{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's make a maze!" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import math, numpy as np, matplotlib.pyplot as plt\n", "\n", "class Maze():\n", " def __init__(self,size=10,fill=0.1):\n", " self.size = size\n", " self.board = np.zeros([size,size])\n", " for row in self.board:\n", " for i,item in enumerate(row):\n", " row[i] = np.random.random() < fill #1 designates filled, 0 is empty\n", " def view(self):\n", " print(self.board)\n", " def find_path(self,start=(0,0),end=(-1,-1)):\n", " start_i,start_j = start[0] % self.size, start[1] % self.size\n", " end_i,end_j = end[0] % self.size, end[1] % self.size\n", " result = self._recurse_find_path(start_i,start_j,end_i,end_j) if self.board[start_i][start_j] == 0 and self.board[end_i][end_j] == 0 else False\n", " self._remove_7s()\n", " return result\n", " def _recurse_find_path(self,i,j,end_i,end_j):\n", " self.board[i][j] = 3 #3 designates path\n", " if i == end_i and j == end_j:\n", " return True\n", " options = [(i,j+1),(i+1,j),(i-1,j),(i,j-1)]\n", " for x,y in options:\n", " if self._ij_legal(x,y) and self.board[x][y] == 0:\n", " if self._recurse_find_path(x,y,end_i,end_j):\n", " return True\n", " self.board[i][j] = 7 #7 designates visited\n", " return False\n", " def _ij_legal(self,i,j):\n", " return i == int(i) and j == int(j) and i >=0 and j >=0 and i < self.size and j < self.size\n", " def _remove_7s(self):\n", " for row in self.board:\n", " for i,item in enumerate(row):\n", " if item == 7:\n", " row[i] = 0\n", " def clear_path(self):\n", " for row in self.board:\n", " for i,item in enumerate(row):\n", " if item != 1:\n", " row[i] = 0 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Okay!\n", "\n", "Use `Maze(arg1,arg2)` to make a maze of size `arg1`x`arg1`, where each square has fill probability `arg2`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 1.]\n", " [ 0. 0. 1. 0. 1. 1. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 1. 1.]]\n" ] } ], "source": [ "x = Maze(8,0.2)\n", "x.view()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Path-finding\n", "The method `find_path()` will attempt to find a path through the maze and return success or failure. If successful, the path will be populated with 3s." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "False\n", "[[ 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 1.]\n", " [ 0. 0. 1. 0. 1. 1. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 1. 1.]]\n" ] } ], "source": [ "print(x.find_path())\n", "x.view()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 1.]\n", " [ 0. 0. 1. 0. 1. 1. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 1. 1.]]\n" ] } ], "source": [ "x.clear_path()\n", "x.view()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use `find_path(start_coord,end_coord)` to find a path between specific coordinates (default is top left corner to bottom right corner)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "True\n", "[[ 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 1.]\n", " [ 0. 0. 3. 3. 3. 3. 3. 3.]\n", " [ 0. 0. 1. 3. 3. 3. 3. 3.]\n", " [ 0. 0. 0. 3. 3. 3. 1. 1.]\n", " [ 0. 0. 1. 3. 1. 1. 0. 0.]\n", " [ 1. 0. 1. 3. 3. 3. 3. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 1. 1.]]\n" ] } ], "source": [ "print(x.find_path((2,2),(-2,-2)))\n", "x.view()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Careful! The path will persist on the board unless you remove it with `clear_path`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 1.]\n", " [ 0. 0. 1. 0. 1. 1. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 1. 1.]]\n", "False\n", "[[ 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 1.]\n", " [ 0. 0. 1. 0. 1. 1. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 1. 0. 0. 0. 1. 1.]]\n" ] } ], "source": [ "x.clear_path()\n", "x.view()\n", "print(x.find_path((5,5),(6,7)))\n", "x.view()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Path Statistics\n", "How likely are you to find a path from the top left corner to the bottom right corner? One can conduct an experiment and watch how path success varies with fill probability and board size." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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aWQfg32bWzTn3kxOBT5o0adfPPXv2pGfPntWVc3c33xwcAnPZZdCwYcXbi4hE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KYG4bXC2TFzh+soIiJSiEdebcrUzL9x/+LBPDj/VtdxRESKpVwPfoSGwtixnrU/cnJcpxERkcLk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\nherVO+PlVR2Azz9fUfoFVI0h6vnnWTZnDteePs20nBye9/Fhq6cn/Vu1Y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import division\n", "sizes = [3,5,10,20,25]\n", "splits = 30\n", "trials = 2000\n", "averages = []\n", "colors = ['r-*','y-*','g-*','b-*','m-*']\n", "fig, axes = plt.subplots(figsize=(15,9))\n", "fig.tight_layout()\n", "for k,size in enumerate(sizes):\n", " averages.append([0]*splits)\n", " for j,fill in [(i,i/splits) for i in range(0,splits)]:\n", " for _ in range(trials):\n", " x = Maze(size,fill)\n", " if x.find_path():\n", " averages[k][j] += 1\n", " averages[k] = [i/trials for i in averages[k]]\n", " plt.subplot(231+k)\n", " plt.xlabel(\"Fill probability\")\n", " plt.ylabel(\"Probability of successful path\")\n", " plt.title(\"Chance of Path, \" + str(sizes[k]) + \"x\" + str(sizes[k]) + \" Boards\")\n", " plt.plot([i/splits for i in range(0,splits)],averages[k],colors[k % len(colors)])\n", "for k in range(len(averages)):\n", " plt.subplot(236)\n", " plt.xlabel(\"Fill probability\")\n", " plt.ylabel(\"Probability of successful path\")\n", " plt.title(\"Chance of Path, All Size Boards\")\n", " plt.plot([i/splits for i in range(0,splits)],averages[k],colors[k % len(colors)])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Approximations\n", "Here I've tried to approximate the plots shown above with different curves. It seems like the path probability generally varies linearly with fill probability. When the path chance is near zero, smaller-size boards have better luck. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LZvgKu8aNqRDwFEur7uZPh1Gkp1oYDG42Hnh2SCasxCf6D05ERERERG4LFXy5\n6L333rv2QHaAUaM4lLCWtJTxJKYlM5M5JJ1LJnZNZX5YtoO3Nwfmea4iIiIiIgVJSkoKPXr0oGLF\niri6ulK/fn1CQ0Mz28PCwqhevTpOTk40b96cqKioHMX95JNPaNCgAW5ubnh5eTFs2DDS0tIy28+d\nO8ezzz6Ls7MzFStWZMmSJbd9bHlJBV8u+HuGzsXFJdsD2bG1pfcPq3gm/U822NhxkXe5l3q0bNqE\nLwP7MXXTFEIjvs2HzEVERERE/seyLIYPn/avVqDdaoxLly7h7e3Nxo0bSUhIYNKkSXTo0IGoqChi\nYmJ47rnnmDx5MrGxsTRo0ICOHTvmKG5ycjIzZszg7NmzbN26lbCwMKZPn57Z3r9/fxwdHTl9+jSf\nfvopr7zyCvv27bup3AsSFXy32YozZ+h18CAA3bt3x9PTk6lTp17T79Pvv+dXpyKkpLvyHW/iYVXF\nfY0DxzdXYsp91eiyogMHYg7kdfoiIiIiIpmWL/+OOXP+jxUrvs/zGMWKFWPcuHF4e3sD0Lp1aypV\nqsRvv/3GihUrqF27Nu3atcPe3p7AwEDCw8M5dOgQKSkp1K9fn1mzZgGQlpZG48aNmTRpEgB9+/al\ncePG2NraUrZsWTp37szmzZsBOH/+PCtWrGDixIkUK1aMxo0b07ZtWxYuXHjL489vKvhus8dKlCD0\n3Dl+iovDGMO8efOYMWPGNUs7O/fuTZ2WbXnS4UtWc5CZ2PCf1EdoU/MFXmyykl6VoM2nT3Au+Vw+\njURERERE7lZBQYvw9W3DyJE/kZj4DiNGbMTXtw1BQYvyNEZWp06d4tChQ9SqVYu9e/dSt27dzLZi\nxYrh4+PD3r17sbe3Z9GiRYwdO5YDBw4wZcoULMti1KhR2cbdsGEDtWrVAuDQoUPY2tri4+OT2V63\nbl327t17SzkXBCr4bjMXW1ve9fHhlUOHSE1Px8vLiylTplyztNMYQ8fnmlLRPpXvHDdR0iaJNVW9\nOfDyAexSK/DfJu/wYIlkOnzxPKlpqTd4ooiIiIjI7dW7d2cCA/tz4UI6YIiISGffvgD69u2MMeTo\nq2/fzuzb15+IiMsxLlxIZ/z4AHr37nzT+aSmptK5c2e6du1KtWrVOH/+PK6urlf0cXV1JTExEQBf\nX19Gjx5N27Zteeedd1i4cGG2x58FBwezY8cOhgwZAkBSUtI1cV1cXDLjFkYq+HLB856elHdw4L0/\n/gAuL+0VgPvTAAAgAElEQVRs3bo1CQkJV/SLjoigZUgIbx88yATn8Xx+zJPEaiU4/OphypTpyZC6\n93PpYhQDvxuYH8MQERERkbuUMQZjDHFxF6hZcxAuLsksW2awLINlkcMvwxdfGFxcLseIi0vOjHsz\n0tPTeemll3B0dMxcpuns7HzN363j4+NxcXHJ/Ozv709UVBRPPvkkVapUuSbuypUrGTlyJN9++y3u\n7u45jlvYqODLBcYYZlWtytSoKKIuXMAYw4QJEyhZsuQV/XqNGMET7dphvL15dtUiltn1ps+Oipzb\nEEfMlzHUrP4xI6olsPbIGub+OjefRiMiIiIid6OIiGhCQlqyZ8/bhIS0IiIiOs9jWJZFjx49OHPm\nDMuXL6dIkSLA5Rm88PDwzH7nz5/nyJEj+Pr6Zl7r168fbdq0ITQ0NPMdvb+FhobSu3dvVq9efcU9\n1apV49KlSxw+fDjzWnh4eOaSz8JIB6/noq9iYmjk6oqnvX3Obnj/fV6bWBLqtKL9nv002NmABNvV\nbNg9mIAdySxut4TmlZrnbtIiIiIiclcpyAev9+3bl/DwcNauXYuTk1Pm9ZiYGHx8fAgODubJJ59k\n7NixbNq0iZ9//hmAhQsXMmHCBMLDw1m1ahVjxowhPDwcJycn1q1bR/v27Vm1ahVNmjS55pkvvPAC\nxhg++ugjduzYQZs2bfjll1+oUaNGnoz5dh+8roKvILEs/urSm/pfj+fdxy9Q/nwStb+pzYED/vwa\nk8jQrb+wuftmfNx9/jmWiIiIiEgOFNSCLzIykkqVKuHo6Jg5swfw4Ycf8sILLxAWFkZAQACRkZE0\nbNiQ+fPn4+3tTVRUFH5+fnz99dc0atQIgE6dOuHm5kZQUBDNmzdn06ZNODg4ZMZ8+OGHWbNmDQCx\nsbF0796dH374AQ8PD6ZMmUKnTp3ybNwq+O50yclsqf8K7U7MZLnPIbx63UOpXk789lsdfk55ho/2\n/MCWHltwc3TL70xFRERE5A5QUAu+u9XtLvj0Dl8+SExM5NVXX732QHaAokVp+P0E/K35BJlSHB93\nnNSj9lSvHkIjuxU0r9CETss7kZaelveJi4iIiIhIoaKCLx84Oztz8ODBbA9kB8Dbm8AVdfhtdxKn\nm5Zkf5f9uDk/gqdnO/pUTOBS+iWG/jA0b5MWEREREZFCRwVfHjmVksKrERFYlnXDA9n/5vB4Uz55\n9Xf6rPQkzakIkRMiqVx5Chf+2sWsph1ZfWg1H+/4OI9HISIiIiIihYkKvjziYWfHpvh4Fp06BYCX\nlxdvvvnmNQeyZ+X31gv0993AtP3pnJx3kqStKVSvvpCY6JEsazePEWEj+Cnyp7wchoiIiIiIFCIq\n+PJIEWP4oFo1Xj96lNiMAq9Hjx54enpef2mnMYz8qRXHEosSVeUv9r+0n2KmHuXK9cc68yYLn11I\nh2UdOB53PO8GIiIiIiIihYYKvjx0v6srz3p4MPLYMYDMpZ2Ojo7XvcfOtSgLvirOgF/8sC1/kcMD\nD+PtPZJLl85Rq+gRRjQZwVNLniLxYmJeDUNERERERAoJHcuQx+JSU6n566+srFWLB1xdc3zf1N5H\nWB9yksAyhirv34vT4+fYsaMx9ev/zMB10/kz6U++7PglRWyK/HMwEREREZEMOpahYNGxDIVccTs7\nZvj4EH3x4k3dN2RuFeLL+bA3OZxDfQ5RJKEiFSuO48ABf95v+R4JFxMYvW50LmUtIiIiIiKFkWb4\nCpFDBy3+UzeJUK8l2FdrSK2vfdm9uyVubk1xLtWXBz96kPHNxtOlTpf8TlVERERECgnN8BUsmuG7\ni1W71zB2sgODTt5PSvgf/DnvFPfeG8KJE+/jkBbFV52+YtB3g9jyx5b8TlVERERE5F9JSUmhR48e\nVKxYEVdXV+rXr09oaCgAx48fx8bGBhcXl8yvyZMn5yjuJ598QoMGDXBzc8PLy4thw4aRlpaW2d6s\nWTOKFi2aGbdGjRq5Mr68ooKvgNm8eTOzZs26bnvAQHuK1KnBL7F7OTbsIOlR7vj4vMv+/S9RvWQV\ngtsG0+7zdkTHR+dh1iIiIiJyJ7Isi8nDJ/+rGcBbjXHp0iW8vb3ZuHEjCQkJTJo0iQ4dOhAVFZXZ\nJyEhgcTERBITExk1alSO4iYnJzNjxgzOnj3L1q1bCQsLY/r06Zntxhhmz56dGXf//v03lXdBo4Kv\ngPH29mb8+PHXPZDdxgaCFzsywe5VHFK/YX+HnXiU6ISTky/Hjo2kTbU2DGw4kLafteV8yvk8zl5E\nRERE7iRrlq9h95zdfLPimzyPUaxYMcaNG4e3tzcArVu3plKlSmzfvj2zT3p6+jX3paSkUL9+/cxJ\nlLS0NBo3bsykSZMA6Nu3L40bN8bW1payZcvSuXNnNm/efEWMO2mJqwq+fGZZFp+eOsWFjGlkLy8v\npkyZcsMD2StVgsnT7OlbYjBFju4mavwRqlWby+nTS4mNXc/gRoOpU7oOL698mXTr2v8IRERERERu\nZH7QfFr4tmDVyFX0SezDyhEraeHbgvlB8/M0RlanTp3i0KFD+Pr6Zl6rUKECXl5edO/enbNnzwJg\nb2/PokWLGDt2LAcOHGDKlClYlnXdGcANGzZQq1atK66NGDECT09PmjRpwoYNG24p34JCm7YUAM/t\n2UNdZ2fGVawIXC4CW7VqRZMmTRg9OvudNy0LWrWyeCTqS5occ6T2+sakVv2ZQ4de4f77w0nDkeYL\nmvNopUcZ/8j4PByNiIiIiBQm2W0SYlkWq5et5svBX+If7c885lGXutzP/Rhytm+IhcU2trGLXfSi\nFwu8FvDcO8/Rul1rjLm5vUdSU1Np1aoVVatWZe7cuZw/f56DBw9Sr149YmJi6N+/P4mJiZnv+AG8\n8847BAUFERMTw7Zt26hSpco1cYODgwkMDGTnzp24u7sDsG3bNnx9fbG3t2fJkiUEBASwc+dOKleu\nfFM536rbvWmLCr4CIPrCBer/9htb/PzwKVbs8rXoaPz8/AgLC6NOnTrZ3vfHH+BX32K1/SislIe5\n79ijHDkRQHr6BWrUmM+ppFM8+NGDTH10Kh1rdczLIYmIiIhIIXG9AmP1stUs6r4IRy9HkqOT8Q/x\np3W71jcV+3bESE9P58UXXyQpKYlVq1ZRpMi1506fOnWKMmXKkJiYiJOTEwAxMTF4eXnx/PPPs3Dh\nwmvuWblyJX379iUsLOyKWcOrtWrVitatWxMQEHBTed8q7dJ5B/JydGS4tzf9IyIy/3C9vLyYM2cO\nf/3113XvK18e3n7H0NMlEOek3zjS6SeqVJlOfPwmzpz5ktLOpVnVaRUB3wbw28nf8mo4IiIiInIH\niIyI5KWQlwjZE4J/iD+REZF5HsOyLHr06MGZM2dYvnx5tsVeVlnf6evXrx9t2rQhNDT0mnf0QkND\n6d27N6tXr75hsXcn0AxfAZGano7f9u2MqVCBDqVK5fg+y4Jnn4U6tkd58svf8AmqhV37OPbubUeD\nBjuxty/Nl/u/ZEDoALb23EoZ5zKMmDCCN8e+edNT6SIiIiJy5ynI5/D17duX8PBw1q5dmzlzB5eX\nXbq5uVG1alViY2Pp168fMTExhIWFAbBw4UImTJhAeHg4q1atYsyYMYSHh+Pk5MS6deto3749q1at\nokmTJlc8Lz4+ni1bttC0aVNsbW1ZunQpffr0YefOnfj4+OTJmAvVkk5jTEvgPaAI8JFlWVOvavcA\nFgH3ALbAdMuy5mcT544v+AA2x8czLSqKVbVr39R9p05B3bqw4qFlsNKeBhFN+SN9KufP76FWrVUY\nY3jjpzdYeWAlr5V8jb4z+hIyJIR2T7XLpZGIiIiISGFRUAu+yMhIKlWqhKOj4xUze0FBQdjY2DBy\n5EhOnz6Nq6srjz/+ONOmTaNUqVJERUXh5+fH119/TaNGjQDo1KkTbm5uBAUF0bx5czZt2oSDg0Nm\nzIcffpg1a9Zw5swZWrduzYEDByhSpAg1atRg4sSJtGjRIs/GXWgKPmNMEeAg8ChwAvgVeMGyrP1Z\n+gQCDpZljcgo/g4CpS3LunRVrLui4IPL09a3MvP2xRcwZozFKjOLlCRXah7ryI7fG1K+/ADKlOlO\nUHAQr7/3Ouml0klqkkTV8KrYnbZjQM8B9OnWJxdGIiIiIiKFQUEt+O5WhekdvgeAw5ZlHbcsKxX4\nDGh7VZ//A1wzvncFzl5d7N1tbnWZZfv2UK+e4cNHenPxbBFOdf6cGjUWcfToMJKTj9G7W2/mjJvD\nxdSLYOBCygXGDxtP7669b/MIRERERESkoMjNgq8cEJ3l8x8Z17KaB/gaY04C4cCruZhPoTdhwoTr\nHsgOMHs2LFnpwPkJTTj2RXFsvjyNl9cwDhx4GUjHwc4BO8sOux/siEuKwxij9/hERERERO5gtrkY\nOyfzwiOBnZZlNTPGVAF+MMbUtSwr8eqOgYGBmd83a9aMZs2a3a48C41y5crRrVs3tmzZgp2d3TXt\nJUtCUBB0f60i3/c8zoEeh6i371nO8jXR0e8ScSyVBUMX8GHch5Q/U56IYxH5MAoREREREfknP/74\nIz/++OO/jpOb7/A1BAIty2qZ8XkEkJ514xZjzDfAZMuyNmd8DgOGWZb121Wx7pp3+LI6m5oKQMmM\n4i4nB7IDdOsGRR0t+oR9jVvSZkrvfZkd+5pSt+46nJ1rE/5nOE8seoKI/0bg4uCSJ2MRERERkYJJ\n7/AVLIXpHb7fgKrGmIrGGHugI/DVVX0OcHlTF4wxpYF7gaO5mFOh8m50NIMOH878bIxh3rx5zJgx\n44ZLO997D1avMZwe9zgnzjUj9cUPqVxpCvv3v0Ra2gVWf7yExyo/xvSfp+fFMEREREREJJ/kWsGX\nsflKAPAdsA9YalnWfmNMH2PM39tCvgE0MMaEA2uB1y3LOpdbORU2w729WRcXx4a4uMxrXl5eTJky\nhW7dupGaMQN4NTc3+Ogj6DHCkXLv1WL/+v/guTAJR8cKfPLJi+zePYdH+A+zfp3Fn0l/5tVwRERE\nREQkj+ng9QJu+ZkzjDl2jJ0NGmBvc7k+tyyLqVOn0q9fP1xdXa977yuvwIULMDT2Vw5/9wUz6i2h\nrM//0b17GosXV+U7zuJTvRbrBm/Iq+GIiIiISAGjJZ0FS6E5h+92upsLPsuyaL17Nw+7uTG8QoWb\nujcpCerUgRmTU/F4bROxKRNZ+NhWXG1tSEiz46kX3mbAoaH83ONnqpWslksjEBEREZGCTAVfwVKY\n3uGT28AYw6yqVXnnjz+Ivc4SzutxdoaQEOgz2I5Dz53iUkIAMfsc+fPzhzh57C/mDB1LiyIPMTJs\nZC5lLyIiIiJy6w4ePEi9evVwdXVl1qxZ+Z1OoaSCrxCoXLQou++/nxLZHMXwT5o2hY4d4aPfLjDe\nbiLue5vxWtpQPI48SNxZBx4t+iRbT2xlyx9bciFzEREREZFbN23aNFq0aEFCQgIBAQGsX7+eRx55\nhOLFi1OpUqX8Tq9QUMFXSJS2t7/le994A04nvEz15p2xoQgGA4l2vDQgHv8ezzC+2Xhe/+F1TeWL\niIiISIESGRlJzZo1Mz87OzvTs2dP3nrrrXzM6lppaWn5ncJ1qeC7A8TGxtKrV6/r7tpZtCgsWGD4\ndl1FLtheYgYzsVKL8Vd0cQ4f7od/HX/OJZ9jTcSaPM5cRERERCR7zZs358cffyQgIABXV1cOHz7M\n/fffT+fOnXM8u9e+fXvKlClD8eLFadq0Kfv27cts69q1K3379uXxxx/H1dWVZs2aERUVldluY2PD\nzJkzqVKlCp6enrz++v8mSObPn0/jxo0ZNGgQHh4ejB8/noSEBPz9/SlVqhQVK1Zk8uTJWJbFuXPn\n8PLyYvXq1QAkJSXh4+PDokWLbuNP6/pU8N0BihcvTnR0NFOnTr1un507F+FgM431RYryCwuoZR5g\nQ3BZFoVs42zMUt5s8SbD1w4nLb3g/uuEiIiIiNw91q1bx0MPPcTs2bNJSEjAx8fnpmO0bt2aw4cP\nc+bMGfz8/OjcufMV7YsXL2bs2LHExMRQr169a9pXrlzJ9u3b2bFjB6tWrSI4ODizbdu2bVSpUoXT\np08zcuRIAgICSExM5NixY2zYsIEFCxYQEhKCu7s7wcHB9OrVizNnzjBw4ED8/Pzo0qXLrf1gbpJ2\n6SykUtPTsbP5X70eHR2Nn58fYWFh1KlT55r+lmWxZEkoXbtuJDX1TRqWnszkxAZUrTyDqDm/4tdg\nO0981oWu9brSvX73vByKiIiIiOSjf9qlM/DYMcZHRl5zfVyFCgRmM9OWXf/r9f0njzzyCF26dKFH\njx5XXF+7di29evXi2LFjOY4VFxeHu7s78fHxuLi40LVrV1JSUli8eDEA58+fx83NjcjISMqVK4eN\njQ2hoaE8/vjjAMydO5fly5ezdu1a5s+fz7hx44jMGGdaWhrFihUjPDyc6tWrA/Dhhx+yZMkS1q9f\nD8CAAQNYv349cXFx7Nq1ixIlSmSb5+3epdP2Zm+Q/PdjbCyBx4+zvl49jLn8Z571QPYtW7Zgd9UG\nL8YY7O0N9vYXSE8fxK7EdBJHG6ImvobHR9M56NyNqY9OocOyjnSq1YlidsXyY2giIiIiUsAEVqp0\nU8Xazfb/J3//ffdmpaenM3LkSJYtW8aZM2ewyZgsiYmJwcXFBWMM5cuXz+zv5OSEu7s7J0+epFy5\ncsDlv2P/zdvbm5MnT2Z+ztoWExNDamoqFbIco+bt7c2JEycyP/fq1YtZs2YxatSo6xZ7uUFLOguh\nh4oX53x6OgtOnbrievfu3fH09Lzu0s6IiGg++aQlK1a8jaNjK7YlRVFjhR8xn71KalgiXmY7D5Z7\nkJlbZ+bFMEREREREcs2nn37KV199RVhYGPHx8ZmzgX/PnlmWRXR0dGb/pKQkzp07R9myZTOvZX2n\nLyoqKrMQhCsLUQ8PD+zs7Dh+/PgV/f8uKNPS0ujduzf+/v7Mnj2bI0eO3N7B3oAKvkKoiDHMrVqV\nYUeOcC7LRi3GGObNm0epUqWyvW/EiF60a/cETz9t6NfvCX7+uSeuj3pQ9cNapIwayfGwmYxq1IPp\nv0zn7F9n82o4IiIiIiLXlXV5o2VZXLhwgdTUVCzL4uLFi6SkpGR7X1JSEg4ODri7u3P+/HlGjrz2\n7OlvvvmGzZs3k5KSwpgxY2jUqNEVRd306dOJi4sjOjqa999/n44dO2b7rCJFitChQwdGjRpFUlIS\nkZGRvPvuu5nv6b3xxhsUKVKEkJAQhg4dir+/P+np6f/mx5JjKvgKqQaurjzv6cmIo0evuO7l5UXv\n3r3/8f7AQLC3h5EjodTLFag0thIETODSL+NpV+M53vjpjVzKXEREREQk57LOpG3YsIFixYrRunVr\noqOjKVq0KC1btsz2Pn9/fypUqEC5cuWoVasWjRo1uiKWMYYXX3yR8ePHU7JkSX7//fdrds5s27Yt\n9913H/Xr16dNmzaZ7xIaY65Zajpz5kycnJyoXLkyDz30EJ07d6Zbt25s376dd999lwULFmCMYdiw\nYRhjbrjh4u2kTVsKsbjUVGr++isrfH1p6OZ20/efPQsNGsBbb8Hzz0Nkr3VEro7CMWQbrXYtZXvv\n7VQsXvH2Jy4iIiIiBcY/bdpyp+rWrRvly5dn4sSJ2bbb2Nhw+PBhKleunKd53e5NWzTDV4gVt7Nj\nha8vVYvd2gYrJUvCsmXwyiuwfz94f/gIpWvbkfxqbfpWfIax68fe5oxFRERERAqGu6XIVcFXyDV0\nc6PkVTty3oz77oOpU+G55yApyVAt9AXcnC/y6GRf1h0MI/zP8NuYrYiIiIhIwZDdssyr2+8EWtJ5\nh/vhhx/Ys2cPAwcOvGG/3r0hNhY+/xys5ItsbfQe0TaGkIHr+db/2zzKVkRERETy2t26pLOg0pJO\nuSnVq1fnjTfeYNeuXTfs9/77cPw4vP022BRzwG/Vs5S6ZEvDmX6EHQnLm2RFREREROS2UsF3h8t6\nIHtqliMcruboCMuXw/TpsH49OFSshu9sZ/xivNjQ+wfSrbzZNlZERERERG4fFXx3kMRLl3h+zx6S\n09KuuP5PB7L/zdsbFi2CF1+EP/4Az4d7U2Xqd9TYVZ3V/b/IzdRFRERERCQXqOC7g7jY2mIBU6Ki\nrrj+94HsM2bM+MelnY8+CgMGQPv2cPEi3NtuEYnjJ5Cy2CJ69tEb3isiIiIiIgWLCr47zHs+Psw+\ncYJDf/11xXUvLy/mzZuXoxjDh8M998CgQVCkiBOdOi/mk37DODBsN2eWn86NtEVEREREJBeo4LvD\neDk6MrJCBfpHRFyzu88zzzxDnTp1/jGGMTB/PvzwAyxYAK5uDXml7aOM9B/KwZd3cm7tuVzKXkRE\nRETkfw4ePEi9evVwdXVl1qxZ+Z1OoaSC7w40oFw5TqeksPT0rc/GubnBihUweDDs3Akt7/+A0vXO\nsP6Jkex/ficJ2xJuY8YiIiIiIteaNm0aLVq0ICEhgYCAAN566y1q166Nq6srlStXZvr06fmdYoGn\ngu8OZGtjQ1C1av/6sMhatWDmTGjXDuLj7Zj+1BdM99uBm+eb7H7yd87vO3+bMhYRERERuVZkZCQ1\na9a84trChQuJi4sjNDSUWbNmsXTp0nzK7n/Srto0sSBRwXeHaujmRsdSpf51nE6d4OmnoUsXqFb6\nUV6o3ozAQduoUiSIXY/v5ELkhduQrYiIiIjIlZo3b86PP/5IQEAArq6uHD58mKFDh1KvXj1sbGyo\nVq0abdu2ZfPmzdeN0b59e8qUKUPx4sVp2rQp+/bty2zr2rUrffv25fHHH8fV1ZVmzZoRlWXzQxsb\nG2bOnEmVKlXw9PTk9ddfz3xlav78+TRu3JhBgwbh4eHB+PHjSUhIwN/fn1KlSlGxYkUmT56MZVmc\nO3cOLy8vVq9eDUBSUhI+Pj4sWrQol35yV1LBdxcbPHjwP+7aCTBtGiQkwKRJMLnV54TFJbNvzCG8\nin1N+KM7STmVkgfZioiIiMjdZN26dTz00EPMnj2bhIQEfHx8rmi3LIuNGzdSq1at68Zo3bo1hw8f\n5syZM/j5+dG5c+cr2hcvXszYsWOJiYmhXr1617SvXLmS7du3s2PHDlatWkVwcHBm27Zt26hSpQqn\nT59m5MiRBAQEkJiYyLFjx9iwYQMLFiwgJCQEd3d3goOD6dWrF2fOnGHgwIH4+fnRpUuX2/BT+mcq\n+O5iNWvW/McD2QHs7ODzz+HDD2HbBg+G/GcI421249Z4M6WKb2dXy11cir+UR1mLiIiISF4KDAzE\nGHPNV2BgYI77X69vTly9EWHW5wB069btuvd27doVJycn7OzsGDduHOHh4SQmJma2t2nThiZNmmBv\nb8/kyZP55ZdfOHHiRGb7sGHDKF68OF5eXrz22mssWbIks61s2bL0798fGxsb7OzsWLp0KW+++SZO\nTk5UqFCBwYMHs3DhQgAee+wx2rdvT/PmzQkNDSUoKOiWfx43SwXfXSynB7IDlCkDn30GXbvCs/eM\n5XCyM593+AOv5PdxKx7N7qd2k5ZccNcui4iIiMitCQwMxLKsa75uVPDltG9OZLcvxaxZs1i0aBFr\n1qzBzs4u2/vS09MZPnw4Pj4+uLm5UalSJQBiYmIy45YvXz6zv5OTE+7u7pw8eTLzmpeXV+b33t7e\n122LiYkhNTWVChUqXNE/a/HYq1cv9u7dS9euXSlRokSOx/9vqeC7S3x08iSnUq5cenkzB7IDNGkC\no0ZB506OjP3Pu8w5ksjxkCb47H0FB/t49nXYR3pqem4NQURERESE4OBgpk2bRlhYGGXLlr1uv08/\n/ZSvvvqKsLAw4uPjOXbsGPC/GUPLsoiOjs7sn5SUxLlz566ImfWdvqioKMqVK5f5OWsh6uHhgZ2d\nHcePH7+i/98FZVpaGr1798bf35/Zs2dz5MiRWxz9zVPB9//s3XmYzWUfx/H3PTtmsu8m+9hHxhJR\nWdKiRaVIwliiiBSi8GSpLCFFxCSiRElpkRRpU8k6dmMbY9+ZxRgz537+OENkmTMz50yYz+u6fpfO\n79zL93c9PNd8575/9zeb2HL6NH0v8xcrODiYESNGuLS1E6BHD6hUCZa99xSJphCf7/2Ck7NeouK6\nNti4eLZ03IJ1XH7ZXUREREQkvS7c0vnxxx8zYMAAFi1aRKlSpa7aLy4uDn9/f/Lly0d8fDyvvPLK\nJW0WLFjA77//TlJSEoMGDaJevXoXJXWjR4/mxIkTxMTE8M4779CqVavLzuXt7U3Lli0ZMGAAcXFx\nREdH89Zbb51/T++NN97A29ubadOm0bdvX9q1a4fDkTULJUr4solXS5Zk6YkT/HT8+CXfdezYkfbt\n27uU8BkDERGwapUXDY/M4YPdgazP+Q6O/z1PlUPdSNwez7Ze266411pEREREJD0uXEkbNGgQx44d\no3bt2gQFBREUFES3bt0u269du3aULFmS4sWLU7VqVerVq3fRWMYYnnzySYYMGUL+/PlZvXr1JSdn\nNm/enJo1a1KjRg0eeOABOnXqdL7vv7eajh8/nly5clGmTBluv/122rRpQ4cOHVi5ciVvvfUWM2bM\nwBhDv379MMa49FqVO5jr4QdzY4y9HuK81n1x+DCv7NzJ2lq18PPKXK4fFQX161tKdO3GI3XX83jZ\n8lQc68PZPSdYs68vBR8pSKlXS2Gt5Y2X3+CV4a9kui6giIiIiLifMSZb/rK+Q4cOlChRgmHDhl32\ney8vL7Zt20aZMmWyNK4r/e+Rej/dP1BrhS8bebhAAcoGBDD6gr3KGVW+PEREGPZ9MI6JK05y4OgS\njgy9B9+4A4TeuYCDHx1kz/g9fPv5t6ybuI4F8xa44QlERERERNwjuyS5SviyEWMM48uXZ9nJk275\nC968OXQK9yfls1n8GHsfW3c8R9Kcyfh/NZ3IGh/R8sWWzOsxj66xXfny5S9pUqUJ0ydPz/yDiIiI\niEgJO6IAACAASURBVIhk0uW2Zf77+xuBtnRKpqSkwJ13xbPSTuWXd7eSw+6lSspgaNKEuU8N4Mvx\nK3ja8TQzgmfw6NhHub/F/TfMPx4RERGRG0F23dJ5rdKWTvG4w4cP06ZNG5cOcfH2hi8/y4XvpjYM\n/qQGp09v52DhNZiICHLMHMMZr0Te4S1OHjmZ5m9RRERERETEvZTwySUKFCjA0aNHXT45qEAB+Owz\n+G7cQ+xPGM/27X345NgmhiY68OcHBnInwd7JDH22Fx9Nnuzh6EVERERE5Bxt6ZTLiomJISwsjMWL\nFxMaGupSn4f6zufn2bVYtnAOSUlfcyCqK7+078CgxAL85jURx4Sz3PPMI1rlExEREbmGaEvntUVb\nOsWtDiUlseP06Uvup7cgO8DHrzXmbPGl9OofjsNxFp+c33Ha25sHgvYS5TUP34hAd4cvIiIiIm5w\n7tUbXf/95W5K+LK5L48cof3mzTgu81uEjh07UrBgQZe3dgb5BzF8dBx/rT/Cjz9+iZf/XAr2fpxC\nTf05WeAbkvee5dCcQ+5+BBERERHJBGutrmvscidt6czmUqyl3qpVPFusGB2KFr3k+5iYGH7//Xee\neOIJl8Y7m3KW8q/dxeGxX1OuVAdCQ78hJSUnOU+eJWlTVdode407d9yJbz5fdz+KiIiIiMgNK6Nb\nOpXwCatiY2kWGcmGOnXI75v5ROyzDZ/x8pQlHJs5lnLlqrBhQyPq1PmB3lviCLn1cxz5ilJxakU3\nRC4iIiIikj0o4ZNM6RkVxWmHg4gKFTI9lrWW0u2qcmh+Ac7E18ThGENgYCvy5tjJoOQTVM05nYoz\nK5O3UV43RC4iIiIicuPToS2SKcNKl+b7Y8eITkzM9FjGGKYPfRevezbj7eMNGHx9A7n7oRp0fuQO\nylf6ga1dt5JyOiXzgYuIiIiIyBUp4RMAcvv4sLF2bUoGBLhlvIalG1KhWAWsiQWeIzbWlzvuqIR5\n6y0KbPuQXAVjiX492i1ziYiIiIjI5Snhk/MCfXzSbDN//nxGjx6dZrvJ0yaz84v9JJf5GDr/QbK9\nix59pvDeZx/DtGmU3/48+yfvJW5dnDtCFxERERGRy1DCJ+kSFhbGyJEjWbdu3VXbdQnvwuTxbxBU\n1ECJVeSpsJZcfl/Q5I4UaNgQ/yeaUrrUT2x5egs2Re9nioiIiIh4ghI+SZdzBdnDw8OvWpD9fOHI\nZAj4MYCEPKMpWdLQu3dukpIOwvDhFD31CV4nj7J30t4sfAIRERERkexDCZ9cUWxy8mXvnyvIPmrU\nqKv2j9oZxbQ+04j8MhK/ir7UaPIBGzbcw9ixX0GOHJgZ0wk51J9d/9tJYkzmD4sREREREZGLqSyD\nXNa6uDgeWb+edbVrk8Pb+5LvY2JiCAsLY8mSJVSrVi3N8T5c8yFvLnuTqXWWcm9Tw4IFMdSrdwsM\nHMiuz3ISW+FBqs6v6lwVFBERERGRi6gOn7jd4xs2UDFnToaVLn3Z77/55hsqVKhA+fLl0xzLWkub\neW3IE5CHituf4q23ihIZeTNB/ik4atVjxZHhlHrnFgo9VsjdjyEiIiIict1Twidut/fMGar//Te/\nh4VRIWfOTI93MvEkNSbXYMzdY5jxii/WhvDFFyGYdZGcuKM7GwPeoPbmuvjm8XVD9CIiIiIiNw4V\nXhe3K+7vz4CSJem+dSvuSLhzB+Tm40c/5plvn2HImJysX3+WCRNiITSUPP2aUcDnL3a8tN0NkYuI\niIiICCjhkzT0KF6cI2fP8unhw24Zr15wPXrU6UGvX19jwrvzePVVWLEC6NuXMkW/4ehnMZz49YRb\n5hIRERERye60pVPStDUhgUK+vuTxdc9WyxRHCo1nNObu0g3ht31ERIxn9eoA8h7eyuGaL7Cz0MvU\n2ngbXv76fYSIiIiICGhLp3hQSM6cLiV7Xbp0SbMgO4C3lzcfPfIR7/z9HjUeKEbdul/QoYPFlg+h\nwOv3kuP4WqJf3+WGyEVEREREsjclfOI2derUSbMg+znBuYOZdP8kev78MU8/9y67dx9izBgwz3Un\npNIi9o3dTvzG+CyIWkRERETkxqUtneI21lruu+8+br/9dgYMGOBSn65fd+XU6b085r2Xbt1W8vnn\nXjQIjmZvlVc4GPIsNVbUx3ipNp+IiIiIZG/a0in/OWMMERERjBs3zqWtnQBv3fsWaw5vZ2dQQYYO\nnUjr1nAoR0mKjWsCW6LYNzHGw1GLiIiIiNy4lPBJuiQ7HDRZs4YDZ85c9vvg4GCGDx/u8tbOnL45\nmd1iNiPXrCJv2SG0bLmfNm3AEd6BCrV/Zle/zZzZe/m5RERERETk6pTwSbr4eHlRKyiIPtuvXC+v\nU6dOPPvsszgcDpfGrF6kOgPvGMSIrUE8+tijnD1ree11Q65PhlOMr4l6arm7whcRERERyVb0Dp+k\nW3xKCpWXL2daxYo0zpvXLWNaa7l/VjOKEEnPKm9y//1PMn06ND74KSs6Oigz83YKtirulrlERERE\nRK43GX2HTwmfZMj8I0fot307a2vXxt/LPQvFh+IPUX1SFV6ukELlHLto2/YmVqyAXG1fYNPfd1N7\nb1N8bvJxy1wiIiIiItcTHdoiWap5gQKE5MzJ6Bj3HapSKFchPnzkY4ZvTiKo8Av06AGtWkGuWQPJ\n5/iTHe1+c9tcIiIiIiLZgRI+ybDx5ctTJiDArWPeXfZuWlcLp++vH9Gt2ypuugleGZOfMh/U4cg3\nxzn54363ziciIiIiciNTwicZVjIggNaFC6fZbt++fTz66KMundoJMPyuMRx3FGbkkseYMcPBp5/C\ngoD7KXfHOra0/AtHkmuHwYiIiIiIZHdK+MTjihYtSkJCAqNGjXKpvb+PP5+1+p73tsSw/uBw5syB\np5+G2LG9CEjcxe7OP3o4YhERERGRG4MObZEsERMTQ1hYGEuWLKFatWou9Xl32SDe+mMEq7vF8MGU\nIsycCYufX8r68FPUWFaLnLcW83DUIiIiIiLXBp3SKde8999/n0mTJvHnn3/i6+ubZntrLfdPK0f+\nHIHMeGItjz8OhQrBKxve5vCmgtxyoDXGK91/50VERERErjs6pVP+c1P27SMyLu6K33fq1ImCBQu6\nvLXTGMP0xxbx4+71fBb5DlOnwg8/wC/tuuKIPcP+bt+4K3QRERERkRuSEj5xGws8u3Urjiusxhpj\niIiIoEaNGi6PWeimsky660W6fdeHOLOXuXPh+f4B+A4OZecUB2ci97gpehERERGRG4+2dIrbOKzl\ntlWreLpYMToVLeq2ca1N4ZlPgtmckI+fOkXywVQvxo2Dubk+JGVPIlX2dAGjrZ0iIiIicuPSlk75\nz3kZw6SQEF7ZsYMjSUluG9cYb96471NOxEcx6rfX6NQJataEUaVbE3skH0de+NRtc4mIiIiI3EiU\n8Ilb1QgKonWhQvTbscOt4+bP24CxDR7mzd9HsHL/CiZOhOXr/djeMpSo8d4kb9zl1vlERERERG4E\nSvjE7YaWLk1cSgpJDvcWSL+92gSeD/Hhic9a4PCJZe5c6LWwAjbEj533fApunk9ERERE5HqXZsJn\njClkjBlgjIkwxkxLvT7IiuDk+nSTjw9zqlTBzyvt3yfMmjWLkSNHujSun19BOtZ5g6o3JdHjux5U\nrAjjx0O3M/dy8EAlTvT9gAfrNsWhxE9EREREBHDh0BZjzB/AL8BK4NxP0tZa+7mHY7swBh3acoNK\nb0F2hyOZ3/6qQce/jjKsyRhaV2tN9+5w0y/R5F7/Dn+yidp9ajLgzWFZEL2IiIiISNbw5KEtOay1\n/ay1n1pr56ZeWZbsyY0tODiY4cOHEx4eztmzZ9Ns7+XlQ/XK7zGgYjLPL+zJzuM7ST7amZnr27Ca\nfTxPX1aO+5MQ/1I826ZTFjyBiIiIiMi1y5WE7xtjzP0ej0SyrfQWZM+duz51S95H54pVaTOvDeM/\nmkirjk05gcVgSEn2od1zbXh3ZoSHIxcRERERubZdcUunMSYOZy1tgFxAEnBuCcZaa2/yfHjnY9GW\nzuvYvjNn2HvmDLVvuvJfmfRu7UxKOshfy6swZHsF/NcWI/LD7VQ7FkwSgQRxmhX+Gxn49kC6dn3K\nnY8iIiIiIvKfcPuWTmttoLU2KPXystYGXPA5y5I9uf5tiI+n5caNJKSkXLFNcHAwH330Efny5XNp\nTD+/wpQuNYj+FQwri/1KseJ+rAz05SdmUI5Q6ibnoYvXaXc9goiIiIjIdcmVUzoXu3JP5Eqa5svH\nrUFBvB4dfdV299xzD8WLF3d53GLFupPb+xRj7+zA9rD9JJji5MnfnoV40TnHa6QMHA4LF2Y2fBER\nERGR69YVEz5jTA5jTH6goDEm3wVXKcD1n8pFgLHlyjF53z42xce7bUwvLx/Kl59A6eSPCaEqRZr8\nTFLl+ZR8MC+/p8Sz/fYPoV07WL3abXOKiIiIiFxPrrbC1xVYAVTAWZLh3PUVMMHzocmNpJi/P4NK\nlaJbVBTufB8zT547+H5JUQ5t+IvdJzYR1ziOLV7jifDNx7ZvUojtMwUefBB273bbnCIiIiIi14ur\nvcM3zlpbGuhrrS19wRVqrVXCJ+nWvVgx4lNSWB0X59Zx+/f+gnYtzpDPPzcYOJV4koGjY5nmU4HI\nj4KxL/SGZs3gxAm3zisiIiIicq1L8x0+a+07xpiqxpiWxph2566sCE5uLD5eXvxeowZhQUEutW/V\nqhXr1q1Ls11AQDEKFXqU2Phj5F4YxKGTh0jKsYW6rxZhe4wXe/0fhyZN4NFHISkps48hIiIiInLd\ncOXQlsHAeJzbOBsBo4CHPBuW3Kh8vVwp/ejUtGlTlwuyHztVnscr5+bu4LM8eFszhnw1hBYd9zCr\nSAhbXonmTN8RkDs3dOoEKvEhIiIiItmEKz99PwbcBey31nYAqgN5PBqVCK4XZJ8+fTKLv/4Er+Sc\nPPtsIoVPbaFgDn8aTL6VPlOS+TqlKBt77oSPP4aoKPjf/7LoCURERERE/luuJHynrbUpQLIxJjdw\nCAj2bFgizuKSERERjBs37qpbO9u370KvXoOx1mAMJCYe4K3H3+WJmq0ZHHU/tn0x9vxwimO/JcLX\nX8Mnn8D772fhk4iIiIiI/DdcSfj+NsbkBSJwntq5Gljm0agk2zhw5sxVvw8ODmb48OFX3dppjMEY\nQ0LCCaZNq8Dp0wnExf3Nm3e/Sak8pYiq3Y4pOcqxtsNWUgLzwYIFMHCgavSJiIiIyA3PlUNbullr\nj1tr3wOaAu1St3aKZMreM2eotmIF+9NI+jp16kSfPn0wxlyxTXR0FG3bTmP69E20bDmUNWsmknz2\nCB80/4AU35Oc6fIJq04FsmPYbggJgXnzVKNPRERERG54Jq2aaMb5U/ajQAPAAr9aa7/IgtgujMG6\ns3abXDte3rGD6MREZlWu7NZxt2/vR0LCFqpW/YL4s/E0+rARvlPfZ3BkLA1Wh5GzQk74/HN4/nlY\ntgxuvtmt84uIiIiIuJMxBmvtlVdArsCVLZ0TcRZhjwTWA12NMRNdDOpeY8xmY0yUMabfFdo0NMas\nNsasN8YsdTVwuTEMKlmSZSdP8uOxY24dt3TpoSQm7uTAgQ8J9Avk2ye/5cAD3fjQFmN1+63O4u8t\nWkBv1egTERERkRuXKyt8m4HK1lpH6mcvYKO1tmIa/byBLThP+NwL/A20ttZuuqBNHuB34B5r7R5j\nTAFr7ZHLjKUVvhvYV0eO0Hf7diJr18Y/HWUb0hIXF8natU0IC/ubHDlKsfP4Tmp2nsy4BQ/TdEpp\nirYt7CzR0KsXrFvnfKfPz89t84uIiIiIuIsnV/i2ARfud7s59V5a6gDbrLW7rLVngdlA83+1eRL4\n3Fq7B+ByyZ7c+B4qUICKOXMyfs8et44bGBhKcHAfNm8Ox1oHpfOW5sfxT/BmXsvabls4e/wsGANj\nx6pGn4iIiIjckFxJ+G4CNhljfk7dcrkRCDLGfG2M+eoq/YoDMRd83pN670LlgXzGmJ+MMSuMMW3T\nEbvcQKZUqEDXYsVcartr1y6aNWvmUkH24OA+QAp79owDIKzYLbwwzYvvE/PwS5eVzkbe3qrRJyIi\nIiI3JB8X2lzuJ2ALmNQ/r8SVpRJfIAxoAuQE/jDG/Gmtjfp3w8GDB5//74YNG9KwYUMXhpfrReF0\nbKUsWbIkDoeDkSNHMnDgwKu2NcabihU/ZNWqW8mX7x5y5apCx3tupfVT6znxUQKbF22m4t0VIWdO\nZ42+evWgZEno3DmzjyQiIiIikmFLly5l6dKlmR4nzXf4MjywMXWBwdbae1M/vww4rLUjL2jTD8hh\nrR2c+vl9YKG1du6/xtI7fHKRmJgYwsLCWLJkCdWqVUuz/b59EezbN4mwsD/x8vIjMRFaF99Jc9bQ\nbEd9CuUu5Gy4dSvccQdMnw733uvZhxARERERcZEn3+HLqBVAeWNMKWOMH9AK+PcW0PlAA2OMtzEm\nJ3Arzi2jIlflSkH2CxUt2hl//+Ls2jUUgIAAeH5uKU7EBjO8w1jikuKcDVWjT0RERERuIB5L+Ky1\nycBzwPc4k7g51tpNxpiuxpiuqW02Awtxlnz4C4iw1irhE1xZ0e3UqRMFCxZk5MiRabY1xhASEsH+\n/e9z8uQfADRsZNjxYCWafHMP4ZPCSUpJcja+7TaYNAkefBB2787Uc4iIiIiI/Jc8tqXTnbSlM3ux\n1tJozRreLl+e6oGBV20bExNDdHQ0DRo0cGnsw4c/Z8eO/tSqtQZv71wcPQqvltpJpZv/5I9h3zLj\nkRl4mdTfg7z1FkydCr/9BnnyZPaxREREREQyLKNbOq+Y8Blj1l2ln7XWhqZ3soxSwpf9ROzbx7QD\nB/itRg28TLr/Xl/Vpk3t8PYOJCRkIgCzpqfg03UF3z0dQf6H8jD67tHOhqrRJyIiIiLXCE8kfKWu\n1tFauyu9k2WUEr7sx2EtDVavpmORInR2sVyDq5KTT/L336GEhEwmf/57sRaeqX2Mh7dv5uVXu/FU\nnafoc1sfZ+OUFHjsMQgMhBkznHX7RERERESymNsTvmuJEr7saW1cHHevXcuG2rUp4ObVtePHl7Bp\nUztq147E1zcfO3bAx5U2csdTZ2lb9UFeb/w6baunloVMSIDGjaFpUxg2zK1xiIiIiIi4wmOndBpj\n4owxsanXGWOMwxhzKmNhiriuemAgbQoX5qUdO9w+dt68jSlY8DG2bu0GQJkyEPhSWeJmxvFV2Nf0\n+aEPC7ctdDY+V6Pvk0+c7/SJiIiIiFwn0rXCZ4zxAh4C6lpr+3ssqkvn1QpfNhWbnMyi48dpUbCg\nS+3ff/99Dh48yIABA9Jsm5JympUra1Ky5CAKF27N2bPQq/ReHsp1iMBFCTz86cMseHIBtYvXdnY4\nV6Pvww/hnnsy81giIiIiIumSpVs6jTFrrLW3pLtjBinhE1edK8i+ePFiQkPTPlcoNnYlkZH3UavW\navz9i7P8T0vkHau4c3QxNt3zN12/6crP4T8Tkj/E2WHZMnj4YVi0CG7Jsn8CIiIiIpLNeXJLZ4sL\nrseNMSOA0xmKUsTDgoODGTFihMsF2YOCalK8+HNs3twRay116hp2twhhW78d3Jv/XoY1GsY9H93D\n/tj9zg633QYTJ8IDD2CjoxnVv79LNQNFRERERP4LrhRef+CC624gFmjuyaBEMqNjx44ULlzYpYLs\nADff/ArJySfYt89ZpqHvlCB+9inM72130DmsM51rdOa+j+/jZOJJZ4fHHoMXX+T7Bg3Y/+67LJo3\nz1OPIiIiIiKSKVcryzDSWtvPGNPSWvtpFsf171i0pVPSJb1bOxMStrBqVX3CwpaRM2cIX81OJrnt\n3zT4rhIFm+Smx3c92HB4A9+1+Y65Uz9k9jvvUH3vXl47eZKB5cuz1teXJ3r25KmuXbPg6UREREQk\nu/FEHb71QDVglbW2RibjyxQlfHLOtP37KeznR7P8+dNs+9NPPxEaGkp+F9oC7NkzgYMHZ1Kjxu94\nefnQr95hbt+2k2Z7a2F9LE98/gTWWma3mM0P877gl969GR4Tw8t583LnlCnc06IFRnX6RERERMQD\nPPEO33fAcaDaBWUZzl0qyyD/iWB/f7pHRZGQkpJm20aNGrmc7AEUL94NH5/c7N49HICecwuw9WQA\nK/vF4O3lzcxHZnL09FGeX/g8AIknTvBi2bKcPn4cc/Sokj0RERERueakeUqnMeYra+1DWRTPlWLQ\nCp+c13rjRkoHBPBGmTJuHzsxcQ8rV4YRGvodQUE1eX/YaYoOXUnDzTXJVTYHJxNPcuf0Oyl1pCDP\nVOzK0g0raLhxJ3vWrKHz5s2gpE9EREREPMBjp3QCTxpjvFMnCTHGPGSM8U13hCJuMrZsWSL272dT\nfLzbxw4IKEG5cuPYtKktKSmn6TggB78VC+anh6Ow1pI7IDfftfmOyKDtzN+zmIlLJhLf6lE6BwTA\nrFluj0dEREREJDNcSfh+BvyNMcWBRUBbYLongxK5mqL+/rxasiTdoqLSVRLB1baFCrUmV65q7Nz5\nCl5e0GZ+MCc2JbJ16hEAvpr7FV6feBHxRQSxjWJ5eeYgqvjEMrnHM3DoUIaeSURERETEE1xJ+Lys\ntQnAo8BEa+3jQFXPhiVydc8WL07VXLk45cK7fOBM9u6//34iIyPTbGuMISRkIocOfcbx4z9R9RYv\nDjwZwtae20iOTaZLeBeGvzycAjkKgIHTSacZ8uoounR6Bnr2zOyjiYiIiIi4jSsJH8aYekAb4Nv0\n9BPxFG9jGF++PLl9fFxqb4yhRYsWLhdk9/XNT4UKEWzeHE5y8kmem5KHSJ+8LGm7C2MMxhgSTicQ\n9FMQh08edt4bOhRWroT58zP7eCIiIiIibuFK4tYLeBn4wlq7wRhTFvjJs2GJuF96C7Lnz38f+fM3\nIyqqJwEBUG96GU5/fZCDv8UStTOKaX2m8f3M7wmqEsSWHVsgRw54/33o3h1OnPDw04iIiIiIpC3N\nUzovamyMFxBorc3Ssgw6pVPcJb0F2VNS4lmx4hbKlBlJwYKP8nr9/VTavo9H9oZhvJ2HJNX/oD69\nbu3F41Ued3Z69llIToaICE8+ioiIiIhkIx47pdMY84kx5iZjTC5gPbDJGPNSRoIU+a8FBwczYsQI\nl7d2envnomLFGWzd2o0zZw7Q9csiHDpm+GPAvvNtetfrzZg/xvxzKMzIkfD997B4saceQ0RERETE\nJa5s6aycuqL3MM5i7KVwntQpcs3Ye+YMC44edaltx44dGTJkCD4uvv+XO3c9ihbtxNatT5O/AOQZ\nEsKx0buI35MEQPMKzTmScIRlMcucHW66CSZNgi5dwAOlI0REREREXOVKwueTWnfvYeBra+1ZQPsr\n5ZoSm5xM+82b2XfmTJptjTE8+OCDmHQUSS9V6lXOnNnDgQMf0Kp/IOuCi7DgwSia1n0Qg+GFui8w\n5o8x/3S4/36oVw8GDcrI44iIiIiIuIUrCd9kYBcQCPxijCkFnPRcSCLpVzFXLroULcqL27Z5ZHwv\nLz8qVpzJjh39SUzcwWNflWL1mm8I+MuHV/sNJ/yWcH7d/Svbjl0w/7hx8Mkn8OefHolJRERERCQt\n6Tq0BcA4l0W8rbXJngnpsnPq0BZJU0JKClX+/pspISE0zZfPI3PExIzh+a6TWLXYi8pnQ+lruzPc\nZzxbvdaTv0F+6r4Yxrv3v/tPhzlzYOhQWLUK/P09EpOIiIiI3Pg8eWhLEWPMVGPMwtRblYD26Z1I\nxNNyenszvlw5ukVFkehiQfZzXP2FQokSLzBgWDEeaFuRFC8HBkNQsi9PPdeOr+bNZdb6WRxNuOBd\nwpYtoVw5eOONdMUjIiIiIuIOrmzpnA4sAoqlfo4CXvBUQCKZ8UCBAoQFBrLslOuVQ7Zu3Urjxo1d\nOrXTGC8qV55BfNzfeKc4eNm8gSUZny3eFM9dnIcrPsx7K967sIPzAJeJEyEyMiOPJCIiIiKSYa4k\nfAWstXOAFIDUQ1uybDunSHrNrlyZxnnzuty+fPnyBAQEuFyQPUeOUhw9UBXbcBUlWvzBtpzVOLHw\nMKd3nebFui8y4e8JnEm+4PCYYsVg+HDo1MlZn09EREREJIu4kvDFGWPyn/tgjKmLDm2Ra1h6Tt88\n137KlCm8/fbbRLqwCjd9+mTivfdRMPgY3brFUez2PRz1asvPTZdSJX8Vqheuzqx1sy7u1KmTs1zD\nuHHpik1EREREJDNcSfh6A18DZYwxy4CZQE+PRiWSxdJTkL19+y706jUYb+88GAOFC3/LmvLFsf7F\niB4WfWkhdnBu7YyIgBEjwEMniYqIiIiI/FuaCZ+1diVwJ1Af6IqzEPtaTwcmktU6duxI4cKF09za\naYzBGMPp06eIiChCfPxh2oVvoP+Jiuybsp9ae2vh7eXN99u/v7hjmTIwYAB07gwOhwefRERERETE\nyZVTOp8DAq21662164BAY0w3z4cm4h5bEhJcameMISIigoceeijNttHRUbRtO42ZM2O4446bsXYy\nN9fwZ8uDFdjcdjN9Kve5uBD7OT17QmKic7VPRERERMTD0qzDZ4xZa62t/q97a6y1t3g0sovnUx0+\nyZDY5GTK/fUXC0NDqREU5JE5Tp78gw0bHiMgYAvNmgWy+OEoHEcSubfevSxos4DqRapf3GHDBmjY\nEFavhhIlPBKTiIiIiNxYPFaHD/AyxpxvZ4zxBnzTO5HIfyHIx4fXS5fm2a1bcXjolwa5c9cjX767\nuemmwdx1F8wrWIbEqESGHhrK2D/HXtqhShXo0QOeeQb0iwwRERER8SBXEr7vgdnGmCbGmLuA2cDC\nNPqIXDM6Fi2KlzFE7N/vsTnKlBnJwYMf0q9fFG9P8qboxMqEfBDCql9XsS9236Ud+veH3bvhk088\nFpOIiIiIiCtbOr2BLkCT1Fs/AO9ba1M8HNuFMWhLp2RKZFwcd61dy/ratSnk55euvtZal0o9ydB7\nBgAAIABJREFU7NkzniNHvmDKlMXkyGF4sfxe/n7zb5aPX84bzd64tMPff8ODD8K6dVCwYLpiEhER\nEZHsJaNbOl1J+HIBiecSvNQE0N9a69pJGG6ghE/cofe2bVhgbLlyLvd56623iI+PZ+DAgWm2dTiS\nWbmyJgEBQ2nYsDmrV1v2d1vOpyc/ZcjiIQT6BV7aqW9f2LNHK30iIiIiclWeTPj+AppYa+NSPwcB\n31trb8tQpBmghE/cIT7FuSidy9vb5T4xMTGEhYWxePFiQkND02x/4sRvbNrUmvnzt3P0qB8TR5xl\nYYWFHB54mI69Ol7aISEBqleHMWPAhdNBRURERCR78uShLf7nkj0Aa20skDO9E4n813J5e6cr2YP0\nFWQHyJOnAXnyNKJlyzf48kvYccSXfO/mI9+r+Ti9//SlHXLmdJZo6NYNTpxIV2wiIiIiImlxJeGL\nN8bUPPfBGFMLuMxPriI3JlcLsp9TpswoTp9+l549DzFoENRvVZ/VDVbza8tfsY7LrFQ3bAgPPAAv\nveTewEVEREQk23NlS2dtnCdznjvisCjQylq7wsOxXRiDtnTKf+rc1s4lS5ZQrVo1F9qPY+/eH2nR\n4mu++soQ7TuPuEfiaNSjEcG9gi/tcOoUVK0K06dD48bufwARERERua557B2+1MH9gAqABbZYa9Pe\n2+ZGSvjEE5IcDvy8XFnkdlq2bBmhoaEEBl7m8JV/cR7gUoOffvqQxYvDWPBdCvUH12fEuyOo+WNN\ngmpcpgj8t99Cz54QGQm5cqXnUURERETkBufJQ1va40z0zg1uAay1M9I7WUYp4RNPeCAyki7FivFQ\ngQIeGf/EiV9Yty6cDh22ERHhxYZcE9g7cy8P//AwtVbWwjvXZd4nbNMGihRxHuIiIiIiIpLKkwnf\nBFKTPCAAZz2+Vdbax9IdZQYp4RNPWHL8OB03b2ZDnTrpPszFVRs3tmHRooeYPbsVP/4cT+l3SvHt\nim/JnTs3FaZUuLTDkSPOrZ3z58Ott3okJhERERG5/njslE5r7XPW2h6p19NAGHCZ/Wgi15fGefNS\nP3duhu3a5bE5ypZ9k7Cw54iPP8OP3+Xi6bCnmfX4LI4vOc6huYcu7VCgAIwbB506wZkzHotLRERE\nRLIHl97hu6iD832+9dbaEM+EdNk5tcInHnHgzBmqrVjB0ltuoUo635tzOBx4ufAOYEzMGL788iTv\nvTeEhb/vJ3RyFdbVW0f0Y9HUXFGTgJsDLu5gLTRvDmFhMHhwumISERERkRuTx1b4jDFfX3B9C2wB\nvshIkCLXmiL+/gwuVYpnt24lPb9UsNZy5513EhkZmWbb4sV7UqfOXIKCjvLTV8VoXqE5M8wMSrxY\ngk1PbcKm/GteY2DSJHj3XVi3Lr2PJCIiIiJynivv8DW84ONZINpau8eTQV0mBq3wicekWMuS48e5\nK29ejHH9lyZTp05l4sSJ/Pnnn/j6+l617fHjS5gzZyIjRnzK579s5MHP7mZHjx1svm8zeRrmodSg\nUpd2iohwXsuWgY9POp9KRERERG4kHlvhA1YAv1prlwJHgDBjzNV/uhW5jngbQ9N8+dKV7IGzIHvB\nggVdKsieN29jbr/dmzJlolg2vyrVCldj9sbZVJpRib3v7uXkspOXdurcGQID4e230xWXiIiIiMg5\nrqzwrQIaAHmB34G/gSRrbRvPh3c+Bq3wyTXpXEH2xYsXExoaetW2iYl7mD27Df36LWbKDz8z8Pde\nRD4TydGvjrKt1zZqrq6Jb55//S5l+3bnaZ1//gnlynnwSURERETkWubJFT5jrU0AHgUmWmsfB6qm\ndyKRG1FwcDAjRowgPDyc5OTkq7YNCChB48bNqFXrNyLnN8ZgWLR9EQWaFyBfs3xsfeYy7xGWLQuv\nvAJPPw0OhwefRERERERuRK4kfBhj6gFtgG/T008kO+jYsSNjxozBx4X37EqUeIGOHV9n3LizdKn0\nMmP+cBZYLzu6LPHr4znw4YFLOz3/PCQkYCMiGNW/f7oOlxERERGR7M2VLZ13Ar2B3621I40xZYHn\nrbU9syLA1Bi0pVOyzCcHD3I8OZluxYt7ZPxjx36gc+dD3FyqBZ8WL8PCpxYSWjiUuHVxrG28lhq/\n1yBnSM6LO61fz8J69fgeuHf6dO5p0cIjsYmIiIjItSmjWzrTXYfvv6CET7LSloQE6q9axdratSnu\n7++ROZYseZoWLd6m6/sfcMB7BdMfng7A3nf3sn/afsKWheHl51xI/2jyZGa/8w7VDxzgtWPHGFiu\nHGv9/HiiZ0+e6trVI/GJiIiIyLVFCZ+IGw3auZMtCQl8WqWKR8ZPTNxN585fYL3b8F3lENZ3W0+x\noGJYa1nffD05K+ak7KiygLPm38K5c/mld2+Gx8Twsp8fd06axD0dOqT7ZFERERERuT558tAWkWzn\nlZtvZmVsLN8fO5ah/o40DlgJCLiZl15K4buvfWmWrxcTlk8AnP+QK3xQgYOzDnLsh2Pn7xljSDxx\nghcrV+Y0YAYOxERHZyg2EREREck+rpjwGWNGpv7ZMuvCEbk25PD2ZkL58nTfupXTKSnp6rt+/Xpu\nv/12zp49e9V2Vat254kn3ufgl08xZeUU4pLiAPAr4EelDyuxOXwzSYeTAIiJiuLeadMYs349982a\nRUytWtCgAaxdm7EHFBEREZFs4YpbOo0x64FqwCprbY0sjerSWLSlU/4TI3fvJrxIEQr7+bncx1pL\ns2bNqF+/PgMHDrxq2927f6BmzVCq9R7JI41K0+PWHue/295vO/Eb4qn2dbXLb9389FN47jnnnw0b\nuhyfiIiIiFx/3P4OnzHmTeBpIBA4/a+vrbX2pnRHmUFK+OR6k56C7AMHTubbxfU51bo5W5/bireX\nNwCOJAer66+mcLvClOhR4vKdlyyBJ56Ad9+Fxx9392OIiIiIyDXC7e/wWWv7WmvzAAustUH/urIs\n2RO5Hl1YkD2trZ19+97Dod258N/dhC83f3n+vpefF5U+qUT00GjiIuMu37lxY1i0CHr1ggkT3PkI\nIiIiInIDSPPQFmvtQ8aYwsaYB1KvQlkRmMj1rmPHjhQuXJhRo0ZdtV3u3KXo23c1Cd/2YPSyMRd9\nl7NcTsqOKcvG1htJjk/m9f6vX1p4/ZZb4LffYPx4GDAAtBouIiIiIqnSTPhSD21ZDrQEWgHLjTHa\nOyaSBmMM77//Pk888USabbt3b4ZPsg87/gjhj5g/LvqucNvCBFYPZNoj01g3cR0L5i24dIDSpZ1J\n348/QseOkMaqooiIiIhkD2nW4TPGRAJ3WWsPpX4uCCy21l79xSQ30jt8ci3Yd+YM3x07RqeiRT0y\n/qxZy+nZL4g7Rg1iXuu55+9PnzydmW/NpNj2YnRM7sis8rPY4buDtj3bEt41/OJB4uOd7/IZ4zzM\nJVcuj8QqIiIiIlnLk3X4DHD4gs9HU++JZCt+xvDKjh2sio31yPitW9ehWH4H33+Rh+3Htp+/375L\ne3oN64V3Pm8MhpTEFF4Y8gLtu7S/dJBcuWD+fChYEJo0gSNHPBKriIiIiFwfXEn4FgLfG2PCjTEd\ngAXAd54NS+TaU8DPj+FlyvDM1q2keGDF2RgYOzov5qeBjFw6/IL7qYXXTyfyXs73iDscd/7eZfn6\nwrRp0KgR1K8Pu3a5PVYRERERuT64cmhLX2AyEIqzLt9ka+1Lng5M5FoUXqQIfsYwZd++DPW31pJy\nlULud91VjNBKp5k5LRfHTh87fz86Kpq209oyftZ4bi92O9FR0VefyBgYPhy6d1eBdhEREZFsLM13\n+K4FeodPriXr4uJovHYt62vXTldBdoBhw4ZhjLlqQfaVKxOp3/gEz88YysjmEy/6zjosyyssp8IH\nFchzex7XJlWBdhEREZHrniff4RORC1QLDOSZYsX44+TJdPcNDw/n7bffJjIy8optatYMoH6Dk0yY\nmJ/EsxfX3zNehhIvlGDP2D2uT9qyJcye7fzzs8/SHbOIiIiIXL+0wieSxaZOncq7777LX3/9ha+v\n72XbREVZKocd5X8f9mPQo1Mv+i4lPoU/S/1JjWU1yFk+p+sTr1kD998PL7/sXPETERERkeuGx1b4\njDEPGWO0EijiJucKso8cOfKKbcqXNzS57whjxlciMfHi1TzvXN4U7VKUPW+nY5UP/inQ/s47KtAu\nIiIikk24UofvY6AeMBf4wFq7OSsC+1cMWuGTG0pMTAxhYWEsXbqUKlWqXLbN3r2Wm0OOM/yDLrzU\nau5F353Zd4a/q/zNrdtvxTff5VcJr+jwYedKX5UqMGWK81RPEREREbmmZXSFz6UtncaY3EBrIByw\nwDTgE2utZwqSXTq/Ej654axYsYLQ0FD8rnLwy33tV7Ny+0q2fF2WvHkbXfTdpvabyFkpJyX7l0z/\n5CrQLiIiInJd8eihLdbakzhX+OYAxYBHgNXGmJ7pnVDkRpSRA1xq1ap11WQP4IM3K3NkzcNM++o1\nHI6zF30X/GIwe8fvxZHkSPfcKtAuIiIikj248g5fc2PMF8BSwBeoba29D2ddvhc9G57Ite+sw0HH\nLVuY74GkqWghf5q0XseYiT3Zs+cdXn+9P+dWuwOrB5KzUk4OzTmUscFVoF1ERETkhufKO3wfAlOt\ntb9c5ru7rLU/eiq4C+bRlk65pv10/DjhmzezoXZtAn183Dp2zJFjlCyTRKcOjxJ7cB1t207n/vtb\nAHB0wVF2DthJzVU1MSbdK/z/eOcdGDUKvv0Wqld3U+QiIiIi4i6e3NJ58N/JnjFmJEBWJHsi14NG\nefNyR548DI2OzvAYycnJl72/+JvPuKnaGD758n9EbvRh3rx+NGlShenTJ5Pv3nw4Eh2cWHoiw/MC\n0LMnjB0LTZvC0qWZG0tERERErhmuJHxNL3OvmbsDEbnejS5blukHDrA+Li7txv+SkpJCnTp1LluQ\nvX37Lrz+XCniDx5k04bH+XPFCV54YQjt23fJWCH2K/lXgXZrLaP6/7OFVERERESuP1dM+Iwxzxpj\n1gEVjDHrLrh2AZf+VCqSzRX282NIqVKM2L073X29vb3p3r074eHhnD178eEsT4V3pVeHt8HxMzgm\ns2lLQx557BWeCu/qnLdtYU4tP0X85vjMP0TjxrBoEfTqxfedO7N/4kQWzZuX+XFFRERE5D9xxXf4\nUksx5AVGAP2Ac/tFY621R7MmvPOx6B0+uS6kWEuSw0EOb+9097XW0qxZM+rXr8/AgQPP33c4HDS5\n9z5+/qUg9sxH4NOVurd+x28/78Q7dZ6dr+4k6WASFd6rkOln+GjyZGaPHk316GheO3uWgeXLs9bX\nlyd69uSprl0zPb6IiIiIpJ8n3uGz1tpdQHcgFjiVelljTL4MRSlyg/M2JkPJHjj/EU+ZMoW33377\noq2dXl5ehNWoi032xwQ8DMkBFC+Rm0OHZp5vU7xbcQ7POUzSkaRMP0ObLl3o/sYbOAoWxACOY8d4\nbsgQ2nTpkumxRURERCRrXS3h+yT1z5VXuETEzYKDgxkxYgQdOnTA4finvt76Ddvo0yeYrXtG41UC\nfvv1IXbs6EtiovOQGL/CfhR4tAD73tuX6RiMMRhjSIyN5cUyZTh99CgmOjpzp4CKiIiIyH8izbIM\n1wJt6ZTsxFrLihUrqF279mW/7zV/EBGdXmTG5G8pW3Yq1asvxhgv4jfEs/autdy681a8AzK2ynhO\nxPDh3BwSwt2PPsqi3r2JmTaNzlu3Ogu1i4iIiEiWy+iWzqu9wxd2tY7W2lXpnSyjlPDJ9SohJQU/\nY/DxcuVAXNecTDxJyaf7UHDFO3w0/R6KF29BiRLPA7D23rUUalWIoh2Kum0+AF5+Gf74A374wVmw\nXURERESylCcSvqXAFbMsa22j9E6WUUr45HoVvmkT1QMDeSE42K3jTlw+iUGdatHnyVLcfnslatT4\njVy5KnJs0TG2995Orcha7t2CmZICDz0EpUvDhAnuG1dEREREXOL2hO9aooRPrldbExK4bdUq1tSq\nRYmAALeNm+xIpuLQBzn09nwWL5qNl9d4atRYhjE+rAhdQdmxZcnX1M1nK508CXXqQN++0Lmze8cW\nERERkavyxApfY2vtEmNMCy6z0metzbLiXEr45Hr26s6dbExI4LMqVTI8xtmzZ/H911bKhdsW8lSP\n7dyZ61n+N6gZuXPfRqlS/2P/tP0cmnOI6gurZzb0S23eDHfcAV9+Cbfd5v7xRUREROSyPFGW4c7U\nPx+8wiUiLuh/882sio1l4dGMla9cuXIl9evXv6Qg+73l7qXG49/zy1+n2L37I/bunUBs7EoKP1mY\n+LXxxK2Pc0f4F6tYEaZNg8cegz173D++iIiIiLiVtnSKZIGFR4/SPSqKTXXq4JfOA1ystdx33300\naNDgooLsAOsPrafBK6+T76ePWLJ4LocODaFmzZXEvHGQxOhEKr5f0Z2P8Y/hw2HePPjlF8iRwzNz\niIiIiMh5HnuHzxhTAHgVaIBza+evwFBrbcaWKzJACZ/cCFacOkWtm27KUN+YmBjCwsJYvHgxoaGh\nF3337DfP8uPIZ3iycSgtW7bC3z+Ym3MPZ3nIcupsroNfYT93hH8xa6F1a/Dzgw8/BNXoExEREfEo\nT2zpPGc2cAh4FHgMOAzMSe9EItldRpM9cBZkHz58OOHh4Zds7RzSaAhH72jLOxMcwHscOjSbBN8/\nKNiqIHsn7c1k1FdgDEydCuvWwbhxnplDRERERDLNlRW+9dbaqv+6t85aW82jkV08n1b4JNs7t7Wz\nYcOG9O/f/6LvRv0+ihnvFaT4oQ589NE3bN/eg8qBy1nXZCt1d9XFO0fmCrFfUXQ01K0LM2ZA06ae\nmUNEREREPLqlcyzwN/+s6j0O1LHW9k53lBmkhE/Ead++fXh5eVGkSJGL7icmJ1LxnWp4TVnNyGGB\nVKvWGWMMZ3r3oEDzAhR7upjngvr5Z2jZEpYtg7JlPTePiIiISDbmibIMcfxTjiEX4Ej9by8g3lob\nlJFAM0IJn0jaPt3wKQOnLyThk6msWxfLli3VKbJ/IocG5Kf2+toYLw++ZzdxovP64w8IyrL/axAR\nERHJNtz+Dp+1NtBaG5R6eVlrfVIvr6xM9kRuRF8dOULvbdvcOubjlR+nYKUtlK61jddeu4mKFaez\nt1AnjJ+DY98fc+tcl3j2WahXD9q1A4cj7fYiIiIikiVcOh/eGJPXGFPHGHPHucvFfvcaYzYbY6KM\nMf2u0q62MSbZGPOoq4GLXM8a5M7NxwcPsuLUKbeNaYxh7N1j2RbWghkzLbt330nhwq3xavU1MWNi\n3DbPFSaHCRPg0CEYNsyzc4mIiIiIy9JM+IwxTwO/AIuAIcD3wGAX+nkDE4B7gcpAa2NMpSu0Gwks\nBHS2u2QL+Xx9GVGmDM9GRZGSie3KDoeD5OTk859vLXErjatW49a2X/Pss1Cy5Osk3/E1cRuOErfW\nA4XYL+TvD59/7jy984svPDuXiIiIiLjElRW+54E6wC5rbSOgBnDShX51gG3W2l3W2rM4yzs0v0y7\nHsBcnOUeRLKN9kWKkMPLi8n79mV4jFdeeYURI0ZcdG94k+EsK9iR00lnmDkzgMqh03A0n0P06C2Z\nDTltRYo4C7J36QLr13t+PhERERG5KlcSvkRr7WkAY0yAtXYzUMGFfsWBC/eR7Um9d54xpjjOJHBS\n6i2dzCLZhjGGSSEhvLprFwfOnMnQGN27d+ftt98mMjLy/L2bc99MtzrPUOyJ13j5ZUhKqknxZ0px\n5KtDJO5LdFf4V1arFowdCw8/DMc8/O6giIiIiFyVjwttYowxeYEvgR+MMceBXS70cyV5Gwf0t9Za\nY4zhKls6Bw8efP6/GzZsSMOGDV0YXuTaViVXLt4qW5aMHnMSHBzMiBEjCA8P56+//sLX1xeA/g36\nE7I6hEYPPkf//oWZPLkvB+4ZxZaR8VR/+zH3PcCVtG0La9dCq1bw3Xfg48r/1YiIiIjIOUuXLmXp\n0qWZHifNOnwXNTamIXATsNBam5RG27rAYGvtvamfXwYc1tqRF7TZwT9JXgEgAXjaWvvVv8ZSWQaR\nK7DW0qxZM+rXr8/AgQPP35+6aipT/5hL9BsLmDvXEJJzPevu3E7NqEoEFQzxfGDJydCsGVSt6lzx\nExEREZEM81jh9dTBawINcK7a/WatXeVCHx9gC9AE2AcsB1pbazddof004Gtr7bzLfKeET+QqYmJi\nCAsL49dff6VixYoApDhSqDmlJo3iJvPTR7eyYgWsvn8+KWFLufWN0TjPS/KwY8egTh343/+cJRtE\nREREJEPcXofvgoH/B0wH8uFchZtmjBmUVj9rbTLwHM5TPTcCc6y1m4wxXY0xXdMbqIhcWXBwMD/9\n9BPly5c/f8/by5sxd49hvu+T5MvvYMIEKDfgDpJmNWB39OisCSxfPpg/H3r3huXLs2ZOERERETkv\nzRU+Y8xWINRam5j6OQew1lqbBXvCzsegFT6RDHrok4eoSHM+6NGJNWss+5v/QWLLodToPorAwNCs\nCWL+fHjuOWfSV7Ro1swpIiIicgPx2AofsBfIccHnAJwnboqImx1KSmLwzp248xccbzZ9k2l7+tO+\nUzx9+hhu7lMWv/m92LSpLQ5Hxk4HTbfmzeHpp6FFC8jgiaQiIiIikn5XTPiMMeONMeNx1tzbYIyZ\nboyZDqzHtTp8IpJOeXx8+PTwYb44csRtY1YoUIEnqz5JfN2BLF8OkXkK4tiTG58dddi1a4jb5knT\nwIHOOn3du4NW7EVERESyxBW3dBpjwvmntIL5939baz/0eHT/xKItnZJtLD1+nHabN7Oxdm0CM1HO\n4MyZM/j7+wNwNOEold6txJDiKxj76s1833E3CeuOcLJ7M6pW/YLcueu5K/yri42F226DZ55xJn4i\nIiIi4hJPn9LpD5x7Z2+ztfZseifKDCV8kt2027SJQr6+jC5XLkP9k5OTqVatGnPmzCE01Pme3rg/\nx/HDjh/wn/sttSqe5Y73/qLMT4eJSXyJWrXW4O2dy52PcGU7dkC9ejBnDqiepoiIyP/Zu/OoLMv1\n7ePf+wFkEsUBZ8gBFMUh53aDQzZotbUyS1MTzTCzcE4tfw6VY6lZqZkpzmWaWZk5ZaZZmjOiojjj\niCMiMzz3+wft3tq7FHkmwOOzFmuF3c95HbRarU6u675OkVxx5C2dLYDDwLTfv+IMw2h+2wlFJNfe\nq1aN+RcuEH3jRp4+7+7uzqBBgwgPDyczM+f3M680foXDlw/zdP9NTP7EA692ZUn9rC7Fiv2Lo0df\nt2f8m6taFRYtgk6d4MQJ560rIiIicgfKzS2du8iZn3fo9++rA5+bptnACfn+k0E7fHLHmXPuHF4W\nC8+XLZunz//dQPYVsSsYvmE4XZL2svf7DPrE7KRRXE12x9anRo1PKVnyEXv+CDf3/vswdy5s2QK+\nTtpdFBERESmgHHlLp/t/mj0A0zQPA3l/sUhEcqVH+fJ5bvYg5z8Kn3zyCVOnTiU6OhqAdjXaEeAb\nQLHmUURf9CalegkuLUylRo3ZHDr0IpmZV+0V/9b69oW774bu3XWJi4iIiIiD5Kbh22kYxqeGYbQw\nDKOlYRifAjscHUxEbBcYGMj48ePp2bMnpmliGAaTHpnE21v+j/emJjP+aCXip5ymRPGHKF36SY4c\niXReOMOAjz+Gkydh/HhM02Ti0KF2HUkhIiIicqfLzZFOT+BV4L7f/2gzMN00TacN09KRTpG8M02T\ngwcPUqtWrT/+rPvX3SnnW46zC8bx5Lpd3D8tkJJtfdmx426qVBlLmTLPOC/gmTPQpAmrX3iBNdOm\n0Toqikfbt3fe+iIiIiIFgENu6TQMwx2IMU0z1JZwtlLDJ2JfZ5POUndGXVY/tYu3GnnxerXT3L+r\nAYmJW4mJeZJGjfbg6VnOKVkWzpzJ5+PHU+/UKd6xWhkeEsJeDw86RkbSpVcvp2QQERERye8c8g6f\naZpZwCHDMO7KczIRsZlpmqy8dIlMq9Uu9Sr4VSCyaSTv7X2dx8aW5uKBDBK3Xqd48XsoX/5FDh+O\ncNrRys4REfSZOBFr8eIYgDU1lVdHj6ZzRIRT1hcREREpzHLzDl9JYL9hGBsMw/j2969vHB1MRP7q\ngzNn+ODMGbvVG3TvILbEb6H249vYXKYiP/eNB6By5ZGkpZ3i3Lk5jBnj+HfqDMPAMAzSsrIYULw4\nqRcu/PFnIiIiImKb3DR8w4HHgbeASX/6EhEnMQyDaSEhjDt5kvi0NJvrpaam4uPhw9gHxzJofX86\nzi+LdftVzu9Nw2IpQs2aC/jss35ER3/EqlXL7fAT3Fx8XByto6KYdOoUbUqVIn7pUoevKSIiInIn\n+Md3+AzD8AZeBoKBaGCOaZqZTsz25yx6h08EGHX8OPuSk/mydu0819iyZQuRkZFs3boVN3c3mn7a\nlAH3DCDphcZYreDV/wcWLPiAoKAEXnjhEosXB3PsWBG6do0kPNwJ79Tt2QMPPwy//AIhIY5fT0RE\nRKQAcMQ7fPOAhuQ0e48B7+Uxm4jYydCgIKKTk1l1+XKea9x7770EBAQwYcIELIaFyY9MZugPQ2k9\npzQV952nRmAP+vUbhWF4YxiQlnae/v1H062bk96pu/tuGD0annsO0p12GbCIiIhIoXSzhq+maZpd\nTNOcCbQHmjkpk4j8Ay83N6aFhPChDe/yGYbBrFmz/hjI/sBdD9C4QmMW3piOW9OSLOl2HqvVICXl\nGlFRNUhNTebatY3Ofaeud2+oWhUGD3bemiIiIiKF0M2OdO42TbP+P33vTDrSKfJXWVYr7pbcvIL7\nz2bPns20adPYtm0bp5JO0fTTpvzWeDvRj51n8WNJdOuRxGOPPc1XX01l27Y3efPNnyhWrJGdfoJc\nuHYN6teHyZPhqaect66IiIhIPmT3OXyGYWQDKX/6I28g9fe/Nk3TLHbbKfNIDZ+I/ZkW+3+SAAAg\nAElEQVSmSZs2bXjooYcYNGgQg9cO5lraNcJHv8L4uIrMjA3ggw/eZdy4wVy6tJwjRwbQsOEOihQJ\ncF7Ibdvg3/+G7dvhLk2HERERkTuXQwav5xdq+EQc4/z583h5eeHv78+1tGvU+KgGK0ut5MxwC5Oq\nXGRv9BqiolrTvv2jHDv2Btevb6Nu3TVYLO7OC/nee/Dll7BpE3h4OG9dERERkXzEIYPXRaRwK1eu\nHP7+/gD4e/kzsvlIXvjxZTIunuL61miSkiYzbNgmwsKeYN26UAzDg2PHhjo35IABULIkDB/u3HVF\nRERECgE1fCIFXFJWFtezsuxSK6JhBDRJ4VLby3S0BFKUsaSmZjN69KtERHSlVq3FXLq0nAsXPrfL\nerliscC8ebB4Maxe7bx1RURERAoBNXwiBdw7J08y7Ngxu9Ryt7gz6dFJvOszlbTMYzRnB4kXjmAY\nBoZh4OFRktq1v+LIkde4cSPaLmvmSunSsHAhdO8OZ886b10RERGRAk4Nn0gBNzQoiOWXLrH9+nWb\na2VkZHB23VmsK1I44L2XgUTSKNuTt3q/wdyZcwEoWrQewcFTiYl5iszMKzavmWvNm+eMa+jcGbKz\nnbeuiIiISAGmhk+kgCvh4cGEqlXpffgw2TZebjRw4EDOXT7HkMkDuW4kYmDg6+ZG/Zaj6RbR7Y/n\nypZ9ntKl23HwYGdM04nN15tvgmHAO+84b00RERGRAky3dIoUAqZp0nLPHp4JCODVSpXyXCc+Pp5a\ntWpRolQJ6pyuQ5pXGsWSi7PWeI5Rk9MZ3O+FP561WrOIjn6YYsXuo2pVJzZg585Bgwbw2WfQooXz\n1hURERFxId3SKXIHMwyD6dWrM/rkSa5lZua5TmBgIFOmTCE1KZXddXazsf9GQjyDaV4hhqOxXf/y\nrMXiTq1aS7hwYQEXL35l64+Qe+XLw9y50KULXLzovHVFRERECiDt8IkUIsdSU6nq7W1TDdM0qd+w\nPgevHKRsaFkCTgUwPmEi4bTgh5/dCA396/PXr29n377HuPvuTfj61rRp7dsybBjs2QPffZdzk6eI\niIhIIaYdPhGxudmDnP+YPNr2UbyuerHhow0Ua1+Mg8X3M7FBPEOG/O/zxYo1pmrVCcTEPEVWlu0X\nx+TaW2/B9es5g9lFRERE5G9ph09E/lZcXBzBwcFcT79Oy7Etee+DSbzu9y8mL/KiWbP/ff7w4d6k\np5+jdu3lGIaTfpd06hQ0bgwrVsC//uWcNUVERERcIK87fGr4ROSWNhzfwFe9v+KRyz1526jHtm05\nl2X+mdWawZ49LSlZsg2VKw93Xrivv4a+fWH3bihRwnnrioiIiDiRjnSKyP+w2ukXJQ9WeRC3l93g\n5CmqXrvKF1/87zMWSxHCwpZy9uzHXL78vV3WzZV27XK+evQA/WJIRERE5C/U8IkUUj9du8aTMTHY\na3d87ONjWdB2AV2T9zJ8qJX09P99xtOzAmFhS4iNDScl5Yhd1s2ViRNzjndOm+a8NUVEREQKADV8\nIoXUvcWKcSw1lS/tNLrAmm6l34h+HPWNpoPXKaZP//vnihe/j8qVR7J//1NkZd2wy9q35OkJS5bA\n6NGwa5dz1hQREREpANTwiRRSHhYLM6pXp//RoyRlZdlUKz09nbp16+KX6Mf1Ide5L/4Q08akc/Xq\n3z9foUJv/PwacejQi3bbYbyl4GD48EN47jlISnLOmiIiIiL5nBo+kULsAX9/HipRgpEnTthUx9PT\nkzfffJPw8HD6Pd+Pbfds4ZWiexk37u+fNwyDkJAZpKYeJT5+kk1r35aOHaFlS+jVS+/ziYiIiKBb\nOkUKvYsZGdTevp219epRr2jRPNcxTZM2bdpw//338/hzj3O8wSnGW5qzNNqfu+76+8+kpZ1i166m\n1Ky5kBIlWuV57duSkgJNmkD//vDii85ZU0RERMTBNJZBRP7RD1evUtPHhwqenjbViY+Pp0GDBmzY\nsIGti7dimRnEj20eZuGifz4scPXqjxw8+DwNGmzFy+sfOkN7O3AAmjeHjRshLMw5a4qIiIg4kMYy\niMg/alWihM3NHkBgYCDjx4/n5Zdfpttb3XAvfpGUb+LZufOfP1OiREsCAwcTE/M02dmpNmfIlVq1\ncm7ufPbZnB0/ERERkTuUdvhE5LaYpsmJEyeoUqUK+9bt43DbM3x49738+Eux/xnG/ufPHDz4PIZR\nhNDQuRj/9KB9g0LXruDlBZ9+6vj1RERERBxIO3wi4hSGYVClShUA6jxcB7NVMnX3xfHtyuybfqZG\njU+5cWMPZ844aVaeYcCMGbBpEyxe7Jw1RURERPIZ7fCJiE3SLqSxrsomRpaoxW8nK+Hu/s/PpqYe\nZdeuewkLW4a//wPOCbhnDzz8MPzyC4SEOGdNERERETvTDp+I5Mr1rCx6xsaSabXapZ5XWS8C/68s\nna8eZczU0zd91tu7GqGh8zhwoCPp6Wfssv4t3X03jBqVM58vPd05a4qIiIjkE2r4RO4wfm5unE5P\nZ8rpmzdnt6NKr8rUKJnFjyPSuHY986bPlirVmooV+7B//zNYrU5qwF55BapUgcGDnbOeiIiISD6h\nhk/kDmMYBh+FhDDx1ClOpqXZXG/9+vU8+PCDNP60Nq9kn6ZDn59v+ZmgoGEUKVKeuLhIm9fPFcOA\n2bPh22/hq6+cs6aIiIhIPqCGT+QOFOzjQ2SlSvQ7csTmWq1atSIgIIBZO2ZR7gE/yi8px+o9e276\nGcMwCA2dS2LiJs6eddINmv7+8Nln0KsXnDjhnDVFREREXEwNn8gdakhQEPuTk1l56ZJNdQzDYNas\nWUydOhWfQSYdLQlEvnSYtKyb7x66uxejdu0VHD/+Btevb7MpQ67dcw+8/jp06oSZkcHEoUPRhVAi\nIiJSmKnhE7lDeVosfFy9Ohczb/7OXW78ZyB7rzd6UfHV8nTZU53ec6fe8nM+PjWoUWMW+/d3ID39\nPGPGOKEBGzAASpRgTYcOnJs+nbXLlzt2PREREREXUsMncgd7sEQJupcvb5daPXr0ICAggB/Lr6Kx\nXwoH3qnP5pObb/m50qXbUa5cOLNmPci+fdNZtcqxDdjCWbN44uhRNn/3HZOTktg0bBhPhIWxcOZM\nh64rIiIi4gqawycidpOQkEDRokW59k0yP3Q9xrBe7xM7eRZFixT9x8/MnTuTBQs+oGLFk3Tvnszi\nxSEcO+ZB166RhIf3sntG0zRZvWwZmyIjGXf+PMO8vGj+7rs82qcPhnHbo21EREREnEJz+ETE5cqU\nKYOPjw/lnytNmVAvHvxiKINWv37Tz3TrFkG/fqNwc/PHMCAj4xL9+4+mW7cIh2Q0DAPDMEhLTmZA\nzZqkmibGsGEYY8ZoTp+IiIgUOmr4RMTuDMPg3s+CefZqEmsXerHmyJqbPmsYBqmp15kzpxrJyVdJ\nSTng0N22+Lg4WkdFMWn/ftosWkT8K6/Ab7/lDGn/6SeHrSsiIiLibDrSKSJ/WJKQwCMlSlDCw8Mu\n9TZ2OMKG79OZM7It+17dQQnvEn/73LRp46hcuTqPPfY0S5eOZufOSYwatRdv76p2yZErpgkrVkBk\nJDz0ELz7LpQu7bz1RURERG4ir0c61fCJyB96Hz4MwIzq1e1SL/FsIj9W2ctnba5SpNsyFjy1IFef\nO3NmOmfOTKNBg19xdy9mlyy5lpQEI0bA4sUwfjyEh+cMbhcRERFxIb3DJyI2G1ulCisuXeK369ft\nUm/giIGseeA7Wn1XiV9jY1l+MHc3cFas+Ar+/s05cKATppltlyy55ucHU6bA99/D9OnQogUcPOjc\nDCIiIiJ2ooZPRP5QwsODd6tW5eXDh8myWm2uN3LkSJbtnUOS3xE6r5tPn1V9SEhOyNVng4OnYrWm\ncezYUJtz5EmDBrB1K3ToAM2awfDhkJrqmiwiIiIieaSGT0T+onPZsvi7uzP97Fmba/1nIHtUyXGE\n/XiRZ4oNpNfKXrkarm6xeBAWtpRLl1Zw7txcm7PkiZsbvPoq7N0Lhw9DnTqwdq1rsoiIiIjkgRo+\nEfkLwzCYHhLCV5cu5aoxu5UePXpQKbgcy8p9SbXJ7Th65SgLoxfm6rMeHiWpXfsbjh17ncTELTZn\nybMKFeCLL+CDD+Dll6FTJzh/3nV5RERERHJJDZ+I/I9QX1821Ktnl9EIhmEwa9YsNmQsxu9QNMM9\nPmPg2oGcvn46V5/39a1JaOh89u/vQFraSZvz2OSxxyAmBipXztntmzED7HD0VURERMRRdEuniDjF\n6dOn+aW/SdIPVzi7/Ft+Pr2Z1Z1X57qpjI9/n/Pno6hffwvu7kUdnDYXYmJydvuysmDmTKhXz9WJ\nREREpBDTLZ0ikq9VqlSJJ+dXxCc5nYbrIriaepWPd3x8G5/vi59fY2Jju2Ka+WBXrXZt2LQJevaE\nhx+GQYPgxg1XpxIRERH5CzV8IuI0RbwtFB8eTMq7x5j98DxGbBzB0StHc/VZwzCoXn06mZmXOX78\n/xycNJcslpyGLyYGEhIgLAy++cbVqURERET+oCOdInJLiVlZJGdnU8HT0+ZapgkzysRQ5r6inB66\ngmUHlvFT+E+4Wdxy9fmMjIvs2tWUKlXeoWzZ523OY1cbNkDv3lCrVs4FL4GBrk4kIiIihYSOdIqI\nw8w7f54esbF2ubXTMKDhp9XI/OYgXf0jcLe4M2XrlFx/vkiRAGrX/pojR/px/fo2m/PY1YMPQnQ0\n3H031K+fM8A9KwsA0zSZOHSoXf4ZioiIiOSWGj4RuaXeFSpwJiODZRcv2qVe3Uegt1sPop5YQ1S7\nKCZsmUDMhRiGjs5dQ1S0aB1q1PiUmJinSUvL3W2fTuPpCSNHwi+/wHffQePG8NtvrPnyS85Nn87a\n5ctdnVBERETuIGr4ROSWPCwWZoSE0P/IEa7/vmNlC29vb4aMeIvpR4eRvs6XsQ+Ope07bZm+YTrL\nV+auISpdui2VKkUSE9OO7OwUmzPZXfXqsG4dC+vX54l772Vzz55MTkpi07BhPBEWxsKZM12dUERE\nRO4AeodPRHKtR2wsxdzceD8kxOZapmkSWrYV9a5V5WCjbRzzPkbKAymE7A3BI8GDyJ6R9Ore65Y1\nYmO7YbWmUavWErvMDbQ30zRZPW8em159lXHJyQwrV47mH37Io+3b58u8IiIikj/pHT4RcbiJVavy\neUICp9LSbK5lGAZL189lVeaXdCr6Gv6e/mDAjfQbjB4ymojwiFzVqF79E9LT4zl58i2bMzmCYRgY\nRYuSZrEwoHx5Us+fx/jtNzV7IiIi4hRq+EQk10oXKUJM48YEeXnZpV7dukG0e3QMn6//GK5Amagy\nJFxLyGmSctkQubl5ERb2FefOzSEhYaldctlbfFwcraOimHTmDG3Gjyf+k0/gzTchO9vV0URERKSQ\n05FOEXGp1FST/v4b8Q/cTmz8r/zywBba3t+WT0d9elt1kpJ2Ex39CHXrrsHPr4GD0tpJQgJ07AhF\nisDixVCypKsTiYiISD6nI50iUiAtmT+PnaXe4dTRaPpmRHJf9P2sn7meOTPm3FYdP7/6VK/+MTEx\nT5Kefs5Bae2kTBlYuxZq1865xXPvXlcnEhERkUJKDZ+IuFSa6cY1SxpJpGNgkHoFrqV78v3xn267\nVkBAe8qXf4mYmCfJzk51QFo7cneH996DMWPgoYdg0SJXJxIREZFCSEc6RcQmGVYrRSx5/92RaZoM\nH/QOeybvwp0imGRQ6ZUqfHHXfA70OUAZ3zK3Xe/AgU4Yhjs1ay4oGJejREfD00/DE0/Au++Ch4er\nE4mIiEg+oyOdIuJ00Tdu0HjnTjKs1jzXMAyDK+cv86uXG2e9alOH+qSdTaZbvW688cMbeaoXGhpF\nauohTp2akOdcTlW3LmzfDocPw8MPw4ULrk4kIiIihYQaPhHJszq+vlT09GTK6dM21QmqHcashS8x\nf9dwjlvc2LB+PW/c9war4lax/cz2267n5uZN7dorOHPmIy5d+tqmbE5TogSsXAnNmuW81/fbb65O\nJCIiIoWAjnSKiE2OpabSZOdOdjZqxF12GNcwsGsqPy1uwRP921C5S2U+3vExv7z4Cxbj9n8/df36\ndvbte4x69X6gaNG6Nmdzmq+/hpdegrFjoWdPV6cRERGRfEBHOkXEJap6e9OvUiUi4+LsUm/IJG9C\nPaYw9YMPqG+pD8CCvQvyVKtYscYEB39ITEw7MjIS7JLPKdq1g82bYfJkiIiA9HRXJxIREZECSg2f\niNhscFAQh1JS+ObSJZtrlSkDdd9oShfjZbp16MaUh6Yw7IdhJKYl5qle2bIdKVu2CzExT2O1FqDG\nqUYN2LYNrlyB5s3BxmOzIiIicmdSwyciNvO0WFgSFkbTYsXsUu+1wW6c9etLkdPe7Fm1hzbBbXh7\n09t5rle58miKFCnD4cO9KVDHw/38YOlSePJJaNIENm1ydSIREREpYPQOn4jkSwsXmFx55SfaTqiC\nTzdvwqaHsSl8EzUDauapXlbWDXbvvp9y5V4gMHCAndM6wdq18MIL8MYb8NprUBDGTYiIiIjd6B0+\nESlUnu9ssK5SQ46+cZoSmSV484E36bemX5536Nzdi1KnzjfEx7/H5curME2TMWOGFpwdv0cegV9/\nhago6NoVUlJcnUhEREQKADV8IpIvWSwwcIYfm7NLc3TESfo07sPp66f5+lDexyx4eQURFraM2Nhw\nli9/n337prNq1XI7pnawKlVgy5ac3b377oPjx12dSERERPI5NXwikm+1aAGx91Uhfs4FMg5n8EHr\nDxiwZgCpmal5rvnVV/t4800PVqx4nV69klixYhitWoUxd+5M+wV3JB8fmD8fevSAe+7JOeopIiIi\n8g/U8ImI3WVarTwVE8OVzEyba416vwiLCOLgq0e4u/jd3B1wN+/98l6e63XrFsHAge9jGN4YBmRl\npdC//2i6dYuwOavTGEbOe3xLl0J4OIwbBwXlaKqIiIg4lRo+EbE7D4uFCkWKMOzYMZtrhYZC0S4V\nObc7jd4delPlQBWmbpvKqcRTeapnGAaGYZCRAZ98UoKkpHOYZgpGQbwEpVkz2L49Z1D7M89AUpKr\nE4mIiEg+o4ZPRBxiTJUqfHv5MlsT8zY/789GvGVhalYwz8Z1Yf7M+Txb+lkGrR2U53onT8bRtWsU\nCxdeonXrR9i6dThZWddtzukSFSvCTz9BQEDO6IZDhwAwTZOJQwvQpTQiIiLiEBrLICIOs+jCBd49\ndYodDRvibrHt90vjx0PZqdFcemANi48s5krnK8x9ei4tq7S0qa5pmsTF9eHGjT3Urbsad3f7zBJ0\nidmzYdgwmDWL1ZmZrOnRg9ZRUTzavr2rk4mIiIiN8jqWQQ2fiDiMaZo8tHcv/y5Vin6BgTbVSk2F\n5tVSmJC8i3EN36J0ndLsC93H7l67cbe425jT+nvTF/170+dnUz1XWjhsGJ+/9x71ihXjnStXGB4S\nwl4PDzpGRtKlVy9XxxMREZE80hw+Ecl3DMNgWkgIRd3cbK7l7Q2RE33Y7FOOYQHD+OHzH/DP9GfG\n9hl2yGkhJGQavr61iY5uQ1ZWwX0XrvPYsfSZMQNrcjIGYE1J4dXRo+kcUYAupRERERG7UcMnIg4V\n6utLzwoV7FLr+edhTdnKWNcUYeuirczsNJO3Nr3FxeSLNtc2DAvVq8/A17cm+/Y9TlbWDTskdj7D\nMDD8/UkrUoQBpUuTevYsxoEDBfNSGhEREbGZGj4RKTAsFhjzvjvz3atwZcRVapauSZc6XXhzw5t2\nqZ/T9M3E2zuEffseJzs72S51nS0+Lo7WUVFMSkigzRtvEP/uuzBhAlitro4mIiIiTqZ3+ESkwHmy\nrclLu3bS6L1AvJ70InRaKN92+pZGFRrZpb5pWjl06EXS0k5Qp85K3Nx87VLXZeLjoWNH8PfPGdpe\nqpSrE4mIiMhtyrfv8BmG0dowjFjDMOIMwxjyN3+/s2EYew3DiDYMY4thGHUdnUlECrbxEw3G3wjm\nyKBjFLUWZcyDY4j8PhKraZ8dLMOwUKPGp3h63sW+ff8mOzvFLnVdJjAQNm6EsDBo0AB+/dXViURE\nRMRJHNrwGYbhBnwEtAZqAZ0Mw6j5X48dA5qZplkXeBv4xJGZRMS1Fl+4QFyKbQ1UaCjU7ezPcd/i\nnJp4ivC7w0m9msrC6IV2SgmG4UZo6Gw8PSsVjqbPwwMmToSPPoInn4QpU0AnJ0RERAo9hx7pNAzj\nX8BI0zRb//79UADTNMf/w/MlgH2maVb6rz/XkU6RQmJSfDxrrlxhTd26Nl0kkpAAzWqk8Qk7qPlz\nDUJbhmJ5wcLRMUcp5mm/WXqmmc3Bg93IzLxA7drf4ObmbbfaLnPiBDz7bM7Q9jlzoEQJVycSERGR\nW8ivRzorAvF/+v7073/2T14EVjk0kYi4VGTFipzPyOCLi7bdrFmmDIQP8eLX8pVIeCuBieMmYn5l\nMuqHUfYJ+jvDcKNmzXl4eJQhJqYd2dmpdq3vEpUrw88/Q1AQNGwIO3a4OpGIiIg4iKN3+NoDrU3T\nfOn377sATU3TfO1vnm0JTAPuM03z6n/9PXPkyJF/fN+iRQtatGjhsNwi4lhbEhN5dv9+DjZpQjH3\nvA9NT02FutWzmZX5G/WWhNL+nfZsc9vGzoU7CS0dasfEYLVmERvblczMq9SuvQI3Ny+71neZL7+E\n3r1h5Eh45RXQ+AYREZF8YePGjWzcuPGP70ePHp2nHT5HN3z3AKP+dKRzGGA1TXPCfz1XF1hOTnN4\n5G/q6EinSCHTMzYWXzc3poaE2FRn4UL4aVQCvfxOUearMtSqX4t6r9fj56E/2332nNWaxcGDncnO\nvk5Y2FeFp+k7ehQ6dIDgYPj0UyhmvyOxIiIiYh/59UjnDiDEMIzKhmEUAZ4DvvnzA4ZhBJHT7HX5\nu2ZPRAqnCdWqcSglhQwbZ8M9/zzsKhbAlTQ33Ne5M3niZPYu2Mu3h7+1U9L/z2Jxp2bNRbi5+bF/\nf3us1nS7r+ES1arBL7/kjGto2BD27HF1IhEREbETh8/hMwyjDfA+4AbMNk1znGEYvQBM05xpGMan\nwFPAqd8/kmmaZpP/qqEdPhH5Rxs3wsjnkxhrjabxwcZ8e+xbXt/yOvtf2Y+Xu/134azWTA4c6ITV\nmkbt2l9isXjafQ2X+ewziIyEsWOhZ08d8RQREckn8rrDp8HrIlIotGsHXS4cov69bgRPDubpJU/T\nsHxD3mz2pkPWy2n6nsM0swgLW4bFUsQh67jEoUM5Rzzr1oWPP4aiRV2dSERE5I6XX490iog4xYQJ\nMDSuCufmXyA5NpnJj05mytYpxCfG3/rDeWCxeFCr1ucYhhv79z+L1ZrhkHVcokYN2LoVPD2hcWOI\niXF1IhEREckjNXwiUiiEhkLrjkXYUyuIowOOUtm/Mn0a92HwusEOW9NiKUKtWksAkwMHnsNqzXTY\nWk7n4wOzZ8PQodCyJcyb5+pEIiIikgc60iki+cKVzEzOZWQQ5uub5xoJCVC3ppVlxbdT86NgvB/2\npuaHNZnywBSebvy0HdP+ldWawf79z2AYObt+FouHw9ZyiZiYnCOe//oXfPRRTjMoIiIiTqUjnSJS\noG1OTOSZ/ftturWzTBnoO8jC8vLBHOl/BC/Tiw6WDnRu35nUdMcNTLdYihAWthSrNf33y1wK0U4f\nQO3asH07ZGZC06YQG+vqRCIiIpJLavhEJF9oW6oU1by8mBRv2zt3/frBl6dLkVbSmzMfnWFi5ER8\n/H14tu+zdkr69ywWT2rX/hKrNZWDBztjtWY5dD2nK1oU5s+Hvn3hgQdg8WJXJxIREZFcUMMnIvmC\nYRh8GBLCpPh4jqfmfTfO2xvGjIGJycGcGneKrItZLJm3hO8Wfsem3zbZMfH/slg8CQv7kuzsJA4e\n7FL4mj7DyBnVsG4djBwJL78MaWkAmKbJxKFD0fF7ERGR/EUNn4jkG1W8vRkQGEjkkSM2NQ7PPw/n\nPXy41rQsx4cf56H6D/HgSw/S/vn2ZGY69rilm5sXYWFfkZV1ldjYroWv6QO4+27YuROuXMl5r+/I\nEdZ8+SXnpk9n7fLlrk4nIiIif6KGT0TylUGBgRxLTWXPjRt5rmGxwKRJMDj6Li59e4mkXUksHbuU\n6+7XGTNtjB3T/j03Ny9q115BZuZlYmO7YZrZmKbJmDGFaAesWDFYsoSFoaE8ERrK5shIJiclsWnY\nMJ4IC2PhzJmuTigiIiKo4RORfKaIxcL2hg2p7+dnU50WLSCkvgdxD1ThSN8j+Hv5897M91hbdK1T\nmi43N29q1/6azMwEYmPD+e67pezbN51VqwrRDphh0HnxYvq88w7WhAQMwJqayqujR9M5IsLV6URE\nRAQ1fCKSD/m4udmlzoQJMOTH8qQnZnPxi4v0adaHTDOTRfsW2aX+rbi5ebNrV1t69lzO0qU96dUr\niRUrhtGqVRhz5xaOHTDDMDCCg0nz9maAnx+pZ89inD2LYdz2rdEiIiLiAGr4RKTQCg2FZ54zWFcj\nmKOvH8VMNfmwzYcMWT+E62nXGTra8Ucsw8NfZciQmWRnZ2AYkJ2dRv/+o+nWrfDsgMXHxdF67lwm\nXbtGm549iR82LOdGTxEREXE5DV4XkUItIQFq1YLvmu6nTGMfqoyqQviKcK7uu8qP638kalAU7f/d\n3qEZVq5cxsKFPTDNDKxWk/DwxTz+uGPXdKl9++DZZ6FJE5g2LWekg4iIiNhEg9dFpNBKzMr7TZdl\nysDAgTDdWo0zH55h9nuz+XXCr6xcv5KkRkkM/XQoYfeFMTPKcUcsT56Mo2vXKObPP8G99/oTE7PQ\nYWvlC3XqwI4d4OYGjRrB3r2uTiQiInLH0g6fiORrZ9LTabxzJ/saN6aUh0eeaqSm5hzvnN/qOKVT\nUjjQ6QC9PurF1bNXKZpZlKj3cnb5nPHeWUrKEfbsaUZIyHQCAp50+Hout2gR9MM5MuEAACAASURB\nVOsHo0dD7945s/xERETktmmHT0QKpYqenjwTEMDQY8fyXOM/w9jfjA7i+i/X8TjgQVZGFgElA7hx\n/AY7Duxw2iUjPj7B1KmzksOHI7h2zbGD4POFzp1hyxb49FPo0AGuXXN1IhERkTuKdvhEJN9LzMqi\n1m+/sTQsjHuLF89TDasVGjeG/7v/Au7Lt5P2QRqHth1i/cn1bFq9iW3R22gU2MjOyf/ZlSvrOXiw\nM/Xqrado0TpOW9dl0tNh8GD49lv47DO45x5XJxIRESlQtMMnIoVWcXd3JlWrRu/Dh8myWvNU4z/D\n2Pt/XYbyQRVJXZvKvun7GNh+IHXC6tDipRZsO73Nzsn/WcmSDxEcPJV9+x4jLe2k09Z1GU9P+OAD\nmDIF2rWDiRNzunARERFxKO3wiUiBYJomj0RH80SpUvStVCnPdZrWm0vm6XmEJVaiR3YPFocs5gAH\n2Ht+L14DvPgy/EuaV25ux+Q3d/r0VM6e/Zj69X/Gw6OU09Z1qVOnoFMn8PPLGd9QpoyrE4mIiOR7\n2uETkULNMAzm1KhBZxubg7mfd+N0xgBMTzAwyE7LZtjYYZyJP8MX3b6gw9IOrD6y2k6pb61Spb6U\nKtWO6OjHyc5Odtq6LhUUBBs3QsOG0KABbNjg6kQiIiKFlho+ESkwAr28KF2kiE01atY0uPc+g+vp\nqXzARyReSMQwDIoXL86DVR5kRccVdFvRja8OfmWn1LdWteo4fHxC2b//WazWTKet61IeHjk36URF\nQZcuMGIE2DB+Q0RERP6eGj4RuaPMnLmQfTveYn22J6f4mLCs+gx+eQwzZ+bMxrs38F6+7/w9r6x6\nhUXRi5ySyTAMatSYBcChQy9xRx1hf/hh2LULfv0VHnwQTp92dSIREZFCRQ2fiNxRIiI6M37GaDz9\ng9hJaazeQUwOe5uIiM5/PNOgfAN+eOEHhqwfwqyds5ySy2LxICzsC1JSYjl+/A2nrJlvlCsHa9ZA\n69Y5g9pXrnR1IhERkUJDDZ+I3FEMw8AwDLKz0/DzG8AH6XvxiLVw+ZvLf3nO+4Y3G8M3MmbzGN7f\n+r5Tsrm5+VKnzkouXvyK06enOmXNfMNigTfegC+/hD59oH9/yMhwdSoREZECTw2fiBRIpmnSJjqa\nQykpt/3ZuLh4oqJac+bMJIqXe4QvQ85w+OXDZFzMaTCuXr1K06ZNST2Tyqbum5i+fTrvbHrHKUct\nixQpTb16a4iPf48LFz53+Hr5zn33we7dcPw43HsvHD3q6kQiIiIFmsYyiEiBNSU+npWXL7O+Xj0M\n47ZvKQbgyJGcHuOLVkcplZFK2NIwDMNg9uzZTJ8+na1bt3I5/TIPL3iYJ0KeYGyrsXle63bcuLGP\nvXtbUbPmYkqWfMjh6+U7pgkffQRvvQUffggdO7o6kYiIiEtpLIOI3HFeq1iRy5mZfJaQkOcawcEw\ndy5021iZ6zEpJHyWU6tHjx4EBAQwYcIEyhUtx8ZuG1l3bB2R30diNR0/MLxo0TqEhS3j4MHnSUra\n5fD18h3DgNdey3m3b8QIiIiAPOzmioiI3OnU8IlIgeVusTCjenUGHT3Ktcy8jzNo0wYiXnVjkkdN\n4vodIf1MOoZhMGvWLKZOncq+ffso5VOKH174gd3nd9Pzm55kW7Pt+JP8PX//ZlSvPpN9+54gNfUO\nPdrYoAHs3JnT7DVpAvv3AzlHeicOHXpn3WgqIiKSBzrSKSIF3kuHDuFlsfBhSEiea5gmdOgADxw7\nQYuy16m7qs4fRzu//fZbVqxYAUByRjJPLnmSUt6lWPDUAjzcPOz1Y/yjs2dncurUuzRosIUiRco6\nfL18yTRztmJffx3GjWN18eKsefFFWkdF8Wj79q5OJyIi4nB5PdKphk9ECrzLmZl8fekSPcqXt6nO\njRtwb1MrE27sot6bFagQUQHTNElOTqZo0aJ/PJeWlUaHpR0wMPiiwxd4uXvZ+iPc0vHjo7h8+Vvu\nvnsj7u5+Dl8vv1o4ahSfjx9PPQ8P3rlxg+EhIez18KBjZCRdevVydTwRERGHUcMnImIHcXHwbNNk\npph7aLqzAd5Vvf/2uczsTLp81YUrqVdY8dwKfIv4OjSXaZocPtybtLSj1KnzHRZLEYeul1+Zpsnq\nxYvZ1Ls345KSGObvT/MZM3j0ueeccpmOiIiIq+jSFhEROwgJgTELfVlkDSK6cyym9e9/2eTh5sHi\npxdTqVglHl34KIlpiQ7NZRgG1atPw83Nj9jYcEwnXByTHxmGgeHpSRowoFo1UpOSMAYMwPjuu5xj\nnyIiIvIXavhERP7LY49B5UGVOLAfTkw6/Y/PuVncmN12NvXL1afV/FZcTrn8j8/ag2G4UbPmYtLT\nT3PkyIA79sKS+Lg4WkdFMSkujjZLlhD/6KMwaFDO7TsHD7o6noiISL6iI50iIn/DNKFH61Se27SL\nB3bdjW/NnCObaWlpXLx4kcDAwD89azLsh2F8F/cd67quo1zRcg7Nlpl5jT17HqBs2S4EBQ1x6FoF\nRmYmTJsGY8bA88/DyJFQsqSrU4mIiNiNjnSKiPzuswsX+OnaNZtqGAZ8sMybr/wrs6lNLNasnCOU\nK1as4MknnyTzT2MgDMNgXKtxPBf2HM2imhGfGG/T2rfi4eFP3bqrOXNmBufPz3PoWgWGhwf06wcH\nDkBGBtSsCdOnQ1aWq5OJiIi4lBo+ESl0fNzc6HXoEOlW295z8/ODgT9V4NBZd37ufQqA55577o+B\n7H9mGAbDmw2nd6PeNJvbjCNXjti09q14elakbt3VHD06hMuXVzl0rQIlIABmzIB162DZMqhfH9av\nd3UqERERl9GRThEpdEzTpG1MDP8qVow37rrL5nrfz08jo/tO6nxfl6qP+BEfH0+DBg3YsGEDderU\n+Z/nP9n5CW/99BZru66lVkAtm9e/mcTErcTEtKV27W8oXvweh65V4JgmrFgBAwdC3brw3nsQHOzq\nVCIiInmiI50iIr8zDIMPg4OZHB/P8dRUm+u1ecGLC09X47cnY0m9biUwMJDx48cTHh7+l6Od/xHR\nMILxD42n1fxW7D632+b1b6Z48XsIDY0iJuZJkpNjHbpWgWMY8NRTOcc877kn52vIELh+3dXJRERE\nnEYNn4gUSpW9vRkYGMhrcXF2uc3yxc/LcsPfmznNjgPQo0cPAgICWL58+d8+36VuF6Y/Np3Wi1rz\na/yvmKbJ0NFDHXKzZqlSj1Ot2gSio1uTnn7G7vULPC8vGDoU9u2DhASoUQNmz4bsbFcnExERcTg1\nfCJSaA0MDMTf3Z3rdvgfezc3g6d/rk6l/ReYPyQRwzBYvnw5zz777D9+5qmaTzHvyXm0+7wdo2eP\nZvqG6Sxf+fcNoq3KletGxYq9iY5uTWbmNUzTZMwYxzSYBVb58hAVBd98A3PmQJMm8PPPrk4lIiLi\nUGr4RKTQKmKxsLBWLYq7u9ulXsmqRajyfggek2LZ8kM2Pj4+GMbNj9Kf3HwSn6U+vL3gbZJaJjFs\nzjDC7gtjZtRMu2T6s8DA1/H3b0VMTDtWrvyMffums2qVYxrMAq1x45xGb9Ag6NQJOnaEU6dcnUpE\nRMQh1PCJiNyGun0CKN2sGN+1O8rZs7d+PiI8gnfffJcA7wAw4HLyZUYPGU1EeITdsxmGwZYtoURG\n7mHZsgh69UpixYphtGoVxty59m8wCzTDyGn2YmMhNDTnNs+RIyE52dXJRERE7EoNn4jIbWqxPJjm\nbpcZ8tAV0tNv/qxhGBiGQUpqCtV+q8bVpKt8f+T7W+4M5lW3br0YPHgG2dlWDAPS0s7Ru3d3unWz\nf4NZKPj6wqhRsHs3HD6c0/wtWpRzw6eIiEghoIZPROQ2efh70HBJDTqcOMTAl///YO+jR4/+7a2d\nccfjiBoURdzKOKb1ncaK31bw1k9vOeT9OsMwsFiKkJXlzpw5waSlZRAfP4GdOxtw+vQHZGRcsvua\nhUJQEHz2Wc7X5Mlw332wfTuQM+Zj4lC9DykiIgWT5vCJyB3jYkYGB1NSaObvb5d6MT0P8+0yK6Um\nhhIRAU899RQNGzZk+PDhN/3chRsXaL2oNc2CmjGl9RQshn1/9zZt2jgqV67OY489zapVyzl58jCd\nOjXh3LkoLl9eSYkSrShXrjslS7bGYrHP+42FitUKc+fC8OHwyCOsvvde1gwaROuoKB5t397V6URE\n5A6V1zl8avhE5I6xOymJ1tHRHGjShFIeHjbXy7qRxa+1djA2MZgRq0tTqdLNB7L/2bW0a/z7s39T\nxb8Ks9vOxsPN9jy5ypyVSELCF5w/H0Va2nHKlu1KuXLd8fWt6ZT1C5KF77/P5++8Q72rV3nHamV4\n1ars9fKiY2QkXXr1cnU8ERG5w2jwuojILdT386NjmTIMOXrULvXci7pTZ1Eog90P0/3pDNzcbj6Q\n/c/8vfxZ02UNl1Mv0/6L9qRm2j4gPleZ3YtTocJLNGjwC/Xq/QhY2Lv3IXbubMqZMx+TmXnNKTkK\ngs59+9JnxgysZctiANbjx3m1WDE6BwVphp+IiBQYavhE5I7ydpUqfH/lClsSE+1Sz/8Bf+7qUZa3\nS8XxTHuTLl1yBrJPmDDhlp/18fBhxXMr8PP0o/Wi1iSm2SdTbvn6hlKt2njuuecklSuP4tq1DWzd\nWpkDBzpx5cpaTPPObmr+c+FO2o0bDKhVi1RfX4w6dTBGjIAqVWDECDh+3NUxRUREbkoNn4jcUYq5\nuzM5OJjehw+TabXapWbltytzl5nMA1kJ9O1rMGvWLGbNmkViLppKDzcPFjy1gDpl6tByXksSkhPs\nkul2WCzulCrVhrCwL7jnnqMUK3Yfx469wdatVTh2bDgpKUecnim/iI+Lo3VUFJNiYmgzdy7xVavm\nXOby7beQmJgzvP2hh3Iue0lLc3VcERGR/6F3+ETkjmOaJo/t28fASpV4qGRJu9RM2pnE3jbRDC7e\niB6ve9KlSyre3t63lWnkxpEs2b+EdV3XEVQ8yC65bHHjRjTnz8/lwoVF+PhUp1y57gQEdMDd3c/V\n0fKPtDT4+mv49NOc0Q6dOkHPnlCvnquTiYhIIaNLW0REbkOW1Yq7xb6HHI6POs75H5Nod6AOX39j\n8K9/3X6NqVunMnnrZFZ3Xk3NgPxxkYrVmsHly6s4f34uiYk/UapUO8qVC8ffvxnG7zeMmqbJ2LHD\neOONcQ6bMZjvnTgBUVE5X2XKwIsv5jSAdroVVkRE7mxq+EREXMyaaWXXPbu4dG8Fen5Vge3boXz5\n268zf+98hqwfwredvqVRhUb2D2qDjIwLXLiwiPPno8jOTqZcuXDKlevG+vXbWbiwB127RvH443f4\n6ILsbFi/HmbPhrVr4d//zmn+mjeHO7UZFhERm6nhExHJB5L3J7OnxR62dG3A19u8+fFHKFLk9ut8\nc+gben7TkyXPLKFllZb2D2oj0zRJStrJxx8PYsWKzQQHe9K9eyqLF4dw7JgHXbtGEh6u0QVcugQL\nF+Y0f6mp0KMHhIdDhQquTiYiIgWMxjKIiOQDvmG+BA4J5OFdsZQJMOnbN6c5OnDgwG3VaVujLV90\n+ILnlj3HitgVDkqbd4ZhUKxYIwYP/pGhQ+djGF4YBqSnJ9Cv3wi6dYtwdcT8oXRp6NcPoqNh0aKc\nY59hYfDEE/DVV3CL8R0iIiK2UsMnIgKcSU+3W63A/oGQDe/ec5qNG+H99y/RvHlzevToz+2cVmhR\nuQXfd/6e3t/1Zu6euXbLZ0+GYWCxeJKensWcOSGkpt7gxInhpKQccnW0/MUwoGlT+OQTOH0annkG\nJk+GwEB4/XWIjf3jUdM0mTh06G39uyIiIvJP1PCJyB3velYW9XfsIDY52S71DDeD0LmhXJh0imWT\nkxk3LoAHHujCvHmL+eKLVbdVq2GFhvzY7UdGbhzJlF+n2CWfvZ08GUfXrlHMm3eI8PDPSU4OY/fu\n+zl9eiqmaZ/RF4WKr2/Osc7Nm+Gnn3KawZYt4f77ISqKNQsXcm76dNYuX+7qpCIiUgjoHT4REWDq\n6dN8fekSP9SrZ7dbJs/MOEP0hP30zv6Q+LN1sFp3UapUKmXL+hEZ2ZFevbrkutapxFM8suARnqn1\nDG+3fDvf34SZkhJHbGw4FosnoaFReHnd5epI+VtmJgsjI/l84ULqJSfzjmky/K672OvrS8fISLr0\n0vuQIiJ3Or3DJyJigz4VKnA1K4vFCfYbfF7h5QpUqF6WafdFUrSoFR/qcPXqdnr0eJyIiM63VSuo\neBCbu29m9ZHVvPLdK2Rbs+2W0xF8fEKoX38TJUs+ys6djTh3LkpHFG/Gw4PO06fTZ84crOXLYwDW\n+Hhe9fSkc3Aw6J+diIjkkRo+ERHA3WLh4+rVGXz0KNfsdJGGYRjUmFMD7+/dKZ92lhbE4WatybJl\nS/K0QxfgG8CGbhuIvRxL5+WdycjOsEtORzEMN4KChlCv3gZOn55KTEw70tPPuzpWvmUYBoZhkJaU\nxIBatUj19cVo2hTjtdegQYOc2z51yYuIiNwmNXwiIr9rWqwYbUuVYsypU3ar+fl3nzPYfJ2GViuD\n6Esr7xqc3pHIrA/n5qleMc9ifN/5e1KzUmn3eTtSMlPsltVRihatQ8OGv+HrW4cdO+4mIWGZqyPl\nW/FxcbSOimJSTAxtoqKIv+suiImBd96BOXOgalV49124ds3VUUVEpIDQO3wiIn9yLTMTEyjh4WGX\neqZpsnLpSr4I/4IXU19kXqX5nKv2NKbn43zzjYGnZ97qZlmz6PlNT+KuxLGy00pKeJewS15HS0zc\nSmxsN/z8GhES8hEeHgUjd76xa1fO7Z6rVkG3btC3L1Su7OpUIiLiBHqHT0TEDvw9POzW7MHvx/Qs\nBpnumXzs9zFJ567zcncTPz+DTp0gKytvdd0t7sxpN4cmFZrQYl4Lzt8oGEclixe/h0aNduPhUYod\nO+py5coaV0cqWP5ztHPvXnB3h4YNoWNH2L7d1clERCSfUsMnIuJgJ+NO0jWqK4uvLObRFo+y/c2t\nzPswk9RU6N4drHmcXGAxLEx+dDIdanXg/jn3c/zqcfsGdxA3Nx9CQj4gNHQuhw5FcOjQy2Rl3XB1\nrIIlMDDnaOfx4znz/Z55Bpo1g6+/zvu/UCIiUijpSKeIiBOZpsnxN45z6etLVP+6Lo+HZ1K58iUW\nLqyCLZMWpm+fztjNY1ndZTW1y9S2X2AHy8pK5MiRfly7tonQ0Hn4+9/v6kgFU1YWLFsGkyZBYiIM\nGAAvvAA+Pq5OJiIidqIjnSIiDmC18y+bDMOg6riqlOtejthH9tC5zResWNGegQMzbbp5/5XGr/Du\nw+/San4rtp7eimmaDB09NN+PQnB3L05oaBTBwZM5cOBZjh59nezsNFfHKnjc3XOOdv72G3z6KXz/\nfc67fSNGwIULrk4nIiIupIZPROQmno6JYf2VK3avGzQ4iKA3g6g3LZQmtUuxaNF43n7btpqd6nQi\nql0UbT9ry4hZI5i+YTrLVy63T2AHK126HY0a7SU19Sg7dzYiKWm3qyMVTIbx/492bt4MCQkQGgo9\ne8KBA65OJyIiLqCGT0TkJnqUL0+fuDjSHfBeVIWeFaj+UXUij7xCVtpUZs+OZsoU22rG/xyP71Jf\nxi4aS1LLJIbOHkrYfWHMjJppn9AOVKRIAGFhywgKGkp09KOcOPE2Vmseb7URqFEDPv4YDh+GoCB4\n8EF4/HHYsOEvg9xN02Ti0Py/GywiInmjhk9E5Cbali5NqI8PE+04m+/PAtoH0HxJcyKsL+FLF6ZO\nzWTWrLzXiwiPYOKbEynrWxYMOHH1BE++8CQR4RH2C+1AhmFQrlwXGjbcRWLiZnbvvpfk5FhXxyrY\nAgJyjnaeOAFPPQV9+vxlkPuaL7/k3PTprF1eMHaDRUTk9qjhExG5hQ9CQph6+jRHU1MdUr/kQyUZ\num4oxc770L/lYkaPhsWL81bLMAwMw+BG8g1q7ayFh9WD2btn89SSpwrMLZ4AXl6VqFt3DeXKdWf3\n7vuJj38f09Ttkzbx8so52rl/P7zzDgvffpsnfHzY3Ls3k5OS2DRsGE+EhbFwZv7fDRYRkdxTwyci\ncgt3eXkxOCiIV+PiHHbsrfg9xfl+2/c0WV+dFd1OM2BAzmtYeRF3PI6oQVHEfB3DgtcX8GqNV2lS\nsQmNZzVm1MZRpGY6pnG1N8MwqFixNw0abOXixaXs3duK1NQTQM4xxDFjdAwxTywWePxxOsfG0mfM\nGP5fe3ceH1V1/3/89clkErKSBKIsCUvYd1kVpIK4sCkooFAWC4i1KqJ1+4K2lvpT0K9frRZsFSiL\nBQoao1JEQEDcAoKACaBgIBASZAtmAtmTmfP7YyYhGzDBTBKSz/PxuMydO2fuPXO5JPPmnHuOIysL\nARwpKUwfMoQJEydWdw2VUkpVIp2WQSml3JDvcPBhair3hIcjv2b+hMvIPppN/G3x2G+5lrs+aM6K\nlcJtt1XOvo+lH+OpjU+x8+ed/G3w3xjZbqRHP0tlMsZOcvJrJCe/SlTUy+zaFczy5fczadIShg8f\nXd3Vu2qtj45mw9SpSJMmOJKSGNq2LYOTkpz3+o0dC4MHg69vdVdTKaUUVz4tgwY+pZSqYfJO5RE3\nOI6sNiHcu7U1H3wo9K/E6ek2J27m0U8fpXlIc94c8iZtG7StvJ172DvvPM+77/4vrVpZmDIli5Ur\nW5GY6MukSTOYPPnB6q7eVWfh3Lk0a9uW20eNYmNMDMkJCUybOhU++ABWrYK9e2HkSOeUD4MGgdVa\n3VVWSqk6SwOfUkrVIvm2fPbesRebnx8Tvm/H2vVe9OxZifu35zNvxzzmfDWHB3o8wHM3PUegT2Dl\nHcBDjDH897+riI5+mKlTbSxcKFx/fTOGDh1NWNit1K//G7y9a/7nuGocPw7vvw+rV8OhQzB6tLPl\n76abwGKp7toppVSdohOvK6VULWINseL1uhf1LVm823I/dw2zs39/Je7fYuWJvk+w96G9HD9/nA5v\ndWD1vtU1/p44EcHLy0penp2lSztSUBBI48YPYLWGcOzYK8TGNmL37v4cOfIXbLYvcTjyqrvKV7em\nTeHxx2HbNti5E6Ki4MknISICHnsMYmPBA1OWKKWUqjzawqeUUjXUiBEj6NWjF2N+GkPynlwesXVh\n/VfetG5d+cf6+tjXTF83nVC/UOYNnUfnazpX/kEqyVtvzaVFi7YMGzaKdetiSEpK4OGHZwJgt2eR\nnv41aWmbsdm2kJV1kODgfoSGDiI09BYCA69DRFumfrWffnK2+q1aBRkZcO+9zm6fPXo4J39XSilV\n6bRLp1JKVaEPzpwh225nYqNGHjtGSkoK3bt3Z9Nnm/Bb6Efif8/xtOnKulgfIiMr/3gFjgIW7FrA\n7K2zmdBlArMHzqZ+vfqVf6AqlJ+fhs221RUAN5OXd5qQkIGEht5CSMgg/P3bXTUD19RY+/Y5g9/q\n1c4J3ceNcy6da+5/Giil1NVIu3QqpVQValWvHk8ePkxqnue6DEZERPDKK68wZeoUWvytBe0mN+DV\n3D3cMyCHU6cq/3jeXt483Pth9j+8n4y8DNq/1Z5l3y/DcRXPf2e1hhIefjdt286nT58f6d17Lw0b\n3s358zuJj7+dbdsi+fHH+zh5chk5OSnl7kOngLiMzp3hxRcvtPrl5sKwYdCpE7zwgnN7McYY/nem\nnk+llKoq2sKnlFJX6I+HDpFeUMDi9u09dgxjDMOGDaNfv378+c9/JvmNZPbPTuH/runKe9sDCAvz\n2KHZcXwH09dNx9vLm/nD5tOjcQ/PHawaGGPIzj6MzbbZ1QL4Od7eYYSGDiIk5BZCQ2/Gam3A2rXR\nLF8+VaeAqAiHA7ZvdwbA996Dxo2dg72MHcv6775jw9SpDFmyhMGj9XwqpZS7tEunUkpVsfMFBXTY\nsYNVHTvSPyTEY8dJSUlh0KBB7N69m8DAQE4sO0ncI4ksaN6ZZduDCQry2KFxGAdL9izhuS3PcXf7\nu3lx0Is08G/guQNWI2McZGTEY7NtIS1tM++9t4XPPze0aePH735nY8WKKI4cqadTQFSU3Q5ffcXy\n559nVWws3axWXszJ4U+RkcQFBjLusceY+KCeT6WUuhwNfEopVQ3eP32aF5KS2N2zJ1Yvz/WSz8/P\nx1psDrQzH6eya9xBVrXtyD+2heLv77FDA5CWncbznz/Pez+8xwsDX2Baj2lYvGr34Cd2ex7R0a/w\nySevMXVqOgsXCj16BDBoUG+CgroRENCVwMCu+Pt3xGLxq+7q1njGGNavXs2XM2Yw98wZZlmtDPDy\nYnDv3shvfgP9+0PfvhAaWt1VVUqpGknv4VNKqWowJjyc4WFhpObne/Q41lITXoePbEifTzoy9uAP\nzOx/htxcjx7eOXrnsHlsnLiR5XuX02dRH7Ylbyt63RjDzL/WrvuyLBYfAgI6kJfnKJoConXrv9G8\n+f/g49MEm20LBw5M5ZtvwtixowP7948lKeklUlPXkpNzrFadi8ogIoi3Nzk5OTzRsSPZ9eohixYh\nf/kL+PjA669D8+bQtSs89BCsWAFJSc6BYJRSSl0xbeFTSqmrmO3b83wzYC+xnVvy1+2N8fb2/DGN\nMazYu4JnPnuGwa0H8/ItL/PVlq+Y+tpUljy1hNF31p77si41BUQhhyOPrKyDZGTEkZkZT0ZGPJmZ\n8djtWQQGdi1qCQwI6EpAQOfLTgxvjGHOnFk8++zcWjeC6MK5c2nWti23jxrFxpgYkhMSmDaz2PnM\nz4e4OPj66wuL1eps/StcOnfWSd+VUnWSdulUSqk6yhafyRfXx3OgUwRP74jEgz1LSziXe47Rz43m\n87WfE9YijDM3nKFNXBusp63MmDaDB6fU7fuy8vLOkJm5tygAZmTEk5X1Az4+TcoEQT+/KEScf3E6\nSEwxxsDhwxfC3zffwIkTzq6fhQGwd2883qdZKaVqAA18SilVRzgcDnbv6Dk4uQAAGMBJREFU3k2v\nXr2KtqUdzGFT9zjOdAjnDztbIgJzZs3h2bnPerSVyBjDG8vf4LnFz5E9MBvLFgs39r+RcXeNo19k\nPzpf07nW3+tXEQ5HAdnZh1wB8EKLYH7+WbZuDeezz2y0bu3DffedZuXKKBITdZCYMs6cgdjYCyEw\nPh66dLkQAG+8EcLDi4obY3h11iyenlv7WkyVUnWLBj6llKojTp48SZcuXdi8eTNdu3Yt2n42MY9P\nu8RjbxtM2MyDLL5vCdNW3M/wMcM9Wp/oNdFMfW0qEfUjOGY7xqTRk8htkUtsciwnMk7Qu0lv+kX2\no19kP26IuIGQep4b0fRqlZ9vIyMjnjVrlrFp02ruvz+ThQuF667z4+abOxEQ0B5///b4+7fDz68d\nfn6tsVjqVXe1a4asLNi580IA3LYNGjUqCoDrMzLY8OyzVTYNhAZMpZSnaOBTSqka4HReHl/YbNxz\nzTUePc7ixYuZP38+3377bYkBXebPWcKSPy2ilaUlDxXcz4LGizgdepJJMyYx+cHJHqnL3Dfn0jaq\nLaPuGEXM2hgSjiQwc4bzvqyzWWfZnrKd2ORYtqVsY+fPO2lWvxn9IvrRN7Iv/SL70bZBW7xExxCD\nC90569WLJDs7mfHj32TAgDZkZx8kK+vCkpNzFF/fJiVCoL+/c/HxaVy3g4bdDvv2sfzll1m1bh3d\nMjN50W7nTyLEWSyMCwtjYkQEBARAYODFHy/1WuFjvXpQ6lyvj47WeQaVUh6hgU8ppWqAE7m5dP3u\nO7687jo6BAR47DilJ2Qv9Pbb/+a12QvocqoJM3iIf/AO4hvETffcxoP/uBvvoCoY1eUSChwF7D21\nl9jkWGJTYtmWvA1bjs0Z/lwhsE/TPgT6XHpgk9rKnUFiAByOfHJyEkuEwMJQ6HDklAmBzudtsFjK\n3utWWweJMcawPjqaL598krnJycxq2pQBf/4zg2+6CcnKgowMyMx07/Fir+XlOcNfQADL7XZWnTtH\nNxHnPIMNGhDn58e4Bx5g4nPP6UAzSqlfTQOfUkrVEPNSUohJTWVLt24e/QKdkpJC9+7dS3TtNMbw\np6de5Pu/7eaMqc81pFO/QR9uPDeEqILzpIUFIr1CaTk6lO4TgvHxr/6WtRPnT7AtZRvbkrcRmxJL\n3Mk42jZoS98IZwtg38i+tAxpWeJcGmOY9cIs5j5fu0JKZcjP/6VMCMzKOkB2diI+Po1KhcB2fPHF\nYVavfrpWDhJT2NomkZE4kpMZWtmtbnZ7UQA0GRms/+gjvnztNeaePs2soCAGtGnD4F9+QU6dgvbt\nnSOMdu4MnTo5H5s1K9NCqJRSF6OBTymlagi7MfTZtYvHIyKY1KiRR4+1ePFiYmNjWbRoUdG2hyY8\nzuqYFBq1jOTkkWTGjY7grX+/QeKPdnYtTSd1YxoBB22E52RxIiwY6RFK81Gh9BkfSFD96v/ymVuQ\ny56Te4q6gcYmx2J32J3hzxUCk3Yl8Yc3/lDrpoHwJIejgJyco0UhcOXKD1mzZjdRUblMnWpnyZJ6\nHDlSj9GjhzJlyiMEBHTB2zu4uqv9q1x2GohKdtGAmZEBP/wA+/Y5l/37nY/nz18If4WPnTvDtddq\nEFRKlaGBTymlapCd584xYt8+fujdm9BSk6ZXJmMMdrsd72IT8M2du5C2bZsxatTtxMRsJCEhmZkz\np5V57+nD+exabOP0+jT8frRRLzuPpJAQTPdQIu8K4YZ7/GncuPq/dBpjOJZ+jG0p21iweAHbNmwj\np0EODAL/r/zxTfVl0B2DGD9xPK1CWxEVGkWQb1B1V7vGM8awdm00H374JPfdl8zSpddw883Duf56\nLzIz95KZuR8fn/AS00cEBnbFz681Ito9sTwVDpi//OIMf4UBsHCBsiGwUycICyuzCx0kRqm6QwOf\nUkrVMDMSEhgQEsLoYkPE12TnEnP5fkkaJz+1UW9/Gvm5hoMBodi7hRI5IoQbRtSjXbvyGx6MMcya\n9Spz5z7t8WkgotdE88SCJ0jpk0J4bDh33n4nwZ2CSbQlkpjmXAKsAUSFRtEqrFVRCCx8bBzUuEKD\nxNTm7qOlB4m5774L3TqNsZOdnVhiMvmMjDjy8k4RENCRgIBuxYJgF6zWBtX8aWoJY+DUqbIhcP9+\n50AxhQHQtaw/eJANjzyig8QoVQdo4FNKqRrGGHPVBgRjDFkJ2fyw3MaJT9Kw7reRbvcm3juUvC4h\nNB0eSt/BVnr0AB8feP/9T/nDhFd5Z+UzjBkzxKN1K5wGIrJ+JMnpyWW6dRpjOJlxksS0RA6nHS75\n+Mth0nPTaRnSklZhrYgKcYbCwkDYMrQl9bzrlXu82th91N1BYoorKDhHZua+EhPKZ2bGY7EEl5lQ\n3t+/HV5eJVu4a+sgMR5nDCQnFwXA5TExrIqLo1tODi8Cf7JanaOQRkUxsXt3Z2tggwbOx+LrhY/1\n64NXxe/hreoWRW3BVOqCGhn4RGQI8AZgA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f1(x):\n", " y = 1 - x/(splits*math.exp(-1)) #e^-1 is roughly 0.36787944117144233\n", " return max(y,0)\n", "def f2(x):\n", " y = 1 - x/(splits*0.4)\n", " return max(y,0)\n", "\n", "fig = plt.figure(figsize=(15,9))\n", "for k in range(len(averages)):\n", " plt.plot([i/splits for i in range(0,splits)],averages[k],colors[k % len(colors)])\n", "plt.plot([i/splits for i in range(0,splits)],[f1(x) for x in range(0,splits)], 'c--')\n", "plt.plot([i/splits for i in range(0,splits)],[f2(x) for x in range(0,splits)], 'k--')\n", "plt.xlabel(\"Fill probability\")\n", "plt.ylabel(\"Probability of successful path\")\n", "plt.title(\"Chance of Path\")\n", "legend = [str(size) + \"x\" + str(size) for size in sizes]\n", "legend.append(\"f1 approx\")\n", "legend.append(\"f2 approx\")\n", "plt.legend(legend)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cool!\n", "Future work involves probability theory to predict the true chance of a path given the board size. We can validate this theoretical work with the simulations above. For now, we can make and play with the mazes. Thanks for playing!" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 0. 0. 1. 0. 0. 0. 1. 1. 0.]\n", " [ 0. 0. 0. 1. 1. 0. 0. 0. 0. 1.]\n", " [ 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n", " [ 1. 1. 0. 0. 1. 0. 0. 1. 0. 0.]\n", " [ 0. 1. 1. 0. 0. 0. 0. 0. 0. 0.]\n", " [ 0. 0. 0. 1. 0. 0. 0. 1. 1. 1.]\n", " [ 0. 0. 0. 1. 0. 0. 0. 0. 0. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]]\n", "True\n", "[[ 3. 3. 3. 1. 0. 0. 0. 1. 1. 0.]\n", " [ 0. 0. 3. 1. 1. 0. 0. 0. 0. 1.]\n", " [ 0. 0. 3. 3. 1. 0. 0. 0. 0. 0.]\n", " [ 1. 0. 0. 3. 3. 3. 3. 1. 0. 0.]\n", " [ 0. 0. 0. 0. 0. 1. 3. 3. 3. 3.]\n", " [ 1. 1. 0. 0. 1. 0. 0. 1. 0. 3.]\n", " [ 0. 1. 1. 0. 0. 0. 3. 3. 3. 3.]\n", " [ 0. 0. 0. 1. 0. 0. 3. 1. 1. 1.]\n", " [ 0. 0. 0. 1. 0. 0. 3. 3. 3. 1.]\n", " [ 0. 0. 0. 0. 0. 0. 1. 0. 3. 3.]]\n" ] } ], "source": [ "x = Maze(10,0.2)\n", "x.view()\n", "print(x.find_path())\n", "x.view()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }