{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "![Callysto.ca Banner](https://github.com/callysto/curriculum-notebooks/blob/master/callysto-notebook-banner-top.jpg?raw=true)\n", "\n", "\"Open" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "# 3D Plotting with matplotlib\n", "\n", "Matplotlib is a rich collection of commands to create mathematical plots in a Jupyter notebook. It is best to search online for extensive examples.\n", "\n", "In this notebook, we will show a few examples on how to do 3D graphs. The basic idea is to set up some data for variables x,y,z, then let the computer plot this into a surface in 3D.\n", "\n", "We first import some useful tools from matplotlib:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2020-07-08T04:44:20.980979Z", "iopub.status.busy": "2020-07-08T04:44:20.978508Z", "iopub.status.idle": "2020-07-08T04:44:21.170058Z", "shell.execute_reply": "2020-07-08T04:44:21.169678Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib.pyplot import *\n", "from numpy import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1. A simple 3D plot\n", "\n", "We will plot a hyperboloid which comes from the quadratic equation $$z = x^2 - y^2.$$\n", "\n", "The key idea is to define a range of values for variables x and y, combine them as a \"meshgrid\" which is just an array of values, then evaluate the quadratic above to give the z values. \n", "\n", "From this data, we then create the 3D figure and plot. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2020-07-08T04:44:21.173481Z", "iopub.status.busy": "2020-07-08T04:44:21.173125Z", "iopub.status.idle": "2020-07-08T04:44:21.292636Z", "shell.execute_reply": "2020-07-08T04:44:21.292899Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "/home/mikel/Documents/CallystoShortsJBook/_build/jupyter_execute/shorts/Matplot3D_4_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Make data.\n", "X = [-2,-1,0,1,2]\n", "Y = [-2,-1,0,1,2]\n", "X, Y = meshgrid(X, Y)\n", "Z = X**2 - Y**2\n", "\n", "# create the 3D figure\n", "fig = figure()\n", "ax = fig.gca(projection='3d')\n", "\n", "\n", "# Plot the surface.\n", "surf = ax.plot_surface(X, Y, Z,\n", " linewidth=0, antialiased=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2. A better 3D plot\n", "\n", "Let's plot the same hyperboloid $$z = x^2 - y^2$$ but with a smoother surface.\n", "\n", "The key idea is enrich the range of values for variables x and y, combine them as a \"meshgrid\" which is just an array of values, then evaluate the quadratic above to give the z values. We use the numpy function \"linspace\" to get more data points into the picture. \n", "\n", "From this data, we then create the 3D figure and plot. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2020-07-08T04:44:21.296349Z", "iopub.status.busy": "2020-07-08T04:44:21.296029Z", "iopub.status.idle": "2020-07-08T04:44:21.436802Z", "shell.execute_reply": "2020-07-08T04:44:21.436505Z" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "/home/mikel/Documents/CallystoShortsJBook/_build/jupyter_execute/shorts/Matplot3D_6_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Make data.\n", "X = linspace(-2,2,25)\n", "Y = linspace(-2,2,25)\n", "X, Y = meshgrid(X, Y)\n", "Z = X**2 - Y**2\n", "\n", "# create the 3D figure\n", "fig = figure()\n", "ax = fig.gca(projection='3d')\n", "\n", "\n", "# Plot the surface.\n", "surf = ax.plot_surface(X, Y, Z,\n", " linewidth=0, antialiased=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3. A parametric 3D plot\n", "\n", "We can also plot parametrized surfaces. For instance, a sphere of radius one can be defined in parametric form as\n", "$$\n", "\\begin{eqnarray}\n", "x & = & \\cos(u)\\sin(v) \\\\\n", "y & = & \\sin(u)\\sin(v) \\\\\n", "x & = & \\cos(v)\n", "\\end{eqnarray}\n", "$$\n", "where $u\\in[0,2\\pi]$ is the azimuthal angle and $v\\in[0,\\pi]$ is the polar angle. \n", "\n", "The \"outer\" function from numpy gives a fast way to compute the products of these functions of u and v." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2020-07-08T04:44:21.446171Z", "iopub.status.busy": "2020-07-08T04:44:21.445578Z", "iopub.status.idle": "2020-07-08T04:44:21.552480Z", "shell.execute_reply": "2020-07-08T04:44:21.552819Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nOydebQc5Xnmf1XVe99Fu9CClnuvJCQhJBYJyRN7MJjDgD1KnLExOI6NCYZ4xhknORObxMuMPU6MZ3LsmQwe4wQM5HgGHGcBZuLIK+CJbSQDWgAJI91dd1/79t61zR/VX3d136ru6r59JV3o55w+uuqu/mrpqqfeer/nfV7JNE2aaKKJJpq4MJAv9gY00UQTTbyV0CTdJppoookLiCbpNtFEE01cQDRJt4kmmmjiAqJJuk000UQTFxC+Kp83pQ1NNNFEE7VDcvugGek20UQTTVxANEm3iSaaaOICokm6TTTRRBMXEE3SbaKJJpq4gGiSbhNNNNHEBUSTdJtoookmLiCapNtEE000cQHRJN0mmmiiiQuIJuk20UQTTVxANEm3iSaaaOICokm6TTTRRBMXEE3SbaKJJpq4gGiSbhNNNNHEBUQ1l7EmmnCFaZoYhkE2m0XTNHw+H7IsoygKsiwjyzKS5Gq21EQTb0lIVRpTNq0dm5gH0zTRdR1N00r+Fp/ZiVaQsHg1ybiJtwhcT/Am6TbhGeVkK0kSmUyG3t5eNE2jpaWFSCRCNBolEAgUvmOaJi+//DJXX311gWybZNzEmxyuJ3IzvdBEVZimiaZpTE9PE4/H2bhxI6lUip6eHlKpFJs2bUJRFNLpNFNTUwwMDJDL5VAUhWg0SjQaRdM0crkc4XC4MK6maaiqWrKuJhk38WZHM9JtwhWCbEXqYGpqipGRkUK0u3XrVlauXFn4vyyXzstqmkYqlSKZTNLd3U1rayvZbBZZlgtkLCLjUChUsl7xEmQrSRKGYeDz+QgGgwVybpJxE5comumFJrzDMIySPC3A7Owsr7/+OqqqsnfvXpYtW1b4TNd1VFWdR7p2vPTSS+zbtw9FUdB1vUDG4pXJZJBluUDCgpDtkfH58+eRJInLLrsMSZIwTbNiZNwk5CYuIprphSaqwzAMNE1D1/XCe5OTk/T29hIKhdi8eTOxWKyEcL1CkCSAoii0trbS2tpasoyu66TTaZLJJHNzc4yMjJDJZACIRCJomkYoFCKbzRIOhwskX36DEOuTZRmfz9ck4yYuKTRJ9y0O8RivqiqGYRTeGxsbo7+/n7a2Nvbs2UMkEmF2dpbZ2dkFrasSFEWhpaWFlpaWkvcNwyCdTjMwMEA2m6W3t5d0Og1AOBwuiYwjkUiBVIWczQ5JkojH46xYsaIgcWuScRMXEk3SfYtCaGw1TeO1115j27ZtKIrC8PAwAwMDrFy5kquvvrok12qPVmvFQghN5IBbW1uRJIkNGzYAFqlmMplCimJiYoJUKoVpmiVkHI1GCYfDKIqCaZr86le/4tprryWXy5Wsx56mENFxk4ybaDSapPsWg51sDcNAkiRSqRQDAwOMjo5y2WWXsX///oLkyw5ZlgvRcK1YCGHbxyjfHhHdrl69uvC+aZqk0+lC3nhqaopUKoVhGIRCIXK5HBMTE4XoWJCxyGWXa42dcsZNRUUT9aJJum8ROGlsVVVlcHCQ2dlZli1bxsGDB/H53E+JhUa6CyXdWtYlyHjVqlWF903TJJPJcOLECXK5HDMzM6RSKXRdJxgMlkTGkUgEn8/nSsaappFMJlm1alVT3tZETWiS7pscTmSby+Xo6+tjamqKTZs2sXLlSjZs2FCRcGHpkG6lbQiHw/h8PjZt2lR43zRNcrkciUSCVCrF8PAwyWQSXdcJBALzyNjv95NOpxkeHqa9vZ1cLteswmvCM5qk+yaF0NjaIzRRPTY3N8eWLVvYvn07siwzPT3tKW2wUOJsBOkuBnFLkkQwGCQYDLJy5cqSdeVyOZLJJKlUitHRUZLJZEGTrGkao6OjBUL2+/2F7WsWfjThhibpvskgyHZ0dBRN01i3bh3JZJKenh4ymQxbt25l165d8yIzL2TmltP1QhqNIJYLHS3byXjFihUln01PTzMwMADA+Pg4yWQSVVXx+XwlkbEgY4FyMs5kMuRyuXlqimbhx5sXTdJ9k6C8oEHTNGZnZxkdHcUwDDo6Oli+fLnjhSyqvaphqacXGgm/308wGCwoKQRUVS2oKSYnJ+nv759XEi1egUCATCbD9PQ07e3tJSmgZuHHmxdN0l3icCpomJ6epqenB4A9e/bQ3t5ecQyvqoTyiNg0zcK6MpnMvMmoaDRayBO/2Ui3XOEg4Pf7WbZs2bwCEjHxlkwmmZ6eZnBwkGw2i2EYyLLM+fPnC8csGAwWvtcs/HjzoUm6SxBOBQ0AExMT9Pb2Eo1G2bx5M+l0uirhgvf0goiITdNkcnKSnp4ewuEwO3bswO/3lxDLyMhIYTIqGAySTqcZHx9n5cqVBWXAUoYb6brB5/PR3t4+7/cYGxtjZmYGv9/P7OwsQ0NDjiXR5f4U5YUfuVyOeDzOmjVrUBSlWfhxCWNpn/lvMZRrbMV7o6Oj9Pf3s2zZMvbu3Us4HGZqaopkMulpXK/pBYBsNsvRo0dpaWnhyiuvJBqNYhgGuVzOMf8pJqNOnz6NrusMDQ25yrSi0SiKolQ9BpcCaiVdN0iSRCgUYt26dSXv2/0pYrEYIyMjpNPpghyuvPBDVVWmpqZYtWoVuq43Cz8uYTRJdwlAkG08HmdiYoLLL78cwzAYGhri/PnzrF69mmuvvbbksbSWQoZqywpi7+3tRVVV9u/fX2JEUwliMioUCrF27dqC34JpmmSz2UJkPDQ0RDKZxDCMEjIWHr2X2sRSo0hXpBfK4eZPYRhGgYzj8ThjY2Ok0+mCSqW/v7+EjMVTTLnWWPzbLPy48GiS7iWMco2tpmlMTk6iaRrDw8OsW7eOAwcOlMyOC9RKuk4RpGEYjIyM0N/fz4oVK7j66qs5fvy4Z8K1ozynKyK8UCg0T6aVyWQKxDI4OFioJgMrZ+r3+0uqyS4GGkW6tY4jy7KjP8XU1BTj4+NEo9GSkmiAUCg0T2tcqQpveHiYjRs3NuVti4Qm6V6CcCpo0DSNgYEBpqenWblyJYcOHapIOAuJdEUUPTAwwOrVq7nuuuscy4LtqHYxep1IEwUM4XB4HhkPDAyQTqfJZrNMT0+XlPaWR8aVbCYbgcWOdOvZnmAwyJo1a+aNb/enmJycJJ1OzztudjIeGRlhw4YNqKraLPxYBDRJ9xKCU0FDNpulr6+PmZkZ1q9fT3t7O5s3b646Vi2kK3K6uq5z/vx5zp8/z9q1a12j6IsBSZIIBALIsszll19eeF9ExslkkkQiUfBZcDK9aSQZNyq3LKRhC4UbeVfyp7CTsf0mlk6n6enpcSyJhmbhx0LRJN1LAOUdGiRJKpz4yWSSLVu2cMUVV6DrOuPj457GrNWcZnx8nN7eXtavX8/1119fs7qgWuTXKMlY+Rj2yLjcZ0F484oIT5BxJpOZRyr1EF+jIt1GpEhqjZjdjpumaRw/fpzly5cXcu32ic/ySbxKZDw7O0soFKKlpcVR3vZWRZN0LyJEVDEzM8PKlSsLXq89PT3kcjk6OjoK74NFpHY9biV4IV1VVRkYGGBgYIBly5ZVTVlUQqPSCwtZR/mybhHesWPHaG1tLSFjwNEO0o3IGpnTXcxIt57t8fl8rFy50rUkulwS6Pf7S5qSiiq8mZkZli9fTjgcdi38sEvb3iqKiibpXgTYCxqEwYqiKPT09CBJUqF6rBy1EFcl0s3lcvT39zM+Ps7ll19OV1cXuq4vGuGKZS4FuZcoLFi9enUJGYsboCCV8fFxR6N0QcaNzOleSrlht/PArSRa6MXFcRsbGyv4U6iqSjqdJp1Ol1ThifPgrVr40STdCwS3goa5uTkmJycB2LFjxzyJkB21znKXk67oujA9Pc2mTZs4dOgQsiwzMjIy7+R/q8HeLNMONzIWPgtACRnXSgyNjHQbUXCi63rNaYpAIEAgEJgXKLz66qusXLkSwzCYmJigr6+vxJ/CHhnbJ2qdOn6Mj4+zbt26N0XhR5N0FxlOBQ1gVSL19fUVTrq9e/c2dL120k2n0/T29jI7O1viLiZQS3FEvVisnO5iw42MR0ZGSCQShMNh4vE4o6OjFYsX3IjhUlNBNCrHDNa+LVu2bJ7EUFXVEoP5gYGBef4U4hgGg0EkSWJwcJC1a9dWLfwQQU1bW1tD9mEx0CTdRYJThwbTNBkZGWFgYKCge/X5fLz00ksNX78g0ldffZV4PM7WrVvZuXOn4wW+kI4QYEXQk5OTFfOgFzqneyEgCj7sKC9ecCLjlpaWQllvI8lyMdMLjRzL7/c7lkRrmlY4djMzM5w/f55sNossy2QyGc6fP184hqFQqHBOCeUNwPe//31OnjzJn/3ZnzVkHxYDTdJtMESllaZphSoqUf46NDTEmjVrSnSvQpPbSCQSCXp6ekin02zfvp3du3dXJKx6SVf484oJE3se1B7ttbS0FNIrbxa4RahuxQuCjBOJBLFYjOHhYTKZTKEqb25ursRjodYbzKVG3lA7gft8Ptra2uZFqblcjuPHjxMIBEqOnV0OF41GSaVSzMzMePIbuZhokm6DYC9oGBoaQlVVNm7cWOg95ibFamT0Fo/H6e7uJpfL0dnZWTBAqYZao1A72W7dupUdO3agqmphX5yivVgsxvj4OBMTE4VIr6WlhUAgcMlFsF5Q6w3EjYzPnDlTyIU6EYo4VvZHbSdcipFuIwk8GAxy2WWXlbyn63oh3x6Px/nKV77CCy+8gGEYnDp1il27dvGJT3zClYTvvvtu/u///b+sWbOGV199dd7npmnyyU9+ku9973tEIhEee+wxrrnmGgAef/xxvvSlLwHw2c9+lo985COe96VJuguEU0EDWDnb4eFhLr/8cg4ePNiwE1mkDewncywWo7u7u+CbK2aXvZKZ10g3k8mQTqd5+eWX6ejo4IorrnAkbCeC6evrK1RAJRKJksdH0Xq93GvWCZdStNyom4XodGyHULaUHyt7jtlOxo0k3UZW8zXiGGma5jhJKM4bcZ5985vf5Ctf+Qq7du1i7969nD59umIl5V133cUnPvEJPvzhDzt+/k//9E+cPXuWs2fPcvToUT7+8Y9z9OhRpqen+cIXvsCLL76IJElce+21HD582FFx5IQm6dYJp4IGEQFOTU0RjUY5cOBAw8tRBUHKsszMzAzd3d3IskxHR8c8D9dax3SDmIiLxWL4/X4OHDhQ80y5mGV2MnERlpCJRKJkllt4LAhCXuzJvlrQSNWBEzG5Gd7oul5QUtjJOJvNoqoqy5YtK7lx1ZOmuFh+Fm4QqToviMVirFq1it27d7N79+6Ky77jHe+gr6/P9fOnn36aD3/4w0iSxMGDB5mdnWVkZITnnnuOm2++uRDc3HzzzRw5coQ777zT0zY2SbdGlHdokCSp0A4nnU6zdetW1q1bx+jo6KLU/8uyzOTkJAMDAwQCAbZv377gmVo3wxtRFTc3N0dHRwc7d+7k2LFjda2jUgrDzWu2XIw/OzuLpmnEYjFHF7ILiYtVHKEoimPe89SpU4XZfbtJulvHCrdtb2R6oVFwi3SdMDc3V3fwUY6hoaGSkvONGzcW5mac3veKJul6RHmHBkmSiMVi9PT0oOt64bFekiTm5uZqnhyrdhEL4/C5uTlGRkbYtWvXvPxgPeOKfbFHkalUip6eHuLxOB0dHSU91RaiQqj1e+X6T9GLbP369SQSiXkuZPYihpaWlooVZQvFxXIZq4S2trYSo3Mo7VjhJs8Sx8vv92MYRlVzIy9oZBpI1/WaSLdRE2lO++B2/tdkaL+grXqTw17QcObMGbq6ulAUhZmZGXp6evD5fHR2ds77kX0+X03FBuLx3inCME2T8fFxenp6aG1tpb29nW3btnkiXBHBVjshxPoF2SYSCTo6OhxVD/UqHWollnTa4OWX05w8maK7O8vkZIZsNk02qxEMZlFVE00z0XXQ9TCaZpDLGajqLLo+gapqhEI5wmFYscLHunUhNm+Osn17K5qmcc01BopSPyFfivpap3HcniLKybi/vx9VVVFVlZaWFlRVrZpfr4RGRsy1RLqxWMxzbrUaNm7cyODgYOH/58+fZ/369WzcuJHnnnuu5P0bbrjB87hN0nWAU0FDIpFgbGyMoaEhwuEwO3fudCU+RVFqinTF8vaTVBiH9/X10d7ezr59+wiHw7zyyis1WzZWu6iz2SyxWIxTp07R2dlZUWJWb6Rb/r2xMZWXXkrz6qtpzp1TGRzMMTamMTOjkUgYZLMGPp9EIGARsGlKgAT48PkyGIaG02Hw+630j2FIQND2SQ5IA2OAAfwEv98kFDIJBiEa9bFihZ/9+5dx882reNe71lYk5Ust0q2VvN3I+I033ihI1pyqyMojYzc0mnRryek2Kr1w+PBhHnzwQe644w6OHj1Ke3s769at45ZbbuFP/uRPmJmZAeAHP/gBX/7ylz2P2yRdG4Tsy7poiwUNY2NjxGIxAoEAe/bsIRKJVBynHtIVRGoYBsPDwyUFFPZHxkZ2hEgmk3R3d5NMJgkEAlx//fWLZlxz/LjB00+rvPRSH319OtbhMQkErJeugyXx9QEmigKSpJJKlT8xGGia2Ccdi4iLUFXxnrWN4bBBOp3Jf6oAcv4Fqmq9EgmTeNxkfDzL6dPDfOtb/cgytLX52LgxyKFDK3nPe9bxa7+2qnB8lkqkWytM03QkY7u/gujFp2laYbKzvOV8o0nX3hWlEoQBjxfceeedPPfcc0xOTrJx40a+8IUvFFzSfvd3f5fbbruN733ve3R1dRGJRHj00UcBWLFiBZ/73OfYv38/AJ///OdL/CiqoUm6OJuGC/IbHBxk1apVrFq1iq1bt1YlXKiddGVZRlVVxsfHGRwcrGgcXsvYbqQryDadTtPZ2UlbWxsnT570RCJeSf+VV7I8/nicF15I09enkckYKIqELIPfbwIW8eZy1mv+ekxUVcYiSjvx6likKY5NjuJpnKMY3eqATjrtzy+r5j9X858VYZoS2WwxkrZeGpOTOWZn05w5M8Njj3Xj80m0tChs3hxhzx4/997bic0zpy4slYjZrcuxfbLTbnYjHPGGhoZKyLgeeM3p1hoMPPHEExU/lySJr3/9646f3X333dx99901rU/gLU26bmQ7ODjI0NBQSTucM2fOeM7T1nLyC4H38ePHWb9+fVXj8FojXTtBJxIJuru7yWQydHZ2FmwjRWTvBW6R7uioziOPJHn++Sx9fTqplEkqZaDrMhDCIjphYqLkX24wkKQMimJiGDJ+vw9FMTFNA8NQ0DSFYNBAlk2SST8tLQaJhEQ4rKDrBsEgpFIQCikoCui6QTrtxzACSJIBqJhmliKZm/mX/XeztlvTwDQ1FCVHOm0Qj2uMjMzxwgvw2GOTrF0rs3t3kDvv3MTNN2+qWUnRKJcxaIwmttYI1c3sZnx8nLGxscKToiBjYQNZ7slbCV5zuuK8vNSLbd6SpGuaJslkElVVC/krTdMKdocbNmyY5y1b6+RYNYj2O8PDw/h8Pnbt2lViJu2GeiLdRCLBuXPnCpVqQmUhUIvhjSBd0zT54Q/TPPZYipMnswwNaWQyJUtSjFIziMd9RQG/H3w+K+oFCV0HTTPRNNB18PmS5HIiRWCSy5mF71vQSKfFezqJBIBKOm3tgxU5S4hmyNGojGGogIJpyoAf8CPLGpDK53/doet+dN1HW5vO3NxcYVtUVeL8eYXz59M8++wZotFXuewyiX/xL1p43/vWcNllKzwZpV9KJNEona4o4ti4cWPhPTEpLZQndk/eQCAwL00hiNZrTjeTyXh6Er3YeEuRrr2gYXJykmQyycaNGwslrXa7w3LUmjJwg6qq9Pf3MzY2ViD3c+fOef5+LZGuruu8/vrrmKZZiGyd4DVPG4vpPP54iP/3/+K88UacTMZ6hBc5VL8fZNnIF0IoqKqPcFglHi+mSSy1QfnIBoJg29pM5ubsuVrx2C/nlxHLis/FbxXIb0v55+R/T7FSqfAdwwhgTa4ZJdtQul6l8PfcnI/W1jbi8fLW9pZyIpeDmRmDM2dm+Na3Jti3r53f+Z0NXHNNZJ5Ruoj2GikZawQaVZHmFDELG8gVK1bM8+R1M0gPBoMFhYWu64XWQU6YnZ29pN3FBN4SpOtU0GAYBqOjo0xMTLB169ZCSasbFhrp5nI5+vr6Ci3U7eRun0irBi+kG4/HOXfuHLFYjK1bt1btqVbton/55Qz33RfjlVd0oBUrejWQZYlgUMY0fWSzEqpaPk6KeFy8Z0WlzqRWPA3jcSP/nmFbVs4vI8hR5HpVrNRFLv9eECuqlvPbaBG1ptnHUfLboeW/L35TCSsCLocgeusVj8OyZSFmZ+fyy9v3Q8DSu7788iynT8dYsybEzTdv4LOfvZZQyCjxpEilUrz44os1+Sw4oVG62EZNgNUyTiWDdGF2Y5rmvNZB5f3vGqlcWEy8qUnXqaBBtMNJpVKEQiGuvfZaTye38Or0CkHsgmynp6fZvHkzXV1d8yKJWqLoSsvOzc3R3d2Nrut0dnYyNjbmSc/rhhMnstx33ywnT4rjJxMOG6RSFjkZhlAclEOQWpZSxYDTRWhikZ+J3y/nibsdSGCRmX3iS5BcLv9vCEXJoOsiktaBEMGgSjZrvRcK6XlpmSBU+2SaIO3y7RYEJra9NAc9O6tjEbzYdoPiJJz4bWUUpRVJSjMwkOSv//os3/1uDzt2tPOHf7iXd7+7A4Bjx45x9dVXO1oa2gsYBCE3onChEhoVeddS0OAGQcayLLNp06YS5YhwZxN93P7qr/6KH//4x0iSxB//8R+ze/dubrnllpLuIOU4cuQIn/zkJ9F1nXvuuYf777+/5PM/+IM/4NlnnwWsgqHx8XFmZ2cB6zrcs2cPAJs2beKZZ57xvF9vOtJ16tAgSRKzs7P09PQA0NHRgd/vp7u72/MJ5vP5CraFXnH69Gnm5uYKTlxu66q191k5+c/NzXHu3DkMw6Czs7MwqTExMVFXIcOpUzl+93dnOHFCJxTyEQqFyGRkTFMnlXKQGmBQJCsfFsEFKFUW2PdBz0+ESWQyMrpuEaLYLVnOIMsKuu5DkqwJNCsXm8qPLRQKaRvhgkWAAbJZPxbhy2Qy1voVJYuupwEdSZIxzQDgIxrVkSSDZFLCNMsn+Mz8fokIXXwujqlEUUVhX976XNcV0ukQoKGqBqqq8ctfTvGhD/2EtjYfv/EbW3jPexRXnwV7AcPk5GSJZtbu1BaJRBqaomiUSU15ddxCUD4HEQqFCIVChZTZV7/6Vf7pn/6JZ599lne84x289tprzM7OupKuruv8u3/37/jhD3/Ixo0b2b9/P4cPH2bXrl2FZb72ta8V/v4f/+N/cPz48cL/w+EwJ06cqGtf3jSk69ahYWpqit7eXgKBANu2bSvkfITnrVd4TS+Iqi6RL67mZQv1R7rCXUzkbMsfrWqtHnvllRz33x/j5ZchmfRhGEHyqUgsIrGITOQ+o1GJZFJHTEyVIxCIkMtl8ftNfD4dTTNRVQXDUEiny6Neg2g0RzKpYxjhfL4VTDOIRbY6EKGYFhBEaL8BCYWEyM0KApQxDBloAbJ55QJYk20+h+8GKKYNSvdNUUza2gxyOZls1qD0lHBKUWhYN4lUYRldh5kZjUcfPcfjj5v8q381w1/8xTtZs6a0O4VbAYN9Mmp0dLTw94kTJ+YpAy6Wj8LF8HCYm5tj06ZN3Hrrrdx6660Vlz127BhdXV10dFhPHHfccQdPP/10Cena8cQTT/CFL3yhIdu55ElXyL5Eg8ctW7YAlmSlr6+PlpYWdu/ePa/dSq052mrEaDcO7+joQNM0li9f7jl1Ud6CxA2yLJNKpQrdJpzI1r6sF9J9/XWd//AfNnLyZLwQdc6HICoTkS6w1AFup1COXM5KG1hFCG7jisd8hWSy/NHZAOJYKQDxfRHlzmGRsB0J5pNeDjDzFW3i+0Egmd8XsbxiG08oLux6YGt7dD3GzIwPkXrw+3N5L2F/PhovR1H3W4yaQZC6YUj84Afj7Nv3bX7t19bxjW/czMqVYYdxivD7/SxfvrzwRKNpGidPnmTnzp0Ft7ahoSGSySSGYRQsNQUh19tyvhY0inRrSXfUYnbjZFpz9OhRx2X7+/vp7e3lxhtvLLyXyWS47rrr8Pl83H///fzGb/yGp/XCEibdco2taZpMTEzg9/sZGBhg+fLl7Nu3z/URp5ZHenAnaWEcrqpqienN2NhYQ/K0dszOzhakX/v27atq7FGNdHt6dO69N8err+aYnXWa9RWTSAqRiM8W9brBoJSsBKFZ0qzSR/dcfnmRiihHLj+WkwQoQWkuVsCJSAL5caBUhxvNrz+BdRnYt82HFRWL7RA55BSll4yEqlokbppi30XkX0o4waBCNqvbvm8gSSaKYqJpMomEj2efPc+OHQ9z660dPPjgu2hv91aFJWRebpNRmUymQMZOLecFGZf3MlsILsaEXCwWY926dZ6WrcW05sknn+R973tfyXYMDAywfv16enp6uPHGG9mzZw+dnZ2e1r3kSNepoEH4FMzOzrJ8+XLXai47as1blROj3Tjcnkd1W77a2JXI0e6bu2nTJmZnZz05KbmR7tCQzsc+luPZZ00CAcvnoJSQDEIh0DQ/mmYRmXWd5sqWE8hgEVgQcLpwfUAbljwrTXHSyQ1xLOJyGkuoEpzg9n6ISCRZmAAsXb4NK9JO4UzkIkL157dZx3lCUKZ4gxAELG4qMtls+ZOMjGla+uRIRCKVyuYn/1I8/fRZjhzp4b3v3caf//k7aWurTL6VSoAlSSIcDhMOh0t04PYux/ZebqlUitOnT5eQca1KCmgc6dZqduM10nUzs3HCk08+Oa8yTSzb0dHBDTfcwPHjx9+8pKvreqE1jK7rJe1wotEo27ZtW5T1ikjXToBODmMCtRYxOC0r1qUoSsE3d25ujunp6brGnZiwItsjR8Tjtplvda1g5WgNDMNHOh0gkym/yPxYRCIuJKFO8DneJUIAACAASURBVFFqLOOGFEWS07EIXOhxLcKQJJ2WlgzxuPsETEtLmkTCeX2BgJ9czjlllEpFiUYTDikMsPatHeuGIL6fpihVE+sLYUX/WdzJF+YTcJpi+XL5cZXyN7RgftIwCOTIZnWefPJ1/vZvf8W9917FAw+802Vd9fku2DtQiJZOIk1x+eWXk0wmmZ2ddVRS2FstueFiRbpeSXf//v2cPXuW3t5eNmzYwJNPPsn//t//e95yv/rVr5iZmeHQoUOF92ZmZohEIgSDQSYnJ/nZz37Gpz71KW87xBIkXTF739fXx+TkZEk7nJGRkZrH85IzMk2T2dlZYrEY/f397NixY95MczkWIgObnp6mu7sbn883b121krmqqsRiFtn+n/9j5quvrP1taUnnyVVH0/wuhFQyIpGIMKEJ4vzoXwqfL4vPZ5DJ2MdWKEax1gRdJJImlcrmCynKS3IF0iQS7iXSuZyY5HP+PZPJKBAr2+4cFolaZCvLPny+HLmckKeVw5KqWRDphGqkkM2vU/g/iIKLUlg3wiCSFMA0Z7E0xjL/83+e4IUXhvjHf7ydaHT+b9To9utuSgrRPshuBWlXUpQb3ixUMibWuxiRrs/n48EHH+SWW25B13Xuvvtudu/ezec//3muu+46Dh8+DFgTaHfccUcJR5w5c4b77ruv8CR5//33u07AOa7b85KXCGKxGCdOnGDLli1s27ZtQSebeKx3u5OKPHFvby/hcJhQKMS+ffs8jV3LRJ0gUkG2fr+fK664wpHYa/VeeOihEA8+mEXXi2RrIUMioVDUvlaCCeSQpCDZrCC1am5klr+BpoXQtEqkZBFlKhXCyrNCMRIWGlixzgxWjlakQ8ojRyn/XR/FfLSlcvD7QVVFOfJ0/rtCmSAm1yztcS4nJtqqEapFvsGgit+vkUiUHxMdi+QFUYr12TXMTuQr5Gng85lomsHLL09y5ZV/xT/8w2+yb19p3vJCNKV069Qr3MeE9anwWEin03R3d5cQcj2Rb61dI2rx0r3tttu47bbbSt774he/WPL///Sf/tO8773tbW/jlVde8byeciw50m1ra+PQoUOO0alT08ZKEMRYfjIIk47e3l5aW1sLdo4///nPPW+n14jUNE3m5uaYmpoCcCXbWsdVVYM77ojywgulxOT3a/kChAjuOVo7cvm8eQDTBF2PIkk6ihJH05wIWwPS+cdkLzrNJPPJR0TC9pxuDCs1UQ57+a7QC9tLh4s2jkXyExK0SudJFIv0kzhP9BWRzfrz2uBE/jthZFklGMyQTjt9VygahEytmGIph6ZJSJKPaFRmairHTTc9wZe+9Gt8/OMHikfgItpDOrmPmabJsWPHWLlyZaF4oVxJYdcYV1rnxfLSXUwsOdKVZdk1HeD3+1FV1bP3pqIoJV6dpmkyMjJCX18fy5YtKxiH14NqMjDTNEsi20gk4imK9hLpnj2r8y//pcb0dJF0wKSlxSSRCFEkOA03QgmFNGTZJJXyUz7Ra5oKmrYMi7xUrOjNoFi84PWYCeWAl0kaMZlVjvILVnZ4rxwRYIrqNwWR643h7YmgJb+d0xhGLl8YUQlCplZKvrIslRi0myYkEka+ItDHZz7zM55/vo8nnnh/zYFGJTQqDytJErIsO3osCCWF8FOopKQQRlReI91arv2LiSVHupUgIlevB97v9xeKKYRx+MqVK7n22mtdx/CqG3SLSE3TZGpqiu7ubsLhMLt27SISiXhu+FiNdB99VOMTnzAIhYSe1no0l2W/w+Pv/J8/GFTJ5cpzsG6I5MefzP9bSwVSnGoRZBFzeCdyr1gBzFB9ElAClmHdIIQvhBPSKIqokGvFOh5zeLsJWOQrSQammZl3kxMwTSlvBgT//M+j7N//EE8//Vv56r5Lh3Td4EVJIdIU9upPkdpraWlxVVI0sifbYmPJkW4lwhORrlcoisLw8DDT09OsWbOmqtRMqAG83HlFFC0gGkv29PQQDoe58sorCwUboprOC9w695qmyQc/mOOppyyiTSbFeFbpqvPwQQKBDLmcMI8xCp4F3mBgEUsbRU8EUdXlFhkKbWwtEYmK11PVutl5WVLCIvJKEjQ7WrD2L0XxZqFiKRMA/Oi6/cYgPCSyZd9xh1VcESEczhAIBJmdzeB8DBXm5mBuLsX+/f+TRx+9lR07Ft6MsZFpilpgV1KUj/PGG2+gKAqxWIzh4WEymUxheXtULK7bS8mxzQ2LW5aySHA7sF4nr3Rdp6+vj+HhYXK5HAcOHGDbtm1Vtb0+n8+zckAsKybjjh49yujoKFdeeSVXXXVVyQm20BNldFRn794c//APSr5QRBBJgMoTQXJeYiWkYLUQbhaLPCMUiUFEeW35vzWK0jAAg0AgRS2EqyhJaolydb2WiCdM2XVeBUI+lsBKOYjUSqWOCEFgOaKTRWWYQIxUSmN2VkZR/Ph8lfZHIZHQueeeI/zgB31ed8IVjYp0G+nJK8syq1atorOzk6uuuooDBw6wb98+NmzYgKIoTE1N8eijj3LttdcyMjLC7/3e7/HNb36zql3qkSNH2LFjB11dXTzwwAPzPn/sscdYvXo1+/btY9++fTz88MOFzx5//HG2bdvGtm3bePzxx2veryUX6VZCNdIVxuEjIyOsX7+eLVu2EAwGPbcRqSV9IcsyyWSSo0eP0tLSwlVXXbUoBsvnz+vs2aPlvQzEZJLwDqiGNFYEl6KS1Go+hK1hpXSCQrGqy0SW0xhGPC/rUik6eFWGrqcoqhq8oLY4IplswcrvlhO7jnUzUlEUS0qm6z4MQwGW5TW/tRC8KMJI4HxzEyXPRbKySrJ9+e84Kx1AIhbT+c//+SiZjI9//+9/rYZtKtuCBuaGGyEXA2f1QrmSYtu2bfzmb/4m9957L7fffjuvvvoqo6OjdHV1uW5fNbMbgA984AM8+OCDJe9NT0/zhS98gRdffBFJkrj22ms5fPhwTaqJNxXpuqUX7MbhGzduLOh6h4aGGuq/AEWZmSjXPXDgwKKQrWmaDA6O87a3hUmnRW5ViPmr7ZPwOxBE00LxUblStKsRDCbJZmvNr0oYRob56gOr2qulRSeREI/SIuJWsJQDtR47oQrwAiEp82PdSMT3FKwI1YpinYzXLbKepbpG1w4/VtQbp+haBtZxSOI8loT19CDKop0DhFhM50tf+inHj5/lj/7o+hIXskAg4OlpqpFVZI3KDXsl8FgsxurVq3n729/O29/+9orL1mp2Y8f3v/99br755sIE4c0338yRI0e48847PeyNhSVJum6dDnw+X77CyoLdONypK4TP5yNT2mOmIipF0qZpMj4+Tk9PD21tbezevZs33nij4YQrbCtfeOEFPvGJK5icFIRb9A+QpFzeptAJmfyy5VGqeEwWUW/p92U5hWHodRAuWBNWbuXBvny7HXs0K6q+khQnA+2fUfZ/e5cJUYJb3uJHIhgkX/IsjNOFVWNrfn21WhEuo3bihaIRfDz/f3ulnxuEl0USZ40yZDLw1FMjpNMv89Wv3ljizStaqNvJuJzMDMNoSITa6E7AXrZpbm7OU2k8eDe7+bu/+zt++tOfsn37dr72ta9x+eWXO353aGjI03oFliTpusHv95NIJMhkMlWNw6E+p7Hy5e2a3ra2toLMTNhM1oJKyggxEdfd3Y2maXzzm/t57TUh1Qpgf6x2drsS1ozVSFNImJKIybCWlmS+kKKe0yVG7WQmIt4otROaU5NJC7b7sQOWYxForfu4DGsfqxeM2OH3a4RCPnRdI5Xy+j2J0qeS+cdG1+F73+tnYuJ7/OAHHy2QX3kRgzC7Fx0YWlpaSKVSnomrEhpNul7G8upHAt7Mbv71v/7X3HnnnQSDQR566CE+8pGP8JOf/KQmoxw3LEnSddtJXdcZHx9namqKLVu2VDQOh9pJ1z6RZifb9vZ2rr766hJHM699xwRE6qL8rm5XPUSjUa666ip+//dH+fu/V5BlMIwg8y92f74iTLwviiC8RqkKViogBSRJJOwdEWqB0OHWgxlqJ2soRru1XvRuOVMvEFpesX43qFhpDAlVDaGqdlN00XLIC8RTiUhTzPdz+OUvx7nqqgc5evR3aWkJuhYxiA4MiUSC2dlZpqenGRwcJBwOl0TFooGrFzSSdE3T9JRnbrTZjb2f4Mc+9jE+/elPF7773HPPlXz3hhtu8LRegSVJuuVIJpP09vYSi8Xw+/0cOHDAs5a2VtJVVZWRkRF6e3tZvnz5PLIVqMfFzC61set5I5FIoSru7/5O53/9r3W0tvqIx90mAGVaWnTicQXr0dVeEOEVwvu1Nf9vimKBgpeJRyGlqndiZiG6y3q/uxxLc1xPS5x2LEItJ0ExQSZaAznd+MIUJ8y8XpKiU4cfN8IeHEzy9rd/nZdf/gPXCk57B4ZcLseqVatob28nnU6TSCSIx+OMjIw4SrXcTG9qKWhoFGZnZxtqdjMyMlKwiXzmmWfYuXMnALfccgt/8id/wszMDAA/+MEP+PKXv1zTti5J0hUnULlxeGdnJ6dPn/ZMeKI4wgtM0yQejzMxMcHatWu55pprGtqOxD5JJ8g2FAqV6HlPnTL45Cd1TDNIPF75p4vHDWTZ6sJQO1SsVIS4oETeE6wLPUWxFY+bF66QU9WOYDBVZ+7YQjisuPRuqwbLcKZ+0m7Lu6AJvXKS4jGqdizs1W/VLksxqSYiZZmij3EpentneM97HuYf//FjVbdeRKhuulld1wtRsd30xu/3lxCxqqoXpWuEm1qhHF7Mbv7iL/6CZ555Bp/Px4oVK3jssccAWLFiBZ/73OfYv38/AJ///OdLqu68QKryCHxJlnnEYjHOnDmDpmklxuGapvHSSy9x/fXXexpH13VefPHFisvbS4NF/uuKK67wNP7Pf/5z3va2t3la9uTJk6xatYrh4WECgQCdnZ0lTSWzWYNt23TGx4VRiztCIR1Ns17FdjFeIQjT6/04k38JwtKpvfihHEMUSb4eTFBftGohGJwmm62FNER6IEdrq0w8LirR6klXWFrdSpVvkqQ55O11inaURUhSEtOEe+45wFe/+usV13z69Gk2bdpUczPTXC5XaBmUSCQKUWBLS0sJGYfD4ZokaYZh8NJLLxUIrhL+43/8j9x00028+93vrmnbFxGuP/6SjHQBtmzZsiDjcKjcPcIwDEZGRujv72fFihVce+21xOPxgjGNV3gpG56ZmWF6eppcLsfOnTsdT/rf/E2T8XHhsOUOSdLQdfJmNGKiTZi2VDvhhU9sLadFCJF79flUwuEYqmqSy6Xzfcn8HtZrh8bCS34XVmySzQaxbjxO49j1uxKyrKBpvjwJhojHAVahKFN5Z7daIcqO4xTbzQsksFoPOR1P4eOQonRS1Up3PPLIMa64Yg333nvI4bv5PaszFxsIBEp8Fnp7e4lGo7S2thbIeGJiolDaK9rNVzNJr0XvW0urnouNJUm6ra2tDcmjOi1vJ9tyH4Z0Ol2XrtftxBHtdxRFYcWKFVx++eWOhPvf/pvBCy8IZyqhLXW68FRMU0ZV7Z/JFHWeWdwjUNHpoP7HQk2bIx4vL2QQDSLtzSSFOsGpVHia+ibQGokoMIZ1vDMU86dCQ+yu3xXQ9RX4fJNoWr2XWCtFQyGZYDCdV19UuoHJ+W1PFpYLBv1ksxqmCX/8x99j+/bV3HCD82N4oyrJxDkvfBbsHXkNwyj48pa3m7dHxdFotGYv3UYoLy4EliTpLgaE6U1/fz+rVq1y9GGot5ll+YkTi8U4d+4csiwXOkK88cYbjlH3mTMGDzyg2LrWyjhPnKhUNlexWo4XpWD2i0skQBdywaVxPp3md9QtwvLp9fmyaFou/3/RvUGyvWTbv14MZJwlc1ZH4izWzUW8RAbNvj4Fi/iFf289qQoJTVuOVe1Wb6ojkt+GGbJZr5I0S1YWCuXIZLQSzw1VNfjgB7/NP//zJ+joWDXvm7quL7pxjizLhSjXDk3TClGx8OXNZrMYhsG5c+dKrCCdxo7FYjVVhV1MLEnSrRbR1lLOaFV2DTIwMMDq1avZv3+/qwdDrekLp75q586dQ5KkknbwYtlyoxBdNzh8WGZ2tvRnCoelsokiUVZb7aIUUa+KUDXIcgrTlG3ysnogTGxqr1SDIJomom8xOVRtW+yEaf9bvIRVolzysszUaylWKUaM9UH0hqtHOpem2GUiit+fRlW9T7FkMgHCYQnTVLEXaSYSKu9610OcOvUfaGkpfaK4EKTrBp/PN0/SNj09zdjYGMuXLyeZTDI4OEgqlcIwDCKRSKFLxdzcXKE/4lLAkiTdShCKhGrmNYZhMDQ0RCqVIpVKVSRbgXoj3bm5Oc6dO4dpmnR1dTk+Bjnll3/rtyTOn5//E6XTfoopBqEiqIU0rcgzGp3Ju5HVP+lkwcm7oB5MexynWrRba17aDVGs47sQhPNjeHEzs8qBFUVG1+3KEEFgCQ9jFJFOiw4cpZicTPOhDz3OU0/dN++zS8ki0jAMgsEgK1euLNHNmqZJKpUimUzS3d3Nn/3Zn9Hb28tNN93Erl27eM973sN73/te13GPHDnCJz/5SXRd55577uH+++8v+fyrX/0qDz/8MD6fj9WrV/Otb32LzZs3A9Y1vWfPHgA2bdrEM888U/N+velIVxCjG4EahsH58+cZHBxkzZo1LFu2jC1btlQlXKg90tV1nTNnziDLMl1dXRUT/eVjf/vbBk895WZcI8hWo3bCFUiTTAbzY4nIUOg+a7nwFqpUsMP7sa0MpUFjtQKj1Ct9K6IdS//rhiRFiV3AMU+sqn4ikRZSKa/Em8J6Aojg82XQtNKnqOeeO8cbb4yyfftl3nahBjRKp+s2jiRJJU01n3nmGd7xjnfwox/9iDNnzlS0lvRidnP11Vfz4osvEolE+MY3vsGnPvUpvvOd7wCWt++JEycWtF9vKmtHcI9GDcNgYGCAX/ziFyV2jrVodd28bMsRj8c5ceIEc3NzBZ/eajOrdtIdGzP5+MerdSoQBjf1EK5KaeQlHrujWCQudLpejHOc9aH1bVNjfCqCwYWSpB0LfQoQWEVp1KlilR0LeZm4AbojlfIjScJNrhKSFPvIgaYFKQ88DcPgYx/7X563vhZcjPbrANFolOuuu44DBw64LmM3uwkEAgWzGzve+c53FjxTDh48yPnz5+vbARcsSdIFd+ItdxrTdZ3+/n5+8YtfoKoqBw4coKurq2DnWAvpVkMikeDEiRO8/vrrbN68mQ0bNnhu92Mn3bvuUqrIjUSbHWE+Xouc2t5Wxwky1iNxFAgSDgujcidjIC8tb7xiikadjpU9FmrFcny+2ky53SGkYLNYBCyczLzDNNuo/Hsn8v+WNuyUpBClckOJ48fP88tf9ta0fi/wWrpbDV5JVxRoeEGthjWPPPIIt956a+H/mUyG6667joMHD/LUU095Wmc53rTpBV3XGRwcZGhoiMsuu4zrr7/e8QesNU/rhGQyyblz58hms3R2dhbyT7OzszW1YTcMg74+k2efVWhtFWW85RCTReIzhUhEJZMx8l6v1RDDe/5VyjdWFBU3aYpGK43Q09ohSKgRaORpLeUfzWslEdExQigxRMfhZRSj23ohVBGl+xkKZchknG/WmiZsP3UsE6MgiUSKu+9+jEceeTeBQIBMJsPo6KinhpEXAl4j5lgsNq9LsRtqMaz59re/zYsvvsjzzz9feG9gYID169fT09PDjTfeyJ49e+js7PS0boElS7puhjKKojAyMsLZs2dZv369K9kK1EO6ouBBJPLT6TRdXV2Fyjj7tnglXTGR9rGPWbP38bjbCZ+j/JE3lRITazkqN1CshXCdIDr0GoRCk+i6hqapBQF+seS11otVp7HaXGEi0yjSWIEVnbqNl0UUlkSjfpJJsI6Dk/l6iKKl40KwEitP7Ef0Y8tkql3OIazUAyQSlvylv3+ObHY5e/Zs5OTJk2Sz2ZKGkUIlIGReboUMiwGvkW6jzW4AfvSjH/Gnf/qnPP/88yVNC8SyHR0d3HDDDRw/fvytQ7rl0DSNwcFB+vv7aW1t5eDBg3X1MqsGWZZJJBL09fWRSqUKka3TiagoiueebYqicPaswrFj4s4uOizY98HuhzBvBCBMMJghmzUdlhP63EZggkxGkHc5iVva22IxBFj7IrS6849TJJLI3zgaiUZWsPspTlrmKLYgEvtV9Ce2CLcaVqEok3VWrNmxEqvkOY333zZC0ZPXOka/93vf4Ze//DTBYLAwSw+lhQyxWIyhoaF53ryikGExDG5qIV2vhRFezG6OHz/Offfdx5EjR1izZk3h/ZmZGSKRCMFgkMnJSX72s5/xqU99qradYgmTriA5QbZDQ0Ns2LCBHTt2kEgkPJ8EtTSzTKfTpNNpXnnlFbZt28aqVasq3vUVRfFskq4oCp/73CYMwz6eXfqkIcs+lwaTRWSzIYp+uKJ/mVAmNMKERKsyjv1RuhxCJaFRnOhR8PnEZJyXwgev8EK6om+ZRtFVzV4wAcWiDD9FHfFCo3Ip38QyTf0lyyJ9Ecz/7X3d1nlRnNTr6ZniH//xFFu3ll4zboUMdm/ekZERkskkuq4TCoUKlWTJZJJIJLKgqNgr6dbiMObF7OaP/uiPSCQSvP/97weK0rAzZ85w3333FTpy33///Z66Tczbhpq/cYlA0zR6e3sZHh5m48aNHDp0CEVRmJ6eZnZ21vM4XrpHpNNpenp6iMfjhU6+XkxBakldnDjh41e/Kh9TkJtJIGDmu/Z6gd0PV3RhaFS+dJL6VQZWNF6ObNZePCCKG+zFD/Z/7S9s3xEQF3na9pn1ns9noGmi4szeOUK056mGYQ/LeEULtRdNiCIUkY6xP23UoicWN+DiHfzrX3+Wr33tX3n6tps3byaTIRaLYZomvb29pFIpz3aQTvBqYF5rNdptt93GbbfdVvLeF7/4xcLfP/rRjxy/97a3vY1XXnnF83rcsGRJd2RkBFmWC2QrUI8xudvymUyGnp4eYrEYnZ2d7Nq1i1dffdVzi2mvPdVGRkb4t/92mUNVmJ9AQCWX08jl6iHNCFbBAfj9KUwzsAAvAHDKJy8cGbJZ+zaJ3PDCxy2PyBcuUmn05bIaKz1QeVy/X6e11WBmJodpOh3/FqybYfWnBEUxMM0shhHASgFZ6O6eWNDEmSRJhMNhJEmipaWFK6+8EijaQSaTSUc7SPFyKu/1OpE2NzfneSLtUsCSJd1NmzY5kmUt6QJwJt1MJkNvby+zs7N0dHSwc+fOwmNSLaReiXRF54menh4GBtZz9qxzTiqXy1Hv5Jffn0HTQnkTHCj2DxNm5LUS6CTFDr+NQoKFuoI5YzFcSdsotuZpBESqwul8EtI+A1X1Mz0tInQ3iH5t7sSpKEa+u7IYJ4CIkKemUuRyCy8oKSdKRVFKOvcKCDvIRCIxr7xXELHX4CYWi7Fp06YFb/uFwpIlXTfUE+kKks5ms/T09DAzM0NHRwdXXHHFvJxULYoEp2VF+51z587R3t7ONddcw1/+pVuOUEyIiRr82nKyqpqmlLBlSlMDGYplxNUi6TSNKl6wIxhUyWYbHT1DJOInlWo08Yawnhwaedksw6p6E2PmKJoH1bIe8Ru6BRwqplmejxddJ6zz8oc/PMu+fXtqWOd8eI1Oy+0gwZq4Ex0rYrEY2WyWX/7yl/McyMqbas7OznLVVVctaLsvJN50xRH1ku7rr7/OSy+9xLJlyzh06BCXXXaZ4zoWEulOTU1x7NgxRkdH2bt3L7t27SIUCvGLX8g4++RmKV5MMrVNmHiRh4WworcIxTbgaZyjxBkW43RpbCFDEamU96edWhAON/7GY/0GcYpt4IPUN+nZivN5ZCkunALHUKgoa/vpT7vrWGcpFlKNJvK/a9eupaOjg3A4zIEDB9i7d2/hehwbG+PkyZMcO3aMU6dO8ZnPfIaenh5mZ2c9XZdHjhxhx44ddHV18cADD8z7PJvN8oEPfICuri6uv/56+vr6Cp99+ctfpqurix07dvD973+/rn2EN2GkW8tsaS6XK6QRhPKh2vdrkZgJgp6ZmeHcuXMEAoGS9jsC58+7rbPcFzeERbzVol4hyK8FdsWB6DYLEMrX7jtpThcKYZ24GFiceCKdFnaL9Y4vIlnxG/mxjnuARqREfL4VaNq0bfuEWsR5ezMZCIcDpNMap0+PLXj9jfJdsHv7+nw+2tvbS2RhpmmSTqfZu3cvJ06c4IknnuC///f/zubNm/n7v/97xzG9+C488sgjLF++nHPnzvHkk0/y6U9/mu985zucPn2aJ598ktdee43h4WHe9a538cYbb9R1g1myke5CkMvleOONN3jxxRdpbW0lEomwfv16T4Rt7whcDaKxX19fH1dccQV79+6dR7gvv2yi68JDoXjRBQKi0KEcVvffcNi9CZiixFkYmfmxoqZWQCYQSNLWlqa1NUU4nEGSGlM23ZgiATcsloA/gFczHUXRiEYztLQkUJRZivsbxjq2LRRvdMup1hXECzRNRpat397nE1rpypd5Om0QjQaZnEzW1MHaCRfKd0GSJCKRCLfffjuRSIS//Mu/5KWXXuK73/2u63e8+C48/fTTfOQjHwHgfe97Hz/+8Y8xTZOnn36aO+64g2AwyNatW+nq6uLYsWN17duSjXSrEaRTmxxVVenr62N8fJzNmzdz8OBBZFmmv7/f83p9Pl+h7Ygb4vE4586dK1jTXX311a7LPvGE2MbS1uGVd0/JR1xCFG8/yXP5tuyNgk4q5dTmXRQJiK4KMkXDb6/38hyL1yViMaumgswnSDX/RJBFaJV1PUAyaT8ulVBvm/v5MIxWYCRfvuzlOARJJi2Z5XPPvc4737mz7nU3knS9jjM3N1eQjFX6jpPvwtGjR12XERH21NQUQ0NDHDx4sOS7lTwbKmHJkm4llHdsUFWV/v5+xsbG2Lx5M4cOHapbR48kiQAAIABJREFUHlNpIk14MORyObq6uli+fDk///nPK473/PP2i0JEGRrZrJcKozAW6dl1uFlMs5HVXTGcI243IhEKiRz2Aghnc5fFfNByy5MvBDpW6iWAJfUS41tVaZYZe/03PElajmkuxPgnh6V4EKqIWloiW6Xkzz13ZsGk61WHW20cr2mKVCrlyVjKi++C2zK1eDZUw5Il3Uo7bJeN9ff3Mzo6yqZNmyqSrZcGkuA8kZZKpeju7iaVStHV1VViuFwNvb327SlNMXiDmOVOY5FCIwm3HtISLmVOF4HdMlK1vSQiESk/+VXelke8ao2eKv2Wgjx128updY993T7bvz7b/xsH0/Tj9ys1dYiwtjlJseuzeHLwYxGwF2IQOWqT3t4BTp06VaKhFfpbL7jQto6CDL0EUV58F8QyGzduRNM0YrEYK1as8OzZ4AVLlnTB/Q4kyzJ9fX1MT09z+eWXV41shcOXl5PFPpFmL57o6uqqWhZcjtFRg3jc/hPIFGv8a0UYMfsty+QdxxZ68s/RWBK390qbwi5Bs/xVKqUa7H3NRIPL8mo1KFariagPQCIYVMhmDeaTZ73wsRhaYFVtwTru1c4jlWI7IdH/rhylBRDOEKXI1rxCa+tytm3bVtDQjo2NkU6nURSlRLJVLtsSuFheul6uOy++C4cPH+bxxx/n0KFD/O3f/i033ngjkiRx+PBhPvjBD/KHf/iHDA8Pc/bs2Yq+vZWwpEm3HJqmMTAwwNTUFOvWrePgwYOeTgARvXpdVkjMpqen5xVPlEOSJNeebadPO33DzIvY67EStAjNkgYZhMNpFMUgmQximvX81I0sH3YauxZCF2kK0UW4Guawk2LjpWnCOKbRCGMVOTifi5GIRjqdzKeQquXDW7B0xW6EJAhXfC6TTGYdu/gKPwVBxN3d3QW/BTsRN7JrhJfrsZbcrxffhd/5nd/ht3/7twuugU8++SQAu3fv5vbbb2fXrl34fD6+/vWv131zkarMVi5GWU/DkMvlME0TXdcZGBhgeHiYDRs2kM1mWb58eYlDUCWcPHmSzs7Oqn4KqqrS3d3N4OAgu3fvZt26dVXvsMeOHePqq692NFk+ccLk4MHyiNTKFweDGtlsLYRXKSo1KbZvEfKkahCGKos1IXWexSN0CATS5HKxRRvfOqbDNDrFYCFJKaFrFPuj1ZovncE5TWSvTBPIcsst2/nudz/haWThtyCiYtFWPRQK0dbWVjUqroTBwUF8Ph/r1q2ruNzU1BQf/ehHefbZZ2sa/wLA9cJZ0pGuYRj09/czNDTE+vXrC5Ftb29vzQUSlWRgmqaV5Iaj0ajnfI6YeHMiXSv1W1QsFM1ZJLLZALKcwTDK1QlOMKosI1H0dhUELHKAbsQXY/E0tOSbLy7a8ORyix0veG2JXg+iwBzhMKTTc5TmausZq1yal8T50veRTHp/JBB+C/ao+NSpU3R2dhZaqleKiivlijVNIxSqvs+1eOleKljSpHv27Fl8Pt88o/JG+C8AJRG0PTdsT6hXQ6ViilWrxF8W2QYCGrlccT8s6ZfoQ+Z+Ara0ZEgkvKYjhLWfQJrijLxYh1epUb3Q8t1uFxOLL0H3+QINa/Vk/c4p7DnYdFpl4d05AkQiAVIp4ULmRrgACqq6sDuhUC9Eo9F5xQz2qFjkiu32kfaoeDG8dC8VLGnS3blzp2OE6vP5yNaQxCsnXcMwGBwcLMxQes0Nu43ttI3ZbJbe3m5gFyJSNQyn6EykH9IU+6KVIpEQpFkP7EoDIfUSXg+LhcUyubFjMbffgqaFqa/AQ8f6PQURilJv+5NHBBijEcfJupGLdFHlS36hTwhuE2lOUTG454pVVUXTNFRVrRgVN0n3EkE9ka6qqhiGwdDQEAMDAxX7qtWCcl2vqqr09vYyOTlJR0dH/l2LdC2vVzcINyqV0qjXrXKtHoTyr1EggKKohEKWOiCV0jFNGUXxoesLXZ8wdFlMXIhiyyiVJr0s6EhShnAYFEUimyXvi1ytYELojBuhBPDhhXAB4vGFeVbU2pTSrcT31KlTtLa2kkwmXaPiYDDYTC9caDTK9EZRlILX55o1azhw4EDV7qJedb2CdIWyYmRkpKQaTpbB5zPJ5aA6UQiZUxIrOpUpRsCNQyDgI5eT0HXfvPYz1v3DrrcVvcgCeDdqqVcWVwtEq/LFjagtNzMxUSXsGEWHZqtnnGn685K4WuG95NgZKVpaFBIJsS2VIcvMa9V+MSCkoGvWrCkptCiPiv/Lf/kvHDt2rGADedVVV3H48OGSnmZumJ6e5gMf+AB9fX1s2bKFv/mbv5lnhH7ixAk+/vGPMzc3h6IofOYzn+EDH/gAAHfddRfPP/984Wbx2GOPsW/fPk/796b0XvAa6ZqmyejoaKG55P79+9m2bVtVwhXtOrxAlmVGR0d54YUXkGWZgwcPsnHjxkI0EAya5HKiH5rXnyNC0ZSm0T9hykOHCh9WlNeO5RnQTjFFkcaahJvGmjmPU1tXg0sVJsVjnsDaxxkCARNrX2MUTd6jWHKtEAv7fdqpXUCkYylZEoBCIgGW/ra1yvcMgkGDi9wAuACnnK6IioU51SOPPMI999zDXXfdxf79+3n99dc96+QfeOABbrrpJs6ePctNN93k6DgWiUT467/+a1577TWOHDnC7//+75d0pfmv//W/cuLECU6cOOGZcGGJR7puqBbpmqbJxMQE3d3dtLe3s337dubm5jyXL3rR9ZqmyfDwMIODg7S3t7s2ygwETCwrh1qrvwIUDcmFKXkjwpQE9acrhBOa06RfjmJ0LBpXQjESlYhEFFKpLEKo71yVVkvk6hbp2nuiiVd5C6Dy9QpvBHuBh+Wz0Xhjd4EAioJHlUeGovZ5fqQXj1d68jOALOm0QiSyeIqVWuCmbS9HPB7nyiuv5PDhwxw+fNjz+E8//TTPPfccAB/5yEe44YYb+MpXvlKyzPbt2wt/r1+/njVr1jAxMbHgdMaSJt1a0wumaTI1NUV3dzfRaJR9+/YRDoeJxWJMT097Xm+1jhDj4+N0d3ezYsUKtm7diiRJrrnhvXtNfvpTsE580f3XK7HYJ9BELzSDYofaetDoUmIBQVZZnFuTi6q0Suu2V6SJv8v7p4nlQGhdrScT0eRTTEwutCLNgq5H8FZBVu/4pb3MSlHsLlFdVhbEWXetY584XQjpGoZxwdqzC8zNzdU1kTY2NlbQAK9bt47x8fGKyx87doxcLlfSbv0zn/kMX/ziFwuRspe0Bixx0nWDLMvzyoNnZmY4e/YsoVBonqetvXuEF7iRuugI0drayjXXXEMoFGJkZKSiK9nHPiZIV+g+Vbx3idBtywlvVrDIJ0MwCKbpK5GhVYYok11MeOuO7A7vHYP9/jSqStUOyguDQmnX5kajFSt1YYe9u4TXG6RTjruUcC1ojI+P1+y5AI0rAa4FlSbS3vWudzE6Ojrv/T/90z+taR0jIyP89m//No8//ngh+v7yl7/MZZddRi6X49577+UrX/kKn//85z2Nt6RJ18sJEYvFOHv2LIqisHPnTsfcVi0euWJ5O+nOzs5y9uxZAoEAe/bsKSH0au19/s2/kbnrLsP2CGnNWre1GczN1RtxSkDAVvqaJhg0yWbF478bKmk4G4NoVJs3ObdYsDSnF4IEFrMQI4zlU6FQjGq9lAA7oXizUhQTw9AwzdLj09YWKVEMCM+F1tbWQssct6e2RpGu10lqqNwJ2K2rL8DatWsZGRlh3bp1jIyMuFavzs3N8e53v5svfelLJdaOIkoOBoN89KMf5c///M89bS8scdKtBF3XefnllzFNk+3bt1fsFlqP2kHXdeLxOGfPngXgiiuucCT0aqQryzK7d+ucOmV/V2JuDqyosFKu1usJHrQRcBIrmg4yX3ifYjGr0ACSSeEBfCFwYarYw+Ew6XSjiiTssHeZEK2bFgIRlWvounM3ieXLW9i6dWvh/0IxEI/HGRkZIZFIYBgG4XCYlpaWAhkHg8GL4qVba/t1AWFsc//99/P444/z67/+6/OWyeVyvPe97+XDH/4w73//+0s+E4RtmiZPPfVUofuxF7zpSDeRSHDu3Dmy2Sy7du3yZLMoy3JNka5hGPT09CBJEtu2bav4o3tpZHnnnXDqlNOd3UdxoqecDEUaolbYiyEEAQewFBGL+hyex2LljJ1wYfKLVTztPUGWdQxD/B5QjGbDWMTbCMeeAJaaxL19T3lOt1KrnHg8TiwWY2hoiGw2WzB3GhkZKUTF9fhW1+Klm0gkqnqmOOH+++/n9ttv55FHHmHTpk2FjhMvvvgiDz30EA8//DB/8zd/w09/+lOmpqZ47LHHgKI07Ld+67eYmJjANE327dvHQw895HndS5p07Y8g5Z62uq7Pa43jZZxKEFaOExMTrFmzxrFbcDm8RNH33Sfx2c+aLrPU4qTNIEkBTFP8P8fCScVOwEJfKi5IkS9sNHFd0h5KdSLK/LxrJYjS7qKe1zBEGbZT2iDAwknXpOgj7HazNlm71v2JUEC0yolEIqxdu7bw/vj4OOPj46iqyuDgIMl8HqncErKaSmgxvHTLsXLlSn784x/Pe/+6667j4YcfBuBDH/oQH/rQhxy//5Of/KTmdQosadIFiwi7u7uJx+N0dnYWPG3Pnz/fsLp40cByamqKjo4O2tra0DStpuKIysuoXH65Rl9fpZuED9NUiUZlkkk/kYhGKtXoiLG0060k6QQCGqqq5XXJdjKu9zHyEhGCNhQR3LslFztpSBIoSgBNE/aUXn+/IPX3k9MobenuTriyrHH33W+vcz0WGUejUTZt2lR4zzCMQkGDKEDK5XLzzG8ikUjheloML91LCUuedM+dO8fq1avZtWtXycGvNU8L8xP4dnexzZs3s23btkKxQybjbRa+EulqmkZvby8TExPceutOvvGNapG5QjJp0tqaJB5v9GP6/EjKNKV826Dy9VjqCFGRZrlhQWXXMoElf8o5QKJYOZal2KpI3KAswjNNqC8O8FOs/PMGWc4SDIrfRUTPzgodSQLTVFmzpo2VK6sVUbjDKacryzKtra0l8x2maZLNZgvmNxMTE6RSqUKZrxirGvleDIlaI7Dkr4CrrrrKsTqsVv8Fe/cIwzAYGBjg/PnzbNy4cV7niVrUDk6kK8YXTfAOHjzI1q0Gjz6qkclU+0kk4vEgRc9V0X9sYSefJOXmzWRX2gZ7pFaa0xQifVFwIHwGQtSfh64XjbggDf4/e18eH0V9v//M7H1kcxISkkDuAwKEhKD4tS1g0dJvPYuK1pZ6oq0K2CIoVqGtglb92mot2KJYLdKWitiWYlUEfyoJ4VKU3PdNssne98z8/ph8JrOb3c1sskGu5/XKC7KZnZ3dnXnm/Xm/n/fzFjdTyOXc0PBJsS6YxnChS4bxO4ONFUS3S4FllUFyzcFy9hw0GhoOB43vfEd6MSgYpBbSKIqCWq2GWq1G0rDVHhiGgc1mQ1dXF5xOJz7//HMwDCMU7ciPWq0GRVGwWq0SOu3OPpzzpBsKkUa6xJlsYGAAra2tSElJCdlFFsm+xS3DpEutpaVlhKFOaiqNhAQXurqIz214wuB76kkESqbyjp2AOY48f7wItWxmwJvD2DGy+8tfPxoTI4fVKp5qEDizLNhPMAS+RmAnWuCYH/HriJsohm8y/NcejFStYY4jGgi9b14OaMWw/0UoBObT+dZmh4Ofj7Z69VXjOsLxDqWUyWSIjY2FzWaDwWBAWlqaULSz2WywWq3o6uqC2+3GoUOHcPz4cXg8Hhw7dgzTp0+X5L8LSPNdIMczc+ZMAMDUqVPx7rvvAgCam5uxbNkyDAwMoLS0FG+88UZE7/ucT7CF60qTGulyHAev14tjx47BbrejvLwcOTk5IZc2UvK04uMjbccVFRWwWq0h9//NbxICIe2yoWGzid83IVs5eAK2g8/jRVK0mmjlAmntJRV5rehH5/e71aoE7ztgAN8coB/aRoPhqcKkJZgnDopyg6adkMsdUCjsUCpt0GpZKBQu0DTxDAaGbRS1Q/uNGfoRv5YWw5+nVEx0BB+4f96MXi53wu0mvrujHcPw+cBfNsN+HwaDEllZ0iathEI0R/WQ/ZCiXXJyMrKzszF79mzMmzcPt912Gy6//HIAwIsvvohvfvObOHTokKT9S/FdAHgpIPFWIIQLAGvXrsXq1atRX1+P+Ph4bNu2LaL3d86TbigoFIpRo1GO49Df34/Kykr4fD4UFBSgoKBg1LtWJJGuyWSCw+FAT08PSkpKUFhYGHL/q1fzEQf/tTDgyTfSar943LkHgA007QRFff2qAZlsooidBsfxCgCfTwWvVw2PRwOHA/B6ZWDZSFqrx4qJJV2djiyjyegeXsPN2zZKe29EDkbTAMcRjwse8+dnjvsYz6RONzExEfn5+SgvL8drr72Gw4cPY/78+ZL2v2fPHixfvhwA77vwzjvvSD42juOwf/9+LF26dEzPB87z9EK4SFfcFjxr1iy0t7dLlp6EmwZBYLPZUFdXBwBQq9XCMiUcZs+WQ6PxwOkUX0huKBRKeL1juT/yS2Q+u0EKPCTnGLi/ic+1hhLknx+QY7TVydjhgd3uAE+2o6UQQsPhcA25iI1MJd199/+M7xARPdKVqtMdq5euVN8Fl8uFuXPnQi6XY926dbjuuutgNBoRFxcnHF96ejo6Ozsjev1znnRDpRdCRbriLjJxW3Ak6YhwhTSn04mGhgY4HA7k5+cjPj4en332meTWxuJiC6qqEkSP0PB6iTWiOGcVaeQmNngRT4fQiP4+0WBwvpKuVquFwzFeXwlgWOLlBWnnHh6xPt5BnhzUamqEt69eL0NcHIempiahw4wUqyLBmR6/Hs7sJhq+C21tbZgyZQqampqwaNEizJw5M2hna6Sf0zlPuqEQmAJwOByor6+Hx+NBXl7eiDtkpMWxQEMdj8eDpqYmDAwMIDc3F5MmTRK+DFJMk3JCfv/7pwNIFxgmKgfG79EK+BOwF4AdcrkHLMsNDcKcqNPiTHS8fT1wOMaSviFje8RdaKGaJMaTHvIBcMFgkMFiCQwsGKxduxhTpkyBSqUS2n1dLhfkcrlAwlI6zM406ZpMJr/RP2JEw3eBDJ/Nzs7GggULcPz4cXz/+9+HyWQSjpGM9IoE5zzphot0vV6vX/NEbm6un0RFjEidxggYhkFrayu6u7uRmZmJgoKCEcdECm9STshLL3VAqeTg8YRqC3YjuqkAGQB1wA2HaHD5C10ul4GmFUNuZePJjZ7pvDIptJ0JhK8DUBQHjYaD220bSrMEm4sWDmN5Hy4Mt5CrYbEYA/7OYObMKbj66lmCfEtMYl6vV1ANiDvMxPKtmJgYgSDPtPeCxWJBbm5uxPuX4rswODgIrVYLlUqF/v5+fPrpp3j44YdBURQWLlyIXbt2YdmyZSGfHw7nPOmGAsuysFqtOHbsGHJyckY0TwRCLpdLbngA+IR6e3s72trakJaWFnZ4JYmipchKZDIZFi1isG9fKMNuYtHHiH4fLwKjF3+v2WE+9oJPS5DXJlIqVZB9BMPXX8ybOMgxLDvjMGzUzjc1cJwSDgeFsWt4pX52LIYniohXLWS0EjmnGNA0hb/+9X44ncag565CoUB8fLyfnIphGDgcDlitVvT19aGpqUnQ0trtdgwODsJgMEClUo25cSGSnO5YzG6k+C5UV1djxYoVwip13bp1mD59OgDg6aefxrJly/DYY49hzpw5uPPOOyN6/fOOdH0+H1paWtDb2wuKojB//nxJX77U9ALHcejt7YXdbofT6ZQ0Ty0SiRnDMPjpT0/iwIFCuFyhyIyQnRcAaQ0mLbpjgdSLI5Q1JFkmE+0rDbVaCZeLtLuebyAeBoGaXzLlmDRJjDcHOwyNRj6KsY4Xej0Nm43ovAPhhphwAWDFim8hPT0BtbV9kiNUmUwWtMPM6XTixIkTQnrC7XZDoVD4OZFptVpJxWqp9Y+xFtKk+C5cdtllOHnyZNDnZ2dn4/DhwxG/LsE5T7rky2EYRhibnpGRgfnz56OiokLy3VZKesFoNKK+vh4GgwF6vR45OTmSTlYppEvUDk6nEyUlxXj8cTUefdQ91CgQ7GsiUxjoIX9aEuGQv0Xy1Y5XTkUh8EIfXjQ4wC9zyWQMUiAChm8oRMMbrAli7OCJKtx3SlYMhDzF0yj4yFKvV8BmI0VH0iwhE/2IYRn3MYeCyxXM8MZ/Wgg/gDLU+UiKsfx5mJioxebN/JBFhmHGZBpDQLS0CoXCb7KCx+MRWn1bW1vhcDgEfwZxrnis2t6xRrpfN8550mVZFh0dHaN2kY2GcJGuxWJBXV0d5HK5YFJ+5MgRybmncKTrdrvR0NAAm82G/Px8dHR0QKVS4aGHVNi61YPWVr6Lyt9hLOQrDf3LE7Bezw51rY2W1iD64InQsopHjZsgzXxbTIYs/MlQTIrizjby7/B74LWoFv5RioJMJgNNU+A4GixLgWEI2Yee1MEPdoxexDpW+BduiYZb6uqGfJ7D5+Cf/7xCCEikFnkjhVKpREJCAhIShgvDDMMI/ry9vb1obGwEwzDQarUCCbMsKynaHeuonq8b5zzpUhQFj8cTdJlP/D2l3MWDycCI4sHr9SIvL8/vC44kZRBsW7HZTXZ2tpBz7u7uFrZ9+20N5s51gON4ApHLiRieh0pFiczJR7wqbDZyIdmG/hUTYCAmflx5+OMNhvCEOBrkci/IPLaxm82cLRDniaXcSMUgXhgAQOHb3y7EN75RIPx1vJEuEHhTCA2ZTAaDweAnvRL785pMJrjdblRVVUGpVPoV7MROZAAv/7xIul8DaJpGTk5O0C89kgKWONJ1u91obGyExWJBXl5eUCP0SCRm4m1JZN7e3i6Y3YhPeGK4AwAzZshx881y7NzpA0DB5/NBpWLgdisBUHC7VfDP1YXC8PunaRvUahYOhxoTPSUiEG73mZWMnS3jxMcGDjTthVLJDBV4HeAj27FE3STXQyEpSYs33rjX76/RUB1EMmInEGJ/3vj4eNhsNpSUlPg5kfX39wtOZC6XC5WVlaAoCi6XKyITcym+Cx999BFWr14t/F5TU4OdO3fiuuuuw49//GMcPHhQIHtiah4JzunTcjRE4jRG0zR8Ph/q6+tx9OhRJCQk4JJLLgk5eSLSSNfn86GnpwcVFRVwu9245JJLMHXq1BERRuB+t21TQ6xyc7s5KBRuaDREdiR94gUAsKxyiHABfultBh9Bnc/KgjOF8awUvOBXJGZotW4ALrAsNeQ6p8fYvh83eB8O3vA+MVGDY8d+CZ3On7ilrgbDYSI0uiqVComJiZg2bRqKi4sxb948zJkzRzDCGRgYwJVXXonS0lK8+eabkvYvxXdh4cKFgufC/v37odVqceWVVwp//81vfiP8PVLCBc6DSBcYNpUJhNRolFgt2u12qFSqEdFnMEQS6bpcLnR3dyMpKQllZWVhRzUHkq5MRuPFF9W45RbiugV4vbyGUql0w+MJsSNJIOTLgS/CEdIgy3oFzuX7ciQjmM4syOQIfgUz7LvLnxd8x5j/507TUqcaswA8UChk8HrlIGPo4+JUqKragLi4kZ7NHMeNm3SjaXYTjrxlMhmysrLw0EMPYc+ePfjss8/g8/nCTtwWY8+ePThw4AAA3jdhwYIFePrpp0Nuv2vXLixZsgRarTbkNpHi3L2iJGA0YuQ4Dp2dnTh06JAw3idY9DmWfQO8IuHYsWMwGo1ITk7GjBkzwhIuEHxe2/XXK7F2rQz+HV0UPB4ZNBqS6xtPpEoUAyTnS8iW72Qa9u51QKNxgabHlhyNiTmzBSmP52wgXaIqIasKO4YbFrTgdbujyepcEgiXtA/z5va8VwefA46JUeCNN25BU1MNjhw5gtraWnR2dsJisUTtxnSmfRdsNptfC79UX12pvgsEO3fuxC233OL32Pr16zFr1iysXr0a7siKFPzxRvyMcwih0gvEarGxsRHx8fEoLy+HUqlEb2+v5NxUuPSCy+VCQ0MD7HY78vPz4fP5MDAwIOmYQ+1340Y93G4LXniBFFJ4OJ0q6PUO2GzEkYxEqJEudYNdMCMLWXxAwdsKDov/yXYqhMsTW62+sH+PNvgR7GdqsgC56bkxPPuMeCf4N5tEjlBNOxwUCnboHJdj5Gdrg8GgwqefPob09AShsEzypJ2dnbDb7bDb7Th16pQg4xJ3mUnFmW4BNpvNISd8R8N3AeAn/p48eRJXXTXsM7xp0yakpKTA4/HgnnvuwdNPP43HH388ov2eF6QbzlM3MBol7mIajQYlJSXQaIY7hAjhSfnSg+l6xYqEnJwczJgxAxRFYXBwMKL8b+B+iQXltdc2oK8vDX/5iwb8Bca/b5tNOTT5gUi/yEUqA0UpwHFSiEeJyFyyQpmVEy8B8n79l85nEvwSe7zFu1DG58MrC51ODbudTMyIblMED/8cEk1z0Gop2GxeeL3BG1D0ehYUpcAnn/CEy3GcUKDV6XTQarVITU0FRVGoqqpCRkZG0C4zMRGHW6V9HaQbSrkQDd8FAPjb3/6G66+/3k8VRaJklUqF22+/Hc8+++yoxxqI84J0Q0GhUAjhv9hqUewuJgYhaSlfukwmE9qGpSgSxiovs1gsqK2thUqlwuzZs/HKKyro9RZs3eqEVquCw8EL9jlOfGGS1+bAcU4Mz+sKN1VCC375O97IMFRUR9qHHVAoSBTqP9mBoigolTLw1y4HiqLBcRR8PkChoGG3kxyouIFChlBZMn/C5SCTcaBpFjTNQi7n/RBYloXPx8DnY0HT3JCsTNxVJp4iERx8c0q0PTHEIBG7DzTNgOPkQ/rhUK/HIjaWw759jyM7e5hUCOmyLCv89PXx3WhkfE5ycrJg6OR2u4Ux6x0dHfB4PFAqlUJHml6vh0ajAUVRZ9x3wWQyjakbTYrvAsFbb72FTZs2+T1GCJvjOLzLEkJFAAAgAElEQVTzzjsoLo58xNF5QbrhIl2z2YyTJ0/C6XQiLy8vbAdLpDIwr9eLnp4eNDU1ITk52W/8jhiRkC7J6bpcLtTX18PlciE/Px96vV6IVp57LgYsS+GPf3RheBpDKPmYmDDCEbAMMhkDhpmoU2K4y4wP5EdGZxyHkDpevmAYLDUhbqIgRM5BraaHuriIh68MDEMNjbknemFC3vx7llaoCoXxjkgPBeJ3wQFQDBmyh8eUKUr8618/8SNcYHhUOU3TcDqdqKmpgVKpRElJCWQyGTiOA8dxwrmqUCiQkJCAxMREv0m9VqtVaG5wOp2Qy+WgKAoKhQJWq3VUN7JwYBhm1LoHMPYWYCm+CwDQ0tKC9vZ2fOtb3/J7/g9+8AP09fWB4ziUlJRgy5YtER/DeUG6weDxeNDV1YWBgQEUFxf7WS2GQiQDJx0OB7q6usAwTMSKhNFgNBphNBoFVzQSlVAUJZzML7wQA5YFtm1zgifT4XRDaAQjYCK0p0BRE1tXjYlRwWqN3MltdIzMPfOLkNBRcPQRrc4LsakQheHx6aODphlMnqzC009/A2ZzB2pqzH5RKTFvaW9vR3d3N/Lz8/26xcQgXWHif/nXoGEwGBAXFweKooQot7m5GR6PR3AjE7f7kteXEsFGkl6YKN8FAMjMzAxqTr5///6IXzMQ5x3pMgyDlpYW9PT0ICUlBRRFhc3biCFVkVBXVwefz4e4uDjMmDFD0n5HI12WZdHZ2Ynm5mYolUqUl5cL7weAcIKL8bvfxUClYvHyy24ML2+lGoWPJGCNhoXVConPjxxW65nWAp/J1xuLCoAF4IbBoIDF4sBwnlwl/F2hsCO81JxXr6hUKmg0Kuzb9wByc5MFW0aLxYK2tjbYbDawLAuPxwODwYD8/Pyw3Vzk5i4mylBEDPDnZ3x8vHDNcRwntPv29PTAZrMJ7b5iIg5sXJpo0j0bcF6QLqnKkrxqWloa5s+fD7fbjerqasn7CWd6E6hIUKvVkvcdbrwPKZLV19cjKSkJs2bNQn19veDSFIxsxdi4UYHc3E6sXx8Pp5PCcKGH+ApIOkIAsiFStIIs0TUaCgzDweMhxZrx5uwUmLiRNl83RrvZEWkf8Skm1osKWCwAn1P3h0zmGMp9h3o9MnZHCYWCxiefPIisLN4PV2zL6PP5hA7L7OxsoVGnoaEBLMsKEanBYEBMTExI17xgROxyuVBXVweGYZCRkeFHxhqNBmq1WiBilmWFPLHRaERrayu8Xi/UarVQrHO73ZJSExaLBZmZmaNudzbivCBdh8OBqqoqTJo0yc+DIZKONCB4pBtKkeDxeCKaCBwM4iLZnDlzoFQq4fP5oNPp8MUXXwiRAelVF18QXq8XTU1NMJvNuPHGXPzgB7G47joTDh3ip+MCzJBDFp8LlEbASgznfBFgJejFsFsY4C/ql0rGKgw7oZ1fkMloiE8HmYyBUskNifYJwUbiI8GBYexBHvdBJsOQWQ8fJep0MlRUrEZW1kiD/r6+PjQ0NCAjIwP5+fkjzkWWZYWIlCgXvF6vX0RK/HH9jo7j0NPTg5aWFmRnZ2Py5Ml++yT/BkbFSqUSiYmJSEpKEo6FuJFZrVZYLBZ89dVXgu8COYZA34WLke7XDI1GEzSvGmkuVRzpktwXsYoMVCREUnQLBIkO3G73iCKZTCZDQQFvRkKWaBaLBadPnxYcmQDeH2LKlCmYM2eOQMQffJCIF1+04Re/cMDrBWw2YqNIjjOUzEsMLQIlSjwIyQbCB7ncDYbxDnUFku1Ik4UYSpwJY51hnInX4r11GcYNnU4BlmXg9QI+HzV00xqrablV9H9yI+U/W/EprdPROHx4NTIz/QnX7XajpqYGFEWhtLQ0ZM2BpumQ/rjEgKa9vR1utxsqlUog4N7eXmg0GsydO3dEZCwu2IkRKj0hl8sRFxeH+Ph4DAwMYPbs2eA4TiDi/v5+OJ1OUBSFmJgYfPTRRzh9+rSf3FMK/v73v2PDhg2orq7G4cOHMXfu3KDb7du3DytXrgTDMLjrrruwbt06AEBzczOWLVuGgYEBlJaW4o033pDk6xKI84J0aZoOelJFPDBOLofT6ZSkSAg2J200+Hw+NDU1ob+/XzDSCVYkEx8/cVlKTU31a+jQ6/Ww2Ww4ceIEGIYRooLbbjPgyisNuP56K1pbScME+Rx8EF+8wQlYB77xQfqp4fMFi+BYkO4rlYqvivNpCuJNSwX8RB86nQp2eyR90v5KCJ1ODofDLfqexXI18p5p8CsAGex28WSG8YC0ZbMYVl+M/K60WhmOHHkIU6cO+4NwHIeOjg50dnaGHU8VDmIDGhLBchwHl8uF5uZmdHZ2QqPRwGKx4PPPP/eLiMMZlYfLExM/bKKgIARrMBiEFBtp7LBaraitrcUDDzwAuVyOq6++Gk888cSo76u4uBhvv/02VqxYEXIbfojAT/H+++8jPT0d5eXluOaaazB9+nSsXbsWq1evxrJly3Dvvfdi27ZtuO+++yL5aAGcJ6Q7VnejQDidTrS3tyM5OXlURUIkIAWMyspKTJ06FZdccgmA8EUyMSwWizAuPljUQpaIFosFPT09sFqt2LaNxf/932R8+qkcJpN4azEBe6BQ0OA4GXw+8R1bgegUoXjNrlgGRlG+IM0afB5aJqMgl1NDellGlM/0PxaDQQmLhew0kLypoaYIDna7E8MkyuepKYqCRiODx8NAoZCD4wCPhwPLBpKpYkh/O/olYjCwQ3nZaIAFH+V6EPrGyCItTYPt278PvZ6C1+uFQqGAzWZDdXU1YmNjUV5eHlWPXLvdjurqasTFxeHyyy8X9u3xeAQJWVNTk+AERoh4NOUCTdPCccfHx2PevHkAELJgp9PpsGrVKrz//vt49913ERsbi76+PknvoaioaNRtDh8+jNzcXGRnZwMAli1bhj179qCoqAj79+/Hjh07APC+DRs2bLhwSXc0jNbaOxZFgtTXJTk1juMwd+5cyOVy4SQajWxJ8Y6kIUL1l4tP8rS0NAA8EW/bZsc77wxg40YW3d3BvmqimWUA2IZITwW32wBgABMh9pfLlfB6Awmdj4AYBoKONlR0ByBk4YlgOI3PIjCPynHEUEYWNX9di8U6+kYhQcb+kGMlLdYj37tKRYNlffjJTy7Do49+GxaLRVj9OBwOcByHlJQUJCQkRK1ZgWVZNDc3w2g0orCwcETrLcnRit34fD6foJzo6OiAzWYDx3HQ6/VCbSImJgY0TaO1tRV9fX1B9x0YEQP8NfH888+jvb0dKpUKSqVSOOejgc7OTmRkZAi/p6eno7KyEkajEXFxccKqNz09PaikTArOG9IdzWksWEU2UJGgVCpRX18f0euGInSz2Yy6ujqo1WrMmTMHX3zxBQYHBxEbGyuoEkKByN5I8U5cdJAKQsQ//GEMrruOxc0396Cy0geXK9R+ZEOkx5NATAw1NIQQiEwJER5erwLBc8bnKiJpiiCz1UjkFlhcYwH0w/+z5qdlaDQKJCVpsWfP3Sgo4Jf8er0eRqMRg4ODyMzMRFJSEqxWKwYHB9Ha2gqPxwO1Wi0QXaQDI00mE2prazF58mTMnTtXcsMDydGKC10kNUBWYzU1NXA4HEIKw+v1Ch1vwUDTNE6cOIGVK1fimmuuQXNzc9BrOpzvgpSpvcE4JBS3jHWFfd6QbigEI91QigS32x1R4Y2IzcV3ZKfTKUi+SHTKsiyysrJw+vRpNDc3g2VZ4a5PLgjSEdTV1YW2tjakp6dj3rx547bcA4CYGBr//ncqXnihHZs32+DzKcAwxIkqGOSwWmnw43VoUBQHmQzw+TgYDHJYLMTLN3JjHblcD59PmvnP+HEmCmm2EI9zUKsBimLgdJI8djBTmuHt5XKLKPomI3ZoKJUK3HvvfPz611cLW3s8HmF1VlJSArWat+nU6XRISUnh9zCUhyWqgM7OTrhcLqhUKj+JGGnlJfD5fEIwMnPmzKjYGpKmCr1ej6amJsjlcsybNw8URQnFsubmZni9XsHzISYmBna7HSkpKXj22Wdx4MABbNu2DbNmzQr5OuF8F6QgPT0d7e3twu8dHR2YMmUKkpKSYDKZBB0xeXwsOG9IN9TdiMjGNBqNJEVCJBIzor8l/zY1NQmdZKRIxjAMKIryW4KRHKzZbEZXVxdsNhu8Xi+8Xi9iYmKQn5+P+Pj4qBAuwI81qaurw1VXaXDTTdNw662nceSIA3K5DFqtAhZLsCGQNHjzbLvgfwBQsFjYob8Ry0KSLxW31IYmY5+PaHXPl1OPRLo+6HQyyGS8EQ3L0kOrilATlP2h03mGin5kHhxP0gUFCfjrX3+MvDy+wYfjOHR3d6O1tRU5OTlhG3/4/LUGGo3Gbzu32w2LxSJM7nU6nVAoFMLyvq+vD9OmTUNBQUHU6iUAv/qrqakRImeyb1IoJu/P5XLBYrHAaDTi3nvvRWtrK2JjY3HttdeOasU4XpSXl6O+vh7Nzc1IS0vDzp07sWPHDlAUhYULF2LXrl1YtmzZqL4N4UCNUoE/Z8YJeL1ev4Q7QXV1NZKTkwVda3JyMjIzM4MqEjiOw6FDh3DZZZdJes3jx48jLy8PAwMDaG9vx9SpU4W7n9S8rd1uR319PSiKEizjLBYLbDabXwXXYDBE3NNOxg45nc4ROeGXXzbi0Uf7hvKfHPR6ObxewO0O1N3aEHlDA4nS+NNHp1PCbudAUSpwHAWFomvIHWtiQdPd4/RTAIY9HVjodDLY7Q6QopxMBqhUNrjdHCJYII0ARTmhUtnhcnlBUjkGgwIPPHA5Hn102FbQbrejpqYGOp0Oubm5UTENF++7urpaCFBcLpcwbp1ExGP1VGAYRmjOKCoqgk430kg9EG63G5s3b8Ynn3yCrVu3IikpCcePHwfHcfjud787lreI3bt344EHHkBfXx/i4uJQUlKC9957D11dXbjrrruwd+9eAMDevXuxatUqMAyDO+64A+vXrwcANDU1CZKxOXPm4M033wxXbA950Z83pOvz+YKmBk6ePAmTyYTExETk5OSMqkj47LPPJJEux3GoqqqC2+1GSkoKMjMzhXQDMDrZejweNDU1wWq1Ii8vL6jQm2EYYWlIiFh8IRAiDiZ4b2trQ09PD7Kzs0P6TvT0eHH11W04dYof5zL0zqDT8YoGh4OYmQ8iOst0DjyBm6FSMVAqZWAYDg5HIKlTUCppyOU0HA5+O36cEh9R81H36Hlmmazbjwz5NAk7pK8enjAsl9PQauXwelk4ncTJTMoYeCP4HO1YwMvTaJoBRdmGjpNDeroW991XhqVLS4TlOAAhx19YWBjVYYziJofAyFncSmy1WmGz2UDTtF9BbDRPhcHBQdTW1iItLQ3p6emSIuejR49i1apVuPHGG/Hzn/88qjeXM4gLj3SJIsHpdCI1NVWQgIwGKaRrNptRW1sLt9uNvLw8TJo0STLZEkLs7u5GZmam0CIpFT6fTyBhi8UCh8PhN2HV6/Wis7MTqampkqdg/PGPRjz3nBHt7YGm3zwBU5QMTqd9qAsqGvCAzxePl8iJry1PnryzGE+Cer0cNls3AApyOV8klOYrLBVejCx6hTtOcQGNl6bRtB0s64JMBixYkI2nn74G+fmThBstaU4gwxdTU1MRGxsr2TxmNDidTlRXV0OtViMvLy9k+68YJBAgx2jjPSYFnTghY47j0NDQAIfDgaKiIkmNDC6XC5s2bcKhQ4ewdevWqKmIviZcOKQbqEiw2+3w+XyS+7Q/++wzzJ8/PygROp1O1NXVwev1Ij8/H93d3ZDJZEhJSYFarQ5LnhzHCYW0yZMnY+rUqVHTUXq9XvT29qKlpQUcx0EmkwndQ+RntOMDgOPH7XjiidP4+GMnGIYOWJr7oFI5oVDweUuLxQeOI8WhyMlMqewZapaYKDAApOk3x4Y+hDK5oSgWHOdDTIwSVqsbIz8jHyjKioQEJW66aTY2bvwOdDr/vK/X6xWsPfPy8sCyrN+KB8AICZbU84njOLS3t6OrqwsFBQVh7U6lQKxMIOoJp9MJvV6PyZMnj+rpAABVVVV46KGHcPPNN+Ohhx46V6NbMc5/0iX+s/39/cIyiaIo9Pb2wmq1Ijc3V9J+KisrUVZW5velk3zwwMCA0OXDMAzsdju6u7thsVjg8Xj8fBIMBoNwkpnNZtTX10Or1UpKcUSCUHlbkhu2WCwwm81C1TqQiIPB6WSxcWMX9uyx4PRpZmgiLTHTCazWc1CpKMjlNBiGg9sNiWRswtiX5qNDofDB6+2foH0z8HoJoZOUCblUwqckDAYgPV2GBx/8H/zwh/NG/J3jOPT29qK5uTnsSohl2RERp1gVQ4g4kLzEjQhZWVlRbaDwer1CUFJQUACGYQQitlgs8Pl8wjWi0+nAMAzi4uLw1FNPoaqqClu3bpXUwHCO4PwnXWIfl5aW5rekNhqNQi5MCo4ePYoZM2ZArVb7qR2mTZuGKVOm+HXIiFMJHMfB4XD4Lf29Xi8YhgFN08jKysLkyZOjdpKL87ZZWVnCTSYcSFWY/Ljdbmg0Gj8iJjpJo9GI+vp6fPFFLLZvZ1BT44XbTdzGHBieZBsKw2Qsl/NEzjCyIZN0on7ow0TZSKrVbrhcg1HYEzcUubJQKin4fF6wLBlbT3K/o0f6ajWFyy9PwcaNC1FSElxqJDYWz8/Pl7TcF0PcmUjITuwiZrVa4XA4MH36dMmDHKWCNAGFu1GQa8RqtaK9vR0PPvggurq6MHnyZCxduhRXXXUV5s+fH9Xj+hpx/pMuy7JB5V4WiwWtra2YOXOmpP18/vnnyM7OhsPhQGNjI5KTkzFt2rSIimQ+nw8tLS3o7+8XbgLii4Dkvkh+LpKKMOlya2pqGneaQizPERMxP95dKQjuFQoF7HYGL7zQhT17TOjsZIfabINNqhj1VQEwoCgOcrkDFMVCJqOGPlOAN1OnAHDw+TiwLEQ/0r0atFoXHA5TwKPDOWCaBpRKwOUKnKRMif4NRqqEcENDJuNfh2EYJCaqsXRpETZsWACDIfjKQnwDjcZyP3DfPT09aGxshFqtFoIGEnGSczFSgifweDyora0Fx3EoLCyUZADjdDrx61//GseOHcPWrVuhUqlw7NgxaLVaLFmyZEzHcRbiwiVdh8OB2tpazJkzR9J+jh07BpfLBYPBgNzcXCgUCslkS0a6k1lpU6ZMCeq0JFYkWK1WoXssNjY2pCIBGNbbqtVq5ObmRjVNQRpGBgYGMHXqVAAQjk+8LOSLdRo8/3wv9uwxwmTygab5eWZ2OwOfj46gYMWCVwBEGu1yoGmAZTnQNDdkksLvTybjlQ9OpxUaDa+KcLkYkQPa2Itper0XNttIIpfLKWi1MthsnqE8OIXMTD3uvbcQCxcmj6j6E1UCTdNCUTYxMRFZWVlR02YDw00ODocDhYWFQpOD2GCcfMfEzlHcsDMagfb29qKpqWmEtWM4HDp0CGvWrMEPf/hDPPjgg1FNb5xlOP9Jl3exGhmBeL1enDhxQpjEEAoOhwP19fUwmUzIzs5GWlqaYLgxGtkC/HK8oaEBCQkJyMrKiqgQQOZOkfyrWJEQGxsLjUaDjo4OIW8bavT0WCCWDGVkZCAtLW3EexVbTJKLlDib2e1avPqqGwcOWNDRwXvlyuW8UoCmqSE3Ngo+nwwsO5JQVCoX3G4bot05ptVa4XBE07vXBcCC4WiZg0olh9tNLhEOBoMC5eUpeOaZb6OwcJLfs8XyP5KLJUNT09PTMWnSpIhXPeFAlvvTpk0Tpv6Gg3jpT47R4/EI6SdxGzGxjSQ2pFKiZIfDgV/+8pf44osv8MorryA/Pz8q7/MsxoVLuqM1PIiLZHl5eTCZTKBpGmlpaZDJZKOerDabDfX19ZDL5cjNzY3Y4zMUvF6v4GVqNpshl8uh1WqFaDhcIUwqiD9ETEwMcnJyIlpiBssftrUx+NvfKHzyiQcWC4uRp5bYIpGGWk1akQfBMNE91WJirLBaIyFdDhTFR84qFQ2XyzO0wiGNHnaII+WYGAXS0vQoLZ2Mq67Kxf/+by40GmmfH/FGTk9PF3KtYlWCWHpFjGGkwuPxoKamBgBQUFAwrtWQ2FeXfM9EDZSUlITU1FRhNHuo64Rcf2vWrMHtt9+On/70p+dzdCvGhUu6QHDtbagiGU8ebX4dYcGW/R6PB42NjbDZbKPOmxrLewmWt3W73TCbzZIKYeHgdrvR0NAAl8uFgoICQYA/XpDUSWdnJ3p6elFXR+Hzz2VobKRx+jSHnh4GVutIz1mZjENcnAdOpwcyGQWPh4HbLZZj+W+v08ngcBBSH87BKpUyeDxk/0YQ/a5KJYNSSQ3JtwDxaS2TUeA4aihf7A+K8kEmc4GifEhJ0WP69ERcdlkGli4tRGZm5N+3y+VCbW0taJpGQUFB0O8qlA5W7FkbjIgjaQ8eC1wuF6qrq6FUKjF16lS/qFhscE48dbVaLZxOJzZu3IhTp07hlVdekawgOk9w/pMuAGG5Fggx6RK9rJQiGZG8BC77Af4kzMzMHKGWGC8iyduSQpiYiL1eL3Q6nR8Rk1SH1E61scJms6G2thYajQa5ublQKpUjuuqMRguOH2dQU0OjsZFFezuLvj5maHqvE8OqgPGABW9NGcl++JSBQsFPY8jKUmD6dD2++90cLFlSOO6IcTzG4gzDCDrYYESsUqnQ3t4OrVYr1CGiBVKn6OjoEIz3g20j9nM4cOAAnn/+eTidTsyaNQt33XUXFixYEJUbwR133IF//etfSE5Oxpdffhn0WFauXIm9e/dCq9Vi+/btKC0tBQC8/vrr+PWvfw0AeOyxx7B8+fJxH08YXBik6/F4gprekIYHspwWn5yRFMlI4SA2NhZqtRoWiwUul0uwzyMR8VhGeHg8HqHoMZ68bWD+1WKxgGXZIQWCHUlJSQIhRgviwYdSon6SwyY3C4fDAZ+PQnW1HNXVPtTWutDe7sTp025wHB8Ju1w+uN18FMtP2aACvjNKSGfI5V54PBZhCgEAUBSgVNJQqWTQauXQ6+VISFAjIUEBinIhM1OG66+ficsu4zsXA1UdRIctbsGW8hlarVbU1NQgLi4O2dnZUVtak5tZa2srBgcHoVAoIJfLRxTrxvN6DocD1dXV0Ov1yM3NlbQvm82GJ554AnV1dfjVr36FwcFBHD16FN/4xjewcOHCMR8Lwccffwy9Xo8f/ehHQUl37969ePHFF7F3715UVlZi5cqVqKysxMDAAObOnYsjR46AoiiUlZXh6NGjUVWKBOAi6RKXsfz8fOh0uoiKZCaTCfX19YiJiUF2drbfxRZMdiWuBMfGxgYVqROMRW8bCex2O2prawEA8fHxQo4OgJ90bSxmJuIlLTH7Geuxe73eEe3N4jl02dl54DgtBgY8MJk8GBz0wGzm/282e2G1emG1+uB2+6DRMEhO1mDqVD2ysgzIyYlFSop2xLERLXJqaioyMjLCvn+S3xTnsMM1xDAMg6amJphMJhQWFkZdF0vIXNzkECoijpSIxR1rhYWFkgZAchyH//f//h/WrVuHe+65B/fee29UV4BitLS04Hvf+15Q0l2xYgUWLFiAW265BQCf1z5w4IDws3Xr1qDbTQBCXgjnfK+dGIH2jl6vV3DVz8zMRGpqKhiGEewWRzspiDcuwzAoKioKmvsU2+eJ50mRaLO3txf19fUj9Lk6nQ5Go1HI20Z7vAqxmjSZTMjPzx9x4YiX/a2trX5mOiRiD5zAKobFYkFdXR30en3Q4YSRQqFQCPaXZDne1taG5ORk0DSN7m5evaFSqZCcbEBurgEGQ9KYiolutxt1dXVgWdbPizYcxHPDxH61JLdpNBrR3NwsWH06HA4kJydj9uzZUV1VMAyD5uZmDA4OjiBzmUyG2NhYv5WGmIjJFAcgNBETt7FIRv5YrVY8/vjjaGpqwjvvvPO1jkYPNvmhs7Mz5ONfB84r0iUg0WNnZ6cg8NfpdELUNFp06/V60dLSIrT9BstjhYN4oKTY6pGQHFFL0DSNSZMmQaVSweVyhSU5qRBHnxkZGcjLywu6T5lMNsLd3+v1CsdIUh1KpdIvkpPJZGhsbITdbkdBQUHUIziiW42Pj8ell1464qIXryo6OjrgdruF9A65oYUiOULmHR0dyM3NxaRJk4JuJxUURUGn0wnG4UQ54PV6kZWVBafTic8//xwMw4yIiMfiLUAcu1JTU/38aMNhNCLu7OyE1WoVVn0ejwfZ2dlISUmRFBEfPHgQjzzyCO677z784Q9/mLDoVirOxOSH8eK8Il2iOSXR4yWXXCJMEf3yyy9B07QQxRH9q/iDZ1lWKBpMnToVubm5UftiaJqGRqNBZ2cnfD4f5s6dC61WKxAIITIxycXGxkY0XoXkrA0Gw5iiT4VCgYSEBCQkJAiPeTweIfdKBg9qtVpMmjQJLpcLSqUyKk0axODF6XRi+vTpIRUVarUaarVaKMqI0zsmkwltbW1Bl/2kxZYMP4zmqkI88SOYckC88iFFXIZh/Aqe4VJQPp9P+Gxmz549blliIBFbrVacOnVKsGo0m83o6OgAENpUx2q14rHHHkNbWxveffddTJs2bVzHFC2EmvyQnp6OAwcO+D2+YMGCM3+AOM9yuqdOnYLL5RI0p4FFMnHe0Gw2C8tVMua5t7c3rMn5WCG2c8zOzg6btxWTHCnUEVkYuWEEkqnb7UZ9fT08Hg/y8/OjJgEjMJlMqKurQ3x8PDIzM8EwjN8xhsttjgYxYRF/imhE+yT/ajKZcPr0aWHoaEJCwriizUCM1Vg8XMOJuBnBaDSisbFRcpNDJBAPnSwqKhqxagk01bFarXj55ZcxMDCA2tpa3HbbbXjssceier7t27cPK1euBMMwuOuuu7Bu3Tq/v69evRrvvfcempubkZGRgdOnT8M0NO5aJpNh2rRp6O/vx7e+9S2sX78eDz74IA4fPoyBgWX2S14AACAASURBVAGUlZXh2LFjAIDS0lIcPXrUL8CIMi6cQhrDMJKLZBzHCcUUjuMgl8uFCETchDAeb4Px+iQEk4X5fD7BxMTpdMJkMiEnJyfqEjCPxyPMeysoKAjp+B/M7EccyZFiYuB7J8Ugg8GAnJycqN7oiDSwqakJU6dORWpqqt8xBpKceFadFIgJq6CgICo6bXHDyeDgIPr7+8FxHBITExEXFxfxMYaDxWIRpqoQ2aSU56xfvx5dXV341re+hebmZnz++ef44IMPokK8DMMgPz8f77//PtLT01FeXo633noL06dPF7a55ZZbcODAAfT390On06G4uBi33XYbAODnP/85rFYr7r//fuzbtw9arRavvfYa5s6dCwB49dVX8dRTTwEA1q9fj9tvv33cxxwGFwbprlmzRijslJWVISYmJiQJEUtEh8OBvLw84aIRRyBms1nId0Va6Z9InwRSXW5tbfXLX45XjUDAsqygKx0rmQfrWCNjuHU6nSCqn4jKvsPhQE1NDVQqFfLy8kLmeEO5collYcEaEUhuNSUlRbJRvFSIc/KknkDm6ZGoUzzOPFJpmFhVMX36dEmjcziOw/79+7F+/XqsXLkSt99++4Tkbg8dOoQNGzbgvffeAwBs2rQJAPDII48E3f6yyy7Dxo0bsXjxYgB8KoQUCs8CXBikW1tbi4qKClRWVuLYsWPweDwoLi5GWVkZysvLMWPGDLjdblRVVUGj0UhuEBBX+s1mM+x2u19eTGwSHi29bSjY7XbU1dVBoVAgNzdXqLyT4giJiIkaQbzkl1KoGxgYQH19PZKSkpCZmRnV3CcZLd/Z2QmNRiPYXkox+5EClmWFsTZkuOdY9hE4IgmAMCNscHAQDMNg+vTpUWv5JiA3C6IjDyczDJSGBRJxsJuFyWRCTU0NpkyZgoyMDEmfs9lsxqOPPorTp09jy5YtfgqAaGPXrl3Yt28f/vSnPwEA3njjDVRWVuKll14asW1raysuvfRSdHR0COeoXC5HSUkJ5HI51q1bh+uuu27CjlUCLgzJWEFBAQoKCoROE5fLhRMnTqCiogIvvfQSPv30U7hcLixatAjf+c53MHnyZCQlJY168oWq9BMS7urqgsvlAsdx8Hq9SEtLi3oDAvGIMJvNQSVgwarURI1gNptx+vRpQY0QzL+BmMAzDBO1sdtikG41rVaL+fPnCzlfsdkPKdTJ5XK/m0VgwTMYBgYGUFdXJ8jvxhqJkWKr+HP0+XxobW1FS0sLtFotGIbByZMn/Y5xvDcLotWWoosl48zFN3TxzYJIw8QqGrPZDLfbjVmzZkn6bjmOw/vvv4/HH38cDz30EH70ox9NuDIhEoXBzp07sXTpUr+goK2tDVOmTEFTUxMWLVqEmTNnIicnZ8KOd6w4ryLdcFi5ciUA4P7770djYyMqKipQVVWF1tZWIX9UVlaGuXPnIj4+XvIFRPK2jY2NSExMFAxMzGYzfD4f9Hq9QHJjyceJC03jbUAAhsdvk4jY7XYLN4uMjAxkZGREtY2U6IXNZjMKCgokRf7hCp6BNwuPxyNMKygsLIx69Blqjpj4ZkGMYMaysrBaraiurp4Qa0eGYdDV1YXm5mbBS5cQcbg0lMlkwiOPPIKBgQFs2bIFaWlpUTumcIgkvTBnzhz8/ve/D2lk9eMf/xjf+973sHTp0ok74PC4MNIL4cAwTFDCI0vSyspKVFZW4siRI7BarSgqKhJIePbs2UEF9KPlbcU5Q5KTA+AnCQsXIRHVQFxcHLKysqJKhgDQ39+P+vp6JCYmQq/XCyQyngITgXjsTCjLyEgQzOwH4Ek3LS0NGRkZUc2bj8VYPFhXXaDOmaShxLnVUI034wGRmblcLhQVFfmloQLTJzRNw2634/PPP4darcZrr72GNWvW4LbbbovqTWA0ZcK2bdtwzz33CFMzBgcHsW/fPsyYMcPPN+HOO+/Eli1b0NzcLJxTg4OD0Gq1UKlU6O/vx/z587Fnzx6/ItwZxkXSjQRerxcnT54UiPiLL76AXC5HaWkpSktLkZmZid27d+Omm25CUVFRRHlbctKbzWbBREcul/vphzmOQ2NjozAAU0qxIxI4nU7B7So/P3/EDSXUzSIw9xrqgiStx+RmFM00CzAcHep0OsTHxwv5zXBmP5HAbDajpqYGkyZNQmZm5riIRzyrzmKxwOl0gqZpuFwuJCUlITs7W9LQ0EhAbqZSZWYMw+DEiRN46qmnhAkTMTExeOCBB7Bs2bKoHJMUZcL27duxa9cu1NXVgWEY3HHHHVi/fj3WrFmDP//5z6iurgZFUcjOzsby5cvxwgsvCM/97LPPsGLFCsG8atWqVbjzzjujcuxjxIWR040WFAqFQLD33XefYPl46NAh/Pa3v0VFRQWKiopQW1uLuXPnCj9SNKbB8sPkwhwcHBQsF/V6PZKTk4UGhGhEuaSQ1d/fj7y8vJAaRVLciomJEZaW4gippaXFbzktNvohnXzB8s7jhThVEUxXGtiE0NDQ4DescbTx5WTSgt1uR3FxcVRudkqlEklJSUhKShIaQBwOB3JycgS7xEi66sLB6/WitrYWDMOgtLRUUuTPcRzee+89bNy4EWvXrsWtt94KmqaFeWrRwuHDh5Gbm4vsbN5QaNmyZUEj0czMTPzrX//ye6y0tBQWi0U4X2+66SZccsklfttcdtllOHnyZNSOdyJxkXQlgKIoGAwGxMfH4/LLL8fbb78NlUqFrq4uIRr+wx/+IJAZkayVlpZKyuuRRg6j0SgslUnutb+/H01NTX5LfqJ7lRqBifPOU6ZMGVOhabRiIvFv0Gg0SE5OhtfrFXxWowHSyRWutTlU+3Vgy2uwvGZ/fz8aGxsxdepUFBQURL1FlBx/ZmYmioqK/PYvtasu3I2X7D+SBpOBgQGsXbsWTqcT//3vf5Gamir8jdx0o4Vg3geVlZUjtvvHP/6Bjz/+GPn5+fi///s/ZGRknFW+CdHARdKNAPPmzcO8ecNjs9PS0nDDDTfghhtuAMBHg9XV1aisrMTu3bvxi1/8AgzDYNasWUI0XFRU5LfktdlsqKurg0qlwpw5cwSSCjRXIUt+0qJJqtPi6CgYwZOlvlKplBz9SIVCoYBGo0FbWxt0Oh1KSkrAcZxAxIHkQSLiSJb8JBUil8tRVlYWcQQYrNIvjtqJDwZFUYK5Dml1jgbxktE2NE2HPP5Qpkmkq46Y6QRLn7Asi5qaGsGuUMrnw3Ec/v3vf+NXv/oVHn30USxbtmzCfQikKBOuvvpq3HLLLVCpVNiyZQuWL1+O/fv3n1W+CdHARdKNImQyGYqLi1FcXIw777xTuHCOHj2Kw4cP47nnnkNNTQ1iY2NRXFyMtrY25Ofn4+c///mohRrxkj89PR2Avy+t2LuBRG8mkwlWq3VClvriVEWgJjbQG4F0gpFom0TtYlVHsAGepJCVn58f1XZNIq8jOdZZs2bBYDCMavYTSe5VrDrJy8uL2Lg8lKuZOH1SXV0tDFGdPHmyYLIfruhpNBqxZs0a+Hw+fPDBB5IHSo4XoTwRxBAbS919991Yu3at8NyzxTchGrhYSDvD4DgOL730Ep5//nmUlpbCarWiq6sLmZmZQjRcWlqK2NjYMd3NXS4X2tra0NXVBaVSKVy8Y400g6G/vx8NDQ2SfGiDQRy1k04w8WgkAIKt43gLWcEg1Vg8mA+GlNwrMf+O1I9BKlwuF2pqaoQGGXGxLlhXnUqlgkqlwrvvvounnnoK69evx8033xy1aHE0VcLzzz+PP/7xj2hsbMTcuXPx+uuvY+nSpdixYwdmzZqFmTNnAgCSk5Px3//+FwCwe/duPP3006ioqPg6fBOigYvqhbMJ//3vfzF//nwhZ8ayLBoaGlBZWYnDhw/j6NGjcDgcmDFjhkDExcXFo6YGxA0IOTk5UCqVfpEmIZBAb1+pU2idTifq6upAUVRQ1cN4wDAMBgYG0NTUBJfLBYVCIUSagV1/43mNxsZGmM3mMbUfk7E0ocx+YmJiYDab0d/fj4KCgqivLsTRc35+fkjLUXEee3BwEHfccQesVisUCgV+8pOfYPHixZg1a1ZUjkmKKuGjjz7CJZdcggMHDuD222+H3W7HI488gvXr10OpVGLXrl245ppr8Mgjj+Ddd9+FXC5HQkIC/vCHP6CwsBDAGfdNiAYuku65Bo/HgxMnTghE/OWXX0KtVmPOnDkCEWdnZ4OmaRiNRvT19cFqtUpqQCAXpTjSFAv7A20vWZZFa2srent7Q87JGg/EfgNiFzZxBGc2myVHmsFAovO0tDSkp6dHLcojN7Xe3l60t7eDpmkoFIpRzX4iBWnS0Gg0yMvLkxQ9cxyHd955B5s3b8bDDz+MnJwcHD16FH19ffjlL385ruMhiNQv4fjx47j//vvx6aefAjjr/BKiiYuSsXMNSqXSr3DHcRxMJhOqqqpQWVmJd955B42NjZDL5UIH0Xe+8x1J0Vuw4pLP5xPIjbQMq1QqKBQKmM1mTJ48GfPmzYv6Ut9ms6GmpgZ6vR7l5eV+ZCKWW5HPgESa4ip/OG3uWKZERAKWZdHV1QWTyYSysjLo9Xo/nXN3dzfq6uoEbwQStUtdXYiHWkaS2z59+jR+9rOfQaFQYP/+/YJhe6gOrrFCqiqBYNu2bViyZInwu8vlwty5c88Wv4Qzgouke46AoijEx8fjyiuvxJVXXgmXy4WrrroKubm5uPzyy/Hll19ix44dMJlMKCgoEEx+iOn1aJEdWdKRi5poSJ1OJxITE2GxWFBZWekXwY3H9pJ0ZJGxM1IaTCiKEkzMxVV+h8Mh3CzE2lyO42A2m5GXlzchBSPi9zBlyhS/SQ7BdM5ib4T29nZYrVa/m18w/waHw4FTp07BYDBIHp3DcRzefvttPPPMM9iwYQNuuOGGCa30R6IsePPNN3HkyBEcPHhQeOxc8UuIJi6S7jkKtVqNv/zlL4KSgcDn8+Grr75CRUUF3nrrLaxduxYURaGkpERoay4oKAh5AbMsi/b2dnR3d48YFy4mODL7bSy2l0TFkJaWhvLy8nGRgnhkDqmGWywWnDp1Suj0a25uRmtr66jyOqkgTQ5ut1vyJIdQRjrBzH5iYmIEDXRRUZFkt7Te3l787Gc/g0ajwUcffRSxYmIskKJKAIAPPvgATz75JA4ePOhXmyDbZmdnY8GCBTh+/Ph5T7rnZE7373//OzZs2IDq6mocPnxYMCkORKiqanNzM5YtW4aBgQGUlpbijTfeiHqr6tkCjuNgs9lw9OhRVFZWoqqqCnV1dUhMTERZWRnKysowb948pKSk4OOPP4ZKpRLaX6VEViSCC2YpSUiGFMBcLhdqa2tBURQKCgqiqhkGhmVswYzFg419D2y/ljIaqbe3F01NTcjMzERKSkrUo8jBwUFUV1dDqVRCLpeHNfshYFkW//jHP/Dss8/il7/8Ja677rozpmP1+XzIz8/Hhx9+KNxEd+zYgRkzZgjbHD9+HEuXLsW+ffuQl5fn917PMr+EaOL8KqRVV1eDpmmsWLECzz77bFDSDVdVvemmm3DDDTdg2bJluPfeezF79mzcd999X8M7+XpAZskdPnwYFRUV+OSTT1BbW4vk5GTceOONuOSSSzBnzhzo9foxXbziTjWihRU7maWnp0f9JkeW+pHI2EihjhwnKdSJrS/JcZIbhkwmQ35+ftSPnxQr+/r6RqRbgpn9aDQafPjhh0hKSsI///lPJCYm4oUXXoh6kXM0OZjb7cbixYtRUVEBmqZx//3349lnn8Xjjz+OlpYWfPbZZ+ju7oZSqRTmqE2dOhXvvvvu2eiXEE2cX6RLsGDBgpCkG6qqum7dOkyaNAk9PT2Qy+UjtrvQYDQasXjxYvziF79AQUGBoJY4fvw4PB4PZs6cKeSHp0+fHrEHBDGPIeNmiGqCjBwab4WfjBTyeDzjtnYUt+MSkvN6vYJBzbRp05CRkRFVY3dg2MCHGMePdsMgaZ4nn3wSBw4cEBz0ioqK8Oabb0bt+KTIwV5++WV88cUX2LJlC3bu3Indu3fjr3/9K06dOoVbbrkFhw8fRldXF7797W+jrq4u6p/dWYwLT70QqqpqNBoRFxcnVLjP9T7u8SIxMRGVlZUCmU6fPl3QQLpcLhw/fhwVFRV48cUX8dVXX0Gv1wu54blz54YcV+P1eoXOrmDmMaS7ymw2o7u7G7W1tQCGncxGs70k0XpLS0vUBloGtuPa7XbBS3fKlClCmmasSoRAsCwrFBPDTUAORG9vL1auXImEhATs378fCQkJQmEymqQmxaRmz5492LBhAwBg6dKluP/++8FxHPbs2YNly5ZBpVIhKysLubm5OHz4MObPnx+14ztXcdaS7re//W309PSMePzJJ5/EtddeO+rzQ1VVxY8PDAzg1ltvRX19PRYvXoy//e1vI4oWH330EVavXi38XlNTg507d+K6667Dj3/8Yxw8eFDIHW7fvh0lJSWS3+PZglDRq1qtxvz584ULhQzyrKqqQkVFBXbu3CmYqxOTnzlz5mD37t3IyclBUVERCgsLRzWnCeZk1tzcDLvdLkyREDdIkHHqarV6TKPmRwNZ6p8+fRqFhYUjhk6KlQhtbW1CHltsfTlaoY6sACZPnuynfBjtuHbu3Inf/e53eOqpp/C///u/wvNkMplfvjQakCIHE29DcuRGoxGdnZ249NJL/Z57IQc3Ypy1pPvBBx+M6/mhqqpJSUkwmUzw+XzYvHkziouLodVqsXDhQmzevBlPP/20334WLlyIEydOAOBJOjc3F1deeaXw99/85jdfpzv9GQVFUUhKSsKSJUsErSWZiltZWYl//OMfuP322zFt2jQUFBQI0fCsWbMk6WPD2V6azWbBJYxlWUyePHlCZGAWiwU1NTVISkoK6cYmViIQwiE652DeDeIbBumKs1gsEdlHdnd3Y+XKlZg0aRIOHjw4pvlvkUKKHExKcBPquRcqzlrSHS/Ky8tRX1+P5uZmpKWlYefOndixYwcoisLChQuxa9cu7NmzB/PmzcO1116L66+/HgsWLBhBumLs2rULS5Ysifr8sHMZNE0jJycHaWlpeP311/Gf//wHc+bMEUzgX3vtNZw8eRIKhQJz5swR8sO5ubmSluSkQUIul6O/vx/p6elISUmB1WqF0WgMansZyXRcAjEZRrLUJwjUOQPDo5HI3DKHwwGv14u4uDhkZmZKKsaxLIsdO3bgpZdewqZNm/Dd7373jJGXFDkY2SY9PR0+nw9msxkJCQmSpWQXIs7JQtru3bvxwAMPoK+vD3FxcSgpKcF7772Hrq4u3HXXXdi7dy8AYO/evVi1apWfCz0ANDU1YdmyZTh69ChuuOEGvPnmm1CpVIiPj8fg4GDI1120aBEeeughfO973wPAz2E6dOgQVCoVrrjiCmzevDnqMqjzAcTu8ciRI0KhrrGxEZMnT/bLD5P2XzHEueHCwsKgkeFoBjqjDY4kyodotwgTiM3Rs7Oz/ebUMQwDnU4XdI5eV1cXHnzwQaSmpuK5556LupcDwcDAAG6++Wa0tLQgMzNTSLOJ5WD9/f1YsGABUlJSoNPpBNOc3//+9/jd734Hj8cDlmVhNptx4MABKBQK3HrrrUIh7YorrkB9ff3FQhrOUdKNBOFyw8uXL4fJZBIeC0e63d3dmDVrFrq6uoQcIpHC3HTTTaiqqsKkSZNw5MiRoEs/mUwmuCkRyQxwYWmGxeA4Dp2dnaisrBSGhBqNRuTn5wtOa7W1tfD5fLjmmmskjZ0Rg2EYP98GYnsZ2E1XV1cHj8fjN0csmjAajairqws5VDRwNJLNZsPatWuh0+lQV1eHRx99FHfffXfU89ZiPPzww0hISMC6deuwefNmDA4OCis+Eri4XC4sXboUzz//PFavXo3t27cLAy8LCwvhcrkwdepU7Ny5Uyi8Pfnkk3j11Vchl8vxwgsv+LX/XgC4cEk3HAoKCnDgwAGkpqaiu7sbCxYsEKrogfjtb3+Lr776Cq+88orf4+SEvfTSS3Hvvffi2muvDZqiCGXscaFrhsVgGAanTp3Cf/7zH7z88svC6mP69OlCNFxYWDhmq0Ri1UicwOx2uzAWKVq2lwRer3dMhN7R0YEHH3wQsbGxKCsrw8mTJ9Ha2oqDBw9OWFohkuuAYPbs2di1axfy8vLOhsm7ZyMukm4wrFmzBomJicIdfmBgAM8880zQbS+99FJs2rQJCxcuFB4jJ+hHH32EZ555Bj6fD++//37QEzYY6XIcd1EzHARr167F4sWLccUVV8DhcAgm8JWVlaitrUV8fLzQTVdeXh7RpGHiRSuXy5GXlweGYfwaD6QYrI+Gvr4+NDQ0RNS1xrIs/vznP2Pr1q34zW9+g8WLF5+x3G1cXJzkFR/AS8mWL1+Or776CjRNX0yzBcdF0g0Go9GIm266SZA9/f3vf0dCQgKOHDmCLVu24E9/+hMAoKWlBf/zP/8jWPcRLFq0CAcPHkRRURFKSkqwZcsWZGRkBD1h5XI5SkpK/NyU+vv7cemll6KhoQEA0N7ejiVLluDLL788Mx/AOQgy743MpiM5w6ysLD8TeIPBMGIOWWdnJzo6OsLaU4q9aMkkZGJMM5oczOPxoLa2FhzHRdTm3N7ejgceeADZ2dl45plnIpouLRXRTLMtWLAAr7/+uiAJ6+7uRkpKCjweD+655x7k5OTg8ccfj/p7OMdwkXTHg2icsF1dXX5uSh9++CEMBgPmz5+PhoYGDAwM4Nprr8Xhw4fxzW9+M6hm+MSJE7jvvvtgsVggk8mEYgaA80YzPBYQE/iKigrBBN7lcgkm8ElJSdi7dy/WrFmD3NzciIs5YjmY2WwWbC/FRGwymdDU1ITs7GzJUjaWZbF9+3b88Y9/xHPPPYcrrrjia5FVSU0vWCwWLFiwAI888ghuvPHGoPs6cOAAnn322RETfS9AXCTdicJY8mEkB/b9739fSC88+uijsFqtaGpqwsKFC/2KGQRkakNeXh66urpQVlaG6upqxMXFXcyrBcDtduPIkSPYtGkTqqqqhFRCaWmpEBFnZWWN2R+Y+CEMDAygp6cHHMchLi4O8fHxQX19A9HW1ob7778f+fn5eOaZZyKWqEUTUtJsHo8HS5YswdVXX41Vq1b5/a27uxupqangOA6rV6+GWq3G5s2bz+RbOBtx4bUBnylcc801eP3117Fu3Tq8/vrrQbvlAt2UPv30Uzz88MMRa4bz8/OF/0+ZMgXJycmCbO4i/KFSqaDT6XDZZZdh9+7dgtk7yQ2//fbbgoabkHBZWRkSExMlRZtKpRI+nw+Dg4OYMWMGkpKShLFIYl9fIluLiYmBWq2GQqHAtm3b8Nprr+G5557DokWLJiy6DSUFC8Rzzz0HnU6HJ554AgaDQQga9uzZg7vvvhuxsbFITEzE0aNHYTQasX37dgDDq6kf/OAH6OvrA8dxQprtIsKA47hwPxcxCvr7+7lFixZxubm53KJFizij0chxHMdVVVVxd955J8dxHPfpp59yxcXF3KxZs7ji4mLuT3/6k/D8xsZGrry8nKNpmlu6dCnncrk4juO4uLi4sK9bWVnJFRYWcgzDcBzHccuXL+fy8/O5mTNncqtWrRL2cxGhwTAM19zczL311lvc6tWrucsvv5ybOXMmd+ONN3KbN2/mPvzwQ66/v5+z2+1+P0ajkfvkk0+4qqoqzmQyjfg7+bFarVxXVxdXU1PD/fOf/+Ryc3O59PR0bvbs2dyrr77KNTU1Tej7W7NmDbdp0yaO4zhu06ZN3MMPPxx0O51OF/TxG2+8kXvrrbc4juO4FStWcC+//PLEHOj5iZC8ejG9cAYxkcWMHTt2/P/2zj8mqiuL498HCDXRWlBpcZeUGQYUBphSQaBNW8cUSEg1kgBZ2gRC05S2GNMmmnWb6C4/KtukrSlCg7ooSgIjpBVtrGgTaPqHf4AtGhl/FIdatZCKM4aWWpGR7/4BczsDMyPWGX7eT/IS7nn3vXfvkJx33znnnoPi4mJYrVYsWbIEGzdudHBmDA0NIS8vD9999x2WLl2Kw4cPIywsDMBoBraamhr4+vqioqIC6enpHpz17GJ4eFgkge/o6MDZs2fh4+OD+Ph4PPvsszCZTPD398dbb7016TSK9+/fR01NDWpra1FaWoqFCxeio6MDIyMjYsOON5is6UtG1ngF158v7jTyNLwd5i2RkZHs7e0lSfb29jIyMtJpv4GBAcbHx7OxsVHIrFYr1Wo1TSYTh4aGqFar+eKLLzpcV1VVxcLCQpJkQ0MDc3JySJJGo5FxcXG8e/cue3p6qFarabVavTHFWcnIyAh//fVX1tfXU6PRUKfTUafTUa/Xc8uWLTQYDDSZTBwcHHS62u3q6qJer+fmzZs5ODg4pWNfsmSJQ9vV15Ovry9Xr17NpKQkHjlyhCTZ39/P8PBw0efatWvUarXeG+zcw6VelTbdGcJkbMP37t1DZmYm8vLyHLzH7e3tCA0NhVqtBkk89dRTE66VKfj+GrbtxAMDA6itrcXzzz8vqhfbksDv3bsXN2/ehEajEduadTodGhoaUFdXh08//RQvvPCCV2y37r6eJouzOmXOwtZkwhoP4U4jT/3LYf4yGdtwXV0d/fz8xGpLp9Oxs7OTTU1NDAkJYUxMDLVaLVNSUvjmm2863F+r1fL69euirVar2d/fz6KiItbV1Ql5WloaQ0JCGB4eLuyB9nz88ceMiopibGws161bx6tXr4pzPj4+Ylzr16/36O8z07FarTQajdy/fz8LCwv59NNPMzs7m7///vu0jWmyX0/25Ofns6mpiSMjI1y6dCmHh4dJkqdPn2ZaWppXxzvHcKlXpdKdAzQ2NgrFTJKHDh3ipk2bHPpER0dPULq3bt3iO++8I5Su1Wrl4sWLWVVVxaGhIcbFxdFoNDrcp7W1VSiSzz77TJgpSNcOmfnIyMjI7wipFQAAB15JREFUdA+BW7ZscXCkbd26dUIfi8UinK79/f3UaDTif56VleXgSKuqqpqikc8JXOrVvxakKJlRPEwKPgAuU/C1t7fD398f8fHx8Pf3F5UC7NHr9SK1ZXJyMm7cuOHNqc1avPkpbrFYkJqaioiICKSmpjp1uLa1teHEiRP44IMPEBAQgPfff18kXHrllVewePFiPPPMM1izZg1iYmKg0+mg1+uxbds2URniww8/xCeffAKNRgOz2TyX6pdNL+408rS8HyQPzfDwMFUqFXt6esQKtaury6FPZWWlgyMtOzubJNnV1SUcaZWVlVy0aJFwpB06dIhFRUUun1tUVMTS0lLRduaQkXieyYaC2TCbzQwMDBRfKDYTgsSrSPPCXOf48eOMiIigWq1mWVkZSXL79u08evQoSfKPP/5gVlYWw8PDmZiYSJPJJK4tKyujWq1mSEiIg93OmZnCRl1dHZOSkhzigX/++WeSo7HHwcHBVKlULm3DBw4c4LJly4QNeN++feJcbW0tNRoNNRoNa2trH+FXmZs8rK12z549fPXVV0VbKt0pQSpdyYMZ7yzZuXMnd+7cOaHf119/zVWrVvGXX35xeh+r1cpFixaxsrLSpW34wIEDTlfRZrOZKpWKZrOZFouFKpWKFovlEWc2t5hsKJgNvV7PL7/8UrTlRpopQdp0JQ/GvsTRvXv3YDAYsGHDBoc+nZ2dKCwsxLFjxxAcHCzkt2/fxtDQEADg1KlTuH//PvR6vUvbsCtOnjyJ1NRUBAUFITAwEKmpqWhpafHcJGcJL7/8MmJiYiYck/0dbfT19eH8+fMOG17Ky8tx6dIldHR0wGKxuC1RJfE8Mk5XIvDz80NlZSXS09NFiSOtVosdO3YgISEBGzZswNatWzE4OCjihG1VMC5evIjCwkL4+Pjg9u3bWL16tXDIOKsiCwCff/45vv32W0RGRmLXrl0IDQ11WoF2PlaRdVeY9cknnxRJZvr6+hxefuNpbGxEZmamQ+WJkJAQAKP5KQoKCvDRRx95buCSByKVrsSBjIwMZGRkOMhKSkrE366UwXPPPYfz588DAJqamiZsFx3vzV+/fj1yc3MREBCA6upq5Ofno7W1dUIV2e7ubrS0tKC6uhpvvPEGtm3b5nD+vffeQ1tbGwDgzp07uHnzpthO7apE0mxnMhtpbDQ0NKC8vNxBZp8VrLm5GTExMd4essQed7aHabCDSOYAk7UN27BarXz88cdJkvX19WJjhy1ueNeuXS5tw/ZUVFSwoKBAtGdb3HBjYyOjo6OpKAo7Ojpc9jt8+DAXLlzIBQsWMDw8XGykaW5u5vLly6nRaJiTk8PLly9zxYoVIimSDb1eLzbSvPbaa/ztt9+8Oq95inSkSaaOyYSw2bzvJPnFF18wKSmJ5KgjLSwsjBaLhS0tLXzssceEUnmQ8k5JSeGpU6dEe7Yp3QsXLvDSpUt86aWXXCrd8Xk27F9EMivYjEI60iRTh71tOCoqCjk5OcI2bPvEr6iogFarhU6nQ0VFhcjRGhQUhO3btyMxMRH5+flITExEUFAQAPf23Z9++gk//vgj1q1bJ2R3795FQkICkpOT0dzc7N1Je4CoqCisXLnSbZ/29nZoNBqo1WoHJyVJtLa2iiT2+fn5s2LO8xGpdCVeISMjAz/88ANMJpNIX1hSUiKiIcrLy2E0GnHu3Dm0tbVh1apV4trXX38dV65cwe7dux0StwOud3oZDAZkZWU5lOK5du0azpw5g/r6erz77rvIzs5GcHCwSxsmSWzevBkajQZxcXH4/vvvxbmDBw8iIiICEREROHjw4F/7UTyAK0ej2WzGE088IapVzFcH5GxAKl3JjGUy25ttGAwG5ObmOshsfdVqNdauXYvY2Fi34WcnTpxAd3c3uru7sXfvXrz99tsARrfdFhcXi0KYxcXFbqvluuNRQ8HoJP+1oigu5ZIZiDvbgzzkMZ0HRqNregCoAPgDOAdA66TfSgBXMVbzb0wWCCBg7O9lALoBRAMIA9Dl4nl7AOTatS8DCAGQC2CPq35emPc3ABJcnEsBcNKu/a+xQwFwC4Cfs37ymDmHXOlKZiwkrQA2ATgJ4CKARpJGRVFKFEWx37WRC8DAMW0zRhSAM4qinAPQBuC/JC884JF/A3Ddrn1jTOZKPh10AIhQFEWlKIo/gH8AODY29zYAtsqk+QAebieFZEqQcbqSGQ3JrwB8NU62Y1z7P06uOw0g9iEf5+x7nG7kHkVRlEwAuwEsB3BcUZSzJNMVRVkB4H8kM0haFUWxvYh8AewnaRy7xT8BGBRFKQPQCaDG02OUPDpS6Uokf3IDQKhd++8Aesfka8fJv/H0w0keAXDEibwXQIZde8KLaEzeA2CNp8cl8SzSvCCR/MkxAHnKKMkABkj2YXRVmaYoSqCiKIEA0sZkEslDI1e6knmDoigNGF2xLlMU5QaAfwNYAAAkqzG6eswAcAXAHQAFY+csiqKUYtSeCgAlJC1TO3rJXOFBJdglEolE4kH+DwVVi4MYEpD1AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "filenames": { "image/png": "/home/mikel/Documents/CallystoShortsJBook/_build/jupyter_execute/shorts/Matplot3D_8_0.png" }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Make data\n", "u = linspace(0, 2 * pi, 20)\n", "v = linspace(0, pi, 20)\n", "x = outer(cos(u), sin(v))\n", "y = outer(sin(u), sin(v))\n", "z = outer(ones(size(u)), cos(v))\n", "\n", "## Create a 3D figure\n", "fig = figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "# Plot the surface\n", "ax.plot_surface(x, y, z, color='b')\n", "\n", "show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More examples\n", "\n", "More information on 3D plotting here:\n", "https://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[![Callysto.ca License](https://github.com/callysto/curriculum-notebooks/blob/master/callysto-notebook-banner-bottom.jpg?raw=true)](https://github.com/callysto/curriculum-notebooks/blob/master/LICENSE.md)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }