4IioMrmehEkGiRMGIGyUoCcS9guBKdB0Rw4hh3HgjiiQykt3gxkXGECExCDEgJhsvC2HcRT4X3eDYzuWc7jqnbs8DB7qr///vb6rfqq6vq3o6X06SU6dO5fLly3spbhtXr16dZF2wS3LPGsk9ayX7rNEccz+FJm8j3X0hyYUkOXfuXJ8/f37cgq7j4E7e+bHLgL2Se9ZI7lkr2WeN5pj7KfwvGq8lueua908fbgMAAGBLU2jynk1ypqruqao7kjyY5KmRawIAAJil0R/X7O7Xq+rRJM/k4E8oPNHdL45cFgAAwCyN3uQlSXdfSnJp7DoAAADmbgqPawIAADAQTR4AAMCCVHePXcPWqupvSf58kyFvS/LPDZfbdOwm496R5O8bft652mbf7tIu6xhy7ZOsdZy5Q2df7g+sIfdDrj/33G8ybg25T6aRfbk/+RzXOtuR+/2tte1cuf9fd3f3O6/7ke5e3CvJhaHHbjIuyZWx/+1T2rdzrWPItU+y1nHmDp19uR8+E1OuY6j15577TcatIfdDZmLKNcj9duPWkH25399a286V+81fS31c8+kdjN1mzSWbyn7YZR1Drn2StY4zd+jsT+XrPbap7Idd1zHU+nPP/XHrWKIp7Ae5P/kcud/OFPbDXHJ/0rW2nSv3G5rl45pTVVVXuvvc2HXAPsk9ayT3rJXss0ZzzP1S7+SN5cLYBcAI5J41knvWSvZZo9nl3p08AACABXEnDwAAYEE0eQAAAAuiyQMAAFgQTd6eVNWnqur7VfXTqvrY2PXAPlTVvVX1g6p6cuxaYJeq6s1V9cPD8/znx64H9sE5nrWaw3W9Jm8DVfVEVf21ql44sv2+qvpjVb1cVV+92Rrd/cvu/lKSh5N8dpf1whAGyv0r3f3QbiuF3djyGHggyZOH5/n7914sDGSb3DvHsyRbZn/y1/WavM1cTHLftRuq6vYk303y8SRnk3yuqs5W1fur6ldHXu+6ZurXD+fB1F3McLmHObqYDY+BJKeT/OVw2L/3WCMM7WI2zz0sycVsn/3JXte/YewC5qC7f1NV7z6y+cNJXu7uV5Kkqn6S5JPd/a0knzi6RlVVkm8n+XV3P7fbiuHkhsg9zNk2x0CSV3PQ6D0fP0BlxrbM/R/2Wx3szjbZr6qXMvHret+Iju/O/PentsnBN/g7bzL+K0k+kuQzVfXwLguDHdoq91X19qp6PMmHqupruy4O9uBGx8Avkny6qr6X5OkxCoMdum7uneNZgRud8yd/Xe9O3p5092NJHhu7Dtin7v5HDp5Xh0Xr7n8l+eLYdcA+cwruKAAAAZFJREFUOcezVnO4rncn7/heS3LXNe+fPtwGSyb3rJ1jgDWSe9ZqttnX5B3fs0nOVNU9VXVHkgeTPDVyTbBrcs/aOQZYI7lnrWabfU3eBqrqx0l+m+Q9VfVqVT3U3a8neTTJM0leSvKz7n5xzDphSHLP2jkGWCO5Z62Wlv3q7rFrAAAAYCDu5AEAACyIJg8AAGBBNHkAAAALoskDAABYEE0eAADAgmjyAAAAFkSTBwAAsCCaPAAAgAXR5AHABqrq/qr6+ZFtj1TVd8aqCQCuR5MHAJv5ZpJvHNn2pyTvHaEWALghTR4A3EJVfSDJbd39QlXdXVWPHH7ojUl6xNIA4P9o8gDg1j6Y5HeHb380yZnDt88m+f0oFQHADWjyAODWbkvylqq6PckDSd5aVW9K8oUkPxqzMAA4SpMHALd2Kcm9SZ5P8niS9yW5kuRCdz83ZmEAcFR1+1UCAACApXAnDwAAYEE0eQAAAAuiyQMAAFgQTR4AAMCCaPIAAAAWRJMHAACwIJo8AACABdHkAQAALMh/AEKck7baxx9DAAAAAElFTkSuQmCC\n", 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